LMFDB - Embedded newform 75.10.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,10,Mod(1,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("75.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	75.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:	$38.6276877123$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{241}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 60 $ x^2 - x - 60
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 15)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-7.26209$ of defining polynomial
Character	$\chi$	$=$	75.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+7.78626 q^{2} +81.0000 q^{3} -451.374 q^{4} +630.687 q^{6} -1839.88 q^{7} -7501.08 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+7.78626 q^{2} +81.0000 q^{3} -451.374 q^{4} +630.687 q^{6} -1839.88 q^{7} -7501.08 q^{8} +6561.00 q^{9} +44385.9 q^{11} -36561.3 q^{12} -136584. q^{13} -14325.8 q^{14} +172698. q^{16} +253591. q^{17} +51085.7 q^{18} +85435.7 q^{19} -149030. q^{21} +345600. q^{22} +979409. q^{23} -607588. q^{24} -1.06348e6 q^{26} +531441. q^{27} +830473. q^{28} +2.58640e6 q^{29} +8.94787e6 q^{31} +5.18523e6 q^{32} +3.59526e6 q^{33} +1.97452e6 q^{34} -2.96147e6 q^{36} -1.56064e7 q^{37} +665225. q^{38} -1.10633e7 q^{39} +2.44893e7 q^{41} -1.16039e6 q^{42} -1.27592e7 q^{43} -2.00346e7 q^{44} +7.62593e6 q^{46} +6.16764e7 q^{47} +1.39886e7 q^{48} -3.69685e7 q^{49} +2.05408e7 q^{51} +6.16504e7 q^{52} -5.70418e6 q^{53} +4.13794e6 q^{54} +1.38011e7 q^{56} +6.92029e6 q^{57} +2.01384e7 q^{58} +8.35095e7 q^{59} +1.48622e8 q^{61} +6.96704e7 q^{62} -1.20714e7 q^{63} -4.80479e7 q^{64} +2.79936e7 q^{66} +1.68003e8 q^{67} -1.14464e8 q^{68} +7.93321e7 q^{69} +2.10986e8 q^{71} -4.92146e7 q^{72} +1.43534e8 q^{73} -1.21515e8 q^{74} -3.85635e7 q^{76} -8.16646e7 q^{77} -8.61416e7 q^{78} -4.55960e8 q^{79} +4.30467e7 q^{81} +1.90680e8 q^{82} +3.55106e8 q^{83} +6.72683e7 q^{84} -9.93465e7 q^{86} +2.09498e8 q^{87} -3.32942e8 q^{88} -4.24540e8 q^{89} +2.51297e8 q^{91} -4.42080e8 q^{92} +7.24777e8 q^{93} +4.80228e8 q^{94} +4.20003e8 q^{96} -1.19905e9 q^{97} -2.87846e8 q^{98} +2.91216e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 31 q^{2} + 162 q^{3} + 541 q^{4} - 2511 q^{6} - 14112 q^{7} - 26133 q^{8} + 13122 q^{9}+O(q^{10}) $ 2 * q - 31 * q^2 + 162 * q^3 + 541 * q^4 - 2511 * q^6 - 14112 * q^7 - 26133 * q^8 + 13122 * q^9	\( 2 q - 31 q^{2} + 162 q^{3} + 541 q^{4} - 2511 q^{6} - 14112 q^{7} - 26133 q^{8} + 13122 q^{9} - 21512 q^{11} + 43821 q^{12} - 24284 q^{13} + 461664 q^{14} + 387265 q^{16} + 156956 q^{17} - 203391 q^{18} - 95896 q^{19} - 1143072 q^{21} + 2901532 q^{22} + 735264 q^{23} - 2116773 q^{24} - 5419166 q^{26} + 1062882 q^{27} - 11348064 q^{28} - 2678212 q^{29} + 10782432 q^{31} + 6402523 q^{32} - 1742472 q^{33} + 5722622 q^{34} + 3549501 q^{36} - 21968332 q^{37} + 7698404 q^{38} - 1967004 q^{39} + 26060372 q^{41} + 37394784 q^{42} + 7191160 q^{43} - 85429972 q^{44} + 17095392 q^{46} + 31580240 q^{47} + 31368465 q^{48} + 73282930 q^{49} + 12713436 q^{51} + 173093786 q^{52} - 3131116 q^{53} - 16474671 q^{54} + 242454240 q^{56} - 7767576 q^{57} + 224332958 q^{58} - 35494664 q^{59} + 341497340 q^{61} - 1485504 q^{62} - 92588832 q^{63} - 205120471 q^{64} + 235024092 q^{66} + 288195816 q^{67} - 210362042 q^{68} + 59556384 q^{69} + 210286064 q^{71} - 171458613 q^{72} + 232663084 q^{73} + 125240234 q^{74} - 218512364 q^{76} + 727042176 q^{77} - 438952446 q^{78} - 24755040 q^{79} + 86093442 q^{81} + 129742346 q^{82} + 372082152 q^{83} - 919193184 q^{84} - 873146372 q^{86} - 216935172 q^{87} + 894861492 q^{88} - 427639116 q^{89} - 1126859328 q^{91} - 684362592 q^{92} + 873376992 q^{93} + 1647543896 q^{94} + 518604363 q^{96} - 1771658884 q^{97} - 4564085351 q^{98} - 141140232 q^{99}+O(q^{100}) \) 2 * q - 31 * q^2 + 162 * q^3 + 541 * q^4 - 2511 * q^6 - 14112 * q^7 - 26133 * q^8 + 13122 * q^9 - 21512 * q^11 + 43821 * q^12 - 24284 * q^13 + 461664 * q^14 + 387265 * q^16 + 156956 * q^17 - 203391 * q^18 - 95896 * q^19 - 1143072 * q^21 + 2901532 * q^22 + 735264 * q^23 - 2116773 * q^24 - 5419166 * q^26 + 1062882 * q^27 - 11348064 * q^28 - 2678212 * q^29 + 10782432 * q^31 + 6402523 * q^32 - 1742472 * q^33 + 5722622 * q^34 + 3549501 * q^36 - 21968332 * q^37 + 7698404 * q^38 - 1967004 * q^39 + 26060372 * q^41 + 37394784 * q^42 + 7191160 * q^43 - 85429972 * q^44 + 17095392 * q^46 + 31580240 * q^47 + 31368465 * q^48 + 73282930 * q^49 + 12713436 * q^51 + 173093786 * q^52 - 3131116 * q^53 - 16474671 * q^54 + 242454240 * q^56 - 7767576 * q^57 + 224332958 * q^58 - 35494664 * q^59 + 341497340 * q^61 - 1485504 * q^62 - 92588832 * q^63 - 205120471 * q^64 + 235024092 * q^66 + 288195816 * q^67 - 210362042 * q^68 + 59556384 * q^69 + 210286064 * q^71 - 171458613 * q^72 + 232663084 * q^73 + 125240234 * q^74 - 218512364 * q^76 + 727042176 * q^77 - 438952446 * q^78 - 24755040 * q^79 + 86093442 * q^81 + 129742346 * q^82 + 372082152 * q^83 - 919193184 * q^84 - 873146372 * q^86 - 216935172 * q^87 + 894861492 * q^88 - 427639116 * q^89 - 1126859328 * q^91 - 684362592 * q^92 + 873376992 * q^93 + 1647543896 * q^94 + 518604363 * q^96 - 1771658884 * q^97 - 4564085351 * q^98 - 141140232 * q^99

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 $

$2$	7.78626	0.344107	0.172054	−	0.985088i	$-0.444960\pi$
$2$	7.78626	0.344107	0.172054	+	0.985088i	$0.444960\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−451.374	−0.881590
$5$	0	0
$5$	0	0
$6$	630.687	0.198671
$7$	−1839.88	−0.289633	−0.144816	−	0.989459i	$-0.546259\pi$
$7$	−1839.88	−0.289633	−0.144816	+	0.989459i	$0.546259\pi$
$8$	−7501.08	−0.647469
$9$	6561.00	0.333333
$10$	0	0
$11$	44385.9	0.914066	0.457033	−	0.889450i	$-0.348912\pi$
$11$	44385.9	0.914066	0.457033	+	0.889450i	$0.348912\pi$
$12$	−36561.3	−0.508986
$13$	−136584.	−1.32634	−0.663169	−	0.748470i	$-0.730789\pi$
$13$	−136584.	−1.32634	−0.663169	+	0.748470i	$0.730789\pi$
$14$	−14325.8	−0.0996648
$15$	0	0
$16$	172698.	0.658791
$17$	253591.	0.736399	0.368199	−	0.929747i	$-0.379974\pi$
$17$	253591.	0.736399	0.368199	+	0.929747i	$0.379974\pi$
$18$	51085.7	0.114702
$19$	85435.7	0.150400	0.0752001	−	0.997168i	$-0.476040\pi$
$19$	85435.7	0.150400	0.0752001	+	0.997168i	$0.476040\pi$
$20$	0	0
$21$	−149030.	−0.167220
$22$	345600.	0.314537
