LMFDB - Embedded newform 1935.2.a.u.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1935,2,Mod(1,1935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1935, 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("1935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1935 = 3^{2} \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1935.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:	$15.4510527911$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1933097.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 13x^{2} + 5x - 4 $ x^5 - 2x^4 - 7x^3 + 13x^2 + 5x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 215)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.434772$ of defining polynomial
Character	$\chi$	$=$	1935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.434772 q^{2} -1.81097 q^{4} -1.00000 q^{5} +3.42802 q^{7} +1.65691 q^{8} +O(q^{10})$	\(q-0.434772 q^{2} -1.81097 q^{4} -1.00000 q^{5} +3.42802 q^{7} +1.65691 q^{8} +0.434772 q^{10} +3.52645 q^{11} +4.34418 q^{13} -1.49041 q^{14} +2.90157 q^{16} -0.147314 q^{17} -8.29463 q^{19} +1.81097 q^{20} -1.53320 q^{22} -3.47463 q^{23} +1.00000 q^{25} -1.88873 q^{26} -6.20805 q^{28} +10.4780 q^{29} +2.52243 q^{31} -4.57533 q^{32} +0.0640482 q^{34} -3.42802 q^{35} -4.80422 q^{37} +3.60628 q^{38} -1.65691 q^{40} +0.513408 q^{41} -1.00000 q^{43} -6.38631 q^{44} +1.51067 q^{46} -6.75240 q^{47} +4.75132 q^{49} -0.434772 q^{50} -7.86719 q^{52} +8.14731 q^{53} -3.52645 q^{55} +5.67991 q^{56} -4.55554 q^{58} -2.09168 q^{59} +10.6884 q^{61} -1.09668 q^{62} -3.81391 q^{64} -4.34418 q^{65} -4.06976 q^{67} +0.266782 q^{68} +1.49041 q^{70} +11.1507 q^{71} +5.53027 q^{73} +2.08874 q^{74} +15.0213 q^{76} +12.0887 q^{77} +2.32623 q^{79} -2.90157 q^{80} -0.223216 q^{82} +4.60509 q^{83} +0.147314 q^{85} +0.434772 q^{86} +5.84300 q^{88} -15.6084 q^{89} +14.8919 q^{91} +6.29246 q^{92} +2.93576 q^{94} +8.29463 q^{95} +17.7693 q^{97} -2.06574 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 8 q^{4} - 5 q^{5} + 5 q^{7} - 3 q^{8}+O(q^{10}) $ 5 * q - 2 * q^2 + 8 * q^4 - 5 * q^5 + 5 * q^7 - 3 * q^8	$ 5 q - 2 q^{2} + 8 q^{4} - 5 q^{5} + 5 q^{7} - 3 q^{8} + 2 q^{10} + 6 q^{11} + 5 q^{13} - q^{14} + 14 q^{16} + 17 q^{17} - 6 q^{19} - 8 q^{20} - 8 q^{22} - q^{23} + 5 q^{25} - 22 q^{26} + 26 q^{28} - 6 q^{29} + 6 q^{31} + 7 q^{32} - 5 q^{35} + 5 q^{37} + 16 q^{38} + 3 q^{40} - 2 q^{41} - 5 q^{43} + 15 q^{44} - 14 q^{46} + 18 q^{49} - 2 q^{50} - 38 q^{52} + 23 q^{53} - 6 q^{55} + 19 q^{56} + 12 q^{58} + q^{59} + 20 q^{61} + 3 q^{62} - 25 q^{64} - 5 q^{65} + 21 q^{67} + 48 q^{68} + q^{70} - 4 q^{71} + 5 q^{73} - 24 q^{74} + 32 q^{76} + 26 q^{77} + 41 q^{79} - 14 q^{80} + 38 q^{82} + 7 q^{83} - 17 q^{85} + 2 q^{86} + 12 q^{88} - 20 q^{89} - 42 q^{91} + 52 q^{92} - 42 q^{94} + 6 q^{95} + 37 q^{97} + 26 q^{98}+O(q^{100}) $ 5 * q - 2 * q^2 + 8 * q^4 - 5 * q^5 + 5 * q^7 - 3 * q^8 + 2 * q^10 + 6 * q^11 + 5 * q^13 - q^14 + 14 * q^16 + 17 * q^17 - 6 * q^19 - 8 * q^20 - 8 * q^22 - q^23 + 5 * q^25 - 22 * q^26 + 26 * q^28 - 6 * q^29 + 6 * q^31 + 7 * q^32 - 5 * q^35 + 5 * q^37 + 16 * q^38 + 3 * q^40 - 2 * q^41 - 5 * q^43 + 15 * q^44 - 14 * q^46 + 18 * q^49 - 2 * q^50 - 38 * q^52 + 23 * q^53 - 6 * q^55 + 19 * q^56 + 12 * q^58 + q^59 + 20 * q^61 + 3 * q^62 - 25 * q^64 - 5 * q^65 + 21 * q^67 + 48 * q^68 + q^70 - 4 * q^71 + 5 * q^73 - 24 * q^74 + 32 * q^76 + 26 * q^77 + 41 * q^79 - 14 * q^80 + 38 * q^82 + 7 * q^83 - 17 * q^85 + 2 * q^86 + 12 * q^88 - 20 * q^89 - 42 * q^91 + 52 * q^92 - 42 * q^94 + 6 * q^95 + 37 * q^97 + 26 * q^98

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 $

$2$	−0.434772	−0.307431	−0.153715	−	0.988115i	$-0.549124\pi$
$2$	−0.434772	−0.307431	−0.153715	+	0.988115i	$0.549124\pi$
$3$	0	0
$3$	0	0
$4$	−1.81097	−0.905486
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	3.42802	1.29567	0.647835	−	0.761781i	$-0.275675\pi$
$7$	3.42802	1.29567	0.647835	+	0.761781i	$0.275675\pi$
$8$	1.65691	0.585805
$9$	0	0
$10$	0.434772	0.137487
$11$	3.52645	1.06326	0.531632	−	0.846975i	$-0.321579\pi$
$11$	3.52645	1.06326	0.531632	+	0.846975i	$0.321579\pi$
$12$	0	0
$13$	4.34418	1.20486	0.602429	−	0.798173i	$-0.294200\pi$
$13$	4.34418	1.20486	0.602429	+	0.798173i	$0.294200\pi$
$14$	−1.49041	−0.398328
$15$	0	0
$16$	2.90157	0.725392
$17$	−0.147314	−0.0357290	−0.0178645	−	0.999840i	$-0.505687\pi$
$17$	−0.147314	−0.0357290	−0.0178645	+	0.999840i	$0.505687\pi$
$18$	0	0
$19$	−8.29463	−1.90292	−0.951459	−	0.307775i	$-0.900416\pi$
$19$	−8.29463	−1.90292	−0.951459	+	0.307775i	$0.900416\pi$
$20$	1.81097	0.404946
$21$	0	0
$22$	−1.53320	−0.326880
$23$	−3.47463	−0.724511	−0.362255	−	0.932079i	$-0.617993\pi$
$23$	−3.47463	−0.724511	−0.362255	+	0.932079i	$0.617993\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	−1.88873	−0.370410
$27$	0	0
$28$	−6.20805	−1.17321
$29$	10.4780	1.94571	0.972857	−	0.231409i	$-0.0743336\pi$
$29$	10.4780	1.94571	0.972857	+	0.231409i	$0.0743336\pi$
$30$	0	0
$31$	2.52243	0.453042	0.226521	−	0.974006i	$-0.427265\pi$
$31$	2.52243	0.453042	0.226521	+	0.974006i	$0.427265\pi$
$32$	−4.57533	−0.808812
$33$	0	0
$34$	0.0640482	0.0109842
$35$	−3.42802	−0.579441
$36$	0	0
$37$	−4.80422	−0.789809	−0.394904	−	0.918722i	$-0.629222\pi$
$37$	−4.80422	−0.789809	−0.394904	+	0.918722i	$0.629222\pi$
$38$	3.60628	0.585015
$39$	0	0
$40$	−1.65691	−0.261980
