LMFDB - Embedded newform 289.10.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 122690 x^{10} + 5157152560 x^{8} - 87983684680032 x^{6} + \cdots + 20\!\cdots\!28 $ x^12 - 122690x^10 + 5157152560x^8 - 87983684680032x^6 + 612743619071665152x^4 - 1335826553351738886144*x^2 + 203949399568932198678528
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{17}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-59.5904$ of defining polynomial
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.8575 q^{2} +59.5904 q^{3} -371.399 q^{4} -633.821 q^{5} -706.595 q^{6} +10932.1 q^{7} +10474.9 q^{8} -16132.0 q^{9} +O(q^{10})$	\(q-11.8575 q^{2} +59.5904 q^{3} -371.399 q^{4} -633.821 q^{5} -706.595 q^{6} +10932.1 q^{7} +10474.9 q^{8} -16132.0 q^{9} +7515.55 q^{10} +26182.2 q^{11} -22131.8 q^{12} -132465. q^{13} -129628. q^{14} -37769.6 q^{15} +65949.4 q^{16} +191286. q^{18} +834785. q^{19} +235400. q^{20} +651448. q^{21} -310456. q^{22} -1.27202e6 q^{23} +624205. q^{24} -1.55140e6 q^{25} +1.57071e6 q^{26} -2.13423e6 q^{27} -4.06017e6 q^{28} +6.34953e6 q^{29} +447855. q^{30} -8.52001e6 q^{31} -6.14516e6 q^{32} +1.56021e6 q^{33} -6.92899e6 q^{35} +5.99140e6 q^{36} -8.05093e6 q^{37} -9.89850e6 q^{38} -7.89366e6 q^{39} -6.63923e6 q^{40} +2.36819e7 q^{41} -7.72457e6 q^{42} -2.89782e6 q^{43} -9.72403e6 q^{44} +1.02248e7 q^{45} +1.50830e7 q^{46} +2.63358e7 q^{47} +3.92995e6 q^{48} +7.91572e7 q^{49} +1.83957e7 q^{50} +4.91975e7 q^{52} -2.45299e6 q^{53} +2.53067e7 q^{54} -1.65948e7 q^{55} +1.14513e8 q^{56} +4.97452e7 q^{57} -7.52898e7 q^{58} +8.84531e6 q^{59} +1.40276e7 q^{60} -6.18808e7 q^{61} +1.01026e8 q^{62} -1.76356e8 q^{63} +3.91004e7 q^{64} +8.39593e7 q^{65} -1.85002e7 q^{66} +1.46096e8 q^{67} -7.58002e7 q^{69} +8.21608e7 q^{70} -2.08285e8 q^{71} -1.68981e8 q^{72} -7.44027e7 q^{73} +9.54641e7 q^{74} -9.24483e7 q^{75} -3.10038e8 q^{76} +2.86226e8 q^{77} +9.35993e7 q^{78} +1.47713e8 q^{79} -4.18001e7 q^{80} +1.90346e8 q^{81} -2.80809e8 q^{82} +5.69010e7 q^{83} -2.41947e8 q^{84} +3.43609e7 q^{86} +3.78371e8 q^{87} +2.74256e8 q^{88} +1.03356e9 q^{89} -1.21241e8 q^{90} -1.44812e9 q^{91} +4.72427e8 q^{92} -5.07710e8 q^{93} -3.12277e8 q^{94} -5.29104e8 q^{95} -3.66193e8 q^{96} +1.03075e9 q^{97} -9.38609e8 q^{98} -4.22370e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9}+O(q^{10}) $ 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9	$ 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9} - 63204 q^{13} + 243480 q^{15} + 38978 q^{16} + 547706 q^{18} - 1110672 q^{19} - 172580 q^{21} + 4441796 q^{25} - 1336332 q^{26} - 500496 q^{30} + 1934850 q^{32} - 6557404 q^{33} + 3519864 q^{35} - 30244102 q^{36} + 28748136 q^{38} + 11901296 q^{42} - 10004616 q^{43} - 112552440 q^{47} - 121354720 q^{49} - 164889018 q^{50} - 59093180 q^{52} - 76804272 q^{53} + 300732568 q^{55} - 11618904 q^{59} - 101609232 q^{60} - 260062974 q^{64} - 18429632 q^{66} - 304208752 q^{67} - 211308236 q^{69} - 460311456 q^{70} + 493218954 q^{72} - 416024248 q^{76} - 138357828 q^{77} - 363335792 q^{81} + 845042136 q^{83} + 958037984 q^{84} + 127952904 q^{86} - 610860648 q^{87} - 938223804 q^{89} - 1635779524 q^{93} + 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) $ 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9 - 63204 * q^13 + 243480 * q^15 + 38978 * q^16 + 547706 * q^18 - 1110672 * q^19 - 172580 * q^21 + 4441796 * q^25 - 1336332 * q^26 - 500496 * q^30 + 1934850 * q^32 - 6557404 * q^33 + 3519864 * q^35 - 30244102 * q^36 + 28748136 * q^38 + 11901296 * q^42 - 10004616 * q^43 - 112552440 * q^47 - 121354720 * q^49 - 164889018 * q^50 - 59093180 * q^52 - 76804272 * q^53 + 300732568 * q^55 - 11618904 * q^59 - 101609232 * q^60 - 260062974 * q^64 - 18429632 * q^66 - 304208752 * q^67 - 211308236 * q^69 - 460311456 * q^70 + 493218954 * q^72 - 416024248 * q^76 - 138357828 * q^77 - 363335792 * q^81 + 845042136 * q^83 + 958037984 * q^84 + 127952904 * q^86 - 610860648 * q^87 - 938223804 * q^89 - 1635779524 * q^93 + 238629952 * q^94 - 152046078 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−11.8575	−0.524034	−0.262017	−	0.965063i	$-0.584388\pi$
$2$	−11.8575	−0.524034	−0.262017	+	0.965063i	$0.584388\pi$
$3$	59.5904	0.424747	0.212374	−	0.977189i	$-0.431881\pi$
$3$	59.5904	0.424747	0.212374	+	0.977189i	$0.431881\pi$
$4$	−371.399	−0.725388
$5$	−633.821	−0.453525	−0.226763	−	0.973950i	$-0.572814\pi$
$5$	−633.821	−0.453525	−0.226763	+	0.973950i	$0.572814\pi$
$6$	−706.595	−0.222582
$7$	10932.1	1.72093	0.860463	−	0.509512i	$-0.170174\pi$
$7$	10932.1	1.72093	0.860463	+	0.509512i	$0.170174\pi$
$8$	10474.9	0.904162
$9$	−16132.0	−0.819590
$10$	7515.55	0.237663
$11$	26182.2	0.539186	0.269593	−	0.962974i	$-0.413111\pi$
$11$	26182.2	0.539186	0.269593	+	0.962974i	$0.413111\pi$
$12$	−22131.8	−0.308107
$13$	−132465.	−1.28634	−0.643172	−	0.765722i	$-0.722382\pi$
$13$	−132465.	−1.28634	−0.643172	+	0.765722i	$0.722382\pi$
$14$	−129628.	−0.901824
$15$	−37769.6	−0.192634
$16$	65949.4	0.251577
$17$	0	0
$17$	0	0
$18$	191286.	0.429493
$19$	834785.	1.46955	0.734774	−	0.678312i	$-0.237288\pi$
$19$	834785.	1.46955	0.734774	+	0.678312i	$0.237288\pi$
$20$	235400.	0.328982
$21$	651448.	0.730959
$22$	−310456.	−0.282552
$23$	−1.27202e6	−0.947805	−0.473902	−	0.880577i	$-0.657155\pi$
$23$	−1.27202e6	−0.947805	−0.473902	+	0.880577i	$0.657155\pi$
$24$	624205.	0.384040
$25$	−1.55140e6	−0.794315
$26$	1.57071e6	0.674088
$27$	−2.13423e6	−0.772866
$28$	−4.06017e6	−1.24834
$29$	6.34953e6	1.66706	0.833529	−	0.552476i	$-0.186317\pi$
$29$	6.34953e6	1.66706	0.833529	+	0.552476i	$0.186317\pi$
$30$	447855.	0.100947
$31$	−8.52001e6	−1.65696	−0.828480	−	0.560018i	$-0.810794\pi$
$31$	−8.52001e6	−1.65696	−0.828480	+	0.560018i	$0.810794\pi$
$32$	−6.14516e6	−1.03600
$33$	1.56021e6	0.229018
$34$	0	0
$35$	−6.92899e6	−0.780484
$36$	5.99140e6	0.594521
$37$	−8.05093e6	−0.706217	−0.353109	−	0.935582i	$-0.614875\pi$
$37$	−8.05093e6	−0.706217	−0.353109	+	0.935582i	$0.614875\pi$
$38$	−9.89850e6	−0.770093
$39$	−7.89366e6	−0.546371
$40$	−6.63923e6	−0.410060
$41$	2.36819e7	1.30885	0.654425	−	0.756127i	$-0.272911\pi$
$41$	2.36819e7	1.30885	0.654425	+	0.756127i	$0.272911\pi$
$42$	−7.72457e6	−0.383047
$43$	−2.89782e6	−0.129260	−0.0646298	−	0.997909i	$-0.520587\pi$
$43$	−2.89782e6	−0.129260	−0.0646298	+	0.997909i	$0.520587\pi$
$44$	−9.72403e6	−0.391119
$45$	1.02248e7	0.371705
