LMFDB - Embedded newform 503.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(1,503)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("503.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.a (trivial)

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:	yes
Analytic conductor:	$4.01647522167$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 $ x^10 - 2x^9 - 9x^8 + 14x^7 + 27x^6 - 27x^5 - 34x^4 + 14x^3 + 17x^2 + x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.07636$ of defining polynomial
Character	$\chi$	$=$	503.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.37178 q^{2} +0.0763625 q^{3} -0.118218 q^{4} +1.17276 q^{5} -0.104753 q^{6} +0.469303 q^{7} +2.90573 q^{8} -2.99417 q^{9} +O(q^{10})$	\(q-1.37178 q^{2} +0.0763625 q^{3} -0.118218 q^{4} +1.17276 q^{5} -0.104753 q^{6} +0.469303 q^{7} +2.90573 q^{8} -2.99417 q^{9} -1.60876 q^{10} -5.74596 q^{11} -0.00902740 q^{12} -1.85873 q^{13} -0.643780 q^{14} +0.0895546 q^{15} -3.74959 q^{16} +5.22916 q^{17} +4.10734 q^{18} +2.12602 q^{19} -0.138641 q^{20} +0.0358371 q^{21} +7.88220 q^{22} +0.171951 q^{23} +0.221889 q^{24} -3.62464 q^{25} +2.54977 q^{26} -0.457730 q^{27} -0.0554799 q^{28} -6.19149 q^{29} -0.122849 q^{30} -0.396234 q^{31} -0.667846 q^{32} -0.438776 q^{33} -7.17326 q^{34} +0.550377 q^{35} +0.353964 q^{36} -8.17999 q^{37} -2.91644 q^{38} -0.141937 q^{39} +3.40771 q^{40} -12.4282 q^{41} -0.0491607 q^{42} -4.97920 q^{43} +0.679275 q^{44} -3.51143 q^{45} -0.235879 q^{46} -0.521599 q^{47} -0.286328 q^{48} -6.77976 q^{49} +4.97222 q^{50} +0.399312 q^{51} +0.219735 q^{52} +8.76106 q^{53} +0.627905 q^{54} -6.73861 q^{55} +1.36367 q^{56} +0.162349 q^{57} +8.49336 q^{58} +3.35297 q^{59} -0.0105869 q^{60} -5.38243 q^{61} +0.543546 q^{62} -1.40517 q^{63} +8.41532 q^{64} -2.17983 q^{65} +0.601905 q^{66} +8.42823 q^{67} -0.618179 q^{68} +0.0131306 q^{69} -0.754997 q^{70} +7.47643 q^{71} -8.70025 q^{72} -4.60009 q^{73} +11.2212 q^{74} -0.276787 q^{75} -0.251334 q^{76} -2.69660 q^{77} +0.194707 q^{78} -17.1992 q^{79} -4.39735 q^{80} +8.94755 q^{81} +17.0487 q^{82} +5.97721 q^{83} -0.00423658 q^{84} +6.13253 q^{85} +6.83038 q^{86} -0.472798 q^{87} -16.6962 q^{88} -4.25595 q^{89} +4.81691 q^{90} -0.872306 q^{91} -0.0203277 q^{92} -0.0302574 q^{93} +0.715520 q^{94} +2.49331 q^{95} -0.0509984 q^{96} -2.64532 q^{97} +9.30034 q^{98} +17.2044 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9} - 4 q^{10} - 3 q^{11} - 7 q^{12} - 18 q^{13} + q^{14} - 2 q^{15} - 4 q^{16} - 11 q^{17} - q^{18} - 3 q^{20} + q^{21} - 18 q^{22} - 2 q^{23} + 10 q^{24} - 27 q^{25} + 11 q^{26} - 2 q^{27} - 22 q^{28} - 9 q^{29} + 12 q^{30} - 22 q^{31} - 10 q^{32} - 10 q^{33} - 10 q^{34} - 6 q^{35} + 2 q^{36} - 35 q^{37} + 2 q^{38} + 8 q^{39} - 19 q^{40} - 4 q^{41} + 4 q^{42} - 20 q^{43} + 9 q^{44} + 2 q^{45} - q^{46} + 7 q^{47} - 27 q^{49} + 16 q^{50} + 9 q^{51} - 7 q^{52} - 24 q^{53} + 17 q^{54} - 11 q^{55} + 12 q^{56} - 23 q^{57} + 2 q^{58} + 17 q^{59} - 4 q^{61} + 8 q^{62} + 10 q^{63} + 3 q^{64} - 16 q^{65} + 46 q^{66} - 6 q^{67} + 28 q^{68} - 2 q^{69} + 26 q^{70} - q^{71} - q^{72} - 31 q^{73} + 11 q^{74} + 30 q^{75} + 20 q^{76} + 3 q^{77} + 11 q^{78} - 10 q^{79} + 24 q^{80} - 6 q^{81} - 9 q^{82} + 22 q^{83} + 22 q^{84} - 6 q^{85} + 38 q^{86} + 25 q^{87} - 3 q^{88} + q^{89} + 2 q^{90} + 10 q^{91} + 27 q^{92} - 6 q^{93} + 33 q^{94} + 39 q^{95} + 46 q^{96} - 57 q^{97} + 40 q^{98} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9 - 4 * q^10 - 3 * q^11 - 7 * q^12 - 18 * q^13 + q^14 - 2 * q^15 - 4 * q^16 - 11 * q^17 - q^18 - 3 * q^20 + q^21 - 18 * q^22 - 2 * q^23 + 10 * q^24 - 27 * q^25 + 11 * q^26 - 2 * q^27 - 22 * q^28 - 9 * q^29 + 12 * q^30 - 22 * q^31 - 10 * q^32 - 10 * q^33 - 10 * q^34 - 6 * q^35 + 2 * q^36 - 35 * q^37 + 2 * q^38 + 8 * q^39 - 19 * q^40 - 4 * q^41 + 4 * q^42 - 20 * q^43 + 9 * q^44 + 2 * q^45 - q^46 + 7 * q^47 - 27 * q^49 + 16 * q^50 + 9 * q^51 - 7 * q^52 - 24 * q^53 + 17 * q^54 - 11 * q^55 + 12 * q^56 - 23 * q^57 + 2 * q^58 + 17 * q^59 - 4 * q^61 + 8 * q^62 + 10 * q^63 + 3 * q^64 - 16 * q^65 + 46 * q^66 - 6 * q^67 + 28 * q^68 - 2 * q^69 + 26 * q^70 - q^71 - q^72 - 31 * q^73 + 11 * q^74 + 30 * q^75 + 20 * q^76 + 3 * q^77 + 11 * q^78 - 10 * q^79 + 24 * q^80 - 6 * q^81 - 9 * q^82 + 22 * q^83 + 22 * q^84 - 6 * q^85 + 38 * q^86 + 25 * q^87 - 3 * q^88 + q^89 + 2 * q^90 + 10 * q^91 + 27 * q^92 - 6 * q^93 + 33 * q^94 + 39 * q^95 + 46 * q^96 - 57 * q^97 + 40 * q^98 + 35 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.37178	−0.969995	−0.484998	−	0.874515i	$-0.661180\pi$
$2$	−1.37178	−0.969995	−0.484998	+	0.874515i	$0.661180\pi$
$3$	0.0763625	0.0440879	0.0220440	−	0.999757i	$-0.492983\pi$
$3$	0.0763625	0.0440879	0.0220440	+	0.999757i	$0.492983\pi$
$4$	−0.118218	−0.0591089
$5$	1.17276	0.524472	0.262236	−	0.965004i	$-0.415540\pi$
$5$	1.17276	0.524472	0.262236	+	0.965004i	$0.415540\pi$
$6$	−0.104753	−0.0427651
$7$	0.469303	0.177380	0.0886899	−	0.996059i	$-0.471732\pi$
$7$	0.469303	0.177380	0.0886899	+	0.996059i	$0.471732\pi$
$8$	2.90573	1.02733
$9$	−2.99417	−0.998056
$10$	−1.60876	−0.508736
$11$	−5.74596	−1.73247	−0.866237	−	0.499634i	$-0.833468\pi$
$11$	−5.74596	−1.73247	−0.866237	+	0.499634i	$0.833468\pi$
$12$	−0.00902740	−0.00260599
$13$	−1.85873	−0.515518	−0.257759	−	0.966209i	$-0.582984\pi$
$13$	−1.85873	−0.515518	−0.257759	+	0.966209i	$0.582984\pi$
$14$	−0.643780	−0.172058
$15$	0.0895546	0.0231229
$16$	−3.74959	−0.937397
$17$	5.22916	1.26826	0.634129	−	0.773228i	$-0.281359\pi$
$17$	5.22916	1.26826	0.634129	+	0.773228i	$0.281359\pi$
$18$	4.10734	0.968110
$19$	2.12602	0.487743	0.243872	−	0.969808i	$-0.421582\pi$
$19$	2.12602	0.487743	0.243872	+	0.969808i	$0.421582\pi$
$20$	−0.138641	−0.0310010
$21$	0.0358371	0.00782030
$22$	7.88220	1.68049
$23$	0.171951	0.0358543	0.0179271	−	0.999839i	$-0.494293\pi$
$23$	0.171951	0.0358543	0.0179271	+	0.999839i	$0.494293\pi$
$24$	0.221889	0.0452929
$25$	−3.62464	−0.724929
$26$	2.54977	0.500050
$27$	−0.457730	−0.0880902
$28$	−0.0554799	−0.0104847
$29$	−6.19149	−1.14973	−0.574865	−	0.818248i	$-0.694946\pi$
$29$	−6.19149	−1.14973	−0.574865	+	0.818248i	$0.694946\pi$
$30$	−0.122849	−0.0224291
$31$	−0.396234	−0.0711658	−0.0355829	−	0.999367i	$-0.511329\pi$
$31$	−0.396234	−0.0711658	−0.0355829	+	0.999367i	$0.511329\pi$
