LMFDB - Embedded newform 845.2.c.h.506.4

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			506.4
Root			$1.03381i$ of defining polynomial
Character	$\chi$	$=$	845.506
Dual form			845.2.c.h.506.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28079i q^{2} +3.21428 q^{3} -3.20199 q^{4} +1.00000i q^{5} -7.33108i q^{6} -2.30369i q^{7} +2.74149i q^{8} +7.33158 q^{9} +O(q^{10})$	\(q-2.28079i q^{2} +3.21428 q^{3} -3.20199 q^{4} +1.00000i q^{5} -7.33108i q^{6} -2.30369i q^{7} +2.74149i q^{8} +7.33158 q^{9} +2.28079 q^{10} -1.25954i q^{11} -10.2921 q^{12} -5.25423 q^{14} +3.21428i q^{15} -0.151230 q^{16} -2.43159 q^{17} -16.7218i q^{18} +0.586893i q^{19} -3.20199i q^{20} -7.40470i q^{21} -2.87274 q^{22} +8.37020 q^{23} +8.81191i q^{24} -1.00000 q^{25} +13.9229 q^{27} +7.37640i q^{28} -3.09157 q^{29} +7.33108 q^{30} +0.394069i q^{31} +5.82790i q^{32} -4.04850i q^{33} +5.54595i q^{34} +2.30369 q^{35} -23.4757 q^{36} +2.01774i q^{37} +1.33858 q^{38} -2.74149 q^{40} -5.58749i q^{41} -16.8886 q^{42} -5.87653 q^{43} +4.03303i q^{44} +7.33158i q^{45} -19.0907i q^{46} +1.92869i q^{47} -0.486096 q^{48} +1.69301 q^{49} +2.28079i q^{50} -7.81582 q^{51} -13.6727 q^{53} -31.7552i q^{54} +1.25954 q^{55} +6.31554 q^{56} +1.88644i q^{57} +7.05121i q^{58} +14.6844i q^{59} -10.2921i q^{60} +5.85222 q^{61} +0.898789 q^{62} -16.8897i q^{63} +12.9897 q^{64} -9.23378 q^{66} +1.99420i q^{67} +7.78594 q^{68} +26.9042 q^{69} -5.25423i q^{70} -9.59141i q^{71} +20.0994i q^{72} +4.38231i q^{73} +4.60204 q^{74} -3.21428 q^{75} -1.87923i q^{76} -2.90159 q^{77} -0.217237 q^{79} -0.151230i q^{80} +22.7573 q^{81} -12.7439 q^{82} +11.0119i q^{83} +23.7098i q^{84} -2.43159i q^{85} +13.4031i q^{86} -9.93715 q^{87} +3.45301 q^{88} -6.37458i q^{89} +16.7218 q^{90} -26.8013 q^{92} +1.26665i q^{93} +4.39894 q^{94} -0.586893 q^{95} +18.7325i q^{96} +16.3061i q^{97} -3.86139i q^{98} -9.23440i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 2.28079i	− 1.61276i	−0.591397	−	0.806380i	$-0.701424\pi$
$2$	− 2.28079i	− 1.61276i	0.591397	−	0.806380i	$-0.298576\pi$
$3$	3.21428	1.85576	0.927882	−	0.372874i	$-0.121628\pi$
$3$	3.21428	1.85576	0.927882	+	0.372874i	$0.121628\pi$
$4$	−3.20199	−1.60100
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	− 7.33108i	− 2.99290i
$7$	− 2.30369i	− 0.870714i	−0.900258	−	0.435357i	$-0.856622\pi$
$7$	− 2.30369i	− 0.870714i	0.900258	−	0.435357i	$-0.143378\pi$
$8$	2.74149i	0.969263i
$9$	7.33158	2.44386
$10$	2.28079	0.721248
$11$	− 1.25954i	− 0.379765i	−0.981807	−	0.189882i	$-0.939189\pi$
$11$	− 1.25954i	− 0.379765i	0.981807	−	0.189882i	$-0.0608107\pi$
$12$	−10.2921	−2.97107
$13$	0	0
$13$	0	0
$14$	−5.25423	−1.40425
$15$	3.21428i	0.829923i
$16$	−0.151230	−0.0378075
$17$	−2.43159	−0.589748	−0.294874	−	0.955536i	$-0.595278\pi$
$17$	−2.43159	−0.589748	−0.294874	+	0.955536i	$0.595278\pi$
$18$	− 16.7218i	− 3.94136i
$19$	0.586893i	0.134643i	0.997731	+	0.0673213i	$0.0214453\pi$
$19$	0.586893i	0.134643i	−0.997731	+	0.0673213i	$0.978555\pi$
$20$	− 3.20199i	− 0.715987i
$21$	− 7.40470i	− 1.61584i
$22$	−2.87274	−0.612470
$23$	8.37020	1.74531	0.872654	−	0.488339i	$-0.162397\pi$
$23$	8.37020	1.74531	0.872654	+	0.488339i	$0.162397\pi$
$24$	8.81191i	1.79872i
$25$	−1.00000	−0.200000
$26$	0	0
$27$	13.9229	2.67946
$28$	7.37640i	1.39401i
$29$	−3.09157	−0.574090	−0.287045	−	0.957917i	$-0.592673\pi$
$29$	−3.09157	−0.574090	−0.287045	+	0.957917i	$0.592673\pi$
$30$	7.33108	1.33847
$31$	0.394069i	0.0707770i	0.999374	+	0.0353885i	$0.0112669\pi$
$31$	0.394069i	0.0707770i	−0.999374	+	0.0353885i	$0.988733\pi$
$32$	5.82790i	1.03024i
$33$	− 4.04850i	− 0.704754i
$34$	5.54595i	0.951122i
$35$	2.30369	0.389395
$36$	−23.4757	−3.91261
$37$	2.01774i	0.331715i	0.986150	+	0.165857i	$0.0530391\pi$
$37$	2.01774i	0.331715i	−0.986150	+	0.165857i	$0.946961\pi$
$38$	1.33858	0.217146
$39$	0	0
$40$	−2.74149	−0.433467
$41$	− 5.58749i	− 0.872619i	−0.899797	−	0.436309i	$-0.856285\pi$
$41$	− 5.58749i	− 0.872619i	0.899797	−	0.436309i	$-0.143715\pi$
$42$	−16.8886	−2.60596
$43$	−5.87653	−0.896162	−0.448081	−	0.893993i	$-0.647892\pi$
$43$	−5.87653	−0.896162	−0.448081	+	0.893993i	$0.647892\pi$
$44$	4.03303i	0.608002i
$45$	7.33158i	1.09293i
$46$	− 19.0907i	− 2.81476i
$47$	1.92869i	0.281329i	0.990057	+	0.140664i	$0.0449239\pi$
$47$	1.92869i	0.281329i	−0.990057	+	0.140664i	$0.955076\pi$
$48$	−0.486096	−0.0701619
$49$	1.69301	0.241858
$50$	2.28079i	0.322552i
$51$	−7.81582	−1.09443
$52$	0	0
$53$	−13.6727	−1.87809	−0.939044	−	0.343797i	$-0.888287\pi$
$53$	−13.6727	−1.87809	−0.939044	+	0.343797i	$0.888287\pi$
$54$	− 31.7552i	− 4.32133i
$55$	1.25954	0.169836
$56$	6.31554	0.843950
$57$	1.88644i	0.249865i
$58$	7.05121i	0.925869i
$59$	14.6844i	1.91175i	0.293770	+	0.955876i	$0.405090\pi$
$59$	14.6844i	1.91175i	−0.293770	+	0.955876i	$0.594910\pi$
$60$	− 10.2921i	− 1.32870i
$61$	5.85222	0.749300	0.374650	−	0.927166i	$-0.377763\pi$
$61$	5.85222	0.749300	0.374650	+	0.927166i	$0.377763\pi$
$62$	0.898789	0.114146
$63$	− 16.8897i	− 2.12790i
$64$	12.9897	1.62372
$65$	0	0
$66$	−9.23378	−1.13660
$67$	1.99420i	0.243630i	0.992553	+	0.121815i	$0.0388715\pi$
$67$	1.99420i	0.243630i	−0.992553	+	0.121815i	$0.961128\pi$
$68$	7.78594	0.944184
$69$	26.9042	3.23888
$70$	− 5.25423i	− 0.628001i
$71$	− 9.59141i	− 1.13829i	−0.822237	−	0.569146i	$-0.807274\pi$
$71$	− 9.59141i	− 1.13829i	0.822237	−	0.569146i	$-0.192726\pi$
$72$	20.0994i	2.36874i
$73$	4.38231i	0.512910i	0.966556	+	0.256455i	$0.0825546\pi$
$73$	4.38231i	0.512910i	−0.966556	+	0.256455i	$0.917445\pi$
$74$	4.60204	0.534976
$75$	−3.21428	−0.371153
$76$	− 1.87923i	− 0.215562i
$77$	−2.90159	−0.330666
$78$	0	0
$79$	−0.217237	−0.0244411	−0.0122206	−	0.999925i	$-0.503890\pi$
