LMFDB - Embedded newform 460.2.o.b.19.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.10
Character	$\chi$	$=$	460.19
Dual form			460.2.o.b.339.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27640 - 0.608942i) q^{2} +(1.81640 - 0.533344i) q^{3} +(1.25838 + 1.55450i) q^{4} +(0.889872 + 2.05137i) q^{5} +(-2.64323 - 0.425324i) q^{6} +(-4.44634 + 0.639287i) q^{7} +(-0.659592 - 2.75044i) q^{8} +(0.491100 - 0.315611i) q^{9} +O(q^{10})$	\(q+(-1.27640 - 0.608942i) q^{2} +(1.81640 - 0.533344i) q^{3} +(1.25838 + 1.55450i) q^{4} +(0.889872 + 2.05137i) q^{5} +(-2.64323 - 0.425324i) q^{6} +(-4.44634 + 0.639287i) q^{7} +(-0.659592 - 2.75044i) q^{8} +(0.491100 - 0.315611i) q^{9} +(0.113335 - 3.16025i) q^{10} +(-2.52706 + 5.53349i) q^{11} +(3.11481 + 2.15245i) q^{12} +(3.23662 + 0.465356i) q^{13} +(6.06458 + 1.89158i) q^{14} +(2.71045 + 3.25151i) q^{15} +(-0.832958 + 3.91231i) q^{16} +(1.09298 + 1.26136i) q^{17} +(-0.819028 + 0.103794i) q^{18} +(-0.839282 + 0.968583i) q^{19} +(-2.06907 + 3.96472i) q^{20} +(-7.73538 + 3.53263i) q^{21} +(6.59511 - 5.52410i) q^{22} +(1.98282 - 4.36674i) q^{23} +(-2.66502 - 4.64412i) q^{24} +(-3.41625 + 3.65092i) q^{25} +(-3.84784 - 2.56489i) q^{26} +(-2.99542 + 3.45689i) q^{27} +(-6.58896 - 6.10738i) q^{28} +(-1.38089 - 1.59363i) q^{29} +(-1.47964 - 5.80072i) q^{30} +(-0.385664 + 1.31345i) q^{31} +(3.44555 - 4.48644i) q^{32} +(-1.63891 + 11.3988i) q^{33} +(-0.626977 - 2.27556i) q^{34} +(-5.26809 - 8.55221i) q^{35} +(1.10861 + 0.366258i) q^{36} +(-0.315022 + 0.202452i) q^{37} +(1.66107 - 0.725223i) q^{38} +(6.12720 - 0.880959i) q^{39} +(5.05523 - 3.80061i) q^{40} +(7.33870 + 4.71629i) q^{41} +(12.0246 + 0.201355i) q^{42} +(-1.62226 - 5.52493i) q^{43} +(-11.7818 + 3.03491i) q^{44} +(1.08445 + 0.726576i) q^{45} +(-5.18996 + 4.36627i) q^{46} +6.84242 q^{47} +(0.573621 + 7.55058i) q^{48} +(12.6448 - 3.71285i) q^{49} +(6.58369 - 2.57972i) q^{50} +(2.65803 + 1.70821i) q^{51} +(3.34951 + 5.61693i) q^{52} +(0.507342 + 3.52864i) q^{53} +(5.92839 - 2.58834i) q^{54} +(-13.6000 - 0.259841i) q^{55} +(4.69109 + 11.8077i) q^{56} +(-1.00789 + 2.20696i) q^{57} +(0.792136 + 2.87499i) q^{58} +(11.1053 + 1.59671i) q^{59} +(-1.64370 + 8.30504i) q^{60} +(2.55769 - 8.71069i) q^{61} +(1.29208 - 1.44164i) q^{62} +(-1.98183 + 1.71727i) q^{63} +(-7.12988 + 3.62834i) q^{64} +(1.92556 + 7.05362i) q^{65} +(9.03312 - 13.5514i) q^{66} +(-14.2897 + 6.52589i) q^{67} +(-0.585411 + 3.28631i) q^{68} +(1.27263 - 8.98928i) q^{69} +(1.51638 + 14.1240i) q^{70} +(9.93470 - 4.53703i) q^{71} +(-1.19200 - 1.14257i) q^{72} +(-5.89120 - 5.10476i) q^{73} +(0.525374 - 0.0665796i) q^{74} +(-4.25810 + 8.45357i) q^{75} +(-2.56180 - 0.0858202i) q^{76} +(7.69868 - 26.2193i) q^{77} +(-8.35720 - 2.60666i) q^{78} +(0.0473234 - 0.329141i) q^{79} +(-8.76683 + 1.77275i) q^{80} +(-4.32469 + 9.46975i) q^{81} +(-6.49515 - 10.4887i) q^{82} +(0.591417 + 0.920263i) q^{83} +(-15.2255 - 7.57928i) q^{84} +(-1.61491 + 3.36455i) q^{85} +(-1.29370 + 8.03987i) q^{86} +(-3.35821 - 2.15819i) q^{87} +(16.8864 + 3.30069i) q^{88} +(2.11466 + 7.20188i) q^{89} +(-0.941750 - 1.58777i) q^{90} -14.6886 q^{91} +(9.28325 - 2.41272i) q^{92} +2.59145i q^{93} +(-8.73365 - 4.16663i) q^{94} +(-2.73378 - 0.859764i) q^{95} +(3.86570 - 9.98685i) q^{96} +(9.54731 + 6.13568i) q^{97} +(-18.4007 - 2.96087i) q^{98} +(0.505391 + 3.51507i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−1.27640	−	0.608942i	−0.902549	−	0.430587i
$2$	−1.27640	−	0.608942i	−0.902549	−	0.430587i
$3$	1.81640	−	0.533344i	1.04870	−	0.307926i	0.288408	−	0.957508i	$-0.406874\pi$
$3$	1.81640	−	0.533344i	1.04870	−	0.307926i	0.760292	+	0.649581i	$0.225056\pi$
$4$	1.25838	+	1.55450i	0.629190	+	0.777251i
$5$	0.889872	+	2.05137i	0.397963	+	0.917401i
$5$	0.889872	+	2.05137i	0.397963	+	0.917401i
$6$	−2.64323	−	0.425324i	−1.07909	−	0.173638i
$7$	−4.44634	+	0.639287i	−1.68056	+	0.241628i	−0.915496	−	0.402328i	$-0.868201\pi$
$7$	−4.44634	+	0.639287i	−1.68056	+	0.241628i	−0.765063	+	0.643956i	$0.777292\pi$
$8$	−0.659592	−	2.75044i	−0.233201	−	0.972429i
$9$	0.491100	−	0.315611i	0.163700	−	0.105204i
$10$	0.113335	−	3.16025i	0.0358397	−	0.999358i
$11$	−2.52706	+	5.53349i	−0.761937	+	1.66841i	−0.0182948	+	0.999833i	$0.505824\pi$
$11$	−2.52706	+	5.53349i	−0.761937	+	1.66841i	−0.743643	+	0.668577i	$0.766904\pi$
$12$	3.11481	+	2.15245i	0.899168	+	0.621360i
$13$	3.23662	+	0.465356i	0.897678	+	0.129067i	0.575681	−	0.817674i	$-0.304737\pi$
$13$	3.23662	+	0.465356i	0.897678	+	0.129067i	0.321997	+	0.946741i	$0.395646\pi$
$14$	6.06458	+	1.89158i	1.62083	+	0.505545i
$15$	2.71045	+	3.25151i	0.699836	+	0.839536i
$16$	−0.832958	+	3.91231i	−0.208239	+	0.978078i
$17$	1.09298	+	1.26136i	0.265086	+	0.305925i	0.872651	−	0.488345i	$-0.162399\pi$
$17$	1.09298	+	1.26136i	0.265086	+	0.305925i	−0.607565	+	0.794270i	$0.707854\pi$
$18$	−0.819028	+	0.103794i	−0.193047	+	0.0244644i
$19$	−0.839282	+	0.968583i	−0.192544	+	0.222208i	−0.843810	−	0.536641i	$-0.819693\pi$
$19$	−0.839282	+	0.968583i	−0.192544	+	0.222208i	0.651266	+	0.758850i	$0.274238\pi$
$20$	−2.06907	+	3.96472i	−0.462657	+	0.886537i
$21$	−7.73538	+	3.53263i	−1.68800	+	0.770883i
$22$	6.59511	−	5.52410i	1.40608	−	1.17774i
$23$	1.98282	−	4.36674i	0.413447	−	0.910528i
$23$	1.98282	−	4.36674i	0.413447	−	0.910528i
$24$	−2.66502	−	4.64412i	−0.543994	−	0.947977i
$25$	−3.41625	+	3.65092i	−0.683251	+	0.730184i
$26$	−3.84784	−	2.56489i	−0.754624	−	0.503017i
$27$	−2.99542	+	3.45689i	−0.576468	+	0.665279i
$28$	−6.58896	−	6.10738i	−1.24520	−	1.15419i
$29$	−1.38089	−	1.59363i	−0.256425	−	0.295930i	0.612911	−	0.790152i	$-0.289999\pi$
$29$	−1.38089	−	1.59363i	−0.256425	−	0.295930i	−0.869336	+	0.494222i	$0.835453\pi$
$30$	−1.47964	−	5.80072i	−0.270143	−	1.05906i
$31$	−0.385664	+	1.31345i	−0.0692674	+	0.235903i	−0.986849	−	0.161644i	$-0.948320\pi$
$31$	−0.385664	+	1.31345i	−0.0692674	+	0.235903i	0.917582	+	0.397547i	$0.130139\pi$
$32$	3.44555	−	4.48644i	0.609094	−	0.793098i
$33$	−1.63891	+	11.3988i	−0.285297	+	1.98428i
$34$	−0.626977	−	2.27556i	−0.107526	−	0.390255i
$35$	−5.26809	−	8.55221i	−0.890470	−	1.44559i
$36$	1.10861	+	0.366258i	0.184768	+	0.0610430i
$37$	−0.315022	+	0.202452i	−0.0517892	+	0.0332829i	−0.566279	−	0.824213i	$-0.691618\pi$
$37$	−0.315022	+	0.202452i	−0.0517892	+	0.0332829i	0.514490	+	0.857496i	$0.327981\pi$
$38$	1.66107	−	0.725223i	0.269461	−	0.117647i
$39$	6.12720	−	0.880959i	0.981138	−	0.141066i
$40$	5.05523	−	3.80061i	0.799302	−	0.600930i
$41$	7.33870	+	4.71629i	1.14611	+	0.736561i	0.968861	−	0.247604i	$-0.0796433\pi$
$41$	7.33870	+	4.71629i	1.14611	+	0.736561i	0.177251	+	0.984166i	$0.443280\pi$
$42$	12.0246	+	0.201355i	1.85543	+	0.0310698i
$43$	−1.62226	−	5.52493i	−0.247393	−	0.842543i	−0.985762	−	0.168146i	$-0.946222\pi$
$43$	−1.62226	−	5.52493i	−0.247393	−	0.842543i	0.738369	−	0.674397i	$-0.235596\pi$
$44$	−11.7818	+	3.03491i	−1.77618	+	0.457530i
$45$	1.08445	+	0.726576i	0.161661	+	0.108312i
$46$	−5.18996	+	4.36627i	−0.765217	+	0.643772i
$47$	6.84242			0.998070			0.499035	−	0.866582i	$-0.333688\pi$
$47$	6.84242			0.998070			0.499035	+	0.866582i	$0.333688\pi$
$48$	0.573621	+	7.55058i	0.0827951	+	1.08983i
$49$	12.6448	−	3.71285i	1.80640	−	0.530407i
$50$	6.58369	−	2.57972i	0.931075	−	0.364828i
$51$	2.65803	+	1.70821i	0.372198	+	0.239197i
$52$	3.34951	+	5.61693i	0.464493	+	0.778929i
$53$	0.507342	+	3.52864i	0.0696887	+	0.484696i	0.994539	+	0.104365i	$0.0332809\pi$
$53$	0.507342	+	3.52864i	0.0696887	+	0.484696i	−0.924850	+	0.380331i	$0.875810\pi$
$54$	5.92839	−	2.58834i	0.806751	−	0.352228i
$55$	−13.6000	−	0.259841i	−1.83382	−	0.0350370i
$56$	4.69109	+	11.8077i	0.626874	+	1.57788i
$57$	−1.00789	+	2.20696i	−0.133498	+	0.292319i
$58$	0.792136	+	2.87499i	0.104013	+	0.377505i
$59$	11.1053	+	1.59671i	1.44579	+	0.207873i	0.820110	−	0.572205i	$-0.193912\pi$
$59$	11.1053	+	1.59671i	1.44579	+	0.207873i	0.625681	+	0.780079i	$0.284821\pi$
$60$	−1.64370	+	8.30504i	−0.212201	+	1.07218i
$61$	2.55769	−	8.71069i	0.327479	−	1.11529i	−0.617067	−	0.786910i	$-0.711679\pi$
$61$	2.55769	−	8.71069i	0.327479	−	1.11529i	0.944546	−	0.328379i	$-0.106502\pi$
$62$	1.29208	−	1.44164i	0.164094	−	0.183089i
$63$	−1.98183	+	1.71727i	−0.249688	+	0.216355i
$64$	−7.12988	+	3.62834i	−0.891235	+	0.453543i
$65$	1.92556	+	7.05362i	0.238837	+	0.874894i
$66$	9.03312	−	13.5514i	1.11190	−	1.66807i
$67$	−14.2897	+	6.52589i	−1.74577	+	0.797265i	−0.755999	+	0.654573i	$0.772848\pi$
$67$	−14.2897	+	6.52589i	−1.74577	+	0.797265i	−0.989767	+	0.142692i	$0.954424\pi$
$68$	−0.585411	+	3.28631i	−0.0709915	+	0.398524i
$69$	1.27263	−	8.98928i	0.153206	−	1.08218i
$70$	1.51638	+	14.1240i	0.181242	+	1.68814i
$71$	9.93470	−	4.53703i	1.17903	−	0.538446i	0.273148	−	0.961972i	$-0.411935\pi$
$71$	9.93470	−	4.53703i	1.17903	−	0.538446i	0.905884	+	0.423526i	$0.139208\pi$
$72$	−1.19200	−	1.14257i	−0.140478	−	0.134653i
$73$	−5.89120	−	5.10476i	−0.689513	−	0.597467i	0.237996	−	0.971266i	$-0.423509\pi$
$73$	−5.89120	−	5.10476i	−0.689513	−	0.597467i	−0.927510	+	0.373799i	$0.878055\pi$
$74$	0.525374	−	0.0665796i	0.0610735	−	0.00773972i
$75$	−4.25810	+	8.45357i	−0.491683	+	0.976135i
$76$	−2.56180	−	0.0858202i	−0.293859	−	0.00984426i
$77$	7.69868	−	26.2193i	0.877346	−	2.98797i
$78$	−8.35720	−	2.60666i	−0.946266	−	0.295146i
