LMFDB - Embedded newform 847.2.f.s.323.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			323.1
Root			$-0.628998 - 0.456994i$ of defining polynomial
Character	$\chi$	$=$	847.323
Dual form			847.2.f.s.729.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.628998 - 0.456994i) q^{2} +(0.190983 - 0.587785i) q^{3} +(-0.431239 - 1.32722i) q^{4} +(0.180019 - 0.130791i) q^{5} +(-0.388742 + 0.282438i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.815793 + 2.51075i) q^{8} +(2.11803 + 1.53884i) q^{9} +O(q^{10})$	\(q+(-0.628998 - 0.456994i) q^{2} +(0.190983 - 0.587785i) q^{3} +(-0.431239 - 1.32722i) q^{4} +(0.180019 - 0.130791i) q^{5} +(-0.388742 + 0.282438i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.815793 + 2.51075i) q^{8} +(2.11803 + 1.53884i) q^{9} -0.173002 q^{10} -0.862478 q^{12} +(5.28251 + 3.83797i) q^{13} +(0.240256 - 0.739431i) q^{14} +(-0.0424967 - 0.130791i) q^{15} +(-0.597465 + 0.434084i) q^{16} +(-3.50678 + 2.54782i) q^{17} +(-0.628998 - 1.93586i) q^{18} +(-0.900787 + 2.77234i) q^{19} +(-0.251220 - 0.182522i) q^{20} +0.618034 q^{21} -3.89796 q^{23} +(1.31998 + 0.959022i) q^{24} +(-1.52978 + 4.70819i) q^{25} +(-1.56876 - 4.82815i) q^{26} +(2.80902 - 2.04087i) q^{27} +(1.12900 - 0.820265i) q^{28} +(1.16623 + 3.58928i) q^{29} +(-0.0330405 + 0.101688i) q^{30} +(5.57379 + 4.04959i) q^{31} +5.85410 q^{32} +3.37009 q^{34} +(0.180019 + 0.130791i) q^{35} +(1.12900 - 3.47470i) q^{36} +(-1.74703 - 5.37681i) q^{37} +(1.83353 - 1.33214i) q^{38} +(3.26477 - 2.37200i) q^{39} +(0.181527 + 0.558682i) q^{40} +(-0.413499 + 1.27262i) q^{41} +(-0.388742 - 0.282438i) q^{42} +4.70820 q^{43} +0.582554 q^{45} +(2.45181 + 1.78134i) q^{46} +(1.86817 - 5.74965i) q^{47} +(0.141042 + 0.434084i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(3.11385 - 2.26234i) q^{50} +(0.827838 + 2.54782i) q^{51} +(2.81579 - 8.66612i) q^{52} +(1.38982 + 1.00977i) q^{53} -2.69953 q^{54} -2.63996 q^{56} +(1.45750 + 1.05894i) q^{57} +(0.906723 - 2.79061i) q^{58} +(-2.94587 - 9.06646i) q^{59} +(-0.155262 + 0.112805i) q^{60} +(-7.79037 + 5.66003i) q^{61} +(-1.65526 - 5.09437i) q^{62} +(-0.809017 + 2.48990i) q^{63} +(-2.48729 - 1.80712i) q^{64} +1.45293 q^{65} +1.27155 q^{67} +(4.89377 + 3.55553i) q^{68} +(-0.744444 + 2.29116i) q^{69} +(-0.0534607 - 0.164535i) q^{70} +(7.53129 - 5.47180i) q^{71} +(-5.59153 + 4.06248i) q^{72} +(-1.72713 - 5.31556i) q^{73} +(-1.35829 + 4.18039i) q^{74} +(2.47524 + 1.79837i) q^{75} +4.06794 q^{76} -3.13752 q^{78} +(-3.66448 - 2.66240i) q^{79} +(-0.0507806 + 0.156287i) q^{80} +(1.76393 + 5.42882i) q^{81} +(0.841669 - 0.611508i) q^{82} +(9.12876 - 6.63243i) q^{83} +(-0.266520 - 0.820265i) q^{84} +(-0.298053 + 0.917313i) q^{85} +(-2.96145 - 2.15162i) q^{86} +2.33245 q^{87} +7.92157 q^{89} +(-0.366425 - 0.266223i) q^{90} +(-2.01774 + 6.20997i) q^{91} +(1.68095 + 5.17343i) q^{92} +(3.44479 - 2.50279i) q^{93} +(-3.80263 + 2.76277i) q^{94} +(0.200439 + 0.616888i) q^{95} +(1.11803 - 3.44095i) q^{96} +(7.32477 + 5.32176i) q^{97} +0.777484 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 + 2 * q^6 - 2 * q^7 + 12 * q^8 + 8 * q^9	$ 8 q + q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{7} + 12 q^{8} + 8 q^{9} + 28 q^{10} - 14 q^{12} + 5 q^{13} + q^{14} - 9 q^{15} + 7 q^{16} - 14 q^{17} + q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{21} - 16 q^{23} + 9 q^{24} - 5 q^{25} - 9 q^{26} + 18 q^{27} + 3 q^{28} - 6 q^{29} + 26 q^{30} + 14 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} + 3 q^{36} + q^{37} - 15 q^{38} - 29 q^{40} - 18 q^{41} + 2 q^{42} - 16 q^{43} + 18 q^{45} + 26 q^{46} + 7 q^{47} - q^{48} - 2 q^{49} - q^{50} - 8 q^{51} + 4 q^{52} + 7 q^{53} - 4 q^{54} - 18 q^{56} + 3 q^{57} + 36 q^{58} + 17 q^{60} - 12 q^{61} + 5 q^{62} - 2 q^{63} - 4 q^{64} - 24 q^{65} - 30 q^{67} + 7 q^{68} - 22 q^{69} - 12 q^{70} + 21 q^{71} - 3 q^{72} - 8 q^{73} - q^{74} + 52 q^{76} - 18 q^{78} - q^{79} + 37 q^{80} + 32 q^{81} - 34 q^{82} + 22 q^{83} + 11 q^{84} + 5 q^{85} + 13 q^{86} - 12 q^{87} - 34 q^{89} + 18 q^{90} - 5 q^{91} + 51 q^{92} + 3 q^{93} - 50 q^{94} + 41 q^{95} - 15 q^{97} - 4 q^{98}+O(q^{100}) $ 8 * q + q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 + 2 * q^6 - 2 * q^7 + 12 * q^8 + 8 * q^9 + 28 * q^10 - 14 * q^12 + 5 * q^13 + q^14 - 9 * q^15 + 7 * q^16 - 14 * q^17 + q^18 - 6 * q^19 - 4 * q^20 - 4 * q^21 - 16 * q^23 + 9 * q^24 - 5 * q^25 - 9 * q^26 + 18 * q^27 + 3 * q^28 - 6 * q^29 + 26 * q^30 + 14 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 + 3 * q^36 + q^37 - 15 * q^38 - 29 * q^40 - 18 * q^41 + 2 * q^42 - 16 * q^43 + 18 * q^45 + 26 * q^46 + 7 * q^47 - q^48 - 2 * q^49 - q^50 - 8 * q^51 + 4 * q^52 + 7 * q^53 - 4 * q^54 - 18 * q^56 + 3 * q^57 + 36 * q^58 + 17 * q^60 - 12 * q^61 + 5 * q^62 - 2 * q^63 - 4 * q^64 - 24 * q^65 - 30 * q^67 + 7 * q^68 - 22 * q^69 - 12 * q^70 + 21 * q^71 - 3 * q^72 - 8 * q^73 - q^74 + 52 * q^76 - 18 * q^78 - q^79 + 37 * q^80 + 32 * q^81 - 34 * q^82 + 22 * q^83 + 11 * q^84 + 5 * q^85 + 13 * q^86 - 12 * q^87 - 34 * q^89 + 18 * q^90 - 5 * q^91 + 51 * q^92 + 3 * q^93 - 50 * q^94 + 41 * q^95 - 15 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.628998	−	0.456994i	−0.444769	−	0.323143i	0.342758	−	0.939424i	$-0.388639\pi$
$2$	−0.628998	−	0.456994i	−0.444769	−	0.323143i	−0.787527	+	0.616280i	$0.788639\pi$
$3$	0.190983	−	0.587785i	0.110264	−	0.339358i	−0.880666	−	0.473738i	$-0.842904\pi$
$3$	0.190983	−	0.587785i	0.110264	−	0.339358i	0.990930	+	0.134380i	$0.0429043\pi$
$4$	−0.431239	−	1.32722i	−0.215619	−	0.663608i
$5$	0.180019	−	0.130791i	0.0805070	−	0.0584917i	−0.546804	−	0.837261i	$-0.684156\pi$
$5$	0.180019	−	0.130791i	0.0805070	−	0.0584917i	0.627311	+	0.778769i	$0.284156\pi$
$6$	−0.388742	+	0.282438i	−0.158703	+	0.115305i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$7$	0.309017	+	0.951057i	0.116797	+	0.359466i
$8$	−0.815793	+	2.51075i	−0.288426	+	0.887685i
$9$	2.11803	+	1.53884i	0.706011	+	0.512947i
$10$	−0.173002			−0.0547082
$11$		0			0
$11$		0			0
$12$	−0.862478			−0.248976
$13$	5.28251	+	3.83797i	1.46511	+	1.06446i	0.981996	+	0.188901i	$0.0604926\pi$
$13$	5.28251	+	3.83797i	1.46511	+	1.06446i	0.483109	+	0.875560i	$0.339507\pi$
$14$	0.240256	−	0.739431i	0.0642111	−	0.197621i
$15$	−0.0424967	−	0.130791i	−0.0109726	−	0.0337702i
$16$	−0.597465	+	0.434084i	−0.149366	+	0.108521i
$17$	−3.50678	+	2.54782i	−0.850518	+	0.617938i	−0.925289	−	0.379263i	$-0.876178\pi$
$17$	−3.50678	+	2.54782i	−0.850518	+	0.617938i	0.0747707	+	0.997201i	$0.476178\pi$
$18$	−0.628998	−	1.93586i	−0.148256	−	0.456286i
$19$	−0.900787	+	2.77234i	−0.206655	+	0.636017i	0.792987	+	0.609239i	$0.208525\pi$
$19$	−0.900787	+	2.77234i	−0.206655	+	0.636017i	−0.999641	+	0.0267786i	$0.991475\pi$
$20$	−0.251220	−	0.182522i	−0.0561745	−	0.0408131i
$21$	0.618034			0.134866
$22$		0			0
$23$	−3.89796			−0.812780			−0.406390	−	0.913700i	$-0.633213\pi$
$23$	−3.89796			−0.812780			−0.406390	+	0.913700i	$0.633213\pi$
$24$	1.31998	+	0.959022i	0.269440	+	0.195760i
$25$	−1.52978	+	4.70819i	−0.305957	+	0.941639i
$26$	−1.56876	−	4.82815i	−0.307659	−	0.946878i
$27$	2.80902	−	2.04087i	0.540596	−	0.392766i
$28$	1.12900	−	0.820265i	0.213361	−	0.155016i
$29$	1.16623	+	3.58928i	0.216563	+	0.666512i	0.999039	+	0.0438312i	$0.0139564\pi$
$29$	1.16623	+	3.58928i	0.216563	+	0.666512i	−0.782476	+	0.622681i	$0.786044\pi$
$30$	−0.0330405	+	0.101688i	−0.00603235	+	0.0185657i
$31$	5.57379	+	4.04959i	1.00108	+	0.727329i	0.962320	−	0.271920i	$-0.0876585\pi$
$31$	5.57379	+	4.04959i	1.00108	+	0.727329i	0.0387621	+	0.999248i	$0.487659\pi$
$32$	5.85410			1.03487
$33$		0			0
$34$	3.37009			0.577966
$35$	0.180019	+	0.130791i	0.0304288	+	0.0221078i
$36$	1.12900	−	3.47470i	0.188166	−	0.579116i
$37$	−1.74703	−	5.37681i	−0.287210	−	0.883942i	−0.985727	−	0.168349i	$-0.946156\pi$
$37$	−1.74703	−	5.37681i	−0.287210	−	0.883942i	0.698517	−	0.715593i	$-0.253844\pi$
$38$	1.83353	−	1.33214i	0.297438	−	0.216102i
$39$	3.26477	−	2.37200i	0.522782	−	0.379823i
$40$	0.181527	+	0.558682i	0.0287019	+	0.0883354i
$41$	−0.413499	+	1.27262i	−0.0645777	+	0.198750i	−0.978139	−	0.207951i	$-0.933321\pi$
$41$	−0.413499	+	1.27262i	−0.0645777	+	0.198750i	0.913562	+	0.406700i	$0.133321\pi$
$42$	−0.388742	−	0.282438i	−0.0599842	−	0.0435811i
$43$	4.70820			0.717994			0.358997	−	0.933339i	$-0.383119\pi$
$43$	4.70820			0.717994			0.358997	+	0.933339i	$0.383119\pi$
$44$		0			0
$45$	0.582554			0.0868420
$46$	2.45181	+	1.78134i	0.361499	+	0.262645i
$47$	1.86817	−	5.74965i	0.272501	−	0.838672i	−0.717369	−	0.696694i	$-0.754654\pi$
$47$	1.86817	−	5.74965i	0.272501	−	0.838672i	0.989870	−	0.141978i	$-0.0453463\pi$
$48$	0.141042	+	0.434084i	0.0203577	+	0.0626546i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	3.11385	−	2.26234i	0.440364	−	0.319943i
$51$	0.827838	+	2.54782i	0.115920	+	0.356766i
$52$	2.81579	−	8.66612i	0.390480	−	1.20177i
$53$	1.38982	+	1.00977i	0.190907	+	0.138702i	0.679133	−	0.734015i	$-0.262356\pi$
$53$	1.38982	+	1.00977i	0.190907	+	0.138702i	−0.488226	+	0.872717i	$0.662356\pi$
$54$	−2.69953			−0.367360
$55$		0			0
$56$	−2.63996			−0.352780
