LMFDB - Embedded newform 3850.2.a.z.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:	$0$
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)

$f(q)$

$=$

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

\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} -2.00000 q^{18} +8.00000 q^{19} +1.00000 q^{21} -1.00000 q^{22} +1.00000 q^{24} +2.00000 q^{26} -5.00000 q^{27} +1.00000 q^{28} -6.00000 q^{29} +11.0000 q^{31} +1.00000 q^{32} -1.00000 q^{33} +3.00000 q^{34} -2.00000 q^{36} -7.00000 q^{37} +8.00000 q^{38} +2.00000 q^{39} +6.00000 q^{41} +1.00000 q^{42} -7.00000 q^{43} -1.00000 q^{44} +9.00000 q^{47} +1.00000 q^{48} +1.00000 q^{49} +3.00000 q^{51} +2.00000 q^{52} +3.00000 q^{53} -5.00000 q^{54} +1.00000 q^{56} +8.00000 q^{57} -6.00000 q^{58} -3.00000 q^{59} -10.0000 q^{61} +11.0000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -1.00000 q^{66} +8.00000 q^{67} +3.00000 q^{68} +6.00000 q^{71} -2.00000 q^{72} +5.00000 q^{73} -7.00000 q^{74} +8.00000 q^{76} -1.00000 q^{77} +2.00000 q^{78} -1.00000 q^{79} +1.00000 q^{81} +6.00000 q^{82} +6.00000 q^{83} +1.00000 q^{84} -7.00000 q^{86} -6.00000 q^{87} -1.00000 q^{88} +2.00000 q^{91} +11.0000 q^{93} +9.00000 q^{94} +1.00000 q^{96} -10.0000 q^{97} +1.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	−2.00000	−0.471405
$19$	8.00000	1.83533	0.917663	−	0.397360i	$-0.130073\pi$
$19$	8.00000	1.83533	0.917663	+	0.397360i	$0.130073\pi$
$20$	0	0
$21$	1.00000	0.218218
$22$	−1.00000	−0.213201
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	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	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	11.0000	1.97566	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	11.0000	1.97566	0.987829	+	0.155543i	$0.0497126\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	3.00000	0.514496
$35$	0	0
$36$	−2.00000	−0.333333
$37$	−7.00000	−1.15079	−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000	−1.15079	−0.575396	+	0.817875i	$0.695152\pi$
$38$	8.00000	1.29777
$39$	2.00000	0.320256
$40$	0	0
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	1.00000	0.154303
$43$	−7.00000	−1.06749	−0.533745	−	0.845645i	$-0.679216\pi$
$43$	−7.00000	−1.06749	−0.533745	+	0.845645i	$0.679216\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	0	0
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	0	0
$51$	3.00000	0.420084
$52$	2.00000	0.277350
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	1.00000	0.133631
$57$	8.00000	1.05963
$58$	−6.00000	−0.787839
$59$	−3.00000	−0.390567	−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000	−0.390567	−0.195283	+	0.980747i	$0.562563\pi$
$60$	0	0
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	11.0000	1.39700
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.00000	−0.123091
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	3.00000	0.363803
$69$	0	0
$70$	0	0
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	−2.00000	−0.235702
$73$	5.00000	0.585206	0.292603	−	0.956234i	$-0.405479\pi$
$73$	5.00000	0.585206	0.292603	+	0.956234i	$0.405479\pi$
$74$	−7.00000	−0.813733
$75$	0	0
$76$	8.00000	0.917663
$77$	−1.00000	−0.113961
$78$	2.00000	0.226455
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	6.00000	0.662589
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	1.00000	0.109109
$85$	0	0
$86$	−7.00000	−0.754829
$87$	−6.00000	−0.643268
$88$	−1.00000	−0.106600
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	0	0
$93$	11.0000	1.14065
$94$	9.00000	0.928279
$95$	0	0
$96$	1.00000	0.102062
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	1.00000	0.101015
$99$	2.00000	0.201008
$100$	0	0
$101$	15.0000	1.49256	0.746278	−	0.665635i	$-0.231839\pi$
$101$	15.0000	1.49256	0.746278	+	0.665635i	$0.231839\pi$
$102$	3.00000	0.297044
$103$	5.00000	0.492665	0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000	0.492665	0.246332	+	0.969185i	$0.420775\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	3.00000	0.291386
$107$	3.00000	0.290021	0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000	0.290021	0.145010	+	0.989430i	$0.453678\pi$
$108$	−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
$111$	−7.00000	−0.664411
$112$	1.00000	0.0944911
$113$	21.0000	1.97551	0.987757	−	0.156001i	$-0.0498603\pi$
