LMFDB - Embedded newform 3850.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3850,2,Mod(1,3850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3850, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3850.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:	$30.7424047782$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	3850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +7.00000 q^{17} +2.00000 q^{18} -4.00000 q^{19} -1.00000 q^{21} +1.00000 q^{22} -8.00000 q^{23} -1.00000 q^{24} -2.00000 q^{26} -5.00000 q^{27} -1.00000 q^{28} +6.00000 q^{29} +5.00000 q^{31} -1.00000 q^{32} -1.00000 q^{33} -7.00000 q^{34} -2.00000 q^{36} -1.00000 q^{37} +4.00000 q^{38} +2.00000 q^{39} +2.00000 q^{41} +1.00000 q^{42} -13.0000 q^{43} -1.00000 q^{44} +8.00000 q^{46} +1.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +7.00000 q^{51} +2.00000 q^{52} -11.0000 q^{53} +5.00000 q^{54} +1.00000 q^{56} -4.00000 q^{57} -6.00000 q^{58} +3.00000 q^{59} +10.0000 q^{61} -5.00000 q^{62} +2.00000 q^{63} +1.00000 q^{64} +1.00000 q^{66} +4.00000 q^{67} +7.00000 q^{68} -8.00000 q^{69} -10.0000 q^{71} +2.00000 q^{72} +1.00000 q^{73} +1.00000 q^{74} -4.00000 q^{76} +1.00000 q^{77} -2.00000 q^{78} -5.00000 q^{79} +1.00000 q^{81} -2.00000 q^{82} -14.0000 q^{83} -1.00000 q^{84} +13.0000 q^{86} +6.00000 q^{87} +1.00000 q^{88} +4.00000 q^{89} -2.00000 q^{91} -8.00000 q^{92} +5.00000 q^{93} -1.00000 q^{94} -1.00000 q^{96} +2.00000 q^{97} -1.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	0	0
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	7.00000	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$18$	2.00000	0.471405
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	1.00000	0.213201
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−2.00000	−0.392232
$27$	−5.00000	−0.962250
$28$	−1.00000	−0.188982
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−7.00000	−1.20049
$35$	0	0
$36$	−2.00000	−0.333333
$37$	−1.00000	−0.164399	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000	−0.164399	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	4.00000	0.648886
$39$	2.00000	0.320256
$40$	0	0
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	1.00000	0.154303
$43$	−13.0000	−1.98248	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−13.0000	−1.98248	−0.991241	+	0.132068i	$0.957838\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	8.00000	1.17954
$47$	1.00000	0.145865	0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000	0.145865	0.0729325	+	0.997337i	$0.476764\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	0	0
$51$	7.00000	0.980196
$52$	2.00000	0.277350
$53$	−11.0000	−1.51097	−0.755483	−	0.655168i	$-0.772598\pi$
$53$	−11.0000	−1.51097	−0.755483	+	0.655168i	$0.772598\pi$
$54$	5.00000	0.680414
$55$	0	0
$56$	1.00000	0.133631
$57$	−4.00000	−0.529813
$58$	−6.00000	−0.787839
$59$	3.00000	0.390567	0.195283	−	0.980747i	$-0.437437\pi$
$59$	3.00000	0.390567	0.195283	+	0.980747i	$0.437437\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	−5.00000	−0.635001
$63$	2.00000	0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	1.00000	0.123091
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	7.00000	0.848875
$69$	−8.00000	−0.963087
$70$	0	0
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	2.00000	0.235702
$73$	1.00000	0.117041	0.0585206	−	0.998286i	$-0.481362\pi$
$73$	1.00000	0.117041	0.0585206	+	0.998286i	$0.481362\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	−4.00000	−0.458831
$77$	1.00000	0.113961
$78$	−2.00000	−0.226455
$79$	−5.00000	−0.562544	−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000	−0.562544	−0.281272	+	0.959628i	$0.590756\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	−14.0000	−1.53670	−0.768350	−	0.640030i	$-0.778922\pi$
$83$	−14.0000	−1.53670	−0.768350	+	0.640030i	$0.778922\pi$
$84$	−1.00000	−0.109109
$85$	0	0
$86$	13.0000	1.40183
$87$	6.00000	0.643268
$88$	1.00000	0.106600
$89$	4.00000	0.423999	0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000	0.423999	0.212000	+	0.977270i	$0.432002\pi$
$90$	0	0
$91$	−2.00000	−0.209657
$92$	−8.00000	−0.834058
$93$	5.00000	0.518476
$94$	−1.00000	−0.103142
$95$	0	0
$96$	−1.00000	−0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−1.00000	−0.101015
$99$	2.00000	0.201008
$100$	0	0
$101$	−3.00000	−0.298511	−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000	−0.298511	−0.149256	+	0.988799i	$0.547688\pi$
$102$	−7.00000	−0.693103
$103$	−11.0000	−1.08386	−0.541931	−	0.840423i	$-0.682307\pi$
