LMFDB - Embedded newform 43.6.e.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(4,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(14))

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

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

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

chi := DirichletCharacter("43.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.e (of order $7$, degree $6$, 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:	$6.89650425196$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	43.4
Dual form			43.6.e.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.37139 + 6.73550i) q^{2} +(15.6252 + 19.5934i) q^{3} +(-9.39457 - 41.1603i) q^{4} +(-42.9010 - 20.6600i) q^{5} -215.900 q^{6} -55.8448 q^{7} +(79.3171 + 38.1971i) q^{8} +(-85.6808 + 375.392i) q^{9} +O(q^{10})$	\(q+(-5.37139 + 6.73550i) q^{2} +(15.6252 + 19.5934i) q^{3} +(-9.39457 - 41.1603i) q^{4} +(-42.9010 - 20.6600i) q^{5} -215.900 q^{6} -55.8448 q^{7} +(79.3171 + 38.1971i) q^{8} +(-85.6808 + 375.392i) q^{9} +(369.594 - 177.987i) q^{10} +(-41.5992 + 182.258i) q^{11} +(659.677 - 827.208i) q^{12} +(-716.393 - 344.997i) q^{13} +(299.964 - 376.143i) q^{14} +(-265.537 - 1163.39i) q^{15} +(533.891 - 257.108i) q^{16} +(820.073 - 394.926i) q^{17} +(-2068.23 - 2593.48i) q^{18} +(255.615 + 1119.92i) q^{19} +(-447.337 + 1959.91i) q^{20} +(-872.585 - 1094.19i) q^{21} +(-1004.15 - 1259.17i) q^{22} +(-1089.96 + 4775.44i) q^{23} +(490.935 + 2150.93i) q^{24} +(-534.747 - 670.551i) q^{25} +(6171.75 - 2972.16i) q^{26} +(-3207.27 + 1544.54i) q^{27} +(524.638 + 2298.59i) q^{28} +(-623.919 + 782.370i) q^{29} +(9262.33 + 4460.50i) q^{30} +(854.013 - 1070.90i) q^{31} +(-1762.85 + 7723.55i) q^{32} +(-4221.04 + 2032.75i) q^{33} +(-1744.90 + 7644.91i) q^{34} +(2395.80 + 1153.76i) q^{35} +16256.2 q^{36} -14114.5 q^{37} +(-8916.26 - 4293.85i) q^{38} +(-4434.13 - 19427.2i) q^{39} +(-2613.63 - 3277.39i) q^{40} +(-10233.1 + 12831.8i) q^{41} +12056.9 q^{42} +(5571.44 - 10768.8i) q^{43} +7892.59 q^{44} +(11431.4 - 14334.5i) q^{45} +(-26310.4 - 32992.2i) q^{46} +(4589.11 + 20106.2i) q^{47} +(13379.8 + 6443.35i) q^{48} -13688.4 q^{49} +7388.83 q^{50} +(20551.7 + 9897.19i) q^{51} +(-7469.96 + 32728.0i) q^{52} +(18101.7 - 8717.31i) q^{53} +(6824.22 - 29898.9i) q^{54} +(5550.10 - 6959.60i) q^{55} +(-4429.45 - 2133.11i) q^{56} +(-17949.0 + 22507.4i) q^{57} +(-1918.34 - 8404.82i) q^{58} +(4506.67 - 2170.30i) q^{59} +(-45390.9 + 21859.1i) q^{60} +(-21795.9 - 27331.2i) q^{61} +(2625.81 + 11504.4i) q^{62} +(4784.83 - 20963.7i) q^{63} +(-30730.2 - 38534.5i) q^{64} +(23606.3 + 29601.4i) q^{65} +(8981.26 - 39349.5i) q^{66} +(15178.3 + 66500.3i) q^{67} +(-23959.5 - 30044.3i) q^{68} +(-110598. + 53261.1i) q^{69} +(-20639.9 + 9939.64i) q^{70} +(-3101.79 - 13589.8i) q^{71} +(-21134.9 + 26502.3i) q^{72} +(45887.5 + 22098.3i) q^{73} +(75814.5 - 95068.4i) q^{74} +(4782.83 - 20955.0i) q^{75} +(43695.0 - 21042.4i) q^{76} +(2323.10 - 10178.2i) q^{77} +(154669. + 74484.8i) q^{78} +44702.3 q^{79} -28216.3 q^{80} +(3923.45 + 1889.44i) q^{81} +(-31463.3 - 137850. i) q^{82} +(27673.0 + 34700.8i) q^{83} +(-36839.5 + 46195.3i) q^{84} -43341.2 q^{85} +(42607.1 + 95369.9i) q^{86} -25078.1 q^{87} +(-10261.3 + 12867.2i) q^{88} +(-20172.2 - 25295.1i) q^{89} +(35147.8 + 153993. i) q^{90} +(40006.8 + 19266.3i) q^{91} +206798. q^{92} +34326.6 q^{93} +(-160075. - 77088.1i) q^{94} +(12171.5 - 53326.9i) q^{95} +(-178875. + 86141.8i) q^{96} +(-21059.8 + 92269.0i) q^{97} +(73525.5 - 92198.0i) q^{98} +(-64853.9 - 31232.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) $ 108 * q - 3 * q^2 - 9 * q^3 - 331 * q^4 + 67 * q^5 - 20 * q^6 - 624 * q^7 + 589 * q^8 - 579 * q^9	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9} + 627 q^{10} - 220 q^{11} - 663 q^{12} - 1266 q^{13} + 2353 q^{14} + 1471 q^{15} - 4583 q^{16} - 1490 q^{17} + 4728 q^{18} + 946 q^{19} + 14589 q^{20} + 776 q^{21} + 963 q^{22} - 3018 q^{23} - 17761 q^{24} - 11939 q^{25} + 1315 q^{26} + 11277 q^{27} - 10787 q^{28} + 7283 q^{29} - 55324 q^{30} + 18676 q^{31} - 10965 q^{32} + 8776 q^{33} + 23815 q^{34} - 13340 q^{35} + 136240 q^{36} + 4994 q^{37} + 39351 q^{38} - 21251 q^{39} + 14719 q^{40} - 10519 q^{41} - 199326 q^{42} + 7026 q^{43} - 180280 q^{44} + 65996 q^{45} - 5266 q^{46} + 34102 q^{47} + 69385 q^{48} + 232252 q^{49} + 17850 q^{50} + 4116 q^{51} + 32385 q^{52} + 46774 q^{53} - 30267 q^{54} + 83643 q^{55} - 231565 q^{56} + 79511 q^{57} - 222889 q^{58} - 142070 q^{59} + 42019 q^{60} + 4715 q^{61} - 150121 q^{62} - 53547 q^{63} + 163605 q^{64} - 106653 q^{65} - 56111 q^{66} + 370962 q^{67} - 579312 q^{68} - 245635 q^{69} - 91242 q^{70} + 16922 q^{71} + 586300 q^{72} + 97842 q^{73} + 535946 q^{74} + 245407 q^{75} + 942280 q^{76} + 43381 q^{77} + 173684 q^{78} + 187210 q^{79} - 752974 q^{80} - 791814 q^{81} + 387227 q^{82} - 444471 q^{83} - 688442 q^{84} + 255432 q^{85} - 244075 q^{86} - 1418850 q^{87} + 196837 q^{88} + 408972 q^{89} - 495568 q^{90} - 25764 q^{91} + 200120 q^{92} + 692536 q^{93} + 161449 q^{94} + 406105 q^{95} + 1096556 q^{96} + 266261 q^{97} + 527485 q^{98} + 212416 q^{99}+O(q^{100}) \) 108 * q - 3 * q^2 - 9 * q^3 - 331 * q^4 + 67 * q^5 - 20 * q^6 - 624 * q^7 + 589 * q^8 - 579 * q^9 + 627 * q^10 - 220 * q^11 - 663 * q^12 - 1266 * q^13 + 2353 * q^14 + 1471 * q^15 - 4583 * q^16 - 1490 * q^17 + 4728 * q^18 + 946 * q^19 + 14589 * q^20 + 776 * q^21 + 963 * q^22 - 3018 * q^23 - 17761 * q^24 - 11939 * q^25 + 1315 * q^26 + 11277 * q^27 - 10787 * q^28 + 7283 * q^29 - 55324 * q^30 + 18676 * q^31 - 10965 * q^32 + 8776 * q^33 + 23815 * q^34 - 13340 * q^35 + 136240 * q^36 + 4994 * q^37 + 39351 * q^38 - 21251 * q^39 + 14719 * q^40 - 10519 * q^41 - 199326 * q^42 + 7026 * q^43 - 180280 * q^44 + 65996 * q^45 - 5266 * q^46 + 34102 * q^47 + 69385 * q^48 + 232252 * q^49 + 17850 * q^50 + 4116 * q^51 + 32385 * q^52 + 46774 * q^53 - 30267 * q^54 + 83643 * q^55 - 231565 * q^56 + 79511 * q^57 - 222889 * q^58 - 142070 * q^59 + 42019 * q^60 + 4715 * q^61 - 150121 * q^62 - 53547 * q^63 + 163605 * q^64 - 106653 * q^65 - 56111 * q^66 + 370962 * q^67 - 579312 * q^68 - 245635 * q^69 - 91242 * q^70 + 16922 * q^71 + 586300 * q^72 + 97842 * q^73 + 535946 * q^74 + 245407 * q^75 + 942280 * q^76 + 43381 * q^77 + 173684 * q^78 + 187210 * q^79 - 752974 * q^80 - 791814 * q^81 + 387227 * q^82 - 444471 * q^83 - 688442 * q^84 + 255432 * q^85 - 244075 * q^86 - 1418850 * q^87 + 196837 * q^88 + 408972 * q^89 - 495568 * q^90 - 25764 * q^91 + 200120 * q^92 + 692536 * q^93 + 161449 * q^94 + 406105 * q^95 + 1096556 * q^96 + 266261 * q^97 + 527485 * q^98 + 212416 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{7}\right)$

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 $

$2$	−5.37139	+	6.73550i	−0.949536	+	1.19068i	0.0320167	+	0.999487i	$0.489807\pi$
$2$	−5.37139	+	6.73550i	−0.949536	+	1.19068i	−0.981552	+	0.191193i	$0.938764\pi$
$3$	15.6252	+	19.5934i	1.00236	+	1.25691i	0.966261	+	0.257566i	$0.0829206\pi$
$3$	15.6252	+	19.5934i	1.00236	+	1.25691i	0.0360953	+	0.999348i	$0.488508\pi$
$4$	−9.39457	−	41.1603i	−0.293580	−	1.28626i
$5$	−42.9010	−	20.6600i	−0.767436	−	0.369578i	0.00884786	−	0.999961i	$-0.497184\pi$
$5$	−42.9010	−	20.6600i	−0.767436	−	0.369578i	−0.776284	+	0.630383i	$0.782898\pi$
$6$	−215.900			−2.44836
$7$	−55.8448			−0.430762			−0.215381	−	0.976530i	$-0.569099\pi$
$7$	−55.8448			−0.430762			−0.215381	+	0.976530i	$0.569099\pi$
$8$	79.3171	+	38.1971i	0.438169	+	0.211011i
$9$	−85.6808	+	375.392i	−0.352596	+	1.54482i
$10$	369.594	−	177.987i	1.16876	−	0.562844i
$11$	−41.5992	+	182.258i	−0.103658	+	0.454155i	0.896285	+	0.443479i	$0.146256\pi$
$11$	−41.5992	+	182.258i	−0.103658	+	0.454155i	−0.999943	+	0.0106769i	$0.996601\pi$
$12$	659.677	−	827.208i	1.32245	−	1.65829i
$13$	−716.393	−	344.997i	−1.17569	−	0.566183i	−0.259038	−	0.965867i	$-0.583405\pi$
$13$	−716.393	−	344.997i	−1.17569	−	0.566183i	−0.916653	+	0.399685i	$0.869120\pi$
$14$	299.964	−	376.143i	0.409024	−	0.512900i
$15$	−265.537	−	1163.39i	−0.304717	−	1.33505i
$16$	533.891	−	257.108i	0.521378	−	0.251082i
$17$	820.073	−	394.926i	0.688225	−	0.331432i	−0.0568781	−	0.998381i	$-0.518115\pi$
$17$	820.073	−	394.926i	0.688225	−	0.331432i	0.745103	+	0.666950i	$0.232400\pi$
$18$	−2068.23	−	2593.48i	−1.50459	−	1.88669i
$19$	255.615	+	1119.92i	0.162444	+	0.711713i	0.988884	+	0.148688i	$0.0475051\pi$
$19$	255.615	+	1119.92i	0.162444	+	0.711713i	−0.826440	+	0.563024i	$0.809638\pi$
$20$	−447.337	+	1959.91i	−0.250069	+	1.09562i
$21$	−872.585	−	1094.19i	−0.431777	−	0.541431i
$22$	−1004.15	−	1259.17i	−0.442327	−	0.554660i
$23$	−1089.96	+	4775.44i	−0.429628	+	1.88232i	0.0395495	+	0.999218i	$0.487408\pi$
$23$	−1089.96	+	4775.44i	−0.429628	+	1.88232i	−0.469177	+	0.883104i	$0.655449\pi$
$24$	490.935	+	2150.93i	0.173979	+	0.762250i
$25$	−534.747	−	670.551i	−0.171119	−	0.214576i
$26$	6171.75	−	2972.16i	1.79050	−	0.862261i
$27$	−3207.27	+	1544.54i	−0.846692	+	0.407745i
$28$	524.638	+	2298.59i	0.126463	+	0.554072i
$29$	−623.919	+	782.370i	−0.137763	+	0.172750i	−0.845927	−	0.533298i	$-0.820952\pi$
$29$	−623.919	+	782.370i	−0.137763	+	0.172750i	0.708164	+	0.706048i	$0.249524\pi$
$30$	9262.33	+	4460.50i	1.87896	+	0.904858i
$31$	854.013	−	1070.90i	0.159610	−	0.200145i	−0.695596	−	0.718434i	$-0.744859\pi$
$31$	854.013	−	1070.90i	0.159610	−	0.200145i	0.855206	+	0.518289i	$0.173431\pi$
$32$	−1762.85	+	7723.55i	−0.304327	+	1.33334i
$33$	−4221.04	+	2032.75i	−0.674737	+	0.324936i
$34$	−1744.90	+	7644.91i	−0.258865	+	1.13416i
$35$	2395.80	+	1153.76i	0.330583	+	0.159200i
$36$	16256.2			2.09056
$37$	−14114.5			−1.69497			−0.847484	−	0.530820i	$-0.821884\pi$
$37$	−14114.5			−1.69497			−0.847484	+	0.530820i	$0.821884\pi$
$38$	−8916.26	−	4293.85i	−1.00167	−	0.482378i
$39$	−4434.13	−	19427.2i	−0.466817	−	2.04526i
$40$	−2613.63	−	3277.39i	−0.258282	−	0.323875i
$41$	−10233.1	+	12831.8i	−0.950705	+	1.19215i	0.0305699	+	0.999533i	$0.490268\pi$
