LMFDB - Embedded newform 7605.2.a.cp.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7605,2,Mod(1,7605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7605, 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("7605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7605 = 3^{2} \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7605.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:	$60.7262307372$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 17x^{7} - 9x^{6} + 59x^{5} + 32x^{4} - 44x^{3} - 23x^{2} + x + 1 $ x^9 - 17x^7 - 9x^6 + 59x^5 + 32x^4 - 44x^3 - 23x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 845)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.07331$ of defining polynomial
Character	$\chi$	$=$	7605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.271374 q^{2} -1.92636 q^{4} -1.00000 q^{5} -3.38151 q^{7} -1.06551 q^{8} +O(q^{10})$	$q+0.271374 q^{2} -1.92636 q^{4} -1.00000 q^{5} -3.38151 q^{7} -1.06551 q^{8} -0.271374 q^{10} +1.75204 q^{11} -0.917654 q^{14} +3.56356 q^{16} -1.95419 q^{17} +7.13261 q^{19} +1.92636 q^{20} +0.475459 q^{22} -7.61420 q^{23} +1.00000 q^{25} +6.51400 q^{28} -3.98380 q^{29} -4.86923 q^{31} +3.09808 q^{32} -0.530316 q^{34} +3.38151 q^{35} -10.5010 q^{37} +1.93560 q^{38} +1.06551 q^{40} +0.911110 q^{41} +4.58553 q^{43} -3.37506 q^{44} -2.06629 q^{46} -8.58491 q^{47} +4.43464 q^{49} +0.271374 q^{50} -11.9646 q^{53} -1.75204 q^{55} +3.60304 q^{56} -1.08110 q^{58} +3.82297 q^{59} +7.98476 q^{61} -1.32138 q^{62} -6.28638 q^{64} -0.472749 q^{67} +3.76446 q^{68} +0.917654 q^{70} -5.50312 q^{71} -2.93857 q^{73} -2.84969 q^{74} -13.7400 q^{76} -5.92456 q^{77} +4.09938 q^{79} -3.56356 q^{80} +0.247252 q^{82} -11.7733 q^{83} +1.95419 q^{85} +1.24439 q^{86} -1.86682 q^{88} -3.85992 q^{89} +14.6677 q^{92} -2.32972 q^{94} -7.13261 q^{95} +6.95775 q^{97} +1.20345 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 3 q^{2} + 17 q^{4} - 9 q^{5} + 7 q^{7} - 12 q^{8}+O(q^{10}) $ 9 * q - 3 * q^2 + 17 * q^4 - 9 * q^5 + 7 * q^7 - 12 * q^8	$ 9 q - 3 q^{2} + 17 q^{4} - 9 q^{5} + 7 q^{7} - 12 q^{8} + 3 q^{10} + 9 q^{11} + 2 q^{14} + 37 q^{16} + q^{17} - 4 q^{19} - 17 q^{20} + 12 q^{22} - 14 q^{23} + 9 q^{25} + 18 q^{28} - 12 q^{29} - 7 q^{31} - 22 q^{32} - 30 q^{34} - 7 q^{35} - 5 q^{37} + 47 q^{38} + 12 q^{40} + 10 q^{41} + 39 q^{43} + 25 q^{44} + 6 q^{46} - 36 q^{47} + 16 q^{49} - 3 q^{50} + 8 q^{53} - 9 q^{55} + 29 q^{56} + 21 q^{58} + 21 q^{59} - 3 q^{61} + 10 q^{62} + 34 q^{64} + q^{67} + 20 q^{68} - 2 q^{70} + q^{71} + 15 q^{74} - 5 q^{76} + 4 q^{77} + 39 q^{79} - 37 q^{80} - 4 q^{82} - 7 q^{83} - q^{85} + 24 q^{86} + 42 q^{88} + 19 q^{89} + 27 q^{92} + 16 q^{94} + 4 q^{95} - 34 q^{97} - 48 q^{98}+O(q^{100}) $ 9 * q - 3 * q^2 + 17 * q^4 - 9 * q^5 + 7 * q^7 - 12 * q^8 + 3 * q^10 + 9 * q^11 + 2 * q^14 + 37 * q^16 + q^17 - 4 * q^19 - 17 * q^20 + 12 * q^22 - 14 * q^23 + 9 * q^25 + 18 * q^28 - 12 * q^29 - 7 * q^31 - 22 * q^32 - 30 * q^34 - 7 * q^35 - 5 * q^37 + 47 * q^38 + 12 * q^40 + 10 * q^41 + 39 * q^43 + 25 * q^44 + 6 * q^46 - 36 * q^47 + 16 * q^49 - 3 * q^50 + 8 * q^53 - 9 * q^55 + 29 * q^56 + 21 * q^58 + 21 * q^59 - 3 * q^61 + 10 * q^62 + 34 * q^64 + q^67 + 20 * q^68 - 2 * q^70 + q^71 + 15 * q^74 - 5 * q^76 + 4 * q^77 + 39 * q^79 - 37 * q^80 - 4 * q^82 - 7 * q^83 - q^85 + 24 * q^86 + 42 * q^88 + 19 * q^89 + 27 * q^92 + 16 * q^94 + 4 * q^95 - 34 * q^97 - 48 * 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 $

$2$	0.271374	0.191890	0.0959451	−	0.995387i	$-0.469413\pi$
$2$	0.271374	0.191890	0.0959451	+	0.995387i	$0.469413\pi$
$3$	0	0
$3$	0	0
$4$	−1.92636	−0.963178
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	−3.38151	−1.27809	−0.639046	−	0.769168i	$-0.720671\pi$
$7$	−3.38151	−1.27809	−0.639046	+	0.769168i	$0.720671\pi$
$8$	−1.06551	−0.376715
$9$	0	0
$10$	−0.271374	−0.0858159
$11$	1.75204	0.528261	0.264131	−	0.964487i	$-0.414915\pi$
$11$	1.75204	0.528261	0.264131	+	0.964487i	$0.414915\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	−0.917654	−0.245253
$15$	0	0
$16$	3.56356	0.890890
$17$	−1.95419	−0.473960	−0.236980	−	0.971514i	$-0.576158\pi$
$17$	−1.95419	−0.473960	−0.236980	+	0.971514i	$0.576158\pi$
$18$	0	0
$19$	7.13261	1.63633	0.818167	−	0.574981i	$-0.194990\pi$
$19$	7.13261	1.63633	0.818167	+	0.574981i	$0.194990\pi$
$20$	1.92636	0.430746
$21$	0	0
$22$	0.475459	0.101368
$23$	−7.61420	−1.58767	−0.793835	−	0.608133i	$-0.791919\pi$
$23$	−7.61420	−1.58767	−0.793835	+	0.608133i	$0.791919\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	6.51400	1.23103
$29$	−3.98380	−0.739773	−0.369886	−	0.929077i	$-0.620603\pi$
$29$	−3.98380	−0.739773	−0.369886	+	0.929077i	$0.620603\pi$
$30$	0	0
$31$	−4.86923	−0.874540	−0.437270	−	0.899330i	$-0.644055\pi$
$31$	−4.86923	−0.874540	−0.437270	+	0.899330i	$0.644055\pi$
$32$	3.09808	0.547668
$33$	0	0
$34$	−0.530316	−0.0909484
$35$	3.38151	0.571580
$36$	0	0
$37$	−10.5010	−1.72635	−0.863176	−	0.504903i	$-0.831528\pi$
$37$	−10.5010	−1.72635	−0.863176	+	0.504903i	$0.831528\pi$
$38$	1.93560	0.313997
$39$	0	0
$40$	1.06551	0.168472
$41$	0.911110	0.142292	0.0711458	−	0.997466i	$-0.477334\pi$
$41$	0.911110	0.142292	0.0711458	+	0.997466i	$0.477334\pi$
$42$	0	0
$43$	4.58553	0.699286	0.349643	−	0.936883i	$-0.386303\pi$
