LMFDB - Embedded newform 1014.2.b.f.337.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1014,2,Mod(337,1014)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1014.337"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1014, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,-6,-6,0,0,0,0,6,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.153664.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 5x^{4} + 6x^{2} + 1 $ x^6 + 5x^4 + 6x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.1
Root			$1.80194i$ of defining polynomial
Character	$\chi$	$=$	1014.337
Dual form			1014.2.b.f.337.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.15883i q^{5} +1.00000i q^{6} +4.69202i q^{7} +1.00000i q^{8} +1.00000 q^{9} -3.15883 q^{10} -0.137063i q^{11} +1.00000 q^{12} +4.69202 q^{14} +3.15883i q^{15} +1.00000 q^{16} +5.60388 q^{17} -1.00000i q^{18} -4.98792i q^{19} +3.15883i q^{20} -4.69202i q^{21} -0.137063 q^{22} +6.09783 q^{23} -1.00000i q^{24} -4.97823 q^{25} -1.00000 q^{27} -4.69202i q^{28} -0.850855 q^{29} +3.15883 q^{30} +6.23490i q^{31} -1.00000i q^{32} +0.137063i q^{33} -5.60388i q^{34} +14.8213 q^{35} -1.00000 q^{36} -11.7017i q^{37} -4.98792 q^{38} +3.15883 q^{40} -4.27413i q^{41} -4.69202 q^{42} +2.09783 q^{43} +0.137063i q^{44} -3.15883i q^{45} -6.09783i q^{46} -4.98792i q^{47} -1.00000 q^{48} -15.0151 q^{49} +4.97823i q^{50} -5.60388 q^{51} -1.82908 q^{53} +1.00000i q^{54} -0.432960 q^{55} -4.69202 q^{56} +4.98792i q^{57} +0.850855i q^{58} +5.89977i q^{59} -3.15883i q^{60} +4.39612 q^{61} +6.23490 q^{62} +4.69202i q^{63} -1.00000 q^{64} +0.137063 q^{66} -4.71379i q^{67} -5.60388 q^{68} -6.09783 q^{69} -14.8213i q^{70} -0.0978347i q^{71} +1.00000i q^{72} +2.32304i q^{73} -11.7017 q^{74} +4.97823 q^{75} +4.98792i q^{76} +0.643104 q^{77} +14.5157 q^{79} -3.15883i q^{80} +1.00000 q^{81} -4.27413 q^{82} -9.85623i q^{83} +4.69202i q^{84} -17.7017i q^{85} -2.09783i q^{86} +0.850855 q^{87} +0.137063 q^{88} -17.0858i q^{89} -3.15883 q^{90} -6.09783 q^{92} -6.23490i q^{93} -4.98792 q^{94} -15.7560 q^{95} +1.00000i q^{96} +2.12737i q^{97} +15.0151i q^{98} -0.137063i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{3} - 6 q^{4} + 6 q^{9} - 2 q^{10} + 6 q^{12} + 18 q^{14} + 6 q^{16} + 16 q^{17} + 10 q^{22} - 36 q^{25} - 6 q^{27} + 22 q^{29} + 2 q^{30} - 8 q^{35} - 6 q^{36} + 8 q^{38} + 2 q^{40} - 18 q^{42}+ \cdots - 16 q^{95}+O(q^{100}) $ 6 * q - 6 * q^3 - 6 * q^4 + 6 * q^9 - 2 * q^10 + 6 * q^12 + 18 * q^14 + 6 * q^16 + 16 * q^17 + 10 * q^22 - 36 * q^25 - 6 * q^27 + 22 * q^29 + 2 * q^30 - 8 * q^35 - 6 * q^36 + 8 * q^38 + 2 * q^40 - 18 * q^42 - 24 * q^43 - 6 * q^48 - 40 * q^49 - 16 * q^51 + 10 * q^53 + 36 * q^55 - 18 * q^56 + 44 * q^61 - 10 * q^62 - 6 * q^64 - 10 * q^66 - 16 * q^68 - 16 * q^74 + 36 * q^75 + 12 * q^77 + 62 * q^79 + 6 * q^81 - 4 * q^82 - 22 * q^87 - 10 * q^88 - 2 * q^90 + 8 * q^94 - 16 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.00000	−0.500000
$5$	− 3.15883i	− 1.41267i	−0.707876	−	0.706337i	$-0.750346\pi$
$5$	− 3.15883i	− 1.41267i	0.707876	−	0.706337i	$-0.249654\pi$
$6$	1.00000i	0.408248i
$7$	4.69202i	1.77342i	0.462329	+	0.886709i	$0.347014\pi$
$7$	4.69202i	1.77342i	−0.462329	+	0.886709i	$0.652986\pi$
$8$	1.00000i	0.353553i
$9$	1.00000	0.333333
$10$	−3.15883	−0.998911
$11$	− 0.137063i	− 0.0413262i	−0.999786	−	0.0206631i	$-0.993422\pi$
$11$	− 0.137063i	− 0.0413262i	0.999786	−	0.0206631i	$-0.00657773\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	4.69202	1.25400
$15$	3.15883i	0.815607i
$16$	1.00000	0.250000
$17$	5.60388	1.35914	0.679570	−	0.733611i	$-0.262167\pi$
$17$	5.60388	1.35914	0.679570	+	0.733611i	$0.262167\pi$
$18$	− 1.00000i	− 0.235702i
$19$	− 4.98792i	− 1.14431i	−0.820147	−	0.572153i	$-0.806108\pi$
$19$	− 4.98792i	− 1.14431i	0.820147	−	0.572153i	$-0.193892\pi$
$20$	3.15883i	0.706337i
$21$	− 4.69202i	− 1.02388i
$22$	−0.137063	−0.0292220
$23$	6.09783	1.27149	0.635743	−	0.771901i	$-0.280694\pi$
$23$	6.09783	1.27149	0.635743	+	0.771901i	$0.280694\pi$
$24$	− 1.00000i	− 0.204124i
$25$	−4.97823	−0.995646
$26$	0	0
$27$	−1.00000	−0.192450
$28$	− 4.69202i	− 0.886709i
$29$	−0.850855	−0.158000	−0.0789999	−	0.996875i	$-0.525173\pi$
$29$	−0.850855	−0.158000	−0.0789999	+	0.996875i	$0.525173\pi$
$30$	3.15883	0.576721
$31$	6.23490i	1.11982i	0.828553	+	0.559910i	$0.189164\pi$
$31$	6.23490i	1.11982i	−0.828553	+	0.559910i	$0.810836\pi$
$32$	− 1.00000i	− 0.176777i
$33$	0.137063i	0.0238597i
$34$	− 5.60388i	− 0.961057i
$35$	14.8213	2.50526
$36$	−1.00000	−0.166667
$37$	− 11.7017i	− 1.92375i	−0.273491	−	0.961875i	$-0.588178\pi$
$37$	− 11.7017i	− 1.92375i	0.273491	−	0.961875i	$-0.411822\pi$
$38$	−4.98792	−0.809147
$39$	0	0
$40$	3.15883	0.499455
$41$	− 4.27413i	− 0.667506i	−0.942660	−	0.333753i	$-0.891685\pi$
$41$	− 4.27413i	− 0.667506i	0.942660	−	0.333753i	$-0.108315\pi$
$42$	−4.69202	−0.723995
$43$	2.09783	0.319917	0.159958	−	0.987124i	$-0.448864\pi$
$43$	2.09783	0.319917	0.159958	+	0.987124i	$0.448864\pi$
$44$	0.137063i	0.0206631i
$45$	− 3.15883i	− 0.470891i
$46$	− 6.09783i	− 0.899077i
$47$	− 4.98792i	− 0.727563i	−0.931484	−	0.363781i	$-0.881486\pi$
$47$	− 4.98792i	− 0.727563i	0.931484	−	0.363781i	$-0.118514\pi$
$48$	−1.00000	−0.144338
$49$	−15.0151	−2.14501
$50$	4.97823i	0.704028i
$51$	−5.60388	−0.784700
$52$	0	0
$53$	−1.82908	−0.251244	−0.125622	−	0.992078i	$-0.540093\pi$
$53$	−1.82908	−0.251244	−0.125622	+	0.992078i	$0.540093\pi$
$54$	1.00000i	0.136083i
$55$	−0.432960	−0.0583804
$56$	−4.69202	−0.626998
$57$	4.98792i	0.660666i
$58$	0.850855i	0.111723i
$59$	5.89977i	0.768085i	0.923315	+	0.384042i	$0.125468\pi$
$59$	5.89977i	0.768085i	−0.923315	+	0.384042i	$0.874532\pi$
$60$	− 3.15883i	− 0.407804i
$61$	4.39612	0.562866	0.281433	−	0.959581i	$-0.409190\pi$
$61$	4.39612	0.562866	0.281433	+	0.959581i	$0.409190\pi$
$62$	6.23490	0.791833
$63$	4.69202i	0.591139i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	0.137063	0.0168713
