LMFDB - Embedded newform 930.2.bk.a.47.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(47,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 4]))

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

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

chi := DirichletCharacter("930.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bk (of order $20$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$64$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.10
Character	$\chi$	$=$	930.47
Dual form			930.2.bk.a.653.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 + 0.987688i) q^{2} +(-0.999352 + 1.41467i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-2.01289 + 0.973791i) q^{5} +(-1.24092 - 1.20835i) q^{6} +(-2.22585 + 1.13413i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-1.00259 - 2.82751i) q^{9} +O(q^{10})$	\(q+(-0.156434 + 0.987688i) q^{2} +(-0.999352 + 1.41467i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-2.01289 + 0.973791i) q^{5} +(-1.24092 - 1.20835i) q^{6} +(-2.22585 + 1.13413i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-1.00259 - 2.82751i) q^{9} +(-0.646917 - 2.14044i) q^{10} +(-3.82916 - 1.24417i) q^{11} +(1.38760 - 1.03662i) q^{12} +(5.57842 - 0.883534i) q^{13} +(-0.771963 - 2.37586i) q^{14} +(0.633992 - 3.82074i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-2.28923 - 1.16642i) q^{17} +(2.94954 - 0.547929i) q^{18} +(-0.452261 - 0.622484i) q^{19} +(2.21529 - 0.304113i) q^{20} +(0.619988 - 4.28223i) q^{21} +(1.82786 - 3.58738i) q^{22} +(-2.24056 + 4.39735i) q^{23} +(0.806785 + 1.53268i) q^{24} +(3.10346 - 3.92027i) q^{25} +5.64795i q^{26} +(5.00194 + 1.40734i) q^{27} +(2.46737 - 0.390793i) q^{28} +(2.51984 - 1.83077i) q^{29} +(3.67452 + 1.22388i) q^{30} +(-5.15306 + 2.10855i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.58677 - 4.17364i) q^{33} +(1.51017 - 2.07858i) q^{34} +(3.37598 - 4.45038i) q^{35} +(0.0797732 + 2.99894i) q^{36} +(5.76396 + 5.76396i) q^{37} +(0.685570 - 0.349315i) q^{38} +(-4.32489 + 8.77459i) q^{39} +(-0.0461792 + 2.23559i) q^{40} +(1.32976 + 1.83026i) q^{41} +(4.13252 + 1.28224i) q^{42} +(1.52231 - 9.61150i) q^{43} +(3.25728 + 2.36655i) q^{44} +(4.77151 + 4.71515i) q^{45} +(-3.99271 - 2.90088i) q^{46} +(2.28123 - 0.361311i) q^{47} +(-1.64002 + 0.557089i) q^{48} +(-0.446347 + 0.614344i) q^{49} +(3.38652 + 3.67852i) q^{50} +(3.93785 - 2.07284i) q^{51} +(-5.57842 - 0.883534i) q^{52} +(0.109773 - 0.215441i) q^{53} +(-2.17249 + 4.72020i) q^{54} +(8.91924 - 1.22442i) q^{55} +2.49813i q^{56} +(1.33258 - 0.0177205i) q^{57} +(1.41404 + 2.77521i) q^{58} +(-7.34028 - 5.33303i) q^{59} +(-1.78364 + 3.43783i) q^{60} +3.22095 q^{61} +(-1.27647 - 5.41947i) q^{62} +(5.43836 + 5.15653i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-10.3684 + 7.21067i) q^{65} +(3.24829 + 6.17089i) q^{66} +(-1.86320 - 1.86320i) q^{67} +(1.81674 + 1.81674i) q^{68} +(-3.98170 - 7.56416i) q^{69} +(3.86747 + 4.03061i) q^{70} +(9.17102 - 2.97985i) q^{71} +(-2.97450 - 0.390346i) q^{72} +(-5.78701 - 11.3577i) q^{73} +(-6.59468 + 4.79131i) q^{74} +(2.44445 + 8.30811i) q^{75} +(0.237768 + 0.731774i) q^{76} +(9.93416 - 1.57342i) q^{77} +(-7.99000 - 5.64429i) q^{78} +(6.26446 - 2.03545i) q^{79} +(-2.20084 - 0.395334i) q^{80} +(-6.98962 + 5.66968i) q^{81} +(-2.01575 + 1.02708i) q^{82} +(-1.48890 - 0.235819i) q^{83} +(-1.91293 + 3.88106i) q^{84} +(5.74382 + 0.118646i) q^{85} +(9.25502 + 3.00714i) q^{86} +(0.0717332 + 5.39433i) q^{87} +(-2.84696 + 2.84696i) q^{88} +(1.67656 - 5.15991i) q^{89} +(-5.40353 + 3.97515i) q^{90} +(-11.4147 + 8.29323i) q^{91} +(3.48976 - 3.48976i) q^{92} +(2.16681 - 9.39707i) q^{93} +2.30966i q^{94} +(1.51652 + 0.812585i) q^{95} +(-0.293676 - 1.70697i) q^{96} +(15.4846 - 7.88980i) q^{97} +(-0.536957 - 0.536957i) q^{98} +(0.321184 + 12.0744i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) $ 512 * q + 8 * q^3 - 12 * q^7	$ 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) $ 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$3$	−0.999352	+	1.41467i	−0.576976	+	0.816761i
$3$	−0.999352	+	1.41467i	−0.576976	+	0.816761i
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	−2.01289	+	0.973791i	−0.900192	+	0.435493i
$5$	−2.01289	+	0.973791i	−0.900192	+	0.435493i
$6$	−1.24092	−	1.20835i	−0.506604	−	0.493307i
$7$	−2.22585	+	1.13413i	−0.841291	+	0.428659i	−0.820858	−	0.571132i	$-0.806504\pi$
$7$	−2.22585	+	1.13413i	−0.841291	+	0.428659i	−0.0204325	+	0.999791i	$0.506504\pi$
$8$	0.453990	−	0.891007i	0.160510	−	0.315018i
$9$	−1.00259	−	2.82751i	−0.334197	−	0.942503i
$10$	−0.646917	−	2.14044i	−0.204573	−	0.676868i
$11$	−3.82916	−	1.24417i	−1.15453	−	0.375131i	−0.331685	−	0.943390i	$-0.607617\pi$
$11$	−3.82916	−	1.24417i	−1.15453	−	0.375131i	−0.822850	+	0.568259i	$0.807617\pi$
$12$	1.38760	−	1.03662i	0.400565	−	0.299245i
$13$	5.57842	−	0.883534i	1.54717	−	0.245048i	0.676327	−	0.736602i	$-0.263571\pi$
$13$	5.57842	−	0.883534i	1.54717	−	0.245048i	0.870847	+	0.491554i	$0.163571\pi$
$14$	−0.771963	−	2.37586i	−0.206316	−	0.634975i
$15$	0.633992	−	3.82074i	0.163696	−	0.986511i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−2.28923	−	1.16642i	−0.555220	−	0.282898i	0.153783	−	0.988105i	$-0.450854\pi$
$17$	−2.28923	−	1.16642i	−0.555220	−	0.282898i	−0.709002	+	0.705206i	$0.750854\pi$
$18$	2.94954	−	0.547929i	0.695213	−	0.129148i
$19$	−0.452261	−	0.622484i	−0.103756	−	0.142808i	0.753982	−	0.656895i	$-0.228131\pi$
$19$	−0.452261	−	0.622484i	−0.103756	−	0.142808i	−0.857738	+	0.514088i	$0.828131\pi$
$20$	2.21529	−	0.304113i	0.495354	−	0.0680017i
$21$	0.619988	−	4.28223i	0.135293	−	0.934459i
$22$	1.82786	−	3.58738i	0.389702	−	0.764833i
$23$	−2.24056	+	4.39735i	−0.467190	+	0.916912i	0.530415	+	0.847738i	$0.322036\pi$
$23$	−2.24056	+	4.39735i	−0.467190	+	0.916912i	−0.997605	+	0.0691734i	$0.977964\pi$
$24$	0.806785	+	1.53268i	0.164684	+	0.312856i
$25$	3.10346	−	3.92027i	0.620692	−	0.784054i
$26$			5.64795i			1.10765i
$27$	5.00194	+	1.40734i	0.962624	+	0.270842i
$28$	2.46737	−	0.390793i	0.466289	−	0.0738529i
$29$	2.51984	−	1.83077i	0.467923	−	0.339966i	−0.328709	−	0.944431i	$-0.606613\pi$
$29$	2.51984	−	1.83077i	0.467923	−	0.339966i	0.796631	+	0.604466i	$0.206613\pi$
$30$	3.67452	+	1.22388i	0.670873	+	0.223449i
$31$	−5.15306	+	2.10855i	−0.925517	+	0.378707i
$31$	−5.15306	+	2.10855i	−0.925517	+	0.378707i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	5.58677	−	4.17364i	0.972531	−	0.726537i
$34$	1.51017	−	2.07858i	0.258993	−	0.356473i
$35$	3.37598	−	4.45038i	0.570645	−	0.752251i
$36$	0.0797732	+	2.99894i	0.0132955	+	0.499823i
$37$	5.76396	+	5.76396i	0.947589	+	0.947589i	0.998693	−	0.0511045i	$-0.0162742\pi$
$37$	5.76396	+	5.76396i	0.947589	+	0.947589i	−0.0511045	+	0.998693i	$0.516274\pi$
$38$	0.685570	−	0.349315i	0.111214	−	0.0566664i
$39$	−4.32489	+	8.77459i	−0.692536	+	1.40506i
$40$	−0.0461792	+	2.23559i	−0.00730157	+	0.353478i
$41$	1.32976	+	1.83026i	0.207674	+	0.285839i	0.900130	−	0.435621i	$-0.143471\pi$
$41$	1.32976	+	1.83026i	0.207674	+	0.285839i	−0.692456	+	0.721460i	$0.743471\pi$
$42$	4.13252	+	1.28224i	0.637662	+	0.197854i
$43$	1.52231	−	9.61150i	0.232150	−	1.46574i	−0.546065	−	0.837743i	$-0.683875\pi$
$43$	1.52231	−	9.61150i	0.232150	−	1.46574i	0.778216	−	0.627997i	$-0.216125\pi$
$44$	3.25728	+	2.36655i	0.491053	+	0.356771i
$45$	4.77151	+	4.71515i	0.711295	+	0.702894i
$46$	−3.99271	−	2.90088i	−0.588693	−	0.427711i
$47$	2.28123	−	0.361311i	0.332751	−	0.0527026i	0.0121764	−	0.999926i	$-0.496124\pi$
$47$	2.28123	−	0.361311i	0.332751	−	0.0527026i	0.320575	+	0.947223i	$0.396124\pi$
$48$	−1.64002	+	0.557089i	−0.236716	+	0.0804089i
$49$	−0.446347	+	0.614344i	−0.0637639	+	0.0877635i
$50$	3.38652	+	3.67852i	0.478926	+	0.520221i
$51$	3.93785	−	2.07284i	0.551409	−	0.290256i
$52$	−5.57842	−	0.883534i	−0.773587	−	0.122524i
$53$	0.109773	−	0.215441i	0.0150784	−	0.0295931i	−0.883344	−	0.468724i	$-0.844714\pi$
$53$	0.109773	−	0.215441i	0.0150784	−	0.0295931i	0.898423	+	0.439131i	$0.144714\pi$
$54$	−2.17249	+	4.72020i	−0.295638	+	0.642338i
$55$	8.91924	−	1.22442i	1.20267	−	0.165101i
$56$			2.49813i			0.333826i
$57$	1.33258	−	0.0177205i	0.176504	−	0.00234714i
$58$	1.41404	+	2.77521i	0.185673	+	0.364403i
$59$	−7.34028	−	5.33303i	−0.955623	−	0.694301i	−0.00349322	−	0.999994i	$-0.501112\pi$
$59$	−7.34028	−	5.33303i	−0.955623	−	0.694301i	−0.952130	+	0.305693i	$0.901112\pi$
$60$	−1.78364	+	3.43783i	−0.230266	+	0.443821i
$61$	3.22095			0.412401			0.206200	−	0.978510i	$-0.433890\pi$
$61$	3.22095			0.412401			0.206200	+	0.978510i	$0.433890\pi$
$62$	−1.27647	−	5.41947i	−0.162112	−	0.688273i
$63$	5.43836	+	5.15653i	0.685169	+	0.649662i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	−10.3684	+	7.21067i	−1.28604	+	0.894373i
$66$	3.24829	+	6.17089i	0.399837	+	0.759584i
$67$	−1.86320	−	1.86320i	−0.227626	−	0.227626i	0.584074	−	0.811700i	$-0.301458\pi$
$67$	−1.86320	−	1.86320i	−0.227626	−	0.227626i	−0.811700	+	0.584074i	$0.801458\pi$
$68$	1.81674	+	1.81674i	0.220312	+	0.220312i
$69$	−3.98170	−	7.56416i	−0.479340	−	0.910618i
$70$	3.86747	+	4.03061i	0.462251	+	0.481750i
$71$	9.17102	−	2.97985i	1.08840	−	0.353643i	0.290772	−	0.956792i	$-0.406088\pi$
$71$	9.17102	−	2.97985i	1.08840	−	0.353643i	0.797628	+	0.603150i	$0.206088\pi$
$72$	−2.97450	−	0.390346i	−0.350548	−	0.0460028i
$73$	−5.78701	−	11.3577i	−0.677319	−	1.32931i	−0.932060	−	0.362303i	$-0.881990\pi$