$79$	−0.217237	−0.0244411	−0.0122206	+	0.999925i	$0.503890\pi$
$80$	− 0.151230i	− 0.0169080i
$81$	22.7573	2.52859
$82$	−12.7439	−1.40733
$83$	11.0119i	1.20871i	0.796716	+	0.604354i	$0.206569\pi$
$83$	11.0119i	1.20871i	−0.796716	+	0.604354i	$0.793431\pi$
$84$	23.7098i	2.58695i
$85$	− 2.43159i	− 0.263743i
$86$	13.4031i	1.44529i
$87$	−9.93715	−1.06537
$88$	3.45301	0.368092
$89$	− 6.37458i	− 0.675704i	−0.941199	−	0.337852i	$-0.890300\pi$
$89$	− 6.37458i	− 0.675704i	0.941199	−	0.337852i	$-0.109700\pi$
$90$	16.7218	1.76263
$91$	0	0
$92$	−26.8013	−2.79423
$93$	1.26665i	0.131345i
$94$	4.39894	0.453716
$95$	−0.586893	−0.0602140
$96$	18.7325i	1.91188i
$97$	16.3061i	1.65563i	0.560998	+	0.827817i	$0.310418\pi$
$97$	16.3061i	1.65563i	−0.560998	+	0.827817i	$0.689582\pi$
$98$	− 3.86139i	− 0.390059i
$99$	− 9.23440i	− 0.928092i
$100$	3.20199	0.320199
$101$	6.90971	0.687541	0.343771	−	0.939054i	$-0.388296\pi$
$101$	6.90971	0.687541	0.343771	+	0.939054i	$0.388296\pi$
$102$	17.8262i	1.76506i
$103$	−9.09928	−0.896579	−0.448289	−	0.893888i	$-0.647967\pi$
$103$	−9.09928	−0.896579	−0.448289	+	0.893888i	$0.647967\pi$
$104$	0	0
$105$	7.40470	0.722625
$106$	31.1845i	3.02891i
$107$	8.96050	0.866244	0.433122	−	0.901335i	$-0.357412\pi$
$107$	8.96050	0.866244	0.433122	+	0.901335i	$0.357412\pi$
$108$	−44.5810	−4.28981
$109$	4.39646i	0.421105i	0.977583	+	0.210552i	$0.0675262\pi$
$109$	4.39646i	0.421105i	−0.977583	+	0.210552i	$0.932474\pi$
$110$	− 2.87274i	− 0.273905i
$111$	6.48558i	0.615584i
$112$	0.348388i	0.0329195i
$113$	10.4452	0.982600	0.491300	−	0.870990i	$-0.336522\pi$
$113$	10.4452	0.982600	0.491300	+	0.870990i	$0.336522\pi$
$114$	4.30256	0.402972
$115$	8.37020i	0.780525i
$116$	9.89917	0.919115
$117$	0	0
$118$	33.4921	3.08320
$119$	5.60164i	0.513502i
$120$	−8.81191	−0.804413
$121$	9.41357	0.855779
$122$	− 13.3477i	− 1.20844i
$123$	− 17.9597i	− 1.61937i
$124$	− 1.26181i	− 0.113314i
$125$	− 1.00000i	− 0.0894427i
$126$	−38.5218	−3.43180
$127$	−14.9712	−1.32848	−0.664240	−	0.747520i	$-0.731245\pi$
$127$	−14.9712	−1.32848	−0.664240	+	0.747520i	$0.731245\pi$
$128$	− 17.9710i	− 1.58843i
$129$	−18.8888	−1.66306
$130$	0	0
$131$	10.7370	0.938098	0.469049	−	0.883172i	$-0.344597\pi$
$131$	10.7370	0.938098	0.469049	+	0.883172i	$0.344597\pi$
$132$	12.9633i	1.12831i
$133$	1.35202	0.117235
$134$	4.54835	0.392918
$135$	13.9229i	1.19829i
$136$	− 6.66619i	− 0.571621i
$137$	2.89958i	0.247728i	0.992299	+	0.123864i	$0.0395286\pi$
$137$	2.89958i	0.247728i	−0.992299	+	0.123864i	$0.960471\pi$
$138$	− 61.3627i	− 5.22354i
$139$	−16.4802	−1.39784	−0.698918	−	0.715202i	$-0.746335\pi$
$139$	−16.4802	−1.39784	−0.698918	+	0.715202i	$0.746335\pi$
$140$	−7.37640	−0.623420
$141$	6.19936i	0.522080i
$142$	−21.8760	−1.83579
$143$	0	0
$144$	−1.10876	−0.0923963
$145$	− 3.09157i	− 0.256741i
$146$	9.99512	0.827202
$147$	5.44179	0.448831
$148$	− 6.46079i	− 0.531074i
$149$	1.08944i	0.0892501i	0.999004	+	0.0446251i	$0.0142093\pi$
$149$	1.08944i	0.0892501i	−0.999004	+	0.0446251i	$0.985791\pi$
$150$	7.33108i	0.598580i
$151$	18.9559i	1.54261i	0.636466	+	0.771305i	$0.280396\pi$
$151$	18.9559i	1.54261i	−0.636466	+	0.771305i	$0.719604\pi$
$152$	−1.60896	−0.130504
$153$	−17.8274	−1.44126
$154$	6.61790i	0.533286i
$155$	−0.394069	−0.0316524
$156$	0	0
$157$	5.27488	0.420981	0.210491	−	0.977596i	$-0.432494\pi$
$157$	5.27488	0.420981	0.210491	+	0.977596i	$0.432494\pi$
$158$	0.495472i	0.0394177i
$159$	−43.9478	−3.48529
$160$	−5.82790	−0.460736
$161$	− 19.2824i	− 1.51966i
$162$	− 51.9046i	− 4.07801i
$163$	20.4979i	1.60552i	0.596300	+	0.802762i	$0.296637\pi$
$163$	20.4979i	1.60552i	−0.596300	+	0.802762i	$0.703363\pi$
$164$	17.8911i	1.39706i
$165$	4.04850	0.315176
$166$	25.1157	1.94936
$167$	− 19.1053i	− 1.47841i	−0.673479	−	0.739206i	$-0.735201\pi$
$167$	− 19.1053i	− 1.47841i	0.673479	−	0.739206i	$-0.264799\pi$
$168$	20.2999	1.56617
$169$	0	0
$170$	−5.54595	−0.425355
$171$	4.30285i	0.329048i
$172$	18.8166	1.43475
$173$	−5.28584	−0.401875	−0.200937	−	0.979604i	$-0.564399\pi$
$173$	−5.28584	−0.401875	−0.200937	+	0.979604i	$0.564399\pi$
$174$	22.6645i	1.71819i
$175$	2.30369i	0.174143i
$176$	0.190480i	0.0143580i
$177$	47.1999i	3.54776i
$178$	−14.5391	−1.08975
$179$	10.8357	0.809896	0.404948	−	0.914340i	$-0.367290\pi$
$179$	10.8357	0.809896	0.404948	+	0.914340i	$0.367290\pi$
$180$	− 23.4757i	− 1.74977i
$181$	−13.4202	−0.997517	−0.498758	−	0.866741i	$-0.666211\pi$
$181$	−13.4202	−0.997517	−0.498758	+	0.866741i	$0.666211\pi$
$182$	0	0
$183$	18.8107	1.39052
$184$	22.9468i	1.69166i
$185$	−2.01774	−0.148347
$186$	2.88896	0.211829
$187$	3.06268i	0.223966i
$188$	− 6.17566i	− 0.450406i
$189$	− 32.0740i	− 2.33304i
$190$	1.33858i	0.0971107i
$191$	7.19596	0.520681	0.260341	−	0.965517i	$-0.416165\pi$
$191$	7.19596	0.520681	0.260341	+	0.965517i	$0.416165\pi$
$192$	41.7526	3.01324
$193$	− 12.6806i	− 0.912770i	−0.889782	−	0.456385i	$-0.849144\pi$
$193$	− 12.6806i	− 0.912770i	0.889782	−	0.456385i	$-0.150856\pi$
$194$	37.1908	2.67014
$195$	0	0
$196$	−5.42099	−0.387214
$197$	− 18.9898i	− 1.35296i	−0.736459	−	0.676482i	$-0.763504\pi$
$197$	− 18.9898i	− 1.35296i	0.736459	−	0.676482i	$-0.236496\pi$
$198$	−21.0617	−1.49679
$199$	−10.1534	−0.719757	−0.359878	−	0.932999i	$-0.617182\pi$
$199$	−10.1534	−0.719757	−0.359878	+	0.932999i	$0.617182\pi$
$200$	− 2.74149i	− 0.193853i
$201$	6.40992i	0.452121i
$202$	− 15.7596i	− 1.10884i
$203$	7.12202i	0.499868i
$204$	25.0262	1.75218
$205$	5.58749	0.390247
$206$	20.7535i	1.44597i
$207$	61.3668	4.26529
$208$	0	0
$209$	0.739214	0.0511325
$210$	− 16.8886i	− 1.16542i
$211$	3.78159	0.260336	0.130168	−	0.991492i	$-0.458448\pi$
$211$	3.78159	0.260336	0.130168	+	0.991492i	$0.458448\pi$
$212$	43.7798	3.00681
$213$	− 30.8295i	− 2.11240i
