LMFDB - Embedded newform 9280.2.a.bf.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9280,2,Mod(1,9280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9280, 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("9280.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9280 = 2^{6} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9280.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:	$74.1011730757$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.621.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 3 $ x^3 - 6*x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.14510$ of defining polynomial
Character	$\chi$	$=$	9280.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.14510 q^{3} +1.00000 q^{5} -3.89167 q^{7} +6.89167 q^{9} +O(q^{10})$	$q-3.14510 q^{3} +1.00000 q^{5} -3.89167 q^{7} +6.89167 q^{9} +4.29021 q^{11} -4.34803 q^{13} -3.14510 q^{15} +1.60147 q^{17} +1.20293 q^{19} +12.2397 q^{21} -8.34803 q^{23} +1.00000 q^{25} -12.2397 q^{27} +1.00000 q^{29} -2.39853 q^{31} -13.4931 q^{33} -3.89167 q^{35} +9.78334 q^{37} +13.6750 q^{39} +5.78334 q^{41} -3.60147 q^{43} +6.89167 q^{45} +8.58041 q^{47} +8.14510 q^{49} -5.03677 q^{51} -4.80440 q^{53} +4.29021 q^{55} -3.78334 q^{57} +4.05783 q^{59} -11.4353 q^{61} -26.8201 q^{63} -4.34803 q^{65} -9.08727 q^{67} +26.2554 q^{69} -12.0000 q^{71} -2.39853 q^{73} -3.14510 q^{75} -16.6961 q^{77} +7.55096 q^{79} +17.8201 q^{81} -2.79707 q^{83} +1.60147 q^{85} -3.14510 q^{87} -4.29021 q^{89} +16.9211 q^{91} +7.54364 q^{93} +1.20293 q^{95} -0.348034 q^{97} +29.5667 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 3 q^{5} + 3 q^{7} + 6 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 3 * q^5 + 3 * q^7 + 6 * q^9	$ 3 q - 3 q^{3} + 3 q^{5} + 3 q^{7} + 6 q^{9} - 3 q^{13} - 3 q^{15} + 3 q^{17} + 12 q^{21} - 15 q^{23} + 3 q^{25} - 12 q^{27} + 3 q^{29} - 9 q^{31} - 24 q^{33} + 3 q^{35} - 3 q^{39} - 12 q^{41} - 9 q^{43} + 6 q^{45} + 18 q^{49} + 6 q^{51} - 9 q^{53} + 18 q^{57} + 15 q^{59} - 15 q^{61} - 30 q^{63} - 3 q^{65} - 18 q^{67} + 9 q^{69} - 36 q^{71} - 9 q^{73} - 3 q^{75} - 30 q^{77} + 9 q^{79} + 3 q^{81} - 12 q^{83} + 3 q^{85} - 3 q^{87} + 24 q^{91} + 18 q^{93} + 9 q^{97} + 30 q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 + 3 * q^5 + 3 * q^7 + 6 * q^9 - 3 * q^13 - 3 * q^15 + 3 * q^17 + 12 * q^21 - 15 * q^23 + 3 * q^25 - 12 * q^27 + 3 * q^29 - 9 * q^31 - 24 * q^33 + 3 * q^35 - 3 * q^39 - 12 * q^41 - 9 * q^43 + 6 * q^45 + 18 * q^49 + 6 * q^51 - 9 * q^53 + 18 * q^57 + 15 * q^59 - 15 * q^61 - 30 * q^63 - 3 * q^65 - 18 * q^67 + 9 * q^69 - 36 * q^71 - 9 * q^73 - 3 * q^75 - 30 * q^77 + 9 * q^79 + 3 * q^81 - 12 * q^83 + 3 * q^85 - 3 * q^87 + 24 * q^91 + 18 * q^93 + 9 * q^97 + 30 * 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
$3$	−3.14510	−1.81583	−0.907913	−	0.419159i	$-0.862325\pi$
$3$	−3.14510	−1.81583	−0.907913	+	0.419159i	$0.862325\pi$
$4$	0	0
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−3.89167	−1.47091	−0.735457	−	0.677572i	$-0.763032\pi$
$7$	−3.89167	−1.47091	−0.735457	+	0.677572i	$0.763032\pi$
$8$	0	0
$9$	6.89167	2.29722
$10$	0	0
$11$	4.29021	1.29355	0.646773	−	0.762683i	$-0.276118\pi$
$11$	4.29021	1.29355	0.646773	+	0.762683i	$0.276118\pi$
$12$	0	0
$13$	−4.34803	−1.20593	−0.602964	−	0.797769i	$-0.706014\pi$
$13$	−4.34803	−1.20593	−0.602964	+	0.797769i	$0.706014\pi$
$14$	0	0
$15$	−3.14510	−0.812062
$16$	0	0
$17$	1.60147	0.388412	0.194206	−	0.980961i	$-0.437787\pi$
$17$	1.60147	0.388412	0.194206	+	0.980961i	$0.437787\pi$
$18$	0	0
$19$	1.20293	0.275971	0.137986	−	0.990434i	$-0.455937\pi$
$19$	1.20293	0.275971	0.137986	+	0.990434i	$0.455937\pi$
$20$	0	0
$21$	12.2397	2.67092
$22$	0	0
$23$	−8.34803	−1.74069	−0.870343	−	0.492447i	$-0.836103\pi$
$23$	−8.34803	−1.74069	−0.870343	+	0.492447i	$0.836103\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	−12.2397	−2.35553
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	−2.39853	−0.430790	−0.215395	−	0.976527i	$-0.569104\pi$
$31$	−2.39853	−0.430790	−0.215395	+	0.976527i	$0.569104\pi$
$32$	0	0
$33$	−13.4931	−2.34885
$34$	0	0
$35$	−3.89167	−0.657812
$36$	0	0
$37$	9.78334	1.60837	0.804186	−	0.594378i	$-0.202602\pi$
$37$	9.78334	1.60837	0.804186	+	0.594378i	$0.202602\pi$
$38$	0	0
$39$	13.6750	2.18975
$40$	0	0
$41$	5.78334	0.903206	0.451603	−	0.892219i	$-0.350852\pi$
$41$	5.78334	0.903206	0.451603	+	0.892219i	$0.350852\pi$
$42$	0	0
$43$	−3.60147	−0.549218	−0.274609	−	0.961556i	$-0.588548\pi$
$43$	−3.60147	−0.549218	−0.274609	+	0.961556i	$0.588548\pi$
$44$	0	0
$45$	6.89167	1.02735
$46$	0	0
$47$	8.58041	1.25158	0.625791	−	0.779991i	$-0.284776\pi$
$47$	8.58041	1.25158	0.625791	+	0.779991i	$0.284776\pi$
$48$	0	0
$49$	8.14510	1.16359
$50$	0	0
$51$	−5.03677	−0.705289
$52$	0	0
$53$	−4.80440	−0.659935	−0.329967	−	0.943992i	$-0.607038\pi$
