LMFDB - Embedded newform 950.2.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(1,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("950.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.993.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x + 3 $ x^3 - x^2 - 6*x + 3
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			1.1
Root			$2.77339$ of defining polynomial
Character	$\chi$	$=$	950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -1.77339 q^{3} +1.00000 q^{4} -1.77339 q^{6} -2.69168 q^{7} +1.00000 q^{8} +0.144903 q^{9} +5.54677 q^{11} -1.77339 q^{12} -2.91829 q^{13} -2.69168 q^{14} +1.00000 q^{16} +4.91829 q^{17} +0.144903 q^{18} +1.00000 q^{19} +4.77339 q^{21} +5.54677 q^{22} +3.60997 q^{23} -1.77339 q^{24} -2.91829 q^{26} +5.06319 q^{27} -2.69168 q^{28} +1.08171 q^{29} +7.54677 q^{31} +1.00000 q^{32} -9.83658 q^{33} +4.91829 q^{34} +0.144903 q^{36} +4.54677 q^{37} +1.00000 q^{38} +5.17526 q^{39} +4.77339 q^{42} -9.54677 q^{43} +5.54677 q^{44} +3.60997 q^{46} -0.836581 q^{47} -1.77339 q^{48} +0.245129 q^{49} -8.72203 q^{51} -2.91829 q^{52} +9.78523 q^{53} +5.06319 q^{54} -2.69168 q^{56} -1.77339 q^{57} +1.08171 q^{58} +12.9933 q^{59} -7.38336 q^{61} +7.54677 q^{62} -0.390032 q^{63} +1.00000 q^{64} -9.83658 q^{66} +2.85510 q^{67} +4.91829 q^{68} -6.40187 q^{69} +14.4769 q^{71} +0.144903 q^{72} +5.15674 q^{73} +4.54677 q^{74} +1.00000 q^{76} -14.9301 q^{77} +5.17526 q^{78} -3.09355 q^{79} -9.41371 q^{81} +1.71019 q^{83} +4.77339 q^{84} -9.54677 q^{86} -1.91829 q^{87} +5.54677 q^{88} -5.09355 q^{89} +7.85510 q^{91} +3.60997 q^{92} -13.3834 q^{93} -0.836581 q^{94} -1.77339 q^{96} -17.2570 q^{97} +0.245129 q^{98} +0.803744 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 2 q^{7} + 3 q^{8} + 5 q^{9} + 2 q^{11} + 2 q^{12} - 6 q^{13} + 2 q^{14} + 3 q^{16} + 12 q^{17} + 5 q^{18} + 3 q^{19} + 7 q^{21} + 2 q^{22} - 2 q^{23} + 2 q^{24}+ \cdots - 36 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 2 * q^7 + 3 * q^8 + 5 * q^9 + 2 * q^11 + 2 * q^12 - 6 * q^13 + 2 * q^14 + 3 * q^16 + 12 * q^17 + 5 * q^18 + 3 * q^19 + 7 * q^21 + 2 * q^22 - 2 * q^23 + 2 * q^24 - 6 * q^26 + 17 * q^27 + 2 * q^28 + 6 * q^29 + 8 * q^31 + 3 * q^32 - 24 * q^33 + 12 * q^34 + 5 * q^36 - q^37 + 3 * q^38 - 11 * q^39 + 7 * q^42 - 14 * q^43 + 2 * q^44 - 2 * q^46 + 3 * q^47 + 2 * q^48 + 9 * q^49 + 15 * q^51 - 6 * q^52 - 10 * q^53 + 17 * q^54 + 2 * q^56 + 2 * q^57 + 6 * q^58 + 6 * q^59 - 2 * q^61 + 8 * q^62 - 14 * q^63 + 3 * q^64 - 24 * q^66 + 4 * q^67 + 12 * q^68 - 6 * q^71 + 5 * q^72 - 12 * q^73 - q^74 + 3 * q^76 - 10 * q^77 - 11 * q^78 + 20 * q^79 + 23 * q^81 - 4 * q^83 + 7 * q^84 - 14 * q^86 - 3 * q^87 + 2 * q^88 + 14 * q^89 + 19 * q^91 - 2 * q^92 - 20 * q^93 + 3 * q^94 + 2 * q^96 - 28 * q^97 + 9 * q^98 - 36 * q^99

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.77339	−1.02387	−0.511933	−	0.859025i	$-0.671070\pi$
$3$	−1.77339	−1.02387	−0.511933	+	0.859025i	$0.671070\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.77339	−0.723982
$7$	−2.69168	−1.01736	−0.508679	−	0.860956i	$-0.669866\pi$
$7$	−2.69168	−1.01736	−0.508679	+	0.860956i	$0.669866\pi$
$8$	1.00000	0.353553
$9$	0.144903	0.0483010
$10$	0	0
$11$	5.54677	1.67242	0.836208	−	0.548413i	$-0.184768\pi$
$11$	5.54677	1.67242	0.836208	+	0.548413i	$0.184768\pi$
$12$	−1.77339	−0.511933
$13$	−2.91829	−0.809388	−0.404694	−	0.914452i	$-0.632622\pi$
$13$	−2.91829	−0.809388	−0.404694	+	0.914452i	$0.632622\pi$
$14$	−2.69168	−0.719381
$15$	0	0
$16$	1.00000	0.250000
$17$	4.91829	1.19286	0.596430	−	0.802665i	$-0.296585\pi$
$17$	4.91829	1.19286	0.596430	+	0.802665i	$0.296585\pi$
$18$	0.144903	0.0341539
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	4.77339	1.04164
$22$	5.54677	1.18258
$23$	3.60997	0.752730	0.376365	−	0.926471i	$-0.377174\pi$
$23$	3.60997	0.752730	0.376365	+	0.926471i	$0.377174\pi$
$24$	−1.77339	−0.361991
$25$	0	0
$26$	−2.91829	−0.572324
$27$	5.06319	0.974412
$28$	−2.69168	−0.508679
$29$	1.08171	0.200868	0.100434	−	0.994944i	$-0.467977\pi$
$29$	1.08171	0.200868	0.100434	+	0.994944i	$0.467977\pi$
$30$	0	0
$31$	7.54677	1.35544	0.677720	−	0.735320i	$-0.262968\pi$
$31$	7.54677	1.35544	0.677720	+	0.735320i	$0.262968\pi$
$32$	1.00000	0.176777
$33$	−9.83658	−1.71233
$34$	4.91829	0.843480
$35$	0	0
$36$	0.144903	0.0241505
$37$	4.54677	0.747485	0.373743	−	0.927532i	$-0.378074\pi$
$37$	4.54677	0.747485	0.373743	+	0.927532i	$0.378074\pi$
$38$	1.00000	0.162221
$39$	5.17526	0.828705
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	4.77339	0.736550
$43$	−9.54677	−1.45587	−0.727935	−	0.685646i	$-0.759520\pi$
$43$	−9.54677	−1.45587	−0.727935	+	0.685646i	$0.759520\pi$
$44$	5.54677	0.836208
$45$	0	0
$46$	3.60997	0.532261
$47$	−0.836581	−0.122028	−0.0610139	−	0.998137i	$-0.519433\pi$
$47$	−0.836581	−0.122028	−0.0610139	+	0.998137i	$0.519433\pi$
$48$	−1.77339	−0.255966
$49$	0.245129	0.0350184
$50$	0	0
$51$	−8.72203	−1.22133
$52$	−2.91829	−0.404694
$53$	9.78523	1.34410	0.672052	−	0.740504i	$-0.265413\pi$
$53$	9.78523	1.34410	0.672052	+	0.740504i	$0.265413\pi$
$54$	5.06319	0.689013
$55$	0	0
$56$	−2.69168	−0.359691
$57$	−1.77339	−0.234891
$58$	1.08171	0.142035
$59$	12.9933	1.69159	0.845793	−	0.533511i	$-0.179128\pi$
$59$	12.9933	1.69159	0.845793	+	0.533511i	$0.179128\pi$
$60$	0	0
$61$	−7.38336	−0.945342	−0.472671	−	0.881239i	$-0.656710\pi$
