LMFDB - Embedded newform 1445.2.d.j.866.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1445,2,Mod(866,1445)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1445, 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("1445.866");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1445 = 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1445.d (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:	$11.5383830921$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			866.17
Character	$\chi$	$=$	1445.866
Dual form			1445.2.d.j.866.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.55555 q^{2} -3.00797i q^{3} +0.419729 q^{4} +1.00000i q^{5} -4.67904i q^{6} +3.45467i q^{7} -2.45819 q^{8} -6.04787 q^{9} +O(q^{10})$	\(q+1.55555 q^{2} -3.00797i q^{3} +0.419729 q^{4} +1.00000i q^{5} -4.67904i q^{6} +3.45467i q^{7} -2.45819 q^{8} -6.04787 q^{9} +1.55555i q^{10} +4.24326i q^{11} -1.26253i q^{12} -0.127392 q^{13} +5.37391i q^{14} +3.00797 q^{15} -4.66329 q^{16} -9.40776 q^{18} -2.57338 q^{19} +0.419729i q^{20} +10.3916 q^{21} +6.60059i q^{22} +3.25221i q^{23} +7.39415i q^{24} -1.00000 q^{25} -0.198164 q^{26} +9.16791i q^{27} +1.45003i q^{28} +4.90337i q^{29} +4.67904 q^{30} +5.36372i q^{31} -2.33759 q^{32} +12.7636 q^{33} -3.45467 q^{35} -2.53847 q^{36} +1.77167i q^{37} -4.00302 q^{38} +0.383191i q^{39} -2.45819i q^{40} -10.0623i q^{41} +16.1646 q^{42} -2.53465 q^{43} +1.78102i q^{44} -6.04787i q^{45} +5.05897i q^{46} -4.59479 q^{47} +14.0270i q^{48} -4.93477 q^{49} -1.55555 q^{50} -0.0534701 q^{52} -1.63860 q^{53} +14.2611i q^{54} -4.24326 q^{55} -8.49224i q^{56} +7.74066i q^{57} +7.62743i q^{58} -6.14174 q^{59} +1.26253 q^{60} -4.04195i q^{61} +8.34352i q^{62} -20.8934i q^{63} +5.69034 q^{64} -0.127392i q^{65} +19.8544 q^{66} +6.88856 q^{67} +9.78255 q^{69} -5.37391 q^{70} +7.21741i q^{71} +14.8668 q^{72} -14.6252i q^{73} +2.75592i q^{74} +3.00797i q^{75} -1.08012 q^{76} -14.6591 q^{77} +0.596072i q^{78} +5.15061i q^{79} -4.66329i q^{80} +9.43315 q^{81} -15.6525i q^{82} +14.4462 q^{83} +4.36164 q^{84} -3.94276 q^{86} +14.7492 q^{87} -10.4307i q^{88} -0.600876 q^{89} -9.40776i q^{90} -0.440098i q^{91} +1.36505i q^{92} +16.1339 q^{93} -7.14741 q^{94} -2.57338i q^{95} +7.03140i q^{96} +7.67639i q^{97} -7.67628 q^{98} -25.6627i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9	$ 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9} - 16 q^{13} + 16 q^{15} + 24 q^{16} + 8 q^{18} + 32 q^{21} - 24 q^{25} - 32 q^{26} - 16 q^{30} + 56 q^{32} - 32 q^{35} - 24 q^{36} - 48 q^{38} + 32 q^{43} - 64 q^{47} - 40 q^{49} - 8 q^{50} - 48 q^{52} - 32 q^{55} - 16 q^{59} + 32 q^{60} + 72 q^{64} - 80 q^{66} - 16 q^{67} + 96 q^{69} - 32 q^{70} + 24 q^{72} - 32 q^{76} - 48 q^{77} + 72 q^{81} + 80 q^{83} + 64 q^{84} - 16 q^{86} + 64 q^{87} + 16 q^{89} - 48 q^{93} + 32 q^{94} - 120 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9 - 16 * q^13 + 16 * q^15 + 24 * q^16 + 8 * q^18 + 32 * q^21 - 24 * q^25 - 32 * q^26 - 16 * q^30 + 56 * q^32 - 32 * q^35 - 24 * q^36 - 48 * q^38 + 32 * q^43 - 64 * q^47 - 40 * q^49 - 8 * q^50 - 48 * q^52 - 32 * q^55 - 16 * q^59 + 32 * q^60 + 72 * q^64 - 80 * q^66 - 16 * q^67 + 96 * q^69 - 32 * q^70 + 24 * q^72 - 32 * q^76 - 48 * q^77 + 72 * q^81 + 80 * q^83 + 64 * q^84 - 16 * q^86 + 64 * q^87 + 16 * q^89 - 48 * q^93 + 32 * q^94 - 120 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1445\mathbb{Z}\right)^\times$.

$n$	$581$	$1157$
$\chi(n)$	$-1$	$1$

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 $

$2$	1.55555	1.09994	0.549969	−	0.835185i	$-0.314639\pi$
$2$	1.55555	1.09994	0.549969	+	0.835185i	$0.314639\pi$
$3$	− 3.00797i	− 1.73665i	−0.495995	−	0.868326i	$-0.665196\pi$
$3$	− 3.00797i	− 1.73665i	0.495995	−	0.868326i	$-0.334804\pi$
$4$	0.419729	0.209865
$5$	1.00000i	0.447214i
$5$	1.00000i	0.447214i
$6$	− 4.67904i	− 1.91021i
$7$	3.45467i	1.30574i	0.757468	+	0.652872i	$0.226436\pi$
$7$	3.45467i	1.30574i	−0.757468	+	0.652872i	$0.773564\pi$
$8$	−2.45819	−0.869100
$9$	−6.04787	−2.01596
$10$	1.55555i	0.491907i
$11$	4.24326i	1.27939i	0.768629	+	0.639695i	$0.220939\pi$
$11$	4.24326i	1.27939i	−0.768629	+	0.639695i	$0.779061\pi$
$12$	− 1.26253i	− 0.364461i
$13$	−0.127392	−0.0353322	−0.0176661	−	0.999844i	$-0.505624\pi$
$13$	−0.127392	−0.0353322	−0.0176661	+	0.999844i	$0.505624\pi$
$14$	5.37391i	1.43624i
$15$	3.00797	0.776654
$16$	−4.66329	−1.16582
$17$	0	0
$17$	0	0
$18$	−9.40776	−2.21743
$19$	−2.57338	−0.590375	−0.295187	−	0.955439i	$-0.595382\pi$
$19$	−2.57338	−0.590375	−0.295187	+	0.955439i	$0.595382\pi$
$20$	0.419729i	0.0938543i
$21$	10.3916	2.26762
$22$	6.60059i	1.40725i
$23$	3.25221i	0.678133i	0.940762	+	0.339066i	$0.110111\pi$
$23$	3.25221i	0.678133i	−0.940762	+	0.339066i	$0.889889\pi$
$24$	7.39415i	1.50932i
$25$	−1.00000	−0.200000
$26$	−0.198164	−0.0388632
$27$	9.16791i	1.76436i
$28$	1.45003i	0.274029i
$29$	4.90337i	0.910534i	0.890355	+	0.455267i	$0.150456\pi$
$29$	4.90337i	0.910534i	−0.890355	+	0.455267i	$0.849544\pi$
$30$	4.67904	0.854272
$31$	5.36372i	0.963352i	0.876349	+	0.481676i	$0.159972\pi$
$31$	5.36372i	0.963352i	−0.876349	+	0.481676i	$0.840028\pi$
$32$	−2.33759	−0.413231
$33$	12.7636	2.22185
$34$	0	0
$35$	−3.45467	−0.583947
$36$	−2.53847	−0.423078
$37$	1.77167i	0.291261i	0.989339	+	0.145631i	$0.0465211\pi$
$37$	1.77167i	0.291261i	−0.989339	+	0.145631i	$0.953479\pi$
$38$	−4.00302	−0.649376
$39$	0.383191i	0.0613597i
$40$	− 2.45819i	− 0.388674i
$41$	− 10.0623i	− 1.57147i	−0.618561	−	0.785737i	$-0.712284\pi$
$41$	− 10.0623i	− 1.57147i	0.618561	−	0.785737i	$-0.287716\pi$
$42$	16.1646	2.49424
$43$	−2.53465	−0.386530	−0.193265	−	0.981147i	$-0.561908\pi$
$43$	−2.53465	−0.386530	−0.193265	+	0.981147i	$0.561908\pi$
$44$	1.78102i	0.268499i
$45$	− 6.04787i	− 0.901564i
$46$	5.05897i	0.745905i
$47$	−4.59479	−0.670219	−0.335109	−	0.942179i	$-0.608773\pi$
$47$	−4.59479	−0.670219	−0.335109	+	0.942179i	$0.608773\pi$
$48$	14.0270i	2.02463i
$49$	−4.93477	−0.704968
$50$	−1.55555	−0.219988
$51$	0	0
$52$	−0.0534701	−0.00741498
$53$	−1.63860	−0.225078	−0.112539	−	0.993647i	$-0.535898\pi$
