LMFDB - Embedded newform 7350.2.a.z.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7350,2,Mod(1,7350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7350, 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("7350.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7350.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:	$58.6900454856$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1050)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7350.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} +1.00000 q^{16} -5.00000 q^{17} -1.00000 q^{18} -4.00000 q^{19} +2.00000 q^{22} +5.00000 q^{23} -1.00000 q^{24} +4.00000 q^{26} +1.00000 q^{27} -6.00000 q^{29} -11.0000 q^{31} -1.00000 q^{32} -2.00000 q^{33} +5.00000 q^{34} +1.00000 q^{36} +8.00000 q^{37} +4.00000 q^{38} -4.00000 q^{39} +5.00000 q^{41} -2.00000 q^{44} -5.00000 q^{46} -1.00000 q^{47} +1.00000 q^{48} -5.00000 q^{51} -4.00000 q^{52} +12.0000 q^{53} -1.00000 q^{54} -4.00000 q^{57} +6.00000 q^{58} -2.00000 q^{59} +10.0000 q^{61} +11.0000 q^{62} +1.00000 q^{64} +2.00000 q^{66} -5.00000 q^{68} +5.00000 q^{69} -1.00000 q^{71} -1.00000 q^{72} +2.00000 q^{73} -8.00000 q^{74} -4.00000 q^{76} +4.00000 q^{78} +9.00000 q^{79} +1.00000 q^{81} -5.00000 q^{82} +6.00000 q^{83} -6.00000 q^{87} +2.00000 q^{88} +11.0000 q^{89} +5.00000 q^{92} -11.0000 q^{93} +1.00000 q^{94} -1.00000 q^{96} -1.00000 q^{97} -2.00000 q^{99} +O(q^{100})\)

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
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	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	$0.687167\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−5.00000	−1.21268	−0.606339	−	0.795206i	$-0.707363\pi$
$17$	−5.00000	−1.21268	−0.606339	+	0.795206i	$0.707363\pi$
$18$	−1.00000	−0.235702
$19$	−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
$21$	0	0
$22$	2.00000	0.426401
$23$	5.00000	1.04257	0.521286	−	0.853382i	$-0.325452\pi$
$23$	5.00000	1.04257	0.521286	+	0.853382i	$0.325452\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	4.00000	0.784465
$27$	1.00000	0.192450
$28$	0	0
$29$	−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	$-0.950287\pi$
$31$	−11.0000	−1.97566	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−1.00000	−0.176777
$33$	−2.00000	−0.348155
$34$	5.00000	0.857493
$35$	0	0
$36$	1.00000	0.166667
$37$	8.00000	1.31519	0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000	1.31519	0.657596	+	0.753371i	$0.271573\pi$
$38$	4.00000	0.648886
$39$	−4.00000	−0.640513
$40$	0	0
$41$	5.00000	0.780869	0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000	0.780869	0.390434	+	0.920631i	$0.372325\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	−5.00000	−0.737210
$47$	−1.00000	−0.145865	−0.0729325	−	0.997337i	$-0.523236\pi$
$47$	−1.00000	−0.145865	−0.0729325	+	0.997337i	$0.523236\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	0	0
$51$	−5.00000	−0.700140
$52$	−4.00000	−0.554700
$53$	12.0000	1.64833	0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000	1.64833	0.824163	+	0.566352i	$0.191646\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	0	0
$57$	−4.00000	−0.529813
$58$	6.00000	0.787839
$59$	−2.00000	−0.260378	−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000	−0.260378	−0.130189	+	0.991489i	$0.541558\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	11.0000	1.39700
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	2.00000	0.246183
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	−5.00000	−0.606339
$69$	5.00000	0.601929
$70$	0	0
$71$	−1.00000	−0.118678	−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000	−0.118678	−0.0593391	+	0.998238i	$0.518899\pi$
$72$	−1.00000	−0.117851
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	−4.00000	−0.458831
$77$	0	0
$78$	4.00000	0.452911
$79$	9.00000	1.01258	0.506290	−	0.862364i	$-0.331017\pi$
$79$	9.00000	1.01258	0.506290	+	0.862364i	$0.331017\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−5.00000	−0.552158
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−6.00000	−0.643268
$88$	2.00000	0.213201
$89$	11.0000	1.16600	0.582999	−	0.812473i	$-0.301879\pi$
$89$	11.0000	1.16600	0.582999	+	0.812473i	$0.301879\pi$
$90$	0	0
$91$	0	0
$92$	5.00000	0.521286
$93$	−11.0000	−1.14065
$94$	1.00000	0.103142
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−1.00000	−0.101535	−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000	−0.101535	−0.0507673	+	0.998711i	$0.516167\pi$
