LMFDB - Embedded newform 845.2.c.h.506.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(506,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("845.506");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 34x^{16} + 407x^{14} + 2175x^{12} + 5555x^{10} + 6664x^{8} + 3544x^{6} + 681x^{4} + 47x^{2} + 1 $ x^18 + 34x^16 + 407x^14 + 2175x^12 + 5555x^10 + 6664x^8 + 3544x^6 + 681x^4 + 47x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			506.2
Root			$3.88295i$ of defining polynomial
Character	$\chi$	$=$	845.506
Dual form			845.2.c.h.506.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63597i q^{2} +1.98944 q^{3} -4.94835 q^{4} -1.00000i q^{5} -5.24412i q^{6} -3.28231i q^{7} +7.77176i q^{8} +0.957886 q^{9} +O(q^{10})$	\(q-2.63597i q^{2} +1.98944 q^{3} -4.94835 q^{4} -1.00000i q^{5} -5.24412i q^{6} -3.28231i q^{7} +7.77176i q^{8} +0.957886 q^{9} -2.63597 q^{10} -3.22850i q^{11} -9.84446 q^{12} -8.65206 q^{14} -1.98944i q^{15} +10.5894 q^{16} +4.25510 q^{17} -2.52496i q^{18} +2.87293i q^{19} +4.94835i q^{20} -6.52996i q^{21} -8.51023 q^{22} -6.09907 q^{23} +15.4615i q^{24} -1.00000 q^{25} -4.06267 q^{27} +16.2420i q^{28} +5.77280 q^{29} -5.24412 q^{30} +0.835435i q^{31} -12.3700i q^{32} -6.42292i q^{33} -11.2163i q^{34} -3.28231 q^{35} -4.73995 q^{36} -5.59588i q^{37} +7.57297 q^{38} +7.77176 q^{40} -2.18667i q^{41} -17.2128 q^{42} -2.48711 q^{43} +15.9757i q^{44} -0.957886i q^{45} +16.0770i q^{46} +10.5761i q^{47} +21.0671 q^{48} -3.77353 q^{49} +2.63597i q^{50} +8.46528 q^{51} -5.08351 q^{53} +10.7091i q^{54} -3.22850 q^{55} +25.5093 q^{56} +5.71554i q^{57} -15.2169i q^{58} -0.144765i q^{59} +9.84446i q^{60} +6.06541 q^{61} +2.20218 q^{62} -3.14407i q^{63} -11.4280 q^{64} -16.9306 q^{66} -12.6133i q^{67} -21.0557 q^{68} -12.1338 q^{69} +8.65206i q^{70} +9.02740i q^{71} +7.44446i q^{72} -5.70395i q^{73} -14.7506 q^{74} -1.98944 q^{75} -14.2163i q^{76} -10.5969 q^{77} +14.1043 q^{79} -10.5894i q^{80} -10.9561 q^{81} -5.76401 q^{82} -7.41467i q^{83} +32.3125i q^{84} -4.25510i q^{85} +6.55595i q^{86} +11.4847 q^{87} +25.0911 q^{88} -13.0912i q^{89} -2.52496 q^{90} +30.1803 q^{92} +1.66205i q^{93} +27.8783 q^{94} +2.87293 q^{95} -24.6093i q^{96} -2.97494i q^{97} +9.94691i q^{98} -3.09253i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9}+O(q^{10}) $ 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9	$ 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9} - 6 q^{10} - 24 q^{12} - 4 q^{14} + 74 q^{16} + 2 q^{17} + 24 q^{22} - 28 q^{23} - 18 q^{25} + 44 q^{27} + 24 q^{29} + 4 q^{30} + 14 q^{35} - 6 q^{36} + 94 q^{38} + 24 q^{40} - 22 q^{42} - 78 q^{43} - 6 q^{48} - 32 q^{49} - 86 q^{51} - 16 q^{53} - 18 q^{55} + 58 q^{56} - 6 q^{61} + 20 q^{62} - 68 q^{64} - 98 q^{66} - 40 q^{68} + 26 q^{69} - 30 q^{74} - 14 q^{75} + 8 q^{77} + 78 q^{79} + 58 q^{81} + 8 q^{82} + 32 q^{87} - 84 q^{88} + 20 q^{90} - 54 q^{92} + 32 q^{94} + 8 q^{95}+O(q^{100}) $ 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9 - 6 * q^10 - 24 * q^12 - 4 * q^14 + 74 * q^16 + 2 * q^17 + 24 * q^22 - 28 * q^23 - 18 * q^25 + 44 * q^27 + 24 * q^29 + 4 * q^30 + 14 * q^35 - 6 * q^36 + 94 * q^38 + 24 * q^40 - 22 * q^42 - 78 * q^43 - 6 * q^48 - 32 * q^49 - 86 * q^51 - 16 * q^53 - 18 * q^55 + 58 * q^56 - 6 * q^61 + 20 * q^62 - 68 * q^64 - 98 * q^66 - 40 * q^68 + 26 * q^69 - 30 * q^74 - 14 * q^75 + 8 * q^77 + 78 * q^79 + 58 * q^81 + 8 * q^82 + 32 * q^87 - 84 * q^88 + 20 * q^90 - 54 * q^92 + 32 * q^94 + 8 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$171$	$677$
$\chi(n)$	$-1$	$1$

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 $

$2$	− 2.63597i	− 1.86391i	−0.362569	−	0.931957i	$-0.618100\pi$
$2$	− 2.63597i	− 1.86391i	0.362569	−	0.931957i	$-0.381900\pi$
$3$	1.98944	1.14861	0.574303	−	0.818643i	$-0.305273\pi$
$3$	1.98944	1.14861	0.574303	+	0.818643i	$0.305273\pi$
$4$	−4.94835	−2.47417
$5$	− 1.00000i	− 0.447214i
$5$	− 1.00000i	− 0.447214i
$6$	− 5.24412i	− 2.14090i
$7$	− 3.28231i	− 1.24059i	−0.784367	−	0.620297i	$-0.787012\pi$
$7$	− 3.28231i	− 1.24059i	0.784367	−	0.620297i	$-0.212988\pi$
$8$	7.77176i	2.74773i
$9$	0.957886	0.319295
$10$	−2.63597	−0.833567
$11$	− 3.22850i	− 0.973429i	−0.873561	−	0.486715i	$-0.838195\pi$
$11$	− 3.22850i	− 0.973429i	0.873561	−	0.486715i	$-0.161805\pi$
$12$	−9.84446	−2.84185
$13$	0	0
$13$	0	0
$14$	−8.65206	−2.31236
$15$	− 1.98944i	− 0.513672i
$16$	10.5894	2.64736
$17$	4.25510	1.03201	0.516007	−	0.856584i	$-0.327418\pi$
$17$	4.25510	1.03201	0.516007	+	0.856584i	$0.327418\pi$
$18$	− 2.52496i	− 0.595139i
$19$	2.87293i	0.659096i	0.944139	+	0.329548i	$0.106896\pi$
$19$	2.87293i	0.659096i	−0.944139	+	0.329548i	$0.893104\pi$
$20$	4.94835i	1.10648i
$21$	− 6.52996i	− 1.42495i
$22$	−8.51023	−1.81439
$23$	−6.09907	−1.27174	−0.635872	−	0.771795i	$-0.719359\pi$
$23$	−6.09907	−1.27174	−0.635872	+	0.771795i	$0.719359\pi$
$24$	15.4615i	3.15606i
$25$	−1.00000	−0.200000
$26$	0	0
$27$	−4.06267	−0.781861
$28$	16.2420i	3.06945i
$29$	5.77280	1.07198	0.535991	−	0.844224i	$-0.319938\pi$
$29$	5.77280	1.07198	0.535991	+	0.844224i	$0.319938\pi$
$30$	−5.24412	−0.957440
$31$	0.835435i	0.150048i	0.997182	+	0.0750242i	$0.0239034\pi$
$31$	0.835435i	0.150048i	−0.997182	+	0.0750242i	$0.976097\pi$
$32$	− 12.3700i	− 2.18672i
$33$	− 6.42292i	− 1.11809i
$34$	− 11.2163i	− 1.92358i
$35$	−3.28231	−0.554811
$36$	−4.73995	−0.789992
$37$	− 5.59588i	− 0.919957i	−0.887930	−	0.459978i	$-0.847857\pi$
$37$	− 5.59588i	− 0.919957i	0.887930	−	0.459978i	$-0.152143\pi$
$38$	7.57297	1.22850
$39$	0	0
$40$	7.77176	1.22882
$41$	− 2.18667i	− 0.341501i	−0.985314	−	0.170750i	$-0.945381\pi$
$41$	− 2.18667i	− 0.341501i	0.985314	−	0.170750i	$-0.0546192\pi$
$42$	−17.2128	−2.65599
$43$	−2.48711	−0.379280	−0.189640	−	0.981854i	$-0.560732\pi$
$43$	−2.48711	−0.379280	−0.189640	+	0.981854i	$0.560732\pi$
$44$	15.9757i	2.40843i
$45$	− 0.957886i	− 0.142793i
$46$	16.0770i	2.37042i
$47$	10.5761i	1.54268i	0.636422	+	0.771341i	$0.280414\pi$
$47$	10.5761i	1.54268i	−0.636422	+	0.771341i	$0.719586\pi$
$48$	21.0671	3.04078
