LMFDB - Embedded newform 7803.2.a.ca.1.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7803,2,Mod(1,7803)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7803.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7803, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7803 = 3^{3} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7803.a (trivial)

Newform invariants

comment:select newform

sage:traces = [15,6,0,12,3,0,-3,18,0,0,-6,0,-3,-3,0,6,0,0,-3,-6,0,12,3,0,6, -24,0,-9,6,0,0,42,0,0,33,0,0,36,0,-15,0,0,-3,18,0,-12,24,0,18,42,0,-12, 48,0,-3,15,0,12,18,0,0,-63,0,30,-24,0,12,0,0,51,21,0,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(73)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$62.3072686972$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 6 x^{14} - 3 x^{13} + 76 x^{12} - 69 x^{11} - 354 x^{10} + 523 x^{9} + 720 x^{8} - 1437 x^{7} + \cdots - 51 $ x^15 - 6x^14 - 3x^13 + 76x^12 - 69x^11 - 354x^10 + 523x^9 + 720x^8 - 1437x^7 - 529x^6 + 1752x^5 - 111x^4 - 902x^3 + 258x^2 + 135x - 51
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$2.01902$ of defining polynomial
Character	$\chi$	$=$	7803.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+2.01902 q^{2} +2.07645 q^{4} -0.707464 q^{5} -4.62694 q^{7} +0.154349 q^{8} -1.42838 q^{10} +1.79601 q^{11} -0.836114 q^{13} -9.34190 q^{14} -3.84126 q^{16} +5.70342 q^{19} -1.46901 q^{20} +3.62619 q^{22} +2.03224 q^{23} -4.49949 q^{25} -1.68813 q^{26} -9.60761 q^{28} -3.20042 q^{29} +3.11899 q^{31} -8.06429 q^{32} +3.27340 q^{35} -5.94714 q^{37} +11.5153 q^{38} -0.109197 q^{40} -10.7502 q^{41} +4.96676 q^{43} +3.72933 q^{44} +4.10314 q^{46} +12.0304 q^{47} +14.4086 q^{49} -9.08458 q^{50} -1.73615 q^{52} +6.29645 q^{53} -1.27061 q^{55} -0.714165 q^{56} -6.46172 q^{58} +14.0008 q^{59} +12.5071 q^{61} +6.29732 q^{62} -8.59945 q^{64} +0.591521 q^{65} +2.58698 q^{67} +6.60906 q^{70} -5.37900 q^{71} +2.99116 q^{73} -12.0074 q^{74} +11.8429 q^{76} -8.31005 q^{77} +10.2295 q^{79} +2.71755 q^{80} -21.7048 q^{82} -9.16954 q^{83} +10.0280 q^{86} +0.277213 q^{88} +3.32288 q^{89} +3.86866 q^{91} +4.21984 q^{92} +24.2897 q^{94} -4.03497 q^{95} +10.6214 q^{97} +29.0913 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 6 q^{2} + 12 q^{4} + 3 q^{5} - 3 q^{7} + 18 q^{8} - 6 q^{11} - 3 q^{13} - 3 q^{14} + 6 q^{16} - 3 q^{19} - 6 q^{20} + 12 q^{22} + 3 q^{23} + 6 q^{25} - 24 q^{26} - 9 q^{28} + 6 q^{29} + 42 q^{32}+ \cdots + 15 q^{98}+O(q^{100}) $ 15 * q + 6 * q^2 + 12 * q^4 + 3 * q^5 - 3 * q^7 + 18 * q^8 - 6 * q^11 - 3 * q^13 - 3 * q^14 + 6 * q^16 - 3 * q^19 - 6 * q^20 + 12 * q^22 + 3 * q^23 + 6 * q^25 - 24 * q^26 - 9 * q^28 + 6 * q^29 + 42 * q^32 + 33 * q^35 + 36 * q^38 - 15 * q^40 - 3 * q^43 + 18 * q^44 - 12 * q^46 + 24 * q^47 + 18 * q^49 + 42 * q^50 - 12 * q^52 + 48 * q^53 - 3 * q^55 + 15 * q^56 + 12 * q^58 + 18 * q^59 - 63 * q^62 + 30 * q^64 - 24 * q^65 + 12 * q^67 + 51 * q^70 + 21 * q^71 + 18 * q^73 + 48 * q^74 + 60 * q^76 + 54 * q^77 + 39 * q^79 - 6 * q^80 - 39 * q^82 + 51 * q^83 + 48 * q^86 + 48 * q^88 + 36 * q^89 - 9 * q^91 + 3 * q^92 + 36 * q^94 - 39 * q^95 - 3 * q^97 + 15 * q^98

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 $

$2$	2.01902	1.42766	0.713832	−	0.700317i	$-0.246958\pi$
$2$	2.01902	1.42766	0.713832	+	0.700317i	$0.246958\pi$
$3$	0	0
$3$	0	0
$4$	2.07645	1.03822
$5$	−0.707464	−0.316388	−0.158194	−	0.987408i	$-0.550567\pi$
$5$	−0.707464	−0.316388	−0.158194	+	0.987408i	$0.550567\pi$
$6$	0	0
$7$	−4.62694	−1.74882	−0.874410	−	0.485187i	$-0.838751\pi$
$7$	−4.62694	−1.74882	−0.874410	+	0.485187i	$0.838751\pi$
$8$	0.154349	0.0545707
$9$	0	0
$10$	−1.42838	−0.451695
$11$	1.79601	0.541518	0.270759	−	0.962647i	$-0.412725\pi$
$11$	1.79601	0.541518	0.270759	+	0.962647i	$0.412725\pi$
$12$	0	0
$13$	−0.836114	−0.231896	−0.115948	−	0.993255i	$-0.536991\pi$
$13$	−0.836114	−0.231896	−0.115948	+	0.993255i	$0.536991\pi$
$14$	−9.34190	−2.49673
$15$	0	0
$16$	−3.84126	−0.960315
$17$	0	0
$17$	0	0
$18$	0	0
$19$	5.70342	1.30845	0.654227	−	0.756298i	$-0.272994\pi$
$19$	5.70342	1.30845	0.654227	+	0.756298i	$0.272994\pi$
$20$	−1.46901	−0.328481
$21$	0	0
$22$	3.62619	0.773106
$23$	2.03224	0.423751	0.211876	−	0.977297i	$-0.432043\pi$
$23$	2.03224	0.423751	0.211876	+	0.977297i	$0.432043\pi$
$24$	0	0
$25$	−4.49949	−0.899899
$26$	−1.68813	−0.331070
$27$	0	0
$28$	−9.60761	−1.81567
$29$	−3.20042	−0.594304	−0.297152	−	0.954830i	$-0.596037\pi$
$29$	−3.20042	−0.594304	−0.297152	+	0.954830i	$0.596037\pi$
$30$	0	0
$31$	3.11899	0.560188	0.280094	−	0.959973i	$-0.409634\pi$
$31$	3.11899	0.560188	0.280094	+	0.959973i	$0.409634\pi$
$32$	−8.06429	−1.42558
$33$	0	0
$34$	0	0
$35$	3.27340	0.553305
$36$	0	0
$37$	−5.94714	−0.977704	−0.488852	−	0.872367i	$-0.662584\pi$
$37$	−5.94714	−0.977704	−0.488852	+	0.872367i	$0.662584\pi$
$38$	11.5153	1.86803
$39$	0	0
$40$	−0.109197	−0.0172655
$41$	−10.7502	−1.67889	−0.839446	−	0.543443i	$-0.817120\pi$
$41$	−10.7502	−1.67889	−0.839446	+	0.543443i	$0.817120\pi$
$42$	0	0
$43$	4.96676	0.757424	0.378712	−	0.925514i	$-0.376367\pi$
