LMFDB - Embedded newform 69.6.e.a.58.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,6,Mod(4,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0664835671$
Analytic rank:	$0$
Dimension:	$100$
Relative dimension:	$10$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			58.8
Character	$\chi$	$=$	69.58
Dual form			69.6.e.a.25.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.07977 - 2.62191i) q^{2} +(1.28083 - 8.90839i) q^{3} +(-3.52316 + 7.71464i) q^{4} +(-65.8664 + 19.3401i) q^{5} +(-18.1315 - 39.7024i) q^{6} +(72.9578 + 84.1978i) q^{7} +(27.9390 + 194.320i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})$	\(q+(4.07977 - 2.62191i) q^{2} +(1.28083 - 8.90839i) q^{3} +(-3.52316 + 7.71464i) q^{4} +(-65.8664 + 19.3401i) q^{5} +(-18.1315 - 39.7024i) q^{6} +(72.9578 + 84.1978i) q^{7} +(27.9390 + 194.320i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(-218.012 + 251.599i) q^{10} +(475.114 + 305.338i) q^{11} +(64.2125 + 41.2668i) q^{12} +(-378.634 + 436.967i) q^{13} +(518.410 + 152.219i) q^{14} +(87.9255 + 611.535i) q^{15} +(445.749 + 514.422i) q^{16} +(-457.976 - 1002.83i) q^{17} +(-376.908 + 110.670i) q^{18} +(-46.8199 + 102.521i) q^{19} +(82.8557 - 576.274i) q^{20} +(843.514 - 542.094i) q^{21} +2738.93 q^{22} +(-1547.63 + 2010.27i) q^{23} +1766.86 q^{24} +(1335.42 - 858.225i) q^{25} +(-399.052 + 2775.47i) q^{26} +(-302.838 + 663.122i) q^{27} +(-906.598 + 266.201i) q^{28} +(-669.400 - 1465.78i) q^{29} +(1962.11 + 2264.39i) q^{30} +(1247.22 + 8674.57i) q^{31} +(-2860.39 - 839.886i) q^{32} +(3328.61 - 3841.42i) q^{33} +(-4497.76 - 2890.54i) q^{34} +(-6433.87 - 4134.79i) q^{35} +(449.867 - 519.174i) q^{36} +(-4956.57 - 1455.38i) q^{37} +(77.7871 + 541.021i) q^{38} +(3407.71 + 3932.70i) q^{39} +(-5598.41 - 12258.8i) q^{40} +(11740.1 - 3447.21i) q^{41} +(2020.02 - 4423.24i) q^{42} +(-1524.73 + 10604.8i) q^{43} +(-4029.47 + 2589.58i) q^{44} +5560.41 q^{45} +(-1043.23 + 12259.2i) q^{46} +11225.2 q^{47} +(5153.60 - 3312.02i) q^{48} +(625.456 - 4350.14i) q^{49} +(3198.04 - 7002.73i) q^{50} +(-9520.17 + 2795.38i) q^{51} +(-2037.06 - 4460.53i) q^{52} +(-15599.1 - 18002.3i) q^{53} +(503.137 + 3499.40i) q^{54} +(-37199.3 - 10922.7i) q^{55} +(-14323.0 + 16529.6i) q^{56} +(853.332 + 548.403i) q^{57} +(-6574.15 - 4224.95i) q^{58} +(27098.8 - 31273.6i) q^{59} +(-5027.55 - 1476.22i) q^{60} +(-871.088 - 6058.55i) q^{61} +(27832.3 + 32120.2i) q^{62} +(-3748.78 - 8208.69i) q^{63} +(-34771.2 + 10209.8i) q^{64} +(16488.3 - 36104.3i) q^{65} +(3508.11 - 24399.4i) q^{66} +(13767.6 - 8847.90i) q^{67} +9349.98 q^{68} +(15926.0 + 16361.7i) q^{69} -37089.8 q^{70} +(21430.6 - 13772.6i) q^{71} +(2263.06 - 15739.9i) q^{72} +(10892.5 - 23851.2i) q^{73} +(-24037.6 + 7058.06i) q^{74} +(-5934.95 - 12995.7i) q^{75} +(-625.961 - 722.398i) q^{76} +(8954.57 + 62280.4i) q^{77} +(24213.9 + 7109.83i) q^{78} +(-61838.0 + 71364.9i) q^{79} +(-39308.9 - 25262.3i) q^{80} +(5519.46 + 3547.14i) q^{81} +(38858.7 - 44845.4i) q^{82} +(101646. + 29845.8i) q^{83} +(1210.22 + 8417.29i) q^{84} +(49560.0 + 57195.3i) q^{85} +(21584.1 + 47262.7i) q^{86} +(-13915.2 + 4085.86i) q^{87} +(-46059.0 + 100855. i) q^{88} +(-2264.42 + 15749.4i) q^{89} +(22685.2 - 14578.9i) q^{90} -64416.0 q^{91} +(-10056.0 - 19021.9i) q^{92} +78874.0 q^{93} +(45796.4 - 29431.6i) q^{94} +(1101.09 - 7658.22i) q^{95} +(-11145.7 + 24405.7i) q^{96} +(-19685.7 + 5780.23i) q^{97} +(-8853.97 - 19387.5i) q^{98} +(-29957.5 - 34572.8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q - 8 q^{2} + 90 q^{3} - 148 q^{4} + 6 q^{5} + 171 q^{6} + 118 q^{7} + 1616 q^{8} - 810 q^{9}+O(q^{10}) $ 100 * q - 8 * q^2 + 90 * q^3 - 148 * q^4 + 6 * q^5 + 171 * q^6 + 118 * q^7 + 1616 * q^8 - 810 * q^9	\( 100 q - 8 q^{2} + 90 q^{3} - 148 q^{4} + 6 q^{5} + 171 q^{6} + 118 q^{7} + 1616 q^{8} - 810 q^{9} - 262 q^{10} + 724 q^{11} + 1332 q^{12} + 2730 q^{13} + 328 q^{14} - 1143 q^{15} - 8596 q^{16} - 5699 q^{17} - 648 q^{18} + 1993 q^{19} + 28263 q^{20} - 1062 q^{21} - 19378 q^{22} + 9084 q^{23} + 1296 q^{24} - 4752 q^{25} - 7828 q^{26} + 7290 q^{27} - 29888 q^{28} - 37644 q^{29} + 2358 q^{30} - 2471 q^{31} + 42352 q^{32} + 1305 q^{33} + 47233 q^{34} + 9062 q^{35} - 21789 q^{36} + 1170 q^{37} - 133648 q^{38} - 24570 q^{39} + 135509 q^{40} - 8556 q^{41} - 17208 q^{42} + 39714 q^{43} + 108207 q^{44} - 44064 q^{45} + 87076 q^{46} + 56898 q^{47} + 60237 q^{48} + 35646 q^{49} + 12207 q^{50} - 48600 q^{51} - 368495 q^{52} + 11912 q^{53} - 34263 q^{54} - 231697 q^{55} + 235302 q^{56} + 4437 q^{57} - 201743 q^{58} + 116756 q^{59} + 209349 q^{60} - 191952 q^{61} - 91633 q^{62} + 9558 q^{63} + 383796 q^{64} + 120963 q^{65} + 92925 q^{66} - 7699 q^{67} - 486648 q^{68} + 9522 q^{69} + 340272 q^{70} + 60029 q^{71} + 130896 q^{72} + 110721 q^{73} - 290458 q^{74} + 48906 q^{75} + 30961 q^{76} - 325750 q^{77} + 51444 q^{78} - 267838 q^{79} - 519366 q^{80} - 65610 q^{81} - 739402 q^{82} - 236288 q^{83} - 382428 q^{84} + 72669 q^{85} + 643772 q^{86} + 62784 q^{87} + 976500 q^{88} + 455688 q^{89} - 21222 q^{90} + 267512 q^{91} + 70711 q^{92} - 12906 q^{93} + 1298755 q^{94} + 1815505 q^{95} + 461520 q^{96} + 271324 q^{97} - 1533115 q^{98} - 11745 q^{99}+O(q^{100}) \) 100 * q - 8 * q^2 + 90 * q^3 - 148 * q^4 + 6 * q^5 + 171 * q^6 + 118 * q^7 + 1616 * q^8 - 810 * q^9 - 262 * q^10 + 724 * q^11 + 1332 * q^12 + 2730 * q^13 + 328 * q^14 - 1143 * q^15 - 8596 * q^16 - 5699 * q^17 - 648 * q^18 + 1993 * q^19 + 28263 * q^20 - 1062 * q^21 - 19378 * q^22 + 9084 * q^23 + 1296 * q^24 - 4752 * q^25 - 7828 * q^26 + 7290 * q^27 - 29888 * q^28 - 37644 * q^29 + 2358 * q^30 - 2471 * q^31 + 42352 * q^32 + 1305 * q^33 + 47233 * q^34 + 9062 * q^35 - 21789 * q^36 + 1170 * q^37 - 133648 * q^38 - 24570 * q^39 + 135509 * q^40 - 8556 * q^41 - 17208 * q^42 + 39714 * q^43 + 108207 * q^44 - 44064 * q^45 + 87076 * q^46 + 56898 * q^47 + 60237 * q^48 + 35646 * q^49 + 12207 * q^50 - 48600 * q^51 - 368495 * q^52 + 11912 * q^53 - 34263 * q^54 - 231697 * q^55 + 235302 * q^56 + 4437 * q^57 - 201743 * q^58 + 116756 * q^59 + 209349 * q^60 - 191952 * q^61 - 91633 * q^62 + 9558 * q^63 + 383796 * q^64 + 120963 * q^65 + 92925 * q^66 - 7699 * q^67 - 486648 * q^68 + 9522 * q^69 + 340272 * q^70 + 60029 * q^71 + 130896 * q^72 + 110721 * q^73 - 290458 * q^74 + 48906 * q^75 + 30961 * q^76 - 325750 * q^77 + 51444 * q^78 - 267838 * q^79 - 519366 * q^80 - 65610 * q^81 - 739402 * q^82 - 236288 * q^83 - 382428 * q^84 + 72669 * q^85 + 643772 * q^86 + 62784 * q^87 + 976500 * q^88 + 455688 * q^89 - 21222 * q^90 + 267512 * q^91 + 70711 * q^92 - 12906 * q^93 + 1298755 * q^94 + 1815505 * q^95 + 461520 * q^96 + 271324 * q^97 - 1533115 * q^98 - 11745 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	4.07977	−	2.62191i	0.721208	−	0.463493i	−0.127849	−	0.991794i	$-0.540807\pi$
$2$	4.07977	−	2.62191i	0.721208	−	0.463493i	0.849057	+	0.528301i	$0.177171\pi$
$3$	1.28083	−	8.90839i	0.0821655	−	0.571474i
$3$	1.28083	−	8.90839i	0.0821655	−	0.571474i
$4$	−3.52316	+	7.71464i	−0.110099	+	0.241082i
$5$	−65.8664	+	19.3401i	−1.17825	+	0.345967i	−0.811501	−	0.584352i	$-0.801349\pi$
$5$	−65.8664	+	19.3401i	−1.17825	+	0.345967i	−0.366753	+	0.930318i	$0.619531\pi$
$6$	−18.1315	−	39.7024i	−0.205615	−	0.450235i
$7$	72.9578	+	84.1978i	0.562765	+	0.649465i	0.963809	−	0.266594i	$-0.0858981\pi$
$7$	72.9578	+	84.1978i	0.562765	+	0.649465i	−0.401044	+	0.916059i	$0.631353\pi$
$8$	27.9390	+	194.320i	0.154343	+	1.07348i
$9$	−77.7189	−	22.8203i	−0.319831	−	0.0939109i
$10$	−218.012	+	251.599i	−0.689414	+	0.795626i
$11$	475.114	+	305.338i	1.18390	+	0.760849i	0.976100	−	0.217322i	$-0.0697320\pi$
$11$	475.114	+	305.338i	1.18390	+	0.760849i	0.207804	+	0.978170i	$0.433368\pi$
$12$	64.2125	+	41.2668i	0.128726	+	0.0827272i
$13$	−378.634	+	436.967i	−0.621386	+	0.717117i	−0.975970	−	0.217907i	$-0.930077\pi$
$13$	−378.634	+	436.967i	−0.621386	+	0.717117i	0.354584	+	0.935024i	$0.384623\pi$
$14$	518.410	+	152.219i	0.706893	+	0.207562i
$15$	87.9255	+	611.535i	0.100899	+	0.701768i
$16$	445.749	+	514.422i	0.435302	+	0.502365i
$17$	−457.976	−	1002.83i	−0.384344	−	0.841597i	−0.998621	−	0.0525057i	$-0.983279\pi$
$17$	−457.976	−	1002.83i	−0.384344	−	0.841597i	0.614276	−	0.789091i	$-0.289448\pi$
$18$	−376.908	+	110.670i	−0.274192	+	0.0805100i
$19$	−46.8199	+	102.521i	−0.0297541	+	0.0651524i	−0.923926	−	0.382572i	$-0.875038\pi$
$19$	−46.8199	+	102.521i	−0.0297541	+	0.0651524i	0.894171	+	0.447725i	$0.147766\pi$
$20$	82.8557	−	576.274i	0.0463177	−	0.322147i
$21$	843.514	−	542.094i	0.417392	−	0.268242i
$22$	2738.93			1.20649
$23$	−1547.63	+	2010.27i	−0.610025	+	0.792382i
$23$	−1547.63	+	2010.27i	−0.610025	+	0.792382i
$24$	1766.86			0.626145
$25$	1335.42	−	858.225i	0.427336	−	0.274632i
$26$	−399.052	+	2775.47i	−0.115770	+	0.805199i
$27$	−302.838	+	663.122i	−0.0799467	+	0.175059i
$28$	−906.598	+	266.201i	−0.218534	+	0.0641675i
$29$	−669.400	−	1465.78i	−0.147806	−	0.323649i	0.821219	−	0.570613i	$-0.193294\pi$
$29$	−669.400	−	1465.78i	−0.147806	−	0.323649i	−0.969025	+	0.246964i	$0.920567\pi$
$30$	1962.11	+	2264.39i	0.398033	+	0.459355i
$31$	1247.22	+	8674.57i	0.233097	+	1.62123i	0.684573	+	0.728944i	$0.259989\pi$
$31$	1247.22	+	8674.57i	0.233097	+	1.62123i	−0.451476	+	0.892283i	$0.649102\pi$
$32$	−2860.39	−	839.886i	−0.493799	−	0.144992i
$33$	3328.61	−	3841.42i	0.532081	−	0.614054i
$34$	−4497.76	−	2890.54i	−0.667266	−	0.428826i
$35$	−6433.87	−	4134.79i	−0.887773	−	0.570537i
$36$	449.867	−	519.174i	0.0578532	−	0.0667662i
$37$	−4956.57	−	1455.38i	−0.595219	−	0.174772i	−0.0297722	−	0.999557i	$-0.509478\pi$
$37$	−4956.57	−	1455.38i	−0.595219	−	0.174772i	−0.565447	+	0.824785i	$0.691296\pi$
$38$	77.7871	+	541.021i	0.00873874	+	0.0607793i
$39$	3407.71	+	3932.70i	0.358757	+	0.414028i
$40$	−5598.41	−	12258.8i	−0.553242	−	1.21143i
$41$	11740.1	−	3447.21i	1.09072	−	0.320264i	0.313560	−	0.949568i	$-0.398478\pi$
$41$	11740.1	−	3447.21i	1.09072	−	0.320264i	0.777159	+	0.629304i	$0.216660\pi$
$42$	2020.02	−	4423.24i	0.176699	−	0.386916i
$43$	−1524.73	+	10604.8i	−0.125754	+	0.874640i	0.825097	+	0.564991i	$0.191121\pi$
$43$	−1524.73	+	10604.8i	−0.125754	+	0.874640i	−0.950851	+	0.309649i	$0.899789\pi$
