LMFDB - Embedded newform 115.2.l.a.102.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			102.5
Character	$\chi$	$=$	115.102
Dual form			115.2.l.a.53.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.00772212 - 0.107969i) q^{2} +(1.79434 - 0.390334i) q^{3} +(1.96805 + 0.282962i) q^{4} +(-0.759367 - 2.10318i) q^{5} +(-0.0282880 - 0.196748i) q^{6} +(-4.32296 + 2.36052i) q^{7} +(0.0917670 - 0.421846i) q^{8} +(0.338390 - 0.154538i) q^{9} +O(q^{10})$	\(q+(0.00772212 - 0.107969i) q^{2} +(1.79434 - 0.390334i) q^{3} +(1.96805 + 0.282962i) q^{4} +(-0.759367 - 2.10318i) q^{5} +(-0.0282880 - 0.196748i) q^{6} +(-4.32296 + 2.36052i) q^{7} +(0.0917670 - 0.421846i) q^{8} +(0.338390 - 0.154538i) q^{9} +(-0.232943 + 0.0657474i) q^{10} +(-0.599394 - 0.519378i) q^{11} +(3.64179 - 0.260466i) q^{12} +(-1.18632 + 2.17257i) q^{13} +(0.221481 + 0.484976i) q^{14} +(-2.18350 - 3.47741i) q^{15} +(3.77065 + 1.10716i) q^{16} +(4.22639 + 3.16383i) q^{17} +(-0.0140722 - 0.0377291i) q^{18} +(0.409398 - 2.84742i) q^{19} +(-0.899349 - 4.35402i) q^{20} +(-6.83547 + 5.92297i) q^{21} +(-0.0607055 + 0.0607055i) q^{22} +(-0.829644 - 4.72353i) q^{23} -0.792754i q^{24} +(-3.84672 + 3.19417i) q^{25} +(0.225410 + 0.144862i) q^{26} +(-3.86324 + 2.89199i) q^{27} +(-9.17573 + 3.42237i) q^{28} +(3.49570 - 0.502606i) q^{29} +(-0.392314 + 0.208898i) q^{30} +(0.250636 - 0.161074i) q^{31} +(0.450393 - 1.20755i) q^{32} +(-1.27825 - 0.697975i) q^{33} +(0.374233 - 0.431888i) q^{34} +(8.24731 + 7.29947i) q^{35} +(0.709695 - 0.208385i) q^{36} +(-3.62537 - 1.35219i) q^{37} +(-0.304273 - 0.0661905i) q^{38} +(-1.28062 + 4.36139i) q^{39} +(-0.956902 + 0.127334i) q^{40} +(1.87241 - 4.10001i) q^{41} +(0.586714 + 0.783758i) q^{42} +(-0.809890 - 3.72300i) q^{43} +(-1.03267 - 1.19177i) q^{44} +(-0.581983 - 0.594344i) q^{45} +(-0.516402 + 0.0531004i) q^{46} +(-3.24360 - 3.24360i) q^{47} +(7.19798 + 0.514810i) q^{48} +(9.33150 - 14.5201i) q^{49} +(0.315168 + 0.439994i) q^{50} +(8.81852 + 4.02728i) q^{51} +(-2.94948 + 3.94004i) q^{52} +(-2.04509 - 3.74531i) q^{53} +(0.282413 + 0.439444i) q^{54} +(-0.637184 + 1.65503i) q^{55} +(0.599069 + 2.04024i) q^{56} +(-0.376849 - 5.26904i) q^{57} +(-0.0272718 - 0.381310i) q^{58} +(1.87184 + 6.37491i) q^{59} +(-3.31326 - 7.46154i) q^{60} +(5.28454 + 8.22290i) q^{61} +(-0.0154556 - 0.0283048i) q^{62} +(-1.09806 + 1.46684i) q^{63} +(7.02251 + 3.20707i) q^{64} +(5.47016 + 0.845251i) q^{65} +(-0.0852307 + 0.132622i) q^{66} +(7.69208 + 0.550148i) q^{67} +(7.42247 + 7.42247i) q^{68} +(-3.33241 - 8.15176i) q^{69} +(0.851805 - 0.834089i) q^{70} +(-10.1464 - 11.7096i) q^{71} +(-0.0341380 - 0.156930i) q^{72} +(2.93063 + 3.91486i) q^{73} +(-0.173991 + 0.380987i) q^{74} +(-5.65552 + 7.23293i) q^{75} +(1.61143 - 5.48801i) q^{76} +(3.81716 + 0.830373i) q^{77} +(0.461007 + 0.171947i) q^{78} +(-13.6014 + 3.99372i) q^{79} +(-0.534748 - 8.77109i) q^{80} +(-6.53396 + 7.54059i) q^{81} +(-0.428217 - 0.233824i) q^{82} +(-1.57366 + 4.21914i) q^{83} +(-15.1285 + 9.72249i) q^{84} +(3.44473 - 11.2914i) q^{85} +(-0.408224 + 0.0586938i) q^{86} +(6.07629 - 2.26634i) q^{87} +(-0.274102 + 0.205190i) q^{88} +(5.37985 + 3.45742i) q^{89} +(-0.0686650 + 0.0582466i) q^{90} -12.1923i q^{91} +(-0.296197 - 9.53087i) q^{92} +(0.386853 - 0.386853i) q^{93} +(-0.375256 + 0.325161i) q^{94} +(-6.29952 + 1.30120i) q^{95} +(0.336809 - 2.34255i) q^{96} +(1.36068 + 3.64812i) q^{97} +(-1.49567 - 1.11964i) q^{98} +(-0.283093 - 0.0831235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	0.00772212	−	0.107969i	0.00546036	−	0.0763458i	−0.993991	−	0.109460i	$-0.965088\pi$
$2$	0.00772212	−	0.107969i	0.00546036	−	0.0763458i	0.999452	+	0.0331140i	$0.0105424\pi$
$3$	1.79434	−	0.390334i	1.03596	−	0.225360i	0.337738	−	0.941240i	$-0.390338\pi$
$3$	1.79434	−	0.390334i	1.03596	−	0.225360i	0.698223	+	0.715880i	$0.253974\pi$
$4$	1.96805	+	0.282962i	0.984023	+	0.141481i
$5$	−0.759367	−	2.10318i	−0.339599	−	0.940570i
$5$	−0.759367	−	2.10318i	−0.339599	−	0.940570i
$6$	−0.0282880	−	0.196748i	−0.0115485	−	0.0803218i
$7$	−4.32296	+	2.36052i	−1.63393	+	0.892192i	−0.641812	+	0.766862i	$0.721817\pi$
$7$	−4.32296	+	2.36052i	−1.63393	+	0.892192i	−0.992115	+	0.125330i	$0.960001\pi$
$8$	0.0917670	−	0.421846i	0.0324445	−	0.149145i
$9$	0.338390	−	0.154538i	0.112797	−	0.0515125i
$10$	−0.232943	+	0.0657474i	−0.0736629	+	0.0207911i
$11$	−0.599394	−	0.519378i	−0.180724	−	0.156598i	0.559801	−	0.828627i	$-0.310878\pi$
$11$	−0.599394	−	0.519378i	−0.180724	−	0.156598i	−0.740525	+	0.672029i	$0.765423\pi$
$12$	3.64179	−	0.260466i	1.05129	−	0.0751900i
$13$	−1.18632	+	2.17257i	−0.329025	+	0.602564i	−0.988860	−	0.148846i	$-0.952444\pi$
$13$	−1.18632	+	2.17257i	−0.329025	+	0.602564i	0.659836	+	0.751410i	$0.270626\pi$
$14$	0.221481	+	0.484976i	0.0591933	+	0.129615i
$15$	−2.18350	−	3.47741i	−0.563778	−	0.897862i
$16$	3.77065	+	1.10716i	0.942662	+	0.276791i
$17$	4.22639	+	3.16383i	1.02505	+	0.767342i	0.972883	−	0.231296i	$-0.0742966\pi$
$17$	4.22639	+	3.16383i	1.02505	+	0.767342i	0.0521660	+	0.998638i	$0.483388\pi$
$18$	−0.0140722	−	0.0377291i	−0.00331685	−	0.00889283i
$19$	0.409398	−	2.84742i	0.0939222	−	0.653244i	−0.887418	−	0.460965i	$-0.847503\pi$
$19$	0.409398	−	2.84742i	0.0939222	−	0.653244i	0.981340	−	0.192278i	$-0.0615876\pi$
$20$	−0.899349	−	4.35402i	−0.201101	−	0.973589i
$21$	−6.83547	+	5.92297i	−1.49162	+	1.29250i
$22$	−0.0607055	+	0.0607055i	−0.0129424	+	0.0129424i
$23$	−0.829644	−	4.72353i	−0.172993	−	0.984923i
$23$	−0.829644	−	4.72353i	−0.172993	−	0.984923i
$24$		−	0.792754i		−	0.161820i
$25$	−3.84672	+	3.19417i	−0.769344	+	0.638834i
$26$	0.225410	+	0.144862i	0.0442066	+	0.0284099i
$27$	−3.86324	+	2.89199i	−0.743482	+	0.556563i
$28$	−9.17573	+	3.42237i	−1.73405	+	0.646767i
$29$	3.49570	−	0.502606i	0.649136	−	0.0933317i	0.190122	−	0.981761i	$-0.439112\pi$
$29$	3.49570	−	0.502606i	0.649136	−	0.0933317i	0.459014	+	0.888429i	$0.348203\pi$
$30$	−0.392314	+	0.208898i	−0.0716264	+	0.0381395i
$31$	0.250636	−	0.161074i	0.0450155	−	0.0289297i	−0.517940	−	0.855417i	$-0.673301\pi$
$31$	0.250636	−	0.161074i	0.0450155	−	0.0289297i	0.562955	+	0.826488i	$0.309664\pi$
$32$	0.450393	−	1.20755i	0.0796189	−	0.213467i
$33$	−1.27825	−	0.697975i	−0.222514	−	0.121502i
$34$	0.374233	−	0.431888i	0.0641805	−	0.0740683i
$35$	8.24731	+	7.29947i	1.39405	+	1.23384i
$36$	0.709695	−	0.208385i	0.118283	−	0.0347309i
$37$	−3.62537	−	1.35219i	−0.596007	−	0.222299i	0.0333136	−	0.999445i	$-0.489394\pi$
$37$	−3.62537	−	1.35219i	−0.596007	−	0.222299i	−0.629321	+	0.777146i	$0.716667\pi$
$38$	−0.304273	−	0.0661905i	−0.0493596	−	0.0107375i
$39$	−1.28062	+	4.36139i	−0.205063	+	0.698381i
$40$	−0.956902	+	0.127334i	−0.151300	+	0.0201332i
$41$	1.87241	−	4.10001i	0.292422	−	0.640315i	−0.705217	−	0.708991i	$-0.749150\pi$
$41$	1.87241	−	4.10001i	0.292422	−	0.640315i	0.997639	+	0.0686768i	$0.0218777\pi$
$42$	0.586714	+	0.783758i	0.0905319	+	0.120937i
$43$	−0.809890	−	3.72300i	−0.123507	−	0.567753i	−0.996756	−	0.0804789i	$-0.974355\pi$
$43$	−0.809890	−	3.72300i	−0.123507	−	0.567753i	0.873249	−	0.487274i	$-0.162009\pi$
$44$	−1.03267	−	1.19177i	−0.155681	−	0.179665i
$45$	−0.581983	−	0.594344i	−0.0867568	−	0.0885996i
$46$	−0.516402	+	0.0531004i	−0.0761394	+	0.00782923i
$47$	−3.24360	−	3.24360i	−0.473127	−	0.473127i	0.429798	−	0.902925i	$-0.358585\pi$
$47$	−3.24360	−	3.24360i	−0.473127	−	0.473127i	−0.902925	+	0.429798i	$0.858585\pi$
$48$	7.19798	+	0.514810i	1.03894	+	0.0743064i
$49$	9.33150	−	14.5201i	1.33307	−	2.07430i
$50$	0.315168	+	0.439994i	0.0445714	+	0.0622245i
$51$	8.81852	+	4.02728i	1.23484	+	0.563932i
$52$	−2.94948	+	3.94004i	−0.409019	+	0.546385i
$53$	−2.04509	−	3.74531i	−0.280915	−	0.514458i	0.698681	−	0.715433i	$-0.253771\pi$
$53$	−2.04509	−	3.74531i	−0.280915	−	0.514458i	−0.979596	+	0.200975i	$0.935589\pi$
$54$	0.282413	+	0.439444i	0.0384316	+	0.0598007i
$55$	−0.637184	+	1.65503i	−0.0859179	+	0.223164i
$56$	0.599069	+	2.04024i	0.0800540	+	0.272639i
$57$	−0.376849	−	5.26904i	−0.0499149	−	0.697901i
$58$	−0.0272718	−	0.381310i	−0.00358097	−	0.0500684i
$59$	1.87184	+	6.37491i	0.243693	+	0.829943i	0.986962	+	0.160951i	$0.0514560\pi$
$59$	1.87184	+	6.37491i	0.243693	+	0.829943i	−0.743269	+	0.668992i	$0.766726\pi$
$60$	−3.31326	−	7.46154i	−0.427740	−	0.963281i
$61$	5.28454	+	8.22290i	0.676616	+	1.05283i	0.994503	+	0.104706i	$0.0333903\pi$
$61$	5.28454	+	8.22290i	0.676616	+	1.05283i	−0.317887	+	0.948128i	$0.602973\pi$
$62$	−0.0154556	−	0.0283048i	−0.00196286	−	0.00359471i
$63$	−1.09806	+	1.46684i	−0.138343	+	0.184804i
$64$	7.02251	+	3.20707i	0.877813	+	0.400884i
$65$	5.47016	+	0.845251i	0.678490	+	0.104840i
$66$	−0.0852307	+	0.132622i	−0.0104912	+	0.0163246i
$67$	7.69208	+	0.550148i	0.939737	+	0.0672113i	0.532797	−	0.846243i	$-0.321141\pi$
$67$	7.69208	+	0.550148i	0.939737	+	0.0672113i	0.406941	+	0.913455i	$0.366596\pi$
$68$	7.42247	+	7.42247i	0.900107	+	0.900107i
$69$	−3.33241	−	8.15176i	−0.401176	−	0.981357i
$70$	0.851805	−	0.834089i	0.101810	−	0.0996927i
$71$	−10.1464	−	11.7096i	−1.20416	−	1.38967i	−0.899335	−	0.437260i	$-0.855949\pi$
$71$	−10.1464	−	11.7096i	−1.20416	−	1.38967i	−0.304820	−	0.952410i	$-0.598596\pi$
$72$	−0.0341380	−	0.156930i	−0.00402320	−	0.0184944i
$73$	2.93063	+	3.91486i	0.343004	+	0.458200i	0.938561	−	0.345113i	$-0.112159\pi$
$73$	2.93063	+	3.91486i	0.343004	+	0.458200i	−0.595557	+	0.803313i	$0.703069\pi$
$74$	−0.173991	+	0.380987i	−0.0202260	+	0.0442888i
$75$	−5.65552	+	7.23293i	−0.653044	+	0.835187i