$57$	1.45750	+	1.05894i	0.193051	+	0.140260i
$58$	0.906723	−	2.79061i	0.119059	−	0.366424i
$59$	−2.94587	−	9.06646i	−0.383520	−	1.18035i	−0.937548	−	0.347855i	$-0.886910\pi$
$59$	−2.94587	−	9.06646i	−0.383520	−	1.18035i	0.554029	−	0.832498i	$-0.313090\pi$
$60$	−0.155262	+	0.112805i	−0.0200443	+	0.0145630i
$61$	−7.79037	+	5.66003i	−0.997455	+	0.724693i	−0.961541	−	0.274662i	$-0.911434\pi$
$61$	−7.79037	+	5.66003i	−0.997455	+	0.724693i	−0.0359136	+	0.999355i	$0.511434\pi$
$62$	−1.65526	−	5.09437i	−0.210219	−	0.646986i
$63$	−0.809017	+	2.48990i	−0.101927	+	0.313698i
$64$	−2.48729	−	1.80712i	−0.310911	−	0.225890i
$65$	1.45293			0.180213
$66$		0			0
$67$	1.27155			0.155344			0.0776722	−	0.996979i	$-0.475251\pi$
$67$	1.27155			0.155344			0.0776722	+	0.996979i	$0.475251\pi$
$68$	4.89377	+	3.55553i	0.593457	+	0.431172i
$69$	−0.744444	+	2.29116i	−0.0896205	+	0.275824i
$70$	−0.0534607	−	0.164535i	−0.00638978	−	0.0196657i
$71$	7.53129	−	5.47180i	0.893800	−	0.649384i	−0.0430661	−	0.999072i	$-0.513713\pi$
$71$	7.53129	−	5.47180i	0.893800	−	0.649384i	0.936866	+	0.349689i	$0.113713\pi$
$72$	−5.59153	+	4.06248i	−0.658968	+	0.478768i
$73$	−1.72713	−	5.31556i	−0.202145	−	0.622140i	−0.999819	−	0.0190495i	$-0.993936\pi$
$73$	−1.72713	−	5.31556i	−0.202145	−	0.622140i	0.797673	−	0.603090i	$-0.206064\pi$
$74$	−1.35829	+	4.18039i	−0.157898	+	0.485960i
$75$	2.47524	+	1.79837i	0.285816	+	0.207658i
$76$	4.06794			0.466625
$77$		0			0
$78$	−3.13752			−0.355254
$79$	−3.66448	−	2.66240i	−0.412286	−	0.299543i	0.362241	−	0.932085i	$-0.382012\pi$
$79$	−3.66448	−	2.66240i	−0.412286	−	0.299543i	−0.774527	+	0.632541i	$0.782012\pi$
$80$	−0.0507806	+	0.156287i	−0.00567745	+	0.0174734i
$81$	1.76393	+	5.42882i	0.195992	+	0.603203i
$82$	0.841669	−	0.611508i	0.0929467	−	0.0675298i
$83$	9.12876	−	6.63243i	1.00201	−	0.728004i	0.0394928	−	0.999220i	$-0.487426\pi$
$83$	9.12876	−	6.63243i	1.00201	−	0.728004i	0.962519	+	0.271216i	$0.0874258\pi$
$84$	−0.266520	−	0.820265i	−0.0290797	−	0.0894983i
$85$	−0.298053	+	0.917313i	−0.0323284	+	0.0994965i
$86$	−2.96145	−	2.15162i	−0.319341	−	0.232015i
$87$	2.33245			0.250065
$88$		0			0
$89$	7.92157			0.839684			0.419842	−	0.907597i	$-0.362085\pi$
$89$	7.92157			0.839684			0.419842	+	0.907597i	$0.362085\pi$
$90$	−0.366425	−	0.266223i	−0.0386246	−	0.0280624i
$91$	−2.01774	+	6.20997i	−0.211517	+	0.650981i
$92$	1.68095	+	5.17343i	0.175251	+	0.539368i
$93$	3.44479	−	2.50279i	0.357208	−	0.259527i
$94$	−3.80263	+	2.76277i	−0.392211	+	0.284958i
$95$	0.200439	+	0.616888i	0.0205646	+	0.0632914i
$96$	1.11803	−	3.44095i	0.114109	−	0.351191i
$97$	7.32477	+	5.32176i	0.743718	+	0.540342i	0.893873	−	0.448320i	$-0.147977\pi$
$97$	7.32477	+	5.32176i	0.743718	+	0.540342i	−0.150156	+	0.988662i	$0.547977\pi$
$98$	0.777484			0.0785378
$99$		0			0
$100$	6.90849			0.690849
$101$	−15.5413	−	11.2915i	−1.54642	−	1.12354i	−0.946142	−	0.323751i	$-0.895056\pi$
$101$	−15.5413	−	11.2915i	−1.54642	−	1.12354i	−0.600280	−	0.799790i	$-0.704944\pi$
$102$	0.643631	−	1.98089i	0.0637289	−	0.196137i
$103$	5.01791	+	15.4435i	0.494430	+	1.52170i	0.817844	+	0.575440i	$0.195169\pi$
$103$	5.01791	+	15.4435i	0.494430	+	1.52170i	−0.323414	+	0.946258i	$0.604831\pi$
$104$	−13.9456	+	10.1321i	−1.36748	+	0.993534i
$105$	0.111258	−	0.0808336i	0.0108577	−	0.00788855i
$106$	−0.412739	−	1.27028i	−0.0400888	−	0.123381i
$107$	1.66664	−	5.12939i	0.161120	−	0.495877i	−0.837609	−	0.546270i	$-0.816047\pi$
$107$	1.66664	−	5.12939i	0.161120	−	0.495877i	0.998729	+	0.0503930i	$0.0160474\pi$
$108$	−3.92003	−	2.84807i	−0.377205	−	0.274056i
$109$	−5.39901			−0.517132			−0.258566	−	0.965994i	$-0.583250\pi$
$109$	−5.39901			−0.517132			−0.258566	+	0.965994i	$0.583250\pi$
$110$		0			0
$111$	−3.49406			−0.331642
$112$	−0.597465	−	0.434084i	−0.0564552	−	0.0410171i
$113$	−5.09761	+	15.6888i	−0.479543	+	1.47588i	0.360188	+	0.932880i	$0.382713\pi$
$113$	−5.09761	+	15.6888i	−0.479543	+	1.47588i	−0.839731	+	0.543002i	$0.817287\pi$
$114$	−0.432838	−	1.33214i	−0.0405390	−	0.124766i
$115$	−0.701707	+	0.509820i	−0.0654345	+	0.0475409i
$116$	4.26082	−	3.09567i	0.395608	−	0.287426i
$117$	5.28251	+	16.2579i	0.488368	+	1.50304i
$118$	−2.29037	+	7.04903i	−0.210846	+	0.648916i
$119$	−3.50678	−	2.54782i	−0.321466	−	0.233558i
$120$	0.363054			0.0331421
$121$		0			0
$122$	7.48673			0.677816
$123$	0.669055	+	0.486097i	0.0603267	+	0.0438299i
$124$	2.97106	−	9.14397i	0.266809	−	0.821153i
$125$	0.684207	+	2.10577i	0.0611973	+	0.188346i
$126$	1.64674	−	1.19643i	0.146703	−	0.106586i
$127$	1.61583	−	1.17397i	0.143382	−	0.104173i	−0.513782	−	0.857921i	$-0.671756\pi$
$127$	1.61583	−	1.17397i	0.143382	−	0.104173i	0.657164	+	0.753748i	$0.271756\pi$
$128$	−2.87938	−	8.86181i	−0.254503	−	0.783281i
$129$	0.899187	−	2.76741i	0.0791690	−	0.243657i
$130$	−0.913888	−	0.663978i	−0.0801533	−	0.0582348i
$131$	−1.37009			−0.119706			−0.0598528	−	0.998207i	$-0.519063\pi$
$131$	−1.37009			−0.119706			−0.0598528	+	0.998207i	$0.519063\pi$
$132$		0			0
$133$	−2.91501			−0.252763
$134$	−0.799801	−	0.581090i	−0.0690923	−	0.0501985i
$135$	0.238748	−	0.734791i	0.0205482	−	0.0632407i
$136$	−3.53615	−	10.8831i	−0.303222	−	0.933222i
$137$	−2.02193	+	1.46902i	−0.172745	+	0.125507i	−0.670798	−	0.741640i	$-0.734048\pi$
$137$	−2.02193	+	1.46902i	−0.172745	+	0.125507i	0.498053	+	0.867146i	$0.334048\pi$
$138$	1.51530	−	1.10093i	0.128991	−	0.0937174i
$139$	1.47172	+	4.52950i	0.124830	+	0.384187i	0.993870	−	0.110555i	$-0.0352627\pi$
$139$	1.47172	+	4.52950i	0.124830	+	0.384187i	−0.869040	+	0.494742i	$0.835263\pi$
$140$	0.0959574	−	0.295327i	0.00810988	−	0.0249597i
$141$	−3.02277	−	2.19617i	−0.254563	−	0.184951i
$142$	−7.23775			−0.607378
$143$		0			0
$144$	−1.93344			−0.161120
$145$	0.679390	+	0.493605i	0.0564202	+	0.0409917i
$146$	−1.34282	+	4.13277i	−0.111132	+	0.342030i
$147$	0.190983	+	0.587785i	0.0157520	+	0.0484797i
$148$	−6.38281	+	4.63738i	−0.524663	+	0.381190i
$149$	−5.84907	+	4.24960i	−0.479175	+	0.348141i	−0.801006	−	0.598656i	$-0.795702\pi$
$149$	−5.84907	+	4.24960i	−0.479175	+	0.348141i	0.321831	+	0.946797i	$0.395702\pi$
$150$	−0.735079	−	2.26234i	−0.0600190	−	0.184719i
$151$	−2.51530	+	7.74130i	−0.204692	+	0.629978i	0.795034	+	0.606565i	$0.207453\pi$
$151$	−2.51530	+	7.74130i	−0.204692	+	0.629978i	−0.999726	+	0.0234126i	$0.992547\pi$
$152$	−6.22580	−	4.52331i	−0.504979	−	0.366888i
$153$	−11.3482			−0.917445
$154$		0			0
$155$	1.53304			0.123137
$156$	−4.55605	−	3.31016i	−0.364776	−	0.265025i
$157$	6.22713	−	19.1651i	0.496979	−	1.52954i	−0.316870	−	0.948469i	$-0.602632\pi$
$157$	6.22713	−	19.1651i	0.496979	−	1.52954i	0.813850	−	0.581076i	$-0.197368\pi$
$158$	1.08825	+	3.34929i	0.0865765	+	0.266455i
$159$	0.858958	−	0.624069i	0.0681198	−	0.0494919i
$160$	1.05385	−	0.765667i	0.0833141	−	0.0605313i
$161$	−1.20454	−	3.70718i	−0.0949307	−	0.292167i
$162$	1.37143	−	4.22083i	0.107750	−	0.331619i
$163$	−6.01463	−	4.36989i	−0.471102	−	0.342276i	0.326768	−	0.945104i	$-0.394040\pi$
$163$	−6.01463	−	4.36989i	−0.471102	−	0.342276i	−0.797871	+	0.602829i	$0.794040\pi$
$164$	1.86736			0.145816
$165$		0			0
$166$	−8.77295			−0.680913
$167$	−1.78884	−	1.29967i	−0.138424	−	0.100571i	0.516418	−	0.856337i	$-0.327265\pi$
$167$	−1.78884	−	1.29967i	−0.138424	−	0.100571i	−0.654843	+	0.755765i	$0.727265\pi$
$168$	−0.504188	+	1.55173i	−0.0388989	+	0.119719i
$169$	9.15770	+	28.1845i	0.704439	+	2.16804i
$170$	0.606681	−	0.440780i	0.0465303	−	0.0338062i
$171$	−6.17408	+	4.48573i	−0.472144	+	0.343033i
$172$	−2.03036	−	6.24881i	−0.154814	−	0.476467i
$173$	3.20210	−	9.85504i	0.243451	−	0.749265i	−0.752437	−	0.658665i	$-0.771122\pi$
$173$	3.20210	−	9.85504i	0.243451	−	0.749265i	0.995887	−	0.0905998i	$-0.0288784\pi$
$174$	−1.46711	−	1.06592i	−0.111221	−	0.0808069i
$175$	−4.95049			−0.374222
$176$		0			0
$177$	−5.89174			−0.442851
$178$	−4.98265	−	3.62011i	−0.373465	−	0.271338i
$179$	−7.23391	+	22.2637i	−0.540688	+	1.66407i	0.190341	+	0.981718i	$0.439041\pi$
$179$	−7.23391	+	22.2637i	−0.540688	+	1.66407i	−0.731028	+	0.682347i	$0.760959\pi$
$180$	−0.251220	−	0.773175i	−0.0187248	−	0.0576291i
$181$	11.0966	−	8.06212i	0.824801	−	0.599253i	−0.0932830	−	0.995640i	$-0.529736\pi$
$181$	11.0966	−	8.06212i	0.824801	−	0.599253i	0.918084	+	0.396387i	$0.129736\pi$
$182$	4.10707	−	2.98396i	0.304436	−	0.221186i
$183$	1.83906	+	5.66003i	0.135947	+	0.418402i
$184$	3.17993	−	9.78681i	0.234427	−	0.721493i
$185$	−1.01774	−	0.739431i	−0.0748257	−	0.0543641i
$186$	−3.31052			−0.242739
$187$		0			0
$188$	−8.43666			−0.615306
$189$	2.80902	+	2.04087i	0.204326	+	0.148451i
$190$	0.155838	−	0.479621i	0.0113057	−	0.0347954i
$191$	−3.71591	−	11.4364i	−0.268874	−	0.827509i	−0.990776	−	0.135513i	$-0.956732\pi$
$191$	−3.71591	−	11.4364i	−0.268874	−	0.827509i	0.721902	−	0.691996i	$-0.243268\pi$
$192$	−1.53723	+	1.11686i	−0.110940	+	0.0806026i
$193$	12.8504	−	9.33634i	0.924990	−	0.672044i	−0.0197714	−	0.999805i	$-0.506294\pi$
$193$	12.8504	−	9.33634i	0.924990	−	0.672044i	0.944761	+	0.327760i	$0.106294\pi$
$194$	−2.17526	−	6.69475i	−0.156174	−	0.480655i
$195$	0.277484	−	0.854009i	0.0198711	−	0.0611568i
