LMFDB - Embedded newform 930.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(1,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, 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("930.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.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:	$7.42608738798$
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	$\chi$	$=$	930.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -2.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -4.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} +2.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} -8.00000 q^{19} +1.00000 q^{20} -2.00000 q^{21} +4.00000 q^{22} -8.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} +1.00000 q^{27} -2.00000 q^{28} +4.00000 q^{29} -1.00000 q^{30} -1.00000 q^{31} -1.00000 q^{32} -4.00000 q^{33} -2.00000 q^{34} -2.00000 q^{35} +1.00000 q^{36} -12.0000 q^{37} +8.00000 q^{38} -4.00000 q^{39} -1.00000 q^{40} +10.0000 q^{41} +2.00000 q^{42} +8.00000 q^{43} -4.00000 q^{44} +1.00000 q^{45} +8.00000 q^{46} -4.00000 q^{47} +1.00000 q^{48} -3.00000 q^{49} -1.00000 q^{50} +2.00000 q^{51} -4.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} -4.00000 q^{55} +2.00000 q^{56} -8.00000 q^{57} -4.00000 q^{58} +2.00000 q^{59} +1.00000 q^{60} +10.0000 q^{61} +1.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} +4.00000 q^{66} -6.00000 q^{67} +2.00000 q^{68} -8.00000 q^{69} +2.00000 q^{70} +6.00000 q^{71} -1.00000 q^{72} -4.00000 q^{73} +12.0000 q^{74} +1.00000 q^{75} -8.00000 q^{76} +8.00000 q^{77} +4.00000 q^{78} -8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -10.0000 q^{82} +4.00000 q^{83} -2.00000 q^{84} +2.00000 q^{85} -8.00000 q^{86} +4.00000 q^{87} +4.00000 q^{88} -1.00000 q^{90} +8.00000 q^{91} -8.00000 q^{92} -1.00000 q^{93} +4.00000 q^{94} -8.00000 q^{95} -1.00000 q^{96} -18.0000 q^{97} +3.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)

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
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	1.00000	0.288675
$13$	−4.00000	−1.10940	−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000	−1.10940	−0.554700	+	0.832050i	$0.687167\pi$
$14$	2.00000	0.534522
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	−1.00000	−0.235702
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	1.00000	0.223607
$21$	−2.00000	−0.436436
$22$	4.00000	0.852803
$23$	−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
$25$	1.00000	0.200000
$26$	4.00000	0.784465
$27$	1.00000	0.192450
$28$	−2.00000	−0.377964
$29$	4.00000	0.742781	0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000	0.742781	0.371391	+	0.928477i	$0.378881\pi$
$30$	−1.00000	−0.182574
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	−4.00000	−0.696311
$34$	−2.00000	−0.342997
$35$	−2.00000	−0.338062
$36$	1.00000	0.166667
$37$	−12.0000	−1.97279	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	−12.0000	−1.97279	−0.986394	+	0.164399i	$0.947432\pi$
$38$	8.00000	1.29777
$39$	−4.00000	−0.640513
$40$	−1.00000	−0.158114
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	2.00000	0.308607
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	−4.00000	−0.603023
$45$	1.00000	0.149071
$46$	8.00000	1.17954
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	1.00000	0.144338
$49$	−3.00000	−0.428571
$50$	−1.00000	−0.141421
$51$	2.00000	0.280056
$52$	−4.00000	−0.554700
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	−1.00000	−0.136083
$55$	−4.00000	−0.539360
$56$	2.00000	0.267261
$57$	−8.00000	−1.05963
$58$	−4.00000	−0.525226
$59$	2.00000	0.260378	0.130189	−	0.991489i	$-0.458442\pi$
$59$	2.00000	0.260378	0.130189	+	0.991489i	$0.458442\pi$
$60$	1.00000	0.129099
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	1.00000	0.127000
$63$	−2.00000	−0.251976
$64$	1.00000	0.125000
$65$	−4.00000	−0.496139
$66$	4.00000	0.492366
$67$	−6.00000	−0.733017	−0.366508	−	0.930415i	$-0.619447\pi$
$67$	−6.00000	−0.733017	−0.366508	+	0.930415i	$0.619447\pi$
$68$	2.00000	0.242536
$69$	−8.00000	−0.963087
$70$	2.00000	0.239046
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	−1.00000	−0.117851
$73$	−4.00000	−0.468165	−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000	−0.468165	−0.234082	+	0.972217i	$0.575209\pi$
$74$	12.0000	1.39497
$75$	1.00000	0.115470
$76$	−8.00000	−0.917663
$77$	8.00000	0.911685
$78$	4.00000	0.452911
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−10.0000	−1.10432
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−2.00000	−0.218218
$85$	2.00000	0.216930
$86$	−8.00000	−0.862662
$87$	4.00000	0.428845
$88$	4.00000	0.426401
$89$	0	0		−	1.00000i	$-0.5\pi$
$89$	0	0			1.00000i	$0.5\pi$
$90$	−1.00000	−0.105409
$91$	8.00000	0.838628
$92$	−8.00000	−0.834058
$93$	−1.00000	−0.103695
$94$	4.00000	0.412568