$41$	0.513408	0.0801809	0.0400905	−	0.999196i	$-0.487235\pi$
$41$	0.513408	0.0801809	0.0400905	+	0.999196i	$0.487235\pi$
$42$	0	0
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−6.38631	−0.962772
$45$	0	0
$46$	1.51067	0.222737
$47$	−6.75240	−0.984939	−0.492469	−	0.870330i	$-0.663906\pi$
$47$	−6.75240	−0.984939	−0.492469	+	0.870330i	$0.663906\pi$
$48$	0	0
$49$	4.75132	0.678760
$50$	−0.434772	−0.0614861
$51$	0	0
$52$	−7.86719	−1.09098
$53$	8.14731	1.11912	0.559560	−	0.828790i	$-0.310970\pi$
$53$	8.14731	1.11912	0.559560	+	0.828790i	$0.310970\pi$
$54$	0	0
$55$	−3.52645	−0.475507
$56$	5.67991	0.759009
$57$	0	0
$58$	−4.55554	−0.598172
$59$	−2.09168	−0.272313	−0.136157	−	0.990687i	$-0.543475\pi$
$59$	−2.09168	−0.272313	−0.136157	+	0.990687i	$0.543475\pi$
$60$	0	0
$61$	10.6884	1.36850	0.684252	−	0.729246i	$-0.260129\pi$
$61$	10.6884	1.36850	0.684252	+	0.729246i	$0.260129\pi$
$62$	−1.09668	−0.139279
$63$	0	0
$64$	−3.81391	−0.476739
$65$	−4.34418	−0.538829
$66$	0	0
$67$	−4.06976	−0.497200	−0.248600	−	0.968606i	$-0.579971\pi$
$67$	−4.06976	−0.497200	−0.248600	+	0.968606i	$0.579971\pi$
$68$	0.266782	0.0323521
$69$	0	0
$70$	1.49041	0.178138
$71$	11.1507	1.32334	0.661670	−	0.749795i	$-0.269848\pi$
$71$	11.1507	1.32334	0.661670	+	0.749795i	$0.269848\pi$
$72$	0	0
$73$	5.53027	0.647269	0.323634	−	0.946182i	$-0.395095\pi$
$73$	5.53027	0.647269	0.323634	+	0.946182i	$0.395095\pi$
$74$	2.08874	0.242811
$75$	0	0
$76$	15.0213	1.72307
$77$	12.0887	1.37764
$78$	0	0
$79$	2.32623	0.261722	0.130861	−	0.991401i	$-0.458226\pi$
$79$	2.32623	0.261722	0.130861	+	0.991401i	$0.458226\pi$
$80$	−2.90157	−0.324405
$81$	0	0
$82$	−0.223216	−0.0246501
$83$	4.60509	0.505474	0.252737	−	0.967535i	$-0.418669\pi$
$83$	4.60509	0.505474	0.252737	+	0.967535i	$0.418669\pi$
$84$	0	0
$85$	0.147314	0.0159785
$86$	0.434772	0.0468827
$87$	0	0
$88$	5.84300	0.622866
$89$	−15.6084	−1.65449	−0.827246	−	0.561840i	$-0.810094\pi$
$89$	−15.6084	−1.65449	−0.827246	+	0.561840i	$0.810094\pi$
$90$	0	0
$91$	14.8919	1.56110
$92$	6.29246	0.656035
$93$	0	0
$94$	2.93576	0.302800
$95$	8.29463	0.851011
$96$	0	0
$97$	17.7693	1.80420	0.902098	−	0.431532i	$-0.142027\pi$
$97$	17.7693	1.80420	0.902098	+	0.431532i	$0.142027\pi$
$98$	−2.06574	−0.208671
$99$	0	0
$100$	−1.81097	−0.181097
$101$	−7.57533	−0.753774	−0.376887	−	0.926259i	$-0.623005\pi$
$101$	−7.57533	−0.753774	−0.376887	+	0.926259i	$0.623005\pi$
$102$	0	0
$103$	10.4419	1.02888	0.514438	−	0.857528i	$-0.328001\pi$
$103$	10.4419	1.02888	0.514438	+	0.857528i	$0.328001\pi$
$104$	7.19789	0.705811
$105$	0	0
$106$	−3.54223	−0.344052
$107$	−1.24173	−0.120042	−0.0600211	−	0.998197i	$-0.519117\pi$
$107$	−1.24173	−0.120042	−0.0600211	+	0.998197i	$0.519117\pi$
$108$	0	0
$109$	19.4202	1.86012	0.930060	−	0.367407i	$-0.119754\pi$
$109$	19.4202	1.86012	0.930060	+	0.367407i	$0.119754\pi$
$110$	1.53320	0.146185
$111$	0	0
$112$	9.94664	0.939869
$113$	−0.936529	−0.0881012	−0.0440506	−	0.999029i	$-0.514026\pi$
$113$	−0.936529	−0.0881012	−0.0440506	+	0.999029i	$0.514026\pi$
$114$	0	0
$115$	3.47463	0.324011
$116$	−18.9753	−1.76182
$117$	0	0
$118$	0.909404	0.0837174
$119$	−0.504996	−0.0462929
$120$	0	0
$121$	1.43585	0.130532
$122$	−4.64700	−0.420720
$123$	0	0
$124$	−4.56806	−0.410224
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	15.8729	1.40849	0.704246	−	0.709956i	$-0.251285\pi$
$127$	15.8729	1.40849	0.704246	+	0.709956i	$0.251285\pi$
$128$	10.8089	0.955376
$129$	0	0
$130$	1.88873	0.165652
$131$	12.6748	1.10741	0.553703	−	0.832714i	$-0.313214\pi$
$131$	12.6748	1.10741	0.553703	+	0.832714i	$0.313214\pi$
$132$	0	0
$133$	−28.4341	−2.46555
$134$	1.76942	0.152855
$135$	0	0
$136$	−0.244086	−0.0209302
$137$	−3.49655	−0.298730	−0.149365	−	0.988782i	$-0.547723\pi$
$137$	−3.49655	−0.298730	−0.149365	+	0.988782i	$0.547723\pi$
$138$	0	0
$139$	2.99727	0.254225	0.127112	−	0.991888i	$-0.459429\pi$
$139$	2.99727	0.254225	0.127112	+	0.991888i	$0.459429\pi$
$140$	6.20805	0.524676
$141$	0	0
$142$	−4.84800	−0.406835
$143$	15.3195	1.28108
$144$	0	0
$145$	−10.4780	−0.870149
$146$	−2.40441	−0.198990
$147$	0	0
$148$	8.70031	0.715161
$149$	8.86367	0.726140	0.363070	−	0.931762i	$-0.381729\pi$
$149$	8.86367	0.726140	0.363070	+	0.931762i	$0.381729\pi$
$150$	0	0
$151$	−16.8717	−1.37300	−0.686500	−	0.727130i	$-0.740854\pi$
$151$	−16.8717	−1.37300	−0.686500	+	0.727130i	$0.740854\pi$
$152$	−13.7434	−1.11474
$153$	0	0
$154$	−5.25585	−0.423529
$155$	−2.52243	−0.202607
$156$	0	0
$157$	0.686807	0.0548132	0.0274066	−	0.999624i	$-0.491275\pi$
$157$	0.686807	0.0548132	0.0274066	+	0.999624i	$0.491275\pi$
$158$	−1.01138	−0.0804613
$159$	0	0
$160$	4.57533	0.361712
$161$	−11.9111	−0.938727
$162$	0	0
$163$	6.91549	0.541663	0.270832	−	0.962627i	$-0.412701\pi$
$163$	6.91549	0.541663	0.270832	+	0.962627i	$0.412701\pi$
$164$	−0.929769	−0.0726027
$165$	0	0
$166$	−2.00216	−0.155398
$167$	7.18000	0.555605	0.277803	−	0.960638i	$-0.410394\pi$
$167$	7.18000	0.555605	0.277803	+	0.960638i	$0.410394\pi$
$168$	0	0
$169$	5.87187	0.451682
$170$	−0.0640482	−0.00491227
$171$	0	0
$172$	1.81097	0.138085
$173$	−14.2811	−1.08577	−0.542887	−	0.839806i	$-0.682669\pi$
$173$	−14.2811	−1.08577	−0.542887	+	0.839806i	$0.682669\pi$
$174$	0	0
$175$	3.42802	0.259134
$176$	10.2322	0.771284
$177$	0	0
$178$	6.78612	0.508641
$179$	−10.1134	−0.755914	−0.377957	−	0.925823i	$-0.623373\pi$
