LMFDB - Embedded newform 3700.2.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3700,2,Mod(1,3700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3700, 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("3700.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3700 = 2^{2} \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3700.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:	$29.5446487479$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 148)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	3700.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.56155 q^{3} -2.56155 q^{7} +3.56155 q^{9} +2.56155 q^{11} -2.00000 q^{13} -7.12311 q^{17} -7.12311 q^{19} -6.56155 q^{21} +2.00000 q^{23} +1.43845 q^{27} -8.24621 q^{29} -0.876894 q^{31} +6.56155 q^{33} +1.00000 q^{37} -5.12311 q^{39} +4.56155 q^{41} -8.24621 q^{43} -10.5616 q^{47} -0.438447 q^{49} -18.2462 q^{51} +6.80776 q^{53} -18.2462 q^{57} +3.12311 q^{59} -11.1231 q^{61} -9.12311 q^{63} +14.2462 q^{67} +5.12311 q^{69} +5.43845 q^{71} +15.9309 q^{73} -6.56155 q^{77} -9.36932 q^{79} -7.00000 q^{81} -1.43845 q^{83} -21.1231 q^{87} +4.87689 q^{89} +5.12311 q^{91} -2.24621 q^{93} +0.876894 q^{97} +9.12311 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} - q^{7} + 3 q^{9} + q^{11} - 4 q^{13} - 6 q^{17} - 6 q^{19} - 9 q^{21} + 4 q^{23} + 7 q^{27} - 10 q^{31} + 9 q^{33} + 2 q^{37} - 2 q^{39} + 5 q^{41} - 17 q^{47} - 5 q^{49} - 20 q^{51} - 7 q^{53}+ \cdots + 10 q^{99}+O(q^{100}) $ 2 * q + q^3 - q^7 + 3 * q^9 + q^11 - 4 * q^13 - 6 * q^17 - 6 * q^19 - 9 * q^21 + 4 * q^23 + 7 * q^27 - 10 * q^31 + 9 * q^33 + 2 * q^37 - 2 * q^39 + 5 * q^41 - 17 * q^47 - 5 * q^49 - 20 * q^51 - 7 * q^53 - 20 * q^57 - 2 * q^59 - 14 * q^61 - 10 * q^63 + 12 * q^67 + 2 * q^69 + 15 * q^71 + 3 * q^73 - 9 * q^77 + 6 * q^79 - 14 * q^81 - 7 * q^83 - 34 * q^87 + 18 * q^89 + 2 * q^91 + 12 * q^93 + 10 * q^97 + 10 * q^99

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 $

$2$	0	0
$2$	0	0
$3$	2.56155	1.47891	0.739457	−	0.673204i	$-0.235083\pi$
$3$	2.56155	1.47891	0.739457	+	0.673204i	$0.235083\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−2.56155	−0.968176	−0.484088	−	0.875019i	$-0.660849\pi$
$7$	−2.56155	−0.968176	−0.484088	+	0.875019i	$0.660849\pi$
$8$	0	0
$9$	3.56155	1.18718
$10$	0	0
$11$	2.56155	0.772337	0.386169	−	0.922428i	$-0.373798\pi$
$11$	2.56155	0.772337	0.386169	+	0.922428i	$0.373798\pi$
$12$	0	0
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	−7.12311	−1.72761	−0.863803	−	0.503829i	$-0.831924\pi$
$17$	−7.12311	−1.72761	−0.863803	+	0.503829i	$0.831924\pi$
$18$	0	0
$19$	−7.12311	−1.63415	−0.817076	−	0.576530i	$-0.804407\pi$
$19$	−7.12311	−1.63415	−0.817076	+	0.576530i	$0.804407\pi$
$20$	0	0
$21$	−6.56155	−1.43185
$22$	0	0
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	1.43845	0.276829
$28$	0	0
$29$	−8.24621	−1.53128	−0.765641	−	0.643268i	$-0.777578\pi$
$29$	−8.24621	−1.53128	−0.765641	+	0.643268i	$0.777578\pi$
$30$	0	0
$31$	−0.876894	−0.157495	−0.0787474	−	0.996895i	$-0.525092\pi$
$31$	−0.876894	−0.157495	−0.0787474	+	0.996895i	$0.525092\pi$
$32$	0	0
$33$	6.56155	1.14222
$34$	0	0
$35$	0	0
$36$	0	0
$37$	1.00000	0.164399
$37$	1.00000	0.164399
$38$	0	0
$39$	−5.12311	−0.820353
$40$	0	0
$41$	4.56155	0.712395	0.356197	−	0.934411i	$-0.384073\pi$
$41$	4.56155	0.712395	0.356197	+	0.934411i	$0.384073\pi$
$42$	0	0
$43$	−8.24621	−1.25754	−0.628768	−	0.777593i	$-0.716440\pi$
$43$	−8.24621	−1.25754	−0.628768	+	0.777593i	$0.716440\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−10.5616	−1.54056	−0.770280	−	0.637705i	$-0.779884\pi$
$47$	−10.5616	−1.54056	−0.770280	+	0.637705i	$0.779884\pi$
$48$	0	0
$49$	−0.438447	−0.0626353
$50$	0	0
$51$	−18.2462	−2.55498
$52$	0	0
$53$	6.80776	0.935118	0.467559	−	0.883962i	$-0.345133\pi$
$53$	6.80776	0.935118	0.467559	+	0.883962i	$0.345133\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	−18.2462	−2.41677
$58$	0	0
$59$	3.12311	0.406594	0.203297	−	0.979117i	$-0.434834\pi$
$59$	3.12311	0.406594	0.203297	+	0.979117i	$0.434834\pi$
$60$	0	0
$61$	−11.1231	−1.42417	−0.712084	−	0.702094i	$-0.752248\pi$
$61$	−11.1231	−1.42417	−0.712084	+	0.702094i	$0.752248\pi$
$62$	0	0
$63$	−9.12311	−1.14940
$64$	0	0
$65$	0	0
$66$	0	0
$67$	14.2462	1.74045	0.870226	−	0.492653i	$-0.163973\pi$
$67$	14.2462	1.74045	0.870226	+	0.492653i	$0.163973\pi$
$68$	0	0
$69$	5.12311	0.616749
$70$	0	0
$71$	5.43845	0.645425	0.322712	−	0.946497i	$-0.395405\pi$
$71$	5.43845	0.645425	0.322712	+	0.946497i	$0.395405\pi$
$72$	0	0