$113$	21.0000	1.97551	0.987757	+	0.156001i	$0.0498603\pi$
$114$	8.00000	0.749269
$115$	0	0
$116$	−6.00000	−0.557086
$117$	−4.00000	−0.369800
$118$	−3.00000	−0.276172
$119$	3.00000	0.275010
$120$	0	0
$121$	1.00000	0.0909091
$122$	−10.0000	−0.905357
$123$	6.00000	0.541002
$124$	11.0000	0.987829
$125$	0	0
$126$	−2.00000	−0.178174
$127$	17.0000	1.50851	0.754253	−	0.656584i	$-0.227999\pi$
$127$	17.0000	1.50851	0.754253	+	0.656584i	$0.227999\pi$
$128$	1.00000	0.0883883
$129$	−7.00000	−0.616316
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	−1.00000	−0.0870388
$133$	8.00000	0.693688
$134$	8.00000	0.691095
$135$	0	0
$136$	3.00000	0.257248
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	−22.0000	−1.86602	−0.933008	−	0.359856i	$-0.882826\pi$
$139$	−22.0000	−1.86602	−0.933008	+	0.359856i	$0.882826\pi$
$140$	0	0
$141$	9.00000	0.757937
$142$	6.00000	0.503509
$143$	−2.00000	−0.167248
$144$	−2.00000	−0.166667
$145$	0	0
$146$	5.00000	0.413803
$147$	1.00000	0.0824786
$148$	−7.00000	−0.575396
$149$	12.0000	0.983078	0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000	0.983078	0.491539	+	0.870855i	$0.336434\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	8.00000	0.648886
$153$	−6.00000	−0.485071
$154$	−1.00000	−0.0805823
$155$	0	0
$156$	2.00000	0.160128
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	−1.00000	−0.0795557
$159$	3.00000	0.237915
$160$	0	0
$161$	0	0
$162$	1.00000	0.0785674
$163$	−10.0000	−0.783260	−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000	−0.783260	−0.391630	+	0.920123i	$0.628089\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	6.00000	0.465690
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	1.00000	0.0771517
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−16.0000	−1.22355
$172$	−7.00000	−0.533745
$173$	−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
$178$	0	0
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	2.00000	0.148250
$183$	−10.0000	−0.739221
$184$	0	0
$185$	0	0
$186$	11.0000	0.806559
$187$	−3.00000	−0.219382
$188$	9.00000	0.656392
$189$	−5.00000	−0.363696
$190$	0	0
$191$	24.0000	1.73658	0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000	1.73658	0.868290	+	0.496058i	$0.165220\pi$
$192$	1.00000	0.0721688
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	−10.0000	−0.717958
$195$	0	0
$196$	1.00000	0.0714286
$197$	−6.00000	−0.427482	−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000	−0.427482	−0.213741	+	0.976890i	$0.568565\pi$
$198$	2.00000	0.142134
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	0	0
$201$	8.00000	0.564276
$202$	15.0000	1.05540
$203$	−6.00000	−0.421117
$204$	3.00000	0.210042
$205$	0	0
$206$	5.00000	0.348367
$207$	0	0
$208$	2.00000	0.138675
$209$	−8.00000	−0.553372
$210$	0	0
$211$	−13.0000	−0.894957	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000	−0.894957	−0.447478	+	0.894295i	$0.647678\pi$
$212$	3.00000	0.206041
$213$	6.00000	0.411113
$214$	3.00000	0.205076
$215$	0	0
$216$	−5.00000	−0.340207
$217$	11.0000	0.746729
$218$	−16.0000	−1.08366
$219$	5.00000	0.337869
$220$	0	0
$221$	6.00000	0.403604
$222$	−7.00000	−0.469809
$223$	−16.0000	−1.07144	−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000	−1.07144	−0.535720	+	0.844396i	$0.679960\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	21.0000	1.39690
$227$	−18.0000	−1.19470	−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000	−1.19470	−0.597351	+	0.801980i	$0.703780\pi$
$228$	8.00000	0.529813
$229$	−4.00000	−0.264327	−0.132164	−	0.991228i	$-0.542192\pi$
$229$	−4.00000	−0.264327	−0.132164	+	0.991228i	$0.542192\pi$
$230$	0	0
$231$	−1.00000	−0.0657952
$232$	−6.00000	−0.393919
$233$	−24.0000	−1.57229	−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000	−1.57229	−0.786146	+	0.618041i	$0.787927\pi$
$234$	−4.00000	−0.261488
$235$	0	0
$236$	−3.00000	−0.195283
$237$	−1.00000	−0.0649570
$238$	3.00000	0.194461
$239$	−27.0000	−1.74648	−0.873242	−	0.487286i	$-0.837987\pi$
$239$	−27.0000	−1.74648	−0.873242	+	0.487286i	$0.837987\pi$
$240$	0	0
$241$	−25.0000	−1.61039	−0.805196	−	0.593009i	$-0.797940\pi$
$241$	−25.0000	−1.61039	−0.805196	+	0.593009i	$0.797940\pi$
$242$	1.00000	0.0642824
$243$	16.0000	1.02640
$244$	−10.0000	−0.640184
$245$	0	0
