LMFDB - Embedded newform 144.3.v.a.43.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(43,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("144.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.v (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.9
Character	$\chi$	$=$	144.43
Dual form			144.3.v.a.67.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62235 + 1.16960i) q^{2} +(-0.520377 + 2.95452i) q^{3} +(1.26405 - 3.79502i) q^{4} +(-1.70362 + 6.35798i) q^{5} +(-2.61139 - 5.40191i) q^{6} +(-0.581649 + 1.00744i) q^{7} +(2.38794 + 7.63530i) q^{8} +(-8.45841 - 3.07493i) q^{9} +O(q^{10})$	\(q+(-1.62235 + 1.16960i) q^{2} +(-0.520377 + 2.95452i) q^{3} +(1.26405 - 3.79502i) q^{4} +(-1.70362 + 6.35798i) q^{5} +(-2.61139 - 5.40191i) q^{6} +(-0.581649 + 1.00744i) q^{7} +(2.38794 + 7.63530i) q^{8} +(-8.45841 - 3.07493i) q^{9} +(-4.67246 - 12.3074i) q^{10} +(0.720261 + 2.68805i) q^{11} +(10.5547 + 5.70951i) q^{12} +(0.641258 + 0.171825i) q^{13} +(-0.234673 - 2.31473i) q^{14} +(-17.8983 - 8.34192i) q^{15} +(-12.8044 - 9.59420i) q^{16} -1.67347 q^{17} +(17.3190 - 4.90437i) q^{18} +(-11.7691 - 11.7691i) q^{19} +(21.9752 + 14.5021i) q^{20} +(-2.67384 - 2.24275i) q^{21} +(-4.31248 - 3.51855i) q^{22} +(-17.9147 - 31.0292i) q^{23} +(-23.8013 + 3.08198i) q^{24} +(-15.8710 - 9.16310i) q^{25} +(-1.24131 + 0.471259i) q^{26} +(13.4865 - 23.3905i) q^{27} +(3.08804 + 3.48083i) q^{28} +(10.7737 + 40.2079i) q^{29} +(38.7940 - 7.40037i) q^{30} +(-18.1310 + 10.4679i) q^{31} +(31.9946 + 0.589138i) q^{32} +(-8.31672 + 0.729228i) q^{33} +(2.71496 - 1.95730i) q^{34} +(-5.41441 - 5.41441i) q^{35} +(-22.3613 + 28.2130i) q^{36} +(23.8924 + 23.8924i) q^{37} +(32.8587 + 5.32841i) q^{38} +(-0.841356 + 1.80520i) q^{39} +(-52.6132 + 2.17484i) q^{40} +(-67.9164 + 39.2116i) q^{41} +(6.96104 + 0.511185i) q^{42} +(3.91706 + 14.6187i) q^{43} +(11.1117 + 0.664429i) q^{44} +(33.9603 - 48.5399i) q^{45} +(65.3558 + 29.3871i) q^{46} +(52.9130 + 30.5493i) q^{47} +(35.0094 - 32.8381i) q^{48} +(23.8234 + 41.2633i) q^{49} +(36.4655 - 3.69697i) q^{50} +(0.870837 - 4.94431i) q^{51} +(1.46266 - 2.21639i) q^{52} +(64.3295 + 64.3295i) q^{53} +(5.47768 + 53.7215i) q^{54} -18.3176 q^{55} +(-9.08108 - 2.03534i) q^{56} +(40.8963 - 28.6476i) q^{57} +(-64.5061 - 52.6304i) q^{58} +(-66.9370 - 17.9357i) q^{59} +(-54.2821 + 57.3797i) q^{60} +(-3.29732 - 12.3058i) q^{61} +(17.1715 - 38.1887i) q^{62} +(8.01765 - 6.73286i) q^{63} +(-52.5955 + 36.4652i) q^{64} +(-2.18492 + 3.78438i) q^{65} +(12.6397 - 10.9103i) q^{66} +(6.45622 - 24.0949i) q^{67} +(-2.11535 + 6.35086i) q^{68} +(100.999 - 36.7825i) q^{69} +(15.1168 + 2.45136i) q^{70} -97.4205 q^{71} +(3.27988 - 71.9253i) q^{72} -77.4165i q^{73} +(-66.7064 - 10.8172i) q^{74} +(35.3315 - 42.1228i) q^{75} +(-59.5405 + 29.7871i) q^{76} +(-3.12700 - 0.837878i) q^{77} +(-0.746393 - 3.91272i) q^{78} +(113.247 + 65.3833i) q^{79} +(82.8134 - 65.0650i) q^{80} +(62.0896 + 52.0181i) q^{81} +(64.3223 - 143.050i) q^{82} +(-108.976 + 29.2000i) q^{83} +(-11.8911 + 7.31234i) q^{84} +(2.85095 - 10.6399i) q^{85} +(-23.4529 - 19.1352i) q^{86} +(-124.402 + 10.9078i) q^{87} +(-18.8041 + 11.9183i) q^{88} -11.8648i q^{89} +(1.67703 + 118.469i) q^{90} +(-0.546091 + 0.546091i) q^{91} +(-140.401 + 28.7642i) q^{92} +(-21.4928 - 59.0156i) q^{93} +(-121.574 + 12.3255i) q^{94} +(94.8773 - 54.7774i) q^{95} +(-18.3899 + 94.2221i) q^{96} +(-79.8339 + 138.276i) q^{97} +(-86.9116 - 39.0797i) q^{98} +(2.17331 - 24.9514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8}+O(q^{10}) $ 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8	\( 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8} - 8 q^{10} - 2 q^{11} + 56 q^{12} - 2 q^{13} + 14 q^{14} - 2 q^{16} - 16 q^{17} + 38 q^{18} - 8 q^{19} - 44 q^{20} + 14 q^{21} - 2 q^{22} - 4 q^{23} + 120 q^{24} - 104 q^{26} - 52 q^{27} + 56 q^{28} - 2 q^{29} - 130 q^{30} - 182 q^{32} - 8 q^{33} - 10 q^{34} + 92 q^{35} - 2 q^{36} - 8 q^{37} - 254 q^{38} + 184 q^{39} - 2 q^{40} - 252 q^{42} - 2 q^{43} - 140 q^{44} - 54 q^{45} + 176 q^{46} + 162 q^{48} - 480 q^{49} - 96 q^{50} - 120 q^{51} - 2 q^{52} - 8 q^{53} + 94 q^{54} - 16 q^{55} + 260 q^{56} + 88 q^{58} + 142 q^{59} - 434 q^{60} - 2 q^{61} - 636 q^{62} + 244 q^{64} - 4 q^{65} - 100 q^{66} - 2 q^{67} - 112 q^{68} + 14 q^{69} - 100 q^{70} - 16 q^{71} + 98 q^{72} + 82 q^{74} - 296 q^{75} + 154 q^{76} + 194 q^{77} + 228 q^{78} + 592 q^{80} - 8 q^{81} - 420 q^{82} + 238 q^{83} - 22 q^{84} - 52 q^{85} - 170 q^{86} - 456 q^{87} - 26 q^{88} + 808 q^{90} + 188 q^{91} + 176 q^{92} + 26 q^{93} - 18 q^{94} - 202 q^{96} - 4 q^{97} + 408 q^{98} - 38 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8 - 8 * q^10 - 2 * q^11 + 56 * q^12 - 2 * q^13 + 14 * q^14 - 2 * q^16 - 16 * q^17 + 38 * q^18 - 8 * q^19 - 44 * q^20 + 14 * q^21 - 2 * q^22 - 4 * q^23 + 120 * q^24 - 104 * q^26 - 52 * q^27 + 56 * q^28 - 2 * q^29 - 130 * q^30 - 182 * q^32 - 8 * q^33 - 10 * q^34 + 92 * q^35 - 2 * q^36 - 8 * q^37 - 254 * q^38 + 184 * q^39 - 2 * q^40 - 252 * q^42 - 2 * q^43 - 140 * q^44 - 54 * q^45 + 176 * q^46 + 162 * q^48 - 480 * q^49 - 96 * q^50 - 120 * q^51 - 2 * q^52 - 8 * q^53 + 94 * q^54 - 16 * q^55 + 260 * q^56 + 88 * q^58 + 142 * q^59 - 434 * q^60 - 2 * q^61 - 636 * q^62 + 244 * q^64 - 4 * q^65 - 100 * q^66 - 2 * q^67 - 112 * q^68 + 14 * q^69 - 100 * q^70 - 16 * q^71 + 98 * q^72 + 82 * q^74 - 296 * q^75 + 154 * q^76 + 194 * q^77 + 228 * q^78 + 592 * q^80 - 8 * q^81 - 420 * q^82 + 238 * q^83 - 22 * q^84 - 52 * q^85 - 170 * q^86 - 456 * q^87 - 26 * q^88 + 808 * q^90 + 188 * q^91 + 176 * q^92 + 26 * q^93 - 18 * q^94 - 202 * q^96 - 4 * q^97 + 408 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.62235	+	1.16960i	−0.811176	+	0.584802i
$2$	−1.62235	+	1.16960i	−0.811176	+	0.584802i
$3$	−0.520377	+	2.95452i	−0.173459	+	0.984841i
$3$	−0.520377	+	2.95452i	−0.173459	+	0.984841i
$4$	1.26405	−	3.79502i	0.316013	−	0.948755i
$5$	−1.70362	+	6.35798i	−0.340723	+	1.27160i	0.556807	+	0.830642i	$0.312026\pi$
$5$	−1.70362	+	6.35798i	−0.340723	+	1.27160i	−0.897530	+	0.440954i	$0.854640\pi$
$6$	−2.61139	−	5.40191i	−0.435231	−	0.900319i
$7$	−0.581649	+	1.00744i	−0.0830926	+	0.143921i	−0.904577	−	0.426311i	$-0.859813\pi$
$7$	−0.581649	+	1.00744i	−0.0830926	+	0.143921i	0.821484	+	0.570231i	$0.193146\pi$
$8$	2.38794	+	7.63530i	0.298492	+	0.954412i
$9$	−8.45841	−	3.07493i	−0.939824	−	0.341659i
$10$	−4.67246	−	12.3074i	−0.467246	−	1.23074i
$11$	0.720261	+	2.68805i	0.0654783	+	0.244368i	0.990906	−	0.134556i	$-0.0429608\pi$
$11$	0.720261	+	2.68805i	0.0654783	+	0.244368i	−0.925428	+	0.378924i	$0.876294\pi$
$12$	10.5547	+	5.70951i	0.879558	+	0.475793i
$13$	0.641258	+	0.171825i	0.0493276	+	0.0132173i	0.283398	−	0.959002i	$-0.408538\pi$
$13$	0.641258	+	0.171825i	0.0493276	+	0.0132173i	−0.234071	+	0.972220i	$0.575205\pi$
$14$	−0.234673	−	2.31473i	−0.0167624	−	0.165338i
$15$	−17.8983	−	8.34192i	−1.19322	−	0.556128i
$16$	−12.8044	−	9.59420i	−0.800272	−	0.599637i
$17$	−1.67347			−0.0984395			−0.0492198	−	0.998788i	$-0.515673\pi$
$17$	−1.67347			−0.0984395			−0.0492198	+	0.998788i	$0.515673\pi$
$18$	17.3190	−	4.90437i	0.962166	−	0.272465i
$19$	−11.7691	−	11.7691i	−0.619424	−	0.619424i	0.325960	−	0.945384i	$-0.394313\pi$
$19$	−11.7691	−	11.7691i	−0.619424	−	0.619424i	−0.945384	+	0.325960i	$0.894313\pi$
$20$	21.9752	+	14.5021i	1.09876	+	0.725103i
$21$	−2.67384	−	2.24275i	−0.127326	−	0.106797i
$22$	−4.31248	−	3.51855i	−0.196022	−	0.159934i
$23$	−17.9147	−	31.0292i	−0.778900	−	1.34909i	−0.932577	−	0.360972i	$-0.882445\pi$
$23$	−17.9147	−	31.0292i	−0.778900	−	1.34909i	0.153677	−	0.988121i	$-0.450888\pi$
$24$	−23.8013	+	3.08198i	−0.991720	+	0.128416i
$25$	−15.8710	−	9.16310i	−0.634838	−	0.366524i
$26$	−1.24131	+	0.471259i	−0.0477428	+	0.0181253i
$27$	13.4865	−	23.3905i	0.499501	−	0.866313i
$28$	3.08804	+	3.48083i	0.110287	+	0.124315i
$29$	10.7737	+	40.2079i	0.371506	+	1.38648i	0.858383	+	0.513009i	$0.171469\pi$
$29$	10.7737	+	40.2079i	0.371506	+	1.38648i	−0.486877	+	0.873471i	$0.661864\pi$
$30$	38.7940	−	7.40037i	1.29313	−	0.246679i
$31$	−18.1310	+	10.4679i	−0.584870	+	0.337675i	−0.763066	−	0.646320i	$-0.776307\pi$
$31$	−18.1310	+	10.4679i	−0.584870	+	0.337675i	0.178196	+	0.983995i	$0.442974\pi$
$32$	31.9946	+	0.589138i	0.999831	+	0.0184106i
$33$	−8.31672	+	0.729228i	−0.252022	+	0.0220978i
$34$	2.71496	−	1.95730i	0.0798518	−	0.0575676i
$35$	−5.41441	−	5.41441i	−0.154697	−	0.154697i
$36$	−22.3613	+	28.2130i	−0.621147	+	0.783694i
$37$	23.8924	+	23.8924i	0.645740	+	0.645740i	0.951961	−	0.306221i	$-0.0990646\pi$
$37$	23.8924	+	23.8924i	0.645740	+	0.645740i	−0.306221	+	0.951961i	$0.599065\pi$
$38$	32.8587	+	5.32841i	0.864702	+	0.140221i
$39$	−0.841356	+	1.80520i	−0.0215732	+	0.0462872i
$40$	−52.6132	+	2.17484i	−1.31533	+	0.0543710i
$41$	−67.9164	+	39.2116i	−1.65650	+	0.956380i	−0.682186	+	0.731178i	$0.738971\pi$
$41$	−67.9164	+	39.2116i	−1.65650	+	0.956380i	−0.974312	+	0.225202i	$0.927696\pi$
$42$	6.96104	+	0.511185i	0.165739	+	0.0121711i
$43$	3.91706	+	14.6187i	0.0910944	+	0.339969i	0.996398	−	0.0847954i	$-0.0270237\pi$
$43$	3.91706	+	14.6187i	0.0910944	+	0.339969i	−0.905304	+	0.424764i	$0.860357\pi$
$44$	11.1117	+	0.664429i	0.252538	+	0.0151007i
$45$	33.9603	−	48.5399i	0.754672	−	1.07866i
$46$	65.3558	+	29.3871i	1.42078	+	0.638850i
$47$	52.9130	+	30.5493i	1.12581	+	0.649986i	0.942877	−	0.333140i	$-0.108108\pi$
$47$	52.9130	+	30.5493i	1.12581	+	0.649986i	0.182931	+	0.983126i	$0.441441\pi$
$48$	35.0094	−	32.8381i	0.729362	−	0.684128i
$49$	23.8234	+	41.2633i	0.486191	+	0.842108i
$50$	36.4655	−	3.69697i	0.729309	−	0.0739393i
$51$	0.870837	−	4.94431i	0.0170752	−	0.0969473i
$52$	1.46266	−	2.21639i	0.0281281	−	0.0426229i
$53$	64.3295	+	64.3295i	1.21376	+	1.21376i	0.969779	+	0.243985i	$0.0784546\pi$
