LMFDB - Embedded newform 1935.2.a.u.1.5

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			1.5
Root			$-2.48695$ 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)

$f(q)$	$=$	$q+2.48695 q^{2} +4.18492 q^{4} -1.00000 q^{5} +3.60359 q^{7} +5.43378 q^{8} +O(q^{10})$	\(q+2.48695 q^{2} +4.18492 q^{4} -1.00000 q^{5} +3.60359 q^{7} +5.43378 q^{8} -2.48695 q^{10} +1.45988 q^{11} -6.81557 q^{13} +8.96194 q^{14} +5.14371 q^{16} +6.52816 q^{17} +5.05632 q^{19} -4.18492 q^{20} +3.63066 q^{22} +1.84167 q^{23} +1.00000 q^{25} -16.9500 q^{26} +15.0807 q^{28} -1.16266 q^{29} +0.155661 q^{31} +1.92457 q^{32} +16.2352 q^{34} -3.60359 q^{35} -1.90562 q^{37} +12.5748 q^{38} -5.43378 q^{40} +0.185392 q^{41} -1.00000 q^{43} +6.10949 q^{44} +4.58015 q^{46} -0.604062 q^{47} +5.98585 q^{49} +2.48695 q^{50} -28.5226 q^{52} +1.47184 q^{53} -1.45988 q^{55} +19.5811 q^{56} -2.89147 q^{58} -2.94683 q^{59} -11.6311 q^{61} +0.387121 q^{62} -5.50110 q^{64} +6.81557 q^{65} +12.5823 q^{67} +27.3198 q^{68} -8.96194 q^{70} -1.84915 q^{71} -7.31667 q^{73} -4.73918 q^{74} +21.1603 q^{76} +5.26082 q^{77} +11.0683 q^{79} -5.14371 q^{80} +0.461060 q^{82} +5.13222 q^{83} -6.52816 q^{85} -2.48695 q^{86} +7.93269 q^{88} -9.81124 q^{89} -24.5605 q^{91} +7.70726 q^{92} -1.50227 q^{94} -5.05632 q^{95} -0.897999 q^{97} +14.8865 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.48695	1.75854	0.879269	−	0.476325i	$-0.158031\pi$
$2$	2.48695	1.75854	0.879269	+	0.476325i	$0.158031\pi$
$3$	0	0
$3$	0	0
$4$	4.18492	2.09246
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	3.60359	1.36203	0.681014	−	0.732270i	$-0.261539\pi$
$7$	3.60359	1.36203	0.681014	+	0.732270i	$0.261539\pi$
$8$	5.43378	1.92113
$9$	0	0
$10$	−2.48695	−0.786443
$11$	1.45988	0.440171	0.220086	−	0.975481i	$-0.429366\pi$
$11$	1.45988	0.440171	0.220086	+	0.975481i	$0.429366\pi$
$12$	0	0
$13$	−6.81557	−1.89030	−0.945150	−	0.326636i	$-0.894085\pi$
$13$	−6.81557	−1.89030	−0.945150	+	0.326636i	$0.894085\pi$
$14$	8.96194	2.39518
$15$	0	0
$16$	5.14371	1.28593
$17$	6.52816	1.58331	0.791656	−	0.610967i	$-0.209219\pi$
$17$	6.52816	1.58331	0.791656	+	0.610967i	$0.209219\pi$
$18$	0	0
$19$	5.05632	1.16000	0.580000	−	0.814616i	$-0.303052\pi$
$19$	5.05632	1.16000	0.580000	+	0.814616i	$0.303052\pi$
$20$	−4.18492	−0.935776
$21$	0	0
$22$	3.63066	0.774058
$23$	1.84167	0.384016	0.192008	−	0.981393i	$-0.438500\pi$
$23$	1.84167	0.384016	0.192008	+	0.981393i	$0.438500\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	−16.9500	−3.32417
$27$	0	0
$28$	15.0807	2.84999
$29$	−1.16266	−0.215900	−0.107950	−	0.994156i	$-0.534429\pi$
$29$	−1.16266	−0.215900	−0.107950	+	0.994156i	$0.534429\pi$
$30$	0	0
$31$	0.155661	0.0279575	0.0139788	−	0.999902i	$-0.495550\pi$
$31$	0.155661	0.0279575	0.0139788	+	0.999902i	$0.495550\pi$
$32$	1.92457	0.340220
$33$	0	0
$34$	16.2352	2.78432
$35$	−3.60359	−0.609118
$36$	0	0
$37$	−1.90562	−0.313282	−0.156641	−	0.987656i	$-0.550067\pi$
$37$	−1.90562	−0.313282	−0.156641	+	0.987656i	$0.550067\pi$
$38$	12.5748	2.03991
$39$	0	0
$40$	−5.43378	−0.859156
$41$	0.185392	0.0289533	0.0144767	−	0.999895i	$-0.495392\pi$
$41$	0.185392	0.0289533	0.0144767	+	0.999895i	$0.495392\pi$
$42$	0	0
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	6.10949	0.921041
$45$	0	0
$46$	4.58015	0.675307
$47$	−0.604062	−0.0881115	−0.0440558	−	0.999029i	$-0.514028\pi$
$47$	−0.604062	−0.0881115	−0.0440558	+	0.999029i	$0.514028\pi$
$48$	0	0
$49$	5.98585	0.855122
$50$	2.48695	0.351708
$51$	0	0
$52$	−28.5226	−3.95538
$53$	1.47184	0.202172	0.101086	−	0.994878i	$-0.467768\pi$
$53$	1.47184	0.202172	0.101086	+	0.994878i	$0.467768\pi$
$54$	0	0
$55$	−1.45988	−0.196851
$56$	19.5811	2.61664
$57$	0	0
$58$	−2.89147	−0.379669
$59$	−2.94683	−0.383645	−0.191822	−	0.981430i	$-0.561440\pi$
$59$	−2.94683	−0.383645	−0.191822	+	0.981430i	$0.561440\pi$
$60$	0	0
$61$	−11.6311	−1.48922	−0.744608	−	0.667502i	$-0.767364\pi$
$61$	−11.6311	−1.48922	−0.744608	+	0.667502i	$0.767364\pi$
$62$	0.387121	0.0491644
$63$	0	0
$64$	−5.50110	−0.687637
$65$	6.81557	0.845368
$66$	0	0
$67$	12.5823	1.53717	0.768586	−	0.639746i	$-0.220961\pi$
$67$	12.5823	1.53717	0.768586	+	0.639746i	$0.220961\pi$
$68$	27.3198	3.31302
$69$	0	0
$70$	−8.96194	−1.07116
$71$	−1.84915	−0.219453	−0.109727	−	0.993962i	$-0.534998\pi$
$71$	−1.84915	−0.219453	−0.109727	+	0.993962i	$0.534998\pi$
$72$	0	0
$73$	−7.31667	−0.856351	−0.428176	−	0.903696i	$-0.640844\pi$
$73$	−7.31667	−0.856351	−0.428176	+	0.903696i	$0.640844\pi$
$74$	−4.73918	−0.550919
$75$	0	0
$76$	21.1603	2.42725
$77$	5.26082	0.599526
$78$	0	0
$79$	11.0683	1.24528	0.622639	−	0.782509i	$-0.286060\pi$
$79$	11.0683	1.24528	0.622639	+	0.782509i	$0.286060\pi$
$80$	−5.14371	−0.575084
$81$	0	0
$82$	0.461060	0.0509155
$83$	5.13222	0.563335	0.281667	−	0.959512i	$-0.409113\pi$
$83$	5.13222	0.563335	0.281667	+	0.959512i	$0.409113\pi$