$76$	1.61143	−	5.48801i	0.184843	−	0.629518i
$77$	3.81716	+	0.830373i	0.435006	+	0.0946297i
$78$	0.461007	+	0.171947i	0.0521988	+	0.0194691i
$79$	−13.6014	+	3.99372i	−1.53027	+	0.449329i	−0.935134	−	0.354294i	$-0.884721\pi$
$79$	−13.6014	+	3.99372i	−1.53027	+	0.449329i	−0.595139	+	0.803623i	$0.702903\pi$
$80$	−0.534748	−	8.77109i	−0.0597866	−	0.980638i
$81$	−6.53396	+	7.54059i	−0.725996	+	0.837844i
$82$	−0.428217	−	0.233824i	−0.0472886	−	0.0258215i
$83$	−1.57366	+	4.21914i	−0.172731	+	0.463111i	−0.994252	−	0.107068i	$-0.965854\pi$
$83$	−1.57366	+	4.21914i	−0.172731	+	0.463111i	0.821520	+	0.570179i	$0.193126\pi$
$84$	−15.1285	+	9.72249i	−1.65065	+	1.06081i
$85$	3.44473	−	11.2914i	0.373633	−	1.22472i
$86$	−0.408224	+	0.0586938i	−0.0440199	+	0.00632911i
$87$	6.07629	−	2.26634i	0.651447	−	0.242977i
$88$	−0.274102	+	0.205190i	−0.0292194	+	0.0218734i
$89$	5.37985	+	3.45742i	0.570263	+	0.366486i	0.793771	−	0.608216i	$-0.208115\pi$
$89$	5.37985	+	3.45742i	0.570263	+	0.366486i	−0.223508	+	0.974702i	$0.571751\pi$
$90$	−0.0686650	+	0.0582466i	−0.00723793	+	0.00613974i
$91$		−	12.1923i		−	1.27810i
$92$	−0.296197	−	9.53087i	−0.0308807	−	0.993662i
$93$	0.386853	−	0.386853i	0.0401148	−	0.0401148i
$94$	−0.375256	+	0.325161i	−0.0387047	+	0.0335378i
$95$	−6.29952	+	1.30120i	−0.646317	+	0.133501i
$96$	0.336809	−	2.34255i	0.0343754	−	0.239086i
$97$	1.36068	+	3.64812i	0.138156	+	0.370411i	0.987541	−	0.157364i	$-0.0502994\pi$
$97$	1.36068	+	3.64812i	0.138156	+	0.370411i	−0.849385	+	0.527774i	$0.823027\pi$
$98$	−1.49567	−	1.11964i	−0.151085	−	0.113101i
$99$	−0.283093	−	0.0831235i	−0.0284519	−	0.00835422i
$100$	−8.47435	+	5.19780i	−0.847435	+	0.519780i
$101$	1.09056	+	2.38800i	0.108515	+	0.237615i	0.956097	−	0.293049i	$-0.0946700\pi$
$101$	1.09056	+	2.38800i	0.108515	+	0.237615i	−0.847582	+	0.530664i	$0.821943\pi$
$102$	0.502920	−	0.921030i	0.0497965	−	0.0911955i
$103$	11.3254	−	0.810011i	1.11593	−	0.0798128i	0.498831	−	0.866699i	$-0.333763\pi$
$103$	11.3254	−	0.810011i	1.11593	−	0.0798128i	0.617098	+	0.786886i	$0.288308\pi$
$104$	0.807627	+	0.699813i	0.0791944	+	0.0686223i
$105$	17.6477	+	9.87850i	1.72224	+	0.964043i
$106$	−0.420171	+	0.191886i	−0.0408106	+	0.0186376i
$107$	−2.09802	+	9.64444i	−0.202823	+	0.932363i	0.757361	+	0.652996i	$0.226488\pi$
$107$	−2.09802	+	9.64444i	−0.202823	+	0.932363i	−0.960184	+	0.279367i	$0.909875\pi$
$108$	−8.42136	+	4.59841i	−0.810346	+	0.442482i
$109$	2.53793	+	17.6517i	0.243090	+	1.69073i	0.636430	+	0.771334i	$0.280410\pi$
$109$	2.53793	+	17.6517i	0.243090	+	1.69073i	−0.393340	+	0.919393i	$0.628681\pi$
$110$	0.173772	+	0.0815767i	0.0165685	+	0.00777803i
$111$	−7.03294	−	1.01118i	−0.667537	−	0.0959774i
$112$	−18.9139	+	4.11446i	−1.78719	+	0.388780i
$113$	1.16536	−	16.2938i	0.109628	−	1.53280i	−0.583578	−	0.812057i	$-0.698348\pi$
$113$	1.16536	−	16.2938i	0.109628	−	1.53280i	0.693206	−	0.720739i	$-0.256198\pi$
$114$	−0.571804			−0.0535544
$115$	−9.30441	+	5.33178i	−0.867641	+	0.497191i
$116$	7.02192			0.651969
$117$	−0.0656930	+	0.918508i	−0.00607332	+	0.0849161i
$118$	0.702749	−	0.152874i	0.0646933	−	0.0140732i
$119$	−25.7388	−	3.70068i	−2.35947	−	0.339241i
$120$	−1.66730	+	0.601992i	−0.152203	+	0.0549541i
$121$	−1.47594	−	10.2654i	−0.134177	−	0.933219i
$122$	0.928629	−	0.507070i	0.0840741	−	0.0459079i
$123$	1.75937	−	8.08768i	0.158637	−	0.729241i
$124$	0.538841	−	0.246080i	0.0483893	−	0.0220987i
$125$	9.63899	+	5.66479i	0.862137	+	0.506675i
$126$	0.149894	+	0.129884i	0.0133536	+	0.0115710i
$127$	9.91857	−	0.709390i	0.880131	−	0.0629482i	0.376045	−	0.926602i	$-0.377284\pi$
$127$	9.91857	−	0.709390i	0.880131	−	0.0629482i	0.504086	+	0.863653i	$0.331829\pi$
$128$	1.63581	−	2.99577i	0.144587	−	0.264791i
$129$	−2.90643	−	6.36420i	−0.255897	−	0.560336i
$130$	0.133502	−	0.584082i	0.0117089	−	0.0512274i
$131$	−11.5421	−	3.38907i	−1.00844	−	0.296105i	−0.264525	−	0.964379i	$-0.585215\pi$
$131$	−11.5421	−	3.38907i	−1.00844	−	0.296105i	−0.743915	+	0.668274i	$0.767033\pi$
$132$	−2.31815	−	1.73534i	−0.201769	−	0.151042i
$133$	4.95158	+	13.2757i	0.429356	+	1.15115i
$134$	0.118798	−	0.826260i	0.0102626	−	0.0713780i
$135$	9.01599	+	5.92901i	0.775973	+	0.510288i
$136$	1.72249	−	1.49255i	0.147703	−	0.127985i
$137$	8.24135	−	8.24135i	0.704106	−	0.704106i	−0.261184	−	0.965289i	$-0.584113\pi$
$137$	8.24135	−	8.24135i	0.704106	−	0.704106i	0.965289	+	0.261184i	$0.0841128\pi$
$138$	−0.905873	+	0.296850i	−0.0771130	+	0.0252695i
$139$			10.2903i			0.872812i	0.899750	+	0.436406i	$0.143749\pi$
$139$			10.2903i			0.872812i	−0.899750	+	0.436406i	$0.856251\pi$
$140$	14.1656	+	16.6994i	1.19721	+	1.41135i
$141$	−7.08619	−	4.55402i	−0.596765	−	0.383518i
$142$	−1.34262	+	1.00508i	−0.112671	+	0.0843441i
$143$	1.83946	−	0.686082i	0.153823	−	0.0573731i
$144$	1.44705	−	0.208054i	0.120587	−	0.0173378i
$145$	−3.71160	−	6.97043i	−0.308231	−	0.578863i
$146$	0.445316	−	0.286187i	0.0368546	−	0.0236850i
$147$	11.0762	−	29.6963i	0.913547	−	2.44931i
$148$	−6.75227	−	3.68702i	−0.555033	−	0.303071i
$149$	5.87592	−	6.78117i	0.481374	−	0.555535i	−0.462166	−	0.886793i	$-0.652928\pi$
$149$	5.87592	−	6.78117i	0.481374	−	0.555535i	0.943540	+	0.331258i	$0.107473\pi$
$150$	0.737261	+	0.666476i	0.0601971	+	0.0544176i
$151$	−4.52333	+	1.32817i	−0.368103	+	0.108085i	−0.460552	−	0.887633i	$-0.652349\pi$
$151$	−4.52333	+	1.32817i	−0.368103	+	0.108085i	0.0924491	+	0.995717i	$0.470530\pi$
$152$	−1.16360	−	0.434002i	−0.0943808	−	0.0352022i
$153$	1.91910	+	0.417474i	0.155150	+	0.0337508i
$154$	0.119131	−	0.405724i	0.00959987	−	0.0326942i
$155$	−0.529092	−	0.404818i	−0.0424977	−	0.0325158i
$156$	−3.75443	+	8.22105i	−0.300595	+	0.658210i
$157$	0.795493	+	1.06265i	0.0634873	+	0.0848091i	0.831161	−	0.556032i	$-0.187677\pi$
$157$	0.795493	+	1.06265i	0.0634873	+	0.0848091i	−0.767674	+	0.640841i	$0.778586\pi$
$158$	0.326168	+	1.49937i	0.0259485	+	0.119283i
$159$	−5.13151	−	5.92208i	−0.406955	−	0.469652i
$160$	−2.88171	−	0.0302825i	−0.227819	−	0.00239404i
$161$	14.7365	+	18.4612i	1.16140	+	1.45495i
$162$	0.763696	+	0.763696i	0.0600016	+	0.0600016i
$163$	−2.22602	−	0.159208i	−0.174356	−	0.0124702i	−0.0161116	−	0.999870i	$-0.505129\pi$
$163$	−2.22602	−	0.159208i	−0.174356	−	0.0124702i	−0.158244	+	0.987400i	$0.550583\pi$
$164$	4.84514	−	7.53919i	0.378342	−	0.588712i
$165$	−0.497308	+	3.21840i	−0.0387154	+	0.250552i
$166$	0.443386	+	0.202487i	0.0344134	+	0.0157161i
$167$	−9.35351	+	12.4948i	−0.723796	+	0.966878i	0.276187	+	0.961104i	$0.410929\pi$
$167$	−9.35351	+	12.4948i	−0.723796	+	0.966878i	−0.999983	+	0.00577449i	$0.998162\pi$
$168$	1.87131	+	3.42705i	0.144375	+	0.264402i
$169$	3.71560	+	5.78158i	0.285815	+	0.444737i
$170$	−1.19252	−	0.459118i	−0.0914621	−	0.0352127i
$171$	−0.301498	−	1.02681i	−0.0230561	−	0.0785219i
$172$	−0.540431	−	7.55621i	−0.0412074	−	0.576155i
$173$	0.261787	+	3.66026i	0.0199033	+	0.278285i	0.997651	+	0.0685006i	$0.0218215\pi$
$173$	0.261787	+	3.66026i	0.0199033	+	0.278285i	−0.977748	+	0.209784i	$0.932724\pi$
$174$	−0.197773	−	0.673554i	−0.0149931	−	0.0510620i
$175$	9.08935	−	22.8885i	0.687090	−	1.73021i
$176$	−1.68507	−	2.62202i	−0.127017	−	0.197642i
$177$	5.84707	+	10.7081i	0.439492	+	0.804870i
$178$	0.414839	−	0.554160i	0.0310935	−	0.0415361i
$179$	−9.98011	−	4.55776i	−0.745949	−	0.340663i	0.00591453	−	0.999983i	$-0.498117\pi$
$179$	−9.98011	−	4.55776i	−0.745949	−	0.340663i	−0.751863	+	0.659319i	$0.770845\pi$
$180$	−0.977191	−	1.33438i	−0.0728355	−	0.0994584i
$181$	−1.60058	+	2.49055i	−0.118970	+	0.185121i	−0.895631	−	0.444798i	$-0.853276\pi$
$181$	−1.60058	+	2.49055i	−0.118970	+	0.185121i	0.776661	+	0.629919i	$0.216912\pi$
$182$	−1.31639	−	0.0941502i	−0.0975774	−	0.00697888i
$183$	12.6919	+	12.6919i	0.938214	+	0.938214i
$184$	−2.06873	−	0.0834818i	−0.152509	−	0.00615436i
$185$	−0.0909157	+	8.65161i	−0.00668426	+	0.636079i
$186$	−0.0387809	−	0.0447555i	−0.00284355	−	0.00328163i
$187$	−0.890046	−	4.09148i	−0.0650866	−	0.299198i
$188$	−5.46573	−	7.30136i	−0.398629	−	0.532506i
$189$	9.87408	−	21.6212i	0.718233	−	1.57271i
$190$	0.0918444	+	0.690203i	0.00666309	+	0.0500726i
$191$	−5.69734	+	19.4034i	−0.412245	+	1.40398i	0.447971	+	0.894048i	$0.352147\pi$
$191$	−5.69734	+	19.4034i	−0.412245	+	1.40398i	−0.860216	+	0.509929i	$0.829672\pi$
$192$	13.8526	+	3.01344i	0.999724	+	0.217477i
$193$	13.7353	+	5.12298i	0.988685	+	0.368760i	0.791208	−	0.611547i	$-0.209453\pi$
$193$	13.7353	+	5.12298i	0.988685	+	0.368760i	0.197477	+	0.980308i	$0.436725\pi$
$194$	0.404392	−	0.118740i	0.0290337	−	0.00852506i
$195$	10.1452	−	0.618526i	0.726516	−	0.0442935i
$196$	22.4734	−	25.9357i	1.60525	−	1.85255i
$197$	−7.57076	−	4.13395i	−0.539394	−	0.294531i	0.186365	−	0.982481i	$-0.440329\pi$
$197$	−7.57076	−	4.13395i	−0.539394	−	0.294531i	−0.725759	+	0.687949i	$0.758511\pi$
$198$	−0.0111609	+	0.0299234i	−0.000793167	+	0.00212656i
$199$	5.12646	−	3.29457i	0.363405	−	0.233546i	−0.346177	−	0.938169i	$-0.612520\pi$
$199$	5.12646	−	3.29457i	0.363405	−	0.233546i	0.709582	+	0.704623i	$0.248884\pi$
$200$	0.994446	+	1.91584i	0.0703180	+	0.135471i
$201$	14.0169	−	2.01533i	0.988678	−	0.142150i
$202$	0.266252	−	0.0993068i	0.0187334	−	0.00698720i
$203$	−13.9254	+	10.4244i	−0.977371	+	0.731651i
$204$	16.2157	+	10.4212i	1.13532	+	0.729628i
$205$	−10.0449	−	0.824603i	−0.701567	−	0.0575928i
$206$		−	1.22905i		−	0.0856323i
$207$	−1.01071	−	1.47018i	−0.0702489	−	0.102185i
$208$	−6.87857	+	6.87857i	−0.476943	+	0.476943i
$209$	−1.72428	+	1.49410i	−0.119271	+	0.103349i