$196$	1.12900	+	0.820265i	0.0806427	+	0.0585904i
$197$	−12.3035			−0.876590			−0.438295	−	0.898831i	$-0.644418\pi$
$197$	−12.3035			−0.876590			−0.438295	+	0.898831i	$0.644418\pi$
$198$		0			0
$199$	15.2615			1.08186			0.540929	−	0.841068i	$-0.318073\pi$
$199$	15.2615			1.08186			0.540929	+	0.841068i	$0.318073\pi$
$200$	−10.5731	−	7.68182i	−0.747633	−	0.543187i
$201$	0.242844	−	0.747397i	0.0171289	−	0.0527173i
$202$	4.61535	+	14.2046i	0.324735	+	0.999432i
$203$	−3.05322	+	2.21829i	−0.214294	+	0.155694i
$204$	3.02452	−	2.19744i	0.211758	−	0.153852i
$205$	0.0920100	+	0.283178i	0.00642626	+	0.0197780i
$206$	3.90135	−	12.0071i	0.271820	−	0.836575i
$207$	−8.25601	−	5.99834i	−0.573832	−	0.416913i
$208$	−4.82212			−0.334354
$209$		0			0
$210$	−0.106921			−0.00737828
$211$	7.22730	+	5.25094i	0.497548	+	0.361490i	0.808080	−	0.589073i	$-0.200507\pi$
$211$	7.22730	+	5.25094i	0.497548	+	0.361490i	−0.310532	+	0.950563i	$0.600507\pi$
$212$	0.740832	−	2.28005i	0.0508805	−	0.156594i
$213$	−1.77790	−	5.47180i	−0.121819	−	0.374922i
$214$	−3.39241	+	2.46473i	−0.231900	+	0.168486i
$215$	0.847566	−	0.615793i	0.0578035	−	0.0419967i
$216$	2.83254	+	8.71768i	0.192730	+	0.593163i
$217$	−2.12900	+	6.55238i	−0.144526	+	0.444805i
$218$	3.39597	+	2.46732i	0.230004	+	0.167108i
$219$	−3.45426			−0.233417
$220$		0			0
$221$	−28.3031			−1.90387
$222$	2.19776	+	1.59677i	0.147504	+	0.107168i
$223$	0.221023	−	0.680238i	0.0148008	−	0.0455521i	−0.943383	−	0.331704i	$-0.892376\pi$
$223$	0.221023	−	0.680238i	0.0148008	−	0.0455521i	0.958184	+	0.286152i	$0.0923763\pi$
$224$	1.80902	+	5.56758i	0.120870	+	0.372000i
$225$	−10.4853	+	7.61802i	−0.699020	+	0.507868i
$226$	10.3761	−	7.53867i	0.690207	−	0.501465i
$227$	1.64447	+	5.06116i	0.109147	+	0.335921i	0.990681	−	0.136199i	$-0.0434888\pi$
$227$	1.64447	+	5.06116i	0.109147	+	0.335921i	−0.881534	+	0.472120i	$0.843489\pi$
$228$	0.776908	−	2.39108i	0.0514520	−	0.158353i
$229$	5.34625	+	3.88427i	0.353290	+	0.256680i	0.750248	−	0.661157i	$-0.229934\pi$
$229$	5.34625	+	3.88427i	0.353290	+	0.256680i	−0.396958	+	0.917837i	$0.629934\pi$
$230$	0.674356			0.0444657
$231$		0			0
$232$	−9.96318			−0.654115
$233$	−7.73188	−	5.61754i	−0.506532	−	0.368017i	0.304974	−	0.952361i	$-0.401352\pi$
$233$	−7.73188	−	5.61754i	−0.506532	−	0.368017i	−0.811507	+	0.584343i	$0.801352\pi$
$234$	4.10707	−	12.6403i	0.268488	−	0.826320i
$235$	−0.415698	−	1.27939i	−0.0271171	−	0.0834580i
$236$	−10.7628	+	7.81962i	−0.700598	+	0.509014i
$237$	−2.26477	+	1.64545i	−0.147113	+	0.106884i
$238$	1.04142	+	3.20515i	0.0675050	+	0.207759i
$239$	−8.29606	+	25.5327i	−0.536628	+	1.65157i	0.203478	+	0.979080i	$0.434776\pi$
$239$	−8.29606	+	25.5327i	−0.536628	+	1.65157i	−0.740105	+	0.672491i	$0.765224\pi$
$240$	0.0821648	+	0.0596962i	0.00530371	+	0.00385337i
$241$	−18.8663			−1.21529			−0.607643	−	0.794210i	$-0.707885\pi$
$241$	−18.8663			−1.21529			−0.607643	+	0.794210i	$0.707885\pi$
$242$		0			0
$243$	13.9443			0.894525
$244$	10.8716	+	7.89868i	0.695983	+	0.505661i
$245$	−0.0687611	+	0.211625i	−0.00439299	+	0.0135202i
$246$	−0.198691	−	0.611508i	−0.0126681	−	0.0389883i
$247$	−15.3986	+	11.1877i	−0.979787	+	0.711857i
$248$	−14.7146	+	10.6908i	−0.934377	+	0.678865i
$249$	−2.15501	−	6.63243i	−0.136568	−	0.420313i
$250$	0.531960	−	1.63720i	0.0336441	−	0.103546i
$251$	−23.7634	−	17.2651i	−1.49993	−	1.08976i	−0.970409	−	0.241468i	$-0.922371\pi$
$251$	−23.7634	−	17.2651i	−1.49993	−	1.08976i	−0.529523	−	0.848296i	$-0.677629\pi$
$252$	3.65351			0.230150
$253$		0			0
$254$	−1.55285			−0.0974348
$255$	0.482260	+	0.350382i	0.0302003	+	0.0219418i
$256$	−4.13879	+	12.7379i	−0.258674	+	0.796118i
$257$	−5.22745	−	16.0884i	−0.326079	−	1.00357i	−0.970951	−	0.239278i	$-0.923089\pi$
$257$	−5.22745	−	16.0884i	−0.326079	−	1.00357i	0.644872	−	0.764291i	$-0.276911\pi$
$258$	−1.83028	+	1.32977i	−0.113948	+	0.0827881i
$259$	4.57379	−	3.32305i	0.284201	−	0.206484i
$260$	−0.626558	−	1.92835i	−0.0388575	−	0.119591i
$261$	−3.05322	+	9.39685i	−0.188990	+	0.581650i
$262$	0.861786	+	0.626124i	0.0532413	+	0.0386821i
$263$	8.18034			0.504421			0.252211	−	0.967672i	$-0.418842\pi$
$263$	8.18034			0.504421			0.252211	+	0.967672i	$0.418842\pi$
$264$		0			0
$265$	0.382263			0.0234822
$266$	1.83353	+	1.33214i	0.112421	+	0.0816787i
$267$	1.51288	−	4.65618i	0.0925870	−	0.284954i
$268$	−0.548341	−	1.68762i	−0.0334953	−	0.103088i
$269$	5.05406	−	3.67199i	0.308151	−	0.223885i	−0.422951	−	0.906152i	$-0.639006\pi$
$269$	5.05406	−	3.67199i	0.308151	−	0.223885i	0.731103	+	0.682267i	$0.239006\pi$
$270$	−0.485967	+	0.353076i	−0.0295750	+	0.0214875i
$271$	−2.43100	−	7.48184i	−0.147673	−	0.454490i	0.849672	−	0.527311i	$-0.176800\pi$
$271$	−2.43100	−	7.48184i	−0.147673	−	0.454490i	−0.997345	+	0.0728213i	$0.976800\pi$
$272$	0.989208	−	3.04447i	0.0599796	−	0.184598i
$273$	3.26477	+	2.37200i	0.197593	+	0.143560i
$274$	1.94312			0.117388
$275$		0			0
$276$	3.36190			0.202363
$277$	9.74675	+	7.08143i	0.585626	+	0.425482i	0.840748	−	0.541427i	$-0.182116\pi$
$277$	9.74675	+	7.08143i	0.585626	+	0.425482i	−0.255122	+	0.966909i	$0.582116\pi$
$278$	1.14424	−	3.52161i	0.0686271	−	0.211212i
$279$	5.57379	+	17.1544i	0.333694	+	1.02700i
$280$	−0.475243	+	0.345285i	−0.0284012	+	0.0206347i
$281$	17.1147	−	12.4345i	1.02098	−	0.741783i	0.0544937	−	0.998514i	$-0.482646\pi$
$281$	17.1147	−	12.4345i	1.02098	−	0.741783i	0.966483	+	0.256731i	$0.0826455\pi$
$282$	0.897679	+	2.76277i	0.0534560	+	0.164521i
$283$	7.72646	−	23.7796i	0.459291	−	1.41355i	−0.406733	−	0.913547i	$-0.633332\pi$
$283$	7.72646	−	23.7796i	0.459291	−	1.41355i	0.866023	−	0.500004i	$-0.166668\pi$
$284$	−10.5101	−	7.63600i	−0.623657	−	0.453113i
$285$	0.400878			0.0237460
$286$		0			0
$287$	−1.33811			−0.0789861
$288$	12.3992	+	9.00854i	0.730629	+	0.530833i
$289$	0.552793	−	1.70132i	0.0325172	−	0.100078i
$290$	−0.201760	−	0.620954i	−0.0118478	−	0.0364637i
$291$	4.52696	−	3.28903i	0.265375	−	0.192806i
$292$	−6.31010	+	4.58455i	−0.369271	+	0.268291i
$293$	0.140630	+	0.432814i	0.00821568	+	0.0252852i	0.955080	−	0.296347i	$-0.0957685\pi$
$293$	0.140630	+	0.432814i	0.00821568	+	0.0252852i	−0.946865	+	0.321632i	$0.895769\pi$
$294$	0.148486	−	0.456994i	0.00865990	−	0.0266524i
$295$	−1.71613	−	1.24684i	−0.0999169	−	0.0725939i
$296$	14.9251			0.867502
$297$		0			0
$298$	5.62110			0.325621
$299$	−20.5910	−	14.9602i	−1.19081	−	0.865173i
$300$	1.31941	−	4.06071i	0.0761759	−	0.234445i
$301$	1.45492	+	4.47777i	0.0838599	+	0.258094i
$302$	5.11984	−	3.71978i	0.294614	−	0.214050i
$303$	−9.60508	+	6.97850i	−0.551798	+	0.400904i
$304$	−0.665238	−	2.04739i	−0.0381540	−	0.117426i
$305$	−0.662130	+	2.03783i	−0.0379135	+	0.116686i
$306$	7.13797	+	5.18604i	0.408051	+	0.296466i
$307$	8.03578			0.458626			0.229313	−	0.973353i	$-0.426352\pi$
$307$	8.03578			0.458626			0.229313	+	0.973353i	$0.426352\pi$
$308$		0			0
$309$	10.0358			0.570918
$310$	−0.964279	−	0.700590i	−0.0547674	−	0.0397908i
$311$	0.0423244	−	0.130261i	0.00240000	−	0.00738644i	−0.949849	−	0.312708i	$-0.898764\pi$
$311$	0.0423244	−	0.130261i	0.00240000	−	0.00738644i	0.952249	+	0.305321i	$0.0987639\pi$
$312$	3.29212	+	10.1321i	0.186379	+	0.573617i
$313$	12.3698	−	8.98720i	0.699183	−	0.507986i	−0.180483	−	0.983578i	$-0.557766\pi$
$313$	12.3698	−	8.98720i	0.699183	−	0.507986i	0.879666	+	0.475592i	$0.157766\pi$
$314$	−12.6752	+	9.20907i	−0.715303	+	0.519698i
$315$	0.180019	+	0.554042i	0.0101429	+	0.0312167i
$316$	−1.95332	+	6.01169i	−0.109883	+	0.338184i
$317$	26.6915	+	19.3925i	1.49914	+	1.08919i	0.970720	+	0.240212i	$0.0772170\pi$
$317$	26.6915	+	19.3925i	1.49914	+	1.08919i	0.528424	+	0.848980i	$0.322783\pi$
$318$	−0.825478			−0.0462905
$319$		0			0
$320$	−0.684115			−0.0382432
$321$	−2.69668	−	1.95925i	−0.150514	−	0.109355i
$322$	−0.936507	+	2.88227i	−0.0521895	+	0.160623i
$323$	−3.90456	−	12.0170i	−0.217256	−	0.668644i
$324$	6.44455	−	4.68224i	0.358031	−	0.260124i
$325$	−26.1510	+	18.9998i	−1.45060	+	1.05392i
$326$	1.78618	+	5.49730i	0.0989274	+	0.304467i
$327$	−1.03112	+	3.17346i	−0.0570211	+	0.175493i
$328$	−2.85790	−	2.07639i	−0.157801	−	0.114649i
$329$	6.04554			0.333301
$330$		0			0
$331$	29.5335			1.62331			0.811653	−	0.584140i	$-0.198568\pi$
$331$	29.5335			1.62331			0.811653	+	0.584140i	$0.198568\pi$
$332$	−12.7393	−	9.25568i	−0.699163	−	0.507971i
$333$	4.57379	−	14.0767i	0.250642	−	0.771397i
$334$	0.531236	+	1.63497i	0.0290679	+	0.0894619i
$335$	0.228903	−	0.166308i	0.0125063	−	0.00908636i
$336$	−0.369254	+	0.268279i	−0.0201444	+	0.0146358i
$337$	−1.73984	−	5.35469i	−0.0947753	−	0.291688i	0.892420	−	0.451206i	$-0.149006\pi$
$337$	−1.73984	−	5.35469i	−0.0947753	−	0.291688i	−0.987195	+	0.159518i	$0.949006\pi$
$338$	7.11997	−	21.9130i	0.387275	−	1.19191i
$339$	8.24811	+	5.99260i	0.447976	+	0.325474i
$340$	1.34600			0.0729974
$341$		0			0
$342$	5.93344			0.320844
$343$	−0.809017	−	0.587785i	−0.0436828	−	0.0317374i
$344$	−3.84092	+	11.8211i	−0.207089	+	0.637353i
$345$	0.165650	+	0.509820i	0.00891832	+	0.0274478i
$346$	−6.51780	+	4.73546i	−0.350399	+	0.254580i
$347$	7.06321	−	5.13173i	0.379173	−	0.275485i	−0.381831	−	0.924232i	$-0.624706\pi$
