LMFDB - Embedded newform 9450.2.a.ds.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9450,2,Mod(1,9450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9450, 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("9450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9450.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:	$75.4586299101$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1890)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} +2.00000 q^{11} +1.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} +6.00000 q^{19} +2.00000 q^{22} +6.00000 q^{23} +1.00000 q^{28} +3.00000 q^{29} +5.00000 q^{31} +1.00000 q^{32} +2.00000 q^{34} -5.00000 q^{37} +6.00000 q^{38} -5.00000 q^{41} -4.00000 q^{43} +2.00000 q^{44} +6.00000 q^{46} -1.00000 q^{47} +1.00000 q^{49} -2.00000 q^{53} +1.00000 q^{56} +3.00000 q^{58} -7.00000 q^{59} +7.00000 q^{61} +5.00000 q^{62} +1.00000 q^{64} -6.00000 q^{67} +2.00000 q^{68} +13.0000 q^{71} -5.00000 q^{73} -5.00000 q^{74} +6.00000 q^{76} +2.00000 q^{77} -8.00000 q^{79} -5.00000 q^{82} -4.00000 q^{83} -4.00000 q^{86} +2.00000 q^{88} +2.00000 q^{89} +6.00000 q^{92} -1.00000 q^{94} -2.00000 q^{97} +1.00000 q^{98} +O(q^{100})$

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
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	0	0
$10$	0	0
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0	0
$13$	0	0		−	1.00000i	$-0.5\pi$
$13$	0	0			1.00000i	$0.5\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	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	$0.422021\pi$
$18$	0	0
$19$	6.00000	1.37649	0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000	1.37649	0.688247	+	0.725476i	$0.258380\pi$
$20$	0	0
$21$	0	0
$22$	2.00000	0.426401
$23$	6.00000	1.25109	0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000	1.25109	0.625543	+	0.780189i	$0.284877\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	0	0
$28$	1.00000	0.188982
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	2.00000	0.342997
$35$	0	0
$36$	0	0
$37$	−5.00000	−0.821995	−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000	−0.821995	−0.410997	+	0.911636i	$0.634819\pi$
$38$	6.00000	0.973329
$39$	0	0
$40$	0	0
$41$	−5.00000	−0.780869	−0.390434	−	0.920631i	$-0.627675\pi$
$41$	−5.00000	−0.780869	−0.390434	+	0.920631i	$0.627675\pi$
$42$	0	0
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	2.00000	0.301511
$45$	0	0
$46$	6.00000	0.884652
$47$	−1.00000	−0.145865	−0.0729325	−	0.997337i	$-0.523236\pi$
$47$	−1.00000	−0.145865	−0.0729325	+	0.997337i	$0.523236\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	0	0
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	3.00000	0.393919
$59$	−7.00000	−0.911322	−0.455661	−	0.890153i	$-0.650597\pi$
$59$	−7.00000	−0.911322	−0.455661	+	0.890153i	$0.650597\pi$
$60$	0	0
$61$	7.00000	0.896258	0.448129	−	0.893969i	$-0.352090\pi$
$61$	7.00000	0.896258	0.448129	+	0.893969i	$0.352090\pi$
$62$	5.00000	0.635001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	−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
$69$	0	0
$70$	0	0
$71$	13.0000	1.54282	0.771408	−	0.636341i	$-0.219553\pi$
$71$	13.0000	1.54282	0.771408	+	0.636341i	$0.219553\pi$
$72$	0	0
$73$	−5.00000	−0.585206	−0.292603	−	0.956234i	$-0.594521\pi$
$73$	−5.00000	−0.585206	−0.292603	+	0.956234i	$0.594521\pi$
$74$	−5.00000	−0.581238
$75$	0	0
$76$	6.00000	0.688247
$77$	2.00000	0.227921
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	0	0
$82$	−5.00000	−0.552158
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	0	0
$85$	0	0
$86$	−4.00000	−0.431331
$87$	0	0
$88$	2.00000	0.213201
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	0	0
$91$	0	0
$92$	6.00000	0.625543
$93$	0	0
$94$	−1.00000	−0.103142
$95$	0	0
$96$	0	0
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	1.00000	0.101015
$99$	0	0
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	0	0
$105$	0	0
$106$	−2.00000	−0.194257