$214$	− 20.4370i	− 1.39704i
$215$	− 5.87653i	− 0.400776i
$216$	38.1695i	2.59710i
$217$	0.907814	0.0616265
$218$	10.0274	0.679141
$219$	14.0860i	0.951841i
$220$	−4.03303	−0.271907
$221$	0	0
$222$	14.7922	0.992789
$223$	− 3.03624i	− 0.203322i	−0.994819	−	0.101661i	$-0.967584\pi$
$223$	− 3.03624i	− 0.203322i	0.994819	−	0.101661i	$-0.0324157\pi$
$224$	13.4257	0.897042
$225$	−7.33158	−0.488772
$226$	− 23.8232i	− 1.58470i
$227$	5.63181i	0.373796i	0.982379	+	0.186898i	$0.0598434\pi$
$227$	5.63181i	0.373796i	−0.982379	+	0.186898i	$0.940157\pi$
$228$	− 6.04036i	− 0.400033i
$229$	− 13.5479i	− 0.895269i	−0.894217	−	0.447635i	$-0.852267\pi$
$229$	− 13.5479i	− 0.895269i	0.894217	−	0.447635i	$-0.147733\pi$
$230$	19.0907	1.25880
$231$	−9.32650	−0.613639
$232$	− 8.47550i	− 0.556444i
$233$	18.8311	1.23367	0.616834	−	0.787093i	$-0.288415\pi$
$233$	18.8311	1.23367	0.616834	+	0.787093i	$0.288415\pi$
$234$	0	0
$235$	−1.92869	−0.125814
$236$	− 47.0195i	− 3.06071i
$237$	−0.698261	−0.0453569
$238$	12.7762	0.828155
$239$	− 13.0244i	− 0.842477i	−0.906950	−	0.421239i	$-0.861596\pi$
$239$	− 13.0244i	− 0.842477i	0.906950	−	0.421239i	$-0.138404\pi$
$240$	− 0.486096i	− 0.0313773i
$241$	18.1149i	1.16688i	0.812154	+	0.583442i	$0.198295\pi$
$241$	18.1149i	1.16688i	−0.812154	+	0.583442i	$0.801705\pi$
$242$	− 21.4703i	− 1.38017i
$243$	31.3796	2.01300
$244$	−18.7388	−1.19963
$245$	1.69301i	0.108162i
$246$	−40.9623	−2.61166
$247$	0	0
$248$	−1.08034	−0.0686015
$249$	35.3952i	2.24308i
$250$	−2.28079	−0.144250
$251$	−0.814081	−0.0513844	−0.0256922	−	0.999670i	$-0.508179\pi$
$251$	−0.814081	−0.0513844	−0.0256922	+	0.999670i	$0.508179\pi$
$252$	54.0807i	3.40676i
$253$	− 10.5426i	− 0.662807i
$254$	34.1461i	2.14252i
$255$	− 7.81582i	− 0.489445i
$256$	−15.0087	−0.938041
$257$	−5.91635	−0.369052	−0.184526	−	0.982828i	$-0.559075\pi$
$257$	−5.91635	−0.369052	−0.184526	+	0.982828i	$0.559075\pi$
$258$	43.0813i	2.68212i
$259$	4.64825	0.288828
$260$	0	0
$261$	−22.6661	−1.40299
$262$	− 24.4889i	− 1.51293i
$263$	−22.8064	−1.40630	−0.703151	−	0.711041i	$-0.748224\pi$
$263$	−22.8064	−1.40630	−0.703151	+	0.711041i	$0.748224\pi$
$264$	11.0989	0.683092
$265$	− 13.6727i	− 0.839907i
$266$	− 3.08367i	− 0.189072i
$267$	− 20.4897i	− 1.25395i
$268$	− 6.38542i	− 0.390051i
$269$	−11.4958	−0.700914	−0.350457	−	0.936579i	$-0.613974\pi$
$269$	−11.4958	−0.700914	−0.350457	+	0.936579i	$0.613974\pi$
$270$	31.7552	1.93256
$271$	3.85160i	0.233968i	0.993134	+	0.116984i	$0.0373227\pi$
$271$	3.85160i	0.233968i	−0.993134	+	0.116984i	$0.962677\pi$
$272$	0.367730	0.0222969
$273$	0	0
$274$	6.61332	0.399525
$275$	1.25954i	0.0759530i
$276$	−86.1469	−5.18543
$277$	−14.2174	−0.854238	−0.427119	−	0.904195i	$-0.640472\pi$
$277$	−14.2174	−0.854238	−0.427119	+	0.904195i	$0.640472\pi$
$278$	37.5879i	2.25437i
$279$	2.88915i	0.172969i
$280$	6.31554i	0.377426i
$281$	− 27.3326i	− 1.63053i	−0.579090	−	0.815264i	$-0.696592\pi$
$281$	− 27.3326i	− 1.63053i	0.579090	−	0.815264i	$-0.303408\pi$
$282$	14.1394	0.841990
$283$	12.4611	0.740736	0.370368	−	0.928885i	$-0.379232\pi$
$283$	12.4611	0.740736	0.370368	+	0.928885i	$0.379232\pi$
$284$	30.7116i	1.82240i
$285$	−1.88644	−0.111743
$286$	0	0
$287$	−12.8718	−0.759801
$288$	42.7277i	2.51775i
$289$	−11.0874	−0.652197
$290$	−7.05121	−0.414061
$291$	52.4123i	3.07247i
$292$	− 14.0321i	− 0.821168i
$293$	− 19.1635i	− 1.11955i	−0.828646	−	0.559773i	$-0.810889\pi$
$293$	− 19.1635i	− 1.11955i	0.828646	−	0.559773i	$-0.189111\pi$
$294$	− 12.4116i	− 0.723857i
$295$	−14.6844	−0.854962
$296$	−5.53161	−0.321519
$297$	− 17.5364i	− 1.01757i
$298$	2.48477	0.143939
$299$	0	0
$300$	10.2921	0.594214
$301$	13.5377i	0.780300i
$302$	43.2344	2.48786
$303$	22.2097	1.27591
$304$	− 0.0887560i	− 0.00509050i
$305$	5.85222i	0.335097i
$306$	40.6606i	2.32441i
$307$	− 25.3229i	− 1.44526i	−0.691237	−	0.722628i	$-0.742934\pi$
$307$	− 25.3229i	− 1.44526i	0.691237	−	0.722628i	$-0.257066\pi$
$308$	9.29086	0.529396
$309$	−29.2476	−1.66384
$310$	0.898789i	0.0510478i
$311$	8.34852	0.473401	0.236701	−	0.971583i	$-0.423934\pi$
$311$	8.34852	0.473401	0.236701	+	0.971583i	$0.423934\pi$
$312$	0	0
$313$	−18.9850	−1.07310	−0.536548	−	0.843870i	$-0.680272\pi$
$313$	−18.9850	−1.07310	−0.536548	+	0.843870i	$0.680272\pi$
$314$	− 12.0309i	− 0.678942i
$315$	16.8897	0.951626
$316$	0.695592	0.0391301
$317$	− 22.0449i	− 1.23816i	−0.785326	−	0.619082i	$-0.787505\pi$
$317$	− 22.0449i	− 1.23816i	0.785326	−	0.619082i	$-0.212495\pi$
$318$	100.236i	5.62093i
$319$	3.89395i	0.218019i
$320$	12.9897i	0.726149i
$321$	28.8015	1.60754
$322$	−43.9790	−2.45085
$323$	− 1.42709i	− 0.0794052i
$324$	−72.8687	−4.04826
$325$	0	0
$326$	46.7515	2.58932
$327$	14.1314i	0.781471i
$328$	15.3180	0.845797
$329$	4.44312	0.244957
$330$	− 9.23378i	− 0.508303i
$331$	− 11.8953i	− 0.653826i	−0.945054	−	0.326913i	$-0.893992\pi$
$331$	− 11.8953i	− 0.653826i	0.945054	−	0.326913i	$-0.106008\pi$
$332$	− 35.2599i	− 1.93514i
$333$	14.7932i	0.810664i
$334$	−43.5751	−2.38433
$335$	−1.99420	−0.108955
$336$	1.11981i	0.0610909i
$337$	−35.1499	−1.91474	−0.957368	−	0.288871i	$-0.906720\pi$
$337$	−35.1499	−1.91474	−0.957368	+	0.288871i	$0.906720\pi$
$338$	0	0
$339$	33.5737	1.82347
$340$	7.78594i	0.422252i
$341$	0.496345	0.0268786
$342$	9.81390	0.530675
$343$	− 20.0260i	− 1.08130i
$344$	− 16.1104i	− 0.868616i
$345$	26.9042i	1.44847i
$346$	12.0559i	0.648128i
$347$	17.7972	0.955405	0.477702	−	0.878522i	$-0.341470\pi$
$347$	17.7972	0.955405	0.477702	+	0.878522i	$0.341470\pi$
$348$	31.8187	1.70566
$349$	17.0901i	0.914814i	0.889257	+	0.457407i	$0.151222\pi$
$349$	17.0901i	0.914814i	−0.889257	+	0.457407i	$0.848778\pi$
$350$	5.25423	0.280850
$351$	0	0
$352$	7.34046	0.391248
$353$	− 8.20354i	− 0.436630i	−0.975878	−	0.218315i	$-0.929944\pi$
