LMFDB - Embedded newform 7605.2.a.cs.1.9

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			1.9
Root			$0.987478$ 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)

$f(q)$	$=$	$q+2.78942 q^{2} +5.78084 q^{4} +1.00000 q^{5} -0.269601 q^{7} +10.5463 q^{8} +O(q^{10})$	$q+2.78942 q^{2} +5.78084 q^{4} +1.00000 q^{5} -0.269601 q^{7} +10.5463 q^{8} +2.78942 q^{10} +1.81080 q^{11} -0.752028 q^{14} +17.8564 q^{16} +0.737366 q^{17} +2.17965 q^{19} +5.78084 q^{20} +5.05108 q^{22} +2.75116 q^{23} +1.00000 q^{25} -1.55852 q^{28} +7.21253 q^{29} -6.19428 q^{31} +28.7163 q^{32} +2.05682 q^{34} -0.269601 q^{35} -7.66406 q^{37} +6.07995 q^{38} +10.5463 q^{40} -8.37897 q^{41} -1.16916 q^{43} +10.4679 q^{44} +7.67414 q^{46} -0.121132 q^{47} -6.92732 q^{49} +2.78942 q^{50} -3.85022 q^{53} +1.81080 q^{55} -2.84330 q^{56} +20.1187 q^{58} -10.6308 q^{59} -4.24380 q^{61} -17.2784 q^{62} +44.3888 q^{64} +9.55095 q^{67} +4.26259 q^{68} -0.752028 q^{70} +8.12097 q^{71} +0.692889 q^{73} -21.3782 q^{74} +12.6002 q^{76} -0.488193 q^{77} +6.65811 q^{79} +17.8564 q^{80} -23.3724 q^{82} -9.19337 q^{83} +0.737366 q^{85} -3.26128 q^{86} +19.0973 q^{88} -6.57163 q^{89} +15.9040 q^{92} -0.337889 q^{94} +2.17965 q^{95} +17.4402 q^{97} -19.3232 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.78942	1.97241	0.986207	−	0.165515i	$-0.0529287\pi$
$2$	2.78942	1.97241	0.986207	+	0.165515i	$0.0529287\pi$
$3$	0	0
$3$	0	0
$4$	5.78084	2.89042
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−0.269601	−0.101899	−0.0509497	−	0.998701i	$-0.516225\pi$
$7$	−0.269601	−0.101899	−0.0509497	+	0.998701i	$0.516225\pi$
$8$	10.5463	3.72869
$9$	0	0
$10$	2.78942	0.882091
$11$	1.81080	0.545977	0.272989	−	0.962017i	$-0.411988\pi$
$11$	1.81080	0.545977	0.272989	+	0.962017i	$0.411988\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	−0.752028	−0.200988
$15$	0	0
$16$	17.8564	4.46410
$17$	0.737366	0.178838	0.0894188	−	0.995994i	$-0.471499\pi$
$17$	0.737366	0.178838	0.0894188	+	0.995994i	$0.471499\pi$
$18$	0	0
$19$	2.17965	0.500046	0.250023	−	0.968240i	$-0.419562\pi$
$19$	2.17965	0.500046	0.250023	+	0.968240i	$0.419562\pi$
$20$	5.78084	1.29263
$21$	0	0
$22$	5.05108	1.07689
$23$	2.75116	0.573657	0.286829	−	0.957982i	$-0.407399\pi$
$23$	2.75116	0.573657	0.286829	+	0.957982i	$0.407399\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	−1.55852	−0.294532
$29$	7.21253	1.33933	0.669667	−	0.742662i	$-0.266437\pi$
$29$	7.21253	1.33933	0.669667	+	0.742662i	$0.266437\pi$
$30$	0	0
$31$	−6.19428	−1.11253	−0.556263	−	0.831007i	$-0.687765\pi$
$31$	−6.19428	−1.11253	−0.556263	+	0.831007i	$0.687765\pi$
$32$	28.7163	5.07637
$33$	0	0
$34$	2.05682	0.352742
$35$	−0.269601	−0.0455708
$36$	0	0
$37$	−7.66406	−1.25996	−0.629982	−	0.776610i	$-0.716938\pi$
$37$	−7.66406	−1.25996	−0.629982	+	0.776610i	$0.716938\pi$
$38$	6.07995	0.986299
$39$	0	0
$40$	10.5463	1.66752
$41$	−8.37897	−1.30857	−0.654287	−	0.756246i	$-0.727031\pi$
$41$	−8.37897	−1.30857	−0.654287	+	0.756246i	$0.727031\pi$
$42$	0	0
$43$	−1.16916	−0.178296	−0.0891478	−	0.996018i	$-0.528414\pi$
$43$	−1.16916	−0.178296	−0.0891478	+	0.996018i	$0.528414\pi$
$44$	10.4679	1.57810
$45$	0	0
$46$	7.67414	1.13149
$47$	−0.121132	−0.0176690	−0.00883449	−	0.999961i	$-0.502812\pi$
$47$	−0.121132	−0.0176690	−0.00883449	+	0.999961i	$0.502812\pi$
$48$	0	0
$49$	−6.92732	−0.989617
$50$	2.78942	0.394483
$51$	0	0
$52$	0	0
$53$	−3.85022	−0.528868	−0.264434	−	0.964404i	$-0.585185\pi$
$53$	−3.85022	−0.528868	−0.264434	+	0.964404i	$0.585185\pi$
$54$	0	0
$55$	1.81080	0.244168
$56$	−2.84330	−0.379951
$57$	0	0
$58$	20.1187	2.64172
$59$	−10.6308	−1.38401	−0.692003	−	0.721894i	$-0.743272\pi$
$59$	−10.6308	−1.38401	−0.692003	+	0.721894i	$0.743272\pi$
$60$	0	0
$61$	−4.24380	−0.543363	−0.271681	−	0.962387i	$-0.587580\pi$
$61$	−4.24380	−0.543363	−0.271681	+	0.962387i	$0.587580\pi$
$62$	−17.2784	−2.19436
$63$	0	0
$64$	44.3888	5.54860
$65$	0	0
$66$	0	0
$67$	9.55095	1.16683	0.583417	−	0.812173i	$-0.301715\pi$
$67$	9.55095	1.16683	0.583417	+	0.812173i	$0.301715\pi$
$68$	4.26259	0.516915
$69$	0	0
$70$	−0.752028	−0.0898845
$71$	8.12097	0.963781	0.481891	−	0.876231i	$-0.339950\pi$
$71$	8.12097	0.963781	0.481891	+	0.876231i	$0.339950\pi$
$72$	0	0
$73$	0.692889	0.0810966	0.0405483	−	0.999178i	$-0.487090\pi$
$73$	0.692889	0.0810966	0.0405483	+	0.999178i	$0.487090\pi$
$74$	−21.3782	−2.48517
$75$	0	0
$76$	12.6002	1.44534
$77$	−0.488193	−0.0556348
$78$	0	0
$79$	6.65811	0.749096	0.374548	−	0.927207i	$-0.377798\pi$
$79$	6.65811	0.749096	0.374548	+	0.927207i	$0.377798\pi$
$80$	17.8564	1.99641
$81$	0	0
$82$	−23.3724	−2.58105
$83$	−9.19337	−1.00910	−0.504552	−	0.863381i	$-0.668342\pi$
$83$	−9.19337	−1.00910	−0.504552	+	0.863381i	$0.668342\pi$
$84$	0	0
$85$	0.737366	0.0799786
$86$	−3.26128	−0.351673
$87$	0	0