$43$	4.58553	0.699286	0.349643	+	0.936883i	$0.386303\pi$
$44$	−3.37506	−0.508810
$45$	0	0
$46$	−2.06629	−0.304658
$47$	−8.58491	−1.25224	−0.626119	−	0.779728i	$-0.715357\pi$
$47$	−8.58491	−1.25224	−0.626119	+	0.779728i	$0.715357\pi$
$48$	0	0
$49$	4.43464	0.633520
$50$	0.271374	0.0383781
$51$	0	0
$52$	0	0
$53$	−11.9646	−1.64347	−0.821734	−	0.569871i	$-0.806993\pi$
$53$	−11.9646	−1.64347	−0.821734	+	0.569871i	$0.806993\pi$
$54$	0	0
$55$	−1.75204	−0.236246
$56$	3.60304	0.481476
$57$	0	0
$58$	−1.08110	−0.141955
$59$	3.82297	0.497708	0.248854	−	0.968541i	$-0.419946\pi$
$59$	3.82297	0.497708	0.248854	+	0.968541i	$0.419946\pi$
$60$	0	0
$61$	7.98476	1.02234	0.511172	−	0.859479i	$-0.329212\pi$
$61$	7.98476	1.02234	0.511172	+	0.859479i	$0.329212\pi$
$62$	−1.32138	−0.167816
$63$	0	0
$64$	−6.28638	−0.785798
$65$	0	0
$66$	0	0
$67$	−0.472749	−0.0577554	−0.0288777	−	0.999583i	$-0.509193\pi$
$67$	−0.472749	−0.0577554	−0.0288777	+	0.999583i	$0.509193\pi$
$68$	3.76446	0.456508
$69$	0	0
$70$	0.917654	0.109681
$71$	−5.50312	−0.653101	−0.326550	−	0.945180i	$-0.605886\pi$
$71$	−5.50312	−0.653101	−0.326550	+	0.945180i	$0.605886\pi$
$72$	0	0
$73$	−2.93857	−0.343934	−0.171967	−	0.985103i	$-0.555012\pi$
$73$	−2.93857	−0.343934	−0.171967	+	0.985103i	$0.555012\pi$
$74$	−2.84969	−0.331270
$75$	0	0
$76$	−13.7400	−1.57608
$77$	−5.92456	−0.675167
$78$	0	0
$79$	4.09938	0.461216	0.230608	−	0.973047i	$-0.425928\pi$
$79$	4.09938	0.461216	0.230608	+	0.973047i	$0.425928\pi$
$80$	−3.56356	−0.398418
$81$	0	0
$82$	0.247252	0.0273044
$83$	−11.7733	−1.29229	−0.646144	−	0.763215i	$-0.723619\pi$
$83$	−11.7733	−1.29229	−0.646144	+	0.763215i	$0.723619\pi$
$84$	0	0
$85$	1.95419	0.211961
$86$	1.24439	0.134186
$87$	0	0
$88$	−1.86682	−0.199004
$89$	−3.85992	−0.409151	−0.204576	−	0.978851i	$-0.565581\pi$
$89$	−3.85992	−0.409151	−0.204576	+	0.978851i	$0.565581\pi$
$90$	0	0
$91$	0	0
$92$	14.6677	1.52921
$93$	0	0
$94$	−2.32972	−0.240292
$95$	−7.13261	−0.731791
$96$	0	0
$97$	6.95775	0.706453	0.353226	−	0.935538i	$-0.385085\pi$
$97$	6.95775	0.706453	0.353226	+	0.935538i	$0.385085\pi$
$98$	1.20345	0.121566
$99$	0	0
$100$	−1.92636	−0.192636
$101$	17.8923	1.78035	0.890175	−	0.455619i	$-0.150582\pi$
$101$	17.8923	1.78035	0.890175	+	0.455619i	$0.150582\pi$
$102$	0	0
$103$	10.2561	1.01056	0.505281	−	0.862955i	$-0.331389\pi$
$103$	10.2561	1.01056	0.505281	+	0.862955i	$0.331389\pi$
$104$	0	0
$105$	0	0
$106$	−3.24689	−0.315366
$107$	−12.8986	−1.24696	−0.623478	−	0.781841i	$-0.714281\pi$
$107$	−12.8986	−1.24696	−0.623478	+	0.781841i	$0.714281\pi$
$108$	0	0
$109$	−10.4476	−1.00070	−0.500348	−	0.865825i	$-0.666794\pi$
$109$	−10.4476	−1.00070	−0.500348	+	0.865825i	$0.666794\pi$
$110$	−0.475459	−0.0453332
$111$	0	0
$112$	−12.0502	−1.13864
$113$	18.9766	1.78516	0.892582	−	0.450884i	$-0.148891\pi$
$113$	18.9766	1.78516	0.892582	+	0.450884i	$0.148891\pi$
$114$	0	0
$115$	7.61420	0.710028
$116$	7.67421	0.712533
$117$	0	0
$118$	1.03745	0.0955054
$119$	6.60812	0.605765
$120$	0	0
$121$	−7.93034	−0.720940
$122$	2.16685	0.196178
$123$	0	0
$124$	9.37987	0.842337
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−9.88489	−0.877142	−0.438571	−	0.898697i	$-0.644515\pi$
$127$	−9.88489	−0.877142	−0.438571	+	0.898697i	$0.644515\pi$
$128$	−7.90212	−0.698455
$129$	0	0
$130$	0	0
$131$	11.4705	1.00218	0.501089	−	0.865396i	$-0.332933\pi$
$131$	11.4705	1.00218	0.501089	+	0.865396i	$0.332933\pi$
$132$	0	0
$133$	−24.1190	−2.09139
$134$	−0.128292	−0.0110827
$135$	0	0
$136$	2.08221	0.178548
$137$	−13.0826	−1.11772	−0.558861	−	0.829261i	$-0.688761\pi$
$137$	−13.0826	−1.11772	−0.558861	+	0.829261i	$0.688761\pi$
$138$	0	0
$139$	11.9762	1.01581	0.507904	−	0.861414i	$-0.330421\pi$
$139$	11.9762	1.01581	0.507904	+	0.861414i	$0.330421\pi$
$140$	−6.51400	−0.550534
$141$	0	0
$142$	−1.49340	−0.125324
$143$	0	0
$144$	0	0
$145$	3.98380	0.330836
$146$	−0.797452	−0.0659976
$147$	0	0
$148$	20.2287	1.66278
$149$	16.3052	1.33577	0.667887	−	0.744262i	$-0.267199\pi$
$149$	16.3052	1.33577	0.667887	+	0.744262i	$0.267199\pi$
$150$	0	0
$151$	−8.75415	−0.712402	−0.356201	−	0.934409i	$-0.615928\pi$
$151$	−8.75415	−0.712402	−0.356201	+	0.934409i	$0.615928\pi$
$152$	−7.59987	−0.616431
$153$	0	0
$154$	−1.60777	−0.129558
$155$	4.86923	0.391106
$156$	0	0
$157$	6.48821	0.517816	0.258908	−	0.965902i	$-0.416637\pi$
$157$	6.48821	0.517816	0.258908	+	0.965902i	$0.416637\pi$
$158$	1.11246	0.0885029
$159$	0	0
$160$	−3.09808	−0.244925
$161$	25.7475	2.02919
$162$	0	0
$163$	3.84933	0.301503	0.150751	−	0.988572i	$-0.451831\pi$
$163$	3.84933	0.301503	0.150751	+	0.988572i	$0.451831\pi$
$164$	−1.75512	−0.137052
$165$	0	0
$166$	−3.19497	−0.247977
$167$	−6.85894	−0.530760	−0.265380	−	0.964144i	$-0.585497\pi$
$167$	−6.85894	−0.530760	−0.265380	+	0.964144i	$0.585497\pi$
$168$	0	0
$169$	0	0
$170$	0.530316	0.0406733
$171$	0	0
$172$	−8.83336	−0.673537
$173$	−16.0204	−1.21801	−0.609005	−	0.793166i	$-0.708431\pi$
$173$	−16.0204	−1.21801	−0.609005	+	0.793166i	$0.708431\pi$
$174$	0	0
$175$	−3.38151	−0.255618
$176$	6.24352	0.470623
$177$	0	0
$178$	−1.04748	−0.0785121
$179$	8.08309	0.604158	0.302079	−	0.953283i	$-0.402319\pi$
$179$	8.08309	0.604158	0.302079	+	0.953283i	$0.402319\pi$
$180$	0	0
$181$	11.0898	0.824298	0.412149	−	0.911117i	$-0.364778\pi$