$43$	4.96676	0.757424	0.378712	+	0.925514i	$0.376367\pi$
$44$	3.72933	0.562217
$45$	0	0
$46$	4.10314	0.604974
$47$	12.0304	1.75482	0.877409	−	0.479743i	$-0.159270\pi$
$47$	12.0304	1.75482	0.877409	+	0.479743i	$0.159270\pi$
$48$	0	0
$49$	14.4086	2.05837
$50$	−9.08458	−1.28475
$51$	0	0
$52$	−1.73615	−0.240760
$53$	6.29645	0.864884	0.432442	−	0.901662i	$-0.357652\pi$
$53$	6.29645	0.864884	0.432442	+	0.901662i	$0.357652\pi$
$54$	0	0
$55$	−1.27061	−0.171330
$56$	−0.714165	−0.0954344
$57$	0	0
$58$	−6.46172	−0.848466
$59$	14.0008	1.82274	0.911372	−	0.411584i	$-0.135024\pi$
$59$	14.0008	1.82274	0.911372	+	0.411584i	$0.135024\pi$
$60$	0	0
$61$	12.5071	1.60136	0.800682	−	0.599089i	$-0.204470\pi$
$61$	12.5071	1.60136	0.800682	+	0.599089i	$0.204470\pi$
$62$	6.29732	0.799760
$63$	0	0
$64$	−8.59945	−1.07493
$65$	0.591521	0.0733691
$66$	0	0
$67$	2.58698	0.316050	0.158025	−	0.987435i	$-0.449487\pi$
$67$	2.58698	0.316050	0.158025	+	0.987435i	$0.449487\pi$
$68$	0	0
$69$	0	0
$70$	6.60906	0.789933
$71$	−5.37900	−0.638370	−0.319185	−	0.947692i	$-0.603409\pi$
$71$	−5.37900	−0.638370	−0.319185	+	0.947692i	$0.603409\pi$
$72$	0	0
$73$	2.99116	0.350089	0.175044	−	0.984561i	$-0.443993\pi$
$73$	2.99116	0.350089	0.175044	+	0.984561i	$0.443993\pi$
$74$	−12.0074	−1.39583
$75$	0	0
$76$	11.8429	1.35847
$77$	−8.31005	−0.947019
$78$	0	0
$79$	10.2295	1.15091	0.575453	−	0.817835i	$-0.304826\pi$
$79$	10.2295	1.15091	0.575453	+	0.817835i	$0.304826\pi$
$80$	2.71755	0.303832
$81$	0	0
$82$	−21.7048	−2.39689
$83$	−9.16954	−1.00649	−0.503244	−	0.864145i	$-0.667860\pi$
$83$	−9.16954	−1.00649	−0.503244	+	0.864145i	$0.667860\pi$
$84$	0	0
$85$	0	0
$86$	10.0280	1.08135
$87$	0	0
$88$	0.277213	0.0295510
$89$	3.32288	0.352225	0.176112	−	0.984370i	$-0.443648\pi$
$89$	3.32288	0.352225	0.176112	+	0.984370i	$0.443648\pi$
$90$	0	0
$91$	3.86866	0.405545
$92$	4.21984	0.439949
$93$	0	0
$94$	24.2897	2.50529
$95$	−4.03497	−0.413979
$96$	0	0
$97$	10.6214	1.07844	0.539218	−	0.842166i	$-0.318720\pi$
$97$	10.6214	1.07844	0.539218	+	0.842166i	$0.318720\pi$
$98$	29.0913	2.93867
$99$	0	0
$100$	−9.34296	−0.934296
$101$	18.6725	1.85799	0.928993	−	0.370098i	$-0.120676\pi$
$101$	18.6725	1.85799	0.928993	+	0.370098i	$0.120676\pi$
$102$	0	0
$103$	5.48731	0.540680	0.270340	−	0.962765i	$-0.412864\pi$
$103$	5.48731	0.540680	0.270340	+	0.962765i	$0.412864\pi$
$104$	−0.129054	−0.0126548
$105$	0	0
$106$	12.7127	1.23476
$107$	−9.79042	−0.946476	−0.473238	−	0.880935i	$-0.656915\pi$
$107$	−9.79042	−0.946476	−0.473238	+	0.880935i	$0.656915\pi$
$108$	0	0
$109$	−2.33350	−0.223509	−0.111755	−	0.993736i	$-0.535647\pi$
$109$	−2.33350	−0.223509	−0.111755	+	0.993736i	$0.535647\pi$
$110$	−2.56540	−0.244601
$111$	0	0
$112$	17.7733	1.67942
$113$	−6.17484	−0.580880	−0.290440	−	0.956893i	$-0.593802\pi$
$113$	−6.17484	−0.580880	−0.290440	+	0.956893i	$0.593802\pi$
$114$	0	0
$115$	−1.43774	−0.134070
$116$	−6.64551	−0.617020
$117$	0	0
$118$	28.2678	2.60226
$119$	0	0
$120$	0	0
$121$	−7.77434	−0.706758
$122$	25.2520	2.28621
$123$	0	0
$124$	6.47643	0.581600
$125$	6.72055	0.601104
$126$	0	0
$127$	−13.1806	−1.16959	−0.584795	−	0.811181i	$-0.698825\pi$
$127$	−13.1806	−1.16959	−0.584795	+	0.811181i	$0.698825\pi$
$128$	−1.23389	−0.109062
$129$	0	0
$130$	1.19429	0.104746
$131$	−12.1634	−1.06272	−0.531360	−	0.847146i	$-0.678319\pi$
$131$	−12.1634	−1.06272	−0.531360	+	0.847146i	$0.678319\pi$
$132$	0	0
$133$	−26.3894	−2.28825
$134$	5.22316	0.451212
$135$	0	0
$136$	0	0
$137$	19.1327	1.63462	0.817309	−	0.576200i	$-0.195465\pi$
$137$	19.1327	1.63462	0.817309	+	0.576200i	$0.195465\pi$
$138$	0	0
$139$	10.7175	0.909048	0.454524	−	0.890735i	$-0.349809\pi$
$139$	10.7175	0.909048	0.454524	+	0.890735i	$0.349809\pi$
$140$	6.79704	0.574454
$141$	0	0
$142$	−10.8603	−0.911377
$143$	−1.50167	−0.125576
$144$	0	0
$145$	2.26418	0.188030
$146$	6.03922	0.499809
$147$	0	0
$148$	−12.3489	−1.01508
$149$	−14.1781	−1.16151	−0.580757	−	0.814077i	$-0.697243\pi$
$149$	−14.1781	−1.16151	−0.580757	+	0.814077i	$0.697243\pi$
$150$	0	0
$151$	10.1345	0.824733	0.412367	−	0.911018i	$-0.364702\pi$
$151$	10.1345	0.824733	0.412367	+	0.911018i	$0.364702\pi$
$152$	0.880319	0.0714033
$153$	0	0
$154$	−16.7782	−1.35202
$155$	−2.20658	−0.177236
$156$	0	0
$157$	−7.24708	−0.578380	−0.289190	−	0.957272i	$-0.593386\pi$
$157$	−7.24708	−0.578380	−0.289190	+	0.957272i	$0.593386\pi$
$158$	20.6535	1.64311
$159$	0	0
$160$	5.70519	0.451035
$161$	−9.40306	−0.741065
$162$	0	0
$163$	25.1848	1.97263	0.986313	−	0.164884i	$-0.0527250\pi$
$163$	25.1848	1.97263	0.986313	+	0.164884i	$0.0527250\pi$
$164$	−22.3221	−1.74307
$165$	0	0
$166$	−18.5135	−1.43693
$167$	−5.38433	−0.416652	−0.208326	−	0.978059i	$-0.566801\pi$
$167$	−5.38433	−0.416652	−0.208326	+	0.978059i	$0.566801\pi$
$168$	0	0
$169$	−12.3009	−0.946224
$170$	0	0
$171$	0	0
$172$	10.3132	0.786376
$173$	6.99021	0.531456	0.265728	−	0.964048i	$-0.414388\pi$
$173$	6.99021	0.531456	0.265728	+	0.964048i	$0.414388\pi$
$174$	0	0
$175$	20.8189	1.57376
$176$	−6.89896	−0.520028
$177$	0	0
$178$	6.70897	0.502858
$179$	−13.9188	−1.04034	−0.520168	−	0.854064i	$-0.674131\pi$