$73$	−5.78701	−	11.3577i	−0.677319	−	1.32931i	0.254742	−	0.967009i	$-0.418010\pi$
$74$	−6.59468	+	4.79131i	−0.766615	+	0.556979i
$75$	2.44445	+	8.30811i	0.282260	+	0.959338i
$76$	0.237768	+	0.731774i	0.0272738	+	0.0839403i
$77$	9.93416	−	1.57342i	1.13210	−	0.179307i
$78$	−7.99000	−	5.64429i	−0.904689	−	0.639090i
$79$	6.26446	−	2.03545i	0.704807	−	0.229006i	0.0653831	−	0.997860i	$-0.479173\pi$
$79$	6.26446	−	2.03545i	0.704807	−	0.229006i	0.639424	+	0.768855i	$0.279173\pi$
$80$	−2.20084	−	0.395334i	−0.246062	−	0.0441997i
$81$	−6.98962	+	5.66968i	−0.776624	+	0.629964i
$82$	−2.01575	+	1.02708i	−0.222603	+	0.113422i
$83$	−1.48890	−	0.235819i	−0.163428	−	0.0258845i	0.0741840	−	0.997245i	$-0.476365\pi$
$83$	−1.48890	−	0.235819i	−0.163428	−	0.0258845i	−0.237612	+	0.971360i	$0.576365\pi$
$84$	−1.91293	+	3.88106i	−0.208717	+	0.423458i
$85$	5.74382	+	0.118646i	0.623005	+	0.0128690i
$86$	9.25502	+	3.00714i	0.997995	+	0.324268i
$87$	0.0717332	+	5.39433i	0.00769061	+	0.578333i
$88$	−2.84696	+	2.84696i	−0.303487	+	0.303487i
$89$	1.67656	−	5.15991i	0.177715	−	0.546949i	−0.822032	−	0.569441i	$-0.807160\pi$
$89$	1.67656	−	5.15991i	0.177715	−	0.546949i	0.999747	+	0.0224915i	$0.00715986\pi$
$90$	−5.40353	+	3.97515i	−0.569582	+	0.419018i
$91$	−11.4147	+	8.29323i	−1.19658	+	0.869367i
$92$	3.48976	−	3.48976i	0.363833	−	0.363833i
$93$	2.16681	−	9.39707i	0.224688	−	0.974431i
$94$			2.30966i			0.238223i
$95$	1.51652	+	0.812585i	0.155592	+	0.0833695i
$96$	−0.293676	−	1.70697i	−0.0299731	−	0.174217i
$97$	15.4846	−	7.88980i	1.57222	−	0.801088i	0.572401	−	0.819974i	$-0.306012\pi$
$97$	15.4846	−	7.88980i	1.57222	−	0.801088i	0.999822	+	0.0188859i	$0.00601191\pi$
$98$	−0.536957	−	0.536957i	−0.0542408	−	0.0542408i
$99$	0.321184	+	12.0744i	0.0322802	+	1.21352i
$100$	−4.16300	+	2.76938i	−0.416300	+	0.276938i
$101$	−7.97186	+	2.59022i	−0.793230	+	0.257736i	−0.677479	−	0.735542i	$-0.736927\pi$
$101$	−7.97186	+	2.59022i	−0.793230	+	0.257736i	−0.115751	+	0.993278i	$0.536927\pi$
$102$	1.43131	+	4.21363i	0.141721	+	0.417211i
$103$	3.00321	−	18.9615i	0.295915	−	1.86833i	−0.172760	−	0.984964i	$-0.555269\pi$
$103$	3.00321	−	18.9615i	0.295915	−	1.86833i	0.468675	−	0.883371i	$-0.344731\pi$
$104$	1.74531	−	5.37152i	0.171142	−	0.526721i
$105$	2.92203	+	9.22340i	0.285161	+	0.900112i
$106$	0.195616	+	0.142123i	0.0189999	+	0.0138042i
$107$	6.49816	+	3.31098i	0.628201	+	0.320084i	0.738946	−	0.673764i	$-0.235324\pi$
$107$	6.49816	+	3.31098i	0.628201	+	0.320084i	−0.110745	+	0.993849i	$0.535324\pi$
$108$	−4.32224	−	2.88414i	−0.415907	−	0.277527i
$109$	5.46917	−	7.52766i	0.523851	−	0.721019i	−0.462327	−	0.886710i	$-0.652985\pi$
$109$	5.46917	−	7.52766i	0.523851	−	0.721019i	0.986178	+	0.165690i	$0.0529852\pi$
$110$	−0.185927	+	9.00097i	−0.0177275	+	0.858209i
$111$	−13.9143	+	2.39389i	−1.32069	+	0.227218i
$112$	−2.46737	−	0.390793i	−0.233144	−	0.0369265i
$113$	−7.67354	+	3.90986i	−0.721865	+	0.367809i	−0.776007	−	0.630724i	$-0.782758\pi$
$113$	−7.67354	+	3.90986i	−0.721865	+	0.367809i	0.0541414	+	0.998533i	$0.482758\pi$
$114$	−0.190959	+	1.31895i	−0.0178850	+	0.123531i
$115$	0.227906	−	11.0332i	0.0212524	−	1.02885i
$116$	−2.96225	+	0.962493i	−0.275038	+	0.0893652i
$117$	−8.09108	−	14.8872i	−0.748020	−	1.37632i
$118$	6.41564	−	6.41564i	0.590608	−	0.590608i
$119$	6.41834			0.588368
$120$	−3.11648	−	2.29947i	−0.284494	−	0.209912i
$121$	4.21531	+	3.06260i	0.383210	+	0.278419i
$122$	−0.503868	+	3.18130i	−0.0456181	+	0.288021i
$123$	−3.91813	+	0.0521028i	−0.353286	+	0.00469795i
$124$	5.55243	−	0.412968i	0.498623	−	0.0370856i
$125$	−2.42940	+	10.9132i	−0.217293	+	0.976107i
$126$	−5.94380	+	4.56475i	−0.529516	+	0.406660i
$127$	1.15732	+	7.30702i	0.102695	+	0.648393i	0.984313	+	0.176429i	$0.0564547\pi$
$127$	1.15732	+	7.30702i	0.102695	+	0.648393i	−0.881618	+	0.471964i	$0.843545\pi$
$128$	0.891007	−	0.453990i	0.0787546	−	0.0401275i
$129$	12.0758	+	11.7588i	1.06321	+	1.03531i
$130$	−5.49992	−	11.3687i	−0.482375	−	0.997102i
$131$	−16.7616	−	5.44618i	−1.46447	−	0.475835i	−0.535038	−	0.844828i	$-0.679703\pi$
$131$	−16.7616	−	5.44618i	−1.46447	−	0.475835i	−0.929432	+	0.368993i	$0.879703\pi$
$132$	−6.60306	+	2.24296i	−0.574722	+	0.195225i
$133$	1.71264	+	0.872633i	0.148505	+	0.0756669i
$134$	2.13173	−	1.54879i	0.184153	−	0.133795i
$135$	−11.4388	+	2.03803i	−0.984496	+	0.175405i
$136$	−2.07858	+	1.51017i	−0.178236	+	0.129496i
$137$	20.4784	−	3.24347i	1.74959	−	0.277108i	0.802170	−	0.597096i	$-0.203679\pi$
$137$	20.4784	−	3.24347i	1.74959	−	0.277108i	0.947422	+	0.319988i	$0.103679\pi$
$138$	8.09391	−	2.74938i	0.689000	−	0.234043i
$139$	−9.67051	+	13.3103i	−0.820242	+	1.12897i	0.169420	+	0.985544i	$0.445811\pi$
$139$	−9.67051	+	13.3103i	−0.820242	+	1.12897i	−0.989662	+	0.143422i	$0.954189\pi$
$140$	−4.58599	+	3.18933i	−0.387587	+	0.269547i
$141$	−1.76861	+	3.58826i	−0.148944	+	0.302186i
$142$	1.50850	+	9.52426i	0.126590	+	0.799258i
$143$	−22.4599	−	3.55730i	−1.87819	−	0.297476i
$144$	0.850854	−	2.87681i	0.0709045	−	0.239734i
$145$	−3.28937	+	6.13894i	−0.273168	+	0.509811i
$146$	12.1231	−	3.93904i	1.00332	−	0.325997i
$147$	−0.423038	−	1.24538i	−0.0348916	−	0.102717i
$148$	−3.70069	−	7.26301i	−0.304195	−	0.597016i
$149$	−10.5645			−0.865481			−0.432740	−	0.901519i	$-0.642453\pi$
$149$	−10.5645			−0.865481			−0.432740	+	0.901519i	$0.642453\pi$
$150$	−8.58822	+	1.11468i	−0.701225	+	0.0910130i
$151$	1.52703	−	4.69972i	0.124268	−	0.382458i	−0.869499	−	0.493935i	$-0.835558\pi$
$151$	1.52703	−	4.69972i	0.124268	−	0.382458i	0.993767	+	0.111477i	$0.0355581\pi$
$152$	−0.759960	+	0.120366i	−0.0616409	+	0.00976296i
$153$	−1.00290	+	7.64226i	−0.0810798	+	0.617840i
$154$			10.0580i			0.810496i
$155$	8.31926	−	9.26229i	0.668219	−	0.743965i
$156$	6.82471	−	7.00866i	0.546414	−	0.561142i
$157$	−10.3797	−	1.64399i	−0.828392	−	0.131204i	−0.272182	−	0.962246i	$-0.587745\pi$
$157$	−10.3797	−	1.64399i	−0.828392	−	0.131204i	−0.556210	+	0.831041i	$0.687745\pi$
$158$	1.03041	+	6.50575i	0.0819750	+	0.517569i
$159$	0.195077	+	0.370593i	0.0154706	+	0.0293899i
$160$	0.734755	−	2.11190i	0.0580875	−	0.166961i
$161$		−	12.3289i		−	0.971654i
$162$	−4.50646	−	7.79050i	−0.354061	−	0.612079i
$163$	−1.33435	−	0.679884i	−0.104514	−	0.0532526i	0.400952	−	0.916099i	$-0.368679\pi$
$163$	−1.33435	−	0.679884i	−0.104514	−	0.0532526i	−0.505466	+	0.862846i	$0.668679\pi$
$164$	−0.699099	−	2.15160i	−0.0545904	−	0.168012i
$165$	−7.18130	+	13.8414i	−0.559064	+	1.07755i
$166$	0.465831	−	1.43368i	0.0361555	−	0.111275i
$167$	1.36568	−	8.62256i	0.105679	−	0.667234i	−0.876799	−	0.480857i	$-0.840326\pi$
$167$	1.36568	−	8.62256i	0.105679	−	0.667234i	0.982478	−	0.186377i	$-0.0596745\pi$
$168$	−3.53403	−	2.49651i	−0.272656	−	0.192610i
$169$	17.9743	−	5.84022i	1.38264	−	0.449248i
$170$	−1.01572	+	5.65454i	−0.0779019	+	0.433684i
$171$	−1.30665	+	1.90287i	−0.0999218	+	0.145516i
$172$	−4.41792	+	8.67066i	−0.336863	+	0.661131i
$173$	−2.87802	−	18.1711i	−0.218812	−	1.38152i	−0.815364	−	0.578948i	$-0.803463\pi$
$173$	−2.87802	−	18.1711i	−0.218812	−	1.38152i	0.596553	−	0.802574i	$-0.296537\pi$
$174$	−5.33914	−	0.773009i	−0.404759	−	0.0586017i
$175$	−2.46175	+	12.2456i	−0.186091	+	0.925683i
$176$	−2.36655	−	3.25728i	−0.178385	−	0.245526i
$177$	14.8800	−	5.05452i	1.11845	−	0.379921i
$178$	4.83411	+	2.46310i	0.362332	+	0.184617i
$179$	4.04104	−	12.4371i	0.302042	−	0.929589i	−0.678723	−	0.734395i	$-0.737466\pi$
$179$	4.04104	−	12.4371i	0.302042	−	0.929589i	0.980765	−	0.195194i	$-0.0625338\pi$
$180$	−3.08092	−	5.95886i	−0.229638	−	0.444147i
$181$	−5.21423			−0.387571			−0.193785	−	0.981044i	$-0.562077\pi$
$181$	−5.21423			−0.387571			−0.193785	+	0.981044i	$0.562077\pi$
$182$	−6.40548	−	12.5715i	−0.474806	−	0.931859i
$183$	−3.21887	+	4.55659i	−0.237945	+	0.336833i
$184$	2.90088	+	3.99271i	0.213855	+	0.294347i
$185$	−17.2151	−	5.98933i	−1.26568	−	0.440344i
$186$	8.94241	+	3.61016i	0.655689	+	0.264710i
$187$	7.31460	+	7.31460i	0.534896	+	0.534896i
$188$	−2.28123	−	0.361311i	−0.166375	−	0.0263513i
$189$	−12.7296	+	2.54031i	−0.925945	+	0.184780i
$190$	−1.03982	+	1.37074i	−0.0754363	+	0.0994436i
$191$		−	25.2969i		−	1.83042i	−0.402977	−	0.915210i	$-0.632025\pi$
$191$		−	25.2969i		−	1.83042i	0.402977	−	0.915210i	$-0.367975\pi$
$192$	1.73190	−	0.0230306i	0.124989	−	0.00166209i
$193$	6.55018	+	12.8555i	0.471492	+	0.925356i	0.997206	+	0.0746946i	$0.0237982\pi$
$193$	6.55018	+	12.8555i	0.471492	+	0.925356i	−0.525714	+	0.850661i	$0.676202\pi$
$194$	5.37034	+	16.5282i	0.385568	+	1.18666i
$195$	0.160914	−	21.8738i	0.0115233	−	1.56642i
$196$	0.614344	−	0.446347i	0.0438817	−	0.0318819i
$197$	−3.47577	−	6.82158i	−0.247638	−	0.486017i	0.733409	−	0.679788i	$-0.237928\pi$
$197$	−3.47577	−	6.82158i	−0.247638	−	0.486017i	−0.981047	+	0.193771i	$0.937928\pi$
$198$	−11.9760	−	1.57162i	−0.851095	−	0.111690i
$199$	4.53310	−	6.23927i	0.321343	−	0.442290i	−0.617534	−	0.786544i	$-0.711868\pi$
$199$	4.53310	−	6.23927i	0.321343	−	0.442290i	0.938877	+	0.344254i	$0.111868\pi$
$200$	−2.08405	−	4.54497i	−0.147364	−	0.321378i
$201$	4.49781	−	0.773824i	0.317251	−	0.0545813i
$202$	−1.31125	−	8.27891i	−0.0922593	−	0.582502i
$203$	−3.53245	+	6.93283i	−0.247930	+	0.486589i
$204$	−4.38566	+	0.754529i	−0.307058	+	0.0528276i
$205$	−4.45897	−	2.38921i	−0.311428	−	0.166870i
$206$	18.2583	+	5.93247i	1.27211	+	0.413335i