$246$	6.00000	0.382546
$247$	16.0000	1.01806
$248$	11.0000	0.698501
$249$	6.00000	0.380235
$250$	0	0
$251$	−15.0000	−0.946792	−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000	−0.946792	−0.473396	+	0.880850i	$0.656972\pi$
$252$	−2.00000	−0.125988
$253$	0	0
$254$	17.0000	1.06667
$255$	0	0
$256$	1.00000	0.0625000
$257$	30.0000	1.87135	0.935674	−	0.352865i	$-0.114792\pi$
$257$	30.0000	1.87135	0.935674	+	0.352865i	$0.114792\pi$
$258$	−7.00000	−0.435801
$259$	−7.00000	−0.434959
$260$	0	0
$261$	12.0000	0.742781
$262$	0	0
$263$	21.0000	1.29492	0.647458	−	0.762101i	$-0.275832\pi$
$263$	21.0000	1.29492	0.647458	+	0.762101i	$0.275832\pi$
$264$	−1.00000	−0.0615457
$265$	0	0
$266$	8.00000	0.490511
$267$	0	0
$268$	8.00000	0.488678
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	2.00000	0.121491	0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000	0.121491	0.0607457	+	0.998153i	$0.480652\pi$
$272$	3.00000	0.181902
$273$	2.00000	0.121046
$274$	6.00000	0.362473
$275$	0	0
$276$	0	0
$277$	−28.0000	−1.68236	−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−28.0000	−1.68236	−0.841178	+	0.540758i	$0.818138\pi$
$278$	−22.0000	−1.31947
$279$	−22.0000	−1.31711
$280$	0	0
$281$	12.0000	0.715860	0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000	0.715860	0.357930	+	0.933748i	$0.383483\pi$
$282$	9.00000	0.535942
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	6.00000	0.356034
$285$	0	0
$286$	−2.00000	−0.118262
$287$	6.00000	0.354169
$288$	−2.00000	−0.117851
$289$	−8.00000	−0.470588
$290$	0	0
$291$	−10.0000	−0.586210
$292$	5.00000	0.292603
$293$	9.00000	0.525786	0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000	0.525786	0.262893	+	0.964825i	$0.415323\pi$
$294$	1.00000	0.0583212
$295$	0	0
$296$	−7.00000	−0.406867
$297$	5.00000	0.290129
$298$	12.0000	0.695141
$299$	0	0
$300$	0	0
$301$	−7.00000	−0.403473
$302$	8.00000	0.460348
$303$	15.0000	0.861727
$304$	8.00000	0.458831
$305$	0	0
$306$	−6.00000	−0.342997
$307$	8.00000	0.456584	0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000	0.456584	0.228292	+	0.973593i	$0.426686\pi$
$308$	−1.00000	−0.0569803
$309$	5.00000	0.284440
$310$	0	0
$311$	−33.0000	−1.87126	−0.935629	−	0.352985i	$-0.885167\pi$
$311$	−33.0000	−1.87126	−0.935629	+	0.352985i	$0.885167\pi$
$312$	2.00000	0.113228
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	−10.0000	−0.564333
$315$	0	0
$316$	−1.00000	−0.0562544
$317$	−27.0000	−1.51647	−0.758236	−	0.651981i	$-0.773938\pi$
$317$	−27.0000	−1.51647	−0.758236	+	0.651981i	$0.773938\pi$
$318$	3.00000	0.168232
$319$	6.00000	0.335936
$320$	0	0
$321$	3.00000	0.167444
$322$	0	0
$323$	24.0000	1.33540
$324$	1.00000	0.0555556
$325$	0	0
$326$	−10.0000	−0.553849
$327$	−16.0000	−0.884802
$328$	6.00000	0.331295
$329$	9.00000	0.496186
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	6.00000	0.329293
$333$	14.0000	0.767195
$334$	12.0000	0.656611
$335$	0	0
$336$	1.00000	0.0545545
$337$	32.0000	1.74315	0.871576	−	0.490261i	$-0.163099\pi$
$337$	32.0000	1.74315	0.871576	+	0.490261i	$0.163099\pi$
$338$	−9.00000	−0.489535
$339$	21.0000	1.14056
$340$	0	0
$341$	−11.0000	−0.595683
$342$	−16.0000	−0.865181
$343$	1.00000	0.0539949
$344$	−7.00000	−0.377415
$345$	0	0
$346$	−6.00000	−0.322562
$347$	9.00000	0.483145	0.241573	−	0.970383i	$-0.422337\pi$
$347$	9.00000	0.483145	0.241573	+	0.970383i	$0.422337\pi$
$348$	−6.00000	−0.321634
$349$	−7.00000	−0.374701	−0.187351	−	0.982293i	$-0.559990\pi$
$349$	−7.00000	−0.374701	−0.187351	+	0.982293i	$0.559990\pi$
$350$	0	0
$351$	−10.0000	−0.533761
$352$	−1.00000	−0.0533002
$353$	0	0		−	1.00000i	$-0.5\pi$
$353$	0	0			1.00000i	$0.5\pi$
$354$	−3.00000	−0.159448
$355$	0	0
$356$	0	0
$357$	3.00000	0.158777
$358$	−12.0000	−0.634220
$359$	−36.0000	−1.90001	−0.950004	−	0.312239i	$-0.898921\pi$
$359$	−36.0000	−1.90001	−0.950004	+	0.312239i	$0.898921\pi$
$360$	0	0
$361$	45.0000	2.36842
$362$	2.00000	0.105118
$363$	1.00000	0.0524864
$364$	2.00000	0.104828
$365$	0	0
$366$	−10.0000	−0.522708
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	0	0
$369$	−12.0000	−0.624695
$370$	0	0
$371$	3.00000	0.155752
$372$	11.0000	0.570323
$373$	−4.00000	−0.207112	−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000	−0.207112	−0.103556	+	0.994624i	$0.533022\pi$
