LMFDB - Embedded newform 845.2.k.d.577.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(268,845)]

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, 1]))

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

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

chi := DirichletCharacter("845.268");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.k (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			577.8
Root			$-1.02262i$ of defining polynomial
Character	$\chi$	$=$	845.577
Dual form			845.2.k.d.268.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.02262 q^{2} +(-1.97063 + 1.97063i) q^{3} -0.954253 q^{4} +(1.69584 - 1.45744i) q^{5} +(-2.01520 + 2.01520i) q^{6} -0.963574i q^{7} -3.02107 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} +(-0.469810 + 6.21394i) q^{15} -1.18090 q^{16} +(5.12686 - 5.12686i) q^{17} -4.87456i q^{18} +(1.93291 + 1.93291i) q^{19} +(-1.61826 + 1.39076i) 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} +0.919493i q^{28} -0.292263i q^{29} +(-0.480436 + 6.35448i) q^{30} +(0.125649 - 0.125649i) q^{31} +4.83454 q^{32} -4.63538 q^{33} +(5.24282 - 5.24282i) q^{34} +(-1.40435 - 1.63407i) q^{35} +4.54868i q^{36} +4.08121i 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} +(-6.94722 - 8.08364i) q^{45} +(2.78642 + 2.78642i) q^{46} +7.84582i q^{47} +(2.32710 - 2.32710i) q^{48} +6.07153 q^{49} +(0.768765 - 5.05497i) 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} -7.61811 q^{57} -0.298873i q^{58} +(3.57185 - 3.57185i) q^{59} +(0.448318 - 5.92967i) q^{60} +2.08337 q^{61} +(0.128491 - 0.128491i) q^{62} -4.59311 q^{63} +7.30568 q^{64} -4.74023 q^{66} -7.29829 q^{67} +(-4.89232 + 4.89232i) q^{68} -10.7391 q^{69} +(-1.43611 - 1.67103i) q^{70} +(9.22988 - 9.22988i) q^{71} +14.4007i q^{72} -3.22747 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} +(-2.00261 + 1.72108i) q^{80} +0.578392 q^{81} +(5.00872 - 5.00872i) q^{82} -8.56854i q^{83} +(-1.81198 - 1.81198i) q^{84} +(1.22228 - 16.1664i) 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} +0.495216i q^{93} +8.02328i q^{94} +(6.09502 + 0.460819i) q^{95} +(-9.52707 + 9.52707i) q^{96} -7.51320 q^{97} +6.20885 q^{98} +(5.60626 - 5.60626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 8 q^{2} + 4 q^{3} + 12 q^{4} + 6 q^{5} - 4 q^{6} - 12 q^{8} + 8 q^{10} - 8 q^{11} + 24 q^{12} + 24 q^{15} + 4 q^{16} + 14 q^{17} + 4 q^{19} + 22 q^{20} - 4 q^{21} - 32 q^{22} - 8 q^{23} - 4 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q - 8 * q^2 + 4 * q^3 + 12 * q^4 + 6 * q^5 - 4 * q^6 - 12 * q^8 + 8 * q^10 - 8 * q^11 + 24 * q^12 + 24 * q^15 + 4 * q^16 + 14 * q^17 + 4 * q^19 + 22 * q^20 - 4 * q^21 - 32 * q^22 - 8 * q^23 - 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 - 12 * q^32 - 36 * q^33 + 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 + 32 * q^43 - 36 * q^44 + 20 * q^45 - 4 * q^46 + 28 * q^48 + 36 * q^49 + 52 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 12 * q^57 + 8 * q^59 + 92 * q^60 + 32 * q^61 - 4 * q^62 - 64 * q^63 - 20 * q^64 - 32 * q^66 - 116 * q^67 - 50 * q^68 - 32 * q^69 - 32 * q^70 + 40 * q^71 - 72 * q^73 - 4 * q^75 + 16 * q^76 + 28 * q^77 + 34 * q^80 + 28 * q^81 + 34 * q^82 + 8 * q^84 - 60 * q^86 - 28 * q^87 + 32 * q^88 + 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 - 56 * q^96 - 44 * q^97 + 8 * q^98 + 60 * q^99

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.02262			0.723100			0.361550	−	0.932353i	$-0.382248\pi$
$2$	1.02262			0.723100			0.361550	+	0.932353i	$0.382248\pi$
$3$	−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
$5$	1.69584	−	1.45744i	0.758404	−	0.651785i
$5$	1.69584	−	1.45744i	0.758404	−	0.651785i
$6$	−2.01520	+	2.01520i	−0.822701	+	0.822701i
$7$		−	0.963574i		−	0.364197i	−0.983280	−	0.182098i	$-0.941711\pi$
$7$		−	0.963574i		−	0.364197i	0.983280	−	0.182098i	$-0.0582889\pi$
$8$	−3.02107			−1.06811
$9$		−	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	$-0.169323\pi$
$11$	1.17612	+	1.17612i	0.354613	+	0.354613i	−0.507210	+	0.861823i	$0.669323\pi$
$12$	1.88048	−	1.88048i	0.542847	−	0.542847i
$13$		0			0
$13$		0			0
$14$		−	0.985368i		−	0.263351i
$15$	−0.469810	+	6.21394i	−0.121305	+	1.60443i
$16$	−1.18090			−0.295224
$17$	5.12686	−	5.12686i	1.24345	−	1.24345i	0.284884	−	0.958562i	$-0.408045\pi$
$17$	5.12686	−	5.12686i	1.24345	−	1.24345i	0.958562	−	0.284884i	$-0.0919552\pi$
$18$		−	4.87456i		−	1.14894i
$19$	1.93291	+	1.93291i	0.443441	+	0.443441i	0.893167	−	0.449726i	$-0.148478\pi$
$19$	1.93291	+	1.93291i	0.443441	+	0.443441i	−0.449726	+	0.893167i	$0.648478\pi$
$20$	−1.61826	+	1.39076i	−0.361854	+	0.310984i
$21$	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	0.931612	−	0.363453i	$-0.118402\pi$
$23$	2.72480	+	2.72480i	0.568159	+	0.568159i	−0.363453	+	0.931612i	$0.618402\pi$
$24$	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
$28$			0.919493i			0.173768i
$29$		−	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	$-0.744920\pi$
$31$	0.125649	−	0.125649i	0.0225673	−	0.0225673i	0.718300	+	0.695733i	$0.244920\pi$
$32$	4.83454			0.854634
$33$	−4.63538			−0.806917
$34$	5.24282	−	5.24282i	0.899136	−	0.899136i
$35$	−1.40435	−	1.63407i	−0.237378	−	0.276208i
$36$			4.54868i			0.758113i
$37$			4.08121i			0.670947i	0.942050	+	0.335474i	$0.108896\pi$
$37$			4.08121i			0.670947i	−0.942050	+	0.335474i	$0.891104\pi$
$38$	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	$-0.568089\pi$
$41$	4.89794	−	4.89794i	0.764930	−	0.764930i	0.977209	+	0.212279i	$0.0680886\pi$
$42$	1.94179	+	1.94179i	0.299625	+	0.299625i
$43$	5.62000	+	5.62000i	0.857043	+	0.857043i	0.990989	−	0.133946i	$-0.0427649\pi$
$43$	5.62000	+	5.62000i	0.857043	+	0.857043i	−0.133946	+	0.990989i	$0.542765\pi$
$44$	−1.12232	−	1.12232i	−0.169195	−	0.169195i
$45$	−6.94722	−	8.08364i	−1.03563	−	1.20504i
$46$	2.78642	+	2.78642i	0.410836	+	0.410836i
$47$			7.84582i			1.14443i	0.820103	+	0.572215i	$0.193916\pi$
$47$			7.84582i			1.14443i	−0.820103	+	0.572215i	$0.806084\pi$
$48$	2.32710	−	2.32710i	0.335889	−	0.335889i
$49$	6.07153			0.867361
$50$	0.768765	−	5.05497i	0.108720	−	0.714880i
$51$			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
$57$	−7.61811			−1.00904
$58$		−	0.298873i		−	0.0392440i
$59$	3.57185	−	3.57185i	0.465015	−	0.465015i	−0.435280	−	0.900295i	$-0.643351\pi$
