LMFDB - Embedded newform 65.6.a.e.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,6,Mod(1,65)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("65.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	65.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:	$10.4249482878$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 161x^{4} + 328x^{3} + 6584x^{2} - 10688x - 47440 $ x^6 - 2x^5 - 161x^4 + 328x^3 + 6584x^2 - 10688*x - 47440
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$7.62628$ of defining polynomial
Character	$\chi$	$=$	65.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+7.62628 q^{2} -29.7832 q^{3} +26.1601 q^{4} +25.0000 q^{5} -227.135 q^{6} +171.199 q^{7} -44.5366 q^{8} +644.042 q^{9} +190.657 q^{10} +452.811 q^{11} -779.133 q^{12} -169.000 q^{13} +1305.61 q^{14} -744.581 q^{15} -1176.77 q^{16} +1469.49 q^{17} +4911.64 q^{18} +2007.18 q^{19} +654.003 q^{20} -5098.87 q^{21} +3453.26 q^{22} -763.605 q^{23} +1326.44 q^{24} +625.000 q^{25} -1288.84 q^{26} -11944.3 q^{27} +4478.59 q^{28} -6493.90 q^{29} -5678.38 q^{30} +5299.68 q^{31} -7549.22 q^{32} -13486.2 q^{33} +11206.7 q^{34} +4279.98 q^{35} +16848.2 q^{36} -4537.59 q^{37} +15307.3 q^{38} +5033.37 q^{39} -1113.42 q^{40} +13699.1 q^{41} -38885.4 q^{42} +3824.25 q^{43} +11845.6 q^{44} +16101.0 q^{45} -5823.46 q^{46} +15653.3 q^{47} +35048.1 q^{48} +12502.1 q^{49} +4766.42 q^{50} -43766.2 q^{51} -4421.06 q^{52} -16260.1 q^{53} -91090.7 q^{54} +11320.3 q^{55} -7624.63 q^{56} -59780.3 q^{57} -49524.3 q^{58} +16817.3 q^{59} -19478.3 q^{60} +9690.04 q^{61} +40416.8 q^{62} +110259. q^{63} -19915.7 q^{64} -4225.00 q^{65} -102849. q^{66} -5726.95 q^{67} +38442.0 q^{68} +22742.6 q^{69} +32640.3 q^{70} +12847.1 q^{71} -28683.4 q^{72} -41868.8 q^{73} -34604.9 q^{74} -18614.5 q^{75} +52508.0 q^{76} +77520.8 q^{77} +38385.9 q^{78} -33399.1 q^{79} -29419.3 q^{80} +199239. q^{81} +104473. q^{82} -58851.7 q^{83} -133387. q^{84} +36737.3 q^{85} +29164.8 q^{86} +193409. q^{87} -20166.7 q^{88} -94010.3 q^{89} +122791. q^{90} -28932.7 q^{91} -19976.0 q^{92} -157842. q^{93} +119377. q^{94} +50179.4 q^{95} +224840. q^{96} -126692. q^{97} +95344.8 q^{98} +291629. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 20 q^{3} + 134 q^{4} + 150 q^{5} - 52 q^{6} + 172 q^{7} - 138 q^{8} + 1034 q^{9} + 50 q^{10} + 800 q^{11} - 832 q^{12} - 1014 q^{13} + 2108 q^{14} + 500 q^{15} + 322 q^{16} + 4396 q^{17}+ \cdots + 301264 q^{99}+O(q^{100}) $ 6 * q + 2 * q^2 + 20 * q^3 + 134 * q^4 + 150 * q^5 - 52 * q^6 + 172 * q^7 - 138 * q^8 + 1034 * q^9 + 50 * q^10 + 800 * q^11 - 832 * q^12 - 1014 * q^13 + 2108 * q^14 + 500 * q^15 + 322 * q^16 + 4396 * q^17 + 6142 * q^18 + 5304 * q^19 + 3350 * q^20 + 1072 * q^21 + 8008 * q^22 - 1140 * q^23 + 4756 * q^24 + 3750 * q^25 - 338 * q^26 + 800 * q^27 + 524 * q^28 - 3664 * q^29 - 1300 * q^30 + 16664 * q^31 - 9894 * q^32 - 13092 * q^33 + 1380 * q^34 + 4300 * q^35 + 1818 * q^36 + 4488 * q^37 - 30112 * q^38 - 3380 * q^39 - 3450 * q^40 + 12436 * q^41 - 68336 * q^42 + 1516 * q^43 - 35124 * q^44 + 25850 * q^45 - 4556 * q^46 + 212 * q^47 - 16712 * q^48 - 27842 * q^49 + 1250 * q^50 - 27664 * q^51 - 22646 * q^52 - 15612 * q^53 - 132912 * q^54 + 20000 * q^55 + 44420 * q^56 - 86796 * q^57 - 39664 * q^58 - 11896 * q^59 - 20800 * q^60 + 57232 * q^61 - 95488 * q^62 + 207956 * q^63 - 39914 * q^64 - 25350 * q^65 + 9908 * q^66 - 25428 * q^67 - 16236 * q^68 + 72404 * q^69 + 52700 * q^70 + 214104 * q^71 - 130806 * q^72 + 60808 * q^73 - 182104 * q^74 + 12500 * q^75 + 366636 * q^76 - 5192 * q^77 + 8788 * q^78 + 36024 * q^79 + 8050 * q^80 + 350514 * q^81 - 1124 * q^82 + 34684 * q^83 + 6024 * q^84 + 109900 * q^85 + 29204 * q^86 - 8640 * q^87 - 40520 * q^88 - 52028 * q^89 + 153550 * q^90 - 29068 * q^91 - 283232 * q^92 + 26508 * q^93 + 157572 * q^94 + 132600 * q^95 + 547908 * q^96 + 129316 * q^97 - 113942 * q^98 + 301264 * q^99

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 $

$2$	7.62628	1.34815	0.674074	−	0.738664i	$-0.264543\pi$
$2$	7.62628	1.34815	0.674074	+	0.738664i	$0.264543\pi$
$3$	−29.7832	−1.91060	−0.955298	−	0.295645i	$-0.904466\pi$
$3$	−29.7832	−1.91060	−0.955298	+	0.295645i	$0.904466\pi$
$4$	26.1601	0.817503
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−227.135	−2.57577
$7$	171.199	1.32055	0.660277	−	0.751022i	$-0.270439\pi$
$7$	171.199	1.32055	0.660277	+	0.751022i	$0.270439\pi$
$8$	−44.5366	−0.246032
$9$	644.042	2.65038
$10$	190.657	0.602910
$11$	452.811	1.12833	0.564163	−	0.825663i	$-0.309199\pi$
$11$	452.811	1.12833	0.564163	+	0.825663i	$0.309199\pi$
$12$	−779.133	−1.56192
$13$	−169.000	−0.277350
$13$	−169.000	−0.277350
$14$	1305.61	1.78030
$15$	−744.581	−0.854445
$16$	−1176.77	−1.14919
$17$	1469.49	1.23323	0.616615	−	0.787264i	$-0.288503\pi$
$17$	1469.49	1.23323	0.616615	+	0.787264i	$0.288503\pi$
$18$	4911.64	3.57310
$19$	2007.18	1.27556	0.637781	−	0.770218i	$-0.279852\pi$
$19$	2007.18	1.27556	0.637781	+	0.770218i	$0.279852\pi$
$20$	654.003	0.365599
$21$	−5098.87	−2.52305
$22$	3453.26	1.52115
$23$	−763.605	−0.300988	−0.150494	−	0.988611i	$-0.548086\pi$
$23$	−763.605	−0.300988	−0.150494	+	0.988611i	$0.548086\pi$
$24$	1326.44	0.470068
$25$	625.000	0.200000
$26$	−1288.84	−0.373909
$27$	−11944.3	−3.15320
$28$	4478.59	1.07956
$29$	−6493.90	−1.43387	−0.716936	−	0.697139i	$-0.754456\pi$
$29$	−6493.90	−1.43387	−0.716936	+	0.697139i	$0.754456\pi$
$30$	−5678.38	−1.15192
$31$	5299.68	0.990479	0.495239	−	0.868757i	$-0.335080\pi$
$31$	5299.68	0.990479	0.495239	+	0.868757i	$0.335080\pi$
$32$	−7549.22	−1.30325
$33$	−13486.2	−2.15578
$34$	11206.7	1.66258
$35$	4279.98	0.590570
$36$	16848.2	2.16669
$37$	−4537.59	−0.544906	−0.272453	−	0.962169i	$-0.587835\pi$
$37$	−4537.59	−0.544906	−0.272453	+	0.962169i	$0.587835\pi$
$38$	15307.3	1.71965
$39$	5033.37	0.529904
$40$	−1113.42	−0.110029
$41$	13699.1	1.27272	0.636359	−	0.771393i	$-0.280440\pi$
$41$	13699.1	1.27272	0.636359	+	0.771393i	$0.280440\pi$
$42$	−38885.4	−3.40144
$43$	3824.25	0.315409	0.157705	−	0.987486i	$-0.449591\pi$
$43$	3824.25	0.315409	0.157705	+	0.987486i	$0.449591\pi$
$44$	11845.6	0.922411
$45$	16101.0	1.18528
$46$	−5823.46	−0.405776