$181$	11.0898	0.824298	0.412149	+	0.911117i	$0.364778\pi$
$182$	0	0
$183$	0	0
$184$	8.11301	0.598099
$185$	10.5010	0.772048
$186$	0	0
$187$	−3.42382	−0.250375
$188$	16.5376	1.20613
$189$	0	0
$190$	−1.93560	−0.140424
$191$	−21.7532	−1.57401	−0.787003	−	0.616949i	$-0.788369\pi$
$191$	−21.7532	−1.57401	−0.787003	+	0.616949i	$0.788369\pi$
$192$	0	0
$193$	22.5285	1.62164	0.810820	−	0.585296i	$-0.199022\pi$
$193$	22.5285	1.62164	0.810820	+	0.585296i	$0.199022\pi$
$194$	1.88815	0.135561
$195$	0	0
$196$	−8.54270	−0.610193
$197$	17.2749	1.23078	0.615392	−	0.788221i	$-0.288998\pi$
$197$	17.2749	1.23078	0.615392	+	0.788221i	$0.288998\pi$
$198$	0	0
$199$	17.4901	1.23984	0.619919	−	0.784666i	$-0.287166\pi$
$199$	17.4901	1.23984	0.619919	+	0.784666i	$0.287166\pi$
$200$	−1.06551	−0.0753430
$201$	0	0
$202$	4.85550	0.341632
$203$	13.4713	0.945498
$204$	0	0
$205$	−0.911110	−0.0636347
$206$	2.78323	0.193917
$207$	0	0
$208$	0	0
$209$	12.4967	0.864412
$210$	0	0
$211$	6.33563	0.436163	0.218081	−	0.975931i	$-0.430020\pi$
$211$	6.33563	0.436163	0.218081	+	0.975931i	$0.430020\pi$
$212$	23.0481	1.58295
$213$	0	0
$214$	−3.50034	−0.239279
$215$	−4.58553	−0.312730
$216$	0	0
$217$	16.4654	1.11774
$218$	−2.83520	−0.192024
$219$	0	0
$220$	3.37506	0.227547
$221$	0	0
$222$	0	0
$223$	23.4948	1.57333	0.786664	−	0.617381i	$-0.211806\pi$
$223$	23.4948	1.57333	0.786664	+	0.617381i	$0.211806\pi$
$224$	−10.4762	−0.699970
$225$	0	0
$226$	5.14974	0.342556
$227$	−9.59397	−0.636774	−0.318387	−	0.947961i	$-0.603141\pi$
$227$	−9.59397	−0.636774	−0.318387	+	0.947961i	$0.603141\pi$
$228$	0	0
$229$	−7.23000	−0.477772	−0.238886	−	0.971048i	$-0.576782\pi$
$229$	−7.23000	−0.477772	−0.238886	+	0.971048i	$0.576782\pi$
$230$	2.06629	0.136247
$231$	0	0
$232$	4.24478	0.278683
$233$	0.429924	0.0281652	0.0140826	−	0.999901i	$-0.495517\pi$
$233$	0.429924	0.0281652	0.0140826	+	0.999901i	$0.495517\pi$
$234$	0	0
$235$	8.58491	0.560017
$236$	−7.36440	−0.479382
$237$	0	0
$238$	1.79327	0.116240
$239$	12.7450	0.824405	0.412203	−	0.911092i	$-0.364760\pi$
$239$	12.7450	0.824405	0.412203	+	0.911092i	$0.364760\pi$
$240$	0	0
$241$	19.1338	1.23252	0.616258	−	0.787545i	$-0.288648\pi$
$241$	19.1338	1.23252	0.616258	+	0.787545i	$0.288648\pi$
$242$	−2.15209	−0.138341
$243$	0	0
$244$	−15.3815	−0.984699
$245$	−4.43464	−0.283319
$246$	0	0
$247$	0	0
$248$	5.18821	0.329452
$249$	0	0
$250$	−0.271374	−0.0171632
$251$	−0.411815	−0.0259935	−0.0129968	−	0.999916i	$-0.504137\pi$
$251$	−0.411815	−0.0259935	−0.0129968	+	0.999916i	$0.504137\pi$
$252$	0	0
$253$	−13.3404	−0.838705
$254$	−2.68250	−0.168315
$255$	0	0
$256$	10.4283	0.651771
$257$	2.47556	0.154421	0.0772105	−	0.997015i	$-0.475399\pi$
$257$	2.47556	0.154421	0.0772105	+	0.997015i	$0.475399\pi$
$258$	0	0
$259$	35.5093	2.20644
$260$	0	0
$261$	0	0
$262$	3.11278	0.192308
$263$	11.3591	0.700430	0.350215	−	0.936669i	$-0.386108\pi$
$263$	11.3591	0.700430	0.350215	+	0.936669i	$0.386108\pi$
$264$	0	0
$265$	11.9646	0.734981
$266$	−6.54527	−0.401317
$267$	0	0
$268$	0.910682	0.0556288
$269$	29.6888	1.81016	0.905078	−	0.425245i	$-0.139812\pi$
$269$	29.6888	1.81016	0.905078	+	0.425245i	$0.139812\pi$
$270$	0	0
$271$	−14.7761	−0.897583	−0.448792	−	0.893636i	$-0.648145\pi$
$271$	−14.7761	−0.897583	−0.448792	+	0.893636i	$0.648145\pi$
$272$	−6.96387	−0.422247
$273$	0	0
$274$	−3.55028	−0.214480
$275$	1.75204	0.105652
$276$	0	0
$277$	−1.94652	−0.116955	−0.0584774	−	0.998289i	$-0.518625\pi$
$277$	−1.94652	−0.116955	−0.0584774	+	0.998289i	$0.518625\pi$
$278$	3.25002	0.194924
$279$	0	0
$280$	−3.60304	−0.215323
$281$	−18.5256	−1.10515	−0.552573	−	0.833464i	$-0.686354\pi$
$281$	−18.5256	−1.10515	−0.552573	+	0.833464i	$0.686354\pi$
$282$	0	0
$283$	13.0952	0.778427	0.389214	−	0.921148i	$-0.372747\pi$
$283$	13.0952	0.778427	0.389214	+	0.921148i	$0.372747\pi$
$284$	10.6010	0.629052
$285$	0	0
$286$	0	0
$287$	−3.08093	−0.181862
$288$	0	0
$289$	−13.1811	−0.775362
$290$	1.08110	0.0634843
$291$	0	0
$292$	5.66074	0.331270
$293$	1.20753	0.0705445	0.0352722	−	0.999378i	$-0.488770\pi$
$293$	1.20753	0.0705445	0.0352722	+	0.999378i	$0.488770\pi$
$294$	0	0
$295$	−3.82297	−0.222582
$296$	11.1889	0.650342
$297$	0	0
$298$	4.42481	0.256322
$299$	0	0
$300$	0	0
$301$	−15.5060	−0.893752
$302$	−2.37565	−0.136703
$303$	0	0
$304$	25.4175	1.45779
$305$	−7.98476	−0.457206
$306$	0	0
$307$	−21.9275	−1.25147	−0.625733	−	0.780037i	$-0.715200\pi$
$307$	−21.9275	−1.25147	−0.625733	+	0.780037i	$0.715200\pi$
$308$	11.4128	0.650306
$309$	0	0
$310$	1.32138	0.0750494
$311$	12.5966	0.714288	0.357144	−	0.934049i	$-0.383751\pi$
$311$	12.5966	0.714288	0.357144	+	0.934049i	$0.383751\pi$
$312$	0	0
$313$	26.8268	1.51634	0.758169	−	0.652058i	$-0.226094\pi$
$313$	26.8268	1.51634	0.758169	+	0.652058i	$0.226094\pi$
$314$	1.76073	0.0993638
$315$	0	0
$316$	−7.89687	−0.444234
$317$	−17.1279	−0.961999	−0.481000	−	0.876721i	$-0.659726\pi$
$317$	−17.1279	−0.961999	−0.481000	+	0.876721i	$0.659726\pi$
$318$	0	0
$319$	−6.97979	−0.390793
$320$	6.28638	0.351420
$321$	0	0
$322$	6.98720	0.389382
$323$	−13.9385	−0.775557
$324$	0	0
$325$	0	0
$326$	1.04461	0.0578555
$327$	0	0
$328$	−0.970798	−0.0536033
$329$	29.0300	1.60047
$330$	0	0
$331$	−1.43062	−0.0786338	−0.0393169	−	0.999227i	$-0.512518\pi$