$53$	−1.63860	−0.225078	−0.112539	+	0.993647i	$0.535898\pi$
$54$	14.2611i	1.94069i
$55$	−4.24326	−0.572161
$56$	− 8.49224i	− 1.13482i
$57$	7.74066i	1.02528i
$58$	7.62743i	1.00153i
$59$	−6.14174	−0.799587	−0.399793	−	0.916605i	$-0.630918\pi$
$59$	−6.14174	−0.799587	−0.399793	+	0.916605i	$0.630918\pi$
$60$	1.26253	0.162992
$61$	− 4.04195i	− 0.517519i	−0.965942	−	0.258760i	$-0.916686\pi$
$61$	− 4.04195i	− 0.517519i	0.965942	−	0.258760i	$-0.0833138\pi$
$62$	8.34352i	1.05963i
$63$	− 20.8934i	− 2.63232i
$64$	5.69034	0.711292
$65$	− 0.127392i	− 0.0158010i
$66$	19.8544	2.44390
$67$	6.88856	0.841571	0.420786	−	0.907160i	$-0.361754\pi$
$67$	6.88856	0.841571	0.420786	+	0.907160i	$0.361754\pi$
$68$	0	0
$69$	9.78255	1.17768
$70$	−5.37391	−0.642305
$71$	7.21741i	0.856549i	0.903649	+	0.428274i	$0.140878\pi$
$71$	7.21741i	0.856549i	−0.903649	+	0.428274i	$0.859122\pi$
$72$	14.8668	1.75207
$73$	− 14.6252i	− 1.71175i	−0.517184	−	0.855874i	$-0.673020\pi$
$73$	− 14.6252i	− 1.71175i	0.517184	−	0.855874i	$-0.326980\pi$
$74$	2.75592i	0.320369i
$75$	3.00797i	0.347330i
$76$	−1.08012	−0.123899
$77$	−14.6591	−1.67056
$78$	0.596072i	0.0674919i
$79$	5.15061i	0.579489i	0.957104	+	0.289744i	$0.0935703\pi$
$79$	5.15061i	0.579489i	−0.957104	+	0.289744i	$0.906430\pi$
$80$	− 4.66329i	− 0.521371i
$81$	9.43315	1.04813
$82$	− 15.6525i	− 1.72852i
$83$	14.4462	1.58567	0.792837	−	0.609434i	$-0.208603\pi$
$83$	14.4462	1.58567	0.792837	+	0.609434i	$0.208603\pi$
$84$	4.36164	0.475893
$85$	0	0
$86$	−3.94276	−0.425159
$87$	14.7492	1.58128
$88$	− 10.4307i	− 1.11192i
$89$	−0.600876	−0.0636927	−0.0318463	−	0.999493i	$-0.510139\pi$
$89$	−0.600876	−0.0636927	−0.0318463	+	0.999493i	$0.510139\pi$
$90$	− 9.40776i	− 0.991665i
$91$	− 0.440098i	− 0.0461348i
$92$	1.36505i	0.142316i
$93$	16.1339	1.67301
$94$	−7.14741	−0.737199
$95$	− 2.57338i	− 0.264024i
$96$	7.03140i	0.717639i
$97$	7.67639i	0.779420i	0.920938	+	0.389710i	$0.127425\pi$
$97$	7.67639i	0.779420i	−0.920938	+	0.389710i	$0.872575\pi$
$98$	−7.67628	−0.775421
$99$	− 25.6627i	− 2.57920i
$100$	−0.419729	−0.0419729
$101$	−16.8485	−1.67649	−0.838243	−	0.545297i	$-0.816417\pi$
$101$	−16.8485	−1.67649	−0.838243	+	0.545297i	$0.816417\pi$
$102$	0	0
$103$	4.32255	0.425914	0.212957	−	0.977062i	$-0.431691\pi$
$103$	4.32255	0.425914	0.212957	+	0.977062i	$0.431691\pi$
$104$	0.313154	0.0307072
$105$	10.3916i	1.01411i
$106$	−2.54891	−0.247572
$107$	4.72053i	0.456351i	0.973620	+	0.228175i	$0.0732760\pi$
$107$	4.72053i	0.456351i	−0.973620	+	0.228175i	$0.926724\pi$
$108$	3.84804i	0.370277i
$109$	15.3281i	1.46816i	0.679061	+	0.734082i	$0.262387\pi$
$109$	15.3281i	1.46816i	−0.679061	+	0.734082i	$0.737613\pi$
$110$	−6.60059	−0.629342
$111$	5.32914	0.505819
$112$	− 16.1101i	− 1.52226i
$113$	7.37161i	0.693463i	0.937964	+	0.346732i	$0.112709\pi$
$113$	7.37161i	0.693463i	−0.937964	+	0.346732i	$0.887291\pi$
$114$	12.0410i	1.12774i
$115$	−3.25221	−0.303270
$116$	2.05809i	0.191089i
$117$	0.770451	0.0712282
$118$	−9.55378	−0.879496
$119$	0	0
$120$	−7.39415	−0.674990
$121$	−7.00523	−0.636839
$122$	− 6.28745i	− 0.569239i
$123$	−30.2672	−2.72910
$124$	2.25131i	0.202173i
$125$	− 1.00000i	− 0.0894427i
$126$	− 32.5007i	− 2.89540i
$127$	−8.02005	−0.711664	−0.355832	−	0.934550i	$-0.615803\pi$
$127$	−8.02005	−0.711664	−0.355832	+	0.934550i	$0.615803\pi$
$128$	13.5268	1.19561
$129$	7.62413i	0.671268i
$130$	− 0.198164i	− 0.0173802i
$131$	− 14.2092i	− 1.24146i	−0.784023	−	0.620731i	$-0.786836\pi$
$131$	− 14.2092i	− 1.24146i	0.784023	−	0.620731i	$-0.213164\pi$
$132$	5.35725	0.466288
$133$	− 8.89020i	− 0.770878i
$134$	10.7155	0.925677
$135$	−9.16791	−0.789048
$136$	0	0
$137$	8.53083	0.728838	0.364419	−	0.931235i	$-0.381268\pi$
$137$	8.53083	0.728838	0.364419	+	0.931235i	$0.381268\pi$
$138$	15.2172	1.29538
$139$	− 6.83721i	− 0.579925i	−0.957038	−	0.289962i	$-0.906357\pi$
$139$	− 6.83721i	− 0.579925i	0.957038	−	0.289962i	$-0.0936428\pi$
$140$	−1.45003	−0.122550
$141$	13.8210i	1.16394i
$142$	11.2270i	0.942151i
$143$	− 0.540557i	− 0.0452037i
$144$	28.2030	2.35025
$145$	−4.90337	−0.407203
$146$	− 22.7502i	− 1.88282i
$147$	14.8436i	1.22428i
$148$	0.743623i	0.0611254i
$149$	7.04072	0.576798	0.288399	−	0.957510i	$-0.406877\pi$
$149$	7.04072	0.576798	0.288399	+	0.957510i	$0.406877\pi$
$150$	4.67904i	0.382042i
$151$	6.35689	0.517316	0.258658	−	0.965969i	$-0.416720\pi$
$151$	6.35689	0.517316	0.258658	+	0.965969i	$0.416720\pi$
$152$	6.32586	0.513095
$153$	0	0
$154$	−22.8029	−1.83751
$155$	−5.36372	−0.430824
$156$	0.160837i	0.0128772i
$157$	−16.7739	−1.33870	−0.669351	−	0.742947i	$-0.733428\pi$
$157$	−16.7739	−1.33870	−0.669351	+	0.742947i	$0.733428\pi$
$158$	8.01202i	0.637402i
$159$	4.92885i	0.390883i
$160$	− 2.33759i	− 0.184803i
$161$	−11.2353	−0.885468
$162$	14.6737	1.15288
$163$	− 4.59441i	− 0.359862i	−0.983679	−	0.179931i	$-0.942413\pi$
$163$	− 4.59441i	− 0.359862i	0.983679	−	0.179931i	$-0.0575874\pi$
$164$	− 4.22346i	− 0.329797i
$165$	12.7636i	0.993644i
$166$	22.4717	1.74414
$167$	21.0265i	1.62708i	0.581509	+	0.813540i	$0.302463\pi$
$167$	21.0265i	1.62708i	−0.581509	+	0.813540i	$0.697537\pi$
$168$	−25.5444	−1.97079
$169$	−12.9838	−0.998752
$170$	0	0
$171$	15.5635	1.19017
$172$	−1.06386	−0.0811189
$173$	12.5524i	0.954343i	0.878810	+	0.477171i	$0.158338\pi$
$173$	12.5524i	0.954343i	−0.878810	+	0.477171i	$0.841662\pi$
$174$	22.9431	1.73931
$175$	− 3.45467i	− 0.261149i
$176$	− 19.7875i	− 1.49154i
$177$	18.4742i	1.38860i
$178$	−0.934691	−0.0700580
$179$	12.1536	0.908404	0.454202	−	0.890899i	$-0.349925\pi$
$179$	12.1536	0.908404	0.454202	+	0.890899i	$0.349925\pi$
$180$	− 2.53847i	− 0.189206i
$181$	15.2624i	1.13445i	0.823563	+	0.567224i	$0.191983\pi$
$181$	15.2624i	1.13445i	−0.823563	+	0.567224i	$0.808017\pi$
$182$	− 0.684594i	− 0.0507455i
$183$	−12.1581	−0.898750
$184$	− 7.99454i	− 0.589366i
$185$	−1.77167	−0.130256
$186$	25.0970	1.84020
$187$	0	0
$188$	−1.92857	−0.140655
$189$	−31.6721	−2.30381
$190$	− 4.00302i	− 0.290410i
$191$	8.89972	0.643961	0.321981	−	0.946746i	$-0.395651\pi$
$191$	8.89972	0.643961	0.321981	+	0.946746i	$0.395651\pi$
$192$	− 17.1164i	− 1.23527i