$61$	−7.38336	−0.945342	−0.472671	+	0.881239i	$0.656710\pi$
$62$	7.54677	0.958441
$63$	−0.390032	−0.0491394
$64$	1.00000	0.125000
$65$	0	0
$66$	−9.83658	−1.21080
$67$	2.85510	0.348806	0.174403	−	0.984674i	$-0.444201\pi$
$67$	2.85510	0.348806	0.174403	+	0.984674i	$0.444201\pi$
$68$	4.91829	0.596430
$69$	−6.40187	−0.770695
$70$	0	0
$71$	14.4769	1.71809	0.859046	−	0.511898i	$-0.171057\pi$
$71$	14.4769	1.71809	0.859046	+	0.511898i	$0.171057\pi$
$72$	0.144903	0.0170770
$73$	5.15674	0.603551	0.301776	−	0.953379i	$-0.402421\pi$
$73$	5.15674	0.603551	0.301776	+	0.953379i	$0.402421\pi$
$74$	4.54677	0.528552
$75$	0	0
$76$	1.00000	0.114708
$77$	−14.9301	−1.70145
$78$	5.17526	0.585983
$79$	−3.09355	−0.348052	−0.174026	−	0.984741i	$-0.555678\pi$
$79$	−3.09355	−0.348052	−0.174026	+	0.984741i	$0.555678\pi$
$80$	0	0
$81$	−9.41371	−1.04597
$82$	0	0
$83$	1.71019	0.187718	0.0938591	−	0.995585i	$-0.470080\pi$
$83$	1.71019	0.187718	0.0938591	+	0.995585i	$0.470080\pi$
$84$	4.77339	0.520819
$85$	0	0
$86$	−9.54677	−1.02946
$87$	−1.91829	−0.205662
$88$	5.54677	0.591288
$89$	−5.09355	−0.539915	−0.269958	−	0.962872i	$-0.587010\pi$
$89$	−5.09355	−0.539915	−0.269958	+	0.962872i	$0.587010\pi$
$90$	0	0
$91$	7.85510	0.823438
$92$	3.60997	0.376365
$93$	−13.3834	−1.38779
$94$	−0.836581	−0.0862867
$95$	0	0
$96$	−1.77339	−0.180996
$97$	−17.2570	−1.75218	−0.876090	−	0.482148i	$-0.839857\pi$
$97$	−17.2570	−1.75218	−0.876090	+	0.482148i	$0.839857\pi$
$98$	0.245129	0.0247618
$99$	0.803744	0.0807793
$100$	0	0
$101$	−9.38336	−0.933679	−0.466839	−	0.884342i	$-0.654607\pi$
$101$	−9.38336	−0.933679	−0.466839	+	0.884342i	$0.654607\pi$
$102$	−8.72203	−0.863610
$103$	−12.9301	−1.27404	−0.637022	−	0.770846i	$-0.719834\pi$
$103$	−12.9301	−1.27404	−0.637022	+	0.770846i	$0.719834\pi$
$104$	−2.91829	−0.286162
$105$	0	0
$106$	9.78523	0.950425
$107$	18.9420	1.83119	0.915595	−	0.402102i	$-0.131720\pi$
$107$	18.9420	1.83119	0.915595	+	0.402102i	$0.131720\pi$
$108$	5.06319	0.487206
$109$	−2.69168	−0.257816	−0.128908	−	0.991657i	$-0.541147\pi$
$109$	−2.69168	−0.257816	−0.128908	+	0.991657i	$0.541147\pi$
$110$	0	0
$111$	−8.06319	−0.765324
$112$	−2.69168	−0.254340
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	−1.77339	−0.166093
$115$	0	0
$116$	1.08171	0.100434
$117$	−0.422869	−0.0390942
$118$	12.9933	1.19613
$119$	−13.2385	−1.21357
$120$	0	0
$121$	19.7667	1.79697
$122$	−7.38336	−0.668458
$123$	0	0
$124$	7.54677	0.677720
$125$	0	0
$126$	−0.390032	−0.0347468
$127$	−1.87361	−0.166256	−0.0831282	−	0.996539i	$-0.526491\pi$
$127$	−1.87361	−0.166256	−0.0831282	+	0.996539i	$0.526491\pi$
$128$	1.00000	0.0883883
$129$	16.9301	1.49061
$130$	0	0
$131$	−11.5468	−1.00885	−0.504423	−	0.863457i	$-0.668295\pi$
$131$	−11.5468	−1.00885	−0.504423	+	0.863457i	$0.668295\pi$
$132$	−9.83658	−0.856164
$133$	−2.69168	−0.233398
$134$	2.85510	0.246643
$135$	0	0
$136$	4.91829	0.421740
$137$	4.23845	0.362115	0.181058	−	0.983472i	$-0.442048\pi$
$137$	4.23845	0.362115	0.181058	+	0.983472i	$0.442048\pi$
$138$	−6.40187	−0.544964
$139$	9.21994	0.782025	0.391012	−	0.920385i	$-0.372125\pi$
$139$	9.21994	0.782025	0.391012	+	0.920385i	$0.372125\pi$
$140$	0	0
$141$	1.48358	0.124940
$142$	14.4769	1.21487
$143$	−16.1871	−1.35363
$144$	0.144903	0.0120752
$145$	0	0
$146$	5.15674	0.426775
$147$	−0.434709	−0.0358542
$148$	4.54677	0.373743
$149$	−7.25697	−0.594514	−0.297257	−	0.954797i	$-0.596072\pi$
$149$	−7.25697	−0.594514	−0.297257	+	0.954797i	$0.596072\pi$
$150$	0	0
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	1.00000	0.0811107
$153$	0.712675	0.0576163
$154$	−14.9301	−1.20310
$155$	0	0
$156$	5.17526	0.414352
$157$	−9.54677	−0.761916	−0.380958	−	0.924592i	$-0.624406\pi$
$157$	−9.54677	−0.761916	−0.380958	+	0.924592i	$0.624406\pi$
$158$	−3.09355	−0.246110
$159$	−17.3530	−1.37618
$160$	0	0
$161$	−9.71687	−0.765797
$162$	−9.41371	−0.739611
$163$	15.7102	1.23052	0.615259	−	0.788325i	$-0.289052\pi$
$163$	15.7102	1.23052	0.615259	+	0.788325i	$0.289052\pi$
$164$	0	0
$165$	0	0
$166$	1.71019	0.132737
$167$	6.45323	0.499366	0.249683	−	0.968328i	$-0.419674\pi$
$167$	6.45323	0.499366	0.249683	+	0.968328i	$0.419674\pi$
$168$	4.77339	0.368275
$169$	−4.48358	−0.344891
$170$	0	0
$171$	0.144903	0.0110810
$172$	−9.54677	−0.727935
$173$	−0.873614	−0.0664196	−0.0332098	−	0.999448i	$-0.510573\pi$
$173$	−0.873614	−0.0664196	−0.0332098	+	0.999448i	$0.510573\pi$
$174$	−1.91829	−0.145425
$175$	0	0
$176$	5.54677	0.418104
$177$	−23.0422	−1.73196
$178$	−5.09355	−0.381778
$179$	−12.3834	−0.925575	−0.462788	−	0.886469i	$-0.653151\pi$
$179$	−12.3834	−0.925575	−0.462788	+	0.886469i	$0.653151\pi$
$180$	0	0
$181$	−17.6403	−1.31119	−0.655597	−	0.755111i	$-0.727583\pi$
$181$	−17.6403	−1.31119	−0.655597	+	0.755111i	$0.727583\pi$
$182$	7.85510	0.582259
$183$	13.0935	0.967903
$184$	3.60997	0.266130
$185$	0	0
$186$	−13.3834	−0.981315
$187$	27.2806	1.99496
$188$	−0.836581	−0.0610139
$189$	−13.6285	−0.991326
$190$	0	0
$191$	−15.1567	−1.09670	−0.548352	−	0.836248i	$-0.684744\pi$
$191$	−15.1567	−1.09670	−0.548352	+	0.836248i	$0.684744\pi$
$192$	−1.77339	−0.127983
$193$	23.3834	1.68317	0.841585	−	0.540124i	$-0.181623\pi$
$193$	23.3834	1.68317	0.841585	+	0.540124i	$0.181623\pi$
$194$	−17.2570	−1.23898
$195$	0	0
$196$	0.245129	0.0175092
$197$	−23.0935	−1.64535	−0.822674	−	0.568514i	$-0.807519\pi$