$67$	− 4.71379i	− 0.575881i	−0.957648	−	0.287941i	$-0.907029\pi$
$67$	− 4.71379i	− 0.575881i	0.957648	−	0.287941i	$-0.0929706\pi$
$68$	−5.60388	−0.679570
$69$	−6.09783	−0.734093
$70$	− 14.8213i	− 1.77149i
$71$	− 0.0978347i	− 0.0116108i	−0.999983	−	0.00580542i	$-0.998152\pi$
$71$	− 0.0978347i	− 0.0116108i	0.999983	−	0.00580542i	$-0.00184793\pi$
$72$	1.00000i	0.117851i
$73$	2.32304i	0.271892i	0.990716	+	0.135946i	$0.0434073\pi$
$73$	2.32304i	0.271892i	−0.990716	+	0.135946i	$0.956593\pi$
$74$	−11.7017	−1.36030
$75$	4.97823	0.574836
$76$	4.98792i	0.572153i
$77$	0.643104	0.0732885
$78$	0	0
$79$	14.5157	1.63315	0.816574	−	0.577241i	$-0.195871\pi$
$79$	14.5157	1.63315	0.816574	+	0.577241i	$0.195871\pi$
$80$	− 3.15883i	− 0.353168i
$81$	1.00000	0.111111
$82$	−4.27413	−0.471998
$83$	− 9.85623i	− 1.08186i	−0.841067	−	0.540931i	$-0.818072\pi$
$83$	− 9.85623i	− 1.08186i	0.841067	−	0.540931i	$-0.181928\pi$
$84$	4.69202i	0.511942i
$85$	− 17.7017i	− 1.92002i
$86$	− 2.09783i	− 0.226215i
$87$	0.850855	0.0912212
$88$	0.137063	0.0146110
$89$	− 17.0858i	− 1.81109i	−0.424254	−	0.905543i	$-0.639464\pi$
$89$	− 17.0858i	− 1.81109i	0.424254	−	0.905543i	$-0.360536\pi$
$90$	−3.15883	−0.332970
$91$	0	0
$92$	−6.09783	−0.635743
$93$	− 6.23490i	− 0.646529i
$94$	−4.98792	−0.514465
$95$	−15.7560	−1.61653
$96$	1.00000i	0.102062i
$97$	2.12737i	0.216002i	0.994151	+	0.108001i	$0.0344450\pi$
$97$	2.12737i	0.216002i	−0.994151	+	0.108001i	$0.965555\pi$
$98$	15.0151i	1.51675i
$99$	− 0.137063i	− 0.0137754i
$100$	4.97823	0.497823
$101$	9.18598	0.914039	0.457020	−	0.889457i	$-0.348917\pi$
$101$	9.18598	0.914039	0.457020	+	0.889457i	$0.348917\pi$
$102$	5.60388i	0.554866i
$103$	−0.225209	−0.0221905	−0.0110953	−	0.999938i	$-0.503532\pi$
$103$	−0.225209	−0.0221905	−0.0110953	+	0.999938i	$0.503532\pi$
$104$	0	0
$105$	−14.8213	−1.44641
$106$	1.82908i	0.177656i
$107$	11.2838	1.09085	0.545424	−	0.838160i	$-0.316369\pi$
$107$	11.2838	1.09085	0.545424	+	0.838160i	$0.316369\pi$
$108$	1.00000	0.0962250
$109$	− 0.195669i	− 0.0187417i	−0.999956	−	0.00937086i	$-0.997017\pi$
$109$	− 0.195669i	− 0.0187417i	0.999956	−	0.00937086i	$-0.00298288\pi$
$110$	0.432960i	0.0412811i
$111$	11.7017i	1.11068i
$112$	4.69202i	0.443354i
$113$	−0.439665	−0.0413602	−0.0206801	−	0.999786i	$-0.506583\pi$
$113$	−0.439665	−0.0413602	−0.0206801	+	0.999786i	$0.506583\pi$
$114$	4.98792	0.467161
$115$	− 19.2620i	− 1.79619i
$116$	0.850855	0.0789999
$117$	0	0
$118$	5.89977	0.543118
$119$	26.2935i	2.41032i
$120$	−3.15883	−0.288361
$121$	10.9812	0.998292
$122$	− 4.39612i	− 0.398006i
$123$	4.27413i	0.385385i
$124$	− 6.23490i	− 0.559910i
$125$	− 0.0687686i	− 0.00615085i
$126$	4.69202	0.417998
$127$	7.87263	0.698583	0.349291	−	0.937014i	$-0.386422\pi$
$127$	7.87263	0.698583	0.349291	+	0.937014i	$0.386422\pi$
$128$	1.00000i	0.0883883i
$129$	−2.09783	−0.184704
$130$	0	0
$131$	−0.621334	−0.0542862	−0.0271431	−	0.999632i	$-0.508641\pi$
$131$	−0.621334	−0.0542862	−0.0271431	+	0.999632i	$0.508641\pi$
$132$	− 0.137063i	− 0.0119298i
$133$	23.4034	2.02933
$134$	−4.71379	−0.407210
$135$	3.15883i	0.271869i
$136$	5.60388i	0.480528i
$137$	− 4.00000i	− 0.341743i	−0.985293	−	0.170872i	$-0.945342\pi$
$137$	− 4.00000i	− 0.341743i	0.985293	−	0.170872i	$-0.0546583\pi$
$138$	6.09783i	0.519082i
$139$	−13.6582	−1.15847	−0.579235	−	0.815160i	$-0.696649\pi$
$139$	−13.6582	−1.15847	−0.579235	+	0.815160i	$0.696649\pi$
$140$	−14.8213	−1.25263
$141$	4.98792i	0.420059i
$142$	−0.0978347	−0.00821010
$143$	0	0
$144$	1.00000	0.0833333
$145$	2.68771i	0.223202i
$146$	2.32304	0.192256
$147$	15.0151	1.23842
$148$	11.7017i	0.961875i
$149$	16.0586i	1.31557i	0.753205	+	0.657786i	$0.228507\pi$
$149$	16.0586i	1.31557i	−0.753205	+	0.657786i	$0.771493\pi$
$150$	− 4.97823i	− 0.406471i
$151$	21.8823i	1.78076i	0.455221	+	0.890379i	$0.349560\pi$
$151$	21.8823i	1.78076i	−0.455221	+	0.890379i	$0.650440\pi$
$152$	4.98792	0.404574
$153$	5.60388	0.453046
$154$	− 0.643104i	− 0.0518228i
$155$	19.6950	1.58194
$156$	0	0
$157$	−7.90217	−0.630661	−0.315331	−	0.948982i	$-0.602115\pi$
$157$	−7.90217	−0.630661	−0.315331	+	0.948982i	$0.602115\pi$
$158$	− 14.5157i	− 1.15481i
$159$	1.82908	0.145056
$160$	−3.15883	−0.249728
$161$	28.6112i	2.25488i
$162$	− 1.00000i	− 0.0785674i
$163$	− 8.01938i	− 0.628126i	−0.949402	−	0.314063i	$-0.898310\pi$
$163$	− 8.01938i	− 0.628126i	0.949402	−	0.314063i	$-0.101690\pi$
$164$	4.27413i	0.333753i
$165$	0.432960	0.0337059
$166$	−9.85623	−0.764992
$167$	17.0858i	1.32214i	0.750326	+	0.661068i	$0.229896\pi$
$167$	17.0858i	1.32214i	−0.750326	+	0.661068i	$0.770104\pi$
$168$	4.69202	0.361997
$169$	0	0
$170$	−17.7017	−1.35766
$171$	− 4.98792i	− 0.381436i
$172$	−2.09783	−0.159958
$173$	15.3448	1.16664	0.583322	−	0.812241i	$-0.301752\pi$
$173$	15.3448	1.16664	0.583322	+	0.812241i	$0.301752\pi$
$174$	− 0.850855i	− 0.0645032i
$175$	− 23.3580i	− 1.76570i
$176$	− 0.137063i	− 0.0103315i
$177$	− 5.89977i	− 0.443454i
$178$	−17.0858	−1.28063
$179$	−0.523499	−0.0391282	−0.0195641	−	0.999809i	$-0.506228\pi$
$179$	−0.523499	−0.0391282	−0.0195641	+	0.999809i	$0.506228\pi$
$180$	3.15883i	0.235446i
$181$	−8.89008	−0.660795	−0.330397	−	0.943842i	$-0.607183\pi$
$181$	−8.89008	−0.660795	−0.330397	+	0.943842i	$0.607183\pi$
$182$	0	0
$183$	−4.39612	−0.324971
$184$	6.09783i	0.449538i
$185$	−36.9638	−2.71763
$186$	−6.23490	−0.457165
$187$	− 0.768086i	− 0.0561680i
$188$	4.98792i	0.363781i
$189$	− 4.69202i	− 0.341294i
$190$	15.7560i	1.14306i
$191$	−7.03146	−0.508779	−0.254389	−	0.967102i	$-0.581874\pi$
$191$	−7.03146	−0.508779	−0.254389	+	0.967102i	$0.581874\pi$
$192$	1.00000	0.0721688
$193$	17.7560i	1.27811i	0.769163	+	0.639053i	$0.220673\pi$
$193$	17.7560i	1.27811i	−0.769163	+	0.639053i	$0.779327\pi$
$194$	2.12737	0.152737
$195$	0	0
$196$	15.0151	1.07250
$197$	18.6571i	1.32926i	0.747171	+	0.664632i	$0.231412\pi$
$197$	18.6571i	1.32926i	−0.747171	+	0.664632i	$0.768588\pi$
$198$	−0.137063	−0.00974067
