LMFDB - Embedded newform 7120.2.a.bj.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7120,2,Mod(1,7120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7120, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7120.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7120 = 2^{4} \cdot 5 \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7120.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$56.8534862392$
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} - x^{6} - 8x^{5} + 6x^{4} + 19x^{3} - 10x^{2} - 12x + 6 $ x^7 - x^6 - 8x^5 + 6x^4 + 19x^3 - 10x^2 - 12*x + 6
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 445)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.96388$ of defining polynomial
Character	$\chi$	$=$	7120.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.931146 q^{3} +1.00000 q^{5} +0.580377 q^{7} -2.13297 q^{9} +O(q^{10})$	$q+0.931146 q^{3} +1.00000 q^{5} +0.580377 q^{7} -2.13297 q^{9} +4.74359 q^{11} +6.25246 q^{13} +0.931146 q^{15} -5.87935 q^{17} +5.41445 q^{19} +0.540416 q^{21} +8.56239 q^{23} +1.00000 q^{25} -4.77954 q^{27} -3.96542 q^{29} -5.68893 q^{31} +4.41697 q^{33} +0.580377 q^{35} +0.495300 q^{37} +5.82195 q^{39} +11.8503 q^{41} +4.78767 q^{43} -2.13297 q^{45} +3.78707 q^{47} -6.66316 q^{49} -5.47453 q^{51} -7.91925 q^{53} +4.74359 q^{55} +5.04164 q^{57} -10.6416 q^{59} +9.77193 q^{61} -1.23793 q^{63} +6.25246 q^{65} -1.35061 q^{67} +7.97283 q^{69} +10.7514 q^{71} +1.31208 q^{73} +0.931146 q^{75} +2.75307 q^{77} -0.492431 q^{79} +1.94845 q^{81} -1.62413 q^{83} -5.87935 q^{85} -3.69239 q^{87} +1.00000 q^{89} +3.62878 q^{91} -5.29722 q^{93} +5.41445 q^{95} -9.61533 q^{97} -10.1179 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 8 q^{3} + 7 q^{5} + 16 q^{7} + 11 q^{9}+O(q^{10}) $ 7 * q + 8 * q^3 + 7 * q^5 + 16 * q^7 + 11 * q^9	$ 7 q + 8 q^{3} + 7 q^{5} + 16 q^{7} + 11 q^{9} + 10 q^{11} - 7 q^{13} + 8 q^{15} - 13 q^{17} + 7 q^{19} + 16 q^{21} + 13 q^{23} + 7 q^{25} + 23 q^{27} - 4 q^{29} - q^{31} - 6 q^{33} + 16 q^{35} - 5 q^{37} + 13 q^{39} + 5 q^{41} + 31 q^{43} + 11 q^{45} + 14 q^{47} + 19 q^{49} + q^{51} - 13 q^{53} + 10 q^{55} + 21 q^{57} + 14 q^{59} + 3 q^{61} + 54 q^{63} - 7 q^{65} - q^{67} + 31 q^{69} + 8 q^{71} + 9 q^{73} + 8 q^{75} + 42 q^{77} - 9 q^{79} + 35 q^{81} + 42 q^{83} - 13 q^{85} - 6 q^{87} + 7 q^{89} - 31 q^{91} + 24 q^{93} + 7 q^{95} - 7 q^{97} - 5 q^{99}+O(q^{100}) $ 7 * q + 8 * q^3 + 7 * q^5 + 16 * q^7 + 11 * q^9 + 10 * q^11 - 7 * q^13 + 8 * q^15 - 13 * q^17 + 7 * q^19 + 16 * q^21 + 13 * q^23 + 7 * q^25 + 23 * q^27 - 4 * q^29 - q^31 - 6 * q^33 + 16 * q^35 - 5 * q^37 + 13 * q^39 + 5 * q^41 + 31 * q^43 + 11 * q^45 + 14 * q^47 + 19 * q^49 + q^51 - 13 * q^53 + 10 * q^55 + 21 * q^57 + 14 * q^59 + 3 * q^61 + 54 * q^63 - 7 * q^65 - q^67 + 31 * q^69 + 8 * q^71 + 9 * q^73 + 8 * q^75 + 42 * q^77 - 9 * q^79 + 35 * q^81 + 42 * q^83 - 13 * q^85 - 6 * q^87 + 7 * q^89 - 31 * q^91 + 24 * q^93 + 7 * q^95 - 7 * q^97 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0	0
$2$	0	0
$3$	0.931146	0.537597	0.268799	−	0.963196i	$-0.413373\pi$
$3$	0.931146	0.537597	0.268799	+	0.963196i	$0.413373\pi$
$4$	0	0
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	0.580377	0.219362	0.109681	−	0.993967i	$-0.465017\pi$
$7$	0.580377	0.219362	0.109681	+	0.993967i	$0.465017\pi$
$8$	0	0
$9$	−2.13297	−0.710989
$10$	0	0
$11$	4.74359	1.43025	0.715123	−	0.698998i	$-0.246371\pi$
$11$	4.74359	1.43025	0.715123	+	0.698998i	$0.246371\pi$
$12$	0	0
$13$	6.25246	1.73412	0.867060	−	0.498204i	$-0.166007\pi$
$13$	6.25246	1.73412	0.867060	+	0.498204i	$0.166007\pi$
$14$	0	0
$15$	0.931146	0.240421
$16$	0	0
$17$	−5.87935	−1.42595	−0.712976	−	0.701189i	$-0.752653\pi$
$17$	−5.87935	−1.42595	−0.712976	+	0.701189i	$0.752653\pi$
$18$	0	0
$19$	5.41445	1.24216	0.621080	−	0.783747i	$-0.286694\pi$
$19$	5.41445	1.24216	0.621080	+	0.783747i	$0.286694\pi$
$20$	0	0
$21$	0.540416	0.117928
$22$	0	0
$23$	8.56239	1.78538	0.892691	−	0.450669i	$-0.148815\pi$
$23$	8.56239	1.78538	0.892691	+	0.450669i	$0.148815\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	−4.77954	−0.919823
$28$	0	0
$29$	−3.96542	−0.736361	−0.368180	−	0.929754i	$-0.620019\pi$
$29$	−3.96542	−0.736361	−0.368180	+	0.929754i	$0.620019\pi$
$30$	0	0
$31$	−5.68893	−1.02176	−0.510881	−	0.859652i	$-0.670681\pi$
$31$	−5.68893	−1.02176	−0.510881	+	0.859652i	$0.670681\pi$
$32$	0	0
$33$	4.41697	0.768897
$34$	0	0
$35$	0.580377	0.0981017
$36$	0	0
$37$	0.495300	0.0814269	0.0407134	−	0.999171i	$-0.487037\pi$
$37$	0.495300	0.0814269	0.0407134	+	0.999171i	$0.487037\pi$
$38$	0	0
$39$	5.82195	0.932258
$40$	0	0
$41$	11.8503	1.85071	0.925356	−	0.379098i	$-0.123766\pi$
$41$	11.8503	1.85071	0.925356	+	0.379098i	$0.123766\pi$
$42$	0	0
$43$	4.78767	0.730113	0.365056	−	0.930985i	$-0.381050\pi$
$43$	4.78767	0.730113	0.365056	+	0.930985i	$0.381050\pi$