$103$	−11.0000	−1.08386	−0.541931	+	0.840423i	$0.682307\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	11.0000	1.06841
$107$	−15.0000	−1.45010	−0.725052	−	0.688694i	$-0.758184\pi$
$107$	−15.0000	−1.45010	−0.725052	+	0.688694i	$0.758184\pi$
$108$	−5.00000	−0.481125
$109$	−16.0000	−1.53252	−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000	−1.53252	−0.766261	+	0.642529i	$0.777885\pi$
$110$	0	0
$111$	−1.00000	−0.0949158
$112$	−1.00000	−0.0944911
$113$	11.0000	1.03479	0.517396	−	0.855746i	$-0.326901\pi$
$113$	11.0000	1.03479	0.517396	+	0.855746i	$0.326901\pi$
$114$	4.00000	0.374634
$115$	0	0
$116$	6.00000	0.557086
$117$	−4.00000	−0.369800
$118$	−3.00000	−0.276172
$119$	−7.00000	−0.641689
$120$	0	0
$121$	1.00000	0.0909091
$122$	−10.0000	−0.905357
$123$	2.00000	0.180334
$124$	5.00000	0.449013
$125$	0	0
$126$	−2.00000	−0.178174
$127$	−21.0000	−1.86345	−0.931724	−	0.363166i	$-0.881696\pi$
$127$	−21.0000	−1.86345	−0.931724	+	0.363166i	$0.881696\pi$
$128$	−1.00000	−0.0883883
$129$	−13.0000	−1.14459
$130$	0	0
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	−1.00000	−0.0870388
$133$	4.00000	0.346844
$134$	−4.00000	−0.345547
$135$	0	0
$136$	−7.00000	−0.600245
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	8.00000	0.681005
$139$	−6.00000	−0.508913	−0.254457	−	0.967084i	$-0.581897\pi$
$139$	−6.00000	−0.508913	−0.254457	+	0.967084i	$0.581897\pi$
$140$	0	0
$141$	1.00000	0.0842152
$142$	10.0000	0.839181
$143$	−2.00000	−0.167248
$144$	−2.00000	−0.166667
$145$	0	0
$146$	−1.00000	−0.0827606
$147$	1.00000	0.0824786
$148$	−1.00000	−0.0821995
$149$	−4.00000	−0.327693	−0.163846	−	0.986486i	$-0.552390\pi$
$149$	−4.00000	−0.327693	−0.163846	+	0.986486i	$0.552390\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	4.00000	0.324443
$153$	−14.0000	−1.13183
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	2.00000	0.160128
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	5.00000	0.397779
$159$	−11.0000	−0.872357
$160$	0	0
$161$	8.00000	0.630488
$162$	−1.00000	−0.0785674
$163$	−2.00000	−0.156652	−0.0783260	−	0.996928i	$-0.524958\pi$
$163$	−2.00000	−0.156652	−0.0783260	+	0.996928i	$0.524958\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	14.0000	1.08661
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	1.00000	0.0771517
$169$	−9.00000	−0.692308
$170$	0	0
$171$	8.00000	0.611775
$172$	−13.0000	−0.991241
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	−6.00000	−0.454859
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	3.00000	0.225494
$178$	−4.00000	−0.299813
$179$	−16.0000	−1.19590	−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000	−1.19590	−0.597948	+	0.801535i	$0.704017\pi$
$180$	0	0
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	2.00000	0.148250
$183$	10.0000	0.739221
$184$	8.00000	0.589768
$185$	0	0
$186$	−5.00000	−0.366618
$187$	−7.00000	−0.511891
$188$	1.00000	0.0729325
$189$	5.00000	0.363696
$190$	0	0
$191$	−4.00000	−0.289430	−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000	−0.289430	−0.144715	+	0.989473i	$0.546227\pi$
$192$	1.00000	0.0721688
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	1.00000	0.0714286
$197$	−22.0000	−1.56744	−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000	−1.56744	−0.783718	+	0.621117i	$0.786679\pi$
$198$	−2.00000	−0.142134
$199$	24.0000	1.70131	0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000	1.70131	0.850657	+	0.525720i	$0.176204\pi$
$200$	0	0
$201$	4.00000	0.282138
$202$	3.00000	0.211079
$203$	−6.00000	−0.421117
$204$	7.00000	0.490098
$205$	0	0
$206$	11.0000	0.766406
$207$	16.0000	1.11208
$208$	2.00000	0.138675
$209$	4.00000	0.276686
$210$	0	0
$211$	15.0000	1.03264	0.516321	−	0.856395i	$-0.327301\pi$
$211$	15.0000	1.03264	0.516321	+	0.856395i	$0.327301\pi$
$212$	−11.0000	−0.755483
$213$	−10.0000	−0.685189
$214$	15.0000	1.02538
$215$	0	0
$216$	5.00000	0.340207
$217$	−5.00000	−0.339422
$218$	16.0000	1.08366
$219$	1.00000	0.0675737
$220$	0	0
$221$	14.0000	0.941742
$222$	1.00000	0.0671156
$223$	24.0000	1.60716	0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000	1.60716	0.803579	+	0.595198i	$0.202926\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−11.0000	−0.731709
$227$	−14.0000	−0.929213	−0.464606	−	0.885517i	$-0.653804\pi$
$227$	−14.0000	−0.929213	−0.464606	+	0.885517i	$0.653804\pi$
$228$	−4.00000	−0.264906
$229$	−12.0000	−0.792982	−0.396491	−	0.918039i	$-0.629772\pi$
$229$	−12.0000	−0.792982	−0.396491	+	0.918039i	$0.629772\pi$
$230$	0	0
$231$	1.00000	0.0657952
$232$	−6.00000	−0.393919
$233$	−16.0000	−1.04819	−0.524097	−	0.851658i	$-0.675597\pi$
$233$	−16.0000	−1.04819	−0.524097	+	0.851658i	$0.675597\pi$
