LMFDB - Embedded newform 7605.2.a.bh.1.2

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:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
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			1.2
Root			$2.56155$ 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)

$f(q)$	$=$	$q+2.56155 q^{2} +4.56155 q^{4} +1.00000 q^{5} +3.56155 q^{7} +6.56155 q^{8} +2.56155 q^{10} +5.56155 q^{11} +9.12311 q^{14} +7.68466 q^{16} -0.438447 q^{17} +1.12311 q^{19} +4.56155 q^{20} +14.2462 q^{22} +5.56155 q^{23} +1.00000 q^{25} +16.2462 q^{28} -8.24621 q^{29} -6.00000 q^{31} +6.56155 q^{32} -1.12311 q^{34} +3.56155 q^{35} -5.56155 q^{37} +2.87689 q^{38} +6.56155 q^{40} +0.438447 q^{41} -7.12311 q^{43} +25.3693 q^{44} +14.2462 q^{46} -4.00000 q^{47} +5.68466 q^{49} +2.56155 q^{50} +9.80776 q^{53} +5.56155 q^{55} +23.3693 q^{56} -21.1231 q^{58} +4.00000 q^{59} -8.43845 q^{61} -15.3693 q^{62} +1.43845 q^{64} +2.87689 q^{67} -2.00000 q^{68} +9.12311 q^{70} -8.68466 q^{71} -11.1231 q^{73} -14.2462 q^{74} +5.12311 q^{76} +19.8078 q^{77} -5.56155 q^{79} +7.68466 q^{80} +1.12311 q^{82} -13.3693 q^{83} -0.438447 q^{85} -18.2462 q^{86} +36.4924 q^{88} +1.31534 q^{89} +25.3693 q^{92} -10.2462 q^{94} +1.12311 q^{95} -14.9309 q^{97} +14.5616 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 5 q^{4} + 2 q^{5} + 3 q^{7} + 9 q^{8} + q^{10} + 7 q^{11} + 10 q^{14} + 3 q^{16} - 5 q^{17} - 6 q^{19} + 5 q^{20} + 12 q^{22} + 7 q^{23} + 2 q^{25} + 16 q^{28} - 12 q^{31} + 9 q^{32} + 6 q^{34}+ \cdots + 25 q^{98}+O(q^{100}) $ 2 * q + q^2 + 5 * q^4 + 2 * q^5 + 3 * q^7 + 9 * q^8 + q^10 + 7 * q^11 + 10 * q^14 + 3 * q^16 - 5 * q^17 - 6 * q^19 + 5 * q^20 + 12 * q^22 + 7 * q^23 + 2 * q^25 + 16 * q^28 - 12 * q^31 + 9 * q^32 + 6 * q^34 + 3 * q^35 - 7 * q^37 + 14 * q^38 + 9 * q^40 + 5 * q^41 - 6 * q^43 + 26 * q^44 + 12 * q^46 - 8 * q^47 - q^49 + q^50 - q^53 + 7 * q^55 + 22 * q^56 - 34 * q^58 + 8 * q^59 - 21 * q^61 - 6 * q^62 + 7 * q^64 + 14 * q^67 - 4 * q^68 + 10 * q^70 - 5 * q^71 - 14 * q^73 - 12 * q^74 + 2 * q^76 + 19 * q^77 - 7 * q^79 + 3 * q^80 - 6 * q^82 - 2 * q^83 - 5 * q^85 - 20 * q^86 + 40 * q^88 + 15 * q^89 + 26 * q^92 - 4 * q^94 - 6 * q^95 - q^97 + 25 * q^98

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 $

$2$	2.56155	1.81129	0.905646	−	0.424035i	$-0.139387\pi$
$2$	2.56155	1.81129	0.905646	+	0.424035i	$0.139387\pi$
$3$	0	0
$3$	0	0
$4$	4.56155	2.28078
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	3.56155	1.34614	0.673070	−	0.739579i	$-0.264975\pi$
$7$	3.56155	1.34614	0.673070	+	0.739579i	$0.264975\pi$
$8$	6.56155	2.31986
$9$	0	0
$10$	2.56155	0.810034
$11$	5.56155	1.67687	0.838436	−	0.545001i	$-0.183471\pi$
$11$	5.56155	1.67687	0.838436	+	0.545001i	$0.183471\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	9.12311	2.43825
$15$	0	0
$16$	7.68466	1.92116
$17$	−0.438447	−0.106339	−0.0531695	−	0.998586i	$-0.516932\pi$
$17$	−0.438447	−0.106339	−0.0531695	+	0.998586i	$0.516932\pi$
$18$	0	0
$19$	1.12311	0.257658	0.128829	−	0.991667i	$-0.458878\pi$
$19$	1.12311	0.257658	0.128829	+	0.991667i	$0.458878\pi$
$20$	4.56155	1.01999
$21$	0	0
$22$	14.2462	3.03730
$23$	5.56155	1.15966	0.579832	−	0.814736i	$-0.303118\pi$
$23$	5.56155	1.15966	0.579832	+	0.814736i	$0.303118\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	16.2462	3.07025
$29$	−8.24621	−1.53128	−0.765641	−	0.643268i	$-0.777578\pi$
$29$	−8.24621	−1.53128	−0.765641	+	0.643268i	$0.777578\pi$
$30$	0	0
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	6.56155	1.15993
$33$	0	0
$34$	−1.12311	−0.192611
$35$	3.56155	0.602012
$36$	0	0
$37$	−5.56155	−0.914314	−0.457157	−	0.889386i	$-0.651132\pi$
$37$	−5.56155	−0.914314	−0.457157	+	0.889386i	$0.651132\pi$
$38$	2.87689	0.466694
$39$	0	0
$40$	6.56155	1.03747
$41$	0.438447	0.0684739	0.0342370	−	0.999414i	$-0.489100\pi$
$41$	0.438447	0.0684739	0.0342370	+	0.999414i	$0.489100\pi$
$42$	0	0
$43$	−7.12311	−1.08626	−0.543132	−	0.839648i	$-0.682762\pi$
$43$	−7.12311	−1.08626	−0.543132	+	0.839648i	$0.682762\pi$
$44$	25.3693	3.82457
$45$	0	0
$46$	14.2462	2.10049
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	0	0
$49$	5.68466	0.812094
$50$	2.56155	0.362258
$51$	0	0
$52$	0	0
$53$	9.80776	1.34720	0.673600	−	0.739096i	$-0.264747\pi$
$53$	9.80776	1.34720	0.673600	+	0.739096i	$0.264747\pi$
$54$	0	0
$55$	5.56155	0.749920
$56$	23.3693	3.12286
$57$	0	0
$58$	−21.1231	−2.77360
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	0	0
$61$	−8.43845	−1.08043	−0.540216	−	0.841526i	$-0.681658\pi$
$61$	−8.43845	−1.08043	−0.540216	+	0.841526i	$0.681658\pi$
$62$	−15.3693	−1.95191
$63$	0	0
$64$	1.43845	0.179806
$65$	0	0
$66$	0	0
$67$	2.87689	0.351469	0.175734	−	0.984438i	$-0.443770\pi$
$67$	2.87689	0.351469	0.175734	+	0.984438i	$0.443770\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	9.12311	1.09042
$71$	−8.68466	−1.03068	−0.515340	−	0.856986i	$-0.672334\pi$