$210$	1.20285	−	1.82913i	0.0830047	−	0.126222i
$211$	2.23555	−	15.5486i	0.153901	−	1.07041i	−0.755698	−	0.654921i	$-0.772702\pi$
$211$	2.23555	−	15.5486i	0.153901	−	1.07041i	0.909599	−	0.415487i	$-0.136389\pi$
$212$	−2.96506	−	7.94963i	−0.203641	−	0.545983i
$213$	−22.7767	−	17.0504i	−1.56063	−	1.16828i
$214$	1.02510	+	0.300997i	0.0700745	+	0.0205757i
$215$	−7.21514	+	4.53047i	−0.492068	+	0.308976i
$216$	0.865455	+	1.89508i	0.0588868	+	0.128944i
$217$	−0.703272	+	1.28795i	−0.0477412	+	0.0874316i
$218$	1.92544	−	0.137710i	0.130407	−	0.00932691i
$219$	6.78664	+	5.88066i	0.458599	+	0.397378i
$220$	−1.72232	+	3.07688i	−0.116119	+	0.207443i
$221$	−11.8875	+	5.42883i	−0.799639	+	0.365183i
$222$	−0.163486	+	0.751533i	−0.0109725	+	0.0504396i
$223$	7.38740	−	4.03383i	0.494697	−	0.270125i	−0.212475	−	0.977166i	$-0.568152\pi$
$223$	7.38740	−	4.03383i	0.494697	−	0.270125i	0.707172	+	0.707042i	$0.249971\pi$
$224$	0.903410	+	6.28335i	0.0603616	+	0.419824i
$225$	−0.808073	+	1.67534i	−0.0538715	+	0.111689i
$226$	−1.75024	−	0.251646i	−0.116424	−	0.0167392i
$227$	−5.45972	+	1.18769i	−0.362375	+	0.0788298i	−0.390066	−	0.920787i	$-0.627548\pi$
$227$	−5.45972	+	1.18769i	−0.362375	+	0.0788298i	0.0276918	+	0.999617i	$0.491184\pi$
$228$	0.749283	−	10.4763i	0.0496225	−	0.693813i
$229$	−17.9294			−1.18481			−0.592406	−	0.805640i	$-0.701822\pi$
$229$	−17.9294			−1.18481			−0.592406	+	0.805640i	$0.701822\pi$
$230$	0.503819	+	1.04576i	0.0332208	+	0.0689556i
$231$	7.17340			0.471975
$232$	0.108768	−	1.52077i	0.00714095	−	0.0998436i
$233$	−19.0781	+	4.15019i	−1.24985	+	0.271888i	−0.788336	−	0.615245i	$-0.789057\pi$
$233$	−19.0781	+	4.15019i	−1.24985	+	0.271888i	−0.461513	+	0.887133i	$0.652693\pi$
$234$	0.0986633	+	0.0141856i	0.00644982	+	0.000927345i
$235$	−4.35878	+	9.28494i	−0.284336	+	0.605683i
$236$	1.88001	+	13.0758i	0.122378	+	0.851161i
$237$	−22.8465	+	12.4752i	−1.48404	+	0.810349i
$238$	−0.598318	+	2.75042i	−0.0387832	+	0.178283i
$239$	−5.20394	+	2.37656i	−0.336615	+	0.153727i	−0.576550	−	0.817062i	$-0.695601\pi$
$239$	−5.20394	+	2.37656i	−0.336615	+	0.153727i	0.239935	+	0.970789i	$0.422874\pi$
$240$	−4.38318	−	15.5296i	−0.282933	−	1.00243i
$241$	−11.1657	−	9.67514i	−0.719246	−	0.623230i	0.216344	−	0.976317i	$-0.430587\pi$
$241$	−11.1657	−	9.67514i	−0.719246	−	0.623230i	−0.935591	+	0.353087i	$0.885132\pi$
$242$	−1.11975	+	0.0800858i	−0.0719800	+	0.00514811i
$243$	−1.84251	+	3.37431i	−0.118197	+	0.216462i
$244$	8.07344	+	17.6784i	0.516849	+	1.13174i
$245$	−37.6244	−	8.59972i	−2.40373	−	0.549416i
$246$	−0.859634	−	0.252411i	−0.0548083	−	0.0160932i
$247$	5.70056	+	4.26739i	0.362718	+	0.271527i
$248$	−0.0449483	−	0.120511i	−0.00285422	−	0.00765246i
$249$	−1.17680	+	8.18482i	−0.0745766	+	0.518692i
$250$	0.686057	−	0.996970i	0.0433901	−	0.0630539i
$251$	−11.2092	+	9.71281i	−0.707517	+	0.613067i	−0.932446	−	0.361308i	$-0.882330\pi$
$251$	−11.2092	+	9.71281i	−0.707517	+	0.613067i	0.224930	+	0.974375i	$0.427785\pi$
$252$	−2.57609	+	2.57609i	−0.162278	+	0.162278i
$253$	−1.95601	+	3.26215i	−0.122973	+	0.205090i
$254$		−	1.07638i		−	0.0675380i
$255$	1.77360	−	21.6051i	0.111067	−	1.35296i
$256$	12.6784	+	8.14792i	0.792401	+	0.509245i
$257$	−11.3570	+	8.50171i	−0.708427	+	0.530322i	−0.891637	−	0.452752i	$-0.850442\pi$
$257$	−11.3570	+	8.50171i	−0.708427	+	0.530322i	0.183209	+	0.983074i	$0.441351\pi$
$258$	−0.709581	+	0.264660i	−0.0441766	+	0.0164770i
$259$	18.8642	−	2.71226i	1.17217	−	0.168532i
$260$	10.5263	+	3.21134i	0.652816	+	0.199159i
$261$	1.10524	−	0.710295i	0.0684127	−	0.0439661i
$262$	−0.455045	+	1.22002i	−0.0281128	+	0.0753733i
$263$	15.1179	+	8.25499i	0.932209	+	0.509024i	0.872187	−	0.489173i	$-0.162701\pi$
$263$	15.1179	+	8.25499i	0.932209	+	0.509024i	0.0600217	+	0.998197i	$0.480883\pi$
$264$	−0.411739	+	0.475172i	−0.0253408	+	0.0292448i
$265$	−6.32408	+	7.14527i	−0.388485	+	0.438930i
$266$	1.47160	−	0.432102i	0.0902298	−	0.0264939i
$267$	11.0028	+	4.10384i	0.673362	+	0.251151i
$268$	14.9827	+	3.25928i	0.915213	+	0.199093i
$269$	1.46335	−	4.98370i	0.0892218	−	0.303862i	−0.902777	−	0.430109i	$-0.858475\pi$
$269$	1.46335	−	4.98370i	0.0892218	−	0.303862i	0.991999	+	0.126247i	$0.0402933\pi$
$270$	0.709773	−	0.927665i	0.0431954	−	0.0564559i
$271$	0.696019	−	1.52407i	0.0422801	−	0.0925806i	−0.887313	−	0.461167i	$-0.847431\pi$
$271$	0.696019	−	1.52407i	0.0422801	−	0.0925806i	0.929593	+	0.368586i	$0.120158\pi$
$272$	12.4333	+	16.6090i	0.753882	+	1.00707i
$273$	−4.75906	−	21.8771i	−0.288032	−	1.32406i
$274$	−0.826171	−	0.953453i	−0.0499108	−	0.0576002i
$275$	3.96469	+	0.0833353i	0.239080	+	0.00502531i
$276$	−4.25170	−	16.9860i	−0.255922	−	1.02244i
$277$	−15.8354	−	15.8354i	−0.951459	−	0.951459i	0.0474157	−	0.998875i	$-0.484901\pi$
$277$	−15.8354	−	15.8354i	−0.951459	−	0.951459i	−0.998875	+	0.0474157i	$0.984901\pi$
$278$	1.11104	+	0.0794629i	0.0666356	+	0.00476587i
$279$	0.0599207	−	0.0932385i	0.00358736	−	0.00558204i
$280$	3.83608	−	2.80924i	0.229250	−	0.167884i
$281$	−1.97290	−	0.900995i	−0.117694	−	0.0537488i	0.355698	−	0.934601i	$-0.384243\pi$
$281$	−1.97290	−	0.900995i	−0.117694	−	0.0537488i	−0.473392	+	0.880852i	$0.656970\pi$
$282$	−0.546415	+	0.729924i	−0.0325385	+	0.0434664i
$283$	−11.9625	−	21.9077i	−0.711099	−	1.30228i	−0.944053	−	0.329792i	$-0.893021\pi$
$283$	−11.9625	−	21.9077i	−0.711099	−	1.30228i	0.232955	−	0.972488i	$-0.425161\pi$
$284$	−16.6552	−	25.9160i	−0.988304	−	1.53783i
$285$	−10.7956	+	4.79372i	−0.639474	+	0.283955i
$286$	−0.0598713	−	0.203903i	−0.00354026	−	0.0120570i
$287$	1.58378	+	22.1441i	0.0934873	+	1.30712i
$288$	−0.0342034	−	0.478225i	−0.00201545	−	0.0281797i
$289$	3.06305	+	10.4318i	0.180179	+	0.613635i
$290$	−0.781254	+	0.346912i	−0.0458768	+	0.0203714i
$291$	3.86550	+	6.01484i	0.226600	+	0.352596i
$292$	4.65985	+	8.53389i	0.272697	+	0.499408i
$293$	0.915037	−	1.22235i	0.0534570	−	0.0714102i	−0.773016	−	0.634386i	$-0.781253\pi$
$293$	0.915037	−	1.22235i	0.0534570	−	0.0714102i	0.826473	+	0.562976i	$0.190344\pi$
$294$	−3.12076	−	1.42520i	−0.182007	−	0.0831196i
$295$	11.9862	−	8.77772i	0.697862	−	0.511059i
$296$	−0.903106	+	1.40526i	−0.0524920	+	0.0816791i
$297$	3.81764	+	0.273043i	0.221522	+	0.0158436i
$298$	−0.686784	−	0.686784i	−0.0397843	−	0.0397843i
$299$	11.2464	+	3.80113i	0.650398	+	0.219825i
$300$	−13.1770	+	12.6344i	−0.760773	+	0.729449i
$301$	12.2893	+	14.1827i	0.708346	+	0.817475i
$302$	0.108472	+	0.498637i	0.00624185	+	0.0286933i
$303$	2.88895	+	3.85919i	0.165966	+	0.221705i
$304$	4.69625	−	10.2834i	0.269349	−	0.589791i
$305$	13.2813	−	17.3585i	0.760487	−	0.993947i
$306$	0.0598939	−	0.203980i	0.00342391	−	0.0116608i
$307$	−6.07281	−	1.32106i	−0.346594	−	0.0753968i	0.0358989	−	0.999355i	$-0.488571\pi$
$307$	−6.07281	−	1.32106i	−0.346594	−	0.0753968i	−0.382492	+	0.923959i	$0.624934\pi$
$308$	7.27738	+	2.71432i	0.414667	+	0.154663i
$309$	20.0055	−	5.87414i	1.13807	−	0.334168i
$310$	−0.0477936	+	0.0539996i	−0.00271449	+	0.00306697i
$311$	2.69973	−	3.11566i	0.153088	−	0.176673i	−0.674025	−	0.738708i	$-0.735436\pi$
$311$	2.69973	−	3.11566i	0.153088	−	0.176673i	0.827113	+	0.562035i	$0.189982\pi$
$312$	1.72232	+	0.940456i	0.0975070	+	0.0532428i
$313$	1.78340	−	4.78149i	0.100804	−	0.270266i	−0.876752	−	0.480943i	$-0.840294\pi$
$313$	1.78340	−	4.78149i	0.100804	−	0.270266i	0.977556	+	0.210677i	$0.0675670\pi$
$314$	0.120877	−	0.0776829i	0.00682148	−	0.00438390i
$315$	3.91885	+	1.19555i	0.220802	+	0.0673615i
$316$	−27.8982	+	4.01115i	−1.56939	+	0.225645i
$317$	29.3201	−	10.9358i	1.64678	−	0.614218i	0.656630	−	0.754213i	$-0.271982\pi$
$317$	29.3201	−	10.9358i	1.64678	−	0.614218i	0.990152	+	0.139995i	$0.0447088\pi$
$318$	−0.679029	+	0.508315i	−0.0380781	+	0.0285049i
$319$	−2.35635	−	1.51433i	−0.131930	−	0.0847864i
$320$	1.41238	−	17.2049i	0.0789545	−	0.961785i
$321$			18.1243i			1.01160i
$322$	2.10704	−	1.44853i	0.117421	−	0.0807233i
$323$	10.7390	−	10.7390i	0.597536	−	0.597536i
$324$	−14.9928	+	12.9914i	−0.832935	+	0.721742i
$325$	−2.37615	−	12.1466i	−0.131805	−	0.673771i
$326$	−0.0343792	+	0.239113i	−0.00190409	+	0.0132432i
$327$	11.4440	+	30.6825i	0.632853	+	1.69675i
$328$	−1.55775	−	1.16612i	−0.0860123	−	0.0643880i
$329$	21.6785	+	6.36539i	1.19518	+	0.350935i
$330$	0.343648	+	0.0785469i	0.0189172	+	0.00432386i
$331$	8.14271	+	17.8300i	0.447564	+	0.980028i	0.990148	+	0.140026i	$0.0447187\pi$
$331$	8.14271	+	17.8300i	0.447564	+	0.980028i	−0.542584	+	0.840002i	$0.682554\pi$
$332$	−4.29089	+	7.85818i	−0.235493	+	0.431273i
$333$	−1.43575	+	0.102687i	−0.0786788	+	0.00562722i
$334$	1.27683	+	1.10638i	0.0698649	+	0.0605383i
$335$	−4.68406	−	16.5956i	−0.255917	−	0.906714i
$336$	−32.3318	+	14.7655i	−1.76385	+	0.805522i
$337$	2.89813	−	13.3225i	0.157871	−	0.725722i	−0.828340	−	0.560226i	$-0.810714\pi$
$337$	2.89813	−	13.3225i	0.157871	−	0.725722i	0.986211	−	0.165495i	$-0.0529222\pi$
$338$	0.652925	−	0.356524i	0.0355145	−	0.0193924i
$339$	−4.26900	−	29.6915i	−0.231860	−	1.61262i
$340$	9.97441	−	21.2472i	0.540938	−	1.15229i
$341$	−0.233888	−	0.0336280i	−0.0126657	−	0.00182106i
$342$	−0.113192	+	0.0246234i	−0.00612071	+	0.00133148i
$343$	−3.60516	+	50.4067i	−0.194660	+	2.72171i
$344$	−1.64486			−0.0886846
$345$	−14.6141	+	13.1988i	−0.786796	+	0.710602i
$346$	0.397217			0.0213545
$347$	1.72022	−	24.0519i	0.0923465	−	1.29117i	−0.714175	−	0.699967i	$-0.753198\pi$
$347$	1.72022	−	24.0519i	0.0923465	−	1.29117i	0.806521	−	0.591205i	$-0.201348\pi$
$348$	12.5997	−	2.74090i	0.675415	−	0.146928i