$197$	−23.0935	−1.64535	−0.822674	+	0.568514i	$0.807519\pi$
$198$	0.803744	0.0571196
$199$	−25.7852	−1.82787	−0.913933	−	0.405865i	$-0.866970\pi$
$199$	−25.7852	−1.82787	−0.913933	+	0.405865i	$0.866970\pi$
$200$	0	0
$201$	−5.06319	−0.357130
$202$	−9.38336	−0.660211
$203$	−2.91161	−0.204355
$204$	−8.72203	−0.610665
$205$	0	0
$206$	−12.9301	−0.900885
$207$	0.523095	0.0363576
$208$	−2.91829	−0.202347
$209$	5.54677	0.383678
$210$	0	0
$211$	14.2266	0.979400	0.489700	−	0.871891i	$-0.337106\pi$
$211$	14.2266	0.979400	0.489700	+	0.871891i	$0.337106\pi$
$212$	9.78523	0.672052
$213$	−25.6732	−1.75910
$214$	18.9420	1.29485
$215$	0	0
$216$	5.06319	0.344507
$217$	−20.3135	−1.37897
$218$	−2.69168	−0.182303
$219$	−9.14490	−0.617955
$220$	0	0
$221$	−14.3530	−0.965487
$222$	−8.06319	−0.541166
$223$	−4.45323	−0.298210	−0.149105	−	0.988821i	$-0.547639\pi$
$223$	−4.45323	−0.298210	−0.149105	+	0.988821i	$0.547639\pi$
$224$	−2.69168	−0.179845
$225$	0	0
$226$	−6.00000	−0.399114
$227$	5.94865	0.394826	0.197413	−	0.980320i	$-0.436746\pi$
$227$	5.94865	0.394826	0.197413	+	0.980320i	$0.436746\pi$
$228$	−1.77339	−0.117445
$229$	1.09355	0.0722638	0.0361319	−	0.999347i	$-0.488496\pi$
$229$	1.09355	0.0722638	0.0361319	+	0.999347i	$0.488496\pi$
$230$	0	0
$231$	26.4769	1.74205
$232$	1.08171	0.0710177
$233$	14.0935	0.923299	0.461650	−	0.887062i	$-0.347258\pi$
$233$	14.0935	0.923299	0.461650	+	0.887062i	$0.347258\pi$
$234$	−0.422869	−0.0276438
$235$	0	0
$236$	12.9933	0.845793
$237$	5.48606	0.356358
$238$	−13.2385	−0.858121
$239$	15.6100	1.00972	0.504862	−	0.863200i	$-0.331543\pi$
$239$	15.6100	1.00972	0.504862	+	0.863200i	$0.331543\pi$
$240$	0	0
$241$	−5.21994	−0.336246	−0.168123	−	0.985766i	$-0.553771\pi$
$241$	−5.21994	−0.336246	−0.168123	+	0.985766i	$0.553771\pi$
$242$	19.7667	1.27065
$243$	1.50458	0.0965188
$244$	−7.38336	−0.472671
$245$	0	0
$246$	0	0
$247$	−2.91829	−0.185686
$248$	7.54677	0.479221
$249$	−3.03284	−0.192198
$250$	0	0
$251$	−28.6403	−1.80776	−0.903881	−	0.427785i	$-0.859294\pi$
$251$	−28.6403	−1.80776	−0.903881	+	0.427785i	$0.859294\pi$
$252$	−0.390032	−0.0245697
$253$	20.0237	1.25888
$254$	−1.87361	−0.117561
$255$	0	0
$256$	1.00000	0.0625000
$257$	6.45323	0.402541	0.201271	−	0.979536i	$-0.435493\pi$
$257$	6.45323	0.402541	0.201271	+	0.979536i	$0.435493\pi$
$258$	16.9301	1.05402
$259$	−12.2385	−0.760460
$260$	0	0
$261$	0.156743	0.00970214
$262$	−11.5468	−0.713362
$263$	22.1871	1.36812	0.684058	−	0.729428i	$-0.260214\pi$
$263$	22.1871	1.36812	0.684058	+	0.729428i	$0.260214\pi$
$264$	−9.83658	−0.605400
$265$	0	0
$266$	−2.69168	−0.165037
$267$	9.03284	0.552801
$268$	2.85510	0.174403
$269$	−20.4070	−1.24424	−0.622119	−	0.782922i	$-0.713728\pi$
$269$	−20.4070	−1.24424	−0.622119	+	0.782922i	$0.713728\pi$
$270$	0	0
$271$	15.9368	0.968092	0.484046	−	0.875043i	$-0.339167\pi$
$271$	15.9368	0.968092	0.484046	+	0.875043i	$0.339167\pi$
$272$	4.91829	0.298215
$273$	−13.9301	−0.843090
$274$	4.23845	0.256054
$275$	0	0
$276$	−6.40187	−0.385347
$277$	4.02368	0.241759	0.120880	−	0.992667i	$-0.461428\pi$
$277$	4.02368	0.241759	0.120880	+	0.992667i	$0.461428\pi$
$278$	9.21994	0.552975
$279$	1.09355	0.0654691
$280$	0	0
$281$	1.67316	0.0998124	0.0499062	−	0.998754i	$-0.484108\pi$
$281$	1.67316	0.0998124	0.0499062	+	0.998754i	$0.484108\pi$
$282$	1.48358	0.0883460
$283$	16.8931	1.00419	0.502095	−	0.864812i	$-0.332563\pi$
$283$	16.8931	1.00419	0.502095	+	0.864812i	$0.332563\pi$
$284$	14.4769	0.859046
$285$	0	0
$286$	−16.1871	−0.957163
$287$	0	0
$288$	0.144903	0.00853849
$289$	7.18958	0.422916
$290$	0	0
$291$	30.6033	1.79400
$292$	5.15674	0.301776
$293$	−1.08171	−0.0631942	−0.0315971	−	0.999501i	$-0.510059\pi$
$293$	−1.08171	−0.0631942	−0.0315971	+	0.999501i	$0.510059\pi$
$294$	−0.434709	−0.0253527
$295$	0	0
$296$	4.54677	0.264276
$297$	28.0844	1.62962
$298$	−7.25697	−0.420385
$299$	−10.5349	−0.609251
$300$	0	0
$301$	25.6968	1.48114
$302$	20.0000	1.15087
$303$	16.6403	0.955962
$304$	1.00000	0.0573539
$305$	0	0
$306$	0.712675	0.0407409
$307$	2.38336	0.136025	0.0680126	−	0.997684i	$-0.478334\pi$
$307$	2.38336	0.136025	0.0680126	+	0.997684i	$0.478334\pi$
$308$	−14.9301	−0.850723
$309$	22.9301	1.30445
$310$	0	0
$311$	−29.4584	−1.67043	−0.835216	−	0.549922i	$-0.814657\pi$
$311$	−29.4584	−1.67043	−0.835216	+	0.549922i	$0.814657\pi$
$312$	5.17526	0.292991
$313$	32.0355	1.81075	0.905377	−	0.424608i	$-0.139588\pi$
$313$	32.0355	1.81075	0.905377	+	0.424608i	$0.139588\pi$
$314$	−9.54677	−0.538756
$315$	0	0
$316$	−3.09355	−0.174026
$317$	−26.6665	−1.49774	−0.748870	−	0.662717i	$-0.769403\pi$
$317$	−26.6665	−1.49774	−0.748870	+	0.662717i	$0.769403\pi$
$318$	−17.3530	−0.973108
$319$	6.00000	0.335936
$320$	0	0
$321$	−33.5915	−1.87489
$322$	−9.71687	−0.541500
$323$	4.91829	0.273661
$324$	−9.41371	−0.522984
$325$	0	0
$326$	15.7102	0.870107
$327$	4.77339	0.263969
$328$	0	0
$329$	2.25181	0.124146
$330$	0	0
$331$	−19.8721	−1.09227	−0.546135	−	0.837697i	$-0.683901\pi$
$331$	−19.8721	−1.09227	−0.546135	+	0.837697i	$0.683901\pi$
$332$	1.71019	0.0938591
$333$	0.658841	0.0361043
$334$	6.45323	0.353105
$335$	0	0
$336$	4.77339	0.260410
$337$	27.5705	1.50186	0.750929	−	0.660383i	$-0.229606\pi$
$337$	27.5705	1.50186	0.750929	+	0.660383i	$0.229606\pi$
$338$	−4.48358	−0.243875
$339$	10.6403	0.577903
$340$	0	0
$341$	41.8603	2.26686
$342$	0.144903	0.00783545
$343$	18.1819	0.981732
