LMFDB - Embedded newform 7105.2.a.s.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7105,2,Mod(1,7105)] 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("7105.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7105, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7105 = 5 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7105.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,3,-1,7,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$56.7337106361$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 21x^{4} + 3x^{3} - 31x^{2} + 14x - 1 $ x^7 - 3x^6 - 6x^5 + 21x^4 + 3x^3 - 31x^2 + 14x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1015)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.19292$ of defining polynomial
Character	$\chi$	$=$	7105.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.19292 q^{2} +0.358243 q^{3} +2.80892 q^{4} +1.00000 q^{5} -0.785599 q^{6} -1.77389 q^{8} -2.87166 q^{9} -2.19292 q^{10} -2.01627 q^{11} +1.00627 q^{12} +1.14384 q^{13} +0.358243 q^{15} -1.72782 q^{16} -3.27769 q^{17} +6.29734 q^{18} +4.79354 q^{19} +2.80892 q^{20} +4.42153 q^{22} +4.15011 q^{23} -0.635484 q^{24} +1.00000 q^{25} -2.50836 q^{26} -2.10348 q^{27} +1.00000 q^{29} -0.785599 q^{30} +2.36657 q^{31} +7.33677 q^{32} -0.722314 q^{33} +7.18772 q^{34} -8.06626 q^{36} -5.74059 q^{37} -10.5119 q^{38} +0.409773 q^{39} -1.77389 q^{40} +6.03010 q^{41} +5.69672 q^{43} -5.66353 q^{44} -2.87166 q^{45} -9.10089 q^{46} -1.67453 q^{47} -0.618979 q^{48} -2.19292 q^{50} -1.17421 q^{51} +3.21296 q^{52} +6.74992 q^{53} +4.61277 q^{54} -2.01627 q^{55} +1.71725 q^{57} -2.19292 q^{58} -5.87726 q^{59} +1.00627 q^{60} -0.0951547 q^{61} -5.18970 q^{62} -12.6333 q^{64} +1.14384 q^{65} +1.58398 q^{66} -14.9900 q^{67} -9.20675 q^{68} +1.48675 q^{69} +8.10157 q^{71} +5.09402 q^{72} -10.8937 q^{73} +12.5887 q^{74} +0.358243 q^{75} +13.4647 q^{76} -0.898600 q^{78} -2.88376 q^{79} -1.72782 q^{80} +7.86143 q^{81} -13.2236 q^{82} +4.53577 q^{83} -3.27769 q^{85} -12.4925 q^{86} +0.358243 q^{87} +3.57665 q^{88} -2.05948 q^{89} +6.29734 q^{90} +11.6573 q^{92} +0.847805 q^{93} +3.67212 q^{94} +4.79354 q^{95} +2.62834 q^{96} -5.56537 q^{97} +5.79005 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 3 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + 4 q^{6} + 6 q^{8} + 12 q^{9} + 3 q^{10} + 7 q^{11} + 3 q^{12} - 5 q^{13} - q^{15} + 7 q^{16} - 14 q^{17} + 29 q^{18} + 9 q^{19} + 7 q^{20} + 9 q^{22} + 12 q^{23}+ \cdots - 7 q^{99}+O(q^{100}) $ 7 * q + 3 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + 4 * q^6 + 6 * q^8 + 12 * q^9 + 3 * q^10 + 7 * q^11 + 3 * q^12 - 5 * q^13 - q^15 + 7 * q^16 - 14 * q^17 + 29 * q^18 + 9 * q^19 + 7 * q^20 + 9 * q^22 + 12 * q^23 - 12 * q^24 + 7 * q^25 + 3 * q^26 - 4 * q^27 + 7 * q^29 + 4 * q^30 + 7 * q^31 + 20 * q^32 - 14 * q^33 - 17 * q^34 + 15 * q^36 + 23 * q^37 + q^38 - 5 * q^39 + 6 * q^40 - 13 * q^41 + 31 * q^43 + 6 * q^44 + 12 * q^45 + 5 * q^46 + 6 * q^47 - 12 * q^48 + 3 * q^50 - 10 * q^51 + 7 * q^52 + 23 * q^53 + 15 * q^54 + 7 * q^55 + 29 * q^57 + 3 * q^58 - 4 * q^59 + 3 * q^60 + 4 * q^61 + 5 * q^62 - 20 * q^64 - 5 * q^65 + 5 * q^66 + 13 * q^67 - 24 * q^68 + 29 * q^69 - 11 * q^71 + 53 * q^72 - 8 * q^73 + 50 * q^74 - q^75 + 43 * q^76 - 64 * q^78 + 7 * q^80 + 19 * q^81 - 32 * q^82 + 6 * q^83 - 14 * q^85 + 23 * q^86 - q^87 + 13 * q^88 + 5 * q^89 + 29 * q^90 + 11 * q^92 - 24 * q^93 + 44 * q^94 + 9 * q^95 - 13 * q^96 - 4 * q^97 - 7 * q^99

Coefficient data

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

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

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

$2$	−2.19292	−1.55063	−0.775316	−	0.631574i	$-0.782409\pi$
$2$	−2.19292	−1.55063	−0.775316	+	0.631574i	$0.782409\pi$
$3$	0.358243	0.206831	0.103416	−	0.994638i	$-0.467023\pi$
$3$	0.358243	0.206831	0.103416	+	0.994638i	$0.467023\pi$
$4$	2.80892	1.40446
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.785599	−0.320719
$7$	0	0
$7$	0	0
$8$	−1.77389	−0.627166
$9$	−2.87166	−0.957221
$10$	−2.19292	−0.693464
$11$	−2.01627	−0.607928	−0.303964	−	0.952683i	$-0.598310\pi$
$11$	−2.01627	−0.607928	−0.303964	+	0.952683i	$0.598310\pi$
$12$	1.00627	0.290486
$13$	1.14384	0.317245	0.158622	−	0.987339i	$-0.449295\pi$
$13$	1.14384	0.317245	0.158622	+	0.987339i	$0.449295\pi$
$14$	0	0
$15$	0.358243	0.0924978
$16$	−1.72782	−0.431955
$17$	−3.27769	−0.794956	−0.397478	−	0.917612i	$-0.630114\pi$
$17$	−3.27769	−0.794956	−0.397478	+	0.917612i	$0.630114\pi$
$18$	6.29734	1.48430
$19$	4.79354	1.09971	0.549857	−	0.835259i	$-0.314682\pi$
$19$	4.79354	1.09971	0.549857	+	0.835259i	$0.314682\pi$
$20$	2.80892	0.628093
$21$	0	0
$22$	4.42153	0.942673
$23$	4.15011	0.865359	0.432679	−	0.901548i	$-0.357568\pi$
$23$	4.15011	0.865359	0.432679	+	0.901548i	$0.357568\pi$
$24$	−0.635484	−0.129718
$25$	1.00000	0.200000
$26$	−2.50836	−0.491929
$27$	−2.10348	−0.404815
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−0.785599	−0.143430
$31$	2.36657	0.425048	0.212524	−	0.977156i	$-0.431832\pi$
$31$	2.36657	0.425048	0.212524	+	0.977156i	$0.431832\pi$
$32$	7.33677	1.29697
$33$	−0.722314	−0.125739
$34$	7.18772	1.23268
$35$	0	0
$36$	−8.06626	−1.34438
$37$	−5.74059	−0.943748	−0.471874	−	0.881666i	$-0.656422\pi$
$37$	−5.74059	−0.943748	−0.471874	+	0.881666i	$0.656422\pi$
$38$	−10.5119	−1.70525
$39$	0.409773	0.0656161
$40$	−1.77389	−0.280477
$41$	6.03010	0.941744	0.470872	−	0.882202i	$-0.343939\pi$
$41$	6.03010	0.941744	0.470872	+	0.882202i	$0.343939\pi$
$42$	0	0
$43$	5.69672	0.868741	0.434371	−	0.900734i	$-0.356971\pi$
$43$	5.69672	0.868741	0.434371	+	0.900734i	$0.356971\pi$