$47$	15653.3	1.03362	0.516811	−	0.856099i	$-0.327119\pi$
$47$	15653.3	1.03362	0.516811	+	0.856099i	$0.327119\pi$
$48$	35048.1	2.19564
$49$	12502.1	0.743865
$50$	4766.42	0.269630
$51$	−43766.2	−2.35621
$52$	−4421.06	−0.226735
$53$	−16260.1	−0.795120	−0.397560	−	0.917576i	$-0.630143\pi$
$53$	−16260.1	−0.795120	−0.397560	+	0.917576i	$0.630143\pi$
$54$	−91090.7	−4.25099
$55$	11320.3	0.504603
$56$	−7624.63	−0.324899
$57$	−59780.3	−2.43708
$58$	−49524.3	−1.93307
$59$	16817.3	0.628965	0.314483	−	0.949263i	$-0.398169\pi$
$59$	16817.3	0.628965	0.314483	+	0.949263i	$0.398169\pi$
$60$	−19478.3	−0.698511
$61$	9690.04	0.333427	0.166714	−	0.986005i	$-0.446684\pi$
$61$	9690.04	0.333427	0.166714	+	0.986005i	$0.446684\pi$
$62$	40416.8	1.33531
$63$	110259.	3.49997
$64$	−19915.7	−0.607780
$65$	−4225.00	−0.124035
$66$	−102849.	−2.90631
$67$	−5726.95	−0.155861	−0.0779303	−	0.996959i	$-0.524831\pi$
$67$	−5726.95	−0.155861	−0.0779303	+	0.996959i	$0.524831\pi$
$68$	38442.0	1.00817
$69$	22742.6	0.575067
$70$	32640.3	0.796176
$71$	12847.1	0.302455	0.151227	−	0.988499i	$-0.451677\pi$
$71$	12847.1	0.302455	0.151227	+	0.988499i	$0.451677\pi$
$72$	−28683.4	−0.652079
$73$	−41868.8	−0.919566	−0.459783	−	0.888031i	$-0.652073\pi$
$73$	−41868.8	−0.919566	−0.459783	+	0.888031i	$0.652073\pi$
$74$	−34604.9	−0.734614
$75$	−18614.5	−0.382119
$76$	52508.0	1.04278
$77$	77520.8	1.49002
$78$	38385.9	0.714389
$79$	−33399.1	−0.602097	−0.301049	−	0.953609i	$-0.597337\pi$
$79$	−33399.1	−0.602097	−0.301049	+	0.953609i	$0.597337\pi$
$80$	−29419.3	−0.513934
$81$	199239.	3.37412
$82$	104473.	1.71581
$83$	−58851.7	−0.937700	−0.468850	−	0.883278i	$-0.655331\pi$
$83$	−58851.7	−0.937700	−0.468850	+	0.883278i	$0.655331\pi$
$84$	−133387.	−2.06260
$85$	36737.3	0.551518
$86$	29164.8	0.425219
$87$	193409.	2.73955
$88$	−20166.7	−0.277605
$89$	−94010.3	−1.25806	−0.629029	−	0.777382i	$-0.716547\pi$
$89$	−94010.3	−1.25806	−0.629029	+	0.777382i	$0.716547\pi$
$90$	122791.	1.59794
$91$	−28932.7	−0.366256
$92$	−19976.0	−0.246059
$93$	−157842.	−1.89241
$94$	119377.	1.39348
$95$	50179.4	0.570449
$96$	224840.	2.48998
$97$	−126692.	−1.36716	−0.683581	−	0.729874i	$-0.739579\pi$
$97$	−126692.	−1.36716	−0.683581	+	0.729874i	$0.739579\pi$
$98$	95344.8	1.00284
$99$	291629.	2.99049
$100$	16350.1	0.163501
$101$	35394.0	0.345245	0.172622	−	0.984988i	$-0.444776\pi$
$101$	35394.0	0.345245	0.172622	+	0.984988i	$0.444776\pi$
$102$	−333773.	−3.17652
$103$	−33346.8	−0.309714	−0.154857	−	0.987937i	$-0.549492\pi$
$103$	−33346.8	−0.309714	−0.154857	+	0.987937i	$0.549492\pi$
$104$	7526.69	0.0682371
$105$	−127472.	−1.12834
$106$	−124004.	−1.07194
$107$	−1497.08	−0.0126411	−0.00632054	−	0.999980i	$-0.502012\pi$
$107$	−1497.08	−0.0126411	−0.00632054	+	0.999980i	$0.502012\pi$
$108$	−312465.	−2.57776
$109$	−7731.80	−0.0623325	−0.0311662	−	0.999514i	$-0.509922\pi$
$109$	−7731.80	−0.0623325	−0.0311662	+	0.999514i	$0.509922\pi$
$110$	86331.5	0.680280
$111$	135144.	1.04109
$112$	−201462.	−1.51757
$113$	−149733.	−1.10312	−0.551558	−	0.834136i	$-0.685967\pi$
$113$	−149733.	−1.10312	−0.551558	+	0.834136i	$0.685967\pi$
$114$	−455901.	−3.28555
$115$	−19090.1	−0.134606
$116$	−169881.	−1.17220
$117$	−108843.	−0.735082
$118$	128254.	0.847938
$119$	251575.	1.62855
$120$	33161.1	0.210221
$121$	43986.5	0.273122
$122$	73898.9	0.449509
$123$	−408003.	−2.43165
$124$	138640.	0.809720
$125$	15625.0	0.0894427
$126$	840869.	4.71848
$127$	239284.	1.31645	0.658224	−	0.752822i	$-0.271308\pi$
$127$	239284.	1.31645	0.658224	+	0.752822i	$0.271308\pi$
$128$	89692.1	0.483871
$129$	−113898.	−0.602620
$130$	−32221.0	−0.167217
$131$	243815.	1.24132	0.620659	−	0.784081i	$-0.286865\pi$
$131$	243815.	1.24132	0.620659	+	0.784081i	$0.286865\pi$
$132$	−352800.	−1.76236
$133$	343627.	1.68445
$134$	−43675.3	−0.210123
$135$	−298608.	−1.41016
$136$	−65446.1	−0.303415
$137$	−164453.	−0.748583	−0.374292	−	0.927311i	$-0.622114\pi$
$137$	−164453.	−0.748583	−0.374292	+	0.927311i	$0.622114\pi$
$138$	173442.	0.775275
$139$	101444.	0.445338	0.222669	−	0.974894i	$-0.428523\pi$
$139$	101444.	0.445338	0.222669	+	0.974894i	$0.428523\pi$
$140$	111965.	0.482793
$141$	−466207.	−1.97484
$142$	97975.8	0.407754
$143$	−76525.0	−0.312942
$144$	−757890.	−3.04579
$145$	−162347.	−0.641247
$146$	−319303.	−1.23971
$147$	−372354.	−1.42123
$148$	−118704.	−0.445462
$149$	−56069.7	−0.206901	−0.103450	−	0.994635i	$-0.532988\pi$
$149$	−56069.7	−0.206901	−0.103450	+	0.994635i	$0.532988\pi$
$150$	−141960.	−0.515153
$151$	−103359.	−0.368897	−0.184449	−	0.982842i	$-0.559050\pi$
$151$	−103359.	−0.368897	−0.184449	+	0.982842i	$0.559050\pi$
$152$	−89392.9	−0.313830
$153$	946413.	3.26853
$154$	591195.	2.00876
$155$	132492.	0.442956
$156$	131673.	0.433198
$157$	−290816.	−0.941606	−0.470803	−	0.882238i	$-0.656036\pi$
$157$	−290816.	−0.941606	−0.470803	+	0.882238i	$0.656036\pi$
$158$	−254711.	−0.811716
$159$	484278.	1.51915
$160$	−188730.	−0.582830
$161$	−130729.	−0.397471
$162$	1.51945e6	4.54882
$163$	−265789.	−0.783553	−0.391777	−	0.920060i	$-0.628139\pi$
$163$	−265789.	−0.783553	−0.391777	+	0.920060i	$0.628139\pi$
$164$	358370.	1.04045
$165$	−337154.	−0.964093
$166$	−448819.	−1.26416
$167$	−279706.	−0.776087	−0.388043	−	0.921641i	$-0.626849\pi$
$167$	−279706.	−0.776087	−0.388043	+	0.921641i	$0.626849\pi$
$168$	227086.	0.620751
$169$	28561.0	0.0769231
$170$	280169.	0.743528
$171$	1.29271e6	3.38072
$172$	100043.	0.257848
$173$	−657222.	−1.66954	−0.834770	−	0.550599i	$-0.814399\pi$
$173$	−657222.	−1.66954	−0.834770	+	0.550599i	$0.814399\pi$
$174$	1.47499e6	3.69332
$175$	106999.	0.264111
$176$	−532855.	−1.29666
$177$	−500874.	−1.20170
$178$	−716949.	−1.69605
$179$	−140536.	−0.327836	−0.163918	−	0.986474i	$-0.552413\pi$
$179$	−140536.	−0.327836	−0.163918	+	0.986474i	$0.552413\pi$
$180$	421205.	0.968974
$181$	554170.	1.25732	0.628662	−	0.777679i	$-0.283603\pi$
$181$	554170.	1.25732	0.628662	+	0.777679i	$0.283603\pi$
$182$	−220648.	−0.493767
$183$	−288601.	−0.637045
$184$	34008.4	0.0740528
$185$	−113440.	−0.243689
$186$	−1.20374e6	−2.55124
$187$	665401.	1.39149
$188$	409493.	0.844990
$189$	−2.04486e6	−4.16398
$190$	382682.	0.769050
$191$	379250.	0.752215	0.376107	−	0.926576i	$-0.377262\pi$