$44$	−4029.47	+	2589.58i	−0.313774	+	0.201650i
$45$	5560.41			0.409332
$46$	−1043.23	+	12259.2i	−0.0726918	+	0.854215i
$47$	11225.2			0.741226			0.370613	−	0.928787i	$-0.379148\pi$
$47$	11225.2			0.741226			0.370613	+	0.928787i	$0.379148\pi$
$48$	5153.60	−	3312.02i	0.322855	−	0.207487i
$49$	625.456	−	4350.14i	0.0372140	−	0.258829i
$50$	3198.04	−	7002.73i	0.180908	−	0.396134i
$51$	−9520.17	+	2795.38i	−0.512530	+	0.150492i
$52$	−2037.06	−	4460.53i	−0.104471	−	0.228759i
$53$	−15599.1	−	18002.3i	−0.762798	−	0.880316i	0.232945	−	0.972490i	$-0.425164\pi$
$53$	−15599.1	−	18002.3i	−0.762798	−	0.880316i	−0.995743	+	0.0921737i	$0.970618\pi$
$54$	503.137	+	3499.40i	0.0234802	+	0.163309i
$55$	−37199.3	−	10922.7i	−1.65817	−	0.486882i
$56$	−14323.0	+	16529.6i	−0.610327	+	0.704355i
$57$	853.332	+	548.403i	0.0347881	+	0.0223570i
$58$	−6574.15	−	4224.95i	−0.256608	−	0.164912i
$59$	27098.8	−	31273.6i	1.01349	−	1.16963i	0.0280498	−	0.999607i	$-0.491070\pi$
$59$	27098.8	−	31273.6i	1.01349	−	1.16963i	0.985440	−	0.170023i	$-0.0543842\pi$
$60$	−5027.55	−	1476.22i	−0.180293	−	0.0529387i
$61$	−871.088	−	6058.55i	−0.0299735	−	0.208470i	0.969331	−	0.245759i	$-0.0790371\pi$
$61$	−871.088	−	6058.55i	−0.0299735	−	0.208470i	−0.999305	+	0.0372884i	$0.988128\pi$
$62$	27832.3	+	32120.2i	0.919539	+	1.06120i
$63$	−3748.78	−	8208.69i	−0.118998	−	0.260569i
$64$	−34771.2	+	10209.8i	−1.06113	+	0.311577i
$65$	16488.3	−	36104.3i	0.484052	−	1.05993i
$66$	3508.11	−	24399.4i	0.0991318	−	0.689477i
$67$	13767.6	−	8847.90i	0.374689	−	0.240798i	−0.339719	−	0.940527i	$-0.610332\pi$
$67$	13767.6	−	8847.90i	0.374689	−	0.240798i	0.714409	+	0.699729i	$0.246696\pi$
$68$	9349.98			0.245210
$69$	15926.0	+	16361.7i	0.402703	+	0.413720i
$70$	−37089.8			−0.904709
$71$	21430.6	−	13772.6i	0.504532	−	0.324243i	−0.263495	−	0.964661i	$-0.584875\pi$
$71$	21430.6	−	13772.6i	0.504532	−	0.324243i	0.768027	+	0.640418i	$0.221239\pi$
$72$	2263.06	−	15739.9i	0.0514476	−	0.357826i
$73$	10892.5	−	23851.2i	0.239232	−	0.523845i	−0.751491	−	0.659743i	$-0.770665\pi$
$73$	10892.5	−	23851.2i	0.239232	−	0.523845i	0.990723	+	0.135899i	$0.0433922\pi$
$74$	−24037.6	+	7058.06i	−0.510283	+	0.149833i
$75$	−5934.95	−	12995.7i	−0.121833	−	0.266777i
$76$	−625.961	−	722.398i	−0.0124312	−	0.0143464i
$77$	8954.57	+	62280.4i	0.172115	+	1.19708i
$78$	24213.9	+	7109.83i	0.450638	+	0.132319i
$79$	−61838.0	+	71364.9i	−1.11478	+	1.28652i	−0.160686	+	0.987006i	$0.551371\pi$
$79$	−61838.0	+	71364.9i	−1.11478	+	1.28652i	−0.954091	+	0.299516i	$0.903175\pi$
$80$	−39308.9	−	25262.3i	−0.686698	−	0.441314i
$81$	5519.46	+	3547.14i	0.0934726	+	0.0600712i
$82$	38858.7	−	44845.4i	0.638196	−	0.736517i
$83$	101646.	+	29845.8i	1.61955	+	0.475542i	0.960896	−	0.276908i	$-0.0893097\pi$
$83$	101646.	+	29845.8i	1.61955	+	0.475542i	0.658650	+	0.752450i	$0.271128\pi$
$84$	1210.22	+	8417.29i	0.0187140	+	0.130159i
$85$	49560.0	+	57195.3i	0.744020	+	0.858644i
$86$	21584.1	+	47262.7i	0.314694	+	0.689084i
$87$	−13915.2	+	4085.86i	−0.197101	+	0.0578742i
$88$	−46059.0	+	100855.i	−0.634027	+	1.38832i
$89$	−2264.42	+	15749.4i	−0.0303028	+	0.210761i	−0.999347	−	0.0361257i	$-0.988498\pi$
$89$	−2264.42	+	15749.4i	−0.0303028	+	0.210761i	0.969044	+	0.246886i	$0.0794074\pi$
$90$	22685.2	−	14578.9i	0.295214	−	0.189722i
$91$	−64416.0			−0.815437
$92$	−10056.0	−	19021.9i	−0.123867	−	0.234307i
$93$	78874.0			0.945641
$94$	45796.4	−	29431.6i	0.534579	−	0.343553i
$95$	1101.09	−	7658.22i	0.0125173	−	0.0870600i
$96$	−11145.7	+	24405.7i	−0.123433	+	0.270280i
$97$	−19685.7	+	5780.23i	−0.212432	+	0.0623757i	−0.386217	−	0.922408i	$-0.626218\pi$
$97$	−19685.7	+	5780.23i	−0.212432	+	0.0623757i	0.173785	+	0.984784i	$0.444400\pi$
$98$	−8853.97	−	19387.5i	−0.0931264	−	0.203918i
$99$	−29957.5	−	34572.8i	−0.307197	−	0.354525i
$100$	1915.99	+	13326.0i	0.0191599	+	0.133260i
$101$	111534.	+	32749.3i	1.08793	+	0.319446i	0.776049	−	0.630673i	$-0.217221\pi$
$101$	111534.	+	32749.3i	1.08793	+	0.319446i	0.311886	+	0.950119i	$0.399039\pi$
$102$	−31510.9	+	36365.5i	−0.299889	+	0.346090i
$103$	103433.	+	66472.6i	0.960655	+	0.617376i	0.924179	−	0.381959i	$-0.124750\pi$
$103$	103433.	+	66472.6i	0.960655	+	0.617376i	0.0364758	+	0.999335i	$0.488387\pi$
$104$	−95490.1	−	61367.8i	−0.865715	−	0.556361i
$105$	−45075.1	+	52019.4i	−0.398991	+	0.460460i
$106$	−110841.	−	32545.9i	−0.958157	−	0.281340i
$107$	27679.3	+	192514.i	0.233720	+	1.62556i	0.681782	+	0.731555i	$0.261205\pi$
$107$	27679.3	+	192514.i	0.233720	+	1.62556i	−0.448063	+	0.894002i	$0.647886\pi$
$108$	−4048.80	−	4672.56i	−0.0334016	−	0.0385475i
$109$	2614.82	+	5725.67i	0.0210803	+	0.0461594i	0.919879	−	0.392202i	$-0.128286\pi$
$109$	2614.82	+	5725.67i	0.0210803	+	0.0461594i	−0.898799	+	0.438361i	$0.855559\pi$
$110$	−180403.	+	52971.1i	−1.42155	+	0.417405i
$111$	−19313.6	+	42291.0i	−0.148784	+	0.325792i
$112$	−10792.3	+	75062.2i	−0.0812961	+	0.565427i
$113$	113697.	−	73068.9i	0.837634	−	0.538315i	−0.0500611	−	0.998746i	$-0.515942\pi$
$113$	113697.	−	73068.9i	0.837634	−	0.538315i	0.887695	+	0.460431i	$0.152305\pi$
$114$	4919.26			0.0354518
$115$	63057.9	−	162341.i	0.444626	−	1.14468i
$116$	13666.4			0.0942993
$117$	39398.8	−	25320.1i	0.266084	−	0.171002i
$118$	28560.1	−	198640.i	0.188823	−	1.31329i
$119$	51023.0	−	111725.i	0.330292	−	0.723239i
$120$	−116377.	+	34171.4i	−0.737758	+	0.216625i
$121$	65599.7	+	143643.i	0.407323	+	0.891912i
$122$	−19438.8	−	22433.6i	−0.118242	−	0.136458i
$123$	−15672.0	−	109001.i	−0.0934029	−	0.649632i
$124$	−71315.3	−	20940.1i	−0.416513	−	0.122299i
$125$	69120.7	−	79769.5i	0.395670	−	0.456627i
$126$	−36816.6	−	23660.6i	−0.206594	−	0.132770i
$127$	−56274.6	−	36165.5i	−0.309601	−	0.198969i	0.376608	−	0.926373i	$-0.377090\pi$
$127$	−56274.6	−	36165.5i	−0.309601	−	0.198969i	−0.686209	+	0.727404i	$0.740727\pi$
$128$	−52618.0	+	60724.4i	−0.283864	+	0.327596i
$129$	92518.4	+	27165.8i	0.489501	+	0.143730i
$130$	−27393.8	−	190528.i	−0.142165	−	0.988781i
$131$	−146904.	−	169536.i	−0.747918	−	0.863144i	0.246447	−	0.969156i	$-0.420737\pi$
$131$	−146904.	−	169536.i	−0.747918	−	0.863144i	−0.994365	+	0.106013i	$0.966192\pi$
$132$	17908.0	+	39212.9i	0.0894563	+	0.195882i
$133$	−12048.0	+	3537.60i	−0.0590588	+	0.0173412i
$134$	32970.3	−	72194.9i	0.158621	−	0.347332i
$135$	7121.96	−	49534.4i	0.0336330	−	0.233923i
$136$	182074.	−	117012.i	0.844114	−	0.542479i
$137$	−246921.			−1.12398			−0.561988	−	0.827145i	$-0.689963\pi$
$137$	−246921.			−1.12398			−0.561988	+	0.827145i	$0.689963\pi$
$138$	107873.	+	24995.5i	0.482189	+	0.111728i
$139$	286844.			1.25924			0.629621	−	0.776903i	$-0.283210\pi$
$139$	286844.			1.25924			0.629621	+	0.776903i	$0.283210\pi$
$140$	54566.0	−	35067.4i	0.235289	−	0.151211i
$141$	14377.7	−	99998.8i	0.0609032	−	0.423591i
$142$	51321.4	−	112378.i	0.213589	−	0.467694i
$143$	−313317.	+	91998.2i	−1.28128	+	0.376218i
$144$	−22903.9	−	50152.5i	−0.0920455	−	0.201552i
$145$	72439.4	+	83599.5i	0.286124	+	0.330205i
$146$	−18096.9	−	125866.i	−0.0702621	−	0.488683i
$147$	−37951.7	−	11143.6i	−0.144856	−	0.0425337i
$148$	28690.5	−	33110.6i	0.107667	−	0.124255i
$149$	−245330.	−	157664.i	−0.905285	−	0.581791i	0.00306823	−	0.999995i	$-0.499023\pi$
$149$	−245330.	−	157664.i	−0.905285	−	0.581791i	−0.908353	+	0.418204i	$0.862660\pi$
$150$	−58286.9	−	37458.7i	−0.211516	−	0.135933i
$151$	251846.	−	290646.i	0.898861	−	1.03734i	−0.100241	−	0.994963i	$-0.531961\pi$
$151$	251846.	−	290646.i	0.898861	−	1.03734i	0.999102	−	0.0423773i	$-0.0134931\pi$
$152$	−21230.1	−	6233.71i	−0.0745319	−	0.0218845i
$153$	12708.5	+	88389.9i	0.0438902	+	0.305263i
$154$	199826.	+	230612.i	0.678970	+	0.783573i
$155$	−249917.	−	547242.i	−0.835538	−	1.82957i
$156$	−42345.3	+	12433.7i	−0.139314	+	0.0409062i
$157$	−212039.	+	464300.i	−0.686540	+	1.50331i	0.169022	+	0.985612i	$0.445939\pi$
$157$	−212039.	+	464300.i	−0.686540	+	1.50331i	−0.855562	+	0.517701i	$0.826788\pi$
$158$	−65172.7	+	453286.i	−0.207694	+	1.44454i
$159$	−180352.	+	115905.i	−0.565753	+	0.363588i
$160$	204647.			0.631983
$161$	−282172.	+	16357.9i	−0.857925	+	0.0497350i
$162$	31818.4			0.0952558
$163$	−381679.	+	245290.i	−1.12520	+	0.723121i	−0.964553	−	0.263891i	$-0.914994\pi$
$163$	−381679.	+	245290.i	−1.12520	+	0.723121i	−0.160646	+	0.987012i	$0.551358\pi$
$164$	−14768.3	+	102716.i	−0.0428767	+	0.298214i
$165$	−144950.	+	317396.i	−0.414484	+	0.907594i
$166$	492944.	−	144741.i	1.38844	−	0.407683i
$167$	242169.	+	530277.i	0.671936	+	1.47133i	0.870967	+	0.491341i	$0.163493\pi$
$167$	242169.	+	530277.i	0.671936	+	1.47133i	−0.199031	+	0.979993i	$0.563780\pi$
$168$	128907.	+	148766.i	0.352373	+	0.406660i
$169$	5264.09	+	36612.6i	0.0141777	+	0.0986083i
$170$	352155.	+	103402.i	0.934568	+	0.274414i
$171$	5978.37	−	6899.40i	0.0156348	−	0.0180435i
$172$	−76440.0	−	49125.0i	−0.197015	−	0.126614i
$173$	−368564.	−	236862.i	−0.936262	−	0.601699i	−0.0189294	−	0.999821i	$-0.506026\pi$
$173$	−368564.	−	236862.i	−0.936262	−	0.601699i	−0.917333	+	0.398122i	$0.869662\pi$
$174$	−46057.9	+	53153.6i	−0.115327	+	0.133094i
$175$	169690.	+	49825.6i	0.418854	+	0.122987i
$176$	54709.6	+	380513.i	0.133132	+	0.925951i
$177$	−243889.	−	281463.i	−0.585139	−	0.675286i
$178$	32055.2	+	70191.1i	0.0758313	+	0.166047i
$179$	626124.	−	183847.i	1.46059	−	0.428867i	0.547561	−	0.836766i	$-0.315557\pi$
$179$	626124.	−	183847.i	1.46059	−	0.428867i	0.913027	+	0.407899i	$0.133738\pi$
$180$	−19590.2	+	42896.6i	−0.0450669	+	0.0986828i
$181$	−12338.1	+	85813.3i	−0.0279931	+	0.194697i	−0.999019	−	0.0442766i	$-0.985902\pi$
$181$	−12338.1	+	85813.3i	−0.0279931	+	0.194697i	0.971026	+	0.238973i	$0.0768108\pi$
$182$	−262803.	+	168893.i	−0.588100	+	0.377949i
$183$	−55087.7			−0.121598
$184$	−433875.	−	244571.i	−0.944757	−	0.532549i
$185$	354619.			0.761785
$186$	321788.	−	206800.i	0.682005	−	0.438298i
$187$	88609.9	−	616295.i	0.185301	−	1.28880i
$188$	−39548.3	+	86598.7i	−0.0816080	+	0.178697i
$189$	−77927.8	+	22881.7i	−0.158686	+	0.0465943i
$190$	−15587.0	−	34130.7i	−0.0313240	−	0.0685901i
$191$	471101.	+	543680.i	0.934396	+	1.07835i	0.996771	+	0.0802977i	$0.0255871\pi$
$191$	471101.	+	543680.i	0.934396	+	1.07835i	−0.0623749	+	0.998053i	$0.519867\pi$
$192$	46416.3	+	322833.i	0.0908694	+	0.632011i