$44$	−5.66353	−0.853810
$45$	−2.87166	−0.428082
$46$	−9.10089	−1.34185
$47$	−1.67453	−0.244256	−0.122128	−	0.992514i	$-0.538972\pi$
$47$	−1.67453	−0.244256	−0.122128	+	0.992514i	$0.538972\pi$
$48$	−0.618979	−0.0893419
$49$	0	0
$50$	−2.19292	−0.310126
$51$	−1.17421	−0.164422
$52$	3.21296	0.445557
$53$	6.74992	0.927173	0.463586	−	0.886052i	$-0.346562\pi$
$53$	6.74992	0.927173	0.463586	+	0.886052i	$0.346562\pi$
$54$	4.61277	0.627719
$55$	−2.01627	−0.271874
$56$	0	0
$57$	1.71725	0.227456
$58$	−2.19292	−0.287945
$59$	−5.87726	−0.765154	−0.382577	−	0.923924i	$-0.624963\pi$
$59$	−5.87726	−0.765154	−0.382577	+	0.923924i	$0.624963\pi$
$60$	1.00627	0.129909
$61$	−0.0951547	−0.0121833	−0.00609165	−	0.999981i	$-0.501939\pi$
$61$	−0.0951547	−0.0121833	−0.00609165	+	0.999981i	$0.501939\pi$
$62$	−5.18970	−0.659093
$63$	0	0
$64$	−12.6333	−1.57917
$65$	1.14384	0.141876
$66$	1.58398	0.194974
$67$	−14.9900	−1.83132	−0.915662	−	0.401949i	$-0.868333\pi$
$67$	−14.9900	−1.83132	−0.915662	+	0.401949i	$0.868333\pi$
$68$	−9.20675	−1.11648
$69$	1.48675	0.178983
$70$	0	0
$71$	8.10157	0.961479	0.480740	−	0.876863i	$-0.340368\pi$
$71$	8.10157	0.961479	0.480740	+	0.876863i	$0.340368\pi$
$72$	5.09402	0.600336
$73$	−10.8937	−1.27501	−0.637505	−	0.770446i	$-0.720034\pi$
$73$	−10.8937	−1.27501	−0.637505	+	0.770446i	$0.720034\pi$
$74$	12.5887	1.46341
$75$	0.358243	0.0413663
$76$	13.4647	1.54450
$77$	0	0
$78$	−0.898600	−0.101746
$79$	−2.88376	−0.324449	−0.162224	−	0.986754i	$-0.551867\pi$
$79$	−2.88376	−0.324449	−0.162224	+	0.986754i	$0.551867\pi$
$80$	−1.72782	−0.193176
$81$	7.86143	0.873492
$82$	−13.2236	−1.46030
$83$	4.53577	0.497865	0.248933	−	0.968521i	$-0.419920\pi$
$83$	4.53577	0.497865	0.248933	+	0.968521i	$0.419920\pi$
$84$	0	0
$85$	−3.27769	−0.355515
$86$	−12.4925	−1.34710
$87$	0.358243	0.0384076
$88$	3.57665	0.381272
$89$	−2.05948	−0.218304	−0.109152	−	0.994025i	$-0.534814\pi$
$89$	−2.05948	−0.218304	−0.109152	+	0.994025i	$0.534814\pi$
$90$	6.29734	0.663798
$91$	0	0
$92$	11.6573	1.21536
$93$	0.847805	0.0879133
$94$	3.67212	0.378751
$95$	4.79354	0.491807
$96$	2.62834	0.268254
$97$	−5.56537	−0.565078	−0.282539	−	0.959256i	$-0.591177\pi$
$97$	−5.56537	−0.565078	−0.282539	+	0.959256i	$0.591177\pi$
$98$	0	0
$99$	5.79005	0.581922
$100$	2.80892	0.280892
$101$	−17.6755	−1.75878	−0.879391	−	0.476100i	$-0.842050\pi$
$101$	−17.6755	−1.75878	−0.879391	+	0.476100i	$0.842050\pi$
$102$	2.57495	0.254958
$103$	−15.7538	−1.55226	−0.776132	−	0.630570i	$-0.782821\pi$
$103$	−15.7538	−1.55226	−0.776132	+	0.630570i	$0.782821\pi$
$104$	−2.02905	−0.198965
$105$	0	0
$106$	−14.8021	−1.43770
$107$	−2.01072	−0.194384	−0.0971919	−	0.995266i	$-0.530986\pi$
$107$	−2.01072	−0.194384	−0.0971919	+	0.995266i	$0.530986\pi$
$108$	−5.90850	−0.568546
$109$	12.8513	1.23093	0.615463	−	0.788166i	$-0.288969\pi$
$109$	12.8513	1.23093	0.615463	+	0.788166i	$0.288969\pi$
$110$	4.42153	0.421576
$111$	−2.05653	−0.195197
$112$	0	0
$113$	20.0736	1.88837	0.944183	−	0.329422i	$-0.106854\pi$
$113$	20.0736	1.88837	0.944183	+	0.329422i	$0.106854\pi$
$114$	−3.76580	−0.352700
$115$	4.15011	0.387000
$116$	2.80892	0.260801
$117$	−3.28473	−0.303673
$118$	12.8884	1.18647
$119$	0	0
$120$	−0.635484	−0.0580115
$121$	−6.93465	−0.630423
$122$	0.208667	0.0188918
$123$	2.16024	0.194782
$124$	6.64749	0.596962
$125$	1.00000	0.0894427
$126$	0	0
$127$	11.5376	1.02380	0.511900	−	0.859045i	$-0.328942\pi$
$127$	11.5376	1.02380	0.511900	+	0.859045i	$0.328942\pi$
$128$	13.0304	1.15174
$129$	2.04081	0.179683
$130$	−2.50836	−0.219998
$131$	−6.62167	−0.578538	−0.289269	−	0.957248i	$-0.593412\pi$
$131$	−6.62167	−0.578538	−0.289269	+	0.957248i	$0.593412\pi$
$132$	−2.02892	−0.176595
$133$	0	0
$134$	32.8720	2.83971
$135$	−2.10348	−0.181039
$136$	5.81426	0.498569
$137$	8.78833	0.750838	0.375419	−	0.926855i	$-0.377499\pi$
$137$	8.78833	0.750838	0.375419	+	0.926855i	$0.377499\pi$
$138$	−3.26033	−0.277537
$139$	−4.17955	−0.354504	−0.177252	−	0.984165i	$-0.556721\pi$
$139$	−4.17955	−0.354504	−0.177252	+	0.984165i	$0.556721\pi$
$140$	0	0
$141$	−0.599889	−0.0505198
$142$	−17.7661	−1.49090
$143$	−2.30629	−0.192862
$144$	4.96172	0.413476
$145$	1.00000	0.0830455
$146$	23.8890	1.97707
$147$	0	0
$148$	−16.1248	−1.32545
$149$	9.66419	0.791721	0.395861	−	0.918311i	$-0.370446\pi$
$149$	9.66419	0.791721	0.395861	+	0.918311i	$0.370446\pi$
$150$	−0.785599	−0.0641439
$151$	−7.76795	−0.632147	−0.316073	−	0.948735i	$-0.602365\pi$
$151$	−7.76795	−0.632147	−0.316073	+	0.948735i	$0.602365\pi$
$152$	−8.50323	−0.689703
$153$	9.41241	0.760948
$154$	0	0
$155$	2.36657	0.190087
$156$	1.15102	0.0921551
$157$	14.5507	1.16127	0.580636	−	0.814163i	$-0.302804\pi$
$157$	14.5507	1.16127	0.580636	+	0.814163i	$0.302804\pi$
$158$	6.32388	0.503101
$159$	2.41811	0.191768
$160$	7.33677	0.580022
$161$	0	0
$162$	−17.2395	−1.35446
$163$	19.7800	1.54929	0.774643	−	0.632399i	$-0.217930\pi$
$163$	19.7800	1.54929	0.774643	+	0.632399i	$0.217930\pi$
$164$	16.9381	1.32264
$165$	−0.722314	−0.0562321
$166$	−9.94660	−0.772006
$167$	10.2176	0.790664	0.395332	−	0.918538i	$-0.370629\pi$
$167$	10.2176	0.790664	0.395332	+	0.918538i	$0.370629\pi$
$168$	0	0
$169$	−11.6916	−0.899356
$170$	7.18772	0.551273
$171$	−13.7654	−1.05267
$172$	16.0016	1.22011
$173$	18.7111	1.42258	0.711288	−	0.702901i	$-0.248112\pi$
$173$	18.7111	1.42258	0.711288	+	0.702901i	$0.248112\pi$
$174$	−0.785599	−0.0595561
$175$	0	0
$176$	3.48375	0.262598
$177$	−2.10548	−0.158258
$178$	4.51627	0.338509
$179$	2.11476	0.158064	0.0790322	−	0.996872i	$-0.474817\pi$
$179$	2.11476	0.158064	0.0790322	+	0.996872i	$0.474817\pi$
$180$	−8.06626	−0.601223
