LMFDB - Embedded newform 74.4.f.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,4,Mod(7,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("74.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	74.f (of order $9$, 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:	$4.36614134042$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	74.7
Dual form			74.4.f.b.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.87939 + 0.684040i) q^{2} +(-1.99226 - 0.725122i) q^{3} +(3.06418 - 2.57115i) q^{4} +(1.44178 + 8.17673i) q^{5} +4.24023 q^{6} +(-1.26639 - 7.18203i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-17.2399 - 14.4660i) q^{9} +O(q^{10})$	\(q+(-1.87939 + 0.684040i) q^{2} +(-1.99226 - 0.725122i) q^{3} +(3.06418 - 2.57115i) q^{4} +(1.44178 + 8.17673i) q^{5} +4.24023 q^{6} +(-1.26639 - 7.18203i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-17.2399 - 14.4660i) q^{9} +(-8.30287 - 14.3810i) q^{10} +(-32.0217 + 55.4632i) q^{11} +(-7.96903 + 2.90049i) q^{12} +(-38.7809 + 32.5410i) q^{13} +(7.29283 + 12.6315i) q^{14} +(3.05674 - 17.3356i) q^{15} +(2.77837 - 15.7569i) q^{16} +(-75.3459 - 63.2227i) q^{17} +(42.2958 + 15.3944i) q^{18} +(-93.0044 - 33.8508i) q^{19} +(25.4415 + 21.3479i) q^{20} +(-2.68488 + 15.2267i) q^{21} +(22.2420 - 126.141i) q^{22} +(92.9105 + 160.926i) q^{23} +(12.9928 - 10.9023i) q^{24} +(52.6814 - 19.1745i) q^{25} +(50.6249 - 87.6849i) q^{26} +(52.4783 + 90.8950i) q^{27} +(-22.3465 - 18.7510i) q^{28} +(16.8768 - 29.2315i) q^{29} +(6.11347 + 34.6712i) q^{30} +120.154 q^{31} +(5.55674 + 31.5138i) q^{32} +(104.013 - 87.2773i) q^{33} +(184.851 + 67.2802i) q^{34} +(56.8997 - 20.7098i) q^{35} -90.0204 q^{36} +(-196.807 + 109.179i) q^{37} +197.946 q^{38} +(100.858 - 36.7092i) q^{39} +(-62.4172 - 22.7180i) q^{40} +(249.864 - 209.661i) q^{41} +(-5.36977 - 30.4535i) q^{42} -434.268 q^{43} +(44.4841 + 252.282i) q^{44} +(93.4285 - 161.823i) q^{45} +(-284.694 - 238.887i) q^{46} +(-29.1937 - 50.5649i) q^{47} +(-16.9609 + 29.3772i) q^{48} +(272.337 - 99.1225i) q^{49} +(-85.8925 + 72.0724i) q^{50} +(104.264 + 180.591i) q^{51} +(-35.1637 + 199.423i) q^{52} +(-9.57467 + 54.3006i) q^{53} +(-160.803 - 134.930i) q^{54} +(-499.676 - 181.867i) q^{55} +(54.8241 + 19.9544i) q^{56} +(160.743 + 134.879i) q^{57} +(-11.7225 + 66.4817i) q^{58} +(-121.163 + 687.149i) q^{59} +(-35.2061 - 60.9787i) q^{60} +(58.2716 - 48.8956i) q^{61} +(-225.815 + 82.1901i) q^{62} +(-82.0630 + 142.137i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(-321.993 - 270.184i) q^{65} +(-135.779 + 235.177i) q^{66} +(-114.897 - 651.612i) q^{67} -393.428 q^{68} +(-68.4108 - 387.977i) q^{69} +(-92.7701 + 77.8434i) q^{70} +(492.472 + 179.245i) q^{71} +(169.183 - 61.5776i) q^{72} -616.359 q^{73} +(295.194 - 339.813i) q^{74} -118.859 q^{75} +(-372.018 + 135.403i) q^{76} +(438.890 + 159.743i) q^{77} +(-164.440 + 137.982i) q^{78} +(82.0574 + 465.370i) q^{79} +132.846 q^{80} +(66.8750 + 379.267i) q^{81} +(-326.175 + 564.951i) q^{82} +(486.456 + 408.185i) q^{83} +(30.9233 + 53.5607i) q^{84} +(408.323 - 707.236i) q^{85} +(816.157 - 297.057i) q^{86} +(-54.8194 + 45.9989i) q^{87} +(-256.174 - 443.706i) q^{88} +(93.8600 - 532.306i) q^{89} +(-64.8948 + 368.036i) q^{90} +(282.823 + 237.316i) q^{91} +(698.459 + 254.218i) q^{92} +(-239.377 - 87.1262i) q^{93} +(89.4546 + 75.0613i) q^{94} +(142.697 - 809.277i) q^{95} +(11.7809 - 66.8130i) q^{96} +(5.20096 + 9.00833i) q^{97} +(-444.022 + 372.579i) q^{98} +(1354.38 - 492.955i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9}+O(q^{10}) $ 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9} + 54 q^{10} - 21 q^{11} + 24 q^{12} - 159 q^{13} + 6 q^{14} - 69 q^{15} - 171 q^{17} + 192 q^{18} - 45 q^{19} - 24 q^{20} + 579 q^{21} + 42 q^{22} + 459 q^{23} + 48 q^{24} - 204 q^{25} + 264 q^{26} + 435 q^{27} + 96 q^{28} + 273 q^{29} - 138 q^{30} - 258 q^{31} - 318 q^{33} - 558 q^{34} - 753 q^{35} + 1296 q^{36} - 891 q^{37} - 2556 q^{38} - 504 q^{39} + 96 q^{40} + 648 q^{41} + 1158 q^{42} - 216 q^{43} + 84 q^{44} + 1731 q^{45} - 6 q^{46} + 48 q^{47} + 144 q^{48} + 1731 q^{49} + 240 q^{50} + 972 q^{51} + 48 q^{52} - 135 q^{53} + 360 q^{54} + 765 q^{55} + 408 q^{56} - 405 q^{57} - 762 q^{58} + 1836 q^{59} + 108 q^{60} - 684 q^{61} - 204 q^{62} - 3264 q^{63} - 960 q^{64} - 1350 q^{65} + 252 q^{66} + 1095 q^{67} - 432 q^{68} - 5823 q^{69} - 1146 q^{70} + 4179 q^{71} + 768 q^{72} - 2658 q^{73} - 1692 q^{74} - 10416 q^{75} - 180 q^{76} + 267 q^{77} + 1530 q^{78} + 4866 q^{79} - 864 q^{80} - 2076 q^{81} + 1800 q^{82} - 186 q^{83} + 504 q^{84} + 753 q^{85} + 648 q^{86} - 525 q^{87} - 168 q^{88} + 687 q^{89} + 768 q^{90} + 3990 q^{91} + 132 q^{92} + 3753 q^{93} + 6210 q^{94} + 9000 q^{95} - 384 q^{96} + 7428 q^{97} - 1542 q^{98} + 6324 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9 + 54 * q^10 - 21 * q^11 + 24 * q^12 - 159 * q^13 + 6 * q^14 - 69 * q^15 - 171 * q^17 + 192 * q^18 - 45 * q^19 - 24 * q^20 + 579 * q^21 + 42 * q^22 + 459 * q^23 + 48 * q^24 - 204 * q^25 + 264 * q^26 + 435 * q^27 + 96 * q^28 + 273 * q^29 - 138 * q^30 - 258 * q^31 - 318 * q^33 - 558 * q^34 - 753 * q^35 + 1296 * q^36 - 891 * q^37 - 2556 * q^38 - 504 * q^39 + 96 * q^40 + 648 * q^41 + 1158 * q^42 - 216 * q^43 + 84 * q^44 + 1731 * q^45 - 6 * q^46 + 48 * q^47 + 144 * q^48 + 1731 * q^49 + 240 * q^50 + 972 * q^51 + 48 * q^52 - 135 * q^53 + 360 * q^54 + 765 * q^55 + 408 * q^56 - 405 * q^57 - 762 * q^58 + 1836 * q^59 + 108 * q^60 - 684 * q^61 - 204 * q^62 - 3264 * q^63 - 960 * q^64 - 1350 * q^65 + 252 * q^66 + 1095 * q^67 - 432 * q^68 - 5823 * q^69 - 1146 * q^70 + 4179 * q^71 + 768 * q^72 - 2658 * q^73 - 1692 * q^74 - 10416 * q^75 - 180 * q^76 + 267 * q^77 + 1530 * q^78 + 4866 * q^79 - 864 * q^80 - 2076 * q^81 + 1800 * q^82 - 186 * q^83 + 504 * q^84 + 753 * q^85 + 648 * q^86 - 525 * q^87 - 168 * q^88 + 687 * q^89 + 768 * q^90 + 3990 * q^91 + 132 * q^92 + 3753 * q^93 + 6210 * q^94 + 9000 * q^95 - 384 * q^96 + 7428 * q^97 - 1542 * q^98 + 6324 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$39$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$2$	−1.87939	+	0.684040i	−0.664463	+	0.241845i
$3$	−1.99226	−	0.725122i	−0.383410	−	0.139550i	0.143122	−	0.989705i	$-0.454286\pi$
$3$	−1.99226	−	0.725122i	−0.383410	−	0.139550i	−0.526532	+	0.850155i	$0.676508\pi$
$4$	3.06418	−	2.57115i	0.383022	−	0.321394i
$5$	1.44178	+	8.17673i	0.128957	+	0.731349i	0.978879	+	0.204441i	$0.0655376\pi$
$5$	1.44178	+	8.17673i	0.128957	+	0.731349i	−0.849922	+	0.526908i	$0.823351\pi$
$6$	4.24023			0.288511
$7$	−1.26639	−	7.18203i	−0.0683784	−	0.387793i	−0.999720	−	0.0236475i	$-0.992472\pi$
$7$	−1.26639	−	7.18203i	−0.0683784	−	0.387793i	0.931342	−	0.364146i	$-0.118639\pi$
$8$	−4.00000	+	6.92820i	−0.176777	+	0.306186i
$9$	−17.2399	−	14.4660i	−0.638515	−	0.535778i
$10$	−8.30287	−	14.3810i	−0.262560	−	0.454767i
$11$	−32.0217	+	55.4632i	−0.877719	+	1.52025i	−0.0238806	+	0.999715i	$0.507602\pi$
$11$	−32.0217	+	55.4632i	−0.877719	+	1.52025i	−0.853838	+	0.520539i	$0.825731\pi$
$12$	−7.96903	+	2.90049i	−0.191705	+	0.0697749i
$13$	−38.7809	+	32.5410i	−0.827376	+	0.694251i	−0.954687	−	0.297612i	$-0.903810\pi$
$13$	−38.7809	+	32.5410i	−0.827376	+	0.694251i	0.127311	+	0.991863i	$0.459365\pi$
$14$	7.29283	+	12.6315i	0.139221	+	0.241137i
$15$	3.05674	−	17.3356i	0.0526164	−	0.298402i
$16$	2.77837	−	15.7569i	0.0434120	−	0.246202i
$17$	−75.3459	−	63.2227i	−1.07495	−	0.901986i	−0.0794537	−	0.996839i	$-0.525318\pi$
$17$	−75.3459	−	63.2227i	−1.07495	−	0.901986i	−0.995491	+	0.0948525i	$0.969762\pi$
$18$	42.2958	+	15.3944i	0.553845	+	0.201583i
$19$	−93.0044	−	33.8508i	−1.12298	−	0.408732i	−0.287243	−	0.957858i	$-0.592739\pi$
$19$	−93.0044	−	33.8508i	−1.12298	−	0.408732i	−0.835740	+	0.549126i	$0.814961\pi$
$20$	25.4415	+	21.3479i	0.284444	+	0.238677i
$21$	−2.68488	+	15.2267i	−0.0278995	+	0.158226i
$22$	22.2420	−	126.141i	0.215546	−	1.22242i
$23$	92.9105	+	160.926i	0.842312	+	1.45893i	0.887935	+	0.459969i	$0.152140\pi$
$23$	92.9105	+	160.926i	0.842312	+	1.45893i	−0.0456224	+	0.998959i	$0.514527\pi$
$24$	12.9928	−	10.9023i	0.110506	−	0.0927257i
$25$	52.6814	−	19.1745i	0.421451	−	0.153396i
$26$	50.6249	−	87.6849i	0.381860	−	0.661401i
$27$	52.4783	+	90.8950i	0.374054	+	0.647880i
$28$	−22.3465	−	18.7510i	−0.150825	−	0.126557i
$29$	16.8768	−	29.2315i	0.108067	−	0.187178i	−0.806920	−	0.590661i	$-0.798867\pi$
$29$	16.8768	−	29.2315i	0.108067	−	0.187178i	0.914987	+	0.403483i	$0.132201\pi$
$30$	6.11347	+	34.6712i	0.0372054	+	0.211002i
$31$	120.154			0.696138			0.348069	−	0.937469i	$-0.386838\pi$
$31$	120.154			0.696138			0.348069	+	0.937469i	$0.386838\pi$
$32$	5.55674	+	31.5138i	0.0306970	+	0.174091i
$33$	104.013	−	87.2773i	0.548677	−	0.460395i
$34$	184.851	+	67.2802i	0.932402	+	0.339367i
$35$	56.8997	−	20.7098i	0.274794	−	0.100017i
$36$	−90.0204			−0.416761
$37$	−196.807	+	109.179i	−0.874456	+	0.485104i
$37$	−196.807	+	109.179i	−0.874456	+	0.485104i
$38$	197.946			0.845030
$39$	100.858	−	36.7092i	0.414107	−	0.150723i
$40$	−62.4172	−	22.7180i	−0.246725	−	0.0898007i
$41$	249.864	−	209.661i	0.951763	−	0.798624i	−0.0278309	−	0.999613i	$-0.508860\pi$
$41$	249.864	−	209.661i	0.951763	−	0.798624i	0.979593	+	0.200989i	$0.0644156\pi$
$42$	−5.36977	−	30.4535i	−0.0197279	−	0.111883i
$43$	−434.268			−1.54012			−0.770062	−	0.637970i	$-0.779775\pi$
$43$	−434.268			−1.54012			−0.770062	+	0.637970i	$0.779775\pi$
$44$	44.4841	+	252.282i	0.152414	+	0.864384i
$45$	93.4285	−	161.823i	0.309500	−	0.536070i
$46$	−284.694	−	238.887i	−0.912520	−	0.765695i
$47$	−29.1937	−	50.5649i	−0.0906029	−	0.156929i	0.817162	−	0.576408i	$-0.195546\pi$
$47$	−29.1937	−	50.5649i	−0.0906029	−	0.156929i	−0.907765	+	0.419479i	$0.862213\pi$