$199$	−7.66248	−0.543179	−0.271589	−	0.962413i	$-0.587549\pi$
$199$	−7.66248	−0.543179	−0.271589	+	0.962413i	$0.587549\pi$
$200$	− 4.97823i	− 0.352014i
$201$	4.71379i	0.332485i
$202$	− 9.18598i	− 0.646323i
$203$	− 3.99223i	− 0.280200i
$204$	5.60388	0.392350
$205$	−13.5013	−0.942969
$206$	0.225209i	0.0156911i
$207$	6.09783	0.423829
$208$	0	0
$209$	−0.683661	−0.0472898
$210$	14.8213i	1.02277i
$211$	11.1642	0.768576	0.384288	−	0.923213i	$-0.374447\pi$
$211$	11.1642	0.768576	0.384288	+	0.923213i	$0.374447\pi$
$212$	1.82908	0.125622
$213$	0.0978347i	0.00670352i
$214$	− 11.2838i	− 0.771346i
$215$	− 6.62671i	− 0.451938i
$216$	− 1.00000i	− 0.0680414i
$217$	−29.2543	−1.98591
$218$	−0.195669	−0.0132524
$219$	− 2.32304i	− 0.156977i
$220$	0.432960	0.0291902
$221$	0	0
$222$	11.7017	0.785367
$223$	− 24.6353i	− 1.64970i	−0.565349	−	0.824852i	$-0.691258\pi$
$223$	− 24.6353i	− 1.64970i	0.565349	−	0.824852i	$-0.308742\pi$
$224$	4.69202	0.313499
$225$	−4.97823	−0.331882
$226$	0.439665i	0.0292461i
$227$	7.47650i	0.496233i	0.968730	+	0.248116i	$0.0798115\pi$
$227$	7.47650i	0.496233i	−0.968730	+	0.248116i	$0.920188\pi$
$228$	− 4.98792i	− 0.330333i
$229$	− 19.2271i	− 1.27056i	−0.772280	−	0.635282i	$-0.780884\pi$
$229$	− 19.2271i	− 1.27056i	0.772280	−	0.635282i	$-0.219116\pi$
$230$	−19.2620	−1.27010
$231$	−0.643104	−0.0423131
$232$	− 0.850855i	− 0.0558614i
$233$	−3.70171	−0.242507	−0.121254	−	0.992622i	$-0.538691\pi$
$233$	−3.70171	−0.242507	−0.121254	+	0.992622i	$0.538691\pi$
$234$	0	0
$235$	−15.7560	−1.02781
$236$	− 5.89977i	− 0.384042i
$237$	−14.5157	−0.942898
$238$	26.2935	1.70435
$239$	− 8.51334i	− 0.550682i	−0.961347	−	0.275341i	$-0.911209\pi$
$239$	− 8.51334i	− 0.550682i	0.961347	−	0.275341i	$-0.0887908\pi$
$240$	3.15883i	0.203902i
$241$	17.4330i	1.12296i	0.827492	+	0.561478i	$0.189767\pi$
$241$	17.4330i	1.12296i	−0.827492	+	0.561478i	$0.810233\pi$
$242$	− 10.9812i	− 0.705899i
$243$	−1.00000	−0.0641500
$244$	−4.39612	−0.281433
$245$	47.4301i	3.03020i
$246$	4.27413	0.272508
$247$	0	0
$248$	−6.23490	−0.395916
$249$	9.85623i	0.624613i
$250$	−0.0687686	−0.00434931
$251$	3.48427	0.219925	0.109963	−	0.993936i	$-0.464927\pi$
$251$	3.48427	0.219925	0.109963	+	0.993936i	$0.464927\pi$
$252$	− 4.69202i	− 0.295570i
$253$	− 0.835790i	− 0.0525456i
$254$	− 7.87263i	− 0.493972i
$255$	17.7017i	1.10852i
$256$	1.00000	0.0625000
$257$	13.6039	0.848586	0.424293	−	0.905525i	$-0.360523\pi$
$257$	13.6039	0.848586	0.424293	+	0.905525i	$0.360523\pi$
$258$	2.09783i	0.130605i
$259$	54.9047	3.41161
$260$	0	0
$261$	−0.850855	−0.0526666
$262$	0.621334i	0.0383861i
$263$	11.4577	0.706513	0.353256	−	0.935527i	$-0.385074\pi$
$263$	11.4577	0.706513	0.353256	+	0.935527i	$0.385074\pi$
$264$	−0.137063	−0.00843567
$265$	5.77777i	0.354926i
$266$	− 23.4034i	− 1.43496i
$267$	17.0858i	1.04563i
$268$	4.71379i	0.287941i
$269$	22.3666	1.36371	0.681857	−	0.731485i	$-0.261172\pi$
$269$	22.3666	1.36371	0.681857	+	0.731485i	$0.261172\pi$
$270$	3.15883	0.192240
$271$	− 3.87263i	− 0.235245i	−0.993058	−	0.117623i	$-0.962473\pi$
$271$	− 3.87263i	− 0.235245i	0.993058	−	0.117623i	$-0.0375273\pi$
$272$	5.60388	0.339785
$273$	0	0
$274$	−4.00000	−0.241649
$275$	0.682333i	0.0411462i
$276$	6.09783	0.367047
$277$	−28.7090	−1.72496	−0.862478	−	0.506094i	$-0.831089\pi$
$277$	−28.7090	−1.72496	−0.862478	+	0.506094i	$0.831089\pi$
$278$	13.6582i	0.819163i
$279$	6.23490i	0.373274i
$280$	14.8213i	0.885743i
$281$	29.0858i	1.73511i	0.497341	+	0.867555i	$0.334310\pi$
$281$	29.0858i	1.73511i	−0.497341	+	0.867555i	$0.665690\pi$
$282$	4.98792	0.297026
$283$	−13.7560	−0.817710	−0.408855	−	0.912599i	$-0.634072\pi$
$283$	−13.7560	−0.817710	−0.408855	+	0.912599i	$0.634072\pi$
$284$	0.0978347i	0.00580542i
$285$	15.7560	0.933305
$286$	0	0
$287$	20.0543	1.18377
$288$	− 1.00000i	− 0.0589256i
$289$	14.4034	0.847260
$290$	2.68771	0.157828
$291$	− 2.12737i	− 0.124709i
$292$	− 2.32304i	− 0.135946i
$293$	− 27.7362i	− 1.62036i	−0.586179	−	0.810182i	$-0.699368\pi$
$293$	− 27.7362i	− 1.62036i	0.586179	−	0.810182i	$-0.300632\pi$
$294$	− 15.0151i	− 0.875696i
$295$	18.6364	1.08505
$296$	11.7017	0.680148
$297$	0.137063i	0.00795322i
$298$	16.0586	0.930250
$299$	0	0
$300$	−4.97823	−0.287418
$301$	9.84309i	0.567346i
$302$	21.8823	1.25919
$303$	−9.18598	−0.527721
$304$	− 4.98792i	− 0.286077i
$305$	− 13.8866i	− 0.795146i
$306$	− 5.60388i	− 0.320352i
$307$	12.4590i	0.711075i	0.934662	+	0.355538i	$0.115702\pi$
$307$	12.4590i	0.711075i	−0.934662	+	0.355538i	$0.884298\pi$
$308$	−0.643104	−0.0366443
$309$	0.225209	0.0128117
$310$	− 19.6950i	− 1.11860i
$311$	6.09783	0.345776	0.172888	−	0.984941i	$-0.444690\pi$
$311$	6.09783	0.345776	0.172888	+	0.984941i	$0.444690\pi$
$312$	0	0
$313$	−12.7385	−0.720025	−0.360013	−	0.932947i	$-0.617228\pi$
$313$	−12.7385	−0.720025	−0.360013	+	0.932947i	$0.617228\pi$
$314$	7.90217i	0.445945i
$315$	14.8213	0.835087
$316$	−14.5157	−0.816574
$317$	14.8140i	0.832038i	0.909356	+	0.416019i	$0.136575\pi$
$317$	14.8140i	0.832038i	−0.909356	+	0.416019i	$0.863425\pi$
$318$	− 1.82908i	− 0.102570i
$319$	0.116621i	0.00652952i
$320$	3.15883i	0.176584i
$321$	−11.2838	−0.629801
$322$	28.6112	1.59444
$323$	− 27.9517i	− 1.55527i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−8.01938	−0.444152
$327$	0.195669i	0.0108205i
$328$	4.27413	0.235999
$329$	23.4034	1.29027
$330$	− 0.432960i	− 0.0238337i
$331$	7.70171i	0.423324i	0.977343	+	0.211662i	$0.0678876\pi$
$331$	7.70171i	0.423324i	−0.977343	+	0.211662i	$0.932112\pi$
$332$	9.85623i	0.540931i
$333$	− 11.7017i	− 0.641250i
$334$	17.0858	0.934891
$335$	−14.8901	−0.813532
$336$	− 4.69202i	− 0.255971i
$337$	−26.5961	−1.44878	−0.724391	−	0.689389i	$-0.757879\pi$
$337$	−26.5961	−1.44878	−0.724391	+	0.689389i	$0.757879\pi$
$338$	0	0
$339$	0.439665	0.0238793
$340$	17.7017i	0.960010i
$341$	0.854576	0.0462779
$342$	−4.98792	−0.269716
$343$	− 37.6069i	− 2.03058i
$344$	2.09783i	0.113108i
$345$	19.2620i	1.03703i
$346$	− 15.3448i	− 0.824942i