$107$	−9.00000	−0.870063	−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000	−0.870063	−0.435031	+	0.900415i	$0.643263\pi$
$108$	0	0
$109$	0	0		−	1.00000i	$-0.5\pi$
$109$	0	0			1.00000i	$0.5\pi$
$110$	0	0
$111$	0	0
$112$	1.00000	0.0944911
$113$	5.00000	0.470360	0.235180	−	0.971952i	$-0.424432\pi$
$113$	5.00000	0.470360	0.235180	+	0.971952i	$0.424432\pi$
$114$	0	0
$115$	0	0
$116$	3.00000	0.278543
$117$	0	0
$118$	−7.00000	−0.644402
$119$	2.00000	0.183340
$120$	0	0
$121$	−7.00000	−0.636364
$122$	7.00000	0.633750
$123$	0	0
$124$	5.00000	0.449013
$125$	0	0
$126$	0	0
$127$	−7.00000	−0.621150	−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000	−0.621150	−0.310575	+	0.950549i	$0.600522\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	0	0
$131$	13.0000	1.13582	0.567908	−	0.823092i	$-0.307753\pi$
$131$	13.0000	1.13582	0.567908	+	0.823092i	$0.307753\pi$
$132$	0	0
$133$	6.00000	0.520266
$134$	−6.00000	−0.518321
$135$	0	0
$136$	2.00000	0.171499
$137$	9.00000	0.768922	0.384461	−	0.923141i	$-0.374387\pi$
$137$	9.00000	0.768922	0.384461	+	0.923141i	$0.374387\pi$
$138$	0	0
$139$	22.0000	1.86602	0.933008	−	0.359856i	$-0.117174\pi$
$139$	22.0000	1.86602	0.933008	+	0.359856i	$0.117174\pi$
$140$	0	0
$141$	0	0
$142$	13.0000	1.09094
$143$	0	0
$144$	0	0
$145$	0	0
$146$	−5.00000	−0.413803
$147$	0	0
$148$	−5.00000	−0.410997
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	0	0
$151$	−4.00000	−0.325515	−0.162758	−	0.986666i	$-0.552039\pi$
$151$	−4.00000	−0.325515	−0.162758	+	0.986666i	$0.552039\pi$
$152$	6.00000	0.486664
$153$	0	0
$154$	2.00000	0.161165
$155$	0	0
$156$	0	0
$157$	−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
$159$	0	0
$160$	0	0
$161$	6.00000	0.472866
$162$	0	0
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	−5.00000	−0.390434
$165$	0	0
$166$	−4.00000	−0.310460
$167$	3.00000	0.232147	0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000	0.232147	0.116073	+	0.993241i	$0.462969\pi$
$168$	0	0
$169$	−13.0000	−1.00000
$170$	0	0
$171$	0	0
$172$	−4.00000	−0.304997
$173$	−7.00000	−0.532200	−0.266100	−	0.963945i	$-0.585735\pi$
$173$	−7.00000	−0.532200	−0.266100	+	0.963945i	$0.585735\pi$
$174$	0	0
$175$	0	0
$176$	2.00000	0.150756
$177$	0	0
$178$	2.00000	0.149906
$179$	18.0000	1.34538	0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000	1.34538	0.672692	+	0.739923i	$0.265138\pi$
$180$	0	0
$181$	25.0000	1.85824	0.929118	−	0.369784i	$-0.120568\pi$
$181$	25.0000	1.85824	0.929118	+	0.369784i	$0.120568\pi$
$182$	0	0
$183$	0	0
$184$	6.00000	0.442326
$185$	0	0
$186$	0	0
$187$	4.00000	0.292509
$188$	−1.00000	−0.0729325
$189$	0	0
$190$	0	0
$191$	24.0000	1.73658	0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000	1.73658	0.868290	+	0.496058i	$0.165220\pi$
$192$	0	0
$193$	10.0000	0.719816	0.359908	−	0.932988i	$-0.382808\pi$
$193$	10.0000	0.719816	0.359908	+	0.932988i	$0.382808\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	1.00000	0.0714286
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	0	0
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	3.00000	0.210559
$204$	0	0
$205$	0	0
$206$	8.00000	0.557386
$207$	0	0
$208$	0	0
$209$	12.0000	0.830057
$210$	0	0
$211$	13.0000	0.894957	0.447478	−	0.894295i	$-0.352322\pi$
$211$	13.0000	0.894957	0.447478	+	0.894295i	$0.352322\pi$
$212$	−2.00000	−0.137361
$213$	0	0
$214$	−9.00000	−0.615227
$215$	0	0
$216$	0	0
$217$	5.00000	0.339422
$218$	0	0
$219$	0	0
$220$	0	0
$221$	0	0
$222$	0	0
$223$	2.00000	0.133930	0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000	0.133930	0.0669650	+	0.997755i	$0.478668\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	5.00000	0.332595
$227$	20.0000	1.32745	0.663723	−	0.747978i	$-0.268975\pi$
$227$	20.0000	1.32745	0.663723	+	0.747978i	$0.268975\pi$
$228$	0	0
$229$	−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
$232$	3.00000	0.196960
$233$	21.0000	1.37576	0.687878	−	0.725826i	$-0.258542\pi$
$233$	21.0000	1.37576	0.687878	+	0.725826i	$0.258542\pi$
$234$	0	0
$235$	0	0