$193$	18.3838i	1.32330i	0.749814	+	0.661648i	$0.230143\pi$
$193$	18.3838i	1.32330i	−0.749814	+	0.661648i	$0.769857\pi$
$194$	11.9410i	0.857314i
$195$	−0.383191	−0.0274409
$196$	−2.07127	−0.147948
$197$	10.6896i	0.761603i	0.924657	+	0.380801i	$0.124352\pi$
$197$	10.6896i	0.761603i	−0.924657	+	0.380801i	$0.875648\pi$
$198$	− 39.9195i	− 2.83696i
$199$	− 15.5191i	− 1.10012i	−0.835126	−	0.550058i	$-0.814605\pi$
$199$	− 15.5191i	− 1.10012i	0.835126	−	0.550058i	$-0.185395\pi$
$200$	2.45819	0.173820
$201$	− 20.7206i	− 1.46152i
$202$	−26.2086	−1.84403
$203$	−16.9396	−1.18892
$204$	0	0
$205$	10.0623	0.702785
$206$	6.72393	0.468479
$207$	− 19.6690i	− 1.36709i
$208$	0.594066	0.0411910
$209$	− 10.9195i	− 0.755320i
$210$	16.1646i	1.11546i
$211$	− 8.75387i	− 0.602641i	−0.953523	−	0.301321i	$-0.902573\pi$
$211$	− 8.75387i	− 0.602641i	0.953523	−	0.301321i	$-0.0974274\pi$
$212$	−0.687766	−0.0472360
$213$	21.7097	1.48753
$214$	7.34301i	0.501958i
$215$	− 2.53465i	− 0.172861i
$216$	− 22.5364i	− 1.53341i
$217$	−18.5299	−1.25789
$218$	23.8436i	1.61489i
$219$	−43.9921	−2.97271
$220$	−1.78102	−0.120076
$221$	0	0
$222$	8.28973	0.556370
$223$	21.1596	1.41695	0.708475	−	0.705736i	$-0.249384\pi$
$223$	21.1596	1.41695	0.708475	+	0.705736i	$0.249384\pi$
$224$	− 8.07561i	− 0.539574i
$225$	6.04787	0.403192
$226$	11.4669i	0.762767i
$227$	− 25.6333i	− 1.70134i	−0.525699	−	0.850671i	$-0.676196\pi$
$227$	− 25.6333i	− 1.70134i	0.525699	−	0.850671i	$-0.323804\pi$
$228$	3.24898i	0.215169i
$229$	−7.10038	−0.469206	−0.234603	−	0.972091i	$-0.575379\pi$
$229$	−7.10038	−0.469206	−0.234603	+	0.972091i	$0.575379\pi$
$230$	−5.05897	−0.333579
$231$	44.0940i	2.90117i
$232$	− 12.0534i	− 0.791345i
$233$	23.7142i	1.55357i	0.629766	+	0.776785i	$0.283151\pi$
$233$	23.7142i	1.55357i	−0.629766	+	0.776785i	$0.716849\pi$
$234$	1.19847	0.0783467
$235$	− 4.59479i	− 0.299731i
$236$	−2.57787	−0.167805
$237$	15.4929	1.00637
$238$	0	0
$239$	0.109315	0.00707103	0.00353551	−	0.999994i	$-0.498875\pi$
$239$	0.109315	0.00707103	0.00353551	+	0.999994i	$0.498875\pi$
$240$	−14.0270	−0.905440
$241$	− 17.4869i	− 1.12643i	−0.826311	−	0.563215i	$-0.809564\pi$
$241$	− 17.4869i	− 1.12643i	0.826311	−	0.563215i	$-0.190436\pi$
$242$	−10.8970	−0.700484
$243$	− 0.870897i	− 0.0558681i
$244$	− 1.69653i	− 0.108609i
$245$	− 4.93477i	− 0.315271i
$246$	−47.0821	−3.00184
$247$	0.327829	0.0208592
$248$	− 13.1850i	− 0.837249i
$249$	− 43.4536i	− 2.75376i
$250$	− 1.55555i	− 0.0983815i
$251$	−3.28782	−0.207525	−0.103763	−	0.994602i	$-0.533088\pi$
$251$	−3.28782	−0.207525	−0.103763	+	0.994602i	$0.533088\pi$
$252$	− 8.76958i	− 0.552432i
$253$	−13.8000	−0.867597
$254$	−12.4756	−0.782787
$255$	0	0
$256$	9.66087	0.603804
$257$	−21.3981	−1.33478	−0.667388	−	0.744710i	$-0.732588\pi$
$257$	−21.3981	−1.33478	−0.667388	+	0.744710i	$0.732588\pi$
$258$	11.8597i	0.738353i
$259$	−6.12055	−0.380313
$260$	− 0.0534701i	− 0.00331608i
$261$	− 29.6550i	− 1.83560i
$262$	− 22.1031i	− 1.36553i
$263$	10.1371	0.625079	0.312540	−	0.949905i	$-0.398820\pi$
$263$	10.1371	0.625079	0.312540	+	0.949905i	$0.398820\pi$
$264$	−31.3753	−1.93101
$265$	− 1.63860i	− 0.100658i
$266$	− 13.8291i	− 0.847919i
$267$	1.80741i	0.110612i
$268$	2.89133	0.176616
$269$	− 15.0776i	− 0.919299i	−0.888100	−	0.459649i	$-0.847975\pi$
$269$	− 15.0776i	− 0.919299i	0.888100	−	0.459649i	$-0.152025\pi$
$270$	−14.2611	−0.867904
$271$	6.80304	0.413255	0.206628	−	0.978420i	$-0.433751\pi$
$271$	6.80304	0.413255	0.206628	+	0.978420i	$0.433751\pi$
$272$	0	0
$273$	−1.32380	−0.0801201
$274$	13.2701	0.801676
$275$	− 4.24326i	− 0.255878i
$276$	4.10602	0.247153
$277$	17.3218i	1.04077i	0.853933	+	0.520383i	$0.174211\pi$
$277$	17.3218i	1.04077i	−0.853933	+	0.520383i	$0.825789\pi$
$278$	− 10.6356i	− 0.637882i
$279$	− 32.4391i	− 1.94208i
$280$	8.49224	0.507508
$281$	−18.0221	−1.07511	−0.537555	−	0.843228i	$-0.680652\pi$
$281$	−18.0221	−1.07511	−0.537555	+	0.843228i	$0.680652\pi$
$282$	21.4992i	1.28026i
$283$	18.9013i	1.12357i	0.827284	+	0.561784i	$0.189885\pi$
$283$	18.9013i	1.12357i	−0.827284	+	0.561784i	$0.810115\pi$
$284$	3.02936i	0.179759i
$285$	−7.74066	−0.458517
$286$	− 0.840863i	− 0.0497213i
$287$	34.7621	2.05194
$288$	14.1374	0.833057
$289$	0	0
$290$	−7.62743	−0.447898
$291$	23.0903	1.35358
$292$	− 6.13862i	− 0.359235i
$293$	7.53184	0.440015	0.220007	−	0.975498i	$-0.429392\pi$
$293$	7.53184	0.440015	0.220007	+	0.975498i	$0.429392\pi$
$294$	23.0900i	1.34664i
$295$	− 6.14174i	− 0.357586i
$296$	− 4.35510i	− 0.253135i
$297$	−38.9018	−2.25731
$298$	10.9522	0.634442
$299$	− 0.414306i	− 0.0239599i
$300$	1.26253i	0.0728923i
$301$	− 8.75638i	− 0.504709i
$302$	9.88844	0.569016
$303$	50.6797i	2.91147i
$304$	12.0004	0.688272
$305$	4.04195	0.231442
$306$	0	0
$307$	−7.77074	−0.443499	−0.221750	−	0.975104i	$-0.571177\pi$
$307$	−7.77074	−0.443499	−0.221750	+	0.975104i	$0.571177\pi$
$308$	−6.15284	−0.350590
$309$	− 13.0021i	− 0.739663i
$310$	−8.34352	−0.473880
$311$	8.64484i	0.490204i	0.969497	+	0.245102i	$0.0788214\pi$
$311$	8.64484i	0.490204i	−0.969497	+	0.245102i	$0.921179\pi$
$312$	− 0.941956i	− 0.0533278i
$313$	12.3380i	0.697383i	0.937238	+	0.348691i	$0.113374\pi$
$313$	12.3380i	0.697383i	−0.937238	+	0.348691i	$0.886626\pi$
$314$	−26.0926	−1.47249
$315$	20.8934	1.17721
$316$	2.16186i	0.121614i
$317$	8.17256i	0.459016i	0.973307	+	0.229508i	$0.0737118\pi$
$317$	8.17256i	0.459016i	−0.973307	+	0.229508i	$0.926288\pi$
$318$	7.66705i	0.429947i
$319$	−20.8063	−1.16493
$320$	5.69034i	0.318100i
$321$	14.1992	0.792522
$322$	−17.4771	−0.973960
$323$	0	0
$324$	3.95937	0.219965
$325$	0.127392	0.00706644
$326$	− 7.14682i	− 0.395826i
$327$	46.1064	2.54969
$328$	24.7351i	1.36577i
$329$	− 15.8735i	− 0.875134i
$330$	19.8544i	1.09295i
$331$	23.4664	1.28983	0.644916	−	0.764254i	$-0.276892\pi$
$331$	23.4664	1.28983	0.644916	+	0.764254i	$0.276892\pi$
$332$	6.06348	0.332777
$333$	− 10.7149i	− 0.587170i
$334$	32.7077i	1.78969i
$335$	6.88856i	0.376362i
$336$	−48.4588	−2.64364
$337$	− 23.7182i	− 1.29201i	−0.763333	−	0.646005i	$-0.776438\pi$
$337$	− 23.7182i	− 1.29201i	0.763333	−	0.646005i	$-0.223562\pi$
$338$	−20.1969	−1.09857
$339$	22.1736	1.20430