$32$	−0.667846	−0.118060
$33$	−0.438776	−0.0763812
$34$	−7.17326	−1.23020
$35$	0.550377	0.0930307
$36$	0.353964	0.0589940
$37$	−8.17999	−1.34478	−0.672391	−	0.740196i	$-0.734733\pi$
$37$	−8.17999	−1.34478	−0.672391	+	0.740196i	$0.734733\pi$
$38$	−2.91644	−0.473109
$39$	−0.141937	−0.0227281
$40$	3.40771	0.538807
$41$	−12.4282	−1.94095	−0.970477	−	0.241193i	$-0.922461\pi$
$41$	−12.4282	−1.94095	−0.970477	+	0.241193i	$0.922461\pi$
$42$	−0.0491607	−0.00758566
$43$	−4.97920	−0.759321	−0.379661	−	0.925126i	$-0.623959\pi$
$43$	−4.97920	−0.759321	−0.379661	+	0.925126i	$0.623959\pi$
$44$	0.679275	0.102405
$45$	−3.51143	−0.523453
$46$	−0.235879	−0.0347785
$47$	−0.521599	−0.0760831	−0.0380415	−	0.999276i	$-0.512112\pi$
$47$	−0.521599	−0.0760831	−0.0380415	+	0.999276i	$0.512112\pi$
$48$	−0.286328	−0.0413279
$49$	−6.77976	−0.968536
$50$	4.97222	0.703178
$51$	0.399312	0.0559148
$52$	0.219735	0.0304717
$53$	8.76106	1.20342	0.601712	−	0.798713i	$-0.294486\pi$
$53$	8.76106	1.20342	0.601712	+	0.798713i	$0.294486\pi$
$54$	0.627905	0.0854470
$55$	−6.73861	−0.908634
$56$	1.36367	0.182228
$57$	0.162349	0.0215036
$58$	8.49336	1.11523
$59$	3.35297	0.436519	0.218260	−	0.975891i	$-0.429962\pi$
$59$	3.35297	0.436519	0.218260	+	0.975891i	$0.429962\pi$
$60$	−0.0105869	−0.00136677
$61$	−5.38243	−0.689150	−0.344575	−	0.938759i	$-0.611977\pi$
$61$	−5.38243	−0.689150	−0.344575	+	0.938759i	$0.611977\pi$
$62$	0.543546	0.0690305
$63$	−1.40517	−0.177035
$64$	8.41532	1.05191
$65$	−2.17983	−0.270375
$66$	0.601905	0.0740894
$67$	8.42823	1.02967	0.514836	−	0.857289i	$-0.327853\pi$
$67$	8.42823	1.02967	0.514836	+	0.857289i	$0.327853\pi$
$68$	−0.618179	−0.0749653
$69$	0.0131306	0.00158074
$70$	−0.754997	−0.0902394
$71$	7.47643	0.887289	0.443644	−	0.896203i	$-0.353685\pi$
$71$	7.47643	0.887289	0.443644	+	0.896203i	$0.353685\pi$
$72$	−8.70025	−1.02533
$73$	−4.60009	−0.538400	−0.269200	−	0.963084i	$-0.586759\pi$
$73$	−4.60009	−0.538400	−0.269200	+	0.963084i	$0.586759\pi$
$74$	11.2212	1.30443
$75$	−0.276787	−0.0319606
$76$	−0.251334	−0.0288299
$77$	−2.69660	−0.307306
$78$	0.194707	0.0220462
$79$	−17.1992	−1.93506	−0.967530	−	0.252758i	$-0.918662\pi$
$79$	−17.1992	−1.93506	−0.967530	+	0.252758i	$0.918662\pi$
$80$	−4.39735	−0.491639
$81$	8.94755	0.994173
$82$	17.0487	1.88272
$83$	5.97721	0.656084	0.328042	−	0.944663i	$-0.393611\pi$
$83$	5.97721	0.656084	0.328042	+	0.944663i	$0.393611\pi$
$84$	−0.00423658	−0.000462249 0
$85$	6.13253	0.665166
$86$	6.83038	0.736538
$87$	−0.472798	−0.0506892
$88$	−16.6962	−1.77982
$89$	−4.25595	−0.451130	−0.225565	−	0.974228i	$-0.572423\pi$
$89$	−4.25595	−0.451130	−0.225565	+	0.974228i	$0.572423\pi$
$90$	4.81691	0.507747
$91$	−0.872306	−0.0914425
$92$	−0.0203277	−0.00211930
$93$	−0.0302574	−0.00313755
$94$	0.715520	0.0738002
$95$	2.49331	0.255808
$96$	−0.0509984	−0.00520501
$97$	−2.64532	−0.268592	−0.134296	−	0.990941i	$-0.542877\pi$
$97$	−2.64532	−0.268592	−0.134296	+	0.990941i	$0.542877\pi$
$98$	9.30034	0.939476
$99$	17.2044	1.72911
$100$	0.428497	0.0428497
$101$	6.39045	0.635873	0.317937	−	0.948112i	$-0.397010\pi$
$101$	6.39045	0.635873	0.317937	+	0.948112i	$0.397010\pi$
$102$	−0.547768	−0.0542371
$103$	−16.6014	−1.63578	−0.817890	−	0.575375i	$-0.804856\pi$
$103$	−16.6014	−1.63578	−0.817890	+	0.575375i	$0.804856\pi$
$104$	−5.40096	−0.529608
$105$	0.0420282	0.00410153
$106$	−12.0182	−1.16732
$107$	9.15760	0.885299	0.442649	−	0.896695i	$-0.354039\pi$
$107$	9.15760	0.885299	0.442649	+	0.896695i	$0.354039\pi$
$108$	0.0541118	0.00520691
$109$	6.51891	0.624398	0.312199	−	0.950017i	$-0.398934\pi$
$109$	6.51891	0.624398	0.312199	+	0.950017i	$0.398934\pi$
$110$	9.24390	0.881371
$111$	−0.624645	−0.0592887
$112$	−1.75969	−0.166275
$113$	1.36694	0.128591	0.0642954	−	0.997931i	$-0.479520\pi$
$113$	1.36694	0.128591	0.0642954	+	0.997931i	$0.479520\pi$
$114$	−0.222707	−0.0208584
$115$	0.201656	0.0188046
$116$	0.731944	0.0679593
$117$	5.56535	0.514516
$118$	−4.59954	−0.423422
$119$	2.45406	0.224963
$120$	0.260221	0.0237549
$121$	22.0161	2.00146
$122$	7.38352	0.668473
$123$	−0.949047	−0.0855726
$124$	0.0468419	0.00420653
$125$	−10.1146	−0.904677
$126$	1.92759	0.171723
$127$	6.77469	0.601157	0.300578	−	0.953757i	$-0.402820\pi$
$127$	6.77469	0.601157	0.300578	+	0.953757i	$0.402820\pi$
$128$	−10.2083	−0.902293
$129$	−0.380225	−0.0334769
$130$	2.99025	0.262263
$131$	16.6839	1.45768	0.728838	−	0.684687i	$-0.240061\pi$
$131$	16.6839	1.45768	0.728838	+	0.684687i	$0.240061\pi$
$132$	0.0518711	0.00451480
$133$	0.997748	0.0865158
$134$	−11.5617	−0.998777
$135$	−0.536805	−0.0462008
$136$	15.1945	1.30292
$137$	13.0662	1.11632	0.558162	−	0.829732i	$-0.311507\pi$
$137$	13.0662	1.11632	0.558162	+	0.829732i	$0.311507\pi$
$138$	−0.0180123	−0.00153331
$139$	−10.8468	−0.920017	−0.460008	−	0.887915i	$-0.652154\pi$
$139$	−10.8468	−0.920017	−0.460008	+	0.887915i	$0.652154\pi$
$140$	−0.0650644	−0.00549894
$141$	−0.0398306	−0.00335434
$142$	−10.2560	−0.860666
$143$	10.6802	0.893122
$144$	11.2269	0.935575
$145$	−7.26110	−0.603002
$146$	6.31032	0.522245
$147$	−0.517719	−0.0427008
$148$	0.967020	0.0794886
$149$	0.0210826	0.00172716	0.000863578	−	1.00000i	$-0.499725\pi$
$149$	0.0210826	0.00172716	0.000863578		1.00000i	$0.499725\pi$
$150$	0.379691	0.0310016
$151$	15.1704	1.23455	0.617276	−	0.786746i	$-0.288236\pi$
$151$	15.1704	1.23455	0.617276	+	0.786746i	$0.288236\pi$
$152$	6.17765	0.501074
$153$	−15.6570	−1.26579
$154$	3.69914	0.298085
$155$	−0.464686	−0.0373245
$156$	0.0167795	0.00134343
$157$	11.1437	0.889367	0.444684	−	0.895688i	$-0.353316\pi$
$157$	11.1437	0.889367	0.444684	+	0.895688i	$0.353316\pi$
$158$	23.5935	1.87700
$159$	0.669016	0.0530565
$160$	−0.783221	−0.0619190
$161$	0.0806970	0.00635982
$162$	−12.2741	−0.964343
$163$	−10.3388	−0.809797	−0.404899	−	0.914362i	$-0.632693\pi$
$163$	−10.3388	−0.809797	−0.404899	+	0.914362i	$0.632693\pi$
$164$	1.46923	0.114728
$165$	−0.514578	−0.0400598
$166$	−8.19942	−0.636398
$167$	−15.6444	−1.21060	−0.605300	−	0.795998i	$-0.706947\pi$
$167$	−15.6444	−1.21060	−0.605300	+	0.795998i	$0.706947\pi$
$168$	0.104133	0.00803404
$169$	−9.54513	−0.734241
$170$	−8.41248	−0.645208
$171$	−6.36567	−0.486795
$172$	0.588630	0.0448826
$173$	−5.69316	−0.432843	−0.216422	−	0.976300i	$-0.569439\pi$