$71$	−8.68466	−1.03068	−0.515340	+	0.856986i	$0.672334\pi$
$72$	0	0
$73$	−11.1231	−1.30186	−0.650931	−	0.759137i	$-0.725621\pi$
$73$	−11.1231	−1.30186	−0.650931	+	0.759137i	$0.725621\pi$
$74$	−14.2462	−1.65609
$75$	0	0
$76$	5.12311	0.587661
$77$	19.8078	2.25730
$78$	0	0
$79$	−5.56155	−0.625724	−0.312862	−	0.949799i	$-0.601288\pi$
$79$	−5.56155	−0.625724	−0.312862	+	0.949799i	$0.601288\pi$
$80$	7.68466	0.859171
$81$	0	0
$82$	1.12311	0.124026
$83$	−13.3693	−1.46747	−0.733737	−	0.679434i	$-0.762225\pi$
$83$	−13.3693	−1.46747	−0.733737	+	0.679434i	$0.762225\pi$
$84$	0	0
$85$	−0.438447	−0.0475563
$86$	−18.2462	−1.96754
$87$	0	0
$88$	36.4924	3.89011
$89$	1.31534	0.139426	0.0697130	−	0.997567i	$-0.477792\pi$
$89$	1.31534	0.139426	0.0697130	+	0.997567i	$0.477792\pi$
$90$	0	0
$91$	0	0
$92$	25.3693	2.64493
$93$	0	0
$94$	−10.2462	−1.05682
$95$	1.12311	0.115228
$96$	0	0
$97$	−14.9309	−1.51600	−0.758000	−	0.652254i	$-0.773823\pi$
$97$	−14.9309	−1.51600	−0.758000	+	0.652254i	$0.773823\pi$
$98$	14.5616	1.47094
$99$	0	0
$100$	4.56155	0.456155
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	0	0
$106$	25.1231	2.44017
$107$	−0.684658	−0.0661884	−0.0330942	−	0.999452i	$-0.510536\pi$
$107$	−0.684658	−0.0661884	−0.0330942	+	0.999452i	$0.510536\pi$
$108$	0	0
$109$	4.87689	0.467122	0.233561	−	0.972342i	$-0.424962\pi$
$109$	4.87689	0.467122	0.233561	+	0.972342i	$0.424962\pi$
$110$	14.2462	1.35832
$111$	0	0
$112$	27.3693	2.58616
$113$	20.2462	1.90460	0.952302	−	0.305158i	$-0.0987093\pi$
$113$	20.2462	1.90460	0.952302	+	0.305158i	$0.0987093\pi$
$114$	0	0
$115$	5.56155	0.518617
$116$	−37.6155	−3.49251
$117$	0	0
$118$	10.2462	0.943240
$119$	−1.56155	−0.143147
$120$	0	0
$121$	19.9309	1.81190
$122$	−21.6155	−1.95698
$123$	0	0
$124$	−27.3693	−2.45784
$125$	1.00000	0.0894427
$126$	0	0
$127$	−17.3693	−1.54128	−0.770639	−	0.637272i	$-0.780063\pi$
$127$	−17.3693	−1.54128	−0.770639	+	0.637272i	$0.780063\pi$
$128$	−9.43845	−0.834249
$129$	0	0
$130$	0	0
$131$	2.24621	0.196252	0.0981262	−	0.995174i	$-0.468715\pi$
$131$	2.24621	0.196252	0.0981262	+	0.995174i	$0.468715\pi$
$132$	0	0
$133$	4.00000	0.346844
$134$	7.36932	0.636612
$135$	0	0
$136$	−2.87689	−0.246692
$137$	−0.246211	−0.0210352	−0.0105176	−	0.999945i	$-0.503348\pi$
$137$	−0.246211	−0.0210352	−0.0105176	+	0.999945i	$0.503348\pi$
$138$	0	0
$139$	17.5616	1.48955	0.744776	−	0.667315i	$-0.232556\pi$
$139$	17.5616	1.48955	0.744776	+	0.667315i	$0.232556\pi$
$140$	16.2462	1.37306
$141$	0	0
$142$	−22.2462	−1.86686
$143$	0	0
$144$	0	0
$145$	−8.24621	−0.684811
$146$	−28.4924	−2.35805
$147$	0	0
$148$	−25.3693	−2.08535
$149$	−12.9309	−1.05934	−0.529669	−	0.848204i	$-0.677684\pi$
$149$	−12.9309	−1.05934	−0.529669	+	0.848204i	$0.677684\pi$
$150$	0	0
$151$	−0.246211	−0.0200364	−0.0100182	−	0.999950i	$-0.503189\pi$
$151$	−0.246211	−0.0200364	−0.0100182	+	0.999950i	$0.503189\pi$
$152$	7.36932	0.597731
$153$	0	0
$154$	50.7386	4.08864
$155$	−6.00000	−0.481932
$156$	0	0
$157$	−13.1231	−1.04734	−0.523669	−	0.851922i	$-0.675437\pi$
$157$	−13.1231	−1.04734	−0.523669	+	0.851922i	$0.675437\pi$
$158$	−14.2462	−1.13337
$159$	0	0
$160$	6.56155	0.518736
$161$	19.8078	1.56107
$162$	0	0
$163$	3.56155	0.278962	0.139481	−	0.990225i	$-0.455457\pi$
$163$	3.56155	0.278962	0.139481	+	0.990225i	$0.455457\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	−34.2462	−2.65802
$167$	2.24621	0.173817	0.0869085	−	0.996216i	$-0.472301\pi$
$167$	2.24621	0.173817	0.0869085	+	0.996216i	$0.472301\pi$
$168$	0	0
$169$	0	0
$170$	−1.12311	−0.0861383
$171$	0	0
$172$	−32.4924	−2.47752
$173$	−12.2462	−0.931062	−0.465531	−	0.885032i	$-0.654137\pi$
$173$	−12.2462	−0.931062	−0.465531	+	0.885032i	$0.654137\pi$
$174$	0	0
$175$	3.56155	0.269228
$176$	42.7386	3.22155
$177$	0	0
$178$	3.36932	0.252541
$179$	2.24621	0.167890	0.0839449	−	0.996470i	$-0.473248\pi$
$179$	2.24621	0.167890	0.0839449	+	0.996470i	$0.473248\pi$
$180$	0	0
$181$	7.56155	0.562046	0.281023	−	0.959701i	$-0.409326\pi$
$181$	7.56155	0.562046	0.281023	+	0.959701i	$0.409326\pi$
$182$	0	0
$183$	0	0
$184$	36.4924	2.69026
$185$	−5.56155	−0.408893
$186$	0	0
$187$	−2.43845	−0.178317
$188$	−18.2462	−1.33074
$189$	0	0
$190$	2.87689	0.208712
$191$	−5.75379	−0.416330	−0.208165	−	0.978094i	$-0.566749\pi$
$191$	−5.75379	−0.416330	−0.208165	+	0.978094i	$0.566749\pi$
$192$	0	0
$193$	2.93087	0.210969	0.105484	−	0.994421i	$-0.466361\pi$
$193$	2.93087	0.210969	0.105484	+	0.994421i	$0.466361\pi$
$194$	−38.2462	−2.74592
$195$	0	0
$196$	25.9309	1.85220
$197$	12.2462	0.872506	0.436253	−	0.899824i	$-0.356305\pi$
$197$	12.2462	0.872506	0.436253	+	0.899824i	$0.356305\pi$
$198$	0	0
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	6.56155	0.463972
$201$	0	0
$202$	−5.12311	−0.360460
$203$	−29.3693	−2.06132
$204$	0	0
$205$	0.438447	0.0306225
$206$	0	0
$207$	0	0
$208$	0	0
$209$	6.24621	0.432059
$210$	0	0
$211$	4.00000	0.275371	0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000	0.275371	0.137686	+	0.990476i	$0.456034\pi$
