LMFDB - Embedded newform 7605.2.a.bu.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:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*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			$0.311108$ 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)

$f(q)$	$=$	$q-2.21432 q^{2} +2.90321 q^{4} +1.00000 q^{5} -3.83654 q^{7} -2.00000 q^{8} +O(q^{10})$	$q-2.21432 q^{2} +2.90321 q^{4} +1.00000 q^{5} -3.83654 q^{7} -2.00000 q^{8} -2.21432 q^{10} -5.80642 q^{11} +8.49532 q^{14} -1.37778 q^{16} +3.59210 q^{17} +2.14764 q^{19} +2.90321 q^{20} +12.8573 q^{22} +6.23506 q^{23} +1.00000 q^{25} -11.1383 q^{28} -2.06668 q^{29} -5.28100 q^{31} +7.05086 q^{32} -7.95407 q^{34} -3.83654 q^{35} -4.75557 q^{37} -4.75557 q^{38} -2.00000 q^{40} +11.1175 q^{41} -9.49532 q^{43} -16.8573 q^{44} -13.8064 q^{46} -2.21432 q^{47} +7.71900 q^{49} -2.21432 q^{50} +0.815792 q^{53} -5.80642 q^{55} +7.67307 q^{56} +4.57628 q^{58} +9.97481 q^{59} +5.28100 q^{61} +11.6938 q^{62} -12.8573 q^{64} -3.55554 q^{67} +10.4286 q^{68} +8.49532 q^{70} -5.73975 q^{71} -2.78568 q^{73} +10.5303 q^{74} +6.23506 q^{76} +22.2766 q^{77} +12.3319 q^{79} -1.37778 q^{80} -24.6178 q^{82} -0.622216 q^{83} +3.59210 q^{85} +21.0257 q^{86} +11.6128 q^{88} +16.1684 q^{89} +18.1017 q^{92} +4.90321 q^{94} +2.14764 q^{95} +4.25088 q^{97} -17.0923 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8}+O(q^{10}) $ 3 * q + 2 * q^4 + 3 * q^5 - 5 * q^7 - 6 * q^8	$ 3 q + 2 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8} - 4 q^{11} + 12 q^{14} - 4 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{22} - 8 q^{23} + 3 q^{25} - 6 q^{29} - 9 q^{31} + 8 q^{32} - 4 q^{34} - 5 q^{35} - 14 q^{37} - 14 q^{38} - 6 q^{40} + 20 q^{41} - 15 q^{43} - 24 q^{44} - 28 q^{46} + 30 q^{49} + 16 q^{53} - 4 q^{55} + 10 q^{56} - 6 q^{58} - 10 q^{59} + 9 q^{61} + 2 q^{62} - 12 q^{64} - 11 q^{67} + 18 q^{68} + 12 q^{70} - 4 q^{71} - 15 q^{73} - 8 q^{74} - 8 q^{76} + 17 q^{79} - 4 q^{80} - 14 q^{82} - 2 q^{83} + 4 q^{85} + 10 q^{86} + 8 q^{88} + 22 q^{89} + 28 q^{92} + 8 q^{94} - q^{97} + 2 q^{98}+O(q^{100}) $ 3 * q + 2 * q^4 + 3 * q^5 - 5 * q^7 - 6 * q^8 - 4 * q^11 + 12 * q^14 - 4 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^22 - 8 * q^23 + 3 * q^25 - 6 * q^29 - 9 * q^31 + 8 * q^32 - 4 * q^34 - 5 * q^35 - 14 * q^37 - 14 * q^38 - 6 * q^40 + 20 * q^41 - 15 * q^43 - 24 * q^44 - 28 * q^46 + 30 * q^49 + 16 * q^53 - 4 * q^55 + 10 * q^56 - 6 * q^58 - 10 * q^59 + 9 * q^61 + 2 * q^62 - 12 * q^64 - 11 * q^67 + 18 * q^68 + 12 * q^70 - 4 * q^71 - 15 * q^73 - 8 * q^74 - 8 * q^76 + 17 * q^79 - 4 * q^80 - 14 * q^82 - 2 * q^83 + 4 * q^85 + 10 * q^86 + 8 * q^88 + 22 * q^89 + 28 * q^92 + 8 * q^94 - q^97 + 2 * 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 $

$2$	−2.21432	−1.56576	−0.782880	−	0.622172i	$-0.786250\pi$
$2$	−2.21432	−1.56576	−0.782880	+	0.622172i	$0.786250\pi$
$3$	0	0
$3$	0	0
$4$	2.90321	1.45161
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	−3.83654	−1.45007	−0.725037	−	0.688710i	$-0.758177\pi$
$7$	−3.83654	−1.45007	−0.725037	+	0.688710i	$0.758177\pi$
$8$	−2.00000	−0.707107
$9$	0	0
$10$	−2.21432	−0.700229
$11$	−5.80642	−1.75070	−0.875351	−	0.483487i	$-0.839370\pi$
$11$	−5.80642	−1.75070	−0.875351	+	0.483487i	$0.839370\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	8.49532	2.27047
$15$	0	0
$16$	−1.37778	−0.344446
$17$	3.59210	0.871213	0.435607	−	0.900137i	$-0.356534\pi$
$17$	3.59210	0.871213	0.435607	+	0.900137i	$0.356534\pi$
$18$	0	0
$19$	2.14764	0.492703	0.246352	−	0.969181i	$-0.420768\pi$
$19$	2.14764	0.492703	0.246352	+	0.969181i	$0.420768\pi$
$20$	2.90321	0.649178
$21$	0	0
$22$	12.8573	2.74118
$23$	6.23506	1.30010	0.650050	−	0.759891i	$-0.274748\pi$
$23$	6.23506	1.30010	0.650050	+	0.759891i	$0.274748\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	−11.1383	−2.10494
$29$	−2.06668	−0.383772	−0.191886	−	0.981417i	$-0.561460\pi$
$29$	−2.06668	−0.383772	−0.191886	+	0.981417i	$0.561460\pi$
$30$	0	0
$31$	−5.28100	−0.948495	−0.474247	−	0.880392i	$-0.657280\pi$
$31$	−5.28100	−0.948495	−0.474247	+	0.880392i	$0.657280\pi$
$32$	7.05086	1.24643
$33$	0	0
$34$	−7.95407	−1.36411
$35$	−3.83654	−0.648493
$36$	0	0
$37$	−4.75557	−0.781811	−0.390905	−	0.920431i	$-0.627838\pi$
$37$	−4.75557	−0.781811	−0.390905	+	0.920431i	$0.627838\pi$
$38$	−4.75557	−0.771455
$39$	0	0
$40$	−2.00000	−0.316228
$41$	11.1175	1.73627	0.868133	−	0.496331i	$-0.165320\pi$
$41$	11.1175	1.73627	0.868133	+	0.496331i	$0.165320\pi$
$42$	0	0
$43$	−9.49532	−1.44802	−0.724011	−	0.689788i	$-0.757704\pi$
$43$	−9.49532	−1.44802	−0.724011	+	0.689788i	$0.757704\pi$
$44$	−16.8573	−2.54133
$45$	0	0
$46$	−13.8064	−2.03565
$47$	−2.21432	−0.322992	−0.161496	−	0.986873i	$-0.551632\pi$
$47$	−2.21432	−0.322992	−0.161496	+	0.986873i	$0.551632\pi$
$48$	0	0
$49$	7.71900	1.10271
$50$	−2.21432	−0.313152
$51$	0	0
$52$	0	0
$53$	0.815792	0.112058	0.0560288	−	0.998429i	$-0.482156\pi$
$53$	0.815792	0.112058	0.0560288	+	0.998429i	$0.482156\pi$
$54$	0	0
$55$	−5.80642	−0.782938
$56$	7.67307	1.02536
$57$	0	0
$58$	4.57628	0.600895
$59$	9.97481	1.29861	0.649305	−	0.760528i	$-0.275060\pi$