$73$	15.9309	1.86457	0.932284	−	0.361728i	$-0.117813\pi$
$73$	15.9309	1.86457	0.932284	+	0.361728i	$0.117813\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	−6.56155	−0.747758
$78$	0	0
$79$	−9.36932	−1.05413	−0.527065	−	0.849825i	$-0.676708\pi$
$79$	−9.36932	−1.05413	−0.527065	+	0.849825i	$0.676708\pi$
$80$	0	0
$81$	−7.00000	−0.777778
$82$	0	0
$83$	−1.43845	−0.157890	−0.0789450	−	0.996879i	$-0.525155\pi$
$83$	−1.43845	−0.157890	−0.0789450	+	0.996879i	$0.525155\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−21.1231	−2.26463
$88$	0	0
$89$	4.87689	0.516950	0.258475	−	0.966018i	$-0.416780\pi$
$89$	4.87689	0.516950	0.258475	+	0.966018i	$0.416780\pi$
$90$	0	0
$91$	5.12311	0.537047
$92$	0	0
$93$	−2.24621	−0.232921
$94$	0	0
$95$	0	0
$96$	0	0
$97$	0.876894	0.0890351	0.0445176	−	0.999009i	$-0.485825\pi$
$97$	0.876894	0.0890351	0.0445176	+	0.999009i	$0.485825\pi$
$98$	0	0
$99$	9.12311	0.916907
$100$	0	0
$101$	10.8078	1.07541	0.537706	−	0.843132i	$-0.319291\pi$
$101$	10.8078	1.07541	0.537706	+	0.843132i	$0.319291\pi$
$102$	0	0
$103$	−2.00000	−0.197066	−0.0985329	−	0.995134i	$-0.531415\pi$
$103$	−2.00000	−0.197066	−0.0985329	+	0.995134i	$0.531415\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	18.2462	1.76393	0.881964	−	0.471317i	$-0.156221\pi$
$107$	18.2462	1.76393	0.881964	+	0.471317i	$0.156221\pi$
$108$	0	0
$109$	7.12311	0.682270	0.341135	−	0.940014i	$-0.389189\pi$
$109$	7.12311	0.682270	0.341135	+	0.940014i	$0.389189\pi$
$110$	0	0
$111$	2.56155	0.243132
$112$	0	0
$113$	−4.24621	−0.399450	−0.199725	−	0.979852i	$-0.564005\pi$
$113$	−4.24621	−0.399450	−0.199725	+	0.979852i	$0.564005\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−7.12311	−0.658531
$118$	0	0
$119$	18.2462	1.67263
$120$	0	0
$121$	−4.43845	−0.403495
$122$	0	0
$123$	11.6847	1.05357
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−13.4384	−1.19247	−0.596235	−	0.802810i	$-0.703337\pi$
$127$	−13.4384	−1.19247	−0.596235	+	0.802810i	$0.703337\pi$
$128$	0	0
$129$	−21.1231	−1.85979
$130$	0	0
$131$	−11.1231	−0.971830	−0.485915	−	0.874006i	$-0.661514\pi$
$131$	−11.1231	−0.971830	−0.485915	+	0.874006i	$0.661514\pi$
$132$	0	0
$133$	18.2462	1.58215
$134$	0	0
$135$	0	0
$136$	0	0
$137$	4.24621	0.362778	0.181389	−	0.983411i	$-0.441941\pi$
$137$	4.24621	0.362778	0.181389	+	0.983411i	$0.441941\pi$
$138$	0	0
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	0	0
$141$	−27.0540	−2.27836
$142$	0	0
$143$	−5.12311	−0.428416
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−1.12311	−0.0926322
$148$	0	0
$149$	−3.43845	−0.281689	−0.140844	−	0.990032i	$-0.544982\pi$
$149$	−3.43845	−0.281689	−0.140844	+	0.990032i	$0.544982\pi$
$150$	0	0
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	0	0
$153$	−25.3693	−2.05099
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−14.8078	−1.18179	−0.590894	−	0.806749i	$-0.701225\pi$
$157$	−14.8078	−1.18179	−0.590894	+	0.806749i	$0.701225\pi$
$158$	0	0
$159$	17.4384	1.38296
$160$	0	0
$161$	−5.12311	−0.403757
$162$	0	0
$163$	−12.2462	−0.959197	−0.479599	−	0.877488i	$-0.659218\pi$
$163$	−12.2462	−0.959197	−0.479599	+	0.877488i	$0.659218\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	9.36932	0.725020	0.362510	−	0.931980i	$-0.381920\pi$
$167$	9.36932	0.725020	0.362510	+	0.931980i	$0.381920\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−25.3693	−1.94004
$172$	0	0
$173$	−15.4384	−1.17376	−0.586882	−	0.809673i	$-0.699645\pi$
$173$	−15.4384	−1.17376	−0.586882	+	0.809673i	$0.699645\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	8.00000	0.601317
$178$	0	0
$179$	−3.75379	−0.280571	−0.140286	−	0.990111i	$-0.544802\pi$
$179$	−3.75379	−0.280571	−0.140286	+	0.990111i	$0.544802\pi$
$180$	0	0
$181$	7.93087	0.589497	0.294748	−	0.955575i	$-0.404764\pi$
$181$	7.93087	0.589497	0.294748	+	0.955575i	$0.404764\pi$
$182$	0	0
$183$	−28.4924	−2.10622
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−18.2462	−1.33430
$188$	0	0
$189$	−3.68466	−0.268019
$190$	0	0
$191$	−7.12311	−0.515410	−0.257705	−	0.966224i	$-0.582966\pi$
$191$	−7.12311	−0.515410	−0.257705	+	0.966224i	$0.582966\pi$
$192$	0	0
$193$	−10.0000	−0.719816	−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000	−0.719816	−0.359908	+	0.932988i	$0.617192\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−12.5616	−0.894974	−0.447487	−	0.894291i	$-0.647681\pi$
$197$	−12.5616	−0.894974	−0.447487	+	0.894291i	$0.647681\pi$
$198$	0	0
$199$	20.2462	1.43522	0.717608	−	0.696447i	$-0.245237\pi$
$199$	20.2462	1.43522	0.717608	+	0.696447i	$0.245237\pi$
$200$	0	0
$201$	36.4924	2.57398
