LMFDB - Embedded newform 845.2.k.d.577.1

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			577.1
Root			$2.64975i$ of defining polynomial
Character	$\chi$	$=$	845.577
Dual form			845.2.k.d.268.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64975 q^{2} +(0.917096 - 0.917096i) q^{3} +5.02120 q^{4} +(1.30391 + 1.81654i) q^{5} +(-2.43008 + 2.43008i) q^{6} +0.112348i q^{7} -8.00544 q^{8} +1.31787i q^{9} +O(q^{10})$	\(q-2.64975 q^{2} +(0.917096 - 0.917096i) q^{3} +5.02120 q^{4} +(1.30391 + 1.81654i) q^{5} +(-2.43008 + 2.43008i) q^{6} +0.112348i q^{7} -8.00544 q^{8} +1.31787i q^{9} +(-3.45504 - 4.81339i) q^{10} +(-1.31019 - 1.31019i) q^{11} +(4.60492 - 4.60492i) q^{12} -0.297695i q^{14} +(2.86175 + 0.470132i) q^{15} +11.1700 q^{16} +(-1.93019 + 1.93019i) q^{17} -3.49203i q^{18} +(4.92146 + 4.92146i) q^{19} +(6.54719 + 9.12121i) q^{20} +(0.103034 + 0.103034i) q^{21} +(3.47169 + 3.47169i) q^{22} +(-2.27175 - 2.27175i) q^{23} +(-7.34175 + 7.34175i) q^{24} +(-1.59964 + 4.73721i) q^{25} +(3.95990 + 3.95990i) q^{27} +0.564122i q^{28} +4.65499i q^{29} +(-7.58294 - 1.24574i) q^{30} +(0.624367 - 0.624367i) q^{31} -13.5870 q^{32} -2.40314 q^{33} +(5.11454 - 5.11454i) q^{34} +(-0.204085 + 0.146492i) q^{35} +6.61729i q^{36} -1.47487i q^{37} +(-13.0407 - 13.0407i) q^{38} +(-10.4384 - 14.5422i) q^{40} +(-3.83645 + 3.83645i) q^{41} +(-0.273014 - 0.273014i) q^{42} +(-2.75555 - 2.75555i) q^{43} +(-6.57874 - 6.57874i) q^{44} +(-2.39396 + 1.71838i) q^{45} +(6.01959 + 6.01959i) q^{46} +0.345095i q^{47} +(10.2440 - 10.2440i) q^{48} +6.98738 q^{49} +(4.23866 - 12.5524i) q^{50} +3.54034i q^{51} +(-3.59144 + 3.59144i) q^{53} +(-10.4928 - 10.4928i) q^{54} +(0.671646 - 4.08839i) q^{55} -0.899394i q^{56} +9.02691 q^{57} -12.3346i q^{58} +(0.908390 - 0.908390i) q^{59} +(14.3694 + 2.36063i) q^{60} -2.78301 q^{61} +(-1.65442 + 1.65442i) q^{62} -0.148060 q^{63} +13.6621 q^{64} +6.36774 q^{66} +0.144329 q^{67} +(-9.69188 + 9.69188i) q^{68} -4.16683 q^{69} +(0.540774 - 0.388167i) q^{70} +(3.87045 - 3.87045i) q^{71} -10.5501i q^{72} -9.06221 q^{73} +3.90805i q^{74} +(2.87745 + 5.81150i) q^{75} +(24.7116 + 24.7116i) q^{76} +(0.147197 - 0.147197i) q^{77} +15.1689i q^{79} +(14.5647 + 20.2908i) q^{80} +3.30961 q^{81} +(10.1657 - 10.1657i) q^{82} +8.53853i q^{83} +(0.517354 + 0.517354i) q^{84} +(-6.02307 - 0.989478i) q^{85} +(7.30152 + 7.30152i) q^{86} +(4.26907 + 4.26907i) q^{87} +(10.4887 + 10.4887i) q^{88} +(-0.402434 + 0.402434i) q^{89} +(6.34342 - 4.55329i) q^{90} +(-11.4069 - 11.4069i) q^{92} -1.14521i q^{93} -0.914416i q^{94} +(-2.52290 + 15.3572i) q^{95} +(-12.4606 + 12.4606i) q^{96} +14.9645 q^{97} -18.5148 q^{98} +(1.72666 - 1.72666i) 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}+O(q^{10}) $ 20 * q - 8 * q^2 + 4 * q^3 + 12 * q^4 + 6 * q^5 - 4 * q^6 - 12 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.64975			−1.87366			−0.936830	−	0.349786i	$-0.886254\pi$
$2$	−2.64975			−1.87366			−0.936830	+	0.349786i	$0.886254\pi$
$3$	0.917096	−	0.917096i	0.529486	−	0.529486i	−0.390933	−	0.920419i	$-0.627848\pi$
$3$	0.917096	−	0.917096i	0.529486	−	0.529486i	0.920419	+	0.390933i	$0.127848\pi$
$4$	5.02120			2.51060
$5$	1.30391	+	1.81654i	0.583126	+	0.812382i
$5$	1.30391	+	1.81654i	0.583126	+	0.812382i
$6$	−2.43008	+	2.43008i	−0.992076	+	0.992076i
$7$			0.112348i			0.0424635i	0.999775	+	0.0212318i	$0.00675879\pi$
$7$			0.112348i			0.0424635i	−0.999775	+	0.0212318i	$0.993241\pi$
$8$	−8.00544			−2.83035
$9$			1.31787i			0.439290i
$10$	−3.45504	−	4.81339i	−1.09258	−	1.52213i
$11$	−1.31019	−	1.31019i	−0.395038	−	0.395038i	0.481441	−	0.876479i	$-0.340114\pi$
$11$	−1.31019	−	1.31019i	−0.395038	−	0.395038i	−0.876479	+	0.481441i	$0.840114\pi$
$12$	4.60492	−	4.60492i	1.32933	−	1.32933i
$13$		0			0
$13$		0			0
$14$		−	0.297695i		−	0.0795622i
$15$	2.86175	+	0.470132i	0.738901	+	0.121388i
$16$	11.1700			2.79251
$17$	−1.93019	+	1.93019i	−0.468140	+	0.468140i	−0.901312	−	0.433171i	$-0.857395\pi$
$17$	−1.93019	+	1.93019i	−0.468140	+	0.468140i	0.433171	+	0.901312i	$0.357395\pi$
$18$		−	3.49203i		−	0.823080i
$19$	4.92146	+	4.92146i	1.12906	+	1.12906i	0.990330	+	0.138731i	$0.0443022\pi$
$19$	4.92146	+	4.92146i	1.12906	+	1.12906i	0.138731	+	0.990330i	$0.455698\pi$
$20$	6.54719	+	9.12121i	1.46400	+	2.03957i
$21$	0.103034	+	0.103034i	0.0224838	+	0.0224838i
$22$	3.47169	+	3.47169i	0.740166	+	0.740166i
$23$	−2.27175	−	2.27175i	−0.473693	−	0.473693i	0.429414	−	0.903108i	$-0.358720\pi$
$23$	−2.27175	−	2.27175i	−0.473693	−	0.473693i	−0.903108	+	0.429414i	$0.858720\pi$
$24$	−7.34175	+	7.34175i	−1.49863	+	1.49863i
$25$	−1.59964	+	4.73721i	−0.319928	+	0.947442i
$26$		0			0
$27$	3.95990	+	3.95990i	0.762083	+	0.762083i
$28$			0.564122i			0.106609i
$29$			4.65499i			0.864410i	0.901775	+	0.432205i	$0.142264\pi$
$29$			4.65499i			0.864410i	−0.901775	+	0.432205i	$0.857736\pi$
$30$	−7.58294	−	1.24574i	−1.38445	−	0.227439i
$31$	0.624367	−	0.624367i	0.112140	−	0.112140i	−0.648810	−	0.760950i	$-0.724733\pi$
$31$	0.624367	−	0.624367i	0.112140	−	0.112140i	0.760950	+	0.648810i	$0.224733\pi$
$32$	−13.5870			−2.40186
$33$	−2.40314			−0.418334
$34$	5.11454	−	5.11454i	0.877136	−	0.877136i
$35$	−0.204085	+	0.146492i	−0.0344966	+	0.0247616i
$36$			6.61729i			1.10288i
$37$		−	1.47487i		−	0.242467i	−0.992624	−	0.121234i	$-0.961315\pi$
$37$		−	1.47487i		−	0.242467i	0.992624	−	0.121234i	$-0.0386850\pi$
$38$	−13.0407	−	13.0407i	−2.11548	−	2.11548i
$39$		0			0
$40$	−10.4384	−	14.5422i	−1.65045	−	2.29932i
$41$	−3.83645	+	3.83645i	−0.599153	+	0.599153i	−0.940087	−	0.340934i	$-0.889257\pi$
$41$	−3.83645	+	3.83645i	−0.599153	+	0.599153i	0.340934	+	0.940087i	$0.389257\pi$
$42$	−0.273014	−	0.273014i	−0.0421270	−	0.0421270i
$43$	−2.75555	−	2.75555i	−0.420217	−	0.420217i	0.465062	−	0.885278i	$-0.346032\pi$
$43$	−2.75555	−	2.75555i	−0.420217	−	0.420217i	−0.885278	+	0.465062i	$0.846032\pi$
$44$	−6.57874	−	6.57874i	−0.991782	−	0.991782i
$45$	−2.39396	+	1.71838i	−0.356871	+	0.256161i
$46$	6.01959	+	6.01959i	0.887540	+	0.887540i
$47$			0.345095i			0.0503372i	0.999683	+	0.0251686i	$0.00801227\pi$
$47$			0.345095i			0.0503372i	−0.999683	+	0.0251686i	$0.991988\pi$
$48$	10.2440	−	10.2440i	1.47859	−	1.47859i
$49$	6.98738			0.998197
$50$	4.23866	−	12.5524i	0.599436	−	1.77518i
$51$			3.54034i			0.495747i
$52$		0			0
$53$	−3.59144	+	3.59144i	−0.493322	+	0.493322i	−0.909351	−	0.416029i	$-0.863421\pi$
$53$	−3.59144	+	3.59144i	−0.493322	+	0.493322i	0.416029	+	0.909351i	$0.363421\pi$
$54$	−10.4928	−	10.4928i	−1.42788	−	1.42788i
$55$	0.671646	−	4.08839i	0.0905647	−	0.551278i
$56$		−	0.899394i		−	0.120187i
$57$	9.02691			1.19564
$58$		−	12.3346i		−	1.61961i
$59$	0.908390	−	0.908390i	0.118262	−	0.118262i	−0.645499	−	0.763761i	$-0.723351\pi$
$59$	0.908390	−	0.908390i	0.118262	−	0.118262i	0.763761	+	0.645499i	$0.223351\pi$
$60$	14.3694	+	2.36063i	1.85508	+	0.304756i
$61$	−2.78301			−0.356328			−0.178164	−	0.984001i	$-0.557016\pi$
$61$	−2.78301			−0.356328			−0.178164	+	0.984001i	$0.557016\pi$
$62$	−1.65442	+	1.65442i	−0.210111	+	0.210111i
$63$	−0.148060			−0.0186538
$64$	13.6621			1.70776
$65$		0			0
$66$	6.36774			0.783815
$67$	0.144329			0.0176325			0.00881627	−	0.999961i	$-0.497194\pi$
$67$	0.144329			0.0176325			0.00881627	+	0.999961i	$0.497194\pi$
$68$	−9.69188	+	9.69188i	−1.17531	+	1.17531i
$69$	−4.16683			−0.501628
$70$	0.540774	−	0.388167i	0.0646349	−	0.0463948i
$71$	3.87045	−	3.87045i	0.459338	−	0.459338i	−0.439100	−	0.898438i	$-0.644703\pi$
$71$	3.87045	−	3.87045i	0.459338	−	0.459338i	0.898438	+	0.439100i	$0.144703\pi$
$72$		−	10.5501i		−	1.24334i
$73$	−9.06221			−1.06065			−0.530326	−	0.847794i	$-0.677930\pi$
$73$	−9.06221			−1.06065			−0.530326	+	0.847794i	$0.677930\pi$
$74$			3.90805i			0.454301i
$75$	2.87745	+	5.81150i	0.332259	+	0.671054i
$76$	24.7116	+	24.7116i	2.83462	+	2.83462i
$77$	0.147197	−	0.147197i	0.0167747	−	0.0167747i
$78$		0			0
$79$			15.1689i			1.70664i	0.521388	+	0.853320i	$0.325414\pi$
$79$			15.1689i			1.70664i	−0.521388	+	0.853320i	$0.674586\pi$
$80$	14.5647	+	20.2908i	1.62839	+	2.26858i
$81$	3.30961			0.367734
$82$	10.1657	−	10.1657i	1.12261	−	1.12261i
$83$			8.53853i			0.937226i	0.883404	+	0.468613i	$0.155246\pi$