$349$	16.4605	+	2.36666i	0.881108	+	0.126684i	0.567996	−	0.823032i	$-0.307719\pi$
$349$	16.4605	+	2.36666i	0.881108	+	0.126684i	0.313113	+	0.949716i	$0.398628\pi$
$350$	−2.40107	−	1.15812i	−0.128343	−	0.0619040i
$351$	−1.70003	−	11.8240i	−0.0907411	−	0.631118i
$352$	−0.897137	+	0.489874i	−0.0478176	+	0.0261104i
$353$	−0.706041	+	3.24562i	−0.0375787	+	0.172747i	−0.992111	−	0.125360i	$-0.959991\pi$
$353$	−0.706041	+	3.24562i	−0.0375787	+	0.172747i	0.954533	+	0.298107i	$0.0963551\pi$
$354$	1.20130	−	0.548614i	0.0638483	−	0.0291585i
$355$	−16.9225	+	30.2315i	−0.898151	+	1.60452i
$356$	9.60947	+	8.32666i	0.509301	+	0.441312i
$357$	−47.6286	+	3.40647i	−2.52077	+	0.180289i
$358$	−0.569166	+	1.04235i	−0.0300814	+	0.0550899i
$359$	−12.7982	−	28.0241i	−0.675462	−	1.47906i	−0.867380	−	0.497646i	$-0.834198\pi$
$359$	−12.7982	−	28.0241i	−0.675462	−	1.47906i	0.191918	−	0.981411i	$-0.438529\pi$
$360$	−0.304128	+	0.190966i	−0.0160290	+	0.0100648i
$361$	10.2902	+	3.02146i	0.541587	+	0.159024i
$362$	0.256543	+	0.192046i	0.0134836	+	0.0100937i
$363$	−6.65528	−	17.8435i	−0.349312	−	0.936541i
$364$	3.44995	−	23.9950i	0.180827	−	1.25768i
$365$	6.00823	−	9.13646i	0.314485	−	0.478224i
$366$	1.46835	−	1.27233i	0.0767517	−	0.0665057i
$367$	19.6376	−	19.6376i	1.02508	−	1.02508i	0.0253980	−	0.999677i	$-0.491915\pi$
$367$	19.6376	−	19.6376i	1.02508	−	1.02508i	0.999677	−	0.0253980i	$-0.00808532\pi$
$368$	2.10142	−	18.7293i	0.109544	−	0.976333i
$369$		−	1.67676i		−	0.0872888i
$370$	0.933406	+	0.0766248i	0.0485255	+	0.00398354i
$371$	17.6817	+	11.3634i	0.917990	+	0.589957i
$372$	0.870808	−	0.651879i	0.0451493	−	0.0337984i
$373$	−6.70708	+	2.50161i	−0.347280	+	0.129529i	−0.517050	−	0.855955i	$-0.672970\pi$
$373$	−6.70708	+	2.50161i	−0.347280	+	0.129529i	0.169771	+	0.985484i	$0.445697\pi$
$374$	−0.448627	+	0.0645028i	−0.0231979	+	0.00333536i
$375$	19.5068	+	6.40213i	1.00732	+	0.330604i
$376$	−1.66595	+	1.07064i	−0.0859150	+	0.0552142i
$377$	−3.05506	+	8.19093i	−0.157343	+	0.421854i
$378$	−2.25818	−	1.23306i	−0.116148	−	0.0634217i
$379$	−8.34078	+	9.62577i	−0.428437	+	0.494443i	−0.928389	−	0.371611i	$-0.878806\pi$
$379$	−8.34078	+	9.62577i	−0.428437	+	0.494443i	0.499952	+	0.866053i	$0.333351\pi$
$380$	−12.7659	+	0.778302i	−0.654879	+	0.0399260i
$381$	17.5204	−	5.14444i	0.897595	−	0.263558i
$382$	2.05097	+	0.764972i	0.104937	+	0.0391394i
$383$	19.6542	+	4.27550i	1.00428	+	0.218468i	0.684492	−	0.729020i	$-0.260024\pi$
$383$	19.6542	+	4.27550i	1.00428	+	0.218468i	0.319790	+	0.947489i	$0.396388\pi$
$384$	1.76585	−	6.01394i	0.0901133	−	0.306898i
$385$	−1.15221	−	8.65873i	−0.0587219	−	0.441290i
$386$	0.659190	−	1.44342i	0.0335519	−	0.0734684i
$387$	−0.849403	−	1.13467i	−0.0431776	−	0.0576785i
$388$	1.64560	+	7.56469i	0.0835426	+	0.384039i
$389$	14.8609	+	17.1504i	0.753477	+	0.869559i	0.994901	−	0.100861i	$-0.0321596\pi$
$389$	14.8609	+	17.1504i	0.753477	+	0.869559i	−0.241423	+	0.970420i	$0.577614\pi$
$390$	0.0115610	−	1.10015i	0.000585413	−	0.0557083i
$391$	11.4381	−	22.5883i	0.578447	−	1.14234i
$392$	−5.26892	−	5.26892i	−0.266121	−	0.266121i
$393$	−22.0333	−	1.57586i	−1.11143	−	0.0794914i
$394$	−0.504801	+	0.785486i	−0.0254315	+	0.0395722i
$395$	18.7279	+	25.5734i	0.942305	+	1.28674i
$396$	−0.533618	−	0.243695i	−0.0268153	−	0.0122461i
$397$	−10.8104	+	14.4410i	−0.542560	+	0.724775i	−0.985102	−	0.171973i	$-0.944986\pi$
$397$	−10.8104	+	14.4410i	−0.542560	+	0.724775i	0.442542	+	0.896748i	$0.354077\pi$
$398$	−0.316126	−	0.578941i	−0.0158459	−	0.0290197i
$399$	14.0668	+	21.8883i	0.704219	+	1.09579i
$400$	−18.0411	+	7.78515i	−0.902055	+	0.389258i
$401$	−5.90383	−	20.1066i	−0.294823	−	1.00408i	−0.965082	−	0.261948i	$-0.915635\pi$
$401$	−5.90383	−	20.1066i	−0.294823	−	1.00408i	0.670259	−	0.742128i	$-0.266183\pi$
$402$	−0.109353	−	1.52896i	−0.00545405	−	0.0762576i
$403$	0.0526118	+	0.735609i	0.00262078	+	0.0366433i
$404$	1.47056	+	5.00828i	0.0731632	+	0.249171i
$405$	20.8209	+	8.01601i	1.03460	+	0.398319i
$406$	1.01798	+	1.58401i	0.0505217	+	0.0786133i
$407$	1.47073	+	2.69343i	0.0729012	+	0.133509i
$408$	2.50814	−	3.35048i	0.124172	−	0.165874i
$409$	6.64652	+	3.03536i	0.328649	+	0.150089i	0.572905	−	0.819622i	$-0.305816\pi$
$409$	6.64652	+	3.03536i	0.328649	+	0.150089i	−0.244256	+	0.969711i	$0.578544\pi$
$410$	−0.166600	+	1.07817i	−0.00822778	+	0.0532472i
$411$	11.5709	−	18.0046i	0.570749	−	0.888103i
$412$	22.5182	+	1.61053i	1.10939	+	0.0793452i
$413$	−23.1400	−	23.1400i	−1.13865	−	1.13865i
$414$	−0.166539	+	0.0977722i	−0.00818496	+	0.00480524i
$415$	10.0686	+	0.105806i	0.494248	+	0.00519382i
$416$	2.08918	+	2.41105i	0.102431	+	0.118211i
$417$	4.01666	+	18.4643i	0.196697	+	0.904200i
$418$	0.148001	+	0.197707i	0.00723899	+	0.00967015i
$419$	−9.29391	+	20.3508i	−0.454037	+	0.994203i	0.534769	+	0.844998i	$0.320399\pi$
$419$	−9.29391	+	20.3508i	−0.454037	+	0.994203i	−0.988806	+	0.149205i	$0.952329\pi$
$420$	31.9362	+	24.4350i	1.55833	+	1.19230i
$421$	9.30346	−	31.6847i	0.453423	−	1.54422i	−0.342916	−	0.939366i	$-0.611415\pi$
$421$	9.30346	−	31.6847i	0.453423	−	1.54422i	0.796339	−	0.604851i	$-0.206767\pi$
$422$	−1.66150	−	0.361438i	−0.0808808	−	0.0175945i
$423$	−1.59886	−	0.596343i	−0.0777392	−	0.0289952i
$424$	−1.76762	+	0.519019i	−0.0858431	+	0.0252058i
$425$	−26.3636	+	1.32941i	−1.27882	+	0.0644861i
$426$	−2.01681	+	2.32752i	−0.0977146	+	0.112769i
$427$	−42.2552	−	23.0731i	−2.04487	−	1.11658i
$428$	−6.85801	+	18.3870i	−0.331494	+	0.888770i
$429$	3.03281	−	1.94907i	0.146425	−	0.0941018i
$430$	0.433436	+	0.813998i	0.0209021	+	0.0392545i
$431$	−4.45996	+	0.641246i	−0.214829	+	0.0308877i	−0.248889	−	0.968532i	$-0.580065\pi$
$431$	−4.45996	+	0.641246i	−0.214829	+	0.0308877i	0.0340599	+	0.999420i	$0.489156\pi$
$432$	−17.7688	+	6.62743i	−0.854904	+	0.318863i
$433$	−9.13018	+	6.83477i	−0.438768	+	0.328458i	−0.795720	−	0.605665i	$-0.792907\pi$
$433$	−9.13018	+	6.83477i	−0.438768	+	0.328458i	0.356951	+	0.934123i	$0.383816\pi$
$434$	0.133628	+	0.0858775i	0.00641435	+	0.00412225i
$435$	−9.38065	−	11.0585i	−0.449768	−	0.530216i
$436$			35.4575i			1.69811i
$437$	−13.7895	+	0.428546i	−0.659643	+	0.0205001i
$438$	0.687338	−	0.687338i	0.0328423	−	0.0328423i
$439$	−3.81470	+	3.30545i	−0.182066	+	0.157761i	−0.741125	−	0.671367i	$-0.765708\pi$
$439$	−3.81470	+	3.30545i	−0.182066	+	0.157761i	0.559060	+	0.829127i	$0.311162\pi$
$440$	0.639696	+	0.420671i	0.0304963	+	0.0200547i
$441$	0.913786	−	6.35552i	0.0435136	−	0.302644i
$442$	0.494351	+	1.32541i	0.0235139	+	0.0630431i
$443$	5.92369	+	4.43442i	0.281443	+	0.210686i	0.730668	−	0.682733i	$-0.239209\pi$
$443$	5.92369	+	4.43442i	0.281443	+	0.210686i	−0.449225	+	0.893419i	$0.648300\pi$
$444$	−13.5550	−	3.98011i	−0.643293	−	0.188888i
$445$	3.18629	−	13.9402i	0.151045	−	0.660831i
$446$	−0.378483	−	0.828762i	−0.0179217	−	0.0392430i
$447$	7.89646	−	14.4613i	0.373490	−	0.683995i
$448$	−37.9284	+	2.71269i	−1.79195	+	0.128163i
$449$	3.25668	+	2.82193i	0.153692	+	0.133175i	0.728313	−	0.685245i	$-0.240305\pi$
$449$	3.25668	+	2.82193i	0.153692	+	0.133175i	−0.574620	+	0.818420i	$0.694850\pi$
$450$	0.174645	+	0.100184i	0.00823285	+	0.00472273i
$451$	−3.25177	+	1.48503i	−0.153120	+	0.0699275i
$452$	6.90402	−	31.7373i	0.324738	−	1.49280i
$453$	−7.59795	+	4.14879i	−0.356983	+	0.194927i
$454$	0.0860734	+	0.598654i	0.00403963	+	0.0280962i
$455$	−25.6425	+	9.25842i	−1.20214	+	0.434041i
$456$	−2.25731	−	0.324552i	−0.105708	−	0.0151985i
$457$	−13.7102	+	2.98247i	−0.641335	+	0.139514i	−0.521461	−	0.853275i	$-0.674613\pi$
$457$	−13.7102	+	2.98247i	−0.641335	+	0.139514i	−0.119874	+	0.992789i	$0.538249\pi$
$458$	−0.138453	+	1.93583i	−0.00646949	+	0.0904554i
$459$	−25.4773			−1.18918
$460$	−19.8202	+	7.86039i	−0.924122	+	0.366492i
$461$	−14.1608			−0.659534			−0.329767	−	0.944062i	$-0.606970\pi$
$461$	−14.1608			−0.659534			−0.329767	+	0.944062i	$0.606970\pi$
$462$	0.0553938	−	0.774507i	0.00257715	−	0.0360333i
$463$	−14.6658	+	3.19035i	−0.681578	+	0.148268i	−0.540008	−	0.841660i	$-0.681579\pi$
$463$	−14.6658	+	3.19035i	−0.681578	+	0.148268i	−0.141570	+	0.989928i	$0.545215\pi$
$464$	13.7375	+	1.97516i	0.637750	+	0.0916945i
$465$	−1.10738	−	0.519857i	−0.0513537	−	0.0241078i
$466$	0.300770	+	2.09190i	0.0139329	+	0.0969054i
$467$	13.2860	−	7.25468i	0.614801	−	0.335707i	−0.141493	−	0.989939i	$-0.545190\pi$
$467$	13.2860	−	7.25468i	0.614801	−	0.335707i	0.756293	+	0.654233i	$0.227008\pi$
$468$	−0.389190	+	1.78908i	−0.0179903	+	0.0827001i
$469$	−34.5512	+	15.7790i	−1.59543	+	0.728607i
$470$	0.968830	+	0.542314i	0.0446888	+	0.0250151i
$471$	1.84217	+	1.59625i	0.0848829	+	0.0735514i
$472$	2.86101	−	0.204623i	0.131688	−	0.00941854i
$473$	−1.44820	+	2.65219i	−0.0665884	+	0.121948i
$474$	1.17051	+	2.56306i	0.0537633	+	0.117725i
$475$	7.52032	+	12.2609i	0.345056	+	0.562570i
$476$	−49.6080	−	14.5662i	−2.27378	−	0.667641i
$477$	−1.27083	−	0.951332i	−0.0581874	−	0.0435585i
$478$	0.216410	+	0.580218i	0.00989837	+	0.0265385i
$479$	0.160132	−	1.11374i	0.00731661	−	0.0508881i	−0.985836	−	0.167712i	$-0.946362\pi$
$479$	0.160132	−	1.11374i	0.00731661	−	0.0508881i	0.993153	+	0.116824i	$0.0372713\pi$
$480$	−5.18257	+	1.07049i	−0.236551	+	0.0488610i
$481$	7.23857	−	6.27225i	0.330050	−	0.285990i
$482$	−1.13084	+	1.13084i	−0.0515084	+	0.0515084i
$483$	33.6483	+	27.3736i	1.53105	+	1.24554i
$484$		−	20.6204i		−	0.937292i
$485$	6.63940	−	5.63202i	0.301480	−	0.255737i
$486$	0.350094	+	0.224992i	0.0158806	+	0.0102058i
$487$	22.0259	−	16.4884i	0.998089	−	0.747160i	0.0304601	−	0.999536i	$-0.490303\pi$
