LMFDB - Embedded newform 6003.2.a.m.1.2

Newspace parameters

Level:	$ N $	$=$	$ 6003 = 3^{2} \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6003.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$47.9341963334$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
Defining polynomial:	$x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} - 93 x^{2} - 369 x - 108$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 2001)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.70316$ of defining polynomial
Character	$\chi$	$=$	6003.1

$q$-expansion

$f(q)$	$=$	$q-2.70316 q^{2} +5.30708 q^{4} -2.79988 q^{5} +0.880738 q^{7} -8.93955 q^{8} +O(q^{10})$	\(q-2.70316 q^{2} +5.30708 q^{4} -2.79988 q^{5} +0.880738 q^{7} -8.93955 q^{8} +7.56852 q^{10} +5.67616 q^{11} -3.71641 q^{13} -2.38078 q^{14} +13.5509 q^{16} -4.80704 q^{17} +6.68378 q^{19} -14.8592 q^{20} -15.3436 q^{22} -1.00000 q^{23} +2.83932 q^{25} +10.0460 q^{26} +4.67414 q^{28} +1.00000 q^{29} +0.779005 q^{31} -18.7511 q^{32} +12.9942 q^{34} -2.46596 q^{35} -8.14977 q^{37} -18.0673 q^{38} +25.0297 q^{40} -6.06174 q^{41} +9.54562 q^{43} +30.1238 q^{44} +2.70316 q^{46} +7.68018 q^{47} -6.22430 q^{49} -7.67515 q^{50} -19.7233 q^{52} +9.73506 q^{53} -15.8926 q^{55} -7.87341 q^{56} -2.70316 q^{58} -5.14558 q^{59} -7.99562 q^{61} -2.10578 q^{62} +23.5855 q^{64} +10.4055 q^{65} -8.36073 q^{67} -25.5113 q^{68} +6.66589 q^{70} -8.52656 q^{71} -12.6677 q^{73} +22.0301 q^{74} +35.4713 q^{76} +4.99921 q^{77} +15.1051 q^{79} -37.9409 q^{80} +16.3859 q^{82} +0.302272 q^{83} +13.4591 q^{85} -25.8033 q^{86} -50.7423 q^{88} +10.7142 q^{89} -3.27318 q^{91} -5.30708 q^{92} -20.7608 q^{94} -18.7138 q^{95} -0.884027 q^{97} +16.8253 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + O(q^{10}) $	$ 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + 14q^{10} - 11q^{11} - 5q^{13} - 17q^{14} + 20q^{16} - 15q^{17} - 6q^{19} - 21q^{20} - 10q^{22} - 11q^{23} + 3q^{25} + 5q^{26} + 7q^{28} + 11q^{29} + 35q^{31} - 28q^{32} + 28q^{34} - 15q^{35} - 28q^{37} + 2q^{38} - q^{40} - 10q^{41} - 6q^{43} - 18q^{44} + 2q^{46} - 15q^{47} + 22q^{49} - 15q^{50} - 36q^{52} + 7q^{53} - 12q^{55} - 56q^{56} - 2q^{58} + 20q^{59} - 20q^{61} + 11q^{62} + 36q^{64} - 11q^{65} - 39q^{67} - 35q^{68} + 38q^{70} - 49q^{71} - 3q^{73} - 37q^{74} - 18q^{76} - 25q^{77} + 41q^{79} - 51q^{80} - 19q^{82} - 13q^{83} - 62q^{86} - 40q^{88} - 34q^{89} + 2q^{91} - 18q^{92} - 14q^{94} - 25q^{95} - 11q^{97} - 53q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.70316	−1.91142	−0.955711	−	0.294305i	$-0.904912\pi$
$2$	−2.70316	−1.91142	−0.955711	+	0.294305i	$0.904912\pi$
$3$	0	0
$3$	0	0
$4$	5.30708	2.65354
$5$	−2.79988	−1.25214	−0.626072	−	0.779765i	$-0.715338\pi$
$5$	−2.79988	−1.25214	−0.626072	+	0.779765i	$0.715338\pi$
$6$	0	0
$7$	0.880738	0.332888	0.166444	−	0.986051i	$-0.446772\pi$
$7$	0.880738	0.332888	0.166444	+	0.986051i	$0.446772\pi$
$8$	−8.93955	−3.16061
$9$	0	0
$10$	7.56852	2.39338
$11$	5.67616	1.71143	0.855713	−	0.517451i	$-0.173119\pi$
$11$	5.67616	1.71143	0.855713	+	0.517451i	$0.173119\pi$
$12$	0	0
$13$	−3.71641	−1.03075	−0.515373	−	0.856966i	$-0.672347\pi$
$13$	−3.71641	−1.03075	−0.515373	+	0.856966i	$0.672347\pi$
$14$	−2.38078	−0.636289
$15$	0	0
$16$	13.5509	3.38772
$17$	−4.80704	−1.16588	−0.582939	−	0.812516i	$-0.698097\pi$
$17$	−4.80704	−1.16588	−0.582939	+	0.812516i	$0.698097\pi$
$18$	0	0
$19$	6.68378	1.53336	0.766682	−	0.642027i	$-0.221907\pi$
$19$	6.68378	1.53336	0.766682	+	0.642027i	$0.221907\pi$
$20$	−14.8592	−3.32261
$21$	0	0
$22$	−15.3436	−3.27126
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	2.83932	0.567865
$26$	10.0460	1.97019
$27$	0	0
$28$	4.67414	0.883330
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	0.779005	0.139913	0.0699567	−	0.997550i	$-0.477714\pi$
$31$	0.779005	0.139913	0.0699567	+	0.997550i	$0.477714\pi$
$32$	−18.7511	−3.31476
$33$	0	0
$34$	12.9942	2.22849
$35$	−2.46596	−0.416823
$36$	0	0
$37$	−8.14977	−1.33981	−0.669907	−	0.742445i	$-0.733666\pi$
$37$	−8.14977	−1.33981	−0.669907	+	0.742445i	$0.733666\pi$
$38$	−18.0673	−2.93091
$39$	0	0
$40$	25.0297	3.95754
$41$	−6.06174	−0.946686	−0.473343	−	0.880878i	$-0.656953\pi$
$41$	−6.06174	−0.946686	−0.473343	+	0.880878i	$0.656953\pi$
$42$	0	0
$43$	9.54562	1.45569	0.727847	−	0.685740i	$-0.240521\pi$
$43$	9.54562	1.45569	0.727847	+	0.685740i	$0.240521\pi$
$44$	30.1238	4.54133
$45$	0	0
$46$	2.70316	0.398559
$47$	7.68018	1.12027	0.560135	−	0.828402i	$-0.310749\pi$
$47$	7.68018	1.12027	0.560135	+	0.828402i	$0.310749\pi$
$48$	0	0
$49$	−6.22430	−0.889186
$50$	−7.67515	−1.08543
$51$	0	0
$52$	−19.7233	−2.73512
$53$	9.73506	1.33721	0.668607	−	0.743616i	$-0.266891\pi$
$53$	9.73506	1.33721	0.668607	+	0.743616i	$0.266891\pi$
$54$	0	0
$55$	−15.8926	−2.14295
$56$	−7.87341	−1.05213
$57$	0	0
$58$	−2.70316	−0.354942
$59$	−5.14558	−0.669898	−0.334949	−	0.942236i	$-0.608719\pi$
$59$	−5.14558	−0.669898	−0.334949	+	0.942236i	$0.608719\pi$
$60$	0	0