$44$	0	0
$45$	−2.13297	−0.317964
$46$	0	0
$47$	3.78707	0.552401	0.276201	−	0.961100i	$-0.410925\pi$
$47$	3.78707	0.552401	0.276201	+	0.961100i	$0.410925\pi$
$48$	0	0
$49$	−6.66316	−0.951880
$50$	0	0
$51$	−5.47453	−0.766588
$52$	0	0
$53$	−7.91925	−1.08779	−0.543897	−	0.839152i	$-0.683052\pi$
$53$	−7.91925	−1.08779	−0.543897	+	0.839152i	$0.683052\pi$
$54$	0	0
$55$	4.74359	0.639626
$56$	0	0
$57$	5.04164	0.667782
$58$	0	0
$59$	−10.6416	−1.38542	−0.692711	−	0.721216i	$-0.743584\pi$
$59$	−10.6416	−1.38542	−0.692711	+	0.721216i	$0.743584\pi$
$60$	0	0
$61$	9.77193	1.25117	0.625584	−	0.780157i	$-0.284861\pi$
$61$	9.77193	1.25117	0.625584	+	0.780157i	$0.284861\pi$
$62$	0	0
$63$	−1.23793	−0.155964
$64$	0	0
$65$	6.25246	0.775522
$66$	0	0
$67$	−1.35061	−0.165004	−0.0825019	−	0.996591i	$-0.526291\pi$
$67$	−1.35061	−0.165004	−0.0825019	+	0.996591i	$0.526291\pi$
$68$	0	0
$69$	7.97283	0.959816
$70$	0	0
$71$	10.7514	1.27595	0.637976	−	0.770056i	$-0.279772\pi$
$71$	10.7514	1.27595	0.637976	+	0.770056i	$0.279772\pi$
$72$	0	0
$73$	1.31208	0.153567	0.0767834	−	0.997048i	$-0.475535\pi$
$73$	1.31208	0.153567	0.0767834	+	0.997048i	$0.475535\pi$
$74$	0	0
$75$	0.931146	0.107519
$76$	0	0
$77$	2.75307	0.313742
$78$	0	0
$79$	−0.492431	−0.0554028	−0.0277014	−	0.999616i	$-0.508819\pi$
$79$	−0.492431	−0.0554028	−0.0277014	+	0.999616i	$0.508819\pi$
$80$	0	0
$81$	1.94845	0.216495
$82$	0	0
$83$	−1.62413	−0.178272	−0.0891359	−	0.996019i	$-0.528411\pi$
$83$	−1.62413	−0.178272	−0.0891359	+	0.996019i	$0.528411\pi$
$84$	0	0
$85$	−5.87935	−0.637705
$86$	0	0
$87$	−3.69239	−0.395866
$88$	0	0
$89$	1.00000	0.106000
$89$	1.00000	0.106000
$90$	0	0
$91$	3.62878	0.380400
$92$	0	0
$93$	−5.29722	−0.549296
$94$	0	0
$95$	5.41445	0.555511
$96$	0	0
$97$	−9.61533	−0.976289	−0.488144	−	0.872763i	$-0.662326\pi$
$97$	−9.61533	−0.976289	−0.488144	+	0.872763i	$0.662326\pi$
$98$	0	0
$99$	−10.1179	−1.01689
$100$	0	0
$101$	4.72415	0.470070	0.235035	−	0.971987i	$-0.424479\pi$
$101$	4.72415	0.470070	0.235035	+	0.971987i	$0.424479\pi$
$102$	0	0
$103$	−5.17345	−0.509755	−0.254877	−	0.966973i	$-0.582035\pi$
$103$	−5.17345	−0.509755	−0.254877	+	0.966973i	$0.582035\pi$
$104$	0	0
$105$	0.540416	0.0527392
$106$	0	0
$107$	−5.68158	−0.549259	−0.274630	−	0.961550i	$-0.588555\pi$
$107$	−5.68158	−0.549259	−0.274630	+	0.961550i	$0.588555\pi$
$108$	0	0
$109$	−6.48821	−0.621458	−0.310729	−	0.950499i	$-0.600573\pi$
$109$	−6.48821	−0.621458	−0.310729	+	0.950499i	$0.600573\pi$
$110$	0	0
$111$	0.461197	0.0437749
$112$	0	0
$113$	9.49005	0.892749	0.446375	−	0.894846i	$-0.352715\pi$
$113$	9.49005	0.892749	0.446375	+	0.894846i	$0.352715\pi$
$114$	0	0
$115$	8.56239	0.798447
$116$	0	0
$117$	−13.3363	−1.23294
$118$	0	0
$119$	−3.41224	−0.312800
$120$	0	0
$121$	11.5017	1.04561
$122$	0	0
$123$	11.0344	0.994938
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	8.22863	0.730173	0.365087	−	0.930974i	$-0.381039\pi$
$127$	8.22863	0.730173	0.365087	+	0.930974i	$0.381039\pi$
$128$	0	0
$129$	4.45802	0.392507
$130$	0	0
$131$	4.92961	0.430702	0.215351	−	0.976537i	$-0.430910\pi$
$131$	4.92961	0.430702	0.215351	+	0.976537i	$0.430910\pi$
$132$	0	0
$133$	3.14242	0.272483
$134$	0	0
$135$	−4.77954	−0.411357
$136$	0	0
$137$	−11.9905	−1.02442	−0.512211	−	0.858860i	$-0.671173\pi$
$137$	−11.9905	−1.02442	−0.512211	+	0.858860i	$0.671173\pi$
$138$	0	0
$139$	−18.0960	−1.53488	−0.767440	−	0.641120i	$-0.778470\pi$
$139$	−18.0960	−1.53488	−0.767440	+	0.641120i	$0.778470\pi$
$140$	0	0
$141$	3.52632	0.296969
$142$	0	0
$143$	29.6591	2.48022
$144$	0	0
$145$	−3.96542	−0.329311
$146$	0	0
$147$	−6.20438	−0.511728
$148$	0	0
$149$	−19.9604	−1.63522	−0.817609	−	0.575773i	$-0.804701\pi$
$149$	−19.9604	−1.63522	−0.817609	+	0.575773i	$0.804701\pi$
$150$	0	0
$151$	9.01450	0.733589	0.366795	−	0.930302i	$-0.380455\pi$
$151$	9.01450	0.733589	0.366795	+	0.930302i	$0.380455\pi$
$152$	0	0
$153$	12.5405	1.01384
$154$	0	0
$155$	−5.68893	−0.456946
$156$	0	0
$157$	−9.23610	−0.737121	−0.368561	−	0.929604i	$-0.620149\pi$
$157$	−9.23610	−0.737121	−0.368561	+	0.929604i	$0.620149\pi$
$158$	0	0
$159$	−7.37398	−0.584795
$160$	0	0
$161$	4.96942	0.391645
$162$	0	0
$163$	19.2838	1.51043	0.755213	−	0.655479i	$-0.227533\pi$
$163$	19.2838	1.51043	0.755213	+	0.655479i	$0.227533\pi$
$164$	0	0
$165$	4.41697	0.343861
$166$	0	0
$167$	24.8161	1.92033	0.960163	−	0.279439i	$-0.0901485\pi$
$167$	24.8161	1.92033	0.960163	+	0.279439i	$0.0901485\pi$
$168$	0	0
$169$	26.0932	2.00717
$170$	0	0
$171$	−11.5488	−0.883163
$172$	0	0
$173$	−17.0185	−1.29389	−0.646945	−	0.762537i	$-0.723954\pi$
$173$	−17.0185	−1.29389	−0.646945	+	0.762537i	$0.723954\pi$
$174$	0	0
$175$	0.580377	0.0438724
$176$	0	0
$177$	−9.90890	−0.744799
$178$	0	0
$179$	6.10678	0.456442	0.228221	−	0.973609i	$-0.426709\pi$
$179$	6.10678	0.456442	0.228221	+	0.973609i	$0.426709\pi$
$180$	0	0
