LMFDB - Embedded newform 9675.2.a.bq.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9675,2,Mod(1,9675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9675, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9675.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9675 = 3^{2} \cdot 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9675.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:	$77.2552639556$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x - 2 $ x^3 - x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 129)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.363328$ of defining polynomial
Character	$\chi$	$=$	9675.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.36333 q^{2} -0.141336 q^{4} -4.14134 q^{7} +2.91934 q^{8} +O(q^{10})$	$q-1.36333 q^{2} -0.141336 q^{4} -4.14134 q^{7} +2.91934 q^{8} +1.77801 q^{11} -3.00000 q^{13} +5.64600 q^{14} -3.69735 q^{16} +3.14134 q^{17} +2.86799 q^{19} -2.42401 q^{22} -6.15066 q^{23} +4.08998 q^{26} +0.585320 q^{28} -1.36333 q^{29} -5.86799 q^{31} -0.797984 q^{32} -4.28267 q^{34} +7.00933 q^{37} -3.91002 q^{38} +3.58532 q^{41} +1.00000 q^{43} -0.251297 q^{44} +8.38538 q^{46} +12.6553 q^{47} +10.1507 q^{49} +0.424008 q^{52} -5.86799 q^{53} -12.0900 q^{56} +1.85866 q^{58} -8.28267 q^{59} -9.55602 q^{61} +8.00000 q^{62} +8.48262 q^{64} +14.8773 q^{67} -0.443984 q^{68} -11.5560 q^{71} -0.282672 q^{73} -9.55602 q^{74} -0.405351 q^{76} -7.36333 q^{77} +15.0093 q^{79} -4.88797 q^{82} -10.0607 q^{83} -1.36333 q^{86} +5.19062 q^{88} +11.2733 q^{89} +12.4240 q^{91} +0.869311 q^{92} -17.2534 q^{94} -4.55602 q^{97} -13.8387 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 2 q^{2} + 8 q^{4} - 4 q^{7} - 6 q^{8}+O(q^{10}) $ 3 * q - 2 * q^2 + 8 * q^4 - 4 * q^7 - 6 * q^8	$ 3 q - 2 q^{2} + 8 q^{4} - 4 q^{7} - 6 q^{8} - q^{11} - 9 q^{13} - 2 q^{14} + 10 q^{16} + q^{17} - 4 q^{19} + 18 q^{22} + 11 q^{23} + 6 q^{26} + 6 q^{28} - 2 q^{29} - 5 q^{31} - 34 q^{32} + 4 q^{34} - 18 q^{38} + 15 q^{41} + 3 q^{43} - 24 q^{44} + 4 q^{46} - 2 q^{47} + q^{49} - 24 q^{52} - 5 q^{53} - 30 q^{56} + 14 q^{58} - 8 q^{59} - 16 q^{61} + 24 q^{62} + 34 q^{64} + 11 q^{67} - 14 q^{68} - 22 q^{71} + 16 q^{73} - 16 q^{74} - 18 q^{76} - 20 q^{77} + 24 q^{79} - 40 q^{82} - 7 q^{83} - 2 q^{86} + 62 q^{88} + 38 q^{89} + 12 q^{91} + 70 q^{92} - 18 q^{94} - q^{97} - 12 q^{98}+O(q^{100}) $ 3 * q - 2 * q^2 + 8 * q^4 - 4 * q^7 - 6 * q^8 - q^11 - 9 * q^13 - 2 * q^14 + 10 * q^16 + q^17 - 4 * q^19 + 18 * q^22 + 11 * q^23 + 6 * q^26 + 6 * q^28 - 2 * q^29 - 5 * q^31 - 34 * q^32 + 4 * q^34 - 18 * q^38 + 15 * q^41 + 3 * q^43 - 24 * q^44 + 4 * q^46 - 2 * q^47 + q^49 - 24 * q^52 - 5 * q^53 - 30 * q^56 + 14 * q^58 - 8 * q^59 - 16 * q^61 + 24 * q^62 + 34 * q^64 + 11 * q^67 - 14 * q^68 - 22 * q^71 + 16 * q^73 - 16 * q^74 - 18 * q^76 - 20 * q^77 + 24 * q^79 - 40 * q^82 - 7 * q^83 - 2 * q^86 + 62 * q^88 + 38 * q^89 + 12 * q^91 + 70 * q^92 - 18 * q^94 - q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.36333	−0.964019	−0.482009	−	0.876166i	$-0.660093\pi$
$2$	−1.36333	−0.964019	−0.482009	+	0.876166i	$0.660093\pi$
$3$	0	0
$3$	0	0
$4$	−0.141336	−0.0706681
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−4.14134	−1.56528	−0.782639	−	0.622476i	$-0.786127\pi$
$7$	−4.14134	−1.56528	−0.782639	+	0.622476i	$0.786127\pi$
$8$	2.91934	1.03214
$9$	0	0
$10$	0	0
$11$	1.77801	0.536090	0.268045	−	0.963406i	$-0.413622\pi$
$11$	1.77801	0.536090	0.268045	+	0.963406i	$0.413622\pi$
$12$	0	0
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	5.64600	1.50896
$15$	0	0
$16$	−3.69735	−0.924338
$17$	3.14134	0.761886	0.380943	−	0.924599i	$-0.375599\pi$
$17$	3.14134	0.761886	0.380943	+	0.924599i	$0.375599\pi$
$18$	0	0
$19$	2.86799	0.657963	0.328981	−	0.944336i	$-0.393295\pi$
$19$	2.86799	0.657963	0.328981	+	0.944336i	$0.393295\pi$
$20$	0	0
$21$	0	0
$22$	−2.42401	−0.516800
$23$	−6.15066	−1.28250	−0.641251	−	0.767331i	$-0.721584\pi$
$23$	−6.15066	−1.28250	−0.641251	+	0.767331i	$0.721584\pi$
$24$	0	0
$25$	0	0
$26$	4.08998	0.802112
$27$	0	0
$28$	0.585320	0.110615
$29$	−1.36333	−0.253164	−0.126582	−	0.991956i	$-0.540401\pi$
$29$	−1.36333	−0.253164	−0.126582	+	0.991956i	$0.540401\pi$
$30$	0	0
$31$	−5.86799	−1.05392	−0.526961	−	0.849889i	$-0.676669\pi$
$31$	−5.86799	−1.05392	−0.526961	+	0.849889i	$0.676669\pi$
$32$	−0.797984	−0.141065
$33$	0	0
$34$	−4.28267	−0.734472
$35$	0	0
$36$	0	0
$37$	7.00933	1.15233	0.576163	−	0.817335i	$-0.304549\pi$
$37$	7.00933	1.15233	0.576163	+	0.817335i	$0.304549\pi$
$38$	−3.91002	−0.634288
$39$	0	0
$40$	0	0
$41$	3.58532	0.559933	0.279966	−	0.960010i	$-0.409677\pi$
$41$	3.58532	0.559933	0.279966	+	0.960010i	$0.409677\pi$
$42$	0	0
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−0.251297	−0.0378844
$45$	0	0
$46$	8.38538	1.23636
$47$	12.6553	1.84597	0.922985	−	0.384837i	$-0.125742\pi$
$47$	12.6553	1.84597	0.922985	+	0.384837i	$0.125742\pi$
$48$	0	0
$49$	10.1507	1.45009
$50$	0	0
$51$	0	0