$331$	−1.43062	−0.0786338	−0.0393169	+	0.999227i	$0.512518\pi$
$332$	22.6796	1.24470
$333$	0	0
$334$	−1.86134	−0.101848
$335$	0.472749	0.0258290
$336$	0	0
$337$	−7.48872	−0.407937	−0.203968	−	0.978977i	$-0.565384\pi$
$337$	−7.48872	−0.407937	−0.203968	+	0.978977i	$0.565384\pi$
$338$	0	0
$339$	0	0
$340$	−3.76446	−0.204157
$341$	−8.53111	−0.461985
$342$	0	0
$343$	8.67480	0.468395
$344$	−4.88593	−0.263431
$345$	0	0
$346$	−4.34752	−0.233724
$347$	−6.96813	−0.374069	−0.187034	−	0.982353i	$-0.559888\pi$
$347$	−6.96813	−0.374069	−0.187034	+	0.982353i	$0.559888\pi$
$348$	0	0
$349$	−21.9738	−1.17623	−0.588116	−	0.808777i	$-0.700130\pi$
$349$	−21.9738	−1.17623	−0.588116	+	0.808777i	$0.700130\pi$
$350$	−0.917654	−0.0490507
$351$	0	0
$352$	5.42797	0.289312
$353$	13.0184	0.692899	0.346450	−	0.938069i	$-0.387387\pi$
$353$	13.0184	0.692899	0.346450	+	0.938069i	$0.387387\pi$
$354$	0	0
$355$	5.50312	0.292075
$356$	7.43559	0.394085
$357$	0	0
$358$	2.19354	0.115932
$359$	9.99211	0.527363	0.263682	−	0.964610i	$-0.415063\pi$
$359$	9.99211	0.527363	0.263682	+	0.964610i	$0.415063\pi$
$360$	0	0
$361$	31.8742	1.67759
$362$	3.00948	0.158175
$363$	0	0
$364$	0	0
$365$	2.93857	0.153812
$366$	0	0
$367$	25.2882	1.32004	0.660018	−	0.751250i	$-0.270549\pi$
$367$	25.2882	1.32004	0.660018	+	0.751250i	$0.270549\pi$
$368$	−27.1337	−1.41444
$369$	0	0
$370$	2.84969	0.148149
$371$	40.4586	2.10050
$372$	0	0
$373$	14.2703	0.738887	0.369444	−	0.929253i	$-0.379548\pi$
$373$	14.2703	0.738887	0.369444	+	0.929253i	$0.379548\pi$
$374$	−0.929136	−0.0480445
$375$	0	0
$376$	9.14730	0.471736
$377$	0	0
$378$	0	0
$379$	−7.01341	−0.360255	−0.180127	−	0.983643i	$-0.557651\pi$
$379$	−7.01341	−0.360255	−0.180127	+	0.983643i	$0.557651\pi$
$380$	13.7400	0.704845
$381$	0	0
$382$	−5.90325	−0.302036
$383$	4.69336	0.239820	0.119910	−	0.992785i	$-0.461739\pi$
$383$	4.69336	0.239820	0.119910	+	0.992785i	$0.461739\pi$
$384$	0	0
$385$	5.92456	0.301944
$386$	6.11365	0.311177
$387$	0	0
$388$	−13.4031	−0.680440
$389$	9.34682	0.473902	0.236951	−	0.971522i	$-0.423852\pi$
$389$	9.34682	0.473902	0.236951	+	0.971522i	$0.423852\pi$
$390$	0	0
$391$	14.8796	0.752493
$392$	−4.72515	−0.238656
$393$	0	0
$394$	4.68795	0.236176
$395$	−4.09938	−0.206262
$396$	0	0
$397$	21.2133	1.06467	0.532334	−	0.846535i	$-0.321315\pi$
$397$	21.2133	1.06467	0.532334	+	0.846535i	$0.321315\pi$
$398$	4.74634	0.237913
$399$	0	0
$400$	3.56356	0.178178
$401$	18.2172	0.909725	0.454863	−	0.890562i	$-0.349688\pi$
$401$	18.2172	0.909725	0.454863	+	0.890562i	$0.349688\pi$
$402$	0	0
$403$	0	0
$404$	−34.4669	−1.71479
$405$	0	0
$406$	3.65575	0.181432
$407$	−18.3982	−0.911965
$408$	0	0
$409$	4.36136	0.215655	0.107828	−	0.994170i	$-0.465611\pi$
$409$	4.36136	0.215655	0.107828	+	0.994170i	$0.465611\pi$
$410$	−0.247252	−0.0122109
$411$	0	0
$412$	−19.7569	−0.973351
$413$	−12.9274	−0.636117
$414$	0	0
$415$	11.7733	0.577929
$416$	0	0
$417$	0	0
$418$	3.39127	0.165872
$419$	−17.0555	−0.833214	−0.416607	−	0.909087i	$-0.636781\pi$
$419$	−17.0555	−0.833214	−0.416607	+	0.909087i	$0.636781\pi$
$420$	0	0
$421$	−1.27996	−0.0623816	−0.0311908	−	0.999513i	$-0.509930\pi$
$421$	−1.27996	−0.0623816	−0.0311908	+	0.999513i	$0.509930\pi$
$422$	1.71932	0.0836954
$423$	0	0
$424$	12.7484	0.619119
$425$	−1.95419	−0.0947921
$426$	0	0
$427$	−27.0006	−1.30665
$428$	24.8473	1.20104
$429$	0	0
$430$	−1.24439	−0.0600099
$431$	−32.8733	−1.58345	−0.791725	−	0.610878i	$-0.790817\pi$
$431$	−32.8733	−1.58345	−0.791725	+	0.610878i	$0.790817\pi$
$432$	0	0
$433$	−28.2622	−1.35819	−0.679097	−	0.734048i	$-0.737628\pi$
$433$	−28.2622	−1.35819	−0.679097	+	0.734048i	$0.737628\pi$
$434$	4.46827	0.214484
$435$	0	0
$436$	20.1257	0.963848
$437$	−54.3091	−2.59796
$438$	0	0
$439$	26.2621	1.25342	0.626711	−	0.779252i	$-0.284401\pi$
$439$	26.2621	1.25342	0.626711	+	0.779252i	$0.284401\pi$
$440$	1.86682	0.0889972
$441$	0	0
$442$	0	0
$443$	14.0477	0.667427	0.333714	−	0.942674i	$-0.391698\pi$
$443$	14.0477	0.667427	0.333714	+	0.942674i	$0.391698\pi$
$444$	0	0
$445$	3.85992	0.182978
$446$	6.37588	0.301906
$447$	0	0
$448$	21.2575	1.00432
$449$	4.45904	0.210435	0.105218	−	0.994449i	$-0.466446\pi$
$449$	4.45904	0.210435	0.105218	+	0.994449i	$0.466446\pi$
$450$	0	0
$451$	1.59631	0.0751671
$452$	−36.5556	−1.71943
$453$	0	0
$454$	−2.60355	−0.122191
$455$	0	0
$456$	0	0
$457$	16.4149	0.767855	0.383927	−	0.923363i	$-0.374571\pi$
$457$	16.4149	0.767855	0.383927	+	0.923363i	$0.374571\pi$
$458$	−1.96203	−0.0916798
$459$	0	0
$460$	−14.6677	−0.683883
$461$	−20.5455	−0.956899	−0.478449	−	0.878115i	$-0.658801\pi$
$461$	−20.5455	−0.956899	−0.478449	+	0.878115i	$0.658801\pi$
$462$	0	0
$463$	1.58359	0.0735958	0.0367979	−	0.999323i	$-0.488284\pi$
$463$	1.58359	0.0735958	0.0367979	+	0.999323i	$0.488284\pi$
$464$	−14.1965	−0.659056
$465$	0	0
$466$	0.116670	0.00540463
$467$	−5.14277	−0.237979	−0.118990	−	0.992896i	$-0.537966\pi$
$467$	−5.14277	−0.237979	−0.118990	+	0.992896i	$0.537966\pi$
$468$	0	0
$469$	1.59861	0.0738168
$470$	2.32972	0.107462
$471$	0	0
$472$	−4.07341	−0.187494
$473$	8.03405	0.369406
$474$	0	0
$475$	7.13261	0.327267
$476$	−12.7296	−0.583460
$477$	0	0
$478$	3.45866	0.158195
$479$	−22.2914	−1.01852	−0.509260	−	0.860613i	$-0.670081\pi$
$479$	−22.2914	−1.01852	−0.509260	+	0.860613i	$0.670081\pi$