$83$			8.53853i			0.937226i	−0.883404	+	0.468613i	$0.844754\pi$
$84$	0.517354	+	0.517354i	0.0564479	+	0.0564479i
$85$	−6.02307	−	0.989478i	−0.653294	−	0.107324i
$86$	7.30152	+	7.30152i	0.787343	+	0.787343i
$87$	4.26907	+	4.26907i	0.457692	+	0.457692i
$88$	10.4887	+	10.4887i	1.11809	+	1.11809i
$89$	−0.402434	+	0.402434i	−0.0426579	+	0.0426579i	−0.728114	−	0.685456i	$-0.759603\pi$
$89$	−0.402434	+	0.402434i	−0.0426579	+	0.0426579i	0.685456	+	0.728114i	$0.259603\pi$
$90$	6.34342	−	4.55329i	0.668655	−	0.479959i
$91$		0			0
$92$	−11.4069	−	11.4069i	−1.18925	−	1.18925i
$93$		−	1.14521i		−	0.118753i
$94$		−	0.914416i		−	0.0943148i
$95$	−2.52290	+	15.3572i	−0.258844	+	1.57561i
$96$	−12.4606	+	12.4606i	−1.27175	+	1.27175i
$97$	14.9645			1.51941			0.759705	−	0.650268i	$-0.225343\pi$
$97$	14.9645			1.51941			0.759705	+	0.650268i	$0.225343\pi$
$98$	−18.5148			−1.87028
$99$	1.72666	−	1.72666i	0.173536	−	0.173536i
$100$	−8.03212	+	23.7865i	−0.803212	+	2.37865i
$101$			8.31058i			0.826934i	0.910519	+	0.413467i	$0.135682\pi$
$101$			8.31058i			0.826934i	−0.910519	+	0.413467i	$0.864318\pi$
$102$		−	9.38104i		−	0.928862i
$103$	7.72940	+	7.72940i	0.761600	+	0.761600i	0.976612	−	0.215011i	$-0.0689789\pi$
$103$	7.72940	+	7.72940i	0.761600	+	0.761600i	−0.215011	+	0.976612i	$0.568979\pi$
$104$		0			0
$105$	−0.0528184	+	0.321512i	−0.00515455	+	0.0313764i
$106$	9.51643	−	9.51643i	0.924317	−	0.924317i
$107$	−5.23546	−	5.23546i	−0.506131	−	0.506131i	0.407205	−	0.913337i	$-0.366503\pi$
$107$	−5.23546	−	5.23546i	−0.506131	−	0.506131i	−0.913337	+	0.407205i	$0.866503\pi$
$108$	19.8835	+	19.8835i	1.91329	+	1.91329i
$109$	3.34544	+	3.34544i	0.320435	+	0.320435i	0.848934	−	0.528499i	$-0.177245\pi$
$109$	3.34544	+	3.34544i	0.320435	+	0.320435i	−0.528499	+	0.848934i	$0.677245\pi$
$110$	−1.77970	+	10.8332i	−0.169687	+	1.03291i
$111$	−1.35260	−	1.35260i	−0.128383	−	0.128383i
$112$			1.25493i			0.118580i
$113$	4.32414	−	4.32414i	0.406780	−	0.406780i	−0.473834	−	0.880614i	$-0.657130\pi$
$113$	4.32414	−	4.32414i	0.406780	−	0.406780i	0.880614	+	0.473834i	$0.157130\pi$
$114$	−23.9191			−2.24023
$115$	1.16457	−	7.08889i	0.108597	−	0.661043i
$116$			23.3736i			2.17019i
$117$		0			0
$118$	−2.40701	+	2.40701i	−0.221583	+	0.221583i
$119$	−0.216853	−	0.216853i	−0.0198789	−	0.0198789i
$120$	−22.9096	−	3.76361i	−2.09135	−	0.343569i
$121$		−	7.56679i		−	0.687890i
$122$	7.37430			0.667638
$123$			7.03679i			0.634486i
$124$	3.13507	−	3.13507i	0.281538	−	0.281538i
$125$	−10.6911	+	3.27108i	−0.956243	+	0.292574i
$126$	0.392323			0.0349509
$127$	8.25062	−	8.25062i	0.732124	−	0.732124i	−0.238916	−	0.971040i	$-0.576792\pi$
$127$	8.25062	−	8.25062i	0.732124	−	0.732124i	0.971040	+	0.238916i	$0.0767920\pi$
$128$	−9.02727			−0.797905
$129$	−5.05420			−0.444997
$130$		0			0
$131$	7.46380			0.652115			0.326058	−	0.945350i	$-0.394280\pi$
$131$	7.46380			0.652115			0.326058	+	0.945350i	$0.394280\pi$
$132$	−12.0667			−1.05027
$133$	−0.552916	+	0.552916i	−0.0479439	+	0.0479439i
$134$	−0.382435			−0.0330374
$135$	−2.02997	+	12.3567i	−0.174712	+	1.06349i
$136$	15.4520	−	15.4520i	1.32500	−	1.32500i
$137$			18.4843i			1.57922i	0.613611	+	0.789608i	$0.289716\pi$
$137$			18.4843i			1.57922i	−0.613611	+	0.789608i	$0.710284\pi$
$138$	11.0411			0.939879
$139$		−	10.9103i		−	0.925402i	−0.886515	−	0.462701i	$-0.846880\pi$
$139$		−	10.9103i		−	0.925402i	0.886515	−	0.462701i	$-0.153120\pi$
$140$	−1.02475	+	0.735563i	−0.0866072	+	0.0621664i
$141$	0.316485	+	0.316485i	0.0266528	+	0.0266528i
$142$	−10.2557	+	10.2557i	−0.860643	+	0.860643i
$143$		0			0
$144$			14.7207i			1.22672i
$145$	−8.45598	+	6.06968i	−0.702231	+	0.504060i
$146$	24.0126			1.98730
$147$	6.40810	−	6.40810i	0.528531	−	0.528531i
$148$		−	7.40562i		−	0.608738i
$149$	−9.84377	−	9.84377i	−0.806433	−	0.806433i	0.177659	−	0.984092i	$-0.443148\pi$
$149$	−9.84377	−	9.84377i	−0.806433	−	0.806433i	−0.984092	+	0.177659i	$0.943148\pi$
$150$	−7.62454	−	15.3990i	−0.622541	−	1.25733i
$151$	8.49593	+	8.49593i	0.691389	+	0.691389i	0.962537	−	0.271149i	$-0.0874035\pi$
$151$	8.49593	+	8.49593i	0.691389	+	0.691389i	−0.271149	+	0.962537i	$0.587404\pi$
$152$	−39.3984	−	39.3984i	−3.19564	−	3.19564i
$153$	−2.54374	−	2.54374i	−0.205649	−	0.205649i
$154$	−0.390037	+	0.390037i	−0.0314301	+	0.0314301i
$155$	1.94830	+	0.320070i	0.156492	+	0.0257086i
$156$		0			0
$157$	−5.14491	−	5.14491i	−0.410609	−	0.410609i	0.471342	−	0.881951i	$-0.343770\pi$
$157$	−5.14491	−	5.14491i	−0.410609	−	0.410609i	−0.881951	+	0.471342i	$0.843770\pi$
$158$		−	40.1940i		−	3.19766i
$159$			6.58739i			0.522414i
$160$	−17.7162	−	24.6813i	−1.40059	−	1.95123i
$161$	0.255227	−	0.255227i	0.0201147	−	0.0201147i
$162$	−8.76965			−0.689009
$163$	20.5175			1.60705			0.803526	−	0.595270i	$-0.202955\pi$
$163$	20.5175			1.60705			0.803526	+	0.595270i	$0.202955\pi$
$164$	−19.2636	+	19.2636i	−1.50423	+	1.50423i
$165$	−3.13348	−	4.36541i	−0.243941	−	0.339847i
$166$		−	22.6250i		−	1.75604i
$167$			2.54101i			0.196629i	0.995155	+	0.0983146i	$0.0313451\pi$
$167$			2.54101i			0.196629i	−0.995155	+	0.0983146i	$0.968655\pi$
$168$	−0.824831	−	0.824831i	−0.0636371	−	0.0636371i
$169$		0			0
$170$	15.9597	+	2.62187i	1.22405	+	0.201088i
$171$	−6.48585	+	6.48585i	−0.495985	+	0.495985i
$172$	−13.8361	−	13.8361i	−1.05500	−	1.05500i
$173$	−0.0557881	−	0.0557881i	−0.00424149	−	0.00424149i	0.704983	−	0.709224i	$-0.250955\pi$
$173$	−0.0557881	−	0.0557881i	−0.00424149	−	0.00424149i	−0.709224	+	0.704983i	$0.750955\pi$
$174$	−11.3120	−	11.3120i	−0.857560	−	0.857560i
$175$	−0.532216	−	0.179716i	−0.0402317	−	0.0135853i
$176$	−14.6349	−	14.6349i	−1.10315	−	1.10315i
$177$		−	1.66616i		−	0.125236i
$178$	1.06635	−	1.06635i	0.0799264	−	0.0799264i
$179$	21.2241			1.58636			0.793181	−	0.608987i	$-0.208424\pi$
$179$	21.2241			1.58636			0.793181	+	0.608987i	$0.208424\pi$
$180$	−12.0206	+	8.62834i	−0.895961	+	0.643119i
$181$		−	22.5267i		−	1.67440i	−0.546899	−	0.837198i	$-0.684192\pi$
$181$		−	22.5267i		−	1.67440i	0.546899	−	0.837198i	$-0.315808\pi$
$182$		0			0
$183$	−2.55229	+	2.55229i	−0.188671	+	0.188671i
$184$	18.1864	+	18.1864i	1.34072	+	1.34072i
$185$	2.67916	−	1.92310i	0.196976	−	0.141389i
$186$			3.03452i			0.222502i
$187$	5.05785			0.369866
$188$			1.73279i			0.126377i
$189$	−0.444887	+	0.444887i	−0.0323608	+	0.0323608i
$190$	6.68506	−	40.6927i	0.484985	−	2.95216i
$191$	19.6065			1.41868			0.709339	−	0.704868i	$-0.248994\pi$
$191$	19.6065			1.41868			0.709339	+	0.704868i	$0.248994\pi$
$192$	12.5295	−	12.5295i	0.904237	−	0.904237i
$193$	−16.7120			−1.20296			−0.601479	−	0.798889i	$-0.705421\pi$
$193$	−16.7120			−1.20296			−0.601479	+	0.798889i	$0.705421\pi$
$194$	−39.6521			−2.84686
$195$		0			0
$196$	35.0850			2.50607
$197$	15.1863			1.08198			0.540990	−	0.841029i	$-0.318050\pi$
$197$	15.1863			1.08198			0.540990	+	0.841029i	$0.318050\pi$
$198$	−4.57523	+	4.57523i	−0.325148	+	0.325148i
$199$	−13.9471			−0.988686			−0.494343	−	0.869267i	$-0.664591\pi$
$199$	−13.9471			−0.988686			−0.494343	+	0.869267i	$0.664591\pi$
$200$	12.8058	−	37.9234i	0.905508	−	2.68159i
$201$	0.132363	−	0.132363i	0.00933618	−	0.00933618i
$202$		−	22.0210i		−	1.54939i
$203$	−0.522979			−0.0367059
$204$			17.7768i			1.24462i
$205$	−11.9715	−	1.96669i	−0.836123	−	0.137359i
$206$	−20.4810	−	20.4810i	−1.42698	−	1.42698i
$207$	2.99388	−	2.99388i	0.208089	−	0.208089i
$208$		0			0
$209$		−	12.8961i		−	0.892044i
$210$	0.139956	−	0.851928i	0.00965787	−	0.0587886i
$211$	−23.6181			−1.62594			−0.812969	−	0.582307i	$-0.802150\pi$
$211$	−23.6181			−1.62594			−0.812969	+	0.582307i	$0.802150\pi$
$212$	−18.0333	+	18.0333i	−1.23853	+	1.23853i
$213$		−	7.09915i		−	0.486426i
$214$	13.8727	+	13.8727i	0.948318	+	0.948318i
$215$	1.41258	−	8.59854i	0.0963371	−	0.586416i
$216$	−31.7007	−	31.7007i	−2.15696	−	2.15696i
$217$	0.0701463	+	0.0701463i	0.00476184	+	0.00476184i
$218$	−8.86460	−	8.86460i	−0.600387	−	0.600387i
$219$	−8.31092	+	8.31092i	−0.561600	+	0.561600i
$220$	3.37247	−	20.5286i	0.227372	−	1.38404i
$221$		0			0
$222$	3.58405	+	3.58405i	0.240546	+	0.240546i
$223$			9.72639i			0.651327i	0.945486	+	0.325664i	$0.105588\pi$