$53$	−4.80440	−0.659935	−0.329967	+	0.943992i	$0.607038\pi$
$54$	0	0
$55$	4.29021	0.578491
$56$	0	0
$57$	−3.78334	−0.501116
$58$	0	0
$59$	4.05783	0.528284	0.264142	−	0.964484i	$-0.414911\pi$
$59$	4.05783	0.528284	0.264142	+	0.964484i	$0.414911\pi$
$60$	0	0
$61$	−11.4353	−1.46414	−0.732071	−	0.681229i	$-0.761446\pi$
$61$	−11.4353	−1.46414	−0.732071	+	0.681229i	$0.761446\pi$
$62$	0	0
$63$	−26.8201	−3.37902
$64$	0	0
$65$	−4.34803	−0.539307
$66$	0	0
$67$	−9.08727	−1.11019	−0.555094	−	0.831788i	$-0.687318\pi$
$67$	−9.08727	−1.11019	−0.555094	+	0.831788i	$0.687318\pi$
$68$	0	0
$69$	26.2554	3.16078
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	0	0
$73$	−2.39853	−0.280727	−0.140364	−	0.990100i	$-0.544827\pi$
$73$	−2.39853	−0.280727	−0.140364	+	0.990100i	$0.544827\pi$
$74$	0	0
$75$	−3.14510	−0.363165
$76$	0	0
$77$	−16.6961	−1.90269
$78$	0	0
$79$	7.55096	0.849550	0.424775	−	0.905299i	$-0.360353\pi$
$79$	7.55096	0.849550	0.424775	+	0.905299i	$0.360353\pi$
$80$	0	0
$81$	17.8201	1.98001
$82$	0	0
$83$	−2.79707	−0.307018	−0.153509	−	0.988147i	$-0.549057\pi$
$83$	−2.79707	−0.307018	−0.153509	+	0.988147i	$0.549057\pi$
$84$	0	0
$85$	1.60147	0.173703
$86$	0	0
$87$	−3.14510	−0.337190
$88$	0	0
$89$	−4.29021	−0.454761	−0.227380	−	0.973806i	$-0.573016\pi$
$89$	−4.29021	−0.454761	−0.227380	+	0.973806i	$0.573016\pi$
$90$	0	0
$91$	16.9211	1.77382
$92$	0	0
$93$	7.54364	0.782239
$94$	0	0
$95$	1.20293	0.123418
$96$	0	0
$97$	−0.348034	−0.0353375	−0.0176687	−	0.999844i	$-0.505624\pi$
$97$	−0.348034	−0.0353375	−0.0176687	+	0.999844i	$0.505624\pi$
$98$	0	0
$99$	29.5667	2.97156
$100$	0	0
$101$	18.4216	1.83302	0.916508	−	0.400017i	$-0.130996\pi$
$101$	18.4216	1.83302	0.916508	+	0.400017i	$0.130996\pi$
$102$	0	0
$103$	12.0735	1.18964	0.594821	−	0.803858i	$-0.297223\pi$
$103$	12.0735	1.18964	0.594821	+	0.803858i	$0.297223\pi$
$104$	0	0
$105$	12.2397	1.19447
$106$	0	0
$107$	5.78334	0.559097	0.279548	−	0.960132i	$-0.409815\pi$
$107$	5.78334	0.559097	0.279548	+	0.960132i	$0.409815\pi$
$108$	0	0
$109$	−10.7971	−1.03417	−0.517086	−	0.855934i	$-0.672983\pi$
$109$	−10.7971	−1.03417	−0.517086	+	0.855934i	$0.672983\pi$
$110$	0	0
$111$	−30.7696	−2.92052
$112$	0	0
$113$	12.2324	1.15073	0.575363	−	0.817898i	$-0.304861\pi$
$113$	12.2324	1.15073	0.575363	+	0.817898i	$0.304861\pi$
$114$	0	0
$115$	−8.34803	−0.778458
$116$	0	0
$117$	−29.9652	−2.77029
$118$	0	0
$119$	−6.23238	−0.571321
$120$	0	0
$121$	7.40586	0.673260
$122$	0	0
$123$	−18.1892	−1.64007
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	0	0
$129$	11.3270	0.997285
$130$	0	0
$131$	20.9863	1.83358	0.916790	−	0.399371i	$-0.130771\pi$
$131$	20.9863	1.83358	0.916790	+	0.399371i	$0.130771\pi$
$132$	0	0
$133$	−4.68141	−0.405930
$134$	0	0
$135$	−12.2397	−1.05343
$136$	0	0
$137$	3.65197	0.312009	0.156004	−	0.987756i	$-0.450139\pi$
$137$	3.65197	0.312009	0.156004	+	0.987756i	$0.450139\pi$
$138$	0	0
$139$	−13.6750	−1.15990	−0.579950	−	0.814652i	$-0.696928\pi$
$139$	−13.6750	−1.15990	−0.579950	+	0.814652i	$0.696928\pi$
$140$	0	0
$141$	−26.9863	−2.27265
$142$	0	0
$143$	−18.6540	−1.55992
$144$	0	0
$145$	1.00000	0.0830455
$146$	0	0
$147$	−25.6172	−2.11287
$148$	0	0
$149$	−7.27648	−0.596112	−0.298056	−	0.954548i	$-0.596338\pi$
$149$	−7.27648	−0.596112	−0.298056	+	0.954548i	$0.596338\pi$
$150$	0	0
$151$	−8.69607	−0.707676	−0.353838	−	0.935307i	$-0.615124\pi$
$151$	−8.69607	−0.707676	−0.353838	+	0.935307i	$0.615124\pi$
$152$	0	0
$153$	11.0368	0.892270
$154$	0	0
$155$	−2.39853	−0.192655
$156$	0	0
$157$	10.0000	0.798087	0.399043	−	0.916932i	$-0.369342\pi$
$157$	10.0000	0.798087	0.399043	+	0.916932i	$0.369342\pi$
$158$	0	0
$159$	15.1103	1.19833
$160$	0	0
$161$	32.4878	2.56040
$162$	0	0
$163$	0.580411	0.0454613	0.0227306	−	0.999742i	$-0.492764\pi$
$163$	0.580411	0.0454613	0.0227306	+	0.999742i	$0.492764\pi$
$164$	0	0
$165$	−13.4931	−1.05044
$166$	0	0
$167$	20.2554	1.56741	0.783706	−	0.621132i	$-0.213327\pi$
$167$	20.2554	1.56741	0.783706	+	0.621132i	$0.213327\pi$
$168$	0	0
$169$	5.90540	0.454261
$170$	0	0
$171$	8.29021	0.633968
$172$	0	0
$173$	1.94217	0.147661	0.0738303	−	0.997271i	$-0.476478\pi$
$173$	1.94217	0.147661	0.0738303	+	0.997271i	$0.476478\pi$
$174$	0	0
$175$	−3.89167	−0.294183
$176$	0	0
$177$	−12.7623	−0.959272
$178$	0	0
$179$	10.9284	0.816830	0.408415	−	0.912796i	$-0.366082\pi$
$179$	10.9284	0.816830	0.408415	+	0.912796i	$0.366082\pi$
$180$	0	0
$181$	1.20293	0.0894132	0.0447066	−	0.999000i	$-0.485765\pi$
$181$	1.20293	0.0894132	0.0447066	+	0.999000i	$0.485765\pi$
$182$	0	0
$183$	35.9652	2.65863
$184$	0	0
$185$	9.78334	0.719286
$186$	0	0
$187$	6.87062	0.502429
$188$	0	0
$189$	47.6329	3.46478
$190$	0	0
$191$	−15.7760	−1.14151	−0.570756	−	0.821120i	$-0.693350\pi$
$191$	−15.7760	−1.14151	−0.570756	+	0.821120i	$0.693350\pi$
