LMFDB - Embedded newform 7605.2.a.bs.1.3

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:	$3$
Coefficient field:	3.3.564.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 3 $ x^3 - x^2 - 5*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.08613$ 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)

$f(q)$	$=$	$q+2.08613 q^{2} +2.35194 q^{4} +1.00000 q^{5} +1.35194 q^{7} +0.734191 q^{8} +O(q^{10})$	$q+2.08613 q^{2} +2.35194 q^{4} +1.00000 q^{5} +1.35194 q^{7} +0.734191 q^{8} +2.08613 q^{10} -3.73419 q^{11} +2.82032 q^{14} -3.17226 q^{16} +2.70388 q^{17} -0.438069 q^{19} +2.35194 q^{20} -7.79001 q^{22} +5.08613 q^{23} +1.00000 q^{25} +3.17968 q^{28} +1.35194 q^{29} +6.43807 q^{31} -8.08613 q^{32} +5.64064 q^{34} +1.35194 q^{35} +7.35194 q^{37} -0.913870 q^{38} +0.734191 q^{40} +6.87614 q^{41} -0.209991 q^{43} -8.78259 q^{44} +10.6103 q^{46} +1.35194 q^{47} -5.17226 q^{49} +2.08613 q^{50} +1.46838 q^{53} -3.73419 q^{55} +0.992582 q^{56} +2.82032 q^{58} +2.26581 q^{59} +3.52420 q^{61} +13.4307 q^{62} -10.5242 q^{64} +11.5242 q^{67} +6.35936 q^{68} +2.82032 q^{70} +0.438069 q^{71} -3.69646 q^{73} +15.3371 q^{74} -1.03031 q^{76} -5.04840 q^{77} +15.0484 q^{79} -3.17226 q^{80} +14.3445 q^{82} -0.475800 q^{83} +2.70388 q^{85} -0.438069 q^{86} -2.74161 q^{88} +11.0484 q^{89} +11.9623 q^{92} +2.82032 q^{94} -0.438069 q^{95} -3.29612 q^{97} -10.7900 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} + 5 q^{4} + 3 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) $ 3 * q - q^2 + 5 * q^4 + 3 * q^5 + 2 * q^7 - 3 * q^8	$ 3 q - q^{2} + 5 q^{4} + 3 q^{5} + 2 q^{7} - 3 q^{8} - q^{10} - 6 q^{11} - 4 q^{14} + 5 q^{16} + 4 q^{17} + 8 q^{19} + 5 q^{20} - 12 q^{22} + 8 q^{23} + 3 q^{25} + 22 q^{28} + 2 q^{29} + 10 q^{31} - 17 q^{32} - 8 q^{34} + 2 q^{35} + 20 q^{37} - 10 q^{38} - 3 q^{40} + 2 q^{41} - 12 q^{43} + 12 q^{44} + 8 q^{46} + 2 q^{47} - q^{49} - q^{50} - 6 q^{53} - 6 q^{55} - 24 q^{56} - 4 q^{58} + 12 q^{59} - 6 q^{61} + 4 q^{62} - 15 q^{64} + 18 q^{67} + 44 q^{68} - 4 q^{70} - 8 q^{71} + 20 q^{73} - 10 q^{74} - 2 q^{76} + 18 q^{77} + 12 q^{79} + 5 q^{80} + 14 q^{82} - 18 q^{83} + 4 q^{85} + 8 q^{86} - 30 q^{88} + 10 q^{92} - 4 q^{94} + 8 q^{95} - 14 q^{97} - 21 q^{98}+O(q^{100}) $ 3 * q - q^2 + 5 * q^4 + 3 * q^5 + 2 * q^7 - 3 * q^8 - q^10 - 6 * q^11 - 4 * q^14 + 5 * q^16 + 4 * q^17 + 8 * q^19 + 5 * q^20 - 12 * q^22 + 8 * q^23 + 3 * q^25 + 22 * q^28 + 2 * q^29 + 10 * q^31 - 17 * q^32 - 8 * q^34 + 2 * q^35 + 20 * q^37 - 10 * q^38 - 3 * q^40 + 2 * q^41 - 12 * q^43 + 12 * q^44 + 8 * q^46 + 2 * q^47 - q^49 - q^50 - 6 * q^53 - 6 * q^55 - 24 * q^56 - 4 * q^58 + 12 * q^59 - 6 * q^61 + 4 * q^62 - 15 * q^64 + 18 * q^67 + 44 * q^68 - 4 * q^70 - 8 * q^71 + 20 * q^73 - 10 * q^74 - 2 * q^76 + 18 * q^77 + 12 * q^79 + 5 * q^80 + 14 * q^82 - 18 * q^83 + 4 * q^85 + 8 * q^86 - 30 * q^88 + 10 * q^92 - 4 * q^94 + 8 * q^95 - 14 * q^97 - 21 * 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 $

$2$	2.08613	1.47512	0.737558	−	0.675283i	$-0.235979\pi$
$2$	2.08613	1.47512	0.737558	+	0.675283i	$0.235979\pi$
$3$	0	0
$3$	0	0
$4$	2.35194	1.17597
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	1.35194	0.510985	0.255492	−	0.966811i	$-0.417762\pi$
$7$	1.35194	0.510985	0.255492	+	0.966811i	$0.417762\pi$
$8$	0.734191	0.259576
$9$	0	0
$10$	2.08613	0.659692
$11$	−3.73419	−1.12590	−0.562950	−	0.826491i	$-0.690334\pi$
$11$	−3.73419	−1.12590	−0.562950	+	0.826491i	$0.690334\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	2.82032	0.753763
$15$	0	0
$16$	−3.17226	−0.793065
$17$	2.70388	0.655787	0.327893	−	0.944715i	$-0.393661\pi$
$17$	2.70388	0.655787	0.327893	+	0.944715i	$0.393661\pi$
$18$	0	0
$19$	−0.438069	−0.100500	−0.0502500	−	0.998737i	$-0.516002\pi$
$19$	−0.438069	−0.100500	−0.0502500	+	0.998737i	$0.516002\pi$
$20$	2.35194	0.525910
$21$	0	0
$22$	−7.79001	−1.66084
$23$	5.08613	1.06053	0.530266	−	0.847832i	$-0.322092\pi$
$23$	5.08613	1.06053	0.530266	+	0.847832i	$0.322092\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	3.17968	0.600903
$29$	1.35194	0.251049	0.125524	−	0.992091i	$-0.459939\pi$
$29$	1.35194	0.251049	0.125524	+	0.992091i	$0.459939\pi$
$30$	0	0
$31$	6.43807	1.15631	0.578156	−	0.815926i	$-0.303773\pi$
$31$	6.43807	1.15631	0.578156	+	0.815926i	$0.303773\pi$
$32$	−8.08613	−1.42944
$33$	0	0
$34$	5.64064	0.967362
$35$	1.35194	0.228519
$36$	0	0
$37$	7.35194	1.20865	0.604326	−	0.796737i	$-0.293443\pi$
$37$	7.35194	1.20865	0.604326	+	0.796737i	$0.293443\pi$
$38$	−0.913870	−0.148249
$39$	0	0
$40$	0.734191	0.116086
$41$	6.87614	1.07387	0.536936	−	0.843623i	$-0.319582\pi$
$41$	6.87614	1.07387	0.536936	+	0.843623i	$0.319582\pi$
$42$	0	0
$43$	−0.209991	−0.0320234	−0.0160117	−	0.999872i	$-0.505097\pi$
$43$	−0.209991	−0.0320234	−0.0160117	+	0.999872i	$0.505097\pi$
$44$	−8.78259	−1.32403
$45$	0	0
$46$	10.6103	1.56441
$47$	1.35194	0.197201	0.0986003	−	0.995127i	$-0.468563\pi$
$47$	1.35194	0.197201	0.0986003	+	0.995127i	$0.468563\pi$
$48$	0	0
$49$	−5.17226	−0.738894
$50$	2.08613	0.295023
$51$	0	0
$52$	0	0
$53$	1.46838	0.201698	0.100849	−	0.994902i	$-0.467844\pi$
$53$	1.46838	0.201698	0.100849	+	0.994902i	$0.467844\pi$
$54$	0	0
$55$	−3.73419	−0.503518
$56$	0.992582	0.132639
$57$	0	0
$58$	2.82032	0.370326