$374$	−3.00000	−0.155126
$375$	0	0
$376$	9.00000	0.464140
$377$	−12.0000	−0.618031
$378$	−5.00000	−0.257172
$379$	−28.0000	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$380$	0	0
$381$	17.0000	0.870936
$382$	24.0000	1.22795
$383$	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
$386$	−10.0000	−0.508987
$387$	14.0000	0.711660
$388$	−10.0000	−0.507673
$389$	−9.00000	−0.456318	−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000	−0.456318	−0.228159	+	0.973624i	$0.573271\pi$
$390$	0	0
$391$	0	0
$392$	1.00000	0.0505076
$393$	0	0
$394$	−6.00000	−0.302276
$395$	0	0
$396$	2.00000	0.100504
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	−16.0000	−0.802008
$399$	8.00000	0.400501
$400$	0	0
$401$	3.00000	0.149813	0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000	0.149813	0.0749064	+	0.997191i	$0.476134\pi$
$402$	8.00000	0.399004
$403$	22.0000	1.09590
$404$	15.0000	0.746278
$405$	0	0
$406$	−6.00000	−0.297775
$407$	7.00000	0.346977
$408$	3.00000	0.148522
$409$	5.00000	0.247234	0.123617	−	0.992330i	$-0.460551\pi$
$409$	5.00000	0.247234	0.123617	+	0.992330i	$0.460551\pi$
$410$	0	0
$411$	6.00000	0.295958
$412$	5.00000	0.246332
$413$	−3.00000	−0.147620
$414$	0	0
$415$	0	0
$416$	2.00000	0.0980581
$417$	−22.0000	−1.07734
$418$	−8.00000	−0.391293
$419$	−3.00000	−0.146560	−0.0732798	−	0.997311i	$-0.523347\pi$
$419$	−3.00000	−0.146560	−0.0732798	+	0.997311i	$0.523347\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−13.0000	−0.632830
$423$	−18.0000	−0.875190
$424$	3.00000	0.145693
$425$	0	0
$426$	6.00000	0.290701
$427$	−10.0000	−0.483934
$428$	3.00000	0.145010
$429$	−2.00000	−0.0965609
$430$	0	0
$431$	−21.0000	−1.01153	−0.505767	−	0.862670i	$-0.668791\pi$
$431$	−21.0000	−1.01153	−0.505767	+	0.862670i	$0.668791\pi$
$432$	−5.00000	−0.240563
$433$	26.0000	1.24948	0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000	1.24948	0.624740	+	0.780833i	$0.285205\pi$
$434$	11.0000	0.528017
$435$	0	0
$436$	−16.0000	−0.766261
$437$	0	0
$438$	5.00000	0.238909
$439$	26.0000	1.24091	0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000	1.24091	0.620456	+	0.784241i	$0.286947\pi$
$440$	0	0
$441$	−2.00000	−0.0952381
$442$	6.00000	0.285391
$443$	−24.0000	−1.14027	−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000	−1.14027	−0.570137	+	0.821549i	$0.693110\pi$
$444$	−7.00000	−0.332205
$445$	0	0
$446$	−16.0000	−0.757622
$447$	12.0000	0.567581
$448$	1.00000	0.0472456
$449$	15.0000	0.707894	0.353947	−	0.935266i	$-0.384839\pi$
$449$	15.0000	0.707894	0.353947	+	0.935266i	$0.384839\pi$
$450$	0	0
$451$	−6.00000	−0.282529
$452$	21.0000	0.987757
$453$	8.00000	0.375873
$454$	−18.0000	−0.844782
$455$	0	0
$456$	8.00000	0.374634
$457$	−28.0000	−1.30978	−0.654892	−	0.755722i	$-0.727286\pi$
$457$	−28.0000	−1.30978	−0.654892	+	0.755722i	$0.727286\pi$
$458$	−4.00000	−0.186908
$459$	−15.0000	−0.700140
$460$	0	0
$461$	−27.0000	−1.25752	−0.628758	−	0.777601i	$-0.716436\pi$
$461$	−27.0000	−1.25752	−0.628758	+	0.777601i	$0.716436\pi$
$462$	−1.00000	−0.0465242
$463$	−22.0000	−1.02243	−0.511213	−	0.859454i	$-0.670804\pi$
$463$	−22.0000	−1.02243	−0.511213	+	0.859454i	$0.670804\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	−24.0000	−1.11178
$467$	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
$469$	8.00000	0.369406
$470$	0	0
$471$	−10.0000	−0.460776
$472$	−3.00000	−0.138086
$473$	7.00000	0.321860
$474$	−1.00000	−0.0459315
$475$	0	0
$476$	3.00000	0.137505
$477$	−6.00000	−0.274721
$478$	−27.0000	−1.23495
$479$	18.0000	0.822441	0.411220	−	0.911536i	$-0.365103\pi$
$479$	18.0000	0.822441	0.411220	+	0.911536i	$0.365103\pi$
$480$	0	0
$481$	−14.0000	−0.638345
$482$	−25.0000	−1.13872
$483$	0	0
$484$	1.00000	0.0454545
$485$	0	0
$486$	16.0000	0.725775
$487$	−34.0000	−1.54069	−0.770344	−	0.637629i	$-0.779915\pi$
$487$	−34.0000	−1.54069	−0.770344	+	0.637629i	$0.779915\pi$
$488$	−10.0000	−0.452679
$489$	−10.0000	−0.452216
$490$	0	0
$491$	−27.0000	−1.21849	−0.609246	−	0.792981i	$-0.708528\pi$
$491$	−27.0000	−1.21849	−0.609246	+	0.792981i	$0.708528\pi$
$492$	6.00000	0.270501
$493$	−18.0000	−0.810679
$494$	16.0000	0.719874
$495$	0	0
$496$	11.0000	0.493915
$497$	6.00000	0.269137
$498$	6.00000	0.268866
