LMFDB - Embedded newform 2925.2.a.bo.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2925,2,Mod(1,2925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2925, 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("2925.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2925 = 3^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2925.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:	$23.3562425912$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.12730624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 8x^{4} + 13x^{2} - 4 $ x^6 - 8x^4 + 13x^2 - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 585)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.29632$ of defining polynomial
Character	$\chi$	$=$	2925.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.29632 q^{2} -0.319551 q^{4} -2.25879 q^{7} +3.00688 q^{8} +O(q^{10})$	$q-1.29632 q^{2} -0.319551 q^{4} -2.25879 q^{7} +3.00688 q^{8} -4.86001 q^{11} -1.00000 q^{13} +2.92811 q^{14} -3.25879 q^{16} -6.57057 q^{17} -7.87847 q^{19} +6.30013 q^{22} -1.04982 q^{23} +1.29632 q^{26} +0.721797 q^{28} +0.639102 q^{31} -1.78933 q^{32} +8.51757 q^{34} +8.89789 q^{37} +10.2130 q^{38} -0.818289 q^{41} +11.8785 q^{43} +1.55302 q^{44} +1.36090 q^{46} +5.90982 q^{47} -1.89789 q^{49} +0.319551 q^{52} -9.00567 q^{53} -6.79191 q^{56} -7.23132 q^{59} -6.89789 q^{61} -0.828481 q^{62} +8.83712 q^{64} +7.36090 q^{67} +2.09963 q^{68} -13.4664 q^{71} -9.75694 q^{73} -11.5345 q^{74} +2.51757 q^{76} +10.9777 q^{77} +9.49815 q^{79} +1.06077 q^{82} +0.724539 q^{83} -15.3983 q^{86} -14.6135 q^{88} -7.78812 q^{89} +2.25879 q^{91} +0.335469 q^{92} -7.66103 q^{94} +4.38032 q^{97} +2.46027 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{4} + 10 q^{7}+O(q^{10}) $ 6 * q + 4 * q^4 + 10 * q^7	$ 6 q + 4 q^{4} + 10 q^{7} - 6 q^{13} + 4 q^{16} - 12 q^{19} + 32 q^{22} + 28 q^{28} - 8 q^{31} + 4 q^{34} + 18 q^{37} + 36 q^{43} + 20 q^{46} + 24 q^{49} - 4 q^{52} - 6 q^{61} + 56 q^{67} + 12 q^{73} - 32 q^{76} + 10 q^{79} + 24 q^{82} + 36 q^{88} - 10 q^{91} - 52 q^{94} + 38 q^{97}+O(q^{100}) $ 6 * q + 4 * q^4 + 10 * q^7 - 6 * q^13 + 4 * q^16 - 12 * q^19 + 32 * q^22 + 28 * q^28 - 8 * q^31 + 4 * q^34 + 18 * q^37 + 36 * q^43 + 20 * q^46 + 24 * q^49 - 4 * q^52 - 6 * q^61 + 56 * q^67 + 12 * q^73 - 32 * q^76 + 10 * q^79 + 24 * q^82 + 36 * q^88 - 10 * q^91 - 52 * q^94 + 38 * q^97

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 $

$2$	−1.29632	−0.916638	−0.458319	−	0.888788i	$-0.651548\pi$
$2$	−1.29632	−0.916638	−0.458319	+	0.888788i	$0.651548\pi$
$3$	0	0
$3$	0	0
$4$	−0.319551	−0.159775
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−2.25879	−0.853741	−0.426870	−	0.904313i	$-0.640384\pi$
$7$	−2.25879	−0.853741	−0.426870	+	0.904313i	$0.640384\pi$
$8$	3.00688	1.06309
$9$	0	0
$10$	0	0
$11$	−4.86001	−1.46535	−0.732674	−	0.680580i	$-0.761728\pi$
$11$	−4.86001	−1.46535	−0.732674	+	0.680580i	$0.761728\pi$
$12$	0	0
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.92811	0.782571
$15$	0	0
$16$	−3.25879	−0.814696
$17$	−6.57057	−1.59360	−0.796799	−	0.604245i	$-0.793475\pi$
$17$	−6.57057	−1.59360	−0.796799	+	0.604245i	$0.793475\pi$
$18$	0	0
$19$	−7.87847	−1.80744	−0.903722	−	0.428119i	$-0.859176\pi$
$19$	−7.87847	−1.80744	−0.903722	+	0.428119i	$0.859176\pi$
$20$	0	0
$21$	0	0
$22$	6.30013	1.34319
$23$	−1.04982	−0.218902	−0.109451	−	0.993992i	$-0.534909\pi$
$23$	−1.04982	−0.218902	−0.109451	+	0.993992i	$0.534909\pi$
$24$	0	0
$25$	0	0
$26$	1.29632	0.254230
$27$	0	0
$28$	0.721797	0.136407
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	0.639102	0.114786	0.0573930	−	0.998352i	$-0.481721\pi$
$31$	0.639102	0.114786	0.0573930	+	0.998352i	$0.481721\pi$
$32$	−1.78933	−0.316312
$33$	0	0
$34$	8.51757	1.46075
$35$	0	0
$36$	0	0
$37$	8.89789	1.46280	0.731402	−	0.681947i	$-0.238866\pi$
$37$	8.89789	1.46280	0.731402	+	0.681947i	$0.238866\pi$
$38$	10.2130	1.65677
$39$	0	0
$40$	0	0
$41$	−0.818289	−0.127795	−0.0638976	−	0.997956i	$-0.520353\pi$
$41$	−0.818289	−0.127795	−0.0638976	+	0.997956i	$0.520353\pi$
$42$	0	0
$43$	11.8785	1.81145	0.905725	−	0.423866i	$-0.139327\pi$
$43$	11.8785	1.81145	0.905725	+	0.423866i	$0.139327\pi$
$44$	1.55302	0.234127
$45$	0	0
$46$	1.36090	0.200654
$47$	5.90982	0.862036	0.431018	−	0.902343i	$-0.358154\pi$
$47$	5.90982	0.862036	0.431018	+	0.902343i	$0.358154\pi$
$48$	0	0
$49$	−1.89789	−0.271127
$50$	0	0
$51$	0	0
$52$	0.319551	0.0443137
$53$	−9.00567	−1.23702	−0.618512	−	0.785775i	$-0.712264\pi$
$53$	−9.00567	−1.23702	−0.618512	+	0.785775i	$0.712264\pi$
$54$	0	0
$55$	0	0
$56$	−6.79191	−0.907606
$57$	0	0
$58$	0	0
$59$	−7.23132	−0.941437	−0.470719	−	0.882283i	$-0.656005\pi$
$59$	−7.23132	−0.941437	−0.470719	+	0.882283i	$0.656005\pi$
$60$	0	0
