LMFDB - Embedded newform 7605.2.a.cg.1.1

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:	$1$
Dimension:	$4$
Coefficient field:	4.4.7488.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 2x + 1 $ x^4 - 2x^3 - 4x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.698857$ 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)

$f(q)$	$=$	$q-2.43091 q^{2} +3.90931 q^{4} -1.00000 q^{5} +1.30114 q^{7} -4.64136 q^{8} +O(q^{10})$	$q-2.43091 q^{2} +3.90931 q^{4} -1.00000 q^{5} +1.30114 q^{7} -4.64136 q^{8} +2.43091 q^{10} -3.17726 q^{11} -3.16296 q^{14} +3.46410 q^{16} -0.651360 q^{17} -2.51160 q^{19} -3.90931 q^{20} +7.72363 q^{22} -1.77955 q^{23} +1.00000 q^{25} +5.08658 q^{28} +8.37930 q^{29} -8.50318 q^{31} +0.861816 q^{32} +1.58340 q^{34} -1.30114 q^{35} -1.39771 q^{37} +6.10547 q^{38} +4.64136 q^{40} +11.6229 q^{41} +3.27383 q^{43} -12.4209 q^{44} +4.32592 q^{46} -12.2105 q^{47} -5.30703 q^{49} -2.43091 q^{50} +6.35452 q^{53} +3.17726 q^{55} -6.03908 q^{56} -20.3693 q^{58} +5.98570 q^{59} +12.9875 q^{61} +20.6704 q^{62} -9.02320 q^{64} +13.1545 q^{67} -2.54637 q^{68} +3.16296 q^{70} -1.09657 q^{71} +12.2293 q^{73} +3.39771 q^{74} -9.81863 q^{76} -4.13407 q^{77} -1.33022 q^{79} -3.46410 q^{80} -28.2543 q^{82} -14.2668 q^{83} +0.651360 q^{85} -7.95839 q^{86} +14.7468 q^{88} -9.60386 q^{89} -6.95681 q^{92} +29.6825 q^{94} +2.51160 q^{95} -7.94681 q^{97} +12.9009 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{4} - 4 q^{5} + 6 q^{7}+O(q^{10}) $ 4 * q - 2 * q^2 + 4 * q^4 - 4 * q^5 + 6 * q^7	$ 4 q - 2 q^{2} + 4 q^{4} - 4 q^{5} + 6 q^{7} + 2 q^{10} - 8 q^{11} + 2 q^{14} + 2 q^{17} - 4 q^{20} - 4 q^{23} + 4 q^{25} + 4 q^{28} - 6 q^{29} - 12 q^{32} + 24 q^{34} - 6 q^{35} - 4 q^{37} - 8 q^{38} - 10 q^{41} + 6 q^{43} - 28 q^{44} - 12 q^{46} - 38 q^{47} - 8 q^{49} - 2 q^{50} + 16 q^{53} + 8 q^{55} - 4 q^{56} - 28 q^{58} + 14 q^{59} + 30 q^{62} - 16 q^{64} + 14 q^{67} + 16 q^{68} - 2 q^{70} - 2 q^{71} + 22 q^{73} + 12 q^{74} - 16 q^{76} - 4 q^{77} + 28 q^{79} - 24 q^{82} - 20 q^{83} - 2 q^{85} - 14 q^{86} + 8 q^{88} - 30 q^{89} - 20 q^{92} + 16 q^{94} - 10 q^{97} + 16 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^4 - 4 * q^5 + 6 * q^7 + 2 * q^10 - 8 * q^11 + 2 * q^14 + 2 * q^17 - 4 * q^20 - 4 * q^23 + 4 * q^25 + 4 * q^28 - 6 * q^29 - 12 * q^32 + 24 * q^34 - 6 * q^35 - 4 * q^37 - 8 * q^38 - 10 * q^41 + 6 * q^43 - 28 * q^44 - 12 * q^46 - 38 * q^47 - 8 * q^49 - 2 * q^50 + 16 * q^53 + 8 * q^55 - 4 * q^56 - 28 * q^58 + 14 * q^59 + 30 * q^62 - 16 * q^64 + 14 * q^67 + 16 * q^68 - 2 * q^70 - 2 * q^71 + 22 * q^73 + 12 * q^74 - 16 * q^76 - 4 * q^77 + 28 * q^79 - 24 * q^82 - 20 * q^83 - 2 * q^85 - 14 * q^86 + 8 * q^88 - 30 * q^89 - 20 * q^92 + 16 * q^94 - 10 * q^97 + 16 * 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 $

$2$	−2.43091	−1.71891	−0.859456	−	0.511210i	$-0.829197\pi$
$2$	−2.43091	−1.71891	−0.859456	+	0.511210i	$0.829197\pi$
$3$	0	0
$3$	0	0
$4$	3.90931	1.95466
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	1.30114	0.491786	0.245893	−	0.969297i	$-0.420919\pi$
$7$	1.30114	0.491786	0.245893	+	0.969297i	$0.420919\pi$
$8$	−4.64136	−1.64097
$9$	0	0
$10$	2.43091	0.768721
$11$	−3.17726	−0.957981	−0.478990	−	0.877820i	$-0.658997\pi$
$11$	−3.17726	−0.957981	−0.478990	+	0.877820i	$0.658997\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	−3.16296	−0.845336
$15$	0	0
$16$	3.46410	0.866025
$17$	−0.651360	−0.157978	−0.0789890	−	0.996875i	$-0.525169\pi$
$17$	−0.651360	−0.157978	−0.0789890	+	0.996875i	$0.525169\pi$
$18$	0	0
$19$	−2.51160	−0.576200	−0.288100	−	0.957600i	$-0.593024\pi$
$19$	−2.51160	−0.576200	−0.288100	+	0.957600i	$0.593024\pi$
$20$	−3.90931	−0.874149
$21$	0	0
$22$	7.72363	1.64668
$23$	−1.77955	−0.371061	−0.185531	−	0.982638i	$-0.559400\pi$
$23$	−1.77955	−0.371061	−0.185531	+	0.982638i	$0.559400\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	5.08658	0.961272
$29$	8.37930	1.55600	0.777998	−	0.628266i	$-0.216235\pi$
$29$	8.37930	1.55600	0.777998	+	0.628266i	$0.216235\pi$
$30$	0	0
$31$	−8.50318	−1.52722	−0.763608	−	0.645680i	$-0.776574\pi$
$31$	−8.50318	−1.52722	−0.763608	+	0.645680i	$0.776574\pi$
$32$	0.861816	0.152349
$33$	0	0
$34$	1.58340	0.271550
$35$	−1.30114	−0.219933
$36$	0	0
$37$	−1.39771	−0.229783	−0.114891	−	0.993378i	$-0.536652\pi$
$37$	−1.39771	−0.229783	−0.114891	+	0.993378i	$0.536652\pi$
$38$	6.10547	0.990437
$39$	0	0
$40$	4.64136	0.733864
$41$	11.6229	1.81520	0.907600	−	0.419836i	$-0.137913\pi$
$41$	11.6229	1.81520	0.907600	+	0.419836i	$0.137913\pi$
$42$	0	0
$43$	3.27383	0.499255	0.249627	−	0.968342i	$-0.419692\pi$
$43$	3.27383	0.499255	0.249627	+	0.968342i	$0.419692\pi$
$44$	−12.4209	−1.87252
$45$	0	0
$46$	4.32592	0.637822
$47$	−12.2105	−1.78108	−0.890539	−	0.454907i	$-0.849673\pi$
$47$	−12.2105	−1.78108	−0.890539	+	0.454907i	$0.849673\pi$
$48$	0	0
$49$	−5.30703	−0.758147
$50$	−2.43091	−0.343782
$51$	0	0
$52$	0	0
$53$	6.35452	0.872861	0.436431	−	0.899738i	$-0.356242\pi$
$53$	6.35452	0.872861	0.436431	+	0.899738i	$0.356242\pi$
$54$	0	0
$55$	3.17726	0.428422
$56$	−6.03908	−0.807006
$57$	0	0
$58$	−20.3693	−2.67462