$173$	−5.69316	−0.432843	−0.216422	+	0.976300i	$0.569439\pi$
$174$	0.648575	0.0491683
$175$	−1.70105	−0.128588
$176$	21.5450	1.62402
$177$	0.256041	0.0192452
$178$	5.83823	0.437594
$179$	10.8571	0.811495	0.405748	−	0.913985i	$-0.367011\pi$
$179$	10.8571	0.811495	0.405748	+	0.913985i	$0.367011\pi$
$180$	0.415113	0.0309407
$181$	6.26595	0.465744	0.232872	−	0.972507i	$-0.425188\pi$
$181$	6.26595	0.465744	0.232872	+	0.972507i	$0.425188\pi$
$182$	1.19661	0.0886988
$183$	−0.411016	−0.0303832
$184$	0.499643	0.0368342
$185$	−9.59313	−0.705301
$186$	0.0415066	0.00304341
$187$	−30.0466	−2.19722
$188$	0.0616623	0.00449718
$189$	−0.214814	−0.0156254
$190$	−3.42027	−0.248132
$191$	8.26296	0.597887	0.298943	−	0.954271i	$-0.403366\pi$
$191$	8.26296	0.597887	0.298943	+	0.954271i	$0.403366\pi$
$192$	0.642615	0.0463767
$193$	−19.8469	−1.42861	−0.714306	−	0.699833i	$-0.753258\pi$
$193$	−19.8469	−1.42861	−0.714306	+	0.699833i	$0.753258\pi$
$194$	3.62880	0.260533
$195$	−0.166458	−0.0119203
$196$	0.801487	0.0572491
$197$	−4.24866	−0.302704	−0.151352	−	0.988480i	$-0.548363\pi$
$197$	−4.24866	−0.302704	−0.151352	+	0.988480i	$0.548363\pi$
$198$	−23.6006	−1.67723
$199$	4.63286	0.328415	0.164207	−	0.986426i	$-0.447493\pi$
$199$	4.63286	0.328415	0.164207	+	0.986426i	$0.447493\pi$
$200$	−10.5322	−0.744742
$201$	0.643601	0.0453961
$202$	−8.76630	−0.616794
$203$	−2.90568	−0.203939
$204$	−0.0472057	−0.00330506
$205$	−14.5752	−1.01798
$206$	22.7734	1.58670
$207$	−0.514850	−0.0357846
$208$	6.96947	0.483246
$209$	−12.2161	−0.845002
$210$	−0.0576535	−0.00397847
$211$	10.2699	0.707007	0.353503	−	0.935433i	$-0.384990\pi$
$211$	10.2699	0.707007	0.353503	+	0.935433i	$0.384990\pi$
$212$	−1.03571	−0.0711330
$213$	0.570919	0.0391187
$214$	−12.5622	−0.858736
$215$	−5.83939	−0.398243
$216$	−1.33004	−0.0904977
$217$	−0.185954	−0.0126234
$218$	−8.94251	−0.605663
$219$	−0.351275	−0.0237369
$220$	0.796624	0.0537083
$221$	−9.71958	−0.653810
$222$	0.856876	0.0575097
$223$	14.7887	0.990326	0.495163	−	0.868800i	$-0.335108\pi$
$223$	14.7887	0.990326	0.495163	+	0.868800i	$0.335108\pi$
$224$	−0.313422	−0.0209414
$225$	10.8528	0.723520
$226$	−1.87514	−0.124732
$227$	14.9154	0.989969	0.494984	−	0.868902i	$-0.335174\pi$
$227$	14.9154	0.989969	0.494984	+	0.868902i	$0.335174\pi$
$228$	−0.0191925	−0.00127105
$229$	−18.2488	−1.20592	−0.602959	−	0.797772i	$-0.706012\pi$
$229$	−18.2488	−1.20592	−0.602959	+	0.797772i	$0.706012\pi$
$230$	−0.276628	−0.0182403
$231$	−0.205919	−0.0135485
$232$	−17.9908	−1.18115
$233$	−16.6741	−1.09235	−0.546177	−	0.837670i	$-0.683918\pi$
$233$	−16.6741	−1.09235	−0.546177	+	0.837670i	$0.683918\pi$
$234$	−7.63443	−0.499079
$235$	−0.611708	−0.0399035
$236$	−0.396380	−0.0258022
$237$	−1.31337	−0.0853127
$238$	−3.36643	−0.218213
$239$	24.3691	1.57631	0.788153	−	0.615479i	$-0.211037\pi$
$239$	24.3691	1.57631	0.788153	+	0.615479i	$0.211037\pi$
$240$	−0.335793	−0.0216753
$241$	18.1071	1.16638	0.583190	−	0.812336i	$-0.301804\pi$
$241$	18.1071	1.16638	0.583190	+	0.812336i	$0.301804\pi$
$242$	−30.2013	−1.94141
$243$	2.05645	0.131921
$244$	0.636299	0.0407349
$245$	−7.95100	−0.507971
$246$	1.30188	0.0830051
$247$	−3.95170	−0.251441
$248$	−1.15135	−0.0731108
$249$	0.456435	0.0289254
$250$	13.8750	0.877533
$251$	26.9687	1.70225	0.851124	−	0.524965i	$-0.175922\pi$
$251$	26.9687	1.70225	0.851124	+	0.524965i	$0.175922\pi$
$252$	0.166116	0.0104643
$253$	−0.988024	−0.0621165
$254$	−9.29340	−0.583119
$255$	0.468295	0.0293258
$256$	−2.82712	−0.176695
$257$	20.3022	1.26642	0.633208	−	0.773982i	$-0.281738\pi$
$257$	20.3022	1.26642	0.633208	+	0.773982i	$0.281738\pi$
$258$	0.521585	0.0324724
$259$	−3.83889	−0.238537
$260$	0.257695	0.0159816
$261$	18.5384	1.14750
$262$	−22.8866	−1.41394
$263$	−12.0595	−0.743622	−0.371811	−	0.928309i	$-0.621263\pi$
$263$	−12.0595	−0.743622	−0.371811	+	0.928309i	$0.621263\pi$
$264$	−1.27497	−0.0784687
$265$	10.2746	0.631162
$266$	−1.36869	−0.0839199
$267$	−0.324995	−0.0198894
$268$	−0.996366	−0.0608628
$269$	−25.0120	−1.52501	−0.762506	−	0.646982i	$-0.776031\pi$
$269$	−25.0120	−1.52501	−0.762506	+	0.646982i	$0.776031\pi$
$270$	0.736379	0.0448146
$271$	−18.0354	−1.09557	−0.547787	−	0.836618i	$-0.684530\pi$
$271$	−18.0354	−1.09557	−0.547787	+	0.836618i	$0.684530\pi$
$272$	−19.6072	−1.18886
$273$	−0.0666115	−0.00403151
$274$	−17.9240	−1.08283
$275$	20.8271	1.25592
$276$	−0.00155227	−9.34357e−5 0
$277$	−29.3688	−1.76460	−0.882301	−	0.470686i	$-0.844006\pi$
$277$	−29.3688	−1.76460	−0.882301	+	0.470686i	$0.844006\pi$
$278$	14.8795	0.892412
$279$	1.18639	0.0710274
$280$	1.59925	0.0955733
$281$	12.0977	0.721686	0.360843	−	0.932626i	$-0.382489\pi$
$281$	12.0977	0.721686	0.360843	+	0.932626i	$0.382489\pi$
$282$	0.0546389	0.00325370
$283$	−8.04149	−0.478017	−0.239009	−	0.971017i	$-0.576822\pi$
$283$	−8.04149	−0.478017	−0.239009	+	0.971017i	$0.576822\pi$
$284$	−0.883846	−0.0524466
$285$	0.190395	0.0112780
$286$	−14.6509	−0.866324
$287$	−5.83257	−0.344286
$288$	1.99964	0.117830
$289$	10.3441	0.608477
$290$	9.96064	0.584909
$291$	−0.202003	−0.0118416
$292$	0.543812	0.0318242
$293$	−13.5236	−0.790056	−0.395028	−	0.918669i	$-0.629265\pi$
$293$	−13.5236	−0.790056	−0.395028	+	0.918669i	$0.629265\pi$
$294$	0.710197	0.0414195
$295$	3.93221	0.228942
$296$	−23.7688	−1.38154
$297$	2.63010	0.152614
$298$	−0.0289207	−0.00167533
$299$	−0.319610	−0.0184835
$300$	0.0327211	0.00188916
$301$	−2.33675	−0.134688
$302$	−20.8105	−1.19751
$303$	0.487991	0.0280343
$304$	−7.97171	−0.457209
$305$	−6.31228	−0.361440
$306$	21.4780	1.22781
$307$	3.60632	0.205824	0.102912	−	0.994690i	$-0.467184\pi$
$307$	3.60632	0.205824	0.102912	+	0.994690i	$0.467184\pi$
$308$	0.318785	0.0181645
$309$	−1.26772	−0.0721181
$310$	0.637447	0.0362046
$311$	−27.5438	−1.56187	−0.780934	−	0.624613i	$-0.785257\pi$
$311$	−27.5438	−1.56187	−0.780934	+	0.624613i	$0.785257\pi$
$312$	−0.412431	−0.0233493
$313$	−30.2190	−1.70808	−0.854039	−	0.520209i	$-0.825854\pi$
$313$	−30.2190	−1.70808	−0.854039	+	0.520209i	$0.825854\pi$
$314$	−15.2868	−0.862682
$315$	−1.64792	−0.0928499
$316$	2.03325	0.114379
$317$	−5.23152	−0.293831	−0.146916	−	0.989149i	$-0.546935\pi$
$317$	−5.23152	−0.293831	−0.146916	+	0.989149i	$0.546935\pi$
$318$	−0.917744	−0.0514645
$319$	35.5761	1.99188
$320$	9.86911	0.551700
