LMFDB - Embedded newform 74.5.g.b.45.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,5,Mod(23,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("74.23");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	74.g (of order $12$, degree $4$, 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:	$7.64937726820$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			45.6
Character	$\chi$	$=$	74.45
Dual form			74.5.g.b.51.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.73205 + 0.732051i) q^{2} +(9.05180 + 5.22606i) q^{3} +(6.92820 + 4.00000i) q^{4} +(8.32031 - 2.22942i) q^{5} +(20.9042 + 20.9042i) q^{6} +(41.9891 - 72.7273i) q^{7} +(16.0000 + 16.0000i) q^{8} +(14.1234 + 24.4624i) q^{9} +O(q^{10})$	\(q+(2.73205 + 0.732051i) q^{2} +(9.05180 + 5.22606i) q^{3} +(6.92820 + 4.00000i) q^{4} +(8.32031 - 2.22942i) q^{5} +(20.9042 + 20.9042i) q^{6} +(41.9891 - 72.7273i) q^{7} +(16.0000 + 16.0000i) q^{8} +(14.1234 + 24.4624i) q^{9} +24.3635 q^{10} +207.159i q^{11} +(41.8085 + 72.4144i) q^{12} +(-148.606 + 39.8189i) q^{13} +(167.957 - 167.957i) q^{14} +(86.9648 + 23.3022i) q^{15} +(32.0000 + 55.4256i) q^{16} +(65.3228 - 243.788i) q^{17} +(20.6781 + 77.1716i) q^{18} +(-517.100 + 138.557i) q^{19} +(66.5625 + 17.8354i) q^{20} +(760.154 - 438.875i) q^{21} +(-151.651 + 565.969i) q^{22} +(278.754 + 278.754i) q^{23} +(61.2119 + 228.446i) q^{24} +(-477.009 + 275.401i) q^{25} -435.149 q^{26} -551.383i q^{27} +(581.818 - 335.913i) q^{28} +(567.557 - 567.557i) q^{29} +(220.534 + 127.325i) q^{30} +(347.201 - 347.201i) q^{31} +(46.8513 + 174.851i) q^{32} +(-1082.62 + 1875.16i) q^{33} +(356.930 - 618.221i) q^{34} +(187.223 - 698.725i) q^{35} +225.974i q^{36} +(-761.188 - 1137.87i) q^{37} -1514.17 q^{38} +(-1553.25 - 416.192i) q^{39} +(168.796 + 97.4542i) q^{40} +(-1862.31 - 1075.20i) q^{41} +(2398.06 - 642.558i) q^{42} +(1403.59 + 1403.59i) q^{43} +(-828.636 + 1435.24i) q^{44} +(172.048 + 172.048i) q^{45} +(557.508 + 965.633i) q^{46} -2179.87 q^{47} +668.936i q^{48} +(-2325.67 - 4028.19i) q^{49} +(-1504.82 + 403.215i) q^{50} +(1865.34 - 1865.34i) q^{51} +(-1188.85 - 318.551i) q^{52} +(1871.89 + 3242.20i) q^{53} +(403.640 - 1506.41i) q^{54} +(461.844 + 1723.63i) q^{55} +(1835.46 - 491.811i) q^{56} +(-5404.79 - 1448.21i) q^{57} +(1966.07 - 1135.11i) q^{58} +(962.555 - 3592.30i) q^{59} +(509.301 + 509.301i) q^{60} +(-78.0603 - 291.325i) q^{61} +(1202.74 - 694.403i) q^{62} +2372.12 q^{63} +512.000i q^{64} +(-1147.68 + 662.611i) q^{65} +(-4330.50 + 4330.50i) q^{66} +(1528.15 + 882.279i) q^{67} +(1427.72 - 1427.72i) q^{68} +(1066.44 + 3980.01i) q^{69} +(1023.00 - 1771.90i) q^{70} +(-1345.22 + 2330.00i) q^{71} +(-165.425 + 617.373i) q^{72} +8297.65i q^{73} +(-1246.62 - 3665.95i) q^{74} -5757.05 q^{75} +(-4136.80 - 1108.45i) q^{76} +(15066.1 + 8698.42i) q^{77} +(-3938.88 - 2274.11i) q^{78} +(7427.56 - 1990.21i) q^{79} +(389.817 + 389.817i) q^{80} +(4025.55 - 6972.46i) q^{81} +(-4300.81 - 4300.81i) q^{82} +(-3892.71 - 6742.37i) q^{83} +7022.01 q^{84} -2174.02i q^{85} +(2807.18 + 4862.17i) q^{86} +(8103.50 - 2171.33i) q^{87} +(-3314.54 + 3314.54i) q^{88} +(3647.87 + 977.444i) q^{89} +(344.096 + 595.992i) q^{90} +(-3343.92 + 12479.7i) q^{91} +(816.249 + 3046.28i) q^{92} +(4957.29 - 1328.30i) q^{93} +(-5955.51 - 1595.77i) q^{94} +(-3993.53 + 2305.67i) q^{95} +(-489.695 + 1827.57i) q^{96} +(10517.2 + 10517.2i) q^{97} +(-3405.02 - 12707.7i) q^{98} +(-5067.61 + 2925.79i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{2} - 102 q^{5} + 40 q^{6} - 48 q^{7} + 448 q^{8} + 556 q^{9}+O(q^{10}) $ 28 * q + 28 * q^2 - 102 * q^5 + 40 * q^6 - 48 * q^7 + 448 * q^8 + 556 * q^9	\( 28 q + 28 q^{2} - 102 q^{5} + 40 q^{6} - 48 q^{7} + 448 q^{8} + 556 q^{9} - 120 q^{10} + 80 q^{12} - 88 q^{13} - 192 q^{14} + 12 q^{15} + 896 q^{16} - 540 q^{17} - 1112 q^{18} + 976 q^{19} - 816 q^{20} - 618 q^{21} + 752 q^{22} + 1996 q^{23} - 160 q^{24} + 414 q^{25} - 2504 q^{26} + 1584 q^{28} + 852 q^{29} + 804 q^{30} + 300 q^{31} - 1792 q^{32} + 316 q^{33} + 300 q^{34} + 796 q^{35} - 3678 q^{37} - 328 q^{38} + 3630 q^{39} - 2784 q^{40} - 6426 q^{41} - 1348 q^{42} - 5548 q^{43} - 1280 q^{44} + 10164 q^{45} + 3992 q^{46} - 7624 q^{47} - 7388 q^{49} + 1768 q^{50} + 15382 q^{51} - 704 q^{52} + 13538 q^{53} - 1108 q^{54} - 10352 q^{55} + 2400 q^{56} - 12946 q^{57} + 3000 q^{58} + 5540 q^{59} - 3024 q^{60} - 26794 q^{61} + 2880 q^{62} - 61204 q^{63} + 39498 q^{65} + 1264 q^{66} + 23910 q^{67} + 1200 q^{68} + 19510 q^{69} + 524 q^{70} - 15992 q^{71} + 8896 q^{72} - 16780 q^{74} + 56644 q^{75} + 7808 q^{76} + 18960 q^{77} + 11892 q^{78} - 1792 q^{79} - 1920 q^{80} - 62170 q^{81} - 2128 q^{82} - 2516 q^{83} - 896 q^{84} - 11096 q^{86} + 39608 q^{87} - 5120 q^{88} + 25460 q^{89} + 20328 q^{90} - 20162 q^{91} - 20512 q^{92} + 8394 q^{93} - 31552 q^{94} + 7470 q^{95} + 1280 q^{96} - 12272 q^{97} + 14752 q^{98} + 23376 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 - 102 * q^5 + 40 * q^6 - 48 * q^7 + 448 * q^8 + 556 * q^9 - 120 * q^10 + 80 * q^12 - 88 * q^13 - 192 * q^14 + 12 * q^15 + 896 * q^16 - 540 * q^17 - 1112 * q^18 + 976 * q^19 - 816 * q^20 - 618 * q^21 + 752 * q^22 + 1996 * q^23 - 160 * q^24 + 414 * q^25 - 2504 * q^26 + 1584 * q^28 + 852 * q^29 + 804 * q^30 + 300 * q^31 - 1792 * q^32 + 316 * q^33 + 300 * q^34 + 796 * q^35 - 3678 * q^37 - 328 * q^38 + 3630 * q^39 - 2784 * q^40 - 6426 * q^41 - 1348 * q^42 - 5548 * q^43 - 1280 * q^44 + 10164 * q^45 + 3992 * q^46 - 7624 * q^47 - 7388 * q^49 + 1768 * q^50 + 15382 * q^51 - 704 * q^52 + 13538 * q^53 - 1108 * q^54 - 10352 * q^55 + 2400 * q^56 - 12946 * q^57 + 3000 * q^58 + 5540 * q^59 - 3024 * q^60 - 26794 * q^61 + 2880 * q^62 - 61204 * q^63 + 39498 * q^65 + 1264 * q^66 + 23910 * q^67 + 1200 * q^68 + 19510 * q^69 + 524 * q^70 - 15992 * q^71 + 8896 * q^72 - 16780 * q^74 + 56644 * q^75 + 7808 * q^76 + 18960 * q^77 + 11892 * q^78 - 1792 * q^79 - 1920 * q^80 - 62170 * q^81 - 2128 * q^82 - 2516 * q^83 - 896 * q^84 - 11096 * q^86 + 39608 * q^87 - 5120 * q^88 + 25460 * q^89 + 20328 * q^90 - 20162 * q^91 - 20512 * q^92 + 8394 * q^93 - 31552 * q^94 + 7470 * q^95 + 1280 * q^96 - 12272 * q^97 + 14752 * q^98 + 23376 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	2.73205	+	0.732051i	0.683013	+	0.183013i
$2$	2.73205	+	0.732051i	0.683013	+	0.183013i
$3$	9.05180	+	5.22606i	1.00576	+	0.580673i	0.909946	−	0.414726i	$-0.136123\pi$
$3$	9.05180	+	5.22606i	1.00576	+	0.580673i	0.0958094	+	0.995400i	$0.469456\pi$
$4$	6.92820	+	4.00000i	0.433013	+	0.250000i
$5$	8.32031	−	2.22942i	0.332812	−	0.0891768i	−0.0885432	−	0.996072i	$-0.528221\pi$
$5$	8.32031	−	2.22942i	0.332812	−	0.0891768i	0.421355	+	0.906896i	$0.361554\pi$
$6$	20.9042	+	20.9042i	0.580673	+	0.580673i
$7$	41.9891	−	72.7273i	0.856921	−	1.48423i	−0.0179303	−	0.999839i	$-0.505708\pi$
$7$	41.9891	−	72.7273i	0.856921	−	1.48423i	0.874851	−	0.484392i	$-0.160959\pi$
$8$	16.0000	+	16.0000i	0.250000	+	0.250000i
$9$	14.1234	+	24.4624i	0.174363	+	0.302005i
$10$	24.3635			0.243635
$11$			207.159i			1.71206i	0.516928	+	0.856029i	$0.327075\pi$
$11$			207.159i			1.71206i	−0.516928	+	0.856029i	$0.672925\pi$
$12$	41.8085	+	72.4144i	0.290337	+	0.502878i
$13$	−148.606	+	39.8189i	−0.879326	+	0.235615i	−0.670116	−	0.742256i	$-0.733756\pi$
$13$	−148.606	+	39.8189i	−0.879326	+	0.235615i	−0.209210	+	0.977871i	$0.567089\pi$
$14$	167.957	−	167.957i	0.856921	−	0.856921i
$15$	86.9648	+	23.3022i	0.386510	+	0.103565i
$16$	32.0000	+	55.4256i	0.125000	+	0.216506i
$17$	65.3228	−	243.788i	0.226030	−	0.843557i	−0.755959	−	0.654619i	$-0.772829\pi$
$17$	65.3228	−	243.788i	0.226030	−	0.843557i	0.981989	−	0.188938i	$-0.0605044\pi$
$18$	20.6781	+	77.1716i	0.0638212	+	0.238184i
$19$	−517.100	+	138.557i	−1.43241	+	0.383813i	−0.889869	−	0.456216i	$-0.849204\pi$
$19$	−517.100	+	138.557i	−1.43241	+	0.383813i	−0.542541	+	0.840029i	$0.682538\pi$
$20$	66.5625	+	17.8354i	0.166406	+	0.0445884i
$21$	760.154	−	438.875i	1.72371	−	0.995182i
$22$	−151.651	+	565.969i	−0.313328	+	1.16936i
$23$	278.754	+	278.754i	0.526946	+	0.526946i	0.919660	−	0.392715i	$-0.128464\pi$
$23$	278.754	+	278.754i	0.526946	+	0.526946i	−0.392715	+	0.919660i	$0.628464\pi$
$24$	61.2119	+	228.446i	0.106271	+	0.396607i
$25$	−477.009	+	275.401i	−0.763214	+	0.440642i
$26$	−435.149			−0.643711
$27$		−	551.383i		−	0.756355i
$28$	581.818	−	335.913i	0.742115	−	0.428461i
$29$	567.557	−	567.557i	0.674860	−	0.674860i	−0.283973	−	0.958832i	$-0.591653\pi$
$29$	567.557	−	567.557i	0.674860	−	0.674860i	0.958832	+	0.283973i	$0.0916525\pi$
$30$	220.534	+	127.325i	0.245038	+	0.141473i
$31$	347.201	−	347.201i	0.361292	−	0.361292i	−0.502997	−	0.864288i	$-0.667769\pi$
$31$	347.201	−	347.201i	0.361292	−	0.361292i	0.864288	+	0.502997i	$0.167769\pi$
$32$	46.8513	+	174.851i	0.0457532	+	0.170753i
$33$	−1082.62	+	1875.16i	−0.994146	+	1.72191i
$34$	356.930	−	618.221i	0.308763	−	0.534794i
$35$	187.223	−	698.725i	0.152835	−	0.570388i
$36$			225.974i			0.174363i
$37$	−761.188	−	1137.87i	−0.556018	−	0.831171i
$37$	−761.188	−	1137.87i	−0.556018	−	0.831171i
$38$	−1514.17			−1.04860
$39$	−1553.25	−	416.192i	−1.02120	−	0.273630i
$40$	168.796	+	97.4542i	0.105497	+	0.0609089i
$41$	−1862.31	−	1075.20i	−1.10786	−	0.639621i	−0.169583	−	0.985516i	$-0.554242\pi$
$41$	−1862.31	−	1075.20i	−1.10786	−	0.639621i	−0.938273	+	0.345894i	$0.887576\pi$
$42$	2398.06	−	642.558i	1.35944	−	0.364262i
$43$	1403.59	+	1403.59i	0.759106	+	0.759106i	0.976160	−	0.217053i	$-0.0696446\pi$
$43$	1403.59	+	1403.59i	0.759106	+	0.759106i	−0.217053	+	0.976160i	$0.569645\pi$