$487$	22.0259	−	16.4884i	0.998089	−	0.747160i	0.967629	+	0.252376i	$0.0812118\pi$
$488$	3.95374	−	1.47467i	0.178978	−	0.0667552i
$489$	−4.05638	+	0.583220i	−0.183436	+	0.0263741i
$490$	−1.21905	+	3.99587i	−0.0550709	+	0.180515i
$491$	21.9542	−	14.1091i	0.990779	−	0.636735i	0.0584288	−	0.998292i	$-0.481391\pi$
$491$	21.9542	−	14.1091i	0.990779	−	0.636735i	0.932350	+	0.361557i	$0.117755\pi$
$492$	5.75102	−	15.4191i	0.259276	−	0.695146i
$493$	16.3644	+	8.93562i	0.737014	+	0.402440i
$494$	0.504767	−	0.582532i	0.0227105	−	0.0262094i
$495$	0.0401477	+	0.658515i	0.00180451	+	0.0295981i
$496$	1.12340	−	0.329859i	0.0504419	−	0.0148111i
$497$	71.5031	+	26.6693i	3.20735	+	1.19628i
$498$	0.874621	+	0.190262i	0.0391927	+	0.00852586i
$499$	3.59093	−	12.2296i	0.160752	−	0.547471i	−0.839241	−	0.543760i	$-0.817000\pi$
$499$	3.59093	−	12.2296i	0.160752	−	0.547471i	0.999993	−	0.00371164i	$-0.00118145\pi$
$500$	17.3670	+	13.8760i	0.776678	+	0.620555i
$501$	−11.9062	+	26.0709i	−0.531929	+	1.16476i
$502$	0.962126	+	1.28525i	0.0429418	+	0.0573635i
$503$	−5.18456	−	23.8331i	−0.231168	−	1.06266i	−0.935647	−	0.352938i	$-0.885183\pi$
$503$	−5.18456	−	23.8331i	−0.231168	−	1.06266i	0.704478	−	0.709725i	$-0.251181\pi$
$504$	0.518013	+	0.597819i	0.0230742	+	0.0266290i
$505$	4.19425	−	4.10701i	0.186642	−	0.182760i
$506$	0.337108	+	0.236380i	0.0149863	+	0.0105084i
$507$	8.92378	+	8.92378i	0.396319	+	0.396319i
$508$	19.7209	+	1.41047i	0.874974	+	0.0625794i
$509$	−15.5147	+	24.1413i	−0.687677	+	1.07005i	0.305359	+	0.952237i	$0.401223\pi$
$509$	−15.5147	+	24.1413i	−0.687677	+	1.07005i	−0.993036	+	0.117809i	$0.962413\pi$
$510$	−2.31899	−	0.358331i	−0.102687	−	0.0158672i
$511$	−21.9101	−	10.0060i	−0.969246	−	0.442640i
$512$	5.06864	−	6.77092i	0.224005	−	0.299235i
$513$	6.65311	+	12.1843i	0.293742	+	0.537948i
$514$	0.830224	+	1.29185i	0.0366196	+	0.0569812i
$515$	−10.3038	−	23.2043i	−0.454038	−	1.02250i
$516$	−3.91916	−	13.3474i	−0.172531	−	0.587588i
$517$	0.259540	+	3.62885i	0.0114146	+	0.159596i
$518$	−0.147170	−	2.05770i	−0.00646626	−	0.0904102i
$519$	1.89846	+	6.46556i	0.0833331	+	0.283807i
$520$	0.858546	−	2.23000i	0.0376497	−	0.0977919i
$521$	13.3721	+	20.8074i	0.585842	+	0.911588i	0.999999	+	0.00138259i	$0.000440093\pi$
$521$	13.3721	+	20.8074i	0.585842	+	0.911588i	−0.414157	+	0.910205i	$0.635924\pi$
$522$	−0.0681552	−	0.124817i	−0.00298307	−	0.00546309i
$523$	6.43190	−	8.59201i	0.281247	−	0.375702i	−0.637565	−	0.770396i	$-0.720058\pi$
$523$	6.43190	−	8.59201i	0.281247	−	0.375702i	0.918813	+	0.394694i	$0.129149\pi$
$524$	−21.7564	−	9.93583i	−0.950434	−	0.434049i
$525$	7.37517	−	44.6177i	0.321879	−	1.94727i
$526$	1.00803	−	1.56852i	0.0439521	−	0.0683908i
$527$	1.56890	+	0.112210i	0.0683422	+	0.00488793i
$528$	−4.04705	−	4.04705i	−0.176125	−	0.176125i
$529$	−21.6234	+	7.83768i	−0.940147	+	0.340769i
$530$	0.722634	+	0.737983i	0.0313892	+	0.0320559i
$531$	1.61858	+	1.86794i	0.0702403	+	0.0810616i
$532$	5.98841	+	27.5283i	0.259631	+	1.19350i
$533$	6.68631	+	8.93187i	0.289616	+	0.386882i
$534$	0.528054	−	1.15628i	0.0228511	−	0.0500370i
$535$	21.8771	−	2.91116i	0.945831	−	0.125861i
$536$	0.937957	−	3.19439i	0.0405136	−	0.137977i
$537$	−19.6867	−	4.28259i	−0.849546	−	0.184807i
$538$	−0.526786	−	0.196481i	−0.0227114	−	0.00847090i
$539$	−13.1347	+	3.85668i	−0.565750	+	0.166119i
$540$	16.0662	+	14.2197i	0.691379	+	0.611920i
$541$	−0.956634	+	1.10401i	−0.0411289	+	0.0474653i	−0.775941	−	0.630805i	$-0.782725\pi$
$541$	−0.956634	+	1.10401i	−0.0411289	+	0.0474653i	0.734812	+	0.678270i	$0.237270\pi$
$542$	−0.159178	−	0.0869177i	−0.00683728	−	0.00373344i
$543$	−1.89983	+	5.09365i	−0.0815296	+	0.218589i
$544$	5.72402	−	3.67860i	0.245415	−	0.157719i
$545$	35.1975	−	18.7419i	1.50769	−	0.802813i
$546$	−2.39880	+	0.344895i	−0.102659	+	0.0147602i
$547$	−28.8241	+	10.7508i	−1.23243	+	0.459673i	−0.879465	−	0.475963i	$-0.842100\pi$
$547$	−28.8241	+	10.7508i	−1.23243	+	0.459673i	−0.352966	+	0.935636i	$0.614827\pi$
$548$	18.5513	−	13.8874i	0.792473	−	0.593238i
$549$	3.05898	+	1.96589i	0.130554	+	0.0839021i
$550$	0.0396134	−	0.427421i	0.00168912	−	0.0182253i
$551$		−	10.1595i		−	0.432810i
$552$	−3.74459	+	0.657703i	−0.159380	+	0.0279937i
$553$	49.3710	−	49.3710i	2.09947	−	2.09947i
$554$	−1.83202	+	1.58746i	−0.0778353	+	0.0674446i
$555$	3.21389	+	15.5594i	0.136422	+	0.660460i
$556$	−2.91177	+	20.2518i	−0.123486	+	0.858867i
$557$	−11.6452	−	31.2219i	−0.493422	−	1.32292i	−0.910298	−	0.413953i	$-0.864148\pi$
$557$	−11.6452	−	31.2219i	−0.493422	−	1.32292i	0.416876	−	0.908963i	$-0.363125\pi$
$558$	−0.00960418	−	0.00718960i	−0.000406577	−	0.000304360i
$559$	9.04928	+	2.65711i	0.382744	+	0.112384i
$560$	23.0160	+	36.6548i	0.972604	+	1.54895i
$561$	−3.19409	−	6.99407i	−0.134854	−	0.295290i
$562$	−0.112515	+	0.206055i	−0.00474615	+	0.00869192i
$563$	19.4551	−	1.39146i	0.819935	−	0.0586429i	0.344933	−	0.938627i	$-0.387902\pi$
$563$	19.4551	−	1.39146i	0.819935	−	0.0586429i	0.475002	+	0.879985i	$0.342447\pi$
$564$	−12.6573	−	10.9676i	−0.532970	−	0.461821i
$565$	−35.1538	+	9.92206i	−1.47893	+	0.417424i
$566$	−2.45774	+	1.12241i	−0.103306	+	0.0471785i
$567$	10.4464	−	48.0212i	0.438707	−	2.01670i
$568$	−5.87074	+	3.20567i	−0.246331	+	0.134507i
$569$	−3.68129	−	25.6039i	−0.154328	−	1.07337i	−0.908857	−	0.417107i	$-0.863044\pi$
$569$	−3.68129	−	25.6039i	−0.154328	−	1.07337i	0.754530	−	0.656266i	$-0.227865\pi$
$570$	0.434210	+	1.20261i	0.0181870	+	0.0503717i
$571$	−12.1361	−	1.74491i	−0.507881	−	0.0730223i	−0.116389	−	0.993204i	$-0.537132\pi$
$571$	−12.1361	−	1.74491i	−0.507881	−	0.0730223i	−0.391492	+	0.920181i	$0.628041\pi$
$572$	3.81427	−	0.829744i	0.159483	−	0.0346933i
$573$	−2.64916	+	37.0400i	−0.110670	+	1.54737i
$574$	2.40311			0.100304
$575$	18.2792	+	15.5201i	0.762294	+	0.647231i
$576$	2.87196			0.119665
$577$	−2.87042	+	40.1338i	−0.119497	+	1.67079i	0.485252	+	0.874374i	$0.338728\pi$
$577$	−2.87042	+	40.1338i	−0.119497	+	1.67079i	−0.604749	+	0.796416i	$0.706727\pi$
$578$	1.14997	−	0.250160i	0.0478323	−	0.0104053i
$579$	26.6454	+	3.83102i	1.10734	+	0.159212i
$580$	−5.33222	−	14.7684i	−0.221408	−	0.613223i
$581$	−3.15649	−	21.9539i	−0.130953	−	0.910799i
$582$	0.679268	−	0.370908i	0.0281566	−	0.0153746i
$583$	−0.719415	+	3.30710i	−0.0297951	+	0.136966i
$584$	1.92040	−	0.877019i	0.0794669	−	0.0362913i
$585$	1.98167	−	0.559321i	0.0819320	−	0.0231251i
$586$	−0.124910	−	0.108235i	−0.00515998	−	0.00447114i
$587$	−18.4064	+	1.31646i	−0.759715	+	0.0543359i	−0.445821	−	0.895122i	$-0.647088\pi$
$587$	−18.4064	+	1.31646i	−0.759715	+	0.0543359i	−0.313894	+	0.949458i	$0.601634\pi$
$588$	30.2013	−	55.3096i	1.24548	−	2.28093i
$589$	−0.356036	−	0.779610i	−0.0146702	−	0.0321233i
$590$	−0.855166	−	1.36192i	−0.0352066	−	0.0560694i
$591$	−15.1981	−	4.46257i	−0.625167	−	0.183566i
$592$	−12.1729	−	9.11252i	−0.500303	−	0.374522i
$593$	8.98529	+	24.0905i	0.368982	+	0.989278i	0.980234	+	0.197842i	$0.0633934\pi$
$593$	8.98529	+	24.0905i	0.368982	+	0.989278i	−0.611252	+	0.791436i	$0.709334\pi$
$594$	0.0589605	−	0.410079i	0.00241918	−	0.0168258i
$595$	11.7620	+	56.9435i	0.482196	+	2.33446i
$596$	13.4829	−	11.6830i	0.552280	−	0.478554i
$597$	7.91261	−	7.91261i	0.323841	−	0.323841i
$598$	0.497251	−	1.18492i	0.0203341	−	0.0484548i
$599$			27.1547i			1.10951i	0.832013	+	0.554756i	$0.187188\pi$
$599$			27.1547i			1.10951i	−0.832013	+	0.554756i	$0.812812\pi$
$600$	2.53219	+	3.04950i	0.103376	+	0.124495i
$601$	−12.7595	−	8.20004i	−0.520471	−	0.334487i	0.253887	−	0.967234i	$-0.418291\pi$
$601$	−12.7595	−	8.20004i	−0.520471	−	0.334487i	−0.774358	+	0.632747i	$0.781927\pi$
$602$	1.62619	−	1.21735i	0.0662786	−	0.0496155i
$603$	2.68794	−	1.00255i	0.109461	−	0.0408270i
$604$	−9.27794	+	1.33397i	−0.377514	+	0.0542783i
$605$	−20.4692	+	10.8994i	−0.832192	+	0.443123i
$606$	0.438983	−	0.282117i	0.0178325	−	0.0114602i
$607$	7.56379	−	20.2793i	0.307005	−	0.823111i	−0.688220	−	0.725502i	$-0.741608\pi$
$607$	7.56379	−	20.2793i	0.307005	−	0.823111i	0.995225	−	0.0976093i	$-0.0311195\pi$
$608$	−3.25401	−	1.77683i	−0.131968	−	0.0720598i
$609$	−20.9179	+	24.1405i	−0.847634	+	0.978222i
$610$	−1.77163	−	1.56802i	−0.0717311	−	0.0634873i
$611$	10.8949	−	3.19903i	0.440760	−	0.129419i
$612$	3.65874	+	1.36464i	0.147896	+	0.0551623i
$613$	2.48229	+	0.539989i	0.100259	+	0.0218100i	0.262415	−	0.964955i	$-0.415481\pi$
$613$	2.48229	+	0.539989i	0.100259	+	0.0218100i	−0.162156	+	0.986765i	$0.551845\pi$
$614$	−0.189529	+	0.645476i	−0.00764876	+	0.0260493i
$615$	−18.3458	+	2.44126i	−0.739775	+	0.0984410i
$616$	0.700579	−	1.53405i	0.0282271	−	0.0618088i
$617$	−4.51549	−	6.03199i	−0.181787	−	0.242839i	0.700386	−	0.713764i	$-0.253011\pi$
$617$	−4.51549	−	6.03199i	−0.181787	−	0.242839i	−0.882173	+	0.470925i	$0.843920\pi$
$618$	−0.479742	−	2.20534i	−0.0192981	−	0.0887117i
$619$	−4.64039	−	5.35530i	−0.186513	−	0.215248i	0.654791	−	0.755810i	$-0.272757\pi$
$619$	−4.64039	−	5.35530i	−0.186513	−	0.215248i	−0.841304	+	0.540563i	$0.818211\pi$
$620$	−0.926729	−	0.946413i	−0.0372183	−	0.0380089i
$621$	16.8655	+	15.8488i	0.676789	+	0.635991i
$622$	−0.315548	−	0.315548i	−0.0126523	−	0.0126523i
$623$	−31.4182	−	2.24708i	−1.25874	−	0.0900272i
$624$	−9.65754	+	15.0274i	−0.386611	+	0.601578i
$625$	4.59454	−	24.5742i	0.183782	−	0.982967i
$626$	−0.502483	−	0.229476i	−0.0200832	−	0.00917171i
$627$	−2.51074	+	3.35396i	−0.100269	+	0.133944i
$628$	1.26488	+	2.31645i	0.0504740	+	0.0924363i