$98$	0	0
$99$	−2.00000	−0.201008
$100$	0	0
$101$	12.0000	1.19404	0.597022	−	0.802225i	$-0.296350\pi$
$101$	12.0000	1.19404	0.597022	+	0.802225i	$0.296350\pi$
$102$	5.00000	0.495074
$103$	13.0000	1.28093	0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000	1.28093	0.640464	+	0.767988i	$0.278742\pi$
$104$	4.00000	0.392232
$105$	0	0
$106$	−12.0000	−1.16554
$107$	2.00000	0.193347	0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000	0.193347	0.0966736	+	0.995316i	$0.469180\pi$
$108$	1.00000	0.0962250
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	0	0
$113$	5.00000	0.470360	0.235180	−	0.971952i	$-0.424432\pi$
$113$	5.00000	0.470360	0.235180	+	0.971952i	$0.424432\pi$
$114$	4.00000	0.374634
$115$	0	0
$116$	−6.00000	−0.557086
$117$	−4.00000	−0.369800
$118$	2.00000	0.184115
$119$	0	0
$120$	0	0
$121$	−7.00000	−0.636364
$122$	−10.0000	−0.905357
$123$	5.00000	0.450835
$124$	−11.0000	−0.987829
$125$	0	0
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	6.00000	0.524222	0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000	0.524222	0.262111	+	0.965038i	$0.415581\pi$
$132$	−2.00000	−0.174078
$133$	0	0
$134$	0	0
$135$	0	0
$136$	5.00000	0.428746
$137$	23.0000	1.96502	0.982511	−	0.186203i	$-0.0596182\pi$
$137$	23.0000	1.96502	0.982511	+	0.186203i	$0.0596182\pi$
$138$	−5.00000	−0.425628
$139$	2.00000	0.169638	0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000	0.169638	0.0848189	+	0.996396i	$0.472969\pi$
$140$	0	0
$141$	−1.00000	−0.0842152
$142$	1.00000	0.0839181
$143$	8.00000	0.668994
$144$	1.00000	0.0833333
$145$	0	0
$146$	−2.00000	−0.165521
$147$	0	0
$148$	8.00000	0.657596
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	0	0
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	4.00000	0.324443
$153$	−5.00000	−0.404226
$154$	0	0
$155$	0	0
$156$	−4.00000	−0.320256
$157$	−14.0000	−1.11732	−0.558661	−	0.829396i	$-0.688685\pi$
$157$	−14.0000	−1.11732	−0.558661	+	0.829396i	$0.688685\pi$
$158$	−9.00000	−0.716002
$159$	12.0000	0.951662
$160$	0	0
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	24.0000	1.87983	0.939913	−	0.341415i	$-0.110906\pi$
$163$	24.0000	1.87983	0.939913	+	0.341415i	$0.110906\pi$
$164$	5.00000	0.390434
$165$	0	0
$166$	−6.00000	−0.465690
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	0	0
$169$	3.00000	0.230769
$170$	0	0
$171$	−4.00000	−0.305888
$172$	0	0
$173$	−2.00000	−0.152057	−0.0760286	−	0.997106i	$-0.524224\pi$
$173$	−2.00000	−0.152057	−0.0760286	+	0.997106i	$0.524224\pi$
$174$	6.00000	0.454859
$175$	0	0
$176$	−2.00000	−0.150756
$177$	−2.00000	−0.150329
$178$	−11.0000	−0.824485
$179$	22.0000	1.64436	0.822179	−	0.569230i	$-0.192758\pi$
$179$	22.0000	1.64436	0.822179	+	0.569230i	$0.192758\pi$
$180$	0	0
$181$	−22.0000	−1.63525	−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000	−1.63525	−0.817624	+	0.575753i	$0.804709\pi$
$182$	0	0
$183$	10.0000	0.739221
$184$	−5.00000	−0.368605
$185$	0	0
$186$	11.0000	0.806559
$187$	10.0000	0.731272
$188$	−1.00000	−0.0729325
$189$	0	0
$190$	0	0
$191$	−25.0000	−1.80894	−0.904468	−	0.426541i	$-0.859732\pi$
$191$	−25.0000	−1.80894	−0.904468	+	0.426541i	$0.859732\pi$
$192$	1.00000	0.0721688
$193$	11.0000	0.791797	0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000	0.791797	0.395899	+	0.918294i	$0.370433\pi$
$194$	1.00000	0.0717958
$195$	0	0
$196$	0	0
$197$	−24.0000	−1.70993	−0.854965	−	0.518686i	$-0.826421\pi$
$197$	−24.0000	−1.70993	−0.854965	+	0.518686i	$0.826421\pi$
$198$	2.00000	0.142134
$199$	5.00000	0.354441	0.177220	−	0.984171i	$-0.443289\pi$
$199$	5.00000	0.354441	0.177220	+	0.984171i	$0.443289\pi$
$200$	0	0
$201$	0	0
$202$	−12.0000	−0.844317
$203$	0	0
$204$	−5.00000	−0.350070
$205$	0	0
$206$	−13.0000	−0.905753
$207$	5.00000	0.347524
$208$	−4.00000	−0.277350
$209$	8.00000	0.553372
$210$	0	0
$211$	−16.0000	−1.10149	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000	−1.10149	−0.550743	+	0.834675i	$0.685655\pi$
$212$	12.0000	0.824163
$213$	−1.00000	−0.0685189
$214$	−2.00000	−0.136717
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−4.00000	−0.270914
$219$	2.00000	0.135147
$220$	0	0
$221$	20.0000	1.34535
$222$	−8.00000	−0.536925
$223$	21.0000	1.40626	0.703132	−	0.711059i	$-0.251784\pi$
$223$	21.0000	1.40626	0.703132	+	0.711059i	$0.251784\pi$
$224$	0	0
$225$	0	0
$226$	−5.00000	−0.332595
$227$	18.0000	1.19470	0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000	1.19470	0.597351	+	0.801980i	$0.296220\pi$