$53$	64.3295	+	64.3295i	1.21376	+	1.21376i	0.243985	+	0.969779i	$0.421545\pi$
$54$	5.47768	+	53.7215i	0.101439	+	0.994842i
$55$	−18.3176			−0.333048
$56$	−9.08108	−	2.03534i	−0.162162	−	0.0363454i
$57$	40.8963	−	28.6476i	0.717479	−	0.502589i
$58$	−64.5061	−	52.6304i	−1.11217	−	0.907422i
$59$	−66.9370	−	17.9357i	−1.13452	−	0.303995i	−0.357777	−	0.933807i	$-0.616465\pi$
$59$	−66.9370	−	17.9357i	−1.13452	−	0.303995i	−0.776748	+	0.629812i	$0.783132\pi$
$60$	−54.2821	+	57.3797i	−0.904701	+	0.956328i
$61$	−3.29732	−	12.3058i	−0.0540545	−	0.201734i	0.933618	−	0.358271i	$-0.116634\pi$
$61$	−3.29732	−	12.3058i	−0.0540545	−	0.201734i	−0.987672	+	0.156537i	$0.949967\pi$
$62$	17.1715	−	38.1887i	0.276959	−	0.615947i
$63$	8.01765	−	6.73286i	0.127264	−	0.106871i
$64$	−52.5955	+	36.4652i	−0.821805	+	0.569769i
$65$	−2.18492	+	3.78438i	−0.0336141	+	0.0582213i
$66$	12.6397	−	10.9103i	0.191511	−	0.165308i
$67$	6.45622	−	24.0949i	0.0963615	−	0.359626i	−0.900861	−	0.434108i	$-0.857064\pi$
$67$	6.45622	−	24.0949i	0.0963615	−	0.359626i	0.997222	+	0.0744820i	$0.0237303\pi$
$68$	−2.11535	+	6.35086i	−0.0311081	+	0.0933950i
$69$	100.999	−	36.7825i	1.46375	−	0.533080i
$70$	15.1168	+	2.45136i	0.215954	+	0.0350194i
$71$	−97.4205			−1.37212			−0.686060	−	0.727545i	$-0.740661\pi$
$71$	−97.4205			−1.37212			−0.686060	+	0.727545i	$0.740661\pi$
$72$	3.27988	−	71.9253i	0.0455539	−	0.998962i
$73$		−	77.4165i		−	1.06050i	−0.847841	−	0.530250i	$-0.822098\pi$
$73$		−	77.4165i		−	1.06050i	0.847841	−	0.530250i	$-0.177902\pi$
$74$	−66.7064	−	10.8172i	−0.901438	−	0.146178i
$75$	35.3315	−	42.1228i	0.471086	−	0.561638i
$76$	−59.5405	+	29.7871i	−0.783427	+	0.391936i
$77$	−3.12700	−	0.837878i	−0.0406104	−	0.0108815i
$78$	−0.746393	−	3.91272i	−0.00956914	−	0.0501631i
$79$	113.247	+	65.3833i	1.43351	+	0.827636i	0.997386	−	0.0722517i	$-0.0230185\pi$
$79$	113.247	+	65.3833i	1.43351	+	0.827636i	0.436121	+	0.899888i	$0.356352\pi$
$80$	82.8134	−	65.0650i	1.03517	−	0.813312i
$81$	62.0896	+	52.0181i	0.766538	+	0.642199i
$82$	64.3223	−	143.050i	0.784419	−	1.74452i
$83$	−108.976	+	29.2000i	−1.31296	+	0.351807i	−0.846336	−	0.532649i	$-0.821197\pi$
$83$	−108.976	+	29.2000i	−1.31296	+	0.351807i	−0.466624	+	0.884456i	$0.654530\pi$
$84$	−11.8911	+	7.31234i	−0.141561	+	0.0870517i
$85$	2.85095	−	10.6399i	0.0335406	−	0.125175i
$86$	−23.4529	−	19.1352i	−0.272708	−	0.222502i
$87$	−124.402	+	10.9078i	−1.42990	+	0.125377i
$88$	−18.8041	+	11.9183i	−0.213683	+	0.135435i
$89$		−	11.8648i		−	0.133313i	−0.997776	−	0.0666563i	$-0.978767\pi$
$89$		−	11.8648i		−	0.133313i	0.997776	−	0.0666563i	$-0.0212331\pi$
$90$	1.67703	+	118.469i	0.0186336	+	1.31632i
$91$	−0.546091	+	0.546091i	−0.00600100	+	0.00600100i
$92$	−140.401	+	28.7642i	−1.52610	+	0.312654i
$93$	−21.4928	−	59.0156i	−0.231105	−	0.634577i
$94$	−121.574	+	12.3255i	−1.29334	+	0.131122i
$95$	94.8773	−	54.7774i	0.998708	−	0.576605i
$96$	−18.3899	+	94.2221i	−0.191561	+	0.981481i
$97$	−79.8339	+	138.276i	−0.823030	+	1.42553i	0.0803857	+	0.996764i	$0.474385\pi$
$97$	−79.8339	+	138.276i	−0.823030	+	1.42553i	−0.903416	+	0.428766i	$0.858949\pi$
$98$	−86.9116	−	39.0797i	−0.886853	−	0.398772i
$99$	2.17331	−	24.9514i	0.0219527	−	0.252035i
$100$	−54.8358	+	48.6480i	−0.548358	+	0.486480i
$101$	6.80684	−	1.82389i	0.0673945	−	0.0180583i	−0.224964	−	0.974367i	$-0.572227\pi$
$101$	6.80684	−	1.82389i	0.0673945	−	0.0180583i	0.292359	+	0.956309i	$0.405560\pi$
$102$	4.37008	+	9.03995i	0.0428440	+	0.0886269i
$103$	55.7083	+	96.4896i	0.540857	+	0.936792i	0.998855	+	0.0478388i	$0.0152334\pi$
$103$	55.7083	+	96.4896i	0.540857	+	0.936792i	−0.457998	+	0.888953i	$0.651433\pi$
$104$	0.219352	+	5.30650i	0.00210915	+	0.0510241i
$105$	18.8145	−	13.1795i	0.179186	−	0.125519i
$106$	−179.605	−	29.1250i	−1.69439	−	0.274764i
$107$	79.5065	−	79.5065i	0.743051	−	0.743051i	−0.230113	−	0.973164i	$-0.573910\pi$
$107$	79.5065	−	79.5065i	0.743051	−	0.743051i	0.973164	+	0.230113i	$0.0739095\pi$
$108$	−71.7196	−	80.7484i	−0.664070	−	0.747670i
$109$	−6.67460	+	6.67460i	−0.0612348	+	0.0612348i	−0.737061	−	0.675826i	$-0.763787\pi$
$109$	−6.67460	+	6.67460i	−0.0612348	+	0.0612348i	0.675826	+	0.737061i	$0.263787\pi$
$110$	29.7176	−	21.4244i	0.270160	−	0.194767i
$111$	−83.0236	+	58.1575i	−0.747960	+	0.523941i
$112$	17.1133	−	7.31923i	0.152797	−	0.0653502i
$113$	−83.4406	−	144.523i	−0.738413	−	1.27897i	−0.953210	−	0.302310i	$-0.902242\pi$
$113$	−83.4406	−	144.523i	−0.738413	−	1.27897i	0.214797	−	0.976659i	$-0.431091\pi$
$114$	−32.8418	+	94.3089i	−0.288086	+	0.827271i
$115$	227.802	−	61.0395i	1.98089	−	0.530778i
$116$	166.208	+	9.93853i	1.43283	+	0.0856770i
$117$	−4.89568	−	3.42519i	−0.0418434	−	0.0292751i
$118$	129.573	−	49.1917i	1.09808	−	0.416879i
$119$	0.973372	−	1.68593i	0.00817960	−	0.0141675i
$120$	20.9531	−	156.579i	0.174609	−	1.30482i
$121$	98.0822	−	56.6278i	0.810597	−	0.467998i
$122$	19.7423	+	16.1077i	0.161822	+	0.132031i
$123$	−80.5093	−	221.066i	−0.654547	−	1.79728i
$124$	16.8075	+	82.0394i	0.135544	+	0.661608i
$125$	−31.0623	+	31.0623i	−0.248498	+	0.248498i
$126$	−5.13267	+	20.3005i	−0.0407355	+	0.161115i
$127$		−	1.53110i		−	0.0120559i	−0.999982	−	0.00602794i	$-0.998081\pi$
$127$		−	1.53110i		−	0.0120559i	0.999982	−	0.00602794i	$-0.00191877\pi$
$128$	42.6786	−	120.675i	0.333426	−	0.942776i
$129$	−45.2295	+	3.96582i	−0.350616	+	0.0307428i
$130$	−0.881531	−	8.69509i	−0.00678101	−	0.0668853i
$131$	26.0628	−	97.2677i	0.198953	−	0.742502i	−0.792255	−	0.610190i	$-0.791093\pi$
$131$	26.0628	−	97.2677i	0.198953	−	0.742502i	0.991208	−	0.132312i	$-0.0422401\pi$
$132$	−7.74533	+	32.4839i	−0.0586767	+	0.246090i
$133$	18.7021	−	5.01122i	0.140617	−	0.0376783i
$134$	17.7073	+	46.6417i	0.132144	+	0.348072i
$135$	125.740	+	125.595i	0.931409	+	0.930336i
$136$	−3.99614	−	12.7775i	−0.0293834	−	0.0939519i
$137$	69.0315	+	39.8554i	0.503880	+	0.290915i	0.730314	−	0.683111i	$-0.239374\pi$
$137$	69.0315	+	39.8554i	0.503880	+	0.290915i	−0.226435	+	0.974026i	$0.572707\pi$
$138$	−120.835	+	177.803i	−0.875613	+	1.28843i
$139$	123.997	+	33.2248i	0.892063	+	0.239028i	0.675605	−	0.737264i	$-0.263883\pi$
$139$	123.997	+	33.2248i	0.892063	+	0.239028i	0.216459	+	0.976292i	$0.430549\pi$
$140$	−27.3919	+	13.7037i	−0.195656	+	0.0978835i
$141$	−117.793	+	140.436i	−0.835415	+	0.995997i
$142$	158.050	−	113.943i	1.11303	−	0.802418i
$143$			1.84749i			0.0129195i
$144$	78.8030	+	120.524i	0.547243	+	0.836974i
$145$	−273.995			−1.88962
$146$	90.5466	+	125.597i	0.620183	+	0.860252i
$147$	−134.310	+	48.9142i	−0.913677	+	0.332750i
$148$	120.873	−	60.4708i	0.816711	−	0.408587i
$149$	−43.7878	+	163.418i	−0.293878	+	1.09677i	0.648227	+	0.761447i	$0.275511\pi$
$149$	−43.7878	+	163.418i	−0.293878	+	1.09677i	−0.942105	+	0.335319i	$0.891156\pi$
$150$	−8.05303	+	109.662i	−0.0536869	+	0.731079i
$151$	41.0374	−	71.0788i	0.271771	−	0.470720i	−0.697545	−	0.716541i	$-0.745724\pi$
$151$	41.0374	−	71.0788i	0.271771	−	0.470720i	0.969315	+	0.245821i	$0.0790575\pi$
$152$	61.7565	−	117.964i	0.406292	−	0.776079i
$153$	14.1549	+	5.14582i	0.0925158	+	0.0336328i
$154$	6.05309	−	2.29802i	0.0393058	−	0.0149222i
$155$	−35.6666	−	133.110i	−0.230107	−	0.858772i
$156$	5.78725	+	5.47483i	0.0370978	+	0.0350951i
$157$	166.872	+	44.7133i	1.06288	+	0.284798i	0.747565	−	0.664188i	$-0.231223\pi$
$157$	166.872	+	44.7133i	1.06288	+	0.284798i	0.315316	+	0.948987i	$0.397889\pi$
$158$	−260.199	+	26.3797i	−1.64683	+	0.166960i
$159$	−223.539	+	156.587i	−1.40590	+	0.984826i
$160$	−58.2522	+	202.417i	−0.364076	+	1.26511i
$161$	41.6802			0.258883
$162$	−161.572	−	11.7715i	−0.997357	−	0.0726636i
$163$	168.279	+	168.279i	1.03238	+	1.03238i	0.999458	+	0.0329269i	$0.0104829\pi$
$163$	168.279	+	168.279i	1.03238	+	1.03238i	0.0329269	+	0.999458i	$0.489517\pi$
$164$	62.9589	+	307.310i	0.383896	+	1.87384i
$165$	9.53208	−	54.1199i	0.0577702	−	0.327999i
$166$	142.645	−	174.831i	0.859305	−	1.05320i
$167$	86.5980	+	149.992i	0.518551	+	0.898156i	0.999768	+	0.0215548i	$0.00686163\pi$
$167$	86.5980	+	149.992i	0.518551	+	0.898156i	−0.481217	+	0.876602i	$0.659805\pi$
$168$	10.7391	−	25.7711i	0.0639230	−	0.153399i
$169$	−145.977	−	84.2796i	−0.863767	−	0.498696i
$170$	7.81922	+	20.5961i	0.0459954	+	0.121154i
$171$	63.3585	+	135.737i	0.370517	+	0.793781i
$172$	60.4295	+	3.61342i	0.351334	+	0.0210082i
$173$	−0.206504	−	0.770682i	−0.00119366	−	0.00445481i	0.965326	−	0.261046i	$-0.0840673\pi$
$173$	−0.206504	−	0.770682i	−0.00119366	−	0.00445481i	−0.966520	+	0.256591i	$0.917401\pi$
$174$	189.065	−	163.197i	1.08658	−	0.937914i
$175$	18.4626	−	10.6594i	0.105501	−	0.0609109i
$176$	16.5672	−	41.3291i	0.0941320	−	0.234824i
$177$	87.8239	−	188.433i	0.496181	−	1.06460i
$178$	13.8771	+	19.2489i	0.0779614	+	0.108140i
$179$	36.3703	+	36.3703i	0.203186	+	0.203186i	0.801363	−	0.598178i	$-0.204108\pi$
$179$	36.3703	+	36.3703i	0.203186	+	0.203186i	−0.598178	+	0.801363i	$0.704108\pi$
$180$	−141.282	−	190.237i	−0.784903	−	1.05687i
$181$	−51.1897	−	51.1897i	−0.282816	−	0.282816i	0.551415	−	0.834231i	$-0.314088\pi$
$181$	−51.1897	−	51.1897i	−0.282816	−	0.282816i	−0.834231	+	0.551415i	$0.814088\pi$
$182$	0.247241	−	1.52466i	0.00135847	−	0.00837726i
$183$	38.0735	−	3.33837i	0.208052	−	0.0182424i
$184$	194.138	−	210.880i	1.05510	−	1.14608i
$185$	−192.611	+	111.204i	−1.04114	+	0.601101i
$186$	103.894	+	70.6061i	0.558569	+	0.379603i
$187$	−1.20534	−	4.49838i	−0.00644565	−	0.0240555i
$188$	182.820	−	162.190i	0.972447	−	0.862713i
$189$	15.7202	+	27.1920i	0.0831755	+	0.143873i
$190$	−89.8564	+	199.837i	−0.472929	+	1.05177i
$191$	−39.3843	−	22.7385i	−0.206200	−	0.119050i	0.393344	−	0.919391i	$-0.371318\pi$
$191$	−39.3843	−	22.7385i	−0.206200	−	0.119050i	−0.599544	+	0.800342i	$0.704651\pi$
$192$	−80.3678	−	174.370i	−0.418582	−	0.908179i
$193$	−40.8327	−	70.7243i	−0.211568	−	0.366447i	0.740637	−	0.671905i	$-0.234524\pi$