$344$	−9.54677	−0.514728
$345$	0	0
$346$	−0.873614	−0.0469658
$347$	−27.2806	−1.46450	−0.732251	−	0.681035i	$-0.761530\pi$
$347$	−27.2806	−1.46450	−0.732251	+	0.681035i	$0.761530\pi$
$348$	−1.91829	−0.102831
$349$	30.9538	1.65692	0.828460	−	0.560049i	$-0.189218\pi$
$349$	30.9538	1.65692	0.828460	+	0.560049i	$0.189218\pi$
$350$	0	0
$351$	−14.7759	−0.788677
$352$	5.54677	0.295644
$353$	11.1819	0.595154	0.297577	−	0.954698i	$-0.403821\pi$
$353$	11.1819	0.595154	0.297577	+	0.954698i	$0.403821\pi$
$354$	−23.0422	−1.22468
$355$	0	0
$356$	−5.09355	−0.269958
$357$	23.4769	1.24253
$358$	−12.3834	−0.654481
$359$	20.3387	1.07343	0.536717	−	0.843762i	$-0.319664\pi$
$359$	20.3387	1.07343	0.536717	+	0.843762i	$0.319664\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	−17.6403	−0.927155
$363$	−35.0540	−1.83986
$364$	7.85510	0.411719
$365$	0	0
$366$	13.0935	0.684411
$367$	−32.9538	−1.72017	−0.860087	−	0.510147i	$-0.829591\pi$
$367$	−32.9538	−1.72017	−0.860087	+	0.510147i	$0.829591\pi$
$368$	3.60997	0.188183
$369$	0	0
$370$	0	0
$371$	−26.3387	−1.36744
$372$	−13.3834	−0.693895
$373$	−10.0869	−0.522278	−0.261139	−	0.965301i	$-0.584098\pi$
$373$	−10.0869	−0.522278	−0.261139	+	0.965301i	$0.584098\pi$
$374$	27.2806	1.41065
$375$	0	0
$376$	−0.836581	−0.0431434
$377$	−3.15674	−0.162581
$378$	−13.6285	−0.700974
$379$	−18.4256	−0.946457	−0.473229	−	0.880940i	$-0.656912\pi$
$379$	−18.4256	−0.946457	−0.473229	+	0.880940i	$0.656912\pi$
$380$	0	0
$381$	3.32264	0.170224
$382$	−15.1567	−0.775486
$383$	28.1871	1.44029	0.720147	−	0.693822i	$-0.244074\pi$
$383$	28.1871	1.44029	0.720147	+	0.693822i	$0.244074\pi$
$384$	−1.77339	−0.0904978
$385$	0	0
$386$	23.3834	1.19018
$387$	−1.38336	−0.0703199
$388$	−17.2570	−0.876090
$389$	20.0237	1.01524	0.507620	−	0.861581i	$-0.330525\pi$
$389$	20.0237	1.01524	0.507620	+	0.861581i	$0.330525\pi$
$390$	0	0
$391$	17.7549	0.897902
$392$	0.245129	0.0123809
$393$	20.4769	1.03292
$394$	−23.0935	−1.16344
$395$	0	0
$396$	0.803744	0.0403896
$397$	−8.32684	−0.417912	−0.208956	−	0.977925i	$-0.567007\pi$
$397$	−8.32684	−0.417912	−0.208956	+	0.977925i	$0.567007\pi$
$398$	−25.7852	−1.29250
$399$	4.77339	0.238968
$400$	0	0
$401$	−22.1501	−1.10612	−0.553061	−	0.833141i	$-0.686540\pi$
$401$	−22.1501	−1.10612	−0.553061	+	0.833141i	$0.686540\pi$
$402$	−5.06319	−0.252529
$403$	−22.0237	−1.09708
$404$	−9.38336	−0.466839
$405$	0	0
$406$	−2.91161	−0.144501
$407$	25.2199	1.25011
$408$	−8.72203	−0.431805
$409$	34.0237	1.68236	0.841181	−	0.540753i	$-0.181861\pi$
$409$	34.0237	1.68236	0.841181	+	0.540753i	$0.181861\pi$
$410$	0	0
$411$	−7.51642	−0.370758
$412$	−12.9301	−0.637022
$413$	−34.9738	−1.72095
$414$	0.523095	0.0257087
$415$	0	0
$416$	−2.91829	−0.143081
$417$	−16.3505	−0.800688
$418$	5.54677	0.271302
$419$	37.5334	1.83363	0.916814	−	0.399315i	$-0.130752\pi$
$419$	37.5334	1.83363	0.916814	+	0.399315i	$0.130752\pi$
$420$	0	0
$421$	33.8341	1.64897	0.824487	−	0.565882i	$-0.191464\pi$
$421$	33.8341	1.64897	0.824487	+	0.565882i	$0.191464\pi$
$422$	14.2266	0.692541
$423$	−0.121223	−0.00589406
$424$	9.78523	0.475213
$425$	0	0
$426$	−25.6732	−1.24387
$427$	19.8736	0.961752
$428$	18.9420	0.915595
$429$	28.7060	1.38594
$430$	0	0
$431$	24.8037	1.19475	0.597377	−	0.801960i	$-0.296210\pi$
$431$	24.8037	1.19475	0.597377	+	0.801960i	$0.296210\pi$
$432$	5.06319	0.243603
$433$	1.68651	0.0810487	0.0405244	−	0.999179i	$-0.487097\pi$
$433$	1.68651	0.0810487	0.0405244	+	0.999179i	$0.487097\pi$
$434$	−20.3135	−0.975079
$435$	0	0
$436$	−2.69168	−0.128908
$437$	3.60997	0.172688
$438$	−9.14490	−0.436960
$439$	0.326839	0.0155992	0.00779958	−	0.999970i	$-0.497517\pi$
$439$	0.326839	0.0155992	0.00779958	+	0.999970i	$0.497517\pi$
$440$	0	0
$441$	0.0355199	0.00169142
$442$	−14.3530	−0.682703
$443$	0.490258	0.0232929	0.0116464	−	0.999932i	$-0.496293\pi$
$443$	0.490258	0.0232929	0.0116464	+	0.999932i	$0.496293\pi$
$444$	−8.06319	−0.382662
$445$	0	0
$446$	−4.45323	−0.210866
$447$	12.8694	0.608703
$448$	−2.69168	−0.127170
$449$	23.5468	1.11124	0.555621	−	0.831436i	$-0.312481\pi$
$449$	23.5468	1.11124	0.555621	+	0.831436i	$0.312481\pi$
$450$	0	0
$451$	0	0
$452$	−6.00000	−0.282216
$453$	−35.4677	−1.66642
$454$	5.94865	0.279184
$455$	0	0
$456$	−1.77339	−0.0830465
$457$	−8.01184	−0.374778	−0.187389	−	0.982286i	$-0.560003\pi$
$457$	−8.01184	−0.374778	−0.187389	+	0.982286i	$0.560003\pi$
$458$	1.09355	0.0510982
$459$	24.9023	1.16234
$460$	0	0
$461$	3.83658	0.178687	0.0893437	−	0.996001i	$-0.471523\pi$
$461$	3.83658	0.178687	0.0893437	+	0.996001i	$0.471523\pi$
$462$	26.4769	1.23182
$463$	−6.58381	−0.305975	−0.152988	−	0.988228i	$-0.548890\pi$
$463$	−6.58381	−0.305975	−0.152988	+	0.988228i	$0.548890\pi$
$464$	1.08171	0.0502171
$465$	0	0
$466$	14.0935	0.652871
$467$	22.6033	1.04596	0.522978	−	0.852346i	$-0.324821\pi$
$467$	22.6033	1.04596	0.522978	+	0.852346i	$0.324821\pi$
$468$	−0.422869	−0.0195471
$469$	−7.68500	−0.354860
$470$	0	0
$471$	16.9301	0.780099
$472$	12.9933	0.598066
$473$	−52.9538	−2.43482
$474$	5.48606	0.251983
$475$	0	0
$476$	−13.2385	−0.606783
$477$	1.41791	0.0649215
$478$	15.6100	0.713983
$479$	−35.7904	−1.63530	−0.817652	−	0.575712i	$-0.804725\pi$
$479$	−35.7904	−1.63530	−0.817652	+	0.575712i	$0.804725\pi$
$480$	0	0
$481$	−13.2688	−0.605006
$482$	−5.21994	−0.237762
$483$	17.2318	0.784073
$484$	19.7667	0.898487
$485$	0	0