$79$	0.0473234	−	0.329141i	0.00532429	−	0.0370313i	−0.986986	−	0.160806i	$-0.948591\pi$
$79$	0.0473234	−	0.329141i	0.00532429	−	0.0370313i	0.992310	+	0.123774i	$0.0394999\pi$
$80$	−8.76683	+	1.77275i	−0.980162	+	0.198200i
$81$	−4.32469	+	9.46975i	−0.480521	+	1.05219i
$82$	−6.49515	−	10.4887i	−0.717269	−	1.15828i
$83$	0.591417	+	0.920263i	0.0649165	+	0.101012i	0.872194	−	0.489160i	$-0.162696\pi$
$83$	0.591417	+	0.920263i	0.0649165	+	0.101012i	−0.807278	+	0.590172i	$0.799060\pi$
$84$	−15.2255	−	7.57928i	−1.66124	−	0.826967i
$85$	−1.61491	+	3.36455i	−0.175162	+	0.364937i
$86$	−1.29370	+	8.03987i	−0.139504	+	0.866961i
$87$	−3.35821	−	2.15819i	−0.360038	−	0.231382i
$88$	16.8864	+	3.30069i	1.80009	+	0.351855i
$89$	2.11466	+	7.20188i	0.224154	+	0.763397i	0.992380	+	0.123218i	$0.0393216\pi$
$89$	2.11466	+	7.20188i	0.224154	+	0.763397i	−0.768226	+	0.640179i	$0.778860\pi$
$90$	−0.941750	−	1.58777i	−0.0992692	−	0.167365i
$91$	−14.6886			−1.53979
$92$	9.28325	−	2.41272i	0.967846	−	0.251543i
$93$			2.59145i			0.268721i
$94$	−8.73365	−	4.16663i	−0.900807	−	0.429756i
$95$	−2.73378	−	0.859764i	−0.280480	−	0.0882099i
$96$	3.86570	−	9.98685i	0.394541	−	1.01928i
$97$	9.54731	+	6.13568i	0.969383	+	0.622984i	0.926579	−	0.376099i	$-0.122735\pi$
$97$	9.54731	+	6.13568i	0.969383	+	0.622984i	0.0428032	+	0.999084i	$0.486371\pi$
$98$	−18.4007	−	2.96087i	−1.85875	−	0.299093i
$99$	0.505391	+	3.51507i	0.0507937	+	0.353278i
$100$	−9.97431	−	0.716333i	−0.997431	−	0.0716333i
$101$	3.60221	−	2.31500i	0.358433	−	0.230351i	−0.349013	−	0.937118i	$-0.613483\pi$
$101$	3.60221	−	2.31500i	0.358433	−	0.230351i	0.707447	+	0.706767i	$0.249847\pi$
$102$	−2.35250	−	3.79894i	−0.232932	−	0.376151i
$103$	−0.0967008	−	0.0441618i	−0.00952822	−	0.00435139i	0.410645	−	0.911795i	$-0.365303\pi$
$103$	−0.0967008	−	0.0441618i	−0.00952822	−	0.00435139i	−0.420173	+	0.907444i	$0.638031\pi$
$104$	−0.854915	−	9.20909i	−0.0838313	−	0.903026i
$105$	−14.1302	−	12.7246i	−1.37897	−	1.24179i
$106$	1.50116	−	4.81289i	0.145806	−	0.467469i
$107$	1.90083	−	6.47365i	0.183761	−	0.625831i	−0.815154	−	0.579245i	$-0.803348\pi$
$107$	1.90083	−	6.47365i	0.183761	−	0.625831i	0.998914	−	0.0465863i	$-0.0148342\pi$
$108$	−9.14312	−	0.306294i	−0.879797	−	0.0294732i
$109$	1.10656	−	0.958842i	0.105989	−	0.0918404i	−0.600254	−	0.799809i	$-0.704934\pi$
$109$	1.10656	−	0.958842i	0.105989	−	0.0918404i	0.706243	+	0.707969i	$0.250388\pi$
$110$	17.2008	+	8.61327i	1.64003	+	0.821243i
$111$	−0.464229	+	0.535749i	−0.0440627	+	0.0508511i
$112$	1.20252	−	17.9280i	0.113628	−	1.69403i
$113$	4.43184	+	9.70438i	0.416913	+	0.912912i	0.995272	+	0.0971293i	$0.0309660\pi$
$113$	4.43184	+	9.70438i	0.416913	+	0.912912i	−0.578359	+	0.815782i	$0.696307\pi$
$114$	2.63037	−	2.20322i	0.246357	−	0.206350i
$115$	10.7223	+	0.181663i	0.999857	+	0.0169402i
$116$	0.739621	−	4.15200i	0.0686721	−	0.385503i
$117$	1.73638	−	0.792978i	0.160528	−	0.0733108i
$118$	−13.2025	−	8.80053i	−1.21539	−	0.810155i
$119$	−5.66612	−	4.90972i	−0.519412	−	0.450073i
$120$	7.15530	−	9.59962i	0.653186	−	0.876321i
$121$	−17.0300	−	19.6537i	−1.54818	−	1.78670i
$122$	−8.56893	+	9.56082i	−0.775794	+	0.865596i
$123$	15.8454	+	4.65264i	1.42873	+	0.419514i
$124$	−2.52708	+	1.05331i	−0.226938	+	0.0945897i
$125$	−10.5294	−	3.75916i	−0.941780	−	0.336229i
$126$	3.57532	−	0.985096i	0.318515	−	0.0877593i
$127$	7.64360	−	16.7371i	0.678259	−	1.48518i	−0.186217	−	0.982509i	$-0.559623\pi$
$127$	7.64360	−	16.7371i	0.678259	−	1.48518i	0.864477	−	0.502673i	$-0.167650\pi$
$128$	11.3100	−	0.289527i	0.999673	−	0.0255908i
$129$	−5.89337	−	9.17026i	−0.518882	−	0.807397i
$130$	1.83746	−	10.1758i	0.161156	−	0.892475i
$131$	−4.83574	+	0.695275i	−0.422501	+	0.0607465i	−0.350286	−	0.936643i	$-0.613916\pi$
$131$	−4.83574	+	0.695275i	−0.422501	+	0.0607465i	−0.0722146	+	0.997389i	$0.523007\pi$
$132$	−19.7819	+	11.7964i	−1.72179	+	1.02674i
$133$	3.11253	−	4.84319i	0.269891	−	0.419958i
$134$	22.2132	+	0.371967i	1.91893	+	0.0321331i
$135$	−9.75691	−	3.06852i	−0.839741	−	0.264096i
$136$	2.74839	−	3.83816i	0.235672	−	0.329119i
$137$	2.33927			0.199858			0.0999288	−	0.994995i	$-0.468138\pi$
$137$	2.33927			0.199858			0.0999288	+	0.994995i	$0.468138\pi$
$138$	−7.09833	+	10.6989i	−0.604250	+	0.910754i
$139$			14.3178i			1.21442i	0.794540	+	0.607212i	$0.207712\pi$
$139$			14.3178i			1.21442i	−0.794540	+	0.607212i	$0.792288\pi$
$140$	6.66518	−	18.9512i	0.563310	−	1.60167i
$141$	12.4286	−	3.64936i	1.04668	−	0.307332i
$142$	−15.4434	−	0.258604i	−1.29598	−	0.0217016i
$143$	−10.7542	+	16.7338i	−0.899310	+	1.39935i
$144$	0.825703	+	2.18423i	0.0688086	+	0.182019i
$145$	2.04032	−	4.25085i	0.169439	−	0.353014i
$146$	4.41102	+	10.1031i	0.365058	+	0.836138i
$147$	20.9878	−	13.4880i	1.73105	−	1.11248i
$148$	−0.711129	−	0.234940i	−0.0584545	−	0.0193120i
$149$	1.97648	+	0.902629i	0.161920	+	0.0739462i	0.494726	−	0.869049i	$-0.335268\pi$
$149$	1.97648	+	0.902629i	0.161920	+	0.0739462i	−0.332807	+	0.942995i	$0.607996\pi$
$150$	10.5828	−	8.19719i	0.864078	−	0.669297i
$151$	−4.48023	−	0.644159i	−0.364596	−	0.0524210i	−0.0424175	−	0.999100i	$-0.513506\pi$
$151$	−4.48023	−	0.644159i	−0.364596	−	0.0524210i	−0.322178	+	0.946679i	$0.604415\pi$
$152$	3.21762	+	1.66953i	0.260983	+	0.135417i
$153$	0.934861	+	0.274500i	0.0755791	+	0.0221920i
$154$	−25.7926	+	28.7782i	−2.07843	+	2.31901i
$155$	−3.03757	+	0.377664i	−0.243984	+	0.0303347i
$156$	9.07981	+	8.41617i	0.726966	+	0.673833i
$157$	−8.36438	+	9.65301i	−0.667550	+	0.770394i	−0.983991	−	0.178218i	$-0.942967\pi$
$157$	−8.36438	+	9.65301i	−0.667550	+	0.770394i	0.316441	+	0.948612i	$0.397512\pi$
$158$	−0.260831	+	0.391298i	−0.0207506	+	0.0311300i
$159$	2.80351	+	6.13884i	0.222333	+	0.486842i
$160$	12.2695	+	3.07575i	0.969986	+	0.243160i
$161$	−6.02470	+	20.6836i	−0.474813	+	1.63010i
$162$	11.2865	−	9.45368i	0.886755	−	0.742751i
$163$	−0.558151	−	1.22218i	−0.0437177	−	0.0957285i	0.886513	−	0.462704i	$-0.153121\pi$
$163$	−0.558151	−	1.22218i	−0.0437177	−	0.0957285i	−0.930231	+	0.366975i	$0.880393\pi$
$164$	1.90338	+	17.3429i	0.148629	+	1.35425i
$165$	−24.8417	+	6.78150i	−1.93392	+	0.527939i
$166$	−0.194497	−	1.53476i	−0.0150959	−	0.119120i
$167$	10.3269	+	11.9179i	0.799119	+	0.922232i	0.998333	−	0.0577238i	$-0.0183843\pi$
$167$	10.3269	+	11.9179i	0.799119	+	0.922232i	−0.199214	+	0.979956i	$0.563839\pi$
$168$	14.8185	+	18.9456i	1.14327	+	1.46169i
$169$	−2.21424	−	0.650159i	−0.170326	−	0.0500122i
$170$	4.11009	−	3.31112i	0.315229	−	0.253951i
$171$	−0.106476	+	0.740558i	−0.00814244	+	0.0566319i
$172$	6.54709	−	9.47427i	0.499211	−	0.722407i
$173$	−18.3413	−	8.37620i	−1.39446	−	0.636830i	−0.430434	−	0.902622i	$-0.641639\pi$
$173$	−18.3413	−	8.37620i	−1.39446	−	0.636830i	−0.964030	+	0.265792i	$0.914367\pi$
$174$	2.97220	+	4.79966i	0.225322	+	0.363861i
$175$	12.8558	−	18.4172i	0.971810	−	1.39221i
$176$	−19.5438	−	14.4958i	−1.47317	−	1.09266i
$177$	21.0233	−	3.02270i	1.58021	−	0.227200i
$178$	1.68637	−	10.4802i	0.126399	−	0.785521i
$179$	−0.253177	+	0.393952i	−0.0189234	+	0.0294453i	−0.850586	−	0.525835i	$-0.823753\pi$
$179$	−0.253177	+	0.393952i	−0.0189234	+	0.0294453i	0.831663	+	0.555281i	$0.187389\pi$
$180$	0.235189	+	2.60009i	0.0175300	+	0.193800i
$181$	0.502778	+	1.71230i	0.0373712	+	0.127274i	0.976066	−	0.217475i	$-0.0697821\pi$
$181$	0.502778	+	1.71230i	0.0373712	+	0.127274i	−0.938695	+	0.344749i	$0.887964\pi$
$182$	18.7485	+	8.94451i	1.38973	+	0.663011i
$183$		−	17.1862i		−	1.27044i
$184$	−13.3183	−	2.57337i	−0.981840	−	0.189711i
$185$	−0.695634	−	0.466070i	−0.0511440	−	0.0342662i
$186$	1.57804	−	3.30772i	0.115708	−	0.242534i
$187$	−9.74176	+	2.86044i	−0.712388	+	0.209176i
$188$	8.61037	+	10.6366i	0.627976	+	0.775751i
$189$	11.1087	−	17.2855i	0.808038	−	1.25733i
$190$	2.96584	+	2.76211i	0.215165	+	0.200385i
$191$	−1.97287	−	13.7216i	−0.142752	−	0.992863i	−0.927707	−	0.373310i	$-0.878223\pi$
$191$	−1.97287	−	13.7216i	−0.142752	−	0.992863i	0.784955	−	0.619553i	$-0.212686\pi$
$192$	−11.0156	+	10.3932i	−0.794980	+	0.750065i
$193$	−3.97523	−	6.18558i	−0.286143	−	0.445248i	0.668190	−	0.743990i	$-0.267069\pi$
$193$	−3.97523	−	6.18558i	−0.286143	−	0.445248i	−0.954334	+	0.298743i	$0.903433\pi$
$194$	−8.44989	−	13.6453i	−0.606667	−	0.979677i
$195$	7.25960	+	11.7852i	0.519871	+	0.843958i
$196$	21.6836	+	14.9842i	1.54883	+	1.07030i
$197$	−9.63211	−	1.38489i	−0.686259	−	0.0986692i	−0.209639	−	0.977779i	$-0.567229\pi$
$197$	−9.63211	−	1.38489i	−0.686259	−	0.0986692i	−0.476620	+	0.879110i	$0.658138\pi$
$198$	1.49539	−	4.79438i	0.106273	−	0.340722i
$199$	6.71471	+	1.97162i	0.475993	+	0.139764i	0.510925	−	0.859626i	$-0.329303\pi$
$199$	6.71471	+	1.97162i	0.475993	+	0.139764i	−0.0349315	+	0.999390i	$0.511121\pi$
$200$	12.2950	+	6.98810i	0.869386	+	0.494133i
$201$	−22.4753	+	19.4750i	−1.58529	+	1.37366i
$202$	−6.00755	+	0.761324i	−0.422690	+	0.0535666i
$203$	7.15870	+	6.20305i	0.502442	+	0.435369i
$204$	0.689391	+	6.28148i	0.0482670	+	0.439792i
$205$	−3.14437	+	19.2513i	−0.219612	+	1.34457i
$206$	0.0965367	+	0.115253i	0.00672603	+	0.00803007i
$207$	−0.404427	−	2.77031i	−0.0281096	−	0.192550i
$208$	−4.51659	+	12.2751i	−0.313169	+	0.851122i
$209$	−3.23873	−	7.09182i	−0.224027	−	0.490552i
$210$	10.2873	+	24.8461i	0.709891	+	1.71454i
$211$	13.6298	+	11.8103i	0.938312	+	0.813052i	0.982556	−	0.185969i	$-0.0595424\pi$