$499$	32.0000	1.43252	0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000	1.43252	0.716258	+	0.697835i	$0.245853\pi$
$500$	0	0
$501$	12.0000	0.536120
$502$	−15.0000	−0.669483
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	−2.00000	−0.0890871
$505$	0	0
$506$	0	0
$507$	−9.00000	−0.399704
$508$	17.0000	0.754253
$509$	12.0000	0.531891	0.265945	−	0.963988i	$-0.414316\pi$
$509$	12.0000	0.531891	0.265945	+	0.963988i	$0.414316\pi$
$510$	0	0
$511$	5.00000	0.221187
$512$	1.00000	0.0441942
$513$	−40.0000	−1.76604
$514$	30.0000	1.32324
$515$	0	0
$516$	−7.00000	−0.308158
$517$	−9.00000	−0.395820
$518$	−7.00000	−0.307562
$519$	−6.00000	−0.263371
$520$	0	0
$521$	−36.0000	−1.57719	−0.788594	−	0.614914i	$-0.789191\pi$
$521$	−36.0000	−1.57719	−0.788594	+	0.614914i	$0.789191\pi$
$522$	12.0000	0.525226
$523$	−22.0000	−0.961993	−0.480996	−	0.876723i	$-0.659725\pi$
$523$	−22.0000	−0.961993	−0.480996	+	0.876723i	$0.659725\pi$
$524$	0	0
$525$	0	0
$526$	21.0000	0.915644
$527$	33.0000	1.43750
$528$	−1.00000	−0.0435194
$529$	−23.0000	−1.00000
$530$	0	0
$531$	6.00000	0.260378
$532$	8.00000	0.346844
$533$	12.0000	0.519778
$534$	0	0
$535$	0	0
$536$	8.00000	0.345547
$537$	−12.0000	−0.517838
$538$	−6.00000	−0.258678
$539$	−1.00000	−0.0430730
$540$	0	0
$541$	−22.0000	−0.945854	−0.472927	−	0.881102i	$-0.656803\pi$
$541$	−22.0000	−0.945854	−0.472927	+	0.881102i	$0.656803\pi$
$542$	2.00000	0.0859074
$543$	2.00000	0.0858282
$544$	3.00000	0.128624
$545$	0	0
$546$	2.00000	0.0855921
$547$	35.0000	1.49649	0.748246	−	0.663421i	$-0.230896\pi$
$547$	35.0000	1.49649	0.748246	+	0.663421i	$0.230896\pi$
$548$	6.00000	0.256307
$549$	20.0000	0.853579
$550$	0	0
$551$	−48.0000	−2.04487
$552$	0	0
$553$	−1.00000	−0.0425243
$554$	−28.0000	−1.18961
$555$	0	0
$556$	−22.0000	−0.933008
$557$	36.0000	1.52537	0.762684	−	0.646771i	$-0.223881\pi$
$557$	36.0000	1.52537	0.762684	+	0.646771i	$0.223881\pi$
$558$	−22.0000	−0.931334
$559$	−14.0000	−0.592137
$560$	0	0
$561$	−3.00000	−0.126660
$562$	12.0000	0.506189
$563$	42.0000	1.77009	0.885044	−	0.465506i	$-0.154128\pi$
$563$	42.0000	1.77009	0.885044	+	0.465506i	$0.154128\pi$
$564$	9.00000	0.378968
$565$	0	0
$566$	14.0000	0.588464
$567$	1.00000	0.0419961
$568$	6.00000	0.251754
$569$	18.0000	0.754599	0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000	0.754599	0.377300	+	0.926091i	$0.376853\pi$
$570$	0	0
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	−2.00000	−0.0836242
$573$	24.0000	1.00261
$574$	6.00000	0.250435
$575$	0	0
$576$	−2.00000	−0.0833333
$577$	−22.0000	−0.915872	−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000	−0.915872	−0.457936	+	0.888985i	$0.651411\pi$
$578$	−8.00000	−0.332756
$579$	−10.0000	−0.415586
$580$	0	0
$581$	6.00000	0.248922
$582$	−10.0000	−0.414513
$583$	−3.00000	−0.124247
$584$	5.00000	0.206901
$585$	0	0
$586$	9.00000	0.371787
$587$	−36.0000	−1.48588	−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000	−1.48588	−0.742940	+	0.669359i	$0.766569\pi$
$588$	1.00000	0.0412393
$589$	88.0000	3.62598
$590$	0	0
$591$	−6.00000	−0.246807
$592$	−7.00000	−0.287698
$593$	18.0000	0.739171	0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000	0.739171	0.369586	+	0.929197i	$0.379500\pi$
$594$	5.00000	0.205152
$595$	0	0
$596$	12.0000	0.491539
$597$	−16.0000	−0.654836
$598$	0	0
$599$	−6.00000	−0.245153	−0.122577	−	0.992459i	$-0.539116\pi$
$599$	−6.00000	−0.245153	−0.122577	+	0.992459i	$0.539116\pi$
$600$	0	0
$601$	−37.0000	−1.50926	−0.754631	−	0.656150i	$-0.772184\pi$
$601$	−37.0000	−1.50926	−0.754631	+	0.656150i	$0.772184\pi$
$602$	−7.00000	−0.285299
$603$	−16.0000	−0.651570
$604$	8.00000	0.325515
$605$	0	0
$606$	15.0000	0.609333
$607$	14.0000	0.568242	0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000	0.568242	0.284121	+	0.958788i	$0.408298\pi$
$608$	8.00000	0.324443
$609$	−6.00000	−0.243132
$610$	0	0
$611$	18.0000	0.728202
$612$	−6.00000	−0.242536
$613$	−28.0000	−1.13091	−0.565455	−	0.824779i	$-0.691299\pi$
$613$	−28.0000	−1.13091	−0.565455	+	0.824779i	$0.691299\pi$
$614$	8.00000	0.322854
$615$	0	0
$616$	−1.00000	−0.0402911
$617$	−33.0000	−1.32853	−0.664265	−	0.747497i	$-0.731255\pi$
$617$	−33.0000	−1.32853	−0.664265	+	0.747497i	$0.731255\pi$
$618$	5.00000	0.201129
$619$	−13.0000	−0.522514	−0.261257	−	0.965269i	$-0.584137\pi$