$223$			9.72639i			0.651327i	−0.945486	+	0.325664i	$0.894412\pi$
$224$		−	1.52647i		−	0.101992i
$225$	−6.24303	−	2.10812i	−0.416202	−	0.140541i
$226$	−11.4579	+	11.4579i	−0.762168	+	0.762168i
$227$	−9.17580			−0.609019			−0.304510	−	0.952509i	$-0.598493\pi$
$227$	−9.17580			−0.609019			−0.304510	+	0.952509i	$0.598493\pi$
$228$	45.3259			3.00178
$229$	12.5270	−	12.5270i	0.827811	−	0.827811i	−0.159403	−	0.987214i	$-0.550957\pi$
$229$	12.5270	−	12.5270i	0.827811	−	0.827811i	0.987214	+	0.159403i	$0.0509569\pi$
$230$	−3.08583	+	18.7838i	−0.203474	+	1.23857i
$231$		−	0.269988i		−	0.0177639i
$232$		−	37.2652i		−	2.44658i
$233$	11.8637	+	11.8637i	0.777214	+	0.777214i	0.979356	−	0.202142i	$-0.0647903\pi$
$233$	11.8637	+	11.8637i	0.777214	+	0.777214i	−0.202142	+	0.979356i	$0.564790\pi$
$234$		0			0
$235$	−0.626879	+	0.449972i	−0.0408931	+	0.0293530i
$236$	4.56120	−	4.56120i	0.296909	−	0.296909i
$237$	13.9114	+	13.9114i	0.903641	+	0.903641i
$238$	0.574608	+	0.574608i	0.0372463	+	0.0372463i
$239$	−18.2161	−	18.2161i	−1.17830	−	1.17830i	−0.980177	−	0.198124i	$-0.936515\pi$
$239$	−18.2161	−	18.2161i	−1.17830	−	1.17830i	−0.198124	−	0.980177i	$-0.563485\pi$
$240$	31.9659	+	5.25140i	2.06339	+	0.338976i
$241$	−3.86818	−	3.86818i	−0.249171	−	0.249171i	0.571459	−	0.820630i	$-0.306378\pi$
$241$	−3.86818	−	3.86818i	−0.249171	−	0.249171i	−0.820630	+	0.571459i	$0.806378\pi$
$242$			20.0501i			1.28887i
$243$	−8.84448	+	8.84448i	−0.567373	+	0.567373i
$244$	−13.9741			−0.894597
$245$	9.11091	+	12.6929i	0.582075	+	0.810917i
$246$		−	18.6458i		−	1.18881i
$247$		0			0
$248$	−4.99833	+	4.99833i	−0.317394	+	0.317394i
$249$	7.83065	+	7.83065i	0.496247	+	0.496247i
$250$	28.3288	−	8.66755i	1.79167	−	0.548184i
$251$		−	13.0677i		−	0.824824i	−0.910997	−	0.412412i	$-0.864686\pi$
$251$		−	13.0677i		−	0.824824i	0.910997	−	0.412412i	$-0.135314\pi$
$252$	−0.743439			−0.0468322
$253$			5.95287i			0.374254i
$254$	−21.8621	+	21.8621i	−1.37175	+	1.37175i
$255$	−6.43118	+	4.61629i	−0.402736	+	0.289083i
$256$	−3.40419			−0.212762
$257$	−12.3380	+	12.3380i	−0.769625	+	0.769625i	−0.978040	−	0.208415i	$-0.933170\pi$
$257$	−12.3380	+	12.3380i	−0.769625	+	0.769625i	0.208415	+	0.978040i	$0.433170\pi$
$258$	13.3924			0.833774
$259$	0.165699			0.0102960
$260$		0			0
$261$	−6.13467			−0.379727
$262$	−19.7772			−1.22184
$263$	14.7419	−	14.7419i	0.909027	−	0.909027i	−0.0871665	−	0.996194i	$-0.527781\pi$
$263$	14.7419	−	14.7419i	0.909027	−	0.909027i	0.996194	+	0.0871665i	$0.0277812\pi$
$264$	19.2382			1.18403
$265$	−11.2069	−	1.84108i	−0.688434	−	0.113097i
$266$	1.46509	−	1.46509i	0.0898306	−	0.0898306i
$267$			0.738141i			0.0451735i
$268$	0.724703			0.0442683
$269$		−	10.5665i		−	0.644252i	−0.946697	−	0.322126i	$-0.895602\pi$
$269$		−	10.5665i		−	0.644252i	0.946697	−	0.322126i	$-0.104398\pi$
$270$	5.37892	−	32.7422i	0.327351	−	1.99262i
$271$	5.59357	+	5.59357i	0.339785	+	0.339785i	0.856286	−	0.516501i	$-0.172766\pi$
$271$	5.59357	+	5.59357i	0.339785	+	0.339785i	−0.516501	+	0.856286i	$0.672766\pi$
$272$	−21.5603	+	21.5603i	−1.30729	+	1.30729i
$273$		0			0
$274$		−	48.9787i		−	2.95891i
$275$	8.30249	−	4.11082i	0.500659	−	0.247892i
$276$	−20.9225			−1.25939
$277$	7.22248	−	7.22248i	0.433957	−	0.433957i	−0.456015	−	0.889972i	$-0.650724\pi$
$277$	7.22248	−	7.22248i	0.433957	−	0.433957i	0.889972	+	0.456015i	$0.150724\pi$
$278$			28.9097i			1.73389i
$279$	0.822834	+	0.822834i	0.0492618	+	0.0492618i
$280$	1.63379	−	1.17273i	0.0976374	−	0.0700840i
$281$	−12.4763	−	12.4763i	−0.744271	−	0.744271i	0.229126	−	0.973397i	$-0.426413\pi$
$281$	−12.4763	−	12.4763i	−0.744271	−	0.744271i	−0.973397	+	0.229126i	$0.926413\pi$
$282$	−0.838608	−	0.838608i	−0.0499384	−	0.0499384i
$283$	−5.84527	−	5.84527i	−0.347465	−	0.347465i	0.511700	−	0.859164i	$-0.329016\pi$
$283$	−5.84527	−	5.84527i	−0.347465	−	0.347465i	−0.859164	+	0.511700i	$0.829016\pi$
$284$	19.4343	−	19.4343i	1.15321	−	1.15321i
$285$	11.7703	+	16.3977i	0.697210	+	0.971318i
$286$		0			0
$287$	−0.431018	−	0.431018i	−0.0254422	−	0.0254422i
$288$		−	17.9059i		−	1.05511i
$289$			9.54871i			0.561689i
$290$	22.4063	−	16.0832i	1.31574	−	0.944436i
$291$	13.7238	−	13.7238i	0.804506	−	0.804506i
$292$	−45.5032			−2.66287
$293$	−6.37832			−0.372625			−0.186313	−	0.982491i	$-0.559654\pi$
$293$	−6.37832			−0.372625			−0.186313	+	0.982491i	$0.559654\pi$
$294$	−16.9799	+	16.9799i	−0.990287	+	0.990287i
$295$	2.83458	+	0.465669i	0.165036	+	0.0271123i
$296$			11.8070i			0.686267i
$297$		−	10.3765i		−	0.602104i
$298$	26.0836	+	26.0836i	1.51098	+	1.51098i
$299$		0			0
$300$	14.4483	+	29.1807i	0.834170	+	1.68475i
$301$	0.309580	−	0.309580i	0.0178439	−	0.0178439i
$302$	−22.5121	−	22.5121i	−1.29543	−	1.29543i
$303$	7.62160	+	7.62160i	0.437850	+	0.437850i
$304$	54.9729	+	54.9729i	3.15291	+	3.15291i
$305$	−3.62880	−	5.05546i	−0.207784	−	0.289475i
$306$	6.74029	+	6.74029i	0.385317	+	0.385317i
$307$			26.5460i			1.51506i	0.652801	+	0.757530i	$0.273594\pi$
$307$			26.5460i			1.51506i	−0.652801	+	0.757530i	$0.726406\pi$
$308$	0.739108	−	0.739108i	0.0421146	−	0.0421146i
$309$	14.1772			0.806512
$310$	−5.16253	−	0.848107i	−0.293212	−	0.0481692i
$311$		−	3.54417i		−	0.200972i	−0.994938	−	0.100486i	$-0.967960\pi$
$311$		−	3.54417i		−	0.200972i	0.994938	−	0.100486i	$-0.0320397\pi$
$312$		0			0
$313$	−6.21088	+	6.21088i	−0.351060	+	0.351060i	−0.860504	−	0.509444i	$-0.829851\pi$
$313$	−6.21088	+	6.21088i	−0.351060	+	0.351060i	0.509444	+	0.860504i	$0.329851\pi$
$314$	13.6328	+	13.6328i	0.769341	+	0.769341i
$315$	−0.193057	−	0.268957i	−0.0108775	−	0.0151540i
$316$			76.1663i			4.28469i
$317$	8.52812			0.478987			0.239494	−	0.970898i	$-0.423019\pi$
$317$	8.52812			0.478987			0.239494	+	0.970898i	$0.423019\pi$
$318$		−	17.4550i		−	0.978825i
$319$	6.09893	−	6.09893i	0.341474	−	0.341474i
$320$	17.8142	+	24.8178i	0.995842	+	1.38736i
$321$	−9.60284			−0.535978
$322$	−0.676289	+	0.676289i	−0.0376881	+	0.0376881i
$323$	−18.9987			−1.05712
$324$	16.6182			0.923233
$325$		0			0
$326$	−54.3663			−3.01107
$327$	6.13618			0.339332
$328$	30.7125	−	30.7125i	1.69581	−	1.69581i
$329$	−0.0387707			−0.00213750
$330$	8.30296	+	11.5673i	0.457063	+	0.636757i
$331$	−12.7328	+	12.7328i	−0.699860	+	0.699860i	−0.964380	−	0.264520i	$-0.914786\pi$
$331$	−12.7328	+	12.7328i	−0.699860	+	0.699860i	0.264520	+	0.964380i	$0.414786\pi$
$332$			42.8737i			2.35300i
$333$	1.94369			0.106513
$334$		−	6.73305i		−	0.368416i
$335$	0.188191	+	0.262179i	0.0102820	+	0.0143244i
$336$	1.15089	+	1.15089i	0.0627863	+	0.0627863i
$337$	20.0865	−	20.0865i	1.09418	−	1.09418i	0.0991030	−	0.995077i	$-0.468403\pi$
$337$	20.0865	−	20.0865i	1.09418	−	1.09418i	0.995077	−	0.0991030i	$-0.0315973\pi$
$338$		0			0
$339$		−	7.93129i		−	0.430769i
$340$	−30.2430	−	4.96836i	−1.64016	−	0.269447i
$341$	−1.63608			−0.0885987
$342$	17.1859	−	17.1859i	0.929307	−	0.929307i
$343$			1.57145i			0.0848505i
$344$	22.0593	+	22.0593i	1.18936	+	1.18936i
$345$	−5.43317	−	7.56922i	−0.292512	−	0.407513i
$346$	0.147825	+	0.147825i	0.00794710	+	0.00794710i
$347$	−5.07459	−	5.07459i	−0.272418	−	0.272418i	0.557655	−	0.830073i	$-0.311701\pi$
$347$	−5.07459	−	5.07459i	−0.272418	−	0.272418i	−0.830073	+	0.557655i	$0.811701\pi$
$348$	21.4359	+	21.4359i	1.14908	+	1.14908i
$349$	−2.58330	+	2.58330i	−0.138281	+	0.138281i	−0.772859	−	0.634578i	$-0.781174\pi$
$349$	−2.58330	+	2.58330i	−0.138281	+	0.138281i	0.634578	+	0.772859i	$0.281174\pi$
$350$	1.41024	+	0.476204i	0.0753806	+	0.0254542i
$351$		0			0
$352$	17.8016	+	17.8016i	0.948827	+	0.948827i
$353$			1.76326i			0.0938487i	0.998898	+	0.0469243i	$0.0149420\pi$
$353$			1.76326i			0.0938487i	−0.998898	+	0.0469243i	$0.985058\pi$
$354$			4.41492i			0.234650i
$355$	12.0775	+	1.98411i	0.641010	+	0.105306i
$356$	−2.02070	+	2.02070i	−0.107097	+	0.107097i
$357$	−0.397750			−0.0210512
$358$	−56.2386			−2.97230
$359$	8.58021	−	8.58021i	0.452846	−	0.452846i	−0.443452	−	0.896298i	$-0.646246\pi$
$359$	8.58021	−	8.58021i	0.452846	−	0.452846i	0.896298	+	0.443452i	$0.146246\pi$
$360$	19.1647	−	13.7564i	1.01007	−	0.725026i
$361$			29.4416i			1.54956i
$362$			59.6902i			3.13725i
$363$	−6.93947	−	6.93947i	−0.364228	−	0.364228i
$364$		0			0