$61$	−7.99562	−1.02373	−0.511867	−	0.859065i	$-0.671046\pi$
$61$	−7.99562	−1.02373	−0.511867	+	0.859065i	$0.671046\pi$
$62$	−2.10578	−0.267434
$63$	0	0
$64$	23.5855	2.94819
$65$	10.4055	1.29064
$66$	0	0
$67$	−8.36073	−1.02143	−0.510713	−	0.859751i	$-0.670619\pi$
$67$	−8.36073	−1.02143	−0.510713	+	0.859751i	$0.670619\pi$
$68$	−25.5113	−3.09370
$69$	0	0
$70$	6.66589	0.796726
$71$	−8.52656	−1.01192	−0.505958	−	0.862558i	$-0.668861\pi$
$71$	−8.52656	−1.01192	−0.505958	+	0.862558i	$0.668861\pi$
$72$	0	0
$73$	−12.6677	−1.48264	−0.741321	−	0.671150i	$-0.765801\pi$
$73$	−12.6677	−1.48264	−0.741321	+	0.671150i	$0.765801\pi$
$74$	22.0301	2.56095
$75$	0	0
$76$	35.4713	4.06884
$77$	4.99921	0.569713
$78$	0	0
$79$	15.1051	1.69945	0.849726	−	0.527224i	$-0.176767\pi$
$79$	15.1051	1.69945	0.849726	+	0.527224i	$0.176767\pi$
$80$	−37.9409	−4.24192
$81$	0	0
$82$	16.3859	1.80952
$83$	0.302272	0.0331786	0.0165893	−	0.999862i	$-0.494719\pi$
$83$	0.302272	0.0331786	0.0165893	+	0.999862i	$0.494719\pi$
$84$	0	0
$85$	13.4591	1.45985
$86$	−25.8033	−2.78245
$87$	0	0
$88$	−50.7423	−5.40915
$89$	10.7142	1.13570	0.567852	−	0.823131i	$-0.307775\pi$
$89$	10.7142	1.13570	0.567852	+	0.823131i	$0.307775\pi$
$90$	0	0
$91$	−3.27318	−0.343123
$92$	−5.30708	−0.553301
$93$	0	0
$94$	−20.7608	−2.14131
$95$	−18.7138	−1.91999
$96$	0	0
$97$	−0.884027	−0.0897593	−0.0448797	−	0.998992i	$-0.514290\pi$
$97$	−0.884027	−0.0897593	−0.0448797	+	0.998992i	$0.514290\pi$
$98$	16.8253	1.69961
$99$	0	0
$100$	15.0685	1.50685
$101$	1.36093	0.135418	0.0677089	−	0.997705i	$-0.478431\pi$
$101$	1.36093	0.135418	0.0677089	+	0.997705i	$0.478431\pi$
$102$	0	0
$103$	−5.31264	−0.523470	−0.261735	−	0.965140i	$-0.584295\pi$
$103$	−5.31264	−0.523470	−0.261735	+	0.965140i	$0.584295\pi$
$104$	33.2230	3.25779
$105$	0	0
$106$	−26.3154	−2.55598
$107$	−7.83080	−0.757032	−0.378516	−	0.925595i	$-0.623566\pi$
$107$	−7.83080	−0.757032	−0.378516	+	0.925595i	$0.623566\pi$
$108$	0	0
$109$	11.2420	1.07679	0.538393	−	0.842694i	$-0.319032\pi$
$109$	11.2420	1.07679	0.538393	+	0.842694i	$0.319032\pi$
$110$	42.9601	4.09609
$111$	0	0
$112$	11.9348	1.12773
$113$	17.4918	1.64549	0.822745	−	0.568411i	$-0.192442\pi$
$113$	17.4918	1.64549	0.822745	+	0.568411i	$0.192442\pi$
$114$	0	0
$115$	2.79988	0.261090
$116$	5.30708	0.492750
$117$	0	0
$118$	13.9093	1.28046
$119$	−4.23374	−0.388106
$120$	0	0
$121$	21.2188	1.92898
$122$	21.6134	1.95679
$123$	0	0
$124$	4.13424	0.371266
$125$	6.04963	0.541095
$126$	0	0
$127$	0.206399	0.0183149	0.00915747	−	0.999958i	$-0.497085\pi$
$127$	0.206399	0.0183149	0.00915747	+	0.999958i	$0.497085\pi$
$128$	−26.2532	−2.32048
$129$	0	0
$130$	−28.1277	−2.46696
$131$	−9.50384	−0.830354	−0.415177	−	0.909741i	$-0.636280\pi$
$131$	−9.50384	−0.830354	−0.415177	+	0.909741i	$0.636280\pi$
$132$	0	0
$133$	5.88666	0.510438
$134$	22.6004	1.95238
$135$	0	0
$136$	42.9728	3.68488
$137$	−4.27725	−0.365430	−0.182715	−	0.983166i	$-0.558489\pi$
$137$	−4.27725	−0.365430	−0.182715	+	0.983166i	$0.558489\pi$
$138$	0	0
$139$	−9.47109	−0.803327	−0.401663	−	0.915787i	$-0.631568\pi$
$139$	−9.47109	−0.803327	−0.401663	+	0.915787i	$0.631568\pi$
$140$	−13.0870	−1.10606
$141$	0	0
$142$	23.0487	1.93420
$143$	−21.0949	−1.76405
$144$	0	0
$145$	−2.79988	−0.232517
$146$	34.2428	2.83396
$147$	0	0
$148$	−43.2514	−3.55525
$149$	20.3448	1.66671	0.833354	−	0.552740i	$-0.186418\pi$
$149$	20.3448	1.66671	0.833354	+	0.552740i	$0.186418\pi$
$150$	0	0
$151$	−14.3715	−1.16953	−0.584766	−	0.811202i	$-0.698814\pi$
$151$	−14.3715	−1.16953	−0.584766	+	0.811202i	$0.698814\pi$
$152$	−59.7500	−4.84636
$153$	0	0
$154$	−13.5137	−1.08896
$155$	−2.18112	−0.175192
$156$	0	0
$157$	−18.9351	−1.51118	−0.755592	−	0.655043i	$-0.772651\pi$
$157$	−18.9351	−1.51118	−0.755592	+	0.655043i	$0.772651\pi$
$158$	−40.8314	−3.24837
$159$	0	0
$160$	52.5009	4.15056
$161$	−0.880738	−0.0694119
$162$	0	0
$163$	12.4920	0.978447	0.489224	−	0.872158i	$-0.337280\pi$
$163$	12.4920	0.978447	0.489224	+	0.872158i	$0.337280\pi$
$164$	−32.1701	−2.51207
$165$	0	0
$166$	−0.817089	−0.0634184
$167$	−8.77674	−0.679165	−0.339582	−	0.940576i	$-0.610286\pi$
$167$	−8.77674	−0.679165	−0.339582	+	0.940576i	$0.610286\pi$
$168$	0	0
$169$	0.811682	0.0624371
$170$	−36.3822	−2.79038
$171$	0	0
$172$	50.6593	3.86274
$173$	−14.7668	−1.12270	−0.561351	−	0.827578i	$-0.689718\pi$
$173$	−14.7668	−1.12270	−0.561351	+	0.827578i	$0.689718\pi$
$174$	0	0
$175$	2.50070	0.189035
$176$	76.9170	5.79784
$177$	0	0
$178$	−28.9622	−2.17081
$179$	7.96536	0.595359	0.297679	−	0.954666i	$-0.403787\pi$
$179$	7.96536	0.595359	0.297679	+	0.954666i	$0.403787\pi$
$180$	0	0
$181$	10.2864	0.764579	0.382289	−	0.924043i	$-0.375136\pi$
$181$	10.2864	0.764579	0.382289	+	0.924043i	$0.375136\pi$
$182$	8.84794	0.655853
$183$	0	0
$184$	8.93955	0.659033
$185$	22.8184	1.67764
$186$	0	0
$187$	−27.2855	−1.99531
$188$	40.7593	2.97268
$189$	0	0
$190$	50.5863	3.66992
$191$	−23.0537	−1.66811	−0.834054	−	0.551683i	$-0.813986\pi$
$191$	−23.0537	−1.66811	−0.834054	+	0.551683i	$0.813986\pi$
$192$	0	0