$347$	0.911854	0.0489509	0.0244754	−	0.999700i	$-0.492208\pi$
$347$	0.911854	0.0489509	0.0244754	+	0.999700i	$0.492208\pi$
$348$	−0.850855	−0.0456106
$349$	17.7211i	0.948588i	0.880366	+	0.474294i	$0.157297\pi$
$349$	17.7211i	0.948588i	−0.880366	+	0.474294i	$0.842703\pi$
$350$	−23.3580	−1.24854
$351$	0	0
$352$	−0.137063	−0.00730550
$353$	− 26.4349i	− 1.40699i	−0.710702	−	0.703493i	$-0.751622\pi$
$353$	− 26.4349i	− 1.40699i	0.710702	−	0.703493i	$-0.248378\pi$
$354$	−5.89977	−0.313569
$355$	−0.309043	−0.0164023
$356$	17.0858i	0.905543i
$357$	− 26.2935i	− 1.39160i
$358$	0.523499i	0.0276678i
$359$	− 7.76941i	− 0.410054i	−0.978756	−	0.205027i	$-0.934272\pi$
$359$	− 7.76941i	− 0.410054i	0.978756	−	0.205027i	$-0.0657282\pi$
$360$	3.15883	0.166485
$361$	−5.87933	−0.309438
$362$	8.89008i	0.467252i
$363$	−10.9812	−0.576364
$364$	0	0
$365$	7.33811	0.384094
$366$	4.39612i	0.229789i
$367$	−13.3274	−0.695682	−0.347841	−	0.937553i	$-0.613085\pi$
$367$	−13.3274	−0.695682	−0.347841	+	0.937553i	$0.613085\pi$
$368$	6.09783	0.317872
$369$	− 4.27413i	− 0.222502i
$370$	36.9638i	1.92165i
$371$	− 8.58211i	− 0.445561i
$372$	6.23490i	0.323264i
$373$	6.70304	0.347070	0.173535	−	0.984828i	$-0.444481\pi$
$373$	6.70304	0.347070	0.173535	+	0.984828i	$0.444481\pi$
$374$	−0.768086	−0.0397168
$375$	0.0687686i	0.00355120i
$376$	4.98792	0.257232
$377$	0	0
$378$	−4.69202	−0.241332
$379$	2.41550i	0.124076i	0.998074	+	0.0620380i	$0.0197600\pi$
$379$	2.41550i	0.124076i	−0.998074	+	0.0620380i	$0.980240\pi$
$380$	15.7560	0.808266
$381$	−7.87263	−0.403327
$382$	7.03146i	0.359761i
$383$	10.0978i	0.515975i	0.966148	+	0.257988i	$0.0830594\pi$
$383$	10.0978i	0.515975i	−0.966148	+	0.257988i	$0.916941\pi$
$384$	− 1.00000i	− 0.0510310i
$385$	− 2.03146i	− 0.103533i
$386$	17.7560	0.903757
$387$	2.09783	0.106639
$388$	− 2.12737i	− 0.108001i
$389$	−25.1336	−1.27432	−0.637162	−	0.770730i	$-0.719892\pi$
$389$	−25.1336	−1.27432	−0.637162	+	0.770730i	$0.719892\pi$
$390$	0	0
$391$	34.1715	1.72813
$392$	− 15.0151i	− 0.758375i
$393$	0.621334	0.0313421
$394$	18.6571	0.939931
$395$	− 45.8528i	− 2.30710i
$396$	0.137063i	0.00688769i
$397$	− 20.8358i	− 1.04572i	−0.852419	−	0.522859i	$-0.824865\pi$
$397$	− 20.8358i	− 1.04572i	0.852419	−	0.522859i	$-0.175135\pi$
$398$	7.66248i	0.384085i
$399$	−23.4034	−1.17164
$400$	−4.97823	−0.248911
$401$	5.95646i	0.297451i	0.988878	+	0.148726i	$0.0475171\pi$
$401$	5.95646i	0.297451i	−0.988878	+	0.148726i	$0.952483\pi$
$402$	4.71379	0.235103
$403$	0	0
$404$	−9.18598	−0.457020
$405$	− 3.15883i	− 0.156964i
$406$	−3.99223	−0.198131
$407$	−1.60388	−0.0795012
$408$	− 5.60388i	− 0.277433i
$409$	− 1.80194i	− 0.0891001i	−0.999007	−	0.0445500i	$-0.985815\pi$
$409$	− 1.80194i	− 0.0891001i	0.999007	−	0.0445500i	$-0.0141854\pi$
$410$	13.5013i	0.666779i
$411$	4.00000i	0.197305i
$412$	0.225209	0.0110953
$413$	−27.6819	−1.36214
$414$	− 6.09783i	− 0.299692i
$415$	−31.1342	−1.52832
$416$	0	0
$417$	13.6582	0.668843
$418$	0.683661i	0.0334389i
$419$	−28.4499	−1.38987	−0.694935	−	0.719072i	$-0.744567\pi$
$419$	−28.4499	−1.38987	−0.694935	+	0.719072i	$0.744567\pi$
$420$	14.8213	0.723206
$421$	13.9323i	0.679019i	0.940603	+	0.339509i	$0.110261\pi$
$421$	13.9323i	0.679019i	−0.940603	+	0.339509i	$0.889739\pi$
$422$	− 11.1642i	− 0.543465i
$423$	− 4.98792i	− 0.242521i
$424$	− 1.82908i	− 0.0888282i
$425$	−27.8974	−1.35322
$426$	0.0978347	0.00474011
$427$	20.6267i	0.998196i
$428$	−11.2838	−0.545424
$429$	0	0
$430$	−6.62671	−0.319568
$431$	− 15.9022i	− 0.765980i	−0.923752	−	0.382990i	$-0.874894\pi$
$431$	− 15.9022i	− 0.765980i	0.923752	−	0.382990i	$-0.125106\pi$
$432$	−1.00000	−0.0481125
$433$	−4.77718	−0.229577	−0.114788	−	0.993390i	$-0.536619\pi$
$433$	−4.77718	−0.229577	−0.114788	+	0.993390i	$0.536619\pi$
$434$	29.2543i	1.40425i
$435$	− 2.68771i	− 0.128866i
$436$	0.195669i	0.00937086i
$437$	− 30.4155i	− 1.45497i
$438$	−2.32304	−0.110999
$439$	33.6316	1.60515	0.802575	−	0.596552i	$-0.203463\pi$
$439$	33.6316	1.60515	0.802575	+	0.596552i	$0.203463\pi$
$440$	− 0.432960i	− 0.0206406i
$441$	−15.0151	−0.715003
$442$	0	0
$443$	−35.3749	−1.68071	−0.840357	−	0.542033i	$-0.817655\pi$
$443$	−35.3749	−1.68071	−0.840357	+	0.542033i	$0.817655\pi$
$444$	− 11.7017i	− 0.555339i
$445$	−53.9711	−2.55847
$446$	−24.6353	−1.16652
$447$	− 16.0586i	− 0.759546i
$448$	− 4.69202i	− 0.221677i
$449$	− 18.0629i	− 0.852442i	−0.904619	−	0.426221i	$-0.859845\pi$
$449$	− 18.0629i	− 0.852442i	0.904619	−	0.426221i	$-0.140155\pi$
$450$	4.97823i	0.234676i
$451$	−0.585826	−0.0275855
$452$	0.439665	0.0206801
$453$	− 21.8823i	− 1.02812i
$454$	7.47650	0.350890
$455$	0	0
$456$	−4.98792	−0.233581
$457$	15.4668i	0.723507i	0.932274	+	0.361753i	$0.117822\pi$
$457$	15.4668i	0.723507i	−0.932274	+	0.361753i	$0.882178\pi$
$458$	−19.2271	−0.898425
$459$	−5.60388	−0.261567
$460$	19.2620i	0.898097i
$461$	18.8092i	0.876033i	0.898967	+	0.438017i	$0.144319\pi$
$461$	18.8092i	0.876033i	−0.898967	+	0.438017i	$0.855681\pi$
$462$	0.643104i	0.0299199i
$463$	− 15.8431i	− 0.736291i	−0.929768	−	0.368145i	$-0.879993\pi$
$463$	− 15.8431i	− 0.736291i	0.929768	−	0.368145i	$-0.120007\pi$
$464$	−0.850855	−0.0395000
$465$	−19.6950	−0.913334
$466$	3.70171i	0.171478i
$467$	−22.0006	−1.01807	−0.509033	−	0.860747i	$-0.669997\pi$
$467$	−22.0006	−1.01807	−0.509033	+	0.860747i	$0.669997\pi$
$468$	0	0
$469$	22.1172	1.02128
$470$	15.7560i	0.726770i
$471$	7.90217	0.364113
$472$	−5.89977	−0.271559
$473$	− 0.287536i	− 0.0132209i
$474$	14.5157i	0.666730i
$475$	24.8310i	1.13932i
$476$	− 26.2935i	− 1.20516i
$477$	−1.82908	−0.0837480
$478$	−8.51334	−0.389391
$479$	− 21.3491i	− 0.975466i	−0.872993	−	0.487733i	$-0.837824\pi$
$479$	− 21.3491i	− 0.975466i	0.872993	−	0.487733i	$-0.162176\pi$
$480$	3.15883	0.144180
$481$	0	0
$482$	17.4330	0.794050
$483$	− 28.6112i	− 1.30185i
$484$	−10.9812	−0.499146
$485$	6.72002	0.305141
$486$	1.00000i	0.0453609i
$487$	31.6394i	1.43372i	0.697219	+	0.716859i	$0.254421\pi$
