LMFDB - Embedded newform 845.2.f.e.437.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(408,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("845.408");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.f (of order $4$, degree $2$, 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:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.3
Root			$-1.02262i$ of defining polynomial
Character	$\chi$	$=$	845.437
Dual form			845.2.f.e.408.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.02262i q^{2} +(-1.97063 + 1.97063i) q^{3} +0.954253 q^{4} +(-1.45744 - 1.69584i) q^{5} +(2.01520 + 2.01520i) q^{6} +0.963574 q^{7} -3.02107i q^{8} -4.76674i q^{9} +O(q^{10})$	\(q-1.02262i q^{2} +(-1.97063 + 1.97063i) q^{3} +0.954253 q^{4} +(-1.45744 - 1.69584i) q^{5} +(2.01520 + 2.01520i) q^{6} +0.963574 q^{7} -3.02107i q^{8} -4.76674i q^{9} +(-1.73420 + 1.49040i) q^{10} +(-1.17612 + 1.17612i) q^{11} +(-1.88048 + 1.88048i) q^{12} -0.985368i q^{14} +(6.21394 + 0.469810i) q^{15} -1.18090 q^{16} +(-5.12686 + 5.12686i) q^{17} -4.87456 q^{18} +(1.93291 - 1.93291i) q^{19} +(-1.39076 - 1.61826i) q^{20} +(-1.89884 + 1.89884i) q^{21} +(1.20272 + 1.20272i) q^{22} +(-2.72480 - 2.72480i) q^{23} +(5.95341 + 5.95341i) q^{24} +(-0.751762 + 4.94316i) q^{25} +(3.48159 + 3.48159i) q^{27} +0.919493 q^{28} -0.292263i q^{29} +(0.480436 - 6.35448i) q^{30} +(-0.125649 - 0.125649i) q^{31} -4.83454i q^{32} -4.63538i q^{33} +(5.24282 + 5.24282i) q^{34} +(-1.40435 - 1.63407i) q^{35} -4.54868i q^{36} -4.08121 q^{37} +(-1.97663 - 1.97663i) q^{38} +(-5.12326 + 4.40302i) q^{40} +(-4.89794 - 4.89794i) q^{41} +(1.94179 + 1.94179i) q^{42} +(-5.62000 - 5.62000i) q^{43} +(-1.12232 + 1.12232i) q^{44} +(-8.08364 + 6.94722i) q^{45} +(-2.78642 + 2.78642i) q^{46} -7.84582 q^{47} +(2.32710 - 2.32710i) q^{48} -6.07153 q^{49} +(5.05497 + 0.768765i) q^{50} -20.2063i q^{51} +(-1.99855 + 1.99855i) q^{53} +(3.56034 - 3.56034i) q^{54} +(3.70863 + 0.280394i) q^{55} -2.91103i q^{56} +7.61811i q^{57} -0.298873 q^{58} +(3.57185 + 3.57185i) q^{59} +(5.92967 + 0.448318i) q^{60} +2.08337 q^{61} +(-0.128491 + 0.128491i) q^{62} -4.59311i q^{63} -7.30568 q^{64} -4.74023 q^{66} +7.29829i q^{67} +(-4.89232 + 4.89232i) q^{68} +10.7391 q^{69} +(-1.67103 + 1.43611i) q^{70} +(-9.22988 - 9.22988i) q^{71} -14.4007 q^{72} -3.22747i q^{73} +4.17352i q^{74} +(-8.25969 - 11.2226i) q^{75} +(1.84449 - 1.84449i) q^{76} +(-1.13328 + 1.13328i) q^{77} -13.5845i q^{79} +(1.72108 + 2.00261i) q^{80} +0.578392 q^{81} +(-5.00872 + 5.00872i) q^{82} -8.56854 q^{83} +(-1.81198 + 1.81198i) q^{84} +(16.1664 + 1.22228i) q^{85} +(-5.74712 + 5.74712i) q^{86} +(0.575942 + 0.575942i) q^{87} +(3.55314 + 3.55314i) q^{88} +(-0.366660 - 0.366660i) q^{89} +(7.10435 + 8.26648i) q^{90} +(-2.60014 - 2.60014i) q^{92} +0.495216 q^{93} +8.02328i q^{94} +(-6.09502 - 0.460819i) q^{95} +(9.52707 + 9.52707i) q^{96} +7.51320i q^{97} +6.20885i q^{98} +(5.60626 + 5.60626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7}+O(q^{10}) $ 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7	$ 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7} - 8 q^{10} + 8 q^{11} - 24 q^{12} + 28 q^{15} + 4 q^{16} - 14 q^{17} + 4 q^{19} - 12 q^{20} + 4 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{24} + 18 q^{25} + 4 q^{27} - 36 q^{28} + 40 q^{30} + 2 q^{34} - 20 q^{35} + 8 q^{37} - 8 q^{38} - 16 q^{40} - 38 q^{41} + 16 q^{42} - 32 q^{43} - 36 q^{44} - 6 q^{45} + 4 q^{46} - 40 q^{47} + 28 q^{48} - 36 q^{49} + 42 q^{50} - 10 q^{53} + 36 q^{54} - 16 q^{55} + 8 q^{59} + 28 q^{60} + 32 q^{61} + 4 q^{62} + 20 q^{64} - 32 q^{66} - 50 q^{68} + 32 q^{69} - 12 q^{70} - 40 q^{71} - 8 q^{72} + 4 q^{75} - 16 q^{76} - 28 q^{77} + 112 q^{80} + 28 q^{81} - 34 q^{82} + 48 q^{83} + 8 q^{84} - 2 q^{85} + 60 q^{86} - 28 q^{87} - 32 q^{88} + 12 q^{89} + 46 q^{90} - 8 q^{92} - 64 q^{93} + 40 q^{95} + 56 q^{96} + 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7 - 8 * q^10 + 8 * q^11 - 24 * q^12 + 28 * q^15 + 4 * q^16 - 14 * q^17 + 4 * q^19 - 12 * q^20 + 4 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^24 + 18 * q^25 + 4 * q^27 - 36 * q^28 + 40 * q^30 + 2 * q^34 - 20 * q^35 + 8 * q^37 - 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 - 32 * q^43 - 36 * q^44 - 6 * q^45 + 4 * q^46 - 40 * q^47 + 28 * q^48 - 36 * q^49 + 42 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 8 * q^59 + 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 - 12 * q^70 - 40 * q^71 - 8 * q^72 + 4 * q^75 - 16 * q^76 - 28 * q^77 + 112 * q^80 + 28 * q^81 - 34 * q^82 + 48 * q^83 + 8 * q^84 - 2 * q^85 + 60 * q^86 - 28 * q^87 - 32 * q^88 + 12 * q^89 + 46 * q^90 - 8 * q^92 - 64 * q^93 + 40 * q^95 + 56 * q^96 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.02262i		−	0.723100i	−0.932353	−	0.361550i	$-0.882248\pi$
$2$		−	1.02262i		−	0.723100i	0.932353	−	0.361550i	$-0.117752\pi$
$3$	−1.97063	+	1.97063i	−1.13774	+	1.13774i	−0.148888	+	0.988854i	$0.547569\pi$
$3$	−1.97063	+	1.97063i	−1.13774	+	1.13774i	−0.988854	+	0.148888i	$0.952431\pi$
$4$	0.954253			0.477126
$5$	−1.45744	−	1.69584i	−0.651785	−	0.758404i
$5$	−1.45744	−	1.69584i	−0.651785	−	0.758404i
$6$	2.01520	+	2.01520i	0.822701	+	0.822701i
$7$	0.963574			0.364197			0.182098	−	0.983280i	$-0.441711\pi$
$7$	0.963574			0.364197			0.182098	+	0.983280i	$0.441711\pi$
$8$		−	3.02107i		−	1.06811i
$9$		−	4.76674i		−	1.58891i
$10$	−1.73420	+	1.49040i	−0.548402	+	0.471306i
$11$	−1.17612	+	1.17612i	−0.354613	+	0.354613i	−0.861823	−	0.507210i	$-0.830677\pi$
$11$	−1.17612	+	1.17612i	−0.354613	+	0.354613i	0.507210	+	0.861823i	$0.330677\pi$
$12$	−1.88048	+	1.88048i	−0.542847	+	0.542847i
$13$		0			0
$13$		0			0
$14$		−	0.985368i		−	0.263351i
$15$	6.21394	+	0.469810i	1.60443	+	0.121305i
$16$	−1.18090			−0.295224
$17$	−5.12686	+	5.12686i	−1.24345	+	1.24345i	−0.284884	+	0.958562i	$0.591955\pi$
$17$	−5.12686	+	5.12686i	−1.24345	+	1.24345i	−0.958562	+	0.284884i	$0.908045\pi$
$18$	−4.87456			−1.14894
$19$	1.93291	−	1.93291i	0.443441	−	0.443441i	−0.449726	−	0.893167i	$-0.648478\pi$
$19$	1.93291	−	1.93291i	0.443441	−	0.443441i	0.893167	+	0.449726i	$0.148478\pi$
$20$	−1.39076	−	1.61826i	−0.310984	−	0.361854i
$21$	−1.89884	+	1.89884i	−0.414362	+	0.414362i
$22$	1.20272	+	1.20272i	0.256421	+	0.256421i
$23$	−2.72480	−	2.72480i	−0.568159	−	0.568159i	0.363453	−	0.931612i	$-0.381598\pi$
$23$	−2.72480	−	2.72480i	−0.568159	−	0.568159i	−0.931612	+	0.363453i	$0.881598\pi$
$24$	5.95341	+	5.95341i	1.21523	+	1.21523i
$25$	−0.751762	+	4.94316i	−0.150352	+	0.988632i
$26$		0			0
$27$	3.48159	+	3.48159i	0.670033	+	0.670033i
$28$	0.919493			0.173768
$29$		−	0.292263i		−	0.0542719i	−0.999632	−	0.0271360i	$-0.991361\pi$
$29$		−	0.292263i		−	0.0542719i	0.999632	−	0.0271360i	$-0.00863870\pi$
$30$	0.480436	−	6.35448i	0.0877153	−	1.16016i
$31$	−0.125649	−	0.125649i	−0.0225673	−	0.0225673i	0.695733	−	0.718300i	$-0.255080\pi$
$31$	−0.125649	−	0.125649i	−0.0225673	−	0.0225673i	−0.718300	+	0.695733i	$0.755080\pi$
$32$		−	4.83454i		−	0.854634i
$33$		−	4.63538i		−	0.806917i
$34$	5.24282	+	5.24282i	0.899136	+	0.899136i
$35$	−1.40435	−	1.63407i	−0.237378	−	0.276208i
$36$		−	4.54868i		−	0.758113i
$37$	−4.08121			−0.670947			−0.335474	−	0.942050i	$-0.608896\pi$
$37$	−4.08121			−0.670947			−0.335474	+	0.942050i	$0.608896\pi$
$38$	−1.97663	−	1.97663i	−0.320652	−	0.320652i
$39$		0			0
$40$	−5.12326	+	4.40302i	−0.810059	+	0.696178i
$41$	−4.89794	−	4.89794i	−0.764930	−	0.764930i	0.212279	−	0.977209i	$-0.431911\pi$
$41$	−4.89794	−	4.89794i	−0.764930	−	0.764930i	−0.977209	+	0.212279i	$0.931911\pi$
$42$	1.94179	+	1.94179i	0.299625	+	0.299625i
$43$	−5.62000	−	5.62000i	−0.857043	−	0.857043i	0.133946	−	0.990989i	$-0.457235\pi$
$43$	−5.62000	−	5.62000i	−0.857043	−	0.857043i	−0.990989	+	0.133946i	$0.957235\pi$
$44$	−1.12232	+	1.12232i	−0.169195	+	0.169195i
$45$	−8.08364	+	6.94722i	−1.20504	+	1.03563i
$46$	−2.78642	+	2.78642i	−0.410836	+	0.410836i
$47$	−7.84582			−1.14443			−0.572215	−	0.820103i	$-0.693916\pi$
$47$	−7.84582			−1.14443			−0.572215	+	0.820103i	$0.693916\pi$
$48$	2.32710	−	2.32710i	0.335889	−	0.335889i
$49$	−6.07153			−0.867361
$50$	5.05497	+	0.768765i	0.714880	+	0.108720i
$51$		−	20.2063i		−	2.82944i
$52$		0			0
$53$	−1.99855	+	1.99855i	−0.274522	+	0.274522i	−0.830918	−	0.556395i	$-0.812184\pi$
$53$	−1.99855	+	1.99855i	−0.274522	+	0.274522i	0.556395	+	0.830918i	$0.312184\pi$
$54$	3.56034	−	3.56034i	0.484501	−	0.484501i
$55$	3.70863	+	0.280394i	0.500072	+	0.0378084i
$56$		−	2.91103i		−	0.389002i