$84$	0	0
$85$	−6.52816	−0.708079
$86$	−2.48695	−0.268175
$87$	0	0
$88$	7.93269	0.845627
$89$	−9.81124	−1.03999	−0.519995	−	0.854169i	$-0.674066\pi$
$89$	−9.81124	−1.03999	−0.519995	+	0.854169i	$0.674066\pi$
$90$	0	0
$91$	−24.5605	−2.57464
$92$	7.70726	0.803537
$93$	0	0
$94$	−1.50227	−0.154948
$95$	−5.05632	−0.518768
$96$	0	0
$97$	−0.897999	−0.0911780	−0.0455890	−	0.998960i	$-0.514516\pi$
$97$	−0.897999	−0.0911780	−0.0455890	+	0.998960i	$0.514516\pi$
$98$	14.8865	1.50377
$99$	0	0
$100$	4.18492	0.418492
$101$	−1.07543	−0.107009	−0.0535045	−	0.998568i	$-0.517039\pi$
$101$	−1.07543	−0.107009	−0.0535045	+	0.998568i	$0.517039\pi$
$102$	0	0
$103$	−9.58449	−0.944388	−0.472194	−	0.881495i	$-0.656538\pi$
$103$	−9.58449	−0.944388	−0.472194	+	0.881495i	$0.656538\pi$
$104$	−37.0343	−3.63152
$105$	0	0
$106$	3.66039	0.355528
$107$	7.97609	0.771078	0.385539	−	0.922692i	$-0.374016\pi$
$107$	7.97609	0.771078	0.385539	+	0.922692i	$0.374016\pi$
$108$	0	0
$109$	−7.03284	−0.673624	−0.336812	−	0.941572i	$-0.609349\pi$
$109$	−7.03284	−0.673624	−0.336812	+	0.941572i	$0.609349\pi$
$110$	−3.63066	−0.346169
$111$	0	0
$112$	18.5358	1.75147
$113$	−18.9473	−1.78241	−0.891207	−	0.453596i	$-0.850141\pi$
$113$	−18.9473	−1.78241	−0.891207	+	0.453596i	$0.850141\pi$
$114$	0	0
$115$	−1.84167	−0.171737
$116$	−4.86563	−0.451763
$117$	0	0
$118$	−7.32862	−0.674655
$119$	23.5248	2.15652
$120$	0	0
$121$	−8.86874	−0.806249
$122$	−28.9261	−2.61884
$123$	0	0
$124$	0.651428	0.0584999
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	3.70512	0.328776	0.164388	−	0.986396i	$-0.447435\pi$
$127$	3.70512	0.328776	0.164388	+	0.986396i	$0.447435\pi$
$128$	−17.5301	−1.54946
$129$	0	0
$130$	16.9500	1.48661
$131$	−3.45007	−0.301434	−0.150717	−	0.988577i	$-0.548158\pi$
$131$	−3.45007	−0.301434	−0.150717	+	0.988577i	$0.548158\pi$
$132$	0	0
$133$	18.2209	1.57995
$134$	31.2915	2.70318
$135$	0	0
$136$	35.4726	3.04175
$137$	−15.6875	−1.34027	−0.670135	−	0.742239i	$-0.733764\pi$
$137$	−15.6875	−1.34027	−0.670135	+	0.742239i	$0.733764\pi$
$138$	0	0
$139$	6.39476	0.542397	0.271198	−	0.962524i	$-0.412580\pi$
$139$	6.39476	0.542397	0.271198	+	0.962524i	$0.412580\pi$
$140$	−15.0807	−1.27455
$141$	0	0
$142$	−4.59873	−0.385917
$143$	−9.94994	−0.832056
$144$	0	0
$145$	1.16266	0.0965536
$146$	−18.1962	−1.50593
$147$	0	0
$148$	−7.97487	−0.655530
$149$	−12.3459	−1.01142	−0.505709	−	0.862704i	$-0.668769\pi$
$149$	−12.3459	−1.01142	−0.505709	+	0.862704i	$0.668769\pi$
$150$	0	0
$151$	3.73748	0.304152	0.152076	−	0.988369i	$-0.451404\pi$
$151$	3.73748	0.304152	0.152076	+	0.988369i	$0.451404\pi$
$152$	27.4750	2.22851
$153$	0	0
$154$	13.0834	1.05429
$155$	−0.155661	−0.0125030
$156$	0	0
$157$	−9.79379	−0.781629	−0.390815	−	0.920469i	$-0.627807\pi$
$157$	−9.79379	−0.781629	−0.390815	+	0.920469i	$0.627807\pi$
$158$	27.5263	2.18987
$159$	0	0
$160$	−1.92457	−0.152151
$161$	6.63664	0.523040
$162$	0	0
$163$	−11.0444	−0.865062	−0.432531	−	0.901619i	$-0.642379\pi$
$163$	−11.0444	−0.865062	−0.432531	+	0.901619i	$0.642379\pi$
$164$	0.775849	0.0605836
$165$	0	0
$166$	12.7636	0.990646
$167$	15.2146	1.17734	0.588672	−	0.808372i	$-0.299651\pi$
$167$	15.2146	1.17734	0.588672	+	0.808372i	$0.299651\pi$
$168$	0	0
$169$	33.4521	2.57323
$170$	−16.2352	−1.24518
$171$	0	0
$172$	−4.18492	−0.319097
$173$	−7.12475	−0.541685	−0.270842	−	0.962624i	$-0.587302\pi$
$173$	−7.12475	−0.541685	−0.270842	+	0.962624i	$0.587302\pi$
$174$	0	0
$175$	3.60359	0.272406
$176$	7.50921	0.566028
$177$	0	0
$178$	−24.4001	−1.82886
$179$	19.7136	1.47346	0.736731	−	0.676186i	$-0.236368\pi$
$179$	19.7136	1.47346	0.736731	+	0.676186i	$0.236368\pi$
$180$	0	0
$181$	−14.1018	−1.04818	−0.524090	−	0.851663i	$-0.675594\pi$
$181$	−14.1018	−1.04818	−0.524090	+	0.851663i	$0.675594\pi$
$182$	−61.0808	−4.52761
$183$	0	0
$184$	10.0073	0.737745
$185$	1.90562	0.140104
$186$	0	0
$187$	9.53035	0.696928
$188$	−2.52795	−0.184370
$189$	0	0
$190$	−12.5748	−0.912274
$191$	22.4685	1.62576	0.812881	−	0.582429i	$-0.197898\pi$
$191$	22.4685	1.62576	0.812881	+	0.582429i	$0.197898\pi$
$192$	0	0
$193$	25.7895	1.85637	0.928183	−	0.372123i	$-0.121370\pi$
$193$	25.7895	1.85637	0.928183	+	0.372123i	$0.121370\pi$
$194$	−2.23328	−0.160340
$195$	0	0
$196$	25.0503	1.78931
$197$	1.09891	0.0782942	0.0391471	−	0.999233i	$-0.487536\pi$
$197$	1.09891	0.0782942	0.0391471	+	0.999233i	$0.487536\pi$
$198$	0	0
$199$	−22.9500	−1.62688	−0.813441	−	0.581648i	$-0.802408\pi$
$199$	−22.9500	−1.62688	−0.813441	+	0.581648i	$0.802408\pi$
$200$	5.43378	0.384226
$201$	0	0
$202$	−2.67453	−0.188179
$203$	−4.18975	−0.294062
$204$	0	0
$205$	−0.185392	−0.0129483
$206$	−23.8361	−1.66074
$207$	0	0
$208$	−35.0573	−2.43079
$209$	7.38164	0.510599
$210$	0	0
$211$	27.1636	1.87002	0.935011	−	0.354618i	$-0.115389\pi$
$211$	27.1636	1.87002	0.935011	+	0.354618i	$0.115389\pi$