$211$	13.6298	+	11.8103i	0.938312	+	0.813052i	−0.0442439	+	0.999021i	$0.514088\pi$
$212$	−4.84685	+	5.22903i	−0.332883	+	0.359131i
$213$	15.6256	−	13.5397i	1.07065	−	0.927723i
$214$	−6.36829	+	7.10545i	−0.435327	+	0.485718i
$215$	9.89007	−	8.24435i	0.674497	−	0.562260i
$216$	11.4837	+	5.95858i	0.781370	+	0.405430i
$217$	0.875122	−	6.08661i	0.0594071	−	0.413186i
$218$	−1.99629	+	0.550031i	−0.135206	+	0.0372528i
$219$	−13.4234	−	6.13026i	−0.907068	−	0.414244i
$220$	−16.7101	−	21.4682i	−1.12659	−	1.44739i
$221$	2.95057	+	4.59118i	0.198477	+	0.308836i
$222$	0.918781	−	0.401140i	0.0616646	−	0.0269228i
$223$	0.435878	+	3.03159i	0.0291885	+	0.203011i	0.999197	−	0.0400592i	$-0.0127547\pi$
$223$	0.435878	+	3.03159i	0.0291885	+	0.203011i	−0.970009	+	0.243070i	$0.921846\pi$
$224$	−12.4520	+	22.1509i	−0.831983	+	1.48002i
$225$	−0.525454	+	2.87118i	−0.0350303	+	0.191412i
$226$	0.252609	−	15.0854i	0.0168033	−	1.00346i
$227$	3.90040	+	13.2835i	0.258879	+	0.881659i	0.981669	+	0.190592i	$0.0610409\pi$
$227$	3.90040	+	13.2835i	0.258879	+	0.881659i	−0.722791	+	0.691067i	$0.757141\pi$
$228$	−4.69903	+	1.21044i	−0.311201	+	0.0801631i
$229$		−	10.4747i		−	0.692190i	−0.938200	−	0.346095i	$-0.887508\pi$
$229$		−	10.4747i		−	0.692190i	0.938200	−	0.346095i	$-0.112492\pi$
$230$	−13.5753	−	6.76111i	−0.895125	−	0.445814i
$231$		−	51.7308i		−	3.40364i
$232$	−3.47237	+	4.84921i	−0.227972	+	0.318366i
$233$	−8.18562	−	27.8777i	−0.536258	−	1.82633i	−0.562680	−	0.826675i	$-0.690230\pi$
$233$	−8.18562	−	27.8777i	−0.536258	−	1.82633i	0.0264220	−	0.999651i	$-0.491589\pi$
$234$	−2.69919	−	0.0451987i	−0.176451	−	0.00295473i
$235$	6.08888	+	14.0364i	0.397195	+	0.915631i
$236$	11.4927	+	19.2725i	0.748108	+	1.25454i
$237$	−0.0895872	−	0.623092i	−0.00581931	−	0.0404742i
$238$	4.24249	+	9.71709i	0.275000	+	0.629865i
$239$	6.88921	+	10.7198i	0.445626	+	0.693407i	0.989301	−	0.145888i	$-0.0466041\pi$
$239$	6.88921	+	10.7198i	0.445626	+	0.693407i	−0.543675	+	0.839296i	$0.682968\pi$
$240$	−14.9786	+	7.89577i	−0.966865	+	0.509669i
$241$	8.61171	+	3.93284i	0.554729	+	0.253336i	0.672997	−	0.739645i	$-0.265007\pi$
$241$	8.61171	+	3.93284i	0.554729	+	0.253336i	−0.118268	+	0.992982i	$0.537734\pi$
$242$	9.76912	+	35.4562i	0.627983	+	2.27921i
$243$	−0.851845	+	5.92471i	−0.0546459	+	0.380071i
$244$	16.7593	−	6.98543i	1.07291	−	0.447196i
$245$	18.8687	+	22.6352i	1.20548	+	1.44611i
$246$	−17.3919	−	15.5876i	−1.10887	−	0.993826i
$247$	−3.16717	+	2.74437i	−0.201522	+	0.174620i
$248$	3.86696	+	0.194405i	0.245552	+	0.0123448i
$249$	1.56507	+	1.35614i	0.0991822	+	0.0859418i
$250$	11.1506	+	11.2100i	0.705227	+	0.708982i
$251$	−1.67211	−	3.66141i	−0.105543	−	0.231106i	0.849491	−	0.527603i	$-0.176909\pi$
$251$	−1.67211	−	3.66141i	−0.105543	−	0.231106i	−0.955034	+	0.296497i	$0.904182\pi$
$252$	−5.16340	−	0.919789i	−0.325264	−	0.0579412i
$253$	19.1526	+	22.0069i	1.20411	+	1.38356i
$254$	−19.9482	+	16.7087i	−1.25166	+	1.04840i
$255$	−1.13887	+	6.97269i	−0.0713188	+	0.436647i
$256$	−14.6124	−	6.51758i	−0.913273	−	0.407349i
$257$	19.1374	+	16.5827i	1.19376	+	1.03440i	0.998561	+	0.0536348i	$0.0170807\pi$
$257$	19.1374	+	16.5827i	1.19376	+	1.03440i	0.195199	+	0.980764i	$0.437465\pi$
$258$	1.93813	+	15.2936i	0.120663	+	0.952139i
$259$	1.27127	−	1.10156i	0.0789928	−	0.0684476i
$260$	−8.54179	+	11.8694i	−0.529739	+	0.736111i
$261$	−1.18112	−	0.346810i	−0.0731098	−	0.0214670i
$262$	6.59571	+	2.05724i	0.407484	+	0.127097i
$263$	−1.15052	−	0.165419i	−0.0709438	−	0.0102002i	0.106752	−	0.994286i	$-0.465955\pi$
$263$	−1.15052	−	0.165419i	−0.0709438	−	0.0102002i	−0.177695	+	0.984086i	$0.556864\pi$
$264$	32.4329	−	3.01087i	1.99610	−	0.185306i
$265$	−6.78708	+	4.18078i	−0.416927	+	0.256823i
$266$	−6.92204	+	4.28649i	−0.424418	+	0.262821i
$267$	7.68215	+	11.9537i	0.470140	+	0.731552i
$268$	−28.1264	−	14.0013i	−1.71809	−	0.855268i
$269$	2.69963	+	18.7764i	0.164599	+	1.14481i	0.889825	+	0.456303i	$0.150827\pi$
$269$	2.69963	+	18.7764i	0.164599	+	1.14481i	−0.725225	+	0.688512i	$0.758264\pi$
$270$	10.5851	+	9.85804i	0.644192	+	0.599941i
$271$	−10.9180	+	16.9888i	−0.663223	+	1.03200i	0.332808	+	0.942994i	$0.392004\pi$
$271$	−10.9180	+	16.9888i	−0.663223	+	1.03200i	−0.996032	+	0.0890008i	$0.971633\pi$
$272$	−5.84525	+	3.22540i	−0.354420	+	0.195569i
$273$	−26.6804	+	7.83408i	−1.61477	+	0.474140i
$274$	−2.98584	−	1.42448i	−0.180381	−	0.0860560i
$275$	−11.5692	−	28.1299i	−0.697651	−	1.69630i
$276$	15.5753	−	9.33363i	0.937524	−	0.561819i
$277$			8.45102i			0.507773i	0.967234	+	0.253886i	$0.0817089\pi$
$277$			8.45102i			0.507773i	−0.967234	+	0.253886i	$0.918291\pi$
$278$	8.71873	−	18.2753i	0.522915	−	1.09608i
$279$	0.225140	+	0.766757i	0.0134788	+	0.0459046i
$280$	−20.0476	+	20.1306i	−1.19807	+	1.20303i
$281$	12.4431	−	19.3618i	0.742290	−	1.15503i	−0.240562	−	0.970634i	$-0.577332\pi$
$281$	12.4431	−	19.3618i	0.742290	−	1.15503i	0.982853	−	0.184393i	$-0.0590318\pi$
$282$	−18.0861	−	2.91025i	−1.07701	−	0.173303i
$283$	12.8930	−	1.85374i	0.766412	−	0.110193i	0.251989	−	0.967730i	$-0.418915\pi$
$283$	12.8930	−	1.85374i	0.766412	−	0.110193i	0.514423	+	0.857537i	$0.328006\pi$
$284$	19.5545	+	9.73422i	1.16034	+	0.577620i
$285$	−5.42419	−	0.103634i	−0.321301	−	0.00613877i
$286$	23.9165	−	14.8104i	1.41421	−	0.875755i
$287$	−35.6454	−	16.2787i	−2.10408	−	0.960902i
$288$	0.276142	−	3.29075i	0.0162718	−	0.193909i
$289$	2.02292	−	14.0697i	0.118995	−	0.827629i
$290$	−5.19278	+	4.18334i	−0.304930	+	0.245654i
$291$	20.6142	+	6.05287i	1.20843	+	0.354826i
$292$	0.521984	−	15.5816i	0.0305468	−	0.911845i
$293$	−2.92845	−	3.37962i	−0.171082	−	0.197439i	0.663733	−	0.747969i	$-0.268971\pi$
$293$	−2.92845	−	3.37962i	−0.171082	−	0.197439i	−0.834815	+	0.550530i	$0.814426\pi$
$294$	−35.0022	+	4.43576i	−2.04137	+	0.258699i
$295$	6.60689	+	24.2020i	0.384668	+	1.40910i
$296$	0.764619	+	0.732913i	0.0444426	+	0.0425997i
$297$	−11.5591	−	25.3109i	−0.670726	−	1.46869i
$298$	−1.97313	−	2.35567i	−0.114300	−	0.136461i
$299$	8.44973	−	13.2108i	0.488661	−	0.763999i
$300$	−18.4994	+	4.01859i	−1.06806	+	0.232013i
$301$	10.7452	+	23.5286i	0.619340	+	1.35617i
$302$	5.32629	+	3.55040i	0.306494	+	0.204303i
$303$	5.30837	−	6.12619i	0.304958	−	0.351940i
$304$	−3.09031	−	4.09032i	−0.177242	−	0.234596i
$305$	20.1449	−	2.50463i	1.15349	−	0.143415i
$306$	−1.02610	−	0.919647i	−0.0586582	−	0.0525727i
$307$	13.6163	+	3.99811i	0.777125	+	0.228184i	0.646159	−	0.763203i	$-0.276374\pi$
$307$	13.6163	+	3.99811i	0.777125	+	0.228184i	0.130965	+	0.991387i	$0.458192\pi$
$308$	50.4458	−	21.0262i	2.87442	−	1.19808i
$309$	−0.199201	−	0.0286408i	−0.0113322	−	0.00162932i
$310$	4.10712	+	1.36765i	0.233269	+	0.0776776i
$311$	0.777922	+	0.355265i	0.0441119	+	0.0201452i	0.437349	−	0.899292i	$-0.355918\pi$
$311$	0.777922	+	0.355265i	0.0441119	+	0.0201452i	−0.393237	+	0.919437i	$0.628645\pi$
$312$	−6.46448	−	16.2715i	−0.365979	−	0.921190i
$313$	22.2818	−	14.3197i	1.25944	−	0.809396i	0.271236	−	0.962513i	$-0.412568\pi$
$313$	22.2818	−	14.3197i	1.25944	−	0.809396i	0.988208	+	0.153117i	$0.0489312\pi$
$314$	16.5544	−	7.22766i	0.934218	−	0.407880i
$315$	−5.28634	−	2.53733i	−0.297851	−	0.142962i
$316$	0.571202	−	0.340621i	0.0321326	−	0.0191614i
$317$	2.72977	−	4.24761i	0.153319	−	0.238569i	−0.756094	−	0.654463i	$-0.772895\pi$
$317$	2.72977	−	4.24761i	0.153319	−	0.238569i	0.909413	+	0.415894i	$0.136531\pi$
$318$	0.159796	−	9.54277i	0.00896094	−	0.535132i
$319$	12.3080	−	3.61394i	0.689113	−	0.202342i
$320$	−13.7878	−	11.3973i	−0.770759	−	0.637127i
$321$		−	12.7725i		−	0.712894i
$322$	20.2850	−	22.7318i	1.13044	−	1.26679i
$323$	−2.13905			−0.119020
$324$	−20.1629	+	5.19380i	−1.12016	+	0.288545i
$325$	−12.7561	+	10.2269i	−0.707581	+	0.567285i
$326$	−0.0318138	+	1.89987i	−0.00176200	+	0.105224i
$327$	1.49857	−	2.33182i	0.0828711	−	0.128950i
$328$	8.13135	−	23.2955i	0.448979	−	1.28628i
$329$	−30.4237	+	4.37427i	−1.67731	+	0.241161i
$330$	35.8374	+	6.47123i	1.97278	+	0.356230i
$331$	−9.48606	−	14.7606i	−0.521401	−	0.811316i	0.476286	−	0.879290i	$-0.341983\pi$
$331$	−9.48606	−	14.7606i	−0.521401	−	0.811316i	−0.997687	+	0.0679746i	$0.978346\pi$
$332$	−0.686324	+	2.07740i	−0.0376669	+	0.114012i
$333$	−0.0908111	+	0.198849i	−0.00497642	+	0.0108968i
$334$	−5.92393	−	21.5004i	−0.324143	−	1.17645i
$335$	−26.1030	−	23.5063i	−1.42616	−	1.28429i
$336$	−7.37750	−	33.2058i	−0.402476	−	1.81152i
$337$	−28.9629	−	8.50426i	−1.57771	−	0.463257i	−0.628474	−	0.777830i	$-0.716320\pi$
$337$	−28.9629	−	8.50426i	−1.57771	−	0.463257i	−0.949233	+	0.314573i	$0.898139\pi$
$338$	2.43034	+	2.17820i	0.132193	+	0.118479i
$339$	13.2258	+	15.2634i	0.718326	+	0.828992i
$340$	−7.26238	+	1.72350i	−0.393858	+	0.0934699i
$341$	−6.29338	−	5.45324i	−0.340806	−	0.295310i
$342$	0.586863	−	0.880409i	0.0317339	−	0.0476071i
$343$	−25.2466	+	11.5297i	−1.36319	+	0.622548i
$344$	−14.1260	+	8.10615i	−0.761621	+	0.437054i
$345$	19.5728	−	5.38868i	1.05377	−	0.290117i
$346$	18.3102	+	21.8601i	0.984362	+	1.17521i
$347$	−3.56860	−	7.81415i	−0.191573	−	0.419485i	0.789334	−	0.613964i	$-0.210426\pi$
$347$	−3.56860	−	7.81415i	−0.191573	−	0.419485i	−0.980907	+	0.194478i	$0.937699\pi$
$348$	−0.870992	−	7.93617i	−0.0466901	−	0.425423i
$349$	4.17906	−	4.82289i	0.223700	−	0.258164i	−0.632794	−	0.774320i	$-0.718092\pi$
$349$	4.17906	−	4.82289i	0.223700	−	0.258164i	0.856494	+	0.516156i	$0.172638\pi$