$44$	−828.636	+	1435.24i	−0.428014	+	0.741343i
$45$	172.048	+	172.048i	0.0849620	+	0.0849620i
$46$	557.508	+	965.633i	0.263473	+	0.456348i
$47$	−2179.87			−0.986812			−0.493406	−	0.869799i	$-0.664248\pi$
$47$	−2179.87			−0.986812			−0.493406	+	0.869799i	$0.664248\pi$
$48$			668.936i			0.290337i
$49$	−2325.67	−	4028.19i	−0.968627	−	1.67771i
$50$	−1504.82	+	403.215i	−0.601928	+	0.161286i
$51$	1865.34	−	1865.34i	0.717162	−	0.717162i
$52$	−1188.85	−	318.551i	−0.439663	−	0.117807i
$53$	1871.89	+	3242.20i	0.666389	+	1.15422i	0.978907	+	0.204307i	$0.0654942\pi$
$53$	1871.89	+	3242.20i	0.666389	+	1.15422i	−0.312518	+	0.949912i	$0.601172\pi$
$54$	403.640	−	1506.41i	0.138423	−	0.516600i
$55$	461.844	+	1723.63i	0.152676	+	0.569794i
$56$	1835.46	−	491.811i	0.585288	−	0.156827i
$57$	−5404.79	−	1448.21i	−1.66352	−	0.445740i
$58$	1966.07	−	1135.11i	0.584446	−	0.337430i
$59$	962.555	−	3592.30i	0.276517	−	1.03197i	−0.678301	−	0.734784i	$-0.737284\pi$
$59$	962.555	−	3592.30i	0.276517	−	1.03197i	0.954818	−	0.297191i	$-0.0960498\pi$
$60$	509.301	+	509.301i	0.141473	+	0.141473i
$61$	−78.0603	−	291.325i	−0.0209783	−	0.0782921i	0.954643	−	0.297752i	$-0.0962370\pi$
$61$	−78.0603	−	291.325i	−0.0209783	−	0.0782921i	−0.975621	+	0.219460i	$0.929570\pi$
$62$	1202.74	−	694.403i	0.312888	−	0.180646i
$63$	2372.12			0.597661
$64$			512.000i			0.125000i
$65$	−1147.68	+	662.611i	−0.271639	+	0.156831i
$66$	−4330.50	+	4330.50i	−0.994146	+	0.994146i
$67$	1528.15	+	882.279i	0.340422	+	0.196543i	0.660458	−	0.750863i	$-0.270362\pi$
$67$	1528.15	+	882.279i	0.340422	+	0.196543i	−0.320037	+	0.947405i	$0.603695\pi$
$68$	1427.72	−	1427.72i	0.308763	−	0.308763i
$69$	1066.44	+	3980.01i	0.223995	+	0.835962i
$70$	1023.00	−	1771.90i	0.208776	−	0.361611i
$71$	−1345.22	+	2330.00i	−0.266857	+	0.462209i	−0.968048	−	0.250763i	$-0.919318\pi$
$71$	−1345.22	+	2330.00i	−0.266857	+	0.462209i	0.701192	+	0.712973i	$0.252652\pi$
$72$	−165.425	+	617.373i	−0.0319106	+	0.119092i
$73$			8297.65i			1.55707i	0.627598	+	0.778537i	$0.284038\pi$
$73$			8297.65i			1.55707i	−0.627598	+	0.778537i	$0.715962\pi$
$74$	−1246.62	−	3665.95i	−0.227652	−	0.669458i
$75$	−5757.05			−1.02348
$76$	−4136.80	−	1108.45i	−0.716205	−	0.191907i
$77$	15066.1	+	8698.42i	2.54109	+	1.46710i
$78$	−3938.88	−	2274.11i	−0.647416	−	0.373786i
$79$	7427.56	−	1990.21i	1.19012	−	0.318893i	0.391189	−	0.920310i	$-0.372064\pi$
$79$	7427.56	−	1990.21i	1.19012	−	0.318893i	0.798935	+	0.601418i	$0.205397\pi$
$80$	389.817	+	389.817i	0.0609089	+	0.0609089i
$81$	4025.55	−	6972.46i	0.613558	−	1.06271i
$82$	−4300.81	−	4300.81i	−0.639621	−	0.639621i
$83$	−3892.71	−	6742.37i	−0.565062	−	0.978716i	−0.997044	−	0.0768337i	$-0.975519\pi$
$83$	−3892.71	−	6742.37i	−0.565062	−	0.978716i	0.431982	−	0.901882i	$-0.357814\pi$
$84$	7022.01			0.995182
$85$		−	2174.02i		−	0.300903i
$86$	2807.18	+	4862.17i	0.379553	+	0.657405i
$87$	8103.50	−	2171.33i	1.07062	−	0.286871i
$88$	−3314.54	+	3314.54i	−0.428014	+	0.428014i
$89$	3647.87	+	977.444i	0.460532	+	0.123399i	0.481623	−	0.876378i	$-0.340047\pi$
$89$	3647.87	+	977.444i	0.460532	+	0.123399i	−0.0210914	+	0.999778i	$0.506714\pi$
$90$	344.096	+	595.992i	0.0424810	+	0.0735792i
$91$	−3343.92	+	12479.7i	−0.403806	+	1.50703i
$92$	816.249	+	3046.28i	0.0964377	+	0.359911i
$93$	4957.29	−	1328.30i	0.573164	−	0.153579i
$94$	−5955.51	−	1595.77i	−0.674005	−	0.180599i
$95$	−3993.53	+	2305.67i	−0.442496	+	0.255475i
$96$	−489.695	+	1827.57i	−0.0531353	+	0.198304i
$97$	10517.2	+	10517.2i	1.11778	+	1.11778i	0.992066	+	0.125718i	$0.0401235\pi$
$97$	10517.2	+	10517.2i	1.11778	+	1.11778i	0.125718	+	0.992066i	$0.459876\pi$
$98$	−3405.02	−	12707.7i	−0.354542	−	1.32317i
$99$	−5067.61	+	2925.79i	−0.517050	+	0.298519i
$100$	−4406.42			−0.440642
$101$			3453.56i			0.338551i	0.985569	+	0.169276i	$0.0541428\pi$
$101$			3453.56i			0.338551i	−0.985569	+	0.169276i	$0.945857\pi$
$102$	6461.72	−	3730.68i	0.621081	−	0.358581i
$103$	−1273.77	+	1273.77i	−0.120065	+	0.120065i	−0.764586	−	0.644521i	$-0.777057\pi$
$103$	−1273.77	+	1273.77i	−0.120065	+	0.120065i	0.644521	+	0.764586i	$0.277057\pi$
$104$	−3014.80	−	1740.60i	−0.278735	−	0.160928i
$105$	5346.28	−	5346.28i	0.484923	−	0.484923i
$106$	2740.63	+	10228.2i	0.243915	+	0.910304i
$107$	−862.347	+	1493.63i	−0.0753207	+	0.130459i	−0.901226	−	0.433350i	$-0.857331\pi$
$107$	−862.347	+	1493.63i	−0.0753207	+	0.130459i	0.825905	+	0.563809i	$0.190665\pi$
$108$	2205.53	−	3820.09i	0.189089	−	0.327511i
$109$	−336.405	+	1255.48i	−0.0283146	+	0.105671i	−0.978637	−	0.205596i	$-0.934087\pi$
$109$	−336.405	+	1255.48i	−0.0283146	+	0.105671i	0.950322	+	0.311267i	$0.100753\pi$
$110$			5047.13i			0.417118i
$111$	−943.534	−	14277.8i	−0.0765793	−	1.15882i
$112$	5374.61			0.428461
$113$	2864.73	+	767.602i	0.224350	+	0.0601145i	0.369243	−	0.929333i	$-0.379617\pi$
$113$	2864.73	+	767.602i	0.224350	+	0.0601145i	−0.144893	+	0.989447i	$0.546284\pi$
$114$	−13706.0	−	7913.16i	−1.05463	−	0.608892i
$115$	2940.78	+	1697.86i	0.222365	+	0.128383i
$116$	6202.38	−	1661.92i	0.460938	−	0.123508i
$117$	−3072.89	−	3072.89i	−0.224479	−	0.224479i
$118$	5259.50	−	9109.72i	0.377729	−	0.654246i
$119$	−14987.2	−	14987.2i	−1.05834	−	1.05834i
$120$	1018.60	+	1764.27i	0.0707363	+	0.122519i
$121$	−28273.8			−1.93114
$122$		−	853.059i		−	0.0573138i
$123$	−11238.2	−	19465.1i	−0.742822	−	1.28661i
$124$	3794.29	−	1016.68i	0.246767	−	0.0661210i
$125$	−7161.68	+	7161.68i	−0.458347	+	0.458347i
$126$	6480.74	+	1736.51i	0.408210	+	0.109380i
$127$	−14845.5	−	25713.2i	−0.920425	−	1.59422i	−0.798759	−	0.601651i	$-0.794510\pi$
$127$	−14845.5	−	25713.2i	−0.920425	−	1.59422i	−0.121665	−	0.992571i	$-0.538823\pi$
$128$	−374.810	+	1398.81i	−0.0228766	+	0.0853766i
$129$	5369.76	+	20040.2i	0.322683	+	1.20427i
$130$	−3620.57	+	970.130i	−0.214235	+	0.0574041i
$131$	5572.72	+	1493.21i	0.324732	+	0.0870116i	0.417502	−	0.908676i	$-0.362906\pi$
$131$	5572.72	+	1493.21i	0.324732	+	0.0870116i	−0.0927705	+	0.995688i	$0.529572\pi$
$132$	−15001.3	+	8661.00i	−0.860956	+	0.497073i
$133$	−11635.7	+	43425.2i	−0.657795	+	2.45492i
$134$	3529.12	+	3529.12i	0.196543	+	0.196543i
$135$	−1229.26	−	4587.67i	−0.0674493	−	0.251724i
$136$	4945.77	−	2855.44i	0.267397	−	0.154382i
$137$	−13137.4			−0.699953			−0.349976	−	0.936758i	$-0.613810\pi$
$137$	−13137.4			−0.699953			−0.349976	+	0.936758i	$0.613810\pi$
$138$			11654.3i			0.611966i
$139$	2009.64	−	1160.27i	0.104013	−	0.0600521i	−0.447091	−	0.894489i	$-0.647540\pi$
$139$	2009.64	−	1160.27i	0.104013	−	0.0600521i	0.551104	+	0.834436i	$0.314207\pi$
$140$	4092.02	−	4092.02i	0.208776	−	0.208776i
$141$	−19731.7	−	11392.1i	−0.992491	−	0.573015i
$142$	−5380.90	+	5380.90i	−0.266857	+	0.266857i
$143$	−8248.84	−	30785.1i	−0.403386	−	1.50546i
$144$	−903.897	+	1565.60i	−0.0435907	+	0.0755013i
$145$	3456.93	−	5987.57i	0.164420	−	0.284783i
$146$	−6074.30	+	22669.6i	−0.284964	+	1.06350i
$147$		−	48616.4i		−	2.24982i
$148$	−722.176	−	10928.2i	−0.0329701	−	0.498912i
$149$	21388.4			0.963399			0.481700	−	0.876336i	$-0.340020\pi$
$149$	21388.4			0.963399			0.481700	+	0.876336i	$0.340020\pi$
$150$	−15728.6	−	4214.45i	−0.699047	−	0.187309i
$151$	28263.4	+	16317.9i	1.23957	+	0.715666i	0.969006	−	0.247036i	$-0.0794566\pi$
$151$	28263.4	+	16317.9i	1.23957	+	0.715666i	0.270564	+	0.962702i	$0.412790\pi$
$152$	−10490.5	−	6056.69i	−0.454056	−	0.262149i
$153$	6886.22	−	1845.16i	0.294170	−	0.0788226i
$154$	34793.7	+	34793.7i	1.46710	+	1.46710i
$155$	2114.76	−	3662.88i	0.0880235	−	0.152461i
$156$	−9096.46	−	9096.46i	−0.373786	−	0.373786i
$157$	11033.4	+	19110.4i	0.447620	+	0.775301i	0.998231	−	0.0594614i	$-0.0189383\pi$
$157$	11033.4	+	19110.4i	0.447620	+	0.775301i	−0.550610	+	0.834762i	$0.685605\pi$
$158$	21749.4			0.871231
$159$			39130.4i			1.54782i
$160$	779.634	+	1350.36i	0.0304544	+	0.0527486i
$161$	31977.7	−	8568.40i	1.23366	−	0.330558i
$162$	16102.2	−	16102.2i	0.613558	−	0.613558i
$163$	15042.5	+	4030.63i	0.566168	+	0.151704i	0.530538	−	0.847661i	$-0.321990\pi$
$163$	15042.5	+	4030.63i	0.566168	+	0.151704i	0.0356292	+	0.999365i	$0.488656\pi$
$164$	−8601.63	−	14898.5i	−0.319811	−	0.553928i
$165$	−4827.25	+	18015.5i	−0.177309	+	0.661728i
$166$	−5699.33	−	21270.2i	−0.206827	−	0.771889i
$167$	481.932	−	129.133i	0.0172803	−	0.00463026i	−0.250169	−	0.968202i	$-0.580486\pi$
$167$	481.932	−	129.133i	0.0172803	−	0.00463026i	0.267449	+	0.963572i	$0.413819\pi$
$168$	19184.5	+	5140.47i	0.679722	+	0.182131i
$169$	−4236.31	+	2445.84i	−0.148325	+	0.0856355i
$170$	1591.49	−	5939.54i	0.0550690	−	0.205520i
$171$	−10692.6	−	10692.6i	−0.365673	−	0.365673i
$172$	4109.99	+	15338.7i	0.138926	+	0.518479i
$173$	29985.9	−	17312.4i	1.00190	−	0.578448i	0.0930907	−	0.995658i	$-0.470325\pi$
$173$	29985.9	−	17312.4i	1.00190	−	0.578448i	0.908810	+	0.417210i	$0.136992\pi$
$174$	23728.7			0.783746
$175$			46255.4i			1.51038i
$176$	−11481.9	+	6629.09i	−0.370671	+	0.214007i
$177$	27486.5	−	27486.5i	0.877349	−	0.877349i
$178$	9250.63	+	5340.85i	0.291965	+	0.168566i
$179$	−14268.2	+	14268.2i	−0.445311	+	0.445311i	−0.893792	−	0.448481i	$-0.851965\pi$
$179$	−14268.2	+	14268.2i	−0.445311	+	0.445311i	0.448481	+	0.893792i	$0.351965\pi$
$180$	503.791	+	1880.18i	0.0155491	+	0.0580301i
$181$	−15235.8	+	26389.1i	−0.465058	+	0.805504i	−0.999204	−	0.0398881i	$-0.987300\pi$
$181$	−15235.8	+	26389.1i	−0.465058	+	0.805504i	0.534146	+	0.845392i	$0.320633\pi$
$182$	−18271.5	+	31647.2i	−0.551610	+	0.955416i
$183$	815.895	−	3044.96i	0.0243631	−	0.0909243i
$184$			8920.13i			0.263473i
$185$	−8870.11	−	7770.44i	−0.259171	−	0.227040i
$186$	14516.0			0.419585