$181$	−1.02757	−0.0763785	−0.0381892	−	0.999271i	$-0.512159\pi$
$181$	−1.02757	−0.0763785	−0.0381892	+	0.999271i	$0.512159\pi$
$182$	0	0
$183$	9.09909	0.672624
$184$	0	0
$185$	0.495300	0.0364152
$186$	0	0
$187$	−27.8892	−2.03946
$188$	0	0
$189$	−2.77394	−0.201774
$190$	0	0
$191$	11.3023	0.817808	0.408904	−	0.912577i	$-0.365911\pi$
$191$	11.3023	0.817808	0.408904	+	0.912577i	$0.365911\pi$
$192$	0	0
$193$	−19.0759	−1.37311	−0.686555	−	0.727077i	$-0.740878\pi$
$193$	−19.0759	−1.37311	−0.686555	+	0.727077i	$0.740878\pi$
$194$	0	0
$195$	5.82195	0.416918
$196$	0	0
$197$	20.1996	1.43916	0.719580	−	0.694409i	$-0.244334\pi$
$197$	20.1996	1.43916	0.719580	+	0.694409i	$0.244334\pi$
$198$	0	0
$199$	11.2701	0.798915	0.399457	−	0.916752i	$-0.369199\pi$
$199$	11.2701	0.798915	0.399457	+	0.916752i	$0.369199\pi$
$200$	0	0
$201$	−1.25762	−0.0887055
$202$	0	0
$203$	−2.30144	−0.161530
$204$	0	0
$205$	11.8503	0.827664
$206$	0	0
$207$	−18.2633	−1.26939
$208$	0	0
$209$	25.6839	1.77660
$210$	0	0
$211$	−6.09599	−0.419665	−0.209833	−	0.977737i	$-0.567292\pi$
$211$	−6.09599	−0.419665	−0.209833	+	0.977737i	$0.567292\pi$
$212$	0	0
$213$	10.0111	0.685948
$214$	0	0
$215$	4.78767	0.326516
$216$	0	0
$217$	−3.30172	−0.224136
$218$	0	0
$219$	1.22173	0.0825571
$220$	0	0
$221$	−36.7604	−2.47277
$222$	0	0
$223$	−7.65809	−0.512824	−0.256412	−	0.966568i	$-0.582540\pi$
$223$	−7.65809	−0.512824	−0.256412	+	0.966568i	$0.582540\pi$
$224$	0	0
$225$	−2.13297	−0.142198
$226$	0	0
$227$	29.5274	1.95980	0.979900	−	0.199490i	$-0.0639285\pi$
$227$	29.5274	1.95980	0.979900	+	0.199490i	$0.0639285\pi$
$228$	0	0
$229$	7.14724	0.472303	0.236151	−	0.971716i	$-0.424114\pi$
$229$	7.14724	0.472303	0.236151	+	0.971716i	$0.424114\pi$
$230$	0	0
$231$	2.56351	0.168667
$232$	0	0
$233$	−10.9605	−0.718045	−0.359023	−	0.933329i	$-0.616890\pi$
$233$	−10.9605	−0.718045	−0.359023	+	0.933329i	$0.616890\pi$
$234$	0	0
$235$	3.78707	0.247041
$236$	0	0
$237$	−0.458525	−0.0297844
$238$	0	0
$239$	−19.7441	−1.27714	−0.638571	−	0.769563i	$-0.720474\pi$
$239$	−19.7441	−1.27714	−0.638571	+	0.769563i	$0.720474\pi$
$240$	0	0
$241$	−19.2285	−1.23862	−0.619309	−	0.785148i	$-0.712587\pi$
$241$	−19.2285	−1.23862	−0.619309	+	0.785148i	$0.712587\pi$
$242$	0	0
$243$	16.1529	1.03621
$244$	0	0
$245$	−6.66316	−0.425694
$246$	0	0
$247$	33.8536	2.15405
$248$	0	0
$249$	−1.51231	−0.0958385
$250$	0	0
$251$	2.44743	0.154481	0.0772403	−	0.997013i	$-0.475389\pi$
$251$	2.44743	0.154481	0.0772403	+	0.997013i	$0.475389\pi$
$252$	0	0
$253$	40.6165	2.55354
$254$	0	0
$255$	−5.47453	−0.342828
$256$	0	0
$257$	20.5627	1.28267	0.641333	−	0.767263i	$-0.278382\pi$
$257$	20.5627	1.28267	0.641333	+	0.767263i	$0.278382\pi$
$258$	0	0
$259$	0.287461	0.0178620
$260$	0	0
$261$	8.45812	0.523545
$262$	0	0
$263$	−10.4549	−0.644679	−0.322340	−	0.946624i	$-0.604469\pi$
$263$	−10.4549	−0.644679	−0.322340	+	0.946624i	$0.604469\pi$
$264$	0	0
$265$	−7.91925	−0.486476
$266$	0	0
$267$	0.931146	0.0569852
$268$	0	0
$269$	26.2193	1.59862	0.799308	−	0.600921i	$-0.205199\pi$
$269$	26.2193	1.59862	0.799308	+	0.600921i	$0.205199\pi$
$270$	0	0
$271$	−20.6659	−1.25536	−0.627681	−	0.778470i	$-0.715996\pi$
$271$	−20.6659	−1.25536	−0.627681	+	0.778470i	$0.715996\pi$
$272$	0	0
$273$	3.37893	0.204502
$274$	0	0
$275$	4.74359	0.286049
$276$	0	0
$277$	0.433915	0.0260714	0.0130357	−	0.999915i	$-0.495850\pi$
$277$	0.433915	0.0260714	0.0130357	+	0.999915i	$0.495850\pi$
$278$	0	0
$279$	12.1343	0.726461
$280$	0	0
$281$	16.7226	0.997585	0.498793	−	0.866721i	$-0.333777\pi$
$281$	16.7226	0.997585	0.498793	+	0.866721i	$0.333777\pi$
$282$	0	0
$283$	10.4735	0.622587	0.311293	−	0.950314i	$-0.399238\pi$
$283$	10.4735	0.622587	0.311293	+	0.950314i	$0.399238\pi$
$284$	0	0
$285$	5.04164	0.298641
$286$	0	0
$287$	6.87767	0.405976
$288$	0	0
$289$	17.5668	1.03334
$290$	0	0
$291$	−8.95327	−0.524850
$292$	0	0
$293$	7.94600	0.464210	0.232105	−	0.972691i	$-0.425439\pi$
$293$	7.94600	0.464210	0.232105	+	0.972691i	$0.425439\pi$
$294$	0	0
$295$	−10.6416	−0.619579
$296$	0	0
$297$	−22.6722	−1.31557
$298$	0	0
$299$	53.5360	3.09607
$300$	0	0
$301$	2.77865	0.160159
$302$	0	0
$303$	4.39887	0.252708
$304$	0	0
$305$	9.77193	0.559539
$306$	0	0
$307$	2.11312	0.120602	0.0603011	−	0.998180i	$-0.480794\pi$
$307$	2.11312	0.120602	0.0603011	+	0.998180i	$0.480794\pi$
$308$	0	0
$309$	−4.81723	−0.274043
$310$	0	0
$311$	8.66507	0.491351	0.245675	−	0.969352i	$-0.420990\pi$
$311$	8.66507	0.491351	0.245675	+	0.969352i	$0.420990\pi$
$312$	0	0
$313$	16.0660	0.908105	0.454052	−	0.890975i	$-0.349978\pi$
$313$	16.0660	0.908105	0.454052	+	0.890975i	$0.349978\pi$
$314$	0	0
$315$	−1.23793	−0.0697492
$316$	0	0
$317$	−1.70619	−0.0958291	−0.0479146	−	0.998851i	$-0.515258\pi$
$317$	−1.70619	−0.0958291	−0.0479146	+	0.998851i	$0.515258\pi$
$318$	0	0
$319$	−18.8104	−1.05318
$320$	0	0
$321$	−5.29038	−0.295280
$322$	0	0
$323$	−31.8335	−1.77126