$59$	9.97481	1.29861	0.649305	+	0.760528i	$0.275060\pi$
$60$	0	0
$61$	5.28100	0.676162	0.338081	−	0.941117i	$-0.390222\pi$
$61$	5.28100	0.676162	0.338081	+	0.941117i	$0.390222\pi$
$62$	11.6938	1.48512
$63$	0	0
$64$	−12.8573	−1.60716
$65$	0	0
$66$	0	0
$67$	−3.55554	−0.434378	−0.217189	−	0.976130i	$-0.569689\pi$
$67$	−3.55554	−0.434378	−0.217189	+	0.976130i	$0.569689\pi$
$68$	10.4286	1.26466
$69$	0	0
$70$	8.49532	1.01538
$71$	−5.73975	−0.681183	−0.340591	−	0.940211i	$-0.610627\pi$
$71$	−5.73975	−0.681183	−0.340591	+	0.940211i	$0.610627\pi$
$72$	0	0
$73$	−2.78568	−0.326039	−0.163020	−	0.986623i	$-0.552123\pi$
$73$	−2.78568	−0.326039	−0.163020	+	0.986623i	$0.552123\pi$
$74$	10.5303	1.22413
$75$	0	0
$76$	6.23506	0.715211
$77$	22.2766	2.53865
$78$	0	0
$79$	12.3319	1.38744	0.693721	−	0.720244i	$-0.255970\pi$
$79$	12.3319	1.38744	0.693721	+	0.720244i	$0.255970\pi$
$80$	−1.37778	−0.154041
$81$	0	0
$82$	−24.6178	−2.71858
$83$	−0.622216	−0.0682970	−0.0341485	−	0.999417i	$-0.510872\pi$
$83$	−0.622216	−0.0682970	−0.0341485	+	0.999417i	$0.510872\pi$
$84$	0	0
$85$	3.59210	0.389618
$86$	21.0257	2.26726
$87$	0	0
$88$	11.6128	1.23793
$89$	16.1684	1.71385	0.856923	−	0.515445i	$-0.172373\pi$
$89$	16.1684	1.71385	0.856923	+	0.515445i	$0.172373\pi$
$90$	0	0
$91$	0	0
$92$	18.1017	1.88723
$93$	0	0
$94$	4.90321	0.505728
$95$	2.14764	0.220344
$96$	0	0
$97$	4.25088	0.431612	0.215806	−	0.976436i	$-0.430762\pi$
$97$	4.25088	0.431612	0.215806	+	0.976436i	$0.430762\pi$
$98$	−17.0923	−1.72659
$99$	0	0
$100$	2.90321	0.290321
$101$	2.23506	0.222397	0.111199	−	0.993798i	$-0.464531\pi$
$101$	2.23506	0.222397	0.111199	+	0.993798i	$0.464531\pi$
$102$	0	0
$103$	−2.44446	−0.240860	−0.120430	−	0.992722i	$-0.538427\pi$
$103$	−2.44446	−0.240860	−0.120430	+	0.992722i	$0.538427\pi$
$104$	0	0
$105$	0	0
$106$	−1.80642	−0.175455
$107$	−1.65233	−0.159736	−0.0798682	−	0.996805i	$-0.525450\pi$
$107$	−1.65233	−0.159736	−0.0798682	+	0.996805i	$0.525450\pi$
$108$	0	0
$109$	−2.61285	−0.250265	−0.125133	−	0.992140i	$-0.539936\pi$
$109$	−2.61285	−0.250265	−0.125133	+	0.992140i	$0.539936\pi$
$110$	12.8573	1.22589
$111$	0	0
$112$	5.28592	0.499472
$113$	−2.42864	−0.228467	−0.114234	−	0.993454i	$-0.536441\pi$
$113$	−2.42864	−0.228467	−0.114234	+	0.993454i	$0.536441\pi$
$114$	0	0
$115$	6.23506	0.581423
$116$	−6.00000	−0.557086
$117$	0	0
$118$	−22.0874	−2.03331
$119$	−13.7812	−1.26332
$120$	0	0
$121$	22.7146	2.06496
$122$	−11.6938	−1.05871
$123$	0	0
$124$	−15.3319	−1.37684
$125$	1.00000	0.0894427
$126$	0	0
$127$	19.2558	1.70868	0.854338	−	0.519717i	$-0.173963\pi$
$127$	19.2558	1.70868	0.854338	+	0.519717i	$0.173963\pi$
$128$	14.3684	1.27000
$129$	0	0
$130$	0	0
$131$	−13.4128	−1.17188	−0.585942	−	0.810353i	$-0.699275\pi$
$131$	−13.4128	−1.17188	−0.585942	+	0.810353i	$0.699275\pi$
$132$	0	0
$133$	−8.23951	−0.714456
$134$	7.87310	0.680132
$135$	0	0
$136$	−7.18421	−0.616041
$137$	4.73483	0.404523	0.202262	−	0.979332i	$-0.435171\pi$
$137$	4.73483	0.404523	0.202262	+	0.979332i	$0.435171\pi$
$138$	0	0
$139$	−11.0415	−0.936527	−0.468263	−	0.883589i	$-0.655120\pi$
$139$	−11.0415	−0.936527	−0.468263	+	0.883589i	$0.655120\pi$
$140$	−11.1383	−0.941356
$141$	0	0
$142$	12.7096	1.06657
$143$	0	0
$144$	0	0
$145$	−2.06668	−0.171628
$146$	6.16839	0.510499
$147$	0	0
$148$	−13.8064	−1.13488
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	0	0
$151$	8.81135	0.717057	0.358529	−	0.933519i	$-0.383279\pi$
$151$	8.81135	0.717057	0.358529	+	0.933519i	$0.383279\pi$
$152$	−4.29529	−0.348394
$153$	0	0
$154$	−49.3274	−3.97492
$155$	−5.28100	−0.424180
$156$	0	0
$157$	−2.73975	−0.218656	−0.109328	−	0.994006i	$-0.534870\pi$
$157$	−2.73975	−0.218656	−0.109328	+	0.994006i	$0.534870\pi$
$158$	−27.3067	−2.17240
$159$	0	0
$160$	7.05086	0.557419
$161$	−23.9210	−1.88524
$162$	0	0
$163$	−24.6938	−1.93417	−0.967084	−	0.254456i	$-0.918104\pi$
$163$	−24.6938	−1.93417	−0.967084	+	0.254456i	$0.918104\pi$
$164$	32.2766	2.52038
$165$	0	0
$166$	1.37778	0.106937
$167$	−7.90813	−0.611950	−0.305975	−	0.952040i	$-0.598982\pi$
$167$	−7.90813	−0.611950	−0.305975	+	0.952040i	$0.598982\pi$
$168$	0	0
$169$	0	0
$170$	−7.95407	−0.610049
$171$	0	0
$172$	−27.5669	−2.10196
$173$	3.65233	0.277681	0.138841	−	0.990315i	$-0.455662\pi$
$173$	3.65233	0.277681	0.138841	+	0.990315i	$0.455662\pi$
$174$	0	0
$175$	−3.83654	−0.290015
$176$	8.00000	0.603023
$177$	0	0
$178$	−35.8020	−2.68347
$179$	5.84146	0.436611	0.218306	−	0.975880i	$-0.429947\pi$
$179$	5.84146	0.436611	0.218306	+	0.975880i	$0.429947\pi$
$180$	0	0
$181$	10.0874	0.749792	0.374896	−	0.927067i	$-0.377678\pi$
$181$	10.0874	0.749792	0.374896	+	0.927067i	$0.377678\pi$
$182$	0	0
$183$	0	0
$184$	−12.4701	−0.919310
$185$	−4.75557	−0.349636
$186$	0	0
$187$	−20.8573	−1.52524
$188$	−6.42864	−0.468857
$189$	0	0
$190$	−4.75557	−0.345005
$191$	−15.9748	−1.15590	−0.577948	−	0.816073i	$-0.696147\pi$
$191$	−15.9748	−1.15590	−0.577948	+	0.816073i	$0.696147\pi$
$192$	0	0
$193$	−3.70318	−0.266561	−0.133280	−	0.991078i	$-0.542551\pi$
$193$	−3.70318	−0.266561	−0.133280	+	0.991078i	$0.542551\pi$
$194$	−9.41282	−0.675801
$195$	0	0