$187$	50502.9	+	13532.2i	1.44422	+	0.386977i
$188$	−15102.6	−	8719.47i	−0.427302	−	0.246703i
$189$	−40100.6	−	23152.1i	−1.12261	−	0.648137i
$190$	−12598.4	+	3375.73i	−0.348986	+	0.0935105i
$191$	−44639.6	−	44639.6i	−1.22364	−	1.22364i	−0.966329	−	0.257310i	$-0.917164\pi$
$191$	−44639.6	−	44639.6i	−1.22364	−	1.22364i	−0.257310	−	0.966329i	$-0.582836\pi$
$192$	−2675.74	+	4634.52i	−0.0725842	+	0.125719i
$193$	20083.7	+	20083.7i	0.539173	+	0.539173i	0.923286	−	0.384113i	$-0.125493\pi$
$193$	20083.7	+	20083.7i	0.539173	+	0.539173i	−0.384113	+	0.923286i	$0.625493\pi$
$194$	21034.5	+	36432.8i	0.558892	+	0.968030i
$195$	−13851.4			−0.364270
$196$		−	37210.8i		−	0.968627i
$197$	10906.0	+	18889.8i	0.281018	+	0.486737i	0.971636	−	0.236483i	$-0.0759947\pi$
$197$	10906.0	+	18889.8i	0.281018	+	0.486737i	−0.690618	+	0.723220i	$0.742661\pi$
$198$	−15986.8	+	4283.65i	−0.407785	+	0.109266i
$199$	−16257.7	+	16257.7i	−0.410538	+	0.410538i	−0.881926	−	0.471388i	$-0.843753\pi$
$199$	−16257.7	+	16257.7i	−0.410538	+	0.410538i	0.471388	+	0.881926i	$0.343753\pi$
$200$	−12038.6	−	3225.72i	−0.300964	−	0.0806430i
$201$	9221.69	+	15972.4i	0.228254	+	0.395347i
$202$	−2528.18	+	9435.31i	−0.0619592	+	0.231235i
$203$	−17445.7	−	65108.1i	−0.423346	−	1.57995i
$204$	20384.8	−	5462.09i	0.489831	−	0.131250i
$205$	−17892.0	−	4794.16i	−0.425748	−	0.114079i
$206$	−4412.47	+	2547.54i	−0.103979	+	0.0600325i
$207$	−2882.05	+	10756.0i	−0.0672606	+	0.251020i
$208$	−6962.38	−	6962.38i	−0.160928	−	0.160928i
$209$	−28703.2	−	107122.i	−0.657110	−	2.45237i
$210$	18520.1	−	10692.6i	0.419956	−	0.242462i
$211$	34322.9			0.770938			0.385469	−	0.922721i	$-0.374040\pi$
$211$	34322.9			0.770938			0.385469	+	0.922721i	$0.374040\pi$
$212$			29950.2i			0.666389i
$213$	−24353.4	+	14060.4i	−0.536785	+	0.309913i
$214$	−3449.39	+	3449.39i	−0.0753207	+	0.0753207i
$215$	14807.5	+	8549.09i	0.320335	+	0.184945i
$216$	8822.13	−	8822.13i	0.189089	−	0.189089i
$217$	−10672.3	−	39829.7i	−0.226642	−	0.845839i
$218$	−1838.15	+	3183.78i	−0.0386784	+	0.0669930i
$219$	−43364.0	+	75108.7i	−0.904151	+	1.56604i
$220$	−3694.75	+	13789.0i	−0.0763379	+	0.284897i
$221$			38829.5i			0.795018i
$222$	7874.30	−	39698.4i	0.159774	−	0.805503i
$223$	−80972.5			−1.62828			−0.814138	−	0.580672i	$-0.802790\pi$
$223$	−80972.5			−1.62828			−0.814138	+	0.580672i	$0.802790\pi$
$224$	14683.7	+	3934.49i	0.292644	+	0.0784137i
$225$	−13474.0	−	7779.19i	−0.266152	−	0.153663i
$226$	7264.66	+	4194.25i	0.142232	+	0.0821179i
$227$	61342.8	−	16436.8i	1.19045	−	0.318981i	0.391387	−	0.920226i	$-0.371995\pi$
$227$	61342.8	−	16436.8i	1.19045	−	0.318981i	0.799064	+	0.601245i	$0.205329\pi$
$228$	−31652.6	−	31652.6i	−0.608892	−	0.608892i
$229$	−8402.19	+	14553.0i	−0.160222	+	0.277512i	−0.934948	−	0.354784i	$-0.884554\pi$
$229$	−8402.19	+	14553.0i	−0.160222	+	0.277512i	0.774726	+	0.632297i	$0.217888\pi$
$230$	6791.44	+	6791.44i	0.128383	+	0.128383i
$231$	90917.0	+	157473.i	1.70381	+	2.95108i
$232$	18161.8			0.337430
$233$		−	20276.1i		−	0.373485i	−0.982409	−	0.186742i	$-0.940207\pi$
$233$		−	20276.1i		−	0.373485i	0.982409	−	0.186742i	$-0.0597930\pi$
$234$	−6145.78	−	10644.8i	−0.112239	−	0.194404i
$235$	−18137.2	+	4859.84i	−0.328423	+	0.0880007i
$236$	21038.0	−	21038.0i	0.377729	−	0.377729i
$237$	77633.8	+	20801.9i	1.38215	+	0.370345i
$238$	−29974.4	−	51917.2i	−0.529171	−	0.916552i
$239$	1823.22	−	6804.36i	0.0319186	−	0.119122i	−0.948128	−	0.317887i	$-0.897027\pi$
$239$	1823.22	−	6804.36i	0.0319186	−	0.119122i	0.980047	+	0.198766i	$0.0636932\pi$
$240$	1491.34	+	5565.75i	0.0258913	+	0.0966276i
$241$	−26394.7	+	7072.44i	−0.454446	+	0.121769i	−0.478779	−	0.877935i	$-0.658921\pi$
$241$	−26394.7	+	7072.44i	−0.454446	+	0.121769i	0.0243328	+	0.999704i	$0.492254\pi$
$242$	−77245.5	−	20697.9i	−1.31899	−	0.353423i
$243$	34198.6	−	19744.6i	0.579156	−	0.334376i
$244$	624.482	−	2330.60i	0.0104892	−	0.0391461i
$245$	−28330.8	−	28330.8i	−0.471984	−	0.471984i
$246$	−16453.8	−	61406.4i	−0.271892	−	1.01471i
$247$	71327.1	−	41180.7i	1.16912	−	0.674994i
$248$	11110.4			0.180646
$249$		−	81374.2i		−	1.31247i
$250$	−24808.8	+	14323.4i	−0.396941	+	0.229174i
$251$	72483.3	−	72483.3i	1.15051	−	1.15051i	0.164060	−	0.986450i	$-0.447541\pi$
$251$	72483.3	−	72483.3i	1.15051	−	1.15051i	0.986450	−	0.164060i	$-0.0524590\pi$
$252$	16434.5	+	9488.46i	0.258795	+	0.149415i
$253$	−57746.4	+	57746.4i	−0.902161	+	0.902161i
$254$	−21735.4	−	81117.5i	−0.336899	−	1.25732i
$255$	11361.6	−	19678.8i	0.174726	−	0.302635i
$256$	−2048.00	+	3547.24i	−0.0312500	+	0.0541266i
$257$	−7108.87	+	26530.7i	−0.107630	+	0.401681i	−0.998630	−	0.0523217i	$-0.983338\pi$
$257$	−7108.87	+	26530.7i	−0.107630	+	0.401681i	0.891000	+	0.454003i	$0.150005\pi$
$258$			58681.9i			0.881586i
$259$	−114716.	+	7580.89i	−1.71011	+	0.113011i
$260$	−10601.8			−0.156831
$261$	21899.6	+	5867.99i	0.321482	+	0.0861407i
$262$	14131.9	+	8159.03i	0.205872	+	0.118860i
$263$	83230.5	+	48053.2i	1.20329	+	0.694721i	0.961286	−	0.275553i	$-0.0888611\pi$
$263$	83230.5	+	48053.2i	1.20329	+	0.694721i	0.242007	+	0.970275i	$0.422194\pi$
$264$	−47324.6	+	12680.6i	−0.679014	+	0.181941i
$265$	22802.9	+	22802.9i	0.324712	+	0.324712i
$266$	−63578.8	+	110122.i	−0.898565	+	1.55636i
$267$	27911.6	+	27911.6i	0.391528	+	0.391528i
$268$	7058.24	+	12225.2i	0.0982713	+	0.170211i
$269$	29656.9			0.409847			0.204923	−	0.978778i	$-0.434305\pi$
$269$	29656.9			0.409847			0.204923	+	0.978778i	$0.434305\pi$
$270$		−	13433.6i		−	0.184275i
$271$	−48914.7	−	84722.8i	−0.666041	−	1.15362i	−0.979002	−	0.203851i	$-0.934654\pi$
$271$	−48914.7	−	84722.8i	−0.666041	−	1.15362i	0.312961	−	0.949766i	$-0.398679\pi$
$272$	15602.4	−	4180.66i	0.210889	−	0.0565076i
$273$	−95488.1	+	95488.1i	−1.28122	+	1.28122i
$274$	−35892.1	−	9617.26i	−0.478077	−	0.128100i
$275$	−57051.8	−	98816.6i	−0.754404	−	1.30667i
$276$	−8531.53	+	31840.1i	−0.111998	+	0.417981i
$277$	−1338.29	−	4994.58i	−0.0174418	−	0.0650938i	0.956656	−	0.291219i	$-0.0940608\pi$
$277$	−1338.29	−	4994.58i	−0.0174418	−	0.0650938i	−0.974098	+	0.226125i	$0.927394\pi$
$278$	6339.82	−	1698.75i	0.0820327	−	0.0219806i
$279$	13397.0	+	3589.73i	0.172108	+	0.0461162i
$280$	14175.2	−	8184.03i	0.180806	−	0.104388i
$281$	−4249.19	+	15858.2i	−0.0538138	+	0.200836i	−0.987599	−	0.156999i	$-0.949818\pi$
$281$	−4249.19	+	15858.2i	−0.0538138	+	0.200836i	0.933785	+	0.357835i	$0.116485\pi$
$282$	−45568.5	−	45568.5i	−0.573015	−	0.573015i
$283$	1562.03	+	5829.56i	0.0195036	+	0.0727885i	0.974992	−	0.222241i	$-0.0713372\pi$
$283$	1562.03	+	5829.56i	0.0195036	+	0.0727885i	−0.955488	+	0.295030i	$0.904671\pi$
$284$	−18640.0	+	10761.8i	−0.231105	+	0.133428i
$285$	−48198.2			−0.593391
$286$		−	90145.0i		−	1.10207i
$287$	−156393.	+	90293.7i	−1.89869	+	1.09621i
$288$	−3615.59	+	3615.59i	−0.0435907	+	0.0435907i
$289$	17165.8	+	9910.69i	0.205527	+	0.118661i
$290$	13827.7	−	13827.7i	0.164420	−	0.164420i
$291$	40236.2	+	150164.i	0.475150	+	1.77329i
$292$	−33190.6	+	57487.8i	−0.389269	+	0.674233i
$293$	56072.7	−	97120.7i	0.653155	−	1.13130i	−0.329198	−	0.944261i	$-0.606779\pi$
$293$	56072.7	−	97120.7i	0.653155	−	1.13130i	0.982353	−	0.187036i	$-0.0598882\pi$
$294$	35589.7	−	132823.i	0.411746	−	1.53666i
$295$		−	32035.0i		−	0.368113i
$296$	6026.95	−	30385.0i	0.0687882	−	0.346797i
$297$	114224.			1.29492
$298$	58434.3	+	15657.4i	0.658014	+	0.176314i
$299$	−52524.3	−	30324.9i	−0.587513	−	0.339201i
$300$	−39886.0	−	23028.2i	−0.443178	−	0.255869i
$301$	161015.	−	43143.7i	1.77718	−	0.476195i
$302$	65271.6	+	65271.6i	0.715666	+	0.715666i
$303$	−18048.5	+	31260.9i	−0.196588	+	0.340500i
$304$	−24226.8	−	24226.8i	−0.262149	−	0.262149i
$305$	−1298.97	−	2249.88i	−0.0139637	−	0.0241858i
$306$	20164.3			0.215347
$307$		−	56666.6i		−	0.601244i	−0.953743	−	0.300622i	$-0.902806\pi$
$307$		−	56666.6i		−	0.601244i	0.953743	−	0.300622i	$-0.0971942\pi$
$308$	69587.4	+	120529.i	0.733549	+	1.27054i
$309$	−18186.7	+	4873.12i	−0.190475	+	0.0510376i
$310$	8459.06	−	8459.06i	0.0880235	−	0.0880235i
$311$	99668.7	+	26706.2i	1.03048	+	0.276115i	0.734162	−	0.678975i	$-0.237575\pi$
$311$	99668.7	+	26706.2i	1.03048	+	0.276115i	0.296315	+	0.955090i	$0.404242\pi$
$312$	−18192.9	−	31511.1i	−0.186893	−	0.323708i
$313$	28232.4	−	105365.i	0.288177	−	1.07549i	−0.658309	−	0.752748i	$-0.728728\pi$
$313$	28232.4	−	105365.i	0.288177	−	1.07549i	0.946486	−	0.322744i	$-0.104605\pi$
$314$	16154.0	+	60287.6i	0.163840	+	0.611461i
$315$	19736.7	−	5288.44i	0.198909	−	0.0532975i
$316$	59420.5	+	15921.7i	0.595062	+	0.159446i
$317$	−87601.3	+	50576.7i	−0.871751	+	0.503305i	−0.867930	−	0.496687i	$-0.834550\pi$
$317$	−87601.3	+	50576.7i	−0.871751	+	0.503305i	−0.00382102	+	0.999993i	$0.501216\pi$
$318$	−28645.4	+	106906.i	−0.283270	+	1.05718i
$319$	117574.	+	117574.i	1.15540	+	1.15540i
$320$	1141.46	+	4260.00i	0.0111471	+	0.0416015i
$321$	−15611.6	+	9013.36i	−0.151509	+	0.0874735i
$322$	93637.2			0.903101
$323$			135114.i			1.29507i
$324$	55779.7	−	32204.4i	0.531357	−	0.306779i
$325$	59920.2	−	59920.2i	0.567292	−	0.567292i
$326$	38146.3	+	22023.8i	0.358936	+	0.207232i
$327$	−9606.30	+	9606.30i	−0.0898381	+	0.0898381i
$328$	−12593.7	−	47000.2i	−0.117059	−	0.436870i
$329$	−91530.7	+	158536.i	−0.845620	+	1.46466i
$330$	−26376.6	+	45685.6i	−0.242209	+	0.419519i
$331$	53276.8	−	198832.i	0.486275	−	1.81480i	−0.0879741	−	0.996123i	$-0.528039\pi$
$331$	53276.8	−	198832.i	0.486275	−	1.81480i	0.574249	−	0.818681i	$-0.305294\pi$
$332$		−	62283.4i		−	0.565062i
$333$	17084.6	−	34691.1i	0.154069	−	0.312846i
$334$	1411.19			0.0126501
$335$	14681.7	+	3933.94i	0.130824	+	0.0350541i