$88$	19.0973	2.03578
$89$	−6.57163	−0.696591	−0.348296	−	0.937385i	$-0.613239\pi$
$89$	−6.57163	−0.696591	−0.348296	+	0.937385i	$0.613239\pi$
$90$	0	0
$91$	0	0
$92$	15.9040	1.65811
$93$	0	0
$94$	−0.337889	−0.0348506
$95$	2.17965	0.223627
$96$	0	0
$97$	17.4402	1.77079	0.885394	−	0.464840i	$-0.153888\pi$
$97$	17.4402	1.77079	0.885394	+	0.464840i	$0.153888\pi$
$98$	−19.3232	−1.95193
$99$	0	0
$100$	5.78084	0.578084
$101$	11.8007	1.17421	0.587107	−	0.809509i	$-0.300267\pi$
$101$	11.8007	1.17421	0.587107	+	0.809509i	$0.300267\pi$
$102$	0	0
$103$	−8.03859	−0.792066	−0.396033	−	0.918236i	$-0.629613\pi$
$103$	−8.03859	−0.792066	−0.396033	+	0.918236i	$0.629613\pi$
$104$	0	0
$105$	0	0
$106$	−10.7399	−1.04315
$107$	−17.2977	−1.67223	−0.836115	−	0.548554i	$-0.815179\pi$
$107$	−17.2977	−1.67223	−0.836115	+	0.548554i	$0.815179\pi$
$108$	0	0
$109$	15.1297	1.44916	0.724581	−	0.689189i	$-0.242033\pi$
$109$	15.1297	1.44916	0.724581	+	0.689189i	$0.242033\pi$
$110$	5.05108	0.481601
$111$	0	0
$112$	−4.81410	−0.454889
$113$	−12.4686	−1.17294	−0.586472	−	0.809969i	$-0.699484\pi$
$113$	−12.4686	−1.17294	−0.586472	+	0.809969i	$0.699484\pi$
$114$	0	0
$115$	2.75116	0.256547
$116$	41.6945	3.87123
$117$	0	0
$118$	−29.6536	−2.72984
$119$	−0.198794	−0.0182234
$120$	0	0
$121$	−7.72100	−0.701909
$122$	−11.8377	−1.07174
$123$	0	0
$124$	−35.8081	−3.21566
$125$	1.00000	0.0894427
$126$	0	0
$127$	11.8876	1.05485	0.527425	−	0.849601i	$-0.323157\pi$
$127$	11.8876	1.05485	0.527425	+	0.849601i	$0.323157\pi$
$128$	66.3863	5.86778
$129$	0	0
$130$	0	0
$131$	−13.7794	−1.20391	−0.601955	−	0.798530i	$-0.705611\pi$
$131$	−13.7794	−1.20391	−0.601955	+	0.798530i	$0.705611\pi$
$132$	0	0
$133$	−0.587635	−0.0509544
$134$	26.6416	2.30148
$135$	0	0
$136$	7.77650	0.666830
$137$	14.1604	1.20981	0.604903	−	0.796299i	$-0.293212\pi$
$137$	14.1604	1.20981	0.604903	+	0.796299i	$0.293212\pi$
$138$	0	0
$139$	4.53645	0.384777	0.192388	−	0.981319i	$-0.438377\pi$
$139$	4.53645	0.384777	0.192388	+	0.981319i	$0.438377\pi$
$140$	−1.55852	−0.131719
$141$	0	0
$142$	22.6527	1.90098
$143$	0	0
$144$	0	0
$145$	7.21253	0.598968
$146$	1.93276	0.159956
$147$	0	0
$148$	−44.3047	−3.64182
$149$	−3.51921	−0.288305	−0.144152	−	0.989556i	$-0.546046\pi$
$149$	−3.51921	−0.288305	−0.144152	+	0.989556i	$0.546046\pi$
$150$	0	0
$151$	4.49258	0.365601	0.182801	−	0.983150i	$-0.441484\pi$
$151$	4.49258	0.365601	0.182801	+	0.983150i	$0.441484\pi$
$152$	22.9873	1.86452
$153$	0	0
$154$	−1.36177	−0.109735
$155$	−6.19428	−0.497536
$156$	0	0
$157$	10.2430	0.817480	0.408740	−	0.912651i	$-0.365968\pi$
$157$	10.2430	0.817480	0.408740	+	0.912651i	$0.365968\pi$
$158$	18.5722	1.47753
$159$	0	0
$160$	28.7163	2.27022
$161$	−0.741716	−0.0584554
$162$	0	0
$163$	1.68819	0.132229	0.0661147	−	0.997812i	$-0.478940\pi$
$163$	1.68819	0.132229	0.0661147	+	0.997812i	$0.478940\pi$
$164$	−48.4374	−3.78233
$165$	0	0
$166$	−25.6441	−1.99037
$167$	−4.29869	−0.332642	−0.166321	−	0.986072i	$-0.553189\pi$
$167$	−4.29869	−0.332642	−0.166321	+	0.986072i	$0.553189\pi$
$168$	0	0
$169$	0	0
$170$	2.05682	0.157751
$171$	0	0
$172$	−6.75874	−0.515349
$173$	11.1912	0.850855	0.425427	−	0.904993i	$-0.360124\pi$
$173$	11.1912	0.850855	0.425427	+	0.904993i	$0.360124\pi$
$174$	0	0
$175$	−0.269601	−0.0203799
$176$	32.3344	2.43730
$177$	0	0
$178$	−18.3310	−1.37397
$179$	−7.68201	−0.574180	−0.287090	−	0.957904i	$-0.592688\pi$
$179$	−7.68201	−0.574180	−0.287090	+	0.957904i	$0.592688\pi$
$180$	0	0
$181$	6.44731	0.479225	0.239612	−	0.970869i	$-0.422980\pi$
$181$	6.44731	0.479225	0.239612	+	0.970869i	$0.422980\pi$
$182$	0	0
$183$	0	0
$184$	29.0147	2.13899
$185$	−7.66406	−0.563473
$186$	0	0
$187$	1.33522	0.0976412
$188$	−0.700247	−0.0510708
$189$	0	0
$190$	6.07995	0.441086
$191$	18.5320	1.34093	0.670465	−	0.741941i	$-0.266095\pi$
$191$	18.5320	1.34093	0.670465	+	0.741941i	$0.266095\pi$
$192$	0	0
$193$	−3.96905	−0.285699	−0.142849	−	0.989744i	$-0.545626\pi$
$193$	−3.96905	−0.285699	−0.142849	+	0.989744i	$0.545626\pi$
$194$	48.6481	3.49273
$195$	0	0
$196$	−40.0457	−2.86041
$197$	1.71586	0.122250	0.0611251	−	0.998130i	$-0.480531\pi$
$197$	1.71586	0.122250	0.0611251	+	0.998130i	$0.480531\pi$
$198$	0	0
$199$	20.2513	1.43557	0.717787	−	0.696263i	$-0.245155\pi$
$199$	20.2513	1.43557	0.717787	+	0.696263i	$0.245155\pi$
$200$	10.5463	0.745738
$201$	0	0
$202$	32.9171	2.31604
$203$	−1.94450	−0.136477
$204$	0	0
$205$	−8.37897	−0.585212
$206$	−22.4230	−1.56228
$207$	0	0
$208$	0	0
$209$	3.94692	0.273014
$210$	0	0
$211$	6.77781	0.466604	0.233302	−	0.972404i	$-0.425047\pi$
$211$	6.77781	0.466604	0.233302	+	0.972404i	$0.425047\pi$
$212$	−22.2575	−1.52865
$213$	0	0
$214$	−48.2504	−3.29833
$215$	−1.16916	−0.0797362
$216$	0	0
$217$	1.66998	0.113366
$218$	42.2030	2.85835
$219$	0	0
$220$	10.4679	0.705749
$221$	0	0
$222$	0	0