$353$	− 8.20354i	− 0.436630i	0.975878	−	0.218315i	$-0.0700561\pi$
$354$	107.653	5.72169
$355$	9.59141	0.509059
$356$	20.4114i	1.08180i
$357$	18.0052i	0.952938i
$358$	− 24.7139i	− 1.30617i
$359$	− 4.83618i	− 0.255244i	−0.991823	−	0.127622i	$-0.959266\pi$
$359$	− 4.83618i	− 0.255244i	0.991823	−	0.127622i	$-0.0407344\pi$
$360$	−20.0994	−1.05933
$361$	18.6556	0.981871
$362$	30.6087i	1.60876i
$363$	30.2578	1.58812
$364$	0	0
$365$	−4.38231	−0.229381
$366$	− 42.9031i	− 2.24258i
$367$	−19.9703	−1.04244	−0.521221	−	0.853421i	$-0.674523\pi$
$367$	−19.9703	−1.04244	−0.521221	+	0.853421i	$0.674523\pi$
$368$	−1.26583	−0.0659858
$369$	− 40.9651i	− 2.13256i
$370$	4.60204i	0.239249i
$371$	31.4977i	1.63528i
$372$	− 4.05580i	− 0.210283i
$373$	−20.4576	−1.05925	−0.529626	−	0.848231i	$-0.677668\pi$
$373$	−20.4576	−1.05925	−0.529626	+	0.848231i	$0.677668\pi$
$374$	6.98533	0.361203
$375$	− 3.21428i	− 0.165985i
$376$	−5.28749	−0.272682
$377$	0	0
$378$	−73.1541	−3.76264
$379$	− 0.189284i	− 0.00972284i	−0.999988	−	0.00486142i	$-0.998453\pi$
$379$	− 0.189284i	− 0.00972284i	0.999988	−	0.00486142i	$-0.00154744\pi$
$380$	1.87923	0.0964024
$381$	−48.1216	−2.46534
$382$	− 16.4125i	− 0.839735i
$383$	16.8652i	0.861773i	0.902406	+	0.430886i	$0.141799\pi$
$383$	16.8652i	0.861773i	−0.902406	+	0.430886i	$0.858201\pi$
$384$	− 57.7639i	− 2.94775i
$385$	− 2.90159i	− 0.147879i
$386$	−28.9218	−1.47208
$387$	−43.0842	−2.19009
$388$	− 52.2120i	− 2.65066i
$389$	0.569132	0.0288561	0.0144281	−	0.999896i	$-0.495407\pi$
$389$	0.569132	0.0288561	0.0144281	+	0.999896i	$0.495407\pi$
$390$	0	0
$391$	−20.3529	−1.02929
$392$	4.64136i	0.234424i
$393$	34.5118	1.74089
$394$	−43.3116	−2.18201
$395$	− 0.217237i	− 0.0109304i
$396$	29.5685i	1.48587i
$397$	22.0794i	1.10813i	0.832472	+	0.554067i	$0.186925\pi$
$397$	22.0794i	1.10813i	−0.832472	+	0.554067i	$0.813075\pi$
$398$	23.1578i	1.16080i
$399$	4.34577	0.217561
$400$	0.151230	0.00756151
$401$	− 16.2825i	− 0.813107i	−0.913627	−	0.406554i	$-0.866730\pi$
$401$	− 16.2825i	− 0.813107i	0.913627	−	0.406554i	$-0.133270\pi$
$402$	14.6197	0.729162
$403$	0	0
$404$	−22.1248	−1.10075
$405$	22.7573i	1.13082i
$406$	16.2438	0.806167
$407$	2.54142	0.125974
$408$	− 21.4270i	− 1.06079i
$409$	− 21.9413i	− 1.08493i	−0.840079	−	0.542464i	$-0.817492\pi$
$409$	− 21.9413i	− 1.08493i	0.840079	−	0.542464i	$-0.182508\pi$
$410$	− 12.7439i	− 0.629375i
$411$	9.32005i	0.459724i
$412$	29.1358	1.43542
$413$	33.8284	1.66459
$414$	− 139.965i	− 6.87889i
$415$	−11.0119	−0.540551
$416$	0	0
$417$	−52.9721	−2.59405
$418$	− 1.68599i	− 0.0824645i
$419$	−12.6663	−0.618788	−0.309394	−	0.950934i	$-0.600126\pi$
$419$	−12.6663	−0.618788	−0.309394	+	0.950934i	$0.600126\pi$
$420$	−23.7098	−1.15692
$421$	18.8977i	0.921018i	0.887655	+	0.460509i	$0.152333\pi$
$421$	18.8977i	0.921018i	−0.887655	+	0.460509i	$0.847667\pi$
$422$	− 8.62501i	− 0.419859i
$423$	14.1404i	0.687528i
$424$	− 37.4835i	− 1.82036i
$425$	2.43159	0.117950
$426$	−70.3154	−3.40679
$427$	− 13.4817i	− 0.652426i
$428$	−28.6914	−1.38685
$429$	0	0
$430$	−13.4031	−0.646355
$431$	− 31.7845i	− 1.53100i	−0.643434	−	0.765502i	$-0.722491\pi$
$431$	− 31.7845i	− 1.53100i	0.643434	−	0.765502i	$-0.277509\pi$
$432$	−2.10556	−0.101304
$433$	26.4695	1.27204	0.636021	−	0.771671i	$-0.280579\pi$
$433$	26.4695	1.27204	0.636021	+	0.771671i	$0.280579\pi$
$434$	− 2.07053i	− 0.0993887i
$435$	− 9.93715i	− 0.476450i
$436$	− 14.0774i	− 0.674187i
$437$	4.91242i	0.234993i
$438$	32.1271	1.53509
$439$	−10.7064	−0.510988	−0.255494	−	0.966811i	$-0.582238\pi$
$439$	−10.7064	−0.510988	−0.255494	+	0.966811i	$0.582238\pi$
$440$	3.45301i	0.164616i
$441$	12.4124	0.591067
$442$	0	0
$443$	−2.14146	−0.101744	−0.0508718	−	0.998705i	$-0.516200\pi$
$443$	−2.14146	−0.101744	−0.0508718	+	0.998705i	$0.516200\pi$
$444$	− 20.7668i	− 0.985547i
$445$	6.37458	0.302184
$446$	−6.92503	−0.327910
$447$	3.50175i	0.165627i
$448$	− 29.9244i	− 1.41379i
$449$	1.10953i	0.0523620i	0.999657	+	0.0261810i	$0.00833462\pi$
$449$	1.10953i	0.0523620i	−0.999657	+	0.0261810i	$0.991665\pi$
$450$	16.7218i	0.788272i
$451$	−7.03765	−0.331390
$452$	−33.4454	−1.57314
$453$	60.9295i	2.86272i
$454$	12.8450	0.602844
$455$	0	0
$456$	−5.17165	−0.242185
$457$	7.94953i	0.371863i	0.982563	+	0.185932i	$0.0595303\pi$
$457$	7.94953i	0.371863i	−0.982563	+	0.185932i	$0.940470\pi$
$458$	−30.8998	−1.44385
$459$	−33.8548	−1.58021
$460$	− 26.8013i	− 1.24962i
$461$	18.2179i	0.848494i	0.905546	+	0.424247i	$0.139461\pi$
$461$	18.2179i	0.848494i	−0.905546	+	0.424247i	$0.860539\pi$
$462$	21.2718i	0.989652i
$463$	− 25.1740i	− 1.16993i	−0.811057	−	0.584967i	$-0.801107\pi$
$463$	− 25.1740i	− 1.16993i	0.811057	−	0.584967i	$-0.198893\pi$
$464$	0.467538	0.0217049
$465$	−1.26665	−0.0587394
$466$	− 42.9498i	− 1.98961i
$467$	−0.530268	−0.0245379	−0.0122689	−	0.999925i	$-0.503905\pi$
$467$	−0.530268	−0.0245379	−0.0122689	+	0.999925i	$0.503905\pi$
$468$	0	0
$469$	4.59402	0.212132
$470$	4.39894i	0.202908i
$471$	16.9549	0.781242
$472$	−40.2572	−1.85299
$473$	7.40170i	0.340331i
$474$	1.59259i	0.0731499i
$475$	− 0.586893i	− 0.0269285i
$476$	− 17.9364i	− 0.822114i
$477$	−100.242	−4.58978
$478$	−29.7058	−1.35871
$479$	− 17.8049i	− 0.813525i	−0.913534	−	0.406762i	$-0.866658\pi$
$479$	− 17.8049i	− 0.813525i	0.913534	−	0.406762i	$-0.133342\pi$
$480$	−18.7325	−0.855017
$481$	0	0
$482$	41.3163	1.88191
$483$	− 61.9789i	− 2.82014i
$484$	−30.1422	−1.37010
$485$	−16.3061	−0.740422
$486$	− 71.5702i	− 3.24649i
$487$	− 24.3801i	− 1.10477i	−0.833590	−	0.552384i	$-0.813718\pi$
$487$	− 24.3801i	− 1.10477i	0.833590	−	0.552384i	$-0.186282\pi$
$488$	16.0438i	0.726269i
$489$	65.8861i	2.97947i
$490$	3.86139	0.174440