$181$	7.29316	0.542096	0.271048	−	0.962566i	$-0.412630\pi$
$181$	7.29316	0.542096	0.271048	+	0.962566i	$0.412630\pi$
$182$	0	0
$183$	−0.0340885	−0.00251989
$184$	−7.36186	−0.542723
$185$	−5.74059	−0.422057
$186$	−1.85917	−0.136321
$187$	6.60870	0.483276
$188$	−4.70362	−0.343047
$189$	0	0
$190$	−10.5119	−0.762612
$191$	−7.52467	−0.544466	−0.272233	−	0.962231i	$-0.587762\pi$
$191$	−7.52467	−0.544466	−0.272233	+	0.962231i	$0.587762\pi$
$192$	−4.52580	−0.326621
$193$	19.7894	1.42447	0.712236	−	0.701940i	$-0.247683\pi$
$193$	19.7894	1.42447	0.712236	+	0.701940i	$0.247683\pi$
$194$	12.2044	0.876227
$195$	0.409773	0.0293444
$196$	0	0
$197$	−3.17854	−0.226462	−0.113231	−	0.993569i	$-0.536120\pi$
$197$	−3.17854	−0.226462	−0.113231	+	0.993569i	$0.536120\pi$
$198$	−12.6971	−0.902346
$199$	−24.0686	−1.70618	−0.853088	−	0.521766i	$-0.825273\pi$
$199$	−24.0686	−1.70618	−0.853088	+	0.521766i	$0.825273\pi$
$200$	−1.77389	−0.125433
$201$	−5.37007	−0.378775
$202$	38.7611	2.72722
$203$	0	0
$204$	−3.29825	−0.230924
$205$	6.03010	0.421161
$206$	34.5468	2.40699
$207$	−11.9177	−0.828339
$208$	−1.97635	−0.137035
$209$	−9.66508	−0.668548
$210$	0	0
$211$	1.02627	0.0706511	0.0353256	−	0.999376i	$-0.488753\pi$
$211$	1.02627	0.0706511	0.0353256	+	0.999376i	$0.488753\pi$
$212$	18.9600	1.30218
$213$	2.90233	0.198864
$214$	4.40936	0.301418
$215$	5.69672	0.388513
$216$	3.73135	0.253886
$217$	0	0
$218$	−28.1818	−1.90871
$219$	−3.90258	−0.263712
$220$	−5.66353	−0.381835
$221$	−3.74915	−0.252195
$222$	4.50980	0.302678
$223$	17.6685	1.18317	0.591586	−	0.806242i	$-0.298502\pi$
$223$	17.6685	1.18317	0.591586	+	0.806242i	$0.298502\pi$
$224$	0	0
$225$	−2.87166	−0.191444
$226$	−44.0199	−2.92816
$227$	11.6086	0.770489	0.385244	−	0.922815i	$-0.374117\pi$
$227$	11.6086	0.770489	0.385244	+	0.922815i	$0.374117\pi$
$228$	4.82362	0.319452
$229$	−6.53287	−0.431704	−0.215852	−	0.976426i	$-0.569253\pi$
$229$	−6.53287	−0.431704	−0.215852	+	0.976426i	$0.569253\pi$
$230$	−9.10089	−0.600095
$231$	0	0
$232$	−1.77389	−0.116462
$233$	−3.47069	−0.227372	−0.113686	−	0.993517i	$-0.536266\pi$
$233$	−3.47069	−0.227372	−0.113686	+	0.993517i	$0.536266\pi$
$234$	7.20316	0.470885
$235$	−1.67453	−0.109234
$236$	−16.5087	−1.07463
$237$	−1.03309	−0.0671062
$238$	0	0
$239$	−6.80972	−0.440484	−0.220242	−	0.975445i	$-0.570685\pi$
$239$	−6.80972	−0.440484	−0.220242	+	0.975445i	$0.570685\pi$
$240$	−0.618979	−0.0399549
$241$	28.1225	1.81153	0.905765	−	0.423780i	$-0.139297\pi$
$241$	28.1225	1.81153	0.905765	+	0.423780i	$0.139297\pi$
$242$	15.2072	0.977554
$243$	9.12674	0.585480
$244$	−0.267282	−0.0171109
$245$	0	0
$246$	−4.73724	−0.302035
$247$	5.48305	0.348878
$248$	−4.19804	−0.266576
$249$	1.62491	0.102974
$250$	−2.19292	−0.138693
$251$	8.52703	0.538221	0.269111	−	0.963109i	$-0.413270\pi$
$251$	8.52703	0.538221	0.269111	+	0.963109i	$0.413270\pi$
$252$	0	0
$253$	−8.36775	−0.526076
$254$	−25.3012	−1.58754
$255$	−1.17421	−0.0735317
$256$	−3.30803	−0.206752
$257$	−16.0368	−1.00035	−0.500175	−	0.865924i	$-0.666731\pi$
$257$	−16.0368	−1.00035	−0.500175	+	0.865924i	$0.666731\pi$
$258$	−4.47533	−0.278622
$259$	0	0
$260$	3.21296	0.199259
$261$	−2.87166	−0.177751
$262$	14.5208	0.897099
$263$	15.4289	0.951384	0.475692	−	0.879612i	$-0.342198\pi$
$263$	15.4289	0.951384	0.475692	+	0.879612i	$0.342198\pi$
$264$	1.28131	0.0788590
$265$	6.74992	0.414644
$266$	0	0
$267$	−0.737792	−0.0451521
$268$	−42.1057	−2.57202
$269$	8.89120	0.542106	0.271053	−	0.962564i	$-0.412628\pi$
$269$	8.89120	0.542106	0.271053	+	0.962564i	$0.412628\pi$
$270$	4.61277	0.280724
$271$	5.46715	0.332106	0.166053	−	0.986117i	$-0.446898\pi$
$271$	5.46715	0.332106	0.166053	+	0.986117i	$0.446898\pi$
$272$	5.66325	0.343385
$273$	0	0
$274$	−19.2721	−1.16427
$275$	−2.01627	−0.121586
$276$	4.17615	0.251375
$277$	11.5331	0.692956	0.346478	−	0.938058i	$-0.387377\pi$
$277$	11.5331	0.692956	0.346478	+	0.938058i	$0.387377\pi$
$278$	9.16543	0.549706
$279$	−6.79598	−0.406865
$280$	0	0
$281$	1.07613	0.0641963	0.0320981	−	0.999485i	$-0.489781\pi$
$281$	1.07613	0.0641963	0.0320981	+	0.999485i	$0.489781\pi$
$282$	1.31551	0.0783375
$283$	8.36849	0.497455	0.248728	−	0.968573i	$-0.419988\pi$
$283$	8.36849	0.497455	0.248728	+	0.968573i	$0.419988\pi$
$284$	22.7566	1.35036
$285$	1.71725	0.101721
$286$	5.05753	0.299058
$287$	0	0
$288$	−21.0687	−1.24149
$289$	−6.25677	−0.368045
$290$	−2.19292	−0.128773
$291$	−1.99375	−0.116876
$292$	−30.5995	−1.79070
$293$	−7.98654	−0.466579	−0.233289	−	0.972407i	$-0.574949\pi$
$293$	−7.98654	−0.466579	−0.233289	+	0.972407i	$0.574949\pi$
$294$	0	0
$295$	−5.87726	−0.342187
$296$	10.1832	0.591886
$297$	4.24118	0.246098
$298$	−21.1928	−1.22767
$299$	4.74707	0.274530
$300$	1.00627	0.0580972
$301$	0	0
$302$	17.0345	0.980227
$303$	−6.33213	−0.363771
$304$	−8.28239	−0.475027
$305$	−0.0951547	−0.00544854
$306$	−20.6407	−1.17995
$307$	−8.04298	−0.459037	−0.229519	−	0.973304i	$-0.573715\pi$
$307$	−8.04298	−0.459037	−0.229519	+	0.973304i	$0.573715\pi$
$308$	0	0
$309$	−5.64367	−0.321057
$310$	−5.18970	−0.294755
$311$	0.275080	0.0155984	0.00779919	−	0.999970i	$-0.497517\pi$
$311$	0.275080	0.0155984	0.00779919	+	0.999970i	$0.497517\pi$
$312$	−0.726893	−0.0411522
$313$	19.8205	1.12032	0.560161	−	0.828384i	$-0.310739\pi$
$313$	19.8205	1.12032	0.560161	+	0.828384i	$0.310739\pi$
$314$	−31.9086	−1.80071
$315$	0	0
$316$	−8.10025	−0.455675
$317$	−1.55345	−0.0872505	−0.0436253	−	0.999048i	$-0.513891\pi$
$317$	−1.55345	−0.0872505	−0.0436253	+	0.999048i	$0.513891\pi$
$318$	−5.30273	−0.297362
$319$	−2.01627	−0.112889
$320$	−12.6333	−0.706225
$321$	−0.720326	−0.0402047
$322$	0	0