$212$	6.15952	0.423038
$213$	0	0
$214$	19.8361	1.35597
$215$	1.00000	0.0681994
$216$	0	0
$217$	0.560937	0.0380789
$218$	−17.4903	−1.18459
$219$	0	0
$220$	−6.10949	−0.411902
$221$	−44.4932	−2.99293
$222$	0	0
$223$	5.84382	0.391331	0.195665	−	0.980671i	$-0.437313\pi$
$223$	5.84382	0.391331	0.195665	+	0.980671i	$0.437313\pi$
$224$	6.93537	0.463389
$225$	0	0
$226$	−47.1210	−3.13445
$227$	−14.9147	−0.989927	−0.494963	−	0.868914i	$-0.664819\pi$
$227$	−14.9147	−0.989927	−0.494963	+	0.868914i	$0.664819\pi$
$228$	0	0
$229$	−23.4662	−1.55069	−0.775345	−	0.631538i	$-0.782424\pi$
$229$	−23.4662	−1.55069	−0.775345	+	0.631538i	$0.782424\pi$
$230$	−4.58015	−0.302006
$231$	0	0
$232$	−6.31764	−0.414773
$233$	7.26682	0.476065	0.238033	−	0.971257i	$-0.423497\pi$
$233$	7.26682	0.476065	0.238033	+	0.971257i	$0.423497\pi$
$234$	0	0
$235$	0.604062	0.0394047
$236$	−12.3323	−0.802761
$237$	0	0
$238$	58.5050	3.79232
$239$	−17.5557	−1.13558	−0.567791	−	0.823173i	$-0.692202\pi$
$239$	−17.5557	−1.13558	−0.567791	+	0.823173i	$0.692202\pi$
$240$	0	0
$241$	4.45321	0.286856	0.143428	−	0.989661i	$-0.454187\pi$
$241$	4.45321	0.286856	0.143428	+	0.989661i	$0.454187\pi$
$242$	−22.0561	−1.41782
$243$	0	0
$244$	−48.6754	−3.11612
$245$	−5.98585	−0.382422
$246$	0	0
$247$	−34.4618	−2.19275
$248$	0.845827	0.0537101
$249$	0	0
$250$	−2.48695	−0.157289
$251$	−4.33940	−0.273901	−0.136950	−	0.990578i	$-0.543730\pi$
$251$	−4.33940	−0.273901	−0.136950	+	0.990578i	$0.543730\pi$
$252$	0	0
$253$	2.68863	0.169033
$254$	9.21444	0.578165
$255$	0	0
$256$	−32.5943	−2.03714
$257$	−13.6972	−0.854410	−0.427205	−	0.904155i	$-0.640502\pi$
$257$	−13.6972	−0.854410	−0.427205	+	0.904155i	$0.640502\pi$
$258$	0	0
$259$	−6.86707	−0.426699
$260$	28.5226	1.76890
$261$	0	0
$262$	−8.58015	−0.530084
$263$	1.05961	0.0653384	0.0326692	−	0.999466i	$-0.489599\pi$
$263$	1.05961	0.0653384	0.0326692	+	0.999466i	$0.489599\pi$
$264$	0	0
$265$	−1.47184	−0.0904143
$266$	45.3145	2.77841
$267$	0	0
$268$	52.6559	3.21647
$269$	−27.2774	−1.66313	−0.831567	−	0.555424i	$-0.812556\pi$
$269$	−27.2774	−1.66313	−0.831567	+	0.555424i	$0.812556\pi$
$270$	0	0
$271$	−11.4511	−0.695604	−0.347802	−	0.937568i	$-0.613072\pi$
$271$	−11.4511	−0.695604	−0.347802	+	0.937568i	$0.613072\pi$
$272$	33.5789	2.03602
$273$	0	0
$274$	−39.0139	−2.35692
$275$	1.45988	0.0880343
$276$	0	0
$277$	−13.2630	−0.796898	−0.398449	−	0.917190i	$-0.630451\pi$
$277$	−13.2630	−0.796898	−0.398449	+	0.917190i	$0.630451\pi$
$278$	15.9034	0.953825
$279$	0	0
$280$	−19.5811	−1.17020
$281$	20.8481	1.24370	0.621848	−	0.783138i	$-0.286382\pi$
$281$	20.8481	1.24370	0.621848	+	0.783138i	$0.286382\pi$
$282$	0	0
$283$	−10.3015	−0.612360	−0.306180	−	0.951974i	$-0.599051\pi$
$283$	−10.3015	−0.612360	−0.306180	+	0.951974i	$0.599051\pi$
$284$	−7.73853	−0.459197
$285$	0	0
$286$	−24.7450	−1.46320
$287$	0.668076	0.0394353
$288$	0	0
$289$	25.6169	1.50688
$290$	2.89147	0.169793
$291$	0	0
$292$	−30.6197	−1.79188
$293$	−11.1008	−0.648518	−0.324259	−	0.945968i	$-0.605115\pi$
$293$	−11.1008	−0.648518	−0.324259	+	0.945968i	$0.605115\pi$
$294$	0	0
$295$	2.94683	0.171571
$296$	−10.3547	−0.601856
$297$	0	0
$298$	−30.7037	−1.77862
$299$	−12.5521	−0.725905
$300$	0	0
$301$	−3.60359	−0.207707
$302$	9.29493	0.534863
$303$	0	0
$304$	26.0082	1.49168
$305$	11.6311	0.665998
$306$	0	0
$307$	17.7636	1.01382	0.506912	−	0.861998i	$-0.330787\pi$
$307$	17.7636	1.01382	0.506912	+	0.861998i	$0.330787\pi$
$308$	22.0161	1.25448
$309$	0	0
$310$	−0.387121	−0.0219870
$311$	−2.39476	−0.135794	−0.0678972	−	0.997692i	$-0.521629\pi$
$311$	−2.39476	−0.135794	−0.0678972	+	0.997692i	$0.521629\pi$
$312$	0	0
$313$	28.9005	1.63355	0.816775	−	0.576956i	$-0.195760\pi$
$313$	28.9005	1.63355	0.816775	+	0.576956i	$0.195760\pi$
$314$	−24.3567	−1.37453
$315$	0	0
$316$	46.3198	2.60569
$317$	−1.44793	−0.0813238	−0.0406619	−	0.999173i	$-0.512947\pi$
$317$	−1.44793	−0.0813238	−0.0406619	+	0.999173i	$0.512947\pi$
$318$	0	0
$319$	−1.69735	−0.0950331
$320$	5.50110	0.307521
$321$	0	0
$322$	16.5050	0.919787
$323$	33.0085	1.83664
$324$	0	0
$325$	−6.81557	−0.378060
$326$	−27.4668	−1.52124
$327$	0	0
$328$	1.00738	0.0556232
$329$	−2.17679	−0.120010
$330$	0	0
$331$	−16.7938	−0.923071	−0.461536	−	0.887122i	$-0.652701\pi$
$331$	−16.7938	−0.923071	−0.461536	+	0.887122i	$0.652701\pi$
$332$	21.4779	1.17876
$333$	0	0
$334$	37.8381	2.07041
$335$	−12.5823	−0.687444
$336$	0	0
$337$	−8.70495	−0.474189	−0.237095	−	0.971487i	$-0.576195\pi$
$337$	−8.70495	−0.474189	−0.237095	+	0.971487i	$0.576195\pi$
$338$	83.1936	4.52513
$339$	0	0
$340$	−27.3198	−1.48163
$341$	0.227247	0.0123061
$342$	0	0
$343$	−3.65457	−0.197328
$344$	−5.43378	−0.292970
$345$	0	0
$346$	−17.7189	−0.952574
$347$	−14.7277	−0.790625	−0.395313	−	0.918547i	$-0.629364\pi$
$347$	−14.7277	−0.790625	−0.395313	+	0.918547i	$0.629364\pi$
$348$	0	0