$212$	44.7386	3.07266
$213$	0	0
$214$	−1.75379	−0.119887
$215$	−7.12311	−0.485792
$216$	0	0
$217$	−21.3693	−1.45064
$218$	12.4924	0.846094
$219$	0	0
$220$	25.3693	1.71040
$221$	0	0
$222$	0	0
$223$	2.87689	0.192651	0.0963255	−	0.995350i	$-0.469291\pi$
$223$	2.87689	0.192651	0.0963255	+	0.995350i	$0.469291\pi$
$224$	23.3693	1.56143
$225$	0	0
$226$	51.8617	3.44979
$227$	26.7386	1.77471	0.887353	−	0.461091i	$-0.152542\pi$
$227$	26.7386	1.77471	0.887353	+	0.461091i	$0.152542\pi$
$228$	0	0
$229$	19.1231	1.26369	0.631845	−	0.775095i	$-0.282298\pi$
$229$	19.1231	1.26369	0.631845	+	0.775095i	$0.282298\pi$
$230$	14.2462	0.939367
$231$	0	0
$232$	−54.1080	−3.55236
$233$	22.6847	1.48612	0.743061	−	0.669224i	$-0.233373\pi$
$233$	22.6847	1.48612	0.743061	+	0.669224i	$0.233373\pi$
$234$	0	0
$235$	−4.00000	−0.260931
$236$	18.2462	1.18773
$237$	0	0
$238$	−4.00000	−0.259281
$239$	13.5616	0.877224	0.438612	−	0.898677i	$-0.355470\pi$
$239$	13.5616	0.877224	0.438612	+	0.898677i	$0.355470\pi$
$240$	0	0
$241$	19.6155	1.26355	0.631774	−	0.775153i	$-0.282327\pi$
$241$	19.6155	1.26355	0.631774	+	0.775153i	$0.282327\pi$
$242$	51.0540	3.28187
$243$	0	0
$244$	−38.4924	−2.46422
$245$	5.68466	0.363180
$246$	0	0
$247$	0	0
$248$	−39.3693	−2.49995
$249$	0	0
$250$	2.56155	0.162007
$251$	−1.36932	−0.0864305	−0.0432153	−	0.999066i	$-0.513760\pi$
$251$	−1.36932	−0.0864305	−0.0432153	+	0.999066i	$0.513760\pi$
$252$	0	0
$253$	30.9309	1.94461
$254$	−44.4924	−2.79170
$255$	0	0
$256$	−27.0540	−1.69087
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	0	0
$259$	−19.8078	−1.23079
$260$	0	0
$261$	0	0
$262$	5.75379	0.355470
$263$	26.2462	1.61841	0.809205	−	0.587526i	$-0.199898\pi$
$263$	26.2462	1.61841	0.809205	+	0.587526i	$0.199898\pi$
$264$	0	0
$265$	9.80776	0.602486
$266$	10.2462	0.628236
$267$	0	0
$268$	13.1231	0.801621
$269$	13.6155	0.830153	0.415077	−	0.909786i	$-0.363755\pi$
$269$	13.6155	0.830153	0.415077	+	0.909786i	$0.363755\pi$
$270$	0	0
$271$	−28.2462	−1.71584	−0.857918	−	0.513787i	$-0.828242\pi$
$271$	−28.2462	−1.71584	−0.857918	+	0.513787i	$0.828242\pi$
$272$	−3.36932	−0.204295
$273$	0	0
$274$	−0.630683	−0.0381010
$275$	5.56155	0.335374
$276$	0	0
$277$	−2.87689	−0.172856	−0.0864279	−	0.996258i	$-0.527545\pi$
$277$	−2.87689	−0.172856	−0.0864279	+	0.996258i	$0.527545\pi$
$278$	44.9848	2.69801
$279$	0	0
$280$	23.3693	1.39658
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	0	0
$283$	−25.8617	−1.53732	−0.768660	−	0.639657i	$-0.779076\pi$
$283$	−25.8617	−1.53732	−0.768660	+	0.639657i	$0.779076\pi$
$284$	−39.6155	−2.35075
$285$	0	0
$286$	0	0
$287$	1.56155	0.0921755
$288$	0	0
$289$	−16.8078	−0.988692
$290$	−21.1231	−1.24039
$291$	0	0
$292$	−50.7386	−2.96925
$293$	8.24621	0.481749	0.240874	−	0.970556i	$-0.422566\pi$
$293$	8.24621	0.481749	0.240874	+	0.970556i	$0.422566\pi$
$294$	0	0
$295$	4.00000	0.232889
$296$	−36.4924	−2.12108
$297$	0	0
$298$	−33.1231	−1.91877
$299$	0	0
$300$	0	0
$301$	−25.3693	−1.46226
$302$	−0.630683	−0.0362917
$303$	0	0
$304$	8.63068	0.495004
$305$	−8.43845	−0.483184
$306$	0	0
$307$	3.06913	0.175165	0.0875823	−	0.996157i	$-0.472086\pi$
$307$	3.06913	0.175165	0.0875823	+	0.996157i	$0.472086\pi$
$308$	90.3542	5.14841
$309$	0	0
$310$	−15.3693	−0.872919
$311$	15.1231	0.857553	0.428776	−	0.903411i	$-0.358945\pi$
$311$	15.1231	0.857553	0.428776	+	0.903411i	$0.358945\pi$
$312$	0	0
$313$	17.1231	0.967855	0.483928	−	0.875108i	$-0.339210\pi$
$313$	17.1231	0.967855	0.483928	+	0.875108i	$0.339210\pi$
$314$	−33.6155	−1.89703
$315$	0	0
$316$	−25.3693	−1.42714
$317$	6.00000	0.336994	0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000	0.336994	0.168497	+	0.985702i	$0.446109\pi$
$318$	0	0
$319$	−45.8617	−2.56776
$320$	1.43845	0.0804116
$321$	0	0
$322$	50.7386	2.82755
$323$	−0.492423	−0.0273991
$324$	0	0
$325$	0	0
$326$	9.12311	0.505282
$327$	0	0
$328$	2.87689	0.158850
$329$	−14.2462	−0.785419
$330$	0	0
$331$	9.61553	0.528517	0.264259	−	0.964452i	$-0.414873\pi$
$331$	9.61553	0.528517	0.264259	+	0.964452i	$0.414873\pi$
$332$	−60.9848	−3.34698
$333$	0	0
$334$	5.75379	0.314833
$335$	2.87689	0.157182
$336$	0	0
$337$	26.0000	1.41631	0.708155	−	0.706057i	$-0.249528\pi$
$337$	26.0000	1.41631	0.708155	+	0.706057i	$0.249528\pi$
$338$	0	0
$339$	0	0
$340$	−2.00000	−0.108465
$341$	−33.3693	−1.80705
$342$	0	0
$343$	−4.68466	−0.252948
$344$	−46.7386	−2.51998
$345$	0	0
$346$	−31.3693	−1.68642
$347$	−10.9309	−0.586800	−0.293400	−	0.955990i	$-0.594787\pi$
$347$	−10.9309	−0.586800	−0.293400	+	0.955990i	$0.594787\pi$
$348$	0	0
$349$	−8.87689	−0.475169	−0.237585	−	0.971367i	$-0.576356\pi$
$349$	−8.87689	−0.475169	−0.237585	+	0.971367i	$0.576356\pi$
$350$	9.12311	0.487651
$351$	0	0
$352$	36.4924	1.94505
$353$	18.8769	1.00472	0.502358	−	0.864660i	$-0.332466\pi$
$353$	18.8769	1.00472	0.502358	+	0.864660i	$0.332466\pi$
$354$	0	0
$355$	−8.68466	−0.460934
