LMFDB - Embedded newform 845.2.f.d.437.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("845.408");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			437.1
Root			$-2.64975i$ of defining polynomial
Character	$\chi$	$=$	845.437
Dual form			845.2.f.d.408.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64975i q^{2} +(0.917096 - 0.917096i) q^{3} -5.02120 q^{4} +(-1.81654 + 1.30391i) q^{5} +(-2.43008 - 2.43008i) q^{6} +0.112348 q^{7} +8.00544i q^{8} +1.31787i q^{9} +O(q^{10})$	\(q-2.64975i q^{2} +(0.917096 - 0.917096i) q^{3} -5.02120 q^{4} +(-1.81654 + 1.30391i) q^{5} +(-2.43008 - 2.43008i) q^{6} +0.112348 q^{7} +8.00544i 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} +(-0.470132 + 2.86175i) q^{15} +11.1700 q^{16} +(1.93019 - 1.93019i) q^{17} +3.49203 q^{18} +(-4.92146 + 4.92146i) q^{19} +(9.12121 - 6.54719i) 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} -0.564122 q^{28} +4.65499i q^{29} +(7.58294 + 1.24574i) q^{30} +(0.624367 + 0.624367i) q^{31} -13.5870i q^{32} +2.40314i q^{33} +(-5.11454 - 5.11454i) q^{34} +(-0.204085 + 0.146492i) q^{35} -6.61729i q^{36} -1.47487 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} +(-1.71838 - 2.39396i) q^{45} +(6.01959 - 6.01959i) q^{46} +0.345095 q^{47} +(10.2440 - 10.2440i) q^{48} -6.98738 q^{49} +(-12.5524 - 4.23866i) 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} +9.02691i q^{57} +12.3346 q^{58} +(-0.908390 - 0.908390i) q^{59} +(2.36063 - 14.3694i) q^{60} -2.78301 q^{61} +(1.65442 - 1.65442i) q^{62} +0.148060i q^{63} -13.6621 q^{64} +6.36774 q^{66} +0.144329i q^{67} +(-9.69188 + 9.69188i) q^{68} +4.16683 q^{69} +(0.388167 + 0.540774i) q^{70} +(3.87045 + 3.87045i) q^{71} -10.5501 q^{72} +9.06221i 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} +(-20.2908 + 14.5647i) q^{80} +3.30961 q^{81} +(-10.1657 + 10.1657i) q^{82} -8.53853 q^{83} +(-0.517354 + 0.517354i) q^{84} +(-0.989478 + 6.02307i) 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} +1.14521 q^{93} -0.914416i q^{94} +(2.52290 - 15.3572i) q^{95} +(-12.4606 - 12.4606i) q^{96} +14.9645i q^{97} +18.5148i q^{98} +(-1.72666 - 1.72666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} - 12 q^{4} - 4 q^{6} - 4 q^{7}+O(q^{10}) $ 20 * q + 4 * q^3 - 12 * q^4 - 4 * q^6 - 4 * q^7	$ 20 q + 4 q^{3} - 12 q^{4} - 4 q^{6} - 4 q^{7} - 8 q^{10} - 8 q^{11} - 24 q^{12} - 28 q^{15} + 4 q^{16} - 14 q^{17} - 4 q^{19} + 12 q^{20} - 4 q^{21} - 32 q^{22} + 8 q^{23} + 4 q^{24} + 18 q^{25} + 4 q^{27} + 36 q^{28} + 40 q^{30} - 2 q^{34} - 20 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{40} + 38 q^{41} + 16 q^{42} - 32 q^{43} + 36 q^{44} + 6 q^{45} - 4 q^{46} + 40 q^{47} + 28 q^{48} - 36 q^{49} - 42 q^{50} - 10 q^{53} - 36 q^{54} - 16 q^{55} - 8 q^{59} - 28 q^{60} + 32 q^{61} + 4 q^{62} + 20 q^{64} - 32 q^{66} - 50 q^{68} + 32 q^{69} + 12 q^{70} + 40 q^{71} + 8 q^{72} + 4 q^{75} + 16 q^{76} - 28 q^{77} - 112 q^{80} + 28 q^{81} - 34 q^{82} - 48 q^{83} - 8 q^{84} + 2 q^{85} - 60 q^{86} - 28 q^{87} - 32 q^{88} - 12 q^{89} + 46 q^{90} - 8 q^{92} + 64 q^{93} + 40 q^{95} - 56 q^{96} - 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^3 - 12 * q^4 - 4 * q^6 - 4 * q^7 - 8 * q^10 - 8 * q^11 - 24 * q^12 - 28 * q^15 + 4 * q^16 - 14 * q^17 - 4 * q^19 + 12 * q^20 - 4 * q^21 - 32 * q^22 + 8 * q^23 + 4 * q^24 + 18 * q^25 + 4 * q^27 + 36 * q^28 + 40 * q^30 - 2 * q^34 - 20 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 - 32 * q^43 + 36 * q^44 + 6 * q^45 - 4 * q^46 + 40 * q^47 + 28 * q^48 - 36 * q^49 - 42 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 8 * q^59 - 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 + 12 * q^70 + 40 * q^71 + 8 * q^72 + 4 * q^75 + 16 * q^76 - 28 * q^77 - 112 * q^80 + 28 * q^81 - 34 * q^82 - 48 * q^83 - 8 * q^84 + 2 * q^85 - 60 * q^86 - 28 * q^87 - 32 * q^88 - 12 * q^89 + 46 * q^90 - 8 * q^92 + 64 * q^93 + 40 * q^95 - 56 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	2.64975i		−	1.87366i	−0.349786	−	0.936830i	$-0.613746\pi$
$2$		−	2.64975i		−	1.87366i	0.349786	−	0.936830i	$-0.386254\pi$
$3$	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
$5$	−1.81654	+	1.30391i	−0.812382	+	0.583126i
$5$	−1.81654	+	1.30391i	−0.812382	+	0.583126i
$6$	−2.43008	−	2.43008i	−0.992076	−	0.992076i
$7$	0.112348			0.0424635			0.0212318	−	0.999775i	$-0.493241\pi$
$7$	0.112348			0.0424635			0.0212318	+	0.999775i	$0.493241\pi$
$8$			8.00544i			2.83035i
$9$			1.31787i			0.439290i
$10$	3.45504	+	4.81339i	1.09258	+	1.52213i
$11$	−1.31019	+	1.31019i	−0.395038	+	0.395038i	−0.876479	−	0.481441i	$-0.840114\pi$
$11$	−1.31019	+	1.31019i	−0.395038	+	0.395038i	0.481441	+	0.876479i	$0.340114\pi$
$12$	−4.60492	+	4.60492i	−1.32933	+	1.32933i
$13$		0			0
$13$		0			0
$14$		−	0.297695i		−	0.0795622i
$15$	−0.470132	+	2.86175i	−0.121388	+	0.738901i
$16$	11.1700			2.79251
$17$	1.93019	−	1.93019i	0.468140	−	0.468140i	−0.433171	−	0.901312i	$-0.642605\pi$
$17$	1.93019	−	1.93019i	0.468140	−	0.468140i	0.901312	+	0.433171i	$0.142605\pi$
$18$	3.49203			0.823080
$19$	−4.92146	+	4.92146i	−1.12906	+	1.12906i	−0.138731	+	0.990330i	$0.544302\pi$
$19$	−4.92146	+	4.92146i	−1.12906	+	1.12906i	−0.990330	+	0.138731i	$0.955698\pi$
$20$	9.12121	−	6.54719i	2.03957	−	1.46400i
$21$	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	0.903108	−	0.429414i	$-0.141280\pi$
$23$	2.27175	+	2.27175i	0.473693	+	0.473693i	−0.429414	+	0.903108i	$0.641280\pi$
$24$	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
$28$	−0.564122			−0.106609
$29$			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	0.760950	−	0.648810i	$-0.224733\pi$
$31$	0.624367	+	0.624367i	0.112140	+	0.112140i	−0.648810	+	0.760950i	$0.724733\pi$
$32$		−	13.5870i		−	2.40186i
$33$			2.40314i			0.418334i
$34$	−5.11454	−	5.11454i	−0.877136	−	0.877136i
$35$	−0.204085	+	0.146492i	−0.0344966	+	0.0247616i
$36$		−	6.61729i		−	1.10288i
$37$	−1.47487			−0.242467			−0.121234	−	0.992624i	$-0.538685\pi$
$37$	−1.47487			−0.242467			−0.121234	+	0.992624i	$0.538685\pi$
$38$	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	0.340934	−	0.940087i	$-0.389257\pi$
$41$	−3.83645	−	3.83645i	−0.599153	−	0.599153i	−0.940087	+	0.340934i	$0.889257\pi$
$42$	−0.273014	−	0.273014i	−0.0421270	−	0.0421270i
$43$	2.75555	+	2.75555i	0.420217	+	0.420217i	0.885278	−	0.465062i	$-0.153968\pi$
$43$	2.75555	+	2.75555i	0.420217	+	0.420217i	−0.465062	+	0.885278i	$0.653968\pi$
$44$	6.57874	−	6.57874i	0.991782	−	0.991782i