$179$	−13.9188	−1.04034	−0.520168	+	0.854064i	$0.674131\pi$
$180$	0	0
$181$	−9.81987	−0.729905	−0.364953	−	0.931026i	$-0.618915\pi$
$181$	−9.81987	−0.729905	−0.364953	+	0.931026i	$0.618915\pi$
$182$	7.81090	0.578982
$183$	0	0
$184$	0.313675	0.0231244
$185$	4.20739	0.309333
$186$	0	0
$187$	0	0
$188$	24.9805	1.82189
$189$	0	0
$190$	−8.14668	−0.591022
$191$	2.14803	0.155426	0.0777131	−	0.996976i	$-0.475238\pi$
$191$	2.14803	0.155426	0.0777131	+	0.996976i	$0.475238\pi$
$192$	0	0
$193$	−0.0412451	−0.00296889	−0.00148444	−	0.999999i	$-0.500473\pi$
$193$	−0.0412451	−0.00296889	−0.00148444	+	0.999999i	$0.500473\pi$
$194$	21.4447	1.53964
$195$	0	0
$196$	29.9187	2.13705
$197$	26.1372	1.86220	0.931099	−	0.364767i	$-0.118851\pi$
$197$	26.1372	1.86220	0.931099	+	0.364767i	$0.118851\pi$
$198$	0	0
$199$	17.1302	1.21433	0.607163	−	0.794577i	$-0.292307\pi$
$199$	17.1302	1.21433	0.607163	+	0.794577i	$0.292307\pi$
$200$	−0.694494	−0.0491081
$201$	0	0
$202$	37.7002	2.65258
$203$	14.8082	1.03933
$204$	0	0
$205$	7.60535	0.531181
$206$	11.0790	0.771910
$207$	0	0
$208$	3.21173	0.222694
$209$	10.2434	0.708552
$210$	0	0
$211$	−7.09038	−0.488122	−0.244061	−	0.969760i	$-0.578480\pi$
$211$	−7.09038	−0.488122	−0.244061	+	0.969760i	$0.578480\pi$
$212$	13.0742	0.897943
$213$	0	0
$214$	−19.7671	−1.35125
$215$	−3.51381	−0.239640
$216$	0	0
$217$	−14.4314	−0.979668
$218$	−4.71139	−0.319096
$219$	0	0
$220$	−2.63836	−0.177879
$221$	0	0
$222$	0	0
$223$	21.8855	1.46556	0.732781	−	0.680465i	$-0.238222\pi$
$223$	21.8855	1.46556	0.732781	+	0.680465i	$0.238222\pi$
$224$	37.3130	2.49308
$225$	0	0
$226$	−12.4671	−0.829301
$227$	19.1300	1.26970	0.634850	−	0.772635i	$-0.281062\pi$
$227$	19.1300	1.26970	0.634850	+	0.772635i	$0.281062\pi$
$228$	0	0
$229$	−17.0884	−1.12923	−0.564616	−	0.825354i	$-0.690976\pi$
$229$	−17.0884	−1.12923	−0.564616	+	0.825354i	$0.690976\pi$
$230$	−2.90282	−0.191406
$231$	0	0
$232$	−0.493983	−0.0324316
$233$	19.9326	1.30583	0.652915	−	0.757431i	$-0.273546\pi$
$233$	19.9326	1.30583	0.652915	+	0.757431i	$0.273546\pi$
$234$	0	0
$235$	−8.51109	−0.555202
$236$	29.0718	1.89242
$237$	0	0
$238$	0	0
$239$	−0.546129	−0.0353261	−0.0176631	−	0.999844i	$-0.505623\pi$
$239$	−0.546129	−0.0353261	−0.0176631	+	0.999844i	$0.505623\pi$
$240$	0	0
$241$	−18.8594	−1.21484	−0.607421	−	0.794380i	$-0.707796\pi$
$241$	−18.8594	−1.21484	−0.607421	+	0.794380i	$0.707796\pi$
$242$	−15.6966	−1.00901
$243$	0	0
$244$	25.9703	1.66258
$245$	−10.1936	−0.651244
$246$	0	0
$247$	−4.76871	−0.303426
$248$	0.481414	0.0305698
$249$	0	0
$250$	13.5689	0.858175
$251$	4.22900	0.266932	0.133466	−	0.991053i	$-0.457389\pi$
$251$	4.22900	0.266932	0.133466	+	0.991053i	$0.457389\pi$
$252$	0	0
$253$	3.64993	0.229469
$254$	−26.6119	−1.66978
$255$	0	0
$256$	14.7076	0.919227
$257$	−15.2767	−0.952933	−0.476467	−	0.879193i	$-0.658083\pi$
$257$	−15.2767	−0.952933	−0.476467	+	0.879193i	$0.658083\pi$
$258$	0	0
$259$	27.5171	1.70983
$260$	1.22826	0.0761736
$261$	0	0
$262$	−24.5581	−1.51721
$263$	31.0995	1.91768	0.958838	−	0.283953i	$-0.0916461\pi$
$263$	31.0995	1.91768	0.958838	+	0.283953i	$0.0916461\pi$
$264$	0	0
$265$	−4.45451	−0.273638
$266$	−53.2808	−3.26685
$267$	0	0
$268$	5.37172	0.328130
$269$	16.1906	0.987157	0.493578	−	0.869701i	$-0.335689\pi$
$269$	16.1906	0.987157	0.493578	+	0.869701i	$0.335689\pi$
$270$	0	0
$271$	−0.190222	−0.0115552	−0.00577759	−	0.999983i	$-0.501839\pi$
$271$	−0.190222	−0.0115552	−0.00577759	+	0.999983i	$0.501839\pi$
$272$	0	0
$273$	0	0
$274$	38.6293	2.33368
$275$	−8.08115	−0.487312
$276$	0	0
$277$	15.3476	0.922150	0.461075	−	0.887361i	$-0.347464\pi$
$277$	15.3476	0.922150	0.461075	+	0.887361i	$0.347464\pi$
$278$	21.6389	1.29781
$279$	0	0
$280$	0.505246	0.0301942
$281$	−9.65856	−0.576181	−0.288091	−	0.957603i	$-0.593020\pi$
$281$	−9.65856	−0.576181	−0.288091	+	0.957603i	$0.593020\pi$
$282$	0	0
$283$	−15.6189	−0.928447	−0.464224	−	0.885718i	$-0.653667\pi$
$283$	−15.6189	−0.928447	−0.464224	+	0.885718i	$0.653667\pi$
$284$	−11.1692	−0.662771
$285$	0	0
$286$	−3.03191	−0.179281
$287$	49.7404	2.93608
$288$	0	0
$289$	0	0
$290$	4.57144	0.268444
$291$	0	0
$292$	6.21099	0.363471
$293$	21.5424	1.25852	0.629260	−	0.777195i	$-0.283358\pi$
$293$	21.5424	1.25852	0.629260	+	0.777195i	$0.283358\pi$
$294$	0	0
$295$	−9.90503	−0.576693
$296$	−0.917937	−0.0533540
$297$	0	0
$298$	−28.6259	−1.65825
$299$	−1.69919	−0.0982664
$300$	0	0
$301$	−22.9809	−1.32460
$302$	20.4618	1.17744
$303$	0	0
$304$	−21.9083	−1.25653
$305$	−8.84829	−0.506652
$306$	0	0
$307$	13.6192	0.777289	0.388645	−	0.921388i	$-0.372943\pi$
$307$	13.6192	0.777289	0.388645	+	0.921388i	$0.372943\pi$
$308$	−17.2554	−0.983217
$309$	0	0
$310$	−4.45512	−0.253034
$311$	−0.570591	−0.0323552	−0.0161776	−	0.999869i	$-0.505150\pi$
$311$	−0.570591	−0.0323552	−0.0161776	+	0.999869i	$0.505150\pi$
$312$	0	0
$313$	−22.1153	−1.25003	−0.625015	−	0.780612i	$-0.714907\pi$
$313$	−22.1153	−1.25003	−0.625015	+	0.780612i	$0.714907\pi$
$314$	−14.6320	−0.825732
$315$	0	0
$316$	21.2410	1.19490
$317$	−4.38226	−0.246132	−0.123066	−	0.992398i	$-0.539273\pi$