$193$	510732.	+	149965.i	0.986961	+	0.289798i	0.735095	−	0.677964i	$-0.237138\pi$
$193$	510732.	+	149965.i	0.986961	+	0.289798i	0.251866	+	0.967762i	$0.418956\pi$
$194$	−65157.7	+	75196.0i	−0.124297	+	0.143447i
$195$	−300512.	−	193128.i	−0.565947	−	0.363712i
$196$	31356.2	+	20151.4i	0.0583020	+	0.0374684i
$197$	−86120.3	+	99388.2i	−0.158103	+	0.182461i	−0.829274	−	0.558842i	$-0.811246\pi$
$197$	−86120.3	+	99388.2i	−0.158103	+	0.182461i	0.671171	+	0.741302i	$0.265791\pi$
$198$	−212866.	−	62503.2i	−0.385873	−	0.113302i
$199$	−129399.	−	899988.i	−0.231631	−	1.61103i	−0.691047	−	0.722810i	$-0.742850\pi$
$199$	−129399.	−	899988.i	−0.231631	−	1.61103i	0.459416	−	0.888221i	$-0.348059\pi$
$200$	204081.	+	235522.i	0.360767	+	0.416348i
$201$	−61186.6	−	133980.i	−0.106823	−	0.233910i
$202$	540898.	−	158822.i	0.932689	−	0.273862i
$203$	74577.7	−	163302.i	0.127019	−	0.278133i
$204$	11975.8	−	83293.3i	0.0201478	−	0.140131i
$205$	−706610.	+	454111.i	−1.17434	+	0.754704i
$206$	596269.			0.978982
$207$	166155.	−	120919.i	0.269518	−	0.196140i
$208$	−393561.			−0.630745
$209$	−53548.4	+	34413.5i	−0.0847971	+	0.0544958i
$210$	−47505.8	+	330410.i	−0.0743359	+	0.517017i
$211$	−400955.	+	877968.i	−0.619997	+	1.35760i	0.295525	+	0.955335i	$0.404505\pi$
$211$	−400955.	+	877968.i	−0.619997	+	1.35760i	−0.915522	+	0.402268i	$0.868222\pi$
$212$	193839.	−	56916.4i	0.296212	−	0.0869757i
$213$	−95242.9	−	208553.i	−0.143841	−	0.314968i
$214$	617679.	+	712839.i	0.921994	+	1.06404i
$215$	−104668.	−	727985.i	−0.154426	−	1.07405i
$216$	−137319.	−	40320.4i	−0.200261	−	0.0588018i
$217$	−639386.	+	737891.i	−0.921752	+	1.06376i
$218$	25680.1	+	16503.6i	0.0365978	+	0.0235200i
$219$	−198524.	−	127584.i	−0.279707	−	0.179757i
$220$	215324.	−	248497.i	0.299941	−	0.346150i
$221$	611608.	+	179584.i	0.842350	+	0.247336i
$222$	32087.9	+	223176.i	0.0436977	+	0.303924i
$223$	444747.	+	513265.i	0.598895	+	0.691162i	0.971557	−	0.236805i	$-0.0761003\pi$
$223$	444747.	+	513265.i	0.598895	+	0.691162i	−0.372662	+	0.927967i	$0.621555\pi$
$224$	−137971.	−	302115.i	−0.183725	−	0.402302i
$225$	−123373.	+	36225.5i	−0.162466	+	0.0477044i
$226$	272279.	−	596209.i	0.354604	−	0.776475i
$227$	56224.8	−	391052.i	0.0724208	−	0.503698i	−0.921035	−	0.389480i	$-0.872655\pi$
$227$	56224.8	−	391052.i	0.0724208	−	0.503698i	0.993456	−	0.114218i	$-0.0364362\pi$
$228$	−7237.16	+	4651.04i	−0.00922000	+	0.00592533i
$229$	−595200.			−0.750023			−0.375011	−	0.927020i	$-0.622361\pi$
$229$	−595200.			−0.750023			−0.375011	+	0.927020i	$0.622361\pi$
$230$	−168380.	−	827645.i	−0.209880	−	1.03163i
$231$	566287.			0.698244
$232$	266128.	−	171030.i	0.324617	−	0.208619i
$233$	39765.3	−	276574.i	0.0479860	−	0.333750i	−0.951660	−	0.307153i	$-0.900624\pi$
$233$	39765.3	−	276574.i	0.0479860	−	0.333750i	0.999646	−	0.0265973i	$-0.00846718\pi$
$234$	94351.1	−	206600.i	0.112644	−	0.246655i
$235$	−739366.	+	217097.i	−0.873353	+	0.256440i
$236$	145792.	+	319239.i	0.170393	+	0.373109i
$237$	556542.	+	642284.i	0.643617	+	0.742773i
$238$	−84770.1	−	589589.i	−0.0970064	−	0.674694i
$239$	−713472.	−	209494.i	−0.807945	−	0.237234i	−0.148428	−	0.988923i	$-0.547421\pi$
$239$	−713472.	−	209494.i	−0.807945	−	0.237234i	−0.659518	+	0.751689i	$0.729239\pi$
$240$	−275394.	+	317822.i	−0.308622	+	0.356169i
$241$	−849030.	−	545639.i	−0.941631	−	0.605149i	−0.0227740	−	0.999741i	$-0.507250\pi$
$241$	−849030.	−	545639.i	−0.941631	−	0.605149i	−0.918857	+	0.394591i	$0.870886\pi$
$242$	644252.	+	414036.i	0.707159	+	0.454464i
$243$	38668.9	−	44626.3i	0.0420093	−	0.0484814i
$244$	49808.5	+	14625.1i	0.0535586	+	0.0157262i
$245$	42935.8	+	298625.i	0.0456987	+	0.317841i
$246$	−349728.	−	403608.i	−0.368462	−	0.425228i
$247$	−27070.8	−	59276.9i	−0.0282331	−	0.0618220i
$248$	−1.65080e6	+	484718.i	−1.70437	+	0.500449i
$249$	396070.	−	867271.i	0.404830	−	0.886455i
$250$	72848.1	−	506670.i	0.0737171	−	0.512714i
$251$	−32292.5	+	20753.1i	−0.0323532	+	0.0207921i	−0.556717	−	0.830702i	$-0.687939\pi$
$251$	−32292.5	+	20753.1i	−0.0323532	+	0.0207921i	0.524364	+	0.851494i	$0.324303\pi$
$252$	76534.6			0.0759201
$253$	−1.34911e6	+	482559.i	−1.32509	+	0.473968i
$254$	−324410.			−0.315508
$255$	572997.	−	368243.i	0.551825	−	0.354637i
$256$	109580.	−	762148.i	0.104504	−	0.726841i
$257$	−174166.	+	381371.i	−0.164487	+	0.360176i	−0.973870	−	0.227104i	$-0.927074\pi$
$257$	−174166.	+	381371.i	−0.164487	+	0.360176i	0.809383	+	0.587280i	$0.199801\pi$
$258$	448680.	−	131744.i	0.419650	−	0.123220i
$259$	−239081.	−	523514.i	−0.221460	−	0.484930i
$260$	220441.	+	254402.i	0.202236	+	0.233393i
$261$	18575.4	+	129195.i	0.0168786	+	0.117394i
$262$	−1.04384e6	−	306499.i	−0.939466	−	0.275852i
$263$	−565036.	+	652086.i	−0.503717	+	0.581320i	−0.949479	−	0.313831i	$-0.898387\pi$
$263$	−565036.	+	652086.i	−0.503717	+	0.581320i	0.445762	+	0.895152i	$0.352933\pi$
$264$	839463.	+	539490.i	0.741296	+	0.476402i
$265$	1.37562e6	+	884059.i	1.20333	+	0.773333i
$266$	−39877.6	+	46021.3i	−0.0345562	+	0.0398799i
$267$	137402.	+	40344.8i	0.117954	+	0.0346345i
$268$	19752.9	+	137385.i	0.0167994	+	0.116843i
$269$	−1.23951e6	−	1.43047e6i	−1.04441	−	1.20531i	−0.978235	−	0.207500i	$-0.933467\pi$
$269$	−1.23951e6	−	1.43047e6i	−1.04441	−	1.20531i	−0.0661708	−	0.997808i	$-0.521078\pi$
$270$	−100819.	−	220762.i	−0.0841650	−	0.184296i
$271$	230835.	−	67779.1i	0.190931	−	0.0560625i	−0.184869	−	0.982763i	$-0.559186\pi$
$271$	230835.	−	67779.1i	0.190931	−	0.0560625i	0.375800	+	0.926701i	$0.377368\pi$
$272$	311734.	−	682603.i	0.255483	−	0.559430i
$273$	−82506.2	+	573843.i	−0.0670008	+	0.466001i
$274$	−1.00738e6	+	647405.i	−0.810621	+	0.520954i
$275$	896528.			0.714878
$276$	−182335.	+	65218.6i	−0.144078	+	0.0515346i
$277$	1.83498e6			1.43692			0.718460	−	0.695568i	$-0.244847\pi$
$277$	1.83498e6			1.43692			0.718460	+	0.695568i	$0.244847\pi$
$278$	1.17026e6	−	752079.i	0.908176	−	0.583649i
$279$	101024.	−	702641.i	0.0776991	−	0.540409i
$280$	623718.	−	1.36575e6i	0.475437	−	1.04106i
$281$	−79302.3	+	23285.2i	−0.0599128	+	0.0175920i	−0.311552	−	0.950229i	$-0.600849\pi$
$281$	−79302.3	+	23285.2i	−0.0599128	+	0.0175920i	0.251639	+	0.967821i	$0.419031\pi$
$282$	−203530.	−	445669.i	−0.152408	−	0.333726i
$283$	143034.	+	165071.i	0.106163	+	0.122519i	0.806344	−	0.591446i	$-0.201443\pi$
$283$	143034.	+	165071.i	0.106163	+	0.122519i	−0.700181	+	0.713965i	$0.746897\pi$
$284$	30747.4	+	213853.i	0.0226210	+	0.157333i
$285$	−66812.1	−	19617.8i	−0.0487240	−	0.0143067i
$286$	−1.03705e6	+	1.19682e6i	−0.749695	+	0.865195i
$287$	1.14678e6	+	736992.i	0.821818	+	0.528151i
$288$	203140.	+	130550.i	0.144316	+	0.0927462i
$289$	133887.	−	154514.i	0.0942963	−	0.108824i
$290$	514726.	+	151137.i	0.359403	+	0.105530i
$291$	26278.5	+	182771.i	0.0181915	+	0.126525i
$292$	145627.	+	168063.i	0.0999507	+	0.115349i
$293$	−660239.	−	1.44572e6i	−0.449296	−	0.983820i	−0.989798	−	0.142478i	$-0.954493\pi$
$293$	−660239.	−	1.44572e6i	−0.449296	−	0.983820i	0.540502	−	0.841343i	$-0.318234\pi$
$294$	−184052.	+	54042.5i	−0.124186	+	0.0364642i
$295$	−1.18006e6	+	2.58398e6i	−0.789496	+	1.72875i
$296$	144328.	−	1.00382e6i	0.0957461	−	0.665929i
$297$	−346358.	+	222591.i	−0.227842	+	0.146425i
$298$	−1.41427e6			−0.922555
$299$	−292436.	−	1.43742e6i	−0.189170	−	0.929835i
$300$	121167.			0.0777288
$301$	−1.00414e6	+	645321.i	−0.638818	+	0.410544i
$302$	265427.	−	1.84608e6i	0.167466	−	1.16475i
$303$	434599.	−	951640.i	0.271946	−	0.595479i
$304$	−73609.2	+	21613.6i	−0.0456823	+	0.0134135i
$305$	174549.	+	382208.i	0.107440	+	0.235261i
$306$	283598.	+	327290.i	0.173141	+	0.199815i
$307$	−323744.	−	2.25169e6i	−0.196045	−	1.36352i	−0.815622	−	0.578585i	$-0.803605\pi$
$307$	−323744.	−	2.25169e6i	−0.196045	−	1.36352i	0.619577	−	0.784936i	$-0.287304\pi$
$308$	−512019.	−	150342.i	−0.307545	−	0.0903035i
$309$	724645.	−	836285.i	0.431747	−	0.498262i
$310$	−2.45442e6	−	1.57736e6i	−1.45059	−	0.932238i
$311$	1.13894e6	+	731951.i	0.667727	+	0.429122i	0.830105	−	0.557607i	$-0.188280\pi$
$311$	1.13894e6	+	731951.i	0.667727	+	0.429122i	−0.162378	+	0.986729i	$0.551917\pi$
$312$	−668995.	+	772062.i	−0.389078	+	0.449020i
$313$	1.89578e6	+	556650.i	1.09377	+	0.321160i	0.778375	−	0.627800i	$-0.216044\pi$
$313$	1.89578e6	+	556650.i	1.09377	+	0.321160i	0.315396	+	0.948960i	$0.397863\pi$
$314$	352283.	+	2.45018e6i	0.201636	+	1.40241i
$315$	405676.	+	468175.i	0.230358	+	0.265847i
$316$	−332689.	−	728488.i	−0.187422	−	0.410398i
$317$	−1.05980e6	+	311187.i	−0.592349	+	0.173929i	−0.564149	−	0.825673i	$-0.690796\pi$
$317$	−1.05980e6	+	311187.i	−0.592349	+	0.173929i	−0.0281997	+	0.999602i	$0.508977\pi$
$318$	−431901.	+	945731.i	−0.239506	+	0.524445i
$319$	129517.	−	900807.i	0.0712604	−	0.495627i
$320$	2.09280e6	−	1.34496e6i	1.14249	−	0.734233i
$321$	1.75044e6			0.948167
$322$	−1.10831e6	+	806566.i	−0.595691	+	0.433511i
$323$	124254.			0.0662679
$324$	−46810.9	+	30083.5i	−0.0247733	+	0.0159208i
$325$	−130621.	+	908490.i	−0.0685970	+	0.477103i
$326$	−914034.	+	2.00146e6i	−0.476342	+	1.04304i
$327$	54355.6	−	15960.3i	0.0281109	−	0.00825412i
$328$	997869.	+	2.18503e6i	0.512140	+	1.12143i
$329$	818969.	+	945141.i	0.417136	+	0.481401i
$330$	240821.	+	1.67495e6i	0.121734	+	0.846675i
$331$	2.84247e6	+	834623.i	1.42602	+	0.418717i	0.901536	−	0.432704i	$-0.142441\pi$
$331$	2.84247e6	+	834623.i	1.42602	+	0.418717i	0.524483	+	0.851421i	$0.324259\pi$
$332$	−588363.	+	679008.i	−0.292955	+	0.338088i
$333$	352007.	+	226221.i	0.173957	+	0.111795i
$334$	2.37833e6	+	1.52846e6i	1.16656	+	0.749702i
$335$	−735703.	+	849047.i	−0.358171	+	0.413352i
$336$	654861.	+	192284.i	0.316447	+	0.0929172i
$337$	99656.7	+	693127.i	0.0478004	+	0.332459i	0.999664	+	0.0259360i	$0.00825661\pi$
$337$	99656.7	+	693127.i	0.0478004	+	0.332459i	−0.951863	+	0.306523i	$0.900834\pi$
$338$	117471.	+	135569.i	0.0559293	+	0.0645458i
$339$	−505299.	−	1.10645e6i	−0.238808	−	0.522917i
$340$	−615849.	+	180830.i	−0.288920	+	0.0848345i
$341$	−2.05610e6	+	4.50224e6i	−0.957544	+	2.09673i
$342$	6300.76	−	43822.7i	0.00291291	−	0.0202598i
$343$	1.98712e6	−	1.27704e6i	0.911988	−	0.586099i
$344$	−2.10332e6			−0.958315
$345$	−1.36543e6	−	769676.i	−0.617619	−	0.348145i