$202$	0	0
$203$	21.1231	1.48255
$204$	0	0
$205$	0	0
$206$	0	0
$207$	7.12311	0.495090
$208$	0	0
$209$	−18.2462	−1.26212
$210$	0	0
$211$	12.3153	0.847823	0.423912	−	0.905704i	$-0.360657\pi$
$211$	12.3153	0.847823	0.423912	+	0.905704i	$0.360657\pi$
$212$	0	0
$213$	13.9309	0.954527
$214$	0	0
$215$	0	0
$216$	0	0
$217$	2.24621	0.152483
$218$	0	0
$219$	40.8078	2.75753
$220$	0	0
$221$	14.2462	0.958304
$222$	0	0
$223$	5.43845	0.364185	0.182093	−	0.983281i	$-0.441713\pi$
$223$	5.43845	0.364185	0.182093	+	0.983281i	$0.441713\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	17.3693	1.15284	0.576421	−	0.817153i	$-0.304449\pi$
$227$	17.3693	1.15284	0.576421	+	0.817153i	$0.304449\pi$
$228$	0	0
$229$	−13.6847	−0.904308	−0.452154	−	0.891940i	$-0.649344\pi$
$229$	−13.6847	−0.904308	−0.452154	+	0.891940i	$0.649344\pi$
$230$	0	0
$231$	−16.8078	−1.10587
$232$	0	0
$233$	−14.0000	−0.917170	−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000	−0.917170	−0.458585	+	0.888650i	$0.651644\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−24.0000	−1.55897
$238$	0	0
$239$	−10.0000	−0.646846	−0.323423	−	0.946254i	$-0.604834\pi$
$239$	−10.0000	−0.646846	−0.323423	+	0.946254i	$0.604834\pi$
$240$	0	0
$241$	−3.75379	−0.241803	−0.120901	−	0.992665i	$-0.538578\pi$
$241$	−3.75379	−0.241803	−0.120901	+	0.992665i	$0.538578\pi$
$242$	0	0
$243$	−22.2462	−1.42710
$244$	0	0
$245$	0	0
$246$	0	0
$247$	14.2462	0.906465
$248$	0	0
$249$	−3.68466	−0.233506
$250$	0	0
$251$	−3.75379	−0.236937	−0.118469	−	0.992958i	$-0.537798\pi$
$251$	−3.75379	−0.236937	−0.118469	+	0.992958i	$0.537798\pi$
$252$	0	0
$253$	5.12311	0.322087
$254$	0	0
$255$	0	0
$256$	0	0
$257$	15.6155	0.974070	0.487035	−	0.873382i	$-0.338078\pi$
$257$	15.6155	0.974070	0.487035	+	0.873382i	$0.338078\pi$
$258$	0	0
$259$	−2.56155	−0.159167
$260$	0	0
$261$	−29.3693	−1.81792
$262$	0	0
$263$	1.43845	0.0886985	0.0443492	−	0.999016i	$-0.485879\pi$
$263$	1.43845	0.0886985	0.0443492	+	0.999016i	$0.485879\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	12.4924	0.764524
$268$	0	0
$269$	28.7386	1.75223	0.876113	−	0.482106i	$-0.160128\pi$
$269$	28.7386	1.75223	0.876113	+	0.482106i	$0.160128\pi$
$270$	0	0
$271$	−2.56155	−0.155603	−0.0778016	−	0.996969i	$-0.524790\pi$
$271$	−2.56155	−0.155603	−0.0778016	+	0.996969i	$0.524790\pi$
$272$	0	0
$273$	13.1231	0.794246
$274$	0	0
$275$	0	0
$276$	0	0
$277$	16.8769	1.01403	0.507017	−	0.861936i	$-0.330748\pi$
$277$	16.8769	1.01403	0.507017	+	0.861936i	$0.330748\pi$
$278$	0	0
$279$	−3.12311	−0.186975
$280$	0	0
$281$	11.6155	0.692924	0.346462	−	0.938064i	$-0.387383\pi$
$281$	11.6155	0.692924	0.346462	+	0.938064i	$0.387383\pi$
$282$	0	0
$283$	−11.6155	−0.690471	−0.345236	−	0.938516i	$-0.612201\pi$
$283$	−11.6155	−0.690471	−0.345236	+	0.938516i	$0.612201\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−11.6847	−0.689724
$288$	0	0
$289$	33.7386	1.98463
$290$	0	0
$291$	2.24621	0.131675
$292$	0	0
$293$	−20.2462	−1.18280	−0.591398	−	0.806380i	$-0.701424\pi$
$293$	−20.2462	−1.18280	−0.591398	+	0.806380i	$0.701424\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	3.68466	0.213806
$298$	0	0
$299$	−4.00000	−0.231326
$300$	0	0
$301$	21.1231	1.21752
$302$	0	0
$303$	27.6847	1.59044
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−8.31534	−0.474582	−0.237291	−	0.971439i	$-0.576259\pi$
$307$	−8.31534	−0.474582	−0.237291	+	0.971439i	$0.576259\pi$
$308$	0	0
$309$	−5.12311	−0.291443
$310$	0	0
$311$	−0.876894	−0.0497241	−0.0248621	−	0.999691i	$-0.507915\pi$
$311$	−0.876894	−0.0497241	−0.0248621	+	0.999691i	$0.507915\pi$
$312$	0	0
$313$	26.4924	1.49744	0.748720	−	0.662886i	$-0.230669\pi$
$313$	26.4924	1.49744	0.748720	+	0.662886i	$0.230669\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−10.4924	−0.589313	−0.294657	−	0.955603i	$-0.595205\pi$
$317$	−10.4924	−0.589313	−0.294657	+	0.955603i	$0.595205\pi$
$318$	0	0
$319$	−21.1231	−1.18267
$320$	0	0
$321$	46.7386	2.60870
$322$	0	0
$323$	50.7386	2.82317
$324$	0	0
$325$	0	0
$326$	0	0
$327$	18.2462	1.00902
$328$	0	0
$329$	27.0540	1.49153
$330$	0	0
$331$	−32.7386	−1.79948	−0.899739	−	0.436428i	$-0.856243\pi$
$331$	−32.7386	−1.79948	−0.899739	+	0.436428i	$0.856243\pi$
$332$	0	0
$333$	3.56155	0.195172
$334$	0	0
$335$	0	0
$336$	0	0
$337$	3.43845	0.187304	0.0936521	−	0.995605i	$-0.470146\pi$
$337$	3.43845	0.187304	0.0936521	+	0.995605i	$0.470146\pi$
$338$	0	0
$339$	−10.8769	−0.590752
$340$	0	0
$341$	−2.24621	−0.121639
$342$	0	0
$343$	19.0540	1.02882
$344$	0	0
$345$	0	0
$346$	0	0
$347$	1.50758	0.0809310	0.0404655	−	0.999181i	$-0.487116\pi$