$317$	−4.38226	−0.246132	−0.123066	+	0.992398i	$0.539273\pi$
$318$	0	0
$319$	−5.74800	−0.321826
$320$	6.08380	0.340095
$321$	0	0
$322$	−18.9850	−1.05799
$323$	0	0
$324$	0	0
$325$	3.76209	0.208683
$326$	50.8487	2.81625
$327$	0	0
$328$	−1.65928	−0.0916183
$329$	−55.6641	−3.06886
$330$	0	0
$331$	−13.5453	−0.744516	−0.372258	−	0.928129i	$-0.621416\pi$
$331$	−13.5453	−0.744516	−0.372258	+	0.928129i	$0.621416\pi$
$332$	−19.0401	−1.04496
$333$	0	0
$334$	−10.8711	−0.594839
$335$	−1.83019	−0.0999941
$336$	0	0
$337$	18.9459	1.03205	0.516024	−	0.856574i	$-0.327412\pi$
$337$	18.9459	1.03205	0.516024	+	0.856574i	$0.327412\pi$
$338$	−24.8358	−1.35089
$339$	0	0
$340$	0	0
$341$	5.60176	0.303352
$342$	0	0
$343$	−34.2792	−1.85091
$344$	0.766616	0.0413332
$345$	0	0
$346$	14.1134	0.758740
$347$	22.7527	1.22143	0.610714	−	0.791852i	$-0.290883\pi$
$347$	22.7527	1.22143	0.610714	+	0.791852i	$0.290883\pi$
$348$	0	0
$349$	10.7432	0.575068	0.287534	−	0.957770i	$-0.407165\pi$
$349$	10.7432	0.575068	0.287534	+	0.957770i	$0.407165\pi$
$350$	42.0338	2.24680
$351$	0	0
$352$	−14.4836	−0.771977
$353$	−23.4054	−1.24575	−0.622873	−	0.782323i	$-0.714035\pi$
$353$	−23.4054	−1.24575	−0.622873	+	0.782323i	$0.714035\pi$
$354$	0	0
$355$	3.80545	0.201972
$356$	6.89979	0.365688
$357$	0	0
$358$	−28.1023	−1.48525
$359$	−30.2112	−1.59449	−0.797243	−	0.603659i	$-0.793709\pi$
$359$	−30.2112	−1.59449	−0.797243	+	0.603659i	$0.793709\pi$
$360$	0	0
$361$	13.5290	0.712053
$362$	−19.8265	−1.04206
$363$	0	0
$364$	8.03306	0.421047
$365$	−2.11614	−0.110764
$366$	0	0
$367$	−12.6255	−0.659048	−0.329524	−	0.944147i	$-0.606888\pi$
$367$	−12.6255	−0.659048	−0.329524	+	0.944147i	$0.606888\pi$
$368$	−7.80636	−0.406935
$369$	0	0
$370$	8.49481	0.441624
$371$	−29.1333	−1.51253
$372$	0	0
$373$	12.8657	0.666160	0.333080	−	0.942899i	$-0.391912\pi$
$373$	12.8657	0.666160	0.333080	+	0.942899i	$0.391912\pi$
$374$	0	0
$375$	0	0
$376$	1.85689	0.0957616
$377$	2.67592	0.137817
$378$	0	0
$379$	21.8112	1.12037	0.560184	−	0.828368i	$-0.310731\pi$
$379$	21.8112	1.12037	0.560184	+	0.828368i	$0.310731\pi$
$380$	−8.37839	−0.429803
$381$	0	0
$382$	4.33693	0.221896
$383$	12.1588	0.621284	0.310642	−	0.950527i	$-0.399456\pi$
$383$	12.1588	0.621284	0.310642	+	0.950527i	$0.399456\pi$
$384$	0	0
$385$	5.87906	0.299625
$386$	−0.0832747	−0.00423857
$387$	0	0
$388$	22.0547	1.11966
$389$	−13.2604	−0.672327	−0.336164	−	0.941804i	$-0.609130\pi$
$389$	−13.2604	−0.672327	−0.336164	+	0.941804i	$0.609130\pi$
$390$	0	0
$391$	0	0
$392$	2.22396	0.112327
$393$	0	0
$394$	52.7715	2.65859
$395$	−7.23698	−0.364132
$396$	0	0
$397$	−25.3045	−1.27000	−0.634998	−	0.772514i	$-0.718999\pi$
$397$	−25.3045	−1.27000	−0.634998	+	0.772514i	$0.718999\pi$
$398$	34.5862	1.73365
$399$	0	0
$400$	17.2837	0.864187
$401$	−19.1195	−0.954782	−0.477391	−	0.878691i	$-0.658418\pi$
$401$	−19.1195	−0.954782	−0.477391	+	0.878691i	$0.658418\pi$
$402$	0	0
$403$	−2.60784	−0.129906
$404$	38.7725	1.92900
$405$	0	0
$406$	29.8980	1.48381
$407$	−10.6811	−0.529445
$408$	0	0
$409$	3.23164	0.159794	0.0798971	−	0.996803i	$-0.474541\pi$
$409$	3.23164	0.159794	0.0798971	+	0.996803i	$0.474541\pi$
$410$	15.3554	0.758347
$411$	0	0
$412$	11.3941	0.561347
$413$	−64.7807	−3.18765
$414$	0	0
$415$	6.48712	0.318440
$416$	6.74267	0.330586
$417$	0	0
$418$	20.6817	1.01157
$419$	−29.8593	−1.45872	−0.729360	−	0.684130i	$-0.760182\pi$
$419$	−29.8593	−1.45872	−0.729360	+	0.684130i	$0.760182\pi$
$420$	0	0
$421$	−20.2363	−0.986255	−0.493127	−	0.869957i	$-0.664146\pi$
$421$	−20.2363	−0.986255	−0.493127	+	0.869957i	$0.664146\pi$
$422$	−14.3156	−0.696874
$423$	0	0
$424$	0.971852	0.0471973
$425$	0	0
$426$	0	0
$427$	−57.8695	−2.80050
$428$	−20.3293	−0.982654
$429$	0	0
$430$	−7.09445	−0.342125
$431$	23.7095	1.14205	0.571024	−	0.820933i	$-0.306546\pi$
$431$	23.7095	1.14205	0.571024	+	0.820933i	$0.306546\pi$
$432$	0	0
$433$	33.1115	1.59124	0.795619	−	0.605797i	$-0.207146\pi$
$433$	33.1115	1.59124	0.795619	+	0.605797i	$0.207146\pi$
$434$	−29.1373	−1.39864
$435$	0	0
$436$	−4.84540	−0.232052
$437$	11.5907	0.554459
$438$	0	0
$439$	−19.9929	−0.954207	−0.477104	−	0.878847i	$-0.658313\pi$
$439$	−19.9929	−0.954207	−0.477104	+	0.878847i	$0.658313\pi$
$440$	−0.196118	−0.00934958
$441$	0	0
$442$	0	0
$443$	14.2792	0.678425	0.339213	−	0.940710i	$-0.389839\pi$
$443$	14.2792	0.678425	0.339213	+	0.940710i	$0.389839\pi$
$444$	0	0
$445$	−2.35082	−0.111439
$446$	44.1873	2.09233
$447$	0	0
$448$	39.7892	1.87986
$449$	29.5108	1.39270	0.696349	−	0.717703i	$-0.254806\pi$
$449$	29.5108	1.39270	0.696349	+	0.717703i	$0.254806\pi$
$450$	0	0
$451$	−19.3074	−0.909151
$452$	−12.8217	−0.603083
$453$	0	0
$454$	38.6238	1.81271
$455$	−2.73693	−0.128309
$456$	0	0
$457$	−16.3770	−0.766085	−0.383042	−	0.923731i	$-0.625124\pi$
$457$	−16.3770	−0.766085	−0.383042	+	0.923731i	$0.625124\pi$
$458$	−34.5018	−1.61216
$459$	0	0
$460$	−2.98538	−0.139194
$461$	−3.30178	−0.153779	−0.0768897	−	0.997040i	$-0.524499\pi$
$461$	−3.30178	−0.153779	−0.0768897	+	0.997040i	$0.524499\pi$
$462$	0	0
$463$	−23.1054	−1.07380	−0.536899	−	0.843646i	$-0.680405\pi$
