LMFDB - Embedded newform 5850.2.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5850,2,Mod(1,5850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5850, 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("5850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5850.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:	$46.7124851824$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 650)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	5850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} +5.00000 q^{7} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} +5.00000 q^{7} -1.00000 q^{8} +3.00000 q^{11} +1.00000 q^{13} -5.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} -4.00000 q^{19} -3.00000 q^{22} -6.00000 q^{23} -1.00000 q^{26} +5.00000 q^{28} -9.00000 q^{29} +5.00000 q^{31} -1.00000 q^{32} +3.00000 q^{34} +2.00000 q^{37} +4.00000 q^{38} +2.00000 q^{43} +3.00000 q^{44} +6.00000 q^{46} +9.00000 q^{47} +18.0000 q^{49} +1.00000 q^{52} +9.00000 q^{53} -5.00000 q^{56} +9.00000 q^{58} +9.00000 q^{59} -1.00000 q^{61} -5.00000 q^{62} +1.00000 q^{64} +5.00000 q^{67} -3.00000 q^{68} +14.0000 q^{73} -2.00000 q^{74} -4.00000 q^{76} +15.0000 q^{77} -16.0000 q^{79} +15.0000 q^{83} -2.00000 q^{86} -3.00000 q^{88} +6.00000 q^{89} +5.00000 q^{91} -6.00000 q^{92} -9.00000 q^{94} +8.00000 q^{97} -18.0000 q^{98} +O(q^{100})$

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
$7$	5.00000	1.88982	0.944911	−	0.327327i	$-0.106148\pi$
$7$	5.00000	1.88982	0.944911	+	0.327327i	$0.106148\pi$
$8$	−1.00000	−0.353553
$9$	0	0
$10$	0	0
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	0	0
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−5.00000	−1.33631
$15$	0	0
$16$	1.00000	0.250000
$17$	−3.00000	−0.727607	−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000	−0.727607	−0.363803	+	0.931476i	$0.618522\pi$
$18$	0	0
$19$	−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
$22$	−3.00000	−0.639602
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	0	0
$26$	−1.00000	−0.196116
$27$	0	0
$28$	5.00000	0.944911
$29$	−9.00000	−1.67126	−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000	−1.67126	−0.835629	+	0.549294i	$0.814897\pi$
$30$	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
$34$	3.00000	0.514496
$35$	0	0
$36$	0	0
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	4.00000	0.648886
$39$	0	0
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	3.00000	0.452267
$45$	0	0
$46$	6.00000	0.884652
$47$	9.00000	1.31278	0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000	1.31278	0.656392	+	0.754420i	$0.272082\pi$
$48$	0	0
$49$	18.0000	2.57143
$50$	0	0
$51$	0	0
$52$	1.00000	0.138675
$53$	9.00000	1.23625	0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000	1.23625	0.618123	+	0.786082i	$0.287894\pi$
$54$	0	0
$55$	0	0
$56$	−5.00000	−0.668153
$57$	0	0
$58$	9.00000	1.18176
$59$	9.00000	1.17170	0.585850	−	0.810419i	$-0.300761\pi$
$59$	9.00000	1.17170	0.585850	+	0.810419i	$0.300761\pi$
$60$	0	0
$61$	−1.00000	−0.128037	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000	−0.128037	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	−5.00000	−0.635001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	5.00000	0.610847	0.305424	−	0.952217i	$-0.401202\pi$
$67$	5.00000	0.610847	0.305424	+	0.952217i	$0.401202\pi$
$68$	−3.00000	−0.363803
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	0	0
$73$	14.0000	1.63858	0.819288	−	0.573382i	$-0.194369\pi$
$73$	14.0000	1.63858	0.819288	+	0.573382i	$0.194369\pi$
$74$	−2.00000	−0.232495
$75$	0	0
$76$	−4.00000	−0.458831
$77$	15.0000	1.70941
$78$	0	0
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	0	0
$81$	0	0
$82$	0	0
$83$	15.0000	1.64646	0.823232	−	0.567705i	$-0.192169\pi$
$83$	15.0000	1.64646	0.823232	+	0.567705i	$0.192169\pi$
$84$	0	0
$85$	0	0
$86$	−2.00000	−0.215666
$87$	0	0
$88$	−3.00000	−0.319801
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	0	0
$91$	5.00000	0.524142