$228$	−4.00000	−0.264906
$229$	−14.0000	−0.925146	−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000	−0.925146	−0.462573	+	0.886581i	$0.653074\pi$
$230$	0	0
$231$	0	0
$232$	6.00000	0.393919
$233$	26.0000	1.70332	0.851658	−	0.524097i	$-0.175597\pi$
$233$	26.0000	1.70332	0.851658	+	0.524097i	$0.175597\pi$
$234$	4.00000	0.261488
$235$	0	0
$236$	−2.00000	−0.130189
$237$	9.00000	0.584613
$238$	0	0
$239$	11.0000	0.711531	0.355765	−	0.934575i	$-0.384220\pi$
$239$	11.0000	0.711531	0.355765	+	0.934575i	$0.384220\pi$
$240$	0	0
$241$	−6.00000	−0.386494	−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000	−0.386494	−0.193247	+	0.981150i	$0.561902\pi$
$242$	7.00000	0.449977
$243$	1.00000	0.0641500
$244$	10.0000	0.640184
$245$	0	0
$246$	−5.00000	−0.318788
$247$	16.0000	1.01806
$248$	11.0000	0.698501
$249$	6.00000	0.380235
$250$	0	0
$251$	−8.00000	−0.504956	−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000	−0.504956	−0.252478	+	0.967603i	$0.581245\pi$
$252$	0	0
$253$	−10.0000	−0.628695
$254$	0	0
$255$	0	0
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−6.00000	−0.371391
$262$	−6.00000	−0.370681
$263$	−21.0000	−1.29492	−0.647458	−	0.762101i	$-0.724168\pi$
$263$	−21.0000	−1.29492	−0.647458	+	0.762101i	$0.724168\pi$
$264$	2.00000	0.123091
$265$	0	0
$266$	0	0
$267$	11.0000	0.673189
$268$	0	0
$269$	−24.0000	−1.46331	−0.731653	−	0.681677i	$-0.761251\pi$
$269$	−24.0000	−1.46331	−0.731653	+	0.681677i	$0.761251\pi$
$270$	0	0
$271$	−9.00000	−0.546711	−0.273356	−	0.961913i	$-0.588134\pi$
$271$	−9.00000	−0.546711	−0.273356	+	0.961913i	$0.588134\pi$
$272$	−5.00000	−0.303170
$273$	0	0
$274$	−23.0000	−1.38948
$275$	0	0
$276$	5.00000	0.300965
$277$	−2.00000	−0.120168	−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000	−0.120168	−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−2.00000	−0.119952
$279$	−11.0000	−0.658553
$280$	0	0
$281$	−29.0000	−1.72999	−0.864997	−	0.501776i	$-0.832680\pi$
$281$	−29.0000	−1.72999	−0.864997	+	0.501776i	$0.832680\pi$
$282$	1.00000	0.0595491
$283$	−26.0000	−1.54554	−0.772770	−	0.634686i	$-0.781129\pi$
$283$	−26.0000	−1.54554	−0.772770	+	0.634686i	$0.781129\pi$
$284$	−1.00000	−0.0593391
$285$	0	0
$286$	−8.00000	−0.473050
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	8.00000	0.470588
$290$	0	0
$291$	−1.00000	−0.0586210
$292$	2.00000	0.117041
$293$	18.0000	1.05157	0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000	1.05157	0.525786	+	0.850617i	$0.323771\pi$
$294$	0	0
$295$	0	0
$296$	−8.00000	−0.464991
$297$	−2.00000	−0.116052
$298$	−18.0000	−1.04271
$299$	−20.0000	−1.15663
$300$	0	0
$301$	0	0
$302$	16.0000	0.920697
$303$	12.0000	0.689382
$304$	−4.00000	−0.229416
$305$	0	0
$306$	5.00000	0.285831
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	0	0
$309$	13.0000	0.739544
$310$	0	0
$311$	29.0000	1.64444	0.822220	−	0.569170i	$-0.192736\pi$
$311$	29.0000	1.64444	0.822220	+	0.569170i	$0.192736\pi$
$312$	4.00000	0.226455
$313$	−1.00000	−0.0565233	−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000	−0.0565233	−0.0282617	+	0.999601i	$0.508997\pi$
$314$	14.0000	0.790066
$315$	0	0
$316$	9.00000	0.506290
$317$	4.00000	0.224662	0.112331	−	0.993671i	$-0.464168\pi$
$317$	4.00000	0.224662	0.112331	+	0.993671i	$0.464168\pi$
$318$	−12.0000	−0.672927
$319$	12.0000	0.671871
$320$	0	0
$321$	2.00000	0.111629
$322$	0	0
$323$	20.0000	1.11283
$324$	1.00000	0.0555556
$325$	0	0
$326$	−24.0000	−1.32924
$327$	4.00000	0.221201
$328$	−5.00000	−0.276079
$329$	0	0
$330$	0	0
$331$	10.0000	0.549650	0.274825	−	0.961494i	$-0.411380\pi$
$331$	10.0000	0.549650	0.274825	+	0.961494i	$0.411380\pi$
$332$	6.00000	0.329293
$333$	8.00000	0.438397
$334$	−16.0000	−0.875481
$335$	0	0
$336$	0	0
$337$	13.0000	0.708155	0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000	0.708155	0.354078	+	0.935216i	$0.384795\pi$
$338$	−3.00000	−0.163178
$339$	5.00000	0.271563
$340$	0	0
$341$	22.0000	1.19137
$342$	4.00000	0.216295
$343$	0	0
$344$	0	0
$345$	0	0
$346$	2.00000	0.107521
$347$	−18.0000	−0.966291	−0.483145	−	0.875540i	$-0.660506\pi$
$347$	−18.0000	−0.966291	−0.483145	+	0.875540i	$0.660506\pi$
$348$	−6.00000	−0.321634
$349$	−4.00000	−0.214115	−0.107058	−	0.994253i	$-0.534143\pi$
$349$	−4.00000	−0.214115	−0.107058	+	0.994253i	$0.534143\pi$
$350$	0	0
$351$	−4.00000	−0.213504
$352$	2.00000	0.106600
$353$	9.00000	0.479022	0.239511	−	0.970894i	$-0.423013\pi$
$353$	9.00000	0.479022	0.239511	+	0.970894i	$0.423013\pi$