$207$	14.6799	+	1.92646i	1.02033	+	0.133898i
$208$	5.03236	+	2.56412i	0.348931	+	0.177789i
$209$	0.957305	+	2.94628i	0.0662182	+	0.203799i
$210$	−9.56695	+	1.44320i	−0.660183	+	0.0995900i
$211$	−28.1423			−1.93740			−0.968700	−	0.248236i	$-0.920149\pi$
$211$	−28.1423			−1.93740			−0.968700	+	0.248236i	$0.920149\pi$
$212$	−0.170975	+	0.170975i	−0.0117426	+	0.0117426i
$213$	−4.94957	+	15.9519i	−0.339139	+	1.09301i
$214$	−4.28675	+	5.90021i	−0.293036	+	0.403330i
$215$	6.29534	+	20.8293i	0.429339	+	1.42055i
$216$	3.52478	−	3.81784i	0.239831	−	0.259771i
$217$	9.07855	−	10.5375i	0.616292	−	0.715334i
$218$	6.57942	+	6.57942i	0.445614	+	0.445614i
$219$	21.8506	+	3.16357i	1.47653	+	0.213774i
$220$	−8.86107	−	1.59170i	−0.597413	−	0.107312i
$221$	−13.8008	−	4.48416i	−0.928345	−	0.301638i
$222$	−0.187733	−	14.1175i	−0.0125998	−	0.947505i
$223$	−7.79644	+	7.79644i	−0.522088	+	0.522088i	−0.918202	−	0.396113i	$-0.870359\pi$
$223$	−7.79644	+	7.79644i	−0.522088	+	0.522088i	0.396113	+	0.918202i	$0.370359\pi$
$224$	0.771963	−	2.37586i	0.0515790	−	0.158744i
$225$	−14.1961	−	4.84463i	−0.946407	−	0.322976i
$226$	−2.66132	−	8.19070i	−0.177028	−	0.544837i
$227$	−2.82087	+	17.8103i	−0.187228	+	1.18211i	0.697703	+	0.716388i	$0.254206\pi$
$227$	−2.82087	+	17.8103i	−0.187228	+	1.18211i	−0.884930	+	0.465723i	$0.845794\pi$
$228$	−1.27283	−	0.394936i	−0.0842955	−	0.0261553i
$229$	−3.82825	−	5.26913i	−0.252978	−	0.348194i	0.663574	−	0.748111i	$-0.269039\pi$
$229$	−3.82825	−	5.26913i	−0.252978	−	0.348194i	−0.916551	+	0.399917i	$0.869039\pi$
$230$	10.8617	+	1.95108i	0.716202	+	0.128650i
$231$	−7.70185	+	15.6260i	−0.506745	+	1.02811i
$232$	−0.487245	−	3.07635i	−0.0319892	−	0.201972i
$233$	−3.76413	−	23.7658i	−0.246596	−	1.55695i	−0.731169	−	0.682197i	$-0.761025\pi$
$233$	−3.76413	−	23.7658i	−0.246596	−	1.55695i	0.484573	−	0.874751i	$-0.338975\pi$
$234$	15.9696	−	5.66259i	1.04397	−	0.370175i
$235$	−4.24002	+	2.94872i	−0.276588	+	0.192353i
$236$	5.33303	+	7.34028i	0.347151	+	0.477812i
$237$	−3.38091	+	10.8963i	−0.219614	+	0.707789i
$238$	−1.00405	+	6.33932i	−0.0650828	+	0.410917i
$239$	−6.16746	−	18.9815i	−0.398940	−	1.22781i	−0.925851	−	0.377890i	$-0.876650\pi$
$239$	−6.16746	−	18.9815i	−0.398940	−	1.22781i	0.526911	−	0.849921i	$-0.323350\pi$
$240$	2.75868	−	2.71839i	0.178072	−	0.175471i
$241$	5.81013	−	17.8817i	0.374263	−	1.15186i	−0.569711	−	0.821845i	$-0.692945\pi$
$241$	5.81013	−	17.8817i	0.374263	−	1.15186i	0.943974	−	0.330019i	$-0.107055\pi$
$242$	−3.68432	+	3.68432i	−0.236837	+	0.236837i
$243$	−1.03564	−	15.5540i	−0.0664365	−	0.997791i
$244$	−3.06331	−	0.995329i	−0.196108	−	0.0637194i
$245$	0.300205	−	1.67126i	0.0191794	−	0.106773i
$246$	0.561469	−	3.87804i	0.0357979	−	0.247255i
$247$	−3.07289	−	3.07289i	−0.195523	−	0.195523i
$248$	−0.460708	+	5.54867i	−0.0292550	+	0.352341i
$249$	1.82154	−	1.87064i	0.115436	−	0.118547i
$250$	−10.3988	−	4.10670i	−0.657678	−	0.259730i
$251$	1.87895	−	2.58615i	0.118598	−	0.163236i	−0.745590	−	0.666405i	$-0.767832\pi$
$251$	1.87895	−	2.58615i	0.118598	−	0.163236i	0.864188	+	0.503168i	$0.167832\pi$
$252$	−3.57873	−	6.58470i	−0.225439	−	0.414797i
$253$	14.0505	−	14.0505i	0.883349	−	0.883349i
$254$	−7.39810			−0.464198
$255$	−5.90794	+	8.00705i	−0.369970	+	0.501421i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	2.56872	+	1.30883i	0.160233	+	0.0816426i	0.532268	−	0.846576i	$-0.321340\pi$
$257$	2.56872	+	1.30883i	0.160233	+	0.0816426i	−0.372035	+	0.928219i	$0.621340\pi$
$258$	−13.5031	+	10.0876i	−0.840669	+	0.628028i
$259$	−19.3667	−	6.29263i	−1.20339	−	0.391005i
$260$	12.0891	−	3.65375i	0.749735	−	0.226596i
$261$	−7.70289	−	5.28935i	−0.476797	−	0.327403i
$262$	8.00123	−	15.7033i	0.494318	−	0.970153i
$263$	3.45836	+	21.8352i	0.213251	+	1.34642i	0.829342	+	0.558741i	$0.188716\pi$
$263$	3.45836	+	21.8352i	0.213251	+	1.34642i	−0.616090	+	0.787675i	$0.711284\pi$
$264$	−1.18240	−	6.87264i	−0.0727718	−	0.422982i
$265$	−0.0111659	+	0.540554i	−0.000685915	+	0.0332060i
$266$	−1.12981	+	1.55504i	−0.0692728	+	0.0953459i
$267$	5.62411	+	7.52834i	0.344190	+	0.460727i
$268$	1.19625	+	2.34777i	0.0730725	+	0.143413i
$269$	−10.6116	+	7.70977i	−0.647000	+	0.470073i	−0.862248	−	0.506486i	$-0.830944\pi$
$269$	−10.6116	+	7.70977i	−0.647000	+	0.470073i	0.215248	+	0.976559i	$0.430944\pi$
$270$	−0.223510	−	11.6168i	−0.0136024	−	0.706976i
$271$	2.28867	+	7.04379i	0.139027	+	0.427880i	0.996195	−	0.0871572i	$-0.0277782\pi$
$271$	2.28867	+	7.04379i	0.139027	+	0.427880i	−0.857168	+	0.515037i	$0.827778\pi$
$272$	−1.16642	−	2.28923i	−0.0707246	−	0.138805i
$273$	−0.324945	−	24.4358i	−0.0196666	−	1.47892i
$274$			20.7337i			1.25257i
$275$	−16.7611	+	11.1501i	−1.01073	+	0.672377i
$276$	1.44937	+	8.42436i	0.0872416	+	0.507087i
$277$	−24.0408	−	3.80768i	−1.44447	−	0.228782i	−0.615527	−	0.788116i	$-0.711057\pi$
$277$	−24.0408	−	3.80768i	−1.44447	−	0.228782i	−0.828942	+	0.559334i	$0.811057\pi$
$278$	−11.6336	−	11.6336i	−0.697739	−	0.697739i
$279$	11.1284	+	12.4563i	0.666238	+	0.745740i
$280$	−2.43265	−	5.02845i	−0.145379	−	0.300508i
$281$	18.5597	+	25.5453i	1.10718	+	1.52390i	0.825507	+	0.564391i	$0.190889\pi$
$281$	18.5597	+	25.5453i	1.10718	+	1.52390i	0.281672	+	0.959511i	$0.409111\pi$
$282$	−3.26741	−	2.30816i	−0.194572	−	0.137449i
$283$	10.4719	+	20.5523i	0.622490	+	1.22170i	0.959899	+	0.280347i	$0.0904494\pi$
$283$	10.4719	+	20.5523i	0.622490	+	1.22170i	−0.337409	+	0.941358i	$0.609551\pi$
$284$	−9.64298			−0.572206
$285$	−2.66508	+	1.33332i	−0.157866	+	0.0789793i
$286$	7.02701	−	21.6269i	0.415516	−	1.27883i
$287$	−5.03560	−	2.56577i	−0.297242	−	0.151452i
$288$	2.70829	+	1.29041i	0.159588	+	0.0760382i
$289$	−6.11232	−	8.41288i	−0.359548	−	0.494875i
$290$	−5.54879	−	4.20922i	−0.325836	−	0.247174i
$291$	−4.31309	+	29.7903i	−0.252838	+	1.74634i
$292$	1.99407	+	12.5901i	0.116694	+	0.736777i
$293$	6.36451	−	12.4911i	0.371819	−	0.729735i	−0.626965	−	0.779048i	$-0.715703\pi$
$293$	6.36451	−	12.4911i	0.371819	−	0.729735i	0.998783	+	0.0493125i	$0.0157030\pi$
$294$	1.29623	−	0.223009i	0.0755974	−	0.0130061i
$295$	19.9684	+	3.58690i	1.16261	+	0.208837i
$296$	7.75251	−	2.51894i	0.450605	−	0.146411i
$297$	−17.4023	−	11.6122i	−1.00978	−	0.673807i
$298$	1.65266	−	10.4345i	0.0957359	−	0.604453i
$299$	−8.61358	+	26.5099i	−0.498136	+	1.53311i
$300$	0.242540	−	8.65686i	0.0140030	−	0.499804i
$301$	7.51221	+	23.1202i	0.432997	+	1.33263i
$302$	4.40298	+	2.24343i	0.253363	+	0.129095i
$303$	4.30239	−	13.8661i	0.247166	−	0.796587i
$304$		−	0.769433i		−	0.0441300i
$305$	−6.48343	+	3.13654i	−0.371240	+	0.179598i
$306$	−7.39128	−	2.18607i	−0.422531	−	0.124969i
$307$	1.25296	+	7.91087i	0.0715102	+	0.451497i	0.997299	+	0.0734552i	$0.0234026\pi$
$307$	1.25296	+	7.91087i	0.0715102	+	0.451497i	−0.925788	+	0.378042i	$0.876597\pi$
$308$	−9.93416	−	1.57342i	−0.566051	−	0.0896537i
$309$	23.8231	+	23.1978i	1.35525	+	1.31968i
$310$	7.84683	+	9.66578i	0.445670	+	0.548979i
$311$		−	0.568537i		−	0.0322388i	−0.999870	−	0.0161194i	$-0.994869\pi$
$311$		−	0.568537i		−	0.0322388i	0.999870	−	0.0161194i	$-0.00513118\pi$
$312$	5.85476	+	7.83708i	0.331460	+	0.443687i
$313$	−6.17028	+	0.977276i	−0.348765	+	0.0552389i	−0.328359	−	0.944553i	$-0.606496\pi$
$313$	−6.17028	+	0.977276i	−0.348765	+	0.0552389i	−0.0204054	+	0.999792i	$0.506496\pi$
$314$	3.24749	−	9.99476i	0.183267	−	0.564037i
$315$	−15.9682	−	5.08371i	−0.899707	−	0.286435i
$316$	−6.58684			−0.370539
$317$	2.48859	+	4.88413i	0.139773	+	0.274320i	0.950273	−	0.311419i	$-0.100804\pi$
$317$	2.48859	+	4.88413i	0.139773	+	0.274320i	−0.810500	+	0.585739i	$0.800804\pi$
$318$	−0.396547	+	0.134701i	−0.0222373	+	0.00755367i
$319$	−11.9267	+	3.87521i	−0.667764	+	0.216970i
$320$	1.97096	+	1.05608i	0.110180	+	0.0590368i
$321$	−11.1779	+	5.88393i	−0.623889	+	0.328409i
$322$	12.1771	+	1.92867i	0.678604	+	0.107480i
$323$	0.309251	+	1.95254i	0.0172072	+	0.108642i
$324$	8.39955	−	3.23227i	0.466642	−	0.179571i
$325$	13.8487	−	24.6109i	0.768188	−	1.36517i
$326$	0.880251	−	1.21156i	0.0487526	−	0.0671022i
$327$	5.18355	+	15.2599i	0.286651	+	0.843872i
$328$	2.23448	−	0.353907i	0.123378	−	0.0195412i
$329$	−4.66789	+	3.39142i	−0.257349	+	0.186975i
$330$	−12.5476	−	9.25816i	−0.690723	−	0.509645i
$331$	−3.32046	+	2.41245i	−0.182509	+	0.132600i	−0.675288	−	0.737554i	$-0.735981\pi$
$331$	−3.32046	+	2.41245i	−0.182509	+	0.132600i	0.492780	+	0.870154i	$0.335981\pi$
$332$	1.34316	+	0.684373i	0.0737154	+	0.0375599i
$333$	10.5187	−	22.0765i	0.576424	−	1.20979i
$334$	8.30276	+	2.69773i	0.454307	+	0.147613i
$335$	5.56478	+	1.93605i	0.304037	+	0.105778i
$336$	3.01861	−	3.09998i	0.164679	−	0.169118i
$337$	−15.3944	+	7.84383i	−0.838586	+	0.427281i	−0.819874	−	0.572544i	$-0.805957\pi$
$337$	−15.3944	+	7.84383i	−0.838586	+	0.427281i	−0.0187120	+	0.999825i	$0.505957\pi$
$338$	2.95651	+	18.6667i	0.160813	+	1.01533i
$339$	2.13739	−	14.7629i	0.116087	−	0.801809i
$340$	−5.42603	−	1.88778i	−0.294268	−	0.102379i
$341$	22.3553	−	1.66270i	1.21061	−	0.0900401i
$342$	−1.67504	−	1.58823i	−0.0905757	−	0.0858819i
$343$	3.03231	−	19.1452i	0.163729	−	1.03375i
$344$	−7.87279	−	5.71992i	−0.424473	−	0.308397i
$345$	15.3806	+	11.3485i	0.828066	+	0.610982i
$346$	18.3976			0.989061
$347$	3.09685	−	3.09685i	0.166248	−	0.166248i	−0.619080	−	0.785328i	$-0.712494\pi$
$347$	3.09685	−	3.09685i	0.166248	−	0.166248i	0.785328	+	0.619080i	$0.212494\pi$