$48$	−16.9609	+	29.3772i	−0.0510020	+	0.0883381i
$49$	272.337	−	99.1225i	0.793985	−	0.288987i
$50$	−85.8925	+	72.0724i	−0.242941	+	0.203852i
$51$	104.264	+	180.591i	0.286273	+	0.495839i
$52$	−35.1637	+	199.423i	−0.0937755	+	0.531827i
$53$	−9.57467	+	54.3006i	−0.0248147	+	0.140731i	−0.994698	−	0.102839i	$-0.967207\pi$
$53$	−9.57467	+	54.3006i	−0.0248147	+	0.140731i	0.969883	+	0.243570i	$0.0783186\pi$
$54$	−160.803	−	134.930i	−0.405231	−	0.340029i
$55$	−499.676	−	181.867i	−1.22502	−	0.445872i
$56$	54.8241	+	19.9544i	0.130825	+	0.0476163i
$57$	160.743	+	134.879i	0.373524	+	0.313424i
$58$	−11.7225	+	66.4817i	−0.0265386	+	0.150508i
$59$	−121.163	+	687.149i	−0.267357	+	1.51626i	0.494881	+	0.868961i	$0.335212\pi$
$59$	−121.163	+	687.149i	−0.267357	+	1.51626i	−0.762238	+	0.647297i	$0.775899\pi$
$60$	−35.2061	−	60.9787i	−0.0757514	−	0.131205i
$61$	58.2716	−	48.8956i	0.122310	−	0.102630i	−0.579581	−	0.814915i	$-0.696784\pi$
$61$	58.2716	−	48.8956i	0.122310	−	0.102630i	0.701891	+	0.712284i	$0.252339\pi$
$62$	−225.815	+	82.1901i	−0.462558	+	0.168357i
$63$	−82.0630	+	142.137i	−0.164110	+	0.284248i
$64$	−32.0000	−	55.4256i	−0.0625000	−	0.108253i
$65$	−321.993	−	270.184i	−0.614435	−	0.515572i
$66$	−135.779	+	235.177i	−0.253232	+	0.438610i
$67$	−114.897	−	651.612i	−0.209506	−	1.18817i	−0.890190	−	0.455589i	$-0.849429\pi$
$67$	−114.897	−	651.612i	−0.209506	−	1.18817i	0.680685	−	0.732577i	$-0.261682\pi$
$68$	−393.428			−0.701621
$69$	−68.4108	−	387.977i	−0.119358	−	0.676912i
$70$	−92.7701	+	77.8434i	−0.158402	+	0.132915i
$71$	492.472	+	179.245i	0.823179	+	0.299613i	0.719056	−	0.694952i	$-0.244574\pi$
$71$	492.472	+	179.245i	0.823179	+	0.299613i	0.104123	+	0.994564i	$0.466797\pi$
$72$	169.183	−	61.5776i	0.276922	−	0.100792i
$73$	−616.359			−0.988211			−0.494105	−	0.869402i	$-0.664504\pi$
$73$	−616.359			−0.988211			−0.494105	+	0.869402i	$0.664504\pi$
$74$	295.194	−	339.813i	0.463724	−	0.533817i
$75$	−118.859			−0.182995
$76$	−372.018	+	135.403i	−0.561491	+	0.204366i
$77$	438.890	+	159.743i	0.649561	+	0.236421i
$78$	−164.440	+	137.982i	−0.238707	+	0.200299i
$79$	82.0574	+	465.370i	0.116863	+	0.662763i	0.985811	+	0.167859i	$0.0536855\pi$
$79$	82.0574	+	465.370i	0.116863	+	0.662763i	−0.868948	+	0.494903i	$0.835203\pi$
$80$	132.846			0.185658
$81$	66.8750	+	379.267i	0.0917353	+	0.520257i
$82$	−326.175	+	564.951i	−0.439268	+	0.760835i
$83$	486.456	+	408.185i	0.643319	+	0.539809i	0.905036	−	0.425336i	$-0.139844\pi$
$83$	486.456	+	408.185i	0.643319	+	0.539809i	−0.261716	+	0.965145i	$0.584288\pi$
$84$	30.9233	+	53.5607i	0.0401667	+	0.0695708i
$85$	408.323	−	707.236i	0.521045	−	0.902477i
$86$	816.157	−	297.057i	1.02335	−	0.372471i
$87$	−54.8194	+	45.9989i	−0.0675546	+	0.0566851i
$88$	−256.174	−	443.706i	−0.310320	−	0.537491i
$89$	93.8600	−	532.306i	0.111788	−	0.633982i	−0.876502	−	0.481397i	$-0.840129\pi$
$89$	93.8600	−	532.306i	0.111788	−	0.633982i	0.988290	−	0.152584i	$-0.0487595\pi$
$90$	−64.8948	+	368.036i	−0.0760056	+	0.431049i
$91$	282.823	+	237.316i	0.325801	+	0.273379i
$92$	698.459	+	254.218i	0.791515	+	0.288088i
$93$	−239.377	−	87.1262i	−0.266906	−	0.0971459i
$94$	89.4546	+	75.0613i	0.0981547	+	0.0823616i
$95$	142.697	−	809.277i	0.154110	−	0.874001i
$96$	11.7809	−	66.8130i	0.0125249	−	0.0710320i
$97$	5.20096	+	9.00833i	0.00544410	+	0.00942946i	0.868735	−	0.495278i	$-0.164934\pi$
$97$	5.20096	+	9.00833i	0.00544410	+	0.00942946i	−0.863291	+	0.504707i	$0.831600\pi$
$98$	−444.022	+	372.579i	−0.457683	+	0.384042i
$99$	1354.38	−	492.955i	1.37496	−	0.500443i
$100$	112.125	−	194.206i	0.112125	−	0.194206i
$101$	−286.158	−	495.641i	−0.281919	−	0.488298i	0.689938	−	0.723868i	$-0.257638\pi$
$101$	−286.158	−	495.641i	−0.281919	−	0.488298i	−0.971857	+	0.235570i	$0.924304\pi$
$102$	−319.484	−	268.079i	−0.310134	−	0.260233i
$103$	−384.563	+	666.083i	−0.367885	+	0.637195i	−0.989235	−	0.146338i	$-0.953251\pi$
$103$	−384.563	+	666.083i	−0.367885	+	0.637195i	0.621350	+	0.783533i	$0.286585\pi$
$104$	−70.3274	−	398.846i	−0.0663093	−	0.376059i
$105$	−128.376			−0.119316
$106$	−19.1493	−	108.601i	−0.0175467	−	0.0995121i
$107$	−1054.91	+	885.177i	−0.953106	+	0.799751i	−0.979818	−	0.199892i	$-0.935941\pi$
$107$	−1054.91	+	885.177i	−0.953106	+	0.799751i	0.0267121	+	0.999643i	$0.491496\pi$
$108$	394.508	+	143.589i	0.351495	+	0.127934i
$109$	1490.56	−	542.519i	1.30981	−	0.476733i	0.409633	−	0.912250i	$-0.365657\pi$
$109$	1490.56	−	542.519i	1.30981	−	0.476733i	0.900180	+	0.435517i	$0.143434\pi$
$110$	1063.49			0.921815
$111$	471.258	−	74.8028i	0.402971	−	0.0639636i
$112$	−116.685			−0.0984439
$113$	−768.761	+	279.806i	−0.639991	+	0.232938i	−0.641574	−	0.767061i	$-0.721718\pi$
$113$	−768.761	+	279.806i	−0.639991	+	0.232938i	0.00158329	+	0.999999i	$0.499496\pi$
$114$	−394.360	−	143.535i	−0.323993	−	0.117924i
$115$	−1181.89	+	991.724i	−0.958364	+	0.804163i
$116$	−23.4450	−	132.963i	−0.0187657	−	0.106425i
$117$	1139.32			0.900257
$118$	−242.326	−	1374.30i	−0.189050	−	1.07216i
$119$	−358.651	+	621.201i	−0.276281	+	0.478533i
$120$	107.878	+	90.5201i	0.0820653	+	0.0688610i
$121$	−1385.28	−	2399.37i	−1.04078	−	1.80268i
$122$	−76.0681	+	131.754i	−0.0564499	+	0.0977740i
$123$	−649.824	+	236.517i	−0.476363	+	0.173382i
$124$	368.173	−	308.934i	0.266636	−	0.223734i
$125$	751.669	+	1301.93i	0.537850	+	0.931584i
$126$	57.0003	−	323.265i	0.0403015	−	0.228561i
$127$	−29.9274	+	169.727i	−0.0209105	+	0.118589i	−0.993476	−	0.114039i	$-0.963621\pi$
$127$	−29.9274	+	169.727i	−0.0209105	+	0.118589i	0.972566	+	0.232628i	$0.0747324\pi$
$128$	98.0537	+	82.2768i	0.0677094	+	0.0568149i
$129$	865.174	+	314.898i	0.590499	+	0.214924i
$130$	789.965	+	287.524i	0.532958	+	0.193981i
$131$	114.856	+	96.3754i	0.0766030	+	0.0642775i	0.680285	−	0.732948i	$-0.261856\pi$
$131$	114.856	+	96.3754i	0.0766030	+	0.0642775i	−0.603682	+	0.797225i	$0.706300\pi$
$132$	94.3114	−	534.866i	0.0621875	−	0.352683i
$133$	−125.338	+	710.829i	−0.0817159	+	0.463434i
$134$	661.664	+	1146.04i	0.426560	+	0.738824i
$135$	−667.562	+	560.151i	−0.425590	+	0.357112i
$136$	739.403	−	269.121i	0.466201	−	0.169683i
$137$	−398.760	+	690.673i	−0.248675	+	0.430717i	−0.963158	−	0.268935i	$-0.913328\pi$
$137$	−398.760	+	690.673i	−0.248675	+	0.430717i	0.714484	+	0.699652i	$0.246662\pi$
$138$	393.962	+	682.362i	0.243017	+	0.420917i
$139$	917.234	+	769.650i	0.559703	+	0.469647i	0.878211	−	0.478274i	$-0.158737\pi$
$139$	917.234	+	769.650i	0.559703	+	0.469647i	−0.318508	+	0.947920i	$0.603182\pi$
$140$	121.103	−	209.756i	0.0731075	−	0.126626i
$141$	21.4956	+	121.907i	0.0128387	+	0.0728117i
$142$	−1048.16			−0.619432
$143$	−563.000	−	3192.93i	−0.329234	−	1.86718i
$144$	−275.839	+	231.456i	−0.159629	+	0.133945i
$145$	263.351	+	95.8518i	0.150828	+	0.0548970i
$146$	1158.38	−	421.614i	0.656629	−	0.238994i
$147$	−614.440			−0.344750
$148$	−322.337	+	840.563i	−0.179027	+	0.466851i
$149$	−2349.01			−1.29153			−0.645765	−	0.763536i	$-0.723461\pi$
$149$	−2349.01			−1.29153			−0.645765	+	0.763536i	$0.723461\pi$
$150$	223.381	−	81.3041i	0.121593	−	0.0442564i
$151$	−1332.63	−	485.039i	−0.718200	−	0.261403i	−0.0430386	−	0.999073i	$-0.513704\pi$
$151$	−1332.63	−	485.039i	−0.718200	−	0.261403i	−0.675161	+	0.737670i	$0.735926\pi$
$152$	606.543	−	508.950i	0.323665	−	0.271587i
$153$	384.377	+	2179.91i	0.203105	+	1.15186i
$154$	−934.115			−0.488787
$155$	173.235	+	982.465i	0.0897715	+	0.509120i
$156$	214.661	−	371.804i	0.110171	−	0.190821i
$157$	−2243.91	−	1882.87i	−1.14066	−	0.957129i	−0.141202	−	0.989981i	$-0.545097\pi$
$157$	−2243.91	−	1882.87i	−1.14066	−	0.957129i	−0.999460	+	0.0328520i	$0.989541\pi$
$158$	−472.550	−	818.480i	−0.237937	−	0.412119i
$159$	58.4498	−	101.238i	0.0291533	−	0.0504949i
$160$	−249.669	+	90.8719i	−0.123363	+	0.0449004i
$161$	1038.11	−	871.081i	0.508167	−	0.426402i
$162$	−385.118	−	667.044i	−0.186776	−	0.323506i
$163$	−142.046	+	805.580i	−0.0682569	+	0.387104i	0.931472	+	0.363813i	$0.118525\pi$
$163$	−142.046	+	805.580i	−0.0682569	+	0.387104i	−0.999729	+	0.0232905i	$0.992586\pi$
$164$	226.559	−	1284.88i	0.107874	−	0.611781i
$165$	863.607	+	724.652i	0.407465	+	0.341904i
$166$	−1193.45	−	434.382i	−0.558012	−	0.203100i
$167$	389.511	+	141.770i	0.180487	+	0.0656918i	0.430683	−	0.902503i	$-0.358273\pi$
$167$	389.511	+	141.770i	0.180487	+	0.0656918i	−0.250196	+	0.968195i	$0.580495\pi$
$168$	−94.7544	−	79.5084i	−0.0435146	−	0.0365131i
$169$	63.5342	−	360.321i	0.0289186	−	0.164006i
$170$	−283.618	+	1608.48i	−0.127956	+	0.725675i
$171$	1113.70	+	1928.99i	0.498052	+	0.862651i
$172$	−1330.68	+	1116.57i	−0.589901	+	0.494986i
$173$	−3420.17	+	1244.84i	−1.50307	+	0.547072i	−0.956853	−	0.290573i	$-0.906154\pi$
$173$	−3420.17	+	1244.84i	−1.50307	+	0.547072i	−0.546215	+	0.837645i	$0.683932\pi$
$174$	71.5616	−	123.948i	0.0311786	−	0.0540029i
$175$	−204.427	−	354.077i	−0.0883040	−	0.152947i
$176$	784.961	+	658.661i	0.336186	+	0.282093i
$177$	739.655	−	1281.12i	0.314101	−	0.544039i
$178$	187.720	+	1064.61i	0.0790461	+	0.448293i
$179$	−1783.83			−0.744857			−0.372429	−	0.928061i	$-0.621475\pi$
$179$	−1783.83			−0.744857			−0.372429	+	0.928061i	$0.621475\pi$
$180$	−129.790	−	736.073i	−0.0537441	−	0.304798i
$181$	−1135.86	+	953.096i	−0.466450	+	0.391398i	−0.845498	−	0.533979i	$-0.820696\pi$
$181$	−1135.86	+	953.096i	−0.466450	+	0.391398i	0.379047	+	0.925377i	$0.376252\pi$
$182$	−693.866	−	252.547i	−0.282598	−	0.102857i
$183$	−151.547	+	55.1587i	−0.0612169	+	0.0222811i
$184$	−1486.57			−0.595605
$185$	−1176.48	−	1451.83i	−0.467547	−	0.576975i
$186$	509.480			0.200843
$187$	5919.24	−	2154.43i	2.31475	−	0.842499i
$188$	−219.465	−	79.8786i	−0.0851389	−	0.0309880i
$189$	586.353	−	492.009i	0.225666	−	0.189357i