$347$	1.50758	0.0809310	0.0404655	+	0.999181i	$0.487116\pi$
$348$	0	0
$349$	7.75379	0.415051	0.207525	−	0.978230i	$-0.433459\pi$
$349$	7.75379	0.415051	0.207525	+	0.978230i	$0.433459\pi$
$350$	0	0
$351$	−2.87689	−0.153557
$352$	0	0
$353$	13.3693	0.711577	0.355788	−	0.934567i	$-0.384212\pi$
$353$	13.3693	0.711577	0.355788	+	0.934567i	$0.384212\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	46.7386	2.47367
$358$	0	0
$359$	−18.5616	−0.979641	−0.489821	−	0.871823i	$-0.662938\pi$
$359$	−18.5616	−0.979641	−0.489821	+	0.871823i	$0.662938\pi$
$360$	0	0
$361$	31.7386	1.67045
$362$	0	0
$363$	−11.3693	−0.596734
$364$	0	0
$365$	0	0
$366$	0	0
$367$	−26.7386	−1.39575	−0.697873	−	0.716222i	$-0.745870\pi$
$367$	−26.7386	−1.39575	−0.697873	+	0.716222i	$0.745870\pi$
$368$	0	0
$369$	16.2462	0.845744
$370$	0	0
$371$	−17.4384	−0.905359
$372$	0	0
$373$	−1.68466	−0.0872283	−0.0436142	−	0.999048i	$-0.513887\pi$
$373$	−1.68466	−0.0872283	−0.0436142	+	0.999048i	$0.513887\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	16.4924	0.849403
$378$	0	0
$379$	2.06913	0.106284	0.0531420	−	0.998587i	$-0.483076\pi$
$379$	2.06913	0.106284	0.0531420	+	0.998587i	$0.483076\pi$
$380$	0	0
$381$	−34.4233	−1.76356
$382$	0	0
$383$	−16.8769	−0.862369	−0.431185	−	0.902264i	$-0.641904\pi$
$383$	−16.8769	−0.862369	−0.431185	+	0.902264i	$0.641904\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−29.3693	−1.49293
$388$	0	0
$389$	−29.3693	−1.48908	−0.744542	−	0.667576i	$-0.767332\pi$
$389$	−29.3693	−1.48908	−0.744542	+	0.667576i	$0.767332\pi$
$390$	0	0
$391$	−14.2462	−0.720462
$392$	0	0
$393$	−28.4924	−1.43725
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−34.8078	−1.74695	−0.873476	−	0.486868i	$-0.838139\pi$
$397$	−34.8078	−1.74695	−0.873476	+	0.486868i	$0.838139\pi$
$398$	0	0
$399$	46.7386	2.33986
$400$	0	0
$401$	−24.2462	−1.21080	−0.605399	−	0.795922i	$-0.706986\pi$
$401$	−24.2462	−1.21080	−0.605399	+	0.795922i	$0.706986\pi$
$402$	0	0
$403$	1.75379	0.0873624
$404$	0	0
$405$	0	0
$406$	0	0
$407$	2.56155	0.126971
$408$	0	0
$409$	7.12311	0.352215	0.176107	−	0.984371i	$-0.443649\pi$
$409$	7.12311	0.352215	0.176107	+	0.984371i	$0.443649\pi$
$410$	0	0
$411$	10.8769	0.536518
$412$	0	0
$413$	−8.00000	−0.393654
$414$	0	0
$415$	0	0
$416$	0	0
$417$	30.7386	1.50528
$418$	0	0
$419$	27.0540	1.32167	0.660837	−	0.750530i	$-0.270202\pi$
$419$	27.0540	1.32167	0.660837	+	0.750530i	$0.270202\pi$
$420$	0	0
$421$	7.12311	0.347159	0.173579	−	0.984820i	$-0.444467\pi$
$421$	7.12311	0.347159	0.173579	+	0.984820i	$0.444467\pi$
$422$	0	0
$423$	−37.6155	−1.82893
$424$	0	0
$425$	0	0
$426$	0	0
$427$	28.4924	1.37884
$428$	0	0
$429$	−13.1231	−0.633590
$430$	0	0
$431$	30.4924	1.46877	0.734384	−	0.678734i	$-0.237471\pi$
$431$	30.4924	1.46877	0.734384	+	0.678734i	$0.237471\pi$
$432$	0	0
$433$	2.80776	0.134933	0.0674663	−	0.997722i	$-0.478508\pi$
$433$	2.80776	0.134933	0.0674663	+	0.997722i	$0.478508\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	−14.2462	−0.681489
$438$	0	0
$439$	7.12311	0.339967	0.169984	−	0.985447i	$-0.445629\pi$
$439$	7.12311	0.339967	0.169984	+	0.985447i	$0.445629\pi$
$440$	0	0
$441$	−1.56155	−0.0743597
$442$	0	0
$443$	−7.68466	−0.365109	−0.182555	−	0.983196i	$-0.558437\pi$
$443$	−7.68466	−0.365109	−0.182555	+	0.983196i	$0.558437\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−8.80776	−0.416593
$448$	0	0
$449$	37.8617	1.78681	0.893403	−	0.449256i	$-0.148311\pi$
$449$	37.8617	1.78681	0.893403	+	0.449256i	$0.148311\pi$
$450$	0	0
$451$	11.6847	0.550209
$452$	0	0
$453$	−40.9848	−1.92564
$454$	0	0
$455$	0	0
$456$	0	0
$457$	8.24621	0.385741	0.192871	−	0.981224i	$-0.438220\pi$
$457$	8.24621	0.385741	0.192871	+	0.981224i	$0.438220\pi$
$458$	0	0
$459$	−10.2462	−0.478252
$460$	0	0
$461$	−10.4924	−0.488681	−0.244340	−	0.969690i	$-0.578571\pi$
$461$	−10.4924	−0.488681	−0.244340	+	0.969690i	$0.578571\pi$
$462$	0	0
$463$	2.00000	0.0929479	0.0464739	−	0.998920i	$-0.485202\pi$
$463$	2.00000	0.0929479	0.0464739	+	0.998920i	$0.485202\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	−0.246211	−0.0113933	−0.00569665	−	0.999984i	$-0.501813\pi$
$467$	−0.246211	−0.0113933	−0.00569665	+	0.999984i	$0.501813\pi$
$468$	0	0
$469$	−36.4924	−1.68506
$470$	0	0
$471$	−37.9309	−1.74776
$472$	0	0
$473$	−21.1231	−0.971241
$474$	0	0
$475$	0	0
$476$	0	0
$477$	24.2462	1.11016
$478$	0	0
$479$	−8.73863	−0.399278	−0.199639	−	0.979869i	$-0.563977\pi$
$479$	−8.73863	−0.399278	−0.199639	+	0.979869i	$0.563977\pi$
$480$	0	0
$481$	−2.00000	−0.0911922