$59$	3.57185	−	3.57185i	0.465015	−	0.465015i	0.900295	+	0.435280i	$0.143351\pi$
$60$	0.448318	−	5.92967i	0.0578776	−	0.765517i
$61$	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
$63$	−4.59311			−0.578677
$64$	7.30568			0.913209
$65$		0			0
$66$	−4.74023			−0.583482
$67$	−7.29829			−0.891628			−0.445814	−	0.895126i	$-0.647086\pi$
$67$	−7.29829			−0.891628			−0.445814	+	0.895126i	$0.647086\pi$
$68$	−4.89232	+	4.89232i	−0.593281	+	0.593281i
$69$	−10.7391			−1.29284
$70$	−1.43611	−	1.67103i	−0.171648	−	0.199726i
$71$	9.22988	−	9.22988i	1.09538	−	1.09538i	0.100442	−	0.994943i	$-0.467974\pi$
$71$	9.22988	−	9.22988i	1.09538	−	1.09538i	0.994943	−	0.100442i	$-0.0320257\pi$
$72$			14.4007i			1.69714i
$73$	−3.22747			−0.377746			−0.188873	−	0.982001i	$-0.560483\pi$
$73$	−3.22747			−0.377746			−0.188873	+	0.982001i	$0.560483\pi$
$74$			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	$-0.276861\pi$
$80$	−2.00261	+	1.72108i	−0.223899	+	0.192423i
$81$	0.578392			0.0642658
$82$	5.00872	−	5.00872i	0.553121	−	0.553121i
$83$		−	8.56854i		−	0.940519i	−0.882528	−	0.470260i	$-0.844160\pi$
$83$		−	8.56854i		−	0.940519i	0.882528	−	0.470260i	$-0.155840\pi$
$84$	−1.81198	−	1.81198i	−0.197703	−	0.197703i
$85$	1.22228	−	16.1664i	0.132575	−	1.75349i
$86$	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	−0.726273	−	0.687407i	$-0.758749\pi$
$89$	−0.366660	+	0.366660i	−0.0388659	+	0.0388659i	0.687407	+	0.726273i	$0.258749\pi$
$90$	−7.10435	−	8.26648i	−0.748864	−	0.871363i
$91$		0			0
$92$	−2.60014	−	2.60014i	−0.271084	−	0.271084i
$93$			0.495216i			0.0513516i
$94$			8.02328i			0.827538i
$95$	6.09502	+	0.460819i	0.625336	+	0.0472791i
$96$	−9.52707	+	9.52707i	−0.972353	+	0.972353i
$97$	−7.51320			−0.762850			−0.381425	−	0.924400i	$-0.624567\pi$
$97$	−7.51320			−0.762850			−0.381425	+	0.924400i	$0.624567\pi$
$98$	6.20885			0.627189
$99$	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	$-0.838725\pi$
$101$		−	9.75358i		−	0.970518i	0.874371	−	0.485259i	$-0.161275\pi$
$102$			20.6633i			2.04597i
$103$	−2.52321	−	2.52321i	−0.248619	−	0.248619i	0.571784	−	0.820404i	$-0.306251\pi$
$103$	−2.52321	−	2.52321i	−0.248619	−	0.248619i	−0.820404	+	0.571784i	$0.806251\pi$
$104$		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	0.944258	−	0.329206i	$-0.106781\pi$
$109$	6.42134	+	6.42134i	0.615053	+	0.615053i	−0.329206	+	0.944258i	$0.606781\pi$
$110$	3.79251	+	0.286736i	0.361602	+	0.0273392i
$111$	−8.04255	−	8.04255i	−0.763365	−	0.763365i
$112$			1.13788i			0.107520i
$113$	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
$115$	8.59204	+	0.649609i	0.801212	+	0.0605763i
$116$			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
$122$	2.13050			0.192886
$123$			19.3040i			1.74059i
$124$	−0.119901	+	0.119901i	−0.0107675	+	0.0107675i
$125$	−5.92947	−	9.47847i	−0.530348	−	0.847780i
$126$	−4.69699			−0.418442
$127$	−1.53806	+	1.53806i	−0.136480	+	0.136480i	−0.772046	−	0.635566i	$-0.780767\pi$
$127$	−1.53806	+	1.53806i	−0.136480	+	0.136480i	0.635566	+	0.772046i	$0.280767\pi$
$128$	−2.19816			−0.194292
$129$	−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	$0.500866\pi$
$132$	4.42333			0.385001
$133$	1.86251	−	1.86251i	0.161500	−	0.161500i
$134$	−7.46336			−0.644736
$135$	10.9784	+	0.830034i	0.944872	+	0.0714380i
$136$	−15.4886	+	15.4886i	−1.32814	+	1.32814i
$137$			4.41747i			0.377410i	0.982034	+	0.188705i	$0.0604289\pi$
$137$			4.41747i			0.377410i	−0.982034	+	0.188705i	$0.939571\pi$
$138$	−10.9820			−0.934850
$139$			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
$145$	−0.425955	−	0.495632i	−0.0353736	−	0.0411600i
$146$	−3.30046			−0.273148
$147$	−11.9647	+	11.9647i	−0.986833	+	0.986833i
$148$		−	3.89451i		−	0.320127i
$149$	3.06342	+	3.06342i	0.250965	+	0.250965i	0.821366	−	0.570401i	$-0.193212\pi$
$149$	3.06342	+	3.06342i	0.250965	+	0.250965i	−0.570401	+	0.821366i	$0.693212\pi$
$150$	8.44650	+	11.4764i	0.689654	+	0.937044i
$151$	−4.74990	−	4.74990i	−0.386542	−	0.386542i	0.486910	−	0.873452i	$-0.338124\pi$
$151$	−4.74990	−	4.74990i	−0.386542	−	0.386542i	−0.873452	+	0.486910i	$0.838124\pi$
$152$	−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	$0.446522\pi$
$158$		−	13.8918i		−	1.10517i
$159$		−	7.87680i		−	0.624671i
$160$	8.19861	−	7.04603i	0.648157	−	0.557037i
$161$	2.62554	−	2.62554i	0.206922	−	0.206922i
$162$	0.591474			0.0464706
$163$	−21.3852			−1.67502			−0.837508	−	0.546425i	$-0.815989\pi$
$163$	−21.3852			−1.67502			−0.837508	+	0.546425i	$0.815989\pi$
$164$	−4.67387	+	4.67387i	−0.364968	+	0.364968i
$165$	−7.86088	+	6.75578i	−0.611969	+	0.525936i
$166$		−	8.76234i		−	0.680090i
$167$			1.71444i			0.132667i	0.997797	+	0.0663337i	$0.0211302\pi$
$167$			1.71444i			0.132667i	−0.997797	+	0.0663337i	$0.978870\pi$
$168$	−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	0.169604	−	0.985512i	$-0.445751\pi$
$173$	−10.7316	−	10.7316i	−0.815908	−	0.815908i	−0.985512	+	0.169604i	$0.945751\pi$
$174$	0.588968	+	0.588968i	0.0446496	+	0.0446496i
$175$	−4.76310	−	0.724378i	−0.360057	−	0.0547578i
$176$	−1.38887	−	1.38887i	−0.104690	−	0.104690i
$177$			14.0776i			1.05814i
$178$	−0.374954	+	0.374954i	−0.0281040	+	0.0281040i
$179$	−2.75923			−0.206234			−0.103117	−	0.994669i	$-0.532882\pi$
$179$	−2.75923			−0.206234			−0.103117	+	0.994669i	$0.532882\pi$
$180$	6.62941	+	7.71384i	0.494127	+	0.574956i
$181$		−	10.3568i		−	0.769818i	−0.922954	−	0.384909i	$-0.874233\pi$
$181$		−	10.3568i		−	0.769818i	0.922954	−	0.384909i	$-0.125767\pi$
$182$		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
$187$	12.0596			0.881885
$188$		−	7.48690i		−	0.546038i
$189$	3.35477	−	3.35477i	0.244024	−	0.244024i
$190$	6.23287	+	0.471242i	0.452180	+	0.0341875i
$191$	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
$193$	−12.5715			−0.904917			−0.452459	−	0.891785i	$-0.649453\pi$
$193$	−12.5715			−0.904917			−0.452459	+	0.891785i	$0.649453\pi$
$194$	−7.68313			−0.551617
$195$		0			0
$196$	−5.79377			−0.413841
$197$	−14.2862			−1.01785			−0.508924	−	0.860812i	$-0.669956\pi$
$197$	−14.2862			−1.01785			−0.508924	+	0.860812i	$0.669956\pi$
$198$	5.73306	−	5.73306i	0.407431	−	0.407431i
$199$	14.7356			1.04458			0.522291	−	0.852768i	$-0.325078\pi$
$199$	14.7356			1.04458			0.522291	+	0.852768i	$0.325078\pi$