$324$	0	0
$325$	6.25246	0.346824
$326$	0	0
$327$	−6.04147	−0.334094
$328$	0	0
$329$	2.19793	0.121176
$330$	0	0
$331$	7.90149	0.434305	0.217153	−	0.976138i	$-0.430323\pi$
$331$	7.90149	0.434305	0.217153	+	0.976138i	$0.430323\pi$
$332$	0	0
$333$	−1.05646	−0.0578936
$334$	0	0
$335$	−1.35061	−0.0737919
$336$	0	0
$337$	7.99703	0.435626	0.217813	−	0.975991i	$-0.430108\pi$
$337$	7.99703	0.435626	0.217813	+	0.975991i	$0.430108\pi$
$338$	0	0
$339$	8.83662	0.479939
$340$	0	0
$341$	−26.9859	−1.46137
$342$	0	0
$343$	−7.92979	−0.428168
$344$	0	0
$345$	7.97283	0.429243
$346$	0	0
$347$	−6.24790	−0.335405	−0.167702	−	0.985838i	$-0.553635\pi$
$347$	−6.24790	−0.335405	−0.167702	+	0.985838i	$0.553635\pi$
$348$	0	0
$349$	7.07360	0.378641	0.189320	−	0.981915i	$-0.439372\pi$
$349$	7.07360	0.378641	0.189320	+	0.981915i	$0.439372\pi$
$350$	0	0
$351$	−29.8839	−1.59508
$352$	0	0
$353$	17.2887	0.920184	0.460092	−	0.887871i	$-0.347816\pi$
$353$	17.2887	0.920184	0.460092	+	0.887871i	$0.347816\pi$
$354$	0	0
$355$	10.7514	0.570623
$356$	0	0
$357$	−3.17729	−0.168160
$358$	0	0
$359$	−12.3384	−0.651193	−0.325597	−	0.945509i	$-0.605565\pi$
$359$	−12.3384	−0.651193	−0.325597	+	0.945509i	$0.605565\pi$
$360$	0	0
$361$	10.3163	0.542962
$362$	0	0
$363$	10.7097	0.562115
$364$	0	0
$365$	1.31208	0.0686771
$366$	0	0
$367$	−30.6605	−1.60047	−0.800233	−	0.599689i	$-0.795291\pi$
$367$	−30.6605	−1.60047	−0.800233	+	0.599689i	$0.795291\pi$
$368$	0	0
$369$	−25.2764	−1.31584
$370$	0	0
$371$	−4.59616	−0.238621
$372$	0	0
$373$	−5.45234	−0.282312	−0.141156	−	0.989987i	$-0.545082\pi$
$373$	−5.45234	−0.282312	−0.141156	+	0.989987i	$0.545082\pi$
$374$	0	0
$375$	0.931146	0.0480842
$376$	0	0
$377$	−24.7936	−1.27694
$378$	0	0
$379$	35.5232	1.82471	0.912353	−	0.409405i	$-0.134264\pi$
$379$	35.5232	1.82471	0.912353	+	0.409405i	$0.134264\pi$
$380$	0	0
$381$	7.66206	0.392539
$382$	0	0
$383$	12.8946	0.658882	0.329441	−	0.944176i	$-0.393140\pi$
$383$	12.8946	0.658882	0.329441	+	0.944176i	$0.393140\pi$
$384$	0	0
$385$	2.75307	0.140310
$386$	0	0
$387$	−10.2119	−0.519102
$388$	0	0
$389$	−28.2948	−1.43460	−0.717300	−	0.696764i	$-0.754622\pi$
$389$	−28.2948	−1.43460	−0.717300	+	0.696764i	$0.754622\pi$
$390$	0	0
$391$	−50.3413	−2.54587
$392$	0	0
$393$	4.59018	0.231544
$394$	0	0
$395$	−0.492431	−0.0247769
$396$	0	0
$397$	−32.7862	−1.64549	−0.822745	−	0.568411i	$-0.807558\pi$
$397$	−32.7862	−1.64549	−0.822745	+	0.568411i	$0.807558\pi$
$398$	0	0
$399$	2.92606	0.146486
$400$	0	0
$401$	19.8756	0.992538	0.496269	−	0.868169i	$-0.334703\pi$
$401$	19.8756	0.992538	0.496269	+	0.868169i	$0.334703\pi$
$402$	0	0
$403$	−35.5698	−1.77186
$404$	0	0
$405$	1.94845	0.0968194
$406$	0	0
$407$	2.34950	0.116461
$408$	0	0
$409$	24.6891	1.22080	0.610398	−	0.792095i	$-0.291009\pi$
$409$	24.6891	1.22080	0.610398	+	0.792095i	$0.291009\pi$
$410$	0	0
$411$	−11.1649	−0.550726
$412$	0	0
$413$	−6.17616	−0.303909
$414$	0	0
$415$	−1.62413	−0.0797256
$416$	0	0
$417$	−16.8500	−0.825148
$418$	0	0
$419$	23.6692	1.15632	0.578159	−	0.815924i	$-0.303771\pi$
$419$	23.6692	1.15632	0.578159	+	0.815924i	$0.303771\pi$
$420$	0	0
$421$	15.9257	0.776169	0.388085	−	0.921624i	$-0.373137\pi$
$421$	15.9257	0.776169	0.388085	+	0.921624i	$0.373137\pi$
$422$	0	0
$423$	−8.07770	−0.392751
$424$	0	0
$425$	−5.87935	−0.285190
$426$	0	0
$427$	5.67141	0.274459
$428$	0	0
$429$	27.6169	1.33336
$430$	0	0
$431$	−7.78225	−0.374858	−0.187429	−	0.982278i	$-0.560015\pi$
$431$	−7.78225	−0.374858	−0.187429	+	0.982278i	$0.560015\pi$
$432$	0	0
$433$	−3.59930	−0.172971	−0.0864856	−	0.996253i	$-0.527564\pi$
$433$	−3.59930	−0.172971	−0.0864856	+	0.996253i	$0.527564\pi$
$434$	0	0
$435$	−3.69239	−0.177036
$436$	0	0
$437$	46.3606	2.21773
$438$	0	0
$439$	−30.2840	−1.44538	−0.722689	−	0.691173i	$-0.757094\pi$
$439$	−30.2840	−1.44538	−0.722689	+	0.691173i	$0.757094\pi$
$440$	0	0
$441$	14.2123	0.676777
$442$	0	0
$443$	−15.1094	−0.717870	−0.358935	−	0.933362i	$-0.616860\pi$
$443$	−15.1094	−0.717870	−0.358935	+	0.933362i	$0.616860\pi$
$444$	0	0
$445$	1.00000	0.0474045
$446$	0	0
$447$	−18.5860	−0.879089
$448$	0	0
$449$	18.3101	0.864106	0.432053	−	0.901848i	$-0.357789\pi$
$449$	18.3101	0.864106	0.432053	+	0.901848i	$0.357789\pi$
$450$	0	0
$451$	56.2132	2.64698
$452$	0	0
$453$	8.39381	0.394376
$454$	0	0
$455$	3.62878	0.170120
$456$	0	0
$457$	−21.0509	−0.984720	−0.492360	−	0.870392i	$-0.663866\pi$
$457$	−21.0509	−0.984720	−0.492360	+	0.870392i	$0.663866\pi$
$458$	0	0
$459$	28.1006	1.31162
$460$	0	0
$461$	−38.8056	−1.80735	−0.903677	−	0.428214i	$-0.859143\pi$
$461$	−38.8056	−1.80735	−0.903677	+	0.428214i	$0.859143\pi$
$462$	0	0
$463$	12.1126	0.562921	0.281460	−	0.959573i	$-0.409181\pi$
$463$	12.1126	0.562921	0.281460	+	0.959573i	$0.409181\pi$
$464$	0	0
$465$	−5.29722	−0.245653
$466$	0	0
$467$	−2.25635	−0.104411	−0.0522056	−	0.998636i	$-0.516625\pi$