$45$	−1.71838	−	2.39396i	−0.256161	−	0.356871i
$46$	6.01959	−	6.01959i	0.887540	−	0.887540i
$47$	0.345095			0.0503372			0.0251686	−	0.999683i	$-0.491988\pi$
$47$	0.345095			0.0503372			0.0251686	+	0.999683i	$0.491988\pi$
$48$	10.2440	−	10.2440i	1.47859	−	1.47859i
$49$	−6.98738			−0.998197
$50$	−12.5524	−	4.23866i	−1.77518	−	0.599436i
$51$		−	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
$57$			9.02691i			1.19564i
$58$	12.3346			1.61961
$59$	−0.908390	−	0.908390i	−0.118262	−	0.118262i	0.645499	−	0.763761i	$-0.276649\pi$
$59$	−0.908390	−	0.908390i	−0.118262	−	0.118262i	−0.763761	+	0.645499i	$0.776649\pi$
$60$	2.36063	−	14.3694i	0.304756	−	1.85508i
$61$	−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
$63$			0.148060i			0.0186538i
$64$	−13.6621			−1.70776
$65$		0			0
$66$	6.36774			0.783815
$67$			0.144329i			0.0176325i	0.999961	+	0.00881627i	$0.00280634\pi$
$67$			0.144329i			0.0176325i	−0.999961	+	0.00881627i	$0.997194\pi$
$68$	−9.69188	+	9.69188i	−1.17531	+	1.17531i
$69$	4.16683			0.501628
$70$	0.388167	+	0.540774i	0.0463948	+	0.0646349i
$71$	3.87045	+	3.87045i	0.459338	+	0.459338i	0.898438	−	0.439100i	$-0.144703\pi$
$71$	3.87045	+	3.87045i	0.459338	+	0.459338i	−0.439100	+	0.898438i	$0.644703\pi$
$72$	−10.5501			−1.24334
$73$			9.06221i			1.06065i	0.847794	+	0.530326i	$0.177930\pi$
$73$			9.06221i			1.06065i	−0.847794	+	0.530326i	$0.822070\pi$
$74$			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	$0.674586\pi$
$80$	−20.2908	+	14.5647i	−2.26858	+	1.62839i
$81$	3.30961			0.367734
$82$	−10.1657	+	10.1657i	−1.12261	+	1.12261i
$83$	−8.53853			−0.937226			−0.468613	−	0.883404i	$-0.655246\pi$
$83$	−8.53853			−0.937226			−0.468613	+	0.883404i	$0.655246\pi$
$84$	−0.517354	+	0.517354i	−0.0564479	+	0.0564479i
$85$	−0.989478	+	6.02307i	−0.107324	+	0.653294i
$86$	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	$-0.240397\pi$
$89$	0.402434	+	0.402434i	0.0426579	+	0.0426579i	−0.685456	+	0.728114i	$0.740397\pi$
$90$	−6.34342	+	4.55329i	−0.668655	+	0.479959i
$91$		0			0
$92$	−11.4069	−	11.4069i	−1.18925	−	1.18925i
$93$	1.14521			0.118753
$94$		−	0.914416i		−	0.0943148i
$95$	2.52290	−	15.3572i	0.258844	−	1.57561i
$96$	−12.4606	−	12.4606i	−1.27175	−	1.27175i
$97$			14.9645i			1.51941i	0.650268	+	0.759705i	$0.274657\pi$
$97$			14.9645i			1.51941i	−0.650268	+	0.759705i	$0.725343\pi$
$98$			18.5148i			1.87028i
$99$	−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	$-0.864318\pi$
$101$		−	8.31058i		−	0.826934i	0.910519	−	0.413467i	$-0.135682\pi$
$102$	−9.38104			−0.928862
$103$	−7.72940	−	7.72940i	−0.761600	−	0.761600i	0.215011	−	0.976612i	$-0.431021\pi$
$103$	−7.72940	−	7.72940i	−0.761600	−	0.761600i	−0.976612	+	0.215011i	$0.931021\pi$
$104$		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	$-0.822755\pi$
$109$	−3.34544	+	3.34544i	−0.320435	+	0.320435i	0.528499	+	0.848934i	$0.322755\pi$
$110$	−10.8332	−	1.77970i	−1.03291	−	0.169687i
$111$	−1.35260	+	1.35260i	−0.128383	+	0.128383i
$112$	1.25493			0.118580
$113$	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
$115$	−7.08889	−	1.16457i	−0.661043	−	0.108597i
$116$		−	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
$122$			7.37430i			0.667638i
$123$	−7.03679			−0.634486
$124$	−3.13507	−	3.13507i	−0.281538	−	0.281538i
$125$	3.27108	+	10.6911i	0.292574	+	0.956243i
$126$	0.392323			0.0349509
$127$	−8.25062	+	8.25062i	−0.732124	+	0.732124i	−0.971040	−	0.238916i	$-0.923208\pi$
$127$	−8.25062	+	8.25062i	−0.732124	+	0.732124i	0.238916	+	0.971040i	$0.423208\pi$
$128$			9.02727i			0.797905i
$129$	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	$0.394280\pi$
$132$		−	12.0667i		−	1.05027i
$133$	−0.552916	+	0.552916i	−0.0479439	+	0.0479439i
$134$	0.382435			0.0330374
$135$	−12.3567	−	2.02997i	−1.06349	−	0.174712i
$136$	15.4520	+	15.4520i	1.32500	+	1.32500i
$137$	18.4843			1.57922			0.789608	−	0.613611i	$-0.210284\pi$
$137$	18.4843			1.57922			0.789608	+	0.613611i	$0.210284\pi$
$138$		−	11.0411i		−	0.939879i
$139$		−	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
$145$	−6.06968	−	8.45598i	−0.504060	−	0.702231i
$146$	24.0126			1.98730
$147$	−6.40810	+	6.40810i	−0.528531	+	0.528531i
$148$	7.40562			0.608738
$149$	9.84377	−	9.84377i	0.806433	−	0.806433i	−0.177659	−	0.984092i	$-0.556852\pi$
$149$	9.84377	−	9.84377i	0.806433	−	0.806433i	0.984092	+	0.177659i	$0.0568525\pi$
$150$	−15.3990	+	7.62454i	−1.25733	+	0.622541i
$151$	8.49593	−	8.49593i	0.691389	−	0.691389i	−0.271149	−	0.962537i	$-0.587404\pi$
$151$	8.49593	−	8.49593i	0.691389	−	0.691389i	0.962537	+	0.271149i	$0.0874035\pi$
$152$	−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	$0.843770\pi$
$158$	40.1940			3.19766
$159$			6.58739i			0.522414i
$160$	17.7162	+	24.6813i	1.40059	+	1.95123i
$161$	0.255227	+	0.255227i	0.0201147	+	0.0201147i
$162$		−	8.76965i		−	0.689009i
$163$		−	20.5175i		−	1.60705i	−0.595270	−	0.803526i	$-0.702955\pi$
$163$		−	20.5175i		−	1.60705i	0.595270	−	0.803526i	$-0.297045\pi$
$164$	19.2636	+	19.2636i	1.50423	+	1.50423i
$165$	−3.13348	−	4.36541i	−0.243941	−	0.339847i
$166$			22.6250i			1.75604i
$167$	2.54101			0.196629			0.0983146	−	0.995155i	$-0.468655\pi$
$167$	2.54101			0.196629			0.0983146	+	0.995155i	$0.468655\pi$
$168$	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	0.709224	−	0.704983i	$-0.249045\pi$
$173$	0.0557881	+	0.0557881i	0.00424149	+	0.00424149i	−0.704983	+	0.709224i	$0.749045\pi$
$174$	11.3120	−	11.3120i	0.857560	−	0.857560i
$175$	0.179716	−	0.532216i	0.0135853	−	0.0402317i
$176$	−14.6349	+	14.6349i	−1.10315	+	1.10315i
$177$	−1.66616			−0.125236
$178$	1.06635	−	1.06635i	0.0799264	−	0.0799264i
$179$	−21.2241			−1.58636			−0.793181	−	0.608987i	$-0.791576\pi$
$179$	−21.2241			−1.58636			−0.793181	+	0.608987i	$0.791576\pi$
$180$	8.62834	+	12.0206i	0.643119	+	0.895961i
$181$			22.5267i			1.67440i	0.546899	+	0.837198i	$0.315808\pi$
$181$			22.5267i			1.67440i	−0.546899	+	0.837198i	$0.684192\pi$
$182$		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
$187$			5.05785i			0.369866i
$188$	−1.73279			−0.126377
$189$	0.444887	+	0.444887i	0.0323608	+	0.0323608i
$190$	−40.6927	−	6.68506i	−2.95216	−	0.484985i
$191$	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
$193$			16.7120i			1.20296i	0.798889	+	0.601479i	$0.205421\pi$
$193$			16.7120i			1.20296i	−0.798889	+	0.601479i	$0.794579\pi$
$194$	39.6521			2.84686
$195$		0			0
$196$	35.0850			2.50607
$197$			15.1863i			1.08198i	0.841029	+	0.540990i	$0.181950\pi$