$52$	0.424008	0.0587994
$53$	−5.86799	−0.806031	−0.403015	−	0.915193i	$-0.632038\pi$
$53$	−5.86799	−0.806031	−0.403015	+	0.915193i	$0.632038\pi$
$54$	0	0
$55$	0	0
$56$	−12.0900	−1.61559
$57$	0	0
$58$	1.85866	0.244055
$59$	−8.28267	−1.07831	−0.539156	−	0.842206i	$-0.681257\pi$
$59$	−8.28267	−1.07831	−0.539156	+	0.842206i	$0.681257\pi$
$60$	0	0
$61$	−9.55602	−1.22352	−0.611761	−	0.791042i	$-0.709539\pi$
$61$	−9.55602	−1.22352	−0.611761	+	0.791042i	$0.709539\pi$
$62$	8.00000	1.01600
$63$	0	0
$64$	8.48262	1.06033
$65$	0	0
$66$	0	0
$67$	14.8773	1.81755	0.908777	−	0.417282i	$-0.137017\pi$
$67$	14.8773	1.81755	0.908777	+	0.417282i	$0.137017\pi$
$68$	−0.443984	−0.0538410
$69$	0	0
$70$	0	0
$71$	−11.5560	−1.37145	−0.685723	−	0.727862i	$-0.740514\pi$
$71$	−11.5560	−1.37145	−0.685723	+	0.727862i	$0.740514\pi$
$72$	0	0
$73$	−0.282672	−0.0330843	−0.0165421	−	0.999863i	$-0.505266\pi$
$73$	−0.282672	−0.0330843	−0.0165421	+	0.999863i	$0.505266\pi$
$74$	−9.55602	−1.11086
$75$	0	0
$76$	−0.405351	−0.0464969
$77$	−7.36333	−0.839129
$78$	0	0
$79$	15.0093	1.68868	0.844341	−	0.535807i	$-0.179992\pi$
$79$	15.0093	1.68868	0.844341	+	0.535807i	$0.179992\pi$
$80$	0	0
$81$	0	0
$82$	−4.88797	−0.539786
$83$	−10.0607	−1.10430	−0.552152	−	0.833744i	$-0.686193\pi$
$83$	−10.0607	−1.10430	−0.552152	+	0.833744i	$0.686193\pi$
$84$	0	0
$85$	0	0
$86$	−1.36333	−0.147011
$87$	0	0
$88$	5.19062	0.553322
$89$	11.2733	1.19497	0.597486	−	0.801879i	$-0.296166\pi$
$89$	11.2733	1.19497	0.597486	+	0.801879i	$0.296166\pi$
$90$	0	0
$91$	12.4240	1.30239
$92$	0.869311	0.0906319
$93$	0	0
$94$	−17.2534	−1.77955
$95$	0	0
$96$	0	0
$97$	−4.55602	−0.462593	−0.231297	−	0.972883i	$-0.574297\pi$
$97$	−4.55602	−0.462593	−0.231297	+	0.972883i	$0.574297\pi$
$98$	−13.8387	−1.39792
$99$	0	0
$100$	0	0
$101$	1.86799	0.185872	0.0929361	−	0.995672i	$-0.470375\pi$
$101$	1.86799	0.185872	0.0929361	+	0.995672i	$0.470375\pi$
$102$	0	0
$103$	5.42401	0.534443	0.267222	−	0.963635i	$-0.413894\pi$
$103$	5.42401	0.534443	0.267222	+	0.963635i	$0.413894\pi$
$104$	−8.75803	−0.858796
$105$	0	0
$106$	8.00000	0.777029
$107$	5.64600	0.545819	0.272910	−	0.962040i	$-0.412014\pi$
$107$	5.64600	0.545819	0.272910	+	0.962040i	$0.412014\pi$
$108$	0	0
$109$	−2.27334	−0.217747	−0.108873	−	0.994056i	$-0.534724\pi$
$109$	−2.27334	−0.217747	−0.108873	+	0.994056i	$0.534724\pi$
$110$	0	0
$111$	0	0
$112$	15.3120	1.44685
$113$	−12.3727	−1.16392	−0.581961	−	0.813217i	$-0.697714\pi$
$113$	−12.3727	−1.16392	−0.581961	+	0.813217i	$0.697714\pi$
$114$	0	0
$115$	0	0
$116$	0.192688	0.0178906
$117$	0	0
$118$	11.2920	1.03951
$119$	−13.0093	−1.19256
$120$	0	0
$121$	−7.83869	−0.712608
$122$	13.0280	1.17950
$123$	0	0
$124$	0.829359	0.0744787
$125$	0	0
$126$	0	0
$127$	−12.8773	−1.14268	−0.571339	−	0.820714i	$-0.693576\pi$
$127$	−12.8773	−1.14268	−0.571339	+	0.820714i	$0.693576\pi$
$128$	−9.96862	−0.881110
$129$	0	0
$130$	0	0
$131$	19.4720	1.70127	0.850637	−	0.525753i	$-0.176217\pi$
$131$	19.4720	1.70127	0.850637	+	0.525753i	$0.176217\pi$
$132$	0	0
$133$	−11.8773	−1.02989
$134$	−20.2827	−1.75216
$135$	0	0
$136$	9.17064	0.786376
$137$	3.54330	0.302724	0.151362	−	0.988478i	$-0.451634\pi$
$137$	3.54330	0.302724	0.151362	+	0.988478i	$0.451634\pi$
$138$	0	0
$139$	5.03863	0.427371	0.213686	−	0.976902i	$-0.431453\pi$
$139$	5.03863	0.427371	0.213686	+	0.976902i	$0.431453\pi$
$140$	0	0
$141$	0	0
$142$	15.7546	1.32210
$143$	−5.33402	−0.446053
$144$	0	0
$145$	0	0
$146$	0.385375	0.0318939
$147$	0	0
$148$	−0.990671	−0.0814327
$149$	9.55602	0.782859	0.391430	−	0.920208i	$-0.371981\pi$
$149$	9.55602	0.782859	0.391430	+	0.920208i	$0.371981\pi$
$150$	0	0
$151$	−11.7360	−0.955061	−0.477530	−	0.878615i	$-0.658468\pi$
$151$	−11.7360	−0.955061	−0.477530	+	0.878615i	$0.658468\pi$
$152$	8.37266	0.679112
$153$	0	0
$154$	10.0386	0.808936
$155$	0	0
$156$	0	0
$157$	6.74531	0.538335	0.269167	−	0.963093i	$-0.413252\pi$
$157$	6.74531	0.538335	0.269167	+	0.963093i	$0.413252\pi$
$158$	−20.4626	−1.62792
$159$	0	0
$160$	0	0
$161$	25.4720	2.00747
$162$	0	0
$163$	14.7067	1.15192	0.575958	−	0.817479i	$-0.304629\pi$
$163$	14.7067	1.15192	0.575958	+	0.817479i	$0.304629\pi$
$164$	−0.506735	−0.0395694
$165$	0	0
$166$	13.7160	1.06457
$167$	14.5047	1.12240	0.561202	−	0.827679i	$-0.310339\pi$
$167$	14.5047	1.12240	0.561202	+	0.827679i	$0.310339\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	0	0
$171$	0	0
$172$	−0.141336	−0.0107768
$173$	9.11203	0.692775	0.346387	−	0.938092i	$-0.387408\pi$
$173$	9.11203	0.692775	0.346387	+	0.938092i	$0.387408\pi$
$174$	0	0
$175$	0	0
$176$	−6.57392	−0.495528
$177$	0	0
$178$	−15.3693	−1.15198
$179$	4.72666	0.353287	0.176643	−	0.984275i	$-0.443476\pi$
$179$	4.72666	0.353287	0.176643	+	0.984275i	$0.443476\pi$
$180$	0	0
$181$	23.9987	1.78381	0.891904	−	0.452225i	$-0.149370\pi$
$181$	23.9987	1.78381	0.891904	+	0.452225i	$0.149370\pi$
$182$	−16.9380	−1.25553
$183$	0	0
$184$	−17.9559	−1.32373
$185$	0	0
$186$	0	0
$187$	5.58532	0.408439
$188$	−1.78866	−0.130451