$196$	22.4099	1.60071
$197$	−16.3970	−1.16824	−0.584119	−	0.811668i	$-0.698560\pi$
$197$	−16.3970	−1.16824	−0.584119	+	0.811668i	$0.698560\pi$
$198$	0	0
$199$	5.29529	0.375373	0.187686	−	0.982229i	$-0.439901\pi$
$199$	5.29529	0.375373	0.187686	+	0.982229i	$0.439901\pi$
$200$	−2.00000	−0.141421
$201$	0	0
$202$	−4.94914	−0.348221
$203$	7.92888	0.556498
$204$	0	0
$205$	11.1175	0.776482
$206$	5.41282	0.377129
$207$	0	0
$208$	0	0
$209$	−12.4701	−0.862577
$210$	0	0
$211$	7.99063	0.550098	0.275049	−	0.961430i	$-0.411306\pi$
$211$	7.99063	0.550098	0.275049	+	0.961430i	$0.411306\pi$
$212$	2.36842	0.162664
$213$	0	0
$214$	3.65878	0.250109
$215$	−9.49532	−0.647575
$216$	0	0
$217$	20.2607	1.37539
$218$	5.78568	0.391856
$219$	0	0
$220$	−16.8573	−1.13652
$221$	0	0
$222$	0	0
$223$	−9.37778	−0.627983	−0.313991	−	0.949426i	$-0.601666\pi$
$223$	−9.37778	−0.627983	−0.313991	+	0.949426i	$0.601666\pi$
$224$	−27.0509	−1.80741
$225$	0	0
$226$	5.37778	0.357725
$227$	−14.4079	−0.956286	−0.478143	−	0.878282i	$-0.658690\pi$
$227$	−14.4079	−0.956286	−0.478143	+	0.878282i	$0.658690\pi$
$228$	0	0
$229$	−17.9541	−1.18644	−0.593219	−	0.805041i	$-0.702143\pi$
$229$	−17.9541	−1.18644	−0.593219	+	0.805041i	$0.702143\pi$
$230$	−13.8064	−0.910369
$231$	0	0
$232$	4.13335	0.271368
$233$	−27.5210	−1.80296	−0.901480	−	0.432821i	$-0.857518\pi$
$233$	−27.5210	−1.80296	−0.901480	+	0.432821i	$0.857518\pi$
$234$	0	0
$235$	−2.21432	−0.144446
$236$	28.9590	1.88507
$237$	0	0
$238$	30.5161	1.97806
$239$	19.0321	1.23109	0.615543	−	0.788104i	$-0.288937\pi$
$239$	19.0321	1.23109	0.615543	+	0.788104i	$0.288937\pi$
$240$	0	0
$241$	23.2815	1.49969	0.749846	−	0.661613i	$-0.230128\pi$
$241$	23.2815	1.49969	0.749846	+	0.661613i	$0.230128\pi$
$242$	−50.2973	−3.23323
$243$	0	0
$244$	15.3319	0.981521
$245$	7.71900	0.493149
$246$	0	0
$247$	0	0
$248$	10.5620	0.670687
$249$	0	0
$250$	−2.21432	−0.140046
$251$	26.7239	1.68680	0.843400	−	0.537287i	$-0.180551\pi$
$251$	26.7239	1.68680	0.843400	+	0.537287i	$0.180551\pi$
$252$	0	0
$253$	−36.2034	−2.27609
$254$	−42.6385	−2.67538
$255$	0	0
$256$	−6.10171	−0.381357
$257$	11.9190	0.743489	0.371744	−	0.928335i	$-0.378760\pi$
$257$	11.9190	0.743489	0.371744	+	0.928335i	$0.378760\pi$
$258$	0	0
$259$	18.2449	1.13368
$260$	0	0
$261$	0	0
$262$	29.7003	1.83489
$263$	−15.9289	−0.982217	−0.491108	−	0.871099i	$-0.663408\pi$
$263$	−15.9289	−0.982217	−0.491108	+	0.871099i	$0.663408\pi$
$264$	0	0
$265$	0.815792	0.0501137
$266$	18.2449	1.11867
$267$	0	0
$268$	−10.3225	−0.630546
$269$	9.58766	0.584570	0.292285	−	0.956331i	$-0.405584\pi$
$269$	9.58766	0.584570	0.292285	+	0.956331i	$0.405584\pi$
$270$	0	0
$271$	13.7239	0.833669	0.416835	−	0.908982i	$-0.363139\pi$
$271$	13.7239	0.833669	0.416835	+	0.908982i	$0.363139\pi$
$272$	−4.94914	−0.300086
$273$	0	0
$274$	−10.4844	−0.633387
$275$	−5.80642	−0.350141
$276$	0	0
$277$	11.8064	0.709379	0.354690	−	0.934984i	$-0.384587\pi$
$277$	11.8064	0.709379	0.354690	+	0.934984i	$0.384587\pi$
$278$	24.4494	1.46638
$279$	0	0
$280$	7.67307	0.458554
$281$	10.7906	0.643713	0.321857	−	0.946788i	$-0.395693\pi$
$281$	10.7906	0.643713	0.321857	+	0.946788i	$0.395693\pi$
$282$	0	0
$283$	−31.1956	−1.85438	−0.927192	−	0.374585i	$-0.877785\pi$
$283$	−31.1956	−1.85438	−0.927192	+	0.374585i	$0.877785\pi$
$284$	−16.6637	−0.988809
$285$	0	0
$286$	0	0
$287$	−42.6528	−2.51772
$288$	0	0
$289$	−4.09679	−0.240988
$290$	4.57628	0.268729
$291$	0	0
$292$	−8.08742	−0.473280
$293$	−5.91903	−0.345794	−0.172897	−	0.984940i	$-0.555313\pi$
$293$	−5.91903	−0.345794	−0.172897	+	0.984940i	$0.555313\pi$
$294$	0	0
$295$	9.97481	0.580756
$296$	9.51114	0.552824
$297$	0	0
$298$	−4.42864	−0.256544
$299$	0	0
$300$	0	0
$301$	36.4291	2.09974
$302$	−19.5111	−1.12274
$303$	0	0
$304$	−2.95899	−0.169710
$305$	5.28100	0.302389
$306$	0	0
$307$	14.5877	0.832562	0.416281	−	0.909236i	$-0.363333\pi$
$307$	14.5877	0.832562	0.416281	+	0.909236i	$0.363333\pi$
$308$	64.6735	3.68512
$309$	0	0
$310$	11.6938	0.664164
$311$	−17.9748	−1.01926	−0.509629	−	0.860394i	$-0.670217\pi$
$311$	−17.9748	−1.01926	−0.509629	+	0.860394i	$0.670217\pi$
$312$	0	0
$313$	−5.79060	−0.327304	−0.163652	−	0.986518i	$-0.552327\pi$
$313$	−5.79060	−0.327304	−0.163652	+	0.986518i	$0.552327\pi$
$314$	6.06668	0.342362
$315$	0	0
$316$	35.8020	2.01402
$317$	−4.78415	−0.268705	−0.134352	−	0.990934i	$-0.542895\pi$
$317$	−4.78415	−0.268705	−0.134352	+	0.990934i	$0.542895\pi$
$318$	0	0
$319$	12.0000	0.671871
$320$	−12.8573	−0.718744
$321$	0	0
$322$	52.9688	2.95184
$323$	7.71456	0.429249
$324$	0	0
$325$	0	0
$326$	54.6800	3.02845
$327$	0	0
$328$	−22.2351	−1.22773
$329$	8.49532	0.468362
$330$	0	0
$331$	2.67307	0.146925	0.0734626	−	0.997298i	$-0.476595\pi$
$331$	2.67307	0.146925	0.0734626	+	0.997298i	$0.476595\pi$
$332$	−1.80642	−0.0991404
$333$	0	0
$334$	17.5111	0.958167
$335$	−3.55554	−0.194260
$336$	0	0
$337$	−29.0350	−1.58164	−0.790820	−	0.612049i	$-0.790345\pi$
$337$	−29.0350	−1.58164	−0.790820	+	0.612049i	$0.790345\pi$
$338$	0	0
$339$	0	0
$340$	10.4286	0.565572
$341$	30.6637	1.66053
$342$	0	0
$343$	−2.75848	−0.148944
$344$	18.9906	1.02391
$345$	0	0