$190$	285.395	+	1618.55i	0.108972	+	0.618012i
$191$	−3495.43			−1.32419			−0.662096	−	0.749419i	$-0.730333\pi$
$191$	−3495.43			−1.32419			−0.662096	+	0.749419i	$0.730333\pi$
$192$	23.5619	+	133.626i	0.00885641	+	0.0502272i
$193$	−290.175	+	502.597i	−0.108224	+	0.187449i	−0.915051	−	0.403339i	$-0.867850\pi$
$193$	−290.175	+	502.597i	−0.108224	+	0.187449i	0.806827	+	0.590788i	$0.201183\pi$
$194$	−15.9367	−	13.3725i	−0.00589787	−	0.00494890i
$195$	445.576	+	771.760i	0.163633	+	0.283420i
$196$	579.629	−	1003.95i	0.211235	−	0.365870i
$197$	4975.42	−	1810.90i	1.79941	−	0.654932i	0.800994	−	0.598672i	$-0.204305\pi$
$197$	4975.42	−	1810.90i	1.79941	−	0.654932i	0.998416	−	0.0562596i	$-0.0179175\pi$
$198$	−2208.21	+	1852.90i	−0.792577	+	0.665051i
$199$	858.801	+	1487.49i	0.305923	+	0.529875i	0.977467	−	0.211091i	$-0.0677015\pi$
$199$	858.801	+	1487.49i	0.305923	+	0.529875i	−0.671543	+	0.740966i	$0.734368\pi$
$200$	−77.8810	+	441.685i	−0.0275351	+	0.156159i
$201$	−243.594	+	1381.49i	−0.0854817	+	0.484791i
$202$	876.840	+	735.756i	0.305417	+	0.256275i
$203$	−231.314	−	84.1915i	−0.0799757	−	0.0291088i
$204$	783.810	+	285.284i	0.269008	+	0.0979110i
$205$	2074.59	+	1740.79i	0.706809	+	0.593083i
$206$	267.115	−	1514.88i	0.0903435	−	0.512363i
$207$	726.183	−	4118.39i	0.243832	−	1.38284i
$208$	404.999	+	701.479i	0.135008	+	0.233840i
$209$	4855.63	−	4074.36i	1.60704	−	1.34847i
$210$	241.268	−	87.8143i	0.0792813	−	0.0288560i
$211$	556.695	−	964.225i	0.181633	−	0.314597i	−0.760804	−	0.648982i	$-0.775195\pi$
$211$	556.695	−	964.225i	0.181633	−	0.314597i	0.942437	+	0.334385i	$0.108528\pi$
$212$	110.277	+	191.005i	0.0357256	+	0.0618786i
$213$	−851.156	−	714.205i	−0.273804	−	0.229749i
$214$	1377.09	−	2385.19i	0.439888	−	0.761908i
$215$	−626.119	−	3550.89i	−0.198609	−	1.12637i
$216$	−839.652			−0.264496
$217$	−152.161	−	862.949i	−0.0476008	−	0.269958i
$218$	−2430.23	+	2039.21i	−0.755027	+	0.633543i
$219$	1227.95	+	446.936i	0.378890	+	0.137905i
$220$	−1998.70	+	727.469i	−0.612512	+	0.222936i
$221$	4979.32			1.51559
$222$	−834.507	+	462.943i	−0.252290	+	0.139958i
$223$	3020.06			0.906897			0.453448	−	0.891282i	$-0.350194\pi$
$223$	3020.06			0.906897			0.453448	+	0.891282i	$0.350194\pi$
$224$	219.297	−	79.8174i	0.0654123	−	0.0238081i
$225$	−1185.60	−	431.523i	−0.351289	−	0.127859i
$226$	1253.40	−	1051.73i	0.368915	−	0.309557i
$227$	549.889	+	3118.57i	0.160782	+	0.911837i	0.953308	+	0.302000i	$0.0976542\pi$
$227$	549.889	+	3118.57i	0.160782	+	0.911837i	−0.792527	+	0.609837i	$0.791235\pi$
$228$	839.338			0.243801
$229$	886.283	+	5026.36i	0.255752	+	1.45044i	0.794135	+	0.607742i	$0.207924\pi$
$229$	886.283	+	5026.36i	0.255752	+	1.45044i	−0.538383	+	0.842701i	$0.680964\pi$
$230$	1542.85	−	2672.29i	0.442315	−	0.766112i
$231$	−758.549	−	636.498i	−0.216056	−	0.181292i
$232$	135.015	+	233.852i	0.0382075	+	0.0661773i
$233$	−3121.65	+	5406.86i	−0.877709	+	1.52024i	−0.0238600	+	0.999715i	$0.507596\pi$
$233$	−3121.65	+	5406.86i	−0.877709	+	1.52024i	−0.853849	+	0.520521i	$0.825738\pi$
$234$	−2141.22	+	779.340i	−0.598187	+	0.217722i
$235$	371.365	−	311.612i	0.103086	−	0.0864993i
$236$	1395.50	+	2417.07i	0.384912	+	0.666687i
$237$	173.971	−	986.639i	0.0476820	−	0.270418i
$238$	249.116	−	1412.81i	0.0678479	−	0.384785i
$239$	−2871.89	−	2409.80i	−0.777267	−	0.652205i	0.165292	−	0.986245i	$-0.447144\pi$
$239$	−2871.89	−	2409.80i	−0.777267	−	0.652205i	−0.942559	+	0.334040i	$0.891588\pi$
$240$	−264.663	−	96.3295i	−0.0711831	−	0.0259085i
$241$	3892.87	+	1416.89i	1.04050	+	0.378713i	0.805072	−	0.593178i	$-0.202127\pi$
$241$	3892.87	+	1416.89i	1.04050	+	0.378713i	0.235433	+	0.971890i	$0.424349\pi$
$242$	4244.74	+	3561.76i	1.12753	+	0.946110i
$243$	633.872	−	3594.86i	0.167337	−	0.949015i
$244$	52.8364	−	299.650i	0.0138627	−	0.0786193i
$245$	1203.15	+	2083.91i	0.313740	+	0.543413i
$246$	1059.48	−	889.012i	0.274594	−	0.230412i
$247$	4708.34	−	1713.69i	1.21289	−	0.441457i
$248$	−480.615	+	832.450i	−0.123061	+	0.213148i
$249$	−673.161	−	1165.95i	−0.171325	−	0.296743i
$250$	−2303.25	−	1932.65i	−0.582680	−	0.488927i
$251$	2196.62	−	3804.65i	0.552388	−	0.956763i	−0.445714	−	0.895175i	$-0.647050\pi$
$251$	2196.62	−	3804.65i	0.552388	−	0.956763i	0.998102	−	0.0615879i	$-0.0196165\pi$
$252$	114.001	+	646.530i	0.0284975	+	0.161617i
$253$	−11900.6			−2.95725
$254$	−59.8548	−	339.454i	−0.0147859	−	0.0838552i
$255$	−1326.32	+	1112.91i	−0.325714	+	0.273307i
$256$	−240.561	−	87.5572i	−0.0587308	−	0.0213763i
$257$	−6065.04	+	2207.49i	−1.47209	+	0.535797i	−0.948667	−	0.316277i	$-0.897567\pi$
$257$	−6065.04	+	2207.49i	−1.47209	+	0.535797i	−0.523422	+	0.852073i	$0.675345\pi$
$258$	−1841.40			−0.444343
$259$	1033.36	+	1275.21i	0.247914	+	0.305938i
$260$	−1681.33			−0.401044
$261$	−713.818	+	259.809i	−0.169288	+	0.0616159i
$262$	−281.783	−	102.561i	−0.0664450	−	0.0241840i
$263$	−2720.77	+	2283.00i	−0.637909	+	0.535269i	−0.903375	−	0.428851i	$-0.858918\pi$
$263$	−2720.77	+	2283.00i	−0.637909	+	0.535269i	0.265466	+	0.964120i	$0.414474\pi$
$264$	188.623	+	1069.73i	0.0439732	+	0.249384i
$265$	−457.806			−0.106124
$266$	−250.677	−	1421.66i	−0.0577818	−	0.327697i
$267$	−572.980	+	992.431i	−0.131333	+	0.227475i
$268$	−2027.46	−	1701.24i	−0.462114	−	0.387760i
$269$	−2050.08	−	3550.84i	−0.464667	−	0.804828i	0.534519	−	0.845156i	$-0.320493\pi$
$269$	−2050.08	−	3550.84i	−0.464667	−	0.804828i	−0.999186	+	0.0403289i	$0.987159\pi$
$270$	871.440	−	1509.38i	0.196423	−	0.340214i
$271$	4662.60	−	1697.05i	1.04514	−	0.380400i	0.238313	−	0.971188i	$-0.423405\pi$
$271$	4662.60	−	1697.05i	1.04514	−	0.380400i	0.806826	+	0.590789i	$0.201183\pi$
$272$	−1205.53	+	1011.56i	−0.268736	+	0.225497i
$273$	−391.372	−	677.876i	−0.0867652	−	0.150282i
$274$	276.976	−	1570.81i	0.0610684	−	0.346336i
$275$	−623.471	+	3535.88i	−0.136715	+	0.775351i
$276$	−1207.17	−	1012.94i	−0.263272	−	0.220911i
$277$	3400.39	+	1237.64i	0.737581	+	0.268457i	0.683370	−	0.730072i	$-0.260514\pi$
$277$	3400.39	+	1237.64i	0.737581	+	0.268457i	0.0542107	+	0.998530i	$0.482736\pi$
$278$	−2250.31	−	819.045i	−0.485484	−	0.176702i
$279$	−2071.44	−	1738.15i	−0.444495	−	0.372975i
$280$	−84.1171	+	477.052i	−0.0179534	+	0.101819i
$281$	−964.654	+	5470.82i	−0.204792	+	1.16143i	0.692976	+	0.720961i	$0.256299\pi$
$281$	−964.654	+	5470.82i	−0.204792	+	1.16143i	−0.897767	+	0.440470i	$0.854812\pi$
$282$	−123.788	−	214.407i	−0.0261399	−	0.0452757i
$283$	−527.539	+	442.658i	−0.110809	+	0.0929798i	−0.696509	−	0.717548i	$-0.745264\pi$
$283$	−527.539	+	442.658i	−0.110809	+	0.0929798i	0.585700	+	0.810528i	$0.300820\pi$
$284$	1969.89	−	716.981i	0.411589	−	0.149806i
$285$	−871.115	+	1508.81i	−0.181054	+	0.313595i
$286$	3242.19	+	5615.64i	0.670331	+	1.16105i
$287$	−1822.22	−	1529.02i	−0.374781	−	0.314479i
$288$	360.082	−	623.680i	0.0736737	−	0.127607i
$289$	826.759	+	4688.79i	0.168280	+	0.954363i
$290$	−560.504			−0.113496
$291$	−3.82951	−	21.7182i	−0.000771443	−	0.00437507i
$292$	−1888.63	+	1584.75i	−0.378507	+	0.317605i
$293$	−3878.07	−	1411.50i	−0.773240	−	0.281436i	−0.0748888	−	0.997192i	$-0.523860\pi$
$293$	−3878.07	−	1411.50i	−0.773240	−	0.281436i	−0.698351	+	0.715756i	$0.746082\pi$
$294$	1154.77	−	420.302i	0.229073	−	0.0833759i
$295$	−5793.32			−1.14339
$296$	30.8163	−	1800.23i	0.00605122	−	0.353502i
$297$	−6721.77			−1.31326
$298$	4414.69	−	1606.81i	0.858174	−	0.312350i
$299$	−8839.85	−	3217.44i	−1.70977	−	0.622306i
$300$	−364.204	+	305.604i	−0.0700911	+	0.0588134i
$301$	549.951	+	3118.93i	0.105311	+	0.597250i
$302$	2836.32			0.540436
$303$	210.701	+	1194.94i	0.0399487	+	0.226560i
$304$	−791.786	+	1371.41i	−0.149382	+	0.258737i
$305$	483.821	+	405.974i	0.0908312	+	0.0762164i
$306$	−2213.54	−	3833.96i	−0.413528	−	0.716251i
$307$	3567.48	−	6179.06i	0.663215	−	1.14872i	−0.316551	−	0.948575i	$-0.602525\pi$
$307$	3567.48	−	6179.06i	0.663215	−	1.14872i	0.979766	−	0.200146i	$-0.0641417\pi$
$308$	1755.56	−	638.972i	0.324781	−	0.118210i
$309$	1249.14	−	1048.15i	0.229971	−	0.192969i
$310$	−997.622	−	1727.93i	−0.182778	−	0.316580i
$311$	1309.61	−	7427.14i	0.238781	−	1.35419i	−0.595722	−	0.803191i	$-0.703134\pi$
$311$	1309.61	−	7427.14i	0.238781	−	1.35419i	0.834503	−	0.551004i	$-0.185755\pi$
$312$	−149.102	+	845.600i	−0.0270553	+	0.153438i
$313$	5452.51	+	4575.20i	0.984646	+	0.826216i	0.984784	−	0.173784i	$-0.0555995\pi$
$313$	5452.51	+	4575.20i	0.984646	+	0.826216i	−0.000138044		1.00000i	$0.500044\pi$
$314$	5505.14	+	2003.71i	0.989404	+	0.360114i
$315$	−1280.53	−	466.076i	−0.229047	−	0.0833664i
$316$	1447.98	+	1215.00i	0.257769	+	0.216294i
$317$	329.574	−	1869.11i	0.0583934	−	0.331166i	−0.941591	−	0.336759i	$-0.890669\pi$
$317$	329.574	−	1869.11i	0.0583934	−	0.331166i	0.999984	+	0.00559329i	$0.00178041\pi$
$318$	−40.5988	+	230.247i	−0.00715933	+	0.0406026i
$319$	1080.85	+	1872.08i	0.189705	+	0.328579i
$320$	407.063	−	341.567i	0.0711111	−	0.0596693i
$321$	2743.52	−	998.560i	0.477035	−	0.173627i
$322$	−1355.16	+	2347.21i	−0.234535	+	0.406226i
$323$	4867.36	+	8430.51i	0.838474	+	1.45228i
$324$	1180.07	+	990.196i	0.202344	+	0.169787i
$325$	−1419.08	+	2457.91i	−0.242204	+	0.419509i
$326$	−284.091	−	1611.16i	−0.0482649	−	0.273724i
$327$	−3362.97			−0.568724
$328$	453.117	+	2569.76i	0.0762781	+	0.432595i
$329$	−326.189	+	273.705i	−0.0546607	+	0.0458657i
$330$	−2118.74	−	771.159i	−0.353433	−	0.128639i
$331$	−2039.79	+	742.421i	−0.338721	+	0.123284i	−0.505780	−	0.862662i	$-0.668795\pi$
$331$	−2039.79	+	742.421i	−0.338721	+	0.123284i	0.167059	+	0.985947i	$0.446573\pi$
$332$	2540.09			0.419897
$333$	4972.32	+	964.781i	0.818262	+	0.158768i
$334$	−829.018			−0.135814
$335$	5162.40	−	1878.96i	0.841947	−	0.306443i
$336$	232.467	+	84.6111i	0.0377444	+	0.0137378i