$354$	2.00000	0.106299
$355$	0	0
$356$	11.0000	0.582999
$357$	0	0
$358$	−22.0000	−1.16274
$359$	−20.0000	−1.05556	−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000	−1.05556	−0.527780	+	0.849381i	$0.676975\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	22.0000	1.15629
$363$	−7.00000	−0.367405
$364$	0	0
$365$	0	0
$366$	−10.0000	−0.522708
$367$	−4.00000	−0.208798	−0.104399	−	0.994535i	$-0.533292\pi$
$367$	−4.00000	−0.208798	−0.104399	+	0.994535i	$0.533292\pi$
$368$	5.00000	0.260643
$369$	5.00000	0.260290
$370$	0	0
$371$	0	0
$372$	−11.0000	−0.570323
$373$	−32.0000	−1.65690	−0.828449	−	0.560065i	$-0.810776\pi$
$373$	−32.0000	−1.65690	−0.828449	+	0.560065i	$0.810776\pi$
$374$	−10.0000	−0.517088
$375$	0	0
$376$	1.00000	0.0515711
$377$	24.0000	1.23606
$378$	0	0
$379$	−2.00000	−0.102733	−0.0513665	−	0.998680i	$-0.516358\pi$
$379$	−2.00000	−0.102733	−0.0513665	+	0.998680i	$0.516358\pi$
$380$	0	0
$381$	0	0
$382$	25.0000	1.27911
$383$	3.00000	0.153293	0.0766464	−	0.997058i	$-0.475579\pi$
$383$	3.00000	0.153293	0.0766464	+	0.997058i	$0.475579\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−11.0000	−0.559885
$387$	0	0
$388$	−1.00000	−0.0507673
$389$	24.0000	1.21685	0.608424	−	0.793612i	$-0.291802\pi$
$389$	24.0000	1.21685	0.608424	+	0.793612i	$0.291802\pi$
$390$	0	0
$391$	−25.0000	−1.26430
$392$	0	0
$393$	6.00000	0.302660
$394$	24.0000	1.20910
$395$	0	0
$396$	−2.00000	−0.100504
$397$	−34.0000	−1.70641	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000	−1.70641	−0.853206	+	0.521575i	$0.825345\pi$
$398$	−5.00000	−0.250627
$399$	0	0
$400$	0	0
$401$	−6.00000	−0.299626	−0.149813	−	0.988714i	$-0.547867\pi$
$401$	−6.00000	−0.299626	−0.149813	+	0.988714i	$0.547867\pi$
$402$	0	0
$403$	44.0000	2.19180
$404$	12.0000	0.597022
$405$	0	0
$406$	0	0
$407$	−16.0000	−0.793091
$408$	5.00000	0.247537
$409$	−35.0000	−1.73064	−0.865319	−	0.501221i	$-0.832884\pi$
$409$	−35.0000	−1.73064	−0.865319	+	0.501221i	$0.832884\pi$
$410$	0	0
$411$	23.0000	1.13451
$412$	13.0000	0.640464
$413$	0	0
$414$	−5.00000	−0.245737
$415$	0	0
$416$	4.00000	0.196116
$417$	2.00000	0.0979404
$418$	−8.00000	−0.391293
$419$	0	0		−	1.00000i	$-0.5\pi$
$419$	0	0			1.00000i	$0.5\pi$
$420$	0	0
$421$	28.0000	1.36464	0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000	1.36464	0.682318	+	0.731055i	$0.260972\pi$
$422$	16.0000	0.778868
$423$	−1.00000	−0.0486217
$424$	−12.0000	−0.582772
$425$	0	0
$426$	1.00000	0.0484502
$427$	0	0
$428$	2.00000	0.0966736
$429$	8.00000	0.386244
$430$	0	0
$431$	−3.00000	−0.144505	−0.0722525	−	0.997386i	$-0.523019\pi$
$431$	−3.00000	−0.144505	−0.0722525	+	0.997386i	$0.523019\pi$
$432$	1.00000	0.0481125
$433$	−9.00000	−0.432512	−0.216256	−	0.976337i	$-0.569385\pi$
$433$	−9.00000	−0.432512	−0.216256	+	0.976337i	$0.569385\pi$
$434$	0	0
$435$	0	0
$436$	4.00000	0.191565
$437$	−20.0000	−0.956730
$438$	−2.00000	−0.0955637
$439$	35.0000	1.67046	0.835229	−	0.549902i	$-0.185335\pi$
$439$	35.0000	1.67046	0.835229	+	0.549902i	$0.185335\pi$
$440$	0	0
$441$	0	0
$442$	−20.0000	−0.951303
$443$	−8.00000	−0.380091	−0.190046	−	0.981775i	$-0.560864\pi$
$443$	−8.00000	−0.380091	−0.190046	+	0.981775i	$0.560864\pi$
$444$	8.00000	0.379663
$445$	0	0
$446$	−21.0000	−0.994379
$447$	18.0000	0.851371
$448$	0	0
$449$	37.0000	1.74614	0.873069	−	0.487597i	$-0.162126\pi$
$449$	37.0000	1.74614	0.873069	+	0.487597i	$0.162126\pi$
$450$	0	0
$451$	−10.0000	−0.470882
$452$	5.00000	0.235180
$453$	−16.0000	−0.751746
$454$	−18.0000	−0.844782
$455$	0	0
$456$	4.00000	0.187317
$457$	14.0000	0.654892	0.327446	−	0.944870i	$-0.393812\pi$
$457$	14.0000	0.654892	0.327446	+	0.944870i	$0.393812\pi$
$458$	14.0000	0.654177
$459$	−5.00000	−0.233380
$460$	0	0
$461$	20.0000	0.931493	0.465746	−	0.884918i	$-0.345786\pi$
$461$	20.0000	0.931493	0.465746	+	0.884918i	$0.345786\pi$
$462$	0	0
$463$	13.0000	0.604161	0.302081	−	0.953282i	$-0.402319\pi$
$463$	13.0000	0.604161	0.302081	+	0.953282i	$0.402319\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	−26.0000	−1.20443
$467$	−34.0000	−1.57333	−0.786666	−	0.617379i	$-0.788195\pi$
$467$	−34.0000	−1.57333	−0.786666	+	0.617379i	$0.788195\pi$
$468$	−4.00000	−0.184900
$469$	0	0
$470$	0	0
$471$	−14.0000	−0.645086
$472$	2.00000	0.0920575
$473$	0	0
$474$	−9.00000	−0.413384
$475$	0	0
$476$	0	0
$477$	12.0000	0.549442
$478$	−11.0000	−0.503128
$479$	−3.00000	−0.137073	−0.0685367	−	0.997649i	$-0.521833\pi$
$479$	−3.00000	−0.137073	−0.0685367	+	0.997649i	$0.521833\pi$