$234$	4.00000	0.261488
$235$	0	0
$236$	3.00000	0.195283
$237$	−5.00000	−0.324785
$238$	7.00000	0.453743
$239$	9.00000	0.582162	0.291081	−	0.956698i	$-0.405985\pi$
$239$	9.00000	0.582162	0.291081	+	0.956698i	$0.405985\pi$
$240$	0	0
$241$	29.0000	1.86805	0.934027	−	0.357202i	$-0.116269\pi$
$241$	29.0000	1.86805	0.934027	+	0.357202i	$0.116269\pi$
$242$	−1.00000	−0.0642824
$243$	16.0000	1.02640
$244$	10.0000	0.640184
$245$	0	0
$246$	−2.00000	−0.127515
$247$	−8.00000	−0.509028
$248$	−5.00000	−0.317500
$249$	−14.0000	−0.887214
$250$	0	0
$251$	15.0000	0.946792	0.473396	−	0.880850i	$-0.343028\pi$
$251$	15.0000	0.946792	0.473396	+	0.880850i	$0.343028\pi$
$252$	2.00000	0.125988
$253$	8.00000	0.502956
$254$	21.0000	1.31766
$255$	0	0
$256$	1.00000	0.0625000
$257$	−10.0000	−0.623783	−0.311891	−	0.950118i	$-0.600963\pi$
$257$	−10.0000	−0.623783	−0.311891	+	0.950118i	$0.600963\pi$
$258$	13.0000	0.809345
$259$	1.00000	0.0621370
$260$	0	0
$261$	−12.0000	−0.742781
$262$	12.0000	0.741362
$263$	23.0000	1.41824	0.709120	−	0.705087i	$-0.249092\pi$
$263$	23.0000	1.41824	0.709120	+	0.705087i	$0.249092\pi$
$264$	1.00000	0.0615457
$265$	0	0
$266$	−4.00000	−0.245256
$267$	4.00000	0.244796
$268$	4.00000	0.244339
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	0	0
$271$	−26.0000	−1.57939	−0.789694	−	0.613501i	$-0.789761\pi$
$271$	−26.0000	−1.57939	−0.789694	+	0.613501i	$0.789761\pi$
$272$	7.00000	0.424437
$273$	−2.00000	−0.121046
$274$	−2.00000	−0.120824
$275$	0	0
$276$	−8.00000	−0.481543
$277$	−16.0000	−0.961347	−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000	−0.961347	−0.480673	+	0.876900i	$0.659608\pi$
$278$	6.00000	0.359856
$279$	−10.0000	−0.598684
$280$	0	0
$281$	8.00000	0.477240	0.238620	−	0.971113i	$-0.423305\pi$
$281$	8.00000	0.477240	0.238620	+	0.971113i	$0.423305\pi$
$282$	−1.00000	−0.0595491
$283$	26.0000	1.54554	0.772770	−	0.634686i	$-0.218871\pi$
$283$	26.0000	1.54554	0.772770	+	0.634686i	$0.218871\pi$
$284$	−10.0000	−0.593391
$285$	0	0
$286$	2.00000	0.118262
$287$	−2.00000	−0.118056
$288$	2.00000	0.117851
$289$	32.0000	1.88235
$290$	0	0
$291$	2.00000	0.117242
$292$	1.00000	0.0585206
$293$	−19.0000	−1.10999	−0.554996	−	0.831853i	$-0.687280\pi$
$293$	−19.0000	−1.10999	−0.554996	+	0.831853i	$0.687280\pi$
$294$	−1.00000	−0.0583212
$295$	0	0
$296$	1.00000	0.0581238
$297$	5.00000	0.290129
$298$	4.00000	0.231714
$299$	−16.0000	−0.925304
$300$	0	0
$301$	13.0000	0.749308
$302$	0	0
$303$	−3.00000	−0.172345
$304$	−4.00000	−0.229416
$305$	0	0
$306$	14.0000	0.800327
$307$	32.0000	1.82634	0.913168	−	0.407583i	$-0.133628\pi$
$307$	32.0000	1.82634	0.913168	+	0.407583i	$0.133628\pi$
$308$	1.00000	0.0569803
$309$	−11.0000	−0.625768
$310$	0	0
$311$	−15.0000	−0.850572	−0.425286	−	0.905059i	$-0.639826\pi$
$311$	−15.0000	−0.850572	−0.425286	+	0.905059i	$0.639826\pi$
$312$	−2.00000	−0.113228
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	−18.0000	−1.01580
$315$	0	0
$316$	−5.00000	−0.281272
$317$	3.00000	0.168497	0.0842484	−	0.996445i	$-0.473151\pi$
$317$	3.00000	0.168497	0.0842484	+	0.996445i	$0.473151\pi$
$318$	11.0000	0.616849
$319$	−6.00000	−0.335936
$320$	0	0
$321$	−15.0000	−0.837218
$322$	−8.00000	−0.445823
$323$	−28.0000	−1.55796
$324$	1.00000	0.0555556
$325$	0	0
$326$	2.00000	0.110770
$327$	−16.0000	−0.884802
$328$	−2.00000	−0.110432
$329$	−1.00000	−0.0551318
$330$	0	0
$331$	−8.00000	−0.439720	−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000	−0.439720	−0.219860	+	0.975531i	$0.570560\pi$
$332$	−14.0000	−0.768350
$333$	2.00000	0.109599
$334$	0	0
$335$	0	0
$336$	−1.00000	−0.0545545
$337$	−20.0000	−1.08947	−0.544735	−	0.838608i	$-0.683370\pi$
$337$	−20.0000	−1.08947	−0.544735	+	0.838608i	$0.683370\pi$
$338$	9.00000	0.489535
$339$	11.0000	0.597438
$340$	0	0
$341$	−5.00000	−0.270765
$342$	−8.00000	−0.432590
$343$	−1.00000	−0.0539949
$344$	13.0000	0.700913
$345$	0	0
$346$	6.00000	0.322562
$347$	−21.0000	−1.12734	−0.563670	−	0.826000i	$-0.690611\pi$
$347$	−21.0000	−1.12734	−0.563670	+	0.826000i	$0.690611\pi$
$348$	6.00000	0.321634
$349$	−29.0000	−1.55233	−0.776167	−	0.630527i	$-0.782839\pi$
$349$	−29.0000	−1.55233	−0.776167	+	0.630527i	$0.782839\pi$
$350$	0	0
$351$	−10.0000	−0.533761
$352$	1.00000	0.0533002
$353$	−36.0000	−1.91609	−0.958043	−	0.286623i	$-0.907467\pi$
$353$	−36.0000	−1.91609	−0.958043	+	0.286623i	$0.907467\pi$
$354$	−3.00000	−0.159448
$355$	0	0
$356$	4.00000	0.212000
$357$	−7.00000	−0.370479
$358$	16.0000	0.845626
$359$	20.0000	1.05556	0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000	1.05556	0.527780	+	0.849381i	$0.323025\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	−10.0000	−0.525588