$337$	5135.93	−	4309.56i	0.830184	−	0.696607i	−0.125149	−	0.992138i	$-0.539941\pi$
$337$	5135.93	−	4309.56i	0.830184	−	0.696607i	0.955333	+	0.295531i	$0.0954964\pi$
$338$	127.068	+	720.641i	0.0204486	+	0.115970i
$339$	1734.46			0.277885
$340$	−567.236	−	3216.96i	−0.0904786	−	0.513129i
$341$	−3847.53	+	6664.12i	−0.611013	+	1.05831i
$342$	−3412.58	−	2863.49i	−0.539565	−	0.452749i
$343$	−2307.50	−	3996.71i	−0.363246	−	0.629161i
$344$	1737.07	−	3008.70i	0.272258	−	0.471564i
$345$	3073.75	−	1118.75i	0.479667	−	0.174584i
$346$	5576.30	−	4679.07i	0.866427	−	0.727018i
$347$	3371.26	+	5839.20i	0.521553	+	0.903356i	0.999686	+	0.0250684i	$0.00798036\pi$
$347$	3371.26	+	5839.20i	0.521553	+	0.903356i	−0.478133	+	0.878287i	$0.658686\pi$
$348$	−49.7062	+	281.898i	−0.00765670	+	0.0434233i
$349$	1831.48	−	10386.8i	0.280908	−	1.59311i	−0.438638	−	0.898664i	$-0.644539\pi$
$349$	1831.48	−	10386.8i	0.280908	−	1.59311i	0.719546	−	0.694445i	$-0.244350\pi$
$350$	626.399	+	525.612i	0.0956642	+	0.0802718i
$351$	−4992.97	−	1817.29i	−0.759274	−	0.276353i
$352$	−1925.80	−	700.932i	−0.291606	−	0.106136i
$353$	3010.04	+	2525.73i	0.453848	+	0.380824i	0.840862	−	0.541250i	$-0.182049\pi$
$353$	3010.04	+	2525.73i	0.453848	+	0.380824i	−0.387013	+	0.922074i	$0.626493\pi$
$354$	−513.759	+	2913.67i	−0.0771355	+	0.437457i
$355$	−755.604	+	4285.24i	−0.112967	+	0.640668i
$356$	−1081.04	−	1872.41i	−0.160940	−	0.278757i
$357$	1164.97	−	977.527i	0.172708	−	0.144919i
$358$	3352.50	−	1220.21i	0.494930	−	0.180140i
$359$	−2033.02	+	3521.30i	−0.298883	+	0.517680i	−0.975881	−	0.218305i	$-0.929947\pi$
$359$	−2033.02	+	3521.30i	−0.298883	+	0.517680i	0.676998	+	0.735985i	$0.263281\pi$
$360$	747.428	+	1294.58i	0.109425	+	0.189529i
$361$	2249.64	+	1887.67i	0.327984	+	0.275211i
$362$	1482.75	−	2568.21i	0.215281	−	0.372878i
$363$	1019.99	+	5784.66i	0.147481	+	0.836408i
$364$	1476.79			0.212651
$365$	−888.653	−	5039.80i	−0.127436	−	0.722727i
$366$	247.085	−	207.329i	0.0352878	−	0.0296100i
$367$	−963.867	−	350.819i	−0.137094	−	0.0498981i	0.272562	−	0.962138i	$-0.412129\pi$
$367$	−963.867	−	350.819i	−0.137094	−	0.0498981i	−0.409656	+	0.912240i	$0.634351\pi$
$368$	2793.84	−	1016.87i	0.395757	−	0.144044i
$369$	−7340.60			−1.03560
$370$	3204.16	+	1923.78i	0.450206	+	0.270305i
$371$	402.114			0.0562715
$372$	−957.509	+	348.505i	−0.133453	+	0.0485729i
$373$	−8124.32	−	2957.01i	−1.12778	−	0.410478i	−0.290293	−	0.956938i	$-0.593753\pi$
$373$	−8124.32	−	2957.01i	−1.12778	−	0.410478i	−0.837485	+	0.546460i	$0.815975\pi$
$374$	−9650.82	+	8098.00i	−1.33431	+	1.11962i
$375$	−553.460	−	3138.83i	−0.0762148	−	0.432235i
$376$	467.099			0.0640659
$377$	296.725	+	1682.81i	0.0405362	+	0.229892i
$378$	−765.430	+	1325.76i	−0.104152	+	0.180397i
$379$	4524.47	+	3796.48i	0.613209	+	0.514544i	0.895661	−	0.444738i	$-0.146703\pi$
$379$	4524.47	+	3796.48i	0.613209	+	0.514544i	−0.282452	+	0.959282i	$0.591148\pi$
$380$	−1643.52	−	2846.67i	−0.221871	−	0.384292i
$381$	182.696	−	316.438i	0.0245664	−	0.0425502i
$382$	6569.26	−	2391.02i	0.879877	−	0.320249i
$383$	6639.46	−	5571.17i	0.885798	−	0.743273i	−0.0815650	−	0.996668i	$-0.525992\pi$
$383$	6639.46	−	5571.17i	0.885798	−	0.743273i	0.967363	+	0.253395i	$0.0815474\pi$
$384$	−135.687	−	235.017i	−0.0180319	−	0.0312322i
$385$	−673.393	+	3819.00i	−0.0891410	+	0.505544i
$386$	201.553	−	1143.07i	0.0265772	−	0.150727i
$387$	7486.75	+	6282.13i	0.983392	+	0.825164i
$388$	39.0985	+	14.2307i	0.00511578	+	0.00186199i
$389$	6288.36	+	2288.77i	0.819620	+	0.298317i	0.717592	−	0.696464i	$-0.245244\pi$
$389$	6288.36	+	2288.77i	0.819620	+	0.298317i	0.102029	+	0.994781i	$0.467467\pi$
$390$	−1365.32	−	1145.64i	−0.177271	−	0.148748i
$391$	3173.74	−	17999.2i	0.410493	−	2.32802i
$392$	−402.606	+	2283.29i	−0.0518742	+	0.294193i
$393$	−158.938	−	275.289i	−0.0204004	−	0.0353346i
$394$	−8112.00	+	6806.77i	−1.03725	+	0.870356i
$395$	−3686.90	+	1341.92i	−0.469641	+	0.170935i
$396$	2882.61	−	4992.82i	0.365799	−	0.633583i
$397$	−1505.26	−	2607.20i	−0.190295	−	0.329600i	0.755053	−	0.655664i	$-0.227611\pi$
$397$	−1505.26	−	2607.20i	−0.190295	−	0.329600i	−0.945348	+	0.326063i	$0.894278\pi$
$398$	−2631.52	−	2208.11i	−0.331422	−	0.278096i
$399$	765.144	−	1325.27i	0.0960028	−	0.166282i
$400$	−155.762	−	883.370i	−0.0194703	−	0.110421i
$401$	−518.798			−0.0646073			−0.0323037	−	0.999478i	$-0.510284\pi$
$401$	−518.798			−0.0646073			−0.0323037	+	0.999478i	$0.510284\pi$
$402$	−487.189	−	2762.99i	−0.0604447	−	0.342799i
$403$	−4659.68	+	3909.93i	−0.575968	+	0.483294i
$404$	−2151.21	−	782.975i	−0.264917	−	0.0964220i
$405$	−3004.75	+	1093.64i	−0.368659	+	0.134181i
$406$	492.319			0.0601807
$407$	246.698	−	14411.6i	0.0300451	−	1.75518i
$408$	−1668.23			−0.202425
$409$	7286.64	−	2652.12i	0.880932	−	0.320633i	0.138346	−	0.990384i	$-0.455821\pi$
$409$	7286.64	−	2652.12i	0.880932	−	0.320633i	0.742586	+	0.669751i	$0.233599\pi$
$410$	−5089.73	−	1852.51i	−0.613082	−	0.223144i
$411$	1295.26	−	1086.85i	0.155451	−	0.130439i
$412$	534.229	+	3029.76i	0.0638825	+	0.362296i
$413$	5088.57			0.606276
$414$	1452.37	+	8236.78i	0.172415	+	0.977816i
$415$	−2636.26	+	4566.13i	−0.311829	+	0.540103i
$416$	−1240.99	−	1041.31i	−0.146261	−	0.122727i
$417$	−1269.27	−	2198.45i	−0.149057	−	0.258174i
$418$	−6338.58	+	10978.7i	−0.741699	+	1.28466i
$419$	6738.06	−	2452.45i	0.785622	−	0.285943i	0.0821074	−	0.996623i	$-0.473835\pi$
$419$	6738.06	−	2452.45i	0.785622	−	0.285943i	0.703515	+	0.710680i	$0.251613\pi$
$420$	−393.367	+	330.074i	−0.0457008	+	0.0383475i
$421$	5247.83	+	9089.51i	0.607515	+	1.05225i	0.991649	+	0.128969i	$0.0411668\pi$
$421$	5247.83	+	9089.51i	0.607515	+	1.05225i	−0.384134	+	0.923277i	$0.625500\pi$
$422$	−386.677	+	2192.95i	−0.0446045	+	0.252965i
$423$	−228.176	+	1294.05i	−0.0262277	+	0.148745i
$424$	−337.907	−	283.538i	−0.0387034	−	0.0324760i
$425$	−5181.59	−	1885.94i	−0.591398	−	0.215251i
$426$	2088.20	+	760.041i	0.237496	+	0.0864416i
$427$	−424.964	−	356.587i	−0.0481627	−	0.0404133i
$428$	−956.518	+	5424.68i	−0.108026	+	0.612645i
$429$	−1193.63	+	6769.39i	−0.134333	+	0.761839i
$430$	3605.67	+	6245.21i	0.404374	+	0.700397i
$431$	−12171.0	+	10212.7i	−1.36022	+	1.14136i	−0.384311	+	0.923204i	$0.625561\pi$
$431$	−12171.0	+	10212.7i	−1.36022	+	1.14136i	−0.975913	+	0.218160i	$0.929995\pi$
$432$	1578.03	−	574.356i	0.175748	−	0.0639669i
$433$	3564.27	−	6173.50i	0.395584	−	0.685172i	−0.597591	−	0.801801i	$-0.703875\pi$
$433$	3564.27	−	6173.50i	0.395584	−	0.685172i	0.993176	+	0.116629i	$0.0372087\pi$
$434$	876.261	+	1517.73i	0.0969168	+	0.167865i
$435$	−455.158	−	381.923i	−0.0501682	−	0.0420961i
$436$	3172.44	−	5494.83i	0.348469	−	0.603565i
$437$	−3193.62	−	18111.9i	−0.349591	−	1.98263i
$438$	−2613.50			−0.285110
$439$	124.927	+	708.497i	0.0135819	+	0.0770267i	0.990845	−	0.135002i	$-0.0431041\pi$
$439$	124.927	+	708.497i	0.0135819	+	0.0770267i	−0.977263	+	0.212029i	$0.931993\pi$
$440$	3258.72	−	2734.39i	0.353075	−	0.296265i
$441$	−6128.97	−	2230.76i	−0.661804	−	0.240877i
$442$	−9358.05	+	3406.05i	−1.00705	+	0.366537i
$443$	−10174.9			−1.09125			−0.545624	−	0.838030i	$-0.683707\pi$
$443$	−10174.9			−1.09125			−0.545624	+	0.838030i	$0.683707\pi$
$444$	1251.69	−	1440.88i	0.133790	−	0.154012i
$445$	4487.85			0.478078
$446$	−5675.85	+	2065.84i	−0.602599	+	0.219328i
$447$	4679.82	+	1703.32i	0.495186	+	0.180233i
$448$	−357.544	+	300.015i	−0.0377062	+	0.0316393i
$449$	−552.105	−	3131.14i	−0.0580299	−	0.329104i	0.941948	−	0.335759i	$-0.108993\pi$
$449$	−552.105	−	3131.14i	−0.0580299	−	0.329104i	−0.999978	+	0.00665501i	$0.997882\pi$
$450$	2523.38			0.264341
$451$	3627.40	+	20572.0i	0.378730	+	2.14789i
$452$	−1636.20	+	2833.98i	−0.170266	+	0.294909i
$453$	2303.24	+	1932.64i	0.238886	+	0.200449i
$454$	−3166.68	−	5484.86i	−0.327356	−	0.566998i
$455$	−1532.70	+	2654.72i	−0.157921	+	0.273528i
$456$	−1577.44	+	574.141i	−0.161997	+	0.0589619i
$457$	−11057.8	+	9278.63i	−1.13187	+	0.949751i	−0.999143	−	0.0414020i	$-0.986818\pi$
$457$	−11057.8	+	9278.63i	−1.13187	+	0.949751i	−0.132726	+	0.991153i	$0.542373\pi$
$458$	−5103.90	−	8840.22i	−0.520720	−	0.901913i
$459$	1792.61	−	10166.4i	0.182291	−	1.03383i
$460$	−1071.65	+	6077.63i	−0.108622	+	0.616024i
$461$	−479.351	−	402.224i	−0.0484287	−	0.0406365i	0.618252	−	0.785980i	$-0.287841\pi$
$461$	−479.351	−	402.224i	−0.0484287	−	0.0406365i	−0.666681	+	0.745343i	$0.732286\pi$
$462$	1861.00	+	677.347i	0.187406	+	0.0682101i
$463$	−3834.89	−	1395.78i	−0.384929	−	0.140103i	0.142305	−	0.989823i	$-0.454549\pi$
$463$	−3834.89	−	1395.78i	−0.384929	−	0.140103i	−0.527234	+	0.849720i	$0.676771\pi$
$464$	−413.709	−	347.143i	−0.0413921	−	0.0347321i
$465$	367.279	−	2082.94i	0.0366282	−	0.207729i
$466$	2168.28	−	12296.9i	0.215544	−	1.22241i
$467$	8876.35	+	15374.3i	0.879547	+	1.52342i	0.851839	+	0.523804i	$0.175488\pi$
$467$	8876.35	+	15374.3i	0.879547	+	1.52342i	0.0277087	+	0.999616i	$0.491179\pi$
$468$	3491.07	−	2929.36i	0.344818	−	0.289337i
$469$	−4534.40	+	1650.39i	−0.446437	+	0.162490i
$470$	−484.783	+	839.668i	−0.0475774	+	0.0824064i
$471$	3105.14	+	5378.27i	0.303774	+	0.526152i
$472$	−4276.06	−	3588.04i	−0.416995	−	0.349900i
$473$	13906.0	−	24085.9i	1.35179	−	2.34138i
$474$	347.942	+	1973.28i	0.0337163	+	0.191214i
$475$	−5548.67			−0.535980
$476$	498.232	+	2825.62i	0.0479757	+	0.272084i
$477$	950.580	−	797.631i	0.0912454	−	0.0765640i
$478$	7045.78	+	2564.45i	0.674198	+	0.245388i
$479$	1191.45	−	433.651i	0.113651	−	0.0413654i	−0.284569	−	0.958656i	$-0.591850\pi$
$479$	1191.45	−	433.651i	0.113651	−	0.0413654i	0.398219	+	0.917290i	$0.369628\pi$
$480$	563.297			0.0535643
$481$	4079.57	−	10638.4i	0.386720	−	1.00846i
$482$	−8285.41			−0.782967