$236$	−7.00000	−0.455661
$237$	0	0
$238$	2.00000	0.129641
$239$	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
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−7.00000	−0.449977
$243$	0	0
$244$	7.00000	0.448129
$245$	0	0
$246$	0	0
$247$	0	0
$248$	5.00000	0.317500
$249$	0	0
$250$	0	0
$251$	24.0000	1.51487	0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000	1.51487	0.757433	+	0.652913i	$0.226453\pi$
$252$	0	0
$253$	12.0000	0.754434
$254$	−7.00000	−0.439219
$255$	0	0
$256$	1.00000	0.0625000
$257$	20.0000	1.24757	0.623783	−	0.781598i	$-0.285595\pi$
$257$	20.0000	1.24757	0.623783	+	0.781598i	$0.285595\pi$
$258$	0	0
$259$	−5.00000	−0.310685
$260$	0	0
$261$	0	0
$262$	13.0000	0.803143
$263$	−28.0000	−1.72655	−0.863277	−	0.504730i	$-0.831592\pi$
$263$	−28.0000	−1.72655	−0.863277	+	0.504730i	$0.831592\pi$
$264$	0	0
$265$	0	0
$266$	6.00000	0.367884
$267$	0	0
$268$	−6.00000	−0.366508
$269$	−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
$271$	3.00000	0.182237	0.0911185	−	0.995840i	$-0.470956\pi$
$271$	3.00000	0.182237	0.0911185	+	0.995840i	$0.470956\pi$
$272$	2.00000	0.121268
$273$	0	0
$274$	9.00000	0.543710
$275$	0	0
$276$	0	0
$277$	−30.0000	−1.80253	−0.901263	−	0.433273i	$-0.857359\pi$
$277$	−30.0000	−1.80253	−0.901263	+	0.433273i	$0.857359\pi$
$278$	22.0000	1.31947
$279$	0	0
$280$	0	0
$281$	10.0000	0.596550	0.298275	−	0.954480i	$-0.403589\pi$
$281$	10.0000	0.596550	0.298275	+	0.954480i	$0.403589\pi$
$282$	0	0
$283$	13.0000	0.772770	0.386385	−	0.922338i	$-0.373724\pi$
$283$	13.0000	0.772770	0.386385	+	0.922338i	$0.373724\pi$
$284$	13.0000	0.771408
$285$	0	0
$286$	0	0
$287$	−5.00000	−0.295141
$288$	0	0
$289$	−13.0000	−0.764706
$290$	0	0
$291$	0	0
$292$	−5.00000	−0.292603
$293$	−17.0000	−0.993151	−0.496575	−	0.867994i	$-0.665409\pi$
$293$	−17.0000	−0.993151	−0.496575	+	0.867994i	$0.665409\pi$
$294$	0	0
$295$	0	0
$296$	−5.00000	−0.290619
$297$	0	0
$298$	−6.00000	−0.347571
$299$	0	0
$300$	0	0
$301$	−4.00000	−0.230556
$302$	−4.00000	−0.230174
$303$	0	0
$304$	6.00000	0.344124
$305$	0	0
$306$	0	0
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	2.00000	0.113961
$309$	0	0
$310$	0	0
$311$	−6.00000	−0.340229	−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000	−0.340229	−0.170114	+	0.985424i	$0.554414\pi$
$312$	0	0
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	−22.0000	−1.24153
$315$	0	0
$316$	−8.00000	−0.450035
$317$	10.0000	0.561656	0.280828	−	0.959758i	$-0.409391\pi$
$317$	10.0000	0.561656	0.280828	+	0.959758i	$0.409391\pi$
$318$	0	0
$319$	6.00000	0.335936
$320$	0	0
$321$	0	0
$322$	6.00000	0.334367
$323$	12.0000	0.667698
$324$	0	0
$325$	0	0
$326$	4.00000	0.221540
$327$	0	0
$328$	−5.00000	−0.276079
$329$	−1.00000	−0.0551318
$330$	0	0
$331$	−11.0000	−0.604615	−0.302307	−	0.953211i	$-0.597757\pi$
$331$	−11.0000	−0.604615	−0.302307	+	0.953211i	$0.597757\pi$
$332$	−4.00000	−0.219529
$333$	0	0
$334$	3.00000	0.164153
$335$	0	0
$336$	0	0
$337$	8.00000	0.435788	0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000	0.435788	0.217894	+	0.975972i	$0.430081\pi$
$338$	−13.0000	−0.707107
$339$	0	0
$340$	0	0
$341$	10.0000	0.541530
$342$	0	0
$343$	1.00000	0.0539949
$344$	−4.00000	−0.215666
$345$	0	0
$346$	−7.00000	−0.376322
$347$	25.0000	1.34207	0.671035	−	0.741426i	$-0.265850\pi$
$347$	25.0000	1.34207	0.671035	+	0.741426i	$0.265850\pi$
$348$	0	0
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	0	0
$351$	0	0
$352$	2.00000	0.106600
$353$	18.0000	0.958043	0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000	0.958043	0.479022	+	0.877803i	$0.340992\pi$
$354$	0	0
$355$	0	0
$356$	2.00000	0.106000
$357$	0	0
$358$	18.0000	0.951330
$359$	−32.0000	−1.68890	−0.844448	−	0.535638i	$-0.820071\pi$
$359$	−32.0000	−1.68890	−0.844448	+	0.535638i	$0.820071\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	25.0000	1.31397
$363$	0	0
$364$	0	0
$365$	0	0
$366$	0	0
$367$	14.0000	0.730794	0.365397	−	0.930852i	$-0.380933\pi$