$346$	−2.12469e6			−0.954123
$347$	1.12127e6	−	720595.i	0.499903	−	0.321268i	−0.266275	−	0.963897i	$-0.585793\pi$
$347$	1.12127e6	−	720595.i	0.499903	−	0.321268i	0.766177	+	0.642629i	$0.222156\pi$
$348$	17504.4	−	121745.i	0.00774815	−	0.0538896i
$349$	−107008.	+	234316.i	−0.0470278	+	0.102976i	−0.931688	−	0.363261i	$-0.881663\pi$
$349$	−107008.	+	234316.i	−0.0470278	+	0.102976i	0.884660	+	0.466237i	$0.154391\pi$
$350$	822936.	−	241636.i	0.359084	−	0.105437i
$351$	−175098.	−	383411.i	−0.0758600	−	0.166110i
$352$	−1.10256e6	−	1.27243e6i	−0.474293	−	0.547364i
$353$	−52824.7	−	367404.i	−0.0225632	−	0.156930i	0.975425	−	0.220332i	$-0.0707141\pi$
$353$	−52824.7	−	367404.i	−0.0225632	−	0.156930i	−0.997988	+	0.0634018i	$0.979805\pi$
$354$	−1.73298e6	−	508849.i	−0.734997	−	0.215815i
$355$	−1.14519e6	+	1.32162e6i	−0.482290	+	0.556592i
$356$	−113523.	−	72956.9i	−0.0474744	−	0.0305099i
$357$	−929936.	−	597634.i	−0.386174	−	0.248179i
$358$	2.07241e6	−	2.39169e6i	0.854611	−	0.986274i
$359$	1.93800e6	+	569048.i	0.793629	+	0.233031i	0.653325	−	0.757078i	$-0.273374\pi$
$359$	1.93800e6	+	569048.i	0.793629	+	0.233031i	0.140305	+	0.990108i	$0.455192\pi$
$360$	155352.	+	1.08050e6i	0.0631774	+	0.439409i
$361$	1.61318e6	+	1.86171e6i	0.651501	+	0.751872i
$362$	174658.	+	382448.i	0.0700515	+	0.153391i
$363$	1.36365e6	−	400405.i	0.543172	−	0.159490i
$364$	226948.	−	496946.i	0.0897785	−	0.196588i
$365$	−256163.	+	1.78165e6i	−0.100643	+	0.699988i
$366$	−224745.	+	144435.i	−0.0876975	+	0.0563598i
$367$	1.76492e6			0.684005			0.342003	−	0.939699i	$-0.388895\pi$
$367$	1.76492e6			0.684005			0.342003	+	0.939699i	$0.388895\pi$
$368$	−1.72398e6	+	99941.4i	−0.663610	+	0.0384703i
$369$	−991096.			−0.378922
$370$	1.44676e6	−	929778.i	0.549406	−	0.353082i
$371$	377680.	−	2.62682e6i	0.142459	−	0.990822i
$372$	−277886.	+	608484.i	−0.104114	+	0.227978i
$373$	350850.	−	103019.i	0.130572	−	0.0383394i	−0.215794	−	0.976439i	$-0.569234\pi$
$373$	350850.	−	103019.i	0.130572	−	0.0383394i	0.346366	+	0.938100i	$0.387416\pi$
$374$	−1.25436e6	−	2.74667e6i	−0.463707	−	1.01538i
$375$	−622086.	−	717926.i	−0.228440	−	0.263634i
$376$	313622.	+	2.18129e6i	0.114403	+	0.795689i
$377$	893956.	+	262489.i	0.323939	+	0.0951170i
$378$	−257934.	+	297672.i	−0.0928494	+	0.107154i
$379$	−3.87944e6	−	2.49317e6i	−1.38730	−	0.891565i	−0.387759	−	0.921761i	$-0.626751\pi$
$379$	−3.87944e6	−	2.49317e6i	−1.38730	−	0.891565i	−0.999544	+	0.0301954i	$0.990387\pi$
$380$	55201.1	+	35475.6i	0.0196105	+	0.0126029i
$381$	−394254.	+	454994.i	−0.139144	+	0.160581i
$382$	3.34747e6	+	982905.i	1.17370	+	0.344630i
$383$	168879.	+	1.17458e6i	0.0588274	+	0.409153i	0.997863	+	0.0653346i	$0.0208115\pi$
$383$	168879.	+	1.17458e6i	0.0588274	+	0.409153i	−0.939036	+	0.343819i	$0.888279\pi$
$384$	473562.	+	546520.i	0.163889	+	0.189138i
$385$	−1.79431e6	−	3.92900e6i	−0.616946	−	1.35092i
$386$	2.47686e6	−	727273.i	0.846124	−	0.248444i
$387$	360505.	−	789395.i	0.122358	−	0.267927i
$388$	24763.3	−	172232.i	0.00835081	−	0.0580812i
$389$	−3.02563e6	+	1.94446e6i	−1.01378	+	0.651515i	−0.938368	−	0.345638i	$-0.887663\pi$
$389$	−3.02563e6	+	1.94446e6i	−1.01378	+	0.651515i	−0.0754089	+	0.997153i	$0.524026\pi$
$390$	−1.73238e6			−0.576744
$391$	2.72473e6	+	631351.i	0.901326	+	0.208847i
$392$	862795.			0.283591
$393$	−1.69845e6	+	1.09153e6i	−0.554717	+	0.356495i
$394$	−90764.5	+	631281.i	−0.0294561	+	0.204872i
$395$	2.69284e6	−	5.89650e6i	0.868397	−	1.90152i
$396$	372261.	−	109306.i	0.119292	−	0.0350272i
$397$	−591258.	−	1.29467e6i	−0.188278	−	0.412272i	0.791828	−	0.610744i	$-0.209130\pi$
$397$	−591258.	−	1.29467e6i	−0.188278	−	0.412272i	−0.980107	+	0.198472i	$0.936402\pi$
$398$	−2.88760e6	−	3.33247e6i	−0.913755	−	1.05453i
$399$	16082.9	+	111859.i	0.00505746	+	0.0351754i
$400$	1.03675e6	+	304419.i	0.323986	+	0.0951308i
$401$	859133.	−	991493.i	0.266809	−	0.307913i	−0.606498	−	0.795085i	$-0.707426\pi$
$401$	859133.	−	991493.i	0.266809	−	0.307913i	0.873306	+	0.487172i	$0.161971\pi$
$402$	−600911.	−	386182.i	−0.185458	−	0.119186i
$403$	−4.26274e6	−	2.73950e6i	−1.30745	−	0.840250i
$404$	−645600.	+	745062.i	−0.196793	+	0.227111i
$405$	−432149.	−	126891.i	−0.130917	−	0.0384407i
$406$	−123904.	−	861772.i	−0.0373053	−	0.259464i
$407$	−1.91056e6	−	2.20490e6i	−0.571707	−	0.659785i
$408$	−809182.	−	1.77186e6i	−0.240655	−	0.526962i
$409$	4.20966e6	−	1.23607e6i	1.24434	−	0.365371i	0.407696	−	0.913118i	$-0.366332\pi$
$409$	4.20966e6	−	1.23607e6i	1.24434	−	0.365371i	0.836644	+	0.547747i	$0.184514\pi$
$410$	−1.69217e6	+	3.70533e6i	−0.497146	+	1.08860i
$411$	−316265.	+	2.19967e6i	−0.0923520	+	0.642323i
$412$	−877224.	+	563758.i	−0.254605	+	0.163625i
$413$	4.61024e6			1.32999
$414$	360837.	−	928964.i	0.103469	−	0.266378i
$415$	−7.27225e6			−2.07276
$416$	1.45004e6	−	931886.i	0.410816	−	0.264016i
$417$	367400.	−	2.55532e6i	0.103466	−	0.719623i
$418$	−128236.	+	280798.i	−0.0358980	+	0.0786057i
$419$	−2.16534e6	+	635802.i	−0.602548	+	0.176924i	−0.568758	−	0.822505i	$-0.692576\pi$
$419$	−2.16534e6	+	635802.i	−0.602548	+	0.176924i	−0.0337898	+	0.999429i	$0.510758\pi$
$420$	−242504.	−	531011.i	−0.0670805	−	0.146886i
$421$	2.18010e6	+	2.51597e6i	0.599475	+	0.691831i	0.971675	−	0.236321i	$-0.0759418\pi$
$421$	2.18010e6	+	2.51597e6i	0.599475	+	0.691831i	−0.372200	+	0.928153i	$0.621396\pi$
$422$	666150.	+	4.63318e6i	0.182092	+	1.26648i
$423$	−872413.	−	256164.i	−0.237067	−	0.0696092i
$424$	3.06239e6	−	3.53418e6i	0.827267	−	0.954717i
$425$	−1.47224e6	−	946154.i	−0.395374	−	0.254091i
$426$	−935376.	−	601129.i	−0.249725	−	0.160489i
$427$	446564.	−	515362.i	0.118526	−	0.136786i
$428$	−1.58269e6	−	464720.i	−0.417626	−	0.122626i
$429$	418249.	+	2.90898e6i	0.109721	+	0.763129i
$430$	−2.33574e6	−	2.69558e6i	−0.609190	−	0.703042i
$431$	469552.	+	1.02818e6i	0.121756	+	0.266609i	0.960689	−	0.277626i	$-0.0895475\pi$
$431$	469552.	+	1.02818e6i	0.121756	+	0.266609i	−0.838933	+	0.544234i	$0.816820\pi$
$432$	−476114.	+	139800.i	−0.122744	+	0.0360410i
$433$	−2.36351e6	+	5.17536e6i	−0.605811	+	1.32654i	0.319592	+	0.947555i	$0.396454\pi$
$433$	−2.36351e6	+	5.17536e6i	−0.605811	+	1.32654i	−0.925403	+	0.378985i	$0.876273\pi$
$434$	−673866.	+	4.68684e6i	−0.171731	+	1.19442i
$435$	837520.	−	538241.i	0.212213	−	0.136381i
$436$	−53383.9			−0.0134491
$437$	−133636.	−	252786.i	−0.0334749	−	0.0633212i
$438$	−1.14445e6			−0.285043
$439$	6.60628e6	−	4.24560e6i	1.63605	−	1.05142i	0.691848	−	0.722043i	$-0.256797\pi$
$439$	6.60628e6	−	4.24560e6i	1.63605	−	1.05142i	0.944197	−	0.329380i	$-0.106840\pi$
$440$	1.08319e6	−	7.53375e6i	0.266730	−	1.85515i
$441$	−147882.	+	323815.i	−0.0362091	+	0.0792868i
$442$	2.96607e6	−	870918.i	0.722148	−	0.212042i
$443$	−2.45587e6	−	5.37760e6i	−0.594560	−	1.30191i	−0.932647	−	0.360790i	$-0.882507\pi$
$443$	−2.45587e6	−	5.37760e6i	−0.594560	−	1.30191i	0.338087	−	0.941115i	$-0.390220\pi$
$444$	−258215.	−	297996.i	−0.0621618	−	0.0717385i
$445$	−155446.	−	1.08115e6i	−0.0372117	−	0.258813i
$446$	3.16020e6	+	927919.i	0.752277	+	0.220888i
$447$	−1.71876e6	+	1.98356e6i	−0.406862	+	0.469543i
$448$	−3.39647e6	−	2.18278e6i	−0.799527	−	0.513825i
$449$	457615.	+	294091.i	0.107123	+	0.0688440i	0.593106	−	0.805125i	$-0.297902\pi$
$449$	457615.	+	294091.i	0.107123	+	0.0688440i	−0.485982	+	0.873969i	$0.661538\pi$
$450$	−408353.	+	471264.i	−0.0950614	+	0.109707i
$451$	6.63046e6	+	1.94688e6i	1.53498	+	0.450710i
$452$	163126.	+	1.13457e6i	0.0375559	+	0.261207i
$453$	−2.26661e6	−	2.61581e6i	−0.518957	−	0.598909i
$454$	−795919.	−	1.74282e6i	−0.181230	−	0.396838i
$455$	4.24285e6	−	1.24581e6i	0.960792	−	0.282114i
$456$	−82724.5	+	181141.i	−0.0186304	+	0.0407949i
$457$	−418937.	+	2.91377e6i	−0.0938335	+	0.652626i	0.887570	+	0.460672i	$0.152392\pi$
$457$	−418937.	+	2.91377e6i	−0.0938335	+	0.652626i	−0.981404	+	0.191954i	$0.938517\pi$
$458$	−2.42828e6	+	1.56056e6i	−0.540923	+	0.347630i
$459$	803689.			0.178056
$460$	1.03024e6	+	1.05842e6i	0.227009	+	0.233219i
$461$	−4.88422e6			−1.07039			−0.535196	−	0.844728i	$-0.679762\pi$
$461$	−4.88422e6			−1.07039			−0.535196	+	0.844728i	$0.679762\pi$
$462$	2.31032e6	−	1.48475e6i	0.503579	−	0.323631i
$463$	502431.	−	3.49448e6i	0.108924	−	0.757583i	−0.860012	−	0.510273i	$-0.829544\pi$
$463$	502431.	−	3.49448e6i	0.108924	−	0.757583i	0.968936	−	0.247310i	$-0.0795466\pi$
$464$	455646.	−	997725.i	0.0982500	−	0.215137i
$465$	−5.19515e6	+	1.52543e6i	−1.11421	+	0.327160i
$466$	−562918.	−	1.23262e6i	−0.120083	−	0.262945i
$467$	2.89625e6	+	3.34245e6i	0.614530	+	0.709206i	0.974659	−	0.223697i	$-0.0718126\pi$
$467$	2.89625e6	+	3.34245e6i	0.614530	+	0.709206i	−0.360128	+	0.932903i	$0.617267\pi$
$468$	56527.0	+	393154.i	0.0119300	+	0.0829751i
$469$	1.74943e6	+	513679.i	0.367252	+	0.107835i
$470$	−2.44723e6	+	2.82426e6i	−0.511012	+	0.589739i
$471$	3.86458e6	+	2.48361e6i	0.802694	+	0.515860i
$472$	6.83421e6	+	4.39208e6i	1.41199	+	0.907434i
$473$	−3.96245e6	+	4.57291e6i	−0.814350	+	0.939810i
$474$	3.95458e6	+	1.16117e6i	0.808452	+	0.237383i
$475$	25461.9	+	177092.i	0.00517794	+	0.0360134i
$476$	682154.	+	787248.i	0.137996	+	0.159255i
$477$	801526.	+	1.75510e6i	0.161295	+	0.353187i
$478$	−3.46008e6	+	1.01597e6i	−0.692653	+	0.203381i
$479$	−2.29826e6	+	5.03249e6i	−0.457678	+	1.00218i	0.530332	+	0.847790i	$0.322067\pi$
$479$	−2.29826e6	+	5.03249e6i	−0.457678	+	1.00218i	−0.988011	+	0.154386i	$0.950660\pi$
$480$	262119.	−	1.82308e6i	0.0519272	−	0.361162i
$481$	2.51268e6	−	1.61480e6i	0.495193	−	0.318241i
$482$	−4.89446e6			−0.959594
$483$	−215693.	+	2.53465e6i	−0.0420696	+	0.494368i
$484$	−1.33927e6			−0.259870
$485$	1.18483e6	−	761446.i	0.228719	−	0.146989i
$486$	40754.1	−	283451.i	0.00782674	−	0.0544362i
$487$	−2.72908e6	+	5.97586e6i	−0.521428	+	1.14177i	0.447468	+	0.894300i	$0.352326\pi$
$487$	−2.72908e6	+	5.97586e6i	−0.521428	+	1.14177i	−0.968896	+	0.247468i	$0.920401\pi$
$488$	1.15296e6	−	338540.i	0.219162	−	0.0643517i
$489$	1.69627e6	+	3.71432e6i	0.320792	+	0.702437i
$490$	958135.	+	1.10575e6i	0.180275	+	0.208049i
$491$	−400570.	−	2.78603e6i	−0.0749851	−	0.521532i	−0.992347	−	0.123479i	$-0.960595\pi$
$491$	−400570.	−	2.78603e6i	−0.0749851	−	0.521532i	0.917362	−	0.398054i	$-0.130314\pi$
$492$	896117.	+	263124.i	0.166898	+	0.0490058i