$348$	1.59872	−	5.15248i	0.0857002	−	0.276202i
$349$	0.0629064	−	0.0204395i	0.00336730	−	0.00109410i	−0.307333	−	0.951602i	$-0.599436\pi$
$349$	0.0629064	−	0.0204395i	0.00336730	−	0.00109410i	0.310700	+	0.950508i	$0.399436\pi$
$350$	−11.7098	−	4.34708i	−0.625913	−	0.232361i
$351$	29.1463	+	3.43133i	1.55572	+	0.183151i
$352$	3.58738	−	1.82786i	0.191208	−	0.0974255i
$353$	14.9821	+	2.37293i	0.797416	+	0.126298i	0.541830	−	0.840488i	$-0.317732\pi$
$353$	14.9821	+	2.37293i	0.797416	+	0.126298i	0.255586	+	0.966786i	$0.417732\pi$
$354$	2.66454	+	15.4875i	0.141619	+	0.823152i
$355$	−15.5585	+	14.9288i	−0.825761	+	0.792337i
$356$	−3.18900	+	4.38928i	−0.169017	+	0.232631i
$357$	−6.41418	+	9.07984i	−0.339474	+	0.480556i
$358$	11.6518	+	5.93687i	0.615815	+	0.313774i
$359$	21.2508	+	15.4396i	1.12157	+	0.814871i	0.984447	−	0.175682i	$-0.0562132\pi$
$359$	21.2508	+	15.4396i	1.12157	+	0.814871i	0.137127	+	0.990553i	$0.456213\pi$
$360$	6.36745	−	2.11081i	0.335594	−	0.111250i
$361$	5.68838	−	17.5070i	0.299388	−	0.921422i
$362$	0.815686	−	5.15004i	0.0428715	−	0.270680i
$363$	−8.54516	+	2.90266i	−0.448505	+	0.152350i
$364$	13.4187	−	4.36001i	0.703333	−	0.228527i
$365$	22.7086	+	17.2264i	1.18862	+	0.901670i
$366$	−3.99695	−	3.89204i	−0.208924	−	0.203440i
$367$	7.66141	+	7.66141i	0.399923	+	0.399923i	0.878206	−	0.478283i	$-0.158741\pi$
$367$	7.66141	+	7.66141i	0.399923	+	0.399923i	−0.478283	+	0.878206i	$0.658741\pi$
$368$	−4.39735	+	2.24056i	−0.229228	+	0.116797i
$369$	3.84188	−	5.59493i	0.200000	−	0.291260i
$370$	8.60863	−	16.0662i	0.447541	−	0.835243i
$371$			0.604034i			0.0313599i
$372$	−4.96462	+	8.26756i	−0.257403	+	0.428653i
$373$	6.80299	−	6.80299i	0.352246	−	0.352246i	−0.508699	−	0.860945i	$-0.669873\pi$
$373$	6.80299	−	6.80299i	0.352246	−	0.352246i	0.860945	+	0.508699i	$0.169873\pi$
$374$	−8.36880	+	6.08029i	−0.432740	+	0.314404i
$375$	−13.0108	−	14.3429i	−0.671873	−	0.740666i
$376$	0.713725	−	2.19662i	0.0368075	−	0.113282i
$377$	12.4392	−	12.4392i	0.640650	−	0.640650i
$378$	−0.517677	−	12.9703i	−0.0266264	−	0.667121i
$379$	11.1532	+	3.62389i	0.572901	+	0.186147i	0.581118	−	0.813819i	$-0.302616\pi$
$379$	11.1532	+	3.62389i	0.572901	+	0.186147i	−0.00821677	+	0.999966i	$0.502616\pi$
$380$	−1.19120	−	1.24145i	−0.0611071	−	0.0636848i
$381$	−11.4936	−	5.66506i	−0.588835	−	0.290230i
$382$	24.9855	+	3.95731i	1.27837	+	0.202474i
$383$	4.60343	−	2.34556i	0.235224	−	0.119853i	−0.332406	−	0.943136i	$-0.607860\pi$
$383$	4.60343	−	2.34556i	0.235224	−	0.119853i	0.567630	+	0.823284i	$0.307860\pi$
$384$	−0.248181	+	1.71418i	−0.0126650	+	0.0874763i
$385$	−18.4642	+	12.8409i	−0.941023	+	0.654434i
$386$	−13.7219	+	4.45850i	−0.698424	+	0.226932i
$387$	−28.7029	+	5.33206i	−1.45905	+	0.271044i
$388$	−17.1648	+	2.71864i	−0.871411	+	0.138018i
$389$	−2.50783	−	7.71832i	−0.127152	−	0.391334i	0.867135	−	0.498073i	$-0.165959\pi$
$389$	−2.50783	−	7.71832i	−0.127152	−	0.391334i	−0.994287	+	0.106739i	$0.965959\pi$
$390$	21.5794	+	3.58075i	1.09271	+	0.181318i
$391$	10.2583	−	7.45311i	0.518786	−	0.376920i
$392$	0.344747	+	0.676605i	0.0174124	+	0.0341737i
$393$	24.4553	−	18.2695i	1.23361	−	0.921577i
$394$	7.28132	−	2.36585i	0.366828	−	0.119190i
$395$	−10.6276	+	10.1974i	−0.534731	+	0.513087i
$396$	3.42572	−	11.5827i	0.172149	−	0.582051i
$397$	5.08208	+	5.08208i	0.255062	+	0.255062i	0.823042	−	0.567980i	$-0.192275\pi$
$397$	5.08208	+	5.08208i	0.255062	+	0.255062i	−0.567980	+	0.823042i	$0.692275\pi$
$398$	5.45332	+	5.45332i	0.273350	+	0.273350i
$399$	−2.94602	+	1.55075i	−0.147485	+	0.0776348i
$400$	4.81503	−	1.34740i	0.240752	−	0.0673699i
$401$	−9.22997	−	12.7040i	−0.460923	−	0.634406i	0.513777	−	0.857924i	$-0.328246\pi$
$401$	−9.22997	−	12.7040i	−0.460923	−	0.634406i	−0.974700	+	0.223518i	$0.928246\pi$
$402$	0.0606847	+	4.56348i	0.00302668	+	0.227606i
$403$	−26.8829	+	16.3153i	−1.33913	+	0.812722i
$404$	8.38211			0.417026
$405$	8.54826	−	18.2189i	0.424766	−	0.905303i
$406$	−6.29487	−	4.57349i	−0.312409	−	0.226979i
$407$	−14.8998	−	29.2424i	−0.738554	−	1.44949i
$408$	−0.0591716	−	4.44970i	−0.00292943	−	0.220293i
$409$			16.1226i			0.797209i	0.917123	+	0.398605i	$0.130505\pi$
$409$			16.1226i			0.797209i	−0.917123	+	0.398605i	$0.869495\pi$
$410$	3.05733	−	4.03032i	0.150991	−	0.199043i
$411$	−15.8767	+	32.2116i	−0.783141	+	1.58888i
$412$	−8.71566	+	17.1054i	−0.429390	+	0.842724i
$413$	22.3867	+	3.54570i	1.10158	+	0.174472i
$414$	−4.19919	+	14.1978i	−0.206379	+	0.697785i
$415$	3.22664	−	0.975202i	0.158389	−	0.0478708i
$416$	−3.31978	+	4.56929i	−0.162766	+	0.224028i
$417$	−9.16548	−	26.9823i	−0.448836	−	1.32133i
$418$	−3.05976	+	0.484619i	−0.149658	+	0.0237035i
$419$	7.44663	+	5.41029i	0.363792	+	0.264310i	0.754632	−	0.656148i	$-0.227816\pi$
$419$	7.44663	+	5.41029i	0.363792	+	0.264310i	−0.390840	+	0.920459i	$0.627816\pi$
$420$	0.0711732	−	9.67493i	0.00347290	−	0.472088i
$421$	−26.0845	−	18.9515i	−1.27128	−	0.923639i	−0.272028	−	0.962289i	$-0.587694\pi$
$421$	−26.0845	−	18.9515i	−1.27128	−	0.923639i	−0.999253	+	0.0386499i	$0.987694\pi$
$422$	4.40243	−	27.7959i	0.214307	−	1.35308i
$423$	−3.30875	−	6.08794i	−0.160877	−	0.296006i
$424$	−0.142123	−	0.195616i	−0.00690212	−	0.00949996i
$425$	−11.6772	+	5.35446i	−0.566428	+	0.259729i
$426$	−14.9812	−	7.38406i	−0.725843	−	0.357759i
$427$	−7.16935	+	3.65296i	−0.346949	+	0.176779i
$428$	−5.15697	−	5.15697i	−0.249272	−	0.249272i
$429$	27.4778	−	28.2184i	1.32664	−	1.36240i
$430$	−21.5577	+	2.95942i	−1.03960	+	0.142716i
$431$	−12.3937	+	17.0585i	−0.596985	+	0.821680i	−0.995428	−	0.0955134i	$-0.969551\pi$
$431$	−12.3937	+	17.0585i	−0.596985	+	0.821680i	0.398443	+	0.917193i	$0.369551\pi$
$432$	3.21944	+	4.07863i	0.154895	+	0.196233i
$433$	−25.1698	+	25.1698i	−1.20958	+	1.20958i	−0.238423	+	0.971161i	$0.576630\pi$
$433$	−25.1698	+	25.1698i	−1.20958	+	1.20958i	−0.971161	+	0.238423i	$0.923370\pi$
$434$	8.98759	+	10.6152i	0.431418	+	0.509547i
$435$	−5.39734	−	10.7883i	−0.258783	−	0.517262i
$436$	−7.52766	+	5.46917i	−0.360510	+	0.261926i
$437$	3.75060	−	0.594037i	0.179416	−	0.0284167i
$438$	−6.54281	+	21.0867i	−0.312627	+	1.00756i
$439$			36.0234i			1.71930i	0.510882	+	0.859651i	$0.329319\pi$
$439$			36.0234i			1.71930i	−0.510882	+	0.859651i	$0.670681\pi$
$440$	2.95828	−	8.50298i	0.141030	−	0.405364i
$441$	2.18457	+	0.646114i	0.104027	+	0.0307674i
$442$	6.58788	−	12.9295i	0.313354	−	0.614991i
$443$	2.90884	−	5.70892i	0.138203	−	0.271239i	−0.811523	−	0.584320i	$-0.801361\pi$
$443$	2.90884	−	5.70892i	0.138203	−	0.271239i	0.949726	+	0.313081i	$0.101361\pi$
$444$	13.9731	+	2.02304i	0.663132	+	0.0960094i
$445$	1.64995	+	12.0189i	0.0782151	+	0.569753i
$446$	−6.48082	−	8.92009i	−0.306876	−	0.422378i
$447$	10.5577	−	14.9454i	0.499362	−	0.706891i
$448$	2.22585	+	1.13413i	0.105161	+	0.0535824i
$449$	21.1658	+	15.3779i	0.998876	+	0.725726i	0.961847	−	0.273588i	$-0.0882106\pi$
$449$	21.1658	+	15.3779i	0.998876	+	0.725726i	0.0370290	+	0.999314i	$0.488211\pi$
$450$	7.00575	−	13.2635i	0.330254	−	0.625246i
$451$	−2.81472	−	8.66283i	−0.132540	−	0.407917i
$452$	8.50618	−	1.34725i	0.400097	−	0.0633691i
$453$	5.12252	+	6.85693i	0.240677	+	0.322167i
$454$	−17.1497	−	5.57229i	−0.804877	−	0.261520i
$455$	14.9006	−	27.8089i	0.698550	−	1.30370i
$456$	0.589189	−	1.19538i	0.0275913	−	0.0559789i
$457$	−3.71660	+	7.29423i	−0.173855	+	0.341210i	−0.961448	−	0.274986i	$-0.911327\pi$
$457$	−3.71660	+	7.29423i	−0.173855	+	0.341210i	0.787593	+	0.616195i	$0.211327\pi$
$458$	5.80313	−	2.95684i	0.271162	−	0.138164i
$459$	−9.80904	−	9.05608i	−0.457847	−	0.422702i
$460$	−3.62621	+	10.4228i	−0.169073	+	0.485966i
$461$	29.2650	+	9.50878i	1.36301	+	0.442868i	0.897046	−	0.441937i	$-0.145708\pi$
$461$	29.2650	+	9.50878i	1.36301	+	0.442868i	0.465962	+	0.884805i	$0.345708\pi$
$462$	−14.2288	−	10.0515i	−0.661982	−	0.467637i
$463$	−2.73617	+	17.2755i	−0.127161	+	0.802860i	0.838851	+	0.544361i	$0.183228\pi$
$463$	−2.73617	+	17.2755i	−0.127161	+	0.802860i	−0.966012	+	0.258499i	$0.916772\pi$
$464$	3.11469			0.144596
$465$	4.78923	+	21.0253i	0.222095	+	0.975025i
$466$	24.0620			1.11465
$467$	−3.25001	+	20.5197i	−0.150392	+	0.949540i	0.790900	+	0.611946i	$0.209613\pi$
$467$	−3.25001	+	20.5197i	−0.150392	+	0.949540i	−0.941292	+	0.337594i	$0.890387\pi$
$468$	3.09467	+	16.6588i	0.143051	+	0.770055i
$469$	6.26030	+	2.03409i	0.289074	+	0.0939257i
$470$	−2.24913	−	4.64910i	−0.103745	−	0.214447i
$471$	12.6987	−	13.0410i	0.585125	−	0.600897i
$472$	−8.08418	+	4.11910i	−0.372105	+	0.189597i
$473$	−17.7875	+	34.9099i	−0.817870	+	1.60516i
$474$	−10.2332	−	5.04384i	−0.470028	−	0.231671i
$475$	−3.84388	−	0.158869i	−0.176369	−	0.00728941i
$476$	−6.10420	−	1.98338i	−0.279786	−	0.0909078i
$477$	−0.719218	−	0.0943837i	−0.0329307	−	0.00432153i
$478$	19.7126	−	3.12217i	0.901633	−	0.142805i
$479$	−3.72832	−	11.4746i	−0.170351	−	0.524288i	0.829039	−	0.559190i	$-0.188888\pi$
$479$	−3.72832	−	11.4746i	−0.170351	−	0.524288i	−0.999391	+	0.0349025i	$0.988888\pi$
$480$	2.25337	+	3.14997i	0.102852	+	0.143776i
$481$	37.2464	+	27.0611i	1.69829	+	1.23388i
$482$	16.7527	+	8.53591i	0.763063	+	0.388800i
$483$	17.4414	+	12.3209i	0.793609	+	0.560621i
$484$	−3.06260	−	4.21531i	−0.139209	−	0.191605i
$485$	−23.4858	+	30.9601i	−1.06644	+	1.40582i
$486$	15.5245	+	1.41029i	0.704207	+	0.0639721i
$487$	−5.72154	+	11.2292i	−0.259268	+	0.508842i	−0.983544	−	0.180668i	$-0.942174\pi$