$367$	14.0000	0.730794	0.365397	+	0.930852i	$0.380933\pi$
$368$	6.00000	0.312772
$369$	0	0
$370$	0	0
$371$	−2.00000	−0.103835
$372$	0	0
$373$	31.0000	1.60512	0.802560	−	0.596572i	$-0.203471\pi$
$373$	31.0000	1.60512	0.802560	+	0.596572i	$0.203471\pi$
$374$	4.00000	0.206835
$375$	0	0
$376$	−1.00000	−0.0515711
$377$	0	0
$378$	0	0
$379$	−21.0000	−1.07870	−0.539349	−	0.842082i	$-0.681330\pi$
$379$	−21.0000	−1.07870	−0.539349	+	0.842082i	$0.681330\pi$
$380$	0	0
$381$	0	0
$382$	24.0000	1.22795
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	0	0
$385$	0	0
$386$	10.0000	0.508987
$387$	0	0
$388$	−2.00000	−0.101535
$389$	−29.0000	−1.47036	−0.735179	−	0.677873i	$-0.762902\pi$
$389$	−29.0000	−1.47036	−0.735179	+	0.677873i	$0.762902\pi$
$390$	0	0
$391$	12.0000	0.606866
$392$	1.00000	0.0505076
$393$	0	0
$394$	−10.0000	−0.503793
$395$	0	0
$396$	0	0
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	8.00000	0.401004
$399$	0	0
$400$	0	0
$401$	−16.0000	−0.799002	−0.399501	−	0.916733i	$-0.630817\pi$
$401$	−16.0000	−0.799002	−0.399501	+	0.916733i	$0.630817\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	0	0
$406$	3.00000	0.148888
$407$	−10.0000	−0.495682
$408$	0	0
$409$	18.0000	0.890043	0.445021	−	0.895520i	$-0.353196\pi$
$409$	18.0000	0.890043	0.445021	+	0.895520i	$0.353196\pi$
$410$	0	0
$411$	0	0
$412$	8.00000	0.394132
$413$	−7.00000	−0.344447
$414$	0	0
$415$	0	0
$416$	0	0
$417$	0	0
$418$	12.0000	0.586939
$419$	−27.0000	−1.31904	−0.659518	−	0.751689i	$-0.729240\pi$
$419$	−27.0000	−1.31904	−0.659518	+	0.751689i	$0.729240\pi$
$420$	0	0
$421$	−34.0000	−1.65706	−0.828529	−	0.559946i	$-0.810822\pi$
$421$	−34.0000	−1.65706	−0.828529	+	0.559946i	$0.810822\pi$
$422$	13.0000	0.632830
$423$	0	0
$424$	−2.00000	−0.0971286
$425$	0	0
$426$	0	0
$427$	7.00000	0.338754
$428$	−9.00000	−0.435031
$429$	0	0
$430$	0	0
$431$	15.0000	0.722525	0.361262	−	0.932464i	$-0.382346\pi$
$431$	15.0000	0.722525	0.361262	+	0.932464i	$0.382346\pi$
$432$	0	0
$433$	−17.0000	−0.816968	−0.408484	−	0.912766i	$-0.633942\pi$
$433$	−17.0000	−0.816968	−0.408484	+	0.912766i	$0.633942\pi$
$434$	5.00000	0.240008
$435$	0	0
$436$	0	0
$437$	36.0000	1.72211
$438$	0	0
$439$	−32.0000	−1.52728	−0.763638	−	0.645644i	$-0.776589\pi$
$439$	−32.0000	−1.52728	−0.763638	+	0.645644i	$0.776589\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−17.0000	−0.807694	−0.403847	−	0.914826i	$-0.632327\pi$
$443$	−17.0000	−0.807694	−0.403847	+	0.914826i	$0.632327\pi$
$444$	0	0
$445$	0	0
$446$	2.00000	0.0947027
$447$	0	0
$448$	1.00000	0.0472456
$449$	−24.0000	−1.13263	−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000	−1.13263	−0.566315	+	0.824189i	$0.691631\pi$
$450$	0	0
$451$	−10.0000	−0.470882
$452$	5.00000	0.235180
$453$	0	0
$454$	20.0000	0.938647
$455$	0	0
$456$	0	0
$457$	8.00000	0.374224	0.187112	−	0.982339i	$-0.440087\pi$
$457$	8.00000	0.374224	0.187112	+	0.982339i	$0.440087\pi$
$458$	−14.0000	−0.654177
$459$	0	0
$460$	0	0
$461$	32.0000	1.49039	0.745194	−	0.666847i	$-0.232357\pi$
$461$	32.0000	1.49039	0.745194	+	0.666847i	$0.232357\pi$
$462$	0	0
$463$	7.00000	0.325318	0.162659	−	0.986682i	$-0.447993\pi$
$463$	7.00000	0.325318	0.162659	+	0.986682i	$0.447993\pi$
$464$	3.00000	0.139272
$465$	0	0
$466$	21.0000	0.972806
$467$	2.00000	0.0925490	0.0462745	−	0.998929i	$-0.485265\pi$
$467$	2.00000	0.0925490	0.0462745	+	0.998929i	$0.485265\pi$
$468$	0	0
$469$	−6.00000	−0.277054
$470$	0	0
$471$	0	0
$472$	−7.00000	−0.322201
$473$	−8.00000	−0.367840
$474$	0	0
$475$	0	0
$476$	2.00000	0.0916698
$477$	0	0
$478$	11.0000	0.503128
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	0	0
$481$	0	0
$482$	−14.0000	−0.637683
$483$	0	0
$484$	−7.00000	−0.318182
$485$	0	0
$486$	0	0
$487$	−5.00000	−0.226572	−0.113286	−	0.993562i	$-0.536138\pi$
$487$	−5.00000	−0.226572	−0.113286	+	0.993562i	$0.536138\pi$
$488$	7.00000	0.316875
$489$	0	0
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	6.00000	0.270226
$494$	0	0
$495$	0	0
$496$	5.00000	0.224507