$486$	1.50458	0.0682491
$487$	−21.4070	−0.970045	−0.485023	−	0.874502i	$-0.661189\pi$
$487$	−21.4070	−0.970045	−0.485023	+	0.874502i	$0.661189\pi$
$488$	−7.38336	−0.334229
$489$	−27.8603	−1.25988
$490$	0	0
$491$	−4.32684	−0.195267	−0.0976337	−	0.995222i	$-0.531127\pi$
$491$	−4.32684	−0.195267	−0.0976337	+	0.995222i	$0.531127\pi$
$492$	0	0
$493$	5.32016	0.239608
$494$	−2.91829	−0.131300
$495$	0	0
$496$	7.54677	0.338860
$497$	−38.9672	−1.74792
$498$	−3.03284	−0.135905
$499$	−37.6968	−1.68754	−0.843771	−	0.536703i	$-0.819670\pi$
$499$	−37.6968	−1.68754	−0.843771	+	0.536703i	$0.819670\pi$
$500$	0	0
$501$	−11.4441	−0.511283
$502$	−28.6403	−1.27828
$503$	−16.9183	−0.754349	−0.377175	−	0.926142i	$-0.623104\pi$
$503$	−16.9183	−0.754349	−0.377175	+	0.926142i	$0.623104\pi$
$504$	−0.390032	−0.0173734
$505$	0	0
$506$	20.0237	0.890161
$507$	7.95113	0.353122
$508$	−1.87361	−0.0831282
$509$	−6.79955	−0.301385	−0.150692	−	0.988581i	$-0.548150\pi$
$509$	−6.79955	−0.301385	−0.150692	+	0.988581i	$0.548150\pi$
$510$	0	0
$511$	−13.8803	−0.614028
$512$	1.00000	0.0441942
$513$	5.06319	0.223545
$514$	6.45323	0.284640
$515$	0	0
$516$	16.9301	0.745307
$517$	−4.64032	−0.204081
$518$	−12.2385	−0.537727
$519$	1.54926	0.0680048
$520$	0	0
$521$	−1.35968	−0.0595685	−0.0297842	−	0.999556i	$-0.509482\pi$
$521$	−1.35968	−0.0595685	−0.0297842	+	0.999556i	$0.509482\pi$
$522$	0.156743	0.00686045
$523$	−21.9486	−0.959747	−0.479874	−	0.877338i	$-0.659318\pi$
$523$	−21.9486	−0.959747	−0.479874	+	0.877338i	$0.659318\pi$
$524$	−11.5468	−0.504423
$525$	0	0
$526$	22.1871	0.967404
$527$	37.1172	1.61685
$528$	−9.83658	−0.428082
$529$	−9.96813	−0.433397
$530$	0	0
$531$	1.88277	0.0817053
$532$	−2.69168	−0.116699
$533$	0	0
$534$	9.03284	0.390889
$535$	0	0
$536$	2.85510	0.123321
$537$	21.9605	0.947665
$538$	−20.4070	−0.879810
$539$	1.35968	0.0585654
$540$	0	0
$541$	−39.8973	−1.71532	−0.857659	−	0.514218i	$-0.828082\pi$
$541$	−39.8973	−1.71532	−0.857659	+	0.514218i	$0.828082\pi$
$542$	15.9368	0.684544
$543$	31.2831	1.34249
$544$	4.91829	0.210870
$545$	0	0
$546$	−13.9301	−0.596155
$547$	−7.34632	−0.314106	−0.157053	−	0.987590i	$-0.550199\pi$
$547$	−7.34632	−0.314106	−0.157053	+	0.987590i	$0.550199\pi$
$548$	4.23845	0.181058
$549$	−1.06987	−0.0456609
$550$	0	0
$551$	1.08171	0.0460824
$552$	−6.40187	−0.272482
$553$	8.32684	0.354093
$554$	4.02368	0.170950
$555$	0	0
$556$	9.21994	0.391012
$557$	−26.9672	−1.14264	−0.571318	−	0.820729i	$-0.693568\pi$
$557$	−26.9672	−1.14264	−0.571318	+	0.820729i	$0.693568\pi$
$558$	1.09355	0.0462936
$559$	27.8603	1.17836
$560$	0	0
$561$	−48.3792	−2.04257
$562$	1.67316	0.0705780
$563$	−44.8973	−1.89220	−0.946098	−	0.323881i	$-0.895012\pi$
$563$	−44.8973	−1.89220	−0.946098	+	0.323881i	$0.895012\pi$
$564$	1.48358	0.0624701
$565$	0	0
$566$	16.8931	0.710070
$567$	25.3387	1.06412
$568$	14.4769	0.607437
$569$	31.1172	1.30450	0.652251	−	0.758003i	$-0.273825\pi$
$569$	31.1172	1.30450	0.652251	+	0.758003i	$0.273825\pi$
$570$	0	0
$571$	33.2570	1.39176	0.695880	−	0.718158i	$-0.255014\pi$
$571$	33.2570	1.39176	0.695880	+	0.718158i	$0.255014\pi$
$572$	−16.1871	−0.676817
$573$	26.8788	1.12288
$574$	0	0
$575$	0	0
$576$	0.144903	0.00603762
$577$	23.4702	0.977078	0.488539	−	0.872542i	$-0.337530\pi$
$577$	23.4702	0.977078	0.488539	+	0.872542i	$0.337530\pi$
$578$	7.18958	0.299047
$579$	−41.4677	−1.72334
$580$	0	0
$581$	−4.60329	−0.190977
$582$	30.6033	1.26855
$583$	54.2765	2.24790
$584$	5.15674	0.213388
$585$	0	0
$586$	−1.08171	−0.0446850
$587$	−10.1501	−0.418938	−0.209469	−	0.977815i	$-0.567174\pi$
$587$	−10.1501	−0.418938	−0.209469	+	0.977815i	$0.567174\pi$
$588$	−0.434709	−0.0179271
$589$	7.54677	0.310959
$590$	0	0
$591$	40.9538	1.68461
$592$	4.54677	0.186871
$593$	−16.6732	−0.684685	−0.342342	−	0.939575i	$-0.611220\pi$
$593$	−16.6732	−0.684685	−0.342342	+	0.939575i	$0.611220\pi$
$594$	28.0844	1.15232
$595$	0	0
$596$	−7.25697	−0.297257
$597$	45.7272	1.87149
$598$	−10.5349	−0.430806
$599$	18.2765	0.746756	0.373378	−	0.927679i	$-0.378200\pi$
$599$	18.2765	0.746756	0.373378	+	0.927679i	$0.378200\pi$
$600$	0	0
$601$	7.96297	0.324816	0.162408	−	0.986724i	$-0.448074\pi$
$601$	7.96297	0.324816	0.162408	+	0.986724i	$0.448074\pi$
$602$	25.6968	1.04733
$603$	0.413712	0.0168477
$604$	20.0000	0.813788
$605$	0	0
$606$	16.6403	0.675967
$607$	−6.93013	−0.281285	−0.140643	−	0.990060i	$-0.544917\pi$
$607$	−6.93013	−0.281285	−0.140643	+	0.990060i	$0.544917\pi$
$608$	1.00000	0.0405554
$609$	5.16342	0.209232
$610$	0	0
$611$	2.44139	0.0987679
$612$	0.712675	0.0288082
$613$	−34.2765	−1.38441	−0.692206	−	0.721700i	$-0.743361\pi$
$613$	−34.2765	−1.38441	−0.692206	+	0.721700i	$0.743361\pi$
$614$	2.38336	0.0961844
$615$	0	0
$616$	−14.9301	−0.601552
$617$	35.5139	1.42974	0.714869	−	0.699259i	$-0.246486\pi$
$617$	35.5139	1.42974	0.714869	+	0.699259i	$0.246486\pi$
$618$	22.9301	0.922385
$619$	−29.5334	−1.18705	−0.593524	−	0.804816i	$-0.702264\pi$
$619$	−29.5334	−1.18705	−0.593524	+	0.804816i	$0.702264\pi$
$620$	0	0
$621$	18.2780	0.733470
$622$	−29.4584	−1.18117
$623$	13.7102	0.549287
$624$	5.17526	0.207176
$625$	0	0
$626$	32.0355	1.28040
$627$	−9.83658	−0.392835
$628$	−9.54677	−0.380958
$629$	22.3624	0.891646
$630$	0	0
$631$	−15.1634	−0.603646	−0.301823	−	0.953364i	$-0.597595\pi$
$631$	−15.1634	−0.603646	−0.301823	+	0.953364i	$0.597595\pi$
$632$	−3.09355	−0.123055