$347$	7.06321	−	5.13173i	0.379173	−	0.275485i	0.761005	+	0.648747i	$0.224706\pi$
$348$	−1.00584	−	3.09567i	−0.0539189	−	0.165945i
$349$	−5.70660	+	17.5631i	−0.305468	+	0.940132i	0.674035	+	0.738700i	$0.264560\pi$
$349$	−5.70660	+	17.5631i	−0.305468	+	0.940132i	−0.979502	+	0.201433i	$0.935440\pi$
$350$	3.11385	+	2.26234i	0.166442	+	0.120927i
$351$	22.6715			1.21011
$352$		0			0
$353$	−23.4857			−1.25002			−0.625009	−	0.780618i	$-0.714905\pi$
$353$	−23.4857			−1.25002			−0.625009	+	0.780618i	$0.714905\pi$
$354$	3.70589	+	2.69249i	0.196966	+	0.143104i
$355$	0.640111	−	1.97006i	0.0339735	−	0.104560i
$356$	−3.41609	−	10.5136i	−0.181052	−	0.557222i
$357$	−2.16731	+	1.57464i	−0.114706	+	0.0833388i
$358$	14.7245	−	10.6980i	0.778213	−	0.565405i
$359$	−4.59855	−	14.1529i	−0.242702	−	0.746960i	−0.996006	−	0.0892873i	$-0.971541\pi$
$359$	−4.59855	−	14.1529i	−0.242702	−	0.746960i	0.753304	−	0.657673i	$-0.228459\pi$
$360$	−0.475243	+	1.46265i	−0.0250475	+	0.0770884i
$361$	8.49689	+	6.17335i	0.447205	+	0.324913i
$362$	−10.6641			−0.560490
$363$		0			0
$364$	9.11210			0.477604
$365$	−1.00615	−	0.731008i	−0.0526641	−	0.0382627i
$366$	1.42984	−	4.40059i	0.0747388	−	0.230022i
$367$	−10.5764	−	32.5508i	−0.552083	−	1.69914i	−0.703524	−	0.710671i	$-0.748391\pi$
$367$	−10.5764	−	32.5508i	−0.552083	−	1.69914i	0.151441	−	0.988466i	$-0.451609\pi$
$368$	2.32889	−	1.69204i	0.121402	−	0.0882037i
$369$	−2.83416	+	2.05914i	−0.147541	+	0.107195i
$370$	0.302241	+	0.930202i	0.0157128	+	0.0483589i
$371$	−0.530865	+	1.63383i	−0.0275611	+	0.0848245i
$372$	−4.80727	−	3.49269i	−0.249245	−	0.181087i
$373$	−3.01739			−0.156235			−0.0781173	−	0.996944i	$-0.524891\pi$
$373$	−3.01739			−0.156235			−0.0781173	+	0.996944i	$0.524891\pi$
$374$		0			0
$375$	1.36841			0.0706646
$376$	12.9119	+	9.38104i	0.665880	+	0.483790i
$377$	−7.61493	+	23.4363i	−0.392189	+	1.20703i
$378$	−0.834201	−	2.56741i	−0.0429067	−	0.132053i
$379$	4.95467	−	3.59978i	0.254505	−	0.184908i	−0.453216	−	0.891401i	$-0.649723\pi$
$379$	4.95467	−	3.59978i	0.254505	−	0.184908i	0.707721	+	0.706492i	$0.249723\pi$
$380$	0.732307	−	0.532053i	0.0375666	−	0.0272937i
$381$	−0.381447	−	1.17397i	−0.0195421	−	0.0601444i
$382$	−2.88906	+	8.89162i	−0.147817	+	0.454935i
$383$	−3.55238	−	2.58096i	−0.181518	−	0.131881i	0.493316	−	0.869850i	$-0.335785\pi$
$383$	−3.55238	−	2.58096i	−0.181518	−	0.131881i	−0.674834	+	0.737970i	$0.735785\pi$
$384$	−5.75876			−0.293875
$385$		0			0
$386$	−12.3495			−0.628573
$387$	9.97214	+	7.24518i	0.506912	+	0.368293i
$388$	3.90440	−	12.0165i	0.198216	−	0.610046i
$389$	3.24344	+	9.98229i	0.164449	+	0.506122i	0.998995	−	0.0448157i	$-0.0142701\pi$
$389$	3.24344	+	9.98229i	0.164449	+	0.506122i	−0.834546	+	0.550938i	$0.814270\pi$
$390$	−0.564814	+	0.410361i	−0.0286005	+	0.0207794i
$391$	13.6693	−	9.93130i	0.691284	−	0.502248i
$392$	−0.815793	−	2.51075i	−0.0412038	−	0.126812i
$393$	−0.261665	+	0.805321i	−0.0131992	+	0.0406231i
$394$	7.73890	+	5.62264i	0.389880	+	0.283264i
$395$	−1.00789			−0.0507127
$396$		0			0
$397$	11.3888			0.571589			0.285794	−	0.958291i	$-0.407743\pi$
$397$	11.3888			0.571589			0.285794	+	0.958291i	$0.407743\pi$
$398$	−9.59945	−	6.97441i	−0.481177	−	0.349595i
$399$	−0.556717	+	1.71340i	−0.0278707	+	0.0857772i
$400$	−1.12976	−	3.47704i	−0.0564879	−	0.173852i
$401$	3.82257	−	2.77726i	0.190890	−	0.138690i	−0.488235	−	0.872712i	$-0.662359\pi$
$401$	3.82257	−	2.77726i	0.190890	−	0.138690i	0.679125	+	0.734022i	$0.262359\pi$
$402$	−0.494304	+	0.359133i	−0.0246537	+	0.0179119i
$403$	13.9014	+	42.7841i	0.692477	+	2.13123i
$404$	−8.28417	+	25.4960i	−0.412153	+	1.26848i
$405$	1.02759	+	0.746584i	0.0510611	+	0.0370981i
$406$	2.93422			0.145623
$407$		0			0
$408$	−7.07230			−0.350131
$409$	1.99458	+	1.44915i	0.0986258	+	0.0716558i	0.636005	−	0.771685i	$-0.280586\pi$
$409$	1.99458	+	1.44915i	0.0986258	+	0.0716558i	−0.537379	+	0.843341i	$0.680586\pi$
$410$	0.0715363	−	0.220166i	0.00353293	−	0.0108732i
$411$	0.477312	+	1.46902i	0.0235441	+	0.0724612i
$412$	18.3330	−	13.3197i	0.903203	−	0.656215i
$413$	7.71239	−	5.60338i	0.379502	−	0.275724i
$414$	2.45181	+	7.54589i	0.120500	+	0.370860i
$415$	0.775885	−	2.38793i	0.0380867	−	0.117219i
$416$	30.9244	+	22.4679i	1.51619	+	1.10158i
$417$	2.94345			0.144141
$418$		0			0
$419$	−14.3399			−0.700548			−0.350274	−	0.936647i	$-0.613912\pi$
$419$	−14.3399			−0.700548			−0.350274	+	0.936647i	$0.613912\pi$
$420$	−0.155262	−	0.112805i	−0.00757603	−	0.00550431i
$421$	−5.35086	+	16.4683i	−0.260785	+	0.802614i	0.731850	+	0.681466i	$0.238657\pi$
$421$	−5.35086	+	16.4683i	−0.260785	+	0.802614i	−0.992635	+	0.121147i	$0.961343\pi$
$422$	−2.14631	−	6.60567i	−0.104481	−	0.321559i
$423$	12.8047	−	9.30312i	0.622583	−	0.452333i
$424$	−3.66908	+	2.66574i	−0.178186	+	0.129460i
$425$	−6.63102	−	20.4082i	−0.321652	−	0.989943i
$426$	−1.38229	+	4.25424i	−0.0669720	+	0.206119i
$427$	−7.79037	−	5.66003i	−0.377002	−	0.273908i
$428$	−7.52653			−0.363808
$429$		0			0
$430$	−0.814531			−0.0392802
$431$	22.5653	+	16.3947i	1.08693	+	0.789704i	0.978879	−	0.204441i	$-0.0655376\pi$
$431$	22.5653	+	16.3947i	1.08693	+	0.789704i	0.108055	+	0.994145i	$0.465538\pi$
$432$	−0.792381	+	2.43870i	−0.0381235	+	0.117332i
$433$	−9.13053	−	28.1009i	−0.438785	−	1.35044i	−0.889158	−	0.457601i	$-0.848709\pi$
$433$	−9.13053	−	28.1009i	−0.438785	−	1.35044i	0.450372	−	0.892841i	$-0.351291\pi$
$434$	4.33353	−	3.14850i	0.208016	−	0.151133i
$435$	0.419886	−	0.305065i	0.0201320	−	0.0146267i
$436$	2.32826	+	7.16566i	0.111504	+	0.343173i
$437$	3.51123	−	10.8064i	0.167965	−	0.516943i
$438$	2.17272	+	1.57858i	0.103817	+	0.0754273i
$439$	33.6655			1.60677			0.803384	−	0.595461i	$-0.203030\pi$
$439$	33.6655			1.60677			0.803384	+	0.595461i	$0.203030\pi$
$440$		0			0
$441$	−2.61803			−0.124668
$442$	17.8026	+	12.9343i	0.846782	+	0.615223i
$443$	3.19113	−	9.82129i	0.151615	−	0.466624i	−0.846187	−	0.532886i	$-0.821107\pi$
$443$	3.19113	−	9.82129i	0.151615	−	0.466624i	0.997802	+	0.0662624i	$0.0211074\pi$
$444$	1.50678	+	4.63738i	0.0715084	+	0.220080i
$445$	1.42603	−	1.03607i	0.0676004	−	0.0491146i
$446$	−0.449887	+	0.326862i	−0.0213028	+	0.0154774i
$447$	1.38078	+	4.24960i	0.0653086	+	0.200999i
$448$	0.950059	−	2.92398i	0.0448861	−	0.138145i
$449$	2.23115	+	1.62103i	0.105294	+	0.0765009i	0.639187	−	0.769052i	$-0.279271\pi$
$449$	2.23115	+	1.62103i	0.105294	+	0.0765009i	−0.533892	+	0.845553i	$0.679271\pi$
$450$	10.0766			0.475016
$451$		0			0
$452$	23.0208			1.08281
$453$	4.06984	+	2.95691i	0.191218	+	0.138928i
$454$	1.27855	−	3.93497i	0.0600053	−	0.184677i
$455$	0.448979	+	1.38182i	0.0210485	+	0.0647805i
$456$	−3.84775	+	2.79556i	−0.180188	+	0.130914i
$457$	−32.6281	+	23.7057i	−1.52628	+	1.10890i	−0.568012	+	0.823020i	$0.692287\pi$
$457$	−32.6281	+	23.7057i	−1.52628	+	1.10890i	−0.958264	+	0.285884i	$0.907713\pi$
$458$	−1.58769	−	4.88640i	−0.0741878	−	0.228327i
$459$	−4.65082	+	14.3138i	−0.217082	+	0.668109i
$460$	0.979244	+	0.711463i	0.0456575	+	0.0331721i
$461$	34.2251			1.59402			0.797011	−	0.603965i	$-0.206413\pi$
$461$	34.2251			1.59402			0.797011	+	0.603965i	$0.206413\pi$
$462$		0			0
$463$	0.707349			0.0328733			0.0164367	−	0.999865i	$-0.494768\pi$
$463$	0.707349			0.0328733			0.0164367	+	0.999865i	$0.494768\pi$
$464$	−2.25483	−	1.63823i	−0.104678	−	0.0760528i
$465$	0.292785	−	0.901099i	0.0135776	−	0.0417874i
$466$	2.29616	+	7.06684i	0.106367	+	0.327365i
$467$	23.1318	−	16.8062i	1.07041	−	0.777698i	0.0944242	−	0.995532i	$-0.469899\pi$
$467$	23.1318	−	16.8062i	1.07041	−	0.777698i	0.975986	+	0.217834i	$0.0698990\pi$
$468$	19.2997	−	14.0221i	0.892130	−	0.648171i
$469$	0.392930	+	1.20931i	0.0181438	+	0.0558409i
$470$	−0.323199	+	0.994703i	−0.0149080	+	0.0458822i
$471$	−10.0757	−	7.32043i	−0.464264	−	0.337308i
$472$	25.1669			1.15840
$473$		0			0
$474$	2.17650			0.0999699
$475$	−11.6747	−	8.48215i	−0.535671	−	0.389188i
$476$	−1.86925	+	5.75297i	−0.0856771	+	0.263687i
$477$	1.38982	+	4.27743i	0.0636356	+	0.195850i
$478$	16.8865	−	12.2687i	0.772369	−	0.561159i
$479$	−4.12369	+	2.99604i	−0.188416	+	0.136892i	−0.677995	−	0.735067i	$-0.737151\pi$
$479$	−4.12369	+	2.99604i	−0.188416	+	0.136892i	0.489578	+	0.871959i	$0.337151\pi$
$480$	−0.248780	−	0.765667i	−0.0113552	−	0.0349477i
$481$	11.4073	−	35.1081i	0.520129	−	1.60079i
$482$	11.8669	+	8.62179i	0.540521	+	0.392712i
$483$	−2.40907			−0.109617
$484$		0			0
$485$	2.01464			0.0914800
$486$	−8.77092	−	6.37245i	−0.397857	−	0.289060i
$487$	9.01968	−	27.7597i	0.408720	−	1.25791i	−0.509028	−	0.860750i	$-0.669995\pi$
$487$	9.01968	−	27.7597i	0.408720	−	1.25791i	0.917748	−	0.397162i	$-0.130005\pi$
$488$	−7.85562	−	24.1771i	−0.355607	−	1.09445i
$489$	−3.71725	+	2.70074i	−0.168100	+	0.122132i
$490$	0.139962	−	0.101688i	0.00632284	−	0.00459381i
$491$	−9.31499	−	28.6686i	−0.420380	−	1.29380i	−0.907350	−	0.420377i	$-0.861898\pi$
$491$	−9.31499	−	28.6686i	−0.420380	−	1.29380i	0.486970	−	0.873419i	$-0.338102\pi$
$492$	0.356633	−	1.09760i	0.0160783	−	0.0494839i
$493$	−13.2345	−	9.61545i	−0.596053	−	0.433058i
$494$	14.7984			0.665810
$495$		0			0
$496$	−5.08801			−0.228458