$363$	1.00000	0.0524864
$364$	−2.00000	−0.104828
$365$	0	0
$366$	−10.0000	−0.522708
$367$	0	0		−	1.00000i	$-0.5\pi$
$367$	0	0			1.00000i	$0.5\pi$
$368$	−8.00000	−0.417029
$369$	−4.00000	−0.208232
$370$	0	0
$371$	11.0000	0.571092
$372$	5.00000	0.259238
$373$	12.0000	0.621336	0.310668	−	0.950518i	$-0.399447\pi$
$373$	12.0000	0.621336	0.310668	+	0.950518i	$0.399447\pi$
$374$	7.00000	0.361961
$375$	0	0
$376$	−1.00000	−0.0515711
$377$	12.0000	0.618031
$378$	−5.00000	−0.257172
$379$	−8.00000	−0.410932	−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000	−0.410932	−0.205466	+	0.978664i	$0.565871\pi$
$380$	0	0
$381$	−21.0000	−1.07586
$382$	4.00000	0.204658
$383$	15.0000	0.766464	0.383232	−	0.923652i	$-0.374811\pi$
$383$	15.0000	0.766464	0.383232	+	0.923652i	$0.374811\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	22.0000	1.11977
$387$	26.0000	1.32165
$388$	2.00000	0.101535
$389$	−17.0000	−0.861934	−0.430967	−	0.902368i	$-0.641828\pi$
$389$	−17.0000	−0.861934	−0.430967	+	0.902368i	$0.641828\pi$
$390$	0	0
$391$	−56.0000	−2.83204
$392$	−1.00000	−0.0505076
$393$	−12.0000	−0.605320
$394$	22.0000	1.10834
$395$	0	0
$396$	2.00000	0.100504
$397$	6.00000	0.301131	0.150566	−	0.988600i	$-0.451890\pi$
$397$	6.00000	0.301131	0.150566	+	0.988600i	$0.451890\pi$
$398$	−24.0000	−1.20301
$399$	4.00000	0.200250
$400$	0	0
$401$	−21.0000	−1.04869	−0.524345	−	0.851506i	$-0.675690\pi$
$401$	−21.0000	−1.04869	−0.524345	+	0.851506i	$0.675690\pi$
$402$	−4.00000	−0.199502
$403$	10.0000	0.498135
$404$	−3.00000	−0.149256
$405$	0	0
$406$	6.00000	0.297775
$407$	1.00000	0.0495682
$408$	−7.00000	−0.346552
$409$	−1.00000	−0.0494468	−0.0247234	−	0.999694i	$-0.507871\pi$
$409$	−1.00000	−0.0494468	−0.0247234	+	0.999694i	$0.507871\pi$
$410$	0	0
$411$	2.00000	0.0986527
$412$	−11.0000	−0.541931
$413$	−3.00000	−0.147620
$414$	−16.0000	−0.786357
$415$	0	0
$416$	−2.00000	−0.0980581
$417$	−6.00000	−0.293821
$418$	−4.00000	−0.195646
$419$	−13.0000	−0.635092	−0.317546	−	0.948243i	$-0.602859\pi$
$419$	−13.0000	−0.635092	−0.317546	+	0.948243i	$0.602859\pi$
$420$	0	0
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−15.0000	−0.730189
$423$	−2.00000	−0.0972433
$424$	11.0000	0.534207
$425$	0	0
$426$	10.0000	0.484502
$427$	−10.0000	−0.483934
$428$	−15.0000	−0.725052
$429$	−2.00000	−0.0965609
$430$	0	0
$431$	7.00000	0.337178	0.168589	−	0.985686i	$-0.446079\pi$
$431$	7.00000	0.337178	0.168589	+	0.985686i	$0.446079\pi$
$432$	−5.00000	−0.240563
$433$	−22.0000	−1.05725	−0.528626	−	0.848855i	$-0.677293\pi$
$433$	−22.0000	−1.05725	−0.528626	+	0.848855i	$0.677293\pi$
$434$	5.00000	0.240008
$435$	0	0
$436$	−16.0000	−0.766261
$437$	32.0000	1.53077
$438$	−1.00000	−0.0477818
$439$	34.0000	1.62273	0.811366	−	0.584539i	$-0.198725\pi$
$439$	34.0000	1.62273	0.811366	+	0.584539i	$0.198725\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	−14.0000	−0.665912
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	−1.00000	−0.0474579
$445$	0	0
$446$	−24.0000	−1.13643
$447$	−4.00000	−0.189194
$448$	−1.00000	−0.0472456
$449$	39.0000	1.84052	0.920262	−	0.391303i	$-0.127976\pi$
$449$	39.0000	1.84052	0.920262	+	0.391303i	$0.127976\pi$
$450$	0	0
$451$	−2.00000	−0.0941763
$452$	11.0000	0.517396
$453$	0	0
$454$	14.0000	0.657053
$455$	0	0
$456$	4.00000	0.187317
$457$	−16.0000	−0.748448	−0.374224	−	0.927338i	$-0.622091\pi$
$457$	−16.0000	−0.748448	−0.374224	+	0.927338i	$0.622091\pi$
$458$	12.0000	0.560723
$459$	−35.0000	−1.63366
$460$	0	0
$461$	−25.0000	−1.16437	−0.582183	−	0.813058i	$-0.697801\pi$
$461$	−25.0000	−1.16437	−0.582183	+	0.813058i	$0.697801\pi$
$462$	−1.00000	−0.0465242
$463$	14.0000	0.650635	0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000	0.650635	0.325318	+	0.945605i	$0.394529\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	16.0000	0.741186
$467$	21.0000	0.971764	0.485882	−	0.874024i	$-0.338498\pi$
$467$	21.0000	0.971764	0.485882	+	0.874024i	$0.338498\pi$
$468$	−4.00000	−0.184900
$469$	−4.00000	−0.184703
$470$	0	0
$471$	18.0000	0.829396
$472$	−3.00000	−0.138086
$473$	13.0000	0.597741
$474$	5.00000	0.229658
$475$	0	0
$476$	−7.00000	−0.320844
$477$	22.0000	1.00731
$478$	−9.00000	−0.411650
$479$	−18.0000	−0.822441	−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000	−0.822441	−0.411220	+	0.911536i	$0.634897\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	−29.0000	−1.32091
$483$	8.00000	0.364013
$484$	1.00000	0.0454545
$485$	0	0
$486$	−16.0000	−0.725775
$487$	6.00000	0.271886	0.135943	−	0.990717i	$-0.456594\pi$