$189$	0	0
$190$	0	0
$191$	−25.7360	−1.86219	−0.931095	−	0.364776i	$-0.881146\pi$
$191$	−25.7360	−1.86219	−0.931095	+	0.364776i	$0.881146\pi$
$192$	0	0
$193$	−11.8680	−0.854277	−0.427138	−	0.904186i	$-0.640478\pi$
$193$	−11.8680	−0.854277	−0.427138	+	0.904186i	$0.640478\pi$
$194$	6.21134	0.445949
$195$	0	0
$196$	−1.43466	−0.102475
$197$	−18.4626	−1.31541	−0.657704	−	0.753276i	$-0.728472\pi$
$197$	−18.4626	−1.31541	−0.657704	+	0.753276i	$0.728472\pi$
$198$	0	0
$199$	22.8480	1.61965	0.809826	−	0.586669i	$-0.199561\pi$
$199$	22.8480	1.61965	0.809826	+	0.586669i	$0.199561\pi$
$200$	0	0
$201$	0	0
$202$	−2.54669	−0.179184
$203$	5.64600	0.396272
$204$	0	0
$205$	0	0
$206$	−7.39470	−0.515213
$207$	0	0
$208$	11.0921	0.769096
$209$	5.09931	0.352727
$210$	0	0
$211$	16.7067	1.15014	0.575068	−	0.818106i	$-0.304976\pi$
$211$	16.7067	1.15014	0.575068	+	0.818106i	$0.304976\pi$
$212$	0.829359	0.0569606
$213$	0	0
$214$	−7.69735	−0.526180
$215$	0	0
$216$	0	0
$217$	24.3013	1.64968
$218$	3.09931	0.209912
$219$	0	0
$220$	0	0
$221$	−9.42401	−0.633927
$222$	0	0
$223$	5.41468	0.362594	0.181297	−	0.983428i	$-0.441971\pi$
$223$	5.41468	0.362594	0.181297	+	0.983428i	$0.441971\pi$
$224$	3.30472	0.220806
$225$	0	0
$226$	16.8680	1.12204
$227$	−12.8480	−0.852753	−0.426376	−	0.904546i	$-0.640210\pi$
$227$	−12.8480	−0.852753	−0.426376	+	0.904546i	$0.640210\pi$
$228$	0	0
$229$	18.1507	1.19943	0.599715	−	0.800214i	$-0.295281\pi$
$229$	18.1507	1.19943	0.599715	+	0.800214i	$0.295281\pi$
$230$	0	0
$231$	0	0
$232$	−3.98002	−0.261301
$233$	12.9193	0.846374	0.423187	−	0.906042i	$-0.360911\pi$
$233$	12.9193	0.846374	0.423187	+	0.906042i	$0.360911\pi$
$234$	0	0
$235$	0	0
$236$	1.17064	0.0762022
$237$	0	0
$238$	17.7360	1.14965
$239$	−18.9193	−1.22379	−0.611895	−	0.790939i	$-0.709593\pi$
$239$	−18.9193	−1.22379	−0.611895	+	0.790939i	$0.709593\pi$
$240$	0	0
$241$	−2.01866	−0.130033	−0.0650166	−	0.997884i	$-0.520710\pi$
$241$	−2.01866	−0.130033	−0.0650166	+	0.997884i	$0.520710\pi$
$242$	10.6867	0.686967
$243$	0	0
$244$	1.35061	0.0864640
$245$	0	0
$246$	0	0
$247$	−8.60398	−0.547458
$248$	−17.1307	−1.08780
$249$	0	0
$250$	0	0
$251$	−9.49534	−0.599340	−0.299670	−	0.954043i	$-0.596877\pi$
$251$	−9.49534	−0.599340	−0.299670	+	0.954043i	$0.596877\pi$
$252$	0	0
$253$	−10.9359	−0.687536
$254$	17.5560	1.10156
$255$	0	0
$256$	−3.37473	−0.210920
$257$	−16.0314	−1.00001	−0.500005	−	0.866023i	$-0.666668\pi$
$257$	−16.0314	−1.00001	−0.500005	+	0.866023i	$0.666668\pi$
$258$	0	0
$259$	−29.0280	−1.80371
$260$	0	0
$261$	0	0
$262$	−26.5467	−1.64006
$263$	21.8573	1.34778	0.673891	−	0.738831i	$-0.264622\pi$
$263$	21.8573	1.34778	0.673891	+	0.738831i	$0.264622\pi$
$264$	0	0
$265$	0	0
$266$	16.1927	0.992837
$267$	0	0
$268$	−2.10270	−0.128443
$269$	6.33063	0.385986	0.192993	−	0.981200i	$-0.438181\pi$
$269$	6.33063	0.385986	0.192993	+	0.981200i	$0.438181\pi$
$270$	0	0
$271$	8.43334	0.512289	0.256144	−	0.966639i	$-0.417548\pi$
$271$	8.43334	0.512289	0.256144	+	0.966639i	$0.417548\pi$
$272$	−11.6146	−0.704240
$273$	0	0
$274$	−4.83068	−0.291832
$275$	0	0
$276$	0	0
$277$	−10.4626	−0.628639	−0.314320	−	0.949317i	$-0.601776\pi$
$277$	−10.4626	−0.628639	−0.314320	+	0.949317i	$0.601776\pi$
$278$	−6.86931	−0.411994
$279$	0	0
$280$	0	0
$281$	1.40535	0.0838362	0.0419181	−	0.999121i	$-0.486653\pi$
$281$	1.40535	0.0838362	0.0419181	+	0.999121i	$0.486653\pi$
$282$	0	0
$283$	−17.2627	−1.02616	−0.513080	−	0.858341i	$-0.671496\pi$
$283$	−17.2627	−1.02616	−0.513080	+	0.858341i	$0.671496\pi$
$284$	1.63328	0.0969175
$285$	0	0
$286$	7.27203	0.430004
$287$	−14.8480	−0.876451
$288$	0	0
$289$	−7.13201	−0.419530
$290$	0	0
$291$	0	0
$292$	0.0399518	0.00233800
$293$	−21.5747	−1.26041	−0.630203	−	0.776430i	$-0.717028\pi$
$293$	−21.5747	−1.26041	−0.630203	+	0.776430i	$0.717028\pi$
$294$	0	0
$295$	0	0
$296$	20.4626	1.18937
$297$	0	0
$298$	−13.0280	−0.754691
$299$	18.4520	1.06711
$300$	0	0
$301$	−4.14134	−0.238703
$302$	16.0000	0.920697
$303$	0	0
$304$	−10.6040	−0.608180
$305$	0	0
$306$	0	0
$307$	13.7067	0.782282	0.391141	−	0.920331i	$-0.372081\pi$
$307$	13.7067	0.782282	0.391141	+	0.920331i	$0.372081\pi$
$308$	1.04070	0.0592996
$309$	0	0
$310$	0	0
$311$	−13.2313	−0.750279	−0.375140	−	0.926968i	$-0.622405\pi$
$311$	−13.2313	−0.750279	−0.375140	+	0.926968i	$0.622405\pi$
$312$	0	0
$313$	8.28267	0.468164	0.234082	−	0.972217i	$-0.424792\pi$
$313$	8.28267	0.468164	0.234082	+	0.972217i	$0.424792\pi$
$314$	−9.19608	−0.518965
$315$	0	0
$316$	−2.12136	−0.119336
$317$	−25.7067	−1.44383	−0.721916	−	0.691981i	$-0.756738\pi$
$317$	−25.7067	−1.44383	−0.721916	+	0.691981i	$0.756738\pi$
$318$	0	0
$319$	−2.42401	−0.135718
$320$	0	0
$321$	0	0
$322$	−34.7267	−1.93524
$323$	9.00933	0.501292
$324$	0	0
$325$	0	0
$326$	−20.0500	−1.11047
$327$	0	0
$328$	10.4668	0.577931
$329$	−52.4100	−2.88946
$330$	0	0
$331$	−25.5106	−1.40219	−0.701095	−	0.713068i	$-0.747305\pi$
$331$	−25.5106	−1.40219	−0.701095	+	0.713068i	$0.747305\pi$