$323$	−15.7117	−0.874224
$324$	22.0821	1.22678
$325$	1.14384	0.0634489
$326$	−43.3759	−2.40237
$327$	4.60387	0.254594
$328$	−10.6968	−0.590629
$329$	0	0
$330$	1.58398	0.0871952
$331$	−13.3947	−0.736238	−0.368119	−	0.929779i	$-0.619998\pi$
$331$	−13.3947	−0.736238	−0.368119	+	0.929779i	$0.619998\pi$
$332$	12.7406	0.699231
$333$	16.4850	0.903375
$334$	−22.4065	−1.22603
$335$	−14.9900	−0.818993
$336$	0	0
$337$	26.4308	1.43978	0.719889	−	0.694089i	$-0.244193\pi$
$337$	26.4308	1.43978	0.719889	+	0.694089i	$0.244193\pi$
$338$	25.6389	1.39457
$339$	7.19122	0.390573
$340$	−9.20675	−0.499306
$341$	−4.77164	−0.258399
$342$	30.1866	1.63230
$343$	0	0
$344$	−10.1054	−0.544845
$345$	1.48675	0.0800438
$346$	−41.0320	−2.20589
$347$	−19.0104	−1.02053	−0.510267	−	0.860016i	$-0.670453\pi$
$347$	−19.0104	−1.02053	−0.510267	+	0.860016i	$0.670453\pi$
$348$	1.00627	0.0539419
$349$	−15.3433	−0.821306	−0.410653	−	0.911792i	$-0.634699\pi$
$349$	−15.3433	−0.821306	−0.410653	+	0.911792i	$0.634699\pi$
$350$	0	0
$351$	−2.40605	−0.128425
$352$	−14.7929	−0.788464
$353$	3.20821	0.170756	0.0853780	−	0.996349i	$-0.472790\pi$
$353$	3.20821	0.170756	0.0853780	+	0.996349i	$0.472790\pi$
$354$	4.61717	0.245400
$355$	8.10157	0.429987
$356$	−5.78489	−0.306599
$357$	0	0
$358$	−4.63750	−0.245100
$359$	8.13970	0.429597	0.214799	−	0.976658i	$-0.431091\pi$
$359$	8.13970	0.429597	0.214799	+	0.976658i	$0.431091\pi$
$360$	5.09402	0.268478
$361$	3.97807	0.209372
$362$	−15.9933	−0.840591
$363$	−2.48429	−0.130391
$364$	0	0
$365$	−10.8937	−0.570202
$366$	0.0747534	0.00390742
$367$	29.8332	1.55728	0.778640	−	0.627471i	$-0.215910\pi$
$367$	29.8332	1.55728	0.778640	+	0.627471i	$0.215910\pi$
$368$	−7.17066	−0.373796
$369$	−17.3164	−0.901457
$370$	12.5887	0.654455
$371$	0	0
$372$	2.38141	0.123471
$373$	11.2070	0.580279	0.290139	−	0.956984i	$-0.406298\pi$
$373$	11.2070	0.580279	0.290139	+	0.956984i	$0.406298\pi$
$374$	−14.4924	−0.749383
$375$	0.358243	0.0184996
$376$	2.97044	0.153189
$377$	1.14384	0.0589108
$378$	0	0
$379$	−8.17474	−0.419908	−0.209954	−	0.977711i	$-0.567331\pi$
$379$	−8.17474	−0.419908	−0.209954	+	0.977711i	$0.567331\pi$
$380$	13.4647	0.690723
$381$	4.13327	0.211754
$382$	16.5010	0.844266
$383$	−2.81414	−0.143796	−0.0718978	−	0.997412i	$-0.522906\pi$
$383$	−2.81414	−0.143796	−0.0718978	+	0.997412i	$0.522906\pi$
$384$	4.66804	0.238215
$385$	0	0
$386$	−43.3967	−2.20883
$387$	−16.3590	−0.831577
$388$	−15.6327	−0.793628
$389$	19.4529	0.986302	0.493151	−	0.869944i	$-0.335845\pi$
$389$	19.4529	0.986302	0.493151	+	0.869944i	$0.335845\pi$
$390$	−0.898600	−0.0455024
$391$	−13.6028	−0.687922
$392$	0	0
$393$	−2.37216	−0.119660
$394$	6.97031	0.351159
$395$	−2.88376	−0.145098
$396$	16.2638	0.817285
$397$	−26.1153	−1.31069	−0.655345	−	0.755329i	$-0.727477\pi$
$397$	−26.1153	−1.31069	−0.655345	+	0.755329i	$0.727477\pi$
$398$	52.7806	2.64565
$399$	0	0
$400$	−1.72782	−0.0863910
$401$	38.1998	1.90761	0.953804	−	0.300428i	$-0.0971296\pi$
$401$	38.1998	1.90761	0.953804	+	0.300428i	$0.0971296\pi$
$402$	11.7762	0.587341
$403$	2.70698	0.134844
$404$	−49.6491	−2.47014
$405$	7.86143	0.390638
$406$	0	0
$407$	11.5746	0.573731
$408$	2.08292	0.103120
$409$	−9.38199	−0.463909	−0.231955	−	0.972727i	$-0.574512\pi$
$409$	−9.38199	−0.463909	−0.231955	+	0.972727i	$0.574512\pi$
$410$	−13.2236	−0.653065
$411$	3.14835	0.155297
$412$	−44.2510	−2.18009
$413$	0	0
$414$	26.1347	1.28445
$415$	4.53577	0.222652
$416$	8.39210	0.411456
$417$	−1.49729	−0.0733227
$418$	21.1948	1.03667
$419$	33.0177	1.61302	0.806509	−	0.591222i	$-0.201354\pi$
$419$	33.0177	1.61302	0.806509	+	0.591222i	$0.201354\pi$
$420$	0	0
$421$	−23.7106	−1.15558	−0.577791	−	0.816185i	$-0.696085\pi$
$421$	−23.7106	−1.15558	−0.577791	+	0.816185i	$0.696085\pi$
$422$	−2.25053	−0.109554
$423$	4.80869	0.233807
$424$	−11.9736	−0.581491
$425$	−3.27769	−0.158991
$426$	−6.36458	−0.308365
$427$	0	0
$428$	−5.64795	−0.273004
$429$	−0.826212	−0.0398899
$430$	−12.4925	−0.602440
$431$	10.7713	0.518833	0.259417	−	0.965766i	$-0.416470\pi$
$431$	10.7713	0.518833	0.259417	+	0.965766i	$0.416470\pi$
$432$	3.63444	0.174862
$433$	−17.7730	−0.854115	−0.427058	−	0.904224i	$-0.640450\pi$
$433$	−17.7730	−0.854115	−0.427058	+	0.904224i	$0.640450\pi$
$434$	0	0
$435$	0.358243	0.0171764
$436$	36.0981	1.72879
$437$	19.8938	0.951648
$438$	8.55807	0.408921
$439$	−5.53503	−0.264173	−0.132086	−	0.991238i	$-0.542168\pi$
$439$	−5.53503	−0.264173	−0.132086	+	0.991238i	$0.542168\pi$
$440$	3.57665	0.170510
$441$	0	0
$442$	8.22161	0.391062
$443$	8.99012	0.427134	0.213567	−	0.976928i	$-0.431492\pi$
$443$	8.99012	0.427134	0.213567	+	0.976928i	$0.431492\pi$
$444$	−5.77661	−0.274146
$445$	−2.05948	−0.0976285
$446$	−38.7457	−1.83466
$447$	3.46212	0.163753
$448$	0	0
$449$	36.7082	1.73237	0.866184	−	0.499726i	$-0.166566\pi$
$449$	36.7082	1.73237	0.866184	+	0.499726i	$0.166566\pi$
$450$	6.29734	0.296859
$451$	−12.1583	−0.572513
$452$	56.3851	2.65213
$453$	−2.78281	−0.130748
$454$	−25.4567	−1.19474
$455$	0	0
$456$	−3.04622	−0.142652
$457$	25.8694	1.21012	0.605059	−	0.796181i	$-0.293150\pi$
$457$	25.8694	1.21012	0.605059	+	0.796181i	$0.293150\pi$
$458$	14.3261	0.669414
$459$	6.89455	0.321810
$460$	11.6573	0.543526
$461$	−19.8430	−0.924181	−0.462091	−	0.886833i	$-0.652900\pi$
$461$	−19.8430	−0.924181	−0.462091	+	0.886833i	$0.652900\pi$
$462$	0	0
$463$	7.06378	0.328281	0.164141	−	0.986437i	$-0.447515\pi$
$463$	7.06378	0.328281	0.164141	+	0.986437i	$0.447515\pi$
$464$	−1.72782	−0.0802121
$465$	0.847805	0.0393160
$466$	7.61095	0.352570
$467$	−13.9400	−0.645066	−0.322533	−	0.946558i	$-0.604534\pi$
$467$	−13.9400	−0.645066	−0.322533	+	0.946558i	$0.604534\pi$