$365$	−11.8163	−	16.4619i	−0.618493	−	0.861654i
$366$	6.76294	−	6.76294i	0.353505	−	0.353505i
$367$	−9.90736	−	9.90736i	−0.517160	−	0.517160i	0.399551	−	0.916711i	$-0.369166\pi$
$367$	−9.90736	−	9.90736i	−0.517160	−	0.517160i	−0.916711	+	0.399551i	$0.869166\pi$
$368$	−25.3756	−	25.3756i	−1.32279	−	1.32279i
$369$	−5.05594	−	5.05594i	−0.263202	−	0.263202i
$370$	−7.09912	+	5.09574i	−0.369066	+	0.264915i
$371$	−0.403491	−	0.403491i	−0.0209482	−	0.0209482i
$372$		−	5.75032i		−	0.298140i
$373$	−20.4300	+	20.4300i	−1.05782	+	1.05782i	−0.0596011	+	0.998222i	$0.518983\pi$
$373$	−20.4300	+	20.4300i	−1.05782	+	1.05782i	−0.998222	+	0.0596011i	$0.981017\pi$
$374$	−13.4021			−0.693004
$375$	−6.80489	+	12.8047i	−0.351403	+	0.661231i
$376$		−	2.76263i		−	0.142472i
$377$		0			0
$378$	1.17884	−	1.17884i	0.0606330	−	0.0606330i
$379$	6.70112	+	6.70112i	0.344213	+	0.344213i	0.857949	−	0.513735i	$-0.171739\pi$
$379$	6.70112	+	6.70112i	0.344213	+	0.344213i	−0.513735	+	0.857949i	$0.671739\pi$
$380$	−12.6680	+	77.1114i	−0.649853	+	3.95573i
$381$		−	15.1332i		−	0.775299i
$382$	−51.9525			−2.65812
$383$		−	21.0722i		−	1.07674i	−0.842709	−	0.538369i	$-0.819041\pi$
$383$		−	21.0722i		−	1.07674i	0.842709	−	0.538369i	$-0.180959\pi$
$384$	−8.27887	+	8.27887i	−0.422479	+	0.422479i
$385$	0.459322	+	0.0754581i	0.0234092	+	0.00384570i
$386$	44.2827			2.25393
$387$	3.63145	−	3.63145i	0.184597	−	0.184597i
$388$	75.1395			3.81463
$389$	−0.0604806			−0.00306649			−0.00153324	−	0.999999i	$-0.500488\pi$
$389$	−0.0604806			−0.00306649			−0.00153324	+	0.999999i	$0.500488\pi$
$390$		0			0
$391$	8.76984			0.443510
$392$	−55.9370			−2.82525
$393$	6.84502	−	6.84502i	0.345286	−	0.345286i
$394$	−40.2400			−2.02726
$395$	−27.5550	+	19.7789i	−1.38644	+	0.995186i
$396$	8.66992	−	8.66992i	0.435680	−	0.435680i
$397$		−	8.21625i		−	0.412362i	−0.978514	−	0.206181i	$-0.933896\pi$
$397$		−	8.21625i		−	0.412362i	0.978514	−	0.206181i	$-0.0661035\pi$
$398$	36.9565			1.85246
$399$			1.01415i			0.0507712i
$400$	−17.8681	+	52.9148i	−0.893403	+	2.64574i
$401$	6.36306	+	6.36306i	0.317756	+	0.317756i	0.847905	−	0.530149i	$-0.177864\pi$
$401$	6.36306	+	6.36306i	0.317756	+	0.317756i	−0.530149	+	0.847905i	$0.677864\pi$
$402$	−0.350730	+	0.350730i	−0.0174928	+	0.0174928i
$403$		0			0
$404$			41.7291i			2.07610i
$405$	4.31543	+	6.01204i	0.214435	+	0.298741i
$406$	1.38576			0.0687743
$407$	−1.93236	+	1.93236i	−0.0957837	+	0.0957837i
$408$		−	28.3420i		−	1.40314i
$409$	−25.3299	−	25.3299i	−1.25248	−	1.25248i	−0.954604	−	0.297878i	$-0.903721\pi$
$409$	−25.3299	−	25.3299i	−1.25248	−	1.25248i	−0.297878	−	0.954604i	$-0.596279\pi$
$410$	31.7214	+	5.21123i	1.56661	+	0.257365i
$411$	16.9518	+	16.9518i	0.836173	+	0.836173i
$412$	38.8108	+	38.8108i	1.91207	+	1.91207i
$413$	0.102056	+	0.102056i	0.00502183	+	0.00502183i
$414$	−7.93304	+	7.93304i	−0.389887	+	0.389887i
$415$	−15.5106	+	11.1335i	−0.761385	+	0.546521i
$416$		0			0
$417$	−10.0058	−	10.0058i	−0.489987	−	0.489987i
$418$			34.1716i			1.67139i
$419$			13.0807i			0.639036i	0.947580	+	0.319518i	$0.103521\pi$
$419$			13.0807i			0.639036i	−0.947580	+	0.319518i	$0.896479\pi$
$420$	−0.265212	+	1.61438i	−0.0129410	+	0.0787735i
$421$	13.7924	−	13.7924i	0.672203	−	0.672203i	−0.286021	−	0.958223i	$-0.592333\pi$
$421$	13.7924	−	13.7924i	0.672203	−	0.672203i	0.958223	+	0.286021i	$0.0923326\pi$
$422$	62.5822			3.04645
$423$	−0.454790			−0.0221126
$424$	28.7510	−	28.7510i	1.39627	−	1.39627i
$425$	−6.05611	−	12.2313i	−0.293765	−	0.593307i
$426$			18.8110i			0.911396i
$427$		−	0.312666i		−	0.0151310i
$428$	−26.2883	−	26.2883i	−1.27069	−	1.27069i
$429$		0			0
$430$	−3.74299	+	22.7840i	−0.180503	+	1.09874i
$431$	15.7112	−	15.7112i	0.756782	−	0.756782i	−0.218953	−	0.975735i	$-0.570264\pi$
$431$	15.7112	−	15.7112i	0.756782	−	0.756782i	0.975735	+	0.218953i	$0.0702642\pi$
$432$	44.2323	+	44.2323i	2.12813	+	2.12813i
$433$	−0.129788	−	0.129788i	−0.00623723	−	0.00623723i	0.703981	−	0.710219i	$-0.251404\pi$
$433$	−0.129788	−	0.129788i	−0.00623723	−	0.00623723i	−0.710219	+	0.703981i	$0.751404\pi$
$434$	−0.185871	−	0.185871i	−0.00892207	−	0.00892207i
$435$	−2.18846	+	13.3214i	−0.104929	+	0.638713i
$436$	16.7981	+	16.7981i	0.804485	+	0.804485i
$437$		−	22.3607i		−	1.06966i
$438$	22.0219	−	22.0219i	1.05225	−	1.05225i
$439$	−17.2936			−0.825380			−0.412690	−	0.910871i	$-0.635411\pi$
$439$	−17.2936			−0.825380			−0.412690	+	0.910871i	$0.635411\pi$
$440$	−5.37682	+	32.7293i	−0.256330	+	1.56031i
$441$			9.20846i			0.438498i
$442$		0			0
$443$	24.4472	−	24.4472i	1.16152	−	1.16152i	0.177377	−	0.984143i	$-0.443239\pi$
$443$	24.4472	−	24.4472i	1.16152	−	1.16152i	0.984143	−	0.177377i	$-0.0567611\pi$
$444$	−6.79166	−	6.79166i	−0.322318	−	0.322318i
$445$	−1.25578	−	0.206300i	−0.0595295	−	0.00977958i
$446$		−	25.7725i		−	1.22037i
$447$	−18.0554			−0.853989
$448$			1.53491i			0.0725177i
$449$	26.2934	−	26.2934i	1.24086	−	1.24086i	0.281221	−	0.959643i	$-0.409261\pi$
$449$	26.2934	−	26.2934i	1.24086	−	1.24086i	0.959643	−	0.281221i	$-0.0907394\pi$
$450$	16.5425	+	5.58600i	0.779820	+	0.263326i
$451$	10.0530			0.473376
$452$	21.7123	−	21.7123i	1.02126	−	1.02126i
$453$	15.5832			0.732161
$454$	24.3136			1.14109
$455$		0			0
$456$	−72.2643			−3.38409
$457$	−9.42691			−0.440972			−0.220486	−	0.975390i	$-0.570764\pi$
$457$	−9.42691			−0.440972			−0.220486	+	0.975390i	$0.570764\pi$
$458$	−33.1936	+	33.1936i	−1.55104	+	1.55104i
$459$	−15.2867			−0.713524
$460$	5.84755	−	35.5947i	0.272643	−	1.65961i
$461$	23.2538	−	23.2538i	1.08304	−	1.08304i	0.0868134	−	0.996225i	$-0.472332\pi$
$461$	23.2538	−	23.2538i	1.08304	−	1.08304i	0.996225	−	0.0868134i	$-0.0276684\pi$
$462$			0.715403i			0.0332836i
$463$	−18.6729			−0.867805			−0.433903	−	0.900960i	$-0.642864\pi$
$463$	−18.6729			−0.867805			−0.433903	+	0.900960i	$0.642864\pi$
$464$			51.9964i			2.41387i
$465$	2.08032	−	1.49325i	0.0964724	−	0.0692477i
$466$	−31.4358	−	31.4358i	−1.45623	−	1.45623i
$467$	12.1678	−	12.1678i	0.563057	−	0.563057i	−0.367118	−	0.930175i	$-0.619655\pi$
$467$	12.1678	−	12.1678i	0.563057	−	0.563057i	0.930175	+	0.367118i	$0.119655\pi$
$468$		0			0
$469$			0.0162150i			0.000748740i
$470$	1.66107	−	1.19232i	0.0766197	−	0.0549974i
$471$	−9.43676			−0.434823
$472$	−7.27205	+	7.27205i	−0.334723	+	0.334723i
$473$			7.22059i			0.332003i
$474$	−36.8617	−	36.8617i	−1.69312	−	1.69312i
$475$	−31.1866	+	15.4414i	−1.43094	+	0.708501i
$476$	−1.08886	−	1.08886i	−0.0499080	−	0.0499080i
$477$	−4.73305	−	4.73305i	−0.216711	−	0.216711i
$478$	48.2682	+	48.2682i	2.20773	+	2.20773i
$479$	23.3087	−	23.3087i	1.06500	−	1.06500i	0.0672673	−	0.997735i	$-0.478572\pi$
$479$	23.3087	−	23.3087i	1.06500	−	1.06500i	0.997735	−	0.0672673i	$-0.0214280\pi$
$480$	−38.8826	−	6.38768i	−1.77474	−	0.291557i
$481$		0			0
$482$	10.2497	+	10.2497i	0.466862	+	0.466862i
$483$		−	0.468135i		−	0.0213009i
$484$		−	37.9944i		−	1.72702i
$485$	19.5123	+	27.1835i	0.886008	+	1.23434i
$486$	23.4357	−	23.4357i	1.06306	−	1.06306i
$487$	−32.9863			−1.49475			−0.747376	−	0.664402i	$-0.768686\pi$
$487$	−32.9863			−1.49475			−0.747376	+	0.664402i	$0.768686\pi$
$488$	22.2792			1.00853
$489$	18.8165	−	18.8165i	0.850911	−	0.850911i
$490$	−24.1417	−	33.6330i	−1.09061	−	1.51938i
$491$		−	21.2958i		−	0.961065i	−0.876977	−	0.480533i	$-0.840443\pi$
$491$		−	21.2958i		−	0.961065i	0.876977	−	0.480533i	$-0.159557\pi$
$492$			35.3331i			1.59294i
$493$	−8.98502	−	8.98502i	−0.404665	−	0.404665i
$494$		0			0
$495$	5.38797	+	0.885142i	0.242171	+	0.0397842i
$496$	6.97420	−	6.97420i	0.313151	−	0.313151i
$497$	0.434837	+	0.434837i	0.0195051	+	0.0195051i
$498$	−20.7493	−	20.7493i	−0.929799	−	0.929799i
$499$	−14.9199	−	14.9199i	−0.667904	−	0.667904i	0.289326	−	0.957231i	$-0.406569\pi$
$499$	−14.9199	−	14.9199i	−0.667904	−	0.667904i	−0.957231	+	0.289326i	$0.906569\pi$
$500$	−53.6822	+	16.4247i	−2.40074	+	0.734536i
$501$	2.33035	+	2.33035i	0.104112	+	0.104112i
$502$			34.6261i			1.54544i
$503$	30.8883	−	30.8883i	1.37724	−	1.37724i	0.527996	−	0.849247i	$-0.322944\pi$
$503$	30.8883	−	30.8883i	1.37724	−	1.37724i	0.849247	−	0.527996i	$-0.177056\pi$
$504$	1.18529			0.0527968
$505$	−15.0965	+	10.8362i	−0.671786	+	0.482207i