$95$	−8.00000	−0.820783
$96$	−1.00000	−0.102062
$97$	−18.0000	−1.82762	−0.913812	−	0.406138i	$-0.866875\pi$
$97$	−18.0000	−1.82762	−0.913812	+	0.406138i	$0.866875\pi$
$98$	3.00000	0.303046
$99$	−4.00000	−0.402015
$100$	1.00000	0.100000
$101$	−18.0000	−1.79107	−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000	−1.79107	−0.895533	+	0.444994i	$0.853206\pi$
$102$	−2.00000	−0.198030
$103$	−14.0000	−1.37946	−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000	−1.37946	−0.689730	+	0.724066i	$0.742271\pi$
$104$	4.00000	0.392232
$105$	−2.00000	−0.195180
$106$	−6.00000	−0.582772
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	1.00000	0.0962250
$109$	18.0000	1.72409	0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000	1.72409	0.862044	+	0.506834i	$0.169184\pi$
$110$	4.00000	0.381385
$111$	−12.0000	−1.13899
$112$	−2.00000	−0.188982
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	8.00000	0.749269
$115$	−8.00000	−0.746004
$116$	4.00000	0.371391
$117$	−4.00000	−0.369800
$118$	−2.00000	−0.184115
$119$	−4.00000	−0.366679
$120$	−1.00000	−0.0912871
$121$	5.00000	0.454545
$122$	−10.0000	−0.905357
$123$	10.0000	0.901670
$124$	−1.00000	−0.0898027
$125$	1.00000	0.0894427
$126$	2.00000	0.178174
$127$	4.00000	0.354943	0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000	0.354943	0.177471	+	0.984126i	$0.443208\pi$
$128$	−1.00000	−0.0883883
$129$	8.00000	0.704361
$130$	4.00000	0.350823
$131$	10.0000	0.873704	0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000	0.873704	0.436852	+	0.899533i	$0.356093\pi$
$132$	−4.00000	−0.348155
$133$	16.0000	1.38738
$134$	6.00000	0.518321
$135$	1.00000	0.0860663
$136$	−2.00000	−0.171499
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	8.00000	0.681005
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	−2.00000	−0.169031
$141$	−4.00000	−0.336861
$142$	−6.00000	−0.503509
$143$	16.0000	1.33799
$144$	1.00000	0.0833333
$145$	4.00000	0.332182
$146$	4.00000	0.331042
$147$	−3.00000	−0.247436
$148$	−12.0000	−0.986394
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	−1.00000	−0.0816497
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	8.00000	0.648886
$153$	2.00000	0.161690
$154$	−8.00000	−0.644658
$155$	−1.00000	−0.0803219
$156$	−4.00000	−0.320256
$157$	−22.0000	−1.75579	−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000	−1.75579	−0.877896	+	0.478852i	$0.841053\pi$
$158$	8.00000	0.636446
$159$	6.00000	0.475831
$160$	−1.00000	−0.0790569
$161$	16.0000	1.26098
$162$	−1.00000	−0.0785674
$163$	−6.00000	−0.469956	−0.234978	−	0.972001i	$-0.575502\pi$
$163$	−6.00000	−0.469956	−0.234978	+	0.972001i	$0.575502\pi$
$164$	10.0000	0.780869
$165$	−4.00000	−0.311400
$166$	−4.00000	−0.310460
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	2.00000	0.154303
$169$	3.00000	0.230769
$170$	−2.00000	−0.153393
$171$	−8.00000	−0.611775
$172$	8.00000	0.609994
$173$	22.0000	1.67263	0.836315	−	0.548250i	$-0.184706\pi$
$173$	22.0000	1.67263	0.836315	+	0.548250i	$0.184706\pi$
$174$	−4.00000	−0.303239
$175$	−2.00000	−0.151186
$176$	−4.00000	−0.301511
$177$	2.00000	0.150329
$178$	0	0
$179$	−20.0000	−1.49487	−0.747435	−	0.664335i	$-0.768715\pi$
$179$	−20.0000	−1.49487	−0.747435	+	0.664335i	$0.768715\pi$
$180$	1.00000	0.0745356
$181$	18.0000	1.33793	0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000	1.33793	0.668965	+	0.743294i	$0.266738\pi$
$182$	−8.00000	−0.592999
$183$	10.0000	0.739221
$184$	8.00000	0.589768
$185$	−12.0000	−0.882258
$186$	1.00000	0.0733236
$187$	−8.00000	−0.585018
$188$	−4.00000	−0.291730
$189$	−2.00000	−0.145479
$190$	8.00000	0.580381
$191$	18.0000	1.30243	0.651217	−	0.758891i	$-0.274259\pi$
$191$	18.0000	1.30243	0.651217	+	0.758891i	$0.274259\pi$
$192$	1.00000	0.0721688
$193$	−2.00000	−0.143963	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000	−0.143963	−0.0719816	+	0.997406i	$0.522932\pi$
$194$	18.0000	1.29232
$195$	−4.00000	−0.286446
$196$	−3.00000	−0.214286
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	4.00000	0.284268
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	−1.00000	−0.0707107
$201$	−6.00000	−0.423207
$202$	18.0000	1.26648
$203$	−8.00000	−0.561490
$204$	2.00000	0.140028
$205$	10.0000	0.698430
$206$	14.0000	0.975426
$207$	−8.00000	−0.556038
$208$	−4.00000	−0.277350
$209$	32.0000	2.21349
$210$	2.00000	0.138013
$211$	24.0000	1.65223	0.826114	−	0.563503i	$-0.190547\pi$
$211$	24.0000	1.65223	0.826114	+	0.563503i	$0.190547\pi$
$212$	6.00000	0.412082
$213$	6.00000	0.411113
$214$	−8.00000	−0.546869
$215$	8.00000	0.545595
$216$	−1.00000	−0.0680414
$217$	2.00000	0.135769
$218$	−18.0000	−1.21911
$219$	−4.00000	−0.270295
$220$	−4.00000	−0.269680
$221$	−8.00000	−0.538138
$222$	12.0000	0.805387
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	2.00000	0.133631
$225$	1.00000	0.0666667