$332$	1.42194	0.0780390
$333$	0	0
$334$	−19.7746	−1.08202
$335$	0	0
$336$	0	0
$337$	−22.0280	−1.19994	−0.599970	−	0.800022i	$-0.704821\pi$
$337$	−22.0280	−1.19994	−0.599970	+	0.800022i	$0.704821\pi$
$338$	5.45331	0.296621
$339$	0	0
$340$	0	0
$341$	−10.4333	−0.564997
$342$	0	0
$343$	−13.0480	−0.704524
$344$	2.91934	0.157400
$345$	0	0
$346$	−12.4227	−0.667848
$347$	36.6867	1.96945	0.984723	−	0.174130i	$-0.0557112\pi$
$347$	36.6867	1.96945	0.984723	+	0.174130i	$0.0557112\pi$
$348$	0	0
$349$	−19.6774	−1.05331	−0.526653	−	0.850080i	$-0.676553\pi$
$349$	−19.6774	−1.05331	−0.526653	+	0.850080i	$0.676553\pi$
$350$	0	0
$351$	0	0
$352$	−1.41882	−0.0756234
$353$	23.4240	1.24673	0.623367	−	0.781929i	$-0.285764\pi$
$353$	23.4240	1.24673	0.623367	+	0.781929i	$0.285764\pi$
$354$	0	0
$355$	0	0
$356$	−1.59333	−0.0844464
$357$	0	0
$358$	−6.44398	−0.340575
$359$	24.1693	1.27561	0.637804	−	0.770199i	$-0.279843\pi$
$359$	24.1693	1.27561	0.637804	+	0.770199i	$0.279843\pi$
$360$	0	0
$361$	−10.7746	−0.567085
$362$	−32.7181	−1.71962
$363$	0	0
$364$	−1.75596	−0.0920374
$365$	0	0
$366$	0	0
$367$	9.17064	0.478704	0.239352	−	0.970933i	$-0.423065\pi$
$367$	9.17064	0.478704	0.239352	+	0.970933i	$0.423065\pi$
$368$	22.7412	1.18547
$369$	0	0
$370$	0	0
$371$	24.3013	1.26166
$372$	0	0
$373$	−27.1893	−1.40781	−0.703904	−	0.710295i	$-0.748562\pi$
$373$	−27.1893	−1.40781	−0.703904	+	0.710295i	$0.748562\pi$
$374$	−7.61462	−0.393743
$375$	0	0
$376$	36.9453	1.90531
$377$	4.08998	0.210645
$378$	0	0
$379$	16.5360	0.849399	0.424700	−	0.905334i	$-0.360380\pi$
$379$	16.5360	0.849399	0.424700	+	0.905334i	$0.360380\pi$
$380$	0	0
$381$	0	0
$382$	35.0866	1.79519
$383$	−8.46264	−0.432421	−0.216210	−	0.976347i	$-0.569370\pi$
$383$	−8.46264	−0.432421	−0.216210	+	0.976347i	$0.569370\pi$
$384$	0	0
$385$	0	0
$386$	16.1800	0.823539
$387$	0	0
$388$	0.643930	0.0326906
$389$	−29.8446	−1.51318	−0.756591	−	0.653888i	$-0.773137\pi$
$389$	−29.8446	−1.51318	−0.756591	+	0.653888i	$0.773137\pi$
$390$	0	0
$391$	−19.3213	−0.977120
$392$	29.6333	1.49671
$393$	0	0
$394$	25.1706	1.26808
$395$	0	0
$396$	0	0
$397$	−30.5199	−1.53175	−0.765876	−	0.642989i	$-0.777694\pi$
$397$	−30.5199	−1.53175	−0.765876	+	0.642989i	$0.777694\pi$
$398$	−31.1493	−1.56138
$399$	0	0
$400$	0	0
$401$	−26.0480	−1.30077	−0.650387	−	0.759603i	$-0.725393\pi$
$401$	−26.0480	−1.30077	−0.650387	+	0.759603i	$0.725393\pi$
$402$	0	0
$403$	17.6040	0.876917
$404$	−0.264015	−0.0131352
$405$	0	0
$406$	−7.69735	−0.382013
$407$	12.4626	0.617750
$408$	0	0
$409$	2.10270	0.103972	0.0519860	−	0.998648i	$-0.483445\pi$
$409$	2.10270	0.103972	0.0519860	+	0.998648i	$0.483445\pi$
$410$	0	0
$411$	0	0
$412$	−0.766608	−0.0377681
$413$	34.3013	1.68786
$414$	0	0
$415$	0	0
$416$	2.39395	0.117373
$417$	0	0
$418$	−6.95204	−0.340035
$419$	−13.1120	−0.640565	−0.320282	−	0.947322i	$-0.603778\pi$
$419$	−13.1120	−0.640565	−0.320282	+	0.947322i	$0.603778\pi$
$420$	0	0
$421$	11.9414	0.581988	0.290994	−	0.956725i	$-0.406014\pi$
$421$	11.9414	0.581988	0.290994	+	0.956725i	$0.406014\pi$
$422$	−22.7767	−1.10875
$423$	0	0
$424$	−17.1307	−0.831940
$425$	0	0
$426$	0	0
$427$	39.5747	1.91515
$428$	−0.797984	−0.0385720
$429$	0	0
$430$	0	0
$431$	−13.1286	−0.632383	−0.316192	−	0.948695i	$-0.602404\pi$
$431$	−13.1286	−0.632383	−0.316192	+	0.948695i	$0.602404\pi$
$432$	0	0
$433$	26.8480	1.29023	0.645117	−	0.764084i	$-0.276809\pi$
$433$	26.8480	1.29023	0.645117	+	0.764084i	$0.276809\pi$
$434$	−33.1307	−1.59032
$435$	0	0
$436$	0.321306	0.0153877
$437$	−17.6401	−0.843839
$438$	0	0
$439$	−0.433337	−0.0206820	−0.0103410	−	0.999947i	$-0.503292\pi$
$439$	−0.433337	−0.0206820	−0.0103410	+	0.999947i	$0.503292\pi$
$440$	0	0
$441$	0	0
$442$	12.8480	0.611118
$443$	−0.475360	−0.0225850	−0.0112925	−	0.999936i	$-0.503595\pi$
$443$	−0.475360	−0.0225850	−0.0112925	+	0.999936i	$0.503595\pi$
$444$	0	0
$445$	0	0
$446$	−7.38199	−0.349547
$447$	0	0
$448$	−35.1294	−1.65971
$449$	−21.0407	−0.992972	−0.496486	−	0.868045i	$-0.665377\pi$
$449$	−21.0407	−0.992972	−0.496486	+	0.868045i	$0.665377\pi$
$450$	0	0
$451$	6.37473	0.300174
$452$	1.74870	0.0822521
$453$	0	0
$454$	17.5161	0.822070
$455$	0	0
$456$	0	0
$457$	−1.55602	−0.0727873	−0.0363937	−	0.999338i	$-0.511587\pi$
$457$	−1.55602	−0.0727873	−0.0363937	+	0.999338i	$0.511587\pi$
$458$	−24.7453	−1.15627
$459$	0	0
$460$	0	0
$461$	19.8387	0.923980	0.461990	−	0.886885i	$-0.347136\pi$
$461$	19.8387	0.923980	0.461990	+	0.886885i	$0.347136\pi$
$462$	0	0
$463$	15.9987	0.743522	0.371761	−	0.928329i	$-0.378754\pi$
$463$	15.9987	0.743522	0.371761	+	0.928329i	$0.378754\pi$
$464$	5.04070	0.234009
$465$	0	0
$466$	−17.6133	−0.815921
$467$	−34.4626	−1.59474	−0.797370	−	0.603490i	$-0.793776\pi$
$467$	−34.4626	−1.59474	−0.797370	+	0.603490i	$0.793776\pi$
$468$	0	0
$469$	−61.6120	−2.84498
$470$	0	0
$471$	0	0
$472$	−24.1800	−1.11297
$473$	1.77801	0.0817529
$474$	0	0
$475$	0	0
$476$	1.83869	0.0842761
$477$	0	0
$478$	25.7933	1.17976
$479$	22.9673	1.04940	0.524701	−	0.851286i	$-0.324177\pi$