$336$	48649.9	+	28088.0i	0.430927	+	0.248796i
$337$	−30922.1	−	17852.9i	−0.272276	−	0.157199i	0.357646	−	0.933857i	$-0.383580\pi$
$337$	−30922.1	−	17852.9i	−0.272276	−	0.157199i	−0.629921	+	0.776659i	$0.716913\pi$
$338$	−13364.3	+	3580.95i	−0.116980	+	0.0313448i
$339$	21919.4	+	21919.4i	0.190735	+	0.190735i
$340$	8696.09	−	15062.1i	0.0752257	−	0.130295i
$341$	71925.9	+	71925.9i	0.618552	+	0.618552i
$342$	−21385.3	−	37040.4i	−0.182836	−	0.316682i
$343$	−188980.			−1.60631
$344$			44914.8i			0.379553i
$345$	17746.2	+	30737.4i	0.149097	+	0.258243i
$346$	94596.5	−	25347.1i	0.790174	−	0.211727i
$347$	80679.3	−	80679.3i	0.670043	−	0.670043i	−0.287682	−	0.957726i	$-0.592885\pi$
$347$	80679.3	−	80679.3i	0.670043	−	0.670043i	0.957726	+	0.287682i	$0.0928848\pi$
$348$	64828.0	+	17370.6i	0.535308	+	0.143435i
$349$	−17907.9	−	31017.4i	−0.147026	−	0.254656i	0.783101	−	0.621894i	$-0.213637\pi$
$349$	−17907.9	−	31017.4i	−0.147026	−	0.254656i	−0.930127	+	0.367238i	$0.880303\pi$
$350$	−33861.3	+	126372.i	−0.276419	+	1.03161i
$351$	21955.5	+	81938.9i	0.178208	+	0.665083i
$352$	−36222.0	+	9705.66i	−0.292339	+	0.0783321i
$353$	−223510.	−	59889.2i	−1.79369	−	0.480617i	−0.800724	−	0.599034i	$-0.795552\pi$
$353$	−223510.	−	59889.2i	−1.79369	−	0.480617i	−0.992964	+	0.118416i	$0.962218\pi$
$354$	95215.9	−	54972.9i	0.759806	−	0.438674i
$355$	−5998.14	+	22385.4i	−0.0475948	+	0.177626i
$356$	21363.4	+	21363.4i	0.168566	+	0.168566i
$357$	−57337.1	−	213985.i	−0.449883	−	1.67899i
$358$	−49426.6	+	28536.4i	−0.385651	+	0.222656i
$359$	−96177.8			−0.746253			−0.373127	−	0.927780i	$-0.621714\pi$
$359$	−96177.8			−0.746253			−0.373127	+	0.927780i	$0.621714\pi$
$360$			5505.53i			0.0424810i
$361$	135333.	−	78134.6i	1.03846	−	0.599555i
$362$	−60943.1	+	60943.1i	−0.465058	+	0.465058i
$363$	−255929.	−	147761.i	−1.94226	−	1.12136i
$364$	−73086.1	+	73086.1i	−0.551610	+	0.551610i
$365$	18498.9	+	69039.0i	0.138855	+	0.518213i
$366$	4458.13	−	7721.72i	0.0332806	−	0.0576437i
$367$	−63267.0	+	109582.i	−0.469727	+	0.813591i	−0.999401	−	0.0346106i	$-0.988981\pi$
$367$	−63267.0	+	109582.i	−0.469727	+	0.813591i	0.529674	+	0.848201i	$0.322314\pi$
$368$	−6529.99	+	24370.3i	−0.0482189	+	0.179955i
$369$		−	60742.1i		−	0.446105i
$370$	−18545.2	−	27722.6i	−0.135466	−	0.202503i
$371$	314395.			2.28417
$372$	39658.3	+	10626.4i	0.286582	+	0.0767894i
$373$	−148161.	−	85541.0i	−1.06492	−	0.614832i	−0.138132	−	0.990414i	$-0.544110\pi$
$373$	−148161.	−	85541.0i	−1.06492	−	0.614832i	−0.926789	+	0.375582i	$0.877443\pi$
$374$	128070.	+	73941.3i	0.915597	+	0.528620i
$375$	−102253.	+	27398.7i	−0.727136	+	0.194835i
$376$	−34877.9	−	34877.9i	−0.246703	−	0.246703i
$377$	−61742.9	+	106942.i	−0.434415	+	0.752429i
$378$	−92608.4	−	92608.4i	−0.648137	−	0.648137i
$379$	3525.13	+	6105.70i	0.0245412	+	0.0425067i	0.878035	−	0.478596i	$-0.158854\pi$
$379$	3525.13	+	6105.70i	0.0245412	+	0.0425067i	−0.853494	+	0.521103i	$0.825521\pi$
$380$	−36890.6			−0.255475
$381$		−	310334.i		−	2.13786i
$382$	−89279.1	−	154636.i	−0.611819	−	1.05970i
$383$	−55200.0	+	14790.8i	−0.376306	+	0.100831i	−0.442014	−	0.897008i	$-0.645736\pi$
$383$	−55200.0	+	14790.8i	−0.376306	+	0.100831i	0.0657082	+	0.997839i	$0.479069\pi$
$384$	−10703.0	+	10703.0i	−0.0725842	+	0.0725842i
$385$	144747.	+	38784.9i	0.976536	+	0.261662i
$386$	40167.3	+	69571.8i	0.269586	+	0.466937i
$387$	−14511.7	+	54158.6i	−0.0968942	+	0.361614i
$388$	30796.6	+	114934.i	0.204569	+	0.763461i
$389$	119458.	−	32008.6i	0.789433	−	0.211528i	0.158493	−	0.987360i	$-0.449336\pi$
$389$	119458.	−	32008.6i	0.789433	−	0.211528i	0.630939	+	0.775832i	$0.282670\pi$
$390$	−37842.7	−	10139.9i	−0.248801	−	0.0666661i
$391$	86165.9	−	49747.9i	0.563614	−	0.325403i
$392$	27240.2	−	101662.i	0.177271	−	0.661585i
$393$	42639.6	+	42639.6i	0.276075	+	0.276075i
$394$	15967.5	+	59591.6i	0.102860	+	0.383877i
$395$	57362.6	−	33118.3i	0.367650	−	0.212263i
$396$	−46812.6			−0.298519
$397$			255973.i			1.62410i	0.583587	+	0.812050i	$0.301649\pi$
$397$			255973.i			1.62410i	−0.583587	+	0.812050i	$0.698351\pi$
$398$	−56318.4	+	32515.5i	−0.355537	+	0.205269i
$399$	−332267.	+	332267.i	−2.08709	+	2.08709i
$400$	−30528.6	−	17625.7i	−0.190803	−	0.110160i
$401$	126244.	−	126244.i	0.785094	−	0.785094i	−0.195591	−	0.980686i	$-0.562663\pi$
$401$	126244.	−	126244.i	0.785094	−	0.785094i	0.980686	+	0.195591i	$0.0626625\pi$
$402$	13501.5	+	50388.2i	0.0835468	+	0.311801i
$403$	−37771.1	+	65421.4i	−0.232568	+	0.402819i
$404$	−13814.2	+	23927.0i	−0.0846378	+	0.146597i
$405$	17949.3	−	66987.7i	0.109430	−	0.408399i
$406$		−	190650.i		−	1.15660i
$407$	235720.	−	157687.i	1.42301	−	0.951934i
$408$	59690.8			0.358581
$409$	−129555.	−	34714.3i	−0.774478	−	0.207521i	−0.150129	−	0.988666i	$-0.547969\pi$
$409$	−129555.	−	34714.3i	−0.774478	−	0.207521i	−0.624349	+	0.781146i	$0.714636\pi$
$410$	−45372.4	−	26195.8i	−0.269913	−	0.155834i
$411$	−118917.	−	68656.9i	−0.703982	−	0.406444i
$412$	−13920.0	+	3729.86i	−0.0820060	+	0.0219734i
$413$	−220842.	−	220842.i	−1.29474	−	1.29474i
$414$	−15747.8	+	27276.0i	−0.0918797	+	0.159140i
$415$	−47420.1	−	47420.1i	−0.275338	−	0.275338i
$416$	−13924.8	−	24118.4i	−0.0804639	−	0.139368i
$417$	24254.5			0.139483
$418$		−	313675.i		−	1.79526i
$419$	−36778.9	−	63703.0i	−0.209494	−	0.362854i	0.742061	−	0.670332i	$-0.233848\pi$
$419$	−36778.9	−	63703.0i	−0.209494	−	0.362854i	−0.951555	+	0.307478i	$0.900515\pi$
$420$	58425.2	−	15655.0i	0.331209	−	0.0887471i
$421$	−173961.	+	173961.i	−0.981497	+	0.981497i	−0.999832	−	0.0183353i	$-0.994163\pi$
$421$	−173961.	+	173961.i	−0.981497	+	0.981497i	0.0183353	+	0.999832i	$0.494163\pi$
$422$	93772.0	+	25126.1i	0.526561	+	0.141091i
$423$	−30787.1	−	53324.9i	−0.172063	−	0.298022i
$424$	−21925.1	+	81825.4i	−0.121958	+	0.455152i
$425$	35979.9	+	134279.i	0.199197	+	0.743413i
$426$	−76827.7	+	20585.9i	−0.423349	+	0.113436i
$427$	−24465.0	−	6555.37i	−0.134180	−	0.0359535i
$428$	−11949.0	+	6898.78i	−0.0652297	+	0.0376604i
$429$	86217.8	−	321769.i	0.468471	−	1.74836i
$430$	34196.4	+	34196.4i	0.184945	+	0.184945i
$431$	77074.2	+	287645.i	0.414910	+	1.54847i	0.785015	+	0.619477i	$0.212655\pi$
$431$	77074.2	+	287645.i	0.414910	+	1.54847i	−0.370104	+	0.928990i	$0.620678\pi$
$432$	30560.7	−	17644.3i	0.163756	−	0.0945444i
$433$	−227504.			−1.21343			−0.606714	−	0.794921i	$-0.707512\pi$
$433$	−227504.			−1.21343			−0.606714	+	0.794921i	$0.707512\pi$
$434$		−	116629.i		−	0.619197i
$435$	62582.8	−	36132.2i	0.330732	−	0.190948i
$436$	−7352.61	+	7352.61i	−0.0386784	+	0.0386784i
$437$	−182767.	−	105521.i	−0.957051	−	0.552553i
$438$	−173456.	+	173456.i	−0.904151	+	0.904151i
$439$	6557.98	+	24474.7i	0.0340284	+	0.126996i	0.980851	−	0.194761i	$-0.0623933\pi$
$439$	6557.98	+	24474.7i	0.0340284	+	0.126996i	−0.946822	+	0.321757i	$0.895727\pi$
$440$	−20188.5	+	34967.5i	−0.104279	+	0.180617i
$441$	65692.8	−	113783.i	0.337785	−	0.585061i
$442$	−28425.1	+	106084.i	−0.145498	+	0.543007i
$443$			242800.i			1.23721i	0.785704	+	0.618603i	$0.212301\pi$
$443$			242800.i			1.23721i	−0.785704	+	0.618603i	$0.787699\pi$
$444$	50574.2	−	102694.i	0.256545	−	0.520928i
$445$	32530.5			0.164275
$446$	−221221.	−	59276.0i	−1.11213	−	0.297995i
$447$	193604.	+	111777.i	0.968944	+	0.559420i
$448$	37236.4	+	21498.4i	0.185529	+	0.107115i
$449$	248272.	−	66524.4i	1.23150	−	0.329981i	0.416339	−	0.909209i	$-0.363313\pi$
$449$	248272.	−	66524.4i	1.23150	−	0.329981i	0.815165	+	0.579229i	$0.196646\pi$
$450$	−31116.8	−	31116.8i	−0.153663	−	0.153663i
$451$	222738.	−	385794.i	1.09507	−	1.89671i
$452$	16777.0	+	16777.0i	0.0821179	+	0.0821179i
$453$	170557.	+	295413.i	0.831136	+	1.43957i
$454$	179624.			0.871471
$455$			111290.i			0.537567i
$456$	−63305.3	−	109648.i	−0.304446	−	0.527316i
$457$	−231577.	+	62050.9i	−1.10883	+	0.297109i	−0.766354	−	0.642419i	$-0.777931\pi$
$457$	−231577.	+	62050.9i	−1.10883	+	0.297109i	−0.342472	+	0.939528i	$0.611264\pi$
$458$	−33608.8	+	33608.8i	−0.160222	+	0.160222i
$459$	−134420.	−	36017.9i	−0.638029	−	0.170959i
$460$	13582.9	+	23526.2i	0.0641913	+	0.111183i
$461$	137.473	−	513.057i	0.000646869	−	0.00241415i	−0.965602	−	0.260026i	$-0.916269\pi$
$461$	137.473	−	513.057i	0.000646869	−	0.00241415i	0.966249	+	0.257612i	$0.0829356\pi$
$462$	133112.	+	496779.i	0.623637	+	2.32745i
$463$	88008.2	−	23581.7i	0.410545	−	0.110005i	−0.0476344	−	0.998865i	$-0.515168\pi$
$463$	88008.2	−	23581.7i	0.410545	−	0.110005i	0.458180	+	0.888860i	$0.348502\pi$
$464$	49619.0	+	13295.4i	0.230469	+	0.0617539i
$465$	38284.8	−	22103.8i	0.177060	−	0.102226i
$466$	14843.2	−	55395.4i	0.0683525	−	0.255095i
$467$	−18453.2	−	18453.2i	−0.0846133	−	0.0846133i	0.663533	−	0.748147i	$-0.269056\pi$
$467$	−18453.2	−	18453.2i	−0.0846133	−	0.0846133i	−0.748147	+	0.663533i	$0.769056\pi$
$468$	−8998.05	−	33581.2i	−0.0410825	−	0.153322i
$469$	128332.	−	74092.3i	0.583429	−	0.336843i
$470$	−53109.3			−0.240422
$471$			230645.i			1.03968i
$472$	72877.8	−	42076.0i	0.327123	−	0.188865i
$473$	−290766.	+	290766.i	−1.29963	+	1.29963i
$474$	196871.	+	113664.i	0.876246	+	0.505901i
$475$	208503.	−	208503.i	0.924111	−	0.924111i
$476$	−43885.5	−	163783.i	−0.193690	−	0.722862i
$477$	−52874.8	+	91581.8i	−0.232387	+	0.402506i
$478$	9962.28	−	17255.2i	0.0436016	−	0.0755203i
$479$	−4902.66	+	18297.0i	−0.0213678	+	0.0797458i	−0.975786	−	0.218726i	$-0.929810\pi$
$479$	−4902.66	+	18297.0i	−0.0213678	+	0.0797458i	0.954419	+	0.298471i	$0.0964767\pi$
$480$			16297.6i			0.0707363i
$481$	158426.	+	138785.i	0.684757	+	0.599864i
$482$	−77289.0			−0.332678
$483$	334235.	+	89557.9i	1.43271	+	0.383892i