$226$	6.00000	0.399114
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	−8.00000	−0.529813
$229$	22.0000	1.45380	0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000	1.45380	0.726900	+	0.686743i	$0.240960\pi$
$230$	8.00000	0.527504
$231$	8.00000	0.526361
$232$	−4.00000	−0.262613
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	4.00000	0.261488
$235$	−4.00000	−0.260931
$236$	2.00000	0.130189
$237$	−8.00000	−0.519656
$238$	4.00000	0.259281
$239$	−4.00000	−0.258738	−0.129369	−	0.991596i	$-0.541295\pi$
$239$	−4.00000	−0.258738	−0.129369	+	0.991596i	$0.541295\pi$
$240$	1.00000	0.0645497
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	−5.00000	−0.321412
$243$	1.00000	0.0641500
$244$	10.0000	0.640184
$245$	−3.00000	−0.191663
$246$	−10.0000	−0.637577
$247$	32.0000	2.03611
$248$	1.00000	0.0635001
$249$	4.00000	0.253490
$250$	−1.00000	−0.0632456
$251$	20.0000	1.26239	0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000	1.26239	0.631194	+	0.775625i	$0.282565\pi$
$252$	−2.00000	−0.125988
$253$	32.0000	2.01182
$254$	−4.00000	−0.250982
$255$	2.00000	0.125245
$256$	1.00000	0.0625000
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	−8.00000	−0.498058
$259$	24.0000	1.49129
$260$	−4.00000	−0.248069
$261$	4.00000	0.247594
$262$	−10.0000	−0.617802
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	4.00000	0.246183
$265$	6.00000	0.368577
$266$	−16.0000	−0.981023
$267$	0	0
$268$	−6.00000	−0.366508
$269$	−12.0000	−0.731653	−0.365826	−	0.930683i	$-0.619214\pi$
$269$	−12.0000	−0.731653	−0.365826	+	0.930683i	$0.619214\pi$
$270$	−1.00000	−0.0608581
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	2.00000	0.121268
$273$	8.00000	0.484182
$274$	−6.00000	−0.362473
$275$	−4.00000	−0.241209
$276$	−8.00000	−0.481543
$277$	8.00000	0.480673	0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000	0.480673	0.240337	+	0.970690i	$0.422742\pi$
$278$	−4.00000	−0.239904
$279$	−1.00000	−0.0598684
$280$	2.00000	0.119523
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	4.00000	0.238197
$283$	2.00000	0.118888	0.0594438	−	0.998232i	$-0.481067\pi$
$283$	2.00000	0.118888	0.0594438	+	0.998232i	$0.481067\pi$
$284$	6.00000	0.356034
$285$	−8.00000	−0.473879
$286$	−16.0000	−0.946100
$287$	−20.0000	−1.18056
$288$	−1.00000	−0.0589256
$289$	−13.0000	−0.764706
$290$	−4.00000	−0.234888
$291$	−18.0000	−1.05518
$292$	−4.00000	−0.234082
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	3.00000	0.174964
$295$	2.00000	0.116445
$296$	12.0000	0.697486
$297$	−4.00000	−0.232104
$298$	18.0000	1.04271
$299$	32.0000	1.85061
$300$	1.00000	0.0577350
$301$	−16.0000	−0.922225
$302$	16.0000	0.920697
$303$	−18.0000	−1.03407
$304$	−8.00000	−0.458831
$305$	10.0000	0.572598
$306$	−2.00000	−0.114332
$307$	−2.00000	−0.114146	−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000	−0.114146	−0.0570730	+	0.998370i	$0.518177\pi$
$308$	8.00000	0.455842
$309$	−14.0000	−0.796432
$310$	1.00000	0.0567962
$311$	−30.0000	−1.70114	−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000	−1.70114	−0.850572	+	0.525859i	$0.823744\pi$
$312$	4.00000	0.226455
$313$	20.0000	1.13047	0.565233	−	0.824931i	$-0.308786\pi$
$313$	20.0000	1.13047	0.565233	+	0.824931i	$0.308786\pi$
$314$	22.0000	1.24153
$315$	−2.00000	−0.112687
$316$	−8.00000	−0.450035
$317$	−22.0000	−1.23564	−0.617822	−	0.786318i	$-0.711985\pi$
$317$	−22.0000	−1.23564	−0.617822	+	0.786318i	$0.711985\pi$
$318$	−6.00000	−0.336463
$319$	−16.0000	−0.895828
$320$	1.00000	0.0559017
$321$	8.00000	0.446516
$322$	−16.0000	−0.891645
$323$	−16.0000	−0.890264
$324$	1.00000	0.0555556
$325$	−4.00000	−0.221880
$326$	6.00000	0.332309
$327$	18.0000	0.995402
$328$	−10.0000	−0.552158
$329$	8.00000	0.441054
$330$	4.00000	0.220193
$331$	−12.0000	−0.659580	−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000	−0.659580	−0.329790	+	0.944054i	$0.606978\pi$
$332$	4.00000	0.219529
$333$	−12.0000	−0.657596
$334$	8.00000	0.437741
$335$	−6.00000	−0.327815
$336$	−2.00000	−0.109109
$337$	−32.0000	−1.74315	−0.871576	−	0.490261i	$-0.836901\pi$
$337$	−32.0000	−1.74315	−0.871576	+	0.490261i	$0.836901\pi$
$338$	−3.00000	−0.163178
$339$	−6.00000	−0.325875
$340$	2.00000	0.108465
$341$	4.00000	0.216612
$342$	8.00000	0.432590
$343$	20.0000	1.07990
$344$	−8.00000	−0.431331
$345$	−8.00000	−0.430706
$346$	−22.0000	−1.18273
$347$	−4.00000	−0.214731	−0.107366	−	0.994220i	$-0.534242\pi$
$347$	−4.00000	−0.214731	−0.107366	+	0.994220i	$0.534242\pi$
$348$	4.00000	0.214423
$349$	−30.0000	−1.60586	−0.802932	−	0.596071i	$-0.796728\pi$
$349$	−30.0000	−1.60586	−0.802932	+	0.596071i	$0.796728\pi$
$350$	2.00000	0.106904
$351$	−4.00000	−0.213504
$352$	4.00000	0.213201
$353$	34.0000	1.80964	0.904819	−	0.425797i	$-0.140006\pi$
$353$	34.0000	1.80964	0.904819	+	0.425797i	$0.140006\pi$
$354$	−2.00000	−0.106299
$355$	6.00000	0.318447