$346$	−8.08742	−0.434782
$347$	−28.3082	−1.51966	−0.759832	−	0.650120i	$-0.774719\pi$
$347$	−28.3082	−1.51966	−0.759832	+	0.650120i	$0.774719\pi$
$348$	0	0
$349$	−32.0464	−1.71540	−0.857702	−	0.514146i	$-0.828109\pi$
$349$	−32.0464	−1.71540	−0.857702	+	0.514146i	$0.828109\pi$
$350$	8.49532	0.454094
$351$	0	0
$352$	−40.9403	−2.18212
$353$	14.4889	0.771164	0.385582	−	0.922674i	$-0.374001\pi$
$353$	14.4889	0.771164	0.385582	+	0.922674i	$0.374001\pi$
$354$	0	0
$355$	−5.73975	−0.304634
$356$	46.9403	2.48783
$357$	0	0
$358$	−12.9349	−0.683628
$359$	24.2701	1.28093	0.640463	−	0.767989i	$-0.278742\pi$
$359$	24.2701	1.28093	0.640463	+	0.767989i	$0.278742\pi$
$360$	0	0
$361$	−14.3876	−0.757244
$362$	−22.3368	−1.17399
$363$	0	0
$364$	0	0
$365$	−2.78568	−0.145809
$366$	0	0
$367$	−2.23798	−0.116821	−0.0584107	−	0.998293i	$-0.518603\pi$
$367$	−2.23798	−0.116821	−0.0584107	+	0.998293i	$0.518603\pi$
$368$	−8.59057	−0.447815
$369$	0	0
$370$	10.5303	0.547447
$371$	−3.12981	−0.162492
$372$	0	0
$373$	28.1131	1.45564	0.727820	−	0.685768i	$-0.240534\pi$
$373$	28.1131	1.45564	0.727820	+	0.685768i	$0.240534\pi$
$374$	46.1847	2.38815
$375$	0	0
$376$	4.42864	0.228390
$377$	0	0
$378$	0	0
$379$	−19.6178	−1.00770	−0.503849	−	0.863792i	$-0.668083\pi$
$379$	−19.6178	−1.00770	−0.503849	+	0.863792i	$0.668083\pi$
$380$	6.23506	0.319852
$381$	0	0
$382$	35.3733	1.80986
$383$	19.4400	0.993338	0.496669	−	0.867940i	$-0.334556\pi$
$383$	19.4400	0.993338	0.496669	+	0.867940i	$0.334556\pi$
$384$	0	0
$385$	22.2766	1.13532
$386$	8.20003	0.417371
$387$	0	0
$388$	12.3412	0.626530
$389$	2.81579	0.142766	0.0713832	−	0.997449i	$-0.477259\pi$
$389$	2.81579	0.142766	0.0713832	+	0.997449i	$0.477259\pi$
$390$	0	0
$391$	22.3970	1.13266
$392$	−15.4380	−0.779737
$393$	0	0
$394$	36.3082	1.82918
$395$	12.3319	0.620483
$396$	0	0
$397$	−12.6795	−0.636367	−0.318184	−	0.948029i	$-0.603073\pi$
$397$	−12.6795	−0.636367	−0.318184	+	0.948029i	$0.603073\pi$
$398$	−11.7255	−0.587744
$399$	0	0
$400$	−1.37778	−0.0688892
$401$	−0.907658	−0.0453263	−0.0226631	−	0.999743i	$-0.507215\pi$
$401$	−0.907658	−0.0453263	−0.0226631	+	0.999743i	$0.507215\pi$
$402$	0	0
$403$	0	0
$404$	6.48886	0.322833
$405$	0	0
$406$	−17.5571	−0.871343
$407$	27.6128	1.36872
$408$	0	0
$409$	−33.5763	−1.66024	−0.830120	−	0.557585i	$-0.811728\pi$
$409$	−33.5763	−1.66024	−0.830120	+	0.557585i	$0.811728\pi$
$410$	−24.6178	−1.21578
$411$	0	0
$412$	−7.09679	−0.349634
$413$	−38.2687	−1.88308
$414$	0	0
$415$	−0.622216	−0.0305434
$416$	0	0
$417$	0	0
$418$	27.6128	1.35059
$419$	−22.9525	−1.12130	−0.560652	−	0.828051i	$-0.689450\pi$
$419$	−22.9525	−1.12130	−0.560652	+	0.828051i	$0.689450\pi$
$420$	0	0
$421$	−31.0874	−1.51511	−0.757554	−	0.652772i	$-0.773606\pi$
$421$	−31.0874	−1.51511	−0.757554	+	0.652772i	$0.773606\pi$
$422$	−17.6938	−0.861321
$423$	0	0
$424$	−1.63158	−0.0792367
$425$	3.59210	0.174243
$426$	0	0
$427$	−20.2607	−0.980485
$428$	−4.79706	−0.231874
$429$	0	0
$430$	21.0257	1.01395
$431$	−17.0509	−0.821311	−0.410655	−	0.911791i	$-0.634700\pi$
$431$	−17.0509	−0.821311	−0.410655	+	0.911791i	$0.634700\pi$
$432$	0	0
$433$	−2.59210	−0.124569	−0.0622843	−	0.998058i	$-0.519839\pi$
$433$	−2.59210	−0.124569	−0.0622843	+	0.998058i	$0.519839\pi$
$434$	−44.8637	−2.15353
$435$	0	0
$436$	−7.58565	−0.363287
$437$	13.3907	0.640564
$438$	0	0
$439$	−13.7699	−0.657200	−0.328600	−	0.944469i	$-0.606577\pi$
$439$	−13.7699	−0.657200	−0.328600	+	0.944469i	$0.606577\pi$
$440$	11.6128	0.553621
$441$	0	0
$442$	0	0
$443$	−4.71609	−0.224068	−0.112034	−	0.993704i	$-0.535737\pi$
$443$	−4.71609	−0.224068	−0.112034	+	0.993704i	$0.535737\pi$
$444$	0	0
$445$	16.1684	0.766455
$446$	20.7654	0.983271
$447$	0	0
$448$	49.3274	2.33050
$449$	10.3368	0.487823	0.243911	−	0.969798i	$-0.421569\pi$
$449$	10.3368	0.487823	0.243911	+	0.969798i	$0.421569\pi$
$450$	0	0
$451$	−64.5531	−3.03969
$452$	−7.05086	−0.331644
$453$	0	0
$454$	31.9037	1.49731
$455$	0	0
$456$	0	0
$457$	−19.6287	−0.918190	−0.459095	−	0.888387i	$-0.651826\pi$
$457$	−19.6287	−0.918190	−0.459095	+	0.888387i	$0.651826\pi$
$458$	39.7560	1.85768
$459$	0	0
$460$	18.1017	0.843997
$461$	−25.2005	−1.17370	−0.586852	−	0.809694i	$-0.699633\pi$
$461$	−25.2005	−1.17370	−0.586852	+	0.809694i	$0.699633\pi$
$462$	0	0
$463$	28.8129	1.33905	0.669524	−	0.742790i	$-0.266498\pi$
$463$	28.8129	1.33905	0.669524	+	0.742790i	$0.266498\pi$
$464$	2.84743	0.132189
$465$	0	0
$466$	60.9403	2.82300
$467$	32.3575	1.49733	0.748664	−	0.662950i	$-0.230696\pi$
$467$	32.3575	1.49733	0.748664	+	0.662950i	$0.230696\pi$
$468$	0	0
$469$	13.6410	0.629881
$470$	4.90321	0.226168
$471$	0	0
$472$	−19.9496	−0.918256
$473$	55.1338	2.53506
$474$	0	0
$475$	2.14764	0.0985406
$476$	−40.0098	−1.83385
$477$	0	0
$478$	−42.1432	−1.92758
$479$	−5.93332	−0.271100	−0.135550	−	0.990770i	$-0.543280\pi$
$479$	−5.93332	−0.271100	−0.135550	+	0.990770i	$0.543280\pi$
$480$	0	0
$481$	0	0
$482$	−51.5526	−2.34816
$483$	0	0
$484$	65.9452	2.99751
$485$	4.25088	0.193023
$486$	0	0
$487$	−4.84299	−0.219457	−0.109728	−	0.993962i	$-0.534998\pi$
$487$	−4.84299	−0.219457	−0.109728	+	0.993962i	$0.534998\pi$
$488$	−10.5620	−0.478119
