LMFDB - Embedded newform 289.10.a.c.1.8

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			1.8
Root			$-105.759$ 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)

$f(q)$	$=$	$q+9.15386 q^{2} +105.759 q^{3} -428.207 q^{4} -1752.99 q^{5} +968.101 q^{6} -5869.78 q^{7} -8606.52 q^{8} -8498.07 q^{9} +O(q^{10})$	\(q+9.15386 q^{2} +105.759 q^{3} -428.207 q^{4} -1752.99 q^{5} +968.101 q^{6} -5869.78 q^{7} -8606.52 q^{8} -8498.07 q^{9} -16046.7 q^{10} +57216.5 q^{11} -45286.7 q^{12} +183293. q^{13} -53731.1 q^{14} -185395. q^{15} +140459. q^{16} -77790.1 q^{18} -269437. q^{19} +750644. q^{20} -620781. q^{21} +523752. q^{22} +1.82770e6 q^{23} -910216. q^{24} +1.11987e6 q^{25} +1.67784e6 q^{26} -2.98040e6 q^{27} +2.51348e6 q^{28} -1.33534e6 q^{29} -1.69708e6 q^{30} +5.82494e6 q^{31} +5.69228e6 q^{32} +6.05116e6 q^{33} +1.02897e7 q^{35} +3.63893e6 q^{36} -1.79478e7 q^{37} -2.46639e6 q^{38} +1.93849e7 q^{39} +1.50872e7 q^{40} +1.95813e7 q^{41} -5.68254e6 q^{42} -1.23432e7 q^{43} -2.45005e7 q^{44} +1.48971e7 q^{45} +1.67305e7 q^{46} +3.64169e7 q^{47} +1.48548e7 q^{48} -5.89930e6 q^{49} +1.02511e7 q^{50} -7.84873e7 q^{52} +4.39657e7 q^{53} -2.72821e7 q^{54} -1.00300e8 q^{55} +5.05184e7 q^{56} -2.84954e7 q^{57} -1.22235e7 q^{58} -6.25259e7 q^{59} +7.93873e7 q^{60} -1.82975e8 q^{61} +5.33206e7 q^{62} +4.98818e7 q^{63} -1.98087e7 q^{64} -3.21312e8 q^{65} +5.53914e7 q^{66} +1.37491e8 q^{67} +1.93295e8 q^{69} +9.41904e7 q^{70} +5.84225e7 q^{71} +7.31388e7 q^{72} -1.40109e8 q^{73} -1.64291e8 q^{74} +1.18436e8 q^{75} +1.15375e8 q^{76} -3.35848e8 q^{77} +1.77446e8 q^{78} +1.26401e8 q^{79} -2.46224e8 q^{80} -1.47936e8 q^{81} +1.79245e8 q^{82} -9.17904e7 q^{83} +2.65823e8 q^{84} -1.12988e8 q^{86} -1.41224e8 q^{87} -4.92435e8 q^{88} -5.55730e8 q^{89} +1.36366e8 q^{90} -1.07589e9 q^{91} -7.82634e8 q^{92} +6.16038e8 q^{93} +3.33355e8 q^{94} +4.72322e8 q^{95} +6.02009e8 q^{96} -6.97429e8 q^{97} -5.40014e7 q^{98} -4.86230e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	9.15386	0.404547	0.202274	−	0.979329i	$-0.435167\pi$
$2$	9.15386	0.404547	0.202274	+	0.979329i	$0.435167\pi$
$3$	105.759	0.753826	0.376913	−	0.926249i	$-0.376986\pi$
$3$	105.759	0.753826	0.376913	+	0.926249i	$0.376986\pi$
$4$	−428.207	−0.836342
$5$	−1752.99	−1.25434	−0.627171	−	0.778882i	$-0.715787\pi$
$5$	−1752.99	−1.25434	−0.627171	+	0.778882i	$0.715787\pi$
$6$	968.101	0.304958
$7$	−5869.78	−0.924018	−0.462009	−	0.886875i	$-0.652871\pi$
$7$	−5869.78	−0.924018	−0.462009	+	0.886875i	$0.652871\pi$
$8$	−8606.52	−0.742887
$9$	−8498.07	−0.431747
$10$	−16046.7	−0.507440