$497$	13.0000	0.583130
$498$	0	0
$499$	−39.0000	−1.74588	−0.872940	−	0.487828i	$-0.837789\pi$
$499$	−39.0000	−1.74588	−0.872940	+	0.487828i	$0.837789\pi$
$500$	0	0
$501$	0	0
$502$	24.0000	1.07117
$503$	36.0000	1.60516	0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000	1.60516	0.802580	+	0.596544i	$0.203460\pi$
$504$	0	0
$505$	0	0
$506$	12.0000	0.533465
$507$	0	0
$508$	−7.00000	−0.310575
$509$	−4.00000	−0.177297	−0.0886484	−	0.996063i	$-0.528255\pi$
$509$	−4.00000	−0.177297	−0.0886484	+	0.996063i	$0.528255\pi$
$510$	0	0
$511$	−5.00000	−0.221187
$512$	1.00000	0.0441942
$513$	0	0
$514$	20.0000	0.882162
$515$	0	0
$516$	0	0
$517$	−2.00000	−0.0879599
$518$	−5.00000	−0.219687
$519$	0	0
$520$	0	0
$521$	22.0000	0.963837	0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000	0.963837	0.481919	+	0.876216i	$0.339940\pi$
$522$	0	0
$523$	−4.00000	−0.174908	−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000	−0.174908	−0.0874539	+	0.996169i	$0.527873\pi$
$524$	13.0000	0.567908
$525$	0	0
$526$	−28.0000	−1.22086
$527$	10.0000	0.435607
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	0	0
$532$	6.00000	0.260133
$533$	0	0
$534$	0	0
$535$	0	0
$536$	−6.00000	−0.259161
$537$	0	0
$538$	−6.00000	−0.258678
$539$	2.00000	0.0861461
$540$	0	0
$541$	18.0000	0.773880	0.386940	−	0.922105i	$-0.373532\pi$
$541$	18.0000	0.773880	0.386940	+	0.922105i	$0.373532\pi$
$542$	3.00000	0.128861
$543$	0	0
$544$	2.00000	0.0857493
$545$	0	0
$546$	0	0
$547$	−12.0000	−0.513083	−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000	−0.513083	−0.256541	+	0.966533i	$0.582583\pi$
$548$	9.00000	0.384461
$549$	0	0
$550$	0	0
$551$	18.0000	0.766826
$552$	0	0
$553$	−8.00000	−0.340195
$554$	−30.0000	−1.27458
$555$	0	0
$556$	22.0000	0.933008
$557$	22.0000	0.932170	0.466085	−	0.884740i	$-0.345664\pi$
$557$	22.0000	0.932170	0.466085	+	0.884740i	$0.345664\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	0	0
$562$	10.0000	0.421825
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	0	0
$565$	0	0
$566$	13.0000	0.546431
$567$	0	0
$568$	13.0000	0.545468
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	0	0
$571$	−45.0000	−1.88319	−0.941596	−	0.336746i	$-0.890674\pi$
$571$	−45.0000	−1.88319	−0.941596	+	0.336746i	$0.890674\pi$
$572$	0	0
$573$	0	0
$574$	−5.00000	−0.208696
$575$	0	0
$576$	0	0
$577$	−7.00000	−0.291414	−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000	−0.291414	−0.145707	+	0.989328i	$0.546546\pi$
$578$	−13.0000	−0.540729
$579$	0	0
$580$	0	0
$581$	−4.00000	−0.165948
$582$	0	0
$583$	−4.00000	−0.165663
$584$	−5.00000	−0.206901
$585$	0	0
$586$	−17.0000	−0.702264
$587$	−28.0000	−1.15568	−0.577842	−	0.816149i	$-0.696105\pi$
$587$	−28.0000	−1.15568	−0.577842	+	0.816149i	$0.696105\pi$
$588$	0	0
$589$	30.0000	1.23613
$590$	0	0
$591$	0	0
$592$	−5.00000	−0.205499
$593$	−12.0000	−0.492781	−0.246390	−	0.969171i	$-0.579245\pi$
$593$	−12.0000	−0.492781	−0.246390	+	0.969171i	$0.579245\pi$
$594$	0	0
$595$	0	0
$596$	−6.00000	−0.245770
$597$	0	0
$598$	0	0
$599$	−15.0000	−0.612883	−0.306442	−	0.951889i	$-0.599138\pi$
$599$	−15.0000	−0.612883	−0.306442	+	0.951889i	$0.599138\pi$
$600$	0	0
$601$	36.0000	1.46847	0.734235	−	0.678895i	$-0.237541\pi$
$601$	36.0000	1.46847	0.734235	+	0.678895i	$0.237541\pi$
$602$	−4.00000	−0.163028
$603$	0	0
$604$	−4.00000	−0.162758
$605$	0	0
$606$	0	0
$607$	44.0000	1.78590	0.892952	−	0.450151i	$-0.148630\pi$
$607$	44.0000	1.78590	0.892952	+	0.450151i	$0.148630\pi$
$608$	6.00000	0.243332
$609$	0	0
$610$	0	0
$611$	0	0
$612$	0	0
$613$	−6.00000	−0.242338	−0.121169	−	0.992632i	$-0.538664\pi$
$613$	−6.00000	−0.242338	−0.121169	+	0.992632i	$0.538664\pi$
$614$	−16.0000	−0.645707
$615$	0	0
$616$	2.00000	0.0805823
$617$	−7.00000	−0.281809	−0.140905	−	0.990023i	$-0.545001\pi$
$617$	−7.00000	−0.281809	−0.140905	+	0.990023i	$0.545001\pi$
$618$	0	0
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	0	0
$621$	0	0
$622$	−6.00000	−0.240578
$623$	2.00000	0.0801283