$349$	4.37517	0.234197	0.117099	−	0.993120i	$-0.462641\pi$
$349$	4.37517	0.234197	0.117099	+	0.993120i	$0.462641\pi$
$350$	8.96194	0.479036
$351$	0	0
$352$	2.80965	0.149755
$353$	7.73629	0.411761	0.205880	−	0.978577i	$-0.433994\pi$
$353$	7.73629	0.411761	0.205880	+	0.978577i	$0.433994\pi$
$354$	0	0
$355$	1.84915	0.0981425
$356$	−41.0592	−2.17614
$357$	0	0
$358$	49.0267	2.59114
$359$	−24.4434	−1.29007	−0.645036	−	0.764152i	$-0.723158\pi$
$359$	−24.4434	−1.29007	−0.645036	+	0.764152i	$0.723158\pi$
$360$	0	0
$361$	6.56642	0.345601
$362$	−35.0705	−1.84326
$363$	0	0
$364$	−102.784	−5.38734
$365$	7.31667	0.382972
$366$	0	0
$367$	18.4924	0.965295	0.482648	−	0.875815i	$-0.339675\pi$
$367$	18.4924	0.965295	0.482648	+	0.875815i	$0.339675\pi$
$368$	9.47303	0.493816
$369$	0	0
$370$	4.73918	0.246378
$371$	5.30390	0.275365
$372$	0	0
$373$	7.66966	0.397120	0.198560	−	0.980089i	$-0.436374\pi$
$373$	7.66966	0.397120	0.198560	+	0.980089i	$0.436374\pi$
$374$	23.7015	1.22558
$375$	0	0
$376$	−3.28234	−0.169274
$377$	7.92419	0.408116
$378$	0	0
$379$	8.70058	0.446919	0.223460	−	0.974713i	$-0.428265\pi$
$379$	8.70058	0.446919	0.223460	+	0.974713i	$0.428265\pi$
$380$	−21.1603	−1.08550
$381$	0	0
$382$	55.8780	2.85897
$383$	12.9425	0.661328	0.330664	−	0.943748i	$-0.392727\pi$
$383$	12.9425	0.661328	0.330664	+	0.943748i	$0.392727\pi$
$384$	0	0
$385$	−5.26082	−0.268116
$386$	64.1371	3.26449
$387$	0	0
$388$	−3.75805	−0.190786
$389$	11.1852	0.567112	0.283556	−	0.958956i	$-0.408486\pi$
$389$	11.1852	0.567112	0.283556	+	0.958956i	$0.408486\pi$
$390$	0	0
$391$	12.0228	0.608017
$392$	32.5258	1.64280
$393$	0	0
$394$	2.73294	0.137683
$395$	−11.0683	−0.556906
$396$	0	0
$397$	−12.1960	−0.612101	−0.306050	−	0.952015i	$-0.599008\pi$
$397$	−12.1960	−0.612101	−0.306050	+	0.952015i	$0.599008\pi$
$398$	−57.0755	−2.86093
$399$	0	0
$400$	5.14371	0.257185
$401$	−22.5471	−1.12595	−0.562973	−	0.826475i	$-0.690343\pi$
$401$	−22.5471	−1.12595	−0.562973	+	0.826475i	$0.690343\pi$
$402$	0	0
$403$	−1.06092	−0.0528481
$404$	−4.50057	−0.223912
$405$	0	0
$406$	−10.4197	−0.517120
$407$	−2.78198	−0.137898
$408$	0	0
$409$	2.60406	0.128763	0.0643813	−	0.997925i	$-0.479493\pi$
$409$	2.60406	0.128763	0.0643813	+	0.997925i	$0.479493\pi$
$410$	−0.461060	−0.0227701
$411$	0	0
$412$	−40.1103	−1.97609
$413$	−10.6192	−0.522535
$414$	0	0
$415$	−5.13222	−0.251931
$416$	−13.1171	−0.643117
$417$	0	0
$418$	18.3578	0.897908
$419$	−37.6853	−1.84105	−0.920523	−	0.390688i	$-0.872237\pi$
$419$	−37.6853	−1.84105	−0.920523	+	0.390688i	$0.872237\pi$
$420$	0	0
$421$	27.5929	1.34480	0.672399	−	0.740189i	$-0.265264\pi$
$421$	27.5929	1.34480	0.672399	+	0.740189i	$0.265264\pi$
$422$	67.5546	3.28851
$423$	0	0
$424$	7.99765	0.388400
$425$	6.52816	0.316662
$426$	0	0
$427$	−41.9139	−2.02835
$428$	33.3793	1.61345
$429$	0	0
$430$	2.48695	0.119931
$431$	25.4467	1.22572	0.612862	−	0.790190i	$-0.290018\pi$
$431$	25.4467	1.22572	0.612862	+	0.790190i	$0.290018\pi$
$432$	0	0
$433$	26.9619	1.29571	0.647854	−	0.761764i	$-0.275667\pi$
$433$	26.9619	1.29571	0.647854	+	0.761764i	$0.275667\pi$
$434$	1.39502	0.0669633
$435$	0	0
$436$	−29.4319	−1.40953
$437$	9.31211	0.445458
$438$	0	0
$439$	38.2034	1.82335	0.911675	−	0.410912i	$-0.134790\pi$
$439$	38.2034	1.82335	0.911675	+	0.410912i	$0.134790\pi$
$440$	−7.93269	−0.378176
$441$	0	0
$442$	−110.652	−5.26319
$443$	11.2101	0.532606	0.266303	−	0.963889i	$-0.414198\pi$
$443$	11.2101	0.532606	0.266303	+	0.963889i	$0.414198\pi$
$444$	0	0
$445$	9.81124	0.465097
$446$	14.5333	0.688171
$447$	0	0
$448$	−19.8237	−0.936581
$449$	30.1289	1.42187	0.710935	−	0.703258i	$-0.248272\pi$
$449$	30.1289	1.42187	0.710935	+	0.703258i	$0.248272\pi$
$450$	0	0
$451$	0.270650	0.0127444
$452$	−79.2930	−3.72963
$453$	0	0
$454$	−37.0922	−1.74082
$455$	24.5605	1.15142
$456$	0	0
$457$	21.5120	1.00629	0.503145	−	0.864202i	$-0.332176\pi$
$457$	21.5120	1.00629	0.503145	+	0.864202i	$0.332176\pi$
$458$	−58.3593	−2.72695
$459$	0	0
$460$	−7.70726	−0.359353
$461$	−4.84930	−0.225854	−0.112927	−	0.993603i	$-0.536023\pi$
$461$	−4.84930	−0.225854	−0.112927	+	0.993603i	$0.536023\pi$
$462$	0	0
$463$	28.9986	1.34768	0.673840	−	0.738877i	$-0.264644\pi$
$463$	28.9986	1.34768	0.673840	+	0.738877i	$0.264644\pi$
$464$	−5.98038	−0.277632
$465$	0	0
$466$	18.0722	0.837179
$467$	27.1124	1.25461	0.627306	−	0.778773i	$-0.284158\pi$
$467$	27.1124	1.25461	0.627306	+	0.778773i	$0.284158\pi$
$468$	0	0
$469$	45.3414	2.09367
$470$	1.50227	0.0692947
$471$	0	0
$472$	−16.0124	−0.737033
$473$	−1.45988	−0.0671255
$474$	0	0
$475$	5.05632	0.232000
$476$	98.4494	4.51242
$477$	0	0
$478$	−43.6601	−1.99697
$479$	22.1035	1.00993	0.504966	−	0.863139i	$-0.331505\pi$
$479$	22.1035	1.00993	0.504966	+	0.863139i	$0.331505\pi$
$480$	0	0
$481$	12.9879	0.592197
$482$	11.0749	0.504448
$483$	0	0
$484$	−37.1150	−1.68704
$485$	0.897999	0.0407760
$486$	0	0