$468$	−9.22652	−0.426496
$469$	0	0
$470$	3.67212	0.169382
$471$	5.21268	0.240188
$472$	10.4256	0.479878
$473$	−11.4861	−0.528132
$474$	2.26548	0.104057
$475$	4.79354	0.219943
$476$	0	0
$477$	−19.3835	−0.887509
$478$	14.9332	0.683028
$479$	32.7564	1.49668	0.748340	−	0.663316i	$-0.230851\pi$
$479$	32.7564	1.49668	0.748340	+	0.663316i	$0.230851\pi$
$480$	2.62834	0.119967
$481$	−6.56633	−0.299399
$482$	−61.6705	−2.80902
$483$	0	0
$484$	−19.4789	−0.885403
$485$	−5.56537	−0.252710
$486$	−20.0142	−0.907865
$487$	−21.6531	−0.981194	−0.490597	−	0.871387i	$-0.663221\pi$
$487$	−21.6531	−0.981194	−0.490597	+	0.871387i	$0.663221\pi$
$488$	0.168794	0.00764095
$489$	7.08602	0.320441
$490$	0	0
$491$	31.9418	1.44151	0.720756	−	0.693189i	$-0.243795\pi$
$491$	31.9418	1.44151	0.720756	+	0.693189i	$0.243795\pi$
$492$	6.06793	0.273563
$493$	−3.27769	−0.147620
$494$	−12.0239	−0.540982
$495$	5.79005	0.260243
$496$	−4.08900	−0.183602
$497$	0	0
$498$	−3.56330	−0.159675
$499$	−25.3188	−1.13342	−0.566712	−	0.823916i	$-0.691785\pi$
$499$	−25.3188	−1.13342	−0.566712	+	0.823916i	$0.691785\pi$
$500$	2.80892	0.125619
$501$	3.66039	0.163534
$502$	−18.6991	−0.834583
$503$	−13.4540	−0.599886	−0.299943	−	0.953957i	$-0.596968\pi$
$503$	−13.4540	−0.599886	−0.299943	+	0.953957i	$0.596968\pi$
$504$	0	0
$505$	−17.6755	−0.786551
$506$	18.3498	0.815750
$507$	−4.18844	−0.186015
$508$	32.4083	1.43788
$509$	26.6570	1.18155	0.590774	−	0.806837i	$-0.298822\pi$
$509$	26.6570	1.18155	0.590774	+	0.806837i	$0.298822\pi$
$510$	2.57495	0.114021
$511$	0	0
$512$	−18.8066	−0.831140
$513$	−10.0831	−0.445181
$514$	35.1676	1.55117
$515$	−15.7538	−0.694194
$516$	5.73246	0.252357
$517$	3.37631	0.148490
$518$	0	0
$519$	6.70310	0.294233
$520$	−2.02905	−0.0889798
$521$	−31.1154	−1.36319	−0.681596	−	0.731729i	$-0.738714\pi$
$521$	−31.1154	−1.36319	−0.681596	+	0.731729i	$0.738714\pi$
$522$	6.29734	0.275627
$523$	29.8286	1.30431	0.652156	−	0.758084i	$-0.273865\pi$
$523$	29.8286	1.30431	0.652156	+	0.758084i	$0.273865\pi$
$524$	−18.5997	−0.812532
$525$	0	0
$526$	−33.8343	−1.47525
$527$	−7.75687	−0.337894
$528$	1.24803	0.0543135
$529$	−5.77655	−0.251154
$530$	−14.8021	−0.642960
$531$	16.8775	0.732421
$532$	0	0
$533$	6.89748	0.298763
$534$	1.61792	0.0700143
$535$	−2.01072	−0.0869311
$536$	26.5907	1.14854
$537$	0.757596	0.0326927
$538$	−19.4977	−0.840607
$539$	0	0
$540$	−5.90850	−0.254261
$541$	−6.86550	−0.295171	−0.147585	−	0.989049i	$-0.547150\pi$
$541$	−6.86550	−0.295171	−0.147585	+	0.989049i	$0.547150\pi$
$542$	−11.9890	−0.514974
$543$	2.61272	0.112123
$544$	−24.0476	−1.03103
$545$	12.8513	0.550487
$546$	0	0
$547$	33.2888	1.42333	0.711664	−	0.702520i	$-0.247942\pi$
$547$	33.2888	1.42333	0.711664	+	0.702520i	$0.247942\pi$
$548$	24.6857	1.05452
$549$	0.273252	0.0116621
$550$	4.42153	0.188535
$551$	4.79354	0.204212
$552$	−2.63733	−0.112252
$553$	0	0
$554$	−25.2912	−1.07452
$555$	−2.05653	−0.0872946
$556$	−11.7400	−0.497887
$557$	9.13204	0.386937	0.193469	−	0.981106i	$-0.438026\pi$
$557$	9.13204	0.386937	0.193469	+	0.981106i	$0.438026\pi$
$558$	14.9031	0.630897
$559$	6.51614	0.275603
$560$	0	0
$561$	2.36752	0.0999567
$562$	−2.35986	−0.0995447
$563$	−12.9457	−0.545598	−0.272799	−	0.962071i	$-0.587949\pi$
$563$	−12.9457	−0.545598	−0.272799	+	0.962071i	$0.587949\pi$
$564$	−1.68504	−0.0709529
$565$	20.0736	0.844503
$566$	−18.3515	−0.771370
$567$	0	0
$568$	−14.3713	−0.603007
$569$	28.0710	1.17680	0.588398	−	0.808571i	$-0.299759\pi$
$569$	28.0710	1.17680	0.588398	+	0.808571i	$0.299759\pi$
$570$	−3.76580	−0.157732
$571$	−28.3423	−1.18609	−0.593044	−	0.805170i	$-0.702074\pi$
$571$	−28.3423	−1.18609	−0.593044	+	0.805170i	$0.702074\pi$
$572$	−6.47819	−0.270867
$573$	−2.69566	−0.112613
$574$	0	0
$575$	4.15011	0.173072
$576$	36.2787	1.51161
$577$	7.10016	0.295583	0.147792	−	0.989019i	$-0.452783\pi$
$577$	7.10016	0.295583	0.147792	+	0.989019i	$0.452783\pi$
$578$	13.7206	0.570703
$579$	7.08941	0.294626
$580$	2.80892	0.116634
$581$	0	0
$582$	4.37215	0.181231
$583$	−13.6097	−0.563655
$584$	19.3242	0.799643
$585$	−3.28473	−0.135807
$586$	17.5139	0.723492
$587$	19.7143	0.813695	0.406847	−	0.913496i	$-0.366628\pi$
$587$	19.7143	0.813695	0.406847	+	0.913496i	$0.366628\pi$
$588$	0	0
$589$	11.3442	0.467431
$590$	12.8884	0.530606
$591$	−1.13869	−0.0468395
$592$	9.91872	0.407657
$593$	19.2204	0.789288	0.394644	−	0.918834i	$-0.370868\pi$
$593$	19.2204	0.789288	0.394644	+	0.918834i	$0.370868\pi$
$594$	−9.30059	−0.381608
$595$	0	0
$596$	27.1459	1.11194
$597$	−8.62239	−0.352891
$598$	−10.4100	−0.425695
$599$	−23.8329	−0.973786	−0.486893	−	0.873462i	$-0.661870\pi$
$599$	−23.8329	−0.973786	−0.486893	+	0.873462i	$0.661870\pi$
$600$	−0.635484	−0.0259435
$601$	4.66075	0.190116	0.0950580	−	0.995472i	$-0.469696\pi$
$601$	4.66075	0.190116	0.0950580	+	0.995472i	$0.469696\pi$
$602$	0	0
$603$	43.0463	1.75298
$604$	−21.8195	−0.887824
$605$	−6.93465	−0.281934
$606$	13.8859	0.564075
$607$	35.5010	1.44094	0.720472	−	0.693484i	$-0.243925\pi$
$607$	35.5010	1.44094	0.720472	+	0.693484i	$0.243925\pi$
$608$	35.1691	1.42630
$609$	0	0
$610$	0.208667	0.00844868
$611$	−1.91540	−0.0774888
$612$	26.4387	1.06872
$613$	−4.54439	−0.183546	−0.0917731	−	0.995780i	$-0.529253\pi$
$613$	−4.54439	−0.183546	−0.0917731	+	0.995780i	$0.529253\pi$
$614$	17.6376	0.711798
$615$	2.16024	0.0871093
$616$	0	0
$617$	25.4471	1.02446	0.512230	−	0.858848i	$-0.328819\pi$
$617$	25.4471	1.02446	0.512230	+	0.858848i	$0.328819\pi$
$618$	12.3761	0.497841
$619$	18.7532	0.753756	0.376878	−	0.926263i	$-0.376998\pi$
$619$	18.7532	0.753756	0.376878	+	0.926263i	$0.376998\pi$