$191$	379250.	0.752215	0.376107	+	0.926576i	$0.377262\pi$
$192$	593155.	1.16122
$193$	884530.	1.70930	0.854652	−	0.519201i	$-0.173770\pi$
$193$	884530.	1.70930	0.854652	+	0.519201i	$0.173770\pi$
$194$	−966189.	−1.84314
$195$	125834.	0.236980
$196$	327057.	0.608112
$197$	−529090.	−0.971323	−0.485661	−	0.874147i	$-0.661421\pi$
$197$	−529090.	−0.971323	−0.485661	+	0.874147i	$0.661421\pi$
$198$	2.22404e6	4.03163
$199$	8938.89	0.0160011	0.00800057	−	0.999968i	$-0.497453\pi$
$199$	8938.89	0.0160011	0.00800057	+	0.999968i	$0.497453\pi$
$200$	−27835.4	−0.0492065
$201$	170567.	0.297786
$202$	269925.	0.465441
$203$	−1.11175e6	−1.89351
$204$	−1.14493e6	−1.92621
$205$	342477.	0.569177
$206$	−254312.	−0.417541
$207$	−491794.	−0.797732
$208$	198874.	0.318728
$209$	908871.	1.43925
$210$	−972134.	−1.52117
$211$	−1.11242e6	−1.72013	−0.860066	−	0.510183i	$-0.829578\pi$
$211$	−1.11242e6	−1.72013	−0.860066	+	0.510183i	$0.829578\pi$
$212$	−425365.	−0.650014
$213$	−382629.	−0.577869
$214$	−11417.1	−0.0170421
$215$	95606.2	0.141055
$216$	531960.	0.775790
$217$	907300.	1.30798
$218$	−58964.9	−0.0840334
$219$	1.24699e6	1.75692
$220$	296139.	0.412515
$221$	−248344.	−0.342037
$222$	1.03065e6	1.40355
$223$	1.27817e6	1.72118	0.860588	−	0.509301i	$-0.170096\pi$
$223$	1.27817e6	1.72118	0.860588	+	0.509301i	$0.170096\pi$
$224$	−1.29242e6	−1.72101
$225$	402526.	0.530075
$226$	−1.14191e6	−1.48716
$227$	−1.31606e6	−1.69516	−0.847579	−	0.530669i	$-0.821941\pi$
$227$	−1.31606e6	−1.69516	−0.847579	+	0.530669i	$0.821941\pi$
$228$	−1.56386e6	−1.99233
$229$	−10410.5	−0.0131185	−0.00655925	−	0.999978i	$-0.502088\pi$
$229$	−10410.5	−0.0131185	−0.00655925	+	0.999978i	$0.502088\pi$
$230$	−145587.	−0.181469
$231$	−2.30882e6	−2.84682
$232$	289216.	0.352779
$233$	1.42470e6	1.71923	0.859616	−	0.510941i	$-0.170703\pi$
$233$	1.42470e6	1.71923	0.859616	+	0.510941i	$0.170703\pi$
$234$	−830067.	−0.991000
$235$	391333.	0.462250
$236$	439943.	0.514181
$237$	994733.	1.15036
$238$	1.91858e6	2.19553
$239$	−336053.	−0.380552	−0.190276	−	0.981731i	$-0.560938\pi$
$239$	−336053.	−0.380552	−0.190276	+	0.981731i	$0.560938\pi$
$240$	876202.	0.981920
$241$	1.13898e6	1.26320	0.631599	−	0.775295i	$-0.282399\pi$
$241$	1.13898e6	1.26320	0.631599	+	0.775295i	$0.282399\pi$
$242$	335453.	0.368208
$243$	−3.03150e6	−3.29338
$244$	253493.	0.272578
$245$	312554.	0.332667
$246$	−3.11155e6	−3.27822
$247$	−339213.	−0.353777
$248$	−236030.	−0.243690
$249$	1.75279e6	1.79157
$250$	119161.	0.120582
$251$	−1.58387e6	−1.58684	−0.793421	−	0.608673i	$-0.791702\pi$
$251$	−1.58387e6	−1.58684	−0.793421	+	0.608673i	$0.791702\pi$
$252$	2.88440e6	2.86124
$253$	−345769.	−0.339613
$254$	1.82484e6	1.77477
$255$	−1.09415e6	−1.05373
$256$	1.32132e6	1.26011
$257$	−1.60657e6	−1.51729	−0.758643	−	0.651507i	$-0.774137\pi$
$257$	−1.60657e6	−1.51729	−0.758643	+	0.651507i	$0.774137\pi$
$258$	−868621.	−0.812421
$259$	−776832.	−0.719578
$260$	−110526.	−0.101399
$261$	−4.18234e6	−3.80030
$262$	1.85940e6	1.67348
$263$	1.09488e6	0.976064	0.488032	−	0.872826i	$-0.337715\pi$
$263$	1.09488e6	0.976064	0.488032	+	0.872826i	$0.337715\pi$
$264$	600628.	0.530391
$265$	−406502.	−0.355589
$266$	2.62059e6	2.27089
$267$	2.79993e6	2.40364
$268$	−149818.	−0.127417
$269$	1.40894e6	1.18716	0.593582	−	0.804774i	$-0.297713\pi$
$269$	1.40894e6	1.18716	0.593582	+	0.804774i	$0.297713\pi$
$270$	−2.27727e6	−1.90110
$271$	−416084.	−0.344158	−0.172079	−	0.985083i	$-0.555048\pi$
$271$	−416084.	−0.344158	−0.172079	+	0.985083i	$0.555048\pi$
$272$	−1.72926e6	−1.41722
$273$	861708.	0.699767
$274$	−1.25416e6	−1.00920
$275$	283007.	0.225665
$276$	594950.	0.470119
$277$	1.07825e6	0.844349	0.422174	−	0.906515i	$-0.361267\pi$
$277$	1.07825e6	0.844349	0.422174	+	0.906515i	$0.361267\pi$
$278$	773641.	0.600382
$279$	3.41321e6	2.62514
$280$	−190616.	−0.145299
$281$	−1.78529e6	−1.34879	−0.674393	−	0.738372i	$-0.735595\pi$
$281$	−1.78529e6	−1.34879	−0.674393	+	0.738372i	$0.735595\pi$
$282$	−3.55542e6	−2.66237
$283$	171905.	0.127591	0.0637957	−	0.997963i	$-0.479679\pi$
$283$	171905.	0.127591	0.0637957	+	0.997963i	$0.479679\pi$
$284$	336082.	0.247258
$285$	−1.49451e6	−1.08990
$286$	−583601.	−0.421892
$287$	2.34527e6	1.68069
$288$	−4.86201e6	−3.45410
$289$	739545.	0.520859
$290$	−1.23811e6	−0.864496
$291$	3.77330e6	2.61210
$292$	−1.09529e6	−0.751749
$293$	976888.	0.664776	0.332388	−	0.943143i	$-0.392146\pi$
$293$	976888.	0.664776	0.332388	+	0.943143i	$0.392146\pi$
$294$	−2.83968e6	−1.91602
$295$	420433.	0.281282
$296$	202089.	0.134064
$297$	−5.40852e6	−3.55784
$298$	−427603.	−0.278933
$299$	129049.	0.0834791
$300$	−486958.	−0.312384
$301$	654708.	0.416515
$302$	−788243.	−0.497328
$303$	−1.05415e6	−0.659623
$304$	−2.36199e6	−1.46587
$305$	242251.	0.149113
$306$	7.21761e6	4.40646
$307$	1.74098e6	1.05426	0.527131	−	0.849784i	$-0.323268\pi$
$307$	1.74098e6	1.05426	0.527131	+	0.849784i	$0.323268\pi$
$308$	2.02795e6	1.21809
$309$	993176.	0.591739
$310$	1.01042e6	0.597170
$311$	1.00483e6	0.589104	0.294552	−	0.955635i	$-0.404830\pi$
$311$	1.00483e6	0.589104	0.294552	+	0.955635i	$0.404830\pi$
$312$	−224169.	−0.130374
$313$	458407.	0.264478	0.132239	−	0.991218i	$-0.457783\pi$
$313$	458407.	0.264478	0.132239	+	0.991218i	$0.457783\pi$
$314$	−2.21784e6	−1.26942
$315$	2.75648e6	1.56523
$316$	−873724.	−0.492217
$317$	383397.	0.214289	0.107145	−	0.994243i	$-0.465829\pi$
$317$	383397.	0.214289	0.107145	+	0.994243i	$0.465829\pi$
$318$	3.69324e6	2.04804
$319$	−2.94051e6	−1.61788
$320$	−497893.	−0.271807
$321$	44587.8	0.0241520
$322$	−996972.	−0.535850
$323$	2.94953e6	1.57306
$324$	5.21210e6	2.75836
$325$	−105625.	−0.0554700
$326$	−2.02698e6	−1.05635
$327$	230278.	0.119092
$328$	−610111.	−0.313130
$329$	2.67984e6	1.36496
$330$	−2.57123e6	−1.29974
$331$	622094.	0.312095	0.156047	−	0.987750i	$-0.450125\pi$
$331$	622094.	0.312095	0.156047	+	0.987750i	$0.450125\pi$
$332$	−1.53957e6	−0.766573
$333$	−2.92240e6	−1.44421
$334$	−2.13311e6	−1.04628
$335$	−143174.	−0.0697029
$336$	6.00020e6	2.89946
$337$	−624562.	−0.299572	−0.149786	−	0.988718i	$-0.547858\pi$
$337$	−624562.	−0.299572	−0.149786	+	0.988718i	$0.547858\pi$
$338$	217814.	0.103704
$339$	4.45953e6	2.10761