$92$	−6.00000	−0.625543
$93$	0	0
$94$	−9.00000	−0.928279
$95$	0	0
$96$	0	0
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	−18.0000	−1.81827
$99$	0	0
$100$	0	0
$101$	3.00000	0.298511	0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000	0.298511	0.149256	+	0.988799i	$0.452312\pi$
$102$	0	0
$103$	−16.0000	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	−9.00000	−0.874157
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	0	0
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	0	0
$112$	5.00000	0.472456
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	0	0
$115$	0	0
$116$	−9.00000	−0.835629
$117$	0	0
$118$	−9.00000	−0.828517
$119$	−15.0000	−1.37505
$120$	0	0
$121$	−2.00000	−0.181818
$122$	1.00000	0.0905357
$123$	0	0
$124$	5.00000	0.449013
$125$	0	0
$126$	0	0
$127$	20.0000	1.77471	0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000	1.77471	0.887357	+	0.461084i	$0.152539\pi$
$128$	−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	$0.415581\pi$
$132$	0	0
$133$	−20.0000	−1.73422
$134$	−5.00000	−0.431934
$135$	0	0
$136$	3.00000	0.257248
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	0	0
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	3.00000	0.250873
$144$	0	0
$145$	0	0
$146$	−14.0000	−1.15865
$147$	0	0
$148$	2.00000	0.164399
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	−7.00000	−0.569652	−0.284826	−	0.958579i	$-0.591936\pi$
$151$	−7.00000	−0.569652	−0.284826	+	0.958579i	$0.591936\pi$
$152$	4.00000	0.324443
$153$	0	0
$154$	−15.0000	−1.20873
$155$	0	0
$156$	0	0
$157$	17.0000	1.35675	0.678374	−	0.734717i	$-0.262685\pi$
$157$	17.0000	1.35675	0.678374	+	0.734717i	$0.262685\pi$
$158$	16.0000	1.27289
$159$	0	0
$160$	0	0
$161$	−30.0000	−2.36433
$162$	0	0
$163$	−16.0000	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$164$	0	0
$165$	0	0
$166$	−15.0000	−1.16423
$167$	24.0000	1.85718	0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000	1.85718	0.928588	+	0.371113i	$0.121024\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	0	0
$172$	2.00000	0.152499
$173$	3.00000	0.228086	0.114043	−	0.993476i	$-0.463620\pi$
$173$	3.00000	0.228086	0.114043	+	0.993476i	$0.463620\pi$
$174$	0	0
$175$	0	0
$176$	3.00000	0.226134
$177$	0	0
$178$	−6.00000	−0.449719
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	11.0000	0.817624	0.408812	−	0.912619i	$-0.365943\pi$
$181$	11.0000	0.817624	0.408812	+	0.912619i	$0.365943\pi$
$182$	−5.00000	−0.370625
$183$	0	0
$184$	6.00000	0.442326
$185$	0	0
$186$	0	0
$187$	−9.00000	−0.658145
$188$	9.00000	0.656392
$189$	0	0
$190$	0	0
$191$	−12.0000	−0.868290	−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000	−0.868290	−0.434145	+	0.900843i	$0.642949\pi$
$192$	0	0
$193$	20.0000	1.43963	0.719816	−	0.694165i	$-0.244226\pi$
$193$	20.0000	1.43963	0.719816	+	0.694165i	$0.244226\pi$
$194$	−8.00000	−0.574367
$195$	0	0
$196$	18.0000	1.28571
$197$	24.0000	1.70993	0.854965	−	0.518686i	$-0.173579\pi$
$197$	24.0000	1.70993	0.854965	+	0.518686i	$0.173579\pi$
$198$	0	0
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	0	0
$201$	0	0
$202$	−3.00000	−0.211079
$203$	−45.0000	−3.15838
$204$	0	0
$205$	0	0
$206$	16.0000	1.11477
$207$	0	0
$208$	1.00000	0.0693375
$209$	−12.0000	−0.830057
$210$	0	0
$211$	14.0000	0.963800	0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000	0.963800	0.481900	+	0.876226i	$0.339947\pi$
$212$	9.00000	0.618123
$213$	0	0
$214$	6.00000	0.410152
$215$	0	0
$216$	0	0
$217$	25.0000	1.69711
$218$	−2.00000	−0.135457
$219$	0	0
$220$	0	0
$221$	−3.00000	−0.201802
$222$	0	0
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	−5.00000	−0.334077
$225$	0	0
$226$	−6.00000	−0.399114
$227$	9.00000	0.597351	0.298675	−	0.954355i	$-0.403455\pi$
$227$	9.00000	0.597351	0.298675	+	0.954355i	$0.403455\pi$
$228$	0	0
$229$	−16.0000	−1.05731	−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000	−1.05731	−0.528655	+	0.848837i	$0.677303\pi$
$230$	0	0
$231$	0	0
$232$	9.00000	0.590879