$193$	−40.8327	−	70.7243i	−0.211568	−	0.366447i	−0.952205	+	0.305458i	$0.901190\pi$
$194$	−32.2100	−	317.707i	−0.166031	−	1.63767i
$195$	−10.0441	−	8.42469i	−0.0515081	−	0.0432035i
$196$	186.709	−	38.2513i	0.952597	−	0.195160i
$197$	75.3287	+	75.3287i	0.382379	+	0.382379i	0.871959	−	0.489579i	$-0.162850\pi$
$197$	75.3287	+	75.3287i	0.382379	+	0.382379i	−0.489579	+	0.871959i	$0.662850\pi$
$198$	25.6574	+	43.0219i	0.129583	+	0.217282i
$199$	−162.505			−0.816609			−0.408305	−	0.912846i	$-0.633880\pi$
$199$	−162.505			−0.816609			−0.408305	+	0.912846i	$0.633880\pi$
$200$	32.0642	−	143.060i	0.160321	−	0.715302i
$201$	67.8294	+	31.6135i	0.337460	+	0.157281i
$202$	−8.90986	+	10.9203i	−0.0441082	+	0.0540609i
$203$	−46.7738	−	12.5330i	−0.230413	−	0.0617389i
$204$	−17.6630	−	9.55470i	−0.0865832	−	0.0468368i
$205$	−133.603	−	498.613i	−0.651721	−	2.43226i
$206$	−203.233	−	91.3834i	−0.986568	−	0.443609i
$207$	56.1173	+	317.544i	0.271098	+	1.53403i
$208$	−6.56238	−	8.35246i	−0.0315499	−	0.0401561i
$209$	23.1590	−	40.1126i	0.110809	−	0.191926i
$210$	−15.1090	+	43.3873i	−0.0719478	+	0.206606i
$211$	−58.3823	+	217.886i	−0.276694	+	1.03263i	0.678004	+	0.735058i	$0.262845\pi$
$211$	−58.3823	+	217.886i	−0.276694	+	1.03263i	−0.954698	+	0.297577i	$0.903822\pi$
$212$	325.447	−	162.816i	1.53513	−	0.767999i
$213$	50.6954	−	287.831i	0.238007	−	1.35132i
$214$	−35.9963	+	221.979i	−0.168207	+	1.03728i
$215$	−99.6183			−0.463341
$216$	210.798	+	47.1188i	0.975917	+	0.218142i
$217$		−	24.3546i		−	0.112233i
$218$	3.02191	−	18.6352i	0.0138620	−	0.0854825i
$219$	228.729	+	40.2858i	1.04442	+	0.183953i
$220$	−23.1544	+	69.5158i	−0.105247	+	0.315981i
$221$	−1.07313	−	0.287544i	−0.00485578	−	0.00130110i
$222$	66.6722	−	191.457i	0.300325	−	0.862418i
$223$	−288.678	−	166.668i	−1.29452	−	0.747391i	−0.315068	−	0.949069i	$-0.602027\pi$
$223$	−288.678	−	166.668i	−1.29452	−	0.747391i	−0.979452	+	0.201678i	$0.935361\pi$
$224$	−19.2031	+	31.8901i	−0.0857282	+	0.142367i
$225$	106.067	+	126.307i	0.471410	+	0.561366i
$226$	304.405	+	136.875i	1.34693	+	0.605643i
$227$	−155.843	+	41.7581i	−0.686535	+	0.183957i	−0.585192	−	0.810895i	$-0.698981\pi$
$227$	−155.843	+	41.7581i	−0.686535	+	0.183957i	−0.101343	+	0.994852i	$0.532314\pi$
$228$	−57.0232	−	191.414i	−0.250102	−	0.839536i
$229$	−14.5951	+	54.4695i	−0.0637339	+	0.237858i	−0.990443	−	0.137921i	$-0.955958\pi$
$229$	−14.5951	+	54.4695i	−0.0637339	+	0.237858i	0.926709	+	0.375779i	$0.122625\pi$
$230$	−298.184	+	365.466i	−1.29645	+	1.58898i
$231$	4.10275	−	8.80279i	0.0177608	−	0.0381073i
$232$	−281.273	+	178.274i	−1.21238	+	0.768423i
$233$		−	276.106i		−	1.18500i	−0.805570	−	0.592501i	$-0.798141\pi$
$233$		−	276.106i		−	1.18500i	0.805570	−	0.592501i	$-0.201859\pi$
$234$	11.9486	−	0.169143i	0.0510625	−	0.000722833i
$235$	−284.375	+	284.375i	−1.21011	+	1.21011i
$236$	−152.678	+	231.355i	−0.646941	+	0.980320i
$237$	−252.108	+	300.567i	−1.06375	+	1.26822i
$238$	0.392719	+	3.87363i	0.00165008	+	0.0162758i
$239$	388.242	−	224.152i	1.62444	−	0.937874i	0.638734	−	0.769428i	$-0.279458\pi$
$239$	388.242	−	224.152i	1.62444	−	0.937874i	0.985711	−	0.168446i	$-0.0538748\pi$
$240$	149.142	+	278.532i	0.621424	+	1.16055i
$241$	−10.1255	+	17.5379i	−0.0420147	+	0.0727715i	−0.886268	−	0.463173i	$-0.846711\pi$
$241$	−10.1255	+	17.5379i	−0.0420147	+	0.0727715i	0.844253	+	0.535944i	$0.180044\pi$
$242$	−92.8918	+	206.588i	−0.383850	+	0.853668i
$243$	−185.999	+	156.376i	−0.765427	+	0.643523i
$244$	−50.8686	−	3.04172i	−0.208478	−	0.0124661i
$245$	−302.937	+	81.1717i	−1.23648	+	0.331313i
$246$	389.174	+	264.482i	1.58201	+	1.07513i
$247$	−5.52479	−	9.56922i	−0.0223676	−	0.0387418i
$248$	−123.221	−	113.439i	−0.496860	−	0.457414i
$249$	−29.5635	−	337.166i	−0.118729	−	1.35408i
$250$	14.0634	−	86.7246i	0.0562535	−	0.346898i
$251$	9.72696	−	9.72696i	0.0387528	−	0.0387528i	−0.687465	−	0.726218i	$-0.741276\pi$
$251$	9.72696	−	9.72696i	0.0387528	−	0.0387528i	0.726218	+	0.687465i	$0.241276\pi$
$252$	−15.4166	−	38.9378i	−0.0611770	−	0.154515i
$253$	70.5047	−	70.5047i	0.278675	−	0.278675i
$254$	1.79078	+	2.48398i	0.00705031	+	0.00977944i
$255$	29.9523	+	13.9600i	0.117460	+	0.0547450i
$256$	71.9028	+	245.695i	0.280870	+	0.959746i
$257$	64.6572	+	111.990i	0.251584	+	0.435757i	0.963962	−	0.266039i	$-0.0857151\pi$
$257$	64.6572	+	111.990i	0.251584	+	0.435757i	−0.712378	+	0.701796i	$0.752382\pi$
$258$	68.7398	−	59.3346i	0.266433	−	0.229979i
$259$	−37.9672	+	10.1733i	−0.146592	+	0.0392791i
$260$	11.6000	+	13.0755i	0.0446153	+	0.0502902i
$261$	32.5085	−	373.224i	0.124553	−	1.42998i
$262$	71.4817	+	188.286i	0.272831	+	0.718647i
$263$	128.843	−	223.163i	0.489899	−	0.848529i	−0.510034	−	0.860154i	$-0.670367\pi$
$263$	128.843	−	223.163i	0.489899	−	0.848529i	0.999932	+	0.0116252i	$0.00370049\pi$
$264$	−25.4277	−	61.7593i	−0.0963169	−	0.233937i
$265$	−518.598	+	299.413i	−1.95697	+	1.12986i
$266$	−24.4803	+	30.0040i	−0.0920311	+	0.112797i
$267$	35.0549	+	6.17418i	0.131292	+	0.0231243i
$268$	−83.2798	−	54.9587i	−0.310745	−	0.205070i
$269$	137.235	−	137.235i	0.510167	−	0.510167i	−0.404410	−	0.914578i	$-0.632523\pi$
$269$	137.235	−	137.235i	0.510167	−	0.510167i	0.914578	+	0.404410i	$0.132523\pi$
$270$	−350.892	−	56.6937i	−1.29960	−	0.209977i
$271$		−	229.284i		−	0.846067i	−0.906114	−	0.423034i	$-0.860965\pi$
$271$		−	229.284i		−	0.846067i	0.906114	−	0.423034i	$-0.139035\pi$
$272$	21.4277	+	16.0556i	0.0787784	+	0.0590280i
$273$	−1.32926	−	1.89761i	−0.00486910	−	0.00695096i
$274$	−158.608	+	16.0801i	−0.578863	+	0.0586867i
$275$	13.1997	−	49.2618i	0.0479987	−	0.179134i
$276$	−11.9227	−	429.787i	−0.0431983	−	1.55720i
$277$	281.517	−	75.4324i	1.01631	−	0.272319i	0.288045	−	0.957617i	$-0.406995\pi$
$277$	281.517	−	75.4324i	1.01631	−	0.272319i	0.728263	+	0.685298i	$0.240328\pi$
$278$	−240.026	+	91.1248i	−0.863404	+	0.327787i
$279$	185.547	−	32.7905i	0.665044	−	0.117529i
$280$	28.4113	−	54.2699i	0.101469	−	0.193821i
$281$	396.230	+	228.763i	1.41007	+	0.814104i	0.995394	−	0.0958648i	$-0.0305616\pi$
$281$	396.230	+	228.763i	1.41007	+	0.814104i	0.414676	+	0.909969i	$0.363895\pi$
$282$	26.8484	−	365.608i	0.0952072	−	1.29648i
$283$	−100.322	−	26.8812i	−0.354495	−	0.0949867i	0.0771767	−	0.997017i	$-0.475409\pi$
$283$	−100.322	−	26.8812i	−0.354495	−	0.0949867i	−0.431672	+	0.902031i	$0.642076\pi$
$284$	−123.144	+	369.713i	−0.433607	+	1.30180i
$285$	112.469	+	308.822i	0.394629	+	1.08359i
$286$	−2.16084	−	2.99729i	−0.00755538	−	0.0104800i
$287$		−	91.2294i		−	0.317873i
$288$	−268.812	−	103.364i	−0.933374	−	0.358904i
$289$	−286.199			−0.990310
$290$	444.517	−	320.466i	1.53282	−	1.10506i
$291$	−366.997	−	307.827i	−1.26116	−	1.05782i
$292$	−293.797	−	97.8584i	−1.00615	−	0.335131i
$293$	6.96552	−	25.9957i	0.0237731	−	0.0887224i	−0.953020	−	0.302907i	$-0.902043\pi$
$293$	6.96552	−	25.9957i	0.0237731	−	0.0887224i	0.976793	+	0.214185i	$0.0687095\pi$
$294$	160.689	−	236.446i	0.546560	−	0.804239i
$295$	228.070	−	395.028i	0.773118	−	1.33908i
$296$	−125.372	+	239.479i	−0.423554	+	0.809050i
$297$	72.5886	+	19.4053i	0.244406	+	0.0653376i
$298$	−120.095	−	316.336i	−0.403005	−	1.06153i
$299$	−6.15637	−	22.9759i	−0.0205899	−	0.0768424i
$300$	−115.196	−	187.329i	−0.383987	−	0.624430i
$301$	−17.0058	−	4.55670i	−0.0564978	−	0.0151385i
$302$	16.5570	+	163.312i	0.0548246	+	0.540769i
$303$	1.84659	+	21.0601i	0.00609436	+	0.0695052i
$304$	37.7805	+	263.610i	0.124278	+	0.867137i
$305$	83.8572			0.274942
$306$	−28.9828	+	8.20733i	−0.0947151	+	0.0268213i
$307$	279.295	+	279.295i	0.909757	+	0.909757i	0.996252	−	0.0864953i	$-0.0275668\pi$
$307$	279.295	+	279.295i	0.909757	+	0.909757i	−0.0864953	+	0.996252i	$0.527567\pi$
$308$	−7.13246	+	10.8079i	−0.0231573	+	0.0350906i
$309$	−314.070	+	114.380i	−1.01641	+	0.370163i
$310$	213.549	+	174.235i	0.688869	+	0.562048i
$311$	32.1575	+	55.6984i	0.103400	+	0.179095i	0.913084	−	0.407773i	$-0.133694\pi$
$311$	32.1575	+	55.6984i	0.103400	+	0.179095i	−0.809683	+	0.586867i	$0.800361\pi$
$312$	−15.7923	−	2.11330i	−0.0506165	−	0.00677341i
$313$	266.640	+	153.944i	0.851884	+	0.491835i	0.861286	−	0.508121i	$-0.169660\pi$
$313$	266.640	+	153.944i	0.851884	+	0.491835i	−0.00940237	+	0.999956i	$0.502993\pi$
$314$	−323.023	+	122.634i	−1.02873	+	0.390554i
$315$	29.1484	+	62.4462i	0.0925345	+	0.198242i
$316$	391.281	−	347.127i	1.23823	−	1.09850i
$317$	119.172	+	444.757i	0.375938	+	1.40302i	0.851970	+	0.523591i	$0.175408\pi$
$317$	119.172	+	444.757i	0.375938	+	1.40302i	−0.476032	+	0.879428i	$0.657925\pi$
$318$	179.513	−	515.491i	0.564506	−	1.62104i
$319$	−100.321	+	57.9204i	−0.314486	+	0.181569i
$320$	−142.242	−	396.524i	−0.444508	−	1.23914i
$321$	193.530	+	276.277i	0.602898	+	0.860676i
$322$	−67.6200	+	48.7494i	−0.210000	+	0.151396i
$323$	19.6952	+	19.6952i	0.0609758	+	0.0609758i
$324$	275.894	−	169.878i	0.851525	−	0.524313i
$325$	−8.60294	−	8.60294i	−0.0264706	−	0.0264706i
$326$	−469.827	−	76.1877i	−1.44119	−	0.233705i
$327$	−16.2469	−	23.1936i	−0.0496848	−	0.0709283i
$328$	−461.572	−	424.927i	−1.40723	−	1.29551i
$329$	−61.5535	+	35.5380i	−0.187093	+	0.108018i
$330$	47.8344	+	98.9502i	0.144953	+	0.299849i
$331$	41.6337	+	155.379i	0.125782	+	0.469423i	0.999866	−	0.0163504i	$-0.00520471\pi$
$331$	41.6337	+	155.379i	0.125782	+	0.469423i	−0.874085	+	0.485773i	$0.838538\pi$
$332$	−26.9365	+	450.475i	−0.0811339	+	1.35685i
$333$	−128.624	−	275.559i	−0.386259	−	0.827505i
$334$	−315.924	−	142.055i	−0.945880	−	0.425313i
$335$	142.196	+	82.0970i	0.424466	+	0.245066i
$336$	12.7195	+	54.3703i	0.0378556	+	0.161816i
$337$	86.7045	+	150.177i	0.257283	+	0.445628i	0.965513	−	0.260354i	$-0.0838393\pi$
$337$	86.7045	+	150.177i	0.257283	+	0.445628i	−0.708230	+	0.705982i	$0.750506\pi$
$338$	335.399	−	34.0037i	0.992305	−	0.100603i