$467$	−2.25635	−0.104411	−0.0522056	+	0.998636i	$0.516625\pi$
$468$	0	0
$469$	−0.783866	−0.0361955
$470$	0	0
$471$	−8.60016	−0.396274
$472$	0	0
$473$	22.7107	1.04424
$474$	0	0
$475$	5.41445	0.248432
$476$	0	0
$477$	16.8915	0.773409
$478$	0	0
$479$	−0.237254	−0.0108404	−0.00542022	−	0.999985i	$-0.501725\pi$
$479$	−0.237254	−0.0108404	−0.00542022	+	0.999985i	$0.501725\pi$
$480$	0	0
$481$	3.09684	0.141204
$482$	0	0
$483$	4.62725	0.210547
$484$	0	0
$485$	−9.61533	−0.436610
$486$	0	0
$487$	−1.69314	−0.0767237	−0.0383619	−	0.999264i	$-0.512214\pi$
$487$	−1.69314	−0.0767237	−0.0383619	+	0.999264i	$0.512214\pi$
$488$	0	0
$489$	17.9561	0.812001
$490$	0	0
$491$	18.2064	0.821641	0.410821	−	0.911716i	$-0.365242\pi$
$491$	18.2064	0.821641	0.410821	+	0.911716i	$0.365242\pi$
$492$	0	0
$493$	23.3141	1.05002
$494$	0	0
$495$	−10.1179	−0.454767
$496$	0	0
$497$	6.23985	0.279896
$498$	0	0
$499$	−20.0254	−0.896462	−0.448231	−	0.893918i	$-0.647946\pi$
$499$	−20.0254	−0.896462	−0.448231	+	0.893918i	$0.647946\pi$
$500$	0	0
$501$	23.1074	1.03236
$502$	0	0
$503$	−33.4990	−1.49365	−0.746824	−	0.665021i	$-0.768422\pi$
$503$	−33.4990	−1.49365	−0.746824	+	0.665021i	$0.768422\pi$
$504$	0	0
$505$	4.72415	0.210222
$506$	0	0
$507$	24.2966	1.07905
$508$	0	0
$509$	−15.2860	−0.677541	−0.338770	−	0.940869i	$-0.610011\pi$
$509$	−15.2860	−0.677541	−0.338770	+	0.940869i	$0.610011\pi$
$510$	0	0
$511$	0.761499	0.0336867
$512$	0	0
$513$	−25.8786	−1.14257
$514$	0	0
$515$	−5.17345	−0.227969
$516$	0	0
$517$	17.9643	0.790070
$518$	0	0
$519$	−15.8467	−0.695592
$520$	0	0
$521$	−23.7850	−1.04204	−0.521021	−	0.853544i	$-0.674449\pi$
$521$	−23.7850	−1.04204	−0.521021	+	0.853544i	$0.674449\pi$
$522$	0	0
$523$	−26.9989	−1.18058	−0.590290	−	0.807192i	$-0.700986\pi$
$523$	−26.9989	−1.18058	−0.590290	+	0.807192i	$0.700986\pi$
$524$	0	0
$525$	0.540416	0.0235857
$526$	0	0
$527$	33.4472	1.45698
$528$	0	0
$529$	50.3145	2.18759
$530$	0	0
$531$	22.6982	0.985020
$532$	0	0
$533$	74.0938	3.20936
$534$	0	0
$535$	−5.68158	−0.245636
$536$	0	0
$537$	5.68630	0.245382
$538$	0	0
$539$	−31.6073	−1.36142
$540$	0	0
$541$	−21.0584	−0.905370	−0.452685	−	0.891671i	$-0.649534\pi$
$541$	−21.0584	−0.905370	−0.452685	+	0.891671i	$0.649534\pi$
$542$	0	0
$543$	−0.956815	−0.0410609
$544$	0	0
$545$	−6.48821	−0.277924
$546$	0	0
$547$	−12.6410	−0.540491	−0.270245	−	0.962792i	$-0.587105\pi$
$547$	−12.6410	−0.540491	−0.270245	+	0.962792i	$0.587105\pi$
$548$	0	0
$549$	−20.8432	−0.889567
$550$	0	0
$551$	−21.4706	−0.914678
$552$	0	0
$553$	−0.285796	−0.0121533
$554$	0	0
$555$	0.461197	0.0195767
$556$	0	0
$557$	7.81870	0.331289	0.165644	−	0.986186i	$-0.447030\pi$
$557$	7.81870	0.331289	0.165644	+	0.986186i	$0.447030\pi$
$558$	0	0
$559$	29.9347	1.26610
$560$	0	0
$561$	−25.9689	−1.09641
$562$	0	0
$563$	20.7792	0.875737	0.437869	−	0.899039i	$-0.355734\pi$
$563$	20.7792	0.875737	0.437869	+	0.899039i	$0.355734\pi$
$564$	0	0
$565$	9.49005	0.399250
$566$	0	0
$567$	1.13084	0.0474908
$568$	0	0
$569$	−19.4719	−0.816307	−0.408153	−	0.912913i	$-0.633827\pi$
$569$	−19.4719	−0.816307	−0.408153	+	0.912913i	$0.633827\pi$
$570$	0	0
$571$	9.07799	0.379902	0.189951	−	0.981794i	$-0.439167\pi$
$571$	9.07799	0.379902	0.189951	+	0.981794i	$0.439167\pi$
$572$	0	0
$573$	10.5241	0.439651
$574$	0	0
$575$	8.56239	0.357076
$576$	0	0
$577$	9.99714	0.416186	0.208093	−	0.978109i	$-0.433274\pi$
$577$	9.99714	0.416186	0.208093	+	0.978109i	$0.433274\pi$
$578$	0	0
$579$	−17.7624	−0.738181
$580$	0	0
$581$	−0.942611	−0.0391061
$582$	0	0
$583$	−37.5657	−1.55581
$584$	0	0
$585$	−13.3363	−0.551388
$586$	0	0
$587$	29.0697	1.19984	0.599918	−	0.800062i	$-0.295200\pi$
$587$	29.0697	1.19984	0.599918	+	0.800062i	$0.295200\pi$
$588$	0	0
$589$	−30.8024	−1.26919
$590$	0	0
$591$	18.8088	0.773689
$592$	0	0
$593$	−7.26916	−0.298509	−0.149254	−	0.988799i	$-0.547687\pi$
$593$	−7.26916	−0.298509	−0.149254	+	0.988799i	$0.547687\pi$
$594$	0	0
$595$	−3.41224	−0.139888
$596$	0	0
$597$	10.4941	0.429494
$598$	0	0
$599$	−15.9436	−0.651438	−0.325719	−	0.945467i	$-0.605606\pi$
$599$	−15.9436	−0.651438	−0.325719	+	0.945467i	$0.605606\pi$
$600$	0	0
$601$	−7.56369	−0.308530	−0.154265	−	0.988030i	$-0.549301\pi$
$601$	−7.56369	−0.308530	−0.154265	+	0.988030i	$0.549301\pi$
$602$	0	0
$603$	2.88081	0.117316
$604$	0	0
$605$	11.5017	0.467609
$606$	0	0
$607$	1.88969	0.0767000	0.0383500	−	0.999264i	$-0.487790\pi$
$607$	1.88969	0.0767000	0.0383500	+	0.999264i	$0.487790\pi$
$608$	0	0
$609$	−2.14298	−0.0868379
$610$	0	0
$611$	23.6785	0.957930
$612$	0	0
$613$	−12.4920	−0.504548	−0.252274	−	0.967656i	$-0.581178\pi$
$613$	−12.4920	−0.504548	−0.252274	+	0.967656i	$0.581178\pi$
$614$	0	0
$615$	11.0344	0.444950
$616$	0	0
$617$	−10.0989	−0.406567	−0.203284	−	0.979120i	$-0.565161\pi$
$617$	−10.0989	−0.406567	−0.203284	+	0.979120i	$0.565161\pi$
$618$	0	0
$619$	30.5158	1.22653	0.613266	−	0.789876i	$-0.289855\pi$