$487$	31.6394i	1.43372i	−0.697219	+	0.716859i	$0.745579\pi$
$488$	4.39612i	0.199003i
$489$	8.01938i	0.362649i
$490$	47.4301	2.14267
$491$	1.39911	0.0631409	0.0315704	−	0.999502i	$-0.489949\pi$
$491$	1.39911	0.0631409	0.0315704	+	0.999502i	$0.489949\pi$
$492$	− 4.27413i	− 0.192693i
$493$	−4.76809	−0.214744
$494$	0	0
$495$	−0.432960	−0.0194601
$496$	6.23490i	0.279955i
$497$	0.459042	0.0205909
$498$	9.85623	0.441668
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	0.0687686i	0.00307543i
$501$	− 17.0858i	− 0.763335i
$502$	− 3.48427i	− 0.155511i
$503$	−18.3827	−0.819645	−0.409822	−	0.912165i	$-0.634409\pi$
$503$	−18.3827	−0.819645	−0.409822	+	0.912165i	$0.634409\pi$
$504$	−4.69202	−0.208999
$505$	− 29.0170i	− 1.29124i
$506$	−0.835790	−0.0371554
$507$	0	0
$508$	−7.87263	−0.349291
$509$	− 0.132751i	− 0.00588411i	−0.999996	−	0.00294205i	$-0.999064\pi$
$509$	− 0.132751i	− 0.00588411i	0.999996	−	0.00294205i	$-0.000936486\pi$
$510$	17.7017	0.783845
$511$	−10.8998	−0.482178
$512$	− 1.00000i	− 0.0441942i
$513$	4.98792i	0.220222i
$514$	− 13.6039i	− 0.600041i
$515$	0.711399i	0.0313480i
$516$	2.09783	0.0923520
$517$	−0.683661	−0.0300674
$518$	− 54.9047i	− 2.41237i
$519$	−15.3448	−0.673563
$520$	0	0
$521$	37.0508	1.62323	0.811613	−	0.584195i	$-0.198590\pi$
$521$	37.0508	1.62323	0.811613	+	0.584195i	$0.198590\pi$
$522$	0.850855i	0.0372409i
$523$	−3.15346	−0.137891	−0.0689455	−	0.997620i	$-0.521963\pi$
$523$	−3.15346	−0.137891	−0.0689455	+	0.997620i	$0.521963\pi$
$524$	0.621334	0.0271431
$525$	23.3580i	1.01942i
$526$	− 11.4577i	− 0.499580i
$527$	34.9396i	1.52199i
$528$	0.137063i	0.00596492i
$529$	14.1836	0.616678
$530$	5.77777	0.250970
$531$	5.89977i	0.256028i
$532$	−23.4034	−1.01467
$533$	0	0
$534$	17.0858	0.739373
$535$	− 35.6437i	− 1.54101i
$536$	4.71379	0.203605
$537$	0.523499	0.0225907
$538$	− 22.3666i	− 0.964292i
$539$	2.05802i	0.0886450i
$540$	− 3.15883i	− 0.135935i
$541$	− 4.07846i	− 0.175347i	−0.996149	−	0.0876733i	$-0.972057\pi$
$541$	− 4.07846i	− 0.175347i	0.996149	−	0.0876733i	$-0.0279432\pi$
$542$	−3.87263	−0.166344
$543$	8.89008	0.381510
$544$	− 5.60388i	− 0.240264i
$545$	−0.618087	−0.0264759
$546$	0	0
$547$	−23.0508	−0.985583	−0.492791	−	0.870148i	$-0.664023\pi$
$547$	−23.0508	−0.985583	−0.492791	+	0.870148i	$0.664023\pi$
$548$	4.00000i	0.170872i
$549$	4.39612	0.187622
$550$	0.682333	0.0290948
$551$	4.24400i	0.180800i
$552$	− 6.09783i	− 0.259541i
$553$	68.1081i	2.89625i
$554$	28.7090i	1.21973i
$555$	36.9638	1.56902
$556$	13.6582	0.579235
$557$	− 20.4155i	− 0.865033i	−0.901626	−	0.432516i	$-0.857626\pi$
$557$	− 20.4155i	− 0.865033i	0.901626	−	0.432516i	$-0.142374\pi$
$558$	6.23490	0.263944
$559$	0	0
$560$	14.8213	0.626315
$561$	0.768086i	0.0324286i
$562$	29.0858	1.22691
$563$	−21.5609	−0.908685	−0.454342	−	0.890827i	$-0.650126\pi$
$563$	−21.5609	−0.908685	−0.454342	+	0.890827i	$0.650126\pi$
$564$	− 4.98792i	− 0.210029i
$565$	1.38883i	0.0584285i
$566$	13.7560i	0.578208i
$567$	4.69202i	0.197046i
$568$	0.0978347	0.00410505
$569$	−8.98792	−0.376793	−0.188397	−	0.982093i	$-0.560329\pi$
$569$	−8.98792	−0.376793	−0.188397	+	0.982093i	$0.560329\pi$
$570$	− 15.7560i	− 0.659946i
$571$	−13.5603	−0.567482	−0.283741	−	0.958901i	$-0.591576\pi$
$571$	−13.5603	−0.567482	−0.283741	+	0.958901i	$0.591576\pi$
$572$	0	0
$573$	7.03146	0.293743
$574$	− 20.0543i	− 0.837050i
$575$	−30.3564	−1.26595
$576$	−1.00000	−0.0416667
$577$	16.2825i	0.677849i	0.940814	+	0.338924i	$0.110063\pi$
$577$	16.2825i	0.677849i	−0.940814	+	0.338924i	$0.889937\pi$
$578$	− 14.4034i	− 0.599103i
$579$	− 17.7560i	− 0.737914i
$580$	− 2.68771i	− 0.111601i
$581$	46.2457	1.91859
$582$	−2.12737	−0.0881825
$583$	0.250700i	0.0103830i
$584$	−2.32304	−0.0961282
$585$	0	0
$586$	−27.7362	−1.14577
$587$	47.5706i	1.96345i	0.190307	+	0.981725i	$0.439052\pi$
$587$	47.5706i	1.96345i	−0.190307	+	0.981725i	$0.560948\pi$
$588$	−15.0151	−0.619211
$589$	31.0992	1.28142
$590$	− 18.6364i	− 0.767248i
$591$	− 18.6571i	− 0.767451i
$592$	− 11.7017i	− 0.480937i
$593$	− 31.0267i	− 1.27411i	−0.770817	−	0.637056i	$-0.780152\pi$
$593$	− 31.0267i	− 1.27411i	0.770817	−	0.637056i	$-0.219848\pi$
$594$	0.137063	0.00562378
$595$	83.0568	3.40500
$596$	− 16.0586i	− 0.657786i
$597$	7.66248	0.313604
$598$	0	0
$599$	22.3263	0.912228	0.456114	−	0.889921i	$-0.349241\pi$
$599$	22.3263	0.912228	0.456114	+	0.889921i	$0.349241\pi$
$600$	4.97823i	0.203235i
$601$	−8.18060	−0.333694	−0.166847	−	0.985983i	$-0.553359\pi$
$601$	−8.18060	−0.333694	−0.166847	+	0.985983i	$0.553359\pi$
$602$	9.84309	0.401174
$603$	− 4.71379i	− 0.191960i
$604$	− 21.8823i	− 0.890379i
$605$	− 34.6878i	− 1.41026i
$606$	9.18598i	0.373155i
$607$	3.30798	0.134267	0.0671334	−	0.997744i	$-0.478615\pi$
$607$	3.30798	0.134267	0.0671334	+	0.997744i	$0.478615\pi$
$608$	−4.98792	−0.202287
$609$	3.99223i	0.161773i
$610$	−13.8866	−0.562253
$611$	0	0
$612$	−5.60388	−0.226523
$613$	− 10.8853i	− 0.439653i	−0.975539	−	0.219827i	$-0.929451\pi$
$613$	− 10.8853i	− 0.439653i	0.975539	−	0.219827i	$-0.0705491\pi$
$614$	12.4590	0.502806
$615$	13.5013	0.544423
$616$	0.643104i	0.0259114i
$617$	− 34.5676i	− 1.39164i	−0.718216	−	0.695820i	$-0.755041\pi$
$617$	− 34.5676i	− 1.39164i	0.718216	−	0.695820i	$-0.244959\pi$
$618$	− 0.225209i	− 0.00905925i
$619$	− 2.86592i	− 0.115191i	−0.998340	−	0.0575955i	$-0.981657\pi$
$619$	− 2.86592i	− 0.115191i	0.998340	−	0.0575955i	$-0.0183434\pi$
$620$	−19.6950	−0.790970
$621$	−6.09783	−0.244698
$622$	− 6.09783i	− 0.244501i
$623$	80.1667	3.21181
$624$	0	0
$625$	−25.1084	−1.00434
$626$	12.7385i	0.509135i
$627$	0.683661	0.0273028
$628$	7.90217	0.315331
$629$	− 65.5749i	− 2.61464i
$630$	− 14.8213i	− 0.590495i
$631$	42.6631i	1.69839i	0.528079	+	0.849195i	$0.322912\pi$
$631$	42.6631i	1.69839i	−0.528079	+	0.849195i	$0.677088\pi$
$632$	14.5157i	0.577405i
$633$	−11.1642	−0.443738
$634$	14.8140	0.588340
$635$	− 24.8683i	− 0.986869i
$636$	−1.82908	−0.0725279
$637$	0	0
$638$	0.116621	0.00461707