$59$	5.98570	0.779271	0.389636	−	0.920969i	$-0.372601\pi$
$59$	5.98570	0.779271	0.389636	+	0.920969i	$0.372601\pi$
$60$	0	0
$61$	12.9875	1.66287	0.831437	−	0.555618i	$-0.187518\pi$
$61$	12.9875	1.66287	0.831437	+	0.555618i	$0.187518\pi$
$62$	20.6704	2.62515
$63$	0	0
$64$	−9.02320	−1.12790
$65$	0	0
$66$	0	0
$67$	13.1545	1.60708	0.803541	−	0.595249i	$-0.202947\pi$
$67$	13.1545	1.60708	0.803541	+	0.595249i	$0.202947\pi$
$68$	−2.54637	−0.308793
$69$	0	0
$70$	3.16296	0.378046
$71$	−1.09657	−0.130139	−0.0650695	−	0.997881i	$-0.520727\pi$
$71$	−1.09657	−0.130139	−0.0650695	+	0.997881i	$0.520727\pi$
$72$	0	0
$73$	12.2293	1.43134	0.715668	−	0.698440i	$-0.246122\pi$
$73$	12.2293	1.43134	0.715668	+	0.698440i	$0.246122\pi$
$74$	3.39771	0.394976
$75$	0	0
$76$	−9.81863	−1.12627
$77$	−4.13407	−0.471121
$78$	0	0
$79$	−1.33022	−0.149662	−0.0748310	−	0.997196i	$-0.523842\pi$
$79$	−1.33022	−0.149662	−0.0748310	+	0.997196i	$0.523842\pi$
$80$	−3.46410	−0.387298
$81$	0	0
$82$	−28.2543	−3.12017
$83$	−14.2668	−1.56599	−0.782995	−	0.622028i	$-0.786309\pi$
$83$	−14.2668	−1.56599	−0.782995	+	0.622028i	$0.786309\pi$
$84$	0	0
$85$	0.651360	0.0706499
$86$	−7.95839	−0.858175
$87$	0	0
$88$	14.7468	1.57202
$89$	−9.60386	−1.01801	−0.509004	−	0.860764i	$-0.669986\pi$
$89$	−9.60386	−1.01801	−0.509004	+	0.860764i	$0.669986\pi$
$90$	0	0
$91$	0	0
$92$	−6.95681	−0.725298
$93$	0	0
$94$	29.6825	3.06152
$95$	2.51160	0.257685
$96$	0	0
$97$	−7.94681	−0.806877	−0.403438	−	0.915007i	$-0.632185\pi$
$97$	−7.94681	−0.806877	−0.403438	+	0.915007i	$0.632185\pi$
$98$	12.9009	1.30319
$99$	0	0
$100$	3.90931	0.390931
$101$	2.12546	0.211491	0.105745	−	0.994393i	$-0.466277\pi$
$101$	2.12546	0.211491	0.105745	+	0.994393i	$0.466277\pi$
$102$	0	0
$103$	−0.985697	−0.0971236	−0.0485618	−	0.998820i	$-0.515464\pi$
$103$	−0.985697	−0.0971236	−0.0485618	+	0.998820i	$0.515464\pi$
$104$	0	0
$105$	0	0
$106$	−15.4473	−1.50037
$107$	12.3359	1.19256	0.596279	−	0.802777i	$-0.296645\pi$
$107$	12.3359	1.19256	0.596279	+	0.802777i	$0.296645\pi$
$108$	0	0
$109$	−0.870235	−0.0833534	−0.0416767	−	0.999131i	$-0.513270\pi$
$109$	−0.870235	−0.0833534	−0.0416767	+	0.999131i	$0.513270\pi$
$110$	−7.72363	−0.736419
$111$	0	0
$112$	4.50729	0.425899
$113$	15.1014	1.42062	0.710308	−	0.703891i	$-0.248556\pi$
$113$	15.1014	1.42062	0.710308	+	0.703891i	$0.248556\pi$
$114$	0	0
$115$	1.77955	0.165944
$116$	32.7573	3.04144
$117$	0	0
$118$	−14.5507	−1.33950
$119$	−0.847512	−0.0776913
$120$	0	0
$121$	−0.905006	−0.0822732
$122$	−31.5713	−2.85833
$123$	0	0
$124$	−33.2416	−2.98518
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−2.89631	−0.257006	−0.128503	−	0.991709i	$-0.541017\pi$
$127$	−2.89631	−0.257006	−0.128503	+	0.991709i	$0.541017\pi$
$128$	20.2109	1.78641
$129$	0	0
$130$	0	0
$131$	−15.7570	−1.37670	−0.688349	−	0.725380i	$-0.741664\pi$
$131$	−15.7570	−1.37670	−0.688349	+	0.725380i	$0.741664\pi$
$132$	0	0
$133$	−3.26795	−0.283367
$134$	−31.9775	−2.76243
$135$	0	0
$136$	3.02320	0.259237
$137$	−0.737739	−0.0630293	−0.0315147	−	0.999503i	$-0.510033\pi$
$137$	−0.737739	−0.0630293	−0.0315147	+	0.999503i	$0.510033\pi$
$138$	0	0
$139$	−19.7468	−1.67490	−0.837452	−	0.546511i	$-0.815956\pi$
$139$	−19.7468	−1.67490	−0.837452	+	0.546511i	$0.815956\pi$
$140$	−5.08658	−0.429894
$141$	0	0
$142$	2.66566	0.223697
$143$	0	0
$144$	0	0
$145$	−8.37930	−0.695863
$146$	−29.7284	−2.46034
$147$	0	0
$148$	−5.46410	−0.449146
$149$	−3.16549	−0.259327	−0.129664	−	0.991558i	$-0.541390\pi$
$149$	−3.16549	−0.259327	−0.129664	+	0.991558i	$0.541390\pi$
$150$	0	0
$151$	−0.168843	−0.0137402	−0.00687011	−	0.999976i	$-0.502187\pi$
$151$	−0.168843	−0.0137402	−0.00687011	+	0.999976i	$0.502187\pi$
$152$	11.6572	0.945527
$153$	0	0
$154$	10.0495	0.809816
$155$	8.50318	0.682992
$156$	0	0
$157$	13.5512	1.08150	0.540750	−	0.841183i	$-0.318141\pi$
$157$	13.5512	1.08150	0.540750	+	0.841183i	$0.318141\pi$
$158$	3.23365	0.257256
$159$	0	0
$160$	−0.861816	−0.0681325
$161$	−2.31545	−0.182483
$162$	0	0
$163$	−15.2061	−1.19104	−0.595519	−	0.803341i	$-0.703053\pi$
$163$	−15.2061	−1.19104	−0.595519	+	0.803341i	$0.703053\pi$
$164$	45.4377	3.54809
$165$	0	0
$166$	34.6814	2.69180
$167$	7.47587	0.578500	0.289250	−	0.957254i	$-0.406594\pi$
$167$	7.47587	0.578500	0.289250	+	0.957254i	$0.406594\pi$
$168$	0	0
$169$	0	0
$170$	−1.58340	−0.121441
$171$	0	0
$172$	12.7984	0.975872
$173$	9.29402	0.706611	0.353306	−	0.935508i	$-0.385058\pi$
$173$	9.29402	0.706611	0.353306	+	0.935508i	$0.385058\pi$
$174$	0	0
$175$	1.30114	0.0983572
$176$	−11.0064	−0.829636
$177$	0	0
$178$	23.3461	1.74986
$179$	−10.8475	−0.810781	−0.405391	−	0.914144i	$-0.632864\pi$
$179$	−10.8475	−0.810781	−0.405391	+	0.914144i	$0.632864\pi$
$180$	0	0
$181$	0.759361	0.0564428	0.0282214	−	0.999602i	$-0.491016\pi$
$181$	0.759361	0.0564428	0.0282214	+	0.999602i	$0.491016\pi$
$182$	0	0
$183$	0	0
$184$	8.25953	0.608901
$185$	1.39771	0.102762
$186$	0	0
$187$	2.06954	0.151340
$188$	−47.7345	−3.48140
$189$	0	0
$190$	−6.10547	−0.442937
$191$	−6.68298	−0.483563	−0.241782	−	0.970331i	$-0.577732\pi$
$191$	−6.68298	−0.483563	−0.241782	+	0.970331i	$0.577732\pi$
$192$	0	0