$350$	−27.6242	+	15.6792i	−1.47657	+	0.838088i
$351$	−11.3037	+	9.79472i	−0.603348	+	0.522804i
$352$	16.1186	+	30.4034i	0.859122	+	1.62051i
$353$	−4.86773	+	16.5780i	−0.259083	+	0.882357i	0.722508	+	0.691363i	$0.242989\pi$
$353$	−4.86773	+	16.5780i	−0.259083	+	0.882357i	−0.981591	+	0.190994i	$0.938829\pi$
$354$	−28.6748	−	8.94382i	−1.52405	−	0.475359i
$355$	18.1477	+	16.3424i	0.963182	+	0.867364i
$356$	−8.53429	+	12.3499i	−0.452316	+	0.654546i
$357$	−12.9105	−	5.89604i	−0.683297	−	0.312051i
$358$	0.563049	−	0.348669i	0.0297580	−	0.0184277i
$359$	−2.33429	+	1.50016i	−0.123199	+	0.0791754i	−0.600789	−	0.799408i	$-0.705147\pi$
$359$	−2.33429	+	1.50016i	−0.123199	+	0.0791754i	0.477590	+	0.878583i	$0.341511\pi$
$360$	1.28311	−	3.46197i	0.0676259	−	0.182462i
$361$	2.47022	+	17.1808i	0.130012	+	0.904252i
$362$	0.400949	−	2.49174i	0.0210734	−	0.130963i
$363$	−41.4155	−	26.6161i	−2.17375	−	1.39698i
$364$	−18.4839	−	22.8335i	−0.968818	−	1.19680i
$365$	5.22934	−	16.6276i	0.273716	−	0.870330i
$366$	−10.4654	+	21.9365i	−0.547036	+	1.14664i
$367$			8.83132i			0.460991i	0.973073	+	0.230495i	$0.0740347\pi$
$367$			8.83132i			0.460991i	−0.973073	+	0.230495i	$0.925965\pi$
$368$	15.4324	+	11.3947i	0.804472	+	0.593991i
$369$	5.09255			0.265108
$370$	0.604095	+	1.01849i	0.0314054	+	0.0529488i
$371$	−4.51163	−	15.3652i	−0.234232	−	0.797721i
$372$	−4.02842	+	3.26103i	−0.208864	+	0.169077i
$373$	10.0484	+	6.45774i	0.520288	+	0.334369i	0.774286	−	0.632836i	$-0.218109\pi$
$373$	10.0484	+	6.45774i	0.520288	+	0.334369i	−0.253998	+	0.967205i	$0.581746\pi$
$374$	14.1762	+	2.28110i	0.733033	+	0.117953i
$375$	−21.1306	−	1.21234i	−1.09118	−	0.0626050i
$376$	−4.51321	−	18.8197i	−0.232751	−	0.970551i
$377$	−3.72782	−	5.80060i	−0.191992	−	0.298746i
$378$	−24.7049	+	15.2986i	−1.27068	+	0.786873i
$379$	−5.92045	+	12.9640i	−0.304113	+	0.665915i	−0.998561	−	0.0536283i	$-0.982921\pi$
$379$	−5.92045	+	12.9640i	−0.304113	+	0.665915i	0.694448	+	0.719543i	$0.255649\pi$
$380$	−2.10363	−	5.33157i	−0.107914	−	0.273504i
$381$	4.95719	−	34.4780i	0.253965	−	1.76636i
$382$	−5.83751	+	18.7156i	−0.298673	+	0.957575i
$383$	3.50773	−	11.9462i	0.179237	−	0.610425i	−0.820037	−	0.572311i	$-0.806047\pi$
$383$	3.50773	−	11.9462i	0.179237	−	0.610425i	0.999273	−	0.0381135i	$-0.0121348\pi$
$384$	20.3891	−	6.55802i	1.04048	−	0.334662i
$385$	60.6364	−	7.53897i	3.09032	−	0.384221i
$386$	1.30732	+	10.3159i	0.0665407	+	0.525068i
$387$	−2.54042	−	2.20129i	−0.129137	−	0.111898i
$388$	2.47621	+	22.5623i	0.125711	+	1.14543i
$389$	29.5929	−	13.5146i	1.50042	−	0.685218i	0.515286	−	0.857018i	$-0.327686\pi$
$389$	29.5929	−	13.5146i	1.50042	−	0.685218i	0.985132	+	0.171800i	$0.0549584\pi$
$390$	−2.08962	−	19.4633i	−0.105812	−	0.985563i
$391$	7.67522	−	2.27169i	0.388153	−	0.114884i
$392$	−18.5524	−	32.3298i	−0.937037	−	1.63290i
$393$	−8.41283	+	3.84201i	−0.424371	+	0.193804i
$394$	11.4511	+	7.63306i	0.576897	+	0.384548i
$395$	0.717303	−	0.195816i	0.0360914	−	0.00985256i
$396$	−4.82821	+	5.20892i	−0.242627	+	0.261758i
$397$	−18.5241	+	16.0512i	−0.929698	+	0.805588i	−0.981182	−	0.193086i	$-0.938150\pi$
$397$	−18.5241	+	16.0512i	−0.929698	+	0.805588i	0.0514836	+	0.998674i	$0.483605\pi$
$398$	−7.37004	−	6.60543i	−0.369427	−	0.331100i
$399$	3.07052	−	10.4572i	0.153718	−	0.523516i
$400$	−11.4379	−	16.4065i	−0.571897	−	0.820326i
$401$	−0.734264	−	0.105571i	−0.0366674	−	0.00527198i	0.123957	−	0.992288i	$-0.460442\pi$
$401$	−0.734264	−	0.105571i	−0.0366674	−	0.00527198i	−0.160624	+	0.987016i	$0.551351\pi$
$402$	40.5466	−	11.1716i	2.02228	−	0.557191i
$403$	−1.85947	+	4.07168i	−0.0926270	+	0.202825i
$404$	8.13162	+	2.68650i	0.404563	+	0.133658i
$405$	−23.2744	−	0.444680i	−1.15651	−	0.0220963i
$406$	−5.36005	−	12.2768i	−0.266015	−	0.609287i
$407$	−0.324188	−	2.25478i	−0.0160694	−	0.111765i
$408$	2.94512	−	8.43747i	0.145805	−	0.417717i
$409$	5.70096	+	3.66378i	0.281894	+	0.181163i	0.673946	−	0.738781i	$-0.264598\pi$
$409$	5.70096	+	3.66378i	0.281894	+	0.181163i	−0.392051	+	0.919943i	$0.628234\pi$
$410$	15.7364	−	22.6576i	0.777164	−	1.11898i
$411$	4.24906	−	1.24764i	0.209591	−	0.0615414i
$412$	−0.0530368	−	0.205894i	−0.00261294	−	0.0101437i
$413$	−50.3988			−2.47997
$414$	−1.17075	+	3.78229i	−0.0575390	+	0.185889i
$415$	−1.36152	+	2.03213i	−0.0668342	+	0.0997535i
$416$	13.2398	−	12.9175i	0.649132	−	0.633333i
$417$	7.63633	+	26.0070i	0.373953	+	1.27357i
$418$	−0.184603	+	11.0242i	−0.00902923	+	0.539210i
$419$	31.6826	+	20.3612i	1.54780	+	0.994709i	0.985868	+	0.167525i	$0.0535773\pi$
$419$	31.6826	+	20.3612i	1.54780	+	0.994709i	0.561930	+	0.827185i	$0.310059\pi$
$420$	1.99914	−	37.9778i	0.0975480	−	1.85313i
$421$	−2.20646	+	0.317242i	−0.107536	+	0.0154614i	−0.195873	−	0.980629i	$-0.562754\pi$
$421$	−2.20646	+	0.317242i	−0.107536	+	0.0154614i	0.0883365	+	0.996091i	$0.471845\pi$
$422$	−10.2052	−	23.3743i	−0.496783	−	1.13784i
$423$	3.36032	−	2.15954i	0.163384	−	0.105001i
$424$	9.37068	−	3.72288i	0.455080	−	0.180799i
$425$	−8.33902	−	0.318766i	−0.404502	−	0.0154624i
$426$	−28.1894	+	7.76692i	−1.36578	+	0.376308i
$427$	−5.80372	+	40.3658i	−0.280862	+	1.95344i
$428$	12.4553	−	5.19146i	0.602048	−	0.250939i
$429$	−10.6090	+	36.1311i	−0.512209	+	1.74442i
$430$	−17.6440	+	4.50059i	−0.850869	+	0.217038i
$431$	−3.56189	−	4.11064i	−0.171570	−	0.198003i	0.663452	−	0.748219i	$-0.269091\pi$
$431$	−3.56189	−	4.11064i	−0.171570	−	0.198003i	−0.835022	+	0.550216i	$0.814545\pi$
$432$	−11.0294	−	14.5984i	−0.530652	−	0.702368i
$433$	15.0512	−	17.3700i	0.723313	−	0.834748i	−0.268388	−	0.963311i	$-0.586491\pi$
$433$	15.0512	−	17.3700i	0.723313	−	0.834748i	0.991701	+	0.128563i	$0.0410364\pi$
$434$	−4.82339	+	7.23603i	−0.231530	+	0.347341i
$435$	1.43887	−	8.80945i	0.0689887	−	0.422381i
$436$	2.88300	+	0.513567i	0.138071	+	0.0245954i
$437$	2.56540	+	5.58545i	0.122720	+	0.267188i
$438$	13.4006	+	15.9987i	0.640306	+	0.764447i
$439$	30.0998	−	13.7461i	1.43658	−	0.656066i	0.463411	−	0.886143i	$-0.346625\pi$
$439$	30.0998	−	13.7461i	1.43658	−	0.656066i	0.973172	+	0.230078i	$0.0738980\pi$
$440$	8.25578	+	37.5774i	0.393579	+	1.79143i
$441$	5.03805	−	5.81422i	0.239907	−	0.276868i
$442$	−0.970342	−	7.65689i	−0.0461545	−	0.364201i
$443$	0.954204	+	1.10121i	0.0453356	+	0.0523201i	0.777964	−	0.628308i	$-0.216252\pi$
$443$	0.954204	+	1.10121i	0.0453356	+	0.0523201i	−0.732629	+	0.680628i	$0.761707\pi$
$444$	−1.41700	−	0.0474695i	−0.0672479	−	0.00225280i
$445$	−12.8919	+	10.7467i	−0.611137	+	0.509443i
$446$	1.28971	−	4.13494i	0.0610696	−	0.195795i
$447$	4.07150	+	0.585393i	0.192575	+	0.0276881i
$448$	29.3823	−	20.6909i	1.38818	−	0.977552i
$449$	1.47815	−	3.23671i	0.0697584	−	0.152750i	−0.871541	−	0.490323i	$-0.836879\pi$
$449$	1.47815	−	3.23671i	0.0697584	−	0.152750i	0.941299	+	0.337573i	$0.109606\pi$
$450$	2.41907	−	3.34479i	0.114036	−	0.157675i
$451$	−44.6429	+	28.6902i	−2.10215	+	1.35097i
$452$	−9.50855	+	19.1011i	−0.447244	+	0.898441i
$453$	−8.48145	+	1.21945i	−0.398493	+	0.0572947i
$454$	3.11044	−	19.3302i	0.145980	−	0.907211i
$455$	−13.0710	−	30.1318i	−0.612778	−	1.41260i
$456$	6.73492	+	1.31644i	0.315391	+	0.0616479i
$457$	−0.527601	+	0.154918i	−0.0246801	+	0.00724674i	−0.294049	−	0.955790i	$-0.595003\pi$
$457$	−0.527601	+	0.154918i	−0.0246801	+	0.00724674i	0.269369	+	0.963037i	$0.413185\pi$
$458$	−6.37850	+	13.3699i	−0.298048	+	0.624735i
$459$	−7.63431			−0.356339
$460$	13.2103	+	16.8964i	0.615933	+	0.787798i
$461$	−28.0466			−1.30626			−0.653131	−	0.757245i	$-0.726545\pi$
$461$	−28.0466			−1.30626			−0.653131	+	0.757245i	$0.726545\pi$
$462$	−31.5010	+	66.0291i	−1.46556	+	3.07195i
$463$	−17.4327	+	5.11870i	−0.810167	+	0.237886i	−0.660477	−	0.750847i	$-0.729646\pi$
$463$	−17.4327	+	5.11870i	−0.810167	+	0.237886i	−0.149690	+	0.988733i	$0.547828\pi$
$464$	7.38501	−	4.07505i	0.342841	−	0.189179i
$465$	−5.31603	+	2.30606i	−0.246525	+	0.106941i
$466$	−6.52776	+	40.5675i	−0.302393	+	1.87925i
$467$	24.4600	−	3.51682i	1.13187	−	0.162739i	0.449178	−	0.893442i	$-0.351717\pi$
$467$	24.4600	−	3.51682i	1.13187	−	0.162739i	0.682695	+	0.730703i	$0.260808\pi$
$468$	3.41771	+	1.70134i	0.157984	+	0.0786444i
$469$	59.3650	−	38.1516i	2.74122	−	1.76168i
$470$	0.775486	−	21.6237i	0.0357705	−	0.997428i
$471$	−10.0447	+	21.9948i	−0.462836	+	1.01347i
$472$	−2.93334	−	31.5978i	−0.135018	−	1.45441i
$473$	34.6717	+	4.98504i	1.59421	+	0.229212i
$474$	−0.265078	+	0.849867i	−0.0121754	+	0.0390357i
$475$	−0.669016	−	6.37307i	−0.0306966	−	0.292417i
$476$	0.502040	−	14.9863i	0.0230110	−	0.686896i
$477$	1.36283	+	1.57279i	0.0623998	+	0.0720133i
$478$	−2.26562	−	17.8779i	−0.103627	−	0.817715i
$479$	6.95803	−	8.03000i	0.317921	−	0.366900i	−0.574186	−	0.818725i	$-0.694681\pi$
$479$	6.95803	−	8.03000i	0.317921	−	0.366900i	0.892107	+	0.451825i	$0.149227\pi$
$480$	23.9267	−	0.957038i	1.09210	−	0.0436826i
$481$	−1.11382	+	0.508664i	−0.0507858	+	0.0231931i
$482$	−8.59710	−	10.2639i	−0.391587	−	0.467508i
$483$	0.0881991	+	40.7830i	0.00401320	+	1.85569i
$484$	9.12147	−	51.2050i	0.414612	−	2.32750i
$485$	−4.09068	+	25.0451i	−0.185748	+	1.13724i
$486$	4.69510	−	7.04357i	0.212974	−	0.319503i
$487$	−1.26532	+	1.46025i	−0.0573370	+	0.0661704i	−0.783694	−	0.621148i	$-0.786667\pi$
$487$	−1.26532	+	1.46025i	−0.0573370	+	0.0661704i	0.726357	+	0.687318i	$0.241212\pi$