$491$	−26.3116	−1.18742	−0.593712	−	0.804677i	$-0.702338\pi$
$491$	−26.3116	−1.18742	−0.593712	+	0.804677i	$0.702338\pi$
$492$	57.5069i	2.59261i
$493$	7.51744	0.338568
$494$	0	0
$495$	9.23440	0.415055
$496$	− 0.0595952i	− 0.00267590i
$497$	−22.0957	−0.991126
$498$	80.7289	3.61755
$499$	24.0669i	1.07738i	0.842504	+	0.538691i	$0.181081\pi$
$499$	24.0669i	1.07738i	−0.842504	+	0.538691i	$0.818919\pi$
$500$	3.20199i	0.143197i
$501$	− 61.4097i	− 2.74358i
$502$	1.85675i	0.0828707i
$503$	−20.1923	−0.900332	−0.450166	−	0.892945i	$-0.648635\pi$
$503$	−20.1923	−0.900332	−0.450166	+	0.892945i	$0.648635\pi$
$504$	46.3029	2.06250
$505$	6.90971i	0.307478i
$506$	−24.0454	−1.06895
$507$	0	0
$508$	47.9377	2.12689
$509$	29.7451i	1.31843i	0.751955	+	0.659214i	$0.229111\pi$
$509$	29.7451i	1.31843i	−0.751955	+	0.659214i	$0.770889\pi$
$510$	−17.8262	−0.789358
$511$	10.0955	0.446598
$512$	− 1.71055i	− 0.0755962i
$513$	8.17125i	0.360770i
$514$	13.4939i	0.595192i
$515$	− 9.09928i	− 0.400962i
$516$	60.4817	2.66256
$517$	2.42926	0.106839
$518$	− 10.6017i	− 0.465811i
$519$	−16.9901	−0.745785
$520$	0	0
$521$	32.9231	1.44239	0.721194	−	0.692733i	$-0.243594\pi$
$521$	32.9231	1.44239	0.721194	+	0.692733i	$0.243594\pi$
$522$	51.6965i	2.26269i
$523$	20.9654	0.916751	0.458375	−	0.888759i	$-0.348432\pi$
$523$	20.9654	0.916751	0.458375	+	0.888759i	$0.348432\pi$
$524$	−34.3799	−1.50189
$525$	7.40470i	0.323168i
$526$	52.0165i	2.26803i
$527$	− 0.958217i	− 0.0417406i
$528$	0.612256i	0.0266450i
$529$	47.0603	2.04610
$530$	−31.1845	−1.35457
$531$	107.660i	4.67205i
$532$	−4.32916	−0.187693
$533$	0	0
$534$	−46.7326	−2.02232
$535$	8.96050i	0.387396i
$536$	−5.46708	−0.236142
$537$	34.8289	1.50298
$538$	26.2196i	1.13041i
$539$	− 2.13240i	− 0.0918491i
$540$	− 44.5810i	− 1.91846i
$541$	0.397145i	0.0170746i	0.999964	+	0.00853729i	$0.00271754\pi$
$541$	0.397145i	0.0170746i	−0.999964	+	0.00853729i	$0.997282\pi$
$542$	8.78469	0.377335
$543$	−43.1363	−1.85116
$544$	− 14.1711i	− 0.607580i
$545$	−4.39646	−0.188324
$546$	0	0
$547$	−20.7287	−0.886295	−0.443147	−	0.896449i	$-0.646138\pi$
$547$	−20.7287	−0.886295	−0.443147	+	0.896449i	$0.646138\pi$
$548$	− 9.28443i	− 0.396611i
$549$	42.9060	1.83118
$550$	2.87274	0.122494
$551$	− 1.81442i	− 0.0772969i
$552$	73.7574i	3.13932i
$553$	0.500448i	0.0212812i
$554$	32.4268i	1.37768i
$555$	−6.48558	−0.275297
$556$	52.7696	2.23793
$557$	14.0049i	0.593406i	0.954970	+	0.296703i	$0.0958872\pi$
$557$	14.0049i	0.593406i	−0.954970	+	0.296703i	$0.904113\pi$
$558$	6.58954	0.278957
$559$	0	0
$560$	−0.348388	−0.0147221
$561$	9.84431i	0.415627i
$562$	−62.3399	−2.62965
$563$	−28.1488	−1.18633	−0.593164	−	0.805081i	$-0.702122\pi$
$563$	−28.1488	−1.18633	−0.593164	+	0.805081i	$0.702122\pi$
$564$	− 19.8503i	− 0.835848i
$565$	10.4452i	0.439432i
$566$	− 28.4211i	− 1.19463i
$567$	− 52.4258i	− 2.20168i
$568$	26.2948	1.10330
$569$	1.24816	0.0523254	0.0261627	−	0.999658i	$-0.491671\pi$
$569$	1.24816	0.0523254	0.0261627	+	0.999658i	$0.491671\pi$
$570$	4.30256i	0.180215i
$571$	−29.0651	−1.21633	−0.608167	−	0.793809i	$-0.708095\pi$
$571$	−29.0651	−1.21633	−0.608167	+	0.793809i	$0.708095\pi$
$572$	0	0
$573$	23.1298	0.966262
$574$	29.3579i	1.22538i
$575$	−8.37020	−0.349062
$576$	95.2353	3.96814
$577$	26.7191i	1.11233i	0.831072	+	0.556165i	$0.187728\pi$
$577$	26.7191i	1.11233i	−0.831072	+	0.556165i	$0.812272\pi$
$578$	25.2879i	1.05184i
$579$	− 40.7590i	− 1.69389i
$580$	9.89917i	0.411041i
$581$	25.3679	1.05244
$582$	119.541	4.95515
$583$	17.2213i	0.713232i
$584$	−12.0141	−0.497145
$585$	0	0
$586$	−43.7079	−1.80556
$587$	26.1925i	1.08108i	0.841319	+	0.540539i	$0.181780\pi$
$587$	26.1925i	1.08108i	−0.841319	+	0.540539i	$0.818220\pi$
$588$	−17.4246	−0.718577
$589$	−0.231277	−0.00952959
$590$	33.4921i	1.37885i
$591$	− 61.0384i	− 2.51078i
$592$	− 0.305143i	− 0.0125413i
$593$	− 14.8254i	− 0.608806i	−0.952543	−	0.304403i	$-0.901543\pi$
$593$	− 14.8254i	− 0.608806i	0.952543	−	0.304403i	$-0.0984570\pi$
$594$	−39.9968	−1.64109
$595$	−5.60164	−0.229645
$596$	− 3.48837i	− 0.142889i
$597$	−32.6359	−1.33570
$598$	0	0
$599$	12.0326	0.491639	0.245820	−	0.969316i	$-0.420943\pi$
$599$	12.0326	0.491639	0.245820	+	0.969316i	$0.420943\pi$
$600$	− 8.81191i	− 0.359745i
$601$	14.9028	0.607899	0.303950	−	0.952688i	$-0.401695\pi$
$601$	14.9028	0.607899	0.303950	+	0.952688i	$0.401695\pi$
$602$	30.8766	1.25844
$603$	14.6206i	0.595399i
$604$	− 60.6966i	− 2.46971i
$605$	9.41357i	0.382716i
$606$	− 50.6556i	− 2.05774i
$607$	29.2262	1.18626	0.593128	−	0.805108i	$-0.297893\pi$
$607$	29.2262	1.18626	0.593128	+	0.805108i	$0.297893\pi$
$608$	−3.42036	−0.138714
$609$	22.8921i	0.927636i
$610$	13.3477	0.540432
$611$	0	0
$612$	57.0833	2.30745
$613$	− 32.1313i	− 1.29777i	−0.760887	−	0.648885i	$-0.775236\pi$
$613$	− 32.1313i	− 1.29777i	0.760887	−	0.648885i	$-0.224764\pi$
$614$	−57.7562	−2.33085
$615$	17.9597	0.724206
$616$	− 7.95467i	− 0.320503i
$617$	13.0350i	0.524771i	0.964963	+	0.262385i	$0.0845092\pi$
$617$	13.0350i	0.524771i	−0.964963	+	0.262385i	$0.915491\pi$
$618$	66.7076i	2.68337i
$619$	28.6664i	1.15220i	0.817379	+	0.576100i	$0.195426\pi$
$619$	28.6664i	1.15220i	−0.817379	+	0.576100i	$0.804574\pi$
$620$	1.26181	0.0506754
$621$	116.537	4.67649
$622$	− 19.0412i	− 0.763483i
$623$	−14.6851	−0.588345
$624$	0	0
$625$	1.00000	0.0400000
$626$	43.3008i	1.73065i
$627$	2.37604	0.0948899
$628$	−16.8901	−0.673990
$629$	− 4.90633i	− 0.195628i
$630$	− 38.5218i	− 1.53475i
$631$	26.4497i	1.05295i	0.850191	+	0.526474i	$0.176486\pi$
$631$	26.4497i	1.05295i	−0.850191	+	0.526474i	$0.823514\pi$
$632$	− 0.595554i	− 0.0236899i
$633$	12.1551	0.483121
$634$	−50.2797	−1.99686
$635$	− 14.9712i	− 0.594114i
$636$	140.721	5.57993
$637$	0	0
$638$	8.88126	0.351613
$639$	− 70.3202i	− 2.78182i