$193$	15.8288	1.13938	0.569692	−	0.821859i	$-0.307063\pi$
$193$	15.8288	1.13938	0.569692	+	0.821859i	$0.307063\pi$
$194$	19.3180	1.38695
$195$	0	0
$196$	−20.7468	−1.48192
$197$	−6.83451	−0.486938	−0.243469	−	0.969909i	$-0.578285\pi$
$197$	−6.83451	−0.486938	−0.243469	+	0.969909i	$0.578285\pi$
$198$	0	0
$199$	−17.2427	−1.22230	−0.611151	−	0.791514i	$-0.709293\pi$
$199$	−17.2427	−1.22230	−0.611151	+	0.791514i	$0.709293\pi$
$200$	−4.64136	−0.328194
$201$	0	0
$202$	−5.16679	−0.363534
$203$	10.9027	0.765217
$204$	0	0
$205$	−11.6229	−0.811782
$206$	2.39614	0.166947
$207$	0	0
$208$	0	0
$209$	7.98001	0.551989
$210$	0	0
$211$	−23.8132	−1.63937	−0.819685	−	0.572815i	$-0.805851\pi$
$211$	−23.8132	−1.63937	−0.819685	+	0.572815i	$0.805851\pi$
$212$	24.8418	1.70614
$213$	0	0
$214$	−29.9875	−2.04990
$215$	−3.27383	−0.223274
$216$	0	0
$217$	−11.0639	−0.751063
$218$	2.11546	0.143277
$219$	0	0
$220$	12.4209	0.837418
$221$	0	0
$222$	0	0
$223$	−10.7954	−0.722915	−0.361458	−	0.932389i	$-0.617721\pi$
$223$	−10.7954	−0.722915	−0.361458	+	0.932389i	$0.617721\pi$
$224$	1.12135	0.0749230
$225$	0	0
$226$	−36.7100	−2.44191
$227$	−10.5532	−0.700441	−0.350221	−	0.936667i	$-0.613893\pi$
$227$	−10.5532	−0.700441	−0.350221	+	0.936667i	$0.613893\pi$
$228$	0	0
$229$	−15.3248	−1.01269	−0.506346	−	0.862330i	$-0.669004\pi$
$229$	−15.3248	−1.01269	−0.506346	+	0.862330i	$0.669004\pi$
$230$	−4.32592	−0.285243
$231$	0	0
$232$	−38.8914	−2.55334
$233$	9.96092	0.652562	0.326281	−	0.945273i	$-0.394204\pi$
$233$	9.96092	0.652562	0.326281	+	0.945273i	$0.394204\pi$
$234$	0	0
$235$	12.2105	0.796522
$236$	23.4000	1.52321
$237$	0	0
$238$	2.06022	0.133544
$239$	2.47998	0.160417	0.0802083	−	0.996778i	$-0.474441\pi$
$239$	2.47998	0.160417	0.0802083	+	0.996778i	$0.474441\pi$
$240$	0	0
$241$	28.4748	1.83422	0.917111	−	0.398633i	$-0.130515\pi$
$241$	28.4748	1.83422	0.917111	+	0.398633i	$0.130515\pi$
$242$	2.19999	0.141420
$243$	0	0
$244$	50.7721	3.25035
$245$	5.30703	0.339054
$246$	0	0
$247$	0	0
$248$	39.4663	2.50612
$249$	0	0
$250$	2.43091	0.153744
$251$	−26.9591	−1.70164	−0.850820	−	0.525457i	$-0.823894\pi$
$251$	−26.9591	−1.70164	−0.850820	+	0.525457i	$0.823894\pi$
$252$	0	0
$253$	5.65409	0.355470
$254$	7.04065	0.441770
$255$	0	0
$256$	−31.0845	−1.94278
$257$	8.59229	0.535972	0.267986	−	0.963423i	$-0.413642\pi$
$257$	8.59229	0.535972	0.267986	+	0.963423i	$0.413642\pi$
$258$	0	0
$259$	−1.81863	−0.113004
$260$	0	0
$261$	0	0
$262$	38.3039	2.36642
$263$	14.6345	0.902403	0.451202	−	0.892422i	$-0.350996\pi$
$263$	14.6345	0.902403	0.451202	+	0.892422i	$0.350996\pi$
$264$	0	0
$265$	−6.35452	−0.390355
$266$	7.94408	0.487083
$267$	0	0
$268$	51.4252	3.14129
$269$	−7.37519	−0.449673	−0.224837	−	0.974396i	$-0.572185\pi$
$269$	−7.37519	−0.449673	−0.224837	+	0.974396i	$0.572185\pi$
$270$	0	0
$271$	11.7902	0.716205	0.358102	−	0.933682i	$-0.383424\pi$
$271$	11.7902	0.716205	0.358102	+	0.933682i	$0.383424\pi$
$272$	−2.25638	−0.136813
$273$	0	0
$274$	1.79338	0.108342
$275$	−3.17726	−0.191596
$276$	0	0
$277$	−19.2510	−1.15668	−0.578339	−	0.815796i	$-0.696299\pi$
$277$	−19.2510	−1.15668	−0.578339	+	0.815796i	$0.696299\pi$
$278$	48.0027	2.87901
$279$	0	0
$280$	6.03908	0.360904
$281$	−25.4911	−1.52067	−0.760336	−	0.649529i	$-0.774966\pi$
$281$	−25.4911	−1.52067	−0.760336	+	0.649529i	$0.774966\pi$
$282$	0	0
$283$	−5.17268	−0.307484	−0.153742	−	0.988111i	$-0.549132\pi$
$283$	−5.17268	−0.307484	−0.153742	+	0.988111i	$0.549132\pi$
$284$	−4.28684	−0.254377
$285$	0	0
$286$	0	0
$287$	15.1231	0.892689
$288$	0	0
$289$	−16.5757	−0.975043
$290$	20.3693	1.19613
$291$	0	0
$292$	47.8083	2.79777
$293$	25.9923	1.51848	0.759242	−	0.650809i	$-0.225570\pi$
$293$	25.9923	1.51848	0.759242	+	0.650809i	$0.225570\pi$
$294$	0	0
$295$	−5.98570	−0.348501
$296$	6.48730	0.377067
$297$	0	0
$298$	7.69502	0.445761
$299$	0	0
$300$	0	0
$301$	4.25973	0.245526
$302$	0.410441	0.0236182
$303$	0	0
$304$	−8.70043	−0.499004
$305$	−12.9875	−0.743660
$306$	0	0
$307$	20.7454	1.18400	0.592001	−	0.805937i	$-0.298338\pi$
$307$	20.7454	1.18400	0.592001	+	0.805937i	$0.298338\pi$
$308$	−16.1614	−0.920880
$309$	0	0
$310$	−20.6704	−1.17400
$311$	1.72617	0.0978819	0.0489410	−	0.998802i	$-0.484415\pi$
$311$	1.72617	0.0978819	0.0489410	+	0.998802i	$0.484415\pi$
$312$	0	0
$313$	6.29703	0.355929	0.177965	−	0.984037i	$-0.443049\pi$
$313$	6.29703	0.355929	0.177965	+	0.984037i	$0.443049\pi$
$314$	−32.9416	−1.85900
$315$	0	0
$316$	−5.20026	−0.292538
$317$	−10.5750	−0.593950	−0.296975	−	0.954885i	$-0.595978\pi$
$317$	−10.5750	−0.593950	−0.296975	+	0.954885i	$0.595978\pi$
$318$	0	0
$319$	−26.6232	−1.49061
$320$	9.02320	0.504412
$321$	0	0
$322$	5.62864	0.313672
$323$	1.63595	0.0910269
$324$	0	0
$325$	0	0
$326$	36.9647	2.04729
$327$	0	0
$328$	−53.9463	−2.97869
$329$	−15.8875	−0.875909
$330$	0	0
$331$	5.77243	0.317281	0.158641	−	0.987336i	$-0.449289\pi$
$331$	5.77243	0.317281	0.158641	+	0.987336i	$0.449289\pi$
$332$	−55.7736	−3.06097
$333$	0	0
$334$	−18.1732	−0.994391
$335$	−13.1545	−0.718709
$336$	0	0
$337$	−2.08610	−0.113637	−0.0568186	−	0.998385i	$-0.518096\pi$
$337$	−2.08610	−0.113637	−0.0568186	+	0.998385i	$0.518096\pi$
$338$	0	0
$339$	0	0