$41$	−10233.1	+	12831.8i	−0.950705	+	1.19215i	−0.981275	+	0.192613i	$0.938304\pi$
$42$	12056.9			1.05466
$43$	5571.44	−	10768.8i	0.459511	−	0.888172i
$43$	5571.44	−	10768.8i	0.459511	−	0.888172i
$44$	7892.59			0.614594
$45$	11431.4	−	14334.5i	0.841528	−	1.05524i
$46$	−26310.4	−	32992.2i	−1.83330	−	2.29888i
$47$	4589.11	+	20106.2i	0.303028	+	1.32765i	0.865530	+	0.500858i	$0.166982\pi$
$47$	4589.11	+	20106.2i	0.303028	+	1.32765i	−0.562501	+	0.826797i	$0.690161\pi$
$48$	13379.8	+	6443.35i	0.838195	+	0.403654i
$49$	−13688.4			−0.814444
$50$	7388.83			0.417975
$51$	20551.7	+	9897.19i	1.10643	+	0.532827i
$52$	−7469.96	+	32728.0i	−0.383098	+	1.67846i
$53$	18101.7	−	8717.31i	0.885175	−	0.426278i	0.0646630	−	0.997907i	$-0.479403\pi$
$53$	18101.7	−	8717.31i	0.885175	−	0.426278i	0.820512	+	0.571629i	$0.193688\pi$
$54$	6824.22	−	29898.9i	0.318470	−	1.39531i
$55$	5550.10	−	6959.60i	0.247397	−	0.310226i
$56$	−4429.45	−	2133.11i	−0.188747	−	0.0908957i
$57$	−17949.0	+	22507.4i	−0.731736	+	0.917567i
$58$	−1918.34	−	8404.82i	−0.0748784	−	0.328064i
$59$	4506.67	−	2170.30i	0.168549	−	0.0811689i	−0.347707	−	0.937603i	$-0.613040\pi$
$59$	4506.67	−	2170.30i	0.168549	−	0.0811689i	0.516256	+	0.856434i	$0.327325\pi$
$60$	−45390.9	+	21859.1i	−1.62776	+	0.783889i
$61$	−21795.9	−	27331.2i	−0.749980	−	0.940446i	0.249631	−	0.968341i	$-0.419691\pi$
$61$	−21795.9	−	27331.2i	−0.749980	−	0.940446i	−0.999611	+	0.0278956i	$0.991119\pi$
$62$	2625.81	+	11504.4i	0.0867528	+	0.380089i
$63$	4784.83	−	20963.7i	0.151885	−	0.665452i
$64$	−30730.2	−	38534.5i	−0.937812	−	1.17598i
$65$	23606.3	+	29601.4i	0.693019	+	0.869018i
$66$	8981.26	−	39349.5i	0.253792	−	1.11193i
$67$	15178.3	+	66500.3i	0.413081	+	1.80983i	0.569331	+	0.822108i	$0.307202\pi$
$67$	15178.3	+	66500.3i	0.413081	+	1.80983i	−0.156250	+	0.987717i	$0.549941\pi$
$68$	−23959.5	−	30044.3i	−0.628356	−	0.787934i
$69$	−110598.	+	53261.1i	−2.79656	+	1.34675i
$70$	−20639.9	+	9939.64i	−0.503457	+	0.242452i
$71$	−3101.79	−	13589.8i	−0.0730242	−	0.319940i	0.925202	−	0.379475i	$-0.123895\pi$
$71$	−3101.79	−	13589.8i	−0.0730242	−	0.319940i	−0.998226	+	0.0595351i	$0.981038\pi$
$72$	−21134.9	+	26502.3i	−0.480472	+	0.602493i
$73$	45887.5	+	22098.3i	1.00783	+	0.485345i	0.863588	−	0.504197i	$-0.168212\pi$
$73$	45887.5	+	22098.3i	1.00783	+	0.485345i	0.144241	+	0.989543i	$0.453926\pi$
$74$	75814.5	−	95068.4i	1.60943	−	2.01817i
$75$	4782.83	−	20955.0i	0.0981821	−	0.430164i
$76$	43695.0	−	21042.4i	0.867757	−	0.417890i
$77$	2323.10	−	10178.2i	0.0446520	−	0.195633i
$78$	154669.	+	74484.8i	2.87851	+	1.38622i
$79$	44702.3			0.805866			0.402933	−	0.915230i	$-0.367991\pi$
$79$	44702.3			0.805866			0.402933	+	0.915230i	$0.367991\pi$
$80$	−28216.3			−0.492919
$81$	3923.45	+	1889.44i	0.0664440	+	0.0319978i
$82$	−31463.3	−	137850.i	−0.516737	−	2.26397i
$83$	27673.0	+	34700.8i	0.440921	+	0.552897i	0.951786	−	0.306764i	$-0.0992462\pi$
$83$	27673.0	+	34700.8i	0.440921	+	0.552897i	−0.510865	+	0.859661i	$0.670675\pi$
$84$	−36839.5	+	46195.3i	−0.569660	+	0.714331i
$85$	−43341.2			−0.650659
$86$	42607.1	+	95369.9i	0.621207	+	1.39048i
$87$	−25078.1			−0.355219
$88$	−10261.3	+	12867.2i	−0.141252	+	0.177124i
$89$	−20172.2	−	25295.1i	−0.269947	−	0.338502i	0.628319	−	0.777956i	$-0.283743\pi$
$89$	−20172.2	−	25295.1i	−0.269947	−	0.338502i	−0.898265	+	0.439454i	$0.855172\pi$
$90$	35147.8	+	153993.i	0.457396	+	2.00398i
$91$	40006.8	+	19266.3i	0.506443	+	0.243890i
$92$	206798.			2.54728
$93$	34326.6			0.411551
$94$	−160075.	−	77088.1i	−1.86855	−	0.899845i
$95$	12171.5	−	53326.9i	0.138368	−	0.606230i
$96$	−178875.	+	86141.8i	−1.98094	+	0.953972i
$97$	−21059.8	+	92269.0i	−0.227261	+	0.995695i	0.724601	+	0.689168i	$0.242024\pi$
$97$	−21059.8	+	92269.0i	−0.227261	+	0.995695i	−0.951862	+	0.306527i	$0.900833\pi$
$98$	73525.5	−	92198.0i	0.773344	−	0.969742i
$99$	−64853.9	−	31232.0i	−0.665041	−	0.320267i
$100$	−22576.4	+	28309.9i	−0.225764	+	0.283099i
$101$	−12218.9	−	53534.3i	−0.119187	−	0.522191i	−0.998909	−	0.0467027i	$-0.985129\pi$
$101$	−12218.9	−	53534.3i	−0.119187	−	0.522191i	0.879722	−	0.475488i	$-0.157728\pi$
$102$	−177054.	+	85264.6i	−1.68502	+	0.811463i
$103$	−41152.8	+	19818.1i	−0.382213	+	0.184064i	−0.615118	−	0.788435i	$-0.710891\pi$
$103$	−41152.8	+	19818.1i	−0.382213	+	0.184064i	0.232904	+	0.972500i	$0.425177\pi$
$104$	−43644.4	−	54728.3i	−0.395681	−	0.496168i
$105$	14828.8	+	64969.4i	0.131260	+	0.575089i
$106$	−38515.6	+	168748.i	−0.332945	+	1.45873i
$107$	38731.3	+	48567.5i	0.327041	+	0.410097i	0.917984	−	0.396616i	$-0.129816\pi$
$107$	38731.3	+	48567.5i	0.327041	+	0.410097i	−0.590943	+	0.806713i	$0.701244\pi$
$108$	93704.5	+	117502.i	0.773038	+	0.969359i
$109$	26795.3	−	117398.i	0.216019	−	0.946441i	−0.744368	−	0.667770i	$-0.767249\pi$
$109$	26795.3	−	117398.i	0.216019	−	0.946441i	0.960387	−	0.278671i	$-0.0898939\pi$
$110$	17064.7	+	74765.4i	0.134468	+	0.589141i
$111$	−220542.	−	276551.i	−1.69896	−	2.13043i
$112$	−29815.0	+	14358.2i	−0.224590	+	0.108157i
$113$	98145.2	−	47264.2i	0.723057	−	0.348206i	−0.0358920	−	0.999356i	$-0.511427\pi$
$113$	98145.2	−	47264.2i	0.723057	−	0.348206i	0.758949	+	0.651150i	$0.225713\pi$
$114$	−55187.4	−	241792.i	−0.397720	−	1.74253i
$115$	145421.	−	182353.i	1.02538	−	1.28578i
$116$	38064.0	+	18330.7i	0.262645	+	0.126483i
$117$	190890.	−	239369.i	1.28920	−	1.61660i
$118$	−9589.02	+	42012.2i	−0.0633971	+	0.277761i
$119$	−45796.8	+	22054.6i	−0.296461	+	0.142768i
$120$	23376.6	−	102420.i	0.148193	−	0.649277i
$121$	113614.	+	54713.9i	0.705457	+	0.339730i
$122$	301163.			1.83190
$123$	−411312.			−2.45137
$124$	−52101.6	−	25090.8i	−0.304296	−	0.146541i
$125$	42199.0	+	184886.i	0.241561	+	1.05835i
$126$	115500.	+	144832.i	0.648120	+	0.812717i
$127$	−55635.3	+	69764.4i	−0.306084	+	0.383818i	−0.910955	−	0.412506i	$-0.864653\pi$
$127$	−55635.3	+	69764.4i	−0.306084	+	0.383818i	0.604870	+	0.796324i	$0.293225\pi$
$128$	171103.			0.923068
$129$	298052.	−	59101.7i	1.57695	−	0.312698i
$130$	−326179.			−1.69277
$131$	−134394.	+	168525.i	−0.684230	+	0.857998i	−0.995736	−	0.0922465i	$-0.970595\pi$
$131$	−134394.	+	168525.i	−0.684230	+	0.857998i	0.311506	+	0.950244i	$0.399167\pi$
$132$	123323.	+	154642.i	0.616042	+	0.772492i
$133$	−14274.8	−	62541.9i	−0.0699746	−	0.306579i
$134$	−529442.	−	254966.i	−2.54716	−	1.22665i
$135$	169505.			0.800476
$136$	80130.9			0.371495
$137$	−163478.	−	78726.8i	−0.744145	−	0.358361i	0.0230848	−	0.999734i	$-0.492651\pi$
$137$	−163478.	−	78726.8i	−0.744145	−	0.358361i	−0.767230	+	0.641372i	$0.778366\pi$
$138$	235323.	−	1.03102e6i	1.05188	−	4.60859i
$139$	265111.	−	127670.i	1.16383	−	0.560472i	0.250671	−	0.968072i	$-0.419349\pi$
$139$	265111.	−	127670.i	1.16383	−	0.560472i	0.913160	+	0.407601i	$0.133635\pi$
$140$	24981.4	−	109451.i	0.107720	−	0.471953i
$141$	−322242.	+	404079.i	−1.36501	+	1.71166i
$142$	108195.	+	52104.1i	0.450285	+	0.216846i
$143$	92679.7	−	116217.i	0.379005	−	0.475257i
$144$	50772.2	+	222448.i	0.204042	+	0.893967i
$145$	42930.5	−	20674.3i	0.169569	−	0.0816601i
$146$	−395322.	+	190377.i	−1.53486	+	0.739150i
$147$	−213883.	−	268201.i	−0.816363	−	1.02369i
$148$	132600.	+	580958.i	0.497609	+	2.18017i
$149$	4733.80	−	20740.2i	0.0174681	−	0.0765326i	−0.965443	−	0.260616i	$-0.916074\pi$
$149$	4733.80	−	20740.2i	0.0174681	−	0.0765326i	0.982911	+	0.184083i	$0.0589316\pi$
$150$	115452.	+	144772.i	0.418960	+	0.525359i
$151$	23216.8	+	29113.0i	0.0828630	+	0.103907i	0.821535	−	0.570158i	$-0.193118\pi$
$151$	23216.8	+	29113.0i	0.0828630	+	0.103907i	−0.738672	+	0.674065i	$0.764547\pi$
$152$	−22503.2	+	98593.0i	−0.0790015	+	0.346128i
$153$	77987.8	+	341687.i	0.269338	+	1.18005i
$154$	56076.7	+	70318.0i	0.190538	+	0.238927i
$155$	−58762.8	+	28298.7i	−0.196460	+	0.0946099i
$156$	−757972.	+	365020.i	−2.49368	+	1.20090i
$157$	105533.	+	462369.i	0.341695	+	1.49706i	0.795496	+	0.605959i	$0.207211\pi$
$157$	105533.	+	462369.i	0.341695	+	1.49706i	−0.453801	+	0.891103i	$0.649932\pi$
$158$	−240114.	+	301093.i	−0.765198	+	0.959528i
$159$	453643.	+	218463.i	1.42306	+	0.685307i
$160$	235197.	−	294928.i	0.726326	−	0.910784i
$161$	60868.8	−	266684.i	0.185067	−	0.810833i
$162$	−33800.7	+	16277.6i	−0.101190	+	0.0487306i
$163$	−31985.9	+	140139.i	−0.0942951	+	0.413134i	−0.999941	−	0.0109018i	$-0.996530\pi$
$163$	−31985.9	+	140139.i	−0.0942951	+	0.413134i	0.905645	+	0.424036i	$0.139387\pi$
$164$	624298.	+	300646.i	1.81252	+	0.872862i
$165$	223083.			0.637907
$166$	−382370.			−1.07699
$167$	−133523.	−	64301.4i	−0.370481	−	0.178414i	0.239374	−	0.970928i	$-0.423058\pi$
$167$	−133523.	−	64301.4i	−0.370481	−	0.178414i	−0.609855	+	0.792513i	$0.708772\pi$
$168$	−27416.2	−	120118.i	−0.0749434	−	0.328348i
$169$	162699.	+	204018.i	0.438195	+	0.549479i
$170$	232802.	−	291925.i	0.617824	−	0.774726i
$171$	−442312.			−1.15675
$172$	−495589.	−	128154.i	−1.27732	−	0.330301i
$173$	423603.			1.07608			0.538039	−	0.842920i	$-0.319165\pi$
$173$	423603.			1.07608			0.538039	+	0.842920i	$0.319165\pi$
$174$	134704.	−	168914.i	0.337293	−	0.422953i
$175$	29862.8	+	37446.8i	0.0737116	+	0.0924314i
$176$	24650.6	+	108001.i	0.0599854	+	0.262813i
$177$	112941.	+	54389.5i	0.270968	+	0.130492i
$178$	278728.			0.659372
$179$	147445.			0.343952			0.171976	−	0.985101i	$-0.444985\pi$
$179$	147445.			0.343952			0.171976	+	0.985101i	$0.444985\pi$
$180$	−697407.	−	335853.i	−1.60437	−	0.772624i
$181$	156935.	−	687575.i	0.356059	−	1.56000i	−0.406852	−	0.913494i	$-0.633373\pi$
$181$	156935.	−	687575.i	0.356059	−	1.56000i	0.762911	−	0.646503i	$-0.223769\pi$
$182$	−344660.	+	165980.i	−0.771281	+	0.371429i
$183$	194945.	−	854109.i	0.430313	−	1.88532i
$184$	−268861.	+	337141.i	−0.585441	+	0.734119i
$185$	605527.	+	291606.i	1.30078	+	0.626423i
$186$	−184381.	+	231207.i	−0.390782	+	0.490025i
$187$	37864.1	+	165893.i	0.0791814	+	0.346917i
$188$	784464.	−	377778.i	1.61874	−	0.779546i
$189$	179109.	−	86254.4i	0.364723	−	0.175641i
$190$	293806.	+	368421.i	0.590441	+	0.740389i
$191$	−139713.	−	612122.i	−0.277110	−	1.21410i	−0.901428	−	0.432929i	$-0.857480\pi$