$197$			15.1863i			1.08198i	−0.841029	+	0.540990i	$0.818050\pi$
$198$	−4.57523	+	4.57523i	−0.325148	+	0.325148i
$199$	13.9471			0.988686			0.494343	−	0.869267i	$-0.335409\pi$
$199$	13.9471			0.988686			0.494343	+	0.869267i	$0.335409\pi$
$200$	37.9234	+	12.8058i	2.68159	+	0.905508i
$201$	0.132363	+	0.132363i	0.00933618	+	0.00933618i
$202$	−22.0210			−1.54939
$203$			0.522979i			0.0367059i
$204$			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
$210$	0.851928	+	0.139956i	0.0587886	+	0.00965787i
$211$	−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
$213$	7.09915			0.486426
$214$	−13.8727	+	13.8727i	−0.948318	+	0.948318i
$215$	−8.59854	−	1.41258i	−0.586416	−	0.0963371i
$216$	−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
$223$	−9.72639			−0.651327			−0.325664	−	0.945486i	$-0.605588\pi$
$223$	−9.72639			−0.651327			−0.325664	+	0.945486i	$0.605588\pi$
$224$		−	1.52647i		−	0.101992i
$225$	6.24303	+	2.10812i	0.416202	+	0.140541i
$226$	−11.4579	−	11.4579i	−0.762168	−	0.762168i
$227$		−	9.17580i		−	0.609019i	−0.952509	−	0.304510i	$-0.901507\pi$
$227$		−	9.17580i		−	0.609019i	0.952509	−	0.304510i	$-0.0984925\pi$
$228$		−	45.3259i		−	3.00178i
$229$	−12.5270	−	12.5270i	−0.827811	−	0.827811i	0.159403	−	0.987214i	$-0.449043\pi$
$229$	−12.5270	−	12.5270i	−0.827811	−	0.827811i	−0.987214	+	0.159403i	$0.949043\pi$
$230$	−3.08583	+	18.7838i	−0.203474	+	1.23857i
$231$			0.269988i			0.0177639i
$232$	−37.2652			−2.44658
$233$	−11.8637	−	11.8637i	−0.777214	−	0.777214i	0.202142	−	0.979356i	$-0.435210\pi$
$233$	−11.8637	−	11.8637i	−0.777214	−	0.777214i	−0.979356	+	0.202142i	$0.935210\pi$
$234$		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	0.198124	−	0.980177i	$-0.436515\pi$
$239$	18.2161	−	18.2161i	1.17830	−	1.17830i	0.980177	−	0.198124i	$-0.0634848\pi$
$240$	−5.25140	+	31.9659i	−0.338976	+	2.06339i
$241$	−3.86818	+	3.86818i	−0.249171	+	0.249171i	−0.820630	−	0.571459i	$-0.806378\pi$
$241$	−3.86818	+	3.86818i	−0.249171	+	0.249171i	0.571459	+	0.820630i	$0.306378\pi$
$242$	20.0501			1.28887
$243$	−8.84448	+	8.84448i	−0.567373	+	0.567373i
$244$	13.9741			0.894597
$245$	12.6929	−	9.11091i	0.810917	−	0.582075i
$246$			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	$0.135314\pi$
$251$			13.0677i			0.824824i	−0.910997	+	0.412412i	$0.864686\pi$
$252$		−	0.743439i		−	0.0468322i
$253$	−5.95287			−0.374254
$254$	21.8621	+	21.8621i	1.37175	+	1.37175i
$255$	4.61629	+	6.43118i	0.289083	+	0.402736i
$256$	−3.40419			−0.212762
$257$	12.3380	−	12.3380i	0.769625	−	0.769625i	−0.208415	−	0.978040i	$-0.566830\pi$
$257$	12.3380	−	12.3380i	0.769625	−	0.769625i	0.978040	+	0.208415i	$0.0668305\pi$
$258$		−	13.3924i		−	0.833774i
$259$	−0.165699			−0.0102960
$260$		0			0
$261$	−6.13467			−0.379727
$262$		−	19.7772i		−	1.22184i
$263$	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
$265$	1.84108	−	11.2069i	0.113097	−	0.688434i
$266$	1.46509	+	1.46509i	0.0898306	+	0.0898306i
$267$	0.738141			0.0451735
$268$		−	0.724703i		−	0.0442683i
$269$		−	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	−0.516501	−	0.856286i	$-0.672766\pi$
$271$	5.59357	−	5.59357i	0.339785	−	0.339785i	0.856286	+	0.516501i	$0.172766\pi$
$272$	21.5603	−	21.5603i	1.30729	−	1.30729i
$273$		0			0
$274$		−	48.9787i		−	2.95891i
$275$	4.11082	+	8.30249i	0.247892	+	0.500659i
$276$	−20.9225			−1.25939
$277$	−7.22248	+	7.22248i	−0.433957	+	0.433957i	−0.889972	−	0.456015i	$-0.849276\pi$
$277$	−7.22248	+	7.22248i	−0.433957	+	0.433957i	0.456015	+	0.889972i	$0.349276\pi$
$278$	−28.9097			−1.73389
$279$	−0.822834	+	0.822834i	−0.0492618	+	0.0492618i
$280$	−1.17273	−	1.63379i	−0.0700840	−	0.0976374i
$281$	−12.4763	+	12.4763i	−0.744271	+	0.744271i	−0.973397	−	0.229126i	$-0.926413\pi$
$281$	−12.4763	+	12.4763i	−0.744271	+	0.744271i	0.229126	+	0.973397i	$0.426413\pi$
$282$	−0.838608	−	0.838608i	−0.0499384	−	0.0499384i
$283$	5.84527	+	5.84527i	0.347465	+	0.347465i	0.859164	−	0.511700i	$-0.170984\pi$
$283$	5.84527	+	5.84527i	0.347465	+	0.347465i	−0.511700	+	0.859164i	$0.670984\pi$
$284$	−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
$288$	17.9059			1.05511
$289$			9.54871i			0.561689i
$290$	−22.4063	+	16.0832i	−1.31574	+	0.944436i
$291$	13.7238	+	13.7238i	0.804506	+	0.804506i
$292$		−	45.5032i		−	2.66287i
$293$			6.37832i			0.372625i	0.982491	+	0.186313i	$0.0596537\pi$
$293$			6.37832i			0.372625i	−0.982491	+	0.186313i	$0.940346\pi$
$294$	16.9799	+	16.9799i	0.990287	+	0.990287i
$295$	2.83458	+	0.465669i	0.165036	+	0.0271123i
$296$		−	11.8070i		−	0.686267i
$297$	−10.3765			−0.602104
$298$	−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
$305$	5.05546	−	3.62880i	0.289475	−	0.207784i
$306$	6.74029	−	6.74029i	0.385317	−	0.385317i
$307$	26.5460			1.51506			0.757530	−	0.652801i	$-0.226406\pi$
$307$	26.5460			1.51506			0.757530	+	0.652801i	$0.226406\pi$
$308$	0.739108	−	0.739108i	0.0421146	−	0.0421146i
$309$	−14.1772			−0.806512
$310$	−0.848107	+	5.16253i	−0.0481692	+	0.293212i
$311$			3.54417i			0.200972i	0.994938	+	0.100486i	$0.0320397\pi$
$311$			3.54417i			0.200972i	−0.994938	+	0.100486i	$0.967960\pi$
$312$		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
$317$			8.52812i			0.478987i	0.970898	+	0.239494i	$0.0769814\pi$
$317$			8.52812i			0.478987i	−0.970898	+	0.239494i	$0.923019\pi$
$318$	17.4550			0.978825
$319$	−6.09893	−	6.09893i	−0.341474	−	0.341474i
$320$	24.8178	−	17.8142i	1.38736	−	0.995842i
$321$	−9.60284			−0.535978
$322$	0.676289	−	0.676289i	0.0376881	−	0.0376881i
$323$			18.9987i			1.05712i
$324$	−16.6182			−0.923233
$325$		0			0
$326$	−54.3663			−3.01107
$327$			6.13618i			0.339332i
$328$	30.7125	−	30.7125i	1.69581	−	1.69581i
$329$	0.0387707			0.00213750
$330$	−11.5673	+	8.30296i	−0.636757	+	0.457063i
$331$	−12.7328	−	12.7328i	−0.699860	−	0.699860i	0.264520	−	0.964380i	$-0.414786\pi$
$331$	−12.7328	−	12.7328i	−0.699860	−	0.699860i	−0.964380	+	0.264520i	$0.914786\pi$
$332$	42.8737			2.35300
$333$		−	1.94369i		−	0.106513i
$334$		−	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	$0.531597\pi$
$337$	−20.0865	+	20.0865i	−1.09418	+	1.09418i	−0.995077	+	0.0991030i	$0.968403\pi$
$338$		0			0
$339$		−	7.93129i		−	0.430769i
$340$	4.96836	−	30.2430i	0.269447	−	1.64016i
$341$	−1.63608			−0.0885987
$342$	−17.1859	+	17.1859i	−0.929307	+	0.929307i
$343$	−1.57145			−0.0848505
$344$	−22.0593	+	22.0593i	−1.18936	+	1.18936i
$345$	−7.56922	+	5.43317i	−0.407513	+	0.292512i