$340$	2.54637	0.138096
$341$	27.0168	1.46304
$342$	0	0
$343$	−16.0132	−0.864632
$344$	−15.1951	−0.819262
$345$	0	0
$346$	−22.5929	−1.21460
$347$	7.68326	0.412459	0.206229	−	0.978504i	$-0.433881\pi$
$347$	7.68326	0.412459	0.206229	+	0.978504i	$0.433881\pi$
$348$	0	0
$349$	16.7973	0.899141	0.449570	−	0.893245i	$-0.351577\pi$
$349$	16.7973	0.899141	0.449570	+	0.893245i	$0.351577\pi$
$350$	−3.16296	−0.169067
$351$	0	0
$352$	−2.73821	−0.145947
$353$	−0.162679	−0.00865854	−0.00432927	−	0.999991i	$-0.501378\pi$
$353$	−0.162679	−0.00865854	−0.00432927	+	0.999991i	$0.501378\pi$
$354$	0	0
$355$	1.09657	0.0582000
$356$	−37.5445	−1.98985
$357$	0	0
$358$	26.3693	1.39366
$359$	−19.3374	−1.02059	−0.510295	−	0.860000i	$-0.670464\pi$
$359$	−19.3374	−1.02059	−0.510295	+	0.860000i	$0.670464\pi$
$360$	0	0
$361$	−12.6919	−0.667993
$362$	−1.84594	−0.0970202
$363$	0	0
$364$	0	0
$365$	−12.2293	−0.640113
$366$	0	0
$367$	−2.26842	−0.118411	−0.0592054	−	0.998246i	$-0.518857\pi$
$367$	−2.26842	−0.118411	−0.0592054	+	0.998246i	$0.518857\pi$
$368$	−6.16454	−0.321349
$369$	0	0
$370$	−3.39771	−0.176639
$371$	8.26814	0.429261
$372$	0	0
$373$	−11.9287	−0.617644	−0.308822	−	0.951120i	$-0.599935\pi$
$373$	−11.9287	−0.617644	−0.308822	+	0.951120i	$0.599935\pi$
$374$	−5.03086	−0.260140
$375$	0	0
$376$	56.6732	2.92270
$377$	0	0
$378$	0	0
$379$	−11.5204	−0.591761	−0.295880	−	0.955225i	$-0.595613\pi$
$379$	−11.5204	−0.591761	−0.295880	+	0.955225i	$0.595613\pi$
$380$	9.81863	0.503685
$381$	0	0
$382$	16.2457	0.831202
$383$	−13.8105	−0.705683	−0.352841	−	0.935683i	$-0.614784\pi$
$383$	−13.8105	−0.705683	−0.352841	+	0.935683i	$0.614784\pi$
$384$	0	0
$385$	4.13407	0.210692
$386$	−38.4784	−1.95850
$387$	0	0
$388$	−31.0666	−1.57717
$389$	−13.9037	−0.704946	−0.352473	−	0.935822i	$-0.614659\pi$
$389$	−13.9037	−0.704946	−0.352473	+	0.935822i	$0.614659\pi$
$390$	0	0
$391$	1.15913	0.0586195
$392$	24.6318	1.24410
$393$	0	0
$394$	16.6141	0.837004
$395$	1.33022	0.0669309
$396$	0	0
$397$	24.9732	1.25337	0.626684	−	0.779274i	$-0.284412\pi$
$397$	24.9732	1.25337	0.626684	+	0.779274i	$0.284412\pi$
$398$	41.9154	2.10103
$399$	0	0
$400$	3.46410	0.173205
$401$	−9.14134	−0.456497	−0.228248	−	0.973603i	$-0.573300\pi$
$401$	−9.14134	−0.456497	−0.228248	+	0.973603i	$0.573300\pi$
$402$	0	0
$403$	0	0
$404$	8.30908	0.413392
$405$	0	0
$406$	−26.5034	−1.31534
$407$	4.44090	0.220127
$408$	0	0
$409$	24.4168	1.20733	0.603667	−	0.797237i	$-0.293706\pi$
$409$	24.4168	1.20733	0.603667	+	0.797237i	$0.293706\pi$
$410$	28.2543	1.39538
$411$	0	0
$412$	−3.85340	−0.189843
$413$	7.78825	0.383235
$414$	0	0
$415$	14.2668	0.700332
$416$	0	0
$417$	0	0
$418$	−19.3987	−0.948820
$419$	−6.97427	−0.340715	−0.170358	−	0.985382i	$-0.554492\pi$
$419$	−6.97427	−0.340715	−0.170358	+	0.985382i	$0.554492\pi$
$420$	0	0
$421$	0.673176	0.0328086	0.0164043	−	0.999865i	$-0.494778\pi$
$421$	0.673176	0.0328086	0.0164043	+	0.999865i	$0.494778\pi$
$422$	57.8877	2.81793
$423$	0	0
$424$	−29.4937	−1.43234
$425$	−0.651360	−0.0315956
$426$	0	0
$427$	16.8986	0.817778
$428$	48.2249	2.33104
$429$	0	0
$430$	7.95839	0.383787
$431$	−28.0309	−1.35020	−0.675099	−	0.737727i	$-0.735899\pi$
$431$	−28.0309	−1.35020	−0.675099	+	0.737727i	$0.735899\pi$
$432$	0	0
$433$	2.66633	0.128136	0.0640679	−	0.997946i	$-0.479593\pi$
$433$	2.66633	0.128136	0.0640679	+	0.997946i	$0.479593\pi$
$434$	26.8952	1.29101
$435$	0	0
$436$	−3.40202	−0.162927
$437$	4.46951	0.213806
$438$	0	0
$439$	22.0739	1.05353	0.526765	−	0.850011i	$-0.323405\pi$
$439$	22.0739	1.05353	0.526765	+	0.850011i	$0.323405\pi$
$440$	−14.7468	−0.703027
$441$	0	0
$442$	0	0
$443$	−14.6927	−0.698070	−0.349035	−	0.937110i	$-0.613491\pi$
$443$	−14.6927	−0.698070	−0.349035	+	0.937110i	$0.613491\pi$
$444$	0	0
$445$	9.60386	0.455267
$446$	26.2427	1.24263
$447$	0	0
$448$	−11.7405	−0.554685
$449$	5.63725	0.266038	0.133019	−	0.991113i	$-0.457533\pi$
$449$	5.63725	0.266038	0.133019	+	0.991113i	$0.457533\pi$
$450$	0	0
$451$	−36.9292	−1.73893
$452$	59.0359	2.77682
$453$	0	0
$454$	25.6539	1.20400
$455$	0	0
$456$	0	0
$457$	−5.07323	−0.237316	−0.118658	−	0.992935i	$-0.537859\pi$
$457$	−5.07323	−0.237316	−0.118658	+	0.992935i	$0.537859\pi$
$458$	37.2532	1.74073
$459$	0	0
$460$	6.95681	0.324363
$461$	33.0893	1.54112	0.770561	−	0.637366i	$-0.219976\pi$
$461$	33.0893	1.54112	0.770561	+	0.637366i	$0.219976\pi$
$462$	0	0
$463$	−24.4976	−1.13850	−0.569251	−	0.822164i	$-0.692767\pi$
$463$	−24.4976	−1.13850	−0.569251	+	0.822164i	$0.692767\pi$
$464$	29.0267	1.34753
$465$	0	0
$466$	−24.2141	−1.12170
$467$	−30.5932	−1.41569	−0.707843	−	0.706370i	$-0.750332\pi$
$467$	−30.5932	−1.41569	−0.707843	+	0.706370i	$0.750332\pi$
$468$	0	0
$469$	17.1159	0.790341
$470$	−29.6825	−1.36915
$471$	0	0
$472$	−27.7818	−1.27876
$473$	−10.4018	−0.478276
$474$	0	0
$475$	−2.51160	−0.115240
$476$	−3.31319	−0.151860
$477$	0	0
$478$	−6.02861	−0.275742
$479$	13.9180	0.635930	0.317965	−	0.948102i	$-0.397001\pi$
$479$	13.9180	0.635930	0.317965	+	0.948102i	$0.397001\pi$
$480$	0	0
$481$	0	0
$482$	−69.2195	−3.15286
$483$	0	0
$484$	−3.53795	−0.160816
$485$	7.94681	0.360846
$486$	0	0
$487$	30.5516	1.38443	0.692213	−	0.721693i	$-0.256636\pi$