$487$	−16.4402	−0.744976	−0.372488	−	0.928037i	$-0.621495\pi$
$487$	−16.4402	−0.744976	−0.372488	+	0.928037i	$0.621495\pi$
$488$	−63.2011	−2.86098
$489$	0	0
$490$	−14.8865	−0.672504
$491$	−1.42711	−0.0644045	−0.0322022	−	0.999481i	$-0.510252\pi$
$491$	−1.42711	−0.0644045	−0.0322022	+	0.999481i	$0.510252\pi$
$492$	0	0
$493$	−7.59003	−0.341838
$494$	−85.7046	−3.85603
$495$	0	0
$496$	0.800673	0.0359513
$497$	−6.66356	−0.298902
$498$	0	0
$499$	−26.3837	−1.18110	−0.590549	−	0.807002i	$-0.701089\pi$
$499$	−26.3837	−1.18110	−0.590549	+	0.807002i	$0.701089\pi$
$500$	−4.18492	−0.187155
$501$	0	0
$502$	−10.7919	−0.481665
$503$	−23.0839	−1.02926	−0.514630	−	0.857413i	$-0.672071\pi$
$503$	−23.0839	−1.02926	−0.514630	+	0.857413i	$0.672071\pi$
$504$	0	0
$505$	1.07543	0.0478559
$506$	6.68649	0.297251
$507$	0	0
$508$	15.5056	0.687950
$509$	26.0935	1.15658	0.578288	−	0.815833i	$-0.303721\pi$
$509$	26.0935	1.15658	0.578288	+	0.815833i	$0.303721\pi$
$510$	0	0
$511$	−26.3663	−1.16638
$512$	−46.0001	−2.03294
$513$	0	0
$514$	−34.0643	−1.50251
$515$	9.58449	0.422343
$516$	0	0
$517$	−0.881860	−0.0387842
$518$	−17.0781	−0.750367
$519$	0	0
$520$	37.0343	1.62406
$521$	−1.90891	−0.0836307	−0.0418154	−	0.999125i	$-0.513314\pi$
$521$	−1.90891	−0.0836307	−0.0418154	+	0.999125i	$0.513314\pi$
$522$	0	0
$523$	−23.1616	−1.01279	−0.506393	−	0.862303i	$-0.669022\pi$
$523$	−23.1616	−1.01279	−0.506393	+	0.862303i	$0.669022\pi$
$524$	−14.4383	−0.630739
$525$	0	0
$526$	2.63520	0.114900
$527$	1.01618	0.0442654
$528$	0	0
$529$	−19.6082	−0.852532
$530$	−3.66039	−0.158997
$531$	0	0
$532$	76.2530	3.30599
$533$	−1.26355	−0.0547305
$534$	0	0
$535$	−7.97609	−0.344836
$536$	68.3695	2.95311
$537$	0	0
$538$	−67.8376	−2.92469
$539$	8.73865	0.376400
$540$	0	0
$541$	12.9286	0.555845	0.277923	−	0.960603i	$-0.410354\pi$
$541$	12.9286	0.555845	0.277923	+	0.960603i	$0.410354\pi$
$542$	−28.4783	−1.22325
$543$	0	0
$544$	12.5639	0.538674
$545$	7.03284	0.301254
$546$	0	0
$547$	24.4280	1.04447	0.522234	−	0.852802i	$-0.325099\pi$
$547$	24.4280	1.04447	0.522234	+	0.852802i	$0.325099\pi$
$548$	−65.6507	−2.80446
$549$	0	0
$550$	3.63066	0.154812
$551$	−5.87878	−0.250444
$552$	0	0
$553$	39.8855	1.69611
$554$	−32.9845	−1.40138
$555$	0	0
$556$	26.7616	1.13494
$557$	35.5724	1.50725	0.753626	−	0.657304i	$-0.228303\pi$
$557$	35.5724	1.50725	0.753626	+	0.657304i	$0.228303\pi$
$558$	0	0
$559$	6.81557	0.288268
$560$	−18.5358	−0.783281
$561$	0	0
$562$	51.8483	2.18709
$563$	−1.12690	−0.0474930	−0.0237465	−	0.999718i	$-0.507559\pi$
$563$	−1.12690	−0.0474930	−0.0237465	+	0.999718i	$0.507559\pi$
$564$	0	0
$565$	18.9473	0.797120
$566$	−25.6193	−1.07686
$567$	0	0
$568$	−10.0479	−0.421599
$569$	−30.4523	−1.27663	−0.638313	−	0.769777i	$-0.720367\pi$
$569$	−30.4523	−1.27663	−0.638313	+	0.769777i	$0.720367\pi$
$570$	0	0
$571$	−11.1779	−0.467782	−0.233891	−	0.972263i	$-0.575146\pi$
$571$	−11.1779	−0.467782	−0.233891	+	0.972263i	$0.575146\pi$
$572$	−41.6397	−1.74104
$573$	0	0
$574$	1.66147	0.0693484
$575$	1.84167	0.0768032
$576$	0	0
$577$	29.2730	1.21865	0.609325	−	0.792921i	$-0.291441\pi$
$577$	29.2730	1.21865	0.609325	+	0.792921i	$0.291441\pi$
$578$	63.7079	2.64990
$579$	0	0
$580$	4.86563	0.202034
$581$	18.4944	0.767278
$582$	0	0
$583$	2.14871	0.0889905
$584$	−39.7572	−1.64516
$585$	0	0
$586$	−27.6072	−1.14044
$587$	0.466894	0.0192708	0.00963539	−	0.999954i	$-0.496933\pi$
$587$	0.466894	0.0192708	0.00963539	+	0.999954i	$0.496933\pi$
$588$	0	0
$589$	0.787071	0.0324307
$590$	7.32862	0.301715
$591$	0	0
$592$	−9.80195	−0.402858
$593$	−1.90991	−0.0784304	−0.0392152	−	0.999231i	$-0.512486\pi$
$593$	−1.90991	−0.0784304	−0.0392152	+	0.999231i	$0.512486\pi$
$594$	0	0
$595$	−23.5248	−0.964423
$596$	−51.6667	−2.11635
$597$	0	0
$598$	−31.2164	−1.27653
$599$	31.4276	1.28410	0.642048	−	0.766665i	$-0.278085\pi$
$599$	31.4276	1.28410	0.642048	+	0.766665i	$0.278085\pi$
$600$	0	0
$601$	−2.01962	−0.0823822	−0.0411911	−	0.999151i	$-0.513115\pi$
$601$	−2.01962	−0.0823822	−0.0411911	+	0.999151i	$0.513115\pi$
$602$	−8.96194	−0.365262
$603$	0	0
$604$	15.6411	0.636426
$605$	8.86874	0.360566
$606$	0	0
$607$	−1.19634	−0.0485579	−0.0242789	−	0.999705i	$-0.507729\pi$
$607$	−1.19634	−0.0485579	−0.0242789	+	0.999705i	$0.507729\pi$
$608$	9.73127	0.394655
$609$	0	0
$610$	28.9261	1.17118
$611$	4.11703	0.166557
$612$	0	0
$613$	1.35570	0.0547564	0.0273782	−	0.999625i	$-0.491284\pi$
$613$	1.35570	0.0547564	0.0273782	+	0.999625i	$0.491284\pi$
$614$	44.1773	1.78285
$615$	0	0
$616$	28.5861	1.15177
$617$	−9.83729	−0.396034	−0.198017	−	0.980199i	$-0.563450\pi$
$617$	−9.83729	−0.396034	−0.198017	+	0.980199i	$0.563450\pi$
$618$	0	0
$619$	7.70757	0.309793	0.154897	−	0.987931i	$-0.450496\pi$
$619$	7.70757	0.309793	0.154897	+	0.987931i	$0.450496\pi$
$620$	−0.651428	−0.0261620
$621$	0	0
$622$	−5.95565	−0.238800
$623$	−35.3557	−1.41650
$624$	0	0