$193$	5.67387	0.408414	0.204207	−	0.978928i	$-0.434538\pi$
$193$	5.67387	0.408414	0.204207	+	0.978928i	$0.434538\pi$
$194$	2.38967	0.171568
$195$	0	0
$196$	−33.0328	−2.35949
$197$	−7.96762	−0.567669	−0.283835	−	0.958873i	$-0.591607\pi$
$197$	−7.96762	−0.567669	−0.283835	+	0.958873i	$0.591607\pi$
$198$	0	0
$199$	−6.95306	−0.492889	−0.246445	−	0.969157i	$-0.579262\pi$
$199$	−6.95306	−0.492889	−0.246445	+	0.969157i	$0.579262\pi$
$200$	−25.3823	−1.79480
$201$	0	0
$202$	−3.67882	−0.258841
$203$	0.880738	0.0618157
$204$	0	0
$205$	16.9722	1.18539
$206$	14.3609	1.00057
$207$	0	0
$208$	−50.3607	−3.49188
$209$	37.9382	2.62424
$210$	0	0
$211$	5.75864	0.396441	0.198221	−	0.980157i	$-0.436484\pi$
$211$	5.75864	0.396441	0.198221	+	0.980157i	$0.436484\pi$
$212$	51.6647	3.54835
$213$	0	0
$214$	21.1679	1.44701
$215$	−26.7266	−1.82274
$216$	0	0
$217$	0.686100	0.0465755
$218$	−30.3889	−2.05819
$219$	0	0
$220$	−84.3430	−5.68640
$221$	17.8649	1.20172
$222$	0	0
$223$	12.0916	0.809713	0.404856	−	0.914380i	$-0.367322\pi$
$223$	12.0916	0.809713	0.404856	+	0.914380i	$0.367322\pi$
$224$	−16.5148	−1.10344
$225$	0	0
$226$	−47.2831	−3.14523
$227$	27.0451	1.79505	0.897523	−	0.440968i	$-0.145365\pi$
$227$	27.0451	1.79505	0.897523	+	0.440968i	$0.145365\pi$
$228$	0	0
$229$	−5.32014	−0.351565	−0.175782	−	0.984429i	$-0.556245\pi$
$229$	−5.32014	−0.351565	−0.175782	+	0.984429i	$0.556245\pi$
$230$	−7.56852	−0.499054
$231$	0	0
$232$	−8.93955	−0.586911
$233$	−23.8743	−1.56406	−0.782028	−	0.623244i	$-0.785814\pi$
$233$	−23.8743	−1.56406	−0.782028	+	0.623244i	$0.785814\pi$
$234$	0	0
$235$	−21.5036	−1.40274
$236$	−27.3080	−1.77760
$237$	0	0
$238$	11.4445	0.741836
$239$	8.24781	0.533506	0.266753	−	0.963765i	$-0.414049\pi$
$239$	8.24781	0.533506	0.266753	+	0.963765i	$0.414049\pi$
$240$	0	0
$241$	10.5594	0.680192	0.340096	−	0.940391i	$-0.389540\pi$
$241$	10.5594	0.680192	0.340096	+	0.940391i	$0.389540\pi$
$242$	−57.3577	−3.68709
$243$	0	0
$244$	−42.4334	−2.71652
$245$	17.4273	1.11339
$246$	0	0
$247$	−24.8396	−1.58051
$248$	−6.96396	−0.442212
$249$	0	0
$250$	−16.3531	−1.03426
$251$	15.9674	1.00785	0.503927	−	0.863746i	$-0.331888\pi$
$251$	15.9674	1.00785	0.503927	+	0.863746i	$0.331888\pi$
$252$	0	0
$253$	−5.67616	−0.356857
$254$	−0.557929	−0.0350076
$255$	0	0
$256$	23.7956	1.48722
$257$	5.13834	0.320521	0.160260	−	0.987075i	$-0.448767\pi$
$257$	5.13834	0.320521	0.160260	+	0.987075i	$0.448767\pi$
$258$	0	0
$259$	−7.17782	−0.446008
$260$	55.2227	3.42477
$261$	0	0
$262$	25.6904	1.58716
$263$	−22.1102	−1.36337	−0.681687	−	0.731644i	$-0.738754\pi$
$263$	−22.1102	−1.36337	−0.681687	+	0.731644i	$0.738754\pi$
$264$	0	0
$265$	−27.2570	−1.67438
$266$	−15.9126	−0.975663
$267$	0	0
$268$	−44.3710	−2.71039
$269$	−20.1023	−1.22566	−0.612828	−	0.790216i	$-0.709968\pi$
$269$	−20.1023	−1.22566	−0.612828	+	0.790216i	$0.709968\pi$
$270$	0	0
$271$	6.90145	0.419233	0.209617	−	0.977784i	$-0.432778\pi$
$271$	6.90145	0.419233	0.209617	+	0.977784i	$0.432778\pi$
$272$	−65.1397	−3.94967
$273$	0	0
$274$	11.5621	0.698491
$275$	16.1165	0.971859
$276$	0	0
$277$	24.5794	1.47683	0.738416	−	0.674345i	$-0.235574\pi$
$277$	24.5794	1.47683	0.738416	+	0.674345i	$0.235574\pi$
$278$	25.6019	1.53550
$279$	0	0
$280$	22.0446	1.31742
$281$	17.2690	1.03018	0.515090	−	0.857136i	$-0.327759\pi$
$281$	17.2690	1.03018	0.515090	+	0.857136i	$0.327759\pi$
$282$	0	0
$283$	−7.22081	−0.429232	−0.214616	−	0.976698i	$-0.568850\pi$
$283$	−7.22081	−0.429232	−0.214616	+	0.976698i	$0.568850\pi$
$284$	−45.2511	−2.68516
$285$	0	0
$286$	57.0229	3.37184
$287$	−5.33881	−0.315140
$288$	0	0
$289$	6.10760	0.359271
$290$	7.56852	0.444439
$291$	0	0
$292$	−67.2285	−3.93425
$293$	18.2359	1.06535	0.532677	−	0.846319i	$-0.321186\pi$
$293$	18.2359	1.06535	0.532677	+	0.846319i	$0.321186\pi$
$294$	0	0
$295$	14.4070	0.838809
$296$	72.8553	4.23463
$297$	0	0
$298$	−54.9951	−3.18578
$299$	3.71641	0.214925
$300$	0	0
$301$	8.40720	0.484583
$302$	38.8484	2.23547
$303$	0	0
$304$	90.5712	5.19461
$305$	22.3868	1.28186
$306$	0	0
$307$	−14.8966	−0.850193	−0.425097	−	0.905148i	$-0.639760\pi$
$307$	−14.8966	−0.850193	−0.425097	+	0.905148i	$0.639760\pi$
$308$	26.5312	1.51175
$309$	0	0
$310$	5.89592	0.334866
$311$	1.07620	0.0610259	0.0305129	−	0.999534i	$-0.490286\pi$
$311$	1.07620	0.0610259	0.0305129	+	0.999534i	$0.490286\pi$
$312$	0	0
$313$	−24.6270	−1.39200	−0.696000	−	0.718042i	$-0.745039\pi$
$313$	−24.6270	−1.39200	−0.696000	+	0.718042i	$0.745039\pi$
$314$	51.1846	2.88851
$315$	0	0
$316$	80.1637	4.50956
$317$	−10.3442	−0.580988	−0.290494	−	0.956877i	$-0.593820\pi$
$317$	−10.3442	−0.580988	−0.290494	+	0.956877i	$0.593820\pi$
$318$	0	0
$319$	5.67616	0.317804
$320$	−66.0367	−3.69156
$321$	0	0
$322$	2.38078	0.132676
$323$	−32.1292	−1.78771
$324$	0	0
$325$	−10.5521	−0.585324
$326$	−33.7678	−1.87023
$327$	0	0
$328$	54.1893	2.99210
$329$	6.76423	0.372924
$330$	0	0
$331$	−14.0821	−0.774025	−0.387012	−	0.922075i	$-0.626493\pi$
$331$	−14.0821	−0.774025	−0.387012	+	0.922075i	$0.626493\pi$