$356$	0	0
$357$	−4.00000	−0.211702
$358$	20.0000	1.05703
$359$	10.0000	0.527780	0.263890	−	0.964553i	$-0.414994\pi$
$359$	10.0000	0.527780	0.263890	+	0.964553i	$0.414994\pi$
$360$	−1.00000	−0.0527046
$361$	45.0000	2.36842
$362$	−18.0000	−0.946059
$363$	5.00000	0.262432
$364$	8.00000	0.419314
$365$	−4.00000	−0.209370
$366$	−10.0000	−0.522708
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	−8.00000	−0.417029
$369$	10.0000	0.520579
$370$	12.0000	0.623850
$371$	−12.0000	−0.623009
$372$	−1.00000	−0.0518476
$373$	34.0000	1.76045	0.880227	−	0.474554i	$-0.157390\pi$
$373$	34.0000	1.76045	0.880227	+	0.474554i	$0.157390\pi$
$374$	8.00000	0.413670
$375$	1.00000	0.0516398
$376$	4.00000	0.206284
$377$	−16.0000	−0.824042
$378$	2.00000	0.102869
$379$	16.0000	0.821865	0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000	0.821865	0.410932	+	0.911666i	$0.365203\pi$
$380$	−8.00000	−0.410391
$381$	4.00000	0.204926
$382$	−18.0000	−0.920960
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	−1.00000	−0.0510310
$385$	8.00000	0.407718
$386$	2.00000	0.101797
$387$	8.00000	0.406663
$388$	−18.0000	−0.913812
$389$	−28.0000	−1.41966	−0.709828	−	0.704375i	$-0.751227\pi$
$389$	−28.0000	−1.41966	−0.709828	+	0.704375i	$0.751227\pi$
$390$	4.00000	0.202548
$391$	−16.0000	−0.809155
$392$	3.00000	0.151523
$393$	10.0000	0.504433
$394$	−10.0000	−0.503793
$395$	−8.00000	−0.402524
$396$	−4.00000	−0.201008
$397$	−34.0000	−1.70641	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000	−1.70641	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−16.0000	−0.802008
$399$	16.0000	0.801002
$400$	1.00000	0.0500000
$401$	4.00000	0.199750	0.0998752	−	0.995000i	$-0.468156\pi$
$401$	4.00000	0.199750	0.0998752	+	0.995000i	$0.468156\pi$
$402$	6.00000	0.299253
$403$	4.00000	0.199254
$404$	−18.0000	−0.895533
$405$	1.00000	0.0496904
$406$	8.00000	0.397033
$407$	48.0000	2.37927
$408$	−2.00000	−0.0990148
$409$	6.00000	0.296681	0.148340	−	0.988936i	$-0.452607\pi$
$409$	6.00000	0.296681	0.148340	+	0.988936i	$0.452607\pi$
$410$	−10.0000	−0.493865
$411$	6.00000	0.295958
$412$	−14.0000	−0.689730
$413$	−4.00000	−0.196827
$414$	8.00000	0.393179
$415$	4.00000	0.196352
$416$	4.00000	0.196116
$417$	4.00000	0.195881
$418$	−32.0000	−1.56517
$419$	−10.0000	−0.488532	−0.244266	−	0.969708i	$-0.578547\pi$
$419$	−10.0000	−0.488532	−0.244266	+	0.969708i	$0.578547\pi$
$420$	−2.00000	−0.0975900
$421$	2.00000	0.0974740	0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000	0.0974740	0.0487370	+	0.998812i	$0.484480\pi$
$422$	−24.0000	−1.16830
$423$	−4.00000	−0.194487
$424$	−6.00000	−0.291386
$425$	2.00000	0.0970143
$426$	−6.00000	−0.290701
$427$	−20.0000	−0.967868
$428$	8.00000	0.386695
$429$	16.0000	0.772487
$430$	−8.00000	−0.385794
$431$	−30.0000	−1.44505	−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000	−1.44505	−0.722525	+	0.691345i	$0.757018\pi$
$432$	1.00000	0.0481125
$433$	4.00000	0.192228	0.0961139	−	0.995370i	$-0.469359\pi$
$433$	4.00000	0.192228	0.0961139	+	0.995370i	$0.469359\pi$
$434$	−2.00000	−0.0960031
$435$	4.00000	0.191785
$436$	18.0000	0.862044
$437$	64.0000	3.06154
$438$	4.00000	0.191127
$439$	−40.0000	−1.90910	−0.954548	−	0.298057i	$-0.903661\pi$
$439$	−40.0000	−1.90910	−0.954548	+	0.298057i	$0.903661\pi$
$440$	4.00000	0.190693
$441$	−3.00000	−0.142857
$442$	8.00000	0.380521
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	−12.0000	−0.569495
$445$	0	0
$446$	8.00000	0.378811
$447$	−18.0000	−0.851371
$448$	−2.00000	−0.0944911
$449$	28.0000	1.32140	0.660701	−	0.750649i	$-0.270259\pi$
$449$	28.0000	1.32140	0.660701	+	0.750649i	$0.270259\pi$
$450$	−1.00000	−0.0471405
$451$	−40.0000	−1.88353
$452$	−6.00000	−0.282216
$453$	−16.0000	−0.751746
$454$	−4.00000	−0.187729
$455$	8.00000	0.375046
$456$	8.00000	0.374634
$457$	36.0000	1.68401	0.842004	−	0.539471i	$-0.181376\pi$
$457$	36.0000	1.68401	0.842004	+	0.539471i	$0.181376\pi$
$458$	−22.0000	−1.02799
$459$	2.00000	0.0933520
$460$	−8.00000	−0.373002
$461$	−40.0000	−1.86299	−0.931493	−	0.363760i	$-0.881493\pi$
$461$	−40.0000	−1.86299	−0.931493	+	0.363760i	$0.881493\pi$
$462$	−8.00000	−0.372194
$463$	−36.0000	−1.67306	−0.836531	−	0.547920i	$-0.815420\pi$
$463$	−36.0000	−1.67306	−0.836531	+	0.547920i	$0.815420\pi$
$464$	4.00000	0.185695
$465$	−1.00000	−0.0463739
$466$	10.0000	0.463241
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	−4.00000	−0.184900
$469$	12.0000	0.554109
$470$	4.00000	0.184506
$471$	−22.0000	−1.01371
$472$	−2.00000	−0.0920575
$473$	−32.0000	−1.47136
$474$	8.00000	0.367452
$475$	−8.00000	−0.367065
$476$	−4.00000	−0.183340
$477$	6.00000	0.274721
$478$	4.00000	0.182956
$479$	−10.0000	−0.456912	−0.228456	−	0.973554i	$-0.573368\pi$
$479$	−10.0000	−0.456912	−0.228456	+	0.973554i	$0.573368\pi$
$480$	−1.00000	−0.0456435
$481$	48.0000	2.18861