$625$	1.00000	0.0400000
$626$	71.8740	2.87266
$627$	0	0
$628$	−40.9862	−1.63553
$629$	−12.4402	−0.496023
$630$	0	0
$631$	15.9152	0.633575	0.316787	−	0.948497i	$-0.397396\pi$
$631$	15.9152	0.633575	0.316787	+	0.948497i	$0.397396\pi$
$632$	60.1426	2.39234
$633$	0	0
$634$	−3.60092	−0.143011
$635$	−3.70512	−0.147033
$636$	0	0
$637$	−40.7970	−1.61644
$638$	−4.22121	−0.167119
$639$	0	0
$640$	17.5301	0.692938
$641$	33.1091	1.30773	0.653865	−	0.756611i	$-0.273146\pi$
$641$	33.1091	1.30773	0.653865	+	0.756611i	$0.273146\pi$
$642$	0	0
$643$	24.9889	0.985465	0.492733	−	0.870181i	$-0.335998\pi$
$643$	24.9889	0.985465	0.492733	+	0.870181i	$0.335998\pi$
$644$	27.7738	1.09444
$645$	0	0
$646$	82.0905	3.22981
$647$	−31.3986	−1.23441	−0.617204	−	0.786803i	$-0.711735\pi$
$647$	−31.3986	−1.23441	−0.617204	+	0.786803i	$0.711735\pi$
$648$	0	0
$649$	−4.30203	−0.168869
$650$	−16.9500	−0.664833
$651$	0	0
$652$	−46.2198	−1.81011
$653$	43.0599	1.68506	0.842532	−	0.538647i	$-0.181064\pi$
$653$	43.0599	1.68506	0.842532	+	0.538647i	$0.181064\pi$
$654$	0	0
$655$	3.45007	0.134805
$656$	0.953600	0.0372318
$657$	0	0
$658$	−5.41357	−0.211043
$659$	40.5509	1.57964	0.789819	−	0.613340i	$-0.210174\pi$
$659$	40.5509	1.57964	0.789819	+	0.613340i	$0.210174\pi$
$660$	0	0
$661$	11.6223	0.452054	0.226027	−	0.974121i	$-0.427426\pi$
$661$	11.6223	0.452054	0.226027	+	0.974121i	$0.427426\pi$
$662$	−41.7654	−1.62326
$663$	0	0
$664$	27.8874	1.08224
$665$	−18.2209	−0.706577
$666$	0	0
$667$	−2.14124	−0.0829091
$668$	63.6721	2.46355
$669$	0	0
$670$	−31.2915	−1.20890
$671$	−16.9801	−0.655510
$672$	0	0
$673$	38.8426	1.49727	0.748636	−	0.662981i	$-0.230709\pi$
$673$	38.8426	1.49727	0.748636	+	0.662981i	$0.230709\pi$
$674$	−21.6488	−0.833880
$675$	0	0
$676$	139.994	5.38439
$677$	12.7171	0.488759	0.244379	−	0.969680i	$-0.421416\pi$
$677$	12.7171	0.488759	0.244379	+	0.969680i	$0.421416\pi$
$678$	0	0
$679$	−3.23602	−0.124187
$680$	−35.4726	−1.36031
$681$	0	0
$682$	0.565151	0.0216407
$683$	19.7382	0.755262	0.377631	−	0.925956i	$-0.376739\pi$
$683$	19.7382	0.755262	0.377631	+	0.925956i	$0.376739\pi$
$684$	0	0
$685$	15.6875	0.599387
$686$	−9.08872	−0.347009
$687$	0	0
$688$	−5.14371	−0.196102
$689$	−10.0314	−0.382167
$690$	0	0
$691$	−29.8228	−1.13451	−0.567256	−	0.823541i	$-0.691995\pi$
$691$	−29.8228	−1.13451	−0.567256	+	0.823541i	$0.691995\pi$
$692$	−29.8165	−1.13345
$693$	0	0
$694$	−36.6271	−1.39035
$695$	−6.39476	−0.242567
$696$	0	0
$697$	1.21027	0.0458421
$698$	10.8808	0.411845
$699$	0	0
$700$	15.0807	0.569998
$701$	−1.49993	−0.0566516	−0.0283258	−	0.999599i	$-0.509018\pi$
$701$	−1.49993	−0.0566516	−0.0283258	+	0.999599i	$0.509018\pi$
$702$	0	0
$703$	−9.63543	−0.363407
$704$	−8.03096	−0.302678
$705$	0	0
$706$	19.2398	0.724098
$707$	−3.87540	−0.145749
$708$	0	0
$709$	−40.6060	−1.52499	−0.762495	−	0.646995i	$-0.776026\pi$
$709$	−40.6060	−1.52499	−0.762495	+	0.646995i	$0.776026\pi$
$710$	4.59873	0.172587
$711$	0	0
$712$	−53.3121	−1.99796
$713$	0.286677	0.0107361
$714$	0	0
$715$	9.94994	0.372107
$716$	82.4997	3.08316
$717$	0	0
$718$	−60.7895	−2.26864
$719$	13.1004	0.488564	0.244282	−	0.969704i	$-0.421448\pi$
$719$	13.1004	0.488564	0.244282	+	0.969704i	$0.421448\pi$
$720$	0	0
$721$	−34.5386	−1.28628
$722$	16.3303	0.607753
$723$	0	0
$724$	−59.0149	−2.19327
$725$	−1.16266	−0.0431801
$726$	0	0
$727$	46.4388	1.72232	0.861161	−	0.508333i	$-0.169738\pi$
$727$	46.4388	1.72232	0.861161	+	0.508333i	$0.169738\pi$
$728$	−133.457	−4.94623
$729$	0	0
$730$	18.1962	0.673471
$731$	−6.52816	−0.241453
$732$	0	0
$733$	−28.1169	−1.03852	−0.519261	−	0.854616i	$-0.673793\pi$
$733$	−28.1169	−1.03852	−0.519261	+	0.854616i	$0.673793\pi$
$734$	45.9897	1.69751
$735$	0	0
$736$	3.54444	0.130650
$737$	18.3687	0.676619
$738$	0	0
$739$	9.67995	0.356083	0.178041	−	0.984023i	$-0.443024\pi$
$739$	9.67995	0.356083	0.178041	+	0.984023i	$0.443024\pi$
$740$	7.97487	0.293162
$741$	0	0
$742$	13.1905	0.484240
$743$	−3.62606	−0.133027	−0.0665136	−	0.997786i	$-0.521188\pi$
$743$	−3.62606	−0.133027	−0.0665136	+	0.997786i	$0.521188\pi$
$744$	0	0
$745$	12.3459	0.452320
$746$	19.0741	0.698351
$747$	0	0
$748$	39.8838	1.45829
$749$	28.7426	1.05023
$750$	0	0
$751$	36.4063	1.32848	0.664242	−	0.747518i	$-0.268754\pi$
$751$	36.4063	1.32848	0.664242	+	0.747518i	$0.268754\pi$
$752$	−3.10712	−0.113305
$753$	0	0
$754$	19.7071	0.717689
$755$	−3.73748	−0.136021
$756$	0	0
$757$	4.37156	0.158887	0.0794434	−	0.996839i	$-0.474686\pi$
$757$	4.37156	0.158887	0.0794434	+	0.996839i	$0.474686\pi$
$758$	21.6379	0.785925
$759$	0	0
$760$	−27.4750	−0.996622
$761$	28.8090	1.04433	0.522164	−	0.852845i	$-0.325125\pi$
$761$	28.8090	1.04433	0.522164	+	0.852845i	$0.325125\pi$
$762$	0	0
$763$	−25.3435	−0.917495
$764$	94.0288	3.40184
$765$	0	0
$766$	32.1872	1.16297
$767$	20.0844	0.725204
$768$	0	0
$769$	2.26852	0.0818049	0.0409025	−	0.999163i	$-0.486977\pi$