$640$	17.9710	0.710368
$641$	26.6673	1.05330	0.526648	−	0.850084i	$-0.323449\pi$
$641$	26.6673	1.05330	0.526648	+	0.850084i	$0.323449\pi$
$642$	− 65.6902i	− 2.59258i
$643$	− 28.0533i	− 1.10631i	−0.833077	−	0.553157i	$-0.813423\pi$
$643$	− 28.0533i	− 1.10631i	0.833077	−	0.553157i	$-0.186577\pi$
$644$	61.7420i	2.43297i
$645$	− 18.8888i	− 0.743745i
$646$	−3.25488	−0.128062
$647$	23.1563	0.910368	0.455184	−	0.890397i	$-0.349573\pi$
$647$	23.1563	0.910368	0.455184	+	0.890397i	$0.349573\pi$
$648$	62.3889i	2.45087i
$649$	18.4956	0.726016
$650$	0	0
$651$	2.91797	0.114364
$652$	− 65.6343i	− 2.57044i
$653$	−23.7386	−0.928962	−0.464481	−	0.885583i	$-0.653759\pi$
$653$	−23.7386	−0.928962	−0.464481	+	0.885583i	$0.653759\pi$
$654$	32.2308	1.26032
$655$	10.7370i	0.419530i
$656$	0.844996i	0.0329916i
$657$	32.1292i	1.25348i
$658$	− 10.1338i	− 0.395057i
$659$	4.26802	0.166259	0.0831293	−	0.996539i	$-0.473509\pi$
$659$	4.26802	0.166259	0.0831293	+	0.996539i	$0.473509\pi$
$660$	−12.9633	−0.504595
$661$	− 12.0531i	− 0.468812i	−0.972139	−	0.234406i	$-0.924685\pi$
$661$	− 12.0531i	− 0.468812i	0.972139	−	0.234406i	$-0.0753145\pi$
$662$	−27.1307	−1.05446
$663$	0	0
$664$	−30.1889	−1.17156
$665$	1.35202i	0.0524291i
$666$	33.7402	1.30741
$667$	−25.8770	−1.00196
$668$	61.1750i	2.36693i
$669$	− 9.75933i	− 0.377318i
$670$	4.54835i	0.175718i
$671$	− 7.37109i	− 0.284558i
$672$	43.1539	1.66470
$673$	2.44006	0.0940576	0.0470288	−	0.998894i	$-0.485025\pi$
$673$	2.44006	0.0940576	0.0470288	+	0.998894i	$0.485025\pi$
$674$	80.1694i	3.08801i
$675$	−13.9229	−0.535892
$676$	0	0
$677$	−17.5620	−0.674964	−0.337482	−	0.941332i	$-0.609575\pi$
$677$	−17.5620	−0.674964	−0.337482	+	0.941332i	$0.609575\pi$
$678$	− 76.5745i	− 2.94083i
$679$	37.5642	1.44158
$680$	6.66619	0.255637
$681$	18.1022i	0.693677i
$682$	− 1.13206i	− 0.0433487i
$683$	− 35.9632i	− 1.37609i	−0.725667	−	0.688046i	$-0.758469\pi$
$683$	− 35.9632i	− 1.37609i	0.725667	−	0.688046i	$-0.241531\pi$
$684$	− 13.7777i	− 0.526804i
$685$	−2.89958	−0.110787
$686$	−45.6751	−1.74388
$687$	− 43.5467i	− 1.66141i
$688$	0.888708	0.0338817
$689$	0	0
$690$	61.3627	2.33604
$691$	40.6980i	1.54822i	0.633049	+	0.774112i	$0.281803\pi$
$691$	40.6980i	1.54822i	−0.633049	+	0.774112i	$0.718197\pi$
$692$	16.9252	0.643400
$693$	−21.2732	−0.808102
$694$	− 40.5917i	− 1.54084i
$695$	− 16.4802i	− 0.625131i
$696$	− 27.2426i	− 1.03263i
$697$	13.5865i	0.514625i
$698$	38.9790	1.47538
$699$	60.5285	2.28940
$700$	− 7.37640i	− 0.278802i
$701$	42.3583	1.59985	0.799926	−	0.600099i	$-0.204872\pi$
$701$	42.3583	1.59985	0.799926	+	0.600099i	$0.204872\pi$
$702$	0	0
$703$	−1.18420	−0.0446629
$704$	− 16.3611i	− 0.616631i
$705$	−6.19936	−0.233481
$706$	−18.7105	−0.704180
$707$	− 15.9178i	− 0.598652i
$708$	− 151.134i	− 5.67995i
$709$	− 10.5529i	− 0.396322i	−0.980169	−	0.198161i	$-0.936503\pi$
$709$	− 10.5529i	− 0.396322i	0.980169	−	0.198161i	$-0.0634969\pi$
$710$	− 21.8760i	− 0.820991i
$711$	−1.59269	−0.0597306
$712$	17.4758	0.654935
$713$	3.29844i	0.123528i
$714$	41.0661	1.53686
$715$	0	0
$716$	−34.6958	−1.29664
$717$	− 41.8640i	− 1.56344i
$718$	−11.0303	−0.411647
$719$	−39.9389	−1.48947	−0.744734	−	0.667361i	$-0.767424\pi$
$719$	−39.9389	−1.48947	−0.744734	+	0.667361i	$0.767424\pi$
$720$	− 1.10876i	− 0.0413209i
$721$	20.9619i	0.780663i
$722$	− 42.5494i	− 1.58352i
$723$	58.2264i	2.16546i
$724$	42.9714	1.59702
$725$	3.09157	0.114818
$726$	− 69.0116i	− 2.56126i
$727$	−16.4466	−0.609969	−0.304985	−	0.952357i	$-0.598651\pi$
$727$	−16.4466	−0.609969	−0.304985	+	0.952357i	$0.598651\pi$
$728$	0	0
$729$	32.5908	1.20707
$730$	9.99512i	0.369936i
$731$	14.2893	0.528510
$732$	−60.2316	−2.22622
$733$	34.8676i	1.28786i	0.765083	+	0.643931i	$0.222698\pi$
$733$	34.8676i	1.28786i	−0.765083	+	0.643931i	$0.777302\pi$
$734$	45.5481i	1.68121i
$735$	5.44179i	0.200723i
$736$	48.7807i	1.79808i
$737$	2.51177	0.0925223
$738$	−93.4327	−3.43930
$739$	3.02112i	0.111134i	0.998455	+	0.0555669i	$0.0176966\pi$
$739$	3.02112i	0.111134i	−0.998455	+	0.0555669i	$0.982303\pi$
$740$	6.46079	0.237503
$741$	0	0
$742$	71.8395	2.63731
$743$	43.9749i	1.61328i	0.591042	+	0.806641i	$0.298717\pi$
$743$	43.9749i	1.61328i	−0.591042	+	0.806641i	$0.701283\pi$
$744$	−3.47250	−0.127308
$745$	−1.08944	−0.0399139
$746$	46.6594i	1.70832i
$747$	80.7343i	2.95391i
$748$	− 9.80669i	− 0.358568i
$749$	− 20.6422i	− 0.754250i
$750$	−7.33108	−0.267693
$751$	−2.30363	−0.0840606	−0.0420303	−	0.999116i	$-0.513383\pi$
$751$	−2.30363	−0.0840606	−0.0420303	+	0.999116i	$0.513383\pi$
$752$	− 0.291677i	− 0.0106364i
$753$	−2.61668	−0.0953572
$754$	0	0
$755$	−18.9559	−0.689876
$756$	102.701i	3.73519i
$757$	−20.2683	−0.736665	−0.368332	−	0.929694i	$-0.620071\pi$
$757$	−20.2683	−0.736665	−0.368332	+	0.929694i	$0.620071\pi$
$758$	−0.431716	−0.0156806
$759$	− 33.8868i	− 1.23001i
$760$	− 1.60896i	− 0.0583632i
$761$	15.0956i	0.547214i	0.961842	+	0.273607i	$0.0882168\pi$
$761$	15.0956i	0.547214i	−0.961842	+	0.273607i	$0.911783\pi$
$762$	109.755i	3.97601i
$763$	10.1281	0.366661
$764$	−23.0414	−0.833609
$765$	− 17.8274i	− 0.644552i
$766$	38.4660	1.38983
$767$	0	0
$768$	−48.2420	−1.74078
$769$	− 19.9278i	− 0.718616i	−0.933219	−	0.359308i	$-0.883013\pi$
$769$	− 19.9278i	− 0.718616i	0.933219	−	0.359308i	$-0.116987\pi$
$770$	−6.61790	−0.238493
$771$	−19.0168	−0.684873
$772$	40.6032i	1.46134i
$773$	− 2.92060i	− 0.105047i	−0.998620	−	0.0525233i	$-0.983274\pi$
$773$	− 2.92060i	− 0.105047i	0.998620	−	0.0525233i	$-0.0167264\pi$
$774$	98.2659i	3.53210i
$775$	− 0.394069i	− 0.0141554i
$776$	−44.7030	−1.60474
$777$	14.9408	0.535997
$778$	− 1.29807i	− 0.0465380i
$779$	3.27926	0.117492
$780$	0	0
$781$	−12.0807	−0.432283
$782$	46.4207i	1.66000i
$783$	−43.0436	−1.53825