$619$	30.5158	1.22653	0.613266	+	0.789876i	$0.289855\pi$
$620$	0	0
$621$	−40.9243	−1.64224
$622$	0	0
$623$	0.580377	0.0232523
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	23.9155	0.955093
$628$	0	0
$629$	−2.91204	−0.116111
$630$	0	0
$631$	15.5337	0.618386	0.309193	−	0.950999i	$-0.399941\pi$
$631$	15.5337	0.618386	0.309193	+	0.950999i	$0.399941\pi$
$632$	0	0
$633$	−5.67625	−0.225611
$634$	0	0
$635$	8.22863	0.326543
$636$	0	0
$637$	−41.6611	−1.65067
$638$	0	0
$639$	−22.9323	−0.907188
$640$	0	0
$641$	−17.5661	−0.693818	−0.346909	−	0.937899i	$-0.612769\pi$
$641$	−17.5661	−0.693818	−0.346909	+	0.937899i	$0.612769\pi$
$642$	0	0
$643$	40.7523	1.60712	0.803558	−	0.595227i	$-0.202938\pi$
$643$	40.7523	1.60712	0.803558	+	0.595227i	$0.202938\pi$
$644$	0	0
$645$	4.45802	0.175534
$646$	0	0
$647$	20.1397	0.791775	0.395887	−	0.918299i	$-0.370437\pi$
$647$	20.1397	0.791775	0.395887	+	0.918299i	$0.370437\pi$
$648$	0	0
$649$	−50.4795	−1.98149
$650$	0	0
$651$	−3.07439	−0.120495
$652$	0	0
$653$	−31.5360	−1.23410	−0.617050	−	0.786924i	$-0.711672\pi$
$653$	−31.5360	−1.23410	−0.617050	+	0.786924i	$0.711672\pi$
$654$	0	0
$655$	4.92961	0.192616
$656$	0	0
$657$	−2.79861	−0.109184
$658$	0	0
$659$	−7.91412	−0.308290	−0.154145	−	0.988048i	$-0.549262\pi$
$659$	−7.91412	−0.308290	−0.154145	+	0.988048i	$0.549262\pi$
$660$	0	0
$661$	−39.7578	−1.54640	−0.773200	−	0.634163i	$-0.781345\pi$
$661$	−39.7578	−1.54640	−0.773200	+	0.634163i	$0.781345\pi$
$662$	0	0
$663$	−34.2293	−1.32935
$664$	0	0
$665$	3.14242	0.121858
$666$	0	0
$667$	−33.9535	−1.31469
$668$	0	0
$669$	−7.13080	−0.275693
$670$	0	0
$671$	46.3540	1.78948
$672$	0	0
$673$	21.6297	0.833763	0.416882	−	0.908961i	$-0.363123\pi$
$673$	21.6297	0.833763	0.416882	+	0.908961i	$0.363123\pi$
$674$	0	0
$675$	−4.77954	−0.183965
$676$	0	0
$677$	−16.7735	−0.644658	−0.322329	−	0.946628i	$-0.604466\pi$
$677$	−16.7735	−0.644658	−0.322329	+	0.946628i	$0.604466\pi$
$678$	0	0
$679$	−5.58052	−0.214161
$680$	0	0
$681$	27.4943	1.05358
$682$	0	0
$683$	−24.7665	−0.947663	−0.473832	−	0.880615i	$-0.657129\pi$
$683$	−24.7665	−0.947663	−0.473832	+	0.880615i	$0.657129\pi$
$684$	0	0
$685$	−11.9905	−0.458135
$686$	0	0
$687$	6.65512	0.253909
$688$	0	0
$689$	−49.5148	−1.88636
$690$	0	0
$691$	−47.4194	−1.80392	−0.901959	−	0.431822i	$-0.857871\pi$
$691$	−47.4194	−1.80392	−0.901959	+	0.431822i	$0.857871\pi$
$692$	0	0
$693$	−5.87222	−0.223067
$694$	0	0
$695$	−18.0960	−0.686420
$696$	0	0
$697$	−69.6723	−2.63903
$698$	0	0
$699$	−10.2058	−0.386019
$700$	0	0
$701$	34.9075	1.31844	0.659218	−	0.751952i	$-0.270887\pi$
$701$	34.9075	1.31844	0.659218	+	0.751952i	$0.270887\pi$
$702$	0	0
$703$	2.68178	0.101145
$704$	0	0
$705$	3.52632	0.132809
$706$	0	0
$707$	2.74179	0.103116
$708$	0	0
$709$	48.6918	1.82866	0.914330	−	0.404970i	$-0.132718\pi$
$709$	48.6918	1.82866	0.914330	+	0.404970i	$0.132718\pi$
$710$	0	0
$711$	1.05034	0.0393908
$712$	0	0
$713$	−48.7108	−1.82423
$714$	0	0
$715$	29.6591	1.10919
$716$	0	0
$717$	−18.3847	−0.686588
$718$	0	0
$719$	−35.5414	−1.32547	−0.662736	−	0.748853i	$-0.730605\pi$
$719$	−35.5414	−1.32547	−0.662736	+	0.748853i	$0.730605\pi$
$720$	0	0
$721$	−3.00255	−0.111821
$722$	0	0
$723$	−17.9045	−0.665877
$724$	0	0
$725$	−3.96542	−0.147272
$726$	0	0
$727$	−2.22393	−0.0824812	−0.0412406	−	0.999149i	$-0.513131\pi$
$727$	−2.22393	−0.0824812	−0.0412406	+	0.999149i	$0.513131\pi$
$728$	0	0
$729$	9.19536	0.340569
$730$	0	0
$731$	−28.1484	−1.04111
$732$	0	0
$733$	−9.92710	−0.366666	−0.183333	−	0.983051i	$-0.558689\pi$
$733$	−9.92710	−0.366666	−0.183333	+	0.983051i	$0.558689\pi$
$734$	0	0
$735$	−6.20438	−0.228852
$736$	0	0
$737$	−6.40676	−0.235996
$738$	0	0
$739$	10.1642	0.373896	0.186948	−	0.982370i	$-0.440140\pi$
$739$	10.1642	0.373896	0.186948	+	0.982370i	$0.440140\pi$
$740$	0	0
$741$	31.5227	1.15801
$742$	0	0
$743$	43.3395	1.58997	0.794985	−	0.606629i	$-0.207478\pi$
$743$	43.3395	1.58997	0.794985	+	0.606629i	$0.207478\pi$
$744$	0	0
$745$	−19.9604	−0.731292
$746$	0	0
$747$	3.46423	0.126749
$748$	0	0
$749$	−3.29746	−0.120487
$750$	0	0
$751$	3.92124	0.143088	0.0715440	−	0.997437i	$-0.477207\pi$
$751$	3.92124	0.143088	0.0715440	+	0.997437i	$0.477207\pi$
$752$	0	0
$753$	2.27892	0.0830484
$754$	0	0
$755$	9.01450	0.328071
$756$	0	0
$757$	7.19956	0.261672	0.130836	−	0.991404i	$-0.458234\pi$
$757$	7.19956	0.261672	0.130836	+	0.991404i	$0.458234\pi$
$758$	0	0
$759$	37.8199	1.37277
$760$	0	0
$761$	40.8629	1.48128	0.740639	−	0.671903i	$-0.234523\pi$
$761$	40.8629	1.48128	0.740639	+	0.671903i	$0.234523\pi$
$762$	0	0
$763$	−3.76561	−0.136324
$764$	0	0
$765$	12.5405	0.453401
$766$	0	0
$767$	−66.5363	−2.40249
$768$	0	0
$769$	51.3277	1.85092	0.925462	−	0.378840i	$-0.123677\pi$
$769$	51.3277	1.85092	0.925462	+	0.378840i	$0.123677\pi$
$770$	0	0
$771$	19.1469	0.689558
$772$	0	0
$773$	−2.66946	−0.0960137	−0.0480069	−	0.998847i	$-0.515287\pi$