$483$	−2699.83	+	982.657i	−0.254341	+	0.0925724i
$484$	−10413.9	−	3790.35i	−0.978014	−	0.355968i
$485$	−66.1601	+	55.5149i	−0.00619417	+	0.00519753i
$486$	1267.74	+	7189.73i	0.118325	+	0.671055i
$487$	1584.73			0.147456			0.0737279	−	0.997278i	$-0.476510\pi$
$487$	1584.73			0.147456			0.0737279	+	0.997278i	$0.476510\pi$
$488$	105.673	+	599.300i	0.00980242	+	0.0555923i
$489$	867.135	−	1501.92i	0.0801906	−	0.138894i
$490$	−3686.66	−	3093.47i	−0.339890	−	0.285202i
$491$	3029.14	+	5246.63i	0.278418	+	0.482234i	0.970992	−	0.239113i	$-0.0768566\pi$
$491$	3029.14	+	5246.63i	0.278418	+	0.482234i	−0.692574	+	0.721347i	$0.743523\pi$
$492$	−1383.06	+	2395.52i	−0.126734	+	0.219509i
$493$	−3119.69	+	1135.48i	−0.284998	+	0.103731i
$494$	−7676.54	+	6441.38i	−0.699158	+	0.586663i
$495$	5983.48	+	10363.7i	0.543308	+	0.941037i
$496$	333.832	−	1893.25i	0.0302208	−	0.171390i
$497$	663.685	−	3763.95i	0.0599001	−	0.339710i
$498$	2062.69	+	1730.80i	0.185605	+	0.155741i
$499$	−15922.5	−	5795.31i	−1.42843	−	0.519907i	−0.491951	−	0.870623i	$-0.663716\pi$
$499$	−15922.5	−	5795.31i	−1.42843	−	0.519907i	−0.936482	+	0.350716i	$0.885938\pi$
$500$	5650.70	+	2056.69i	0.505414	+	0.183956i
$501$	−673.205	−	564.886i	−0.0600331	−	0.0503738i
$502$	−1525.75	+	8652.98i	−0.135653	+	0.769326i
$503$	−2398.52	+	13602.7i	−0.212613	+	1.20579i	0.672387	+	0.740200i	$0.265269\pi$
$503$	−2398.52	+	13602.7i	−0.212613	+	1.20579i	−0.885000	+	0.465591i	$0.845842\pi$
$504$	−656.504	−	1137.10i	−0.0580218	−	0.100497i
$505$	3640.14	−	3054.44i	0.320761	−	0.269150i
$506$	22365.8	−	8140.50i	1.96499	−	0.715196i
$507$	−387.853	+	671.781i	−0.0339747	+	0.0588458i
$508$	344.690	+	597.021i	0.0301046	+	0.0521428i
$509$	−8719.47	−	7316.51i	−0.759300	−	0.637129i	0.178644	−	0.983914i	$-0.442829\pi$
$509$	−8719.47	−	7316.51i	−0.759300	−	0.637129i	−0.937945	+	0.346785i	$0.887273\pi$
$510$	1731.38	−	2998.84i	0.150327	−	0.260375i
$511$	780.549	+	4426.71i	0.0675723	+	0.383222i
$512$	512.000			0.0441942
$513$	−1803.84	−	10230.1i	−0.155246	−	0.880446i
$514$	9888.53	−	8297.47i	0.848569	−	0.712034i
$515$	−6000.83	−	2184.12i	−0.513453	−	0.186882i
$516$	3460.70	−	1259.59i	0.295249	−	0.107462i
$517$	3739.33			0.318095
$518$	−2814.38	−	1689.76i	−0.238719	−	0.143328i
$519$	7716.52			0.652635
$520$	3159.86	−	1150.10i	0.266479	−	0.0969904i
$521$	6760.05	+	2460.46i	0.568452	+	0.206900i	0.610226	−	0.792228i	$-0.291079\pi$
$521$	6760.05	+	2460.46i	0.568452	+	0.206900i	−0.0417740	+	0.999127i	$0.513301\pi$
$522$	1163.82	−	976.561i	0.0975843	−	0.0818829i
$523$	−1761.27	−	9988.68i	−0.147256	−	0.835133i	−0.965528	−	0.260301i	$-0.916178\pi$
$523$	−1761.27	−	9988.68i	−0.147256	−	0.835133i	0.818271	−	0.574832i	$-0.194933\pi$
$524$	599.734			0.0499990
$525$	150.521	+	853.647i	0.0125129	+	0.0709642i
$526$	3551.72	−	6151.75i	0.294415	−	0.509941i
$527$	−9053.10	−	7596.45i	−0.748310	−	0.627906i
$528$	−1086.24	−	1881.41i	−0.0895309	−	0.155072i
$529$	−11181.2	+	19366.5i	−0.918981	+	1.59172i
$530$	860.394	−	313.158i	0.0705153	−	0.0256655i
$531$	12029.1	−	10093.6i	0.983089	−	0.824910i
$532$	1443.59	+	2500.37i	0.117646	+	0.203768i
$533$	−2867.38	+	16261.7i	−0.233020	+	1.32152i
$534$	397.988	−	2257.10i	0.0322521	−	0.182911i
$535$	−8758.81	−	7349.51i	−0.707806	−	0.593920i
$536$	4974.09	+	1810.42i	0.400836	+	0.145892i
$537$	3553.84	+	1293.49i	0.285586	+	0.103945i
$538$	6281.81	+	5271.06i	0.503398	+	0.422401i
$539$	−3223.03	+	18278.7i	−0.257562	+	1.46071i
$540$	−605.296	+	3432.81i	−0.0482367	+	0.273564i
$541$	−3073.31	−	5323.12i	−0.244236	−	0.423030i	0.717680	−	0.696373i	$-0.245204\pi$
$541$	−3073.31	−	5323.12i	−0.244236	−	0.423030i	−0.961917	+	0.273343i	$0.911871\pi$
$542$	−7601.98	+	6378.82i	−0.602459	+	0.505523i
$543$	2954.03	−	1075.18i	0.233461	−	0.0849730i
$544$	1573.71	−	2725.75i	0.124030	−	0.214827i
$545$	6585.09	+	11405.7i	0.517567	+	0.896453i
$546$	1199.23	+	1006.28i	0.0939971	+	0.0788729i
$547$	1072.87	−	1858.27i	0.0838624	−	0.145254i	−0.821044	−	0.570866i	$-0.806608\pi$
$547$	1072.87	−	1858.27i	0.0838624	−	0.145254i	0.904906	+	0.425612i	$0.139941\pi$
$548$	553.952	+	3141.62i	0.0431819	+	0.244897i
$549$	−1711.92			−0.133084
$550$	−1246.94	−	7071.76i	−0.0966723	−	0.548256i
$551$	−2559.13	+	2147.36i	−0.197863	+	0.166027i
$552$	2961.63	+	1077.94i	0.228361	+	0.0831165i
$553$	3238.39	−	1178.68i	0.249024	−	0.0906374i
$554$	−7237.25			−0.555020
$555$	1291.09	+	3745.50i	0.0987455	+	0.286464i
$556$	4789.45			0.365320
$557$	19049.4	−	6933.42i	1.44910	−	0.527430i	0.506762	−	0.862086i	$-0.330842\pi$
$557$	19049.4	−	6933.42i	1.44910	−	0.527430i	0.942340	+	0.334656i	$0.108620\pi$
$558$	5082.00	+	1849.70i	0.385552	+	0.140330i
$559$	16841.3	−	14131.5i	1.27426	−	1.06923i
$560$	−168.234	−	954.104i	−0.0126950	−	0.0719969i
$561$	−13354.9			−1.00507
$562$	−1929.31	−	10941.6i	−0.144809	−	0.821255i
$563$	3621.93	−	6273.36i	0.271130	−	0.469611i	−0.698022	−	0.716077i	$-0.745936\pi$
$563$	3621.93	−	6273.36i	0.271130	−	0.469611i	0.969151	+	0.246466i	$0.0792694\pi$
$564$	379.308	+	318.277i	0.0283187	+	0.0237622i
$565$	−3396.28	−	5882.53i	−0.252890	−	0.438018i
$566$	688.654	−	1192.78i	0.0511418	−	0.0885803i
$567$	2639.22	−	960.598i	0.195479	−	0.0711487i
$568$	−3211.74	+	2694.97i	−0.237256	+	0.199081i
$569$	39.7341	+	68.8214i	0.00292749	+	0.00507055i	0.867485	−	0.497463i	$-0.165735\pi$
$569$	39.7341	+	68.8214i	0.00292749	+	0.00507055i	−0.864558	+	0.502533i	$0.832401\pi$
$570$	605.070	−	3431.52i	0.0444624	−	0.252159i
$571$	626.439	−	3552.71i	0.0459119	−	0.260379i	−0.953208	−	0.302314i	$-0.902241\pi$
$571$	626.439	−	3552.71i	0.0459119	−	0.260379i	0.999120	+	0.0419346i	$0.0133521\pi$
$572$	−9934.65	−	8336.16i	−0.726204	−	0.609357i
$573$	6963.80	+	2534.62i	0.507708	+	0.184791i
$574$	4470.56	+	1627.15i	0.325083	+	0.118321i
$575$	7980.32	+	6696.28i	0.578787	+	0.485660i
$576$	−250.110	+	1418.45i	−0.0180925	+	0.102607i
$577$	−3440.76	+	19513.5i	−0.248250	+	1.40790i	0.564571	+	0.825385i	$0.309042\pi$
$577$	−3440.76	+	19513.5i	−0.248250	+	1.40790i	−0.812821	+	0.582514i	$0.802069\pi$
$578$	−4761.12	−	8246.50i	−0.342624	−	0.593441i
$579$	942.547	−	790.891i	0.0676527	−	0.0567674i
$580$	1053.40	−	383.407i	0.0754141	−	0.0274485i
$581$	2315.56	−	4010.66i	0.165345	−	0.286386i
$582$	22.0533	+	38.1974i	0.00157068	+	0.00272050i
$583$	−2705.09	−	2269.84i	−0.192167	−	0.161247i
$584$	2465.44	−	4270.26i	0.174693	−	0.302576i
$585$	1642.64	+	9315.90i	0.116094	+	0.658402i
$586$	8253.91			0.581853
$587$	−85.6875	−	485.958i	−0.00602505	−	0.0341697i	0.981647	−	0.190707i	$-0.0610780\pi$
$587$	−85.6875	−	485.958i	−0.00602505	−	0.0341697i	−0.987672	+	0.156537i	$0.949967\pi$
$588$	−1882.75	+	1579.82i	−0.132047	+	0.110800i
$589$	−11174.8	−	4067.31i	−0.781750	−	0.284534i
$590$	10887.9	−	3962.87i	0.759741	−	0.276523i
$591$	−11225.4			−0.781307
$592$	1173.52	+	3404.41i	0.0814717	+	0.236352i
$593$	14357.3			0.994240			0.497120	−	0.867682i	$-0.334391\pi$
$593$	14357.3			0.994240			0.497120	+	0.867682i	$0.334391\pi$
$594$	12632.8	−	4597.96i	0.872610	−	0.317604i
$595$	−5596.49	−	2036.96i	−0.385603	−	0.140348i
$596$	−7197.77	+	6039.65i	−0.494685	+	0.415090i
$597$	−632.342	−	3586.19i	−0.0433501	−	0.245851i
$598$	18814.3			1.28658
$599$	3345.96	+	18975.9i	0.228234	+	1.29438i	0.856406	+	0.516304i	$0.172692\pi$
$599$	3345.96	+	18975.9i	0.228234	+	1.29438i	−0.628172	+	0.778075i	$0.716196\pi$
$600$	475.435	−	823.477i	0.0323492	−	0.0560305i
$601$	−14166.4	−	11887.1i	−0.961500	−	0.806794i	0.0196965	−	0.999806i	$-0.493730\pi$
$601$	−14166.4	−	11887.1i	−0.961500	−	0.806794i	−0.981196	+	0.193012i	$0.938174\pi$
$602$	−3167.04	−	5485.48i	−0.214417	−	0.371381i
$603$	−7445.41	+	12895.8i	−0.502820	+	0.870911i
$604$	−5330.54	+	1940.16i	−0.359100	+	0.130702i
$605$	17621.8	−	14786.4i	1.18418	−	0.993642i
$606$	−1213.38	−	2101.63i	−0.0813368	−	0.140879i
$607$	−1021.49	+	5793.17i	−0.0683049	+	0.387376i	0.931421	+	0.363945i	$0.118570\pi$
$607$	−1021.49	+	5793.17i	−0.0683049	+	0.387376i	−0.999725	+	0.0234316i	$0.992541\pi$
$608$	549.969	−	3119.03i	0.0366845	−	0.208048i
$609$	399.788	+	335.462i	0.0266014	+	0.0223212i
$610$	−1186.99	−	432.029i	−0.0787865	−	0.0286759i
$611$	2777.59	+	1010.96i	0.183911	+	0.0669380i
$612$	6782.67	+	5691.34i	0.447996	+	0.375913i
$613$	3329.21	−	18880.9i	0.219356	−	1.24403i	−0.653828	−	0.756643i	$-0.726838\pi$
$613$	3329.21	−	18880.9i	0.219356	−	1.24403i	0.873185	−	0.487389i	$-0.162051\pi$
$614$	−2477.95	+	14053.1i	−0.162869	+	0.923678i
$615$	−2870.83	−	4972.43i	−0.188233	−	0.326029i
$616$	−2862.29	+	2401.75i	−0.187216	+	0.157093i
$617$	8248.04	−	3002.04i	0.538174	−	0.195879i	−0.0586103	−	0.998281i	$-0.518667\pi$
$617$	8248.04	−	3002.04i	0.538174	−	0.195879i	0.596784	+	0.802402i	$0.296445\pi$
$618$	−1630.64	+	2824.34i	−0.106139	+	0.183838i
$619$	1880.60	+	3257.29i	0.122112	+	0.211505i	0.920601	−	0.390506i	$-0.127700\pi$
$619$	1880.60	+	3257.29i	0.122112	+	0.211505i	−0.798488	+	0.602011i	$0.794367\pi$
$620$	3056.89	+	2565.04i	0.198012	+	0.166152i
$621$	−9751.57	+	16890.2i	−0.630140	+	1.09143i
$622$	2619.21	+	14854.3i	0.168844	+	0.957560i
$623$	−3941.90			−0.253498
$624$	−298.204	−	1691.20i	−0.0191310	−	0.108497i
$625$	−4193.49	+	3518.76i	−0.268383	+	0.225200i
$626$	−13377.0	−	4868.83i	−0.854077	−	0.310858i
$627$	−12628.1	+	4596.25i	−0.804333	+	0.292753i
$628$	−11716.9			−0.744514
$629$	21731.2	+	4216.51i	1.37755	+	0.267287i
$630$	2725.43			0.172355
$631$	−26793.8	+	9752.15i	−1.69040	+	0.615257i	−0.994676	−	0.103049i	$-0.967140\pi$
$631$	−26793.8	+	9752.15i	−1.69040	+	0.615257i	−0.695727	+	0.718306i	$0.744918\pi$
$632$	−3552.41	−	1292.97i	−0.223588	−	0.0813792i
$633$	−1808.26	+	1517.31i	−0.113542	+	0.0952728i
$634$	659.148	+	3738.21i	0.0412904	+	0.234169i