$497$	7.53129	+	5.47180i	0.337825	+	0.245444i
$498$	−1.67548	+	5.15661i	−0.0750802	+	0.231073i
$499$	1.83897	+	5.65978i	0.0823238	+	0.253367i	0.983743	−	0.179580i	$-0.0574739\pi$
$499$	1.83897	+	5.65978i	0.0823238	+	0.253367i	−0.901420	+	0.432947i	$0.857474\pi$
$500$	2.49976	−	1.81618i	0.111793	−	0.0812221i
$501$	−1.10556	+	0.803238i	−0.0493929	+	0.0358860i
$502$	7.05707	+	21.7194i	0.314973	+	0.969386i
$503$	1.53846	−	4.73489i	0.0685964	−	0.211118i	−0.910882	−	0.412667i	$-0.864597\pi$
$503$	1.53846	−	4.73489i	0.0685964	−	0.211118i	0.979479	+	0.201549i	$0.0645974\pi$
$504$	−5.59153	−	4.06248i	−0.249067	−	0.180957i
$505$	−4.27456			−0.190216
$506$		0			0
$507$	18.3154			0.813416
$508$	−2.25493	−	1.63830i	−0.100046	−	0.0726878i
$509$	−6.59088	+	20.2846i	−0.292135	+	0.899100i	0.692033	+	0.721866i	$0.256715\pi$
$509$	−6.59088	+	20.2846i	−0.292135	+	0.899100i	−0.984169	+	0.177235i	$0.943285\pi$
$510$	−0.143218	−	0.440780i	−0.00634180	−	0.0195180i
$511$	4.52169	−	3.28520i	0.200028	−	0.145329i
$512$	−6.65219	+	4.83310i	−0.293988	+	0.213595i
$513$	3.12765	+	9.62593i	0.138089	+	0.424995i
$514$	−4.06426	+	12.5085i	−0.179267	+	0.551727i
$515$	2.92320	+	2.12383i	0.128812	+	0.0935872i
$516$	−4.06072			−0.178763
$517$		0			0
$518$	−4.39552			−0.193128
$519$	−5.18110	−	3.76429i	−0.227425	−	0.165234i
$520$	−1.18529	+	3.64794i	−0.0519783	+	0.159973i
$521$	−6.84113	−	21.0548i	−0.299715	−	0.922428i	−0.981597	−	0.190966i	$-0.938838\pi$
$521$	−6.84113	−	21.0548i	−0.299715	−	0.922428i	0.681882	−	0.731463i	$-0.261162\pi$
$522$	6.21477	−	4.51529i	0.272013	−	0.197629i
$523$	3.97346	−	2.88689i	0.173747	−	0.126235i	−0.497513	−	0.867456i	$-0.665753\pi$
$523$	3.97346	−	2.88689i	0.173747	−	0.126235i	0.671260	+	0.741222i	$0.265753\pi$
$524$	0.590838	+	1.81841i	0.0258109	+	0.0794377i
$525$	−0.945459	+	2.90982i	−0.0412632	+	0.126995i
$526$	−5.14542	−	3.73836i	−0.224351	−	0.163000i
$527$	−29.8637			−1.30088
$528$		0			0
$529$	−7.80592			−0.339388
$530$	−0.240443	−	0.174692i	−0.0104442	−	0.00758813i
$531$	7.71239	−	23.7363i	0.334689	−	1.03007i
$532$	1.25706	+	3.86885i	0.0545006	+	0.167736i
$533$	−7.06858	+	5.13563i	−0.306174	+	0.222449i
$534$	−3.07945	+	2.23735i	−0.133261	+	0.0968195i
$535$	−0.370853	−	1.14137i	−0.0160334	−	0.0493457i
$536$	−1.03732	+	3.19254i	−0.0448054	+	0.137897i
$537$	11.7047	+	8.50397i	0.505095	+	0.366973i
$538$	−4.85707			−0.209403
$539$		0			0
$540$	−1.07818			−0.0463977
$541$	15.6824	+	11.3939i	0.674238	+	0.489862i	0.871441	−	0.490500i	$-0.163186\pi$
$541$	15.6824	+	11.3939i	0.674238	+	0.489862i	−0.197203	+	0.980363i	$0.563186\pi$
$542$	−1.89006	+	5.81702i	−0.0811852	+	0.249862i
$543$	−2.61954	−	8.06212i	−0.112415	−	0.345979i
$544$	−20.5290	+	14.9152i	−0.880175	+	0.639484i
$545$	−0.971925	+	0.706145i	−0.0416327	+	0.0302479i
$546$	−0.969548	−	2.98396i	−0.0414928	−	0.127702i
$547$	−4.46532	+	13.7428i	−0.190923	+	0.587601i	−1.00000		0.000101747i	$-0.999968\pi$
$547$	−4.46532	+	13.7428i	−0.190923	+	0.587601i	0.809077	+	0.587703i	$0.199968\pi$
$548$	2.82164	+	2.05004i	0.120534	+	0.0875733i
$549$	−25.2102			−1.07594
$550$		0			0
$551$	−11.0012			−0.468667
$552$	−5.14523	−	3.73823i	−0.218996	−	0.159110i
$553$	1.39971	−	4.30785i	0.0595216	−	0.183189i
$554$	−2.89452	−	8.90841i	−0.122976	−	0.378482i
$555$	−0.628998	+	0.456994i	−0.0266995	+	0.0193983i
$556$	5.37696	−	3.90659i	0.228034	−	0.165676i
$557$	−5.70780	−	17.5668i	−0.241847	−	0.744329i	−0.996139	−	0.0877900i	$-0.972020\pi$
$557$	−5.70780	−	17.5668i	−0.241847	−	0.744329i	0.754292	−	0.656539i	$-0.227980\pi$
$558$	4.33353	−	13.3372i	0.183453	−	0.564611i
$559$	24.8711	+	18.0699i	1.05194	+	0.764277i
$560$	−0.164330			−0.00694419
$561$		0			0
$562$	−16.4476			−0.693801
$563$	25.3092	+	18.3882i	1.06665	+	0.774969i	0.975308	−	0.220850i	$-0.0708831\pi$
$563$	25.3092	+	18.3882i	1.06665	+	0.774969i	0.0913461	+	0.995819i	$0.470883\pi$
$564$	−1.61126	+	4.95894i	−0.0678462	+	0.208809i
$565$	1.13430	+	3.49101i	0.0477203	+	0.146868i
$566$	−15.7271	+	11.4264i	−0.661058	+	0.480287i
$567$	−4.61803	+	3.35520i	−0.193939	+	0.140905i
$568$	7.59437	+	23.3731i	0.318653	+	0.980712i
$569$	−0.536469	+	1.65108i	−0.0224899	+	0.0692169i	−0.961672	−	0.274204i	$-0.911586\pi$
$569$	−0.536469	+	1.65108i	−0.0224899	+	0.0692169i	0.939182	+	0.343421i	$0.111586\pi$
$570$	−0.252152	−	0.183199i	−0.0105615	−	0.00767336i
$571$	−12.5309			−0.524403			−0.262201	−	0.965013i	$-0.584449\pi$
$571$	−12.5309			−0.524403			−0.262201	+	0.965013i	$0.584449\pi$
$572$		0			0
$573$	−7.43182			−0.310469
$574$	0.841669	+	0.611508i	0.0351306	+	0.0255238i
$575$	5.96304	−	18.3523i	0.248676	−	0.765345i
$576$	−2.48729	−	7.65508i	−0.103637	−	0.318962i
$577$	−16.3337	+	11.8672i	−0.679983	+	0.494036i	−0.873352	−	0.487090i	$-0.838058\pi$
$577$	−16.3337	+	11.8672i	−0.679983	+	0.494036i	0.193369	+	0.981126i	$0.438058\pi$
$578$	−1.12520	+	0.817505i	−0.0468021	+	0.0340037i
$579$	−3.03356	−	9.33634i	−0.126070	−	0.388005i
$580$	0.362142	−	1.11456i	0.0150371	−	0.0462795i
$581$	9.12876	+	6.63243i	0.378725	+	0.275160i
$582$	−4.35051			−0.180334
$583$		0			0
$584$	14.7550			0.610568
$585$	3.07735	+	2.23582i	0.127233	+	0.0924399i
$586$	0.109337	−	0.336506i	0.00451669	−	0.0139009i
$587$	−0.00258825	−	0.00796580i	−0.000106828	−	0.000328784i	0.951003	−	0.309181i	$-0.100055\pi$
$587$	−0.00258825	−	0.00796580i	−0.000106828	−	0.000328784i	−0.951110	+	0.308853i	$0.900055\pi$
$588$	0.697759	−	0.506952i	0.0287751	−	0.0209063i
$589$	−16.2476	+	11.8046i	−0.669472	+	0.486400i
$590$	0.509643	+	1.56852i	0.0209817	+	0.0645750i
$591$	−2.34977	+	7.23183i	−0.0966564	+	0.297478i
$592$	3.37778	+	2.45410i	0.138826	+	0.100863i
$593$	0.439298			0.0180398			0.00901989	−	0.999959i	$-0.497129\pi$
$593$	0.439298			0.0180398			0.00901989	+	0.999959i	$0.497129\pi$
$594$		0			0
$595$	−0.964520			−0.0395415
$596$	8.16249	+	5.93040i	0.334349	+	0.242918i
$597$	2.91469	−	8.97048i	0.119290	−	0.367137i
$598$	6.11496	+	18.8199i	0.250060	+	0.769604i
$599$	−36.5403	+	26.5481i	−1.49300	+	1.08473i	−0.519930	+	0.854209i	$0.674042\pi$
$599$	−36.5403	+	26.5481i	−1.49300	+	1.08473i	−0.973068	+	0.230518i	$0.925958\pi$
$600$	−6.53455	+	4.74763i	−0.266772	+	0.193821i
$601$	−3.44358	−	10.5983i	−0.140467	−	0.432312i	0.855934	−	0.517086i	$-0.172983\pi$
$601$	−3.44358	−	10.5983i	−0.140467	−	0.432312i	−0.996400	+	0.0847740i	$0.972983\pi$
$602$	1.13117	−	3.48139i	0.0461032	−	0.141891i
$603$	2.69318	+	1.95671i	0.109675	+	0.0796834i
$604$	11.3591			0.462194
$605$		0			0
$606$	9.23071			0.374972
$607$	−28.8817	−	20.9838i	−1.17227	−	0.851706i	−0.180994	−	0.983484i	$-0.557931\pi$
$607$	−28.8817	−	20.9838i	−1.17227	−	0.851706i	−0.991279	+	0.131778i	$0.957931\pi$
$608$	−5.27330	+	16.2295i	−0.213860	+	0.658195i
$609$	0.720768	+	2.21829i	0.0292070	+	0.0898898i
$610$	1.34775	−	0.979200i	0.0545689	−	0.0396466i
$611$	31.9356	−	23.2026i	1.29198	−	0.938676i
$612$	4.89377	+	15.0615i	0.197819	+	0.608824i
$613$	−5.31447	+	16.3563i	−0.214650	+	0.660623i	0.784529	+	0.620092i	$0.212905\pi$
$613$	−5.31447	+	16.3563i	−0.214650	+	0.660623i	−0.999178	+	0.0405309i	$0.987095\pi$
$614$	−5.05449	−	3.67230i	−0.203983	−	0.148202i
$615$	0.184020			0.00742040
$616$		0			0
$617$	−16.8852			−0.679774			−0.339887	−	0.940466i	$-0.610389\pi$
$617$	−16.8852			−0.679774			−0.339887	+	0.940466i	$0.610389\pi$
$618$	−6.31251	−	4.58631i	−0.253927	−	0.184488i
$619$	9.60092	−	29.5486i	0.385893	−	1.18766i	−0.549937	−	0.835206i	$-0.685348\pi$
$619$	9.60092	−	29.5486i	0.385893	−	1.18766i	0.935830	−	0.352452i	$-0.114652\pi$
$620$	−0.661107	−	2.03468i	−0.0265507	−	0.0817146i
$621$	−10.9494	+	7.95523i	−0.439385	+	0.319232i
$622$	−0.0861506	+	0.0625921i	−0.00345432	+	0.00250971i
$623$	2.44790	+	7.53386i	0.0980730	+	0.301838i
$624$	−0.920943	+	2.83437i	−0.0368672	+	0.113466i
$625$	−19.6266	−	14.2595i	−0.785062	−	0.570381i
$626$	−11.8877			−0.475127
$627$		0			0
$628$	−28.1217			−1.12218
$629$	19.8256	+	14.4041i	0.790499	+	0.574331i
$630$	0.139962	−	0.430759i	0.00557622	−	0.0171618i
$631$	2.24150	+	6.89863i	0.0892327	+	0.274630i	0.985708	−	0.168464i	$-0.0538807\pi$
$631$	2.24150	+	6.89863i	0.0892327	+	0.274630i	−0.896475	+	0.443094i	$0.853881\pi$
$632$	9.67408	−	7.02863i	0.384814	−	0.279584i
$633$	4.46672	−	3.24526i	0.177536	−	0.128988i
$634$	−7.92665	−	24.3957i	−0.314807	−	0.968877i
$635$	0.137335	−	0.422675i	0.00544999	−	0.0167733i
$636$	−1.19869	−	0.870900i	−0.0475312	−	0.0345334i
$637$	−6.52954			−0.258710
$638$		0			0
$639$	24.3718			0.964132
$640$	−1.67739	−	1.21870i	−0.0663048	−	0.0481732i
$641$	−6.41207	+	19.7343i	−0.253262	+	0.779459i	0.740906	+	0.671609i	$0.234397\pi$
$641$	−6.41207	+	19.7343i	−0.253262	+	0.779459i	−0.994167	+	0.107850i	$0.965603\pi$
$642$	0.800840	+	2.46473i	0.0316066	+	0.0972752i
$643$	−5.75314	+	4.17990i	−0.226882	+	0.164839i	−0.695419	−	0.718605i	$-0.744781\pi$
$643$	−5.75314	+	4.17990i	−0.226882	+	0.164839i	0.468537	+	0.883444i	$0.344781\pi$
$644$	−4.40079	+	3.19736i	−0.173415	+	0.125994i
$645$	−0.200083	−	0.615793i	−0.00787827	−	0.0242468i
$646$	−3.03574	+	9.34303i	−0.119439	+	0.367597i