$23$	979409.	0.729775	0.364887	−	0.931052i	$-0.381108\pi$
$23$	979409.	0.729775	0.364887	+	0.931052i	$0.381108\pi$
$24$	−607588.	−0.373816
$25$	0	0
$26$	−1.06348e6	−0.456403
$27$	531441.	0.192450
$28$	830473.	0.255337
$29$	2.58640e6	0.679054	0.339527	−	0.940596i	$-0.389733\pi$
$29$	2.58640e6	0.679054	0.339527	+	0.940596i	$0.389733\pi$
$30$	0	0
$31$	8.94787e6	1.74017	0.870085	−	0.492901i	$-0.164064\pi$
$31$	8.94787e6	1.74017	0.870085	+	0.492901i	$0.164064\pi$
$32$	5.18523e6	0.874164
$33$	3.59526e6	0.527736
$34$	1.97452e6	0.253400
$35$	0	0
$36$	−2.96147e6	−0.293863
$37$	−1.56064e7	−1.36897	−0.684486	−	0.729026i	$-0.739974\pi$
$37$	−1.56064e7	−1.36897	−0.684486	+	0.729026i	$0.739974\pi$
$38$	665225.	0.0517538
$39$	−1.10633e7	−0.765761
$40$	0	0
$41$	2.44893e7	1.35347	0.676735	−	0.736227i	$-0.263394\pi$
$41$	2.44893e7	1.35347	0.676735	+	0.736227i	$0.263394\pi$
$42$	−1.16039e6	−0.0575415
$43$	−1.27592e7	−0.569135	−0.284568	−	0.958656i	$-0.591850\pi$
$43$	−1.27592e7	−0.569135	−0.284568	+	0.958656i	$0.591850\pi$
$44$	−2.00346e7	−0.805832
$45$	0	0
$46$	7.62593e6	0.251121
$47$	6.16764e7	1.84365	0.921825	−	0.387607i	$-0.126698\pi$
$47$	6.16764e7	1.84365	0.921825	+	0.387607i	$0.126698\pi$
$48$	1.39886e7	0.380353
$49$	−3.69685e7	−0.916113
$50$	0	0
$51$	2.05408e7	0.425160
$52$	6.16504e7	1.16929
$53$	−5.70418e6	−0.0993006	−0.0496503	−	0.998767i	$-0.515811\pi$
$53$	−5.70418e6	−0.0993006	−0.0496503	+	0.998767i	$0.515811\pi$
$54$	4.13794e6	0.0662235
$55$	0	0
$56$	1.38011e7	0.187528
$57$	6.92029e6	0.0868336
$58$	2.01384e7	0.233668
$59$	8.35095e7	0.897226	0.448613	−	0.893726i	$-0.351918\pi$
$59$	8.35095e7	0.897226	0.448613	+	0.893726i	$0.351918\pi$
$60$	0	0
$61$	1.48622e8	1.37435	0.687177	−	0.726490i	$-0.258850\pi$
$61$	1.48622e8	1.37435	0.687177	+	0.726490i	$0.258850\pi$
$62$	6.96704e7	0.598806
$63$	−1.20714e7	−0.0965443
$64$	−4.80479e7	−0.357985
$65$	0	0
$66$	2.79936e7	0.181598
$67$	1.68003e8	1.01854	0.509272	−	0.860606i	$-0.329915\pi$
$67$	1.68003e8	1.01854	0.509272	+	0.860606i	$0.329915\pi$
$68$	−1.14464e8	−0.649202
$69$	7.93321e7	0.421336
$70$	0	0
$71$	2.10986e8	0.985349	0.492675	−	0.870214i	$-0.336019\pi$
$71$	2.10986e8	0.985349	0.492675	+	0.870214i	$0.336019\pi$
$72$	−4.92146e7	−0.215823
$73$	1.43534e8	0.591566	0.295783	−	0.955255i	$-0.404420\pi$
$73$	1.43534e8	0.591566	0.295783	+	0.955255i	$0.404420\pi$
$74$	−1.21515e8	−0.471074
$75$	0	0
$76$	−3.85635e7	−0.132591
$77$	−8.16646e7	−0.264744
$78$	−8.61416e7	−0.263504
$79$	−4.55960e8	−1.31706	−0.658529	−	0.752555i	$-0.728821\pi$
$79$	−4.55960e8	−1.31706	−0.658529	+	0.752555i	$0.728821\pi$
$80$	0	0
$81$	4.30467e7	0.111111
$82$	1.90680e8	0.465739
$83$	3.55106e8	0.821309	0.410655	−	0.911791i	$-0.365300\pi$
$83$	3.55106e8	0.821309	0.410655	+	0.911791i	$0.365300\pi$
$84$	6.72683e7	0.147419
$85$	0	0
$86$	−9.93465e7	−0.195844
$87$	2.09498e8	0.392052
$88$	−3.32942e8	−0.591830
$89$	−4.24540e8	−0.717239	−0.358620	−	0.933484i	$-0.616752\pi$
$89$	−4.24540e8	−0.717239	−0.358620	+	0.933484i	$0.616752\pi$
$90$	0	0
$91$	2.51297e8	0.384151
$92$	−4.42080e8	−0.643362
$93$	7.24777e8	1.00469
$94$	4.80228e8	0.634413
$95$	0	0
$96$	4.20003e8	0.504699
$97$	−1.19905e9	−1.37520	−0.687598	−	0.726092i	$-0.741335\pi$
$97$	−1.19905e9	−1.37520	−0.687598	+	0.726092i	$0.741335\pi$
$98$	−2.87846e8	−0.315241
$99$	2.91216e8	0.304689
$100$	0	0
$101$	−1.77085e9	−1.69331	−0.846654	−	0.532144i	$-0.821387\pi$
$101$	−1.77085e9	−1.69331	−0.846654	+	0.532144i	$0.821387\pi$
$102$	1.59936e8	0.146301
$103$	−3.03322e8	−0.265544	−0.132772	−	0.991147i	$-0.542388\pi$
$103$	−3.03322e8	−0.265544	−0.132772	+	0.991147i	$0.542388\pi$
$104$	1.02453e9	0.858763
$105$	0	0
$106$	−4.44142e7	−0.0341701
$107$	1.95414e8	0.144121	0.0720607	−	0.997400i	$-0.477042\pi$
$107$	1.95414e8	0.144121	0.0720607	+	0.997400i	$0.477042\pi$
$108$	−2.39879e8	−0.169662
$109$	2.31494e9	1.57080	0.785401	−	0.618988i	$-0.212457\pi$
$109$	2.31494e9	1.57080	0.785401	+	0.618988i	$0.212457\pi$
$110$	0	0
$111$	−1.26412e9	−0.790377
$112$	−3.17743e8	−0.190808
$113$	−1.31945e9	−0.761270	−0.380635	−	0.924725i	$-0.624294\pi$
$113$	−1.31945e9	−0.761270	−0.380635	+	0.924725i	$0.624294\pi$
$114$	5.38832e7	0.0298801
$115$	0	0
$116$	−1.16743e9	−0.598648
$117$	−8.96126e8	−0.442113
$118$	6.50227e8	0.308742
$119$	−4.66576e8	−0.213285
$120$	0	0
$121$	−3.87842e8	−0.164483
$122$	1.15721e9	0.472925
$123$	1.98363e9	0.781426
$124$	−4.03884e9	−1.53412
$125$	0	0
$126$	−9.39914e7	−0.0332216
$127$	−3.18960e9	−1.08798	−0.543988	−	0.839093i	$-0.683086\pi$
$127$	−3.18960e9	−1.08798	−0.543988	+	0.839093i	$0.683086\pi$
$128$	−3.02895e9	−0.997349
$129$	−1.03350e9	−0.328590
$130$	0	0
$131$	−5.40115e9	−1.60238	−0.801190	−	0.598410i	$-0.795799\pi$
$131$	−5.40115e9	−1.60238	−0.801190	+	0.598410i	$0.795799\pi$
$132$	−1.62281e9	−0.465247
$133$	−1.57191e8	−0.0435608
$134$	1.30811e9	0.350488
$135$	0	0
$136$	−1.90220e9	−0.476796
$137$	−1.19903e7	−0.00290795	−0.00145398	−	0.999999i	$-0.500463\pi$
$137$	−1.19903e7	−0.00290795	−0.00145398	+	0.999999i	$0.500463\pi$
$138$	6.17701e8	0.144985
$139$	9.15482e8	0.208010	0.104005	−	0.994577i	$-0.466834\pi$
$139$	9.15482e8	0.208010	0.104005	+	0.994577i	$0.466834\pi$
$140$	0	0
$141$	4.99578e9	1.06443
$142$	1.64279e9	0.339066
$143$	−6.06239e9	−1.21236
$144$	1.13307e9	0.219597
$145$	0	0
$146$	1.11760e9	0.203562
$147$	−2.99445e9	−0.528918
$148$	7.04432e9	1.20687
$149$	5.00462e9	0.831827	0.415913	−	0.909404i	$-0.363462\pi$
$149$	5.00462e9	0.831827	0.415913	+	0.909404i	$0.363462\pi$
$150$	0	0
$151$	3.20554e9	0.501770	0.250885	−	0.968017i	$-0.419278\pi$
$151$	3.20554e9	0.501770	0.250885	+	0.968017i	$0.419278\pi$
$152$	−6.40860e8	−0.0973794
$153$	1.66381e9	0.245466
$154$	−6.35862e8	−0.0911002
$155$	0	0
$156$	4.99368e9	0.675088
$157$	4.63430e8	0.0608745	0.0304373	−	0.999537i	$-0.490310\pi$
$157$	4.63430e8	0.0608745	0.0304373	+	0.999537i	$0.490310\pi$
$158$	−3.55023e9	−0.453210
$159$	−4.62038e8	−0.0573312
$160$	0	0
$161$	−1.80199e9	−0.211367
$162$	3.35173e8	0.0382342
$163$	1.27948e10	1.41968	0.709840	−	0.704363i	$-0.248767\pi$
$163$	1.27948e10	1.41968	0.709840	+	0.704363i	$0.248767\pi$
$164$	−1.10538e10	−1.19320
$165$	0	0
$166$	2.76495e9	0.282619
$167$	1.85699e10	1.84750	0.923752	−	0.382992i	$-0.125106\pi$
$167$	1.85699e10	1.84750	0.923752	+	0.382992i	$0.125106\pi$
$168$	1.11789e9	0.108269
$169$	8.05063e9	0.759171
$170$	0	0
$171$	5.60544e8	0.0501334