$479$	22.9673	1.04940	0.524701	+	0.851286i	$0.324177\pi$
$480$	0	0
$481$	−21.0280	−0.958794
$482$	2.75209	0.125354
$483$	0	0
$484$	1.10789	0.0503586
$485$	0	0
$486$	0	0
$487$	19.0093	0.861395	0.430697	−	0.902496i	$-0.358268\pi$
$487$	19.0093	0.861395	0.430697	+	0.902496i	$0.358268\pi$
$488$	−27.8973	−1.26285
$489$	0	0
$490$	0	0
$491$	6.64939	0.300083	0.150041	−	0.988680i	$-0.452059\pi$
$491$	6.64939	0.300083	0.150041	+	0.988680i	$0.452059\pi$
$492$	0	0
$493$	−4.28267	−0.192882
$494$	11.7300	0.527760
$495$	0	0
$496$	21.6960	0.974181
$497$	47.8573	2.14670
$498$	0	0
$499$	18.3400	0.821009	0.410505	−	0.911858i	$-0.365353\pi$
$499$	18.3400	0.821009	0.410505	+	0.911858i	$0.365353\pi$
$500$	0	0
$501$	0	0
$502$	12.9453	0.577775
$503$	−15.2733	−0.681005	−0.340502	−	0.940244i	$-0.610597\pi$
$503$	−15.2733	−0.681005	−0.340502	+	0.940244i	$0.610597\pi$
$504$	0	0
$505$	0	0
$506$	14.9093	0.662798
$507$	0	0
$508$	1.82003	0.0807508
$509$	−5.58532	−0.247565	−0.123782	−	0.992309i	$-0.539503\pi$
$509$	−5.58532	−0.247565	−0.123782	+	0.992309i	$0.539503\pi$
$510$	0	0
$511$	1.17064	0.0517861
$512$	24.5381	1.08444
$513$	0	0
$514$	21.8560	0.964028
$515$	0	0
$516$	0	0
$517$	22.5013	0.989605
$518$	39.5747	1.73881
$519$	0	0
$520$	0	0
$521$	27.5620	1.20751	0.603756	−	0.797169i	$-0.293670\pi$
$521$	27.5620	1.20751	0.603756	+	0.797169i	$0.293670\pi$
$522$	0	0
$523$	−35.9987	−1.57411	−0.787056	−	0.616881i	$-0.788396\pi$
$523$	−35.9987	−1.57411	−0.787056	+	0.616881i	$0.788396\pi$
$524$	−2.75209	−0.120226
$525$	0	0
$526$	−29.7987	−1.29929
$527$	−18.4333	−0.802969
$528$	0	0
$529$	14.8307	0.644812
$530$	0	0
$531$	0	0
$532$	1.67869	0.0727806
$533$	−10.7560	−0.465892
$534$	0	0
$535$	0	0
$536$	43.4320	1.87598
$537$	0	0
$538$	−8.63073	−0.372097
$539$	18.0480	0.777381
$540$	0	0
$541$	1.94526	0.0836332	0.0418166	−	0.999125i	$-0.486685\pi$
$541$	1.94526	0.0836332	0.0418166	+	0.999125i	$0.486685\pi$
$542$	−11.4974	−0.493856
$543$	0	0
$544$	−2.50674	−0.107475
$545$	0	0
$546$	0	0
$547$	24.0666	1.02901	0.514507	−	0.857486i	$-0.327975\pi$
$547$	24.0666	1.02901	0.514507	+	0.857486i	$0.327975\pi$
$548$	−0.500796	−0.0213929
$549$	0	0
$550$	0	0
$551$	−3.91002	−0.166572
$552$	0	0
$553$	−62.1587	−2.64326
$554$	14.2640	0.606020
$555$	0	0
$556$	−0.712141	−0.0302015
$557$	−5.84934	−0.247844	−0.123922	−	0.992292i	$-0.539547\pi$
$557$	−5.84934	−0.247844	−0.123922	+	0.992292i	$0.539547\pi$
$558$	0	0
$559$	−3.00000	−0.126886
$560$	0	0
$561$	0	0
$562$	−1.91595	−0.0808197
$563$	−43.3400	−1.82656	−0.913281	−	0.407330i	$-0.866460\pi$
$563$	−43.3400	−1.82656	−0.913281	+	0.407330i	$0.866460\pi$
$564$	0	0
$565$	0	0
$566$	23.5347	0.989238
$567$	0	0
$568$	−33.7360	−1.41553
$569$	−3.12268	−0.130910	−0.0654548	−	0.997856i	$-0.520850\pi$
$569$	−3.12268	−0.130910	−0.0654548	+	0.997856i	$0.520850\pi$
$570$	0	0
$571$	18.1413	0.759191	0.379596	−	0.925152i	$-0.376063\pi$
$571$	18.1413	0.759191	0.379596	+	0.925152i	$0.376063\pi$
$572$	0.753890	0.0315217
$573$	0	0
$574$	20.2427	0.844915
$575$	0	0
$576$	0	0
$577$	−23.3107	−0.970435	−0.485218	−	0.874393i	$-0.661260\pi$
$577$	−23.3107	−0.970435	−0.485218	+	0.874393i	$0.661260\pi$
$578$	9.72327	0.404435
$579$	0	0
$580$	0	0
$581$	41.6647	1.72854
$582$	0	0
$583$	−10.4333	−0.432105
$584$	−0.825217	−0.0341477
$585$	0	0
$586$	29.4134	1.21505
$587$	−12.9321	−0.533763	−0.266882	−	0.963729i	$-0.585993\pi$
$587$	−12.9321	−0.533763	−0.266882	+	0.963729i	$0.585993\pi$
$588$	0	0
$589$	−16.8294	−0.693442
$590$	0	0
$591$	0	0
$592$	−25.9160	−1.06514
$593$	−4.40403	−0.180852	−0.0904260	−	0.995903i	$-0.528823\pi$
$593$	−4.40403	−0.180852	−0.0904260	+	0.995903i	$0.528823\pi$
$594$	0	0
$595$	0	0
$596$	−1.35061	−0.0553231
$597$	0	0
$598$	−25.1561	−1.02871
$599$	−27.9953	−1.14386	−0.571928	−	0.820304i	$-0.693804\pi$
$599$	−27.9953	−1.14386	−0.571928	+	0.820304i	$0.693804\pi$
$600$	0	0
$601$	6.48130	0.264378	0.132189	−	0.991225i	$-0.457799\pi$
$601$	6.48130	0.264378	0.132189	+	0.991225i	$0.457799\pi$
$602$	5.64600	0.230114
$603$	0	0
$604$	1.65872	0.0674923
$605$	0	0
$606$	0	0
$607$	−31.7746	−1.28969	−0.644846	−	0.764313i	$-0.723078\pi$
$607$	−31.7746	−1.28969	−0.644846	+	0.764313i	$0.723078\pi$
$608$	−2.28861	−0.0928155
$609$	0	0
$610$	0	0
$611$	−37.9660	−1.53594
$612$	0	0
$613$	−20.2241	−0.816842	−0.408421	−	0.912794i	$-0.633920\pi$
$613$	−20.2241	−0.816842	−0.408421	+	0.912794i	$0.633920\pi$
$614$	−18.6867	−0.754134
$615$	0	0
$616$	−21.4961	−0.866102
$617$	−15.8867	−0.639572	−0.319786	−	0.947490i	$-0.603611\pi$
$617$	−15.8867	−0.639572	−0.319786	+	0.947490i	$0.603611\pi$
$618$	0	0
$619$	−32.2827	−1.29755	−0.648775	−	0.760980i	$-0.724718\pi$
$619$	−32.2827	−1.29755	−0.648775	+	0.760980i	$0.724718\pi$
$620$	0	0
$621$	0	0
$622$	18.0386	0.723283
$623$	−46.6867	−1.87046
$624$	0	0
$625$	0	0
$626$	−11.2920	−0.451319
$627$	0	0
$628$	−0.953356	−0.0380431
$629$	22.0187	0.877941
$630$	0	0
$631$	−11.4134	−0.454359	−0.227179	−	0.973853i	$-0.572950\pi$