$487$	30.5516	1.38443	0.692213	+	0.721693i	$0.256636\pi$
$488$	−60.2796	−2.72873
$489$	0	0
$490$	−12.9009	−0.582803
$491$	14.6843	0.662692	0.331346	−	0.943509i	$-0.392497\pi$
$491$	14.6843	0.662692	0.331346	+	0.943509i	$0.392497\pi$
$492$	0	0
$493$	−5.45794	−0.245813
$494$	0	0
$495$	0	0
$496$	−29.4559	−1.32261
$497$	−1.42680	−0.0640005
$498$	0	0
$499$	16.1489	0.722922	0.361461	−	0.932387i	$-0.382278\pi$
$499$	16.1489	0.722922	0.361461	+	0.932387i	$0.382278\pi$
$500$	−3.90931	−0.174830
$501$	0	0
$502$	65.5350	2.92497
$503$	2.00861	0.0895597	0.0447799	−	0.998997i	$-0.485741\pi$
$503$	2.00861	0.0895597	0.0447799	+	0.998997i	$0.485741\pi$
$504$	0	0
$505$	−2.12546	−0.0945816
$506$	−13.7446	−0.611021
$507$	0	0
$508$	−11.3226	−0.502358
$509$	38.3971	1.70192	0.850962	−	0.525228i	$-0.176020\pi$
$509$	38.3971	1.70192	0.850962	+	0.525228i	$0.176020\pi$
$510$	0	0
$511$	15.9121	0.703911
$512$	35.1417	1.55306
$513$	0	0
$514$	−20.8871	−0.921289
$515$	0.985697	0.0434350
$516$	0	0
$517$	38.7958	1.70624
$518$	4.42091	0.194244
$519$	0	0
$520$	0	0
$521$	−31.2138	−1.36750	−0.683751	−	0.729716i	$-0.739652\pi$
$521$	−31.2138	−1.36750	−0.683751	+	0.729716i	$0.739652\pi$
$522$	0	0
$523$	33.2081	1.45209	0.726045	−	0.687647i	$-0.241357\pi$
$523$	33.2081	1.45209	0.726045	+	0.687647i	$0.241357\pi$
$524$	−61.5991	−2.69097
$525$	0	0
$526$	−35.5752	−1.55115
$527$	5.53863	0.241266
$528$	0	0
$529$	−19.8332	−0.862313
$530$	15.4473	0.670986
$531$	0	0
$532$	−12.7754	−0.553885
$533$	0	0
$534$	0	0
$535$	−12.3359	−0.533328
$536$	−61.0550	−2.63717
$537$	0	0
$538$	17.9284	0.772948
$539$	16.8618	0.726290
$540$	0	0
$541$	−39.1911	−1.68496	−0.842478	−	0.538731i	$-0.818904\pi$
$541$	−39.1911	−1.68496	−0.842478	+	0.538731i	$0.818904\pi$
$542$	−28.6609	−1.23109
$543$	0	0
$544$	−0.561352	−0.0240678
$545$	0.870235	0.0372768
$546$	0	0
$547$	8.26842	0.353532	0.176766	−	0.984253i	$-0.443436\pi$
$547$	8.26842	0.353532	0.176766	+	0.984253i	$0.443436\pi$
$548$	−2.88405	−0.123201
$549$	0	0
$550$	7.72363	0.329337
$551$	−21.0454	−0.896566
$552$	0	0
$553$	−1.73081	−0.0736016
$554$	46.7973	1.98823
$555$	0	0
$556$	−77.1965	−3.27386
$557$	−45.0632	−1.90939	−0.954695	−	0.297586i	$-0.903819\pi$
$557$	−45.0632	−1.90939	−0.954695	+	0.297586i	$0.903819\pi$
$558$	0	0
$559$	0	0
$560$	−4.50729	−0.190468
$561$	0	0
$562$	61.9666	2.61390
$563$	45.8777	1.93352	0.966758	−	0.255693i	$-0.0823036\pi$
$563$	45.8777	1.93352	0.966758	+	0.255693i	$0.0823036\pi$
$564$	0	0
$565$	−15.1014	−0.635319
$566$	12.5743	0.528537
$567$	0	0
$568$	5.08959	0.213554
$569$	−6.12068	−0.256592	−0.128296	−	0.991736i	$-0.540951\pi$
$569$	−6.12068	−0.256592	−0.128296	+	0.991736i	$0.540951\pi$
$570$	0	0
$571$	19.2267	0.804611	0.402306	−	0.915505i	$-0.368209\pi$
$571$	19.2267	0.804611	0.402306	+	0.915505i	$0.368209\pi$
$572$	0	0
$573$	0	0
$574$	−36.7629	−1.53445
$575$	−1.77955	−0.0742123
$576$	0	0
$577$	−9.40689	−0.391614	−0.195807	−	0.980642i	$-0.562733\pi$
$577$	−9.40689	−0.391614	−0.195807	+	0.980642i	$0.562733\pi$
$578$	40.2941	1.67601
$579$	0	0
$580$	−32.7573	−1.36017
$581$	−18.5632	−0.770132
$582$	0	0
$583$	−20.1900	−0.836184
$584$	−56.7608	−2.34878
$585$	0	0
$586$	−63.1848	−2.61014
$587$	37.2286	1.53659	0.768294	−	0.640097i	$-0.221106\pi$
$587$	37.2286	1.53659	0.768294	+	0.640097i	$0.221106\pi$
$588$	0	0
$589$	21.3566	0.879982
$590$	14.5507	0.599042
$591$	0	0
$592$	−4.84182	−0.198998
$593$	−18.1214	−0.744157	−0.372078	−	0.928201i	$-0.621355\pi$
$593$	−18.1214	−0.744157	−0.372078	+	0.928201i	$0.621355\pi$
$594$	0	0
$595$	0.847512	0.0347446
$596$	−12.3749	−0.506896
$597$	0	0
$598$	0	0
$599$	7.18204	0.293450	0.146725	−	0.989177i	$-0.453127\pi$
$599$	7.18204	0.293450	0.146725	+	0.989177i	$0.453127\pi$
$600$	0	0
$601$	−33.0739	−1.34911	−0.674556	−	0.738223i	$-0.735665\pi$
$601$	−33.0739	−1.34911	−0.674556	+	0.738223i	$0.735665\pi$
$602$	−10.3550	−0.422038
$603$	0	0
$604$	−0.660059	−0.0268574
$605$	0.905006	0.0367937
$606$	0	0
$607$	21.6142	0.877295	0.438648	−	0.898659i	$-0.355458\pi$
$607$	21.6142	0.877295	0.438648	+	0.898659i	$0.355458\pi$
$608$	−2.16454	−0.0877835
$609$	0	0
$610$	31.5713	1.27829
$611$	0	0
$612$	0	0
$613$	−27.3537	−1.10481	−0.552403	−	0.833577i	$-0.686289\pi$
$613$	−27.3537	−1.10481	−0.552403	+	0.833577i	$0.686289\pi$
$614$	−50.4301	−2.03519
$615$	0	0
$616$	19.1877	0.773096
$617$	−16.3304	−0.657436	−0.328718	−	0.944428i	$-0.606617\pi$
$617$	−16.3304	−0.657436	−0.328718	+	0.944428i	$0.606617\pi$
$618$	0	0
$619$	35.8801	1.44214	0.721072	−	0.692860i	$-0.243650\pi$
$619$	35.8801	1.44214	0.721072	+	0.692860i	$0.243650\pi$
$620$	33.2416	1.33501
$621$	0	0
$622$	−4.19615	−0.168250
$623$	−12.4960	−0.500642
$624$	0	0
$625$	1.00000	0.0400000
$626$	−15.3075	−0.611811
$627$	0	0
$628$	52.9757	2.11396
$629$	0.910415	0.0363006
$630$	0	0
$631$	−7.04769	−0.280564	−0.140282	−	0.990112i	$-0.544801\pi$
$631$	−7.04769	−0.280564	−0.140282	+	0.990112i	$0.544801\pi$
$632$	6.17406	0.245591
$633$	0	0
$634$	25.7068	1.02095
$635$	2.89631	0.114936
$636$	0	0
$637$	0	0
$638$	64.7186	2.56223
$639$	0	0
$640$	−20.2109	−0.798907
$641$	−40.9504	−1.61745	−0.808723	−	0.588190i	$-0.799841\pi$