$200$	−2.27113	+	14.9336i	−0.160593	+	1.05597i
$201$	14.3822	−	14.3822i	1.01444	−	1.01444i
$202$		−	9.97419i		−	0.701781i
$203$	−0.281617			−0.0197656
$204$		−	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
$210$	6.12301	+	0.462936i	0.422528	+	0.0319456i
$211$	−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
$213$			36.3773i			2.49253i
$214$	−0.321422	−	0.321422i	−0.0219719	−	0.0219719i
$215$	17.7214	+	1.33985i	1.20859	+	0.0913767i
$216$	−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
$223$			7.06079i			0.472826i	0.971653	+	0.236413i	$0.0759718\pi$
$223$			7.06079i			0.472826i	−0.971653	+	0.236413i	$0.924028\pi$
$224$		−	4.65843i		−	0.311255i
$225$	−23.5628	−	3.58346i	−1.57085	−	0.238897i
$226$	1.39889	−	1.39889i	0.0930527	−	0.0930527i
$227$	17.1755			1.13998			0.569989	−	0.821652i	$-0.306948\pi$
$227$	17.1755			1.13998			0.569989	+	0.821652i	$0.306948\pi$
$228$	7.26960			0.481441
$229$	−8.90647	+	8.90647i	−0.588556	+	0.588556i	−0.937240	−	0.348684i	$-0.886629\pi$
$229$	−8.90647	+	8.90647i	−0.588556	+	0.588556i	0.348684	+	0.937240i	$0.386629\pi$
$230$	8.78637	+	0.664302i	0.579356	+	0.0438028i
$231$			4.46654i			0.293876i
$232$			0.882948i			0.0579684i
$233$	17.5822	+	17.5822i	1.15185	+	1.15185i	0.986182	+	0.165666i	$0.0529773\pi$
$233$	17.5822	+	17.5822i	1.15185	+	1.15185i	0.165666	+	0.986182i	$0.447023\pi$
$234$		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	0.631122	−	0.775684i	$-0.282595\pi$
$239$	−2.23488	−	2.23488i	−0.144562	−	0.144562i	−0.775684	+	0.631122i	$0.782595\pi$
$240$	0.554797	−	7.33801i	0.0358120	−	0.473666i
$241$	12.7412	+	12.7412i	0.820734	+	0.820734i	0.986213	−	0.165479i	$-0.0529171\pi$
$241$	12.7412	+	12.7412i	0.820734	+	0.820734i	−0.165479	+	0.986213i	$0.552917\pi$
$242$		−	8.41971i		−	0.541239i
$243$	−11.5846	+	11.5846i	−0.743150	+	0.743150i
$244$	−1.98807			−0.127273
$245$	10.2963	−	8.84886i	0.657810	−	0.565333i
$246$			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	$0.145369\pi$
$251$			13.9729i			0.881960i	−0.897517	+	0.440980i	$0.854631\pi$
$252$	4.38299			0.276102
$253$			6.40937i			0.402954i
$254$	−1.57284	+	1.57284i	−0.0986889	+	0.0986889i
$255$	29.4493	+	34.2666i	1.84419	+	2.14586i
$256$	−16.8592			−1.05370
$257$	−16.3892	+	16.3892i	−1.02233	+	1.02233i	−0.0225869	+	0.999745i	$0.507190\pi$
$257$	−16.3892	+	16.3892i	−1.02233	+	1.02233i	−0.999745	+	0.0225869i	$0.992810\pi$
$258$	−22.6508			−1.41018
$259$	3.93255			0.244357
$260$		0			0
$261$	−1.39314			−0.0862334
$262$	−0.0636572			−0.00393276
$263$	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
$265$	−0.476468	+	6.30199i	−0.0292692	+	0.387128i
$266$	1.90463	−	1.90463i	0.116780	−	0.116780i
$267$		−	1.44510i		−	0.0884388i
$268$	6.96441			0.425419
$269$			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	$-0.258659\pi$
$271$	−0.633254	−	0.633254i	−0.0384674	−	0.0384674i	−0.726079	+	0.687611i	$0.758659\pi$
$272$	−6.05429	+	6.05429i	−0.367095	+	0.367095i
$273$		0			0
$274$			4.51738i			0.272905i
$275$	6.69791	−	4.92959i	0.403899	−	0.297265i
$276$	10.2478			0.616847
$277$	−6.75631	+	6.75631i	−0.405948	+	0.405948i	−0.880323	−	0.474375i	$-0.842674\pi$
$277$	−6.75631	+	6.75631i	−0.405948	+	0.405948i	0.474375	+	0.880323i	$0.342674\pi$
$278$			14.0596i			0.843236i
$279$	−0.598939	−	0.598939i	−0.0358575	−	0.0358575i
$280$	4.24263	+	4.93664i	0.253546	+	0.295021i
$281$	−5.58408	−	5.58408i	−0.333118	−	0.333118i	0.520651	−	0.853769i	$-0.325689\pi$
$281$	−5.58408	−	5.58408i	−0.333118	−	0.333118i	−0.853769	+	0.520651i	$0.825689\pi$
$282$	−15.8109	−	15.8109i	−0.941525	−	0.941525i
$283$	14.9230	+	14.9230i	0.887078	+	0.887078i	0.994241	−	0.107163i	$-0.0341768\pi$
$283$	14.9230	+	14.9230i	0.887078	+	0.887078i	−0.107163	+	0.994241i	$0.534177\pi$
$284$	−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
$288$		−	23.0450i		−	1.35794i
$289$		−	35.5694i		−	2.09232i
$290$	−0.435589	−	0.506842i	−0.0255787	−	0.0297628i
$291$	14.8057	−	14.8057i	0.867927	−	0.867927i
$292$	3.07982			0.180233
$293$	−4.02159			−0.234944			−0.117472	−	0.993076i	$-0.537479\pi$
$293$	−4.02159			−0.234944			−0.117472	+	0.993076i	$0.537479\pi$
$294$	−12.2353	+	12.2353i	−0.713579	+	0.713579i
$295$	0.851553	−	11.2630i	0.0495793	−	0.655760i
$296$		−	12.3296i		−	0.716645i
$297$			8.18953i			0.475205i
$298$	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
$305$	3.53307	−	3.03638i	0.202303	−	0.173863i
$306$	−24.9912	−	24.9912i	−1.42865	−	1.42865i
$307$		−	24.2191i		−	1.38226i	−0.722732	−	0.691128i	$-0.757114\pi$
$307$		−	24.2191i		−	1.38226i	0.722732	−	0.691128i	$-0.242886\pi$
$308$	−1.08143	+	1.08143i	−0.0616204	+	0.0616204i
$309$	9.94462			0.565730
$310$	0.0306332	−	0.405169i	0.00173985	−	0.0230121i
$311$			7.87243i			0.446405i	0.974772	+	0.223202i	$0.0716511\pi$
$311$			7.87243i			0.446405i	−0.974772	+	0.223202i	$0.928349\pi$
$312$		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
$317$	−22.9255			−1.28762			−0.643812	−	0.765184i	$-0.722648\pi$
$317$	−22.9255			−1.28762			−0.643812	+	0.765184i	$0.722648\pi$
$318$		−	8.05496i		−	0.451700i
$319$	0.343736	−	0.343736i	0.0192455	−	0.0192455i
$320$	12.3893	−	10.6476i	0.692581	−	0.595216i
$321$	1.23879			0.0691423
$322$	2.68493	−	2.68493i	0.149625	−	0.149625i
$323$	19.8196			1.10279
$324$	−0.551932			−0.0306629
$325$		0			0
$326$	−21.8689			−1.21120
$327$	−25.3081			−1.39954
$328$	−14.7970	+	14.7970i	−0.817029	+	0.817029i
$329$	7.56003			0.416798
$330$	−8.03868	+	6.90858i	−0.442515	+	0.380305i
$331$	−23.7270	+	23.7270i	−1.30416	+	1.30416i	−0.378594	+	0.925563i	$0.623592\pi$
$331$	−23.7270	+	23.7270i	−1.30416	+	1.30416i	−0.925563	+	0.378594i	$0.876408\pi$
$332$			8.17655i			0.448747i
$333$	19.4541			1.06608
$334$			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	−0.189126	−	0.981953i	$-0.560566\pi$
$337$	14.5544	−	14.5544i	0.792826	−	0.792826i	0.981953	+	0.189126i	$0.0605656\pi$
$338$		0			0
$339$			5.39143i			0.292822i
$340$	−1.16636	+	15.4268i	−0.0632548	+	0.836638i
$341$	0.295557			0.0160053
$342$	9.42210	−	9.42210i	0.509489	−	0.509489i
$343$		−	12.5954i		−	0.680087i
$344$	−16.9784	−	16.9784i	−0.915416	−	0.915416i
$345$	−18.2118	+	15.6516i	−0.980492	+	0.842652i
$346$	−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	−0.875790	−	0.482692i	$-0.839659\pi$