$635$	−1430.96			−0.0894266
$636$	−81.1976	−	460.494i	−0.00506241	−	0.0287104i
$637$	−7335.92	+	12706.2i	−0.456295	+	0.790325i
$638$	−3311.91	−	2779.02i	−0.205517	−	0.172449i
$639$	−5897.22	−	10214.3i	−0.365086	−	0.632348i
$640$	−531.384	+	920.383i	−0.0328200	+	0.0568459i
$641$	2601.46	−	946.853i	0.160298	−	0.0583439i	−0.260625	−	0.965440i	$-0.583928\pi$
$641$	2601.46	−	946.853i	0.160298	−	0.0583439i	0.420923	+	0.907096i	$0.361706\pi$
$642$	−4473.08	+	3753.36i	−0.274982	+	0.230737i
$643$	884.736	+	1532.41i	0.0542622	+	0.0939848i	0.891881	−	0.452271i	$-0.149386\pi$
$643$	884.736	+	1532.41i	0.0542622	+	0.0939848i	−0.837618	+	0.546256i	$0.816053\pi$
$644$	941.285	−	5338.29i	0.0575960	−	0.326643i
$645$	−1327.44	+	7528.31i	−0.0810357	+	0.459576i
$646$	−14914.5	−	12514.7i	−0.908361	−	0.762205i
$647$	−14315.7	−	5210.48i	−0.869871	−	0.316607i	−0.131756	−	0.991282i	$-0.542062\pi$
$647$	−14315.7	−	5210.48i	−0.869871	−	0.316607i	−0.738115	+	0.674675i	$0.764284\pi$
$648$	−2895.14	−	1053.74i	−0.175512	−	0.0638812i
$649$	−34231.7	−	28723.8i	−2.07043	−	1.73730i
$650$	985.679	−	5590.07i	0.0594793	−	0.337324i
$651$	−322.599	+	1829.55i	−0.0194219	+	0.110147i
$652$	1636.02	+	2833.66i	0.0982689	+	0.170207i
$653$	5582.87	−	4684.58i	0.334570	−	0.280738i	−0.459989	−	0.887925i	$-0.652147\pi$
$653$	5582.87	−	4684.58i	0.334570	−	0.280738i	0.794559	+	0.607187i	$0.207702\pi$
$654$	6320.32	−	2300.41i	0.377896	−	0.137543i
$655$	−622.439	+	1078.10i	−0.0371309	+	0.0643125i
$656$	−2609.40	−	4519.61i	−0.155305	−	0.268996i
$657$	10626.0	+	8916.25i	0.630988	+	0.529462i
$658$	425.809	−	737.523i	0.0252276	−	0.0436955i
$659$	−2469.82	−	14007.0i	−0.145995	−	0.827976i	−0.966563	−	0.256428i	$-0.917454\pi$
$659$	−2469.82	−	14007.0i	−0.145995	−	0.827976i	0.820569	−	0.571548i	$-0.193657\pi$
$660$	4509.43			0.265954
$661$	2030.21	+	11513.9i	0.119464	+	0.677516i	0.984443	+	0.175706i	$0.0562209\pi$
$661$	2030.21	+	11513.9i	0.119464	+	0.677516i	−0.864978	+	0.501809i	$0.832668\pi$
$662$	3325.70	−	2790.59i	0.195252	−	0.163836i
$663$	−9920.08	−	3610.61i	−0.581092	−	0.211500i
$664$	−4773.81	+	1737.53i	−0.279006	+	0.101550i
$665$	−5992.97			−0.349470
$666$	−10004.8	+	1588.07i	−0.582102	+	0.0923970i
$667$	6272.14			0.364105
$668$	1558.04	−	567.082i	0.0902433	−	0.0328459i
$669$	−6016.73	−	2189.91i	−0.347713	−	0.126557i
$670$	−8416.86	+	7062.58i	−0.485331	+	0.407241i
$671$	845.955	+	4797.65i	0.0486702	+	0.276023i
$672$	−494.772			−0.0284022
$673$	691.713	+	3922.90i	0.0396190	+	0.224690i	0.998188	−	0.0601694i	$-0.0191641\pi$
$673$	691.713	+	3922.90i	0.0396190	+	0.224690i	−0.958569	+	0.284860i	$0.908053\pi$
$674$	−6704.48	+	11612.5i	−0.383156	+	0.663646i
$675$	4507.49	+	3782.23i	0.257027	+	0.215672i
$676$	−731.758	−	1267.44i	−0.0416339	−	0.0721121i
$677$	5605.27	−	9708.61i	0.318210	−	0.551155i	−0.661905	−	0.749588i	$-0.730252\pi$
$677$	5605.27	−	9708.61i	0.318210	−	0.551155i	0.980115	+	0.198432i	$0.0635850\pi$
$678$	−3259.72	+	1186.44i	−0.184644	+	0.0672051i
$679$	58.1117	−	48.7615i	0.00328442	−	0.00275596i
$680$	3266.58	+	5657.89i	0.184217	+	0.319074i
$681$	1165.83	−	6611.74i	0.0656015	−	0.372045i
$682$	2672.47	−	15156.3i	0.150050	−	0.850975i
$683$	10042.0	+	8426.21i	0.562584	+	0.472064i	0.879176	−	0.476498i	$-0.158094\pi$
$683$	10042.0	+	8426.21i	0.562584	+	0.472064i	−0.316591	+	0.948562i	$0.602538\pi$
$684$	8372.30	+	3047.27i	0.468016	+	0.170344i
$685$	−6222.37	−	2264.76i	−0.347073	−	0.126324i
$686$	7070.60	+	5932.94i	0.393523	+	0.330205i
$687$	1879.02	−	10656.5i	0.104351	−	0.591804i
$688$	−1206.56	+	6842.73i	−0.0668599	+	0.379181i
$689$	−1395.69	−	2417.40i	−0.0771718	−	0.133665i
$690$	−5011.49	+	4205.14i	−0.276499	+	0.232010i
$691$	−8728.36	+	3176.86i	−0.480525	+	0.174897i	−0.570914	−	0.821010i	$-0.693411\pi$
$691$	−8728.36	+	3176.86i	−0.480525	+	0.174897i	0.0903894	+	0.995907i	$0.471189\pi$
$692$	−7279.34	+	12608.2i	−0.399883	+	0.692618i
$693$	−5255.59	−	9102.95i	−0.288086	−	0.498979i
$694$	−10330.1	−	8668.02i	−0.565024	−	0.474112i
$695$	−4970.78	+	8609.64i	−0.271298	+	0.469902i
$696$	−99.4123	−	563.795i	−0.00541410	−	0.0307049i
$697$	−32081.6			−1.74344
$698$	3662.96	+	20773.7i	0.198632	+	1.12650i
$699$	10139.8	−	8508.27i	0.548671	−	0.460390i
$700$	−1536.79	−	559.344i	−0.0829786	−	0.0302017i
$701$	−21784.6	+	7928.94i	−1.17374	+	0.427207i	−0.853987	−	0.520294i	$-0.825822\pi$
$701$	−21784.6	+	7928.94i	−1.17374	+	0.427207i	−0.319754	+	0.947501i	$0.603600\pi$
$702$	10626.8			0.571344
$703$	21999.7	−	3492.01i	1.18028	−	0.187345i
$704$	4098.78			0.219430
$705$	−965.811	+	351.527i	−0.0515951	+	0.0187791i
$706$	−7384.73	−	2687.82i	−0.393666	−	0.143283i
$707$	−3197.32	+	2682.87i	−0.170082	+	0.142715i
$708$	−1027.52	−	5827.34i	−0.0545430	−	0.309329i
$709$	23492.2			1.24439			0.622193	−	0.782864i	$-0.286242\pi$
$709$	23492.2			1.24439			0.622193	+	0.782864i	$0.286242\pi$
$710$	−1511.21	−	8570.49i	−0.0798798	−	0.453021i
$711$	5317.39	−	9209.99i	0.280475	−	0.485797i
$712$	3312.49	+	2779.51i	0.174355	+	0.146301i
$713$	11163.6	+	19335.8i	0.586365	+	1.01561i
$714$	−1520.76	+	2634.04i	−0.0797102	+	0.138062i
$715$	25296.0	−	9207.00i	1.32310	−	0.481570i
$716$	−5465.96	+	4586.49i	−0.285297	+	0.239392i
$717$	3974.14	+	6883.41i	0.206997	+	0.358529i
$718$	1412.12	−	8008.55i	0.0733983	−	0.416262i
$719$	−588.044	+	3334.96i	−0.0305012	+	0.172981i	−0.996253	−	0.0864868i	$-0.972436\pi$
$719$	−588.044	+	3334.96i	−0.0305012	+	0.172981i	0.965752	+	0.259468i	$0.0835471\pi$
$720$	−2290.25	−	1921.75i	−0.118545	−	0.0994714i
$721$	5270.83	+	1918.43i	0.272255	+	0.0990928i
$722$	−5519.18	−	2008.82i	−0.284491	−	0.103546i
$723$	−6728.18	−	5645.61i	−0.346091	−	0.290405i
$724$	−1029.91	+	5840.91i	−0.0528679	+	0.299828i
$725$	328.596	−	1863.56i	0.0168328	−	0.0954633i
$726$	−5873.90	−	10173.9i	−0.300277	−	0.520095i
$727$	19706.3	−	16535.6i	1.00532	−	0.843564i	0.0176074	−	0.999845i	$-0.494395\pi$
$727$	19706.3	−	16535.6i	1.00532	−	0.843564i	0.987713	+	0.156281i	$0.0499507\pi$
$728$	−2775.47	+	1010.19i	−0.141299	+	0.0514286i
$729$	1329.54	−	2302.83i	0.0675477	−	0.116996i
$730$	5117.55	+	8863.85i	0.259464	+	0.449405i
$731$	32720.3	+	27455.6i	1.65555	+	1.38917i
$732$	−322.546	+	558.667i	−0.0162864	+	0.0282089i
$733$	−474.930	−	2693.46i	−0.0239317	−	0.135724i	0.970501	−	0.241097i	$-0.0775073\pi$
$733$	−474.930	−	2693.46i	−0.0239317	−	0.135724i	−0.994433	+	0.105374i	$0.966396\pi$
$734$	2051.45			0.103161
$735$	−885.887	−	5024.11i	−0.0444577	−	0.252132i
$736$	−4555.11	+	3822.19i	−0.228130	+	0.191424i
$737$	39819.7	+	14493.2i	1.99020	+	0.724374i
$738$	13795.8	−	5021.27i	0.688118	−	0.250454i
$739$	36265.1			1.80519			0.902594	−	0.430493i	$-0.141660\pi$
$739$	36265.1			1.80519			0.902594	+	0.430493i	$0.141660\pi$
$740$	−7337.80	−	1423.76i	−0.364517	−	0.0707275i
$741$	−10622.9			−0.526640
$742$	−755.727	+	275.062i	−0.0373903	+	0.0136090i
$743$	16703.6	+	6079.63i	0.824761	+	0.300188i	0.719707	−	0.694278i	$-0.244276\pi$
$743$	16703.6	+	6079.63i	0.824761	+	0.300188i	0.105054	+	0.994467i	$0.466498\pi$
$744$	1561.14	−	1309.95i	0.0769275	−	0.0645498i
$745$	−3386.74	−	19207.2i	−0.166551	−	0.944559i
$746$	17291.4			0.848639
$747$	−2481.65	−	14074.2i	−0.121551	−	0.689353i
$748$	12598.2	−	21820.8i	0.615826	−	1.06664i
$749$	7693.30	+	6455.45i	0.375310	+	0.314922i
$750$	3187.25	+	5520.48i	0.155176	+	0.268772i
$751$	−8167.02	+	14145.7i	−0.396829	+	0.687328i	−0.993333	−	0.115282i	$-0.963223\pi$
$751$	−8167.02	+	14145.7i	−0.396829	+	0.687328i	0.596504	+	0.802610i	$0.296556\pi$
$752$	−877.859	+	319.514i	−0.0425694	+	0.0154940i
$753$	−7135.06	+	5987.03i	−0.345307	+	0.289747i
$754$	−1708.77	−	2959.68i	−0.0825330	−	0.142951i
$755$	2044.67	−	11595.9i	0.0985605	−	0.558965i
$756$	531.662	−	3015.21i	0.0255772	−	0.145056i
$757$	9619.73	+	8071.91i	0.461869	+	0.387554i	0.843818	−	0.536629i	$-0.180303\pi$
$757$	9619.73	+	8071.91i	0.461869	+	0.387554i	−0.381949	+	0.924183i	$0.624747\pi$
$758$	−11100.2	−	4040.13i	−0.531895	−	0.193594i
$759$	23709.1	+	8629.40i	1.13384	+	0.412684i
$760$	5036.05	+	4225.75i	0.240364	+	0.201689i
$761$	5198.14	−	29480.1i	0.247612	−	1.40427i	−0.566737	−	0.823899i	$-0.691794\pi$
$761$	5198.14	−	29480.1i	0.247612	−	1.40427i	0.814349	−	0.580376i	$-0.197094\pi$
$762$	−126.899	+	719.681i	−0.00603290	+	0.0342143i
$763$	−5784.02	−	10018.2i	−0.274437	−	0.475339i
$764$	−10710.6	+	8987.28i	−0.507195	+	0.425587i
$765$	−17270.3	+	6285.89i	−0.816223	+	0.297081i
$766$	−8667.20	+	15012.0i	−0.408823	+	0.708103i
$767$	−17661.7	−	30591.0i	−0.831458	−	1.44013i
$768$	415.770	+	348.873i	0.0195349	+	0.0163917i
$769$	7282.61	−	12613.8i	0.341505	−	0.591504i	−0.643207	−	0.765692i	$-0.722397\pi$
$769$	7282.61	−	12613.8i	0.341505	−	0.591504i	0.984712	+	0.174188i	$0.0557300\pi$
$770$	−1346.79	−	7638.01i	−0.0630322	−	0.357474i
$771$	13683.8			0.639184
$772$	403.107	+	2286.13i	0.0187929	+	0.106580i
$773$	7712.13	−	6471.25i	0.358844	−	0.301106i	−0.445486	−	0.895289i	$-0.646969\pi$
$773$	7712.13	−	6471.25i	0.358844	−	0.301106i	0.804330	+	0.594183i	$0.202525\pi$
$774$	−18367.7	−	6685.30i	−0.852989	−	0.310463i
$775$	6329.87	−	2303.88i	0.293388	−	0.106784i
$776$	−83.2154			−0.00384956
$777$	−1134.03	−	3289.86i	−0.0523592	−	0.151896i
$778$	−13383.9			−0.616754
$779$	−30335.7	+	11041.3i	−1.39524	+	0.507824i
$780$	3349.64	+	1219.17i	0.153764	+	0.0559656i
$781$	−25711.3	+	21574.4i	−1.17801	+	0.988465i
$782$	6347.47	+	35998.3i	0.290262	+	1.64616i
$783$	3542.66			0.161692
$784$	−805.213	−	4566.59i	−0.0366806	−	0.208026i
$785$	12160.5	−	21062.6i	0.552899	−	0.957650i
$786$	487.015	+	408.654i	0.0221008	+	0.0185448i
$787$	−8506.50	−	14733.7i	−0.385291	−	0.667343i	0.606519	−	0.795069i	$-0.292566\pi$
$787$	−8506.50	−	14733.7i	−0.385291	−	0.667343i	−0.991810	+	0.127726i	$0.959232\pi$