$482$	−10.0000	−0.455488
$483$	16.0000	0.728025
$484$	5.00000	0.227273
$485$	−18.0000	−0.817338
$486$	−1.00000	−0.0453609
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	−10.0000	−0.452679
$489$	−6.00000	−0.271329
$490$	3.00000	0.135526
$491$	−8.00000	−0.361035	−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000	−0.361035	−0.180517	+	0.983572i	$0.557777\pi$
$492$	10.0000	0.450835
$493$	8.00000	0.360302
$494$	−32.0000	−1.43975
$495$	−4.00000	−0.179787
$496$	−1.00000	−0.0449013
$497$	−12.0000	−0.538274
$498$	−4.00000	−0.179244
$499$	−36.0000	−1.61158	−0.805791	−	0.592200i	$-0.798259\pi$
$499$	−36.0000	−1.61158	−0.805791	+	0.592200i	$0.798259\pi$
$500$	1.00000	0.0447214
$501$	−8.00000	−0.357414
$502$	−20.0000	−0.892644
$503$	12.0000	0.535054	0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000	0.535054	0.267527	+	0.963550i	$0.413794\pi$
$504$	2.00000	0.0890871
$505$	−18.0000	−0.800989
$506$	−32.0000	−1.42257
$507$	3.00000	0.133235
$508$	4.00000	0.177471
$509$	16.0000	0.709188	0.354594	−	0.935020i	$-0.384619\pi$
$509$	16.0000	0.709188	0.354594	+	0.935020i	$0.384619\pi$
$510$	−2.00000	−0.0885615
$511$	8.00000	0.353899
$512$	−1.00000	−0.0441942
$513$	−8.00000	−0.353209
$514$	18.0000	0.793946
$515$	−14.0000	−0.616914
$516$	8.00000	0.352180
$517$	16.0000	0.703679
$518$	−24.0000	−1.05450
$519$	22.0000	0.965693
$520$	4.00000	0.175412
$521$	18.0000	0.788594	0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000	0.788594	0.394297	+	0.918983i	$0.370988\pi$
$522$	−4.00000	−0.175075
$523$	0	0		−	1.00000i	$-0.5\pi$
$523$	0	0			1.00000i	$0.5\pi$
$524$	10.0000	0.436852
$525$	−2.00000	−0.0872872
$526$	0	0
$527$	−2.00000	−0.0871214
$528$	−4.00000	−0.174078
$529$	41.0000	1.78261
$530$	−6.00000	−0.260623
$531$	2.00000	0.0867926
$532$	16.0000	0.693688
$533$	−40.0000	−1.73259
$534$	0	0
$535$	8.00000	0.345870
$536$	6.00000	0.259161
$537$	−20.0000	−0.863064
$538$	12.0000	0.517357
$539$	12.0000	0.516877
$540$	1.00000	0.0430331
$541$	2.00000	0.0859867	0.0429934	−	0.999075i	$-0.486311\pi$
$541$	2.00000	0.0859867	0.0429934	+	0.999075i	$0.486311\pi$
$542$	−8.00000	−0.343629
$543$	18.0000	0.772454
$544$	−2.00000	−0.0857493
$545$	18.0000	0.771035
$546$	−8.00000	−0.342368
$547$	2.00000	0.0855138	0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000	0.0855138	0.0427569	+	0.999086i	$0.486386\pi$
$548$	6.00000	0.256307
$549$	10.0000	0.426790
$550$	4.00000	0.170561
$551$	−32.0000	−1.36325
$552$	8.00000	0.340503
$553$	16.0000	0.680389
$554$	−8.00000	−0.339887
$555$	−12.0000	−0.509372
$556$	4.00000	0.169638
$557$	6.00000	0.254228	0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000	0.254228	0.127114	+	0.991888i	$0.459429\pi$
$558$	1.00000	0.0423334
$559$	−32.0000	−1.35346
$560$	−2.00000	−0.0845154
$561$	−8.00000	−0.337760
$562$	−6.00000	−0.253095
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	−4.00000	−0.168430
$565$	−6.00000	−0.252422
$566$	−2.00000	−0.0840663
$567$	−2.00000	−0.0839921
$568$	−6.00000	−0.251754
$569$	−28.0000	−1.17382	−0.586911	−	0.809652i	$-0.699656\pi$
$569$	−28.0000	−1.17382	−0.586911	+	0.809652i	$0.699656\pi$
$570$	8.00000	0.335083
$571$	−12.0000	−0.502184	−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000	−0.502184	−0.251092	+	0.967963i	$0.580790\pi$
$572$	16.0000	0.668994
$573$	18.0000	0.751961
$574$	20.0000	0.834784
$575$	−8.00000	−0.333623
$576$	1.00000	0.0416667
$577$	−6.00000	−0.249783	−0.124892	−	0.992170i	$-0.539858\pi$
$577$	−6.00000	−0.249783	−0.124892	+	0.992170i	$0.539858\pi$
$578$	13.0000	0.540729
$579$	−2.00000	−0.0831172
$580$	4.00000	0.166091
$581$	−8.00000	−0.331896
$582$	18.0000	0.746124
$583$	−24.0000	−0.993978
$584$	4.00000	0.165521
$585$	−4.00000	−0.165380
$586$	6.00000	0.247858
$587$	28.0000	1.15568	0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000	1.15568	0.577842	+	0.816149i	$0.303895\pi$
$588$	−3.00000	−0.123718
$589$	8.00000	0.329634
$590$	−2.00000	−0.0823387
$591$	10.0000	0.411345
$592$	−12.0000	−0.493197
$593$	−30.0000	−1.23195	−0.615976	−	0.787765i	$-0.711238\pi$
$593$	−30.0000	−1.23195	−0.615976	+	0.787765i	$0.711238\pi$
$594$	4.00000	0.164122
$595$	−4.00000	−0.163984
$596$	−18.0000	−0.737309
$597$	16.0000	0.654836
$598$	−32.0000	−1.30858
$599$	−30.0000	−1.22577	−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000	−1.22577	−0.612883	+	0.790173i	$0.709990\pi$
$600$	−1.00000	−0.0408248
$601$	−26.0000	−1.06056	−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000	−1.06056	−0.530281	+	0.847822i	$0.677914\pi$
$602$	16.0000	0.652111
$603$	−6.00000	−0.244339
$604$	−16.0000	−0.651031
$605$	5.00000	0.203279
$606$	18.0000	0.731200
$607$	−14.0000	−0.568242	−0.284121	−	0.958788i	$-0.591702\pi$
$607$	−14.0000	−0.568242	−0.284121	+	0.958788i	$0.591702\pi$
$608$	8.00000	0.324443
$609$	−8.00000	−0.324176