$57$			7.61811i			1.00904i
$58$	−0.298873			−0.0392440
$59$	3.57185	+	3.57185i	0.465015	+	0.465015i	0.900295	−	0.435280i	$-0.143351\pi$
$59$	3.57185	+	3.57185i	0.465015	+	0.465015i	−0.435280	+	0.900295i	$0.643351\pi$
$60$	5.92967	+	0.448318i	0.765517	+	0.0578776i
$61$	2.08337			0.266749			0.133374	−	0.991066i	$-0.457419\pi$
$61$	2.08337			0.266749			0.133374	+	0.991066i	$0.457419\pi$
$62$	−0.128491	+	0.128491i	−0.0163184	+	0.0163184i
$63$		−	4.59311i		−	0.578677i
$64$	−7.30568			−0.913209
$65$		0			0
$66$	−4.74023			−0.583482
$67$			7.29829i			0.891628i	0.895126	+	0.445814i	$0.147086\pi$
$67$			7.29829i			0.891628i	−0.895126	+	0.445814i	$0.852914\pi$
$68$	−4.89232	+	4.89232i	−0.593281	+	0.593281i
$69$	10.7391			1.29284
$70$	−1.67103	+	1.43611i	−0.199726	+	0.171648i
$71$	−9.22988	−	9.22988i	−1.09538	−	1.09538i	−0.994943	−	0.100442i	$-0.967974\pi$
$71$	−9.22988	−	9.22988i	−1.09538	−	1.09538i	−0.100442	−	0.994943i	$-0.532026\pi$
$72$	−14.4007			−1.69714
$73$		−	3.22747i		−	0.377746i	−0.982001	−	0.188873i	$-0.939517\pi$
$73$		−	3.22747i		−	0.377746i	0.982001	−	0.188873i	$-0.0604835\pi$
$74$			4.17352i			0.485162i
$75$	−8.25969	−	11.2226i	−0.953747	−	1.29587i
$76$	1.84449	−	1.84449i	0.211577	−	0.211577i
$77$	−1.13328	+	1.13328i	−0.129149	+	0.129149i
$78$		0			0
$79$		−	13.5845i		−	1.52838i	−0.644992	−	0.764190i	$-0.723139\pi$
$79$		−	13.5845i		−	1.52838i	0.644992	−	0.764190i	$-0.276861\pi$
$80$	1.72108	+	2.00261i	0.192423	+	0.223899i
$81$	0.578392			0.0642658
$82$	−5.00872	+	5.00872i	−0.553121	+	0.553121i
$83$	−8.56854			−0.940519			−0.470260	−	0.882528i	$-0.655840\pi$
$83$	−8.56854			−0.940519			−0.470260	+	0.882528i	$0.655840\pi$
$84$	−1.81198	+	1.81198i	−0.197703	+	0.197703i
$85$	16.1664	+	1.22228i	1.75349	+	0.132575i
$86$	−5.74712	+	5.74712i	−0.619728	+	0.619728i
$87$	0.575942	+	0.575942i	0.0617474	+	0.0617474i
$88$	3.55314	+	3.55314i	0.378766	+	0.378766i
$89$	−0.366660	−	0.366660i	−0.0388659	−	0.0388659i	0.687407	−	0.726273i	$-0.258749\pi$
$89$	−0.366660	−	0.366660i	−0.0388659	−	0.0388659i	−0.726273	+	0.687407i	$0.758749\pi$
$90$	7.10435	+	8.26648i	0.748864	+	0.871363i
$91$		0			0
$92$	−2.60014	−	2.60014i	−0.271084	−	0.271084i
$93$	0.495216			0.0513516
$94$			8.02328i			0.827538i
$95$	−6.09502	−	0.460819i	−0.625336	−	0.0472791i
$96$	9.52707	+	9.52707i	0.972353	+	0.972353i
$97$			7.51320i			0.762850i	0.924400	+	0.381425i	$0.124567\pi$
$97$			7.51320i			0.762850i	−0.924400	+	0.381425i	$0.875433\pi$
$98$			6.20885i			0.627189i
$99$	5.60626	+	5.60626i	0.563450	+	0.563450i
$100$	−0.717371	+	4.71703i	−0.0717371	+	0.471703i
$101$			9.75358i			0.970518i	0.874371	+	0.485259i	$0.161275\pi$
$101$			9.75358i			0.970518i	−0.874371	+	0.485259i	$0.838725\pi$
$102$	−20.6633			−2.04597
$103$	2.52321	+	2.52321i	0.248619	+	0.248619i	0.820404	−	0.571784i	$-0.193749\pi$
$103$	2.52321	+	2.52321i	0.248619	+	0.248619i	−0.571784	+	0.820404i	$0.693749\pi$
$104$		0			0
$105$	5.98759	+	0.452697i	0.584329	+	0.0441787i
$106$	2.04375	+	2.04375i	0.198507	+	0.198507i
$107$	−0.314313	−	0.314313i	−0.0303858	−	0.0303858i	0.691751	−	0.722136i	$-0.256840\pi$
$107$	−0.314313	−	0.314313i	−0.0303858	−	0.0303858i	−0.722136	+	0.691751i	$0.756840\pi$
$108$	3.32232	+	3.32232i	0.319690	+	0.319690i
$109$	6.42134	−	6.42134i	0.615053	−	0.615053i	−0.329206	−	0.944258i	$-0.606781\pi$
$109$	6.42134	−	6.42134i	0.615053	−	0.615053i	0.944258	+	0.329206i	$0.106781\pi$
$110$	0.286736	−	3.79251i	0.0273392	−	0.361602i
$111$	8.04255	−	8.04255i	0.763365	−	0.763365i
$112$	−1.13788			−0.107520
$113$	1.36795	−	1.36795i	0.128686	−	0.128686i	−0.639830	−	0.768516i	$-0.720995\pi$
$113$	1.36795	−	1.36795i	0.128686	−	0.128686i	0.768516	+	0.639830i	$0.220995\pi$
$114$	7.79041			0.729639
$115$	−0.649609	+	8.59204i	−0.0605763	+	0.801212i
$116$		−	0.278893i		−	0.0258946i
$117$		0			0
$118$	3.65264	−	3.65264i	0.336253	−	0.336253i
$119$	−4.94011	+	4.94011i	−0.452859	+	0.452859i
$120$	1.41933	−	18.7727i	0.129567	−	1.71371i
$121$			8.23349i			0.748499i
$122$		−	2.13050i		−	0.192886i
$123$	19.3040			1.74059
$124$	−0.119901	−	0.119901i	−0.0107675	−	0.0107675i
$125$	9.47847	−	5.92947i	0.847780	−	0.530348i
$126$	−4.69699			−0.418442
$127$	1.53806	−	1.53806i	0.136480	−	0.136480i	−0.635566	−	0.772046i	$-0.719233\pi$
$127$	1.53806	−	1.53806i	0.136480	−	0.136480i	0.772046	+	0.635566i	$0.219233\pi$
$128$		−	2.19816i		−	0.194292i
$129$	22.1499			1.95019
$130$		0			0
$131$	−0.0622493			−0.00543874			−0.00271937	−	0.999996i	$-0.500866\pi$
$131$	−0.0622493			−0.00543874			−0.00271937	+	0.999996i	$0.500866\pi$
$132$		−	4.42333i		−	0.385001i
$133$	1.86251	−	1.86251i	0.161500	−	0.161500i
$134$	7.46336			0.644736
$135$	0.830034	−	10.9784i	0.0714380	−	0.944872i
$136$	15.4886	+	15.4886i	1.32814	+	1.32814i
$137$	−4.41747			−0.377410			−0.188705	−	0.982034i	$-0.560429\pi$
$137$	−4.41747			−0.377410			−0.188705	+	0.982034i	$0.560429\pi$
$138$		−	10.9820i		−	0.934850i
$139$			13.7486i			1.16614i	0.812422	+	0.583070i	$0.198149\pi$
$139$			13.7486i			1.16614i	−0.812422	+	0.583070i	$0.801851\pi$
$140$	−1.34010	−	1.55932i	−0.113259	−	0.131786i
$141$	15.4612	−	15.4612i	1.30207	−	1.30207i
$142$	−9.43864	+	9.43864i	−0.792073	+	0.792073i
$143$		0			0
$144$			5.62903i			0.469085i
$145$	−0.495632	+	0.425955i	−0.0411600	+	0.0353736i
$146$	−3.30046			−0.273148
$147$	11.9647	−	11.9647i	0.986833	−	0.986833i
$148$	−3.89451			−0.320127
$149$	3.06342	−	3.06342i	0.250965	−	0.250965i	−0.570401	−	0.821366i	$-0.693212\pi$
$149$	3.06342	−	3.06342i	0.250965	−	0.250965i	0.821366	+	0.570401i	$0.193212\pi$
$150$	−11.4764	+	8.44650i	−0.937044	+	0.689654i
$151$	4.74990	−	4.74990i	0.386542	−	0.386542i	−0.486910	−	0.873452i	$-0.661876\pi$
$151$	4.74990	−	4.74990i	0.386542	−	0.386542i	0.873452	+	0.486910i	$0.161876\pi$
$152$	−5.83947	−	5.83947i	−0.473644	−	0.473644i
$153$	24.4384	+	24.4384i	1.97573	+	1.97573i
$154$	1.15891	+	1.15891i	0.0933876	+	0.0933876i
$155$	−0.0299556	+	0.396208i	−0.00240610	+	0.0318242i
$156$		0			0
$157$	14.4488	+	14.4488i	1.15314	+	1.15314i	0.985920	+	0.167218i	$0.0534784\pi$
$157$	14.4488	+	14.4488i	1.15314	+	1.15314i	0.167218	+	0.985920i	$0.446522\pi$
$158$	−13.8918			−1.10517
$159$		−	7.87680i		−	0.624671i
$160$	−8.19861	+	7.04603i	−0.648157	+	0.557037i
$161$	−2.62554	−	2.62554i	−0.206922	−	0.206922i
$162$		−	0.591474i		−	0.0464706i
$163$		−	21.3852i		−	1.67502i	−0.546425	−	0.837508i	$-0.684011\pi$
$163$		−	21.3852i		−	1.67502i	0.546425	−	0.837508i	$-0.315989\pi$
$164$	−4.67387	−	4.67387i	−0.364968	−	0.364968i
$165$	−7.86088	+	6.75578i	−0.611969	+	0.525936i
$166$			8.76234i			0.680090i
$167$	−1.71444			−0.132667			−0.0663337	−	0.997797i	$-0.521130\pi$
$167$	−1.71444			−0.132667			−0.0663337	+	0.997797i	$0.521130\pi$
$168$	5.73655	+	5.73655i	0.442584	+	0.442584i
$169$		0			0
$170$	1.24992	−	16.5321i	0.0958646	−	1.26795i
$171$	−9.21371	−	9.21371i	−0.704590	−	0.704590i
$172$	−5.36291	−	5.36291i	−0.408918	−	0.408918i
$173$	10.7316	+	10.7316i	0.815908	+	0.815908i	0.985512	−	0.169604i	$-0.0542489\pi$
$173$	10.7316	+	10.7316i	0.815908	+	0.815908i	−0.169604	+	0.985512i	$0.554249\pi$
$174$	0.588968	−	0.588968i	0.0446496	−	0.0446496i
$175$	−0.724378	+	4.76310i	−0.0547578	+	0.360057i
$176$	1.38887	−	1.38887i	0.104690	−	0.104690i
$177$	−14.0776			−1.05814
$178$	−0.374954	+	0.374954i	−0.0281040	+	0.0281040i
$179$	2.75923			0.206234			0.103117	−	0.994669i	$-0.467118\pi$
$179$	2.75923			0.206234			0.103117	+	0.994669i	$0.467118\pi$
$180$	−7.71384	+	6.62941i	−0.574956	+	0.494127i
$181$			10.3568i			0.769818i	0.922954	+	0.384909i	$0.125767\pi$
$181$			10.3568i			0.769818i	−0.922954	+	0.384909i	$0.874233\pi$
$182$		0			0
$183$	−4.10555	+	4.10555i	−0.303491	+	0.303491i
$184$	−8.23180	+	8.23180i	−0.606856	+	0.606856i
$185$	5.94810	+	6.92109i	0.437313	+	0.508849i
$186$		−	0.506417i		−	0.0371323i
$187$		−	12.0596i		−	0.881885i
$188$	−7.48690			−0.546038
$189$	3.35477	+	3.35477i	0.244024	+	0.244024i
$190$	−0.471242	+	6.23287i	−0.0341875	+	0.452180i
$191$	18.5797			1.34438			0.672189	−	0.740380i	$-0.265354\pi$
$191$	18.5797			1.34438			0.672189	+	0.740380i	$0.265354\pi$
$192$	14.3968	−	14.3968i	1.03900	−	1.03900i
$193$		−	12.5715i		−	0.904917i	−0.891785	−	0.452459i	$-0.850547\pi$
$193$		−	12.5715i		−	0.904917i	0.891785	−	0.452459i	$-0.149453\pi$
$194$	7.68313			0.551617
$195$		0			0
$196$	−5.79377			−0.413841
$197$			14.2862i			1.01785i	0.860812	+	0.508924i	$0.169956\pi$
$197$			14.2862i			1.01785i	−0.860812	+	0.508924i	$0.830044\pi$