$488$	−25.6453	−	1.28928i	−1.16091	−	0.0583629i
$489$	−1.66567	−	1.92228i	−0.0753241	−	0.0869286i
$490$	−10.3004	−	40.3815i	−0.465325	−	1.82425i
$491$	−10.6209	+	36.1716i	−0.479316	+	1.63240i	0.264766	+	0.964313i	$0.414705\pi$
$491$	−10.6209	+	36.1716i	−0.479316	+	1.63240i	−0.744082	+	0.668088i	$0.767113\pi$
$492$	12.7070	+	30.4866i	0.572878	+	1.37444i
$493$	0.500867	−	3.48361i	0.0225579	−	0.156894i
$494$	5.71374	−	1.57429i	0.257073	−	0.0708304i
$495$	−6.76098	+	4.16471i	−0.303883	+	0.187190i
$496$	−4.81739	−	2.60289i	−0.216307	−	0.116873i
$497$	−41.2726	+	26.5243i	−1.85133	+	1.18978i
$498$	−1.17184	−	2.68401i	−0.0525114	−	0.120273i
$499$	9.32542	−	1.34079i	0.417463	−	0.0600221i	0.0696170	−	0.997574i	$-0.477822\pi$
$499$	9.32542	−	1.34079i	0.417463	−	0.0600221i	0.347846	+	0.937552i	$0.386913\pi$
$500$	−7.40640	−	21.0985i	−0.331224	−	0.943552i
$501$	25.1141	+	16.1399i	1.12202	+	0.721076i
$502$	−0.0953080	+	5.69163i	−0.00425380	+	0.254030i
$503$	9.35984	+	31.8767i	0.417334	+	1.42131i	0.853334	+	0.521364i	$0.174577\pi$
$503$	9.35984	+	31.8767i	0.417334	+	1.42131i	−0.436000	+	0.899947i	$0.643605\pi$
$504$	6.03045	+	4.31822i	0.268618	+	0.192349i
$505$	7.95443	+	5.32942i	0.353968	+	0.237156i
$506$	−11.0454	−	39.7524i	−0.491028	−	1.76721i
$507$	−4.36871			−0.194021
$508$	35.6365	−	9.17970i	1.58111	−	0.407283i
$509$	−20.9462	+	6.15035i	−0.928423	+	0.272609i	−0.710776	−	0.703418i	$-0.751656\pi$
$509$	−20.9462	+	6.15035i	−0.928423	+	0.272609i	−0.217646	+	0.976028i	$0.569838\pi$
$510$	5.69961	−	8.20641i	0.252383	−	0.363386i
$511$	29.4577	+	18.9313i	1.30313	+	0.837472i
$512$	14.6824	+	17.2171i	0.648875	+	0.760895i
$513$	−0.834290	−	5.80262i	−0.0368348	−	0.256192i
$514$	−14.3291	−	32.8196i	−0.632028	−	1.44761i
$515$	0.00454087	−	0.237668i	0.000200095	−	0.0104729i
$516$	6.83910	−	20.7009i	0.301075	−	0.911308i
$517$	−17.2912	+	37.8625i	−0.760467	+	1.66519i
$518$	−2.29343	+	0.631900i	−0.100767	+	0.0277641i
$519$	−37.7826	−	5.43232i	−1.65847	−	0.238452i
$520$	18.1305	−	9.94866i	0.795075	−	0.436278i
$521$	2.20302	−	7.50280i	0.0965161	−	0.328704i	−0.897054	−	0.441921i	$-0.854297\pi$
$521$	2.20302	−	7.50280i	0.0965161	−	0.328704i	0.993570	+	0.113217i	$0.0361155\pi$
$522$	1.29640	+	1.16190i	0.0567418	+	0.0508551i
$523$	8.62249	−	7.47143i	0.377035	−	0.326703i	−0.445642	−	0.895211i	$-0.647025\pi$
$523$	8.62249	−	7.47143i	0.377035	−	0.326703i	0.822678	+	0.568508i	$0.192479\pi$
$524$	−7.16601	−	6.64226i	−0.313049	−	0.290168i
$525$	13.5287	−	40.3096i	0.590440	−	1.75926i
$526$	1.36778	+	0.911737i	0.0596382	+	0.0397536i
$527$	−2.07826	+	0.949111i	−0.0905305	+	0.0413439i
$528$	−43.2307	−	15.9067i	−1.88137	−	0.692248i
$529$	−15.1368	−	17.3169i	−0.658123	−	0.752910i
$530$	11.2089	−	1.20341i	0.486882	−	0.0522726i
$531$	5.95777	−	2.72082i	0.258545	−	0.118074i
$532$	11.4455	−	1.25614i	0.496225	−	0.0544606i
$533$	21.5578	+	18.6800i	0.933774	+	0.809119i
$534$	−2.52640	−	19.9356i	−0.109328	−	0.862698i
$535$	14.9714	−	1.86140i	0.647268	−	0.0804754i
$536$	27.3745	+	34.9986i	1.18240	+	1.51171i
$537$	−0.249760	+	0.850606i	−0.0107780	+	0.0367063i
$538$	7.98790	−	25.6100i	0.344383	−	1.10413i
$539$	−11.4092	+	79.3525i	−0.491427	+	3.41795i
$540$	−7.50789	−	19.0285i	−0.323088	−	0.818857i
$541$	−4.05376	+	8.87649i	−0.174285	+	0.381630i	−0.976535	−	0.215357i	$-0.930908\pi$
$541$	−4.05376	+	8.87649i	−0.174285	+	0.381630i	0.802251	+	0.596987i	$0.203636\pi$
$542$	24.2809	−	15.0360i	1.04295	−	0.645851i
$543$	1.82649	+	2.84208i	0.0783823	+	0.121965i
$544$	9.42494	−	0.557484i	0.404091	−	0.0239019i
$545$	2.95164	+	1.41672i	0.126434	+	0.0606858i
$546$	38.8253	+	6.24742i	1.66157	+	0.267365i
$547$	−24.5377	−	15.7694i	−1.04916	−	0.674251i	−0.101921	−	0.994793i	$-0.532499\pi$
$547$	−24.5377	−	15.7694i	−1.04916	−	0.674251i	−0.947235	+	0.320541i	$0.896135\pi$
$548$	2.94370	+	3.63641i	0.125748	+	0.155340i
$549$	−1.49311	−	5.08506i	−0.0637243	−	0.217025i
$550$	−2.36252	+	42.9499i	−0.100738	+	1.83139i
$551$	2.70252			0.115131
$552$	−25.5639	+	2.42897i	−1.08807	+	0.103384i
$553$			1.49373i			0.0635197i
$554$	5.14618	−	10.7869i	0.218640	−	0.458290i
$555$	−1.51213	−	0.475559i	−0.0641862	−	0.0201863i
$556$	−22.2571	+	18.0173i	−0.943912	+	0.764103i
$557$	12.3771	+	7.95428i	0.524434	+	0.337034i	0.775924	−	0.630827i	$-0.217284\pi$
$557$	12.3771	+	7.95428i	0.524434	+	0.337034i	−0.251490	+	0.967860i	$0.580920\pi$
$558$	0.179542	−	1.11578i	0.00760062	−	0.0472349i
$559$	−2.67960	−	18.6370i	−0.113335	−	0.788263i
$560$	37.8470	−	13.4868i	1.59933	−	0.569920i
$561$	−16.1693	+	10.3914i	−0.682670	+	0.438726i
$562$	−27.6725	+	17.1362i	−1.16729	+	0.722848i
$563$	39.3175	+	17.9557i	1.65703	+	0.756742i	0.999996	+	0.00288536i	$0.000918440\pi$
$563$	39.3175	+	17.9557i	1.65703	+	0.756742i	0.657039	+	0.753857i	$0.271809\pi$
$564$	21.3128	+	14.7280i	0.897432	+	0.620160i
$565$	−15.9635	+	17.7270i	−0.671591	+	0.745781i
$566$	−17.5855	−	5.48500i	−0.739172	−	0.230552i
$567$	13.1751	−	44.8704i	0.553304	−	1.88438i
$568$	−19.0317	−	24.3322i	−0.798552	−	1.02096i
$569$	−4.49805	+	3.89758i	−0.188568	+	0.163395i	−0.744029	−	0.668148i	$-0.767087\pi$
$569$	−4.49805	+	3.89758i	−0.188568	+	0.163395i	0.555461	+	0.831543i	$0.312542\pi$
$570$	6.86031	+	3.43529i	0.287347	+	0.143889i
$571$	11.7414	−	13.5503i	0.491361	−	0.567060i	−0.454868	−	0.890559i	$-0.650314\pi$
$571$	11.7414	−	13.5503i	0.491361	−	0.567060i	0.946229	+	0.323498i	$0.104859\pi$
$572$	−39.5457	+	4.34012i	−1.65349	+	0.181470i
$573$	−10.9019	−	23.8718i	−0.455433	−	0.997259i
$574$	35.5849	+	42.4841i	1.48529	+	1.77325i
$575$	9.16879	+	22.1570i	0.382365	+	0.924011i
$576$	−2.35634	+	4.03215i	−0.0981809	+	0.168006i
$577$	3.72264	−	1.70007i	0.154976	−	0.0707750i	−0.336417	−	0.941713i	$-0.609215\pi$
$577$	3.72264	−	1.70007i	0.154976	−	0.0707750i	0.491393	+	0.870938i	$0.336488\pi$
$578$	−11.1497	+	16.7267i	−0.463765	+	0.695738i
$579$	−10.5197	−	9.11534i	−0.437182	−	0.378820i
$580$	9.17546	−	2.17751i	0.380990	−	0.0904161i
$581$	−3.21795	−	3.71372i	−0.133503	−	0.154071i
$582$	−22.6260	−	20.2787i	−0.937880	−	0.840579i
$583$	−20.8078	−	6.10971i	−0.861770	−	0.253038i
$584$	−10.1546	+	19.5705i	−0.420198	+	0.809832i
$585$	3.17185	+	2.85631i	0.131140	+	0.118094i
$586$	1.67988	+	6.09699i	0.0693953	+	0.251864i
$587$	−8.98282	+	19.6696i	−0.370760	+	0.811852i	0.628656	+	0.777684i	$0.283606\pi$
$587$	−8.98282	+	19.6696i	−0.370760	+	0.811852i	−0.999416	+	0.0341684i	$0.989122\pi$
$588$	47.3779	+	15.6525i	1.95383	+	0.645499i
$589$	−0.948506	−	1.47590i	−0.0390825	−	0.0608136i
$590$	6.30461	−	34.9146i	0.259557	−	1.43741i
$591$	−18.2344	+	2.62171i	−0.750063	+	0.107843i
$592$	−0.529656	−	1.40110i	−0.0217687	−	0.0575847i
$593$	3.65914	−	5.69373i	0.150263	−	0.233813i	−0.757959	−	0.652302i	$-0.773804\pi$
$593$	3.65914	−	5.69373i	0.150263	−	0.233813i	0.908222	+	0.418488i	$0.137440\pi$
$594$	−0.658853	+	39.3455i	−0.0270330	+	1.61437i
$595$	5.02954	−	15.9923i	0.206191	−	0.655622i
$596$	1.08403	+	4.20830i	0.0444034	+	0.172378i
$597$	13.2482			0.542211
$598$	−18.8298	+	11.7168i	−0.770008	+	0.479136i
$599$		−	35.7925i		−	1.46244i	−0.682142	−	0.731220i	$-0.738951\pi$
$599$		−	35.7925i		−	1.46244i	0.682142	−	0.731220i	$-0.261049\pi$
$600$	26.0597	+	6.13575i	1.06388	+	0.250491i
$601$	7.16410	−	2.10357i	0.292230	−	0.0858064i	−0.132332	−	0.991205i	$-0.542246\pi$
$601$	7.16410	−	2.10357i	0.292230	−	0.0858064i	0.424562	+	0.905399i	$0.360428\pi$
$602$	0.612459	−	36.5750i	0.0249620	−	1.49069i
$603$	−4.95804	+	7.71486i	−0.201907	+	0.314173i
$604$	−4.63648	−	7.77512i	−0.188656	−	0.316365i
$605$	25.1625	−	52.4242i	1.02300	−	2.13135i
$606$	−10.5061	+	4.58696i	−0.426780	+	0.186333i
$607$	21.6587	−	13.9192i	0.879101	−	0.564964i	−0.0214228	−	0.999771i	$-0.506820\pi$
$607$	21.6587	−	13.9192i	0.879101	−	0.564964i	0.900524	+	0.434807i	$0.143183\pi$
$608$	1.45370	+	7.10269i	0.0589553	+	0.288052i
$609$	16.3114	+	7.44918i	0.660973	+	0.301856i
$610$	−27.2380	−	9.07015i	−1.10284	−	0.367240i
$611$	22.1463	+	3.18416i	0.895945	+	0.128817i
$612$	0.749700	+	1.79867i	0.0303048	+	0.0727069i
$613$	22.7945	+	6.69305i	0.920659	+	0.270330i	0.707521	−	0.706692i	$-0.249813\pi$
$613$	22.7945	+	6.69305i	0.920659	+	0.270330i	0.213138	+	0.977022i	$0.431632\pi$
$614$	−14.9452	−	13.3947i	−0.603140	−	0.540567i
$615$	4.55612	+	36.6451i	0.183720	+	1.47767i
$616$	−77.1927	−	3.88074i	−3.11018	−	0.156360i
$617$	−24.3596	+	28.1125i	−0.980682	+	1.13177i	0.0105915	+	0.999944i	$0.496629\pi$
$617$	−24.3596	+	28.1125i	−0.980682	+	1.13177i	−0.991273	+	0.131823i	$0.957917\pi$
$618$	0.236819	+	0.157859i	0.00952626	+	0.00635001i
$619$	−17.9678	−	39.3441i	−0.722188	−	1.58137i	−0.810812	−	0.585306i	$-0.800974\pi$
$619$	−17.9678	−	39.3441i	−0.722188	−	1.58137i	0.0886241	−	0.996065i	$-0.471753\pi$
$620$	−4.40950	−	4.24667i	−0.177090	−	0.170550i
$621$	9.15598	+	19.9346i	0.367417	+	0.799948i
$622$	−0.776602	−	0.927168i	−0.0311389	−	0.0371761i
$623$	−14.0066	−	30.6701i	−0.561161	−	1.22877i
$624$	−1.65712	+	24.7053i	−0.0663377	+	0.989005i
$625$	−1.65841	−	24.9449i	−0.0663363	−	0.997797i
$626$	−37.1603	+	4.70925i	−1.48523	+	0.188219i
$627$	−9.66521	−	11.1543i	−0.385991	−	0.445458i
$628$	−25.5312	−	0.855295i	−1.01881	−	0.0341300i
$629$	−0.599677	−	0.176081i	−0.0239107	−	0.00702081i
$630$	5.20238	+	6.45771i	0.207268	+	0.257281i
$631$	5.62327	−	39.1107i	0.223859	−	1.55697i	−0.499386	−	0.866380i	$-0.666441\pi$