$356$	6.00000	0.317999
$357$	0	0
$358$	5.75379	0.304097
$359$	26.2462	1.38522	0.692611	−	0.721311i	$-0.256460\pi$
$359$	26.2462	1.38522	0.692611	+	0.721311i	$0.256460\pi$
$360$	0	0
$361$	−17.7386	−0.933612
$362$	19.3693	1.01803
$363$	0	0
$364$	0	0
$365$	−11.1231	−0.582210
$366$	0	0
$367$	−11.1231	−0.580621	−0.290311	−	0.956932i	$-0.593759\pi$
$367$	−11.1231	−0.580621	−0.290311	+	0.956932i	$0.593759\pi$
$368$	42.7386	2.22791
$369$	0	0
$370$	−14.2462	−0.740625
$371$	34.9309	1.81352
$372$	0	0
$373$	33.6155	1.74055	0.870273	−	0.492570i	$-0.163942\pi$
$373$	33.6155	1.74055	0.870273	+	0.492570i	$0.163942\pi$
$374$	−6.24621	−0.322984
$375$	0	0
$376$	−26.2462	−1.35354
$377$	0	0
$378$	0	0
$379$	−3.75379	−0.192819	−0.0964096	−	0.995342i	$-0.530736\pi$
$379$	−3.75379	−0.192819	−0.0964096	+	0.995342i	$0.530736\pi$
$380$	5.12311	0.262810
$381$	0	0
$382$	−14.7386	−0.754094
$383$	−5.36932	−0.274359	−0.137180	−	0.990546i	$-0.543804\pi$
$383$	−5.36932	−0.274359	−0.137180	+	0.990546i	$0.543804\pi$
$384$	0	0
$385$	19.8078	1.00950
$386$	7.50758	0.382126
$387$	0	0
$388$	−68.1080	−3.45766
$389$	12.7386	0.645874	0.322937	−	0.946420i	$-0.395330\pi$
$389$	12.7386	0.645874	0.322937	+	0.946420i	$0.395330\pi$
$390$	0	0
$391$	−2.43845	−0.123318
$392$	37.3002	1.88394
$393$	0	0
$394$	31.3693	1.58036
$395$	−5.56155	−0.279832
$396$	0	0
$397$	−24.3002	−1.21959	−0.609796	−	0.792559i	$-0.708749\pi$
$397$	−24.3002	−1.21959	−0.609796	+	0.792559i	$0.708749\pi$
$398$	20.4924	1.02719
$399$	0	0
$400$	7.68466	0.384233
$401$	6.49242	0.324216	0.162108	−	0.986773i	$-0.448171\pi$
$401$	6.49242	0.324216	0.162108	+	0.986773i	$0.448171\pi$
$402$	0	0
$403$	0	0
$404$	−9.12311	−0.453891
$405$	0	0
$406$	−75.2311	−3.73365
$407$	−30.9309	−1.53319
$408$	0	0
$409$	12.0000	0.593362	0.296681	−	0.954977i	$-0.404120\pi$
$409$	12.0000	0.593362	0.296681	+	0.954977i	$0.404120\pi$
$410$	1.12311	0.0554662
$411$	0	0
$412$	0	0
$413$	14.2462	0.701010
$414$	0	0
$415$	−13.3693	−0.656274
$416$	0	0
$417$	0	0
$418$	16.0000	0.782586
$419$	−27.6155	−1.34911	−0.674553	−	0.738226i	$-0.735664\pi$
$419$	−27.6155	−1.34911	−0.674553	+	0.738226i	$0.735664\pi$
$420$	0	0
$421$	−25.3693	−1.23642	−0.618212	−	0.786011i	$-0.712143\pi$
$421$	−25.3693	−1.23642	−0.618212	+	0.786011i	$0.712143\pi$
$422$	10.2462	0.498778
$423$	0	0
$424$	64.3542	3.12531
$425$	−0.438447	−0.0212678
$426$	0	0
$427$	−30.0540	−1.45441
$428$	−3.12311	−0.150961
$429$	0	0
$430$	−18.2462	−0.879910
$431$	−30.7386	−1.48063	−0.740314	−	0.672261i	$-0.765323\pi$
$431$	−30.7386	−1.48063	−0.740314	+	0.672261i	$0.765323\pi$
$432$	0	0
$433$	20.7386	0.996635	0.498318	−	0.866995i	$-0.333951\pi$
$433$	20.7386	0.996635	0.498318	+	0.866995i	$0.333951\pi$
$434$	−54.7386	−2.62754
$435$	0	0
$436$	22.2462	1.06540
$437$	6.24621	0.298797
$438$	0	0
$439$	−12.1922	−0.581904	−0.290952	−	0.956738i	$-0.593972\pi$
$439$	−12.1922	−0.581904	−0.290952	+	0.956738i	$0.593972\pi$
$440$	36.4924	1.73971
$441$	0	0
$442$	0	0
$443$	5.56155	0.264237	0.132119	−	0.991234i	$-0.457822\pi$
$443$	5.56155	0.264237	0.132119	+	0.991234i	$0.457822\pi$
$444$	0	0
$445$	1.31534	0.0623532
$446$	7.36932	0.348947
$447$	0	0
$448$	5.12311	0.242044
$449$	−3.56155	−0.168080	−0.0840400	−	0.996462i	$-0.526782\pi$
$449$	−3.56155	−0.168080	−0.0840400	+	0.996462i	$0.526782\pi$
$450$	0	0
$451$	2.43845	0.114822
$452$	92.3542	4.34397
$453$	0	0
$454$	68.4924	3.21451
$455$	0	0
$456$	0	0
$457$	−26.4384	−1.23674	−0.618369	−	0.785888i	$-0.712206\pi$
$457$	−26.4384	−1.23674	−0.618369	+	0.785888i	$0.712206\pi$
$458$	48.9848	2.28891
$459$	0	0
$460$	25.3693	1.18285
$461$	19.1771	0.893166	0.446583	−	0.894742i	$-0.352641\pi$
$461$	19.1771	0.893166	0.446583	+	0.894742i	$0.352641\pi$
$462$	0	0
$463$	41.8078	1.94297	0.971486	−	0.237098i	$-0.0761962\pi$
$463$	41.8078	1.94297	0.971486	+	0.237098i	$0.0761962\pi$
$464$	−63.3693	−2.94185
$465$	0	0
$466$	58.1080	2.69180
$467$	−26.9309	−1.24621	−0.623106	−	0.782137i	$-0.714129\pi$
$467$	−26.9309	−1.24621	−0.623106	+	0.782137i	$0.714129\pi$
$468$	0	0
$469$	10.2462	0.473126
$470$	−10.2462	−0.472622
$471$	0	0
$472$	26.2462	1.20808
$473$	−39.6155	−1.82152
$474$	0	0
$475$	1.12311	0.0515316
$476$	−7.12311	−0.326487
$477$	0	0
$478$	34.7386	1.58891
$479$	−18.0540	−0.824907	−0.412454	−	0.910979i	$-0.635328\pi$
$479$	−18.0540	−0.824907	−0.412454	+	0.910979i	$0.635328\pi$
$480$	0	0
$481$	0	0
$482$	50.2462	2.28865
$483$	0	0
$484$	90.9157	4.13253
$485$	−14.9309	−0.677976
$486$	0	0
$487$	−4.05398	−0.183703	−0.0918516	−	0.995773i	$-0.529279\pi$
$487$	−4.05398	−0.183703	−0.0918516	+	0.995773i	$0.529279\pi$
$488$	−55.3693	−2.50645
$489$	0	0
$490$	14.5616	0.657824
$491$	−36.4924	−1.64688	−0.823440	−	0.567403i	$-0.807948\pi$
$491$	−36.4924	−1.64688	−0.823440	+	0.567403i	$0.807948\pi$
$492$	0	0
$493$	3.61553	0.162835
$494$	0	0
$495$	0	0
$496$	−46.1080	−2.07031
$497$	−30.9309	−1.38744
$498$	0	0