$198$	5.73306	−	5.73306i	0.407431	−	0.407431i
$199$	−14.7356			−1.04458			−0.522291	−	0.852768i	$-0.674922\pi$
$199$	−14.7356			−1.04458			−0.522291	+	0.852768i	$0.674922\pi$
$200$	14.9336	+	2.27113i	1.05597	+	0.160593i
$201$	−14.3822	−	14.3822i	−1.01444	−	1.01444i
$202$	9.97419			0.701781
$203$		−	0.281617i		−	0.0197656i
$204$		−	19.2819i		−	1.35000i
$205$	−1.16770	+	15.4446i	−0.0815558	+	1.07870i
$206$	2.58028	−	2.58028i	0.179777	−	0.179777i
$207$	−12.9884	+	12.9884i	−0.902756	+	0.902756i
$208$		0			0
$209$			4.54668i			0.314500i
$210$	0.462936	−	6.12301i	0.0319456	−	0.422528i
$211$	−8.53209			−0.587373			−0.293686	−	0.955902i	$-0.594882\pi$
$211$	−8.53209			−0.587373			−0.293686	+	0.955902i	$0.594882\pi$
$212$	−1.90712	+	1.90712i	−0.130982	+	0.130982i
$213$	36.3773			2.49253
$214$	−0.321422	+	0.321422i	−0.0219719	+	0.0219719i
$215$	−1.33985	+	17.7214i	−0.0913767	+	1.20859i
$216$	10.5181	−	10.5181i	0.715669	−	0.715669i
$217$	−0.121073	−	0.121073i	−0.00821894	−	0.00821894i
$218$	−6.56657	−	6.56657i	−0.444745	−	0.444745i
$219$	6.36013	+	6.36013i	0.429778	+	0.429778i
$220$	3.53897	+	0.267567i	0.238597	+	0.0180394i
$221$		0			0
$222$	−8.22445	−	8.22445i	−0.551989	−	0.551989i
$223$	7.06079			0.472826			0.236413	−	0.971653i	$-0.424028\pi$
$223$	7.06079			0.472826			0.236413	+	0.971653i	$0.424028\pi$
$224$		−	4.65843i		−	0.311255i
$225$	23.5628	+	3.58346i	1.57085	+	0.238897i
$226$	−1.39889	−	1.39889i	−0.0930527	−	0.0930527i
$227$		−	17.1755i		−	1.13998i	−0.821652	−	0.569989i	$-0.806948\pi$
$227$		−	17.1755i		−	1.13998i	0.821652	−	0.569989i	$-0.193052\pi$
$228$			7.26960i			0.481441i
$229$	−8.90647	−	8.90647i	−0.588556	−	0.588556i	0.348684	−	0.937240i	$-0.386629\pi$
$229$	−8.90647	−	8.90647i	−0.588556	−	0.588556i	−0.937240	+	0.348684i	$0.886629\pi$
$230$	8.78637	+	0.664302i	0.579356	+	0.0438028i
$231$		−	4.46654i		−	0.293876i
$232$	−0.882948			−0.0579684
$233$	−17.5822	−	17.5822i	−1.15185	−	1.15185i	−0.986182	−	0.165666i	$-0.947023\pi$
$233$	−17.5822	−	17.5822i	−1.15185	−	1.15185i	−0.165666	−	0.986182i	$-0.552977\pi$
$234$		0			0
$235$	11.4348	+	13.3053i	0.745923	+	0.867940i
$236$	3.40845	+	3.40845i	0.221871	+	0.221871i
$237$	26.7700	+	26.7700i	1.73890	+	1.73890i
$238$	5.05184	+	5.05184i	0.327462	+	0.327462i
$239$	−2.23488	+	2.23488i	−0.144562	+	0.144562i	−0.775684	−	0.631122i	$-0.782595\pi$
$239$	−2.23488	+	2.23488i	−0.144562	+	0.144562i	0.631122	+	0.775684i	$0.282595\pi$
$240$	−7.33801	−	0.554797i	−0.473666	−	0.0358120i
$241$	−12.7412	+	12.7412i	−0.820734	+	0.820734i	−0.986213	−	0.165479i	$-0.947083\pi$
$241$	−12.7412	+	12.7412i	−0.820734	+	0.820734i	0.165479	+	0.986213i	$0.447083\pi$
$242$	8.41971			0.541239
$243$	−11.5846	+	11.5846i	−0.743150	+	0.743150i
$244$	1.98807			0.127273
$245$	8.84886	+	10.2963i	0.565333	+	0.657810i
$246$		−	19.7406i		−	1.25862i
$247$		0			0
$248$	−0.379596	+	0.379596i	−0.0241044	+	0.0241044i
$249$	16.8854	−	16.8854i	1.07007	−	1.07007i
$250$	−6.06358	−	9.69285i	−0.383495	−	0.613030i
$251$		−	13.9729i		−	0.881960i	−0.897517	−	0.440980i	$-0.854631\pi$
$251$		−	13.9729i		−	0.881960i	0.897517	−	0.440980i	$-0.145369\pi$
$252$		−	4.38299i		−	0.276102i
$253$	6.40937			0.402954
$254$	−1.57284	−	1.57284i	−0.0986889	−	0.0986889i
$255$	−34.2666	+	29.4493i	−2.14586	+	1.84419i
$256$	−16.8592			−1.05370
$257$	16.3892	−	16.3892i	1.02233	−	1.02233i	0.0225869	−	0.999745i	$-0.492810\pi$
$257$	16.3892	−	16.3892i	1.02233	−	1.02233i	0.999745	−	0.0225869i	$-0.00719024\pi$
$258$		−	22.6508i		−	1.41018i
$259$	−3.93255			−0.244357
$260$		0			0
$261$	−1.39314			−0.0862334
$262$			0.0636572i			0.00393276i
$263$	0.919982	−	0.919982i	0.0567285	−	0.0567285i	−0.678173	−	0.734902i	$-0.737228\pi$
$263$	0.919982	−	0.919982i	0.0567285	−	0.0567285i	0.734902	+	0.678173i	$0.237228\pi$
$264$	−14.0038			−0.861876
$265$	6.30199	+	0.476468i	0.387128	+	0.0292692i
$266$	−1.90463	−	1.90463i	−0.116780	−	0.116780i
$267$	1.44510			0.0884388
$268$			6.96441i			0.425419i
$269$			7.93774i			0.483973i	0.970280	+	0.241986i	$0.0777989\pi$
$269$			7.93774i			0.483973i	−0.970280	+	0.241986i	$0.922201\pi$
$270$	−11.2267	−	0.848808i	−0.683237	−	0.0516568i
$271$	0.633254	−	0.633254i	0.0384674	−	0.0384674i	−0.687611	−	0.726079i	$-0.741341\pi$
$271$	0.633254	−	0.633254i	0.0384674	−	0.0384674i	0.726079	+	0.687611i	$0.241341\pi$
$272$	6.05429	−	6.05429i	0.367095	−	0.367095i
$273$		0			0
$274$			4.51738i			0.272905i
$275$	−4.92959	−	6.69791i	−0.297265	−	0.403899i
$276$	10.2478			0.616847
$277$	6.75631	−	6.75631i	0.405948	−	0.405948i	−0.474375	−	0.880323i	$-0.657326\pi$
$277$	6.75631	−	6.75631i	0.405948	−	0.405948i	0.880323	+	0.474375i	$0.157326\pi$
$278$	14.0596			0.843236
$279$	−0.598939	+	0.598939i	−0.0358575	+	0.0358575i
$280$	−4.93664	+	4.24263i	−0.295021	+	0.253546i
$281$	5.58408	−	5.58408i	0.333118	−	0.333118i	−0.520651	−	0.853769i	$-0.674311\pi$
$281$	5.58408	−	5.58408i	0.333118	−	0.333118i	0.853769	+	0.520651i	$0.174311\pi$
$282$	−15.8109	−	15.8109i	−0.941525	−	0.941525i
$283$	−14.9230	−	14.9230i	−0.887078	−	0.887078i	0.107163	−	0.994241i	$-0.465823\pi$
$283$	−14.9230	−	14.9230i	−0.887078	−	0.887078i	−0.994241	+	0.107163i	$0.965823\pi$
$284$	−8.80764	−	8.80764i	−0.522637	−	0.522637i
$285$	12.9191	−	11.1029i	0.765262	−	0.657679i
$286$		0			0
$287$	−4.71953	−	4.71953i	−0.278585	−	0.278585i
$288$	−23.0450			−1.35794
$289$		−	35.5694i		−	2.09232i
$290$	0.435589	+	0.506842i	0.0255787	+	0.0297628i
$291$	−14.8057	−	14.8057i	−0.867927	−	0.867927i
$292$		−	3.07982i		−	0.180233i
$293$		−	4.02159i		−	0.234944i	−0.993076	−	0.117472i	$-0.962521\pi$
$293$		−	4.02159i		−	0.234944i	0.993076	−	0.117472i	$-0.0374790\pi$
$294$	−12.2353	−	12.2353i	−0.713579	−	0.713579i
$295$	0.851553	−	11.2630i	0.0495793	−	0.655760i
$296$			12.3296i			0.716645i
$297$	−8.18953			−0.475205
$298$	−3.13271	−	3.13271i	−0.181473	−	0.181473i
$299$		0			0
$300$	−7.88183	−	10.7092i	−0.455058	−	0.618294i
$301$	−5.41529	−	5.41529i	−0.312132	−	0.312132i
$302$	−4.85734	−	4.85734i	−0.279508	−	0.279508i
$303$	−19.2207	−	19.2207i	−1.10420	−	1.10420i
$304$	−2.28257	+	2.28257i	−0.130914	+	0.130914i
$305$	−3.03638	−	3.53307i	−0.173863	−	0.202303i
$306$	24.9912	−	24.9912i	1.42865	−	1.42865i
$307$	24.2191			1.38226			0.691128	−	0.722732i	$-0.257114\pi$
$307$	24.2191			1.38226			0.691128	+	0.722732i	$0.257114\pi$
$308$	−1.08143	+	1.08143i	−0.0616204	+	0.0616204i
$309$	−9.94462			−0.565730
$310$	0.405169	+	0.0306332i	0.0230121	+	0.00173985i
$311$		−	7.87243i		−	0.446405i	−0.974772	−	0.223202i	$-0.928349\pi$
$311$		−	7.87243i		−	0.446405i	0.974772	−	0.223202i	$-0.0716511\pi$
$312$		0			0
$313$	3.39121	−	3.39121i	0.191683	−	0.191683i	−0.604740	−	0.796423i	$-0.706723\pi$
$313$	3.39121	−	3.39121i	0.191683	−	0.191683i	0.796423	+	0.604740i	$0.206723\pi$
$314$	14.7756	−	14.7756i	0.833834	−	0.833834i
$315$	−7.78919	+	6.69416i	−0.438871	+	0.377173i
$316$		−	12.9631i		−	0.729230i
$317$			22.9255i			1.28762i	0.765184	+	0.643812i	$0.222648\pi$
$317$			22.9255i			1.28762i	−0.765184	+	0.643812i	$0.777352\pi$
$318$	−8.05496			−0.451700
$319$	0.343736	+	0.343736i	0.0192455	+	0.0192455i
$320$	10.6476	+	12.3893i	0.595216	+	0.692581i
$321$	1.23879			0.0691423
$322$	−2.68493	+	2.68493i	−0.149625	+	0.149625i
$323$			19.8196i			1.10279i
$324$	0.551932			0.0306629
$325$		0			0
$326$	−21.8689			−1.21120
$327$			25.3081i			1.39954i
$328$	−14.7970	+	14.7970i	−0.817029	+	0.817029i
$329$	−7.56003			−0.416798
$330$	6.90858	+	8.03868i	0.380305	+	0.442515i
$331$	23.7270	+	23.7270i	1.30416	+	1.30416i	0.925563	+	0.378594i	$0.123592\pi$
$331$	23.7270	+	23.7270i	1.30416	+	1.30416i	0.378594	+	0.925563i	$0.376408\pi$
$332$	−8.17655			−0.448747
$333$			19.4541i			1.06608i
$334$			1.75322i			0.0959318i
$335$	12.3767	−	10.6368i	0.676214	−	0.581150i
$336$	2.24234	−	2.24234i	0.122330	−	0.122330i
$337$	−14.5544	+	14.5544i	−0.792826	+	0.792826i	−0.981953	−	0.189126i	$-0.939434\pi$
$337$	−14.5544	+	14.5544i	−0.792826	+	0.792826i	0.189126	+	0.981953i	$0.439434\pi$
$338$		0			0
$339$			5.39143i			0.292822i
$340$	15.4268	+	1.16636i	0.836638	+	0.0632548i
$341$	0.295557			0.0160053
$342$	−9.42210	+	9.42210i	−0.509489	+	0.509489i
$343$	−12.5954			−0.680087
$344$	−16.9784	+	16.9784i	−0.915416	+	0.915416i
$345$	−15.6516	−	18.2118i	−0.842652	−	0.980492i
$346$	10.9743	−	10.9743i	0.589983	−	0.589983i
$347$	16.1312	+	16.1312i	0.865967	+	0.865967i	0.992023	−	0.126056i	$-0.0402319\pi$
$347$	16.1312	+	16.1312i	0.865967	+	0.865967i	−0.126056	+	0.992023i	$0.540232\pi$
$348$	0.549594	+	0.549594i	0.0294613	+	0.0294613i