$631$	5.62327	−	39.1107i	0.223859	−	1.55697i	0.723245	−	0.690592i	$-0.242650\pi$
$632$	−0.936498	+	0.0869387i	−0.0372519	+	0.00345824i
$633$	31.0561	+	14.1828i	1.23437	+	0.563717i
$634$	−6.07082	+	3.75936i	−0.241103	+	0.149303i
$635$	41.1359	+	0.785942i	1.63243	+	0.0311891i
$636$	−6.01495	+	12.0831i	−0.238508	+	0.479125i
$637$	42.6542	−	6.13275i	1.69002	−	0.242989i
$638$	−17.9105	−	2.88200i	−0.709084	−	0.114099i
$639$	3.44700	−	5.36364i	0.136361	−	0.212182i
$640$	10.6584	+	22.9434i	0.421310	+	0.906917i
$641$	−2.17703	−	7.41430i	−0.0859877	−	0.292847i	0.905261	−	0.424856i	$-0.139675\pi$
$641$	−2.17703	−	7.41430i	−0.0859877	−	0.292847i	−0.991249	+	0.132009i	$0.957857\pi$
$642$	−7.77773	+	16.3028i	−0.306963	+	0.643422i
$643$		−	22.9582i		−	0.905384i	−0.891667	−	0.452692i	$-0.850464\pi$
$643$		−	22.9582i		−	0.905384i	0.891667	−	0.452692i	$-0.149536\pi$
$644$	−39.7341	+	16.6624i	−1.56574	+	0.656592i
$645$	13.5673	−	20.2499i	0.534211	−	0.797337i
$646$	2.73028	+	1.30256i	0.107421	+	0.0512484i
$647$	4.42414	−	1.29904i	0.173931	−	0.0510707i	−0.193607	−	0.981079i	$-0.562019\pi$
$647$	4.42414	−	1.29904i	0.173931	−	0.0510707i	0.367538	+	0.930008i	$0.380201\pi$
$648$	28.8985	+	5.64864i	1.13524	+	0.221900i
$649$	−36.8992	+	57.4163i	−1.44842	+	2.25379i
$650$	22.5094	−	5.28583i	0.882892	−	0.207327i
$651$	−1.65668	−	11.5225i	−0.0649304	−	0.451601i
$652$	1.19752	−	2.40561i	0.0468983	−	0.0942111i
$653$	−4.05179	−	6.30470i	−0.158559	−	0.246722i	0.752880	−	0.658158i	$-0.228664\pi$
$653$	−4.05179	−	6.30470i	−0.158559	−	0.246722i	−0.911439	+	0.411435i	$0.865028\pi$
$654$	−3.33271	+	2.06379i	−0.130319	+	0.0807005i
$655$	−5.72946	−	9.30120i	−0.223869	−	0.363428i
$656$	−24.5644	+	24.7828i	−0.959080	+	0.967606i
$657$	−4.50429	−	0.647619i	−0.175729	−	0.0252660i
$658$	41.4964	+	12.9430i	1.61770	+	0.504569i
$659$	−27.4194	−	8.05105i	−1.06811	−	0.313624i	−0.299995	−	0.953941i	$-0.596985\pi$
$659$	−27.4194	−	8.05105i	−1.06811	−	0.313624i	−0.768111	+	0.640316i	$0.778803\pi$
$660$	−41.8021	−	30.0827i	−1.62715	−	1.17097i
$661$	23.8783	−	20.6906i	0.928757	−	0.804773i	−0.0522718	−	0.998633i	$-0.516646\pi$
$661$	23.8783	−	20.6906i	0.928757	−	0.804773i	0.981029	+	0.193860i	$0.0621008\pi$
$662$	3.11964	+	24.6168i	0.121248	+	0.956761i
$663$	7.80810	+	6.76576i	0.303241	+	0.262760i
$664$	2.14104	−	2.23366i	0.0830884	−	0.0866827i
$665$	12.7049	+	2.07514i	0.492676	+	0.0804703i
$666$	0.236998	−	0.198511i	0.00918350	−	0.00769215i
$667$	−9.69704	+	2.87010i	−0.375471	+	0.111131i
$668$	−5.53120	+	31.0504i	−0.214009	+	1.20138i
$669$	2.40861	+	5.27412i	0.0931223	+	0.203909i
$670$	19.0039	+	45.8986i	0.734185	+	1.77322i
$671$	41.7371	+	36.1654i	1.61124	+	1.39615i
$672$	−10.8037	+	46.8762i	−0.416763	+	1.80829i
$673$	−30.2892	+	26.2458i	−1.16756	+	1.01170i	−0.167900	+	0.985804i	$0.553698\pi$
$673$	−30.2892	+	26.2458i	−1.16756	+	1.01170i	−0.999665	+	0.0258961i	$0.991756\pi$
$674$	31.7895	+	28.4915i	1.22449	+	1.09745i
$675$	−2.38773	−	22.7456i	−0.0919039	−	0.875480i
$676$	−1.77568	−	4.26019i	−0.0682954	−	0.163853i
$677$	0.321350	−	2.23504i	0.0123505	−	0.0858996i	−0.982714	−	0.185131i	$-0.940729\pi$
$677$	0.321350	−	2.23504i	0.0123505	−	0.0858996i	0.995064	+	0.0992310i	$0.0316383\pi$
$678$	−7.58686	−	27.5359i	−0.291371	−	1.05751i
$679$	−46.3731	−	21.1779i	−1.77963	−	0.812732i
$680$	10.3192	+	2.22250i	0.395723	+	0.0852288i
$681$	14.1694	+	22.0480i	0.542972	+	0.844881i
$682$	4.71215	+	10.7928i	0.180437	+	0.413278i
$683$	−6.07497	−	42.2523i	−0.232452	−	1.61674i	−0.687439	−	0.726242i	$-0.741265\pi$
$683$	−6.07497	−	42.2523i	−0.232452	−	1.61674i	0.454986	−	0.890498i	$-0.349644\pi$
$684$	−1.28519	+	0.766386i	−0.0491404	+	0.0293035i
$685$	2.08165	+	4.79872i	0.0795359	+	0.183350i
$686$	39.2457	+	0.657180i	1.49841	+	0.0250913i
$687$	−5.58663	−	19.0263i	−0.213143	−	0.725899i
$688$	22.9665	−	1.74478i	0.875590	−	0.0665189i
$689$			11.6570i			0.444095i
$690$	−28.2641	−	5.04062i	−1.07600	−	0.191893i
$691$			17.3578i			0.660324i	0.943924	+	0.330162i	$0.107103\pi$
$691$			17.3578i			0.660324i	−0.943924	+	0.330162i	$0.892897\pi$
$692$	−10.0595	−	39.0521i	−0.382406	−	1.48454i
$693$	−4.49428	−	15.3061i	−0.170723	−	0.581431i
$694$	−0.203406	+	12.1470i	−0.00772117	+	0.461095i
$695$	−29.3712	+	12.7411i	−1.11411	+	0.483296i
$696$	−3.72093	+	10.6601i	−0.141041	+	0.404070i
$697$	2.07207	+	14.4116i	0.0784852	+	0.545877i
$698$	−8.27100	+	3.61113i	−0.313062	+	0.136683i
$699$	−29.7367	−	46.2713i	−1.12475	−	1.75014i
$700$	44.8071	−	3.19139i	1.69355	−	0.120623i
$701$	−42.8431	−	19.5658i	−1.61816	−	0.738990i	−0.619231	−	0.785209i	$-0.712556\pi$
$701$	−42.8431	−	19.5658i	−1.61816	−	0.738990i	−0.998931	+	0.0462186i	$0.985283\pi$
$702$	20.3924	−	5.61866i	0.769663	−	0.212063i
$703$	0.0683003	−	0.475039i	0.00257599	−	0.0179164i
$704$	−2.05976	−	48.6221i	−0.0776302	−	1.83252i
$705$	18.5461	+	22.2482i	0.698485	+	0.837915i
$706$	16.3082	−	18.1959i	0.613766	−	0.684812i
$707$	−14.5367	+	12.5961i	−0.546709	+	0.473726i
$708$	31.1542	+	28.8771i	1.17085	+	1.08527i
$709$	−2.57781	−	2.23369i	−0.0968119	−	0.0838879i	0.605110	−	0.796142i	$-0.293129\pi$
$709$	−2.57781	−	2.23369i	−0.0968119	−	0.0838879i	−0.701922	+	0.712254i	$0.747675\pi$
$710$	−13.2122	−	31.9103i	−0.495844	−	1.19757i
$711$	−0.0806401	−	0.176577i	−0.00302424	−	0.00662216i
$712$	18.4135	−	10.5666i	0.690076	−	0.395998i
$713$	4.97080	+	4.28844i	0.186158	+	0.160603i
$714$	12.8886	+	15.3874i	0.482344	+	0.575860i
$715$	−43.8972	−	7.16985i	−1.64166	−	0.268137i
$716$	−0.930993	+	0.102176i	−0.0347928	+	0.00381850i
$717$	18.2309	+	15.7972i	0.680846	+	0.589956i
$718$	3.89299	−	0.493351i	0.145285	−	0.0184117i
$719$	−34.4457	+	29.8474i	−1.28461	+	1.11312i	−0.297220	+	0.954809i	$0.596059\pi$
$719$	−34.4457	+	29.8474i	−1.28461	+	1.11312i	−0.987389	+	0.158311i	$0.949395\pi$
$720$	−3.74590	+	3.63751i	−0.139601	+	0.135562i
$721$	0.458197	+	0.134539i	0.0170641	+	0.00501048i
$722$	7.30910	−	23.4337i	0.272017	−	0.872113i
$723$	17.7399	+	2.55061i	0.659754	+	0.0948582i
$724$	−2.02909	+	2.93630i	−0.0754107	+	0.109127i
$725$	10.5357	+	0.402737i	0.391286	+	0.0149573i
$726$	36.6550	+	59.1924i	1.36039	+	2.19684i
$727$	−12.3913	−	19.2812i	−0.459567	−	0.715100i	0.531706	−	0.846929i	$-0.321551\pi$
$727$	−12.3913	−	19.2812i	−0.459567	−	0.715100i	−0.991272	+	0.131829i	$0.957915\pi$
$728$	9.68850	+	40.4002i	0.359080	+	1.49733i
$729$	−2.83210	−	19.6977i	−0.104893	−	0.729544i
$730$	−16.8000	+	18.0391i	−0.621795	+	0.667657i
$731$	5.19584	−	8.08488i	0.192175	−	0.299030i
$732$	26.7161	−	21.6268i	0.987454	−	0.799351i
$733$	19.7763	−	5.80684i	0.730454	−	0.214481i	0.104703	−	0.994504i	$-0.466611\pi$
$733$	19.7763	−	5.80684i	0.730454	−	0.214481i	0.625751	+	0.780023i	$0.284793\pi$
$734$	5.37776	−	11.2723i	0.198497	−	0.416067i
$735$	46.3455	+	31.0512i	1.70948	+	1.14534i
$736$	−12.7592	−	23.9417i	−0.470311	−	0.882501i
$737$		−	95.5633i		−	3.52012i
$738$	−6.50012	−	3.10107i	−0.239273	−	0.114152i
$739$	5.72024	+	19.4813i	0.210422	+	0.716633i	0.995288	+	0.0969662i	$0.0309139\pi$
$739$	5.72024	+	19.4813i	0.210422	+	0.716633i	−0.784865	+	0.619666i	$0.787268\pi$
$740$	−0.150865	−	1.66786i	−0.00554589	−	0.0613117i
$741$	−4.28917	+	6.67408i	−0.157567	+	0.245178i
$742$	−3.59787	+	22.3594i	−0.132082	+	0.820839i
$743$	−40.8898	+	5.87907i	−1.50010	+	0.215682i	−0.842915	−	0.538046i	$-0.819163\pi$
$743$	−40.8898	+	5.87907i	−1.50010	+	0.215682i	−0.657186	+	0.753728i	$0.728253\pi$
$744$	7.12764	−	1.70930i	0.261312	−	0.0626660i
$745$	−0.0928115	+	4.85772i	−0.00340035	+	0.177973i
$746$	−8.89341	−	14.3615i	−0.325611	−	0.525814i
$747$	0.580891	+	0.265284i	0.0212537	+	0.00970623i
$748$	−16.7054	−	11.5441i	−0.610810	−	0.422093i
$749$	−4.31323	+	29.9992i	−0.157602	+	1.09615i
$750$	26.2328	+	14.4147i	0.957886	+	0.526351i
$751$	29.3781	+	8.62620i	1.07202	+	0.314775i	0.769684	−	0.638425i	$-0.220414\pi$
$751$	29.3781	+	8.62620i	1.07202	+	0.314775i	0.302340	+	0.953200i	$0.402232\pi$
$752$	−5.69945	+	26.7697i	−0.207837	+	0.976190i
$753$	−4.99001	−	5.75878i	−0.181846	−	0.209862i
$754$	1.22595	+	9.67389i	0.0446465	+	0.352302i
$755$	−2.66542	−	9.76383i	−0.0970045	−	0.355342i
$756$	40.8492	−	4.48319i	1.48567	−	0.163052i
$757$	1.00727	+	2.20562i	0.0366100	+	0.0801646i	0.927053	−	0.374929i	$-0.122333\pi$
$757$	1.00727	+	2.20562i	0.0366100	+	0.0801646i	−0.890443	+	0.455094i	$0.849606\pi$
$758$	15.4511	−	12.9420i	0.561211	−	0.470074i
$759$	46.5261	+	29.7585i	1.68879	+	1.08017i
$760$	−0.561555	+	8.08619i	−0.0203697	+	0.293317i
$761$	−17.2330	−	37.7350i	−0.624695	−	1.36789i	−0.912055	−	0.410069i	$-0.865505\pi$
$761$	−17.2330	−	37.7350i	−0.624695	−	1.36789i	0.287359	−	0.957823i	$-0.407223\pi$
$762$	−27.3225	+	40.9890i	−0.989788	+	1.48488i
$763$	−4.30718	+	4.97075i	−0.155930	+	0.179953i
$764$	18.8477	−	20.3339i	0.681886	−	0.735654i
$765$	0.268805	+	2.16202i	0.00971868	+	0.0781680i
$766$	−11.7518	+	13.1122i	−0.424611	+	0.473761i
$767$	35.2007	+	10.3359i	1.27103	+	0.373207i
$768$	−30.0180	−	4.04513i	−1.08318	−	0.145966i
$769$	−52.2853	−	7.51750i	−1.88546	−	0.271088i	−0.899354	−	0.437220i	$-0.855963\pi$
$769$	−52.2853	−	7.51750i	−1.88546	−	0.271088i	−0.986103	+	0.166133i	$0.946872\pi$
$770$	−81.9869	−	27.3013i	−2.95460	−	0.983870i
$771$	43.6055	+	19.9140i	1.57041	+	0.717184i
$772$	4.61315	−	13.9633i	0.166031	−	0.502551i