$340$	0	0
$341$	−22.7596	−1.23250
$342$	24.2098	1.30911
$343$	7.13468i	0.385237i
$344$	6.23063	0.335933
$345$	9.78255i	0.526675i
$346$	19.5259i	1.04972i
$347$	− 7.01884i	− 0.376791i	−0.982093	−	0.188395i	$-0.939671\pi$
$347$	− 7.01884i	− 0.376791i	0.982093	−	0.188395i	$-0.0603287\pi$
$348$	6.19067	0.331854
$349$	29.3836	1.57287	0.786434	−	0.617674i	$-0.211925\pi$
$349$	29.3836	1.57287	0.786434	+	0.617674i	$0.211925\pi$
$350$	− 5.37391i	− 0.287248i
$351$	− 1.16792i	− 0.0623389i
$352$	− 9.91899i	− 0.528684i
$353$	9.09110	0.483870	0.241935	−	0.970292i	$-0.422218\pi$
$353$	9.09110	0.483870	0.241935	+	0.970292i	$0.422218\pi$
$354$	28.7375i	1.52738i
$355$	−7.21741	−0.383060
$356$	−0.252205	−0.0133668
$357$	0	0
$358$	18.9055	0.999188
$359$	−5.24008	−0.276561	−0.138280	−	0.990393i	$-0.544157\pi$
$359$	−5.24008	−0.276561	−0.138280	+	0.990393i	$0.544157\pi$
$360$	14.8668i	0.783549i
$361$	−12.3777	−0.651458
$362$	23.7415i	1.24782i
$363$	21.0715i	1.10597i
$364$	− 0.184722i	− 0.00968206i
$365$	14.6252	0.765517
$366$	−18.9125	−0.988570
$367$	− 18.2327i	− 0.951740i	−0.879516	−	0.475870i	$-0.842133\pi$
$367$	− 18.2327i	− 0.951740i	0.879516	−	0.475870i	$-0.157867\pi$
$368$	− 15.1660i	− 0.790582i
$369$	60.8558i	3.16803i
$370$	−2.75592	−0.143274
$371$	− 5.66082i	− 0.293895i
$372$	6.77186	0.351105
$373$	−18.5489	−0.960428	−0.480214	−	0.877151i	$-0.659441\pi$
$373$	−18.5489	−0.960428	−0.480214	+	0.877151i	$0.659441\pi$
$374$	0	0
$375$	−3.00797	−0.155331
$376$	11.2948	0.582487
$377$	− 0.624651i	− 0.0321712i
$378$	−49.2675	−2.53405
$379$	− 20.0619i	− 1.03051i	−0.857037	−	0.515255i	$-0.827697\pi$
$379$	− 20.0619i	− 1.03051i	0.857037	−	0.515255i	$-0.172303\pi$
$380$	− 1.08012i	− 0.0554092i
$381$	24.1241i	1.23591i
$382$	13.8439	0.708317
$383$	10.9283	0.558412	0.279206	−	0.960231i	$-0.409929\pi$
$383$	10.9283	0.558412	0.279206	+	0.960231i	$0.409929\pi$
$384$	− 40.6881i	− 2.07636i
$385$	− 14.6591i	− 0.747095i
$386$	28.5969i	1.45555i
$387$	15.3292	0.779228
$388$	3.22200i	0.163573i
$389$	23.7513	1.20424	0.602120	−	0.798405i	$-0.294323\pi$
$389$	23.7513	1.20424	0.602120	+	0.798405i	$0.294323\pi$
$390$	−0.596072	−0.0301833
$391$	0	0
$392$	12.1306	0.612688
$393$	−42.7408	−2.15599
$394$	16.6282i	0.837716i
$395$	−5.15061	−0.259155
$396$	− 10.7714i	− 0.541282i
$397$	− 28.3867i	− 1.42469i	−0.701830	−	0.712344i	$-0.747633\pi$
$397$	− 28.3867i	− 1.42469i	0.701830	−	0.712344i	$-0.252367\pi$
$398$	− 24.1406i	− 1.21006i
$399$	−26.7415	−1.33875
$400$	4.66329	0.233164
$401$	− 8.72614i	− 0.435763i	−0.975975	−	0.217881i	$-0.930085\pi$
$401$	− 8.72614i	− 0.435763i	0.975975	−	0.217881i	$-0.0699146\pi$
$402$	− 32.2318i	− 1.60758i
$403$	− 0.683295i	− 0.0340373i
$404$	−7.07179	−0.351835
$405$	9.43315i	0.468737i
$406$	−26.3503	−1.30774
$407$	−7.51766	−0.372637
$408$	0	0
$409$	10.5572	0.522020	0.261010	−	0.965336i	$-0.415944\pi$
$409$	10.5572	0.522020	0.261010	+	0.965336i	$0.415944\pi$
$410$	15.6525	0.773020
$411$	− 25.6605i	− 1.26574i
$412$	1.81430	0.0893841
$413$	− 21.2177i	− 1.04406i
$414$	− 30.5960i	− 1.50371i
$415$	14.4462i	0.709135i
$416$	0.297790	0.0146004
$417$	−20.5661	−1.00713
$418$	− 16.9859i	− 0.830805i
$419$	− 14.2887i	− 0.698051i	−0.937113	−	0.349025i	$-0.886513\pi$
$419$	− 14.2887i	− 0.698051i	0.937113	−	0.349025i	$-0.113487\pi$
$420$	4.36164i	0.212826i
$421$	18.2694	0.890398	0.445199	−	0.895432i	$-0.353133\pi$
$421$	18.2694	0.890398	0.445199	+	0.895432i	$0.353133\pi$
$422$	− 13.6171i	− 0.662868i
$423$	27.7887	1.35113
$424$	4.02798	0.195616
$425$	0	0
$426$	33.7705	1.63619
$427$	13.9636	0.675748
$428$	1.98134i	0.0957718i
$429$	−1.62598	−0.0785030
$430$	− 3.94276i	− 0.190137i
$431$	21.0425i	1.01358i	0.862069	+	0.506791i	$0.169168\pi$
$431$	21.0425i	1.01358i	−0.862069	+	0.506791i	$0.830832\pi$
$432$	− 42.7526i	− 2.05693i
$433$	3.57657	0.171879	0.0859395	−	0.996300i	$-0.472611\pi$
$433$	3.57657	0.171879	0.0859395	+	0.996300i	$0.472611\pi$
$434$	−28.8241	−1.38360
$435$	14.7492i	0.707170i
$436$	6.43364i	0.308115i
$437$	− 8.36919i	− 0.400353i
$438$	−68.4318	−3.26980
$439$	3.28791i	0.156923i	0.996917	+	0.0784617i	$0.0250008\pi$
$439$	3.28791i	0.156923i	−0.996917	+	0.0784617i	$0.974999\pi$
$440$	10.4307	0.497265
$441$	29.8449	1.42119
$442$	0	0
$443$	−24.9391	−1.18489	−0.592447	−	0.805609i	$-0.701838\pi$
$443$	−24.9391	−1.18489	−0.592447	+	0.805609i	$0.701838\pi$
$444$	2.23679	0.106154
$445$	− 0.600876i	− 0.0284842i
$446$	32.9147	1.55856
$447$	− 21.1783i	− 1.00170i
$448$	19.6583i	0.928766i
$449$	− 9.65637i	− 0.455712i	−0.973695	−	0.227856i	$-0.926828\pi$
$449$	− 9.65637i	− 0.455712i	0.973695	−	0.227856i	$-0.0731716\pi$
$450$	9.40776	0.443486
$451$	42.6971	2.01053
$452$	3.09408i	0.145533i
$453$	− 19.1213i	− 0.898397i
$454$	− 39.8738i	− 1.87137i
$455$	0.440098	0.0206321
$456$	− 19.0280i	− 0.891067i
$457$	20.4776	0.957900	0.478950	−	0.877842i	$-0.341018\pi$
$457$	20.4776	0.957900	0.478950	+	0.877842i	$0.341018\pi$
$458$	−11.0450	−0.516098
$459$	0	0
$460$	−1.36505	−0.0636457
$461$	18.8498	0.877923	0.438961	−	0.898506i	$-0.355346\pi$
$461$	18.8498	0.877923	0.438961	+	0.898506i	$0.355346\pi$
$462$	68.5904i	3.19111i
$463$	2.13430	0.0991892	0.0495946	−	0.998769i	$-0.484207\pi$
$463$	2.13430	0.0991892	0.0495946	+	0.998769i	$0.484207\pi$
$464$	− 22.8658i	− 1.06152i
$465$	16.1339i	0.748191i
$466$	36.8886i	1.70883i
$467$	23.2636	1.07651	0.538255	−	0.842782i	$-0.319084\pi$
$467$	23.2636	1.07651	0.538255	+	0.842782i	$0.319084\pi$
$468$	0.323381	0.0149483
$469$	23.7977i	1.09888i
$470$	− 7.14741i	− 0.329686i
$471$	50.4553i	2.32486i
$472$	15.0976	0.694921
$473$	− 10.7552i	− 0.494523i
$474$	24.0999	1.10694
$475$	2.57338	0.118075
$476$	0	0
$477$	9.91002	0.453749
$478$	0.170045	0.00777770
$479$	31.2128i	1.42615i	0.701088	+	0.713074i	$0.252698\pi$
$479$	31.2128i	1.42615i	−0.701088	+	0.713074i	$0.747302\pi$
$480$	−7.03140	−0.320938
$481$	− 0.225697i	− 0.0102909i
$482$	− 27.2017i	− 1.23900i
$483$	33.7955i	1.53775i
$484$	−2.94030	−0.133650
$485$	−7.67639	−0.348567
$486$	− 1.35472i	− 0.0614514i
$487$	− 14.6528i	− 0.663980i	−0.943283	−	0.331990i	$-0.892280\pi$