$480$	0	0
$481$	0	0
$482$	5.19241	0.236508
$483$	0	0
$484$	15.2767	0.694394
$485$	−6.95775	−0.315935
$486$	0	0
$487$	−23.4185	−1.06119	−0.530597	−	0.847624i	$-0.678032\pi$
$487$	−23.4185	−1.06119	−0.530597	+	0.847624i	$0.678032\pi$
$488$	−8.50784	−0.385132
$489$	0	0
$490$	−1.20345	−0.0543661
$491$	−3.39791	−0.153345	−0.0766727	−	0.997056i	$-0.524430\pi$
$491$	−3.39791	−0.153345	−0.0766727	+	0.997056i	$0.524430\pi$
$492$	0	0
$493$	7.78509	0.350623
$494$	0	0
$495$	0	0
$496$	−17.3518	−0.779119
$497$	18.6089	0.834723
$498$	0	0
$499$	−4.87712	−0.218330	−0.109165	−	0.994024i	$-0.534818\pi$
$499$	−4.87712	−0.218330	−0.109165	+	0.994024i	$0.534818\pi$
$500$	1.92636	0.0861493
$501$	0	0
$502$	−0.111756	−0.00498791
$503$	13.9853	0.623572	0.311786	−	0.950152i	$-0.399073\pi$
$503$	13.9853	0.623572	0.311786	+	0.950152i	$0.399073\pi$
$504$	0	0
$505$	−17.8923	−0.796196
$506$	−3.62024	−0.160939
$507$	0	0
$508$	19.0418	0.844844
$509$	−37.0157	−1.64069	−0.820347	−	0.571866i	$-0.806220\pi$
$509$	−37.0157	−1.64069	−0.820347	+	0.571866i	$0.806220\pi$
$510$	0	0
$511$	9.93683	0.439579
$512$	18.6342	0.823524
$513$	0	0
$514$	0.671801	0.0296319
$515$	−10.2561	−0.451937
$516$	0	0
$517$	−15.0411	−0.661508
$518$	9.63628	0.423394
$519$	0	0
$520$	0	0
$521$	−21.5328	−0.943370	−0.471685	−	0.881767i	$-0.656354\pi$
$521$	−21.5328	−0.943370	−0.471685	+	0.881767i	$0.656354\pi$
$522$	0	0
$523$	36.0055	1.57441	0.787204	−	0.616692i	$-0.211528\pi$
$523$	36.0055	1.57441	0.787204	+	0.616692i	$0.211528\pi$
$524$	−22.0962	−0.965277
$525$	0	0
$526$	3.08255	0.134406
$527$	9.51539	0.414497
$528$	0	0
$529$	34.9760	1.52070
$530$	3.24689	0.141036
$531$	0	0
$532$	46.4619	2.01438
$533$	0	0
$534$	0	0
$535$	12.8986	0.557656
$536$	0.503718	0.0217573
$537$	0	0
$538$	8.05676	0.347351
$539$	7.76969	0.334664
$540$	0	0
$541$	0.123280	0.00530020	0.00265010	−	0.999996i	$-0.499156\pi$
$541$	0.123280	0.00530020	0.00265010	+	0.999996i	$0.499156\pi$
$542$	−4.00984	−0.172238
$543$	0	0
$544$	−6.05423	−0.259573
$545$	10.4476	0.447525
$546$	0	0
$547$	2.52166	0.107818	0.0539092	−	0.998546i	$-0.482832\pi$
$547$	2.52166	0.107818	0.0539092	+	0.998546i	$0.482832\pi$
$548$	25.2018	1.07657
$549$	0	0
$550$	0.475459	0.0202736
$551$	−28.4149	−1.21052
$552$	0	0
$553$	−13.8621	−0.589477
$554$	−0.528233	−0.0224425
$555$	0	0
$556$	−23.0704	−0.978403
$557$	0.974960	0.0413104	0.0206552	−	0.999787i	$-0.493425\pi$
$557$	0.974960	0.0413104	0.0206552	+	0.999787i	$0.493425\pi$
$558$	0	0
$559$	0	0
$560$	12.0502	0.509215
$561$	0	0
$562$	−5.02737	−0.212067
$563$	31.5376	1.32915	0.664576	−	0.747220i	$-0.268612\pi$
$563$	31.5376	1.32915	0.664576	+	0.747220i	$0.268612\pi$
$564$	0	0
$565$	−18.9766	−0.798350
$566$	3.55369	0.149373
$567$	0	0
$568$	5.86363	0.246033
$569$	−24.8762	−1.04287	−0.521433	−	0.853292i	$-0.674602\pi$
$569$	−24.8762	−1.04287	−0.521433	+	0.853292i	$0.674602\pi$
$570$	0	0
$571$	−7.92958	−0.331843	−0.165921	−	0.986139i	$-0.553060\pi$
$571$	−7.92958	−0.331843	−0.165921	+	0.986139i	$0.553060\pi$
$572$	0	0
$573$	0	0
$574$	−0.836085	−0.0348975
$575$	−7.61420	−0.317534
$576$	0	0
$577$	19.0769	0.794180	0.397090	−	0.917780i	$-0.370020\pi$
$577$	19.0769	0.794180	0.397090	+	0.917780i	$0.370020\pi$
$578$	−3.57702	−0.148784
$579$	0	0
$580$	−7.67421	−0.318654
$581$	39.8116	1.65166
$582$	0	0
$583$	−20.9626	−0.868181
$584$	3.13108	0.129565
$585$	0	0
$586$	0.327691	0.0135368
$587$	19.1196	0.789149	0.394574	−	0.918864i	$-0.370892\pi$
$587$	19.1196	0.789149	0.394574	+	0.918864i	$0.370892\pi$
$588$	0	0
$589$	−34.7303	−1.43104
$590$	−1.03745	−0.0427113
$591$	0	0
$592$	−37.4209	−1.53799
$593$	36.9354	1.51676	0.758379	−	0.651814i	$-0.225992\pi$
$593$	36.9354	1.51676	0.758379	+	0.651814i	$0.225992\pi$
$594$	0	0
$595$	−6.60812	−0.270906
$596$	−31.4096	−1.28659
$597$	0	0
$598$	0	0
$599$	5.19953	0.212447	0.106224	−	0.994342i	$-0.466124\pi$
$599$	5.19953	0.212447	0.106224	+	0.994342i	$0.466124\pi$
$600$	0	0
$601$	−28.3207	−1.15523	−0.577613	−	0.816311i	$-0.696016\pi$
$601$	−28.3207	−1.15523	−0.577613	+	0.816311i	$0.696016\pi$
$602$	−4.20793	−0.171502
$603$	0	0
$604$	16.8636	0.686170
$605$	7.93034	0.322414
$606$	0	0
$607$	20.1615	0.818332	0.409166	−	0.912460i	$-0.365820\pi$
$607$	20.1615	0.818332	0.409166	+	0.912460i	$0.365820\pi$
$608$	22.0974	0.896168
$609$	0	0
$610$	−2.16685	−0.0877333
$611$	0	0
$612$	0	0
$613$	−18.8190	−0.760094	−0.380047	−	0.924967i	$-0.624092\pi$
$613$	−18.8190	−0.760094	−0.380047	+	0.924967i	$0.624092\pi$
$614$	−5.95054	−0.240144
$615$	0	0
$616$	6.31268	0.254345
$617$	−2.82492	−0.113727	−0.0568634	−	0.998382i	$-0.518110\pi$
$617$	−2.82492	−0.113727	−0.0568634	+	0.998382i	$0.518110\pi$
$618$	0	0
$619$	−15.6686	−0.629773	−0.314886	−	0.949129i	$-0.601966\pi$
$619$	−15.6686	−0.629773	−0.314886	+	0.949129i	$0.601966\pi$
$620$	−9.37987	−0.376705
$621$	0	0
$622$	3.41839	0.137065
$623$	13.0524	0.522933
$624$	0	0
$625$	1.00000	0.0400000
$626$	7.28008	0.290971
$627$	0	0
$628$	−12.4986	−0.498749
$629$	20.5209	0.818223
$630$	0	0
$631$	−10.1149	−0.402667	−0.201333	−	0.979523i	$-0.564527\pi$
$631$	−10.1149	−0.402667	−0.201333	+	0.979523i	$0.564527\pi$
$632$	−4.36793	−0.173747
$633$	0	0
$634$	−4.64807	−0.184598
$635$	9.88489	0.392270
$636$	0	0
$637$	0	0
$638$	−1.89413	−0.0749894
$639$	0	0