$484$	−195887.	−	113095.i	−0.836208	−	0.482785i
$485$	110954.	+	64059.3i	0.471693	+	0.272332i
$486$	107886.	−	28908.0i	0.456766	−	0.122390i
$487$	−37888.0	−	37888.0i	−0.159751	−	0.159751i	0.622705	−	0.782457i	$-0.286034\pi$
$487$	−37888.0	−	37888.0i	−0.159751	−	0.159751i	−0.782457	+	0.622705i	$0.786034\pi$
$488$	3412.23	−	5910.16i	0.0143285	−	0.0248176i
$489$	115097.	+	115097.i	0.481336	+	0.481336i
$490$	−56661.7	−	98140.9i	−0.235992	−	0.408750i
$491$	−239325.			−0.992715			−0.496357	−	0.868118i	$-0.665329\pi$
$491$	−239325.			−0.992715			−0.496357	+	0.868118i	$0.665329\pi$
$492$		−	179811.i		−	0.742822i
$493$	−101289.	−	175438.i	−0.416744	−	0.721821i
$494$	225015.	−	60292.7i	0.922059	−	0.247065i
$495$	−35641.3	+	35641.3i	−0.145460	+	0.145460i
$496$	30354.3	+	8133.41i	0.123383	+	0.0330605i
$497$	112970.	+	195669.i	0.457350	+	0.792154i
$498$	59570.0	−	222318.i	0.240198	−	0.896431i
$499$	93071.5	+	347347.i	0.373779	+	1.39496i	0.855120	+	0.518430i	$0.173483\pi$
$499$	93071.5	+	347347.i	0.373779	+	1.39496i	−0.481340	+	0.876534i	$0.659850\pi$
$500$	−78264.3	+	20970.9i	−0.313057	+	0.0838834i
$501$	5037.21	+	1349.72i	0.0200685	+	0.00537733i
$502$	251090.	−	144967.i	0.996371	−	0.575255i
$503$	114324.	−	426664.i	0.451858	−	1.68636i	−0.245306	−	0.969446i	$-0.578889\pi$
$503$	114324.	−	426664.i	0.451858	−	1.68636i	0.697164	−	0.716911i	$-0.254445\pi$
$504$	37953.9	+	37953.9i	0.149415	+	0.149415i
$505$	7699.44	+	28734.7i	0.0301909	+	0.112674i
$506$	−200039.	+	115493.i	−0.781294	+	0.451080i
$507$	−51128.3			−0.198905
$508$		−	237528.i		−	0.920425i
$509$	27437.2	−	15840.9i	0.105902	−	0.0611426i	−0.446113	−	0.894976i	$-0.647192\pi$
$509$	27437.2	−	15840.9i	0.105902	−	0.0611426i	0.552016	+	0.833834i	$0.313859\pi$
$510$	45446.3	−	45446.3i	0.174726	−	0.174726i
$511$	603466.	+	348411.i	2.31106	+	1.33429i
$512$	−8192.00	+	8192.00i	−0.0312500	+	0.0312500i
$513$	76397.7	+	285120.i	0.290299	+	1.08341i
$514$	−38843.6	+	67279.1i	−0.147026	+	0.254656i
$515$	−7758.39	+	13437.9i	−0.0292521	+	0.0506662i
$516$	−42958.1	+	160322.i	−0.161341	+	0.602134i
$517$		−	451579.i		−	1.68948i
$518$	−318960.	−	63266.6i	−1.18871	−	0.235784i
$519$	361902.			1.34356
$520$	−28964.6	−	7761.04i	−0.107118	−	0.0287021i
$521$	−442098.	−	255245.i	−1.62871	−	0.940335i	−0.984479	−	0.175502i	$-0.943845\pi$
$521$	−442098.	−	255245.i	−1.62871	−	0.940335i	−0.644229	−	0.764833i	$-0.722822\pi$
$522$	55535.3	+	32063.3i	0.203811	+	0.117670i
$523$	−346910.	+	92954.4i	−1.26828	+	0.339834i	−0.829370	−	0.558699i	$-0.811301\pi$
$523$	−346910.	+	92954.4i	−1.26828	+	0.339834i	−0.438906	+	0.898533i	$0.644634\pi$
$524$	32636.1	+	32636.1i	0.118860	+	0.118860i
$525$	−241734.	+	418695.i	−0.877038	+	1.51907i
$526$	192213.	+	192213.i	0.694721	+	0.694721i
$527$	−61963.3	−	107324.i	−0.223107	−	0.386433i
$528$	−138576.			−0.497073
$529$		−	124433.i		−	0.444657i
$530$	45605.8	+	78991.5i	0.162356	+	0.281209i
$531$	101471.	−	27189.1i	0.359876	−	0.0964285i
$532$	−254315.	+	254315.i	−0.898565	+	0.898565i
$533$	319564.	+	85626.8i	1.12487	+	0.301409i
$534$	55823.2	+	96688.7i	0.195764	+	0.339073i
$535$	−3845.07	+	14350.0i	−0.0134337	+	0.0501353i
$536$	10334.0	+	38566.9i	0.0359698	+	0.134241i
$537$	−203720.	+	54586.5i	−0.706455	+	0.189294i
$538$	81024.2	+	21710.4i	0.279931	+	0.0750072i
$539$	834475.	−	481784.i	2.87234	−	1.65835i
$540$	9834.11	−	36701.4i	0.0337247	−	0.125862i
$541$	159469.	+	159469.i	0.544858	+	0.544858i	0.924949	−	0.380091i	$-0.124107\pi$
$541$	159469.	+	159469.i	0.544858	+	0.544858i	−0.380091	+	0.924949i	$0.624107\pi$
$542$	−71616.1	−	267275.i	−0.243788	−	0.909829i
$543$	−275822.	+	159246.i	−0.935469	+	0.540093i
$544$	45687.1			0.154382
$545$			11196.0i			0.0376937i
$546$	−330780.	+	190976.i	−1.10957	+	0.640610i
$547$	−306505.	+	306505.i	−1.02438	+	1.02438i	−0.0246885	+	0.999695i	$0.507859\pi$
$547$	−306505.	+	306505.i	−1.02438	+	1.02438i	−0.999695	+	0.0246885i	$0.992141\pi$
$548$	−91018.7	−	52549.7i	−0.303089	−	0.174988i
$549$	6024.04	−	6024.04i	0.0199868	−	0.0199868i
$550$	−83529.6	−	311737.i	−0.276131	−	1.03053i
$551$	−214845.	+	372122.i	−0.707656	+	1.22570i
$552$	−46617.2	+	80743.3i	−0.152992	+	0.264989i
$553$	167134.	−	623754.i	0.546532	−	2.03968i
$554$		−	14625.2i		−	0.0476520i
$555$	−39681.7	−	116692.i	−0.128826	−	0.378840i
$556$	18564.3			0.0600521
$557$	470993.	+	126202.i	1.51811	+	0.406778i	0.919121	−	0.393976i	$-0.128901\pi$
$557$	470993.	+	126202.i	1.51811	+	0.406778i	0.598994	+	0.800754i	$0.295567\pi$
$558$	33973.6	+	19614.6i	0.109112	+	0.0629958i
$559$	−264471.	−	152692.i	−0.846359	−	0.488646i
$560$	44718.4	−	11982.3i	0.142597	−	0.0382087i
$561$	386422.	+	386422.i	1.22782	+	1.22782i
$562$	−23218.0	+	40214.8i	−0.0735111	+	0.127325i
$563$	−273265.	−	273265.i	−0.862119	−	0.862119i	0.129465	−	0.991584i	$-0.458674\pi$
$563$	−273265.	−	273265.i	−0.862119	−	0.862119i	−0.991584	+	0.129465i	$0.958674\pi$
$564$	−91136.9	−	157854.i	−0.286508	−	0.496246i
$565$	25546.7			0.0800273
$566$			17070.1i			0.0532849i
$567$	−338059.	−	585535.i	−1.05154	−	1.82132i
$568$	−58803.5	+	15756.4i	−0.182266	+	0.0488382i
$569$	56415.3	−	56415.3i	0.174250	−	0.174250i	−0.614594	−	0.788844i	$-0.710680\pi$
$569$	56415.3	−	56415.3i	0.174250	−	0.174250i	0.788844	+	0.614594i	$0.210680\pi$
$570$	−131680.	−	35283.5i	−0.405293	−	0.108598i
$571$	−297249.	−	514851.i	−0.911693	−	1.57910i	−0.811672	−	0.584113i	$-0.801442\pi$
$571$	−297249.	−	514851.i	−0.911693	−	1.57910i	−0.100021	−	0.994985i	$-0.531891\pi$
$572$	65990.7	−	246281.i	0.201693	−	0.752728i
$573$	−170779.	−	637358.i	−0.520147	−	1.94122i
$574$	−493374.	+	132199.i	−1.49745	+	0.401241i
$575$	−209737.	−	56199.0i	−0.634366	−	0.169978i
$576$	−12524.8	+	7231.18i	−0.0377507	+	0.0217954i
$577$	−36340.4	+	135624.i	−0.109153	+	0.407366i	−0.998783	−	0.0493162i	$-0.984296\pi$
$577$	−36340.4	+	135624.i	−0.109153	+	0.407366i	0.889630	+	0.456683i	$0.150962\pi$
$578$	39642.7	+	39642.7i	0.118661	+	0.118661i
$579$	76834.8	+	286752.i	0.229193	+	0.855359i
$580$	47900.6	−	27655.4i	0.142392	−	0.0822099i
$581$	−653806.			−1.93685
$582$			439709.i			1.29813i
$583$	−671651.	+	387778.i	−1.97609	+	1.14090i
$584$	−132762.	+	132762.i	−0.389269	+	0.389269i
$585$	−32418.1	−	18716.6i	−0.0947276	−	0.0546910i
$586$	224291.	−	224291.i	0.653155	−	0.653155i
$587$	−5889.16	−	21978.6i	−0.0170914	−	0.0637859i	0.956853	−	0.290571i	$-0.0938452\pi$
$587$	−5889.16	−	21978.6i	−0.0170914	−	0.0637859i	−0.973945	+	0.226785i	$0.927179\pi$
$588$	194466.	−	336825.i	0.562456	−	0.974202i
$589$	−131431.	+	227645.i	−0.378849	+	0.656186i
$590$	23451.3	−	87521.3i	0.0673693	−	0.251426i
$591$			227982.i			0.652718i
$592$	38709.3	−	78601.2i	0.110451	−	0.224278i
$593$	228469.			0.649708			0.324854	−	0.945764i	$-0.394685\pi$
$593$	228469.			0.649708			0.324854	+	0.945764i	$0.394685\pi$
$594$	312065.	+	83617.7i	0.884449	+	0.236987i
$595$	−158111.	−	91285.3i	−0.446609	−	0.257850i
$596$	148183.	+	85553.7i	0.417164	+	0.240850i
$597$	−232126.	+	62197.9i	−0.651290	+	0.174513i
$598$	−121300.	−	121300.i	−0.339201	−	0.339201i
$599$	−190084.	+	329235.i	−0.529776	+	0.917599i	0.469621	+	0.882868i	$0.344391\pi$
$599$	−190084.	+	329235.i	−0.529776	+	0.917599i	−0.999397	+	0.0347308i	$0.988943\pi$
$600$	−92112.8	−	92112.8i	−0.255869	−	0.255869i
$601$	320945.	+	555893.i	0.888549	+	1.53901i	0.841591	+	0.540115i	$0.181619\pi$
$601$	320945.	+	555893.i	0.888549	+	1.53901i	0.0469582	+	0.998897i	$0.485047\pi$
$602$	471483.			1.30099
$603$			49843.1i			0.137079i
$604$	130543.	+	226107.i	0.357833	+	0.619785i
$605$	−235247.	+	63034.2i	−0.642707	+	0.172213i
$606$	−72194.1	+	72194.1i	−0.196588	+	0.196588i
$607$	347237.	+	93042.0i	0.942430	+	0.252523i	0.697147	−	0.716928i	$-0.254452\pi$
$607$	347237.	+	93042.0i	0.942430	+	0.252523i	0.245283	+	0.969451i	$0.421119\pi$
$608$	−48453.6	−	83924.0i	−0.131075	−	0.227028i
$609$	182344.	−	680518.i	0.491651	−	1.83487i
$610$	−1901.83	−	7097.71i	−0.00511106	−	0.0190747i
$611$	323942.	−	86799.9i	0.867729	−	0.232507i
$612$	55089.8	+	14761.3i	0.147085	+	0.0394113i
$613$	−46657.5	+	26937.7i	−0.124165	+	0.0716870i	−0.560796	−	0.827954i	$-0.689505\pi$
$613$	−46657.5	+	26937.7i	−0.124165	+	0.0716870i	0.436631	+	0.899641i	$0.356172\pi$
$614$	41482.8	−	154816.i	0.110035	−	0.410657i
$615$	−136901.	−	136901.i	−0.361956	−	0.361956i
$616$	101883.	+	380233.i	0.268498	+	1.00205i
$617$	−377783.	+	218113.i	−0.992365	+	0.572942i	−0.905981	−	0.423319i	$-0.860865\pi$
$617$	−377783.	+	218113.i	−0.992365	+	0.572942i	−0.0863849	+	0.996262i	$0.527531\pi$
$618$	−53254.4			−0.139437
$619$		−	318838.i		−	0.832126i	−0.909336	−	0.416063i	$-0.863410\pi$
$619$		−	318838.i		−	0.832126i	0.909336	−	0.416063i	$-0.136590\pi$
$620$	29303.0	−	16918.1i	0.0762306	−	0.0440117i
$621$	153700.	−	153700.i	0.398558	−	0.398558i
$622$	252750.	+	145925.i	0.653296	+	0.377181i
$623$	224258.	−	224258.i	0.577792	−	0.577792i
$624$	−26636.3	−	99407.9i	−0.0684076	−	0.255301i
$625$	128505.	−	222577.i	0.328972	−	0.569796i
$626$	154265.	−	267195.i	0.393657	−	0.681834i
$627$	300009.	−	1.11965e6i	0.763132	−	2.84805i
$628$			176534.i			0.447620i
$629$	−327123.	+	111239.i	−0.826816	+	0.281163i
$630$	57793.2			0.145611
$631$	−490098.	−	131321.i	−1.23090	−	0.329820i	−0.415973	−	0.909377i	$-0.636559\pi$
$631$	−490098.	−	131321.i	−1.23090	−	0.329820i	−0.814931	+	0.579557i	$0.803225\pi$
$632$	150684.	+	86997.7i	0.377254	+	0.217808i
$633$	310684.	+	179374.i	0.775375	+	0.447663i
$634$	−276356.	+	74049.4i	−0.687528	+	0.184223i
$635$	−180845.	−	180845.i	−0.448496	−	0.448496i
$636$	−156521.	+	271103.i	−0.386954	+	0.670224i