$61$	−6.89789	−0.883184	−0.441592	−	0.897216i	$-0.645586\pi$
$61$	−6.89789	−0.883184	−0.441592	+	0.897216i	$0.645586\pi$
$62$	−0.828481	−0.105217
$63$	0	0
$64$	8.83712	1.10464
$65$	0	0
$66$	0	0
$67$	7.36090	0.899277	0.449638	−	0.893211i	$-0.351553\pi$
$67$	7.36090	0.899277	0.449638	+	0.893211i	$0.351553\pi$
$68$	2.09963	0.254618
$69$	0	0
$70$	0	0
$71$	−13.4664	−1.59817	−0.799085	−	0.601218i	$-0.794682\pi$
$71$	−13.4664	−1.59817	−0.799085	+	0.601218i	$0.794682\pi$
$72$	0	0
$73$	−9.75694	−1.14196	−0.570982	−	0.820963i	$-0.693437\pi$
$73$	−9.75694	−1.14196	−0.570982	+	0.820963i	$0.693437\pi$
$74$	−11.5345	−1.34086
$75$	0	0
$76$	2.51757	0.288785
$77$	10.9777	1.25103
$78$	0	0
$79$	9.49815	1.06863	0.534313	−	0.845287i	$-0.320570\pi$
$79$	9.49815	1.06863	0.534313	+	0.845287i	$0.320570\pi$
$80$	0	0
$81$	0	0
$82$	1.06077	0.117142
$83$	0.724539	0.0795284	0.0397642	−	0.999209i	$-0.487339\pi$
$83$	0.724539	0.0795284	0.0397642	+	0.999209i	$0.487339\pi$
$84$	0	0
$85$	0	0
$86$	−15.3983	−1.66044
$87$	0	0
$88$	−14.6135	−1.55780
$89$	−7.78812	−0.825539	−0.412770	−	0.910835i	$-0.635439\pi$
$89$	−7.78812	−0.825539	−0.412770	+	0.910835i	$0.635439\pi$
$90$	0	0
$91$	2.25879	0.236785
$92$	0.335469	0.0349751
$93$	0	0
$94$	−7.66103	−0.790175
$95$	0	0
$96$	0	0
$97$	4.38032	0.444754	0.222377	−	0.974961i	$-0.428618\pi$
$97$	4.38032	0.444754	0.222377	+	0.974961i	$0.428618\pi$
$98$	2.46027	0.248525
$99$	0	0
$100$	0	0
$101$	15.5762	1.54989	0.774947	−	0.632026i	$-0.217777\pi$
$101$	15.5762	1.54989	0.774947	+	0.632026i	$0.217777\pi$
$102$	0	0
$103$	16.3960	1.61555	0.807775	−	0.589491i	$-0.200672\pi$
$103$	16.3960	1.61555	0.807775	+	0.589491i	$0.200672\pi$
$104$	−3.00688	−0.294849
$105$	0	0
$106$	11.6742	1.13390
$107$	−4.47094	−0.432222	−0.216111	−	0.976369i	$-0.569337\pi$
$107$	−4.47094	−0.432222	−0.216111	+	0.976369i	$0.569337\pi$
$108$	0	0
$109$	−9.75694	−0.934545	−0.467273	−	0.884113i	$-0.654763\pi$
$109$	−9.75694	−0.934545	−0.467273	+	0.884113i	$0.654763\pi$
$110$	0	0
$111$	0	0
$112$	7.36090	0.695540
$113$	−16.8773	−1.58769	−0.793844	−	0.608122i	$-0.791923\pi$
$113$	−16.8773	−1.58769	−0.793844	+	0.608122i	$0.791923\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	0	0
$118$	9.37411	0.862957
$119$	14.8415	1.36052
$120$	0	0
$121$	12.6197	1.14724
$122$	8.94188	0.809560
$123$	0	0
$124$	−0.204225	−0.0183400
$125$	0	0
$126$	0	0
$127$	13.2782	1.17825	0.589125	−	0.808042i	$-0.299473\pi$
$127$	13.2782	1.17825	0.589125	+	0.808042i	$0.299473\pi$
$128$	−7.87708	−0.696242
$129$	0	0
$130$	0	0
$131$	−7.49280	−0.654649	−0.327325	−	0.944912i	$-0.606147\pi$
$131$	−7.49280	−0.654649	−0.327325	+	0.944912i	$0.606147\pi$
$132$	0	0
$133$	17.7958	1.54309
$134$	−9.54209	−0.824311
$135$	0	0
$136$	−19.7569	−1.69414
$137$	8.37488	0.715515	0.357757	−	0.933815i	$-0.383542\pi$
$137$	8.37488	0.715515	0.357757	+	0.933815i	$0.383542\pi$
$138$	0	0
$139$	0.341481	0.0289640	0.0144820	−	0.999895i	$-0.495390\pi$
$139$	0.341481	0.0289640	0.0144820	+	0.999895i	$0.495390\pi$
$140$	0	0
$141$	0	0
$142$	17.4568	1.46494
$143$	4.86001	0.406414
$144$	0	0
$145$	0	0
$146$	12.6481	1.04677
$147$	0	0
$148$	−2.84333	−0.233720
$149$	3.56847	0.292341	0.146170	−	0.989259i	$-0.453305\pi$
$149$	3.56847	0.292341	0.146170	+	0.989259i	$0.453305\pi$
$150$	0	0
$151$	5.15667	0.419644	0.209822	−	0.977740i	$-0.432712\pi$
$151$	5.15667	0.419644	0.209822	+	0.977740i	$0.432712\pi$
$152$	−23.6896	−1.92148
$153$	0	0
$154$	−14.2307	−1.14674
$155$	0	0
$156$	0	0
$157$	−4.51757	−0.360541	−0.180271	−	0.983617i	$-0.557697\pi$
$157$	−4.51757	−0.360541	−0.180271	+	0.983617i	$0.557697\pi$
$158$	−12.3127	−0.979543
$159$	0	0
$160$	0	0
$161$	2.37131	0.186885
$162$	0	0
$163$	11.0194	0.863107	0.431554	−	0.902087i	$-0.357966\pi$
$163$	11.0194	0.863107	0.431554	+	0.902087i	$0.357966\pi$
$164$	0.261485	0.0204185
$165$	0	0
$166$	−0.939235	−0.0728988
$167$	13.4026	1.03713	0.518563	−	0.855039i	$-0.326467\pi$
$167$	13.4026	1.03713	0.518563	+	0.855039i	$0.326467\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	0	0
$171$	0	0
$172$	−3.79577	−0.289425
$173$	−4.07168	−0.309564	−0.154782	−	0.987949i	$-0.549468\pi$
$173$	−4.07168	−0.309564	−0.154782	+	0.987949i	$0.549468\pi$
$174$	0	0
$175$	0	0
$176$	15.8377	1.19381
$177$	0	0
$178$	10.0959	0.756720
$179$	6.96983	0.520950	0.260475	−	0.965481i	$-0.416121\pi$
$179$	6.96983	0.520950	0.260475	+	0.965481i	$0.416121\pi$
$180$	0	0
$181$	−8.13726	−0.604837	−0.302419	−	0.953175i	$-0.597794\pi$
$181$	−8.13726	−0.604837	−0.302419	+	0.953175i	$0.597794\pi$
$182$	−2.92811	−0.217046
$183$	0	0
$184$	−3.15667	−0.232713
$185$	0	0
$186$	0	0
$187$	31.9330	2.33517
$188$	−1.88849	−0.137732
$189$	0	0
$190$	0	0
$191$	19.9630	1.44447	0.722236	−	0.691647i	$-0.243114\pi$
$191$	19.9630	1.44447	0.722236	+	0.691647i	$0.243114\pi$
$192$	0	0