$620$	6.64749	0.266970
$621$	−8.72968	−0.350310
$622$	−0.603230	−0.0241873
$623$	0	0
$624$	−0.708014	−0.0283432
$625$	1.00000	0.0400000
$626$	−43.4649	−1.73721
$627$	−3.46244	−0.138277
$628$	40.8717	1.63096
$629$	18.8159	0.750238
$630$	0	0
$631$	−1.51110	−0.0601558	−0.0300779	−	0.999548i	$-0.509576\pi$
$631$	−1.51110	−0.0601558	−0.0300779	+	0.999548i	$0.509576\pi$
$632$	5.11549	0.203483
$633$	0.367652	0.0146129
$634$	3.40660	0.135293
$635$	11.5376	0.457857
$636$	6.79227	0.269331
$637$	0	0
$638$	4.42153	0.175050
$639$	−23.2650	−0.920348
$640$	13.0304	0.515072
$641$	−27.8164	−1.09868	−0.549340	−	0.835599i	$-0.685121\pi$
$641$	−27.8164	−1.09868	−0.549340	+	0.835599i	$0.685121\pi$
$642$	1.57962	0.0623426
$643$	−25.3347	−0.999102	−0.499551	−	0.866285i	$-0.666502\pi$
$643$	−25.3347	−0.999102	−0.499551	+	0.866285i	$0.666502\pi$
$644$	0	0
$645$	2.04081	0.0803567
$646$	34.4546	1.35560
$647$	17.8486	0.701700	0.350850	−	0.936432i	$-0.385893\pi$
$647$	17.8486	0.701700	0.350850	+	0.936432i	$0.385893\pi$
$648$	−13.9453	−0.547824
$649$	11.8501	0.465159
$650$	−2.50836	−0.0983859
$651$	0	0
$652$	55.5602	2.17591
$653$	−0.578609	−0.0226427	−0.0113214	−	0.999936i	$-0.503604\pi$
$653$	−0.578609	−0.0226427	−0.0113214	+	0.999936i	$0.503604\pi$
$654$	−10.0959	−0.394782
$655$	−6.62167	−0.258730
$656$	−10.4189	−0.406791
$657$	31.2830	1.22047
$658$	0	0
$659$	−12.8202	−0.499404	−0.249702	−	0.968323i	$-0.580333\pi$
$659$	−12.8202	−0.499404	−0.249702	+	0.968323i	$0.580333\pi$
$660$	−2.02892	−0.0789756
$661$	−38.8314	−1.51037	−0.755184	−	0.655513i	$-0.772452\pi$
$661$	−38.8314	−1.51037	−0.755184	+	0.655513i	$0.772452\pi$
$662$	29.3735	1.14163
$663$	−1.34311	−0.0521619
$664$	−8.04597	−0.312244
$665$	0	0
$666$	−36.1505	−1.40080
$667$	4.15011	0.160693
$668$	28.7005	1.11046
$669$	6.32962	0.244717
$670$	32.8720	1.26996
$671$	0.191858	0.00740658
$672$	0	0
$673$	34.6158	1.33434	0.667171	−	0.744904i	$-0.267505\pi$
$673$	34.6158	1.33434	0.667171	+	0.744904i	$0.267505\pi$
$674$	−57.9608	−2.23257
$675$	−2.10348	−0.0809630
$676$	−32.8408	−1.26311
$677$	44.2441	1.70044	0.850219	−	0.526430i	$-0.176470\pi$
$677$	44.2441	1.70044	0.850219	+	0.526430i	$0.176470\pi$
$678$	−15.7698	−0.605635
$679$	0	0
$680$	5.81426	0.222967
$681$	4.15869	0.159361
$682$	10.4638	0.400681
$683$	24.0701	0.921018	0.460509	−	0.887655i	$-0.347667\pi$
$683$	24.0701	0.921018	0.460509	+	0.887655i	$0.347667\pi$
$684$	−38.6660	−1.47843
$685$	8.78833	0.335785
$686$	0	0
$687$	−2.34035	−0.0892900
$688$	−9.84291	−0.375257
$689$	7.72084	0.294140
$690$	−3.26033	−0.124118
$691$	−18.3274	−0.697206	−0.348603	−	0.937270i	$-0.613344\pi$
$691$	−18.3274	−0.697206	−0.348603	+	0.937270i	$0.613344\pi$
$692$	52.5578	1.99795
$693$	0	0
$694$	41.6884	1.58247
$695$	−4.17955	−0.158539
$696$	−0.635484	−0.0240880
$697$	−19.7648	−0.748644
$698$	33.6466	1.27354
$699$	−1.24335	−0.0470277
$700$	0	0
$701$	4.68603	0.176989	0.0884944	−	0.996077i	$-0.471794\pi$
$701$	4.68603	0.176989	0.0884944	+	0.996077i	$0.471794\pi$
$702$	5.27628	0.199140
$703$	−27.5178	−1.03785
$704$	25.4722	0.960020
$705$	−0.599889	−0.0225931
$706$	−7.03537	−0.264780
$707$	0	0
$708$	−5.91413	−0.222267
$709$	31.1993	1.17171	0.585857	−	0.810414i	$-0.300758\pi$
$709$	31.1993	1.17171	0.585857	+	0.810414i	$0.300758\pi$
$710$	−17.7661	−0.666751
$711$	8.28120	0.310569
$712$	3.65329	0.136913
$713$	9.82153	0.367819
$714$	0	0
$715$	−2.30629	−0.0862505
$716$	5.94018	0.221995
$717$	−2.43953	−0.0911059
$718$	−17.8497	−0.666147
$719$	41.7530	1.55712	0.778562	−	0.627568i	$-0.215949\pi$
$719$	41.7530	1.55712	0.778562	+	0.627568i	$0.215949\pi$
$720$	4.96172	0.184912
$721$	0	0
$722$	−8.72360	−0.324659
$723$	10.0747	0.374681
$724$	20.4859	0.761351
$725$	1.00000	0.0371391
$726$	5.44786	0.202189
$727$	25.7038	0.953300	0.476650	−	0.879093i	$-0.341851\pi$
$727$	25.7038	0.953300	0.476650	+	0.879093i	$0.341851\pi$
$728$	0	0
$729$	−20.3147	−0.752397
$730$	23.8890	0.884173
$731$	−18.6721	−0.690611
$732$	−0.0957516	−0.00353908
$733$	−33.1773	−1.22543	−0.612715	−	0.790304i	$-0.709923\pi$
$733$	−33.1773	−1.22543	−0.612715	+	0.790304i	$0.709923\pi$
$734$	−65.4219	−2.41477
$735$	0	0
$736$	30.4484	1.12234
$737$	30.2240	1.11331
$738$	37.9736	1.39783
$739$	−11.3783	−0.418559	−0.209280	−	0.977856i	$-0.567112\pi$
$739$	−11.3783	−0.418559	−0.209280	+	0.977856i	$0.567112\pi$
$740$	−16.1248	−0.592761
$741$	1.96426	0.0721590
$742$	0	0
$743$	−23.3059	−0.855012	−0.427506	−	0.904013i	$-0.640608\pi$
$743$	−23.3059	−0.855012	−0.427506	+	0.904013i	$0.640608\pi$
$744$	−1.50392	−0.0551362
$745$	9.66419	0.354068
$746$	−24.5762	−0.899799
$747$	−13.0252	−0.476567
$748$	18.5633	0.678741
$749$	0	0
$750$	−0.785599	−0.0286860
$751$	49.8246	1.81813	0.909063	−	0.416658i	$-0.136799\pi$
$751$	49.8246	1.81813	0.909063	+	0.416658i	$0.136799\pi$
$752$	2.89329	0.105508
$753$	3.05474	0.111321
$754$	−2.50836	−0.0913490
$755$	−7.76795	−0.282705
$756$	0	0
$757$	9.88103	0.359132	0.179566	−	0.983746i	$-0.442531\pi$
$757$	9.88103	0.359132	0.179566	+	0.983746i	$0.442531\pi$
$758$	17.9266	0.651123
$759$	−2.99769	−0.108809
$760$	−8.50323	−0.308445
$761$	−29.2380	−1.05988	−0.529938	−	0.848036i	$-0.677785\pi$
$761$	−29.2380	−1.05988	−0.529938	+	0.848036i	$0.677785\pi$
$762$	−9.06395	−0.328352
$763$	0	0
$764$	−21.1362	−0.764680
$765$	9.41241	0.340306
$766$	6.17119	0.222974
$767$	−6.72265	−0.242741
$768$	−1.18508	−0.0427627
$769$	−17.1071	−0.616897	−0.308449	−	0.951241i	$-0.599810\pi$
$769$	−17.1071	−0.616897	−0.308449	+	0.951241i	$0.599810\pi$
$770$	0	0
$771$	−5.74508	−0.206904
$772$	55.5868	2.00061
$773$	28.5875	1.02822	0.514110	−	0.857725i	$-0.328122\pi$