$480$	0	0
$481$	−32.0000	−1.45907
$482$	6.00000	0.273293
$483$	0	0
$484$	−7.00000	−0.318182
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	−39.0000	−1.76726	−0.883629	−	0.468187i	$-0.844907\pi$
$487$	−39.0000	−1.76726	−0.883629	+	0.468187i	$0.844907\pi$
$488$	−10.0000	−0.452679
$489$	24.0000	1.08532
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	5.00000	0.225417
$493$	30.0000	1.35113
$494$	−16.0000	−0.719874
$495$	0	0
$496$	−11.0000	−0.493915
$497$	0	0
$498$	−6.00000	−0.268866
$499$	22.0000	0.984855	0.492428	−	0.870353i	$-0.336110\pi$
$499$	22.0000	0.984855	0.492428	+	0.870353i	$0.336110\pi$
$500$	0	0
$501$	16.0000	0.714827
$502$	8.00000	0.357057
$503$	8.00000	0.356702	0.178351	−	0.983967i	$-0.442924\pi$
$503$	8.00000	0.356702	0.178351	+	0.983967i	$0.442924\pi$
$504$	0	0
$505$	0	0
$506$	10.0000	0.444554
$507$	3.00000	0.133235
$508$	0	0
$509$	2.00000	0.0886484	0.0443242	−	0.999017i	$-0.485887\pi$
$509$	2.00000	0.0886484	0.0443242	+	0.999017i	$0.485887\pi$
$510$	0	0
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−4.00000	−0.176604
$514$	14.0000	0.617514
$515$	0	0
$516$	0	0
$517$	2.00000	0.0879599
$518$	0	0
$519$	−2.00000	−0.0877903
$520$	0	0
$521$	−3.00000	−0.131432	−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000	−0.131432	−0.0657162	+	0.997838i	$0.520933\pi$
$522$	6.00000	0.262613
$523$	−14.0000	−0.612177	−0.306089	−	0.952003i	$-0.599020\pi$
$523$	−14.0000	−0.612177	−0.306089	+	0.952003i	$0.599020\pi$
$524$	6.00000	0.262111
$525$	0	0
$526$	21.0000	0.915644
$527$	55.0000	2.39584
$528$	−2.00000	−0.0870388
$529$	2.00000	0.0869565
$530$	0	0
$531$	−2.00000	−0.0867926
$532$	0	0
$533$	−20.0000	−0.866296
$534$	−11.0000	−0.476017
$535$	0	0
$536$	0	0
$537$	22.0000	0.949370
$538$	24.0000	1.03471
$539$	0	0
$540$	0	0
$541$	−4.00000	−0.171973	−0.0859867	−	0.996296i	$-0.527404\pi$
$541$	−4.00000	−0.171973	−0.0859867	+	0.996296i	$0.527404\pi$
$542$	9.00000	0.386583
$543$	−22.0000	−0.944110
$544$	5.00000	0.214373
$545$	0	0
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	23.0000	0.982511
$549$	10.0000	0.426790
$550$	0	0
$551$	24.0000	1.02243
$552$	−5.00000	−0.212814
$553$	0	0
$554$	2.00000	0.0849719
$555$	0	0
$556$	2.00000	0.0848189
$557$	38.0000	1.61011	0.805056	−	0.593199i	$-0.202135\pi$
$557$	38.0000	1.61011	0.805056	+	0.593199i	$0.202135\pi$
$558$	11.0000	0.465667
$559$	0	0
$560$	0	0
$561$	10.0000	0.422200
$562$	29.0000	1.22329
$563$	−36.0000	−1.51722	−0.758610	−	0.651546i	$-0.774121\pi$
$563$	−36.0000	−1.51722	−0.758610	+	0.651546i	$0.774121\pi$
$564$	−1.00000	−0.0421076
$565$	0	0
$566$	26.0000	1.09286
$567$	0	0
$568$	1.00000	0.0419591
$569$	9.00000	0.377300	0.188650	−	0.982044i	$-0.439589\pi$
$569$	9.00000	0.377300	0.188650	+	0.982044i	$0.439589\pi$
$570$	0	0
$571$	−44.0000	−1.84134	−0.920671	−	0.390339i	$-0.872358\pi$
$571$	−44.0000	−1.84134	−0.920671	+	0.390339i	$0.872358\pi$
$572$	8.00000	0.334497
$573$	−25.0000	−1.04439
$574$	0	0
$575$	0	0
$576$	1.00000	0.0416667
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	−8.00000	−0.332756
$579$	11.0000	0.457144
$580$	0	0
$581$	0	0
$582$	1.00000	0.0414513
$583$	−24.0000	−0.993978
$584$	−2.00000	−0.0827606
$585$	0	0
$586$	−18.0000	−0.743573
$587$	6.00000	0.247647	0.123823	−	0.992304i	$-0.460484\pi$
$587$	6.00000	0.247647	0.123823	+	0.992304i	$0.460484\pi$
$588$	0	0
$589$	44.0000	1.81299
$590$	0	0
$591$	−24.0000	−0.987228
$592$	8.00000	0.328798
$593$	9.00000	0.369586	0.184793	−	0.982777i	$-0.440839\pi$
$593$	9.00000	0.369586	0.184793	+	0.982777i	$0.440839\pi$
$594$	2.00000	0.0820610
$595$	0	0
$596$	18.0000	0.737309
$597$	5.00000	0.204636
$598$	20.0000	0.817861
$599$	17.0000	0.694601	0.347301	−	0.937754i	$-0.387098\pi$
$599$	17.0000	0.694601	0.347301	+	0.937754i	$0.387098\pi$
$600$	0	0
$601$	−34.0000	−1.38689	−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000	−1.38689	−0.693444	+	0.720510i	$0.743908\pi$
$602$	0	0
$603$	0	0
$604$	−16.0000	−0.651031
$605$	0	0
$606$	−12.0000	−0.487467
$607$	−27.0000	−1.09590	−0.547948	−	0.836512i	$-0.684591\pi$
$607$	−27.0000	−1.09590	−0.547948	+	0.836512i	$0.684591\pi$
$608$	4.00000	0.162221
$609$	0	0
$610$	0	0
$611$	4.00000	0.161823
$612$	−5.00000	−0.202113
$613$	34.0000	1.37325	0.686624	−	0.727013i	$-0.259092\pi$
$613$	34.0000	1.37325	0.686624	+	0.727013i	$0.259092\pi$
$614$	−28.0000	−1.12999
$615$	0	0
$616$	0	0
$617$	29.0000	1.16750	0.583748	−	0.811935i	$-0.301586\pi$