$191$	−139713.	−	612122.i	−0.277110	−	1.21410i	0.624317	−	0.781171i	$-0.285377\pi$
$192$	274855.	−	1.20422e6i	0.538084	−	2.35750i
$193$	−171185.	−	214659.i	−0.330805	−	0.414817i	0.588416	−	0.808559i	$-0.299752\pi$
$193$	−171185.	−	214659.i	−0.330805	−	0.414817i	−0.919221	+	0.393742i	$0.871180\pi$
$194$	−508358.	−	637461.i	−0.969762	−	1.21604i
$195$	−211138.	+	925055.i	−0.397630	+	1.74213i
$196$	128596.	+	563417.i	0.239105	+	1.04759i
$197$	193151.	+	242204.i	0.354594	+	0.444647i	0.926852	−	0.375427i	$-0.122504\pi$
$197$	193151.	+	242204.i	0.354594	+	0.444647i	−0.572258	+	0.820074i	$0.693932\pi$
$198$	558719.	−	269065.i	1.01282	−	0.487746i
$199$	−547032.	+	263437.i	−0.979220	+	0.471568i	−0.853837	−	0.520541i	$-0.825730\pi$
$199$	−547032.	+	263437.i	−0.979220	+	0.471568i	−0.125383	+	0.992108i	$0.540016\pi$
$200$	−16801.4	−	73612.0i	−0.0297010	−	0.130129i
$201$	−1.06580e6	+	1.33647e6i	−1.86074	+	2.33330i
$202$	426213.	+	205253.i	0.734934	+	0.353926i
$203$	34842.6	−	43691.3i	0.0593432	−	0.0744140i
$204$	214297.	−	938895.i	0.360529	−	1.57958i
$205$	704115.	−	339084.i	1.17020	−	0.563537i
$206$	87562.3	−	383635.i	0.143764	−	0.629869i
$207$	−1.69927e6	−	818327.i	−2.75637	−	1.32740i
$208$	−471177.			−0.755137
$209$	−214748.			−0.340067
$210$	−517253.	−	249096.i	−0.809384	−	0.389779i
$211$	−88134.1	−	386141.i	−0.136282	−	0.597090i	−0.996233	−	0.0867139i	$-0.972363\pi$
$211$	−88134.1	−	386141.i	−0.136282	−	0.597090i	0.859951	−	0.510376i	$-0.170494\pi$
$212$	−528864.	−	663175.i	−0.808174	−	1.01342i
$213$	217804.	−	273118.i	0.328941	−	0.412479i
$214$	−535168.			−0.798832
$215$	−461504.	+	346887.i	−0.680894	+	0.511790i
$216$	−313388.			−0.457033
$217$	−47692.2	+	59804.1i	−0.0687540	+	0.0862147i
$218$	646806.	+	811068.i	0.921791	+	1.15589i
$219$	284021.	+	1.24438e6i	0.400167	+	1.75324i
$220$	−338600.	−	163061.i	−0.471662	−	0.227140i
$221$	−723743.			−0.996790
$222$	3.04732e6			4.14989
$223$	−929514.	−	447631.i	−1.25168	−	0.602778i	−0.313720	−	0.949516i	$-0.601575\pi$
$223$	−929514.	−	447631.i	−1.25168	−	0.602778i	−0.937962	+	0.346738i	$0.887289\pi$
$224$	98446.0	−	431320.i	0.131093	−	0.574354i
$225$	297537.	−	143286.i	0.391818	−	0.188690i
$226$	−208827.	+	914931.i	−0.271967	+	1.19156i
$227$	−534990.	+	670856.i	−0.689098	+	0.864102i	−0.996157	−	0.0875887i	$-0.972084\pi$
$227$	−534990.	+	670856.i	−0.689098	+	0.864102i	0.307058	+	0.951691i	$0.400655\pi$
$228$	1.09503e6	+	527341.i	1.39505	+	0.671822i
$229$	493226.	−	618486.i	0.621524	−	0.779366i	−0.367034	−	0.930207i	$-0.619627\pi$
$229$	493226.	−	618486.i	0.621524	−	0.779366i	0.988558	+	0.150841i	$0.0481983\pi$
$230$	447122.	+	1.95897e6i	0.557323	+	2.44179i
$231$	235723.	−	113518.i	0.290651	−	0.139970i
$232$	−79371.7	+	38223.4i	−0.0968157	+	0.0466240i
$233$	−799019.	−	1.00194e6i	−0.964200	−	1.20907i	−0.977881	−	0.209163i	$-0.932926\pi$
$233$	−799019.	−	1.00194e6i	−0.964200	−	1.20907i	0.0136804	−	0.999906i	$-0.495645\pi$
$234$	586924.	+	2.57148e6i	0.700717	+	3.07004i
$235$	218517.	−	957387.i	0.258117	−	1.13088i
$236$	−131668.	−	165107.i	−0.153887	−	0.192968i
$237$	698482.	+	875869.i	0.807764	+	1.01290i
$238$	97443.6	−	426928.i	0.111509	−	0.488554i
$239$	−98010.3	−	429411.i	−0.110988	−	0.486271i	−0.999618	−	0.0276455i	$-0.991199\pi$
$239$	−98010.3	−	429411.i	−0.110988	−	0.486271i	0.888630	−	0.458626i	$-0.151658\pi$
$240$	−440885.	−	552852.i	−0.494080	−	0.619557i
$241$	1.18546e6	−	570887.i	1.31475	−	0.633151i	0.360670	−	0.932694i	$-0.382548\pi$
$241$	1.18546e6	−	570887.i	1.31475	−	0.633151i	0.954083	+	0.299542i	$0.0968339\pi$
$242$	−978793.	+	471362.i	−1.07437	+	0.517387i
$243$	216772.	+	949739.i	0.235498	+	1.03178i
$244$	−920196.	+	1.15389e6i	−0.989477	+	1.24077i
$245$	587244.	+	282802.i	0.625034	+	0.301000i
$246$	2.20932e6	−	2.77040e6i	2.32766	−	2.91880i
$247$	203249.	−	890492.i	0.211976	−	0.928726i
$248$	108643.	−	52319.7i	0.112169	−	0.0540177i
$249$	−247510.	+	1.08441e6i	−0.252985	+	1.10840i
$250$	−1.47197e6	−	708863.i	−1.48953	−	0.717318i
$251$	287450.			0.287991			0.143995	−	0.989578i	$-0.454005\pi$
$251$	287450.			0.287991			0.143995	+	0.989578i	$0.454005\pi$
$252$	−907823.			−0.900534
$253$	−825020.	−	397309.i	−0.810332	−	0.390236i
$254$	−171060.	−	749463.i	−0.166366	−	0.728897i
$255$	−677213.	−	849199.i	−0.652192	−	0.817822i
$256$	64304.8	−	80635.6i	0.0613258	−	0.0769001i
$257$	−1.27806e6			−1.20703			−0.603517	−	0.797350i	$-0.706234\pi$
$257$	−1.27806e6			−1.20703			−0.603517	+	0.797350i	$0.706234\pi$
$258$	−1.20287e6	+	2.32499e6i	−1.12505	+	2.17456i
$259$	788222.			0.730129
$260$	996631.	−	1.24974e6i	0.914326	−	1.14653i
$261$	−240238.	−	301248.i	−0.218293	−	0.273731i
$262$	−413218.	−	1.81043e6i	−0.371900	−	1.62940i
$263$	811410.	+	390754.i	0.723354	+	0.348349i	0.759066	−	0.651013i	$-0.225656\pi$
$263$	811410.	+	390754.i	0.723354	+	0.348349i	−0.0357124	+	0.999362i	$0.511370\pi$
$264$	−412446.			−0.364214
$265$	−956680.			−0.836858
$266$	497927.	+	239789.i	0.431481	+	0.207790i
$267$	180422.	−	790482.i	0.154886	−	0.678600i
$268$	2.59458e6	−	1.24948e6i	2.20663	−	1.06266i
$269$	−391053.	+	1.71332e6i	−0.329500	+	1.44363i	0.490586	+	0.871393i	$0.336783\pi$
$269$	−391053.	+	1.71332e6i	−0.329500	+	1.44363i	−0.820086	+	0.572240i	$0.806074\pi$
$270$	−910477.	+	1.14170e6i	−0.760081	+	0.953111i
$271$	−1.00952e6	−	486158.i	−0.835009	−	0.402119i	−0.0330175	−	0.999455i	$-0.510512\pi$
$271$	−1.00952e6	−	486158.i	−0.835009	−	0.402119i	−0.801991	+	0.597336i	$0.796226\pi$
$272$	336291.	−	421695.i	0.275608	−	0.345602i
$273$	247623.	+	1.08491e6i	0.201087	+	0.881020i
$274$	1.40837e6	−	678234.i	1.13329	−	0.545762i
$275$	144458.	−	69567.4i	0.115189	−	0.0554720i
$276$	3.23126e6	+	4.05187e6i	2.55329	+	3.20172i
$277$	353896.	+	1.55052e6i	0.277126	+	1.21417i	0.901409	+	0.432969i	$0.142534\pi$
$277$	353896.	+	1.55052e6i	0.277126	+	1.21417i	−0.624283	+	0.781198i	$0.714609\pi$
$278$	−564086.	+	2.47142e6i	−0.437757	+	1.91794i
$279$	328834.	+	412345.i	0.252910	+	0.317140i
$280$	145958.	+	183025.i	0.111258	+	0.139513i
$281$	−495394.	+	2.17046e6i	−0.374270	+	1.63978i	0.340370	+	0.940292i	$0.389448\pi$
$281$	−495394.	+	2.17046e6i	−0.374270	+	1.63978i	−0.714640	+	0.699492i	$0.753409\pi$
$282$	−990788.	−	4.34093e6i	−0.741922	−	3.25057i
$283$	445067.	+	558096.i	0.330339	+	0.414231i	0.919068	−	0.394099i	$-0.128943\pi$
$283$	445067.	+	558096.i	0.330339	+	0.414231i	−0.588730	+	0.808330i	$0.700372\pi$
$284$	−530222.	+	255341.i	−0.390087	+	0.187856i
$285$	1.23504e6	−	594762.i	0.900673	−	0.433741i
$286$	284960.	+	1.24849e6i	0.206000	+	0.902547i
$287$	571463.	−	716592.i	0.409528	−	0.513532i
$288$	−2.74832e6	−	1.32352e6i	−1.95248	−	0.940263i
$289$	−368713.	+	462352.i	−0.259683	+	0.325633i
$290$	−91344.9	+	400208.i	−0.0637807	+	0.279442i
$291$	−2.13692e6	+	1.02909e6i	−1.47930	+	0.712393i
$292$	478477.	−	2.09635e6i	0.328401	−	1.43882i
$293$	−97120.4	−	46770.7i	−0.0660909	−	0.0318277i	0.400546	−	0.916276i	$-0.368820\pi$
$293$	−97120.4	−	46770.7i	−0.0660909	−	0.0318277i	−0.466637	+	0.884449i	$0.654535\pi$
$294$	2.95532e6			1.99405
$295$	−238179.			−0.159349
$296$	−1.11952e6	−	539134.i	−0.742683	−	0.357657i
$297$	−148085.	−	648801.i	−0.0974134	−	0.426796i
$298$	114268.	+	143288.i	0.0745393	+	0.0934693i
$299$	2.42835e6	−	3.04506e6i	1.57085	−	1.96978i
$300$	−907445.			−0.582126
$301$	−311136.	+	601383.i	−0.197940	+	0.382591i
$302$	−320797.			−0.202401
$303$	857996.	−	1.07589e6i	0.536882	−	0.673228i
$304$	424413.	+	532196.i	0.263393	+	0.330284i
$305$	370402.	+	1.62284e6i	0.227994	+	0.998908i
$306$	−2.72033e6	−	1.31004e6i	−1.66081	−	0.799802i
$307$	−778.521			−0.000471438			−0.000235719	−	1.00000i	$-0.500075\pi$
$307$	−778.521			−0.000471438			−0.000235719		1.00000i	$0.500075\pi$
$308$	−440760.			−0.264744
$309$	−1.03132e6	−	496659.i	−0.614467	−	0.295912i
$310$	125032.	−	547800.i	0.0738952	−	0.323756i
$311$	−2.37068e6	+	1.14166e6i	−1.38987	+	0.669324i	−0.971078	−	0.238761i	$-0.923259\pi$
$311$	−2.37068e6	+	1.14166e6i	−1.38987	+	0.669324i	−0.418787	+	0.908085i	$0.637545\pi$
$312$	390360.	−	1.71028e6i	0.227028	−	0.994673i
$313$	1.82041e6	−	2.28273e6i	1.05029	−	1.31702i	0.103690	−	0.994610i	$-0.466935\pi$
$313$	1.82041e6	−	2.28273e6i	1.05029	−	1.31702i	0.946599	−	0.322412i	$-0.104494\pi$
$314$	−3.68115e6	−	1.77275e6i	−2.10697	−	1.01467i
$315$	−638385.	+	800509.i	−0.362498	+	0.454559i
$316$	−419959.	−	1.83996e6i	−0.236586	−	1.03655i
$317$	−42897.3	+	20658.2i	−0.0239763	+	0.0115464i	−0.445833	−	0.895116i	$-0.647093\pi$
$317$	−42897.3	+	20658.2i	−0.0239763	+	0.0115464i	0.421857	+	0.906662i	$0.361378\pi$
$318$	−3.90815e6	+	1.88207e6i	−2.16722	+	1.04368i
$319$	−116639.	−	146260.i	−0.0641749	−	0.0804728i
$320$	522234.	+	2.28806e6i	0.285095	+	1.24908i
$321$	−346417.	+	1.51775e6i	−0.187645	+	0.822126i
$322$	1.46930e6	+	1.84244e6i	0.789715	+	0.990271i
$323$	651911.	+	817471.i	0.347682	+	0.435979i
$324$	40910.6	−	179241.i	0.0216508	−	0.0948582i
$325$	151751.	+	664864.i	0.0796935	+	0.349160i
$326$	−772100.	−	968183.i	−0.402374	−	0.504561i
$327$	2.71890e6	−	1.30935e6i	1.40612	−	0.677154i
$328$	−1.30180e6	+	626912.i	−0.668126	+	0.321753i
$329$	−256278.	−	1.12283e6i	−0.130533	−	0.571903i
$330$	−1.19827e6	+	1.50258e6i	−0.605715	+	0.759543i
$331$	1.14239e6	+	550146.i	0.573118	+	0.275999i	0.697912	−	0.716184i	$-0.254113\pi$
$331$	1.14239e6	+	550146.i	0.573118	+	0.275999i	−0.124794	+	0.992183i	$0.539827\pi$
$332$	1.16832e6	−	1.46503e6i	0.581723	−	0.729458i
$333$	1.20934e6	−	5.29848e6i	0.597639	−	2.61843i
$334$	1.15031e6	−	553959.i	0.564219	−	0.271714i
$335$	722736.	−	3.16651e6i	0.351858	−	1.54159i
$336$	−747190.	−	359828.i	−0.361063	−	0.173879i
$337$	−103775.			−0.0497759			−0.0248880	−	0.999690i	$-0.507923\pi$
$337$	−103775.			−0.0497759			−0.0248880	+	0.999690i	$0.507923\pi$
$338$	−2.24808e6			−1.07034
$339$	2.45960e6	+	1.18448e6i	1.16243	+	0.559795i
$340$	407171.	+	1.78393e6i	0.191021	+	0.836916i
$341$	159653.	+	200199.i	0.0743519	+	0.0932343i
$342$	2.37583e6	−	2.97920e6i	1.09837	−	1.37732i
$343$	1.70301e6			0.781594