$223$	−10.2132	−0.683928	−0.341964	−	0.939713i	$-0.611092\pi$
$223$	−10.2132	−0.683928	−0.341964	+	0.939713i	$0.611092\pi$
$224$	−7.74193	−0.517279
$225$	0	0
$226$	−34.7800	−2.31353
$227$	−9.09196	−0.603455	−0.301727	−	0.953394i	$-0.597563\pi$
$227$	−9.09196	−0.603455	−0.301727	+	0.953394i	$0.597563\pi$
$228$	0	0
$229$	−7.80962	−0.516074	−0.258037	−	0.966135i	$-0.583076\pi$
$229$	−7.80962	−0.516074	−0.258037	+	0.966135i	$0.583076\pi$
$230$	7.67414	0.506018
$231$	0	0
$232$	76.0657	4.99396
$233$	3.62746	0.237643	0.118821	−	0.992916i	$-0.462088\pi$
$233$	3.62746	0.237643	0.118821	+	0.992916i	$0.462088\pi$
$234$	0	0
$235$	−0.121132	−0.00790181
$236$	−61.4547	−4.00036
$237$	0	0
$238$	−0.554520	−0.0359442
$239$	−19.0089	−1.22959	−0.614793	−	0.788688i	$-0.710761\pi$
$239$	−19.0089	−1.22959	−0.614793	+	0.788688i	$0.710761\pi$
$240$	0	0
$241$	−10.1458	−0.653550	−0.326775	−	0.945102i	$-0.605962\pi$
$241$	−10.1458	−0.653550	−0.326775	+	0.945102i	$0.605962\pi$
$242$	−21.5371	−1.38446
$243$	0	0
$244$	−24.5327	−1.57055
$245$	−6.92732	−0.442570
$246$	0	0
$247$	0	0
$248$	−65.3269	−4.14826
$249$	0	0
$250$	2.78942	0.176418
$251$	−0.128762	−0.00812739	−0.00406370	−	0.999992i	$-0.501294\pi$
$251$	−0.128762	−0.00812739	−0.00406370	+	0.999992i	$0.501294\pi$
$252$	0	0
$253$	4.98181	0.313204
$254$	33.1594	2.08060
$255$	0	0
$256$	96.4013	6.02508
$257$	−6.73869	−0.420348	−0.210174	−	0.977664i	$-0.567403\pi$
$257$	−6.73869	−0.420348	−0.210174	+	0.977664i	$0.567403\pi$
$258$	0	0
$259$	2.06624	0.128390
$260$	0	0
$261$	0	0
$262$	−38.4364	−2.37461
$263$	−17.8067	−1.09801	−0.549005	−	0.835819i	$-0.684993\pi$
$263$	−17.8067	−1.09801	−0.549005	+	0.835819i	$0.684993\pi$
$264$	0	0
$265$	−3.85022	−0.236517
$266$	−1.63916	−0.100503
$267$	0	0
$268$	55.2125	3.37264
$269$	0.205114	0.0125060	0.00625302	−	0.999980i	$-0.498010\pi$
$269$	0.205114	0.0125060	0.00625302	+	0.999980i	$0.498010\pi$
$270$	0	0
$271$	−26.5928	−1.61540	−0.807699	−	0.589595i	$-0.799287\pi$
$271$	−26.5928	−1.61540	−0.807699	+	0.589595i	$0.799287\pi$
$272$	13.1667	0.798349
$273$	0	0
$274$	39.4993	2.38624
$275$	1.81080	0.109195
$276$	0	0
$277$	25.2149	1.51502	0.757510	−	0.652824i	$-0.226416\pi$
$277$	25.2149	1.51502	0.757510	+	0.652824i	$0.226416\pi$
$278$	12.6540	0.758939
$279$	0	0
$280$	−2.84330	−0.169919
$281$	−12.7906	−0.763025	−0.381513	−	0.924364i	$-0.624597\pi$
$281$	−12.7906	−0.763025	−0.381513	+	0.924364i	$0.624597\pi$
$282$	0	0
$283$	22.4737	1.33592	0.667961	−	0.744196i	$-0.267167\pi$
$283$	22.4737	1.33592	0.667961	+	0.744196i	$0.267167\pi$
$284$	46.9460	2.78573
$285$	0	0
$286$	0	0
$287$	2.25897	0.133343
$288$	0	0
$289$	−16.4563	−0.968017
$290$	20.1187	1.18141
$291$	0	0
$292$	4.00548	0.234403
$293$	19.4096	1.13392	0.566960	−	0.823745i	$-0.308119\pi$
$293$	19.4096	1.13392	0.566960	+	0.823745i	$0.308119\pi$
$294$	0	0
$295$	−10.6308	−0.618947
$296$	−80.8277	−4.69801
$297$	0	0
$298$	−9.81653	−0.568656
$299$	0	0
$300$	0	0
$301$	0.315207	0.0181682
$302$	12.5317	0.721117
$303$	0	0
$304$	38.9207	2.23226
$305$	−4.24380	−0.242999
$306$	0	0
$307$	−20.9899	−1.19796	−0.598978	−	0.800765i	$-0.704426\pi$
$307$	−20.9899	−1.19796	−0.598978	+	0.800765i	$0.704426\pi$
$308$	−2.82217	−0.160808
$309$	0	0
$310$	−17.2784	−0.981348
$311$	−12.5265	−0.710311	−0.355155	−	0.934807i	$-0.615572\pi$
$311$	−12.5265	−0.710311	−0.355155	+	0.934807i	$0.615572\pi$
$312$	0	0
$313$	−8.46526	−0.478485	−0.239242	−	0.970960i	$-0.576899\pi$
$313$	−8.46526	−0.478485	−0.239242	+	0.970960i	$0.576899\pi$
$314$	28.5720	1.61241
$315$	0	0
$316$	38.4895	2.16520
$317$	−15.3660	−0.863043	−0.431522	−	0.902103i	$-0.642023\pi$
$317$	−15.3660	−0.863043	−0.431522	+	0.902103i	$0.642023\pi$
$318$	0	0
$319$	13.0605	0.731246
$320$	44.3888	2.48141
$321$	0	0
$322$	−2.06895	−0.115298
$323$	1.60720	0.0894270
$324$	0	0
$325$	0	0
$326$	4.70907	0.260811
$327$	0	0
$328$	−88.3673	−4.87927
$329$	0.0326574	0.00180046
$330$	0	0
$331$	−6.88564	−0.378469	−0.189234	−	0.981932i	$-0.560601\pi$
$331$	−6.88564	−0.378469	−0.189234	+	0.981932i	$0.560601\pi$
$332$	−53.1454	−2.91673
$333$	0	0
$334$	−11.9908	−0.656109
$335$	9.55095	0.521824
$336$	0	0
$337$	−12.4209	−0.676609	−0.338305	−	0.941037i	$-0.609853\pi$
$337$	−12.4209	−0.676609	−0.338305	+	0.941037i	$0.609853\pi$
$338$	0	0
$339$	0	0
$340$	4.26259	0.231172
$341$	−11.2166	−0.607413
$342$	0	0
$343$	3.75481	0.202741
$344$	−12.3304	−0.664809
$345$	0	0
$346$	31.2170	1.67824
$347$	−23.4882	−1.26091	−0.630455	−	0.776226i	$-0.717132\pi$
$347$	−23.4882	−1.26091	−0.630455	+	0.776226i	$0.717132\pi$
$348$	0	0
$349$	−17.5281	−0.938259	−0.469129	−	0.883129i	$-0.655432\pi$
$349$	−17.5281	−0.938259	−0.469129	+	0.883129i	$0.655432\pi$
$350$	−0.752028	−0.0401976
$351$	0	0
$352$	51.9995	2.77158
$353$	4.01241	0.213559	0.106780	−	0.994283i	$-0.465946\pi$