$346$	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	$-0.218826\pi$
$349$	2.58330	+	2.58330i	0.138281	+	0.138281i	−0.634578	+	0.772859i	$0.718826\pi$
$350$	−1.41024	−	0.476204i	−0.0753806	−	0.0254542i
$351$		0			0
$352$	17.8016	+	17.8016i	0.948827	+	0.948827i
$353$	−1.76326			−0.0938487			−0.0469243	−	0.998898i	$-0.514942\pi$
$353$	−1.76326			−0.0938487			−0.0469243	+	0.998898i	$0.514942\pi$
$354$			4.41492i			0.234650i
$355$	−12.0775	−	1.98411i	−0.641010	−	0.105306i
$356$	−2.02070	−	2.02070i	−0.107097	−	0.107097i
$357$		−	0.397750i		−	0.0210512i
$358$			56.2386i			2.97230i
$359$	−8.58021	−	8.58021i	−0.452846	−	0.452846i	0.443452	−	0.896298i	$-0.353754\pi$
$359$	−8.58021	−	8.58021i	−0.452846	−	0.452846i	−0.896298	+	0.443452i	$0.853754\pi$
$360$	19.1647	−	13.7564i	1.01007	−	0.725026i
$361$		−	29.4416i		−	1.54956i
$362$	59.6902			3.13725
$363$	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
$370$	−5.09574	−	7.09912i	−0.264915	−	0.369066i
$371$	−0.403491	+	0.403491i	−0.0209482	+	0.0209482i
$372$	−5.75032			−0.298140
$373$	−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
$375$	12.8047	+	6.80489i	0.661231	+	0.351403i
$376$			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	$-0.828261\pi$
$379$	−6.70112	+	6.70112i	−0.344213	+	0.344213i	0.513735	+	0.857949i	$0.328261\pi$
$380$	−12.6680	+	77.1114i	−0.649853	+	3.95573i
$381$			15.1332i			0.775299i
$382$		−	51.9525i		−	2.65812i
$383$	21.0722			1.07674			0.538369	−	0.842709i	$-0.319041\pi$
$383$	21.0722			1.07674			0.538369	+	0.842709i	$0.319041\pi$
$384$	8.27887	+	8.27887i	0.422479	+	0.422479i
$385$	0.0754581	−	0.459322i	0.00384570	−	0.0234092i
$386$	44.2827			2.25393
$387$	−3.63145	+	3.63145i	−0.184597	+	0.184597i
$388$		−	75.1395i		−	3.81463i
$389$	0.0604806			0.00306649			0.00153324	−	0.999999i	$-0.499512\pi$
$389$	0.0604806			0.00306649			0.00153324	+	0.999999i	$0.499512\pi$
$390$		0			0
$391$	8.76984			0.443510
$392$		−	55.9370i		−	2.82525i
$393$	6.84502	−	6.84502i	0.345286	−	0.345286i
$394$	40.2400			2.02726
$395$	−19.7789	−	27.5550i	−0.995186	−	1.38644i
$396$	8.66992	+	8.66992i	0.435680	+	0.435680i
$397$	−8.21625			−0.412362			−0.206181	−	0.978514i	$-0.566104\pi$
$397$	−8.21625			−0.412362			−0.206181	+	0.978514i	$0.566104\pi$
$398$		−	36.9565i		−	1.85246i
$399$			1.01415i			0.0507712i
$400$	17.8681	−	52.9148i	0.893403	−	2.64574i
$401$	6.36306	−	6.36306i	0.317756	−	0.317756i	−0.530149	−	0.847905i	$-0.677864\pi$
$401$	6.36306	−	6.36306i	0.317756	−	0.317756i	0.847905	+	0.530149i	$0.177864\pi$
$402$	0.350730	−	0.350730i	0.0174928	−	0.0174928i
$403$		0			0
$404$			41.7291i			2.07610i
$405$	−6.01204	+	4.31543i	−0.298741	+	0.214435i
$406$	1.38576			0.0687743
$407$	1.93236	−	1.93236i	0.0957837	−	0.0957837i
$408$	28.3420			1.40314
$409$	25.3299	−	25.3299i	1.25248	−	1.25248i	0.297878	−	0.954604i	$-0.403721\pi$
$409$	25.3299	−	25.3299i	1.25248	−	1.25248i	0.954604	−	0.297878i	$-0.0962789\pi$
$410$	5.21123	−	31.7214i	0.257365	−	1.56661i
$411$	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
$418$	−34.1716			−1.67139
$419$			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	0.958223	−	0.286021i	$-0.0923326\pi$
$421$	13.7924	+	13.7924i	0.672203	+	0.672203i	−0.286021	+	0.958223i	$0.592333\pi$
$422$			62.5822i			3.04645i
$423$			0.454790i			0.0221126i
$424$	−28.7510	−	28.7510i	−1.39627	−	1.39627i
$425$	−6.05611	−	12.2313i	−0.293765	−	0.593307i
$426$		−	18.8110i		−	0.911396i
$427$	−0.312666			−0.0151310
$428$	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	0.975735	−	0.218953i	$-0.0702642\pi$
$431$	15.7112	+	15.7112i	0.756782	+	0.756782i	−0.218953	+	0.975735i	$0.570264\pi$
$432$	44.2323	+	44.2323i	2.12813	+	2.12813i
$433$	0.129788	+	0.129788i	0.00623723	+	0.00623723i	0.710219	−	0.703981i	$-0.248596\pi$
$433$	0.129788	+	0.129788i	0.00623723	+	0.00623723i	−0.703981	+	0.710219i	$0.748596\pi$
$434$	0.185871	−	0.185871i	0.00892207	−	0.00892207i
$435$	−13.3214	−	2.18846i	−0.638713	−	0.104929i
$436$	16.7981	−	16.7981i	0.804485	−	0.804485i
$437$	−22.3607			−1.06966
$438$	22.0219	−	22.0219i	1.05225	−	1.05225i
$439$	17.2936			0.825380			0.412690	−	0.910871i	$-0.364589\pi$
$439$	17.2936			0.825380			0.412690	+	0.910871i	$0.364589\pi$
$440$	32.7293	+	5.37682i	1.56031	+	0.256330i
$441$		−	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
$447$		−	18.0554i		−	0.853989i
$448$	−1.53491			−0.0725177
$449$	−26.2934	−	26.2934i	−1.24086	−	1.24086i	−0.959643	−	0.281221i	$-0.909261\pi$
$449$	−26.2934	−	26.2934i	−1.24086	−	1.24086i	−0.281221	−	0.959643i	$-0.590739\pi$
$450$	5.58600	−	16.5425i	0.263326	−	0.779820i
$451$	10.0530			0.473376
$452$	−21.7123	+	21.7123i	−1.02126	+	1.02126i
$453$		−	15.5832i		−	0.732161i
$454$	−24.3136			−1.14109
$455$		0			0
$456$	−72.2643			−3.38409
$457$		−	9.42691i		−	0.440972i	−0.975390	−	0.220486i	$-0.929236\pi$
$457$		−	9.42691i		−	0.440972i	0.975390	−	0.220486i	$-0.0707643\pi$
$458$	−33.1936	+	33.1936i	−1.55104	+	1.55104i
$459$	15.2867			0.713524
$460$	35.5947	+	5.84755i	1.65961	+	0.272643i
$461$	23.2538	+	23.2538i	1.08304	+	1.08304i	0.996225	+	0.0868134i	$0.0276684\pi$
$461$	23.2538	+	23.2538i	1.08304	+	1.08304i	0.0868134	+	0.996225i	$0.472332\pi$
$462$	0.715403			0.0332836
$463$			18.6729i			0.867805i	0.900960	+	0.433903i	$0.142864\pi$
$463$			18.6729i			0.867805i	−0.900960	+	0.433903i	$0.857136\pi$
$464$			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	−0.930175	−	0.367118i	$-0.880345\pi$
$467$	−12.1678	+	12.1678i	−0.563057	+	0.563057i	0.367118	+	0.930175i	$0.380345\pi$
$468$		0			0
$469$			0.0162150i			0.000748740i
$470$	1.19232	+	1.66107i	0.0549974	+	0.0766197i
$471$	−9.43676			−0.434823
$472$	7.27205	−	7.27205i	0.334723	−	0.334723i
$473$	−7.22059			−0.332003
$474$	36.8617	−	36.8617i	1.69312	−	1.69312i
$475$	15.4414	+	31.1866i	0.708501	+	1.43094i
$476$	−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	−0.997735	−	0.0672673i	$-0.978572\pi$
$479$	−23.3087	−	23.3087i	−1.06500	−	1.06500i	−0.0672673	−	0.997735i	$-0.521428\pi$
$480$	38.8826	+	6.38768i	1.77474	+	0.291557i
$481$		0			0
$482$	10.2497	+	10.2497i	0.466862	+	0.466862i
$483$	0.468135			0.0213009
$484$		−	37.9944i		−	1.72702i
$485$	−19.5123	−	27.1835i	−0.886008	−	1.23434i
$486$	23.4357	+	23.4357i	1.06306	+	1.06306i
$487$		−	32.9863i		−	1.49475i	−0.664402	−	0.747376i	$-0.731314\pi$
$487$		−	32.9863i		−	1.49475i	0.664402	−	0.747376i	$-0.268686\pi$
$488$		−	22.2792i		−	1.00853i