$192$	0	0
$193$	9.94217	0.715653	0.357827	−	0.933788i	$-0.383518\pi$
$193$	9.94217	0.715653	0.357827	+	0.933788i	$0.383518\pi$
$194$	0	0
$195$	13.6750	0.979288
$196$	0	0
$197$	25.1681	1.79316	0.896578	−	0.442885i	$-0.146045\pi$
$197$	25.1681	1.79316	0.896578	+	0.442885i	$0.146045\pi$
$198$	0	0
$199$	−18.7696	−1.33054	−0.665271	−	0.746602i	$-0.731684\pi$
$199$	−18.7696	−1.33054	−0.665271	+	0.746602i	$0.731684\pi$
$200$	0	0
$201$	28.5804	2.01591
$202$	0	0
$203$	−3.89167	−0.273142
$204$	0	0
$205$	5.78334	0.403926
$206$	0	0
$207$	−57.5319	−3.99874
$208$	0	0
$209$	5.16082	0.356981
$210$	0	0
$211$	−12.2902	−0.846093	−0.423046	−	0.906108i	$-0.639039\pi$
$211$	−12.2902	−0.846093	−0.423046	+	0.906108i	$0.639039\pi$
$212$	0	0
$213$	37.7412	2.58599
$214$	0	0
$215$	−3.60147	−0.245618
$216$	0	0
$217$	9.33431	0.633654
$218$	0	0
$219$	7.54364	0.509752
$220$	0	0
$221$	−6.96323	−0.468397
$222$	0	0
$223$	20.2324	1.35486	0.677430	−	0.735587i	$-0.263094\pi$
$223$	20.2324	1.35486	0.677430	+	0.735587i	$0.263094\pi$
$224$	0	0
$225$	6.89167	0.459445
$226$	0	0
$227$	−8.98627	−0.596440	−0.298220	−	0.954497i	$-0.596393\pi$
$227$	−8.98627	−0.596440	−0.298220	+	0.954497i	$0.596393\pi$
$228$	0	0
$229$	21.2692	1.40551	0.702753	−	0.711434i	$-0.251954\pi$
$229$	21.2692	1.40551	0.702753	+	0.711434i	$0.251954\pi$
$230$	0	0
$231$	52.5108	3.45496
$232$	0	0
$233$	11.1608	0.731170	0.365585	−	0.930778i	$-0.380869\pi$
$233$	11.1608	0.731170	0.365585	+	0.930778i	$0.380869\pi$
$234$	0	0
$235$	8.58041	0.559724
$236$	0	0
$237$	−23.7486	−1.54263
$238$	0	0
$239$	−1.92645	−0.124612	−0.0623059	−	0.998057i	$-0.519845\pi$
$239$	−1.92645	−0.124612	−0.0623059	+	0.998057i	$0.519845\pi$
$240$	0	0
$241$	−17.7255	−1.14180	−0.570900	−	0.821019i	$-0.693406\pi$
$241$	−17.7255	−1.14180	−0.570900	+	0.821019i	$0.693406\pi$
$242$	0	0
$243$	−19.3270	−1.23983
$244$	0	0
$245$	8.14510	0.520372
$246$	0	0
$247$	−5.23039	−0.332801
$248$	0	0
$249$	8.79707	0.557492
$250$	0	0
$251$	14.3638	0.906632	0.453316	−	0.891350i	$-0.350241\pi$
$251$	14.3638	0.906632	0.453316	+	0.891350i	$0.350241\pi$
$252$	0	0
$253$	−35.8148	−2.25166
$254$	0	0
$255$	−5.03677	−0.315415
$256$	0	0
$257$	−14.3638	−0.895986	−0.447993	−	0.894037i	$-0.647861\pi$
$257$	−14.3638	−0.895986	−0.447993	+	0.894037i	$0.647861\pi$
$258$	0	0
$259$	−38.0735	−2.36578
$260$	0	0
$261$	6.89167	0.426584
$262$	0	0
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	0	0
$265$	−4.80440	−0.295132
$266$	0	0
$267$	13.4931	0.825767
$268$	0	0
$269$	12.1083	0.738258	0.369129	−	0.929378i	$-0.379656\pi$
$269$	12.1083	0.738258	0.369129	+	0.929378i	$0.379656\pi$
$270$	0	0
$271$	3.49314	0.212193	0.106096	−	0.994356i	$-0.466165\pi$
$271$	3.49314	0.212193	0.106096	+	0.994356i	$0.466165\pi$
$272$	0	0
$273$	−53.2186	−3.22094
$274$	0	0
$275$	4.29021	0.258709
$276$	0	0
$277$	−22.1471	−1.33069	−0.665345	−	0.746536i	$-0.731716\pi$
$277$	−22.1471	−1.33069	−0.665345	+	0.746536i	$0.731716\pi$
$278$	0	0
$279$	−16.5299	−0.989620
$280$	0	0
$281$	−14.8779	−0.887544	−0.443772	−	0.896140i	$-0.646360\pi$
$281$	−14.8779	−0.887544	−0.443772	+	0.896140i	$0.646360\pi$
$282$	0	0
$283$	−5.20293	−0.309282	−0.154641	−	0.987971i	$-0.549422\pi$
$283$	−5.20293	−0.309282	−0.154641	+	0.987971i	$0.549422\pi$
$284$	0	0
$285$	−3.78334	−0.224106
$286$	0	0
$287$	−22.5069	−1.32854
$288$	0	0
$289$	−14.4353	−0.849136
$290$	0	0
$291$	1.09460	0.0641667
$292$	0	0
$293$	−17.7833	−1.03891	−0.519457	−	0.854497i	$-0.673866\pi$
$293$	−17.7833	−1.03891	−0.519457	+	0.854497i	$0.673866\pi$
$294$	0	0
$295$	4.05783	0.236256
$296$	0	0
$297$	−52.5108	−3.04699
$298$	0	0
$299$	36.2975	2.09914
$300$	0	0
$301$	14.0157	0.807853
$302$	0	0
$303$	−57.9378	−3.32844
$304$	0	0
$305$	−11.4353	−0.654784
$306$	0	0
$307$	−2.40586	−0.137310	−0.0686549	−	0.997640i	$-0.521871\pi$
$307$	−2.40586	−0.137310	−0.0686549	+	0.997640i	$0.521871\pi$
$308$	0	0
$309$	−37.9725	−2.16018
$310$	0	0
$311$	16.2470	0.921285	0.460642	−	0.887586i	$-0.347619\pi$
$311$	16.2470	0.921285	0.460642	+	0.887586i	$0.347619\pi$
$312$	0	0
$313$	−12.1745	−0.688146	−0.344073	−	0.938943i	$-0.611807\pi$
$313$	−12.1745	−0.688146	−0.344073	+	0.938943i	$0.611807\pi$
$314$	0	0
$315$	−26.8201	−1.51114
$316$	0	0
$317$	13.6823	0.768477	0.384238	−	0.923234i	$-0.374464\pi$
$317$	13.6823	0.768477	0.384238	+	0.923234i	$0.374464\pi$
$318$	0	0
$319$	4.29021	0.240205
$320$	0	0
$321$	−18.1892	−1.01522
$322$	0	0
$323$	1.92645	0.107191
$324$	0	0
$325$	−4.34803	−0.241186
$326$	0	0
$327$	33.9579	1.87788
$328$	0	0
$329$	−33.3921	−1.84097
$330$	0	0
$331$	−8.87062	−0.487573	−0.243787	−	0.969829i	$-0.578390\pi$
$331$	−8.87062	−0.487573	−0.243787	+	0.969829i	$0.578390\pi$
$332$	0	0
$333$	67.4236	3.69479
$334$	0	0
$335$	−9.08727	−0.496491
$336$	0	0
$337$	−14.1819	−0.772536	−0.386268	−	0.922387i	$-0.626236\pi$