$349$	−7.34369	−	7.34369i	−0.393099	−	0.393099i	0.482692	−	0.875790i	$-0.339659\pi$
$349$	−7.34369	−	7.34369i	−0.393099	−	0.393099i	−0.875790	+	0.482692i	$0.839659\pi$
$350$	4.87083	+	0.740762i	0.260357	+	0.0395954i
$351$		0			0
$352$	5.68599	+	5.68599i	0.303064	+	0.303064i
$353$	4.30033			0.228884			0.114442	−	0.993430i	$-0.463492\pi$
$353$	4.30033			0.228884			0.114442	+	0.993430i	$0.463492\pi$
$354$			14.3960i			0.765138i
$355$	−2.20046	+	29.1044i	−0.116788	+	1.54470i
$356$	−0.349887	−	0.349887i	−0.0185440	−	0.0185440i
$357$		−	19.4702i		−	1.03047i
$358$		−	2.82163i		−	0.149128i
$359$	−10.4273	−	10.4273i	−0.550333	−	0.550333i	0.376204	−	0.926537i	$-0.377229\pi$
$359$	−10.4273	−	10.4273i	−0.550333	−	0.550333i	−0.926537	+	0.376204i	$0.877229\pi$
$360$	20.9881	+	24.4213i	1.10617	+	1.28711i
$361$			11.5277i			0.606720i
$362$	10.5911			0.556656
$363$	−16.2251	−	16.2251i	−0.851599	−	0.851599i
$364$		0			0
$365$	−5.47327	+	4.70382i	−0.286484	+	0.246209i
$366$	4.19841	+	4.19841i	0.219454	+	0.219454i
$367$	8.07749	+	8.07749i	0.421641	+	0.421641i	0.885769	−	0.464127i	$-0.153632\pi$
$367$	8.07749	+	8.07749i	0.421641	+	0.421641i	−0.464127	+	0.885769i	$0.653632\pi$
$368$	3.21770	+	3.21770i	0.167734	+	0.167734i
$369$	−23.3472	+	23.3472i	−1.21541	+	1.21541i
$370$	7.07763	−	6.08264i	0.367949	−	0.316221i
$371$	−1.92575	+	1.92575i	−0.0999801	+	0.0999801i
$372$	0.472562			0.0245012
$373$	19.9100	−	19.9100i	1.03090	−	1.03090i	0.0313915	−	0.999507i	$-0.490006\pi$
$373$	19.9100	−	19.9100i	1.03090	−	1.03090i	0.999507	−	0.0313915i	$-0.00999387\pi$
$374$	−12.3324			−0.637691
$375$	−6.99375	+	30.3633i	−0.361156	+	1.56795i
$376$			23.7028i			1.22238i
$377$		0			0
$378$	3.43065	−	3.43065i	0.176453	−	0.176453i
$379$	−11.9727	+	11.9727i	−0.614998	+	0.614998i	−0.944244	−	0.329246i	$-0.893205\pi$
$379$	−11.9727	+	11.9727i	−0.614998	+	0.614998i	0.329246	+	0.944244i	$0.393205\pi$
$380$	−5.81619	−	0.439738i	−0.298364	−	0.0225581i
$381$			6.06187i			0.310559i
$382$		−	18.9999i		−	0.972119i
$383$	6.60394			0.337446			0.168723	−	0.985664i	$-0.446036\pi$
$383$	6.60394			0.337446			0.168723	+	0.985664i	$0.446036\pi$
$384$	4.33176	+	4.33176i	0.221054	+	0.221054i
$385$	3.57354	+	0.270181i	0.182124	+	0.0137697i
$386$	−12.8559			−0.654346
$387$	−26.7891	+	26.7891i	−1.36177	+	1.36177i
$388$			7.16950i			0.363976i
$389$	33.6949			1.70840			0.854199	−	0.519946i	$-0.174048\pi$
$389$	33.6949			1.70840			0.854199	+	0.519946i	$0.174048\pi$
$390$		0			0
$391$	27.9393			1.41295
$392$			18.3425i			0.926437i
$393$	0.122670	−	0.122670i	0.00618789	−	0.00618789i
$394$	14.6093			0.736005
$395$	−23.0372	+	19.7986i	−1.15913	+	0.996175i
$396$	5.34979	+	5.34979i	0.268837	+	0.268837i
$397$	5.82089			0.292142			0.146071	−	0.989274i	$-0.453337\pi$
$397$	5.82089			0.292142			0.146071	+	0.989274i	$0.453337\pi$
$398$			15.0689i			0.755337i
$399$			7.34061i			0.367490i
$400$	0.887752	−	5.83736i	0.0443876	−	0.291868i
$401$	−0.186676	+	0.186676i	−0.00932213	+	0.00932213i	−0.711752	−	0.702430i	$-0.752098\pi$
$401$	−0.186676	+	0.186676i	−0.00932213	+	0.00932213i	0.702430	+	0.711752i	$0.252098\pi$
$402$	−14.7075	+	14.7075i	−0.733544	+	0.733544i
$403$		0			0
$404$			9.30738i			0.463060i
$405$	−0.842969	−	0.980861i	−0.0418875	−	0.0487394i
$406$	−0.287987			−0.0142925
$407$	4.79999	−	4.79999i	0.237927	−	0.237927i
$408$	−61.0446			−3.02216
$409$	−26.2788	+	26.2788i	−1.29940	+	1.29940i	−0.370619	+	0.928785i	$0.620855\pi$
$409$	−26.2788	+	26.2788i	−1.29940	+	1.29940i	−0.928785	+	0.370619i	$0.879145\pi$
$410$	15.7939	+	1.19411i	0.780005	+	0.0589730i
$411$	8.70518	−	8.70518i	0.429395	−	0.429395i
$412$	2.40778	+	2.40778i	0.118623	+	0.118623i
$413$	3.44174	+	3.44174i	0.169357	+	0.169357i
$414$	13.2822	+	13.2822i	0.652783	+	0.652783i
$415$	12.4881	+	14.5309i	0.613016	+	0.713293i
$416$		0			0
$417$	−27.0934	−	27.0934i	−1.32677	−	1.32677i
$418$	4.64951			0.227415
$419$			33.9159i			1.65690i	0.560062	+	0.828451i	$0.310777\pi$
$419$			33.9159i			1.65690i	−0.560062	+	0.828451i	$0.689223\pi$
$420$	5.71367	+	0.431987i	0.278799	+	0.0210788i
$421$	−21.5599	−	21.5599i	−1.05076	−	1.05076i	−0.998641	−	0.0521230i	$-0.983401\pi$
$421$	−21.5599	−	21.5599i	−1.05076	−	1.05076i	−0.0521230	−	0.998641i	$-0.516599\pi$
$422$			8.72506i			0.424729i
$423$			37.3990i			1.81840i
$424$	6.03777	+	6.03777i	0.293220	+	0.293220i
$425$	−21.4887	−	29.1971i	−1.04236	−	1.41627i
$426$		−	37.2001i		−	1.80235i
$427$	2.00748			0.0971490
$428$	−0.299934	−	0.299934i	−0.0144979	−	0.0144979i
$429$		0			0
$430$	18.1223	+	1.37015i	0.873933	+	0.0660745i
$431$	3.25153	+	3.25153i	0.156621	+	0.156621i	0.781067	−	0.624447i	$-0.214676\pi$
$431$	3.25153	+	3.25153i	0.156621	+	0.156621i	−0.624447	+	0.781067i	$0.714676\pi$
$432$	−4.11140	−	4.11140i	−0.197810	−	0.197810i
$433$	2.83031	+	2.83031i	0.136016	+	0.136016i	0.771837	−	0.635821i	$-0.219338\pi$
$433$	2.83031	+	2.83031i	0.136016	+	0.136016i	−0.635821	+	0.771837i	$0.719338\pi$
$434$	−0.123811	+	0.123811i	−0.00594311	+	0.00594311i
$435$	0.137308	−	1.81610i	0.00658343	−	0.0870755i
$436$	6.12758	−	6.12758i	0.293458	−	0.293458i
$437$	−10.5336			−0.503890
$438$	6.50398	−	6.50398i	0.310772	−	0.310772i
$439$	−22.7237			−1.08454			−0.542271	−	0.840203i	$-0.682436\pi$
$439$	−22.7237			−1.08454			−0.542271	+	0.840203i	$0.682436\pi$
$440$	0.847092	−	11.2040i	0.0403835	−	0.534132i
$441$			28.9414i			1.37816i
$442$		0			0
$443$	1.84874	−	1.84874i	0.0878361	−	0.0878361i	−0.661824	−	0.749660i	$-0.730217\pi$
$443$	1.84874	−	1.84874i	0.0878361	−	0.0878361i	0.749660	+	0.661824i	$0.230217\pi$
$444$	7.67462	−	7.67462i	0.364222	−	0.364222i
$445$	−0.0874142	+	1.15618i	−0.00414383	+	0.0548083i
$446$		−	7.22049i		−	0.341900i
$447$			12.0737i			0.571067i
$448$	−7.03956			−0.332588
$449$	−22.7499	−	22.7499i	−1.07364	−	1.07364i	−0.997064	−	0.0765713i	$-0.975603\pi$
$449$	−22.7499	−	22.7499i	−1.07364	−	1.07364i	−0.0765713	−	0.997064i	$-0.524397\pi$
$450$	3.66451	−	24.0957i	0.172746	−	1.13588i
$451$	11.5211			0.542509
$452$	1.30537	−	1.30537i	0.0613994	−	0.0613994i
$453$			18.7206i			0.879569i
$454$	−17.5640			−0.824318
$455$		0			0
$456$	23.0149			1.07777
$457$		−	28.3674i		−	1.32697i	−0.748189	−	0.663486i	$-0.769076\pi$
$457$		−	28.3674i		−	1.32697i	0.748189	−	0.663486i	$-0.230924\pi$
$458$	−9.10792	+	9.10792i	−0.425585	+	0.425585i
$459$	−35.6993			−1.66630
$460$	−0.619891	+	8.19898i	−0.0289026	+	0.382279i
$461$	8.13851	+	8.13851i	0.379048	+	0.379048i	0.870759	−	0.491710i	$-0.163628\pi$
$461$	8.13851	+	8.13851i	0.379048	+	0.379048i	−0.491710	+	0.870759i	$0.663628\pi$
$462$	−4.56756			−0.212502
$463$		−	29.9456i		−	1.39169i	−0.718192	−	0.695845i	$-0.755030\pi$
$463$		−	29.9456i		−	1.39169i	0.718192	−	0.695845i	$-0.244970\pi$
$464$			0.345132i			0.0160224i
$465$	−0.721746	−	0.839809i	−0.0334702	−	0.0389452i
$466$	−17.9799	+	17.9799i	−0.832901	+	0.832901i
$467$	16.1332	−	16.1332i	0.746557	−	0.746557i	−0.227274	−	0.973831i	$-0.572981\pi$
$467$	16.1332	−	16.1332i	0.746557	−	0.746557i	0.973831	+	0.227274i	$0.0729812\pi$
$468$		0			0
$469$			7.03244i			0.324728i
$470$	13.6062	−	11.6934i	0.627608	−	0.539377i
$471$	−56.9463			−2.62395
$472$	10.7908	−	10.7908i	0.496688	−	0.496688i
$473$	13.2196			0.607837
$474$	27.3755	−	27.3755i	1.25740	−	1.25740i
$475$	8.10162	+	11.0078i	0.371728	+	0.505073i
$476$	−4.71411	+	4.71411i	−0.216071	+	0.216071i
$477$	9.52658	+	9.52658i	0.436192	+	0.436192i
$478$	2.28542	+	2.28542i	0.104533	+	0.104533i
$479$	−27.4551	−	27.4551i	−1.25445	−	1.25445i	−0.953703	−	0.300751i	$-0.902763\pi$
$479$	−27.4551	−	27.4551i	−1.25445	−	1.25445i	−0.300751	−	0.953703i	$-0.597237\pi$
$480$	2.27132	−	30.0415i	0.103671	−	1.37120i
$481$		0			0
$482$	13.0294	+	13.0294i	0.593473	+	0.593473i
$483$	10.3479			0.470847
$484$			7.85683i			0.357129i
$485$	12.7412	−	10.9500i	0.578548	−	0.497214i
$486$	11.8466	+	11.8466i	0.537372	+	0.537372i
$487$			28.9437i			1.31156i	0.754951	+	0.655782i	$0.227661\pi$
$487$			28.9437i			1.31156i	−0.754951	+	0.655782i	$0.772339\pi$
$488$		−	6.29402i		−	0.284917i
$489$	42.1422	+	42.1422i	1.90574	+	1.90574i
$490$	10.5292	−	9.04900i	0.475662	−	0.408792i
$491$			7.27465i			0.328300i	0.986435	+	0.164150i	$0.0524882\pi$
$491$			7.27465i			0.328300i	−0.986435	+	0.164150i	$0.947512\pi$
$492$	18.4209			0.830480
$493$	1.49839	+	1.49839i	0.0674842	+	0.0674842i
$494$		0			0
$495$	1.33657	−	17.6781i	0.0600743	−	0.794571i
$496$	0.148379	+	0.148379i	0.00666241	+	0.00666241i
$497$	−8.89367	−	8.89367i	−0.398936	−	0.398936i