$332$	1.60418	0.0880408
$333$	0	0
$334$	23.7249	1.29817
$335$	23.4090	1.27897
$336$	0	0
$337$	−0.569964	−0.0310479	−0.0155240	−	0.999879i	$-0.504942\pi$
$337$	−0.569964	−0.0310479	−0.0155240	+	0.999879i	$0.504942\pi$
$338$	−2.19411	−0.119344
$339$	0	0
$340$	71.4286	3.87376
$341$	4.42176	0.239452
$342$	0	0
$343$	−11.6471	−0.628887
$344$	−85.3336	−4.60088
$345$	0	0
$346$	39.9171	2.14596
$347$	12.4225	0.666877	0.333438	−	0.942772i	$-0.391791\pi$
$347$	12.4225	0.666877	0.333438	+	0.942772i	$0.391791\pi$
$348$	0	0
$349$	−28.4638	−1.52363	−0.761816	−	0.647793i	$-0.775692\pi$
$349$	−28.4638	−1.52363	−0.761816	+	0.647793i	$0.775692\pi$
$350$	−6.75980	−0.361326
$351$	0	0
$352$	−106.434	−5.67297
$353$	−27.0042	−1.43729	−0.718644	−	0.695378i	$-0.755237\pi$
$353$	−27.0042	−1.43729	−0.718644	+	0.695378i	$0.755237\pi$
$354$	0	0
$355$	23.8733	1.26706
$356$	56.8611	3.01363
$357$	0	0
$358$	−21.5316	−1.13798
$359$	−14.0693	−0.742551	−0.371276	−	0.928523i	$-0.621079\pi$
$359$	−14.0693	−0.742551	−0.371276	+	0.928523i	$0.621079\pi$
$360$	0	0
$361$	25.6729	1.35120
$362$	−27.8057	−1.46143
$363$	0	0
$364$	−17.3710	−0.910489
$365$	35.4680	1.85648
$366$	0	0
$367$	34.8397	1.81862	0.909310	−	0.416120i	$-0.136610\pi$
$367$	34.8397	1.81862	0.909310	+	0.416120i	$0.136610\pi$
$368$	−13.5509	−0.706389
$369$	0	0
$370$	−61.6817	−3.20668
$371$	8.57404	0.445142
$372$	0	0
$373$	22.0794	1.14323	0.571613	−	0.820523i	$-0.306318\pi$
$373$	22.0794	1.14323	0.571613	+	0.820523i	$0.306318\pi$
$374$	73.7571	3.81389
$375$	0	0
$376$	−68.6574	−3.54073
$377$	−3.71641	−0.191405
$378$	0	0
$379$	−7.46769	−0.383590	−0.191795	−	0.981435i	$-0.561431\pi$
$379$	−7.46769	−0.383590	−0.191795	+	0.981435i	$0.561431\pi$
$380$	−99.3154	−5.09477
$381$	0	0
$382$	62.3178	3.18846
$383$	30.9640	1.58218	0.791092	−	0.611697i	$-0.209513\pi$
$383$	30.9640	1.58218	0.791092	+	0.611697i	$0.209513\pi$
$384$	0	0
$385$	−13.9972	−0.713363
$386$	−15.3374	−0.780652
$387$	0	0
$388$	−4.69160	−0.238180
$389$	20.5067	1.03973	0.519864	−	0.854249i	$-0.325982\pi$
$389$	20.5067	1.03973	0.519864	+	0.854249i	$0.325982\pi$
$390$	0	0
$391$	4.80704	0.243102
$392$	55.6425	2.81037
$393$	0	0
$394$	21.5378	1.08506
$395$	−42.2924	−2.12796
$396$	0	0
$397$	−18.4473	−0.925843	−0.462922	−	0.886399i	$-0.653199\pi$
$397$	−18.4473	−0.925843	−0.462922	+	0.886399i	$0.653199\pi$
$398$	18.7952	0.942120
$399$	0	0
$400$	38.4754	1.92377
$401$	15.7291	0.785475	0.392738	−	0.919651i	$-0.371528\pi$
$401$	15.7291	0.785475	0.392738	+	0.919651i	$0.371528\pi$
$402$	0	0
$403$	−2.89510	−0.144215
$404$	7.22257	0.359336
$405$	0	0
$406$	−2.38078	−0.118156
$407$	−46.2594	−2.29299
$408$	0	0
$409$	−7.14903	−0.353497	−0.176748	−	0.984256i	$-0.556558\pi$
$409$	−7.14903	−0.353497	−0.176748	+	0.984256i	$0.556558\pi$
$410$	−45.8785	−2.26578
$411$	0	0
$412$	−28.1946	−1.38905
$413$	−4.53191	−0.223001
$414$	0	0
$415$	−0.846325	−0.0415444
$416$	69.6869	3.41668
$417$	0	0
$418$	−102.553	−5.01603
$419$	14.7980	0.722928	0.361464	−	0.932386i	$-0.382277\pi$
$419$	14.7980	0.722928	0.361464	+	0.932386i	$0.382277\pi$
$420$	0	0
$421$	6.98352	0.340356	0.170178	−	0.985413i	$-0.445566\pi$
$421$	6.98352	0.340356	0.170178	+	0.985413i	$0.445566\pi$
$422$	−15.5665	−0.757767
$423$	0	0
$424$	−87.0271	−4.22641
$425$	−13.6487	−0.662061
$426$	0	0
$427$	−7.04205	−0.340789
$428$	−41.5586	−2.00881
$429$	0	0
$430$	72.2463	3.48402
$431$	−18.2431	−0.878737	−0.439368	−	0.898307i	$-0.644798\pi$
$431$	−18.2431	−0.878737	−0.439368	+	0.898307i	$0.644798\pi$
$432$	0	0
$433$	−6.54148	−0.314364	−0.157182	−	0.987570i	$-0.550241\pi$
$433$	−6.54148	−0.314364	−0.157182	+	0.987570i	$0.550241\pi$
$434$	−1.85464	−0.0890255
$435$	0	0
$436$	59.6620	2.85729
$437$	−6.68378	−0.319728
$438$	0	0
$439$	−24.9232	−1.18952	−0.594760	−	0.803904i	$-0.702753\pi$
$439$	−24.9232	−1.18952	−0.594760	+	0.803904i	$0.702753\pi$
$440$	142.072	6.77303
$441$	0	0
$442$	−48.2917	−2.29700
$443$	31.7227	1.50719	0.753594	−	0.657340i	$-0.228318\pi$
$443$	31.7227	1.50719	0.753594	+	0.657340i	$0.228318\pi$
$444$	0	0
$445$	−29.9985	−1.42207
$446$	−32.6855	−1.54770
$447$	0	0
$448$	20.7727	0.981417
$449$	−27.6235	−1.30363	−0.651816	−	0.758377i	$-0.725992\pi$
$449$	−27.6235	−1.30363	−0.651816	+	0.758377i	$0.725992\pi$
$450$	0	0
$451$	−34.4074	−1.62018
$452$	92.8303	4.36637
$453$	0	0
$454$	−73.1072	−3.43109
$455$	9.16452	0.429639
$456$	0	0
$457$	3.37558	0.157903	0.0789516	−	0.996878i	$-0.474843\pi$
$457$	3.37558	0.157903	0.0789516	+	0.996878i	$0.474843\pi$
$458$	14.3812	0.671989
$459$	0	0
$460$	14.8592	0.692812
$461$	−39.9849	−1.86228	−0.931140	−	0.364661i	$-0.881185\pi$
$461$	−39.9849	−1.86228	−0.931140	+	0.364661i	$0.881185\pi$
$462$	0	0
$463$	9.18722	0.426966	0.213483	−	0.976947i	$-0.431519\pi$
$463$	9.18722	0.426966	0.213483	+	0.976947i	$0.431519\pi$
$464$	13.5509	0.629085
$465$	0	0
$466$	64.5360	2.98957
$467$	−13.0823	−0.605378	−0.302689	−	0.953089i	$-0.597884\pi$
$467$	−13.0823	−0.605378	−0.302689	+	0.953089i	$0.597884\pi$
$468$	0	0
$469$	−7.36362	−0.340020