$493$	−1.16336e6	+	1.34259e6i	−0.215574	+	0.248785i
$494$	−265861.	−	170859.i	−0.0490160	−	0.0315007i
$495$	2.64183e6	+	1.69780e6i	0.484610	+	0.311440i
$496$	−3.90645e6	+	4.50828e6i	−0.712981	+	0.822824i
$497$	2.72316e6	+	799591.i	0.494517	+	0.145203i
$498$	−658034.	−	4.57673e6i	−0.118898	−	0.826955i
$499$	5.20012e6	+	6.00126e6i	0.934894	+	1.07892i	0.996727	+	0.0808384i	$0.0257598\pi$
$499$	5.20012e6	+	6.00126e6i	0.934894	+	1.07892i	−0.0618334	+	0.998086i	$0.519695\pi$
$500$	371870.	+	814282.i	0.0665221	+	0.145663i
$501$	5.03409e6	−	1.47814e6i	0.896039	−	0.263101i
$502$	−77333.2	+	169336.i	−0.0136964	+	0.0299909i
$503$	−670342.	+	4.66233e6i	−0.118134	+	0.821643i	0.841473	+	0.540300i	$0.181689\pi$
$503$	−670342.	+	4.66233e6i	−0.118134	+	0.821643i	−0.959607	+	0.281343i	$0.909220\pi$
$504$	1.49038e6	−	957806.i	0.261348	−	0.167958i
$505$	−7.97970e6			−1.39238
$506$	−4.23884e6	+	5.50598e6i	−0.735989	+	0.956001i
$507$	332901.			0.0575169
$508$	477268.	−	306721.i	0.0820545	−	0.0527333i
$509$	−250624.	+	1.74313e6i	−0.0428774	+	0.298219i	0.957087	+	0.289800i	$0.0935889\pi$
$509$	−250624.	+	1.74313e6i	−0.0428774	+	0.298219i	−0.999965	+	0.00841865i	$0.997320\pi$
$510$	1.37220e6	−	3.00469e6i	0.233610	−	0.511534i
$511$	2.80291e6	−	823008.i	0.474850	−	0.139429i
$512$	−2.61934e6	−	5.73554e6i	−0.441587	−	0.966940i
$513$	−53805.3	−	62094.6i	−0.00902676	−	0.0104174i
$514$	289362.	+	2.01256e6i	0.0483096	+	0.336001i
$515$	−8.09837e6	−	2.37790e6i	−1.34549	−	0.395071i
$516$	−535531.	+	618036.i	−0.0885443	+	0.102186i
$517$	5.33327e6	+	3.42749e6i	0.877541	+	0.563961i
$518$	−2.34800e6	−	1.50897e6i	−0.384480	−	0.247090i
$519$	−2.58212e6	+	2.97993e6i	−0.420784	+	0.485610i
$520$	7.47645e6	+	2.19528e6i	1.21251	+	0.356026i
$521$	−1.25755e6	−	8.74642e6i	−0.202969	−	1.41168i	−0.795413	−	0.606068i	$-0.792746\pi$
$521$	−1.25755e6	−	8.74642e6i	−0.202969	−	1.41168i	0.592444	−	0.805611i	$-0.298163\pi$
$522$	414521.	+	478383.i	0.0665841	+	0.0768421i
$523$	−1.22707e6	−	2.68691e6i	−0.196163	−	0.429536i	0.785833	−	0.618438i	$-0.212234\pi$
$523$	−1.22707e6	−	2.68691e6i	−0.196163	−	0.429536i	−0.981996	+	0.188902i	$0.939507\pi$
$524$	1.82547e6	−	536007.i	0.290434	−	0.0852790i
$525$	661211.	−	1.44785e6i	0.104699	−	0.229259i
$526$	−595506.	+	4.14183e6i	−0.0938473	+	0.652722i
$527$	8.12791e6	−	5.22349e6i	1.27483	−	0.819283i
$528$	3.45984e6			0.540096
$529$	−1.64603e6	−	6.22231e6i	−0.255739	−	0.966746i
$530$	7.93015e6			1.22629
$531$	−2.81976e6	+	1.81215e6i	−0.433986	+	0.278906i
$532$	15155.6	−	105409.i	0.00232163	−	0.0161473i
$533$	−2.93889e6	+	6.43528e6i	−0.448090	+	0.981181i
$534$	666348.	−	195657.i	0.101122	−	0.0296922i
$535$	−5.54637e6	−	1.21449e7i	−0.837770	−	1.83446i
$536$	2.10398e6	+	2.42812e6i	0.316322	+	0.365055i
$537$	−835817.	−	5.81323e6i	−0.125076	−	0.869925i
$538$	−8.80748e6	−	2.58611e6i	−1.31189	−	0.385204i
$539$	1.62543e6	−	1.87584e6i	0.240988	−	0.278115i
$540$	357048.	+	229461.i	0.0526917	+	0.0338629i
$541$	7.24953e6	+	4.65899e6i	1.06492	+	0.684382i	0.951026	−	0.309111i	$-0.100032\pi$
$541$	7.24953e6	+	4.65899e6i	1.06492	+	0.684382i	0.113893	+	0.993493i	$0.463668\pi$
$542$	764041.	−	881751.i	0.111717	−	0.128928i
$543$	748656.	+	219825.i	0.108964	+	0.0319947i
$544$	467729.	+	3.25313e6i	0.0677637	+	0.471307i
$545$	−282964.	−	326558.i	−0.0408075	−	0.0470944i
$546$	1.16796e6	+	2.55747e6i	0.167666	+	0.367138i
$547$	−1.14384e7	+	3.35862e6i	−1.63455	+	0.479946i	−0.964874	−	0.262712i	$-0.915383\pi$
$547$	−1.14384e7	+	3.35862e6i	−1.63455	+	0.479946i	−0.669671	+	0.742658i	$0.733565\pi$
$548$	869942.	−	1.90491e6i	0.123748	−	0.270971i
$549$	−70558.1	+	490743.i	−0.00999117	+	0.0694901i
$550$	3.65763e6	−	2.35062e6i	0.515576	−	0.331341i
$551$	181615.			0.0254843
$552$	−2.73445e6	+	3.55187e6i	−0.381964	+	0.496146i
$553$	−1.05203e7			−1.46291
$554$	7.48631e6	−	4.81116e6i	1.03632	−	0.666002i
$555$	454208.	−	3.15908e6i	0.0625924	−	0.435340i
$556$	−1.01060e6	+	2.21290e6i	−0.138641	+	0.303581i
$557$	1.17029e7	−	3.43629e6i	1.59829	−	0.469301i	0.643222	−	0.765679i	$-0.277597\pi$
$557$	1.17029e7	−	3.43629e6i	1.59829	−	0.469301i	0.955071	+	0.296378i	$0.0957789\pi$
$558$	−1.43010e6	−	3.13149e6i	−0.194438	−	0.425761i
$559$	−4.05661e6	−	4.68158e6i	−0.549078	−	0.633669i
$560$	−740861.	−	5.15280e6i	−0.0998313	−	0.694342i
$561$	−5.37671e6	−	1.57874e6i	−0.721289	−	0.211789i
$562$	−262483.	+	302922.i	−0.0350559	+	0.0404566i
$563$	−7.13604e6	−	4.58606e6i	−0.948826	−	0.609773i	−0.0279414	−	0.999610i	$-0.508895\pi$
$563$	−7.13604e6	−	4.58606e6i	−0.948826	−	0.609773i	−0.920884	+	0.389836i	$0.872532\pi$
$564$	720800.	+	463230.i	0.0954151	+	0.0613196i
$565$	−6.07568e6	+	7.01171e6i	−0.800707	+	0.924065i
$566$	1.01635e6	+	298427.i	0.133353	+	0.0391558i
$567$	104026.	+	723519.i	0.0135889	+	0.0945132i
$568$	3.27505e6	+	3.77960e6i	0.425938	+	0.491559i
$569$	441606.	+	966982.i	0.0571813	+	0.125210i	0.936066	−	0.351825i	$-0.114439\pi$
$569$	441606.	+	966982.i	0.0571813	+	0.125210i	−0.878884	+	0.477035i	$0.841712\pi$
$570$	−324014.	+	95139.1i	−0.0417712	+	0.0122651i
$571$	2.17178e6	−	4.75554e6i	0.278757	−	0.610393i	−0.717526	−	0.696532i	$-0.754726\pi$
$571$	2.17178e6	−	4.75554e6i	0.278757	−	0.610393i	0.996283	+	0.0861388i	$0.0274529\pi$
$572$	394132.	−	2.74125e6i	0.0503677	−	0.350315i
$573$	5.44672e6	−	3.50039e6i	0.693024	−	0.445379i
$574$	6.61093e6			0.837496
$575$	−341479.	+	4.01278e6i	−0.0430719	+	0.506146i
$576$	2.93537e6			0.368644
$577$	1.09237e6	−	702023.i	0.136594	−	0.0877833i	−0.470559	−	0.882368i	$-0.655948\pi$
$577$	1.09237e6	−	702023.i	0.136594	−	0.0877833i	0.607153	+	0.794585i	$0.292312\pi$
$578$	141107.	−	981423.i	0.0175683	−	0.122190i
$579$	1.99011e6	−	4.35772e6i	0.246706	−	0.540211i
$580$	−900155.	+	264309.i	−0.111109	+	0.0326244i
$581$	4.90289e6	+	1.07358e7i	0.602576	+	1.31946i
$582$	586419.	+	676764.i	0.0717631	+	0.0828190i
$583$	−1.91457e6	−	1.33162e7i	−0.233292	−	1.62258i
$584$	4.93909e6	+	1.45025e6i	0.599259	+	0.175958i
$585$	−2.10536e6	+	2.42972e6i	−0.254353	+	0.293539i
$586$	−6.48418e6	−	4.16713e6i	−0.780029	−	0.501294i
$587$	6.26484e6	+	4.02617e6i	0.750438	+	0.482277i	0.859104	−	0.511801i	$-0.171022\pi$
$587$	6.26484e6	+	4.02617e6i	0.750438	+	0.482277i	−0.108666	+	0.994078i	$0.534658\pi$
$588$	219679.	−	253523.i	0.0262026	−	0.0302394i
$589$	−947724.	−	278277.i	−0.112562	−	0.0330513i
$590$	1.96057e6	+	1.36360e7i	0.231874	+	1.61272i
$591$	775083.	+	894494.i	0.0912808	+	0.105344i
$592$	−1.46071e6	−	3.19850e6i	−0.171301	−	0.375096i
$593$	1.58886e7	−	4.66532e6i	1.85545	−	0.544810i	0.855831	−	0.517255i	$-0.173046\pi$
$593$	1.58886e7	−	4.66532e6i	1.85545	−	0.544810i	0.999620	−	0.0275542i	$-0.00877190\pi$
$594$	−829450.	+	1.81624e6i	−0.0964548	+	0.211207i
$595$	−1.19993e6	+	8.34570e6i	−0.138952	+	0.966429i
$596$	2.08066e6	−	1.33716e6i	0.239930	−	0.154194i
$597$	−8.18318e6			−0.939694
$598$	−4.96186e6	−	5.09760e6i	−0.567403	−	0.582925i
$599$	−1.50580e7			−1.71474			−0.857372	−	0.514698i	$-0.827904\pi$
$599$	−1.50580e7			−1.71474			−0.857372	+	0.514698i	$0.827904\pi$
$600$	2.35951e6	−	1.51637e6i	0.267574	−	0.171960i
$601$	163773.	−	1.13907e6i	0.0184951	−	0.128636i	−0.978482	−	0.206332i	$-0.933847\pi$
$601$	163773.	−	1.13907e6i	0.0184951	−	0.128636i	0.996977	+	0.0776959i	$0.0247563\pi$
$602$	−2.40468e6	+	5.26552e6i	−0.270437	+	0.592175i
$603$	−1.27192e6	+	373468.i	−0.142451	+	0.0418274i
$604$	1.35493e6	+	2.96689e6i	0.151121	+	0.330909i
$605$	−7.09890e6	−	8.19256e6i	−0.788501	−	0.909979i
$606$	−722048.	−	5.02195e6i	−0.0798702	−	0.555509i
$607$	−7.43931e6	−	2.18438e6i	−0.819523	−	0.240634i	−0.155012	−	0.987913i	$-0.549542\pi$
$607$	−7.43931e6	−	2.18438e6i	−0.819523	−	0.240634i	−0.664510	+	0.747279i	$0.731360\pi$
$608$	220030.	−	253928.i	0.0241392	−	0.0278581i
$609$	−1.35924e6	−	873530.i	−0.148509	−	0.0954410i
$610$	1.71423e6	+	1.10167e6i	0.186528	+	0.119875i
$611$	−4.25026e6	+	4.90506e6i	−0.460588	+	0.531546i
$612$	−726670.	−	213370.i	−0.0784258	−	0.0230279i
$613$	−2.17836e6	−	1.51509e7i	−0.234142	−	1.62849i	−0.679875	−	0.733328i	$-0.737966\pi$
$613$	−2.17836e6	−	1.51509e7i	−0.234142	−	1.62849i	0.445733	−	0.895166i	$-0.352943\pi$
$614$	−7.22452e6	−	8.33754e6i	−0.773371	−	0.892518i
$615$	3.14035e6	+	6.87640e6i	0.334803	+	0.733117i
$616$	−1.18521e7	+	3.48010e6i	−1.25848	+	0.369522i
$617$	1.10525e6	−	2.42017e6i	0.116882	−	0.255937i	−0.842144	−	0.539252i	$-0.818707\pi$
$617$	1.10525e6	−	2.42017e6i	0.116882	−	0.255937i	0.959027	+	0.283315i	$0.0914343\pi$
$618$	763722.	−	5.31180e6i	0.0804385	−	0.559462i
$619$	−1.29446e7	+	8.31900e6i	−1.35788	+	0.872659i	−0.998174	−	0.0604053i	$-0.980761\pi$
$619$	−1.29446e7	+	8.31900e6i	−1.35788	+	0.872659i	−0.359710	+	0.933064i	$0.617124\pi$
$620$	5.10227e6			0.533070
$621$	−864373.	−	1.63505e6i	−0.0899440	−	0.170139i
$622$	6.56571e6			0.680465
$623$	−1.49127e6	+	958384.i	−0.153935	+	0.0989280i
$624$	−504087.	+	3.50600e6i	−0.0518255	+	0.360454i
$625$	−5.07073e6	+	1.11033e7i	−0.519242	+	1.13698i
$626$	9.19382e6	−	2.69955e6i	0.937692	−	0.275331i
$627$	237982.	+	521109.i	0.0241755	+	0.0529370i
$628$	−2.83486e6	−	3.27160e6i	−0.286835	−	0.331026i
$629$	810495.	+	5.63712e6i	0.0816815	+	0.568107i
$630$	2.88258e6	+	846401.i	0.289354	+	0.0849620i
$631$	−1.36779e6	+	1.57852e6i	−0.136756	+	0.157825i	−0.819996	−	0.572369i	$-0.806025\pi$
$631$	−1.36779e6	+	1.57852e6i	−0.136756	+	0.157825i	0.683240	+	0.730194i	$0.260570\pi$
$632$	−1.55953e7	−	1.00225e7i	−1.55311	−	0.998122i
$633$	7.30773e6	+	4.69639e6i	0.724892	+	0.465860i
$634$	−3.50785e6	+	4.04828e6i	−0.346592	+	0.399988i
$635$	4.40605e6	+	1.29373e6i	0.433625	+	0.127324i
$636$	−258758.	−	1.79970e6i	−0.0253659	−	0.176424i
$637$	1.66405e6	+	1.92042e6i	0.162487	+	0.187520i
$638$	−1.83344e6	−	4.01467e6i	−0.178326	−	0.390479i
$639$	−1.97986e6	+	581339.i	−0.191815	+	0.0563219i
$640$	2.29134e6	−	5.01734e6i	0.221126	−	0.484199i
$641$	−281735.	+	1.95951e6i	−0.0270829	+	0.188366i	−0.998872	−	0.0474863i	$-0.984879\pi$
$641$	−281735.	+	1.95951e6i	−0.0270829	+	0.188366i	0.971789	+	0.235852i	$0.0757880\pi$
$642$	7.14140e6	−	4.58950e6i	0.683826	−	0.439468i
$643$	−7.29347e6			−0.695676			−0.347838	−	0.937555i	$-0.613084\pi$