$339$	470.418	−	171.321i	1.38766	−	0.505370i
$340$	−36.7749	−	24.2688i	−0.108161	−	0.0713788i
$341$	−41.1973	−	41.1973i	−0.120813	−	0.120813i
$342$	−261.548	−	146.108i	−0.764760	−	0.427217i
$343$	−112.429			−0.327781
$344$	−102.264	+	64.8163i	−0.297279	+	0.188420i
$345$	61.7993	+	704.811i	0.179128	+	2.04293i
$346$	1.23641	+	1.00879i	0.00357345	+	0.00291558i
$347$	252.549	+	67.6704i	0.727808	+	0.195015i	0.603653	−	0.797247i	$-0.293711\pi$
$347$	252.549	+	67.6704i	0.727808	+	0.195015i	0.124155	+	0.992263i	$0.460378\pi$
$348$	−115.855	+	485.895i	−0.332916	+	1.39625i
$349$	−38.3257	−	143.034i	−0.109816	−	0.409838i	0.889031	−	0.457847i	$-0.151379\pi$
$349$	−38.3257	−	143.034i	−0.109816	−	0.409838i	−0.998847	+	0.0480086i	$0.984713\pi$
$350$	−17.4856	+	38.8873i	−0.0499588	+	0.111107i
$351$	12.6674	−	12.6820i	0.0360895	−	0.0361311i
$352$	21.4608	+	86.4274i	0.0609683	+	0.245532i
$353$	274.592	−	475.607i	0.777880	−	1.34733i	−0.155282	−	0.987870i	$-0.549629\pi$
$353$	274.592	−	475.607i	0.777880	−	1.34733i	0.933162	−	0.359457i	$-0.117038\pi$
$354$	77.9113	+	408.425i	0.220088	+	1.15374i
$355$	165.967	−	619.397i	0.467513	−	1.74478i
$356$	−45.0272	−	14.9977i	−0.126481	−	0.0421284i
$357$	4.47460	+	3.75317i	0.0125339	+	0.0105131i
$358$	−101.544	−	16.4665i	−0.283643	−	0.0459959i
$359$	197.661			0.550589			0.275294	−	0.961360i	$-0.411225\pi$
$359$	197.661			0.550589			0.275294	+	0.961360i	$0.411225\pi$
$360$	451.712	+	143.386i	1.25475	+	0.398295i
$361$		−	83.9789i		−	0.232629i
$362$	142.920	+	23.1760i	0.394805	+	0.0640222i
$363$	116.268	+	319.254i	0.320299	+	0.879488i
$364$	1.38214	+	2.76271i	0.00379709	+	0.00758987i
$365$	492.212	+	131.888i	1.34853	+	0.361337i
$366$	−57.8641	+	49.9470i	−0.158099	+	0.136467i
$367$	−340.786	−	196.753i	−0.928572	−	0.536112i	−0.0422126	−	0.999109i	$-0.513441\pi$
$367$	−340.786	−	196.753i	−0.928572	−	0.536112i	−0.886360	+	0.462997i	$0.846774\pi$
$368$	−68.3138	+	569.185i	−0.185635	+	1.54670i
$369$	695.038	−	122.829i	1.88357	−	0.332870i
$370$	182.418	−	405.690i	0.493021	−	1.09646i
$371$	−102.226	+	27.3913i	−0.275541	+	0.0738309i
$372$	−251.133	+	6.96670i	−0.675090	+	0.0187277i
$373$	−49.6894	+	185.443i	−0.133216	+	0.497167i	−0.999999	−	0.00151788i	$-0.999517\pi$
$373$	−49.6894	+	185.443i	−0.133216	+	0.497167i	0.866783	+	0.498685i	$0.166184\pi$
$374$	7.21681	+	5.88819i	0.0192963	+	0.0157438i
$375$	−75.6102	−	107.938i	−0.201627	−	0.287836i
$376$	−106.900	+	476.956i	−0.284309	+	1.26850i
$377$			27.6349i			0.0733020i
$378$	−57.3075	−	25.7285i	−0.151607	−	0.0680649i
$379$	−115.446	+	115.446i	−0.304607	+	0.304607i	−0.842813	−	0.538206i	$-0.819102\pi$
$379$	−115.446	+	115.446i	−0.304607	+	0.304607i	0.538206	+	0.842813i	$0.319102\pi$
$380$	−87.9517	−	429.303i	−0.231452	−	1.12974i
$381$	4.52366	+	0.796748i	0.0118731	+	0.00209120i
$382$	90.4902	−	9.17413i	0.236885	−	0.0240161i
$383$	297.108	−	171.535i	0.775739	−	0.447873i	−0.0591794	−	0.998247i	$-0.518848\pi$
$383$	297.108	−	171.535i	0.775739	−	0.447873i	0.834918	+	0.550375i	$0.185515\pi$
$384$	334.329	+	188.892i	0.870649	+	0.491905i
$385$	10.6544	−	18.4540i	0.0276738	−	0.0479325i
$386$	148.964	+	66.9816i	0.385918	+	0.173527i
$387$	11.8193	−	135.695i	0.0305409	−	0.350634i
$388$	423.847	+	477.760i	1.09239	+	1.23134i
$389$	8.19164	−	2.19494i	0.0210582	−	0.00564252i	−0.248275	−	0.968690i	$-0.579864\pi$
$389$	8.19164	−	2.19494i	0.0210582	−	0.00564252i	0.269333	+	0.963047i	$0.413197\pi$
$390$	26.1486	+	1.92022i	0.0670476	+	0.00492365i
$391$	29.9797	+	51.9264i	0.0766745	+	0.132804i
$392$	−258.169	+	280.433i	−0.658594	+	0.715389i
$393$	273.817	+	127.619i	0.696736	+	0.324731i
$394$	−210.315	−	34.1049i	−0.533793	−	0.0865606i
$395$	−608.635	+	608.635i	−1.54085	+	1.54085i
$396$	−91.9439	−	39.7876i	−0.232182	−	0.100474i
$397$	−89.2611	+	89.2611i	−0.224839	+	0.224839i	−0.810533	−	0.585694i	$-0.800822\pi$
$397$	−89.2611	+	89.2611i	−0.224839	+	0.224839i	0.585694	+	0.810533i	$0.300822\pi$
$398$	263.641	−	190.067i	0.662414	−	0.477555i
$399$	5.07360	+	57.8636i	0.0127158	+	0.145021i
$400$	115.305	+	269.597i	0.288262	+	0.673991i
$401$	−373.730	−	647.319i	−0.931995	−	1.61426i	−0.779907	−	0.625895i	$-0.784734\pi$
$401$	−373.730	−	647.319i	−0.931995	−	1.61426i	−0.152087	−	0.988367i	$-0.548599\pi$
$402$	−147.018	+	28.0453i	−0.365717	+	0.0697644i
$403$	−13.4253	+	3.59729i	−0.0333134	+	0.00892629i
$404$	1.68250	−	28.1376i	0.00416462	−	0.0696475i
$405$	−436.507	+	306.145i	−1.07779	+	0.755914i
$406$	90.5421	−	34.3739i	0.223010	−	0.0846647i
$407$	−47.0152	+	81.4327i	−0.115516	+	0.200080i
$408$	39.8308	−	5.15760i	0.0976245	−	0.0126412i
$409$	336.222	−	194.118i	0.822058	−	0.474615i	−0.0290677	−	0.999577i	$-0.509254\pi$
$409$	336.222	−	194.118i	0.822058	−	0.474615i	0.851126	+	0.524962i	$0.175921\pi$
$410$	799.931	+	652.663i	1.95105	+	1.59186i
$411$	−153.676	+	183.215i	−0.373908	+	0.445780i
$412$	436.598	−	89.4463i	1.05970	−	0.217103i
$413$	57.0030	−	57.0030i	0.138022	−	0.138022i
$414$	−462.443	−	449.533i	−1.11701	−	1.08583i
$415$		−	742.611i		−	1.78942i
$416$	20.4156	+	5.87525i	0.0490759	+	0.0141232i
$417$	−162.689	+	349.062i	−0.390141	+	0.837079i
$418$	9.34380	+	92.1637i	0.0223536	+	0.220487i
$419$	−119.896	+	447.458i	−0.286148	+	1.06792i	0.661849	+	0.749637i	$0.269772\pi$
$419$	−119.896	+	447.458i	−0.286148	+	1.06792i	−0.947997	+	0.318281i	$0.896895\pi$
$420$	−26.2338	−	88.0610i	−0.0624614	−	0.209669i
$421$	−195.708	+	52.4398i	−0.464865	+	0.124560i	−0.483646	−	0.875264i	$-0.660688\pi$
$421$	−195.708	+	52.4398i	−0.464865	+	0.124560i	0.0187818	+	0.999824i	$0.494021\pi$
$422$	−160.124	−	421.772i	−0.379440	−	0.999459i
$423$	−353.623	−	421.103i	−0.835988	−	0.995515i
$424$	−337.560	+	644.789i	−0.796132	+	1.52073i
$425$	26.5596	+	15.3342i	0.0624932	+	0.0360804i
$426$	254.403	+	526.257i	0.597189	+	1.23534i
$427$	14.3153	+	3.83576i	0.0335252	+	0.00898306i
$428$	−201.228	−	402.229i	−0.470160	−	0.939787i
$429$	−5.45847	−	0.961395i	−0.0127237	−	0.00224101i
$430$	161.616	−	116.514i	0.375851	−	0.270963i
$431$			286.835i			0.665511i	0.943013	+	0.332755i	$0.107978\pi$
$431$			286.835i			0.665511i	−0.943013	+	0.332755i	$0.892022\pi$
$432$	−397.099	+	170.107i	−0.919210	+	0.393767i
$433$	440.641			1.01765			0.508823	−	0.860871i	$-0.330081\pi$
$433$	440.641			1.01765			0.508823	+	0.860871i	$0.330081\pi$
$434$	28.4852	+	39.5117i	0.0656342	+	0.0910408i
$435$	142.581	−	809.525i	0.327772	−	1.86098i
$436$	16.8932	+	33.7673i	0.0387459	+	0.0774479i
$437$	−154.345	+	576.023i	−0.353192	+	1.31813i
$438$	−418.197	+	202.164i	−0.954788	+	0.461563i
$439$	−85.8760	+	148.742i	−0.195617	+	0.338819i	−0.947103	−	0.320931i	$-0.896004\pi$
$439$	−85.8760	+	148.742i	−0.195617	+	0.338819i	0.751485	+	0.659750i	$0.229338\pi$
$440$	−43.7413	−	139.861i	−0.0994121	−	0.317865i
$441$	−74.6261	−	422.277i	−0.169220	−	0.957545i
$442$	2.07730	−	0.788638i	0.00469978	−	0.00178425i
$443$	−156.889	−	585.518i	−0.354152	−	1.32171i	−0.881549	−	0.472093i	$-0.843499\pi$
$443$	−156.889	−	585.518i	−0.354152	−	1.32171i	0.527397	−	0.849619i	$-0.323168\pi$
$444$	115.763	+	388.590i	0.260727	+	0.875203i
$445$	75.4362	+	20.2131i	0.169520	+	0.0454226i
$446$	663.273	−	67.2444i	1.48716	−	0.150772i
$447$	−460.036	−	214.411i	−1.02916	−	0.479667i
$448$	−6.14458	−	74.1970i	−0.0137156	−	0.165618i
$449$	342.778			0.763426			0.381713	−	0.924281i	$-0.375334\pi$
$449$	342.778			0.763426			0.381713	+	0.924281i	$0.375334\pi$
$450$	−319.808	−	80.8584i	−0.710684	−	0.179685i
$451$	−154.320	−	154.320i	−0.342174	−	0.342174i
$452$	−653.942	+	133.974i	−1.44678	+	0.296402i
$453$	188.649	+	158.234i	0.416444	+	0.349302i
$454$	203.992	−	250.022i	0.449323	−	0.550708i
$455$	−2.54171	−	4.40236i	−0.00558617	−	0.00967552i
$456$	316.391	+	243.847i	0.693839	+	0.534751i
$457$	435.927	+	251.682i	0.953888	+	0.550728i	0.894287	−	0.447495i	$-0.147684\pi$
$457$	435.927	+	251.682i	0.953888	+	0.550728i	0.0596015	+	0.998222i	$0.481017\pi$
$458$	−40.0295	−	105.439i	−0.0874006	−	0.230217i
$459$	−22.5693	+	39.1433i	−0.0491707	+	0.0852794i
$460$	56.3079	−	941.672i	0.122408	−	2.04711i
$461$	−9.88938	−	36.9077i	−0.0214520	−	0.0800600i	0.954370	−	0.298627i	$-0.0965285\pi$
$461$	−9.88938	−	36.9077i	−0.0214520	−	0.0800600i	−0.975822	+	0.218567i	$0.929862\pi$
$462$	3.63968	+	19.0798i	0.00787809	+	0.0412983i
$463$	−339.905	+	196.244i	−0.734136	+	0.423854i	−0.819933	−	0.572459i	$-0.805990\pi$
$463$	−339.905	+	196.244i	−0.734136	+	0.423854i	0.0857971	+	0.996313i	$0.472656\pi$
$464$	247.813	−	618.201i	0.534079	−	1.33233i
$465$	411.836	−	36.1106i	0.885668	−	0.0776572i
$466$	322.934	+	447.940i	0.692992	+	0.961245i
$467$	217.484	+	217.484i	0.465703	+	0.465703i	0.900519	−	0.434816i	$-0.143187\pi$
$467$	217.484	+	217.484i	0.465703	+	0.465703i	−0.434816	+	0.900519i	$0.643187\pi$
$468$	−19.1871	+	14.2496i	−0.0409980	+	0.0304478i
$469$	20.5191	+	20.5191i	0.0437507	+	0.0437507i
$470$	128.750	−	793.964i	0.273937	−	1.68928i
$471$	−218.943	+	469.761i	−0.464848	+	0.997369i
$472$	−22.8968	−	553.913i	−0.0485101	−	1.17354i
$473$	−36.4744	+	21.0585i	−0.0771129	+	0.0445212i
$474$	57.4624	−	782.492i	0.121229	−	1.65083i
$475$	78.9451	+	294.627i	0.166200	+	0.620267i
$476$	−5.16775	−	5.82507i	−0.0108566	−	0.0122375i
$477$	−346.316	−	741.934i	−0.726030	−	1.55542i
$478$	−367.697	+	817.743i	−0.769240	+	1.71076i
$479$	−323.431	−	186.733i	−0.675222	−	0.389839i	0.122831	−	0.992428i	$-0.460803\pi$
$479$	−323.431	−	186.733i	−0.675222	−	0.389839i	−0.798052	+	0.602588i	$0.794136\pi$
$480$	−567.733	−	277.441i	−1.18278	−	0.578002i
$481$	11.2159	+	19.4265i	0.0233178	+	0.0403877i
$482$	−4.08527	−	40.2956i	−0.00847567	−	0.0836008i
$483$	−21.6894	+	123.145i	−0.0449057	+	0.254959i
$484$	−90.9227	−	443.804i	−0.187857	−	0.916951i
$485$	−743.152	−	743.152i	−1.53227	−	1.53227i
$486$	118.857	−	471.242i	0.244563	−	0.969633i