$49$	−3.77353	−0.539075
$50$	2.63597i	0.372783i
$51$	8.46528	1.18538
$52$	0	0
$53$	−5.08351	−0.698273	−0.349137	−	0.937072i	$-0.613525\pi$
$53$	−5.08351	−0.698273	−0.349137	+	0.937072i	$0.613525\pi$
$54$	10.7091i	1.45732i
$55$	−3.22850	−0.435331
$56$	25.5093	3.40882
$57$	5.71554i	0.757042i
$58$	− 15.2169i	− 1.99808i
$59$	− 0.144765i	− 0.0188468i	−0.999956	−	0.00942338i	$-0.997000\pi$
$59$	− 0.144765i	− 0.0188468i	0.999956	−	0.00942338i	$-0.00299960\pi$
$60$	9.84446i	1.27091i
$61$	6.06541	0.776596	0.388298	−	0.921534i	$-0.373063\pi$
$61$	6.06541	0.776596	0.388298	+	0.921534i	$0.373063\pi$
$62$	2.20218	0.279677
$63$	− 3.14407i	− 0.396116i
$64$	−11.4280	−1.42850
$65$	0	0
$66$	−16.9306	−2.08402
$67$	− 12.6133i	− 1.54096i	−0.637461	−	0.770482i	$-0.720015\pi$
$67$	− 12.6133i	− 1.54096i	0.637461	−	0.770482i	$-0.279985\pi$
$68$	−21.0557	−2.55338
$69$	−12.1338	−1.46073
$70$	8.65206i	1.03412i
$71$	9.02740i	1.07136i	0.844423	+	0.535678i	$0.179944\pi$
$71$	9.02740i	1.07136i	−0.844423	+	0.535678i	$0.820056\pi$
$72$	7.44446i	0.877338i
$73$	− 5.70395i	− 0.667597i	−0.942644	−	0.333798i	$-0.891669\pi$
$73$	− 5.70395i	− 0.667597i	0.942644	−	0.333798i	$-0.108331\pi$
$74$	−14.7506	−1.71472
$75$	−1.98944	−0.229721
$76$	− 14.2163i	− 1.63072i
$77$	−10.5969	−1.20763
$78$	0	0
$79$	14.1043	1.58686	0.793430	−	0.608662i	$-0.208293\pi$
$79$	14.1043	1.58686	0.793430	+	0.608662i	$0.208293\pi$
$80$	− 10.5894i	− 1.18394i
$81$	−10.9561	−1.21735
$82$	−5.76401	−0.636528
$83$	− 7.41467i	− 0.813865i	−0.913458	−	0.406933i	$-0.866598\pi$
$83$	− 7.41467i	− 0.813865i	0.913458	−	0.406933i	$-0.133402\pi$
$84$	32.3125i	3.52558i
$85$	− 4.25510i	− 0.461531i
$86$	6.55595i	0.706946i
$87$	11.4847	1.23128
$88$	25.0911	2.67472
$89$	− 13.0912i	− 1.38766i	−0.720138	−	0.693830i	$-0.755922\pi$
$89$	− 13.0912i	− 1.38766i	0.720138	−	0.693830i	$-0.244078\pi$
$90$	−2.52496	−0.266154
$91$	0	0
$92$	30.1803	3.14652
$93$	1.66205i	0.172347i
$94$	27.8783	2.87543
$95$	2.87293	0.294757
$96$	− 24.6093i	− 2.51168i
$97$	− 2.97494i	− 0.302059i	−0.988529	−	0.151030i	$-0.951741\pi$
$97$	− 2.97494i	− 0.302059i	0.988529	−	0.151030i	$-0.0482589\pi$
$98$	9.94691i	1.00479i
$99$	− 3.09253i	− 0.310811i
$100$	4.94835	0.494835
$101$	−2.24007	−0.222896	−0.111448	−	0.993770i	$-0.535549\pi$
$101$	−2.24007	−0.222896	−0.111448	+	0.993770i	$0.535549\pi$
$102$	− 22.3143i	− 2.20944i
$103$	12.6517	1.24661	0.623305	−	0.781979i	$-0.285790\pi$
$103$	12.6517	1.24661	0.623305	+	0.781979i	$0.285790\pi$
$104$	0	0
$105$	−6.52996	−0.637259
$106$	13.4000i	1.30152i
$107$	5.51892	0.533534	0.266767	−	0.963761i	$-0.414045\pi$
$107$	5.51892	0.533534	0.266767	+	0.963761i	$0.414045\pi$
$108$	20.1035	1.93446
$109$	7.12142i	0.682108i	0.940044	+	0.341054i	$0.110784\pi$
$109$	7.12142i	0.682108i	−0.940044	+	0.341054i	$0.889216\pi$
$110$	8.51023i	0.811419i
$111$	− 11.1327i	− 1.05667i
$112$	− 34.7578i	− 3.28430i
$113$	18.7572	1.76453	0.882264	−	0.470756i	$-0.156019\pi$
$113$	18.7572	1.76453	0.882264	+	0.470756i	$0.156019\pi$
$114$	15.0660	1.41106
$115$	6.09907i	0.568741i
$116$	−28.5658	−2.65227
$117$	0	0
$118$	−0.381596	−0.0351287
$119$	− 13.9665i	− 1.28031i
$120$	15.4615	1.41143
$121$	0.576790	0.0524355
$122$	− 15.9883i	− 1.44751i
$123$	− 4.35026i	− 0.392250i
$124$	− 4.13402i	− 0.371246i
$125$	1.00000i	0.0894427i
$126$	−8.28769	−0.738326
$127$	−0.368129	−0.0326661	−0.0163331	−	0.999867i	$-0.505199\pi$
$127$	−0.368129	−0.0326661	−0.0163331	+	0.999867i	$0.505199\pi$
$128$	5.38392i	0.475875i
$129$	−4.94796	−0.435644
$130$	0	0
$131$	3.09282	0.270221	0.135110	−	0.990831i	$-0.456861\pi$
$131$	3.09282	0.270221	0.135110	+	0.990831i	$0.456861\pi$
$132$	31.7828i	2.76634i
$133$	9.42984	0.817671
$134$	−33.2484	−2.87222
$135$	4.06267i	0.349659i
$136$	33.0696i	2.83570i
$137$	− 15.5865i	− 1.33164i	−0.746111	−	0.665822i	$-0.768081\pi$
$137$	− 15.5865i	− 1.33164i	0.746111	−	0.665822i	$-0.231919\pi$
$138$	31.9842i	2.72268i
$139$	18.7547	1.59075	0.795376	−	0.606116i	$-0.207273\pi$
$139$	18.7547	1.59075	0.795376	+	0.606116i	$0.207273\pi$
$140$	16.2420	1.37270
$141$	21.0405i	1.77193i
$142$	23.7960	1.99691
$143$	0	0
$144$	10.1435	0.845290
$145$	− 5.77280i	− 0.479405i
$146$	−15.0355	−1.24434
$147$	−7.50722	−0.619185
$148$	27.6904i	2.27613i
$149$	− 13.1350i	− 1.07606i	−0.842925	−	0.538032i	$-0.819168\pi$
$149$	− 13.1350i	− 1.07606i	0.842925	−	0.538032i	$-0.180832\pi$
$150$	5.24412i	0.428180i
$151$	1.66546i	0.135533i	0.997701	+	0.0677665i	$0.0215873\pi$
$151$	1.66546i	0.135533i	−0.997701	+	0.0677665i	$0.978413\pi$
$152$	−22.3278	−1.81102
$153$	4.07590	0.329517
$154$	27.9332i	2.25092i
$155$	0.835435	0.0671037
$156$	0	0
$157$	−20.6056	−1.64450	−0.822251	−	0.569125i	$-0.807282\pi$
$157$	−20.6056	−1.64450	−0.822251	+	0.569125i	$0.807282\pi$
$158$	− 37.1786i	− 2.95777i
$159$	−10.1134	−0.802041
$160$	−12.3700	−0.977932
$161$	20.0190i	1.57772i
$162$	28.8800i	2.26903i
$163$	5.62628i	0.440684i	0.975423	+	0.220342i	$0.0707174\pi$
$163$	5.62628i	0.440684i	−0.975423	+	0.220342i	$0.929283\pi$
$164$	10.8204i	0.844933i
$165$	−6.42292	−0.500023
$166$	−19.5449	−1.51697
$167$	14.1216i	1.09276i	0.837537	+	0.546381i	$0.183995\pi$
$167$	14.1216i	1.09276i	−0.837537	+	0.546381i	$0.816005\pi$
$168$	50.7493	3.91539
$169$	0	0
$170$	−11.2163	−0.860253
$171$	2.75194i	0.210446i
$172$	12.3071	0.938406
$173$	9.86557	0.750066	0.375033	−	0.927012i	$-0.377631\pi$
$173$	9.86557	0.750066	0.375033	+	0.927012i	$0.377631\pi$
$174$	− 30.2732i	− 2.29501i
$175$	3.28231i	0.248119i
$176$	− 34.1880i	− 2.57702i
$177$	− 0.288001i	− 0.0216475i
$178$	−34.5079	−2.58648
$179$	−9.25334	−0.691627	−0.345813	−	0.938303i	$-0.612397\pi$
$179$	−9.25334	−0.691627	−0.345813	+	0.938303i	$0.612397\pi$
$180$	4.73995i	0.353295i
$181$	21.6558	1.60967	0.804833	−	0.593501i	$-0.202255\pi$
$181$	21.6558	1.60967	0.804833	+	0.593501i	$0.202255\pi$
$182$	0	0
$183$	12.0668	0.892003
$184$	− 47.4005i	− 3.49441i
$185$	−5.59588	−0.411417
$186$	4.38112	0.321239
$187$	− 13.7376i	− 1.00459i
$188$	− 52.3342i	− 3.81686i
$189$	13.3349i	0.969973i