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	0	0
$235$	0	0
$236$	9.00000	0.585850
$237$	0	0
$238$	15.0000	0.972306
$239$	15.0000	0.970269	0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000	0.970269	0.485135	+	0.874439i	$0.338771\pi$
$240$	0	0
$241$	8.00000	0.515325	0.257663	−	0.966235i	$-0.417048\pi$
$241$	8.00000	0.515325	0.257663	+	0.966235i	$0.417048\pi$
$242$	2.00000	0.128565
$243$	0	0
$244$	−1.00000	−0.0640184
$245$	0	0
$246$	0	0
$247$	−4.00000	−0.254514
$248$	−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
$253$	−18.0000	−1.13165
$254$	−20.0000	−1.25491
$255$	0	0
$256$	1.00000	0.0625000
$257$	15.0000	0.935674	0.467837	−	0.883815i	$-0.345033\pi$
$257$	15.0000	0.935674	0.467837	+	0.883815i	$0.345033\pi$
$258$	0	0
$259$	10.0000	0.621370
$260$	0	0
$261$	0	0
$262$	−6.00000	−0.370681
$263$	−18.0000	−1.10993	−0.554964	−	0.831875i	$-0.687268\pi$
$263$	−18.0000	−1.10993	−0.554964	+	0.831875i	$0.687268\pi$
$264$	0	0
$265$	0	0
$266$	20.0000	1.22628
$267$	0	0
$268$	5.00000	0.305424
$269$	−9.00000	−0.548740	−0.274370	−	0.961624i	$-0.588469\pi$
$269$	−9.00000	−0.548740	−0.274370	+	0.961624i	$0.588469\pi$
$270$	0	0
$271$	−19.0000	−1.15417	−0.577084	−	0.816685i	$-0.695809\pi$
$271$	−19.0000	−1.15417	−0.577084	+	0.816685i	$0.695809\pi$
$272$	−3.00000	−0.181902
$273$	0	0
$274$	6.00000	0.362473
$275$	0	0
$276$	0	0
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	10.0000	0.599760
$279$	0	0
$280$	0	0
$281$	−12.0000	−0.715860	−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000	−0.715860	−0.357930	+	0.933748i	$0.616517\pi$
$282$	0	0
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	0	0
$285$	0	0
$286$	−3.00000	−0.177394
$287$	0	0
$288$	0	0
$289$	−8.00000	−0.470588
$290$	0	0
$291$	0	0
$292$	14.0000	0.819288
$293$	0	0		−	1.00000i	$-0.5\pi$
$293$	0	0			1.00000i	$0.5\pi$
$294$	0	0
$295$	0	0
$296$	−2.00000	−0.116248
$297$	0	0
$298$	0	0
$299$	−6.00000	−0.346989
$300$	0	0
$301$	10.0000	0.576390
$302$	7.00000	0.402805
$303$	0	0
$304$	−4.00000	−0.229416
$305$	0	0
$306$	0	0
$307$	20.0000	1.14146	0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000	1.14146	0.570730	+	0.821138i	$0.306660\pi$
$308$	15.0000	0.854704
$309$	0	0
$310$	0	0
$311$	18.0000	1.02069	0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000	1.02069	0.510343	+	0.859971i	$0.329518\pi$
$312$	0	0
$313$	−19.0000	−1.07394	−0.536972	−	0.843600i	$-0.680432\pi$
$313$	−19.0000	−1.07394	−0.536972	+	0.843600i	$0.680432\pi$
$314$	−17.0000	−0.959366
$315$	0	0
$316$	−16.0000	−0.900070
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	−27.0000	−1.51171
$320$	0	0
$321$	0	0
$322$	30.0000	1.67183
$323$	12.0000	0.667698
$324$	0	0
$325$	0	0
$326$	16.0000	0.886158
$327$	0	0
$328$	0	0
$329$	45.0000	2.48093
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	15.0000	0.823232
$333$	0	0
$334$	−24.0000	−1.31322
$335$	0	0
$336$	0	0
$337$	−13.0000	−0.708155	−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000	−0.708155	−0.354078	+	0.935216i	$0.615205\pi$
$338$	−1.00000	−0.0543928
$339$	0	0
$340$	0	0
$341$	15.0000	0.812296
$342$	0	0
$343$	55.0000	2.96972
$344$	−2.00000	−0.107833
$345$	0	0
$346$	−3.00000	−0.161281
$347$	−30.0000	−1.61048	−0.805242	−	0.592946i	$-0.797965\pi$
$347$	−30.0000	−1.61048	−0.805242	+	0.592946i	$0.797965\pi$
$348$	0	0
$349$	20.0000	1.07058	0.535288	−	0.844670i	$-0.320203\pi$
$349$	20.0000	1.07058	0.535288	+	0.844670i	$0.320203\pi$
$350$	0	0
$351$	0	0
$352$	−3.00000	−0.159901
$353$	6.00000	0.319348	0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000	0.319348	0.159674	+	0.987170i	$0.448956\pi$
$354$	0	0
$355$	0	0
$356$	6.00000	0.317999
$357$	0	0
$358$	0	0
$359$	21.0000	1.10834	0.554169	−	0.832404i	$-0.313036\pi$
$359$	21.0000	1.10834	0.554169	+	0.832404i	$0.313036\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	−11.0000	−0.578147
$363$	0	0
$364$	5.00000	0.262071
$365$	0	0
$366$	0	0
$367$	−10.0000	−0.521996	−0.260998	−	0.965339i	$-0.584052\pi$
$367$	−10.0000	−0.521996	−0.260998	+	0.965339i	$0.584052\pi$