$321$	0.699298	0.0390310
$322$	−0.110699	−0.00616899
$323$	11.1173	0.618584
$324$	−1.05776	−0.0587644
$325$	6.73723	0.373714
$326$	14.1826	0.785500
$327$	0.497800	0.0275284
$328$	−36.1129	−1.99400
$329$	−0.244788	−0.0134956
$330$	0.705888	0.0388578
$331$	−5.56111	−0.305666	−0.152833	−	0.988252i	$-0.548840\pi$
$331$	−5.56111	−0.305666	−0.152833	+	0.988252i	$0.548840\pi$
$332$	−0.706612	−0.0387804
$333$	24.4923	1.34217
$334$	21.4607	1.17428
$335$	9.88426	0.540035
$336$	−0.134375	−0.00733073
$337$	1.20314	0.0655392	0.0327696	−	0.999463i	$-0.489567\pi$
$337$	1.20314	0.0655392	0.0327696	+	0.999463i	$0.489567\pi$
$338$	13.0938	0.712210
$339$	0.104383	0.00566930
$340$	−0.724973	−0.0393172
$341$	2.27675	0.123293
$342$	8.73231	0.472189
$343$	−6.46688	−0.349178
$344$	−14.4682	−0.780074
$345$	0.0153990	0.000829054 0
$346$	7.80977	0.419856
$347$	18.8760	1.01332	0.506659	−	0.862147i	$-0.330880\pi$
$347$	18.8760	1.01332	0.506659	+	0.862147i	$0.330880\pi$
$348$	0.0558931	0.00299618
$349$	18.3633	0.982966	0.491483	−	0.870887i	$-0.336455\pi$
$349$	18.3633	0.982966	0.491483	+	0.870887i	$0.336455\pi$
$350$	2.33347	0.124729
$351$	0.850795	0.0454121
$352$	3.83742	0.204535
$353$	−2.06519	−0.109919	−0.0549596	−	0.998489i	$-0.517503\pi$
$353$	−2.06519	−0.109919	−0.0549596	+	0.998489i	$0.517503\pi$
$354$	−0.351232	−0.0186678
$355$	8.76802	0.465358
$356$	0.503129	0.0266658
$357$	0.187398	0.00991816
$358$	−14.8935	−0.787147
$359$	−7.83605	−0.413571	−0.206786	−	0.978386i	$-0.566300\pi$
$359$	−7.83605	−0.413571	−0.206786	+	0.978386i	$0.566300\pi$
$360$	−10.2033	−0.537759
$361$	−14.4800	−0.762107
$362$	−8.59550	−0.451770
$363$	1.68121	0.0882404
$364$	0.103122	0.00540506
$365$	−5.39478	−0.282376
$366$	0.563824	0.0294716
$367$	27.3479	1.42755	0.713775	−	0.700375i	$-0.246984\pi$
$367$	27.3479	1.42755	0.713775	+	0.700375i	$0.246984\pi$
$368$	−0.644745	−0.0336097
$369$	37.2120	1.93718
$370$	13.1597	0.684139
$371$	4.11159	0.213463
$372$	0.00357697	0.000185457 0
$373$	31.3381	1.62263	0.811313	−	0.584612i	$-0.198753\pi$
$373$	31.3381	1.62263	0.811313	+	0.584612i	$0.198753\pi$
$374$	41.2173	2.13130
$375$	−0.772376	−0.0398853
$376$	−1.51563	−0.0781625
$377$	11.5083	0.592707
$378$	0.294677	0.0151566
$379$	−1.97192	−0.101291	−0.0506454	−	0.998717i	$-0.516128\pi$
$379$	−1.97192	−0.101291	−0.0506454	+	0.998717i	$0.516128\pi$
$380$	−0.294753	−0.0151205
$381$	0.517333	0.0265038
$382$	−11.3350	−0.579948
$383$	−24.9455	−1.27466	−0.637328	−	0.770593i	$-0.719960\pi$
$383$	−24.9455	−1.27466	−0.637328	+	0.770593i	$0.719960\pi$
$384$	−0.779530	−0.0397802
$385$	−3.16245	−0.161173
$386$	27.2256	1.38575
$387$	14.9086	0.757845
$388$	0.312724	0.0158761
$389$	−8.98152	−0.455381	−0.227691	−	0.973734i	$-0.573117\pi$
$389$	−8.98152	−0.455381	−0.227691	+	0.973734i	$0.573117\pi$
$390$	0.228343	0.0115626
$391$	0.899159	0.0454724
$392$	−19.7001	−0.995007
$393$	1.27402	0.0642659
$394$	5.82822	0.293622
$395$	−20.1704	−1.01488
$396$	−2.03386	−0.102205
$397$	−10.3125	−0.517569	−0.258784	−	0.965935i	$-0.583322\pi$
$397$	−10.3125	−0.517569	−0.258784	+	0.965935i	$0.583322\pi$
$398$	−6.35527	−0.318561
$399$	0.0761906	0.00381430
$400$	13.5909	0.679546
$401$	−22.2691	−1.11207	−0.556033	−	0.831160i	$-0.687677\pi$
$401$	−22.2691	−1.11207	−0.556033	+	0.831160i	$0.687677\pi$
$402$	−0.882879	−0.0440340
$403$	0.736492	0.0366873
$404$	−0.755464	−0.0375858
$405$	10.4933	0.521416
$406$	3.98596	0.197820
$407$	47.0019	2.32980
$408$	1.16029	0.0574430
$409$	−9.36108	−0.462876	−0.231438	−	0.972850i	$-0.574343\pi$
$409$	−9.36108	−0.462876	−0.231438	+	0.972850i	$0.574343\pi$
$410$	19.9940	0.987433
$411$	0.997771	0.0492164
$412$	1.96257	0.0966891
$413$	1.57356	0.0774297
$414$	0.706262	0.0347109
$415$	7.00980	0.344098
$416$	1.24134	0.0608619
$417$	−0.828292	−0.0405616
$418$	16.7578	0.819648
$419$	−34.9797	−1.70887	−0.854436	−	0.519557i	$-0.826097\pi$
$419$	−34.9797	−1.70887	−0.854436	+	0.519557i	$0.826097\pi$
$420$	−0.00496848	−0.000242437 0
$421$	15.9244	0.776107	0.388054	−	0.921637i	$-0.373147\pi$
$421$	15.9244	0.776107	0.388054	+	0.921637i	$0.373147\pi$
$422$	−14.0880	−0.685793
$423$	1.56176	0.0759352
$424$	25.4573	1.23631
$425$	−18.9538	−0.919396
$426$	−0.783175	−0.0379450
$427$	−2.52599	−0.122241
$428$	−1.08259	−0.0523290
$429$	0.815566	0.0393759
$430$	8.01036	0.386294
$431$	−37.5257	−1.80755	−0.903775	−	0.428008i	$-0.859215\pi$
$431$	−37.5257	−1.80755	−0.903775	+	0.428008i	$0.859215\pi$
$432$	1.71630	0.0825755
$433$	27.7776	1.33491	0.667454	−	0.744651i	$-0.267384\pi$
$433$	27.7776	1.33491	0.667454	+	0.744651i	$0.267384\pi$
$434$	0.255088	0.0122446
$435$	−0.554476	−0.0265851
$436$	−0.770651	−0.0369075
$437$	0.365572	0.0174877
$438$	0.481872	0.0230247
$439$	37.3507	1.78265	0.891327	−	0.453362i	$-0.149775\pi$
$439$	37.3507	1.78265	0.891327	+	0.453362i	$0.149775\pi$
$440$	−19.5806	−0.933468
$441$	20.2997	0.966654
$442$	13.3331	0.634193
$443$	15.8245	0.751844	0.375922	−	0.926651i	$-0.377326\pi$
$443$	15.8245	0.751844	0.375922	+	0.926651i	$0.377326\pi$
$444$	0.0738441	0.00350449
$445$	−4.99119	−0.236605
$446$	−20.2869	−0.960612
$447$	0.00160992	7.61467e−5 0
$448$	3.94933	0.186588
$449$	−33.0395	−1.55923	−0.779616	−	0.626258i	$-0.784586\pi$
$449$	−33.0395	−1.55923	−0.779616	+	0.626258i	$0.784586\pi$
$450$	−14.8877	−0.701811
$451$	71.4118	3.36265
$452$	−0.161596	−0.00760086
$453$	1.15845	0.0544289
$454$	−20.4606	−0.960265
$455$	−1.02300	−0.0479591
$456$	0.471741	0.0220913
$457$	−6.38585	−0.298717	−0.149359	−	0.988783i	$-0.547721\pi$
$457$	−6.38585	−0.298717	−0.149359	+	0.988783i	$0.547721\pi$
$458$	25.0334	1.16973
$459$	−2.39354	−0.111721
$460$	−0.0238394	−0.00111152
$461$	4.10510	0.191193	0.0955967	−	0.995420i	$-0.469524\pi$
$461$	4.10510	0.191193	0.0955967	+	0.995420i	$0.469524\pi$
$462$	0.282476	0.0131420
$463$	−21.9482	−1.02002	−0.510011	−	0.860168i	$-0.670359\pi$
$463$	−21.9482	−1.02002	−0.510011	+	0.860168i	$0.670359\pi$
$464$	23.2155	1.07775
$465$	−0.0354846	−0.00164556
$466$	22.8732	1.05958
$467$	−20.9539	−0.969633	−0.484816	−	0.874616i	$-0.661114\pi$
$467$	−20.9539	−0.969633	−0.484816	+	0.874616i	$0.661114\pi$
$468$	−0.657922	−0.0304125
$469$	3.95539	0.182643
$470$	0.839130	0.0387062
$471$	0.850964	0.0392104
$472$	9.74282	0.448450
$473$	28.6103	1.31550