$639$	− 0.0978347i	− 0.00387028i
$640$	3.15883	0.124864
$641$	−41.3927	−1.63491	−0.817456	−	0.575991i	$-0.804616\pi$
$641$	−41.3927	−1.63491	−0.817456	+	0.575991i	$0.804616\pi$
$642$	11.2838i	0.445337i
$643$	13.7125i	0.540767i	0.962753	+	0.270383i	$0.0871505\pi$
$643$	13.7125i	0.540767i	−0.962753	+	0.270383i	$0.912850\pi$
$644$	− 28.6112i	− 1.12744i
$645$	6.62671i	0.260926i
$646$	−27.9517	−1.09974
$647$	−18.0086	−0.707992	−0.353996	−	0.935247i	$-0.615177\pi$
$647$	−18.0086	−0.707992	−0.353996	+	0.935247i	$0.615177\pi$
$648$	1.00000i	0.0392837i
$649$	0.808643	0.0317420
$650$	0	0
$651$	29.2543	1.14657
$652$	8.01938i	0.314063i
$653$	46.5652	1.82224	0.911119	−	0.412143i	$-0.135220\pi$
$653$	46.5652	1.82224	0.911119	+	0.412143i	$0.135220\pi$
$654$	0.195669	0.00765128
$655$	1.96269i	0.0766887i
$656$	− 4.27413i	− 0.166877i
$657$	2.32304i	0.0906306i
$658$	− 23.4034i	− 0.912360i
$659$	13.8562	0.539762	0.269881	−	0.962894i	$-0.413016\pi$
$659$	13.8562	0.539762	0.269881	+	0.962894i	$0.413016\pi$
$660$	−0.432960	−0.0168530
$661$	43.1051i	1.67660i	0.545213	+	0.838298i	$0.316449\pi$
$661$	43.1051i	1.67660i	−0.545213	+	0.838298i	$0.683551\pi$
$662$	7.70171	0.299335
$663$	0	0
$664$	9.85623	0.382496
$665$	− 73.9275i	− 2.86679i
$666$	−11.7017	−0.453432
$667$	−5.18837	−0.200895
$668$	− 17.0858i	− 0.661068i
$669$	24.6353i	0.952457i
$670$	14.8901i	0.575254i
$671$	− 0.602548i	− 0.0232611i
$672$	−4.69202	−0.180999
$673$	−30.7415	−1.18500	−0.592499	−	0.805571i	$-0.701859\pi$
$673$	−30.7415	−1.18500	−0.592499	+	0.805571i	$0.701859\pi$
$674$	26.5961i	1.02444i
$675$	4.97823	0.191612
$676$	0	0
$677$	16.5894	0.637582	0.318791	−	0.947825i	$-0.396723\pi$
$677$	16.5894	0.637582	0.318791	+	0.947825i	$0.396723\pi$
$678$	− 0.439665i	− 0.0168852i
$679$	−9.98169	−0.383062
$680$	17.7017	0.678830
$681$	− 7.47650i	− 0.286500i
$682$	− 0.854576i	− 0.0327234i
$683$	34.9885i	1.33880i	0.742903	+	0.669399i	$0.233448\pi$
$683$	34.9885i	1.33880i	−0.742903	+	0.669399i	$0.766552\pi$
$684$	4.98792i	0.190718i
$685$	−12.6353	−0.482771
$686$	−37.6069	−1.43584
$687$	19.2271i	0.733561i
$688$	2.09783	0.0799792
$689$	0	0
$690$	19.2620	0.733294
$691$	14.0871i	0.535898i	0.963433	+	0.267949i	$0.0863458\pi$
$691$	14.0871i	0.535898i	−0.963433	+	0.267949i	$0.913654\pi$
$692$	−15.3448	−0.583322
$693$	0.643104	0.0244295
$694$	− 0.911854i	− 0.0346135i
$695$	43.1439i	1.63654i
$696$	0.850855i	0.0322516i
$697$	− 23.9517i	− 0.907234i
$698$	17.7211	0.670753
$699$	3.70171	0.140012
$700$	23.3580i	0.882848i
$701$	−48.6112	−1.83602	−0.918009	−	0.396559i	$-0.870204\pi$
$701$	−48.6112	−1.83602	−0.918009	+	0.396559i	$0.870204\pi$
$702$	0	0
$703$	−58.3672	−2.20136
$704$	0.137063i	0.00516577i
$705$	15.7560	0.593405
$706$	−26.4349	−0.994890
$707$	43.1008i	1.62097i
$708$	5.89977i	0.221727i
$709$	− 17.2862i	− 0.649197i	−0.945852	−	0.324599i	$-0.894771\pi$
$709$	− 17.2862i	− 0.649197i	0.945852	−	0.324599i	$-0.105229\pi$
$710$	0.309043i	0.0115982i
$711$	14.5157	0.544382
$712$	17.0858	0.640316
$713$	38.0194i	1.42384i
$714$	−26.2935	−0.984010
$715$	0	0
$716$	0.523499	0.0195641
$717$	8.51334i	0.317936i
$718$	−7.76941	−0.289952
$719$	−29.1207	−1.08602	−0.543009	−	0.839727i	$-0.682715\pi$
$719$	−29.1207	−1.08602	−0.543009	+	0.839727i	$0.682715\pi$
$720$	− 3.15883i	− 0.117723i
$721$	− 1.05669i	− 0.0393531i
$722$	5.87933i	0.218806i
$723$	− 17.4330i	− 0.648339i
$724$	8.89008	0.330397
$725$	4.23575	0.157312
$726$	10.9812i	0.407551i
$727$	−45.5666	−1.68997	−0.844985	−	0.534790i	$-0.820391\pi$
$727$	−45.5666	−1.68997	−0.844985	+	0.534790i	$0.820391\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	− 7.33811i	− 0.271596i
$731$	11.7560	0.434812
$732$	4.39612	0.162485
$733$	− 21.7995i	− 0.805185i	−0.915379	−	0.402592i	$-0.868109\pi$
$733$	− 21.7995i	− 0.805185i	0.915379	−	0.402592i	$-0.131891\pi$
$734$	13.3274i	0.491922i
$735$	− 47.4301i	− 1.74949i
$736$	− 6.09783i	− 0.224769i
$737$	−0.646088	−0.0237990
$738$	−4.27413	−0.157333
$739$	41.5663i	1.52904i	0.644599	+	0.764521i	$0.277024\pi$
$739$	41.5663i	1.52904i	−0.644599	+	0.764521i	$0.722976\pi$
$740$	36.9638	1.35881
$741$	0	0
$742$	−8.58211	−0.315059
$743$	28.8224i	1.05739i	0.848812	+	0.528695i	$0.177319\pi$
$743$	28.8224i	1.05739i	−0.848812	+	0.528695i	$0.822681\pi$
$744$	6.23490	0.228582
$745$	50.7265	1.85847
$746$	− 6.70304i	− 0.245416i
$747$	− 9.85623i	− 0.360621i
$748$	0.768086i	0.0280840i
$749$	52.9439i	1.93453i
$750$	0.0687686	0.00251108
$751$	−16.6203	−0.606482	−0.303241	−	0.952914i	$-0.598069\pi$
$751$	−16.6203	−0.606482	−0.303241	+	0.952914i	$0.598069\pi$
$752$	− 4.98792i	− 0.181891i
$753$	−3.48427	−0.126974
$754$	0	0
$755$	69.1226	2.51563
$756$	4.69202i	0.170647i
$757$	−40.3913	−1.46805	−0.734024	−	0.679123i	$-0.762360\pi$
$757$	−40.3913	−1.46805	−0.734024	+	0.679123i	$0.762360\pi$
$758$	2.41550	0.0877350
$759$	0.835790i	0.0303372i
$760$	− 15.7560i	− 0.571530i
$761$	3.29483i	0.119438i	0.998215	+	0.0597188i	$0.0190204\pi$
$761$	3.29483i	0.119438i	−0.998215	+	0.0597188i	$0.980980\pi$
$762$	7.87263i	0.285195i
$763$	0.918085	0.0332369
$764$	7.03146	0.254389
$765$	− 17.7017i	− 0.640007i
$766$	10.0978	0.364850
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	− 2.35258i	− 0.0848363i	−0.999100	−	0.0424182i	$-0.986494\pi$
$769$	− 2.35258i	− 0.0848363i	0.999100	−	0.0424182i	$-0.0135062\pi$
$770$	−2.03146	−0.0732087
$771$	−13.6039	−0.489932
$772$	− 17.7560i	− 0.639053i
$773$	− 20.3937i	− 0.733512i	−0.930317	−	0.366756i	$-0.880468\pi$
$773$	− 20.3937i	− 0.733512i	0.930317	−	0.366756i	$-0.119532\pi$
$774$	− 2.09783i	− 0.0754051i
$775$	− 31.0388i	− 1.11494i
$776$	−2.12737	−0.0763683
$777$	−54.9047	−1.96969
$778$	25.1336i	0.901083i
$779$	−21.3190	−0.763832
$780$	0	0
$781$	−0.0134095	−0.000479831 0
$782$	− 34.1715i	− 1.22197i
$783$	0.850855	0.0304071
$784$	−15.0151	−0.536252
$785$	24.9616i	0.890919i
$786$	− 0.621334i	− 0.0221622i
$787$	− 19.6775i	− 0.701429i	−0.936482	−	0.350714i	$-0.885939\pi$