$179$	−10.1134	−0.755914	−0.377957	+	0.925823i	$0.623373\pi$
$180$	0	0
$181$	−1.20863	−0.0898366	−0.0449183	−	0.998991i	$-0.514303\pi$
$181$	−1.20863	−0.0898366	−0.0449183	+	0.998991i	$0.514303\pi$
$182$	−6.47460	−0.479929
$183$	0	0
$184$	−5.75714	−0.424422
$185$	4.80422	0.353213
$186$	0	0
$187$	−0.519497	−0.0379894
$188$	12.2284	0.891849
$189$	0	0
$190$	−3.60628	−0.261627
$191$	11.7896	0.853068	0.426534	−	0.904472i	$-0.359734\pi$
$191$	11.7896	0.853068	0.426534	+	0.904472i	$0.359734\pi$
$192$	0	0
$193$	8.78628	0.632450	0.316225	−	0.948684i	$-0.397585\pi$
$193$	8.78628	0.632450	0.316225	+	0.948684i	$0.397585\pi$
$194$	−7.72558	−0.554665
$195$	0	0
$196$	−8.60451	−0.614608
$197$	20.7009	1.47488	0.737440	−	0.675412i	$-0.236034\pi$
$197$	20.7009	1.47488	0.737440	+	0.675412i	$0.236034\pi$
$198$	0	0
$199$	−7.88873	−0.559217	−0.279609	−	0.960114i	$-0.590205\pi$
$199$	−7.88873	−0.559217	−0.279609	+	0.960114i	$0.590205\pi$
$200$	1.65691	0.117161
$201$	0	0
$202$	3.29355	0.231733
$203$	35.9187	2.52100
$204$	0	0
$205$	−0.513408	−0.0358580
$206$	−4.53987	−0.316308
$207$	0	0
$208$	12.6049	0.873994
$209$	−29.2506	−2.02331
$210$	0	0
$211$	−18.7883	−1.29344	−0.646719	−	0.762728i	$-0.723860\pi$
$211$	−18.7883	−1.29344	−0.646719	+	0.762728i	$0.723860\pi$
$212$	−14.7546	−1.01335
$213$	0	0
$214$	0.539869	0.0369047
$215$	1.00000	0.0681994
$216$	0	0
$217$	8.64695	0.586993
$218$	−8.44338	−0.571858
$219$	0	0
$220$	6.38631	0.430565
$221$	−0.639959	−0.0430483
$222$	0	0
$223$	−13.0551	−0.874232	−0.437116	−	0.899405i	$-0.644000\pi$
$223$	−13.0551	−0.874232	−0.437116	+	0.899405i	$0.644000\pi$
$224$	−15.6843	−1.04795
$225$	0	0
$226$	0.407177	0.0270850
$227$	−21.6000	−1.43364	−0.716822	−	0.697256i	$-0.754404\pi$
$227$	−21.6000	−1.43364	−0.716822	+	0.697256i	$0.754404\pi$
$228$	0	0
$229$	2.87945	0.190279	0.0951397	−	0.995464i	$-0.469670\pi$
$229$	2.87945	0.190279	0.0951397	+	0.995464i	$0.469670\pi$
$230$	−1.51067	−0.0996109
$231$	0	0
$232$	17.3610	1.13981
$233$	−22.7687	−1.49163	−0.745813	−	0.666155i	$-0.767939\pi$
$233$	−22.7687	−1.49163	−0.745813	+	0.666155i	$0.767939\pi$
$234$	0	0
$235$	6.75240	0.440478
$236$	3.78797	0.246576
$237$	0	0
$238$	0.219558	0.0142319
$239$	21.4719	1.38890	0.694452	−	0.719539i	$-0.255647\pi$
$239$	21.4719	1.38890	0.694452	+	0.719539i	$0.255647\pi$
$240$	0	0
$241$	−2.39827	−0.154486	−0.0772430	−	0.997012i	$-0.524612\pi$
$241$	−2.39827	−0.154486	−0.0772430	+	0.997012i	$0.524612\pi$
$242$	−0.624270	−0.0401296
$243$	0	0
$244$	−19.3563	−1.23916
$245$	−4.75132	−0.303551
$246$	0	0
$247$	−36.0333	−2.29275
$248$	4.17943	0.265394
$249$	0	0
$250$	0.434772	0.0274974
$251$	−3.46113	−0.218464	−0.109232	−	0.994016i	$-0.534839\pi$
$251$	−3.46113	−0.218464	−0.109232	+	0.994016i	$0.534839\pi$
$252$	0	0
$253$	−12.2531	−0.770347
$254$	−6.90110	−0.433013
$255$	0	0
$256$	2.92843	0.183027
$257$	13.9899	0.872668	0.436334	−	0.899785i	$-0.356277\pi$
$257$	13.9899	0.872668	0.436334	+	0.899785i	$0.356277\pi$
$258$	0	0
$259$	−16.4690	−1.02333
$260$	7.86719	0.487902
$261$	0	0
$262$	−5.51067	−0.340451
$263$	26.2315	1.61750	0.808751	−	0.588151i	$-0.200144\pi$
$263$	26.2315	1.61750	0.808751	+	0.588151i	$0.200144\pi$
$264$	0	0
$265$	−8.14731	−0.500486
$266$	12.3624	0.757986
$267$	0	0
$268$	7.37023	0.450208
$269$	−6.72899	−0.410274	−0.205137	−	0.978733i	$-0.565764\pi$
$269$	−6.72899	−0.410274	−0.205137	+	0.978733i	$0.565764\pi$
$270$	0	0
$271$	5.29736	0.321792	0.160896	−	0.986971i	$-0.448562\pi$
$271$	5.29736	0.321792	0.160896	+	0.986971i	$0.448562\pi$
$272$	−0.427443	−0.0259175
$273$	0	0
$274$	1.52020	0.0918388
$275$	3.52645	0.212653
$276$	0	0
$277$	6.76297	0.406348	0.203174	−	0.979143i	$-0.434874\pi$
$277$	6.76297	0.406348	0.203174	+	0.979143i	$0.434874\pi$
$278$	−1.30313	−0.0781564
$279$	0	0
$280$	−5.67991	−0.339439
$281$	16.3690	0.976492	0.488246	−	0.872706i	$-0.337637\pi$
$281$	16.3690	0.976492	0.488246	+	0.872706i	$0.337637\pi$
$282$	0	0
$283$	−28.2202	−1.67752	−0.838759	−	0.544502i	$-0.816719\pi$
$283$	−28.2202	−1.67752	−0.838759	+	0.544502i	$0.816719\pi$
$284$	−20.1936	−1.19827
$285$	0	0
$286$	−6.66051	−0.393844
$287$	1.75997	0.103888
$288$	0	0
$289$	−16.9783	−0.998723
$290$	4.55554	0.267510
$291$	0	0
$292$	−10.0152	−0.586093
$293$	−9.03940	−0.528087	−0.264044	−	0.964511i	$-0.585056\pi$
$293$	−9.03940	−0.528087	−0.264044	+	0.964511i	$0.585056\pi$
$294$	0	0
$295$	2.09168	0.121782
$296$	−7.96014	−0.462674
$297$	0	0
$298$	−3.85368	−0.223238
$299$	−15.0944	−0.872932
$300$	0	0
$301$	−3.42802	−0.197588
$302$	7.33535	0.422102
$303$	0	0
$304$	−24.0674	−1.38036
$305$	−10.6884	−0.612013
$306$	0	0
$307$	13.2061	0.753711	0.376856	−	0.926272i	$-0.377005\pi$
$307$	13.2061	0.753711	0.376856	+	0.926272i	$0.377005\pi$
$308$	−21.8924	−1.24743
$309$	0	0
$310$	1.09668	0.0622875
$311$	1.00273	0.0568599	0.0284299	−	0.999596i	$-0.490949\pi$
$311$	1.00273	0.0568599	0.0284299	+	0.999596i	$0.490949\pi$
$312$	0	0
$313$	5.10184	0.288373	0.144186	−	0.989551i	$-0.453943\pi$
$313$	5.10184	0.288373	0.144186	+	0.989551i	$0.453943\pi$
$314$	−0.298605	−0.0168512
$315$	0	0
$316$	−4.21275	−0.236986
$317$	1.09441	0.0614683	0.0307342	−	0.999528i	$-0.490215\pi$
$317$	1.09441	0.0614683	0.0307342	+	0.999528i	$0.490215\pi$
$318$	0	0
$319$	36.9501	2.06881
$320$	3.81391	0.213204
$321$	0	0
$322$	5.17862	0.288593
$323$	1.22192	0.0679893
$324$	0	0