$487$	−5.72154	+	11.2292i	−0.259268	+	0.508842i	0.724276	+	0.689510i	$0.242174\pi$
$488$	1.46228	−	2.86989i	0.0661944	−	0.129914i
$489$	2.29529	−	1.20822i	0.103797	−	0.0546376i
$490$	1.60372	+	0.557952i	0.0724486	+	0.0252057i
$491$		−	16.7431i		−	0.755605i	−0.925886	−	0.377802i	$-0.876680\pi$
$491$		−	16.7431i		−	0.755605i	0.925886	−	0.377802i	$-0.123320\pi$
$492$	3.74246	+	1.16121i	0.168723	+	0.0523516i
$493$	−7.90394	+	1.25186i	−0.355975	+	0.0563810i
$494$	3.51576	−	2.55435i	0.158182	−	0.114926i
$495$	−12.4044	−	23.9916i	−0.557538	−	1.07834i
$496$	−5.40829	−	1.32304i	−0.242839	−	0.0594062i
$497$	−17.0338	+	17.0338i	−0.764069	+	0.764069i
$498$	1.56266	+	2.09175i	0.0700244	+	0.0937336i
$499$	21.6691	−	29.8249i	0.970040	−	1.33515i	0.0280132	−	0.999608i	$-0.491082\pi$
$499$	21.6691	−	29.8249i	0.970040	−	1.33515i	0.942027	−	0.335538i	$-0.108918\pi$
$500$	5.68287	−	9.62835i	0.254146	−	0.430593i
$501$	10.8333	+	10.5490i	0.483996	+	0.471293i
$502$	2.26038	+	2.26038i	0.100886	+	0.100886i
$503$	30.1259	−	15.3499i	1.34325	−	0.684418i	0.373294	−	0.927713i	$-0.378228\pi$
$503$	30.1259	−	15.3499i	1.34325	−	0.684418i	0.969952	+	0.243295i	$0.0782283\pi$
$504$	7.06347	−	2.50460i	0.314632	−	0.111564i
$505$	13.5242	−	12.9768i	0.601817	−	0.577458i
$506$	11.6796	+	16.0755i	0.519219	+	0.714644i
$507$	−9.70070	+	31.2642i	−0.430823	+	1.38849i
$508$	1.15732	−	7.30702i	0.0513477	−	0.324197i
$509$	−27.8685	−	20.2476i	−1.23525	−	0.897460i	−0.237975	−	0.971271i	$-0.576484\pi$
$509$	−27.8685	−	20.2476i	−1.23525	−	0.897460i	−0.997272	+	0.0738112i	$0.976484\pi$
$510$	−6.98426	−	7.08778i	−0.309268	−	0.313852i
$511$	25.7620	+	18.7172i	1.13964	+	0.827999i
$512$	−0.987688	+	0.156434i	−0.0436501	+	0.00691349i
$513$	−1.38614	−	3.75011i	−0.0611995	−	0.165572i
$514$	−1.69455	+	2.33235i	−0.0747435	+	0.102876i
$515$	12.4194	+	41.0920i	0.547265	+	1.81073i
$516$	−7.85108	−	14.9149i	−0.345624	−	0.656594i
$517$	−9.18471	−	1.45471i	−0.403943	−	0.0639783i
$518$	9.24478	−	18.1439i	0.406192	−	0.797198i
$519$	28.5823	+	14.0879i	1.25462	+	0.618388i
$520$	1.71761	+	12.5119i	0.0753224	+	0.548681i
$521$		−	27.6791i		−	1.21265i	−0.795219	−	0.606323i	$-0.792644\pi$
$521$		−	27.6791i		−	1.21265i	0.795219	−	0.606323i	$-0.207356\pi$
$522$	6.42923	−	6.78062i	0.281400	−	0.296780i
$523$	−19.1276	−	37.5399i	−0.836389	−	1.64151i	−0.764975	−	0.644060i	$-0.777249\pi$
$523$	−19.1276	−	37.5399i	−0.836389	−	1.64151i	−0.0714143	−	0.997447i	$-0.522751\pi$
$524$	14.2583	+	10.3593i	0.622876	+	0.452546i
$525$	−14.8634	−	15.7203i	−0.648692	−	0.686088i
$526$	−22.1074			−0.963928
$527$	14.2560	+	1.18368i	0.621001	+	0.0515618i
$528$	6.97299	−	0.0927261i	0.303461	−	0.00403538i
$529$	−0.797532	−	1.09771i	−0.0346753	−	0.0477265i
$530$	−0.532152	−	0.0955897i	−0.0231152	−	0.00415215i
$531$	−7.71988	+	26.1016i	−0.335014	+	1.13271i
$532$	−1.35916	−	1.35916i	−0.0589270	−	0.0589270i
$533$	9.03508	+	9.03508i	0.391353	+	0.391353i
$534$	−8.31546	+	4.37717i	−0.359845	+	0.189419i
$535$	−16.3043	−	0.336787i	−0.704896	−	0.0145606i
$536$	−2.50600	+	0.814248i	−0.108243	+	0.0351702i
$537$	13.5559	+	18.1457i	0.584981	+	0.783046i
$538$	−5.95483	−	11.6870i	−0.256731	−	0.503863i
$539$	2.47348	−	1.79709i	0.106540	−	0.0774062i
$540$	11.5087	+	1.59651i	0.495257	+	0.0687028i
$541$	−10.6761	−	32.8576i	−0.459001	−	1.41266i	−0.866373	−	0.499398i	$-0.833555\pi$
$541$	−10.6761	−	32.8576i	−0.459001	−	1.41266i	0.407372	−	0.913262i	$-0.366445\pi$
$542$	−7.31509	+	1.15860i	−0.314210	+	0.0497660i
$543$	5.21085	−	7.37643i	0.223619	−	0.316553i
$544$	2.44351	−	0.793945i	0.104765	−	0.0340401i
$545$	−3.67847	+	20.4782i	−0.157568	+	0.877189i
$546$	24.1858	+	3.50166i	1.03506	+	0.149857i
$547$	1.06157	−	0.540897i	0.0453894	−	0.0231271i	−0.431148	−	0.902281i	$-0.641891\pi$
$547$	1.06157	−	0.540897i	0.0453894	−	0.0231271i	0.476538	+	0.879154i	$0.341891\pi$
$548$	−20.4784	−	3.24347i	−0.874796	−	0.138554i
$549$	−3.22930	−	9.10728i	−0.137823	−	0.388689i
$550$	−8.39082	−	18.2990i	−0.357786	−	0.780273i
$551$	−2.27925	−	0.740574i	−0.0970994	−	0.0315495i
$552$	−8.54737	+	0.113662i	−0.363800	+	0.00483778i
$553$	−11.6353	+	11.6353i	−0.494782	+	0.494782i
$554$	7.52161	−	23.1491i	0.319563	−	0.983512i
$555$	25.6769	−	18.3683i	1.08992	−	0.779690i
$556$	13.3103	−	9.67051i	0.564483	−	0.410121i
$557$	31.0153	−	31.0153i	1.31416	−	1.31416i	0.395844	−	0.918318i	$-0.370452\pi$
$557$	31.0153	−	31.0153i	1.31416	−	1.31416i	0.918318	−	0.395844i	$-0.129548\pi$
$558$	−14.0438	+	9.04276i	−0.594522	+	0.382810i
$559$		−	54.9619i		−	2.32464i
$560$	5.34710	−	1.61608i	0.225956	−	0.0682918i
$561$	−17.6576	+	3.03790i	−0.745505	+	0.128260i
$562$	−28.1341	+	14.3351i	−1.18677	+	0.604688i
$563$	−7.47690	−	7.47690i	−0.315114	−	0.315114i	0.531773	−	0.846887i	$-0.321526\pi$
$563$	−7.47690	−	7.47690i	−0.315114	−	0.315114i	−0.846887	+	0.531773i	$0.821526\pi$
$564$	2.79088	−	2.86611i	0.117517	−	0.120685i
$565$	11.6386	−	15.3425i	0.489640	−	0.645466i
$566$	−21.9374	+	7.12789i	−0.922097	+	0.299608i
$567$	9.12769	−	20.5469i	0.383327	−	0.862890i
$568$	1.50850	−	9.52426i	0.0632950	−	0.399629i
$569$	9.44375	−	29.0649i	0.395902	−	1.21846i	−0.532354	−	0.846522i	$-0.678692\pi$
$569$	9.44375	−	29.0649i	0.395902	−	1.21846i	0.928256	−	0.371941i	$-0.121308\pi$
$570$	−0.899997	−	2.84085i	−0.0376967	−	0.118990i
$571$	12.5900	+	9.14718i	0.526875	+	0.382797i	0.819188	−	0.573525i	$-0.194425\pi$
$571$	12.5900	+	9.14718i	0.526875	+	0.382797i	−0.292312	+	0.956323i	$0.594425\pi$
$572$	20.2614	+	10.3237i	0.847170	+	0.431655i
$573$	35.7868	+	25.2805i	1.49502	+	1.05611i
$574$	3.32192	−	4.57223i	0.138654	−	0.190841i
$575$	10.2853	+	22.4306i	0.428927	+	0.935422i
$576$	−1.69819	+	2.47308i	−0.0707581	+	0.103045i
$577$	33.5050	+	5.30668i	1.39483	+	0.220920i	0.808188	−	0.588924i	$-0.200448\pi$
$577$	33.5050	+	5.30668i	1.39483	+	0.220920i	0.586645	+	0.809844i	$0.300448\pi$
$578$	9.26548	−	4.72100i	0.385393	−	0.196368i
$579$	−24.7322	−	3.58077i	−1.02783	−	0.148812i
$580$	5.02542	−	4.82201i	0.208669	−	0.200223i
$581$	3.58152	−	1.16370i	0.148586	−	0.0482786i
$582$	−28.7488	−	8.92022i	−1.19168	−	0.369755i
$583$	−0.688381	+	0.688381i	−0.0285098	+	0.0285098i
$584$	−12.7470			−0.527474
$585$	30.7835	+	22.0873i	1.27274	+	0.913197i
$586$	11.3416	+	8.24018i	0.468519	+	0.340399i
$587$	−6.31924	+	39.8981i	−0.260823	+	1.64677i	0.415084	+	0.909783i	$0.363752\pi$
$587$	−6.31924	+	39.8981i	−0.260823	+	1.64677i	−0.675907	+	0.736987i	$0.736248\pi$
$588$	0.0174888	+	1.31515i	0.000721224	+	0.0542360i
$589$	3.64307	+	2.25408i	0.150110	+	0.0928779i
$590$	−6.66649	+	19.1615i	−0.274455	+	0.788866i
$591$	13.1238	+	1.90009i	0.539841	+	0.0781591i
$592$	1.27517	+	8.05111i	0.0524092	+	0.330899i
$593$	−2.24781	+	1.14532i	−0.0923067	+	0.0470326i	−0.499534	−	0.866294i	$-0.666496\pi$
$593$	−2.24781	+	1.14532i	−0.0923067	+	0.0470326i	0.407228	+	0.913327i	$0.366496\pi$
$594$	14.1915	−	15.3715i	0.582285	−	0.630699i
$595$	−12.9194	+	6.25012i	−0.529644	+	0.256230i
$596$	10.0475	+	3.26462i	0.411561	+	0.133724i
$597$	4.29636	+	12.6481i	0.175838	+	0.517651i
$598$	−24.8360	−	12.6546i	−1.01562	−	0.517485i
$599$	−0.258528	+	0.187832i	−0.0105632	+	0.00767459i	−0.593054	−	0.805162i	$-0.702078\pi$
$599$	−0.258528	+	0.187832i	−0.0105632	+	0.00767459i	0.582491	+	0.812837i	$0.302078\pi$
$600$	8.51234	+	1.59378i	0.347515	+	0.0650660i
$601$	−17.7859	+	12.9222i	−0.725501	+	0.527108i	−0.888137	−	0.459579i	$-0.848000\pi$
$601$	−17.7859	+	12.9222i	−0.725501	+	0.527108i	0.162636	+	0.986686i	$0.448000\pi$
$602$	−24.0107	+	3.80293i	−0.978604	+	0.154996i
$603$	−3.40018	+	7.13624i	−0.138466	+	0.290610i
$604$	−2.90459	+	3.99782i	−0.118186	+	0.162669i
$605$	−11.4673	−	2.05985i	−0.466212	−	0.0837450i
$606$	13.0223	+	6.41856i	0.528997	+	0.260736i
$607$	6.63449	+	41.8885i	0.269286	+	1.70020i	0.637490	+	0.770459i	$0.279973\pi$
$607$	6.63449	+	41.8885i	0.269286	+	1.70020i	−0.368204	+	0.929745i	$0.620027\pi$
$608$	0.759960	+	0.120366i	0.0308205	+	0.00488148i
$609$	−6.27751	−	11.9256i	−0.254378	−	0.483249i
$610$	−2.08369	−	6.89427i	−0.0843661	−	0.279141i
$611$	12.4064	−	4.03108i	0.501909	−	0.163080i
$612$	3.31540	−	6.95831i	0.134017	−	0.281273i
$613$	5.08910	+	9.98792i	0.205547	+	0.403408i	0.970649	−	0.240501i	$-0.0773116\pi$
$613$	5.08910	+	9.98792i	0.205547	+	0.403408i	−0.765102	+	0.643909i	$0.777312\pi$
$614$	−8.00948			−0.323236
$615$	7.83602	−	3.92031i	0.315979	−	0.158082i
$616$	3.10809	−	9.56572i	0.125229	−	0.385414i
$617$	−4.90095	+	0.776234i	−0.197305	+	0.0312500i	−0.254305	−	0.967124i	$-0.581847\pi$
$617$	−4.90095	+	0.776234i	−0.197305	+	0.0312500i	0.0569998	+	0.998374i	$0.481847\pi$
$618$	−26.6389	+	19.9008i	−1.07158	+	0.800529i
$619$		−	13.1246i		−	0.527522i	−0.964588	−	0.263761i	$-0.915037\pi$
$619$		−	13.1246i		−	0.527522i	0.964588	−	0.263761i	$-0.0849630\pi$
$620$	−10.7743	+	6.23816i	−0.432706	+	0.250531i
$621$	−17.3957	+	18.8421i	−0.698066	+	0.756106i
$622$	0.561537	+	0.0889387i	0.0225156	+	0.00356612i
$623$	2.12023	+	13.3866i	0.0849451	+	0.536322i
$624$	−8.65648	+	4.55668i	−0.346537	+	0.182413i
$625$	−5.73705	−	24.3328i	−0.229482	−	0.973313i
$626$		−	6.24719i		−	0.249688i
$627$	−5.12471	−	1.59010i	−0.204661	−	0.0635025i
$628$	9.36368	+	4.77103i	0.373652	+	0.190385i
$629$	−6.47182	−	19.9182i	−0.258048	−	0.794191i
$630$	7.51910	−	14.9764i	0.299568	−	0.596672i
$631$	4.25833	−	13.1058i	0.169521	−	0.521733i	−0.829820	−	0.558032i	$-0.811557\pi$