$773$	28.5875	1.02822	0.514110	+	0.857725i	$0.328122\pi$
$774$	35.8742	1.28947
$775$	2.36657	0.0850096
$776$	9.87237	0.354397
$777$	0	0
$778$	−42.6588	−1.52939
$779$	28.9056	1.03565
$780$	1.15102	0.0412130
$781$	−16.3349	−0.584510
$782$	29.8299	1.06671
$783$	−2.10348	−0.0751722
$784$	0	0
$785$	14.5507	0.519337
$786$	5.20197	0.185548
$787$	19.6440	0.700234	0.350117	−	0.936706i	$-0.386142\pi$
$787$	19.6440	0.700234	0.350117	+	0.936706i	$0.386142\pi$
$788$	−8.92827	−0.318056
$789$	5.52727	0.196776
$790$	6.32388	0.224993
$791$	0	0
$792$	−10.2709	−0.364961
$793$	−0.108842	−0.00386509
$794$	57.2689	2.03240
$795$	2.41811	0.0857615
$796$	−67.6067	−2.39625
$797$	−1.25487	−0.0444498	−0.0222249	−	0.999753i	$-0.507075\pi$
$797$	−1.25487	−0.0444498	−0.0222249	+	0.999753i	$0.507075\pi$
$798$	0	0
$799$	5.48859	0.194172
$800$	7.33677	0.259394
$801$	5.91412	0.208965
$802$	−83.7694	−2.95800
$803$	21.9646	0.775115
$804$	−15.0841	−0.531974
$805$	0	0
$806$	−5.93620	−0.209094
$807$	3.18521	0.112125
$808$	31.3545	1.10305
$809$	10.7880	0.379284	0.189642	−	0.981853i	$-0.439267\pi$
$809$	10.7880	0.379284	0.189642	+	0.981853i	$0.439267\pi$
$810$	−17.2395	−0.605735
$811$	−7.96908	−0.279832	−0.139916	−	0.990163i	$-0.544683\pi$
$811$	−7.96908	−0.279832	−0.139916	+	0.990163i	$0.544683\pi$
$812$	0	0
$813$	1.95857	0.0686899
$814$	−25.3822	−0.889645
$815$	19.7800	0.692862
$816$	2.02882	0.0710229
$817$	27.3075	0.955367
$818$	20.5740	0.719353
$819$	0	0
$820$	16.9381	0.591502
$821$	8.33984	0.291063	0.145531	−	0.989354i	$-0.453511\pi$
$821$	8.33984	0.291063	0.145531	+	0.989354i	$0.453511\pi$
$822$	−6.90410	−0.240808
$823$	45.3487	1.58076	0.790378	−	0.612620i	$-0.209884\pi$
$823$	45.3487	1.58076	0.790378	+	0.612620i	$0.209884\pi$
$824$	27.9455	0.973527
$825$	−0.722314	−0.0251477
$826$	0	0
$827$	28.9150	1.00547	0.502737	−	0.864439i	$-0.332326\pi$
$827$	28.9150	1.00547	0.502737	+	0.864439i	$0.332326\pi$
$828$	−33.4759	−1.16337
$829$	−40.0207	−1.38998	−0.694988	−	0.719021i	$-0.744591\pi$
$829$	−40.0207	−1.38998	−0.694988	+	0.719021i	$0.744591\pi$
$830$	−9.94660	−0.345252
$831$	4.13164	0.143325
$832$	−14.4505	−0.500982
$833$	0	0
$834$	3.28345	0.113696
$835$	10.2176	0.353596
$836$	−27.1484	−0.938947
$837$	−4.97803	−0.172066
$838$	−72.4052	−2.50120
$839$	4.07632	0.140730	0.0703651	−	0.997521i	$-0.477584\pi$
$839$	4.07632	0.140730	0.0703651	+	0.997521i	$0.477584\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	51.9955	1.79188
$843$	0.385514	0.0132778
$844$	2.88270	0.0992265
$845$	−11.6916	−0.402204
$846$	−10.5451	−0.362548
$847$	0	0
$848$	−11.6627	−0.400497
$849$	2.99795	0.102889
$850$	7.18772	0.246537
$851$	−23.8241	−0.816680
$852$	8.15239	0.279296
$853$	−18.3291	−0.627575	−0.313788	−	0.949493i	$-0.601598\pi$
$853$	−18.3291	−0.627575	−0.313788	+	0.949493i	$0.601598\pi$
$854$	0	0
$855$	−13.7654	−0.470768
$856$	3.56680	0.121911
$857$	−6.19875	−0.211745	−0.105873	−	0.994380i	$-0.533764\pi$
$857$	−6.19875	−0.211745	−0.105873	+	0.994380i	$0.533764\pi$
$858$	1.81182	0.0618546
$859$	30.9336	1.05544	0.527721	−	0.849418i	$-0.323047\pi$
$859$	30.9336	1.05544	0.527721	+	0.849418i	$0.323047\pi$
$860$	16.0016	0.545650
$861$	0	0
$862$	−23.6206	−0.804519
$863$	−32.3806	−1.10225	−0.551124	−	0.834423i	$-0.685801\pi$
$863$	−32.3806	−1.10225	−0.551124	+	0.834423i	$0.685801\pi$
$864$	−15.4327	−0.525032
$865$	18.7111	0.636195
$866$	38.9748	1.32442
$867$	−2.24144	−0.0761234
$868$	0	0
$869$	5.81445	0.197242
$870$	−0.785599	−0.0266343
$871$	−17.1462	−0.580977
$872$	−22.7967	−0.771995
$873$	15.9819	0.540904
$874$	−43.6255	−1.47565
$875$	0	0
$876$	−10.9620	−0.370373
$877$	−26.7896	−0.904621	−0.452311	−	0.891860i	$-0.649400\pi$
$877$	−26.7896	−0.904621	−0.452311	+	0.891860i	$0.649400\pi$
$878$	12.1379	0.409635
$879$	−2.86112	−0.0965032
$880$	3.48375	0.117437
$881$	33.6636	1.13416	0.567078	−	0.823664i	$-0.308074\pi$
$881$	33.6636	1.13416	0.567078	+	0.823664i	$0.308074\pi$
$882$	0	0
$883$	−25.3917	−0.854499	−0.427250	−	0.904134i	$-0.640517\pi$
$883$	−25.3917	−0.854499	−0.427250	+	0.904134i	$0.640517\pi$
$884$	−10.5311	−0.354198
$885$	−2.10548	−0.0707751
$886$	−19.7147	−0.662327
$887$	7.95683	0.267164	0.133582	−	0.991038i	$-0.457352\pi$
$887$	7.95683	0.267164	0.133582	+	0.991038i	$0.457352\pi$
$888$	3.64805	0.122421
$889$	0	0
$890$	4.51627	0.151386
$891$	−15.8508	−0.531021
$892$	49.6294	1.66172
$893$	−8.02695	−0.268611
$894$	−7.59218	−0.253920
$895$	2.11476	0.0706885
$896$	0	0
$897$	1.70060	0.0567815
$898$	−80.4983	−2.68626
$899$	2.36657	0.0789294
$900$	−8.06626	−0.268875
$901$	−22.1241	−0.737061
$902$	26.6623	0.887756
$903$	0	0
$904$	−35.6084	−1.18432
$905$	7.29316	0.242433
$906$	6.10249	0.202742
$907$	47.0395	1.56192	0.780961	−	0.624580i	$-0.214730\pi$
$907$	47.0395	1.56192	0.780961	+	0.624580i	$0.214730\pi$
$908$	32.6075	1.08212
$909$	50.7582	1.68354
$910$	0	0
$911$	48.2084	1.59721	0.798607	−	0.601853i	$-0.205571\pi$
$911$	48.2084	1.59721	0.798607	+	0.601853i	$0.205571\pi$
$912$	−2.96710	−0.0982506
$913$	−9.14534	−0.302667
$914$	−56.7296	−1.87645
$915$	−0.0340885	−0.00112693
$916$	−18.3503	−0.606310
$917$	0	0
$918$	−15.1192	−0.499008
$919$	14.6624	0.483668	0.241834	−	0.970318i	$-0.422251\pi$
$919$	14.6624	0.483668	0.241834	+	0.970318i	$0.422251\pi$
$920$	−7.36186	−0.242713
$921$	−2.88134	−0.0949433
$922$	43.5142	1.43306
$923$	9.26691	0.305024
$924$	0	0
$925$	−5.74059	−0.188750
$926$	−15.4903	−0.509044
$927$	45.2395	1.48586
$928$	7.33677	0.240841
$929$	56.9101	1.86716	0.933579	−	0.358371i	$-0.116668\pi$
$929$	56.9101	1.86716	0.933579	+	0.358371i	$0.116668\pi$
$930$	−1.85917	−0.0609647
$931$	0	0
$932$	−9.74887	−0.319335