$193$	−13.4155	−0.965666	−0.482833	−	0.875712i	$-0.660392\pi$
$193$	−13.4155	−0.965666	−0.482833	+	0.875712i	$0.660392\pi$
$194$	−5.67830	−0.407678
$195$	0	0
$196$	0.606471	0.0433194
$197$	8.18738	0.583327	0.291663	−	0.956521i	$-0.405791\pi$
$197$	8.18738	0.583327	0.291663	+	0.956521i	$0.405791\pi$
$198$	0	0
$199$	17.6742	1.25289	0.626447	−	0.779464i	$-0.284508\pi$
$199$	17.6742	1.25289	0.626447	+	0.779464i	$0.284508\pi$
$200$	0	0
$201$	0	0
$202$	−20.1918	−1.42069
$203$	0	0
$204$	0	0
$205$	0	0
$206$	−21.2545	−1.48087
$207$	0	0
$208$	3.25879	0.225956
$209$	38.2894	2.64854
$210$	0	0
$211$	7.36090	0.506745	0.253373	−	0.967369i	$-0.418460\pi$
$211$	7.36090	0.506745	0.253373	+	0.967369i	$0.418460\pi$
$212$	2.87777	0.197646
$213$	0	0
$214$	5.79577	0.396191
$215$	0	0
$216$	0	0
$217$	−1.44359	−0.0979975
$218$	12.6481	0.856639
$219$	0	0
$220$	0	0
$221$	6.57057	0.441984
$222$	0	0
$223$	−3.11784	−0.208786	−0.104393	−	0.994536i	$-0.533290\pi$
$223$	−3.11784	−0.208786	−0.104393	+	0.994536i	$0.533290\pi$
$224$	4.04172	0.270049
$225$	0	0
$226$	21.8785	1.45533
$227$	−1.24751	−0.0828000	−0.0414000	−	0.999143i	$-0.513182\pi$
$227$	−1.24751	−0.0828000	−0.0414000	+	0.999143i	$0.513182\pi$
$228$	0	0
$229$	−3.96116	−0.261761	−0.130881	−	0.991398i	$-0.541780\pi$
$229$	−3.96116	−0.261761	−0.130881	+	0.991398i	$0.541780\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	8.54262	0.559645	0.279823	−	0.960052i	$-0.409724\pi$
$233$	8.54262	0.559645	0.279823	+	0.960052i	$0.409724\pi$
$234$	0	0
$235$	0	0
$236$	2.31077	0.150419
$237$	0	0
$238$	−19.2394	−1.24710
$239$	3.74640	0.242335	0.121167	−	0.992632i	$-0.461336\pi$
$239$	3.74640	0.242335	0.121167	+	0.992632i	$0.461336\pi$
$240$	0	0
$241$	−26.2745	−1.69249	−0.846245	−	0.532794i	$-0.821142\pi$
$241$	−26.2745	−1.69249	−0.846245	+	0.532794i	$0.821142\pi$
$242$	−16.3592	−1.05161
$243$	0	0
$244$	2.20423	0.141111
$245$	0	0
$246$	0	0
$247$	7.87847	0.501295
$248$	1.92170	0.122028
$249$	0	0
$250$	0	0
$251$	10.2430	0.646532	0.323266	−	0.946308i	$-0.395219\pi$
$251$	10.2430	0.646532	0.323266	+	0.946308i	$0.395219\pi$
$252$	0	0
$253$	5.10211	0.320767
$254$	−17.2128	−1.08003
$255$	0	0
$256$	−7.46301	−0.466438
$257$	−6.96983	−0.434766	−0.217383	−	0.976086i	$-0.569752\pi$
$257$	−6.96983	−0.434766	−0.217383	+	0.976086i	$0.569752\pi$
$258$	0	0
$259$	−20.0984	−1.24886
$260$	0	0
$261$	0	0
$262$	9.71308	0.600076
$263$	16.5419	1.02002	0.510008	−	0.860170i	$-0.329642\pi$
$263$	16.5419	1.02002	0.510008	+	0.860170i	$0.329642\pi$
$264$	0	0
$265$	0	0
$266$	−23.0690	−1.41445
$267$	0	0
$268$	−2.35218	−0.143682
$269$	−17.2128	−1.04948	−0.524742	−	0.851261i	$-0.675838\pi$
$269$	−17.2128	−1.04948	−0.524742	+	0.851261i	$0.675838\pi$
$270$	0	0
$271$	−16.6391	−1.01075	−0.505377	−	0.862899i	$-0.668646\pi$
$271$	−16.6391	−1.01075	−0.505377	+	0.862899i	$0.668646\pi$
$272$	21.4121	1.29830
$273$	0	0
$274$	−10.8565	−0.655868
$275$	0	0
$276$	0	0
$277$	5.96116	0.358172	0.179086	−	0.983833i	$-0.442686\pi$
$277$	5.96116	0.358172	0.179086	+	0.983833i	$0.442686\pi$
$278$	−0.442669	−0.0265495
$279$	0	0
$280$	0	0
$281$	−1.55302	−0.0926454	−0.0463227	−	0.998927i	$-0.514750\pi$
$281$	−1.55302	−0.0926454	−0.0463227	+	0.998927i	$0.514750\pi$
$282$	0	0
$283$	−13.5527	−0.805625	−0.402813	−	0.915282i	$-0.631967\pi$
$283$	−13.5527	−0.805625	−0.402813	+	0.915282i	$0.631967\pi$
$284$	4.30320	0.255348
$285$	0	0
$286$	−6.30013	−0.372535
$287$	1.84834	0.109104
$288$	0	0
$289$	26.1724	1.53955
$290$	0	0
$291$	0	0
$292$	3.11784	0.182458
$293$	12.3866	0.723636	0.361818	−	0.932249i	$-0.382156\pi$
$293$	12.3866	0.723636	0.361818	+	0.932249i	$0.382156\pi$
$294$	0	0
$295$	0	0
$296$	26.7549	1.55510
$297$	0	0
$298$	−4.62589	−0.267971
$299$	1.04982	0.0607124
$300$	0	0
$301$	−26.8309	−1.54651
$302$	−6.68471	−0.384662
$303$	0	0
$304$	25.6742	1.47252
$305$	0	0
$306$	0	0
$307$	−12.7375	−0.726969	−0.363484	−	0.931600i	$-0.618413\pi$
$307$	−12.7375	−0.726969	−0.363484	+	0.931600i	$0.618413\pi$
$308$	−3.50794	−0.199883
$309$	0	0
$310$	0	0
$311$	12.4702	0.707120	0.353560	−	0.935412i	$-0.384971\pi$
$311$	12.4702	0.707120	0.353560	+	0.935412i	$0.384971\pi$
$312$	0	0
$313$	24.4787	1.38362	0.691810	−	0.722080i	$-0.256814\pi$
$313$	24.4787	1.38362	0.691810	+	0.722080i	$0.256814\pi$
$314$	5.85622	0.330486
$315$	0	0
$316$	−3.03514	−0.170740
$317$	−27.1644	−1.52570	−0.762851	−	0.646574i	$-0.776201\pi$
$317$	−27.1644	−1.52570	−0.762851	+	0.646574i	$0.776201\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	0	0
$322$	−3.07398	−0.171306
$323$	51.7660	2.88034
$324$	0	0
$325$	0	0
$326$	−14.2847	−0.791157
$327$	0	0
$328$	−2.46050	−0.135858
$329$	−13.3490	−0.735956
$330$	0	0
$331$	12.1530	0.667988	0.333994	−	0.942575i	$-0.391603\pi$
$331$	12.1530	0.667988	0.333994	+	0.942575i	$0.391603\pi$