$487$	6.00000	0.271886	0.135943	+	0.990717i	$0.456594\pi$
$488$	−10.0000	−0.452679
$489$	−2.00000	−0.0904431
$490$	0	0
$491$	17.0000	0.767199	0.383600	−	0.923499i	$-0.374684\pi$
$491$	17.0000	0.767199	0.383600	+	0.923499i	$0.374684\pi$
$492$	2.00000	0.0901670
$493$	42.0000	1.89158
$494$	8.00000	0.359937
$495$	0	0
$496$	5.00000	0.224507
$497$	10.0000	0.448561
$498$	14.0000	0.627355
$499$	4.00000	0.179065	0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000	0.179065	0.0895323	+	0.995984i	$0.471463\pi$
$500$	0	0
$501$	0	0
$502$	−15.0000	−0.669483
$503$	−36.0000	−1.60516	−0.802580	−	0.596544i	$-0.796540\pi$
$503$	−36.0000	−1.60516	−0.802580	+	0.596544i	$0.796540\pi$
$504$	−2.00000	−0.0890871
$505$	0	0
$506$	−8.00000	−0.355643
$507$	−9.00000	−0.399704
$508$	−21.0000	−0.931724
$509$	36.0000	1.59567	0.797836	−	0.602875i	$-0.205978\pi$
$509$	36.0000	1.59567	0.797836	+	0.602875i	$0.205978\pi$
$510$	0	0
$511$	−1.00000	−0.0442374
$512$	−1.00000	−0.0441942
$513$	20.0000	0.883022
$514$	10.0000	0.441081
$515$	0	0
$516$	−13.0000	−0.572293
$517$	−1.00000	−0.0439799
$518$	−1.00000	−0.0439375
$519$	−6.00000	−0.263371
$520$	0	0
$521$	28.0000	1.22670	0.613351	−	0.789810i	$-0.289821\pi$
$521$	28.0000	1.22670	0.613351	+	0.789810i	$0.289821\pi$
$522$	12.0000	0.525226
$523$	18.0000	0.787085	0.393543	−	0.919306i	$-0.371249\pi$
$523$	18.0000	0.787085	0.393543	+	0.919306i	$0.371249\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	−23.0000	−1.00285
$527$	35.0000	1.52462
$528$	−1.00000	−0.0435194
$529$	41.0000	1.78261
$530$	0	0
$531$	−6.00000	−0.260378
$532$	4.00000	0.173422
$533$	4.00000	0.173259
$534$	−4.00000	−0.173097
$535$	0	0
$536$	−4.00000	−0.172774
$537$	−16.0000	−0.690451
$538$	14.0000	0.603583
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	22.0000	0.945854	0.472927	−	0.881102i	$-0.343197\pi$
$541$	22.0000	0.945854	0.472927	+	0.881102i	$0.343197\pi$
$542$	26.0000	1.11680
$543$	10.0000	0.429141
$544$	−7.00000	−0.300123
$545$	0	0
$546$	2.00000	0.0855921
$547$	41.0000	1.75303	0.876517	−	0.481371i	$-0.159861\pi$
$547$	41.0000	1.75303	0.876517	+	0.481371i	$0.159861\pi$
$548$	2.00000	0.0854358
$549$	−20.0000	−0.853579
$550$	0	0
$551$	−24.0000	−1.02243
$552$	8.00000	0.340503
$553$	5.00000	0.212622
$554$	16.0000	0.679775
$555$	0	0
$556$	−6.00000	−0.254457
$557$	8.00000	0.338971	0.169485	−	0.985533i	$-0.445789\pi$
$557$	8.00000	0.338971	0.169485	+	0.985533i	$0.445789\pi$
$558$	10.0000	0.423334
$559$	−26.0000	−1.09968
$560$	0	0
$561$	−7.00000	−0.295540
$562$	−8.00000	−0.337460
$563$	30.0000	1.26435	0.632175	−	0.774826i	$-0.282163\pi$
$563$	30.0000	1.26435	0.632175	+	0.774826i	$0.282163\pi$
$564$	1.00000	0.0421076
$565$	0	0
$566$	−26.0000	−1.09286
$567$	−1.00000	−0.0419961
$568$	10.0000	0.419591
$569$	−26.0000	−1.08998	−0.544988	−	0.838444i	$-0.683466\pi$
$569$	−26.0000	−1.08998	−0.544988	+	0.838444i	$0.683466\pi$
$570$	0	0
$571$	−36.0000	−1.50655	−0.753277	−	0.657704i	$-0.771528\pi$
$571$	−36.0000	−1.50655	−0.753277	+	0.657704i	$0.771528\pi$
$572$	−2.00000	−0.0836242
$573$	−4.00000	−0.167102
$574$	2.00000	0.0834784
$575$	0	0
$576$	−2.00000	−0.0833333
$577$	18.0000	0.749350	0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000	0.749350	0.374675	+	0.927156i	$0.377754\pi$
$578$	−32.0000	−1.33102
$579$	−22.0000	−0.914289
$580$	0	0
$581$	14.0000	0.580818
$582$	−2.00000	−0.0829027
$583$	11.0000	0.455573
$584$	−1.00000	−0.0413803
$585$	0	0
$586$	19.0000	0.784883
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	1.00000	0.0412393
$589$	−20.0000	−0.824086
$590$	0	0
$591$	−22.0000	−0.904959
$592$	−1.00000	−0.0410997
$593$	−22.0000	−0.903432	−0.451716	−	0.892162i	$-0.649188\pi$
$593$	−22.0000	−0.903432	−0.451716	+	0.892162i	$0.649188\pi$
$594$	−5.00000	−0.205152
$595$	0	0
$596$	−4.00000	−0.163846
$597$	24.0000	0.982255
$598$	16.0000	0.654289
$599$	−18.0000	−0.735460	−0.367730	−	0.929933i	$-0.619865\pi$
$599$	−18.0000	−0.735460	−0.367730	+	0.929933i	$0.619865\pi$
$600$	0	0
$601$	−7.00000	−0.285536	−0.142768	−	0.989756i	$-0.545600\pi$
$601$	−7.00000	−0.285536	−0.142768	+	0.989756i	$0.545600\pi$
$602$	−13.0000	−0.529840
$603$	−8.00000	−0.325785
$604$	0	0
$605$	0	0
$606$	3.00000	0.121867
$607$	−26.0000	−1.05531	−0.527654	−	0.849460i	$-0.676928\pi$
$607$	−26.0000	−1.05531	−0.527654	+	0.849460i	$0.676928\pi$
$608$	4.00000	0.162221
$609$	−6.00000	−0.243132
$610$	0	0
$611$	2.00000	0.0809113
$612$	−14.0000	−0.565916
$613$	−24.0000	−0.969351	−0.484675	−	0.874694i	$-0.661062\pi$
$613$	−24.0000	−0.969351	−0.484675	+	0.874694i	$0.661062\pi$
$614$	−32.0000	−1.29141