$190$	− 7.57297i	− 0.549401i
$191$	−21.3578	−1.54539	−0.772697	−	0.634775i	$-0.781093\pi$
$191$	−21.3578	−1.54539	−0.772697	+	0.634775i	$0.781093\pi$
$192$	−22.7353	−1.64078
$193$	− 5.77649i	− 0.415801i	−0.978150	−	0.207901i	$-0.933337\pi$
$193$	− 5.77649i	− 0.415801i	0.978150	−	0.207901i	$-0.0666631\pi$
$194$	−7.84186	−0.563013
$195$	0	0
$196$	18.6727	1.33377
$197$	12.4045i	0.883787i	0.897067	+	0.441894i	$0.145693\pi$
$197$	12.4045i	0.883787i	−0.897067	+	0.441894i	$0.854307\pi$
$198$	−8.15183	−0.579325
$199$	6.03432	0.427762	0.213881	−	0.976860i	$-0.431390\pi$
$199$	6.03432	0.427762	0.213881	+	0.976860i	$0.431390\pi$
$200$	− 7.77176i	− 0.549547i
$201$	− 25.0935i	− 1.76996i
$202$	5.90477i	0.415458i
$203$	− 18.9481i	− 1.32989i
$204$	−41.8892	−2.93283
$205$	−2.18667	−0.152724
$206$	− 33.3495i	− 2.32357i
$207$	−5.84221	−0.406062
$208$	0	0
$209$	9.27526	0.641583
$210$	17.2128i	1.18780i
$211$	−13.6840	−0.942049	−0.471024	−	0.882120i	$-0.656116\pi$
$211$	−13.6840	−0.942049	−0.471024	+	0.882120i	$0.656116\pi$
$212$	25.1550	1.72765
$213$	17.9595i	1.23056i
$214$	− 14.5477i	− 0.994461i
$215$	2.48711i	0.169619i
$216$	− 31.5741i	− 2.14835i
$217$	2.74215	0.186149
$218$	18.7719	1.27139
$219$	− 11.3477i	− 0.766806i
$220$	15.9757	1.07708
$221$	0	0
$222$	−29.3454	−1.96954
$223$	18.6882i	1.25145i	0.780042	+	0.625727i	$0.215198\pi$
$223$	18.6882i	1.25145i	−0.780042	+	0.625727i	$0.784802\pi$
$224$	−40.6020	−2.71284
$225$	−0.957886	−0.0638590
$226$	− 49.4434i	− 3.28893i
$227$	11.5082i	0.763828i	0.924198	+	0.381914i	$0.124735\pi$
$227$	11.5082i	0.763828i	−0.924198	+	0.381914i	$0.875265\pi$
$228$	− 28.2825i	− 1.87305i
$229$	1.98065i	0.130885i	0.997856	+	0.0654424i	$0.0208459\pi$
$229$	1.98065i	0.130885i	−0.997856	+	0.0654424i	$0.979154\pi$
$230$	16.0770	1.06008
$231$	−21.0820	−1.38709
$232$	44.8648i	2.94552i
$233$	−22.1334	−1.45001	−0.725005	−	0.688744i	$-0.758163\pi$
$233$	−22.1334	−1.45001	−0.725005	+	0.688744i	$0.758163\pi$
$234$	0	0
$235$	10.5761	0.689909
$236$	0.716346i	0.0466302i
$237$	28.0597	1.82268
$238$	−36.8154	−2.38639
$239$	− 11.2846i	− 0.729942i	−0.931019	−	0.364971i	$-0.881079\pi$
$239$	− 11.2846i	− 0.729942i	0.931019	−	0.364971i	$-0.118921\pi$
$240$	− 21.0671i	− 1.35988i
$241$	24.9029i	1.60414i	0.597233	+	0.802068i	$0.296267\pi$
$241$	24.9029i	1.60414i	−0.597233	+	0.802068i	$0.703733\pi$
$242$	− 1.52040i	− 0.0977352i
$243$	−9.60855	−0.616389
$244$	−30.0138	−1.92143
$245$	3.77353i	0.241082i
$246$	−11.4672	−0.731120
$247$	0	0
$248$	−6.49280	−0.412293
$249$	− 14.7511i	− 0.934810i
$250$	2.63597	0.166713
$251$	14.1454	0.892848	0.446424	−	0.894821i	$-0.352697\pi$
$251$	14.1454	0.892848	0.446424	+	0.894821i	$0.352697\pi$
$252$	15.5580i	0.980060i
$253$	19.6908i	1.23795i
$254$	0.970377i	0.0608868i
$255$	− 8.46528i	− 0.530117i
$256$	−8.66412	−0.541508
$257$	−3.53245	−0.220348	−0.110174	−	0.993912i	$-0.535141\pi$
$257$	−3.53245	−0.220348	−0.110174	+	0.993912i	$0.535141\pi$
$258$	13.0427i	0.812002i
$259$	−18.3674	−1.14129
$260$	0	0
$261$	5.52968	0.342279
$262$	− 8.15259i	− 0.503669i
$263$	−12.2296	−0.754109	−0.377055	−	0.926191i	$-0.623063\pi$
$263$	−12.2296	−0.754109	−0.377055	+	0.926191i	$0.623063\pi$
$264$	49.9174	3.07220
$265$	5.08351i	0.312277i
$266$	− 24.8568i	− 1.52407i
$267$	− 26.0441i	− 1.59388i
$268$	62.4152i	3.81261i
$269$	−22.4563	−1.36919	−0.684593	−	0.728926i	$-0.740020\pi$
$269$	−22.4563	−1.36919	−0.684593	+	0.728926i	$0.740020\pi$
$270$	10.7091	0.651734
$271$	19.3264i	1.17399i	0.809589	+	0.586997i	$0.199690\pi$
$271$	19.3264i	1.17399i	−0.809589	+	0.586997i	$0.800310\pi$
$272$	45.0592	2.73211
$273$	0	0
$274$	−41.0855	−2.48207
$275$	3.22850i	0.194686i
$276$	60.0420	3.61411
$277$	11.8931	0.714587	0.357294	−	0.933992i	$-0.383700\pi$
$277$	11.8931	0.714587	0.357294	+	0.933992i	$0.383700\pi$
$278$	− 49.4368i	− 2.96502i
$279$	0.800251i	0.0479098i
$280$	− 25.5093i	− 1.52447i
$281$	− 22.7024i	− 1.35431i	−0.735838	−	0.677157i	$-0.763212\pi$
$281$	− 22.7024i	− 1.35431i	0.735838	−	0.677157i	$-0.236788\pi$
$282$	55.4623	3.30273
$283$	8.86050	0.526702	0.263351	−	0.964700i	$-0.415172\pi$
$283$	8.86050	0.526702	0.263351	+	0.964700i	$0.415172\pi$
$284$	− 44.6707i	− 2.65072i
$285$	5.71554	0.338559
$286$	0	0
$287$	−7.17733	−0.423664
$288$	− 11.8490i	− 0.698210i
$289$	1.10589	0.0650525
$290$	−15.2169	−0.893569
$291$	− 5.91848i	− 0.346947i
$292$	28.2251i	1.65175i
$293$	6.40308i	0.374072i	0.982353	+	0.187036i	$0.0598881\pi$
$293$	6.40308i	0.374072i	−0.982353	+	0.187036i	$0.940112\pi$
$294$	19.7888i	1.15411i
$295$	−0.144765	−0.00842853
$296$	43.4898	2.52780
$297$	13.1163i	0.761087i
$298$	−34.6236	−2.00569
$299$	0	0
$300$	9.84446	0.568370
$301$	8.16345i	0.470533i
$302$	4.39010	0.252622
$303$	−4.45650	−0.256019
$304$	30.4228i	1.74487i
$305$	− 6.06541i	− 0.347304i
$306$	− 10.7440i	− 0.614191i
$307$	25.8317i	1.47429i	0.675733	+	0.737146i	$0.263827\pi$
$307$	25.8317i	1.47429i	−0.675733	+	0.737146i	$0.736173\pi$
$308$	52.4372	2.98789
$309$	25.1698	1.43186
$310$	− 2.20218i	− 0.125076i
$311$	3.87202	0.219562	0.109781	−	0.993956i	$-0.464985\pi$
$311$	3.87202	0.219562	0.109781	+	0.993956i	$0.464985\pi$
$312$	0	0
$313$	4.13361	0.233645	0.116823	−	0.993153i	$-0.462729\pi$
$313$	4.13361	0.233645	0.116823	+	0.993153i	$0.462729\pi$
$314$	54.3157i	3.06521i
$315$	−3.14407	−0.177148
$316$	−69.7931	−3.92617
$317$	− 24.9158i	− 1.39941i	−0.714431	−	0.699706i	$-0.753314\pi$
$317$	− 24.9158i	− 1.39941i	0.714431	−	0.699706i	$-0.246686\pi$
$318$	26.6585i	1.49493i
$319$	− 18.6375i	− 1.04350i
$320$	11.4280i	0.638844i
$321$	10.9796	0.612820
$322$	52.7695	2.94073
$323$	12.2246i	0.680196i
$324$	54.2147	3.01193
$325$	0	0
$326$	14.8307	0.821397
$327$	14.1677i	0.783474i
$328$	16.9943	0.938353
$329$	34.7140	1.91384
$330$	16.9306i	0.932001i
$331$	5.56860i	0.306078i	0.988220	+	0.153039i	$0.0489060\pi$
$331$	5.56860i	0.306078i	−0.988220	+	0.153039i	$0.951094\pi$
$332$	36.6903i	2.01364i
$333$	− 5.36021i	− 0.293738i
$334$	37.2241	2.03681
$335$	−12.6133	−0.689140
$336$	− 69.1487i	− 3.77237i
$337$	−16.8799	−0.919507	−0.459753	−	0.888047i	$-0.652062\pi$