$463$	−23.1054	−1.07380	−0.536899	+	0.843646i	$0.680405\pi$
$464$	12.2937	0.570719
$465$	0	0
$466$	40.2444	1.86429
$467$	−39.5702	−1.83109	−0.915545	−	0.402216i	$-0.868240\pi$
$467$	−39.5702	−1.83109	−0.915545	+	0.402216i	$0.868240\pi$
$468$	0	0
$469$	−11.9698	−0.552714
$470$	−17.1841	−0.792642
$471$	0	0
$472$	2.16101	0.0994684
$473$	8.92037	0.410159
$474$	0	0
$475$	−25.6625	−1.17748
$476$	0	0
$477$	0	0
$478$	−1.10265	−0.0504339
$479$	−34.0854	−1.55740	−0.778701	−	0.627396i	$-0.784121\pi$
$479$	−34.0854	−1.55740	−0.778701	+	0.627396i	$0.784121\pi$
$480$	0	0
$481$	4.97249	0.226726
$482$	−38.0776	−1.73439
$483$	0	0
$484$	−16.1430	−0.733773
$485$	−7.51423	−0.341203
$486$	0	0
$487$	40.2231	1.82268	0.911341	−	0.411653i	$-0.135049\pi$
$487$	40.2231	1.82268	0.911341	+	0.411653i	$0.135049\pi$
$488$	1.93046	0.0873876
$489$	0	0
$490$	−20.5810	−0.929757
$491$	21.1648	0.955156	0.477578	−	0.878589i	$-0.341515\pi$
$491$	21.1648	0.955156	0.477578	+	0.878589i	$0.341515\pi$
$492$	0	0
$493$	0	0
$494$	−9.62813	−0.433190
$495$	0	0
$496$	−11.9809	−0.537957
$497$	24.8883	1.11639
$498$	0	0
$499$	−24.1391	−1.08061	−0.540307	−	0.841468i	$-0.681692\pi$
$499$	−24.1391	−1.08061	−0.540307	+	0.841468i	$0.681692\pi$
$500$	13.9549	0.624081
$501$	0	0
$502$	8.53845	0.381089
$503$	19.4903	0.869028	0.434514	−	0.900665i	$-0.356920\pi$
$503$	19.4903	0.869028	0.434514	+	0.900665i	$0.356920\pi$
$504$	0	0
$505$	−13.2101	−0.587843
$506$	7.36929	0.327605
$507$	0	0
$508$	−27.3688	−1.21430
$509$	11.2605	0.499111	0.249555	−	0.968361i	$-0.419716\pi$
$509$	11.2605	0.499111	0.249555	+	0.968361i	$0.419716\pi$
$510$	0	0
$511$	−13.8399	−0.612243
$512$	32.1628	1.42141
$513$	0	0
$514$	−30.8439	−1.36047
$515$	−3.88207	−0.171065
$516$	0	0
$517$	21.6068	0.950266
$518$	55.5576	2.44106
$519$	0	0
$520$	0.0913008	0.00400381
$521$	25.7599	1.12856	0.564280	−	0.825583i	$-0.309154\pi$
$521$	25.7599	1.12856	0.564280	+	0.825583i	$0.309154\pi$
$522$	0	0
$523$	−16.3630	−0.715505	−0.357752	−	0.933816i	$-0.616457\pi$
$523$	−16.3630	−0.715505	−0.357752	+	0.933816i	$0.616457\pi$
$524$	−25.2566	−1.10334
$525$	0	0
$526$	62.7905	2.73780
$527$	0	0
$528$	0	0
$529$	−18.8700	−0.820435
$530$	−8.99375	−0.390664
$531$	0	0
$532$	−54.7962	−2.37572
$533$	8.98836	0.389329
$534$	0	0
$535$	6.92637	0.299453
$536$	0.399298	0.0172470
$537$	0	0
$538$	32.6891	1.40933
$539$	25.8781	1.11465
$540$	0	0
$541$	0.0654823	0.00281530	0.00140765	−	0.999999i	$-0.499552\pi$
$541$	0.0654823	0.00281530	0.00140765	+	0.999999i	$0.499552\pi$
$542$	−0.384063	−0.0164969
$543$	0	0
$544$	0	0
$545$	1.65087	0.0707155
$546$	0	0
$547$	9.71350	0.415319	0.207660	−	0.978201i	$-0.433415\pi$
$547$	9.71350	0.415319	0.207660	+	0.978201i	$0.433415\pi$
$548$	39.7281	1.69710
$549$	0	0
$550$	−16.3160	−0.695717
$551$	−18.2534	−0.777620
$552$	0	0
$553$	−47.3312	−2.01273
$554$	30.9872	1.31652
$555$	0	0
$556$	22.2544	0.943795
$557$	19.1479	0.811322	0.405661	−	0.914024i	$-0.367041\pi$
$557$	19.1479	0.811322	0.405661	+	0.914024i	$0.367041\pi$
$558$	0	0
$559$	−4.15278	−0.175644
$560$	−12.5740	−0.531347
$561$	0	0
$562$	−19.5008	−0.822593
$563$	−5.67364	−0.239115	−0.119558	−	0.992827i	$-0.538148\pi$
$563$	−5.67364	−0.239115	−0.119558	+	0.992827i	$0.538148\pi$
$564$	0	0
$565$	4.36847	0.183783
$566$	−31.5349	−1.32551
$567$	0	0
$568$	−0.830244	−0.0348363
$569$	−6.32590	−0.265195	−0.132598	−	0.991170i	$-0.542332\pi$
$569$	−6.32590	−0.265195	−0.132598	+	0.991170i	$0.542332\pi$
$570$	0	0
$571$	−29.3754	−1.22932	−0.614661	−	0.788791i	$-0.710707\pi$
$571$	−29.3754	−1.22932	−0.614661	+	0.788791i	$0.710707\pi$
$572$	−3.11814	−0.130376
$573$	0	0
$574$	100.427	4.19174
$575$	−9.14405	−0.381333
$576$	0	0
$577$	14.0393	0.584465	0.292233	−	0.956347i	$-0.405602\pi$
$577$	14.0393	0.584465	0.292233	+	0.956347i	$0.405602\pi$
$578$	0	0
$579$	0	0
$580$	4.70146	0.195218
$581$	42.4269	1.76017
$582$	0	0
$583$	11.3085	0.468351
$584$	0.461684	0.0191046
$585$	0	0
$586$	43.4946	1.79674
$587$	−0.612807	−0.0252932	−0.0126466	−	0.999920i	$-0.504026\pi$
$587$	−0.612807	−0.0252932	−0.0126466	+	0.999920i	$0.504026\pi$
$588$	0	0
$589$	17.7889	0.732980
$590$	−19.9985	−0.823324
$591$	0	0
$592$	22.8445	0.938904
$593$	−14.3438	−0.589028	−0.294514	−	0.955647i	$-0.595158\pi$
$593$	−14.3438	−0.589028	−0.294514	+	0.955647i	$0.595158\pi$
$594$	0	0
$595$	0	0
$596$	−29.4401	−1.20591
$597$	0	0
$598$	−3.43069	−0.140291
$599$	35.6635	1.45717	0.728585	−	0.684955i	$-0.240178\pi$
$599$	35.6635	1.45717	0.728585	+	0.684955i	$0.240178\pi$
$600$	0	0
$601$	−32.7304	−1.33510	−0.667550	−	0.744565i	$-0.732657\pi$
$601$	−32.7304	−1.33510	−0.667550	+	0.744565i	$0.732657\pi$
$602$	−46.3990	−1.89108
$603$	0	0
$604$	21.0437	0.856258
$605$	5.50006	0.223609
$606$	0	0
$607$	7.90851	0.320997	0.160498	−	0.987036i	$-0.448690\pi$
$607$	7.90851	0.320997	0.160498	+	0.987036i	$0.448690\pi$
$608$	−45.9940	−1.86530
$609$	0	0
$610$	−17.8649	−0.723328
$611$	−10.0588	−0.406936
$612$	0	0
$613$	29.6052	1.19574	0.597872	−	0.801592i	$-0.296013\pi$
$613$	29.6052	1.19574	0.597872	+	0.801592i	$0.296013\pi$
$614$	27.4975	1.10971
$615$	0	0
$616$	−1.28265	−0.0516795