$647$	−22.3118	−	16.2105i	−0.877166	−	0.637299i	0.0553338	−	0.998468i	$-0.482378\pi$
$647$	−22.3118	−	16.2105i	−0.877166	−	0.637299i	−0.932500	+	0.361169i	$0.882378\pi$
$648$	−15.0694			−0.591984
$649$		0			0
$650$	25.1317			0.985748
$651$	3.44479	+	2.50279i	0.135012	+	0.0980920i
$652$	−3.20604	+	9.86719i	−0.125558	+	0.386429i
$653$	4.99190	+	15.3635i	0.195348	+	0.601220i	0.999972	+	0.00743560i	$0.00236685\pi$
$653$	4.99190	+	15.3635i	0.195348	+	0.601220i	−0.804624	+	0.593785i	$0.797633\pi$
$654$	2.09882	−	1.52489i	0.0820705	−	0.0596277i
$655$	−0.246643	+	0.179197i	−0.00963714	+	0.00700179i
$656$	−0.305372	−	0.939838i	−0.0119228	−	0.0366945i
$657$	4.52169	−	13.9163i	0.176408	−	0.542927i
$658$	−3.80263	−	2.76277i	−0.148242	−	0.107704i
$659$	13.2085			0.514531			0.257266	−	0.966341i	$-0.417178\pi$
$659$	13.2085			0.514531			0.257266	+	0.966341i	$0.417178\pi$
$660$		0			0
$661$	−4.90660			−0.190845			−0.0954223	−	0.995437i	$-0.530420\pi$
$661$	−4.90660			−0.190845			−0.0954223	+	0.995437i	$0.530420\pi$
$662$	−18.5765	−	13.4966i	−0.721996	−	0.524561i
$663$	−5.40540	+	16.6361i	−0.209928	+	0.646093i
$664$	9.20522	+	28.3307i	0.357232	+	1.09945i
$665$	−0.524757	+	0.381258i	−0.0203492	+	0.0147846i
$666$	−9.30986	+	6.76401i	−0.360750	+	0.262100i
$667$	−4.54590	−	13.9908i	−0.176018	−	0.541728i
$668$	−0.953523	+	2.93464i	−0.0368929	+	0.113545i
$669$	−0.357622	−	0.259828i	−0.0138265	−	0.0100455i
$670$	−0.219981			−0.00849861
$671$		0			0
$672$	3.61803			0.139569
$673$	−24.2601	−	17.6260i	−0.935159	−	0.679433i	0.0120914	−	0.999927i	$-0.496151\pi$
$673$	−24.2601	−	17.6260i	−0.935159	−	0.679433i	−0.947251	+	0.320494i	$0.896151\pi$
$674$	−1.35270	+	4.16318i	−0.0521041	+	0.160360i
$675$	5.31162	+	16.3475i	0.204444	+	0.629215i
$676$	33.4578	−	24.3085i	1.28684	−	0.934943i
$677$	10.1847	−	7.39959i	0.391428	−	0.284389i	−0.374612	−	0.927182i	$-0.622224\pi$
$677$	10.1847	−	7.39959i	0.391428	−	0.284389i	0.766040	+	0.642792i	$0.222224\pi$
$678$	−2.44946	−	7.53867i	−0.0940711	−	0.289521i
$679$	−2.79781	+	8.61078i	−0.107370	+	0.330451i
$680$	−2.06000	−	1.49667i	−0.0789973	−	0.0573949i
$681$	3.28894			0.126033
$682$		0			0
$683$	−28.5342			−1.09183			−0.545916	−	0.837840i	$-0.683818\pi$
$683$	−28.5342			−1.09183			−0.545916	+	0.837840i	$0.683818\pi$
$684$	8.61605	+	6.25992i	0.329443	+	0.239354i
$685$	−0.171851	+	0.528902i	−0.00656608	+	0.0202083i
$686$	0.240256	+	0.739431i	0.00917301	+	0.0282316i
$687$	3.30416	−	2.40061i	0.126062	−	0.0915891i
$688$	−2.81299	+	2.04376i	−0.107244	+	0.0779174i
$689$	3.46631	+	10.6682i	0.132056	+	0.406426i
$690$	0.128791	−	0.396377i	0.00490297	−	0.0150898i
$691$	−20.5282	−	14.9146i	−0.780929	−	0.567378i	0.124329	−	0.992241i	$-0.460322\pi$
$691$	−20.5282	−	14.9146i	−0.780929	−	0.567378i	−0.905258	+	0.424863i	$0.860322\pi$
$692$	−14.4606			−0.549711
$693$		0			0
$694$	−6.78791			−0.257666
$695$	0.857358	+	0.622907i	0.0325214	+	0.0236282i
$696$	−1.90280	+	5.85621i	−0.0721254	+	0.221979i
$697$	−1.79236	−	5.51631i	−0.0678904	−	0.208945i
$698$	11.6157	−	8.43929i	0.439660	−	0.319432i
$699$	−4.77856	+	3.47183i	−0.180742	+	0.131317i
$700$	2.13484	+	6.57037i	0.0806895	+	0.248337i
$701$	14.1227	−	43.4653i	0.533409	−	1.64166i	−0.213654	−	0.976909i	$-0.568537\pi$
$701$	14.1227	−	43.4653i	0.533409	−	1.64166i	0.747063	−	0.664753i	$-0.231463\pi$
$702$	−14.2603	−	10.3607i	−0.538221	−	0.391040i
$703$	16.4800			0.621556
$704$		0			0
$705$	−0.831396			−0.0313122
$706$	14.7725	+	10.7328i	0.555968	+	0.403935i
$707$	5.93627	−	18.2700i	0.223256	−	0.687112i
$708$	2.54075	+	7.81962i	0.0954872	+	0.293879i
$709$	−31.1717	+	22.6476i	−1.17068	+	0.850548i	−0.991090	−	0.133193i	$-0.957477\pi$
$709$	−31.1717	+	22.6476i	−1.17068	+	0.850548i	−0.179589	+	0.983742i	$0.557477\pi$
$710$	−1.30293	+	0.946636i	−0.0488982	+	0.0355266i
$711$	−3.66448	−	11.2781i	−0.137429	−	0.422962i
$712$	−6.46236	+	19.8891i	−0.242187	+	0.745375i
$713$	−21.7264	−	15.7851i	−0.813660	−	0.591159i
$714$	2.08283			0.0779480
$715$		0			0
$716$	32.6683			1.22087
$717$	13.4233	+	9.75261i	0.501303	+	0.364218i
$718$	−3.57530	+	11.0036i	−0.133429	+	0.410652i
$719$	1.76205	+	5.42304i	0.0657135	+	0.202245i	0.978522	−	0.206143i	$-0.0660911\pi$
$719$	1.76205	+	5.42304i	0.0657135	+	0.202245i	−0.912808	+	0.408388i	$0.866091\pi$
$720$	−0.348056	+	0.252877i	−0.0129713	+	0.00942418i
$721$	−13.1371	+	9.54464i	−0.489250	+	0.355461i
$722$	−2.52334	−	7.76605i	−0.0939091	−	0.289023i
$723$	−3.60315	+	11.0893i	−0.134002	+	0.412417i
$724$	−15.4854	−	11.2508i	−0.575512	−	0.418134i
$725$	−18.6831			−0.693872
$726$		0			0
$727$	11.8221			0.438458			0.219229	−	0.975673i	$-0.429646\pi$
$727$	11.8221			0.438458			0.219229	+	0.975673i	$0.429646\pi$
$728$	−13.9456	−	10.1321i	−0.516859	−	0.375520i
$729$	−2.62868	+	8.09024i	−0.0973584	+	0.299638i
$730$	0.298798	+	0.919606i	0.0110590	+	0.0340361i
$731$	−16.5106	+	11.9957i	−0.610667	+	0.443676i
$732$	6.71902	−	4.88165i	0.248342	−	0.180431i
$733$	−2.72303	−	8.38064i	−0.100578	−	0.309546i	0.888089	−	0.459671i	$-0.152033\pi$
$733$	−2.72303	−	8.38064i	−0.100578	−	0.309546i	−0.988667	+	0.150125i	$0.952033\pi$
$734$	−8.22298	+	25.3077i	−0.303516	+	0.934125i
$735$	0.111258	+	0.0808336i	0.00410381	+	0.00298159i
$736$	−22.8190			−0.841121
$737$		0			0
$738$	2.72370			0.100261
$739$	0.388983	+	0.282612i	0.0143090	+	0.0103961i	0.594917	−	0.803787i	$-0.297185\pi$
$739$	0.388983	+	0.282612i	0.0143090	+	0.0103961i	−0.580608	+	0.814183i	$0.697185\pi$
$740$	−0.542497	+	1.66963i	−0.0199426	+	0.0613769i
$741$	3.63511	+	11.1877i	0.133539	+	0.410991i
$742$	1.08057	−	0.785077i	0.0396688	−	0.0288211i
$743$	26.8952	−	19.5405i	0.986688	−	0.716871i	0.0274948	−	0.999622i	$-0.491247\pi$
$743$	26.8952	−	19.5405i	0.986688	−	0.716871i	0.959193	+	0.282751i	$0.0912470\pi$
$744$	3.47364	+	10.6908i	0.127350	+	0.391943i
$745$	−0.497133	+	1.53002i	−0.0182135	+	0.0560555i
$746$	1.89793	+	1.37893i	0.0694883	+	0.0504862i
$747$	29.5413			1.08086
$748$		0			0
$749$	5.39336			0.197069
$750$	−0.860729	−	0.625357i	−0.0314294	−	0.0228348i
$751$	8.65453	−	26.6359i	0.315808	−	0.971958i	−0.659612	−	0.751606i	$-0.729280\pi$
$751$	8.65453	−	26.6359i	0.315808	−	0.971958i	0.975421	−	0.220352i	$-0.0707205\pi$
$752$	1.37966	+	4.24616i	0.0503110	+	0.154841i
$753$	−14.6866	+	10.6704i	−0.535209	+	0.388852i
$754$	15.5000	−	11.2614i	0.564478	−	0.410117i
$755$	0.559694	+	1.72256i	0.0203693	+	0.0626904i
$756$	1.49732	−	4.60828i	0.0544570	−	0.167601i
$757$	17.9981	+	13.0764i	0.654151	+	0.475269i	0.864683	−	0.502318i	$-0.167519\pi$
$757$	17.9981	+	13.0764i	0.654151	+	0.475269i	−0.210532	+	0.977587i	$0.567519\pi$
$758$	−4.76156			−0.172948
$759$		0			0
$760$	−1.71237			−0.0621142
$761$	−39.0152	−	28.3462i	−1.41430	−	1.02755i	−0.992680	−	0.120775i	$-0.961462\pi$
$761$	−39.0152	−	28.3462i	−1.41430	−	1.02755i	−0.421619	−	0.906773i	$-0.638538\pi$
$762$	−0.296569	+	0.912745i	−0.0107436	+	0.0330653i
$763$	−1.66839	−	5.13477i	−0.0603997	−	0.185891i
$764$	−13.5761	+	9.86364i	−0.491167	+	0.356854i
$765$	−2.04289	+	1.48424i	−0.0738607	+	0.0536629i
$766$	1.05496	+	3.24683i	0.0381172	+	0.117313i
$767$	19.2352	−	59.1999i	0.694543	−	2.13758i
$768$	6.69670	+	4.86544i	0.241646	+	0.175566i
$769$	−43.6883			−1.57544			−0.787721	−	0.616032i	$-0.788739\pi$
$769$	−43.6883			−1.57544			−0.787721	+	0.616032i	$0.788739\pi$
$770$		0			0
$771$	−10.4549			−0.376524
$772$	−17.9329	−	13.0290i	−0.645420	−	0.468925i
$773$	−0.180951	+	0.556910i	−0.00650835	+	0.0200306i	−0.954258	−	0.298985i	$-0.903352\pi$
$773$	−0.180951	+	0.556910i	−0.00650835	+	0.0200306i	0.947750	+	0.319015i	$0.103352\pi$
$774$	−2.96145	−	9.11441i	−0.106447	−	0.327611i
$775$	−27.5930	+	20.0475i	−0.991169	+	0.720126i
$776$	−19.3371	+	14.0492i	−0.694162	+	0.504338i
$777$	−1.07973	−	3.32305i	−0.0387349	−	0.119214i
$778$	2.52173	−	7.76108i	0.0904083	−	0.278248i
$779$	−3.15565	−	2.29271i	−0.113063	−	0.0821450i
$780$	−1.25312			−0.0448688
$781$		0			0
$782$	−13.1365			−0.469760
$783$	10.6012	+	7.70222i	0.378856	+	0.275255i
$784$	0.228211	−	0.702362i	0.00815041	−	0.0250844i
$785$	−1.38563	−	4.26455i	−0.0494554	−	0.152208i
$786$	0.532613	−	0.386966i	0.0189977	−	0.0138026i
$787$	24.8502	−	18.0548i	0.885815	−	0.643582i	−0.0489683	−	0.998800i	$-0.515593\pi$
$787$	24.8502	−	18.0548i	0.885815	−	0.643582i	0.934784	+	0.355218i	$0.115593\pi$
$788$	5.30576	+	16.3295i	0.189010	+	0.581713i
$789$	1.56231	−	4.80828i	0.0556196	−	0.171179i
$790$	0.633964	+	0.460602i	0.0225554	+	0.0163875i
$791$	−16.4962			−0.586538
$792$		0			0
$793$	−62.8758			−2.23278
$794$	−7.16355	−	5.20462i	−0.254225	−	0.184705i
$795$	0.0730058	−	0.224689i	0.00258925	−	0.00796889i
$796$	−6.58135	−	20.2553i	−0.233270	−	0.717930i
$797$	8.76431	−	6.36765i	0.310448	−	0.225554i	−0.421641	−	0.906763i	$-0.638546\pi$
$797$	8.76431	−	6.36765i	0.310448	−	0.225554i	0.732089	+	0.681209i	$0.238546\pi$
$798$	1.13319	−	0.823308i	0.0401143	−	0.0291448i
$799$	8.09781	+	24.9225i	0.286480	+	0.881695i
$800$	−8.95551	+	27.5622i	−0.316625	+	0.974472i
$801$	16.7781	+	12.1900i	0.592827	+	0.430714i
$802$	−3.67358			−0.129719
$803$		0			0
$804$	−1.09668			−0.0386770