$474$	1.80166	0.0827530
$475$	−7.70608	−0.353579
$476$	−0.290113	−0.0132973
$477$	−26.2321	−1.20108
$478$	−33.4291	−1.52901
$479$	40.1617	1.83503	0.917517	−	0.397698i	$-0.130191\pi$
$479$	40.1617	1.83503	0.917517	+	0.397698i	$0.130191\pi$
$480$	−0.0598087	−0.00272988
$481$	15.2044	0.693260
$482$	−24.8389	−1.13138
$483$	0.00616223	0.000280391 0
$484$	−2.60269	−0.118304
$485$	−3.10232	−0.140869
$486$	−2.82099	−0.127963
$487$	−1.56804	−0.0710547	−0.0355273	−	0.999369i	$-0.511311\pi$
$487$	−1.56804	−0.0710547	−0.0355273	+	0.999369i	$0.511311\pi$
$488$	−15.6399	−0.707985
$489$	−0.789497	−0.0357023
$490$	10.9070	0.492729
$491$	9.66243	0.436059	0.218030	−	0.975942i	$-0.430037\pi$
$491$	9.66243	0.436059	0.218030	+	0.975942i	$0.430037\pi$
$492$	0.112194	0.00505810
$493$	−32.3763	−1.45815
$494$	5.42086	0.243896
$495$	20.1765	0.906868
$496$	1.48572	0.0667106
$497$	3.50871	0.157387
$498$	−0.626128	−0.0280575
$499$	−20.6363	−0.923810	−0.461905	−	0.886930i	$-0.652834\pi$
$499$	−20.6363	−0.923810	−0.461905	+	0.886930i	$0.652834\pi$
$500$	1.19573	0.0534745
$501$	−1.19465	−0.0533728
$502$	−36.9951	−1.65117
$503$	−1.00000	−0.0445878
$503$	−1.00000	−0.0445878
$504$	−4.08305	−0.181873
$505$	7.49444	0.333498
$506$	1.35535	0.0602528
$507$	−0.728890	−0.0323712
$508$	−0.800889	−0.0355337
$509$	−23.3284	−1.03401	−0.517006	−	0.855982i	$-0.672953\pi$
$509$	−23.3284	−1.03401	−0.517006	+	0.855982i	$0.672953\pi$
$510$	−0.642398	−0.0284459
$511$	−2.15883	−0.0955012
$512$	24.2947	1.07369
$513$	−0.973144	−0.0429654
$514$	−27.8501	−1.22842
$515$	−19.4693	−0.857921
$516$	0.0449493	0.00197878
$517$	2.99709	0.131812
$518$	5.26612	0.231380
$519$	−0.434744	−0.0190832
$520$	−6.33401	−0.277765
$521$	−43.2647	−1.89546	−0.947730	−	0.319073i	$-0.896629\pi$
$521$	−43.2647	−1.89546	−0.947730	+	0.319073i	$0.896629\pi$
$522$	−25.4306	−1.11307
$523$	−43.4082	−1.89811	−0.949054	−	0.315112i	$-0.897958\pi$
$523$	−43.4082	−1.89811	−0.949054	+	0.315112i	$0.897958\pi$
$524$	−1.97233	−0.0861615
$525$	−0.129897	−0.00566916
$526$	16.5430	0.721310
$527$	−2.07197	−0.0902565
$528$	1.64523	0.0715995
$529$	−22.9704	−0.998714
$530$	−14.0945	−0.612225
$531$	−10.0394	−0.435671
$532$	−0.117952	−0.00511385
$533$	23.1006	1.00060
$534$	0.445822	0.0192926
$535$	10.7396	0.464315
$536$	24.4902	1.05781
$537$	0.829073	0.0357771
$538$	34.3110	1.47925
$539$	38.9562	1.67796
$540$	0.0634599	0.00273088
$541$	32.5657	1.40011	0.700054	−	0.714090i	$-0.253159\pi$
$541$	32.5657	1.40011	0.700054	+	0.714090i	$0.253159\pi$
$542$	24.7406	1.06270
$543$	0.478484	0.0205337
$544$	−3.49228	−0.149730
$545$	7.64509	0.327480
$546$	0.0913763	0.00391055
$547$	27.8377	1.19025	0.595127	−	0.803631i	$-0.297102\pi$
$547$	27.8377	1.19025	0.595127	+	0.803631i	$0.297102\pi$
$548$	−1.54466	−0.0659847
$549$	16.1159	0.687811
$550$	−28.5702	−1.21824
$551$	−13.1633	−0.560773
$552$	0.0381540	0.00162394
$553$	−8.07162	−0.343240
$554$	40.2876	1.71166
$555$	−0.732556	−0.0310953
$556$	1.28229	0.0543811
$557$	15.7225	0.666182	0.333091	−	0.942895i	$-0.391908\pi$
$557$	15.7225	0.666182	0.333091	+	0.942895i	$0.391908\pi$
$558$	−1.62747	−0.0688963
$559$	9.25498	0.391444
$560$	−2.06369	−0.0872068
$561$	−2.29443	−0.0968710
$562$	−16.5953	−0.700033
$563$	−24.7817	−1.04442	−0.522212	−	0.852816i	$-0.674893\pi$
$563$	−24.7817	−1.04442	−0.522212	+	0.852816i	$0.674893\pi$
$564$	0.00470869	0.000198271 0
$565$	1.60309	0.0674423
$566$	11.0312	0.463674
$567$	4.19911	0.176346
$568$	21.7245	0.911539
$569$	2.95346	0.123816	0.0619078	−	0.998082i	$-0.480282\pi$
$569$	2.95346	0.123816	0.0619078	+	0.998082i	$0.480282\pi$
$570$	−0.261180	−0.0109396
$571$	−10.7926	−0.451656	−0.225828	−	0.974167i	$-0.572509\pi$
$571$	−10.7926	−0.451656	−0.225828	+	0.974167i	$0.572509\pi$
$572$	−1.26259	−0.0527914
$573$	0.630981	0.0263596
$574$	8.00101	0.333956
$575$	−0.623261	−0.0259918
$576$	−25.1969	−1.04987
$577$	−5.92593	−0.246700	−0.123350	−	0.992363i	$-0.539364\pi$
$577$	−5.92593	−0.246700	−0.123350	+	0.992363i	$0.539364\pi$
$578$	−14.1898	−0.590220
$579$	−1.51556	−0.0629845
$580$	0.858391	0.0356428
$581$	2.80512	0.116376
$582$	0.277104	0.0114863
$583$	−50.3407	−2.08490
$584$	−13.3666	−0.553115
$585$	6.52679	0.269850
$586$	18.5514	0.766350
$587$	−14.8090	−0.611234	−0.305617	−	0.952155i	$-0.598863\pi$
$587$	−14.8090	−0.611234	−0.305617	+	0.952155i	$0.598863\pi$
$588$	0.0612036	0.00252399
$589$	−0.842403	−0.0347106
$590$	−5.39414	−0.222073
$591$	−0.324438	−0.0133456
$592$	30.6716	1.26060
$593$	33.4465	1.37348	0.686741	−	0.726902i	$-0.259041\pi$
$593$	33.4465	1.37348	0.686741	+	0.726902i	$0.259041\pi$
$594$	−3.60792	−0.148035
$595$	2.87801	0.117987
$596$	−0.00249234	−0.000102090 0
$597$	0.353777	0.0144791
$598$	0.438435	0.0179289
$599$	9.35823	0.382367	0.191183	−	0.981554i	$-0.438767\pi$
$599$	9.35823	0.382367	0.191183	+	0.981554i	$0.438767\pi$
$600$	−0.804268	−0.0328341
$601$	−6.16182	−0.251346	−0.125673	−	0.992072i	$-0.540109\pi$
$601$	−6.16182	−0.251346	−0.125673	+	0.992072i	$0.540109\pi$
$602$	3.20551	0.130647
$603$	−25.2355	−1.02767
$604$	−1.79341	−0.0729730
$605$	25.8195	1.04971
$606$	−0.669416	−0.0271932
$607$	35.7361	1.45048	0.725242	−	0.688494i	$-0.241728\pi$
$607$	35.7361	1.45048	0.725242	+	0.688494i	$0.241728\pi$
$608$	−1.41986	−0.0575828
$609$	−0.221885	−0.00899124
$610$	8.65907	0.350595
$611$	0.969511	0.0392222
$612$	1.85093	0.0748195
$613$	−1.96528	−0.0793771	−0.0396885	−	0.999212i	$-0.512637\pi$
$613$	−1.96528	−0.0793771	−0.0396885	+	0.999212i	$0.512637\pi$
$614$	−4.94708	−0.199648
$615$	−1.11300	−0.0448805
$616$	−7.83558	−0.315705
$617$	−35.4461	−1.42701	−0.713503	−	0.700652i	$-0.752893\pi$
$617$	−35.4461	−1.42701	−0.713503	+	0.700652i	$0.752893\pi$
$618$	1.73904	0.0699543
$619$	−34.4643	−1.38524	−0.692618	−	0.721304i	$-0.743543\pi$
$619$	−34.4643	−1.38524	−0.692618	+	0.721304i	$0.743543\pi$
$620$	0.0549341	0.00220621
$621$	−0.0787071	−0.00315841
$622$	37.7841	1.51501
$623$	−1.99733	−0.0800213
$624$	0.532206	0.0213053
$625$	6.26126	0.250451
$626$	41.4538	1.65683
$627$	−0.932849	−0.0372544
$628$	−1.31739	−0.0525695
$629$	−42.7745	−1.70553
$630$	2.26059	0.0900640
$631$	−29.7560	−1.18457	−0.592284	−	0.805729i	$-0.701774\pi$
$631$	−29.7560	−1.18457	−0.592284	+	0.805729i	$0.701774\pi$
$632$	−49.9762	−1.98795
$633$	0.784233	0.0311705