$619$	−13.0000	−0.522514	−0.261257	+	0.965269i	$0.584137\pi$
$620$	0	0
$621$	0	0
$622$	−33.0000	−1.32318
$623$	0	0
$624$	2.00000	0.0800641
$625$	0	0
$626$	−10.0000	−0.399680
$627$	−8.00000	−0.319489
$628$	−10.0000	−0.399043
$629$	−21.0000	−0.837325
$630$	0	0
$631$	32.0000	1.27390	0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000	1.27390	0.636950	+	0.770905i	$0.280196\pi$
$632$	−1.00000	−0.0397779
$633$	−13.0000	−0.516704
$634$	−27.0000	−1.07231
$635$	0	0
$636$	3.00000	0.118958
$637$	2.00000	0.0792429
$638$	6.00000	0.237542
$639$	−12.0000	−0.474713
$640$	0	0
$641$	−15.0000	−0.592464	−0.296232	−	0.955116i	$-0.595730\pi$
$641$	−15.0000	−0.592464	−0.296232	+	0.955116i	$0.595730\pi$
$642$	3.00000	0.118401
$643$	−25.0000	−0.985904	−0.492952	−	0.870057i	$-0.664082\pi$
$643$	−25.0000	−0.985904	−0.492952	+	0.870057i	$0.664082\pi$
$644$	0	0
$645$	0	0
$646$	24.0000	0.944267
$647$	−39.0000	−1.53325	−0.766624	−	0.642096i	$-0.778065\pi$
$647$	−39.0000	−1.53325	−0.766624	+	0.642096i	$0.778065\pi$
$648$	1.00000	0.0392837
$649$	3.00000	0.117760
$650$	0	0
$651$	11.0000	0.431124
$652$	−10.0000	−0.391630
$653$	21.0000	0.821794	0.410897	−	0.911682i	$-0.365216\pi$
$653$	21.0000	0.821794	0.410897	+	0.911682i	$0.365216\pi$
$654$	−16.0000	−0.625650
$655$	0	0
$656$	6.00000	0.234261
$657$	−10.0000	−0.390137
$658$	9.00000	0.350857
$659$	24.0000	0.934907	0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000	0.934907	0.467454	+	0.884018i	$0.345171\pi$
$660$	0	0
$661$	−10.0000	−0.388955	−0.194477	−	0.980907i	$-0.562301\pi$
$661$	−10.0000	−0.388955	−0.194477	+	0.980907i	$0.562301\pi$
$662$	20.0000	0.777322
$663$	6.00000	0.233021
$664$	6.00000	0.232845
$665$	0	0
$666$	14.0000	0.542489
$667$	0	0
$668$	12.0000	0.464294
$669$	−16.0000	−0.618596
$670$	0	0
$671$	10.0000	0.386046
$672$	1.00000	0.0385758
$673$	2.00000	0.0770943	0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000	0.0770943	0.0385472	+	0.999257i	$0.487727\pi$
$674$	32.0000	1.23259
$675$	0	0
$676$	−9.00000	−0.346154
$677$	15.0000	0.576497	0.288248	−	0.957556i	$-0.406927\pi$
$677$	15.0000	0.576497	0.288248	+	0.957556i	$0.406927\pi$
$678$	21.0000	0.806500
$679$	−10.0000	−0.383765
$680$	0	0
$681$	−18.0000	−0.689761
$682$	−11.0000	−0.421212
$683$	18.0000	0.688751	0.344375	−	0.938832i	$-0.388091\pi$
$683$	18.0000	0.688751	0.344375	+	0.938832i	$0.388091\pi$
$684$	−16.0000	−0.611775
$685$	0	0
$686$	1.00000	0.0381802
$687$	−4.00000	−0.152610
$688$	−7.00000	−0.266872
$689$	6.00000	0.228582
$690$	0	0
$691$	11.0000	0.418460	0.209230	−	0.977866i	$-0.432904\pi$
$691$	11.0000	0.418460	0.209230	+	0.977866i	$0.432904\pi$
$692$	−6.00000	−0.228086
$693$	2.00000	0.0759737
$694$	9.00000	0.341635
$695$	0	0
$696$	−6.00000	−0.227429
$697$	18.0000	0.681799
$698$	−7.00000	−0.264954
$699$	−24.0000	−0.907763
$700$	0	0
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	−10.0000	−0.377426
$703$	−56.0000	−2.11208
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	0	0
$707$	15.0000	0.564133
$708$	−3.00000	−0.112747
$709$	17.0000	0.638448	0.319224	−	0.947679i	$-0.396578\pi$
$709$	17.0000	0.638448	0.319224	+	0.947679i	$0.396578\pi$
$710$	0	0
$711$	2.00000	0.0750059
$712$	0	0
$713$	0	0
$714$	3.00000	0.112272
$715$	0	0
$716$	−12.0000	−0.448461
$717$	−27.0000	−1.00833
$718$	−36.0000	−1.34351
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	5.00000	0.186210
$722$	45.0000	1.67473
$723$	−25.0000	−0.929760
$724$	2.00000	0.0743294
$725$	0	0
$726$	1.00000	0.0371135
$727$	−19.0000	−0.704671	−0.352335	−	0.935874i	$-0.614612\pi$
$727$	−19.0000	−0.704671	−0.352335	+	0.935874i	$0.614612\pi$
$728$	2.00000	0.0741249
$729$	13.0000	0.481481
$730$	0	0
$731$	−21.0000	−0.776713
$732$	−10.0000	−0.369611
$733$	5.00000	0.184679	0.0923396	−	0.995728i	$-0.470565\pi$
$733$	5.00000	0.184679	0.0923396	+	0.995728i	$0.470565\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	0	0
$737$	−8.00000	−0.294684
$738$	−12.0000	−0.441726
$739$	5.00000	0.183928	0.0919640	−	0.995762i	$-0.470686\pi$
$739$	5.00000	0.183928	0.0919640	+	0.995762i	$0.470686\pi$
$740$	0	0
$741$	16.0000	0.587775
$742$	3.00000	0.110133
$743$	−39.0000	−1.43077	−0.715386	−	0.698730i	$-0.753749\pi$
$743$	−39.0000	−1.43077	−0.715386	+	0.698730i	$0.753749\pi$
$744$	11.0000	0.403280
$745$	0	0