$353$	4.01241	0.213559	0.106780	+	0.994283i	$0.465946\pi$
$354$	0	0
$355$	8.12097	0.431016
$356$	−37.9895	−2.01344
$357$	0	0
$358$	−21.4283	−1.13252
$359$	−5.71225	−0.301481	−0.150740	−	0.988573i	$-0.548166\pi$
$359$	−5.71225	−0.301481	−0.150740	+	0.988573i	$0.548166\pi$
$360$	0	0
$361$	−14.2491	−0.749954
$362$	17.9842	0.945230
$363$	0	0
$364$	0	0
$365$	0.692889	0.0362675
$366$	0	0
$367$	4.43654	0.231585	0.115793	−	0.993273i	$-0.463059\pi$
$367$	4.43654	0.231585	0.115793	+	0.993273i	$0.463059\pi$
$368$	49.1259	2.56087
$369$	0	0
$370$	−21.3782	−1.11140
$371$	1.03802	0.0538914
$372$	0	0
$373$	−7.49142	−0.387891	−0.193946	−	0.981012i	$-0.562129\pi$
$373$	−7.49142	−0.387891	−0.193946	+	0.981012i	$0.562129\pi$
$374$	3.72449	0.192589
$375$	0	0
$376$	−1.27750	−0.0658822
$377$	0	0
$378$	0	0
$379$	−11.5676	−0.594188	−0.297094	−	0.954848i	$-0.596018\pi$
$379$	−11.5676	−0.594188	−0.297094	+	0.954848i	$0.596018\pi$
$380$	12.6002	0.646377
$381$	0	0
$382$	51.6935	2.64487
$383$	26.5665	1.35749	0.678744	−	0.734375i	$-0.262525\pi$
$383$	26.5665	1.35749	0.678744	+	0.734375i	$0.262525\pi$
$384$	0	0
$385$	−0.488193	−0.0248806
$386$	−11.0713	−0.563516
$387$	0	0
$388$	100.819	5.11832
$389$	−32.0328	−1.62413	−0.812063	−	0.583570i	$-0.801656\pi$
$389$	−32.0328	−1.62413	−0.812063	+	0.583570i	$0.801656\pi$
$390$	0	0
$391$	2.02862	0.102591
$392$	−73.0577	−3.68997
$393$	0	0
$394$	4.78625	0.241128
$395$	6.65811	0.335006
$396$	0	0
$397$	−37.9730	−1.90581	−0.952905	−	0.303268i	$-0.901922\pi$
$397$	−37.9730	−1.90581	−0.952905	+	0.303268i	$0.901922\pi$
$398$	56.4892	2.83155
$399$	0	0
$400$	17.8564	0.892820
$401$	−29.0762	−1.45199	−0.725997	−	0.687698i	$-0.758621\pi$
$401$	−29.0762	−1.45199	−0.725997	+	0.687698i	$0.758621\pi$
$402$	0	0
$403$	0	0
$404$	68.2180	3.39397
$405$	0	0
$406$	−5.42403	−0.269190
$407$	−13.8781	−0.687912
$408$	0	0
$409$	26.7221	1.32133	0.660663	−	0.750683i	$-0.270275\pi$
$409$	26.7221	1.32133	0.660663	+	0.750683i	$0.270275\pi$
$410$	−23.3724	−1.15428
$411$	0	0
$412$	−46.4698	−2.28940
$413$	2.86606	0.141030
$414$	0	0
$415$	−9.19337	−0.451285
$416$	0	0
$417$	0	0
$418$	11.0096	0.538497
$419$	−35.3861	−1.72873	−0.864363	−	0.502868i	$-0.832278\pi$
$419$	−35.3861	−1.72873	−0.864363	+	0.502868i	$0.832278\pi$
$420$	0	0
$421$	14.1178	0.688058	0.344029	−	0.938959i	$-0.388208\pi$
$421$	14.1178	0.688058	0.344029	+	0.938959i	$0.388208\pi$
$422$	18.9061	0.920336
$423$	0	0
$424$	−40.6057	−1.97198
$425$	0.737366	0.0357675
$426$	0	0
$427$	1.14413	0.0553684
$428$	−99.9951	−4.83345
$429$	0	0
$430$	−3.26128	−0.157273
$431$	−14.1483	−0.681498	−0.340749	−	0.940154i	$-0.610681\pi$
$431$	−14.1483	−0.681498	−0.340749	+	0.940154i	$0.610681\pi$
$432$	0	0
$433$	−24.8561	−1.19451	−0.597253	−	0.802053i	$-0.703741\pi$
$433$	−24.8561	−1.19451	−0.597253	+	0.802053i	$0.703741\pi$
$434$	4.65827	0.223604
$435$	0	0
$436$	87.4623	4.18869
$437$	5.99658	0.286855
$438$	0	0
$439$	9.76222	0.465926	0.232963	−	0.972486i	$-0.425158\pi$
$439$	9.76222	0.465926	0.232963	+	0.972486i	$0.425158\pi$
$440$	19.0973	0.910428
$441$	0	0
$442$	0	0
$443$	32.5970	1.54873	0.774365	−	0.632740i	$-0.218070\pi$
$443$	32.5970	1.54873	0.774365	+	0.632740i	$0.218070\pi$
$444$	0	0
$445$	−6.57163	−0.311525
$446$	−28.4889	−1.34899
$447$	0	0
$448$	−11.9673	−0.565400
$449$	12.1858	0.575083	0.287542	−	0.957768i	$-0.407162\pi$
$449$	12.1858	0.575083	0.287542	+	0.957768i	$0.407162\pi$
$450$	0	0
$451$	−15.1726	−0.714452
$452$	−72.0788	−3.39030
$453$	0	0
$454$	−25.3613	−1.19026
$455$	0	0
$456$	0	0
$457$	−30.1469	−1.41021	−0.705105	−	0.709103i	$-0.749100\pi$
$457$	−30.1469	−1.41021	−0.705105	+	0.709103i	$0.749100\pi$
$458$	−21.7843	−1.01791
$459$	0	0
$460$	15.9040	0.741530
$461$	31.8382	1.48285	0.741427	−	0.671034i	$-0.234149\pi$
$461$	31.8382	1.48285	0.741427	+	0.671034i	$0.234149\pi$
$462$	0	0
$463$	15.5796	0.724045	0.362023	−	0.932169i	$-0.382086\pi$
$463$	15.5796	0.724045	0.362023	+	0.932169i	$0.382086\pi$
$464$	128.790	5.97892
$465$	0	0
$466$	10.1185	0.468730
$467$	29.7598	1.37712	0.688560	−	0.725179i	$-0.258243\pi$
$467$	29.7598	1.37712	0.688560	+	0.725179i	$0.258243\pi$
$468$	0	0
$469$	−2.57494	−0.118900
$470$	−0.337889	−0.0155856
$471$	0	0
$472$	−112.115	−5.16053
$473$	−2.11712	−0.0973453
$474$	0	0
$475$	2.17965	0.100009
$476$	−1.14920	−0.0526734
$477$	0	0
$478$	−53.0238	−2.42525
$479$	−15.1038	−0.690112	−0.345056	−	0.938582i	$-0.612140\pi$
$479$	−15.1038	−0.690112	−0.345056	+	0.938582i	$0.612140\pi$
$480$	0	0
$481$	0	0
$482$	−28.3009	−1.28907
$483$	0	0
$484$	−44.6338	−2.02881
$485$	17.4402	0.791921
$486$	0	0
$487$	−6.99071	−0.316780	−0.158390	−	0.987377i	$-0.550630\pi$
$487$	−6.99071	−0.316780	−0.158390	+	0.987377i	$0.550630\pi$
$488$	−44.7565	−2.02603
$489$	0	0
$490$	−19.3232	−0.872931
$491$	18.4608	0.833125	0.416563	−	0.909107i	$-0.363235\pi$