$59$	2.26581	0.294983	0.147492	−	0.989063i	$-0.452880\pi$
$59$	2.26581	0.294983	0.147492	+	0.989063i	$0.452880\pi$
$60$	0	0
$61$	3.52420	0.451228	0.225614	−	0.974217i	$-0.427561\pi$
$61$	3.52420	0.451228	0.225614	+	0.974217i	$0.427561\pi$
$62$	13.4307	1.70569
$63$	0	0
$64$	−10.5242	−1.31552
$65$	0	0
$66$	0	0
$67$	11.5242	1.40791	0.703953	−	0.710247i	$-0.251417\pi$
$67$	11.5242	1.40791	0.703953	+	0.710247i	$0.251417\pi$
$68$	6.35936	0.771185
$69$	0	0
$70$	2.82032	0.337093
$71$	0.438069	0.0519893	0.0259946	−	0.999662i	$-0.491725\pi$
$71$	0.438069	0.0519893	0.0259946	+	0.999662i	$0.491725\pi$
$72$	0	0
$73$	−3.69646	−0.432638	−0.216319	−	0.976323i	$-0.569405\pi$
$73$	−3.69646	−0.432638	−0.216319	+	0.976323i	$0.569405\pi$
$74$	15.3371	1.78290
$75$	0	0
$76$	−1.03031	−0.118185
$77$	−5.04840	−0.575318
$78$	0	0
$79$	15.0484	1.69308	0.846539	−	0.532327i	$-0.178682\pi$
$79$	15.0484	1.69308	0.846539	+	0.532327i	$0.178682\pi$
$80$	−3.17226	−0.354669
$81$	0	0
$82$	14.3445	1.58409
$83$	−0.475800	−0.0522259	−0.0261129	−	0.999659i	$-0.508313\pi$
$83$	−0.475800	−0.0522259	−0.0261129	+	0.999659i	$0.508313\pi$
$84$	0	0
$85$	2.70388	0.293277
$86$	−0.438069	−0.0472382
$87$	0	0
$88$	−2.74161	−0.292257
$89$	11.0484	1.17113	0.585564	−	0.810626i	$-0.300873\pi$
$89$	11.0484	1.17113	0.585564	+	0.810626i	$0.300873\pi$
$90$	0	0
$91$	0	0
$92$	11.9623	1.24715
$93$	0	0
$94$	2.82032	0.290894
$95$	−0.438069	−0.0449450
$96$	0	0
$97$	−3.29612	−0.334670	−0.167335	−	0.985900i	$-0.553516\pi$
$97$	−3.29612	−0.334670	−0.167335	+	0.985900i	$0.553516\pi$
$98$	−10.7900	−1.08996
$99$	0	0
$100$	2.35194	0.235194
$101$	−16.1723	−1.60920	−0.804600	−	0.593817i	$-0.797620\pi$
$101$	−16.1723	−1.60920	−0.804600	+	0.593817i	$0.797620\pi$
$102$	0	0
$103$	10.5545	1.03997	0.519983	−	0.854176i	$-0.325938\pi$
$103$	10.5545	1.03997	0.519983	+	0.854176i	$0.325938\pi$
$104$	0	0
$105$	0	0
$106$	3.06324	0.297528
$107$	−13.4307	−1.29839	−0.649195	−	0.760622i	$-0.724894\pi$
$107$	−13.4307	−1.29839	−0.649195	+	0.760622i	$0.724894\pi$
$108$	0	0
$109$	11.6406	1.11497	0.557486	−	0.830187i	$-0.311766\pi$
$109$	11.6406	1.11497	0.557486	+	0.830187i	$0.311766\pi$
$110$	−7.79001	−0.742748
$111$	0	0
$112$	−4.28870	−0.405244
$113$	13.7523	1.29371	0.646853	−	0.762615i	$-0.276085\pi$
$113$	13.7523	1.29371	0.646853	+	0.762615i	$0.276085\pi$
$114$	0	0
$115$	5.08613	0.474284
$116$	3.17968	0.295226
$117$	0	0
$118$	4.72677	0.435135
$119$	3.65548	0.335097
$120$	0	0
$121$	2.94418	0.267653
$122$	7.35194	0.665613
$123$	0	0
$124$	15.1419	1.35979
$125$	1.00000	0.0894427
$126$	0	0
$127$	−3.96227	−0.351595	−0.175797	−	0.984426i	$-0.556250\pi$
$127$	−3.96227	−0.351595	−0.175797	+	0.984426i	$0.556250\pi$
$128$	−5.78259	−0.511114
$129$	0	0
$130$	0	0
$131$	11.0484	0.965303	0.482652	−	0.875812i	$-0.339674\pi$
$131$	11.0484	0.965303	0.482652	+	0.875812i	$0.339674\pi$
$132$	0	0
$133$	−0.592243	−0.0513540
$134$	24.0410	2.07682
$135$	0	0
$136$	1.98516	0.170226
$137$	−12.5168	−1.06938	−0.534690	−	0.845048i	$-0.679572\pi$
$137$	−12.5168	−1.06938	−0.534690	+	0.845048i	$0.679572\pi$
$138$	0	0
$139$	1.64064	0.139157	0.0695787	−	0.997576i	$-0.477834\pi$
$139$	1.64064	0.139157	0.0695787	+	0.997576i	$0.477834\pi$
$140$	3.17968	0.268732
$141$	0	0
$142$	0.913870	0.0766903
$143$	0	0
$144$	0	0
$145$	1.35194	0.112272
$146$	−7.71130	−0.638191
$147$	0	0
$148$	17.2913	1.42134
$149$	3.29612	0.270029	0.135014	−	0.990844i	$-0.456892\pi$
$149$	3.29612	0.270029	0.135014	+	0.990844i	$0.456892\pi$
$150$	0	0
$151$	−9.65873	−0.786016	−0.393008	−	0.919535i	$-0.628566\pi$
$151$	−9.65873	−0.786016	−0.393008	+	0.919535i	$0.628566\pi$
$152$	−0.321627	−0.0260874
$153$	0	0
$154$	−10.5316	−0.848662
$155$	6.43807	0.517118
$156$	0	0
$157$	11.5800	0.924186	0.462093	−	0.886831i	$-0.347099\pi$
$157$	11.5800	0.924186	0.462093	+	0.886831i	$0.347099\pi$
$158$	31.3929	2.49749
$159$	0	0
$160$	−8.08613	−0.639265
$161$	6.87614	0.541916
$162$	0	0
$163$	18.9926	1.48761	0.743807	−	0.668395i	$-0.233018\pi$
$163$	18.9926	1.48761	0.743807	+	0.668395i	$0.233018\pi$
$164$	16.1723	1.26284
$165$	0	0
$166$	−0.992582	−0.0770393
$167$	−16.9320	−1.31023	−0.655117	−	0.755527i	$-0.727381\pi$
$167$	−16.9320	−1.31023	−0.655117	+	0.755527i	$0.727381\pi$
$168$	0	0
$169$	0	0
$170$	5.64064	0.432618
$171$	0	0
$172$	−0.493887	−0.0376585
$173$	10.7645	0.818410	0.409205	−	0.912442i	$-0.365806\pi$
$173$	10.7645	0.818410	0.409205	+	0.912442i	$0.365806\pi$
$174$	0	0
$175$	1.35194	0.102197
$176$	11.8458	0.892913
$177$	0	0
$178$	23.0484	1.72755
$179$	−18.5168	−1.38401	−0.692005	−	0.721893i	$-0.743272\pi$
$179$	−18.5168	−1.38401	−0.692005	+	0.721893i	$0.743272\pi$
$180$	0	0
$181$	−12.2887	−0.913412	−0.456706	−	0.889618i	$-0.650971\pi$
$181$	−12.2887	−0.913412	−0.456706	+	0.889618i	$0.650971\pi$
$182$	0	0
$183$	0	0
$184$	3.73419	0.275288
$185$	7.35194	0.540525
$186$	0	0
$187$	−10.0968	−0.738351
$188$	3.17968	0.231902
$189$	0	0
$190$	−0.913870	−0.0662991
$191$	−5.40776	−0.391292	−0.195646	−	0.980675i	$-0.562680\pi$
$191$	−5.40776	−0.391292	−0.195646	+	0.980675i	$0.562680\pi$
$192$	0	0
$193$	−19.1090	−1.37550	−0.687749	−	0.725949i	$-0.741401\pi$
$193$	−19.1090	−1.37550	−0.687749	+	0.725949i	$0.741401\pi$
$194$	−6.87614	−0.493678
$195$	0	0
$196$	−12.1648	−0.868917