$46$	1.50830e7	0.496682
$47$	2.63358e7	0.787238	0.393619	−	0.919274i	$-0.371223\pi$
$47$	2.63358e7	0.787238	0.393619	+	0.919274i	$0.371223\pi$
$48$	3.92995e6	0.106857
$49$	7.91572e7	1.96159
$50$	1.83957e7	0.416248
$51$	0	0
$52$	4.91975e7	0.933099
$53$	−2.45299e6	−0.0427027	−0.0213513	−	0.999772i	$-0.506797\pi$
$53$	−2.45299e6	−0.0427027	−0.0213513	+	0.999772i	$0.506797\pi$
$54$	2.53067e7	0.405008
$55$	−1.65948e7	−0.244534
$56$	1.14513e8	1.55600
$57$	4.97452e7	0.624186
$58$	−7.52898e7	−0.873595
$59$	8.84531e6	0.0950340	0.0475170	−	0.998870i	$-0.484869\pi$
$59$	8.84531e6	0.0950340	0.0475170	+	0.998870i	$0.484869\pi$
$60$	1.40276e7	0.139734
$61$	−6.18808e7	−0.572231	−0.286116	−	0.958195i	$-0.592364\pi$
$61$	−6.18808e7	−0.572231	−0.286116	+	0.958195i	$0.592364\pi$
$62$	1.01026e8	0.868304
$63$	−1.76356e8	−1.41045
$64$	3.91004e7	0.291320
$65$	8.39593e7	0.583389
$66$	−1.85002e7	−0.120013
$67$	1.46096e8	0.885730	0.442865	−	0.896588i	$-0.353962\pi$
$67$	1.46096e8	0.885730	0.442865	+	0.896588i	$0.353962\pi$
$68$	0	0
$69$	−7.58002e7	−0.402577
$70$	8.21608e7	0.409000
$71$	−2.08285e8	−0.972737	−0.486369	−	0.873754i	$-0.661679\pi$
$71$	−2.08285e8	−0.972737	−0.486369	+	0.873754i	$0.661679\pi$
$72$	−1.68981e8	−0.741042
$73$	−7.44027e7	−0.306645	−0.153323	−	0.988176i	$-0.548997\pi$
$73$	−7.44027e7	−0.306645	−0.153323	+	0.988176i	$0.548997\pi$
$74$	9.54641e7	0.370082
$75$	−9.24483e7	−0.337383
$76$	−3.10038e8	−1.06599
$77$	2.86226e8	0.927899
$78$	9.35993e7	0.286317
$79$	1.47713e8	0.426676	0.213338	−	0.976978i	$-0.431566\pi$
$79$	1.47713e8	0.426676	0.213338	+	0.976978i	$0.431566\pi$
$80$	−4.18001e7	−0.114097
$81$	1.90346e8	0.491317
$82$	−2.80809e8	−0.685882
$83$	5.69010e7	0.131604	0.0658019	−	0.997833i	$-0.479039\pi$
$83$	5.69010e7	0.131604	0.0658019	+	0.997833i	$0.479039\pi$
$84$	−2.41947e8	−0.530229
$85$	0	0
$86$	3.43609e7	0.0677364
$87$	3.78371e8	0.708078
$88$	2.74256e8	0.487511
$89$	1.03356e9	1.74614	0.873071	−	0.487592i	$-0.162125\pi$
$89$	1.03356e9	1.74614	0.873071	+	0.487592i	$0.162125\pi$
$90$	−1.21241e8	−0.194786
$91$	−1.44812e9	−2.21370
$92$	4.72427e8	0.687527
$93$	−5.07710e8	−0.703789
$94$	−3.12277e8	−0.412539
$95$	−5.29104e8	−0.666477
$96$	−3.66193e8	−0.440037
$97$	1.03075e9	1.18217	0.591086	−	0.806609i	$-0.298699\pi$
$97$	1.03075e9	1.18217	0.591086	+	0.806609i	$0.298699\pi$
$98$	−9.38609e8	−1.02794
$99$	−4.22370e8	−0.441911
$100$	5.76187e8	0.576187
$101$	−4.52386e8	−0.432576	−0.216288	−	0.976330i	$-0.569395\pi$
$101$	−4.52386e8	−0.432576	−0.216288	+	0.976330i	$0.569395\pi$
$102$	0	0
$103$	−2.13433e8	−0.186850	−0.0934250	−	0.995626i	$-0.529782\pi$
$103$	−2.13433e8	−0.186850	−0.0934250	+	0.995626i	$0.529782\pi$
$104$	−1.38756e9	−1.16306
$105$	−4.12901e8	−0.331508
$106$	2.90865e7	0.0223776
$107$	−1.25133e9	−0.922881	−0.461440	−	0.887171i	$-0.652667\pi$
$107$	−1.25133e9	−0.922881	−0.461440	+	0.887171i	$0.652667\pi$
$108$	7.92650e8	0.560628
$109$	−9.41035e8	−0.638538	−0.319269	−	0.947664i	$-0.603437\pi$
$109$	−9.41035e8	−0.638538	−0.319269	+	0.947664i	$0.603437\pi$
$110$	1.96773e8	0.128144
$111$	−4.79758e8	−0.299964
$112$	7.20965e8	0.432946
$113$	7.72792e7	0.0445871	0.0222936	−	0.999751i	$-0.492903\pi$
$113$	7.72792e7	0.0445871	0.0222936	+	0.999751i	$0.492903\pi$
$114$	−5.89855e8	−0.327095
$115$	8.06233e8	0.429854
$116$	−2.35821e9	−1.20926
$117$	2.13693e9	1.05427
$118$	−1.04884e8	−0.0498010
$119$	0	0
$120$	−3.95634e8	−0.174172
$121$	−1.67244e9	−0.709279
$122$	7.33754e8	0.299869
$123$	1.41122e9	0.555930
$124$	3.16432e9	1.20194
$125$	2.22124e9	0.813767
$126$	2.09115e9	0.739126
$127$	−3.54892e9	−1.21054	−0.605271	−	0.796020i	$-0.706935\pi$
$127$	−3.54892e9	−1.21054	−0.605271	+	0.796020i	$0.706935\pi$
$128$	2.68269e9	0.883335
$129$	−1.72682e8	−0.0549026
$130$	−9.95550e8	−0.305716
$131$	−2.85977e9	−0.848419	−0.424209	−	0.905564i	$-0.639448\pi$
$131$	−2.85977e9	−0.848419	−0.424209	+	0.905564i	$0.639448\pi$
$132$	−5.79459e8	−0.166127
$133$	9.12596e9	2.52898
$134$	−1.73234e9	−0.464153
$135$	1.35272e9	0.350514
$136$	0	0
$137$	−1.35821e8	−0.0329400	−0.0164700	−	0.999864i	$-0.505243\pi$
$137$	−1.35821e8	−0.0329400	−0.0164700	+	0.999864i	$0.505243\pi$
$138$	8.98803e8	0.210964
$139$	−4.19737e8	−0.0953698	−0.0476849	−	0.998862i	$-0.515184\pi$
$139$	−4.19737e8	−0.0953698	−0.0476849	+	0.998862i	$0.515184\pi$
$140$	2.57342e9	0.566154
$141$	1.56936e9	0.334377
$142$	2.46975e9	0.509747
$143$	−3.46823e9	−0.693578
$144$	−1.06389e9	−0.206190
$145$	−4.02447e9	−0.756053
$146$	8.82233e8	0.160692
$147$	4.71701e9	0.833179
$148$	2.99011e9	0.512282
$149$	−8.05680e9	−1.33913	−0.669567	−	0.742751i	$-0.733520\pi$
$149$	−8.05680e9	−1.33913	−0.669567	+	0.742751i	$0.733520\pi$
$150$	1.09621e9	0.176800
$151$	5.71660e9	0.894832	0.447416	−	0.894326i	$-0.352344\pi$
$151$	5.71660e9	0.894832	0.447416	+	0.894326i	$0.352344\pi$
$152$	8.74432e9	1.32871
$153$	0	0
$154$	−3.39394e9	−0.486251
$155$	5.40016e9	0.751474
$156$	2.93170e9	0.396331
$157$	−3.73112e9	−0.490107	−0.245053	−	0.969510i	$-0.578806\pi$
$157$	−3.73112e9	−0.490107	−0.245053	+	0.969510i	$0.578806\pi$
$158$	−1.75152e9	−0.223593
$159$	−1.46175e8	−0.0181378
$160$	3.89493e9	0.469851
$161$	−1.39059e10	−1.63110
$162$	−2.25704e9	−0.257467
$163$	3.76537e9	0.417795	0.208898	−	0.977938i	$-0.433012\pi$
$163$	3.76537e9	0.417795	0.208898	+	0.977938i	$0.433012\pi$
$164$	−8.79544e9	−0.949425
$165$	−9.88891e8	−0.103865
$166$	−6.74705e8	−0.0689648
$167$	−7.70007e9	−0.766074	−0.383037	−	0.923733i	$-0.625122\pi$
$167$	−7.70007e9	−0.766074	−0.383037	+	0.923733i	$0.625122\pi$
$168$	6.82387e9	0.660905
$169$	6.94255e9	0.654680
$170$	0	0
$171$	−1.34667e10	−1.20443
$172$	1.07625e9	0.0937634
$173$	−5.96147e9	−0.505995	−0.252997	−	0.967467i	$-0.581416\pi$
$173$	−5.96147e9	−0.505995	−0.252997	+	0.967467i	$0.581416\pi$
$174$	−4.48655e9	−0.371057
$175$	−1.69600e10	−1.36696
$176$	1.72670e9	0.135647
$177$	5.27095e8	0.0403654
$178$	−1.22554e10	−0.915038
$179$	−4.90200e9	−0.356890	−0.178445	−	0.983950i	$-0.557107\pi$
$179$	−4.90200e9	−0.356890	−0.178445	+	0.983950i	$0.557107\pi$
$180$	−3.79748e9	−0.269630
$181$	−6.71648e9	−0.465144	−0.232572	−	0.972579i	$-0.574714\pi$
$181$	−6.71648e9	−0.465144	−0.232572	+	0.972579i	$0.574714\pi$
$182$	1.71712e10	1.16006
$183$	−3.68750e9	−0.243054
$184$	−1.33243e10	−0.856969
$185$	5.10285e9	0.320287
$186$	6.02019e9	0.368810
$187$	0	0
$188$	−9.78108e9	−0.571053