$349$	−7.34369	+	7.34369i	−0.393099	+	0.393099i	0.482692	+	0.875790i	$0.339659\pi$
$350$	−4.87083	−	0.740762i	−0.260357	−	0.0395954i
$351$		0			0
$352$	5.68599	+	5.68599i	0.303064	+	0.303064i
$353$			4.30033i			0.228884i	0.993430	+	0.114442i	$0.0365080\pi$
$353$			4.30033i			0.228884i	−0.993430	+	0.114442i	$0.963492\pi$
$354$			14.3960i			0.765138i
$355$	2.20046	−	29.1044i	0.116788	−	1.54470i
$356$	0.349887	−	0.349887i	0.0185440	−	0.0185440i
$357$	19.4702			1.03047
$358$	−2.82163			−0.149128
$359$	−10.4273	+	10.4273i	−0.550333	+	0.550333i	−0.926537	−	0.376204i	$-0.877229\pi$
$359$	−10.4273	+	10.4273i	−0.550333	+	0.550333i	0.376204	+	0.926537i	$0.377229\pi$
$360$	20.9881	+	24.4213i	1.10617	+	1.28711i
$361$		−	11.5277i		−	0.606720i
$362$		−	10.5911i		−	0.556656i
$363$	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
$370$	6.08264	+	7.07763i	0.316221	+	0.367949i
$371$	1.92575	+	1.92575i	0.0999801	+	0.0999801i
$372$		−	0.472562i		−	0.0245012i
$373$	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
$375$	30.3633	+	6.99375i	1.56795	+	0.361156i
$376$		−	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	0.329246	−	0.944244i	$-0.393205\pi$
$379$	−11.9727	−	11.9727i	−0.614998	−	0.614998i	−0.944244	+	0.329246i	$0.893205\pi$
$380$	−5.81619	−	0.439738i	−0.298364	−	0.0225581i
$381$		−	6.06187i		−	0.310559i
$382$	18.9999			0.972119
$383$			6.60394i			0.337446i	0.985664	+	0.168723i	$0.0539643\pi$
$383$			6.60394i			0.337446i	−0.985664	+	0.168723i	$0.946036\pi$
$384$	4.33176	−	4.33176i	0.221054	−	0.221054i
$385$	0.270181	−	3.57354i	0.0137697	−	0.182124i
$386$	−12.8559			−0.654346
$387$	26.7891	−	26.7891i	1.36177	−	1.36177i
$388$	7.16950			0.363976
$389$	−33.6949			−1.70840			−0.854199	−	0.519946i	$-0.825952\pi$
$389$	−33.6949			−1.70840			−0.854199	+	0.519946i	$0.825952\pi$
$390$		0			0
$391$	27.9393			1.41295
$392$	−18.3425			−0.926437
$393$	0.122670	−	0.122670i	0.00618789	−	0.00618789i
$394$	−14.6093			−0.736005
$395$	−19.7986	−	23.0372i	−0.996175	−	1.15913i
$396$	−5.34979	+	5.34979i	−0.268837	+	0.268837i
$397$		−	5.82089i		−	0.292142i	−0.989274	−	0.146071i	$-0.953337\pi$
$397$		−	5.82089i		−	0.292142i	0.989274	−	0.146071i	$-0.0466628\pi$
$398$	15.0689			0.755337
$399$			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	$-0.247902\pi$
$401$	0.186676	+	0.186676i	0.00932213	+	0.00932213i	−0.702430	+	0.711752i	$0.747902\pi$
$402$	14.7075	−	14.7075i	0.733544	−	0.733544i
$403$		0			0
$404$			9.30738i			0.463060i
$405$	0.980861	−	0.842969i	0.0487394	−	0.0418875i
$406$	−0.287987			−0.0142925
$407$	−4.79999	+	4.79999i	−0.237927	+	0.237927i
$408$		−	61.0446i		−	3.02216i
$409$	−26.2788	−	26.2788i	−1.29940	−	1.29940i	−0.928785	−	0.370619i	$-0.879145\pi$
$409$	−26.2788	−	26.2788i	−1.29940	−	1.29940i	−0.370619	−	0.928785i	$-0.620855\pi$
$410$	1.19411	−	15.7939i	0.0589730	−	0.780005i
$411$	−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
$418$			4.64951i			0.227415i
$419$			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	0.0521230	−	0.998641i	$-0.483401\pi$
$421$	21.5599	−	21.5599i	1.05076	−	1.05076i	0.998641	−	0.0521230i	$-0.0165988\pi$
$422$	−8.72506			−0.424729
$423$	37.3990			1.81840
$424$	6.03777	−	6.03777i	0.293220	−	0.293220i
$425$	−21.4887	−	29.1971i	−1.04236	−	1.41627i
$426$			37.2001i			1.80235i
$427$		−	2.00748i		−	0.0971490i
$428$	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	$-0.785324\pi$
$431$	−3.25153	+	3.25153i	−0.156621	+	0.156621i	0.624447	+	0.781067i	$0.285324\pi$
$432$	−4.11140	−	4.11140i	−0.197810	−	0.197810i
$433$	−2.83031	−	2.83031i	−0.136016	−	0.136016i	0.635821	−	0.771837i	$-0.280662\pi$
$433$	−2.83031	−	2.83031i	−0.136016	−	0.136016i	−0.771837	+	0.635821i	$0.780662\pi$
$434$	−0.123811	−	0.123811i	−0.00594311	−	0.00594311i
$435$	1.81610	+	0.137308i	0.0870755	+	0.00658343i
$436$	−6.12758	−	6.12758i	−0.293458	−	0.293458i
$437$			10.5336i			0.503890i
$438$	6.50398	−	6.50398i	0.310772	−	0.310772i
$439$	22.7237			1.08454			0.542271	−	0.840203i	$-0.317564\pi$
$439$	22.7237			1.08454			0.542271	+	0.840203i	$0.317564\pi$
$440$	−11.2040	−	0.847092i	−0.534132	−	0.0403835i
$441$		−	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
$447$	−12.0737			−0.571067
$448$		−	7.03956i		−	0.332588i
$449$	−22.7499	+	22.7499i	−1.07364	+	1.07364i	−0.0765713	+	0.997064i	$0.524397\pi$
$449$	−22.7499	+	22.7499i	−1.07364	+	1.07364i	−0.997064	+	0.0765713i	$0.975603\pi$
$450$	−24.0957	−	3.66451i	−1.13588	−	0.172746i
$451$	11.5211			0.542509
$452$	−1.30537	+	1.30537i	−0.0613994	+	0.0613994i
$453$	18.7206			0.879569
$454$	17.5640			0.824318
$455$		0			0
$456$	23.0149			1.07777
$457$	28.3674			1.32697			0.663486	−	0.748189i	$-0.269076\pi$
$457$	28.3674			1.32697			0.663486	+	0.748189i	$0.269076\pi$
$458$	−9.10792	+	9.10792i	−0.425585	+	0.425585i
$459$	35.6993			1.66630
$460$	−8.19898	−	0.619891i	−0.382279	−	0.0289026i
$461$	−8.13851	+	8.13851i	−0.379048	+	0.379048i	−0.870759	−	0.491710i	$-0.836372\pi$
$461$	−8.13851	+	8.13851i	−0.379048	+	0.379048i	0.491710	+	0.870759i	$0.336372\pi$
$462$			4.56756i			0.212502i
$463$	−29.9456			−1.39169			−0.695845	−	0.718192i	$-0.744970\pi$
$463$	−29.9456			−1.39169			−0.695845	+	0.718192i	$0.744970\pi$
$464$			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	−0.973831	−	0.227274i	$-0.927019\pi$
$467$	−16.1332	+	16.1332i	−0.746557	+	0.746557i	0.227274	+	0.973831i	$0.427019\pi$
$468$		0			0
$469$			7.03244i			0.324728i
$470$	11.6934	+	13.6062i	0.539377	+	0.627608i
$471$	−56.9463			−2.62395
$472$	−10.7908	+	10.7908i	−0.496688	+	0.496688i
$473$			13.2196i			0.607837i
$474$	27.3755	+	27.3755i	1.25740	+	1.25740i
$475$	11.0078	−	8.10162i	0.505073	−	0.371728i
$476$	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	−0.300751	+	0.953703i	$0.597237\pi$
$479$	−27.4551	+	27.4551i	−1.25445	+	1.25445i	−0.953703	+	0.300751i	$0.902763\pi$
$480$	−2.27132	+	30.0415i	−0.103671	+	1.37120i
$481$		0			0
$482$	13.0294	+	13.0294i	0.593473	+	0.593473i
$483$			10.3479i			0.470847i
$484$			7.85683i			0.357129i
$485$	−12.7412	+	10.9500i	−0.578548	+	0.497214i
$486$	−11.8466	+	11.8466i	−0.537372	+	0.537372i
$487$	−28.9437			−1.31156			−0.655782	−	0.754951i	$-0.727661\pi$
$487$	−28.9437			−1.31156			−0.655782	+	0.754951i	$0.727661\pi$