$788$	10589.5	−	18341.5i	0.478723	−	0.829173i
$789$	7075.93	−	2575.43i	0.319277	−	0.116207i
$790$	6011.18	−	5043.98i	0.270719	−	0.227160i
$791$	2983.12	+	5166.92i	0.134093	+	0.232256i
$792$	−2002.24	+	11355.3i	−0.0898314	+	0.509459i
$793$	−668.709	+	3792.43i	−0.0299452	+	0.169828i
$794$	4612.40	+	3870.26i	0.206156	+	0.172985i
$795$	912.067	+	331.965i	0.0406889	+	0.0148096i
$796$	6456.07	+	2349.82i	0.287474	+	0.104632i
$797$	−25769.7	−	21623.4i	−1.14531	−	0.961028i	−0.145710	−	0.989327i	$-0.546547\pi$
$797$	−25769.7	−	21623.4i	−1.14531	−	0.961028i	−0.999600	+	0.0282990i	$0.990991\pi$
$798$	−531.463	+	3014.08i	−0.0235759	+	0.133706i
$799$	−997.229	+	5655.57i	−0.0441545	+	0.250412i
$800$	896.998	+	1553.65i	0.0396421	+	0.0686621i
$801$	−9318.48	+	7819.14i	−0.411052	+	0.344913i
$802$	975.021	−	354.879i	0.0429292	−	0.0156249i
$803$	19736.9	−	34185.3i	0.867371	−	1.50233i
$804$	2805.61	+	4859.46i	0.123067	+	0.213159i
$805$	8619.32	+	7232.47i	0.377380	+	0.316660i
$806$	6082.77	−	10535.7i	0.265827	−	0.460426i
$807$	1509.49	+	8560.75i	0.0658446	+	0.373423i
$808$	4578.53			0.199347
$809$	4997.47	+	28342.1i	0.217184	+	1.23171i	0.877076	+	0.480351i	$0.159491\pi$
$809$	4997.47	+	28342.1i	0.217184	+	1.23171i	−0.659893	+	0.751360i	$0.729398\pi$
$810$	4898.98	−	4110.74i	0.212510	−	0.178317i
$811$	−27807.6	−	10121.2i	−1.20402	−	0.438227i	−0.339393	−	0.940645i	$-0.610222\pi$
$811$	−27807.6	−	10121.2i	−1.20402	−	0.438227i	−0.864625	+	0.502418i	$0.832444\pi$
$812$	−925.257	+	336.766i	−0.0399879	+	0.0145544i
$813$	−10519.7			−0.453802
$814$	9394.50	+	27253.8i	0.404517	+	1.17352i
$815$	−6791.81			−0.291910
$816$	3135.24	−	1141.13i	0.134504	−	0.0489555i
$817$	40388.9	+	14700.3i	1.72953	+	0.629498i
$818$	−11880.2	+	9968.71i	−0.507803	+	0.426098i
$819$	−1442.82	−	8182.62i	−0.0615581	−	0.349114i
$820$	10832.7			0.461337
$821$	6859.60	+	38902.7i	0.291598	+	1.65373i	0.680718	+	0.732545i	$0.261668\pi$
$821$	6859.60	+	38902.7i	0.291598	+	1.65373i	−0.389121	+	0.921187i	$0.627221\pi$
$822$	−1690.84	+	2928.61i	−0.0717454	+	0.124267i
$823$	1111.77	+	932.890i	0.0470887	+	0.0395121i	0.666028	−	0.745926i	$-0.267993\pi$
$823$	1111.77	+	932.890i	0.0470887	+	0.0395121i	−0.618940	+	0.785439i	$0.712437\pi$
$824$	−3076.50	−	5328.66i	−0.130067	−	0.225282i
$825$	3806.06	−	6592.28i	0.160618	−	0.278199i
$826$	−9563.38	+	3480.78i	−0.402848	+	0.146625i
$827$	−12965.4	+	10879.2i	−0.545163	+	0.457446i	−0.873299	−	0.487185i	$-0.838024\pi$
$827$	−12965.4	+	10879.2i	−0.545163	+	0.457446i	0.328136	+	0.944630i	$0.393579\pi$
$828$	−8363.85	−	14486.6i	−0.351043	−	0.608025i
$829$	−2035.76	+	11545.4i	−0.0852893	+	0.483700i	0.912004	+	0.410180i	$0.134534\pi$
$829$	−2035.76	+	11545.4i	−0.0852893	+	0.483700i	−0.997294	+	0.0735194i	$0.976577\pi$
$830$	1831.13	−	10384.8i	0.0765775	−	0.434292i
$831$	−5877.02	−	4931.40i	−0.245333	−	0.205859i
$832$	3044.60	+	1108.14i	0.126866	+	0.0461754i
$833$	−26786.2	−	9749.40i	−1.11415	−	0.405518i
$834$	3889.28	+	3263.49i	0.161481	+	0.135498i
$835$	−597.630	+	3389.33i	−0.0247687	+	0.140470i
$836$	4402.73	−	24969.1i	0.182143	−	1.03299i
$837$	6305.47	+	10921.4i	0.260393	+	0.451014i
$838$	−10985.8	+	9218.21i	−0.452863	+	0.379997i
$839$	−9445.40	+	3437.84i	−0.388667	+	0.141463i	−0.528960	−	0.848647i	$-0.677418\pi$
$839$	−9445.40	+	3437.84i	−0.388667	+	0.141463i	0.140293	+	0.990110i	$0.455196\pi$
$840$	513.504	−	889.415i	0.0210923	−	0.0365330i
$841$	11624.8	+	20134.8i	0.476643	+	0.825570i
$842$	−16080.3	−	13493.0i	−0.658151	−	0.552255i
$843$	5888.85	−	10199.8i	0.240597	−	0.416725i
$844$	−773.353	−	4385.90i	−0.0315402	−	0.178873i
$845$	3037.85			0.123675
$846$	−456.352	−	2588.10i	−0.0185458	−	0.105178i
$847$	−15478.1	+	12987.7i	−0.627902	+	0.526872i
$848$	829.009	+	301.735i	0.0335711	+	0.0122189i
$849$	1371.98	−	499.358i	0.0554606	−	0.0201860i
$850$	11028.3			0.445019
$851$	−35855.1	−	21527.5i	−1.44430	−	0.867159i
$852$	−4444.42			−0.178713
$853$	33522.3	−	12201.1i	1.34558	−	0.489751i	0.434015	−	0.900906i	$-0.357096\pi$
$853$	33522.3	−	12201.1i	1.34558	−	0.489751i	0.911566	+	0.411154i	$0.134874\pi$
$854$	1042.59	+	379.472i	0.0417761	+	0.0152052i
$855$	−14167.1	+	11887.6i	−0.566672	+	0.475494i
$856$	−1913.04	−	10849.4i	−0.0763858	−	0.433205i
$857$	−43677.1			−1.74093			−0.870467	−	0.492227i	$-0.836183\pi$
$857$	−43677.1			−1.74093			−0.870467	+	0.492227i	$0.836183\pi$
$858$	−2387.25	−	13538.8i	−0.0949877	−	0.538702i
$859$	−6925.00	+	11994.4i	−0.275061	+	0.476420i	−0.970151	−	0.242503i	$-0.922032\pi$
$859$	−6925.00	+	11994.4i	−0.275061	+	0.476420i	0.695089	+	0.718924i	$0.255365\pi$
$860$	−11048.4	−	9270.73i	−0.438079	−	0.367592i
$861$	2521.60	+	4367.54i	0.0998093	+	0.172875i
$862$	15888.1	−	27519.0i	0.627786	−	1.08736i
$863$	−17831.7	+	6490.19i	−0.703356	+	0.256001i	−0.668843	−	0.743404i	$-0.733210\pi$
$863$	−17831.7	+	6490.19i	−0.703356	+	0.256001i	−0.0345130	+	0.999404i	$0.510988\pi$
$864$	−2572.84	+	2158.87i	−0.101308	+	0.0850073i
$865$	−15109.9	−	26171.0i	−0.593931	−	1.02872i
$866$	−2475.72	+	14040.5i	−0.0971459	+	0.550942i
$867$	1752.83	−	9940.77i	0.0686610	−	0.389396i
$868$	−2685.02	−	2253.00i	−0.104995	−	0.0881011i
$869$	−28438.6	−	10350.8i	−1.11014	−	0.404058i
$870$	1116.67	+	406.434i	0.0435156	+	0.0158384i
$871$	25659.9	+	21531.3i	0.998225	+	0.837610i
$872$	−2203.55	+	12497.0i	−0.0855754	+	0.485322i
$873$	40.6504	−	230.540i	0.00157596	−	0.00893769i
$874$	18391.3	+	31854.7i	0.711779	+	1.23284i
$875$	8398.59	−	7047.25i	0.324485	−	0.272275i
$876$	4911.78	−	1787.74i	0.189445	−	0.0689523i
$877$	−13856.4	+	24000.1i	−0.533522	+	0.924087i	0.465711	+	0.884937i	$0.345799\pi$
$877$	−13856.4	+	24000.1i	−0.533522	+	0.924087i	−0.999233	+	0.0391506i	$0.987535\pi$
$878$	−719.427	−	1246.08i	−0.0276532	−	0.0478967i
$879$	6702.60	+	5624.15i	0.257193	+	0.215811i
$880$	−4253.95	+	7368.06i	−0.162955	+	0.282247i
$881$	8245.76	+	46764.0i	0.315331	+	1.78833i	0.570356	+	0.821397i	$0.306805\pi$
$881$	8245.76	+	46764.0i	0.315331	+	1.78833i	−0.255025	+	0.966934i	$0.582084\pi$
$882$	13044.6			0.497999
$883$	−3453.98	−	19588.5i	−0.131637	−	0.746552i	−0.977143	−	0.212585i	$-0.931812\pi$
$883$	−3453.98	−	19588.5i	−0.131637	−	0.746552i	0.845505	−	0.533967i	$-0.179299\pi$
$884$	15257.5	−	12802.6i	0.580504	−	0.487101i
$885$	11541.8	+	4200.87i	0.438387	+	0.159560i
$886$	19122.5	−	6960.03i	0.725094	−	0.263913i
$887$	−4789.79			−0.181314			−0.0906569	−	0.995882i	$-0.528897\pi$
$887$	−4789.79			−0.181314			−0.0906569	+	0.995882i	$0.528897\pi$
$888$	−1366.78	+	3564.18i	−0.0516512	+	0.134692i
$889$	1256.88			0.0474179
$890$	−8434.40	+	3069.87i	−0.317665	+	0.115621i
$891$	−23176.8	−	8435.68i	−0.871440	−	0.317178i
$892$	9253.99	−	7765.02i	0.347362	−	0.291471i
$893$	1003.48	+	5690.99i	0.0376036	+	0.213261i
$894$	−9960.32			−0.372621
$895$	−2571.88	−	14585.9i	−0.0960542	−	0.544751i
$896$	466.741	−	808.419i	0.0174026	−	0.0301422i
$897$	15278.2	+	12819.9i	0.568701	+	0.477197i
$898$	3179.44	+	5506.96i	0.118151	+	0.204643i
$899$	2027.81	−	3512.28i	0.0752296	−	0.130301i
$900$	−4742.40	+	1726.09i	−0.175645	+	0.0639294i
$901$	4154.45	−	3485.99i	0.153612	−	0.128896i
$902$	−20889.3	−	36181.4i	−0.771108	−	1.33560i
$903$	1165.96	−	6612.49i	0.0429687	−	0.243688i
$904$	1136.49	−	6445.36i	0.0418132	−	0.237134i
$905$	−9430.86	−	7913.43i	−0.346401	−	0.290665i
$906$	−5650.68	−	2056.68i	−0.207209	−	0.0754178i
$907$	−19340.2	−	7039.26i	−0.708027	−	0.257701i	−0.0371930	−	0.999308i	$-0.511842\pi$
$907$	−19340.2	−	7039.26i	−0.708027	−	0.257701i	−0.670834	+	0.741607i	$0.734064\pi$
$908$	9703.28	+	8142.02i	0.354642	+	0.297580i
$909$	−2236.60	+	12684.4i	−0.0816097	+	0.462832i
$910$	1064.60	−	6037.67i	0.0387817	−	0.219942i
$911$	−14253.5	−	24687.8i	−0.518375	−	0.897853i	−0.999772	−	0.0213497i	$-0.993204\pi$
$911$	−14253.5	−	24687.8i	−0.518375	−	0.897853i	0.481397	−	0.876503i	$-0.340130\pi$
$912$	2571.88	−	2158.07i	0.0933811	−	0.0783560i
$913$	−38216.4	+	13909.6i	−1.38530	+	0.504208i
$914$	14435.0	−	25002.1i	0.522393	−	0.904811i
$915$	−669.515	−	1159.63i	−0.0241896	−	0.0418976i
$916$	15639.3	+	13122.9i	0.564122	+	0.473354i
$917$	546.720	−	946.946i	0.0196884	−	0.0341013i
$918$	3585.22	+	20332.8i	0.128900	+	0.731026i
$919$	28696.8			1.03005			0.515027	−	0.857174i	$-0.327782\pi$
$919$	28696.8			1.03005			0.515027	+	0.857174i	$0.327782\pi$
$920$	−2143.30	−	12155.3i	−0.0768071	−	0.435595i
$921$	−11587.9	+	9723.41i	−0.414587	+	0.347880i
$922$	1176.02	+	428.037i	0.0420068	+	0.0152892i
$923$	−24931.3	+	9074.27i	−0.889085	+	0.323600i
$924$	−3960.86			−0.141020
$925$	−8274.63	+	9525.35i	−0.294128	+	0.338586i
$926$	8162.00			0.289655
$927$	16265.4	−	5920.12i	0.576295	−	0.209754i
$928$	1014.98	+	369.422i	0.0359033	+	0.0130677i
$929$	30694.4	−	25755.6i	1.08401	−	0.909596i	0.0877663	−	0.996141i	$-0.472027\pi$
$929$	30694.4	−	25755.6i	1.08401	−	0.909596i	0.996248	+	0.0865451i	$0.0275827\pi$
$930$	734.557	+	4165.88i	0.0259001	+	0.146887i
$931$	−28683.9			−1.00975
$932$	4336.55	+	24593.8i	0.152413	+	0.864374i
$933$	−7994.66	+	13847.1i	−0.280529	+	0.485890i
$934$	−27198.7	−	22822.4i	−0.952858	−	0.799543i
$935$	26150.4	+	45293.8i	0.914662	+	1.58424i
$936$	−4557.27	+	7893.43i	−0.159144	+	0.275646i
$937$	−39472.2	+	14366.7i	−1.37620	+	0.500896i	−0.921024	−	0.389505i	$-0.872646\pi$
$937$	−39472.2	+	14366.7i	−1.37620	+	0.500896i	−0.455177	+	0.890401i	$0.650424\pi$
$938$	7392.95	−	6203.42i	0.257344	−	0.215937i
$939$	−7545.22	−	13068.7i	−0.262225	−	0.454187i
$940$	336.726	−	1909.67i	0.0116838	−	0.0662623i
$941$	−5507.38	+	31233.9i	−0.190792	+	1.08204i	0.727492	+	0.686116i	$0.240686\pi$
$941$	−5507.38	+	31233.9i	−0.190792	+	1.08204i	−0.918284	+	0.395921i	$0.870425\pi$