$637$	506007.	+	506007.i	1.24703	+	1.24703i
$638$	235149.	+	407290.i	0.577699	+	1.00060i
$639$	−75996.5			−0.186120
$640$			12474.1i			0.0304544i
$641$	−105862.	−	183359.i	−0.257647	−	0.446257i	0.707964	−	0.706248i	$-0.249614\pi$
$641$	−105862.	−	183359.i	−0.257647	−	0.446257i	−0.965611	+	0.259991i	$0.916280\pi$
$642$	−49249.9	+	13196.5i	−0.119491	+	0.0320175i
$643$	−480578.	+	480578.i	−1.16236	+	1.16236i	−0.178406	+	0.983957i	$0.557094\pi$
$643$	−480578.	+	480578.i	−1.16236	+	1.16236i	−0.983957	+	0.178406i	$0.942906\pi$
$644$	255822.	+	68547.2i	0.616830	+	0.165279i
$645$	89356.2	+	154769.i	0.214786	+	0.372019i
$646$	−98910.0	+	369137.i	−0.237015	+	0.884551i
$647$	−151820.	−	566601.i	−0.362678	−	1.35353i	−0.870541	−	0.492095i	$-0.836231\pi$
$647$	−151820.	−	566601.i	−0.362678	−	1.35353i	0.507863	−	0.861438i	$-0.330436\pi$
$648$	175968.	−	47150.6i	0.419068	−	0.112289i
$649$	744178.	+	199402.i	1.76680	+	0.473413i
$650$	207570.	−	119840.i	0.491290	−	0.283646i
$651$	111549.	−	416305.i	0.263210	−	0.982312i
$652$	88095.0	+	88095.0i	0.207232	+	0.207232i
$653$	180376.	+	673174.i	0.423012	+	1.57870i	0.768225	+	0.640179i	$0.221140\pi$
$653$	180376.	+	673174.i	0.423012	+	1.57870i	−0.345213	+	0.938524i	$0.612193\pi$
$654$	−33277.2	+	19212.6i	−0.0778021	+	0.0449191i
$655$	49695.7			0.115834
$656$		−	137626.i		−	0.319811i
$657$	−202981.	+	117191.i	−0.470245	+	0.271496i
$658$	−366123.	+	366123.i	−0.845620	+	0.845620i
$659$	−613880.	−	354424.i	−1.41356	−	0.816116i	−0.417834	−	0.908523i	$-0.637211\pi$
$659$	−613880.	−	354424.i	−1.41356	−	0.816116i	−0.995721	+	0.0924071i	$0.970544\pi$
$660$	−105506.	+	105506.i	−0.242209	+	0.242209i
$661$	−120579.	−	450007.i	−0.275974	−	1.02995i	−0.955186	−	0.296007i	$-0.904345\pi$
$661$	−120579.	−	450007.i	−0.275974	−	1.02995i	0.679212	−	0.733942i	$-0.262322\pi$
$662$	291110.	−	504217.i	0.664264	−	1.15054i
$663$	−202925.	+	351477.i	−0.461646	+	0.799594i
$664$	45594.6	−	170161.i	0.103414	−	0.385944i
$665$			387252.i			0.875689i
$666$	72071.6	−	82271.2i	0.162486	−	0.185481i
$667$	316418.			0.711228
$668$	3855.45	+	1033.07i	0.00864017	+	0.00231513i
$669$	−732947.	−	423167.i	−1.63765	−	0.945496i
$670$	37231.2	+	21495.5i	0.0829388	+	0.0478847i
$671$	60350.6	−	16170.9i	0.134041	−	0.0359161i
$672$	112352.	+	112352.i	0.248796	+	0.248796i
$673$	−161583.	+	279869.i	−0.356750	+	0.617909i	−0.987416	−	0.158145i	$-0.949449\pi$
$673$	−161583.	+	279869.i	−0.356750	+	0.617909i	0.630666	+	0.776055i	$0.282782\pi$
$674$	−71411.5	−	71411.5i	−0.157199	−	0.157199i
$675$	151851.	+	263014.i	0.333282	+	0.577261i
$676$	−39133.4			−0.0856355
$677$		−	249012.i		−	0.543304i	−0.962396	−	0.271652i	$-0.912430\pi$
$677$		−	249012.i		−	0.543304i	0.962396	−	0.271652i	$-0.0875700\pi$
$678$	43838.8	+	75931.1i	0.0953673	+	0.165181i
$679$	1.20650e6	−	323281.i	2.61690	−	0.701197i
$680$	34784.4	−	34784.4i	0.0752257	−	0.0752257i
$681$	641162.	+	171799.i	1.38253	+	0.370447i
$682$	143852.	+	249158.i	0.309276	+	0.535682i
$683$	119628.	−	446457.i	0.256443	−	0.957057i	−0.710840	−	0.703354i	$-0.751685\pi$
$683$	119628.	−	446457.i	0.256443	−	0.957057i	0.967282	−	0.253703i	$-0.0816485\pi$
$684$	−31310.2	−	116851.i	−0.0669227	−	0.249759i
$685$	−109307.	+	29288.8i	−0.232953	+	0.0624195i
$686$	−516304.	−	138343.i	−1.09713	−	0.293974i
$687$	−152110.	+	87820.7i	−0.322288	+	0.186073i
$688$	−32879.9	+	122710.i	−0.0694631	+	0.259240i
$689$	−407275.	−	407275.i	−0.857924	−	0.857924i
$690$	25982.3	+	96967.2i	0.0545732	+	0.203670i
$691$	−373074.	+	215395.i	−0.781339	+	0.451106i	−0.836905	−	0.547349i	$-0.815637\pi$
$691$	−373074.	+	215395.i	−0.781339	+	0.451106i	0.0555657	+	0.998455i	$0.482304\pi$
$692$	276998.			0.578448
$693$			491405.i			1.02323i
$694$	279481.	−	161359.i	0.580275	−	0.335022i
$695$	14134.1	−	14134.1i	0.0292617	−	0.0292617i
$696$	164397.	+	94914.8i	0.339372	+	0.195936i
$697$	−383773.	+	383773.i	−0.789966	+	0.789966i
$698$	−26219.0	−	97850.5i	−0.0538152	−	0.200841i
$699$	105964.	−	183535.i	0.216873	−	0.375635i
$700$	−185022.	+	320467.i	−0.377595	+	0.654014i
$701$	−204161.	+	761941.i	−0.415468	+	1.55055i	0.368428	+	0.929656i	$0.379896\pi$
$701$	−204161.	+	761941.i	−0.415468	+	1.55055i	−0.783896	+	0.620892i	$0.786770\pi$
$702$			239934.i			0.486874i
$703$	551270.	+	482926.i	1.11546	+	0.977170i
$704$	−106065.			−0.214007
$705$	−189572.	−	50795.6i	−0.381413	−	0.102199i
$706$	−566798.	−	327241.i	−1.13715	−	0.656535i
$707$	251168.	+	145012.i	0.502488	+	0.290112i
$708$	300378.	−	80485.9i	0.599240	−	0.160566i
$709$	63435.3	+	63435.3i	0.126194	+	0.126194i	0.767383	−	0.641189i	$-0.221559\pi$
$709$	63435.3	+	63435.3i	0.126194	+	0.126194i	−0.641189	+	0.767383i	$0.721559\pi$
$710$	−32774.4	+	56767.0i	−0.0650158	+	0.112611i
$711$	153588.	+	153588.i	0.303821	+	0.303821i
$712$	42726.8	+	74005.0i	0.0842831	+	0.145983i
$713$	193568.			0.380762
$714$		−	626592.i		−	1.22910i
$715$	−137266.	−	237751.i	−0.268504	−	0.465062i
$716$	−155926.	+	41780.2i	−0.304153	+	0.0814976i
$717$	52063.5	−	52063.5i	0.101273	−	0.101273i
$718$	−262763.	−	70407.1i	−0.509700	−	0.136574i
$719$	14296.6	+	24762.4i	0.0276550	+	0.0478999i	0.879522	−	0.475859i	$-0.157863\pi$
$719$	14296.6	+	24762.4i	0.0276550	+	0.0478999i	−0.851867	+	0.523759i	$0.824529\pi$
$720$	−4030.33	+	15041.4i	−0.00777456	+	0.0290150i
$721$	39153.4	+	146122.i	0.0753180	+	0.281091i
$722$	426935.	−	114397.i	0.819007	−	0.219452i
$723$	−275881.	−	73922.0i	−0.527770	−	0.141415i
$724$	−211113.	+	121886.i	−0.402752	+	0.232529i
$725$	−114424.	+	427035.i	−0.217691	+	0.812433i
$726$	−591043.	−	591043.i	−1.12136	−	1.12136i
$727$	−211460.	−	789180.i	−0.400092	−	1.49316i	−0.812932	−	0.582359i	$-0.802130\pi$
$727$	−211460.	−	789180.i	−0.400092	−	1.49316i	0.412840	−	0.910804i	$-0.364537\pi$
$728$	−253178.	+	146172.i	−0.477708	+	0.275805i
$729$	−239395.			−0.450463
$730$			202160.i			0.379359i
$731$	433864.	−	250492.i	0.811931	−	0.468768i
$732$	17832.5	−	17832.5i	0.0332806	−	0.0332806i
$733$	250334.	+	144530.i	0.465920	+	0.268999i	0.714530	−	0.699604i	$-0.246640\pi$
$733$	250334.	+	144530.i	0.465920	+	0.268999i	−0.248610	+	0.968604i	$0.579974\pi$
$734$	−253068.	+	253068.i	−0.469727	+	0.469727i
$735$	−108386.	−	404504.i	−0.200632	−	0.748769i
$736$	−35680.5	+	61800.5i	−0.0658682	+	0.114087i
$737$	−182772.	+	316570.i	−0.336492	+	0.582821i
$738$	44466.3	−	165950.i	0.0816429	−	0.304695i
$739$			243855.i			0.446523i	0.974759	+	0.223261i	$0.0716703\pi$
$739$			243855.i			0.446523i	−0.974759	+	0.223261i	$0.928330\pi$
$740$	−30372.2	−	89315.6i	−0.0554642	−	0.163104i
$741$	860851.			1.56780
$742$	858944.	+	230153.i	1.56012	+	0.418032i
$743$	368163.	+	212559.i	0.666903	+	0.385037i	0.794902	−	0.606738i	$-0.207522\pi$
$743$	368163.	+	212559.i	0.666903	+	0.385037i	−0.127999	+	0.991774i	$0.540855\pi$
$744$	100569.	+	58063.8i	0.181686	+	0.104896i
$745$	177958.	−	47683.8i	0.320631	−	0.0859128i
$746$	−342164.	−	342164.i	−0.614832	−	0.614832i
$747$	109957.	−	190450.i	0.197052	−	0.341303i
$748$	295765.	+	295765.i	0.528620	+	0.528620i
$749$	72418.4	+	125432.i	0.129088	+	0.223587i
$750$	−299419.			−0.532300
$751$			623510.i			1.10551i	0.833343	+	0.552756i	$0.186424\pi$
$751$			623510.i			1.10551i	−0.833343	+	0.552756i	$0.813576\pi$
$752$	−69755.8	−	120821.i	−0.123351	−	0.213651i
$753$	1.03491e6	−	277302.i	1.82520	−	0.489062i
$754$	−246972.	+	246972.i	−0.434415	+	0.434415i
$755$	271540.	+	72758.9i	0.476365	+	0.127642i
$756$	−185217.	−	320805.i	−0.324068	−	0.561303i
$757$	96419.9	−	359844.i	0.168258	−	0.627946i	−0.829345	−	0.558737i	$-0.811286\pi$
$757$	96419.9	−	359844.i	0.168258	−	0.627946i	0.997602	−	0.0692085i	$-0.0220474\pi$
$758$	5161.14	+	19261.7i	0.00898271	+	0.0335239i
$759$	−824495.	+	220923.i	−1.43121	+	0.383493i
$760$	−100787.	−	27005.8i	−0.174493	−	0.0467552i
$761$	253202.	−	146186.i	0.437218	−	0.252428i	−0.265199	−	0.964194i	$-0.585438\pi$
$761$	253202.	−	146186.i	0.437218	−	0.252428i	0.702417	+	0.711766i	$0.252104\pi$
$762$	227181.	−	847849.i	0.391256	−	1.46019i
$763$	77182.5	+	77182.5i	0.132577	+	0.132577i
$764$	−130714.	−	487830.i	−0.223941	−	0.835761i
$765$	53181.9	−	30704.6i	0.0908742	−	0.0524663i
$766$	−161637.			−0.275475
$767$			572166.i			0.972594i
$768$	−37076.2	+	21405.9i	−0.0628597	+	0.0362921i
$769$	−55793.2	+	55793.2i	−0.0943471	+	0.0943471i	−0.752705	−	0.658358i	$-0.771251\pi$
$769$	−55793.2	+	55793.2i	−0.0943471	+	0.0943471i	0.658358	+	0.752705i	$0.271251\pi$
$770$	367064.	+	211924.i	0.619099	+	0.357437i
$771$	−202999.	+	202999.i	−0.341495	+	0.341495i
$772$	58809.0	+	219478.i	0.0986755	+	0.368262i
$773$	344004.	−	595832.i	0.575711	−	0.997160i	−0.420253	−	0.907407i	$-0.638059\pi$
$773$	344004.	−	595832.i	0.575711	−	0.997160i	0.995964	−	0.0897536i	$-0.0286079\pi$
$774$	−79293.7	+	137341.i	−0.132360	+	0.229254i
$775$	−69998.4	+	261238.i	−0.116543	+	0.434943i
$776$			336551.i			0.558892i
$777$	−1.07800e6	−	530892.i	−1.78558	−	0.879355i
$778$	349797.			0.577905
$779$	1.11198e6	+	297953.i	1.83240	+	0.490990i
$780$	−95965.1	−	55405.5i	−0.157734	−	0.0910675i
$781$	−482680.	−	278675.i	−0.791329	−	0.456874i
$782$	271828.	−	72836.0i	0.444509	−	0.119106i
$783$	−312941.	−	312941.i	−0.510433	−	0.510433i
$784$	148843.	−	257804.i	0.242157	−	0.419428i
$785$	134406.	+	134406.i	0.218112	+	0.218112i
$786$	85279.2	+	147708.i	0.138038	+	0.239088i
$787$	15939.2			0.0257346			0.0128673	−	0.999917i	$-0.495904\pi$
$787$	15939.2			0.0257346			0.0128673	+	0.999917i	$0.495904\pi$
$788$			174496.i			0.281018i
$789$	502257.	+	869935.i	0.806812	+	1.39744i
$790$	180962.	−	48488.6i	0.289956	−	0.0776936i