$488$	−6.29402			−0.284917
$489$	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	$-0.947512\pi$
$491$		−	7.27465i		−	0.328300i	0.986435	−	0.164150i	$-0.0524882\pi$
$492$		−	18.4209i		−	0.830480i
$493$	−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	0.795652	−	0.605754i	$-0.207128\pi$
$499$	4.24201	+	4.24201i	0.189899	+	0.189899i	−0.605754	+	0.795652i	$0.707128\pi$
$500$	5.65822	+	9.04486i	0.253043	+	0.404498i
$501$	−3.37852	−	3.37852i	−0.150941	−	0.150941i
$502$			14.2889i			0.637745i
$503$	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
$505$	−14.2152	−	16.5405i	−0.632569	−	0.736044i
$506$			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	0.970658	−	0.240466i	$-0.0773003\pi$
$509$	16.4739	+	16.4739i	0.730191	+	0.730191i	−0.240466	+	0.970658i	$0.577300\pi$
$510$	30.1154	+	35.0417i	1.33353	+	1.55167i
$511$			3.10990i			0.137574i
$512$	−12.8442			−0.567640
$513$			13.4592i			0.594240i
$514$	−16.7599	+	16.7599i	−0.739248	+	0.739248i
$515$	−7.95639	−	0.601550i	−0.350600	−	0.0265075i
$516$	21.1366			0.930486
$517$	−9.22762	+	9.22762i	−0.405830	+	0.405830i
$518$	4.02150			0.176694
$519$	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	$0.592303\pi$
$522$	−1.42465			−0.0623554
$523$	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
$525$	10.8138	−	7.95882i	0.471952	−	0.347351i
$526$	0.940790	−	0.940790i	0.0410204	−	0.0410204i
$527$		−	1.28837i		−	0.0561225i
$528$	5.47391			0.238221
$529$		−	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
$535$	−0.991116	−	0.0749342i	−0.0428497	−	0.00323969i
$536$	22.0487			0.952357
$537$	5.43741	−	5.43741i	0.234641	−	0.234641i
$538$			8.11728i			0.349961i
$539$	7.14084	+	7.14084i	0.307578	+	0.307578i
$540$	−10.4762	−	0.792062i	−0.450824	−	0.0340849i
$541$	10.9728	+	10.9728i	0.471756	+	0.471756i	0.902483	−	0.430727i	$-0.141743\pi$
$541$	10.9728	+	10.9728i	0.471756	+	0.471756i	−0.430727	+	0.902483i	$0.641743\pi$
$542$	−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	$0.962109\pi$
$548$		−	4.21538i		−	0.180072i
$549$		−	9.93091i		−	0.423841i
$550$	6.84940	−	5.04108i	0.292059	−	0.214952i
$551$	0.564920	−	0.564920i	0.0240664	−	0.0240664i
$552$	32.4436			1.38089
$553$	−13.0897			−0.556631
$554$	−6.90913	+	6.90913i	−0.293541	+	0.293541i
$555$	−25.3604	−	1.91740i	−1.07649	−	0.0813889i
$556$		−	13.1196i		−	0.556397i
$557$			13.5803i			0.575415i	0.957718	+	0.287708i	$0.0928932\pi$
$557$			13.5803i			0.575415i	−0.957718	+	0.287708i	$0.907107\pi$
$558$	−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	0.775677	−	0.631130i	$-0.217409\pi$
$563$	3.42976	+	3.42976i	0.144547	+	0.144547i	−0.631130	+	0.775677i	$0.717409\pi$
$564$	14.7539	+	14.7539i	0.621251	+	0.621251i
$565$	0.326128	−	4.31352i	0.0137203	−	0.181471i
$566$	15.2605	+	15.2605i	0.641446	+	0.641446i
$567$		−	0.557323i		−	0.0234054i
$568$	−27.8841	+	27.8841i	−1.16999	+	1.16999i
$569$	0.248793			0.0104299			0.00521497	−	0.999986i	$-0.498340\pi$
$569$	0.248793			0.0104299			0.00521497	+	0.999986i	$0.498340\pi$
$570$	−13.2113	+	11.3540i	−0.553361	+	0.475568i
$571$			7.72842i			0.323424i	0.986838	+	0.161712i	$0.0517016\pi$
$571$			7.72842i			0.323424i	−0.986838	+	0.161712i	$0.948298\pi$
$572$		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
$577$	12.1339			0.505141			0.252570	−	0.967578i	$-0.418724\pi$
$577$	12.1339			0.505141			0.252570	+	0.967578i	$0.418724\pi$
$578$		−	36.3739i		−	1.51295i
$579$	24.7738	−	24.7738i	1.02956	−	1.02956i
$580$	0.406469	+	0.472958i	0.0168777	+	0.0196385i
$581$	−8.25642			−0.342534
$582$	15.1406	−	15.1406i	0.627598	−	0.627598i
$583$	−4.70107			−0.194698
$584$	9.75040			0.403475
$585$		0			0
$586$	−4.11255			−0.169888
$587$	36.5294			1.50773			0.753865	−	0.657030i	$-0.228187\pi$
$587$	36.5294			1.50773			0.753865	+	0.657030i	$0.228187\pi$
$588$	11.4174	−	11.4174i	0.470844	−	0.470844i
$589$	0.485739			0.0200145
$590$	0.870813	−	11.5178i	0.0358508	−	0.474180i
$591$	28.1527	−	28.1527i	1.15805	−	1.15805i
$592$		−	4.81949i		−	0.198080i
$593$	16.6936			0.685525			0.342762	−	0.939422i	$-0.388637\pi$
$593$	16.6936			0.685525			0.342762	+	0.939422i	$0.388637\pi$
$594$			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	$-0.0872847\pi$
$600$	−24.9531	−	33.9042i	−1.01871	−	1.38413i
$601$	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
$603$			34.7891i			1.41672i
$604$	4.53261	+	4.53261i	0.184429	+	0.184429i
$605$	−11.9998	−	13.9627i	−0.487860	−	0.567664i
$606$	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
$613$			27.9096i			1.12726i	0.826028	+	0.563630i	$0.190596\pi$
$613$			27.9096i			1.12726i	−0.826028	+	0.563630i	$0.809404\pi$
$614$		−	24.7669i		−	0.999510i
$615$	28.1344	+	32.7366i	1.13449	+	1.32007i
$616$	−3.42371	+	3.42371i	−0.137945	+	0.137945i
$617$	−4.38264			−0.176439			−0.0882193	−	0.996101i	$-0.528118\pi$
$617$	−4.38264			−0.176439			−0.0882193	+	0.996101i	$0.528118\pi$
$618$	10.1695			0.409079
$619$	8.67268	−	8.67268i	0.348584	−	0.348584i	−0.510998	−	0.859582i	$-0.670724\pi$
$619$	8.67268	−	8.67268i	0.348584	−	0.348584i	0.859582	+	0.510998i	$0.170724\pi$
$620$	−0.0285853	+	0.378082i	−0.00114801	+	0.0151842i
$621$			18.9732i			0.761370i
$622$			8.05049i			0.322795i
$623$	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
$630$	−7.96536	+	6.84557i	−0.317348	+	0.272734i
$631$	17.9168	+	17.9168i	0.713256	+	0.713256i	0.967215	−	0.253959i	$-0.0817328\pi$
$631$	17.9168	+	17.9168i	0.713256	+	0.713256i	−0.253959	+	0.967215i	$0.581733\pi$
$632$			41.0398i			1.63248i
$633$	16.8136	−	16.8136i	0.668279	−	0.668279i
$634$	−23.4440			−0.931081
$635$	−0.366682	+	4.84992i	−0.0145513	+	0.192463i
$636$			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	$-0.989714\pi$
$641$		−	1.63592i		−	0.0646150i	0.999478	−	0.0323075i	$-0.0102856\pi$
$642$	1.26681			0.0499968
$643$		−	39.6687i		−	1.56438i	−0.623039	−	0.782191i	$-0.714102\pi$
$643$		−	39.6687i		−	1.56438i	0.623039	−	0.782191i	$-0.285898\pi$
$644$	−2.50543	+	2.50543i	−0.0987278	+	0.0987278i
$645$	−37.5627	+	32.2820i	−1.47903	+	1.27110i
$646$	20.2678			0.797428
$647$	−10.5113	+	10.5113i	−0.413244	+	0.413244i	−0.882867	−	0.469623i	$-0.844390\pi$
$647$	−10.5113	+	10.5113i	−0.413244	+	0.413244i	0.469623	+	0.882867i	$0.344390\pi$
$648$	−1.74736			−0.0686429
$649$	8.40185			0.329801
$650$		0			0