$344$	853248.	−	641339.i	0.388758	−	0.292208i
$345$	5.84513e6			2.64391
$346$	−2.27533e6	+	2.85318e6i	−1.02177	+	1.28126i
$347$	−1.19078e6	−	1.49319e6i	−0.530894	−	0.665720i	0.441988	−	0.897021i	$-0.354273\pi$
$347$	−1.19078e6	−	1.49319e6i	−0.530894	−	0.665720i	−0.972882	+	0.231301i	$0.925702\pi$
$348$	235598.	+	1.03222e6i	0.104285	+	0.456904i
$349$	610350.	+	293929.i	0.268235	+	0.129175i	0.563167	−	0.826343i	$-0.309583\pi$
$349$	610350.	+	293929.i	0.268235	+	0.129175i	−0.294932	+	0.955518i	$0.595297\pi$
$350$	−412628.			−0.180048
$351$	2.83052e6			1.22631
$352$	−1.33435e6	−	642587.i	−0.573999	−	0.276424i
$353$	−46119.8	+	202064.i	−0.0196993	+	0.0863083i	−0.983822	−	0.179149i	$-0.942666\pi$
$353$	−46119.8	+	202064.i	−0.0196993	+	0.0863083i	0.964123	+	0.265457i	$0.0855228\pi$
$354$	−972991.	+	468568.i	−0.412668	+	0.198730i
$355$	−147697.	+	647101.i	−0.0622013	+	0.272522i
$356$	−851646.	+	1.06793e6i	−0.356151	+	0.446599i
$357$	−1.14771e6	−	552707.i	−0.476607	−	0.229522i
$358$	−791984.	+	993117.i	−0.326595	+	0.409537i
$359$	−809493.	−	3.54662e6i	−0.331495	−	1.45237i	−0.816237	−	0.577717i	$-0.803944\pi$
$359$	−809493.	−	3.54662e6i	−0.331495	−	1.45237i	0.484742	−	0.874657i	$-0.338913\pi$
$360$	1.45424e6	−	700327.i	0.591400	−	0.284803i
$361$	1.04200e6	−	501799.i	0.420822	−	0.202657i
$362$	3.78821e6	+	4.75027e6i	1.51937	+	1.90523i
$363$	703219.	+	3.08100e6i	0.280107	+	1.22723i
$364$	417158.	−	1.82769e6i	0.165024	−	0.723018i
$365$	−1.51207e6	−	1.89607e6i	−0.594072	−	0.744943i
$366$	4.70573e6	+	5.90080e6i	1.83622	+	2.30255i
$367$	−1.05371e6	+	4.61659e6i	−0.408371	+	1.78919i	0.183351	+	0.983047i	$0.441305\pi$
$367$	−1.05371e6	+	4.61659e6i	−0.408371	+	1.78919i	−0.591722	+	0.806142i	$0.701552\pi$
$368$	645884.	+	2.82980e6i	0.248619	+	1.08927i
$369$	−3.94020e6	−	4.94085e6i	−1.50644	−	1.88902i
$370$	−5.21663e6	+	2.51220e6i	−1.98101	+	0.954003i
$371$	−1.01088e6	+	486816.i	−0.381300	+	0.183624i
$372$	−322484.	−	1.41289e6i	−0.120823	−	0.529361i
$373$	−154368.	+	193571.i	−0.0574492	+	0.0720390i	−0.809726	−	0.586808i	$-0.800384\pi$
$373$	−154368.	+	193571.i	−0.0574492	+	0.0720390i	0.752277	+	0.658847i	$0.228956\pi$
$374$	−1.32076e6	−	636044.i	−0.488252	−	0.235130i
$375$	−2.96317e6	+	3.71570e6i	−1.08812	+	1.36446i
$376$	−404004.	+	1.77006e6i	−0.147372	+	0.645680i
$377$	716886.	−	345234.i	0.259775	−	0.125101i
$378$	−381097.	+	1.66970e6i	−0.137185	+	0.601046i
$379$	−718231.	−	345882.i	−0.256842	−	0.123689i	0.301033	−	0.953614i	$-0.402669\pi$
$379$	−718231.	−	345882.i	−0.256842	−	0.123689i	−0.557875	+	0.829925i	$0.688383\pi$
$380$	−2.30930e6			−0.820391
$381$	−2.23623e6			−0.789231
$382$	4.87340e6	+	2.34691e6i	1.70873	+	0.822882i
$383$	−465651.	−	2.04015e6i	−0.162205	−	0.710665i	−0.988970	−	0.148118i	$-0.952679\pi$
$383$	−465651.	−	2.04015e6i	−0.162205	−	0.710665i	0.826765	−	0.562547i	$-0.190179\pi$
$384$	2.67352e6	+	3.35249e6i	0.925243	+	1.16022i
$385$	−309944.	+	388658.i	−0.106569	+	0.133634i
$386$	2.36534e6			0.808026
$387$	3.56517e6	+	3.01416e6i	1.21005	+	1.02303i
$388$	3.99567e6			1.34744
$389$	−1.88105e6	+	2.35876e6i	−0.630270	+	0.790333i	−0.989749	−	0.142820i	$-0.954383\pi$
$389$	−1.88105e6	+	2.35876e6i	−0.630270	+	0.790333i	0.359479	+	0.933153i	$0.382954\pi$
$390$	−5.09661e6	−	6.39095e6i	−1.69676	−	2.12767i
$391$	992098.	+	4.34667e6i	0.328180	+	1.43785i
$392$	−1.08572e6	−	522856.i	−0.356864	−	0.171857i
$393$	−5.40191e6			−1.76427
$394$	−2.66885e6			−0.866133
$395$	−1.91778e6	−	923552.i	−0.618451	−	0.297830i
$396$	−676244.	+	2.96282e6i	−0.216703	+	0.949439i
$397$	1.09493e6	−	527288.i	0.348665	−	0.167908i	−0.251351	−	0.967896i	$-0.580875\pi$
$397$	1.09493e6	−	527288.i	0.348665	−	0.167908i	0.600016	+	0.799988i	$0.295161\pi$
$398$	1.16394e6	−	5.09956e6i	0.368318	−	1.61371i
$399$	1.00236e6	−	1.25692e6i	0.315204	−	0.395253i
$400$	−457901.	−	220513.i	−0.143094	−	0.0689104i
$401$	−2.64774e6	+	3.32016e6i	−0.822269	+	1.03109i	0.176634	+	0.984277i	$0.443479\pi$
$401$	−2.64774e6	+	3.32016e6i	−0.822269	+	1.03109i	−0.998904	+	0.0468163i	$0.985092\pi$
$402$	−3.27699e6	−	1.43574e7i	−1.01137	−	4.43110i
$403$	−981265.	+	472552.i	−0.300970	+	0.144940i
$404$	−2.08870e6	+	1.00586e6i	−0.636682	+	0.306610i
$405$	−129284.	−	162117.i	−0.0391659	−	0.0491125i
$406$	107130.	+	469365.i	0.0322548	+	0.141318i
$407$	587152.	−	2.57248e6i	0.175697	−	0.769779i
$408$	1.25206e6	+	1.57003e6i	0.372370	+	0.466937i
$409$	−566008.	−	709751.i	−0.167307	−	0.209796i	0.691109	−	0.722751i	$-0.257122\pi$
$409$	−566008.	−	709751.i	−0.167307	−	0.209796i	−0.858416	+	0.512954i	$0.828551\pi$
$410$	−1.49817e6	+	6.56392e6i	−0.440151	+	1.92843i
$411$	−1.01185e6	−	4.43320e6i	−0.295469	−	1.29453i
$412$	1.20233e6	+	1.50768e6i	0.348965	+	0.437588i
$413$	−251674.	+	121200.i	−0.0726045	+	0.0349645i
$414$	1.46393e7	−	7.04992e6i	4.19778	−	2.02154i
$415$	−470278.	−	2.06042e6i	−0.134040	−	0.587268i
$416$	3.92749e6	−	4.92492e6i	1.11271	−	1.39529i
$417$	6.64389e6	+	3.19953e6i	1.87104	+	0.901044i
$418$	1.15350e6	−	1.44644e6i	0.322906	−	0.404911i
$419$	−1.21636e6	+	5.32923e6i	−0.338476	+	1.48296i	0.463764	+	0.885959i	$0.346499\pi$
$419$	−1.21636e6	+	5.32923e6i	−0.338476	+	1.48296i	−0.802240	+	0.597002i	$0.796359\pi$
$420$	2.53485e6	−	1.22072e6i	0.701179	−	0.337670i
$421$	−607407.	+	2.66122e6i	−0.167022	+	0.731772i	0.820155	+	0.572142i	$0.193887\pi$
$421$	−607407.	+	2.66122e6i	−0.167022	+	0.731772i	−0.987177	+	0.159630i	$0.948970\pi$
$422$	3.07426e6	+	1.48048e6i	0.840347	+	0.404690i
$423$	−7.94090e6			−2.15784
$424$	1.76875e6			0.477806
$425$	−703350.	−	338715.i	−0.188886	−	0.0909625i
$426$	669677.	+	2.93405e6i	0.178789	+	0.783327i
$427$	1.21719e6	+	1.52630e6i	0.323063	+	0.405108i
$428$	1.63519e6	−	2.05046e6i	0.431478	−	0.541056i
$429$	3.72521e6			0.977255
$430$	142458.	−	4.97173e6i	0.0371548	−	1.29669i
$431$	7.02818e6			1.82242			0.911212	−	0.411937i	$-0.135148\pi$
$431$	7.02818e6			1.82242			0.911212	+	0.411937i	$0.135148\pi$
$432$	−1.31522e6	+	1.64923e6i	−0.339069	+	0.425179i
$433$	1.25512e6	+	1.57387e6i	0.321710	+	0.403412i	0.916219	−	0.400677i	$-0.131225\pi$
$433$	1.25512e6	+	1.57387e6i	0.321710	+	0.403412i	−0.594509	+	0.804089i	$0.702654\pi$
$434$	−146638.	−	642462.i	−0.0373698	−	0.163728i
$435$	1.07588e6	+	518114.i	0.272608	+	0.131281i
$436$	−5.08386e6			−1.28079
$437$	−5.62674e6			−1.40946
$438$	−9.90711e6	−	4.77101e6i	−2.46753	−	1.18830i
$439$	1.20630e6	−	5.28515e6i	0.298740	−	1.30887i	−0.573265	−	0.819370i	$-0.694323\pi$
$439$	1.20630e6	−	5.28515e6i	0.298740	−	1.30887i	0.872005	−	0.489497i	$-0.162820\pi$
$440$	706055.	−	340018.i	0.173863	−	0.0837279i
$441$	1.17283e6	−	5.13850e6i	0.287170	−	1.25817i
$442$	3.88750e6	−	4.87477e6i	0.946488	−	1.18686i
$443$	684079.	+	329435.i	0.165614	+	0.0797555i	0.514854	−	0.857278i	$-0.327846\pi$
$443$	684079.	+	329435.i	0.165614	+	0.0797555i	−0.349240	+	0.937033i	$0.613560\pi$
$444$	−9.31102e6	+	1.16756e7i	−2.24150	+	2.81076i
$445$	342809.	+	1.50194e6i	0.0820639	+	0.359545i
$446$	8.00780e6	−	3.85635e6i	1.90623	−	0.917993i
$447$	480336.	−	231318.i	0.113704	−	0.0547570i
$448$	1.71612e6	+	2.15195e6i	0.403974	+	0.506567i
$449$	−1.39610e6	−	6.11671e6i	−0.326814	−	1.43186i	−0.825166	−	0.564890i	$-0.808919\pi$
$449$	−1.39610e6	−	6.11671e6i	−0.326814	−	1.43186i	0.498352	−	0.866975i	$-0.333939\pi$
$450$	−633081.	+	2.77371e6i	−0.147376	+	0.645698i
$451$	−1.91302e6	−	2.39885e6i	−0.442872	−	0.555343i
$452$	−2.86744e6	−	3.59566e6i	−0.660159	−	0.827813i
$453$	−207654.	+	909792.i	−0.0475439	+	0.208304i
$454$	−1.64492e6	−	7.20686e6i	−0.374546	−	1.64099i
$455$	−1.31829e6	−	1.65308e6i	−0.298526	−	0.374340i
$456$	−2.28338e6	+	1.09962e6i	−0.514241	+	0.247645i
$457$	−749409.	+	360896.i	−0.167853	+	0.0808336i	−0.515924	−	0.856635i	$-0.672551\pi$
$457$	−749409.	+	360896.i	−0.167853	+	0.0808336i	0.348071	+	0.937468i	$0.386837\pi$
$458$	1.51651e6	+	6.64426e6i	0.337817	+	1.48007i
$459$	−2.02021e6	+	2.53327e6i	−0.447575	+	0.561241i
$460$	−8.87185e6	−	4.27246e6i	−1.95488	−	0.941420i
$461$	4.31761e6	−	5.41411e6i	0.946217	−	1.18652i	−0.0361101	−	0.999348i	$-0.511497\pi$
$461$	4.31761e6	−	5.41411e6i	0.946217	−	1.18652i	0.982327	−	0.187171i	$-0.0599319\pi$
$462$	−501557.	+	2.19746e6i	−0.109324	+	0.478979i
$463$	−7.59962e6	+	3.65979e6i	−1.64755	+	0.793420i	−0.648061	+	0.761589i	$0.724420\pi$
$463$	−7.59962e6	+	3.65979e6i	−1.64755	+	0.793420i	−0.999493	+	0.0318316i	$0.989866\pi$
$464$	−131951.	+	578115.i	−0.0284523	+	0.124658i
$465$	−1.47265e6	−	709189.i	−0.315839	−	0.152100i
$466$	1.10404e7			2.35516
$467$	−1.89845e6			−0.402815			−0.201408	−	0.979507i	$-0.564552\pi$
$467$	−1.89845e6			−0.402815			−0.201408	+	0.979507i	$0.564552\pi$
$468$	−1.16458e7	−	5.60833e6i	−2.45785	−	1.18364i
$469$	−847627.	−	3.71370e6i	−0.177940	−	0.779605i
$470$	5.27474e6	+	6.61432e6i	1.10143	+	1.38115i
$471$	−7.41040e6	+	9.29235e6i	−1.53918	+	1.93007i
$472$	440356.			0.0909805
$473$	1.73094e6	+	1.46341e6i	0.355736	+	0.300756i
$474$	−9.65124e6			−1.97305
$475$	614277.	−	770279.i	0.124919	−	0.156644i
$476$	1.33801e6	+	1.67782e6i	0.270672	+	0.339412i
$477$	1.72144e6	+	7.54213e6i	0.346415	+	1.51774i
$478$	3.41875e6	+	1.64638e6i	0.684381	+	0.329580i
$479$	−970717.			−0.193310			−0.0966548	−	0.995318i	$-0.530814\pi$
$479$	−970717.			−0.193310			−0.0966548	+	0.995318i	$0.530814\pi$
$480$	9.45362e6			1.87282
$481$	1.01115e7	+	4.86946e6i	1.99276	+	0.959662i
$482$	−2.52235e6	+	1.10511e7i	−0.494524	+	2.16665i
$483$	6.17631e6	−	2.97435e6i	1.20465	−	0.580130i
$484$	1.18468e6	−	5.19042e6i	0.229873	−	1.00714i
$485$	2.80977e6	−	3.52334e6i	0.542395	−	0.680142i
$486$	−7.56133e6	−	3.64135e6i	−1.45214	−	0.699312i
$487$	2.69847e6	−	3.38377e6i	0.515579	−	0.646515i	−0.454085	−	0.890958i	$-0.650034\pi$
$487$	2.69847e6	−	3.38377e6i	0.515579	−	0.646515i	0.969664	+	0.244443i	$0.0786052\pi$
$488$	−684815.	−	3.00037e6i	−0.130174	−	0.570329i
$489$	−3.24558e6	+	1.56299e6i	−0.613791	+	0.295586i
$490$	−5.05913e6	+	2.43635e6i	−0.951887	+	0.458405i
$491$	−2.10488e6	−	2.63944e6i	−0.394025	−	0.494092i	0.544761	−	0.838591i	$-0.316620\pi$