$805$	−0.701707	−	0.509820i	−0.0247319	−	0.0179688i
$806$	10.8081	−	33.2639i	0.380699	−	1.17167i
$807$	−1.19310	−	3.67199i	−0.0419992	−	0.129260i
$808$	41.0286	−	29.8090i	1.44338	−	1.04868i
$809$	−31.2200	+	22.6827i	−1.09764	+	0.797480i	−0.980673	−	0.195656i	$-0.937316\pi$
$809$	−31.2200	+	22.6827i	−1.09764	+	0.797480i	−0.116964	+	0.993136i	$0.537316\pi$
$810$	−0.305165	−	0.939200i	−0.0107224	−	0.0330001i
$811$	15.7270	−	48.4026i	0.552248	−	1.69964i	−0.150854	−	0.988556i	$-0.548202\pi$
$811$	15.7270	−	48.4026i	0.552248	−	1.69964i	0.703102	−	0.711089i	$-0.251798\pi$
$812$	4.26082	+	3.09567i	0.149526	+	0.108637i
$813$	−4.86200			−0.170518
$814$		0			0
$815$	−1.65429			−0.0579473
$816$	−1.60057	−	1.16288i	−0.0560312	−	0.0407091i
$817$	−4.24109	+	13.0527i	−0.148377	+	0.456657i
$818$	−0.592336	−	1.82302i	−0.0207106	−	0.0637405i
$819$	−13.8298	+	10.0479i	−0.483252	+	0.351103i
$820$	0.336160	−	0.244234i	0.0117392	−	0.00852903i
$821$	12.4563	+	38.3365i	0.434728	+	1.33795i	0.893365	+	0.449331i	$0.148338\pi$
$821$	12.4563	+	38.3365i	0.434728	+	1.33795i	−0.458637	+	0.888623i	$0.651662\pi$
$822$	0.371103	−	1.14214i	0.0129437	−	0.0398366i
$823$	−20.7770	−	15.0953i	−0.724239	−	0.526191i	0.163496	−	0.986544i	$-0.447723\pi$
$823$	−20.7770	−	15.0953i	−0.724239	−	0.526191i	−0.887736	+	0.460353i	$0.847723\pi$
$824$	−42.8685			−1.49340
$825$		0			0
$826$	−7.41179			−0.257889
$827$	−25.8527	−	18.7831i	−0.898987	−	0.653152i	0.0392187	−	0.999231i	$-0.487513\pi$
$827$	−25.8527	−	18.7831i	−0.898987	−	0.653152i	−0.938206	+	0.346078i	$0.887513\pi$
$828$	−4.40079	+	13.5442i	−0.152938	+	0.470694i
$829$	14.9565	+	46.0313i	0.519460	+	1.59873i	0.775017	+	0.631940i	$0.217741\pi$
$829$	14.9565	+	46.0313i	0.519460	+	1.59873i	−0.255557	+	0.966794i	$0.582259\pi$
$830$	−1.57930	+	1.14743i	−0.0548182	+	0.0398278i
$831$	6.02382	−	4.37656i	0.208964	−	0.151821i
$832$	−6.20345	−	19.0923i	−0.215066	−	0.661905i
$833$	1.33947	−	4.12246i	0.0464099	−	0.142835i
$834$	−1.85142	−	1.34514i	−0.0641095	−	0.0465783i
$835$	−0.492010			−0.0170267
$836$		0			0
$837$	23.9216			0.826850
$838$	9.01975	+	6.55323i	0.311582	+	0.226378i
$839$	−11.6550	+	35.8705i	−0.402377	+	1.23839i	0.520689	+	0.853746i	$0.325675\pi$
$839$	−11.6550	+	35.8705i	−0.402377	+	1.23839i	−0.923066	+	0.384642i	$0.874325\pi$
$840$	0.112190	+	0.345285i	0.00387091	+	0.0119134i
$841$	11.9387	−	8.67396i	0.411679	−	0.299102i
$842$	10.8916	−	7.91319i	0.375348	−	0.272707i
$843$	−4.04023	−	12.4345i	−0.139153	−	0.428269i
$844$	3.85245	−	11.8566i	0.132607	−	0.408121i
$845$	5.33485	+	3.87600i	0.183525	+	0.133338i
$846$	−12.3056			−0.423074
$847$		0			0
$848$	−1.26869			−0.0435671
$849$	−12.5017	−	9.08300i	−0.429057	−	0.311728i
$850$	−5.15552	+	15.8671i	−0.176833	+	0.544235i
$851$	6.80986	+	20.9586i	0.233439	+	0.718451i
$852$	−6.49557	+	4.71931i	−0.222535	+	0.161681i
$853$	7.51467	−	5.45973i	0.257297	−	0.186938i	−0.451657	−	0.892191i	$-0.649167\pi$
$853$	7.51467	−	5.45973i	0.257297	−	0.186938i	0.708955	+	0.705254i	$0.249167\pi$
$854$	2.31353	+	7.12030i	0.0791672	+	0.243652i
$855$	−0.524757	+	1.61503i	−0.0179463	+	0.0552330i
$856$	11.5190	+	8.36904i	0.393711	+	0.286048i
$857$	29.7644			1.01673			0.508365	−	0.861141i	$-0.330250\pi$
$857$	29.7644			1.01673			0.508365	+	0.861141i	$0.330250\pi$
$858$		0			0
$859$	33.2611			1.13485			0.567427	−	0.823424i	$-0.307939\pi$
$859$	33.2611			1.13485			0.567427	+	0.823424i	$0.307939\pi$
$860$	−1.18279	−	0.859350i	−0.0403329	−	0.0293036i
$861$	−0.255556	+	0.786521i	−0.00870933	+	0.0268046i
$862$	−6.70129	−	20.6244i	−0.228247	−	0.702471i
$863$	15.0216	−	10.9138i	0.511340	−	0.371510i	−0.301992	−	0.953311i	$-0.597652\pi$
$863$	15.0216	−	10.9138i	0.511340	−	0.371510i	0.813332	+	0.581800i	$0.197652\pi$
$864$	16.4443	−	11.9475i	0.559445	−	0.406461i
$865$	−0.712517	−	2.19290i	−0.0242263	−	0.0745609i
$866$	−7.09884	+	21.8480i	−0.241229	+	0.742425i
$867$	−0.894438	−	0.649847i	−0.0303767	−	0.0220700i
$868$	9.61454			0.326339
$869$		0			0
$870$	−0.403520			−0.0136806
$871$	6.71697	+	4.88016i	0.227596	+	0.165358i
$872$	4.40448	−	13.5556i	0.149154	−	0.459050i
$873$	7.32477	+	22.5433i	0.247906	+	0.762976i
$874$	−7.14704	+	5.19263i	−0.241752	+	0.175643i
$875$	−1.79128	+	1.30144i	−0.0605562	+	0.0439967i
$876$	1.48961	+	4.58455i	0.0503293	+	0.154898i
$877$	6.95044	−	21.3913i	0.234700	−	0.722332i	−0.762461	−	0.647034i	$-0.776009\pi$
$877$	6.95044	−	21.3913i	0.234700	−	0.722332i	0.997161	−	0.0752979i	$-0.0239908\pi$
$878$	−21.1756	−	15.3849i	−0.714641	−	0.519217i
$879$	0.281259			0.00948664
$880$		0			0
$881$	7.06565			0.238048			0.119024	−	0.992891i	$-0.462023\pi$
$881$	7.06565			0.238048			0.119024	+	0.992891i	$0.462023\pi$
$882$	1.64674	+	1.19643i	0.0554486	+	0.0402857i
$883$	−6.16125	+	18.9624i	−0.207342	+	0.638134i	0.792267	+	0.610175i	$0.208901\pi$
$883$	−6.16125	+	18.9624i	−0.207342	+	0.638134i	−0.999609	+	0.0279593i	$0.991099\pi$
$884$	12.2054	+	37.5643i	0.410511	+	1.26342i
$885$	−1.06063	+	0.770590i	−0.0356525	+	0.0259031i
$886$	−6.49549	+	4.71925i	−0.218220	+	0.158546i
$887$	−2.14915	−	6.61442i	−0.0721615	−	0.222090i	0.908471	−	0.417949i	$-0.137251\pi$
$887$	−2.14915	−	6.61442i	−0.0721615	−	0.222090i	−0.980632	+	0.195858i	$0.937251\pi$
$888$	2.85043	−	8.77273i	0.0956543	−	0.294394i
$889$	1.61583	+	1.17397i	0.0541934	+	0.0393738i
$890$	−1.37045			−0.0459376
$891$		0			0
$892$	−0.998136			−0.0334201
$893$	14.2571	+	10.3584i	0.477097	+	0.346631i
$894$	1.07353	−	3.30400i	0.0359043	−	0.110502i
$895$	1.60966	+	4.95402i	0.0538049	+	0.165595i
$896$	7.53831	−	5.47690i	0.251837	−	0.182970i
$897$	−12.7259	+	9.24594i	−0.424907	+	0.308713i
$898$	−0.662590	−	2.03924i	−0.0221109	−	0.0680504i
$899$	−8.03481	+	24.7286i	−0.267976	+	0.824745i
$900$	14.6324	+	10.6311i	0.487748	+	0.354369i
$901$	−7.44650			−0.248079
$902$		0			0
$903$	2.90983			0.0968331
$904$	−35.2322	−	25.5977i	−1.17181	−	0.851367i
$905$	0.943135	−	2.90267i	0.0313509	−	0.0964880i
$906$	−1.20863	−	3.71978i	−0.0401541	−	0.123582i
$907$	18.9635	−	13.7778i	0.629672	−	0.457483i	−0.226615	−	0.973984i	$-0.572766\pi$
$907$	18.9635	−	13.7778i	0.629672	−	0.457483i	0.856286	+	0.516501i	$0.172766\pi$
$908$	6.00810	−	4.36514i	0.199386	−	0.144862i
$909$	−15.5413	−	47.8314i	−0.515474	−	1.58647i
$910$	0.349074	−	1.07434i	0.0115717	−	0.0356140i
$911$	−37.8698	−	27.5140i	−1.25468	−	0.911580i	−0.256198	−	0.966624i	$-0.582470\pi$
$911$	−37.8698	−	27.5140i	−1.25468	−	0.911580i	−0.998484	+	0.0550445i	$0.982470\pi$
$912$	−1.33048			−0.0440564
$913$		0			0
$914$	31.3563			1.03718
$915$	1.07135	+	0.778381i	0.0354177	+	0.0257325i
$916$	2.84977	−	8.77068i	0.0941589	−	0.289791i
$917$	−0.423382	−	1.30304i	−0.0139813	−	0.0430301i
$918$	9.46665	−	6.87792i	0.312446	−	0.227005i
$919$	8.59768	−	6.24658i	0.283611	−	0.206056i	−0.436880	−	0.899520i	$-0.643916\pi$
$919$	8.59768	−	6.24658i	0.283611	−	0.206056i	0.720491	+	0.693464i	$0.243916\pi$
$920$	−0.707584	−	2.17772i	−0.0233283	−	0.0717973i
$921$	1.53470	−	4.72331i	0.0505700	−	0.155638i
$922$	−21.5275	−	15.6407i	−0.708971	−	0.515098i
$923$	60.7848			2.00075
$924$		0			0
$925$	27.9876			0.920228
$926$	−0.444921	−	0.323254i	−0.0146210	−	0.0106228i
$927$	−13.1371	+	40.4317i	−0.431478	+	1.32795i
$928$	6.82721	+	21.0120i	0.224114	+	0.689752i
$929$	29.6674	−	21.5546i	0.973357	−	0.707185i	0.0171426	−	0.999853i	$-0.494543\pi$
$929$	29.6674	−	21.5546i	0.973357	−	0.707185i	0.956214	+	0.292668i	$0.0945431\pi$
$930$	−0.595957	+	0.432988i	−0.0195422	+	0.0141982i
$931$	−0.900787	−	2.77234i	−0.0295221	−	0.0908596i
$932$	−4.12141	+	12.6844i	−0.135001	+	0.415491i
$933$	−0.0684824	−	0.0497554i	−0.00224201	−	0.00162892i
$934$	−22.2302			−0.727393
$935$		0			0
$936$	−45.1290			−1.47509
$937$	−32.5365	−	23.6392i	−1.06292	−	0.772258i	−0.0882954	−	0.996094i	$-0.528142\pi$
$937$	−32.5365	−	23.6392i	−1.06292	−	0.772258i	−0.974627	+	0.223836i	$0.928142\pi$
$938$	0.305497	−	0.940223i	0.00997483	−	0.0306994i
$939$	−2.92012	−	8.98720i	−0.0952944	−	0.293286i
$940$	−1.51876	+	1.10344i	−0.0495364	+	0.0359903i
$941$	20.1523	−	14.6415i	0.656948	−	0.477300i	−0.208683	−	0.977983i	$-0.566918\pi$
$941$	20.1523	−	14.6415i	0.656948	−	0.477300i	0.865631	+	0.500683i	$0.166918\pi$
$942$	2.99221	+	9.20907i	0.0974914	+	0.300048i
$943$	1.61180	−	4.96061i	0.0524875	−	0.161540i
$944$	5.69566	+	4.13814i	0.185378	+	0.134685i
$945$	0.772605			0.0251328
$946$		0			0
$947$	−32.2061			−1.04656			−0.523279	−	0.852161i	$-0.675292\pi$
$947$	−32.2061			−1.04656			−0.523279	+	0.852161i	$0.675292\pi$
$948$	3.16053	+	2.29626i	0.102649	+	0.0745791i
$949$	11.2774	−	34.7082i	0.366079	−	1.12668i
$950$	3.46706	+	10.6705i	0.112486	+	0.346197i
$951$	16.4963	−	11.9852i	0.534928	−	0.388648i
$952$	9.25776	−	6.72615i	0.300046	−	0.217996i
$953$	−13.9247	−	42.8557i	−0.451064	−	1.38823i	−0.875695	−	0.482865i	$-0.839596\pi$
$953$	−13.9247	−	42.8557i	−0.451064	−	1.38823i	0.424631	−	0.905367i	$-0.360404\pi$
$954$	1.08057	−	3.32564i	0.0349846	−	0.107671i
$955$	−2.16472	−	1.57276i	−0.0700486	−	0.0508933i
$956$	37.4650			1.21170
$957$		0			0
$958$	3.96296			0.128038
$959$	−2.02193	−	1.46902i	−0.0652915	−	0.0474370i