$189$	−2.33316e10	−1.33005
$190$	6.27387e9	0.349257
$191$	−1.84682e10	−1.00409	−0.502046	−	0.864841i	$-0.667419\pi$
$191$	−1.84682e10	−1.00409	−0.502046	+	0.864841i	$0.667419\pi$
$192$	2.33001e9	0.123738
$193$	−3.37714e10	−1.75203	−0.876013	−	0.482287i	$-0.839806\pi$
$193$	−3.37714e10	−1.75203	−0.876013	+	0.482287i	$0.839806\pi$
$194$	−1.22222e10	−0.619498
$195$	5.00316e9	0.247793
$196$	−2.93989e10	−1.42291
$197$	−6.25236e9	−0.295765	−0.147882	−	0.989005i	$-0.547246\pi$
$197$	−6.25236e9	−0.295765	−0.147882	+	0.989005i	$0.547246\pi$
$198$	5.00827e9	0.231576
$199$	−1.46173e10	−0.660735	−0.330368	−	0.943852i	$-0.607173\pi$
$199$	−1.46173e10	−0.660735	−0.330368	+	0.943852i	$0.607173\pi$
$200$	−1.62508e10	−0.718189
$201$	8.70591e9	0.376211
$202$	5.36418e9	0.226685
$203$	6.94137e10	2.86889
$204$	0	0
$205$	−1.50101e10	−0.593597
$206$	2.53078e9	0.0979157
$207$	2.05202e10	0.776811
$208$	−8.73600e9	−0.323614
$209$	2.18565e10	0.792359
$210$	4.89599e9	0.173722
$211$	2.69240e10	0.935122	0.467561	−	0.883961i	$-0.345133\pi$
$211$	2.69240e10	0.935122	0.467561	+	0.883961i	$0.345133\pi$
$212$	9.11039e8	0.0309760
$213$	−1.24118e10	−0.413167
$214$	1.48377e10	0.483621
$215$	1.83670e9	0.0586225
$216$	−2.23559e10	−0.698796
$217$	−9.31416e10	−2.85151
$218$	1.11584e10	0.334616
$219$	−4.43369e9	−0.130247
$220$	6.16329e9	0.177382
$221$	0	0
$222$	5.68874e9	0.157191
$223$	−1.09042e10	−0.295273	−0.147636	−	0.989042i	$-0.547166\pi$
$223$	−1.09042e10	−0.295273	−0.147636	+	0.989042i	$0.547166\pi$
$224$	−6.71795e10	−1.78287
$225$	2.50271e10	0.651012
$226$	−9.16341e8	−0.0233652
$227$	5.73714e10	1.43410	0.717050	−	0.697022i	$-0.245492\pi$
$227$	5.73714e10	1.43410	0.717050	+	0.697022i	$0.245492\pi$
$228$	−1.84753e10	−0.452777
$229$	−4.85190e10	−1.16587	−0.582937	−	0.812517i	$-0.698097\pi$
$229$	−4.85190e10	−1.16587	−0.582937	+	0.812517i	$0.698097\pi$
$230$	−9.55994e9	−0.225258
$231$	1.70563e10	0.394123
$232$	6.65109e10	1.50729
$233$	1.92873e9	0.0428717	0.0214358	−	0.999770i	$-0.493176\pi$
$233$	1.92873e9	0.0428717	0.0214358	+	0.999770i	$0.493176\pi$
$234$	−2.53387e10	−0.552475
$235$	−1.66922e10	−0.357032
$236$	−3.28514e9	−0.0689366
$237$	8.80230e9	0.181229
$238$	0	0
$239$	−9.39248e10	−1.86204	−0.931021	−	0.364965i	$-0.881081\pi$
$239$	−9.39248e10	−1.86204	−0.931021	+	0.364965i	$0.881081\pi$
$240$	−2.49088e9	−0.0484622
$241$	4.52039e10	0.863175	0.431588	−	0.902071i	$-0.357954\pi$
$241$	4.52039e10	0.863175	0.431588	+	0.902071i	$0.357954\pi$
$242$	1.98310e10	0.371686
$243$	5.33508e10	0.981551
$244$	2.29825e10	0.415090
$245$	−5.01715e10	−0.889630
$246$	−1.67335e10	−0.291326
$247$	−1.10580e11	−1.89034
$248$	−8.92465e10	−1.49816
$249$	3.39075e9	0.0558983
$250$	−2.63384e10	−0.426442
$251$	−4.87193e10	−0.774763	−0.387382	−	0.921919i	$-0.626620\pi$
$251$	−4.87193e10	−0.774763	−0.387382	+	0.921919i	$0.626620\pi$
$252$	6.54986e10	1.02313
$253$	−3.33043e10	−0.511043
$254$	4.20814e10	0.634365
$255$	0	0
$256$	−5.18295e10	−0.754218
$257$	−8.25999e10	−1.18108	−0.590542	−	0.807007i	$-0.701086\pi$
$257$	−8.25999e10	−1.18108	−0.590542	+	0.807007i	$0.701086\pi$
$258$	2.04758e9	0.0287708
$259$	−8.80135e10	−1.21535
$260$	−3.11824e10	−0.423184
$261$	−1.02431e11	−1.36630
$262$	3.39098e10	0.444600
$263$	−3.46665e10	−0.446795	−0.223398	−	0.974727i	$-0.571715\pi$
$263$	−3.46665e10	−0.446795	−0.223398	+	0.974727i	$0.571715\pi$
$264$	1.63430e10	0.207069
$265$	1.55476e9	0.0193667
$266$	−1.08211e11	−1.32527
$267$	6.15901e10	0.741669
$268$	−5.42599e10	−0.642499
$269$	−1.26130e11	−1.46871	−0.734353	−	0.678768i	$-0.762514\pi$
$269$	−1.26130e11	−1.46871	−0.734353	+	0.678768i	$0.762514\pi$
$270$	−1.60399e10	−0.183681
$271$	5.63928e10	0.635129	0.317564	−	0.948237i	$-0.397135\pi$
$271$	5.63928e10	0.635129	0.317564	+	0.948237i	$0.397135\pi$
$272$	0	0
$273$	−8.62942e10	−0.940264
$274$	1.61050e9	0.0172617
$275$	−4.06189e10	−0.428283
$276$	2.81521e10	0.292025
$277$	−4.76405e10	−0.486203	−0.243102	−	0.970001i	$-0.578165\pi$
$277$	−4.76405e10	−0.486203	−0.243102	+	0.970001i	$0.578165\pi$
$278$	4.97705e9	0.0499770
$279$	1.37445e11	1.35803
$280$	−7.25807e10	−0.705684
$281$	−1.14333e11	−1.09394	−0.546969	−	0.837153i	$-0.684218\pi$
$281$	−1.14333e11	−1.09394	−0.546969	+	0.837153i	$0.684218\pi$
$282$	−1.86087e10	−0.175225
$283$	2.54590e10	0.235941	0.117970	−	0.993017i	$-0.462361\pi$
$283$	2.54590e10	0.235941	0.117970	+	0.993017i	$0.462361\pi$
$284$	7.73568e10	0.705612
$285$	−3.15295e10	−0.283084
$286$	4.11246e10	0.363459
$287$	2.58893e11	2.25243
$288$	9.91337e10	0.849093
$289$	0	0
$290$	4.77202e10	0.396197
$291$	6.14228e10	0.502124
$292$	2.76331e10	0.222437
$293$	4.43928e10	0.351891	0.175946	−	0.984400i	$-0.443702\pi$
$293$	4.43928e10	0.351891	0.175946	+	0.984400i	$0.443702\pi$
$294$	−5.59321e10	−0.436614
$295$	−5.60634e9	−0.0431003
$296$	−8.43329e10	−0.638535
$297$	−5.58787e10	−0.416718
$298$	9.55337e10	0.701752
$299$	1.68499e11	1.21920
$300$	3.43352e10	0.244734
$301$	−3.16792e10	−0.222446
$302$	−6.77848e10	−0.468922
$303$	−2.69578e10	−0.183735
$304$	5.50536e10	0.369704
$305$	3.92213e10	0.259521
$306$	0	0
$307$	1.77005e11	1.13727	0.568635	−	0.822590i	$-0.307472\pi$
$307$	1.77005e11	1.13727	0.568635	+	0.822590i	$0.307472\pi$
$308$	−1.06304e11	−0.673088
$309$	−1.27185e10	−0.0793640
$310$	−6.40326e10	−0.393798
$311$	−1.16929e11	−0.708764	−0.354382	−	0.935101i	$-0.615309\pi$
$311$	−1.16929e11	−0.708764	−0.354382	+	0.935101i	$0.615309\pi$
$312$	−8.26855e10	−0.494008
$313$	−6.60894e10	−0.389208	−0.194604	−	0.980882i	$-0.562342\pi$
$313$	−6.60894e10	−0.389208	−0.194604	+	0.980882i	$0.562342\pi$
$314$	4.42419e10	0.256833
$315$	1.11778e11	0.639677
$316$	−5.48606e10	−0.309506
$317$	−2.15865e11	−1.20065	−0.600324	−	0.799757i	$-0.704962\pi$
$317$	−2.15865e11	−1.20065	−0.600324	+	0.799757i	$0.704962\pi$
$318$	1.73327e9	0.00950484
$319$	1.66245e11	0.898854
$320$	−2.47826e10	−0.132121
$321$	−7.45674e10	−0.391991
$322$	1.64889e11	0.854753
$323$	0	0
$324$	−7.06945e10	−0.356396
$325$	2.05506e11	1.02176
$326$	−4.46480e10	−0.218939
$327$	−5.60767e10	−0.271217
$328$	2.48067e11	1.18341
$329$	2.87905e11	1.35478
$330$	1.17258e10	0.0544289
$331$	−2.19673e11	−1.00589	−0.502946	−	0.864318i	$-0.667751\pi$
$331$	−2.19673e11	−1.00589	−0.502946	+	0.864318i	$0.667751\pi$
$332$	−2.11330e10	−0.0954639
$333$	1.29877e11	0.578808
$334$	9.13039e10	0.401449
$335$	−9.25987e10	−0.401701