$784$	−0.256033	−0.00914405
$785$	5.27488i	0.188269i
$786$	− 78.7140i	− 2.80764i
$787$	− 5.51034i	− 0.196423i	−0.995166	−	0.0982113i	$-0.968688\pi$
$787$	− 5.51034i	− 0.196423i	0.995166	−	0.0982113i	$-0.0313121\pi$
$788$	60.8051i	2.16609i
$789$	−73.3060	−2.60976
$790$	−0.495472	−0.0176281
$791$	− 24.0625i	− 0.855563i
$792$	25.3160	0.899565
$793$	0	0
$794$	50.3585	1.78716
$795$	− 43.9478i	− 1.55867i
$796$	32.5112	1.15233
$797$	50.5977	1.79226	0.896131	−	0.443789i	$-0.146366\pi$
$797$	50.5977	1.79226	0.896131	+	0.443789i	$0.146366\pi$
$798$	− 9.91178i	− 0.350873i
$799$	− 4.68980i	− 0.165913i
$800$	− 5.82790i	− 0.206047i
$801$	− 46.7357i	− 1.65133i
$802$	−37.1368	−1.31135
$803$	5.51968	0.194785
$804$	− 20.5245i	− 0.723843i
$805$	19.2824	0.679614
$806$	0	0
$807$	−36.9508	−1.30073
$808$	18.9429i	0.666408i
$809$	−24.7359	−0.869670	−0.434835	−	0.900510i	$-0.643193\pi$
$809$	−24.7359	−0.869670	−0.434835	+	0.900510i	$0.643193\pi$
$810$	51.9046	1.82374
$811$	− 45.9957i	− 1.61513i	−0.589780	−	0.807564i	$-0.700786\pi$
$811$	− 45.9957i	− 1.61513i	0.589780	−	0.807564i	$-0.299214\pi$
$812$	− 22.8046i	− 0.800286i
$813$	12.3801i	0.434190i
$814$	− 5.79644i	− 0.203165i
$815$	−20.4979	−0.718012
$816$	1.18199	0.0413778
$817$	− 3.44889i	− 0.120662i
$818$	−50.0435	−1.74973
$819$	0	0
$820$	−17.8911	−0.624784
$821$	1.19931i	0.0418563i	0.999781	+	0.0209281i	$0.00666212\pi$
$821$	1.19931i	0.0418563i	−0.999781	+	0.0209281i	$0.993338\pi$
$822$	21.2570	0.741425
$823$	−22.1824	−0.773229	−0.386615	−	0.922241i	$-0.626356\pi$
$823$	−22.1824	−0.773229	−0.386615	+	0.922241i	$0.626356\pi$
$824$	− 24.9456i	− 0.869020i
$825$	4.04850i	0.140951i
$826$	− 77.1555i	− 2.68458i
$827$	− 46.3610i	− 1.61213i	−0.591828	−	0.806065i	$-0.701593\pi$
$827$	− 46.3610i	− 1.61213i	0.591828	−	0.806065i	$-0.298407\pi$
$828$	−196.496	−6.82871
$829$	20.3120	0.705466	0.352733	−	0.935724i	$-0.385252\pi$
$829$	20.3120	0.705466	0.352733	+	0.935724i	$0.385252\pi$
$830$	25.1157i	0.871779i
$831$	−45.6985	−1.58526
$832$	0	0
$833$	−4.11670	−0.142635
$834$	120.818i	4.18359i
$835$	19.1053	0.661166
$836$	−2.36696	−0.0818630
$837$	5.48659i	0.189644i
$838$	28.8891i	0.997956i
$839$	− 44.2056i	− 1.52615i	−0.646311	−	0.763074i	$-0.723689\pi$
$839$	− 44.2056i	− 1.52615i	0.646311	−	0.763074i	$-0.276311\pi$
$840$	20.2999i	0.700414i
$841$	−19.4422	−0.670421
$842$	43.1017	1.48538
$843$	− 87.8546i	− 3.02587i
$844$	−12.1086	−0.416796
$845$	0	0
$846$	32.2512	1.10882
$847$	− 21.6859i	− 0.745138i
$848$	2.06772	0.0710059
$849$	40.0535	1.37463
$850$	− 5.54595i	− 0.190224i
$851$	16.8889i	0.578944i
$852$	98.7157i	3.38194i
$853$	− 21.5463i	− 0.737731i	−0.929483	−	0.368865i	$-0.879746\pi$
$853$	− 21.5463i	− 0.737731i	0.929483	−	0.368865i	$-0.120254\pi$
$854$	−30.7489	−1.05221
$855$	−4.30285	−0.147155
$856$	24.5651i	0.839618i
$857$	46.4540	1.58684	0.793419	−	0.608676i	$-0.208299\pi$
$857$	46.4540	1.58684	0.793419	+	0.608676i	$0.208299\pi$
$858$	0	0
$859$	12.4901	0.426158	0.213079	−	0.977035i	$-0.431651\pi$
$859$	12.4901	0.426158	0.213079	+	0.977035i	$0.431651\pi$
$860$	18.8166i	0.641640i
$861$	−41.3737	−1.41001
$862$	−72.4936	−2.46914
$863$	15.2521i	0.519187i	0.965718	+	0.259593i	$0.0835886\pi$
$863$	15.2521i	0.519187i	−0.965718	+	0.259593i	$0.916411\pi$
$864$	81.1412i	2.76048i
$865$	− 5.28584i	− 0.179724i
$866$	− 60.3713i	− 2.05150i
$867$	−35.6378	−1.21032
$868$	−2.90681	−0.0986637
$869$	0.273619i	0.00928188i
$870$	−22.6645	−0.768400
$871$	0	0
$872$	−12.0528	−0.408161
$873$	119.549i	4.04614i
$874$	11.2042	0.378987
$875$	−2.30369	−0.0778790
$876$	− 45.1031i	− 1.52389i
$877$	− 53.6346i	− 1.81111i	−0.424227	−	0.905556i	$-0.639454\pi$
$877$	− 53.6346i	− 1.81111i	0.424227	−	0.905556i	$-0.360546\pi$
$878$	24.4190i	0.824102i
$879$	− 61.5969i	− 2.07761i
$880$	−0.190480	−0.00642108
$881$	−37.8813	−1.27625	−0.638127	−	0.769931i	$-0.720290\pi$
$881$	−37.8813	−1.27625	−0.638127	+	0.769931i	$0.720290\pi$
$882$	− 28.3101i	− 0.953249i
$883$	−28.9953	−0.975771	−0.487885	−	0.872908i	$-0.662232\pi$
$883$	−28.9953	−0.975771	−0.487885	+	0.872908i	$0.662232\pi$
$884$	0	0
$885$	−47.1999	−1.58661
$886$	4.88421i	0.164088i
$887$	2.16393	0.0726575	0.0363287	−	0.999340i	$-0.488434\pi$
$887$	2.16393	0.0726575	0.0363287	+	0.999340i	$0.488434\pi$
$888$	−17.7801	−0.596663
$889$	34.4890i	1.15673i
$890$	− 14.5391i	− 0.487350i
$891$	− 28.6637i	− 0.960269i
$892$	9.72203i	0.325518i
$893$	−1.13194	−0.0378788
$894$	7.98675	0.267117
$895$	10.8357i	0.362197i
$896$	−41.3998	−1.38307
$897$	0	0
$898$	2.53060	0.0844474
$899$	− 1.21829i	− 0.0406323i
$900$	23.4757	0.782522
$901$	33.2464	1.10760
$902$	16.0514i	0.534453i
$903$	43.5139i	1.44805i
$904$	28.6354i	0.952398i
$905$	− 13.4202i	− 0.446103i
$906$	138.967	4.61688
$907$	−18.5788	−0.616900	−0.308450	−	0.951241i	$-0.599810\pi$
$907$	−18.5788	−0.616900	−0.308450	+	0.951241i	$0.599810\pi$
$908$	− 18.0330i	− 0.598446i
$909$	50.6590	1.68025
$910$	0	0
$911$	9.55425	0.316546	0.158273	−	0.987395i	$-0.449407\pi$
$911$	9.55425	0.316546	0.158273	+	0.987395i	$0.449407\pi$
$912$	− 0.285286i	− 0.00944677i
$913$	13.8699	0.459025
$914$	18.1312	0.599726
$915$	18.8107i	0.621861i
$916$	43.3802i	1.43332i
$917$	− 24.7348i	− 0.816815i
$918$	77.2156i	2.54850i
$919$	32.9746	1.08773	0.543866	−	0.839172i	$-0.316960\pi$
$919$	32.9746	1.08773	0.543866	+	0.839172i	$0.316960\pi$
$920$	−22.9468	−0.756534
$921$	− 81.3949i	− 2.68205i
$922$	41.5513	1.36842
$923$	0	0
$924$	29.8634	0.982433
$925$	− 2.01774i	− 0.0663429i
$926$	−57.4165	−1.88682
$927$	−66.7121	−2.19111
$928$	− 18.0174i	− 0.591449i
$929$	7.17296i	0.235337i	0.993053	+	0.117669i	$0.0375421\pi$
$929$	7.17296i	0.235337i	−0.993053	+	0.117669i	$0.962458\pi$
$930$	2.88896i	0.0947326i
$931$	0.993614i	0.0325644i