$769$	2.26852	0.0818049	0.0409025	+	0.999163i	$0.486977\pi$
$770$	−13.0834	−0.471493
$771$	0	0
$772$	107.927	3.88437
$773$	41.5361	1.49395	0.746976	−	0.664851i	$-0.231505\pi$
$773$	41.5361	1.49395	0.746976	+	0.664851i	$0.231505\pi$
$774$	0	0
$775$	0.155661	0.00559150
$776$	−4.87953	−0.175165
$777$	0	0
$778$	27.8170	0.997289
$779$	0.937401	0.0335859
$780$	0	0
$781$	−2.69954	−0.0965970
$782$	29.9000	1.06922
$783$	0	0
$784$	30.7895	1.09962
$785$	9.79379	0.349555
$786$	0	0
$787$	18.4465	0.657546	0.328773	−	0.944409i	$-0.393365\pi$
$787$	18.4465	0.657546	0.328773	+	0.944409i	$0.393365\pi$
$788$	4.59886	0.163827
$789$	0	0
$790$	−27.5263	−0.979340
$791$	−68.2784	−2.42770
$792$	0	0
$793$	79.2730	2.81507
$794$	−30.3309	−1.07640
$795$	0	0
$796$	−96.0438	−3.40418
$797$	−21.9800	−0.778570	−0.389285	−	0.921117i	$-0.627278\pi$
$797$	−21.9800	−0.778570	−0.389285	+	0.921117i	$0.627278\pi$
$798$	0	0
$799$	−3.94342	−0.139508
$800$	1.92457	0.0680439
$801$	0	0
$802$	−56.0734	−1.98002
$803$	−10.6815	−0.376941
$804$	0	0
$805$	−6.63664	−0.233911
$806$	−2.63845	−0.0929354
$807$	0	0
$808$	−5.84364	−0.205578
$809$	−53.8587	−1.89357	−0.946785	−	0.321867i	$-0.895689\pi$
$809$	−53.8587	−1.89357	−0.946785	+	0.321867i	$0.895689\pi$
$810$	0	0
$811$	−52.6482	−1.84873	−0.924363	−	0.381513i	$-0.875403\pi$
$811$	−52.6482	−1.84873	−0.924363	+	0.381513i	$0.875403\pi$
$812$	−17.5337	−0.615314
$813$	0	0
$814$	−6.91865	−0.242499
$815$	11.0444	0.386867
$816$	0	0
$817$	−5.05632	−0.176898
$818$	6.47617	0.226434
$819$	0	0
$820$	−0.775849	−0.0270938
$821$	−18.3977	−0.642083	−0.321042	−	0.947065i	$-0.604033\pi$
$821$	−18.3977	−0.642083	−0.321042	+	0.947065i	$0.604033\pi$
$822$	0	0
$823$	55.8227	1.94586	0.972929	−	0.231106i	$-0.0742343\pi$
$823$	55.8227	1.94586	0.972929	+	0.231106i	$0.0742343\pi$
$824$	−52.0800	−1.81429
$825$	0	0
$826$	−26.4094	−0.918899
$827$	−38.0834	−1.32429	−0.662145	−	0.749376i	$-0.730354\pi$
$827$	−38.0834	−1.32429	−0.662145	+	0.749376i	$0.730354\pi$
$828$	0	0
$829$	−42.1893	−1.46530	−0.732648	−	0.680608i	$-0.761716\pi$
$829$	−42.1893	−1.46530	−0.732648	+	0.680608i	$0.761716\pi$
$830$	−12.7636	−0.443030
$831$	0	0
$832$	37.4931	1.29984
$833$	39.0766	1.35392
$834$	0	0
$835$	−15.2146	−0.526525
$836$	30.8916	1.06841
$837$	0	0
$838$	−93.7214	−3.23755
$839$	39.0639	1.34864	0.674318	−	0.738441i	$-0.264438\pi$
$839$	39.0639	1.34864	0.674318	+	0.738441i	$0.264438\pi$
$840$	0	0
$841$	−27.6482	−0.953387
$842$	68.6223	2.36488
$843$	0	0
$844$	113.678	3.91295
$845$	−33.4521	−1.15079
$846$	0	0
$847$	−31.9593	−1.09813
$848$	7.57070	0.259979
$849$	0	0
$850$	16.2352	0.556863
$851$	−3.50953	−0.120305
$852$	0	0
$853$	2.26136	0.0774275	0.0387137	−	0.999250i	$-0.487674\pi$
$853$	2.26136	0.0774275	0.0387137	+	0.999250i	$0.487674\pi$
$854$	−104.238	−3.56694
$855$	0	0
$856$	43.3403	1.48134
$857$	39.5335	1.35044	0.675219	−	0.737617i	$-0.264049\pi$
$857$	39.5335	1.35044	0.675219	+	0.737617i	$0.264049\pi$
$858$	0	0
$859$	7.37491	0.251629	0.125814	−	0.992054i	$-0.459846\pi$
$859$	7.37491	0.251629	0.125814	+	0.992054i	$0.459846\pi$
$860$	4.18492	0.142705
$861$	0	0
$862$	63.2847	2.15548
$863$	−24.4395	−0.831931	−0.415966	−	0.909380i	$-0.636556\pi$
$863$	−24.4395	−0.831931	−0.415966	+	0.909380i	$0.636556\pi$
$864$	0	0
$865$	7.12475	0.242249
$866$	67.0530	2.27855
$867$	0	0
$868$	2.34748	0.0796786
$869$	16.1584	0.548136
$870$	0	0
$871$	−85.7556	−2.90572
$872$	−38.2149	−1.29412
$873$	0	0
$874$	23.1587	0.783356
$875$	−3.60359	−0.121824
$876$	0	0
$877$	−4.58668	−0.154881	−0.0774405	−	0.996997i	$-0.524675\pi$
$877$	−4.58668	−0.154881	−0.0774405	+	0.996997i	$0.524675\pi$
$878$	95.0100	3.20643
$879$	0	0
$880$	−7.50921	−0.253135
$881$	17.5990	0.592925	0.296463	−	0.955044i	$-0.404193\pi$
$881$	17.5990	0.592925	0.296463	+	0.955044i	$0.404193\pi$
$882$	0	0
$883$	−37.3914	−1.25832	−0.629161	−	0.777275i	$-0.716601\pi$
$883$	−37.3914	−1.25832	−0.629161	+	0.777275i	$0.716601\pi$
$884$	−186.200	−6.26259
$885$	0	0
$886$	27.8788	0.936608
$887$	32.5705	1.09361	0.546806	−	0.837259i	$-0.315844\pi$
$887$	32.5705	1.09361	0.546806	+	0.837259i	$0.315844\pi$
$888$	0	0
$889$	13.3517	0.447802
$890$	24.4001	0.817892
$891$	0	0
$892$	24.4559	0.818844
$893$	−3.05433	−0.102209
$894$	0	0
$895$	−19.7136	−0.658952
$896$	−63.1713	−2.11040
$897$	0	0
$898$	74.9290	2.50041
$899$	−0.180980	−0.00603603
$900$	0	0
$901$	9.60840	0.320102
$902$	0.673093	0.0224116
$903$	0	0
$904$	−102.956	−3.42425
$905$	14.1018	0.468760
$906$	0	0
$907$	5.66154	0.187988	0.0939942	−	0.995573i	$-0.470036\pi$
$907$	5.66154	0.187988	0.0939942	+	0.995573i	$0.470036\pi$
$908$	−62.4170	−2.07138
$909$	0	0
$910$	61.0808	2.02481
$911$	−12.7362	−0.421970	−0.210985	−	0.977489i	$-0.567667\pi$
$911$	−12.7362	−0.421970	−0.210985	+	0.977489i	$0.567667\pi$
$912$	0	0
$913$	7.49245	0.247964
$914$	53.4994	1.76960
$915$	0	0