$610$	−10.0000	−0.404888
$611$	16.0000	0.647291
$612$	2.00000	0.0808452
$613$	8.00000	0.323117	0.161558	−	0.986863i	$-0.448348\pi$
$613$	8.00000	0.323117	0.161558	+	0.986863i	$0.448348\pi$
$614$	2.00000	0.0807134
$615$	10.0000	0.403239
$616$	−8.00000	−0.322329
$617$	42.0000	1.69086	0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000	1.69086	0.845428	+	0.534089i	$0.179345\pi$
$618$	14.0000	0.563163
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	−1.00000	−0.0401610
$621$	−8.00000	−0.321029
$622$	30.0000	1.20289
$623$	0	0
$624$	−4.00000	−0.160128
$625$	1.00000	0.0400000
$626$	−20.0000	−0.799361
$627$	32.0000	1.27796
$628$	−22.0000	−0.877896
$629$	−24.0000	−0.956943
$630$	2.00000	0.0796819
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	8.00000	0.318223
$633$	24.0000	0.953914
$634$	22.0000	0.873732
$635$	4.00000	0.158735
$636$	6.00000	0.237915
$637$	12.0000	0.475457
$638$	16.0000	0.633446
$639$	6.00000	0.237356
$640$	−1.00000	−0.0395285
$641$	−4.00000	−0.157991	−0.0789953	−	0.996875i	$-0.525171\pi$
$641$	−4.00000	−0.157991	−0.0789953	+	0.996875i	$0.525171\pi$
$642$	−8.00000	−0.315735
$643$	−8.00000	−0.315489	−0.157745	−	0.987480i	$-0.550422\pi$
$643$	−8.00000	−0.315489	−0.157745	+	0.987480i	$0.550422\pi$
$644$	16.0000	0.630488
$645$	8.00000	0.315000
$646$	16.0000	0.629512
$647$	8.00000	0.314512	0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000	0.314512	0.157256	+	0.987558i	$0.449735\pi$
$648$	−1.00000	−0.0392837
$649$	−8.00000	−0.314027
$650$	4.00000	0.156893
$651$	2.00000	0.0783862
$652$	−6.00000	−0.234978
$653$	−6.00000	−0.234798	−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000	−0.234798	−0.117399	+	0.993085i	$0.537456\pi$
$654$	−18.0000	−0.703856
$655$	10.0000	0.390732
$656$	10.0000	0.390434
$657$	−4.00000	−0.156055
$658$	−8.00000	−0.311872
$659$	−2.00000	−0.0779089	−0.0389545	−	0.999241i	$-0.512403\pi$
$659$	−2.00000	−0.0779089	−0.0389545	+	0.999241i	$0.512403\pi$
$660$	−4.00000	−0.155700
$661$	46.0000	1.78919	0.894596	−	0.446875i	$-0.147463\pi$
$661$	46.0000	1.78919	0.894596	+	0.446875i	$0.147463\pi$
$662$	12.0000	0.466393
$663$	−8.00000	−0.310694
$664$	−4.00000	−0.155230
$665$	16.0000	0.620453
$666$	12.0000	0.464991
$667$	−32.0000	−1.23904
$668$	−8.00000	−0.309529
$669$	−8.00000	−0.309298
$670$	6.00000	0.231800
$671$	−40.0000	−1.54418
$672$	2.00000	0.0771517
$673$	8.00000	0.308377	0.154189	−	0.988041i	$-0.450724\pi$
$673$	8.00000	0.308377	0.154189	+	0.988041i	$0.450724\pi$
$674$	32.0000	1.23259
$675$	1.00000	0.0384900
$676$	3.00000	0.115385
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	6.00000	0.230429
$679$	36.0000	1.38155
$680$	−2.00000	−0.0766965
$681$	4.00000	0.153280
$682$	−4.00000	−0.153168
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	−8.00000	−0.305888
$685$	6.00000	0.229248
$686$	−20.0000	−0.763604
$687$	22.0000	0.839352
$688$	8.00000	0.304997
$689$	−24.0000	−0.914327
$690$	8.00000	0.304555
$691$	28.0000	1.06517	0.532585	−	0.846376i	$-0.321221\pi$
$691$	28.0000	1.06517	0.532585	+	0.846376i	$0.321221\pi$
$692$	22.0000	0.836315
$693$	8.00000	0.303895
$694$	4.00000	0.151838
$695$	4.00000	0.151729
$696$	−4.00000	−0.151620
$697$	20.0000	0.757554
$698$	30.0000	1.13552
$699$	−10.0000	−0.378235
$700$	−2.00000	−0.0755929
$701$	2.00000	0.0755390	0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000	0.0755390	0.0377695	+	0.999286i	$0.487975\pi$
$702$	4.00000	0.150970
$703$	96.0000	3.62071
$704$	−4.00000	−0.150756
$705$	−4.00000	−0.150649
$706$	−34.0000	−1.27961
$707$	36.0000	1.35392
$708$	2.00000	0.0751646
$709$	−42.0000	−1.57734	−0.788672	−	0.614815i	$-0.789231\pi$
$709$	−42.0000	−1.57734	−0.788672	+	0.614815i	$0.789231\pi$
$710$	−6.00000	−0.225176
$711$	−8.00000	−0.300023
$712$	0	0
$713$	8.00000	0.299602
$714$	4.00000	0.149696
$715$	16.0000	0.598366
$716$	−20.0000	−0.747435
$717$	−4.00000	−0.149383
$718$	−10.0000	−0.373197
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	1.00000	0.0372678
$721$	28.0000	1.04277
$722$	−45.0000	−1.67473
$723$	10.0000	0.371904
$724$	18.0000	0.668965
$725$	4.00000	0.148556
$726$	−5.00000	−0.185567
$727$	−2.00000	−0.0741759	−0.0370879	−	0.999312i	$-0.511808\pi$
$727$	−2.00000	−0.0741759	−0.0370879	+	0.999312i	$0.511808\pi$
$728$	−8.00000	−0.296500
$729$	1.00000	0.0370370
$730$	4.00000	0.148047
$731$	16.0000	0.591781
$732$	10.0000	0.369611
$733$	6.00000	0.221615	0.110808	−	0.993842i	$-0.464656\pi$
$733$	6.00000	0.221615	0.110808	+	0.993842i	$0.464656\pi$
$734$	8.00000	0.295285
$735$	−3.00000	−0.110657
$736$	8.00000	0.294884
$737$	24.0000	0.884051
$738$	−10.0000	−0.368105
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	−12.0000	−0.441129
$741$	32.0000	1.17555
$742$	12.0000	0.440534
$743$	−16.0000	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$744$	1.00000	0.0366618
$745$	−18.0000	−0.659469