$489$	−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	$0.159557\pi$
$491$			21.2958i			0.961065i	−0.876977	+	0.480533i	$0.840443\pi$
$492$	35.3331			1.59294
$493$	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	$-0.593431\pi$
$499$	14.9199	−	14.9199i	0.667904	−	0.667904i	0.957231	+	0.289326i	$0.0934312\pi$
$500$	−16.4247	−	53.6822i	−0.734536	−	2.40074i
$501$	2.33035	−	2.33035i	0.104112	−	0.104112i
$502$	34.6261			1.54544
$503$	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
$505$	10.8362	+	15.0965i	0.482207	+	0.671786i
$506$			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	0.189062	−	0.981965i	$-0.439455\pi$
$509$	26.4196	−	26.4196i	1.17103	−	1.17103i	0.981965	−	0.189062i	$-0.0605446\pi$
$510$	17.0410	−	12.2320i	0.754590	−	0.541643i
$511$			1.01812i			0.0450390i
$512$			27.0748i			1.19655i
$513$	−38.9770			−1.72088
$514$	−32.6928	−	32.6928i	−1.44202	−	1.44202i
$515$	24.1192	+	3.96233i	1.06282	+	0.174601i
$516$	−25.3781			−1.11721
$517$	−0.452141	+	0.452141i	−0.0198851	+	0.0198851i
$518$			0.439061i			0.0192912i
$519$	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	$0.785648\pi$
$522$			16.2554i			0.711478i
$523$	−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
$525$	−0.323276	−	0.652910i	−0.0141089	−	0.0284953i
$526$	−39.0625	−	39.0625i	−1.70321	−	1.70321i
$527$	2.41030			0.104994
$528$			26.8432i			1.16820i
$529$		−	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
$535$	16.3370	+	2.68386i	0.706310	+	0.116034i
$536$	−1.15541			−0.0499063
$537$	−19.4645	+	19.4645i	−0.839955	+	0.839955i
$538$	−27.9987			−1.20711
$539$	9.15481	−	9.15481i	0.394326	−	0.394326i
$540$	62.0453	+	10.1929i	2.67001	+	0.438632i
$541$	5.42748	−	5.42748i	0.233345	−	0.233345i	−0.580742	−	0.814088i	$-0.697238\pi$
$541$	5.42748	−	5.42748i	0.233345	−	0.233345i	0.814088	+	0.580742i	$0.197238\pi$
$542$	−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	$0.634973\pi$
$548$	−92.8131			−3.96478
$549$		−	3.66765i		−	0.156531i
$550$	21.9996	−	10.8927i	0.938065	−	0.464464i
$551$	−22.9093	−	22.9093i	−0.975971	−	0.975971i
$552$			33.3573i			1.41978i
$553$			1.70420i			0.0724700i
$554$	19.1378	+	19.1378i	0.813087	+	0.813087i
$555$	0.693384	−	4.22071i	0.0294325	−	0.179159i
$556$			54.7829i			2.32331i
$557$	4.87503			0.206562			0.103281	−	0.994652i	$-0.467066\pi$
$557$	4.87503			0.206562			0.103281	+	0.994652i	$0.467066\pi$
$558$	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	$-0.943346\pi$
$563$	−27.5537	−	27.5537i	−1.16125	−	1.16125i	−0.177047	−	0.984202i	$-0.556654\pi$
$564$	−1.58913	+	1.58913i	−0.0669146	+	0.0669146i
$565$	−2.21669	+	13.4932i	−0.0932568	+	0.567665i
$566$	15.4885	−	15.4885i	0.651031	−	0.651031i
$567$	0.371828			0.0156153
$568$	−30.9846	+	30.9846i	−1.30009	+	1.30009i
$569$	−3.68208			−0.154361			−0.0771804	−	0.997017i	$-0.524592\pi$
$569$	−3.68208			−0.154361			−0.0771804	+	0.997017i	$0.524592\pi$
$570$	−43.4500	+	31.1883i	−1.81992	+	1.30633i
$571$			2.96698i			0.124164i	0.998071	+	0.0620821i	$0.0197741\pi$
$571$			2.96698i			0.124164i	−0.998071	+	0.0620821i	$0.980226\pi$
$572$		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
$577$			35.0533i			1.45929i	0.683827	+	0.729644i	$0.260314\pi$
$577$			35.0533i			1.45929i	−0.683827	+	0.729644i	$0.739686\pi$
$578$	25.3017			1.05241
$579$	15.3265	+	15.3265i	0.636948	+	0.636948i
$580$	30.4771	+	42.4591i	1.26549	+	1.76302i
$581$	−0.959287			−0.0397979
$582$	36.3648	−	36.3648i	1.50737	−	1.50737i
$583$		−	9.41095i		−	0.389762i
$584$	−72.5469			−3.00201
$585$		0			0
$586$	16.9010			0.698173
$587$		−	7.05437i		−	0.291165i	−0.989346	−	0.145583i	$-0.953494\pi$
$587$		−	7.05437i		−	0.291165i	0.989346	−	0.145583i	$-0.0465056\pi$
$588$	32.1763	−	32.1763i	1.32693	−	1.32693i
$589$	−6.14559			−0.253225
$590$	1.23391	−	7.51095i	0.0507992	−	0.309221i
$591$	13.9273	+	13.9273i	0.572892	+	0.572892i
$592$	−16.4744			−0.677092
$593$			40.0169i			1.64330i	0.569993	+	0.821649i	$0.306946\pi$
$593$			40.0169i			1.64330i	−0.569993	+	0.821649i	$0.693054\pi$
$594$			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	$0.908208\pi$
$600$	46.5236	−	23.0352i	1.89932	−	0.940410i
$601$	−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
$603$	−0.190206			−0.00774580
$604$	−42.6597	+	42.6597i	−1.73580	+	1.73580i
$605$	−9.86641	−	13.7454i	−0.401127	−	0.558829i
$606$	−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
$613$	10.6593			0.430524			0.215262	−	0.976556i	$-0.430939\pi$
$613$	10.6593			0.430524			0.215262	+	0.976556i	$0.430939\pi$
$614$		−	70.3403i		−	2.83871i
$615$	12.7826	−	9.17533i	0.515445	−	0.369985i
$616$	−1.17838	−	1.17838i	−0.0474783	−	0.0474783i
$617$			13.7284i			0.552685i	0.961059	+	0.276343i	$0.0891224\pi$
$617$			13.7284i			0.552685i	−0.961059	+	0.276343i	$0.910878\pi$
$618$			37.5661i			1.51113i
$619$	−16.8604	−	16.8604i	−0.677679	−	0.677679i	0.281796	−	0.959474i	$-0.409070\pi$
$619$	−16.8604	−	16.8604i	−0.677679	−	0.677679i	−0.959474	+	0.281796i	$0.909070\pi$
$620$	9.78283	+	1.60714i	0.392888	+	0.0645441i
$621$			17.9918i			0.721988i
$622$	9.39119			0.376552
$623$	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
$630$	−0.712670	+	0.511553i	−0.0283935	+	0.0203808i
$631$	21.6345	−	21.6345i	0.861257	−	0.861257i	−0.130227	−	0.991484i	$-0.541571\pi$
$631$	21.6345	−	21.6345i	0.861257	−	0.861257i	0.991484	+	0.130227i	$0.0415706\pi$
$632$	−121.434			−4.83038
$633$	−21.6601	+	21.6601i	−0.860911	+	0.860911i
$634$	22.5974			0.897459
$635$	4.22953	−	25.7457i	0.167844	−	1.02169i
$636$		−	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	$-0.902299\pi$
$641$		−	15.2991i		−	0.604280i	0.953264	−	0.302140i	$-0.0977010\pi$
$642$			25.4452i			1.00424i
$643$	−22.3480			−0.881319			−0.440660	−	0.897674i	$-0.645255\pi$
$643$	−22.3480			−0.881319			−0.440660	+	0.897674i	$0.645255\pi$
$644$	−1.28154	−	1.28154i	−0.0504999	−	0.0504999i
$645$	−9.18116	+	6.59022i	−0.361508	+	0.259490i
$646$	50.3420			1.98068
$647$	3.30644	−	3.30644i	0.129990	−	0.129990i	−0.639119	−	0.769108i	$-0.720701\pi$
$647$	3.30644	−	3.30644i	0.129990	−	0.129990i	0.769108	+	0.639119i	$0.220701\pi$
$648$			26.4949i			1.04082i
$649$	2.38033			0.0934361
$650$		0			0
$651$	0.128662			0.00504265
$652$			103.022i			4.03466i
$653$	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
$655$	−13.5583	+	9.73212i	−0.529766	+	0.380265i
$656$	−42.8533	−	42.8533i	−1.67314	−	1.67314i
$657$	−11.9428			−0.465934
$658$		−	0.102733i		−	0.00400494i