$337$	−14.1819	−0.772536	−0.386268	+	0.922387i	$0.626236\pi$
$338$	0	0
$339$	−38.4721	−2.08952
$340$	0	0
$341$	−10.2902	−0.557246
$342$	0	0
$343$	−4.45636	−0.240621
$344$	0	0
$345$	26.2554	1.41354
$346$	0	0
$347$	27.1755	1.45886	0.729428	−	0.684058i	$-0.239786\pi$
$347$	27.1755	1.45886	0.729428	+	0.684058i	$0.239786\pi$
$348$	0	0
$349$	−1.31859	−0.0705824	−0.0352912	−	0.999377i	$-0.511236\pi$
$349$	−1.31859	−0.0705824	−0.0352912	+	0.999377i	$0.511236\pi$
$350$	0	0
$351$	53.2186	2.84060
$352$	0	0
$353$	13.8990	0.739769	0.369885	−	0.929078i	$-0.379397\pi$
$353$	13.8990	0.739769	0.369885	+	0.929078i	$0.379397\pi$
$354$	0	0
$355$	−12.0000	−0.636894
$356$	0	0
$357$	19.6015	1.03742
$358$	0	0
$359$	1.26076	0.0665403	0.0332702	−	0.999446i	$-0.489408\pi$
$359$	1.26076	0.0665403	0.0332702	+	0.999446i	$0.489408\pi$
$360$	0	0
$361$	−17.5530	−0.923840
$362$	0	0
$363$	−23.2922	−1.22252
$364$	0	0
$365$	−2.39853	−0.125545
$366$	0	0
$367$	−17.2765	−0.901825	−0.450912	−	0.892568i	$-0.648901\pi$
$367$	−17.2765	−0.901825	−0.450912	+	0.892568i	$0.648901\pi$
$368$	0	0
$369$	39.8569	2.07487
$370$	0	0
$371$	18.6971	0.970707
$372$	0	0
$373$	−32.9515	−1.70616	−0.853082	−	0.521777i	$-0.825269\pi$
$373$	−32.9515	−1.70616	−0.853082	+	0.521777i	$0.825269\pi$
$374$	0	0
$375$	−3.14510	−0.162412
$376$	0	0
$377$	−4.34803	−0.223935
$378$	0	0
$379$	4.87062	0.250187	0.125093	−	0.992145i	$-0.460077\pi$
$379$	4.87062	0.250187	0.125093	+	0.992145i	$0.460077\pi$
$380$	0	0
$381$	−25.1608	−1.28903
$382$	0	0
$383$	−2.06622	−0.105579	−0.0527894	−	0.998606i	$-0.516811\pi$
$383$	−2.06622	−0.105579	−0.0527894	+	0.998606i	$0.516811\pi$
$384$	0	0
$385$	−16.6961	−0.850910
$386$	0	0
$387$	−24.8201	−1.26168
$388$	0	0
$389$	−23.9725	−1.21546	−0.607728	−	0.794145i	$-0.707919\pi$
$389$	−23.9725	−1.21546	−0.607728	+	0.794145i	$0.707919\pi$
$390$	0	0
$391$	−13.3691	−0.676104
$392$	0	0
$393$	−66.0040	−3.32946
$394$	0	0
$395$	7.55096	0.379930
$396$	0	0
$397$	−24.1544	−1.21228	−0.606138	−	0.795360i	$-0.707282\pi$
$397$	−24.1544	−1.21228	−0.606138	+	0.795360i	$0.707282\pi$
$398$	0	0
$399$	14.7235	0.737098
$400$	0	0
$401$	16.2470	0.811338	0.405669	−	0.914020i	$-0.367039\pi$
$401$	16.2470	0.811338	0.405669	+	0.914020i	$0.367039\pi$
$402$	0	0
$403$	10.4289	0.519501
$404$	0	0
$405$	17.8201	0.885489
$406$	0	0
$407$	41.9725	2.08050
$408$	0	0
$409$	9.08727	0.449337	0.224668	−	0.974435i	$-0.427870\pi$
$409$	9.08727	0.449337	0.224668	+	0.974435i	$0.427870\pi$
$410$	0	0
$411$	−11.4858	−0.566553
$412$	0	0
$413$	−15.7917	−0.777060
$414$	0	0
$415$	−2.79707	−0.137303
$416$	0	0
$417$	43.0093	2.10618
$418$	0	0
$419$	−32.4446	−1.58502	−0.792512	−	0.609856i	$-0.791227\pi$
$419$	−32.4446	−1.58502	−0.792512	+	0.609856i	$0.791227\pi$
$420$	0	0
$421$	−25.5667	−1.24604	−0.623022	−	0.782204i	$-0.714095\pi$
$421$	−25.5667	−1.24604	−0.623022	+	0.782204i	$0.714095\pi$
$422$	0	0
$423$	59.1334	2.87516
$424$	0	0
$425$	1.60147	0.0776825
$426$	0	0
$427$	44.5025	2.15362
$428$	0	0
$429$	58.6686	2.83255
$430$	0	0
$431$	−1.70979	−0.0823579	−0.0411790	−	0.999152i	$-0.513111\pi$
$431$	−1.70979	−0.0823579	−0.0411790	+	0.999152i	$0.513111\pi$
$432$	0	0
$433$	−23.7412	−1.14093	−0.570465	−	0.821322i	$-0.693237\pi$
$433$	−23.7412	−1.14093	−0.570465	+	0.821322i	$0.693237\pi$
$434$	0	0
$435$	−3.14510	−0.150796
$436$	0	0
$437$	−10.0421	−0.480379
$438$	0	0
$439$	−8.47941	−0.404700	−0.202350	−	0.979313i	$-0.564858\pi$
$439$	−8.47941	−0.404700	−0.202350	+	0.979313i	$0.564858\pi$
$440$	0	0
$441$	56.1334	2.67302
$442$	0	0
$443$	−18.4490	−0.876540	−0.438270	−	0.898843i	$-0.644409\pi$
$443$	−18.4490	−0.876540	−0.438270	+	0.898843i	$0.644409\pi$
$444$	0	0
$445$	−4.29021	−0.203375
$446$	0	0
$447$	22.8853	1.08244
$448$	0	0
$449$	−11.3775	−0.536936	−0.268468	−	0.963289i	$-0.586517\pi$
$449$	−11.3775	−0.536936	−0.268468	+	0.963289i	$0.586517\pi$
$450$	0	0
$451$	24.8117	1.16834
$452$	0	0
$453$	27.3500	1.28502
$454$	0	0
$455$	16.9211	0.793274
$456$	0	0
$457$	−4.40586	−0.206098	−0.103049	−	0.994676i	$-0.532860\pi$
$457$	−4.40586	−0.206098	−0.103049	+	0.994676i	$0.532860\pi$
$458$	0	0
$459$	−19.6015	−0.914918
$460$	0	0
$461$	−15.3113	−0.713116	−0.356558	−	0.934273i	$-0.616050\pi$
$461$	−15.3113	−0.713116	−0.356558	+	0.934273i	$0.616050\pi$
$462$	0	0
$463$	−17.0873	−0.794113	−0.397056	−	0.917794i	$-0.629968\pi$
$463$	−17.0873	−0.794113	−0.397056	+	0.917794i	$0.629968\pi$
$464$	0	0
$465$	7.54364	0.349828
$466$	0	0
$467$	22.3711	1.03521	0.517605	−	0.855620i	$-0.326824\pi$
$467$	22.3711	1.03521	0.517605	+	0.855620i	$0.326824\pi$
$468$	0	0
$469$	35.3647	1.63299
$470$	0	0
$471$	−31.4510	−1.44919
$472$	0	0
$473$	−15.4510	−0.710439
$474$	0	0
$475$	1.20293	0.0551943
$476$	0	0
$477$	−33.1103	−1.51602
$478$	0	0
$479$	−8.00733	−0.365864	−0.182932	−	0.983126i	$-0.558559\pi$