$631$	4.25833	−	13.1058i	0.169521	−	0.521733i	0.999341	+	0.0362985i	$0.0115567\pi$
$632$	1.03041	−	6.50575i	0.0409875	−	0.258785i
$633$	28.1241	−	39.8122i	1.11783	−	1.58239i
$634$	−5.21330	+	1.69390i	−0.207046	+	0.0672735i
$635$	−9.44507	−	13.5812i	−0.374816	−	0.538955i
$636$	−0.0710092	−	0.412737i	−0.00281570	−	0.0163661i
$637$	−1.94712	+	3.82143i	−0.0771476	+	0.151411i
$638$	−1.96176	−	12.3860i	−0.0776666	−	0.490368i
$639$	−17.6203	−	22.9436i	−0.697050	−	0.907634i
$640$	−1.35141	+	1.78149i	−0.0534191	+	0.0704195i
$641$	−13.3188	−	18.3317i	−0.526061	−	0.724060i	0.460463	−	0.887679i	$-0.347683\pi$
$641$	−13.3188	−	18.3317i	−0.526061	−	0.724060i	−0.986524	+	0.163619i	$0.947683\pi$
$642$	−4.06288	−	11.9607i	−0.160349	−	0.472052i
$643$	7.07939	+	3.60713i	0.279184	+	0.142251i	0.587976	−	0.808878i	$-0.299925\pi$
$643$	7.07939	+	3.60713i	0.279184	+	0.142251i	−0.308792	+	0.951129i	$0.599925\pi$
$644$	−3.80984	+	11.7255i	−0.150129	+	0.462049i
$645$	−35.7579	−	11.9100i	−1.40797	−	0.468954i
$646$	−1.97687			−0.0777791
$647$	−18.5676	−	36.4410i	−0.729968	−	1.43264i	−0.894867	−	0.446332i	$-0.852730\pi$
$647$	−18.5676	−	36.4410i	−0.729968	−	1.43264i	0.164899	−	0.986310i	$-0.447270\pi$
$648$	1.87850	+	8.80178i	0.0737944	+	0.345766i
$649$	21.4719	+	29.5536i	0.842847	+	1.16008i
$650$	22.1415	+	17.5282i	0.868461	+	0.687512i
$651$	5.83446	+	23.3739i	0.228671	+	0.916094i
$652$	1.05894	+	1.05894i	0.0414714	+	0.0414714i
$653$	−8.31640	−	1.31719i	−0.325446	−	0.0515456i	−0.00842609	−	0.999964i	$-0.502682\pi$
$653$	−8.31640	−	1.31719i	−0.325446	−	0.0515456i	−0.317020	+	0.948419i	$0.602682\pi$
$654$	−15.8829	+	2.73256i	−0.621069	+	0.106852i
$655$	39.0428	−	5.35975i	1.52553	−	0.209423i
$656$			2.26233i			0.0883292i
$657$	−26.3119	+	27.7499i	−1.02652	+	1.08263i
$658$	−2.61945	−	5.14095i	−0.102117	−	0.200415i
$659$	−7.41251	−	22.8134i	−0.288751	−	0.888683i	−0.985249	−	0.171125i	$-0.945260\pi$
$659$	−7.41251	−	22.8134i	−0.288751	−	0.888683i	0.696499	−	0.717558i	$-0.254740\pi$
$660$	11.1071	−	10.9448i	0.432342	−	0.426027i
$661$	−15.9817	+	11.6114i	−0.621618	+	0.451632i	−0.853486	−	0.521115i	$-0.825516\pi$
$661$	−15.9817	+	11.6114i	−0.621618	+	0.451632i	0.231868	+	0.972747i	$0.425516\pi$
$662$	−1.86332	−	3.65697i	−0.0724199	−	0.142132i
$663$	20.1355	−	15.0424i	0.781999	−	0.584198i
$664$	−0.886064	+	1.21956i	−0.0343859	+	0.0473282i
$665$	−4.29712	−	0.0887628i	−0.166635	−	0.00344208i
$666$	20.1592	+	13.8428i	0.781155	+	0.536397i
$667$	2.40469	+	15.1826i	0.0931098	+	0.587872i
$668$	−3.96336	+	7.77853i	−0.153347	+	0.300960i
$669$	−3.23802	−	18.8208i	−0.125189	−	0.727654i
$670$	−2.78274	+	5.19341i	−0.107507	+	0.200639i
$671$	−12.3335	−	4.00741i	−0.476131	−	0.154704i
$672$	2.58960	+	3.46639i	0.0998959	+	0.133719i
$673$	−37.4745	−	19.0942i	−1.44453	−	0.736027i	−0.456422	−	0.889763i	$-0.650869\pi$
$673$	−37.4745	−	19.0942i	−1.44453	−	0.736027i	−0.988112	+	0.153737i	$0.950869\pi$
$674$	−5.33905	−	16.4319i	−0.205653	−	0.632933i
$675$	21.0405	−	15.2413i	0.809848	−	0.586639i
$676$	−18.8993			−0.726898
$677$	−17.3116	+	17.3116i	−0.665337	+	0.665337i	−0.956633	−	0.291296i	$-0.905914\pi$
$677$	−17.3116	+	17.3116i	−0.665337	+	0.665337i	0.291296	+	0.956633i	$0.405914\pi$
$678$	14.2467	+	4.42050i	0.547143	+	0.169768i
$679$	−25.5183	+	35.1229i	−0.979303	+	1.34790i
$680$	2.71335	−	5.06391i	0.104052	−	0.194192i
$681$	−22.3767	−	21.7894i	−0.857476	−	0.834970i
$682$	−1.85491	+	22.3401i	−0.0710281	+	0.855448i
$683$	19.8764	+	19.8764i	0.760550	+	0.760550i	0.976422	−	0.215872i	$-0.0692594\pi$
$683$	19.8764	+	19.8764i	0.760550	+	0.760550i	−0.215872	+	0.976422i	$0.569259\pi$
$684$	1.83071	−	1.40596i	0.0699991	−	0.0537583i
$685$	−38.0624	+	26.4705i	−1.45429	+	1.01138i
$686$	18.4352	+	5.98995i	0.703858	+	0.228697i
$687$	11.2799	−	0.149998i	0.430353	−	0.00572279i
$688$	6.88107	−	6.88107i	0.262338	−	0.262338i
$689$	0.422007	−	1.29881i	0.0160772	−	0.0494805i
$690$	−13.6148	+	13.4160i	−0.518308	+	0.510738i
$691$	−1.40224	−	4.31564i	−0.0533436	−	0.164175i	0.920836	−	0.389951i	$-0.127508\pi$
$691$	−1.40224	−	4.31564i	−0.0533436	−	0.164175i	−0.974179	+	0.225776i	$0.927508\pi$
$692$	−2.87802	+	18.1711i	−0.109406	+	0.690761i
$693$	−14.4088	−	26.5114i	−0.547343	−	1.00709i
$694$	2.57427	+	3.54318i	0.0977180	+	0.134497i
$695$	6.50421	−	36.2093i	0.246719	−	1.37350i
$696$	4.83895	+	2.38506i	0.183420	+	0.0904055i
$697$	−0.909279	−	5.74096i	−0.0344414	−	0.217454i
$698$	0.0103472	+	0.0653294i	0.000391646	+	0.00247275i
$699$	37.3825	+	18.4254i	1.41393	+	0.696911i
$700$	6.12537	−	10.8856i	0.231517	−	0.411436i
$701$	10.4554	+	14.3907i	0.394897	+	0.543529i	0.959454	−	0.281865i	$-0.0909531\pi$
$701$	10.4554	+	14.3907i	0.394897	+	0.543529i	−0.564557	+	0.825394i	$0.690953\pi$
$702$	−7.94858	+	28.2507i	−0.300000	+	1.06625i
$703$	0.981158	−	6.19479i	0.0370051	−	0.233641i
$704$	1.24417	+	3.82916i	0.0468914	+	0.144317i
$705$	0.0658038	−	8.94504i	0.00247831	−	0.336890i
$706$	−4.68743	+	14.4264i	−0.176414	+	0.542946i
$707$	14.8065	−	14.8065i	0.556856	−	0.556856i
$708$	−15.7137	+	0.208958i	−0.590556	+	0.00785314i
$709$	−16.9372	−	5.50324i	−0.636091	−	0.206678i	−0.0268194	−	0.999640i	$-0.508538\pi$
$709$	−16.9372	−	5.50324i	−0.636091	−	0.206678i	−0.609271	+	0.792962i	$0.708538\pi$
$710$	−12.3111	−	17.7023i	−0.462027	−	0.664357i
$711$	−12.0359	−	15.6721i	−0.451383	−	0.587750i
$712$	−3.83637	−	3.83637i	−0.143774	−	0.143774i
$713$	2.27371	−	27.3842i	0.0851513	−	1.02554i
$714$	−7.96465	−	7.75561i	−0.298070	−	0.290246i
$715$	48.6734	−	14.7108i	1.82028	−	0.550153i
$716$	−7.68652	+	10.5796i	−0.287259	+	0.395378i
$717$	33.0160	+	10.2443i	1.23301	+	0.382579i
$718$	−18.5739	+	18.5739i	−0.693171	+	0.693171i
$719$	−42.2392			−1.57525			−0.787627	−	0.616152i	$-0.788691\pi$
$719$	−42.2392			−1.57525			−0.787627	+	0.616152i	$0.788691\pi$
$720$	1.08874	+	6.61926i	0.0405748	+	0.246685i
$721$	14.8201	+	45.6114i	0.551928	+	1.69866i
$722$	16.4016	+	8.35704i	0.610405	+	0.311017i
$723$	19.4904	+	26.0896i	0.724857	+	0.970281i
$724$	4.95903	+	1.61129i	0.184301	+	0.0598830i
$725$	0.643108	−	15.5602i	0.0238844	−	0.577891i
$726$	−1.53017	−	8.89403i	−0.0567900	−	0.330088i
$727$	14.3964	−	28.2545i	0.533933	−	1.04790i	−0.453706	−	0.891152i	$-0.649898\pi$
$727$	14.3964	−	28.2545i	0.533933	−	1.04790i	0.987638	−	0.156750i	$-0.0501018\pi$
$728$	2.20718	+	13.9356i	0.0818035	+	0.516487i
$729$	23.0388	+	14.0788i	0.853289	+	0.521438i
$730$	−20.5667	+	19.7342i	−0.761208	+	0.730397i
$731$	−14.6960	+	20.2273i	−0.543550	+	0.748132i
$732$	4.46939	−	3.33889i	0.165193	−	0.123409i
$733$	12.4128	+	24.3616i	0.458479	+	0.899816i	0.998314	+	0.0580448i	$0.0184866\pi$
$733$	12.4128	+	24.3616i	0.458479	+	0.899816i	−0.539835	+	0.841771i	$0.681513\pi$
$734$	−8.76560	+	6.36858i	−0.323544	+	0.235069i
$735$	2.06427	+	2.09487i	0.0761417	+	0.0772703i
$736$	−1.52508	−	4.69372i	−0.0562152	−	0.173013i
$737$	4.81635	+	9.45262i	0.177413	+	0.348192i
$738$	4.92505	+	4.66982i	0.181293	+	0.171898i
$739$		−	50.1687i		−	1.84549i	−0.385416	−	0.922743i	$-0.625942\pi$
$739$		−	50.1687i		−	1.84549i	0.385416	−	0.922743i	$-0.374058\pi$
$740$	14.5217	+	11.0160i	0.533830	+	0.404954i
$741$	7.41802	−	1.27623i	0.272508	−	0.0468835i
$742$	−0.596597	−	0.0944917i	−0.0219018	−	0.00346890i
$743$	2.82038	+	2.82038i	0.103470	+	0.103470i	0.756947	−	0.653477i	$-0.226690\pi$
$743$	2.82038	+	2.82038i	0.103470	+	0.103470i	−0.653477	+	0.756947i	$0.726690\pi$
$744$	−7.38914	−	6.19682i	−0.270899	−	0.227187i
$745$	21.2653	−	10.2877i	0.779099	−	0.376910i
$746$	5.65502	+	7.78346i	0.207045	+	0.284973i
$747$	0.825981	+	4.44632i	0.0302211	+	0.162682i
$748$	−4.69626	−	9.21693i	−0.171712	−	0.337004i
$749$	−18.2190			−0.665707
$750$	16.2017	−	10.6069i	0.591602	−	0.387308i
$751$	7.82714	−	24.0895i	0.285616	−	0.879037i	−0.700597	−	0.713557i	$-0.747083\pi$
$751$	7.82714	−	24.0895i	0.285616	−	0.879037i	0.986213	−	0.165480i	$-0.0529172\pi$
$752$	2.05792	+	1.04856i	0.0750447	+	0.0382372i
$753$	1.78082	+	5.24256i	0.0648968	+	0.191050i
$754$	10.3401	+	14.2319i	0.376564	+	0.518296i
$755$	1.50280	+	10.9470i	0.0546924	+	0.398404i
$756$	12.8916	+	1.51770i	0.468863	+	0.0551982i
$757$	−2.14433	−	13.5388i	−0.0779370	−	0.492075i	−0.995522	−	0.0945342i	$-0.969864\pi$
$757$	−2.14433	−	13.5388i	−0.0779370	−	0.492075i	0.917585	−	0.397540i	$-0.130136\pi$
$758$	−5.32402	+	10.4490i	−0.193377	+	0.379524i
$759$	5.83546	+	33.9183i	0.211814	+	1.23116i
$760$	1.41251	−	0.982326i	0.0512370	−	0.0356327i
$761$	−5.72264	+	1.85940i	−0.207445	+	0.0674031i	−0.410896	−	0.911682i	$-0.634784\pi$
$761$	−5.72264	+	1.85940i	−0.207445	+	0.0674031i	0.203451	+	0.979085i	$0.434784\pi$
$762$	7.39331	−	10.4659i	0.267831	−	0.379139i
$763$	−3.63621	+	22.9581i	−0.131640	+	0.831140i
$764$	−7.81717	+	24.0588i	−0.282815	+	0.870416i
$765$	−5.42323	−	16.3597i	−0.196077	−	0.591485i
$766$	1.59655	+	4.91368i	0.0576857	+	0.177538i
$767$	−45.6591	−	23.2645i	−1.64865	−	0.840031i
$768$	−1.65425	−	0.513282i	−0.0596926	−	0.0185215i
$769$			24.3303i			0.877373i	0.898640	+	0.438686i	$0.144556\pi$
$769$			24.3303i			0.877373i	−0.898640	+	0.438686i	$0.855444\pi$
$770$	−9.79438	−	20.2456i	−0.352965	−	0.729602i
$771$	−4.41862	+	2.32592i	−0.159133	+	0.0837659i
$772$	−2.25704	−	14.2504i	−0.0812326	−	0.512882i
$773$	−41.7374	−	6.61056i	−1.50119	−	0.237765i	−0.648917	−	0.760859i	$-0.724778\pi$