$506$		−	15.7736i		−	0.701224i
$507$		0			0
$508$	41.4280	−	41.4280i	1.83807	−	1.83807i
$509$	−26.4196	−	26.4196i	−1.17103	−	1.17103i	−0.981965	−	0.189062i	$-0.939455\pi$
$509$	−26.4196	−	26.4196i	−1.17103	−	1.17103i	−0.189062	−	0.981965i	$-0.560545\pi$
$510$	17.0410	−	12.2320i	0.754590	−	0.541643i
$511$		−	1.01812i		−	0.0450390i
$512$	27.0748			1.19655
$513$			38.9770i			1.72088i
$514$	32.6928	−	32.6928i	1.44202	−	1.44202i
$515$	−3.96233	+	24.1192i	−0.174601	+	1.06282i
$516$	−25.3781			−1.11721
$517$	0.452141	−	0.452141i	0.0198851	−	0.0198851i
$518$	−0.439061			−0.0192912
$519$	−0.102326			−0.00449161
$520$		0			0
$521$	−35.6853			−1.56340			−0.781701	−	0.623653i	$-0.785648\pi$
$521$	−35.6853			−1.56340			−0.781701	+	0.623653i	$0.785648\pi$
$522$	16.2554			0.711478
$523$	−3.05155	+	3.05155i	−0.133435	+	0.133435i	−0.770670	−	0.637235i	$-0.780078\pi$
$523$	−3.05155	+	3.05155i	−0.133435	+	0.133435i	0.637235	+	0.770670i	$0.280078\pi$
$524$	37.4772			1.63720
$525$	−0.652910	+	0.323276i	−0.0284953	+	0.0141089i
$526$	−39.0625	+	39.0625i	−1.70321	+	1.70321i
$527$			2.41030i			0.104994i
$528$	−26.8432			−1.16820
$529$		−	12.6783i		−	0.551229i
$530$	29.6955	+	4.87842i	1.28989	+	0.211905i
$531$	1.19714	+	1.19714i	0.0519514	+	0.0519514i
$532$	−2.77630	+	2.77630i	−0.120368	+	0.120368i
$533$		0			0
$534$		−	1.95589i		−	0.0846398i
$535$	2.68386	−	16.3370i	0.116034	−	0.706310i
$536$	−1.15541			−0.0499063
$537$	19.4645	−	19.4645i	0.839955	−	0.839955i
$538$			27.9987i			1.20711i
$539$	−9.15481	−	9.15481i	−0.394326	−	0.394326i
$540$	−10.1929	+	62.0453i	−0.438632	+	2.67001i
$541$	5.42748	+	5.42748i	0.233345	+	0.233345i	0.814088	−	0.580742i	$-0.197238\pi$
$541$	5.42748	+	5.42748i	0.233345	+	0.233345i	−0.580742	+	0.814088i	$0.697238\pi$
$542$	−14.8216	−	14.8216i	−0.636641	−	0.636641i
$543$	−20.6591	−	20.6591i	−0.886569	−	0.886569i
$544$	26.2255	−	26.2255i	1.12441	−	1.12441i
$545$	−1.71498	+	10.4393i	−0.0734616	+	0.447170i
$546$		0			0
$547$	11.6940	+	11.6940i	0.500000	+	0.500000i	0.911438	−	0.411438i	$-0.134973\pi$
$547$	11.6940	+	11.6940i	0.500000	+	0.500000i	−0.411438	+	0.911438i	$0.634973\pi$
$548$			92.8131i			3.96478i
$549$		−	3.66765i		−	0.156531i
$550$	−21.9996	+	10.8927i	−0.938065	+	0.464464i
$551$	−22.9093	+	22.9093i	−0.975971	+	0.975971i
$552$	33.3573			1.41978
$553$	−1.70420			−0.0724700
$554$	−19.1378	+	19.1378i	−0.813087	+	0.813087i
$555$	0.693384	−	4.22071i	0.0294325	−	0.179159i
$556$		−	54.7829i		−	2.32331i
$557$			4.87503i			0.206562i	0.994652	+	0.103281i	$0.0329340\pi$
$557$			4.87503i			0.206562i	−0.994652	+	0.103281i	$0.967066\pi$
$558$	−2.18031	−	2.18031i	−0.0922998	−	0.0922998i
$559$		0			0
$560$	−2.27963	+	1.63632i	−0.0963321	+	0.0691470i
$561$	4.63853	−	4.63853i	0.195839	−	0.195839i
$562$	33.0590	+	33.0590i	1.39451	+	1.39451i
$563$	27.5537	+	27.5537i	1.16125	+	1.16125i	0.984202	+	0.177047i	$0.0566545\pi$
$563$	27.5537	+	27.5537i	1.16125	+	1.16125i	0.177047	+	0.984202i	$0.443346\pi$
$564$	1.58913	+	1.58913i	0.0669146	+	0.0669146i
$565$	13.4932	+	2.21669i	0.567665	+	0.0932568i
$566$	15.4885	+	15.4885i	0.651031	+	0.651031i
$567$			0.371828i			0.0156153i
$568$	−30.9846	+	30.9846i	−1.30009	+	1.30009i
$569$	3.68208			0.154361			0.0771804	−	0.997017i	$-0.475408\pi$
$569$	3.68208			0.154361			0.0771804	+	0.997017i	$0.475408\pi$
$570$	−31.1883	−	43.4500i	−1.30633	−	1.81992i
$571$		−	2.96698i		−	0.124164i	−0.998071	−	0.0620821i	$-0.980226\pi$
$571$		−	2.96698i		−	0.124164i	0.998071	−	0.0620821i	$-0.0197741\pi$
$572$		0			0
$573$	17.9811	−	17.9811i	0.751170	−	0.751170i
$574$	1.14209	+	1.14209i	0.0476699	+	0.0476699i
$575$	14.3958	−	7.12778i	0.600345	−	0.297249i
$576$			18.0049i			0.750204i
$577$	35.0533			1.45929			0.729644	−	0.683827i	$-0.239686\pi$
$577$	35.0533			1.45929			0.729644	+	0.683827i	$0.239686\pi$
$578$		−	25.3017i		−	1.05241i
$579$	−15.3265	+	15.3265i	−0.636948	+	0.636948i
$580$	−42.4591	+	30.4771i	−1.76302	+	1.26549i
$581$	−0.959287			−0.0397979
$582$	−36.3648	+	36.3648i	−1.50737	+	1.50737i
$583$	9.41095			0.389762
$584$	72.5469			3.00201
$585$		0			0
$586$	16.9010			0.698173
$587$	−7.05437			−0.291165			−0.145583	−	0.989346i	$-0.546506\pi$
$587$	−7.05437			−0.291165			−0.145583	+	0.989346i	$0.546506\pi$
$588$	32.1763	−	32.1763i	1.32693	−	1.32693i
$589$	6.14559			0.253225
$590$	−7.51095	−	1.23391i	−0.309221	−	0.0507992i
$591$	13.9273	−	13.9273i	0.572892	−	0.572892i
$592$		−	16.4744i		−	0.677092i
$593$	−40.0169			−1.64330			−0.821649	−	0.569993i	$-0.806946\pi$
$593$	−40.0169			−1.64330			−0.821649	+	0.569993i	$0.806946\pi$
$594$			27.4951i			1.12814i
$595$	0.111166	−	0.676680i	0.00455735	−	0.0277412i
$596$	−49.4275	−	49.4275i	−2.02463	−	2.02463i
$597$	−12.7909	+	12.7909i	−0.523495	+	0.523495i
$598$		0			0
$599$			13.9207i			0.568784i	0.958708	+	0.284392i	$0.0917918\pi$
$599$			13.9207i			0.568784i	−0.958708	+	0.284392i	$0.908208\pi$
$600$	−23.0352	−	46.5236i	−0.940410	−	1.89932i
$601$	−2.31378			−0.0943812			−0.0471906	−	0.998886i	$-0.515027\pi$
$601$	−2.31378			−0.0943812			−0.0471906	+	0.998886i	$0.515027\pi$
$602$	−0.820311	+	0.820311i	−0.0334334	+	0.0334334i
$603$			0.190206i			0.00774580i
$604$	42.6597	+	42.6597i	1.73580	+	1.73580i
$605$	13.7454	−	9.86641i	0.558829	−	0.401127i
$606$	−20.1954	−	20.1954i	−0.820381	−	0.820381i
$607$	16.6882	+	16.6882i	0.677353	+	0.677353i	0.959400	−	0.282047i	$-0.0910135\pi$
$607$	16.6882	+	16.6882i	0.677353	+	0.677353i	−0.282047	+	0.959400i	$0.591014\pi$
$608$	−66.8679	−	66.8679i	−2.71185	−	2.71185i
$609$	−0.479621	+	0.479621i	−0.0194352	+	0.0194352i
$610$	9.61542	+	13.3957i	0.389317	+	0.542377i
$611$		0			0
$612$	−12.7726	−	12.7726i	−0.516303	−	0.516303i
$613$		−	10.6593i		−	0.430524i	−0.976556	−	0.215262i	$-0.930939\pi$
$613$		−	10.6593i		−	0.430524i	0.976556	−	0.215262i	$-0.0690606\pi$
$614$		−	70.3403i		−	2.83871i
$615$	−12.7826	+	9.17533i	−0.515445	+	0.369985i
$616$	−1.17838	+	1.17838i	−0.0474783	+	0.0474783i
$617$	13.7284			0.552685			0.276343	−	0.961059i	$-0.410878\pi$
$617$	13.7284			0.552685			0.276343	+	0.961059i	$0.410878\pi$
$618$	−37.5661			−1.51113
$619$	16.8604	−	16.8604i	0.677679	−	0.677679i	−0.281796	−	0.959474i	$-0.590930\pi$
$619$	16.8604	−	16.8604i	0.677679	−	0.677679i	0.959474	+	0.281796i	$0.0909301\pi$
$620$	9.78283	+	1.60714i	0.392888	+	0.0645441i
$621$		−	17.9918i		−	0.721988i
$622$			9.39119i			0.376552i
$623$	−0.0452127	−	0.0452127i	−0.00181141	−	0.00181141i
$624$		0			0
$625$	−19.8823	−	15.1557i	−0.795292	−	0.606227i
$626$	16.4573	−	16.4573i	0.657766	−	0.657766i
$627$	−11.8270	−	11.8270i	−0.472324	−	0.472324i
$628$	−25.8336	−	25.8336i	−1.03087	−	1.03087i
$629$	2.84678	+	2.84678i	0.113509	+	0.113509i
$630$	0.511553	+	0.712670i	0.0203808	+	0.0283935i
$631$	21.6345	+	21.6345i	0.861257	+	0.861257i	0.991484	−	0.130227i	$-0.0415706\pi$
$631$	21.6345	+	21.6345i	0.861257	+	0.861257i	−0.130227	+	0.991484i	$0.541571\pi$
$632$		−	121.434i		−	4.83038i
$633$	−21.6601	+	21.6601i	−0.860911	+	0.860911i
$634$	−22.5974			−0.897459
$635$	25.7457	+	4.22953i	1.02169	+	0.167844i
$636$			33.0766i			1.31157i
$637$		0			0
$638$	−16.1607	+	16.1607i	−0.639807	+	0.639807i
$639$	5.10075	+	5.10075i	0.201783	+	0.201783i
$640$	−11.7707	−	16.3984i	−0.465279	−	0.648204i
$641$			15.2991i			0.604280i	0.953264	+	0.302140i	$0.0977010\pi$
$641$			15.2991i			0.604280i	−0.953264	+	0.302140i	$0.902299\pi$
$642$	25.4452			1.00424
$643$			22.3480i			0.881319i	0.897674	+	0.440660i	$0.145255\pi$
$643$			22.3480i			0.881319i	−0.897674	+	0.440660i	$0.854745\pi$
$644$	1.28154	−	1.28154i	0.0504999	−	0.0504999i
$645$	−6.59022	−	9.18116i	−0.259490	−	0.361508i
$646$	50.3420			1.98068
$647$	−3.30644	+	3.30644i	−0.129990	+	0.129990i	−0.769108	−	0.639119i	$-0.779299\pi$
$647$	−3.30644	+	3.30644i	−0.129990	+	0.129990i	0.639119	+	0.769108i	$0.279299\pi$
$648$	−26.4949			−1.04082
$649$	−2.38033			−0.0934361
$650$		0			0
$651$	0.128662			0.00504265
$652$	103.022			4.03466
$653$	17.3287	−	17.3287i	0.678124	−	0.678124i	−0.281451	−	0.959575i	$-0.590816\pi$
$653$	17.3287	−	17.3287i	0.678124	−	0.678124i	0.959575	+	0.281451i	$0.0908158\pi$
$654$	−16.2594			−0.635792
$655$	9.73212	+	13.5583i	0.380265	+	0.529766i