$487$	− 14.6528i	− 0.663980i	0.943283	−	0.331990i	$-0.107720\pi$
$488$	9.93588i	0.449776i
$489$	−13.8198	−0.624954
$490$	− 7.67628i	− 0.346779i
$491$	13.8614	0.625555	0.312778	−	0.949826i	$-0.398741\pi$
$491$	13.8614	0.625555	0.312778	+	0.949826i	$0.398741\pi$
$492$	−12.7040	−0.572742
$493$	0	0
$494$	0.509953	0.0229439
$495$	25.6627	1.15345
$496$	− 25.0125i	− 1.12310i
$497$	−24.9338	−1.11843
$498$	− 67.5942i	− 3.02897i
$499$	40.0320i	1.79208i	0.443976	+	0.896039i	$0.353567\pi$
$499$	40.0320i	1.79208i	−0.443976	+	0.896039i	$0.646433\pi$
$500$	− 0.419729i	− 0.0187709i
$501$	63.2471	2.82567
$502$	−5.11435	−0.228265
$503$	39.2423i	1.74973i	0.484371	+	0.874863i	$0.339049\pi$
$503$	39.2423i	1.74973i	−0.484371	+	0.874863i	$0.660951\pi$
$504$	51.3600i	2.28775i
$505$	− 16.8485i	− 0.749747i
$506$	−21.4665	−0.954303
$507$	39.0548i	1.73448i
$508$	−3.36625	−0.149353
$509$	26.7005	1.18348	0.591740	−	0.806129i	$-0.298441\pi$
$509$	26.7005	1.18348	0.591740	+	0.806129i	$0.298441\pi$
$510$	0	0
$511$	50.5253	2.23511
$512$	−12.0256	−0.531462
$513$	− 23.5925i	− 1.04164i
$514$	−33.2857	−1.46817
$515$	4.32255i	0.190474i
$516$	3.20007i	0.140875i
$517$	− 19.4969i	− 0.857471i
$518$	−9.52081	−0.418321
$519$	37.7573	1.65736
$520$	0.313154i	0.0137327i
$521$	− 4.64101i	− 0.203326i	−0.994819	−	0.101663i	$-0.967584\pi$
$521$	− 4.64101i	− 0.203326i	0.994819	−	0.101663i	$-0.0324164\pi$
$522$	− 46.1298i	− 2.01904i
$523$	9.21401	0.402900	0.201450	−	0.979499i	$-0.435435\pi$
$523$	9.21401	0.402900	0.201450	+	0.979499i	$0.435435\pi$
$524$	− 5.96401i	− 0.260539i
$525$	−10.3916	−0.453524
$526$	15.7687	0.687549
$527$	0	0
$528$	−59.5202	−2.59029
$529$	12.4231	0.540136
$530$	− 2.54891i	− 0.110718i
$531$	37.1445	1.61193
$532$	− 3.73148i	− 0.161780i
$533$	1.28186i	0.0555236i
$534$	2.81152i	0.121666i
$535$	−4.72053	−0.204086
$536$	−16.9334	−0.731410
$537$	− 36.5577i	− 1.57758i
$538$	− 23.4540i	− 1.01117i
$539$	− 20.9395i	− 0.901929i
$540$	−3.84804	−0.165593
$541$	− 31.9717i	− 1.37457i	−0.726388	−	0.687285i	$-0.758803\pi$
$541$	− 31.9717i	− 1.37457i	0.726388	−	0.687285i	$-0.241197\pi$
$542$	10.5824	0.454555
$543$	45.9089	1.97014
$544$	0	0
$545$	−15.3281	−0.656583
$546$	−2.05924	−0.0881272
$547$	− 8.40850i	− 0.359522i	−0.983710	−	0.179761i	$-0.942468\pi$
$547$	− 8.40850i	− 0.359522i	0.983710	−	0.179761i	$-0.0575324\pi$
$548$	3.58064	0.152957
$549$	24.4452i	1.04330i
$550$	− 6.60059i	− 0.281450i
$551$	− 12.6183i	− 0.537556i
$552$	−24.0473	−1.02352
$553$	−17.7937	−0.756664
$554$	26.9449i	1.14478i
$555$	5.32914i	0.226209i
$556$	− 2.86978i	− 0.121706i
$557$	1.01642	0.0430670	0.0215335	−	0.999768i	$-0.493145\pi$
$557$	1.01642	0.0430670	0.0215335	+	0.999768i	$0.493145\pi$
$558$	− 50.4605i	− 2.13616i
$559$	0.322894	0.0136570
$560$	16.1101	0.680777
$561$	0	0
$562$	−28.0343	−1.18256
$563$	−10.3869	−0.437757	−0.218878	−	0.975752i	$-0.570240\pi$
$563$	−10.3869	−0.437757	−0.218878	+	0.975752i	$0.570240\pi$
$564$	5.80107i	0.244269i
$565$	−7.37161	−0.310126
$566$	29.4019i	1.23585i
$567$	32.5885i	1.36859i
$568$	− 17.7417i	− 0.744427i
$569$	−23.9733	−1.00501	−0.502506	−	0.864574i	$-0.667589\pi$
$569$	−23.9733	−1.00501	−0.502506	+	0.864574i	$0.667589\pi$
$570$	−12.0410	−0.504340
$571$	− 11.8509i	− 0.495944i	−0.968767	−	0.247972i	$-0.920236\pi$
$571$	− 11.8509i	− 0.495944i	0.968767	−	0.247972i	$-0.0797641\pi$
$572$	− 0.226888i	− 0.00948665i
$573$	− 26.7701i	− 1.11834i
$574$	54.0741	2.25701
$575$	− 3.25221i	− 0.135627i
$576$	−34.4144	−1.43394
$577$	−22.5581	−0.939107	−0.469553	−	0.882904i	$-0.655585\pi$
$577$	−22.5581	−0.939107	−0.469553	+	0.882904i	$0.655585\pi$
$578$	0	0
$579$	55.2980	2.29811
$580$	−2.05809	−0.0854575
$581$	49.9068i	2.07048i
$582$	35.9181	1.48885
$583$	− 6.95298i	− 0.287963i
$584$	35.9514i	1.48768i
$585$	0.770451i	0.0318542i
$586$	11.7161	0.483989
$587$	42.1734	1.74068	0.870341	−	0.492449i	$-0.163898\pi$
$587$	42.1734	1.74068	0.870341	+	0.492449i	$0.163898\pi$
$588$	6.23031i	0.256934i
$589$	− 13.8029i	− 0.568739i
$590$	− 9.55378i	− 0.393323i
$591$	32.1540	1.32264
$592$	− 8.26182i	− 0.339559i
$593$	−8.48766	−0.348547	−0.174273	−	0.984697i	$-0.555758\pi$
$593$	−8.48766	−0.348547	−0.174273	+	0.984697i	$0.555758\pi$
$594$	−60.5136	−2.48290
$595$	0	0
$596$	2.95519	0.121049
$597$	−46.6808	−1.91052
$598$	− 0.644473i	− 0.0263545i
$599$	−17.0226	−0.695523	−0.347762	−	0.937583i	$-0.613058\pi$
$599$	−17.0226	−0.695523	−0.347762	+	0.937583i	$0.613058\pi$
$600$	− 7.39415i	− 0.301865i
$601$	− 20.2981i	− 0.827975i	−0.910282	−	0.413988i	$-0.864136\pi$
$601$	− 20.2981i	− 0.827975i	0.910282	−	0.413988i	$-0.135864\pi$
$602$	− 13.6210i	− 0.555149i
$603$	−41.6611	−1.69657
$604$	2.66817	0.108566
$605$	− 7.00523i	− 0.284803i
$606$	78.8346i	3.20244i
$607$	48.8334i	1.98209i	0.133542	+	0.991043i	$0.457365\pi$
$607$	48.8334i	1.98209i	−0.133542	+	0.991043i	$0.542635\pi$
$608$	6.01552	0.243961
$609$	50.9537i	2.06475i
$610$	6.28745	0.254572
$611$	0.585340	0.0236803
$612$	0	0
$613$	−21.5320	−0.869669	−0.434834	−	0.900510i	$-0.643193\pi$
$613$	−21.5320	−0.869669	−0.434834	+	0.900510i	$0.643193\pi$
$614$	−12.0878	−0.487822
$615$	− 30.2672i	− 1.22049i
$616$	36.0347	1.45188
$617$	− 4.62599i	− 0.186235i	−0.995655	−	0.0931177i	$-0.970317\pi$
$617$	− 4.62599i	− 0.186235i	0.995655	−	0.0931177i	$-0.0296833\pi$
$618$	− 20.2254i	− 0.813584i
$619$	− 46.6252i	− 1.87402i	−0.349298	−	0.937012i	$-0.613580\pi$
$619$	− 46.6252i	− 1.87402i	0.349298	−	0.937012i	$-0.386420\pi$
$620$	−2.25131	−0.0904147
$621$	−29.8160	−1.19647
$622$	13.4475i	0.539194i
$623$	− 2.07583i	− 0.0831664i
$624$	− 1.78693i	− 0.0715345i
$625$	1.00000	0.0400000
$626$	19.1923i	0.767078i
$627$	−32.8456	−1.31173
$628$	−7.04048	−0.280946
$629$	0	0
$630$	32.5007	1.29486
$631$	−26.2970	−1.04687	−0.523433	−	0.852067i	$-0.675349\pi$
$631$	−26.2970	−1.04687	−0.523433	+	0.852067i	$0.675349\pi$
$632$	− 12.6612i	− 0.503634i
$633$	−26.3314	−1.04658
$634$	12.7128i	0.504890i
$635$	− 8.02005i	− 0.318266i
$636$	2.06878i	0.0820324i
$637$	0.628651	0.0249081
$638$	−32.3652	−1.28135
$639$	− 43.6500i	− 1.72677i
$640$	13.5268i	0.534693i
$641$	− 6.56445i	− 0.259280i	−0.991561	−	0.129640i	$-0.958618\pi$