$659$			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	−0.901994	−	0.431749i	$-0.857897\pi$
$661$	−12.0900	+	12.0900i	−0.470245	+	0.470245i	0.431749	+	0.901994i	$0.357897\pi$
$662$	−33.7389	+	33.7389i	−1.31130	+	1.31130i
$663$		0			0
$664$		−	68.3547i		−	2.65268i
$665$	0.283442	−	1.72535i	0.0109914	−	0.0669061i
$666$	−5.15030			−0.199570
$667$	−10.5750	+	10.5750i	−0.409465	+	0.409465i
$668$	−12.7589			−0.493657
$669$	−8.92003	+	8.92003i	−0.344868	+	0.344868i
$670$	−0.694709	+	0.498661i	−0.0268390	+	0.0192650i
$671$	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	0.952785	−	0.303645i	$-0.0982037\pi$
$673$	16.8402	+	16.8402i	0.649140	+	0.649140i	−0.303645	+	0.952785i	$0.598204\pi$
$674$	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	$0.498588\pi$
$678$	−21.0160			−0.807114
$679$			1.68123i			0.0645195i
$680$	−48.2173	−	7.92120i	−1.84905	−	0.303764i
$681$	−8.41509	−	8.41509i	−0.322467	−	0.322467i
$682$			4.33521i			0.166004i
$683$			26.7876i			1.02500i	0.858687	+	0.512500i	$0.171280\pi$
$683$			26.7876i			1.02500i	−0.858687	+	0.512500i	$0.828720\pi$
$684$	32.5667	+	32.5667i	1.24522	+	1.24522i
$685$	−33.5774	+	24.1018i	−1.28293	+	0.920882i
$686$			4.16397i			0.158981i
$687$	−22.9770			−0.876628
$688$	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	−0.995955	−	0.0898576i	$-0.971359\pi$
$691$	−28.5426	−	28.5426i	−1.08581	−	1.08581i	−0.0898576	−	0.995955i	$-0.528641\pi$
$692$	−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
$695$	14.2261	+	19.8190i	0.539626	+	0.751779i
$696$	−34.1758	+	34.1758i	−1.29543	+	1.29543i
$697$	−14.8102			−0.560976
$698$	6.84510	−	6.84510i	0.259091	−	0.259091i
$699$	−21.7602			−0.823047
$700$	−0.902392	+	2.67236i	−0.0341072	+	0.101006i
$701$			24.9781i			0.943410i	0.881756	+	0.471705i	$0.156361\pi$
$701$			24.9781i			0.943410i	−0.881756	+	0.471705i	$0.843639\pi$
$702$		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
$707$		−	0.933677i		−	0.0351145i
$708$	8.36612			0.314418
$709$	7.21640	+	7.21640i	0.271018	+	0.271018i	0.829510	−	0.558492i	$-0.188620\pi$
$709$	7.21640	+	7.21640i	0.271018	+	0.271018i	−0.558492	+	0.829510i	$0.688620\pi$
$710$	−5.25742	+	32.0025i	−0.197307	+	1.20103i
$711$	−19.9907			−0.749710
$712$	−3.22166	+	3.22166i	−0.120737	+	0.120737i
$713$			2.83681i			0.106240i
$714$	−1.05394			−0.0394428
$715$		0			0
$716$	106.570			3.98272
$717$		−	33.4118i		−	1.24779i
$718$	−22.7354	+	22.7354i	−0.848479	+	0.848479i
$719$	28.4233			1.06001			0.530005	−	0.847994i	$-0.322190\pi$
$719$	28.4233			1.06001			0.530005	+	0.847994i	$0.322190\pi$
$720$	−19.1944	−	26.7407i	−0.715333	−	0.996566i
$721$	−0.868382	−	0.868382i	−0.0323402	−	0.0323402i
$722$	−78.0130			−2.90334
$723$			7.09498i			0.263865i
$724$		−	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	−0.847812	−	0.530296i	$-0.822081\pi$
$727$	−8.56116	+	8.56116i	−0.317516	+	0.317516i	0.530296	+	0.847812i	$0.322081\pi$
$728$		0			0
$729$			26.1513i			0.968566i
$730$	−43.6199	+	31.3103i	−1.61445	+	1.15885i
$731$	10.6375			0.393441
$732$	12.8156	−	12.8156i	0.473676	−	0.473676i
$733$	17.2200			0.636036			0.318018	−	0.948085i	$-0.396983\pi$
$733$	17.2200			0.636036			0.318018	+	0.948085i	$0.396983\pi$
$734$	−26.2521	+	26.2521i	−0.968982	+	0.968982i
$735$	3.28499	−	19.9961i	0.121169	−	0.737569i
$736$	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	$-0.346954\pi$
$739$	−11.5296	−	11.5296i	−0.424124	−	0.424124i	−0.886621	+	0.462497i	$0.846954\pi$
$740$	−13.4526	+	9.65626i	−0.494528	+	0.354971i
$741$		0			0
$742$	1.06915	+	1.06915i	0.0392498	+	0.0392498i
$743$	33.1199			1.21505			0.607525	−	0.794301i	$-0.292163\pi$
$743$	33.1199			1.21505			0.607525	+	0.794301i	$0.292163\pi$
$744$			9.16789i			0.336111i
$745$	−5.04623	+	30.7170i	−0.184879	+	1.12538i
$746$	54.1344	+	54.1344i	1.98200	+	1.98200i
$747$		−	11.2527i		−	0.411714i
$748$		−	25.3965i		−	0.928586i
$749$	−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	$-0.868939\pi$
$751$		−	21.9348i		−	0.800411i	0.916426	−	0.400205i	$-0.131061\pi$
$752$	3.85472			0.140567
$753$	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
$760$	122.941	+	20.1969i	4.45953	+	0.732618i
$761$	−15.5835	+	15.5835i	−0.564901	+	0.564901i	−0.930696	−	0.365794i	$-0.880797\pi$
$761$	−15.5835	+	15.5835i	−0.564901	+	0.564901i	0.365794	+	0.930696i	$0.380797\pi$
$762$	40.0993			1.45265
$763$	−0.375854	+	0.375854i	−0.0136068	+	0.0136068i
$764$	−98.4482			−3.56173
$765$	−7.93762	−	1.30400i	−0.286985	−	0.0471463i
$766$		−	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	$-0.625625\pi$
$769$	14.9366	−	14.9366i	0.538628	−	0.538628i	0.923126	+	0.384498i	$0.125625\pi$
$770$	−1.21709	−	0.199945i	−0.0438609	−	0.00720553i
$771$		−	22.6303i		−	0.815011i
$772$		−	83.9143i		−	3.02014i
$773$	−18.6956			−0.672435			−0.336217	−	0.941784i	$-0.609148\pi$
$773$	−18.6956			−0.672435			−0.336217	+	0.941784i	$0.609148\pi$
$774$	9.62245	+	9.62245i	0.345872	+	0.345872i
$775$	3.95652	−	1.95899i	0.142122	−	0.0703691i
$776$	−119.797			−4.30046
$777$	−0.151962	+	0.151962i	−0.00545159	+	0.00545159i
$778$		−	0.160259i		−	0.00574555i
$779$	37.7619			1.35296
$780$		0			0
$781$	−10.1421			−0.362912
$782$		−	23.2379i		−	0.830987i
$783$	−18.4333	+	18.4333i	−0.658752	+	0.658752i
$784$	−78.0493			−2.78747
$785$	16.0544	+	2.63744i	0.573008	+	0.0941344i
$786$	−18.1376	−	18.1376i	−0.646947	−	0.646947i
$787$	43.3231			1.54430			0.772150	−	0.635440i	$-0.219181\pi$
$787$	43.3231			1.54430			0.772150	+	0.635440i	$0.219181\pi$
$788$		−	76.2534i		−	2.71642i
$789$		−	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
$795$	−8.58935	−	11.9663i	−0.304633	−	0.424399i
$796$	−70.0314			−2.48220
$797$	24.8641	−	24.8641i	0.880731	−	0.880731i	−0.112877	−	0.993609i	$-0.536007\pi$
$797$	24.8641	−	24.8641i	0.880731	−	0.880731i	0.993609	+	0.112877i	$0.0360067\pi$
$798$	2.68726			0.0951280
$799$	0.666099	−	0.666099i	0.0235649	−	0.0235649i
$800$	−64.3644	−	21.7343i	−2.27563	−	0.768424i
$801$	−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
$808$	66.5298			2.34051
$809$			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	0.978834	−	0.204656i	$-0.0656076\pi$
$811$	22.0471	+	22.0471i	0.774178	+	0.774178i	−0.204656	+	0.978834i	$0.565608\pi$
$812$		−	2.62598i		−	0.0921538i
$813$		−	10.2597i		−	0.359823i
$814$	−5.12029	−	5.12029i	−0.179466	−	0.179466i
$815$	26.7529	+	37.2708i	0.937114	+	1.30554i
$816$		−	39.5458i		−	1.38438i
$817$	−27.1226			−0.948901