$787$	− 19.6775i	− 0.701429i	0.936482	−	0.350714i	$-0.114061\pi$
$788$	− 18.6571i	− 0.664632i
$789$	−11.4577	−0.407905
$790$	−45.8528	−1.63137
$791$	− 2.06292i	− 0.0733489i
$792$	0.137063	0.00487033
$793$	0	0
$794$	−20.8358	−0.739435
$795$	− 5.77777i	− 0.204917i
$796$	7.66248	0.271589
$797$	45.8689	1.62476	0.812380	−	0.583128i	$-0.198172\pi$
$797$	45.8689	1.62476	0.812380	+	0.583128i	$0.198172\pi$
$798$	23.4034i	0.828472i
$799$	− 27.9517i	− 0.988859i
$800$	4.97823i	0.176007i
$801$	− 17.0858i	− 0.603695i
$802$	5.95646	0.210330
$803$	0.318404	0.0112362
$804$	− 4.71379i	− 0.166243i
$805$	90.3779	3.18540
$806$	0	0
$807$	−22.3666	−0.787341
$808$	9.18598i	0.323162i
$809$	38.1414	1.34098	0.670490	−	0.741919i	$-0.266084\pi$
$809$	38.1414	1.34098	0.670490	+	0.741919i	$0.266084\pi$
$810$	−3.15883	−0.110990
$811$	46.6983i	1.63980i	0.572509	+	0.819899i	$0.305970\pi$
$811$	46.6983i	1.63980i	−0.572509	+	0.819899i	$0.694030\pi$
$812$	3.99223i	0.140100i
$813$	3.87263i	0.135819i
$814$	1.60388i	0.0562158i
$815$	−25.3319	−0.887337
$816$	−5.60388	−0.196175
$817$	− 10.4638i	− 0.366083i
$818$	−1.80194	−0.0630033
$819$	0	0
$820$	13.5013	0.471484
$821$	32.6950i	1.14106i	0.821276	+	0.570532i	$0.193263\pi$
$821$	32.6950i	1.14106i	−0.821276	+	0.570532i	$0.806737\pi$
$822$	4.00000	0.139516
$823$	21.6799	0.755715	0.377858	−	0.925864i	$-0.376661\pi$
$823$	21.6799	0.755715	0.377858	+	0.925864i	$0.376661\pi$
$824$	− 0.225209i	− 0.00784554i
$825$	− 0.682333i	− 0.0237558i
$826$	27.6819i	0.963175i
$827$	13.9172i	0.483950i	0.970283	+	0.241975i	$0.0777951\pi$
$827$	13.9172i	0.483950i	−0.970283	+	0.241975i	$0.922205\pi$
$828$	−6.09783	−0.211914
$829$	16.4047	0.569760	0.284880	−	0.958563i	$-0.408046\pi$
$829$	16.4047	0.569760	0.284880	+	0.958563i	$0.408046\pi$
$830$	31.1342i	1.08068i
$831$	28.7090	0.995904
$832$	0	0
$833$	−84.1426	−2.91537
$834$	− 13.6582i	− 0.472944i
$835$	53.9711	1.86775
$836$	0.683661	0.0236449
$837$	− 6.23490i	− 0.215510i
$838$	28.4499i	0.982787i
$839$	− 11.6146i	− 0.400982i	−0.979696	−	0.200491i	$-0.935746\pi$
$839$	− 11.6146i	− 0.400982i	0.979696	−	0.200491i	$-0.0642537\pi$
$840$	− 14.8213i	− 0.511384i
$841$	−28.2760	−0.975036
$842$	13.9323	0.480139
$843$	− 29.0858i	− 1.00177i
$844$	−11.1642	−0.384288
$845$	0	0
$846$	−4.98792	−0.171488
$847$	51.5241i	1.77039i
$848$	−1.82908	−0.0628110
$849$	13.7560	0.472105
$850$	27.8974i	0.956872i
$851$	− 71.3551i	− 2.44602i
$852$	− 0.0978347i	− 0.00335176i
$853$	− 26.2983i	− 0.900436i	−0.892919	−	0.450218i	$-0.851346\pi$
$853$	− 26.2983i	− 0.900436i	0.892919	−	0.450218i	$-0.148654\pi$
$854$	20.6267	0.705832
$855$	−15.7560	−0.538844
$856$	11.2838i	0.385673i
$857$	48.6305	1.66119	0.830594	−	0.556879i	$-0.188001\pi$
$857$	48.6305	1.66119	0.830594	+	0.556879i	$0.188001\pi$
$858$	0	0
$859$	33.6185	1.14705	0.573524	−	0.819189i	$-0.305576\pi$
$859$	33.6185	1.14705	0.573524	+	0.819189i	$0.305576\pi$
$860$	6.62671i	0.225969i
$861$	−20.0543	−0.683449
$862$	−15.9022	−0.541630
$863$	− 5.78879i	− 0.197053i	−0.995134	−	0.0985264i	$-0.968587\pi$
$863$	− 5.78879i	− 0.197053i	0.995134	−	0.0985264i	$-0.0314129\pi$
$864$	1.00000i	0.0340207i
$865$	− 48.4717i	− 1.64809i
$866$	4.77718i	0.162335i
$867$	−14.4034	−0.489166
$868$	29.2543	0.992955
$869$	− 1.98957i	− 0.0674917i
$870$	−2.68771	−0.0911219
$871$	0	0
$872$	0.195669	0.00662620
$873$	2.12737i	0.0720007i
$874$	−30.4155	−1.02882
$875$	0.322664	0.0109080
$876$	2.32304i	0.0784884i
$877$	9.50604i	0.320996i	0.987036	+	0.160498i	$0.0513100\pi$
$877$	9.50604i	0.320996i	−0.987036	+	0.160498i	$0.948690\pi$
$878$	− 33.6316i	− 1.13501i
$879$	27.7362i	0.935517i
$880$	−0.432960	−0.0145951
$881$	46.7875	1.57631	0.788155	−	0.615477i	$-0.211037\pi$
$881$	46.7875	1.57631	0.788155	+	0.615477i	$0.211037\pi$
$882$	15.0151i	0.505584i
$883$	−3.03146	−0.102017	−0.0510084	−	0.998698i	$-0.516244\pi$
$883$	−3.03146	−0.102017	−0.0510084	+	0.998698i	$0.516244\pi$
$884$	0	0
$885$	−18.6364	−0.626456
$886$	35.3749i	1.18844i
$887$	37.0180	1.24294	0.621472	−	0.783436i	$-0.286535\pi$
$887$	37.0180	1.24294	0.621472	+	0.783436i	$0.286535\pi$
$888$	−11.7017	−0.392684
$889$	36.9385i	1.23888i
$890$	53.9711i	1.80911i
$891$	− 0.137063i	− 0.00459179i
$892$	24.6353i	0.824852i
$893$	−24.8793	−0.832555
$894$	−16.0586	−0.537080
$895$	1.65365i	0.0552753i
$896$	−4.69202	−0.156749
$897$	0	0
$898$	−18.0629	−0.602767
$899$	− 5.30499i	− 0.176931i
$900$	4.97823	0.165941
$901$	−10.2500	−0.341476
$902$	0.585826i	0.0195059i
$903$	− 9.84309i	− 0.327557i
$904$	− 0.439665i	− 0.0146230i
$905$	28.0823i	0.933487i
$906$	−21.8823	−0.726991
$907$	−19.0965	−0.634089	−0.317045	−	0.948411i	$-0.602690\pi$
$907$	−19.0965	−0.634089	−0.317045	+	0.948411i	$0.602690\pi$
$908$	− 7.47650i	− 0.248116i
$909$	9.18598	0.304680
$910$	0	0
$911$	−31.3142	−1.03749	−0.518743	−	0.854930i	$-0.673600\pi$
$911$	−31.3142	−1.03749	−0.518743	+	0.854930i	$0.673600\pi$
$912$	4.98792i	0.165166i
$913$	−1.35093	−0.0447092
$914$	15.4668	0.511597
$915$	13.8866i	0.459078i
$916$	19.2271i	0.635282i
$917$	− 2.91531i	− 0.0962721i
$918$	5.60388i	0.184955i
$919$	30.3967	1.00270	0.501348	−	0.865246i	$-0.332838\pi$
$919$	30.3967	1.00270	0.501348	+	0.865246i	$0.332838\pi$
$920$	19.2620	0.635051
$921$	− 12.4590i	− 0.410539i
$922$	18.8092	0.619449
$923$	0	0
$924$	0.643104	0.0211566
$925$	58.2538i	1.91537i
$926$	−15.8431	−0.520636
$927$	−0.225209	−0.00739685
$928$	0.850855i	0.0279307i
$929$	− 40.5810i	− 1.33142i	−0.746210	−	0.665710i	$-0.768129\pi$
$929$	− 40.5810i	− 1.33142i	0.746210	−	0.665710i	$-0.231871\pi$
$930$	19.6950i	0.645825i
$931$	74.8939i	2.45455i
$932$	3.70171	0.121254
$933$	−6.09783	−0.199634
$934$	22.0006i	0.719881i
$935$	−2.42626	−0.0793470
$936$	0	0
$937$	−18.7047	−0.611056	−0.305528	−	0.952183i	$-0.598833\pi$
$937$	−18.7047	−0.611056	−0.305528	+	0.952183i	$0.598833\pi$
$938$	− 22.1172i	− 0.722153i
$939$	12.7385	0.415707
$940$	15.7560	0.513904
$941$	− 4.04998i	− 0.132026i	−0.997819	−	0.0660128i	$-0.978972\pi$