$332$	−0.231527	−0.0127067
$333$	0	0
$334$	−17.3741	−0.950669
$335$	0	0
$336$	0	0
$337$	−23.0351	−1.25480	−0.627402	−	0.778695i	$-0.715882\pi$
$337$	−23.0351	−1.25480	−0.627402	+	0.778695i	$0.715882\pi$
$338$	−1.29632	−0.0705106
$339$	0	0
$340$	0	0
$341$	−3.10604	−0.168201
$342$	0	0
$343$	20.0984	1.08521
$344$	35.7172	1.92574
$345$	0	0
$346$	5.27820	0.283758
$347$	−10.6422	−0.571306	−0.285653	−	0.958333i	$-0.592210\pi$
$347$	−10.6422	−0.571306	−0.285653	+	0.958333i	$0.592210\pi$
$348$	0	0
$349$	3.20053	0.171321	0.0856603	−	0.996324i	$-0.472700\pi$
$349$	3.20053	0.171321	0.0856603	+	0.996324i	$0.472700\pi$
$350$	0	0
$351$	0	0
$352$	8.69617	0.463508
$353$	−32.3496	−1.72180	−0.860899	−	0.508776i	$-0.830098\pi$
$353$	−32.3496	−1.72180	−0.860899	+	0.508776i	$0.830098\pi$
$354$	0	0
$355$	0	0
$356$	2.48870	0.131901
$357$	0	0
$358$	−9.03514	−0.477522
$359$	18.0649	0.953431	0.476716	−	0.879058i	$-0.341827\pi$
$359$	18.0649	0.953431	0.476716	+	0.879058i	$0.341827\pi$
$360$	0	0
$361$	43.0703	2.26686
$362$	10.5485	0.554417
$363$	0	0
$364$	−0.721797	−0.0378324
$365$	0	0
$366$	0	0
$367$	−11.8785	−0.620051	−0.310026	−	0.950728i	$-0.600338\pi$
$367$	−11.8785	−0.620051	−0.310026	+	0.950728i	$0.600338\pi$
$368$	3.42112	0.178338
$369$	0	0
$370$	0	0
$371$	20.3419	1.05610
$372$	0	0
$373$	14.2745	0.739106	0.369553	−	0.929210i	$-0.379511\pi$
$373$	14.2745	0.739106	0.369553	+	0.929210i	$0.379511\pi$
$374$	−41.3955	−2.14051
$375$	0	0
$376$	17.7702	0.916426
$377$	0	0
$378$	0	0
$379$	5.67424	0.291466	0.145733	−	0.989324i	$-0.453446\pi$
$379$	5.67424	0.291466	0.145733	+	0.989324i	$0.453446\pi$
$380$	0	0
$381$	0	0
$382$	−25.8785	−1.32406
$383$	−12.8797	−0.658120	−0.329060	−	0.944309i	$-0.606732\pi$
$383$	−12.8797	−0.658120	−0.329060	+	0.944309i	$0.606732\pi$
$384$	0	0
$385$	0	0
$386$	17.3907	0.885166
$387$	0	0
$388$	−1.39973	−0.0710607
$389$	21.0766	1.06863	0.534313	−	0.845287i	$-0.320570\pi$
$389$	21.0766	1.06863	0.534313	+	0.845287i	$0.320570\pi$
$390$	0	0
$391$	6.89789	0.348841
$392$	−5.70673	−0.288233
$393$	0	0
$394$	−10.6135	−0.534699
$395$	0	0
$396$	0	0
$397$	28.4118	1.42595	0.712973	−	0.701192i	$-0.247348\pi$
$397$	28.4118	1.42595	0.712973	+	0.701192i	$0.247348\pi$
$398$	−22.9115	−1.14845
$399$	0	0
$400$	0	0
$401$	27.3722	1.36690	0.683452	−	0.729995i	$-0.260478\pi$
$401$	27.3722	1.36690	0.683452	+	0.729995i	$0.260478\pi$
$402$	0	0
$403$	−0.639102	−0.0318359
$404$	−4.97740	−0.247635
$405$	0	0
$406$	0	0
$407$	−43.2438	−2.14352
$408$	0	0
$409$	11.0351	0.545653	0.272826	−	0.962063i	$-0.412042\pi$
$409$	11.0351	0.545653	0.272826	+	0.962063i	$0.412042\pi$
$410$	0	0
$411$	0	0
$412$	−5.23937	−0.258125
$413$	16.3340	0.803743
$414$	0	0
$415$	0	0
$416$	1.78933	0.0877293
$417$	0	0
$418$	−49.6354	−2.42775
$419$	−16.6898	−0.815353	−0.407676	−	0.913127i	$-0.633661\pi$
$419$	−16.6898	−0.815353	−0.407676	+	0.913127i	$0.633661\pi$
$420$	0	0
$421$	21.8346	1.06415	0.532077	−	0.846696i	$-0.321412\pi$
$421$	21.8346	1.06415	0.532077	+	0.846696i	$0.321412\pi$
$422$	−9.54209	−0.464502
$423$	0	0
$424$	−27.0790	−1.31507
$425$	0	0
$426$	0	0
$427$	15.5808	0.754010
$428$	1.42869	0.0690584
$429$	0	0
$430$	0	0
$431$	−21.3381	−1.02782	−0.513910	−	0.857844i	$-0.671803\pi$
$431$	−21.3381	−1.02782	−0.513910	+	0.857844i	$0.671803\pi$
$432$	0	0
$433$	12.5564	0.603422	0.301711	−	0.953399i	$-0.402442\pi$
$433$	12.5564	0.603422	0.301711	+	0.953399i	$0.402442\pi$
$434$	1.87136	0.0898282
$435$	0	0
$436$	3.11784	0.149317
$437$	8.27094	0.395653
$438$	0	0
$439$	−2.38032	−0.113606	−0.0568031	−	0.998385i	$-0.518091\pi$
$439$	−2.38032	−0.113606	−0.0568031	+	0.998385i	$0.518091\pi$
$440$	0	0
$441$	0	0
$442$	−8.51757	−0.405140
$443$	14.7139	0.699080	0.349540	−	0.936921i	$-0.386338\pi$
$443$	14.7139	0.699080	0.349540	+	0.936921i	$0.386338\pi$
$444$	0	0
$445$	0	0
$446$	4.04172	0.191381
$447$	0	0
$448$	−19.9612	−0.943076
$449$	−9.42470	−0.444779	−0.222390	−	0.974958i	$-0.571386\pi$
$449$	−9.42470	−0.444779	−0.222390	+	0.974958i	$0.571386\pi$
$450$	0	0
$451$	3.97689	0.187264
$452$	5.39317	0.253673
$453$	0	0
$454$	1.61717	0.0758976
$455$	0	0
$456$	0	0
$457$	−31.2112	−1.46000	−0.730000	−	0.683447i	$-0.760480\pi$
$457$	−31.2112	−1.46000	−0.730000	+	0.683447i	$0.760480\pi$
$458$	5.13494	0.239940
$459$	0	0
$460$	0	0
$461$	5.03794	0.234640	0.117320	−	0.993094i	$-0.462570\pi$
$461$	5.03794	0.234640	0.117320	+	0.993094i	$0.462570\pi$
$462$	0	0
$463$	−2.25879	−0.104975	−0.0524873	−	0.998622i	$-0.516715\pi$
$463$	−2.25879	−0.104975	−0.0524873	+	0.998622i	$0.516715\pi$
$464$	0	0
$465$	0	0
$466$	−11.0740	−0.512992
$467$	−7.89206	−0.365201	−0.182601	−	0.983187i	$-0.558452\pi$
$467$	−7.89206	−0.365201	−0.182601	+	0.983187i	$0.558452\pi$
$468$	0	0
$469$	−16.6267	−0.767749
$470$	0	0
$471$	0	0
$472$	−21.7437	−1.00084