$640$	7.90212	0.312359
$641$	17.6173	0.695843	0.347922	−	0.937524i	$-0.386888\pi$
$641$	17.6173	0.695843	0.347922	+	0.937524i	$0.386888\pi$
$642$	0	0
$643$	19.0312	0.750519	0.375260	−	0.926920i	$-0.377554\pi$
$643$	19.0312	0.750519	0.375260	+	0.926920i	$0.377554\pi$
$644$	−49.5989	−1.95447
$645$	0	0
$646$	−3.78254	−0.148822
$647$	26.6972	1.04957	0.524787	−	0.851233i	$-0.324145\pi$
$647$	26.6972	1.04957	0.524787	+	0.851233i	$0.324145\pi$
$648$	0	0
$649$	6.69802	0.262920
$650$	0	0
$651$	0	0
$652$	−7.41518	−0.290401
$653$	3.16076	0.123690	0.0618451	−	0.998086i	$-0.480302\pi$
$653$	3.16076	0.123690	0.0618451	+	0.998086i	$0.480302\pi$
$654$	0	0
$655$	−11.4705	−0.448188
$656$	3.24680	0.126766
$657$	0	0
$658$	7.87798	0.307116
$659$	18.0060	0.701413	0.350706	−	0.936486i	$-0.385942\pi$
$659$	18.0060	0.701413	0.350706	+	0.936486i	$0.385942\pi$
$660$	0	0
$661$	3.51786	0.136829	0.0684145	−	0.997657i	$-0.478206\pi$
$661$	3.51786	0.136829	0.0684145	+	0.997657i	$0.478206\pi$
$662$	−0.388232	−0.0150891
$663$	0	0
$664$	12.5446	0.486824
$665$	24.1190	0.935296
$666$	0	0
$667$	30.3334	1.17452
$668$	13.2128	0.511217
$669$	0	0
$670$	0.128292	0.00495634
$671$	13.9896	0.540064
$672$	0	0
$673$	−26.0032	−1.00235	−0.501175	−	0.865346i	$-0.667099\pi$
$673$	−26.0032	−1.00235	−0.501175	+	0.865346i	$0.667099\pi$
$674$	−2.03224	−0.0782791
$675$	0	0
$676$	0	0
$677$	28.5157	1.09595	0.547975	−	0.836495i	$-0.315399\pi$
$677$	28.5157	1.09595	0.547975	+	0.836495i	$0.315399\pi$
$678$	0	0
$679$	−23.5277	−0.902912
$680$	−2.08221	−0.0798490
$681$	0	0
$682$	−2.31512	−0.0886505
$683$	−28.9493	−1.10771	−0.553857	−	0.832612i	$-0.686845\pi$
$683$	−28.9493	−1.10771	−0.553857	+	0.832612i	$0.686845\pi$
$684$	0	0
$685$	13.0826	0.499861
$686$	2.35411	0.0898805
$687$	0	0
$688$	16.3408	0.622987
$689$	0	0
$690$	0	0
$691$	21.6566	0.823854	0.411927	−	0.911217i	$-0.364856\pi$
$691$	21.6566	0.823854	0.411927	+	0.911217i	$0.364856\pi$
$692$	30.8611	1.17316
$693$	0	0
$694$	−1.89097	−0.0717801
$695$	−11.9762	−0.454283
$696$	0	0
$697$	−1.78048	−0.0674405
$698$	−5.96312	−0.225707
$699$	0	0
$700$	6.51400	0.246206
$701$	−25.0376	−0.945656	−0.472828	−	0.881155i	$-0.656767\pi$
$701$	−25.0376	−0.945656	−0.472828	+	0.881155i	$0.656767\pi$
$702$	0	0
$703$	−74.8995	−2.82489
$704$	−11.0140	−0.415107
$705$	0	0
$706$	3.53285	0.132961
$707$	−60.5030	−2.27545
$708$	0	0
$709$	25.6247	0.962355	0.481178	−	0.876623i	$-0.340209\pi$
$709$	25.6247	0.962355	0.481178	+	0.876623i	$0.340209\pi$
$710$	1.49340	0.0560464
$711$	0	0
$712$	4.11279	0.154133
$713$	37.0753	1.38848
$714$	0	0
$715$	0	0
$716$	−15.5709	−0.581912
$717$	0	0
$718$	2.71160	0.101196
$719$	−14.8064	−0.552186	−0.276093	−	0.961131i	$-0.589040\pi$
$719$	−14.8064	−0.552186	−0.276093	+	0.961131i	$0.589040\pi$
$720$	0	0
$721$	−34.6811	−1.29159
$722$	8.64982	0.321913
$723$	0	0
$724$	−21.3629	−0.793945
$725$	−3.98380	−0.147955
$726$	0	0
$727$	−30.1688	−1.11890	−0.559449	−	0.828865i	$-0.688987\pi$
$727$	−30.1688	−1.11890	−0.559449	+	0.828865i	$0.688987\pi$
$728$	0	0
$729$	0	0
$730$	0.797452	0.0295150
$731$	−8.96098	−0.331434
$732$	0	0
$733$	−49.8997	−1.84309	−0.921544	−	0.388275i	$-0.873071\pi$
$733$	−49.8997	−1.84309	−0.921544	+	0.388275i	$0.873071\pi$
$734$	6.86257	0.253302
$735$	0	0
$736$	−23.5894	−0.869516
$737$	−0.828276	−0.0305100
$738$	0	0
$739$	31.5796	1.16167	0.580836	−	0.814020i	$-0.302726\pi$
$739$	31.5796	1.16167	0.580836	+	0.814020i	$0.302726\pi$
$740$	−20.2287	−0.743620
$741$	0	0
$742$	10.9794	0.403066
$743$	1.60448	0.0588625	0.0294312	−	0.999567i	$-0.490630\pi$
$743$	1.60448	0.0588625	0.0294312	+	0.999567i	$0.490630\pi$
$744$	0	0
$745$	−16.3052	−0.597377
$746$	3.87258	0.141785
$747$	0	0
$748$	6.59551	0.241156
$749$	43.6168	1.59372
$750$	0	0
$751$	10.7873	0.393634	0.196817	−	0.980440i	$-0.436940\pi$
$751$	10.7873	0.393634	0.196817	+	0.980440i	$0.436940\pi$
$752$	−30.5928	−1.11561
$753$	0	0
$754$	0	0
$755$	8.75415	0.318596
$756$	0	0
$757$	−6.40389	−0.232753	−0.116377	−	0.993205i	$-0.537128\pi$
$757$	−6.40389	−0.232753	−0.116377	+	0.993205i	$0.537128\pi$
$758$	−1.90326	−0.0691294
$759$	0	0
$760$	7.59987	0.275676
$761$	−50.2655	−1.82212	−0.911062	−	0.412269i	$-0.864736\pi$
$761$	−50.2655	−1.82212	−0.911062	+	0.412269i	$0.864736\pi$
$762$	0	0
$763$	35.3286	1.27898
$764$	41.9044	1.51605
$765$	0	0
$766$	1.27366	0.0460191
$767$	0	0
$768$	0	0
$769$	4.10457	0.148015	0.0740074	−	0.997258i	$-0.476421\pi$
$769$	4.10457	0.148015	0.0740074	+	0.997258i	$0.476421\pi$
$770$	1.60777	0.0579401
$771$	0	0
$772$	−43.3980	−1.56193
$773$	1.17851	0.0423882	0.0211941	−	0.999775i	$-0.493253\pi$
$773$	1.17851	0.0423882	0.0211941	+	0.999775i	$0.493253\pi$
$774$	0	0
$775$	−4.86923	−0.174908
$776$	−7.41356	−0.266131
$777$	0	0
$778$	2.53648	0.0909373
$779$	6.49860	0.232836
$780$	0	0
$781$	−9.64172	−0.345008
$782$	4.03793	0.144396
$783$	0	0
$784$	15.8031	0.564397
$785$	−6.48821	−0.231574
$786$	0	0
$787$	33.4916	1.19385	0.596923	−	0.802298i	$-0.296390\pi$
$787$	33.4916	1.19385	0.596923	+	0.802298i	$0.296390\pi$
$788$	−33.2776	−1.18546
$789$	0	0
$790$	−1.11246	−0.0395797
$791$	−64.1695	−2.28161
$792$	0	0
$793$	0	0
$794$	5.75675	0.204299
$795$	0	0
$796$	−33.6921	−1.19418
$797$	24.9394	0.883400	0.441700	−	0.897163i	$-0.354376\pi$