$487$	291.516			0.598596			0.299298	−	0.954160i	$-0.403248\pi$
$487$	291.516			0.598596			0.299298	+	0.954160i	$0.403248\pi$
$488$	86.0844	−	54.5614i	0.176403	−	0.111806i
$489$	−584.752	+	409.615i	−1.19581	+	0.837658i
$490$	396.532	−	486.005i	0.809248	−	0.991848i
$491$	−219.276	−	58.7547i	−0.446590	−	0.119663i	0.0285134	−	0.999593i	$-0.490923\pi$
$491$	−219.276	−	58.7547i	−0.446590	−	0.119663i	−0.475103	+	0.879930i	$0.657589\pi$
$492$	−940.716	+	26.0964i	−1.91202	+	0.0530415i
$493$	−18.0294	−	67.2868i	−0.0365709	−	0.136484i
$494$	20.1554	+	9.06282i	0.0408003	+	0.0183458i
$495$	154.938	+	56.3255i	0.313006	+	0.113789i
$496$	332.587	+	39.9172i	0.670537	+	0.0804782i
$497$	56.6645	−	98.1457i	0.114013	−	0.197476i
$498$	442.314	+	512.425i	0.888180	+	1.02897i
$499$	133.612	−	498.645i	0.267759	−	0.999289i	−0.692782	−	0.721148i	$-0.743615\pi$
$499$	133.612	−	498.645i	0.267759	−	0.999289i	0.960540	−	0.278141i	$-0.0897184\pi$
$500$	78.6177	+	157.146i	0.157235	+	0.314293i
$501$	−488.219	+	177.803i	−0.974489	+	0.354897i
$502$	−4.40385	+	27.1572i	−0.00877262	+	0.0540981i
$503$	−350.224			−0.696270			−0.348135	−	0.937444i	$-0.613185\pi$
$503$	−350.224			−0.696270			−0.348135	+	0.937444i	$0.613185\pi$
$504$	70.5530	+	45.1395i	0.139986	+	0.0895625i
$505$			46.3850i			0.0918514i
$506$	−31.9208	+	196.846i	−0.0630846	+	0.389024i
$507$	324.969	−	387.434i	0.640965	−	0.764170i
$508$	−5.81055	−	1.93539i	−0.0114381	−	0.00380981i
$509$	−357.042	−	95.6690i	−0.701457	−	0.187955i	−0.109574	−	0.993979i	$-0.534949\pi$
$509$	−357.042	−	95.6690i	−0.701457	−	0.187955i	−0.591883	+	0.806024i	$0.701615\pi$
$510$	−64.9207	+	12.3843i	−0.127296	+	0.0242830i
$511$	77.9928	+	45.0292i	0.152628	+	0.0881197i
$512$	−404.017	−	314.506i	−0.789097	−	0.614269i
$513$	−434.007	+	116.560i	−0.846018	+	0.227212i
$514$	−235.880	−	106.063i	−0.458911	−	0.206348i
$515$	−708.384	+	189.811i	−1.37550	+	0.368565i
$516$	−42.1221	+	176.660i	−0.0816319	+	0.342364i
$517$	−44.0070	+	164.236i	−0.0851200	+	0.317672i
$518$	49.6974	−	60.9112i	0.0959410	−	0.117589i
$519$	2.38446	−	0.209074i	0.00459433	−	0.000402841i
$520$	−34.1123	−	7.64561i	−0.0656006	−	0.0147031i
$521$		−	198.941i		−	0.381844i	−0.981605	−	0.190922i	$-0.938852\pi$
$521$		−	198.941i		−	0.381844i	0.981605	−	0.190922i	$-0.0611478\pi$
$522$	383.784	+	643.522i	0.735218	+	1.23280i
$523$	−156.570	+	156.570i	−0.299370	+	0.299370i	−0.840767	−	0.541397i	$-0.817896\pi$
$523$	−156.570	+	156.570i	−0.299370	+	0.299370i	0.541397	+	0.840767i	$0.317896\pi$
$524$	−336.188	−	221.860i	−0.641581	−	0.423397i
$525$	21.8859	+	60.0952i	0.0416875	+	0.114467i
$526$	51.9834	+	512.745i	0.0988278	+	0.974800i
$527$	30.3417	−	17.5178i	0.0575743	−	0.0332405i
$528$	113.487	+	70.4550i	0.214937	+	0.133437i
$529$	−377.372	+	653.628i	−0.713369	+	1.23559i
$530$	491.154	−	1092.31i	0.926706	−	2.06096i
$531$	511.030	+	357.534i	0.962391	+	0.673323i
$532$	4.62276	−	77.3094i	0.00868940	−	0.145318i
$533$	−50.2895	+	13.4750i	−0.0943518	+	0.0252815i
$534$	−64.0927	+	30.9836i	−0.120024	+	0.0580218i
$535$	370.052	+	640.949i	0.691686	+	1.19804i
$536$	199.389	−	8.24203i	0.371994	−	0.0153769i
$537$	−126.383	+	88.5305i	−0.235350	+	0.164861i
$538$	−62.1328	+	383.154i	−0.115488	+	0.712182i
$539$	−93.7588	+	93.7588i	−0.173950	+	0.173950i
$540$	635.579	−	318.427i	1.17700	−	0.589680i
$541$	−294.914	+	294.914i	−0.545128	+	0.545128i	−0.925028	−	0.379900i	$-0.875958\pi$
$541$	−294.914	+	294.914i	−0.545128	+	0.545128i	0.379900	+	0.925028i	$0.375958\pi$
$542$	268.172	+	371.980i	0.494782	+	0.686309i
$543$	177.879	−	124.603i	0.327586	−	0.229472i
$544$	−53.5420	−	0.985906i	−0.0984228	−	0.00181233i
$545$	−31.0660	−	53.8079i	−0.0570018	−	0.0987301i
$546$	4.37599	+	1.52388i	0.00801463	+	0.00279099i
$547$	−785.292	+	210.418i	−1.43563	+	0.384677i	−0.891003	−	0.453998i	$-0.849997\pi$
$547$	−785.292	+	210.418i	−1.43563	+	0.384677i	−0.544632	+	0.838675i	$0.683331\pi$
$548$	238.511	−	211.597i	0.435240	−	0.386125i
$549$	−9.94932	+	114.226i	−0.0181226	+	0.208063i
$550$	36.2023	+	95.3583i	0.0658224	+	0.173379i
$551$	346.413	−	600.005i	0.628699	−	1.08894i
$552$	522.024	+	683.321i	0.945695	+	1.23790i
$553$	−131.740	+	76.0601i	−0.238228	+	0.137541i
$554$	−368.494	+	451.642i	−0.665152	+	0.815238i
$555$	−228.324	−	626.940i	−0.411394	−	1.12962i
$556$	282.827	−	428.572i	0.508682	−	0.770814i
$557$	427.709	−	427.709i	0.767880	−	0.767880i	−0.209853	−	0.977733i	$-0.567298\pi$
$557$	427.709	−	427.709i	0.767880	−	0.767880i	0.977733	+	0.209853i	$0.0672984\pi$
$558$	−262.671	+	270.215i	−0.470737	+	0.484256i
$559$			10.0474i			0.0179739i
$560$	17.3811	+	121.275i	0.0310376	+	0.216562i
$561$	13.9178	−	1.22034i	0.0248089	−	0.00217530i
$562$	−910.387	+	92.2974i	−1.61991	+	0.164230i
$563$	−153.185	+	571.695i	−0.272087	+	1.01544i	0.685681	+	0.727902i	$0.259504\pi$
$563$	−153.185	+	571.695i	−0.272087	+	1.01544i	−0.957768	+	0.287541i	$0.907162\pi$
$564$	384.059	+	624.546i	0.680955	+	1.10735i
$565$	1061.03	−	284.301i	1.87792	−	0.503188i
$566$	194.198	−	73.7264i	0.343106	−	0.130259i
$567$	−88.5197	+	32.2955i	−0.156119	+	0.0569586i
$568$	−232.634	−	743.834i	−0.409567	−	1.30957i
$569$	−812.137	−	468.887i	−1.42731	−	0.824055i	−0.430398	−	0.902639i	$-0.641627\pi$
$569$	−812.137	−	468.887i	−1.42731	−	0.824055i	−0.996907	+	0.0785844i	$0.974960\pi$
$570$	−543.664	−	369.474i	−0.953797	−	0.648199i
$571$	207.187	+	55.5155i	0.362849	+	0.0972251i	0.435637	−	0.900122i	$-0.356523\pi$
$571$	207.187	+	55.5155i	0.362849	+	0.0972251i	−0.0727883	+	0.997347i	$0.523190\pi$
$572$	7.01128	+	2.33533i	0.0122575	+	0.00408274i
$573$	87.6761	−	104.529i	0.153012	−	0.182424i
$574$	106.702	+	148.006i	0.185893	+	0.257851i
$575$			656.616i			1.14194i
$576$	557.003	−	146.710i	0.967019	−	0.254705i
$577$	743.867			1.28920			0.644599	−	0.764521i	$-0.277024\pi$
$577$	743.867			1.28920			0.644599	+	0.764521i	$0.277024\pi$
$578$	464.316	−	334.740i	0.803315	−	0.579135i
$579$	230.205	−	83.8378i	0.397590	−	0.144798i
$580$	−346.344	+	1039.82i	−0.597145	+	1.79279i
$581$	33.9682	−	126.771i	0.0584651	−	0.218195i
$582$	955.434	+	70.1624i	1.64164	+	0.120554i
$583$	−126.587	+	219.255i	−0.217130	+	0.376081i
$584$	591.098	−	184.866i	1.01215	−	0.316551i
$585$	30.1177	−	25.2914i	0.0514832	−	0.0432332i
$586$	19.1041	+	50.3210i	0.0326009	+	0.0858720i
$587$	−73.5191	−	274.377i	−0.125246	−	0.467423i	0.874603	−	0.484840i	$-0.161122\pi$
$587$	−73.5191	−	274.377i	−0.125246	−	0.467423i	−0.999848	+	0.0174175i	$0.994456\pi$
$588$	15.8551	+	571.541i	0.0269645	+	0.972009i
$589$	336.582	+	90.1868i	0.571446	+	0.153119i
$590$	92.0176	+	907.626i	0.155962	+	1.53835i
$591$	−261.760	+	183.361i	−0.442910	+	0.310256i
$592$	−76.6982	−	535.154i	−0.129558	−	0.903977i
$593$	−1094.34			−1.84543			−0.922715	−	0.385482i	$-0.874035\pi$
$593$	−1094.34			−1.84543			−0.922715	+	0.385482i	$0.874035\pi$
$594$	−140.461	+	53.4178i	−0.236466	+	0.0899289i
$595$	9.06086	+	9.06086i	0.0152283	+	0.0152283i
$596$	564.825	+	372.744i	0.947693	+	0.625410i
$597$	84.5641	−	480.126i	0.141648	−	0.804230i
$598$	36.8605	+	30.0745i	0.0616396	+	0.0502917i
$599$	−41.9094	−	72.5892i	−0.0699656	−	0.121184i	0.828920	−	0.559367i	$-0.188956\pi$
$599$	−41.9094	−	72.5892i	−0.0699656	−	0.121184i	−0.898886	+	0.438183i	$0.855622\pi$
$600$	405.990	+	169.180i	0.676649	+	0.281966i
$601$	779.113	+	449.821i	1.29636	+	0.748454i	0.979774	−	0.200109i	$-0.0641297\pi$
$601$	779.113	+	449.821i	1.29636	+	0.748454i	0.316587	+	0.948563i	$0.397463\pi$
$602$	32.9190	−	12.4975i	0.0546827	−	0.0207600i
$603$	−128.700	+	183.953i	−0.213432	+	0.305062i
$604$	−217.872	−	245.585i	−0.360715	−	0.406597i
$605$	192.944	+	720.077i	0.318916	+	1.19021i
$606$	−27.6278	−	32.0071i	−0.0455904	−	0.0528170i
$607$	241.636	−	139.509i	0.398083	−	0.229833i	−0.287574	−	0.957758i	$-0.592849\pi$
$607$	241.636	−	139.509i	0.398083	−	0.229833i	0.685656	+	0.727925i	$0.259515\pi$
$608$	−369.612	−	383.479i	−0.607915	−	0.630723i
$609$	61.3690	−	131.672i	0.100770	−	0.216211i
$610$	−136.046	+	98.0798i	−0.223026	+	0.160786i
$611$	28.6818	+	28.6818i	0.0469424	+	0.0469424i
$612$	37.4210	−	47.2136i	0.0611454	−	0.0771464i
$613$	707.726	+	707.726i	1.15453	+	1.15453i	0.985634	+	0.168894i	$0.0540196\pi$
$613$	707.726	+	707.726i	1.15453	+	1.15453i	0.168894	+	0.985634i	$0.445980\pi$
$614$	−779.781	−	126.450i	−1.27000	−	0.205945i
$615$	1542.69	−	135.266i	2.50843	−	0.219945i
$616$	−1.06964	−	25.8764i	−0.00173643	−	0.0420071i
$617$	410.544	−	237.028i	0.665387	−	0.384161i	−0.128939	−	0.991652i	$-0.541157\pi$
$617$	410.544	−	237.028i	0.665387	−	0.384161i	0.794327	+	0.607491i	$0.207824\pi$
$618$	375.752	−	552.903i	0.608013	−	0.894665i
$619$	31.3235	+	116.901i	0.0506034	+	0.188855i	0.986601	−	0.163152i	$-0.0521661\pi$
$619$	31.3235	+	116.901i	0.0506034	+	0.188855i	−0.935998	+	0.352007i	$0.885499\pi$
$620$	−550.238	−	32.9018i	−0.887481	−	0.0530675i
$621$	−967.393	+	0.557100i	−1.55780	+	0.000897102i
$622$	−117.316	−	52.7509i	−0.188611	−	0.0848085i
$623$	11.9531	+	6.90115i	0.0191864	+	0.0110773i
$624$	28.0925	−	15.0423i	0.0450200	−	0.0241062i
$625$	−373.653	−	647.185i	−0.597844	−	1.03550i
$626$	−612.637	+	62.1108i	−0.978654	+	0.0992185i
$627$	106.462	+	89.2976i	0.169796	+	0.142420i
$628$	380.623	−	576.764i	0.606088	−	0.918414i
$629$	−39.9832	−	39.9832i	−0.0635663	−	0.0635663i
$630$	−120.326	−	67.2177i	−0.190994	−	0.106695i
$631$	−1081.77			−1.71437			−0.857185	−	0.515008i	$-0.827789\pi$
$631$	−1081.77			−1.71437			−0.857185	+	0.515008i	$0.827789\pi$
$632$	−228.794	+	1020.81i	−0.362015	+	1.61520i
$633$	−613.368	−	285.875i	−0.968986	−	0.451619i
$634$	−713.529	−	582.168i	−1.12544	−	0.918246i
$635$	9.73468	+	2.60840i	0.0153302	+	0.00410772i
$636$	311.688	+	1046.27i	0.490075	+	1.64507i
$637$	8.18689	+	30.5539i	0.0128523	+	0.0479653i
$638$	95.0122	−	211.303i	0.148922	−	0.331196i
$639$	824.023	+	299.561i	1.28955	+	0.468797i