$641$	− 6.56445i	− 0.259280i	0.991561	−	0.129640i	$-0.0413822\pi$
$642$	22.0875	0.871726
$643$	− 6.40706i	− 0.252670i	−0.991988	−	0.126335i	$-0.959679\pi$
$643$	− 6.40706i	− 0.252670i	0.991988	−	0.126335i	$-0.0403214\pi$
$644$	−4.71579	−0.185828
$645$	−7.62413	−0.300200
$646$	0	0
$647$	−8.03230	−0.315782	−0.157891	−	0.987457i	$-0.550470\pi$
$647$	−8.03230	−0.315782	−0.157891	+	0.987457i	$0.550470\pi$
$648$	−23.1884	−0.910928
$649$	− 26.0610i	− 1.02298i
$650$	0.198164	0.00777265
$651$	55.7373i	2.18452i
$652$	− 1.92841i	− 0.0755222i
$653$	46.2055i	1.80816i	0.427363	+	0.904080i	$0.359443\pi$
$653$	46.2055i	1.80816i	−0.427363	+	0.904080i	$0.640557\pi$
$654$	71.7207	2.80450
$655$	14.2092	0.555199
$656$	46.9236i	1.83206i
$657$	88.4513i	3.45081i
$658$	− 24.6920i	− 0.962594i
$659$	47.9496	1.86785	0.933926	−	0.357465i	$-0.116359\pi$
$659$	47.9496	1.86785	0.933926	+	0.357465i	$0.116359\pi$
$660$	5.35725i	0.208531i
$661$	−37.8757	−1.47319	−0.736596	−	0.676333i	$-0.763568\pi$
$661$	−37.8757	−1.47319	−0.736596	+	0.676333i	$0.763568\pi$
$662$	36.5032	1.41874
$663$	0	0
$664$	−35.5114	−1.37811
$665$	8.89020	0.344747
$666$	− 16.6675i	− 0.645851i
$667$	−15.9468	−0.617463
$668$	8.82544i	0.341466i
$669$	− 63.6473i	− 2.46075i
$670$	10.7155i	0.413975i
$671$	17.1511	0.662109
$672$	−24.2912	−0.937053
$673$	4.06145i	0.156557i	0.996932	+	0.0782786i	$0.0249424\pi$
$673$	4.06145i	0.156557i	−0.996932	+	0.0782786i	$0.975058\pi$
$674$	− 36.8947i	− 1.42113i
$675$	− 9.16791i	− 0.352873i
$676$	−5.44967	−0.209603
$677$	3.48544i	0.133956i	0.997754	+	0.0669782i	$0.0213358\pi$
$677$	3.48544i	0.133956i	−0.997754	+	0.0669782i	$0.978664\pi$
$678$	34.4921	1.32466
$679$	−26.5194	−1.01772
$680$	0	0
$681$	−77.1041	−2.95464
$682$	−35.4037	−1.35568
$683$	14.0816i	0.538818i	0.963026	+	0.269409i	$0.0868284\pi$
$683$	14.0816i	0.538818i	−0.963026	+	0.269409i	$0.913172\pi$
$684$	6.53245	0.249775
$685$	8.53083i	0.325946i
$686$	11.0983i	0.423737i
$687$	21.3577i	0.814847i
$688$	11.8198	0.450625
$689$	0.208744	0.00795252
$690$	15.2172i	0.579310i
$691$	44.6596i	1.69893i	0.527644	+	0.849465i	$0.323075\pi$
$691$	44.6596i	1.69893i	−0.527644	+	0.849465i	$0.676925\pi$
$692$	5.26861i	0.200283i
$693$	88.6562	3.36777
$694$	− 10.9181i	− 0.414447i
$695$	6.83721	0.259350
$696$	−36.2563	−1.37429
$697$	0	0
$698$	45.7076	1.73006
$699$	71.3316	2.69801
$700$	− 1.45003i	− 0.0548059i
$701$	1.84833	0.0698103	0.0349052	−	0.999391i	$-0.488887\pi$
$701$	1.84833	0.0698103	0.0349052	+	0.999391i	$0.488887\pi$
$702$	− 1.81675i	− 0.0685689i
$703$	− 4.55920i	− 0.171953i
$704$	24.1456i	0.910020i
$705$	−13.8210	−0.520528
$706$	14.1416	0.532228
$707$	− 58.2060i	− 2.18906i
$708$	7.75415i	0.291419i
$709$	− 30.0075i	− 1.12695i	−0.826132	−	0.563477i	$-0.809463\pi$
$709$	− 30.0075i	− 1.12695i	0.826132	−	0.563477i	$-0.190537\pi$
$710$	−11.2270	−0.421343
$711$	− 31.1502i	− 1.16822i
$712$	1.47706	0.0553553
$713$	−17.4439	−0.653281
$714$	0	0
$715$	0.540557	0.0202157
$716$	5.10122	0.190642
$717$	− 0.328817i	− 0.0122799i
$718$	−8.15119	−0.304200
$719$	38.3910i	1.43174i	0.698232	+	0.715872i	$0.253970\pi$
$719$	38.3910i	1.43174i	−0.698232	+	0.715872i	$0.746030\pi$
$720$	28.2030i	1.05106i
$721$	14.9330i	0.556134i
$722$	−19.2541	−0.716563
$723$	−52.6000	−1.95622
$724$	6.40609i	0.238080i
$725$	− 4.90337i	− 0.182107i
$726$	32.7777i	1.21650i
$727$	0.0992434	0.00368073	0.00184037	−	0.999998i	$-0.499414\pi$
$727$	0.0992434	0.00368073	0.00184037	+	0.999998i	$0.499414\pi$
$728$	1.08184i	0.0400958i
$729$	25.6798	0.951104
$730$	22.7502	0.842022
$731$	0	0
$732$	−5.10310	−0.188616
$733$	−14.4487	−0.533674	−0.266837	−	0.963742i	$-0.585979\pi$
$733$	−14.4487	−0.533674	−0.266837	+	0.963742i	$0.585979\pi$
$734$	− 28.3619i	− 1.04686i
$735$	−14.8436	−0.547516
$736$	− 7.60234i	− 0.280226i
$737$	29.2299i	1.07670i
$738$	94.6641i	3.48463i
$739$	−4.56053	−0.167762	−0.0838808	−	0.996476i	$-0.526732\pi$
$739$	−4.56053	−0.167762	−0.0838808	+	0.996476i	$0.526732\pi$
$740$	−0.743623	−0.0273361
$741$	− 0.986098i	− 0.0362252i
$742$	− 8.80567i	− 0.323266i
$743$	− 33.2731i	− 1.22067i	−0.792142	−	0.610337i	$-0.791034\pi$
$743$	− 33.2731i	− 1.22067i	0.792142	−	0.610337i	$-0.208966\pi$
$744$	−39.6601	−1.45401
$745$	7.04072i	0.257952i
$746$	−28.8538	−1.05641
$747$	−87.3686	−3.19665
$748$	0	0
$749$	−16.3079	−0.595877
$750$	−4.67904	−0.170854
$751$	26.4160i	0.963933i	0.876190	+	0.481967i	$0.160077\pi$
$751$	26.4160i	0.963933i	−0.876190	+	0.481967i	$0.839923\pi$
$752$	21.4268	0.781355
$753$	9.88964i	0.360399i
$754$	− 0.971675i	− 0.0353863i
$755$	6.35689i	0.231351i
$756$	−13.2937	−0.483488
$757$	−22.1805	−0.806163	−0.403082	−	0.915164i	$-0.632061\pi$
$757$	−22.1805	−0.806163	−0.403082	+	0.915164i	$0.632061\pi$
$758$	− 31.2072i	− 1.13350i
$759$	41.5099i	1.50671i
$760$	6.32586i	0.229463i
$761$	−23.1817	−0.840337	−0.420168	−	0.907446i	$-0.638029\pi$
$761$	−23.1817	−0.840337	−0.420168	+	0.907446i	$0.638029\pi$
$762$	37.5261i	1.35943i
$763$	−52.9535	−1.91705
$764$	3.73547	0.135145
$765$	0	0
$766$	16.9996	0.614219
$767$	0.782409	0.0282512
$768$	− 29.0596i	− 1.04860i
$769$	16.7701	0.604747	0.302373	−	0.953190i	$-0.402221\pi$
$769$	16.7701	0.604747	0.302373	+	0.953190i	$0.402221\pi$
$770$	− 22.8029i	− 0.821759i
$771$	64.3648i	2.31804i
$772$	7.71623i	0.277713i
$773$	13.6907	0.492419	0.246210	−	0.969217i	$-0.420815\pi$
$773$	13.6907	0.492419	0.246210	+	0.969217i	$0.420815\pi$
$774$	23.8453	0.857103
$775$	− 5.36372i	− 0.192670i
$776$	− 18.8700i	− 0.677394i
$777$	18.4104i	0.660470i
$778$	36.9463	1.32459
$779$	25.8943i	0.927759i
$780$	−0.160837	−0.00575887
$781$	−30.6253	−1.09586
$782$	0	0
$783$	−44.9537	−1.60651
$784$	23.0123	0.821867
$785$	− 16.7739i	− 0.598685i
$786$	−66.4854	−2.37145
$787$	− 29.2308i	− 1.04197i	−0.853567	−	0.520983i	$-0.825565\pi$
$787$	− 29.2308i	− 1.04197i	0.853567	−	0.520983i	$-0.174435\pi$
$788$	4.48674i	0.159833i
$789$	− 30.4920i	− 1.08554i
$790$	−8.01202	−0.285055
$791$	−25.4665	−0.905485
$792$	63.0837i	2.24158i
$793$	0.514913i	0.0182851i
$794$	− 44.1569i	− 1.56707i
$795$	−4.92885	−0.174808
$796$	− 6.51380i	− 0.230875i