$797$	24.9394	0.883400	0.441700	+	0.897163i	$0.354376\pi$
$798$	0	0
$799$	16.7765	0.593511
$800$	3.09808	0.109534
$801$	0	0
$802$	4.94368	0.174567
$803$	−5.14851	−0.181687
$804$	0	0
$805$	−25.7475	−0.907481
$806$	0	0
$807$	0	0
$808$	−19.0644	−0.670684
$809$	−12.8221	−0.450802	−0.225401	−	0.974266i	$-0.572369\pi$
$809$	−12.8221	−0.450802	−0.225401	+	0.974266i	$0.572369\pi$
$810$	0	0
$811$	29.8424	1.04791	0.523954	−	0.851746i	$-0.324456\pi$
$811$	29.8424	1.04791	0.523954	+	0.851746i	$0.324456\pi$
$812$	−25.9505	−0.910683
$813$	0	0
$814$	−4.99279	−0.174997
$815$	−3.84933	−0.134836
$816$	0	0
$817$	32.7068	1.14427
$818$	1.18356	0.0413822
$819$	0	0
$820$	1.75512	0.0612916
$821$	−19.6918	−0.687249	−0.343624	−	0.939107i	$-0.611655\pi$
$821$	−19.6918	−0.687249	−0.343624	+	0.939107i	$0.611655\pi$
$822$	0	0
$823$	41.9069	1.46078	0.730390	−	0.683030i	$-0.239338\pi$
$823$	41.9069	1.46078	0.730390	+	0.683030i	$0.239338\pi$
$824$	−10.9280	−0.380693
$825$	0	0
$826$	−3.50817	−0.122065
$827$	−21.7734	−0.757134	−0.378567	−	0.925574i	$-0.623583\pi$
$827$	−21.7734	−0.757134	−0.378567	+	0.925574i	$0.623583\pi$
$828$	0	0
$829$	−5.87683	−0.204111	−0.102055	−	0.994779i	$-0.532542\pi$
$829$	−5.87683	−0.204111	−0.102055	+	0.994779i	$0.532542\pi$
$830$	3.19497	0.110899
$831$	0	0
$832$	0	0
$833$	−8.66612	−0.300263
$834$	0	0
$835$	6.85894	0.237363
$836$	−24.0730	−0.832583
$837$	0	0
$838$	−4.62841	−0.159886
$839$	54.1116	1.86814	0.934069	−	0.357092i	$-0.116232\pi$
$839$	54.1116	1.86814	0.934069	+	0.357092i	$0.116232\pi$
$840$	0	0
$841$	−13.1294	−0.452736
$842$	−0.347348	−0.0119704
$843$	0	0
$844$	−12.2047	−0.420103
$845$	0	0
$846$	0	0
$847$	26.8166	0.921428
$848$	−42.6367	−1.46415
$849$	0	0
$850$	−0.530316	−0.0181897
$851$	79.9567	2.74088
$852$	0	0
$853$	10.8001	0.369787	0.184893	−	0.982759i	$-0.440806\pi$
$853$	10.8001	0.369787	0.184893	+	0.982759i	$0.440806\pi$
$854$	−7.32725	−0.250733
$855$	0	0
$856$	13.7436	0.469747
$857$	12.0558	0.411817	0.205908	−	0.978571i	$-0.433985\pi$
$857$	12.0558	0.411817	0.205908	+	0.978571i	$0.433985\pi$
$858$	0	0
$859$	−47.6819	−1.62688	−0.813442	−	0.581646i	$-0.802409\pi$
$859$	−47.6819	−1.62688	−0.813442	+	0.581646i	$0.802409\pi$
$860$	8.83336	0.301215
$861$	0	0
$862$	−8.92095	−0.303849
$863$	46.2292	1.57366	0.786831	−	0.617169i	$-0.211721\pi$
$863$	46.2292	1.57366	0.786831	+	0.617169i	$0.211721\pi$
$864$	0	0
$865$	16.0204	0.544711
$866$	−7.66962	−0.260624
$867$	0	0
$868$	−31.7182	−1.07658
$869$	7.18230	0.243643
$870$	0	0
$871$	0	0
$872$	11.1320	0.376977
$873$	0	0
$874$	−14.7381	−0.498523
$875$	3.38151	0.114316
$876$	0	0
$877$	−25.2281	−0.851893	−0.425947	−	0.904748i	$-0.640059\pi$
$877$	−25.2281	−0.851893	−0.425947	+	0.904748i	$0.640059\pi$
$878$	7.12684	0.240519
$879$	0	0
$880$	−6.24352	−0.210469
$881$	12.5086	0.421425	0.210712	−	0.977548i	$-0.432422\pi$
$881$	12.5086	0.421425	0.210712	+	0.977548i	$0.432422\pi$
$882$	0	0
$883$	−11.2289	−0.377881	−0.188941	−	0.981989i	$-0.560505\pi$
$883$	−11.2289	−0.377881	−0.188941	+	0.981989i	$0.560505\pi$
$884$	0	0
$885$	0	0
$886$	3.81218	0.128073
$887$	54.5383	1.83122	0.915609	−	0.402069i	$-0.131709\pi$
$887$	54.5383	1.83122	0.915609	+	0.402069i	$0.131709\pi$
$888$	0	0
$889$	33.4259	1.12107
$890$	1.04748	0.0351117
$891$	0	0
$892$	−45.2594	−1.51540
$893$	−61.2328	−2.04908
$894$	0	0
$895$	−8.08309	−0.270188
$896$	26.7211	0.892690
$897$	0	0
$898$	1.21007	0.0403805
$899$	19.3980	0.646960
$900$	0	0
$901$	23.3811	0.778939
$902$	0.433196	0.0144238
$903$	0	0
$904$	−20.2197	−0.672498
$905$	−11.0898	−0.368637
$906$	0	0
$907$	28.9083	0.959883	0.479942	−	0.877300i	$-0.340658\pi$
$907$	28.9083	0.959883	0.479942	+	0.877300i	$0.340658\pi$
$908$	18.4814	0.613327
$909$	0	0
$910$	0	0
$911$	7.04371	0.233369	0.116684	−	0.993169i	$-0.462773\pi$
$911$	7.04371	0.233369	0.116684	+	0.993169i	$0.462773\pi$
$912$	0	0
$913$	−20.6274	−0.682666
$914$	4.45456	0.147344
$915$	0	0
$916$	13.9276	0.460180
$917$	−38.7875	−1.28088
$918$	0	0
$919$	−17.3638	−0.572780	−0.286390	−	0.958113i	$-0.592455\pi$
$919$	−17.3638	−0.572780	−0.286390	+	0.958113i	$0.592455\pi$
$920$	−8.11301	−0.267478
$921$	0	0
$922$	−5.57551	−0.183620
$923$	0	0
$924$	0	0
$925$	−10.5010	−0.345271
$926$	0.429745	0.0141223
$927$	0	0
$928$	−12.3421	−0.405150
$929$	30.9381	1.01504	0.507522	−	0.861639i	$-0.330561\pi$
$929$	30.9381	1.01504	0.507522	+	0.861639i	$0.330561\pi$
$930$	0	0
$931$	31.6306	1.03665
$932$	−0.828186	−0.0271281
$933$	0	0
$934$	−1.39561	−0.0456659
$935$	3.42382	0.111971
$936$	0	0
$937$	30.5009	0.996422	0.498211	−	0.867056i	$-0.333990\pi$
$937$	30.5009	0.996422	0.498211	+	0.867056i	$0.333990\pi$
$938$	0.433820	0.0141647
$939$	0	0
$940$	−16.5376	−0.539397
$941$	−32.0423	−1.04455	−0.522275	−	0.852777i	$-0.674917\pi$
$941$	−32.0423	−1.04455	−0.522275	+	0.852777i	$0.674917\pi$
$942$	0	0
$943$	−6.93738	−0.225912
$944$	13.6234	0.443404
$945$	0	0
$946$	2.18023	0.0708854
$947$	−8.63395	−0.280566	−0.140283	−	0.990111i	$-0.544801\pi$
$947$	−8.63395	−0.280566	−0.140283	+	0.990111i	$0.544801\pi$
$948$	0	0
$949$	0	0
$950$	1.93560	0.0627993
$951$	0	0
$952$	−7.04102	−0.228201
$953$	32.4260	1.05038	0.525191	−	0.850984i	$-0.323994\pi$
$953$	32.4260	1.05038	0.525191	+	0.850984i	$0.323994\pi$
$954$	0	0
$955$	21.7532	0.703917
$956$	−24.5514	−0.794049
$957$	0	0