$941$	− 4.04998i	− 0.132026i	0.997819	−	0.0660128i	$-0.0210278\pi$
$942$	− 7.90217i	− 0.257466i
$943$	− 26.0629i	− 0.848725i
$944$	5.89977i	0.192021i
$945$	−14.8213	−0.482137
$946$	−0.287536	−0.00934861
$947$	− 11.5356i	− 0.374856i	−0.982278	−	0.187428i	$-0.939985\pi$
$947$	− 11.5356i	− 0.374856i	0.982278	−	0.187428i	$-0.0600151\pi$
$948$	14.5157	0.471449
$949$	0	0
$950$	24.8310	0.805624
$951$	− 14.8140i	− 0.480377i
$952$	−26.2935	−0.852177
$953$	9.57109	0.310038	0.155019	−	0.987911i	$-0.450456\pi$
$953$	9.57109	0.310038	0.155019	+	0.987911i	$0.450456\pi$
$954$	1.82908i	0.0592188i
$955$	22.2112i	0.718738i
$956$	8.51334i	0.275341i
$957$	− 0.116621i	− 0.00376982i
$958$	−21.3491	−0.689759
$959$	18.7681	0.606053
$960$	− 3.15883i	− 0.101951i
$961$	−7.87395	−0.253998
$962$	0	0
$963$	11.2838	0.363616
$964$	− 17.4330i	− 0.561478i
$965$	56.0883	1.80555
$966$	−28.6112	−0.920549
$967$	− 61.2073i	− 1.96829i	−0.177357	−	0.984147i	$-0.556755\pi$
$967$	− 61.2073i	− 1.96829i	0.177357	−	0.984147i	$-0.443245\pi$
$968$	10.9812i	0.352950i
$969$	27.9517i	0.897937i
$970$	− 6.72002i	− 0.215767i
$971$	−28.8595	−0.926145	−0.463072	−	0.886320i	$-0.653253\pi$
$971$	−28.8595	−0.926145	−0.463072	+	0.886320i	$0.653253\pi$
$972$	1.00000	0.0320750
$973$	− 64.0844i	− 2.05445i
$974$	31.6394	1.01379
$975$	0	0
$976$	4.39612	0.140717
$977$	− 46.6305i	− 1.49184i	−0.666034	−	0.745922i	$-0.732009\pi$
$977$	− 46.6305i	− 1.49184i	0.666034	−	0.745922i	$-0.267991\pi$
$978$	8.01938	0.256431
$979$	−2.34183	−0.0748452
$980$	− 47.4301i	− 1.51510i
$981$	− 0.195669i	− 0.00624724i
$982$	− 1.39911i	− 0.0446473i
$983$	55.6883i	1.77618i	0.459669	+	0.888090i	$0.347968\pi$
$983$	55.6883i	1.77618i	−0.459669	+	0.888090i	$0.652032\pi$
$984$	−4.27413	−0.136254
$985$	58.9347	1.87782
$986$	4.76809i	0.151847i
$987$	−23.4034	−0.744939
$988$	0	0
$989$	12.7922	0.406770
$990$	0.432960i	0.0137604i
$991$	−9.32172	−0.296114	−0.148057	−	0.988979i	$-0.547302\pi$
$991$	−9.32172	−0.296114	−0.148057	+	0.988979i	$0.547302\pi$
$992$	6.23490	0.197958
$993$	− 7.70171i	− 0.244406i
$994$	− 0.459042i	− 0.0145599i
$995$	24.2045i	0.767334i
$996$	− 9.85623i	− 0.312307i
$997$	46.0253	1.45764	0.728819	−	0.684707i	$-0.240070\pi$
$997$	46.0253	1.45764	0.728819	+	0.684707i	$0.240070\pi$
$998$	0	0
$999$	11.7017i	0.370226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.b.f.337.1		6
3.2	odd	2		3042.2.b.o.1351.6		6
13.2	odd	12		1014.2.e.n.529.1		6
13.3	even	3		1014.2.i.h.823.4		12
13.4	even	6		1014.2.i.h.361.6		12
13.5	odd	4		1014.2.a.l.1.1	✓	3
13.6	odd	12		1014.2.e.n.991.1		6
13.7	odd	12		1014.2.e.l.991.3		6
13.8	odd	4		1014.2.a.n.1.3	yes	3
13.9	even	3		1014.2.i.h.361.1		12
13.10	even	6		1014.2.i.h.823.3		12
13.11	odd	12		1014.2.e.l.529.3		6
13.12	even	2	inner	1014.2.b.f.337.6		6
39.5	even	4		3042.2.a.bh.1.3		3
39.8	even	4		3042.2.a.ba.1.1		3
39.38	odd	2		3042.2.b.o.1351.1		6
52.31	even	4		8112.2.a.cj.1.1		3
52.47	even	4		8112.2.a.cm.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.l.1.1	✓	3	13.5	odd	4
1014.2.a.n.1.3	yes	3	13.8	odd	4
1014.2.b.f.337.1		6	1.1	even	1	trivial
1014.2.b.f.337.6		6	13.12	even	2	inner
1014.2.e.l.529.3		6	13.11	odd	12
1014.2.e.l.991.3		6	13.7	odd	12
1014.2.e.n.529.1		6	13.2	odd	12
1014.2.e.n.991.1		6	13.6	odd	12
1014.2.i.h.361.1		12	13.9	even	3
1014.2.i.h.361.6		12	13.4	even	6
1014.2.i.h.823.3		12	13.10	even	6
1014.2.i.h.823.4		12	13.3	even	3
3042.2.a.ba.1.1		3	39.8	even	4
3042.2.a.bh.1.3		3	39.5	even	4
3042.2.b.o.1351.1		6	39.38	odd	2
3042.2.b.o.1351.6		6	3.2	odd	2
8112.2.a.cj.1.1		3	52.31	even	4
8112.2.a.cm.1.3		3	52.47	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.15883i q^{5} +1.00000i q^{6} +4.69202i q^{7} +1.00000i q^{8} +1.00000 q^{9} -3.15883 q^{10} -0.137063i q^{11} +1.00000 q^{12} +4.69202 q^{14} +3.15883i q^{15} +1.00000 q^{16} +5.60388 q^{17} -1.00000i q^{18} -4.98792i q^{19} +3.15883i q^{20} -4.69202i q^{21} -0.137063 q^{22} +6.09783 q^{23} -1.00000i q^{24} -4.97823 q^{25} -1.00000 q^{27} -4.69202i q^{28} -0.850855 q^{29} +3.15883 q^{30} +6.23490i q^{31} -1.00000i q^{32} +0.137063i q^{33} -5.60388i q^{34} +14.8213 q^{35} -1.00000 q^{36} -11.7017i q^{37} -4.98792 q^{38} +3.15883 q^{40} -4.27413i q^{41} -4.69202 q^{42} +2.09783 q^{43} +0.137063i q^{44} -3.15883i q^{45} -6.09783i q^{46} -4.98792i q^{47} -1.00000 q^{48} -15.0151 q^{49} +4.97823i q^{50} -5.60388 q^{51} -1.82908 q^{53} +1.00000i q^{54} -0.432960 q^{55} -4.69202 q^{56} +4.98792i q^{57} +0.850855i q^{58} +5.89977i q^{59} -3.15883i q^{60} +4.39612 q^{61} +6.23490 q^{62} +4.69202i q^{63} -1.00000 q^{64} +0.137063 q^{66} -4.71379i q^{67} -5.60388 q^{68} -6.09783 q^{69} -14.8213i q^{70} -0.0978347i q^{71} +1.00000i q^{72} +2.32304i q^{73} -11.7017 q^{74} +4.97823 q^{75} +4.98792i q^{76} +0.643104 q^{77} +14.5157 q^{79} -3.15883i q^{80} +1.00000 q^{81} -4.27413 q^{82} -9.85623i q^{83} +4.69202i q^{84} -17.7017i q^{85} -2.09783i q^{86} +0.850855 q^{87} +0.137063 q^{88} -17.0858i q^{89} -3.15883 q^{90} -6.09783 q^{92} -6.23490i q^{93} -4.98792 q^{94} -15.7560 q^{95} +1.00000i q^{96} +2.12737i q^{97} +15.0151i q^{98} -0.137063i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{3} - 6 q^{4} + 6 q^{9} - 2 q^{10} + 6 q^{12} + 18 q^{14} + 6 q^{16} + 16 q^{17} + 10 q^{22} - 36 q^{25} - 6 q^{27} + 22 q^{29} + 2 q^{30} - 8 q^{35} - 6 q^{36} + 8 q^{38} + 2 q^{40} - 18 q^{42}+ \cdots - 16 q^{95}+O(q^{100}) \) 6 * q - 6 * q^3 - 6 * q^4 + 6 * q^9 - 2 * q^10 + 6 * q^12 + 18 * q^14 + 6 * q^16 + 16 * q^17 + 10 * q^22 - 36 * q^25 - 6 * q^27 + 22 * q^29 + 2 * q^30 - 8 * q^35 - 6 * q^36 + 8 * q^38 + 2 * q^40 - 18 * q^42 - 24 * q^43 - 6 * q^48 - 40 * q^49 - 16 * q^51 + 10 * q^53 + 36 * q^55 - 18 * q^56 + 44 * q^61 - 10 * q^62 - 6 * q^64 - 10 * q^66 - 16 * q^68 - 16 * q^74 + 36 * q^75 + 12 * q^77 + 62 * q^79 + 6 * q^81 - 4 * q^82 - 22 * q^87 - 10 * q^88 - 2 * q^90 + 8 * q^94 - 16 * q^95

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