$498$	−17.2673	−	17.2673i	−0.773766	−	0.773766i
$499$	4.24201	−	4.24201i	0.189899	−	0.189899i	−0.605754	−	0.795652i	$-0.707128\pi$
$499$	4.24201	−	4.24201i	0.189899	−	0.189899i	0.795652	+	0.605754i	$0.207128\pi$
$500$	9.04486	−	5.65822i	0.404498	−	0.253043i
$501$	3.37852	−	3.37852i	0.150941	−	0.150941i
$502$	−14.2889			−0.637745
$503$	2.56713	−	2.56713i	0.114463	−	0.114463i	−0.647555	−	0.762018i	$-0.724209\pi$
$503$	2.56713	−	2.56713i	0.114463	−	0.114463i	0.762018	+	0.647555i	$0.224209\pi$
$504$	−13.8761			−0.618091
$505$	16.5405	−	14.2152i	0.736044	−	0.632569i
$506$		−	6.55433i		−	0.291376i
$507$		0			0
$508$	1.46769	−	1.46769i	0.0651184	−	0.0651184i
$509$	16.4739	−	16.4739i	0.730191	−	0.730191i	−0.240466	−	0.970658i	$-0.577300\pi$
$509$	16.4739	−	16.4739i	0.730191	−	0.730191i	0.970658	+	0.240466i	$0.0773003\pi$
$510$	30.1154	+	35.0417i	1.33353	+	1.55167i
$511$		−	3.10990i		−	0.137574i
$512$			12.8442i			0.567640i
$513$	13.4592			0.594240
$514$	−16.7599	−	16.7599i	−0.739248	−	0.739248i
$515$	0.601550	−	7.95639i	0.0265075	−	0.350600i
$516$	21.1366			0.930486
$517$	9.22762	−	9.22762i	0.405830	−	0.405830i
$518$			4.02150i			0.176694i
$519$	−42.2960			−1.85659
$520$		0			0
$521$	−13.0530			−0.571862			−0.285931	−	0.958250i	$-0.592303\pi$
$521$	−13.0530			−0.571862			−0.285931	+	0.958250i	$0.592303\pi$
$522$			1.42465i			0.0623554i
$523$	12.0352	−	12.0352i	0.526264	−	0.526264i	−0.393192	−	0.919456i	$-0.628629\pi$
$523$	12.0352	−	12.0352i	0.526264	−	0.526264i	0.919456	+	0.393192i	$0.128629\pi$
$524$	−0.0594015			−0.00259497
$525$	−7.95882	−	10.8138i	−0.347351	−	0.471952i
$526$	−0.940790	−	0.940790i	−0.0410204	−	0.0410204i
$527$	1.28837			0.0561225
$528$			5.47391i			0.238221i
$529$		−	8.15098i		−	0.354390i
$530$	0.487244	−	6.44453i	0.0211645	−	0.279932i
$531$	17.0261	−	17.0261i	0.738870	−	0.738870i
$532$	1.77730	−	1.77730i	0.0770558	−	0.0770558i
$533$		0			0
$534$		−	1.47779i		−	0.0639501i
$535$	−0.0749342	+	0.991116i	−0.00323969	+	0.0428497i
$536$	22.0487			0.952357
$537$	−5.43741	+	5.43741i	−0.234641	+	0.234641i
$538$	8.11728			0.349961
$539$	7.14084	−	7.14084i	0.307578	−	0.307578i
$540$	0.792062	−	10.4762i	0.0340849	−	0.450824i
$541$	−10.9728	+	10.9728i	−0.471756	+	0.471756i	−0.902483	−	0.430727i	$-0.858257\pi$
$541$	−10.9728	+	10.9728i	−0.471756	+	0.471756i	0.430727	+	0.902483i	$0.358257\pi$
$542$	−0.647577	−	0.647577i	−0.0278158	−	0.0278158i
$543$	−20.4095	−	20.4095i	−0.875855	−	0.875855i
$544$	24.7860	+	24.7860i	1.06269	+	1.06269i
$545$	−20.2483	−	1.53089i	−0.867340	−	0.0655761i
$546$		0			0
$547$	−20.4450	−	20.4450i	−0.874167	−	0.874167i	0.118756	−	0.992923i	$-0.462109\pi$
$547$	−20.4450	−	20.4450i	−0.874167	−	0.874167i	−0.992923	+	0.118756i	$0.962109\pi$
$548$	−4.21538			−0.180072
$549$		−	9.93091i		−	0.423841i
$550$	−6.84940	+	5.04108i	−0.292059	+	0.214952i
$551$	−0.564920	−	0.564920i	−0.0240664	−	0.0240664i
$552$		−	32.4436i		−	1.38089i
$553$		−	13.0897i		−	0.556631i
$554$	−6.90913	−	6.90913i	−0.293541	−	0.293541i
$555$	−25.3604	−	1.91740i	−1.07649	−	0.0813889i
$556$			13.1196i			0.556397i
$557$	−13.5803			−0.575415			−0.287708	−	0.957718i	$-0.592893\pi$
$557$	−13.5803			−0.575415			−0.287708	+	0.957718i	$0.592893\pi$
$558$	0.612485	+	0.612485i	0.0259286	+	0.0259286i
$559$		0			0
$560$	1.65839	+	1.92967i	0.0700797	+	0.0815432i
$561$	23.7650	+	23.7650i	1.00336	+	1.00336i
$562$	−5.71037	−	5.71037i	−0.240878	−	0.240878i
$563$	−3.42976	−	3.42976i	−0.144547	−	0.144547i	0.631130	−	0.775677i	$-0.282591\pi$
$563$	−3.42976	−	3.42976i	−0.144547	−	0.144547i	−0.775677	+	0.631130i	$0.782591\pi$
$564$	14.7539	−	14.7539i	0.621251	−	0.621251i
$565$	−4.31352	−	0.326128i	−0.181471	−	0.0137203i
$566$	−15.2605	+	15.2605i	−0.641446	+	0.641446i
$567$	0.557323			0.0234054
$568$	−27.8841	+	27.8841i	−1.16999	+	1.16999i
$569$	−0.248793			−0.0104299			−0.00521497	−	0.999986i	$-0.501660\pi$
$569$	−0.248793			−0.0104299			−0.00521497	+	0.999986i	$0.501660\pi$
$570$	−11.3540	−	13.2113i	−0.475568	−	0.553361i
$571$		−	7.72842i		−	0.323424i	−0.986838	−	0.161712i	$-0.948298\pi$
$571$		−	7.72842i		−	0.323424i	0.986838	−	0.161712i	$-0.0517016\pi$
$572$		0			0
$573$	−36.6136	+	36.6136i	−1.52955	+	1.52955i
$574$	−4.82627	+	4.82627i	−0.201445	+	0.201445i
$575$	15.5175	−	11.4207i	0.647125	−	0.476276i
$576$			34.8243i			1.45101i
$577$		−	12.1339i		−	0.505141i	−0.967578	−	0.252570i	$-0.918724\pi$
$577$		−	12.1339i		−	0.505141i	0.967578	−	0.252570i	$-0.0812760\pi$
$578$	−36.3739			−1.51295
$579$	24.7738	+	24.7738i	1.02956	+	1.02956i
$580$	−0.472958	+	0.406469i	−0.0196385	+	0.0168777i
$581$	−8.25642			−0.342534
$582$	−15.1406	+	15.1406i	−0.627598	+	0.627598i
$583$		−	4.70107i		−	0.194698i
$584$	−9.75040			−0.403475
$585$		0			0
$586$	−4.11255			−0.169888
$587$		−	36.5294i		−	1.50773i	−0.657030	−	0.753865i	$-0.728187\pi$
$587$		−	36.5294i		−	1.50773i	0.657030	−	0.753865i	$-0.271813\pi$
$588$	11.4174	−	11.4174i	0.470844	−	0.470844i
$589$	−0.485739			−0.0200145
$590$	−11.5178	−	0.870813i	−0.474180	−	0.0358508i
$591$	−28.1527	−	28.1527i	−1.15805	−	1.15805i
$592$	4.81949			0.198080
$593$			16.6936i			0.685525i	0.939422	+	0.342762i	$0.111363\pi$
$593$			16.6936i			0.685525i	−0.939422	+	0.342762i	$0.888637\pi$
$594$			8.37476i			0.343621i
$595$	15.5775	+	1.17775i	0.638617	+	0.0482832i
$596$	2.92328	−	2.92328i	0.119742	−	0.119742i
$597$	29.0384	−	29.0384i	1.18846	−	1.18846i
$598$		0			0
$599$		−	13.2549i		−	0.541579i	−0.962639	−	0.270789i	$-0.912715\pi$
$599$		−	13.2549i		−	0.541579i	0.962639	−	0.270789i	$-0.0872847\pi$
$600$	−33.9042	+	24.9531i	−1.38413	+	1.01871i
$601$	1.09321			0.0445930			0.0222965	−	0.999751i	$-0.492902\pi$
$601$	1.09321			0.0445930			0.0222965	+	0.999751i	$0.492902\pi$
$602$	−5.53777	+	5.53777i	−0.225703	+	0.225703i
$603$	34.7891			1.41672
$604$	4.53261	−	4.53261i	0.184429	−	0.184429i
$605$	13.9627	−	11.9998i	0.567664	−	0.487860i
$606$	−19.6554	+	19.6554i	−0.798446	+	0.798446i
$607$	−29.6013	−	29.6013i	−1.20148	−	1.20148i	−0.973717	−	0.227761i	$-0.926860\pi$
$607$	−29.6013	−	29.6013i	−1.20148	−	1.20148i	−0.227761	−	0.973717i	$-0.573140\pi$
$608$	−9.34475	−	9.34475i	−0.378980	−	0.378980i
$609$	0.554962	+	0.554962i	0.0224882	+	0.0224882i
$610$	−3.61298	+	3.10506i	−0.146285	+	0.125720i
$611$		0			0
$612$	23.3204	+	23.3204i	0.942673	+	0.942673i
$613$	27.9096			1.12726			0.563630	−	0.826028i	$-0.309404\pi$
$613$	27.9096			1.12726			0.563630	+	0.826028i	$0.309404\pi$
$614$		−	24.7669i		−	0.999510i
$615$	−28.1344	−	32.7366i	−1.13449	−	1.32007i
$616$	3.42371	+	3.42371i	0.137945	+	0.137945i
$617$			4.38264i			0.176439i	0.996101	+	0.0882193i	$0.0281176\pi$
$617$			4.38264i			0.176439i	−0.996101	+	0.0882193i	$0.971882\pi$
$618$			10.1695i			0.409079i
$619$	8.67268	+	8.67268i	0.348584	+	0.348584i	0.859582	−	0.510998i	$-0.170724\pi$
$619$	8.67268	+	8.67268i	0.348584	+	0.348584i	−0.510998	+	0.859582i	$0.670724\pi$
$620$	−0.0285853	+	0.378082i	−0.00114801	+	0.0151842i
$621$		−	18.9732i		−	0.761370i
$622$	−8.05049			−0.322795
$623$	−0.353304	−	0.353304i	−0.0141548	−	0.0141548i
$624$		0			0
$625$	−23.8697	−	7.43216i	−0.954788	−	0.297287i
$626$	−3.46791	−	3.46791i	−0.138606	−	0.138606i
$627$	−8.95980	−	8.95980i	−0.357820	−	0.357820i
$628$	13.7878	+	13.7878i	0.550193	+	0.550193i
$629$	20.9238	−	20.9238i	0.834287	−	0.834287i
$630$	6.84557	+	7.96536i	0.272734	+	0.317348i
$631$	−17.9168	+	17.9168i	−0.713256	+	0.713256i	−0.967215	−	0.253959i	$-0.918267\pi$
$631$	−17.9168	+	17.9168i	−0.713256	+	0.713256i	0.253959	+	0.967215i	$0.418267\pi$
$632$	−41.0398			−1.63248
$633$	16.8136	−	16.8136i	0.668279	−	0.668279i
$634$	23.4440			0.931081
$635$	−4.84992	−	0.366682i	−0.192463	−	0.0145513i
$636$		−	7.51646i		−	0.298047i
$637$		0			0
$638$	0.351511	−	0.351511i	0.0139164	−	0.0139164i
$639$	−43.9964	+	43.9964i	−1.74047	+	1.74047i
$640$	−3.72774	+	3.20368i	−0.147352	+	0.126637i
$641$			1.63592i			0.0646150i	0.999478	+	0.0323075i	$0.0102856\pi$
$641$			1.63592i			0.0646150i	−0.999478	+	0.0323075i	$0.989714\pi$
$642$		−	1.26681i		−	0.0499968i
$643$	−39.6687			−1.56438			−0.782191	−	0.623039i	$-0.785898\pi$
$643$	−39.6687			−1.56438			−0.782191	+	0.623039i	$0.785898\pi$
$644$	−2.50543	−	2.50543i	−0.0987278	−	0.0987278i
$645$	−32.2820	−	37.5627i	−1.27110	−	1.47903i
$646$	20.2678			0.797428
$647$	10.5113	−	10.5113i	0.413244	−	0.413244i	−0.469623	−	0.882867i	$-0.655610\pi$
$647$	10.5113	−	10.5113i	0.413244	−	0.413244i	0.882867	+	0.469623i	$0.155610\pi$
$648$		−	1.74736i		−	0.0686429i