$336$	4.29626e10	0.183892
$337$	3.65398e11	1.54323	0.771617	−	0.636088i	$-0.219448\pi$
$337$	3.65398e11	1.54323	0.771617	+	0.636088i	$0.219448\pi$
$338$	−8.23215e10	−0.343074
$339$	4.60510e9	0.0189383
$340$	0	0
$341$	−2.23072e11	−0.893410
$342$	1.59682e11	0.631160
$343$	4.24205e11	1.65482
$344$	−3.03544e10	−0.116872
$345$	4.80438e10	0.182579
$346$	7.06883e10	0.265158
$347$	−3.18226e11	−1.17829	−0.589147	−	0.808026i	$-0.700536\pi$
$347$	−3.18226e11	−1.17829	−0.589147	+	0.808026i	$0.700536\pi$
$348$	−1.40527e11	−0.513632
$349$	1.05189e11	0.379537	0.189769	−	0.981829i	$-0.439226\pi$
$349$	1.05189e11	0.379537	0.189769	+	0.981829i	$0.439226\pi$
$350$	2.01104e11	0.716332
$351$	2.82711e11	0.994171
$352$	−1.60894e11	−0.558595
$353$	2.74596e11	0.941258	0.470629	−	0.882331i	$-0.344027\pi$
$353$	2.74596e11	0.941258	0.470629	+	0.882331i	$0.344027\pi$
$354$	−6.25005e9	−0.0211529
$355$	1.32015e11	0.441161
$356$	−3.83862e11	−1.26663
$357$	0	0
$358$	5.81256e10	0.187022
$359$	−3.36158e11	−1.06812	−0.534058	−	0.845448i	$-0.679334\pi$
$359$	−3.36158e11	−1.06812	−0.534058	+	0.845448i	$0.679334\pi$
$360$	1.07104e11	0.336081
$361$	3.74179e11	1.15957
$362$	7.96408e10	0.243751
$363$	−9.96614e10	−0.301264
$364$	5.37832e11	1.60579
$365$	4.71580e10	0.139071
$366$	4.37247e10	0.127368
$367$	−4.27664e11	−1.23057	−0.615283	−	0.788306i	$-0.710958\pi$
$367$	−4.27664e11	−1.23057	−0.615283	+	0.788306i	$0.710958\pi$
$368$	−8.38890e10	−0.238446
$369$	−3.82037e11	−1.07272
$370$	−6.05072e10	−0.167841
$371$	−2.68164e10	−0.0734882
$372$	1.88563e11	0.510521
$373$	−6.59774e11	−1.76484	−0.882420	−	0.470463i	$-0.844087\pi$
$373$	−6.59774e11	−1.76484	−0.882420	+	0.470463i	$0.844087\pi$
$374$	0	0
$375$	1.32364e11	0.345645
$376$	2.75866e11	0.711790
$377$	−8.41093e11	−2.14441
$378$	2.76655e11	0.696989
$379$	−3.76630e11	−0.937645	−0.468823	−	0.883292i	$-0.655322\pi$
$379$	−3.76630e11	−0.937645	−0.468823	+	0.883292i	$0.655322\pi$
$380$	1.96509e11	0.483455
$381$	−2.11482e11	−0.514174
$382$	2.18987e11	0.526178
$383$	2.37194e11	0.563261	0.281630	−	0.959523i	$-0.409125\pi$
$383$	2.37194e11	0.563261	0.281630	+	0.959523i	$0.409125\pi$
$384$	1.59862e11	0.375194
$385$	−1.81416e11	−0.420826
$386$	4.00445e11	0.918121
$387$	4.67475e10	0.105940
$388$	−3.82820e11	−0.857534
$389$	3.64753e10	0.0807656	0.0403828	−	0.999184i	$-0.487142\pi$
$389$	3.64753e10	0.0807656	0.0403828	+	0.999184i	$0.487142\pi$
$390$	−5.93252e10	−0.129852
$391$	0	0
$392$	8.29166e11	1.77359
$393$	−1.70415e11	−0.360363
$394$	7.41376e10	0.154991
$395$	−9.36238e10	−0.193508
$396$	1.56868e11	0.320557
$397$	−5.75210e11	−1.16217	−0.581084	−	0.813844i	$-0.697371\pi$
$397$	−5.75210e11	−1.16217	−0.581084	+	0.813844i	$0.697371\pi$
$398$	1.73325e11	0.346248
$399$	5.43819e11	1.07418
$400$	−1.02314e11	−0.199831
$401$	−3.39949e11	−0.656545	−0.328273	−	0.944583i	$-0.606466\pi$
$401$	−3.39949e11	−0.656545	−0.328273	+	0.944583i	$0.606466\pi$
$402$	−1.03231e11	−0.197148
$403$	1.12860e12	2.13142
$404$	1.68015e11	0.313786
$405$	−1.20646e11	−0.222825
$406$	−8.23076e11	−1.50339
$407$	−2.10791e11	−0.380782
$408$	0	0
$409$	−1.12478e11	−0.198752	−0.0993760	−	0.995050i	$-0.531685\pi$
$409$	−1.12478e11	−0.198752	−0.0993760	+	0.995050i	$0.531685\pi$
$410$	1.77983e11	0.311065
$411$	−8.09362e9	−0.0139912
$412$	7.92686e10	0.135539
$413$	9.66978e10	0.163547
$414$	−2.43319e11	−0.407075
$415$	−3.60650e10	−0.0596857
$416$	8.14021e11	1.33265
$417$	−2.50123e10	−0.0405081
$418$	−2.59164e11	−0.415223
$419$	2.86731e10	0.0454477	0.0227239	−	0.999742i	$-0.492766\pi$
$419$	2.86731e10	0.0454477	0.0227239	+	0.999742i	$0.492766\pi$
$420$	1.53351e11	0.240472
$421$	7.41818e11	1.15087	0.575437	−	0.817846i	$-0.304832\pi$
$421$	7.41818e11	1.15087	0.575437	+	0.817846i	$0.304832\pi$
$422$	−3.19252e11	−0.490036
$423$	−4.24849e11	−0.645212
$424$	−2.56949e10	−0.0386101
$425$	0	0
$426$	1.47173e11	0.216514
$427$	−6.76487e11	−0.984768
$428$	4.64743e11	0.669447
$429$	−2.06673e11	−0.294595
$430$	−2.17787e10	−0.0307202
$431$	−9.85196e10	−0.137523	−0.0687614	−	0.997633i	$-0.521905\pi$
$431$	−9.85196e10	−0.137523	−0.0687614	+	0.997633i	$0.521905\pi$
$432$	−1.40751e11	−0.194435
$433$	6.29756e11	0.860948	0.430474	−	0.902603i	$-0.358346\pi$
$433$	6.29756e11	0.860948	0.430474	+	0.902603i	$0.358346\pi$
$434$	1.10443e12	1.49429
$435$	−2.39819e11	−0.321131
$436$	3.49500e11	0.463188
$437$	−1.06186e12	−1.39284
$438$	5.25726e10	0.0682537
$439$	−3.19248e10	−0.0410240	−0.0205120	−	0.999790i	$-0.506530\pi$
$439$	−3.19248e10	−0.0410240	−0.0205120	+	0.999790i	$0.506530\pi$
$440$	−1.73829e11	−0.221099
$441$	−1.27696e12	−1.60770
$442$	0	0
$443$	9.76504e11	1.20464	0.602320	−	0.798255i	$-0.294243\pi$
$443$	9.76504e11	1.20464	0.602320	+	0.798255i	$0.294243\pi$
$444$	1.78182e11	0.217590
$445$	−6.55091e11	−0.791920
$446$	1.29297e11	0.154733
$447$	−4.80108e11	−0.568794
$448$	4.27449e11	0.501341
$449$	3.18417e11	0.369733	0.184867	−	0.982764i	$-0.440815\pi$
$449$	3.18417e11	0.369733	0.184867	+	0.982764i	$0.440815\pi$
$450$	−2.96760e11	−0.341153
$451$	6.20044e11	0.705713
$452$	−2.87014e10	−0.0323430
$453$	3.40654e11	0.380077
$454$	−6.80284e11	−0.751517
$455$	9.17851e11	1.00397
$456$	5.21077e11	0.564365
$457$	−5.17641e11	−0.555144	−0.277572	−	0.960705i	$-0.589530\pi$
$457$	−5.17641e11	−0.555144	−0.277572	+	0.960705i	$0.589530\pi$
$458$	5.75315e11	0.610958
$459$	0	0
$460$	−2.99434e11	−0.311811
$461$	1.03511e12	1.06741	0.533704	−	0.845671i	$-0.320800\pi$
$461$	1.03511e12	1.06741	0.533704	+	0.845671i	$0.320800\pi$
$462$	−2.02246e11	−0.206534
$463$	−4.59441e11	−0.464638	−0.232319	−	0.972640i	$-0.574631\pi$
$463$	−4.59441e11	−0.464638	−0.232319	+	0.972640i	$0.574631\pi$
$464$	4.18748e11	0.419393
$465$	3.21797e11	0.319186
$466$	−2.28700e10	−0.0224662
$467$	1.31601e12	1.28036	0.640182	−	0.768223i	$-0.278859\pi$
$467$	1.31601e12	1.28036	0.640182	+	0.768223i	$0.278859\pi$
$468$	−7.93653e11	−0.764758
$469$	1.59714e12	1.52428
$470$	1.97928e11	0.187097
$471$	−2.22339e11	−0.208171
$472$	9.26540e10	0.0859261
$473$	−7.58711e10	−0.0696949
$474$	−1.04374e11	−0.0949703
$475$	−1.29508e12	−1.16728
$476$	0	0
$477$	3.95717e10	0.0349987
$478$	1.11372e12	0.975773
$479$	2.08121e12	1.80637	0.903185	−	0.429251i	$-0.141223\pi$
$479$	2.08121e12	1.80637	0.903185	+	0.429251i	$0.141223\pi$
$480$	2.32100e11	0.199568
$481$	1.06647e12	0.908438
$482$	−5.36006e11	−0.452333