$482$	0	0
$483$	−13.1231	−0.597122
$484$	0	0
$485$	0	0
$486$	0	0
$487$	7.12311	0.322779	0.161389	−	0.986891i	$-0.448403\pi$
$487$	7.12311	0.322779	0.161389	+	0.986891i	$0.448403\pi$
$488$	0	0
$489$	−31.3693	−1.41857
$490$	0	0
$491$	13.7538	0.620700	0.310350	−	0.950622i	$-0.399554\pi$
$491$	13.7538	0.620700	0.310350	+	0.950622i	$0.399554\pi$
$492$	0	0
$493$	58.7386	2.64546
$494$	0	0
$495$	0	0
$496$	0	0
$497$	−13.9309	−0.624885
$498$	0	0
$499$	10.6307	0.475895	0.237947	−	0.971278i	$-0.423525\pi$
$499$	10.6307	0.475895	0.237947	+	0.971278i	$0.423525\pi$
$500$	0	0
$501$	24.0000	1.07224
$502$	0	0
$503$	35.6155	1.58802	0.794009	−	0.607906i	$-0.207990\pi$
$503$	35.6155	1.58802	0.794009	+	0.607906i	$0.207990\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−23.0540	−1.02386
$508$	0	0
$509$	−37.0540	−1.64239	−0.821194	−	0.570649i	$-0.806692\pi$
$509$	−37.0540	−1.64239	−0.821194	+	0.570649i	$0.806692\pi$
$510$	0	0
$511$	−40.8078	−1.80523
$512$	0	0
$513$	−10.2462	−0.452381
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−27.0540	−1.18983
$518$	0	0
$519$	−39.5464	−1.73589
$520$	0	0
$521$	−20.4233	−0.894761	−0.447380	−	0.894344i	$-0.647643\pi$
$521$	−20.4233	−0.894761	−0.447380	+	0.894344i	$0.647643\pi$
$522$	0	0
$523$	−11.7538	−0.513957	−0.256979	−	0.966417i	$-0.582727\pi$
$523$	−11.7538	−0.513957	−0.256979	+	0.966417i	$0.582727\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	6.24621	0.272089
$528$	0	0
$529$	−19.0000	−0.826087
$530$	0	0
$531$	11.1231	0.482702
$532$	0	0
$533$	−9.12311	−0.395166
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−9.61553	−0.414941
$538$	0	0
$539$	−1.12311	−0.0483756
$540$	0	0
$541$	15.1231	0.650193	0.325097	−	0.945681i	$-0.394603\pi$
$541$	15.1231	0.650193	0.325097	+	0.945681i	$0.394603\pi$
$542$	0	0
$543$	20.3153	0.871815
$544$	0	0
$545$	0	0
$546$	0	0
$547$	27.1231	1.15970	0.579850	−	0.814723i	$-0.303111\pi$
$547$	27.1231	1.15970	0.579850	+	0.814723i	$0.303111\pi$
$548$	0	0
$549$	−39.6155	−1.69075
$550$	0	0
$551$	58.7386	2.50235
$552$	0	0
$553$	24.0000	1.02058
$554$	0	0
$555$	0	0
$556$	0	0
$557$	−32.7386	−1.38718	−0.693590	−	0.720370i	$-0.743972\pi$
$557$	−32.7386	−1.38718	−0.693590	+	0.720370i	$0.743972\pi$
$558$	0	0
$559$	16.4924	0.697555
$560$	0	0
$561$	−46.7386	−1.97331
$562$	0	0
$563$	−16.2462	−0.684696	−0.342348	−	0.939573i	$-0.611222\pi$
$563$	−16.2462	−0.684696	−0.342348	+	0.939573i	$0.611222\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	17.9309	0.753026
$568$	0	0
$569$	−35.1231	−1.47244	−0.736219	−	0.676744i	$-0.763390\pi$
$569$	−35.1231	−1.47244	−0.736219	+	0.676744i	$0.763390\pi$
$570$	0	0
$571$	27.0540	1.13217	0.566087	−	0.824346i	$-0.308457\pi$
$571$	27.0540	1.13217	0.566087	+	0.824346i	$0.308457\pi$
$572$	0	0
$573$	−18.2462	−0.762246
$574$	0	0
$575$	0	0
$576$	0	0
$577$	0.876894	0.0365056	0.0182528	−	0.999833i	$-0.494190\pi$
$577$	0.876894	0.0365056	0.0182528	+	0.999833i	$0.494190\pi$
$578$	0	0
$579$	−25.6155	−1.06455
$580$	0	0
$581$	3.68466	0.152865
$582$	0	0
$583$	17.4384	0.722227
$584$	0	0
$585$	0	0
$586$	0	0
$587$	8.87689	0.366389	0.183194	−	0.983077i	$-0.441356\pi$
$587$	8.87689	0.366389	0.183194	+	0.983077i	$0.441356\pi$
$588$	0	0
$589$	6.24621	0.257371
$590$	0	0
$591$	−32.1771	−1.32359
$592$	0	0
$593$	−29.0540	−1.19310	−0.596552	−	0.802575i	$-0.703463\pi$
$593$	−29.0540	−1.19310	−0.596552	+	0.802575i	$0.703463\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	51.8617	2.12256
$598$	0	0
$599$	1.93087	0.0788932	0.0394466	−	0.999222i	$-0.487440\pi$
$599$	1.93087	0.0788932	0.0394466	+	0.999222i	$0.487440\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	0	0
$603$	50.7386	2.06624
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−3.61553	−0.146750	−0.0733749	−	0.997304i	$-0.523377\pi$
$607$	−3.61553	−0.146750	−0.0733749	+	0.997304i	$0.523377\pi$
$608$	0	0
$609$	54.1080	2.19256
$610$	0	0
$611$	21.1231	0.854549
$612$	0	0
$613$	15.4384	0.623553	0.311777	−	0.950155i	$-0.399076\pi$
$613$	15.4384	0.623553	0.311777	+	0.950155i	$0.399076\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−19.4384	−0.782562	−0.391281	−	0.920271i	$-0.627968\pi$
$617$	−19.4384	−0.782562	−0.391281	+	0.920271i	$0.627968\pi$
$618$	0	0
$619$	−31.6847	−1.27351	−0.636757	−	0.771065i	$-0.719725\pi$
$619$	−31.6847	−1.27351	−0.636757	+	0.771065i	$0.719725\pi$
$620$	0	0
$621$	2.87689	0.115446
$622$	0	0
$623$	−12.4924	−0.500498
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−46.7386	−1.86656
$628$	0	0
$629$	−7.12311	−0.284017
$630$	0	0
$631$	33.3693	1.32841	0.664206	−	0.747550i	$-0.268770\pi$