$491$	−2.10488e6	−	2.63944e6i	−0.394025	−	0.494092i	−0.938787	+	0.344499i	$0.888049\pi$
$492$	3.86410e6	+	1.69297e7i	0.719674	+	3.15310i
$493$	−202681.	+	888002.i	−0.0375574	+	0.164550i
$494$	4.90619e6	+	6.15216e6i	0.904538	+	1.13425i
$495$	2.13704e6	+	2.67977e6i	0.392013	+	0.491569i
$496$	180613.	−	791316.i	0.0329643	−	0.144426i
$497$	173219.	+	758922.i	0.0314561	+	0.137818i
$498$	−5.97459e6	−	7.49191e6i	−1.07953	−	1.35369i
$499$	−2.01537e6	+	970552.i	−0.362330	+	0.174489i	−0.606187	−	0.795322i	$-0.707302\pi$
$499$	−2.01537e6	+	970552.i	−0.362330	+	0.174489i	0.243857	+	0.969811i	$0.421587\pi$
$500$	7.21352e6	−	3.47385e6i	1.29039	−	0.621421i
$501$	−826445.	−	3.62089e6i	−0.147102	−	0.644498i
$502$	−1.54401e6	+	1.93612e6i	−0.273457	+	0.342905i
$503$	225779.	+	108730.i	0.0397891	+	0.0191614i	0.453672	−	0.891168i	$-0.350114\pi$
$503$	225779.	+	108730.i	0.0397891	+	0.0191614i	−0.413883	+	0.910330i	$0.635828\pi$
$504$	1.18027e6	−	1.48001e6i	0.206969	−	0.259531i
$505$	−581820.	+	2.54912e6i	−0.101522	+	0.444797i
$506$	7.10758e6	−	3.42283e6i	1.23409	−	0.594304i
$507$	−1.45520e6	+	6.37563e6i	−0.251421	+	1.10155i
$508$	3.39419e6	+	1.63456e6i	0.583549	+	0.281022i
$509$	−3.52927e6			−0.603796			−0.301898	−	0.953340i	$-0.597620\pi$
$509$	−3.52927e6			−0.603796			−0.301898	+	0.953340i	$0.597620\pi$
$510$	9.35736e6			1.59304
$511$	−2.56258e6	−	1.23407e6i	−0.434135	−	0.209068i
$512$	1.41609e6	+	6.20428e6i	0.238734	+	1.04596i
$513$	−2.54959e6	−	3.19709e6i	−0.427737	−	0.536366i
$514$	6.86497e6	−	8.60840e6i	1.14612	−	1.43719i
$515$	2.17494e6			0.361351
$516$	−5.23271e6	−	1.17127e7i	−0.865172	−	1.93656i
$517$	−3.85541e6			−0.634373
$518$	−4.23385e6	+	5.30908e6i	−0.693283	+	0.869350i
$519$	6.61887e6	+	8.29980e6i	1.07861	+	1.35254i
$520$	741698.	+	3.24959e6i	0.120287	+	0.527012i
$521$	−1.13498e6	−	546577.i	−0.183186	−	0.0882180i	0.340043	−	0.940410i	$-0.389559\pi$
$521$	−1.13498e6	−	546577.i	−0.183186	−	0.0882180i	−0.523229	+	0.852192i	$0.675273\pi$
$522$	3.31947e6			0.533203
$523$	1.69055e6			0.270255			0.135127	−	0.990828i	$-0.456856\pi$
$523$	1.69055e6			0.270255			0.135127	+	0.990828i	$0.456856\pi$
$524$	8.19912e6	+	3.94849e6i	1.30448	+	0.628206i
$525$	−267096.	+	1.17023e6i	−0.0422931	+	0.185298i
$526$	−6.99032e6	+	3.36636e6i	−1.10162	+	0.530514i
$527$	277427.	−	1.21549e6i	0.0435133	−	0.190644i
$528$	−1.73094e6	+	2.17053e6i	−0.270207	+	0.338829i
$529$	−1.58179e7	−	7.61748e6i	−2.45759	−	1.18351i
$530$	5.13870e6	−	6.44372e6i	0.794627	−	0.996431i
$531$	428578.	+	1.87772e6i	0.0659620	+	0.288998i
$532$	−2.44014e6	+	1.17511e6i	−0.373797	+	0.180011i
$533$	1.17578e7	−	5.66227e6i	1.79271	−	0.863322i
$534$	4.35518e6	+	5.46122e6i	0.660926	+	0.828775i
$535$	−658205.	−	2.88379e6i	−0.0994207	−	0.435591i
$536$	−1.33622e6	+	5.85438e6i	−0.200894	+	0.880175i
$537$	2.30386e6	+	2.88894e6i	0.344762	+	0.432318i
$538$	−9.43955e6	−	1.18368e7i	−1.40603	−	1.76311i
$539$	569424.	−	2.49481e6i	0.0844236	−	0.369884i
$540$	−1.59243e6	−	6.97688e6i	−0.235004	−	1.02962i
$541$	2.05772e6	+	2.58029e6i	0.302268	+	0.379032i	0.909648	−	0.415379i	$-0.136351\pi$
$541$	2.05772e6	+	2.58029e6i	0.302268	+	0.379032i	−0.607380	+	0.794411i	$0.707780\pi$
$542$	8.69703e6	−	4.18827e6i	1.27167	−	0.612402i
$543$	1.59240e7	−	7.66862e6i	2.31768	−	1.11614i
$544$	1.60457e6	+	7.03007e6i	0.232467	+	1.01850i
$545$	−3.57499e6	+	4.48289e6i	−0.515565	+	0.646498i
$546$	−8.63747e6	−	4.15959e6i	−1.23995	−	0.597130i
$547$	−4.89255e6	+	6.13506e6i	−0.699144	+	0.876699i	−0.996959	−	0.0779245i	$-0.975171\pi$
$547$	−4.89255e6	+	6.13506e6i	−0.699144	+	0.876699i	0.297815	+	0.954624i	$0.403742\pi$
$548$	−1.70461e6	+	7.46840e6i	−0.242479	+	1.06237i
$549$	1.21274e7	−	5.84025e6i	1.71726	−	0.826990i
$550$	−307369.	+	1.34667e6i	−0.0433265	+	0.189826i
$551$	−1.03568e6	−	498756.i	−0.145327	−	0.0699857i
$552$	−1.08067e7			−1.50955
$553$	−2.49639e6			−0.347136
$554$	−1.23445e7	−	5.94478e6i	−1.70882	−	0.822927i
$555$	3.74792e6	+	1.64207e7i	0.516485	+	2.26287i
$556$	−7.74555e6	−	9.71262e6i	−1.06259	−	1.33245i
$557$	1.64593e6	−	2.06394e6i	0.224789	−	0.281876i	−0.656629	−	0.754214i	$-0.728018\pi$
$557$	1.64593e6	−	2.06394e6i	0.224789	−	0.281876i	0.881418	+	0.472338i	$0.156590\pi$
$558$	−4.54365e6			−0.617759
$559$	−7.70655e6	+	5.79258e6i	−1.04311	+	0.784048i
$560$	1.57573e6			0.212331
$561$	−2.65878e6	+	3.33400e6i	−0.356677	+	0.447258i
$562$	−1.19582e7	−	1.49951e7i	−1.59708	−	2.00267i
$563$	−495648.	−	2.17158e6i	−0.0659026	−	0.288738i	0.931228	−	0.364437i	$-0.118738\pi$
$563$	−495648.	−	2.17158e6i	−0.0659026	−	0.288738i	−0.997131	+	0.0756986i	$0.975881\pi$
$564$	1.96593e7	+	9.46743e6i	2.60238	+	1.25324i
$565$	−5.18701e6			−0.683590
$566$	−6.14969e6			−0.806886
$567$	−219104.	−	105515.i	−0.0286216	−	0.0137834i
$568$	273067.	−	1.19639e6i	0.0355139	−	0.155597i
$569$	−2.59914e6	+	1.25168e6i	−0.336550	+	0.162074i	−0.594524	−	0.804078i	$-0.702659\pi$
$569$	−2.59914e6	+	1.25168e6i	−0.336550	+	0.162074i	0.257974	+	0.966152i	$0.416945\pi$
$570$	−2.62783e6	+	1.15133e7i	−0.338774	+	1.48427i
$571$	3.92113e6	−	4.91694e6i	0.503293	−	0.631109i	−0.463676	−	0.886005i	$-0.653470\pi$
$571$	3.92113e6	−	4.91694e6i	0.503293	−	0.631109i	0.966969	+	0.254896i	$0.0820411\pi$
$572$	−5.65420e6	−	2.72292e6i	−0.722572	−	0.347972i
$573$	9.81049e6	−	1.23020e7i	1.24826	−	1.56526i
$574$	1.75706e6	+	7.69818e6i	0.222591	+	0.975233i
$575$	3.78503e6	−	1.82277e6i	0.477419	−	0.229913i
$576$	1.70985e7	−	8.23422e6i	2.14735	−	1.03411i
$577$	4.70185e6	+	5.89593e6i	0.587935	+	0.737247i	0.983443	−	0.181215i	$-0.0580031\pi$
$577$	4.70185e6	+	5.89593e6i	0.587935	+	0.737247i	−0.395509	+	0.918462i	$0.629432\pi$
$578$	−1.13367e6	−	4.96694e6i	−0.141146	−	0.618400i
$579$	1.53110e6	−	6.70818e6i	0.189805	−	0.831589i
$580$	−1.25427e6	−	1.57281e6i	−0.154818	−	0.194136i
$581$	−1.54539e6	−	1.93786e6i	−0.189932	−	0.238167i
$582$	4.54681e6	−	1.99209e7i	0.556416	−	2.43782i
$583$	835783.	+	3.66181e6i	0.101841	+	0.446194i
$584$	2.79557e6	+	3.50554e6i	0.339187	+	0.425327i
$585$	−1.31347e7	+	6.32536e6i	−1.58684	+	0.764180i
$586$	836696.	−	402931.i	0.100652	−	0.0484716i
$587$	−1.26286e6	−	5.53295e6i	−0.151273	−	0.662768i	−0.992516	−	0.122112i	$-0.961033\pi$
$587$	−1.26286e6	−	5.53295e6i	−0.151273	−	0.662768i	0.841244	−	0.540656i	$-0.181824\pi$
$588$	−9.02989e6	+	1.13231e7i	−1.07706	+	1.35059i
$589$	1.41762e6	+	682692.i	0.168373	+	0.0810842i
$590$	1.27935e6	−	1.60426e6i	0.151307	−	0.189734i
$591$	−1.72757e6	+	7.56896e6i	−0.203454	+	0.891389i
$592$	−7.53561e6	+	3.62896e6i	−0.883719	+	0.425577i
$593$	2.02915e6	−	8.89029e6i	0.236961	−	1.03820i	−0.706760	−	0.707454i	$-0.749844\pi$
$593$	2.02915e6	−	8.89029e6i	0.236961	−	1.03820i	0.943721	−	0.330742i	$-0.107299\pi$
$594$	5.16542e6	+	2.48753e6i	0.600675	+	0.289270i
$595$	2.42038e6			0.280279
$596$	−898143.			−0.103569
$597$	−1.37091e7	−	6.60195e6i	−1.57425	−	0.758117i
$598$	7.46638e6	+	3.27124e7i	0.853802	+	3.74075i
$599$	8.80113e6	+	1.10363e7i	1.00224	+	1.25677i	0.966301	+	0.257414i	$0.0828705\pi$
$599$	8.80113e6	+	1.10363e7i	1.00224	+	1.25677i	0.0359383	+	0.999354i	$0.488558\pi$
$600$	1.17978e6	−	1.47940e6i	0.133790	−	0.167767i
$601$	−1.31501e7			−1.48506			−0.742529	−	0.669814i	$-0.766374\pi$
$601$	−1.31501e7			−1.48506			−0.742529	+	0.669814i	$0.766374\pi$
$602$	−2.37939e6	−	5.32591e6i	−0.267592	−	0.598967i
$603$	−2.62642e7			−2.94151
$604$	980188.	−	1.22912e6i	0.109324	−	0.137088i
$605$	−3.74379e6	−	4.69456e6i	−0.415836	−	0.521442i
$606$	2.63805e6	+	1.15581e7i	0.291811	+	1.27851i
$607$	1.29382e7	+	6.23072e6i	1.42529	+	0.686383i	0.978115	−	0.208064i	$-0.0667163\pi$
$607$	1.29382e7	+	6.23072e6i	1.42529	+	0.686383i	0.447174	+	0.894447i	$0.352431\pi$
$608$	−9.10041e6			−0.998394
$609$	1.40048e6			0.153015
$610$	−1.29202e7	−	6.22204e6i	−1.40587	−	0.677031i
$611$	3.64896e6	−	1.59872e7i	0.395427	−	1.73248i
$612$	1.33313e7	−	6.42000e6i	1.43877	−	0.692877i
$613$	−1.42155e6	+	6.22820e6i	−0.152795	+	0.669439i	0.839270	+	0.543715i	$0.182983\pi$
$613$	−1.42155e6	+	6.22820e6i	−0.152795	+	0.669439i	−0.992065	+	0.125724i	$0.959874\pi$
$614$	4181.74	−	5243.74i	0.000447647	−	0.000561332i
$615$	1.76457e7	+	8.49773e6i	1.88127	+	0.905972i
$616$	573037.	−	718566.i	0.0608459	−	0.0762983i
$617$	2.57972e6	+	1.13025e7i	0.272810	+	1.19526i	0.906680	+	0.421819i	$0.138608\pi$
$617$	2.57972e6	+	1.13025e7i	0.272810	+	1.19526i	−0.633870	+	0.773439i	$0.718535\pi$
$618$	8.88488e6	−	4.27873e6i	0.935794	−	0.450655i
$619$	3.46887e6	−	1.67052e6i	0.363883	−	0.175237i	−0.243003	−	0.970025i	$-0.578133\pi$
$619$	3.46887e6	−	1.67052e6i	0.363883	−	0.175237i	0.606886	+	0.794789i	$0.292418\pi$
$620$	1.71683e6	+	2.15284e6i	0.179370	+	0.224922i
$621$	−3.88005e6	−	1.69996e7i	−0.403746	−	1.76893i
$622$	5.04419e6	−	2.21001e7i	0.522776	−	2.29043i
$623$	1.12651e6	+	1.41260e6i	0.116283	+	0.145814i
$624$	−7.36223e6	−	9.23194e6i	−0.756916	−	0.949143i
$625$	1.41297e6	−	6.19062e6i	0.144688	−	0.633919i
$626$	5.59717e6	+	2.45228e7i	0.570864	+	2.50112i
$627$	−3.35548e6	−	4.20764e6i	−0.340868	−	0.427435i
$628$	1.80398e7	−	8.68752e6i	1.82530	−	0.879016i
$629$	−1.15749e7	+	5.57420e6i	−1.16652	+	0.561766i
$630$	−1.96282e6	−	8.59969e6i	−0.197029	−	0.863239i
$631$	−8.79692e6	+	1.10310e7i	−0.879543	+	1.10291i	0.114446	+	0.993430i	$0.463491\pi$
$631$	−8.79692e6	+	1.10310e7i	−0.879543	+	1.10291i	−0.993989	+	0.109483i	$0.965081\pi$
$632$	3.54566e6	+	1.70750e6i	0.353106	+	0.170047i
$633$	6.18868e6	−	7.76037e6i	0.613888	−	0.769791i
$634$	91274.2	−	399898.i	0.00901830	−	0.0395118i
$635$	3.82815e6	−	1.84354e6i	0.376751	−	0.181434i
$636$	4.73022e6	−	2.07245e7i	0.463702	−	2.03161i
$637$	9.80624e6	+	4.72244e6i	0.957534	+	0.461124i
$638$	1.61165e6			0.156754
$639$	5.36728e6			0.519999
$640$	−7.34051e6	−	3.53500e6i	−0.708396	−	0.341146i
$641$	−299625.	−	1.31274e6i	−0.0288027	−	0.126193i	0.958483	−	0.285151i	$-0.0920437\pi$
$641$	−299625.	−	1.31274e6i	−0.0288027	−	0.126193i	−0.987285	+	0.158958i	$0.949187\pi$
$642$	−8.36209e6	−	1.04857e7i	−0.800714	−	1.00406i