$172$	5.75917e9	0.501744
$173$	−4.90746e9	−0.416533	−0.208266	−	0.978072i	$-0.566782\pi$
$173$	−4.90746e9	−0.416533	−0.208266	+	0.978072i	$0.566782\pi$
$174$	1.63121e9	0.134908
$175$	0	0
$176$	7.66536e9	0.602179
$177$	6.76427e9	0.518014
$178$	−3.30558e9	−0.246807
$179$	−1.28930e10	−0.938678	−0.469339	−	0.883018i	$-0.655508\pi$
$179$	−1.28930e10	−0.938678	−0.469339	+	0.883018i	$0.655508\pi$
$180$	0	0
$181$	2.66233e10	1.84378	0.921889	−	0.387453i	$-0.126645\pi$
$181$	2.66233e10	1.84378	0.921889	+	0.387453i	$0.126645\pi$
$182$	1.95667e9	0.132189
$183$	1.20384e10	0.793483
$184$	−7.34663e9	−0.472506
$185$	0	0
$186$	5.64331e9	0.345721
$187$	1.12558e10	0.673117
$188$	−2.78391e10	−1.62534
$189$	−9.77786e8	−0.0557399
$190$	0	0
$191$	−2.72802e10	−1.48319	−0.741595	−	0.670848i	$-0.765930\pi$
$191$	−2.72802e10	−1.48319	−0.741595	+	0.670848i	$0.765930\pi$
$192$	−3.89188e9	−0.206683
$193$	9.65442e9	0.500862	0.250431	−	0.968134i	$-0.419428\pi$
$193$	9.65442e9	0.500862	0.250431	+	0.968134i	$0.419428\pi$
$194$	−9.33612e9	−0.473215
$195$	0	0
$196$	1.66866e10	0.807636
$197$	−1.21091e10	−0.572812	−0.286406	−	0.958108i	$-0.592461\pi$
$197$	−1.21091e10	−0.572812	−0.286406	+	0.958108i	$0.592461\pi$
$198$	2.26748e9	0.104846
$199$	1.89741e10	0.857673	0.428837	−	0.903382i	$-0.358924\pi$
$199$	1.89741e10	0.857673	0.428837	+	0.903382i	$0.358924\pi$
$200$	0	0
$201$	1.36082e10	0.588056
$202$	−1.37883e10	−0.582680
$203$	−4.75866e9	−0.196676
$204$	−9.27161e9	−0.374817
$205$	0	0
$206$	−2.36174e9	−0.0913757
$207$	6.42590e9	0.243258
$208$	−2.35878e10	−0.873779
$209$	3.79214e9	0.137476
$210$	0	0
$211$	−8.91928e9	−0.309784	−0.154892	−	0.987931i	$-0.549503\pi$
$211$	−8.91928e9	−0.309784	−0.154892	+	0.987931i	$0.549503\pi$
$212$	2.57472e9	0.0875424
$213$	1.70898e10	0.568892
$214$	1.52154e9	0.0495933
$215$	0	0
$216$	−3.98638e9	−0.124605
$217$	−1.64630e10	−0.504010
$218$	1.80248e10	0.540524
$219$	1.16263e10	0.341541
$220$	0	0
$221$	−3.46364e10	−0.976714
$222$	−9.84275e9	−0.271975
$223$	4.42755e10	1.19892	0.599462	−	0.800403i	$-0.295381\pi$
$223$	4.42755e10	1.19892	0.599462	+	0.800403i	$0.295381\pi$
$224$	−9.54018e9	−0.253187
$225$	0	0
$226$	−1.02735e10	−0.261959
$227$	5.40045e10	1.34994	0.674968	−	0.737847i	$-0.264157\pi$
$227$	5.40045e10	1.34994	0.674968	+	0.737847i	$0.264157\pi$
$228$	−3.12364e9	−0.0765516
$229$	5.80250e9	0.139430	0.0697149	−	0.997567i	$-0.477791\pi$
$229$	5.80250e9	0.139430	0.0697149	+	0.997567i	$0.477791\pi$
$230$	0	0
$231$	−6.61483e9	−0.152850
$232$	−1.94008e10	−0.439667
$233$	−5.41865e10	−1.20445	−0.602226	−	0.798326i	$-0.705719\pi$
$233$	−5.41865e10	−1.20445	−0.602226	+	0.798326i	$0.705719\pi$
$234$	−6.97747e9	−0.152134
$235$	0	0
$236$	−3.76940e10	−0.790986
$237$	−3.69328e10	−0.760404
$238$	−3.63288e9	−0.0733930
$239$	7.91761e10	1.56965	0.784826	−	0.619716i	$-0.212752\pi$
$239$	7.91761e10	1.56965	0.784826	+	0.619716i	$0.212752\pi$
$240$	0	0
$241$	−6.14920e10	−1.17420	−0.587100	−	0.809514i	$-0.699730\pi$
$241$	−6.14920e10	−1.17420	−0.587100	+	0.809514i	$0.699730\pi$
$242$	−3.01984e9	−0.0565998
$243$	3.48678e9	0.0641500
$244$	−6.70841e10	−1.21162
$245$	0	0
$246$	1.54451e10	0.268894
$247$	−1.16691e10	−0.199481
$248$	−6.71187e10	−1.12671
$249$	2.87636e10	0.474183
$250$	0	0
$251$	2.89319e10	0.460093	0.230046	−	0.973180i	$-0.426112\pi$
$251$	2.89319e10	0.460093	0.230046	+	0.973180i	$0.426112\pi$
$252$	5.44873e9	0.0851125
$253$	4.34719e10	0.667062
$254$	−2.48350e10	−0.374381
$255$	0	0
$256$	1.01633e9	0.0147896
$257$	−1.22388e11	−1.75001	−0.875005	−	0.484114i	$-0.839142\pi$
$257$	−1.22388e11	−1.75001	−0.875005	+	0.484114i	$0.839142\pi$
$258$	−8.04706e9	−0.113070
$259$	2.87139e10	0.396499
$260$	0	0
$261$	1.69694e10	0.226351
$262$	−4.20548e10	−0.551391
$263$	6.24892e10	0.805386	0.402693	−	0.915335i	$-0.368074\pi$
$263$	6.24892e10	0.805386	0.402693	+	0.915335i	$0.368074\pi$
$264$	−2.69683e10	−0.341693
$265$	0	0
$266$	−1.22393e9	−0.0149896
$267$	−3.43878e10	−0.414098
$268$	−7.58321e10	−0.897938
$269$	1.27214e11	1.48132	0.740659	−	0.671881i	$-0.234513\pi$
$269$	1.27214e11	1.48132	0.740659	+	0.671881i	$0.234513\pi$
$270$	0	0
$271$	1.54116e10	0.173574	0.0867871	−	0.996227i	$-0.472340\pi$
$271$	1.54116e10	0.173574	0.0867871	+	0.996227i	$0.472340\pi$
$272$	4.37946e10	0.485133
$273$	2.03551e10	0.221790
$274$	−9.33596e7	−0.00100065
$275$	0	0
$276$	−3.58085e10	−0.371445
$277$	9.20867e10	0.939806	0.469903	−	0.882718i	$-0.344289\pi$
$277$	9.20867e10	0.939806	0.469903	+	0.882718i	$0.344289\pi$
$278$	7.12818e9	0.0715776
$279$	5.87070e10	0.580057
$280$	0	0
$281$	−7.78782e10	−0.745139	−0.372570	−	0.928004i	$-0.621523\pi$
$281$	−7.78782e10	−0.745139	−0.372570	+	0.928004i	$0.621523\pi$
$282$	3.88985e10	0.366279
$283$	−2.92463e10	−0.271039	−0.135520	−	0.990775i	$-0.543270\pi$
$283$	−2.92463e10	−0.271039	−0.135520	+	0.990775i	$0.543270\pi$
$284$	−9.52334e10	−0.868674
$285$	0	0
$286$	−4.72034e10	−0.417182
$287$	−4.50572e10	−0.392009
$288$	3.40203e10	0.291388
$289$	−5.42796e10	−0.457717
$290$	0	0
$291$	−9.71231e10	−0.793970
$292$	−6.47877e10	−0.521519
$293$	2.27403e11	1.80257	0.901285	−	0.433227i	$-0.142625\pi$
$293$	2.27403e11	1.80257	0.901285	+	0.433227i	$0.142625\pi$
$294$	−2.33155e10	−0.182005
$295$	0	0
$296$	1.17065e11	0.886368
$297$	2.35885e10	0.175912
$298$	3.89673e10	0.286238
$299$	−1.33771e11	−0.967927
$300$	0	0
$301$	2.34754e10	0.164840
$302$	2.49592e10	0.172663
$303$	−1.43439e11	−0.977632
$304$	1.47546e10	0.0990823
$305$	0	0
$306$	1.29548e10	0.0844668
$307$	6.02579e10	0.387160	0.193580	−	0.981084i	$-0.437990\pi$
$307$	6.02579e10	0.387160	0.193580	+	0.981084i	$0.437990\pi$
$308$	3.68613e10	0.233395
$309$	−2.45691e10	−0.153312
$310$	0	0
$311$	1.36816e11	0.829308	0.414654	−	0.909979i	$-0.363903\pi$
$311$	1.36816e11	0.829308	0.414654	+	0.909979i	$0.363903\pi$
$312$	8.29866e10	0.495807
$313$	−2.25535e11	−1.32820	−0.664101	−	0.747643i	$-0.731185\pi$
$313$	−2.25535e11	−1.32820	−0.664101	+	0.747643i	$0.731185\pi$
$314$	3.60839e9	0.0209474
$315$	0	0
$316$	2.05809e11	1.16111
$317$	1.28386e11	0.714089	0.357045	−	0.934087i	$-0.383784\pi$
$317$	1.28386e11	0.714089	0.357045	+	0.934087i	$0.383784\pi$
$318$	−3.59755e9	−0.0197281
$319$	1.14800e11	0.620701
$320$	0	0
$321$	1.58285e10	0.0832086
$322$	−1.40308e10	−0.0727328
$323$	2.16657e10	0.110755
$324$	−1.94302e10	−0.0979545
$325$	0	0
$326$	9.96239e10	0.488522