$337$	−16.8799	−0.919507	−0.459753	+	0.888047i	$0.652062\pi$
$338$	0	0
$339$	37.3164	2.02675
$340$	21.0557i	1.14191i
$341$	2.69720	0.146062
$342$	7.25404	0.392254
$343$	− 10.5903i	− 0.571821i
$344$	− 19.3292i	− 1.04216i
$345$	12.1338i	0.653259i
$346$	− 26.0054i	− 1.39806i
$347$	−12.4254	−0.667031	−0.333516	−	0.942745i	$-0.608235\pi$
$347$	−12.4254	−0.667031	−0.333516	+	0.942745i	$0.608235\pi$
$348$	−56.8301	−3.04641
$349$	− 2.73516i	− 0.146410i	−0.997317	−	0.0732050i	$-0.976677\pi$
$349$	− 2.73516i	− 0.146410i	0.997317	−	0.0732050i	$-0.0233227\pi$
$350$	8.65206	0.462472
$351$	0	0
$352$	−39.9364	−2.12862
$353$	− 22.7460i	− 1.21065i	−0.795980	−	0.605323i	$-0.793044\pi$
$353$	− 22.7460i	− 1.21065i	0.795980	−	0.605323i	$-0.206956\pi$
$354$	−0.759163	−0.0403491
$355$	9.02740	0.479125
$356$	64.7796i	3.43331i
$357$	− 27.7856i	− 1.47057i
$358$	24.3915i	1.28913i
$359$	11.5189i	0.607945i	0.952681	+	0.303973i	$0.0983131\pi$
$359$	11.5189i	0.607945i	−0.952681	+	0.303973i	$0.901687\pi$
$360$	7.44446	0.392357
$361$	10.7463	0.565592
$362$	− 57.0842i	− 3.00028i
$363$	1.14749	0.0602277
$364$	0	0
$365$	−5.70395	−0.298558
$366$	− 31.8077i	− 1.66262i
$367$	14.0733	0.734622	0.367311	−	0.930098i	$-0.380279\pi$
$367$	14.0733	0.734622	0.367311	+	0.930098i	$0.380279\pi$
$368$	−64.5858	−3.36677
$369$	− 2.09458i	− 0.109040i
$370$	14.7506i	0.766846i
$371$	16.6856i	0.866274i
$372$	− 8.22440i	− 0.426415i
$373$	18.4780	0.956753	0.478377	−	0.878155i	$-0.341225\pi$
$373$	18.4780	0.956753	0.478377	+	0.878155i	$0.341225\pi$
$374$	−36.2119	−1.87247
$375$	1.98944i	0.102734i
$376$	−82.1949	−4.23888
$377$	0	0
$378$	35.1505	1.80795
$379$	1.53391i	0.0787918i	0.999224	+	0.0393959i	$0.0125434\pi$
$379$	1.53391i	0.0787918i	−0.999224	+	0.0393959i	$0.987457\pi$
$380$	−14.2163	−0.729279
$381$	−0.732371	−0.0375205
$382$	56.2985i	2.88048i
$383$	30.1620i	1.54120i	0.637317	+	0.770602i	$0.280044\pi$
$383$	30.1620i	1.54120i	−0.637317	+	0.770602i	$0.719956\pi$
$384$	10.7110i	0.546593i
$385$	10.5969i	0.540069i
$386$	−15.2267	−0.775017
$387$	−2.38237	−0.121102
$388$	14.7210i	0.747348i
$389$	−19.8405	−1.00595	−0.502976	−	0.864301i	$-0.667761\pi$
$389$	−19.8405	−1.00595	−0.502976	+	0.864301i	$0.667761\pi$
$390$	0	0
$391$	−25.9522	−1.31246
$392$	− 29.3269i	− 1.48123i
$393$	6.15299	0.310377
$394$	32.6980	1.64730
$395$	− 14.1043i	− 0.709665i
$396$	15.3029i	0.769001i
$397$	5.70766i	0.286459i	0.989689	+	0.143230i	$0.0457487\pi$
$397$	5.70766i	0.286459i	−0.989689	+	0.143230i	$0.954251\pi$
$398$	− 15.9063i	− 0.797311i
$399$	18.7601	0.939182
$400$	−10.5894	−0.529472
$401$	31.3372i	1.56491i	0.622709	+	0.782454i	$0.286032\pi$
$401$	31.3372i	1.56491i	−0.622709	+	0.782454i	$0.713968\pi$
$402$	−66.1458	−3.29905
$403$	0	0
$404$	11.0847	0.551482
$405$	10.9561i	0.544414i
$406$	−49.9466	−2.47881
$407$	−18.0663	−0.895513
$408$	65.7902i	3.25710i
$409$	19.2508i	0.951889i	0.879475	+	0.475944i	$0.157894\pi$
$409$	19.2508i	0.951889i	−0.879475	+	0.475944i	$0.842106\pi$
$410$	5.76401i	0.284664i
$411$	− 31.0084i	− 1.52953i
$412$	−62.6050	−3.08433
$413$	−0.475162	−0.0233812
$414$	15.3999i	0.756864i
$415$	−7.41467	−0.363972
$416$	0	0
$417$	37.3114	1.82715
$418$	− 24.4493i	− 1.19586i
$419$	−12.8466	−0.627596	−0.313798	−	0.949490i	$-0.601601\pi$
$419$	−12.8466	−0.627596	−0.313798	+	0.949490i	$0.601601\pi$
$420$	32.3125	1.57669
$421$	15.5491i	0.757819i	0.925434	+	0.378910i	$0.123701\pi$
$421$	15.5491i	0.757819i	−0.925434	+	0.378910i	$0.876299\pi$
$422$	36.0708i	1.75590i
$423$	10.1307i	0.492571i
$424$	− 39.5078i	− 1.91867i
$425$	−4.25510	−0.206403
$426$	47.3407	2.29367
$427$	− 19.9085i	− 0.963441i
$428$	−27.3095	−1.32006
$429$	0	0
$430$	6.55595	0.316156
$431$	16.4219i	0.791017i	0.918462	+	0.395509i	$0.129432\pi$
$431$	16.4219i	0.791017i	−0.918462	+	0.395509i	$0.870568\pi$
$432$	−43.0214	−2.06987
$433$	15.4378	0.741895	0.370948	−	0.928654i	$-0.379033\pi$
$433$	15.4378	0.741895	0.370948	+	0.928654i	$0.379033\pi$
$434$	− 7.22823i	− 0.346966i
$435$	− 11.4847i	− 0.550647i
$436$	− 35.2393i	− 1.68765i
$437$	− 17.5222i	− 0.838201i
$438$	−29.9122	−1.42926
$439$	39.6616	1.89294	0.946472	−	0.322785i	$-0.104619\pi$
$439$	39.6616	1.89294	0.946472	+	0.322785i	$0.104619\pi$
$440$	− 25.0911i	− 1.19617i
$441$	−3.61461	−0.172124
$442$	0	0
$443$	4.90611	0.233097	0.116548	−	0.993185i	$-0.462817\pi$
$443$	4.90611	0.233097	0.116548	+	0.993185i	$0.462817\pi$
$444$	55.0884i	2.61438i
$445$	−13.0912	−0.620581
$446$	49.2615	2.33260
$447$	− 26.1314i	− 1.23597i
$448$	37.5101i	1.77219i
$449$	28.2902i	1.33510i	0.744566	+	0.667549i	$0.232657\pi$
$449$	28.2902i	1.33510i	−0.744566	+	0.667549i	$0.767343\pi$
$450$	2.52496i	0.119028i
$451$	−7.05967	−0.332427
$452$	−92.8171	−4.36575
$453$	3.31333i	0.155674i
$454$	30.3354	1.42371
$455$	0	0
$456$	−44.4198	−2.08015
$457$	− 32.3338i	− 1.51251i	−0.654275	−	0.756257i	$-0.727026\pi$
$457$	− 32.3338i	− 1.51251i	0.654275	−	0.756257i	$-0.272974\pi$
$458$	5.22093	0.243958
$459$	−17.2871	−0.806892
$460$	− 30.1803i	− 1.40716i
$461$	6.97401i	0.324812i	0.986724	+	0.162406i	$0.0519254\pi$
$461$	6.97401i	0.324812i	−0.986724	+	0.162406i	$0.948075\pi$
$462$	55.5715i	2.58542i
$463$	33.1964i	1.54277i	0.636370	+	0.771384i	$0.280435\pi$
$463$	33.1964i	1.54277i	−0.636370	+	0.771384i	$0.719565\pi$
$464$	61.1307	2.83792
$465$	1.66205	0.0770757
$466$	58.3431i	2.70269i
$467$	31.6108	1.46277	0.731386	−	0.681963i	$-0.238874\pi$
$467$	31.6108	1.46277	0.731386	+	0.681963i	$0.238874\pi$
$468$	0	0
$469$	−41.4008	−1.91171
$470$	− 27.8783i	− 1.28593i
$471$	−40.9936	−1.88889
$472$	1.12508	0.0517859
$473$	8.02963i	0.369203i
$474$	− 73.9647i	− 3.39731i
$475$	− 2.87293i	− 0.131819i
$476$	69.1113i	3.16771i
$477$	−4.86942	−0.222955
$478$	−29.7460	−1.36055
$479$	10.3683i	0.473742i	0.971541	+	0.236871i	$0.0761219\pi$
$479$	10.3683i	0.473742i	−0.971541	+	0.236871i	$0.923878\pi$
$480$	−24.6093	−1.12326
$481$	0	0
$482$	65.6433	2.98997
$483$	39.8267i	1.81218i
$484$	−2.85416	−0.129734
$485$	−2.97494	−0.135085
$486$	25.3279i	1.14890i