$641$	−40.9504	−1.61745	−0.808723	+	0.588190i	$0.799841\pi$
$642$	0	0
$643$	−35.2189	−1.38890	−0.694448	−	0.719543i	$-0.744351\pi$
$643$	−35.2189	−1.38890	−0.694448	+	0.719543i	$0.744351\pi$
$644$	−9.05180	−0.356691
$645$	0	0
$646$	−3.97685	−0.156467
$647$	−28.4718	−1.11934	−0.559670	−	0.828715i	$-0.689072\pi$
$647$	−28.4718	−1.11934	−0.559670	+	0.828715i	$0.689072\pi$
$648$	0	0
$649$	−19.0181	−0.746527
$650$	0	0
$651$	0	0
$652$	−59.4456	−2.32807
$653$	−31.2664	−1.22355	−0.611774	−	0.791033i	$-0.709544\pi$
$653$	−31.2664	−1.22355	−0.611774	+	0.791033i	$0.709544\pi$
$654$	0	0
$655$	15.7570	0.615678
$656$	40.2631	1.57201
$657$	0	0
$658$	38.6212	1.50561
$659$	3.22236	0.125525	0.0627627	−	0.998028i	$-0.480009\pi$
$659$	3.22236	0.125525	0.0627627	+	0.998028i	$0.480009\pi$
$660$	0	0
$661$	−29.9547	−1.16510	−0.582552	−	0.812793i	$-0.697946\pi$
$661$	−29.9547	−1.16510	−0.582552	+	0.812793i	$0.697946\pi$
$662$	−14.0322	−0.545378
$663$	0	0
$664$	66.2176	2.56974
$665$	3.26795	0.126726
$666$	0	0
$667$	−14.9114	−0.577370
$668$	29.2255	1.13077
$669$	0	0
$670$	31.9775	1.23540
$671$	−41.2646	−1.59300
$672$	0	0
$673$	−29.7673	−1.14744	−0.573722	−	0.819050i	$-0.694501\pi$
$673$	−29.7673	−1.14744	−0.573722	+	0.819050i	$0.694501\pi$
$674$	5.07112	0.195332
$675$	0	0
$676$	0	0
$677$	−24.8749	−0.956019	−0.478010	−	0.878355i	$-0.658642\pi$
$677$	−24.8749	−0.956019	−0.478010	+	0.878355i	$0.658642\pi$
$678$	0	0
$679$	−10.3399	−0.396811
$680$	−3.02320	−0.115934
$681$	0	0
$682$	−65.6754	−2.51484
$683$	9.13134	0.349401	0.174701	−	0.984622i	$-0.444104\pi$
$683$	9.13134	0.349401	0.174701	+	0.984622i	$0.444104\pi$
$684$	0	0
$685$	0.737739	0.0281876
$686$	38.9266	1.48623
$687$	0	0
$688$	11.3409	0.432367
$689$	0	0
$690$	0	0
$691$	−32.9873	−1.25490	−0.627449	−	0.778658i	$-0.715901\pi$
$691$	−32.9873	−1.25490	−0.627449	+	0.778658i	$0.715901\pi$
$692$	36.3332	1.38118
$693$	0	0
$694$	−18.6773	−0.708980
$695$	19.7468	0.749040
$696$	0	0
$697$	−7.57072	−0.286762
$698$	−40.8328	−1.54554
$699$	0	0
$700$	5.08658	0.192254
$701$	−24.6223	−0.929971	−0.464985	−	0.885318i	$-0.653940\pi$
$701$	−24.6223	−0.929971	−0.464985	+	0.885318i	$0.653940\pi$
$702$	0	0
$703$	3.51050	0.132401
$704$	28.6691	1.08051
$705$	0	0
$706$	0.395458	0.0148833
$707$	2.76552	0.104008
$708$	0	0
$709$	49.8515	1.87221	0.936107	−	0.351716i	$-0.114402\pi$
$709$	49.8515	1.87221	0.936107	+	0.351716i	$0.114402\pi$
$710$	−2.66566	−0.100041
$711$	0	0
$712$	44.5750	1.67052
$713$	15.1318	0.566691
$714$	0	0
$715$	0	0
$716$	−42.4063	−1.58480
$717$	0	0
$718$	47.0075	1.75430
$719$	12.6725	0.472605	0.236302	−	0.971680i	$-0.424064\pi$
$719$	12.6725	0.472605	0.236302	+	0.971680i	$0.424064\pi$
$720$	0	0
$721$	−1.28253	−0.0477640
$722$	30.8528	1.14822
$723$	0	0
$724$	2.96858	0.110326
$725$	8.37930	0.311199
$726$	0	0
$727$	−26.0757	−0.967093	−0.483547	−	0.875319i	$-0.660652\pi$
$727$	−26.0757	−0.967093	−0.483547	+	0.875319i	$0.660652\pi$
$728$	0	0
$729$	0	0
$730$	29.7284	1.10030
$731$	−2.13244	−0.0788713
$732$	0	0
$733$	3.39408	0.125363	0.0626815	−	0.998034i	$-0.480035\pi$
$733$	3.39408	0.125363	0.0626815	+	0.998034i	$0.480035\pi$
$734$	5.51433	0.203538
$735$	0	0
$736$	−1.53364	−0.0565308
$737$	−41.7954	−1.53955
$738$	0	0
$739$	6.79283	0.249878	0.124939	−	0.992164i	$-0.460126\pi$
$739$	6.79283	0.249878	0.124939	+	0.992164i	$0.460126\pi$
$740$	5.46410	0.200864
$741$	0	0
$742$	−20.0991	−0.737861
$743$	13.7336	0.503838	0.251919	−	0.967748i	$-0.418938\pi$
$743$	13.7336	0.503838	0.251919	+	0.967748i	$0.418938\pi$
$744$	0	0
$745$	3.16549	0.115975
$746$	28.9975	1.06167
$747$	0	0
$748$	8.09048	0.295817
$749$	16.0508	0.586483
$750$	0	0
$751$	−40.7747	−1.48789	−0.743944	−	0.668241i	$-0.767047\pi$
$751$	−40.7747	−1.48789	−0.743944	+	0.668241i	$0.767047\pi$
$752$	−42.2983	−1.54246
$753$	0	0
$754$	0	0
$755$	0.168843	0.00614481
$756$	0	0
$757$	−13.5939	−0.494077	−0.247039	−	0.969006i	$-0.579457\pi$
$757$	−13.5939	−0.494077	−0.247039	+	0.969006i	$0.579457\pi$
$758$	28.0049	1.01718
$759$	0	0
$760$	−11.6572	−0.422853
$761$	−9.80815	−0.355545	−0.177773	−	0.984072i	$-0.556889\pi$
$761$	−9.80815	−0.355545	−0.177773	+	0.984072i	$0.556889\pi$
$762$	0	0
$763$	−1.13230	−0.0409920
$764$	−26.1258	−0.945200
$765$	0	0
$766$	33.5720	1.21301
$767$	0	0
$768$	0	0
$769$	43.2829	1.56082	0.780411	−	0.625267i	$-0.215010\pi$
$769$	43.2829	1.56082	0.780411	+	0.625267i	$0.215010\pi$
$770$	−10.0495	−0.362161
$771$	0	0
$772$	61.8798	2.22710
$773$	−24.2208	−0.871163	−0.435582	−	0.900149i	$-0.643457\pi$
$773$	−24.2208	−0.871163	−0.435582	+	0.900149i	$0.643457\pi$
$774$	0	0
$775$	−8.50318	−0.305443
$776$	36.8841	1.32406
$777$	0	0
$778$	33.7986	1.21174
$779$	−29.1922	−1.04592
$780$	0	0
$781$	3.48409	0.124671
$782$	−2.81773	−0.100762
$783$	0	0
$784$	−18.3841	−0.656574
$785$	−13.5512	−0.483661
$786$	0	0
$787$	10.4775	0.373482	0.186741	−	0.982409i	$-0.440207\pi$
$787$	10.4775	0.373482	0.186741	+	0.982409i	$0.440207\pi$
$788$	−26.7182	−0.951797
$789$	0	0
$790$	−3.23365	−0.115048
$791$	19.6490	0.698639
$792$	0	0
$793$	0	0
$794$	−60.7075	−2.15443
$795$	0	0
$796$	−67.4071	−2.38918