$368$	−6.00000	−0.312772
$369$	0	0
$370$	0	0
$371$	45.0000	2.33628
$372$	0	0
$373$	29.0000	1.50156	0.750782	−	0.660551i	$-0.229677\pi$
$373$	29.0000	1.50156	0.750782	+	0.660551i	$0.229677\pi$
$374$	9.00000	0.465379
$375$	0	0
$376$	−9.00000	−0.464140
$377$	−9.00000	−0.463524
$378$	0	0
$379$	29.0000	1.48963	0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000	1.48963	0.744815	+	0.667271i	$0.232538\pi$
$380$	0	0
$381$	0	0
$382$	12.0000	0.613973
$383$	−36.0000	−1.83951	−0.919757	−	0.392488i	$-0.871614\pi$
$383$	−36.0000	−1.83951	−0.919757	+	0.392488i	$0.871614\pi$
$384$	0	0
$385$	0	0
$386$	−20.0000	−1.01797
$387$	0	0
$388$	8.00000	0.406138
$389$	−18.0000	−0.912636	−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000	−0.912636	−0.456318	+	0.889817i	$0.650832\pi$
$390$	0	0
$391$	18.0000	0.910299
$392$	−18.0000	−0.909137
$393$	0	0
$394$	−24.0000	−1.20910
$395$	0	0
$396$	0	0
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	16.0000	0.802008
$399$	0	0
$400$	0	0
$401$	−12.0000	−0.599251	−0.299626	−	0.954057i	$-0.596862\pi$
$401$	−12.0000	−0.599251	−0.299626	+	0.954057i	$0.596862\pi$
$402$	0	0
$403$	5.00000	0.249068
$404$	3.00000	0.149256
$405$	0	0
$406$	45.0000	2.23331
$407$	6.00000	0.297409
$408$	0	0
$409$	−22.0000	−1.08783	−0.543915	−	0.839140i	$-0.683059\pi$
$409$	−22.0000	−1.08783	−0.543915	+	0.839140i	$0.683059\pi$
$410$	0	0
$411$	0	0
$412$	−16.0000	−0.788263
$413$	45.0000	2.21431
$414$	0	0
$415$	0	0
$416$	−1.00000	−0.0490290
$417$	0	0
$418$	12.0000	0.586939
$419$	−6.00000	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$420$	0	0
$421$	−4.00000	−0.194948	−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000	−0.194948	−0.0974740	+	0.995238i	$0.531076\pi$
$422$	−14.0000	−0.681509
$423$	0	0
$424$	−9.00000	−0.437079
$425$	0	0
$426$	0	0
$427$	−5.00000	−0.241967
$428$	−6.00000	−0.290021
$429$	0	0
$430$	0	0
$431$	−36.0000	−1.73406	−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000	−1.73406	−0.867029	+	0.498257i	$0.833974\pi$
$432$	0	0
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	−25.0000	−1.20004
$435$	0	0
$436$	2.00000	0.0957826
$437$	24.0000	1.14808
$438$	0	0
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	0	0
$441$	0	0
$442$	3.00000	0.142695
$443$	−6.00000	−0.285069	−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000	−0.285069	−0.142534	+	0.989790i	$0.545525\pi$
$444$	0	0
$445$	0	0
$446$	4.00000	0.189405
$447$	0	0
$448$	5.00000	0.236228
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	0	0
$451$	0	0
$452$	6.00000	0.282216
$453$	0	0
$454$	−9.00000	−0.422391
$455$	0	0
$456$	0	0
$457$	26.0000	1.21623	0.608114	−	0.793849i	$-0.291926\pi$
$457$	26.0000	1.21623	0.608114	+	0.793849i	$0.291926\pi$
$458$	16.0000	0.747631
$459$	0	0
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	−1.00000	−0.0464739	−0.0232370	−	0.999730i	$-0.507397\pi$
$463$	−1.00000	−0.0464739	−0.0232370	+	0.999730i	$0.507397\pi$
$464$	−9.00000	−0.417815
$465$	0	0
$466$	6.00000	0.277945
$467$	−30.0000	−1.38823	−0.694117	−	0.719862i	$-0.744205\pi$
$467$	−30.0000	−1.38823	−0.694117	+	0.719862i	$0.744205\pi$
$468$	0	0
$469$	25.0000	1.15439
$470$	0	0
$471$	0	0
$472$	−9.00000	−0.414259
$473$	6.00000	0.275880
$474$	0	0
$475$	0	0
$476$	−15.0000	−0.687524
$477$	0	0
$478$	−15.0000	−0.686084
$479$	15.0000	0.685367	0.342684	−	0.939451i	$-0.388664\pi$
$479$	15.0000	0.685367	0.342684	+	0.939451i	$0.388664\pi$
$480$	0	0
$481$	2.00000	0.0911922
$482$	−8.00000	−0.364390
$483$	0	0
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	0	0
$487$	−7.00000	−0.317200	−0.158600	−	0.987343i	$-0.550698\pi$
$487$	−7.00000	−0.317200	−0.158600	+	0.987343i	$0.550698\pi$
$488$	1.00000	0.0452679
$489$	0	0
$490$	0	0
$491$	−6.00000	−0.270776	−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000	−0.270776	−0.135388	+	0.990793i	$0.543228\pi$
$492$	0	0
$493$	27.0000	1.21602
$494$	4.00000	0.179969
$495$	0	0
$496$	5.00000	0.224507
$497$	0	0
$498$	0	0