$487$	− 34.9155i	− 1.58217i	−0.611705	−	0.791086i	$-0.709516\pi$
$487$	− 34.9155i	− 1.58217i	0.611705	−	0.791086i	$-0.290484\pi$
$488$	47.1389i	2.13388i
$489$	11.1932i	0.506172i
$490$	9.94691	0.449356
$491$	−17.5013	−0.789824	−0.394912	−	0.918719i	$-0.629225\pi$
$491$	−17.5013	−0.789824	−0.394912	+	0.918719i	$0.629225\pi$
$492$	21.5266i	0.970495i
$493$	24.5638	1.10630
$494$	0	0
$495$	−3.09253	−0.138999
$496$	8.84679i	0.397233i
$497$	29.6307	1.32912
$498$	−38.8834	−1.74241
$499$	8.46542i	0.378964i	0.981884	+	0.189482i	$0.0606809\pi$
$499$	8.46542i	0.378964i	−0.981884	+	0.189482i	$0.939319\pi$
$500$	− 4.94835i	− 0.221297i
$501$	28.0941i	1.25515i
$502$	− 37.2868i	− 1.66419i
$503$	−4.00003	−0.178353	−0.0891763	−	0.996016i	$-0.528423\pi$
$503$	−4.00003	−0.178353	−0.0891763	+	0.996016i	$0.528423\pi$
$504$	24.4350	1.08842
$505$	2.24007i	0.0996819i
$506$	51.9045	2.30744
$507$	0	0
$508$	1.82163	0.0808217
$509$	18.2954i	0.810927i	0.914111	+	0.405464i	$0.132890\pi$
$509$	18.2954i	0.810927i	−0.914111	+	0.405464i	$0.867110\pi$
$510$	−22.3143	−0.988092
$511$	−18.7221	−0.828217
$512$	33.6062i	1.48520i
$513$	− 11.6718i	− 0.515322i
$514$	9.31144i	0.410710i
$515$	− 12.6517i	− 0.557501i
$516$	24.4842	1.07786
$517$	34.1449	1.50169
$518$	48.4159i	2.12727i
$519$	19.6270	0.861530
$520$	0	0
$521$	−0.596886	−0.0261500	−0.0130750	−	0.999915i	$-0.504162\pi$
$521$	−0.596886	−0.0261500	−0.0130750	+	0.999915i	$0.504162\pi$
$522$	− 14.5761i	− 0.637978i
$523$	34.0800	1.49021	0.745107	−	0.666945i	$-0.232398\pi$
$523$	34.0800	1.49021	0.745107	+	0.666945i	$0.232398\pi$
$524$	−15.3044	−0.668574
$525$	6.52996i	0.284991i
$526$	32.2369i	1.40559i
$527$	3.55486i	0.154852i
$528$	− 68.0152i	− 2.95998i
$529$	14.1986	0.617332
$530$	13.4000	0.582058
$531$	− 0.138668i	− 0.00601768i
$532$	−46.6621	−2.02306
$533$	0	0
$534$	−68.6516	−2.97085
$535$	− 5.51892i	− 0.238604i
$536$	98.0278	4.23416
$537$	−18.4090	−0.794406
$538$	59.1942i	2.55204i
$539$	12.1828i	0.524752i
$540$	− 20.1035i	− 0.865117i
$541$	42.5430i	1.82907i	0.404510	+	0.914534i	$0.367442\pi$
$541$	42.5430i	1.82907i	−0.404510	+	0.914534i	$0.632558\pi$
$542$	50.9438	2.18822
$543$	43.0831	1.84887
$544$	− 52.6355i	− 2.25673i
$545$	7.12142	0.305048
$546$	0	0
$547$	42.0185	1.79658	0.898291	−	0.439401i	$-0.144809\pi$
$547$	42.0185	1.79658	0.898291	+	0.439401i	$0.144809\pi$
$548$	77.1274i	3.29472i
$549$	5.80997	0.247963
$550$	8.51023	0.362878
$551$	16.5849i	0.706539i
$552$	− 94.3006i	− 4.01370i
$553$	− 46.2947i	− 1.96865i
$554$	− 31.3499i	− 1.33193i
$555$	−11.1327	−0.472556
$556$	−92.8047	−3.93580
$557$	− 36.5703i	− 1.54953i	−0.632247	−	0.774767i	$-0.717867\pi$
$557$	− 36.5703i	− 1.54953i	0.632247	−	0.774767i	$-0.282133\pi$
$558$	2.10944	0.0892997
$559$	0	0
$560$	−34.7578	−1.46879
$561$	− 27.3302i	− 1.15388i
$562$	−59.8430	−2.52433
$563$	−24.6898	−1.04055	−0.520277	−	0.853998i	$-0.674171\pi$
$563$	−24.6898	−1.04055	−0.520277	+	0.853998i	$0.674171\pi$
$564$	− 104.116i	− 4.38407i
$565$	− 18.7572i	− 0.789121i
$566$	− 23.3560i	− 0.981727i
$567$	35.9613i	1.51023i
$568$	−70.1588	−2.94380
$569$	21.7107	0.910162	0.455081	−	0.890450i	$-0.349610\pi$
$569$	21.7107	0.910162	0.455081	+	0.890450i	$0.349610\pi$
$570$	− 15.0660i	− 0.631045i
$571$	−30.8235	−1.28992	−0.644962	−	0.764215i	$-0.723127\pi$
$571$	−30.8235	−1.28992	−0.644962	+	0.764215i	$0.723127\pi$
$572$	0	0
$573$	−42.4901	−1.77505
$574$	18.9192i	0.789674i
$575$	6.09907	0.254349
$576$	−10.9467	−0.456113
$577$	− 32.2437i	− 1.34232i	−0.741311	−	0.671161i	$-0.765796\pi$
$577$	− 32.2437i	− 1.34232i	0.741311	−	0.671161i	$-0.234204\pi$
$578$	− 2.91510i	− 0.121252i
$579$	− 11.4920i	− 0.477592i
$580$	28.5658i	1.18613i
$581$	−24.3372	−1.00968
$582$	−15.6009	−0.646680
$583$	16.4121i	0.679720i
$584$	44.3297	1.83438
$585$	0	0
$586$	16.8783	0.697238
$587$	7.71022i	0.318235i	0.987260	+	0.159117i	$0.0508649\pi$
$587$	7.71022i	0.318235i	−0.987260	+	0.159117i	$0.949135\pi$
$588$	37.1483	1.53197
$589$	−2.40015	−0.0988964
$590$	0.381596i	0.0157101i
$591$	24.6781i	1.01512i
$592$	− 59.2573i	− 2.43546i
$593$	− 17.1507i	− 0.704295i	−0.935945	−	0.352147i	$-0.885452\pi$
$593$	− 17.1507i	− 0.704295i	0.935945	−	0.352147i	$-0.114548\pi$
$594$	34.5743	1.41860
$595$	−13.9665	−0.572572
$596$	64.9967i	2.66237i
$597$	12.0049	0.491330
$598$	0	0
$599$	−14.8111	−0.605163	−0.302582	−	0.953123i	$-0.597849\pi$
$599$	−14.8111	−0.605163	−0.302582	+	0.953123i	$0.597849\pi$
$600$	− 15.4615i	− 0.631212i
$601$	5.70203	0.232591	0.116295	−	0.993215i	$-0.462898\pi$
$601$	5.70203	0.232591	0.116295	+	0.993215i	$0.462898\pi$
$602$	21.5186	0.877033
$603$	− 12.0821i	− 0.492023i
$604$	− 8.24126i	− 0.335332i
$605$	− 0.576790i	− 0.0234499i
$606$	11.7472i	0.477198i
$607$	4.95359	0.201060	0.100530	−	0.994934i	$-0.467946\pi$
$607$	4.95359	0.201060	0.100530	+	0.994934i	$0.467946\pi$
$608$	35.5381	1.44126
$609$	− 37.6961i	− 1.52752i
$610$	−15.9883	−0.647345
$611$	0	0
$612$	−20.1690	−0.815282
$613$	− 20.0157i	− 0.808427i	−0.914665	−	0.404213i	$-0.867545\pi$
$613$	− 20.0157i	− 0.808427i	0.914665	−	0.404213i	$-0.132455\pi$
$614$	68.0916	2.74795
$615$	−4.35026	−0.175420
$616$	− 82.3567i	− 3.31825i
$617$	4.36915i	0.175895i	0.996125	+	0.0879477i	$0.0280308\pi$
$617$	4.36915i	0.175895i	−0.996125	+	0.0879477i	$0.971969\pi$
$618$	− 66.3470i	− 2.66887i
$619$	29.2465i	1.17552i	0.809037	+	0.587758i	$0.199989\pi$
$619$	29.2465i	1.17552i	−0.809037	+	0.587758i	$0.800011\pi$
$620$	−4.13402	−0.166026
$621$	24.7785	0.994327
$622$	− 10.2065i	− 0.409245i
$623$	−42.9692	−1.72152
$624$	0	0
$625$	1.00000	0.0400000
$626$	− 10.8961i	− 0.435495i
$627$	18.4526	0.736926
$628$	101.963	4.06879
$629$	− 23.8110i	− 0.949408i
$630$	8.28769i	0.330189i
$631$	− 2.37642i	− 0.0946038i	−0.998881	−	0.0473019i	$-0.984938\pi$
$631$	− 2.37642i	− 0.0946038i	0.998881	−	0.0473019i	$-0.0150623\pi$
$632$	109.615i	4.36027i
$633$	−27.2236	−1.08204
$634$	−65.6774	−2.60838
$635$	0.368129i	0.0146087i
$636$	50.0444	1.98439
$637$	0	0
$638$	−49.1279	−1.94499
$639$	8.64722i	0.342079i
$640$	5.38392	0.212818