$746$	−34.0000	−1.24483
$747$	4.00000	0.146352
$748$	−8.00000	−0.292509
$749$	−16.0000	−0.584627
$750$	−1.00000	−0.0365148
$751$	16.0000	0.583848	0.291924	−	0.956441i	$-0.405705\pi$
$751$	16.0000	0.583848	0.291924	+	0.956441i	$0.405705\pi$
$752$	−4.00000	−0.145865
$753$	20.0000	0.728841
$754$	16.0000	0.582686
$755$	−16.0000	−0.582300
$756$	−2.00000	−0.0727393
$757$	36.0000	1.30844	0.654221	−	0.756303i	$-0.272997\pi$
$757$	36.0000	1.30844	0.654221	+	0.756303i	$0.272997\pi$
$758$	−16.0000	−0.581146
$759$	32.0000	1.16153
$760$	8.00000	0.290191
$761$	−20.0000	−0.724999	−0.362500	−	0.931984i	$-0.618077\pi$
$761$	−20.0000	−0.724999	−0.362500	+	0.931984i	$0.618077\pi$
$762$	−4.00000	−0.144905
$763$	−36.0000	−1.30329
$764$	18.0000	0.651217
$765$	2.00000	0.0723102
$766$	16.0000	0.578103
$767$	−8.00000	−0.288863
$768$	1.00000	0.0360844
$769$	−34.0000	−1.22607	−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000	−1.22607	−0.613036	+	0.790055i	$0.710052\pi$
$770$	−8.00000	−0.288300
$771$	−18.0000	−0.648254
$772$	−2.00000	−0.0719816
$773$	14.0000	0.503545	0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000	0.503545	0.251773	+	0.967786i	$0.418987\pi$
$774$	−8.00000	−0.287554
$775$	−1.00000	−0.0359211
$776$	18.0000	0.646162
$777$	24.0000	0.860995
$778$	28.0000	1.00385
$779$	−80.0000	−2.86630
$780$	−4.00000	−0.143223
$781$	−24.0000	−0.858788
$782$	16.0000	0.572159
$783$	4.00000	0.142948
$784$	−3.00000	−0.107143
$785$	−22.0000	−0.785214
$786$	−10.0000	−0.356688
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	10.0000	0.356235
$789$	0	0
$790$	8.00000	0.284627
$791$	12.0000	0.426671
$792$	4.00000	0.142134
$793$	−40.0000	−1.42044
$794$	34.0000	1.20661
$795$	6.00000	0.212798
$796$	16.0000	0.567105
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	−16.0000	−0.566394
$799$	−8.00000	−0.283020
$800$	−1.00000	−0.0353553
$801$	0	0
$802$	−4.00000	−0.141245
$803$	16.0000	0.564628
$804$	−6.00000	−0.211604
$805$	16.0000	0.563926
$806$	−4.00000	−0.140894
$807$	−12.0000	−0.422420
$808$	18.0000	0.633238
$809$	28.0000	0.984428	0.492214	−	0.870474i	$-0.336188\pi$
$809$	28.0000	0.984428	0.492214	+	0.870474i	$0.336188\pi$
$810$	−1.00000	−0.0351364
$811$	−16.0000	−0.561836	−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000	−0.561836	−0.280918	+	0.959732i	$0.590639\pi$
$812$	−8.00000	−0.280745
$813$	8.00000	0.280572
$814$	−48.0000	−1.68240
$815$	−6.00000	−0.210171
$816$	2.00000	0.0700140
$817$	−64.0000	−2.23908
$818$	−6.00000	−0.209785
$819$	8.00000	0.279543
$820$	10.0000	0.349215
$821$	−4.00000	−0.139601	−0.0698005	−	0.997561i	$-0.522236\pi$
$821$	−4.00000	−0.139601	−0.0698005	+	0.997561i	$0.522236\pi$
$822$	−6.00000	−0.209274
$823$	28.0000	0.976019	0.488009	−	0.872838i	$-0.337723\pi$
$823$	28.0000	0.976019	0.488009	+	0.872838i	$0.337723\pi$
$824$	14.0000	0.487713
$825$	−4.00000	−0.139262
$826$	4.00000	0.139178
$827$	36.0000	1.25184	0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000	1.25184	0.625921	+	0.779886i	$0.284723\pi$
$828$	−8.00000	−0.278019
$829$	−46.0000	−1.59765	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000	−1.59765	−0.798823	+	0.601566i	$0.794544\pi$
$830$	−4.00000	−0.138842
$831$	8.00000	0.277517
$832$	−4.00000	−0.138675
$833$	−6.00000	−0.207888
$834$	−4.00000	−0.138509
$835$	−8.00000	−0.276851
$836$	32.0000	1.10674
$837$	−1.00000	−0.0345651
$838$	10.0000	0.345444
$839$	42.0000	1.45000	0.725001	−	0.688748i	$-0.241839\pi$
$839$	42.0000	1.45000	0.725001	+	0.688748i	$0.241839\pi$
$840$	2.00000	0.0690066
$841$	−13.0000	−0.448276
$842$	−2.00000	−0.0689246
$843$	6.00000	0.206651
$844$	24.0000	0.826114
$845$	3.00000	0.103203
$846$	4.00000	0.137523
$847$	−10.0000	−0.343604
$848$	6.00000	0.206041
$849$	2.00000	0.0686398
$850$	−2.00000	−0.0685994
$851$	96.0000	3.29084
$852$	6.00000	0.205557
$853$	14.0000	0.479351	0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000	0.479351	0.239675	+	0.970853i	$0.422959\pi$
$854$	20.0000	0.684386
$855$	−8.00000	−0.273594
$856$	−8.00000	−0.273434
$857$	10.0000	0.341593	0.170797	−	0.985306i	$-0.445366\pi$
$857$	10.0000	0.341593	0.170797	+	0.985306i	$0.445366\pi$
$858$	−16.0000	−0.546231
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	8.00000	0.272798
$861$	−20.0000	−0.681598
$862$	30.0000	1.02180
$863$	16.0000	0.544646	0.272323	−	0.962206i	$-0.412208\pi$
$863$	16.0000	0.544646	0.272323	+	0.962206i	$0.412208\pi$
$864$	−1.00000	−0.0340207
$865$	22.0000	0.748022
$866$	−4.00000	−0.135926
$867$	−13.0000	−0.441503
$868$	2.00000	0.0678844
$869$	32.0000	1.08553
$870$	−4.00000	−0.135613
$871$	24.0000	0.813209
$872$	−18.0000	−0.609557
$873$	−18.0000	−0.609208
$874$	−64.0000	−2.16483
$875$	−2.00000	−0.0676123
$876$	−4.00000	−0.135147
$877$	−2.00000	−0.0675352	−0.0337676	−	0.999430i	$-0.510751\pi$