$633$	−25.2293	−1.00277
$634$	−26.6665	−1.05906
$635$	0	0
$636$	−17.3530	−0.688091
$637$	−0.715358	−0.0283435
$638$	6.00000	0.237542
$639$	2.09775	0.0829855
$640$	0	0
$641$	−25.0802	−0.990608	−0.495304	−	0.868720i	$-0.664943\pi$
$641$	−25.0802	−0.990608	−0.495304	+	0.868720i	$0.664943\pi$
$642$	−33.5915	−1.32575
$643$	19.1306	0.754437	0.377218	−	0.926124i	$-0.376881\pi$
$643$	19.1306	0.754437	0.377218	+	0.926124i	$0.376881\pi$
$644$	−9.71687	−0.382898
$645$	0	0
$646$	4.91829	0.193508
$647$	12.4019	0.487568	0.243784	−	0.969830i	$-0.421611\pi$
$647$	12.4019	0.487568	0.243784	+	0.969830i	$0.421611\pi$
$648$	−9.41371	−0.369806
$649$	72.0710	2.82904
$650$	0	0
$651$	36.0237	1.41188
$652$	15.7102	0.615259
$653$	−10.7801	−0.421856	−0.210928	−	0.977502i	$-0.567649\pi$
$653$	−10.7801	−0.421856	−0.210928	+	0.977502i	$0.567649\pi$
$654$	4.77339	0.186654
$655$	0	0
$656$	0	0
$657$	0.747227	0.0291521
$658$	2.25181	0.0877845
$659$	8.56529	0.333656	0.166828	−	0.985986i	$-0.446647\pi$
$659$	8.56529	0.333656	0.166828	+	0.985986i	$0.446647\pi$
$660$	0	0
$661$	−26.2883	−1.02250	−0.511248	−	0.859433i	$-0.670817\pi$
$661$	−26.2883	−1.02250	−0.511248	+	0.859433i	$0.670817\pi$
$662$	−19.8721	−0.772351
$663$	25.4534	0.988529
$664$	1.71019	0.0663684
$665$	0	0
$666$	0.658841	0.0255296
$667$	3.90494	0.151200
$668$	6.45323	0.249683
$669$	7.89729	0.305327
$670$	0	0
$671$	−40.9538	−1.58100
$672$	4.77339	0.184137
$673$	−12.9301	−0.498420	−0.249210	−	0.968449i	$-0.580171\pi$
$673$	−12.9301	−0.498420	−0.249210	+	0.968449i	$0.580171\pi$
$674$	27.5705	1.06197
$675$	0	0
$676$	−4.48358	−0.172445
$677$	−15.9250	−0.612046	−0.306023	−	0.952024i	$-0.598998\pi$
$677$	−15.9250	−0.612046	−0.306023	+	0.952024i	$0.598998\pi$
$678$	10.6403	0.408639
$679$	46.4502	1.78260
$680$	0	0
$681$	−10.5493	−0.404248
$682$	41.8603	1.60291
$683$	13.2898	0.508520	0.254260	−	0.967136i	$-0.418168\pi$
$683$	13.2898	0.508520	0.254260	+	0.967136i	$0.418168\pi$
$684$	0.144903	0.00554050
$685$	0	0
$686$	18.1819	0.694190
$687$	−1.93929	−0.0739884
$688$	−9.54677	−0.363967
$689$	−28.5561	−1.08790
$690$	0	0
$691$	27.2570	1.03690	0.518452	−	0.855107i	$-0.326508\pi$
$691$	27.2570	1.03690	0.518452	+	0.855107i	$0.326508\pi$
$692$	−0.873614	−0.0332098
$693$	−2.16342	−0.0821815
$694$	−27.2806	−1.03556
$695$	0	0
$696$	−1.91829	−0.0727126
$697$	0	0
$698$	30.9538	1.17162
$699$	−24.9933	−0.945334
$700$	0	0
$701$	−41.4441	−1.56532	−0.782660	−	0.622449i	$-0.786138\pi$
$701$	−41.4441	−1.56532	−0.782660	+	0.622449i	$0.786138\pi$
$702$	−14.7759	−0.557679
$703$	4.54677	0.171485
$704$	5.54677	0.209052
$705$	0	0
$706$	11.1819	0.420838
$707$	25.2570	0.949886
$708$	−23.0422	−0.865979
$709$	−36.7904	−1.38169	−0.690846	−	0.723002i	$-0.742762\pi$
$709$	−36.7904	−1.38169	−0.690846	+	0.723002i	$0.742762\pi$
$710$	0	0
$711$	−0.448264	−0.0168112
$712$	−5.09355	−0.190889
$713$	27.2436	1.02028
$714$	23.4769	0.878601
$715$	0	0
$716$	−12.3834	−0.462788
$717$	−27.6825	−1.03382
$718$	20.3387	0.759033
$719$	−4.13726	−0.154294	−0.0771469	−	0.997020i	$-0.524581\pi$
$719$	−4.13726	−0.154294	−0.0771469	+	0.997020i	$0.524581\pi$
$720$	0	0
$721$	34.8037	1.29616
$722$	1.00000	0.0372161
$723$	9.25697	0.344270
$724$	−17.6403	−0.655597
$725$	0	0
$726$	−35.0540	−1.30098
$727$	−40.4374	−1.49974	−0.749870	−	0.661585i	$-0.769884\pi$
$727$	−40.4374	−1.49974	−0.749870	+	0.661585i	$0.769884\pi$
$728$	7.85510	0.291129
$729$	25.5729	0.947146
$730$	0	0
$731$	−46.9538	−1.73665
$732$	13.0935	0.483952
$733$	28.1264	1.03887	0.519436	−	0.854509i	$-0.326142\pi$
$733$	28.1264	1.03887	0.519436	+	0.854509i	$0.326142\pi$
$734$	−32.9538	−1.21635
$735$	0	0
$736$	3.60997	0.133065
$737$	15.8366	0.583348
$738$	0	0
$739$	−38.1501	−1.40337	−0.701686	−	0.712486i	$-0.747569\pi$
$739$	−38.1501	−1.40337	−0.701686	+	0.712486i	$0.747569\pi$
$740$	0	0
$741$	5.17526	0.190118
$742$	−26.3387	−0.966923
$743$	−17.8232	−0.653871	−0.326935	−	0.945047i	$-0.606016\pi$
$743$	−17.8232	−0.653871	−0.326935	+	0.945047i	$0.606016\pi$
$744$	−13.3834	−0.490658
$745$	0	0
$746$	−10.0869	−0.369307
$747$	0.247812	0.00906697
$748$	27.2806	0.997479
$749$	−50.9857	−1.86298
$750$	0	0
$751$	23.6968	0.864710	0.432355	−	0.901703i	$-0.357683\pi$
$751$	23.6968	0.864710	0.432355	+	0.901703i	$0.357683\pi$
$752$	−0.836581	−0.0305070
$753$	50.7904	1.85090
$754$	−3.15674	−0.114962
$755$	0	0
$756$	−13.6285	−0.495663
$757$	−6.51394	−0.236753	−0.118377	−	0.992969i	$-0.537769\pi$
$757$	−6.51394	−0.236753	−0.118377	+	0.992969i	$0.537769\pi$
$758$	−18.4256	−0.669246
$759$	−35.5097	−1.28892
$760$	0	0
$761$	34.7786	1.26072	0.630361	−	0.776302i	$-0.282907\pi$
$761$	34.7786	1.26072	0.630361	+	0.776302i	$0.282907\pi$
$762$	3.32264	0.120367
$763$	7.24513	0.262291
$764$	−15.1567	−0.548352
$765$	0	0
$766$	28.1871	1.01844
$767$	−37.9183	−1.36915
$768$	−1.77339	−0.0639916
$769$	−27.6850	−0.998347	−0.499173	−	0.866502i	$-0.666363\pi$
$769$	−27.6850	−0.998347	−0.499173	+	0.866502i	$0.666363\pi$
$770$	0	0
$771$	−11.4441	−0.412148
$772$	23.3834	0.841585
$773$	−19.9738	−0.718409	−0.359205	−	0.933259i	$-0.616952\pi$
$773$	−19.9738	−0.718409	−0.359205	+	0.933259i	$0.616952\pi$
$774$	−1.38336	−0.0497237
$775$	0	0
$776$	−17.2570	−0.619489
$777$	21.7035	0.778609
$778$	20.0237	0.717884
$779$	0	0
$780$	0	0
$781$	80.3001	2.87336
$782$	17.7549	0.634913
$783$	5.47691	0.195729
$784$	0.245129	0.00875461