$651$	0.477178			0.0187021
$652$	20.4069			0.799195
$653$	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
$655$	−0.105565	+	0.0907243i	−0.00412476	+	0.00354489i
$656$	−5.78396	+	5.78396i	−0.225826	+	0.225826i
$657$			15.3845i			0.600206i
$658$	7.73102			0.301387
$659$		−	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	0.996801	+	0.0799231i	$0.0254675\pi$
$661$	27.6825	+	27.6825i	1.07672	+	1.07672i	0.0799231	+	0.996801i	$0.474533\pi$
$662$	−24.2637	+	24.2637i	−0.943036	+	0.943036i
$663$		0			0
$664$			25.8862i			1.00458i
$665$	0.444034	−	5.87300i	0.0172189	−	0.227745i
$666$	19.8941			0.770881
$667$	0.796357	−	0.796357i	0.0308351	−	0.0308351i
$668$		−	1.63601i		−	0.0632991i
$669$	−13.9142	−	13.9142i	−0.537954	−	0.537954i
$670$	−12.6567	+	10.8774i	−0.488970	+	0.420229i
$671$	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	0.832598	−	0.553878i	$-0.186852\pi$
$673$	7.23064	+	7.23064i	0.278721	+	0.278721i	−0.553878	+	0.832598i	$0.686852\pi$
$674$	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	$0.448167\pi$
$678$			5.51338i			0.211740i
$679$			7.23953i			0.277828i
$680$	−3.69259	+	48.8399i	−0.141604	+	1.87292i
$681$	−33.8465	+	33.8465i	−1.29700	+	1.29700i
$682$	0.302242			0.0115735
$683$	−20.0207			−0.766070			−0.383035	−	0.923734i	$-0.625121\pi$
$683$	−20.0207			−0.766070			−0.383035	+	0.923734i	$0.625121\pi$
$684$	−8.79221	+	8.79221i	−0.336178	+	0.336178i
$685$	6.43817	+	7.49133i	0.245990	+	0.286229i
$686$		−	12.8803i		−	0.491771i
$687$		−	35.1027i		−	1.33925i
$688$	−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	$-0.514965\pi$
$691$	25.0225	−	25.0225i	0.951900	−	0.951900i	0.998895	+	0.0469952i	$0.0149645\pi$
$692$	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
$695$	20.0377	+	23.3155i	0.760073	+	0.884406i
$696$	−1.73996	−	1.73996i	−0.0659531	−	0.0659531i
$697$		−	50.2221i		−	1.90230i
$698$	−7.50978	+	7.50978i	−0.284250	+	0.284250i
$699$	−69.2959			−2.62101
$700$	4.54520	+	0.691240i	0.171793	+	0.0261264i
$701$		−	37.1781i		−	1.40420i	−0.712080	−	0.702098i	$-0.752247\pi$
$701$		−	37.1781i		−	1.40420i	0.712080	−	0.702098i	$-0.247753\pi$
$702$		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
$707$	−9.39830			−0.353459
$708$		−	13.4336i		−	0.504864i
$709$	34.0774	−	34.0774i	1.27980	−	1.27980i	0.339026	−	0.940777i	$-0.389903\pi$
$709$	34.0774	−	34.0774i	1.27980	−	1.27980i	0.940777	−	0.339026i	$-0.110097\pi$
$710$	2.25023	−	29.7626i	0.0844497	−	1.11697i
$711$	−64.7540			−2.42846
$712$	1.10771	−	1.10771i	0.0415131	−	0.0415131i
$713$	0.684738			0.0256436
$714$	19.9106			0.745135
$715$		0			0
$716$	2.63300			0.0983998
$717$	8.80822			0.328949
$718$	−10.6632	+	10.6632i	−0.397946	+	0.397946i
$719$	−33.3985			−1.24555			−0.622777	−	0.782400i	$-0.713996\pi$
$719$	−33.3985			−1.24555			−0.622777	+	0.782400i	$0.713996\pi$
$720$	8.20394	+	9.54594i	0.305743	+	0.355756i
$721$	−2.43130	+	2.43130i	−0.0905464	+	0.0905464i
$722$		−	11.7884i		−	0.438719i
$723$	−50.2164			−1.86757
$724$			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	−0.993232	−	0.116149i	$-0.962945\pi$
$727$	−23.6487	+	23.6487i	−0.877083	+	0.877083i	0.116149	+	0.993232i	$0.462945\pi$
$728$		0			0
$729$		−	43.9226i		−	1.62676i
$730$	−5.59707	+	4.81021i	−0.207157	+	0.178034i
$731$	57.6260			2.13137
$732$	3.91774	−	3.91774i	0.144804	−	0.144804i
$733$		−	14.7049i		−	0.543138i	−0.962419	−	0.271569i	$-0.912458\pi$
$733$		−	14.7049i		−	0.543138i	0.962419	−	0.271569i	$-0.0875424\pi$
$734$	8.26018	+	8.26018i	0.304889	+	0.304889i
$735$	−2.85247	+	37.7281i	−0.105215	+	1.39162i
$736$	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	−0.922084	−	0.386989i	$-0.873515\pi$
$739$	−14.5463	+	14.5463i	−0.535095	+	0.535095i	0.386989	+	0.922084i	$0.373515\pi$
$740$	−5.67600	−	6.60447i	−0.208654	−	0.242785i
$741$		0			0
$742$	1.96931	+	1.96931i	0.0722956	+	0.0722956i
$743$		−	44.6408i		−	1.63771i	−0.573999	−	0.818856i	$-0.694609\pi$
$743$		−	44.6408i		−	1.63771i	0.573999	−	0.818856i	$-0.305391\pi$
$744$		−	1.49608i		−	0.0548491i
$745$	9.65982	+	0.730339i	0.353908	+	0.0267576i
$746$	20.3603	−	20.3603i	0.745443	−	0.745443i
$747$	−40.8440			−1.49440
$748$	−11.5079			−0.420771
$749$	−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	$-0.896065\pi$
$751$		−	17.5799i		−	0.641500i	0.947164	−	0.320750i	$-0.103935\pi$
$752$		−	9.26510i		−	0.337863i
$753$	−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
$760$	−18.4135	−	1.39217i	−0.667927	−	0.0504993i
$761$	8.28144	+	8.28144i	0.300202	+	0.300202i	0.841093	−	0.540891i	$-0.181913\pi$
$761$	8.28144	+	8.28144i	0.300202	+	0.300202i	−0.540891	+	0.841093i	$0.681913\pi$
$762$		−	6.19897i		−	0.224565i
$763$	6.18743	−	6.18743i	0.224000	−	0.224000i
$764$	−17.7297			−0.641438
$765$	−77.0611	−	5.82628i	−2.78615	−	0.210650i
$766$			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	0.422618	−	0.906308i	$-0.361111\pi$
$769$	−13.4131	−	13.4131i	−0.483689	−	0.483689i	−0.906308	+	0.422618i	$0.861111\pi$
$770$	0.276292	−	3.65437i	0.00995686	−	0.131694i
$771$		−	64.5941i		−	2.32630i
$772$	11.9964			0.431760
$773$			16.4099i			0.590224i	0.955463	+	0.295112i	$0.0953570\pi$
$773$			16.4099i			0.590224i	−0.955463	+	0.295112i	$0.904643\pi$
$774$	27.3950	−	27.3950i	0.984694	−	0.984694i
$775$	−0.526647	−	0.715564i	−0.0189177	−	0.0257038i
$776$	22.6979			0.814808
$777$	−7.74959	+	7.74959i	−0.278015	+	0.278015i
$778$	−34.4570			−1.23534
$779$	18.9346			0.678403
$780$		0			0
$781$	21.7109			0.776876
$782$	28.5712			1.02170
$783$	1.01754	−	1.01754i	0.0363639	−	0.0363639i
$784$	−7.16984			−0.256066
$785$	45.5610	+	3.44468i	1.62614	+	0.122946i
$786$	0.125445	−	0.125445i	0.00447446	−	0.00447446i
$787$			13.6002i			0.484794i	0.970177	+	0.242397i	$0.0779336\pi$
$787$			13.6002i			0.484794i	−0.970177	+	0.242397i	$0.922066\pi$
$788$	13.6326			0.485642
$789$			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
$795$	−11.4799	−	13.3578i	−0.407151	−	0.473753i
$796$	−14.0615			−0.498397
$797$	21.1671	−	21.1671i	0.749776	−	0.749776i	−0.224661	−	0.974437i	$-0.572127\pi$
$797$	21.1671	−	21.1671i	0.749776	−	0.749776i	0.974437	+	0.224661i	$0.0721274\pi$
$798$			7.50664i			0.265732i
$799$	40.2244	+	40.2244i	1.42304	+	1.42304i
$800$	3.63442	−	23.8979i	0.128496	−	0.844919i