$641$	28.9687	1.14419	0.572097	−	0.820186i	$-0.306130\pi$
$641$	28.9687	1.14419	0.572097	+	0.820186i	$0.306130\pi$
$642$	− 28.9419i	− 1.14224i
$643$	− 14.0697i	− 0.554855i	−0.960747	−	0.277427i	$-0.910518\pi$
$643$	− 14.0697i	− 0.554855i	0.960747	−	0.277427i	$-0.0894818\pi$
$644$	− 99.0610i	− 3.90355i
$645$	4.94796i	0.194826i
$646$	32.2238	1.26783
$647$	−8.25026	−0.324351	−0.162176	−	0.986762i	$-0.551851\pi$
$647$	−8.25026	−0.324351	−0.162176	+	0.986762i	$0.551851\pi$
$648$	− 85.1483i	− 3.34494i
$649$	−0.467373	−0.0183460
$650$	0	0
$651$	5.45536	0.213812
$652$	− 27.8408i	− 1.09033i
$653$	−13.2659	−0.519136	−0.259568	−	0.965725i	$-0.583580\pi$
$653$	−13.2659	−0.519136	−0.259568	+	0.965725i	$0.583580\pi$
$654$	37.3456	1.46033
$655$	− 3.09282i	− 0.120847i
$656$	− 23.1557i	− 0.904077i
$657$	− 5.46373i	− 0.213161i
$658$	− 91.5051i	− 3.56724i
$659$	28.0173	1.09140	0.545699	−	0.837981i	$-0.316264\pi$
$659$	28.0173	1.09140	0.545699	+	0.837981i	$0.316264\pi$
$660$	31.7828	1.23714
$661$	− 30.0308i	− 1.16806i	−0.811731	−	0.584031i	$-0.801474\pi$
$661$	− 30.0308i	− 1.16806i	0.811731	−	0.584031i	$-0.198526\pi$
$662$	14.6787	0.570503
$663$	0	0
$664$	57.6250	2.23628
$665$	− 9.42984i	− 0.365674i
$666$	−14.1294	−0.547502
$667$	−35.2087	−1.36329
$668$	− 69.8785i	− 2.70368i
$669$	37.1791i	1.43743i
$670$	33.2484i	1.28450i
$671$	− 19.5822i	− 0.755962i
$672$	−80.7754	−3.11598
$673$	−20.1701	−0.777499	−0.388749	−	0.921344i	$-0.627093\pi$
$673$	−20.1701	−0.777499	−0.388749	+	0.921344i	$0.627093\pi$
$674$	44.4949i	1.71388i
$675$	4.06267	0.156372
$676$	0	0
$677$	−28.5492	−1.09723	−0.548616	−	0.836074i	$-0.684845\pi$
$677$	−28.5492	−1.09723	−0.548616	+	0.836074i	$0.684845\pi$
$678$	− 98.3649i	− 3.77768i
$679$	−9.76466	−0.374733
$680$	33.0696	1.26816
$681$	22.8950i	0.877337i
$682$	− 7.10974i	− 0.272246i
$683$	12.4889i	0.477876i	0.971035	+	0.238938i	$0.0767993\pi$
$683$	12.4889i	0.477876i	−0.971035	+	0.238938i	$0.923201\pi$
$684$	− 13.6176i	− 0.520681i
$685$	−15.5865	−0.595529
$686$	−27.9157	−1.06582
$687$	3.94038i	0.150335i
$688$	−26.3371	−1.00409
$689$	0	0
$690$	31.9842	1.21762
$691$	45.5955i	1.73453i	0.497843	+	0.867267i	$0.334126\pi$
$691$	45.5955i	1.73453i	−0.497843	+	0.867267i	$0.665874\pi$
$692$	−48.8183	−1.85579
$693$	−10.1506	−0.385591
$694$	32.7530i	1.24329i
$695$	− 18.7547i	− 0.711406i
$696$	89.2560i	3.38324i
$697$	− 9.30452i	− 0.352434i
$698$	−7.20981	−0.272895
$699$	−44.0332	−1.66549
$700$	− 16.2420i	− 0.613889i
$701$	4.57596	0.172831	0.0864157	−	0.996259i	$-0.472459\pi$
$701$	4.57596	0.172831	0.0864157	+	0.996259i	$0.472459\pi$
$702$	0	0
$703$	16.0766	0.606340
$704$	36.8952i	1.39054i
$705$	21.0405	0.792433
$706$	−59.9578	−2.25654
$707$	7.35260i	0.276523i
$708$	1.42513i	0.0535597i
$709$	− 24.2827i	− 0.911957i	−0.889991	−	0.455979i	$-0.849289\pi$
$709$	− 24.2827i	− 0.911957i	0.889991	−	0.455979i	$-0.150711\pi$
$710$	− 23.7960i	− 0.893047i
$711$	13.5103	0.506677
$712$	101.741	3.81292
$713$	− 5.09537i	− 0.190823i
$714$	−73.2422	−2.74102
$715$	0	0
$716$	45.7887	1.71120
$717$	− 22.4501i	− 0.838416i
$718$	30.3635	1.13316
$719$	13.0137	0.485329	0.242664	−	0.970110i	$-0.421979\pi$
$719$	13.0137	0.485329	0.242664	+	0.970110i	$0.421979\pi$
$720$	− 10.1435i	− 0.378025i
$721$	− 41.5267i	− 1.54654i
$722$	− 28.3268i	− 1.05422i
$723$	49.5429i	1.84252i
$724$	−107.161	−3.98259
$725$	−5.77280	−0.214396
$726$	− 3.02476i	− 0.112259i
$727$	−11.5596	−0.428722	−0.214361	−	0.976755i	$-0.568767\pi$
$727$	−11.5596	−0.428722	−0.214361	+	0.976755i	$0.568767\pi$
$728$	0	0
$729$	13.7527	0.509358
$730$	15.0355i	0.556487i
$731$	−10.5829	−0.391423
$732$	−59.7107	−2.20697
$733$	13.7767i	0.508855i	0.967092	+	0.254427i	$0.0818870\pi$
$733$	13.7767i	0.508855i	−0.967092	+	0.254427i	$0.918113\pi$
$734$	− 37.0969i	− 1.36927i
$735$	7.50722i	0.276908i
$736$	75.4453i	2.78095i
$737$	−40.7222	−1.50002
$738$	−5.52126	−0.203240
$739$	5.83557i	0.214665i	0.994223	+	0.107332i	$0.0342309\pi$
$739$	5.83557i	0.214665i	−0.994223	+	0.107332i	$0.965769\pi$
$740$	27.6904	1.01792
$741$	0	0
$742$	43.9828	1.61466
$743$	− 12.1353i	− 0.445202i	−0.974910	−	0.222601i	$-0.928545\pi$
$743$	− 12.1353i	− 0.445202i	0.974910	−	0.222601i	$-0.0714547\pi$
$744$	−12.9171	−0.473562
$745$	−13.1350	−0.481230
$746$	− 48.7074i	− 1.78331i
$747$	− 7.10240i	− 0.259863i
$748$	67.9784i	2.48554i
$749$	− 18.1148i	− 0.661900i
$750$	5.24412	0.191488
$751$	−45.3878	−1.65622	−0.828112	−	0.560563i	$-0.810585\pi$
$751$	−45.3878	−1.65622	−0.828112	+	0.560563i	$0.810585\pi$
$752$	111.995i	4.08404i
$753$	28.1414	1.02553
$754$	0	0
$755$	1.66546	0.0606122
$756$	− 65.9859i	− 2.39988i
$757$	19.5260	0.709684	0.354842	−	0.934926i	$-0.384535\pi$
$757$	19.5260	0.709684	0.354842	+	0.934926i	$0.384535\pi$
$758$	4.04335	0.146861
$759$	39.1738i	1.42192i
$760$	22.3278i	0.809913i
$761$	− 28.1496i	− 1.02042i	−0.860050	−	0.510210i	$-0.829568\pi$
$761$	− 28.1496i	− 1.02042i	0.860050	−	0.510210i	$-0.170432\pi$
$762$	1.93051i	0.0699350i
$763$	23.3747	0.846220
$764$	105.686	3.82357
$765$	− 4.07590i	− 0.147365i
$766$	79.5061	2.87267
$767$	0	0
$768$	−17.2368	−0.621979
$769$	1.42110i	0.0512463i	0.999672	+	0.0256232i	$0.00815700\pi$
$769$	1.42110i	0.0512463i	−0.999672	+	0.0256232i	$0.991843\pi$
$770$	27.9332	1.00664
$771$	−7.02761	−0.253093
$772$	28.5841i	1.02876i
$773$	13.8186i	0.497020i	0.968629	+	0.248510i	$0.0799409\pi$
$773$	13.8186i	0.497020i	−0.968629	+	0.248510i	$0.920059\pi$
$774$	6.27985i	0.225724i
$775$	− 0.835435i	− 0.0300097i
$776$	23.1205	0.829979
$777$	−36.5409	−1.31090
$778$	52.2989i	1.87501i
$779$	6.28217	0.225082
$780$	0	0
$781$	29.1450	1.04289
$782$	68.4092i	2.44631i
$783$	−23.4530	−0.838141
$784$	−39.9596	−1.42713
$785$	20.6056i	0.735444i
$786$	− 16.2191i	− 0.578517i
$787$	9.96442i	0.355193i	0.984103	+	0.177597i	$0.0568322\pi$
$787$	9.96442i	0.355193i	−0.984103	+	0.177597i	$0.943168\pi$
$788$	− 61.3820i	− 2.18664i
$789$	−24.3301	−0.866174
$790$	−37.1786	−1.32275
$791$	− 61.5668i	− 2.18906i
$792$	24.0344	0.854026
$793$	0	0
$794$	15.0452	0.533935
$795$	10.1134i	0.358684i