$624$	0	0
$625$	0	0
$626$	22.0000	0.879297
$627$	0	0
$628$	−22.0000	−0.877896
$629$	−10.0000	−0.398726
$630$	0	0
$631$	−46.0000	−1.83123	−0.915616	−	0.402055i	$-0.868296\pi$
$631$	−46.0000	−1.83123	−0.915616	+	0.402055i	$0.868296\pi$
$632$	−8.00000	−0.318223
$633$	0	0
$634$	10.0000	0.397151
$635$	0	0
$636$	0	0
$637$	0	0
$638$	6.00000	0.237542
$639$	0	0
$640$	0	0
$641$	−20.0000	−0.789953	−0.394976	−	0.918691i	$-0.629247\pi$
$641$	−20.0000	−0.789953	−0.394976	+	0.918691i	$0.629247\pi$
$642$	0	0
$643$	−43.0000	−1.69575	−0.847877	−	0.530193i	$-0.822120\pi$
$643$	−43.0000	−1.69575	−0.847877	+	0.530193i	$0.822120\pi$
$644$	6.00000	0.236433
$645$	0	0
$646$	12.0000	0.472134
$647$	7.00000	0.275198	0.137599	−	0.990488i	$-0.456061\pi$
$647$	7.00000	0.275198	0.137599	+	0.990488i	$0.456061\pi$
$648$	0	0
$649$	−14.0000	−0.549548
$650$	0	0
$651$	0	0
$652$	4.00000	0.156652
$653$	26.0000	1.01746	0.508729	−	0.860927i	$-0.330115\pi$
$653$	26.0000	1.01746	0.508729	+	0.860927i	$0.330115\pi$
$654$	0	0
$655$	0	0
$656$	−5.00000	−0.195217
$657$	0	0
$658$	−1.00000	−0.0389841
$659$	32.0000	1.24654	0.623272	−	0.782006i	$-0.285803\pi$
$659$	32.0000	1.24654	0.623272	+	0.782006i	$0.285803\pi$
$660$	0	0
$661$	7.00000	0.272268	0.136134	−	0.990690i	$-0.456532\pi$
$661$	7.00000	0.272268	0.136134	+	0.990690i	$0.456532\pi$
$662$	−11.0000	−0.427527
$663$	0	0
$664$	−4.00000	−0.155230
$665$	0	0
$666$	0	0
$667$	18.0000	0.696963
$668$	3.00000	0.116073
$669$	0	0
$670$	0	0
$671$	14.0000	0.540464
$672$	0	0
$673$	2.00000	0.0770943	0.0385472	−	0.999257i	$-0.487727\pi$
$673$	2.00000	0.0770943	0.0385472	+	0.999257i	$0.487727\pi$
$674$	8.00000	0.308148
$675$	0	0
$676$	−13.0000	−0.500000
$677$	27.0000	1.03769	0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000	1.03769	0.518847	+	0.854867i	$0.326361\pi$
$678$	0	0
$679$	−2.00000	−0.0767530
$680$	0	0
$681$	0	0
$682$	10.0000	0.382920
$683$	47.0000	1.79841	0.899203	−	0.437533i	$-0.144148\pi$
$683$	47.0000	1.79841	0.899203	+	0.437533i	$0.144148\pi$
$684$	0	0
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	−4.00000	−0.152499
$689$	0	0
$690$	0	0
$691$	10.0000	0.380418	0.190209	−	0.981744i	$-0.439083\pi$
$691$	10.0000	0.380418	0.190209	+	0.981744i	$0.439083\pi$
$692$	−7.00000	−0.266100
$693$	0	0
$694$	25.0000	0.948987
$695$	0	0
$696$	0	0
$697$	−10.0000	−0.378777
$698$	−26.0000	−0.984115
$699$	0	0
$700$	0	0
$701$	−1.00000	−0.0377695	−0.0188847	−	0.999822i	$-0.506012\pi$
$701$	−1.00000	−0.0377695	−0.0188847	+	0.999822i	$0.506012\pi$
$702$	0	0
$703$	−30.0000	−1.13147
$704$	2.00000	0.0753778
$705$	0	0
$706$	18.0000	0.677439
$707$	0	0
$708$	0	0
$709$	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
$711$	0	0
$712$	2.00000	0.0749532
$713$	30.0000	1.12351
$714$	0	0
$715$	0	0
$716$	18.0000	0.672692
$717$	0	0
$718$	−32.0000	−1.19423
$719$	30.0000	1.11881	0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000	1.11881	0.559406	+	0.828894i	$0.311029\pi$
$720$	0	0
$721$	8.00000	0.297936
$722$	17.0000	0.632674
$723$	0	0
$724$	25.0000	0.929118
$725$	0	0
$726$	0	0
$727$	−24.0000	−0.890111	−0.445055	−	0.895503i	$-0.646816\pi$
$727$	−24.0000	−0.890111	−0.445055	+	0.895503i	$0.646816\pi$
$728$	0	0
$729$	0	0
$730$	0	0
$731$	−8.00000	−0.295891
$732$	0	0
$733$	32.0000	1.18195	0.590973	−	0.806691i	$-0.298744\pi$
$733$	32.0000	1.18195	0.590973	+	0.806691i	$0.298744\pi$
$734$	14.0000	0.516749
$735$	0	0
$736$	6.00000	0.221163
$737$	−12.0000	−0.442026
$738$	0	0
$739$	25.0000	0.919640	0.459820	−	0.888012i	$-0.347914\pi$
$739$	25.0000	0.919640	0.459820	+	0.888012i	$0.347914\pi$
$740$	0	0
$741$	0	0
$742$	−2.00000	−0.0734223
$743$	−42.0000	−1.54083	−0.770415	−	0.637542i	$-0.779951\pi$
$743$	−42.0000	−1.54083	−0.770415	+	0.637542i	$0.779951\pi$
$744$	0	0
$745$	0	0
$746$	31.0000	1.13499
$747$	0	0
$748$	4.00000	0.146254
$749$	−9.00000	−0.328853
$750$	0	0
$751$	−10.0000	−0.364905	−0.182453	−	0.983215i	$-0.558404\pi$
$751$	−10.0000	−0.364905	−0.182453	+	0.983215i	$0.558404\pi$