$801$	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
$808$			29.4663i			1.03662i
$809$		−	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	$-0.882950\pi$
$811$	−16.3366	+	16.3366i	−0.573657	+	0.573657i	0.359492	+	0.933148i	$0.382950\pi$
$812$	0.268734			0.00943071
$813$	2.49581			0.0875320
$814$	−4.90856	+	4.90856i	−0.172045	+	0.172045i
$815$	−36.2659	+	31.1675i	−1.27034	+	1.09175i
$816$		−	23.8615i		−	0.835319i
$817$			21.7260i			0.760096i
$818$	−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	−0.142305	+	0.989823i	$0.545451\pi$
$821$	−32.4390	+	32.4390i	−1.13213	+	1.13213i	−0.989823	+	0.142305i	$0.954549\pi$
$822$	−8.90207	−	8.90207i	−0.310495	−	0.310495i
$823$	−12.5333	−	12.5333i	−0.436885	−	0.436885i	0.454077	−	0.890962i	$-0.349969\pi$
$823$	−12.5333	−	12.5333i	−0.436885	−	0.436885i	−0.890962	+	0.454077i	$0.849969\pi$
$824$	7.62280	+	7.62280i	0.265553	+	0.265553i
$825$	−3.48471	+	22.9135i	−0.121322	+	0.797744i
$826$	−3.51959	−	3.51959i	−0.122462	−	0.122462i
$827$		−	5.79276i		−	0.201434i	−0.994915	−	0.100717i	$-0.967886\pi$
$827$		−	5.79276i		−	0.201434i	0.994915	−	0.100717i	$-0.0321137\pi$
$828$	−12.3942	+	12.3942i	−0.430729	+	0.430729i
$829$	33.7598			1.17252			0.586262	−	0.810121i	$-0.300599\pi$
$829$	33.7598			1.17252			0.586262	+	0.810121i	$0.300599\pi$
$830$	−12.7705	−	14.8595i	−0.443272	−	0.515782i
$831$		−	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
$837$	0.874920			0.0302417
$838$			34.6830i			1.19811i
$839$	−27.7173	+	27.7173i	−0.956909	+	0.956909i	−0.999109	−	0.0422005i	$-0.986563\pi$
$839$	−27.7173	+	27.7173i	−0.956909	+	0.956909i	0.0422005	+	0.999109i	$0.486563\pi$
$840$	−18.0889	−	1.36763i	−0.624127	−	0.0471877i
$841$	28.9146			0.997055
$842$	22.0475	−	22.0475i	0.759807	−	0.759807i
$843$	22.0083			0.758005
$844$	8.14177			0.280251
$845$		0			0
$846$	38.2449			1.31489
$847$	−7.93357			−0.272601
$848$	2.36008	−	2.36008i	0.0810455	−	0.0810455i
$849$	−58.8152			−2.01853
$850$	−21.9748	−	29.8575i	−0.753728	−	1.02410i
$851$	−11.1205	+	11.1205i	−0.381205	+	0.381205i
$852$		−	34.7131i		−	1.18925i
$853$	−40.6417			−1.39154			−0.695772	−	0.718262i	$-0.744938\pi$
$853$	−40.6417			−1.39154			−0.695772	+	0.718262i	$0.744938\pi$
$854$		−	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	−0.0674695	−	0.997721i	$-0.521493\pi$
$857$	27.2327	−	27.2327i	0.930252	−	0.930252i	0.997721	+	0.0674695i	$0.0214925\pi$
$858$		0			0
$859$		−	44.5502i		−	1.52003i	−0.649904	−	0.760016i	$-0.725191\pi$
$859$		−	44.5502i		−	1.52003i	0.649904	−	0.760016i	$-0.274809\pi$
$860$	−16.9107	−	1.27855i	−0.576651	−	0.0435982i
$861$	18.6009			0.633916
$862$	−3.32507	+	3.32507i	−0.113252	+	0.113252i
$863$			55.4497i			1.88753i	0.330615	+	0.943766i	$0.392744\pi$
$863$			55.4497i			1.88753i	−0.330615	+	0.943766i	$0.607256\pi$
$864$	16.8319	+	16.8319i	0.572632	+	0.572632i
$865$	−33.8397	−	2.55848i	−1.15058	−	0.0869910i
$866$	−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
$873$			35.8135i			1.21210i
$874$			10.7718i			0.364363i
$875$	−9.13320	+	5.71348i	−0.308759	+	0.193151i
$876$	−6.06917	+	6.06917i	−0.205058	+	0.205058i
$877$	−5.37699			−0.181568			−0.0907839	−	0.995871i	$-0.528937\pi$
$877$	−5.37699			−0.181568			−0.0907839	+	0.995871i	$0.528937\pi$
$878$	23.2377			0.784233
$879$	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	$0.256516\pi$
$881$			42.8267i			1.44287i	−0.692484	+	0.721434i	$0.743484\pi$
$882$		−	29.5960i		−	0.996549i
$883$	−32.9568	−	32.9568i	−1.10908	−	1.10908i	−0.993271	−	0.115813i	$-0.963053\pi$
$883$	−32.9568	−	32.9568i	−1.10908	−	1.10908i	−0.115813	−	0.993271i	$-0.536947\pi$
$884$		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
$890$	−0.0893914	+	1.18233i	−0.00299641	+	0.0396319i
$891$	0.680258	+	0.680258i	0.0227895	+	0.0227895i
$892$		−	6.73778i		−	0.225598i
$893$	−15.1653	+	15.1653i	−0.507488	+	0.507488i
$894$	−12.3468			−0.412939
$895$	−4.67921	+	4.02140i	−0.156409	+	0.134420i
$896$			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
$902$	11.7817			0.392288
$903$			21.3430i			0.710252i
$904$	−4.13267	+	4.13267i	−0.137451	+	0.137451i
$905$	−15.0944	−	17.5636i	−0.501756	−	0.583833i
$906$	19.1440			0.636017
$907$	7.82336	−	7.82336i	0.259770	−	0.259770i	−0.565190	−	0.824961i	$-0.691197\pi$
$907$	7.82336	−	7.82336i	0.259770	−	0.259770i	0.824961	+	0.565190i	$0.191197\pi$
$908$	−16.3898			−0.543913
$909$	−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	$0.580194\pi$
$912$	8.99619			0.297894
$913$	10.0776	−	10.0776i	0.333521	−	0.333521i
$914$	29.0090			0.959533
$915$	−0.978791	+	12.9459i	−0.0323578	+	0.427980i
$916$	8.49903	−	8.49903i	0.280816	−	0.280816i
$917$			0.0599818i			0.00198077i
$918$	36.5067			1.20490
$919$			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
$925$	20.1741	+	3.06810i	0.663320	+	0.100879i
$926$	−30.6229			−1.00633
$927$	−12.0275	+	12.0275i	−0.395035	+	0.395035i
$928$		−	1.41296i		−	0.0463826i
$929$	−34.4704	−	34.4704i	−1.13094	−	1.13094i	−0.990022	−	0.140915i	$-0.954996\pi$
$929$	−34.4704	−	34.4704i	−1.13094	−	1.13094i	−0.140915	−	0.990022i	$-0.545004\pi$
$930$	0.738070	+	0.858804i	0.0242023	+	0.0281613i
$931$	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	$0.695466\pi$
$938$			7.19150i			0.234811i
$939$			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	$-0.738668\pi$
$941$	1.54410	−	1.54410i	0.0503363	−	0.0503363i	0.731827	+	0.681491i	$0.238668\pi$
$942$	−58.2343			−1.89738
$943$	26.6918			0.869204
$944$	−4.21798	+	4.21798i	−0.137284	+	0.137284i
$945$	0.799799	−	10.5785i	0.0260175	−	0.344119i
$946$			13.5186i			0.439527i
$947$			6.71654i			0.218258i	0.994028	+	0.109129i	$0.0348062\pi$
$947$			6.71654i			0.218258i	−0.994028	+	0.109129i	$0.965194\pi$
$948$	−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	0.469412	−	0.882979i	$-0.344466\pi$
$953$	−12.7671	−	12.7671i	−0.413568	−	0.413568i	−0.882979	+	0.469412i	$0.844466\pi$
$954$	9.74205	+	9.74205i	0.315411	+	0.315411i
$955$	31.5082	−	27.0787i	1.01958	−	0.876245i
$956$	2.13264	+	2.13264i	0.0689744	+	0.0689744i
$957$			1.35475i			0.0437929i
$958$	−28.0760	+	28.0760i	−0.907095	+	0.907095i
$959$	4.25656			0.137451
$960$	−3.43228	+	45.3970i	−0.110776	+	1.46518i
$961$			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
$967$	−60.0570			−1.93130			−0.965651	−	0.259841i	$-0.916330\pi$