$617$	29.0000	1.16750	0.583748	+	0.811935i	$0.301586\pi$
$618$	−13.0000	−0.522937
$619$	−14.0000	−0.562708	−0.281354	−	0.959604i	$-0.590783\pi$
$619$	−14.0000	−0.562708	−0.281354	+	0.959604i	$0.590783\pi$
$620$	0	0
$621$	5.00000	0.200643
$622$	−29.0000	−1.16279
$623$	0	0
$624$	−4.00000	−0.160128
$625$	0	0
$626$	1.00000	0.0399680
$627$	8.00000	0.319489
$628$	−14.0000	−0.558661
$629$	−40.0000	−1.59490
$630$	0	0
$631$	33.0000	1.31371	0.656855	−	0.754017i	$-0.271887\pi$
$631$	33.0000	1.31371	0.656855	+	0.754017i	$0.271887\pi$
$632$	−9.00000	−0.358001
$633$	−16.0000	−0.635943
$634$	−4.00000	−0.158860
$635$	0	0
$636$	12.0000	0.475831
$637$	0	0
$638$	−12.0000	−0.475085
$639$	−1.00000	−0.0395594
$640$	0	0
$641$	−15.0000	−0.592464	−0.296232	−	0.955116i	$-0.595730\pi$
$641$	−15.0000	−0.592464	−0.296232	+	0.955116i	$0.595730\pi$
$642$	−2.00000	−0.0789337
$643$	26.0000	1.02534	0.512670	−	0.858586i	$-0.328656\pi$
$643$	26.0000	1.02534	0.512670	+	0.858586i	$0.328656\pi$
$644$	0	0
$645$	0	0
$646$	−20.0000	−0.786889
$647$	−28.0000	−1.10079	−0.550397	−	0.834903i	$-0.685524\pi$
$647$	−28.0000	−1.10079	−0.550397	+	0.834903i	$0.685524\pi$
$648$	−1.00000	−0.0392837
$649$	4.00000	0.157014
$650$	0	0
$651$	0	0
$652$	24.0000	0.939913
$653$	28.0000	1.09572	0.547862	−	0.836569i	$-0.315442\pi$
$653$	28.0000	1.09572	0.547862	+	0.836569i	$0.315442\pi$
$654$	−4.00000	−0.156412
$655$	0	0
$656$	5.00000	0.195217
$657$	2.00000	0.0780274
$658$	0	0
$659$	−14.0000	−0.545363	−0.272681	−	0.962104i	$-0.587910\pi$
$659$	−14.0000	−0.545363	−0.272681	+	0.962104i	$0.587910\pi$
$660$	0	0
$661$	14.0000	0.544537	0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000	0.544537	0.272268	+	0.962221i	$0.412226\pi$
$662$	−10.0000	−0.388661
$663$	20.0000	0.776736
$664$	−6.00000	−0.232845
$665$	0	0
$666$	−8.00000	−0.309994
$667$	−30.0000	−1.16160
$668$	16.0000	0.619059
$669$	21.0000	0.811907
$670$	0	0
$671$	−20.0000	−0.772091
$672$	0	0
$673$	19.0000	0.732396	0.366198	−	0.930537i	$-0.380659\pi$
$673$	19.0000	0.732396	0.366198	+	0.930537i	$0.380659\pi$
$674$	−13.0000	−0.500741
$675$	0	0
$676$	3.00000	0.115385
$677$	−18.0000	−0.691796	−0.345898	−	0.938272i	$-0.612426\pi$
$677$	−18.0000	−0.691796	−0.345898	+	0.938272i	$0.612426\pi$
$678$	−5.00000	−0.192024
$679$	0	0
$680$	0	0
$681$	18.0000	0.689761
$682$	−22.0000	−0.842424
$683$	−2.00000	−0.0765279	−0.0382639	−	0.999268i	$-0.512183\pi$
$683$	−2.00000	−0.0765279	−0.0382639	+	0.999268i	$0.512183\pi$
$684$	−4.00000	−0.152944
$685$	0	0
$686$	0	0
$687$	−14.0000	−0.534133
$688$	0	0
$689$	−48.0000	−1.82865
$690$	0	0
$691$	−2.00000	−0.0760836	−0.0380418	−	0.999276i	$-0.512112\pi$
$691$	−2.00000	−0.0760836	−0.0380418	+	0.999276i	$0.512112\pi$
$692$	−2.00000	−0.0760286
$693$	0	0
$694$	18.0000	0.683271
$695$	0	0
$696$	6.00000	0.227429
$697$	−25.0000	−0.946943
$698$	4.00000	0.151402
$699$	26.0000	0.983410
$700$	0	0
$701$	0	0		−	1.00000i	$-0.5\pi$
$701$	0	0			1.00000i	$0.5\pi$
$702$	4.00000	0.150970
$703$	−32.0000	−1.20690
$704$	−2.00000	−0.0753778
$705$	0	0
$706$	−9.00000	−0.338719
$707$	0	0
$708$	−2.00000	−0.0751646
$709$	10.0000	0.375558	0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000	0.375558	0.187779	+	0.982211i	$0.439871\pi$
$710$	0	0
$711$	9.00000	0.337526
$712$	−11.0000	−0.412242
$713$	−55.0000	−2.05977
$714$	0	0
$715$	0	0
$716$	22.0000	0.822179
$717$	11.0000	0.410803
$718$	20.0000	0.746393
$719$	−3.00000	−0.111881	−0.0559406	−	0.998434i	$-0.517816\pi$
$719$	−3.00000	−0.111881	−0.0559406	+	0.998434i	$0.517816\pi$
$720$	0	0
$721$	0	0
$722$	3.00000	0.111648
$723$	−6.00000	−0.223142
$724$	−22.0000	−0.817624
$725$	0	0
$726$	7.00000	0.259794
$727$	−33.0000	−1.22390	−0.611951	−	0.790896i	$-0.709615\pi$
$727$	−33.0000	−1.22390	−0.611951	+	0.790896i	$0.709615\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	0	0
$732$	10.0000	0.369611
$733$	30.0000	1.10808	0.554038	−	0.832492i	$-0.313086\pi$
$733$	30.0000	1.10808	0.554038	+	0.832492i	$0.313086\pi$
$734$	4.00000	0.147643
$735$	0	0
$736$	−5.00000	−0.184302
$737$	0	0
$738$	−5.00000	−0.184053
$739$	0	0		−	1.00000i	$-0.5\pi$
$739$	0	0			1.00000i	$0.5\pi$
$740$	0	0
$741$	16.0000	0.587775
$742$	0	0
$743$	−33.0000	−1.21065	−0.605326	−	0.795977i	$-0.706957\pi$
$743$	−33.0000	−1.21065	−0.605326	+	0.795977i	$0.706957\pi$
$744$	11.0000	0.403280
$745$	0	0
$746$	32.0000	1.17160
$747$	6.00000	0.219529
$748$	10.0000	0.365636
$749$	0	0
$750$	0	0
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	−1.00000	−0.0364662