$489$	0	0
$490$	−17.0923	−0.772153
$491$	−0.0765209	−0.00345334	−0.00172667	−	0.999999i	$-0.500550\pi$
$491$	−0.0765209	−0.00345334	−0.00172667	+	0.999999i	$0.500550\pi$
$492$	0	0
$493$	−7.42372	−0.334347
$494$	0	0
$495$	0	0
$496$	7.27607	0.326705
$497$	22.0207	0.987765
$498$	0	0
$499$	38.0687	1.70419	0.852094	−	0.523388i	$-0.175332\pi$
$499$	38.0687	1.70419	0.852094	+	0.523388i	$0.175332\pi$
$500$	2.90321	0.129836
$501$	0	0
$502$	−59.1753	−2.64112
$503$	−13.2543	−0.590979	−0.295489	−	0.955346i	$-0.595483\pi$
$503$	−13.2543	−0.590979	−0.295489	+	0.955346i	$0.595483\pi$
$504$	0	0
$505$	2.23506	0.0994590
$506$	80.1659	3.56381
$507$	0	0
$508$	55.9037	2.48033
$509$	28.4701	1.26192	0.630958	−	0.775817i	$-0.282662\pi$
$509$	28.4701	1.26192	0.630958	+	0.775817i	$0.282662\pi$
$510$	0	0
$511$	10.6874	0.472781
$512$	−15.2257	−0.672887
$513$	0	0
$514$	−26.3926	−1.16413
$515$	−2.44446	−0.107716
$516$	0	0
$517$	12.8573	0.565462
$518$	−40.4001	−1.77508
$519$	0	0
$520$	0	0
$521$	−17.1175	−0.749933	−0.374966	−	0.927038i	$-0.622346\pi$
$521$	−17.1175	−0.749933	−0.374966	+	0.927038i	$0.622346\pi$
$522$	0	0
$523$	0.133353	0.00583112	0.00291556	−	0.999996i	$-0.499072\pi$
$523$	0.133353	0.00583112	0.00291556	+	0.999996i	$0.499072\pi$
$524$	−38.9403	−1.70111
$525$	0	0
$526$	35.2716	1.53792
$527$	−18.9699	−0.826341
$528$	0	0
$529$	15.8760	0.690262
$530$	−1.80642	−0.0784660
$531$	0	0
$532$	−23.9210	−1.03711
$533$	0	0
$534$	0	0
$535$	−1.65233	−0.0714363
$536$	7.11108	0.307152
$537$	0	0
$538$	−21.2301	−0.915296
$539$	−44.8198	−1.93053
$540$	0	0
$541$	−26.3876	−1.13449	−0.567246	−	0.823548i	$-0.691991\pi$
$541$	−26.3876	−1.13449	−0.567246	+	0.823548i	$0.691991\pi$
$542$	−30.3892	−1.30533
$543$	0	0
$544$	25.3274	1.08590
$545$	−2.61285	−0.111922
$546$	0	0
$547$	−0.0573086	−0.00245034	−0.00122517	−	0.999999i	$-0.500390\pi$
$547$	−0.0573086	−0.00245034	−0.00122517	+	0.999999i	$0.500390\pi$
$548$	13.7462	0.587209
$549$	0	0
$550$	12.8573	0.548236
$551$	−4.43848	−0.189086
$552$	0	0
$553$	−47.3116	−2.01189
$554$	−26.1432	−1.11072
$555$	0	0
$556$	−32.0558	−1.35947
$557$	−41.0420	−1.73900	−0.869502	−	0.493930i	$-0.835560\pi$
$557$	−41.0420	−1.73900	−0.869502	+	0.493930i	$0.835560\pi$
$558$	0	0
$559$	0	0
$560$	5.28592	0.223371
$561$	0	0
$562$	−23.8938	−1.00790
$563$	−21.2257	−0.894556	−0.447278	−	0.894395i	$-0.647607\pi$
$563$	−21.2257	−0.894556	−0.447278	+	0.894395i	$0.647607\pi$
$564$	0	0
$565$	−2.42864	−0.102174
$566$	69.0770	2.90352
$567$	0	0
$568$	11.4795	0.481669
$569$	−16.3620	−0.685929	−0.342965	−	0.939348i	$-0.611431\pi$
$569$	−16.3620	−0.685929	−0.342965	+	0.939348i	$0.611431\pi$
$570$	0	0
$571$	−37.7101	−1.57812	−0.789060	−	0.614317i	$-0.789432\pi$
$571$	−37.7101	−1.57812	−0.789060	+	0.614317i	$0.789432\pi$
$572$	0	0
$573$	0	0
$574$	94.4469	3.94214
$575$	6.23506	0.260020
$576$	0	0
$577$	42.7150	1.77825	0.889125	−	0.457664i	$-0.151314\pi$
$577$	42.7150	1.77825	0.889125	+	0.457664i	$0.151314\pi$
$578$	9.07160	0.377329
$579$	0	0
$580$	−6.00000	−0.249136
$581$	2.38715	0.0990358
$582$	0	0
$583$	−4.73683	−0.196180
$584$	5.57136	0.230545
$585$	0	0
$586$	13.1066	0.541430
$587$	−9.62375	−0.397215	−0.198607	−	0.980079i	$-0.563642\pi$
$587$	−9.62375	−0.397215	−0.198607	+	0.980079i	$0.563642\pi$
$588$	0	0
$589$	−11.3417	−0.467326
$590$	−22.0874	−0.909325
$591$	0	0
$592$	6.55215	0.269292
$593$	24.5018	1.00617	0.503084	−	0.864238i	$-0.332199\pi$
$593$	24.5018	1.00617	0.503084	+	0.864238i	$0.332199\pi$
$594$	0	0
$595$	−13.7812	−0.564976
$596$	5.80642	0.237840
$597$	0	0
$598$	0	0
$599$	16.9654	0.693189	0.346595	−	0.938015i	$-0.387338\pi$
$599$	16.9654	0.693189	0.346595	+	0.938015i	$0.387338\pi$
$600$	0	0
$601$	−21.5669	−0.879733	−0.439866	−	0.898063i	$-0.644974\pi$
$601$	−21.5669	−0.879733	−0.439866	+	0.898063i	$0.644974\pi$
$602$	−80.6657	−3.28769
$603$	0	0
$604$	25.5812	1.04088
$605$	22.7146	0.923478
$606$	0	0
$607$	−19.9857	−0.811195	−0.405597	−	0.914052i	$-0.632937\pi$
$607$	−19.9857	−0.811195	−0.405597	+	0.914052i	$0.632937\pi$
$608$	15.1427	0.614118
$609$	0	0
$610$	−11.6938	−0.473469
$611$	0	0
$612$	0	0
$613$	11.2000	0.452365	0.226182	−	0.974085i	$-0.427375\pi$
$613$	11.2000	0.452365	0.226182	+	0.974085i	$0.427375\pi$
$614$	−32.3017	−1.30359
$615$	0	0
$616$	−44.5531	−1.79510
$617$	−0.590573	−0.0237756	−0.0118878	−	0.999929i	$-0.503784\pi$
$617$	−0.590573	−0.0237756	−0.0118878	+	0.999929i	$0.503784\pi$
$618$	0	0
$619$	−12.2573	−0.492664	−0.246332	−	0.969186i	$-0.579225\pi$
$619$	−12.2573	−0.492664	−0.246332	+	0.969186i	$0.579225\pi$
$620$	−15.3319	−0.615742
$621$	0	0
$622$	39.8020	1.59591
$623$	−62.0306	−2.48520
$624$	0	0
$625$	1.00000	0.0400000
$626$	12.8222	0.512480
$627$	0	0
$628$	−7.95407	−0.317402
$629$	−17.0825	−0.681124
$630$	0	0
$631$	36.6400	1.45862	0.729309	−	0.684185i	$-0.239842\pi$
$631$	36.6400	1.45862	0.729309	+	0.684185i	$0.239842\pi$
$632$	−24.6637	−0.981069
$633$	0	0
$634$	10.5936	0.420727
$635$	19.2558	0.764143
$636$	0	0
$637$	0	0
$638$	−26.5718	−1.05199
$639$	0	0
$640$	14.3684	0.567962
$641$	21.1655	0.835986	0.417993	−	0.908450i	$-0.362734\pi$