$649$	−8.40185			−0.329801
$650$		0			0
$651$	0.477178			0.0187021
$652$		−	20.4069i		−	0.799195i
$653$	9.09002	−	9.09002i	0.355720	−	0.355720i	−0.506513	−	0.862233i	$-0.669066\pi$
$653$	9.09002	−	9.09002i	0.355720	−	0.355720i	0.862233	+	0.506513i	$0.169066\pi$
$654$	25.8805			1.01201
$655$	0.0907243	+	0.105565i	0.00354489	+	0.00412476i
$656$	5.78396	+	5.78396i	0.225826	+	0.225826i
$657$	−15.3845			−0.600206
$658$			7.73102i			0.301387i
$659$		−	24.1035i		−	0.938938i	−0.882949	−	0.469469i	$-0.844445\pi$
$659$		−	24.1035i		−	0.938938i	0.882949	−	0.469469i	$-0.155555\pi$
$660$	−7.50127	+	6.44672i	−0.291987	+	0.250938i
$661$	−27.6825	+	27.6825i	−1.07672	+	1.07672i	−0.0799231	+	0.996801i	$0.525467\pi$
$661$	−27.6825	+	27.6825i	−1.07672	+	1.07672i	−0.996801	+	0.0799231i	$0.974533\pi$
$662$	24.2637	−	24.2637i	0.943036	−	0.943036i
$663$		0			0
$664$			25.8862i			1.00458i
$665$	−5.87300	−	0.444034i	−0.227745	−	0.0172189i
$666$	19.8941			0.770881
$667$	−0.796357	+	0.796357i	−0.0308351	+	0.0308351i
$668$	−1.63601			−0.0632991
$669$	−13.9142	+	13.9142i	−0.537954	+	0.537954i
$670$	−10.8774	−	12.6567i	−0.420229	−	0.488970i
$671$	−2.45030	+	2.45030i	−0.0945926	+	0.0945926i
$672$	9.18004	+	9.18004i	0.354128	+	0.354128i
$673$	−7.23064	−	7.23064i	−0.278721	−	0.278721i	0.553878	−	0.832598i	$-0.313148\pi$
$673$	−7.23064	−	7.23064i	−0.278721	−	0.278721i	−0.832598	+	0.553878i	$0.813148\pi$
$674$	14.8835	+	14.8835i	0.573293	+	0.573293i
$675$	−19.8274	+	14.5927i	−0.763157	+	0.561675i
$676$		0			0
$677$	29.8933	+	29.8933i	1.14889	+	1.14889i	0.986771	+	0.162121i	$0.0518333\pi$
$677$	29.8933	+	29.8933i	1.14889	+	1.14889i	0.162121	+	0.986771i	$0.448167\pi$
$678$	5.51338			0.211740
$679$			7.23953i			0.277828i
$680$	3.69259	−	48.8399i	0.141604	−	1.87292i
$681$	33.8465	+	33.8465i	1.29700	+	1.29700i
$682$		−	0.302242i		−	0.0115735i
$683$		−	20.0207i		−	0.766070i	−0.923734	−	0.383035i	$-0.874879\pi$
$683$		−	20.0207i		−	0.766070i	0.923734	−	0.383035i	$-0.125121\pi$
$684$	−8.79221	−	8.79221i	−0.336178	−	0.336178i
$685$	6.43817	+	7.49133i	0.245990	+	0.286229i
$686$			12.8803i			0.491771i
$687$	35.1027			1.33925
$688$	6.63664	+	6.63664i	0.253019	+	0.253019i
$689$		0			0
$690$	−18.6238	+	16.0056i	−0.708994	+	0.609322i
$691$	−25.0225	−	25.0225i	−0.951900	−	0.951900i	0.0469952	−	0.998895i	$-0.485035\pi$
$691$	−25.0225	−	25.0225i	−0.951900	−	0.951900i	−0.998895	+	0.0469952i	$0.985035\pi$
$692$	10.2407	+	10.2407i	0.389291	+	0.389291i
$693$	5.40204	+	5.40204i	0.205207	+	0.205207i
$694$	16.4960	−	16.4960i	0.626181	−	0.626181i
$695$	23.3155	−	20.0377i	0.884406	−	0.760073i
$696$	1.73996	−	1.73996i	0.0659531	−	0.0659531i
$697$	50.2221			1.90230
$698$	−7.50978	+	7.50978i	−0.284250	+	0.284250i
$699$	69.2959			2.62101
$700$	−0.691240	+	4.54520i	−0.0261264	+	0.171793i
$701$			37.1781i			1.40420i	0.712080	+	0.702098i	$0.247753\pi$
$701$			37.1781i			1.40420i	−0.712080	+	0.702098i	$0.752247\pi$
$702$		0			0
$703$	−7.88864	+	7.88864i	−0.297526	+	0.297526i
$704$	8.59235	−	8.59235i	0.323836	−	0.323836i
$705$	−48.7534	−	3.68605i	−1.83616	−	0.138825i
$706$		−	4.39760i		−	0.165506i
$707$			9.39830i			0.353459i
$708$	−13.4336			−0.504864
$709$	34.0774	+	34.0774i	1.27980	+	1.27980i	0.940777	+	0.339026i	$0.110097\pi$
$709$	34.0774	+	34.0774i	1.27980	+	1.27980i	0.339026	+	0.940777i	$0.389903\pi$
$710$	29.7626	+	2.25023i	1.11697	+	0.0844497i
$711$	−64.7540			−2.42846
$712$	−1.10771	+	1.10771i	−0.0415131	+	0.0415131i
$713$			0.684738i			0.0256436i
$714$	−19.9106			−0.745135
$715$		0			0
$716$	2.63300			0.0983998
$717$		−	8.80822i		−	0.328949i
$718$	−10.6632	+	10.6632i	−0.397946	+	0.397946i
$719$	33.3985			1.24555			0.622777	−	0.782400i	$-0.286004\pi$
$719$	33.3985			1.24555			0.622777	+	0.782400i	$0.286004\pi$
$720$	9.54594	−	8.20394i	0.355756	−	0.305743i
$721$	2.43130	+	2.43130i	0.0905464	+	0.0905464i
$722$	11.7884			0.438719
$723$		−	50.2164i		−	1.86757i
$724$			9.88305i			0.367301i
$725$	1.44470	+	0.219712i	0.0536550	+	0.00815991i
$726$	−16.5921	+	16.5921i	−0.615791	+	0.615791i
$727$	23.6487	−	23.6487i	0.877083	−	0.877083i	−0.116149	−	0.993232i	$-0.537055\pi$
$727$	23.6487	−	23.6487i	0.877083	−	0.877083i	0.993232	+	0.116149i	$0.0370549\pi$
$728$		0			0
$729$		−	43.9226i		−	1.62676i
$730$	4.81021	+	5.59707i	0.178034	+	0.207157i
$731$	57.6260			2.13137
$732$	−3.91774	+	3.91774i	−0.144804	+	0.144804i
$733$	−14.7049			−0.543138			−0.271569	−	0.962419i	$-0.587542\pi$
$733$	−14.7049			−0.543138			−0.271569	+	0.962419i	$0.587542\pi$
$734$	8.26018	−	8.26018i	0.304889	−	0.304889i
$735$	−37.7281	−	2.85247i	−1.39162	−	0.105215i
$736$	−13.1731	+	13.1731i	−0.485568	+	0.485568i
$737$	−8.58366	−	8.58366i	−0.316183	−	0.316183i
$738$	23.8753	+	23.8753i	0.878861	+	0.878861i
$739$	−14.5463	−	14.5463i	−0.535095	−	0.535095i	0.386989	−	0.922084i	$-0.373515\pi$
$739$	−14.5463	−	14.5463i	−0.535095	−	0.535095i	−0.922084	+	0.386989i	$0.873515\pi$
$740$	5.67600	+	6.60447i	0.208654	+	0.242785i
$741$		0			0
$742$	1.96931	+	1.96931i	0.0722956	+	0.0722956i
$743$	−44.6408			−1.63771			−0.818856	−	0.573999i	$-0.805391\pi$
$743$	−44.6408			−1.63771			−0.818856	+	0.573999i	$0.805391\pi$
$744$		−	1.49608i		−	0.0548491i
$745$	−9.65982	−	0.730339i	−0.353908	−	0.0267576i
$746$	−20.3603	−	20.3603i	−0.745443	−	0.745443i
$747$			40.8440i			1.49440i
$748$		−	11.5079i		−	0.420771i
$749$	−0.302864	−	0.302864i	−0.0110664	−	0.0110664i
$750$	31.0501	+	7.15193i	1.13379	+	0.261152i
$751$			17.5799i			0.641500i	0.947164	+	0.320750i	$0.103935\pi$
$751$			17.5799i			0.641500i	−0.947164	+	0.320750i	$0.896065\pi$
$752$	9.26510			0.337863
$753$	27.5353	+	27.5353i	1.00344	+	1.00344i
$754$		0			0
$755$	−14.9778	−	1.13241i	−0.545097	−	0.0412125i
$756$	3.20130	+	3.20130i	0.116430	+	0.116430i
$757$	−24.8848	−	24.8848i	−0.904455	−	0.904455i	0.0913630	−	0.995818i	$-0.470878\pi$
$757$	−24.8848	−	24.8848i	−0.904455	−	0.904455i	−0.995818	+	0.0913630i	$0.970878\pi$
$758$	12.2435	+	12.2435i	0.444705	+	0.444705i
$759$	−12.6305	+	12.6305i	−0.458457	+	0.458457i
$760$	−1.39217	+	18.4135i	−0.0504993	+	0.667927i
$761$	−8.28144	+	8.28144i	−0.300202	+	0.300202i	−0.841093	−	0.540891i	$-0.818087\pi$
$761$	−8.28144	+	8.28144i	−0.300202	+	0.300202i	0.540891	+	0.841093i	$0.318087\pi$
$762$	6.19897			0.224565
$763$	6.18743	−	6.18743i	0.224000	−	0.224000i
$764$	17.7297			0.641438
$765$	5.82628	−	77.0611i	0.210650	−	2.78615i
$766$		−	6.75331i		−	0.244007i
$767$		0			0
$768$	33.2233	−	33.2233i	1.19884	−	1.19884i
$769$	−13.4131	+	13.4131i	−0.483689	+	0.483689i	−0.906308	−	0.422618i	$-0.861111\pi$
$769$	−13.4131	+	13.4131i	−0.483689	+	0.483689i	0.422618	+	0.906308i	$0.361111\pi$
$770$	0.276292	−	3.65437i	0.00995686	−	0.131694i
$771$			64.5941i			2.32630i
$772$		−	11.9964i		−	0.431760i
$773$	16.4099			0.590224			0.295112	−	0.955463i	$-0.404643\pi$
$773$	16.4099			0.590224			0.295112	+	0.955463i	$0.404643\pi$
$774$	27.3950	+	27.3950i	0.984694	+	0.984694i
$775$	0.715564	−	0.526647i	0.0257038	−	0.0189177i
$776$	22.6979			0.814808
$777$	7.74959	−	7.74959i	0.278015	−	0.278015i
$778$		−	34.4570i		−	1.23534i
$779$	−18.9346			−0.678403
$780$		0			0
$781$	21.7109			0.776876
$782$		−	28.5712i		−	1.02170i
$783$	1.01754	−	1.01754i	0.0363639	−	0.0363639i
$784$	7.16984			0.256066
$785$	3.44468	−	45.5610i	0.122946	−	1.62614i
$786$	−0.125445	−	0.125445i	−0.00447446	−	0.00447446i
$787$	−13.6002			−0.484794			−0.242397	−	0.970177i	$-0.577934\pi$
$787$	−13.6002			−0.484794			−0.242397	+	0.970177i	$0.577934\pi$
$788$			13.6326i			0.485642i
$789$			3.62588i			0.129085i
$790$	20.2464	+	23.5583i	0.720334	+	0.838166i
$791$	1.31812	−	1.31812i	0.0468669	−	0.0468669i
$792$	16.9369	−	16.9369i	0.601827	−	0.601827i
$793$		0			0
$794$		−	5.95255i		−	0.211248i
$795$	−13.3578	+	11.4799i	−0.473753	+	0.407151i
$796$	−14.0615			−0.498397
$797$	−21.1671	+	21.1671i	−0.749776	+	0.749776i	−0.974437	−	0.224661i	$-0.927873\pi$
$797$	−21.1671	+	21.1671i	−0.749776	+	0.749776i	0.224661	+	0.974437i	$0.427873\pi$
$798$	7.50664			0.265732
$799$	40.2244	−	40.2244i	1.42304	−	1.42304i
$800$	23.8979	+	3.63442i	0.844919	+	0.128496i
$801$	−1.74778	+	1.74778i	−0.0617546	+	0.0617546i
$802$	0.190898	+	0.190898i	0.00674083	+	0.00674083i
$803$	3.79588	+	3.79588i	0.133954	+	0.133954i
$804$	−13.7243	−	13.7243i	−0.484018	−	0.484018i
$805$	−0.625946	+	8.27906i	−0.0220617	+	0.291799i
$806$		0			0
$807$	−15.6423	−	15.6423i	−0.550636	−	0.550636i
$808$	29.4663			1.03662
$809$		−	2.94058i		−	0.103385i	−0.998663	−	0.0516926i	$-0.983538\pi$