$773$	−15.6718	+	10.0717i	−0.563677	+	0.362253i	−0.791236	−	0.611511i	$-0.790562\pi$
$773$	−15.6718	+	10.0717i	−0.563677	+	0.362253i	0.227559	+	0.973764i	$0.426926\pi$
$774$	1.90213	+	4.35669i	0.0683708	+	0.156598i
$775$	−3.47778	−	5.89512i	−0.124926	−	0.211759i
$776$	10.5785	−	30.3064i	0.379747	−	1.08794i
$777$	1.72162	−	2.67890i	0.0617629	−	0.0961050i
$778$	−46.0019	−	0.770315i	−1.64925	−	0.0276171i
$779$	−10.7274	+	3.14984i	−0.384347	+	0.112855i
$780$	−9.18483	+	26.1154i	−0.328870	+	0.935081i
$781$			66.4389i			2.37737i
$782$	−11.1800	−	1.77418i	−0.399794	−	0.0634446i
$783$	9.64536			0.344697
$784$	3.99324	+	52.5630i	0.142616	+	1.87725i
$785$	−27.2451	−	8.56851i	−0.972421	−	0.305823i
$786$	13.0777	+	0.218990i	0.466465	+	0.00781110i
$787$	−9.53963	+	14.8440i	−0.340051	+	0.529130i	−0.968595	−	0.248644i	$-0.920015\pi$
$787$	−9.53963	+	14.8440i	−0.340051	+	0.529130i	0.628544	+	0.777774i	$0.283651\pi$
$788$	−9.96804	−	16.7159i	−0.355097	−	0.595478i
$789$	−2.17802	+	0.313153i	−0.0775397	+	0.0111485i
$790$	−1.03480	−	0.186857i	−0.0368167	−	0.00664806i
$791$	−25.9094	−	40.3158i	−0.921231	−	1.43346i
$792$	9.33464	−	3.70856i	0.331692	−	0.131778i
$793$	12.3318	−	27.0030i	0.437917	−	0.958904i
$794$	33.4184	−	9.20765i	1.18597	−	0.326767i
$795$	−10.0983	+	11.2138i	−0.358149	+	0.397714i
$796$	5.38477	+	12.9191i	0.190858	+	0.457905i
$797$	−39.8744	−	11.7082i	−1.41243	−	0.414726i	−0.515493	−	0.856894i	$-0.672391\pi$
$797$	−39.8744	−	11.7082i	−1.41243	−	0.414726i	−0.896932	+	0.442168i	$0.854209\pi$
$798$	−10.2870	+	11.4778i	−0.364157	+	0.406310i
$799$	7.47861	+	8.63077i	0.264574	+	0.305335i
$800$	4.60874	+	27.9063i	0.162944	+	0.986635i
$801$	3.31150	+	2.86943i	0.117006	+	0.101386i
$802$	0.872926	+	0.581875i	0.0308241	+	0.0205467i
$803$	43.1346	−	19.6989i	1.52219	−	0.695159i
$804$	−58.5564	−	10.4310i	−2.06512	−	0.367874i
$805$	−47.7910	+	6.04687i	−1.68441	+	0.213124i
$806$	4.85284	−	4.06477i	0.170934	−	0.143175i
$807$	14.9179	+	32.6656i	0.525134	+	1.14988i
$808$	−8.74327	−	8.38072i	−0.307587	−	0.294833i
$809$	−23.4166	+	27.0243i	−0.823286	+	0.950122i	−0.999413	−	0.0342451i	$-0.989097\pi$
$809$	−23.4166	+	27.0243i	−0.823286	+	0.950122i	0.176128	+	0.984367i	$0.443643\pi$
$810$	29.4366	+	14.7403i	1.03430	+	0.517923i
$811$	6.66214	−	5.77278i	0.233939	−	0.202710i	−0.530000	−	0.847998i	$-0.677808\pi$
$811$	6.66214	−	5.77278i	0.233939	−	0.202710i	0.763939	+	0.645288i	$0.223263\pi$
$812$	−0.634289	+	18.9340i	−0.0222592	+	0.664454i
$813$	−10.7707	+	36.6815i	−0.377744	+	1.28648i
$814$	−0.959235	+	3.07540i	−0.0336212	+	0.107793i
$815$	2.01046	−	2.23256i	0.0704234	−	0.0782031i
$816$	−8.89707	+	8.97616i	−0.311460	+	0.314228i
$817$	6.71289	+	3.06567i	0.234854	+	0.107254i
$818$	−5.04566	−	8.14800i	−0.176417	−	0.284888i
$819$	−7.21359	+	4.63589i	−0.252063	+	0.161991i
$820$	−33.8830	+	19.3375i	−1.18325	+	0.675296i
$821$	−4.13238	−	28.7413i	−0.144221	−	1.00308i	−0.925460	−	0.378846i	$-0.876321\pi$
$821$	−4.13238	−	28.7413i	−0.144221	−	1.00308i	0.781239	−	0.624232i	$-0.214588\pi$
$822$	−6.18323	−	0.994950i	−0.215665	−	0.0347028i
$823$	16.6489	+	10.6996i	0.580345	+	0.372965i	0.797633	−	0.603143i	$-0.206085\pi$
$823$	16.6489	+	10.6996i	0.580345	+	0.372965i	−0.217289	+	0.976107i	$0.569721\pi$
$824$	−0.0576814	+	0.295099i	−0.00200943	+	0.0102803i
$825$	−36.0173	−	44.9248i	−1.25396	−	1.56408i
$826$	64.3290	+	30.6900i	2.23829	+	1.06784i
$827$			13.9649i			0.485607i	0.970075	+	0.242804i	$0.0780671\pi$
$827$			13.9649i			0.485607i	−0.970075	+	0.242804i	$0.921933\pi$
$828$	3.79753	−	4.11479i	0.131973	−	0.142999i
$829$	42.8180			1.48713			0.743565	−	0.668663i	$-0.233133\pi$
$829$	42.8180			1.48713			0.743565	+	0.668663i	$0.233133\pi$
$830$	2.97529	−	1.76473i	0.103274	−	0.0612545i
$831$	4.50730	+	15.3505i	0.156357	+	0.532502i
$832$	−24.7652	+	8.42564i	−0.858579	+	0.292106i
$833$	18.5037	+	11.8916i	0.641116	+	0.412020i
$834$	6.08972	−	37.8453i	0.210870	−	1.31048i
$835$	−15.2584	+	31.7897i	−0.528038	+	1.10013i
$836$	6.94871	−	13.9588i	0.240326	−	0.482776i
$837$	−3.38524	−	5.26754i	−0.117011	−	0.182073i
$838$	−28.0409	−	45.2818i	−0.968655	−	1.56424i
$839$	12.5691	−	27.5225i	0.433934	−	0.950182i	−0.558739	−	0.829344i	$-0.688715\pi$
$839$	12.5691	−	27.5225i	0.433934	−	0.950182i	0.992672	−	0.120838i	$-0.0385582\pi$
$840$	−25.6780	+	47.2574i	−0.885974	+	1.63054i
$841$	3.49432	−	24.3036i	0.120494	−	0.838054i
$842$	3.00951	+	0.938681i	0.103714	+	0.0323491i
$843$	12.2751	−	41.8052i	0.422777	−	1.43985i
$844$	−1.20765	+	36.0493i	−0.0415691	+	1.24087i
$845$	−0.636671	−	5.12079i	−0.0219022	−	0.176160i
$846$	−5.60414	+	0.710200i	−0.192674	+	0.0244172i
$847$	88.2856	+	76.4999i	3.03353	+	2.62857i
$848$	−14.2277	−	0.954328i	−0.488582	−	0.0327718i
$849$	22.4303	−	10.2436i	0.769805	−	0.351558i
$850$	10.4498	+	5.48485i	0.358425	+	0.188129i
$851$	0.259424	+	1.77704i	0.00889294	+	0.0609163i
$852$	40.7104	+	7.25201i	1.39472	+	0.248450i
$853$	13.2815	−	6.06547i	0.454751	−	0.207678i	−0.174852	−	0.984595i	$-0.555945\pi$
$853$	13.2815	−	6.06547i	0.454751	−	0.207678i	0.629603	+	0.776917i	$0.283217\pi$
$854$	31.9883	−	47.9887i	1.09462	−	1.64214i
$855$	−1.61391	+	0.440580i	−0.0551946	+	0.0150675i
$856$	−19.0592	−	0.958170i	−0.651429	−	0.0327496i
$857$	−4.71668	+	4.08703i	−0.161119	+	0.139610i	−0.731689	−	0.681639i	$-0.761268\pi$
$857$	−4.71668	+	4.08703i	−0.161119	+	0.139610i	0.570570	+	0.821249i	$0.306722\pi$
$858$	35.5430	−	39.6573i	1.21342	−	1.35388i
$859$	−7.54162	+	25.6844i	−0.257317	+	0.876341i	0.724942	+	0.688810i	$0.241867\pi$
$859$	−7.54162	+	25.6844i	−0.257317	+	0.876341i	−0.982259	+	0.187531i	$0.939952\pi$
$860$	25.2613	+	4.99962i	0.861404	+	0.170486i
$861$	−73.4285	−	10.5574i	−2.50244	−	0.359796i
$862$	2.04325	+	7.41579i	0.0695933	+	0.252583i
$863$	11.6917	−	25.6012i	0.397989	−	0.871474i	−0.599482	−	0.800389i	$-0.704627\pi$
$863$	11.6917	−	25.6012i	0.397989	−	0.871474i	0.997470	−	0.0710851i	$-0.0226462\pi$
$864$	5.18829	+	25.3497i	0.176509	+	0.862413i
$865$	0.861270	−	45.0786i	0.0292841	−	1.53272i
$866$	−29.7886	+	13.0057i	−1.01226	+	0.441952i
$867$	−3.82955	−	26.6351i	−0.130058	−	0.904576i
$868$	10.5629	−	6.29889i	0.358528	−	0.213798i
$869$	1.70171	+	1.09362i	0.0577266	+	0.0370986i
$870$	−7.20101	+	10.3682i	−0.244137	+	0.351514i
$871$	−49.2873	+	14.4720i	−1.67004	+	0.490367i
$872$	−3.36712	−	2.41109i	−0.114025	−	0.0816499i
$873$	6.62518			0.224228
$874$	0.126740	−	8.69144i	0.00428703	−	0.293992i
$875$	49.2206	+	9.98317i	1.66396	+	0.337493i
$876$	−7.36223	−	28.5809i	−0.248747	−	0.965659i
$877$	−4.85111	−	16.5214i	−0.163810	−	0.557886i	−0.999956	−	0.00937914i	$-0.997014\pi$
$877$	−4.85111	−	16.5214i	−0.163810	−	0.557886i	0.836146	−	0.548507i	$-0.184804\pi$
$878$	−46.7898	−	0.783509i	−1.57908	−	0.0264422i
$879$	−7.12175	−	4.57687i	−0.240211	−	0.154374i
$880$	12.3448	−	52.9910i	0.416143	−	1.78633i
$881$	40.3713	−	5.80452i	1.36015	−	0.195559i	0.576667	−	0.816979i	$-0.304353\pi$
$881$	40.3713	−	5.80452i	1.36015	−	0.195559i	0.783478	+	0.621420i	$0.213444\pi$
$882$	−9.97107	+	4.35338i	−0.335744	+	0.146586i
$883$	0.904164	−	0.581071i	0.0304275	−	0.0195546i	−0.525339	−	0.850893i	$-0.676061\pi$
$883$	0.904164	−	0.581071i	0.0304275	−	0.0195546i	0.555766	+	0.831339i	$0.312425\pi$
$884$	−3.42406	+	10.3641i	−0.115164	+	0.348583i
$885$	24.9088	+	40.4369i	0.837300	+	1.35927i
$886$	−0.547371	−	1.98664i	−0.0183893	−	0.0667424i
$887$	2.93452	−	20.4101i	0.0985317	−	0.685303i	−0.879355	−	0.476167i	$-0.842026\pi$
$887$	2.93452	−	20.4101i	0.0985317	−	0.685303i	0.977887	−	0.209136i	$-0.0670651\pi$
$888$	1.77975	+	0.923461i	0.0597245	+	0.0309893i
$889$	−23.2862	+	79.3055i	−0.780994	+	2.65982i
$890$	22.9994	−	5.86663i	0.770940	−	0.196650i
$891$	−41.4720	−	47.8612i	−1.38936	−	1.60341i
$892$	−4.16412	+	4.49247i	−0.139425	+	0.150419i
$893$	−5.74272	+	6.62745i	−0.192173	+	0.221779i
$894$	−4.84038	−	3.22650i	−0.161886	−	0.107910i
$895$	−1.03344	−	0.168794i	−0.0345440	−	0.00564217i
$896$	−50.1030	+	8.51767i	−1.67382	+	0.284556i
$897$	8.30223	−	28.5027i	0.277203	−	0.951677i
$898$	−3.85768	+	3.23121i	−0.128732	+	0.107827i
$899$	2.62572	−	1.19913i	0.0875728	−	0.0399931i
$900$	−5.12447	+	2.79621i	−0.170816	+	0.0932071i
$901$	−3.89638	+	4.49666i	−0.129807	+	0.149806i
$902$	74.4528	−	9.43524i	2.47901	−	0.314159i
$903$	32.0664	+	37.0066i	1.06710	+	1.23150i
$904$	23.7681	−	18.5905i	0.790517	−	0.618310i
$905$	−3.06516	+	2.55511i	−0.101889	+	0.0849349i
$906$	11.5683	+	3.60821i	0.384330	+	0.119875i
$907$	−10.4413	−	1.50124i	−0.346699	−	0.0498478i	−0.0332341	−	0.999448i	$-0.510581\pi$
$907$	−10.4413	−	1.50124i	−0.346699	−	0.0498478i	−0.313465	+	0.949600i	$0.601490\pi$
$908$	−15.7411	+	22.7789i	−0.522387	+	0.755945i
$909$	1.03841	−	2.27380i	0.0344418	−	0.0754170i
$910$	−1.66474	+	46.4197i	−0.0551854	+	1.53880i
$911$	7.19412	−	4.62338i	0.238352	−	0.153179i	−0.416012	−	0.909359i	$-0.636573\pi$
$911$	7.19412	−	4.62338i	0.238352	−	0.153179i	0.654364	+	0.756180i	$0.272936\pi$
$912$	−7.79480	−	5.78147i	−0.258111	−	0.191444i
$913$	−6.58681	+	0.947041i	−0.217992	+	0.0313425i
$914$	0.767764	+	0.123542i	0.0253954	+	0.00408640i
$915$	35.2554	−	15.2936i	1.16551	−	0.505590i
$916$	16.2830	−	13.1812i	0.538005	−	0.435519i
$917$	21.0569	−	6.18286i	0.695359	−	0.204176i
$918$	9.74442	+	4.64885i	0.321614	+	0.153435i
$919$	18.4231			0.607722			0.303861	−	0.952716i	$-0.401724\pi$