$325$	4.34418	0.240972
$326$	−3.00667	−0.166524
$327$	0	0
$328$	0.850670	0.0469704
$329$	−23.1474	−1.27616
$330$	0	0
$331$	17.1663	0.943547	0.471774	−	0.881720i	$-0.343614\pi$
$331$	17.1663	0.943547	0.471774	+	0.881720i	$0.343614\pi$
$332$	−8.33969	−0.457700
$333$	0	0
$334$	−3.12167	−0.170810
$335$	4.06976	0.222355
$336$	0	0
$337$	−23.0000	−1.25289	−0.626446	−	0.779465i	$-0.715491\pi$
$337$	−23.0000	−1.25289	−0.626446	+	0.779465i	$0.715491\pi$
$338$	−2.55293	−0.138861
$339$	0	0
$340$	−0.266782	−0.0144683
$341$	8.89523	0.481704
$342$	0	0
$343$	−7.70852	−0.416221
$344$	−1.65691	−0.0893344
$345$	0	0
$346$	6.20904	0.333800
$347$	13.8648	0.744299	0.372150	−	0.928173i	$-0.378621\pi$
$347$	13.8648	0.744299	0.372150	+	0.928173i	$0.378621\pi$
$348$	0	0
$349$	−1.71755	−0.0919382	−0.0459691	−	0.998943i	$-0.514638\pi$
$349$	−1.71755	−0.0919382	−0.0459691	+	0.998943i	$0.514638\pi$
$350$	−1.49041	−0.0796657
$351$	0	0
$352$	−16.1347	−0.859982
$353$	13.3575	0.710947	0.355474	−	0.934686i	$-0.384320\pi$
$353$	13.3575	0.710947	0.355474	+	0.934686i	$0.384320\pi$
$354$	0	0
$355$	−11.1507	−0.591816
$356$	28.2665	1.49812
$357$	0	0
$358$	4.39704	0.232391
$359$	−30.7771	−1.62435	−0.812177	−	0.583412i	$-0.801717\pi$
$359$	−30.7771	−1.62435	−0.812177	+	0.583412i	$0.801717\pi$
$360$	0	0
$361$	49.8009	2.62110
$362$	0.525478	0.0276185
$363$	0	0
$364$	−26.9689	−1.41355
$365$	−5.53027	−0.289467
$366$	0	0
$367$	17.0314	0.889030	0.444515	−	0.895771i	$-0.353376\pi$
$367$	17.0314	0.889030	0.444515	+	0.895771i	$0.353376\pi$
$368$	−10.0819	−0.525554
$369$	0	0
$370$	−2.08874	−0.108589
$371$	27.9292	1.45001
$372$	0	0
$373$	33.5031	1.73472	0.867362	−	0.497677i	$-0.165813\pi$
$373$	33.5031	1.73472	0.867362	+	0.497677i	$0.165813\pi$
$374$	0.225863	0.0116791
$375$	0	0
$376$	−11.1881	−0.576982
$377$	45.5182	2.34431
$378$	0	0
$379$	−1.63225	−0.0838432	−0.0419216	−	0.999121i	$-0.513348\pi$
$379$	−1.63225	−0.0838432	−0.0419216	+	0.999121i	$0.513348\pi$
$380$	−15.0213	−0.770579
$381$	0	0
$382$	−5.12581	−0.262259
$383$	18.8360	0.962477	0.481238	−	0.876590i	$-0.340187\pi$
$383$	18.8360	0.962477	0.481238	+	0.876590i	$0.340187\pi$
$384$	0	0
$385$	−12.0887	−0.616099
$386$	−3.82003	−0.194434
$387$	0	0
$388$	−32.1796	−1.63367
$389$	−20.0472	−1.01643	−0.508217	−	0.861229i	$-0.669695\pi$
$389$	−20.0472	−1.01643	−0.508217	+	0.861229i	$0.669695\pi$
$390$	0	0
$391$	0.511863	0.0258860
$392$	7.87249	0.397621
$393$	0	0
$394$	−9.00019	−0.453423
$395$	−2.32623	−0.117046
$396$	0	0
$397$	9.36558	0.470045	0.235022	−	0.971990i	$-0.424484\pi$
$397$	9.36558	0.470045	0.235022	+	0.971990i	$0.424484\pi$
$398$	3.42980	0.171920
$399$	0	0
$400$	2.90157	0.145078
$401$	−27.6415	−1.38035	−0.690176	−	0.723641i	$-0.742467\pi$
$401$	−27.6415	−1.38035	−0.690176	+	0.723641i	$0.742467\pi$
$402$	0	0
$403$	10.9579	0.545851
$404$	13.7187	0.682532
$405$	0	0
$406$	−15.6165	−0.775033
$407$	−16.9418	−0.839776
$408$	0	0
$409$	8.75240	0.432778	0.216389	−	0.976307i	$-0.430572\pi$
$409$	8.75240	0.432778	0.216389	+	0.976307i	$0.430572\pi$
$410$	0.223216	0.0110238
$411$	0	0
$412$	−18.9101	−0.931633
$413$	−7.17031	−0.352828
$414$	0	0
$415$	−4.60509	−0.226055
$416$	−19.8761	−0.974504
$417$	0	0
$418$	12.7174	0.622026
$419$	−5.38920	−0.263280	−0.131640	−	0.991298i	$-0.542024\pi$
$419$	−5.38920	−0.263280	−0.131640	+	0.991298i	$0.542024\pi$
$420$	0	0
$421$	−34.4283	−1.67793	−0.838966	−	0.544184i	$-0.816839\pi$
$421$	−34.4283	−1.67793	−0.838966	+	0.544184i	$0.816839\pi$
$422$	8.16863	0.397643
$423$	0	0
$424$	13.4993	0.655586
$425$	−0.147314	−0.00714579
$426$	0	0
$427$	36.6399	1.77313
$428$	2.24873	0.108697
$429$	0	0
$430$	−0.434772	−0.0209666
$431$	15.4470	0.744056	0.372028	−	0.928222i	$-0.378663\pi$
$431$	15.4470	0.744056	0.372028	+	0.928222i	$0.378663\pi$
$432$	0	0
$433$	16.5096	0.793400	0.396700	−	0.917948i	$-0.370155\pi$
$433$	16.5096	0.793400	0.396700	+	0.917948i	$0.370155\pi$
$434$	−3.75945	−0.180460
$435$	0	0
$436$	−35.1695	−1.68431
$437$	28.8208	1.37868
$438$	0	0
$439$	−27.0405	−1.29057	−0.645287	−	0.763941i	$-0.723262\pi$
$439$	−27.0405	−1.29057	−0.645287	+	0.763941i	$0.723262\pi$
$440$	−5.84300	−0.278554
$441$	0	0
$442$	0.278237	0.0132344
$443$	1.84327	0.0875762	0.0437881	−	0.999041i	$-0.486057\pi$
$443$	1.84327	0.0875762	0.0437881	+	0.999041i	$0.486057\pi$
$444$	0	0
$445$	15.6084	0.739911
$446$	5.67598	0.268766
$447$	0	0
$448$	−13.0742	−0.617696
$449$	12.2474	0.577991	0.288995	−	0.957330i	$-0.406679\pi$
$449$	12.2474	0.577991	0.288995	+	0.957330i	$0.406679\pi$
$450$	0	0
$451$	1.81051	0.0852536
$452$	1.69603	0.0797745
$453$	0	0
$454$	9.39110	0.440746
$455$	−14.8919	−0.698144
$456$	0	0
$457$	32.9544	1.54154	0.770771	−	0.637112i	$-0.219871\pi$
$457$	32.9544	1.54154	0.770771	+	0.637112i	$0.219871\pi$
$458$	−1.25191	−0.0584977
$459$	0	0
$460$	−6.29246	−0.293388
$461$	−21.0988	−0.982671	−0.491336	−	0.870970i	$-0.663491\pi$
$461$	−21.0988	−0.982671	−0.491336	+	0.870970i	$0.663491\pi$
$462$	0	0
$463$	23.6686	1.09997	0.549986	−	0.835174i	$-0.314633\pi$
$463$	23.6686	1.09997	0.549986	+	0.835174i	$0.314633\pi$
$464$	30.4026	1.41141
$465$	0	0
$466$	9.89920	0.458572
$467$	−17.8786	−0.827323	−0.413662	−	0.910431i	$-0.635750\pi$
$467$	−17.8786	−0.827323	−0.413662	+	0.910431i	$0.635750\pi$
$468$	0	0
$469$	−13.9512	−0.644207
$470$	−2.93576	−0.135416
$471$	0	0
$472$	−3.46571	−0.159522
$473$	−3.52645	−0.162146