$631$	−11.4134	−0.454359	−0.227179	+	0.973853i	$0.572950\pi$
$632$	43.8174	1.74296
$633$	0	0
$634$	35.0466	1.39188
$635$	0	0
$636$	0	0
$637$	−30.4520	−1.20655
$638$	3.30472	0.130835
$639$	0	0
$640$	0	0
$641$	28.9694	1.14422	0.572111	−	0.820176i	$-0.306125\pi$
$641$	28.9694	1.14422	0.572111	+	0.820176i	$0.306125\pi$
$642$	0	0
$643$	−35.5747	−1.40293	−0.701464	−	0.712705i	$-0.747470\pi$
$643$	−35.5747	−1.40293	−0.701464	+	0.712705i	$0.747470\pi$
$644$	−3.60011	−0.141864
$645$	0	0
$646$	−12.2827	−0.483255
$647$	14.4040	0.566281	0.283140	−	0.959078i	$-0.408624\pi$
$647$	14.4040	0.566281	0.283140	+	0.959078i	$0.408624\pi$
$648$	0	0
$649$	−14.7267	−0.578072
$650$	0	0
$651$	0	0
$652$	−2.07859	−0.0814037
$653$	−29.3047	−1.14678	−0.573391	−	0.819282i	$-0.694372\pi$
$653$	−29.3047	−1.14678	−0.573391	+	0.819282i	$0.694372\pi$
$654$	0	0
$655$	0	0
$656$	−13.2562	−0.517567
$657$	0	0
$658$	71.4520	2.78549
$659$	−34.1880	−1.33177	−0.665887	−	0.746052i	$-0.731947\pi$
$659$	−34.1880	−1.33177	−0.665887	+	0.746052i	$0.731947\pi$
$660$	0	0
$661$	−5.46264	−0.212472	−0.106236	−	0.994341i	$-0.533880\pi$
$661$	−5.46264	−0.212472	−0.106236	+	0.994341i	$0.533880\pi$
$662$	34.7793	1.35174
$663$	0	0
$664$	−29.3706	−1.13980
$665$	0	0
$666$	0	0
$667$	8.38538	0.324683
$668$	−2.05003	−0.0793182
$669$	0	0
$670$	0	0
$671$	−16.9907	−0.655918
$672$	0	0
$673$	5.19608	0.200294	0.100147	−	0.994973i	$-0.468069\pi$
$673$	5.19608	0.200294	0.100147	+	0.994973i	$0.468069\pi$
$674$	30.0314	1.15677
$675$	0	0
$676$	0.565344	0.0217440
$677$	−39.2733	−1.50940	−0.754699	−	0.656072i	$-0.772217\pi$
$677$	−39.2733	−1.50940	−0.754699	+	0.656072i	$0.772217\pi$
$678$	0	0
$679$	18.8680	0.724087
$680$	0	0
$681$	0	0
$682$	14.2241	0.544668
$683$	24.4333	0.934916	0.467458	−	0.884015i	$-0.345170\pi$
$683$	24.4333	0.934916	0.467458	+	0.884015i	$0.345170\pi$
$684$	0	0
$685$	0	0
$686$	17.7887	0.679174
$687$	0	0
$688$	−3.69735	−0.140960
$689$	17.6040	0.670658
$690$	0	0
$691$	4.30133	0.163630	0.0818151	−	0.996648i	$-0.473928\pi$
$691$	4.30133	0.163630	0.0818151	+	0.996648i	$0.473928\pi$
$692$	−1.28786	−0.0489571
$693$	0	0
$694$	−50.0160	−1.89858
$695$	0	0
$696$	0	0
$697$	11.2627	0.426605
$698$	26.8267	1.01541
$699$	0	0
$700$	0	0
$701$	9.71733	0.367018	0.183509	−	0.983018i	$-0.441254\pi$
$701$	9.71733	0.367018	0.183509	+	0.983018i	$0.441254\pi$
$702$	0	0
$703$	20.1027	0.758188
$704$	15.0822	0.568430
$705$	0	0
$706$	−31.9346	−1.20187
$707$	−7.73599	−0.290942
$708$	0	0
$709$	−18.1307	−0.680912	−0.340456	−	0.940260i	$-0.610581\pi$
$709$	−18.1307	−0.680912	−0.340456	+	0.940260i	$0.610581\pi$
$710$	0	0
$711$	0	0
$712$	32.9108	1.23338
$713$	36.0921	1.35166
$714$	0	0
$715$	0	0
$716$	−0.668047	−0.0249661
$717$	0	0
$718$	−32.9507	−1.22971
$719$	−45.2080	−1.68597	−0.842986	−	0.537935i	$-0.819204\pi$
$719$	−45.2080	−1.68597	−0.842986	+	0.537935i	$0.819204\pi$
$720$	0	0
$721$	−22.4626	−0.836552
$722$	14.6893	0.546681
$723$	0	0
$724$	−3.39188	−0.126058
$725$	0	0
$726$	0	0
$727$	0.482618	0.0178993	0.00894965	−	0.999960i	$-0.497151\pi$
$727$	0.482618	0.0178993	0.00894965	+	0.999960i	$0.497151\pi$
$728$	36.2700	1.34425
$729$	0	0
$730$	0	0
$731$	3.14134	0.116187
$732$	0	0
$733$	−36.5653	−1.35057	−0.675286	−	0.737556i	$-0.735980\pi$
$733$	−36.5653	−1.35057	−0.675286	+	0.737556i	$0.735980\pi$
$734$	−12.5026	−0.461479
$735$	0	0
$736$	4.90813	0.180916
$737$	26.4520	0.974372
$738$	0	0
$739$	−6.89343	−0.253579	−0.126789	−	0.991930i	$-0.540467\pi$
$739$	−6.89343	−0.253579	−0.126789	+	0.991930i	$0.540467\pi$
$740$	0	0
$741$	0	0
$742$	−33.1307	−1.21627
$743$	−41.5161	−1.52308	−0.761538	−	0.648120i	$-0.775556\pi$
$743$	−41.5161	−1.52308	−0.761538	+	0.648120i	$0.775556\pi$
$744$	0	0
$745$	0	0
$746$	37.0679	1.35715
$747$	0	0
$748$	−0.789407	−0.0288636
$749$	−23.3820	−0.854359
$750$	0	0
$751$	26.3213	0.960478	0.480239	−	0.877138i	$-0.340550\pi$
$751$	26.3213	0.960478	0.480239	+	0.877138i	$0.340550\pi$
$752$	−46.7912	−1.70630
$753$	0	0
$754$	−5.57599	−0.203066
$755$	0	0
$756$	0	0
$757$	−7.61462	−0.276758	−0.138379	−	0.990379i	$-0.544189\pi$
$757$	−7.61462	−0.276758	−0.138379	+	0.990379i	$0.544189\pi$
$758$	−22.5441	−0.818837
$759$	0	0
$760$	0	0
$761$	−19.0466	−0.690440	−0.345220	−	0.938522i	$-0.612196\pi$
$761$	−19.0466	−0.690440	−0.345220	+	0.938522i	$0.612196\pi$
$762$	0	0
$763$	9.41468	0.340834
$764$	3.63742	0.131597
$765$	0	0
$766$	11.5374	0.416862
$767$	24.8480	0.897210
$768$	0	0
$769$	25.3493	0.914119	0.457059	−	0.889436i	$-0.348903\pi$
$769$	25.3493	0.914119	0.457059	+	0.889436i	$0.348903\pi$
$770$	0	0
$771$	0	0
$772$	1.67738	0.0603701
$773$	−16.9193	−0.608547	−0.304273	−	0.952585i	$-0.598414\pi$
$773$	−16.9193	−0.608547	−0.304273	+	0.952585i	$0.598414\pi$
$774$	0	0
$775$	0	0
$776$	−13.3006	−0.477463
$777$	0	0
$778$	40.6880	1.45874
$779$	10.2827	0.368415
$780$	0	0
$781$	−20.5467	−0.735218
$782$	26.3413	0.941962
$783$	0	0
$784$	−37.5306	−1.34038
$785$	0	0
$786$	0	0
$787$	8.03731	0.286499	0.143250	−	0.989687i	$-0.454245\pi$