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	−47.0000	−1.89215	−0.946074	−	0.323949i	$-0.894989\pi$
$617$	−47.0000	−1.89215	−0.946074	+	0.323949i	$0.894989\pi$
$618$	11.0000	0.442485
$619$	−11.0000	−0.442127	−0.221064	−	0.975259i	$-0.570953\pi$
$619$	−11.0000	−0.442127	−0.221064	+	0.975259i	$0.570953\pi$
$620$	0	0
$621$	40.0000	1.60514
$622$	15.0000	0.601445
$623$	−4.00000	−0.160257
$624$	2.00000	0.0800641
$625$	0	0
$626$	−6.00000	−0.239808
$627$	4.00000	0.159745
$628$	18.0000	0.718278
$629$	−7.00000	−0.279108
$630$	0	0
$631$	20.0000	0.796187	0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000	0.796187	0.398094	+	0.917345i	$0.369672\pi$
$632$	5.00000	0.198889
$633$	15.0000	0.596196
$634$	−3.00000	−0.119145
$635$	0	0
$636$	−11.0000	−0.436178
$637$	2.00000	0.0792429
$638$	6.00000	0.237542
$639$	20.0000	0.791188
$640$	0	0
$641$	−15.0000	−0.592464	−0.296232	−	0.955116i	$-0.595730\pi$
$641$	−15.0000	−0.592464	−0.296232	+	0.955116i	$0.595730\pi$
$642$	15.0000	0.592003
$643$	−33.0000	−1.30139	−0.650696	−	0.759338i	$-0.725523\pi$
$643$	−33.0000	−1.30139	−0.650696	+	0.759338i	$0.725523\pi$
$644$	8.00000	0.315244
$645$	0	0
$646$	28.0000	1.10165
$647$	33.0000	1.29736	0.648682	−	0.761060i	$-0.275321\pi$
$647$	33.0000	1.29736	0.648682	+	0.761060i	$0.275321\pi$
$648$	−1.00000	−0.0392837
$649$	−3.00000	−0.117760
$650$	0	0
$651$	−5.00000	−0.195965
$652$	−2.00000	−0.0783260
$653$	43.0000	1.68272	0.841360	−	0.540475i	$-0.181755\pi$
$653$	43.0000	1.68272	0.841360	+	0.540475i	$0.181755\pi$
$654$	16.0000	0.625650
$655$	0	0
$656$	2.00000	0.0780869
$657$	−2.00000	−0.0780274
$658$	1.00000	0.0389841
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	10.0000	0.388955	0.194477	−	0.980907i	$-0.437699\pi$
$661$	10.0000	0.388955	0.194477	+	0.980907i	$0.437699\pi$
$662$	8.00000	0.310929
$663$	14.0000	0.543715
$664$	14.0000	0.543305
$665$	0	0
$666$	−2.00000	−0.0774984
$667$	−48.0000	−1.85857
$668$	0	0
$669$	24.0000	0.927894
$670$	0	0
$671$	−10.0000	−0.386046
$672$	1.00000	0.0385758
$673$	−22.0000	−0.848038	−0.424019	−	0.905653i	$-0.639381\pi$
$673$	−22.0000	−0.848038	−0.424019	+	0.905653i	$0.639381\pi$
$674$	20.0000	0.770371
$675$	0	0
$676$	−9.00000	−0.346154
$677$	35.0000	1.34516	0.672580	−	0.740025i	$-0.265186\pi$
$677$	35.0000	1.34516	0.672580	+	0.740025i	$0.265186\pi$
$678$	−11.0000	−0.422452
$679$	−2.00000	−0.0767530
$680$	0	0
$681$	−14.0000	−0.536481
$682$	5.00000	0.191460
$683$	−30.0000	−1.14792	−0.573959	−	0.818884i	$-0.694593\pi$
$683$	−30.0000	−1.14792	−0.573959	+	0.818884i	$0.694593\pi$
$684$	8.00000	0.305888
$685$	0	0
$686$	1.00000	0.0381802
$687$	−12.0000	−0.457829
$688$	−13.0000	−0.495620
$689$	−22.0000	−0.838133
$690$	0	0
$691$	−11.0000	−0.418460	−0.209230	−	0.977866i	$-0.567096\pi$
$691$	−11.0000	−0.418460	−0.209230	+	0.977866i	$0.567096\pi$
$692$	−6.00000	−0.228086
$693$	−2.00000	−0.0759737
$694$	21.0000	0.797149
$695$	0	0
$696$	−6.00000	−0.227429
$697$	14.0000	0.530288
$698$	29.0000	1.09767
$699$	−16.0000	−0.605176
$700$	0	0
$701$	8.00000	0.302156	0.151078	−	0.988522i	$-0.451726\pi$
$701$	8.00000	0.302156	0.151078	+	0.988522i	$0.451726\pi$
$702$	10.0000	0.377426
$703$	4.00000	0.150863
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	36.0000	1.35488
$707$	3.00000	0.112827
$708$	3.00000	0.112747
$709$	9.00000	0.338002	0.169001	−	0.985616i	$-0.445946\pi$
$709$	9.00000	0.338002	0.169001	+	0.985616i	$0.445946\pi$
$710$	0	0
$711$	10.0000	0.375029
$712$	−4.00000	−0.149906
$713$	−40.0000	−1.49801
$714$	7.00000	0.261968
$715$	0	0
$716$	−16.0000	−0.597948
$717$	9.00000	0.336111
$718$	−20.0000	−0.746393
$719$	48.0000	1.79010	0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000	1.79010	0.895049	+	0.445968i	$0.147140\pi$
$720$	0	0
$721$	11.0000	0.409661
$722$	3.00000	0.111648
$723$	29.0000	1.07852
$724$	10.0000	0.371647
$725$	0	0
$726$	−1.00000	−0.0371135
$727$	45.0000	1.66896	0.834479	−	0.551040i	$-0.185769\pi$
$727$	45.0000	1.66896	0.834479	+	0.551040i	$0.185769\pi$
$728$	2.00000	0.0741249
$729$	13.0000	0.481481
$730$	0	0
$731$	−91.0000	−3.36576
$732$	10.0000	0.369611
$733$	−7.00000	−0.258551	−0.129275	−	0.991609i	$-0.541265\pi$
$733$	−7.00000	−0.258551	−0.129275	+	0.991609i	$0.541265\pi$
$734$	0	0
$735$	0	0
$736$	8.00000	0.294884
$737$	−4.00000	−0.147342
$738$	4.00000	0.147242
$739$	−23.0000	−0.846069	−0.423034	−	0.906114i	$-0.639035\pi$
$739$	−23.0000	−0.846069	−0.423034	+	0.906114i	$0.639035\pi$
$740$	0	0
$741$	−8.00000	−0.293887
$742$	−11.0000	−0.403823
$743$	11.0000	0.403551	0.201775	−	0.979432i	$-0.435329\pi$
$743$	11.0000	0.403551	0.201775	+	0.979432i	$0.435329\pi$