$499$	0.630683	0.0282333	0.0141166	−	0.999900i	$-0.495506\pi$
$499$	0.630683	0.0282333	0.0141166	+	0.999900i	$0.495506\pi$
$500$	4.56155	0.203999
$501$	0	0
$502$	−3.50758	−0.156551
$503$	7.50758	0.334746	0.167373	−	0.985894i	$-0.446472\pi$
$503$	7.50758	0.334746	0.167373	+	0.985894i	$0.446472\pi$
$504$	0	0
$505$	−2.00000	−0.0889988
$506$	79.2311	3.52225
$507$	0	0
$508$	−79.2311	−3.51531
$509$	7.06913	0.313334	0.156667	−	0.987652i	$-0.449925\pi$
$509$	7.06913	0.313334	0.156667	+	0.987652i	$0.449925\pi$
$510$	0	0
$511$	−39.6155	−1.75249
$512$	−50.4233	−2.22842
$513$	0	0
$514$	−5.12311	−0.225971
$515$	0	0
$516$	0	0
$517$	−22.2462	−0.978387
$518$	−50.7386	−2.22933
$519$	0	0
$520$	0	0
$521$	43.3693	1.90004	0.950022	−	0.312183i	$-0.101060\pi$
$521$	43.3693	1.90004	0.950022	+	0.312183i	$0.101060\pi$
$522$	0	0
$523$	27.6155	1.20754	0.603771	−	0.797158i	$-0.293664\pi$
$523$	27.6155	1.20754	0.603771	+	0.797158i	$0.293664\pi$
$524$	10.2462	0.447608
$525$	0	0
$526$	67.2311	2.93141
$527$	2.63068	0.114594
$528$	0	0
$529$	7.93087	0.344820
$530$	25.1231	1.09128
$531$	0	0
$532$	18.2462	0.791074
$533$	0	0
$534$	0	0
$535$	−0.684658	−0.0296004
$536$	18.8769	0.815358
$537$	0	0
$538$	34.8769	1.50365
$539$	31.6155	1.36178
$540$	0	0
$541$	−4.49242	−0.193144	−0.0965722	−	0.995326i	$-0.530788\pi$
$541$	−4.49242	−0.193144	−0.0965722	+	0.995326i	$0.530788\pi$
$542$	−72.3542	−3.10788
$543$	0	0
$544$	−2.87689	−0.123346
$545$	4.87689	0.208903
$546$	0	0
$547$	4.38447	0.187466	0.0937332	−	0.995597i	$-0.470120\pi$
$547$	4.38447	0.187466	0.0937332	+	0.995597i	$0.470120\pi$
$548$	−1.12311	−0.0479767
$549$	0	0
$550$	14.2462	0.607460
$551$	−9.26137	−0.394547
$552$	0	0
$553$	−19.8078	−0.842312
$554$	−7.36932	−0.313092
$555$	0	0
$556$	80.1080	3.39733
$557$	6.49242	0.275093	0.137546	−	0.990495i	$-0.456078\pi$
$557$	6.49242	0.275093	0.137546	+	0.990495i	$0.456078\pi$
$558$	0	0
$559$	0	0
$560$	27.3693	1.15656
$561$	0	0
$562$	56.3542	2.37716
$563$	−13.1771	−0.555348	−0.277674	−	0.960675i	$-0.589563\pi$
$563$	−13.1771	−0.555348	−0.277674	+	0.960675i	$0.589563\pi$
$564$	0	0
$565$	20.2462	0.851765
$566$	−66.2462	−2.78454
$567$	0	0
$568$	−56.9848	−2.39103
$569$	−10.4924	−0.439865	−0.219933	−	0.975515i	$-0.570584\pi$
$569$	−10.4924	−0.439865	−0.219933	+	0.975515i	$0.570584\pi$
$570$	0	0
$571$	−3.31534	−0.138743	−0.0693714	−	0.997591i	$-0.522099\pi$
$571$	−3.31534	−0.138743	−0.0693714	+	0.997591i	$0.522099\pi$
$572$	0	0
$573$	0	0
$574$	4.00000	0.166957
$575$	5.56155	0.231933
$576$	0	0
$577$	−15.4233	−0.642080	−0.321040	−	0.947066i	$-0.604032\pi$
$577$	−15.4233	−0.642080	−0.321040	+	0.947066i	$0.604032\pi$
$578$	−43.0540	−1.79081
$579$	0	0
$580$	−37.6155	−1.56190
$581$	−47.6155	−1.97542
$582$	0	0
$583$	54.5464	2.25908
$584$	−72.9848	−3.02013
$585$	0	0
$586$	21.1231	0.872587
$587$	−7.12311	−0.294002	−0.147001	−	0.989136i	$-0.546962\pi$
$587$	−7.12311	−0.294002	−0.147001	+	0.989136i	$0.546962\pi$
$588$	0	0
$589$	−6.73863	−0.277661
$590$	10.2462	0.421830
$591$	0	0
$592$	−42.7386	−1.75655
$593$	13.5076	0.554690	0.277345	−	0.960770i	$-0.410546\pi$
$593$	13.5076	0.554690	0.277345	+	0.960770i	$0.410546\pi$
$594$	0	0
$595$	−1.56155	−0.0640174
$596$	−58.9848	−2.41611
$597$	0	0
$598$	0	0
$599$	−6.24621	−0.255213	−0.127607	−	0.991825i	$-0.540730\pi$
$599$	−6.24621	−0.255213	−0.127607	+	0.991825i	$0.540730\pi$
$600$	0	0
$601$	4.93087	0.201134	0.100567	−	0.994930i	$-0.467934\pi$
$601$	4.93087	0.201134	0.100567	+	0.994930i	$0.467934\pi$
$602$	−64.9848	−2.64858
$603$	0	0
$604$	−1.12311	−0.0456985
$605$	19.9309	0.810305
$606$	0	0
$607$	−46.2462	−1.87708	−0.938538	−	0.345176i	$-0.887819\pi$
$607$	−46.2462	−1.87708	−0.938538	+	0.345176i	$0.887819\pi$
$608$	7.36932	0.298865
$609$	0	0
$610$	−21.6155	−0.875187
$611$	0	0
$612$	0	0
$613$	3.80776	0.153794	0.0768971	−	0.997039i	$-0.475499\pi$
$613$	3.80776	0.153794	0.0768971	+	0.997039i	$0.475499\pi$
$614$	7.86174	0.317274
$615$	0	0
$616$	129.970	5.23663
$617$	−16.2462	−0.654048	−0.327024	−	0.945016i	$-0.606046\pi$
$617$	−16.2462	−0.654048	−0.327024	+	0.945016i	$0.606046\pi$
$618$	0	0
$619$	30.0000	1.20580	0.602901	−	0.797816i	$-0.294011\pi$
$619$	30.0000	1.20580	0.602901	+	0.797816i	$0.294011\pi$
$620$	−27.3693	−1.09918
$621$	0	0
$622$	38.7386	1.55328
$623$	4.68466	0.187687
$624$	0	0
$625$	1.00000	0.0400000
$626$	43.8617	1.75307
$627$	0	0
$628$	−59.8617	−2.38874
$629$	2.43845	0.0972273
$630$	0	0
$631$	38.9848	1.55196	0.775981	−	0.630756i	$-0.217255\pi$
$631$	38.9848	1.55196	0.775981	+	0.630756i	$0.217255\pi$
$632$	−36.4924	−1.45159
$633$	0	0
$634$	15.3693	0.610394
$635$	−17.3693	−0.689280
$636$	0	0
$637$	0	0
$638$	−117.477	−4.65097
$639$	0	0
$640$	−9.43845	−0.373087
$641$	2.87689	0.113630	0.0568152	−	0.998385i	$-0.481905\pi$
$641$	2.87689	0.113630	0.0568152	+	0.998385i	$0.481905\pi$
$642$	0	0
$643$	19.5616	0.771432	0.385716	−	0.922617i	$-0.373954\pi$
$643$	19.5616	0.771432	0.385716	+	0.922617i	$0.373954\pi$