$773$	−41.7374	−	6.61056i	−1.50119	−	0.237765i	−0.852275	+	0.523094i	$0.824778\pi$
$774$	−0.776298	−	29.1836i	−0.0279034	−	1.04898i
$775$	−7.72623	+	26.7452i	−0.277534	+	0.960716i
$776$		−	17.3788i		−	0.623862i
$777$	28.2562	−	21.1090i	1.01368	−	0.757282i
$778$	8.01560	−	1.26955i	0.287373	−	0.0455155i
$779$	0.537910	−	1.65552i	0.0192726	−	0.0593150i
$780$	−6.91242	+	20.7535i	−0.247504	+	0.743095i
$781$	−38.8247			−1.38926
$782$	5.75659	+	11.2980i	0.205855	+	0.404014i
$783$	15.1806	−	5.61114i	0.542510	−	0.200526i
$784$	−0.722205	+	0.234659i	−0.0257930	+	0.00838067i
$785$	22.4942	−	6.79852i	0.802851	−	0.242649i
$786$	14.2190	+	27.0122i	0.507174	+	0.963494i
$787$	−36.1203	−	5.72090i	−1.28755	−	0.203928i	−0.525137	−	0.851018i	$-0.675986\pi$
$787$	−36.1203	−	5.72090i	−1.28755	−	0.203928i	−0.762414	+	0.647090i	$0.775986\pi$
$788$	1.19767	+	7.56178i	0.0426652	+	0.269377i
$789$	−34.3458	−	16.9286i	−1.22274	−	0.602675i
$790$	−8.40934	−	12.0920i	−0.299191	−	0.430213i
$791$	12.6458	−	17.4055i	0.449634	−	0.618868i
$792$	10.9042	+	5.19547i	0.387463	+	0.184613i
$793$	17.9678	−	2.84582i	0.638056	−	0.101058i
$794$	−5.81452	+	4.22450i	−0.206350	+	0.149922i
$795$	−0.753548	−	0.556000i	−0.0267256	−	0.0197193i
$796$	−6.23927	+	4.53310i	−0.221145	+	0.160671i
$797$	14.3436	+	7.30841i	0.508075	+	0.258877i	0.689185	−	0.724586i	$-0.257969\pi$
$797$	14.3436	+	7.30841i	0.508075	+	0.258877i	−0.181110	+	0.983463i	$0.557969\pi$
$798$	−1.07080	−	3.15234i	−0.0379060	−	0.111592i
$799$	−5.64369	−	1.83375i	−0.199659	−	0.0648732i
$800$	0.577572	+	4.96653i	0.0204202	+	0.175593i
$801$	−16.2706	+	0.432805i	−0.574893	+	0.0152924i
$802$	13.9914	−	7.12900i	0.494055	−	0.251734i
$803$	8.02855	+	50.6903i	0.283321	+	1.78882i
$804$	−4.51679	−	0.653949i	−0.159295	−	0.0230630i
$805$	12.0058	+	24.8168i	0.423148	+	0.874676i
$806$	−11.9090	−	29.1042i	−0.419476	−	1.02515i
$807$	−0.302084	−	22.7167i	−0.0106339	−	0.799665i
$808$	−1.31125	+	8.27891i	−0.0461297	+	0.291251i
$809$	−12.8047	−	9.30319i	−0.450191	−	0.327083i	0.339480	−	0.940613i	$-0.389749\pi$
$809$	−12.8047	−	9.30319i	−0.450191	−	0.327083i	−0.789671	+	0.613530i	$0.789749\pi$
$810$	16.6573	+	11.2931i	0.585279	+	0.396798i
$811$	−26.4611			−0.929176			−0.464588	−	0.885527i	$-0.653798\pi$
$811$	−26.4611			−0.929176			−0.464588	+	0.885527i	$0.653798\pi$
$812$	5.50192	−	5.50192i	0.193080	−	0.193080i
$813$	−12.2518	−	3.80151i	−0.429690	−	0.133325i
$814$	31.2133	−	10.1418i	1.09402	−	0.355470i
$815$	3.34796	+	0.0691567i	0.117274	+	0.00242245i
$816$	4.40417	+	0.637643i	0.154177	+	0.0223220i
$817$	−6.67149	+	3.39929i	−0.233406	+	0.118926i
$818$	−15.9241	−	2.52212i	−0.556772	−	0.0881840i
$819$	34.8934	+	23.9603i	1.21928	+	0.837241i
$820$	3.50242	+	3.65017i	0.122310	+	0.127469i
$821$	10.9873	−	15.1227i	0.383460	−	0.527787i	−0.573037	−	0.819530i	$-0.694235\pi$
$821$	10.9873	−	15.1227i	0.383460	−	0.527787i	0.956497	+	0.291742i	$0.0942349\pi$
$822$	−29.3314	−	20.7203i	−1.02305	−	0.722702i
$823$	3.85882	+	1.96617i	0.134510	+	0.0685363i	0.519950	−	0.854196i	$-0.325950\pi$
$823$	3.85882	+	1.96617i	0.134510	+	0.0685363i	−0.385440	+	0.922733i	$0.625950\pi$
$824$	−15.5314	−	11.2842i	−0.541062	−	0.393105i
$825$	0.976517	−	34.8544i	0.0339980	−	1.21347i
$826$	−7.00409	+	21.5564i	−0.243703	+	0.750042i
$827$	−3.02296	+	19.0862i	−0.105119	+	0.663692i	0.877713	+	0.479187i	$0.159068\pi$
$827$	−3.02296	+	19.0862i	−0.105119	+	0.663692i	−0.982831	+	0.184505i	$0.940932\pi$
$828$	−13.3661	−	6.36852i	−0.464505	−	0.221321i
$829$	−28.4935	+	9.25810i	−0.989621	+	0.321547i	−0.758711	−	0.651428i	$-0.774170\pi$
$829$	−28.4935	+	9.25810i	−0.989621	+	0.321547i	−0.230910	+	0.972975i	$0.574170\pi$
$830$	0.458439	+	3.33947i	0.0159126	+	0.115915i
$831$	29.4118	−	30.2046i	1.02028	−	1.04779i
$832$	−3.99370	−	3.99370i	−0.138457	−	0.138457i
$833$	1.73837	−	0.885746i	0.0602311	−	0.0306893i
$834$	28.0839	−	4.83168i	0.972465	−	0.167307i
$835$	5.64761	+	18.6862i	0.195444	+	0.646661i
$836$		−	3.09790i		−	0.107143i
$837$	−28.7427	+	3.29475i	−0.993494	+	0.113883i
$838$	−6.50859	+	6.50859i	−0.224836	+	0.224836i
$839$	20.0943	−	14.5994i	0.693733	−	0.504027i	−0.184152	−	0.982898i	$-0.558954\pi$
$839$	20.0943	−	14.5994i	0.693733	−	0.504027i	0.877885	+	0.478871i	$0.158954\pi$
$840$	9.54469	+	1.58379i	0.329323	+	0.0546460i
$841$	−5.96362	+	18.3541i	−0.205642	+	0.632901i
$842$	22.7987	−	22.7987i	0.785695	−	0.785695i
$843$	−54.6858	+	0.727206i	−1.88348	+	0.0250463i
$844$	26.7650	+	8.69646i	0.921288	+	0.299345i
$845$	−30.4933	+	29.2590i	−1.04900	+	1.00654i
$846$	6.53059	−	2.31565i	0.224526	−	0.0796136i
$847$	−12.8560	−	2.03619i	−0.441738	−	0.0699644i
$848$	0.215441	−	0.109773i	0.00739826	−	0.00376960i
$849$	−39.5398	−	5.72464i	−1.35700	−	0.196469i
$850$	−3.46182	−	12.3711i	−0.118739	−	0.424324i
$851$	−38.2607	+	12.4316i	−1.31156	+	0.426151i
$852$	9.63673	−	13.6417i	0.330149	−	0.467355i
$853$	10.4973	−	1.66261i	0.359421	−	0.0569267i	0.0258874	−	0.999665i	$-0.491759\pi$
$853$	10.4973	−	1.66261i	0.359421	−	0.0569267i	0.333534	+	0.942738i	$0.391759\pi$
$854$	−2.48646	−	7.65253i	−0.0850848	−	0.261864i
$855$	0.777139	−	5.10267i	0.0265776	−	0.174508i
$856$	5.90021	−	4.28675i	0.201665	−	0.146518i
$857$	11.1558	+	21.8944i	0.381073	+	0.747899i	0.999273	−	0.0381225i	$-0.0121377\pi$
$857$	11.1558	+	21.8944i	0.381073	+	0.747899i	−0.618200	+	0.786021i	$0.712138\pi$
$858$	23.5725	+	31.5538i	0.804752	+	1.07723i
$859$	−1.10566	+	0.359250i	−0.0377246	+	0.0122575i	−0.327819	−	0.944741i	$-0.606313\pi$
$859$	−1.10566	+	0.359250i	−0.0377246	+	0.0122575i	0.290094	+	0.956998i	$0.406313\pi$
$860$	0.449384	−	21.7552i	0.0153239	−	0.741847i
$861$	8.66205	−	4.55962i	0.295202	−	0.155391i
$862$	−14.9097	−	14.9097i	−0.507826	−	0.507826i
$863$	−8.28360	−	8.28360i	−0.281977	−	0.281977i	0.551920	−	0.833897i	$-0.313895\pi$
$863$	−8.28360	−	8.28360i	−0.281977	−	0.281977i	−0.833897	+	0.551920i	$0.813895\pi$
$864$	−4.53204	+	2.54177i	−0.154183	+	0.0864727i
$865$	23.4880	+	33.7738i	0.798615	+	1.14834i
$866$	−20.9225	−	28.7974i	−0.710976	−	0.978574i
$867$	18.0098	−	0.239493i	0.611646	−	0.00813359i
$868$	−11.8905	+	7.21635i	−0.403590	+	0.244939i
$869$	−26.5200			−0.899631
$870$	11.4999	−	3.64322i	0.389882	−	0.123517i
$871$	−12.0399	−	8.74750i	−0.407956	−	0.296398i
$872$	−4.22425	−	8.29055i	−0.143051	−	0.280753i
$873$	−37.8332	−	35.8726i	−1.28046	−	1.21410i
$874$			3.79736i			0.128447i
$875$	−6.96946	−	27.0464i	−0.235611	−	0.914334i
$876$	−19.8036	−	9.76094i	−0.669101	−	0.329792i
$877$	15.7592	−	30.9291i	0.532150	−	1.04440i	−0.455866	−	0.890049i	$-0.650670\pi$
$877$	15.7592	−	30.9291i	0.532150	−	1.04440i	0.988016	−	0.154354i	$-0.0493298\pi$
$878$	−35.5799	−	5.63530i	−1.20076	−	0.190182i
$879$	11.3104	+	21.4866i	0.381489	+	0.724727i
$880$	7.93552	+	4.25202i	0.267506	+	0.143336i
$881$	−19.5890	+	26.9619i	−0.659970	+	0.908370i	−0.999480	−	0.0322318i	$-0.989739\pi$
$881$	−19.5890	+	26.9619i	−0.659970	+	0.908370i	0.339511	+	0.940602i	$0.389739\pi$
$882$	−0.979901	+	2.05660i	−0.0329950	+	0.0692493i
$883$	−51.4679	+	8.15171i	−1.73203	+	0.274327i	−0.941235	−	0.337752i	$-0.890334\pi$
$883$	−51.4679	+	8.15171i	−1.73203	+	0.274327i	−0.790797	+	0.612079i	$0.790334\pi$
$884$	11.7397	+	8.52939i	0.394849	+	0.286874i
$885$	−25.0298	+	24.6642i	−0.841367	+	0.829079i
$886$	5.18359	+	3.76610i	0.174146	+	0.126524i
$887$	1.91493	−	12.0904i	0.0642972	−	0.405957i	−0.934458	−	0.356074i	$-0.884115\pi$
$887$	1.91493	−	12.0904i	0.0642972	−	0.405957i	0.998755	−	0.0498829i	$-0.0158848\pi$
$888$	−4.18400	+	13.4846i	−0.140406	+	0.452512i
$889$	−10.8631	−	14.9518i	−0.364336	−	0.501466i
$890$	−12.1291	−	0.250543i	−0.406568	−	0.00839821i
$891$	33.8184	−	13.0138i	1.13296	−	0.435980i
$892$	9.82409	−	5.00562i	0.328935	−	0.167601i
$893$	−1.25662	−	1.25662i	−0.0420512	−	0.0420512i
$894$	13.1098	+	12.7657i	0.438456	+	0.426948i
$895$	3.97691	+	28.9696i	0.132933	+	0.968346i
$896$	−1.46836	+	2.02103i	−0.0490545	+	0.0675177i
$897$	−28.8948	−	38.6781i	−0.964768	−	1.29142i
$898$	−18.4996	+	18.4996i	−0.617339	+	0.617339i
$899$	−9.12461	+	14.7473i	−0.304323	+	0.491849i
$900$	12.0042	+	8.99436i	0.400141	+	0.299812i
$901$	−0.502589	+	0.365152i	−0.0167437	+	0.0121650i
$902$	8.99649	−	1.42490i	0.299550	−	0.0474441i
$903$	−40.2148	−	12.4779i	−1.33827	−	0.415239i
$904$			8.61221i			0.286438i
$905$	10.4957	−	5.07757i	0.348888	−	0.168784i
$906$	−7.57385	+	3.98680i	−0.251624	+	0.132452i
$907$	18.3207	−	35.9563i	0.608328	−	1.19391i	−0.357302	−	0.933989i	$-0.616303\pi$
$907$	18.3207	−	35.9563i	0.608328	−	1.19391i	0.965630	−	0.259922i	$-0.0836968\pi$
$908$	8.18649	−	16.0669i	0.271678	−	0.533199i
$909$	15.3164	+	19.9436i	0.508012	+	0.661487i
$910$	25.1355	+	19.0674i	0.833234	+	0.632078i
$911$	−4.09568	−	5.63722i	−0.135696	−	0.186770i	0.735761	−	0.677241i	$-0.236825\pi$
$911$	−4.09568	−	5.63722i	−0.135696	−	0.186770i	−0.871457	+	0.490471i	$0.836825\pi$
$912$	1.08850	+	0.768934i	0.0360437	+	0.0254620i
$913$	5.40784	+	2.75543i	0.178974	+	0.0911916i
$914$	−6.62302	−	4.81191i	−0.219070	−	0.159164i
$915$	2.04206	−	12.3064i	0.0675083	−	0.406838i
$916$	2.01263	+	6.19423i	0.0664991	+	0.204663i
$917$	43.4855	−	6.88742i	1.43602	−	0.227443i
$918$	10.4791	−	8.27159i	0.345860	−	0.273003i
$919$	8.46430	+	2.75022i	0.279211	+	0.0907213i	0.445275	−	0.895394i	$-0.353106\pi$
$919$	8.46430	+	2.75022i	0.279211	+	0.0907213i	−0.166064	+	0.986115i	$0.553106\pi$