$470$	58.1276	2.68123
$471$	0	0
$472$	45.9992	2.11729
$473$	54.1825	2.49131
$474$	0	0
$475$	18.9774	0.870743
$476$	−22.4688	−1.02986
$477$	0	0
$478$	−22.2951	−1.01976
$479$	−41.5385	−1.89794	−0.948972	−	0.315361i	$-0.897875\pi$
$479$	−41.5385	−1.89794	−0.948972	+	0.315361i	$0.897875\pi$
$480$	0	0
$481$	30.2879	1.38101
$482$	−28.5438	−1.30013
$483$	0	0
$484$	112.610	5.11862
$485$	2.47517	0.112392
$486$	0	0
$487$	22.4277	1.01630	0.508148	−	0.861270i	$-0.330330\pi$
$487$	22.4277	1.01630	0.508148	+	0.861270i	$0.330330\pi$
$488$	71.4773	3.23563
$489$	0	0
$490$	−47.1088	−2.12816
$491$	−13.8826	−0.626513	−0.313256	−	0.949669i	$-0.601420\pi$
$491$	−13.8826	−0.626513	−0.313256	+	0.949669i	$0.601420\pi$
$492$	0	0
$493$	−4.80704	−0.216498
$494$	67.1455	3.02102
$495$	0	0
$496$	10.5562	0.473988
$497$	−7.50967	−0.336855
$498$	0	0
$499$	−10.9367	−0.489592	−0.244796	−	0.969575i	$-0.578721\pi$
$499$	−10.9367	−0.489592	−0.244796	+	0.969575i	$0.578721\pi$
$500$	32.1059	1.43582
$501$	0	0
$502$	−43.1625	−1.92644
$503$	3.54058	0.157867	0.0789334	−	0.996880i	$-0.474849\pi$
$503$	3.54058	0.157867	0.0789334	+	0.996880i	$0.474849\pi$
$504$	0	0
$505$	−3.81044	−0.169563
$506$	15.3436	0.682105
$507$	0	0
$508$	1.09537	0.0485994
$509$	−12.3607	−0.547878	−0.273939	−	0.961747i	$-0.588327\pi$
$509$	−12.3607	−0.547878	−0.273939	+	0.961747i	$0.588327\pi$
$510$	0	0
$511$	−11.1569	−0.493554
$512$	−11.8168	−0.522233
$513$	0	0
$514$	−13.8898	−0.612651
$515$	14.8748	0.655460
$516$	0	0
$517$	43.5939	1.91726
$518$	19.4028	0.852509
$519$	0	0
$520$	−93.0205	−4.07922
$521$	−34.5365	−1.51307	−0.756535	−	0.653953i	$-0.773109\pi$
$521$	−34.5365	−1.51307	−0.756535	+	0.653953i	$0.773109\pi$
$522$	0	0
$523$	31.4234	1.37405	0.687024	−	0.726634i	$-0.258917\pi$
$523$	31.4234	1.37405	0.687024	+	0.726634i	$0.258917\pi$
$524$	−50.4376	−2.20338
$525$	0	0
$526$	59.7675	2.60599
$527$	−3.74471	−0.163122
$528$	0	0
$529$	1.00000	0.0434783
$530$	73.6801	3.20046
$531$	0	0
$532$	31.2409	1.35447
$533$	22.5279	0.975792
$534$	0	0
$535$	21.9253	0.947913
$536$	74.7412	3.22833
$537$	0	0
$538$	54.3396	2.34275
$539$	−35.3301	−1.52178
$540$	0	0
$541$	28.3717	1.21980	0.609898	−	0.792480i	$-0.291210\pi$
$541$	28.3717	1.21980	0.609898	+	0.792480i	$0.291210\pi$
$542$	−18.6557	−0.801332
$543$	0	0
$544$	90.1374	3.86461
$545$	−31.4762	−1.34829
$546$	0	0
$547$	20.4656	0.875046	0.437523	−	0.899207i	$-0.355856\pi$
$547$	20.4656	0.875046	0.437523	+	0.899207i	$0.355856\pi$
$548$	−22.6997	−0.969682
$549$	0	0
$550$	−43.5653	−1.85763
$551$	6.68378	0.284738
$552$	0	0
$553$	13.3036	0.565727
$554$	−66.4420	−2.82285
$555$	0	0
$556$	−50.2638	−2.13166
$557$	−33.3630	−1.41363	−0.706817	−	0.707396i	$-0.749870\pi$
$557$	−33.3630	−1.41363	−0.706817	+	0.707396i	$0.749870\pi$
$558$	0	0
$559$	−35.4754	−1.50045
$560$	−33.4160	−1.41208
$561$	0	0
$562$	−46.6808	−1.96911
$563$	−21.5508	−0.908257	−0.454129	−	0.890936i	$-0.650049\pi$
$563$	−21.5508	−0.908257	−0.454129	+	0.890936i	$0.650049\pi$
$564$	0	0
$565$	−48.9749	−2.06039
$566$	19.5190	0.820445
$567$	0	0
$568$	76.2236	3.19827
$569$	−12.9510	−0.542934	−0.271467	−	0.962448i	$-0.587509\pi$
$569$	−12.9510	−0.542934	−0.271467	+	0.962448i	$0.587509\pi$
$570$	0	0
$571$	3.76335	0.157491	0.0787456	−	0.996895i	$-0.474909\pi$
$571$	3.76335	0.157491	0.0787456	+	0.996895i	$0.474909\pi$
$572$	−111.952	−4.68096
$573$	0	0
$574$	14.4317	0.602366
$575$	−2.83932	−0.118408
$576$	0	0
$577$	9.05091	0.376794	0.188397	−	0.982093i	$-0.439671\pi$
$577$	9.05091	0.376794	0.188397	+	0.982093i	$0.439671\pi$
$578$	−16.5098	−0.686718
$579$	0	0
$580$	−14.8592	−0.616993
$581$	0.266222	0.0110448
$582$	0	0
$583$	55.2578	2.28854
$584$	113.244	4.68605
$585$	0	0
$586$	−49.2946	−2.03634
$587$	7.59812	0.313608	0.156804	−	0.987630i	$-0.449881\pi$
$587$	7.59812	0.313608	0.156804	+	0.987630i	$0.449881\pi$
$588$	0	0
$589$	5.20670	0.214538
$590$	−38.9445	−1.60332
$591$	0	0
$592$	−110.437	−4.53892
$593$	−7.95422	−0.326641	−0.163320	−	0.986573i	$-0.552220\pi$
$593$	−7.95422	−0.326641	−0.163320	+	0.986573i	$0.552220\pi$
$594$	0	0
$595$	11.8540	0.485965
$596$	107.971	4.42267
$597$	0	0
$598$	−10.0460	−0.410813
$599$	−31.2856	−1.27830	−0.639148	−	0.769084i	$-0.720713\pi$
$599$	−31.2856	−1.27830	−0.639148	+	0.769084i	$0.720713\pi$
$600$	0	0
$601$	14.4217	0.588274	0.294137	−	0.955763i	$-0.404968\pi$
$601$	14.4217	0.588274	0.294137	+	0.955763i	$0.404968\pi$
$602$	−22.7260	−0.926242
$603$	0	0
$604$	−76.2704	−3.10340
$605$	−59.4100	−2.41536
$606$	0	0
$607$	−27.1287	−1.10112	−0.550560	−	0.834796i	$-0.685586\pi$
$607$	−27.1287	−1.10112	−0.550560	+	0.834796i	$0.685586\pi$
$608$	−125.328	−5.08274
$609$	0	0
$610$	−60.5150	−2.45018
$611$	−28.5427	−1.15471
$612$	0	0
$613$	−7.58210	−0.306238	−0.153119	−	0.988208i	$-0.548932\pi$
$613$	−7.58210	−0.306238	−0.153119	+	0.988208i	$0.548932\pi$
$614$	40.2679	1.62508
$615$	0	0
$616$	−44.6907	−1.80064
$617$	−40.3076	−1.62272	−0.811361	−	0.584546i	$-0.801273\pi$
$617$	−40.3076	−1.62272	−0.811361	+	0.584546i	$0.801273\pi$
$618$	0	0