$327$	1.87510e11	0.906902
$328$	−1.83696e11	−0.876329
$329$	−1.13477e11	−0.533981
$330$	0	0
$331$	1.15018e10	0.0526673	0.0263337	−	0.999653i	$-0.491617\pi$
$331$	1.15018e10	0.0526673	0.0263337	+	0.999653i	$0.491617\pi$
$332$	−1.60286e11	−0.724058
$333$	−1.02394e11	−0.456324
$334$	1.44590e11	0.635740
$335$	0	0
$336$	−2.57372e10	−0.110163
$337$	2.79631e11	1.18100	0.590502	−	0.807036i	$-0.298930\pi$
$337$	2.79631e11	1.18100	0.590502	+	0.807036i	$0.298930\pi$
$338$	6.26843e10	0.261236
$339$	−1.06875e11	−0.439519
$340$	0	0
$341$	3.97159e11	1.59063
$342$	4.36454e9	0.0172513
$343$	1.42263e11	0.554969
$344$	9.57078e10	0.368497
$345$	0	0
$346$	−3.82107e10	−0.143332
$347$	−9.07088e10	−0.335867	−0.167933	−	0.985798i	$-0.553709\pi$
$347$	−9.07088e10	−0.335867	−0.167933	+	0.985798i	$0.553709\pi$
$348$	−9.45621e10	−0.345629
$349$	−3.98825e11	−1.43902	−0.719511	−	0.694481i	$-0.755634\pi$
$349$	−3.98825e11	−1.43902	−0.719511	+	0.694481i	$0.755634\pi$
$350$	0	0
$351$	−7.25862e10	−0.255254
$352$	2.30151e11	0.799044
$353$	4.56192e11	1.56373	0.781865	−	0.623448i	$-0.214269\pi$
$353$	4.56192e11	1.56373	0.781865	+	0.623448i	$0.214269\pi$
$354$	5.26684e10	0.178252
$355$	0	0
$356$	1.91627e11	0.632311
$357$	−3.77926e10	−0.123140
$358$	−1.00389e11	−0.323006
$359$	1.89176e11	0.601094	0.300547	−	0.953767i	$-0.402831\pi$
$359$	1.89176e11	0.601094	0.300547	+	0.953767i	$0.402831\pi$
$360$	0	0
$361$	−3.15388e11	−0.977380
$362$	2.07296e11	0.634458
$363$	−3.14152e10	−0.0949643
$364$	−1.13429e11	−0.338664
$365$	0	0
$366$	9.37339e10	0.273044
$367$	3.17920e10	0.0914787	0.0457394	−	0.998953i	$-0.485436\pi$
$367$	3.17920e10	0.0914787	0.0457394	+	0.998953i	$0.485436\pi$
$368$	1.69142e11	0.480769
$369$	1.60674e11	0.451156
$370$	0	0
$371$	1.04950e10	0.0287607
$372$	−3.27146e11	−0.885723
$373$	4.46388e11	1.19405	0.597025	−	0.802222i	$-0.296349\pi$
$373$	4.46388e11	1.19405	0.597025	+	0.802222i	$0.296349\pi$
$374$	8.76409e10	0.231625
$375$	0	0
$376$	−4.62639e11	−1.19371
$377$	−3.53260e11	−0.900655
$378$	−7.61330e9	−0.0191805
$379$	3.53467e11	0.879978	0.439989	−	0.898003i	$-0.354982\pi$
$379$	3.53467e11	0.879978	0.439989	+	0.898003i	$0.354982\pi$
$380$	0	0
$381$	−2.58357e11	−0.628143
$382$	−2.12411e11	−0.510377
$383$	−3.14974e11	−0.747963	−0.373981	−	0.927436i	$-0.622008\pi$
$383$	−3.14974e11	−0.747963	−0.373981	+	0.927436i	$0.622008\pi$
$384$	−2.45345e11	−0.575820
$385$	0	0
$386$	7.51718e10	0.172350
$387$	−8.37131e10	−0.189712
$388$	5.41220e11	1.21236
$389$	−4.20729e11	−0.931600	−0.465800	−	0.884890i	$-0.654233\pi$
$389$	−4.20729e11	−0.931600	−0.465800	+	0.884890i	$0.654233\pi$
$390$	0	0
$391$	2.48369e11	0.537405
$392$	2.77303e11	0.593155
$393$	−4.37493e11	−0.925134
$394$	−9.42843e10	−0.197109
$395$	0	0
$396$	−1.31447e11	−0.268611
$397$	−5.63093e11	−1.13769	−0.568844	−	0.822446i	$-0.692609\pi$
$397$	−5.63093e11	−1.13769	−0.568844	+	0.822446i	$0.692609\pi$
$398$	1.47737e11	0.295132
$399$	−1.27325e10	−0.0251498
$400$	0	0
$401$	2.75897e11	0.532841	0.266420	−	0.963857i	$-0.414159\pi$
$401$	2.75897e11	0.532841	0.266420	+	0.963857i	$0.414159\pi$
$402$	1.05957e11	0.202355
$403$	−1.22213e12	−2.30805
$404$	7.99317e11	1.49280
$405$	0	0
$406$	−3.70521e10	−0.0676778
$407$	−6.92703e11	−1.25133
$408$	−1.54079e11	−0.275278
$409$	−6.54552e10	−0.115662	−0.0578308	−	0.998326i	$-0.518418\pi$
$409$	−6.54552e10	−0.115662	−0.0578308	+	0.998326i	$0.518418\pi$
$410$	0	0
$411$	−9.71214e8	−0.00167891
$412$	1.36912e11	0.234101
$413$	−1.53647e11	−0.259866
$414$	5.00337e10	0.0837069
$415$	0	0
$416$	−7.08218e11	−1.15944
$417$	7.41541e10	0.120094
$418$	2.95266e10	0.0473064
$419$	2.70250e10	0.0428354	0.0214177	−	0.999771i	$-0.493182\pi$
$419$	2.70250e10	0.0428354	0.0214177	+	0.999771i	$0.493182\pi$
$420$	0	0
$421$	−4.29698e11	−0.666644	−0.333322	−	0.942813i	$-0.608170\pi$
$421$	−4.29698e11	−0.666644	−0.333322	+	0.942813i	$0.608170\pi$
$422$	−6.94478e10	−0.106599
$423$	4.04659e11	0.614550
$424$	4.27875e10	0.0642940
$425$	0	0
$426$	1.33066e11	0.195760
$427$	−2.73446e11	−0.398058
$428$	−8.82048e10	−0.127056
$429$	−4.91054e11	−0.699957
$430$	0	0
$431$	−9.44700e11	−1.31870	−0.659350	−	0.751836i	$-0.729169\pi$
$431$	−9.44700e11	−1.31870	−0.659350	+	0.751836i	$0.729169\pi$
$432$	9.17789e10	0.126784
$433$	−2.10762e11	−0.288136	−0.144068	−	0.989568i	$-0.546018\pi$
$433$	−2.10762e11	−0.288136	−0.144068	+	0.989568i	$0.546018\pi$
$434$	−1.28185e11	−0.173434
$435$	0	0
$436$	−1.04491e12	−1.38480
$437$	8.36765e10	0.109758
$438$	9.05253e10	0.117527
$439$	7.69079e11	0.988282	0.494141	−	0.869382i	$-0.335483\pi$
$439$	7.69079e11	0.988282	0.494141	+	0.869382i	$0.335483\pi$
$440$	0	0
$441$	−2.42550e11	−0.305371
$442$	−2.69688e11	−0.336094
$443$	6.49894e11	0.801726	0.400863	−	0.916138i	$-0.368710\pi$
$443$	6.49894e11	0.801726	0.400863	+	0.916138i	$0.368710\pi$
$444$	5.70590e11	0.696788
$445$	0	0
$446$	3.44741e11	0.412559
$447$	4.05374e11	0.480255
$448$	8.84023e10	0.103684
$449$	−4.51858e11	−0.524679	−0.262339	−	0.964976i	$-0.584494\pi$
$449$	−4.51858e11	−0.524679	−0.262339	+	0.964976i	$0.584494\pi$
$450$	0	0
$451$	1.08698e12	1.23716
$452$	5.95564e11	0.671128
$453$	2.59649e11	0.289697
$454$	4.20493e11	0.464523
$455$	0	0
$456$	−5.19097e10	−0.0562220
$457$	6.18434e11	0.663240	0.331620	−	0.943413i	$-0.392405\pi$
$457$	6.18434e11	0.663240	0.331620	+	0.943413i	$0.392405\pi$
$458$	4.51798e10	0.0479788
$459$	1.34768e11	0.141720
$460$	0	0
$461$	−2.76450e11	−0.285078	−0.142539	−	0.989789i	$-0.545527\pi$
$461$	−2.76450e11	−0.285078	−0.142539	+	0.989789i	$0.545527\pi$
$462$	−5.15048e10	−0.0525967
$463$	−6.09969e11	−0.616870	−0.308435	−	0.951245i	$-0.599805\pi$
$463$	−6.09969e11	−0.616870	−0.308435	+	0.951245i	$0.599805\pi$
$464$	4.46666e11	0.447355
$465$	0	0
$466$	−4.21910e11	−0.414461
$467$	−2.83260e11	−0.275587	−0.137794	−	0.990461i	$-0.544001\pi$
$467$	−2.83260e11	−0.275587	−0.137794	+	0.990461i	$0.544001\pi$
$468$	4.04488e11	0.389762
$469$	−3.09104e11	−0.295004
$470$	0	0
$471$	3.75378e10	0.0351459
$472$	−6.26412e11	−0.580926
$473$	−5.66328e11	−0.520227
$474$	−2.87568e11	−0.261661
$475$	0	0
$476$	2.10600e11	0.188030
$477$	−3.74251e10	−0.0331002
$478$	6.16485e11	0.540129
$479$	−1.39149e12	−1.20773	−0.603865	−	0.797087i	$-0.706373\pi$
$479$	−1.39149e12	−1.20773	−0.603865	+	0.797087i	$0.706373\pi$
$480$	0	0
$481$	2.13158e12	1.81572
$482$	−4.78793e11	−0.404051