$773$	−2.66946	−0.0960137	−0.0480069	+	0.998847i	$0.515287\pi$
$774$	0	0
$775$	−5.68893	−0.204352
$776$	0	0
$777$	0.267668	0.00960254
$778$	0	0
$779$	64.1631	2.29888
$780$	0	0
$781$	51.0001	1.82493
$782$	0	0
$783$	18.9529	0.677322
$784$	0	0
$785$	−9.23610	−0.329651
$786$	0	0
$787$	16.3284	0.582043	0.291022	−	0.956716i	$-0.406005\pi$
$787$	16.3284	0.582043	0.291022	+	0.956716i	$0.406005\pi$
$788$	0	0
$789$	−9.73507	−0.346578
$790$	0	0
$791$	5.50781	0.195835
$792$	0	0
$793$	61.0986	2.16967
$794$	0	0
$795$	−7.37398	−0.261528
$796$	0	0
$797$	34.8557	1.23465	0.617325	−	0.786708i	$-0.288216\pi$
$797$	34.8557	1.23465	0.617325	+	0.786708i	$0.288216\pi$
$798$	0	0
$799$	−22.2655	−0.787698
$800$	0	0
$801$	−2.13297	−0.0753647
$802$	0	0
$803$	6.22395	0.219638
$804$	0	0
$805$	4.96942	0.175149
$806$	0	0
$807$	24.4140	0.859412
$808$	0	0
$809$	−41.4204	−1.45626	−0.728132	−	0.685437i	$-0.759611\pi$
$809$	−41.4204	−1.45626	−0.728132	+	0.685437i	$0.759611\pi$
$810$	0	0
$811$	−7.34996	−0.258092	−0.129046	−	0.991639i	$-0.541192\pi$
$811$	−7.34996	−0.258092	−0.129046	+	0.991639i	$0.541192\pi$
$812$	0	0
$813$	−19.2429	−0.674880
$814$	0	0
$815$	19.2838	0.675483
$816$	0	0
$817$	25.9226	0.906917
$818$	0	0
$819$	−7.74008	−0.270460
$820$	0	0
$821$	−38.8242	−1.35498	−0.677488	−	0.735534i	$-0.736931\pi$
$821$	−38.8242	−1.35498	−0.677488	+	0.735534i	$0.736931\pi$
$822$	0	0
$823$	21.4901	0.749099	0.374550	−	0.927207i	$-0.377797\pi$
$823$	21.4901	0.749099	0.374550	+	0.927207i	$0.377797\pi$
$824$	0	0
$825$	4.41697	0.153779
$826$	0	0
$827$	−19.6349	−0.682771	−0.341386	−	0.939923i	$-0.610896\pi$
$827$	−19.6349	−0.682771	−0.341386	+	0.939923i	$0.610896\pi$
$828$	0	0
$829$	−20.8272	−0.723358	−0.361679	−	0.932303i	$-0.617796\pi$
$829$	−20.8272	−0.723358	−0.361679	+	0.932303i	$0.617796\pi$
$830$	0	0
$831$	0.404038	0.0140159
$832$	0	0
$833$	39.1751	1.35734
$834$	0	0
$835$	24.8161	0.858796
$836$	0	0
$837$	27.1905	0.939840
$838$	0	0
$839$	−22.3217	−0.770630	−0.385315	−	0.922785i	$-0.625907\pi$
$839$	−22.3217	−0.770630	−0.385315	+	0.922785i	$0.625907\pi$
$840$	0	0
$841$	−13.2754	−0.457773
$842$	0	0
$843$	15.5712	0.536299
$844$	0	0
$845$	26.0932	0.897634
$846$	0	0
$847$	6.67530	0.229366
$848$	0	0
$849$	9.75238	0.334701
$850$	0	0
$851$	4.24096	0.145378
$852$	0	0
$853$	−4.79245	−0.164090	−0.0820452	−	0.996629i	$-0.526145\pi$
$853$	−4.79245	−0.164090	−0.0820452	+	0.996629i	$0.526145\pi$
$854$	0	0
$855$	−11.5488	−0.394962
$856$	0	0
$857$	49.1822	1.68003	0.840016	−	0.542561i	$-0.182545\pi$
$857$	49.1822	1.68003	0.840016	+	0.542561i	$0.182545\pi$
$858$	0	0
$859$	−45.6426	−1.55731	−0.778653	−	0.627454i	$-0.784097\pi$
$859$	−45.6426	−1.55731	−0.778653	+	0.627454i	$0.784097\pi$
$860$	0	0
$861$	6.40412	0.218252
$862$	0	0
$863$	−16.9728	−0.577761	−0.288880	−	0.957365i	$-0.593283\pi$
$863$	−16.9728	−0.577761	−0.288880	+	0.957365i	$0.593283\pi$
$864$	0	0
$865$	−17.0185	−0.578645
$866$	0	0
$867$	16.3572	0.555520
$868$	0	0
$869$	−2.33589	−0.0792397
$870$	0	0
$871$	−8.44465	−0.286136
$872$	0	0
$873$	20.5092	0.694131
$874$	0	0
$875$	0.580377	0.0196203
$876$	0	0
$877$	−6.47951	−0.218797	−0.109399	−	0.993998i	$-0.534893\pi$
$877$	−6.47951	−0.218797	−0.109399	+	0.993998i	$0.534893\pi$
$878$	0	0
$879$	7.39888	0.249558
$880$	0	0
$881$	−13.0221	−0.438724	−0.219362	−	0.975644i	$-0.570398\pi$
$881$	−13.0221	−0.438724	−0.219362	+	0.975644i	$0.570398\pi$
$882$	0	0
$883$	−24.1962	−0.814268	−0.407134	−	0.913369i	$-0.633472\pi$
$883$	−24.1962	−0.814268	−0.407134	+	0.913369i	$0.633472\pi$
$884$	0	0
$885$	−9.90890	−0.333084
$886$	0	0
$887$	18.6517	0.626264	0.313132	−	0.949710i	$-0.398622\pi$
$887$	18.6517	0.626264	0.313132	+	0.949710i	$0.398622\pi$
$888$	0	0
$889$	4.77571	0.160172
$890$	0	0
$891$	9.24267	0.309641
$892$	0	0
$893$	20.5049	0.686171
$894$	0	0
$895$	6.10678	0.204127
$896$	0	0
$897$	49.8498	1.66444
$898$	0	0
$899$	22.5590	0.752385
$900$	0	0
$901$	46.5601	1.55114
$902$	0	0
$903$	2.58733	0.0861010
$904$	0	0
$905$	−1.02757	−0.0341575
$906$	0	0
$907$	19.1208	0.634896	0.317448	−	0.948276i	$-0.397174\pi$
$907$	19.1208	0.634896	0.317448	+	0.948276i	$0.397174\pi$
$908$	0	0
$909$	−10.0765	−0.334215
$910$	0	0
$911$	−6.04981	−0.200439	−0.100220	−	0.994965i	$-0.531955\pi$
$911$	−6.04981	−0.200439	−0.100220	+	0.994965i	$0.531955\pi$
$912$	0	0
$913$	−7.70423	−0.254973
$914$	0	0
$915$	9.09909	0.300807
$916$	0	0
$917$	2.86103	0.0944796
$918$	0	0
$919$	−19.9158	−0.656962	−0.328481	−	0.944511i	$-0.606537\pi$
$919$	−19.9158	−0.656962	−0.328481	+	0.944511i	$0.606537\pi$
$920$	0	0
$921$	1.96762	0.0648354
$922$	0	0
$923$	67.2224	2.21265
$924$	0	0
$925$	0.495300	0.0162854
$926$	0	0
$927$	11.0348	0.362430
$928$	0	0
$929$	0.333759	0.0109503	0.00547514	−	0.999985i	$-0.498257\pi$
$929$	0.333759	0.0109503	0.00547514	+	0.999985i	$0.498257\pi$
$930$	0	0
$931$	−36.0774	−1.18239
$932$	0	0