$491$	18.4608	0.833125	0.416563	+	0.909107i	$0.363235\pi$
$492$	0	0
$493$	5.31827	0.239523
$494$	0	0
$495$	0	0
$496$	−110.608	−4.96643
$497$	−2.18942	−0.0982088
$498$	0	0
$499$	9.65233	0.432097	0.216049	−	0.976383i	$-0.430683\pi$
$499$	9.65233	0.432097	0.216049	+	0.976383i	$0.430683\pi$
$500$	5.78084	0.258527
$501$	0	0
$502$	−0.359171	−0.0160306
$503$	−6.85353	−0.305584	−0.152792	−	0.988258i	$-0.548826\pi$
$503$	−6.85353	−0.305584	−0.152792	+	0.988258i	$0.548826\pi$
$504$	0	0
$505$	11.8007	0.525125
$506$	13.8963	0.617768
$507$	0	0
$508$	68.7201	3.04896
$509$	−33.8433	−1.50008	−0.750039	−	0.661393i	$-0.769965\pi$
$509$	−33.8433	−1.50008	−0.750039	+	0.661393i	$0.769965\pi$
$510$	0	0
$511$	−0.186803	−0.00826369
$512$	136.131	6.01618
$513$	0	0
$514$	−18.7970	−0.829100
$515$	−8.03859	−0.354223
$516$	0	0
$517$	−0.219347	−0.00964686
$518$	5.76359	0.253238
$519$	0	0
$520$	0	0
$521$	36.7411	1.60966	0.804828	−	0.593508i	$-0.202258\pi$
$521$	36.7411	1.60966	0.804828	+	0.593508i	$0.202258\pi$
$522$	0	0
$523$	32.2229	1.40901	0.704505	−	0.709699i	$-0.251169\pi$
$523$	32.2229	1.40901	0.704505	+	0.709699i	$0.251169\pi$
$524$	−79.6563	−3.47980
$525$	0	0
$526$	−49.6704	−2.16573
$527$	−4.56745	−0.198961
$528$	0	0
$529$	−15.4311	−0.670917
$530$	−10.7399	−0.466510
$531$	0	0
$532$	−3.39702	−0.147280
$533$	0	0
$534$	0	0
$535$	−17.2977	−0.747844
$536$	100.727	4.35076
$537$	0	0
$538$	0.572149	0.0246671
$539$	−12.5440	−0.540308
$540$	0	0
$541$	−9.68462	−0.416375	−0.208187	−	0.978089i	$-0.566756\pi$
$541$	−9.68462	−0.416375	−0.208187	+	0.978089i	$0.566756\pi$
$542$	−74.1784	−3.18623
$543$	0	0
$544$	21.1744	0.907845
$545$	15.1297	0.648085
$546$	0	0
$547$	−5.81447	−0.248609	−0.124304	−	0.992244i	$-0.539670\pi$
$547$	−5.81447	−0.248609	−0.124304	+	0.992244i	$0.539670\pi$
$548$	81.8591	3.49685
$549$	0	0
$550$	5.05108	0.215379
$551$	15.7208	0.669729
$552$	0	0
$553$	−1.79503	−0.0763325
$554$	70.3350	2.98825
$555$	0	0
$556$	26.2245	1.11217
$557$	−30.9894	−1.31306	−0.656531	−	0.754299i	$-0.727977\pi$
$557$	−30.9894	−1.31306	−0.656531	+	0.754299i	$0.727977\pi$
$558$	0	0
$559$	0	0
$560$	−4.81410	−0.203433
$561$	0	0
$562$	−35.6784	−1.50500
$563$	14.0334	0.591437	0.295719	−	0.955275i	$-0.404441\pi$
$563$	14.0334	0.591437	0.295719	+	0.955275i	$0.404441\pi$
$564$	0	0
$565$	−12.4686	−0.524557
$566$	62.6885	2.63499
$567$	0	0
$568$	85.6464	3.59364
$569$	−18.9717	−0.795336	−0.397668	−	0.917529i	$-0.630180\pi$
$569$	−18.9717	−0.795336	−0.397668	+	0.917529i	$0.630180\pi$
$570$	0	0
$571$	18.6462	0.780318	0.390159	−	0.920748i	$-0.372420\pi$
$571$	18.6462	0.780318	0.390159	+	0.920748i	$0.372420\pi$
$572$	0	0
$573$	0	0
$574$	6.30122	0.263008
$575$	2.75116	0.114731
$576$	0	0
$577$	−10.6262	−0.442374	−0.221187	−	0.975231i	$-0.570993\pi$
$577$	−10.6262	−0.442374	−0.221187	+	0.975231i	$0.570993\pi$
$578$	−45.9034	−1.90933
$579$	0	0
$580$	41.6945	1.73127
$581$	2.47854	0.102827
$582$	0	0
$583$	−6.97198	−0.288750
$584$	7.30744	0.302384
$585$	0	0
$586$	54.1414	2.23656
$587$	−14.2936	−0.589962	−0.294981	−	0.955503i	$-0.595313\pi$
$587$	−14.2936	−0.589962	−0.294981	+	0.955503i	$0.595313\pi$
$588$	0	0
$589$	−13.5014	−0.556314
$590$	−29.6536	−1.22082
$591$	0	0
$592$	−136.853	−5.62461
$593$	0.474392	0.0194809	0.00974047	−	0.999953i	$-0.496899\pi$
$593$	0.474392	0.0194809	0.00974047	+	0.999953i	$0.496899\pi$
$594$	0	0
$595$	−0.198794	−0.00814977
$596$	−20.3440	−0.833321
$597$	0	0
$598$	0	0
$599$	32.2915	1.31940	0.659698	−	0.751531i	$-0.270684\pi$
$599$	32.2915	1.31940	0.659698	+	0.751531i	$0.270684\pi$
$600$	0	0
$601$	19.7195	0.804374	0.402187	−	0.915558i	$-0.368250\pi$
$601$	19.7195	0.804374	0.402187	+	0.915558i	$0.368250\pi$
$602$	0.879242	0.0358352
$603$	0	0
$604$	25.9709	1.05674
$605$	−7.72100	−0.313903
$606$	0	0
$607$	24.0765	0.977235	0.488618	−	0.872498i	$-0.337501\pi$
$607$	24.0765	0.977235	0.488618	+	0.872498i	$0.337501\pi$
$608$	62.5915	2.53842
$609$	0	0
$610$	−11.8377	−0.479295
$611$	0	0
$612$	0	0
$613$	13.5949	0.549092	0.274546	−	0.961574i	$-0.411472\pi$
$613$	13.5949	0.549092	0.274546	+	0.961574i	$0.411472\pi$
$614$	−58.5495	−2.36287
$615$	0	0
$616$	−5.14864	−0.207445
$617$	2.41390	0.0971798	0.0485899	−	0.998819i	$-0.484527\pi$
$617$	2.41390	0.0971798	0.0485899	+	0.998819i	$0.484527\pi$
$618$	0	0
$619$	11.6882	0.469790	0.234895	−	0.972021i	$-0.424525\pi$
$619$	11.6882	0.469790	0.234895	+	0.972021i	$0.424525\pi$
$620$	−35.8081	−1.43809
$621$	0	0
$622$	−34.9415	−1.40103
$623$	1.77172	0.0709823
$624$	0	0
$625$	1.00000	0.0400000
$626$	−23.6131	−0.943770
$627$	0	0
$628$	59.2131	2.36286
$629$	−5.65122	−0.225329
$630$	0	0
$631$	38.7427	1.54232	0.771162	−	0.636639i	$-0.219676\pi$
$631$	38.7427	1.54232	0.771162	+	0.636639i	$0.219676\pi$
$632$	70.2186	2.79315
$633$	0	0
$634$	−42.8623	−1.70228
$635$	11.8876	0.471744
$636$	0	0