$753$	−8.00000	−0.291536
$754$	−24.0000	−0.874028
$755$	0	0
$756$	0	0
$757$	28.0000	1.01768	0.508839	−	0.860862i	$-0.330075\pi$
$757$	28.0000	1.01768	0.508839	+	0.860862i	$0.330075\pi$
$758$	2.00000	0.0726433
$759$	−10.0000	−0.362977
$760$	0	0
$761$	17.0000	0.616250	0.308125	−	0.951346i	$-0.400299\pi$
$761$	17.0000	0.616250	0.308125	+	0.951346i	$0.400299\pi$
$762$	0	0
$763$	0	0
$764$	−25.0000	−0.904468
$765$	0	0
$766$	−3.00000	−0.108394
$767$	8.00000	0.288863
$768$	1.00000	0.0360844
$769$	−14.0000	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$770$	0	0
$771$	−14.0000	−0.504198
$772$	11.0000	0.395899
$773$	−4.00000	−0.143870	−0.0719350	−	0.997409i	$-0.522917\pi$
$773$	−4.00000	−0.143870	−0.0719350	+	0.997409i	$0.522917\pi$
$774$	0	0
$775$	0	0
$776$	1.00000	0.0358979
$777$	0	0
$778$	−24.0000	−0.860442
$779$	−20.0000	−0.716574
$780$	0	0
$781$	2.00000	0.0715656
$782$	25.0000	0.893998
$783$	−6.00000	−0.214423
$784$	0	0
$785$	0	0
$786$	−6.00000	−0.214013
$787$	40.0000	1.42585	0.712923	−	0.701242i	$-0.247371\pi$
$787$	40.0000	1.42585	0.712923	+	0.701242i	$0.247371\pi$
$788$	−24.0000	−0.854965
$789$	−21.0000	−0.747620
$790$	0	0
$791$	0	0
$792$	2.00000	0.0710669
$793$	−40.0000	−1.42044
$794$	34.0000	1.20661
$795$	0	0
$796$	5.00000	0.177220
$797$	42.0000	1.48772	0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000	1.48772	0.743858	+	0.668338i	$0.232994\pi$
$798$	0	0
$799$	5.00000	0.176887
$800$	0	0
$801$	11.0000	0.388666
$802$	6.00000	0.211867
$803$	−4.00000	−0.141157
$804$	0	0
$805$	0	0
$806$	−44.0000	−1.54983
$807$	−24.0000	−0.844840
$808$	−12.0000	−0.422159
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	0	0
$811$	−48.0000	−1.68551	−0.842754	−	0.538299i	$-0.819067\pi$
$811$	−48.0000	−1.68551	−0.842754	+	0.538299i	$0.819067\pi$
$812$	0	0
$813$	−9.00000	−0.315644
$814$	16.0000	0.560800
$815$	0	0
$816$	−5.00000	−0.175035
$817$	0	0
$818$	35.0000	1.22375
$819$	0	0
$820$	0	0
$821$	52.0000	1.81481	0.907406	−	0.420255i	$-0.138059\pi$
$821$	52.0000	1.81481	0.907406	+	0.420255i	$0.138059\pi$
$822$	−23.0000	−0.802217
$823$	20.0000	0.697156	0.348578	−	0.937280i	$-0.386665\pi$
$823$	20.0000	0.697156	0.348578	+	0.937280i	$0.386665\pi$
$824$	−13.0000	−0.452876
$825$	0	0
$826$	0	0
$827$	−30.0000	−1.04320	−0.521601	−	0.853189i	$-0.674665\pi$
$827$	−30.0000	−1.04320	−0.521601	+	0.853189i	$0.674665\pi$
$828$	5.00000	0.173762
$829$	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
$831$	−2.00000	−0.0693792
$832$	−4.00000	−0.138675
$833$	0	0
$834$	−2.00000	−0.0692543
$835$	0	0
$836$	8.00000	0.276686
$837$	−11.0000	−0.380216
$838$	0	0
$839$	−9.00000	−0.310715	−0.155357	−	0.987858i	$-0.549653\pi$
$839$	−9.00000	−0.310715	−0.155357	+	0.987858i	$0.549653\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−28.0000	−0.964944
$843$	−29.0000	−0.998813
$844$	−16.0000	−0.550743
$845$	0	0
$846$	1.00000	0.0343807
$847$	0	0
$848$	12.0000	0.412082
$849$	−26.0000	−0.892318
$850$	0	0
$851$	40.0000	1.37118
$852$	−1.00000	−0.0342594
$853$	20.0000	0.684787	0.342393	−	0.939557i	$-0.388762\pi$
$853$	20.0000	0.684787	0.342393	+	0.939557i	$0.388762\pi$
$854$	0	0
$855$	0	0
$856$	−2.00000	−0.0683586
$857$	58.0000	1.98124	0.990621	−	0.136637i	$-0.0436295\pi$
$857$	58.0000	1.98124	0.990621	+	0.136637i	$0.0436295\pi$
$858$	−8.00000	−0.273115
$859$	−10.0000	−0.341196	−0.170598	−	0.985341i	$-0.554570\pi$
$859$	−10.0000	−0.341196	−0.170598	+	0.985341i	$0.554570\pi$
$860$	0	0
$861$	0	0
$862$	3.00000	0.102180
$863$	51.0000	1.73606	0.868030	−	0.496512i	$-0.165386\pi$
$863$	51.0000	1.73606	0.868030	+	0.496512i	$0.165386\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	9.00000	0.305832
$867$	8.00000	0.271694
$868$	0	0
$869$	−18.0000	−0.610608
$870$	0	0
$871$	0	0
$872$	−4.00000	−0.135457
$873$	−1.00000	−0.0338449
$874$	20.0000	0.676510
$875$	0	0
$876$	2.00000	0.0675737
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	−35.0000	−1.18119
$879$	18.0000	0.607125
$880$	0	0
$881$	39.0000	1.31394	0.656972	−	0.753915i	$-0.271837\pi$
$881$	39.0000	1.31394	0.656972	+	0.753915i	$0.271837\pi$
$882$	0	0
$883$	2.00000	0.0673054	0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000	0.0673054	0.0336527	+	0.999434i	$0.489286\pi$
$884$	20.0000	0.672673
$885$	0	0
$886$	8.00000	0.268765
$887$	56.0000	1.88030	0.940148	−	0.340766i	$-0.110687\pi$
$887$	56.0000	1.88030	0.940148	+	0.340766i	$0.110687\pi$
$888$	−8.00000	−0.268462
$889$	0	0
$890$	0	0