$744$	−5.00000	−0.183309
$745$	0	0
$746$	−12.0000	−0.439351
$747$	28.0000	1.02447
$748$	−7.00000	−0.255945
$749$	15.0000	0.548088
$750$	0	0
$751$	2.00000	0.0729810	0.0364905	−	0.999334i	$-0.488382\pi$
$751$	2.00000	0.0729810	0.0364905	+	0.999334i	$0.488382\pi$
$752$	1.00000	0.0364662
$753$	15.0000	0.546630
$754$	−12.0000	−0.437014
$755$	0	0
$756$	5.00000	0.181848
$757$	13.0000	0.472493	0.236247	−	0.971693i	$-0.424083\pi$
$757$	13.0000	0.472493	0.236247	+	0.971693i	$0.424083\pi$
$758$	8.00000	0.290573
$759$	8.00000	0.290382
$760$	0	0
$761$	15.0000	0.543750	0.271875	−	0.962333i	$-0.412356\pi$
$761$	15.0000	0.543750	0.271875	+	0.962333i	$0.412356\pi$
$762$	21.0000	0.760750
$763$	16.0000	0.579239
$764$	−4.00000	−0.144715
$765$	0	0
$766$	−15.0000	−0.541972
$767$	6.00000	0.216647
$768$	1.00000	0.0360844
$769$	−2.00000	−0.0721218	−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000	−0.0721218	−0.0360609	+	0.999350i	$0.511481\pi$
$770$	0	0
$771$	−10.0000	−0.360141
$772$	−22.0000	−0.791797
$773$	−14.0000	−0.503545	−0.251773	−	0.967786i	$-0.581013\pi$
$773$	−14.0000	−0.503545	−0.251773	+	0.967786i	$0.581013\pi$
$774$	−26.0000	−0.934551
$775$	0	0
$776$	−2.00000	−0.0717958
$777$	1.00000	0.0358748
$778$	17.0000	0.609480
$779$	−8.00000	−0.286630
$780$	0	0
$781$	10.0000	0.357828
$782$	56.0000	2.00256
$783$	−30.0000	−1.07211
$784$	1.00000	0.0357143
$785$	0	0
$786$	12.0000	0.428026
$787$	36.0000	1.28326	0.641631	−	0.767014i	$-0.278258\pi$
$787$	36.0000	1.28326	0.641631	+	0.767014i	$0.278258\pi$
$788$	−22.0000	−0.783718
$789$	23.0000	0.818822
$790$	0	0
$791$	−11.0000	−0.391115
$792$	−2.00000	−0.0710669
$793$	20.0000	0.710221
$794$	−6.00000	−0.212932
$795$	0	0
$796$	24.0000	0.850657
$797$	−28.0000	−0.991811	−0.495905	−	0.868377i	$-0.665164\pi$
$797$	−28.0000	−0.991811	−0.495905	+	0.868377i	$0.665164\pi$
$798$	−4.00000	−0.141598
$799$	7.00000	0.247642
$800$	0	0
$801$	−8.00000	−0.282666
$802$	21.0000	0.741536
$803$	−1.00000	−0.0352892
$804$	4.00000	0.141069
$805$	0	0
$806$	−10.0000	−0.352235
$807$	−14.0000	−0.492823
$808$	3.00000	0.105540
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	0	0
$811$	32.0000	1.12367	0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000	1.12367	0.561836	+	0.827249i	$0.310095\pi$
$812$	−6.00000	−0.210559
$813$	−26.0000	−0.911860
$814$	−1.00000	−0.0350500
$815$	0	0
$816$	7.00000	0.245049
$817$	52.0000	1.81925
$818$	1.00000	0.0349642
$819$	4.00000	0.139771
$820$	0	0
$821$	36.0000	1.25641	0.628204	−	0.778048i	$-0.283790\pi$
$821$	36.0000	1.25641	0.628204	+	0.778048i	$0.283790\pi$
$822$	−2.00000	−0.0697580
$823$	32.0000	1.11545	0.557725	−	0.830026i	$-0.311674\pi$
$823$	32.0000	1.11545	0.557725	+	0.830026i	$0.311674\pi$
$824$	11.0000	0.383203
$825$	0	0
$826$	3.00000	0.104383
$827$	−37.0000	−1.28662	−0.643308	−	0.765607i	$-0.722439\pi$
$827$	−37.0000	−1.28662	−0.643308	+	0.765607i	$0.722439\pi$
$828$	16.0000	0.556038
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	0	0
$831$	−16.0000	−0.555034
$832$	2.00000	0.0693375
$833$	7.00000	0.242536
$834$	6.00000	0.207763
$835$	0	0
$836$	4.00000	0.138343
$837$	−25.0000	−0.864126
$838$	13.0000	0.449078
$839$	−24.0000	−0.828572	−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000	−0.828572	−0.414286	+	0.910147i	$0.635969\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	2.00000	0.0689246
$843$	8.00000	0.275535
$844$	15.0000	0.516321
$845$	0	0
$846$	2.00000	0.0687614
$847$	−1.00000	−0.0343604
$848$	−11.0000	−0.377742
$849$	26.0000	0.892318
$850$	0	0
$851$	8.00000	0.274236
$852$	−10.0000	−0.342594
$853$	47.0000	1.60925	0.804625	−	0.593784i	$-0.202367\pi$
$853$	47.0000	1.60925	0.804625	+	0.593784i	$0.202367\pi$
$854$	10.0000	0.342193
$855$	0	0
$856$	15.0000	0.512689
$857$	42.0000	1.43469	0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000	1.43469	0.717346	+	0.696717i	$0.245357\pi$
$858$	2.00000	0.0682789
$859$	41.0000	1.39890	0.699451	−	0.714681i	$-0.253428\pi$
$859$	41.0000	1.39890	0.699451	+	0.714681i	$0.253428\pi$
$860$	0	0
$861$	−2.00000	−0.0681598
$862$	−7.00000	−0.238421
$863$	−22.0000	−0.748889	−0.374444	−	0.927249i	$-0.622167\pi$
$863$	−22.0000	−0.748889	−0.374444	+	0.927249i	$0.622167\pi$
$864$	5.00000	0.170103
$865$	0	0
$866$	22.0000	0.747590
$867$	32.0000	1.08678
$868$	−5.00000	−0.169711
$869$	5.00000	0.169613
$870$	0	0
$871$	8.00000	0.271070
$872$	16.0000	0.541828
$873$	−4.00000	−0.135379
$874$	−32.0000	−1.08242
$875$	0	0
$876$	1.00000	0.0337869
$877$	−8.00000	−0.270141	−0.135070	−	0.990836i	$-0.543126\pi$
$877$	−8.00000	−0.270141	−0.135070	+	0.990836i	$0.543126\pi$