$643$	−7.29347e6			−0.695676			−0.347838	+	0.937555i	$0.613084\pi$
$644$	867942.	−	2.23449e6i	0.0824662	−	0.212306i
$645$	−6.61924e6			−0.626483
$646$	506927.	−	325782.i	0.0477929	−	0.0307147i
$647$	1.46691e6	−	1.02026e7i	0.137767	−	0.958188i	−0.797267	−	0.603627i	$-0.793721\pi$
$647$	1.46691e6	−	1.02026e7i	0.137767	−	0.958188i	0.935033	−	0.354560i	$-0.115369\pi$
$648$	−535073.	+	1.17165e6i	−0.0500582	+	0.109612i
$649$	2.24240e7	−	6.58429e6i	2.08979	−	0.613617i
$650$	1.84907e6	+	4.04891e6i	0.171661	+	0.375885i
$651$	5.75448e6	+	6.64102e6i	0.532174	+	0.614161i
$652$	−547610.	−	3.80871e6i	−0.0504490	−	0.350880i
$653$	−7.19821e6	−	2.11359e6i	−0.660605	−	0.193971i	−0.0657894	−	0.997834i	$-0.520957\pi$
$653$	−7.19821e6	−	2.11359e6i	−0.660605	−	0.193971i	−0.594815	+	0.803863i	$0.702775\pi$
$654$	179912.	−	207630.i	0.0164481	−	0.0189821i
$655$	1.29549e7	+	8.32558e6i	1.17986	+	0.758248i
$656$	7.00647e6	+	4.50278e6i	0.635682	+	0.408528i
$657$	−1.39084e6	+	1.60512e6i	−0.125708	+	0.145075i
$658$	5.81928e6	+	1.70869e6i	0.523968	+	0.153851i
$659$	973411.	+	6.77022e6i	0.0873137	+	0.607280i	0.985755	+	0.168187i	$0.0537912\pi$
$659$	973411.	+	6.77022e6i	0.0873137	+	0.607280i	−0.898441	+	0.439093i	$0.855300\pi$
$660$	−1.93792e6	−	2.23647e6i	−0.173171	−	0.199850i
$661$	−5.94551e6	−	1.30188e7i	−0.529280	−	1.15896i	−0.965805	−	0.259269i	$-0.916518\pi$
$661$	−5.94551e6	−	1.30188e7i	−0.529280	−	1.15896i	0.436525	−	0.899692i	$-0.356209\pi$
$662$	1.37849e7	−	4.04762e6i	1.22253	−	0.358967i
$663$	2.38318e6	−	5.21843e6i	0.210558	−	0.461058i
$664$	−2.95977e6	+	2.05856e7i	−0.260518	+	1.81194i
$665$	725138.	−	466018.i	0.0635867	−	0.0408647i
$666$	2.02924e6			0.177275
$667$	3.98260e6	+	922813.i	0.346619	+	0.0803154i
$668$	−4.94409e6			−0.428692
$669$	5.14202e6	−	3.30457e6i	0.444189	−	0.285463i
$670$	−775377.	+	5.39286e6i	−0.0667307	+	0.464122i
$671$	1.43604e6	−	3.14448e6i	0.123129	−	0.269614i
$672$	−2.86808e6	+	842143.i	−0.245001	+	0.0719387i
$673$	−4.05238e6	−	8.87348e6i	−0.344884	−	0.755190i	0.655116	−	0.755528i	$-0.272620\pi$
$673$	−4.05238e6	−	8.87348e6i	−0.344884	−	0.755190i	−1.00000		0.000337908i	$0.999892\pi$
$674$	2.22389e6	+	2.56651e6i	0.188566	+	0.217617i
$675$	164691.	+	1.14545e6i	0.0139127	+	0.0967648i
$676$	−300999.	−	88381.2i	−0.0253337	−	0.00743864i
$677$	−1.01613e6	+	1.17268e6i	−0.0852077	+	0.0983350i	−0.796752	−	0.604306i	$-0.793450\pi$
$677$	−1.01613e6	+	1.17268e6i	−0.0852077	+	0.0983350i	0.711545	+	0.702641i	$0.247996\pi$
$678$	−4.96252e6	−	3.18922e6i	−0.414599	−	0.266446i
$679$	−1.92291e6	−	1.23578e6i	−0.160060	−	0.102864i
$680$	−9.72954e6	+	1.12285e7i	−0.806901	+	0.931213i
$681$	−3.41163e6	−	1.00175e6i	−0.281900	−	0.0827732i
$682$	3.41603e6	+	2.37590e7i	0.281229	+	1.95599i
$683$	5.61336e6	+	6.47816e6i	0.460438	+	0.531374i	0.937727	−	0.347373i	$-0.112926\pi$
$683$	5.61336e6	+	6.47816e6i	0.460438	+	0.531374i	−0.477289	+	0.878746i	$0.658381\pi$
$684$	32163.7	+	70428.6i	0.00262861	+	0.00575584i
$685$	1.62638e7	−	4.77549e6i	1.32433	−	0.388858i
$686$	4.75870e6	−	1.04201e7i	0.386081	−	0.845399i
$687$	−762352.	+	5.30228e6i	−0.0616260	+	0.428618i
$688$	−6.13497e6	+	3.94270e6i	−0.494130	+	0.317558i
$689$	1.37728e7			1.10528
$690$	−7.58865e6	+	439924.i	−0.606795	+	0.0351766i
$691$	1.02112e7			0.813548			0.406774	−	0.913529i	$-0.366654\pi$
$691$	1.02112e7			0.813548			0.406774	+	0.913529i	$0.366654\pi$
$692$	3.12581e6	−	2.00884e6i	0.248140	−	0.159470i
$693$	725320.	−	5.04471e6i	0.0573715	−	0.399028i
$694$	2.68518e6	−	5.87972e6i	0.211629	−	0.463402i
$695$	−1.88934e7	+	5.54760e6i	−1.48371	+	0.435655i
$696$	−1.18274e6	−	2.58984e6i	−0.0925478	−	0.202651i
$697$	−8.83365e6	−	1.01946e7i	−0.688745	−	0.794854i
$698$	177785.	+	1.23652e6i	0.0138120	+	0.0960646i
$699$	−2.41290e6	−	708490.i	−0.186787	−	0.0548455i
$700$	−982233.	+	1.13356e6i	−0.0757651	+	0.0874376i
$701$	−784753.	−	504330.i	−0.0603167	−	0.0387632i	0.510135	−	0.860094i	$-0.329595\pi$
$701$	−784753.	−	504330.i	−0.0603167	−	0.0387632i	−0.570452	+	0.821331i	$0.693232\pi$
$702$	−1.71963e6	−	1.10514e6i	−0.131702	−	0.0846395i
$703$	381274.	−	440014.i	0.0290970	−	0.0335798i
$704$	−1.96377e7	−	5.76616e6i	−1.49334	−	0.438485i
$705$	986985.	+	6.86463e6i	0.0747890	+	0.520169i
$706$	−1.17881e6	−	1.36042e6i	−0.0890088	−	0.102722i
$707$	5.37984e6	+	1.17802e7i	0.404782	+	0.886349i
$708$	3.03064e6	−	889877.i	0.227223	−	0.0667186i
$709$	5.06850e6	−	1.10985e7i	0.378672	−	0.829177i	−0.620322	−	0.784347i	$-0.712998\pi$
$709$	5.06850e6	−	1.10985e7i	0.378672	−	0.829177i	0.998995	−	0.0448299i	$-0.0142746\pi$
$710$	−1.20695e6	+	8.39452e6i	−0.0898552	+	0.624956i
$711$	6.43456e6	−	4.13524e6i	0.477359	−	0.306780i
$712$	−3.12369e6			−0.230924
$713$	−1.93685e7	−	1.09178e7i	−1.42683	−	0.804287i
$714$	−5.36087e6			−0.393541
$715$	1.88578e7	−	1.21192e7i	1.37951	−	0.886560i
$716$	−787623.	+	5.47804e6i	−0.0574164	+	0.399340i
$717$	−2.78010e6	+	6.08756e6i	−0.201958	+	0.442227i
$718$	9.39859e6	−	2.75968e6i	0.680380	−	0.199778i
$719$	5.19413e6	+	1.13736e7i	0.374706	+	0.820491i	0.999220	+	0.0394782i	$0.0125696\pi$
$719$	5.19413e6	+	1.13736e7i	0.374706	+	0.820491i	−0.624515	+	0.781013i	$0.714703\pi$
$720$	2.47855e6	+	2.86040e6i	0.178183	+	0.205634i
$721$	1.94943e6	+	1.35586e7i	0.139659	+	0.971349i
$722$	1.14626e7	+	3.36574e6i	0.818355	+	0.240291i
$723$	−5.94823e6	+	6.86462e6i	−0.423196	+	0.488395i
$724$	−618550.	−	397518.i	−0.0438559	−	0.0281845i
$725$	−2.15191e6	−	1.38295e6i	−0.152047	−	0.0977147i
$726$	4.51357e6	−	5.20894e6i	0.317818	−	0.366782i
$727$	673049.	+	197625.i	0.0472292	+	0.0138677i	0.305262	−	0.952268i	$-0.401256\pi$
$727$	673049.	+	197625.i	0.0472292	+	0.0138677i	−0.258033	+	0.966136i	$0.583074\pi$
$728$	−1.79972e6	−	1.25173e7i	−0.125857	−	0.875352i
$729$	−348020.	−	401636.i	−0.0242541	−	0.0279907i
$730$	3.62625e6	+	7.94037e6i	0.251855	+	0.551485i
$731$	1.13330e7	−	3.32768e6i	0.784427	−	0.230329i
$732$	194083.	−	424981.i	0.0133878	−	0.0293152i
$733$	−248072.	+	1.72538e6i	−0.0170536	+	0.118611i	−0.996570	−	0.0827538i	$-0.973628\pi$
$733$	−248072.	+	1.72538e6i	−0.0170536	+	0.118611i	0.979516	+	0.201365i	$0.0645376\pi$
$734$	7.20046e6	−	4.62746e6i	0.493310	−	0.317031i
$735$	2.71526e6			0.185393
$736$	6.11522e6	−	4.45032e6i	0.416119	−	0.302829i
$737$	9.24279e6			0.626808
$738$	−4.04344e6	+	2.59856e6i	−0.273282	+	0.175627i
$739$	−1.17855e6	+	8.19697e6i	−0.0793845	+	0.552131i	0.910852	+	0.412733i	$0.135426\pi$
$739$	−1.17855e6	+	8.19697e6i	−0.0793845	+	0.552131i	−0.990236	+	0.139398i	$0.955483\pi$
$740$	−1.24938e6	+	2.73576e6i	−0.0838715	+	0.183653i
$741$	−562735.	+	165234.i	−0.0376494	+	0.0110549i
$742$	−5.34644e6	−	1.17071e7i	−0.356496	−	0.780618i
$743$	−1.24645e6	−	1.43849e6i	−0.0828332	−	0.0955946i	0.712820	−	0.701347i	$-0.247418\pi$
$743$	−1.24645e6	−	1.43849e6i	−0.0828332	−	0.0955946i	−0.795653	+	0.605752i	$0.792872\pi$
$744$	2.20366e6	+	1.53268e7i	0.145953	+	1.01512i
$745$	1.92083e7	+	5.64005e6i	1.26794	+	0.372300i
$746$	1.16128e6	−	1.34019e6i	0.0763996	−	0.0881698i
$747$	−7.21870e6	−	4.63917e6i	−0.473323	−	0.304186i
$748$	4.44231e6	+	2.85490e6i	0.290305	+	0.186568i
$749$	−1.41898e7	+	1.63759e7i	−0.924213	+	1.06660i
$750$	−4.42031e6	−	1.29792e6i	−0.286945	−	0.0842547i
$751$	−1.27391e6	−	8.86021e6i	−0.0824209	−	0.573250i	−0.988624	−	0.150407i	$-0.951941\pi$
$751$	−1.27391e6	−	8.86021e6i	−0.0824209	−	0.573250i	0.906203	−	0.422842i	$-0.138968\pi$
$752$	5.00364e6	+	5.77451e6i	0.322657	+	0.372366i
$753$	143516.	+	314256.i	0.00922384	+	0.0201974i
$754$	4.33536e6	−	1.27298e6i	0.277713	−	0.0815440i
$755$	−1.09671e7	+	2.40145e7i	−0.700201	+	1.53323i
$756$	98028.1	−	681800.i	0.00623801	−	0.0433863i
$757$	−1.94293e7	+	1.24865e7i	−1.23231	+	0.791955i	−0.984248	−	0.176791i	$-0.943428\pi$
$757$	−1.94293e7	+	1.24865e7i	−1.23231	+	0.791955i	−0.248057	+	0.968745i	$0.579792\pi$
$758$	−2.23641e7			−1.41377
$759$	2.57084e6	+	1.26365e7i	0.161983	+	0.796200i
$760$	1.51891e6			0.0953888
$761$	5.48700e6	−	3.52628e6i	0.343458	−	0.220727i	−0.357527	−	0.933903i	$-0.616380\pi$
$761$	5.48700e6	−	3.52628e6i	0.343458	−	0.220727i	0.700985	+	0.713176i	$0.252744\pi$
$762$	−415515.	+	2.88997e6i	−0.0259238	+	0.180304i
$763$	−291317.	+	637895.i	−0.0181157	+	0.0396678i
$764$	−5.85406e6	+	1.71891e6i	−0.362847	+	0.106542i
$765$	−2.54654e6	−	5.57614e6i	−0.157324	−	0.344493i
$766$	3.76863e6	+	4.34924e6i	0.232066	+	0.267819i
$767$	3.40503e6	+	2.36825e7i	0.208994	+	1.45358i
$768$	−6.64916e6	−	1.95237e6i	−0.406784	−	0.119443i
$769$	−1.56058e6	+	1.80100e6i	−0.0951632	+	0.109824i	−0.801334	−	0.598218i	$-0.795876\pi$
$769$	−1.56058e6	+	1.80100e6i	−0.0951632	+	0.109824i	0.706170	+	0.708042i	$0.250421\pi$
$770$	−1.76219e7	−	1.13249e7i	−1.07109	−	0.688347i
$771$	3.17433e6	+	2.04002e6i	0.192316	+	0.123594i
$772$	−2.95631e6	+	3.41177e6i	−0.178528	+	0.206033i
$773$	−2.80056e7	−	8.22318e6i	−1.68576	−	0.494984i	−0.708267	−	0.705945i	$-0.750523\pi$
$773$	−2.80056e7	−	8.22318e6i	−1.68576	−	0.494984i	−0.977494	+	0.210961i	$0.932341\pi$
$774$	−598946.	−	4.16576e6i	−0.0359365	−	0.249944i
$775$	9.11030e6	+	1.05139e7i	0.544852	+	0.628793i
$776$	−1.67321e6	−	3.66382e6i	−0.0997463	−	0.218414i
$777$	−4.96989e6	+	1.45929e6i	−0.295321	+	0.0867141i
$778$	−7.24570e6	+	1.58659e7i	−0.429172	+	0.939756i
$779$	−196259.	+	1.36501e6i	−0.0115874	+	0.0805921i
$780$	2.54866e6	−	1.63793e6i	0.149995	−	0.0963957i
$781$	1.43873e7			0.844018
$782$	1.27716e7	−	4.56823e6i	0.746843	−	0.267135i
$783$	1.17471e6			0.0684742
$784$	2.51661e6	−	1.61732e6i	0.146226	−	0.0939739i
$785$	4.98661e6	−	3.46826e7i	0.288822	−	2.00880i
$786$	−4.06740e6	+	8.90637e6i	−0.234834	+	0.514214i
$787$	−3.35379e6	+	984761.i	−0.193018	+	0.0566753i	−0.376813	−	0.926289i	$-0.622980\pi$
$787$	−3.35379e6	+	984761.i	−0.193018	+	0.0566753i	0.183795	+	0.982965i	$0.441162\pi$
$788$	−463328.	−	1.01455e6i	−0.0265811	−	0.0582045i
$789$	5.08532e6	+	5.86877e6i	0.290821	+	0.335625i
$790$	−4.47392e6	−	3.11168e7i	−0.255047	−	1.77389i
$791$	1.44474e7	+	4.24213e6i	0.821008	+	0.241070i
$792$	5.88120e6	−	6.78727e6i	0.333160	−	0.384487i
$793$	2.97721e6	+	1.91334e6i	0.168123	+	0.108046i
$794$	−5.80672e6	−	3.73175e6i	−0.326873	−	0.210069i
$795$	9.63749e6	−	1.11223e7i	0.540812	−	0.624130i