$617$	−1.93021	−0.0777074	−0.0388537	−	0.999245i	$-0.512371\pi$
$617$	−1.93021	−0.0777074	−0.0388537	+	0.999245i	$0.512371\pi$
$618$	0	0
$619$	26.0074	1.04532	0.522662	−	0.852540i	$-0.324939\pi$
$619$	26.0074	1.04532	0.522662	+	0.852540i	$0.324939\pi$
$620$	−4.58184	−0.184011
$621$	0	0
$622$	−1.15204	−0.0461924
$623$	−15.3748	−0.615978
$624$	0	0
$625$	17.7429	0.709717
$626$	−44.6513	−1.78462
$627$	0	0
$628$	−15.0482	−0.600488
$629$	0	0
$630$	0	0
$631$	−34.5543	−1.37558	−0.687792	−	0.725908i	$-0.741420\pi$
$631$	−34.5543	−1.37558	−0.687792	+	0.725908i	$0.741420\pi$
$632$	1.57891	0.0628057
$633$	0	0
$634$	−8.84788	−0.351394
$635$	9.32480	0.370043
$636$	0	0
$637$	−12.0473	−0.477329
$638$	−11.6053	−0.459460
$639$	0	0
$640$	0.872934	0.0345058
$641$	32.4230	1.28063	0.640316	−	0.768111i	$-0.278803\pi$
$641$	32.4230	1.28063	0.640316	+	0.768111i	$0.278803\pi$
$642$	0	0
$643$	1.37140	0.0540827	0.0270413	−	0.999634i	$-0.491391\pi$
$643$	1.37140	0.0540827	0.0270413	+	0.999634i	$0.491391\pi$
$644$	−19.5250	−0.769391
$645$	0	0
$646$	0	0
$647$	−5.77601	−0.227078	−0.113539	−	0.993534i	$-0.536219\pi$
$647$	−5.77601	−0.227078	−0.113539	+	0.993534i	$0.536219\pi$
$648$	0	0
$649$	25.1455	0.987049
$650$	7.59575	0.297930
$651$	0	0
$652$	52.2949	2.04803
$653$	0.860592	0.0336776	0.0168388	−	0.999858i	$-0.494640\pi$
$653$	0.860592	0.0336776	0.0168388	+	0.999858i	$0.494640\pi$
$654$	0	0
$655$	8.60516	0.336231
$656$	41.2942	1.61227
$657$	0	0
$658$	−112.387	−4.38130
$659$	12.2049	0.475435	0.237718	−	0.971334i	$-0.423601\pi$
$659$	12.2049	0.475435	0.237718	+	0.971334i	$0.423601\pi$
$660$	0	0
$661$	−39.5790	−1.53944	−0.769722	−	0.638380i	$-0.779605\pi$
$661$	−39.5790	−1.53944	−0.769722	+	0.638380i	$0.779605\pi$
$662$	−27.3482	−1.06292
$663$	0	0
$664$	−1.41531	−0.0549247
$665$	18.6696	0.723974
$666$	0	0
$667$	−6.50403	−0.251837
$668$	−11.1803	−0.432578
$669$	0	0
$670$	−3.69520	−0.142758
$671$	22.4628	0.867169
$672$	0	0
$673$	0.737727	0.0284373	0.0142186	−	0.999899i	$-0.495474\pi$
$673$	0.737727	0.0284373	0.0142186	+	0.999899i	$0.495474\pi$
$674$	38.2521	1.47342
$675$	0	0
$676$	−25.5422	−0.982392
$677$	36.0059	1.38382	0.691910	−	0.721984i	$-0.256769\pi$
$677$	36.0059	1.38382	0.691910	+	0.721984i	$0.256769\pi$
$678$	0	0
$679$	−49.1444	−1.88599
$680$	0	0
$681$	0	0
$682$	11.3101	0.433085
$683$	−4.20984	−0.161085	−0.0805425	−	0.996751i	$-0.525665\pi$
$683$	−4.20984	−0.161085	−0.0805425	+	0.996751i	$0.525665\pi$
$684$	0	0
$685$	−13.5357	−0.517172
$686$	−69.2105	−2.64247
$687$	0	0
$688$	−19.0786	−0.727366
$689$	−5.26455	−0.200563
$690$	0	0
$691$	−20.9026	−0.795171	−0.397585	−	0.917565i	$-0.630152\pi$
$691$	−20.9026	−0.795171	−0.397585	+	0.917565i	$0.630152\pi$
$692$	14.5148	0.551770
$693$	0	0
$694$	45.9381	1.74379
$695$	−7.58225	−0.287611
$696$	0	0
$697$	0	0
$698$	21.6907	0.821003
$699$	0	0
$700$	43.2294	1.63392
$701$	1.69253	0.0639260	0.0319630	−	0.999489i	$-0.489824\pi$
$701$	1.69253	0.0639260	0.0319630	+	0.999489i	$0.489824\pi$
$702$	0	0
$703$	−33.9191	−1.27928
$704$	−15.4447	−0.582095
$705$	0	0
$706$	−47.2561	−1.77851
$707$	−86.3967	−3.24928
$708$	0	0
$709$	28.9497	1.08723	0.543614	−	0.839336i	$-0.317056\pi$
$709$	28.9497	1.08723	0.543614	+	0.839336i	$0.317056\pi$
$710$	7.68328	0.288348
$711$	0	0
$712$	0.512884	0.0192211
$713$	6.33854	0.237380
$714$	0	0
$715$	1.06238	0.0397307
$716$	−28.9016	−1.08010
$717$	0	0
$718$	−60.9970	−2.27639
$719$	12.7690	0.476204	0.238102	−	0.971240i	$-0.423475\pi$
$719$	12.7690	0.476204	0.238102	+	0.971240i	$0.423475\pi$
$720$	0	0
$721$	−25.3895	−0.945553
$722$	27.3154	1.01657
$723$	0	0
$724$	−20.3904	−0.757805
$725$	14.4003	0.534813
$726$	0	0
$727$	16.5039	0.612096	0.306048	−	0.952016i	$-0.400993\pi$
$727$	16.5039	0.612096	0.306048	+	0.952016i	$0.400993\pi$
$728$	0.597124	0.0221309
$729$	0	0
$730$	−4.27253	−0.158133
$731$	0	0
$732$	0	0
$733$	−11.1444	−0.411627	−0.205814	−	0.978591i	$-0.565984\pi$
$733$	−11.1444	−0.411627	−0.205814	+	0.978591i	$0.565984\pi$
$734$	−25.4913	−0.940899
$735$	0	0
$736$	−16.3886	−0.604090
$737$	4.64625	0.171147
$738$	0	0
$739$	−18.6191	−0.684913	−0.342456	−	0.939534i	$-0.611259\pi$
$739$	−18.6191	−0.684913	−0.342456	+	0.939534i	$0.611259\pi$
$740$	8.73642	0.321157
$741$	0	0
$742$	−58.8208	−2.15938
$743$	−3.29586	−0.120913	−0.0604566	−	0.998171i	$-0.519256\pi$
$743$	−3.29586	−0.120913	−0.0604566	+	0.998171i	$0.519256\pi$
$744$	0	0
$745$	10.0305	0.367489
$746$	25.9761	0.951052
$747$	0	0
$748$	0	0
$749$	45.2997	1.65522
$750$	0	0
$751$	−28.4579	−1.03844	−0.519222	−	0.854639i	$-0.673778\pi$
$751$	−28.4579	−1.03844	−0.519222	+	0.854639i	$0.673778\pi$
$752$	−46.2120	−1.68518
$753$	0	0
$754$	5.40274	0.196756
$755$	−7.16979	−0.260935
$756$	0	0
$757$	−33.9857	−1.23523	−0.617615	−	0.786480i	$-0.711901\pi$
$757$	−33.9857	−1.23523	−0.617615	+	0.786480i	$0.711901\pi$
$758$	44.0373	1.59951
$759$	0	0
$760$	−0.622794	−0.0225911
$761$	−18.8297	−0.682576	−0.341288	−	0.939959i	$-0.610863\pi$
$761$	−18.8297	−0.682576	−0.341288	+	0.939959i	$0.610863\pi$
$762$	0	0
$763$	10.7970	0.390877
$764$	4.46028	0.161367
$765$	0	0