$634$	7.17650	0.285015
$635$	7.94506	0.315290
$636$	−0.0790896	−0.00313611
$637$	12.6017	0.499298
$638$	−48.8026	−1.93211
$639$	−22.3857	−0.885564
$640$	−11.9718	−0.473228
$641$	−32.9327	−1.30077	−0.650383	−	0.759607i	$-0.725391\pi$
$641$	−32.9327	−1.30077	−0.650383	+	0.759607i	$0.725391\pi$
$642$	−0.959283	−0.0378599
$643$	−0.492253	−0.0194126	−0.00970628	−	0.999953i	$-0.503090\pi$
$643$	−0.492253	−0.0194126	−0.00970628	+	0.999953i	$0.503090\pi$
$644$	−0.00953982	−0.000375922 0
$645$	−0.445911	−0.0175577
$646$	−15.2505	−0.600024
$647$	3.76376	0.147969	0.0739844	−	0.997259i	$-0.476429\pi$
$647$	3.76376	0.147969	0.0739844	+	0.997259i	$0.476429\pi$
$648$	25.9992	1.02134
$649$	−19.2660	−0.756258
$650$	−9.24200	−0.362501
$651$	−0.0141999	−0.000556538 0
$652$	1.22223	0.0478662
$653$	18.5728	0.726809	0.363404	−	0.931631i	$-0.381614\pi$
$653$	18.5728	0.726809	0.363404	+	0.931631i	$0.381614\pi$
$654$	−0.682873	−0.0267024
$655$	19.5661	0.764510
$656$	46.6005	1.81945
$657$	13.7734	0.537353
$658$	0.335795	0.0130907
$659$	−34.1930	−1.33197	−0.665985	−	0.745965i	$-0.731988\pi$
$659$	−34.1930	−1.33197	−0.665985	+	0.745965i	$0.731988\pi$
$660$	0.0608322	0.00236789
$661$	29.5439	1.14912	0.574562	−	0.818461i	$-0.305173\pi$
$661$	29.5439	1.14912	0.574562	+	0.818461i	$0.305173\pi$
$662$	7.62862	0.296495
$663$	−0.742212	−0.0288251
$664$	17.3682	0.674015
$665$	1.17012	0.0453751
$666$	−33.5980	−1.30190
$667$	−1.06463	−0.0412227
$668$	1.84944	0.0715572
$669$	1.12930	0.0436614
$670$	−13.5590	−0.523831
$671$	30.9273	1.19393
$672$	−0.0239337	−0.000923263 0
$673$	−9.15185	−0.352778	−0.176389	−	0.984321i	$-0.556442\pi$
$673$	−9.15185	−0.352778	−0.176389	+	0.984321i	$0.556442\pi$
$674$	−1.65045	−0.0635728
$675$	1.65911	0.0638591
$676$	1.12840	0.0434001
$677$	−33.1256	−1.27312	−0.636561	−	0.771227i	$-0.719644\pi$
$677$	−33.1256	−1.27312	−0.636561	+	0.771227i	$0.719644\pi$
$678$	−0.143190	−0.00549920
$679$	−1.24146	−0.0476427
$680$	17.8195	0.683345
$681$	1.13898	0.0436457
$682$	−3.12320	−0.119593
$683$	49.1452	1.88049	0.940245	−	0.340498i	$-0.110596\pi$
$683$	49.1452	1.88049	0.940245	+	0.340498i	$0.110596\pi$
$684$	0.752535	0.0287739
$685$	15.3235	0.585481
$686$	8.87113	0.338701
$687$	−1.39353	−0.0531664
$688$	18.6700	0.711786
$689$	−16.2844	−0.620387
$690$	−0.0211240	−0.000804179 0
$691$	34.1013	1.29727	0.648637	−	0.761098i	$-0.275339\pi$
$691$	34.1013	1.29727	0.648637	+	0.761098i	$0.275339\pi$
$692$	0.673033	0.0255849
$693$	8.07406	0.306708
$694$	−25.8938	−0.982914
$695$	−12.7207	−0.482523
$696$	−1.37382	−0.0520746
$697$	−64.9889	−2.46163
$698$	−25.1904	−0.953473
$699$	−1.27327	−0.0481596
$700$	0.201095	0.00760067
$701$	26.2590	0.991787	0.495894	−	0.868383i	$-0.334841\pi$
$701$	26.2590	0.991787	0.495894	+	0.868383i	$0.334841\pi$
$702$	−1.16710	−0.0440495
$703$	−17.3909	−0.655909
$704$	−48.3541	−1.82241
$705$	−0.0467116	−0.00175926
$706$	2.83299	0.106621
$707$	2.99905	0.112791
$708$	−0.0302686	−0.00113756
$709$	28.4811	1.06963	0.534815	−	0.844969i	$-0.320381\pi$
$709$	28.4811	1.06963	0.534815	+	0.844969i	$0.320381\pi$
$710$	−12.0278	−0.451395
$711$	51.4973	1.93130
$712$	−12.3666	−0.463460
$713$	−0.0681329	−0.00255160
$714$	−0.257069	−0.00962057
$715$	12.5252	0.468418
$716$	−1.28350	−0.0479666
$717$	1.86089	0.0694961
$718$	10.7493	0.401162
$719$	13.8368	0.516024	0.258012	−	0.966142i	$-0.416933\pi$
$719$	13.8368	0.516024	0.258012	+	0.966142i	$0.416933\pi$
$720$	13.1664	0.490683
$721$	−7.79106	−0.290154
$722$	19.8634	0.739240
$723$	1.38270	0.0514233
$724$	−0.740746	−0.0275296
$725$	22.4419	0.833473
$726$	−2.30625	−0.0855928
$727$	9.61759	0.356697	0.178348	−	0.983967i	$-0.442925\pi$
$727$	9.61759	0.356697	0.178348	+	0.983967i	$0.442925\pi$
$728$	−2.53469	−0.0939417
$729$	−26.6856	−0.988356
$730$	7.40046	0.273903
$731$	−26.0370	−0.963015
$732$	0.0485894	0.00179592
$733$	−16.9530	−0.626175	−0.313087	−	0.949724i	$-0.601363\pi$
$733$	−16.9530	−0.626175	−0.313087	+	0.949724i	$0.601363\pi$
$734$	−37.5153	−1.38472
$735$	−0.607158	−0.0223954
$736$	−0.114837	−0.00423294
$737$	−48.4283	−1.78388
$738$	−51.0468	−1.87906
$739$	9.82452	0.361401	0.180700	−	0.983538i	$-0.442164\pi$
$739$	9.82452	0.361401	0.180700	+	0.983538i	$0.442164\pi$
$740$	1.13408	0.0416895
$741$	−0.301762	−0.0110855
$742$	−5.64019	−0.207058
$743$	28.8650	1.05896	0.529478	−	0.848324i	$-0.322388\pi$
$743$	28.8650	1.05896	0.529478	+	0.848324i	$0.322388\pi$
$744$	−0.0879200	−0.00322330
$745$	0.0247248	0.000905845 0
$746$	−42.9890	−1.57394
$747$	−17.8968	−0.654808
$748$	3.55204	0.129875
$749$	4.29769	0.157034
$750$	1.05953	0.0386886
$751$	−9.70834	−0.354262	−0.177131	−	0.984187i	$-0.556682\pi$
$751$	−9.70834	−0.354262	−0.177131	+	0.984187i	$0.556682\pi$
$752$	1.95578	0.0713200
$753$	2.05940	0.0750486
$754$	−15.7869	−0.574923
$755$	17.7912	0.647489
$756$	0.0253948	0.000923600 0
$757$	−5.99476	−0.217883	−0.108942	−	0.994048i	$-0.534746\pi$
$757$	−5.99476	−0.217883	−0.108942	+	0.994048i	$0.534746\pi$
$758$	2.70505	0.0982517
$759$	−0.0754480	−0.00273859
$760$	7.24488	0.262799
$761$	15.4793	0.561123	0.280562	−	0.959836i	$-0.409479\pi$
$761$	15.4793	0.561123	0.280562	+	0.959836i	$0.409479\pi$
$762$	−0.709667	−0.0257085
$763$	3.05934	0.110756
$764$	−0.976829	−0.0353404
$765$	−18.3618	−0.663873
$766$	34.2198	1.23641
$767$	−6.23226	−0.225034
$768$	−0.215886	−0.00779011
$769$	−27.9740	−1.00877	−0.504384	−	0.863480i	$-0.668280\pi$
$769$	−27.9740	−1.00877	−0.504384	+	0.863480i	$0.668280\pi$
$770$	4.33819	0.156337
$771$	1.55033	0.0558336
$772$	2.34626	0.0844436
$773$	31.7330	1.14136	0.570679	−	0.821173i	$-0.306680\pi$
$773$	31.7330	1.14136	0.570679	+	0.821173i	$0.306680\pi$
$774$	−20.4513	−0.735107
$775$	1.43621	0.0515901
$776$	−7.68659	−0.275932
$777$	−0.293147	−0.0105166
$778$	12.3207	0.441718
$779$	−26.4226	−0.946687
$780$	0.0196782	0.000704594 0
$781$	−42.9593	−1.53720
$782$	−1.23345	−0.0441080
$783$	2.83403	0.101280
$784$	25.4213	0.907903
$785$	13.0689	0.466448
$786$	−1.74768	−0.0623376
$787$	19.1339	0.682051	0.341025	−	0.940054i	$-0.389226\pi$
$787$	19.1339	0.682051	0.341025	+	0.940054i	$0.389226\pi$
$788$	0.502266	0.0178925
$789$	−0.920895	−0.0327847
$790$	27.6694	0.984434
$791$	0.641508	0.0228094
$792$	49.9913	1.77636
$793$	10.0045	0.355270
$794$	14.1465	0.502039