$340$	961051.	0.450868
$341$	2.39975e6	1.11758
$342$	9.85853e6	4.55771
$343$	−736988.	−0.338240
$344$	−170319.	−0.0776009
$345$	568566.	0.257178
$346$	−5.01216e6	−2.25079
$347$	−1.43412e6	−0.639382	−0.319691	−	0.947522i	$-0.603579\pi$
$347$	−1.43412e6	−0.639382	−0.319691	+	0.947522i	$0.603579\pi$
$348$	5.05961e6	2.23959
$349$	−1.80725e6	−0.794247	−0.397124	−	0.917765i	$-0.629992\pi$
$349$	−1.80725e6	−0.794247	−0.397124	+	0.917765i	$0.629992\pi$
$350$	816008.	0.356061
$351$	2.01859e6	0.874541
$352$	−3.41837e6	−1.47049
$353$	−2.71033e6	−1.15767	−0.578835	−	0.815444i	$-0.696493\pi$
$353$	−2.71033e6	−1.15767	−0.578835	+	0.815444i	$0.696493\pi$
$354$	−3.81981e6	−1.62007
$355$	321178.	0.135262
$356$	−2.45932e6	−1.02847
$357$	−7.49273e6	−3.11150
$358$	−1.07177e6	−0.441971
$359$	−1.91002e6	−0.782171	−0.391085	−	0.920354i	$-0.627900\pi$
$359$	−1.91002e6	−0.782171	−0.391085	+	0.920354i	$0.627900\pi$
$360$	−717086.	−0.291618
$361$	1.55266e6	0.627060
$362$	4.22626e6	1.69506
$363$	−1.31006e6	−0.521825
$364$	−756881.	−0.299416
$365$	−1.04672e6	−0.411242
$366$	−2.20095e6	−0.858831
$367$	2.09294e6	0.811131	0.405566	−	0.914066i	$-0.367075\pi$
$367$	2.09294e6	0.811131	0.405566	+	0.914066i	$0.367075\pi$
$368$	898589.	0.345893
$369$	8.82278e6	3.37318
$370$	−865124.	−0.328529
$371$	−2.78371e6	−1.05000
$372$	−4.12915e6	−1.54705
$373$	1.20939e6	0.450083	0.225041	−	0.974349i	$-0.427748\pi$
$373$	1.20939e6	0.450083	0.225041	+	0.974349i	$0.427748\pi$
$374$	5.07453e6	1.87593
$375$	−465363.	−0.170889
$376$	−697146.	−0.254305
$377$	1.09747e6	0.397685
$378$	−1.55947e7	−5.61366
$379$	−594902.	−0.212739	−0.106370	−	0.994327i	$-0.533923\pi$
$379$	−594902.	−0.212739	−0.106370	+	0.994327i	$0.533923\pi$
$380$	1.31270e6	0.466344
$381$	−7.12664e6	−2.51520
$382$	2.89226e6	1.01410
$383$	−2.34526e6	−0.816946	−0.408473	−	0.912770i	$-0.633939\pi$
$383$	−2.34526e6	−0.816946	−0.408473	+	0.912770i	$0.633939\pi$
$384$	−2.67132e6	−0.924481
$385$	1.93802e6	0.666356
$386$	6.74567e6	2.30440
$387$	2.46297e6	0.835954
$388$	−3.31428e6	−1.11766
$389$	−4.27642e6	−1.43287	−0.716434	−	0.697655i	$-0.754227\pi$
$389$	−4.27642e6	−1.43287	−0.716434	+	0.697655i	$0.754227\pi$
$390$	959647.	0.319485
$391$	−1.12211e6	−0.371188
$392$	−556803.	−0.183015
$393$	−7.26161e6	−2.37166
$394$	−4.03498e6	−1.30949
$395$	−834977.	−0.269266
$396$	7.62905e6	2.44474
$397$	4.05375e6	1.29087	0.645433	−	0.763817i	$-0.276677\pi$
$397$	4.05375e6	1.29087	0.645433	+	0.763817i	$0.276677\pi$
$398$	68170.5	0.0215719
$399$	−1.02343e7	−3.21830
$400$	−735483.	−0.229838
$401$	−2.70195e6	−0.839105	−0.419553	−	0.907731i	$-0.637813\pi$
$401$	−2.70195e6	−0.839105	−0.419553	+	0.907731i	$0.637813\pi$
$402$	1.30079e6	0.401460
$403$	−895646.	−0.274709
$404$	925912.	0.282239
$405$	4.98096e6	1.50895
$406$	−8.47851e6	−2.55273
$407$	−2.05467e6	−0.614832
$408$	1.94920e6	0.579703
$409$	−1.61265e6	−0.476686	−0.238343	−	0.971181i	$-0.576604\pi$
$409$	−1.61265e6	−0.476686	−0.238343	+	0.971181i	$0.576604\pi$
$410$	2.61183e6	0.767334
$411$	4.89794e6	1.43024
$412$	−872356.	−0.253192
$413$	2.87911e6	0.830583
$414$	−3.75055e6	−1.07546
$415$	−1.47129e6	−0.419352
$416$	1.27582e6	0.361456
$417$	−3.02133e6	−0.850861
$418$	6.93131e6	1.94032
$419$	−1.08547e6	−0.302054	−0.151027	−	0.988530i	$-0.548258\pi$
$419$	−1.08547e6	−0.302054	−0.151027	+	0.988530i	$0.548258\pi$
$420$	−3.33467e6	−0.922423
$421$	−5.35894e6	−1.47358	−0.736790	−	0.676121i	$-0.763659\pi$
$421$	−5.35894e6	−1.47358	−0.736790	+	0.676121i	$0.763659\pi$
$422$	−8.48361e6	−2.31899
$423$	1.00814e7	2.73949
$424$	724169.	0.195625
$425$	918431.	0.246646
$426$	−2.91804e6	−0.779053
$427$	1.65893e6	0.440309
$428$	−39163.7	−0.0103341
$429$	2.27916e6	0.597905
$430$	729119.	0.190164
$431$	−2.11538e6	−0.548524	−0.274262	−	0.961655i	$-0.588434\pi$
$431$	−2.11538e6	−0.548524	−0.274262	+	0.961655i	$0.588434\pi$
$432$	1.40557e7	3.62364
$433$	5.31501e6	1.36234	0.681168	−	0.732128i	$-0.261473\pi$
$433$	5.31501e6	1.36234	0.681168	+	0.732128i	$0.261473\pi$
$434$	6.91932e6	1.76335
$435$	4.83523e6	1.22516
$436$	−202265.	−0.0509570
$437$	−1.53269e6	−0.383929
$438$	9.50987e6	2.36859
$439$	3.32599e6	0.823682	0.411841	−	0.911256i	$-0.364886\pi$
$439$	3.32599e6	0.823682	0.411841	+	0.911256i	$0.364886\pi$
$440$	−504166.	−0.124149
$441$	8.05190e6	1.97152
$442$	−1.89394e6	−0.461116
$443$	5.41394e6	1.31070	0.655352	−	0.755324i	$-0.272520\pi$
$443$	5.41394e6	1.31070	0.655352	+	0.755324i	$0.272520\pi$
$444$	3.53539e6	0.851098
$445$	−2.35026e6	−0.562620
$446$	9.74766e6	2.32040
$447$	1.66994e6	0.395304
$448$	−3.40956e6	−0.802607
$449$	692641.	0.162141	0.0810704	−	0.996708i	$-0.474166\pi$
$449$	692641.	0.162141	0.0810704	+	0.996708i	$0.474166\pi$
$450$	3.06978e6	0.714620
$451$	6.20309e6	1.43604
$452$	−3.91703e6	−0.901801
$453$	3.07836e6	0.704813
$454$	−1.00366e7	−2.28532
$455$	−723316.	−0.163795
$456$	2.66241e6	0.599602
$457$	3.90454e6	0.874539	0.437270	−	0.899330i	$-0.355946\pi$
$457$	3.90454e6	0.874539	0.437270	+	0.899330i	$0.355946\pi$
$458$	−79393.6	−0.0176857
$459$	−1.75521e7	−3.88863
$460$	−499400.	−0.110041
$461$	−8.82344e6	−1.93368	−0.966842	−	0.255375i	$-0.917801\pi$
$461$	−8.82344e6	−1.93368	−0.966842	+	0.255375i	$0.917801\pi$
$462$	−1.76077e7	−3.83794
$463$	−5.52375e6	−1.19752	−0.598758	−	0.800930i	$-0.704339\pi$
$463$	−5.52375e6	−1.19752	−0.598758	+	0.800930i	$0.704339\pi$
$464$	7.64184e6	1.64779
$465$	−3.94604e6	−0.846309
$466$	1.08652e7	2.31778
$467$	−5.29356e6	−1.12320	−0.561598	−	0.827410i	$-0.689813\pi$
$467$	−5.29356e6	−1.12320	−0.561598	+	0.827410i	$0.689813\pi$
$468$	−2.84735e6	−0.600932
$469$	−980448.	−0.205822
$470$	2.98442e6	0.623182
$471$	8.66145e6	1.79903
$472$	−748986.	−0.154746
$473$	1.73166e6	0.355885
$474$	7.58611e6	1.55086
$475$	1.25449e6	0.255113
$476$	6.58124e6	1.33134
$477$	−1.04722e7	−2.10737
$478$	−2.56284e6	−0.513040
$479$	−4.55616e6	−0.907319	−0.453659	−	0.891175i	$-0.649882\pi$
$479$	−4.55616e6	−0.907319	−0.453659	+	0.891175i	$0.649882\pi$
$480$	5.62101e6	1.11355
$481$	766853.	0.151130
$482$	8.68614e6	1.70298
$483$	3.89352e6	0.759407
$484$	1.15069e6	0.223278
$485$	−3.16730e6	−0.611414
$486$	−2.31191e7	−4.43996