$631$	33.3693	1.32841	0.664206	+	0.747550i	$0.268770\pi$
$632$	0	0
$633$	31.5464	1.25386
$634$	0	0
$635$	0	0
$636$	0	0
$637$	0.876894	0.0347438
$638$	0	0
$639$	19.3693	0.766238
$640$	0	0
$641$	18.8078	0.742862	0.371431	−	0.928461i	$-0.378867\pi$
$641$	18.8078	0.742862	0.371431	+	0.928461i	$0.378867\pi$
$642$	0	0
$643$	30.9848	1.22192	0.610962	−	0.791660i	$-0.290783\pi$
$643$	30.9848	1.22192	0.610962	+	0.791660i	$0.290783\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−15.1231	−0.594551	−0.297275	−	0.954792i	$-0.596078\pi$
$647$	−15.1231	−0.594551	−0.297275	+	0.954792i	$0.596078\pi$
$648$	0	0
$649$	8.00000	0.314027
$650$	0	0
$651$	5.75379	0.225509
$652$	0	0
$653$	−49.3693	−1.93197	−0.965985	−	0.258597i	$-0.916740\pi$
$653$	−49.3693	−1.93197	−0.965985	+	0.258597i	$0.916740\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	56.7386	2.21358
$658$	0	0
$659$	11.1922	0.435988	0.217994	−	0.975950i	$-0.430049\pi$
$659$	11.1922	0.435988	0.217994	+	0.975950i	$0.430049\pi$
$660$	0	0
$661$	12.8769	0.500853	0.250427	−	0.968136i	$-0.419429\pi$
$661$	12.8769	0.500853	0.250427	+	0.968136i	$0.419429\pi$
$662$	0	0
$663$	36.4924	1.41725
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−16.4924	−0.638589
$668$	0	0
$669$	13.9309	0.538599
$670$	0	0
$671$	−28.4924	−1.09994
$672$	0	0
$673$	16.4233	0.633071	0.316536	−	0.948581i	$-0.397480\pi$
$673$	16.4233	0.633071	0.316536	+	0.948581i	$0.397480\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−22.1771	−0.852334	−0.426167	−	0.904644i	$-0.640136\pi$
$677$	−22.1771	−0.852334	−0.426167	+	0.904644i	$0.640136\pi$
$678$	0	0
$679$	−2.24621	−0.0862017
$680$	0	0
$681$	44.4924	1.70495
$682$	0	0
$683$	16.7386	0.640486	0.320243	−	0.947335i	$-0.396235\pi$
$683$	16.7386	0.640486	0.320243	+	0.947335i	$0.396235\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−35.0540	−1.33739
$688$	0	0
$689$	−13.6155	−0.518710
$690$	0	0
$691$	−7.50758	−0.285602	−0.142801	−	0.989751i	$-0.545611\pi$
$691$	−7.50758	−0.285602	−0.142801	+	0.989751i	$0.545611\pi$
$692$	0	0
$693$	−23.3693	−0.887727
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−32.4924	−1.23074
$698$	0	0
$699$	−35.8617	−1.35642
$700$	0	0
$701$	40.1080	1.51486	0.757428	−	0.652918i	$-0.226456\pi$
$701$	40.1080	1.51486	0.757428	+	0.652918i	$0.226456\pi$
$702$	0	0
$703$	−7.12311	−0.268653
$704$	0	0
$705$	0	0
$706$	0	0
$707$	−27.6847	−1.04119
$708$	0	0
$709$	3.61553	0.135784	0.0678920	−	0.997693i	$-0.478373\pi$
$709$	3.61553	0.135784	0.0678920	+	0.997693i	$0.478373\pi$
$710$	0	0
$711$	−33.3693	−1.25145
$712$	0	0
$713$	−1.75379	−0.0656799
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−25.6155	−0.956629
$718$	0	0
$719$	−30.4233	−1.13460	−0.567299	−	0.823512i	$-0.692011\pi$
$719$	−30.4233	−1.13460	−0.567299	+	0.823512i	$0.692011\pi$
$720$	0	0
$721$	5.12311	0.190794
$722$	0	0
$723$	−9.61553	−0.357605
$724$	0	0
$725$	0	0
$726$	0	0
$727$	13.3693	0.495841	0.247920	−	0.968780i	$-0.420253\pi$
$727$	13.3693	0.495841	0.247920	+	0.968780i	$0.420253\pi$
$728$	0	0
$729$	−35.9848	−1.33277
$730$	0	0
$731$	58.7386	2.17253
$732$	0	0
$733$	−4.06913	−0.150297	−0.0751484	−	0.997172i	$-0.523943\pi$
$733$	−4.06913	−0.150297	−0.0751484	+	0.997172i	$0.523943\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	36.4924	1.34422
$738$	0	0
$739$	20.8078	0.765426	0.382713	−	0.923867i	$-0.374990\pi$
$739$	20.8078	0.765426	0.382713	+	0.923867i	$0.374990\pi$
$740$	0	0
$741$	36.4924	1.34058
$742$	0	0
$743$	−29.9309	−1.09806	−0.549029	−	0.835804i	$-0.685002\pi$
$743$	−29.9309	−1.09806	−0.549029	+	0.835804i	$0.685002\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−5.12311	−0.187445
$748$	0	0
$749$	−46.7386	−1.70779
$750$	0	0
$751$	32.1771	1.17416	0.587079	−	0.809530i	$-0.300278\pi$
$751$	32.1771	1.17416	0.587079	+	0.809530i	$0.300278\pi$
$752$	0	0
$753$	−9.61553	−0.350409
$754$	0	0
$755$	0	0
$756$	0	0
$757$	12.7386	0.462994	0.231497	−	0.972836i	$-0.425638\pi$
$757$	12.7386	0.462994	0.231497	+	0.972836i	$0.425638\pi$
$758$	0	0
$759$	13.1231	0.476339
$760$	0	0
$761$	−47.7926	−1.73248	−0.866240	−	0.499627i	$-0.833470\pi$
$761$	−47.7926	−1.73248	−0.866240	+	0.499627i	$0.833470\pi$
$762$	0	0
$763$	−18.2462	−0.660557
$764$	0	0
$765$	0	0
$766$	0	0
$767$	−6.24621	−0.225538
$768$	0	0
$769$	−10.4924	−0.378366	−0.189183	−	0.981942i	$-0.560584\pi$
$769$	−10.4924	−0.378366	−0.189183	+	0.981942i	$0.560584\pi$
$770$	0	0
$771$	40.0000	1.44056
$772$	0	0
$773$	−34.3153	−1.23424	−0.617119	−	0.786870i	$-0.711700\pi$