$479$	−8.00733	−0.365864	−0.182932	+	0.983126i	$0.558559\pi$
$480$	0	0
$481$	−42.5383	−1.93958
$482$	0	0
$483$	−102.177	−4.64924
$484$	0	0
$485$	−0.348034	−0.0158034
$486$	0	0
$487$	−17.0441	−0.772342	−0.386171	−	0.922427i	$-0.626203\pi$
$487$	−17.0441	−0.772342	−0.386171	+	0.922427i	$0.626203\pi$
$488$	0	0
$489$	−1.82545	−0.0825498
$490$	0	0
$491$	−37.0873	−1.67373	−0.836863	−	0.547413i	$-0.815613\pi$
$491$	−37.0873	−1.67373	−0.836863	+	0.547413i	$0.815613\pi$
$492$	0	0
$493$	1.60147	0.0721264
$494$	0	0
$495$	29.5667	1.32892
$496$	0	0
$497$	46.7001	2.09478
$498$	0	0
$499$	23.5089	1.05240	0.526200	−	0.850361i	$-0.323616\pi$
$499$	23.5089	1.05240	0.526200	+	0.850361i	$0.323616\pi$
$500$	0	0
$501$	−63.7054	−2.84615
$502$	0	0
$503$	17.1608	0.765163	0.382582	−	0.923922i	$-0.375035\pi$
$503$	17.1608	0.765163	0.382582	+	0.923922i	$0.375035\pi$
$504$	0	0
$505$	18.4216	0.819750
$506$	0	0
$507$	−18.5731	−0.824860
$508$	0	0
$509$	14.3638	0.636662	0.318331	−	0.947980i	$-0.396878\pi$
$509$	14.3638	0.636662	0.318331	+	0.947980i	$0.396878\pi$
$510$	0	0
$511$	9.33431	0.412925
$512$	0	0
$513$	−14.7235	−0.650059
$514$	0	0
$515$	12.0735	0.532024
$516$	0	0
$517$	36.8117	1.61898
$518$	0	0
$519$	−6.10833	−0.268126
$520$	0	0
$521$	−32.0388	−1.40364	−0.701822	−	0.712352i	$-0.747630\pi$
$521$	−32.0388	−1.40364	−0.701822	+	0.712352i	$0.747630\pi$
$522$	0	0
$523$	26.9442	1.17819	0.589093	−	0.808065i	$-0.299485\pi$
$523$	26.9442	1.17819	0.589093	+	0.808065i	$0.299485\pi$
$524$	0	0
$525$	12.2397	0.534185
$526$	0	0
$527$	−3.84117	−0.167324
$528$	0	0
$529$	46.6897	2.02999
$530$	0	0
$531$	27.9652	1.21359
$532$	0	0
$533$	−25.1462	−1.08920
$534$	0	0
$535$	5.78334	0.250036
$536$	0	0
$537$	−34.3711	−1.48322
$538$	0	0
$539$	34.9442	1.50515
$540$	0	0
$541$	13.5005	0.580430	0.290215	−	0.956961i	$-0.406273\pi$
$541$	13.5005	0.580430	0.290215	+	0.956961i	$0.406273\pi$
$542$	0	0
$543$	−3.78334	−0.162359
$544$	0	0
$545$	−10.7971	−0.462496
$546$	0	0
$547$	−35.1755	−1.50399	−0.751997	−	0.659166i	$-0.770909\pi$
$547$	−35.1755	−1.50399	−0.751997	+	0.659166i	$0.770909\pi$
$548$	0	0
$549$	−78.8084	−3.36346
$550$	0	0
$551$	1.20293	0.0512466
$552$	0	0
$553$	−29.3859	−1.24961
$554$	0	0
$555$	−30.7696	−1.30610
$556$	0	0
$557$	−18.6382	−0.789728	−0.394864	−	0.918740i	$-0.629208\pi$
$557$	−18.6382	−0.789728	−0.394864	+	0.918740i	$0.629208\pi$
$558$	0	0
$559$	15.6593	0.662318
$560$	0	0
$561$	−21.6088	−0.912324
$562$	0	0
$563$	0.421581	0.0177675	0.00888376	−	0.999961i	$-0.497172\pi$
$563$	0.421581	0.0177675	0.00888376	+	0.999961i	$0.497172\pi$
$564$	0	0
$565$	12.2324	0.514620
$566$	0	0
$567$	−69.3500	−2.91243
$568$	0	0
$569$	7.49314	0.314129	0.157064	−	0.987588i	$-0.449797\pi$
$569$	7.49314	0.314129	0.157064	+	0.987588i	$0.449797\pi$
$570$	0	0
$571$	−6.46369	−0.270497	−0.135249	−	0.990812i	$-0.543183\pi$
$571$	−6.46369	−0.270497	−0.135249	+	0.990812i	$0.543183\pi$
$572$	0	0
$573$	49.6172	2.07279
$574$	0	0
$575$	−8.34803	−0.348137
$576$	0	0
$577$	−31.5594	−1.31383	−0.656917	−	0.753963i	$-0.728140\pi$
$577$	−31.5594	−1.31383	−0.656917	+	0.753963i	$0.728140\pi$
$578$	0	0
$579$	−31.2692	−1.29950
$580$	0	0
$581$	10.8853	0.451597
$582$	0	0
$583$	−20.6118	−0.853656
$584$	0	0
$585$	−29.9652	−1.23891
$586$	0	0
$587$	11.5941	0.478541	0.239271	−	0.970953i	$-0.423092\pi$
$587$	11.5941	0.478541	0.239271	+	0.970953i	$0.423092\pi$
$588$	0	0
$589$	−2.88527	−0.118886
$590$	0	0
$591$	−79.1564	−3.25606
$592$	0	0
$593$	−18.4648	−0.758257	−0.379128	−	0.925344i	$-0.623776\pi$
$593$	−18.4648	−0.758257	−0.379128	+	0.925344i	$0.623776\pi$
$594$	0	0
$595$	−6.23238	−0.255503
$596$	0	0
$597$	59.0324	2.41603
$598$	0	0
$599$	−28.3711	−1.15921	−0.579605	−	0.814897i	$-0.696793\pi$
$599$	−28.3711	−1.15921	−0.579605	+	0.814897i	$0.696793\pi$
$600$	0	0
$601$	−34.4648	−1.40585	−0.702923	−	0.711266i	$-0.748122\pi$
$601$	−34.4648	−1.40585	−0.702923	+	0.711266i	$0.748122\pi$
$602$	0	0
$603$	−62.6265	−2.55035
$604$	0	0
$605$	7.40586	0.301091
$606$	0	0
$607$	36.7275	1.49072	0.745362	−	0.666660i	$-0.232277\pi$
$607$	36.7275	1.49072	0.745362	+	0.666660i	$0.232277\pi$
$608$	0	0
$609$	12.2397	0.495978
$610$	0	0
$611$	−37.3079	−1.50932
$612$	0	0
$613$	−8.95149	−0.361547	−0.180774	−	0.983525i	$-0.557860\pi$
$613$	−8.95149	−0.361547	−0.180774	+	0.983525i	$0.557860\pi$
$614$	0	0
$615$	−18.1892	−0.733460
$616$	0	0
$617$	22.3985	0.901731	0.450866	−	0.892592i	$-0.351115\pi$
$617$	22.3985	0.901731	0.450866	+	0.892592i	$0.351115\pi$
$618$	0	0
$619$	−31.5392	−1.26767	−0.633834	−	0.773469i	$-0.718520\pi$
$619$	−31.5392	−1.26767	−0.633834	+	0.773469i	$0.718520\pi$
$620$	0	0
$621$	102.177	4.10024
$622$	0	0
$623$	16.6961	0.668914
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	−16.2313	−0.648216
$628$	0	0
$629$	15.6677	0.624712
$630$	0	0