$629$	−11.0441	−	17.1850i	−0.440357	−	0.685209i
$630$	0.159344	−	0.413883i	0.00634843	−	0.0164895i
$631$	2.60088	+	8.85780i	0.103540	+	0.352623i	0.994925	−	0.100624i	$-0.0320838\pi$
$631$	2.60088	+	8.85780i	0.103540	+	0.352623i	−0.891385	+	0.453247i	$0.850266\pi$
$632$	0.436579	+	6.10417i	0.0173662	+	0.242811i
$633$	−2.05781	−	28.7720i	−0.0817907	−	1.14358i
$634$	−0.954321	−	3.25012i	−0.0379009	−	0.129079i
$635$	−9.02381	−	20.3218i	−0.358099	−	0.806448i
$636$	−8.42332	−	13.1069i	−0.334007	−	0.519724i
$637$	20.4759	+	37.4988i	0.811284	+	1.48576i
$638$	−0.181697	+	0.242719i	−0.00719347	+	0.00960935i
$639$	−5.24301	−	2.39440i	−0.207410	−	0.0947211i
$640$	−7.54283	−	1.16552i	−0.298156	−	0.0460712i
$641$	−4.64508	+	7.22789i	−0.183470	+	0.285485i	−0.920790	−	0.390059i	$-0.872455\pi$
$641$	−4.64508	+	7.22789i	−0.183470	+	0.285485i	0.737320	+	0.675544i	$0.236091\pi$
$642$	1.95687	+	0.139958i	0.0772314	+	0.00552370i
$643$	12.0118	+	12.0118i	0.473699	+	0.473699i	0.903109	−	0.429410i	$-0.141279\pi$
$643$	12.0118	+	12.0118i	0.473699	+	0.473699i	−0.429410	+	0.903109i	$0.641279\pi$
$644$	23.7782	+	40.5024i	0.936994	+	1.59602i
$645$	−11.1780	+	10.9455i	−0.440133	+	0.430979i
$646$	−1.07656	−	1.24241i	−0.0423566	−	0.0488822i
$647$	−3.63470	−	16.7084i	−0.142895	−	0.656876i	−0.991743	−	0.128240i	$-0.959067\pi$
$647$	−3.63470	−	16.7084i	−0.142895	−	0.656876i	0.848848	−	0.528636i	$-0.177296\pi$
$648$	2.58137	+	3.44830i	0.101406	+	0.135462i
$649$	2.18902	−	4.79328i	0.0859265	−	0.188153i
$650$	−1.32981	+	0.162754i	−0.0521593	+	0.00638373i
$651$	−0.759178	+	2.58552i	−0.0297545	+	0.101335i
$652$	−4.33586	−	0.943210i	−0.169806	−	0.0369389i
$653$	−10.2936	−	3.83932i	−0.402820	−	0.150244i	0.139884	−	0.990168i	$-0.455327\pi$
$653$	−10.2936	−	3.83932i	−0.402820	−	0.150244i	−0.542705	+	0.839924i	$0.682600\pi$
$654$	3.40114	−	0.998664i	0.132995	−	0.0390508i
$655$	1.63689	+	26.8487i	0.0639584	+	1.04907i
$656$	11.5996	−	13.3866i	0.452888	−	0.522661i
$657$	1.59669	+	0.871859i	0.0622928	+	0.0340144i
$658$	0.854670	−	2.29146i	0.0333185	−	0.0893304i
$659$	28.3720	−	18.2336i	1.10522	−	0.710280i	0.144972	−	0.989436i	$-0.453691\pi$
$659$	28.3720	−	18.2336i	1.10522	−	0.710280i	0.960246	+	0.279156i	$0.0900545\pi$
$660$	−1.88941	+	6.19324i	−0.0735452	+	0.241071i
$661$	16.6437	−	2.39301i	0.647366	−	0.0930771i	0.189192	−	0.981940i	$-0.439413\pi$
$661$	16.6437	−	2.39301i	0.647366	−	0.0930771i	0.458173	+	0.888863i	$0.348504\pi$
$662$	1.98798	−	0.741477i	0.0772649	−	0.0288183i
$663$	−19.2111	+	14.3813i	−0.746098	+	0.558522i
$664$	1.63542	+	1.05102i	0.0634665	+	0.0407875i
$665$	24.1611	−	20.4952i	0.936927	−	0.794769i
$666$			0.155810i			0.00603752i
$667$	−5.27426	−	16.0951i	−0.204220	−	0.623203i
$668$	−21.9437	+	21.9437i	−0.849027	+	0.849027i
$669$	11.6809	−	10.1216i	0.451612	−	0.391324i
$670$	−1.82798	+	0.377581i	−0.0706212	+	0.0145872i
$671$	1.10327	−	7.67343i	0.0425914	−	0.296230i
$672$	4.07363	+	10.9218i	0.157144	+	0.421319i
$673$	1.27984	+	0.958077i	0.0493342	+	0.0369311i	0.623660	−	0.781696i	$-0.285645\pi$
$673$	1.27984	+	0.958077i	0.0493342	+	0.0369311i	−0.574326	+	0.818627i	$0.694736\pi$
$674$	−1.41604	−	0.415786i	−0.0545438	−	0.0160155i
$675$	5.62332	−	23.4645i	0.216442	−	0.903150i
$676$	5.67649	+	12.4298i	0.218327	+	0.478069i
$677$	0.0442508	−	0.0810392i	0.00170070	−	0.00311459i	−0.876827	−	0.480806i	$-0.840344\pi$
$677$	0.0442508	−	0.0810392i	0.00170070	−	0.00311459i	0.878528	+	0.477691i	$0.158526\pi$
$678$	−3.23874	+	0.231639i	−0.124383	+	0.00889605i
$679$	−14.4936	−	12.5588i	−0.556214	−	0.481962i
$680$	−4.44710	−	2.48932i	−0.170539	−	0.0954610i
$681$	−9.33299	+	4.26223i	−0.357641	+	0.163329i
$682$	−0.00543690	+	0.0249930i	−0.000208190	+	0.000957033i
$683$	−29.4354	+	16.0729i	−1.12631	+	0.615013i	−0.930742	−	0.365676i	$-0.880838\pi$
$683$	−29.4354	+	16.0729i	−1.12631	+	0.615013i	−0.195571	+	0.980690i	$0.562656\pi$
$684$	−0.302814	−	2.10612i	−0.0115784	−	0.0805293i
$685$	−23.5912	−	11.0748i	−0.901375	−	0.423147i
$686$	5.41454	+	0.778493i	0.206728	+	0.0297230i
$687$	−32.1715	+	6.99848i	−1.22742	+	0.267009i
$688$	1.06816	−	14.9348i	0.0407232	−	0.569385i
$689$	10.5631			0.402422
$690$	1.31222	+	1.67979i	0.0499553	+	0.0639487i
$691$	27.8807			1.06063			0.530315	−	0.847801i	$-0.322074\pi$
$691$	27.8807			1.06063			0.530315	+	0.847801i	$0.322074\pi$
$692$	−0.520507	+	7.27764i	−0.0197867	+	0.276654i
$693$	1.42001	−	0.308905i	0.0539418	−	0.0117343i
$694$	−2.58358	−	0.371463i	−0.0980714	−	0.0141005i
$695$	21.6424	−	7.81412i	0.820941	−	0.296407i
$696$	−0.398443	−	2.77123i	−0.0151030	−	0.105043i
$697$	20.8853	−	11.4042i	0.791087	−	0.431966i
$698$	0.382636	−	1.75895i	0.0144830	−	0.0665772i
$699$	−32.6126	+	14.8937i	−1.23352	+	0.563331i
$700$	24.3648	−	42.4737i	0.920904	−	1.60536i
$701$	3.17607	+	2.75208i	0.119958	+	0.103945i	0.712774	−	0.701393i	$-0.247438\pi$
$701$	3.17607	+	2.75208i	0.119958	+	0.103945i	−0.592816	+	0.805338i	$0.701984\pi$
$702$	−1.28976	+	0.0922451i	−0.0486787	+	0.00348157i
$703$	−5.33448	+	9.76937i	−0.201194	+	0.368459i
$704$	−2.54357	−	5.56964i	−0.0958643	−	0.209914i
$705$	−4.19689	+	18.3617i	−0.158064	+	0.691542i
$706$	0.344975	+	0.101294i	0.0129833	+	0.00381224i
$707$	−10.3514	−	7.74894i	−0.389303	−	0.291429i
$708$	8.47730	+	22.7285i	0.318597	+	0.854190i
$709$	−3.48761	+	24.2569i	−0.130980	+	0.910985i	0.813301	+	0.581844i	$0.197668\pi$
$709$	−3.48761	+	24.2569i	−0.130980	+	0.910985i	−0.944281	+	0.329142i	$0.893241\pi$
$710$	3.13340	+	2.06056i	0.117594	+	0.0773314i
$711$	−3.98539	+	3.45336i	−0.149464	+	0.129511i
$712$	1.95219	−	1.95219i	0.0731615	−	0.0731615i
$713$	−0.968775	−	1.05025i	−0.0362809	−	0.0393322i
$714$			5.16873i			0.193435i
$715$	−2.83978	−	3.34772i	−0.106202	−	0.125198i
$716$	−18.3516	−	11.7939i	−0.685833	−	0.440758i
$717$	−8.40997	+	6.29563i	−0.314076	+	0.235115i
$718$	−3.12457	+	1.16541i	−0.116608	+	0.0434925i
$719$	22.1084	−	3.17870i	0.824503	−	0.118546i	0.282867	−	0.959159i	$-0.408714\pi$
$719$	22.1084	−	3.17870i	0.824503	−	0.118546i	0.541635	+	0.840613i	$0.317805\pi$
$720$	−1.53642	−	2.88541i	−0.0572589	−	0.107533i
$721$	−47.0474	+	30.2356i	−1.75214	+	1.12603i
$722$	0.405687	−	1.08769i	0.0150981	−	0.0404796i
$723$	−23.8116	−	13.0021i	−0.885562	−	0.483553i
$724$	−3.85474	+	4.44861i	−0.143260	+	0.165331i
$725$	−11.8416	+	13.0993i	−0.439786	+	0.486495i
$726$	−1.97794	+	0.580776i	−0.0734083	+	0.0215546i
$727$	10.6722	+	3.98054i	0.395811	+	0.147630i	0.539485	−	0.841995i	$-0.318619\pi$
$727$	10.6722	+	3.98054i	0.395811	+	0.147630i	−0.143674	+	0.989625i	$0.545892\pi$
$728$	−5.14326	−	1.11885i	−0.190622	−	0.0414673i
$729$	6.44409	−	21.9466i	0.238670	−	0.812835i
$730$	−0.940061	−	0.719257i	−0.0347932	−	0.0266209i
$731$	8.35605	−	18.2972i	0.309060	−	0.676747i
$732$	21.3869	+	28.5696i	0.790484	+	1.05596i
$733$	8.02610	+	36.8954i	0.296451	+	1.36276i	0.848608	+	0.529022i	$0.177441\pi$
$733$	8.02610	+	36.8954i	0.296451	+	1.36276i	−0.552157	+	0.833740i	$0.686195\pi$
$734$	−1.96862	−	2.27190i	−0.0726629	−	0.0838575i
$735$	−70.8676	−	0.744715i	−2.61399	−	0.0274692i
$736$	−6.07756	−	1.12561i	−0.224022	−	0.0414904i
$737$	−4.32485	−	4.32485i	−0.159308	−	0.159308i
$738$	−0.181039	−	0.0129482i	−0.00666413	−	0.000476628i
$739$	−19.2459	+	29.9472i	−0.707972	+	1.10163i	0.281870	+	0.959453i	$0.409045\pi$
$739$	−19.2459	+	29.9472i	−0.707972	+	1.10163i	−0.989842	+	0.142173i	$0.954591\pi$
$740$	−2.62700	+	17.0010i	−0.0965706	+	0.624970i
$741$	11.8944	+	5.43201i	0.436953	+	0.199550i
$742$	1.36344	−	1.82134i	0.0500533	−	0.0668633i
$743$	7.51580	+	13.7642i	0.275728	+	0.504958i	0.978444	−	0.206512i	$-0.0662114\pi$
$743$	7.51580	+	13.7642i	0.275728	+	0.504958i	−0.702716	+	0.711470i	$0.748030\pi$
$744$	−0.127692	−	0.198693i	−0.00468142	−	0.00728442i
$745$	−18.7240	−	7.20870i	−0.685994	−	0.264106i
$746$	0.218305	+	0.743477i	0.00799270	+	0.0272206i
$747$	0.119506	+	1.67091i	0.00437248	+	0.0611352i
$748$	−0.593918	−	8.30406i	−0.0217158	−	0.303626i
$749$	−13.6962	−	46.6450i	−0.500448	−	1.70437i
$750$	0.841866	−	2.05669i	0.0307406	−	0.0750998i
$751$	19.3947	+	30.1788i	0.707724	+	1.10124i	0.989885	+	0.141873i	$0.0453123\pi$
$751$	19.3947	+	30.1788i	0.707724	+	1.10124i	−0.282161	+	0.959367i	$0.591051\pi$
$752$	−8.63928	−	15.8217i	−0.315042	−	0.576956i
$753$	−16.3218	+	21.8034i	−0.594800	+	0.794559i
$754$	0.860777	+	0.393104i	0.0313476	+	0.0143160i
$755$	6.22825	+	8.50480i	0.226669	+	0.309521i
$756$	25.5506	−	39.7575i	0.929267	−	1.44597i
$757$	−14.3117	−	1.02360i	−0.520169	−	0.0372032i	−0.191213	−	0.981549i	$-0.561242\pi$
$757$	−14.3117	−	1.02360i	−0.520169	−	0.0372032i	−0.328956	+	0.944345i	$0.606697\pi$
$758$	0.974879	+	0.974879i	0.0354092	+	0.0354092i
$759$	−2.23642	+	6.61690i	−0.0811767	+	0.240178i
$760$	−0.0291805	+	2.77684i	−0.00105849	+	0.100726i
$761$	−27.4199	−	31.6442i	−0.993970	−	1.14710i	−0.989120	−	0.147114i	$-0.953002\pi$
$761$	−27.4199	−	31.6442i	−0.993970	−	1.14710i	−0.00485031	−	0.999988i	$-0.501544\pi$
$762$	−0.420147	−	1.93139i	−0.0152203	−	0.0699668i
$763$	−52.6386	−	70.3169i	−1.90564	−	2.54564i
$764$	−16.7030	+	36.5745i	−0.604295	+	1.32322i
$765$	−0.579278	−	4.35322i	−0.0209438	−	0.157391i
$766$	0.613395	−	2.08903i	0.0221629	−	0.0754798i
$767$	−16.0706	−	3.49594i	−0.580275	−	0.126231i
$768$	25.9298	+	9.67130i	0.935660	+	0.348983i
$769$	47.9122	−	14.0683i	1.72776	−	0.507316i	0.741279	−	0.671197i	$-0.234219\pi$
$769$	47.9122	−	14.0683i	1.72776	−	0.507316i	0.986480	+	0.163881i	$0.0524013\pi$
$770$	−0.943774	+	0.0575391i	−0.0340113	+	0.00207357i