$474$	0	0
$475$	−8.29463	−0.380584
$476$	0.914535	0.0419176
$477$	0	0
$478$	−9.33541	−0.426992
$479$	12.7833	0.584086	0.292043	−	0.956405i	$-0.405665\pi$
$479$	12.7833	0.584086	0.292043	+	0.956405i	$0.405665\pi$
$480$	0	0
$481$	−20.8704	−0.951607
$482$	1.04270	0.0474937
$483$	0	0
$484$	−2.60029	−0.118195
$485$	−17.7693	−0.806861
$486$	0	0
$487$	−3.29227	−0.149187	−0.0745935	−	0.997214i	$-0.523766\pi$
$487$	−3.29227	−0.149187	−0.0745935	+	0.997214i	$0.523766\pi$
$488$	17.7096	0.801676
$489$	0	0
$490$	2.06574	0.0933207
$491$	11.2678	0.508509	0.254255	−	0.967137i	$-0.418170\pi$
$491$	11.2678	0.508509	0.254255	+	0.967137i	$0.418170\pi$
$492$	0	0
$493$	−1.54356	−0.0695183
$494$	15.6663	0.704860
$495$	0	0
$496$	7.31901	0.328633
$497$	38.2247	1.71461
$498$	0	0
$499$	−28.7140	−1.28542	−0.642709	−	0.766111i	$-0.722189\pi$
$499$	−28.7140	−1.28542	−0.642709	+	0.766111i	$0.722189\pi$
$500$	1.81097	0.0809892
$501$	0	0
$502$	1.50480	0.0671626
$503$	12.4110	0.553379	0.276690	−	0.960959i	$-0.410763\pi$
$503$	12.4110	0.553379	0.276690	+	0.960959i	$0.410763\pi$
$504$	0	0
$505$	7.57533	0.337098
$506$	5.32732	0.236828
$507$	0	0
$508$	−28.7454	−1.27537
$509$	−20.4592	−0.906839	−0.453419	−	0.891297i	$-0.649796\pi$
$509$	−20.4592	−0.906839	−0.453419	+	0.891297i	$0.649796\pi$
$510$	0	0
$511$	18.9579	0.838647
$512$	−22.8909	−1.01164
$513$	0	0
$514$	−6.08244	−0.268285
$515$	−10.4419	−0.460127
$516$	0	0
$517$	−23.8120	−1.04725
$518$	7.16025	0.314603
$519$	0	0
$520$	−7.19789	−0.315648
$521$	−43.3303	−1.89834	−0.949168	−	0.314770i	$-0.898072\pi$
$521$	−43.3303	−1.89834	−0.949168	+	0.314770i	$0.898072\pi$
$522$	0	0
$523$	−9.83341	−0.429985	−0.214993	−	0.976616i	$-0.568973\pi$
$523$	−9.83341	−0.429985	−0.214993	+	0.976616i	$0.568973\pi$
$524$	−22.9538	−1.00274
$525$	0	0
$526$	−11.4047	−0.497269
$527$	−0.371590	−0.0161867
$528$	0	0
$529$	−10.9269	−0.475084
$530$	3.54223	0.153865
$531$	0	0
$532$	51.4935	2.23253
$533$	2.23034	0.0966066
$534$	0	0
$535$	1.24173	0.0536845
$536$	−6.74321	−0.291262
$537$	0	0
$538$	2.92558	0.126131
$539$	16.7553	0.721701
$540$	0	0
$541$	22.6054	0.971884	0.485942	−	0.873991i	$-0.338477\pi$
$541$	22.6054	0.971884	0.485942	+	0.873991i	$0.338477\pi$
$542$	−2.30315	−0.0989286
$543$	0	0
$544$	0.674012	0.0288980
$545$	−19.4202	−0.831871
$546$	0	0
$547$	−32.7864	−1.40184	−0.700922	−	0.713238i	$-0.747228\pi$
$547$	−32.7864	−1.40184	−0.700922	+	0.713238i	$0.747228\pi$
$548$	6.33216	0.270496
$549$	0	0
$550$	−1.53320	−0.0653760
$551$	−86.9110	−3.70253
$552$	0	0
$553$	7.97438	0.339105
$554$	−2.94035	−0.124924
$555$	0	0
$556$	−5.42797	−0.230197
$557$	21.8974	0.927821	0.463910	−	0.885882i	$-0.346446\pi$
$557$	21.8974	0.927821	0.463910	+	0.885882i	$0.346446\pi$
$558$	0	0
$559$	−4.34418	−0.183739
$560$	−9.94664	−0.420322
$561$	0	0
$562$	−7.11678	−0.300203
$563$	5.29931	0.223339	0.111670	−	0.993745i	$-0.464380\pi$
$563$	5.29931	0.223339	0.111670	+	0.993745i	$0.464380\pi$
$564$	0	0
$565$	0.936529	0.0394001
$566$	12.2694	0.515720
$567$	0	0
$568$	18.4756	0.775219
$569$	9.09310	0.381203	0.190601	−	0.981668i	$-0.438956\pi$
$569$	9.09310	0.381203	0.190601	+	0.981668i	$0.438956\pi$
$570$	0	0
$571$	4.29009	0.179535	0.0897673	−	0.995963i	$-0.471388\pi$
$571$	4.29009	0.179535	0.0897673	+	0.995963i	$0.471388\pi$
$572$	−27.7432	−1.16000
$573$	0	0
$574$	−0.765188	−0.0319383
$575$	−3.47463	−0.144902
$576$	0	0
$577$	−3.56791	−0.148534	−0.0742670	−	0.997238i	$-0.523662\pi$
$577$	−3.56791	−0.148534	−0.0742670	+	0.997238i	$0.523662\pi$
$578$	7.38170	0.307038
$579$	0	0
$580$	18.9753	0.787908
$581$	15.7863	0.654927
$582$	0	0
$583$	28.7311	1.18992
$584$	9.16313	0.379173
$585$	0	0
$586$	3.93008	0.162350
$587$	−42.8506	−1.76863	−0.884317	−	0.466886i	$-0.845376\pi$
$587$	−42.8506	−1.76863	−0.884317	+	0.466886i	$0.845376\pi$
$588$	0	0
$589$	−20.9226	−0.862102
$590$	−0.909404	−0.0374396
$591$	0	0
$592$	−13.9398	−0.572921
$593$	22.3566	0.918078	0.459039	−	0.888416i	$-0.348194\pi$
$593$	22.3566	0.918078	0.459039	+	0.888416i	$0.348194\pi$
$594$	0	0
$595$	0.504996	0.0207028
$596$	−16.0519	−0.657510
$597$	0	0
$598$	6.56263	0.268366
$599$	−32.1107	−1.31201	−0.656005	−	0.754757i	$-0.727755\pi$
$599$	−32.1107	−1.31201	−0.656005	+	0.754757i	$0.727755\pi$
$600$	0	0
$601$	−38.4026	−1.56647	−0.783237	−	0.621723i	$-0.786433\pi$
$601$	−38.4026	−1.56647	−0.783237	+	0.621723i	$0.786433\pi$
$602$	1.49041	0.0607445
$603$	0	0
$604$	30.5542	1.24323
$605$	−1.43585	−0.0583758
$606$	0	0
$607$	−14.6539	−0.594784	−0.297392	−	0.954755i	$-0.596117\pi$
$607$	−14.6539	−0.594784	−0.297392	+	0.954755i	$0.596117\pi$
$608$	37.9507	1.53910
$609$	0	0
$610$	4.64700	0.188152
$611$	−29.3336	−1.18671
$612$	0	0
$613$	−43.2473	−1.74674	−0.873371	−	0.487056i	$-0.838071\pi$
$613$	−43.2473	−1.74674	−0.873371	+	0.487056i	$0.838071\pi$
$614$	−5.74164	−0.231714
$615$	0	0
$616$	20.0299	0.807028
$617$	−11.2697	−0.453702	−0.226851	−	0.973929i	$-0.572843\pi$
$617$	−11.2697	−0.453702	−0.226851	+	0.973929i	$0.572843\pi$
$618$	0	0
$619$	14.7440	0.592611	0.296306	−	0.955093i	$-0.404245\pi$
$619$	14.7440	0.592611	0.296306	+	0.955093i	$0.404245\pi$
$620$	4.56806	0.183458
$621$	0	0
$622$	−0.435961	−0.0174805
$623$	−53.5060	−2.14367
$624$	0	0
$625$	1.00000	0.0400000
$626$	−2.21814	−0.0886546
$627$	0	0
$628$	−1.24379	−0.0496326
$629$	0.707730	0.0282191
$630$	0	0