$499$	−25.0000	−1.11915	−0.559577	−	0.828778i	$-0.689036\pi$
$499$	−25.0000	−1.11915	−0.559577	+	0.828778i	$0.689036\pi$
$500$	0	0
$501$	0	0
$502$	−24.0000	−1.07117
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	0	0
$505$	0	0
$506$	18.0000	0.800198
$507$	0	0
$508$	20.0000	0.887357
$509$	36.0000	1.59567	0.797836	−	0.602875i	$-0.205978\pi$
$509$	36.0000	1.59567	0.797836	+	0.602875i	$0.205978\pi$
$510$	0	0
$511$	70.0000	3.09662
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−15.0000	−0.661622
$515$	0	0
$516$	0	0
$517$	27.0000	1.18746
$518$	−10.0000	−0.439375
$519$	0	0
$520$	0	0
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	0	0
$523$	−40.0000	−1.74908	−0.874539	−	0.484955i	$-0.838836\pi$
$523$	−40.0000	−1.74908	−0.874539	+	0.484955i	$0.838836\pi$
$524$	6.00000	0.262111
$525$	0	0
$526$	18.0000	0.784837
$527$	−15.0000	−0.653410
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	0	0
$532$	−20.0000	−0.867110
$533$	0	0
$534$	0	0
$535$	0	0
$536$	−5.00000	−0.215967
$537$	0	0
$538$	9.00000	0.388018
$539$	54.0000	2.32594
$540$	0	0
$541$	−16.0000	−0.687894	−0.343947	−	0.938989i	$-0.611764\pi$
$541$	−16.0000	−0.687894	−0.343947	+	0.938989i	$0.611764\pi$
$542$	19.0000	0.816120
$543$	0	0
$544$	3.00000	0.128624
$545$	0	0
$546$	0	0
$547$	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
$549$	0	0
$550$	0	0
$551$	36.0000	1.53365
$552$	0	0
$553$	−80.0000	−3.40195
$554$	22.0000	0.934690
$555$	0	0
$556$	−10.0000	−0.424094
$557$	36.0000	1.52537	0.762684	−	0.646771i	$-0.223881\pi$
$557$	36.0000	1.52537	0.762684	+	0.646771i	$0.223881\pi$
$558$	0	0
$559$	2.00000	0.0845910
$560$	0	0
$561$	0	0
$562$	12.0000	0.506189
$563$	0	0		−	1.00000i	$-0.5\pi$
$563$	0	0			1.00000i	$0.5\pi$
$564$	0	0
$565$	0	0
$566$	−14.0000	−0.588464
$567$	0	0
$568$	0	0
$569$	27.0000	1.13190	0.565949	−	0.824440i	$-0.308510\pi$
$569$	27.0000	1.13190	0.565949	+	0.824440i	$0.308510\pi$
$570$	0	0
$571$	−28.0000	−1.17176	−0.585882	−	0.810397i	$-0.699252\pi$
$571$	−28.0000	−1.17176	−0.585882	+	0.810397i	$0.699252\pi$
$572$	3.00000	0.125436
$573$	0	0
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−4.00000	−0.166522	−0.0832611	−	0.996528i	$-0.526534\pi$
$577$	−4.00000	−0.166522	−0.0832611	+	0.996528i	$0.526534\pi$
$578$	8.00000	0.332756
$579$	0	0
$580$	0	0
$581$	75.0000	3.11152
$582$	0	0
$583$	27.0000	1.11823
$584$	−14.0000	−0.579324
$585$	0	0
$586$	0	0
$587$	−15.0000	−0.619116	−0.309558	−	0.950881i	$-0.600181\pi$
$587$	−15.0000	−0.619116	−0.309558	+	0.950881i	$0.600181\pi$
$588$	0	0
$589$	−20.0000	−0.824086
$590$	0	0
$591$	0	0
$592$	2.00000	0.0821995
$593$	6.00000	0.246390	0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000	0.246390	0.123195	+	0.992382i	$0.460686\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	0	0
$598$	6.00000	0.245358
$599$	−30.0000	−1.22577	−0.612883	−	0.790173i	$-0.709990\pi$
$599$	−30.0000	−1.22577	−0.612883	+	0.790173i	$0.709990\pi$
$600$	0	0
$601$	5.00000	0.203954	0.101977	−	0.994787i	$-0.467483\pi$
$601$	5.00000	0.203954	0.101977	+	0.994787i	$0.467483\pi$
$602$	−10.0000	−0.407570
$603$	0	0
$604$	−7.00000	−0.284826
$605$	0	0
$606$	0	0
$607$	−22.0000	−0.892952	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000	−0.892952	−0.446476	+	0.894795i	$0.647321\pi$
$608$	4.00000	0.162221
$609$	0	0
$610$	0	0
$611$	9.00000	0.364101
$612$	0	0
$613$	32.0000	1.29247	0.646234	−	0.763139i	$-0.276343\pi$
$613$	32.0000	1.29247	0.646234	+	0.763139i	$0.276343\pi$
$614$	−20.0000	−0.807134
$615$	0	0
$616$	−15.0000	−0.604367
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	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
$622$	−18.0000	−0.721734
$623$	30.0000	1.20192
$624$	0	0
$625$	0	0
$626$	19.0000	0.759393
$627$	0	0
$628$	17.0000	0.678374
$629$	−6.00000	−0.239236
$630$	0	0
$631$	20.0000	0.796187	0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000	0.796187	0.398094	+	0.917345i	$0.369672\pi$
$632$	16.0000	0.636446
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	18.0000	0.713186