$878$	−34.0000	−1.14744
$879$	−19.0000	−0.640854
$880$	0	0
$881$	28.0000	0.943344	0.471672	−	0.881774i	$-0.343651\pi$
$881$	28.0000	0.943344	0.471672	+	0.881774i	$0.343651\pi$
$882$	2.00000	0.0673435
$883$	2.00000	0.0673054	0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000	0.0673054	0.0336527	+	0.999434i	$0.489286\pi$
$884$	14.0000	0.470871
$885$	0	0
$886$	24.0000	0.806296
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	1.00000	0.0335578
$889$	21.0000	0.704317
$890$	0	0
$891$	−1.00000	−0.0335013
$892$	24.0000	0.803579
$893$	−4.00000	−0.133855
$894$	4.00000	0.133780
$895$	0	0
$896$	1.00000	0.0334077
$897$	−16.0000	−0.534224
$898$	−39.0000	−1.30145
$899$	30.0000	1.00056
$900$	0	0
$901$	−77.0000	−2.56524
$902$	2.00000	0.0665927
$903$	13.0000	0.432613
$904$	−11.0000	−0.365855
$905$	0	0
$906$	0	0
$907$	38.0000	1.26177	0.630885	−	0.775877i	$-0.282692\pi$
$907$	38.0000	1.26177	0.630885	+	0.775877i	$0.282692\pi$
$908$	−14.0000	−0.464606
$909$	6.00000	0.199007
$910$	0	0
$911$	−10.0000	−0.331315	−0.165657	−	0.986183i	$-0.552975\pi$
$911$	−10.0000	−0.331315	−0.165657	+	0.986183i	$0.552975\pi$
$912$	−4.00000	−0.132453
$913$	14.0000	0.463332
$914$	16.0000	0.529233
$915$	0	0
$916$	−12.0000	−0.396491
$917$	12.0000	0.396275
$918$	35.0000	1.15517
$919$	39.0000	1.28649	0.643246	−	0.765660i	$-0.277587\pi$
$919$	39.0000	1.28649	0.643246	+	0.765660i	$0.277587\pi$
$920$	0	0
$921$	32.0000	1.05444
$922$	25.0000	0.823331
$923$	−20.0000	−0.658308
$924$	1.00000	0.0328976
$925$	0	0
$926$	−14.0000	−0.460069
$927$	22.0000	0.722575
$928$	−6.00000	−0.196960
$929$	−36.0000	−1.18112	−0.590561	−	0.806993i	$-0.701093\pi$
$929$	−36.0000	−1.18112	−0.590561	+	0.806993i	$0.701093\pi$
$930$	0	0
$931$	−4.00000	−0.131095
$932$	−16.0000	−0.524097
$933$	−15.0000	−0.491078
$934$	−21.0000	−0.687141
$935$	0	0
$936$	4.00000	0.130744
$937$	49.0000	1.60076	0.800380	−	0.599493i	$-0.204631\pi$
$937$	49.0000	1.60076	0.800380	+	0.599493i	$0.204631\pi$
$938$	4.00000	0.130605
$939$	6.00000	0.195803
$940$	0	0
$941$	−5.00000	−0.162995	−0.0814977	−	0.996674i	$-0.525970\pi$
$941$	−5.00000	−0.162995	−0.0814977	+	0.996674i	$0.525970\pi$
$942$	−18.0000	−0.586472
$943$	−16.0000	−0.521032
$944$	3.00000	0.0976417
$945$	0	0
$946$	−13.0000	−0.422666
$947$	−4.00000	−0.129983	−0.0649913	−	0.997886i	$-0.520702\pi$
$947$	−4.00000	−0.129983	−0.0649913	+	0.997886i	$0.520702\pi$
$948$	−5.00000	−0.162392
$949$	2.00000	0.0649227
$950$	0	0
$951$	3.00000	0.0972817
$952$	7.00000	0.226871
$953$	24.0000	0.777436	0.388718	−	0.921357i	$-0.372918\pi$
$953$	24.0000	0.777436	0.388718	+	0.921357i	$0.372918\pi$
$954$	−22.0000	−0.712276
$955$	0	0
$956$	9.00000	0.291081
$957$	−6.00000	−0.193952
$958$	18.0000	0.581554
$959$	−2.00000	−0.0645834
$960$	0	0
$961$	−6.00000	−0.193548
$962$	2.00000	0.0644826
$963$	30.0000	0.966736
$964$	29.0000	0.934027
$965$	0	0
$966$	−8.00000	−0.257396
$967$	−20.0000	−0.643157	−0.321578	−	0.946883i	$-0.604213\pi$
$967$	−20.0000	−0.643157	−0.321578	+	0.946883i	$0.604213\pi$
$968$	−1.00000	−0.0321412
$969$	−28.0000	−0.899490
$970$	0	0
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	16.0000	0.513200
$973$	6.00000	0.192351
$974$	−6.00000	−0.192252
$975$	0	0
$976$	10.0000	0.320092
$977$	58.0000	1.85558	0.927792	−	0.373097i	$-0.121704\pi$
$977$	58.0000	1.85558	0.927792	+	0.373097i	$0.121704\pi$
$978$	2.00000	0.0639529
$979$	−4.00000	−0.127841
$980$	0	0
$981$	32.0000	1.02168
$982$	−17.0000	−0.542492
$983$	−33.0000	−1.05254	−0.526268	−	0.850319i	$-0.676409\pi$
$983$	−33.0000	−1.05254	−0.526268	+	0.850319i	$0.676409\pi$
$984$	−2.00000	−0.0637577
$985$	0	0
$986$	−42.0000	−1.33755
$987$	−1.00000	−0.0318304
$988$	−8.00000	−0.254514
$989$	104.000	3.30701
$990$	0	0
$991$	−10.0000	−0.317660	−0.158830	−	0.987306i	$-0.550772\pi$
$991$	−10.0000	−0.317660	−0.158830	+	0.987306i	$0.550772\pi$
$992$	−5.00000	−0.158750
$993$	−8.00000	−0.253872
$994$	−10.0000	−0.317181
$995$	0	0
$996$	−14.0000	−0.443607
$997$	−5.00000	−0.158352	−0.0791758	−	0.996861i	$-0.525229\pi$
$997$	−5.00000	−0.158352	−0.0791758	+	0.996861i	$0.525229\pi$
$998$	−4.00000	−0.126618
$999$	5.00000	0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3850.2.a.h.1.1	✓	1
5.2	odd	4		3850.2.c.f.1849.1		2
5.3	odd	4		3850.2.c.f.1849.2		2
5.4	even	2		3850.2.a.p.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3850.2.a.h.1.1	✓	1	1.1	even	1	trivial
3850.2.a.p.1.1	yes	1	5.4	even	2
3850.2.c.f.1849.1		2	5.2	odd	4
3850.2.c.f.1849.2		2	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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