$473$	−57.7295	−2.65440
$474$	0	0
$475$	0	0
$476$	−4.74262	−0.217377
$477$	0	0
$478$	−4.85654	−0.222133
$479$	10.7162	0.489637	0.244819	−	0.969569i	$-0.421272\pi$
$479$	10.7162	0.489637	0.244819	+	0.969569i	$0.421272\pi$
$480$	0	0
$481$	−8.89789	−0.405709
$482$	34.0602	1.55140
$483$	0	0
$484$	−4.03263	−0.183301
$485$	0	0
$486$	0	0
$487$	−15.8115	−0.716487	−0.358244	−	0.933628i	$-0.616624\pi$
$487$	−15.8115	−0.716487	−0.358244	+	0.933628i	$0.616624\pi$
$488$	−20.7411	−0.938907
$489$	0	0
$490$	0	0
$491$	−13.9397	−0.629088	−0.314544	−	0.949243i	$-0.601852\pi$
$491$	−13.9397	−0.629088	−0.314544	+	0.949243i	$0.601852\pi$
$492$	0	0
$493$	0	0
$494$	−10.2130	−0.459506
$495$	0	0
$496$	−2.08270	−0.0935158
$497$	30.4178	1.36442
$498$	0	0
$499$	32.9136	1.47342	0.736708	−	0.676211i	$-0.236379\pi$
$499$	32.9136	1.47342	0.736708	+	0.676211i	$0.236379\pi$
$500$	0	0
$501$	0	0
$502$	−13.2782	−0.592635
$503$	−17.8430	−0.795580	−0.397790	−	0.917477i	$-0.630223\pi$
$503$	−17.8430	−0.795580	−0.397790	+	0.917477i	$0.630223\pi$
$504$	0	0
$505$	0	0
$506$	−6.61398	−0.294027
$507$	0	0
$508$	−4.24306	−0.188255
$509$	32.4937	1.44026	0.720130	−	0.693839i	$-0.244082\pi$
$509$	32.4937	1.44026	0.720130	+	0.693839i	$0.244082\pi$
$510$	0	0
$511$	22.0388	0.974941
$512$	25.4286	1.12380
$513$	0	0
$514$	9.03514	0.398523
$515$	0	0
$516$	0	0
$517$	−28.7218	−1.26318
$518$	26.0540	1.14475
$519$	0	0
$520$	0	0
$521$	−41.3955	−1.81357	−0.906784	−	0.421595i	$-0.861470\pi$
$521$	−41.3955	−1.81357	−0.906784	+	0.421595i	$0.861470\pi$
$522$	0	0
$523$	−20.9136	−0.914488	−0.457244	−	0.889341i	$-0.651163\pi$
$523$	−20.9136	−0.914488	−0.457244	+	0.889341i	$0.651163\pi$
$524$	2.39433	0.104597
$525$	0	0
$526$	−21.4436	−0.934985
$527$	−4.19926	−0.182923
$528$	0	0
$529$	−21.8979	−0.952082
$530$	0	0
$531$	0	0
$532$	−5.68665	−0.246548
$533$	0.818289	0.0354440
$534$	0	0
$535$	0	0
$536$	22.1334	0.956016
$537$	0	0
$538$	22.3133	0.961997
$539$	9.22375	0.397295
$540$	0	0
$541$	−30.7921	−1.32386	−0.661928	−	0.749568i	$-0.730261\pi$
$541$	−30.7921	−1.32386	−0.661928	+	0.749568i	$0.730261\pi$
$542$	21.5696	0.926495
$543$	0	0
$544$	11.7569	0.504075
$545$	0	0
$546$	0	0
$547$	2.84333	0.121572	0.0607859	−	0.998151i	$-0.480639\pi$
$547$	2.84333	0.121572	0.0607859	+	0.998151i	$0.480639\pi$
$548$	−2.67620	−0.114322
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−21.4543	−0.912329
$554$	−7.72759	−0.328314
$555$	0	0
$556$	−0.109120	−0.00462774
$557$	21.9587	0.930420	0.465210	−	0.885200i	$-0.345979\pi$
$557$	21.9587	0.930420	0.465210	+	0.885200i	$0.345979\pi$
$558$	0	0
$559$	−11.8785	−0.502406
$560$	0	0
$561$	0	0
$562$	2.01321	0.0849223
$563$	14.8619	0.626354	0.313177	−	0.949695i	$-0.398607\pi$
$563$	14.8619	0.626354	0.313177	+	0.949695i	$0.398607\pi$
$564$	0	0
$565$	0	0
$566$	17.5687	0.738466
$567$	0	0
$568$	−40.4919	−1.69900
$569$	1.63658	0.0686089	0.0343044	−	0.999411i	$-0.489078\pi$
$569$	1.63658	0.0686089	0.0343044	+	0.999411i	$0.489078\pi$
$570$	0	0
$571$	−12.7375	−0.533049	−0.266524	−	0.963828i	$-0.585875\pi$
$571$	−12.7375	−0.533049	−0.266524	+	0.963828i	$0.585875\pi$
$572$	−1.55302	−0.0649350
$573$	0	0
$574$	−2.39604	−0.100009
$575$	0	0
$576$	0	0
$577$	−22.1761	−0.923203	−0.461601	−	0.887087i	$-0.652725\pi$
$577$	−22.1761	−0.923203	−0.461601	+	0.887087i	$0.652725\pi$
$578$	−33.9278	−1.41121
$579$	0	0
$580$	0	0
$581$	−1.63658	−0.0678967
$582$	0	0
$583$	43.7676	1.81267
$584$	−29.3380	−1.21401
$585$	0	0
$586$	−16.0571	−0.663312
$587$	−30.4076	−1.25505	−0.627527	−	0.778595i	$-0.715933\pi$
$587$	−30.4076	−1.25505	−0.627527	+	0.778595i	$0.715933\pi$
$588$	0	0
$589$	−5.03514	−0.207469
$590$	0	0
$591$	0	0
$592$	−28.9963	−1.19174
$593$	−10.9376	−0.449152	−0.224576	−	0.974457i	$-0.572100\pi$
$593$	−10.9376	−0.449152	−0.224576	+	0.974457i	$0.572100\pi$
$594$	0	0
$595$	0	0
$596$	−1.14031	−0.0467089
$597$	0	0
$598$	−1.36090	−0.0556513
$599$	22.1902	0.906668	0.453334	−	0.891341i	$-0.350235\pi$
$599$	22.1902	0.906668	0.453334	+	0.891341i	$0.350235\pi$
$600$	0	0
$601$	5.61968	0.229232	0.114616	−	0.993410i	$-0.463436\pi$
$601$	5.61968	0.229232	0.114616	+	0.993410i	$0.463436\pi$
$602$	34.7815	1.41759
$603$	0	0
$604$	−1.64782	−0.0670488
$605$	0	0
$606$	0	0
$607$	13.5966	0.551868	0.275934	−	0.961177i	$-0.411013\pi$
$607$	13.5966	0.551868	0.275934	+	0.961177i	$0.411013\pi$
$608$	14.0972	0.571717
$609$	0	0
$610$	0	0
$611$	−5.90982	−0.239086
$612$	0	0
$613$	37.1724	1.50138	0.750690	−	0.660655i	$-0.229721\pi$
$613$	37.1724	1.50138	0.750690	+	0.660655i	$0.229721\pi$
$614$	16.5119	0.666367
$615$	0	0
$616$	33.0087	1.32996
$617$	15.0092	0.604249	0.302125	−	0.953268i	$-0.402304\pi$
$617$	15.0092	0.604249	0.302125	+	0.953268i	$0.402304\pi$
$618$	0	0
$619$	−4.39604	−0.176692	−0.0883459	−	0.996090i	$-0.528158\pi$