$643$	6.64122e6	−	8.32783e6i	0.633462	−	0.794336i	−0.356706	−	0.934217i	$-0.616100\pi$
$643$	6.64122e6	−	8.32783e6i	0.633462	−	0.794336i	0.990168	+	0.139880i	$0.0446717\pi$
$644$	−1.15486e7			−1.09727
$645$	−1.40078e7	−	3.62225e6i	−1.32578	−	0.342830i
$646$	−9.00774e6			−0.849248
$647$	−548433.	+	687714.i	−0.0515066	+	0.0645873i	−0.806918	−	0.590664i	$-0.798866\pi$
$647$	−548433.	+	687714.i	−0.0515066	+	0.0645873i	0.755411	+	0.655251i	$0.227437\pi$
$648$	239026.	+	299729.i	0.0223619	+	0.0280409i
$649$	208080.	+	911659.i	0.0193918	+	0.0849612i
$650$	−5.29331e6	−	2.54912e6i	−0.491410	−	0.236650i
$651$	−1.91696e6			−0.177281
$652$	6.06867e6			0.559080
$653$	1.45273e7	+	6.99599e6i	1.33322	+	0.642046i	0.958500	−	0.285091i	$-0.0920240\pi$
$653$	1.45273e7	+	6.99599e6i	1.33322	+	0.642046i	0.374722	+	0.927137i	$0.377738\pi$
$654$	−5.78510e6	+	2.53462e7i	−0.528892	+	2.31723i
$655$	9.24738e6	−	4.45330e6i	0.842200	−	0.405582i
$656$	−2.16416e6	+	9.48181e6i	−0.196350	+	0.860264i
$657$	−1.22272e7	+	1.53324e7i	−1.10513	+	1.38579i
$658$	8.93937e6	+	4.30497e6i	0.804900	+	0.387619i
$659$	7.58677e6	−	9.51350e6i	0.680523	−	0.853349i	−0.314879	−	0.949132i	$-0.601964\pi$
$659$	7.58677e6	−	9.51350e6i	0.680523	−	0.853349i	0.995402	+	0.0957825i	$0.0305353\pi$
$660$	−2.09577e6	−	9.18218e6i	−0.187277	−	0.820514i
$661$	−2.67595e6	+	1.28867e6i	−0.238218	+	0.114720i	−0.549185	−	0.835701i	$-0.685062\pi$
$661$	−2.67595e6	+	1.28867e6i	−0.238218	+	0.114720i	0.310966	+	0.950421i	$0.399347\pi$
$662$	−9.84172e6	+	4.73952e6i	−0.872823	+	0.420329i
$663$	−1.13086e7	−	1.41806e7i	−0.999138	−	1.25288i
$664$	869470.	+	3.80940e6i	0.0765304	+	0.335302i
$665$	−679716.	+	2.97803e6i	−0.0596037	+	0.261141i
$666$	2.91921e7	+	3.66057e7i	2.55023	+	3.19789i
$667$	−3.05611e6	−	3.83224e6i	−0.265983	−	0.333533i
$668$	−1.39227e6	+	6.09994e6i	−0.120721	+	0.528913i
$669$	−5.75325e6	−	2.52066e7i	−0.496990	−	2.17746i
$670$	1.74460e7	+	2.18766e7i	1.50144	+	1.88275i
$671$	5.88801e6	−	2.83552e6i	0.504850	−	0.243123i
$672$	9.98925e6	−	4.81057e6i	0.853316	−	0.410935i
$673$	2.27462e6	+	9.96576e6i	0.193585	+	0.848151i	0.974656	+	0.223709i	$0.0718164\pi$
$673$	2.27462e6	+	9.96576e6i	0.193585	+	0.848151i	−0.781071	+	0.624442i	$0.785326\pi$
$674$	557417.	−	698979.i	0.0472640	−	0.0592672i
$675$	2.75077e6	+	1.32470e6i	0.232377	+	0.111907i
$676$	6.86895e6	−	8.61339e6i	0.578127	−	0.724949i
$677$	730405.	−	3.20011e6i	0.0612480	−	0.268345i	−0.935027	−	0.354576i	$-0.884625\pi$
$677$	730405.	−	3.20011e6i	0.0612480	−	0.268345i	0.996275	+	0.0862310i	$0.0274823\pi$
$678$	−2.11895e7	+	1.02043e7i	−1.77030	+	0.852533i
$679$	1.17608e6	−	5.15274e6i	0.0978954	−	0.428908i
$680$	−3.43770e6	−	1.65551e6i	−0.285099	−	0.137296i
$681$	−2.15037e7			−1.77682
$682$	−2.20600e6			−0.181612
$683$	1.01037e7	+	4.86567e6i	0.828758	+	0.399109i	0.799649	−	0.600468i	$-0.205019\pi$
$683$	1.01037e7	+	4.86567e6i	0.828758	+	0.399109i	0.0291085	+	0.999576i	$0.490733\pi$
$684$	4.15533e6	+	1.82057e7i	0.339598	+	1.48788i
$685$	5.38687e6	+	6.75492e6i	0.438642	+	0.550039i
$686$	−9.14751e6	+	1.14706e7i	−0.742151	+	0.930628i
$687$	1.98250e7			1.60258
$688$	205785.	−	7.18184e6i	0.0165746	−	0.578448i
$689$	−1.59754e7			−1.28204
$690$	−3.13965e7	+	3.93699e7i	−2.51049	+	3.14805i
$691$	5.45128e6	+	6.83569e6i	0.434313	+	0.544612i	0.950035	−	0.312145i	$-0.101047\pi$
$691$	5.45128e6	+	6.83569e6i	0.434313	+	0.544612i	−0.515721	+	0.856756i	$0.672476\pi$
$692$	−3.97956e6	−	1.74356e7i	−0.315915	−	1.38411i
$693$	3.62175e6	+	1.74415e6i	0.286474	+	0.137959i
$694$	1.64535e7			1.29676
$695$	−1.40112e7			−1.10030
$696$	−1.98912e6	−	957911.i	−0.155646	−	0.0749553i
$697$	−3.32422e6	+	1.45644e7i	−0.259184	+	1.13556i
$698$	−5.25819e6	+	2.53221e6i	−0.408505	+	0.196726i
$699$	7.14652e6	−	3.13109e7i	0.553225	−	2.42384i
$700$	1.26077e6	−	1.58096e6i	0.0972504	−	0.121948i
$701$	1.07182e7	+	5.16160e6i	0.823808	+	0.396725i	0.797789	−	0.602937i	$-0.206003\pi$
$701$	1.07182e7	+	5.16160e6i	0.823808	+	0.396725i	0.0260186	+	0.999661i	$0.491717\pi$
$702$	−1.52038e7	+	1.90650e7i	−1.16442	+	1.46014i
$703$	−3.60789e6	−	1.58072e7i	−0.275337	−	1.20633i
$704$	8.30157e6	−	3.99782e6i	0.631289	−	0.304013i
$705$	2.21728e7	−	1.06779e7i	1.68015	−	0.809117i
$706$	−1.11328e6	−	1.39601e6i	−0.0840604	−	0.105408i
$707$	682360.	+	2.98961e6i	0.0513411	+	0.224940i
$708$	1.17766e6	−	5.15965e6i	0.0882949	−	0.386845i
$709$	−1.85307e6	−	2.32367e6i	−0.138444	−	0.173604i	0.707776	−	0.706437i	$-0.249699\pi$
$709$	−1.85307e6	−	2.32367e6i	−0.138444	−	0.173604i	−0.846220	+	0.532833i	$0.821127\pi$
$710$	−3.56521e6	−	4.47064e6i	−0.265424	−	0.332831i
$711$	−3.83013e6	+	1.67809e7i	−0.284145	+	1.24492i
$712$	−633799.	−	2.77686e6i	−0.0468545	−	0.205283i
$713$	4.18317e6	+	5.24553e6i	0.308164	+	0.386425i
$714$	9.88754e6	−	4.76159e6i	0.725843	−	0.349547i
$715$	−6.37709e6	+	3.07105e6i	−0.466506	+	0.224658i
$716$	−1.38518e6	−	6.06888e6i	−0.100977	−	0.442411i
$717$	6.88218e6	−	8.62998e6i	0.499952	−	0.626919i
$718$	2.82364e7	+	1.35979e7i	2.04408	+	0.984377i
$719$	−1.07317e7	+	1.34571e7i	−0.774188	+	0.970801i	−0.999994	−	0.00337089i	$-0.998927\pi$
$719$	−1.07317e7	+	1.34571e7i	−0.774188	+	0.970801i	0.225806	+	0.974172i	$0.427498\pi$
$720$	2.41760e6	−	1.05922e7i	0.173801	−	0.761473i
$721$	2.29817e6	−	1.10674e6i	0.164643	−	0.0792879i
$722$	−2.21710e6	+	9.71373e6i	−0.158286	+	0.693495i
$723$	2.97086e7	+	1.43069e7i	2.11367	+	1.01789i
$724$	−2.97751e7			−2.11109
$725$	858257.			0.0606419
$726$	−2.45294e7	−	1.18127e7i	−1.72721	−	0.831780i
$727$	−2.40805e6	−	1.05504e7i	−0.168978	−	0.740340i	−0.986408	−	0.164313i	$-0.947459\pi$
$727$	−2.40805e6	−	1.05504e7i	−0.168978	−	0.740340i	0.817431	−	0.576027i	$-0.195398\pi$
$728$	2.43731e6	+	3.05629e6i	0.170444	+	0.213730i
$729$	−1.45617e7	+	1.82598e7i	−1.01483	+	1.27256i
$730$	2.08929e7			1.45108
$731$	316093.	−	1.10315e7i	0.0218787	−	0.763558i
$732$	−3.69868e7			−2.55134
$733$	9.09067e6	−	1.13993e7i	0.624937	−	0.783646i	−0.364093	−	0.931363i	$-0.618621\pi$
$733$	9.09067e6	−	1.13993e7i	0.624937	−	0.783646i	0.989030	+	0.147717i	$0.0471924\pi$
$734$	−2.54352e7	−	3.18947e7i	−1.74259	−	2.18514i
$735$	3.63476e6	+	1.59249e7i	0.248175	+	1.08732i
$736$	−3.49619e7	−	1.68368e7i	−2.37903	−	1.14568i
$737$	−1.27516e7			−0.864761
$738$	5.44435e7			3.67964
$739$	2.39125e7	+	1.15156e7i	1.61070	+	0.775671i	0.999870	−	0.0160942i	$-0.00512316\pi$
$739$	2.39125e7	+	1.15156e7i	1.61070	+	0.775671i	0.610826	+	0.791765i	$0.290837\pi$
$740$	6.31394e6	−	2.76632e7i	0.423859	−	1.85705i
$741$	2.06235e7	−	9.93177e6i	1.37980	−	0.664479i
$742$	2.15090e6	−	9.42369e6i	0.143420	−	0.628364i
$743$	−1.11696e7	+	1.40063e7i	−0.742277	+	0.930786i	−0.999366	−	0.0356017i	$-0.988665\pi$
$743$	−1.11696e7	+	1.40063e7i	−0.742277	+	0.930786i	0.257089	+	0.966388i	$0.417237\pi$
$744$	2.72269e6	+	1.31118e6i	0.180329	+	0.0868418i
$745$	−631577.	+	791973.i	−0.0416904	+	0.0522781i
$746$	−474629.	−	2.07949e6i	−0.0312254	−	0.136807i
$747$	−1.53975e7	+	7.41502e6i	−1.00960	+	0.486196i
$748$	6.47250e6	−	3.11699e6i	0.422979	−	0.203696i
$749$	−2.16294e6	−	2.71224e6i	−0.140877	−	0.176654i
$750$	−9.11077e6	−	3.99169e7i	−0.591428	−	2.59122i
$751$	−4.42790e6	+	1.93999e7i	−0.286483	+	1.25516i	0.602832	+	0.797868i	$0.294039\pi$
$751$	−4.42790e6	+	1.93999e7i	−0.286483	+	1.25516i	−0.889315	+	0.457295i	$0.848818\pi$
$752$	7.61955e6	+	9.55461e6i	0.491343	+	0.616124i
$753$	4.49146e6	+	5.63212e6i	0.288669	+	0.361980i
$754$	−1.52535e6	+	6.68298e6i	−0.0977102	+	0.428096i
$755$	−394550.	−	1.72864e6i	−0.0251904	−	0.110366i
$756$	−5.23291e6	−	6.56186e6i	−0.332996	−	0.417563i
$757$	−1.80939e6	+	871356.i	−0.114760	+	0.0552657i	−0.490383	−	0.871507i	$-0.663143\pi$
$757$	−1.80939e6	+	871356.i	−0.114760	+	0.0552657i	0.375623	+	0.926773i	$0.377429\pi$
$758$	6.18758e6	−	2.97978e6i	0.391154	−	0.188370i
$759$	−5.10648e6	−	2.23729e7i	−0.321749	−	1.40967i
$760$	3.00234e6	−	3.76482e6i	0.188550	−	0.236434i
$761$	−1.07678e7	−	5.18549e6i	−0.674007	−	0.324585i	0.0653846	−	0.997860i	$-0.479173\pi$
$761$	−1.07678e7	−	5.18549e6i	−0.674007	−	0.324585i	−0.739392	+	0.673275i	$0.764887\pi$
$762$	1.20117e7	−	1.50621e7i	0.749403	−	0.939722i
$763$	−1.49638e6	+	6.55606e6i	−0.0930528	+	0.407691i
$764$	−2.38826e7	+	1.15012e7i	−1.48029	+	0.712872i
$765$	3.71351e6	−	1.62699e7i	0.229420	−	1.00515i
$766$	1.62426e7	+	7.82204e6i	1.00019	+	0.481668i
$767$	−3.97729e6			−0.244118
$768$	2.58470e6			0.158127
$769$	354799.	+	170862.i	0.0216355	+	0.0104191i	0.444670	−	0.895694i	$-0.353321\pi$
$769$	354799.	+	170862.i	0.0216355	+	0.0104191i	−0.423035	+	0.906113i	$0.639035\pi$
$770$	−952976.	−	4.17526e6i	−0.0579236	−	0.253780i
$771$	−1.99700e7	−	2.50415e7i	−1.20988	−	1.51714i
$772$	−7.22723e6	+	9.06266e6i	−0.436444	+	0.547284i
$773$	1.38405e7			0.833114			0.416557	−	0.909110i	$-0.363237\pi$
$773$	1.38405e7			0.833114			0.416557	+	0.909110i	$0.363237\pi$
$774$	−3.94517e7	+	7.82301e6i	−2.36708	+	0.469376i
$775$	−1.17477e6			−0.0702586
$776$	−5.19481e6	+	6.51409e6i	−0.309682	+	0.388328i
$777$	1.23161e7	+	1.54439e7i	0.731849	+	0.917709i
$778$	−5.78361e6	−	2.53396e7i	−0.342571	−	1.50090i
$779$	−1.69864e7	−	8.18023e6i	−1.00290	−	0.482972i
$780$	4.00591e7			2.35757
$781$	2.60589e6			0.152872
$782$	−3.46059e7	−	1.66653e7i	−2.02364	−	0.974535i
$783$	792674.	−	3.47293e6i	0.0462051	−	0.202438i
$784$	−7.30809e6	+	3.51939e6i	−0.424633	+	0.204492i
$785$	5.02510e6	−	2.20164e7i	0.291052	−	1.27518i
$786$	2.90157e7	−	3.63846e7i	1.67524	−	2.10068i
$787$	−5.41214e6	−	2.60635e6i	−0.311482	−	0.150002i	0.271612	−	0.962407i	$-0.412443\pi$
$787$	−5.41214e6	−	2.60635e6i	−0.311482	−	0.150002i	−0.583093	+	0.812405i	$0.698158\pi$
$788$	8.15461e6	−	1.02256e7i	0.467830	−	0.586640i
$789$	5.02224e6	+	2.20039e7i	0.287213	+	1.25836i
$790$	1.65217e7	−	7.95643e6i	0.941861	−	0.453577i
$791$	−5.48090e6	+	2.63946e6i	−0.311466	+	0.149994i
$792$	−3.95105e6	−	4.95447e6i	−0.223821	−	0.280662i
$793$	6.18525e6	+	2.70994e7i	0.349281	+	1.53030i
$794$	−2.32971e6	+	1.02071e7i	−0.131145	+	0.574583i