$752$	−1.00000	−0.0364662
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−7.00000	−0.254419	−0.127210	−	0.991876i	$-0.540602\pi$
$757$	−7.00000	−0.254419	−0.127210	+	0.991876i	$0.540602\pi$
$758$	−21.0000	−0.762754
$759$	0	0
$760$	0	0
$761$	−27.0000	−0.978749	−0.489375	−	0.872074i	$-0.662775\pi$
$761$	−27.0000	−0.978749	−0.489375	+	0.872074i	$0.662775\pi$
$762$	0	0
$763$	0	0
$764$	24.0000	0.868290
$765$	0	0
$766$	−24.0000	−0.867155
$767$	0	0
$768$	0	0
$769$	−2.00000	−0.0721218	−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000	−0.0721218	−0.0360609	+	0.999350i	$0.511481\pi$
$770$	0	0
$771$	0	0
$772$	10.0000	0.359908
$773$	33.0000	1.18693	0.593464	−	0.804861i	$-0.297760\pi$
$773$	33.0000	1.18693	0.593464	+	0.804861i	$0.297760\pi$
$774$	0	0
$775$	0	0
$776$	−2.00000	−0.0717958
$777$	0	0
$778$	−29.0000	−1.03970
$779$	−30.0000	−1.07486
$780$	0	0
$781$	26.0000	0.930353
$782$	12.0000	0.429119
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	−49.0000	−1.74666	−0.873331	−	0.487128i	$-0.838045\pi$
$787$	−49.0000	−1.74666	−0.873331	+	0.487128i	$0.838045\pi$
$788$	−10.0000	−0.356235
$789$	0	0
$790$	0	0
$791$	5.00000	0.177780
$792$	0	0
$793$	0	0
$794$	2.00000	0.0709773
$795$	0	0
$796$	8.00000	0.283552
$797$	9.00000	0.318796	0.159398	−	0.987214i	$-0.449045\pi$
$797$	9.00000	0.318796	0.159398	+	0.987214i	$0.449045\pi$
$798$	0	0
$799$	−2.00000	−0.0707549
$800$	0	0
$801$	0	0
$802$	−16.0000	−0.564980
$803$	−10.0000	−0.352892
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	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
$811$	8.00000	0.280918	0.140459	−	0.990086i	$-0.455142\pi$
$811$	8.00000	0.280918	0.140459	+	0.990086i	$0.455142\pi$
$812$	3.00000	0.105279
$813$	0	0
$814$	−10.0000	−0.350500
$815$	0	0
$816$	0	0
$817$	−24.0000	−0.839654
$818$	18.0000	0.629355
$819$	0	0
$820$	0	0
$821$	−18.0000	−0.628204	−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000	−0.628204	−0.314102	+	0.949389i	$0.601703\pi$
$822$	0	0
$823$	29.0000	1.01088	0.505438	−	0.862863i	$-0.331331\pi$
$823$	29.0000	1.01088	0.505438	+	0.862863i	$0.331331\pi$
$824$	8.00000	0.278693
$825$	0	0
$826$	−7.00000	−0.243561
$827$	23.0000	0.799788	0.399894	−	0.916561i	$-0.369047\pi$
$827$	23.0000	0.799788	0.399894	+	0.916561i	$0.369047\pi$
$828$	0	0
$829$	−46.0000	−1.59765	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000	−1.59765	−0.798823	+	0.601566i	$0.794544\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	2.00000	0.0692959
$834$	0	0
$835$	0	0
$836$	12.0000	0.415029
$837$	0	0
$838$	−27.0000	−0.932700
$839$	4.00000	0.138095	0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000	0.138095	0.0690477	+	0.997613i	$0.478004\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	−34.0000	−1.17172
$843$	0	0
$844$	13.0000	0.447478
$845$	0	0
$846$	0	0
$847$	−7.00000	−0.240523
$848$	−2.00000	−0.0686803
$849$	0	0
$850$	0	0
$851$	−30.0000	−1.02839
$852$	0	0
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	7.00000	0.239535
$855$	0	0
$856$	−9.00000	−0.307614
$857$	24.0000	0.819824	0.409912	−	0.912125i	$-0.365559\pi$
$857$	24.0000	0.819824	0.409912	+	0.912125i	$0.365559\pi$
$858$	0	0
$859$	−18.0000	−0.614152	−0.307076	−	0.951685i	$-0.599351\pi$
$859$	−18.0000	−0.614152	−0.307076	+	0.951685i	$0.599351\pi$
$860$	0	0
$861$	0	0
$862$	15.0000	0.510902
$863$	16.0000	0.544646	0.272323	−	0.962206i	$-0.412208\pi$
$863$	16.0000	0.544646	0.272323	+	0.962206i	$0.412208\pi$
$864$	0	0
$865$	0	0
$866$	−17.0000	−0.577684
$867$	0	0
$868$	5.00000	0.169711
$869$	−16.0000	−0.542763
$870$	0	0
$871$	0	0
$872$	0	0
$873$	0	0
$874$	36.0000	1.21772
$875$	0	0
$876$	0	0
$877$	1.00000	0.0337676	0.0168838	−	0.999857i	$-0.494625\pi$
$877$	1.00000	0.0337676	0.0168838	+	0.999857i	$0.494625\pi$
$878$	−32.0000	−1.07995
$879$	0	0
$880$	0	0
$881$	43.0000	1.44871	0.724353	−	0.689429i	$-0.242138\pi$
$881$	43.0000	1.44871	0.724353	+	0.689429i	$0.242138\pi$
$882$	0	0