$631$	−41.0598	−1.63457	−0.817283	−	0.576237i	$-0.804521\pi$
$631$	−41.0598	−1.63457	−0.817283	+	0.576237i	$0.804521\pi$
$632$	0	0
$633$	38.6540	1.53636
$634$	0	0
$635$	8.00000	0.317470
$636$	0	0
$637$	−35.4152	−1.40320
$638$	0	0
$639$	−82.7001	−3.27156
$640$	0	0
$641$	40.5383	1.60117	0.800583	−	0.599221i	$-0.204523\pi$
$641$	40.5383	1.60117	0.800583	+	0.599221i	$0.204523\pi$
$642$	0	0
$643$	35.2765	1.39117	0.695584	−	0.718445i	$-0.255146\pi$
$643$	35.2765	1.39117	0.695584	+	0.718445i	$0.255146\pi$
$644$	0	0
$645$	11.3270	0.445999
$646$	0	0
$647$	−3.69514	−0.145271	−0.0726355	−	0.997359i	$-0.523141\pi$
$647$	−3.69514	−0.145271	−0.0726355	+	0.997359i	$0.523141\pi$
$648$	0	0
$649$	17.4089	0.683360
$650$	0	0
$651$	−29.3574	−1.15061
$652$	0	0
$653$	8.52152	0.333473	0.166736	−	0.986002i	$-0.446677\pi$
$653$	8.52152	0.333473	0.166736	+	0.986002i	$0.446677\pi$
$654$	0	0
$655$	20.9863	0.820002
$656$	0	0
$657$	−16.5299	−0.644893
$658$	0	0
$659$	5.10193	0.198743	0.0993715	−	0.995050i	$-0.468317\pi$
$659$	5.10193	0.198743	0.0993715	+	0.995050i	$0.468317\pi$
$660$	0	0
$661$	14.6961	0.571611	0.285805	−	0.958288i	$-0.407739\pi$
$661$	14.6961	0.571611	0.285805	+	0.958288i	$0.407739\pi$
$662$	0	0
$663$	21.9001	0.850528
$664$	0	0
$665$	−4.68141	−0.181537
$666$	0	0
$667$	−8.34803	−0.323237
$668$	0	0
$669$	−63.6329	−2.46019
$670$	0	0
$671$	−49.0598	−1.89393
$672$	0	0
$673$	−25.5813	−0.986088	−0.493044	−	0.870004i	$-0.664116\pi$
$673$	−25.5813	−0.986088	−0.493044	+	0.870004i	$0.664116\pi$
$674$	0	0
$675$	−12.2397	−0.471106
$676$	0	0
$677$	21.2344	0.816103	0.408052	−	0.912959i	$-0.366208\pi$
$677$	21.2344	0.816103	0.408052	+	0.912959i	$0.366208\pi$
$678$	0	0
$679$	1.35443	0.0519784
$680$	0	0
$681$	28.2628	1.08303
$682$	0	0
$683$	22.1324	0.846874	0.423437	−	0.905925i	$-0.360823\pi$
$683$	22.1324	0.846874	0.423437	+	0.905925i	$0.360823\pi$
$684$	0	0
$685$	3.65197	0.139534
$686$	0	0
$687$	−66.8937	−2.55215
$688$	0	0
$689$	20.8897	0.795833
$690$	0	0
$691$	−8.08088	−0.307411	−0.153705	−	0.988117i	$-0.549121\pi$
$691$	−8.08088	−0.307411	−0.153705	+	0.988117i	$0.549121\pi$
$692$	0	0
$693$	−115.064	−4.37091
$694$	0	0
$695$	−13.6750	−0.518723
$696$	0	0
$697$	9.26182	0.350817
$698$	0	0
$699$	−35.1019	−1.32768
$700$	0	0
$701$	−28.2902	−1.06851	−0.534253	−	0.845325i	$-0.679407\pi$
$701$	−28.2902	−1.06851	−0.534253	+	0.845325i	$0.679407\pi$
$702$	0	0
$703$	11.7687	0.443864
$704$	0	0
$705$	−26.9863	−1.01636
$706$	0	0
$707$	−71.6907	−2.69621
$708$	0	0
$709$	−52.2060	−1.96064	−0.980318	−	0.197423i	$-0.936743\pi$
$709$	−52.2060	−1.96064	−0.980318	+	0.197423i	$0.936743\pi$
$710$	0	0
$711$	52.0388	1.95161
$712$	0	0
$713$	20.0230	0.749869
$714$	0	0
$715$	−18.6540	−0.697618
$716$	0	0
$717$	6.05889	0.226273
$718$	0	0
$719$	27.0177	1.00759	0.503795	−	0.863823i	$-0.331937\pi$
$719$	27.0177	1.00759	0.503795	+	0.863823i	$0.331937\pi$
$720$	0	0
$721$	−46.9863	−1.74986
$722$	0	0
$723$	55.7486	2.07331
$724$	0	0
$725$	1.00000	0.0371391
$726$	0	0
$727$	−33.7559	−1.25194	−0.625968	−	0.779849i	$-0.715296\pi$
$727$	−33.7559	−1.25194	−0.625968	+	0.779849i	$0.715296\pi$
$728$	0	0
$729$	7.32499	0.271296
$730$	0	0
$731$	−5.76762	−0.213323
$732$	0	0
$733$	−9.52059	−0.351651	−0.175826	−	0.984421i	$-0.556259\pi$
$733$	−9.52059	−0.351651	−0.175826	+	0.984421i	$0.556259\pi$
$734$	0	0
$735$	−25.6172	−0.944904
$736$	0	0
$737$	−38.9863	−1.43608
$738$	0	0
$739$	−0.0735473	−0.00270548	−0.00135274	−	0.999999i	$-0.500431\pi$
$739$	−0.0735473	−0.00270548	−0.00135274	+	0.999999i	$0.500431\pi$
$740$	0	0
$741$	16.4501	0.604309
$742$	0	0
$743$	27.4196	1.00593	0.502964	−	0.864308i	$-0.332243\pi$
$743$	27.4196	1.00593	0.502964	+	0.864308i	$0.332243\pi$
$744$	0	0
$745$	−7.27648	−0.266590
$746$	0	0
$747$	−19.2765	−0.705289
$748$	0	0
$749$	−22.5069	−0.822383
$750$	0	0
$751$	−17.0873	−0.623523	−0.311762	−	0.950160i	$-0.600919\pi$
$751$	−17.0873	−0.623523	−0.311762	+	0.950160i	$0.600919\pi$
$752$	0	0
$753$	−45.1755	−1.64629
$754$	0	0
$755$	−8.69607	−0.316482
$756$	0	0
$757$	−25.7833	−0.937111	−0.468556	−	0.883434i	$-0.655225\pi$
$757$	−25.7833	−0.937111	−0.468556	+	0.883434i	$0.655225\pi$
$758$	0	0
$759$	112.641	4.08862
$760$	0	0
$761$	9.28381	0.336538	0.168269	−	0.985741i	$-0.446182\pi$
$761$	9.28381	0.336538	0.168269	+	0.985741i	$0.446182\pi$
$762$	0	0
$763$	42.0186	1.52118
$764$	0	0
$765$	11.0368	0.399035
$766$	0	0
$767$	−17.6436	−0.637073
$768$	0	0
$769$	−33.1019	−1.19369	−0.596843	−	0.802358i	$-0.703579\pi$
$769$	−33.1019	−1.19369	−0.596843	+	0.802358i	$0.703579\pi$
$770$	0	0
$771$	45.1755	1.62696
$772$	0	0
$773$	−25.7687	−0.926835	−0.463418	−	0.886140i	$-0.653377\pi$
$773$	−25.7687	−0.926835	−0.463418	+	0.886140i	$0.653377\pi$
$774$	0	0
$775$	−2.39853	−0.0861579
$776$	0	0
$777$	119.745	4.29584
$778$	0	0
$779$	6.95696	0.249259
$780$	0	0
$781$	−51.4825	−1.84219