$641$	21.1655	0.835986	0.417993	+	0.908450i	$0.362734\pi$
$642$	0	0
$643$	12.1920	0.480807	0.240404	−	0.970673i	$-0.422720\pi$
$643$	12.1920	0.480807	0.240404	+	0.970673i	$0.422720\pi$
$644$	−69.4479	−2.73663
$645$	0	0
$646$	−17.0825	−0.672102
$647$	−9.46076	−0.371941	−0.185970	−	0.982555i	$-0.559543\pi$
$647$	−9.46076	−0.371941	−0.185970	+	0.982555i	$0.559543\pi$
$648$	0	0
$649$	−57.9180	−2.27348
$650$	0	0
$651$	0	0
$652$	−71.6914	−2.80765
$653$	−20.3990	−0.798275	−0.399137	−	0.916891i	$-0.630690\pi$
$653$	−20.3990	−0.798275	−0.399137	+	0.916891i	$0.630690\pi$
$654$	0	0
$655$	−13.4128	−0.524082
$656$	−15.3176	−0.598050
$657$	0	0
$658$	−18.8113	−0.733343
$659$	−34.9719	−1.36231	−0.681156	−	0.732138i	$-0.738522\pi$
$659$	−34.9719	−1.36231	−0.681156	+	0.732138i	$0.738522\pi$
$660$	0	0
$661$	−19.4603	−0.756917	−0.378459	−	0.925618i	$-0.623546\pi$
$661$	−19.4603	−0.756917	−0.378459	+	0.925618i	$0.623546\pi$
$662$	−5.91903	−0.230050
$663$	0	0
$664$	1.24443	0.0482933
$665$	−8.23951	−0.319514
$666$	0	0
$667$	−12.8859	−0.498942
$668$	−22.9590	−0.888310
$669$	0	0
$670$	7.87310	0.304164
$671$	−30.6637	−1.18376
$672$	0	0
$673$	14.2652	0.549882	0.274941	−	0.961461i	$-0.411342\pi$
$673$	14.2652	0.549882	0.274941	+	0.961461i	$0.411342\pi$
$674$	64.2928	2.47647
$675$	0	0
$676$	0	0
$677$	34.0415	1.30832	0.654160	−	0.756356i	$-0.273022\pi$
$677$	34.0415	1.30832	0.654160	+	0.756356i	$0.273022\pi$
$678$	0	0
$679$	−16.3087	−0.625869
$680$	−7.18421	−0.275502
$681$	0	0
$682$	−67.8992	−2.60000
$683$	−29.3383	−1.12260	−0.561300	−	0.827613i	$-0.689698\pi$
$683$	−29.3383	−1.12260	−0.561300	+	0.827613i	$0.689698\pi$
$684$	0	0
$685$	4.73483	0.180908
$686$	6.10816	0.233211
$687$	0	0
$688$	13.0825	0.498766
$689$	0	0
$690$	0	0
$691$	3.18913	0.121320	0.0606601	−	0.998158i	$-0.480679\pi$
$691$	3.18913	0.121320	0.0606601	+	0.998158i	$0.480679\pi$
$692$	10.6035	0.403084
$693$	0	0
$694$	62.6834	2.37943
$695$	−11.0415	−0.418827
$696$	0	0
$697$	39.9353	1.51266
$698$	70.9610	2.68591
$699$	0	0
$700$	−11.1383	−0.420987
$701$	−2.44738	−0.0924361	−0.0462180	−	0.998931i	$-0.514717\pi$
$701$	−2.44738	−0.0924361	−0.0462180	+	0.998931i	$0.514717\pi$
$702$	0	0
$703$	−10.2133	−0.385201
$704$	74.6548	2.81366
$705$	0	0
$706$	−32.0830	−1.20746
$707$	−8.57490	−0.322492
$708$	0	0
$709$	−0.603003	−0.0226463	−0.0113231	−	0.999936i	$-0.503604\pi$
$709$	−0.603003	−0.0226463	−0.0113231	+	0.999936i	$0.503604\pi$
$710$	12.7096	0.476984
$711$	0	0
$712$	−32.3368	−1.21187
$713$	−32.9273	−1.23314
$714$	0	0
$715$	0	0
$716$	16.9590	0.633787
$717$	0	0
$718$	−53.7418	−2.00562
$719$	−43.5975	−1.62591	−0.812956	−	0.582325i	$-0.802143\pi$
$719$	−43.5975	−1.62591	−0.812956	+	0.582325i	$0.802143\pi$
$720$	0	0
$721$	9.37826	0.349265
$722$	31.8588	1.18566
$723$	0	0
$724$	29.2859	1.08840
$725$	−2.06668	−0.0767544
$726$	0	0
$727$	32.8642	1.21887	0.609433	−	0.792838i	$-0.291397\pi$
$727$	32.8642	1.21887	0.609433	+	0.792838i	$0.291397\pi$
$728$	0	0
$729$	0	0
$730$	6.16839	0.228302
$731$	−34.1082	−1.26154
$732$	0	0
$733$	17.4035	0.642811	0.321406	−	0.946942i	$-0.395845\pi$
$733$	17.4035	0.642811	0.321406	+	0.946942i	$0.395845\pi$
$734$	4.95560	0.182914
$735$	0	0
$736$	43.9625	1.62048
$737$	20.6450	0.760467
$738$	0	0
$739$	42.5847	1.56651	0.783253	−	0.621704i	$-0.213559\pi$
$739$	42.5847	1.56651	0.783253	+	0.621704i	$0.213559\pi$
$740$	−13.8064	−0.507534
$741$	0	0
$742$	6.93041	0.254423
$743$	32.8464	1.20502	0.602508	−	0.798113i	$-0.294168\pi$
$743$	32.8464	1.20502	0.602508	+	0.798113i	$0.294168\pi$
$744$	0	0
$745$	2.00000	0.0732743
$746$	−62.2514	−2.27918
$747$	0	0
$748$	−60.5531	−2.21404
$749$	6.33921	0.231630
$750$	0	0
$751$	12.4746	0.455204	0.227602	−	0.973754i	$-0.426912\pi$
$751$	12.4746	0.455204	0.227602	+	0.973754i	$0.426912\pi$
$752$	3.05086	0.111253
$753$	0	0
$754$	0	0
$755$	8.81135	0.320678
$756$	0	0
$757$	−4.87463	−0.177172	−0.0885858	−	0.996069i	$-0.528235\pi$
$757$	−4.87463	−0.177172	−0.0885858	+	0.996069i	$0.528235\pi$
$758$	43.4400	1.57781
$759$	0	0
$760$	−4.29529	−0.155806
$761$	4.10171	0.148687	0.0743434	−	0.997233i	$-0.476314\pi$
$761$	4.10171	0.148687	0.0743434	+	0.997233i	$0.476314\pi$
$762$	0	0
$763$	10.0243	0.362903
$764$	−46.3783	−1.67791
$765$	0	0
$766$	−43.0464	−1.55533
$767$	0	0
$768$	0	0
$769$	−48.0973	−1.73443	−0.867216	−	0.497932i	$-0.834093\pi$
$769$	−48.0973	−1.73443	−0.867216	+	0.497932i	$0.834093\pi$
$770$	−49.3274	−1.77764
$771$	0	0
$772$	−10.7511	−0.386941
$773$	−18.1936	−0.654377	−0.327189	−	0.944959i	$-0.606101\pi$
$773$	−18.1936	−0.654377	−0.327189	+	0.944959i	$0.606101\pi$
$774$	0	0
$775$	−5.28100	−0.189699
$776$	−8.50177	−0.305196
$777$	0	0
$778$	−6.23506	−0.223538
$779$	23.8765	0.855464
$780$	0	0
$781$	33.3274	1.19255
$782$	−49.5941	−1.77348
$783$	0	0
$784$	−10.6351	−0.379826
$785$	−2.73975	−0.0977858
$786$	0	0
$787$	−29.2973	−1.04434	−0.522168	−	0.852843i	$-0.674877\pi$
$787$	−29.2973	−1.04434	−0.522168	+	0.852843i	$0.674877\pi$
$788$	−47.6040	−1.69582
$789$	0	0
$790$	−27.3067	−0.971527
$791$	9.31756	0.331294
$792$	0	0
$793$	0	0
$794$	28.0765	0.996398
$795$	0	0
$796$	15.3733	0.544894
$797$	−26.8780	−0.952068	−0.476034	−	0.879427i	$-0.657926\pi$