$933$	0.0985455	0.00322623
$934$	30.5693	1.00026
$935$	6.60870	0.216128
$936$	5.82675	0.190453
$937$	−59.9509	−1.95851	−0.979256	−	0.202627i	$-0.935052\pi$
$937$	−59.9509	−1.95851	−0.979256	+	0.202627i	$0.935052\pi$
$938$	0	0
$939$	7.10055	0.231718
$940$	−4.70362	−0.153415
$941$	1.97689	0.0644448	0.0322224	−	0.999481i	$-0.489742\pi$
$941$	1.97689	0.0644448	0.0322224	+	0.999481i	$0.489742\pi$
$942$	−11.4310	−0.372443
$943$	25.0256	0.814946
$944$	10.1548	0.330512
$945$	0	0
$946$	25.1882	0.818939
$947$	44.0697	1.43207	0.716036	−	0.698063i	$-0.245954\pi$
$947$	44.0697	1.43207	0.716036	+	0.698063i	$0.245954\pi$
$948$	−2.90186	−0.0942479
$949$	−12.4607	−0.404490
$950$	−10.5119	−0.341050
$951$	−0.556512	−0.0180461
$952$	0	0
$953$	40.7220	1.31912	0.659558	−	0.751653i	$-0.270743\pi$
$953$	40.7220	1.31912	0.659558	+	0.751653i	$0.270743\pi$
$954$	42.5065	1.37620
$955$	−7.52467	−0.243493
$956$	−19.1279	−0.618641
$957$	−0.722314	−0.0233491
$958$	−71.8324	−2.32080
$959$	0	0
$960$	−4.52580	−0.146069
$961$	−25.3994	−0.819334
$962$	14.3995	0.464257
$963$	5.77411	0.186068
$964$	78.9938	2.54422
$965$	19.7894	0.637043
$966$	0	0
$967$	50.3987	1.62071	0.810357	−	0.585937i	$-0.199273\pi$
$967$	50.3987	1.62071	0.810357	+	0.585937i	$0.199273\pi$
$968$	12.3013	0.395380
$969$	−5.62861	−0.180817
$970$	12.2044	0.391861
$971$	23.7796	0.763123	0.381561	−	0.924344i	$-0.375387\pi$
$971$	23.7796	0.763123	0.381561	+	0.924344i	$0.375387\pi$
$972$	25.6362	0.822283
$973$	0	0
$974$	47.4835	1.52147
$975$	0.409773	0.0131232
$976$	0.164410	0.00526264
$977$	5.79575	0.185422	0.0927112	−	0.995693i	$-0.470447\pi$
$977$	5.79575	0.185422	0.0927112	+	0.995693i	$0.470447\pi$
$978$	−15.5391	−0.496886
$979$	4.15246	0.132713
$980$	0	0
$981$	−36.9045	−1.17827
$982$	−70.0459	−2.23525
$983$	25.9651	0.828157	0.414079	−	0.910241i	$-0.364104\pi$
$983$	25.9651	0.828157	0.414079	+	0.910241i	$0.364104\pi$
$984$	−3.83203	−0.122161
$985$	−3.17854	−0.101277
$986$	7.18772	0.228904
$987$	0	0
$988$	15.4014	0.489985
$989$	23.6420	0.751773
$990$	−12.6971	−0.403541
$991$	−37.1998	−1.18169	−0.590846	−	0.806785i	$-0.701206\pi$
$991$	−37.1998	−1.18169	−0.590846	+	0.806785i	$0.701206\pi$
$992$	17.3629	0.551274
$993$	−4.79854	−0.152277
$994$	0	0
$995$	−24.0686	−0.763026
$996$	4.56423	0.144623
$997$	−28.7494	−0.910504	−0.455252	−	0.890363i	$-0.650451\pi$
$997$	−28.7494	−0.910504	−0.455252	+	0.890363i	$0.650451\pi$
$998$	55.5221	1.75752
$999$	12.0752	0.382043

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7105.2.a.s.1.1		7
7.6	odd	2		1015.2.a.k.1.1	✓	7
21.20	even	2		9135.2.a.be.1.7		7
35.34	odd	2		5075.2.a.y.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1015.2.a.k.1.1	✓	7	7.6	odd	2
5075.2.a.y.1.7		7	35.34	odd	2
7105.2.a.s.1.1		7	1.1	even	1	trivial
9135.2.a.be.1.7		7	21.20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7105 = 5 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7105.a (trivial)

\(f(q)\)	\(=\)	\(q-2.19292 q^{2} +0.358243 q^{3} +2.80892 q^{4} +1.00000 q^{5} -0.785599 q^{6} -1.77389 q^{8} -2.87166 q^{9} -2.19292 q^{10} -2.01627 q^{11} +1.00627 q^{12} +1.14384 q^{13} +0.358243 q^{15} -1.72782 q^{16} -3.27769 q^{17} +6.29734 q^{18} +4.79354 q^{19} +2.80892 q^{20} +4.42153 q^{22} +4.15011 q^{23} -0.635484 q^{24} +1.00000 q^{25} -2.50836 q^{26} -2.10348 q^{27} +1.00000 q^{29} -0.785599 q^{30} +2.36657 q^{31} +7.33677 q^{32} -0.722314 q^{33} +7.18772 q^{34} -8.06626 q^{36} -5.74059 q^{37} -10.5119 q^{38} +0.409773 q^{39} -1.77389 q^{40} +6.03010 q^{41} +5.69672 q^{43} -5.66353 q^{44} -2.87166 q^{45} -9.10089 q^{46} -1.67453 q^{47} -0.618979 q^{48} -2.19292 q^{50} -1.17421 q^{51} +3.21296 q^{52} +6.74992 q^{53} +4.61277 q^{54} -2.01627 q^{55} +1.71725 q^{57} -2.19292 q^{58} -5.87726 q^{59} +1.00627 q^{60} -0.0951547 q^{61} -5.18970 q^{62} -12.6333 q^{64} +1.14384 q^{65} +1.58398 q^{66} -14.9900 q^{67} -9.20675 q^{68} +1.48675 q^{69} +8.10157 q^{71} +5.09402 q^{72} -10.8937 q^{73} +12.5887 q^{74} +0.358243 q^{75} +13.4647 q^{76} -0.898600 q^{78} -2.88376 q^{79} -1.72782 q^{80} +7.86143 q^{81} -13.2236 q^{82} +4.53577 q^{83} -3.27769 q^{85} -12.4925 q^{86} +0.358243 q^{87} +3.57665 q^{88} -2.05948 q^{89} +6.29734 q^{90} +11.6573 q^{92} +0.847805 q^{93} +3.67212 q^{94} +4.79354 q^{95} +2.62834 q^{96} -5.56537 q^{97} +5.79005 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 3 q^{2} - q^{3} + 7 q^{4} + 7 q^{5} + 4 q^{6} + 6 q^{8} + 12 q^{9} + 3 q^{10} + 7 q^{11} + 3 q^{12} - 5 q^{13} - q^{15} + 7 q^{16} - 14 q^{17} + 29 q^{18} + 9 q^{19} + 7 q^{20} + 9 q^{22} + 12 q^{23}+ \cdots - 7 q^{99}+O(q^{100}) \) 7 * q + 3 * q^2 - q^3 + 7 * q^4 + 7 * q^5 + 4 * q^6 + 6 * q^8 + 12 * q^9 + 3 * q^10 + 7 * q^11 + 3 * q^12 - 5 * q^13 - q^15 + 7 * q^16 - 14 * q^17 + 29 * q^18 + 9 * q^19 + 7 * q^20 + 9 * q^22 + 12 * q^23 - 12 * q^24 + 7 * q^25 + 3 * q^26 - 4 * q^27 + 7 * q^29 + 4 * q^30 + 7 * q^31 + 20 * q^32 - 14 * q^33 - 17 * q^34 + 15 * q^36 + 23 * q^37 + q^38 - 5 * q^39 + 6 * q^40 - 13 * q^41 + 31 * q^43 + 6 * q^44 + 12 * q^45 + 5 * q^46 + 6 * q^47 - 12 * q^48 + 3 * q^50 - 10 * q^51 + 7 * q^52 + 23 * q^53 + 15 * q^54 + 7 * q^55 + 29 * q^57 + 3 * q^58 - 4 * q^59 + 3 * q^60 + 4 * q^61 + 5 * q^62 - 20 * q^64 - 5 * q^65 + 5 * q^66 + 13 * q^67 - 24 * q^68 + 29 * q^69 - 11 * q^71 + 53 * q^72 - 8 * q^73 + 50 * q^74 - q^75 + 43 * q^76 - 64 * q^78 + 7 * q^80 + 19 * q^81 - 32 * q^82 + 6 * q^83 - 14 * q^85 + 23 * q^86 - q^87 + 13 * q^88 + 5 * q^89 + 29 * q^90 + 11 * q^92 - 24 * q^93 + 44 * q^94 + 9 * q^95 - 13 * q^96 - 4 * q^97 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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