$640$	694.543	+	476.934i	1.08522	+	0.745209i
$641$	−166.559	+	288.489i	−0.259843	+	0.450061i	−0.966200	−	0.257795i	$-0.917004\pi$
$641$	−166.559	+	288.489i	−0.259843	+	0.450061i	0.706357	+	0.707856i	$0.250337\pi$
$642$	−637.109	−	221.865i	−0.992382	−	0.345584i
$643$	−198.632	+	741.303i	−0.308914	+	1.15288i	0.620610	+	0.784120i	$0.286885\pi$
$643$	−198.632	+	741.303i	−0.308914	+	1.15288i	−0.929524	+	0.368763i	$0.879781\pi$
$644$	52.6859	−	158.177i	0.0818104	−	0.245617i
$645$	51.8391	−	294.325i	0.0803707	−	0.456317i
$646$	−54.9881	−	8.91694i	−0.0851208	−	0.0138033i
$647$	545.441			0.843030			0.421515	−	0.906821i	$-0.361498\pi$
$647$	545.441			0.843030			0.421515	+	0.906821i	$0.361498\pi$
$648$	−248.908	+	598.288i	−0.384117	+	0.923284i
$649$		−	192.848i		−	0.297147i
$650$	24.0190	+	3.89496i	0.0369523	+	0.00599224i
$651$	71.9562	+	12.6736i	0.110532	+	0.0194679i
$652$	851.334	−	425.908i	1.30573	−	0.653233i
$653$	−491.583	−	131.719i	−0.752808	−	0.201714i	−0.138045	−	0.990426i	$-0.544082\pi$
$653$	−491.583	−	131.719i	−0.752808	−	0.201714i	−0.614763	+	0.788712i	$0.710748\pi$
$654$	53.4856	+	18.6256i	0.0817822	+	0.0284795i
$655$	574.025	+	331.414i	0.876374	+	0.505975i
$656$	1245.83	+	149.525i	1.89913	+	0.227934i
$657$	−238.051	+	654.821i	−0.362330	+	0.996683i
$658$	58.2962	−	129.648i	0.0885960	−	0.197034i
$659$	1194.74	−	320.129i	1.81295	−	0.485779i	0.817079	−	0.576526i	$-0.195592\pi$
$659$	1194.74	−	320.129i	1.81295	−	0.485779i	0.995874	+	0.0907468i	$0.0289254\pi$
$660$	−193.337	−	104.585i	−0.292935	−	0.158462i
$661$	325.682	−	1215.46i	0.492712	−	1.83882i	−0.0497751	−	0.998760i	$-0.515850\pi$
$661$	325.682	−	1215.46i	0.492712	−	1.83882i	0.542487	−	0.840064i	$-0.317483\pi$
$662$	−249.276	−	203.384i	−0.376551	−	0.307227i
$663$	1.40799	−	3.02095i	0.00212366	−	0.00455649i
$664$	−483.178	−	762.335i	−0.727677	−	1.14809i
$665$			127.445i			0.191646i
$666$	530.969	+	296.614i	0.797250	+	0.445367i
$667$	1054.61	−	1054.61i	1.58113	−	1.58113i
$668$	678.687	−	139.043i	1.01600	−	0.208149i
$669$	642.647	−	766.175i	0.960608	−	1.14525i
$670$	−326.713	+	33.1231i	−0.487632	+	0.0494374i
$671$	30.7036	−	17.7267i	0.0457580	−	0.0264184i
$672$	−84.2272	−	73.3310i	−0.125338	−	0.109123i
$673$	−203.937	+	353.229i	−0.303027	+	0.524858i	−0.976820	−	0.214062i	$-0.931330\pi$
$673$	−203.937	+	353.229i	−0.303027	+	0.524858i	0.673793	+	0.738920i	$0.264664\pi$
$674$	−316.312	−	142.229i	−0.469306	−	0.211023i
$675$	−428.373	+	247.650i	−0.634627	+	0.366889i
$676$	−504.365	+	447.450i	−0.746102	+	0.661909i
$677$	786.070	−	210.627i	1.16111	−	0.311118i	0.373700	−	0.927550i	$-0.378089\pi$
$677$	786.070	−	210.627i	1.16111	−	0.311118i	0.787408	+	0.616432i	$0.211422\pi$
$678$	−562.807	+	828.146i	−0.830099	+	1.22145i
$679$	−92.8705	−	160.857i	−0.136775	−	0.236902i
$680$	88.0467	−	3.63954i	0.129480	−	0.00535226i
$681$	−42.2779	−	482.173i	−0.0620822	−	0.708037i
$682$	115.021	+	18.6520i	0.168653	+	0.0273490i
$683$	−290.330	+	290.330i	−0.425080	+	0.425080i	−0.886949	−	0.461868i	$-0.847179\pi$
$683$	−290.330	+	290.330i	−0.425080	+	0.425080i	0.461868	+	0.886949i	$0.347179\pi$
$684$	595.211	−	68.8687i	0.870192	−	0.100685i
$685$	−371.003	+	371.003i	−0.541610	+	0.541610i
$686$	182.399	−	131.497i	0.265888	−	0.191687i
$687$	−153.337	−	71.4662i	−0.223197	−	0.104026i
$688$	90.0989	−	224.764i	0.130958	−	0.326691i
$689$	30.1984	+	52.3052i	0.0438294	+	0.0759147i
$690$	−924.610	−	1071.17i	−1.34002	−	1.55242i
$691$	−202.302	+	54.2067i	−0.292767	+	0.0784468i	−0.402213	−	0.915546i	$-0.631759\pi$
$691$	−202.302	+	54.2067i	−0.292767	+	0.0784468i	0.109446	+	0.993993i	$0.465092\pi$
$692$	−3.18578	−	0.190496i	−0.00460373	−	0.000275283i
$693$	23.8731	+	16.7024i	0.0344489	+	0.0241017i
$694$	−488.871	+	185.598i	−0.704426	+	0.267432i
$695$	−422.486	+	731.767i	−0.607893	+	1.05290i
$696$	−380.347	−	923.796i	−0.546476	−	1.32729i
$697$	113.656	−	65.6195i	0.163065	−	0.0941456i
$698$	229.470	+	187.225i	0.328754	+	0.268230i
$699$	815.760	+	143.679i	1.16704	+	0.205549i
$700$	−17.1149	−	83.5401i	−0.0244499	−	0.119343i
$701$	−460.602	+	460.602i	−0.657064	+	0.657064i	−0.954684	−	0.297620i	$-0.903807\pi$
$701$	−460.602	+	460.602i	−0.657064	+	0.657064i	0.297620	+	0.954684i	$0.403807\pi$
$702$	−5.71806	+	35.3905i	−0.00814539	+	0.0504139i
$703$		−	562.381i		−	0.799973i
$704$	−135.903	−	115.115i	−0.193044	−	0.163516i
$705$	−692.211	−	988.176i	−0.981860	−	1.40167i
$706$	110.787	+	1092.76i	0.156923	+	1.54783i
$707$	−2.12172	+	7.91838i	−0.00300102	+	0.0112000i
$708$	−604.095	−	571.483i	−0.853241	−	0.807180i
$709$	−628.058	+	168.288i	−0.885836	+	0.237359i	−0.672923	−	0.739712i	$-0.734962\pi$
$709$	−628.058	+	168.288i	−0.885836	+	0.237359i	−0.212913	+	0.977071i	$0.568295\pi$
$710$	455.193	+	1199.00i	0.641117	+	1.68873i
$711$	−756.842	−	901.266i	−1.06448	−	1.26760i
$712$	90.5914	−	28.3324i	0.127235	−	0.0397927i
$713$	649.621	+	375.059i	0.911110	+	0.526029i
$714$	−11.6491	−	0.855453i	−0.0163153	−	0.00119811i
$715$	−11.7463	−	3.14742i	−0.0164284	−	0.00440199i
$716$	184.000	−	92.0520i	0.256983	−	0.128564i
$717$	460.229	+	1263.71i	0.641882	+	1.76250i
$718$	−320.676	+	231.186i	−0.446624	+	0.321985i
$719$			1292.58i			1.79775i	0.438208	+	0.898874i	$0.355614\pi$
$719$			1292.58i			1.79775i	−0.438208	+	0.898874i	$0.644386\pi$
$720$	−900.540	+	295.701i	−1.25075	+	0.410695i
$721$	−129.611			−0.179765
$722$	98.2221	+	136.243i	0.136042	+	0.188703i
$723$	−46.5472	−	39.0425i	−0.0643806	−	0.0540007i
$724$	−258.973	+	129.560i	−0.357697	+	0.178950i
$725$	197.441	−	736.858i	0.272332	−	1.01636i
$726$	−562.029	−	381.954i	−0.774145	−	0.526108i
$727$	147.687	−	255.802i	0.203146	−	0.351860i	−0.746394	−	0.665504i	$-0.768217\pi$
$727$	147.687	−	255.802i	0.203146	−	0.351860i	0.949541	+	0.313644i	$0.101550\pi$
$728$	−5.47360	−	2.86554i	−0.00751868	−	0.00393618i
$729$	−365.227	−	630.912i	−0.500997	−	0.865449i
$730$	−952.798	+	361.725i	−1.30520	+	0.495514i
$731$	−6.55509	−	24.4639i	−0.00896729	−	0.0334664i
$732$	35.4577	−	148.710i	0.0484395	−	0.203155i
$733$	1024.97	+	274.639i	1.39832	+	0.374678i	0.877741	−	0.479136i	$-0.159050\pi$
$733$	1024.97	+	274.639i	1.39832	+	0.374678i	0.520578	+	0.853814i	$0.325717\pi$
$734$	782.998	−	79.3824i	1.06675	−	0.108150i
$735$	−82.1822	−	937.274i	−0.111812	−	1.27520i
$736$	−554.892	−	1003.32i	−0.753930	−	1.36320i
$737$	69.4186			0.0941908
$738$	−983.935	+	1012.19i	−1.33325	+	1.37153i
$739$	214.647	+	214.647i	0.290456	+	0.290456i	0.837260	−	0.546804i	$-0.184156\pi$
$739$	214.647	+	214.647i	0.290456	+	0.290456i	−0.546804	+	0.837260i	$0.684156\pi$
$740$	178.551	+	871.528i	0.241285	+	1.17774i
$741$	31.1474	−	11.3435i	0.0420343	−	0.0153084i
$742$	133.809	−	164.002i	0.180335	−	0.221027i
$743$	−138.018	−	239.054i	−0.185758	−	0.321741i	0.758074	−	0.652169i	$-0.226141\pi$
$743$	−138.018	−	239.054i	−0.185758	−	0.321741i	−0.943832	+	0.330427i	$0.892807\pi$
$744$	399.278	−	305.029i	0.536665	−	0.409985i
$745$	−964.411	−	556.803i	−1.29451	−	0.747387i
$746$	−136.282	−	358.971i	−0.182683	−	0.481195i
$747$	1011.55	+	88.1078i	1.35415	+	0.117949i
$748$	−18.5950	−	1.11190i	−0.0248597	−	0.00148650i
$749$	33.8536	+	126.343i	0.0451983	+	0.168682i
$750$	248.912	+	86.6801i	0.331882	+	0.115573i
$751$	−559.902	+	323.260i	−0.745542	+	0.430439i	−0.824081	−	0.566472i	$-0.808308\pi$
$751$	−559.902	+	323.260i	−0.745542	+	0.430439i	0.0785387	+	0.996911i	$0.474975\pi$
$752$	−384.420	−	898.822i	−0.511197	−	1.19524i
$753$	23.6768	+	33.8002i	0.0314433	+	0.0448874i
$754$	−32.3218	−	44.8335i	−0.0428672	−	0.0594608i
$755$	382.005	+	382.005i	0.505968	+	0.505968i
$756$	123.065	−	25.2863i	0.162785	−	0.0334475i
$757$	8.92142	+	8.92142i	0.0117852	+	0.0117852i	0.712975	−	0.701190i	$-0.247347\pi$
$757$	8.92142	+	8.92142i	0.0117852	+	0.0117852i	−0.701190	+	0.712975i	$0.747347\pi$
$758$	52.2678	−	322.320i	0.0689549	−	0.425224i
$759$	171.619	+	244.997i	0.226112	+	0.322789i
$760$	644.803	+	593.611i	0.848425	+	0.781068i
$761$	−24.5944	+	14.1996i	−0.0323185	+	0.0186591i	−0.516072	−	0.856545i	$-0.672606\pi$
$761$	−24.5944	+	14.1996i	−0.0323185	+	0.0186591i	0.483754	+	0.875204i	$0.339273\pi$
$762$	−8.27085	+	3.99829i	−0.0108541	+	0.00524710i
$763$	−2.84202	−	10.6066i	−0.00372480	−	0.0139011i
$764$	−136.077	+	120.721i	−0.178111	+	0.158012i
$765$	−56.8315	+	81.2302i	−0.0742896	+	0.106183i
$766$	−281.385	+	625.789i	−0.367343	+	0.816957i
$767$	−39.8421	−	23.0028i	−0.0519454	−	0.0299907i
$768$	−763.328	+	84.5843i	−0.993917	+	0.110136i
$769$	−453.525	−	785.528i	−0.589759	−	1.02149i	−0.994264	−	0.106957i	$-0.965889\pi$
$769$	−453.525	−	785.528i	−0.589759	−	1.02149i	0.404505	−	0.914536i	$-0.367444\pi$
$770$	4.29866	+	42.4003i	0.00558267	+	0.0550654i
$771$	−364.522	+	132.754i	−0.472791	+	0.172185i
$772$	−320.015	+	65.5617i	−0.414527	+	0.0849245i
$773$	260.219	+	260.219i	0.336635	+	0.336635i	0.855099	−	0.518465i	$-0.173496\pi$
$773$	260.219	+	260.219i	0.336635	+	0.336635i	−0.518465	+	0.855099i	$0.673496\pi$
$774$	139.535	+	233.970i	0.180278	+	0.302286i
$775$	383.674			0.495064
$776$	−1246.42	−	279.360i	−1.60621	−	0.360000i
$777$	−10.2999	−	117.469i	−0.0132560	−	0.151183i
$778$	−10.7225	+	13.1419i	−0.0137821	+	0.0168920i
$779$	1260.80	+	337.829i	1.61848	+	0.433670i
$780$	−44.6681	+	27.4682i	−0.0572668	+	0.0352157i
$781$	−70.1682	−	261.871i	−0.0898440	−	0.335303i
$782$	−109.371	−	49.1785i	−0.139861	−	0.0628881i
$783$	1085.78	+	290.264i	1.38669	+	0.370708i
$784$	90.8453	−	756.916i	0.115874	−	0.965454i
$785$	−568.573	+	984.797i	−0.724297	+	1.25452i
$786$	−593.492	+	113.215i	−0.755079	+	0.144039i
$787$	174.716	−	652.047i	0.222002	−	0.828523i	−0.761582	−	0.648069i	$-0.775577\pi$
$787$	174.716	−	652.047i	0.222002	−	0.828523i	0.983584	−	0.180454i	$-0.0577566\pi$
$788$	381.093	−	190.655i	0.483621	−	0.241948i
$789$	592.294	+	496.800i	0.750689	+	0.629657i