$797$	−26.8780	−0.952068	−0.476034	+	0.879427i	$0.657926\pi$
$798$	0	0
$799$	−7.95407	−0.281395
$800$	7.05086	0.249285
$801$	0	0
$802$	2.00984	0.0709701
$803$	16.1748	0.570798
$804$	0	0
$805$	−23.9210	−0.843106
$806$	0	0
$807$	0	0
$808$	−4.47013	−0.157259
$809$	28.4572	1.00050	0.500251	−	0.865880i	$-0.333241\pi$
$809$	28.4572	1.00050	0.500251	+	0.865880i	$0.333241\pi$
$810$	0	0
$811$	−16.6316	−0.584014	−0.292007	−	0.956416i	$-0.594323\pi$
$811$	−16.6316	−0.584014	−0.292007	+	0.956416i	$0.594323\pi$
$812$	23.0192	0.807816
$813$	0	0
$814$	−61.1437	−2.14308
$815$	−24.6938	−0.864987
$816$	0	0
$817$	−20.3926	−0.713445
$818$	74.3486	2.59954
$819$	0	0
$820$	32.2766	1.12715
$821$	34.9688	1.22042	0.610210	−	0.792239i	$-0.291085\pi$
$821$	34.9688	1.22042	0.610210	+	0.792239i	$0.291085\pi$
$822$	0	0
$823$	18.6637	0.650576	0.325288	−	0.945615i	$-0.394539\pi$
$823$	18.6637	0.650576	0.325288	+	0.945615i	$0.394539\pi$
$824$	4.88892	0.170314
$825$	0	0
$826$	84.7392	2.94845
$827$	−21.2968	−0.740563	−0.370281	−	0.928920i	$-0.620739\pi$
$827$	−21.2968	−0.740563	−0.370281	+	0.928920i	$0.620739\pi$
$828$	0	0
$829$	−7.19219	−0.249795	−0.124898	−	0.992170i	$-0.539860\pi$
$829$	−7.19219	−0.249795	−0.124898	+	0.992170i	$0.539860\pi$
$830$	1.37778	0.0478236
$831$	0	0
$832$	0	0
$833$	27.7275	0.960700
$834$	0	0
$835$	−7.90813	−0.273672
$836$	−36.2034	−1.25212
$837$	0	0
$838$	50.8243	1.75569
$839$	1.58120	0.0545893	0.0272946	−	0.999627i	$-0.491311\pi$
$839$	1.58120	0.0545893	0.0272946	+	0.999627i	$0.491311\pi$
$840$	0	0
$841$	−24.7288	−0.852719
$842$	68.8375	2.37230
$843$	0	0
$844$	23.1985	0.798525
$845$	0	0
$846$	0	0
$847$	−87.1452	−2.99434
$848$	−1.12399	−0.0385978
$849$	0	0
$850$	−7.95407	−0.272822
$851$	−29.6513	−1.01643
$852$	0	0
$853$	−23.0207	−0.788215	−0.394108	−	0.919064i	$-0.628946\pi$
$853$	−23.0207	−0.788215	−0.394108	+	0.919064i	$0.628946\pi$
$854$	44.8637	1.53521
$855$	0	0
$856$	3.30465	0.112951
$857$	−47.4499	−1.62086	−0.810428	−	0.585838i	$-0.800765\pi$
$857$	−47.4499	−1.62086	−0.810428	+	0.585838i	$0.800765\pi$
$858$	0	0
$859$	−49.0241	−1.67268	−0.836341	−	0.548210i	$-0.815310\pi$
$859$	−49.0241	−1.67268	−0.836341	+	0.548210i	$0.815310\pi$
$860$	−27.5669	−0.940024
$861$	0	0
$862$	37.7560	1.28598
$863$	37.3590	1.27172	0.635858	−	0.771806i	$-0.280646\pi$
$863$	37.3590	1.27172	0.635858	+	0.771806i	$0.280646\pi$
$864$	0	0
$865$	3.65233	0.124183
$866$	5.73975	0.195045
$867$	0	0
$868$	58.8212	1.99652
$869$	−71.6040	−2.42900
$870$	0	0
$871$	0	0
$872$	5.22570	0.176964
$873$	0	0
$874$	−29.6513	−1.00297
$875$	−3.83654	−0.129699
$876$	0	0
$877$	20.7971	0.702267	0.351133	−	0.936325i	$-0.385796\pi$
$877$	20.7971	0.702267	0.351133	+	0.936325i	$0.385796\pi$
$878$	30.4909	1.02902
$879$	0	0
$880$	8.00000	0.269680
$881$	−29.7560	−1.00251	−0.501253	−	0.865301i	$-0.667128\pi$
$881$	−29.7560	−1.00251	−0.501253	+	0.865301i	$0.667128\pi$
$882$	0	0
$883$	−40.5975	−1.36621	−0.683107	−	0.730318i	$-0.739372\pi$
$883$	−40.5975	−1.36621	−0.683107	+	0.730318i	$0.739372\pi$
$884$	0	0
$885$	0	0
$886$	10.4429	0.350837
$887$	−48.4306	−1.62614	−0.813071	−	0.582165i	$-0.802206\pi$
$887$	−48.4306	−1.62614	−0.813071	+	0.582165i	$0.802206\pi$
$888$	0	0
$889$	−73.8756	−2.47771
$890$	−35.8020	−1.20009
$891$	0	0
$892$	−27.2257	−0.911584
$893$	−4.75557	−0.159139
$894$	0	0
$895$	5.84146	0.195258
$896$	−55.1249	−1.84159
$897$	0	0
$898$	−22.8889	−0.763813
$899$	10.9141	0.364006
$900$	0	0
$901$	2.93041	0.0976261
$902$	142.941	4.75942
$903$	0	0
$904$	4.85728	0.161551
$905$	10.0874	0.335317
$906$	0	0
$907$	−10.2997	−0.341997	−0.170998	−	0.985271i	$-0.554699\pi$
$907$	−10.2997	−0.341997	−0.170998	+	0.985271i	$0.554699\pi$
$908$	−41.8292	−1.38815
$909$	0	0
$910$	0	0
$911$	−7.35905	−0.243816	−0.121908	−	0.992541i	$-0.538901\pi$
$911$	−7.35905	−0.243816	−0.121908	+	0.992541i	$0.538901\pi$
$912$	0	0
$913$	3.61285	0.119568
$914$	43.4641	1.43767
$915$	0	0
$916$	−52.1245	−1.72224
$917$	51.4588	1.69932
$918$	0	0
$919$	0.782766	0.0258211	0.0129105	−	0.999917i	$-0.495890\pi$
$919$	0.782766	0.0258211	0.0129105	+	0.999917i	$0.495890\pi$
$920$	−12.4701	−0.411128
$921$	0	0
$922$	55.8020	1.83774
$923$	0	0
$924$	0	0
$925$	−4.75557	−0.156362
$926$	−63.8009	−2.09663
$927$	0	0
$928$	−14.5718	−0.478344
$929$	28.4415	0.933137	0.466568	−	0.884485i	$-0.345490\pi$
$929$	28.4415	0.933137	0.466568	+	0.884485i	$0.345490\pi$
$930$	0	0
$931$	16.5777	0.543311
$932$	−79.8992	−2.61719
$933$	0	0
$934$	−71.6499	−2.34446
$935$	−20.8573	−0.682106
$936$	0	0
$937$	−21.3747	−0.698282	−0.349141	−	0.937070i	$-0.613527\pi$
$937$	−21.3747	−0.698282	−0.349141	+	0.937070i	$0.613527\pi$
$938$	−30.2054	−0.986242
$939$	0	0
$940$	−6.42864	−0.209679
$941$	38.2830	1.24799	0.623995	−	0.781428i	$-0.285508\pi$
$941$	38.2830	1.24799	0.623995	+	0.781428i	$0.285508\pi$
$942$	0	0
$943$	69.3185	2.25732
$944$	−13.7431	−0.447301
$945$	0	0
$946$	−122.084	−3.96929
$947$	−7.60501	−0.247130	−0.123565	−	0.992337i	$-0.539433\pi$
$947$	−7.60501	−0.247130	−0.123565	+	0.992337i	$0.539433\pi$
$948$	0	0
$949$	0	0
$950$	−4.75557	−0.154291
$951$	0	0
$952$	27.5625	0.893305