$637$	0	0
$638$	36.4311	1.44232
$639$	0	0
$640$	66.3863	2.62415
$641$	37.1079	1.46568	0.732838	−	0.680403i	$-0.238195\pi$
$641$	37.1079	1.46568	0.732838	+	0.680403i	$0.238195\pi$
$642$	0	0
$643$	38.5589	1.52061	0.760307	−	0.649564i	$-0.225049\pi$
$643$	38.5589	1.52061	0.760307	+	0.649564i	$0.225049\pi$
$644$	−4.28774	−0.168961
$645$	0	0
$646$	4.48315	0.176387
$647$	41.1658	1.61840	0.809198	−	0.587536i	$-0.199902\pi$
$647$	41.1658	1.61840	0.809198	+	0.587536i	$0.199902\pi$
$648$	0	0
$649$	−19.2502	−0.755636
$650$	0	0
$651$	0	0
$652$	9.75917	0.382199
$653$	7.33411	0.287006	0.143503	−	0.989650i	$-0.454163\pi$
$653$	7.33411	0.287006	0.143503	+	0.989650i	$0.454163\pi$
$654$	0	0
$655$	−13.7794	−0.538405
$656$	−149.618	−5.84161
$657$	0	0
$658$	0.0910950	0.00355125
$659$	−31.5480	−1.22894	−0.614468	−	0.788942i	$-0.710629\pi$
$659$	−31.5480	−1.22894	−0.614468	+	0.788942i	$0.710629\pi$
$660$	0	0
$661$	5.61821	0.218523	0.109262	−	0.994013i	$-0.465151\pi$
$661$	5.61821	0.218523	0.109262	+	0.994013i	$0.465151\pi$
$662$	−19.2069	−0.746497
$663$	0	0
$664$	−96.9563	−3.76263
$665$	−0.587635	−0.0227875
$666$	0	0
$667$	19.8429	0.768319
$668$	−24.8500	−0.961476
$669$	0	0
$670$	26.6416	1.02925
$671$	−7.68468	−0.296664
$672$	0	0
$673$	50.7267	1.95537	0.977686	−	0.210071i	$-0.0673695\pi$
$673$	50.7267	1.95537	0.977686	+	0.210071i	$0.0673695\pi$
$674$	−34.6470	−1.33455
$675$	0	0
$676$	0	0
$677$	−33.0566	−1.27047	−0.635234	−	0.772320i	$-0.719096\pi$
$677$	−33.0566	−1.27047	−0.635234	+	0.772320i	$0.719096\pi$
$678$	0	0
$679$	−4.70190	−0.180442
$680$	7.77650	0.298215
$681$	0	0
$682$	−31.2878	−1.19807
$683$	−15.9036	−0.608536	−0.304268	−	0.952587i	$-0.598412\pi$
$683$	−15.9036	−0.608536	−0.304268	+	0.952587i	$0.598412\pi$
$684$	0	0
$685$	14.1604	0.541042
$686$	10.4737	0.399889
$687$	0	0
$688$	−20.8770	−0.795929
$689$	0	0
$690$	0	0
$691$	19.3916	0.737689	0.368845	−	0.929491i	$-0.379753\pi$
$691$	19.3916	0.737689	0.368845	+	0.929491i	$0.379753\pi$
$692$	64.6948	2.45933
$693$	0	0
$694$	−65.5182	−2.48704
$695$	4.53645	0.172077
$696$	0	0
$697$	−6.17836	−0.234022
$698$	−48.8932	−1.85064
$699$	0	0
$700$	−1.55852	−0.0589064
$701$	−14.2486	−0.538162	−0.269081	−	0.963118i	$-0.586720\pi$
$701$	−14.2486	−0.538162	−0.269081	+	0.963118i	$0.586720\pi$
$702$	0	0
$703$	−16.7050	−0.630040
$704$	80.3794	3.02941
$705$	0	0
$706$	11.1923	0.421227
$707$	−3.18148	−0.119652
$708$	0	0
$709$	17.2978	0.649632	0.324816	−	0.945777i	$-0.394698\pi$
$709$	17.2978	0.649632	0.324816	+	0.945777i	$0.394698\pi$
$710$	22.6527	0.850143
$711$	0	0
$712$	−69.3065	−2.59737
$713$	−17.0415	−0.638208
$714$	0	0
$715$	0	0
$716$	−44.4084	−1.65962
$717$	0	0
$718$	−15.9338	−0.594645
$719$	25.3275	0.944556	0.472278	−	0.881450i	$-0.343432\pi$
$719$	25.3275	0.944556	0.472278	+	0.881450i	$0.343432\pi$
$720$	0	0
$721$	2.16721	0.0807111
$722$	−39.7467	−1.47922
$723$	0	0
$724$	37.2709	1.38516
$725$	7.21253	0.267867
$726$	0	0
$727$	−43.3262	−1.60688	−0.803439	−	0.595387i	$-0.796999\pi$
$727$	−43.3262	−1.60688	−0.803439	+	0.595387i	$0.796999\pi$
$728$	0	0
$729$	0	0
$730$	1.93276	0.0715345
$731$	−0.862100	−0.0318859
$732$	0	0
$733$	−39.9598	−1.47595	−0.737975	−	0.674828i	$-0.764218\pi$
$733$	−39.9598	−1.47595	−0.737975	+	0.674828i	$0.764218\pi$
$734$	12.3753	0.456782
$735$	0	0
$736$	79.0032	2.91210
$737$	17.2949	0.637065
$738$	0	0
$739$	−11.0903	−0.407962	−0.203981	−	0.978975i	$-0.565388\pi$
$739$	−11.0903	−0.407962	−0.203981	+	0.978975i	$0.565388\pi$
$740$	−44.3047	−1.62867
$741$	0	0
$742$	2.89547	0.106296
$743$	19.8685	0.728904	0.364452	−	0.931222i	$-0.381256\pi$
$743$	19.8685	0.728904	0.364452	+	0.931222i	$0.381256\pi$
$744$	0	0
$745$	−3.51921	−0.128934
$746$	−20.8967	−0.765082
$747$	0	0
$748$	7.71871	0.282224
$749$	4.66347	0.170399
$750$	0	0
$751$	7.50398	0.273824	0.136912	−	0.990583i	$-0.456282\pi$
$751$	7.50398	0.273824	0.136912	+	0.990583i	$0.456282\pi$
$752$	−2.16299	−0.0788762
$753$	0	0
$754$	0	0
$755$	4.49258	0.163502
$756$	0	0
$757$	−33.3769	−1.21310	−0.606551	−	0.795044i	$-0.707448\pi$
$757$	−33.3769	−1.21310	−0.606551	+	0.795044i	$0.707448\pi$
$758$	−32.2669	−1.17199
$759$	0	0
$760$	22.9873	0.833837
$761$	−13.6920	−0.496335	−0.248168	−	0.968717i	$-0.579828\pi$
$761$	−13.6920	−0.496335	−0.248168	+	0.968717i	$0.579828\pi$
$762$	0	0
$763$	−4.07898	−0.147669
$764$	107.131	3.87585
$765$	0	0
$766$	74.1051	2.67753
$767$	0	0
$768$	0	0
$769$	−28.0273	−1.01069	−0.505346	−	0.862917i	$-0.668635\pi$
$769$	−28.0273	−1.01069	−0.505346	+	0.862917i	$0.668635\pi$
$770$	−1.36177	−0.0490749
$771$	0	0
$772$	−22.9445	−0.825789
$773$	−13.4760	−0.484699	−0.242349	−	0.970189i	$-0.577918\pi$
$773$	−13.4760	−0.484699	−0.242349	+	0.970189i	$0.577918\pi$
$774$	0	0
$775$	−6.19428	−0.222505
$776$	183.931	6.60272
$777$	0	0
$778$	−89.3527	−3.20345
$779$	−18.2632	−0.654348