$487$	8.00881e6	1.53019	0.765096	−	0.643916i	$-0.222692\pi$
$487$	8.00881e6	1.53019	0.765096	+	0.643916i	$0.222692\pi$
$488$	−431562.	−0.0820339
$489$	7.91607e6	1.49705
$490$	2.38362e6	0.448484
$491$	−5.83743e6	−1.09274	−0.546372	−	0.837543i	$-0.683991\pi$
$491$	−5.83743e6	−1.09274	−0.546372	+	0.837543i	$0.683991\pi$
$492$	−1.06734e7	−1.98788
$493$	−9.54272e6	−1.76830
$494$	−2.58693e6	−0.476944
$495$	7.29072e6	1.33739
$496$	−6.23651e6	−1.13825
$497$	2.19942e6	0.399408
$498$	1.33673e7	2.41530
$499$	−2.89323e6	−0.520153	−0.260077	−	0.965588i	$-0.583748\pi$
$499$	−2.89323e6	−0.520153	−0.260077	+	0.965588i	$0.583748\pi$
$500$	408752.	0.0731197
$501$	8.33055e6	1.48279
$502$	−1.20790e7	−2.13930
$503$	1.02497e7	1.80631	0.903156	−	0.429312i	$-0.141244\pi$
$503$	1.02497e7	1.80631	0.903156	+	0.429312i	$0.141244\pi$
$504$	−4.91058e6	−0.861106
$505$	884851.	0.154398
$506$	−2.63693e6	−0.457849
$507$	−850639.	−0.146969
$508$	6.25969e6	1.07620
$509$	6.87884e6	1.17685	0.588424	−	0.808552i	$-0.299749\pi$
$509$	6.87884e6	1.17685	0.588424	+	0.808552i	$0.299749\pi$
$510$	−8.34433e6	−1.42058
$511$	−7.16790e6	−1.21434
$512$	7.20661e6	1.21494
$513$	−2.39744e7	−4.02211
$514$	−1.22522e7	−2.04553
$515$	−833670.	−0.138508
$516$	−2.97960e6	−0.492644
$517$	7.08799e6	1.16626
$518$	−5.92434e6	−0.970097
$519$	1.95742e7	3.18982
$520$	188167.	0.0305166
$521$	1.11738e6	0.180346	0.0901728	−	0.995926i	$-0.471258\pi$
$521$	1.11738e6	0.180346	0.0901728	+	0.995926i	$0.471258\pi$
$522$	−3.18957e7	−5.12337
$523$	2.65174e6	0.423912	0.211956	−	0.977279i	$-0.432017\pi$
$523$	2.65174e6	0.423912	0.211956	+	0.977279i	$0.432017\pi$
$524$	6.37824e6	1.01478
$525$	−3.18679e6	−0.504609
$526$	8.34988e6	1.31588
$527$	7.78783e6	1.22149
$528$	1.58702e7	2.47740
$529$	−5.85325e6	−0.909406
$530$	−3.10010e6	−0.479386
$531$	1.08311e7	1.66700
$532$	8.98932e6	1.37704
$533$	−2.31515e6	−0.352988
$534$	2.13531e7	3.24046
$535$	−37426.9	−0.00565326
$536$	255059.	0.0383467
$537$	4.18563e6	0.626362
$538$	1.07449e7	1.60047
$539$	5.66110e6	0.839323
$540$	−7.81162e6	−1.15281
$541$	9.63494e6	1.41532	0.707662	−	0.706551i	$-0.249750\pi$
$541$	9.63494e6	1.41532	0.707662	+	0.706551i	$0.249750\pi$
$542$	−3.17317e6	−0.463976
$543$	−1.65050e7	−2.40224
$544$	−1.10935e7	−1.60721
$545$	−193295.	−0.0278759
$546$	6.57163e6	0.943390
$547$	1.83795e6	0.262642	0.131321	−	0.991340i	$-0.458078\pi$
$547$	1.83795e6	0.262642	0.131321	+	0.991340i	$0.458078\pi$
$548$	−4.30211e6	−0.611969
$549$	6.24079e6	0.883708
$550$	2.15829e6	0.304230
$551$	−1.30344e7	−1.82899
$552$	−1.01288e6	−0.141485
$553$	−5.71789e6	−0.795103
$554$	8.22307e6	1.13831
$555$	3.37861e6	0.465592
$556$	2.65379e6	0.364065
$557$	−5.72815e6	−0.782305	−0.391152	−	0.920326i	$-0.627923\pi$
$557$	−5.72815e6	−0.782305	−0.391152	+	0.920326i	$0.627923\pi$
$558$	2.60301e7	3.53908
$559$	−646298.	−0.0874788
$560$	−5.03656e6	−0.678678
$561$	−1.98178e7	−2.65857
$562$	−1.36151e7	−1.81836
$563$	−8.32198e6	−1.10651	−0.553255	−	0.833012i	$-0.686615\pi$
$563$	−8.32198e6	−1.10651	−0.553255	+	0.833012i	$0.686615\pi$
$564$	−1.21960e7	−1.61443
$565$	−3.74332e6	−0.493329
$566$	1.31099e6	0.172012
$567$	3.41095e7	4.45571
$568$	−572168.	−0.0744137
$569$	−1.13277e7	−1.46676	−0.733382	−	0.679817i	$-0.762059\pi$
$569$	−1.13277e7	−1.46676	−0.733382	+	0.679817i	$0.762059\pi$
$570$	−1.13975e7	−1.46934
$571$	−1.31340e7	−1.68581	−0.842904	−	0.538064i	$-0.819156\pi$
$571$	−1.31340e7	−1.68581	−0.842904	+	0.538064i	$0.819156\pi$
$572$	−2.00190e6	−0.255831
$573$	−1.12953e7	−1.43718
$574$	1.78857e7	2.26582
$575$	−477253.	−0.0601976
$576$	−1.28266e7	−1.61085
$577$	−5.24787e6	−0.656211	−0.328105	−	0.944641i	$-0.606410\pi$
$577$	−5.24787e6	−0.656211	−0.328105	+	0.944641i	$0.606410\pi$
$578$	5.63997e6	0.702195
$579$	−2.63442e7	−3.26579
$580$	−4.24703e6	−0.524222
$581$	−1.00754e7	−1.23828
$582$	2.87762e7	3.52149
$583$	−7.36274e6	−0.897156
$584$	1.86469e6	0.226243
$585$	−2.72108e6	−0.328739
$586$	7.45002e6	0.896217
$587$	4.50054e6	0.539100	0.269550	−	0.962986i	$-0.413125\pi$
$587$	4.50054e6	0.539100	0.269550	+	0.962986i	$0.413125\pi$
$588$	−9.74083e6	−1.16186
$589$	1.06374e7	1.26342
$590$	3.20634e6	0.379210
$591$	1.57580e7	1.85581
$592$	5.33971e6	0.626201
$593$	−1.02931e7	−1.20201	−0.601005	−	0.799245i	$-0.705233\pi$
$593$	−1.02931e7	−1.20201	−0.601005	+	0.799245i	$0.705233\pi$
$594$	−4.12468e7	−4.79650
$595$	6.28939e6	0.728309
$596$	−1.46679e6	−0.169142
$597$	−266229.	−0.0305717
$598$	984166.	0.112542
$599$	1.05149e7	1.19740	0.598700	−	0.800973i	$-0.295684\pi$
$599$	1.05149e7	1.19740	0.598700	+	0.800973i	$0.295684\pi$
$600$	829028.	0.0940137
$601$	1.66880e7	1.88460	0.942298	−	0.334774i	$-0.108660\pi$
$601$	1.66880e7	1.88460	0.942298	+	0.334774i	$0.108660\pi$
$602$	4.99298e6	0.561525
$603$	−3.68839e6	−0.413089
$604$	−2.70388e6	−0.301575
$605$	1.09966e6	0.122144
$606$	−8.03924e6	−0.889269
$607$	−5.97807e6	−0.658551	−0.329275	−	0.944234i	$-0.606804\pi$
$607$	−5.97807e6	−0.658551	−0.329275	+	0.944234i	$0.606804\pi$
$608$	−1.51526e7	−1.66237
$609$	3.31115e7	3.61773
$610$	1.84747e6	0.201027
$611$	−2.64541e6	−0.286675
$612$	2.47583e7	2.67203
$613$	−449741.	−0.0483405	−0.0241702	−	0.999708i	$-0.507694\pi$
$613$	−449741.	−0.0483405	−0.0241702	+	0.999708i	$0.507694\pi$
$614$	1.32772e7	1.42130
$615$	−1.02001e7	−1.08747
$616$	−3.45251e6	−0.366593
$617$	3.68155e6	0.389330	0.194665	−	0.980870i	$-0.437638\pi$
$617$	3.68155e6	0.389330	0.194665	+	0.980870i	$0.437638\pi$
$618$	7.57423e6	0.797751
$619$	−1.14389e6	−0.119993	−0.0599967	−	0.998199i	$-0.519109\pi$
$619$	−1.14389e6	−0.119993	−0.0599967	+	0.998199i	$0.519109\pi$
$620$	3.46600e6	0.362118
$621$	9.12075e6	0.949077
$622$	7.66312e6	0.794199
$623$	−1.60945e7	−1.66133
$624$	−5.92313e6	−0.608961
$625$	390625.	0.0400000
$626$	3.49594e6	0.356556
$627$	−2.70691e7	−2.74983
$628$	−7.60778e6	−0.769766
$629$	−6.66795e6	−0.671995
$630$	2.10217e7	2.11017
$631$	−1.75675e6	−0.175646	−0.0878228	−	0.996136i	$-0.527991\pi$
$631$	−1.75675e6	−0.175646	−0.0878228	+	0.996136i	$0.527991\pi$
$632$	1.48748e6	0.148135
$633$	3.31314e7	3.28648
$634$	2.92389e6	0.288894
$635$	5.98209e6	0.588734
$636$	1.26688e7	1.24191
$637$	−2.11286e6	−0.206311
$638$	−2.24251e7	−2.18114