$920$	−9.72722	−	5.21205i	−0.320697	−	0.171836i
$921$	−12.4434	−	6.13322i	−0.410025	−	0.202096i
$922$	−13.9698	+	27.4172i	−0.460070	+	0.902938i
$923$	48.5270	−	24.7257i	1.59728	−	0.813857i
$924$	12.1536	−	12.4812i	0.399824	−	0.410601i
$925$	40.4845	−	4.70806i	1.33112	−	0.154800i
$926$	−16.6348	−	5.40496i	−0.546653	−	0.177618i
$927$	−56.6249	+	10.5191i	−1.85981	+	0.345491i
$928$	−0.487245	+	3.07635i	−0.0159946	+	0.100986i
$929$	−27.4657			−0.901121			−0.450560	−	0.892746i	$-0.648776\pi$
$929$	−27.4657			−0.901121			−0.450560	+	0.892746i	$0.648776\pi$
$930$	−21.5156	+	1.44118i	−0.705526	+	0.0472582i
$931$	0.584285			0.0191492
$932$	−3.76413	+	23.7658i	−0.123298	+	0.778474i
$933$	0.804293	+	0.568168i	0.0263314	+	0.0186010i
$934$	−19.7587	−	6.41998i	−0.646524	−	0.210068i
$935$	−21.8464	−	7.60060i	−0.714453	−	0.248566i
$936$	−16.9379	+	0.450555i	−0.553631	+	0.0147269i
$937$	17.1105	−	8.71824i	0.558976	−	0.284812i	−0.151590	−	0.988444i	$-0.548439\pi$
$937$	17.1105	−	8.71824i	0.558976	−	0.284812i	0.710565	+	0.703631i	$0.248439\pi$
$938$	−2.98838	+	5.86502i	−0.0975739	+	0.191500i
$939$	4.78375	−	9.70556i	0.156112	−	0.316729i
$940$	4.94370	−	1.49416i	0.161246	−	0.0487341i
$941$	−22.9481	−	7.45628i	−0.748086	−	0.243068i	−0.0899286	−	0.995948i	$-0.528664\pi$
$941$	−22.9481	−	7.45628i	−0.748086	−	0.243068i	−0.658157	+	0.752880i	$0.728664\pi$
$942$	10.8939	+	14.5824i	0.354943	+	0.475121i
$943$	−11.0277	+	1.74662i	−0.359113	+	0.0568779i
$944$	−2.80374	−	8.62902i	−0.0912539	−	0.280851i
$945$	23.1497	−	17.5094i	0.753058	−	0.569580i
$946$	−31.6976	−	23.0296i	−1.03058	−	0.748758i
$947$	−31.1189	−	15.8559i	−1.01123	−	0.515247i	−0.131800	−	0.991276i	$-0.542076\pi$
$947$	−31.1189	−	15.8559i	−1.01123	−	0.515247i	−0.879430	+	0.476029i	$0.842076\pi$
$948$	6.58257	−	9.31822i	0.213792	−	0.302642i
$949$	−42.3172	−	58.2447i	−1.37368	−	1.89070i
$950$	0.758229	−	3.77171i	0.0246002	−	0.122370i
$951$	−9.39641	−	1.36043i	−0.304699	−	0.0441149i
$952$	2.91386	−	5.71878i	0.0944389	−	0.185347i
$953$	−4.30437	+	8.44781i	−0.139432	+	0.273651i	−0.950154	−	0.311780i	$-0.899075\pi$
$953$	−4.30437	+	8.44781i	−0.139432	+	0.273651i	0.810722	+	0.585431i	$0.199075\pi$
$954$	0.205732	−	0.695598i	0.00666082	−	0.0225208i
$955$	24.6339	+	50.9199i	0.797134	+	1.64773i
$956$			19.9583i			0.645498i
$957$	6.43678	−	20.7450i	0.208072	−	0.670590i
$958$	11.9166	−	1.88740i	0.385007	−	0.0609791i
$959$	−41.9033	+	30.4446i	−1.35313	+	0.983106i
$960$	−3.46369	+	1.73286i	−0.111790	+	0.0559280i
$961$	22.1080	−	21.7310i	0.713162	−	0.700999i
$962$	−32.5545	+	32.5545i	−1.04960	+	1.04960i
$963$	2.84682	−	21.6932i	0.0917374	−	0.699053i
$964$	−11.0515	+	15.2111i	−0.355945	+	0.489917i
$965$	−25.7033	−	19.4981i	−0.827420	−	0.627667i
$966$	−14.8977	+	15.2992i	−0.479324	+	0.492244i
$967$	−6.79143	−	6.79143i	−0.218398	−	0.218398i	0.589425	−	0.807823i	$-0.299354\pi$
$967$	−6.79143	−	6.79143i	−0.218398	−	0.218398i	−0.807823	+	0.589425i	$0.799354\pi$
$968$	4.64251	−	2.36548i	0.149216	−	0.0760293i
$969$	−3.07125	−	1.51378i	−0.0986627	−	0.0486297i
$970$	−26.9049	−	28.0399i	−0.863865	−	0.900306i
$971$	−28.4016	−	39.0914i	−0.911450	−	1.25450i	−0.966669	−	0.256029i	$-0.917586\pi$
$971$	−28.4016	−	39.0914i	−0.911450	−	1.25450i	0.0552189	−	0.998474i	$-0.482414\pi$
$972$	−3.82150	+	15.1128i	−0.122575	+	0.484743i
$973$	6.42950	−	40.5943i	0.206120	−	1.30139i
$974$	−10.1959	−	7.40773i	−0.326696	−	0.237359i
$975$	20.9766	+	44.1863i	0.671790	+	1.41510i
$976$	2.60581	+	1.89323i	0.0834098	+	0.0606008i
$977$	57.9111	−	9.17221i	1.85274	−	0.293445i	0.872108	−	0.489313i	$-0.162752\pi$
$977$	57.9111	−	9.17221i	1.85274	−	0.293445i	0.980630	+	0.195868i	$0.0627524\pi$
$978$	0.834282	+	2.45604i	0.0266774	+	0.0785356i
$979$	−12.8396	+	17.6722i	−0.410355	+	0.564806i
$980$	−0.801959	+	1.49669i	−0.0256176	+	0.0478101i
$981$	−26.7679	−	7.91695i	−0.854633	−	0.252769i
$982$	16.5369	+	2.61919i	0.527715	+	0.0835819i
$983$	19.0372	−	37.3626i	0.607192	−	1.19168i	−0.358874	−	0.933386i	$-0.616839\pi$
$983$	19.0372	−	37.3626i	0.607192	−	1.19168i	0.966066	−	0.258295i	$-0.0831606\pi$
$984$	−1.73237	+	3.51473i	−0.0552259	+	0.112046i
$985$	13.6391	+	10.3464i	0.434579	+	0.329664i
$986$		−	8.00246i		−	0.254850i
$987$	−0.132882	−	9.99274i	−0.00422969	−	0.318073i
$988$	1.97292	+	3.87207i	0.0627668	+	0.123187i
$989$	38.8543	+	28.2293i	1.23550	+	0.897640i
$990$	25.6367	−	8.49859i	0.814789	−	0.270103i
$991$	27.9515			0.887908			0.443954	−	0.896050i	$-0.353575\pi$
$991$	27.9515			0.887908			0.443954	+	0.896050i	$0.353575\pi$
$992$	2.15279	−	5.13473i	0.0683512	−	0.163028i
$993$	−0.0945246	−	7.10824i	−0.00299965	−	0.225573i
$994$	−14.1594	−	19.4887i	−0.449108	−	0.618145i
$995$	−3.04888	+	16.9733i	−0.0966561	+	0.538089i
$996$	−2.31045	+	1.21620i	−0.0732094	+	0.0385367i
$997$	−36.0211	−	36.0211i	−1.14080	−	1.14080i	−0.988304	−	0.152495i	$-0.951269\pi$
$997$	−36.0211	−	36.0211i	−1.14080	−	1.14080i	−0.152495	−	0.988304i	$-0.548731\pi$
$998$	26.0679	+	26.0679i	0.825165	+	0.825165i
$999$	20.7191	+	36.9428i	0.655524	+	1.16882i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bk.a.47.10	✓	512
3.2	odd	2	inner	930.2.bk.a.47.39	yes	512
5.3	odd	4	inner	930.2.bk.a.233.39	yes	512
15.8	even	4	inner	930.2.bk.a.233.23	yes	512
31.2	even	5	inner	930.2.bk.a.467.23	yes	512
93.2	odd	10	inner	930.2.bk.a.467.39	yes	512
155.33	odd	20	inner	930.2.bk.a.653.39	yes	512
465.188	even	20	inner	930.2.bk.a.653.10	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bk.a.47.10	✓	512	1.1	even	1	trivial
930.2.bk.a.47.39	yes	512	3.2	odd	2	inner
930.2.bk.a.233.23	yes	512	15.8	even	4	inner
930.2.bk.a.233.39	yes	512	5.3	odd	4	inner
930.2.bk.a.467.23	yes	512	31.2	even	5	inner
930.2.bk.a.467.39	yes	512	93.2	odd	10	inner
930.2.bk.a.653.10	yes	512	465.188	even	20	inner
930.2.bk.a.653.39	yes	512	155.33	odd	20	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-0.999352 + 1.41467i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-2.01289 + 0.973791i) q^{5} +(-1.24092 - 1.20835i) q^{6} +(-2.22585 + 1.13413i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-1.00259 - 2.82751i) q^{9} +O(q^{10})\)	\(q+(-0.156434 + 0.987688i) q^{2} +(-0.999352 + 1.41467i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(-2.01289 + 0.973791i) q^{5} +(-1.24092 - 1.20835i) q^{6} +(-2.22585 + 1.13413i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-1.00259 - 2.82751i) q^{9} +(-0.646917 - 2.14044i) q^{10} +(-3.82916 - 1.24417i) q^{11} +(1.38760 - 1.03662i) q^{12} +(5.57842 - 0.883534i) q^{13} +(-0.771963 - 2.37586i) q^{14} +(0.633992 - 3.82074i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-2.28923 - 1.16642i) q^{17} +(2.94954 - 0.547929i) q^{18} +(-0.452261 - 0.622484i) q^{19} +(2.21529 - 0.304113i) q^{20} +(0.619988 - 4.28223i) q^{21} +(1.82786 - 3.58738i) q^{22} +(-2.24056 + 4.39735i) q^{23} +(0.806785 + 1.53268i) q^{24} +(3.10346 - 3.92027i) q^{25} +5.64795i q^{26} +(5.00194 + 1.40734i) q^{27} +(2.46737 - 0.390793i) q^{28} +(2.51984 - 1.83077i) q^{29} +(3.67452 + 1.22388i) q^{30} +(-5.15306 + 2.10855i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(5.58677 - 4.17364i) q^{33} +(1.51017 - 2.07858i) q^{34} +(3.37598 - 4.45038i) q^{35} +(0.0797732 + 2.99894i) q^{36} +(5.76396 + 5.76396i) q^{37} +(0.685570 - 0.349315i) q^{38} +(-4.32489 + 8.77459i) q^{39} +(-0.0461792 + 2.23559i) q^{40} +(1.32976 + 1.83026i) q^{41} +(4.13252 + 1.28224i) q^{42} +(1.52231 - 9.61150i) q^{43} +(3.25728 + 2.36655i) q^{44} +(4.77151 + 4.71515i) q^{45} +(-3.99271 - 2.90088i) q^{46} +(2.28123 - 0.361311i) q^{47} +(-1.64002 + 0.557089i) q^{48} +(-0.446347 + 0.614344i) q^{49} +(3.38652 + 3.67852i) q^{50} +(3.93785 - 2.07284i) q^{51} +(-5.57842 - 0.883534i) q^{52} +(0.109773 - 0.215441i) q^{53} +(-2.17249 + 4.72020i) q^{54} +(8.91924 - 1.22442i) q^{55} +2.49813i q^{56} +(1.33258 - 0.0177205i) q^{57} +(1.41404 + 2.77521i) q^{58} +(-7.34028 - 5.33303i) q^{59} +(-1.78364 + 3.43783i) q^{60} +3.22095 q^{61} +(-1.27647 - 5.41947i) q^{62} +(5.43836 + 5.15653i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(-10.3684 + 7.21067i) q^{65} +(3.24829 + 6.17089i) q^{66} +(-1.86320 - 1.86320i) q^{67} +(1.81674 + 1.81674i) q^{68} +(-3.98170 - 7.56416i) q^{69} +(3.86747 + 4.03061i) q^{70} +(9.17102 - 2.97985i) q^{71} +(-2.97450 - 0.390346i) q^{72} +(-5.78701 - 11.3577i) q^{73} +(-6.59468 + 4.79131i) q^{74} +(2.44445 + 8.30811i) q^{75} +(0.237768 + 0.731774i) q^{76} +(9.93416 - 1.57342i) q^{77} +(-7.99000 - 5.64429i) q^{78} +(6.26446 - 2.03545i) q^{79} +(-2.20084 - 0.395334i) q^{80} +(-6.98962 + 5.66968i) q^{81} +(-2.01575 + 1.02708i) q^{82} +(-1.48890 - 0.235819i) q^{83} +(-1.91293 + 3.88106i) q^{84} +(5.74382 + 0.118646i) q^{85} +(9.25502 + 3.00714i) q^{86} +(0.0717332 + 5.39433i) q^{87} +(-2.84696 + 2.84696i) q^{88} +(1.67656 - 5.15991i) q^{89} +(-5.40353 + 3.97515i) q^{90} +(-11.4147 + 8.29323i) q^{91} +(3.48976 - 3.48976i) q^{92} +(2.16681 - 9.39707i) q^{93} +2.30966i q^{94} +(1.51652 + 0.812585i) q^{95} +(-0.293676 - 1.70697i) q^{96} +(15.4846 - 7.88980i) q^{97} +(-0.536957 - 0.536957i) q^{98} +(0.321184 + 12.0744i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) \) 512 * q + 8 * q^3 - 12 * q^7	\( 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) \) 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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