$960$	−0.130654	+	0.402113i	−0.00421685	+	0.0129781i
$961$	5.08838	+	15.6604i	0.164141	+	0.505175i
$962$	−23.2194	+	16.8699i	−0.748623	+	0.543906i
$963$	11.4233	−	8.29952i	0.368111	−	0.267448i
$964$	8.13589	+	25.0397i	0.262039	+	0.806474i
$965$	1.09220	−	3.36144i	0.0351591	−	0.108208i
$966$	1.51530	+	1.10093i	0.0487540	+	0.0354218i
$967$	−1.81387			−0.0583300			−0.0291650	−	0.999575i	$-0.509285\pi$
$967$	−1.81387			−0.0583300			−0.0291650	+	0.999575i	$0.509285\pi$
$968$		0			0
$969$	−7.80912			−0.250865
$970$	−1.26720	−	0.920677i	−0.0406874	−	0.0295612i
$971$	7.12405	−	21.9256i	0.228622	−	0.703625i	−0.769282	−	0.638909i	$-0.779386\pi$
$971$	7.12405	−	21.9256i	0.228622	−	0.703625i	0.997904	−	0.0647158i	$-0.0206141\pi$
$972$	−6.01331	−	18.5071i	−0.192877	−	0.593615i
$973$	−3.85302	+	2.79938i	−0.123522	+	0.0897441i
$974$	−18.3594	+	13.3389i	−0.588272	+	0.427405i
$975$	6.17342	+	18.9998i	0.197708	+	0.608481i
$976$	2.19754	−	6.76335i	0.0703417	−	0.216489i
$977$	5.73956	+	4.17004i	0.183625	+	0.133411i	0.675800	−	0.737085i	$-0.263798\pi$
$977$	5.73956	+	4.17004i	0.183625	+	0.133411i	−0.492175	+	0.870496i	$0.663798\pi$
$978$	3.57236			0.114232
$979$		0			0
$980$	0.310525			0.00991935
$981$	−11.4353	−	8.30823i	−0.365101	−	0.265261i
$982$	−7.24226	+	22.2894i	−0.231110	+	0.711283i
$983$	11.8509	+	36.4732i	0.377984	+	1.16332i	0.941443	+	0.337172i	$0.109470\pi$
$983$	11.8509	+	36.4732i	0.377984	+	1.16332i	−0.563459	+	0.826144i	$0.690530\pi$
$984$	−1.76628	+	1.28328i	−0.0563069	+	0.0409094i
$985$	−2.21487	+	1.60920i	−0.0705716	+	0.0512733i
$986$	3.93029	+	12.0962i	0.125166	+	0.385221i
$987$	1.15459	−	3.55348i	0.0367512	−	0.113108i
$988$	21.4890	+	15.6126i	0.683655	+	0.496705i
$989$	−18.3524			−0.583572
$990$		0			0
$991$	20.2722			0.643967			0.321984	−	0.946745i	$-0.395650\pi$
$991$	20.2722			0.643967			0.321984	+	0.946745i	$0.395650\pi$
$992$	32.6295	+	23.7067i	1.03599	+	0.752690i
$993$	5.64039	−	17.3593i	0.178992	−	0.550882i
$994$	−2.23659	−	6.88351i	−0.0709402	−	0.218332i
$995$	2.74736	−	1.99607i	0.0870971	−	0.0632798i
$996$	−7.87335	+	5.72032i	−0.249477	+	0.181255i
$997$	−4.76217	−	14.6565i	−0.150820	−	0.464175i	0.846894	−	0.531762i	$-0.178470\pi$
$997$	−4.76217	−	14.6565i	−0.150820	−	0.464175i	−0.997713	+	0.0675872i	$0.978470\pi$
$998$	1.42977	−	4.40039i	0.0452587	−	0.139292i
$999$	−15.8808	−	11.5381i	−0.502447	−	0.365049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.s.323.1		8
11.2	odd	10		77.2.f.a.71.1	yes	8
11.3	even	5	inner	847.2.f.s.729.1		8
11.4	even	5		847.2.f.q.372.2		8
11.5	even	5		847.2.a.k.1.3		4
11.6	odd	10		847.2.a.l.1.2		4
11.7	odd	10		77.2.f.a.64.1	✓	8
11.8	odd	10		847.2.f.p.729.2		8
11.9	even	5		847.2.f.q.148.2		8
11.10	odd	2		847.2.f.p.323.2		8
33.2	even	10		693.2.m.g.379.2		8
33.5	odd	10		7623.2.a.co.1.2		4
33.17	even	10		7623.2.a.ch.1.3		4
33.29	even	10		693.2.m.g.64.2		8
77.2	odd	30		539.2.q.c.214.1		16
77.6	even	10		5929.2.a.bi.1.2		4
77.13	even	10		539.2.f.d.148.1		8
77.18	odd	30		539.2.q.c.471.1		16
77.24	even	30		539.2.q.b.324.2		16
77.27	odd	10		5929.2.a.bb.1.3		4
77.40	even	30		539.2.q.b.361.2		16
77.46	odd	30		539.2.q.c.324.2		16
77.51	odd	30		539.2.q.c.361.2		16
77.62	even	10		539.2.f.d.295.1		8
77.68	even	30		539.2.q.b.214.1		16
77.73	even	30		539.2.q.b.471.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.1	✓	8	11.7	odd	10
77.2.f.a.71.1	yes	8	11.2	odd	10
539.2.f.d.148.1		8	77.13	even	10
539.2.f.d.295.1		8	77.62	even	10
539.2.q.b.214.1		16	77.68	even	30
539.2.q.b.324.2		16	77.24	even	30
539.2.q.b.361.2		16	77.40	even	30
539.2.q.b.471.1		16	77.73	even	30
539.2.q.c.214.1		16	77.2	odd	30
539.2.q.c.324.2		16	77.46	odd	30
539.2.q.c.361.2		16	77.51	odd	30
539.2.q.c.471.1		16	77.18	odd	30
693.2.m.g.64.2		8	33.29	even	10
693.2.m.g.379.2		8	33.2	even	10
847.2.a.k.1.3		4	11.5	even	5
847.2.a.l.1.2		4	11.6	odd	10
847.2.f.p.323.2		8	11.10	odd	2
847.2.f.p.729.2		8	11.8	odd	10
847.2.f.q.148.2		8	11.9	even	5
847.2.f.q.372.2		8	11.4	even	5
847.2.f.s.323.1		8	1.1	even	1	trivial
847.2.f.s.729.1		8	11.3	even	5	inner
5929.2.a.bb.1.3		4	77.27	odd	10
5929.2.a.bi.1.2		4	77.6	even	10
7623.2.a.ch.1.3		4	33.17	even	10
7623.2.a.co.1.2		4	33.5	odd	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.628998 - 0.456994i) q^{2} +(0.190983 - 0.587785i) q^{3} +(-0.431239 - 1.32722i) q^{4} +(0.180019 - 0.130791i) q^{5} +(-0.388742 + 0.282438i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.815793 + 2.51075i) q^{8} +(2.11803 + 1.53884i) q^{9} +O(q^{10})\)	\(q+(-0.628998 - 0.456994i) q^{2} +(0.190983 - 0.587785i) q^{3} +(-0.431239 - 1.32722i) q^{4} +(0.180019 - 0.130791i) q^{5} +(-0.388742 + 0.282438i) q^{6} +(0.309017 + 0.951057i) q^{7} +(-0.815793 + 2.51075i) q^{8} +(2.11803 + 1.53884i) q^{9} -0.173002 q^{10} -0.862478 q^{12} +(5.28251 + 3.83797i) q^{13} +(0.240256 - 0.739431i) q^{14} +(-0.0424967 - 0.130791i) q^{15} +(-0.597465 + 0.434084i) q^{16} +(-3.50678 + 2.54782i) q^{17} +(-0.628998 - 1.93586i) q^{18} +(-0.900787 + 2.77234i) q^{19} +(-0.251220 - 0.182522i) q^{20} +0.618034 q^{21} -3.89796 q^{23} +(1.31998 + 0.959022i) q^{24} +(-1.52978 + 4.70819i) q^{25} +(-1.56876 - 4.82815i) q^{26} +(2.80902 - 2.04087i) q^{27} +(1.12900 - 0.820265i) q^{28} +(1.16623 + 3.58928i) q^{29} +(-0.0330405 + 0.101688i) q^{30} +(5.57379 + 4.04959i) q^{31} +5.85410 q^{32} +3.37009 q^{34} +(0.180019 + 0.130791i) q^{35} +(1.12900 - 3.47470i) q^{36} +(-1.74703 - 5.37681i) q^{37} +(1.83353 - 1.33214i) q^{38} +(3.26477 - 2.37200i) q^{39} +(0.181527 + 0.558682i) q^{40} +(-0.413499 + 1.27262i) q^{41} +(-0.388742 - 0.282438i) q^{42} +4.70820 q^{43} +0.582554 q^{45} +(2.45181 + 1.78134i) q^{46} +(1.86817 - 5.74965i) q^{47} +(0.141042 + 0.434084i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(3.11385 - 2.26234i) q^{50} +(0.827838 + 2.54782i) q^{51} +(2.81579 - 8.66612i) q^{52} +(1.38982 + 1.00977i) q^{53} -2.69953 q^{54} -2.63996 q^{56} +(1.45750 + 1.05894i) q^{57} +(0.906723 - 2.79061i) q^{58} +(-2.94587 - 9.06646i) q^{59} +(-0.155262 + 0.112805i) q^{60} +(-7.79037 + 5.66003i) q^{61} +(-1.65526 - 5.09437i) q^{62} +(-0.809017 + 2.48990i) q^{63} +(-2.48729 - 1.80712i) q^{64} +1.45293 q^{65} +1.27155 q^{67} +(4.89377 + 3.55553i) q^{68} +(-0.744444 + 2.29116i) q^{69} +(-0.0534607 - 0.164535i) q^{70} +(7.53129 - 5.47180i) q^{71} +(-5.59153 + 4.06248i) q^{72} +(-1.72713 - 5.31556i) q^{73} +(-1.35829 + 4.18039i) q^{74} +(2.47524 + 1.79837i) q^{75} +4.06794 q^{76} -3.13752 q^{78} +(-3.66448 - 2.66240i) q^{79} +(-0.0507806 + 0.156287i) q^{80} +(1.76393 + 5.42882i) q^{81} +(0.841669 - 0.611508i) q^{82} +(9.12876 - 6.63243i) q^{83} +(-0.266520 - 0.820265i) q^{84} +(-0.298053 + 0.917313i) q^{85} +(-2.96145 - 2.15162i) q^{86} +2.33245 q^{87} +7.92157 q^{89} +(-0.366425 - 0.266223i) q^{90} +(-2.01774 + 6.20997i) q^{91} +(1.68095 + 5.17343i) q^{92} +(3.44479 - 2.50279i) q^{93} +(-3.80263 + 2.76277i) q^{94} +(0.200439 + 0.616888i) q^{95} +(1.11803 - 3.44095i) q^{96} +(7.32477 + 5.32176i) q^{97} +0.777484 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 + 2 * q^6 - 2 * q^7 + 12 * q^8 + 8 * q^9	\( 8 q + q^{2} + 6 q^{3} - 7 q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{7} + 12 q^{8} + 8 q^{9} + 28 q^{10} - 14 q^{12} + 5 q^{13} + q^{14} - 9 q^{15} + 7 q^{16} - 14 q^{17} + q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{21} - 16 q^{23} + 9 q^{24} - 5 q^{25} - 9 q^{26} + 18 q^{27} + 3 q^{28} - 6 q^{29} + 26 q^{30} + 14 q^{31} + 20 q^{32} - 24 q^{34} + 3 q^{35} + 3 q^{36} + q^{37} - 15 q^{38} - 29 q^{40} - 18 q^{41} + 2 q^{42} - 16 q^{43} + 18 q^{45} + 26 q^{46} + 7 q^{47} - q^{48} - 2 q^{49} - q^{50} - 8 q^{51} + 4 q^{52} + 7 q^{53} - 4 q^{54} - 18 q^{56} + 3 q^{57} + 36 q^{58} + 17 q^{60} - 12 q^{61} + 5 q^{62} - 2 q^{63} - 4 q^{64} - 24 q^{65} - 30 q^{67} + 7 q^{68} - 22 q^{69} - 12 q^{70} + 21 q^{71} - 3 q^{72} - 8 q^{73} - q^{74} + 52 q^{76} - 18 q^{78} - q^{79} + 37 q^{80} + 32 q^{81} - 34 q^{82} + 22 q^{83} + 11 q^{84} + 5 q^{85} + 13 q^{86} - 12 q^{87} - 34 q^{89} + 18 q^{90} - 5 q^{91} + 51 q^{92} + 3 q^{93} - 50 q^{94} + 41 q^{95} - 15 q^{97} - 4 q^{98}+O(q^{100}) \) 8 * q + q^2 + 6 * q^3 - 7 * q^4 + 3 * q^5 + 2 * q^6 - 2 * q^7 + 12 * q^8 + 8 * q^9 + 28 * q^10 - 14 * q^12 + 5 * q^13 + q^14 - 9 * q^15 + 7 * q^16 - 14 * q^17 + q^18 - 6 * q^19 - 4 * q^20 - 4 * q^21 - 16 * q^23 + 9 * q^24 - 5 * q^25 - 9 * q^26 + 18 * q^27 + 3 * q^28 - 6 * q^29 + 26 * q^30 + 14 * q^31 + 20 * q^32 - 24 * q^34 + 3 * q^35 + 3 * q^36 + q^37 - 15 * q^38 - 29 * q^40 - 18 * q^41 + 2 * q^42 - 16 * q^43 + 18 * q^45 + 26 * q^46 + 7 * q^47 - q^48 - 2 * q^49 - q^50 - 8 * q^51 + 4 * q^52 + 7 * q^53 - 4 * q^54 - 18 * q^56 + 3 * q^57 + 36 * q^58 + 17 * q^60 - 12 * q^61 + 5 * q^62 - 2 * q^63 - 4 * q^64 - 24 * q^65 - 30 * q^67 + 7 * q^68 - 22 * q^69 - 12 * q^70 + 21 * q^71 - 3 * q^72 - 8 * q^73 - q^74 + 52 * q^76 - 18 * q^78 - q^79 + 37 * q^80 + 32 * q^81 - 34 * q^82 + 22 * q^83 + 11 * q^84 + 5 * q^85 + 13 * q^86 - 12 * q^87 - 34 * q^89 + 18 * q^90 - 5 * q^91 + 51 * q^92 + 3 * q^93 - 50 * q^94 + 41 * q^95 - 15 * q^97 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more