$639$	8.27409e6	0.801619
$640$	2.24230e6	0.216394
$641$	−9.00917e6	−0.866043	−0.433022	−	0.901384i	$-0.642553\pi$
$641$	−9.00917e6	−0.866043	−0.433022	+	0.901384i	$0.642553\pi$
$642$	340039.	0.0325605
$643$	−1.98773e7	−1.89596	−0.947981	−	0.318327i	$-0.896879\pi$
$643$	−1.98773e7	−1.89596	−0.947981	+	0.318327i	$0.896879\pi$
$644$	−3.41987e6	−0.324934
$645$	−2.84746e6	−0.269500
$646$	2.24939e7	2.12072
$647$	907817.	0.0852585	0.0426293	−	0.999091i	$-0.486427\pi$
$647$	907817.	0.0852585	0.0426293	+	0.999091i	$0.486427\pi$
$648$	−8.87341e6	−0.830143
$649$	7.61506e6	0.709679
$650$	−805526.	−0.0747818
$651$	−2.70223e7	−2.49902
$652$	−6.95308e6	−0.640557
$653$	−4.96671e6	−0.455812	−0.227906	−	0.973683i	$-0.573188\pi$
$653$	−4.96671e6	−0.455812	−0.227906	+	0.973683i	$0.573188\pi$
$654$	1.75616e6	0.160554
$655$	6.09538e6	0.555134
$656$	−1.61207e7	−1.46260
$657$	−2.69652e7	−2.43720
$658$	2.04372e7	1.84016
$659$	1.50643e7	1.35125	0.675625	−	0.737245i	$-0.263874\pi$
$659$	1.50643e7	1.35125	0.675625	+	0.737245i	$0.263874\pi$
$660$	−8.81999e6	−0.788149
$661$	2.41958e6	0.215395	0.107698	−	0.994184i	$-0.465652\pi$
$661$	2.41958e6	0.215395	0.107698	+	0.994184i	$0.465652\pi$
$662$	4.74426e6	0.420750
$663$	7.39649e6	0.653494
$664$	2.62106e6	0.230705
$665$	8.59068e6	0.753309
$666$	−2.22870e7	−1.94700
$667$	4.95877e6	0.431578
$668$	−7.31714e6	−0.634454
$669$	−3.80680e7	−3.28847
$670$	−1.09188e6	−0.0939699
$671$	4.38775e6	0.376215
$672$	3.84925e7	3.28816
$673$	1.65638e7	1.40969	0.704844	−	0.709362i	$-0.251017\pi$
$673$	1.65638e7	1.40969	0.704844	+	0.709362i	$0.251017\pi$
$674$	−4.76308e6	−0.403867
$675$	−7.46520e6	−0.630641
$676$	747159.	0.0628849
$677$	5.75548e6	0.482625	0.241313	−	0.970447i	$-0.422422\pi$
$677$	5.75548e6	0.482625	0.241313	+	0.970447i	$0.422422\pi$
$678$	3.40096e7	2.84137
$679$	−2.16896e7	−1.80541
$680$	−1.63615e6	−0.135691
$681$	3.91965e7	3.23876
$682$	1.83012e7	1.50667
$683$	−5.72848e6	−0.469881	−0.234940	−	0.972010i	$-0.575489\pi$
$683$	−5.72848e6	−0.469881	−0.234940	+	0.972010i	$0.575489\pi$
$684$	3.38173e7	2.76375
$685$	−4.11132e6	−0.334777
$686$	−5.62048e6	−0.455998
$687$	310060.	0.0250642
$688$	−4.50027e6	−0.362466
$689$	2.74795e6	0.220527
$690$	4.33604e6	0.346713
$691$	1.03053e7	0.821041	0.410520	−	0.911851i	$-0.365347\pi$
$691$	1.03053e7	0.821041	0.410520	+	0.911851i	$0.365347\pi$
$692$	−1.71930e7	−1.36485
$693$	4.99266e7	3.94911
$694$	−1.09370e7	−0.861982
$695$	2.53610e6	0.199161
$696$	−8.61380e6	−0.674018
$697$	2.01307e7	1.56955
$698$	−1.37826e7	−1.07076
$699$	−4.24323e7	−3.28476
$700$	2.79912e6	0.215912
$701$	1.51125e7	1.16156	0.580781	−	0.814060i	$-0.302747\pi$
$701$	1.51125e7	1.16156	0.580781	+	0.814060i	$0.302747\pi$
$702$	1.53943e7	1.17901
$703$	−9.10776e6	−0.695061
$704$	−9.01806e6	−0.685775
$705$	−1.16552e7	−0.883173
$706$	−2.06697e7	−1.56071
$707$	6.05943e6	0.455914
$708$	−1.31029e7	−0.982393
$709$	2.17724e7	1.62664	0.813318	−	0.581820i	$-0.197659\pi$
$709$	2.17724e7	1.62664	0.813318	+	0.581820i	$0.197659\pi$
$710$	2.44940e6	0.182353
$711$	−2.15104e7	−1.59579
$712$	4.18690e6	0.309523
$713$	−4.04686e6	−0.298122
$714$	−5.71417e7	−4.19476
$715$	−1.91313e6	−0.139952
$716$	−3.67645e6	−0.268007
$717$	1.00088e7	0.727080
$718$	−1.45663e7	−1.05448
$719$	7.54447e6	0.544260	0.272130	−	0.962260i	$-0.412272\pi$
$719$	7.54447e6	0.544260	0.272130	+	0.962260i	$0.412272\pi$
$720$	−1.89473e7	−1.36212
$721$	−5.70894e6	−0.408995
$722$	1.18410e7	0.845369
$723$	−3.39224e7	−2.41346
$724$	1.44972e7	1.02787
$725$	−4.05869e6	−0.286774
$726$	−9.99089e6	−0.703498
$727$	2.06007e7	1.44559	0.722795	−	0.691063i	$-0.242857\pi$
$727$	2.06007e7	1.44559	0.722795	+	0.691063i	$0.242857\pi$
$728$	1.28856e6	0.0901108
$729$	4.18729e7	2.91820
$730$	−7.98257e6	−0.554416
$731$	5.61969e6	0.388973
$732$	−7.54983e6	−0.520786
$733$	−4.42100e6	−0.303921	−0.151960	−	0.988387i	$-0.548559\pi$
$733$	−4.42100e6	−0.303921	−0.151960	+	0.988387i	$0.548559\pi$
$734$	1.59613e7	1.09353
$735$	−9.30886e6	−0.635591
$736$	5.76462e6	0.392262
$737$	−2.59322e6	−0.175862
$738$	6.72850e7	4.54755
$739$	847676.	0.0570977	0.0285489	−	0.999592i	$-0.490911\pi$
$739$	847676.	0.0570977	0.0285489	+	0.999592i	$0.490911\pi$
$740$	−2.96760e6	−0.199217
$741$	1.01029e7	0.675926
$742$	−2.12294e7	−1.41556
$743$	4.18581e6	0.278168	0.139084	−	0.990281i	$-0.455584\pi$
$743$	4.18581e6	0.278168	0.139084	+	0.990281i	$0.455584\pi$
$744$	7.02973e6	0.465593
$745$	−1.40174e6	−0.0925289
$746$	9.22311e6	0.606778
$747$	−3.79030e7	−2.48526
$748$	1.74070e7	1.13755
$749$	−256298.	−0.0166932
$750$	−3.54899e6	−0.230384
$751$	−2.60568e7	−1.68586	−0.842930	−	0.538023i	$-0.819171\pi$
$751$	−2.60568e7	−1.68586	−0.842930	+	0.538023i	$0.819171\pi$
$752$	−1.84204e7	−1.18783
$753$	4.71726e7	3.03182
$754$	8.36960e6	0.536138
$755$	−2.58397e6	−0.164976
$756$	−5.34937e7	−3.40407
$757$	−1.34084e7	−0.850430	−0.425215	−	0.905092i	$-0.639801\pi$
$757$	−1.34084e7	−0.850430	−0.425215	+	0.905092i	$0.639801\pi$
$758$	−4.53689e6	−0.286804
$759$	1.02981e7	0.648863
$760$	−2.23482e6	−0.140349
$761$	1.74233e7	1.09061	0.545303	−	0.838239i	$-0.316415\pi$
$761$	1.74233e7	1.09061	0.545303	+	0.838239i	$0.316415\pi$
$762$	−5.43498e7	−3.39086
$763$	−1.32368e6	−0.0823135
$764$	9.92122e6	0.614938
$765$	2.36603e7	1.46173
$766$	−1.78856e7	−1.10136
$767$	−2.84213e6	−0.174444
$768$	−3.93532e7	−2.40756
$769$	1.67671e6	0.102245	0.0511227	−	0.998692i	$-0.483720\pi$
$769$	1.67671e6	0.102245	0.0511227	+	0.998692i	$0.483720\pi$
$770$	1.47799e7	0.898347
$771$	4.78489e7	2.89892
$772$	2.31394e7	1.39736
$773$	2.08953e7	1.25776	0.628882	−	0.777501i	$-0.283513\pi$
$773$	2.08953e7	1.25776	0.628882	+	0.777501i	$0.283513\pi$
$774$	1.87833e7	1.12699
$775$	3.31230e6	0.198096
$776$	5.64244e6	0.336366
$777$	2.31366e7	1.37482
$778$	−3.26132e7	−1.93172
$779$	2.74965e7	1.62343
$780$	3.29184e6	0.193732
$781$	5.81732e6	0.341268
$782$	−8.55753e6	−0.500416
$783$	7.75652e7	4.52129
$784$	−1.47122e7	−0.854843
$785$	−7.27040e6	−0.421099
$786$	−5.53791e7	−3.19734
$787$	2.62205e7	1.50905	0.754527	−	0.656269i	$-0.227867\pi$
$787$	2.62205e7	1.50905	0.754527	+	0.656269i	$0.227867\pi$
$788$	−1.38410e7	−0.794060
$789$	−3.26092e7	−1.86486