$638$	27.0000	1.06894
$639$	0	0
$640$	0	0
$641$	−3.00000	−0.118493	−0.0592464	−	0.998243i	$-0.518870\pi$
$641$	−3.00000	−0.118493	−0.0592464	+	0.998243i	$0.518870\pi$
$642$	0	0
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	−30.0000	−1.18217
$645$	0	0
$646$	−12.0000	−0.472134
$647$	6.00000	0.235884	0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000	0.235884	0.117942	+	0.993020i	$0.462370\pi$
$648$	0	0
$649$	27.0000	1.05984
$650$	0	0
$651$	0	0
$652$	−16.0000	−0.626608
$653$	−33.0000	−1.29139	−0.645695	−	0.763596i	$-0.723432\pi$
$653$	−33.0000	−1.29139	−0.645695	+	0.763596i	$0.723432\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	0	0
$658$	−45.0000	−1.75428
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	2.00000	0.0777910	0.0388955	−	0.999243i	$-0.487616\pi$
$661$	2.00000	0.0777910	0.0388955	+	0.999243i	$0.487616\pi$
$662$	−20.0000	−0.777322
$663$	0	0
$664$	−15.0000	−0.582113
$665$	0	0
$666$	0	0
$667$	54.0000	2.09089
$668$	24.0000	0.928588
$669$	0	0
$670$	0	0
$671$	−3.00000	−0.115814
$672$	0	0
$673$	−25.0000	−0.963679	−0.481840	−	0.876259i	$-0.660031\pi$
$673$	−25.0000	−0.963679	−0.481840	+	0.876259i	$0.660031\pi$
$674$	13.0000	0.500741
$675$	0	0
$676$	1.00000	0.0384615
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	0	0
$679$	40.0000	1.53506
$680$	0	0
$681$	0	0
$682$	−15.0000	−0.574380
$683$	15.0000	0.573959	0.286980	−	0.957937i	$-0.407349\pi$
$683$	15.0000	0.573959	0.286980	+	0.957937i	$0.407349\pi$
$684$	0	0
$685$	0	0
$686$	−55.0000	−2.09991
$687$	0	0
$688$	2.00000	0.0762493
$689$	9.00000	0.342873
$690$	0	0
$691$	−1.00000	−0.0380418	−0.0190209	−	0.999819i	$-0.506055\pi$
$691$	−1.00000	−0.0380418	−0.0190209	+	0.999819i	$0.506055\pi$
$692$	3.00000	0.114043
$693$	0	0
$694$	30.0000	1.13878
$695$	0	0
$696$	0	0
$697$	0	0
$698$	−20.0000	−0.757011
$699$	0	0
$700$	0	0
$701$	33.0000	1.24639	0.623196	−	0.782065i	$-0.285834\pi$
$701$	33.0000	1.24639	0.623196	+	0.782065i	$0.285834\pi$
$702$	0	0
$703$	−8.00000	−0.301726
$704$	3.00000	0.113067
$705$	0	0
$706$	−6.00000	−0.225813
$707$	15.0000	0.564133
$708$	0	0
$709$	−40.0000	−1.50223	−0.751116	−	0.660171i	$-0.770484\pi$
$709$	−40.0000	−1.50223	−0.751116	+	0.660171i	$0.770484\pi$
$710$	0	0
$711$	0	0
$712$	−6.00000	−0.224860
$713$	−30.0000	−1.12351
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	−21.0000	−0.783713
$719$	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
$721$	−80.0000	−2.97936
$722$	3.00000	0.111648
$723$	0	0
$724$	11.0000	0.408812
$725$	0	0
$726$	0	0
$727$	20.0000	0.741759	0.370879	−	0.928681i	$-0.379056\pi$
$727$	20.0000	0.741759	0.370879	+	0.928681i	$0.379056\pi$
$728$	−5.00000	−0.185312
$729$	0	0
$730$	0	0
$731$	−6.00000	−0.221918
$732$	0	0
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	10.0000	0.369107
$735$	0	0
$736$	6.00000	0.221163
$737$	15.0000	0.552532
$738$	0	0
$739$	11.0000	0.404642	0.202321	−	0.979319i	$-0.435152\pi$
$739$	11.0000	0.404642	0.202321	+	0.979319i	$0.435152\pi$
$740$	0	0
$741$	0	0
$742$	−45.0000	−1.65200
$743$	33.0000	1.21065	0.605326	−	0.795977i	$-0.293043\pi$
$743$	33.0000	1.21065	0.605326	+	0.795977i	$0.293043\pi$
$744$	0	0
$745$	0	0
$746$	−29.0000	−1.06177
$747$	0	0
$748$	−9.00000	−0.329073
$749$	−30.0000	−1.09618
$750$	0	0
$751$	−22.0000	−0.802791	−0.401396	−	0.915905i	$-0.631475\pi$
$751$	−22.0000	−0.802791	−0.401396	+	0.915905i	$0.631475\pi$
$752$	9.00000	0.328196
$753$	0	0
$754$	9.00000	0.327761
$755$	0	0
$756$	0	0
$757$	23.0000	0.835949	0.417975	−	0.908459i	$-0.362740\pi$
$757$	23.0000	0.835949	0.417975	+	0.908459i	$0.362740\pi$
$758$	−29.0000	−1.05333
$759$	0	0
$760$	0	0
$761$	−12.0000	−0.435000	−0.217500	−	0.976060i	$-0.569790\pi$
$761$	−12.0000	−0.435000	−0.217500	+	0.976060i	$0.569790\pi$
$762$	0	0
$763$	10.0000	0.362024
$764$	−12.0000	−0.434145
$765$	0	0
$766$	36.0000	1.30073
$767$	9.00000	0.324971
$768$	0	0
$769$	−40.0000	−1.44244	−0.721218	−	0.692708i	$-0.756418\pi$
$769$	−40.0000	−1.44244	−0.721218	+	0.692708i	$0.756418\pi$