$795$	−1.49483e7	−	1.87446e7i	−0.838830	−	1.05186i
$796$	1.59823e7	+	2.00411e7i	0.894038	+	1.12109i
$797$	−2.70610e6	+	1.18562e7i	−0.150903	+	0.661150i	0.841720	+	0.539914i	$0.181543\pi$
$797$	−2.70610e6	+	1.18562e7i	−0.150903	+	0.661150i	−0.992624	+	0.121237i	$0.961314\pi$
$798$	3.08193e6	+	1.35028e7i	0.171323	+	0.750614i
$799$	1.17039e7	+	1.46762e7i	0.648578	+	0.813291i
$800$	6.12171e6	−	2.94806e6i	0.338180	−	0.162859i
$801$	1.12240e7	−	5.40518e6i	0.618109	−	0.297665i
$802$	−8.14092e6	−	3.56677e7i	−0.446928	−	1.95812i
$803$	−5.93646e6	+	7.44409e6i	−0.324892	+	0.407401i
$804$	6.50224e7	+	3.13131e7i	3.54750	+	1.70839i
$805$	−8.12102e6	+	1.01834e7i	−0.441693	+	0.553866i
$806$	2.08787e6	−	9.14758e6i	0.113205	−	0.495985i
$807$	−3.96799e7	+	1.91088e7i	−2.14480	+	1.03288i
$808$	1.07569e6	−	4.71292e6i	0.0579642	−	0.253958i
$809$	3.11369e7	+	1.49947e7i	1.67265	+	0.805504i	0.997711	+	0.0676277i	$0.0215430\pi$
$809$	3.11369e7	+	1.49947e7i	1.67265	+	0.805504i	0.674936	+	0.737876i	$0.264171\pi$
$810$	1.78638e6			0.0956667
$811$	−3.09161e7			−1.65056			−0.825282	−	0.564720i	$-0.808984\pi$
$811$	−3.09161e7			−1.65056			−0.825282	+	0.564720i	$0.808984\pi$
$812$	−2.12568e6	−	1.02367e6i	−0.113138	−	0.0544842i
$813$	−6.24843e6	−	2.73762e7i	−0.331547	−	1.45260i
$814$	1.41731e7	+	1.77726e7i	0.749730	+	0.940132i
$815$	4.26751e6	−	5.35129e6i	0.225051	−	0.282205i
$816$	1.35170e7			0.710650
$817$	1.34844e7	+	3.48691e6i	0.706768	+	0.182762i
$818$	7.82078e6			0.408664
$819$	−1.06602e7	+	1.33675e7i	−0.555337	+	0.696371i
$820$	−2.05716e7	−	2.57960e7i	−1.06840	−	1.33973i
$821$	5.83941e6	+	2.55841e7i	0.302351	+	1.32468i	0.866568	+	0.499058i	$0.166321\pi$
$821$	5.83941e6	+	2.55841e7i	0.302351	+	1.32468i	−0.564218	+	0.825626i	$0.690822\pi$
$822$	3.52949e7	+	1.69971e7i	1.82193	+	0.877396i
$823$	2.05269e7			1.05639			0.528194	−	0.849124i	$-0.322870\pi$
$823$	2.05269e7			1.05639			0.528194	+	0.849124i	$0.322870\pi$
$824$	−4.02111e6			−0.206314
$825$	3.62025e6	+	1.74342e6i	0.185184	+	0.0891798i
$826$	535497.	−	2.34616e6i	0.0273091	−	0.119649i
$827$	1.74431e6	−	840017.i	0.0886872	−	0.0427095i	−0.389014	−	0.921232i	$-0.627184\pi$
$827$	1.74431e6	−	840017.i	0.0886872	−	0.0427095i	0.477701	+	0.878522i	$0.341470\pi$
$828$	−1.77186e7	+	7.76305e7i	−0.898162	+	3.93510i
$829$	2.06463e7	−	2.58897e7i	1.04341	−	1.30840i	0.0935904	−	0.995611i	$-0.470166\pi$
$829$	2.06463e7	−	2.58897e7i	1.04341	−	1.30840i	0.949823	−	0.312788i	$-0.101263\pi$
$830$	1.64040e7	+	7.89977e6i	0.826524	+	0.398033i
$831$	−2.48502e7	+	3.11612e7i	−1.24833	+	1.56535i
$832$	8.72065e6	+	3.82077e7i	0.436758	+	1.91356i
$833$	−1.12255e7	+	5.40589e6i	−0.560520	+	0.269932i
$834$	−5.72374e7	+	2.75641e7i	−2.84947	+	1.37223i
$835$	4.39981e6	+	5.51719e6i	0.218383	+	0.273843i
$836$	2.01747e6	+	8.83911e6i	0.0998369	+	0.437414i
$837$	−1.08500e6	+	4.75371e6i	−0.0535325	+	0.234541i
$838$	−2.93615e7	−	3.68182e7i	−1.44434	−	1.81114i
$839$	3.76848e6	+	4.72552e6i	0.184825	+	0.231763i	0.865608	−	0.500721i	$-0.166932\pi$
$839$	3.76848e6	+	4.72552e6i	0.184825	+	0.231763i	−0.680783	+	0.732485i	$0.738360\pi$
$840$	−1.30546e6	+	5.71960e6i	−0.0638360	+	0.279684i
$841$	4.34133e6	+	1.90206e7i	0.211657	+	0.927331i
$842$	−1.46621e7	−	1.83856e7i	−0.712713	−	0.893714i
$843$	−5.02673e7	+	2.42075e7i	−2.43622	+	1.17322i
$844$	−1.50657e7	+	7.25525e6i	−0.728003	+	0.350588i
$845$	−2.76493e6	−	1.21139e7i	−0.133211	−	0.583638i
$846$	4.26537e7	−	5.34860e7i	2.04895	−	2.56930i
$847$	−6.34478e6	−	3.05548e6i	−0.303884	−	0.146343i
$848$	7.42303e6	−	9.30818e6i	0.354480	−	0.444504i
$849$	−3.98073e6	+	1.74407e7i	−0.189537	+	0.830415i
$850$	6.05938e6	−	2.91804e6i	0.287661	−	0.138530i
$851$	1.53843e7	−	6.74030e7i	0.728205	−	3.19048i
$852$	−1.32878e7	−	6.39907e6i	−0.627125	−	0.302008i
$853$	−1.27010e7			−0.597675			−0.298837	−	0.954304i	$-0.596599\pi$
$853$	−1.27010e7			−0.597675			−0.298837	+	0.954304i	$0.596599\pi$
$854$	−1.68184e7			−0.789115
$855$	1.89756e7	+	9.13818e6i	0.887730	+	0.427508i
$856$	1.21692e6	+	5.33166e6i	0.0567645	+	0.248701i
$857$	−3.24638e6	−	4.07083e6i	−0.150990	−	0.189335i	0.700584	−	0.713570i	$-0.252923\pi$
$857$	−3.24638e6	−	4.07083e6i	−0.150990	−	0.189335i	−0.851574	+	0.524235i	$0.824351\pi$
$858$	−2.00096e7	+	2.50912e7i	−0.927938	+	1.16360i
$859$	−1.78984e7			−0.827621			−0.413810	−	0.910363i	$-0.635802\pi$
$859$	−1.78984e7			−0.827621			−0.413810	+	0.910363i	$0.635802\pi$
$860$	1.86136e7	+	1.57368e7i	0.858192	+	0.725555i
$861$	2.29697e7			1.05596
$862$	−3.77511e7	+	4.73383e7i	−1.73046	+	2.16993i
$863$	−6.08178e6	−	7.62631e6i	−0.277974	−	0.348568i	0.623172	−	0.782085i	$-0.285844\pi$
$863$	−6.08178e6	−	7.62631e6i	−0.277974	−	0.348568i	−0.901145	+	0.433517i	$0.857272\pi$
$864$	−6.27539e6	−	2.74943e7i	−0.285994	−	1.25302i
$865$	−1.81730e7	−	8.75165e6i	−0.825821	−	0.397694i
$866$	−1.73425e7			−0.785809
$867$	−1.48202e7			−0.669588
$868$	2.90960e6	+	1.40119e6i	0.131079	+	0.0631245i
$869$	−1.85958e6	+	8.14735e6i	−0.0835344	+	0.365988i
$870$	−9.26870e6	+	4.46357e6i	−0.415165	+	0.199933i
$871$	1.20688e7	−	5.28768e7i	0.539037	−	2.36167i
$872$	6.60958e6	−	8.28815e6i	0.294363	−	0.369119i
$873$	−3.28326e7	−	1.58114e7i	−1.45804	−	0.702156i
$874$	3.02234e7	−	3.78990e7i	1.33834	−	1.67822i
$875$	−2.35660e6	−	1.03249e7i	−0.104056	−	0.455897i
$876$	4.85508e7	−	2.33808e7i	2.13765	−	1.02944i
$877$	−4.01279e6	+	1.93246e6i	−0.176176	+	0.0848419i	−0.519893	−	0.854231i	$-0.674028\pi$
$877$	−4.01279e6	+	1.93246e6i	−0.176176	+	0.0848419i	0.343717	+	0.939073i	$0.388314\pi$
$878$	2.91186e7	+	3.65136e7i	1.27478	+	1.59852i
$879$	−601129.	−	2.63372e6i	−0.0262419	−	0.114973i
$880$	1.17378e6	−	5.14265e6i	0.0510950	−	0.223862i
$881$	1.37776e7	+	1.72765e7i	0.598044	+	0.749923i	0.985072	−	0.172145i	$-0.0550698\pi$
$881$	1.37776e7	+	1.72765e7i	0.598044	+	0.749923i	−0.387028	+	0.922068i	$0.626498\pi$
$882$	2.83107e7	+	3.55005e7i	1.22540	+	1.53661i
$883$	8.00348e6	−	3.50655e7i	0.345444	−	1.51349i	−0.441952	−	0.897039i	$-0.645714\pi$
$883$	8.00348e6	−	3.50655e7i	0.345444	−	1.51349i	0.787395	−	0.616449i	$-0.211429\pi$
$884$	6.79925e6	+	2.97895e7i	0.292638	+	1.28213i
$885$	−3.72159e6	−	4.66673e6i	−0.159724	−	0.200288i
$886$	−5.89336e6	+	2.83809e6i	−0.252220	+	0.121463i
$887$	−2.72701e6	+	1.31326e6i	−0.116380	+	0.0560455i	−0.491168	−	0.871065i	$-0.663430\pi$
$887$	−2.72701e6	+	1.31326e6i	−0.116380	+	0.0560455i	0.374788	+	0.927111i	$0.377716\pi$
$888$	−6.92931e6	−	3.03593e7i	−0.294888	−	1.29199i
$889$	3.10694e6	−	3.89598e6i	0.131850	−	0.165334i
$890$	−1.19577e7	−	5.75853e6i	−0.506026	−	0.243689i
$891$	−507577.	+	636481.i	−0.0214194	+	0.0268591i
$892$	−9.69222e6	+	4.24644e7i	−0.407860	+	1.78695i
$893$	−2.13444e7	+	1.02789e7i	−0.895683	+	0.431338i
$894$	−1.02203e6	+	4.47780e6i	−0.0427680	+	0.187379i
$895$	−6.32554e6	−	3.04622e6i	−0.263961	−	0.127117i
$896$	−9.55524e6			−0.397623
$897$	9.76064e7			4.05039
$898$	4.86981e7	+	2.34518e7i	2.01521	+	0.970476i
$899$	305003.	+	1.33631e6i	0.0125865	+	0.0551451i
$900$	−8.69294e6	−	1.09006e7i	−0.357734	−	0.448584i
$901$	1.14020e7	−	1.42977e7i	0.467917	−	0.586750i
$902$	2.64330e7			1.08176
$903$	−1.66447e7	+	3.30052e6i	−0.679291	+	0.134699i
$904$	9.58995e6			0.390297
$905$	−2.09380e7	+	2.62554e7i	−0.849794	+	1.06561i
$906$	−5.01252e6	−	6.28550e6i	−0.202878	−	0.254401i
$907$	−706390.	−	3.09490e6i	−0.0285119	−	0.124919i	0.958669	−	0.284523i	$-0.0918353\pi$
$907$	−706390.	−	3.09490e6i	−0.0285119	−	0.124919i	−0.987181	+	0.159604i	$0.948978\pi$
$908$	3.26387e7	+	1.57179e7i	1.31376	+	0.632676i
$909$	2.11433e7			0.848717
$910$	1.82154e7			0.729181
$911$	8.76904e6	+	4.22295e6i	0.350071	+	0.168585i	0.600652	−	0.799510i	$-0.294908\pi$
$911$	8.76904e6	+	4.22295e6i	0.350071	+	0.168585i	−0.250582	+	0.968095i	$0.580622\pi$
$912$	−3.79599e6	+	1.66313e7i	−0.151126	+	0.662125i
$913$	−7.47567e6	+	3.60009e6i	−0.296806	+	0.142934i
$914$	1.59455e6	−	6.98616e6i	0.0631352	−	0.276613i
$915$	−2.60093e7	+	3.26146e7i	−1.02701	+	1.28783i
$916$	−3.00907e7	−	1.44909e7i	−1.18493	−	0.570634i
$917$	7.50522e6	−	9.41125e6i	0.294741	−	0.369593i
$918$	−6.21149e6	−	2.72143e7i	−0.243270	−	1.06584i
$919$	1.65318e7	−	7.96131e6i	0.645702	−	0.310954i	−0.0822193	−	0.996614i	$-0.526201\pi$
$919$	1.65318e7	−	7.96131e6i	0.645702	−	0.310954i	0.727922	+	0.685660i	$0.240487\pi$
$920$	1.84997e7	−	8.90900e6i	0.720603	−	0.347024i
$921$	−12164.5	−	15253.9i	−0.000472549	−	0.000592557i
$922$	1.32752e7	+	5.81625e7i	0.514297	+	2.25328i
$923$	−2.46635e6	+	1.08058e7i	−0.0952905	+	0.417495i
$924$	−6.88696e6	−	8.63597e6i	−0.265367	−	0.332760i
$925$	7.54769e6	+	9.46450e6i	0.290041	+	0.363700i
$926$	1.61700e7	−	7.08454e7i	0.619702	−	2.71509i
$927$	−3.91357e6	−	1.71465e7i	−0.149580	−	0.655353i
$928$	−4.94280e6	−	6.19807e6i	−0.188410	−	0.236258i
$929$	2.11597e7	−	1.01900e7i	0.804397	−	0.387377i	0.0139460	−	0.999903i	$-0.495561\pi$
$929$	2.11597e7	−	1.01900e7i	0.804397	−	0.387377i	0.790451	+	0.612526i	$0.209846\pi$
$930$	1.26869e7	−	6.10968e6i	0.481003	−	0.231639i
$931$	−3.49896e6	−	1.53299e7i	−0.132301	−	0.579650i
$932$	−3.37336e7	+	4.23006e7i	−1.27211	+	1.59517i
$933$	−5.94113e7	−	2.86110e7i	−2.23442	−	1.07604i
$934$	1.01973e7	−	1.27870e7i	0.382488	−	0.479624i
$935$	1.80296e6	−	7.89927e6i	0.0674460	−	0.295500i
$936$	2.42841e7	−	1.16946e7i	0.906007	−	0.436310i
$937$	−742385.	+	3.25260e6i	−0.0276236	+	0.121027i	−0.986860	−	0.161578i	$-0.948342\pi$
$937$	−742385.	+	3.25260e6i	−0.0276236	+	0.121027i	0.959236	+	0.282605i	$0.0911987\pi$
$938$	2.95666e7	+	1.42385e7i	1.09722	+	0.528393i
$939$	7.31706e7			2.70815
$940$	−4.14592e7			−1.53039
$941$	−9.06022e6	−	4.36317e6i	−0.333553	−	0.160631i	0.259609	−	0.965714i	$-0.416406\pi$
$941$	−9.06022e6	−	4.36317e6i	−0.333553	−	0.160631i	−0.593162	+	0.805083i	$0.702121\pi$
$942$	−2.27845e7	−	9.98256e7i	−0.836590	−	3.66534i
$943$	−5.01241e7	−	6.28536e7i	−1.83555	−	2.30171i
$944$	1.84807e6	−	2.31741e6i	0.0674976	−	0.0846393i
$945$	−9.46598e6			−0.344815
$946$	−1.91543e7	+	3.79817e6i	−0.695888	+	0.137990i