$790$	275.558	−	1699.28i	0.348807	−	2.15099i
$791$	194.132			0.245427
$792$	195.701	−	42.9885i	0.247098	−	0.0542784i
$793$		−	8.45774i		−	0.0106655i
$794$	40.4127	−	249.213i	0.0508976	−	0.313870i
$795$	−614.755	−	1688.02i	−0.773277	−	2.12329i
$796$	−205.415	+	616.711i	−0.258059	+	0.774762i
$797$	−743.268	−	199.158i	−0.932582	−	0.249885i	−0.239627	−	0.970865i	$-0.577025\pi$
$797$	−743.268	−	199.158i	−0.932582	−	0.249885i	−0.692956	+	0.720980i	$0.743692\pi$
$798$	−75.9087	−	87.9410i	−0.0951236	−	0.110202i
$799$	−88.5484	−	51.1235i	−0.110824	−	0.0639843i
$800$	−502.386	−	302.520i	−0.627983	−	0.378150i
$801$	−36.4835	+	100.358i	−0.0455475	+	0.125290i
$802$	1363.43	+	613.063i	1.70004	+	0.764418i
$803$	208.100	−	55.7601i	0.259153	−	0.0694397i
$804$	205.714	−	217.453i	0.255863	−	0.270464i
$805$	−71.0070	+	265.002i	−0.0882075	+	0.329195i
$806$	17.5731	−	21.5383i	0.0218029	−	0.0267225i
$807$	334.050	+	476.878i	0.413940	+	0.590927i
$808$	30.1802	+	47.6169i	0.0373518	+	0.0589318i
$809$		−	255.211i		−	0.315464i	−0.987482	−	0.157732i	$-0.949582\pi$
$809$		−	255.211i		−	0.315464i	0.987482	−	0.157732i	$-0.0504183\pi$
$810$	350.099	−	1007.22i	0.432221	−	1.24348i
$811$	45.0193	−	45.0193i	0.0555109	−	0.0555109i	−0.678806	−	0.734317i	$-0.737502\pi$
$811$	45.0193	−	45.0193i	0.0555109	−	0.0555109i	0.734317	+	0.678806i	$0.237502\pi$
$812$	−106.687	+	161.665i	−0.131388	+	0.199095i
$813$	677.425	+	119.314i	0.833242	+	0.146758i
$814$	−18.9689	−	187.102i	−0.0233033	−	0.229855i
$815$	−1356.59	+	783.230i	−1.66453	+	0.961019i
$816$	−58.5872	+	54.9537i	−0.0717980	+	0.0673452i
$817$	125.948	−	218.148i	0.154159	−	0.267011i
$818$	−318.429	+	708.174i	−0.389277	+	0.865738i
$819$	6.29826	−	2.93987i	0.00769018	−	0.00358958i
$820$	−2061.13	−	123.246i	−2.51357	−	0.150300i
$821$	639.561	−	171.370i	0.779003	−	0.208733i	0.152658	−	0.988279i	$-0.451217\pi$
$821$	639.561	−	171.370i	0.779003	−	0.208733i	0.626345	+	0.779546i	$0.284550\pi$
$822$	35.0271	−	476.980i	0.0426120	−	0.580268i
$823$	112.200	+	194.337i	0.136331	+	0.236132i	0.926105	−	0.377266i	$-0.123136\pi$
$823$	112.200	+	194.337i	0.136331	+	0.236132i	−0.789774	+	0.613398i	$0.789802\pi$
$824$	−603.699	+	655.760i	−0.732644	+	0.795826i
$825$	138.676	+	64.6334i	0.168092	+	0.0783435i
$826$	−25.8080	+	159.150i	−0.0312445	+	0.192675i
$827$	148.147	−	148.147i	0.179137	−	0.179137i	−0.611842	−	0.790980i	$-0.709571\pi$
$827$	148.147	−	148.147i	0.179137	−	0.179137i	0.790980	+	0.611842i	$0.209571\pi$
$828$	1276.02	+	188.426i	1.54109	+	0.227567i
$829$	−69.4371	+	69.4371i	−0.0837601	+	0.0837601i	−0.747746	−	0.663985i	$-0.768864\pi$
$829$	−69.4371	+	69.4371i	−0.0837601	+	0.0837601i	0.663985	+	0.747746i	$0.268864\pi$
$830$	868.561	+	1204.78i	1.04646	+	1.45154i
$831$	76.3714	+	871.003i	0.0919030	+	1.04814i
$832$	−39.9929	+	14.3464i	−0.0480684	+	0.0172433i
$833$	−39.8677	−	69.0529i	−0.0478604	−	0.0828967i
$834$	−144.326	−	756.583i	−0.173053	−	0.907173i
$835$	−1101.18	+	295.059i	−1.31877	+	0.353364i
$836$	−122.954	−	138.593i	−0.147074	−	0.165782i
$837$	0.325525	+	565.267i	0.000388919	+	0.675349i
$838$	−328.835	−	866.164i	−0.392405	−	1.03361i
$839$	−731.850	+	1267.60i	−0.872289	+	1.51085i	−0.0126661	+	0.999920i	$0.504032\pi$
$839$	−731.850	+	1267.60i	−0.872289	+	1.51085i	−0.859623	+	0.510929i	$0.829301\pi$
$840$	145.557	+	112.183i	0.173282	+	0.133551i
$841$	−772.277	+	445.874i	−0.918284	+	0.530172i
$842$	256.173	−	313.977i	0.304244	−	0.372894i
$843$	−882.076	+	1051.63i	−1.04635	+	1.24748i
$844$	753.083	+	496.981i	0.892278	+	0.588840i
$845$	784.536	−	784.536i	0.928445	−	0.928445i
$846$	1066.22	+	269.578i	1.26031	+	0.318650i
$847$			131.750i			0.155549i
$848$	−206.507	−	1440.89i	−0.243523	−	1.69916i
$849$	131.627	−	282.416i	0.155037	−	0.332645i
$850$	−61.0239	+	6.18677i	−0.0717929	+	0.00727855i
$851$	313.336	−	1169.38i	0.368197	−	1.37413i
$852$	−1028.24	−	556.223i	−1.20686	−	0.652844i
$853$	−751.890	+	201.468i	−0.881465	+	0.236188i	−0.671039	−	0.741422i	$-0.734152\pi$
$853$	−751.890	+	201.468i	−0.881465	+	0.236188i	−0.210426	+	0.977610i	$0.567485\pi$
$854$	−27.7107	+	10.5202i	−0.0324482	+	0.0123188i
$855$	−970.949	+	171.589i	−1.13561	+	0.200689i
$856$	796.912	+	417.199i	0.930972	+	0.487382i
$857$	−1.57126	−	0.907170i	−0.00183345	−	0.00105854i	0.499083	−	0.866554i	$-0.333670\pi$
$857$	−1.57126	−	0.907170i	−0.00183345	−	0.00105854i	−0.500916	+	0.865496i	$0.667004\pi$
$858$	9.98000	−	4.82453i	0.0116317	−	0.00562299i
$859$	−985.809	−	264.147i	−1.14762	−	0.307505i	−0.365611	−	0.930768i	$-0.619140\pi$
$859$	−985.809	−	264.147i	−1.14762	−	0.307505i	−0.782012	+	0.623263i	$0.785807\pi$
$860$	−125.923	+	378.053i	−0.146422	+	0.439597i
$861$	269.539	+	47.4737i	0.313054	+	0.0551379i
$862$	−335.484	−	465.347i	−0.389192	−	0.539846i
$863$		−	1127.45i		−	1.30643i	−0.757174	−	0.653214i	$-0.773420\pi$
$863$		−	1127.45i		−	1.30643i	0.757174	−	0.653214i	$-0.226580\pi$
$864$	445.276	−	740.422i	0.515366	−	0.856970i
$865$	5.25178			0.00607142
$866$	−714.874	+	515.375i	−0.825490	+	0.595122i
$867$	148.932	−	845.583i	0.171778	−	0.975298i
$868$	−92.4262	−	30.7855i	−0.106482	−	0.0354671i
$869$	−94.1861	+	351.507i	−0.108384	+	0.404496i
$870$	715.508	+	1480.10i	0.822423	+	1.70126i
$871$	8.28021	−	14.3417i	0.00950655	−	0.0164658i
$872$	−66.9011	−	35.0240i	−0.0767214	−	0.0401652i
$873$	1100.46	−	924.115i	1.26055	−	1.05855i
$874$	−423.317	−	1115.03i	−0.484344	−	1.27578i
$875$	−13.2262	−	49.3609i	−0.0151157	−	0.0564125i
$876$	442.010	−	817.107i	0.504578	−	0.932770i
$877$	269.507	+	72.2143i	0.307306	+	0.0823424i	0.409177	−	0.912455i	$-0.365816\pi$
$877$	269.507	+	72.2143i	0.307306	+	0.0823424i	−0.101870	+	0.994798i	$0.532483\pi$
$878$	−34.6477	−	341.752i	−0.0394621	−	0.389239i
$879$	73.1801	+	34.1073i	0.0832538	+	0.0388024i
$880$	234.545	+	175.743i	0.266529	+	0.199708i
$881$	541.530			0.614677			0.307338	−	0.951600i	$-0.400562\pi$
$881$	541.530			0.614677			0.307338	+	0.951600i	$0.400562\pi$
$882$	614.967	+	597.799i	0.697242	+	0.677777i
$883$	1032.32	+	1032.32i	1.16910	+	1.16910i	0.982420	+	0.186683i	$0.0597739\pi$
$883$	1032.32	+	1032.32i	1.16910	+	1.16910i	0.186683	+	0.982420i	$0.440226\pi$
$884$	−2.44772	+	3.70907i	−0.00276892	+	0.00419578i
$885$	1048.44	+	879.401i	1.18468	+	0.993673i
$886$	939.354	+	766.419i	1.06022	+	0.865032i
$887$	227.865	+	394.673i	0.256894	+	0.444953i	0.965408	−	0.260743i	$-0.0839677\pi$
$887$	227.865	+	394.673i	0.256894	+	0.444953i	−0.708514	+	0.705696i	$0.750634\pi$
$888$	−642.305	−	495.033i	−0.723316	−	0.557470i
$889$	1.54250	+	0.890561i	0.00173509	+	0.00100176i
$890$	−146.025	+	55.4378i	−0.164073	+	0.0622897i
$891$	−95.1068	+	204.367i	−0.106742	+	0.229368i
$892$	−997.413	+	884.861i	−1.11818	+	0.991997i
$893$	−263.199	−	982.273i	−0.294736	−	1.09997i
$894$	997.117	−	190.211i	1.11534	−	0.212763i
$895$	−293.202	+	169.280i	−0.327600	+	0.189140i
$896$	96.7498	+	113.187i	0.107980	+	0.126325i
$897$	71.0864	−	6.23301i	0.0792491	−	0.00694873i
$898$	−556.107	+	400.915i	−0.619273	+	0.446453i
$899$	−616.230	−	616.230i	−0.685462	−	0.685462i
$900$	613.413	−	242.868i	0.681571	−	0.269853i
$901$	−107.654	−	107.654i	−0.119482	−	0.119482i
$902$	430.856	+	69.8681i	0.477667	+	0.0774591i
$903$	22.3123	−	47.8730i	0.0247091	−	0.0530155i
$904$	904.228	−	982.207i	1.00025	−	1.08651i
$905$	412.671	−	238.256i	0.455990	−	0.263266i
$906$	−491.126	−	36.0659i	−0.542081	−	0.0398078i
$907$	−387.337	−	1445.56i	−0.427053	−	1.59378i	−0.759398	−	0.650626i	$-0.774506\pi$
$907$	−387.337	−	1445.56i	−0.427053	−	1.59378i	0.332345	−	0.943158i	$-0.392160\pi$
$908$	−38.5212	+	644.213i	−0.0424242	+	0.709486i
$909$	−63.1834	−	5.50339i	−0.0695087	−	0.00605434i
$910$	9.27256	+	4.16939i	0.0101896	+	0.00458175i
$911$	111.984	+	64.6541i	0.122925	+	0.0709705i	0.560201	−	0.828356i	$-0.310724\pi$
$911$	111.984	+	64.6541i	0.122925	+	0.0709705i	−0.437277	+	0.899327i	$0.644057\pi$
$912$	−798.501	−	25.5533i	−0.875549	−	0.0280189i
$913$	−156.982	−	271.901i	−0.171941	−	0.297810i
$914$	−1001.60	+	101.544i	−1.09584	+	0.111099i
$915$	−43.6374	+	247.758i	−0.0476911	+	0.270774i
$916$	188.264	+	124.241i	0.205528	+	0.135634i
$917$	82.8325	+	82.8325i	0.0903298	+	0.0903298i
$918$	−9.16674	−	89.9013i	−0.00998556	−	0.0979317i
$919$	−1326.45			−1.44337			−0.721683	−	0.692223i	$-0.756631\pi$
$919$	−1326.45			−1.44337			−0.721683	+	0.692223i	$0.756631\pi$
$920$	1010.03	+	1593.58i	1.09786	+	1.73215i
$921$	−970.524	+	679.846i	−1.05377	+	0.738160i
$922$	59.2114	+	48.3105i	0.0642206	+	0.0523976i
$923$	−62.4717	−	16.7392i	−0.0676833	−	0.0181357i
$924$	−28.2207	−	26.6972i	−0.0305419	−	0.0288931i
$925$	−160.267	−	598.123i	−0.173261	−	0.646619i
$926$	321.917	−	715.932i	0.347643	−	0.773145i
$927$	−174.505	−	987.448i	−0.188247	−	1.06521i
$928$	321.011	+	1292.78i	0.345917	+	1.39308i
$929$	−193.734	+	335.557i	−0.208540	+	0.361203i	−0.951255	−	0.308406i	$-0.900205\pi$
$929$	−193.734	+	335.557i	−0.208540	+	0.361203i	0.742715	+	0.669608i	$0.233538\pi$
$930$	−625.907	+	540.269i	−0.673018	+	0.580934i
$931$	205.251	−	766.008i	0.220463	−	0.822780i
$932$	−1047.83	−	349.011i	−1.12428	−	0.374476i
$933$	−181.296	+	66.0259i	−0.194316	+	0.0707673i
$934$	−607.204	−	98.4651i	−0.650112	−	0.105423i
$935$	30.6540			0.0327851
$936$	14.4618	−	45.5591i	0.0154506	−	0.0486743i
$937$			31.2600i			0.0333618i	0.999861	+	0.0166809i	$0.00530994\pi$
$937$			31.2600i			0.0333618i	−0.999861	+	0.0166809i	$0.994690\pi$
$938$	−57.2883	−	9.28995i	−0.0610750	−	0.00990400i
$939$	−593.586	+	707.684i	−0.632146	+	0.753657i
$940$	719.745	+	1438.68i	0.765687	+	1.53051i
$941$	−1021.89	−	273.814i	−1.08596	−	0.290982i	−0.328924	−	0.944356i	$-0.606686\pi$
$941$	−1021.89	−	273.814i	−1.08596	−	0.290982i	−0.757035	+	0.653375i	$0.773353\pi$
$942$	−194.231	−	1018.19i	−0.206190	−	1.08089i
$943$	2433.40	+	1404.93i	2.58049	+	1.48985i