$770$	0	0
$771$	0	0
$772$	20.0000	0.719816
$773$	−12.0000	−0.431610	−0.215805	−	0.976436i	$-0.569238\pi$
$773$	−12.0000	−0.431610	−0.215805	+	0.976436i	$0.569238\pi$
$774$	0	0
$775$	0	0
$776$	−8.00000	−0.287183
$777$	0	0
$778$	18.0000	0.645331
$779$	0	0
$780$	0	0
$781$	0	0
$782$	−18.0000	−0.643679
$783$	0	0
$784$	18.0000	0.642857
$785$	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	$0.838045\pi$
$788$	24.0000	0.854965
$789$	0	0
$790$	0	0
$791$	30.0000	1.06668
$792$	0	0
$793$	−1.00000	−0.0355110
$794$	22.0000	0.780751
$795$	0	0
$796$	−16.0000	−0.567105
$797$	−3.00000	−0.106265	−0.0531327	−	0.998587i	$-0.516921\pi$
$797$	−3.00000	−0.106265	−0.0531327	+	0.998587i	$0.516921\pi$
$798$	0	0
$799$	−27.0000	−0.955191
$800$	0	0
$801$	0	0
$802$	12.0000	0.423735
$803$	42.0000	1.48215
$804$	0	0
$805$	0	0
$806$	−5.00000	−0.176117
$807$	0	0
$808$	−3.00000	−0.105540
$809$	42.0000	1.47664	0.738321	−	0.674450i	$-0.235619\pi$
$809$	42.0000	1.47664	0.738321	+	0.674450i	$0.235619\pi$
$810$	0	0
$811$	−13.0000	−0.456492	−0.228246	−	0.973604i	$-0.573299\pi$
$811$	−13.0000	−0.456492	−0.228246	+	0.973604i	$0.573299\pi$
$812$	−45.0000	−1.57919
$813$	0	0
$814$	−6.00000	−0.210300
$815$	0	0
$816$	0	0
$817$	−8.00000	−0.279885
$818$	22.0000	0.769212
$819$	0	0
$820$	0	0
$821$	−36.0000	−1.25641	−0.628204	−	0.778048i	$-0.716210\pi$
$821$	−36.0000	−1.25641	−0.628204	+	0.778048i	$0.716210\pi$
$822$	0	0
$823$	−4.00000	−0.139431	−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000	−0.139431	−0.0697156	+	0.997567i	$0.522209\pi$
$824$	16.0000	0.557386
$825$	0	0
$826$	−45.0000	−1.56575
$827$	−9.00000	−0.312961	−0.156480	−	0.987681i	$-0.550015\pi$
$827$	−9.00000	−0.312961	−0.156480	+	0.987681i	$0.550015\pi$
$828$	0	0
$829$	5.00000	0.173657	0.0868286	−	0.996223i	$-0.472327\pi$
$829$	5.00000	0.173657	0.0868286	+	0.996223i	$0.472327\pi$
$830$	0	0
$831$	0	0
$832$	1.00000	0.0346688
$833$	−54.0000	−1.87099
$834$	0	0
$835$	0	0
$836$	−12.0000	−0.415029
$837$	0	0
$838$	6.00000	0.207267
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	52.0000	1.79310
$842$	4.00000	0.137849
$843$	0	0
$844$	14.0000	0.481900
$845$	0	0
$846$	0	0
$847$	−10.0000	−0.343604
$848$	9.00000	0.309061
$849$	0	0
$850$	0	0
$851$	−12.0000	−0.411355
$852$	0	0
$853$	−10.0000	−0.342393	−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000	−0.342393	−0.171197	+	0.985237i	$0.554763\pi$
$854$	5.00000	0.171096
$855$	0	0
$856$	6.00000	0.205076
$857$	54.0000	1.84460	0.922302	−	0.386469i	$-0.126305\pi$
$857$	54.0000	1.84460	0.922302	+	0.386469i	$0.126305\pi$
$858$	0	0
$859$	2.00000	0.0682391	0.0341196	−	0.999418i	$-0.489137\pi$
$859$	2.00000	0.0682391	0.0341196	+	0.999418i	$0.489137\pi$
$860$	0	0
$861$	0	0
$862$	36.0000	1.22616
$863$	45.0000	1.53182	0.765909	−	0.642949i	$-0.222289\pi$
$863$	45.0000	1.53182	0.765909	+	0.642949i	$0.222289\pi$
$864$	0	0
$865$	0	0
$866$	−2.00000	−0.0679628
$867$	0	0
$868$	25.0000	0.848555
$869$	−48.0000	−1.62829
$870$	0	0
$871$	5.00000	0.169419
$872$	−2.00000	−0.0677285
$873$	0	0
$874$	−24.0000	−0.811812
$875$	0	0
$876$	0	0
$877$	−10.0000	−0.337676	−0.168838	−	0.985644i	$-0.554001\pi$
$877$	−10.0000	−0.337676	−0.168838	+	0.985644i	$0.554001\pi$
$878$	−20.0000	−0.674967
$879$	0	0
$880$	0	0
$881$	−9.00000	−0.303218	−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000	−0.303218	−0.151609	+	0.988441i	$0.548445\pi$
$882$	0	0
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	−3.00000	−0.100901
$885$	0	0
$886$	6.00000	0.201574
$887$	−24.0000	−0.805841	−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000	−0.805841	−0.402921	+	0.915235i	$0.632005\pi$
$888$	0	0
$889$	100.000	3.35389
$890$	0	0
$891$	0	0
$892$	−4.00000	−0.133930
$893$	−36.0000	−1.20469
$894$	0	0
$895$	0	0
$896$	−5.00000	−0.167038
$897$	0	0
$898$	6.00000	0.200223
$899$	−45.0000	−1.50083
$900$	0	0
$901$	−27.0000	−0.899500
$902$	0	0
$903$	0	0
$904$	−6.00000	−0.199557
$905$	0	0
$906$	0	0
$907$	44.0000	1.46100	0.730498	−	0.682915i	$-0.239288\pi$