$795$	0.784593	0.0278266
$796$	−0.547686	−0.0194122
$797$	−2.45993	−0.0871352	−0.0435676	−	0.999050i	$-0.513872\pi$
$797$	−2.45993	−0.0871352	−0.0435676	+	0.999050i	$0.513872\pi$
$798$	−0.104517	−0.00369985
$799$	−2.72752	−0.0964929
$800$	2.42071	0.0855849
$801$	12.7430	0.450253
$802$	30.5483	1.07870
$803$	26.4320	0.932764
$804$	−0.0760850	−0.00268331
$805$	0.0946379	0.00333555
$806$	−1.01031	−0.0355865
$807$	−1.90998	−0.0672346
$808$	18.5689	0.653252
$809$	16.9350	0.595404	0.297702	−	0.954659i	$-0.403780\pi$
$809$	16.9350	0.595404	0.297702	+	0.954659i	$0.403780\pi$
$810$	−14.3945	−0.505771
$811$	−23.7584	−0.834269	−0.417135	−	0.908845i	$-0.636966\pi$
$811$	−23.7584	−0.834269	−0.417135	+	0.908845i	$0.636966\pi$
$812$	0.343503	0.0120546
$813$	−1.37723	−0.0483016
$814$	−64.4764	−2.25990
$815$	−12.1249	−0.424716
$816$	−1.49726	−0.0524144
$817$	−10.5859	−0.370354
$818$	12.8413	0.448987
$819$	2.61183	0.0912648
$820$	1.72305	0.0601714
$821$	19.2765	0.672755	0.336378	−	0.941727i	$-0.390798\pi$
$821$	19.2765	0.672755	0.336378	+	0.941727i	$0.390798\pi$
$822$	−1.36872	−0.0477397
$823$	52.8192	1.84116	0.920580	−	0.390553i	$-0.127716\pi$
$823$	52.8192	1.84116	0.920580	+	0.390553i	$0.127716\pi$
$824$	−48.2390	−1.68049
$825$	1.59041	0.0553709
$826$	−2.15858	−0.0751064
$827$	−25.7144	−0.894176	−0.447088	−	0.894490i	$-0.647539\pi$
$827$	−25.7144	−0.894176	−0.447088	+	0.894490i	$0.647539\pi$
$828$	0.0608644	0.00211518
$829$	23.3380	0.810562	0.405281	−	0.914192i	$-0.367174\pi$
$829$	23.3380	0.810562	0.405281	+	0.914192i	$0.367174\pi$
$830$	−9.61591	−0.333773
$831$	−2.24268	−0.0777976
$832$	−15.6418	−0.542281
$833$	−35.4524	−1.22835
$834$	1.13623	0.0393446
$835$	−18.3471	−0.634926
$836$	1.44415	0.0499471
$837$	0.181368	0.00626900
$838$	47.9845	1.65760
$839$	18.8028	0.649144	0.324572	−	0.945861i	$-0.394780\pi$
$839$	18.8028	0.649144	0.324572	+	0.945861i	$0.394780\pi$
$840$	0.122123	0.00421363
$841$	9.33453	0.321880
$842$	−21.8448	−0.752821
$843$	0.923809	0.0318177
$844$	−1.21408	−0.0417904
$845$	−11.1941	−0.385089
$846$	−2.14239	−0.0736568
$847$	10.3322	0.355019
$848$	−32.8504	−1.12809
$849$	−0.614069	−0.0210748
$850$	26.0005	0.891810
$851$	−1.40656	−0.0482162
$852$	−0.0674927	−0.00231226
$853$	−45.0553	−1.54266	−0.771332	−	0.636433i	$-0.780409\pi$
$853$	−45.0553	−1.54266	−0.771332	+	0.636433i	$0.780409\pi$
$854$	3.46511	0.118573
$855$	−7.46538	−0.255311
$856$	26.6095	0.909495
$857$	−33.4362	−1.14216	−0.571079	−	0.820895i	$-0.693475\pi$
$857$	−33.4362	−1.14216	−0.571079	+	0.820895i	$0.693475\pi$
$858$	−1.11878	−0.0381944
$859$	19.4483	0.663567	0.331784	−	0.943355i	$-0.392350\pi$
$859$	19.4483	0.663567	0.331784	+	0.943355i	$0.392350\pi$
$860$	0.690319	0.0235397
$861$	−0.445390	−0.0151789
$862$	51.4770	1.75332
$863$	−16.1628	−0.550186	−0.275093	−	0.961418i	$-0.588709\pi$
$863$	−16.1628	−0.550186	−0.275093	+	0.961418i	$0.588709\pi$
$864$	0.305693	0.0103999
$865$	−6.67669	−0.227014
$866$	−38.1048	−1.29485
$867$	0.789902	0.0268265
$868$	0.0219830	0.000746153 0
$869$	98.8259	3.35244
$870$	0.760620	0.0257874
$871$	−15.6658	−0.530815
$872$	18.9422	0.641463
$873$	7.92054	0.268070
$874$	−0.501484	−0.0169630
$875$	−4.74681	−0.160471
$876$	0.0415269	0.00140306
$877$	−22.3959	−0.756255	−0.378127	−	0.925754i	$-0.623432\pi$
$877$	−22.3959	−0.756255	−0.378127	+	0.925754i	$0.623432\pi$
$878$	−51.2370	−1.72917
$879$	−1.03269	−0.0348319
$880$	25.2670	0.851751
$881$	10.4074	0.350633	0.175316	−	0.984512i	$-0.443905\pi$
$881$	10.4074	0.350633	0.175316	+	0.984512i	$0.443905\pi$
$882$	−27.8468	−0.937650
$883$	−18.3582	−0.617803	−0.308902	−	0.951094i	$-0.599961\pi$
$883$	−18.3582	−0.617803	−0.308902	+	0.951094i	$0.599961\pi$
$884$	1.14903	0.0386460
$885$	0.300274	0.0100936
$886$	−21.7077	−0.729286
$887$	−22.9758	−0.771453	−0.385726	−	0.922613i	$-0.626049\pi$
$887$	−22.9758	−0.771453	−0.385726	+	0.922613i	$0.626049\pi$
$888$	−1.81505	−0.0609091
$889$	3.17938	0.106633
$890$	6.84682	0.229506
$891$	−51.4123	−1.72238
$892$	−1.74829	−0.0585370
$893$	−1.10893	−0.0371090
$894$	−0.00220846	−7.38619e−5 0
$895$	12.7327	0.425607
$896$	−4.79077	−0.160048
$897$	−0.0244062	−0.000814900 0
$898$	45.3230	1.51245
$899$	2.45328	0.0818215
$900$	−1.28299	−0.0427664
$901$	45.8130	1.52625
$902$	−97.9614	−3.26176
$903$	−0.178440	−0.00593812
$904$	3.97196	0.132105
$905$	7.34843	0.244270
$906$	−1.58914	−0.0527957
$907$	0.415835	0.0138076	0.00690378	−	0.999976i	$-0.497802\pi$
$907$	0.415835	0.0138076	0.00690378	+	0.999976i	$0.497802\pi$
$908$	−1.76326	−0.0585159
$909$	−19.1341	−0.634638
$910$	1.40333	0.0465201
$911$	−13.6089	−0.450881	−0.225441	−	0.974257i	$-0.572382\pi$
$911$	−13.6089	−0.450881	−0.225441	+	0.974257i	$0.572382\pi$
$912$	−0.608740	−0.0201574
$913$	−34.3448	−1.13665
$914$	8.75998	0.289754
$915$	−0.482022	−0.0159351
$916$	2.15734	0.0712804
$917$	7.82978	0.258562
$918$	3.28342	0.108369
$919$	−14.8913	−0.491218	−0.245609	−	0.969369i	$-0.578988\pi$
$919$	−14.8913	−0.491218	−0.245609	+	0.969369i	$0.578988\pi$
$920$	0.585959	0.0193185
$921$	0.275388	0.00907433
$922$	−5.63129	−0.185457
$923$	−13.8966	−0.457414
$924$	0.0243433	0.000800835 0
$925$	29.6496	0.974871
$926$	30.1082	0.989416
$927$	49.7072	1.63260
$928$	4.13496	0.135737
$929$	−19.4977	−0.639699	−0.319850	−	0.947468i	$-0.603632\pi$
$929$	−19.4977	−0.639699	−0.319850	+	0.947468i	$0.603632\pi$
$930$	0.0486771	0.00159618
$931$	−14.4139	−0.472397
$932$	1.97117	0.0645678
$933$	−2.10332	−0.0688595
$934$	28.7442	0.940539
$935$	−35.2373	−1.15238
$936$	16.1714	0.528578
$937$	12.5125	0.408764	0.204382	−	0.978891i	$-0.434481\pi$
$937$	12.5125	0.408764	0.204382	+	0.978891i	$0.434481\pi$
$938$	−5.42593	−0.177163
$939$	−2.30760	−0.0753056
$940$	0.0723148	0.00235865
$941$	4.08256	0.133088	0.0665439	−	0.997783i	$-0.478803\pi$
$941$	4.08256	0.133088	0.0665439	+	0.997783i	$0.478803\pi$
$942$	−1.16734	−0.0380339
$943$	−2.13704	−0.0695915
$944$	−12.5723	−0.409192
$945$	−0.251924	−0.00819509
$946$	−39.2471	−1.27603
$947$	−0.698574	−0.0227006	−0.0113503	−	0.999936i	$-0.503613\pi$
$947$	−0.698574	−0.0227006	−0.0113503	+	0.999936i	$0.503613\pi$
$948$	0.155264	0.00504274
$949$	8.55032	0.277555
$950$	10.5710	0.342970
$951$	−0.399492	−0.0129544
$952$	7.13083	0.231112
$953$	7.31223	0.236866	0.118433	−	0.992962i	$-0.462213\pi$