$619$	7.17677	0.288459	0.144229	−	0.989544i	$-0.453930\pi$
$619$	7.17677	0.288459	0.144229	+	0.989544i	$0.453930\pi$
$620$	−11.5754	−0.464878
$621$	0	0
$622$	−2.90915	−0.116646
$623$	9.43642	0.378062
$624$	0	0
$625$	−31.1349	−1.24539
$626$	66.5707	2.66070
$627$	0	0
$628$	−100.490	−4.00998
$629$	39.1762	1.56206
$630$	0	0
$631$	−13.8537	−0.551506	−0.275753	−	0.961229i	$-0.588927\pi$
$631$	−13.8537	−0.551506	−0.275753	+	0.961229i	$0.588927\pi$
$632$	−135.033	−5.37131
$633$	0	0
$634$	27.9620	1.11051
$635$	−0.577892	−0.0229329
$636$	0	0
$637$	23.1320	0.916525
$638$	−15.3436	−0.607457
$639$	0	0
$640$	73.5058	2.90557
$641$	2.14458	0.0847056	0.0423528	−	0.999103i	$-0.486515\pi$
$641$	2.14458	0.0847056	0.0423528	+	0.999103i	$0.486515\pi$
$642$	0	0
$643$	−48.1250	−1.89786	−0.948932	−	0.315481i	$-0.897834\pi$
$643$	−48.1250	−1.89786	−0.948932	+	0.315481i	$0.897834\pi$
$644$	−4.67414	−0.184187
$645$	0	0
$646$	86.8503	3.41708
$647$	−14.6607	−0.576370	−0.288185	−	0.957575i	$-0.593052\pi$
$647$	−14.6607	−0.576370	−0.288185	+	0.957575i	$0.593052\pi$
$648$	0	0
$649$	−29.2071	−1.14648
$650$	28.5240	1.11880
$651$	0	0
$652$	66.2959	2.59635
$653$	−30.0473	−1.17584	−0.587921	−	0.808918i	$-0.700053\pi$
$653$	−30.0473	−1.17584	−0.587921	+	0.808918i	$0.700053\pi$
$654$	0	0
$655$	26.6096	1.03972
$656$	−82.1421	−3.20711
$657$	0	0
$658$	−18.2848	−0.712816
$659$	−17.5722	−0.684516	−0.342258	−	0.939606i	$-0.611192\pi$
$659$	−17.5722	−0.684516	−0.342258	+	0.939606i	$0.611192\pi$
$660$	0	0
$661$	−22.2147	−0.864052	−0.432026	−	0.901861i	$-0.642201\pi$
$661$	−22.2147	−0.864052	−0.432026	+	0.901861i	$0.642201\pi$
$662$	38.0663	1.47949
$663$	0	0
$664$	−2.70218	−0.104865
$665$	−16.4819	−0.639142
$666$	0	0
$667$	−1.00000	−0.0387202
$668$	−46.5788	−1.80219
$669$	0	0
$670$	−63.2784	−2.44466
$671$	−45.3844	−1.75205
$672$	0	0
$673$	28.1597	1.08547	0.542737	−	0.839902i	$-0.317388\pi$
$673$	28.1597	1.08547	0.542737	+	0.839902i	$0.317388\pi$
$674$	1.54070	0.0593457
$675$	0	0
$676$	4.30766	0.165679
$677$	−0.245245	−0.00942553	−0.00471277	−	0.999989i	$-0.501500\pi$
$677$	−0.245245	−0.00942553	−0.00471277	+	0.999989i	$0.501500\pi$
$678$	0	0
$679$	−0.778596	−0.0298798
$680$	−120.319	−4.61401
$681$	0	0
$682$	−11.9527	−0.457693
$683$	−28.9636	−1.10826	−0.554131	−	0.832430i	$-0.686949\pi$
$683$	−28.9636	−1.10826	−0.554131	+	0.832430i	$0.686949\pi$
$684$	0	0
$685$	11.9758	0.457571
$686$	31.4841	1.20207
$687$	0	0
$688$	129.352	4.93149
$689$	−36.1795	−1.37833
$690$	0	0
$691$	−35.3723	−1.34563	−0.672813	−	0.739813i	$-0.734914\pi$
$691$	−35.3723	−1.34563	−0.672813	+	0.739813i	$0.734914\pi$
$692$	−78.3687	−2.97913
$693$	0	0
$694$	−33.5801	−1.27468
$695$	26.5179	1.00588
$696$	0	0
$697$	29.1390	1.10372
$698$	76.9422	2.91231
$699$	0	0
$700$	13.2714	0.501612
$701$	−19.9823	−0.754722	−0.377361	−	0.926066i	$-0.623168\pi$
$701$	−19.9823	−0.754722	−0.377361	+	0.926066i	$0.623168\pi$
$702$	0	0
$703$	−54.4712	−2.05442
$704$	133.875	5.04561
$705$	0	0
$706$	72.9966	2.74726
$707$	1.19862	0.0450789
$708$	0	0
$709$	−13.0449	−0.489911	−0.244956	−	0.969534i	$-0.578773\pi$
$709$	−13.0449	−0.489911	−0.244956	+	0.969534i	$0.578773\pi$
$710$	−64.5334	−2.42190
$711$	0	0
$712$	−95.7803	−3.58952
$713$	−0.779005	−0.0291740
$714$	0	0
$715$	59.0632	2.20884
$716$	42.2727	1.57981
$717$	0	0
$718$	38.0317	1.41933
$719$	−8.19259	−0.305532	−0.152766	−	0.988262i	$-0.548818\pi$
$719$	−8.19259	−0.305532	−0.152766	+	0.988262i	$0.548818\pi$
$720$	0	0
$721$	−4.67905	−0.174257
$722$	−69.3978	−2.58272
$723$	0	0
$724$	54.5905	2.02884
$725$	2.83932	0.105450
$726$	0	0
$727$	−28.0803	−1.04144	−0.520721	−	0.853727i	$-0.674337\pi$
$727$	−28.0803	−1.04144	−0.520721	+	0.853727i	$0.674337\pi$
$728$	29.2608	1.08448
$729$	0	0
$730$	−95.8758	−3.54852
$731$	−45.8862	−1.69716
$732$	0	0
$733$	−32.2797	−1.19228	−0.596140	−	0.802881i	$-0.703300\pi$
$733$	−32.2797	−1.19228	−0.596140	+	0.802881i	$0.703300\pi$
$734$	−94.1774	−3.47615
$735$	0	0
$736$	18.7511	0.691176
$737$	−47.4568	−1.74809
$738$	0	0
$739$	2.56275	0.0942721	0.0471361	−	0.998888i	$-0.484991\pi$
$739$	2.56275	0.0942721	0.0471361	+	0.998888i	$0.484991\pi$
$740$	121.099	4.45168
$741$	0	0
$742$	−23.1770	−0.850855
$743$	−35.8227	−1.31421	−0.657104	−	0.753800i	$-0.728219\pi$
$743$	−35.8227	−1.31421	−0.657104	+	0.753800i	$0.728219\pi$
$744$	0	0
$745$	−56.9629	−2.08696
$746$	−59.6841	−2.18519
$747$	0	0
$748$	−144.806	−5.29464
$749$	−6.89689	−0.252007
$750$	0	0
$751$	−42.9765	−1.56824	−0.784118	−	0.620612i	$-0.786884\pi$
$751$	−42.9765	−1.56824	−0.784118	+	0.620612i	$0.786884\pi$
$752$	104.073	3.79516
$753$	0	0
$754$	10.0460	0.365855
$755$	40.2383	1.46442
$756$	0	0
$757$	−32.0132	−1.16354	−0.581769	−	0.813354i	$-0.697639\pi$
$757$	−32.0132	−1.16354	−0.581769	+	0.813354i	$0.697639\pi$
$758$	20.1864	0.733202
$759$	0	0
$760$	167.293	6.06834
$761$	−11.4559	−0.415278	−0.207639	−	0.978206i	$-0.566578\pi$
$761$	−11.4559	−0.415278	−0.207639	+	0.978206i	$0.566578\pi$
$762$	0	0
$763$	9.90124	0.358449
$764$	−122.348	−4.42639