$11$	57216.5	1.17830	0.589148	−	0.808025i	$-0.299463\pi$
$11$	57216.5	1.17830	0.589148	+	0.808025i	$0.299463\pi$
$12$	−45286.7	−0.630456
$13$	183293.	1.77992	0.889960	−	0.456038i	$-0.150732\pi$
$13$	183293.	1.77992	0.889960	+	0.456038i	$0.150732\pi$
$14$	−53731.1	−0.373809
$15$	−185395.	−0.945555
$16$	140459.	0.535809
$17$	0	0
$17$	0	0
$18$	−77790.1	−0.174662
$19$	−269437.	−0.474315	−0.237157	−	0.971471i	$-0.576216\pi$
$19$	−269437.	−0.474315	−0.237157	+	0.971471i	$0.576216\pi$
$20$	750644.	1.04906
$21$	−620781.	−0.696549
$22$	523752.	0.476677
$23$	1.82770e6	1.36185	0.680925	−	0.732353i	$-0.261578\pi$
$23$	1.82770e6	1.36185	0.680925	+	0.732353i	$0.261578\pi$
$24$	−910216.	−0.560007
$25$	1.11987e6	0.573371
$26$	1.67784e6	0.720062
$27$	−2.98040e6	−1.07929
$28$	2.51348e6	0.772795
$29$	−1.33534e6	−0.350591	−0.175295	−	0.984516i	$-0.556088\pi$
$29$	−1.33534e6	−0.350591	−0.175295	+	0.984516i	$0.556088\pi$
$30$	−1.69708e6	−0.382522
$31$	5.82494e6	1.13283	0.566413	−	0.824121i	$-0.308331\pi$
$31$	5.82494e6	1.13283	0.566413	+	0.824121i	$0.308331\pi$
$32$	5.69228e6	0.959647
$33$	6.05116e6	0.888230
$34$	0	0
$35$	1.02897e7	1.15903
$36$	3.63893e6	0.361088
$37$	−1.79478e7	−1.57436	−0.787178	−	0.616726i	$-0.788459\pi$
$37$	−1.79478e7	−1.57436	−0.787178	+	0.616726i	$0.788459\pi$
$38$	−2.46639e6	−0.191883
$39$	1.93849e7	1.34175
$40$	1.50872e7	0.931833
$41$	1.95813e7	1.08222	0.541108	−	0.840953i	$-0.318005\pi$
$41$	1.95813e7	1.08222	0.541108	+	0.840953i	$0.318005\pi$
$42$	−5.68254e6	−0.281787
$43$	−1.23432e7	−0.550580	−0.275290	−	0.961361i	$-0.588774\pi$
$43$	−1.23432e7	−0.550580	−0.275290	+	0.961361i	$0.588774\pi$
$44$	−2.45005e7	−0.985458
$45$	1.48971e7	0.541557
$46$	1.67305e7	0.550933
$47$	3.64169e7	1.08858	0.544292	−	0.838896i	$-0.316798\pi$
$47$	3.64169e7	1.08858	0.544292	+	0.838896i	$0.316798\pi$
$48$	1.48548e7	0.403907
$49$	−5.89930e6	−0.146190
$50$	1.02511e7	0.231956
$51$	0	0
$52$	−7.84873e7	−1.48862
$53$	4.39657e7	0.765372	0.382686	−	0.923879i	$-0.374999\pi$
$53$	4.39657e7	0.765372	0.382686	+	0.923879i	$0.374999\pi$
$54$	−2.72821e7	−0.436623
$55$	−1.00300e8	−1.47799
$56$	5.05184e7	0.686441
$57$	−2.84954e7	−0.357551
$58$	−1.22235e7	−0.141830
$59$	−6.25259e7	−0.671778	−0.335889	−	0.941902i	$-0.609037\pi$
$59$	−6.25259e7	−0.671778	−0.335889	+	0.941902i	$0.609037\pi$
$60$	7.93873e7	0.790807
$61$	−1.82975e8	−1.69203	−0.846013	−	0.533163i	$-0.821003\pi$
$61$	−1.82975e8	−1.69203	−0.846013	+	0.533163i	$0.821003\pi$
$62$	5.33206e7	0.458282
$63$	4.98818e7	0.398942
$64$	−1.98087e7	−0.147586
$65$	−3.21312e8	−2.23263
$66$	5.53914e7	0.359331
$67$	1.37491e8	0.833560	0.416780	−	0.909007i	$-0.363159\pi$