$790$	−6.36777e6	−0.363011
$791$	−2.56342e7	−1.45673
$792$	−1.29882e7	−0.735758
$793$	−1.63762e6	−0.0924761
$794$	3.09150e7	1.74028
$795$	1.21069e7	0.679386
$796$	233842.	0.0130810
$797$	−2.73769e6	−0.152665	−0.0763324	−	0.997082i	$-0.524321\pi$
$797$	−2.73769e6	−0.152665	−0.0763324	+	0.997082i	$0.524321\pi$
$798$	−7.80498e7	−4.33875
$799$	2.30024e7	1.27470
$800$	−4.71826e6	−0.260650
$801$	−6.05465e7	−3.33433
$802$	−2.06058e7	−1.13124
$803$	−1.89586e7	−1.03757
$804$	4.46205e6	0.243441
$805$	−3.26821e6	−0.177755
$806$	−6.83044e6	−0.370349
$807$	−4.19627e7	−2.26819
$808$	−1.57633e6	−0.0849413
$809$	−2.09569e7	−1.12578	−0.562892	−	0.826530i	$-0.690311\pi$
$809$	−2.09569e7	−1.12578	−0.562892	+	0.826530i	$0.690311\pi$
$810$	3.79862e7	2.03429
$811$	2.72798e6	0.145643	0.0728213	−	0.997345i	$-0.476800\pi$
$811$	2.72798e6	0.145643	0.0728213	+	0.997345i	$0.476800\pi$
$812$	−2.90835e7	−1.54795
$813$	1.23923e7	0.657546
$814$	−1.56695e7	−0.828884
$815$	−6.64473e6	−0.350416
$816$	5.15028e7	2.70773
$817$	7.67594e6	0.402324
$818$	−1.22985e7	−0.642644
$819$	−1.86338e7	−0.970717
$820$	8.95924e6	0.465304
$821$	1.56207e7	0.808801	0.404400	−	0.914582i	$-0.367480\pi$
$821$	1.56207e7	0.808801	0.404400	+	0.914582i	$0.367480\pi$
$822$	3.73531e7	1.92818
$823$	7.04631e6	0.362629	0.181314	−	0.983425i	$-0.441965\pi$
$823$	7.04631e6	0.362629	0.181314	+	0.983425i	$0.441965\pi$
$824$	1.48515e6	0.0761997
$825$	−8.42886e6	−0.431155
$826$	2.19569e7	1.11975
$827$	−3.60941e7	−1.83515	−0.917577	−	0.397559i	$-0.869857\pi$
$827$	−3.60941e7	−1.83515	−0.917577	+	0.397559i	$0.869857\pi$
$828$	−1.28654e7	−0.652149
$829$	−2.15501e7	−1.08909	−0.544543	−	0.838733i	$-0.683297\pi$
$829$	−2.15501e7	−1.08909	−0.544543	+	0.838733i	$0.683297\pi$
$830$	−1.12205e7	−0.565349
$831$	−3.21139e7	−1.61321
$832$	3.36576e6	0.168568
$833$	1.83718e7	0.917357
$834$	−2.30415e7	−1.14709
$835$	−6.99265e6	−0.347077
$836$	2.37762e7	1.17659
$837$	−6.33011e7	−3.12318
$838$	−8.27812e6	−0.407213
$839$	1.21355e7	0.595187	0.297593	−	0.954693i	$-0.403816\pi$
$839$	1.21355e7	0.595187	0.297593	+	0.954693i	$0.403816\pi$
$840$	5.67716e6	0.277608
$841$	2.16596e7	1.05599
$842$	−4.08688e7	−1.98660
$843$	5.31717e7	2.57699
$844$	−2.91010e7	−1.40621
$845$	714025.	0.0344010
$846$	7.68835e7	3.69324
$847$	7.53045e6	0.360672
$848$	1.91344e7	0.913746
$849$	−5.11988e6	−0.243776
$850$	7.00421e6	0.332516
$851$	3.46493e6	0.164010
$852$	−1.00096e7	−0.472410
$853$	3.47231e7	1.63398	0.816990	−	0.576653i	$-0.195641\pi$
$853$	3.47231e7	1.63398	0.816990	+	0.576653i	$0.195641\pi$
$854$	1.26514e7	0.593602
$855$	3.23176e7	1.51190
$856$	66674.7	0.00311012
$857$	−7.91521e6	−0.368138	−0.184069	−	0.982913i	$-0.558927\pi$
$857$	−7.91521e6	−0.368138	−0.184069	+	0.982913i	$0.558927\pi$
$858$	1.73815e7	0.806064
$859$	−2.19414e7	−1.01457	−0.507284	−	0.861779i	$-0.669351\pi$
$859$	−2.19414e7	−1.01457	−0.507284	+	0.861779i	$0.669351\pi$
$860$	2.50107e6	0.115313
$861$	−6.98498e7	−3.21113
$862$	−1.61325e7	−0.739491
$863$	−2.34790e7	−1.07313	−0.536566	−	0.843859i	$-0.680279\pi$
$863$	−2.34790e7	−1.07313	−0.536566	+	0.843859i	$0.680279\pi$
$864$	9.01703e7	4.10941
$865$	−1.64305e7	−0.746641
$866$	4.05337e7	1.83663
$867$	−2.20260e7	−0.995150
$868$	2.37351e7	1.06928
$869$	−1.51235e7	−0.679363
$870$	3.68748e7	1.65170
$871$	967854.	0.0432279
$872$	344348.	0.0153358
$873$	−8.15950e7	−3.62350
$874$	−1.16887e7	−0.517593
$875$	2.67499e6	0.118114
$876$	3.26213e7	1.43629
$877$	2.71398e7	1.19154	0.595768	−	0.803156i	$-0.296848\pi$
$877$	2.71398e7	1.19154	0.595768	+	0.803156i	$0.296848\pi$
$878$	2.53649e7	1.11045
$879$	−2.90949e7	−1.27012
$880$	−1.33214e7	−0.579886
$881$	4.57122e6	0.198423	0.0992115	−	0.995066i	$-0.468368\pi$
$881$	4.57122e6	0.198423	0.0992115	+	0.995066i	$0.468368\pi$
$882$	6.14060e7	2.65791
$883$	3.03713e7	1.31087	0.655437	−	0.755250i	$-0.272484\pi$
$883$	3.03713e7	1.31087	0.655437	+	0.755250i	$0.272484\pi$
$884$	−6.49670e6	−0.279616
$885$	−1.25219e7	−0.537416
$886$	4.12882e7	1.76702
$887$	3.39368e7	1.44831	0.724156	−	0.689636i	$-0.242230\pi$
$887$	3.39368e7	1.44831	0.724156	+	0.689636i	$0.242230\pi$
$888$	−6.01887e6	−0.256143
$889$	4.09652e7	1.73844
$890$	−1.79237e7	−0.758496
$891$	9.02173e7	3.80711
$892$	3.34370e7	1.40707
$893$	3.14190e7	1.31845
$894$	1.27354e7	0.532929
$895$	−3.51341e6	−0.146613
$896$	1.53552e7	0.638978
$897$	−3.84351e6	−0.159495
$898$	5.28227e6	0.218590
$899$	−3.44156e7	−1.42022
$900$	1.05301e7	0.433339
$901$	−2.38940e7	−0.980567
$902$	4.73065e7	1.93600
$903$	−1.94993e7	−0.795793
$904$	6.66860e6	0.271402
$905$	1.38543e7	0.562292
$906$	2.34764e7	0.950193
$907$	−2.55351e7	−1.03067	−0.515334	−	0.856989i	$-0.672332\pi$
$907$	−2.55351e7	−1.03067	−0.515334	+	0.856989i	$0.672332\pi$
$908$	−3.44282e7	−1.38580
$909$	2.27952e7	0.915028
$910$	−5.51621e6	−0.220819
$911$	−2.19240e6	−0.0875233	−0.0437616	−	0.999042i	$-0.513934\pi$
$911$	−2.19240e6	−0.0875233	−0.0437616	+	0.999042i	$0.513934\pi$
$912$	7.03477e7	2.80068
$913$	−2.66487e7	−1.05803
$914$	2.97771e7	1.17901
$915$	−7.21502e6	−0.284895
$916$	−272341.	−0.0107244
$917$	4.17410e7	1.63923
$918$	−1.33857e8	−5.24245
$919$	−1.95519e6	−0.0763659	−0.0381829	−	0.999271i	$-0.512157\pi$
$919$	−1.95519e6	−0.0763659	−0.0381829	+	0.999271i	$0.512157\pi$
$920$	850210.	0.0331174
$921$	−5.18521e7	−2.01427
$922$	−6.72900e7	−2.60689
$923$	−2.17117e6	−0.0838858
$924$	−6.03990e7	−2.32729
$925$	−2.83600e6	−0.108981
$926$	−4.21256e7	−1.61443
$927$	−2.14767e7	−0.820859
$928$	4.90239e7	1.86869
$929$	2.43874e7	0.927099	0.463550	−	0.886071i	$-0.346576\pi$
$929$	2.43874e7	0.927099	0.463550	+	0.886071i	$0.346576\pi$
$930$	−3.00936e7	−1.14095
$931$	2.50940e7	0.948846
$932$	3.72704e7	1.40548
$933$	−2.99271e7	−1.12554
$934$	−4.03702e7	−1.51424
$935$	1.66350e7	0.622292
$936$	4.84750e6	0.180854
$937$	−4.49798e7	−1.67367	−0.836833	−	0.547458i	$-0.815596\pi$
$937$	−4.49798e7	−1.67367	−0.836833	+	0.547458i	$0.815596\pi$
$938$	−7.47717e6	−0.277479
$939$	−1.36528e7	−0.505311
$940$	1.02373e7	0.377891
$941$	2.36994e7	0.872496	0.436248	−	0.899826i	$-0.356307\pi$
$941$	2.36994e7	0.872496	0.436248	+	0.899826i	$0.356307\pi$
$942$	6.60546e7	2.42536
$943$	−1.04607e7	−0.383073
$944$	−1.97902e7	−0.722802