$907$	44.0000	1.46100	0.730498	+	0.682915i	$0.239288\pi$
$908$	9.00000	0.298675
$909$	0	0
$910$	0	0
$911$	−24.0000	−0.795155	−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000	−0.795155	−0.397578	+	0.917568i	$0.630149\pi$
$912$	0	0
$913$	45.0000	1.48928
$914$	−26.0000	−0.860004
$915$	0	0
$916$	−16.0000	−0.528655
$917$	30.0000	0.990687
$918$	0	0
$919$	8.00000	0.263896	0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000	0.263896	0.131948	+	0.991257i	$0.457877\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	0	0
$926$	1.00000	0.0328620
$927$	0	0
$928$	9.00000	0.295439
$929$	−42.0000	−1.37798	−0.688988	−	0.724773i	$-0.741945\pi$
$929$	−42.0000	−1.37798	−0.688988	+	0.724773i	$0.741945\pi$
$930$	0	0
$931$	−72.0000	−2.35970
$932$	−6.00000	−0.196537
$933$	0	0
$934$	30.0000	0.981630
$935$	0	0
$936$	0	0
$937$	−13.0000	−0.424691	−0.212346	−	0.977195i	$-0.568110\pi$
$937$	−13.0000	−0.424691	−0.212346	+	0.977195i	$0.568110\pi$
$938$	−25.0000	−0.816279
$939$	0	0
$940$	0	0
$941$	42.0000	1.36916	0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000	1.36916	0.684580	+	0.728937i	$0.259985\pi$
$942$	0	0
$943$	0	0
$944$	9.00000	0.292925
$945$	0	0
$946$	−6.00000	−0.195077
$947$	3.00000	0.0974869	0.0487435	−	0.998811i	$-0.484478\pi$
$947$	3.00000	0.0974869	0.0487435	+	0.998811i	$0.484478\pi$
$948$	0	0
$949$	14.0000	0.454459
$950$	0	0
$951$	0	0
$952$	15.0000	0.486153
$953$	27.0000	0.874616	0.437308	−	0.899312i	$-0.355932\pi$
$953$	27.0000	0.874616	0.437308	+	0.899312i	$0.355932\pi$
$954$	0	0
$955$	0	0
$956$	15.0000	0.485135
$957$	0	0
$958$	−15.0000	−0.484628
$959$	−30.0000	−0.968751
$960$	0	0
$961$	−6.00000	−0.193548
$962$	−2.00000	−0.0644826
$963$	0	0
$964$	8.00000	0.257663
$965$	0	0
$966$	0	0
$967$	−31.0000	−0.996893	−0.498446	−	0.866921i	$-0.666096\pi$
$967$	−31.0000	−0.996893	−0.498446	+	0.866921i	$0.666096\pi$
$968$	2.00000	0.0642824
$969$	0	0
$970$	0	0
$971$	18.0000	0.577647	0.288824	−	0.957382i	$-0.406736\pi$
$971$	18.0000	0.577647	0.288824	+	0.957382i	$0.406736\pi$
$972$	0	0
$973$	−50.0000	−1.60293
$974$	7.00000	0.224294
$975$	0	0
$976$	−1.00000	−0.0320092
$977$	−6.00000	−0.191957	−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000	−0.191957	−0.0959785	+	0.995383i	$0.530598\pi$
$978$	0	0
$979$	18.0000	0.575282
$980$	0	0
$981$	0	0
$982$	6.00000	0.191468
$983$	−21.0000	−0.669796	−0.334898	−	0.942254i	$-0.608702\pi$
$983$	−21.0000	−0.669796	−0.334898	+	0.942254i	$0.608702\pi$
$984$	0	0
$985$	0	0
$986$	−27.0000	−0.859855
$987$	0	0
$988$	−4.00000	−0.127257
$989$	−12.0000	−0.381578
$990$	0	0
$991$	14.0000	0.444725	0.222362	−	0.974964i	$-0.428623\pi$
$991$	14.0000	0.444725	0.222362	+	0.974964i	$0.428623\pi$
$992$	−5.00000	−0.158750
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	−1.00000	−0.0316703	−0.0158352	−	0.999875i	$-0.505041\pi$
$997$	−1.00000	−0.0316703	−0.0158352	+	0.999875i	$0.505041\pi$
$998$	25.0000	0.791361
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5850.2.a.bb.1.1		1
3.2	odd	2		650.2.a.h.1.1	yes	1
5.2	odd	4		5850.2.e.ba.5149.1		2
5.3	odd	4		5850.2.e.ba.5149.2		2
5.4	even	2		5850.2.a.bc.1.1		1
12.11	even	2		5200.2.a.bc.1.1		1
15.2	even	4		650.2.b.b.599.2		2
15.8	even	4		650.2.b.b.599.1		2
15.14	odd	2		650.2.a.f.1.1	✓	1
39.38	odd	2		8450.2.a.a.1.1		1
60.59	even	2		5200.2.a.i.1.1		1
195.194	odd	2		8450.2.a.x.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.a.f.1.1	✓	1	15.14	odd	2
650.2.a.h.1.1	yes	1	3.2	odd	2
650.2.b.b.599.1		2	15.8	even	4
650.2.b.b.599.2		2	15.2	even	4
5200.2.a.i.1.1		1	60.59	even	2
5200.2.a.bc.1.1		1	12.11	even	2
5850.2.a.bb.1.1		1	1.1	even	1	trivial
5850.2.a.bc.1.1		1	5.4	even	2
5850.2.e.ba.5149.1		2	5.2	odd	4
5850.2.e.ba.5149.2		2	5.3	odd	4
8450.2.a.a.1.1		1	39.38	odd	2
8450.2.a.x.1.1		1	195.194	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:	\( N \)	\(=\)	\( 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5850.a (trivial)

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