$771$	−17.0597	+	19.6879i	−0.614390	+	0.709044i
$772$	25.5820	+	13.9688i	0.920716	+	0.502749i
$773$	−15.7704	+	42.2821i	−0.567223	+	1.52078i	0.263819	+	0.964572i	$0.415018\pi$
$773$	−15.7704	+	42.2821i	−0.567223	+	1.52078i	−0.831042	+	0.556210i	$0.812255\pi$
$774$	−0.129069	+	0.0829473i	−0.00463927	+	0.00298148i
$775$	−0.449629	+	1.42018i	−0.0161512	+	0.0510144i
$776$	1.66381	−	0.239220i	0.0597273	−	0.00858749i
$777$	32.7901	−	12.2301i	1.17634	−	0.438751i
$778$	1.96647	−	1.47208i	0.0705015	−	0.0527767i
$779$	−10.9079	−	7.01009i	−0.390816	−	0.251163i
$780$	20.1413	+	1.65343i	0.721175	+	0.0592024i
$781$			12.2885i			0.439716i
$782$	−2.35052	−	1.40939i	−0.0840543	−	0.0503996i
$783$	−12.0512	+	12.0512i	−0.430676	+	0.430676i
$784$	51.2619	−	44.4187i	1.83078	−	1.58638i
$785$	1.63088	−	2.48001i	0.0582086	−	0.0885153i
$786$	−0.340288	+	2.36675i	−0.0121377	+	0.0844193i
$787$	3.15170	+	8.45004i	0.112346	+	0.301211i	0.980939	−	0.194314i	$-0.0622482\pi$
$787$	3.15170	+	8.45004i	0.112346	+	0.301211i	−0.868593	+	0.495526i	$0.834975\pi$
$788$	−13.7298	−	10.2780i	−0.489105	−	0.366140i
$789$	30.3488	+	8.91121i	1.08045	+	0.317247i
$790$	2.90576	−	1.82456i	0.103382	−	0.0649150i
$791$	33.4241	+	73.1886i	1.18842	+	2.60229i
$792$	−0.0610438	+	0.111793i	−0.00216910	+	0.00397241i
$793$	−24.1340	+	1.72610i	−0.857023	+	0.0612955i
$794$	1.47571	+	1.27871i	0.0523710	+	0.0453797i
$795$	−8.55849	+	15.2895i	−0.303538	+	0.542264i
$796$	11.0213	−	5.03328i	0.390641	−	0.178400i
$797$	4.20965	−	19.3514i	0.149113	−	0.685464i	−0.840512	−	0.541793i	$-0.817746\pi$
$797$	4.20965	−	19.3514i	0.149113	−	0.685464i	0.989626	−	0.143671i	$-0.0458906\pi$
$798$	2.47189	−	1.34975i	0.0875040	−	0.0477808i
$799$	−3.44649	−	23.9709i	−0.121928	−	0.848029i
$800$	2.12458	+	6.08374i	0.0751154	+	0.215093i
$801$	2.35479	+	0.338568i	0.0832024	+	0.0119627i
$802$	−2.21649	+	0.482167i	−0.0782668	+	0.0170259i
$803$	0.276691	−	3.86865i	0.00976423	−	0.136522i
$804$	28.1562			0.992993
$805$	27.6369	−	45.0123i	0.974073	−	1.58648i
$806$	0.0798295			0.00281187
$807$	0.680428	−	9.51363i	0.0239522	−	0.334896i
$808$	1.10744	−	0.240910i	0.0389598	−	0.00847518i
$809$	35.1251	+	5.05023i	1.23493	+	0.177557i	0.728696	−	0.684837i	$-0.240127\pi$
$809$	35.1251	+	5.05023i	1.23493	+	0.177557i	0.506238	+	0.862394i	$0.331036\pi$
$810$	1.02626	−	2.18612i	0.0360592	−	0.0768123i
$811$	−6.00846	−	41.7898i	−0.210986	−	1.46744i	−0.769875	−	0.638195i	$-0.779682\pi$
$811$	−6.00846	−	41.7898i	−0.210986	−	1.46744i	0.558890	−	0.829242i	$-0.311228\pi$
$812$	−30.3555	+	16.5754i	−1.06527	+	0.581682i
$813$	0.653997	−	3.00637i	0.0229367	−	0.105438i
$814$	0.302165	−	0.137994i	0.0105909	−	0.00483669i
$815$	1.35553	+	4.80262i	0.0474820	+	0.168229i
$816$	28.7927	+	24.9490i	1.00795	+	0.873390i
$817$	−10.9325	+	0.781910i	−0.382481	+	0.0273556i
$818$	0.379051	−	0.694180i	0.0132532	−	0.0242714i
$819$	−1.88417	−	4.12575i	−0.0658381	−	0.144165i
$820$	−19.5355	−	4.46519i	−0.682210	−	0.155931i
$821$	42.0954	+	12.3603i	1.46914	+	0.431379i	0.915820	−	0.401589i	$-0.131542\pi$
$821$	42.0954	+	12.3603i	1.46914	+	0.431379i	0.553321	+	0.832968i	$0.313360\pi$
$822$	−1.85460	−	1.38833i	−0.0646865	−	0.0484237i
$823$	−14.6587	−	39.3016i	−0.510971	−	1.36997i	−0.894761	−	0.446546i	$-0.852654\pi$
$823$	−14.6587	−	39.3016i	−0.510971	−	1.36997i	0.383790	−	0.923420i	$-0.374619\pi$
$824$	0.697601	−	4.85192i	0.0243021	−	0.169025i
$825$	7.14651	−	1.39802i	0.248810	−	0.0486728i
$826$	−2.67710	+	2.31972i	−0.0931482	+	0.0807134i
$827$	−26.1573	+	26.1573i	−0.909578	+	0.909578i	−0.996238	−	0.0866596i	$-0.972381\pi$
$827$	−26.1573	+	26.1573i	−0.909578	+	0.909578i	0.0866596	+	0.996238i	$0.472381\pi$
$828$	−1.57311	−	3.17938i	−0.0546693	−	0.110491i
$829$			7.75893i			0.269479i	0.990881	+	0.134739i	$0.0430197\pi$
$829$			7.75893i			0.269479i	−0.990881	+	0.134739i	$0.956980\pi$
$830$	0.0891747	−	1.08628i	0.00309530	−	0.0377054i
$831$	−34.5952	−	22.2330i	−1.20010	−	0.771255i
$832$	−15.2985	+	11.4523i	−0.530380	+	0.397038i
$833$	85.3777	−	31.8442i	2.95816	−	1.10334i
$834$	2.02459	−	0.291092i	0.0701059	−	0.0100797i
$835$	33.3816	+	10.1839i	1.15522	+	0.352430i
$836$	−3.81623	+	2.45254i	−0.131987	+	0.0848230i
$837$	−0.502444	+	1.34710i	−0.0173670	+	0.0465627i
$838$	2.12550	+	1.16061i	0.0734240	+	0.0400925i
$839$	30.0770	−	34.7107i	1.03837	−	1.19835i	0.0585894	−	0.998282i	$-0.481340\pi$
$839$	30.0770	−	34.7107i	1.03837	−	1.19835i	0.979783	−	0.200063i	$-0.0641148\pi$
$840$	5.78668	−	6.53809i	0.199659	−	0.225585i
$841$	−15.8580	+	4.65632i	−0.546826	+	0.160563i
$842$	−3.34913	−	1.24916i	−0.115419	−	0.0430489i
$843$	−3.89174	−	0.846597i	−0.134039	−	0.0291583i
$844$	8.79931	−	29.9677i	0.302885	−	1.03153i
$845$	9.33820	−	12.2049i	0.321244	−	0.419862i
$846$	−0.0767333	+	0.168023i	−0.00263815	+	0.00577673i
$847$	30.6121	+	40.8930i	1.05185	+	1.40510i
$848$	−3.56467	−	16.3865i	−0.122411	−	0.562715i
$849$	−30.0162	−	34.6405i	−1.03015	−	1.18886i
$850$	−0.0600465	+	2.85672i	−0.00205958	+	0.0979847i
$851$	−3.37935	+	18.2464i	−0.115843	+	0.625477i
$852$	−40.0010	−	40.0010i	−1.37041	−	1.37041i
$853$	36.6436	+	2.62080i	1.25465	+	0.0897345i	0.682790	−	0.730615i	$-0.260766\pi$
$853$	36.6436	+	2.62080i	1.25465	+	0.0897345i	0.571863	+	0.820349i	$0.306221\pi$
$854$	−2.81748	+	4.38409i	−0.0964123	+	0.150020i
$855$	−1.93061	+	1.41383i	−0.0660255	+	0.0483519i
$856$	3.87594	+	1.77008i	0.132477	+	0.0605001i
$857$	−33.1587	+	44.2949i	−1.13268	+	1.51308i	−0.304596	+	0.952482i	$0.598521\pi$
$857$	−33.1587	+	44.2949i	−1.13268	+	1.51308i	−0.828085	+	0.560603i	$0.810570\pi$
$858$	−0.187020	−	0.342501i	−0.00638474	−	0.0116928i
$859$	7.98822	+	12.4299i	0.272555	+	0.424103i	0.950367	−	0.311132i	$-0.100708\pi$
$859$	7.98822	+	12.4299i	0.272555	+	0.424103i	−0.677812	+	0.735235i	$0.737072\pi$
$860$	−15.4817	+	6.87456i	−0.527920	+	0.234421i
$861$	11.4854	+	39.1158i	0.391422	+	1.33306i
$862$	0.0347945	+	0.486491i	0.00118511	+	0.0165699i
$863$	−2.64275	−	36.9504i	−0.0899602	−	1.25781i	−0.819183	−	0.573532i	$-0.805573\pi$
$863$	−2.64275	−	36.9504i	−0.0899602	−	1.25781i	0.729223	−	0.684276i	$-0.239882\pi$
$864$	1.75224	+	5.96759i	0.0596125	+	0.203021i
$865$	7.49939	−	3.33007i	0.254987	−	0.113226i
$866$	0.667441	+	1.03856i	0.0226806	+	0.0352916i
$867$	9.56803	+	17.5225i	0.324947	+	0.595097i
$868$	−1.74851	+	2.33574i	−0.0593484	+	0.0792801i
$869$	10.2268	+	4.67044i	0.346921	+	0.158434i
$870$	−1.26642	+	0.927427i	−0.0429357	+	0.0314427i
$871$	−10.3205	+	16.0590i	−0.349696	+	0.544137i
$872$	7.67920	+	0.549227i	0.260051	+	0.0185992i
$873$	1.02421	+	1.02421i	0.0346643	+	0.0346643i
$874$	−0.0602145	+	1.49215i	−0.00203679	+	0.0504729i
$875$	−55.0409	−	1.73571i	−1.86072	−	0.0586776i
$876$	11.6924	+	13.4938i	0.395050	+	0.455912i
$877$	−2.56350	−	11.7842i	−0.0865634	−	0.397925i	0.913395	−	0.407075i	$-0.133451\pi$
$877$	−2.56350	−	11.7842i	−0.0865634	−	0.397925i	−0.999958	+	0.00914951i	$0.997088\pi$
$878$	0.327430	+	0.437395i	0.0110502	+	0.0147614i
$879$	1.16476	−	2.55047i	0.0392864	−	0.0860253i
$880$	−4.23499	+	5.53508i	−0.142761	+	0.186587i
$881$	7.53089	−	25.6479i	0.253722	−	0.864099i	−0.729854	−	0.683603i	$-0.760412\pi$
$881$	7.53089	−	25.6479i	0.253722	−	0.864099i	0.983576	−	0.180495i	$-0.0577700\pi$
$882$	−0.679145	−	0.147739i	−0.0228680	−	0.00497463i
$883$	26.8105	+	9.99980i	0.902245	+	0.336520i	0.757413	−	0.652936i	$-0.226463\pi$
$883$	26.8105	+	9.99980i	0.902245	+	0.336520i	0.144832	+	0.989456i	$0.453736\pi$
$884$	−24.9313	+	7.32048i	−0.838529	+	0.246214i
$885$	18.0810	−	20.4288i	0.607785	−	0.686707i
$886$	0.524525	−	0.605334i	0.0176217	−	0.0203366i
$887$	24.8252	+	13.5556i	0.833549	+	0.455152i	0.838543	−	0.544835i	$-0.183408\pi$
$887$	24.8252	+	13.5556i	0.833549	+	0.455152i	−0.00499390	+	0.999988i	$0.501590\pi$
$888$	−1.07196	+	2.87403i	−0.0359725	+	0.0964460i
$889$	−41.2031	+	26.4796i	−1.38191	+	0.888098i
$890$	−1.48051	−	0.451670i	−0.0496269	−	0.0151400i
$891$	7.83284	−	1.12619i	0.262410	−	0.0377288i
$892$	15.6802	−	5.84840i	0.525010	−	0.195819i
$893$	−10.5638	+	7.90797i	−0.353504	+	0.264630i
$894$	−1.50040	−	0.964246i	−0.0501808	−	0.0322492i
$895$	−2.00722	+	24.4510i	−0.0670940	+	0.817306i
$896$			16.8120i			0.561649i
$897$	21.6636	+	2.43064i	0.723326	+	0.0811567i
$898$	0.329830	−	0.329830i	0.0110066	−	0.0110066i
$899$	0.795192	−	0.689038i	0.0265212	−	0.0229807i
$900$	−2.06438	+	3.06849i	−0.0688127	+	0.102283i
$901$	3.20618	−	22.2995i	0.106813	−	0.742903i
$902$	0.135228	+	0.362559i	0.00450258	+	0.0120719i
$903$	27.5872	+	20.6515i	0.918044	+	0.687239i
$904$	−6.76655	−	1.98684i	−0.225052	−	0.0660813i
$905$	6.45350	+	1.47506i	0.214522	+	0.0490327i
$906$	0.389270	+	0.852382i	0.0129326	+	0.0283185i
$907$	−2.57411	+	4.71412i	−0.0854718	+	0.156530i	−0.916918	−	0.399075i	$-0.869331\pi$
$907$	−2.57411	+	4.71412i	−0.0854718	+	0.156530i	0.831447	+	0.555605i	$0.187513\pi$
$908$	−11.0811	+	0.792532i	−0.367738	+	0.0263011i
$909$	0.738071	+	0.639542i	0.0244803	+	0.0212123i
$910$	0.801610	+	2.84010i	0.0265731	+	0.0941484i
$911$	28.7911	−	13.1485i	0.953892	−	0.435628i	0.123214	−	0.992380i	$-0.460680\pi$
$911$	28.7911	−	13.1485i	0.953892	−	0.435628i	0.830679	+	0.556752i	$0.187953\pi$
$912$	4.41272	−	20.2849i	0.146120	−	0.671701i
$913$	3.13457	−	1.71161i	0.103739	−	0.0566459i
$914$	0.216143	+	1.50331i	0.00714938	+	0.0497250i
$915$	17.0556	−	36.3312i	0.563839	−	1.20107i
$916$	−35.2860	−	5.07335i	−1.16588	−	0.167628i
$917$	57.8962	−	12.5945i	1.91190	−	0.415908i