$782$	0	0
$783$	−12.2397	−0.437411
$784$	0	0
$785$	10.0000	0.356915
$786$	0	0
$787$	33.3500	1.18880	0.594400	−	0.804170i	$-0.297390\pi$
$787$	33.3500	1.18880	0.594400	+	0.804170i	$0.297390\pi$
$788$	0	0
$789$	37.7412	1.34362
$790$	0	0
$791$	−47.6044	−1.69262
$792$	0	0
$793$	49.7211	1.76565
$794$	0	0
$795$	15.1103	0.535908
$796$	0	0
$797$	7.05982	0.250072	0.125036	−	0.992152i	$-0.460095\pi$
$797$	7.05982	0.250072	0.125036	+	0.992152i	$0.460095\pi$
$798$	0	0
$799$	13.7412	0.486130
$800$	0	0
$801$	−29.5667	−1.04469
$802$	0	0
$803$	−10.2902	−0.363133
$804$	0	0
$805$	32.4878	1.14504
$806$	0	0
$807$	−38.0819	−1.34055
$808$	0	0
$809$	18.6814	0.656803	0.328402	−	0.944538i	$-0.393490\pi$
$809$	18.6814	0.656803	0.328402	+	0.944538i	$0.393490\pi$
$810$	0	0
$811$	−36.2133	−1.27162	−0.635811	−	0.771845i	$-0.719334\pi$
$811$	−36.2133	−1.27162	−0.635811	+	0.771845i	$0.719334\pi$
$812$	0	0
$813$	−10.9863	−0.385305
$814$	0	0
$815$	0.580411	0.0203309
$816$	0	0
$817$	−4.33231	−0.151569
$818$	0	0
$819$	116.615	4.07485
$820$	0	0
$821$	36.8706	1.28679	0.643397	−	0.765533i	$-0.277525\pi$
$821$	36.8706	1.28679	0.643397	+	0.765533i	$0.277525\pi$
$822$	0	0
$823$	39.0324	1.36058	0.680291	−	0.732942i	$-0.261853\pi$
$823$	39.0324	1.36058	0.680291	+	0.732942i	$0.261853\pi$
$824$	0	0
$825$	−13.4931	−0.469771
$826$	0	0
$827$	−17.2103	−0.598459	−0.299230	−	0.954181i	$-0.596730\pi$
$827$	−17.2103	−0.598459	−0.299230	+	0.954181i	$0.596730\pi$
$828$	0	0
$829$	−32.7034	−1.13584	−0.567918	−	0.823085i	$-0.692251\pi$
$829$	−32.7034	−1.13584	−0.567918	+	0.823085i	$0.692251\pi$
$830$	0	0
$831$	69.6549	2.41630
$832$	0	0
$833$	13.0441	0.451951
$834$	0	0
$835$	20.2554	0.700968
$836$	0	0
$837$	29.3574	1.01474
$838$	0	0
$839$	−32.3049	−1.11529	−0.557644	−	0.830080i	$-0.688294\pi$
$839$	−32.3049	−1.11529	−0.557644	+	0.830080i	$0.688294\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	0	0
$843$	46.7927	1.61162
$844$	0	0
$845$	5.90540	0.203152
$846$	0	0
$847$	−28.8212	−0.990307
$848$	0	0
$849$	16.3638	0.561603
$850$	0	0
$851$	−81.6717	−2.79967
$852$	0	0
$853$	−46.7422	−1.60042	−0.800211	−	0.599719i	$-0.795279\pi$
$853$	−46.7422	−1.60042	−0.800211	+	0.599719i	$0.795279\pi$
$854$	0	0
$855$	8.29021	0.283519
$856$	0	0
$857$	30.4648	1.04066	0.520328	−	0.853966i	$-0.325810\pi$
$857$	30.4648	1.04066	0.520328	+	0.853966i	$0.325810\pi$
$858$	0	0
$859$	30.7971	1.05078	0.525391	−	0.850861i	$-0.323919\pi$
$859$	30.7971	1.05078	0.525391	+	0.850861i	$0.323919\pi$
$860$	0	0
$861$	70.7864	2.41239
$862$	0	0
$863$	34.9010	1.18804	0.594022	−	0.804449i	$-0.297539\pi$
$863$	34.9010	1.18804	0.594022	+	0.804449i	$0.297539\pi$
$864$	0	0
$865$	1.94217	0.0660358
$866$	0	0
$867$	45.4005	1.54188
$868$	0	0
$869$	32.3952	1.09893
$870$	0	0
$871$	39.5118	1.33881
$872$	0	0
$873$	−2.39853	−0.0811781
$874$	0	0
$875$	−3.89167	−0.131562
$876$	0	0
$877$	−36.9599	−1.24805	−0.624023	−	0.781406i	$-0.714503\pi$
$877$	−36.9599	−1.24805	−0.624023	+	0.781406i	$0.714503\pi$
$878$	0	0
$879$	55.9304	1.88649
$880$	0	0
$881$	25.0009	0.842303	0.421151	−	0.906990i	$-0.361626\pi$
$881$	25.0009	0.842303	0.421151	+	0.906990i	$0.361626\pi$
$882$	0	0
$883$	−52.7696	−1.77584	−0.887919	−	0.459999i	$-0.847850\pi$
$883$	−52.7696	−1.77584	−0.887919	+	0.459999i	$0.847850\pi$
$884$	0	0
$885$	−12.7623	−0.429000
$886$	0	0
$887$	−23.5667	−0.791292	−0.395646	−	0.918403i	$-0.629479\pi$
$887$	−23.5667	−0.791292	−0.395646	+	0.918403i	$0.629479\pi$
$888$	0	0
$889$	−31.1334	−1.04418
$890$	0	0
$891$	76.4520	2.56124
$892$	0	0
$893$	10.3216	0.345401
$894$	0	0
$895$	10.9284	0.365298
$896$	0	0
$897$	−114.159	−3.81167
$898$	0	0
$899$	−2.39853	−0.0799956
$900$	0	0
$901$	−7.69408	−0.256327
$902$	0	0
$903$	−44.0809	−1.46692
$904$	0	0
$905$	1.20293	0.0399868
$906$	0	0
$907$	−25.2103	−0.837093	−0.418546	−	0.908195i	$-0.637460\pi$
$907$	−25.2103	−0.837093	−0.418546	+	0.908195i	$0.637460\pi$
$908$	0	0
$909$	126.955	4.21085
$910$	0	0
$911$	32.5961	1.07996	0.539979	−	0.841679i	$-0.318432\pi$
$911$	32.5961	1.07996	0.539979	+	0.841679i	$0.318432\pi$
$912$	0	0
$913$	−12.0000	−0.397142
$914$	0	0
$915$	35.9652	1.18897
$916$	0	0
$917$	−81.6717	−2.69704
$918$	0	0
$919$	44.0000	1.45143	0.725713	−	0.687998i	$-0.241510\pi$
$919$	44.0000	1.45143	0.725713	+	0.687998i	$0.241510\pi$
$920$	0	0
$921$	7.56668	0.249331
$922$	0	0
$923$	52.1764	1.71741
$924$	0	0
$925$	9.78334	0.321674
$926$	0	0
$927$	83.2069	2.73287
$928$	0	0
$929$	5.05249	0.165767	0.0828835	−	0.996559i	$-0.473587\pi$
$929$	5.05249	0.165767	0.0828835	+	0.996559i	$0.473587\pi$
$930$	0	0
$931$	9.79800	0.321116
$932$	0	0
$933$	−51.0986	−1.67289
$934$	0	0
$935$	6.87062	0.224693
$936$	0	0
$937$	−19.6088	−0.640591	−0.320296	−	0.947318i	$-0.603782\pi$
$937$	−19.6088	−0.640591	−0.320296	+	0.947318i	$0.603782\pi$
$938$	0	0
$939$	38.2902	1.24955