$773$	−34.3153	−1.23424	−0.617119	+	0.786870i	$0.711700\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−6.56155	−0.235394
$778$	0	0
$779$	−32.4924	−1.16416
$780$	0	0
$781$	13.9309	0.498486
$782$	0	0
$783$	−11.8617	−0.423904
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−13.3002	−0.474100	−0.237050	−	0.971497i	$-0.576181\pi$
$787$	−13.3002	−0.474100	−0.237050	+	0.971497i	$0.576181\pi$
$788$	0	0
$789$	3.68466	0.131177
$790$	0	0
$791$	10.8769	0.386738
$792$	0	0
$793$	22.2462	0.789986
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−32.1080	−1.13732	−0.568661	−	0.822572i	$-0.692538\pi$
$797$	−32.1080	−1.13732	−0.568661	+	0.822572i	$0.692538\pi$
$798$	0	0
$799$	75.2311	2.66148
$800$	0	0
$801$	17.3693	0.613715
$802$	0	0
$803$	40.8078	1.44007
$804$	0	0
$805$	0	0
$806$	0	0
$807$	73.6155	2.59139
$808$	0	0
$809$	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
$811$	−42.4233	−1.48968	−0.744842	−	0.667241i	$-0.767475\pi$
$811$	−42.4233	−1.48968	−0.744842	+	0.667241i	$0.767475\pi$
$812$	0	0
$813$	−6.56155	−0.230124
$814$	0	0
$815$	0	0
$816$	0	0
$817$	58.7386	2.05500
$818$	0	0
$819$	18.2462	0.637574
$820$	0	0
$821$	45.6847	1.59441	0.797203	−	0.603712i	$-0.206312\pi$
$821$	45.6847	1.59441	0.797203	+	0.603712i	$0.206312\pi$
$822$	0	0
$823$	1.75379	0.0611332	0.0305666	−	0.999533i	$-0.490269\pi$
$823$	1.75379	0.0611332	0.0305666	+	0.999533i	$0.490269\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	15.7538	0.547813	0.273906	−	0.961756i	$-0.411684\pi$
$827$	15.7538	0.547813	0.273906	+	0.961756i	$0.411684\pi$
$828$	0	0
$829$	−54.3542	−1.88780	−0.943899	−	0.330234i	$-0.892872\pi$
$829$	−54.3542	−1.88780	−0.943899	+	0.330234i	$0.892872\pi$
$830$	0	0
$831$	43.2311	1.49967
$832$	0	0
$833$	3.12311	0.108209
$834$	0	0
$835$	0	0
$836$	0	0
$837$	−1.26137	−0.0435992
$838$	0	0
$839$	2.24621	0.0775478	0.0387739	−	0.999248i	$-0.487655\pi$
$839$	2.24621	0.0775478	0.0387739	+	0.999248i	$0.487655\pi$
$840$	0	0
$841$	39.0000	1.34483
$842$	0	0
$843$	29.7538	1.02477
$844$	0	0
$845$	0	0
$846$	0	0
$847$	11.3693	0.390654
$848$	0	0
$849$	−29.7538	−1.02115
$850$	0	0
$851$	2.00000	0.0685591
$852$	0	0
$853$	−42.9848	−1.47177	−0.735887	−	0.677105i	$-0.763234\pi$
$853$	−42.9848	−1.47177	−0.735887	+	0.677105i	$0.763234\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−31.1231	−1.06315	−0.531573	−	0.847013i	$-0.678399\pi$
$857$	−31.1231	−1.06315	−0.531573	+	0.847013i	$0.678399\pi$
$858$	0	0
$859$	20.1080	0.686074	0.343037	−	0.939322i	$-0.388544\pi$
$859$	20.1080	0.686074	0.343037	+	0.939322i	$0.388544\pi$
$860$	0	0
$861$	−29.9309	−1.02004
$862$	0	0
$863$	−5.26137	−0.179099	−0.0895495	−	0.995982i	$-0.528543\pi$
$863$	−5.26137	−0.179099	−0.0895495	+	0.995982i	$0.528543\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	86.4233	2.93509
$868$	0	0
$869$	−24.0000	−0.814144
$870$	0	0
$871$	−28.4924	−0.965429
$872$	0	0
$873$	3.12311	0.105701
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−28.7386	−0.970435	−0.485217	−	0.874394i	$-0.661260\pi$
$877$	−28.7386	−0.970435	−0.485217	+	0.874394i	$0.661260\pi$
$878$	0	0
$879$	−51.8617	−1.74925
$880$	0	0
$881$	13.5076	0.455082	0.227541	−	0.973769i	$-0.426931\pi$
$881$	13.5076	0.455082	0.227541	+	0.973769i	$0.426931\pi$
$882$	0	0
$883$	55.6155	1.87161	0.935806	−	0.352516i	$-0.114674\pi$
$883$	55.6155	1.87161	0.935806	+	0.352516i	$0.114674\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	16.8078	0.564349	0.282175	−	0.959363i	$-0.408944\pi$
$887$	16.8078	0.564349	0.282175	+	0.959363i	$0.408944\pi$
$888$	0	0
$889$	34.4233	1.15452
$890$	0	0
$891$	−17.9309	−0.600707
$892$	0	0
$893$	75.2311	2.51751
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−10.2462	−0.342111
$898$	0	0
$899$	7.23106	0.241169
$900$	0	0
$901$	−48.4924	−1.61552
$902$	0	0
$903$	54.1080	1.80060
$904$	0	0
$905$	0	0
$906$	0	0
$907$	43.6155	1.44823	0.724115	−	0.689679i	$-0.242249\pi$
$907$	43.6155	1.44823	0.724115	+	0.689679i	$0.242249\pi$
$908$	0	0
$909$	38.4924	1.27671
$910$	0	0
$911$	−7.75379	−0.256894	−0.128447	−	0.991716i	$-0.540999\pi$
$911$	−7.75379	−0.256894	−0.128447	+	0.991716i	$0.540999\pi$
$912$	0	0
$913$	−3.68466	−0.121944
$914$	0	0
$915$	0	0
$916$	0	0
$917$	28.4924	0.940903
$918$	0	0
$919$	39.7538	1.31136	0.655678	−	0.755040i	$-0.272383\pi$
$919$	39.7538	1.31136	0.655678	+	0.755040i	$0.272383\pi$
$920$	0	0
$921$	−21.3002	−0.701865
$922$	0	0
$923$	−10.8769	−0.358017
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−7.12311	−0.233953
$928$	0	0
$929$	−36.2462	−1.18920	−0.594600	−	0.804022i	$-0.702689\pi$
$929$	−36.2462	−1.18920	−0.594600	+	0.804022i	$0.702689\pi$