$483$	−8.28655e11	−0.692806
$484$	6.21143e11	0.514503
$485$	−6.53311e11	−0.536145
$486$	−6.32609e11	−0.514366
$487$	7.18370e11	0.578719	0.289360	−	0.957220i	$-0.406558\pi$
$487$	7.18370e11	0.578719	0.289360	+	0.957220i	$0.406558\pi$
$488$	−6.48197e11	−0.517390
$489$	2.24380e11	0.177457
$490$	5.94910e11	0.466196
$491$	−9.78925e11	−0.760121	−0.380060	−	0.924962i	$-0.624097\pi$
$491$	−9.78925e11	−0.760121	−0.380060	+	0.924962i	$0.624097\pi$
$492$	−5.24124e11	−0.403265
$493$	0	0
$494$	1.31121e12	0.990604
$495$	2.67707e11	0.200418
$496$	−5.61889e11	−0.416853
$497$	−2.27699e12	−1.67401
$498$	−4.02059e10	−0.0292926
$499$	1.70045e12	1.22775	0.613876	−	0.789402i	$-0.289609\pi$
$499$	1.70045e12	1.22775	0.613876	+	0.789402i	$0.289609\pi$
$500$	−8.24966e11	−0.590297
$501$	−4.58850e11	−0.325388
$502$	5.77690e11	0.406002
$503$	1.03194e11	0.0718787	0.0359393	−	0.999354i	$-0.488558\pi$
$503$	1.03194e11	0.0718787	0.0359393	+	0.999354i	$0.488558\pi$
$504$	−1.84732e12	−1.27528
$505$	2.86731e11	0.196184
$506$	3.94906e11	0.267804
$507$	4.13709e11	0.278073
$508$	1.31807e12	0.878113
$509$	7.49118e11	0.494675	0.247338	−	0.968929i	$-0.420444\pi$
$509$	7.49118e11	0.494675	0.247338	+	0.968929i	$0.420444\pi$
$510$	0	0
$511$	−8.13378e11	−0.527714
$512$	−7.58967e11	−0.488099
$513$	−1.78162e12	−1.13576
$514$	9.79431e11	0.618928
$515$	1.35278e11	0.0847412
$516$	6.41339e10	0.0398257
$517$	6.89528e11	0.424467
$518$	1.04362e12	0.636883
$519$	−3.55246e11	−0.214920
$520$	8.79468e11	0.527479
$521$	−1.51334e12	−0.899843	−0.449921	−	0.893068i	$-0.648548\pi$
$521$	−1.51334e12	−0.899843	−0.449921	+	0.893068i	$0.648548\pi$
$522$	1.21457e12	0.715990
$523$	1.87630e12	1.09659	0.548295	−	0.836285i	$-0.315277\pi$
$523$	1.87630e12	1.09659	0.548295	+	0.836285i	$0.315277\pi$
$524$	1.06212e12	0.615433
$525$	−1.01065e12	−0.580611
$526$	4.11059e11	0.234136
$527$	0	0
$528$	1.02895e11	0.0576156
$529$	−1.83116e11	−0.101666
$530$	−1.84356e10	−0.0101488
$531$	−1.42692e11	−0.0778889
$532$	−3.38937e12	−1.83450
$533$	−3.13703e12	−1.68363
$534$	−7.30307e11	−0.388660
$535$	7.93121e11	0.418550
$536$	1.53034e12	0.800844
$537$	−2.92112e11	−0.151588
$538$	1.49560e12	0.769652
$539$	2.07251e12	1.05766
$540$	−5.02398e11	−0.254259
$541$	−2.51866e12	−1.26410	−0.632050	−	0.774927i	$-0.717786\pi$
$541$	−2.51866e12	−1.26410	−0.632050	+	0.774927i	$0.717786\pi$
$542$	−6.68679e11	−0.332829
$543$	−4.00237e11	−0.197569
$544$	0	0
$545$	5.96448e11	0.289593
$546$	1.02324e12	0.492730
$547$	2.33711e12	1.11618	0.558091	−	0.829779i	$-0.311534\pi$
$547$	2.33711e12	1.11618	0.558091	+	0.829779i	$0.311534\pi$
$548$	5.04437e10	0.0238943
$549$	9.98260e11	0.468995
$550$	4.81640e11	0.224435
$551$	5.30050e12	2.44982
$552$	−7.94002e11	−0.363995
$553$	1.61482e12	0.734278
$554$	5.64899e11	0.254787
$555$	3.04081e11	0.136041
$556$	1.55890e11	0.0691802
$557$	7.35788e11	0.323895	0.161948	−	0.986799i	$-0.448222\pi$
$557$	7.35788e11	0.323895	0.161948	+	0.986799i	$0.448222\pi$
$558$	−1.62975e12	−0.711653
$559$	3.83860e11	0.166272
$560$	−4.56963e11	−0.196352
$561$	0	0
$562$	1.35571e12	0.573261
$563$	−2.80471e12	−1.17652	−0.588262	−	0.808670i	$-0.700188\pi$
$563$	−2.80471e12	−1.17652	−0.588262	+	0.808670i	$0.700188\pi$
$564$	−5.82858e11	−0.242553
$565$	−4.89812e10	−0.0202214
$566$	−3.01881e11	−0.123641
$567$	2.08089e12	0.845521
$568$	−2.18177e12	−0.879512
$569$	7.41576e11	0.296586	0.148293	−	0.988943i	$-0.452622\pi$
$569$	7.41576e11	0.296586	0.148293	+	0.988943i	$0.452622\pi$
$570$	3.73862e11	0.148346
$571$	−2.37109e12	−0.933440	−0.466720	−	0.884405i	$-0.654564\pi$
$571$	−2.37109e12	−0.933440	−0.466720	+	0.884405i	$0.654564\pi$
$572$	1.28810e12	0.503114
$573$	−1.10052e12	−0.426485
$574$	−3.06984e12	−1.18035
$575$	1.97341e12	0.752855
$576$	−6.30767e11	−0.238763
$577$	1.64213e12	0.616759	0.308380	−	0.951263i	$-0.400213\pi$
$577$	1.64213e12	0.616759	0.308380	+	0.951263i	$0.400213\pi$
$578$	0	0
$579$	−2.01245e12	−0.744168
$580$	1.49468e12	0.548432
$581$	6.22047e11	0.226481
$582$	−7.28323e11	−0.263130
$583$	−6.42247e10	−0.0230247
$584$	−7.79364e11	−0.277257
$585$	−1.35443e12	−0.478140
$586$	−5.26389e11	−0.184403
$587$	−4.40209e12	−1.53034	−0.765168	−	0.643830i	$-0.777344\pi$
$587$	−4.40209e12	−1.53034	−0.765168	+	0.643830i	$0.777344\pi$
$588$	−1.75189e12	−0.604379
$589$	−7.11238e12	−2.43498
$590$	6.64774e10	0.0225860
$591$	−3.72581e11	−0.125625
$592$	−5.30954e11	−0.177668
$593$	3.23487e12	1.07426	0.537132	−	0.843498i	$-0.319508\pi$
$593$	3.23487e12	1.07426	0.537132	+	0.843498i	$0.319508\pi$
$594$	6.62584e11	0.218374
$595$	0	0
$596$	2.99229e12	0.971393
$597$	−8.71049e11	−0.280645
$598$	−1.99798e12	−0.638904
$599$	4.90816e12	1.55775	0.778875	−	0.627179i	$-0.215791\pi$
$599$	4.90816e12	1.55775	0.778875	+	0.627179i	$0.215791\pi$
$600$	−9.68389e11	−0.305049
$601$	1.05961e12	0.331292	0.165646	−	0.986185i	$-0.447029\pi$
$601$	1.05961e12	0.331292	0.165646	+	0.986185i	$0.447029\pi$
$602$	3.75637e11	0.116569
$603$	−2.35682e12	−0.725936
$604$	−2.12314e12	−0.649101
$605$	1.06003e12	0.321676
$606$	3.19653e11	0.0962836
$607$	5.76988e11	0.172511	0.0862556	−	0.996273i	$-0.472510\pi$
$607$	5.76988e11	0.172511	0.0862556	+	0.996273i	$0.472510\pi$
$608$	−5.12989e12	−1.52245
$609$	4.13639e12	1.21855
$610$	−4.65068e11	−0.135998
$611$	−3.48858e12	−1.01266
$612$	0	0
$613$	−5.09644e12	−1.45779	−0.728895	−	0.684625i	$-0.759966\pi$
$613$	−5.09644e12	−1.45779	−0.728895	+	0.684625i	$0.759966\pi$
$614$	−2.09884e12	−0.595967
$615$	−8.94458e11	−0.252128
$616$	2.99820e12	0.838971
$617$	5.92498e12	1.64590	0.822951	−	0.568113i	$-0.192326\pi$
$617$	5.92498e12	1.64590	0.822951	+	0.568113i	$0.192326\pi$
$618$	1.50810e11	0.0415894
$619$	−3.09980e12	−0.848644	−0.424322	−	0.905511i	$-0.639487\pi$
$619$	−3.09980e12	−0.848644	−0.424322	+	0.905511i	$0.639487\pi$
$620$	−2.00561e12	−0.545110
$621$	2.71478e12	0.732526
$622$	1.38649e12	0.371417
$623$	1.12990e13	3.00498
$624$	−5.20582e11	−0.137454
$625$	1.62220e12	0.425251
$626$	7.83657e11	0.203958
$627$	1.30244e12	0.336552
$628$	1.38573e12	0.355518
$629$	0	0
$630$	−1.32542e12	−0.335212
$631$	3.86695e11	0.0971040	0.0485520	−	0.998821i	$-0.484539\pi$
$631$	3.86695e11	0.0971040	0.0485520	+	0.998821i	$0.484539\pi$
$632$	1.54729e12	0.385784
$633$	1.60441e12	0.397191
$634$	2.55963e12	0.629180
$635$	2.24938e12	0.549011
$636$	5.42892e10	0.0131570
$637$	−1.04856e13	−2.52328