$765$	0	0
$766$	−83.7005	−3.02422
$767$	19.1231	0.690495
$768$	0	0
$769$	−0.0983888	−0.00354799	−0.00177400	−	0.999998i	$-0.500565\pi$
$769$	−0.0983888	−0.00354799	−0.00177400	+	0.999998i	$0.500565\pi$
$770$	37.8366	1.36354
$771$	0	0
$772$	30.1117	1.08374
$773$	−12.4020	−0.446070	−0.223035	−	0.974810i	$-0.571596\pi$
$773$	−12.4020	−0.446070	−0.223035	+	0.974810i	$0.571596\pi$
$774$	0	0
$775$	2.21185	0.0794519
$776$	7.90281	0.283694
$777$	0	0
$778$	−55.4328	−1.98736
$779$	−40.5153	−1.45161
$780$	0	0
$781$	−48.3981	−1.73182
$782$	−12.9942	−0.464671
$783$	0	0
$784$	−84.3449	−3.01232
$785$	53.0159	1.89222
$786$	0	0
$787$	26.7197	0.952455	0.476227	−	0.879322i	$-0.342004\pi$
$787$	26.7197	0.952455	0.476227	+	0.879322i	$0.342004\pi$
$788$	−42.2848	−1.50633
$789$	0	0
$790$	114.323	4.06743
$791$	15.4057	0.547763
$792$	0	0
$793$	29.7150	1.05521
$794$	49.8660	1.76968
$795$	0	0
$796$	−36.9004	−1.30790
$797$	−20.2834	−0.718474	−0.359237	−	0.933246i	$-0.616963\pi$
$797$	−20.2834	−0.718474	−0.359237	+	0.933246i	$0.616963\pi$
$798$	0	0
$799$	−36.9189	−1.30610
$800$	−53.2406	−1.88234
$801$	0	0
$802$	−42.5184	−1.50138
$803$	−71.9039	−2.53743
$804$	0	0
$805$	2.46596	0.0869137
$806$	7.82592	0.275656
$807$	0	0
$808$	−12.1661	−0.428003
$809$	−35.7621	−1.25733	−0.628665	−	0.777676i	$-0.716398\pi$
$809$	−35.7621	−1.25733	−0.628665	+	0.777676i	$0.716398\pi$
$810$	0	0
$811$	26.4097	0.927370	0.463685	−	0.886000i	$-0.346527\pi$
$811$	26.4097	0.927370	0.463685	+	0.886000i	$0.346527\pi$
$812$	4.67414	0.164030
$813$	0	0
$814$	125.047	4.38288
$815$	−34.9760	−1.22516
$816$	0	0
$817$	63.8008	2.23211
$818$	19.3250	0.675682
$819$	0	0
$820$	90.0725	3.14547
$821$	−21.8673	−0.763172	−0.381586	−	0.924333i	$-0.624622\pi$
$821$	−21.8673	−0.763172	−0.381586	+	0.924333i	$0.624622\pi$
$822$	0	0
$823$	−33.6657	−1.17351	−0.586756	−	0.809764i	$-0.699595\pi$
$823$	−33.6657	−1.17351	−0.586756	+	0.809764i	$0.699595\pi$
$824$	47.4927	1.65449
$825$	0	0
$826$	12.2505	0.426249
$827$	49.4034	1.71793	0.858963	−	0.512038i	$-0.171109\pi$
$827$	49.4034	1.71793	0.858963	+	0.512038i	$0.171109\pi$
$828$	0	0
$829$	3.54310	0.123057	0.0615285	−	0.998105i	$-0.480402\pi$
$829$	3.54310	0.123057	0.0615285	+	0.998105i	$0.480402\pi$
$830$	2.28775	0.0794090
$831$	0	0
$832$	−87.6535	−3.03884
$833$	29.9204	1.03668
$834$	0	0
$835$	24.5738	0.850412
$836$	201.341	6.96351
$837$	0	0
$838$	−40.0013	−1.38182
$839$	27.3924	0.945691	0.472846	−	0.881145i	$-0.343227\pi$
$839$	27.3924	0.945691	0.472846	+	0.881145i	$0.343227\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−18.8776	−0.650564
$843$	0	0
$844$	30.5615	1.05197
$845$	−2.27261	−0.0781802
$846$	0	0
$847$	18.6882	0.642133
$848$	131.919	4.53011
$849$	0	0
$850$	36.8947	1.26548
$851$	8.14977	0.279371
$852$	0	0
$853$	18.4109	0.630376	0.315188	−	0.949029i	$-0.397932\pi$
$853$	18.4109	0.630376	0.315188	+	0.949029i	$0.397932\pi$
$854$	19.0358	0.651391
$855$	0	0
$856$	70.0039	2.39268
$857$	−40.3861	−1.37956	−0.689782	−	0.724018i	$-0.742293\pi$
$857$	−40.3861	−1.37956	−0.689782	+	0.724018i	$0.742293\pi$
$858$	0	0
$859$	38.5166	1.31417	0.657085	−	0.753816i	$-0.271789\pi$
$859$	38.5166	1.31417	0.657085	+	0.753816i	$0.271789\pi$
$860$	−141.840	−4.83670
$861$	0	0
$862$	49.3139	1.67964
$863$	−22.4884	−0.765513	−0.382756	−	0.923849i	$-0.625025\pi$
$863$	−22.4884	−0.765513	−0.382756	+	0.923849i	$0.625025\pi$
$864$	0	0
$865$	41.3454	1.40578
$866$	17.6827	0.600882
$867$	0	0
$868$	3.64118	0.123590
$869$	85.7387	2.90849
$870$	0	0
$871$	31.0719	1.05283
$872$	−100.498	−3.40330
$873$	0	0
$874$	18.0673	0.611136
$875$	5.32814	0.180124
$876$	0	0
$877$	−2.78341	−0.0939892	−0.0469946	−	0.998895i	$-0.514964\pi$
$877$	−2.78341	−0.0939892	−0.0469946	+	0.998895i	$0.514964\pi$
$878$	67.3714	2.27367
$879$	0	0
$880$	−215.358	−7.25973
$881$	0.347005	0.0116909	0.00584544	−	0.999983i	$-0.498139\pi$
$881$	0.347005	0.0116909	0.00584544	+	0.999983i	$0.498139\pi$
$882$	0	0
$883$	−31.9999	−1.07688	−0.538442	−	0.842663i	$-0.680987\pi$
$883$	−31.9999	−1.07688	−0.538442	+	0.842663i	$0.680987\pi$
$884$	94.8104	3.18882
$885$	0	0
$886$	−85.7514	−2.88087
$887$	−54.2012	−1.81990	−0.909949	−	0.414721i	$-0.863879\pi$
$887$	−54.2012	−1.81990	−0.909949	+	0.414721i	$0.863879\pi$
$888$	0	0
$889$	0.181783	0.00609682
$890$	81.0907	2.71817
$891$	0	0
$892$	64.1710	2.14860
$893$	51.3326	1.71778
$894$	0	0
$895$	−22.3020	−0.745475
$896$	−23.1222	−0.772459
$897$	0	0
$898$	74.6706	2.49179
$899$	0.779005	0.0259813
$900$	0	0
$901$	−46.7968	−1.55903
$902$	93.0088	3.09685
$903$	0	0
$904$	−156.369	−5.20075
$905$	−28.8005	−0.957363
$906$	0	0
$907$	−8.16651	−0.271164	−0.135582	−	0.990766i	$-0.543290\pi$
$907$	−8.16651	−0.271164	−0.135582	+	0.990766i	$0.543290\pi$
$908$	143.530	4.76322
$909$	0	0
$910$	−24.7732	−0.821222
$911$	−21.0259	−0.696618	−0.348309	−	0.937380i	$-0.613244\pi$
$911$	−21.0259	−0.696618	−0.348309	+	0.937380i	$0.613244\pi$
$912$	0	0
$913$	1.71574	0.0567828
$914$	−9.12474	−0.301820
$915$	0	0
$916$	−28.2344	−0.932890