$644$	90.3542	3.56045
$645$	0	0
$646$	−1.26137	−0.0496278
$647$	−26.5464	−1.04365	−0.521823	−	0.853054i	$-0.674748\pi$
$647$	−26.5464	−1.04365	−0.521823	+	0.853054i	$0.674748\pi$
$648$	0	0
$649$	22.2462	0.873240
$650$	0	0
$651$	0	0
$652$	16.2462	0.636251
$653$	−16.7386	−0.655033	−0.327517	−	0.944845i	$-0.606212\pi$
$653$	−16.7386	−0.655033	−0.327517	+	0.944845i	$0.606212\pi$
$654$	0	0
$655$	2.24621	0.0877667
$656$	3.36932	0.131550
$657$	0	0
$658$	−36.4924	−1.42262
$659$	39.6155	1.54320	0.771601	−	0.636107i	$-0.219456\pi$
$659$	39.6155	1.54320	0.771601	+	0.636107i	$0.219456\pi$
$660$	0	0
$661$	−32.4924	−1.26381	−0.631904	−	0.775046i	$-0.717726\pi$
$661$	−32.4924	−1.26381	−0.631904	+	0.775046i	$0.717726\pi$
$662$	24.6307	0.957299
$663$	0	0
$664$	−87.7235	−3.40433
$665$	4.00000	0.155113
$666$	0	0
$667$	−45.8617	−1.77577
$668$	10.2462	0.396438
$669$	0	0
$670$	7.36932	0.284702
$671$	−46.9309	−1.81175
$672$	0	0
$673$	34.1080	1.31476	0.657382	−	0.753557i	$-0.271664\pi$
$673$	34.1080	1.31476	0.657382	+	0.753557i	$0.271664\pi$
$674$	66.6004	2.56535
$675$	0	0
$676$	0	0
$677$	−37.4233	−1.43829	−0.719147	−	0.694858i	$-0.755467\pi$
$677$	−37.4233	−1.43829	−0.719147	+	0.694858i	$0.755467\pi$
$678$	0	0
$679$	−53.1771	−2.04075
$680$	−2.87689	−0.110324
$681$	0	0
$682$	−85.4773	−3.27309
$683$	19.1231	0.731725	0.365863	−	0.930669i	$-0.380774\pi$
$683$	19.1231	0.731725	0.365863	+	0.930669i	$0.380774\pi$
$684$	0	0
$685$	−0.246211	−0.00940725
$686$	−12.0000	−0.458162
$687$	0	0
$688$	−54.7386	−2.08689
$689$	0	0
$690$	0	0
$691$	18.0000	0.684752	0.342376	−	0.939563i	$-0.388768\pi$
$691$	18.0000	0.684752	0.342376	+	0.939563i	$0.388768\pi$
$692$	−55.8617	−2.12354
$693$	0	0
$694$	−28.0000	−1.06287
$695$	17.5616	0.666148
$696$	0	0
$697$	−0.192236	−0.00728146
$698$	−22.7386	−0.860670
$699$	0	0
$700$	16.2462	0.614049
$701$	19.3693	0.731569	0.365785	−	0.930700i	$-0.380801\pi$
$701$	19.3693	0.731569	0.365785	+	0.930700i	$0.380801\pi$
$702$	0	0
$703$	−6.24621	−0.235580
$704$	8.00000	0.301511
$705$	0	0
$706$	48.3542	1.81983
$707$	−7.12311	−0.267892
$708$	0	0
$709$	48.0000	1.80268	0.901339	−	0.433114i	$-0.142585\pi$
$709$	48.0000	1.80268	0.901339	+	0.433114i	$0.142585\pi$
$710$	−22.2462	−0.834885
$711$	0	0
$712$	8.63068	0.323449
$713$	−33.3693	−1.24969
$714$	0	0
$715$	0	0
$716$	10.2462	0.382919
$717$	0	0
$718$	67.2311	2.50904
$719$	7.12311	0.265647	0.132824	−	0.991140i	$-0.457596\pi$
$719$	7.12311	0.265647	0.132824	+	0.991140i	$0.457596\pi$
$720$	0	0
$721$	0	0
$722$	−45.4384	−1.69104
$723$	0	0
$724$	34.4924	1.28190
$725$	−8.24621	−0.306257
$726$	0	0
$727$	−6.63068	−0.245918	−0.122959	−	0.992412i	$-0.539238\pi$
$727$	−6.63068	−0.245918	−0.122959	+	0.992412i	$0.539238\pi$
$728$	0	0
$729$	0	0
$730$	−28.4924	−1.05455
$731$	3.12311	0.115512
$732$	0	0
$733$	25.1771	0.929937	0.464968	−	0.885327i	$-0.346066\pi$
$733$	25.1771	0.929937	0.464968	+	0.885327i	$0.346066\pi$
$734$	−28.4924	−1.05167
$735$	0	0
$736$	36.4924	1.34513
$737$	16.0000	0.589368
$738$	0	0
$739$	−36.7386	−1.35145	−0.675726	−	0.737153i	$-0.736170\pi$
$739$	−36.7386	−1.35145	−0.675726	+	0.737153i	$0.736170\pi$
$740$	−25.3693	−0.932595
$741$	0	0
$742$	89.4773	3.28481
$743$	24.9848	0.916605	0.458303	−	0.888796i	$-0.348458\pi$
$743$	24.9848	0.916605	0.458303	+	0.888796i	$0.348458\pi$
$744$	0	0
$745$	−12.9309	−0.473750
$746$	86.1080	3.15264
$747$	0	0
$748$	−11.1231	−0.406701
$749$	−2.43845	−0.0890989
$750$	0	0
$751$	48.3002	1.76250	0.881249	−	0.472652i	$-0.156703\pi$
$751$	48.3002	1.76250	0.881249	+	0.472652i	$0.156703\pi$
$752$	−30.7386	−1.12092
$753$	0	0
$754$	0	0
$755$	−0.246211	−0.00896054
$756$	0	0
$757$	14.8769	0.540710	0.270355	−	0.962761i	$-0.412859\pi$
$757$	14.8769	0.540710	0.270355	+	0.962761i	$0.412859\pi$
$758$	−9.61553	−0.349252
$759$	0	0
$760$	7.36932	0.267313
$761$	−0.246211	−0.00892515	−0.00446258	−	0.999990i	$-0.501420\pi$
$761$	−0.246211	−0.00892515	−0.00446258	+	0.999990i	$0.501420\pi$
$762$	0	0
$763$	17.3693	0.628811
$764$	−26.2462	−0.949555
$765$	0	0
$766$	−13.7538	−0.496945
$767$	0	0
$768$	0	0
$769$	−8.00000	−0.288487	−0.144244	−	0.989542i	$-0.546075\pi$
$769$	−8.00000	−0.288487	−0.144244	+	0.989542i	$0.546075\pi$
$770$	50.7386	1.82849
$771$	0	0
$772$	13.3693	0.481172
$773$	22.4924	0.808996	0.404498	−	0.914539i	$-0.367446\pi$
$773$	22.4924	0.808996	0.404498	+	0.914539i	$0.367446\pi$
$774$	0	0
$775$	−6.00000	−0.215526
$776$	−97.9697	−3.51691
$777$	0	0
$778$	32.6307	1.16987
$779$	0.492423	0.0176429
$780$	0	0
$781$	−48.3002	−1.72832
$782$	−6.24621	−0.223364
$783$	0	0
$784$	43.6847	1.56017
$785$	−13.1231	−0.468384
$786$	0	0
$787$	6.87689	0.245135	0.122567	−	0.992460i	$-0.460887\pi$
$787$	6.87689	0.245135	0.122567	+	0.992460i	$0.460887\pi$
$788$	55.8617	1.98999
$789$	0	0
$790$	−14.2462	−0.506857
$791$	72.1080	2.56386
$792$	0	0
$793$	0	0
$794$	−62.2462	−2.20904
$795$	0	0
$796$	36.4924	1.29344