$944$	685.006	+	871.862i	0.725642	+	0.923582i
$945$	−199.667	+	53.6239i	−0.211288	+	0.0567448i
$946$	34.5442	−	76.8250i	0.0365161	−	0.0812103i
$947$	−383.086	+	102.648i	−0.404526	+	0.108392i	−0.455344	−	0.890315i	$-0.650484\pi$
$947$	−383.086	+	102.648i	−0.404526	+	0.108392i	0.0508180	+	0.998708i	$0.483817\pi$
$948$	821.982	+	1336.69i	0.867070	+	1.41001i
$949$	13.3021	−	49.6440i	0.0140169	−	0.0523119i
$950$	−472.674	−	385.654i	−0.497551	−	0.405952i
$951$	−1376.06	+	120.656i	−1.44696	+	0.126873i
$952$	15.1969	+	3.40609i	0.0159632	+	0.00357783i
$953$		−	1093.98i		−	1.14793i	−0.818878	−	0.573967i	$-0.805404\pi$
$953$		−	1093.98i		−	1.14793i	0.818878	−	0.573967i	$-0.194596\pi$
$954$	1429.62	+	798.625i	1.49855	+	0.837133i
$955$	211.667	−	211.667i	0.221640	−	0.221640i
$956$	−359.902	−	1756.73i	−0.376467	−	1.83758i
$957$	−118.922	−	326.542i	−0.124266	−	0.341214i
$958$	743.123	−	75.3398i	0.775703	−	0.0786428i
$959$	−80.3042	+	46.3636i	−0.0837374	+	0.0483458i
$960$	1245.56	−	213.917i	1.29746	−	0.222830i
$961$	−261.345	+	452.663i	−0.271951	+	0.471034i
$962$	−40.9174	−	18.3984i	−0.0425337	−	0.0191252i
$963$	−916.976	+	428.022i	−0.952207	+	0.444467i
$964$	53.7576	+	60.5955i	0.0557652	+	0.0628584i
$965$	519.226	−	139.126i	0.538058	−	0.144172i
$966$	−108.843	−	225.153i	−0.112674	−	0.233077i
$967$	−384.078	−	665.243i	−0.397185	−	0.687945i	0.596192	−	0.802842i	$-0.296680\pi$
$967$	−384.078	−	665.243i	−0.397185	−	0.687945i	−0.993377	+	0.114897i	$0.963346\pi$
$968$	666.584	+	613.663i	0.688620	+	0.633950i
$969$	−68.4388	+	47.9409i	−0.0706282	+	0.0494746i
$970$	2074.85	+	336.460i	2.13902	+	0.346866i
$971$	719.024	−	719.024i	0.740499	−	0.740499i	−0.232175	−	0.972674i	$-0.574584\pi$
$971$	719.024	−	719.024i	0.740499	−	0.740499i	0.972674	+	0.232175i	$0.0745843\pi$
$972$	358.338	+	903.536i	0.368660	+	0.929564i
$973$	−105.595	+	105.595i	−0.108525	+	0.108525i
$974$	−472.942	+	340.959i	−0.485567	+	0.350060i
$975$	29.8943	−	20.9408i	0.0306609	−	0.0214777i
$976$	−75.8439	+	189.203i	−0.0777090	+	0.193855i
$977$	727.704	+	1260.42i	0.744835	+	1.29009i	0.950272	+	0.311422i	$0.100805\pi$
$977$	727.704	+	1260.42i	0.744835	+	1.29009i	−0.205437	+	0.978670i	$0.565862\pi$
$978$	469.586	−	1348.47i	0.480149	−	1.37880i
$979$	31.8932	−	8.54577i	0.0325774	−	0.00872908i
$980$	−74.8795	+	1252.26i	−0.0764077	+	1.27781i
$981$	76.9805	−	35.9326i	0.0784714	−	0.0366285i
$982$	424.462	−	161.145i	0.432242	−	0.164099i
$983$	−146.815	+	254.292i	−0.149354	+	0.258689i	−0.930989	−	0.365047i	$-0.881053\pi$
$983$	−146.815	+	254.292i	−0.149354	+	0.258689i	0.781635	+	0.623737i	$0.214386\pi$
$984$	1495.65	−	1142.60i	1.51997	−	1.16118i
$985$	−607.270	+	350.607i	−0.616517	+	0.355946i
$986$	107.949	+	88.0756i	0.109482	+	0.0893261i
$987$	−72.9666	−	200.355i	−0.0739277	−	0.202993i
$988$	−43.2990	+	8.87071i	−0.0438249	+	0.00897845i
$989$	383.432	−	383.432i	0.387696	−	0.387696i
$990$	−317.243	+	89.8365i	−0.320447	+	0.0907439i
$991$			1522.85i			1.53668i	0.640039	+	0.768342i	$0.278918\pi$
$991$			1522.85i			1.53668i	−0.640039	+	0.768342i	$0.721082\pi$
$992$	−586.260	+	324.235i	−0.590988	+	0.326850i
$993$	−480.736	+	42.1519i	−0.484125	+	0.0424491i
$994$	22.8620	+	225.502i	0.0230000	+	0.226863i
$995$	276.846	−	1033.20i	0.278238	−	1.03840i
$996$	−1316.92	−	314.002i	−1.32221	−	0.315263i
$997$	−805.565	+	215.851i	−0.807989	+	0.216500i	−0.639089	−	0.769133i	$-0.720688\pi$
$997$	−805.565	+	215.851i	−0.807989	+	0.216500i	−0.168900	+	0.985633i	$0.554022\pi$
$998$	366.453	+	965.251i	0.367187	+	0.967185i
$999$	881.079	−	236.628i	0.881961	−	0.236865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.v.a.43.9	✓	184
3.2	odd	2		432.3.w.a.235.38		184
9.4	even	3	inner	144.3.v.a.139.22	yes	184
9.5	odd	6		432.3.w.a.91.25		184
16.3	odd	4	inner	144.3.v.a.115.22	yes	184
48.35	even	4		432.3.w.a.19.25		184
144.67	odd	12	inner	144.3.v.a.67.9	yes	184
144.131	even	12		432.3.w.a.307.38		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.v.a.43.9	✓	184	1.1	even	1	trivial
144.3.v.a.67.9	yes	184	144.67	odd	12	inner
144.3.v.a.115.22	yes	184	16.3	odd	4	inner
144.3.v.a.139.22	yes	184	9.4	even	3	inner
432.3.w.a.19.25		184	48.35	even	4
432.3.w.a.91.25		184	9.5	odd	6
432.3.w.a.235.38		184	3.2	odd	2
432.3.w.a.307.38		184	144.131	even	12

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.62235 + 1.16960i) q^{2} +(-0.520377 + 2.95452i) q^{3} +(1.26405 - 3.79502i) q^{4} +(-1.70362 + 6.35798i) q^{5} +(-2.61139 - 5.40191i) q^{6} +(-0.581649 + 1.00744i) q^{7} +(2.38794 + 7.63530i) q^{8} +(-8.45841 - 3.07493i) q^{9} +O(q^{10})\)	\(q+(-1.62235 + 1.16960i) q^{2} +(-0.520377 + 2.95452i) q^{3} +(1.26405 - 3.79502i) q^{4} +(-1.70362 + 6.35798i) q^{5} +(-2.61139 - 5.40191i) q^{6} +(-0.581649 + 1.00744i) q^{7} +(2.38794 + 7.63530i) q^{8} +(-8.45841 - 3.07493i) q^{9} +(-4.67246 - 12.3074i) q^{10} +(0.720261 + 2.68805i) q^{11} +(10.5547 + 5.70951i) q^{12} +(0.641258 + 0.171825i) q^{13} +(-0.234673 - 2.31473i) q^{14} +(-17.8983 - 8.34192i) q^{15} +(-12.8044 - 9.59420i) q^{16} -1.67347 q^{17} +(17.3190 - 4.90437i) q^{18} +(-11.7691 - 11.7691i) q^{19} +(21.9752 + 14.5021i) q^{20} +(-2.67384 - 2.24275i) q^{21} +(-4.31248 - 3.51855i) q^{22} +(-17.9147 - 31.0292i) q^{23} +(-23.8013 + 3.08198i) q^{24} +(-15.8710 - 9.16310i) q^{25} +(-1.24131 + 0.471259i) q^{26} +(13.4865 - 23.3905i) q^{27} +(3.08804 + 3.48083i) q^{28} +(10.7737 + 40.2079i) q^{29} +(38.7940 - 7.40037i) q^{30} +(-18.1310 + 10.4679i) q^{31} +(31.9946 + 0.589138i) q^{32} +(-8.31672 + 0.729228i) q^{33} +(2.71496 - 1.95730i) q^{34} +(-5.41441 - 5.41441i) q^{35} +(-22.3613 + 28.2130i) q^{36} +(23.8924 + 23.8924i) q^{37} +(32.8587 + 5.32841i) q^{38} +(-0.841356 + 1.80520i) q^{39} +(-52.6132 + 2.17484i) q^{40} +(-67.9164 + 39.2116i) q^{41} +(6.96104 + 0.511185i) q^{42} +(3.91706 + 14.6187i) q^{43} +(11.1117 + 0.664429i) q^{44} +(33.9603 - 48.5399i) q^{45} +(65.3558 + 29.3871i) q^{46} +(52.9130 + 30.5493i) q^{47} +(35.0094 - 32.8381i) q^{48} +(23.8234 + 41.2633i) q^{49} +(36.4655 - 3.69697i) q^{50} +(0.870837 - 4.94431i) q^{51} +(1.46266 - 2.21639i) q^{52} +(64.3295 + 64.3295i) q^{53} +(5.47768 + 53.7215i) q^{54} -18.3176 q^{55} +(-9.08108 - 2.03534i) q^{56} +(40.8963 - 28.6476i) q^{57} +(-64.5061 - 52.6304i) q^{58} +(-66.9370 - 17.9357i) q^{59} +(-54.2821 + 57.3797i) q^{60} +(-3.29732 - 12.3058i) q^{61} +(17.1715 - 38.1887i) q^{62} +(8.01765 - 6.73286i) q^{63} +(-52.5955 + 36.4652i) q^{64} +(-2.18492 + 3.78438i) q^{65} +(12.6397 - 10.9103i) q^{66} +(6.45622 - 24.0949i) q^{67} +(-2.11535 + 6.35086i) q^{68} +(100.999 - 36.7825i) q^{69} +(15.1168 + 2.45136i) q^{70} -97.4205 q^{71} +(3.27988 - 71.9253i) q^{72} -77.4165i q^{73} +(-66.7064 - 10.8172i) q^{74} +(35.3315 - 42.1228i) q^{75} +(-59.5405 + 29.7871i) q^{76} +(-3.12700 - 0.837878i) q^{77} +(-0.746393 - 3.91272i) q^{78} +(113.247 + 65.3833i) q^{79} +(82.8134 - 65.0650i) q^{80} +(62.0896 + 52.0181i) q^{81} +(64.3223 - 143.050i) q^{82} +(-108.976 + 29.2000i) q^{83} +(-11.8911 + 7.31234i) q^{84} +(2.85095 - 10.6399i) q^{85} +(-23.4529 - 19.1352i) q^{86} +(-124.402 + 10.9078i) q^{87} +(-18.8041 + 11.9183i) q^{88} -11.8648i q^{89} +(1.67703 + 118.469i) q^{90} +(-0.546091 + 0.546091i) q^{91} +(-140.401 + 28.7642i) q^{92} +(-21.4928 - 59.0156i) q^{93} +(-121.574 + 12.3255i) q^{94} +(94.8773 - 54.7774i) q^{95} +(-18.3899 + 94.2221i) q^{96} +(-79.8339 + 138.276i) q^{97} +(-86.9116 - 39.0797i) q^{98} +(2.17331 - 24.9514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8}+O(q^{10}) \) 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8	\( 184 q - 2 q^{2} - 4 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} - 8 q^{8} - 8 q^{10} - 2 q^{11} + 56 q^{12} - 2 q^{13} + 14 q^{14} - 2 q^{16} - 16 q^{17} + 38 q^{18} - 8 q^{19} - 44 q^{20} + 14 q^{21} - 2 q^{22} - 4 q^{23} + 120 q^{24} - 104 q^{26} - 52 q^{27} + 56 q^{28} - 2 q^{29} - 130 q^{30} - 182 q^{32} - 8 q^{33} - 10 q^{34} + 92 q^{35} - 2 q^{36} - 8 q^{37} - 254 q^{38} + 184 q^{39} - 2 q^{40} - 252 q^{42} - 2 q^{43} - 140 q^{44} - 54 q^{45} + 176 q^{46} + 162 q^{48} - 480 q^{49} - 96 q^{50} - 120 q^{51} - 2 q^{52} - 8 q^{53} + 94 q^{54} - 16 q^{55} + 260 q^{56} + 88 q^{58} + 142 q^{59} - 434 q^{60} - 2 q^{61} - 636 q^{62} + 244 q^{64} - 4 q^{65} - 100 q^{66} - 2 q^{67} - 112 q^{68} + 14 q^{69} - 100 q^{70} - 16 q^{71} + 98 q^{72} + 82 q^{74} - 296 q^{75} + 154 q^{76} + 194 q^{77} + 228 q^{78} + 592 q^{80} - 8 q^{81} - 420 q^{82} + 238 q^{83} - 22 q^{84} - 52 q^{85} - 170 q^{86} - 456 q^{87} - 26 q^{88} + 808 q^{90} + 188 q^{91} + 176 q^{92} + 26 q^{93} - 18 q^{94} - 202 q^{96} - 4 q^{97} + 408 q^{98} - 38 q^{99}+O(q^{100}) \) 184 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 - 8 * q^8 - 8 * q^10 - 2 * q^11 + 56 * q^12 - 2 * q^13 + 14 * q^14 - 2 * q^16 - 16 * q^17 + 38 * q^18 - 8 * q^19 - 44 * q^20 + 14 * q^21 - 2 * q^22 - 4 * q^23 + 120 * q^24 - 104 * q^26 - 52 * q^27 + 56 * q^28 - 2 * q^29 - 130 * q^30 - 182 * q^32 - 8 * q^33 - 10 * q^34 + 92 * q^35 - 2 * q^36 - 8 * q^37 - 254 * q^38 + 184 * q^39 - 2 * q^40 - 252 * q^42 - 2 * q^43 - 140 * q^44 - 54 * q^45 + 176 * q^46 + 162 * q^48 - 480 * q^49 - 96 * q^50 - 120 * q^51 - 2 * q^52 - 8 * q^53 + 94 * q^54 - 16 * q^55 + 260 * q^56 + 88 * q^58 + 142 * q^59 - 434 * q^60 - 2 * q^61 - 636 * q^62 + 244 * q^64 - 4 * q^65 - 100 * q^66 - 2 * q^67 - 112 * q^68 + 14 * q^69 - 100 * q^70 - 16 * q^71 + 98 * q^72 + 82 * q^74 - 296 * q^75 + 154 * q^76 + 194 * q^77 + 228 * q^78 + 592 * q^80 - 8 * q^81 - 420 * q^82 + 238 * q^83 - 22 * q^84 - 52 * q^85 - 170 * q^86 - 456 * q^87 - 26 * q^88 + 808 * q^90 + 188 * q^91 + 176 * q^92 + 26 * q^93 - 18 * q^94 - 202 * q^96 - 4 * q^97 + 408 * q^98 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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