$953$	7.31223	0.236866	0.118433	+	0.992962i	$0.462213\pi$
$954$	35.9847	1.16505
$955$	9.69044	0.313575
$956$	−2.88086	−0.0931737
$957$	2.71668	0.0878178
$958$	−55.0930	−1.77997
$959$	6.13202	0.198013
$960$	0.753630	0.0243233
$961$	−30.8430	−0.994935
$962$	−20.8571	−0.672459
$963$	−27.4194	−0.883578
$964$	−2.14058	−0.0689434
$965$	−23.2756	−0.749267
$966$	−0.00845323	−0.000271978 0
$967$	38.1107	1.22556	0.612778	−	0.790255i	$-0.290052\pi$
$967$	38.1107	1.22556	0.612778	+	0.790255i	$0.290052\pi$
$968$	63.9729	2.05617
$969$	0.848946	0.0272721
$970$	4.25570	0.136642
$971$	−51.0424	−1.63803	−0.819014	−	0.573773i	$-0.805479\pi$
$971$	−51.0424	−1.63803	−0.819014	+	0.573773i	$0.805479\pi$
$972$	−0.243109	−0.00779771
$973$	−5.09045	−0.163192
$974$	2.15101	0.0689227
$975$	0.514472	0.0164763
$976$	20.1819	0.646007
$977$	53.4134	1.70885	0.854424	−	0.519577i	$-0.173910\pi$
$977$	53.4134	1.70885	0.854424	+	0.519577i	$0.173910\pi$
$978$	1.08302	0.0346310
$979$	24.4546	0.781571
$980$	0.939949	0.0300256
$981$	−19.5187	−0.623185
$982$	−13.2547	−0.422976
$983$	1.20932	0.0385714	0.0192857	−	0.999814i	$-0.493861\pi$
$983$	1.20932	0.0385714	0.0192857	+	0.999814i	$0.493861\pi$
$984$	−2.75767	−0.0879114
$985$	−4.98264	−0.158760
$986$	44.4132	1.41440
$987$	−0.0186926	−0.000594993 0
$988$	0.467161	0.0148624
$989$	−0.856179	−0.0272249
$990$	−27.6778	−0.879658
$991$	−13.3298	−0.423433	−0.211717	−	0.977331i	$-0.567905\pi$
$991$	−13.3298	−0.423433	−0.211717	+	0.977331i	$0.567905\pi$
$992$	0.264624	0.00840181
$993$	−0.424660	−0.0134762
$994$	−4.81318	−0.152665
$995$	5.43321	0.172244
$996$	−0.0539587	−0.00170975
$997$	−39.2475	−1.24298	−0.621490	−	0.783422i	$-0.713472\pi$
$997$	−39.2475	−1.24298	−0.621490	+	0.783422i	$0.713472\pi$
$998$	28.3085	0.896091
$999$	3.74423	0.118462

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.e.1.4	✓	10
3.2	odd	2		4527.2.a.k.1.7		10
4.3	odd	2		8048.2.a.p.1.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.e.1.4	✓	10	1.1	even	1	trivial
4527.2.a.k.1.7		10	3.2	odd	2
8048.2.a.p.1.4		10	4.3	odd	2

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:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.a (trivial)

\(f(q)\)	\(=\)	\(q-1.37178 q^{2} +0.0763625 q^{3} -0.118218 q^{4} +1.17276 q^{5} -0.104753 q^{6} +0.469303 q^{7} +2.90573 q^{8} -2.99417 q^{9} +O(q^{10})\)	\(q-1.37178 q^{2} +0.0763625 q^{3} -0.118218 q^{4} +1.17276 q^{5} -0.104753 q^{6} +0.469303 q^{7} +2.90573 q^{8} -2.99417 q^{9} -1.60876 q^{10} -5.74596 q^{11} -0.00902740 q^{12} -1.85873 q^{13} -0.643780 q^{14} +0.0895546 q^{15} -3.74959 q^{16} +5.22916 q^{17} +4.10734 q^{18} +2.12602 q^{19} -0.138641 q^{20} +0.0358371 q^{21} +7.88220 q^{22} +0.171951 q^{23} +0.221889 q^{24} -3.62464 q^{25} +2.54977 q^{26} -0.457730 q^{27} -0.0554799 q^{28} -6.19149 q^{29} -0.122849 q^{30} -0.396234 q^{31} -0.667846 q^{32} -0.438776 q^{33} -7.17326 q^{34} +0.550377 q^{35} +0.353964 q^{36} -8.17999 q^{37} -2.91644 q^{38} -0.141937 q^{39} +3.40771 q^{40} -12.4282 q^{41} -0.0491607 q^{42} -4.97920 q^{43} +0.679275 q^{44} -3.51143 q^{45} -0.235879 q^{46} -0.521599 q^{47} -0.286328 q^{48} -6.77976 q^{49} +4.97222 q^{50} +0.399312 q^{51} +0.219735 q^{52} +8.76106 q^{53} +0.627905 q^{54} -6.73861 q^{55} +1.36367 q^{56} +0.162349 q^{57} +8.49336 q^{58} +3.35297 q^{59} -0.0105869 q^{60} -5.38243 q^{61} +0.543546 q^{62} -1.40517 q^{63} +8.41532 q^{64} -2.17983 q^{65} +0.601905 q^{66} +8.42823 q^{67} -0.618179 q^{68} +0.0131306 q^{69} -0.754997 q^{70} +7.47643 q^{71} -8.70025 q^{72} -4.60009 q^{73} +11.2212 q^{74} -0.276787 q^{75} -0.251334 q^{76} -2.69660 q^{77} +0.194707 q^{78} -17.1992 q^{79} -4.39735 q^{80} +8.94755 q^{81} +17.0487 q^{82} +5.97721 q^{83} -0.00423658 q^{84} +6.13253 q^{85} +6.83038 q^{86} -0.472798 q^{87} -16.6962 q^{88} -4.25595 q^{89} +4.81691 q^{90} -0.872306 q^{91} -0.0203277 q^{92} -0.0302574 q^{93} +0.715520 q^{94} +2.49331 q^{95} -0.0509984 q^{96} -2.64532 q^{97} +9.30034 q^{98} +17.2044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9	\( 10 q - 4 q^{2} - 8 q^{3} + 4 q^{4} - q^{5} - 2 q^{6} - 5 q^{7} - 3 q^{8} - 2 q^{9} - 4 q^{10} - 3 q^{11} - 7 q^{12} - 18 q^{13} + q^{14} - 2 q^{15} - 4 q^{16} - 11 q^{17} - q^{18} - 3 q^{20} + q^{21} - 18 q^{22} - 2 q^{23} + 10 q^{24} - 27 q^{25} + 11 q^{26} - 2 q^{27} - 22 q^{28} - 9 q^{29} + 12 q^{30} - 22 q^{31} - 10 q^{32} - 10 q^{33} - 10 q^{34} - 6 q^{35} + 2 q^{36} - 35 q^{37} + 2 q^{38} + 8 q^{39} - 19 q^{40} - 4 q^{41} + 4 q^{42} - 20 q^{43} + 9 q^{44} + 2 q^{45} - q^{46} + 7 q^{47} - 27 q^{49} + 16 q^{50} + 9 q^{51} - 7 q^{52} - 24 q^{53} + 17 q^{54} - 11 q^{55} + 12 q^{56} - 23 q^{57} + 2 q^{58} + 17 q^{59} - 4 q^{61} + 8 q^{62} + 10 q^{63} + 3 q^{64} - 16 q^{65} + 46 q^{66} - 6 q^{67} + 28 q^{68} - 2 q^{69} + 26 q^{70} - q^{71} - q^{72} - 31 q^{73} + 11 q^{74} + 30 q^{75} + 20 q^{76} + 3 q^{77} + 11 q^{78} - 10 q^{79} + 24 q^{80} - 6 q^{81} - 9 q^{82} + 22 q^{83} + 22 q^{84} - 6 q^{85} + 38 q^{86} + 25 q^{87} - 3 q^{88} + q^{89} + 2 q^{90} + 10 q^{91} + 27 q^{92} - 6 q^{93} + 33 q^{94} + 39 q^{95} + 46 q^{96} - 57 q^{97} + 40 q^{98} + 35 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 8 * q^3 + 4 * q^4 - q^5 - 2 * q^6 - 5 * q^7 - 3 * q^8 - 2 * q^9 - 4 * q^10 - 3 * q^11 - 7 * q^12 - 18 * q^13 + q^14 - 2 * q^15 - 4 * q^16 - 11 * q^17 - q^18 - 3 * q^20 + q^21 - 18 * q^22 - 2 * q^23 + 10 * q^24 - 27 * q^25 + 11 * q^26 - 2 * q^27 - 22 * q^28 - 9 * q^29 + 12 * q^30 - 22 * q^31 - 10 * q^32 - 10 * q^33 - 10 * q^34 - 6 * q^35 + 2 * q^36 - 35 * q^37 + 2 * q^38 + 8 * q^39 - 19 * q^40 - 4 * q^41 + 4 * q^42 - 20 * q^43 + 9 * q^44 + 2 * q^45 - q^46 + 7 * q^47 - 27 * q^49 + 16 * q^50 + 9 * q^51 - 7 * q^52 - 24 * q^53 + 17 * q^54 - 11 * q^55 + 12 * q^56 - 23 * q^57 + 2 * q^58 + 17 * q^59 - 4 * q^61 + 8 * q^62 + 10 * q^63 + 3 * q^64 - 16 * q^65 + 46 * q^66 - 6 * q^67 + 28 * q^68 - 2 * q^69 + 26 * q^70 - q^71 - q^72 - 31 * q^73 + 11 * q^74 + 30 * q^75 + 20 * q^76 + 3 * q^77 + 11 * q^78 - 10 * q^79 + 24 * q^80 - 6 * q^81 - 9 * q^82 + 22 * q^83 + 22 * q^84 - 6 * q^85 + 38 * q^86 + 25 * q^87 - 3 * q^88 + q^89 + 2 * q^90 + 10 * q^91 + 27 * q^92 - 6 * q^93 + 33 * q^94 + 39 * q^95 + 46 * q^96 - 57 * q^97 + 40 * q^98 + 35 * q^99

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