$483$	−1.45961e11	−0.122033
$484$	1.75062e11	0.145007
$485$	0	0
$486$	2.71490e10	0.0220745
$487$	1.41532e11	0.114018	0.0570092	−	0.998374i	$-0.481844\pi$
$487$	1.41532e11	0.114018	0.0570092	+	0.998374i	$0.481844\pi$
$488$	−1.11483e12	−0.889851
$489$	1.03638e12	0.819652
$490$	0	0
$491$	−4.66246e11	−0.362034	−0.181017	−	0.983480i	$-0.557939\pi$
$491$	−4.66246e11	−0.362034	−0.181017	+	0.983480i	$0.557939\pi$
$492$	−8.95359e11	−0.688897
$493$	6.55887e11	0.500055
$494$	−9.08589e10	−0.0686430
$495$	0	0
$496$	1.54528e12	1.14641
$497$	−3.88188e11	−0.285389
$498$	2.23961e11	0.163170
$499$	−2.21254e12	−1.59749	−0.798746	−	0.601668i	$-0.794503\pi$
$499$	−2.21254e12	−1.59749	−0.798746	+	0.601668i	$0.794503\pi$
$500$	0	0
$501$	1.50416e12	1.06666
$502$	2.25271e11	0.158321
$503$	−3.39574e11	−0.236526	−0.118263	−	0.992982i	$-0.537733\pi$
$503$	−3.39574e11	−0.236526	−0.118263	+	0.992982i	$0.537733\pi$
$504$	9.05488e10	0.0625094
$505$	0	0
$506$	3.38484e11	0.229541
$507$	6.52101e11	0.438308
$508$	1.43970e12	0.959149
$509$	−5.66691e11	−0.374211	−0.187106	−	0.982340i	$-0.559911\pi$
$509$	−5.66691e11	−0.374211	−0.187106	+	0.982340i	$0.559911\pi$
$510$	0	0
$511$	−2.64086e11	−0.171337
$512$	1.55874e12	1.00244
$513$	4.54040e10	0.0289445
$514$	−9.52947e11	−0.602191
$515$	0	0
$516$	4.66493e11	0.289682
$517$	2.73756e12	1.68522
$518$	2.23574e11	0.136438
$519$	−3.97504e11	−0.240485
$520$	0	0
$521$	4.42970e11	0.263393	0.131697	−	0.991290i	$-0.457958\pi$
$521$	4.42970e11	0.263393	0.131697	+	0.991290i	$0.457958\pi$
$522$	1.32128e11	0.0778892
$523$	1.44683e11	0.0845591	0.0422796	−	0.999106i	$-0.486538\pi$
$523$	1.44683e11	0.0845591	0.0422796	+	0.999106i	$0.486538\pi$
$524$	2.43794e12	1.41264
$525$	0	0
$526$	4.86557e11	0.277139
$527$	2.26910e12	1.28146
$528$	6.20894e11	0.347668
$529$	−8.41911e11	−0.467429
$530$	0	0
$531$	5.47906e11	0.299075
$532$	7.09520e10	0.0384028
$533$	−3.34484e12	−1.79516
$534$	−2.67752e11	−0.142494
$535$	0	0
$536$	−1.26020e12	−0.659475
$537$	−1.04434e12	−0.541946
$538$	9.90519e11	0.509733
$539$	−1.64088e12	−0.837388
$540$	0	0
$541$	−3.10308e11	−0.155742	−0.0778710	−	0.996963i	$-0.524812\pi$
$541$	−3.10308e11	−0.155742	−0.0778710	+	0.996963i	$0.524812\pi$
$542$	1.19999e11	0.0597281
$543$	2.15649e12	1.06451
$544$	1.31493e12	0.643733
$545$	0	0
$546$	1.58490e11	0.0763194
$547$	−1.68502e12	−0.804750	−0.402375	−	0.915475i	$-0.631815\pi$
$547$	−1.68502e12	−0.804750	−0.402375	+	0.915475i	$0.631815\pi$
$548$	5.41211e9	0.00256362
$549$	9.75108e11	0.458118
$550$	0	0
$551$	2.20971e11	0.102130
$552$	−5.95077e11	−0.272802
$553$	8.38911e11	0.381463
$554$	7.17011e11	0.323394
$555$	0	0
$556$	−4.13225e11	−0.183379
$557$	2.31328e12	1.01831	0.509156	−	0.860674i	$-0.329958\pi$
$557$	2.31328e12	1.01831	0.509156	+	0.860674i	$0.329958\pi$
$558$	4.57108e11	0.199602
$559$	1.74270e12	0.754865
$560$	0	0
$561$	9.11723e11	0.388624
$562$	−6.06380e11	−0.256408
$563$	−7.03648e11	−0.295167	−0.147583	−	0.989050i	$-0.547150\pi$
$563$	−7.03648e11	−0.295167	−0.147583	+	0.989050i	$0.547150\pi$
$564$	−2.25497e12	−0.938392
$565$	0	0
$566$	−2.27720e11	−0.0932666
$567$	−7.92007e10	−0.0321814
$568$	−1.58262e12	−0.637983
$569$	3.21997e12	1.28779	0.643896	−	0.765113i	$-0.277317\pi$
$569$	3.21997e12	1.28779	0.643896	+	0.765113i	$0.277317\pi$
$570$	0	0
$571$	−1.21116e12	−0.476801	−0.238401	−	0.971167i	$-0.576623\pi$
$571$	−1.21116e12	−0.476801	−0.238401	+	0.971167i	$0.576623\pi$
$572$	2.73641e12	1.06880
$573$	−2.20969e12	−0.856320
$574$	−3.50827e11	−0.134893
$575$	0	0
$576$	−3.15242e11	−0.119328
$577$	−7.30673e11	−0.274430	−0.137215	−	0.990541i	$-0.543815\pi$
$577$	−7.30673e11	−0.274430	−0.137215	+	0.990541i	$0.543815\pi$
$578$	−4.22635e11	−0.157504
$579$	7.82008e11	0.289173
$580$	0	0
$581$	−6.53352e11	−0.237878
$582$	−7.56226e11	−0.273211
$583$	−2.53185e11	−0.0907673
$584$	−1.07666e12	−0.383021
$585$	0	0
$586$	1.77062e12	0.620278
$587$	−4.55331e12	−1.58291	−0.791453	−	0.611230i	$-0.790675\pi$
$587$	−4.55331e12	−1.58291	−0.791453	+	0.611230i	$0.790675\pi$
$588$	1.35162e12	0.466289
$589$	7.64467e11	0.261722
$590$	0	0
$591$	−9.80833e11	−0.330713
$592$	−2.69520e12	−0.901867
$593$	−3.00074e12	−0.996510	−0.498255	−	0.867030i	$-0.666026\pi$
$593$	−3.00074e12	−0.996510	−0.498255	+	0.867030i	$0.666026\pi$
$594$	1.83666e11	0.0605327
$595$	0	0
$596$	−2.25896e12	−0.733330
$597$	1.53690e12	0.495178
$598$	−1.04158e12	−0.333071
$599$	−4.03514e12	−1.28067	−0.640336	−	0.768095i	$-0.721205\pi$
$599$	−4.03514e12	−1.28067	−0.640336	+	0.768095i	$0.721205\pi$
$600$	0	0
$601$	2.04760e12	0.640192	0.320096	−	0.947385i	$-0.396285\pi$
$601$	2.04760e12	0.640192	0.320096	+	0.947385i	$0.396285\pi$
$602$	1.82785e11	0.0567227
$603$	1.10227e12	0.339514
$604$	−1.44690e12	−0.442355
$605$	0	0
$606$	−1.11685e12	−0.336410
$607$	−3.15792e12	−0.944175	−0.472088	−	0.881552i	$-0.656499\pi$
$607$	−3.15792e12	−0.944175	−0.472088	+	0.881552i	$0.656499\pi$
$608$	4.43004e11	0.131474
$609$	−3.85451e11	−0.113551
$610$	0	0
$611$	−8.42399e12	−2.44530
$612$	−7.51000e11	−0.216401
$613$	2.89302e12	0.827520	0.413760	−	0.910386i	$-0.364215\pi$
$613$	2.89302e12	0.827520	0.413760	+	0.910386i	$0.364215\pi$
$614$	4.69183e11	0.133225
$615$	0	0
$616$	6.12573e11	0.171413
$617$	−6.03603e12	−1.67675	−0.838375	−	0.545094i	$-0.816494\pi$
$617$	−6.03603e12	−1.67675	−0.838375	+	0.545094i	$0.816494\pi$
$618$	−1.91301e11	−0.0527558
$619$	4.05606e12	1.11044	0.555222	−	0.831702i	$-0.312633\pi$
$619$	4.05606e12	1.11044	0.555222	+	0.831702i	$0.312633\pi$
$620$	0	0
$621$	5.20498e11	0.140445
$622$	1.06529e12	0.285371
$623$	7.81102e11	0.207736
$624$	−1.91061e12	−0.504477
$625$	0	0
$626$	−1.75607e12	−0.457044
$627$	3.07163e11	0.0793716
$628$	−2.09180e11	−0.0536664
$629$	−3.95764e12	−1.00811
$630$	0	0
$631$	−5.34498e12	−1.34219	−0.671095	−	0.741372i	$-0.734176\pi$
$631$	−5.34498e12	−1.34219	−0.671095	+	0.741372i	$0.734176\pi$
$632$	3.42020e12	0.852755
$633$	−7.22461e11	−0.178854
$634$	9.99651e11	0.245723
$635$	0	0
$636$	2.08552e11	0.0505426
$637$	5.04929e12	1.21507
$638$	8.93859e11	0.213588
$639$	1.38428e12	0.328450
$640$	0	0
$641$	4.81739e12	1.12707	0.563534	−	0.826093i	$-0.309441\pi$
$641$	4.81739e12	1.12707	0.563534	+	0.826093i	$0.309441\pi$
$642$	1.23245e11	0.0286327
$643$	5.85505e11	0.135077	0.0675385	−	0.997717i	$-0.478485\pi$
$643$	5.85505e11	0.135077	0.0675385	+	0.997717i	$0.478485\pi$