$797$	14.1482	0.501153	0.250577	−	0.968097i	$-0.419380\pi$
$797$	14.1482	0.501153	0.250577	+	0.968097i	$0.419380\pi$
$798$	−41.5976	−1.47254
$799$	0	0
$800$	2.33759	0.0826463
$801$	3.63402	0.128402
$802$	− 13.5739i	− 0.479312i
$803$	62.0584	2.18999
$804$	− 8.69702i	− 0.306720i
$805$	− 11.2353i	− 0.395993i
$806$	− 1.06290i	− 0.0374390i
$807$	−45.3530	−1.59650
$808$	41.4167	1.45703
$809$	17.1630i	0.603418i	0.953400	+	0.301709i	$0.0975571\pi$
$809$	17.1630i	0.603418i	−0.953400	+	0.301709i	$0.902443\pi$
$810$	14.6737i	0.515582i
$811$	− 45.2749i	− 1.58982i	−0.606730	−	0.794908i	$-0.707519\pi$
$811$	− 45.2749i	− 1.58982i	0.606730	−	0.794908i	$-0.292481\pi$
$812$	−7.11003	−0.249513
$813$	− 20.4633i	− 0.717680i
$814$	−11.6941	−0.409878
$815$	4.59441	0.160935
$816$	0	0
$817$	6.52262	0.228197
$818$	16.4222	0.574190
$819$	2.66166i	0.0930058i
$820$	4.22346	0.147490
$821$	− 23.9915i	− 0.837309i	−0.908146	−	0.418654i	$-0.862502\pi$
$821$	− 23.9915i	− 0.837309i	0.908146	−	0.418654i	$-0.137498\pi$
$822$	− 39.9161i	− 1.39223i
$823$	− 43.3681i	− 1.51172i	−0.654735	−	0.755858i	$-0.727220\pi$
$823$	− 43.3681i	− 1.51172i	0.654735	−	0.755858i	$-0.272780\pi$
$824$	−10.6256	−0.370162
$825$	−12.7636	−0.444371
$826$	− 33.0052i	− 1.14840i
$827$	38.4929i	1.33853i	0.743024	+	0.669265i	$0.233391\pi$
$827$	38.4929i	1.33853i	−0.743024	+	0.669265i	$0.766609\pi$
$828$	− 8.25563i	− 0.286903i
$829$	−54.4489	−1.89109	−0.945545	−	0.325492i	$-0.894470\pi$
$829$	−54.4489	−1.89109	−0.945545	+	0.325492i	$0.894470\pi$
$830$	22.4717i	0.780004i
$831$	52.1034	1.80745
$832$	−0.724904	−0.0251315
$833$	0	0
$834$	−31.9916	−1.10778
$835$	−21.0265	−0.727652
$836$	− 4.58324i	− 0.158515i
$837$	−49.1740	−1.69970
$838$	− 22.2268i	− 0.767813i
$839$	− 11.8856i	− 0.410335i	−0.978727	−	0.205167i	$-0.934226\pi$
$839$	− 11.8856i	− 0.410335i	0.978727	−	0.205167i	$-0.0657739\pi$
$840$	− 25.5444i	− 0.881365i
$841$	4.95692	0.170928
$842$	28.4190	0.979383
$843$	54.2100i	1.86709i
$844$	− 3.67425i	− 0.126473i
$845$	− 12.9838i	− 0.446655i
$846$	43.2266	1.48616
$847$	− 24.2008i	− 0.831549i
$848$	7.64124	0.262401
$849$	56.8546	1.95124
$850$	0	0
$851$	−5.76186	−0.197514
$852$	9.11221	0.312179
$853$	34.3786i	1.17710i	0.808461	+	0.588550i	$0.200301\pi$
$853$	34.3786i	1.17710i	−0.808461	+	0.588550i	$0.799699\pi$
$854$	21.7211	0.743281
$855$	15.5635i	0.532260i
$856$	− 11.6039i	− 0.396615i
$857$	− 18.4424i	− 0.629980i	−0.949095	−	0.314990i	$-0.897999\pi$
$857$	− 18.4424i	− 0.629980i	0.949095	−	0.314990i	$-0.102001\pi$
$858$	−2.52929	−0.0863485
$859$	−24.4156	−0.833049	−0.416524	−	0.909125i	$-0.636752\pi$
$859$	−24.4156	−0.833049	−0.416524	+	0.909125i	$0.636752\pi$
$860$	− 1.06386i	− 0.0362775i
$861$	− 104.563i	− 3.56351i
$862$	32.7326i	1.11488i
$863$	−22.5253	−0.766770	−0.383385	−	0.923589i	$-0.625242\pi$
$863$	−22.5253	−0.766770	−0.383385	+	0.923589i	$0.625242\pi$
$864$	− 21.4308i	− 0.729091i
$865$	−12.5524	−0.426795
$866$	5.56353	0.189056
$867$	0	0
$868$	−7.77753	−0.263987
$869$	−21.8554	−0.741392
$870$	22.9431i	0.777843i
$871$	−0.877548	−0.0297346
$872$	− 37.6793i	− 1.27598i
$873$	− 46.4258i	− 1.57128i
$874$	− 13.0187i	− 0.440363i
$875$	3.45467	0.116789
$876$	−18.4648	−0.623866
$877$	56.5640i	1.91003i	0.296557	+	0.955015i	$0.404162\pi$
$877$	56.5640i	1.91003i	−0.296557	+	0.955015i	$0.595838\pi$
$878$	5.11450i	0.172606i
$879$	− 22.6555i	− 0.764152i
$880$	19.7875	0.667037
$881$	33.2018i	1.11860i	0.828967	+	0.559298i	$0.188929\pi$
$881$	33.2018i	1.11860i	−0.828967	+	0.559298i	$0.811071\pi$
$882$	46.4252	1.56322
$883$	11.2453	0.378433	0.189217	−	0.981935i	$-0.439405\pi$
$883$	11.2453	0.378433	0.189217	+	0.981935i	$0.439405\pi$
$884$	0	0
$885$	−18.4742	−0.621002
$886$	−38.7940	−1.30331
$887$	1.01177i	0.0339718i	0.999856	+	0.0169859i	$0.00540704\pi$
$887$	1.01177i	0.0339718i	−0.999856	+	0.0169859i	$0.994593\pi$
$888$	−13.1000	−0.439608
$889$	− 27.7067i	− 0.929252i
$890$	− 0.934691i	− 0.0313309i
$891$	40.0273i	1.34096i
$892$	8.88128	0.297367
$893$	11.8242	0.395680
$894$	− 32.9438i	− 1.10180i
$895$	12.1536i	0.406250i
$896$	46.7306i	1.56116i
$897$	−1.24622	−0.0416100
$898$	− 15.0209i	− 0.501255i
$899$	−26.3003	−0.877164
$900$	2.53847	0.0846156
$901$	0	0
$902$	66.4174	2.21146
$903$	−26.3389	−0.876504
$904$	− 18.1208i	− 0.602689i
$905$	−15.2624	−0.507341
$906$	− 29.7441i	− 0.988182i
$907$	18.3308i	0.608663i	0.952566	+	0.304332i	$0.0984331\pi$
$907$	18.3308i	0.608663i	−0.952566	+	0.304332i	$0.901567\pi$
$908$	− 10.7590i	− 0.357051i
$909$	101.897	3.37972
$910$	0.684594	0.0226941
$911$	27.7944i	0.920870i	0.887694	+	0.460435i	$0.152306\pi$
$911$	27.7944i	0.920870i	−0.887694	+	0.460435i	$0.847694\pi$
$912$	− 36.0969i	− 1.19529i
$913$	61.2988i	2.02869i
$914$	31.8538	1.05363
$915$	− 12.1581i	− 0.401933i
$916$	−2.98023	−0.0984697
$917$	49.0881	1.62103
$918$	0	0
$919$	−13.6372	−0.449850	−0.224925	−	0.974376i	$-0.572214\pi$
$919$	−13.6372	−0.449850	−0.224925	+	0.974376i	$0.572214\pi$
$920$	7.99454	0.263572
$921$	23.3741i	0.770204i
$922$	29.3218	0.965661
$923$	− 0.919441i	− 0.0302638i
$924$	18.5075i	0.608853i
$925$	− 1.77167i	− 0.0582522i
$926$	3.32000	0.109102
$927$	−26.1422	−0.858624
$928$	− 11.4621i	− 0.376261i
$929$	52.4121i	1.71959i	0.510642	+	0.859793i	$0.329408\pi$
$929$	52.4121i	1.71959i	−0.510642	+	0.859793i	$0.670592\pi$
$930$	25.0970i	0.822964i
$931$	12.6991	0.416195
$932$	9.95354i	0.326039i
$933$	26.0034	0.851313
$934$	36.1876	1.18409
$935$	0	0
$936$	−1.89391	−0.0619045
$937$	−32.5221	−1.06245	−0.531225	−	0.847231i	$-0.678268\pi$
$937$	−32.5221	−1.06245	−0.531225	+	0.847231i	$0.678268\pi$
$938$	37.0185i	1.20870i
$939$	37.1122	1.21111
$940$	− 1.92857i	− 0.0629029i
$941$	17.3587i	0.565879i	0.959138	+	0.282939i	$0.0913096\pi$
$941$	17.3587i	0.565879i	−0.959138	+	0.282939i	$0.908690\pi$
$942$	78.4856i	2.55720i
$943$	32.7249	1.06567
$944$	28.6407	0.932176
$945$	− 31.6721i	− 1.03029i
$946$	− 16.7302i	− 0.543944i
$947$	− 14.2696i	− 0.463699i	−0.972752	−	0.231849i	$-0.925522\pi$
$947$	− 14.2696i	− 0.463699i	0.972752	−	0.231849i	$-0.0744776\pi$
$948$	6.50280	0.211201
$949$	1.86313i	0.0604799i
$950$	4.00302	0.129875