$656$	−42.8533	+	42.8533i	−1.67314	+	1.67314i
$657$		−	11.9428i		−	0.465934i
$658$	0.102733			0.00400494
$659$			40.7382i			1.58693i	0.608613	+	0.793467i	$0.291726\pi$
$659$			40.7382i			1.58693i	−0.608613	+	0.793467i	$0.708274\pi$
$660$	−15.7338	−	21.9196i	−0.612439	−	0.853219i
$661$	−12.0900	−	12.0900i	−0.470245	−	0.470245i	0.431749	−	0.901994i	$-0.357897\pi$
$661$	−12.0900	−	12.0900i	−0.470245	−	0.470245i	−0.901994	+	0.431749i	$0.857897\pi$
$662$	33.7389	−	33.7389i	1.31130	−	1.31130i
$663$		0			0
$664$		−	68.3547i		−	2.65268i
$665$	−1.72535	−	0.283442i	−0.0669061	−	0.0109914i
$666$	−5.15030			−0.199570
$667$	10.5750	−	10.5750i	0.409465	−	0.409465i
$668$			12.7589i			0.493657i
$669$	8.92003	+	8.92003i	0.344868	+	0.344868i
$670$	−0.498661	−	0.694709i	−0.0192650	−	0.0268390i
$671$	3.64628	+	3.64628i	0.140763	+	0.140763i
$672$	−1.39992	−	1.39992i	−0.0540031	−	0.0540031i
$673$	−16.8402	−	16.8402i	−0.649140	−	0.649140i	0.303645	−	0.952785i	$-0.401796\pi$
$673$	−16.8402	−	16.8402i	−0.649140	−	0.649140i	−0.952785	+	0.303645i	$0.901796\pi$
$674$	−53.2242	+	53.2242i	−2.05012	+	2.05012i
$675$	−25.0933	+	12.4245i	−0.965842	+	0.478218i
$676$		0			0
$677$	26.1344	+	26.1344i	1.00443	+	1.00443i	0.999990	+	0.00443504i	$0.00141172\pi$
$677$	26.1344	+	26.1344i	1.00443	+	1.00443i	0.00443504	+	0.999990i	$0.498588\pi$
$678$			21.0160i			0.807114i
$679$			1.68123i			0.0645195i
$680$	48.2173	+	7.92120i	1.84905	+	0.303764i
$681$	−8.41509	+	8.41509i	−0.322467	+	0.322467i
$682$	4.33521			0.166004
$683$	−26.7876			−1.02500			−0.512500	−	0.858687i	$-0.671280\pi$
$683$	−26.7876			−1.02500			−0.512500	+	0.858687i	$0.671280\pi$
$684$	−32.5667	+	32.5667i	−1.24522	+	1.24522i
$685$	−33.5774	+	24.1018i	−1.28293	+	0.920882i
$686$		−	4.16397i		−	0.158981i
$687$		−	22.9770i		−	0.876628i
$688$	−30.7796	−	30.7796i	−1.17346	−	1.17346i
$689$		0			0
$690$	14.3966	+	20.0566i	0.548068	+	0.763541i
$691$	−28.5426	+	28.5426i	−1.08581	+	1.08581i	−0.0898576	+	0.995955i	$0.528641\pi$
$691$	−28.5426	+	28.5426i	−1.08581	+	1.08581i	−0.995955	+	0.0898576i	$0.971359\pi$
$692$	−0.280123	−	0.280123i	−0.0106487	−	0.0106487i
$693$	0.193987	+	0.193987i	0.00736896	+	0.00736896i
$694$	13.4464	+	13.4464i	0.510419	+	0.510419i
$695$	19.8190	−	14.2261i	0.751779	−	0.539626i
$696$	−34.1758	−	34.1758i	−1.29543	−	1.29543i
$697$		−	14.8102i		−	0.560976i
$698$	6.84510	−	6.84510i	0.259091	−	0.259091i
$699$	21.7602			0.823047
$700$	−2.67236	−	0.902392i	−0.101006	−	0.0341072i
$701$		−	24.9781i		−	0.943410i	−0.881756	−	0.471705i	$-0.843639\pi$
$701$		−	24.9781i		−	0.943410i	0.881756	−	0.471705i	$-0.156361\pi$
$702$		0			0
$703$	7.25852	−	7.25852i	0.273760	−	0.273760i
$704$	−17.9000	−	17.9000i	−0.674632	−	0.674632i
$705$	−0.162240	+	0.987576i	−0.00611032	+	0.0371943i
$706$		−	4.67220i		−	0.175840i
$707$	−0.933677			−0.0351145
$708$		−	8.36612i		−	0.314418i
$709$	−7.21640	+	7.21640i	−0.271018	+	0.271018i	−0.829510	−	0.558492i	$-0.811380\pi$
$709$	−7.21640	+	7.21640i	−0.271018	+	0.271018i	0.558492	+	0.829510i	$0.311380\pi$
$710$	−32.0025	−	5.25742i	−1.20103	−	0.197307i
$711$	−19.9907			−0.749710
$712$	3.22166	−	3.22166i	0.120737	−	0.120737i
$713$	−2.83681			−0.106240
$714$	1.05394			0.0394428
$715$		0			0
$716$	106.570			3.98272
$717$	−33.4118			−1.24779
$718$	−22.7354	+	22.7354i	−0.848479	+	0.848479i
$719$	−28.4233			−1.06001			−0.530005	−	0.847994i	$-0.677810\pi$
$719$	−28.4233			−1.06001			−0.530005	+	0.847994i	$0.677810\pi$
$720$	−26.7407	+	19.1944i	−0.996566	+	0.715333i
$721$	−0.868382	+	0.868382i	−0.0323402	+	0.0323402i
$722$		−	78.0130i		−	2.90334i
$723$	−7.09498			−0.263865
$724$		−	113.111i		−	4.20374i
$725$	−22.0517	−	7.44631i	−0.818978	−	0.276549i
$726$	18.3879	+	18.3879i	0.682439	+	0.682439i
$727$	8.56116	−	8.56116i	0.317516	−	0.317516i	−0.530296	−	0.847812i	$-0.677919\pi$
$727$	8.56116	−	8.56116i	0.317516	−	0.317516i	0.847812	+	0.530296i	$0.177919\pi$
$728$		0			0
$729$			26.1513i			0.968566i
$730$	31.3103	+	43.6199i	1.15885	+	1.61445i
$731$	10.6375			0.393441
$732$	−12.8156	+	12.8156i	−0.473676	+	0.473676i
$733$		−	17.2200i		−	0.636036i	−0.948085	−	0.318018i	$-0.896983\pi$
$733$		−	17.2200i		−	0.636036i	0.948085	−	0.318018i	$-0.103017\pi$
$734$	26.2521	+	26.2521i	0.968982	+	0.968982i
$735$	19.9961	+	3.28499i	0.737569	+	0.121169i
$736$	30.8663	+	30.8663i	1.13775	+	1.13775i
$737$	−0.189098	−	0.189098i	−0.00696552	−	0.00696552i
$738$	13.3970	+	13.3970i	0.493151	+	0.493151i
$739$	11.5296	−	11.5296i	0.424124	−	0.424124i	−0.462497	−	0.886621i	$-0.653046\pi$
$739$	11.5296	−	11.5296i	0.424124	−	0.424124i	0.886621	+	0.462497i	$0.153046\pi$
$740$	13.4526	−	9.65626i	0.494528	−	0.354971i
$741$		0			0
$742$	1.06915	+	1.06915i	0.0392498	+	0.0392498i
$743$		−	33.1199i		−	1.21505i	−0.794301	−	0.607525i	$-0.792163\pi$
$743$		−	33.1199i		−	1.21505i	0.794301	−	0.607525i	$-0.207837\pi$
$744$			9.16789i			0.336111i
$745$	5.04623	−	30.7170i	0.184879	−	1.12538i
$746$	54.1344	−	54.1344i	1.98200	−	1.98200i
$747$	−11.2527			−0.411714
$748$	25.3965			0.928586
$749$	0.588194	−	0.588194i	0.0214921	−	0.0214921i
$750$	18.0313	−	33.9292i	0.658410	−	1.23892i
$751$			21.9348i			0.800411i	0.916426	+	0.400205i	$0.131061\pi$
$751$			21.9348i			0.800411i	−0.916426	+	0.400205i	$0.868939\pi$
$752$			3.85472i			0.140567i
$753$	−11.9843	−	11.9843i	−0.436732	−	0.436732i
$754$		0			0
$755$	−4.35528	+	26.5111i	−0.158505	+	0.964838i
$756$	−2.23387	+	2.23387i	−0.0812449	+	0.0812449i
$757$	2.08399	+	2.08399i	0.0757437	+	0.0757437i	0.743964	−	0.668220i	$-0.232944\pi$
$757$	2.08399	+	2.08399i	0.0757437	+	0.0757437i	−0.668220	+	0.743964i	$0.732944\pi$
$758$	−17.7563	−	17.7563i	−0.644938	−	0.644938i
$759$	5.45935	+	5.45935i	0.198162	+	0.198162i
$760$	20.1969	−	122.941i	0.732618	−	4.45953i
$761$	−15.5835	−	15.5835i	−0.564901	−	0.564901i	0.365794	−	0.930696i	$-0.380797\pi$
$761$	−15.5835	−	15.5835i	−0.564901	−	0.564901i	−0.930696	+	0.365794i	$0.880797\pi$
$762$			40.0993i			1.45265i
$763$	−0.375854	+	0.375854i	−0.0136068	+	0.0136068i
$764$	98.4482			3.56173
$765$	1.30400	−	7.93762i	0.0471463	−	0.286985i
$766$			55.8361i			2.01744i
$767$		0			0
$768$	−3.12197	+	3.12197i	−0.112654	+	0.112654i
$769$	−14.9366	−	14.9366i	−0.538628	−	0.538628i	0.384498	−	0.923126i	$-0.374375\pi$
$769$	−14.9366	−	14.9366i	−0.538628	−	0.538628i	−0.923126	+	0.384498i	$0.874375\pi$
$770$	−1.21709	−	0.199945i	−0.0438609	−	0.00720553i
$771$			22.6303i			0.815011i
$772$	−83.9143			−3.02014
$773$			18.6956i			0.672435i	0.941784	+	0.336217i	$0.109148\pi$
$773$			18.6956i			0.672435i	−0.941784	+	0.336217i	$0.890852\pi$
$774$	−9.62245	+	9.62245i	−0.345872	+	0.345872i
$775$	1.95899	+	3.95652i	0.0703691	+	0.142122i
$776$	−119.797			−4.30046
$777$	0.151962	−	0.151962i	0.00545159	−	0.00545159i
$778$	0.160259			0.00574555
$779$	−37.7619			−1.35296
$780$		0			0
$781$	−10.1421			−0.362912
$782$	−23.2379			−0.830987
$783$	−18.4333	+	18.4333i	−0.658752	+	0.658752i
$784$	78.0493			2.78747
$785$	2.63744	−	16.0544i	0.0941344	−	0.573008i
$786$	−18.1376	+	18.1376i	−0.646947	+	0.646947i
$787$			43.3231i			1.54430i	0.635440	+	0.772150i	$0.280819\pi$
$787$			43.3231i			1.54430i	−0.635440	+	0.772150i	$0.719181\pi$
$788$	76.2534			2.71642
$789$		−	27.0396i		−	0.962634i
$790$	73.0140	−	52.4093i	2.59772	−	1.86464i
$791$	0.485808	+	0.485808i	0.0172733	+	0.0172733i
$792$	−13.8227	+	13.8227i	−0.491168	+	0.491168i
$793$		0			0
$794$			21.7710i			0.772625i
$795$	−11.9663	+	8.58935i	−0.424399	+	0.304633i
$796$	−70.0314			−2.48220
$797$	−24.8641	+	24.8641i	−0.880731	+	0.880731i	−0.993609	−	0.112877i	$-0.963993\pi$
$797$	−24.8641	+	24.8641i	−0.880731	+	0.880731i	0.112877	+	0.993609i	$0.463993\pi$
$798$		−	2.68726i		−	0.0951280i
$799$	−0.666099	−	0.666099i	−0.0235649	−	0.0235649i
$800$	21.7343	−	64.3644i	0.768424	−	2.27563i
$801$	−0.530356	−	0.530356i	−0.0187392	−	0.0187392i
$802$	−16.8606	−	16.8606i	−0.595367	−	0.595367i
$803$	11.8732	+	11.8732i	0.418997	+	0.418997i
$804$	0.664622	−	0.664622i	0.0234394	−	0.0234394i
$805$	0.796423	+	0.130837i	0.0280702	+	0.00461141i
$806$		0			0
$807$	−9.69052	−	9.69052i	−0.341122	−	0.341122i
$808$		−	66.5298i		−	2.34051i