$787$	8.03731	0.286499	0.143250	+	0.989687i	$0.454245\pi$
$788$	2.60944	0.0929574
$789$	0	0
$790$	0	0
$791$	51.2393	1.82186
$792$	0	0
$793$	28.6680	1.01803
$794$	41.6087	1.47664
$795$	0	0
$796$	−3.22925	−0.114458
$797$	39.9787	1.41612	0.708059	−	0.706153i	$-0.249571\pi$
$797$	39.9787	1.41612	0.708059	+	0.706153i	$0.249571\pi$
$798$	0	0
$799$	39.7546	1.40642
$800$	0	0
$801$	0	0
$802$	35.5119	1.25397
$803$	−0.502593	−0.0177361
$804$	0	0
$805$	0	0
$806$	−24.0000	−0.845364
$807$	0	0
$808$	5.45331	0.191847
$809$	−31.9160	−1.12211	−0.561053	−	0.827780i	$-0.689603\pi$
$809$	−31.9160	−1.12211	−0.561053	+	0.827780i	$0.689603\pi$
$810$	0	0
$811$	−12.6027	−0.442539	−0.221270	−	0.975213i	$-0.571020\pi$
$811$	−12.6027	−0.442539	−0.221270	+	0.975213i	$0.571020\pi$
$812$	−0.797984	−0.0280037
$813$	0	0
$814$	−16.9907	−0.595523
$815$	0	0
$816$	0	0
$817$	2.86799	0.100338
$818$	−2.86667	−0.100231
$819$	0	0
$820$	0	0
$821$	−1.22538	−0.0427661	−0.0213831	−	0.999771i	$-0.506807\pi$
$821$	−1.22538	−0.0427661	−0.0213831	+	0.999771i	$0.506807\pi$
$822$	0	0
$823$	−33.8094	−1.17852	−0.589261	−	0.807943i	$-0.700581\pi$
$823$	−33.8094	−1.17852	−0.589261	+	0.807943i	$0.700581\pi$
$824$	15.8345	0.551623
$825$	0	0
$826$	−46.7640	−1.62713
$827$	−1.22067	−0.0424470	−0.0212235	−	0.999775i	$-0.506756\pi$
$827$	−1.22067	−0.0424470	−0.0212235	+	0.999775i	$0.506756\pi$
$828$	0	0
$829$	13.9813	0.485592	0.242796	−	0.970077i	$-0.421935\pi$
$829$	13.9813	0.485592	0.242796	+	0.970077i	$0.421935\pi$
$830$	0	0
$831$	0	0
$832$	−25.4479	−0.882246
$833$	31.8867	1.10481
$834$	0	0
$835$	0	0
$836$	−0.720717	−0.0249265
$837$	0	0
$838$	17.8760	0.617516
$839$	4.08405	0.140997	0.0704985	−	0.997512i	$-0.477541\pi$
$839$	4.08405	0.140997	0.0704985	+	0.997512i	$0.477541\pi$
$840$	0	0
$841$	−27.1413	−0.935908
$842$	−16.2800	−0.561047
$843$	0	0
$844$	−2.36126	−0.0812778
$845$	0	0
$846$	0	0
$847$	32.4626	1.11543
$848$	21.6960	0.745045
$849$	0	0
$850$	0	0
$851$	−43.1120	−1.47786
$852$	0	0
$853$	46.4507	1.59044	0.795220	−	0.606320i	$-0.207355\pi$
$853$	46.4507	1.59044	0.795220	+	0.606320i	$0.207355\pi$
$854$	−53.9533	−1.84624
$855$	0	0
$856$	16.4826	0.563364
$857$	−21.8573	−0.746633	−0.373316	−	0.927704i	$-0.621779\pi$
$857$	−21.8573	−0.746633	−0.373316	+	0.927704i	$0.621779\pi$
$858$	0	0
$859$	7.23471	0.246845	0.123423	−	0.992354i	$-0.460613\pi$
$859$	7.23471	0.246845	0.123423	+	0.992354i	$0.460613\pi$
$860$	0	0
$861$	0	0
$862$	17.8986	0.609629
$863$	−7.91595	−0.269462	−0.134731	−	0.990882i	$-0.543017\pi$
$863$	−7.91595	−0.269462	−0.134731	+	0.990882i	$0.543017\pi$
$864$	0	0
$865$	0	0
$866$	−36.6027	−1.24381
$867$	0	0
$868$	−3.43466	−0.116580
$869$	26.6867	0.905284
$870$	0	0
$871$	−44.6320	−1.51230
$872$	−6.63667	−0.224746
$873$	0	0
$874$	24.0492	0.813476
$875$	0	0
$876$	0	0
$877$	6.98002	0.235699	0.117849	−	0.993031i	$-0.462400\pi$
$877$	6.98002	0.235699	0.117849	+	0.993031i	$0.462400\pi$
$878$	0.590781	0.0199379
$879$	0	0
$880$	0	0
$881$	−12.3120	−0.414801	−0.207401	−	0.978256i	$-0.566500\pi$
$881$	−12.3120	−0.414801	−0.207401	+	0.978256i	$0.566500\pi$
$882$	0	0
$883$	10.0734	0.338997	0.169498	−	0.985530i	$-0.445785\pi$
$883$	10.0734	0.338997	0.169498	+	0.985530i	$0.445785\pi$
$884$	1.33195	0.0447984
$885$	0	0
$886$	0.648071	0.0217724
$887$	−57.1239	−1.91803	−0.959017	−	0.283350i	$-0.908554\pi$
$887$	−57.1239	−1.91803	−0.959017	+	0.283350i	$0.908554\pi$
$888$	0	0
$889$	53.3293	1.78861
$890$	0	0
$891$	0	0
$892$	−0.765290	−0.0256238
$893$	36.2954	1.21458
$894$	0	0
$895$	0	0
$896$	41.2834	1.37918
$897$	0	0
$898$	28.6854	0.957244
$899$	8.00000	0.266815
$900$	0	0
$901$	−18.4333	−0.614103
$902$	−8.69085	−0.289374
$903$	0	0
$904$	−36.1200	−1.20133
$905$	0	0
$906$	0	0
$907$	24.3747	0.809350	0.404675	−	0.914461i	$-0.367385\pi$
$907$	24.3747	0.809350	0.404675	+	0.914461i	$0.367385\pi$
$908$	1.81589	0.0602624
$909$	0	0
$910$	0	0
$911$	−23.4974	−0.778504	−0.389252	−	0.921131i	$-0.627266\pi$
$911$	−23.4974	−0.778504	−0.389252	+	0.921131i	$0.627266\pi$
$912$	0	0
$913$	−17.8880	−0.592005
$914$	2.12136	0.0701684
$915$	0	0
$916$	−2.56534	−0.0847614
$917$	−80.6400	−2.66297
$918$	0	0
$919$	45.9894	1.51705	0.758524	−	0.651645i	$-0.225921\pi$
$919$	45.9894	1.51705	0.758524	+	0.651645i	$0.225921\pi$
$920$	0	0
$921$	0	0
$922$	−27.0466	−0.890734
$923$	34.6680	1.14111
$924$	0	0
$925$	0	0
$926$	−21.8115	−0.716769
$927$	0	0
$928$	1.08791	0.0357125
$929$	−23.7487	−0.779170	−0.389585	−	0.920991i	$-0.627381\pi$
$929$	−23.7487	−0.779170	−0.389585	+	0.920991i	$0.627381\pi$
$930$	0	0
$931$	29.1120	0.954108
$932$	−1.82597	−0.0598116
$933$	0	0
$934$	46.9839	1.53736
$935$	0	0
$936$	0	0
$937$	39.7360	1.29812	0.649059	−	0.760738i	$-0.275163\pi$
$937$	39.7360	1.29812	0.649059	+	0.760738i	$0.275163\pi$
$938$	83.9974	2.74261
$939$	0	0
$940$	0	0
$941$	−6.53604	−0.213069	−0.106534	−	0.994309i	$-0.533975\pi$
$941$	−6.53604	−0.213069	−0.106534	+	0.994309i	$0.533975\pi$
$942$	0	0
$943$	−22.0521	−0.718115