$197$	−12.2839	−0.875191	−0.437596	−	0.899172i	$-0.644170\pi$
$197$	−12.2839	−0.875191	−0.437596	+	0.899172i	$0.644170\pi$
$198$	0	0
$199$	0.764504	0.0541942	0.0270971	−	0.999633i	$-0.491374\pi$
$199$	0.764504	0.0541942	0.0270971	+	0.999633i	$0.491374\pi$
$200$	0.734191	0.0519151
$201$	0	0
$202$	−33.7374	−2.37376
$203$	1.82774	0.128282
$204$	0	0
$205$	6.87614	0.480250
$206$	22.0181	1.53407
$207$	0	0
$208$	0	0
$209$	1.63583	0.113153
$210$	0	0
$211$	−7.92454	−0.545548	−0.272774	−	0.962078i	$-0.587941\pi$
$211$	−7.92454	−0.545548	−0.272774	+	0.962078i	$0.587941\pi$
$212$	3.45355	0.237190
$213$	0	0
$214$	−28.0181	−1.91528
$215$	−0.209991	−0.0143213
$216$	0	0
$217$	8.70388	0.590858
$218$	24.2839	1.64471
$219$	0	0
$220$	−8.78259	−0.592122
$221$	0	0
$222$	0	0
$223$	4.28870	0.287193	0.143596	−	0.989636i	$-0.454133\pi$
$223$	4.28870	0.287193	0.143596	+	0.989636i	$0.454133\pi$
$224$	−10.9320	−0.730422
$225$	0	0
$226$	28.6890	1.90837
$227$	−25.5094	−1.69312	−0.846558	−	0.532297i	$-0.821329\pi$
$227$	−25.5094	−1.69312	−0.846558	+	0.532297i	$0.821329\pi$
$228$	0	0
$229$	25.1090	1.65925	0.829626	−	0.558320i	$-0.188554\pi$
$229$	25.1090	1.65925	0.829626	+	0.558320i	$0.188554\pi$
$230$	10.6103	0.699624
$231$	0	0
$232$	0.992582	0.0651662
$233$	−15.2961	−1.00208	−0.501041	−	0.865423i	$-0.667049\pi$
$233$	−15.2961	−1.00208	−0.501041	+	0.865423i	$0.667049\pi$
$234$	0	0
$235$	1.35194	0.0881908
$236$	5.32905	0.346891
$237$	0	0
$238$	7.62581	0.494308
$239$	−13.6736	−0.884469	−0.442235	−	0.896899i	$-0.645814\pi$
$239$	−13.6736	−0.884469	−0.442235	+	0.896899i	$0.645814\pi$
$240$	0	0
$241$	12.5168	0.806277	0.403138	−	0.915139i	$-0.367919\pi$
$241$	12.5168	0.806277	0.403138	+	0.915139i	$0.367919\pi$
$242$	6.14195	0.394819
$243$	0	0
$244$	8.28870	0.530630
$245$	−5.17226	−0.330444
$246$	0	0
$247$	0	0
$248$	4.72677	0.300150
$249$	0	0
$250$	2.08613	0.131938
$251$	14.6284	0.923337	0.461669	−	0.887052i	$-0.347251\pi$
$251$	14.6284	0.923337	0.461669	+	0.887052i	$0.347251\pi$
$252$	0	0
$253$	−18.9926	−1.19405
$254$	−8.26581	−0.518643
$255$	0	0
$256$	8.98516	0.561573
$257$	−28.0968	−1.75263	−0.876315	−	0.481738i	$-0.840006\pi$
$257$	−28.0968	−1.75263	−0.876315	+	0.481738i	$0.840006\pi$
$258$	0	0
$259$	9.93937	0.617603
$260$	0	0
$261$	0	0
$262$	23.0484	1.42393
$263$	−15.7752	−0.972739	−0.486369	−	0.873753i	$-0.661679\pi$
$263$	−15.7752	−0.972739	−0.486369	+	0.873753i	$0.661679\pi$
$264$	0	0
$265$	1.46838	0.0902020
$266$	−1.23550	−0.0757531
$267$	0	0
$268$	27.1042	1.65565
$269$	4.17226	0.254387	0.127194	−	0.991878i	$-0.459403\pi$
$269$	4.17226	0.254387	0.127194	+	0.991878i	$0.459403\pi$
$270$	0	0
$271$	6.07871	0.369255	0.184628	−	0.982809i	$-0.440892\pi$
$271$	6.07871	0.369255	0.184628	+	0.982809i	$0.440892\pi$
$272$	−8.57741	−0.520082
$273$	0	0
$274$	−26.1116	−1.57746
$275$	−3.73419	−0.225180
$276$	0	0
$277$	−26.1574	−1.57165	−0.785824	−	0.618451i	$-0.787761\pi$
$277$	−26.1574	−1.57165	−0.785824	+	0.618451i	$0.787761\pi$
$278$	3.42259	0.205274
$279$	0	0
$280$	0.992582	0.0593181
$281$	−6.64325	−0.396303	−0.198152	−	0.980171i	$-0.563494\pi$
$281$	−6.64325	−0.396303	−0.198152	+	0.980171i	$0.563494\pi$
$282$	0	0
$283$	17.5423	1.04278	0.521390	−	0.853318i	$-0.325414\pi$
$283$	17.5423	1.04278	0.521390	+	0.853318i	$0.325414\pi$
$284$	1.03031	0.0611378
$285$	0	0
$286$	0	0
$287$	9.29612	0.548733
$288$	0	0
$289$	−9.68904	−0.569944
$290$	2.82032	0.165615
$291$	0	0
$292$	−8.69385	−0.508769
$293$	13.9442	0.814628	0.407314	−	0.913288i	$-0.366465\pi$
$293$	13.9442	0.814628	0.407314	+	0.913288i	$0.366465\pi$
$294$	0	0
$295$	2.26581	0.131921
$296$	5.39773	0.313737
$297$	0	0
$298$	6.87614	0.398324
$299$	0	0
$300$	0	0
$301$	−0.283896	−0.0163635
$302$	−20.1494	−1.15947
$303$	0	0
$304$	1.38967	0.0797031
$305$	3.52420	0.201795
$306$	0	0
$307$	28.2132	1.61021	0.805107	−	0.593129i	$-0.202108\pi$
$307$	28.2132	1.61021	0.805107	+	0.593129i	$0.202108\pi$
$308$	−11.8735	−0.676557
$309$	0	0
$310$	13.4307	0.762810
$311$	−7.23550	−0.410287	−0.205144	−	0.978732i	$-0.565766\pi$
$311$	−7.23550	−0.410287	−0.205144	+	0.978732i	$0.565766\pi$
$312$	0	0
$313$	−21.7523	−1.22951	−0.614756	−	0.788718i	$-0.710745\pi$
$313$	−21.7523	−1.22951	−0.614756	+	0.788718i	$0.710745\pi$
$314$	24.1574	1.36328
$315$	0	0
$316$	35.3929	1.99101
$317$	−14.7449	−0.828154	−0.414077	−	0.910242i	$-0.635896\pi$
$317$	−14.7449	−0.828154	−0.414077	+	0.910242i	$0.635896\pi$
$318$	0	0
$319$	−5.04840	−0.282656
$320$	−10.5242	−0.588321
$321$	0	0
$322$	14.3445	0.799389
$323$	−1.18449	−0.0659066
$324$	0	0
$325$	0	0
$326$	39.6210	2.19440
$327$	0	0
$328$	5.04840	0.278751
$329$	1.82774	0.100767
$330$	0	0
$331$	34.0181	1.86980	0.934902	−	0.354907i	$-0.115488\pi$
$331$	34.0181	1.86980	0.934902	+	0.354907i	$0.115488\pi$
$332$	−1.11905	−0.0614160
$333$	0	0
$334$	−35.3223	−1.93275
$335$	11.5242	0.629634
$336$	0	0
$337$	15.3929	0.838506	0.419253	−	0.907869i	$-0.362292\pi$
$337$	15.3929	0.838506	0.419253	+	0.907869i	$0.362292\pi$
$338$	0	0
$339$	0	0
$340$	6.35936	0.344885
$341$	−24.0410	−1.30189
$342$	0	0
$343$	−16.4562	−0.888549
$344$	−0.154174	−0.00831249
$345$	0	0
$346$	22.4562	1.20725
$347$	2.89903	0.155628	0.0778141	−	0.996968i	$-0.475206\pi$
$347$	2.89903	0.155628	0.0778141	+	0.996968i	$0.475206\pi$
$348$	0	0
$349$	−18.2839	−0.978714	−0.489357	−	0.872083i	$-0.662769\pi$