$916$	−98.2041	−3.24476
$917$	−12.4326	−0.410562
$918$	0	0
$919$	−17.5550	−0.579085	−0.289543	−	0.957165i	$-0.593503\pi$
$919$	−17.5550	−0.579085	−0.289543	+	0.957165i	$0.593503\pi$
$920$	−10.0073	−0.329930
$921$	0	0
$922$	−12.0600	−0.397173
$923$	12.6030	0.414833
$924$	0	0
$925$	−1.90562	−0.0626564
$926$	72.1181	2.36995
$927$	0	0
$928$	−2.23762	−0.0734535
$929$	−12.7382	−0.417926	−0.208963	−	0.977924i	$-0.567009\pi$
$929$	−12.7382	−0.417926	−0.208963	+	0.977924i	$0.567009\pi$
$930$	0	0
$931$	30.2664	0.991942
$932$	30.4111	0.996147
$933$	0	0
$934$	67.4271	2.20628
$935$	−9.53035	−0.311676
$936$	0	0
$937$	−2.11433	−0.0690721	−0.0345360	−	0.999403i	$-0.510995\pi$
$937$	−2.11433	−0.0690721	−0.0345360	+	0.999403i	$0.510995\pi$
$938$	112.762	3.68180
$939$	0	0
$940$	2.52795	0.0824527
$941$	−2.17027	−0.0707487	−0.0353743	−	0.999374i	$-0.511262\pi$
$941$	−2.17027	−0.0707487	−0.0353743	+	0.999374i	$0.511262\pi$
$942$	0	0
$943$	0.341431	0.0111185
$944$	−15.1576	−0.493339
$945$	0	0
$946$	−3.63066	−0.118043
$947$	−25.6147	−0.832366	−0.416183	−	0.909281i	$-0.636632\pi$
$947$	−25.6147	−0.832366	−0.416183	+	0.909281i	$0.636632\pi$
$948$	0	0
$949$	49.8673	1.61876
$950$	12.5748	0.407981
$951$	0	0
$952$	127.829	4.14295
$953$	53.4187	1.73040	0.865201	−	0.501426i	$-0.167191\pi$
$953$	53.4187	1.73040	0.865201	+	0.501426i	$0.167191\pi$
$954$	0	0
$955$	−22.4685	−0.727063
$956$	−73.4691	−2.37616
$957$	0	0
$958$	54.9702	1.77601
$959$	−56.5311	−1.82549
$960$	0	0
$961$	−30.9758	−0.999218
$962$	32.3002	1.04140
$963$	0	0
$964$	18.6363	0.600235
$965$	−25.7895	−0.830193
$966$	0	0
$967$	12.1018	0.389169	0.194584	−	0.980886i	$-0.437664\pi$
$967$	12.1018	0.389169	0.194584	+	0.980886i	$0.437664\pi$
$968$	−48.1908	−1.54891
$969$	0	0
$970$	2.23328	0.0717063
$971$	−10.8393	−0.347849	−0.173924	−	0.984759i	$-0.555645\pi$
$971$	−10.8393	−0.347849	−0.173924	+	0.984759i	$0.555645\pi$
$972$	0	0
$973$	23.0441	0.738760
$974$	−40.8859	−1.31007
$975$	0	0
$976$	−59.8272	−1.91502
$977$	38.8433	1.24271	0.621353	−	0.783531i	$-0.286583\pi$
$977$	38.8433	1.24271	0.621353	+	0.783531i	$0.286583\pi$
$978$	0	0
$979$	−14.3233	−0.457773
$980$	−25.0503	−0.800203
$981$	0	0
$982$	−3.54915	−0.113258
$983$	−11.7345	−0.374271	−0.187136	−	0.982334i	$-0.559920\pi$
$983$	−11.7345	−0.374271	−0.187136	+	0.982334i	$0.559920\pi$
$984$	0	0
$985$	−1.09891	−0.0350142
$986$	−18.8760	−0.601135
$987$	0	0
$988$	−144.220	−4.58824
$989$	−1.84167	−0.0585619
$990$	0	0
$991$	−17.7801	−0.564803	−0.282401	−	0.959296i	$-0.591131\pi$
$991$	−17.7801	−0.564803	−0.282401	+	0.959296i	$0.591131\pi$
$992$	0.299581	0.00951169
$993$	0	0
$994$	−16.5719	−0.525630
$995$	22.9500	0.727564
$996$	0	0
$997$	6.09009	0.192875	0.0964376	−	0.995339i	$-0.469255\pi$
$997$	6.09009	0.192875	0.0964376	+	0.995339i	$0.469255\pi$
$998$	−65.6150	−2.07701
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1935.2.a.u.1.5		5
3.2	odd	2		215.2.a.c.1.1	✓	5
5.4	even	2		9675.2.a.ch.1.1		5
12.11	even	2		3440.2.a.w.1.1		5
15.2	even	4		1075.2.b.h.474.2		10
15.8	even	4		1075.2.b.h.474.9		10
15.14	odd	2		1075.2.a.m.1.5		5
129.128	even	2		9245.2.a.l.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
215.2.a.c.1.1	✓	5	3.2	odd	2
1075.2.a.m.1.5		5	15.14	odd	2
1075.2.b.h.474.2		10	15.2	even	4
1075.2.b.h.474.9		10	15.8	even	4
1935.2.a.u.1.5		5	1.1	even	1	trivial
3440.2.a.w.1.1		5	12.11	even	2
9245.2.a.l.1.5		5	129.128	even	2
9675.2.a.ch.1.1		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)

\(f(q)\)	\(=\)	\(q+2.48695 q^{2} +4.18492 q^{4} -1.00000 q^{5} +3.60359 q^{7} +5.43378 q^{8} +O(q^{10})\)	\(q+2.48695 q^{2} +4.18492 q^{4} -1.00000 q^{5} +3.60359 q^{7} +5.43378 q^{8} -2.48695 q^{10} +1.45988 q^{11} -6.81557 q^{13} +8.96194 q^{14} +5.14371 q^{16} +6.52816 q^{17} +5.05632 q^{19} -4.18492 q^{20} +3.63066 q^{22} +1.84167 q^{23} +1.00000 q^{25} -16.9500 q^{26} +15.0807 q^{28} -1.16266 q^{29} +0.155661 q^{31} +1.92457 q^{32} +16.2352 q^{34} -3.60359 q^{35} -1.90562 q^{37} +12.5748 q^{38} -5.43378 q^{40} +0.185392 q^{41} -1.00000 q^{43} +6.10949 q^{44} +4.58015 q^{46} -0.604062 q^{47} +5.98585 q^{49} +2.48695 q^{50} -28.5226 q^{52} +1.47184 q^{53} -1.45988 q^{55} +19.5811 q^{56} -2.89147 q^{58} -2.94683 q^{59} -11.6311 q^{61} +0.387121 q^{62} -5.50110 q^{64} +6.81557 q^{65} +12.5823 q^{67} +27.3198 q^{68} -8.96194 q^{70} -1.84915 q^{71} -7.31667 q^{73} -4.73918 q^{74} +21.1603 q^{76} +5.26082 q^{77} +11.0683 q^{79} -5.14371 q^{80} +0.461060 q^{82} +5.13222 q^{83} -6.52816 q^{85} -2.48695 q^{86} +7.93269 q^{88} -9.81124 q^{89} -24.5605 q^{91} +7.70726 q^{92} -1.50227 q^{94} -5.05632 q^{95} -0.897999 q^{97} +14.8865 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 8 q^{4} - 5 q^{5} + 5 q^{7} - 3 q^{8}+O(q^{10}) \) 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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