$619$	−4.39604	−0.176692	−0.0883459	+	0.996090i	$0.528158\pi$
$620$	0	0
$621$	0	0
$622$	−16.1654	−0.648173
$623$	17.5917	0.704796
$624$	0	0
$625$	0	0
$626$	−31.7323	−1.26828
$627$	0	0
$628$	1.44359	0.0576057
$629$	−58.4642	−2.33112
$630$	0	0
$631$	−3.08639	−0.122867	−0.0614336	−	0.998111i	$-0.519567\pi$
$631$	−3.08639	−0.122867	−0.0614336	+	0.998111i	$0.519567\pi$
$632$	28.5598	1.13605
$633$	0	0
$634$	35.2137	1.39852
$635$	0	0
$636$	0	0
$637$	1.89789	0.0751970
$638$	0	0
$639$	0	0
$640$	0	0
$641$	47.4865	1.87560	0.937802	−	0.347172i	$-0.112858\pi$
$641$	47.4865	1.87560	0.937802	+	0.347172i	$0.112858\pi$
$642$	0	0
$643$	8.21995	0.324163	0.162082	−	0.986777i	$-0.448179\pi$
$643$	8.21995	0.324163	0.162082	+	0.986777i	$0.448179\pi$
$644$	−0.757753	−0.0298597
$645$	0	0
$646$	−67.1054	−2.64023
$647$	26.6612	1.04816	0.524079	−	0.851670i	$-0.324410\pi$
$647$	26.6612	1.04816	0.524079	+	0.851670i	$0.324410\pi$
$648$	0	0
$649$	35.1443	1.37953
$650$	0	0
$651$	0	0
$652$	−3.52126	−0.137903
$653$	43.1596	1.68897	0.844483	−	0.535582i	$-0.179908\pi$
$653$	43.1596	1.68897	0.844483	+	0.535582i	$0.179908\pi$
$654$	0	0
$655$	0	0
$656$	2.66663	0.104114
$657$	0	0
$658$	17.3046	0.674605
$659$	4.21965	0.164374	0.0821871	−	0.996617i	$-0.473810\pi$
$659$	4.21965	0.164374	0.0821871	+	0.996617i	$0.473810\pi$
$660$	0	0
$661$	−25.0740	−0.975265	−0.487632	−	0.873049i	$-0.662139\pi$
$661$	−25.0740	−0.975265	−0.487632	+	0.873049i	$0.662139\pi$
$662$	−15.7542	−0.612303
$663$	0	0
$664$	2.17860	0.0845462
$665$	0	0
$666$	0	0
$667$	0	0
$668$	−4.28282	−0.165707
$669$	0	0
$670$	0	0
$671$	33.5238	1.29417
$672$	0	0
$673$	35.8661	1.38254	0.691268	−	0.722599i	$-0.257053\pi$
$673$	35.8661	1.38254	0.691268	+	0.722599i	$0.257053\pi$
$674$	29.8609	1.15020
$675$	0	0
$676$	−0.319551	−0.0122904
$677$	0.734731	0.0282380	0.0141190	−	0.999900i	$-0.495506\pi$
$677$	0.734731	0.0282380	0.0141190	+	0.999900i	$0.495506\pi$
$678$	0	0
$679$	−9.89419	−0.379704
$680$	0	0
$681$	0	0
$682$	4.02643	0.154180
$683$	−32.5072	−1.24385	−0.621927	−	0.783076i	$-0.713650\pi$
$683$	−32.5072	−1.24385	−0.621927	+	0.783076i	$0.713650\pi$
$684$	0	0
$685$	0	0
$686$	−26.0540	−0.994747
$687$	0	0
$688$	−38.7094	−1.47578
$689$	9.00567	0.343089
$690$	0	0
$691$	11.3609	0.432189	0.216094	−	0.976372i	$-0.430668\pi$
$691$	11.3609	0.432189	0.216094	+	0.976372i	$0.430668\pi$
$692$	1.30111	0.0494607
$693$	0	0
$694$	13.7958	0.523680
$695$	0	0
$696$	0	0
$697$	5.37662	0.203654
$698$	−4.14892	−0.157039
$699$	0	0
$700$	0	0
$701$	−33.5468	−1.26705	−0.633523	−	0.773724i	$-0.718392\pi$
$701$	−33.5468	−1.26705	−0.633523	+	0.773724i	$0.718392\pi$
$702$	0	0
$703$	−70.1017	−2.64394
$704$	−42.9485	−1.61868
$705$	0	0
$706$	41.9355	1.57826
$707$	−35.1834	−1.32321
$708$	0	0
$709$	−20.5879	−0.773193	−0.386597	−	0.922249i	$-0.626349\pi$
$709$	−20.5879	−0.773193	−0.386597	+	0.922249i	$0.626349\pi$
$710$	0	0
$711$	0	0
$712$	−23.4180	−0.877626
$713$	−0.670939	−0.0251269
$714$	0	0
$715$	0	0
$716$	−2.22722	−0.0832350
$717$	0	0
$718$	−23.4180	−0.873951
$719$	−27.4558	−1.02393	−0.511964	−	0.859007i	$-0.671082\pi$
$719$	−27.4558	−1.02393	−0.511964	+	0.859007i	$0.671082\pi$
$720$	0	0
$721$	−37.0351	−1.37926
$722$	−55.8329	−2.07789
$723$	0	0
$724$	2.60027	0.0966381
$725$	0	0
$726$	0	0
$727$	13.2782	0.492461	0.246231	−	0.969211i	$-0.420808\pi$
$727$	13.2782	0.492461	0.246231	+	0.969211i	$0.420808\pi$
$728$	6.79191	0.251725
$729$	0	0
$730$	0	0
$731$	−78.0483	−2.88672
$732$	0	0
$733$	−47.6511	−1.76003	−0.880017	−	0.474941i	$-0.842469\pi$
$733$	−47.6511	−1.76003	−0.880017	+	0.474941i	$0.842469\pi$
$734$	15.3983	0.568362
$735$	0	0
$736$	1.87847	0.0692413
$737$	−35.7740	−1.31775
$738$	0	0
$739$	−38.9524	−1.43289	−0.716444	−	0.697644i	$-0.754232\pi$
$739$	−38.9524	−1.43289	−0.716444	+	0.697644i	$0.754232\pi$
$740$	0	0
$741$	0	0
$742$	−26.3696	−0.968059
$743$	−45.9838	−1.68698	−0.843491	−	0.537143i	$-0.819503\pi$
$743$	−45.9838	−1.68698	−0.843491	+	0.537143i	$0.819503\pi$
$744$	0	0
$745$	0	0
$746$	−18.5044	−0.677493
$747$	0	0
$748$	−10.2042	−0.373103
$749$	10.0989	0.369006
$750$	0	0
$751$	−1.89419	−0.0691202	−0.0345601	−	0.999403i	$-0.511003\pi$
$751$	−1.89419	−0.0691202	−0.0345601	+	0.999403i	$0.511003\pi$
$752$	−19.2589	−0.702298
$753$	0	0
$754$	0	0
$755$	0	0
$756$	0	0
$757$	14.2745	0.518816	0.259408	−	0.965768i	$-0.416473\pi$
$757$	14.2745	0.518816	0.259408	+	0.965768i	$0.416473\pi$
$758$	−7.35564	−0.267169
$759$	0	0
$760$	0	0
$761$	−38.2059	−1.38496	−0.692481	−	0.721436i	$-0.743482\pi$
$761$	−38.2059	−1.38496	−0.692481	+	0.721436i	$0.743482\pi$
$762$	0	0
$763$	22.0388	0.797859
$764$	−6.37919	−0.230791
$765$	0	0
$766$	16.6962	0.603257
$767$	7.23132	0.261108
$768$	0	0
$769$	−29.2394	−1.05440	−0.527199	−	0.849742i	$-0.676758\pi$