$809$			20.6437i			0.725792i	0.931830	+	0.362896i	$0.118212\pi$
$809$			20.6437i			0.725792i	−0.931830	+	0.362896i	$0.881788\pi$
$810$	−11.4348	−	15.9304i	−0.401779	−	0.559738i
$811$	22.0471	−	22.0471i	0.774178	−	0.774178i	−0.204656	−	0.978834i	$-0.565608\pi$
$811$	22.0471	−	22.0471i	0.774178	−	0.774178i	0.978834	+	0.204656i	$0.0656076\pi$
$812$	−2.62598			−0.0921538
$813$	10.2597			0.359823
$814$	5.12029	−	5.12029i	0.179466	−	0.179466i
$815$	26.7529	+	37.2708i	0.937114	+	1.30554i
$816$			39.5458i			1.38438i
$817$		−	27.1226i		−	0.948901i
$818$	67.1180	+	67.1180i	2.34672	+	2.34672i
$819$		0			0
$820$	−60.1111	−	9.87512i	−2.09917	−	0.344854i
$821$	25.9495	−	25.9495i	0.905644	−	0.905644i	−0.0902727	−	0.995917i	$-0.528774\pi$
$821$	25.9495	−	25.9495i	0.905644	−	0.905644i	0.995917	+	0.0902727i	$0.0287739\pi$
$822$	−44.9182	−	44.9182i	−1.56670	−	1.56670i
$823$	−16.6935	−	16.6935i	−0.581899	−	0.581899i	0.353526	−	0.935425i	$-0.384983\pi$
$823$	−16.6935	−	16.6935i	−0.581899	−	0.581899i	−0.935425	+	0.353526i	$0.884983\pi$
$824$	−61.8772	−	61.8772i	−2.15559	−	2.15559i
$825$	3.84417	−	11.3842i	0.133837	−	0.396347i
$826$	−0.270423	−	0.270423i	−0.00940921	−	0.00940921i
$827$			4.44429i			0.154543i	0.997010	+	0.0772716i	$0.0246209\pi$
$827$			4.44429i			0.154543i	−0.997010	+	0.0772716i	$0.975379\pi$
$828$	15.0328	−	15.0328i	0.522427	−	0.522427i
$829$	−29.3369			−1.01891			−0.509457	−	0.860496i	$-0.670154\pi$
$829$	−29.3369			−1.01891			−0.509457	+	0.860496i	$0.670154\pi$
$830$	41.0993	−	29.5010i	1.42658	−	1.02399i
$831$		−	13.2474i		−	0.459548i
$832$		0			0
$833$	−13.4870	+	13.4870i	−0.467296	+	0.467296i
$834$	26.5129	+	26.5129i	0.918068	+	0.918068i
$835$	−4.61585	+	3.31324i	−0.159738	+	0.114660i
$836$		−	64.7540i		−	2.23956i
$837$	4.94486			0.170919
$838$		−	34.6607i		−	1.19734i
$839$	−6.00111	+	6.00111i	−0.207181	+	0.207181i	−0.803068	−	0.595887i	$-0.796801\pi$
$839$	−6.00111	+	6.00111i	−0.207181	+	0.207181i	0.595887	+	0.803068i	$0.296801\pi$
$840$	0.422834	−	2.57384i	0.0145892	−	0.0888061i
$841$	7.33109			0.252796
$842$	−36.5466	+	36.5466i	−1.25948	+	1.25948i
$843$	−22.8838			−0.788162
$844$	−118.591			−4.08208
$845$		0			0
$846$	1.20508			0.0414316
$847$	0.850114			0.0292103
$848$	−40.1165	+	40.1165i	−1.37761	+	1.37761i
$849$	−10.7213			−0.367955
$850$	16.0472	+	32.4101i	0.550415	+	1.11166i
$851$	−3.35054	+	3.35054i	−0.114855	+	0.114855i
$852$		−	35.6462i		−	1.22122i
$853$	34.3415			1.17583			0.587915	−	0.808923i	$-0.299949\pi$
$853$	34.3415			1.17583			0.587915	+	0.808923i	$0.299949\pi$
$854$			0.828488i			0.0283503i
$855$	−20.2388	−	3.32485i	−0.692151	−	0.113707i
$856$	41.9122	+	41.9122i	1.43253	+	1.43253i
$857$	−24.6090	+	24.6090i	−0.840626	+	0.840626i	−0.988940	−	0.148314i	$-0.952615\pi$
$857$	−24.6090	+	24.6090i	−0.840626	+	0.840626i	0.148314	+	0.988940i	$0.452615\pi$
$858$		0			0
$859$		−	12.8606i		−	0.438798i	−0.975635	−	0.219399i	$-0.929590\pi$
$859$		−	12.8606i		−	0.438798i	0.975635	−	0.219399i	$-0.0704097\pi$
$860$	7.09284	−	43.1750i	0.241864	−	1.47226i
$861$	−0.790569			−0.0269425
$862$	−41.6308	+	41.6308i	−1.41795	+	1.41795i
$863$		−	2.75373i		−	0.0937379i	−0.998901	−	0.0468690i	$-0.985076\pi$
$863$		−	2.75373i		−	0.0937379i	0.998901	−	0.0468690i	$-0.0149243\pi$
$864$	−53.8032	−	53.8032i	−1.83042	−	1.83042i
$865$	0.0285987	−	0.174084i	0.000972386	−	0.00591903i
$866$	0.343907	+	0.343907i	0.0116864	+	0.0116864i
$867$	8.75709	+	8.75709i	0.297406	+	0.297406i
$868$	0.352219	+	0.352219i	0.0119551	+	0.0119551i
$869$	19.8742	−	19.8742i	0.674187	−	0.674187i
$870$	5.79888	−	35.2985i	0.196601	−	1.19673i
$871$		0			0
$872$	−26.7817	−	26.7817i	−0.906944	−	0.906944i
$873$			19.7212i			0.667462i
$874$			59.2504i			2.00417i
$875$	−0.367499	−	1.20113i	−0.0124237	−	0.0406055i
$876$	−41.7308	+	41.7308i	−1.40995	+	1.40995i
$877$	47.2631			1.59596			0.797981	−	0.602683i	$-0.205902\pi$
$877$	47.2631			1.59596			0.797981	+	0.602683i	$0.205902\pi$
$878$	45.8239			1.54648
$879$	−5.84953	+	5.84953i	−0.197300	+	0.197300i
$880$	7.50231	−	45.6675i	0.252903	−	1.53945i
$881$			41.3214i			1.39215i	0.717967	+	0.696077i	$0.245073\pi$
$881$			41.3214i			1.39215i	−0.717967	+	0.696077i	$0.754927\pi$
$882$		−	24.4001i		−	0.821596i
$883$	−13.4808	−	13.4808i	−0.453666	−	0.453666i	0.442903	−	0.896569i	$-0.353949\pi$
$883$	−13.4808	−	13.4808i	−0.453666	−	0.453666i	−0.896569	+	0.442903i	$0.853949\pi$
$884$		0			0
$885$	3.02665	−	2.17252i	0.101740	−	0.0730285i
$886$	−64.7790	+	64.7790i	−2.17629	+	2.17629i
$887$	16.2104	+	16.2104i	0.544292	+	0.544292i	0.924784	−	0.380492i	$-0.124246\pi$
$887$	16.2104	+	16.2104i	0.544292	+	0.544292i	−0.380492	+	0.924784i	$0.624246\pi$
$888$	10.8281	+	10.8281i	0.363368	+	0.363368i
$889$	0.926941	+	0.926941i	0.0310886	+	0.0310886i
$890$	3.32750	+	0.546646i	0.111538	+	0.0183236i
$891$	−4.33622	−	4.33622i	−0.145269	−	0.145269i
$892$			48.8381i			1.63522i
$893$	−1.69837	+	1.69837i	−0.0568338	+	0.0568338i
$894$	47.8423			1.60008
$895$	27.6743	+	38.5544i	0.925048	+	1.28873i
$896$		−	1.01420i		−	0.0338819i
$897$		0			0
$898$	−69.6712	+	69.6712i	−2.32496	+	2.32496i
$899$	2.90642	+	2.90642i	0.0969345	+	0.0969345i
$900$	−31.3475	−	10.5853i	−1.04492	−	0.352843i
$901$		−	13.8643i		−	0.461888i
$902$	−26.6379			−0.886946
$903$		−	0.567829i		−	0.0188962i
$904$	−34.6166	+	34.6166i	−1.15133	+	1.15133i
$905$	40.9207	−	29.3728i	1.36025	−	0.976384i
$906$	−41.2916			−1.37182
$907$	17.0541	−	17.0541i	0.566271	−	0.566271i	−0.364811	−	0.931082i	$-0.618866\pi$
$907$	17.0541	−	17.0541i	0.566271	−	0.566271i	0.931082	+	0.364811i	$0.118866\pi$
$908$	−46.0735			−1.52900
$909$	−10.9523			−0.363264
$910$		0			0
$911$	58.5135			1.93864			0.969320	−	0.245803i	$-0.0790515\pi$
$911$	58.5135			1.93864			0.969320	+	0.245803i	$0.0790515\pi$
$912$	100.831			3.33884
$913$	11.1871	−	11.1871i	0.370240	−	0.370240i
$914$	24.9790			0.826231
$915$	−7.96429	−	1.30838i	−0.263291	−	0.0432538i
$916$	62.9008	−	62.9008i	2.07830	−	2.07830i
$917$			0.838543i			0.0276911i
$918$	40.5061			1.33690
$919$			44.8545i			1.47961i	0.672820	+	0.739806i	$0.265083\pi$
$919$			44.8545i			1.47961i	−0.672820	+	0.739806i	$0.734917\pi$
$920$	−9.32291	+	56.7497i	−0.307367	+	1.87098i
$921$	24.3452	+	24.3452i	0.802202	+	0.802202i
$922$	−61.6169	+	61.6169i	−2.02924	+	2.02924i
$923$		0			0
$924$		−	1.35567i		−	0.0445981i
$925$	6.98677	+	2.35926i	0.229724	+	0.0775721i
$926$	49.4787			1.62597
$927$	−10.1863	+	10.1863i	−0.334563	+	0.334563i
$928$		−	63.2473i		−	2.07619i
$929$	19.8452	+	19.8452i	0.651099	+	0.651099i	0.953258	−	0.302158i	$-0.0977072\pi$
$929$	19.8452	+	19.8452i	0.651099	+	0.651099i	−0.302158	+	0.953258i	$0.597707\pi$
$930$	−5.51233	+	3.95674i	−0.180756	+	0.129747i
$931$	34.3881	+	34.3881i	1.12702	+	1.12702i
$932$	59.5698	+	59.5698i	1.95127	+	1.95127i
$933$	−3.25035	−	3.25035i	−0.106412	−	0.106412i
$934$	−32.2416	+	32.2416i	−1.05498	+	1.05498i
$935$	6.59497	+	9.18779i	0.215679	+	0.300473i
$936$		0			0
$937$	20.7545	+	20.7545i	0.678019	+	0.678019i	0.959552	−	0.281533i	$-0.0908428\pi$
$937$	20.7545	+	20.7545i	0.678019	+	0.678019i	−0.281533	+	0.959552i	$0.590843\pi$
$938$		−	0.0429658i		−	0.00140288i
$939$			11.3919i			0.371762i
$940$	−3.14768	+	2.25940i	−0.102666	+	0.0736935i
$941$	6.70533	−	6.70533i	0.218588	−	0.218588i	−0.589315	−	0.807903i	$-0.700602\pi$
$941$	6.70533	−	6.70533i	0.218588	−	0.218588i	0.807903	+	0.589315i	$0.200602\pi$
$942$	25.0051			0.814710
$943$	17.4309			0.567630
$944$	10.1467	−	10.1467i	0.330249	−	0.330249i
$945$	−1.38825	−	0.228063i	−0.0451597	−	0.00741889i
$946$		−	19.1328i		−	0.622061i
$947$		−	4.51085i		−	0.146583i	−0.997311	−	0.0732915i	$-0.976650\pi$
$947$		−	4.51085i		−	0.146583i	0.997311	−	0.0732915i	$-0.0233503\pi$
$948$	69.8518	+	69.8518i	2.26868	+	2.26868i
$949$		0			0
$950$	82.6367	−	40.9160i	2.68109	−	1.32749i
$951$	7.82111	−	7.82111i	0.253617	−	0.253617i
$952$	1.73600	+	1.73600i	0.0562642	+	0.0562642i
$953$	4.06109	+	4.06109i	0.131552	+	0.131552i	0.769817	−	0.638265i	$-0.220348\pi$
$953$	4.06109	+	4.06109i	0.131552	+	0.131552i	−0.638265	+	0.769817i	$0.720348\pi$
$954$	12.5414	+	12.5414i	0.406043	+	0.406043i
$955$	25.5651	+	35.6160i	0.827268	+	1.15251i
$956$	−91.4666	−	91.4666i	−2.95824	−	2.95824i