$947$	7.55642e6			0.273805			0.136902	−	0.990585i	$-0.456285\pi$
$947$	7.55642e6			0.273805			0.136902	+	0.990585i	$0.456285\pi$
$948$	2.94891e7	−	3.69782e7i	1.06571	−	1.33636i
$949$	−2.52497e7	−	3.16621e7i	−0.910102	−	1.14123i
$950$	1.88870e6	+	8.27493e6i	0.0678975	+	0.297478i
$951$	−1.07504e6	−	517713.i	−0.0385456	−	0.0185626i
$952$	−4.47489e6			−0.160026
$953$	−5.09970e7			−1.81891			−0.909457	−	0.415798i	$-0.863502\pi$
$953$	−5.09970e7			−1.81891			−0.909457	+	0.415798i	$0.863502\pi$
$954$	−6.00466e7	−	2.89169e7i	−2.13608	−	1.02868i
$955$	−6.65264e6	+	2.91471e7i	−0.236040	+	1.03416i
$956$	−1.67539e7	+	8.06826e6i	−0.592887	+	0.285519i
$957$	1.04323e6	−	4.57068e6i	0.0368213	−	0.161325i
$958$	5.21409e6	−	6.53827e6i	0.183554	−	0.230170i
$959$	9.12939e6	+	4.39648e6i	0.320550	+	0.154369i
$960$	−3.66707e7	+	4.59836e7i	−1.28423	+	1.61037i
$961$	5.95310e6	+	2.60822e7i	0.207938	+	0.911038i
$962$	−8.71113e7	+	4.19506e7i	−3.03485	+	1.46150i
$963$	−2.15504e7	+	1.03781e7i	−0.748841	+	0.360623i
$964$	−3.46348e7	−	4.34306e7i	−1.20038	−	1.50523i
$965$	2.90914e6	+	1.27458e7i	0.100565	+	0.440604i
$966$	−1.31416e7	+	5.75770e7i	−0.453111	+	1.98521i
$967$	1.01749e7	+	1.27589e7i	0.349916	+	0.438781i	0.925377	−	0.379049i	$-0.123749\pi$
$967$	1.01749e7	+	1.27589e7i	0.349916	+	0.438781i	−0.575461	+	0.817829i	$0.695177\pi$
$968$	6.92166e6	+	8.67949e6i	0.237423	+	0.297719i
$969$	−5.83077e6	+	2.55463e7i	−0.199488	+	0.874013i
$970$	8.63910e6	+	3.78504e7i	0.294808	+	1.29164i
$971$	2.14406e7	+	2.68857e7i	0.729776	+	0.915110i	0.998847	−	0.0480100i	$-0.0152879\pi$
$971$	2.14406e7	+	2.68857e7i	0.729776	+	0.915110i	−0.269071	+	0.963120i	$0.586717\pi$
$972$	3.70550e7	−	1.78448e7i	1.25800	−	0.605822i
$973$	−1.48050e7	+	7.12973e6i	−0.501334	+	0.241430i
$974$	8.29690e6	+	3.63511e7i	0.280232	+	1.22778i
$975$	−1.06558e7	+	1.33619e7i	−0.358983	+	0.450150i
$976$	−1.86637e7	−	8.98796e6i	−0.627152	−	0.302021i
$977$	−1.81835e7	+	2.28013e7i	−0.609453	+	0.764230i	−0.986818	−	0.161835i	$-0.948259\pi$
$977$	−1.81835e7	+	2.28013e7i	−0.609453	+	0.764230i	0.377365	+	0.926065i	$0.376830\pi$
$978$	6.90575e6	−	3.02561e7i	0.230868	−	1.01150i
$979$	5.44938e6	−	2.62428e6i	0.181715	−	0.0875093i
$980$	6.12330e6	−	2.68280e7i	0.203667	−	0.892323i
$981$	4.17744e7	+	2.01175e7i	1.38592	+	0.667423i
$982$	2.90841e7			0.962447
$983$	−5.11735e7			−1.68912			−0.844561	−	0.535459i	$-0.820139\pi$
$983$	−5.11735e7			−1.68912			−0.844561	+	0.535459i	$0.820139\pi$
$984$	−3.26241e7	−	1.57109e7i	−1.07412	−	0.517267i
$985$	−3.28244e6	−	1.43813e7i	−0.107797	−	0.472289i
$986$	−4.89247e6	−	6.13496e6i	−0.160264	−	0.200965i
$987$	1.79955e7	−	2.25657e7i	0.587993	−	0.737320i
$988$	−3.85624e7			−1.25681
$989$	4.53532e7	+	3.83437e7i	1.47441	+	1.24653i
$990$	−2.95285e7			−0.957532
$991$	1.43649e7	−	1.80130e7i	0.464641	−	0.582642i	−0.493209	−	0.869911i	$-0.664176\pi$
$991$	1.43649e7	−	1.80130e7i	0.464641	−	0.582642i	0.957850	+	0.287269i	$0.0927475\pi$
$992$	6.76564e6	+	8.48384e6i	0.218288	+	0.273724i
$993$	7.07084e6	+	3.09794e7i	0.227561	+	0.997010i
$994$	−6.04215e6	−	2.90974e6i	−0.193966	−	0.0934090i
$995$	2.89108e7			0.925770
$996$	4.69600e7			1.49996
$997$	1.51314e7	+	7.28692e6i	0.482106	+	0.232170i	0.659119	−	0.752038i	$-0.270929\pi$
$997$	1.51314e7	+	7.28692e6i	0.482106	+	0.232170i	−0.177013	+	0.984208i	$0.556644\pi$
$998$	4.28818e6	−	1.87878e7i	0.136285	−	0.597102i
$999$	4.52690e7	−	2.18004e7i	1.43512	−	0.691116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.e.a.4.3	✓	108
43.11	even	7	inner	43.6.e.a.11.3	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.e.a.4.3	✓	108	1.1	even	1	trivial
43.6.e.a.11.3	yes	108	43.11	even	7	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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.e (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.37139 + 6.73550i) q^{2} +(15.6252 + 19.5934i) q^{3} +(-9.39457 - 41.1603i) q^{4} +(-42.9010 - 20.6600i) q^{5} -215.900 q^{6} -55.8448 q^{7} +(79.3171 + 38.1971i) q^{8} +(-85.6808 + 375.392i) q^{9} +O(q^{10})\)	\(q+(-5.37139 + 6.73550i) q^{2} +(15.6252 + 19.5934i) q^{3} +(-9.39457 - 41.1603i) q^{4} +(-42.9010 - 20.6600i) q^{5} -215.900 q^{6} -55.8448 q^{7} +(79.3171 + 38.1971i) q^{8} +(-85.6808 + 375.392i) q^{9} +(369.594 - 177.987i) q^{10} +(-41.5992 + 182.258i) q^{11} +(659.677 - 827.208i) q^{12} +(-716.393 - 344.997i) q^{13} +(299.964 - 376.143i) q^{14} +(-265.537 - 1163.39i) q^{15} +(533.891 - 257.108i) q^{16} +(820.073 - 394.926i) q^{17} +(-2068.23 - 2593.48i) q^{18} +(255.615 + 1119.92i) q^{19} +(-447.337 + 1959.91i) q^{20} +(-872.585 - 1094.19i) q^{21} +(-1004.15 - 1259.17i) q^{22} +(-1089.96 + 4775.44i) q^{23} +(490.935 + 2150.93i) q^{24} +(-534.747 - 670.551i) q^{25} +(6171.75 - 2972.16i) q^{26} +(-3207.27 + 1544.54i) q^{27} +(524.638 + 2298.59i) q^{28} +(-623.919 + 782.370i) q^{29} +(9262.33 + 4460.50i) q^{30} +(854.013 - 1070.90i) q^{31} +(-1762.85 + 7723.55i) q^{32} +(-4221.04 + 2032.75i) q^{33} +(-1744.90 + 7644.91i) q^{34} +(2395.80 + 1153.76i) q^{35} +16256.2 q^{36} -14114.5 q^{37} +(-8916.26 - 4293.85i) q^{38} +(-4434.13 - 19427.2i) q^{39} +(-2613.63 - 3277.39i) q^{40} +(-10233.1 + 12831.8i) q^{41} +12056.9 q^{42} +(5571.44 - 10768.8i) q^{43} +7892.59 q^{44} +(11431.4 - 14334.5i) q^{45} +(-26310.4 - 32992.2i) q^{46} +(4589.11 + 20106.2i) q^{47} +(13379.8 + 6443.35i) q^{48} -13688.4 q^{49} +7388.83 q^{50} +(20551.7 + 9897.19i) q^{51} +(-7469.96 + 32728.0i) q^{52} +(18101.7 - 8717.31i) q^{53} +(6824.22 - 29898.9i) q^{54} +(5550.10 - 6959.60i) q^{55} +(-4429.45 - 2133.11i) q^{56} +(-17949.0 + 22507.4i) q^{57} +(-1918.34 - 8404.82i) q^{58} +(4506.67 - 2170.30i) q^{59} +(-45390.9 + 21859.1i) q^{60} +(-21795.9 - 27331.2i) q^{61} +(2625.81 + 11504.4i) q^{62} +(4784.83 - 20963.7i) q^{63} +(-30730.2 - 38534.5i) q^{64} +(23606.3 + 29601.4i) q^{65} +(8981.26 - 39349.5i) q^{66} +(15178.3 + 66500.3i) q^{67} +(-23959.5 - 30044.3i) q^{68} +(-110598. + 53261.1i) q^{69} +(-20639.9 + 9939.64i) q^{70} +(-3101.79 - 13589.8i) q^{71} +(-21134.9 + 26502.3i) q^{72} +(45887.5 + 22098.3i) q^{73} +(75814.5 - 95068.4i) q^{74} +(4782.83 - 20955.0i) q^{75} +(43695.0 - 21042.4i) q^{76} +(2323.10 - 10178.2i) q^{77} +(154669. + 74484.8i) q^{78} +44702.3 q^{79} -28216.3 q^{80} +(3923.45 + 1889.44i) q^{81} +(-31463.3 - 137850. i) q^{82} +(27673.0 + 34700.8i) q^{83} +(-36839.5 + 46195.3i) q^{84} -43341.2 q^{85} +(42607.1 + 95369.9i) q^{86} -25078.1 q^{87} +(-10261.3 + 12867.2i) q^{88} +(-20172.2 - 25295.1i) q^{89} +(35147.8 + 153993. i) q^{90} +(40006.8 + 19266.3i) q^{91} +206798. q^{92} +34326.6 q^{93} +(-160075. - 77088.1i) q^{94} +(12171.5 - 53326.9i) q^{95} +(-178875. + 86141.8i) q^{96} +(-21059.8 + 92269.0i) q^{97} +(73525.5 - 92198.0i) q^{98} +(-64853.9 - 31232.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9}+O(q^{10}) \) 108 * q - 3 * q^2 - 9 * q^3 - 331 * q^4 + 67 * q^5 - 20 * q^6 - 624 * q^7 + 589 * q^8 - 579 * q^9	\( 108 q - 3 q^{2} - 9 q^{3} - 331 q^{4} + 67 q^{5} - 20 q^{6} - 624 q^{7} + 589 q^{8} - 579 q^{9} + 627 q^{10} - 220 q^{11} - 663 q^{12} - 1266 q^{13} + 2353 q^{14} + 1471 q^{15} - 4583 q^{16} - 1490 q^{17} + 4728 q^{18} + 946 q^{19} + 14589 q^{20} + 776 q^{21} + 963 q^{22} - 3018 q^{23} - 17761 q^{24} - 11939 q^{25} + 1315 q^{26} + 11277 q^{27} - 10787 q^{28} + 7283 q^{29} - 55324 q^{30} + 18676 q^{31} - 10965 q^{32} + 8776 q^{33} + 23815 q^{34} - 13340 q^{35} + 136240 q^{36} + 4994 q^{37} + 39351 q^{38} - 21251 q^{39} + 14719 q^{40} - 10519 q^{41} - 199326 q^{42} + 7026 q^{43} - 180280 q^{44} + 65996 q^{45} - 5266 q^{46} + 34102 q^{47} + 69385 q^{48} + 232252 q^{49} + 17850 q^{50} + 4116 q^{51} + 32385 q^{52} + 46774 q^{53} - 30267 q^{54} + 83643 q^{55} - 231565 q^{56} + 79511 q^{57} - 222889 q^{58} - 142070 q^{59} + 42019 q^{60} + 4715 q^{61} - 150121 q^{62} - 53547 q^{63} + 163605 q^{64} - 106653 q^{65} - 56111 q^{66} + 370962 q^{67} - 579312 q^{68} - 245635 q^{69} - 91242 q^{70} + 16922 q^{71} + 586300 q^{72} + 97842 q^{73} + 535946 q^{74} + 245407 q^{75} + 942280 q^{76} + 43381 q^{77} + 173684 q^{78} + 187210 q^{79} - 752974 q^{80} - 791814 q^{81} + 387227 q^{82} - 444471 q^{83} - 688442 q^{84} + 255432 q^{85} - 244075 q^{86} - 1418850 q^{87} + 196837 q^{88} + 408972 q^{89} - 495568 q^{90} - 25764 q^{91} + 200120 q^{92} + 692536 q^{93} + 161449 q^{94} + 406105 q^{95} + 1096556 q^{96} + 266261 q^{97} + 527485 q^{98} + 212416 q^{99}+O(q^{100}) \) 108 * q - 3 * q^2 - 9 * q^3 - 331 * q^4 + 67 * q^5 - 20 * q^6 - 624 * q^7 + 589 * q^8 - 579 * q^9 + 627 * q^10 - 220 * q^11 - 663 * q^12 - 1266 * q^13 + 2353 * q^14 + 1471 * q^15 - 4583 * q^16 - 1490 * q^17 + 4728 * q^18 + 946 * q^19 + 14589 * q^20 + 776 * q^21 + 963 * q^22 - 3018 * q^23 - 17761 * q^24 - 11939 * q^25 + 1315 * q^26 + 11277 * q^27 - 10787 * q^28 + 7283 * q^29 - 55324 * q^30 + 18676 * q^31 - 10965 * q^32 + 8776 * q^33 + 23815 * q^34 - 13340 * q^35 + 136240 * q^36 + 4994 * q^37 + 39351 * q^38 - 21251 * q^39 + 14719 * q^40 - 10519 * q^41 - 199326 * q^42 + 7026 * q^43 - 180280 * q^44 + 65996 * q^45 - 5266 * q^46 + 34102 * q^47 + 69385 * q^48 + 232252 * q^49 + 17850 * q^50 + 4116 * q^51 + 32385 * q^52 + 46774 * q^53 - 30267 * q^54 + 83643 * q^55 - 231565 * q^56 + 79511 * q^57 - 222889 * q^58 - 142070 * q^59 + 42019 * q^60 + 4715 * q^61 - 150121 * q^62 - 53547 * q^63 + 163605 * q^64 - 106653 * q^65 - 56111 * q^66 + 370962 * q^67 - 579312 * q^68 - 245635 * q^69 - 91242 * q^70 + 16922 * q^71 + 586300 * q^72 + 97842 * q^73 + 535946 * q^74 + 245407 * q^75 + 942280 * q^76 + 43381 * q^77 + 173684 * q^78 + 187210 * q^79 - 752974 * q^80 - 791814 * q^81 + 387227 * q^82 - 444471 * q^83 - 688442 * q^84 + 255432 * q^85 - 244075 * q^86 - 1418850 * q^87 + 196837 * q^88 + 408972 * q^89 - 495568 * q^90 - 25764 * q^91 + 200120 * q^92 + 692536 * q^93 + 161449 * q^94 + 406105 * q^95 + 1096556 * q^96 + 266261 * q^97 + 527485 * q^98 + 212416 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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