$891$	−2.00000	−0.0670025
$892$	21.0000	0.703132
$893$	4.00000	0.133855
$894$	−18.0000	−0.602010
$895$	0	0
$896$	0	0
$897$	−20.0000	−0.667781
$898$	−37.0000	−1.23471
$899$	66.0000	2.20122
$900$	0	0
$901$	−60.0000	−1.99889
$902$	10.0000	0.332964
$903$	0	0
$904$	−5.00000	−0.166298
$905$	0	0
$906$	16.0000	0.531564
$907$	18.0000	0.597680	0.298840	−	0.954303i	$-0.403400\pi$
$907$	18.0000	0.597680	0.298840	+	0.954303i	$0.403400\pi$
$908$	18.0000	0.597351
$909$	12.0000	0.398015
$910$	0	0
$911$	51.0000	1.68971	0.844853	−	0.534999i	$-0.179688\pi$
$911$	51.0000	1.68971	0.844853	+	0.534999i	$0.179688\pi$
$912$	−4.00000	−0.132453
$913$	−12.0000	−0.397142
$914$	−14.0000	−0.463079
$915$	0	0
$916$	−14.0000	−0.462573
$917$	0	0
$918$	5.00000	0.165025
$919$	43.0000	1.41844	0.709220	−	0.704988i	$-0.249047\pi$
$919$	43.0000	1.41844	0.709220	+	0.704988i	$0.249047\pi$
$920$	0	0
$921$	28.0000	0.922631
$922$	−20.0000	−0.658665
$923$	4.00000	0.131662
$924$	0	0
$925$	0	0
$926$	−13.0000	−0.427207
$927$	13.0000	0.426976
$928$	6.00000	0.196960
$929$	34.0000	1.11550	0.557752	−	0.830008i	$-0.311664\pi$
$929$	34.0000	1.11550	0.557752	+	0.830008i	$0.311664\pi$
$930$	0	0
$931$	0	0
$932$	26.0000	0.851658
$933$	29.0000	0.949417
$934$	34.0000	1.11251
$935$	0	0
$936$	4.00000	0.130744
$937$	−30.0000	−0.980057	−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000	−0.980057	−0.490029	+	0.871706i	$0.663014\pi$
$938$	0	0
$939$	−1.00000	−0.0326338
$940$	0	0
$941$	36.0000	1.17357	0.586783	−	0.809744i	$-0.300394\pi$
$941$	36.0000	1.17357	0.586783	+	0.809744i	$0.300394\pi$
$942$	14.0000	0.456145
$943$	25.0000	0.814112
$944$	−2.00000	−0.0650945
$945$	0	0
$946$	0	0
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	9.00000	0.292306
$949$	−8.00000	−0.259691
$950$	0	0
$951$	4.00000	0.129709
$952$	0	0
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	−12.0000	−0.388514
$955$	0	0
$956$	11.0000	0.355765
$957$	12.0000	0.387905
$958$	3.00000	0.0969256
$959$	0	0
$960$	0	0
$961$	90.0000	2.90323
$962$	32.0000	1.03172
$963$	2.00000	0.0644491
$964$	−6.00000	−0.193247
$965$	0	0
$966$	0	0
$967$	−1.00000	−0.0321578	−0.0160789	−	0.999871i	$-0.505118\pi$
$967$	−1.00000	−0.0321578	−0.0160789	+	0.999871i	$0.505118\pi$
$968$	7.00000	0.224989
$969$	20.0000	0.642493
$970$	0	0
$971$	6.00000	0.192549	0.0962746	−	0.995355i	$-0.469307\pi$
$971$	6.00000	0.192549	0.0962746	+	0.995355i	$0.469307\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	39.0000	1.24964
$975$	0	0
$976$	10.0000	0.320092
$977$	−33.0000	−1.05576	−0.527882	−	0.849318i	$-0.677014\pi$
$977$	−33.0000	−1.05576	−0.527882	+	0.849318i	$0.677014\pi$
$978$	−24.0000	−0.767435
$979$	−22.0000	−0.703123
$980$	0	0
$981$	4.00000	0.127710
$982$	−12.0000	−0.382935
$983$	16.0000	0.510321	0.255160	−	0.966899i	$-0.417872\pi$
$983$	16.0000	0.510321	0.255160	+	0.966899i	$0.417872\pi$
$984$	−5.00000	−0.159394
$985$	0	0
$986$	−30.0000	−0.955395
$987$	0	0
$988$	16.0000	0.509028
$989$	0	0
$990$	0	0
$991$	37.0000	1.17534	0.587672	−	0.809099i	$-0.300045\pi$
$991$	37.0000	1.17534	0.587672	+	0.809099i	$0.300045\pi$
$992$	11.0000	0.349250
$993$	10.0000	0.317340
$994$	0	0
$995$	0	0
$996$	6.00000	0.190117
$997$	4.00000	0.126681	0.0633406	−	0.997992i	$-0.479825\pi$
$997$	4.00000	0.126681	0.0633406	+	0.997992i	$0.479825\pi$
$998$	−22.0000	−0.696398
$999$	8.00000	0.253109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7350.2.a.z.1.1		1
5.4	even	2		7350.2.a.bt.1.1		1
7.2	even	3		1050.2.i.k.151.1	yes	2
7.4	even	3		1050.2.i.k.751.1	yes	2
7.6	odd	2		7350.2.a.h.1.1		1
35.2	odd	12		1050.2.o.f.949.1		4
35.4	even	6		1050.2.i.j.751.1	yes	2
35.9	even	6		1050.2.i.j.151.1	✓	2
35.18	odd	12		1050.2.o.f.499.1		4
35.23	odd	12		1050.2.o.f.949.2		4
35.32	odd	12		1050.2.o.f.499.2		4
35.34	odd	2		7350.2.a.cn.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.j.151.1	✓	2	35.9	even	6
1050.2.i.j.751.1	yes	2	35.4	even	6
1050.2.i.k.151.1	yes	2	7.2	even	3
1050.2.i.k.751.1	yes	2	7.4	even	3
1050.2.o.f.499.1		4	35.18	odd	12
1050.2.o.f.499.2		4	35.32	odd	12
1050.2.o.f.949.1		4	35.2	odd	12
1050.2.o.f.949.2		4	35.23	odd	12
7350.2.a.h.1.1		1	7.6	odd	2
7350.2.a.z.1.1		1	1.1	even	1	trivial
7350.2.a.bt.1.1		1	5.4	even	2
7350.2.a.cn.1.1		1	35.34	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:	\( N \)	\(=\)	\( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7350.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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