$796$	7.39897e6	+	2.17253e6i	0.413894	+	0.121530i
$797$	−3.23665e6	−	2.25114e7i	−0.180489	−	1.25533i	−0.855611	−	0.517619i	$-0.826818\pi$
$797$	−3.23665e6	−	2.25114e7i	−0.180489	−	1.25533i	0.675122	−	0.737706i	$-0.264091\pi$
$798$	358899.	+	414191.i	0.0199510	+	0.0230247i
$799$	−5.14089e6	−	1.12570e7i	−0.284886	−	0.623814i
$800$	−4.54065e6	+	1.33325e6i	−0.250838	+	0.0736526i
$801$	535396.	−	1.17235e6i	0.0294845	−	0.0645620i
$802$	905463.	−	6.29763e6i	0.0497090	−	0.345734i
$803$	1.24578e7	−	8.00616e6i	0.681794	−	0.438163i
$804$	1.24918e6			0.0681528
$805$	1.82693e7	−	6.53468e6i	0.993647	−	0.355414i
$806$	−2.45737e7			−1.33240
$807$	−1.43308e7	+	9.20985e6i	−0.774616	+	0.497816i
$808$	−3.24770e6	+	2.25882e7i	−0.175004	+	1.21718i
$809$	273985.	−	599943.i	0.0147182	−	0.0322284i	−0.902130	−	0.431464i	$-0.857997\pi$
$809$	273985.	−	599943.i	0.0147182	−	0.0322284i	0.916848	+	0.399236i	$0.130724\pi$
$810$	−2.09577e6	+	615373.i	−0.112236	+	0.0329553i
$811$	−1.63416e6	−	3.57830e6i	−0.0872452	−	0.191040i	0.860980	−	0.508638i	$-0.169851\pi$
$811$	−1.63416e6	−	3.57830e6i	−0.0872452	−	0.191040i	−0.948225	+	0.317598i	$0.897124\pi$
$812$	997070.	+	1.15068e6i	0.0530683	+	0.0612441i
$813$	−308143.	−	2.14318e6i	−0.0163503	−	0.113719i
$814$	−1.35757e7	−	3.98618e6i	−0.718126	−	0.210861i
$815$	2.03959e7	−	2.35381e7i	1.07559	−	1.24130i
$816$	−5.68161e6	−	3.65135e6i	−0.298708	−	0.191968i
$817$	−1.01583e6	−	652832.i	−0.0532432	−	0.0342173i
$818$	1.39336e7	−	1.60802e7i	0.728082	−	0.840251i
$819$	5.00634e6	+	1.46999e6i	0.260802	+	0.0765784i
$820$	−1.01380e6	−	7.05114e6i	−0.0526524	−	0.366206i
$821$	−1.56659e7	−	1.80794e7i	−0.811143	−	0.936109i	0.187794	−	0.982209i	$-0.439866\pi$
$821$	−1.56659e7	−	1.80794e7i	−0.811143	−	0.936109i	−0.998937	+	0.0460992i	$0.985321\pi$
$822$	4.47705e6	+	9.80337e6i	0.231107	+	0.506053i
$823$	1.54599e7	−	4.53944e6i	0.795624	−	0.233616i	0.141435	−	0.989948i	$-0.454828\pi$
$823$	1.54599e7	−	4.53944e6i	0.795624	−	0.233616i	0.654189	+	0.756331i	$0.273010\pi$
$824$	−1.00271e7	+	2.19563e7i	−0.514468	+	1.12653i
$825$	1.14830e6	−	7.98662e6i	0.0587383	−	0.408534i
$826$	1.88087e7	−	1.20876e7i	0.959200	−	0.616440i
$827$	−2.89090e7			−1.46984			−0.734918	−	0.678156i	$-0.762779\pi$
$827$	−2.89090e7			−1.46984			−0.734918	+	0.678156i	$0.762779\pi$
$828$	347452.	+	1.70784e6i	0.0176124	+	0.0865709i
$829$	3.52253e7			1.78020			0.890099	−	0.455767i	$-0.150635\pi$
$829$	3.52253e7			1.78020			0.890099	+	0.455767i	$0.150635\pi$
$830$	−2.96691e7	+	1.90672e7i	−1.49489	+	0.960708i
$831$	2.35031e6	−	1.63468e7i	0.118065	−	0.821162i
$832$	8.70424e6	−	1.90596e7i	0.435936	−	0.954567i
$833$	−4.64889e6	+	1.36504e6i	−0.232133	+	0.0681604i
$834$	−5.20091e6	−	1.13884e7i	−0.258919	−	0.566954i
$835$	−2.62064e7	−	3.02438e7i	−1.30074	−	1.50114i
$836$	−76828.1	−	534351.i	−0.00380193	−	0.0264430i
$837$	−6.13000e6	−	1.79993e6i	−0.302445	−	0.0888060i
$838$	−7.16709e6	+	8.27126e6i	−0.352560	+	0.406875i
$839$	1.74272e7	+	1.11998e7i	0.854718	+	0.549294i	0.893043	−	0.449971i	$-0.148566\pi$
$839$	1.74272e7	+	1.11998e7i	0.854718	+	0.549294i	−0.0383246	+	0.999265i	$0.512202\pi$
$840$	−1.13678e7	−	7.30562e6i	−0.555875	−	0.357239i
$841$	1.17315e7	−	1.35389e7i	0.571958	−	0.660075i
$842$	1.54910e7	+	4.54856e6i	0.753005	+	0.221102i
$843$	105861.	+	736280.i	0.00513059	+	0.0356841i
$844$	−5.36058e6	−	6.18644e6i	−0.259034	−	0.298941i
$845$	−1.05482e6	−	2.30973e6i	−0.0508201	−	0.111281i
$846$	−4.23089e6	+	1.24230e6i	−0.203238	+	0.0596761i
$847$	−7.30845e6	+	1.60033e7i	−0.350039	+	0.766479i
$848$	2.30750e6	−	1.60490e7i	0.110193	−	0.766407i
$849$	1.65372e6	−	1.06278e6i	0.0787393	−	0.0506027i
$850$	−8.48715e6			−0.402916
$851$	1.05966e7	−	7.71166e6i	0.501585	−	0.365026i
$852$	1.94447e6			0.0917701
$853$	9.29127e6	−	5.97114e6i	0.437223	−	0.280986i	−0.303456	−	0.952845i	$-0.598141\pi$
$853$	9.29127e6	−	5.97114e6i	0.437223	−	0.280986i	0.740679	+	0.671860i	$0.234504\pi$
$854$	470646.	−	3.27341e6i	0.0220826	−	0.153588i
$855$	−260338.	+	570061.i	−0.0121793	+	0.0266690i
$856$	−3.66359e7	+	1.07573e7i	−1.70892	+	0.501786i
$857$	1.29962e7	+	2.84577e7i	0.604454	+	1.32357i	0.926303	+	0.376779i	$0.122968\pi$
$857$	1.29962e7	+	2.84577e7i	0.604454	+	1.32357i	−0.321849	+	0.946791i	$0.604304\pi$
$858$	9.33346e6	+	1.07714e7i	0.432837	+	0.499520i
$859$	−3.05717e6	−	2.12631e7i	−0.141364	−	0.983205i	−0.929794	−	0.368081i	$-0.880015\pi$
$859$	−3.05717e6	−	2.12631e7i	−0.141364	−	0.983205i	0.788430	−	0.615124i	$-0.210894\pi$
$860$	5.98491e6	+	1.75733e6i	0.275938	+	0.0810227i
$861$	8.03425e6	−	9.27201e6i	0.369349	−	0.426252i
$862$	4.61145e6	+	2.96360e6i	0.211383	+	0.135847i
$863$	1.08042e7	+	6.94344e6i	0.493816	+	0.317357i	0.763739	−	0.645526i	$-0.223362\pi$
$863$	1.08042e7	+	6.94344e6i	0.493816	+	0.317357i	−0.269922	+	0.962882i	$0.586998\pi$
$864$	1.42318e6	−	1.64244e6i	0.0648598	−	0.0748522i
$865$	2.88569e7	+	8.47315e6i	1.31132	+	0.385039i
$866$	3.92675e6	+	2.73112e7i	0.177926	+	1.23750i
$867$	−1.20499e6	−	1.39063e6i	−0.0544420	−	0.0628294i
$868$	−3.43990e6	−	7.53234e6i	−0.154970	−	0.339337i
$869$	−5.11705e7	+	1.50250e7i	−2.29864	+	0.674941i
$870$	2.00567e6	−	4.39180e6i	0.0898382	−	0.196718i
$871$	−1.34664e6	+	9.36611e6i	−0.0601461	+	0.418325i
$872$	−1.03956e6	+	668082.i	−0.0462974	+	0.0297535i
$873$	1.66185e6			0.0738002
$874$	−1.20798e6	−	680928.i	−0.0534913	−	0.0301524i
$875$	1.17593e7			0.519233
$876$	1.68369e6	−	1.08204e6i	0.0741315	−	0.0476414i
$877$	−1.31179e6	+	9.12372e6i	−0.0575926	+	0.400565i	0.940551	+	0.339654i	$0.110310\pi$
$877$	−1.31179e6	+	9.12372e6i	−0.0575926	+	0.400565i	−0.998143	+	0.0609115i	$0.980599\pi$
$878$	1.58205e7	−	3.46421e7i	0.692603	−	1.51659i
$879$	−1.37247e7	+	4.02994e6i	−0.599144	+	0.175925i
$880$	−1.09627e7	−	2.40050e7i	−0.477211	−	1.04495i
$881$	1.51903e7	+	1.75306e7i	0.659368	+	0.760951i	0.982674	−	0.185343i	$-0.0593398\pi$
$881$	1.51903e7	+	1.75306e7i	0.659368	+	0.760951i	−0.323306	+	0.946294i	$0.604794\pi$
$882$	245692.	+	1.70882e6i	0.0106346	+	0.0739650i
$883$	−3.18410e7	−	9.34937e6i	−1.37431	−	0.403535i	−0.490527	−	0.871426i	$-0.663196\pi$
$883$	−3.18410e7	−	9.34937e6i	−1.37431	−	0.403535i	−0.883786	+	0.467892i	$0.845014\pi$
$884$	−3.54022e6	+	4.08563e6i	−0.152370	+	0.175844i
$885$	2.15076e7	+	1.38221e7i	0.923068	+	0.593220i
$886$	−2.41190e7	−	1.55003e7i	−1.03223	−	0.663371i
$887$	2.67329e6	−	3.08515e6i	0.114087	−	0.131664i	−0.695833	−	0.718203i	$-0.744965\pi$
$887$	2.67329e6	−	3.08515e6i	0.114087	−	0.131664i	0.809921	+	0.586540i	$0.199510\pi$
$888$	−8.75759e6	−	2.57146e6i	−0.372694	−	0.109433i
$889$	−1.06062e6	−	7.37675e6i	−0.0450095	−	0.313048i
$890$	−3.46887e6	−	4.00329e6i	−0.146795	−	0.169411i
$891$	1.53930e6	+	3.37060e6i	0.0649575	+	0.142237i
$892$	−5.52657e6	+	1.62275e6i	−0.232565	+	0.0682871i
$893$	−525565.	+	1.15083e6i	−0.0220545	+	0.0482927i
$894$	−1.81145e6	+	1.25989e7i	−0.0758022	+	0.527216i
$895$	−3.76849e7	+	2.42186e7i	−1.57257	+	1.01063i
$896$	−8.95177e6			−0.372511
$897$	−1.31797e7	+	764041.i	−0.546919	+	0.0317056i
$898$	2.63804e6			0.109167
$899$	1.18801e7	−	7.63491e6i	0.490256	−	0.315068i
$900$	155195.	−	1.07940e6i	0.00638662	−	0.0444200i
$901$	−1.09092e7	+	2.38878e7i	−0.447694	+	0.980313i
$902$	3.21553e7	−	9.44165e6i	1.31594	−	0.386395i
$903$	4.46264e6	+	9.77181e6i	0.182126	+	0.398800i
$904$	1.73753e7	+	2.00522e7i	0.707151	+	0.816096i
$905$	−846974.	−	5.89084e6i	−0.0343755	−	0.239087i
$906$	−1.61057e7	−	4.72905e6i	−0.651866	−	0.191405i
$907$	−1.68486e7	+	1.94444e7i	−0.680059	+	0.784830i	−0.985915	−	0.167248i	$-0.946512\pi$
$907$	−1.68486e7	+	1.94444e7i	−0.680059	+	0.784830i	0.305856	+	0.952078i	$0.401057\pi$
$908$	2.81874e6	+	1.81149e6i	0.113459	+	0.0729159i
$909$	−7.92093e6	−	5.09048e6i	−0.317956	−	0.204338i
$910$	1.40434e7	−	1.62070e7i	0.562173	−	0.648783i
$911$	2.52371e7	+	7.41027e6i	1.00750	+	0.295827i	0.743528	−	0.668704i	$-0.233151\pi$
$911$	2.52371e7	+	7.41027e6i	1.00750	+	0.295827i	0.263967	+	0.964532i	$0.414969\pi$
$912$	98261.4	+	683423.i	0.00391197	+	0.0272084i
$913$	3.91802e7	+	4.52164e7i	1.55557	+	1.79523i
$914$	5.93047e6	+	1.29859e7i	0.234814	+	0.514171i
$915$	3.62843e6	−	1.06540e6i	0.143273	−	0.0420689i
$916$	2.09698e6	−	4.59175e6i	0.0825765	−	0.180817i
$917$	3.55678e6	−	2.47379e7i	0.139680	−	0.971494i
$918$	3.27887e6	−	2.10720e6i	0.128415	−	0.0825276i
$919$	2.67128e7			1.04335			0.521676	−	0.853144i	$-0.325307\pi$
$919$	2.67128e7			1.04335			0.521676	+	0.853144i	$0.325307\pi$
$920$	3.33078e7	+	7.71779e6i	1.29741	+	0.300624i
$921$	−2.04736e7			−0.795325
$922$	−1.99265e7	+	1.28060e7i	−0.771975	+	0.496118i
$923$	−2.09618e6	+	1.45793e7i	−0.0809887	+	0.563289i
$924$	−1.99512e6	+	4.36870e6i	−0.0768757	+	0.168334i
$925$	−7.86817e6	+	2.31030e6i	−0.302357	+	0.0887799i
$926$	−7.11242e6	−	1.55740e7i	−0.272577	−	0.596861i
$927$	−6.52180e6	−	7.52656e6i	−0.249269	−	0.287672i
$928$	683655.	+	4.75493e6i	0.0260596	+	0.181248i
$929$	3.44401e6	+	1.01125e6i	0.130926	+	0.0384433i	0.346539	−	0.938036i	$-0.387357\pi$
$929$	3.44401e6	+	1.01125e6i	0.130926	+	0.0384433i	−0.215613	+	0.976479i	$0.569175\pi$
$930$	−1.71955e7	+	1.98446e7i	−0.651938	+	0.752377i
$931$	416699.	+	267796.i	0.0157561	+	0.0101258i
$932$	1.99357e6	+	1.28119e6i	0.0751781	+	0.0483140i
$933$	7.97929e6	−	9.20860e6i	0.300096	−	0.346329i
$934$	2.05796e7	+	6.04272e6i	0.771916	+	0.226655i
$935$	6.08281e6	+	4.23069e7i	0.227549	+	1.58264i
$936$	6.02096e6	+	6.94855e6i	0.224634	+	0.259242i
$937$	−1.09355e7	−	2.39454e7i	−0.406902	−	0.890991i	−0.996524	−	0.0833117i	$-0.973450\pi$
$937$	−1.09355e7	−	2.39454e7i	−0.406902	−	0.890991i	0.589621	−	0.807680i	$-0.299277\pi$
$938$	8.48409e6	−	2.49115e6i	0.314846	−	0.0924471i
$939$	7.38703e6	−	1.61753e7i	0.273405	−	0.598673i
$940$	930075.	−	6.46881e6i	0.0343319	−	0.238784i
$941$	2.89635e7	−	1.86137e7i	1.06629	−	0.685265i	0.114941	−	0.993372i	$-0.463332\pi$
$941$	2.89635e7	−	1.86137e7i	1.06629	−	0.685265i	0.951352	+	0.308107i	$0.0996956\pi$
$942$	2.22784e7			0.818007
$943$	−1.12395e7	+	2.89358e7i	−0.411594	+	1.05964i
$944$	2.81671e7			1.02876
$945$	4.69029e6	−	3.01427e6i	0.170852	−	0.109800i
$946$	−4.17613e6	+	2.90456e7i	−0.151721	+	1.05524i
$947$	−6.13189e6	+	1.34270e7i	−0.222187	+	0.486522i	−0.987595	−	0.157024i	$-0.949810\pi$