$809$		−	2.94058i		−	0.103385i	0.998663	−	0.0516926i	$-0.0164616\pi$
$810$	−1.00305	+	0.862035i	−0.0352435	+	0.0302888i
$811$	16.3366	+	16.3366i	0.573657	+	0.573657i	0.933148	−	0.359492i	$-0.117050\pi$
$811$	16.3366	+	16.3366i	0.573657	+	0.573657i	−0.359492	+	0.933148i	$0.617050\pi$
$812$		−	0.268734i		−	0.00943071i
$813$			2.49581i			0.0875320i
$814$	−4.90856	−	4.90856i	−0.172045	−	0.172045i
$815$	−36.2659	+	31.1675i	−1.27034	+	1.09175i
$816$			23.8615i			0.835319i
$817$	−21.7260			−0.760096
$818$	26.8732	+	26.8732i	0.939599	+	0.939599i
$819$		0			0
$820$	−1.11428	+	14.7380i	−0.0389124	+	0.514674i
$821$	32.4390	+	32.4390i	1.13213	+	1.13213i	0.989823	+	0.142305i	$0.0454514\pi$
$821$	32.4390	+	32.4390i	1.13213	+	1.13213i	0.142305	+	0.989823i	$0.454549\pi$
$822$	−8.90207	−	8.90207i	−0.310495	−	0.310495i
$823$	12.5333	+	12.5333i	0.436885	+	0.436885i	0.890962	−	0.454077i	$-0.150031\pi$
$823$	12.5333	+	12.5333i	0.436885	+	0.436885i	−0.454077	+	0.890962i	$0.650031\pi$
$824$	7.62280	−	7.62280i	0.265553	−	0.265553i
$825$	22.9135	+	3.48471i	0.797744	+	0.121322i
$826$	3.51959	−	3.51959i	0.122462	−	0.122462i
$827$	5.79276			0.201434			0.100717	−	0.994915i	$-0.467886\pi$
$827$	5.79276			0.201434			0.100717	+	0.994915i	$0.467886\pi$
$828$	−12.3942	+	12.3942i	−0.430729	+	0.430729i
$829$	−33.7598			−1.17252			−0.586262	−	0.810121i	$-0.699401\pi$
$829$	−33.7598			−1.17252			−0.586262	+	0.810121i	$0.699401\pi$
$830$	14.8595	−	12.7705i	0.515782	−	0.443272i
$831$			26.6284i			0.923727i
$832$		0			0
$833$	31.1279	−	31.1279i	1.07852	−	1.07852i
$834$	−27.7062	+	27.7062i	−0.959386	+	0.959386i
$835$	2.49869	+	2.90742i	0.0864706	+	0.100615i
$836$			4.33868i			0.150056i
$837$		−	0.874920i		−	0.0302417i
$838$	34.6830			1.19811
$839$	−27.7173	−	27.7173i	−0.956909	−	0.956909i	0.0422005	−	0.999109i	$-0.486563\pi$
$839$	−27.7173	−	27.7173i	−0.956909	−	0.956909i	−0.999109	+	0.0422005i	$0.986563\pi$
$840$	1.36763	−	18.0889i	0.0471877	−	0.624127i
$841$	28.9146			0.997055
$842$	−22.0475	+	22.0475i	−0.759807	+	0.759807i
$843$			22.0083i			0.758005i
$844$	−8.14177			−0.280251
$845$		0			0
$846$	38.2449			1.31489
$847$			7.93357i			0.272601i
$848$	2.36008	−	2.36008i	0.0810455	−	0.0810455i
$849$	58.8152			2.01853
$850$	−29.8575	+	21.9748i	−1.02410	+	0.753728i
$851$	11.1205	+	11.1205i	0.381205	+	0.381205i
$852$	34.7131			1.18925
$853$		−	40.6417i		−	1.39154i	−0.718262	−	0.695772i	$-0.755062\pi$
$853$		−	40.6417i		−	1.39154i	0.718262	−	0.695772i	$-0.244938\pi$
$854$		−	2.05289i		−	0.0702484i
$855$	−2.19661	+	29.0534i	−0.0751224	+	0.993605i
$856$	−0.949561	+	0.949561i	−0.0324553	+	0.0324553i
$857$	−27.2327	+	27.2327i	−0.930252	+	0.930252i	−0.997721	−	0.0674695i	$-0.978507\pi$
$857$	−27.2327	+	27.2327i	−0.930252	+	0.930252i	0.0674695	+	0.997721i	$0.478507\pi$
$858$		0			0
$859$		−	44.5502i		−	1.52003i	−0.649904	−	0.760016i	$-0.725191\pi$
$859$		−	44.5502i		−	1.52003i	0.649904	−	0.760016i	$-0.274809\pi$
$860$	−1.27855	+	16.9107i	−0.0435982	+	0.576651i
$861$	18.6009			0.633916
$862$	3.32507	−	3.32507i	0.113252	−	0.113252i
$863$	55.4497			1.88753			0.943766	−	0.330615i	$-0.107256\pi$
$863$	55.4497			1.88753			0.943766	+	0.330615i	$0.107256\pi$
$864$	16.8319	−	16.8319i	0.572632	−	0.572632i
$865$	2.55848	−	33.8397i	0.0869910	−	1.15058i
$866$	2.89432	−	2.89432i	0.0983531	−	0.0983531i
$867$	70.0940	+	70.0940i	2.38052	+	2.38052i
$868$	−0.115534	−	0.115534i	−0.00392147	−	0.00392147i
$869$	15.9770	+	15.9770i	0.541984	+	0.541984i
$870$	−1.85718	−	0.140414i	−0.0629643	−	0.00476048i
$871$		0			0
$872$	−19.3993	−	19.3993i	−0.656944	−	0.656944i
$873$	35.8135			1.21210
$874$			10.7718i			0.364363i
$875$	9.13320	−	5.71348i	0.308759	−	0.193151i
$876$	6.06917	+	6.06917i	0.205058	+	0.205058i
$877$			5.37699i			0.181568i	0.995871	+	0.0907839i	$0.0289373\pi$
$877$			5.37699i			0.181568i	−0.995871	+	0.0907839i	$0.971063\pi$
$878$			23.2377i			0.784233i
$879$	7.92505	+	7.92505i	0.267305	+	0.267305i
$880$	−4.37951	−	0.331117i	−0.147633	−	0.0111619i
$881$		−	42.8267i		−	1.44287i	−0.692484	−	0.721434i	$-0.743484\pi$
$881$		−	42.8267i		−	1.44287i	0.692484	−	0.721434i	$-0.256516\pi$
$882$	29.5960			0.996549
$883$	32.9568	+	32.9568i	1.10908	+	1.10908i	0.993271	+	0.115813i	$0.0369473\pi$
$883$	32.9568	+	32.9568i	1.10908	+	1.10908i	0.115813	+	0.993271i	$0.463053\pi$
$884$		0			0
$885$	20.5172	+	23.8733i	0.689677	+	0.802494i
$886$	−1.89055	−	1.89055i	−0.0635143	−	0.0635143i
$887$	−14.9480	−	14.9480i	−0.501906	−	0.501906i	0.410124	−	0.912030i	$-0.365485\pi$
$887$	−14.9480	−	14.9480i	−0.501906	−	0.501906i	−0.912030	+	0.410124i	$0.865485\pi$
$888$	−24.2971	−	24.2971i	−0.815358	−	0.815358i
$889$	1.48203	−	1.48203i	0.0497057	−	0.0497057i
$890$	1.18233	+	0.0893914i	0.0396319	+	0.00299641i
$891$	−0.680258	+	0.680258i	−0.0227895	+	0.0227895i
$892$	6.73778			0.225598
$893$	−15.1653	+	15.1653i	−0.507488	+	0.507488i
$894$	12.3468			0.412939
$895$	−4.02140	−	4.67921i	−0.134420	−	0.156409i
$896$		−	2.11809i		−	0.0707605i
$897$		0			0
$898$	−23.2645	+	23.2645i	−0.776346	+	0.776346i
$899$	−0.0367227	+	0.0367227i	−0.00122477	+	0.00122477i
$900$	22.4849	+	3.41952i	0.749495	+	0.113984i
$901$		−	20.4926i		−	0.682707i
$902$		−	11.7817i		−	0.392288i
$903$	21.3430			0.710252
$904$	−4.13267	−	4.13267i	−0.137451	−	0.137451i
$905$	17.5636	−	15.0944i	0.583833	−	0.501756i
$906$	19.1440			0.636017
$907$	−7.82336	+	7.82336i	−0.259770	+	0.259770i	−0.824961	−	0.565190i	$-0.808803\pi$
$907$	−7.82336	+	7.82336i	−0.259770	+	0.259770i	0.565190	+	0.824961i	$0.308803\pi$
$908$		−	16.3898i		−	0.543913i
$909$	46.4928			1.54207
$910$		0			0
$911$	−15.0479			−0.498560			−0.249280	−	0.968431i	$-0.580194\pi$
$911$	−15.0479			−0.498560			−0.249280	+	0.968431i	$0.580194\pi$
$912$		−	8.99619i		−	0.297894i
$913$	10.0776	−	10.0776i	0.333521	−	0.333521i
$914$	−29.0090			−0.959533
$915$	12.9459	+	0.978791i	0.427980	+	0.0323578i
$916$	−8.49903	−	8.49903i	−0.280816	−	0.280816i
$917$	−0.0599818			−0.00198077
$918$			36.5067i			1.20490i
$919$			12.5103i			0.412676i	0.978481	+	0.206338i	$0.0661546\pi$
$919$			12.5103i			0.412676i	−0.978481	+	0.206338i	$0.933845\pi$
$920$	25.9572	+	1.96252i	0.855782	+	0.0647022i
$921$	−47.7268	+	47.7268i	−1.57265	+	1.57265i
$922$	8.32259	−	8.32259i	0.274090	−	0.274090i
$923$		0			0
$924$		−	4.26220i		−	0.140216i
$925$	3.06810	−	20.1741i	0.100879	−	0.663320i
$926$	−30.6229			−1.00633
$927$	12.0275	−	12.0275i	0.395035	−	0.395035i
$928$	−1.41296			−0.0463826
$929$	−34.4704	+	34.4704i	−1.13094	+	1.13094i	−0.140915	+	0.990022i	$0.545004\pi$
$929$	−34.4704	+	34.4704i	−1.13094	+	1.13094i	−0.990022	+	0.140915i	$0.954996\pi$
$930$	−0.858804	+	0.738070i	−0.0281613	+	0.0242023i
$931$	−11.7357	+	11.7357i	−0.384623	+	0.384623i
$932$	−16.7779	−	16.7779i	−0.549577	−	0.549577i
$933$	15.5136	+	15.5136i	0.507894	+	0.507894i
$934$	−16.4981	−	16.4981i	−0.539836	−	0.539836i
$935$	−20.4512	+	17.5761i	−0.668825	+	0.574800i
$936$		0			0
$937$	7.38027	+	7.38027i	0.241103	+	0.241103i	0.817306	−	0.576203i	$-0.195466\pi$
$937$	7.38027	+	7.38027i	0.241103	+	0.241103i	−0.576203	+	0.817306i	$0.695466\pi$
$938$	7.19150			0.234811
$939$			13.3656i			0.436171i
$940$	10.9117	+	12.6966i	0.355900	+	0.414117i
$941$	−1.54410	−	1.54410i	−0.0503363	−	0.0503363i	0.681491	−	0.731827i	$-0.261332\pi$
$941$	−1.54410	−	1.54410i	−0.0503363	−	0.0503363i	−0.731827	+	0.681491i	$0.761332\pi$
$942$			58.2343i			1.89738i
$943$			26.6918i			0.869204i
$944$	−4.21798	−	4.21798i	−0.137284	−	0.137284i
$945$	0.799799	−	10.5785i	0.0260175	−	0.344119i
$946$		−	13.5186i		−	0.439527i
$947$	−6.71654			−0.218258			−0.109129	−	0.994028i	$-0.534806\pi$
$947$	−6.71654			−0.218258			−0.109129	+	0.994028i	$0.534806\pi$
$948$	25.5454	+	25.5454i	0.829676	+	0.829676i
$949$		0			0
$950$	11.2568	−	8.28486i	0.365218	−	0.268796i
$951$	−45.1776	−	45.1776i	−1.46498	−	1.46498i
$952$	14.9244	+	14.9244i	0.483703	+	0.483703i
$953$	12.7671	+	12.7671i	0.413568	+	0.413568i	0.882979	−	0.469412i	$-0.155534\pi$
$953$	12.7671	+	12.7671i	0.413568	+	0.413568i	−0.469412	+	0.882979i	$0.655534\pi$
$954$	9.74205	−	9.74205i	0.315411	−	0.315411i
$955$	−27.0787	−	31.5082i	−0.876245	−	1.01958i
$956$	−2.13264	+	2.13264i	−0.0689744	+	0.0689744i
$957$	−1.35475			−0.0437929
$958$	−28.0760	+	28.0760i	−0.907095	+	0.907095i
$959$	−4.25656			−0.137451
$960$	−45.3970	−	3.43228i	−1.46518	−	0.110776i
$961$		−	30.9684i		−	0.998981i
$962$		0			0
$963$	−1.49825	+	1.49825i	−0.0482804	+	0.0482804i
$964$	−12.1583	+	12.1583i	−0.391594	+	0.391594i