$933$	8.06844	0.264149
$934$	0	0
$935$	−27.8892	−0.912075
$936$	0	0
$937$	−14.6611	−0.478957	−0.239479	−	0.970902i	$-0.576977\pi$
$937$	−14.6611	−0.478957	−0.239479	+	0.970902i	$0.576977\pi$
$938$	0	0
$939$	14.9598	0.488194
$940$	0	0
$941$	−4.63624	−0.151137	−0.0755686	−	0.997141i	$-0.524077\pi$
$941$	−4.63624	−0.151137	−0.0755686	+	0.997141i	$0.524077\pi$
$942$	0	0
$943$	101.467	3.30423
$944$	0	0
$945$	−2.77394	−0.0902362
$946$	0	0
$947$	−10.9543	−0.355965	−0.177983	−	0.984034i	$-0.556957\pi$
$947$	−10.9543	−0.355965	−0.177983	+	0.984034i	$0.556957\pi$
$948$	0	0
$949$	8.20369	0.266303
$950$	0	0
$951$	−1.58871	−0.0515175
$952$	0	0
$953$	−26.4968	−0.858315	−0.429158	−	0.903230i	$-0.641190\pi$
$953$	−26.4968	−0.858315	−0.429158	+	0.903230i	$0.641190\pi$
$954$	0	0
$955$	11.3023	0.365735
$956$	0	0
$957$	−17.5152	−0.566185
$958$	0	0
$959$	−6.95904	−0.224719
$960$	0	0
$961$	1.36388	0.0439962
$962$	0	0
$963$	12.1186	0.390517
$964$	0	0
$965$	−19.0759	−0.614074
$966$	0	0
$967$	59.1812	1.90314	0.951569	−	0.307435i	$-0.0994706\pi$
$967$	59.1812	1.90314	0.951569	+	0.307435i	$0.0994706\pi$
$968$	0	0
$969$	−29.6416	−0.952225
$970$	0	0
$971$	5.45699	0.175123	0.0875616	−	0.996159i	$-0.472093\pi$
$971$	5.45699	0.175123	0.0875616	+	0.996159i	$0.472093\pi$
$972$	0	0
$973$	−10.5025	−0.336695
$974$	0	0
$975$	5.82195	0.186452
$976$	0	0
$977$	17.0837	0.546555	0.273278	−	0.961935i	$-0.411892\pi$
$977$	17.0837	0.546555	0.273278	+	0.961935i	$0.411892\pi$
$978$	0	0
$979$	4.74359	0.151606
$980$	0	0
$981$	13.8391	0.441850
$982$	0	0
$983$	−42.1851	−1.34549	−0.672747	−	0.739872i	$-0.734886\pi$
$983$	−42.1851	−1.34549	−0.672747	+	0.739872i	$0.734886\pi$
$984$	0	0
$985$	20.1996	0.643612
$986$	0	0
$987$	2.04659	0.0651438
$988$	0	0
$989$	40.9939	1.30353
$990$	0	0
$991$	11.7224	0.372375	0.186188	−	0.982514i	$-0.440387\pi$
$991$	11.7224	0.372375	0.186188	+	0.982514i	$0.440387\pi$
$992$	0	0
$993$	7.35744	0.233481
$994$	0	0
$995$	11.2701	0.357286
$996$	0	0
$997$	0.629575	0.0199388	0.00996942	−	0.999950i	$-0.496827\pi$
$997$	0.629575	0.0199388	0.00996942	+	0.999950i	$0.496827\pi$
$998$	0	0
$999$	−2.36731	−0.0748983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7120.2.a.bj.1.4		7
4.3	odd	2		445.2.a.f.1.6	✓	7
12.11	even	2		4005.2.a.o.1.2		7
20.19	odd	2		2225.2.a.k.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
445.2.a.f.1.6	✓	7	4.3	odd	2
2225.2.a.k.1.2		7	20.19	odd	2
4005.2.a.o.1.2		7	12.11	even	2
7120.2.a.bj.1.4		7	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:	\( N \)	\(=\)	\( 7120 = 2^{4} \cdot 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7120.a (trivial)

\(f(q)\)	\(=\)	\(q+0.931146 q^{3} +1.00000 q^{5} +0.580377 q^{7} -2.13297 q^{9} +O(q^{10})\)	\(q+0.931146 q^{3} +1.00000 q^{5} +0.580377 q^{7} -2.13297 q^{9} +4.74359 q^{11} +6.25246 q^{13} +0.931146 q^{15} -5.87935 q^{17} +5.41445 q^{19} +0.540416 q^{21} +8.56239 q^{23} +1.00000 q^{25} -4.77954 q^{27} -3.96542 q^{29} -5.68893 q^{31} +4.41697 q^{33} +0.580377 q^{35} +0.495300 q^{37} +5.82195 q^{39} +11.8503 q^{41} +4.78767 q^{43} -2.13297 q^{45} +3.78707 q^{47} -6.66316 q^{49} -5.47453 q^{51} -7.91925 q^{53} +4.74359 q^{55} +5.04164 q^{57} -10.6416 q^{59} +9.77193 q^{61} -1.23793 q^{63} +6.25246 q^{65} -1.35061 q^{67} +7.97283 q^{69} +10.7514 q^{71} +1.31208 q^{73} +0.931146 q^{75} +2.75307 q^{77} -0.492431 q^{79} +1.94845 q^{81} -1.62413 q^{83} -5.87935 q^{85} -3.69239 q^{87} +1.00000 q^{89} +3.62878 q^{91} -5.29722 q^{93} +5.41445 q^{95} -9.61533 q^{97} -10.1179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 8 q^{3} + 7 q^{5} + 16 q^{7} + 11 q^{9}+O(q^{10}) \) 7 * q + 8 * q^3 + 7 * q^5 + 16 * q^7 + 11 * q^9	\( 7 q + 8 q^{3} + 7 q^{5} + 16 q^{7} + 11 q^{9} + 10 q^{11} - 7 q^{13} + 8 q^{15} - 13 q^{17} + 7 q^{19} + 16 q^{21} + 13 q^{23} + 7 q^{25} + 23 q^{27} - 4 q^{29} - q^{31} - 6 q^{33} + 16 q^{35} - 5 q^{37} + 13 q^{39} + 5 q^{41} + 31 q^{43} + 11 q^{45} + 14 q^{47} + 19 q^{49} + q^{51} - 13 q^{53} + 10 q^{55} + 21 q^{57} + 14 q^{59} + 3 q^{61} + 54 q^{63} - 7 q^{65} - q^{67} + 31 q^{69} + 8 q^{71} + 9 q^{73} + 8 q^{75} + 42 q^{77} - 9 q^{79} + 35 q^{81} + 42 q^{83} - 13 q^{85} - 6 q^{87} + 7 q^{89} - 31 q^{91} + 24 q^{93} + 7 q^{95} - 7 q^{97} - 5 q^{99}+O(q^{100}) \) 7 * q + 8 * q^3 + 7 * q^5 + 16 * q^7 + 11 * q^9 + 10 * q^11 - 7 * q^13 + 8 * q^15 - 13 * q^17 + 7 * q^19 + 16 * q^21 + 13 * q^23 + 7 * q^25 + 23 * q^27 - 4 * q^29 - q^31 - 6 * q^33 + 16 * q^35 - 5 * q^37 + 13 * q^39 + 5 * q^41 + 31 * q^43 + 11 * q^45 + 14 * q^47 + 19 * q^49 + q^51 - 13 * q^53 + 10 * q^55 + 21 * q^57 + 14 * q^59 + 3 * q^61 + 54 * q^63 - 7 * q^65 - q^67 + 31 * q^69 + 8 * q^71 + 9 * q^73 + 8 * q^75 + 42 * q^77 - 9 * q^79 + 35 * q^81 + 42 * q^83 - 13 * q^85 - 6 * q^87 + 7 * q^89 - 31 * q^91 + 24 * q^93 + 7 * q^95 - 7 * q^97 - 5 * q^99

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