$967$	−60.0570			−1.93130			−0.965651	+	0.259841i	$0.916330\pi$
$968$			24.8740i			0.799479i
$969$	−39.0570	+	39.0570i	−1.25469	+	1.25469i
$970$	−13.0294	+	11.1977i	−0.418348	+	0.359536i
$971$	−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
$973$	13.2478			0.424705
$974$	−29.5983			−0.948391
$975$		0			0
$976$	−2.46025			−0.0787506
$977$	−37.4959			−1.19960			−0.599800	−	0.800150i	$-0.704753\pi$
$977$	−37.4959			−1.19960			−0.599800	+	0.800150i	$0.704753\pi$
$978$	43.0954	−	43.0954i	1.37804	−	1.37804i
$979$	−0.862473			−0.0275648
$980$	−9.82532	+	8.44405i	−0.313858	+	0.269735i
$981$	30.6089	−	30.6089i	0.977266	−	0.977266i
$982$		−	7.43919i		−	0.237394i
$983$	46.1176			1.47092			0.735461	−	0.677567i	$-0.236966\pi$
$983$	46.1176			1.47092			0.735461	+	0.677567i	$0.236966\pi$
$984$		−	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
$990$	1.36680	−	18.0779i	0.0434397	−	0.574554i
$991$	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
$993$		−	93.5143i		−	2.96759i
$994$	−9.09482	−	9.09482i	−0.288470	−	0.288470i
$995$	24.9893	−	21.4762i	0.792214	−	0.680842i
$996$	−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.k.d.577.8		20
5.3	odd	4		845.2.f.d.408.3		20
13.2	odd	12		845.2.t.f.657.4		20
13.3	even	3		845.2.o.g.357.2		20
13.4	even	6		845.2.o.e.587.4		20
13.5	odd	4		845.2.f.e.437.3		20
13.6	odd	12		65.2.t.a.37.2	yes	20
13.7	odd	12		845.2.t.g.427.4		20
13.8	odd	4		845.2.f.d.437.8		20
13.9	even	3		845.2.o.f.587.2		20
13.10	even	6		65.2.o.a.32.4	✓	20
13.11	odd	12		845.2.t.e.657.2		20
13.12	even	2		845.2.k.e.577.3		20
39.23	odd	6		585.2.cf.a.487.2		20
39.32	even	12		585.2.dp.a.37.4		20
65.3	odd	12		845.2.t.g.188.4		20
65.8	even	4	inner	845.2.k.d.268.8		20
65.18	even	4		845.2.k.e.268.3		20
65.19	odd	12		325.2.x.b.232.4		20
65.23	odd	12		65.2.t.a.58.2	yes	20
65.28	even	12		845.2.o.e.488.4		20
65.32	even	12		325.2.s.b.193.2		20
65.33	even	12		845.2.o.g.258.2		20
65.38	odd	4		845.2.f.e.408.8		20
65.43	odd	12		845.2.t.f.418.4		20
65.48	odd	12		845.2.t.e.418.2		20
65.49	even	6		325.2.s.b.32.2		20
65.58	even	12		65.2.o.a.63.4	yes	20
65.62	odd	12		325.2.x.b.318.4		20
65.63	even	12		845.2.o.f.488.2		20
195.23	even	12		585.2.dp.a.253.4		20
195.188	odd	12		585.2.cf.a.388.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.4	✓	20	13.10	even	6
65.2.o.a.63.4	yes	20	65.58	even	12
65.2.t.a.37.2	yes	20	13.6	odd	12
65.2.t.a.58.2	yes	20	65.23	odd	12
325.2.s.b.32.2		20	65.49	even	6
325.2.s.b.193.2		20	65.32	even	12
325.2.x.b.232.4		20	65.19	odd	12
325.2.x.b.318.4		20	65.62	odd	12
585.2.cf.a.388.2		20	195.188	odd	12
585.2.cf.a.487.2		20	39.23	odd	6
585.2.dp.a.37.4		20	39.32	even	12
585.2.dp.a.253.4		20	195.23	even	12
845.2.f.d.408.3		20	5.3	odd	4
845.2.f.d.437.8		20	13.8	odd	4
845.2.f.e.408.8		20	65.38	odd	4
845.2.f.e.437.3		20	13.5	odd	4
845.2.k.d.268.8		20	65.8	even	4	inner
845.2.k.d.577.8		20	1.1	even	1	trivial
845.2.k.e.268.3		20	65.18	even	4
845.2.k.e.577.3		20	13.12	even	2
845.2.o.e.488.4		20	65.28	even	12
845.2.o.e.587.4		20	13.4	even	6
845.2.o.f.488.2		20	65.63	even	12
845.2.o.f.587.2		20	13.9	even	3
845.2.o.g.258.2		20	65.33	even	12
845.2.o.g.357.2		20	13.3	even	3
845.2.t.e.418.2		20	65.48	odd	12
845.2.t.e.657.2		20	13.11	odd	12
845.2.t.f.418.4		20	65.43	odd	12
845.2.t.f.657.4		20	13.2	odd	12
845.2.t.g.188.4		20	65.3	odd	12
845.2.t.g.427.4		20	13.7	odd	12

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.02262 q^{2} +(-1.97063 + 1.97063i) q^{3} -0.954253 q^{4} +(1.69584 - 1.45744i) q^{5} +(-2.01520 + 2.01520i) q^{6} -0.963574i q^{7} -3.02107 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} +(-0.469810 + 6.21394i) q^{15} -1.18090 q^{16} +(5.12686 - 5.12686i) q^{17} -4.87456i q^{18} +(1.93291 + 1.93291i) q^{19} +(-1.61826 + 1.39076i) 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} +0.919493i q^{28} -0.292263i q^{29} +(-0.480436 + 6.35448i) q^{30} +(0.125649 - 0.125649i) q^{31} +4.83454 q^{32} -4.63538 q^{33} +(5.24282 - 5.24282i) q^{34} +(-1.40435 - 1.63407i) q^{35} +4.54868i q^{36} +4.08121i 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} +(-6.94722 - 8.08364i) q^{45} +(2.78642 + 2.78642i) q^{46} +7.84582i q^{47} +(2.32710 - 2.32710i) q^{48} +6.07153 q^{49} +(0.768765 - 5.05497i) 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} -7.61811 q^{57} -0.298873i q^{58} +(3.57185 - 3.57185i) q^{59} +(0.448318 - 5.92967i) q^{60} +2.08337 q^{61} +(0.128491 - 0.128491i) q^{62} -4.59311 q^{63} +7.30568 q^{64} -4.74023 q^{66} -7.29829 q^{67} +(-4.89232 + 4.89232i) q^{68} -10.7391 q^{69} +(-1.43611 - 1.67103i) q^{70} +(9.22988 - 9.22988i) q^{71} +14.4007i q^{72} -3.22747 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} +(-2.00261 + 1.72108i) q^{80} +0.578392 q^{81} +(5.00872 - 5.00872i) q^{82} -8.56854i q^{83} +(-1.81198 - 1.81198i) q^{84} +(1.22228 - 16.1664i) 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} +0.495216i q^{93} +8.02328i q^{94} +(6.09502 + 0.460819i) q^{95} +(-9.52707 + 9.52707i) q^{96} -7.51320 q^{97} +6.20885 q^{98} +(5.60626 - 5.60626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 8 q^{2} + 4 q^{3} + 12 q^{4} + 6 q^{5} - 4 q^{6} - 12 q^{8} + 8 q^{10} - 8 q^{11} + 24 q^{12} + 24 q^{15} + 4 q^{16} + 14 q^{17} + 4 q^{19} + 22 q^{20} - 4 q^{21} - 32 q^{22} - 8 q^{23} - 4 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q - 8 * q^2 + 4 * q^3 + 12 * q^4 + 6 * q^5 - 4 * q^6 - 12 * q^8 + 8 * q^10 - 8 * q^11 + 24 * q^12 + 24 * q^15 + 4 * q^16 + 14 * q^17 + 4 * q^19 + 22 * q^20 - 4 * q^21 - 32 * q^22 - 8 * q^23 - 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 - 12 * q^32 - 36 * q^33 + 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 + 32 * q^43 - 36 * q^44 + 20 * q^45 - 4 * q^46 + 28 * q^48 + 36 * q^49 + 52 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 12 * q^57 + 8 * q^59 + 92 * q^60 + 32 * q^61 - 4 * q^62 - 64 * q^63 - 20 * q^64 - 32 * q^66 - 116 * q^67 - 50 * q^68 - 32 * q^69 - 32 * q^70 + 40 * q^71 - 72 * q^73 - 4 * q^75 + 16 * q^76 + 28 * q^77 + 34 * q^80 + 28 * q^81 + 34 * q^82 + 8 * q^84 - 60 * q^86 - 28 * q^87 + 32 * q^88 + 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 - 56 * q^96 - 44 * q^97 + 8 * q^98 + 60 * q^99

Introduction

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