$797$	−15.5616	−0.551218	−0.275609	−	0.961270i	$-0.588880\pi$
$797$	−15.5616	−0.551218	−0.275609	+	0.961270i	$0.588880\pi$
$798$	0	0
$799$	1.75379	0.0620446
$800$	6.56155	0.231986
$801$	0	0
$802$	16.6307	0.587250
$803$	−61.8617	−2.18305
$804$	0	0
$805$	19.8078	0.698132
$806$	0	0
$807$	0	0
$808$	−13.1231	−0.461669
$809$	6.87689	0.241779	0.120889	−	0.992666i	$-0.461425\pi$
$809$	6.87689	0.241779	0.120889	+	0.992666i	$0.461425\pi$
$810$	0	0
$811$	2.49242	0.0875208	0.0437604	−	0.999042i	$-0.486066\pi$
$811$	2.49242	0.0875208	0.0437604	+	0.999042i	$0.486066\pi$
$812$	−133.970	−4.70141
$813$	0	0
$814$	−79.2311	−2.77705
$815$	3.56155	0.124756
$816$	0	0
$817$	−8.00000	−0.279885
$818$	30.7386	1.07475
$819$	0	0
$820$	2.00000	0.0698430
$821$	−8.05398	−0.281086	−0.140543	−	0.990075i	$-0.544885\pi$
$821$	−8.05398	−0.281086	−0.140543	+	0.990075i	$0.544885\pi$
$822$	0	0
$823$	−15.6155	−0.544323	−0.272162	−	0.962252i	$-0.587739\pi$
$823$	−15.6155	−0.544323	−0.272162	+	0.962252i	$0.587739\pi$
$824$	0	0
$825$	0	0
$826$	36.4924	1.26973
$827$	34.7386	1.20798	0.603990	−	0.796992i	$-0.293577\pi$
$827$	34.7386	1.20798	0.603990	+	0.796992i	$0.293577\pi$
$828$	0	0
$829$	−36.7386	−1.27599	−0.637993	−	0.770042i	$-0.720235\pi$
$829$	−36.7386	−1.27599	−0.637993	+	0.770042i	$0.720235\pi$
$830$	−34.2462	−1.18870
$831$	0	0
$832$	0	0
$833$	−2.49242	−0.0863573
$834$	0	0
$835$	2.24621	0.0777333
$836$	28.4924	0.985431
$837$	0	0
$838$	−70.7386	−2.44363
$839$	7.31534	0.252554	0.126277	−	0.991995i	$-0.459697\pi$
$839$	7.31534	0.252554	0.126277	+	0.991995i	$0.459697\pi$
$840$	0	0
$841$	39.0000	1.34483
$842$	−64.9848	−2.23953
$843$	0	0
$844$	18.2462	0.628060
$845$	0	0
$846$	0	0
$847$	70.9848	2.43907
$848$	75.3693	2.58819
$849$	0	0
$850$	−1.12311	−0.0385222
$851$	−30.9309	−1.06030
$852$	0	0
$853$	−22.9309	−0.785138	−0.392569	−	0.919723i	$-0.628414\pi$
$853$	−22.9309	−0.785138	−0.392569	+	0.919723i	$0.628414\pi$
$854$	−76.9848	−2.63437
$855$	0	0
$856$	−4.49242	−0.153548
$857$	−7.56155	−0.258298	−0.129149	−	0.991625i	$-0.541225\pi$
$857$	−7.56155	−0.258298	−0.129149	+	0.991625i	$0.541225\pi$
$858$	0	0
$859$	26.5464	0.905751	0.452876	−	0.891574i	$-0.350398\pi$
$859$	26.5464	0.905751	0.452876	+	0.891574i	$0.350398\pi$
$860$	−32.4924	−1.10798
$861$	0	0
$862$	−78.7386	−2.68185
$863$	−13.3693	−0.455097	−0.227548	−	0.973767i	$-0.573071\pi$
$863$	−13.3693	−0.455097	−0.227548	+	0.973767i	$0.573071\pi$
$864$	0	0
$865$	−12.2462	−0.416384
$866$	53.1231	1.80520
$867$	0	0
$868$	−97.4773	−3.30859
$869$	−30.9309	−1.04926
$870$	0	0
$871$	0	0
$872$	32.0000	1.08366
$873$	0	0
$874$	16.0000	0.541208
$875$	3.56155	0.120402
$876$	0	0
$877$	27.1231	0.915882	0.457941	−	0.888983i	$-0.348587\pi$
$877$	27.1231	0.915882	0.457941	+	0.888983i	$0.348587\pi$
$878$	−31.2311	−1.05400
$879$	0	0
$880$	42.7386	1.44072
$881$	−47.3693	−1.59591	−0.797956	−	0.602715i	$-0.794086\pi$
$881$	−47.3693	−1.59591	−0.797956	+	0.602715i	$0.794086\pi$
$882$	0	0
$883$	−8.49242	−0.285793	−0.142896	−	0.989738i	$-0.545642\pi$
$883$	−8.49242	−0.285793	−0.142896	+	0.989738i	$0.545642\pi$
$884$	0	0
$885$	0	0
$886$	14.2462	0.478611
$887$	−7.31534	−0.245625	−0.122813	−	0.992430i	$-0.539191\pi$
$887$	−7.31534	−0.245625	−0.122813	+	0.992430i	$0.539191\pi$
$888$	0	0
$889$	−61.8617	−2.07478
$890$	3.36932	0.112940
$891$	0	0
$892$	13.1231	0.439394
$893$	−4.49242	−0.150333
$894$	0	0
$895$	2.24621	0.0750826
$896$	−33.6155	−1.12302
$897$	0	0
$898$	−9.12311	−0.304442
$899$	49.4773	1.65016
$900$	0	0
$901$	−4.30019	−0.143260
$902$	6.24621	0.207976
$903$	0	0
$904$	132.847	4.41841
$905$	7.56155	0.251355
$906$	0	0
$907$	14.7386	0.489388	0.244694	−	0.969600i	$-0.421312\pi$
$907$	14.7386	0.489388	0.244694	+	0.969600i	$0.421312\pi$
$908$	121.970	4.04771
$909$	0	0
$910$	0	0
$911$	−21.3693	−0.707997	−0.353999	−	0.935246i	$-0.615178\pi$
$911$	−21.3693	−0.707997	−0.353999	+	0.935246i	$0.615178\pi$
$912$	0	0
$913$	−74.3542	−2.46076
$914$	−67.7235	−2.24009
$915$	0	0
$916$	87.2311	2.88220
$917$	8.00000	0.264183
$918$	0	0
$919$	−44.7926	−1.47757	−0.738786	−	0.673940i	$-0.764601\pi$
$919$	−44.7926	−1.47757	−0.738786	+	0.673940i	$0.764601\pi$
$920$	36.4924	1.20312
$921$	0	0
$922$	49.1231	1.61778
$923$	0	0
$924$	0	0
$925$	−5.56155	−0.182863
$926$	107.093	3.51929
$927$	0	0
$928$	−54.1080	−1.77618
$929$	−34.6847	−1.13797	−0.568983	−	0.822349i	$-0.692663\pi$
$929$	−34.6847	−1.13797	−0.568983	+	0.822349i	$0.692663\pi$
$930$	0	0
$931$	6.38447	0.209243
$932$	103.477	3.38951
$933$	0	0
$934$	−68.9848	−2.25725
$935$	−2.43845	−0.0797458
$936$	0	0
$937$	−6.49242	−0.212098	−0.106049	−	0.994361i	$-0.533820\pi$
$937$	−6.49242	−0.212098	−0.106049	+	0.994361i	$0.533820\pi$
$938$	26.2462	0.856969
$939$	0	0
$940$	−18.2462	−0.595126
$941$	9.31534	0.303671	0.151836	−	0.988406i	$-0.451482\pi$
$941$	9.31534	0.303671	0.151836	+	0.988406i	$0.451482\pi$
$942$	0	0
$943$	2.43845	0.0794068
$944$	30.7386	1.00046
$945$	0	0