$791$	176113.	−	176113.i	0.281474	−	0.281474i
$792$	−127894.	−	34269.2i	−0.203892	−	0.0546328i
$793$	23200.5	+	40184.4i	0.0368936	+	0.0639015i
$794$	−187385.	+	699331.i	−0.297231	+	1.10928i
$795$	87238.0	+	325577.i	0.138029	+	0.515132i
$796$	−177668.	+	47605.9i	−0.280403	+	0.0751337i
$797$	716893.	+	192091.i	1.12859	+	0.302406i	0.774356	−	0.632750i	$-0.218074\pi$
$797$	716893.	+	192091.i	1.12859	+	0.302406i	0.354237	+	0.935156i	$0.384740\pi$
$798$	−1.15101e6	+	664534.i	−1.80747	+	1.04354i
$799$	−142395.	+	531425.i	−0.223049	+	0.832432i
$800$	−70502.7	−	70502.7i	−0.110160	−	0.110160i
$801$	27609.7	+	103041.i	0.0430324	+	0.160599i
$802$	437322.	−	252488.i	0.679912	−	0.392547i
$803$	−1.71893e6			−2.66580
$804$			147547.i			0.228254i
$805$	246962.	−	142583.i	0.381099	−	0.220028i
$806$	−151084.	+	151084.i	−0.232568	+	0.232568i
$807$	268449.	+	154989.i	0.412206	+	0.237987i
$808$	−55257.0	+	55257.0i	−0.0846378	+	0.0846378i
$809$	−140495.	−	524335.i	−0.214667	−	0.801146i	−0.986284	−	0.165059i	$-0.947219\pi$
$809$	−140495.	−	524335.i	−0.214667	−	0.801146i	0.771617	−	0.636087i	$-0.219448\pi$
$810$	98076.8	−	169874.i	0.149485	−	0.258915i
$811$	439540.	−	761306.i	0.668277	−	1.15749i	−0.310108	−	0.950701i	$-0.600365\pi$
$811$	439540.	−	761306.i	0.668277	−	1.15749i	0.978386	−	0.206789i	$-0.0663014\pi$
$812$	139565.	−	520865.i	0.211673	−	0.789974i
$813$		−	1.02252e6i		−	1.54701i
$814$	759435.	−	258249.i	1.14615	−	0.389754i
$815$	134144.			0.201956
$816$	163078.	+	43696.7i	0.244915	+	0.0656249i
$817$	−920271.	−	531319.i	−1.37871	−	0.795996i
$818$	−328540.	−	189682.i	−0.490999	−	0.283479i
$819$	−352511.	+	94455.0i	−0.525539	+	0.140818i
$820$	−104783.	−	104783.i	−0.155834	−	0.155834i
$821$	658.565	−	1140.67i	0.000977040	−	0.00169228i	−0.865536	−	0.500846i	$-0.833022\pi$
$821$	658.565	−	1140.67i	0.000977040	−	0.00169228i	0.866514	+	0.499154i	$0.166356\pi$
$822$	−274628.	−	274628.i	−0.406444	−	0.406444i
$823$	−214218.	−	371037.i	−0.316269	−	0.547794i	0.663438	−	0.748232i	$-0.269097\pi$
$823$	−214218.	−	371037.i	−0.316269	−	0.547794i	−0.979706	+	0.200438i	$0.935763\pi$
$824$	−40760.7			−0.0600325
$825$		−	1.19262e6i		−	1.75225i
$826$	−441684.	−	765018.i	−0.647368	−	1.12127i
$827$	−78633.5	+	21069.8i	−0.114973	+	0.0308070i	−0.315847	−	0.948810i	$-0.602289\pi$
$827$	−78633.5	+	21069.8i	−0.114973	+	0.0308070i	0.200874	+	0.979617i	$0.435622\pi$
$828$	−62991.3	+	62991.3i	−0.0918797	+	0.0918797i
$829$	788502.	+	211279.i	1.14734	+	0.307430i	0.781901	−	0.623403i	$-0.214250\pi$
$829$	788502.	+	211279.i	1.14734	+	0.307430i	0.365444	+	0.930833i	$0.380917\pi$
$830$	−94840.3	−	164268.i	−0.137669	−	0.238450i
$831$	13988.0	−	52204.0i	0.0202560	−	0.0755965i
$832$	−20387.3	−	76086.3i	−0.0294518	−	0.109916i
$833$	−1.13394e6	+	303839.i	−1.63418	+	0.437878i
$834$	66264.5	+	17755.5i	0.0952684	+	0.0255271i
$835$	3721.93	−	2148.86i	0.00533820	−	0.00308201i
$836$	229626.	−	856975.i	0.328555	−	1.22618i
$837$	−191441.	−	191441.i	−0.273265	−	0.273265i
$838$	−53848.1	−	200964.i	−0.0766800	−	0.286174i
$839$	−399755.	+	230799.i	−0.567898	+	0.327876i	−0.756309	−	0.654214i	$-0.772999\pi$
$839$	−399755.	+	230799.i	−0.567898	+	0.327876i	0.188412	+	0.982090i	$0.439666\pi$
$840$	171081.			0.242462
$841$			63039.3i			0.0891291i
$842$	−602620.	+	347923.i	−0.850001	+	0.490748i
$843$	−121339.	+	121339.i	−0.170744	+	0.170744i
$844$	237796.	+	137292.i	0.333826	+	0.192735i
$845$	−29794.6	+	29794.6i	−0.0417277	+	0.0417277i
$846$	−45075.5	−	168224.i	−0.0629795	−	0.235043i
$847$	−1.18719e6	+	2.05628e6i	−1.65483	+	2.86626i
$848$	−119801.	+	207501.i	−0.166597	+	0.288555i
$849$	−16326.5	+	60931.3i	−0.0226505	+	0.0845327i
$850$			393196.i			0.544216i
$851$	105002.	−	529371.i	0.144991	−	0.730973i
$852$	−224967.			−0.309913
$853$	−91198.5	−	24436.6i	−0.125340	−	0.0335848i	0.195604	−	0.980683i	$-0.437333\pi$
$853$	−91198.5	−	24436.6i	−0.125340	−	0.0335848i	−0.320944	+	0.947098i	$0.604000\pi$
$854$	−62040.7	−	35819.2i	−0.0850669	−	0.0491134i
$855$	−112804.	−	65127.6i	−0.154310	−	0.0890908i
$856$	−37695.6	+	10100.5i	−0.0514450	+	0.0137847i
$857$	428190.	+	428190.i	0.583008	+	0.583008i	0.935729	−	0.352720i	$-0.114743\pi$
$857$	428190.	+	428190.i	0.583008	+	0.583008i	−0.352720	+	0.935729i	$0.614743\pi$
$858$	471103.	−	815974.i	0.639943	−	1.10841i
$859$	−18479.8	−	18479.8i	−0.0250444	−	0.0250444i	0.694474	−	0.719518i	$-0.255637\pi$
$859$	−18479.8	−	18479.8i	−0.0250444	−	0.0250444i	−0.719518	+	0.694474i	$0.755637\pi$
$860$	68392.8	+	118460.i	0.0924726	+	0.160167i
$861$	−1.88752e6			−2.54616
$862$			842282.i			1.13356i
$863$	70403.5	+	121943.i	0.0945307	+	0.163732i	0.909413	−	0.415895i	$-0.136532\pi$
$863$	70403.5	+	121943.i	0.0945307	+	0.163732i	−0.814882	+	0.579627i	$0.803198\pi$
$864$	96410.0	−	25833.0i	0.129150	−	0.0346056i
$865$	210895.	−	210895.i	0.281861	−	0.281861i
$866$	−621553.	−	166545.i	−0.828786	−	0.222073i
$867$	103588.	+	179419.i	0.137807	+	0.238688i
$868$	85378.7	−	318638.i	0.113321	−	0.422919i
$869$	412290.	+	1.53869e6i	0.545963	+	2.03756i
$870$	197430.	−	52901.2i	0.260840	−	0.0698919i
$871$	−262224.	−	70262.8i	−0.345650	−	0.0926166i
$872$	−25470.2	+	14705.2i	−0.0334965	+	0.0193392i
$873$	−108738.	+	405816.i	−0.142677	+	0.532477i
$874$	−422082.	−	422082.i	−0.552553	−	0.552553i
$875$	220137.	+	821562.i	0.287526	+	1.07306i
$876$	−600869.	+	346912.i	−0.783018	+	0.452076i
$877$	−1.16638e6			−1.51650			−0.758250	−	0.651964i	$-0.773945\pi$
$877$	−1.16638e6			−1.51650			−0.758250	+	0.651964i	$0.773945\pi$
$878$			71667.0i			0.0929672i
$879$	1.01512e6	−	586078.i	1.31383	−	0.758539i
$880$	−80754.0	+	80754.0i	−0.104279	+	0.104279i
$881$	−313158.	−	180802.i	−0.403471	−	0.232944i	0.284510	−	0.958673i	$-0.408169\pi$
$881$	−313158.	−	180802.i	−0.403471	−	0.232944i	−0.687980	+	0.725729i	$0.741503\pi$
$882$	262771.	−	262771.i	0.337785	−	0.337785i
$883$	−379583.	−	1.41662e6i	−0.486839	−	1.81691i	−0.571631	−	0.820511i	$-0.693689\pi$
$883$	−379583.	−	1.41662e6i	−0.486839	−	1.81691i	0.0847914	−	0.996399i	$-0.472978\pi$
$884$	−155318.	+	269018.i	−0.198754	+	0.344253i
$885$	167417.	−	289975.i	0.213753	−	0.370232i
$886$	−177742.	+	663343.i	−0.226424	+	0.845027i
$887$		−	420617.i		−	0.534614i	−0.963611	−	0.267307i	$-0.913866\pi$
$887$		−	420617.i		−	0.534614i	0.963611	−	0.267307i	$-0.0861337\pi$
$888$	213348.	−	243541.i	0.270560	−	0.308850i
$889$	−2.49340e6			−3.15492
$890$	88875.1	+	23814.0i	0.112202	+	0.0300644i
$891$	1.44441e6	+	833930.i	1.81943	+	1.05045i
$892$	−560994.	−	323890.i	−0.705064	−	0.407069i
$893$	1.12721e6	−	302035.i	1.41352	−	0.378751i
$894$	447109.	+	447109.i	0.559420	+	0.559420i
$895$	−86906.1	+	150526.i	−0.108494	+	0.187916i
$896$	85993.7	+	85993.7i	0.107115	+	0.107115i
$897$	−316959.	−	548990.i	−0.393930	−	0.682306i
$898$	726992.			0.901524
$899$		−	394113.i		−	0.487642i
$900$	−62233.6	−	107792.i	−0.0768316	−	0.133076i
$901$	912687.	−	244554.i	1.12427	−	0.301248i
$902$	890952.	−	890952.i	1.09507	−	1.09507i
$903$	1.68294e6	+	450943.i	2.06393	+	0.553027i
$904$	33554.0	+	58117.3i	0.0410589	+	0.0711162i
$905$	−67933.8	+	253532.i	−0.0829447	+	0.309554i
$906$	249712.	+	931939.i	0.304217	+	1.13535i
$907$	717971.	−	192380.i	0.872755	−	0.233854i	0.205476	−	0.978662i	$-0.434126\pi$
$907$	717971.	−	192380.i	0.872755	−	0.233854i	0.667279	+	0.744808i	$0.267459\pi$
$908$	490742.	+	131494.i	0.595226	+	0.159490i
$909$	−84482.5	+	48776.0i	−0.102244	+	0.0590308i
$910$	−81469.8	+	304049.i	−0.0983816	+	0.367165i
$911$	128886.	+	128886.i	0.155299	+	0.155299i	0.780480	−	0.625181i	$-0.214975\pi$
$911$	128886.	+	128886.i	0.155299	+	0.155299i	−0.625181	+	0.780480i	$0.714975\pi$
$912$	−92685.4	−	345907.i	−0.111435	−	0.415881i
$913$	1.39674e6	−	806410.i	1.67562	−	0.967418i
$914$	−678105.			−0.811717
$915$		−	27154.0i		−	0.0324333i
$916$	−116424.	+	67217.6i	−0.138756	+	0.0801109i
$917$	342591.	−	342591.i	0.407415	−	0.407415i
$918$	−340877.	−	196805.i	−0.404494	−	0.233535i
$919$	375242.	−	375242.i	0.444304	−	0.444304i	−0.449152	−	0.893456i	$-0.648274\pi$
$919$	375242.	−	375242.i	0.444304	−	0.444304i	0.893456	+	0.449152i	$0.148274\pi$
$920$	19886.7	+	74218.3i	0.0234957	+	0.0876870i
$921$	296143.	−	512935.i	0.349126	−	0.604704i
$922$	751.168	−	1301.06i	0.000883639	−	0.00153051i
$923$	107131.	−	399817.i	0.125751	−	0.469308i
$924$			1.45467e6i			1.70381i
$925$	676465.	+	333143.i	0.790609	+	0.389356i
$926$	257706.			0.300540
$927$	−49149.5	−	13169.6i	−0.0571952	−	0.0153254i
$928$	125829.	+	72647.3i	0.146111	+	0.0843574i
$929$	−1.34187e6	−	774727.i	−1.55481	−	0.897672i	−0.997739	−	0.0672087i	$-0.978591\pi$
$929$	−1.34187e6	−	774727.i	−1.55481	−	0.897672i	−0.557074	−	0.830463i	$-0.688076\pi$
$930$	120777.	−	32362.2i	0.139643	−	0.0374172i
$931$	1.76074e6	+	1.76074e6i	2.03140	+	2.03140i
$932$	81104.5	−	140477.i	0.0933712	−	0.161724i
$933$	762614.	+	762614.i	0.876075	+	0.876075i
$934$	−36906.5	−	63923.9i	−0.0423066	−	0.0732773i
$935$	450368.			0.515163
$936$		−	98332.5i		−	0.112239i
$937$	−19039.8	−	32977.9i	−0.0216862	−	0.0375616i	0.854979	−	0.518663i	$-0.173570\pi$
$937$	−19039.8	−	32977.9i	−0.0216862	−	0.0375616i	−0.876665	+	0.481102i	$0.840237\pi$
$938$	404848.	−	108479.i	0.460136	−	0.123293i
$939$	806197.	−	806197.i	0.914345	−	0.914345i
$940$	−145097.	−	38878.7i	−0.164212	−	0.0440003i
$941$	−300292.	−	520120.i	−0.339128	−	0.587387i	0.645141	−	0.764064i	$-0.276799\pi$
$941$	−300292.	−	520120.i	−0.339128	−	0.587387i	−0.984269	+	0.176676i	$0.943465\pi$
$942$	−168844.	+	630133.i	−0.190275	+	0.710118i
$943$	−219408.	−	818844.i	−0.246735	−	0.920826i