$940$	0	0
$941$	−6.68141	−0.217808	−0.108904	−	0.994052i	$-0.534734\pi$
$941$	−6.68141	−0.217808	−0.108904	+	0.994052i	$0.534734\pi$
$942$	0	0
$943$	−48.2795	−1.57220
$944$	0	0
$945$	47.6329	1.54950
$946$	0	0
$947$	−33.4667	−1.08752	−0.543762	−	0.839240i	$-0.683000\pi$
$947$	−33.4667	−1.08752	−0.543762	+	0.839240i	$0.683000\pi$
$948$	0	0
$949$	10.4289	0.338537
$950$	0	0
$951$	−43.0324	−1.39542
$952$	0	0
$953$	−43.7412	−1.41692	−0.708459	−	0.705752i	$-0.750609\pi$
$953$	−43.7412	−1.41692	−0.708459	+	0.705752i	$0.750609\pi$
$954$	0	0
$955$	−15.7760	−0.510500
$956$	0	0
$957$	−13.4931	−0.436171
$958$	0	0
$959$	−14.2123	−0.458938
$960$	0	0
$961$	−25.2470	−0.814420
$962$	0	0
$963$	39.8569	1.28437
$964$	0	0
$965$	9.94217	0.320050
$966$	0	0
$967$	−35.9304	−1.15544	−0.577722	−	0.816233i	$-0.696058\pi$
$967$	−35.9304	−1.15544	−0.577722	+	0.816233i	$0.696058\pi$
$968$	0	0
$969$	−6.05889	−0.194640
$970$	0	0
$971$	−26.7971	−0.859959	−0.429979	−	0.902839i	$-0.641479\pi$
$971$	−26.7971	−0.859959	−0.429979	+	0.902839i	$0.641479\pi$
$972$	0	0
$973$	53.2186	1.70611
$974$	0	0
$975$	13.6750	0.437951
$976$	0	0
$977$	−21.4510	−0.686279	−0.343140	−	0.939284i	$-0.611490\pi$
$977$	−21.4510	−0.686279	−0.343140	+	0.939284i	$0.611490\pi$
$978$	0	0
$979$	−18.4059	−0.588254
$980$	0	0
$981$	−74.4098	−2.37572
$982$	0	0
$983$	49.8715	1.59066	0.795328	−	0.606180i	$-0.207299\pi$
$983$	49.8715	1.59066	0.795328	+	0.606180i	$0.207299\pi$
$984$	0	0
$985$	25.1681	0.801924
$986$	0	0
$987$	105.022	3.34288
$988$	0	0
$989$	30.0652	0.956016
$990$	0	0
$991$	−16.2167	−0.515139	−0.257570	−	0.966260i	$-0.582922\pi$
$991$	−16.2167	−0.515139	−0.257570	+	0.966260i	$0.582922\pi$
$992$	0	0
$993$	27.8990	0.885348
$994$	0	0
$995$	−18.7696	−0.595037
$996$	0	0
$997$	−6.31766	−0.200082	−0.100041	−	0.994983i	$-0.531897\pi$
$997$	−6.31766	−0.200082	−0.100041	+	0.994983i	$0.531897\pi$
$998$	0	0
$999$	−119.745	−3.78857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9280.2.a.bf.1.1		3
4.3	odd	2		9280.2.a.by.1.3		3
8.3	odd	2		2320.2.a.l.1.1		3
8.5	even	2		290.2.a.e.1.3	✓	3
24.5	odd	2		2610.2.a.x.1.1		3
40.13	odd	4		1450.2.b.l.349.3		6
40.29	even	2		1450.2.a.p.1.1		3
40.37	odd	4		1450.2.b.l.349.4		6
232.173	even	2		8410.2.a.v.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.a.e.1.3	✓	3	8.5	even	2
1450.2.a.p.1.1		3	40.29	even	2
1450.2.b.l.349.3		6	40.13	odd	4
1450.2.b.l.349.4		6	40.37	odd	4
2320.2.a.l.1.1		3	8.3	odd	2
2610.2.a.x.1.1		3	24.5	odd	2
8410.2.a.v.1.1		3	232.173	even	2
9280.2.a.bf.1.1		3	1.1	even	1	trivial
9280.2.a.by.1.3		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9280 = 2^{6} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9280.a (trivial)

\(f(q)\)	\(=\)	\(q-3.14510 q^{3} +1.00000 q^{5} -3.89167 q^{7} +6.89167 q^{9} +O(q^{10})\)	\(q-3.14510 q^{3} +1.00000 q^{5} -3.89167 q^{7} +6.89167 q^{9} +4.29021 q^{11} -4.34803 q^{13} -3.14510 q^{15} +1.60147 q^{17} +1.20293 q^{19} +12.2397 q^{21} -8.34803 q^{23} +1.00000 q^{25} -12.2397 q^{27} +1.00000 q^{29} -2.39853 q^{31} -13.4931 q^{33} -3.89167 q^{35} +9.78334 q^{37} +13.6750 q^{39} +5.78334 q^{41} -3.60147 q^{43} +6.89167 q^{45} +8.58041 q^{47} +8.14510 q^{49} -5.03677 q^{51} -4.80440 q^{53} +4.29021 q^{55} -3.78334 q^{57} +4.05783 q^{59} -11.4353 q^{61} -26.8201 q^{63} -4.34803 q^{65} -9.08727 q^{67} +26.2554 q^{69} -12.0000 q^{71} -2.39853 q^{73} -3.14510 q^{75} -16.6961 q^{77} +7.55096 q^{79} +17.8201 q^{81} -2.79707 q^{83} +1.60147 q^{85} -3.14510 q^{87} -4.29021 q^{89} +16.9211 q^{91} +7.54364 q^{93} +1.20293 q^{95} -0.348034 q^{97} +29.5667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 3 q^{5} + 3 q^{7} + 6 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 3 * q^5 + 3 * q^7 + 6 * q^9	\( 3 q - 3 q^{3} + 3 q^{5} + 3 q^{7} + 6 q^{9} - 3 q^{13} - 3 q^{15} + 3 q^{17} + 12 q^{21} - 15 q^{23} + 3 q^{25} - 12 q^{27} + 3 q^{29} - 9 q^{31} - 24 q^{33} + 3 q^{35} - 3 q^{39} - 12 q^{41} - 9 q^{43} + 6 q^{45} + 18 q^{49} + 6 q^{51} - 9 q^{53} + 18 q^{57} + 15 q^{59} - 15 q^{61} - 30 q^{63} - 3 q^{65} - 18 q^{67} + 9 q^{69} - 36 q^{71} - 9 q^{73} - 3 q^{75} - 30 q^{77} + 9 q^{79} + 3 q^{81} - 12 q^{83} + 3 q^{85} - 3 q^{87} + 24 q^{91} + 18 q^{93} + 9 q^{97} + 30 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 3 * q^5 + 3 * q^7 + 6 * q^9 - 3 * q^13 - 3 * q^15 + 3 * q^17 + 12 * q^21 - 15 * q^23 + 3 * q^25 - 12 * q^27 + 3 * q^29 - 9 * q^31 - 24 * q^33 + 3 * q^35 - 3 * q^39 - 12 * q^41 - 9 * q^43 + 6 * q^45 + 18 * q^49 + 6 * q^51 - 9 * q^53 + 18 * q^57 + 15 * q^59 - 15 * q^61 - 30 * q^63 - 3 * q^65 - 18 * q^67 + 9 * q^69 - 36 * q^71 - 9 * q^73 - 3 * q^75 - 30 * q^77 + 9 * q^79 + 3 * q^81 - 12 * q^83 + 3 * q^85 - 3 * q^87 + 24 * q^91 + 18 * q^93 + 9 * q^97 + 30 * q^99

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