$644$	8.13372e11	0.186339
$645$	0	0
$646$	1.68695e11	0.0381114
$647$	−4.54903e12	−1.02059	−0.510293	−	0.860001i	$-0.670463\pi$
$647$	−4.54903e12	−1.02059	−0.510293	+	0.860001i	$0.670463\pi$
$648$	−3.22897e11	−0.0719410
$649$	3.70664e12	0.820124
$650$	0	0
$651$	−1.33350e12	−0.290991
$652$	−5.77526e12	−1.25158
$653$	7.04350e12	1.51593	0.757965	−	0.652295i	$-0.226194\pi$
$653$	7.04350e12	1.51593	0.757965	+	0.652295i	$0.226194\pi$
$654$	1.46001e12	0.312072
$655$	0	0
$656$	4.22925e12	0.891653
$657$	9.41729e11	0.197189
$658$	−8.83561e11	−0.183747
$659$	5.23559e12	1.08139	0.540694	−	0.841219i	$-0.318162\pi$
$659$	5.23559e12	1.08139	0.540694	+	0.841219i	$0.318162\pi$
$660$	0	0
$661$	−5.79017e12	−1.17974	−0.589868	−	0.807500i	$-0.700820\pi$
$661$	−5.79017e12	−1.17974	−0.589868	+	0.807500i	$0.700820\pi$
$662$	8.95563e10	0.0181232
$663$	−2.80555e12	−0.563906
$664$	−2.66368e12	−0.531772
$665$	0	0
$666$	−7.97263e11	−0.157025
$667$	2.53314e12	0.495557
$668$	−8.38197e12	−1.62874
$669$	3.58632e12	0.692199
$670$	0	0
$671$	6.59671e12	1.25625
$672$	−7.72755e11	−0.146177
$673$	5.92328e10	0.0111300	0.00556499	−	0.999985i	$-0.498229\pi$
$673$	5.92328e10	0.0111300	0.00556499	+	0.999985i	$0.498229\pi$
$674$	2.17728e12	0.406392
$675$	0	0
$676$	−3.63385e12	−0.669278
$677$	−4.57177e12	−0.836440	−0.418220	−	0.908346i	$-0.637346\pi$
$677$	−4.57177e12	−0.836440	−0.418220	+	0.908346i	$0.637346\pi$
$678$	−8.32157e11	−0.151242
$679$	2.20611e12	0.398302
$680$	0	0
$681$	4.37436e12	0.779386
$682$	3.09238e12	0.547348
$683$	9.71286e12	1.70787	0.853934	−	0.520382i	$-0.174210\pi$
$683$	9.71286e12	1.70787	0.853934	+	0.520382i	$0.174210\pi$
$684$	−2.53015e11	−0.0441971
$685$	0	0
$686$	1.10770e12	0.190969
$687$	4.70003e11	0.0804998
$688$	−2.20349e12	−0.374941
$689$	7.79098e11	0.131706
$690$	0	0
$691$	2.23726e12	0.373306	0.186653	−	0.982426i	$-0.440236\pi$
$691$	2.23726e12	0.373306	0.186653	+	0.982426i	$0.440236\pi$
$692$	2.21510e12	0.367211
$693$	−5.35801e11	−0.0882478
$694$	−7.06282e11	−0.115574
$695$	0	0
$696$	−1.57146e12	−0.253842
$697$	6.21025e12	0.996693
$698$	−3.10535e12	−0.495178
$699$	−4.38911e12	−0.695391
$700$	0	0
$701$	−2.29477e10	−0.00358929	−0.00179464	−	0.999998i	$-0.500571\pi$
$701$	−2.29477e10	−0.00358929	−0.00179464	+	0.999998i	$0.500571\pi$
$702$	−5.65175e11	−0.0878347
$703$	−1.33334e12	−0.205894
$704$	−2.13265e12	−0.327222
$705$	0	0
$706$	3.55203e12	0.538091
$707$	3.25815e12	0.490438
$708$	−3.05322e12	−0.456676
$709$	−9.57637e12	−1.42329	−0.711644	−	0.702540i	$-0.752049\pi$
$709$	−9.57637e12	−1.42329	−0.711644	+	0.702540i	$0.752049\pi$
$710$	0	0
$711$	−2.99156e12	−0.439020
$712$	3.18451e12	0.464390
$713$	8.76362e12	1.26993
$714$	−2.94263e11	−0.0423735
$715$	0	0
$716$	5.81959e12	0.827529
$717$	6.41326e12	0.906239
$718$	1.47298e12	0.206841
$719$	−5.46390e12	−0.762469	−0.381235	−	0.924478i	$-0.624501\pi$
$719$	−5.46390e12	−0.762469	−0.381235	+	0.924478i	$0.624501\pi$
$720$	0	0
$721$	5.58075e11	0.0769102
$722$	−2.45570e12	−0.336324
$723$	−4.98085e12	−0.677925
$724$	−1.20171e13	−1.62546
$725$	0	0
$726$	−2.44607e11	−0.0326779
$727$	−6.59842e12	−0.876062	−0.438031	−	0.898960i	$-0.644324\pi$
$727$	−6.59842e12	−0.876062	−0.438031	+	0.898960i	$0.644324\pi$
$728$	−1.88500e12	−0.248726
$729$	2.82430e11	0.0370370
$730$	0	0
$731$	−3.23561e12	−0.419111
$732$	−5.43381e12	−0.699527
$733$	−6.91041e11	−0.0884170	−0.0442085	−	0.999022i	$-0.514077\pi$
$733$	−6.91041e11	−0.0884170	−0.0442085	+	0.999022i	$0.514077\pi$
$734$	2.47541e11	0.0314785
$735$	0	0
$736$	5.07846e12	0.637943
$737$	7.45694e12	0.931016
$738$	1.25105e12	0.155246
$739$	7.60189e12	0.937608	0.468804	−	0.883302i	$-0.344685\pi$
$739$	7.60189e12	0.937608	0.468804	+	0.883302i	$0.344685\pi$
$740$	0	0
$741$	−9.45200e11	−0.115171
$742$	8.17167e10	0.00989677
$743$	2.23002e12	0.268448	0.134224	−	0.990951i	$-0.457146\pi$
$743$	2.23002e12	0.268448	0.134224	+	0.990951i	$0.457146\pi$
$744$	−5.43661e12	−0.650504
$745$	0	0
$746$	3.47569e12	0.410882
$747$	2.32985e12	0.273770
$748$	−5.08060e12	−0.593414
$749$	−3.59538e11	−0.0417423
$750$	0	0
$751$	1.65708e12	0.190092	0.0950459	−	0.995473i	$-0.469700\pi$
$751$	1.65708e12	0.190092	0.0950459	+	0.995473i	$0.469700\pi$
$752$	1.06514e13	1.21458
$753$	2.34348e12	0.265635
$754$	−2.75058e12	−0.309922
$755$	0	0
$756$	4.41347e11	0.0491397
$757$	1.28420e13	1.42135	0.710675	−	0.703521i	$-0.248390\pi$
$757$	1.28420e13	1.42135	0.710675	+	0.703521i	$0.248390\pi$
$758$	2.75218e12	0.302807
$759$	3.52122e12	0.385129
$760$	0	0
$761$	1.61852e13	1.74939	0.874694	−	0.484676i	$-0.161063\pi$
$761$	1.61852e13	1.74939	0.874694	+	0.484676i	$0.161063\pi$
$762$	−2.01164e12	−0.216149
$763$	−4.25921e12	−0.454955
$764$	1.23136e13	1.30757
$765$	0	0
$766$	−2.45247e12	−0.257380
$767$	−1.14060e13	−1.19002
$768$	8.23228e10	0.00853875
$769$	5.30462e12	0.546998	0.273499	−	0.961872i	$-0.411819\pi$
$769$	5.30462e12	0.546998	0.273499	+	0.961872i	$0.411819\pi$
$770$	0	0
$771$	−9.91345e12	−1.01037
$772$	−4.35775e12	−0.441555
$773$	1.26188e13	1.27119	0.635596	−	0.772022i	$-0.280755\pi$
$773$	1.26188e13	1.27119	0.635596	+	0.772022i	$0.280755\pi$
$774$	−6.51812e11	−0.0652812
$775$	0	0
$776$	8.99418e12	0.890397
$777$	2.32582e12	0.228919
$778$	−3.27591e12	−0.320571
$779$	2.09226e12	0.203562
$780$	0	0
$781$	9.36478e12	0.900675
$782$	1.93387e12	0.184925
$783$	1.37452e12	0.130684
$784$	−6.38438e12	−0.603527
$785$	0	0
$786$	−3.40644e12	−0.318346
$787$	−1.22887e13	−1.14188	−0.570941	−	0.820991i	$-0.693421\pi$
$787$	−1.22887e13	−1.14188	−0.570941	+	0.820991i	$0.693421\pi$
$788$	5.46571e12	0.504985
$789$	5.06162e12	0.464990
$790$	0	0
$791$	2.42762e12	0.220489
$792$	−2.18443e12	−0.197277
$793$	−2.02993e13	−1.82286
$794$	−4.38439e12	−0.391487
$795$	0	0
$796$	−8.56441e12	−0.756116
$797$	3.56495e12	0.312962	0.156481	−	0.987681i	$-0.449985\pi$
$797$	3.56495e12	0.312962	0.156481	+	0.987681i	$0.449985\pi$
$798$	−9.91385e10	−0.00865425
$799$	1.56405e13	1.35766
$800$	0	0
$801$	−2.78541e12	−0.239080
$802$	2.14821e12	0.183354
$803$	6.37090e12	0.540730
$804$	−6.14240e12	−0.518425
$805$	0	0
$806$	−9.51585e12	−0.794218
$807$	1.03043e13	0.855239
$808$	1.32833e13	1.09636
$809$	−3.11624e12	−0.255778	−0.127889	−	0.991789i	$-0.540820\pi$
$809$	−3.11624e12	−0.255778	−0.127889	+	0.991789i	$0.540820\pi$
$810$	0	0
$811$	−2.30256e12	−0.186904	−0.0934518	−	0.995624i	$-0.529790\pi$