$944$	229908.	−	61603.5i	0.257994	−	0.0691292i
$945$	−385265.	−	103231.i	−0.431416	−	0.115597i
$946$	−1.00724e6	+	581531.i	−1.12552	+	0.649817i
$947$	−406245.	+	1.51613e6i	−0.452989	+	1.69058i	0.240944	+	0.970539i	$0.422543\pi$
$947$	−406245.	+	1.51613e6i	−0.452989	+	1.69058i	−0.693933	+	0.720039i	$0.744124\pi$
$948$	454655.	+	454655.i	0.505901	+	0.505901i
$949$	−330403.	−	1.23308e6i	−0.366870	−	1.36918i
$950$	722274.	−	417005.i	0.800304	−	0.462055i
$951$	−1.05727e6			−1.16902
$952$		−	479590.i		−	0.529171i
$953$	1.27510e6	−	736180.i	1.40397	−	0.810584i	0.409175	−	0.912456i	$-0.365817\pi$
$953$	1.27510e6	−	736180.i	1.40397	−	0.810584i	0.994798	+	0.101872i	$0.0324832\pi$
$954$	−211499.	+	211499.i	−0.232387	+	0.232387i
$955$	−470935.	−	271895.i	−0.516362	−	0.298122i
$956$	39849.1	−	39849.1i	0.0436016	−	0.0436016i
$957$	449809.	+	1.67871e6i	0.491139	+	1.83296i
$958$	−26788.6	+	46399.2i	−0.0291890	+	0.0505568i
$959$	−551629.	+	955449.i	−0.599804	+	1.03889i
$960$	−11930.7	+	44526.0i	−0.0129456	+	0.0483138i
$961$			682424.i			0.738937i
$962$	331230.	+	495144.i	0.357915	+	0.535034i
$963$	−48717.1			−0.0525326
$964$	−211158.	−	56579.5i	−0.227223	−	0.0608843i
$965$	211877.	+	122327.i	0.227525	+	0.131362i
$966$	847585.	+	489353.i	0.908299	+	0.524407i
$967$	371981.	−	99671.9i	0.397802	−	0.106591i	−0.0543712	−	0.998521i	$-0.517315\pi$
$967$	371981.	−	99671.9i	0.397802	−	0.106591i	0.452174	+	0.891930i	$0.350649\pi$
$968$	−452381.	−	452381.i	−0.482785	−	0.482785i
$969$	−706112.	+	1.22302e6i	−0.752014	+	1.30253i
$970$	256237.	+	256237.i	0.272332	+	0.272332i
$971$	679380.	+	1.17672e6i	0.720567	+	1.24806i	0.960773	+	0.277336i	$0.0894517\pi$
$971$	679380.	+	1.17672e6i	0.720567	+	1.24806i	−0.240206	+	0.970722i	$0.577215\pi$
$972$	315913.			0.334376
$973$		−	194874.i		−	0.205840i
$974$	−75776.1	−	131248.i	−0.0798756	−	0.138349i
$975$	855533.	−	229239.i	0.899969	−	0.241146i
$976$	13648.9	−	13648.9i	0.0143285	−	0.0143285i
$977$	−883920.	−	236846.i	−0.926028	−	0.248128i	−0.235868	−	0.971785i	$-0.575793\pi$
$977$	−883920.	−	236846.i	−0.926028	−	0.248128i	−0.690160	+	0.723657i	$0.742460\pi$
$978$	230195.	+	398709.i	0.240668	+	0.416849i
$979$	−202486.	+	755689.i	−0.211266	+	0.788457i
$980$	−82958.4	−	309605.i	−0.0863791	−	0.322371i
$981$	−35463.3	+	9502.37i	−0.0368503	+	0.00987402i
$982$	−653847.	−	175198.i	−0.678037	−	0.181679i
$983$	312040.	−	180156.i	0.322926	−	0.186441i	−0.329770	−	0.944061i	$-0.606971\pi$
$983$	312040.	−	180156.i	0.322926	−	0.186441i	0.652696	+	0.757620i	$0.273638\pi$
$984$	131630.	−	491251.i	0.135946	−	0.507357i
$985$	132855.	+	132855.i	0.136932	+	0.136932i
$986$	−148298.	−	553454.i	−0.152539	−	0.569282i
$987$	−1.65704e6	+	956690.i	−1.70097	+	0.982058i
$988$	658891.			0.674994
$989$			782512.i			0.800015i
$990$	−123465.	+	71282.5i	−0.125972	+	0.0727299i
$991$	228998.	−	228998.i	0.233176	−	0.233176i	−0.580841	−	0.814017i	$-0.697276\pi$
$991$	228998.	−	228998.i	0.233176	−	0.233176i	0.814017	+	0.580841i	$0.197276\pi$
$992$	76975.4	+	44441.8i	0.0782219	+	0.0451615i
$993$	1.52136e6	−	1.52136e6i	1.54288	−	1.54288i
$994$	165399.	+	617277.i	0.167402	+	0.624752i
$995$	−99024.0	+	171515.i	−0.100022	+	0.173243i
$996$	325497.	−	563777.i	0.328116	−	0.568314i
$997$	361141.	−	1.34780e6i	0.363318	−	1.35592i	−0.506369	−	0.862317i	$-0.669013\pi$
$997$	361141.	−	1.34780e6i	0.363318	−	1.35592i	0.869687	−	0.493604i	$-0.164321\pi$
$998$			1.01710e6i			1.02118i
$999$	−627403.	+	419706.i	−0.628660	+	0.420547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.5.g.b.45.6	✓	28
37.14	odd	12	inner	74.5.g.b.51.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.5.g.b.45.6	✓	28	1.1	even	1	trivial
74.5.g.b.51.6	yes	28	37.14	odd	12	inner

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	74.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.73205 + 0.732051i) q^{2} +(9.05180 + 5.22606i) q^{3} +(6.92820 + 4.00000i) q^{4} +(8.32031 - 2.22942i) q^{5} +(20.9042 + 20.9042i) q^{6} +(41.9891 - 72.7273i) q^{7} +(16.0000 + 16.0000i) q^{8} +(14.1234 + 24.4624i) q^{9} +O(q^{10})\)	\(q+(2.73205 + 0.732051i) q^{2} +(9.05180 + 5.22606i) q^{3} +(6.92820 + 4.00000i) q^{4} +(8.32031 - 2.22942i) q^{5} +(20.9042 + 20.9042i) q^{6} +(41.9891 - 72.7273i) q^{7} +(16.0000 + 16.0000i) q^{8} +(14.1234 + 24.4624i) q^{9} +24.3635 q^{10} +207.159i q^{11} +(41.8085 + 72.4144i) q^{12} +(-148.606 + 39.8189i) q^{13} +(167.957 - 167.957i) q^{14} +(86.9648 + 23.3022i) q^{15} +(32.0000 + 55.4256i) q^{16} +(65.3228 - 243.788i) q^{17} +(20.6781 + 77.1716i) q^{18} +(-517.100 + 138.557i) q^{19} +(66.5625 + 17.8354i) q^{20} +(760.154 - 438.875i) q^{21} +(-151.651 + 565.969i) q^{22} +(278.754 + 278.754i) q^{23} +(61.2119 + 228.446i) q^{24} +(-477.009 + 275.401i) q^{25} -435.149 q^{26} -551.383i q^{27} +(581.818 - 335.913i) q^{28} +(567.557 - 567.557i) q^{29} +(220.534 + 127.325i) q^{30} +(347.201 - 347.201i) q^{31} +(46.8513 + 174.851i) q^{32} +(-1082.62 + 1875.16i) q^{33} +(356.930 - 618.221i) q^{34} +(187.223 - 698.725i) q^{35} +225.974i q^{36} +(-761.188 - 1137.87i) q^{37} -1514.17 q^{38} +(-1553.25 - 416.192i) q^{39} +(168.796 + 97.4542i) q^{40} +(-1862.31 - 1075.20i) q^{41} +(2398.06 - 642.558i) q^{42} +(1403.59 + 1403.59i) q^{43} +(-828.636 + 1435.24i) q^{44} +(172.048 + 172.048i) q^{45} +(557.508 + 965.633i) q^{46} -2179.87 q^{47} +668.936i q^{48} +(-2325.67 - 4028.19i) q^{49} +(-1504.82 + 403.215i) q^{50} +(1865.34 - 1865.34i) q^{51} +(-1188.85 - 318.551i) q^{52} +(1871.89 + 3242.20i) q^{53} +(403.640 - 1506.41i) q^{54} +(461.844 + 1723.63i) q^{55} +(1835.46 - 491.811i) q^{56} +(-5404.79 - 1448.21i) q^{57} +(1966.07 - 1135.11i) q^{58} +(962.555 - 3592.30i) q^{59} +(509.301 + 509.301i) q^{60} +(-78.0603 - 291.325i) q^{61} +(1202.74 - 694.403i) q^{62} +2372.12 q^{63} +512.000i q^{64} +(-1147.68 + 662.611i) q^{65} +(-4330.50 + 4330.50i) q^{66} +(1528.15 + 882.279i) q^{67} +(1427.72 - 1427.72i) q^{68} +(1066.44 + 3980.01i) q^{69} +(1023.00 - 1771.90i) q^{70} +(-1345.22 + 2330.00i) q^{71} +(-165.425 + 617.373i) q^{72} +8297.65i q^{73} +(-1246.62 - 3665.95i) q^{74} -5757.05 q^{75} +(-4136.80 - 1108.45i) q^{76} +(15066.1 + 8698.42i) q^{77} +(-3938.88 - 2274.11i) q^{78} +(7427.56 - 1990.21i) q^{79} +(389.817 + 389.817i) q^{80} +(4025.55 - 6972.46i) q^{81} +(-4300.81 - 4300.81i) q^{82} +(-3892.71 - 6742.37i) q^{83} +7022.01 q^{84} -2174.02i q^{85} +(2807.18 + 4862.17i) q^{86} +(8103.50 - 2171.33i) q^{87} +(-3314.54 + 3314.54i) q^{88} +(3647.87 + 977.444i) q^{89} +(344.096 + 595.992i) q^{90} +(-3343.92 + 12479.7i) q^{91} +(816.249 + 3046.28i) q^{92} +(4957.29 - 1328.30i) q^{93} +(-5955.51 - 1595.77i) q^{94} +(-3993.53 + 2305.67i) q^{95} +(-489.695 + 1827.57i) q^{96} +(10517.2 + 10517.2i) q^{97} +(-3405.02 - 12707.7i) q^{98} +(-5067.61 + 2925.79i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{2} - 102 q^{5} + 40 q^{6} - 48 q^{7} + 448 q^{8} + 556 q^{9}+O(q^{10}) \) 28 * q + 28 * q^2 - 102 * q^5 + 40 * q^6 - 48 * q^7 + 448 * q^8 + 556 * q^9	\( 28 q + 28 q^{2} - 102 q^{5} + 40 q^{6} - 48 q^{7} + 448 q^{8} + 556 q^{9} - 120 q^{10} + 80 q^{12} - 88 q^{13} - 192 q^{14} + 12 q^{15} + 896 q^{16} - 540 q^{17} - 1112 q^{18} + 976 q^{19} - 816 q^{20} - 618 q^{21} + 752 q^{22} + 1996 q^{23} - 160 q^{24} + 414 q^{25} - 2504 q^{26} + 1584 q^{28} + 852 q^{29} + 804 q^{30} + 300 q^{31} - 1792 q^{32} + 316 q^{33} + 300 q^{34} + 796 q^{35} - 3678 q^{37} - 328 q^{38} + 3630 q^{39} - 2784 q^{40} - 6426 q^{41} - 1348 q^{42} - 5548 q^{43} - 1280 q^{44} + 10164 q^{45} + 3992 q^{46} - 7624 q^{47} - 7388 q^{49} + 1768 q^{50} + 15382 q^{51} - 704 q^{52} + 13538 q^{53} - 1108 q^{54} - 10352 q^{55} + 2400 q^{56} - 12946 q^{57} + 3000 q^{58} + 5540 q^{59} - 3024 q^{60} - 26794 q^{61} + 2880 q^{62} - 61204 q^{63} + 39498 q^{65} + 1264 q^{66} + 23910 q^{67} + 1200 q^{68} + 19510 q^{69} + 524 q^{70} - 15992 q^{71} + 8896 q^{72} - 16780 q^{74} + 56644 q^{75} + 7808 q^{76} + 18960 q^{77} + 11892 q^{78} - 1792 q^{79} - 1920 q^{80} - 62170 q^{81} - 2128 q^{82} - 2516 q^{83} - 896 q^{84} - 11096 q^{86} + 39608 q^{87} - 5120 q^{88} + 25460 q^{89} + 20328 q^{90} - 20162 q^{91} - 20512 q^{92} + 8394 q^{93} - 31552 q^{94} + 7470 q^{95} + 1280 q^{96} - 12272 q^{97} + 14752 q^{98} + 23376 q^{99}+O(q^{100}) \) 28 * q + 28 * q^2 - 102 * q^5 + 40 * q^6 - 48 * q^7 + 448 * q^8 + 556 * q^9 - 120 * q^10 + 80 * q^12 - 88 * q^13 - 192 * q^14 + 12 * q^15 + 896 * q^16 - 540 * q^17 - 1112 * q^18 + 976 * q^19 - 816 * q^20 - 618 * q^21 + 752 * q^22 + 1996 * q^23 - 160 * q^24 + 414 * q^25 - 2504 * q^26 + 1584 * q^28 + 852 * q^29 + 804 * q^30 + 300 * q^31 - 1792 * q^32 + 316 * q^33 + 300 * q^34 + 796 * q^35 - 3678 * q^37 - 328 * q^38 + 3630 * q^39 - 2784 * q^40 - 6426 * q^41 - 1348 * q^42 - 5548 * q^43 - 1280 * q^44 + 10164 * q^45 + 3992 * q^46 - 7624 * q^47 - 7388 * q^49 + 1768 * q^50 + 15382 * q^51 - 704 * q^52 + 13538 * q^53 - 1108 * q^54 - 10352 * q^55 + 2400 * q^56 - 12946 * q^57 + 3000 * q^58 + 5540 * q^59 - 3024 * q^60 - 26794 * q^61 + 2880 * q^62 - 61204 * q^63 + 39498 * q^65 + 1264 * q^66 + 23910 * q^67 + 1200 * q^68 + 19510 * q^69 + 524 * q^70 - 15992 * q^71 + 8896 * q^72 - 16780 * q^74 + 56644 * q^75 + 7808 * q^76 + 18960 * q^77 + 11892 * q^78 - 1792 * q^79 - 1920 * q^80 - 62170 * q^81 - 2128 * q^82 - 2516 * q^83 - 896 * q^84 - 11096 * q^86 + 39608 * q^87 - 5120 * q^88 + 25460 * q^89 + 20328 * q^90 - 20162 * q^91 - 20512 * q^92 + 8394 * q^93 - 31552 * q^94 + 7470 * q^95 + 1280 * q^96 - 12272 * q^97 + 14752 * q^98 + 23376 * q^99

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