$942$	−9514.72	−	7983.79i	−0.329094	−	0.276142i
$943$	56954.9	+	20729.9i	1.96682	+	0.715862i
$944$	10490.7	+	3818.31i	0.361699	+	0.131648i
$945$	4868.42	+	4085.09i	0.167587	+	0.140622i
$946$	−9659.01	+	54779.0i	−0.331968	+	1.88268i
$947$	2354.76	−	13354.5i	0.0808021	−	0.458251i	−0.917382	−	0.398009i	$-0.869701\pi$
$947$	2354.76	−	13354.5i	0.0808021	−	0.458251i	0.998184	−	0.0602427i	$-0.0191875\pi$
$948$	−2003.72	−	3470.54i	−0.0686474	−	0.118901i
$949$	23903.0	−	20057.0i	0.817622	−	0.686066i
$950$	10428.1	−	3795.52i	0.356139	−	0.129624i
$951$	−2011.93	+	3484.76i	−0.0686027	+	0.118823i
$952$	−2869.21	−	4969.61i	−0.0976801	−	0.169187i
$953$	−762.038	−	639.425i	−0.0259022	−	0.0217345i	0.629745	−	0.776802i	$-0.283160\pi$
$953$	−762.038	−	639.425i	−0.0259022	−	0.0217345i	−0.655647	+	0.755068i	$0.727604\pi$
$954$	−1240.89	+	2149.29i	−0.0421126	+	0.0729412i
$955$	−5039.64	−	28581.2i	−0.170763	−	0.968446i
$956$	−14995.9			−0.507325
$957$	−795.838	−	4513.42i	−0.0268817	−	0.152454i
$958$	−1942.55	+	1630.00i	−0.0655126	+	0.0549716i
$959$	5465.42	+	1989.25i	0.184033	+	0.0669826i
$960$	−1058.65	+	385.318i	−0.0355915	+	0.0129543i
$961$	−15354.1			−0.515392
$962$	−390.018	+	22784.2i	−0.0130714	+	0.763608i
$963$	30991.6			1.03706
$964$	15571.5	−	5667.55i	0.520252	−	0.189356i
$965$	−4527.97	−	1648.05i	−0.151047	−	0.0549767i
$966$	4401.84	−	3693.58i	0.146612	−	0.123022i
$967$	168.760	+	957.088i	0.00561217	+	0.0318282i	0.987485	−	0.157711i	$-0.0504116\pi$
$967$	168.760	+	957.088i	0.00561217	+	0.0318282i	−0.981873	+	0.189540i	$0.939300\pi$
$968$	22164.5			0.735943
$969$	−3583.88	−	20325.2i	−0.118814	−	0.673827i
$970$	86.3658	−	149.590i	0.00285880	−	0.00495159i
$971$	15641.6	+	13124.8i	0.516953	+	0.433775i	0.863568	−	0.504232i	$-0.168224\pi$
$971$	15641.6	+	13124.8i	0.516953	+	0.433775i	−0.346615	+	0.938008i	$0.612669\pi$
$972$	−7300.64	−	12645.1i	−0.240914	−	0.417275i
$973$	4366.08	−	7562.28i	0.143854	−	0.249163i
$974$	−2978.32	+	1084.02i	−0.0979789	+	0.0356614i
$975$	4609.45	−	3867.79i	0.151406	−	0.127044i
$976$	−608.545	−	1054.03i	−0.0199580	−	0.0345683i
$977$	2522.77	−	14307.4i	0.0826107	−	0.468509i	−0.915236	−	0.402918i	$-0.867996\pi$
$977$	2522.77	−	14307.4i	0.0826107	−	0.468509i	0.997847	−	0.0655904i	$-0.0208931\pi$
$978$	−602.306	+	3415.85i	−0.0196929	+	0.111684i
$979$	26517.9	+	22251.1i	0.865694	+	0.726404i
$980$	9044.70	+	3292.00i	0.294819	+	0.107305i
$981$	−33545.2	−	12209.5i	−1.09176	−	0.397368i
$982$	−9281.83	−	7788.38i	−0.301624	−	0.253093i
$983$	2222.16	−	12602.5i	0.0721015	−	0.408908i	−0.927300	−	0.374319i	$-0.877877\pi$
$983$	2222.16	−	12602.5i	0.0721015	−	0.408908i	0.999402	−	0.0345893i	$-0.0110123\pi$
$984$	960.661	−	5448.18i	0.0311227	−	0.176506i
$985$	21980.7	+	38071.7i	0.711029	+	1.23154i
$986$	5086.40	−	4267.99i	0.164284	−	0.137850i
$987$	848.321	−	308.764i	0.0273580	−	0.00995750i
$988$	10021.0	−	17356.9i	0.322683	−	0.558904i
$989$	−40348.1	−	69885.0i	−1.29726	−	2.24693i
$990$	−18334.4	−	15384.4i	−0.588593	−	0.493888i
$991$	−27760.1	+	48081.9i	−0.889836	+	1.54124i	−0.0497685	+	0.998761i	$0.515848\pi$
$991$	−27760.1	+	48081.9i	−0.889836	+	1.54124i	−0.840068	+	0.542481i	$0.817485\pi$
$992$	667.664	+	3786.51i	0.0213693	+	0.121191i
$993$	4602.12			0.147073
$994$	1327.37	+	7527.89i	0.0423558	+	0.240211i
$995$	−10924.6	+	9166.81i	−0.348073	+	0.292068i
$996$	−5060.52	−	1841.88i	−0.160993	−	0.0585965i
$997$	37832.5	−	13769.9i	1.20177	−	0.437410i	0.337931	−	0.941171i	$-0.390273\pi$
$997$	37832.5	−	13769.9i	1.20177	−	0.437410i	0.863843	+	0.503761i	$0.168051\pi$
$998$	33888.7			1.07488
$999$	−20251.9	−	12159.3i	−0.641383	−	0.385088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.4.f.b.7.2	✓	30
37.16	even	9	inner	74.4.f.b.53.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.f.b.7.2	✓	30	1.1	even	1	trivial
74.4.f.b.53.2	yes	30	37.16	even	9	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	74.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87939 + 0.684040i) q^{2} +(-1.99226 - 0.725122i) q^{3} +(3.06418 - 2.57115i) q^{4} +(1.44178 + 8.17673i) q^{5} +4.24023 q^{6} +(-1.26639 - 7.18203i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-17.2399 - 14.4660i) q^{9} +O(q^{10})\)	\(q+(-1.87939 + 0.684040i) q^{2} +(-1.99226 - 0.725122i) q^{3} +(3.06418 - 2.57115i) q^{4} +(1.44178 + 8.17673i) q^{5} +4.24023 q^{6} +(-1.26639 - 7.18203i) q^{7} +(-4.00000 + 6.92820i) q^{8} +(-17.2399 - 14.4660i) q^{9} +(-8.30287 - 14.3810i) q^{10} +(-32.0217 + 55.4632i) q^{11} +(-7.96903 + 2.90049i) q^{12} +(-38.7809 + 32.5410i) q^{13} +(7.29283 + 12.6315i) q^{14} +(3.05674 - 17.3356i) q^{15} +(2.77837 - 15.7569i) q^{16} +(-75.3459 - 63.2227i) q^{17} +(42.2958 + 15.3944i) q^{18} +(-93.0044 - 33.8508i) q^{19} +(25.4415 + 21.3479i) q^{20} +(-2.68488 + 15.2267i) q^{21} +(22.2420 - 126.141i) q^{22} +(92.9105 + 160.926i) q^{23} +(12.9928 - 10.9023i) q^{24} +(52.6814 - 19.1745i) q^{25} +(50.6249 - 87.6849i) q^{26} +(52.4783 + 90.8950i) q^{27} +(-22.3465 - 18.7510i) q^{28} +(16.8768 - 29.2315i) q^{29} +(6.11347 + 34.6712i) q^{30} +120.154 q^{31} +(5.55674 + 31.5138i) q^{32} +(104.013 - 87.2773i) q^{33} +(184.851 + 67.2802i) q^{34} +(56.8997 - 20.7098i) q^{35} -90.0204 q^{36} +(-196.807 + 109.179i) q^{37} +197.946 q^{38} +(100.858 - 36.7092i) q^{39} +(-62.4172 - 22.7180i) q^{40} +(249.864 - 209.661i) q^{41} +(-5.36977 - 30.4535i) q^{42} -434.268 q^{43} +(44.4841 + 252.282i) q^{44} +(93.4285 - 161.823i) q^{45} +(-284.694 - 238.887i) q^{46} +(-29.1937 - 50.5649i) q^{47} +(-16.9609 + 29.3772i) q^{48} +(272.337 - 99.1225i) q^{49} +(-85.8925 + 72.0724i) q^{50} +(104.264 + 180.591i) q^{51} +(-35.1637 + 199.423i) q^{52} +(-9.57467 + 54.3006i) q^{53} +(-160.803 - 134.930i) q^{54} +(-499.676 - 181.867i) q^{55} +(54.8241 + 19.9544i) q^{56} +(160.743 + 134.879i) q^{57} +(-11.7225 + 66.4817i) q^{58} +(-121.163 + 687.149i) q^{59} +(-35.2061 - 60.9787i) q^{60} +(58.2716 - 48.8956i) q^{61} +(-225.815 + 82.1901i) q^{62} +(-82.0630 + 142.137i) q^{63} +(-32.0000 - 55.4256i) q^{64} +(-321.993 - 270.184i) q^{65} +(-135.779 + 235.177i) q^{66} +(-114.897 - 651.612i) q^{67} -393.428 q^{68} +(-68.4108 - 387.977i) q^{69} +(-92.7701 + 77.8434i) q^{70} +(492.472 + 179.245i) q^{71} +(169.183 - 61.5776i) q^{72} -616.359 q^{73} +(295.194 - 339.813i) q^{74} -118.859 q^{75} +(-372.018 + 135.403i) q^{76} +(438.890 + 159.743i) q^{77} +(-164.440 + 137.982i) q^{78} +(82.0574 + 465.370i) q^{79} +132.846 q^{80} +(66.8750 + 379.267i) q^{81} +(-326.175 + 564.951i) q^{82} +(486.456 + 408.185i) q^{83} +(30.9233 + 53.5607i) q^{84} +(408.323 - 707.236i) q^{85} +(816.157 - 297.057i) q^{86} +(-54.8194 + 45.9989i) q^{87} +(-256.174 - 443.706i) q^{88} +(93.8600 - 532.306i) q^{89} +(-64.8948 + 368.036i) q^{90} +(282.823 + 237.316i) q^{91} +(698.459 + 254.218i) q^{92} +(-239.377 - 87.1262i) q^{93} +(89.4546 + 75.0613i) q^{94} +(142.697 - 809.277i) q^{95} +(11.7809 - 66.8130i) q^{96} +(5.20096 + 9.00833i) q^{97} +(-444.022 + 372.579i) q^{98} +(1354.38 - 492.955i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9}+O(q^{10}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9	\( 30 q + 6 q^{3} - 6 q^{5} - 36 q^{6} - 75 q^{7} - 120 q^{8} - 48 q^{9} + 54 q^{10} - 21 q^{11} + 24 q^{12} - 159 q^{13} + 6 q^{14} - 69 q^{15} - 171 q^{17} + 192 q^{18} - 45 q^{19} - 24 q^{20} + 579 q^{21} + 42 q^{22} + 459 q^{23} + 48 q^{24} - 204 q^{25} + 264 q^{26} + 435 q^{27} + 96 q^{28} + 273 q^{29} - 138 q^{30} - 258 q^{31} - 318 q^{33} - 558 q^{34} - 753 q^{35} + 1296 q^{36} - 891 q^{37} - 2556 q^{38} - 504 q^{39} + 96 q^{40} + 648 q^{41} + 1158 q^{42} - 216 q^{43} + 84 q^{44} + 1731 q^{45} - 6 q^{46} + 48 q^{47} + 144 q^{48} + 1731 q^{49} + 240 q^{50} + 972 q^{51} + 48 q^{52} - 135 q^{53} + 360 q^{54} + 765 q^{55} + 408 q^{56} - 405 q^{57} - 762 q^{58} + 1836 q^{59} + 108 q^{60} - 684 q^{61} - 204 q^{62} - 3264 q^{63} - 960 q^{64} - 1350 q^{65} + 252 q^{66} + 1095 q^{67} - 432 q^{68} - 5823 q^{69} - 1146 q^{70} + 4179 q^{71} + 768 q^{72} - 2658 q^{73} - 1692 q^{74} - 10416 q^{75} - 180 q^{76} + 267 q^{77} + 1530 q^{78} + 4866 q^{79} - 864 q^{80} - 2076 q^{81} + 1800 q^{82} - 186 q^{83} + 504 q^{84} + 753 q^{85} + 648 q^{86} - 525 q^{87} - 168 q^{88} + 687 q^{89} + 768 q^{90} + 3990 q^{91} + 132 q^{92} + 3753 q^{93} + 6210 q^{94} + 9000 q^{95} - 384 q^{96} + 7428 q^{97} - 1542 q^{98} + 6324 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 6 * q^5 - 36 * q^6 - 75 * q^7 - 120 * q^8 - 48 * q^9 + 54 * q^10 - 21 * q^11 + 24 * q^12 - 159 * q^13 + 6 * q^14 - 69 * q^15 - 171 * q^17 + 192 * q^18 - 45 * q^19 - 24 * q^20 + 579 * q^21 + 42 * q^22 + 459 * q^23 + 48 * q^24 - 204 * q^25 + 264 * q^26 + 435 * q^27 + 96 * q^28 + 273 * q^29 - 138 * q^30 - 258 * q^31 - 318 * q^33 - 558 * q^34 - 753 * q^35 + 1296 * q^36 - 891 * q^37 - 2556 * q^38 - 504 * q^39 + 96 * q^40 + 648 * q^41 + 1158 * q^42 - 216 * q^43 + 84 * q^44 + 1731 * q^45 - 6 * q^46 + 48 * q^47 + 144 * q^48 + 1731 * q^49 + 240 * q^50 + 972 * q^51 + 48 * q^52 - 135 * q^53 + 360 * q^54 + 765 * q^55 + 408 * q^56 - 405 * q^57 - 762 * q^58 + 1836 * q^59 + 108 * q^60 - 684 * q^61 - 204 * q^62 - 3264 * q^63 - 960 * q^64 - 1350 * q^65 + 252 * q^66 + 1095 * q^67 - 432 * q^68 - 5823 * q^69 - 1146 * q^70 + 4179 * q^71 + 768 * q^72 - 2658 * q^73 - 1692 * q^74 - 10416 * q^75 - 180 * q^76 + 267 * q^77 + 1530 * q^78 + 4866 * q^79 - 864 * q^80 - 2076 * q^81 + 1800 * q^82 - 186 * q^83 + 504 * q^84 + 753 * q^85 + 648 * q^86 - 525 * q^87 - 168 * q^88 + 687 * q^89 + 768 * q^90 + 3990 * q^91 + 132 * q^92 + 3753 * q^93 + 6210 * q^94 + 9000 * q^95 - 384 * q^96 + 7428 * q^97 - 1542 * q^98 + 6324 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more