$349$	−18.2839	−0.978714	−0.489357	+	0.872083i	$0.662769\pi$
$350$	2.82032	0.150753
$351$	0	0
$352$	30.1952	1.60941
$353$	−21.1042	−1.12326	−0.561632	−	0.827387i	$-0.689826\pi$
$353$	−21.1042	−1.12326	−0.561632	+	0.827387i	$0.689826\pi$
$354$	0	0
$355$	0.438069	0.0232503
$356$	25.9852	1.37721
$357$	0	0
$358$	−38.6284	−2.04158
$359$	34.5349	1.82268	0.911340	−	0.411654i	$-0.135049\pi$
$359$	34.5349	1.82268	0.911340	+	0.411654i	$0.135049\pi$
$360$	0	0
$361$	−18.8081	−0.989900
$362$	−25.6358	−1.34739
$363$	0	0
$364$	0	0
$365$	−3.69646	−0.193482
$366$	0	0
$367$	1.60291	0.0836713	0.0418356	−	0.999125i	$-0.486679\pi$
$367$	1.60291	0.0836713	0.0418356	+	0.999125i	$0.486679\pi$
$368$	−16.1345	−0.841070
$369$	0	0
$370$	15.3371	0.797338
$371$	1.98516	0.103065
$372$	0	0
$373$	19.5800	1.01381	0.506907	−	0.862000i	$-0.330789\pi$
$373$	19.5800	1.01381	0.506907	+	0.862000i	$0.330789\pi$
$374$	−21.0632	−1.08915
$375$	0	0
$376$	0.992582	0.0511885
$377$	0	0
$378$	0	0
$379$	−6.36261	−0.326825	−0.163413	−	0.986558i	$-0.552250\pi$
$379$	−6.36261	−0.326825	−0.163413	+	0.986558i	$0.552250\pi$
$380$	−1.03031	−0.0528539
$381$	0	0
$382$	−11.2813	−0.577201
$383$	15.9804	0.816558	0.408279	−	0.912857i	$-0.366129\pi$
$383$	15.9804	0.816558	0.408279	+	0.912857i	$0.366129\pi$
$384$	0	0
$385$	−5.04840	−0.257290
$386$	−39.8639	−2.02902
$387$	0	0
$388$	−7.75228	−0.393562
$389$	21.5046	1.09032	0.545162	−	0.838331i	$-0.316468\pi$
$389$	21.5046	1.09032	0.545162	+	0.838331i	$0.316468\pi$
$390$	0	0
$391$	13.7523	0.695483
$392$	−3.79743	−0.191799
$393$	0	0
$394$	−25.6258	−1.29101
$395$	15.0484	0.757167
$396$	0	0
$397$	−15.4636	−0.776095	−0.388047	−	0.921639i	$-0.626850\pi$
$397$	−15.4636	−0.776095	−0.388047	+	0.921639i	$0.626850\pi$
$398$	1.59485	0.0799428
$399$	0	0
$400$	−3.17226	−0.158613
$401$	−25.7523	−1.28601	−0.643004	−	0.765863i	$-0.722312\pi$
$401$	−25.7523	−1.28601	−0.643004	+	0.765863i	$0.722312\pi$
$402$	0	0
$403$	0	0
$404$	−38.0362	−1.89237
$405$	0	0
$406$	3.81290	0.189231
$407$	−27.4535	−1.36082
$408$	0	0
$409$	−10.5316	−0.520755	−0.260377	−	0.965507i	$-0.583847\pi$
$409$	−10.5316	−0.520755	−0.260377	+	0.965507i	$0.583847\pi$
$410$	14.3445	0.708425
$411$	0	0
$412$	24.8236	1.22297
$413$	3.06324	0.150732
$414$	0	0
$415$	−0.475800	−0.0233561
$416$	0	0
$417$	0	0
$418$	3.41256	0.166914
$419$	−7.46838	−0.364854	−0.182427	−	0.983219i	$-0.558395\pi$
$419$	−7.46838	−0.364854	−0.182427	+	0.983219i	$0.558395\pi$
$420$	0	0
$421$	35.4897	1.72966	0.864832	−	0.502062i	$-0.167425\pi$
$421$	35.4897	1.72966	0.864832	+	0.502062i	$0.167425\pi$
$422$	−16.5316	−0.804747
$423$	0	0
$424$	1.07807	0.0523558
$425$	2.70388	0.131157
$426$	0	0
$427$	4.76450	0.230570
$428$	−31.5881	−1.52687
$429$	0	0
$430$	−0.438069	−0.0211256
$431$	0.154174	0.00742629	0.00371315	−	0.999993i	$-0.498818\pi$
$431$	0.154174	0.00742629	0.00371315	+	0.999993i	$0.498818\pi$
$432$	0	0
$433$	5.65548	0.271785	0.135892	−	0.990724i	$-0.456610\pi$
$433$	5.65548	0.271785	0.135892	+	0.990724i	$0.456610\pi$
$434$	18.1574	0.871584
$435$	0	0
$436$	27.3781	1.31117
$437$	−2.22808	−0.106583
$438$	0	0
$439$	26.9729	1.28735	0.643674	−	0.765300i	$-0.277409\pi$
$439$	26.9729	1.28735	0.643674	+	0.765300i	$0.277409\pi$
$440$	−2.74161	−0.130701
$441$	0	0
$442$	0	0
$443$	−29.3700	−1.39541	−0.697706	−	0.716384i	$-0.745796\pi$
$443$	−29.3700	−1.39541	−0.697706	+	0.716384i	$0.745796\pi$
$444$	0	0
$445$	11.0484	0.523744
$446$	8.94679	0.423643
$447$	0	0
$448$	−14.2281	−0.672214
$449$	−31.6768	−1.49492	−0.747461	−	0.664306i	$-0.768727\pi$
$449$	−31.6768	−1.49492	−0.747461	+	0.664306i	$0.768727\pi$
$450$	0	0
$451$	−25.6768	−1.20907
$452$	32.3445	1.52136
$453$	0	0
$454$	−53.2159	−2.49754
$455$	0	0
$456$	0	0
$457$	21.1696	0.990274	0.495137	−	0.868815i	$-0.335118\pi$
$457$	21.1696	0.990274	0.495137	+	0.868815i	$0.335118\pi$
$458$	52.3807	2.44759
$459$	0	0
$460$	11.9623	0.557744
$461$	35.2058	1.63970	0.819849	−	0.572579i	$-0.194057\pi$
$461$	35.2058	1.63970	0.819849	+	0.572579i	$0.194057\pi$
$462$	0	0
$463$	−1.35194	−0.0628299	−0.0314150	−	0.999506i	$-0.510001\pi$
$463$	−1.35194	−0.0628299	−0.0314150	+	0.999506i	$0.510001\pi$
$464$	−4.28870	−0.199098
$465$	0	0
$466$	−31.9097	−1.47819
$467$	31.6635	1.46521	0.732607	−	0.680652i	$-0.238303\pi$
$467$	31.6635	1.46521	0.732607	+	0.680652i	$0.238303\pi$
$468$	0	0
$469$	15.5800	0.719418
$470$	2.82032	0.130092
$471$	0	0
$472$	1.66354	0.0765705
$473$	0.784148	0.0360552
$474$	0	0
$475$	−0.438069	−0.0201000
$476$	8.59746	0.394064
$477$	0	0
$478$	−28.5248	−1.30470
$479$	−13.3142	−0.608342	−0.304171	−	0.952617i	$-0.598379\pi$
$479$	−13.3142	−0.608342	−0.304171	+	0.952617i	$0.598379\pi$
$480$	0	0
$481$	0	0
$482$	26.1116	1.18935
$483$	0	0
$484$	6.92454	0.314752
$485$	−3.29612	−0.149669
$486$	0	0
$487$	8.89578	0.403106	0.201553	−	0.979478i	$-0.435401\pi$
$487$	8.89578	0.403106	0.201553	+	0.979478i	$0.435401\pi$
$488$	2.58744	0.117128
$489$	0	0
$490$	−10.7900	−0.487443
$491$	9.52901	0.430038	0.215019	−	0.976610i	$-0.431019\pi$
$491$	9.52901	0.430038	0.215019	+	0.976610i	$0.431019\pi$
$492$	0	0
$493$	3.65548	0.164635
$494$	0	0
$495$	0	0
$496$	−20.4232	−0.917030
$497$	0.592243	0.0265657
$498$	0	0
$499$	−25.4716	−1.14027	−0.570133	−	0.821552i	$-0.693109\pi$