$746$	−4.00000	−0.146450
$747$	−12.0000	−0.439057
$748$	−3.00000	−0.109691
$749$	3.00000	0.109618
$750$	0	0
$751$	−46.0000	−1.67856	−0.839282	−	0.543696i	$-0.817024\pi$
$751$	−46.0000	−1.67856	−0.839282	+	0.543696i	$0.817024\pi$
$752$	9.00000	0.328196
$753$	−15.0000	−0.546630
$754$	−12.0000	−0.437014
$755$	0	0
$756$	−5.00000	−0.181848
$757$	11.0000	0.399802	0.199901	−	0.979816i	$-0.435938\pi$
$757$	11.0000	0.399802	0.199901	+	0.979816i	$0.435938\pi$
$758$	−28.0000	−1.01701
$759$	0	0
$760$	0	0
$761$	21.0000	0.761249	0.380625	−	0.924730i	$-0.375709\pi$
$761$	21.0000	0.761249	0.380625	+	0.924730i	$0.375709\pi$
$762$	17.0000	0.615845
$763$	−16.0000	−0.579239
$764$	24.0000	0.868290
$765$	0	0
$766$	15.0000	0.541972
$767$	−6.00000	−0.216647
$768$	1.00000	0.0360844
$769$	−22.0000	−0.793340	−0.396670	−	0.917961i	$-0.629834\pi$
$769$	−22.0000	−0.793340	−0.396670	+	0.917961i	$0.629834\pi$
$770$	0	0
$771$	30.0000	1.08042
$772$	−10.0000	−0.359908
$773$	18.0000	0.647415	0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000	0.647415	0.323708	+	0.946157i	$0.395071\pi$
$774$	14.0000	0.503220
$775$	0	0
$776$	−10.0000	−0.358979
$777$	−7.00000	−0.251124
$778$	−9.00000	−0.322666
$779$	48.0000	1.71978
$780$	0	0
$781$	−6.00000	−0.214697
$782$	0	0
$783$	30.0000	1.07211
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	−4.00000	−0.142585	−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000	−0.142585	−0.0712923	+	0.997455i	$0.522712\pi$
$788$	−6.00000	−0.213741
$789$	21.0000	0.747620
$790$	0	0
$791$	21.0000	0.746674
$792$	2.00000	0.0710669
$793$	−20.0000	−0.710221
$794$	2.00000	0.0709773
$795$	0	0
$796$	−16.0000	−0.567105
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	8.00000	0.283197
$799$	27.0000	0.955191
$800$	0	0
$801$	0	0
$802$	3.00000	0.105934
$803$	−5.00000	−0.176446
$804$	8.00000	0.282138
$805$	0	0
$806$	22.0000	0.774917
$807$	−6.00000	−0.211210
$808$	15.0000	0.527698
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	−16.0000	−0.561836	−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000	−0.561836	−0.280918	+	0.959732i	$0.590639\pi$
$812$	−6.00000	−0.210559
$813$	2.00000	0.0701431
$814$	7.00000	0.245350
$815$	0	0
$816$	3.00000	0.105021
$817$	−56.0000	−1.95919
$818$	5.00000	0.174821
$819$	−4.00000	−0.139771
$820$	0	0
$821$	24.0000	0.837606	0.418803	−	0.908077i	$-0.362450\pi$
$821$	24.0000	0.837606	0.418803	+	0.908077i	$0.362450\pi$
$822$	6.00000	0.209274
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	5.00000	0.174183
$825$	0	0
$826$	−3.00000	−0.104383
$827$	9.00000	0.312961	0.156480	−	0.987681i	$-0.449985\pi$
$827$	9.00000	0.312961	0.156480	+	0.987681i	$0.449985\pi$
$828$	0	0
$829$	26.0000	0.903017	0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000	0.903017	0.451509	+	0.892267i	$0.350886\pi$
$830$	0	0
$831$	−28.0000	−0.971309
$832$	2.00000	0.0693375
$833$	3.00000	0.103944
$834$	−22.0000	−0.761798
$835$	0	0
$836$	−8.00000	−0.276686
$837$	−55.0000	−1.90108
$838$	−3.00000	−0.103633
$839$	24.0000	0.828572	0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000	0.828572	0.414286	+	0.910147i	$0.364031\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−10.0000	−0.344623
$843$	12.0000	0.413302
$844$	−13.0000	−0.447478
$845$	0	0
$846$	−18.0000	−0.618853
$847$	1.00000	0.0343604
$848$	3.00000	0.103020
$849$	14.0000	0.480479
$850$	0	0
$851$	0	0
$852$	6.00000	0.205557
$853$	35.0000	1.19838	0.599189	−	0.800608i	$-0.295490\pi$
$853$	35.0000	1.19838	0.599189	+	0.800608i	$0.295490\pi$
$854$	−10.0000	−0.342193
$855$	0	0
$856$	3.00000	0.102538
$857$	−30.0000	−1.02478	−0.512390	−	0.858753i	$-0.671240\pi$
$857$	−30.0000	−1.02478	−0.512390	+	0.858753i	$0.671240\pi$
$858$	−2.00000	−0.0682789
$859$	−1.00000	−0.0341196	−0.0170598	−	0.999854i	$-0.505431\pi$
$859$	−1.00000	−0.0341196	−0.0170598	+	0.999854i	$0.505431\pi$
$860$	0	0
$861$	6.00000	0.204479
$862$	−21.0000	−0.715263
$863$	−42.0000	−1.42970	−0.714848	−	0.699280i	$-0.753504\pi$
$863$	−42.0000	−1.42970	−0.714848	+	0.699280i	$0.753504\pi$
$864$	−5.00000	−0.170103
$865$	0	0
$866$	26.0000	0.883516
$867$	−8.00000	−0.271694
$868$	11.0000	0.373364
$869$	1.00000	0.0339227
$870$	0	0
$871$	16.0000	0.542139
$872$	−16.0000	−0.541828
$873$	20.0000	0.676897
$874$	0	0
$875$	0	0
$876$	5.00000	0.168934