$930$	0	0
$931$	3.12311	0.102356
$932$	0	0
$933$	−2.24621	−0.0735377
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−3.93087	−0.128416	−0.0642080	−	0.997937i	$-0.520452\pi$
$937$	−3.93087	−0.128416	−0.0642080	+	0.997937i	$0.520452\pi$
$938$	0	0
$939$	67.8617	2.21458
$940$	0	0
$941$	−8.24621	−0.268819	−0.134409	−	0.990926i	$-0.542914\pi$
$941$	−8.24621	−0.268819	−0.134409	+	0.990926i	$0.542914\pi$
$942$	0	0
$943$	9.12311	0.297089
$944$	0	0
$945$	0	0
$946$	0	0
$947$	17.3693	0.564427	0.282213	−	0.959352i	$-0.408931\pi$
$947$	17.3693	0.564427	0.282213	+	0.959352i	$0.408931\pi$
$948$	0	0
$949$	−31.8617	−1.03428
$950$	0	0
$951$	−26.8769	−0.871543
$952$	0	0
$953$	−22.6695	−0.734337	−0.367169	−	0.930154i	$-0.619673\pi$
$953$	−22.6695	−0.734337	−0.367169	+	0.930154i	$0.619673\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−54.1080	−1.74906
$958$	0	0
$959$	−10.8769	−0.351233
$960$	0	0
$961$	−30.2311	−0.975195
$962$	0	0
$963$	64.9848	2.09411
$964$	0	0
$965$	0	0
$966$	0	0
$967$	18.0000	0.578841	0.289420	−	0.957202i	$-0.406537\pi$
$967$	18.0000	0.578841	0.289420	+	0.957202i	$0.406537\pi$
$968$	0	0
$969$	129.970	4.17523
$970$	0	0
$971$	32.9848	1.05853	0.529267	−	0.848455i	$-0.322467\pi$
$971$	32.9848	1.05853	0.529267	+	0.848455i	$0.322467\pi$
$972$	0	0
$973$	−30.7386	−0.985435
$974$	0	0
$975$	0	0
$976$	0	0
$977$	40.8769	1.30777	0.653884	−	0.756595i	$-0.273138\pi$
$977$	40.8769	1.30777	0.653884	+	0.756595i	$0.273138\pi$
$978$	0	0
$979$	12.4924	0.399260
$980$	0	0
$981$	25.3693	0.809980
$982$	0	0
$983$	−31.1922	−0.994878	−0.497439	−	0.867499i	$-0.665726\pi$
$983$	−31.1922	−0.994878	−0.497439	+	0.867499i	$0.665726\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	69.3002	2.20585
$988$	0	0
$989$	−16.4924	−0.524429
$990$	0	0
$991$	−12.7386	−0.404656	−0.202328	−	0.979318i	$-0.564851\pi$
$991$	−12.7386	−0.404656	−0.202328	+	0.979318i	$0.564851\pi$
$992$	0	0
$993$	−83.8617	−2.66127
$994$	0	0
$995$	0	0
$996$	0	0
$997$	3.75379	0.118884	0.0594418	−	0.998232i	$-0.481068\pi$
$997$	3.75379	0.118884	0.0594418	+	0.998232i	$0.481068\pi$
$998$	0	0
$999$	1.43845	0.0455105

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3700.2.a.g.1.2		2
5.2	odd	4		3700.2.d.f.149.1		4
5.3	odd	4		3700.2.d.f.149.4		4
5.4	even	2		148.2.a.b.1.1	✓	2
15.14	odd	2		1332.2.a.f.1.2		2
20.19	odd	2		592.2.a.h.1.2		2
35.34	odd	2		7252.2.a.e.1.2		2
40.19	odd	2		2368.2.a.t.1.1		2
40.29	even	2		2368.2.a.x.1.2		2
60.59	even	2		5328.2.a.z.1.1		2
185.184	even	2		5476.2.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
148.2.a.b.1.1	✓	2	5.4	even	2
592.2.a.h.1.2		2	20.19	odd	2
1332.2.a.f.1.2		2	15.14	odd	2
2368.2.a.t.1.1		2	40.19	odd	2
2368.2.a.x.1.2		2	40.29	even	2
3700.2.a.g.1.2		2	1.1	even	1	trivial
3700.2.d.f.149.1		4	5.2	odd	4
3700.2.d.f.149.4		4	5.3	odd	4
5328.2.a.z.1.1		2	60.59	even	2
5476.2.a.d.1.1		2	185.184	even	2
7252.2.a.e.1.2		2	35.34	odd	2

Overview	Random
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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:	\( N \)	\(=\)	\( 3700 = 2^{2} \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3700.a (trivial)

\(f(q)\)	\(=\)	\(q+2.56155 q^{3} -2.56155 q^{7} +3.56155 q^{9} +2.56155 q^{11} -2.00000 q^{13} -7.12311 q^{17} -7.12311 q^{19} -6.56155 q^{21} +2.00000 q^{23} +1.43845 q^{27} -8.24621 q^{29} -0.876894 q^{31} +6.56155 q^{33} +1.00000 q^{37} -5.12311 q^{39} +4.56155 q^{41} -8.24621 q^{43} -10.5616 q^{47} -0.438447 q^{49} -18.2462 q^{51} +6.80776 q^{53} -18.2462 q^{57} +3.12311 q^{59} -11.1231 q^{61} -9.12311 q^{63} +14.2462 q^{67} +5.12311 q^{69} +5.43845 q^{71} +15.9309 q^{73} -6.56155 q^{77} -9.36932 q^{79} -7.00000 q^{81} -1.43845 q^{83} -21.1231 q^{87} +4.87689 q^{89} +5.12311 q^{91} -2.24621 q^{93} +0.876894 q^{97} +9.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} - q^{7} + 3 q^{9} + q^{11} - 4 q^{13} - 6 q^{17} - 6 q^{19} - 9 q^{21} + 4 q^{23} + 7 q^{27} - 10 q^{31} + 9 q^{33} + 2 q^{37} - 2 q^{39} + 5 q^{41} - 17 q^{47} - 5 q^{49} - 20 q^{51} - 7 q^{53}+ \cdots + 10 q^{99}+O(q^{100}) \) 2 * q + q^3 - q^7 + 3 * q^9 + q^11 - 4 * q^13 - 6 * q^17 - 6 * q^19 - 9 * q^21 + 4 * q^23 + 7 * q^27 - 10 * q^31 + 9 * q^33 + 2 * q^37 - 2 * q^39 + 5 * q^41 - 17 * q^47 - 5 * q^49 - 20 * q^51 - 7 * q^53 - 20 * q^57 - 2 * q^59 - 14 * q^61 - 10 * q^63 + 12 * q^67 + 2 * q^69 + 15 * q^71 + 3 * q^73 - 9 * q^77 + 6 * q^79 - 14 * q^81 - 7 * q^83 - 34 * q^87 + 18 * q^89 + 2 * q^91 + 12 * q^93 + 10 * q^97 + 10 * q^99

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