$499$	−25.4716	−1.14027	−0.570133	+	0.821552i	$0.693109\pi$
$500$	2.35194	0.105182
$501$	0	0
$502$	30.5168	1.36203
$503$	32.6661	1.45651	0.728256	−	0.685305i	$-0.240331\pi$
$503$	32.6661	1.45651	0.728256	+	0.685305i	$0.240331\pi$
$504$	0	0
$505$	−16.1723	−0.719656
$506$	−39.6210	−1.76137
$507$	0	0
$508$	−9.31902	−0.413464
$509$	−8.41998	−0.373209	−0.186605	−	0.982435i	$-0.559748\pi$
$509$	−8.41998	−0.373209	−0.186605	+	0.982435i	$0.559748\pi$
$510$	0	0
$511$	−4.99739	−0.221071
$512$	30.3094	1.33950
$513$	0	0
$514$	−58.6136	−2.58533
$515$	10.5545	0.465087
$516$	0	0
$517$	−5.04840	−0.222028
$518$	20.7348	0.911036
$519$	0	0
$520$	0	0
$521$	−27.3371	−1.19766	−0.598830	−	0.800876i	$-0.704368\pi$
$521$	−27.3371	−1.19766	−0.598830	+	0.800876i	$0.704368\pi$
$522$	0	0
$523$	−7.77517	−0.339985	−0.169992	−	0.985445i	$-0.554374\pi$
$523$	−7.77517	−0.339985	−0.169992	+	0.985445i	$0.554374\pi$
$524$	25.9852	1.13517
$525$	0	0
$526$	−32.9091	−1.43490
$527$	17.4078	0.758294
$528$	0	0
$529$	2.86872	0.124727
$530$	3.06324	0.133058
$531$	0	0
$532$	−1.39292	−0.0603907
$533$	0	0
$534$	0	0
$535$	−13.4307	−0.580658
$536$	8.46096	0.365458
$537$	0	0
$538$	8.70388	0.375251
$539$	19.3142	0.831922
$540$	0	0
$541$	2.77934	0.119493	0.0597466	−	0.998214i	$-0.480971\pi$
$541$	2.77934	0.119493	0.0597466	+	0.998214i	$0.480971\pi$
$542$	12.6810	0.544695
$543$	0	0
$544$	−21.8639	−0.937408
$545$	11.6406	0.498630
$546$	0	0
$547$	−38.4184	−1.64265	−0.821327	−	0.570458i	$-0.806766\pi$
$547$	−38.4184	−1.64265	−0.821327	+	0.570458i	$0.806766\pi$
$548$	−29.4387	−1.25756
$549$	0	0
$550$	−7.79001	−0.332167
$551$	−0.592243	−0.0252304
$552$	0	0
$553$	20.3445	0.865137
$554$	−54.5678	−2.31836
$555$	0	0
$556$	3.85869	0.163645
$557$	7.11905	0.301644	0.150822	−	0.988561i	$-0.451808\pi$
$557$	7.11905	0.301644	0.150822	+	0.988561i	$0.451808\pi$
$558$	0	0
$559$	0	0
$560$	−4.28870	−0.181231
$561$	0	0
$562$	−13.8587	−0.584594
$563$	−32.8236	−1.38335	−0.691674	−	0.722210i	$-0.743127\pi$
$563$	−32.8236	−1.38335	−0.691674	+	0.722210i	$0.743127\pi$
$564$	0	0
$565$	13.7523	0.578563
$566$	36.5955	1.53822
$567$	0	0
$568$	0.321627	0.0134952
$569$	−15.4126	−0.646128	−0.323064	−	0.946377i	$-0.604713\pi$
$569$	−15.4126	−0.646128	−0.323064	+	0.946377i	$0.604713\pi$
$570$	0	0
$571$	31.5142	1.31883	0.659413	−	0.751780i	$-0.270805\pi$
$571$	31.5142	1.31883	0.659413	+	0.751780i	$0.270805\pi$
$572$	0	0
$573$	0	0
$574$	19.3929	0.809445
$575$	5.08613	0.212106
$576$	0	0
$577$	−44.3855	−1.84779	−0.923896	−	0.382643i	$-0.875014\pi$
$577$	−44.3855	−1.84779	−0.923896	+	0.382643i	$0.875014\pi$
$578$	−20.2126	−0.840733
$579$	0	0
$580$	3.17968	0.132029
$581$	−0.643253	−0.0266866
$582$	0	0
$583$	−5.48322	−0.227092
$584$	−2.71391	−0.112302
$585$	0	0
$586$	29.0894	1.20167
$587$	13.3519	0.551094	0.275547	−	0.961288i	$-0.411141\pi$
$587$	13.3519	0.551094	0.275547	+	0.961288i	$0.411141\pi$
$588$	0	0
$589$	−2.82032	−0.116209
$590$	4.72677	0.194598
$591$	0	0
$592$	−23.3223	−0.958539
$593$	37.3929	1.53554	0.767772	−	0.640724i	$-0.221366\pi$
$593$	37.3929	1.53554	0.767772	+	0.640724i	$0.221366\pi$
$594$	0	0
$595$	3.65548	0.149860
$596$	7.75228	0.317546
$597$	0	0
$598$	0	0
$599$	−13.8277	−0.564986	−0.282493	−	0.959269i	$-0.591161\pi$
$599$	−13.8277	−0.564986	−0.282493	+	0.959269i	$0.591161\pi$
$600$	0	0
$601$	6.34452	0.258798	0.129399	−	0.991593i	$-0.458695\pi$
$601$	6.34452	0.258798	0.129399	+	0.991593i	$0.458695\pi$
$602$	−0.592243	−0.0241380
$603$	0	0
$604$	−22.7167	−0.924331
$605$	2.94418	0.119698
$606$	0	0
$607$	−16.2462	−0.659411	−0.329706	−	0.944084i	$-0.606950\pi$
$607$	−16.2462	−0.659411	−0.329706	+	0.944084i	$0.606950\pi$
$608$	3.54229	0.143659
$609$	0	0
$610$	7.35194	0.297671
$611$	0	0
$612$	0	0
$613$	22.6890	0.916402	0.458201	−	0.888849i	$-0.348494\pi$
$613$	22.6890	0.916402	0.458201	+	0.888849i	$0.348494\pi$
$614$	58.8565	2.37525
$615$	0	0
$616$	−3.70649	−0.149339
$617$	9.01223	0.362819	0.181409	−	0.983408i	$-0.441934\pi$
$617$	9.01223	0.362819	0.181409	+	0.983408i	$0.441934\pi$
$618$	0	0
$619$	−3.45030	−0.138679	−0.0693395	−	0.997593i	$-0.522089\pi$
$619$	−3.45030	−0.138679	−0.0693395	+	0.997593i	$0.522089\pi$
$620$	15.1419	0.608115
$621$	0	0
$622$	−15.0942	−0.605222
$623$	14.9368	0.598429
$624$	0	0
$625$	1.00000	0.0400000
$626$	−45.3781	−1.81367
$627$	0	0
$628$	27.2355	1.08681
$629$	19.8787	0.792618
$630$	0	0
$631$	24.9549	0.993437	0.496718	−	0.867912i	$-0.334538\pi$
$631$	24.9549	0.993437	0.496718	+	0.867912i	$0.334538\pi$
$632$	11.0484	0.439482
$633$	0	0
$634$	−30.7597	−1.22162
$635$	−3.96227	−0.157238
$636$	0	0
$637$	0	0
$638$	−10.5316	−0.416951
$639$	0	0
$640$	−5.78259	−0.228577
$641$	−41.1304	−1.62455	−0.812276	−	0.583274i	$-0.801772\pi$
$641$	−41.1304	−1.62455	−0.812276	+	0.583274i	$0.801772\pi$
$642$	0	0
$643$	−7.22547	−0.284945	−0.142472	−	0.989799i	$-0.545505\pi$
$643$	−7.22547	−0.284945	−0.142472	+	0.989799i	$0.545505\pi$
$644$	16.1723	0.637276
$645$	0	0
$646$	−2.47099	−0.0972199
$647$	8.45771	0.332507	0.166254	−	0.986083i	$-0.446833\pi$
$647$	8.45771	0.332507	0.166254	+	0.986083i	$0.446833\pi$
$648$	0	0
$649$	−8.46096	−0.332122
$650$	0	0
$651$	0	0
$652$	44.6694	1.74939
$653$	16.3807	0.641026	0.320513	−	0.947244i	$-0.396145\pi$
$653$	16.3807	0.641026	0.320513	+	0.947244i	$0.396145\pi$