$631$	28.9244	1.15146	0.575731	−	0.817639i	$-0.304717\pi$
$631$	28.9244	1.15146	0.575731	+	0.817639i	$0.304717\pi$
$632$	3.85435	0.153318
$633$	0	0
$634$	−0.475821	−0.0188972
$635$	−15.8729	−0.629897
$636$	0	0
$637$	20.6406	0.817809
$638$	−16.0649	−0.636015
$639$	0	0
$640$	−10.8089	−0.427257
$641$	−19.0280	−0.751562	−0.375781	−	0.926708i	$-0.622626\pi$
$641$	−19.0280	−0.751562	−0.375781	+	0.926708i	$0.622626\pi$
$642$	0	0
$643$	−43.1807	−1.70288	−0.851440	−	0.524452i	$-0.824270\pi$
$643$	−43.1807	−1.70288	−0.851440	+	0.524452i	$0.824270\pi$
$644$	21.5707	0.850004
$645$	0	0
$646$	−0.531256	−0.0209020
$647$	18.7593	0.737503	0.368751	−	0.929528i	$-0.379785\pi$
$647$	18.7593	0.737503	0.368751	+	0.929528i	$0.379785\pi$
$648$	0	0
$649$	−7.37620	−0.289541
$650$	−1.88873	−0.0740820
$651$	0	0
$652$	−12.5238	−0.490469
$653$	−22.0692	−0.863636	−0.431818	−	0.901961i	$-0.642128\pi$
$653$	−22.0692	−0.863636	−0.431818	+	0.901961i	$0.642128\pi$
$654$	0	0
$655$	−12.6748	−0.495247
$656$	1.48969	0.0581626
$657$	0	0
$658$	10.0638	0.392329
$659$	−11.3232	−0.441091	−0.220545	−	0.975377i	$-0.570784\pi$
$659$	−11.3232	−0.441091	−0.220545	+	0.975377i	$0.570784\pi$
$660$	0	0
$661$	−16.2409	−0.631697	−0.315849	−	0.948810i	$-0.602289\pi$
$661$	−16.2409	−0.631697	−0.315849	+	0.948810i	$0.602289\pi$
$662$	−7.46345	−0.290075
$663$	0	0
$664$	7.63020	0.296109
$665$	28.4341	1.10263
$666$	0	0
$667$	−36.4071	−1.40969
$668$	−13.0028	−0.503093
$669$	0	0
$670$	−1.76942	−0.0683586
$671$	37.6919	1.45508
$672$	0	0
$673$	20.3835	0.785726	0.392863	−	0.919597i	$-0.371485\pi$
$673$	20.3835	0.785726	0.392863	+	0.919597i	$0.371485\pi$
$674$	9.99979	0.385177
$675$	0	0
$676$	−10.6338	−0.408992
$677$	39.7020	1.52587	0.762936	−	0.646474i	$-0.223757\pi$
$677$	39.7020	1.52587	0.762936	+	0.646474i	$0.223757\pi$
$678$	0	0
$679$	60.9134	2.33764
$680$	0.244086	0.00936027
$681$	0	0
$682$	−3.86740	−0.148090
$683$	3.69595	0.141422	0.0707108	−	0.997497i	$-0.477473\pi$
$683$	3.69595	0.141422	0.0707108	+	0.997497i	$0.477473\pi$
$684$	0	0
$685$	3.49655	0.133596
$686$	3.35145	0.127959
$687$	0	0
$688$	−2.90157	−0.110621
$689$	35.3934	1.34838
$690$	0	0
$691$	7.30957	0.278069	0.139035	−	0.990288i	$-0.455600\pi$
$691$	7.30957	0.278069	0.139035	+	0.990288i	$0.455600\pi$
$692$	25.8627	0.983153
$693$	0	0
$694$	−6.02801	−0.228820
$695$	−2.99727	−0.113693
$696$	0	0
$697$	−0.0756324	−0.00286478
$698$	0.746742	0.0282646
$699$	0	0
$700$	−6.20805	−0.234642
$701$	28.8131	1.08826	0.544128	−	0.839002i	$-0.316861\pi$
$701$	28.8131	1.08826	0.544128	+	0.839002i	$0.316861\pi$
$702$	0	0
$703$	39.8492	1.50294
$704$	−13.4496	−0.506899
$705$	0	0
$706$	−5.80747	−0.218567
$707$	−25.9684	−0.976642
$708$	0	0
$709$	8.59692	0.322864	0.161432	−	0.986884i	$-0.448389\pi$
$709$	8.59692	0.322864	0.161432	+	0.986884i	$0.448389\pi$
$710$	4.84800	0.181942
$711$	0	0
$712$	−25.8617	−0.969209
$713$	−8.76452	−0.328234
$714$	0	0
$715$	−15.3195	−0.572918
$716$	18.3152	0.684470
$717$	0	0
$718$	13.3810	0.499376
$719$	−36.4995	−1.36120	−0.680600	−	0.732655i	$-0.738281\pi$
$719$	−36.4995	−1.36120	−0.680600	+	0.732655i	$0.738281\pi$
$720$	0	0
$721$	35.7952	1.33308
$722$	−21.6520	−0.805806
$723$	0	0
$724$	2.18879	0.0813458
$725$	10.4780	0.389143
$726$	0	0
$727$	−26.8954	−0.997494	−0.498747	−	0.866748i	$-0.666206\pi$
$727$	−26.8954	−0.997494	−0.498747	+	0.866748i	$0.666206\pi$
$728$	24.6745	0.914498
$729$	0	0
$730$	2.40441	0.0889911
$731$	0.147314	0.00544862
$732$	0	0
$733$	25.7501	0.951103	0.475551	−	0.879688i	$-0.342249\pi$
$733$	25.7501	0.951103	0.475551	+	0.879688i	$0.342249\pi$
$734$	−7.40477	−0.273315
$735$	0	0
$736$	15.8976	0.585993
$737$	−14.3518	−0.528656
$738$	0	0
$739$	−28.5152	−1.04895	−0.524474	−	0.851426i	$-0.675738\pi$
$739$	−28.5152	−1.04895	−0.524474	+	0.851426i	$0.675738\pi$
$740$	−8.70031	−0.319830
$741$	0	0
$742$	−12.1428	−0.445777
$743$	−17.1761	−0.630131	−0.315066	−	0.949070i	$-0.602027\pi$
$743$	−17.1761	−0.630131	−0.315066	+	0.949070i	$0.602027\pi$
$744$	0	0
$745$	−8.86367	−0.324740
$746$	−14.5662	−0.533307
$747$	0	0
$748$	0.940794	0.0343988
$749$	−4.25666	−0.155535
$750$	0	0
$751$	−43.6085	−1.59130	−0.795649	−	0.605758i	$-0.792870\pi$
$751$	−43.6085	−1.59130	−0.795649	+	0.605758i	$0.792870\pi$
$752$	−19.5926	−0.714467
$753$	0	0
$754$	−19.7901	−0.720712
$755$	16.8717	0.614024
$756$	0	0
$757$	−17.3185	−0.629452	−0.314726	−	0.949183i	$-0.601913\pi$
$757$	−17.3185	−0.629452	−0.314726	+	0.949183i	$0.601913\pi$
$758$	0.709659	0.0257760
$759$	0	0
$760$	13.7434	0.498526
$761$	37.9806	1.37680	0.688398	−	0.725333i	$-0.258314\pi$
$761$	37.9806	1.37680	0.688398	+	0.725333i	$0.258314\pi$
$762$	0	0
$763$	66.5729	2.41010
$764$	−21.3507	−0.772441
$765$	0	0
$766$	−8.18939	−0.295895
$767$	−9.08662	−0.328099
$768$	0	0
$769$	−13.9857	−0.504338	−0.252169	−	0.967683i	$-0.581144\pi$
$769$	−13.9857	−0.504338	−0.252169	+	0.967683i	$0.581144\pi$
$770$	5.25585	0.189408
$771$	0	0
$772$	−15.9117	−0.572675
$773$	−13.4580	−0.484052	−0.242026	−	0.970270i	$-0.577812\pi$
$773$	−13.4580	−0.484052	−0.242026	+	0.970270i	$0.577812\pi$
$774$	0	0
$775$	2.52243	0.0906084
$776$	29.4420	1.05691
$777$	0	0
$778$	8.71598	0.312483
$779$	−4.25853	−0.152578
$780$	0	0
$781$	39.3223	1.40706
$782$	−0.222544	−0.00795815
$783$	0	0
$784$	13.7863	0.492367
$785$	−0.686807	−0.0245132
$786$	0	0
$787$	23.8454	0.849998	0.424999	−	0.905194i	$-0.360274\pi$