$780$	0	0
$781$	14.7055	0.526203
$782$	5.65865	0.202353
$783$	0	0
$784$	−123.697	−4.41775
$785$	10.2430	0.365588
$786$	0	0
$787$	17.0143	0.606495	0.303247	−	0.952912i	$-0.401929\pi$
$787$	17.0143	0.606495	0.303247	+	0.952912i	$0.401929\pi$
$788$	9.91912	0.353354
$789$	0	0
$790$	18.5722	0.660771
$791$	3.36153	0.119522
$792$	0	0
$793$	0	0
$794$	−105.923	−3.75905
$795$	0	0
$796$	117.069	4.14941
$797$	−24.4948	−0.867650	−0.433825	−	0.900997i	$-0.642836\pi$
$797$	−24.4948	−0.867650	−0.433825	+	0.900997i	$0.642836\pi$
$798$	0	0
$799$	−0.0893190	−0.00315988
$800$	28.7163	1.01527
$801$	0	0
$802$	−81.1055	−2.86393
$803$	1.25468	0.0442769
$804$	0	0
$805$	−0.741716	−0.0261420
$806$	0	0
$807$	0	0
$808$	124.454	4.37828
$809$	11.6571	0.409841	0.204920	−	0.978779i	$-0.434306\pi$
$809$	11.6571	0.409841	0.204920	+	0.978779i	$0.434306\pi$
$810$	0	0
$811$	−40.2610	−1.41376	−0.706878	−	0.707335i	$-0.749897\pi$
$811$	−40.2610	−1.41376	−0.706878	+	0.707335i	$0.749897\pi$
$812$	−11.2409	−0.394477
$813$	0	0
$814$	−38.7118	−1.35685
$815$	1.68819	0.0591348
$816$	0	0
$817$	−2.54837	−0.0891560
$818$	74.5392	2.60620
$819$	0	0
$820$	−48.4374	−1.69151
$821$	−18.3671	−0.641016	−0.320508	−	0.947246i	$-0.603854\pi$
$821$	−18.3671	−0.641016	−0.320508	+	0.947246i	$0.603854\pi$
$822$	0	0
$823$	20.8077	0.725312	0.362656	−	0.931923i	$-0.381870\pi$
$823$	20.8077	0.725312	0.362656	+	0.931923i	$0.381870\pi$
$824$	−84.7776	−2.95337
$825$	0	0
$826$	7.99463	0.278169
$827$	−25.7766	−0.896341	−0.448171	−	0.893948i	$-0.647924\pi$
$827$	−25.7766	−0.896341	−0.448171	+	0.893948i	$0.647924\pi$
$828$	0	0
$829$	46.6288	1.61949	0.809743	−	0.586785i	$-0.199606\pi$
$829$	46.6288	1.61949	0.809743	+	0.586785i	$0.199606\pi$
$830$	−25.6441	−0.890121
$831$	0	0
$832$	0	0
$833$	−5.10797	−0.176981
$834$	0	0
$835$	−4.29869	−0.148762
$836$	22.8165	0.789124
$837$	0	0
$838$	−98.7066	−3.40976
$839$	−8.84041	−0.305205	−0.152602	−	0.988288i	$-0.548765\pi$
$839$	−8.84041	−0.305205	−0.152602	+	0.988288i	$0.548765\pi$
$840$	0	0
$841$	23.0206	0.793814
$842$	39.3803	1.35713
$843$	0	0
$844$	39.1814	1.34868
$845$	0	0
$846$	0	0
$847$	2.08159	0.0715241
$848$	−68.7511	−2.36092
$849$	0	0
$850$	2.05682	0.0705483
$851$	−21.0851	−0.722788
$852$	0	0
$853$	−26.7505	−0.915920	−0.457960	−	0.888973i	$-0.651420\pi$
$853$	−26.7505	−0.915920	−0.457960	+	0.888973i	$0.651420\pi$
$854$	3.19146	0.109209
$855$	0	0
$856$	−182.427	−6.23523
$857$	14.3257	0.489356	0.244678	−	0.969604i	$-0.421318\pi$
$857$	14.3257	0.489356	0.244678	+	0.969604i	$0.421318\pi$
$858$	0	0
$859$	14.9290	0.509370	0.254685	−	0.967024i	$-0.418028\pi$
$859$	14.9290	0.509370	0.254685	+	0.967024i	$0.418028\pi$
$860$	−6.75874	−0.230471
$861$	0	0
$862$	−39.4654	−1.34420
$863$	12.0275	0.409422	0.204711	−	0.978822i	$-0.434375\pi$
$863$	12.0275	0.409422	0.204711	+	0.978822i	$0.434375\pi$
$864$	0	0
$865$	11.1912	0.380514
$866$	−69.3339	−2.35606
$867$	0	0
$868$	9.65389	0.327674
$869$	12.0565	0.408989
$870$	0	0
$871$	0	0
$872$	159.563	5.40348
$873$	0	0
$874$	16.7269	0.565798
$875$	−0.269601	−0.00911416
$876$	0	0
$877$	15.1156	0.510417	0.255208	−	0.966886i	$-0.417856\pi$
$877$	15.1156	0.510417	0.255208	+	0.966886i	$0.417856\pi$
$878$	27.2309	0.918998
$879$	0	0
$880$	32.3344	1.08999
$881$	−17.7055	−0.596514	−0.298257	−	0.954486i	$-0.596405\pi$
$881$	−17.7055	−0.596514	−0.298257	+	0.954486i	$0.596405\pi$
$882$	0	0
$883$	39.3891	1.32555	0.662775	−	0.748818i	$-0.269379\pi$
$883$	39.3891	1.32555	0.662775	+	0.748818i	$0.269379\pi$
$884$	0	0
$885$	0	0
$886$	90.9265	3.05474
$887$	−10.0414	−0.337156	−0.168578	−	0.985688i	$-0.553917\pi$
$887$	−10.0414	−0.337156	−0.168578	+	0.985688i	$0.553917\pi$
$888$	0	0
$889$	−3.20489	−0.107489
$890$	−18.3310	−0.614457
$891$	0	0
$892$	−59.0410	−1.97684
$893$	−0.264027	−0.00883531
$894$	0	0
$895$	−7.68201	−0.256781
$896$	−17.8978	−0.597923
$897$	0	0
$898$	33.9913	1.13430
$899$	−44.6764	−1.49004
$900$	0	0
$901$	−2.83902	−0.0945814
$902$	−42.3228	−1.40920
$903$	0	0
$904$	−131.498	−4.37354
$905$	6.44731	0.214316
$906$	0	0
$907$	3.91233	0.129907	0.0649534	−	0.997888i	$-0.479310\pi$
$907$	3.91233	0.129907	0.0649534	+	0.997888i	$0.479310\pi$
$908$	−52.5592	−1.74424
$909$	0	0
$910$	0	0
$911$	−15.8817	−0.526183	−0.263092	−	0.964771i	$-0.584742\pi$
$911$	−15.8817	−0.526183	−0.263092	+	0.964771i	$0.584742\pi$
$912$	0	0
$913$	−16.6474	−0.550948
$914$	−84.0921	−2.78152
$915$	0	0
$916$	−45.1461	−1.49167
$917$	3.71493	0.122678
$918$	0	0
$919$	25.5893	0.844113	0.422056	−	0.906570i	$-0.361308\pi$
$919$	25.5893	0.844113	0.422056	+	0.906570i	$0.361308\pi$
$920$	29.0147	0.956586
$921$	0	0
$922$	88.8100	2.92480
$923$	0	0
$924$	0	0
$925$	−7.66406	−0.251993
$926$	43.4580	1.42812
$927$	0	0
$928$	207.117	6.79895
$929$	20.2720	0.665104	0.332552	−	0.943085i	$-0.392090\pi$