$638$	−1.97125e12	−0.471030
$639$	3.36005e12	0.797245
$640$	−1.70034e12	−0.400615
$641$	−5.83791e12	−1.36583	−0.682914	−	0.730499i	$-0.739288\pi$
$641$	−5.83791e12	−1.36583	−0.682914	+	0.730499i	$0.739288\pi$
$642$	8.84185e11	0.205417
$643$	−4.53130e12	−1.04538	−0.522689	−	0.852523i	$-0.675071\pi$
$643$	−4.53130e12	−1.04538	−0.522689	+	0.852523i	$0.675071\pi$
$644$	5.16462e12	1.18318
$645$	1.09449e11	0.0248997
$646$	0	0
$647$	−8.18289e12	−1.83585	−0.917925	−	0.396754i	$-0.870137\pi$
$647$	−8.18289e12	−1.83585	−0.917925	+	0.396754i	$0.870137\pi$
$648$	1.99387e12	0.444231
$649$	2.31589e11	0.0512410
$650$	−2.43680e12	−0.535438
$651$	−5.55034e12	−1.21117
$652$	−1.39845e12	−0.303064
$653$	2.43949e12	0.525036	0.262518	−	0.964927i	$-0.415447\pi$
$653$	2.43949e12	0.525036	0.262518	+	0.964927i	$0.415447\pi$
$654$	6.64931e11	0.142127
$655$	1.81258e12	0.384779
$656$	1.56181e12	0.329276
$657$	1.20026e12	0.251323
$658$	−3.41385e12	−0.709950
$659$	−1.61269e12	−0.333094	−0.166547	−	0.986034i	$-0.553262\pi$
$659$	−1.61269e12	−0.333094	−0.166547	+	0.986034i	$0.553262\pi$
$660$	3.67273e11	0.0753427
$661$	−7.30795e11	−0.148898	−0.0744491	−	0.997225i	$-0.523720\pi$
$661$	−7.30795e11	−0.148898	−0.0744491	+	0.997225i	$0.523720\pi$
$662$	2.60478e12	0.527121
$663$	0	0
$664$	5.96034e11	0.118991
$665$	−5.78422e12	−1.14696
$666$	−1.54003e12	−0.303315
$667$	−8.07674e12	−1.58005
$668$	2.85980e12	0.555701
$669$	−6.49787e11	−0.125416
$670$	1.09799e12	0.210505
$671$	−1.62017e12	−0.308539
$672$	−4.00325e12	−0.757271
$673$	−4.80522e12	−0.902911	−0.451456	−	0.892294i	$-0.649095\pi$
$673$	−4.80522e12	−0.902911	−0.451456	+	0.892294i	$0.649095\pi$
$674$	−4.33272e12	−0.808707
$675$	3.31103e12	0.613899
$676$	−2.57846e12	−0.474897
$677$	−2.48514e12	−0.454675	−0.227337	−	0.973816i	$-0.573002\pi$
$677$	−2.48514e12	−0.454675	−0.227337	+	0.973816i	$0.573002\pi$
$678$	−5.46051e10	−0.00992429
$679$	1.12683e13	2.03443
$680$	0	0
$681$	3.41878e12	0.609130
$682$	2.64509e12	0.468177
$683$	−8.09671e11	−0.142369	−0.0711845	−	0.997463i	$-0.522678\pi$
$683$	−8.09671e11	−0.142369	−0.0711845	+	0.997463i	$0.522678\pi$
$684$	5.00154e12	0.873677
$685$	8.60861e10	0.0149391
$686$	−5.03002e12	−0.867184
$687$	−2.89126e12	−0.495202
$688$	−1.91109e11	−0.0325187
$689$	3.24937e11	0.0549303
$690$	−5.69680e11	−0.0956776
$691$	3.01668e12	0.503359	0.251679	−	0.967811i	$-0.419017\pi$
$691$	3.01668e12	0.503359	0.251679	+	0.967811i	$0.419017\pi$
$692$	2.21408e12	0.367043
$693$	−4.61740e12	−0.760497
$694$	3.77338e12	0.617465
$695$	2.66038e11	0.0432526
$696$	3.96341e12	0.640217
$697$	0	0
$698$	−1.24728e12	−0.198890
$699$	1.14934e11	0.0182096
$700$	6.29893e12	0.991575
$701$	−4.71932e12	−0.738156	−0.369078	−	0.929398i	$-0.620326\pi$
$701$	−4.71932e12	−0.738156	−0.369078	+	0.929398i	$0.620326\pi$
$702$	−3.35226e12	−0.520979
$703$	−6.72080e12	−1.03782
$704$	1.02373e12	0.157076
$705$	−9.94693e11	−0.151648
$706$	−3.25604e12	−0.493251
$707$	−4.94552e12	−0.744432
$708$	−1.95763e11	−0.0292806
$709$	8.19568e12	1.21808	0.609041	−	0.793138i	$-0.291554\pi$
$709$	8.19568e12	1.21808	0.609041	+	0.793138i	$0.291554\pi$
$710$	−1.56538e12	−0.231183
$711$	−2.38291e12	−0.349699
$712$	1.08264e13	1.57880
$713$	1.08376e13	1.57048
$714$	0	0
$715$	2.19824e12	0.314555
$716$	1.82060e12	0.258884
$717$	−5.59701e12	−0.790897
$718$	3.98601e12	0.559729
$719$	−1.16808e13	−1.63001	−0.815006	−	0.579452i	$-0.803267\pi$
$719$	−1.16808e13	−1.63001	−0.815006	+	0.579452i	$0.803267\pi$
$720$	6.74319e11	0.0935124
$721$	−2.33327e12	−0.321555
$722$	−4.43684e12	−0.607654
$723$	2.69372e12	0.366631
$724$	2.49449e12	0.337410
$725$	−9.85064e12	−1.32417
$726$	1.18174e12	0.157873
$727$	−5.18587e12	−0.688520	−0.344260	−	0.938874i	$-0.611870\pi$
$727$	−5.18587e12	−0.688520	−0.344260	+	0.938874i	$0.611870\pi$
$728$	−1.51690e13	−2.00155
$729$	−5.67392e11	−0.0744063
$730$	−5.59178e11	−0.0728781
$731$	0	0
$732$	1.36953e12	0.176308
$733$	−9.00169e10	−0.0115175	−0.00575873	−	0.999983i	$-0.501833\pi$
$733$	−9.00169e10	−0.0115175	−0.00575873	+	0.999983i	$0.501833\pi$
$734$	5.07104e12	0.644859
$735$	−2.98974e12	−0.377868
$736$	7.81677e12	0.981923
$737$	3.82511e12	0.477573
$738$	4.53001e12	0.562142
$739$	−1.27401e13	−1.57135	−0.785677	−	0.618638i	$-0.787685\pi$
$739$	−1.27401e13	−1.57135	−0.785677	+	0.618638i	$0.787685\pi$
$740$	−1.89519e12	−0.232333
$741$	−6.58951e12	−0.802918
$742$	3.17976e11	0.0385103
$743$	7.98450e11	0.0961165	0.0480583	−	0.998845i	$-0.484697\pi$
$743$	7.98450e11	0.0961165	0.0480583	+	0.998845i	$0.484697\pi$
$744$	−5.31823e12	−0.636340
$745$	5.10657e12	0.607332
$746$	7.82329e12	0.924836
$747$	−9.17926e11	−0.107861
$748$	0	0
$749$	−1.36797e13	−1.58821
$750$	−1.56952e12	−0.181130
$751$	−9.56992e12	−1.09781	−0.548907	−	0.835883i	$-0.684956\pi$
$751$	−9.56992e12	−1.09781	−0.548907	+	0.835883i	$0.684956\pi$
$752$	1.73683e12	0.198051
$753$	−2.90320e12	−0.329078
$754$	9.97328e12	1.12374
$755$	−3.62330e12	−0.405829
$756$	8.66533e12	0.964799
$757$	−1.18435e13	−1.31084	−0.655418	−	0.755267i	$-0.727507\pi$
$757$	−1.18435e13	−1.31084	−0.655418	+	0.755267i	$0.727507\pi$
$758$	4.46590e12	0.491358
$759$	−1.98461e12	−0.217064
$760$	−5.54233e12	−0.602603
$761$	7.12456e12	0.770064	0.385032	−	0.922903i	$-0.374190\pi$
$761$	7.12456e12	0.770064	0.385032	+	0.922903i	$0.374190\pi$
$762$	2.50765e12	0.269445
$763$	−1.02875e13	−1.09888
$764$	6.85906e12	0.728357
$765$	0	0
$766$	−2.81254e12	−0.295168
$767$	−1.17170e12	−0.122246
$768$	−3.08854e12	−0.320352
$769$	−1.51364e13	−1.56082	−0.780411	−	0.625267i	$-0.784990\pi$
$769$	−1.51364e13	−1.56082	−0.780411	+	0.625267i	$0.784990\pi$
$770$	2.15115e12	0.220527
$771$	−4.92216e12	−0.501662
$772$	1.25426e13	1.27090
$773$	6.55361e12	0.660196	0.330098	−	0.943947i	$-0.392918\pi$
$773$	6.55361e12	0.660196	0.330098	+	0.943947i	$0.392918\pi$
$774$	−5.54310e11	−0.0555161
$775$	1.32179e13	1.31615
$776$	1.07970e13	1.06888
$777$	−5.24476e12	−0.516216
$778$	−4.32508e11	−0.0423239
$779$	1.97693e13	1.92342
$780$	−1.85817e12	−0.179746
$781$	−5.45335e12	−0.524486
$782$	0	0
$783$	−1.35514e13	−1.28841
$784$	5.22037e12	0.493491
$785$	2.36486e12	0.222276
$786$	2.02070e12	0.188843
$787$	1.72441e13	1.60234	0.801168	−	0.598439i	$-0.204212\pi$
$787$	1.72441e13	1.60234	0.801168	+	0.598439i	$0.204212\pi$
$788$	2.32212e12	0.214544
$789$	−2.06579e12	−0.189775
$790$	1.11015e12	0.101405