$965$	−21.3193	+	18.3222i	−0.686293	+	0.589812i
$966$		−	10.5820i		−	0.340469i
$967$			60.0570i			1.93130i	0.259841	+	0.965651i	$0.416330\pi$
$967$			60.0570i			1.93130i	−0.259841	+	0.965651i	$0.583670\pi$
$968$	24.8740			0.799479
$969$	−39.0570	−	39.0570i	−1.25469	−	1.25469i
$970$	−11.1977	−	13.0294i	−0.359536	−	0.418348i
$971$	−40.9179			−1.31312			−0.656558	−	0.754275i	$-0.727988\pi$
$971$	−40.9179			−1.31312			−0.656558	+	0.754275i	$0.727988\pi$
$972$	−11.0546	+	11.0546i	−0.354577	+	0.354577i
$973$			13.2478i			0.424705i
$974$	29.5983			0.948391
$975$		0			0
$976$	−2.46025			−0.0787506
$977$			37.4959i			1.19960i	0.800150	+	0.599800i	$0.204753\pi$
$977$			37.4959i			1.19960i	−0.800150	+	0.599800i	$0.795247\pi$
$978$	43.0954	−	43.0954i	1.37804	−	1.37804i
$979$	0.862473			0.0275648
$980$	8.44405	+	9.82532i	0.269735	+	0.313858i
$981$	−30.6089	−	30.6089i	−0.977266	−	0.977266i
$982$	7.43919			0.237394
$983$			46.1176i			1.47092i	0.677567	+	0.735461i	$0.263034\pi$
$983$			46.1176i			1.47092i	−0.677567	+	0.735461i	$0.736966\pi$
$984$		−	58.3189i		−	1.85914i
$985$	24.2271	−	20.8212i	0.771939	−	0.663418i
$986$	1.53228	−	1.53228i	0.0487978	−	0.0487978i
$987$	14.8980	−	14.8980i	0.474208	−	0.474208i
$988$		0			0
$989$			30.6267i			0.973873i
$990$	−18.0779	−	1.36680i	−0.574554	−	0.0434397i
$991$	0.802199			0.0254827			0.0127413	−	0.999919i	$-0.495944\pi$
$991$	0.802199			0.0254827			0.0127413	+	0.999919i	$0.495944\pi$
$992$	−0.607457	+	0.607457i	−0.0192868	+	0.0192868i
$993$	−93.5143			−2.96759
$994$	−9.09482	+	9.09482i	−0.288470	+	0.288470i
$995$	21.4762	+	24.9893i	0.680842	+	0.792214i
$996$	16.1129	−	16.1129i	0.510558	−	0.510558i
$997$	11.0378	+	11.0378i	0.349571	+	0.349571i	0.859950	−	0.510379i	$-0.170495\pi$
$997$	11.0378	+	11.0378i	0.349571	+	0.349571i	−0.510379	+	0.859950i	$0.670495\pi$
$998$	−4.33796	−	4.33796i	−0.137316	−	0.137316i
$999$	−14.2091	−	14.2091i	−0.449556	−	0.449556i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.f.e.437.3		20
5.3	odd	4		845.2.k.e.268.3		20
13.2	odd	12		65.2.o.a.32.4	✓	20
13.3	even	3		845.2.t.f.657.4		20
13.4	even	6		845.2.t.g.427.4		20
13.5	odd	4		845.2.k.e.577.3		20
13.6	odd	12		845.2.o.e.587.4		20
13.7	odd	12		845.2.o.f.587.2		20
13.8	odd	4		845.2.k.d.577.8		20
13.9	even	3		65.2.t.a.37.2	yes	20
13.10	even	6		845.2.t.e.657.2		20
13.11	odd	12		845.2.o.g.357.2		20
13.12	even	2		845.2.f.d.437.8		20
39.2	even	12		585.2.cf.a.487.2		20
39.35	odd	6		585.2.dp.a.37.4		20
65.2	even	12		325.2.x.b.318.4		20
65.3	odd	12		845.2.o.e.488.4		20
65.8	even	4		845.2.f.d.408.3		20
65.9	even	6		325.2.x.b.232.4		20
65.18	even	4	inner	845.2.f.e.408.8		20
65.22	odd	12		325.2.s.b.193.2		20
65.23	odd	12		845.2.o.f.488.2		20
65.28	even	12		65.2.t.a.58.2	yes	20
65.33	even	12		845.2.t.e.418.2		20
65.38	odd	4		845.2.k.d.268.8		20
65.43	odd	12		845.2.o.g.258.2		20
65.48	odd	12		65.2.o.a.63.4	yes	20
65.54	odd	12		325.2.s.b.32.2		20
65.58	even	12		845.2.t.f.418.4		20
65.63	even	12		845.2.t.g.188.4		20
195.113	even	12		585.2.cf.a.388.2		20
195.158	odd	12		585.2.dp.a.253.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.4	✓	20	13.2	odd	12
65.2.o.a.63.4	yes	20	65.48	odd	12
65.2.t.a.37.2	yes	20	13.9	even	3
65.2.t.a.58.2	yes	20	65.28	even	12
325.2.s.b.32.2		20	65.54	odd	12
325.2.s.b.193.2		20	65.22	odd	12
325.2.x.b.232.4		20	65.9	even	6
325.2.x.b.318.4		20	65.2	even	12
585.2.cf.a.388.2		20	195.113	even	12
585.2.cf.a.487.2		20	39.2	even	12
585.2.dp.a.37.4		20	39.35	odd	6
585.2.dp.a.253.4		20	195.158	odd	12
845.2.f.d.408.3		20	65.8	even	4
845.2.f.d.437.8		20	13.12	even	2
845.2.f.e.408.8		20	65.18	even	4	inner
845.2.f.e.437.3		20	1.1	even	1	trivial
845.2.k.d.268.8		20	65.38	odd	4
845.2.k.d.577.8		20	13.8	odd	4
845.2.k.e.268.3		20	5.3	odd	4
845.2.k.e.577.3		20	13.5	odd	4
845.2.o.e.488.4		20	65.3	odd	12
845.2.o.e.587.4		20	13.6	odd	12
845.2.o.f.488.2		20	65.23	odd	12
845.2.o.f.587.2		20	13.7	odd	12
845.2.o.g.258.2		20	65.43	odd	12
845.2.o.g.357.2		20	13.11	odd	12
845.2.t.e.418.2		20	65.33	even	12
845.2.t.e.657.2		20	13.10	even	6
845.2.t.f.418.4		20	65.58	even	12
845.2.t.f.657.4		20	13.3	even	3
845.2.t.g.188.4		20	65.63	even	12
845.2.t.g.427.4		20	13.4	even	6

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.02262i q^{2} +(-1.97063 + 1.97063i) q^{3} +0.954253 q^{4} +(-1.45744 - 1.69584i) q^{5} +(2.01520 + 2.01520i) q^{6} +0.963574 q^{7} -3.02107i q^{8} -4.76674i q^{9} +O(q^{10})\)	\(q-1.02262i q^{2} +(-1.97063 + 1.97063i) q^{3} +0.954253 q^{4} +(-1.45744 - 1.69584i) q^{5} +(2.01520 + 2.01520i) q^{6} +0.963574 q^{7} -3.02107i q^{8} -4.76674i q^{9} +(-1.73420 + 1.49040i) q^{10} +(-1.17612 + 1.17612i) q^{11} +(-1.88048 + 1.88048i) q^{12} -0.985368i q^{14} +(6.21394 + 0.469810i) q^{15} -1.18090 q^{16} +(-5.12686 + 5.12686i) q^{17} -4.87456 q^{18} +(1.93291 - 1.93291i) q^{19} +(-1.39076 - 1.61826i) q^{20} +(-1.89884 + 1.89884i) q^{21} +(1.20272 + 1.20272i) q^{22} +(-2.72480 - 2.72480i) q^{23} +(5.95341 + 5.95341i) q^{24} +(-0.751762 + 4.94316i) q^{25} +(3.48159 + 3.48159i) q^{27} +0.919493 q^{28} -0.292263i q^{29} +(0.480436 - 6.35448i) q^{30} +(-0.125649 - 0.125649i) q^{31} -4.83454i q^{32} -4.63538i q^{33} +(5.24282 + 5.24282i) q^{34} +(-1.40435 - 1.63407i) q^{35} -4.54868i q^{36} -4.08121 q^{37} +(-1.97663 - 1.97663i) q^{38} +(-5.12326 + 4.40302i) q^{40} +(-4.89794 - 4.89794i) q^{41} +(1.94179 + 1.94179i) q^{42} +(-5.62000 - 5.62000i) q^{43} +(-1.12232 + 1.12232i) q^{44} +(-8.08364 + 6.94722i) q^{45} +(-2.78642 + 2.78642i) q^{46} -7.84582 q^{47} +(2.32710 - 2.32710i) q^{48} -6.07153 q^{49} +(5.05497 + 0.768765i) q^{50} -20.2063i q^{51} +(-1.99855 + 1.99855i) q^{53} +(3.56034 - 3.56034i) q^{54} +(3.70863 + 0.280394i) q^{55} -2.91103i q^{56} +7.61811i q^{57} -0.298873 q^{58} +(3.57185 + 3.57185i) q^{59} +(5.92967 + 0.448318i) q^{60} +2.08337 q^{61} +(-0.128491 + 0.128491i) q^{62} -4.59311i q^{63} -7.30568 q^{64} -4.74023 q^{66} +7.29829i q^{67} +(-4.89232 + 4.89232i) q^{68} +10.7391 q^{69} +(-1.67103 + 1.43611i) q^{70} +(-9.22988 - 9.22988i) q^{71} -14.4007 q^{72} -3.22747i q^{73} +4.17352i q^{74} +(-8.25969 - 11.2226i) q^{75} +(1.84449 - 1.84449i) q^{76} +(-1.13328 + 1.13328i) q^{77} -13.5845i q^{79} +(1.72108 + 2.00261i) q^{80} +0.578392 q^{81} +(-5.00872 + 5.00872i) q^{82} -8.56854 q^{83} +(-1.81198 + 1.81198i) q^{84} +(16.1664 + 1.22228i) q^{85} +(-5.74712 + 5.74712i) q^{86} +(0.575942 + 0.575942i) q^{87} +(3.55314 + 3.55314i) q^{88} +(-0.366660 - 0.366660i) q^{89} +(7.10435 + 8.26648i) q^{90} +(-2.60014 - 2.60014i) q^{92} +0.495216 q^{93} +8.02328i q^{94} +(-6.09502 - 0.460819i) q^{95} +(9.52707 + 9.52707i) q^{96} +7.51320i q^{97} +6.20885i q^{98} +(5.60626 + 5.60626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7}+O(q^{10}) \) 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7	\( 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7} - 8 q^{10} + 8 q^{11} - 24 q^{12} + 28 q^{15} + 4 q^{16} - 14 q^{17} + 4 q^{19} - 12 q^{20} + 4 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{24} + 18 q^{25} + 4 q^{27} - 36 q^{28} + 40 q^{30} + 2 q^{34} - 20 q^{35} + 8 q^{37} - 8 q^{38} - 16 q^{40} - 38 q^{41} + 16 q^{42} - 32 q^{43} - 36 q^{44} - 6 q^{45} + 4 q^{46} - 40 q^{47} + 28 q^{48} - 36 q^{49} + 42 q^{50} - 10 q^{53} + 36 q^{54} - 16 q^{55} + 8 q^{59} + 28 q^{60} + 32 q^{61} + 4 q^{62} + 20 q^{64} - 32 q^{66} - 50 q^{68} + 32 q^{69} - 12 q^{70} - 40 q^{71} - 8 q^{72} + 4 q^{75} - 16 q^{76} - 28 q^{77} + 112 q^{80} + 28 q^{81} - 34 q^{82} + 48 q^{83} + 8 q^{84} - 2 q^{85} + 60 q^{86} - 28 q^{87} - 32 q^{88} + 12 q^{89} + 46 q^{90} - 8 q^{92} - 64 q^{93} + 40 q^{95} + 56 q^{96} + 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7 - 8 * q^10 + 8 * q^11 - 24 * q^12 + 28 * q^15 + 4 * q^16 - 14 * q^17 + 4 * q^19 - 12 * q^20 + 4 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^24 + 18 * q^25 + 4 * q^27 - 36 * q^28 + 40 * q^30 + 2 * q^34 - 20 * q^35 + 8 * q^37 - 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 - 32 * q^43 - 36 * q^44 - 6 * q^45 + 4 * q^46 - 40 * q^47 + 28 * q^48 - 36 * q^49 + 42 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 8 * q^59 + 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 - 12 * q^70 - 40 * q^71 - 8 * q^72 + 4 * q^75 - 16 * q^76 - 28 * q^77 + 112 * q^80 + 28 * q^81 - 34 * q^82 + 48 * q^83 + 8 * q^84 - 2 * q^85 + 60 * q^86 - 28 * q^87 - 32 * q^88 + 12 * q^89 + 46 * q^90 - 8 * q^92 - 64 * q^93 + 40 * q^95 + 56 * q^96 + 60 * q^99

Introduction

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