$654$	0	0
$655$	11.0484	0.431697
$656$	−21.8129	−0.851651
$657$	0	0
$658$	3.81290	0.148642
$659$	0.308348	0.0120115	0.00600576	−	0.999982i	$-0.498088\pi$
$659$	0.308348	0.0120115	0.00600576	+	0.999982i	$0.498088\pi$
$660$	0	0
$661$	32.7858	1.27522	0.637611	−	0.770359i	$-0.279923\pi$
$661$	32.7858	1.27522	0.637611	+	0.770359i	$0.279923\pi$
$662$	70.9662	2.75818
$663$	0	0
$664$	−0.349328	−0.0135566
$665$	−0.592243	−0.0229662
$666$	0	0
$667$	6.87614	0.266245
$668$	−39.8229	−1.54080
$669$	0	0
$670$	24.0410	0.928784
$671$	−13.1600	−0.508037
$672$	0	0
$673$	−21.7523	−0.838489	−0.419244	−	0.907873i	$-0.637705\pi$
$673$	−21.7523	−0.838489	−0.419244	+	0.907873i	$0.637705\pi$
$674$	32.1116	1.23689
$675$	0	0
$676$	0	0
$677$	14.4200	0.554205	0.277102	−	0.960840i	$-0.410626\pi$
$677$	14.4200	0.554205	0.277102	+	0.960840i	$0.410626\pi$
$678$	0	0
$679$	−4.45616	−0.171012
$680$	1.98516	0.0761275
$681$	0	0
$682$	−50.1526	−1.92044
$683$	−39.1797	−1.49917	−0.749584	−	0.661909i	$-0.769747\pi$
$683$	−39.1797	−1.49917	−0.749584	+	0.661909i	$0.769747\pi$
$684$	0	0
$685$	−12.5168	−0.478242
$686$	−34.3297	−1.31071
$687$	0	0
$688$	0.666147	0.0253966
$689$	0	0
$690$	0	0
$691$	5.56193	0.211586	0.105793	−	0.994388i	$-0.466262\pi$
$691$	5.56193	0.211586	0.105793	+	0.994388i	$0.466262\pi$
$692$	25.3175	0.962425
$693$	0	0
$694$	6.04776	0.229570
$695$	1.64064	0.0622331
$696$	0	0
$697$	18.5922	0.704231
$698$	−38.1426	−1.44372
$699$	0	0
$700$	3.17968	0.120181
$701$	9.58002	0.361832	0.180916	−	0.983499i	$-0.442094\pi$
$701$	9.58002	0.361832	0.180916	+	0.983499i	$0.442094\pi$
$702$	0	0
$703$	−3.22066	−0.121469
$704$	39.2994	1.48115
$705$	0	0
$706$	−44.0261	−1.65695
$707$	−21.8639	−0.822277
$708$	0	0
$709$	−12.1574	−0.456582	−0.228291	−	0.973593i	$-0.573314\pi$
$709$	−12.1574	−0.456582	−0.228291	+	0.973593i	$0.573314\pi$
$710$	0.913870	0.0342969
$711$	0	0
$712$	8.11164	0.303996
$713$	32.7449	1.22630
$714$	0	0
$715$	0	0
$716$	−43.5503	−1.62755
$717$	0	0
$718$	72.0442	2.68867
$719$	−21.1452	−0.788583	−0.394291	−	0.918985i	$-0.629010\pi$
$719$	−21.1452	−0.788583	−0.394291	+	0.918985i	$0.629010\pi$
$720$	0	0
$721$	14.2691	0.531408
$722$	−39.2361	−1.46022
$723$	0	0
$724$	−28.9023	−1.07414
$725$	1.35194	0.0502098
$726$	0	0
$727$	−9.72938	−0.360843	−0.180421	−	0.983589i	$-0.557746\pi$
$727$	−9.72938	−0.360843	−0.180421	+	0.983589i	$0.557746\pi$
$728$	0	0
$729$	0	0
$730$	−7.71130	−0.285408
$731$	−0.567791	−0.0210005
$732$	0	0
$733$	4.40515	0.162708	0.0813539	−	0.996685i	$-0.474076\pi$
$733$	4.40515	0.162708	0.0813539	+	0.996685i	$0.474076\pi$
$734$	3.34388	0.123425
$735$	0	0
$736$	−41.1271	−1.51597
$737$	−43.0336	−1.58516
$738$	0	0
$739$	12.4891	0.459418	0.229709	−	0.973259i	$-0.426223\pi$
$739$	12.4891	0.459418	0.229709	+	0.973259i	$0.426223\pi$
$740$	17.2913	0.635641
$741$	0	0
$742$	4.14131	0.152032
$743$	23.7571	0.871563	0.435781	−	0.900053i	$-0.356472\pi$
$743$	23.7571	0.871563	0.435781	+	0.900053i	$0.356472\pi$
$744$	0	0
$745$	3.29612	0.120761
$746$	40.8465	1.49550
$747$	0	0
$748$	−23.7471	−0.868278
$749$	−18.1574	−0.663458
$750$	0	0
$751$	−32.1574	−1.17344	−0.586721	−	0.809789i	$-0.699581\pi$
$751$	−32.1574	−1.17344	−0.586721	+	0.809789i	$0.699581\pi$
$752$	−4.28870	−0.156393
$753$	0	0
$754$	0	0
$755$	−9.65873	−0.351517
$756$	0	0
$757$	−36.1723	−1.31470	−0.657352	−	0.753584i	$-0.728323\pi$
$757$	−36.1723	−1.31470	−0.657352	+	0.753584i	$0.728323\pi$
$758$	−13.2732	−0.482105
$759$	0	0
$760$	−0.321627	−0.0116666
$761$	33.8639	1.22757	0.613783	−	0.789475i	$-0.289647\pi$
$761$	33.8639	1.22757	0.613783	+	0.789475i	$0.289647\pi$
$762$	0	0
$763$	15.7374	0.569734
$764$	−12.7187	−0.460147
$765$	0	0
$766$	33.3371	1.20452
$767$	0	0
$768$	0	0
$769$	21.8639	0.788433	0.394216	−	0.919018i	$-0.371016\pi$
$769$	21.8639	0.788433	0.394216	+	0.919018i	$0.371016\pi$
$770$	−10.5316	−0.379533
$771$	0	0
$772$	−44.9433	−1.61754
$773$	−22.1378	−0.796241	−0.398120	−	0.917333i	$-0.630337\pi$
$773$	−22.1378	−0.796241	−0.398120	+	0.917333i	$0.630337\pi$
$774$	0	0
$775$	6.43807	0.231262
$776$	−2.41998	−0.0868723
$777$	0	0
$778$	44.8613	1.60836
$779$	−3.01223	−0.107924
$780$	0	0
$781$	−1.63583	−0.0585348
$782$	28.6890	1.02592
$783$	0	0
$784$	16.4078	0.585991
$785$	11.5800	0.413309
$786$	0	0
$787$	−15.2616	−0.544019	−0.272009	−	0.962295i	$-0.587688\pi$
$787$	−15.2616	−0.544019	−0.272009	+	0.962295i	$0.587688\pi$
$788$	−28.8910	−1.02920
$789$	0	0
$790$	31.3929	1.11691
$791$	18.5922	0.661064
$792$	0	0
$793$	0	0
$794$	−32.2590	−1.14483
$795$	0	0
$796$	1.79807	0.0637308
$797$	−9.22066	−0.326613	−0.163306	−	0.986575i	$-0.552216\pi$
$797$	−9.22066	−0.326613	−0.163306	+	0.986575i	$0.552216\pi$
$798$	0	0
$799$	3.65548	0.129322
$800$	−8.08613	−0.285888
$801$	0	0
$802$	−53.7226	−1.89701
$803$	13.8033	0.487107
$804$	0	0
$805$	6.87614	0.242352
$806$	0	0
$807$	0	0
$808$	−11.8735	−0.417709
$809$	−0.167453	−0.00588733	−0.00294366	−	0.999996i	$-0.500937\pi$
$809$	−0.167453	−0.00588733	−0.00294366	+	0.999996i	$0.500937\pi$
$810$	0	0
$811$	36.0032	1.26425	0.632123	−	0.774868i	$-0.282184\pi$
$811$	36.0032	1.26425	0.632123	+	0.774868i	$0.282184\pi$
$812$	4.29873	0.150856
$813$	0	0
$814$	−57.2717	−2.00737
$815$	18.9926	0.665281
$816$	0	0
$817$	0.0919908	0.00321835
$818$	−21.9703	−0.768174
$819$	0	0