$791$	8.44824e11	0.0767312
$792$	−4.42430e12	−0.399559
$793$	8.19706e12	0.736086
$794$	6.82057e12	0.609015
$795$	9.26487e10	0.00822597
$796$	5.42884e12	0.479290
$797$	−1.92951e13	−1.69389	−0.846944	−	0.531682i	$-0.821560\pi$
$797$	−1.92951e13	−1.69389	−0.846944	+	0.531682i	$0.821560\pi$
$798$	−6.44835e12	−0.562906
$799$	0	0
$800$	9.53358e12	0.822908
$801$	−1.66733e13	−1.43112
$802$	4.03096e12	0.344052
$803$	−1.94803e12	−0.165339
$804$	−3.23337e12	−0.272899
$805$	8.81382e12	0.739746
$806$	−1.33825e13	−1.11694
$807$	−7.51616e12	−0.623829
$808$	−4.73871e12	−0.391119
$809$	3.75180e12	0.307944	0.153972	−	0.988075i	$-0.450794\pi$
$809$	3.75180e12	0.307944	0.153972	+	0.988075i	$0.450794\pi$
$810$	1.43056e12	0.116768
$811$	−4.21763e12	−0.342353	−0.171177	−	0.985240i	$-0.554757\pi$
$811$	−4.21763e12	−0.342353	−0.171177	+	0.985240i	$0.554757\pi$
$812$	−2.57802e13	−2.08106
$813$	3.36047e12	0.269769
$814$	2.49946e12	0.199543
$815$	−2.38657e12	−0.189481
$816$	0	0
$817$	−2.41905e12	−0.189953
$818$	1.33371e12	0.104153
$819$	2.33611e13	1.81433
$820$	5.57474e12	0.430588
$821$	−2.89064e12	−0.222050	−0.111025	−	0.993818i	$-0.535413\pi$
$821$	−2.89064e12	−0.222050	−0.111025	+	0.993818i	$0.535413\pi$
$822$	9.59704e10	0.00733186
$823$	1.85820e11	0.0141186	0.00705931	−	0.999975i	$-0.497753\pi$
$823$	1.85820e11	0.0141186	0.00705931	+	0.999975i	$0.497753\pi$
$824$	−2.23569e12	−0.168943
$825$	−2.42050e12	−0.181912
$826$	−1.14660e12	−0.0857040
$827$	−2.19451e13	−1.63141	−0.815704	−	0.578470i	$-0.803650\pi$
$827$	−2.19451e13	−1.63141	−0.815704	+	0.578470i	$0.803650\pi$
$828$	−7.62119e12	−0.563490
$829$	7.80531e12	0.573977	0.286989	−	0.957934i	$-0.407346\pi$
$829$	7.80531e12	0.573977	0.286989	+	0.957934i	$0.407346\pi$
$830$	4.27642e11	0.0312773
$831$	−2.83892e12	−0.206513
$832$	−5.17944e12	−0.374738
$833$	0	0
$834$	2.96584e11	0.0212276
$835$	4.88047e12	0.347434
$836$	−8.11748e12	−0.574768
$837$	1.81836e13	1.28061
$838$	−3.39993e11	−0.0238161
$839$	1.83657e13	1.27962	0.639808	−	0.768535i	$-0.279014\pi$
$839$	1.83657e13	1.27962	0.639808	+	0.768535i	$0.279014\pi$
$840$	−4.32511e12	−0.299737
$841$	2.58094e13	1.77908
$842$	−8.79613e12	−0.603097
$843$	−6.81314e12	−0.464647
$844$	−9.99954e12	−0.678327
$845$	−4.40033e12	−0.296914
$846$	5.03766e12	0.338113
$847$	−1.82833e13	−1.22062
$848$	−1.61773e11	−0.0107430
$849$	1.51711e12	0.100215
$850$	0	0
$851$	1.02409e13	0.669356
$852$	4.60972e12	0.299707
$853$	−1.15587e13	−0.747544	−0.373772	−	0.927521i	$-0.621936\pi$
$853$	−1.15587e13	−0.747544	−0.373772	+	0.927521i	$0.621936\pi$
$854$	8.02147e12	0.516052
$855$	8.53551e12	0.546238
$856$	−1.31076e13	−0.834434
$857$	3.67551e12	0.232757	0.116379	−	0.993205i	$-0.462871\pi$
$857$	3.67551e12	0.232757	0.116379	+	0.993205i	$0.462871\pi$
$858$	2.45063e12	0.154378
$859$	2.36948e13	1.48485	0.742426	−	0.669928i	$-0.233675\pi$
$859$	2.36948e13	1.48485	0.742426	+	0.669928i	$0.233675\pi$
$860$	−6.82147e11	−0.0425241
$861$	1.54275e13	0.956715
$862$	1.16820e12	0.0720666
$863$	8.18769e12	0.502473	0.251237	−	0.967926i	$-0.419163\pi$
$863$	8.18769e12	0.502473	0.251237	+	0.967926i	$0.419163\pi$
$864$	1.31152e13	0.800686
$865$	3.77850e12	0.229481
$866$	−7.46736e12	−0.451166
$867$	0	0
$868$	3.45927e13	2.06845
$869$	3.86746e12	0.230058
$870$	2.84367e12	0.168284
$871$	−1.93526e13	−1.13935
$872$	−9.85728e12	−0.577342
$873$	−1.66281e13	−0.968896
$874$	1.25911e13	0.729898
$875$	2.42828e13	1.40043
$876$	1.64667e12	0.0944794
$877$	1.34379e13	0.767064	0.383532	−	0.923528i	$-0.374708\pi$
$877$	1.34379e13	0.767064	0.383532	+	0.923528i	$0.374708\pi$
$878$	3.78549e11	0.0214979
$879$	2.64538e12	0.149465
$880$	−1.09442e12	−0.0615192
$881$	−3.19613e13	−1.78745	−0.893724	−	0.448618i	$-0.851916\pi$
$881$	−3.19613e13	−1.78745	−0.893724	+	0.448618i	$0.851916\pi$
$882$	1.51416e13	0.842489
$883$	9.21484e12	0.510111	0.255056	−	0.966926i	$-0.417906\pi$
$883$	9.21484e12	0.510111	0.255056	+	0.966926i	$0.417906\pi$
$884$	0	0
$885$	−3.34084e11	−0.0183067
$886$	−1.15789e13	−0.631272
$887$	−5.95887e12	−0.323227	−0.161614	−	0.986854i	$-0.551670\pi$
$887$	−5.95887e12	−0.323227	−0.161614	+	0.986854i	$0.551670\pi$
$888$	−5.02543e12	−0.271216
$889$	−3.87972e13	−2.08325
$890$	7.76776e12	0.414993
$891$	4.98368e12	0.264911
$892$	4.04982e12	0.214187
$893$	2.19847e13	1.15688
$894$	5.69289e12	0.298067
$895$	3.10699e12	0.161859
$896$	2.93274e13	1.52016
$897$	1.00409e13	0.517853
$898$	−3.77565e12	−0.193753
$899$	−5.40981e13	−2.76225
$900$	−9.29504e12	−0.472237
$901$	0	0
$902$	−7.35220e12	−0.369818
$903$	−1.88778e12	−0.0944834
$904$	8.09494e11	0.0403140
$905$	4.25704e12	0.210955
$906$	−4.03932e12	−0.199173
$907$	−3.49523e13	−1.71491	−0.857457	−	0.514555i	$-0.827957\pi$
$907$	−3.49523e13	−1.71491	−0.857457	+	0.514555i	$0.827957\pi$
$908$	−2.13077e13	−1.04028
$909$	7.29788e12	0.354535
$910$	−1.08834e13	−0.526115
$911$	−1.82282e12	−0.0876819	−0.0438410	−	0.999039i	$-0.513959\pi$
$911$	−1.82282e12	−0.0876819	−0.0438410	+	0.999039i	$0.513959\pi$
$912$	3.28066e12	0.157031
$913$	1.48979e12	0.0709589
$914$	6.13795e12	0.290914
$915$	2.33721e12	0.110231
$916$	1.80199e13	0.845712
$917$	−3.12633e13	−1.46007
$918$	0	0
$919$	−1.16854e13	−0.540411	−0.270206	−	0.962803i	$-0.587092\pi$
$919$	−1.16854e13	−0.540411	−0.270206	+	0.962803i	$0.587092\pi$
$920$	8.44524e12	0.388657
$921$	1.05478e13	0.483052
$922$	−1.22738e13	−0.559358
$923$	2.75905e13	1.25127
$924$	−6.33470e12	−0.285892
$925$	1.24902e13	0.560959
$926$	5.44783e12	0.243486
$927$	3.44309e12	0.153140
$928$	−3.90189e13	−1.72707
$929$	−2.03224e13	−0.895166	−0.447583	−	0.894242i	$-0.647715\pi$
$929$	−2.03224e13	−0.895166	−0.447583	+	0.894242i	$0.647715\pi$
$930$	−3.81572e12	−0.167264
$931$	6.60793e13	2.88265
$932$	−7.16329e11	−0.0310986
$933$	−6.96787e12	−0.301046
$934$	−1.56046e13	−0.670954
$935$	0	0
$936$	2.23842e13	0.953235
$937$	1.03126e13	0.437061	0.218530	−	0.975830i	$-0.429874\pi$
$937$	1.03126e13	0.437061	0.218530	+	0.975830i	$0.429874\pi$
$938$	−1.89381e13	−0.798773
$939$	−3.93829e12	−0.165315
$940$	6.19945e12	0.258987
$941$	9.97481e12	0.414717	0.207358	−	0.978265i	$-0.433513\pi$
$941$	9.97481e12	0.414717	0.207358	+	0.978265i	$0.433513\pi$
$942$	2.63639e12	0.109089
$943$	−3.01239e13	−1.24053
$944$	5.83343e11	0.0239084
$945$	1.47881e13	0.603209
$946$	8.99644e11	0.0365225
$947$	−7.55330e12	−0.305184	−0.152592	−	0.988289i	$-0.548762\pi$