$766$	24.5488	0.886984
$767$	−11.7062	−0.422688
$768$	0	0
$769$	13.8929	0.500990	0.250495	−	0.968118i	$-0.419407\pi$
$769$	13.8929	0.500990	0.250495	+	0.968118i	$0.419407\pi$
$770$	11.8700	0.427764
$771$	0	0
$772$	−0.0856433	−0.00308237
$773$	0.699415	0.0251562	0.0125781	−	0.999921i	$-0.495996\pi$
$773$	0.699415	0.0251562	0.0125781	+	0.999921i	$0.495996\pi$
$774$	0	0
$775$	−14.0339	−0.504113
$776$	1.63940	0.0588510
$777$	0	0
$778$	−26.7730	−0.959858
$779$	−61.3127	−2.19675
$780$	0	0
$781$	−9.66075	−0.345689
$782$	0	0
$783$	0	0
$784$	−55.3472	−1.97669
$785$	5.12705	0.182992
$786$	0	0
$787$	−31.7384	−1.13135	−0.565676	−	0.824628i	$-0.691385\pi$
$787$	−31.7384	−1.13135	−0.565676	+	0.824628i	$0.691385\pi$
$788$	54.2725	1.93338
$789$	0	0
$790$	−14.6116	−0.519858
$791$	28.5706	1.01585
$792$	0	0
$793$	−10.4573	−0.371351
$794$	−51.0903	−1.81313
$795$	0	0
$796$	35.5699	1.26074
$797$	−14.4932	−0.513374	−0.256687	−	0.966495i	$-0.582631\pi$
$797$	−14.4932	−0.513374	−0.256687	+	0.966495i	$0.582631\pi$
$798$	0	0
$799$	0	0
$800$	36.2852	1.28288
$801$	0	0
$802$	−38.6027	−1.36311
$803$	5.37217	0.189580
$804$	0	0
$805$	6.65233	0.234464
$806$	−5.26528	−0.185461
$807$	0	0
$808$	2.88209	0.101392
$809$	−12.3944	−0.435764	−0.217882	−	0.975975i	$-0.569915\pi$
$809$	−12.3944	−0.435764	−0.217882	+	0.975975i	$0.569915\pi$
$810$	0	0
$811$	−6.89310	−0.242049	−0.121025	−	0.992649i	$-0.538618\pi$
$811$	−6.89310	−0.242049	−0.121025	+	0.992649i	$0.538618\pi$
$812$	30.7484	1.07906
$813$	0	0
$814$	−21.5655	−0.755869
$815$	−17.8173	−0.624114
$816$	0	0
$817$	28.3275	0.991055
$818$	6.52475	0.228133
$819$	0	0
$820$	15.7921	0.551484
$821$	2.01308	0.0702570	0.0351285	−	0.999383i	$-0.488816\pi$
$821$	2.01308	0.0702570	0.0351285	+	0.999383i	$0.488816\pi$
$822$	0	0
$823$	−0.588567	−0.0205161	−0.0102581	−	0.999947i	$-0.503265\pi$
$823$	−0.588567	−0.0205161	−0.0102581	+	0.999947i	$0.503265\pi$
$824$	0.846962	0.0295053
$825$	0	0
$826$	−130.794	−4.55089
$827$	13.9282	0.484330	0.242165	−	0.970235i	$-0.422142\pi$
$827$	13.9282	0.484330	0.242165	+	0.970235i	$0.422142\pi$
$828$	0	0
$829$	−4.52363	−0.157112	−0.0785562	−	0.996910i	$-0.525031\pi$
$829$	−4.52363	−0.157112	−0.0785562	+	0.996910i	$0.525031\pi$
$830$	13.0976	0.454625
$831$	0	0
$832$	7.19012	0.249273
$833$	0	0
$834$	0	0
$835$	3.80922	0.131823
$836$	21.2699	0.735636
$837$	0	0
$838$	−60.2865	−2.08256
$839$	25.8744	0.893284	0.446642	−	0.894713i	$-0.352620\pi$
$839$	25.8744	0.893284	0.446642	+	0.894713i	$0.352620\pi$
$840$	0	0
$841$	−18.7573	−0.646803
$842$	−40.8574	−1.40804
$843$	0	0
$844$	−14.7228	−0.506780
$845$	8.70245	0.299373
$846$	0	0
$847$	35.9714	1.23599
$848$	−24.1863	−0.830561
$849$	0	0
$850$	0	0
$851$	−12.0860	−0.414303
$852$	0	0
$853$	−13.6688	−0.468012	−0.234006	−	0.972235i	$-0.575184\pi$
$853$	−13.6688	−0.468012	−0.234006	+	0.972235i	$0.575184\pi$
$854$	−116.840	−3.99817
$855$	0	0
$856$	−1.51114	−0.0516499
$857$	48.7835	1.66641	0.833207	−	0.552961i	$-0.186502\pi$
$857$	48.7835	1.66641	0.833207	+	0.552961i	$0.186502\pi$
$858$	0	0
$859$	−44.1426	−1.50612	−0.753062	−	0.657949i	$-0.771424\pi$
$859$	−44.1426	−1.50612	−0.753062	+	0.657949i	$0.771424\pi$
$860$	−7.29623	−0.248800
$861$	0	0
$862$	47.8700	1.63046
$863$	47.6997	1.62372	0.811858	−	0.583855i	$-0.198456\pi$
$863$	47.6997	1.62372	0.811858	+	0.583855i	$0.198456\pi$
$864$	0	0
$865$	−4.94532	−0.168146
$866$	66.8529	2.27175
$867$	0	0
$868$	−29.9661	−1.01711
$869$	18.3723	0.623237
$870$	0	0
$871$	−2.16301	−0.0732908
$872$	−0.360174	−0.0121970
$873$	0	0
$874$	23.4019	0.791582
$875$	−31.0956	−1.05122
$876$	0	0
$877$	−16.4688	−0.556111	−0.278056	−	0.960565i	$-0.589690\pi$
$877$	−16.4688	−0.556111	−0.278056	+	0.960565i	$0.589690\pi$
$878$	−40.3660	−1.36229
$879$	0	0
$880$	4.88076	0.164530
$881$	39.5566	1.33270	0.666348	−	0.745640i	$-0.267856\pi$
$881$	39.5566	1.33270	0.666348	+	0.745640i	$0.267856\pi$
$882$	0	0
$883$	−25.0310	−0.842360	−0.421180	−	0.906977i	$-0.638384\pi$
$883$	−25.0310	−0.842360	−0.421180	+	0.906977i	$0.638384\pi$
$884$	0	0
$885$	0	0
$886$	28.8300	0.968563
$887$	44.1968	1.48398	0.741992	−	0.670409i	$-0.233881\pi$
$887$	44.1968	1.48398	0.741992	+	0.670409i	$0.233881\pi$
$888$	0	0
$889$	60.9859	2.04540
$890$	−4.74635	−0.159098
$891$	0	0
$892$	45.4441	1.52158
$893$	68.6146	2.29610
$894$	0	0
$895$	9.84702	0.329150
$896$	5.70915	0.190729
$897$	0	0
$898$	59.5828	1.98831
$899$	−9.98210	−0.332922
$900$	0	0
$901$	0	0
$902$	−38.9821	−1.29796
$903$	0	0
$904$	−0.953081	−0.0316990
$905$	6.94720	0.230933
$906$	0	0
$907$	31.1826	1.03540	0.517700	−	0.855562i	$-0.326788\pi$
$907$	31.1826	1.03540	0.517700	+	0.855562i	$0.326788\pi$
$908$	39.7224	1.31823
$909$	0	0
$910$	−5.52593	−0.183183
$911$	−37.0795	−1.22850	−0.614249	−	0.789112i	$-0.710541\pi$
$911$	−37.0795	−1.22850	−0.614249	+	0.789112i	$0.710541\pi$
$912$	0	0
$913$	−16.4686	−0.545031
$914$	−33.0656	−1.09371
$915$	0	0
$916$	−35.4831	−1.17240
$917$	56.2793	1.85851
$918$	0	0
$919$	31.8291	1.04995	0.524973	−	0.851119i	$-0.324076\pi$
$919$	31.8291	1.04995	0.524973	+	0.851119i	$0.324076\pi$
$920$	−0.221914	−0.00731627