$785$	0	0
$786$	20.4769	0.730387
$787$	42.0118	1.49756	0.748780	−	0.662818i	$-0.230640\pi$
$787$	42.0118	1.49756	0.748780	+	0.662818i	$0.230640\pi$
$788$	−23.0935	−0.822674
$789$	−39.3463	−1.40077
$790$	0	0
$791$	16.1501	0.574230
$792$	0.803744	0.0285598
$793$	21.5468	0.765148
$794$	−8.32684	−0.295508
$795$	0	0
$796$	−25.7852	−0.913933
$797$	−45.1054	−1.59771	−0.798857	−	0.601520i	$-0.794562\pi$
$797$	−45.1054	−1.59771	−0.798857	+	0.601520i	$0.794562\pi$
$798$	4.77339	0.168976
$799$	−4.11455	−0.145562
$800$	0	0
$801$	−0.738070	−0.0260784
$802$	−22.1501	−0.782146
$803$	28.6033	1.00939
$804$	−5.06319	−0.178565
$805$	0	0
$806$	−22.0237	−0.775751
$807$	36.1896	1.27393
$808$	−9.38336	−0.330105
$809$	6.85510	0.241012	0.120506	−	0.992713i	$-0.461548\pi$
$809$	6.85510	0.241012	0.120506	+	0.992713i	$0.461548\pi$
$810$	0	0
$811$	−15.1819	−0.533110	−0.266555	−	0.963820i	$-0.585885\pi$
$811$	−15.1819	−0.533110	−0.266555	+	0.963820i	$0.585885\pi$
$812$	−2.91161	−0.102178
$813$	−28.2621	−0.991196
$814$	25.2199	0.883958
$815$	0	0
$816$	−8.72203	−0.305332
$817$	−9.54677	−0.333999
$818$	34.0237	1.18961
$819$	1.13823	0.0397729
$820$	0	0
$821$	22.5006	0.785276	0.392638	−	0.919693i	$-0.371563\pi$
$821$	22.5006	0.785276	0.392638	+	0.919693i	$0.371563\pi$
$822$	−7.51642	−0.262165
$823$	−16.1896	−0.564333	−0.282167	−	0.959365i	$-0.591053\pi$
$823$	−16.1896	−0.564333	−0.282167	+	0.959365i	$0.591053\pi$
$824$	−12.9301	−0.450442
$825$	0	0
$826$	−34.9738	−1.21690
$827$	−25.0817	−0.872177	−0.436088	−	0.899904i	$-0.643636\pi$
$827$	−25.0817	−0.872177	−0.436088	+	0.899904i	$0.643636\pi$
$828$	0.523095	0.0181788
$829$	21.3068	0.740016	0.370008	−	0.929029i	$-0.379355\pi$
$829$	21.3068	0.740016	0.370008	+	0.929029i	$0.379355\pi$
$830$	0	0
$831$	−7.13554	−0.247529
$832$	−2.91829	−0.101174
$833$	1.20562	0.0417721
$834$	−16.3505	−0.566172
$835$	0	0
$836$	5.54677	0.191839
$837$	38.2108	1.32076
$838$	37.5334	1.29657
$839$	−11.4727	−0.396082	−0.198041	−	0.980194i	$-0.563458\pi$
$839$	−11.4727	−0.396082	−0.198041	+	0.980194i	$0.563458\pi$
$840$	0	0
$841$	−27.8299	−0.959652
$842$	33.8341	1.16600
$843$	−2.96716	−0.102195
$844$	14.2266	0.489700
$845$	0	0
$846$	−0.121223	−0.00416773
$847$	−53.2056	−1.82817
$848$	9.78523	0.336026
$849$	−29.9580	−1.02816
$850$	0	0
$851$	16.4137	0.562655
$852$	−25.6732	−0.879548
$853$	−38.9908	−1.33502	−0.667511	−	0.744600i	$-0.732640\pi$
$853$	−38.9908	−1.33502	−0.667511	+	0.744600i	$0.732640\pi$
$854$	19.8736	0.680061
$855$	0	0
$856$	18.9420	0.647423
$857$	−29.8973	−1.02127	−0.510636	−	0.859797i	$-0.670590\pi$
$857$	−29.8973	−1.02127	−0.510636	+	0.859797i	$0.670590\pi$
$858$	28.7060	0.980007
$859$	−6.47691	−0.220989	−0.110495	−	0.993877i	$-0.535243\pi$
$859$	−6.47691	−0.220989	−0.110495	+	0.993877i	$0.535243\pi$
$860$	0	0
$861$	0	0
$862$	24.8037	0.844819
$863$	−5.09355	−0.173386	−0.0866932	−	0.996235i	$-0.527630\pi$
$863$	−5.09355	−0.173386	−0.0866932	+	0.996235i	$0.527630\pi$
$864$	5.06319	0.172253
$865$	0	0
$866$	1.68651	0.0573101
$867$	−12.7499	−0.433010
$868$	−20.3135	−0.689485
$869$	−17.1592	−0.582087
$870$	0	0
$871$	−8.33200	−0.282319
$872$	−2.69168	−0.0911517
$873$	−2.50059	−0.0846320
$874$	3.60997	0.122109
$875$	0	0
$876$	−9.14490	−0.308978
$877$	−29.8341	−1.00743	−0.503713	−	0.863871i	$-0.668033\pi$
$877$	−29.8341	−1.00743	−0.503713	+	0.863871i	$0.668033\pi$
$878$	0.326839	0.0110303
$879$	1.91829	0.0647023
$880$	0	0
$881$	−11.5796	−0.390127	−0.195064	−	0.980791i	$-0.562491\pi$
$881$	−11.5796	−0.390127	−0.195064	+	0.980791i	$0.562491\pi$
$882$	0.0355199	0.00119602
$883$	−48.0237	−1.61613	−0.808063	−	0.589096i	$-0.799484\pi$
$883$	−48.0237	−1.61613	−0.808063	+	0.589096i	$0.799484\pi$
$884$	−14.3530	−0.482744
$885$	0	0
$886$	0.490258	0.0164705
$887$	9.38336	0.315062	0.157531	−	0.987514i	$-0.449647\pi$
$887$	9.38336	0.315062	0.157531	+	0.987514i	$0.449647\pi$
$888$	−8.06319	−0.270583
$889$	5.04316	0.169142
$890$	0	0
$891$	−52.2157	−1.74929
$892$	−4.45323	−0.149105
$893$	−0.836581	−0.0279951
$894$	12.8694	0.430418
$895$	0	0
$896$	−2.69168	−0.0899226
$897$	18.6825	0.623791
$898$	23.5468	0.785766
$899$	8.16342	0.272265
$900$	0	0
$901$	48.1266	1.60333
$902$	0	0
$903$	−45.5705	−1.51649
$904$	−6.00000	−0.199557
$905$	0	0
$906$	−35.4677	−1.17834
$907$	−19.4347	−0.645319	−0.322659	−	0.946515i	$-0.604577\pi$
$907$	−19.4347	−0.645319	−0.322659	+	0.946515i	$0.604577\pi$
$908$	5.94865	0.197413
$909$	−1.35968	−0.0450976
$910$	0	0
$911$	−19.9866	−0.662187	−0.331094	−	0.943598i	$-0.607418\pi$
$911$	−19.9866	−0.662187	−0.331094	+	0.943598i	$0.607418\pi$
$912$	−1.77339	−0.0587227
$913$	9.48606	0.313943
$914$	−8.01184	−0.265008
$915$	0	0
$916$	1.09355	0.0361319
$917$	31.0802	1.02636
$918$	24.9023	0.821897
$919$	6.15158	0.202922	0.101461	−	0.994840i	$-0.467648\pi$
$919$	6.15158	0.202922	0.101461	+	0.994840i	$0.467648\pi$
$920$	0	0
$921$	−4.22661	−0.139272
$922$	3.83658	0.126351
$923$	−42.2478	−1.39060
$924$	26.4769	0.871026
$925$	0	0
$926$	−6.58381	−0.216357
$927$	−1.87361	−0.0615375
$928$	1.08171	0.0355089
$929$	−7.17010	−0.235243	−0.117622	−	0.993058i	$-0.537527\pi$
$929$	−7.17010	−0.235243	−0.117622	+	0.993058i	$0.537527\pi$
$930$	0	0
$931$	0.245129	0.00803378
$932$	14.0935	0.461650
$933$	52.2411	1.71030
$934$	22.6033	0.739602
$935$	0	0
$936$	−0.422869	−0.0138219