$818$	−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	0.995917	−	0.0902727i	$-0.0287739\pi$
$821$	25.9495	+	25.9495i	0.905644	+	0.905644i	−0.0902727	+	0.995917i	$0.528774\pi$
$822$	−44.9182	−	44.9182i	−1.56670	−	1.56670i
$823$	16.6935	+	16.6935i	0.581899	+	0.581899i	0.935425	−	0.353526i	$-0.115017\pi$
$823$	16.6935	+	16.6935i	0.581899	+	0.581899i	−0.353526	+	0.935425i	$0.615017\pi$
$824$	61.8772	−	61.8772i	2.15559	−	2.15559i
$825$	11.3842	+	3.84417i	0.396347	+	0.133837i
$826$	−0.270423	+	0.270423i	−0.00940921	+	0.00940921i
$827$	4.44429			0.154543			0.0772716	−	0.997010i	$-0.475379\pi$
$827$	4.44429			0.154543			0.0772716	+	0.997010i	$0.475379\pi$
$828$	15.0328	−	15.0328i	0.522427	−	0.522427i
$829$	29.3369			1.01891			0.509457	−	0.860496i	$-0.329846\pi$
$829$	29.3369			1.01891			0.509457	+	0.860496i	$0.329846\pi$
$830$	−29.5010	−	41.0993i	−1.02399	−	1.42658i
$831$			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
$837$			4.94486i			0.170919i
$838$	34.6607			1.19734
$839$	6.00111	+	6.00111i	0.207181	+	0.207181i	0.803068	−	0.595887i	$-0.203199\pi$
$839$	6.00111	+	6.00111i	0.207181	+	0.207181i	−0.595887	+	0.803068i	$0.703199\pi$
$840$	−2.57384	−	0.422834i	−0.0888061	−	0.0145892i
$841$	7.33109			0.252796
$842$	36.5466	−	36.5466i	1.25948	−	1.25948i
$843$			22.8838i			0.788162i
$844$	118.591			4.08208
$845$		0			0
$846$	1.20508			0.0414316
$847$			0.850114i			0.0292103i
$848$	−40.1165	+	40.1165i	−1.37761	+	1.37761i
$849$	10.7213			0.367955
$850$	−32.4101	+	16.0472i	−1.11166	+	0.550415i
$851$	−3.35054	−	3.35054i	−0.114855	−	0.114855i
$852$	−35.6462			−1.22122
$853$		−	34.3415i		−	1.17583i	−0.808923	−	0.587915i	$-0.799949\pi$
$853$		−	34.3415i		−	1.17583i	0.808923	−	0.587915i	$-0.200051\pi$
$854$			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	−0.148314	−	0.988940i	$-0.547385\pi$
$857$	24.6090	−	24.6090i	0.840626	−	0.840626i	0.988940	+	0.148314i	$0.0473847\pi$
$858$		0			0
$859$		−	12.8606i		−	0.438798i	−0.975635	−	0.219399i	$-0.929590\pi$
$859$		−	12.8606i		−	0.438798i	0.975635	−	0.219399i	$-0.0704097\pi$
$860$	43.1750	+	7.09284i	1.47226	+	0.241864i
$861$	−0.790569			−0.0269425
$862$	41.6308	−	41.6308i	1.41795	−	1.41795i
$863$	2.75373			0.0937379			0.0468690	−	0.998901i	$-0.485076\pi$
$863$	2.75373			0.0937379			0.0468690	+	0.998901i	$0.485076\pi$
$864$	53.8032	−	53.8032i	1.83042	−	1.83042i
$865$	−0.174084	−	0.0285987i	−0.00591903	−	0.000972386i
$866$	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
$873$	−19.7212			−0.667462
$874$			59.2504i			2.00417i
$875$	0.367499	+	1.20113i	0.0124237	+	0.0406055i
$876$	−41.7308	−	41.7308i	−1.40995	−	1.40995i
$877$			47.2631i			1.59596i	0.602683	+	0.797981i	$0.294098\pi$
$877$			47.2631i			1.59596i	−0.602683	+	0.797981i	$0.705902\pi$
$878$		−	45.8239i		−	1.54648i
$879$	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	$-0.754927\pi$
$881$		−	41.3214i		−	1.39215i	0.717967	−	0.696077i	$-0.245073\pi$
$882$	−24.4001			−0.821596
$883$	13.4808	+	13.4808i	0.453666	+	0.453666i	0.896569	−	0.442903i	$-0.146051\pi$
$883$	13.4808	+	13.4808i	0.453666	+	0.453666i	−0.442903	+	0.896569i	$0.646051\pi$
$884$		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
$890$	−0.546646	+	3.32750i	−0.0183236	+	0.111538i
$891$	−4.33622	+	4.33622i	−0.145269	+	0.145269i
$892$	48.8381			1.63522
$893$	−1.69837	+	1.69837i	−0.0568338	+	0.0568338i
$894$	−47.8423			−1.60008
$895$	38.5544	−	27.6743i	1.28873	−	0.925048i
$896$			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
$902$		−	26.6379i		−	0.886946i
$903$	0.567829			0.0188962
$904$	34.6166	+	34.6166i	1.15133	+	1.15133i
$905$	−29.3728	−	40.9207i	−0.976384	−	1.36025i
$906$	−41.2916			−1.37182
$907$	−17.0541	+	17.0541i	−0.566271	+	0.566271i	−0.931082	−	0.364811i	$-0.881134\pi$
$907$	−17.0541	+	17.0541i	−0.566271	+	0.566271i	0.364811	+	0.931082i	$0.381134\pi$
$908$			46.0735i			1.52900i
$909$	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	$0.0790515\pi$
$912$			100.831i			3.33884i
$913$	11.1871	−	11.1871i	0.370240	−	0.370240i
$914$	−24.9790			−0.826231
$915$	1.30838	−	7.96429i	0.0432538	−	0.263291i
$916$	62.9008	+	62.9008i	2.07830	+	2.07830i
$917$	0.838543			0.0276911
$918$		−	40.5061i		−	1.33690i
$919$			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
$925$	−2.35926	+	6.98677i	−0.0775721	+	0.229724i
$926$	49.4787			1.62597
$927$	10.1863	−	10.1863i	0.334563	−	0.334563i
$928$	63.2473			2.07619
$929$	−19.8452	+	19.8452i	−0.651099	+	0.651099i	−0.953258	−	0.302158i	$-0.902293\pi$
$929$	−19.8452	+	19.8452i	−0.651099	+	0.651099i	0.302158	+	0.953258i	$0.402293\pi$
$930$	3.95674	+	5.51233i	0.129747	+	0.180756i
$931$	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	$0.590843\pi$
$938$	0.0429658			0.00140288
$939$			11.3919i			0.371762i
$940$	3.14768	−	2.25940i	0.102666	−	0.0736935i
$941$	6.70533	+	6.70533i	0.218588	+	0.218588i	0.807903	−	0.589315i	$-0.200602\pi$
$941$	6.70533	+	6.70533i	0.218588	+	0.218588i	−0.589315	+	0.807903i	$0.700602\pi$
$942$			25.0051i			0.814710i
$943$		−	17.4309i		−	0.567630i
$944$	−10.1467	−	10.1467i	−0.330249	−	0.330249i
$945$	−1.38825	−	0.228063i	−0.0451597	−	0.00741889i
$946$			19.1328i			0.622061i
$947$	−4.51085			−0.146583			−0.0732915	−	0.997311i	$-0.523350\pi$
$947$	−4.51085			−0.146583			−0.0732915	+	0.997311i	$0.523350\pi$
$948$	−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	0.638265	−	0.769817i	$-0.279652\pi$
$953$	−4.06109	−	4.06109i	−0.131552	−	0.131552i	−0.769817	+	0.638265i	$0.779652\pi$
$954$	−12.5414	+	12.5414i	−0.406043	+	0.406043i
$955$	−35.6160	+	25.5651i	−1.15251	+	0.827268i
$956$	−91.4666	+	91.4666i	−2.95824	+	2.95824i
$957$	−11.1866			−0.361612
$958$	−61.7624	+	61.7624i	−1.99545	+	1.99545i
$959$	2.07667			0.0670591
$960$	6.42300	−	39.0976i	0.207302	−	1.26187i
$961$		−	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
$967$			17.6414i			0.567310i	0.958926	+	0.283655i	$0.0915470\pi$
$967$			17.6414i			0.567310i	−0.958926	+	0.283655i	$0.908453\pi$
$968$	−60.5755			−1.94697
$969$	17.4237	+	17.4237i	0.559729	+	0.559729i
$970$	−72.0297	+	51.7028i	−2.31273	+	1.66008i
$971$	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
$973$		−	1.22575i		−	0.0392958i
$974$	−87.4056			−2.80065
$975$		0			0
$976$	−31.0864			−0.995050
$977$			15.3443i			0.490909i	0.969408	+	0.245454i	$0.0789371\pi$
$977$			15.3443i			0.490909i	−0.969408	+	0.245454i	$0.921063\pi$
$978$	−49.8591	+	49.8591i	−1.59432	+	1.59432i
$979$	−1.05453			−0.0337030
$980$	−63.7334	+	45.7477i	−2.03589	+	1.46136i