$951$	24.5828	0.797152
$952$	0	0
$953$	30.1090	0.975326	0.487663	−	0.873032i	$-0.337850\pi$
$953$	30.1090	0.975326	0.487663	+	0.873032i	$0.337850\pi$
$954$	15.4155	0.499096
$955$	8.89972i	0.287988i
$956$	0.0458829	0.00148396
$957$	62.5846i	2.02307i
$958$	48.5530i	1.56868i
$959$	29.4712i	0.951675i
$960$	17.1164	0.552428
$961$	2.23055	0.0719533
$962$	− 0.351083i	− 0.0113194i
$963$	− 28.5492i	− 0.919984i
$964$	− 7.33976i	− 0.236398i
$965$	−18.3838	−0.591796
$966$	52.5705i	1.69143i
$967$	−17.5196	−0.563392	−0.281696	−	0.959504i	$-0.590897\pi$
$967$	−17.5196	−0.563392	−0.281696	+	0.959504i	$0.590897\pi$
$968$	17.2202	0.553477
$969$	0	0
$970$	−11.9410	−0.383402
$971$	11.6359	0.373414	0.186707	−	0.982416i	$-0.440218\pi$
$971$	11.6359	0.373414	0.186707	+	0.982416i	$0.440218\pi$
$972$	− 0.365541i	− 0.0117247i
$973$	23.6203	0.757234
$974$	− 22.7931i	− 0.730337i
$975$	− 0.383191i	− 0.0122719i
$976$	18.8488i	0.603335i
$977$	43.3421	1.38664	0.693319	−	0.720631i	$-0.256148\pi$
$977$	43.3421	1.38664	0.693319	+	0.720631i	$0.256148\pi$
$978$	−21.4974	−0.687411
$979$	− 2.54967i	− 0.0814878i
$980$	− 2.07127i	− 0.0661642i
$981$	− 92.7023i	− 2.95976i
$982$	21.5620	0.688072
$983$	44.3919i	1.41588i	0.706271	+	0.707941i	$0.250376\pi$
$983$	44.3919i	1.41588i	−0.706271	+	0.707941i	$0.749624\pi$
$984$	74.4025	2.37186
$985$	−10.6896	−0.340599
$986$	0	0
$987$	−47.7470	−1.51980
$988$	0.137599	0.00437761
$989$	− 8.24320i	− 0.262119i
$990$	39.9195	1.26873
$991$	− 57.7133i	− 1.83332i	−0.399664	−	0.916662i	$-0.630873\pi$
$991$	− 57.7133i	− 1.83332i	0.399664	−	0.916662i	$-0.369127\pi$
$992$	− 12.5382i	− 0.398087i
$993$	− 70.5863i	− 2.23999i
$994$	−38.7857	−1.23021
$995$	15.5191	0.491987
$996$	− 18.2387i	− 0.577917i
$997$	− 11.6661i	− 0.369471i	−0.982788	−	0.184735i	$-0.940857\pi$
$997$	− 11.6661i	− 0.369471i	0.982788	−	0.184735i	$-0.0591428\pi$
$998$	62.2716i	1.97117i
$999$	−16.2425	−0.513891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1445.2.d.j.866.17		24
17.4	even	4		1445.2.a.p.1.4		12
17.5	odd	16		85.2.l.a.26.3	✓	24
17.10	odd	16		85.2.l.a.36.3	yes	24
17.13	even	4		1445.2.a.q.1.4		12
17.16	even	2	inner	1445.2.d.j.866.18		24
51.5	even	16		765.2.be.b.451.4		24
51.44	even	16		765.2.be.b.631.4		24
85.4	even	4		7225.2.a.bs.1.9		12
85.22	even	16		425.2.n.f.349.3		24
85.27	even	16		425.2.n.c.274.4		24
85.39	odd	16		425.2.m.b.26.4		24
85.44	odd	16		425.2.m.b.376.4		24
85.64	even	4		7225.2.a.bq.1.9		12
85.73	even	16		425.2.n.c.349.4		24
85.78	even	16		425.2.n.f.274.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.3	✓	24	17.5	odd	16
85.2.l.a.36.3	yes	24	17.10	odd	16
425.2.m.b.26.4		24	85.39	odd	16
425.2.m.b.376.4		24	85.44	odd	16
425.2.n.c.274.4		24	85.27	even	16
425.2.n.c.349.4		24	85.73	even	16
425.2.n.f.274.3		24	85.78	even	16
425.2.n.f.349.3		24	85.22	even	16
765.2.be.b.451.4		24	51.5	even	16
765.2.be.b.631.4		24	51.44	even	16
1445.2.a.p.1.4		12	17.4	even	4
1445.2.a.q.1.4		12	17.13	even	4
1445.2.d.j.866.17		24	1.1	even	1	trivial
1445.2.d.j.866.18		24	17.16	even	2	inner
7225.2.a.bq.1.9		12	85.64	even	4
7225.2.a.bs.1.9		12	85.4	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:	\( N \)	\(=\)	\( 1445 = 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1445.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.55555 q^{2} -3.00797i q^{3} +0.419729 q^{4} +1.00000i q^{5} -4.67904i q^{6} +3.45467i q^{7} -2.45819 q^{8} -6.04787 q^{9} +O(q^{10})\)	\(q+1.55555 q^{2} -3.00797i q^{3} +0.419729 q^{4} +1.00000i q^{5} -4.67904i q^{6} +3.45467i q^{7} -2.45819 q^{8} -6.04787 q^{9} +1.55555i q^{10} +4.24326i q^{11} -1.26253i q^{12} -0.127392 q^{13} +5.37391i q^{14} +3.00797 q^{15} -4.66329 q^{16} -9.40776 q^{18} -2.57338 q^{19} +0.419729i q^{20} +10.3916 q^{21} +6.60059i q^{22} +3.25221i q^{23} +7.39415i q^{24} -1.00000 q^{25} -0.198164 q^{26} +9.16791i q^{27} +1.45003i q^{28} +4.90337i q^{29} +4.67904 q^{30} +5.36372i q^{31} -2.33759 q^{32} +12.7636 q^{33} -3.45467 q^{35} -2.53847 q^{36} +1.77167i q^{37} -4.00302 q^{38} +0.383191i q^{39} -2.45819i q^{40} -10.0623i q^{41} +16.1646 q^{42} -2.53465 q^{43} +1.78102i q^{44} -6.04787i q^{45} +5.05897i q^{46} -4.59479 q^{47} +14.0270i q^{48} -4.93477 q^{49} -1.55555 q^{50} -0.0534701 q^{52} -1.63860 q^{53} +14.2611i q^{54} -4.24326 q^{55} -8.49224i q^{56} +7.74066i q^{57} +7.62743i q^{58} -6.14174 q^{59} +1.26253 q^{60} -4.04195i q^{61} +8.34352i q^{62} -20.8934i q^{63} +5.69034 q^{64} -0.127392i q^{65} +19.8544 q^{66} +6.88856 q^{67} +9.78255 q^{69} -5.37391 q^{70} +7.21741i q^{71} +14.8668 q^{72} -14.6252i q^{73} +2.75592i q^{74} +3.00797i q^{75} -1.08012 q^{76} -14.6591 q^{77} +0.596072i q^{78} +5.15061i q^{79} -4.66329i q^{80} +9.43315 q^{81} -15.6525i q^{82} +14.4462 q^{83} +4.36164 q^{84} -3.94276 q^{86} +14.7492 q^{87} -10.4307i q^{88} -0.600876 q^{89} -9.40776i q^{90} -0.440098i q^{91} +1.36505i q^{92} +16.1339 q^{93} -7.14741 q^{94} -2.57338i q^{95} +7.03140i q^{96} +7.67639i q^{97} -7.67628 q^{98} -25.6627i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9	\( 24 q + 8 q^{2} + 24 q^{4} + 24 q^{8} - 24 q^{9} - 16 q^{13} + 16 q^{15} + 24 q^{16} + 8 q^{18} + 32 q^{21} - 24 q^{25} - 32 q^{26} - 16 q^{30} + 56 q^{32} - 32 q^{35} - 24 q^{36} - 48 q^{38} + 32 q^{43} - 64 q^{47} - 40 q^{49} - 8 q^{50} - 48 q^{52} - 32 q^{55} - 16 q^{59} + 32 q^{60} + 72 q^{64} - 80 q^{66} - 16 q^{67} + 96 q^{69} - 32 q^{70} + 24 q^{72} - 32 q^{76} - 48 q^{77} + 72 q^{81} + 80 q^{83} + 64 q^{84} - 16 q^{86} + 64 q^{87} + 16 q^{89} - 48 q^{93} + 32 q^{94} - 120 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^4 + 24 * q^8 - 24 * q^9 - 16 * q^13 + 16 * q^15 + 24 * q^16 + 8 * q^18 + 32 * q^21 - 24 * q^25 - 32 * q^26 - 16 * q^30 + 56 * q^32 - 32 * q^35 - 24 * q^36 - 48 * q^38 + 32 * q^43 - 64 * q^47 - 40 * q^49 - 8 * q^50 - 48 * q^52 - 32 * q^55 - 16 * q^59 + 32 * q^60 + 72 * q^64 - 80 * q^66 - 16 * q^67 + 96 * q^69 - 32 * q^70 + 24 * q^72 - 32 * q^76 - 48 * q^77 + 72 * q^81 + 80 * q^83 + 64 * q^84 - 16 * q^86 + 64 * q^87 + 16 * q^89 - 48 * q^93 + 32 * q^94 - 120 * q^98

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