$797$	−46.2137	−1.63697	−0.818486	−	0.574527i	$-0.805186\pi$
$797$	−46.2137	−1.63697	−0.818486	+	0.574527i	$0.805186\pi$
$798$	0	0
$799$	7.95340	0.281371
$800$	0.861816	0.0304698
$801$	0	0
$802$	22.2217	0.784677
$803$	−38.8558	−1.37119
$804$	0	0
$805$	2.31545	0.0816088
$806$	0	0
$807$	0	0
$808$	−9.86502	−0.347050
$809$	−7.21280	−0.253588	−0.126794	−	0.991929i	$-0.540469\pi$
$809$	−7.21280	−0.253588	−0.126794	+	0.991929i	$0.540469\pi$
$810$	0	0
$811$	−44.8652	−1.57543	−0.787714	−	0.616040i	$-0.788736\pi$
$811$	−44.8652	−1.57543	−0.787714	+	0.616040i	$0.788736\pi$
$812$	42.6219	1.49574
$813$	0	0
$814$	−10.7954	−0.378380
$815$	15.2061	0.532648
$816$	0	0
$817$	−8.22256	−0.287671
$818$	−59.3550	−2.07530
$819$	0	0
$820$	−45.4377	−1.58675
$821$	−45.6331	−1.59261	−0.796304	−	0.604897i	$-0.793214\pi$
$821$	−45.6331	−1.59261	−0.796304	+	0.604897i	$0.793214\pi$
$822$	0	0
$823$	−13.9305	−0.485585	−0.242793	−	0.970078i	$-0.578063\pi$
$823$	−13.9305	−0.485585	−0.242793	+	0.970078i	$0.578063\pi$
$824$	4.57498	0.159377
$825$	0	0
$826$	−18.9325	−0.658746
$827$	−17.8737	−0.621530	−0.310765	−	0.950487i	$-0.600585\pi$
$827$	−17.8737	−0.621530	−0.310765	+	0.950487i	$0.600585\pi$
$828$	0	0
$829$	−35.4471	−1.23113	−0.615565	−	0.788086i	$-0.711072\pi$
$829$	−35.4471	−1.23113	−0.615565	+	0.788086i	$0.711072\pi$
$830$	−34.6814	−1.20381
$831$	0	0
$832$	0	0
$833$	3.45678	0.119770
$834$	0	0
$835$	−7.47587	−0.258713
$836$	31.1963	1.07895
$837$	0	0
$838$	16.9538	0.585659
$839$	7.03052	0.242720	0.121360	−	0.992609i	$-0.461274\pi$
$839$	7.03052	0.242720	0.121360	+	0.992609i	$0.461274\pi$
$840$	0	0
$841$	41.2126	1.42113
$842$	−1.63643	−0.0563951
$843$	0	0
$844$	−93.0933	−3.20440
$845$	0	0
$846$	0	0
$847$	−1.17754	−0.0404608
$848$	22.0127	0.755920
$849$	0	0
$850$	1.58340	0.0543100
$851$	2.48730	0.0852635
$852$	0	0
$853$	−25.7138	−0.880425	−0.440212	−	0.897894i	$-0.645097\pi$
$853$	−25.7138	−0.880425	−0.440212	+	0.897894i	$0.645097\pi$
$854$	−41.0788	−1.40569
$855$	0	0
$856$	−57.2555	−1.95695
$857$	−20.7578	−0.709072	−0.354536	−	0.935042i	$-0.615361\pi$
$857$	−20.7578	−0.709072	−0.354536	+	0.935042i	$0.615361\pi$
$858$	0	0
$859$	−9.79466	−0.334190	−0.167095	−	0.985941i	$-0.553439\pi$
$859$	−9.79466	−0.334190	−0.167095	+	0.985941i	$0.553439\pi$
$860$	−12.7984	−0.436423
$861$	0	0
$862$	68.1404	2.32087
$863$	−23.1995	−0.789720	−0.394860	−	0.918741i	$-0.629207\pi$
$863$	−23.1995	−0.789720	−0.394860	+	0.918741i	$0.629207\pi$
$864$	0	0
$865$	−9.29402	−0.316006
$866$	−6.48161	−0.220254
$867$	0	0
$868$	−43.2521	−1.46807
$869$	4.22647	0.143373
$870$	0	0
$871$	0	0
$872$	4.03908	0.136780
$873$	0	0
$874$	−10.8650	−0.367513
$875$	−1.30114	−0.0439867
$876$	0	0
$877$	57.4364	1.93949	0.969745	−	0.244118i	$-0.0784985\pi$
$877$	57.4364	1.93949	0.969745	+	0.244118i	$0.0784985\pi$
$878$	−53.6596	−1.81092
$879$	0	0
$880$	11.0064	0.371024
$881$	−20.8628	−0.702884	−0.351442	−	0.936210i	$-0.614309\pi$
$881$	−20.8628	−0.702884	−0.351442	+	0.936210i	$0.614309\pi$
$882$	0	0
$883$	−39.9752	−1.34527	−0.672637	−	0.739973i	$-0.734838\pi$
$883$	−39.9752	−1.34527	−0.672637	+	0.739973i	$0.734838\pi$
$884$	0	0
$885$	0	0
$886$	35.7166	1.19992
$887$	−9.71588	−0.326227	−0.163114	−	0.986607i	$-0.552154\pi$
$887$	−9.71588	−0.326227	−0.163114	+	0.986607i	$0.552154\pi$
$888$	0	0
$889$	−3.76851	−0.126392
$890$	−23.3461	−0.782563
$891$	0	0
$892$	−42.2027	−1.41305
$893$	30.6678	1.02626
$894$	0	0
$895$	10.8475	0.362592
$896$	26.2973	0.878531
$897$	0	0
$898$	−13.7036	−0.457296
$899$	−71.2507	−2.37634
$900$	0	0
$901$	−4.13908	−0.137893
$902$	89.7714	2.98906
$903$	0	0
$904$	−70.0909	−2.33119
$905$	−0.759361	−0.0252420
$906$	0	0
$907$	9.89625	0.328600	0.164300	−	0.986410i	$-0.447464\pi$
$907$	9.89625	0.328600	0.164300	+	0.986410i	$0.447464\pi$
$908$	−41.2558	−1.36912
$909$	0	0
$910$	0	0
$911$	48.9981	1.62338	0.811690	−	0.584088i	$-0.198548\pi$
$911$	48.9981	1.62338	0.811690	+	0.584088i	$0.198548\pi$
$912$	0	0
$913$	45.3295	1.50019
$914$	12.3326	0.407925
$915$	0	0
$916$	−59.9095	−1.97947
$917$	−20.5021	−0.677040
$918$	0	0
$919$	5.61295	0.185154	0.0925771	−	0.995706i	$-0.470490\pi$
$919$	5.61295	0.185154	0.0925771	+	0.995706i	$0.470490\pi$
$920$	−8.25953	−0.272309
$921$	0	0
$922$	−80.4370	−2.64905
$923$	0	0
$924$	0	0
$925$	−1.39771	−0.0459566
$926$	59.5515	1.95698
$927$	0	0
$928$	7.22141	0.237054
$929$	−0.763668	−0.0250551	−0.0125276	−	0.999922i	$-0.503988\pi$
$929$	−0.763668	−0.0250551	−0.0125276	+	0.999922i	$0.503988\pi$
$930$	0	0
$931$	13.3291	0.436844
$932$	38.9404	1.27553
$933$	0	0
$934$	74.3693	2.43344
$935$	−2.06954	−0.0676812
$936$	0	0
$937$	−23.8968	−0.780674	−0.390337	−	0.920672i	$-0.627641\pi$
$937$	−23.8968	−0.780674	−0.390337	+	0.920672i	$0.627641\pi$
$938$	−41.6073	−1.35853
$939$	0	0
$940$	47.7345	1.55693
$941$	−5.76615	−0.187971	−0.0939856	−	0.995574i	$-0.529961\pi$
$941$	−5.76615	−0.187971	−0.0939856	+	0.995574i	$0.529961\pi$
$942$	0	0
$943$	−20.6836	−0.673551
$944$	20.7351	0.674869
$945$	0	0
$946$	25.2859	0.822115
$947$	32.7108	1.06296	0.531479	−	0.847071i	$-0.321636\pi$
$947$	32.7108	1.06296	0.531479	+	0.847071i	$0.321636\pi$
$948$	0	0
$949$	0	0
$950$	6.10547	0.198087
$951$	0	0