$946$	−101.477	−3.29931
$947$	15.5076	0.503929	0.251964	−	0.967737i	$-0.418923\pi$
$947$	15.5076	0.503929	0.251964	+	0.967737i	$0.418923\pi$
$948$	0	0
$949$	0	0
$950$	2.87689	0.0933388
$951$	0	0
$952$	−10.2462	−0.332082
$953$	21.3153	0.690472	0.345236	−	0.938516i	$-0.387799\pi$
$953$	21.3153	0.690472	0.345236	+	0.938516i	$0.387799\pi$
$954$	0	0
$955$	−5.75379	−0.186188
$956$	61.8617	2.00075
$957$	0	0
$958$	−46.2462	−1.49415
$959$	−0.876894	−0.0283164
$960$	0	0
$961$	5.00000	0.161290
$962$	0	0
$963$	0	0
$964$	89.4773	2.88187
$965$	2.93087	0.0943480
$966$	0	0
$967$	−38.1080	−1.22547	−0.612735	−	0.790289i	$-0.709931\pi$
$967$	−38.1080	−1.22547	−0.612735	+	0.790289i	$0.709931\pi$
$968$	130.777	4.20335
$969$	0	0
$970$	−38.2462	−1.22801
$971$	−20.8769	−0.669971	−0.334986	−	0.942223i	$-0.608731\pi$
$971$	−20.8769	−0.669971	−0.334986	+	0.942223i	$0.608731\pi$
$972$	0	0
$973$	62.5464	2.00515
$974$	−10.3845	−0.332740
$975$	0	0
$976$	−64.8466	−2.07569
$977$	27.3693	0.875622	0.437811	−	0.899067i	$-0.355754\pi$
$977$	27.3693	0.875622	0.437811	+	0.899067i	$0.355754\pi$
$978$	0	0
$979$	7.31534	0.233799
$980$	25.9309	0.828331
$981$	0	0
$982$	−93.4773	−2.98298
$983$	−42.7386	−1.36315	−0.681575	−	0.731748i	$-0.738705\pi$
$983$	−42.7386	−1.36315	−0.681575	+	0.731748i	$0.738705\pi$
$984$	0	0
$985$	12.2462	0.390197
$986$	9.26137	0.294942
$987$	0	0
$988$	0	0
$989$	−39.6155	−1.25970
$990$	0	0
$991$	−39.9157	−1.26796	−0.633982	−	0.773348i	$-0.718581\pi$
$991$	−39.9157	−1.26796	−0.633982	+	0.773348i	$0.718581\pi$
$992$	−39.3693	−1.24998
$993$	0	0
$994$	−79.2311	−2.51306
$995$	8.00000	0.253617
$996$	0	0
$997$	42.1080	1.33357	0.666786	−	0.745249i	$-0.267669\pi$
$997$	42.1080	1.33357	0.666786	+	0.745249i	$0.267669\pi$
$998$	1.61553	0.0511386
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7605.2.a.bh.1.2		2
3.2	odd	2		2535.2.a.p.1.1		2
13.5	odd	4		585.2.b.e.181.1		4
13.8	odd	4		585.2.b.e.181.4		4
13.12	even	2		7605.2.a.bc.1.1		2
39.5	even	4		195.2.b.c.181.4	yes	4
39.8	even	4		195.2.b.c.181.1	✓	4
39.38	odd	2		2535.2.a.q.1.2		2
156.47	odd	4		3120.2.g.n.961.2		4
156.83	odd	4		3120.2.g.n.961.3		4
195.8	odd	4		975.2.h.e.649.2		4
195.44	even	4		975.2.b.f.376.1		4
195.47	odd	4		975.2.h.g.649.3		4
195.83	odd	4		975.2.h.g.649.4		4
195.122	odd	4		975.2.h.e.649.1		4
195.164	even	4		975.2.b.f.376.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.b.c.181.1	✓	4	39.8	even	4
195.2.b.c.181.4	yes	4	39.5	even	4
585.2.b.e.181.1		4	13.5	odd	4
585.2.b.e.181.4		4	13.8	odd	4
975.2.b.f.376.1		4	195.44	even	4
975.2.b.f.376.4		4	195.164	even	4
975.2.h.e.649.1		4	195.122	odd	4
975.2.h.e.649.2		4	195.8	odd	4
975.2.h.g.649.3		4	195.47	odd	4
975.2.h.g.649.4		4	195.83	odd	4
2535.2.a.p.1.1		2	3.2	odd	2
2535.2.a.q.1.2		2	39.38	odd	2
3120.2.g.n.961.2		4	156.47	odd	4
3120.2.g.n.961.3		4	156.83	odd	4
7605.2.a.bc.1.1		2	13.12	even	2
7605.2.a.bh.1.2		2	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)

\(f(q)\)	\(=\)	\(q+2.56155 q^{2} +4.56155 q^{4} +1.00000 q^{5} +3.56155 q^{7} +6.56155 q^{8} +2.56155 q^{10} +5.56155 q^{11} +9.12311 q^{14} +7.68466 q^{16} -0.438447 q^{17} +1.12311 q^{19} +4.56155 q^{20} +14.2462 q^{22} +5.56155 q^{23} +1.00000 q^{25} +16.2462 q^{28} -8.24621 q^{29} -6.00000 q^{31} +6.56155 q^{32} -1.12311 q^{34} +3.56155 q^{35} -5.56155 q^{37} +2.87689 q^{38} +6.56155 q^{40} +0.438447 q^{41} -7.12311 q^{43} +25.3693 q^{44} +14.2462 q^{46} -4.00000 q^{47} +5.68466 q^{49} +2.56155 q^{50} +9.80776 q^{53} +5.56155 q^{55} +23.3693 q^{56} -21.1231 q^{58} +4.00000 q^{59} -8.43845 q^{61} -15.3693 q^{62} +1.43845 q^{64} +2.87689 q^{67} -2.00000 q^{68} +9.12311 q^{70} -8.68466 q^{71} -11.1231 q^{73} -14.2462 q^{74} +5.12311 q^{76} +19.8078 q^{77} -5.56155 q^{79} +7.68466 q^{80} +1.12311 q^{82} -13.3693 q^{83} -0.438447 q^{85} -18.2462 q^{86} +36.4924 q^{88} +1.31534 q^{89} +25.3693 q^{92} -10.2462 q^{94} +1.12311 q^{95} -14.9309 q^{97} +14.5616 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 5 q^{4} + 2 q^{5} + 3 q^{7} + 9 q^{8} + q^{10} + 7 q^{11} + 10 q^{14} + 3 q^{16} - 5 q^{17} - 6 q^{19} + 5 q^{20} + 12 q^{22} + 7 q^{23} + 2 q^{25} + 16 q^{28} - 12 q^{31} + 9 q^{32} + 6 q^{34}+ \cdots + 25 q^{98}+O(q^{100}) \) 2 * q + q^2 + 5 * q^4 + 2 * q^5 + 3 * q^7 + 9 * q^8 + q^10 + 7 * q^11 + 10 * q^14 + 3 * q^16 - 5 * q^17 - 6 * q^19 + 5 * q^20 + 12 * q^22 + 7 * q^23 + 2 * q^25 + 16 * q^28 - 12 * q^31 + 9 * q^32 + 6 * q^34 + 3 * q^35 - 7 * q^37 + 14 * q^38 + 9 * q^40 + 5 * q^41 - 6 * q^43 + 26 * q^44 + 12 * q^46 - 8 * q^47 - q^49 + q^50 - q^53 + 7 * q^55 + 22 * q^56 - 34 * q^58 + 8 * q^59 - 21 * q^61 - 6 * q^62 + 7 * q^64 + 14 * q^67 - 4 * q^68 + 10 * q^70 - 5 * q^71 - 14 * q^73 - 12 * q^74 + 2 * q^76 + 19 * q^77 - 7 * q^79 + 3 * q^80 - 6 * q^82 - 2 * q^83 - 5 * q^85 - 20 * q^86 + 40 * q^88 + 15 * q^89 + 26 * q^92 - 4 * q^94 - 6 * q^95 - q^97 + 25 * q^98

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