$769$	−29.2394	−1.05440	−0.527199	+	0.849742i	$0.676758\pi$
$770$	0	0
$771$	0	0
$772$	4.28692	0.154290
$773$	42.4051	1.52521	0.762603	−	0.646866i	$-0.223921\pi$
$773$	42.4051	1.52521	0.762603	+	0.646866i	$0.223921\pi$
$774$	0	0
$775$	0	0
$776$	13.1711	0.472815
$777$	0	0
$778$	−27.3221	−0.979543
$779$	6.44686	0.230983
$780$	0	0
$781$	65.4469	2.34187
$782$	−8.94188	−0.319761
$783$	0	0
$784$	6.18481	0.220886
$785$	0	0
$786$	0	0
$787$	28.2307	1.00631	0.503157	−	0.864195i	$-0.332172\pi$
$787$	28.2307	1.00631	0.503157	+	0.864195i	$0.332172\pi$
$788$	−2.61628	−0.0932013
$789$	0	0
$790$	0	0
$791$	38.1223	1.35547
$792$	0	0
$793$	6.89789	0.244951
$794$	−36.8308	−1.30708
$795$	0	0
$796$	−5.64782	−0.200182
$797$	34.1540	1.20980	0.604898	−	0.796303i	$-0.293214\pi$
$797$	34.1540	1.20980	0.604898	+	0.796303i	$0.293214\pi$
$798$	0	0
$799$	−38.8309	−1.37374
$800$	0	0
$801$	0	0
$802$	−35.4832	−1.25296
$803$	47.4188	1.67337
$804$	0	0
$805$	0	0
$806$	0.828481	0.0291820
$807$	0	0
$808$	46.8359	1.64768
$809$	−31.9102	−1.12190	−0.560952	−	0.827848i	$-0.689565\pi$
$809$	−31.9102	−1.12190	−0.560952	+	0.827848i	$0.689565\pi$
$810$	0	0
$811$	33.3997	1.17282	0.586412	−	0.810013i	$-0.300540\pi$
$811$	33.3997	1.17282	0.586412	+	0.810013i	$0.300540\pi$
$812$	0	0
$813$	0	0
$814$	56.0579	1.96483
$815$	0	0
$816$	0	0
$817$	−93.5842	−3.27410
$818$	−14.3051	−0.500166
$819$	0	0
$820$	0	0
$821$	−31.4478	−1.09754	−0.548768	−	0.835975i	$-0.684903\pi$
$821$	−31.4478	−1.09754	−0.548768	+	0.835975i	$0.684903\pi$
$822$	0	0
$823$	−5.64279	−0.196695	−0.0983477	−	0.995152i	$-0.531356\pi$
$823$	−5.64279	−0.196695	−0.0983477	+	0.995152i	$0.531356\pi$
$824$	49.3010	1.71748
$825$	0	0
$826$	−21.1741	−0.736741
$827$	−35.2981	−1.22744	−0.613718	−	0.789525i	$-0.710327\pi$
$827$	−35.2981	−1.22744	−0.613718	+	0.789525i	$0.710327\pi$
$828$	0	0
$829$	9.79577	0.340221	0.170111	−	0.985425i	$-0.445587\pi$
$829$	9.79577	0.340221	0.170111	+	0.985425i	$0.445587\pi$
$830$	0	0
$831$	0	0
$832$	−8.83712	−0.306372
$833$	12.4702	0.432067
$834$	0	0
$835$	0	0
$836$	−12.2354	−0.423171
$837$	0	0
$838$	21.6354	0.747383
$839$	3.74640	0.129340	0.0646701	−	0.997907i	$-0.479401\pi$
$839$	3.74640	0.129340	0.0646701	+	0.997907i	$0.479401\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	−28.3047	−0.975443
$843$	0	0
$844$	−2.35218	−0.0809654
$845$	0	0
$846$	0	0
$847$	−28.5052	−0.979449
$848$	29.3476	1.00780
$849$	0	0
$850$	0	0
$851$	−9.34114	−0.320210
$852$	0	0
$853$	−17.9330	−0.614015	−0.307008	−	0.951707i	$-0.599328\pi$
$853$	−17.9330	−0.614015	−0.307008	+	0.951707i	$0.599328\pi$
$854$	−20.1978	−0.691154
$855$	0	0
$856$	−13.4436	−0.459493
$857$	−16.1426	−0.551421	−0.275711	−	0.961241i	$-0.588913\pi$
$857$	−16.1426	−0.551421	−0.275711	+	0.961241i	$0.588913\pi$
$858$	0	0
$859$	28.9806	0.988805	0.494402	−	0.869233i	$-0.335387\pi$
$859$	28.9806	0.988805	0.494402	+	0.869233i	$0.335387\pi$
$860$	0	0
$861$	0	0
$862$	27.6610	0.942138
$863$	−19.5739	−0.666304	−0.333152	−	0.942873i	$-0.608112\pi$
$863$	−19.5739	−0.666304	−0.333152	+	0.942873i	$0.608112\pi$
$864$	0	0
$865$	0	0
$866$	−16.2771	−0.553120
$867$	0	0
$868$	0.461301	0.0156576
$869$	−46.1611	−1.56591
$870$	0	0
$871$	−7.36090	−0.249415
$872$	−29.3380	−0.993509
$873$	0	0
$874$	−10.7218	−0.362670
$875$	0	0
$876$	0	0
$877$	−12.5564	−0.424000	−0.212000	−	0.977270i	$-0.567998\pi$
$877$	−12.5564	−0.424000	−0.212000	+	0.977270i	$0.567998\pi$
$878$	3.08565	0.104136
$879$	0	0
$880$	0	0
$881$	−43.7898	−1.47532	−0.737658	−	0.675175i	$-0.764068\pi$
$881$	−43.7898	−1.47532	−0.737658	+	0.675175i	$0.764068\pi$
$882$	0	0
$883$	50.3133	1.69318	0.846589	−	0.532246i	$-0.178652\pi$
$883$	50.3133	1.69318	0.846589	+	0.532246i	$0.178652\pi$
$884$	−2.09963	−0.0706182
$885$	0	0
$886$	−19.0740	−0.640803
$887$	−3.92759	−0.131875	−0.0659377	−	0.997824i	$-0.521004\pi$
$887$	−3.92759	−0.131875	−0.0659377	+	0.997824i	$0.521004\pi$
$888$	0	0
$889$	−29.9926	−1.00592
$890$	0	0
$891$	0	0
$892$	0.996308	0.0333588
$893$	−46.5604	−1.55808
$894$	0	0
$895$	0	0
$896$	17.7926	0.594411
$897$	0	0
$898$	12.2174	0.407701
$899$	0	0
$900$	0	0
$901$	59.1724	1.97132
$902$	−5.15533	−0.171654
$903$	0	0
$904$	−50.7482	−1.68786
$905$	0	0
$906$	0	0
$907$	16.4399	0.545878	0.272939	−	0.962031i	$-0.412004\pi$
$907$	16.4399	0.545878	0.272939	+	0.962031i	$0.412004\pi$
$908$	0.398642	0.0132294
$909$	0	0
$910$	0	0
$911$	−9.72002	−0.322039	−0.161019	−	0.986951i	$-0.551478\pi$
$911$	−9.72002	−0.322039	−0.161019	+	0.986951i	$0.551478\pi$
$912$	0	0
$913$	−3.52126	−0.116537
$914$	40.4598	1.33829
$915$	0	0
$916$	1.26579	0.0418230
$917$	16.9246	0.558901
$918$	0	0
$919$	41.0120	1.35286	0.676431	−	0.736506i	$-0.263526\pi$
$919$	41.0120	1.35286	0.676431	+	0.736506i	$0.263526\pi$
$920$	0	0
$921$	0	0
$922$	−6.53078	−0.215080