$929$	20.2720	0.665104	0.332552	+	0.943085i	$0.392090\pi$
$930$	0	0
$931$	−15.0991	−0.494854
$932$	20.9698	0.686888
$933$	0	0
$934$	83.0125	2.71625
$935$	1.33522	0.0436665
$936$	0	0
$937$	8.15562	0.266433	0.133216	−	0.991087i	$-0.457470\pi$
$937$	8.15562	0.266433	0.133216	+	0.991087i	$0.457470\pi$
$938$	−7.18258	−0.234519
$939$	0	0
$940$	−0.700247	−0.0228395
$941$	−48.8847	−1.59359	−0.796797	−	0.604247i	$-0.793474\pi$
$941$	−48.8847	−1.59359	−0.796797	+	0.604247i	$0.793474\pi$
$942$	0	0
$943$	−23.0519	−0.750674
$944$	−189.827	−6.17835
$945$	0	0
$946$	−5.90553	−0.192005
$947$	−28.6198	−0.930019	−0.465010	−	0.885306i	$-0.653949\pi$
$947$	−28.6198	−0.930019	−0.465010	+	0.885306i	$0.653949\pi$
$948$	0	0
$949$	0	0
$950$	6.07995	0.197260
$951$	0	0
$952$	−2.09655	−0.0679496
$953$	42.2431	1.36839	0.684194	−	0.729300i	$-0.260154\pi$
$953$	42.2431	1.36839	0.684194	+	0.729300i	$0.260154\pi$
$954$	0	0
$955$	18.5320	0.599682
$956$	−109.888	−3.55402
$957$	0	0
$958$	−42.1309	−1.36119
$959$	−3.81766	−0.123279
$960$	0	0
$961$	7.36907	0.237712
$962$	0	0
$963$	0	0
$964$	−58.6514	−1.88903
$965$	−3.96905	−0.127768
$966$	0	0
$967$	9.15979	0.294559	0.147280	−	0.989095i	$-0.452948\pi$
$967$	9.15979	0.294559	0.147280	+	0.989095i	$0.452948\pi$
$968$	−81.4282	−2.61720
$969$	0	0
$970$	48.6481	1.56200
$971$	−31.5715	−1.01318	−0.506589	−	0.862187i	$-0.669094\pi$
$971$	−31.5715	−1.01318	−0.506589	+	0.862187i	$0.669094\pi$
$972$	0	0
$973$	−1.22303	−0.0392085
$974$	−19.5000	−0.624820
$975$	0	0
$976$	−75.7790	−2.42563
$977$	−8.46405	−0.270789	−0.135394	−	0.990792i	$-0.543230\pi$
$977$	−8.46405	−0.270789	−0.135394	+	0.990792i	$0.543230\pi$
$978$	0	0
$979$	−11.8999	−0.380323
$980$	−40.0457	−1.27921
$981$	0	0
$982$	51.4949	1.64327
$983$	−5.80225	−0.185063	−0.0925315	−	0.995710i	$-0.529496\pi$
$983$	−5.80225	−0.185063	−0.0925315	+	0.995710i	$0.529496\pi$
$984$	0	0
$985$	1.71586	0.0546719
$986$	14.8349	0.472439
$987$	0	0
$988$	0	0
$989$	−3.21656	−0.102281
$990$	0	0
$991$	−47.0740	−1.49535	−0.747677	−	0.664063i	$-0.768831\pi$
$991$	−47.0740	−1.49535	−0.747677	+	0.664063i	$0.768831\pi$
$992$	−177.877	−5.64759
$993$	0	0
$994$	−6.10719	−0.193708
$995$	20.2513	0.642008
$996$	0	0
$997$	6.46083	0.204616	0.102308	−	0.994753i	$-0.467377\pi$
$997$	6.46083	0.204616	0.102308	+	0.994753i	$0.467377\pi$
$998$	26.9243	0.852275
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7605.2.a.cs.1.9		9
3.2	odd	2		845.2.a.n.1.1	✓	9
13.12	even	2		7605.2.a.cp.1.1		9
15.14	odd	2		4225.2.a.bt.1.9		9
39.2	even	12		845.2.m.j.316.1		36
39.5	even	4		845.2.c.h.506.18		18
39.8	even	4		845.2.c.h.506.1		18
39.11	even	12		845.2.m.j.316.18		36
39.17	odd	6		845.2.e.o.146.1		18
39.20	even	12		845.2.m.j.361.1		36
39.23	odd	6		845.2.e.o.191.1		18
39.29	odd	6		845.2.e.p.191.9		18
39.32	even	12		845.2.m.j.361.18		36
39.35	odd	6		845.2.e.p.146.9		18
39.38	odd	2		845.2.a.o.1.9	yes	9
195.194	odd	2		4225.2.a.bs.1.1		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.n.1.1	✓	9	3.2	odd	2
845.2.a.o.1.9	yes	9	39.38	odd	2
845.2.c.h.506.1		18	39.8	even	4
845.2.c.h.506.18		18	39.5	even	4
845.2.e.o.146.1		18	39.17	odd	6
845.2.e.o.191.1		18	39.23	odd	6
845.2.e.p.146.9		18	39.35	odd	6
845.2.e.p.191.9		18	39.29	odd	6
845.2.m.j.316.1		36	39.2	even	12
845.2.m.j.316.18		36	39.11	even	12
845.2.m.j.361.1		36	39.20	even	12
845.2.m.j.361.18		36	39.32	even	12
4225.2.a.bs.1.1		9	195.194	odd	2
4225.2.a.bt.1.9		9	15.14	odd	2
7605.2.a.cp.1.1		9	13.12	even	2
7605.2.a.cs.1.9		9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.78942 q^{2} +5.78084 q^{4} +1.00000 q^{5} -0.269601 q^{7} +10.5463 q^{8} +O(q^{10})\)	\(q+2.78942 q^{2} +5.78084 q^{4} +1.00000 q^{5} -0.269601 q^{7} +10.5463 q^{8} +2.78942 q^{10} +1.81080 q^{11} -0.752028 q^{14} +17.8564 q^{16} +0.737366 q^{17} +2.17965 q^{19} +5.78084 q^{20} +5.05108 q^{22} +2.75116 q^{23} +1.00000 q^{25} -1.55852 q^{28} +7.21253 q^{29} -6.19428 q^{31} +28.7163 q^{32} +2.05682 q^{34} -0.269601 q^{35} -7.66406 q^{37} +6.07995 q^{38} +10.5463 q^{40} -8.37897 q^{41} -1.16916 q^{43} +10.4679 q^{44} +7.67414 q^{46} -0.121132 q^{47} -6.92732 q^{49} +2.78942 q^{50} -3.85022 q^{53} +1.81080 q^{55} -2.84330 q^{56} +20.1187 q^{58} -10.6308 q^{59} -4.24380 q^{61} -17.2784 q^{62} +44.3888 q^{64} +9.55095 q^{67} +4.26259 q^{68} -0.752028 q^{70} +8.12097 q^{71} +0.692889 q^{73} -21.3782 q^{74} +12.6002 q^{76} -0.488193 q^{77} +6.65811 q^{79} +17.8564 q^{80} -23.3724 q^{82} -9.19337 q^{83} +0.737366 q^{85} -3.26128 q^{86} +19.0973 q^{88} -6.57163 q^{89} +15.9040 q^{92} -0.337889 q^{94} +2.17965 q^{95} +17.4402 q^{97} -19.3232 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 3 q^{2} + 17 q^{4} + 9 q^{5} - 7 q^{7} + 12 q^{8}+O(q^{10}) \) 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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