$981$	−4.40886	−	4.40886i	−0.140764	−	0.140764i
$982$	56.4286			1.80071
$983$		−	4.80751i		−	0.153336i	−0.997057	−	0.0766679i	$-0.975572\pi$
$983$		−	4.80751i		−	0.153336i	0.997057	−	0.0766679i	$-0.0244281\pi$
$984$		−	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
$990$	2.34541	−	14.2768i	0.0745420	−	0.453746i
$991$	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
$993$	−23.3545			−0.741131
$994$	1.15221	−	1.15221i	0.0365459	−	0.0365459i
$995$	−25.3355	+	18.1858i	−0.803191	+	0.576529i
$996$	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.f.d.437.1		20
5.3	odd	4		845.2.k.d.268.1		20
13.2	odd	12		845.2.o.f.357.5		20
13.3	even	3		845.2.t.g.657.5		20
13.4	even	6		845.2.t.f.427.5		20
13.5	odd	4		845.2.k.d.577.1		20
13.6	odd	12		845.2.o.g.587.5		20
13.7	odd	12		65.2.o.a.2.1	✓	20
13.8	odd	4		845.2.k.e.577.10		20
13.9	even	3		845.2.t.e.427.1		20
13.10	even	6		65.2.t.a.7.1	yes	20
13.11	odd	12		845.2.o.e.357.1		20
13.12	even	2		845.2.f.e.437.10		20
39.20	even	12		585.2.cf.a.262.5		20
39.23	odd	6		585.2.dp.a.397.5		20
65.3	odd	12		845.2.o.g.488.5		20
65.7	even	12		325.2.x.b.93.5		20
65.8	even	4		845.2.f.e.408.1		20
65.18	even	4	inner	845.2.f.d.408.10		20
65.23	odd	12		65.2.o.a.33.1	yes	20
65.28	even	12		845.2.t.e.188.1		20
65.33	even	12		65.2.t.a.28.1	yes	20
65.38	odd	4		845.2.k.e.268.10		20
65.43	odd	12		845.2.o.e.258.1		20
65.48	odd	12		845.2.o.f.258.5		20
65.49	even	6		325.2.x.b.7.5		20
65.58	even	12		845.2.t.g.418.5		20
65.59	odd	12		325.2.s.b.132.5		20
65.62	odd	12		325.2.s.b.293.5		20
65.63	even	12		845.2.t.f.188.5		20
195.23	even	12		585.2.cf.a.163.5		20
195.98	odd	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	13.7	odd	12
65.2.o.a.33.1	yes	20	65.23	odd	12
65.2.t.a.7.1	yes	20	13.10	even	6
65.2.t.a.28.1	yes	20	65.33	even	12
325.2.s.b.132.5		20	65.59	odd	12
325.2.s.b.293.5		20	65.62	odd	12
325.2.x.b.7.5		20	65.49	even	6
325.2.x.b.93.5		20	65.7	even	12
585.2.cf.a.163.5		20	195.23	even	12
585.2.cf.a.262.5		20	39.20	even	12
585.2.dp.a.28.5		20	195.98	odd	12
585.2.dp.a.397.5		20	39.23	odd	6
845.2.f.d.408.10		20	65.18	even	4	inner
845.2.f.d.437.1		20	1.1	even	1	trivial
845.2.f.e.408.1		20	65.8	even	4
845.2.f.e.437.10		20	13.12	even	2
845.2.k.d.268.1		20	5.3	odd	4
845.2.k.d.577.1		20	13.5	odd	4
845.2.k.e.268.10		20	65.38	odd	4
845.2.k.e.577.10		20	13.8	odd	4
845.2.o.e.258.1		20	65.43	odd	12
845.2.o.e.357.1		20	13.11	odd	12
845.2.o.f.258.5		20	65.48	odd	12
845.2.o.f.357.5		20	13.2	odd	12
845.2.o.g.488.5		20	65.3	odd	12
845.2.o.g.587.5		20	13.6	odd	12
845.2.t.e.188.1		20	65.28	even	12
845.2.t.e.427.1		20	13.9	even	3
845.2.t.f.188.5		20	65.63	even	12
845.2.t.f.427.5		20	13.4	even	6
845.2.t.g.418.5		20	65.58	even	12
845.2.t.g.657.5		20	13.3	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.64975i q^{2} +(0.917096 - 0.917096i) q^{3} -5.02120 q^{4} +(-1.81654 + 1.30391i) q^{5} +(-2.43008 - 2.43008i) q^{6} +0.112348 q^{7} +8.00544i q^{8} +1.31787i q^{9} +O(q^{10})\)	\(q-2.64975i q^{2} +(0.917096 - 0.917096i) q^{3} -5.02120 q^{4} +(-1.81654 + 1.30391i) q^{5} +(-2.43008 - 2.43008i) q^{6} +0.112348 q^{7} +8.00544i 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} +(-0.470132 + 2.86175i) q^{15} +11.1700 q^{16} +(1.93019 - 1.93019i) q^{17} +3.49203 q^{18} +(-4.92146 + 4.92146i) q^{19} +(9.12121 - 6.54719i) 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} -0.564122 q^{28} +4.65499i q^{29} +(7.58294 + 1.24574i) q^{30} +(0.624367 + 0.624367i) q^{31} -13.5870i q^{32} +2.40314i q^{33} +(-5.11454 - 5.11454i) q^{34} +(-0.204085 + 0.146492i) q^{35} -6.61729i q^{36} -1.47487 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} +(-1.71838 - 2.39396i) q^{45} +(6.01959 - 6.01959i) q^{46} +0.345095 q^{47} +(10.2440 - 10.2440i) q^{48} -6.98738 q^{49} +(-12.5524 - 4.23866i) 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} +9.02691i q^{57} +12.3346 q^{58} +(-0.908390 - 0.908390i) q^{59} +(2.36063 - 14.3694i) q^{60} -2.78301 q^{61} +(1.65442 - 1.65442i) q^{62} +0.148060i q^{63} -13.6621 q^{64} +6.36774 q^{66} +0.144329i q^{67} +(-9.69188 + 9.69188i) q^{68} +4.16683 q^{69} +(0.388167 + 0.540774i) q^{70} +(3.87045 + 3.87045i) q^{71} -10.5501 q^{72} +9.06221i 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} +(-20.2908 + 14.5647i) q^{80} +3.30961 q^{81} +(-10.1657 + 10.1657i) q^{82} -8.53853 q^{83} +(-0.517354 + 0.517354i) q^{84} +(-0.989478 + 6.02307i) 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} +1.14521 q^{93} -0.914416i q^{94} +(2.52290 - 15.3572i) q^{95} +(-12.4606 - 12.4606i) q^{96} +14.9645i q^{97} +18.5148i q^{98} +(-1.72666 - 1.72666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 12 q^{4} - 4 q^{6} - 4 q^{7}+O(q^{10}) \) 20 * q + 4 * q^3 - 12 * q^4 - 4 * q^6 - 4 * q^7	\( 20 q + 4 q^{3} - 12 q^{4} - 4 q^{6} - 4 q^{7} - 8 q^{10} - 8 q^{11} - 24 q^{12} - 28 q^{15} + 4 q^{16} - 14 q^{17} - 4 q^{19} + 12 q^{20} - 4 q^{21} - 32 q^{22} + 8 q^{23} + 4 q^{24} + 18 q^{25} + 4 q^{27} + 36 q^{28} + 40 q^{30} - 2 q^{34} - 20 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{40} + 38 q^{41} + 16 q^{42} - 32 q^{43} + 36 q^{44} + 6 q^{45} - 4 q^{46} + 40 q^{47} + 28 q^{48} - 36 q^{49} - 42 q^{50} - 10 q^{53} - 36 q^{54} - 16 q^{55} - 8 q^{59} - 28 q^{60} + 32 q^{61} + 4 q^{62} + 20 q^{64} - 32 q^{66} - 50 q^{68} + 32 q^{69} + 12 q^{70} + 40 q^{71} + 8 q^{72} + 4 q^{75} + 16 q^{76} - 28 q^{77} - 112 q^{80} + 28 q^{81} - 34 q^{82} - 48 q^{83} - 8 q^{84} + 2 q^{85} - 60 q^{86} - 28 q^{87} - 32 q^{88} - 12 q^{89} + 46 q^{90} - 8 q^{92} + 64 q^{93} + 40 q^{95} - 56 q^{96} - 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^3 - 12 * q^4 - 4 * q^6 - 4 * q^7 - 8 * q^10 - 8 * q^11 - 24 * q^12 - 28 * q^15 + 4 * q^16 - 14 * q^17 - 4 * q^19 + 12 * q^20 - 4 * q^21 - 32 * q^22 + 8 * q^23 + 4 * q^24 + 18 * q^25 + 4 * q^27 + 36 * q^28 + 40 * q^30 - 2 * q^34 - 20 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 - 32 * q^43 + 36 * q^44 + 6 * q^45 - 4 * q^46 + 40 * q^47 + 28 * q^48 - 36 * q^49 - 42 * q^50 - 10 * q^53 - 36 * q^54 - 16 * q^55 - 8 * q^59 - 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 + 12 * q^70 + 40 * q^71 + 8 * q^72 + 4 * q^75 + 16 * q^76 - 28 * q^77 - 112 * q^80 + 28 * q^81 - 34 * q^82 - 48 * q^83 - 8 * q^84 + 2 * q^85 - 60 * q^86 - 28 * q^87 - 32 * q^88 - 12 * q^89 + 46 * q^90 - 8 * q^92 + 64 * q^93 + 40 * q^95 - 56 * q^96 - 60 * q^99

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