$923$	13.4664	0.443253
$924$	0	0
$925$	0	0
$926$	2.92811	0.0962237
$927$	0	0
$928$	0	0
$929$	−33.6073	−1.10262	−0.551311	−	0.834300i	$-0.685872\pi$
$929$	−33.6073	−1.10262	−0.551311	+	0.834300i	$0.685872\pi$
$930$	0	0
$931$	14.9524	0.490047
$932$	−2.72980	−0.0894176
$933$	0	0
$934$	10.2307	0.334757
$935$	0	0
$936$	0	0
$937$	21.3170	0.696397	0.348199	−	0.937421i	$-0.386793\pi$
$937$	21.3170	0.696397	0.348199	+	0.937421i	$0.386793\pi$
$938$	21.5535	0.703748
$939$	0	0
$940$	0	0
$941$	−1.93190	−0.0629780	−0.0314890	−	0.999504i	$-0.510025\pi$
$941$	−1.93190	−0.0629780	−0.0314890	+	0.999504i	$0.510025\pi$
$942$	0	0
$943$	0.859052	0.0279746
$944$	23.5653	0.766986
$945$	0	0
$946$	74.8359	2.43313
$947$	−22.6800	−0.737000	−0.368500	−	0.929628i	$-0.620129\pi$
$947$	−22.6800	−0.737000	−0.368500	+	0.929628i	$0.620129\pi$
$948$	0	0
$949$	9.75694	0.316724
$950$	0	0
$951$	0	0
$952$	44.6267	1.44636
$953$	22.3547	0.724140	0.362070	−	0.932151i	$-0.382070\pi$
$953$	22.3547	0.724140	0.362070	+	0.932151i	$0.382070\pi$
$954$	0	0
$955$	0	0
$956$	−1.19717	−0.0387191
$957$	0	0
$958$	−13.8917	−0.448820
$959$	−18.9171	−0.610864
$960$	0	0
$961$	−30.5915	−0.986824
$962$	11.5345	0.371888
$963$	0	0
$964$	8.39604	0.270418
$965$	0	0
$966$	0	0
$967$	−26.8748	−0.864235	−0.432117	−	0.901817i	$-0.642233\pi$
$967$	−26.8748	−0.864235	−0.432117	+	0.901817i	$0.642233\pi$
$968$	37.9459	1.21963
$969$	0	0
$970$	0	0
$971$	−29.1601	−0.935791	−0.467895	−	0.883784i	$-0.654988\pi$
$971$	−29.1601	−0.935791	−0.467895	+	0.883784i	$0.654988\pi$
$972$	0	0
$973$	−0.771332	−0.0247278
$974$	20.4968	0.656759
$975$	0	0
$976$	22.4787	0.719527
$977$	28.7410	0.919507	0.459753	−	0.888047i	$-0.347938\pi$
$977$	28.7410	0.919507	0.459753	+	0.888047i	$0.347938\pi$
$978$	0	0
$979$	37.8503	1.20970
$980$	0	0
$981$	0	0
$982$	18.0703	0.576646
$983$	37.8608	1.20757	0.603786	−	0.797146i	$-0.293658\pi$
$983$	37.8608	1.20757	0.603786	+	0.797146i	$0.293658\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	0	0
$988$	−2.51757	−0.0800946
$989$	−12.4702	−0.396529
$990$	0	0
$991$	−10.1373	−0.322021	−0.161010	−	0.986953i	$-0.551475\pi$
$991$	−10.1373	−0.322021	−0.161010	+	0.986953i	$0.551475\pi$
$992$	−1.14357	−0.0363082
$993$	0	0
$994$	−39.4312	−1.25068
$995$	0	0
$996$	0	0
$997$	−14.7218	−0.466244	−0.233122	−	0.972447i	$-0.574894\pi$
$997$	−14.7218	−0.466244	−0.233122	+	0.972447i	$0.574894\pi$
$998$	−42.6666	−1.35059
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2925.2.a.bo.1.2		6
3.2	odd	2	inner	2925.2.a.bo.1.5		6
5.2	odd	4		585.2.c.d.469.4	yes	12
5.3	odd	4		585.2.c.d.469.10	yes	12
5.4	even	2		2925.2.a.bn.1.5		6
15.2	even	4		585.2.c.d.469.9	yes	12
15.8	even	4		585.2.c.d.469.3	✓	12
15.14	odd	2		2925.2.a.bn.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.c.d.469.3	✓	12	15.8	even	4
585.2.c.d.469.4	yes	12	5.2	odd	4
585.2.c.d.469.9	yes	12	15.2	even	4
585.2.c.d.469.10	yes	12	5.3	odd	4
2925.2.a.bn.1.2		6	15.14	odd	2
2925.2.a.bn.1.5		6	5.4	even	2
2925.2.a.bo.1.2		6	1.1	even	1	trivial
2925.2.a.bo.1.5		6	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2925.a (trivial)

\(f(q)\)	\(=\)	\(q-1.29632 q^{2} -0.319551 q^{4} -2.25879 q^{7} +3.00688 q^{8} +O(q^{10})\)	\(q-1.29632 q^{2} -0.319551 q^{4} -2.25879 q^{7} +3.00688 q^{8} -4.86001 q^{11} -1.00000 q^{13} +2.92811 q^{14} -3.25879 q^{16} -6.57057 q^{17} -7.87847 q^{19} +6.30013 q^{22} -1.04982 q^{23} +1.29632 q^{26} +0.721797 q^{28} +0.639102 q^{31} -1.78933 q^{32} +8.51757 q^{34} +8.89789 q^{37} +10.2130 q^{38} -0.818289 q^{41} +11.8785 q^{43} +1.55302 q^{44} +1.36090 q^{46} +5.90982 q^{47} -1.89789 q^{49} +0.319551 q^{52} -9.00567 q^{53} -6.79191 q^{56} -7.23132 q^{59} -6.89789 q^{61} -0.828481 q^{62} +8.83712 q^{64} +7.36090 q^{67} +2.09963 q^{68} -13.4664 q^{71} -9.75694 q^{73} -11.5345 q^{74} +2.51757 q^{76} +10.9777 q^{77} +9.49815 q^{79} +1.06077 q^{82} +0.724539 q^{83} -15.3983 q^{86} -14.6135 q^{88} -7.78812 q^{89} +2.25879 q^{91} +0.335469 q^{92} -7.66103 q^{94} +4.38032 q^{97} +2.46027 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{4} + 10 q^{7}+O(q^{10}) \) 6 * q + 4 * q^4 + 10 * q^7	\( 6 q + 4 q^{4} + 10 q^{7} - 6 q^{13} + 4 q^{16} - 12 q^{19} + 32 q^{22} + 28 q^{28} - 8 q^{31} + 4 q^{34} + 18 q^{37} + 36 q^{43} + 20 q^{46} + 24 q^{49} - 4 q^{52} - 6 q^{61} + 56 q^{67} + 12 q^{73} - 32 q^{76} + 10 q^{79} + 24 q^{82} + 36 q^{88} - 10 q^{91} - 52 q^{94} + 38 q^{97}+O(q^{100}) \) 6 * q + 4 * q^4 + 10 * q^7 - 6 * q^13 + 4 * q^16 - 12 * q^19 + 32 * q^22 + 28 * q^28 - 8 * q^31 + 4 * q^34 + 18 * q^37 + 36 * q^43 + 20 * q^46 + 24 * q^49 - 4 * q^52 - 6 * q^61 + 56 * q^67 + 12 * q^73 - 32 * q^76 + 10 * q^79 + 24 * q^82 + 36 * q^88 - 10 * q^91 - 52 * q^94 + 38 * q^97

Introduction

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