$932$	−60.2971	−1.97510
$933$	26.8345	0.878521
$934$	1.20943i	0.0395737i
$935$	−3.06268	−0.100160
$936$	0	0
$937$	48.7912	1.59394	0.796970	−	0.604019i	$-0.206435\pi$
$937$	48.7912	1.59394	0.796970	+	0.604019i	$0.206435\pi$
$938$	− 10.4780i	− 0.342119i
$939$	−61.0231	−1.99141
$940$	6.17566	0.201428
$941$	− 28.4075i	− 0.926059i	−0.886343	−	0.463029i	$-0.846762\pi$
$941$	− 28.4075i	− 0.926059i	0.886343	−	0.463029i	$-0.153238\pi$
$942$	− 38.6706i	− 1.25996i
$943$	− 46.7684i	− 1.52299i
$944$	− 2.22073i	− 0.0722786i
$945$	32.0740	1.04337
$946$	16.8817	0.548872
$947$	− 35.7589i	− 1.16201i	−0.813901	−	0.581004i	$-0.802660\pi$
$947$	− 35.7589i	− 1.16201i	0.813901	−	0.581004i	$-0.197340\pi$
$948$	2.23583	0.0726163
$949$	0	0
$950$	−1.33858	−0.0434292
$951$	− 70.8583i	− 2.29774i
$952$	−15.3568	−0.497718
$953$	6.41209	0.207708	0.103854	−	0.994593i	$-0.466883\pi$
$953$	6.41209	0.207708	0.103854	+	0.994593i	$0.466883\pi$
$954$	228.632i	7.40222i
$955$	7.19596i	0.232856i
$956$	41.7040i	1.34880i
$957$	12.5162i	0.404592i
$958$	−40.6091	−1.31202
$959$	6.67973	0.215700
$960$	41.7526i	1.34756i
$961$	30.8447	0.994991
$962$	0	0
$963$	65.6946	2.11698
$964$	− 58.0039i	− 1.86818i
$965$	12.6806	0.408203
$966$	−141.361	−4.54820
$967$	7.78138i	0.250232i	0.992142	+	0.125116i	$0.0399304\pi$
$967$	7.78138i	0.250232i	−0.992142	+	0.125116i	$0.960070\pi$
$968$	25.8072i	0.829474i
$969$	− 4.58705i	− 0.147357i
$970$	37.1908i	1.19412i
$971$	−45.0741	−1.44650	−0.723249	−	0.690587i	$-0.757352\pi$
$971$	−45.0741	−1.44650	−0.723249	+	0.690587i	$0.757352\pi$
$972$	−100.477	−3.22281
$973$	37.9654i	1.21711i
$974$	−55.6059	−1.78173
$975$	0	0
$976$	−0.885032	−0.0283292
$977$	27.6147i	0.883474i	0.897145	+	0.441737i	$0.145638\pi$
$977$	27.6147i	0.883474i	−0.897145	+	0.441737i	$0.854362\pi$
$978$	150.272	4.80517
$979$	−8.02902	−0.256609
$980$	− 5.42099i	− 0.173167i
$981$	32.2330i	1.02912i
$982$	60.0111i	1.91503i
$983$	− 40.7921i	− 1.30107i	−0.759478	−	0.650533i	$-0.774545\pi$
$983$	− 40.7921i	− 1.30107i	0.759478	−	0.650533i	$-0.225455\pi$
$984$	49.2364	1.56960
$985$	18.9898	0.605064
$986$	− 17.1457i	− 0.546029i
$987$	14.2814	0.454582
$988$	0	0
$989$	−49.1877	−1.56408
$990$	− 21.0617i	− 0.669385i
$991$	48.3304	1.53527	0.767633	−	0.640890i	$-0.221435\pi$
$991$	48.3304	1.53527	0.767633	+	0.640890i	$0.221435\pi$
$992$	−2.29660	−0.0729171
$993$	− 38.2348i	− 1.21335i
$994$	50.3955i	1.59845i
$995$	− 10.1534i	− 0.321885i
$996$	− 113.335i	− 3.59116i
$997$	−9.25930	−0.293245	−0.146622	−	0.989193i	$-0.546840\pi$
$997$	−9.25930	−0.293245	−0.146622	+	0.989193i	$0.546840\pi$
$998$	54.8914	1.73756
$999$	28.0928i	0.888816i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.c.h.506.4		18
13.2	odd	12		845.2.e.o.191.8		18
13.3	even	3		845.2.m.j.316.15		36
13.4	even	6		845.2.m.j.361.15		36
13.5	odd	4		845.2.a.o.1.2	yes	9
13.6	odd	12		845.2.e.o.146.8		18
13.7	odd	12		845.2.e.p.146.2		18
13.8	odd	4		845.2.a.n.1.8	✓	9
13.9	even	3		845.2.m.j.361.4		36
13.10	even	6		845.2.m.j.316.4		36
13.11	odd	12		845.2.e.p.191.2		18
13.12	even	2	inner	845.2.c.h.506.15		18
39.5	even	4		7605.2.a.cp.1.8		9
39.8	even	4		7605.2.a.cs.1.2		9
65.34	odd	4		4225.2.a.bt.1.2		9
65.44	odd	4		4225.2.a.bs.1.8		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.8	✓	9	13.8	odd	4
845.2.a.o.1.2	yes	9	13.5	odd	4
845.2.c.h.506.4		18	1.1	even	1	trivial
845.2.c.h.506.15		18	13.12	even	2	inner
845.2.e.o.146.8		18	13.6	odd	12
845.2.e.o.191.8		18	13.2	odd	12
845.2.e.p.146.2		18	13.7	odd	12
845.2.e.p.191.2		18	13.11	odd	12
845.2.m.j.316.4		36	13.10	even	6
845.2.m.j.316.15		36	13.3	even	3
845.2.m.j.361.4		36	13.9	even	3
845.2.m.j.361.15		36	13.4	even	6
4225.2.a.bs.1.8		9	65.44	odd	4
4225.2.a.bt.1.2		9	65.34	odd	4
7605.2.a.cp.1.8		9	39.5	even	4
7605.2.a.cs.1.2		9	39.8	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)

\(f(q)\)	\(=\)	\(q-2.28079i q^{2} +3.21428 q^{3} -3.20199 q^{4} +1.00000i q^{5} -7.33108i q^{6} -2.30369i q^{7} +2.74149i q^{8} +7.33158 q^{9} +O(q^{10})\)	\(q-2.28079i q^{2} +3.21428 q^{3} -3.20199 q^{4} +1.00000i q^{5} -7.33108i q^{6} -2.30369i q^{7} +2.74149i q^{8} +7.33158 q^{9} +2.28079 q^{10} -1.25954i q^{11} -10.2921 q^{12} -5.25423 q^{14} +3.21428i q^{15} -0.151230 q^{16} -2.43159 q^{17} -16.7218i q^{18} +0.586893i q^{19} -3.20199i q^{20} -7.40470i q^{21} -2.87274 q^{22} +8.37020 q^{23} +8.81191i q^{24} -1.00000 q^{25} +13.9229 q^{27} +7.37640i q^{28} -3.09157 q^{29} +7.33108 q^{30} +0.394069i q^{31} +5.82790i q^{32} -4.04850i q^{33} +5.54595i q^{34} +2.30369 q^{35} -23.4757 q^{36} +2.01774i q^{37} +1.33858 q^{38} -2.74149 q^{40} -5.58749i q^{41} -16.8886 q^{42} -5.87653 q^{43} +4.03303i q^{44} +7.33158i q^{45} -19.0907i q^{46} +1.92869i q^{47} -0.486096 q^{48} +1.69301 q^{49} +2.28079i q^{50} -7.81582 q^{51} -13.6727 q^{53} -31.7552i q^{54} +1.25954 q^{55} +6.31554 q^{56} +1.88644i q^{57} +7.05121i q^{58} +14.6844i q^{59} -10.2921i q^{60} +5.85222 q^{61} +0.898789 q^{62} -16.8897i q^{63} +12.9897 q^{64} -9.23378 q^{66} +1.99420i q^{67} +7.78594 q^{68} +26.9042 q^{69} -5.25423i q^{70} -9.59141i q^{71} +20.0994i q^{72} +4.38231i q^{73} +4.60204 q^{74} -3.21428 q^{75} -1.87923i q^{76} -2.90159 q^{77} -0.217237 q^{79} -0.151230i q^{80} +22.7573 q^{81} -12.7439 q^{82} +11.0119i q^{83} +23.7098i q^{84} -2.43159i q^{85} +13.4031i q^{86} -9.93715 q^{87} +3.45301 q^{88} -6.37458i q^{89} +16.7218 q^{90} -26.8013 q^{92} +1.26665i q^{93} +4.39894 q^{94} -0.586893 q^{95} +18.7325i q^{96} +16.3061i q^{97} -3.86139i q^{98} -9.23440i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 14 q^{3} - 34 q^{4} + 32 q^{9}+O(q^{10}) \) 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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