$918$	−0.196739	+	2.75077i	−0.00649335	+	0.0907889i
$919$	30.2174			0.996779			0.498389	−	0.866953i	$-0.333925\pi$
$919$	30.2174			0.996779			0.498389	+	0.866953i	$0.333925\pi$
$920$	1.39535	+	4.41431i	0.0460034	+	0.145536i
$921$	−11.4123			−0.376049
$922$	−0.109351	+	1.52893i	−0.00360129	+	0.0503526i
$923$	37.4767	−	8.15256i	1.23356	−	0.268345i
$924$	14.1176	+	2.02980i	0.464434	+	0.0667755i
$925$	18.2649	−	6.37854i	0.600547	−	0.209725i
$926$	0.231209	+	1.60809i	0.00759799	+	0.0528452i
$927$	3.70724	−	2.02431i	0.121762	−	0.0664869i
$928$	0.967518	−	4.44761i	0.0317603	−	0.146000i
$929$	47.3922	−	21.6433i	1.55489	−	0.710093i	0.561778	−	0.827288i	$-0.310118\pi$
$929$	47.3922	−	21.6433i	1.55489	−	0.710093i	0.993109	+	0.117195i	$0.0373903\pi$
$930$	−0.0646799	+	0.115549i	−0.00212094	+	0.00378900i
$931$	−37.5246	−	32.5152i	−1.22982	−	1.06564i
$932$	−38.7210	+	2.76938i	−1.26835	+	0.0907140i
$933$	3.62809	−	6.64434i	0.118778	−	0.217526i
$934$	−0.680687	−	1.49050i	−0.0222728	−	0.0487705i
$935$	−7.92923	+	4.97886i	−0.259314	+	0.162826i
$936$	0.381440	+	0.112001i	0.0124678	+	0.00366087i
$937$	−22.2265	−	16.6386i	−0.726108	−	0.543558i	0.171053	−	0.985262i	$-0.445283\pi$
$937$	−22.2265	−	16.6386i	−0.726108	−	0.543558i	−0.897161	+	0.441704i	$0.854374\pi$
$938$	1.43684	+	3.85232i	0.0469145	+	0.125783i
$939$	1.33365	−	9.27573i	0.0435220	−	0.302702i
$940$	−11.2056	+	17.0398i	−0.365485	+	0.555778i
$941$	−40.6073	+	35.1864i	−1.32376	+	1.14704i	−0.345787	+	0.938313i	$0.612388\pi$
$941$	−40.6073	+	35.1864i	−1.32376	+	1.14704i	−0.977973	+	0.208731i	$0.933067\pi$
$942$	0.186572	−	0.186572i	0.00607883	−	0.00607883i
$943$	−20.9200	−	5.44284i	−0.681247	−	0.177243i
$944$			26.1100i			0.849808i
$945$	−52.9713	−	4.34850i	−1.72316	−	0.141457i
$946$	0.275171	+	0.176842i	0.00894659	+	0.00574963i
$947$	−24.1664	+	18.0908i	−0.785303	+	0.587871i	−0.914893	−	0.403697i	$-0.867725\pi$
$947$	−24.1664	+	18.0908i	−0.785303	+	0.587871i	0.129589	+	0.991568i	$0.458634\pi$
$948$	−48.4930	+	18.0870i	−1.57498	+	0.587437i
$949$	−11.9820	+	1.72275i	−0.388952	+	0.0559228i
$950$	1.38188	−	0.717283i	0.0448340	−	0.0232717i
$951$	48.3415	−	31.0672i	1.56758	−	1.00742i
$952$	−3.92309	+	10.5182i	−0.127148	+	0.340897i
$953$	−17.2780	−	9.43451i	−0.559690	−	0.305614i	0.174390	−	0.984677i	$-0.444205\pi$
$953$	−17.2780	−	9.43451i	−0.559690	−	0.305614i	−0.734080	+	0.679063i	$0.762386\pi$
$954$	−0.112528	+	0.129864i	−0.00364323	+	0.00420452i
$955$	45.1351	−	2.75175i	1.46054	−	0.0890447i
$956$	−10.9141	+	3.20466i	−0.352986	+	0.103646i
$957$	−4.81918	−	1.79746i	−0.155782	−	0.0581037i
$958$	−0.119013	−	0.0258898i	−0.00384514	−	0.000836460i
$959$	−16.1732	+	55.0809i	−0.522260	+	1.77865i
$960$	−4.18139	−	31.4228i	−0.134954	−	1.01417i
$961$	−12.8410	+	28.1179i	−0.414226	+	0.907027i
$962$	−0.621314	−	0.829978i	−0.0200320	−	0.0267596i
$963$	0.780479	+	3.58780i	0.0251506	+	0.115615i
$964$	−19.2369	−	22.2006i	−0.619579	−	0.715032i
$965$	0.344448	−	32.7779i	0.0110882	−	1.05516i
$966$	3.21534	−	3.42160i	0.103452	−	0.110088i
$967$	16.8032	+	16.8032i	0.540355	+	0.540355i	0.923633	−	0.383278i	$-0.125205\pi$
$967$	16.8032	+	16.8032i	0.540355	+	0.540355i	−0.383278	+	0.923633i	$0.625205\pi$
$968$	−4.46587	−	0.319405i	−0.143538	−	0.0102661i
$969$	15.0777	−	23.4613i	0.484364	−	0.753685i
$970$	−0.556815	−	0.760342i	−0.0178782	−	0.0244131i
$971$	−34.9478	−	15.9601i	−1.12153	−	0.512185i	−0.233677	−	0.972314i	$-0.575076\pi$
$971$	−34.9478	−	15.9601i	−1.12153	−	0.512185i	−0.887852	+	0.460129i	$0.847803\pi$
$972$	−4.58095	+	6.11944i	−0.146934	+	0.196281i
$973$	−24.2904	−	44.4846i	−0.778716	−	1.42611i
$974$	−1.61015	−	2.50545i	−0.0515926	−	0.0802797i
$975$	−9.00484	−	20.8676i	−0.288386	−	0.668297i
$976$	10.8221	+	36.8565i	0.346405	+	1.17975i
$977$	3.52629	+	49.3040i	0.112816	+	1.57737i	0.667049	+	0.745013i	$0.267557\pi$
$977$	3.52629	+	49.3040i	0.112816	+	1.57737i	−0.554233	+	0.832361i	$0.686988\pi$
$978$	0.0316460	+	0.442468i	0.00101193	+	0.0141486i
$979$	−1.42894	−	4.86654i	−0.0456692	−	0.155535i
$980$	−71.6131	−	27.5709i	−2.28760	−	0.880721i
$981$	3.58666	+	5.58096i	0.114513	+	0.178186i
$982$	−1.35382	−	2.47933i	−0.0432020	−	0.0791186i
$983$	7.00154	−	9.35296i	0.223314	−	0.298313i	−0.674866	−	0.737940i	$-0.735799\pi$
$983$	7.00154	−	9.35296i	0.223314	−	0.298313i	0.898180	+	0.439627i	$0.144889\pi$
$984$	−3.25030	−	1.48436i	−0.103616	−	0.0473198i
$985$	−2.94544	+	19.0618i	−0.0938495	+	0.607361i
$986$	1.09114	−	1.69785i	0.0347490	−	0.0540705i
$987$	41.3832	+	2.95979i	1.31724	+	0.0942110i
$988$	10.0115	+	10.0115i	0.318507	+	0.318507i
$989$	−16.9138	+	6.91430i	−0.537827	+	0.219862i
$990$	0.0714095		0.000750409i	0.00226954		2.38496e-5i
$991$	8.60417	+	9.92974i	0.273320	+	0.315429i	0.875770	−	0.482728i	$-0.160354\pi$
$991$	8.60417	+	9.92974i	0.273320	+	0.315429i	−0.602450	+	0.798157i	$0.705809\pi$
$992$	−0.0816202	−	0.375202i	−0.00259144	−	0.0119127i
$993$	21.5704	+	28.8147i	0.684517	+	0.914408i
$994$	3.43162	−	7.51420i	0.108844	−	0.238336i
$995$	−10.8219	−	8.28006i	−0.343079	−	0.262496i
$996$	−4.63199	+	15.7751i	−0.146770	+	0.499853i
$997$	−16.1824	−	3.52027i	−0.512503	−	0.111488i	−0.0511256	−	0.998692i	$-0.516281\pi$
$997$	−16.1824	−	3.52027i	−0.512503	−	0.111488i	−0.461377	+	0.887204i	$0.652645\pi$
$998$	−1.29269	−	0.482148i	−0.0409194	−	0.0152621i
$999$	17.9162	−	5.26067i	0.566844	−	0.166440i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.102.5	yes	200
5.2	odd	4		575.2.r.b.493.5		200
5.3	odd	4	inner	115.2.l.a.33.6	yes	200
5.4	even	2		575.2.r.b.332.6		200
23.7	odd	22	inner	115.2.l.a.7.6	✓	200
115.7	even	44		575.2.r.b.168.6		200
115.53	even	44	inner	115.2.l.a.53.5	yes	200
115.99	odd	22		575.2.r.b.7.5		200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.7.6	✓	200	23.7	odd	22	inner
115.2.l.a.33.6	yes	200	5.3	odd	4	inner
115.2.l.a.53.5	yes	200	115.53	even	44	inner
115.2.l.a.102.5	yes	200	1.1	even	1	trivial
575.2.r.b.7.5		200	115.99	odd	22
575.2.r.b.168.6		200	115.7	even	44
575.2.r.b.332.6		200	5.4	even	2
575.2.r.b.493.5		200	5.2	odd	4

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.00772212 - 0.107969i) q^{2} +(1.79434 - 0.390334i) q^{3} +(1.96805 + 0.282962i) q^{4} +(-0.759367 - 2.10318i) q^{5} +(-0.0282880 - 0.196748i) q^{6} +(-4.32296 + 2.36052i) q^{7} +(0.0917670 - 0.421846i) q^{8} +(0.338390 - 0.154538i) q^{9} +O(q^{10})\)	\(q+(0.00772212 - 0.107969i) q^{2} +(1.79434 - 0.390334i) q^{3} +(1.96805 + 0.282962i) q^{4} +(-0.759367 - 2.10318i) q^{5} +(-0.0282880 - 0.196748i) q^{6} +(-4.32296 + 2.36052i) q^{7} +(0.0917670 - 0.421846i) q^{8} +(0.338390 - 0.154538i) q^{9} +(-0.232943 + 0.0657474i) q^{10} +(-0.599394 - 0.519378i) q^{11} +(3.64179 - 0.260466i) q^{12} +(-1.18632 + 2.17257i) q^{13} +(0.221481 + 0.484976i) q^{14} +(-2.18350 - 3.47741i) q^{15} +(3.77065 + 1.10716i) q^{16} +(4.22639 + 3.16383i) q^{17} +(-0.0140722 - 0.0377291i) q^{18} +(0.409398 - 2.84742i) q^{19} +(-0.899349 - 4.35402i) q^{20} +(-6.83547 + 5.92297i) q^{21} +(-0.0607055 + 0.0607055i) q^{22} +(-0.829644 - 4.72353i) q^{23} -0.792754i q^{24} +(-3.84672 + 3.19417i) q^{25} +(0.225410 + 0.144862i) q^{26} +(-3.86324 + 2.89199i) q^{27} +(-9.17573 + 3.42237i) q^{28} +(3.49570 - 0.502606i) q^{29} +(-0.392314 + 0.208898i) q^{30} +(0.250636 - 0.161074i) q^{31} +(0.450393 - 1.20755i) q^{32} +(-1.27825 - 0.697975i) q^{33} +(0.374233 - 0.431888i) q^{34} +(8.24731 + 7.29947i) q^{35} +(0.709695 - 0.208385i) q^{36} +(-3.62537 - 1.35219i) q^{37} +(-0.304273 - 0.0661905i) q^{38} +(-1.28062 + 4.36139i) q^{39} +(-0.956902 + 0.127334i) q^{40} +(1.87241 - 4.10001i) q^{41} +(0.586714 + 0.783758i) q^{42} +(-0.809890 - 3.72300i) q^{43} +(-1.03267 - 1.19177i) q^{44} +(-0.581983 - 0.594344i) q^{45} +(-0.516402 + 0.0531004i) q^{46} +(-3.24360 - 3.24360i) q^{47} +(7.19798 + 0.514810i) q^{48} +(9.33150 - 14.5201i) q^{49} +(0.315168 + 0.439994i) q^{50} +(8.81852 + 4.02728i) q^{51} +(-2.94948 + 3.94004i) q^{52} +(-2.04509 - 3.74531i) q^{53} +(0.282413 + 0.439444i) q^{54} +(-0.637184 + 1.65503i) q^{55} +(0.599069 + 2.04024i) q^{56} +(-0.376849 - 5.26904i) q^{57} +(-0.0272718 - 0.381310i) q^{58} +(1.87184 + 6.37491i) q^{59} +(-3.31326 - 7.46154i) q^{60} +(5.28454 + 8.22290i) q^{61} +(-0.0154556 - 0.0283048i) q^{62} +(-1.09806 + 1.46684i) q^{63} +(7.02251 + 3.20707i) q^{64} +(5.47016 + 0.845251i) q^{65} +(-0.0852307 + 0.132622i) q^{66} +(7.69208 + 0.550148i) q^{67} +(7.42247 + 7.42247i) q^{68} +(-3.33241 - 8.15176i) q^{69} +(0.851805 - 0.834089i) q^{70} +(-10.1464 - 11.7096i) q^{71} +(-0.0341380 - 0.156930i) q^{72} +(2.93063 + 3.91486i) q^{73} +(-0.173991 + 0.380987i) q^{74} +(-5.65552 + 7.23293i) q^{75} +(1.61143 - 5.48801i) q^{76} +(3.81716 + 0.830373i) q^{77} +(0.461007 + 0.171947i) q^{78} +(-13.6014 + 3.99372i) q^{79} +(-0.534748 - 8.77109i) q^{80} +(-6.53396 + 7.54059i) q^{81} +(-0.428217 - 0.233824i) q^{82} +(-1.57366 + 4.21914i) q^{83} +(-15.1285 + 9.72249i) q^{84} +(3.44473 - 11.2914i) q^{85} +(-0.408224 + 0.0586938i) q^{86} +(6.07629 - 2.26634i) q^{87} +(-0.274102 + 0.205190i) q^{88} +(5.37985 + 3.45742i) q^{89} +(-0.0686650 + 0.0582466i) q^{90} -12.1923i q^{91} +(-0.296197 - 9.53087i) q^{92} +(0.386853 - 0.386853i) q^{93} +(-0.375256 + 0.325161i) q^{94} +(-6.29952 + 1.30120i) q^{95} +(0.336809 - 2.34255i) q^{96} +(1.36068 + 3.64812i) q^{97} +(-1.49567 - 1.11964i) q^{98} +(-0.283093 - 0.0831235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Introduction

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