$958$	−6.04930	−0.195444
$959$	44.2390	1.42855
$960$	0	0
$961$	−7.29060	−0.235181
$962$	0	0
$963$	0	0
$964$	−36.8585	−1.18713
$965$	−22.5285	−0.725219
$966$	0	0
$967$	27.0744	0.870656	0.435328	−	0.900272i	$-0.356632\pi$
$967$	27.0744	0.870656	0.435328	+	0.900272i	$0.356632\pi$
$968$	8.44986	0.271589
$969$	0	0
$970$	−1.88815	−0.0606249
$971$	−31.8039	−1.02063	−0.510317	−	0.859986i	$-0.670472\pi$
$971$	−31.8039	−1.02063	−0.510317	+	0.859986i	$0.670472\pi$
$972$	0	0
$973$	−40.4977	−1.29830
$974$	−6.35517	−0.203633
$975$	0	0
$976$	28.4542	0.910796
$977$	−31.3672	−1.00353	−0.501763	−	0.865005i	$-0.667315\pi$
$977$	−31.3672	−1.00353	−0.501763	+	0.865005i	$0.667315\pi$
$978$	0	0
$979$	−6.76276	−0.216139
$980$	8.54270	0.272886
$981$	0	0
$982$	−0.922103	−0.0294255
$983$	35.5044	1.13241	0.566207	−	0.824263i	$-0.308410\pi$
$983$	35.5044	1.13241	0.566207	+	0.824263i	$0.308410\pi$
$984$	0	0
$985$	−17.2749	−0.550424
$986$	2.11267	0.0672811
$987$	0	0
$988$	0	0
$989$	−34.9151	−1.11024
$990$	0	0
$991$	−41.0638	−1.30443	−0.652217	−	0.758032i	$-0.726161\pi$
$991$	−41.0638	−1.30443	−0.652217	+	0.758032i	$0.726161\pi$
$992$	−15.0853	−0.478957
$993$	0	0
$994$	5.04997	0.160175
$995$	−17.4901	−0.554472
$996$	0	0
$997$	−44.7904	−1.41853	−0.709264	−	0.704943i	$-0.750972\pi$
$997$	−44.7904	−1.41853	−0.709264	+	0.704943i	$0.750972\pi$
$998$	−1.32352	−0.0418954
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7605.2.a.cp.1.6		9
3.2	odd	2		845.2.a.o.1.4	yes	9
13.12	even	2		7605.2.a.cs.1.4		9
15.14	odd	2		4225.2.a.bs.1.6		9
39.2	even	12		845.2.m.j.316.8		36
39.5	even	4		845.2.c.h.506.11		18
39.8	even	4		845.2.c.h.506.8		18
39.11	even	12		845.2.m.j.316.11		36
39.17	odd	6		845.2.e.p.146.4		18
39.20	even	12		845.2.m.j.361.8		36
39.23	odd	6		845.2.e.p.191.4		18
39.29	odd	6		845.2.e.o.191.6		18
39.32	even	12		845.2.m.j.361.11		36
39.35	odd	6		845.2.e.o.146.6		18
39.38	odd	2		845.2.a.n.1.6	✓	9
195.194	odd	2		4225.2.a.bt.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.6	✓	9	39.38	odd	2
845.2.a.o.1.4	yes	9	3.2	odd	2
845.2.c.h.506.8		18	39.8	even	4
845.2.c.h.506.11		18	39.5	even	4
845.2.e.o.146.6		18	39.35	odd	6
845.2.e.o.191.6		18	39.29	odd	6
845.2.e.p.146.4		18	39.17	odd	6
845.2.e.p.191.4		18	39.23	odd	6
845.2.m.j.316.8		36	39.2	even	12
845.2.m.j.316.11		36	39.11	even	12
845.2.m.j.361.8		36	39.20	even	12
845.2.m.j.361.11		36	39.32	even	12
4225.2.a.bs.1.6		9	15.14	odd	2
4225.2.a.bt.1.4		9	195.194	odd	2
7605.2.a.cp.1.6		9	1.1	even	1	trivial
7605.2.a.cs.1.4		9	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7605.a (trivial)

\(f(q)\)	\(=\)	\(q+0.271374 q^{2} -1.92636 q^{4} -1.00000 q^{5} -3.38151 q^{7} -1.06551 q^{8} +O(q^{10})\)	\(q+0.271374 q^{2} -1.92636 q^{4} -1.00000 q^{5} -3.38151 q^{7} -1.06551 q^{8} -0.271374 q^{10} +1.75204 q^{11} -0.917654 q^{14} +3.56356 q^{16} -1.95419 q^{17} +7.13261 q^{19} +1.92636 q^{20} +0.475459 q^{22} -7.61420 q^{23} +1.00000 q^{25} +6.51400 q^{28} -3.98380 q^{29} -4.86923 q^{31} +3.09808 q^{32} -0.530316 q^{34} +3.38151 q^{35} -10.5010 q^{37} +1.93560 q^{38} +1.06551 q^{40} +0.911110 q^{41} +4.58553 q^{43} -3.37506 q^{44} -2.06629 q^{46} -8.58491 q^{47} +4.43464 q^{49} +0.271374 q^{50} -11.9646 q^{53} -1.75204 q^{55} +3.60304 q^{56} -1.08110 q^{58} +3.82297 q^{59} +7.98476 q^{61} -1.32138 q^{62} -6.28638 q^{64} -0.472749 q^{67} +3.76446 q^{68} +0.917654 q^{70} -5.50312 q^{71} -2.93857 q^{73} -2.84969 q^{74} -13.7400 q^{76} -5.92456 q^{77} +4.09938 q^{79} -3.56356 q^{80} +0.247252 q^{82} -11.7733 q^{83} +1.95419 q^{85} +1.24439 q^{86} -1.86682 q^{88} -3.85992 q^{89} +14.6677 q^{92} -2.32972 q^{94} -7.13261 q^{95} +6.95775 q^{97} +1.20345 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 3 q^{2} + 17 q^{4} - 9 q^{5} + 7 q^{7} - 12 q^{8}+O(q^{10}) \) 9 * q - 3 * q^2 + 17 * q^4 - 9 * q^5 + 7 * q^7 - 12 * q^8	\( 9 q - 3 q^{2} + 17 q^{4} - 9 q^{5} + 7 q^{7} - 12 q^{8} + 3 q^{10} + 9 q^{11} + 2 q^{14} + 37 q^{16} + q^{17} - 4 q^{19} - 17 q^{20} + 12 q^{22} - 14 q^{23} + 9 q^{25} + 18 q^{28} - 12 q^{29} - 7 q^{31} - 22 q^{32} - 30 q^{34} - 7 q^{35} - 5 q^{37} + 47 q^{38} + 12 q^{40} + 10 q^{41} + 39 q^{43} + 25 q^{44} + 6 q^{46} - 36 q^{47} + 16 q^{49} - 3 q^{50} + 8 q^{53} - 9 q^{55} + 29 q^{56} + 21 q^{58} + 21 q^{59} - 3 q^{61} + 10 q^{62} + 34 q^{64} + q^{67} + 20 q^{68} - 2 q^{70} + q^{71} + 15 q^{74} - 5 q^{76} + 4 q^{77} + 39 q^{79} - 37 q^{80} - 4 q^{82} - 7 q^{83} - q^{85} + 24 q^{86} + 42 q^{88} + 19 q^{89} + 27 q^{92} + 16 q^{94} + 4 q^{95} - 34 q^{97} - 48 q^{98}+O(q^{100}) \) 9 * q - 3 * q^2 + 17 * q^4 - 9 * q^5 + 7 * q^7 - 12 * q^8 + 3 * q^10 + 9 * q^11 + 2 * q^14 + 37 * q^16 + q^17 - 4 * q^19 - 17 * q^20 + 12 * q^22 - 14 * q^23 + 9 * q^25 + 18 * q^28 - 12 * q^29 - 7 * q^31 - 22 * q^32 - 30 * q^34 - 7 * q^35 - 5 * q^37 + 47 * q^38 + 12 * q^40 + 10 * q^41 + 39 * q^43 + 25 * q^44 + 6 * q^46 - 36 * q^47 + 16 * q^49 - 3 * q^50 + 8 * q^53 - 9 * q^55 + 29 * q^56 + 21 * q^58 + 21 * q^59 - 3 * q^61 + 10 * q^62 + 34 * q^64 + q^67 + 20 * q^68 - 2 * q^70 + q^71 + 15 * q^74 - 5 * q^76 + 4 * q^77 + 39 * q^79 - 37 * q^80 - 4 * q^82 - 7 * q^83 - q^85 + 24 * q^86 + 42 * q^88 + 19 * q^89 + 27 * q^92 + 16 * q^94 + 4 * q^95 - 34 * q^97 - 48 * q^98

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