$952$	3.93361	0.127489
$953$	−43.4009	−1.40589	−0.702947	−	0.711243i	$-0.748133\pi$
$953$	−43.4009	−1.40589	−0.702947	+	0.711243i	$0.748133\pi$
$954$	0	0
$955$	6.68298	0.216256
$956$	9.69502	0.313559
$957$	0	0
$958$	−33.8334	−1.09311
$959$	−0.959905	−0.0309969
$960$	0	0
$961$	41.3041	1.33239
$962$	0	0
$963$	0	0
$964$	111.317	3.58527
$965$	−15.8288	−0.509548
$966$	0	0
$967$	−43.6204	−1.40274	−0.701369	−	0.712798i	$-0.747427\pi$
$967$	−43.6204	−1.40274	−0.701369	+	0.712798i	$0.747427\pi$
$968$	4.20046	0.135008
$969$	0	0
$970$	−19.3180	−0.620263
$971$	−37.0194	−1.18801	−0.594005	−	0.804461i	$-0.702454\pi$
$971$	−37.0194	−1.18801	−0.594005	+	0.804461i	$0.702454\pi$
$972$	0	0
$973$	−25.6934	−0.823694
$974$	−74.2682	−2.37971
$975$	0	0
$976$	44.9899	1.44009
$977$	−25.0778	−0.802310	−0.401155	−	0.916010i	$-0.631391\pi$
$977$	−25.0778	−0.802310	−0.401155	+	0.916010i	$0.631391\pi$
$978$	0	0
$979$	30.5140	0.975231
$980$	20.7468	0.662733
$981$	0	0
$982$	−35.6961	−1.13911
$983$	21.0019	0.669857	0.334928	−	0.942244i	$-0.391288\pi$
$983$	21.0019	0.669857	0.334928	+	0.942244i	$0.391288\pi$
$984$	0	0
$985$	6.83451	0.217765
$986$	13.2677	0.422531
$987$	0	0
$988$	0	0
$989$	−5.82594	−0.185254
$990$	0	0
$991$	3.03888	0.0965333	0.0482666	−	0.998834i	$-0.484630\pi$
$991$	3.03888	0.0965333	0.0482666	+	0.998834i	$0.484630\pi$
$992$	−7.32817	−0.232670
$993$	0	0
$994$	3.46841	0.110011
$995$	17.2427	0.546630
$996$	0	0
$997$	10.3174	0.326757	0.163378	−	0.986563i	$-0.447761\pi$
$997$	10.3174	0.326757	0.163378	+	0.986563i	$0.447761\pi$
$998$	−39.2564	−1.24264
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7605.2.a.cg.1.1		4
3.2	odd	2		2535.2.a.bl.1.4		4
13.2	odd	12		585.2.bu.b.316.1		8
13.7	odd	12		585.2.bu.b.361.1		8
13.12	even	2		7605.2.a.ck.1.4		4
39.2	even	12		195.2.bb.c.121.4	✓	8
39.20	even	12		195.2.bb.c.166.4	yes	8
39.38	odd	2		2535.2.a.bi.1.1		4
195.2	odd	12		975.2.w.g.199.1		8
195.59	even	12		975.2.bc.i.751.1		8
195.98	odd	12		975.2.w.g.49.1		8
195.119	even	12		975.2.bc.i.901.1		8
195.137	odd	12		975.2.w.j.49.4		8
195.158	odd	12		975.2.w.j.199.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.c.121.4	✓	8	39.2	even	12
195.2.bb.c.166.4	yes	8	39.20	even	12
585.2.bu.b.316.1		8	13.2	odd	12
585.2.bu.b.361.1		8	13.7	odd	12
975.2.w.g.49.1		8	195.98	odd	12
975.2.w.g.199.1		8	195.2	odd	12
975.2.w.j.49.4		8	195.137	odd	12
975.2.w.j.199.4		8	195.158	odd	12
975.2.bc.i.751.1		8	195.59	even	12
975.2.bc.i.901.1		8	195.119	even	12
2535.2.a.bi.1.1		4	39.38	odd	2
2535.2.a.bl.1.4		4	3.2	odd	2
7605.2.a.cg.1.1		4	1.1	even	1	trivial
7605.2.a.ck.1.4		4	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)

\(f(q)\)	\(=\)	\(q-2.43091 q^{2} +3.90931 q^{4} -1.00000 q^{5} +1.30114 q^{7} -4.64136 q^{8} +O(q^{10})\)	\(q-2.43091 q^{2} +3.90931 q^{4} -1.00000 q^{5} +1.30114 q^{7} -4.64136 q^{8} +2.43091 q^{10} -3.17726 q^{11} -3.16296 q^{14} +3.46410 q^{16} -0.651360 q^{17} -2.51160 q^{19} -3.90931 q^{20} +7.72363 q^{22} -1.77955 q^{23} +1.00000 q^{25} +5.08658 q^{28} +8.37930 q^{29} -8.50318 q^{31} +0.861816 q^{32} +1.58340 q^{34} -1.30114 q^{35} -1.39771 q^{37} +6.10547 q^{38} +4.64136 q^{40} +11.6229 q^{41} +3.27383 q^{43} -12.4209 q^{44} +4.32592 q^{46} -12.2105 q^{47} -5.30703 q^{49} -2.43091 q^{50} +6.35452 q^{53} +3.17726 q^{55} -6.03908 q^{56} -20.3693 q^{58} +5.98570 q^{59} +12.9875 q^{61} +20.6704 q^{62} -9.02320 q^{64} +13.1545 q^{67} -2.54637 q^{68} +3.16296 q^{70} -1.09657 q^{71} +12.2293 q^{73} +3.39771 q^{74} -9.81863 q^{76} -4.13407 q^{77} -1.33022 q^{79} -3.46410 q^{80} -28.2543 q^{82} -14.2668 q^{83} +0.651360 q^{85} -7.95839 q^{86} +14.7468 q^{88} -9.60386 q^{89} -6.95681 q^{92} +29.6825 q^{94} +2.51160 q^{95} -7.94681 q^{97} +12.9009 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{4} - 4 q^{5} + 6 q^{7}+O(q^{10}) \) 4 * q - 2 * q^2 + 4 * q^4 - 4 * q^5 + 6 * q^7	\( 4 q - 2 q^{2} + 4 q^{4} - 4 q^{5} + 6 q^{7} + 2 q^{10} - 8 q^{11} + 2 q^{14} + 2 q^{17} - 4 q^{20} - 4 q^{23} + 4 q^{25} + 4 q^{28} - 6 q^{29} - 12 q^{32} + 24 q^{34} - 6 q^{35} - 4 q^{37} - 8 q^{38} - 10 q^{41} + 6 q^{43} - 28 q^{44} - 12 q^{46} - 38 q^{47} - 8 q^{49} - 2 q^{50} + 16 q^{53} + 8 q^{55} - 4 q^{56} - 28 q^{58} + 14 q^{59} + 30 q^{62} - 16 q^{64} + 14 q^{67} + 16 q^{68} - 2 q^{70} - 2 q^{71} + 22 q^{73} + 12 q^{74} - 16 q^{76} - 4 q^{77} + 28 q^{79} - 24 q^{82} - 20 q^{83} - 2 q^{85} - 14 q^{86} + 8 q^{88} - 30 q^{89} - 20 q^{92} + 16 q^{94} - 10 q^{97} + 16 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^4 - 4 * q^5 + 6 * q^7 + 2 * q^10 - 8 * q^11 + 2 * q^14 + 2 * q^17 - 4 * q^20 - 4 * q^23 + 4 * q^25 + 4 * q^28 - 6 * q^29 - 12 * q^32 + 24 * q^34 - 6 * q^35 - 4 * q^37 - 8 * q^38 - 10 * q^41 + 6 * q^43 - 28 * q^44 - 12 * q^46 - 38 * q^47 - 8 * q^49 - 2 * q^50 + 16 * q^53 + 8 * q^55 - 4 * q^56 - 28 * q^58 + 14 * q^59 + 30 * q^62 - 16 * q^64 + 14 * q^67 + 16 * q^68 - 2 * q^70 - 2 * q^71 + 22 * q^73 + 12 * q^74 - 16 * q^76 - 4 * q^77 + 28 * q^79 - 24 * q^82 - 20 * q^83 - 2 * q^85 - 14 * q^86 + 8 * q^88 - 30 * q^89 - 20 * q^92 + 16 * q^94 - 10 * q^97 + 16 * q^98

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