$953$	33.3560	1.08051	0.540253	−	0.841503i	$-0.318328\pi$
$953$	33.3560	1.08051	0.540253	+	0.841503i	$0.318328\pi$
$954$	0	0
$955$	−15.9748	−0.516933
$956$	55.2543	1.78705
$957$	0	0
$958$	13.1383	0.424478
$959$	−18.1653	−0.586589
$960$	0	0
$961$	−3.11108	−0.100357
$962$	0	0
$963$	0	0
$964$	67.5910	2.17696
$965$	−3.70318	−0.119210
$966$	0	0
$967$	−40.8988	−1.31522	−0.657608	−	0.753360i	$-0.728432\pi$
$967$	−40.8988	−1.31522	−0.657608	+	0.753360i	$0.728432\pi$
$968$	−45.4291	−1.46015
$969$	0	0
$970$	−9.41282	−0.302227
$971$	4.23506	0.135910	0.0679548	−	0.997688i	$-0.478353\pi$
$971$	4.23506	0.135910	0.0679548	+	0.997688i	$0.478353\pi$
$972$	0	0
$973$	42.3611	1.35803
$974$	10.7239	0.343617
$975$	0	0
$976$	−7.27607	−0.232901
$977$	38.7882	1.24094	0.620472	−	0.784229i	$-0.286941\pi$
$977$	38.7882	1.24094	0.620472	+	0.784229i	$0.286941\pi$
$978$	0	0
$979$	−93.8805	−3.00043
$980$	22.4099	0.715858
$981$	0	0
$982$	0.169442	0.00540710
$983$	−21.4479	−0.684080	−0.342040	−	0.939685i	$-0.611118\pi$
$983$	−21.4479	−0.684080	−0.342040	+	0.939685i	$0.611118\pi$
$984$	0	0
$985$	−16.3970	−0.522452
$986$	16.4385	0.523508
$987$	0	0
$988$	0	0
$989$	−59.2039	−1.88257
$990$	0	0
$991$	−11.3002	−0.358963	−0.179481	−	0.983761i	$-0.557442\pi$
$991$	−11.3002	−0.358963	−0.179481	+	0.983761i	$0.557442\pi$
$992$	−37.2355	−1.18223
$993$	0	0
$994$	−48.7610	−1.54660
$995$	5.29529	0.167872
$996$	0	0
$997$	−54.2246	−1.71731	−0.858656	−	0.512553i	$-0.828700\pi$
$997$	−54.2246	−1.71731	−0.858656	+	0.512553i	$0.828700\pi$
$998$	−84.2962	−2.66835
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7605.2.a.bu.1.1		3
3.2	odd	2		2535.2.a.y.1.3		3
13.3	even	3		585.2.j.g.451.3		6
13.9	even	3		585.2.j.g.406.3		6
13.12	even	2		7605.2.a.bt.1.3		3
39.29	odd	6		195.2.i.e.61.1	yes	6
39.35	odd	6		195.2.i.e.16.1	✓	6
39.38	odd	2		2535.2.a.z.1.1		3
195.29	odd	6		975.2.i.m.451.3		6
195.68	even	12		975.2.bb.j.724.6		12
195.74	odd	6		975.2.i.m.601.3		6
195.107	even	12		975.2.bb.j.724.1		12
195.113	even	12		975.2.bb.j.874.1		12
195.152	even	12		975.2.bb.j.874.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.e.16.1	✓	6	39.35	odd	6
195.2.i.e.61.1	yes	6	39.29	odd	6
585.2.j.g.406.3		6	13.9	even	3
585.2.j.g.451.3		6	13.3	even	3
975.2.i.m.451.3		6	195.29	odd	6
975.2.i.m.601.3		6	195.74	odd	6
975.2.bb.j.724.1		12	195.107	even	12
975.2.bb.j.724.6		12	195.68	even	12
975.2.bb.j.874.1		12	195.113	even	12
975.2.bb.j.874.6		12	195.152	even	12
2535.2.a.y.1.3		3	3.2	odd	2
2535.2.a.z.1.1		3	39.38	odd	2
7605.2.a.bt.1.3		3	13.12	even	2
7605.2.a.bu.1.1		3	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)

\(f(q)\)	\(=\)	\(q-2.21432 q^{2} +2.90321 q^{4} +1.00000 q^{5} -3.83654 q^{7} -2.00000 q^{8} +O(q^{10})\)	\(q-2.21432 q^{2} +2.90321 q^{4} +1.00000 q^{5} -3.83654 q^{7} -2.00000 q^{8} -2.21432 q^{10} -5.80642 q^{11} +8.49532 q^{14} -1.37778 q^{16} +3.59210 q^{17} +2.14764 q^{19} +2.90321 q^{20} +12.8573 q^{22} +6.23506 q^{23} +1.00000 q^{25} -11.1383 q^{28} -2.06668 q^{29} -5.28100 q^{31} +7.05086 q^{32} -7.95407 q^{34} -3.83654 q^{35} -4.75557 q^{37} -4.75557 q^{38} -2.00000 q^{40} +11.1175 q^{41} -9.49532 q^{43} -16.8573 q^{44} -13.8064 q^{46} -2.21432 q^{47} +7.71900 q^{49} -2.21432 q^{50} +0.815792 q^{53} -5.80642 q^{55} +7.67307 q^{56} +4.57628 q^{58} +9.97481 q^{59} +5.28100 q^{61} +11.6938 q^{62} -12.8573 q^{64} -3.55554 q^{67} +10.4286 q^{68} +8.49532 q^{70} -5.73975 q^{71} -2.78568 q^{73} +10.5303 q^{74} +6.23506 q^{76} +22.2766 q^{77} +12.3319 q^{79} -1.37778 q^{80} -24.6178 q^{82} -0.622216 q^{83} +3.59210 q^{85} +21.0257 q^{86} +11.6128 q^{88} +16.1684 q^{89} +18.1017 q^{92} +4.90321 q^{94} +2.14764 q^{95} +4.25088 q^{97} -17.0923 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8}+O(q^{10}) \) 3 * q + 2 * q^4 + 3 * q^5 - 5 * q^7 - 6 * q^8	\( 3 q + 2 q^{4} + 3 q^{5} - 5 q^{7} - 6 q^{8} - 4 q^{11} + 12 q^{14} - 4 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{22} - 8 q^{23} + 3 q^{25} - 6 q^{29} - 9 q^{31} + 8 q^{32} - 4 q^{34} - 5 q^{35} - 14 q^{37} - 14 q^{38} - 6 q^{40} + 20 q^{41} - 15 q^{43} - 24 q^{44} - 28 q^{46} + 30 q^{49} + 16 q^{53} - 4 q^{55} + 10 q^{56} - 6 q^{58} - 10 q^{59} + 9 q^{61} + 2 q^{62} - 12 q^{64} - 11 q^{67} + 18 q^{68} + 12 q^{70} - 4 q^{71} - 15 q^{73} - 8 q^{74} - 8 q^{76} + 17 q^{79} - 4 q^{80} - 14 q^{82} - 2 q^{83} + 4 q^{85} + 10 q^{86} + 8 q^{88} + 22 q^{89} + 28 q^{92} + 8 q^{94} - q^{97} + 2 q^{98}+O(q^{100}) \) 3 * q + 2 * q^4 + 3 * q^5 - 5 * q^7 - 6 * q^8 - 4 * q^11 + 12 * q^14 - 4 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^22 - 8 * q^23 + 3 * q^25 - 6 * q^29 - 9 * q^31 + 8 * q^32 - 4 * q^34 - 5 * q^35 - 14 * q^37 - 14 * q^38 - 6 * q^40 + 20 * q^41 - 15 * q^43 - 24 * q^44 - 28 * q^46 + 30 * q^49 + 16 * q^53 - 4 * q^55 + 10 * q^56 - 6 * q^58 - 10 * q^59 + 9 * q^61 + 2 * q^62 - 12 * q^64 - 11 * q^67 + 18 * q^68 + 12 * q^70 - 4 * q^71 - 15 * q^73 - 8 * q^74 - 8 * q^76 + 17 * q^79 - 4 * q^80 - 14 * q^82 - 2 * q^83 + 4 * q^85 + 10 * q^86 + 8 * q^88 + 22 * q^89 + 28 * q^92 + 8 * q^94 - q^97 + 2 * q^98

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