$820$	16.1723	0.564760
$821$	−5.04840	−0.176190	−0.0880952	−	0.996112i	$-0.528078\pi$
$821$	−5.04840	−0.176190	−0.0880952	+	0.996112i	$0.528078\pi$
$822$	0	0
$823$	−11.3094	−0.394221	−0.197110	−	0.980381i	$-0.563156\pi$
$823$	−11.3094	−0.394221	−0.197110	+	0.980381i	$0.563156\pi$
$824$	7.74903	0.269950
$825$	0	0
$826$	6.39031	0.222347
$827$	43.8687	1.52546	0.762732	−	0.646714i	$-0.223857\pi$
$827$	43.8687	1.52546	0.762732	+	0.646714i	$0.223857\pi$
$828$	0	0
$829$	−44.4461	−1.54368	−0.771839	−	0.635818i	$-0.780663\pi$
$829$	−44.4461	−1.54368	−0.771839	+	0.635818i	$0.780663\pi$
$830$	−0.992582	−0.0344530
$831$	0	0
$832$	0	0
$833$	−13.9852	−0.484557
$834$	0	0
$835$	−16.9320	−0.585955
$836$	3.84738	0.133065
$837$	0	0
$838$	−15.5800	−0.538203
$839$	1.44068	0.0497378	0.0248689	−	0.999691i	$-0.492083\pi$
$839$	1.44068	0.0497378	0.0248689	+	0.999691i	$0.492083\pi$
$840$	0	0
$841$	−27.1723	−0.936974
$842$	74.0362	2.55146
$843$	0	0
$844$	−18.6380	−0.641548
$845$	0	0
$846$	0	0
$847$	3.98036	0.136767
$848$	−4.65809	−0.159959
$849$	0	0
$850$	5.64064	0.193472
$851$	37.3929	1.28181
$852$	0	0
$853$	0.992582	0.0339853	0.0169927	−	0.999856i	$-0.494591\pi$
$853$	0.992582	0.0339853	0.0169927	+	0.999856i	$0.494591\pi$
$854$	9.93937	0.340118
$855$	0	0
$856$	−9.86066	−0.337031
$857$	10.6071	0.362331	0.181165	−	0.983453i	$-0.442013\pi$
$857$	10.6071	0.362331	0.181165	+	0.983453i	$0.442013\pi$
$858$	0	0
$859$	−40.9123	−1.39591	−0.697955	−	0.716142i	$-0.745906\pi$
$859$	−40.9123	−1.39591	−0.697955	+	0.716142i	$0.745906\pi$
$860$	−0.493887	−0.0168414
$861$	0	0
$862$	0.321627	0.0109546
$863$	48.2494	1.64243	0.821215	−	0.570619i	$-0.193297\pi$
$863$	48.2494	1.64243	0.821215	+	0.570619i	$0.193297\pi$
$864$	0	0
$865$	10.7645	0.366004
$866$	11.7981	0.400915
$867$	0	0
$868$	20.4710	0.694831
$869$	−56.1936	−1.90624
$870$	0	0
$871$	0	0
$872$	8.54645	0.289419
$873$	0	0
$874$	−4.64806	−0.157223
$875$	1.35194	0.0457039
$876$	0	0
$877$	−4.81551	−0.162608	−0.0813042	−	0.996689i	$-0.525909\pi$
$877$	−4.81551	−0.162608	−0.0813042	+	0.996689i	$0.525909\pi$
$878$	56.2691	1.89899
$879$	0	0
$880$	11.8458	0.399323
$881$	−21.6210	−0.728430	−0.364215	−	0.931315i	$-0.618663\pi$
$881$	−21.6210	−0.728430	−0.364215	+	0.931315i	$0.618663\pi$
$882$	0	0
$883$	−21.1616	−0.712144	−0.356072	−	0.934458i	$-0.615884\pi$
$883$	−21.1616	−0.712144	−0.356072	+	0.934458i	$0.615884\pi$
$884$	0	0
$885$	0	0
$886$	−61.2697	−2.05840
$887$	9.10097	0.305581	0.152790	−	0.988259i	$-0.451174\pi$
$887$	9.10097	0.305581	0.152790	+	0.988259i	$0.451174\pi$
$888$	0	0
$889$	−5.35675	−0.179660
$890$	23.0484	0.772584
$891$	0	0
$892$	10.0868	0.337730
$893$	−0.592243	−0.0198187
$894$	0	0
$895$	−18.5168	−0.618948
$896$	−7.81771	−0.261171
$897$	0	0
$898$	−66.0820	−2.20518
$899$	8.70388	0.290291
$900$	0	0
$901$	3.97033	0.132271
$902$	−53.5652	−1.78353
$903$	0	0
$904$	10.0968	0.335815
$905$	−12.2887	−0.408490
$906$	0	0
$907$	43.2436	1.43588	0.717939	−	0.696106i	$-0.245086\pi$
$907$	43.2436	1.43588	0.717939	+	0.696106i	$0.245086\pi$
$908$	−59.9965	−1.99105
$909$	0	0
$910$	0	0
$911$	−23.2058	−0.768843	−0.384422	−	0.923158i	$-0.625599\pi$
$911$	−23.2058	−0.768843	−0.384422	+	0.923158i	$0.625599\pi$
$912$	0	0
$913$	1.77673	0.0588012
$914$	44.1626	1.46077
$915$	0	0
$916$	59.0549	1.95123
$917$	14.9368	0.493255
$918$	0	0
$919$	0.419983	0.0138540	0.00692698	−	0.999976i	$-0.497795\pi$
$919$	0.419983	0.0138540	0.00692698	+	0.999976i	$0.497795\pi$
$920$	3.73419	0.123113
$921$	0	0
$922$	73.4439	2.41875
$923$	0	0
$924$	0	0
$925$	7.35194	0.241730
$926$	−2.82032	−0.0926815
$927$	0	0
$928$	−10.9320	−0.358859
$929$	−39.2207	−1.28679	−0.643394	−	0.765535i	$-0.722474\pi$
$929$	−39.2207	−1.28679	−0.643394	+	0.765535i	$0.722474\pi$
$930$	0	0
$931$	2.26581	0.0742589
$932$	−35.9755	−1.17842
$933$	0	0
$934$	66.0543	2.16136
$935$	−10.0968	−0.330201
$936$	0	0
$937$	−22.5774	−0.737572	−0.368786	−	0.929514i	$-0.620226\pi$
$937$	−22.5774	−0.737572	−0.368786	+	0.929514i	$0.620226\pi$
$938$	32.5019	1.06123
$939$	0	0
$940$	3.17968	0.103710
$941$	−18.0510	−0.588446	−0.294223	−	0.955737i	$-0.595061\pi$
$941$	−18.0510	−0.588446	−0.294223	+	0.955737i	$0.595061\pi$
$942$	0	0
$943$	34.9729	1.13888
$944$	−7.18774	−0.233941
$945$	0	0
$946$	1.63583	0.0531856
$947$	24.5578	0.798020	0.399010	−	0.916947i	$-0.369354\pi$
$947$	24.5578	0.798020	0.399010	+	0.916947i	$0.369354\pi$
$948$	0	0
$949$	0	0
$950$	−0.913870	−0.0296499
$951$	0	0
$952$	2.68382	0.0869831
$953$	−34.9219	−1.13123	−0.565616	−	0.824669i	$-0.691362\pi$
$953$	−34.9219	−1.13123	−0.565616	+	0.824669i	$0.691362\pi$
$954$	0	0
$955$	−5.40776	−0.174991
$956$	−32.1594	−1.04011
$957$	0	0
$958$	−27.7752	−0.897375
$959$	−16.9219	−0.546438
$960$	0	0
$961$	10.4487	0.337056
$962$	0	0
$963$	0	0
$964$	29.4387	0.948157
$965$	−19.1090	−0.615141
$966$	0	0
$967$	5.16484	0.166090	0.0830451	−	0.996546i	$-0.473535\pi$
$967$	5.16484	0.166090	0.0830451	+	0.996546i	$0.473535\pi$
$968$	2.16159	0.0694762
$969$	0	0
$970$	−6.87614	−0.220780
$971$	−14.2935	−0.458701	−0.229350	−	0.973344i	$-0.573660\pi$
$971$	−14.2935	−0.458701	−0.229350	+	0.973344i	$0.573660\pi$
$972$	0	0
$973$	2.21805	0.0711074
$974$	18.5578	0.594629
$975$	0	0
$976$	−11.1797	−0.357853
$977$	−0.424790	−0.0135902	−0.00679512	−	0.999977i	$-0.502163\pi$