$787$	23.8454	0.849998	0.424999	+	0.905194i	$0.360274\pi$
$788$	−37.4888	−1.33548
$789$	0	0
$790$	1.01138	0.0359834
$791$	−3.21044	−0.114150
$792$	0	0
$793$	46.4321	1.64885
$794$	−4.07189	−0.144506
$795$	0	0
$796$	14.2863	0.506364
$797$	30.5648	1.08266	0.541330	−	0.840810i	$-0.317921\pi$
$797$	30.5648	1.08266	0.541330	+	0.840810i	$0.317921\pi$
$798$	0	0
$799$	0.994725	0.0351908
$800$	−4.57533	−0.161762
$801$	0	0
$802$	12.0178	0.424363
$803$	19.5022	0.688218
$804$	0	0
$805$	11.9111	0.419811
$806$	−4.76419	−0.167811
$807$	0	0
$808$	−12.5516	−0.441564
$809$	48.7186	1.71285	0.856427	−	0.516268i	$-0.172679\pi$
$809$	48.7186	1.71285	0.856427	+	0.516268i	$0.172679\pi$
$810$	0	0
$811$	−53.9242	−1.89354	−0.946768	−	0.321917i	$-0.895673\pi$
$811$	−53.9242	−1.89354	−0.946768	+	0.321917i	$0.895673\pi$
$812$	−65.0479	−2.28273
$813$	0	0
$814$	7.36585	0.258173
$815$	−6.91549	−0.242239
$816$	0	0
$817$	8.29463	0.290192
$818$	−3.80530	−0.133049
$819$	0	0
$820$	0.929769	0.0324689
$821$	40.9746	1.43002	0.715011	−	0.699113i	$-0.246422\pi$
$821$	40.9746	1.43002	0.715011	+	0.699113i	$0.246422\pi$
$822$	0	0
$823$	−15.9332	−0.555397	−0.277699	−	0.960668i	$-0.589572\pi$
$823$	−15.9332	−0.555397	−0.277699	+	0.960668i	$0.589572\pi$
$824$	17.3013	0.602720
$825$	0	0
$826$	3.11745	0.108470
$827$	3.73538	0.129892	0.0649460	−	0.997889i	$-0.479312\pi$
$827$	3.73538	0.129892	0.0649460	+	0.997889i	$0.479312\pi$
$828$	0	0
$829$	14.0809	0.489051	0.244526	−	0.969643i	$-0.421368\pi$
$829$	14.0809	0.489051	0.244526	+	0.969643i	$0.421368\pi$
$830$	2.00216	0.0694962
$831$	0	0
$832$	−16.5683	−0.574402
$833$	−0.699937	−0.0242514
$834$	0	0
$835$	−7.18000	−0.248474
$836$	52.9720	1.83208
$837$	0	0
$838$	2.34308	0.0809402
$839$	21.4882	0.741855	0.370928	−	0.928662i	$-0.379040\pi$
$839$	21.4882	0.741855	0.370928	+	0.928662i	$0.379040\pi$
$840$	0	0
$841$	80.7882	2.78580
$842$	14.9685	0.515847
$843$	0	0
$844$	34.0251	1.17119
$845$	−5.87187	−0.201998
$846$	0	0
$847$	4.92214	0.169127
$848$	23.6400	0.811801
$849$	0	0
$850$	0.0640482	0.00219683
$851$	16.6929	0.572225
$852$	0	0
$853$	2.14185	0.0733354	0.0366677	−	0.999328i	$-0.488326\pi$
$853$	2.14185	0.0733354	0.0366677	+	0.999328i	$0.488326\pi$
$854$	−15.9300	−0.545114
$855$	0	0
$856$	−2.05742	−0.0703213
$857$	−18.4102	−0.628881	−0.314441	−	0.949277i	$-0.601817\pi$
$857$	−18.4102	−0.628881	−0.314441	+	0.949277i	$0.601817\pi$
$858$	0	0
$859$	−17.0069	−0.580268	−0.290134	−	0.956986i	$-0.593700\pi$
$859$	−17.0069	−0.580268	−0.290134	+	0.956986i	$0.593700\pi$
$860$	−1.81097	−0.0617537
$861$	0	0
$862$	−6.71593	−0.228745
$863$	−54.0541	−1.84002	−0.920011	−	0.391891i	$-0.871821\pi$
$863$	−54.0541	−1.84002	−0.920011	+	0.391891i	$0.871821\pi$
$864$	0	0
$865$	14.2811	0.485573
$866$	−7.17791	−0.243915
$867$	0	0
$868$	−15.6594	−0.531514
$869$	8.20335	0.278280
$870$	0	0
$871$	−17.6798	−0.599056
$872$	32.1775	1.08967
$873$	0	0
$874$	−12.5305	−0.423850
$875$	−3.42802	−0.115888
$876$	0	0
$877$	18.8141	0.635308	0.317654	−	0.948207i	$-0.397105\pi$
$877$	18.8141	0.635308	0.317654	+	0.948207i	$0.397105\pi$
$878$	11.7565	0.396762
$879$	0	0
$880$	−10.2322	−0.344929
$881$	16.0913	0.542129	0.271065	−	0.962561i	$-0.412624\pi$
$881$	16.0913	0.542129	0.271065	+	0.962561i	$0.412624\pi$
$882$	0	0
$883$	−50.3274	−1.69365	−0.846825	−	0.531871i	$-0.821489\pi$
$883$	−50.3274	−1.69365	−0.846825	+	0.531871i	$0.821489\pi$
$884$	1.15895	0.0389797
$885$	0	0
$886$	−0.801401	−0.0269236
$887$	50.7671	1.70459	0.852297	−	0.523058i	$-0.175209\pi$
$887$	50.7671	1.70459	0.852297	+	0.523058i	$0.175209\pi$
$888$	0	0
$889$	54.4126	1.82494
$890$	−6.78612	−0.227471
$891$	0	0
$892$	23.6424	0.791605
$893$	56.0087	1.87426
$894$	0	0
$895$	10.1134	0.338055
$896$	37.0530	1.23785
$897$	0	0
$898$	−5.32483	−0.177692
$899$	26.4300	0.881490
$900$	0	0
$901$	−1.20022	−0.0399850
$902$	−0.787160	−0.0262095
$903$	0	0
$904$	−1.55174	−0.0516101
$905$	1.20863	0.0401762
$906$	0	0
$907$	19.1876	0.637115	0.318558	−	0.947904i	$-0.396802\pi$
$907$	19.1876	0.637115	0.318558	+	0.947904i	$0.396802\pi$
$908$	39.1171	1.29815
$909$	0	0
$910$	6.47460	0.214631
$911$	−8.14924	−0.269996	−0.134998	−	0.990846i	$-0.543103\pi$
$911$	−8.14924	−0.269996	−0.134998	+	0.990846i	$0.543103\pi$
$912$	0	0
$913$	16.2396	0.537453
$914$	−14.3277	−0.473917
$915$	0	0
$916$	−5.21461	−0.172295
$917$	43.4496	1.43483
$918$	0	0
$919$	12.3979	0.408969	0.204484	−	0.978870i	$-0.434448\pi$
$919$	12.3979	0.408969	0.204484	+	0.978870i	$0.434448\pi$
$920$	5.75714	0.189807
$921$	0	0
$922$	9.17320	0.302103
$923$	48.4405	1.59444
$924$	0	0
$925$	−4.80422	−0.157962
$926$	−10.2904	−0.338165
$927$	0	0
$928$	−47.9403	−1.57372
$929$	13.5123	0.443324	0.221662	−	0.975124i	$-0.428852\pi$
$929$	13.5123	0.443324	0.221662	+	0.975124i	$0.428852\pi$
$930$	0	0
$931$	−39.4104	−1.29162
$932$	41.2335	1.35065
$933$	0	0
$934$	7.77313	0.254344
$935$	0.519497	0.0169894
$936$	0	0
$937$	−12.6732	−0.414017	−0.207008	−	0.978339i	$-0.566373\pi$
$937$	−12.6732	−0.414017	−0.207008	+	0.978339i	$0.566373\pi$
$938$	6.06561	0.198049
$939$	0	0
$940$	−12.2284	−0.398847
$941$	−43.4722	−1.41715	−0.708576	−	0.705635i	$-0.750662\pi$
$941$	−43.4722	−1.41715	−0.708576	+	0.705635i	$0.750662\pi$
$942$	0	0
$943$	−1.78391	−0.0580919
$944$	−6.06915	−0.197534
$945$	0	0
$946$	1.53320	0.0498487
$947$	13.6061	0.442139	0.221070	−	0.975258i	$-0.429045\pi$