$796$	−29.8599	−1.05836
$797$	10.0651	0.356523	0.178262	−	0.983983i	$-0.442953\pi$
$797$	10.0651	0.356523	0.178262	+	0.983983i	$0.442953\pi$
$798$	− 49.4512i	− 1.75055i
$799$	45.0024i	1.59207i
$800$	12.3700i	0.437344i
$801$	− 12.5398i	− 0.443073i
$802$	82.6041	2.91685
$803$	−18.4152	−0.649858
$804$	124.171i	4.37919i
$805$	20.0190	0.705577
$806$	0	0
$807$	−44.6756	−1.57265
$808$	− 17.4093i	− 0.612457i
$809$	−38.1107	−1.33990	−0.669950	−	0.742406i	$-0.733684\pi$
$809$	−38.1107	−1.33990	−0.669950	+	0.742406i	$0.733684\pi$
$810$	28.8800	1.01474
$811$	− 3.57508i	− 0.125538i	−0.998028	−	0.0627690i	$-0.980007\pi$
$811$	− 3.57508i	− 0.125538i	0.998028	−	0.0627690i	$-0.0199932\pi$
$812$	93.7617i	3.29039i
$813$	38.4488i	1.34846i
$814$	47.6222i	1.66916i
$815$	5.62628	0.197080
$816$	89.6427	3.13812
$817$	− 7.14530i	− 0.249982i
$818$	50.7445	1.77424
$819$	0	0
$820$	10.8204	0.377865
$821$	43.5678i	1.52053i	0.649615	+	0.760263i	$0.274930\pi$
$821$	43.5678i	1.52053i	−0.649615	+	0.760263i	$0.725070\pi$
$822$	−81.7374	−2.85092
$823$	4.31879	0.150544	0.0752718	−	0.997163i	$-0.476018\pi$
$823$	4.31879	0.150544	0.0752718	+	0.997163i	$0.476018\pi$
$824$	98.3260i	3.42535i
$825$	6.42292i	0.223617i
$826$	1.25251i	0.0435805i
$827$	− 23.6479i	− 0.822320i	−0.911563	−	0.411160i	$-0.865124\pi$
$827$	− 23.6479i	− 0.822320i	0.911563	−	0.411160i	$-0.134876\pi$
$828$	28.9093	1.00467
$829$	49.9657	1.73538	0.867691	−	0.497105i	$-0.165603\pi$
$829$	49.9657	1.73538	0.867691	+	0.497105i	$0.165603\pi$
$830$	19.5449i	0.678412i
$831$	23.6607	0.820779
$832$	0	0
$833$	−16.0567	−0.556333
$834$	− 98.3518i	− 3.40564i
$835$	14.1216	0.488698
$836$	−45.8972	−1.58739
$837$	− 3.39410i	− 0.117317i
$838$	33.8632i	1.16978i
$839$	− 14.7181i	− 0.508125i	−0.967188	−	0.254063i	$-0.918233\pi$
$839$	− 14.7181i	− 0.508125i	0.967188	−	0.254063i	$-0.0817670\pi$
$840$	− 50.7493i	− 1.75102i
$841$	4.32519	0.149145
$842$	40.9871	1.41251
$843$	− 45.1652i	− 1.55557i
$844$	67.7134	2.33079
$845$	0	0
$846$	26.7042	0.918110
$847$	− 1.89320i	− 0.0650512i
$848$	−53.8315	−1.84858
$849$	17.6275	0.604973
$850$	11.2163i	0.384717i
$851$	34.1297i	1.16995i
$852$	− 88.8699i	− 3.04463i
$853$	− 27.0196i	− 0.925134i	−0.886584	−	0.462567i	$-0.846929\pi$
$853$	− 27.0196i	− 0.925134i	0.886584	−	0.462567i	$-0.153071\pi$
$854$	−52.4783	−1.79577
$855$	2.75194	0.0941144
$856$	42.8917i	1.46601i
$857$	−33.1663	−1.13294	−0.566470	−	0.824083i	$-0.691691\pi$
$857$	−33.1663	−1.13294	−0.566470	+	0.824083i	$0.691691\pi$
$858$	0	0
$859$	−47.4781	−1.61993	−0.809966	−	0.586476i	$-0.800515\pi$
$859$	−47.4781	−1.61993	−0.809966	+	0.586476i	$0.800515\pi$
$860$	− 12.3071i	− 0.419668i
$861$	−14.2789	−0.486623
$862$	43.2878	1.47439
$863$	− 3.65653i	− 0.124470i	−0.998062	−	0.0622349i	$-0.980177\pi$
$863$	− 3.65653i	− 0.124470i	0.998062	−	0.0622349i	$-0.0198228\pi$
$864$	50.2551i	1.70971i
$865$	− 9.86557i	− 0.335440i
$866$	− 40.6937i	− 1.38283i
$867$	2.20011	0.0747196
$868$	−13.5691	−0.460566
$869$	− 45.5358i	− 1.54470i
$870$	−30.2732	−1.02636
$871$	0	0
$872$	−55.3460	−1.87425
$873$	− 2.84965i	− 0.0964461i
$874$	−46.1881	−1.56234
$875$	3.28231	0.110962
$876$	56.1523i	1.89721i
$877$	− 7.26069i	− 0.245176i	−0.992458	−	0.122588i	$-0.960881\pi$
$877$	− 7.26069i	− 0.245176i	0.992458	−	0.122588i	$-0.0391194\pi$
$878$	− 104.547i	− 3.52828i
$879$	12.7386i	0.429661i
$880$	−34.1880	−1.15248
$881$	39.7044	1.33767	0.668837	−	0.743409i	$-0.266792\pi$
$881$	39.7044	1.33767	0.668837	+	0.743409i	$0.266792\pi$
$882$	9.52800i	0.320825i
$883$	−7.48855	−0.252010	−0.126005	−	0.992030i	$-0.540215\pi$
$883$	−7.48855	−0.252010	−0.126005	+	0.992030i	$0.540215\pi$
$884$	0	0
$885$	−0.288001	−0.00968106
$886$	− 12.9324i	− 0.434472i
$887$	−3.24520	−0.108963	−0.0544816	−	0.998515i	$-0.517351\pi$
$887$	−3.24520	−0.108963	−0.0544816	+	0.998515i	$0.517351\pi$
$888$	86.5206	2.90344
$889$	1.20831i	0.0405254i
$890$	34.5079i	1.15671i
$891$	35.3718i	1.18500i
$892$	− 92.4757i	− 3.09631i
$893$	−30.3844	−1.01678
$894$	−68.8816	−2.30375
$895$	9.25334i	0.309305i
$896$	17.6717	0.590369
$897$	0	0
$898$	74.5722	2.48851
$899$	4.82279i	0.160849i
$900$	4.73995	0.157998
$901$	−21.6308	−0.720628
$902$	18.6091i	0.619615i
$903$	16.2407i	0.540457i
$904$	145.776i	4.84845i
$905$	− 21.6558i	− 0.719865i
$906$	8.73385	0.290163
$907$	−28.5229	−0.947087	−0.473544	−	0.880770i	$-0.657025\pi$
$907$	−28.5229	−0.947087	−0.473544	+	0.880770i	$0.657025\pi$
$908$	− 56.9467i	− 1.88984i
$909$	−2.14573	−0.0711695
$910$	0	0
$911$	−49.2789	−1.63268	−0.816341	−	0.577570i	$-0.804001\pi$
$911$	−49.2789	−1.63268	−0.816341	+	0.577570i	$0.804001\pi$
$912$	60.5244i	2.00416i
$913$	−23.9382	−0.792240
$914$	−85.2311	−2.81919
$915$	− 12.0668i	− 0.398916i
$916$	− 9.80092i	− 0.323832i
$917$	− 10.1516i	− 0.335235i
$918$	45.5683i	1.50398i
$919$	−9.83623	−0.324467	−0.162234	−	0.986752i	$-0.551870\pi$
$919$	−9.83623	−0.324467	−0.162234	+	0.986752i	$0.551870\pi$
$920$	−47.4005	−1.56275
$921$	51.3907i	1.69338i
$922$	18.3833	0.605421
$923$	0	0
$924$	104.321	3.43191
$925$	5.59588i	0.183991i
$926$	87.5048	2.87559
$927$	12.1189	0.398036
$928$	− 71.4093i	− 2.34413i
$929$	27.6765i	0.908037i	0.890992	+	0.454018i	$0.150010\pi$
$929$	27.6765i	0.908037i	−0.890992	+	0.454018i	$0.849990\pi$
$930$	− 4.38112i	− 0.143662i
$931$	− 10.8411i	− 0.355302i
$932$	109.524	3.58758
$933$	7.70317	0.252190
$934$	− 83.3251i	− 2.72648i
$935$	−13.7376	−0.449267
$936$	0	0
$937$	−39.8796	−1.30281	−0.651406	−	0.758730i	$-0.725820\pi$
$937$	−39.8796	−1.30281	−0.651406	+	0.758730i	$0.725820\pi$
$938$	109.131i	3.56327i
$939$	8.22358	0.268367
$940$	−52.3342	−1.70695
$941$	2.58047i	0.0841210i	0.999115	+	0.0420605i	$0.0133922\pi$
$941$	2.58047i	0.0841210i	−0.999115	+	0.0420605i	$0.986608\pi$
$942$	108.058i	3.52072i
$943$	13.3367i	0.434302i
$944$	− 1.53298i	− 0.0498942i
$945$	13.3349	0.433785
$946$	21.1659	0.688162
$947$	− 5.28389i	− 0.171703i	−0.996308	−	0.0858517i	$-0.972639\pi$
$947$	− 5.28389i	− 0.171703i	0.996308	−	0.0858517i	$-0.0273611\pi$
$948$	−138.849	−4.50962
$949$	0	0
$950$	−7.57297	−0.245700