$883$	24.0000	0.807664	0.403832	−	0.914833i	$-0.367678\pi$
$883$	24.0000	0.807664	0.403832	+	0.914833i	$0.367678\pi$
$884$	0	0
$885$	0	0
$886$	−17.0000	−0.571126
$887$	−13.0000	−0.436497	−0.218249	−	0.975893i	$-0.570034\pi$
$887$	−13.0000	−0.436497	−0.218249	+	0.975893i	$0.570034\pi$
$888$	0	0
$889$	−7.00000	−0.234772
$890$	0	0
$891$	0	0
$892$	2.00000	0.0669650
$893$	−6.00000	−0.200782
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	−24.0000	−0.800890
$899$	15.0000	0.500278
$900$	0	0
$901$	−4.00000	−0.133259
$902$	−10.0000	−0.332964
$903$	0	0
$904$	5.00000	0.166298
$905$	0	0
$906$	0	0
$907$	−44.0000	−1.46100	−0.730498	−	0.682915i	$-0.760712\pi$
$907$	−44.0000	−1.46100	−0.730498	+	0.682915i	$0.760712\pi$
$908$	20.0000	0.663723
$909$	0	0
$910$	0	0
$911$	45.0000	1.49092	0.745458	−	0.666552i	$-0.232231\pi$
$911$	45.0000	1.49092	0.745458	+	0.666552i	$0.232231\pi$
$912$	0	0
$913$	−8.00000	−0.264761
$914$	8.00000	0.264616
$915$	0	0
$916$	−14.0000	−0.462573
$917$	13.0000	0.429298
$918$	0	0
$919$	−10.0000	−0.329870	−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000	−0.329870	−0.164935	+	0.986304i	$0.552741\pi$
$920$	0	0
$921$	0	0
$922$	32.0000	1.05386
$923$	0	0
$924$	0	0
$925$	0	0
$926$	7.00000	0.230034
$927$	0	0
$928$	3.00000	0.0984798
$929$	14.0000	0.459325	0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000	0.459325	0.229663	+	0.973270i	$0.426238\pi$
$930$	0	0
$931$	6.00000	0.196642
$932$	21.0000	0.687878
$933$	0	0
$934$	2.00000	0.0654420
$935$	0	0
$936$	0	0
$937$	7.00000	0.228680	0.114340	−	0.993442i	$-0.463525\pi$
$937$	7.00000	0.228680	0.114340	+	0.993442i	$0.463525\pi$
$938$	−6.00000	−0.195907
$939$	0	0
$940$	0	0
$941$	22.0000	0.717180	0.358590	−	0.933495i	$-0.383258\pi$
$941$	22.0000	0.717180	0.358590	+	0.933495i	$0.383258\pi$
$942$	0	0
$943$	−30.0000	−0.976934
$944$	−7.00000	−0.227831
$945$	0	0
$946$	−8.00000	−0.260102
$947$	−52.0000	−1.68977	−0.844886	−	0.534946i	$-0.820332\pi$
$947$	−52.0000	−1.68977	−0.844886	+	0.534946i	$0.820332\pi$
$948$	0	0
$949$	0	0
$950$	0	0
$951$	0	0
$952$	2.00000	0.0648204
$953$	30.0000	0.971795	0.485898	−	0.874016i	$-0.338493\pi$
$953$	30.0000	0.971795	0.485898	+	0.874016i	$0.338493\pi$
$954$	0	0
$955$	0	0
$956$	11.0000	0.355765
$957$	0	0
$958$	24.0000	0.775405
$959$	9.00000	0.290625
$960$	0	0
$961$	−6.00000	−0.193548
$962$	0	0
$963$	0	0
$964$	−14.0000	−0.450910
$965$	0	0
$966$	0	0
$967$	−37.0000	−1.18984	−0.594920	−	0.803785i	$-0.702816\pi$
$967$	−37.0000	−1.18984	−0.594920	+	0.803785i	$0.702816\pi$
$968$	−7.00000	−0.224989
$969$	0	0
$970$	0	0
$971$	27.0000	0.866471	0.433236	−	0.901281i	$-0.357372\pi$
$971$	27.0000	0.866471	0.433236	+	0.901281i	$0.357372\pi$
$972$	0	0
$973$	22.0000	0.705288
$974$	−5.00000	−0.160210
$975$	0	0
$976$	7.00000	0.224065
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	0	0
$979$	4.00000	0.127841
$980$	0	0
$981$	0	0
$982$	12.0000	0.382935
$983$	−16.0000	−0.510321	−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000	−0.510321	−0.255160	+	0.966899i	$0.582128\pi$
$984$	0	0
$985$	0	0
$986$	6.00000	0.191079
$987$	0	0
$988$	0	0
$989$	−24.0000	−0.763156
$990$	0	0
$991$	10.0000	0.317660	0.158830	−	0.987306i	$-0.449228\pi$
$991$	10.0000	0.317660	0.158830	+	0.987306i	$0.449228\pi$
$992$	5.00000	0.158750
$993$	0	0
$994$	13.0000	0.412335
$995$	0	0
$996$	0	0
$997$	−38.0000	−1.20347	−0.601736	−	0.798695i	$-0.705524\pi$
$997$	−38.0000	−1.20347	−0.601736	+	0.798695i	$0.705524\pi$
$998$	−39.0000	−1.23452
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9450.2.a.ds.1.1		1
3.2	odd	2		9450.2.a.bg.1.1		1
5.4	even	2		1890.2.a.h.1.1	✓	1
15.14	odd	2		1890.2.a.n.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.2.a.h.1.1	✓	1	5.4	even	2
1890.2.a.n.1.1	yes	1	15.14	odd	2
9450.2.a.bg.1.1		1	3.2	odd	2
9450.2.a.ds.1.1		1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9450.a (trivial)

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L-functions

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