$937$	−24.2646	−0.792690	−0.396345	−	0.918102i	$-0.629722\pi$
$937$	−24.2646	−0.792690	−0.396345	+	0.918102i	$0.629722\pi$
$938$	−7.68500	−0.250924
$939$	−56.8114	−1.85397
$940$	0	0
$941$	−7.44806	−0.242800	−0.121400	−	0.992604i	$-0.538738\pi$
$941$	−7.44806	−0.242800	−0.121400	+	0.992604i	$0.538738\pi$
$942$	16.9301	0.551613
$943$	0	0
$944$	12.9933	0.422897
$945$	0	0
$946$	−52.9538	−1.72168
$947$	−52.9538	−1.72077	−0.860384	−	0.509647i	$-0.829776\pi$
$947$	−52.9538	−1.72077	−0.860384	+	0.509647i	$0.829776\pi$
$948$	5.48606	0.178179
$949$	−15.0489	−0.488507
$950$	0	0
$951$	47.2900	1.53348
$952$	−13.2385	−0.429061
$953$	−12.8694	−0.416881	−0.208441	−	0.978035i	$-0.566839\pi$
$953$	−12.8694	−0.416881	−0.208441	+	0.978035i	$0.566839\pi$
$954$	1.41791	0.0459065
$955$	0	0
$956$	15.6100	0.504862
$957$	−10.6403	−0.343953
$958$	−35.7904	−1.15634
$959$	−11.4085	−0.368401
$960$	0	0
$961$	25.9538	0.837220
$962$	−13.2688	−0.427804
$963$	2.74475	0.0884482
$964$	−5.21994	−0.168123
$965$	0	0
$966$	17.2318	0.554423
$967$	25.8603	0.831610	0.415805	−	0.909454i	$-0.363500\pi$
$967$	25.8603	0.831610	0.415805	+	0.909454i	$0.363500\pi$
$968$	19.7667	0.635326
$969$	−8.72203	−0.280192
$970$	0	0
$971$	35.0935	1.12621	0.563103	−	0.826387i	$-0.309608\pi$
$971$	35.0935	1.12621	0.563103	+	0.826387i	$0.309608\pi$
$972$	1.50458	0.0482594
$973$	−24.8171	−0.795600
$974$	−21.4070	−0.685926
$975$	0	0
$976$	−7.38336	−0.236335
$977$	−42.1737	−1.34926	−0.674629	−	0.738157i	$-0.735696\pi$
$977$	−42.1737	−1.34926	−0.674629	+	0.738157i	$0.735696\pi$
$978$	−27.8603	−0.890873
$979$	−28.2528	−0.902963
$980$	0	0
$981$	−0.390032	−0.0124528
$982$	−4.32684	−0.138075
$983$	−42.6270	−1.35959	−0.679795	−	0.733403i	$-0.737931\pi$
$983$	−42.6270	−1.35959	−0.679795	+	0.733403i	$0.737931\pi$
$984$	0	0
$985$	0	0
$986$	5.32016	0.169428
$987$	−3.99332	−0.127109
$988$	−2.91829	−0.0928432
$989$	−34.4636	−1.09588
$990$	0	0
$991$	−34.1737	−1.08556	−0.542782	−	0.839873i	$-0.682629\pi$
$991$	−34.1737	−1.08556	−0.542782	+	0.839873i	$0.682629\pi$
$992$	7.54677	0.239610
$993$	35.2409	1.11834
$994$	−38.9672	−1.23596
$995$	0	0
$996$	−3.03284	−0.0960991
$997$	29.3834	0.930580	0.465290	−	0.885158i	$-0.345950\pi$
$997$	29.3834	0.930580	0.465290	+	0.885158i	$0.345950\pi$
$998$	−37.6968	−1.19327
$999$	23.0212	0.728359

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.a.l.1.1	yes	3
3.2	odd	2		8550.2.a.ci.1.1		3
4.3	odd	2		7600.2.a.bk.1.3		3
5.2	odd	4		950.2.b.h.799.6		6
5.3	odd	4		950.2.b.h.799.1		6
5.4	even	2		950.2.a.j.1.3	✓	3
15.14	odd	2		8550.2.a.cp.1.3		3
20.19	odd	2		7600.2.a.bz.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.a.j.1.3	✓	3	5.4	even	2
950.2.a.l.1.1	yes	3	1.1	even	1	trivial
950.2.b.h.799.1		6	5.3	odd	4
950.2.b.h.799.6		6	5.2	odd	4
7600.2.a.bk.1.3		3	4.3	odd	2
7600.2.a.bz.1.1		3	20.19	odd	2
8550.2.a.ci.1.1		3	3.2	odd	2
8550.2.a.cp.1.3		3	15.14	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.77339 q^{3} +1.00000 q^{4} -1.77339 q^{6} -2.69168 q^{7} +1.00000 q^{8} +0.144903 q^{9} +5.54677 q^{11} -1.77339 q^{12} -2.91829 q^{13} -2.69168 q^{14} +1.00000 q^{16} +4.91829 q^{17} +0.144903 q^{18} +1.00000 q^{19} +4.77339 q^{21} +5.54677 q^{22} +3.60997 q^{23} -1.77339 q^{24} -2.91829 q^{26} +5.06319 q^{27} -2.69168 q^{28} +1.08171 q^{29} +7.54677 q^{31} +1.00000 q^{32} -9.83658 q^{33} +4.91829 q^{34} +0.144903 q^{36} +4.54677 q^{37} +1.00000 q^{38} +5.17526 q^{39} +4.77339 q^{42} -9.54677 q^{43} +5.54677 q^{44} +3.60997 q^{46} -0.836581 q^{47} -1.77339 q^{48} +0.245129 q^{49} -8.72203 q^{51} -2.91829 q^{52} +9.78523 q^{53} +5.06319 q^{54} -2.69168 q^{56} -1.77339 q^{57} +1.08171 q^{58} +12.9933 q^{59} -7.38336 q^{61} +7.54677 q^{62} -0.390032 q^{63} +1.00000 q^{64} -9.83658 q^{66} +2.85510 q^{67} +4.91829 q^{68} -6.40187 q^{69} +14.4769 q^{71} +0.144903 q^{72} +5.15674 q^{73} +4.54677 q^{74} +1.00000 q^{76} -14.9301 q^{77} +5.17526 q^{78} -3.09355 q^{79} -9.41371 q^{81} +1.71019 q^{83} +4.77339 q^{84} -9.54677 q^{86} -1.91829 q^{87} +5.54677 q^{88} -5.09355 q^{89} +7.85510 q^{91} +3.60997 q^{92} -13.3834 q^{93} -0.836581 q^{94} -1.77339 q^{96} -17.2570 q^{97} +0.245129 q^{98} +0.803744 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{6} + 2 q^{7} + 3 q^{8} + 5 q^{9} + 2 q^{11} + 2 q^{12} - 6 q^{13} + 2 q^{14} + 3 q^{16} + 12 q^{17} + 5 q^{18} + 3 q^{19} + 7 q^{21} + 2 q^{22} - 2 q^{23} + 2 q^{24}+ \cdots - 36 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 2 * q^3 + 3 * q^4 + 2 * q^6 + 2 * q^7 + 3 * q^8 + 5 * q^9 + 2 * q^11 + 2 * q^12 - 6 * q^13 + 2 * q^14 + 3 * q^16 + 12 * q^17 + 5 * q^18 + 3 * q^19 + 7 * q^21 + 2 * q^22 - 2 * q^23 + 2 * q^24 - 6 * q^26 + 17 * q^27 + 2 * q^28 + 6 * q^29 + 8 * q^31 + 3 * q^32 - 24 * q^33 + 12 * q^34 + 5 * q^36 - q^37 + 3 * q^38 - 11 * q^39 + 7 * q^42 - 14 * q^43 + 2 * q^44 - 2 * q^46 + 3 * q^47 + 2 * q^48 + 9 * q^49 + 15 * q^51 - 6 * q^52 - 10 * q^53 + 17 * q^54 + 2 * q^56 + 2 * q^57 + 6 * q^58 + 6 * q^59 - 2 * q^61 + 8 * q^62 - 14 * q^63 + 3 * q^64 - 24 * q^66 + 4 * q^67 + 12 * q^68 - 6 * q^71 + 5 * q^72 - 12 * q^73 - q^74 + 3 * q^76 - 10 * q^77 - 11 * q^78 + 20 * q^79 + 23 * q^81 - 4 * q^83 + 7 * q^84 - 14 * q^86 - 3 * q^87 + 2 * q^88 + 14 * q^89 + 19 * q^91 - 2 * q^92 - 20 * q^93 + 3 * q^94 + 2 * q^96 - 28 * q^97 + 9 * q^98 - 36 * q^99

Introduction

L-functions

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