$977$	−0.424790	−0.0135902	−0.00679512	+	0.999977i	$0.502163\pi$
$978$	0	0
$979$	−41.2568	−1.31857
$980$	−12.1648	−0.388592
$981$	0	0
$982$	19.8787	0.634356
$983$	−17.8081	−0.567990	−0.283995	−	0.958826i	$-0.591660\pi$
$983$	−17.8081	−0.567990	−0.283995	+	0.958826i	$0.591660\pi$
$984$	0	0
$985$	−12.2839	−0.391397
$986$	7.62581	0.242855
$987$	0	0
$988$	0	0
$989$	−1.06804	−0.0339618
$990$	0	0
$991$	−34.7497	−1.10386	−0.551930	−	0.833891i	$-0.686108\pi$
$991$	−34.7497	−1.10386	−0.551930	+	0.833891i	$0.686108\pi$
$992$	−52.0591	−1.65288
$993$	0	0
$994$	1.23550	0.0391876
$995$	0.764504	0.0242364
$996$	0	0
$997$	48.0213	1.52085	0.760425	−	0.649425i	$-0.224990\pi$
$997$	48.0213	1.52085	0.760425	+	0.649425i	$0.224990\pi$
$998$	−53.1371	−1.68203
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7605.2.a.bs.1.3		3
3.2	odd	2		845.2.a.k.1.1		3
13.5	odd	4		585.2.b.g.181.2		6
13.8	odd	4		585.2.b.g.181.5		6
13.12	even	2		7605.2.a.cc.1.1		3
15.14	odd	2		4225.2.a.bc.1.3		3
39.2	even	12		845.2.m.h.316.2		12
39.5	even	4		65.2.c.a.51.5	yes	6
39.8	even	4		65.2.c.a.51.2	✓	6
39.11	even	12		845.2.m.h.316.5		12
39.17	odd	6		845.2.e.k.146.1		6
39.20	even	12		845.2.m.h.361.2		12
39.23	odd	6		845.2.e.k.191.1		6
39.29	odd	6		845.2.e.i.191.3		6
39.32	even	12		845.2.m.h.361.5		12
39.35	odd	6		845.2.e.i.146.3		6
39.38	odd	2		845.2.a.i.1.3		3
156.47	odd	4		1040.2.k.d.961.5		6
156.83	odd	4		1040.2.k.d.961.6		6
195.8	odd	4		325.2.d.f.324.1		6
195.44	even	4		325.2.c.g.51.2		6
195.47	odd	4		325.2.d.e.324.6		6
195.83	odd	4		325.2.d.e.324.5		6
195.122	odd	4		325.2.d.f.324.2		6
195.164	even	4		325.2.c.g.51.5		6
195.194	odd	2		4225.2.a.be.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.c.a.51.2	✓	6	39.8	even	4
65.2.c.a.51.5	yes	6	39.5	even	4
325.2.c.g.51.2		6	195.44	even	4
325.2.c.g.51.5		6	195.164	even	4
325.2.d.e.324.5		6	195.83	odd	4
325.2.d.e.324.6		6	195.47	odd	4
325.2.d.f.324.1		6	195.8	odd	4
325.2.d.f.324.2		6	195.122	odd	4
585.2.b.g.181.2		6	13.5	odd	4
585.2.b.g.181.5		6	13.8	odd	4
845.2.a.i.1.3		3	39.38	odd	2
845.2.a.k.1.1		3	3.2	odd	2
845.2.e.i.146.3		6	39.35	odd	6
845.2.e.i.191.3		6	39.29	odd	6
845.2.e.k.146.1		6	39.17	odd	6
845.2.e.k.191.1		6	39.23	odd	6
845.2.m.h.316.2		12	39.2	even	12
845.2.m.h.316.5		12	39.11	even	12
845.2.m.h.361.2		12	39.20	even	12
845.2.m.h.361.5		12	39.32	even	12
1040.2.k.d.961.5		6	156.47	odd	4
1040.2.k.d.961.6		6	156.83	odd	4
4225.2.a.bc.1.3		3	15.14	odd	2
4225.2.a.be.1.1		3	195.194	odd	2
7605.2.a.bs.1.3		3	1.1	even	1	trivial
7605.2.a.cc.1.1		3	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)

\(f(q)\)	\(=\)	\(q+2.08613 q^{2} +2.35194 q^{4} +1.00000 q^{5} +1.35194 q^{7} +0.734191 q^{8} +O(q^{10})\)	\(q+2.08613 q^{2} +2.35194 q^{4} +1.00000 q^{5} +1.35194 q^{7} +0.734191 q^{8} +2.08613 q^{10} -3.73419 q^{11} +2.82032 q^{14} -3.17226 q^{16} +2.70388 q^{17} -0.438069 q^{19} +2.35194 q^{20} -7.79001 q^{22} +5.08613 q^{23} +1.00000 q^{25} +3.17968 q^{28} +1.35194 q^{29} +6.43807 q^{31} -8.08613 q^{32} +5.64064 q^{34} +1.35194 q^{35} +7.35194 q^{37} -0.913870 q^{38} +0.734191 q^{40} +6.87614 q^{41} -0.209991 q^{43} -8.78259 q^{44} +10.6103 q^{46} +1.35194 q^{47} -5.17226 q^{49} +2.08613 q^{50} +1.46838 q^{53} -3.73419 q^{55} +0.992582 q^{56} +2.82032 q^{58} +2.26581 q^{59} +3.52420 q^{61} +13.4307 q^{62} -10.5242 q^{64} +11.5242 q^{67} +6.35936 q^{68} +2.82032 q^{70} +0.438069 q^{71} -3.69646 q^{73} +15.3371 q^{74} -1.03031 q^{76} -5.04840 q^{77} +15.0484 q^{79} -3.17226 q^{80} +14.3445 q^{82} -0.475800 q^{83} +2.70388 q^{85} -0.438069 q^{86} -2.74161 q^{88} +11.0484 q^{89} +11.9623 q^{92} +2.82032 q^{94} -0.438069 q^{95} -3.29612 q^{97} -10.7900 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} + 5 q^{4} + 3 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) \) 3 * q - q^2 + 5 * q^4 + 3 * q^5 + 2 * q^7 - 3 * q^8	\( 3 q - q^{2} + 5 q^{4} + 3 q^{5} + 2 q^{7} - 3 q^{8} - q^{10} - 6 q^{11} - 4 q^{14} + 5 q^{16} + 4 q^{17} + 8 q^{19} + 5 q^{20} - 12 q^{22} + 8 q^{23} + 3 q^{25} + 22 q^{28} + 2 q^{29} + 10 q^{31} - 17 q^{32} - 8 q^{34} + 2 q^{35} + 20 q^{37} - 10 q^{38} - 3 q^{40} + 2 q^{41} - 12 q^{43} + 12 q^{44} + 8 q^{46} + 2 q^{47} - q^{49} - q^{50} - 6 q^{53} - 6 q^{55} - 24 q^{56} - 4 q^{58} + 12 q^{59} - 6 q^{61} + 4 q^{62} - 15 q^{64} + 18 q^{67} + 44 q^{68} - 4 q^{70} - 8 q^{71} + 20 q^{73} - 10 q^{74} - 2 q^{76} + 18 q^{77} + 12 q^{79} + 5 q^{80} + 14 q^{82} - 18 q^{83} + 4 q^{85} + 8 q^{86} - 30 q^{88} + 10 q^{92} - 4 q^{94} + 8 q^{95} - 14 q^{97} - 21 q^{98}+O(q^{100}) \) 3 * q - q^2 + 5 * q^4 + 3 * q^5 + 2 * q^7 - 3 * q^8 - q^10 - 6 * q^11 - 4 * q^14 + 5 * q^16 + 4 * q^17 + 8 * q^19 + 5 * q^20 - 12 * q^22 + 8 * q^23 + 3 * q^25 + 22 * q^28 + 2 * q^29 + 10 * q^31 - 17 * q^32 - 8 * q^34 + 2 * q^35 + 20 * q^37 - 10 * q^38 - 3 * q^40 + 2 * q^41 - 12 * q^43 + 12 * q^44 + 8 * q^46 + 2 * q^47 - q^49 - q^50 - 6 * q^53 - 6 * q^55 - 24 * q^56 - 4 * q^58 + 12 * q^59 - 6 * q^61 + 4 * q^62 - 15 * q^64 + 18 * q^67 + 44 * q^68 - 4 * q^70 - 8 * q^71 + 20 * q^73 - 10 * q^74 - 2 * q^76 + 18 * q^77 + 12 * q^79 + 5 * q^80 + 14 * q^82 - 18 * q^83 + 4 * q^85 + 8 * q^86 - 30 * q^88 + 10 * q^92 - 4 * q^94 + 8 * q^95 - 14 * q^97 - 21 * q^98

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