$945$	−5.11214e7	−1.86219
$946$	1.32061e7	0.479786
$947$	2.24198e7	0.812376	0.406188	−	0.913789i	$-0.366858\pi$
$947$	2.24198e7	0.812376	0.406188	+	0.913789i	$0.366858\pi$
$948$	2.60223e7	0.940427
$949$	7.07582e6	0.255042
$950$	9.56706e6	0.343929
$951$	−1.14188e7	−0.409420
$952$	−1.12043e7	−0.400676
$953$	1.65747e7	0.591171	0.295585	−	0.955316i	$-0.404485\pi$
$953$	1.65747e7	0.591171	0.295585	+	0.955316i	$0.404485\pi$
$954$	−7.98636e7	−2.84105
$955$	9.48125e6	0.336401
$956$	−8.79119e6	−0.311102
$957$	8.75778e7	3.09111
$958$	−3.47465e7	−1.22320
$959$	−2.81542e7	−0.988545
$960$	1.48289e7	0.519314
$961$	−542563.	−0.0189514
$962$	5.84824e6	0.203745
$963$	−964179.	−0.0335036
$964$	2.97957e7	1.03267
$965$	2.21133e7	0.764424
$966$	2.96931e7	1.02379
$967$	1.57319e7	0.541021	0.270510	−	0.962717i	$-0.412808\pi$
$967$	1.57319e7	0.541021	0.270510	+	0.962717i	$0.412808\pi$
$968$	−1.95901e6	−0.0671968
$969$	−8.78465e7	−3.00549
$970$	−2.41547e7	−0.824276
$971$	−8.18745e6	−0.278677	−0.139338	−	0.990245i	$-0.544498\pi$
$971$	−8.18745e6	−0.278677	−0.139338	+	0.990245i	$0.544498\pi$
$972$	−7.93044e7	−2.69235
$973$	1.73671e7	0.588093
$974$	6.10774e7	2.06292
$975$	3.14586e6	0.105981
$976$	−1.14030e7	−0.383172
$977$	4.04123e7	1.35450	0.677248	−	0.735755i	$-0.263173\pi$
$977$	4.04123e7	1.35450	0.677248	+	0.735755i	$0.263173\pi$
$978$	6.03701e7	2.01825
$979$	−4.25689e7	−1.41950
$980$	8.17643e6	0.271956
$981$	−4.97960e6	−0.165205
$982$	−4.45179e7	−1.47318
$983$	−3.44605e7	−1.13746	−0.568732	−	0.822523i	$-0.692566\pi$
$983$	−3.44605e7	−1.13746	−0.568732	+	0.822523i	$0.692566\pi$
$984$	1.81711e7	0.598264
$985$	−1.32272e7	−0.434389
$986$	−7.27754e7	−2.38392
$987$	−7.98142e7	−2.60788
$988$	−8.87385e6	−0.289214
$989$	−2.92021e6	−0.0949345
$990$	5.56011e7	1.80300
$991$	1.80218e7	0.582927	0.291464	−	0.956582i	$-0.405858\pi$
$991$	1.80218e7	0.582927	0.291464	+	0.956582i	$0.405858\pi$
$992$	−4.00084e7	−1.29084
$993$	−1.85280e7	−0.596287
$994$	1.67734e7	0.538461
$995$	223472.	0.00715593
$996$	4.58533e7	1.46461
$997$	3.07170e7	0.978679	0.489340	−	0.872093i	$-0.337238\pi$
$997$	3.07170e7	0.978679	0.489340	+	0.872093i	$0.337238\pi$
$998$	−2.20646e7	−0.701244
$999$	5.41985e7	1.71820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.6.a.e.1.5	✓	6
3.2	odd	2		585.6.a.k.1.2		6
4.3	odd	2		1040.6.a.r.1.6		6
5.2	odd	4		325.6.b.f.274.10		12
5.3	odd	4		325.6.b.f.274.3		12
5.4	even	2		325.6.a.f.1.2		6
13.12	even	2		845.6.a.g.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.6.a.e.1.5	✓	6	1.1	even	1	trivial
325.6.a.f.1.2		6	5.4	even	2
325.6.b.f.274.3		12	5.3	odd	4
325.6.b.f.274.10		12	5.2	odd	4
585.6.a.k.1.2		6	3.2	odd	2
845.6.a.g.1.2		6	13.12	even	2
1040.6.a.r.1.6		6	4.3	odd	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	65.a (trivial)

\(f(q)\)	\(=\)	\(q+7.62628 q^{2} -29.7832 q^{3} +26.1601 q^{4} +25.0000 q^{5} -227.135 q^{6} +171.199 q^{7} -44.5366 q^{8} +644.042 q^{9} +190.657 q^{10} +452.811 q^{11} -779.133 q^{12} -169.000 q^{13} +1305.61 q^{14} -744.581 q^{15} -1176.77 q^{16} +1469.49 q^{17} +4911.64 q^{18} +2007.18 q^{19} +654.003 q^{20} -5098.87 q^{21} +3453.26 q^{22} -763.605 q^{23} +1326.44 q^{24} +625.000 q^{25} -1288.84 q^{26} -11944.3 q^{27} +4478.59 q^{28} -6493.90 q^{29} -5678.38 q^{30} +5299.68 q^{31} -7549.22 q^{32} -13486.2 q^{33} +11206.7 q^{34} +4279.98 q^{35} +16848.2 q^{36} -4537.59 q^{37} +15307.3 q^{38} +5033.37 q^{39} -1113.42 q^{40} +13699.1 q^{41} -38885.4 q^{42} +3824.25 q^{43} +11845.6 q^{44} +16101.0 q^{45} -5823.46 q^{46} +15653.3 q^{47} +35048.1 q^{48} +12502.1 q^{49} +4766.42 q^{50} -43766.2 q^{51} -4421.06 q^{52} -16260.1 q^{53} -91090.7 q^{54} +11320.3 q^{55} -7624.63 q^{56} -59780.3 q^{57} -49524.3 q^{58} +16817.3 q^{59} -19478.3 q^{60} +9690.04 q^{61} +40416.8 q^{62} +110259. q^{63} -19915.7 q^{64} -4225.00 q^{65} -102849. q^{66} -5726.95 q^{67} +38442.0 q^{68} +22742.6 q^{69} +32640.3 q^{70} +12847.1 q^{71} -28683.4 q^{72} -41868.8 q^{73} -34604.9 q^{74} -18614.5 q^{75} +52508.0 q^{76} +77520.8 q^{77} +38385.9 q^{78} -33399.1 q^{79} -29419.3 q^{80} +199239. q^{81} +104473. q^{82} -58851.7 q^{83} -133387. q^{84} +36737.3 q^{85} +29164.8 q^{86} +193409. q^{87} -20166.7 q^{88} -94010.3 q^{89} +122791. q^{90} -28932.7 q^{91} -19976.0 q^{92} -157842. q^{93} +119377. q^{94} +50179.4 q^{95} +224840. q^{96} -126692. q^{97} +95344.8 q^{98} +291629. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 20 q^{3} + 134 q^{4} + 150 q^{5} - 52 q^{6} + 172 q^{7} - 138 q^{8} + 1034 q^{9} + 50 q^{10} + 800 q^{11} - 832 q^{12} - 1014 q^{13} + 2108 q^{14} + 500 q^{15} + 322 q^{16} + 4396 q^{17}+ \cdots + 301264 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 20 * q^3 + 134 * q^4 + 150 * q^5 - 52 * q^6 + 172 * q^7 - 138 * q^8 + 1034 * q^9 + 50 * q^10 + 800 * q^11 - 832 * q^12 - 1014 * q^13 + 2108 * q^14 + 500 * q^15 + 322 * q^16 + 4396 * q^17 + 6142 * q^18 + 5304 * q^19 + 3350 * q^20 + 1072 * q^21 + 8008 * q^22 - 1140 * q^23 + 4756 * q^24 + 3750 * q^25 - 338 * q^26 + 800 * q^27 + 524 * q^28 - 3664 * q^29 - 1300 * q^30 + 16664 * q^31 - 9894 * q^32 - 13092 * q^33 + 1380 * q^34 + 4300 * q^35 + 1818 * q^36 + 4488 * q^37 - 30112 * q^38 - 3380 * q^39 - 3450 * q^40 + 12436 * q^41 - 68336 * q^42 + 1516 * q^43 - 35124 * q^44 + 25850 * q^45 - 4556 * q^46 + 212 * q^47 - 16712 * q^48 - 27842 * q^49 + 1250 * q^50 - 27664 * q^51 - 22646 * q^52 - 15612 * q^53 - 132912 * q^54 + 20000 * q^55 + 44420 * q^56 - 86796 * q^57 - 39664 * q^58 - 11896 * q^59 - 20800 * q^60 + 57232 * q^61 - 95488 * q^62 + 207956 * q^63 - 39914 * q^64 - 25350 * q^65 + 9908 * q^66 - 25428 * q^67 - 16236 * q^68 + 72404 * q^69 + 52700 * q^70 + 214104 * q^71 - 130806 * q^72 + 60808 * q^73 - 182104 * q^74 + 12500 * q^75 + 366636 * q^76 - 5192 * q^77 + 8788 * q^78 + 36024 * q^79 + 8050 * q^80 + 350514 * q^81 - 1124 * q^82 + 34684 * q^83 + 6024 * q^84 + 109900 * q^85 + 29204 * q^86 - 8640 * q^87 - 40520 * q^88 - 52028 * q^89 + 153550 * q^90 - 29068 * q^91 - 283232 * q^92 + 26508 * q^93 + 157572 * q^94 + 132600 * q^95 + 547908 * q^96 + 129316 * q^97 - 113942 * q^98 + 301264 * q^99

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