$877$	−2.00000	−0.0675352	−0.0337676	+	0.999430i	$0.510751\pi$
$878$	40.0000	1.34993
$879$	−6.00000	−0.202375
$880$	−4.00000	−0.134840
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	3.00000	0.101015
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	−8.00000	−0.269069
$885$	2.00000	0.0672293
$886$	−4.00000	−0.134383
$887$	−56.0000	−1.88030	−0.940148	−	0.340766i	$-0.889313\pi$
$887$	−56.0000	−1.88030	−0.940148	+	0.340766i	$0.889313\pi$
$888$	12.0000	0.402694
$889$	−8.00000	−0.268311
$890$	0	0
$891$	−4.00000	−0.134005
$892$	−8.00000	−0.267860
$893$	32.0000	1.07084
$894$	18.0000	0.602010
$895$	−20.0000	−0.668526
$896$	2.00000	0.0668153
$897$	32.0000	1.06845
$898$	−28.0000	−0.934372
$899$	−4.00000	−0.133407
$900$	1.00000	0.0333333
$901$	12.0000	0.399778
$902$	40.0000	1.33185
$903$	−16.0000	−0.532447
$904$	6.00000	0.199557
$905$	18.0000	0.598340
$906$	16.0000	0.531564
$907$	−10.0000	−0.332045	−0.166022	−	0.986122i	$-0.553092\pi$
$907$	−10.0000	−0.332045	−0.166022	+	0.986122i	$0.553092\pi$
$908$	4.00000	0.132745
$909$	−18.0000	−0.597022
$910$	−8.00000	−0.265197
$911$	24.0000	0.795155	0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000	0.795155	0.397578	+	0.917568i	$0.369851\pi$
$912$	−8.00000	−0.264906
$913$	−16.0000	−0.529523
$914$	−36.0000	−1.19077
$915$	10.0000	0.330590
$916$	22.0000	0.726900
$917$	−20.0000	−0.660458
$918$	−2.00000	−0.0660098
$919$	4.00000	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$920$	8.00000	0.263752
$921$	−2.00000	−0.0659022
$922$	40.0000	1.31733
$923$	−24.0000	−0.789970
$924$	8.00000	0.263181
$925$	−12.0000	−0.394558
$926$	36.0000	1.18303
$927$	−14.0000	−0.459820
$928$	−4.00000	−0.131306
$929$	32.0000	1.04989	0.524943	−	0.851137i	$-0.324087\pi$
$929$	32.0000	1.04989	0.524943	+	0.851137i	$0.324087\pi$
$930$	1.00000	0.0327913
$931$	24.0000	0.786568
$932$	−10.0000	−0.327561
$933$	−30.0000	−0.982156
$934$	0	0
$935$	−8.00000	−0.261628
$936$	4.00000	0.130744
$937$	−2.00000	−0.0653372	−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000	−0.0653372	−0.0326686	+	0.999466i	$0.510401\pi$
$938$	−12.0000	−0.391814
$939$	20.0000	0.652675
$940$	−4.00000	−0.130466
$941$	12.0000	0.391189	0.195594	−	0.980685i	$-0.437336\pi$
$941$	12.0000	0.391189	0.195594	+	0.980685i	$0.437336\pi$
$942$	22.0000	0.716799
$943$	−80.0000	−2.60516
$944$	2.00000	0.0650945
$945$	−2.00000	−0.0650600
$946$	32.0000	1.04041
$947$	28.0000	0.909878	0.454939	−	0.890523i	$-0.349661\pi$
$947$	28.0000	0.909878	0.454939	+	0.890523i	$0.349661\pi$
$948$	−8.00000	−0.259828
$949$	16.0000	0.519382
$950$	8.00000	0.259554
$951$	−22.0000	−0.713399
$952$	4.00000	0.129641
$953$	22.0000	0.712650	0.356325	−	0.934362i	$-0.384030\pi$
$953$	22.0000	0.712650	0.356325	+	0.934362i	$0.384030\pi$
$954$	−6.00000	−0.194257
$955$	18.0000	0.582466
$956$	−4.00000	−0.129369
$957$	−16.0000	−0.517207
$958$	10.0000	0.323085
$959$	−12.0000	−0.387500
$960$	1.00000	0.0322749
$961$	1.00000	0.0322581
$962$	−48.0000	−1.54758
$963$	8.00000	0.257796
$964$	10.0000	0.322078
$965$	−2.00000	−0.0643823
$966$	−16.0000	−0.514792
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	−5.00000	−0.160706
$969$	−16.0000	−0.513994
$970$	18.0000	0.577945
$971$	−2.00000	−0.0641831	−0.0320915	−	0.999485i	$-0.510217\pi$
$971$	−2.00000	−0.0641831	−0.0320915	+	0.999485i	$0.510217\pi$
$972$	1.00000	0.0320750
$973$	−8.00000	−0.256468
$974$	12.0000	0.384505
$975$	−4.00000	−0.128103
$976$	10.0000	0.320092
$977$	−46.0000	−1.47167	−0.735835	−	0.677161i	$-0.763210\pi$
$977$	−46.0000	−1.47167	−0.735835	+	0.677161i	$0.763210\pi$
$978$	6.00000	0.191859
$979$	0	0
$980$	−3.00000	−0.0958315
$981$	18.0000	0.574696
$982$	8.00000	0.255290
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	−10.0000	−0.318788
$985$	10.0000	0.318626
$986$	−8.00000	−0.254772
$987$	8.00000	0.254643
$988$	32.0000	1.01806
$989$	−64.0000	−2.03508
$990$	4.00000	0.127128
$991$	−56.0000	−1.77890	−0.889449	−	0.457034i	$-0.848912\pi$
$991$	−56.0000	−1.77890	−0.889449	+	0.457034i	$0.848912\pi$
$992$	1.00000	0.0317500
$993$	−12.0000	−0.380808
$994$	12.0000	0.380617
$995$	16.0000	0.507234
$996$	4.00000	0.126745
$997$	18.0000	0.570066	0.285033	−	0.958518i	$-0.407995\pi$
$997$	18.0000	0.570066	0.285033	+	0.958518i	$0.407995\pi$
$998$	36.0000	1.13956
$999$	−12.0000	−0.379663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.a.h.1.1	✓	1
3.2	odd	2		2790.2.a.p.1.1		1
4.3	odd	2		7440.2.a.m.1.1		1
5.2	odd	4		4650.2.d.b.3349.1		2
5.3	odd	4		4650.2.d.b.3349.2		2
5.4	even	2		4650.2.a.bg.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.a.h.1.1	✓	1	1.1	even	1	trivial
2790.2.a.p.1.1		1	3.2	odd	2
4650.2.a.bg.1.1		1	5.4	even	2
4650.2.d.b.3349.1		2	5.2	odd	4
4650.2.d.b.3349.2		2	5.3	odd	4
7440.2.a.m.1.1		1	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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