$944$	30.6240	0.996725
$945$	0	0
$946$	−2.42401	−0.0788113
$947$	50.3993	1.63776	0.818879	−	0.573966i	$-0.194596\pi$
$947$	50.3993	1.63776	0.818879	+	0.573966i	$0.194596\pi$
$948$	0	0
$949$	0.848017	0.0275278
$950$	0	0
$951$	0	0
$952$	−37.9787	−1.23090
$953$	−17.4660	−0.565780	−0.282890	−	0.959152i	$-0.591293\pi$
$953$	−17.4660	−0.565780	−0.282890	+	0.959152i	$0.591293\pi$
$954$	0	0
$955$	0	0
$956$	2.67399	0.0864829
$957$	0	0
$958$	−31.3120	−1.01164
$959$	−14.6740	−0.473848
$960$	0	0
$961$	3.43334	0.110753
$962$	28.6680	0.924295
$963$	0	0
$964$	0.285309	0.00918919
$965$	0	0
$966$	0	0
$967$	−0.800055	−0.0257280	−0.0128640	−	0.999917i	$-0.504095\pi$
$967$	−0.800055	−0.0257280	−0.0128640	+	0.999917i	$0.504095\pi$
$968$	−22.8838	−0.735514
$969$	0	0
$970$	0	0
$971$	37.2627	1.19582	0.597908	−	0.801564i	$-0.295999\pi$
$971$	37.2627	1.19582	0.597908	+	0.801564i	$0.295999\pi$
$972$	0	0
$973$	−20.8667	−0.668955
$974$	−25.9160	−0.830401
$975$	0	0
$976$	35.3320	1.13095
$977$	−38.0373	−1.21692	−0.608461	−	0.793584i	$-0.708213\pi$
$977$	−38.0373	−1.21692	−0.608461	+	0.793584i	$0.708213\pi$
$978$	0	0
$979$	20.0441	0.640612
$980$	0	0
$981$	0	0
$982$	−9.06530	−0.289285
$983$	−42.2827	−1.34861	−0.674304	−	0.738454i	$-0.735556\pi$
$983$	−42.2827	−1.34861	−0.674304	+	0.738454i	$0.735556\pi$
$984$	0	0
$985$	0	0
$986$	5.83869	0.185942
$987$	0	0
$988$	1.21605	0.0386878
$989$	−6.15066	−0.195580
$990$	0	0
$991$	38.6040	1.22630	0.613148	−	0.789968i	$-0.289903\pi$
$991$	38.6040	1.22630	0.613148	+	0.789968i	$0.289903\pi$
$992$	4.68256	0.148672
$993$	0	0
$994$	−65.2453	−2.06945
$995$	0	0
$996$	0	0
$997$	−47.1680	−1.49383	−0.746913	−	0.664922i	$-0.768465\pi$
$997$	−47.1680	−1.49383	−0.746913	+	0.664922i	$0.768465\pi$
$998$	−25.0034	−0.791468
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9675.2.a.bq.1.2		3
3.2	odd	2		3225.2.a.t.1.2		3
5.4	even	2		387.2.a.i.1.2		3
15.14	odd	2		129.2.a.d.1.2	✓	3
20.19	odd	2		6192.2.a.bw.1.2		3
60.59	even	2		2064.2.a.x.1.2		3
105.104	even	2		6321.2.a.p.1.2		3
120.29	odd	2		8256.2.a.cr.1.2		3
120.59	even	2		8256.2.a.cu.1.2		3
645.644	even	2		5547.2.a.p.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
129.2.a.d.1.2	✓	3	15.14	odd	2
387.2.a.i.1.2		3	5.4	even	2
2064.2.a.x.1.2		3	60.59	even	2
3225.2.a.t.1.2		3	3.2	odd	2
5547.2.a.p.1.2		3	645.644	even	2
6192.2.a.bw.1.2		3	20.19	odd	2
6321.2.a.p.1.2		3	105.104	even	2
8256.2.a.cr.1.2		3	120.29	odd	2
8256.2.a.cu.1.2		3	120.59	even	2
9675.2.a.bq.1.2		3	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:	\( N \)	\(=\)	\( 9675 = 3^{2} \cdot 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9675.a (trivial)

\(f(q)\)	\(=\)	\(q-1.36333 q^{2} -0.141336 q^{4} -4.14134 q^{7} +2.91934 q^{8} +O(q^{10})\)	\(q-1.36333 q^{2} -0.141336 q^{4} -4.14134 q^{7} +2.91934 q^{8} +1.77801 q^{11} -3.00000 q^{13} +5.64600 q^{14} -3.69735 q^{16} +3.14134 q^{17} +2.86799 q^{19} -2.42401 q^{22} -6.15066 q^{23} +4.08998 q^{26} +0.585320 q^{28} -1.36333 q^{29} -5.86799 q^{31} -0.797984 q^{32} -4.28267 q^{34} +7.00933 q^{37} -3.91002 q^{38} +3.58532 q^{41} +1.00000 q^{43} -0.251297 q^{44} +8.38538 q^{46} +12.6553 q^{47} +10.1507 q^{49} +0.424008 q^{52} -5.86799 q^{53} -12.0900 q^{56} +1.85866 q^{58} -8.28267 q^{59} -9.55602 q^{61} +8.00000 q^{62} +8.48262 q^{64} +14.8773 q^{67} -0.443984 q^{68} -11.5560 q^{71} -0.282672 q^{73} -9.55602 q^{74} -0.405351 q^{76} -7.36333 q^{77} +15.0093 q^{79} -4.88797 q^{82} -10.0607 q^{83} -1.36333 q^{86} +5.19062 q^{88} +11.2733 q^{89} +12.4240 q^{91} +0.869311 q^{92} -17.2534 q^{94} -4.55602 q^{97} -13.8387 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 2 q^{2} + 8 q^{4} - 4 q^{7} - 6 q^{8}+O(q^{10}) \) 3 * q - 2 * q^2 + 8 * q^4 - 4 * q^7 - 6 * q^8	\( 3 q - 2 q^{2} + 8 q^{4} - 4 q^{7} - 6 q^{8} - q^{11} - 9 q^{13} - 2 q^{14} + 10 q^{16} + q^{17} - 4 q^{19} + 18 q^{22} + 11 q^{23} + 6 q^{26} + 6 q^{28} - 2 q^{29} - 5 q^{31} - 34 q^{32} + 4 q^{34} - 18 q^{38} + 15 q^{41} + 3 q^{43} - 24 q^{44} + 4 q^{46} - 2 q^{47} + q^{49} - 24 q^{52} - 5 q^{53} - 30 q^{56} + 14 q^{58} - 8 q^{59} - 16 q^{61} + 24 q^{62} + 34 q^{64} + 11 q^{67} - 14 q^{68} - 22 q^{71} + 16 q^{73} - 16 q^{74} - 18 q^{76} - 20 q^{77} + 24 q^{79} - 40 q^{82} - 7 q^{83} - 2 q^{86} + 62 q^{88} + 38 q^{89} + 12 q^{91} + 70 q^{92} - 18 q^{94} - q^{97} - 12 q^{98}+O(q^{100}) \) 3 * q - 2 * q^2 + 8 * q^4 - 4 * q^7 - 6 * q^8 - q^11 - 9 * q^13 - 2 * q^14 + 10 * q^16 + q^17 - 4 * q^19 + 18 * q^22 + 11 * q^23 + 6 * q^26 + 6 * q^28 - 2 * q^29 - 5 * q^31 - 34 * q^32 + 4 * q^34 - 18 * q^38 + 15 * q^41 + 3 * q^43 - 24 * q^44 + 4 * q^46 - 2 * q^47 + q^49 - 24 * q^52 - 5 * q^53 - 30 * q^56 + 14 * q^58 - 8 * q^59 - 16 * q^61 + 24 * q^62 + 34 * q^64 + 11 * q^67 - 14 * q^68 - 22 * q^71 + 16 * q^73 - 16 * q^74 - 18 * q^76 - 20 * q^77 + 24 * q^79 - 40 * q^82 - 7 * q^83 - 2 * q^86 + 62 * q^88 + 38 * q^89 + 12 * q^91 + 70 * q^92 - 18 * q^94 - q^97 - 12 * q^98

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