$811$	−2.30256e12	−0.186904	−0.0934518	+	0.995624i	$0.529790\pi$
$812$	2.14793e12	0.173388
$813$	1.24834e12	0.100213
$814$	−5.39357e12	−0.430593
$815$	0	0
$816$	3.54737e12	0.280092
$817$	−1.09009e12	−0.0855980
$818$	−5.09651e11	−0.0398000
$819$	1.64876e12	0.128050
$820$	0	0
$821$	−6.28720e12	−0.482962	−0.241481	−	0.970406i	$-0.577633\pi$
$821$	−6.28720e12	−0.482962	−0.241481	+	0.970406i	$0.577633\pi$
$822$	−7.56212e9	−0.000577724 0
$823$	−3.76056e12	−0.285728	−0.142864	−	0.989742i	$-0.545631\pi$
$823$	−3.76056e12	−0.285728	−0.142864	+	0.989742i	$0.545631\pi$
$824$	2.27524e12	0.171932
$825$	0	0
$826$	−1.19634e12	−0.0894219
$827$	−1.75054e13	−1.30136	−0.650679	−	0.759353i	$-0.725516\pi$
$827$	−1.75054e13	−1.30136	−0.650679	+	0.759353i	$0.725516\pi$
$828$	−2.90049e12	−0.214454
$829$	−2.42570e12	−0.178378	−0.0891891	−	0.996015i	$-0.528428\pi$
$829$	−2.42570e12	−0.178378	−0.0891891	+	0.996015i	$0.528428\pi$
$830$	0	0
$831$	7.45902e12	0.542597
$832$	6.56257e12	0.474809
$833$	−9.37486e12	−0.674625
$834$	5.77383e11	0.0413254
$835$	0	0
$836$	−1.71167e12	−0.121197
$837$	4.75526e12	0.334896
$838$	2.10424e11	0.0147400
$839$	9.69596e11	0.0675557	0.0337778	−	0.999429i	$-0.489246\pi$
$839$	9.69596e11	0.0675557	0.0337778	+	0.999429i	$0.489246\pi$
$840$	0	0
$841$	−7.81769e12	−0.538885
$842$	−3.34574e12	−0.229397
$843$	−6.30813e12	−0.430206
$844$	4.02593e12	0.273102
$845$	0	0
$846$	3.15078e12	0.211471
$847$	7.13582e11	0.0476397
$848$	−9.85101e11	−0.0654183
$849$	−2.36895e12	−0.156485
$850$	0	0
$851$	−1.52850e13	−0.999042
$852$	−7.71391e12	−0.501529
$853$	2.11898e13	1.37043	0.685215	−	0.728340i	$-0.259708\pi$
$853$	2.11898e13	1.37043	0.685215	+	0.728340i	$0.259708\pi$
$854$	−2.12912e12	−0.136975
$855$	0	0
$856$	−1.46582e12	−0.0933142
$857$	−8.34904e12	−0.528717	−0.264358	−	0.964425i	$-0.585160\pi$
$857$	−8.34904e12	−0.528717	−0.264358	+	0.964425i	$0.585160\pi$
$858$	−3.82347e12	−0.240860
$859$	−8.24621e12	−0.516755	−0.258378	−	0.966044i	$-0.583188\pi$
$859$	−8.24621e12	−0.516755	−0.258378	+	0.966044i	$0.583188\pi$
$860$	0	0
$861$	−3.64964e12	−0.226326
$862$	−7.35568e12	−0.453775
$863$	−4.35663e12	−0.267364	−0.133682	−	0.991024i	$-0.542680\pi$
$863$	−4.35663e12	−0.267364	−0.133682	+	0.991024i	$0.542680\pi$
$864$	2.75564e12	0.168233
$865$	0	0
$866$	−1.64105e12	−0.0991497
$867$	−4.39665e12	−0.264263
$868$	7.43096e12	0.444331
$869$	−2.02382e13	−1.20388
$870$	0	0
$871$	−2.29464e13	−1.35093
$872$	−1.73646e13	−1.01705
$873$	−7.86697e12	−0.458399
$874$	6.51527e11	0.0377686
$875$	0	0
$876$	−5.24780e12	−0.301099
$877$	1.21873e12	0.0695680	0.0347840	−	0.999395i	$-0.488926\pi$
$877$	1.21873e12	0.0695680	0.0347840	+	0.999395i	$0.488926\pi$
$878$	5.98825e12	0.340075
$879$	1.84197e13	1.04071
$880$	0	0
$881$	3.98577e12	0.222905	0.111453	−	0.993770i	$-0.464450\pi$
$881$	3.98577e12	0.222905	0.111453	+	0.993770i	$0.464450\pi$
$882$	−1.88856e12	−0.105080
$883$	−2.19963e13	−1.21766	−0.608831	−	0.793300i	$-0.708361\pi$
$883$	−2.19963e13	−1.21766	−0.608831	+	0.793300i	$0.708361\pi$
$884$	1.56340e13	0.861061
$885$	0	0
$886$	5.06025e12	0.275880
$887$	−1.39860e13	−0.758640	−0.379320	−	0.925266i	$-0.623842\pi$
$887$	−1.39860e13	−0.758640	−0.379320	+	0.925266i	$0.623842\pi$
$888$	9.48226e12	0.511745
$889$	5.86847e12	0.315113
$890$	0	0
$891$	1.91067e12	0.101563
$892$	−1.99848e13	−1.05696
$893$	5.26936e12	0.277285
$894$	3.15635e12	0.165259
$895$	0	0
$896$	5.57290e12	0.288865
$897$	−1.08355e13	−0.558833
$898$	−3.51829e12	−0.180546
$899$	2.31428e13	1.18167
$900$	0	0
$901$	−1.44653e12	−0.0731248
$902$	8.46349e12	0.425716
$903$	1.90150e12	0.0951705
$904$	9.89727e12	0.492899
$905$	0	0
$906$	2.02169e12	0.0996869
$907$	8.00749e12	0.392884	0.196442	−	0.980515i	$-0.437061\pi$
$907$	8.00749e12	0.392884	0.196442	+	0.980515i	$0.437061\pi$
$908$	−2.43762e13	−1.19009
$909$	−1.16186e13	−0.564436
$910$	0	0
$911$	−4.09248e13	−1.96858	−0.984291	−	0.176555i	$-0.943505\pi$
$911$	−4.09248e13	−1.96858	−0.984291	+	0.176555i	$0.943505\pi$
$912$	1.19512e12	0.0572052
$913$	1.57617e13	0.750731
$914$	4.81529e12	0.228226
$915$	0	0
$916$	−2.61910e12	−0.122920
$917$	9.93745e12	0.464102
$918$	1.04934e12	0.0487669
$919$	8.12730e12	0.375860	0.187930	−	0.982182i	$-0.439822\pi$
$919$	8.12730e12	0.375860	0.187930	+	0.982182i	$0.439822\pi$
$920$	0	0
$921$	4.88089e12	0.223527
$922$	−2.15252e12	−0.0980973
$923$	−2.88172e13	−1.30691
$924$	2.98576e12	0.134751
$925$	0	0
$926$	−4.74938e12	−0.212269
$927$	−1.99010e12	−0.0885147
$928$	1.34111e13	0.593605
$929$	−4.43436e13	−1.95326	−0.976631	−	0.214923i	$-0.931050\pi$
$929$	−4.43436e13	−1.95326	−0.976631	+	0.214923i	$0.931050\pi$
$930$	0	0
$931$	−3.15843e12	−0.137783
$932$	2.44584e13	1.06183
$933$	1.10821e13	0.478801
$934$	−2.20554e12	−0.0948317
$935$	0	0
$936$	6.72192e12	0.286254
$937$	3.56882e13	1.51250	0.756251	−	0.654281i	$-0.227029\pi$
$937$	3.56882e13	1.51250	0.756251	+	0.654281i	$0.227029\pi$
$938$	−2.40677e12	−0.101513
$939$	−1.82683e13	−0.766838
$940$	0	0
$941$	3.76351e13	1.56473	0.782366	−	0.622818i	$-0.214012\pi$
$941$	3.76351e13	1.56473	0.782366	+	0.622818i	$0.214012\pi$
$942$	2.92279e11	0.0120940
$943$	2.39850e13	0.987727
$944$	1.44219e13	0.591085
$945$	0	0
$946$	−4.40958e12	−0.179014
$947$	1.01014e13	0.408139	0.204070	−	0.978956i	$-0.434583\pi$
$947$	1.01014e13	0.408139	0.204070	+	0.978956i	$0.434583\pi$
$948$	1.66705e13	0.670365
$949$	−1.96045e13	−0.784616
$950$	0	0
$951$	1.03993e13	0.412280
$952$	3.49982e12	0.138096
$953$	−1.49469e13	−0.586993	−0.293497	−	0.955960i	$-0.594819\pi$
$953$	−1.49469e13	−0.586993	−0.293497	+	0.955960i	$0.594819\pi$
$954$	−2.91402e11	−0.0113900
$955$	0	0
$956$	−3.57380e13	−1.38379
$957$	9.29876e12	0.358362
$958$	−1.08345e13	−0.415589
$959$	2.20607e10	0.000842238 0
$960$	0	0
$961$	5.36247e13	2.02819
$962$	1.65970e13	0.624803
$963$	1.28211e12	0.0480405
$964$	2.77559e13	1.03516
$965$	0	0
$966$	−1.13649e12	−0.0419923
$967$	−2.42942e13	−0.893475	−0.446738	−	0.894665i	$-0.647414\pi$
$967$	−2.42942e13	−0.893475	−0.446738	+	0.894665i	$0.647414\pi$
$968$	2.90924e12	0.106498
$969$	1.75492e12	0.0639441
$970$	0	0
$971$	−1.07032e13	−0.386392	−0.193196	−	0.981160i	$-0.561885\pi$
$971$	−1.07032e13	−0.386392	−0.193196	+	0.981160i	$0.561885\pi$
$972$	−1.57384e12	−0.0565540
$973$	−1.68437e12	−0.0602464
$974$	1.10201e12	0.0392346
$975$	0	0