$877$	32.0000	1.08056	0.540282	−	0.841484i	$-0.318318\pi$
$877$	32.0000	1.08056	0.540282	+	0.841484i	$0.318318\pi$
$878$	26.0000	0.877457
$879$	9.00000	0.303562
$880$	0	0
$881$	24.0000	0.808581	0.404290	−	0.914631i	$-0.367519\pi$
$881$	24.0000	0.808581	0.404290	+	0.914631i	$0.367519\pi$
$882$	−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	$0.489286\pi$
$884$	6.00000	0.201802
$885$	0	0
$886$	−24.0000	−0.806296
$887$	36.0000	1.20876	0.604381	−	0.796696i	$-0.293421\pi$
$887$	36.0000	1.20876	0.604381	+	0.796696i	$0.293421\pi$
$888$	−7.00000	−0.234905
$889$	17.0000	0.570162
$890$	0	0
$891$	−1.00000	−0.0335013
$892$	−16.0000	−0.535720
$893$	72.0000	2.40939
$894$	12.0000	0.401340
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	15.0000	0.500556
$899$	−66.0000	−2.20122
$900$	0	0
$901$	9.00000	0.299833
$902$	−6.00000	−0.199778
$903$	−7.00000	−0.232945
$904$	21.0000	0.698450
$905$	0	0
$906$	8.00000	0.265782
$907$	26.0000	0.863316	0.431658	−	0.902037i	$-0.357929\pi$
$907$	26.0000	0.863316	0.431658	+	0.902037i	$0.357929\pi$
$908$	−18.0000	−0.597351
$909$	−30.0000	−0.995037
$910$	0	0
$911$	6.00000	0.198789	0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000	0.198789	0.0993944	+	0.995048i	$0.468309\pi$
$912$	8.00000	0.264906
$913$	−6.00000	−0.198571
$914$	−28.0000	−0.926158
$915$	0	0
$916$	−4.00000	−0.132164
$917$	0	0
$918$	−15.0000	−0.495074
$919$	11.0000	0.362857	0.181428	−	0.983404i	$-0.441928\pi$
$919$	11.0000	0.362857	0.181428	+	0.983404i	$0.441928\pi$
$920$	0	0
$921$	8.00000	0.263609
$922$	−27.0000	−0.889198
$923$	12.0000	0.394985
$924$	−1.00000	−0.0328976
$925$	0	0
$926$	−22.0000	−0.722965
$927$	−10.0000	−0.328443
$928$	−6.00000	−0.196960
$929$	12.0000	0.393707	0.196854	−	0.980433i	$-0.436928\pi$
$929$	12.0000	0.393707	0.196854	+	0.980433i	$0.436928\pi$
$930$	0	0
$931$	8.00000	0.262189
$932$	−24.0000	−0.786146
$933$	−33.0000	−1.08037
$934$	21.0000	0.687141
$935$	0	0
$936$	−4.00000	−0.130744
$937$	29.0000	0.947389	0.473694	−	0.880689i	$-0.342920\pi$
$937$	29.0000	0.947389	0.473694	+	0.880689i	$0.342920\pi$
$938$	8.00000	0.261209
$939$	−10.0000	−0.326338
$940$	0	0
$941$	9.00000	0.293392	0.146696	−	0.989182i	$-0.453136\pi$
$941$	9.00000	0.293392	0.146696	+	0.989182i	$0.453136\pi$
$942$	−10.0000	−0.325818
$943$	0	0
$944$	−3.00000	−0.0976417
$945$	0	0
$946$	7.00000	0.227590
$947$	−48.0000	−1.55979	−0.779895	−	0.625910i	$-0.784728\pi$
$947$	−48.0000	−1.55979	−0.779895	+	0.625910i	$0.784728\pi$
$948$	−1.00000	−0.0324785
$949$	10.0000	0.324614
$950$	0	0
$951$	−27.0000	−0.875535
$952$	3.00000	0.0972306
$953$	12.0000	0.388718	0.194359	−	0.980930i	$-0.437737\pi$
$953$	12.0000	0.388718	0.194359	+	0.980930i	$0.437737\pi$
$954$	−6.00000	−0.194257
$955$	0	0
$956$	−27.0000	−0.873242
$957$	6.00000	0.193952
$958$	18.0000	0.581554
$959$	6.00000	0.193750
$960$	0	0
$961$	90.0000	2.90323
$962$	−14.0000	−0.451378
$963$	−6.00000	−0.193347
$964$	−25.0000	−0.805196
$965$	0	0
$966$	0	0
$967$	−4.00000	−0.128631	−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000	−0.128631	−0.0643157	+	0.997930i	$0.520486\pi$
$968$	1.00000	0.0321412
$969$	24.0000	0.770991
$970$	0	0
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	16.0000	0.513200
$973$	−22.0000	−0.705288
$974$	−34.0000	−1.08943
$975$	0	0
$976$	−10.0000	−0.320092
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	−10.0000	−0.319765
$979$	0	0
$980$	0	0
$981$	32.0000	1.02168
$982$	−27.0000	−0.861605
$983$	−33.0000	−1.05254	−0.526268	−	0.850319i	$-0.676409\pi$
$983$	−33.0000	−1.05254	−0.526268	+	0.850319i	$0.676409\pi$
$984$	6.00000	0.191273
$985$	0	0
$986$	−18.0000	−0.573237
$987$	9.00000	0.286473
$988$	16.0000	0.509028
$989$	0	0
$990$	0	0
$991$	−10.0000	−0.317660	−0.158830	−	0.987306i	$-0.550772\pi$
$991$	−10.0000	−0.317660	−0.158830	+	0.987306i	$0.550772\pi$
$992$	11.0000	0.349250
$993$	20.0000	0.634681
$994$	6.00000	0.190308
$995$	0	0
$996$	6.00000	0.190117
$997$	47.0000	1.48850	0.744252	−	0.667898i	$-0.232806\pi$
$997$	47.0000	1.48850	0.744252	+	0.667898i	$0.232806\pi$
$998$	32.0000	1.01294
$999$	35.0000	1.10735

Twists

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

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

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