$919$	18.4231			0.607722			0.303861	+	0.952716i	$0.401724\pi$
$920$	−6.57267	−	29.6108i	−0.216694	−	0.976239i
$921$	26.8651			0.885235
$922$	35.7987	+	17.0788i	1.17897	+	0.562459i
$923$	34.2662	−	10.0615i	1.12789	−	0.331177i
$924$	80.4157	−	65.0971i	2.64548	−	2.14154i
$925$	0.337058	−	1.84175i	0.0110824	−	0.0605562i
$926$	25.3681	+	4.08200i	0.833646	+	0.134143i
$927$	−0.0614278	+	0.00883198i	−0.00201755	+	0.000290080i
$928$	−11.9077	+	0.704338i	−0.390889	+	0.0231210i
$929$	10.2123	−	6.56302i	0.335054	−	0.215326i	−0.362286	−	0.932067i	$-0.618004\pi$
$929$	10.2123	−	6.56302i	0.335054	−	0.215326i	0.697339	+	0.716741i	$0.254367\pi$
$930$	8.18962	+	0.293702i	0.268548	+	0.00963087i
$931$	−7.01635	+	15.3637i	−0.229952	+	0.503524i
$932$	33.0353	−	47.8053i	1.08211	−	1.56591i
$933$	1.60250	+	0.230404i	0.0524634	+	0.00754310i
$934$	−33.3622	−	10.4059i	−1.09164	−	0.340490i
$935$	−14.5367	−	17.4385i	−0.475402	−	0.570301i
$936$	−3.32634	−	4.25277i	−0.108725	−	0.139006i
$937$	−38.3867	−	44.3006i	−1.25404	−	1.44724i	−0.845040	−	0.534704i	$-0.820423\pi$
$937$	−38.3867	−	44.3006i	−1.25404	−	1.44724i	−0.408999	−	0.912535i	$-0.634122\pi$
$938$	−99.0054	+	12.5467i	−3.23264	+	0.409666i
$939$	32.8355	−	37.8942i	1.07155	−	1.23663i
$940$	−14.1574	+	27.1283i	−0.461764	+	0.884826i
$941$	21.9381	−	10.0188i	0.715163	−	0.326604i	−0.0243900	−	0.999703i	$-0.507764\pi$
$941$	21.9381	−	10.0188i	0.715163	−	0.326604i	0.739553	+	0.673099i	$0.235037\pi$
$942$	26.2146	−	21.9575i	0.854118	−	0.715414i
$943$	35.1462	−	22.6946i	1.14452	−	0.739038i
$944$	−15.4971	+	42.1175i	−0.504387	+	1.37081i
$945$	45.3442	+	7.40620i	1.47505	+	0.240924i
$946$	−41.2193	−	27.4759i	−1.34015	−	0.893319i
$947$	−5.52261	+	6.37344i	−0.179461	+	0.207109i	−0.838352	−	0.545130i	$-0.816480\pi$
$947$	−5.52261	+	6.37344i	−0.179461	+	0.207109i	0.658891	+	0.752239i	$0.271026\pi$
$948$	0.855864	−	0.923351i	0.0277972	−	0.0299890i
$949$	−16.6921	−	19.2637i	−0.541848	−	0.625326i
$950$	−3.02690	+	8.54197i	−0.0982056	+	0.277138i
$951$	2.69293	−	9.17127i	0.0873242	−	0.297399i
$952$	−9.76658	+	18.8228i	−0.316537	+	0.610049i
$953$	−5.87755	+	40.8792i	−0.190392	+	1.32421i	0.640579	+	0.767893i	$0.278695\pi$
$953$	−5.87755	+	40.8792i	−0.190392	+	1.32421i	−0.830971	+	0.556316i	$0.812215\pi$
$954$	−0.781777	−	2.83739i	−0.0253110	−	0.0918641i
$955$	26.3926	−	16.2576i	0.854044	−	0.526084i
$956$	−7.99474	+	24.1989i	−0.258568	+	0.782648i
$957$	20.4287	−	13.1287i	0.660367	−	0.424392i
$958$	−13.7710	+	6.01243i	−0.444921	+	0.194253i
$959$	−10.4012	+	1.49547i	−0.335872	+	0.0482912i
$960$	−31.1228	−	13.3484i	−1.00448	−	0.430818i
$961$	24.5024	+	15.7468i	0.790401	+	0.507960i
$962$	1.73142	+	0.0289932i	0.0558233	+	0.000934777i
$963$	−1.10965	−	3.77913i	−0.0357581	−	0.121781i
$964$	4.72320	+	18.3359i	0.152124	+	0.590561i
$965$	9.15148	−	13.6591i	0.294597	−	0.439701i
$966$	24.7219	−	52.1090i	0.795413	−	1.67658i
$967$	−20.8635			−0.670925			−0.335463	−	0.942053i	$-0.608893\pi$
$967$	−20.8635			−0.670925			−0.335463	+	0.942053i	$0.608893\pi$
$968$	−42.8235	+	59.8035i	−1.37640	+	1.92216i
$969$	−3.88537	+	1.14085i	−0.124816	+	0.0366493i
$970$	20.4723	−	29.4765i	0.657327	−	0.946432i
$971$	−22.7983	−	14.6516i	−0.731634	−	0.470192i	0.121033	−	0.992649i	$-0.461379\pi$
$971$	−22.7983	−	14.6516i	−0.731634	−	0.470192i	−0.852666	+	0.522456i	$0.825016\pi$
$972$	−10.2819	+	6.13135i	−0.329793	+	0.196663i
$973$	−9.15321	−	63.6620i	−0.293439	−	2.04091i
$974$	2.50426	−	1.09336i	0.0802416	−	0.0350335i
$975$	−17.7158	+	25.3795i	−0.567359	+	0.812794i
$976$	31.9485	+	17.2621i	1.02265	+	0.552547i
$977$	10.4695	−	22.9251i	0.334951	−	0.733439i	−0.664959	−	0.746880i	$-0.731551\pi$
$977$	10.4695	−	22.9251i	0.334951	−	0.733439i	0.999910	+	0.0134404i	$0.00427834\pi$
$978$	0.955496	+	3.46789i	0.0305534	+	0.110891i
$979$	−45.1954	−	6.49812i	−1.44445	−	0.207681i
$980$	−11.4425	+	57.8151i	−0.365518	+	1.84684i
$981$	0.240812	−	0.820131i	0.00768854	−	0.0261848i
$982$	35.5829	−	39.7018i	1.13550	−	1.26693i
$983$	−24.3706	+	21.1172i	−0.777301	+	0.673535i	−0.950282	−	0.311390i	$-0.899205\pi$
$983$	−24.3706	+	21.1172i	−0.777301	+	0.673535i	0.172981	+	0.984925i	$0.444660\pi$
$984$	2.34530	−	46.6508i	0.0747654	−	1.48717i
$985$	−5.73042	−	20.9914i	−0.182587	−	0.668842i
$986$	−2.76062	+	4.14147i	−0.0879160	+	0.131891i
$987$	−52.9287	+	24.1717i	−1.68474	+	0.769395i
$988$	−8.25164	−	1.46992i	−0.262520	−	0.0467643i
$989$	−27.3426	−	3.87093i	−0.869443	−	0.123089i
$990$	11.1658	−	1.19878i	0.354871	−	0.0380997i
$991$	34.2230	−	15.6291i	1.08713	−	0.496475i	0.210477	−	0.977599i	$-0.432498\pi$
$991$	34.2230	−	15.6291i	1.08713	−	0.496475i	0.876653	+	0.481123i	$0.159771\pi$
$992$	4.56390	+	6.25583i	0.144904	+	0.198623i
$993$	−25.1030	−	21.7518i	−0.796619	−	0.690274i
$994$	68.8320	−	8.72293i	2.18322	−	0.276675i
$995$	1.93071	+	15.5289i	0.0612078	+	0.492298i
$996$	−0.138671	+	4.13944i	−0.00439396	+	0.131163i
$997$	−4.00375	+	13.6355i	−0.126800	+	0.431842i	−0.998282	−	0.0585854i	$-0.981341\pi$
$997$	−4.00375	+	13.6355i	−0.126800	+	0.431842i	0.871482	+	0.490427i	$0.163159\pi$
$998$	−12.7194	−	3.96725i	−0.402626	−	0.125581i
$999$	0.243765	−	1.69542i	0.00771239	−	0.0536409i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.b.19.10	✓	640
4.3	odd	2	inner	460.2.o.b.19.27	yes	640
5.4	even	2	inner	460.2.o.b.19.55	yes	640
20.19	odd	2	inner	460.2.o.b.19.38	yes	640
23.17	odd	22	inner	460.2.o.b.339.38	yes	640
92.63	even	22	inner	460.2.o.b.339.55	yes	640
115.109	odd	22	inner	460.2.o.b.339.27	yes	640
460.339	even	22	inner	460.2.o.b.339.10	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.b.19.10	✓	640	1.1	even	1	trivial
460.2.o.b.19.27	yes	640	4.3	odd	2	inner
460.2.o.b.19.38	yes	640	20.19	odd	2	inner
460.2.o.b.19.55	yes	640	5.4	even	2	inner
460.2.o.b.339.10	yes	640	460.339	even	22	inner
460.2.o.b.339.27	yes	640	115.109	odd	22	inner
460.2.o.b.339.38	yes	640	23.17	odd	22	inner
460.2.o.b.339.55	yes	640	92.63	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.27640 - 0.608942i) q^{2} +(1.81640 - 0.533344i) q^{3} +(1.25838 + 1.55450i) q^{4} +(0.889872 + 2.05137i) q^{5} +(-2.64323 - 0.425324i) q^{6} +(-4.44634 + 0.639287i) q^{7} +(-0.659592 - 2.75044i) q^{8} +(0.491100 - 0.315611i) q^{9} +O(q^{10})\)	\(q+(-1.27640 - 0.608942i) q^{2} +(1.81640 - 0.533344i) q^{3} +(1.25838 + 1.55450i) q^{4} +(0.889872 + 2.05137i) q^{5} +(-2.64323 - 0.425324i) q^{6} +(-4.44634 + 0.639287i) q^{7} +(-0.659592 - 2.75044i) q^{8} +(0.491100 - 0.315611i) q^{9} +(0.113335 - 3.16025i) q^{10} +(-2.52706 + 5.53349i) q^{11} +(3.11481 + 2.15245i) q^{12} +(3.23662 + 0.465356i) q^{13} +(6.06458 + 1.89158i) q^{14} +(2.71045 + 3.25151i) q^{15} +(-0.832958 + 3.91231i) q^{16} +(1.09298 + 1.26136i) q^{17} +(-0.819028 + 0.103794i) q^{18} +(-0.839282 + 0.968583i) q^{19} +(-2.06907 + 3.96472i) q^{20} +(-7.73538 + 3.53263i) q^{21} +(6.59511 - 5.52410i) q^{22} +(1.98282 - 4.36674i) q^{23} +(-2.66502 - 4.64412i) q^{24} +(-3.41625 + 3.65092i) q^{25} +(-3.84784 - 2.56489i) q^{26} +(-2.99542 + 3.45689i) q^{27} +(-6.58896 - 6.10738i) q^{28} +(-1.38089 - 1.59363i) q^{29} +(-1.47964 - 5.80072i) q^{30} +(-0.385664 + 1.31345i) q^{31} +(3.44555 - 4.48644i) q^{32} +(-1.63891 + 11.3988i) q^{33} +(-0.626977 - 2.27556i) q^{34} +(-5.26809 - 8.55221i) q^{35} +(1.10861 + 0.366258i) q^{36} +(-0.315022 + 0.202452i) q^{37} +(1.66107 - 0.725223i) q^{38} +(6.12720 - 0.880959i) q^{39} +(5.05523 - 3.80061i) q^{40} +(7.33870 + 4.71629i) q^{41} +(12.0246 + 0.201355i) q^{42} +(-1.62226 - 5.52493i) q^{43} +(-11.7818 + 3.03491i) q^{44} +(1.08445 + 0.726576i) q^{45} +(-5.18996 + 4.36627i) q^{46} +6.84242 q^{47} +(0.573621 + 7.55058i) q^{48} +(12.6448 - 3.71285i) q^{49} +(6.58369 - 2.57972i) q^{50} +(2.65803 + 1.70821i) q^{51} +(3.34951 + 5.61693i) q^{52} +(0.507342 + 3.52864i) q^{53} +(5.92839 - 2.58834i) q^{54} +(-13.6000 - 0.259841i) q^{55} +(4.69109 + 11.8077i) q^{56} +(-1.00789 + 2.20696i) q^{57} +(0.792136 + 2.87499i) q^{58} +(11.1053 + 1.59671i) q^{59} +(-1.64370 + 8.30504i) q^{60} +(2.55769 - 8.71069i) q^{61} +(1.29208 - 1.44164i) q^{62} +(-1.98183 + 1.71727i) q^{63} +(-7.12988 + 3.62834i) q^{64} +(1.92556 + 7.05362i) q^{65} +(9.03312 - 13.5514i) q^{66} +(-14.2897 + 6.52589i) q^{67} +(-0.585411 + 3.28631i) q^{68} +(1.27263 - 8.98928i) q^{69} +(1.51638 + 14.1240i) q^{70} +(9.93470 - 4.53703i) q^{71} +(-1.19200 - 1.14257i) q^{72} +(-5.89120 - 5.10476i) q^{73} +(0.525374 - 0.0665796i) q^{74} +(-4.25810 + 8.45357i) q^{75} +(-2.56180 - 0.0858202i) q^{76} +(7.69868 - 26.2193i) q^{77} +(-8.35720 - 2.60666i) q^{78} +(0.0473234 - 0.329141i) q^{79} +(-8.76683 + 1.77275i) q^{80} +(-4.32469 + 9.46975i) q^{81} +(-6.49515 - 10.4887i) q^{82} +(0.591417 + 0.920263i) q^{83} +(-15.2255 - 7.57928i) q^{84} +(-1.61491 + 3.36455i) q^{85} +(-1.29370 + 8.03987i) q^{86} +(-3.35821 - 2.15819i) q^{87} +(16.8864 + 3.30069i) q^{88} +(2.11466 + 7.20188i) q^{89} +(-0.941750 - 1.58777i) q^{90} -14.6886 q^{91} +(9.28325 - 2.41272i) q^{92} +2.59145i q^{93} +(-8.73365 - 4.16663i) q^{94} +(-2.73378 - 0.859764i) q^{95} +(3.86570 - 9.98685i) q^{96} +(9.54731 + 6.13568i) q^{97} +(-18.4007 - 2.96087i) q^{98} +(0.505391 + 3.51507i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Introduction

L-functions

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