$976$	2.56667e13	0.905412
$977$	1.53038e13	0.537372	0.268686	−	0.963228i	$-0.413411\pi$
$977$	1.53038e13	0.537372	0.268686	+	0.963228i	$0.413411\pi$
$978$	8.06954e12	0.282048
$979$	−1.88436e13	−0.655604
$980$	0	0
$981$	1.51883e13	0.523600
$982$	−3.63032e12	−0.124578
$983$	−3.27251e13	−1.11787	−0.558934	−	0.829212i	$-0.688790\pi$
$983$	−3.27251e13	−1.11787	−0.558934	+	0.829212i	$0.688790\pi$
$984$	−1.48794e13	−0.505949
$985$	0	0
$986$	5.10691e12	0.172073
$987$	−9.19163e12	−0.308294
$988$	5.26714e12	0.175861
$989$	−1.24965e13	−0.415340
$990$	0	0
$991$	3.05488e13	1.00615	0.503075	−	0.864243i	$-0.332202\pi$
$991$	3.05488e13	1.00615	0.503075	+	0.864243i	$0.332202\pi$
$992$	4.63967e13	1.52119
$993$	9.31649e11	0.0304075
$994$	−3.02253e12	−0.0982046
$995$	0	0
$996$	−1.29831e13	−0.418035
$997$	−4.87857e13	−1.56374	−0.781870	−	0.623441i	$-0.785734\pi$
$997$	−4.87857e13	−1.56374	−0.781870	+	0.623441i	$0.785734\pi$
$998$	−1.72274e13	−0.549709
$999$	−8.29388e12	−0.263459

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.10.a.f.1.2		2
3.2	odd	2		225.10.a.k.1.1		2
5.2	odd	4		75.10.b.f.49.3		4
5.3	odd	4		75.10.b.f.49.2		4
5.4	even	2		15.10.a.d.1.1	✓	2
15.2	even	4		225.10.b.i.199.2		4
15.8	even	4		225.10.b.i.199.3		4
15.14	odd	2		45.10.a.d.1.2		2
20.19	odd	2		240.10.a.r.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.a.d.1.1	✓	2	5.4	even	2
45.10.a.d.1.2		2	15.14	odd	2
75.10.a.f.1.2		2	1.1	even	1	trivial
75.10.b.f.49.2		4	5.3	odd	4
75.10.b.f.49.3		4	5.2	odd	4
225.10.a.k.1.1		2	3.2	odd	2
225.10.b.i.199.2		4	15.2	even	4
225.10.b.i.199.3		4	15.8	even	4
240.10.a.r.1.2		2	20.19	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	75.a (trivial)

\(f(q)\)	\(=\)	\(q+7.78626 q^{2} +81.0000 q^{3} -451.374 q^{4} +630.687 q^{6} -1839.88 q^{7} -7501.08 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+7.78626 q^{2} +81.0000 q^{3} -451.374 q^{4} +630.687 q^{6} -1839.88 q^{7} -7501.08 q^{8} +6561.00 q^{9} +44385.9 q^{11} -36561.3 q^{12} -136584. q^{13} -14325.8 q^{14} +172698. q^{16} +253591. q^{17} +51085.7 q^{18} +85435.7 q^{19} -149030. q^{21} +345600. q^{22} +979409. q^{23} -607588. q^{24} -1.06348e6 q^{26} +531441. q^{27} +830473. q^{28} +2.58640e6 q^{29} +8.94787e6 q^{31} +5.18523e6 q^{32} +3.59526e6 q^{33} +1.97452e6 q^{34} -2.96147e6 q^{36} -1.56064e7 q^{37} +665225. q^{38} -1.10633e7 q^{39} +2.44893e7 q^{41} -1.16039e6 q^{42} -1.27592e7 q^{43} -2.00346e7 q^{44} +7.62593e6 q^{46} +6.16764e7 q^{47} +1.39886e7 q^{48} -3.69685e7 q^{49} +2.05408e7 q^{51} +6.16504e7 q^{52} -5.70418e6 q^{53} +4.13794e6 q^{54} +1.38011e7 q^{56} +6.92029e6 q^{57} +2.01384e7 q^{58} +8.35095e7 q^{59} +1.48622e8 q^{61} +6.96704e7 q^{62} -1.20714e7 q^{63} -4.80479e7 q^{64} +2.79936e7 q^{66} +1.68003e8 q^{67} -1.14464e8 q^{68} +7.93321e7 q^{69} +2.10986e8 q^{71} -4.92146e7 q^{72} +1.43534e8 q^{73} -1.21515e8 q^{74} -3.85635e7 q^{76} -8.16646e7 q^{77} -8.61416e7 q^{78} -4.55960e8 q^{79} +4.30467e7 q^{81} +1.90680e8 q^{82} +3.55106e8 q^{83} +6.72683e7 q^{84} -9.93465e7 q^{86} +2.09498e8 q^{87} -3.32942e8 q^{88} -4.24540e8 q^{89} +2.51297e8 q^{91} -4.42080e8 q^{92} +7.24777e8 q^{93} +4.80228e8 q^{94} +4.20003e8 q^{96} -1.19905e9 q^{97} -2.87846e8 q^{98} +2.91216e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 31 q^{2} + 162 q^{3} + 541 q^{4} - 2511 q^{6} - 14112 q^{7} - 26133 q^{8} + 13122 q^{9}+O(q^{10}) \) 2 * q - 31 * q^2 + 162 * q^3 + 541 * q^4 - 2511 * q^6 - 14112 * q^7 - 26133 * q^8 + 13122 * q^9	\( 2 q - 31 q^{2} + 162 q^{3} + 541 q^{4} - 2511 q^{6} - 14112 q^{7} - 26133 q^{8} + 13122 q^{9} - 21512 q^{11} + 43821 q^{12} - 24284 q^{13} + 461664 q^{14} + 387265 q^{16} + 156956 q^{17} - 203391 q^{18} - 95896 q^{19} - 1143072 q^{21} + 2901532 q^{22} + 735264 q^{23} - 2116773 q^{24} - 5419166 q^{26} + 1062882 q^{27} - 11348064 q^{28} - 2678212 q^{29} + 10782432 q^{31} + 6402523 q^{32} - 1742472 q^{33} + 5722622 q^{34} + 3549501 q^{36} - 21968332 q^{37} + 7698404 q^{38} - 1967004 q^{39} + 26060372 q^{41} + 37394784 q^{42} + 7191160 q^{43} - 85429972 q^{44} + 17095392 q^{46} + 31580240 q^{47} + 31368465 q^{48} + 73282930 q^{49} + 12713436 q^{51} + 173093786 q^{52} - 3131116 q^{53} - 16474671 q^{54} + 242454240 q^{56} - 7767576 q^{57} + 224332958 q^{58} - 35494664 q^{59} + 341497340 q^{61} - 1485504 q^{62} - 92588832 q^{63} - 205120471 q^{64} + 235024092 q^{66} + 288195816 q^{67} - 210362042 q^{68} + 59556384 q^{69} + 210286064 q^{71} - 171458613 q^{72} + 232663084 q^{73} + 125240234 q^{74} - 218512364 q^{76} + 727042176 q^{77} - 438952446 q^{78} - 24755040 q^{79} + 86093442 q^{81} + 129742346 q^{82} + 372082152 q^{83} - 919193184 q^{84} - 873146372 q^{86} - 216935172 q^{87} + 894861492 q^{88} - 427639116 q^{89} - 1126859328 q^{91} - 684362592 q^{92} + 873376992 q^{93} + 1647543896 q^{94} + 518604363 q^{96} - 1771658884 q^{97} - 4564085351 q^{98} - 141140232 q^{99}+O(q^{100}) \) 2 * q - 31 * q^2 + 162 * q^3 + 541 * q^4 - 2511 * q^6 - 14112 * q^7 - 26133 * q^8 + 13122 * q^9 - 21512 * q^11 + 43821 * q^12 - 24284 * q^13 + 461664 * q^14 + 387265 * q^16 + 156956 * q^17 - 203391 * q^18 - 95896 * q^19 - 1143072 * q^21 + 2901532 * q^22 + 735264 * q^23 - 2116773 * q^24 - 5419166 * q^26 + 1062882 * q^27 - 11348064 * q^28 - 2678212 * q^29 + 10782432 * q^31 + 6402523 * q^32 - 1742472 * q^33 + 5722622 * q^34 + 3549501 * q^36 - 21968332 * q^37 + 7698404 * q^38 - 1967004 * q^39 + 26060372 * q^41 + 37394784 * q^42 + 7191160 * q^43 - 85429972 * q^44 + 17095392 * q^46 + 31580240 * q^47 + 31368465 * q^48 + 73282930 * q^49 + 12713436 * q^51 + 173093786 * q^52 - 3131116 * q^53 - 16474671 * q^54 + 242454240 * q^56 - 7767576 * q^57 + 224332958 * q^58 - 35494664 * q^59 + 341497340 * q^61 - 1485504 * q^62 - 92588832 * q^63 - 205120471 * q^64 + 235024092 * q^66 + 288195816 * q^67 - 210362042 * q^68 + 59556384 * q^69 + 210286064 * q^71 - 171458613 * q^72 + 232663084 * q^73 + 125240234 * q^74 - 218512364 * q^76 + 727042176 * q^77 - 438952446 * q^78 - 24755040 * q^79 + 86093442 * q^81 + 129742346 * q^82 + 372082152 * q^83 - 919193184 * q^84 - 873146372 * q^86 - 216935172 * q^87 + 894861492 * q^88 - 427639116 * q^89 - 1126859328 * q^91 - 684362592 * q^92 + 873376992 * q^93 + 1647543896 * q^94 + 518604363 * q^96 - 1771658884 * q^97 - 4564085351 * q^98 - 141140232 * q^99

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