$957$		−	11.1866i		−	0.361612i
$958$	−61.7624	+	61.7624i	−1.99545	+	1.99545i
$959$	−2.07667			−0.0670591
$960$	39.0976	+	6.42300i	1.26187	+	0.207302i
$961$			30.2203i			0.974849i
$962$		0			0
$963$	6.89966	−	6.89966i	0.222338	−	0.222338i
$964$	−19.4229	−	19.4229i	−0.625569	−	0.625569i
$965$	−21.7909	−	30.3581i	−0.701475	−	0.977260i
$966$			1.24044i			0.0399106i
$967$	17.6414			0.567310			0.283655	−	0.958926i	$-0.408453\pi$
$967$	17.6414			0.567310			0.283655	+	0.958926i	$0.408453\pi$
$968$			60.5755i			1.94697i
$969$	−17.4237	+	17.4237i	−0.559729	+	0.559729i
$970$	−51.7028	−	72.0297i	−1.66008	−	2.31273i
$971$	33.3973			1.07177			0.535886	−	0.844290i	$-0.319978\pi$
$971$	33.3973			1.07177			0.535886	+	0.844290i	$0.319978\pi$
$972$	−44.4099	+	44.4099i	−1.42445	+	1.42445i
$973$	1.22575			0.0392958
$974$	87.4056			2.80065
$975$		0			0
$976$	−31.0864			−0.995050
$977$	15.3443			0.490909			0.245454	−	0.969408i	$-0.421063\pi$
$977$	15.3443			0.490909			0.245454	+	0.969408i	$0.421063\pi$
$978$	−49.8591	+	49.8591i	−1.59432	+	1.59432i
$979$	1.05453			0.0337030
$980$	45.7477	+	63.7334i	1.46136	+	2.03589i
$981$	−4.40886	+	4.40886i	−0.140764	+	0.140764i
$982$			56.4286i			1.80071i
$983$	4.80751			0.153336			0.0766679	−	0.997057i	$-0.475572\pi$
$983$	4.80751			0.153336			0.0766679	+	0.997057i	$0.475572\pi$
$984$		−	56.3325i		−	1.79582i
$985$	19.8016	+	27.5865i	0.630930	+	0.878980i
$986$	23.8081	+	23.8081i	0.758205	+	0.758205i
$987$	−0.0355565	+	0.0355565i	−0.00113177	+	0.00113177i
$988$		0			0
$989$			12.5198i			0.398108i
$990$	−14.2768	−	2.34541i	−0.453746	−	0.0745420i
$991$	0.439117			0.0139490			0.00697450	−	0.999976i	$-0.497780\pi$
$991$	0.439117			0.0139490			0.00697450	+	0.999976i	$0.497780\pi$
$992$	−8.48327	+	8.48327i	−0.269344	+	0.269344i
$993$			23.3545i			0.741131i
$994$	−1.15221	−	1.15221i	−0.0365459	−	0.0365459i
$995$	−18.1858	−	25.3355i	−0.576529	−	0.803191i
$996$	39.3193	+	39.3193i	1.24588	+	1.24588i
$997$	−4.64457	−	4.64457i	−0.147095	−	0.147095i	0.629724	−	0.776819i	$-0.283168\pi$
$997$	−4.64457	−	4.64457i	−0.147095	−	0.147095i	−0.776819	+	0.629724i	$0.783168\pi$
$998$	39.5340	+	39.5340i	1.25143	+	1.25143i
$999$	5.84034	−	5.84034i	0.184780	−	0.184780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.k.d.577.1		20
5.3	odd	4		845.2.f.d.408.10		20
13.2	odd	12		65.2.t.a.7.1	yes	20
13.3	even	3		845.2.o.f.357.5		20
13.4	even	6		65.2.o.a.2.1	✓	20
13.5	odd	4		845.2.f.e.437.10		20
13.6	odd	12		845.2.t.f.427.5		20
13.7	odd	12		845.2.t.e.427.1		20
13.8	odd	4		845.2.f.d.437.1		20
13.9	even	3		845.2.o.g.587.5		20
13.10	even	6		845.2.o.e.357.1		20
13.11	odd	12		845.2.t.g.657.5		20
13.12	even	2		845.2.k.e.577.10		20
39.2	even	12		585.2.dp.a.397.5		20
39.17	odd	6		585.2.cf.a.262.5		20
65.2	even	12		325.2.s.b.293.5		20
65.3	odd	12		845.2.t.e.188.1		20
65.4	even	6		325.2.s.b.132.5		20
65.8	even	4	inner	845.2.k.d.268.1		20
65.17	odd	12		325.2.x.b.93.5		20
65.18	even	4		845.2.k.e.268.10		20
65.23	odd	12		845.2.t.f.188.5		20
65.28	even	12		65.2.o.a.33.1	yes	20
65.33	even	12		845.2.o.f.258.5		20
65.38	odd	4		845.2.f.e.408.1		20
65.43	odd	12		65.2.t.a.28.1	yes	20
65.48	odd	12		845.2.t.g.418.5		20
65.54	odd	12		325.2.x.b.7.5		20
65.58	even	12		845.2.o.e.258.1		20
65.63	even	12		845.2.o.g.488.5		20
195.158	odd	12		585.2.cf.a.163.5		20
195.173	even	12		585.2.dp.a.28.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.1	✓	20	13.4	even	6
65.2.o.a.33.1	yes	20	65.28	even	12
65.2.t.a.7.1	yes	20	13.2	odd	12
65.2.t.a.28.1	yes	20	65.43	odd	12
325.2.s.b.132.5		20	65.4	even	6
325.2.s.b.293.5		20	65.2	even	12
325.2.x.b.7.5		20	65.54	odd	12
325.2.x.b.93.5		20	65.17	odd	12
585.2.cf.a.163.5		20	195.158	odd	12
585.2.cf.a.262.5		20	39.17	odd	6
585.2.dp.a.28.5		20	195.173	even	12
585.2.dp.a.397.5		20	39.2	even	12
845.2.f.d.408.10		20	5.3	odd	4
845.2.f.d.437.1		20	13.8	odd	4
845.2.f.e.408.1		20	65.38	odd	4
845.2.f.e.437.10		20	13.5	odd	4
845.2.k.d.268.1		20	65.8	even	4	inner
845.2.k.d.577.1		20	1.1	even	1	trivial
845.2.k.e.268.10		20	65.18	even	4
845.2.k.e.577.10		20	13.12	even	2
845.2.o.e.258.1		20	65.58	even	12
845.2.o.e.357.1		20	13.10	even	6
845.2.o.f.258.5		20	65.33	even	12
845.2.o.f.357.5		20	13.3	even	3
845.2.o.g.488.5		20	65.63	even	12
845.2.o.g.587.5		20	13.9	even	3
845.2.t.e.188.1		20	65.3	odd	12
845.2.t.e.427.1		20	13.7	odd	12
845.2.t.f.188.5		20	65.23	odd	12
845.2.t.f.427.5		20	13.6	odd	12
845.2.t.g.418.5		20	65.48	odd	12
845.2.t.g.657.5		20	13.11	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)

\(f(q)\)	\(=\)	\(q-2.64975 q^{2} +(0.917096 - 0.917096i) q^{3} +5.02120 q^{4} +(1.30391 + 1.81654i) q^{5} +(-2.43008 + 2.43008i) q^{6} +0.112348i q^{7} -8.00544 q^{8} +1.31787i q^{9} +O(q^{10})\)	\(q-2.64975 q^{2} +(0.917096 - 0.917096i) q^{3} +5.02120 q^{4} +(1.30391 + 1.81654i) q^{5} +(-2.43008 + 2.43008i) q^{6} +0.112348i q^{7} -8.00544 q^{8} +1.31787i q^{9} +(-3.45504 - 4.81339i) q^{10} +(-1.31019 - 1.31019i) q^{11} +(4.60492 - 4.60492i) q^{12} -0.297695i q^{14} +(2.86175 + 0.470132i) q^{15} +11.1700 q^{16} +(-1.93019 + 1.93019i) q^{17} -3.49203i q^{18} +(4.92146 + 4.92146i) q^{19} +(6.54719 + 9.12121i) q^{20} +(0.103034 + 0.103034i) q^{21} +(3.47169 + 3.47169i) q^{22} +(-2.27175 - 2.27175i) q^{23} +(-7.34175 + 7.34175i) q^{24} +(-1.59964 + 4.73721i) q^{25} +(3.95990 + 3.95990i) q^{27} +0.564122i q^{28} +4.65499i q^{29} +(-7.58294 - 1.24574i) q^{30} +(0.624367 - 0.624367i) q^{31} -13.5870 q^{32} -2.40314 q^{33} +(5.11454 - 5.11454i) q^{34} +(-0.204085 + 0.146492i) q^{35} +6.61729i q^{36} -1.47487i q^{37} +(-13.0407 - 13.0407i) q^{38} +(-10.4384 - 14.5422i) q^{40} +(-3.83645 + 3.83645i) q^{41} +(-0.273014 - 0.273014i) q^{42} +(-2.75555 - 2.75555i) q^{43} +(-6.57874 - 6.57874i) q^{44} +(-2.39396 + 1.71838i) q^{45} +(6.01959 + 6.01959i) q^{46} +0.345095i q^{47} +(10.2440 - 10.2440i) q^{48} +6.98738 q^{49} +(4.23866 - 12.5524i) q^{50} +3.54034i q^{51} +(-3.59144 + 3.59144i) q^{53} +(-10.4928 - 10.4928i) q^{54} +(0.671646 - 4.08839i) q^{55} -0.899394i q^{56} +9.02691 q^{57} -12.3346i q^{58} +(0.908390 - 0.908390i) q^{59} +(14.3694 + 2.36063i) q^{60} -2.78301 q^{61} +(-1.65442 + 1.65442i) q^{62} -0.148060 q^{63} +13.6621 q^{64} +6.36774 q^{66} +0.144329 q^{67} +(-9.69188 + 9.69188i) q^{68} -4.16683 q^{69} +(0.540774 - 0.388167i) q^{70} +(3.87045 - 3.87045i) q^{71} -10.5501i q^{72} -9.06221 q^{73} +3.90805i q^{74} +(2.87745 + 5.81150i) q^{75} +(24.7116 + 24.7116i) q^{76} +(0.147197 - 0.147197i) q^{77} +15.1689i q^{79} +(14.5647 + 20.2908i) q^{80} +3.30961 q^{81} +(10.1657 - 10.1657i) q^{82} +8.53853i q^{83} +(0.517354 + 0.517354i) q^{84} +(-6.02307 - 0.989478i) q^{85} +(7.30152 + 7.30152i) q^{86} +(4.26907 + 4.26907i) q^{87} +(10.4887 + 10.4887i) q^{88} +(-0.402434 + 0.402434i) q^{89} +(6.34342 - 4.55329i) q^{90} +(-11.4069 - 11.4069i) q^{92} -1.14521i q^{93} -0.914416i q^{94} +(-2.52290 + 15.3572i) q^{95} +(-12.4606 + 12.4606i) q^{96} +14.9645 q^{97} -18.5148 q^{98} +(1.72666 - 1.72666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 8 q^{2} + 4 q^{3} + 12 q^{4} + 6 q^{5} - 4 q^{6} - 12 q^{8}+O(q^{10}) \) 20 * q - 8 * q^2 + 4 * q^3 + 12 * q^4 + 6 * q^5 - 4 * q^6 - 12 * q^8	\( 20 q - 8 q^{2} + 4 q^{3} + 12 q^{4} + 6 q^{5} - 4 q^{6} - 12 q^{8} + 8 q^{10} - 8 q^{11} + 24 q^{12} + 24 q^{15} + 4 q^{16} + 14 q^{17} + 4 q^{19} + 22 q^{20} - 4 q^{21} - 32 q^{22} - 8 q^{23} - 4 q^{24} - 18 q^{25} + 4 q^{27} - 40 q^{30} - 12 q^{32} - 36 q^{33} + 2 q^{34} - 20 q^{35} + 8 q^{38} - 16 q^{40} + 38 q^{41} + 16 q^{42} + 32 q^{43} - 36 q^{44} + 20 q^{45} - 4 q^{46} + 28 q^{48} + 36 q^{49} + 52 q^{50} - 10 q^{53} + 36 q^{54} - 16 q^{55} + 12 q^{57} + 8 q^{59} + 92 q^{60} + 32 q^{61} - 4 q^{62} - 64 q^{63} - 20 q^{64} - 32 q^{66} - 116 q^{67} - 50 q^{68} - 32 q^{69} - 32 q^{70} + 40 q^{71} - 72 q^{73} - 4 q^{75} + 16 q^{76} + 28 q^{77} + 34 q^{80} + 28 q^{81} + 34 q^{82} + 8 q^{84} - 60 q^{86} - 28 q^{87} + 32 q^{88} + 12 q^{89} - 46 q^{90} - 8 q^{92} - 40 q^{95} - 56 q^{96} - 44 q^{97} + 8 q^{98} + 60 q^{99}+O(q^{100}) \) 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

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