$947$	−7.55330e12	−0.305184	−0.152592	+	0.988289i	$0.548762\pi$
$948$	−3.26916e12	−0.131462
$949$	9.85578e12	0.394451
$950$	1.53565e13	0.611696
$951$	−1.28635e13	−0.509972
$952$	0	0
$953$	5.11924e12	0.201042	0.100521	−	0.994935i	$-0.467949\pi$
$953$	5.11924e12	0.201042	0.100521	+	0.994935i	$0.467949\pi$
$954$	−4.69222e11	−0.0183405
$955$	1.17055e13	0.455381
$956$	3.48836e13	1.35070
$957$	9.90657e12	0.381786
$958$	−2.46781e13	−0.946599
$959$	−1.48481e12	−0.0566874
$960$	−1.47681e12	−0.0561181
$961$	4.61509e13	1.74552
$962$	−1.26457e13	−0.476052
$963$	2.01865e13	0.756384
$964$	−1.67887e13	−0.626137
$965$	2.14050e13	0.794588
$966$	9.82581e12	0.363054
$967$	2.96090e13	1.08894	0.544471	−	0.838780i	$-0.316731\pi$
$967$	2.96090e13	1.08894	0.544471	+	0.838780i	$0.316731\pi$
$968$	−1.75187e13	−0.641303
$969$	0	0
$970$	7.74666e12	0.280958
$971$	2.36780e13	0.854790	0.427395	−	0.904065i	$-0.359431\pi$
$971$	2.36780e13	0.854790	0.427395	+	0.904065i	$0.359431\pi$
$972$	−1.98144e13	−0.712006
$973$	−4.58861e12	−0.164124
$974$	−8.51810e12	−0.303269
$975$	1.22462e13	0.433990
$976$	−4.08100e12	−0.143960
$977$	−1.30708e13	−0.458961	−0.229480	−	0.973313i	$-0.573703\pi$
$977$	−1.30708e13	−0.458961	−0.229480	+	0.973313i	$0.573703\pi$
$978$	−2.66059e12	−0.0929937
$979$	2.70608e13	0.941496
$980$	1.86336e13	0.645328
$981$	1.51808e13	0.523339
$982$	1.16076e13	0.398329
$983$	−1.05637e13	−0.360850	−0.180425	−	0.983589i	$-0.557747\pi$
$983$	−1.05637e13	−0.360850	−0.180425	+	0.983589i	$0.557747\pi$
$984$	1.47824e13	0.502651
$985$	3.96288e12	0.134137
$986$	0	0
$987$	1.71564e13	0.575438
$988$	4.10693e13	1.37123
$989$	3.68608e12	0.122513
$990$	−3.17435e12	−0.105026
$991$	4.60965e13	1.51823	0.759113	−	0.650958i	$-0.225633\pi$
$991$	4.60965e13	1.51823	0.759113	+	0.650958i	$0.225633\pi$
$992$	5.23568e13	1.71661
$993$	−1.30904e13	−0.427250
$994$	2.69995e13	0.877238
$995$	9.26473e12	0.299660
$996$	−1.25932e12	−0.0405480
$997$	2.60737e13	0.835748	0.417874	−	0.908505i	$-0.362775\pi$
$997$	2.60737e13	0.835748	0.417874	+	0.908505i	$0.362775\pi$
$998$	−2.01631e13	−0.643384
$999$	1.71825e13	0.545811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.c.1.6		12
17.4	even	4		17.10.b.a.16.7	✓	12
17.13	even	4		17.10.b.a.16.8	yes	12
17.16	even	2	inner	289.10.a.c.1.5		12
51.38	odd	4		153.10.d.b.118.5		12
51.47	odd	4		153.10.d.b.118.6		12
68.47	odd	4		272.10.b.c.33.5		12
68.55	odd	4		272.10.b.c.33.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.b.a.16.7	✓	12	17.4	even	4
17.10.b.a.16.8	yes	12	17.13	even	4
153.10.d.b.118.5		12	51.38	odd	4
153.10.d.b.118.6		12	51.47	odd	4
272.10.b.c.33.5		12	68.47	odd	4
272.10.b.c.33.8		12	68.55	odd	4
289.10.a.c.1.5		12	17.16	even	2	inner
289.10.a.c.1.6		12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-11.8575 q^{2} +59.5904 q^{3} -371.399 q^{4} -633.821 q^{5} -706.595 q^{6} +10932.1 q^{7} +10474.9 q^{8} -16132.0 q^{9} +O(q^{10})\)	\(q-11.8575 q^{2} +59.5904 q^{3} -371.399 q^{4} -633.821 q^{5} -706.595 q^{6} +10932.1 q^{7} +10474.9 q^{8} -16132.0 q^{9} +7515.55 q^{10} +26182.2 q^{11} -22131.8 q^{12} -132465. q^{13} -129628. q^{14} -37769.6 q^{15} +65949.4 q^{16} +191286. q^{18} +834785. q^{19} +235400. q^{20} +651448. q^{21} -310456. q^{22} -1.27202e6 q^{23} +624205. q^{24} -1.55140e6 q^{25} +1.57071e6 q^{26} -2.13423e6 q^{27} -4.06017e6 q^{28} +6.34953e6 q^{29} +447855. q^{30} -8.52001e6 q^{31} -6.14516e6 q^{32} +1.56021e6 q^{33} -6.92899e6 q^{35} +5.99140e6 q^{36} -8.05093e6 q^{37} -9.89850e6 q^{38} -7.89366e6 q^{39} -6.63923e6 q^{40} +2.36819e7 q^{41} -7.72457e6 q^{42} -2.89782e6 q^{43} -9.72403e6 q^{44} +1.02248e7 q^{45} +1.50830e7 q^{46} +2.63358e7 q^{47} +3.92995e6 q^{48} +7.91572e7 q^{49} +1.83957e7 q^{50} +4.91975e7 q^{52} -2.45299e6 q^{53} +2.53067e7 q^{54} -1.65948e7 q^{55} +1.14513e8 q^{56} +4.97452e7 q^{57} -7.52898e7 q^{58} +8.84531e6 q^{59} +1.40276e7 q^{60} -6.18808e7 q^{61} +1.01026e8 q^{62} -1.76356e8 q^{63} +3.91004e7 q^{64} +8.39593e7 q^{65} -1.85002e7 q^{66} +1.46096e8 q^{67} -7.58002e7 q^{69} +8.21608e7 q^{70} -2.08285e8 q^{71} -1.68981e8 q^{72} -7.44027e7 q^{73} +9.54641e7 q^{74} -9.24483e7 q^{75} -3.10038e8 q^{76} +2.86226e8 q^{77} +9.35993e7 q^{78} +1.47713e8 q^{79} -4.18001e7 q^{80} +1.90346e8 q^{81} -2.80809e8 q^{82} +5.69010e7 q^{83} -2.41947e8 q^{84} +3.43609e7 q^{86} +3.78371e8 q^{87} +2.74256e8 q^{88} +1.03356e9 q^{89} -1.21241e8 q^{90} -1.44812e9 q^{91} +4.72427e8 q^{92} -5.07710e8 q^{93} -3.12277e8 q^{94} -5.29104e8 q^{95} -3.66193e8 q^{96} +1.03075e9 q^{97} -9.38609e8 q^{98} -4.22370e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9}+O(q^{10}) \) 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9	\( 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9} - 63204 q^{13} + 243480 q^{15} + 38978 q^{16} + 547706 q^{18} - 1110672 q^{19} - 172580 q^{21} + 4441796 q^{25} - 1336332 q^{26} - 500496 q^{30} + 1934850 q^{32} - 6557404 q^{33} + 3519864 q^{35} - 30244102 q^{36} + 28748136 q^{38} + 11901296 q^{42} - 10004616 q^{43} - 112552440 q^{47} - 121354720 q^{49} - 164889018 q^{50} - 59093180 q^{52} - 76804272 q^{53} + 300732568 q^{55} - 11618904 q^{59} - 101609232 q^{60} - 260062974 q^{64} - 18429632 q^{66} - 304208752 q^{67} - 211308236 q^{69} - 460311456 q^{70} + 493218954 q^{72} - 416024248 q^{76} - 138357828 q^{77} - 363335792 q^{81} + 845042136 q^{83} + 958037984 q^{84} + 127952904 q^{86} - 610860648 q^{87} - 938223804 q^{89} - 1635779524 q^{93} + 238629952 q^{94} - 152046078 q^{98}+O(q^{100}) \) 12 * q - 30 * q^2 + 1874 * q^4 - 23550 * q^8 + 9184 * q^9 - 63204 * q^13 + 243480 * q^15 + 38978 * q^16 + 547706 * q^18 - 1110672 * q^19 - 172580 * q^21 + 4441796 * q^25 - 1336332 * q^26 - 500496 * q^30 + 1934850 * q^32 - 6557404 * q^33 + 3519864 * q^35 - 30244102 * q^36 + 28748136 * q^38 + 11901296 * q^42 - 10004616 * q^43 - 112552440 * q^47 - 121354720 * q^49 - 164889018 * q^50 - 59093180 * q^52 - 76804272 * q^53 + 300732568 * q^55 - 11618904 * q^59 - 101609232 * q^60 - 260062974 * q^64 - 18429632 * q^66 - 304208752 * q^67 - 211308236 * q^69 - 460311456 * q^70 + 493218954 * q^72 - 416024248 * q^76 - 138357828 * q^77 - 363335792 * q^81 + 845042136 * q^83 + 958037984 * q^84 + 127952904 * q^86 - 610860648 * q^87 - 938223804 * q^89 - 1635779524 * q^93 + 238629952 * q^94 - 152046078 * q^98

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