$947$	−6.13189e6	+	1.34270e7i	−0.222187	+	0.486522i	0.765408	+	0.643546i	$0.222537\pi$
$948$	−6.91578e6	+	2.03066e6i	−0.249931	+	0.0733864i
$949$	6.29792e6	+	1.37905e7i	0.227003	+	0.497067i
$950$	568197.	+	655735.i	0.0204263	+	0.0235732i
$951$	1.41474e6	+	9.83973e6i	0.0507254	+	0.352803i
$952$	2.31359e7	+	6.79331e6i	0.827359	+	0.242934i
$953$	1.13714e7	−	1.31233e7i	0.405585	−	0.468071i	−0.515807	−	0.856705i	$-0.672508\pi$
$953$	1.13714e7	−	1.31233e7i	0.405585	−	0.468071i	0.921392	+	0.388635i	$0.127053\pi$
$954$	7.87175e6	+	5.05887e6i	0.280027	+	0.179963i
$955$	−4.15446e7	−	2.66991e7i	−1.47403	−	0.947301i
$956$	4.12985e6	−	4.76610e6i	0.146147	−	0.168662i
$957$	−7.85885e6	−	2.30757e6i	−0.277383	−	0.0814469i
$958$	3.81835e6	+	2.65572e7i	0.134419	+	0.934908i
$959$	−1.80148e7	−	2.07902e7i	−0.632534	−	0.729983i
$960$	−9.30090e6	−	2.03661e7i	−0.325722	−	0.713231i
$961$	−4.62232e7	+	1.35724e7i	−1.61455	+	0.474075i
$962$	6.01730e6	−	1.31760e7i	0.209635	−	0.459037i
$963$	2.24202e6	−	1.55936e7i	0.0779066	−	0.541852i
$964$	7.20067e6	−	4.62759e6i	0.249563	−	0.160385i
$965$	−3.65404e7			−1.26315
$966$	5.76565e6	+	1.09063e7i	0.198795	+	0.376041i
$967$	−4.19374e7			−1.44223			−0.721116	−	0.692815i	$-0.756370\pi$
$967$	−4.19374e7			−1.44223			−0.721116	+	0.692815i	$0.756370\pi$
$968$	−2.60800e7	+	1.67606e7i	−0.894580	+	0.574912i
$969$	159148.	−	1.10690e6i	0.00544493	−	0.0378703i
$970$	2.83740e6	−	6.21305e6i	0.0968260	−	0.212019i
$971$	−3.94112e7	+	1.15722e7i	−1.34144	+	0.393883i	−0.872184	−	0.489178i	$-0.837297\pi$
$971$	−3.94112e7	+	1.15722e7i	−1.34144	+	0.393883i	−0.469258	+	0.883061i	$0.655479\pi$
$972$	208039.	+	455542.i	0.00706283	+	0.0154654i
$973$	2.09275e7	+	2.41517e7i	0.708657	+	0.817833i
$974$	4.53413e6	+	3.15356e7i	0.153143	+	1.06513i
$975$	7.92588e6	+	2.32725e6i	0.267015	+	0.0784028i
$976$	2.72836e6	−	3.14870e6i	0.0916807	−	0.105805i
$977$	2.82930e7	+	1.81828e7i	0.948292	+	0.609430i	0.920734	−	0.390190i	$-0.127591\pi$
$977$	2.82930e7	+	1.81828e7i	0.948292	+	0.609430i	0.0275576	+	0.999620i	$0.491227\pi$
$978$	1.66590e7	+	1.07061e7i	0.556932	+	0.357919i
$979$	−5.88475e6	+	6.79136e6i	−0.196233	+	0.226465i
$980$	−2.45505e6	−	720868.i	−0.0816574	−	0.0239768i
$981$	−72559.7	−	504664.i	−0.00240726	−	0.0167429i
$982$	−8.93894e6	−	1.03161e7i	−0.295806	−	0.341379i
$983$	1.38226e7	+	3.02674e7i	0.456255	+	0.999059i	0.988325	+	0.152359i	$0.0486868\pi$
$983$	1.38226e7	+	3.02674e7i	0.456255	+	0.999059i	−0.532071	+	0.846700i	$0.678586\pi$
$984$	2.07432e7	−	6.09075e6i	0.682948	−	0.200532i
$985$	3.75026e6	−	8.21192e6i	0.123160	−	0.269683i
$986$	−1.22609e6	+	8.52766e6i	−0.0401635	+	0.279343i
$987$	9.46865e6	−	6.08513e6i	0.309382	−	0.198828i
$988$	552674.			0.0180126
$989$	−1.89587e7	−	1.94774e7i	−0.616336	−	0.633198i
$990$	1.52296e7			0.493855
$991$	−915182.	+	588152.i	−0.0296022	+	0.0190242i	−0.555358	−	0.831611i	$-0.687419\pi$
$991$	−915182.	+	588152.i	−0.0296022	+	0.0190242i	0.525756	+	0.850635i	$0.323782\pi$
$992$	3.71813e6	−	2.58602e7i	0.119963	−	0.834358i
$993$	1.10759e7	−	2.42528e7i	0.356455	−	0.780528i
$994$	1.32063e7	−	3.87772e6i	0.423951	−	0.124483i
$995$	2.59289e7	+	5.67764e7i	0.830283	+	1.81807i
$996$	5.29527e6	+	6.11107e6i	0.169137	+	0.195195i
$997$	−1.07484e6	−	7.47568e6i	−0.0342457	−	0.238184i	0.965508	−	0.260373i	$-0.0838456\pi$
$997$	−1.07484e6	−	7.47568e6i	−0.0342457	−	0.238184i	−0.999754	+	0.0221889i	$0.992936\pi$
$998$	3.69501e7	+	1.08495e7i	1.17433	+	0.344814i
$999$	2.46613e6	−	2.84607e6i	0.0781812	−	0.0902259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.6.e.a.58.8	yes	100
23.2	even	11	inner	69.6.e.a.25.8	✓	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.6.e.a.25.8	✓	100	23.2	even	11	inner
69.6.e.a.58.8	yes	100	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(4.07977 - 2.62191i) q^{2} +(1.28083 - 8.90839i) q^{3} +(-3.52316 + 7.71464i) q^{4} +(-65.8664 + 19.3401i) q^{5} +(-18.1315 - 39.7024i) q^{6} +(72.9578 + 84.1978i) q^{7} +(27.9390 + 194.320i) q^{8} +(-77.7189 - 22.8203i) q^{9} +O(q^{10})\)	\(q+(4.07977 - 2.62191i) q^{2} +(1.28083 - 8.90839i) q^{3} +(-3.52316 + 7.71464i) q^{4} +(-65.8664 + 19.3401i) q^{5} +(-18.1315 - 39.7024i) q^{6} +(72.9578 + 84.1978i) q^{7} +(27.9390 + 194.320i) q^{8} +(-77.7189 - 22.8203i) q^{9} +(-218.012 + 251.599i) q^{10} +(475.114 + 305.338i) q^{11} +(64.2125 + 41.2668i) q^{12} +(-378.634 + 436.967i) q^{13} +(518.410 + 152.219i) q^{14} +(87.9255 + 611.535i) q^{15} +(445.749 + 514.422i) q^{16} +(-457.976 - 1002.83i) q^{17} +(-376.908 + 110.670i) q^{18} +(-46.8199 + 102.521i) q^{19} +(82.8557 - 576.274i) q^{20} +(843.514 - 542.094i) q^{21} +2738.93 q^{22} +(-1547.63 + 2010.27i) q^{23} +1766.86 q^{24} +(1335.42 - 858.225i) q^{25} +(-399.052 + 2775.47i) q^{26} +(-302.838 + 663.122i) q^{27} +(-906.598 + 266.201i) q^{28} +(-669.400 - 1465.78i) q^{29} +(1962.11 + 2264.39i) q^{30} +(1247.22 + 8674.57i) q^{31} +(-2860.39 - 839.886i) q^{32} +(3328.61 - 3841.42i) q^{33} +(-4497.76 - 2890.54i) q^{34} +(-6433.87 - 4134.79i) q^{35} +(449.867 - 519.174i) q^{36} +(-4956.57 - 1455.38i) q^{37} +(77.7871 + 541.021i) q^{38} +(3407.71 + 3932.70i) q^{39} +(-5598.41 - 12258.8i) q^{40} +(11740.1 - 3447.21i) q^{41} +(2020.02 - 4423.24i) q^{42} +(-1524.73 + 10604.8i) q^{43} +(-4029.47 + 2589.58i) q^{44} +5560.41 q^{45} +(-1043.23 + 12259.2i) q^{46} +11225.2 q^{47} +(5153.60 - 3312.02i) q^{48} +(625.456 - 4350.14i) q^{49} +(3198.04 - 7002.73i) q^{50} +(-9520.17 + 2795.38i) q^{51} +(-2037.06 - 4460.53i) q^{52} +(-15599.1 - 18002.3i) q^{53} +(503.137 + 3499.40i) q^{54} +(-37199.3 - 10922.7i) q^{55} +(-14323.0 + 16529.6i) q^{56} +(853.332 + 548.403i) q^{57} +(-6574.15 - 4224.95i) q^{58} +(27098.8 - 31273.6i) q^{59} +(-5027.55 - 1476.22i) q^{60} +(-871.088 - 6058.55i) q^{61} +(27832.3 + 32120.2i) q^{62} +(-3748.78 - 8208.69i) q^{63} +(-34771.2 + 10209.8i) q^{64} +(16488.3 - 36104.3i) q^{65} +(3508.11 - 24399.4i) q^{66} +(13767.6 - 8847.90i) q^{67} +9349.98 q^{68} +(15926.0 + 16361.7i) q^{69} -37089.8 q^{70} +(21430.6 - 13772.6i) q^{71} +(2263.06 - 15739.9i) q^{72} +(10892.5 - 23851.2i) q^{73} +(-24037.6 + 7058.06i) q^{74} +(-5934.95 - 12995.7i) q^{75} +(-625.961 - 722.398i) q^{76} +(8954.57 + 62280.4i) q^{77} +(24213.9 + 7109.83i) q^{78} +(-61838.0 + 71364.9i) q^{79} +(-39308.9 - 25262.3i) q^{80} +(5519.46 + 3547.14i) q^{81} +(38858.7 - 44845.4i) q^{82} +(101646. + 29845.8i) q^{83} +(1210.22 + 8417.29i) q^{84} +(49560.0 + 57195.3i) q^{85} +(21584.1 + 47262.7i) q^{86} +(-13915.2 + 4085.86i) q^{87} +(-46059.0 + 100855. i) q^{88} +(-2264.42 + 15749.4i) q^{89} +(22685.2 - 14578.9i) q^{90} -64416.0 q^{91} +(-10056.0 - 19021.9i) q^{92} +78874.0 q^{93} +(45796.4 - 29431.6i) q^{94} +(1101.09 - 7658.22i) q^{95} +(-11145.7 + 24405.7i) q^{96} +(-19685.7 + 5780.23i) q^{97} +(-8853.97 - 19387.5i) q^{98} +(-29957.5 - 34572.8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q - 8 q^{2} + 90 q^{3} - 148 q^{4} + 6 q^{5} + 171 q^{6} + 118 q^{7} + 1616 q^{8} - 810 q^{9}+O(q^{10}) \) 100 * q - 8 * q^2 + 90 * q^3 - 148 * q^4 + 6 * q^5 + 171 * q^6 + 118 * q^7 + 1616 * q^8 - 810 * q^9	\( 100 q - 8 q^{2} + 90 q^{3} - 148 q^{4} + 6 q^{5} + 171 q^{6} + 118 q^{7} + 1616 q^{8} - 810 q^{9} - 262 q^{10} + 724 q^{11} + 1332 q^{12} + 2730 q^{13} + 328 q^{14} - 1143 q^{15} - 8596 q^{16} - 5699 q^{17} - 648 q^{18} + 1993 q^{19} + 28263 q^{20} - 1062 q^{21} - 19378 q^{22} + 9084 q^{23} + 1296 q^{24} - 4752 q^{25} - 7828 q^{26} + 7290 q^{27} - 29888 q^{28} - 37644 q^{29} + 2358 q^{30} - 2471 q^{31} + 42352 q^{32} + 1305 q^{33} + 47233 q^{34} + 9062 q^{35} - 21789 q^{36} + 1170 q^{37} - 133648 q^{38} - 24570 q^{39} + 135509 q^{40} - 8556 q^{41} - 17208 q^{42} + 39714 q^{43} + 108207 q^{44} - 44064 q^{45} + 87076 q^{46} + 56898 q^{47} + 60237 q^{48} + 35646 q^{49} + 12207 q^{50} - 48600 q^{51} - 368495 q^{52} + 11912 q^{53} - 34263 q^{54} - 231697 q^{55} + 235302 q^{56} + 4437 q^{57} - 201743 q^{58} + 116756 q^{59} + 209349 q^{60} - 191952 q^{61} - 91633 q^{62} + 9558 q^{63} + 383796 q^{64} + 120963 q^{65} + 92925 q^{66} - 7699 q^{67} - 486648 q^{68} + 9522 q^{69} + 340272 q^{70} + 60029 q^{71} + 130896 q^{72} + 110721 q^{73} - 290458 q^{74} + 48906 q^{75} + 30961 q^{76} - 325750 q^{77} + 51444 q^{78} - 267838 q^{79} - 519366 q^{80} - 65610 q^{81} - 739402 q^{82} - 236288 q^{83} - 382428 q^{84} + 72669 q^{85} + 643772 q^{86} + 62784 q^{87} + 976500 q^{88} + 455688 q^{89} - 21222 q^{90} + 267512 q^{91} + 70711 q^{92} - 12906 q^{93} + 1298755 q^{94} + 1815505 q^{95} + 461520 q^{96} + 271324 q^{97} - 1533115 q^{98} - 11745 q^{99}+O(q^{100}) \) 100 * q - 8 * q^2 + 90 * q^3 - 148 * q^4 + 6 * q^5 + 171 * q^6 + 118 * q^7 + 1616 * q^8 - 810 * q^9 - 262 * q^10 + 724 * q^11 + 1332 * q^12 + 2730 * q^13 + 328 * q^14 - 1143 * q^15 - 8596 * q^16 - 5699 * q^17 - 648 * q^18 + 1993 * q^19 + 28263 * q^20 - 1062 * q^21 - 19378 * q^22 + 9084 * q^23 + 1296 * q^24 - 4752 * q^25 - 7828 * q^26 + 7290 * q^27 - 29888 * q^28 - 37644 * q^29 + 2358 * q^30 - 2471 * q^31 + 42352 * q^32 + 1305 * q^33 + 47233 * q^34 + 9062 * q^35 - 21789 * q^36 + 1170 * q^37 - 133648 * q^38 - 24570 * q^39 + 135509 * q^40 - 8556 * q^41 - 17208 * q^42 + 39714 * q^43 + 108207 * q^44 - 44064 * q^45 + 87076 * q^46 + 56898 * q^47 + 60237 * q^48 + 35646 * q^49 + 12207 * q^50 - 48600 * q^51 - 368495 * q^52 + 11912 * q^53 - 34263 * q^54 - 231697 * q^55 + 235302 * q^56 + 4437 * q^57 - 201743 * q^58 + 116756 * q^59 + 209349 * q^60 - 191952 * q^61 - 91633 * q^62 + 9558 * q^63 + 383796 * q^64 + 120963 * q^65 + 92925 * q^66 - 7699 * q^67 - 486648 * q^68 + 9522 * q^69 + 340272 * q^70 + 60029 * q^71 + 130896 * q^72 + 110721 * q^73 - 290458 * q^74 + 48906 * q^75 + 30961 * q^76 - 325750 * q^77 + 51444 * q^78 - 267838 * q^79 - 519366 * q^80 - 65610 * q^81 - 739402 * q^82 - 236288 * q^83 - 382428 * q^84 + 72669 * q^85 + 643772 * q^86 + 62784 * q^87 + 976500 * q^88 + 455688 * q^89 - 21222 * q^90 + 267512 * q^91 + 70711 * q^92 - 12906 * q^93 + 1298755 * q^94 + 1815505 * q^95 + 461520 * q^96 + 271324 * q^97 - 1533115 * q^98 - 11745 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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