$951$	− 49.5686i	− 1.60737i
$952$	108.545	3.51795
$953$	−2.22577	−0.0720999	−0.0360499	−	0.999350i	$-0.511478\pi$
$953$	−2.22577	−0.0720999	−0.0360499	+	0.999350i	$0.511478\pi$
$954$	12.8356i	0.415570i
$955$	21.3578i	0.691121i
$956$	55.8403i	1.80600i
$957$	− 37.0782i	− 1.19857i
$958$	27.3307	0.883014
$959$	−51.1596	−1.65203
$960$	22.7353i	0.733780i
$961$	30.3020	0.977485
$962$	0	0
$963$	5.28649	0.170355
$964$	− 123.228i	− 3.96891i
$965$	−5.77649	−0.185952
$966$	104.982	3.37774
$967$	27.6359i	0.888712i	0.895850	+	0.444356i	$0.146567\pi$
$967$	27.6359i	0.888712i	−0.895850	+	0.444356i	$0.853433\pi$
$968$	4.48268i	0.144079i
$969$	24.3202i	0.781277i
$970$	7.84186i	0.251787i
$971$	−49.9320	−1.60239	−0.801197	−	0.598400i	$-0.795803\pi$
$971$	−49.9320	−1.60239	−0.801197	+	0.598400i	$0.795803\pi$
$972$	47.5465	1.52505
$973$	− 61.5586i	− 1.97348i
$974$	−92.0363	−2.94903
$975$	0	0
$976$	64.2294	2.05593
$977$	35.2611i	1.12810i	0.825739	+	0.564052i	$0.190758\pi$
$977$	35.2611i	1.12810i	−0.825739	+	0.564052i	$0.809242\pi$
$978$	29.5049	0.943461
$979$	−42.2648	−1.35079
$980$	− 18.6727i	− 0.596478i
$981$	6.82151i	0.217794i
$982$	46.1330i	1.47216i
$983$	20.6986i	0.660184i	0.943949	+	0.330092i	$0.107080\pi$
$983$	20.6986i	0.660184i	−0.943949	+	0.330092i	$0.892920\pi$
$984$	33.8092	1.07780
$985$	12.4045	0.395242
$986$	− 64.7496i	− 2.06205i
$987$	69.0615	2.19825
$988$	0	0
$989$	15.1690	0.482348
$990$	8.15183i	0.259082i
$991$	12.6676	0.402400	0.201200	−	0.979550i	$-0.435516\pi$
$991$	12.6676	0.402400	0.201200	+	0.979550i	$0.435516\pi$
$992$	10.3343	0.328114
$993$	11.0784i	0.351563i
$994$	− 78.1056i	− 2.47736i
$995$	− 6.03432i	− 0.191301i
$996$	72.9934i	2.31288i
$997$	−47.7614	−1.51262	−0.756309	−	0.654214i	$-0.772999\pi$
$997$	−47.7614	−1.51262	−0.756309	+	0.654214i	$0.772999\pi$
$998$	22.3146	0.706356
$999$	22.7342i	0.719279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.c.h.506.2		18
13.2	odd	12		845.2.e.p.191.8		18
13.3	even	3		845.2.m.j.316.17		36
13.4	even	6		845.2.m.j.361.17		36
13.5	odd	4		845.2.a.n.1.2	✓	9
13.6	odd	12		845.2.e.p.146.8		18
13.7	odd	12		845.2.e.o.146.2		18
13.8	odd	4		845.2.a.o.1.8	yes	9
13.9	even	3		845.2.m.j.361.2		36
13.10	even	6		845.2.m.j.316.2		36
13.11	odd	12		845.2.e.o.191.2		18
13.12	even	2	inner	845.2.c.h.506.17		18
39.5	even	4		7605.2.a.cs.1.8		9
39.8	even	4		7605.2.a.cp.1.2		9
65.34	odd	4		4225.2.a.bs.1.2		9
65.44	odd	4		4225.2.a.bt.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.2	✓	9	13.5	odd	4
845.2.a.o.1.8	yes	9	13.8	odd	4
845.2.c.h.506.2		18	1.1	even	1	trivial
845.2.c.h.506.17		18	13.12	even	2	inner
845.2.e.o.146.2		18	13.7	odd	12
845.2.e.o.191.2		18	13.11	odd	12
845.2.e.p.146.8		18	13.6	odd	12
845.2.e.p.191.8		18	13.2	odd	12
845.2.m.j.316.2		36	13.10	even	6
845.2.m.j.316.17		36	13.3	even	3
845.2.m.j.361.2		36	13.9	even	3
845.2.m.j.361.17		36	13.4	even	6
4225.2.a.bs.1.2		9	65.34	odd	4
4225.2.a.bt.1.8		9	65.44	odd	4
7605.2.a.cp.1.2		9	39.8	even	4
7605.2.a.cs.1.8		9	39.5	even	4

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.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.63597i q^{2} +1.98944 q^{3} -4.94835 q^{4} -1.00000i q^{5} -5.24412i q^{6} -3.28231i q^{7} +7.77176i q^{8} +0.957886 q^{9} +O(q^{10})\)	\(q-2.63597i q^{2} +1.98944 q^{3} -4.94835 q^{4} -1.00000i q^{5} -5.24412i q^{6} -3.28231i q^{7} +7.77176i q^{8} +0.957886 q^{9} -2.63597 q^{10} -3.22850i q^{11} -9.84446 q^{12} -8.65206 q^{14} -1.98944i q^{15} +10.5894 q^{16} +4.25510 q^{17} -2.52496i q^{18} +2.87293i q^{19} +4.94835i q^{20} -6.52996i q^{21} -8.51023 q^{22} -6.09907 q^{23} +15.4615i q^{24} -1.00000 q^{25} -4.06267 q^{27} +16.2420i q^{28} +5.77280 q^{29} -5.24412 q^{30} +0.835435i q^{31} -12.3700i q^{32} -6.42292i q^{33} -11.2163i q^{34} -3.28231 q^{35} -4.73995 q^{36} -5.59588i q^{37} +7.57297 q^{38} +7.77176 q^{40} -2.18667i q^{41} -17.2128 q^{42} -2.48711 q^{43} +15.9757i q^{44} -0.957886i q^{45} +16.0770i q^{46} +10.5761i q^{47} +21.0671 q^{48} -3.77353 q^{49} +2.63597i q^{50} +8.46528 q^{51} -5.08351 q^{53} +10.7091i q^{54} -3.22850 q^{55} +25.5093 q^{56} +5.71554i q^{57} -15.2169i q^{58} -0.144765i q^{59} +9.84446i q^{60} +6.06541 q^{61} +2.20218 q^{62} -3.14407i q^{63} -11.4280 q^{64} -16.9306 q^{66} -12.6133i q^{67} -21.0557 q^{68} -12.1338 q^{69} +8.65206i q^{70} +9.02740i q^{71} +7.44446i q^{72} -5.70395i q^{73} -14.7506 q^{74} -1.98944 q^{75} -14.2163i q^{76} -10.5969 q^{77} +14.1043 q^{79} -10.5894i q^{80} -10.9561 q^{81} -5.76401 q^{82} -7.41467i q^{83} +32.3125i q^{84} -4.25510i q^{85} +6.55595i q^{86} +11.4847 q^{87} +25.0911 q^{88} -13.0912i q^{89} -2.52496 q^{90} +30.1803 q^{92} +1.66205i q^{93} +27.8783 q^{94} +2.87293 q^{95} -24.6093i q^{96} -2.97494i q^{97} +9.94691i q^{98} -3.09253i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9}+O(q^{10}) \) 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9	\( 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9} - 6 q^{10} - 24 q^{12} - 4 q^{14} + 74 q^{16} + 2 q^{17} + 24 q^{22} - 28 q^{23} - 18 q^{25} + 44 q^{27} + 24 q^{29} + 4 q^{30} + 14 q^{35} - 6 q^{36} + 94 q^{38} + 24 q^{40} - 22 q^{42} - 78 q^{43} - 6 q^{48} - 32 q^{49} - 86 q^{51} - 16 q^{53} - 18 q^{55} + 58 q^{56} - 6 q^{61} + 20 q^{62} - 68 q^{64} - 98 q^{66} - 40 q^{68} + 26 q^{69} - 30 q^{74} - 14 q^{75} + 8 q^{77} + 78 q^{79} + 58 q^{81} + 8 q^{82} + 32 q^{87} - 84 q^{88} + 20 q^{90} - 54 q^{92} + 32 q^{94} + 8 q^{95}+O(q^{100}) \) 18 * q + 14 * q^3 - 34 * q^4 + 32 * q^9 - 6 * q^10 - 24 * q^12 - 4 * q^14 + 74 * q^16 + 2 * q^17 + 24 * q^22 - 28 * q^23 - 18 * q^25 + 44 * q^27 + 24 * q^29 + 4 * q^30 + 14 * q^35 - 6 * q^36 + 94 * q^38 + 24 * q^40 - 22 * q^42 - 78 * q^43 - 6 * q^48 - 32 * q^49 - 86 * q^51 - 16 * q^53 - 18 * q^55 + 58 * q^56 - 6 * q^61 + 20 * q^62 - 68 * q^64 - 98 * q^66 - 40 * q^68 + 26 * q^69 - 30 * q^74 - 14 * q^75 + 8 * q^77 + 78 * q^79 + 58 * q^81 + 8 * q^82 + 32 * q^87 - 84 * q^88 + 20 * q^90 - 54 * q^92 + 32 * q^94 + 8 * q^95

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