$947$	13.6061	0.442139	0.221070	+	0.975258i	$0.429045\pi$
$948$	0	0
$949$	24.0245	0.779867
$950$	3.60628	0.117003
$951$	0	0
$952$	−0.836731	−0.0271186
$953$	15.7134	0.509007	0.254503	−	0.967072i	$-0.418088\pi$
$953$	15.7134	0.509007	0.254503	+	0.967072i	$0.418088\pi$
$954$	0	0
$955$	−11.7896	−0.381504
$956$	−38.8851	−1.25763
$957$	0	0
$958$	−5.55784	−0.179566
$959$	−11.9862	−0.387056
$960$	0	0
$961$	−24.6373	−0.794753
$962$	9.07387	0.292553
$963$	0	0
$964$	4.34320	0.139885
$965$	−8.78628	−0.282840
$966$	0	0
$967$	32.8964	1.05788	0.528939	−	0.848660i	$-0.322590\pi$
$967$	32.8964	1.05788	0.528939	+	0.848660i	$0.322590\pi$
$968$	2.37908	0.0764664
$969$	0	0
$970$	7.72558	0.248054
$971$	−20.8625	−0.669510	−0.334755	−	0.942305i	$-0.608654\pi$
$971$	−20.8625	−0.669510	−0.334755	+	0.942305i	$0.608654\pi$
$972$	0	0
$973$	10.2747	0.329391
$974$	1.43139	0.0458646
$975$	0	0
$976$	31.0130	0.992702
$977$	−56.8435	−1.81858	−0.909292	−	0.416160i	$-0.863376\pi$
$977$	−56.8435	−1.81858	−0.909292	+	0.416160i	$0.863376\pi$
$978$	0	0
$979$	−55.0424	−1.75916
$980$	8.60451	0.274861
$981$	0	0
$982$	−4.89893	−0.156331
$983$	−58.0603	−1.85184	−0.925918	−	0.377725i	$-0.876706\pi$
$983$	−58.0603	−1.85184	−0.925918	+	0.377725i	$0.876706\pi$
$984$	0	0
$985$	−20.7009	−0.659587
$986$	0.671096	0.0213720
$987$	0	0
$988$	65.2554	2.07605
$989$	3.47463	0.110487
$990$	0	0
$991$	−30.1239	−0.956916	−0.478458	−	0.878111i	$-0.658804\pi$
$991$	−30.1239	−0.956916	−0.478458	+	0.878111i	$0.658804\pi$
$992$	−11.5410	−0.366426
$993$	0	0
$994$	−16.6190	−0.527124
$995$	7.88873	0.250089
$996$	0	0
$997$	30.3566	0.961405	0.480702	−	0.876884i	$-0.340382\pi$
$997$	30.3566	0.961405	0.480702	+	0.876884i	$0.340382\pi$
$998$	12.4841	0.395177
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1935.2.a.u.1.3		5
3.2	odd	2		215.2.a.c.1.3	✓	5
5.4	even	2		9675.2.a.ch.1.3		5
12.11	even	2		3440.2.a.w.1.2		5
15.2	even	4		1075.2.b.h.474.6		10
15.8	even	4		1075.2.b.h.474.5		10
15.14	odd	2		1075.2.a.m.1.3		5
129.128	even	2		9245.2.a.l.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.a.c.1.3	✓	5	3.2	odd	2
1075.2.a.m.1.3		5	15.14	odd	2
1075.2.b.h.474.5		10	15.8	even	4
1075.2.b.h.474.6		10	15.2	even	4
1935.2.a.u.1.3		5	1.1	even	1	trivial
3440.2.a.w.1.2		5	12.11	even	2
9245.2.a.l.1.3		5	129.128	even	2
9675.2.a.ch.1.3		5	5.4	even	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:	\( N \)	\(=\)	\( 1935 = 3^{2} \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1935.a (trivial)

\(f(q)\)	\(=\)	\(q-0.434772 q^{2} -1.81097 q^{4} -1.00000 q^{5} +3.42802 q^{7} +1.65691 q^{8} +O(q^{10})\)	\(q-0.434772 q^{2} -1.81097 q^{4} -1.00000 q^{5} +3.42802 q^{7} +1.65691 q^{8} +0.434772 q^{10} +3.52645 q^{11} +4.34418 q^{13} -1.49041 q^{14} +2.90157 q^{16} -0.147314 q^{17} -8.29463 q^{19} +1.81097 q^{20} -1.53320 q^{22} -3.47463 q^{23} +1.00000 q^{25} -1.88873 q^{26} -6.20805 q^{28} +10.4780 q^{29} +2.52243 q^{31} -4.57533 q^{32} +0.0640482 q^{34} -3.42802 q^{35} -4.80422 q^{37} +3.60628 q^{38} -1.65691 q^{40} +0.513408 q^{41} -1.00000 q^{43} -6.38631 q^{44} +1.51067 q^{46} -6.75240 q^{47} +4.75132 q^{49} -0.434772 q^{50} -7.86719 q^{52} +8.14731 q^{53} -3.52645 q^{55} +5.67991 q^{56} -4.55554 q^{58} -2.09168 q^{59} +10.6884 q^{61} -1.09668 q^{62} -3.81391 q^{64} -4.34418 q^{65} -4.06976 q^{67} +0.266782 q^{68} +1.49041 q^{70} +11.1507 q^{71} +5.53027 q^{73} +2.08874 q^{74} +15.0213 q^{76} +12.0887 q^{77} +2.32623 q^{79} -2.90157 q^{80} -0.223216 q^{82} +4.60509 q^{83} +0.147314 q^{85} +0.434772 q^{86} +5.84300 q^{88} -15.6084 q^{89} +14.8919 q^{91} +6.29246 q^{92} +2.93576 q^{94} +8.29463 q^{95} +17.7693 q^{97} -2.06574 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 8 q^{4} - 5 q^{5} + 5 q^{7} - 3 q^{8}+O(q^{10}) \) 5 * q - 2 * q^2 + 8 * q^4 - 5 * q^5 + 5 * q^7 - 3 * q^8	\( 5 q - 2 q^{2} + 8 q^{4} - 5 q^{5} + 5 q^{7} - 3 q^{8} + 2 q^{10} + 6 q^{11} + 5 q^{13} - q^{14} + 14 q^{16} + 17 q^{17} - 6 q^{19} - 8 q^{20} - 8 q^{22} - q^{23} + 5 q^{25} - 22 q^{26} + 26 q^{28} - 6 q^{29} + 6 q^{31} + 7 q^{32} - 5 q^{35} + 5 q^{37} + 16 q^{38} + 3 q^{40} - 2 q^{41} - 5 q^{43} + 15 q^{44} - 14 q^{46} + 18 q^{49} - 2 q^{50} - 38 q^{52} + 23 q^{53} - 6 q^{55} + 19 q^{56} + 12 q^{58} + q^{59} + 20 q^{61} + 3 q^{62} - 25 q^{64} - 5 q^{65} + 21 q^{67} + 48 q^{68} + q^{70} - 4 q^{71} + 5 q^{73} - 24 q^{74} + 32 q^{76} + 26 q^{77} + 41 q^{79} - 14 q^{80} + 38 q^{82} + 7 q^{83} - 17 q^{85} + 2 q^{86} + 12 q^{88} - 20 q^{89} - 42 q^{91} + 52 q^{92} - 42 q^{94} + 6 q^{95} + 37 q^{97} + 26 q^{98}+O(q^{100}) \) 5 * q - 2 * q^2 + 8 * q^4 - 5 * q^5 + 5 * q^7 - 3 * q^8 + 2 * q^10 + 6 * q^11 + 5 * q^13 - q^14 + 14 * q^16 + 17 * q^17 - 6 * q^19 - 8 * q^20 - 8 * q^22 - q^23 + 5 * q^25 - 22 * q^26 + 26 * q^28 - 6 * q^29 + 6 * q^31 + 7 * q^32 - 5 * q^35 + 5 * q^37 + 16 * q^38 + 3 * q^40 - 2 * q^41 - 5 * q^43 + 15 * q^44 - 14 * q^46 + 18 * q^49 - 2 * q^50 - 38 * q^52 + 23 * q^53 - 6 * q^55 + 19 * q^56 + 12 * q^58 + q^59 + 20 * q^61 + 3 * q^62 - 25 * q^64 - 5 * q^65 + 21 * q^67 + 48 * q^68 + q^70 - 4 * q^71 + 5 * q^73 - 24 * q^74 + 32 * q^76 + 26 * q^77 + 41 * q^79 - 14 * q^80 + 38 * q^82 + 7 * q^83 - 17 * q^85 + 2 * q^86 + 12 * q^88 - 20 * q^89 - 42 * q^91 + 52 * q^92 - 42 * q^94 + 6 * q^95 + 37 * q^97 + 26 * q^98

Introduction

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