$917$	−8.37039	−0.276415
$918$	0	0
$919$	−12.9335	−0.426638	−0.213319	−	0.976983i	$-0.568427\pi$
$919$	−12.9335	−0.426638	−0.213319	+	0.976983i	$0.568427\pi$
$920$	−25.0297	−0.825204
$921$	0	0
$922$	108.085	3.55961
$923$	31.6882	1.04303
$924$	0	0
$925$	−23.1398	−0.760833
$926$	−24.8345	−0.816113
$927$	0	0
$928$	−18.7511	−0.615536
$929$	13.5273	0.443817	0.221909	−	0.975067i	$-0.428771\pi$
$929$	13.5273	0.443817	0.221909	+	0.975067i	$0.428771\pi$
$930$	0	0
$931$	−41.6018	−1.36344
$932$	−126.703	−4.15028
$933$	0	0
$934$	35.3636	1.15713
$935$	76.3961	2.49842
$936$	0	0
$937$	−4.15878	−0.135862	−0.0679308	−	0.997690i	$-0.521640\pi$
$937$	−4.15878	−0.135862	−0.0679308	+	0.997690i	$0.521640\pi$
$938$	19.9050	0.649923
$939$	0	0
$940$	−114.121	−3.72222
$941$	46.9661	1.53105	0.765525	−	0.643406i	$-0.222479\pi$
$941$	46.9661	1.53105	0.765525	+	0.643406i	$0.222479\pi$
$942$	0	0
$943$	6.06174	0.197398
$944$	−69.7273	−2.26943
$945$	0	0
$946$	−146.464	−4.76195
$947$	6.09656	0.198112	0.0990558	−	0.995082i	$-0.468418\pi$
$947$	6.09656	0.198112	0.0990558	+	0.995082i	$0.468418\pi$
$948$	0	0
$949$	47.0783	1.52823
$950$	−51.2990	−1.66436
$951$	0	0
$952$	37.8478	1.22665
$953$	9.32474	0.302058	0.151029	−	0.988529i	$-0.451741\pi$
$953$	9.32474	0.302058	0.151029	+	0.988529i	$0.451741\pi$
$954$	0	0
$955$	64.5476	2.08871
$956$	43.7717	1.41568
$957$	0	0
$958$	112.285	3.62777
$959$	−3.76713	−0.121647
$960$	0	0
$961$	−30.3932	−0.980424
$962$	−81.8730	−2.63969
$963$	0	0
$964$	56.0396	1.80492
$965$	−15.8862	−0.511393
$966$	0	0
$967$	−43.6266	−1.40294	−0.701468	−	0.712701i	$-0.747472\pi$
$967$	−43.6266	−1.40294	−0.701468	+	0.712701i	$0.747472\pi$
$968$	−189.686	−6.09675
$969$	0	0
$970$	−6.69078	−0.214828
$971$	−19.3929	−0.622347	−0.311173	−	0.950353i	$-0.600722\pi$
$971$	−19.3929	−0.622347	−0.311173	+	0.950353i	$0.600722\pi$
$972$	0	0
$973$	−8.34155	−0.267418
$974$	−60.6256	−1.94257
$975$	0	0
$976$	−108.348	−3.46813
$977$	58.1111	1.85914	0.929569	−	0.368649i	$-0.120180\pi$
$977$	58.1111	1.85914	0.929569	+	0.368649i	$0.120180\pi$
$978$	0	0
$979$	60.8155	1.94367
$980$	92.4879	2.95442
$981$	0	0
$982$	37.5269	1.19753
$983$	−30.4731	−0.971942	−0.485971	−	0.873975i	$-0.661534\pi$
$983$	−30.4731	−0.971942	−0.485971	+	0.873975i	$0.661534\pi$
$984$	0	0
$985$	22.3084	0.710804
$986$	12.9942	0.413819
$987$	0	0
$988$	−131.826	−4.19394
$989$	−9.54562	−0.303533
$990$	0	0
$991$	11.8870	0.377603	0.188802	−	0.982015i	$-0.439540\pi$
$991$	11.8870	0.377603	0.188802	+	0.982015i	$0.439540\pi$
$992$	−14.6072	−0.463780
$993$	0	0
$994$	20.2998	0.643872
$995$	19.4677	0.617168
$996$	0	0
$997$	−33.6336	−1.06519	−0.532593	−	0.846371i	$-0.678782\pi$
$997$	−33.6336	−1.06519	−0.532593	+	0.846371i	$0.678782\pi$
$998$	29.5635	0.935818
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6003.2.a.m.1.2		11
3.2	odd	2		2001.2.a.l.1.10	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.l.1.10	✓	11	3.2	odd	2
6003.2.a.m.1.2		11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.70316 q^{2} +5.30708 q^{4} -2.79988 q^{5} +0.880738 q^{7} -8.93955 q^{8} +O(q^{10})\)	\(q-2.70316 q^{2} +5.30708 q^{4} -2.79988 q^{5} +0.880738 q^{7} -8.93955 q^{8} +7.56852 q^{10} +5.67616 q^{11} -3.71641 q^{13} -2.38078 q^{14} +13.5509 q^{16} -4.80704 q^{17} +6.68378 q^{19} -14.8592 q^{20} -15.3436 q^{22} -1.00000 q^{23} +2.83932 q^{25} +10.0460 q^{26} +4.67414 q^{28} +1.00000 q^{29} +0.779005 q^{31} -18.7511 q^{32} +12.9942 q^{34} -2.46596 q^{35} -8.14977 q^{37} -18.0673 q^{38} +25.0297 q^{40} -6.06174 q^{41} +9.54562 q^{43} +30.1238 q^{44} +2.70316 q^{46} +7.68018 q^{47} -6.22430 q^{49} -7.67515 q^{50} -19.7233 q^{52} +9.73506 q^{53} -15.8926 q^{55} -7.87341 q^{56} -2.70316 q^{58} -5.14558 q^{59} -7.99562 q^{61} -2.10578 q^{62} +23.5855 q^{64} +10.4055 q^{65} -8.36073 q^{67} -25.5113 q^{68} +6.66589 q^{70} -8.52656 q^{71} -12.6677 q^{73} +22.0301 q^{74} +35.4713 q^{76} +4.99921 q^{77} +15.1051 q^{79} -37.9409 q^{80} +16.3859 q^{82} +0.302272 q^{83} +13.4591 q^{85} -25.8033 q^{86} -50.7423 q^{88} +10.7142 q^{89} -3.27318 q^{91} -5.30708 q^{92} -20.7608 q^{94} -18.7138 q^{95} -0.884027 q^{97} +16.8253 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + O(q^{10}) \)	\( 11q - 2q^{2} + 18q^{4} - 2q^{5} + 3q^{7} - 18q^{8} + 14q^{10} - 11q^{11} - 5q^{13} - 17q^{14} + 20q^{16} - 15q^{17} - 6q^{19} - 21q^{20} - 10q^{22} - 11q^{23} + 3q^{25} + 5q^{26} + 7q^{28} + 11q^{29} + 35q^{31} - 28q^{32} + 28q^{34} - 15q^{35} - 28q^{37} + 2q^{38} - q^{40} - 10q^{41} - 6q^{43} - 18q^{44} + 2q^{46} - 15q^{47} + 22q^{49} - 15q^{50} - 36q^{52} + 7q^{53} - 12q^{55} - 56q^{56} - 2q^{58} + 20q^{59} - 20q^{61} + 11q^{62} + 36q^{64} - 11q^{65} - 39q^{67} - 35q^{68} + 38q^{70} - 49q^{71} - 3q^{73} - 37q^{74} - 18q^{76} - 25q^{77} + 41q^{79} - 51q^{80} - 19q^{82} - 13q^{83} - 62q^{86} - 40q^{88} - 34q^{89} + 2q^{91} - 18q^{92} - 14q^{94} - 25q^{95} - 11q^{97} - 53q^{98} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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