$921$	0	0
$922$	−6.66637	−0.219545
$923$	4.49746	0.148036
$924$	0	0
$925$	26.7591	0.879835
$926$	−46.6503	−1.53302
$927$	0	0
$928$	25.8091	0.847226
$929$	15.8917	0.521390	0.260695	−	0.965421i	$-0.416048\pi$
$929$	15.8917	0.521390	0.260695	+	0.965421i	$0.416048\pi$
$930$	0	0
$931$	82.1784	2.69329
$932$	41.3891	1.35574
$933$	0	0
$934$	−79.8931	−2.61418
$935$	0	0
$936$	0	0
$937$	16.2472	0.530773	0.265386	−	0.964142i	$-0.414501\pi$
$937$	16.2472	0.530773	0.265386	+	0.964142i	$0.414501\pi$
$938$	−24.1673	−0.789090
$939$	0	0
$940$	−17.6728	−0.576424
$941$	−3.98317	−0.129848	−0.0649238	−	0.997890i	$-0.520680\pi$
$941$	−3.98317	−0.129848	−0.0649238	+	0.997890i	$0.520680\pi$
$942$	0	0
$943$	−21.8469	−0.711433
$944$	−53.7806	−1.75041
$945$	0	0
$946$	18.0104	0.585569
$947$	−32.1167	−1.04365	−0.521825	−	0.853052i	$-0.674749\pi$
$947$	−32.1167	−1.04365	−0.521825	+	0.853052i	$0.674749\pi$
$948$	0	0
$949$	−2.50095	−0.0811844
$950$	−51.8132	−1.68104
$951$	0	0
$952$	0	0
$953$	35.5808	1.15258	0.576288	−	0.817246i	$-0.304501\pi$
$953$	35.5808	1.15258	0.576288	+	0.817246i	$0.304501\pi$
$954$	0	0
$955$	−1.51966	−0.0491749
$956$	−1.13401	−0.0366764
$957$	0	0
$958$	−68.8191	−2.22344
$959$	−88.5260	−2.85865
$960$	0	0
$961$	−21.2719	−0.686189
$962$	10.0396	0.323689
$963$	0	0
$964$	−39.1606	−1.26128
$965$	0.0291794	0.000939319 0
$966$	0	0
$967$	−49.6209	−1.59570	−0.797851	−	0.602855i	$-0.794030\pi$
$967$	−49.6209	−1.59570	−0.797851	+	0.602855i	$0.794030\pi$
$968$	−1.19996	−0.0385683
$969$	0	0
$970$	−15.1714	−0.487124
$971$	−5.02788	−0.161352	−0.0806762	−	0.996740i	$-0.525708\pi$
$971$	−5.02788	−0.161352	−0.0806762	+	0.996740i	$0.525708\pi$
$972$	0	0
$973$	−49.5893	−1.58976
$974$	81.2112	2.60218
$975$	0	0
$976$	−48.0429	−1.53782
$977$	26.6435	0.852401	0.426201	−	0.904629i	$-0.359852\pi$
$977$	26.6435	0.852401	0.426201	+	0.904629i	$0.359852\pi$
$978$	0	0
$979$	5.96794	0.190736
$980$	−21.1664	−0.676137
$981$	0	0
$982$	42.7323	1.36364
$983$	25.0411	0.798687	0.399343	−	0.916801i	$-0.369238\pi$
$983$	25.0411	0.798687	0.399343	+	0.916801i	$0.369238\pi$
$984$	0	0
$985$	−18.4911	−0.589176
$986$	0	0
$987$	0	0
$988$	−9.90198	−0.315024
$989$	10.0937	0.320960
$990$	0	0
$991$	−25.4643	−0.808901	−0.404450	−	0.914560i	$-0.632537\pi$
$991$	−25.4643	−0.808901	−0.404450	+	0.914560i	$0.632537\pi$
$992$	−25.1525	−0.798592
$993$	0	0
$994$	50.2501	1.59384
$995$	−12.1190	−0.384198
$996$	0	0
$997$	31.7829	1.00657	0.503287	−	0.864119i	$-0.332124\pi$
$997$	31.7829	1.00657	0.503287	+	0.864119i	$0.332124\pi$
$998$	−48.7374	−1.54275
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7803.2.a.ca.1.12	yes	15
3.2	odd	2		7803.2.a.bx.1.4	✓	15
17.16	even	2		7803.2.a.bz.1.12	yes	15
51.50	odd	2		7803.2.a.by.1.4	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7803.2.a.bx.1.4	✓	15	3.2	odd	2
7803.2.a.by.1.4	yes	15	51.50	odd	2
7803.2.a.bz.1.12	yes	15	17.16	even	2
7803.2.a.ca.1.12	yes	15	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7803 = 3^{3} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7803.a (trivial)

\(f(q)\)	\(=\)	\(q+2.01902 q^{2} +2.07645 q^{4} -0.707464 q^{5} -4.62694 q^{7} +0.154349 q^{8} -1.42838 q^{10} +1.79601 q^{11} -0.836114 q^{13} -9.34190 q^{14} -3.84126 q^{16} +5.70342 q^{19} -1.46901 q^{20} +3.62619 q^{22} +2.03224 q^{23} -4.49949 q^{25} -1.68813 q^{26} -9.60761 q^{28} -3.20042 q^{29} +3.11899 q^{31} -8.06429 q^{32} +3.27340 q^{35} -5.94714 q^{37} +11.5153 q^{38} -0.109197 q^{40} -10.7502 q^{41} +4.96676 q^{43} +3.72933 q^{44} +4.10314 q^{46} +12.0304 q^{47} +14.4086 q^{49} -9.08458 q^{50} -1.73615 q^{52} +6.29645 q^{53} -1.27061 q^{55} -0.714165 q^{56} -6.46172 q^{58} +14.0008 q^{59} +12.5071 q^{61} +6.29732 q^{62} -8.59945 q^{64} +0.591521 q^{65} +2.58698 q^{67} +6.60906 q^{70} -5.37900 q^{71} +2.99116 q^{73} -12.0074 q^{74} +11.8429 q^{76} -8.31005 q^{77} +10.2295 q^{79} +2.71755 q^{80} -21.7048 q^{82} -9.16954 q^{83} +10.0280 q^{86} +0.277213 q^{88} +3.32288 q^{89} +3.86866 q^{91} +4.21984 q^{92} +24.2897 q^{94} -4.03497 q^{95} +10.6214 q^{97} +29.0913 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 6 q^{2} + 12 q^{4} + 3 q^{5} - 3 q^{7} + 18 q^{8} - 6 q^{11} - 3 q^{13} - 3 q^{14} + 6 q^{16} - 3 q^{19} - 6 q^{20} + 12 q^{22} + 3 q^{23} + 6 q^{25} - 24 q^{26} - 9 q^{28} + 6 q^{29} + 42 q^{32}+ \cdots + 15 q^{98}+O(q^{100}) \) 15 * q + 6 * q^2 + 12 * q^4 + 3 * q^5 - 3 * q^7 + 18 * q^8 - 6 * q^11 - 3 * q^13 - 3 * q^14 + 6 * q^16 - 3 * q^19 - 6 * q^20 + 12 * q^22 + 3 * q^23 + 6 * q^25 - 24 * q^26 - 9 * q^28 + 6 * q^29 + 42 * q^32 + 33 * q^35 + 36 * q^38 - 15 * q^40 - 3 * q^43 + 18 * q^44 - 12 * q^46 + 24 * q^47 + 18 * q^49 + 42 * q^50 - 12 * q^52 + 48 * q^53 - 3 * q^55 + 15 * q^56 + 12 * q^58 + 18 * q^59 - 63 * q^62 + 30 * q^64 - 24 * q^65 + 12 * q^67 + 51 * q^70 + 21 * q^71 + 18 * q^73 + 48 * q^74 + 60 * q^76 + 54 * q^77 + 39 * q^79 - 6 * q^80 - 39 * q^82 + 51 * q^83 + 48 * q^86 + 48 * q^88 + 36 * q^89 - 9 * q^91 + 3 * q^92 + 36 * q^94 - 39 * q^95 - 3 * q^97 + 15 * q^98

Introduction

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