$67$	1.37491e8	0.833560	0.416780	+	0.909007i	$0.363159\pi$
$68$	0	0
$69$	1.93295e8	1.02660
$70$	9.41904e7	0.468884
$71$	5.84225e7	0.272846	0.136423	−	0.990651i	$-0.456439\pi$
$71$	5.84225e7	0.272846	0.136423	+	0.990651i	$0.456439\pi$
$72$	7.31388e7	0.320739
$73$	−1.40109e8	−0.577450	−0.288725	−	0.957412i	$-0.593231\pi$
$73$	−1.40109e8	−0.577450	−0.288725	+	0.957412i	$0.593231\pi$
$74$	−1.64291e8	−0.636901
$75$	1.18436e8	0.432222
$76$	1.15375e8	0.396689
$77$	−3.35848e8	−1.08877
$78$	1.77446e8	0.542801
$79$	1.26401e8	0.365115	0.182558	−	0.983195i	$-0.441562\pi$
$79$	1.26401e8	0.365115	0.182558	+	0.983195i	$0.441562\pi$
$80$	−2.46224e8	−0.672087
$81$	−1.47936e8	−0.381848
$82$	1.79245e8	0.437808
$83$	−9.17904e7	−0.212298	−0.106149	−	0.994350i	$-0.533852\pi$
$83$	−9.17904e7	−0.212298	−0.106149	+	0.994350i	$0.533852\pi$
$84$	2.65823e8	0.582553
$85$	0	0
$86$	−1.12988e8	−0.222736
$87$	−1.41224e8	−0.264284
$88$	−4.92435e8	−0.875341
$89$	−5.55730e8	−0.938878	−0.469439	−	0.882965i	$-0.655544\pi$
$89$	−5.55730e8	−0.938878	−0.469439	+	0.882965i	$0.655544\pi$
$90$	1.36366e8	0.219086
$91$	−1.07589e9	−1.64468
$92$	−7.82634e8	−1.13897
$93$	6.16038e8	0.853954
$94$	3.33355e8	0.440384
$95$	4.72322e8	0.594952
$96$	6.02009e8	0.723407
$97$	−6.97429e8	−0.799884	−0.399942	−	0.916540i	$-0.630970\pi$
$97$	−6.97429e8	−0.799884	−0.399942	+	0.916540i	$0.630970\pi$
$98$	−5.40014e7	−0.0591408
$99$	−4.86230e8	−0.508725
$100$	−4.79534e8	−0.479534
$101$	−3.83633e8	−0.366834	−0.183417	−	0.983035i	$-0.558716\pi$
$101$	−3.83633e8	−0.366834	−0.183417	+	0.983035i	$0.558716\pi$
$102$	0	0
$103$	−1.47116e9	−1.28793	−0.643967	−	0.765054i	$-0.722712\pi$
$103$	−1.47116e9	−1.28793	−0.643967	+	0.765054i	$0.722712\pi$
$104$	−1.57751e9	−1.32228
$105$	1.08823e9	0.873710
$106$	4.02456e8	0.309629
$107$	4.50065e8	0.331931	0.165966	−	0.986132i	$-0.446926\pi$
$107$	4.50065e8	0.331931	0.165966	+	0.986132i	$0.446926\pi$
$108$	1.27623e9	0.902653
$109$	−3.38904e8	−0.229963	−0.114981	−	0.993368i	$-0.536681\pi$
$109$	−3.38904e8	−0.229963	−0.114981	+	0.993368i	$0.536681\pi$
$110$	−9.18135e8	−0.597915
$111$	−1.89814e9	−1.18679
$112$	−8.24464e8	−0.495097
$113$	8.15980e7	0.0470789	0.0235395	−	0.999723i	$-0.492506\pi$
$113$	8.15980e7	0.0470789	0.0235395	+	0.999723i	$0.492506\pi$
$114$	−2.60843e8	−0.144646
$115$	−3.20395e9	−1.70823
$116$	5.71801e8	0.293214
$117$	−1.55764e9	−0.768475
$118$	−5.72353e8	−0.271766
$119$	0	0
$120$	1.59560e9	0.702440
$121$	9.15786e8	0.388383
$122$	−1.67492e9	−0.684504
$123$	2.07090e9	0.815803
$124$	−2.49428e9	−0.947430
$125$	1.46070e9	0.535138
$126$	4.56611e8	0.161391
$127$	1.33940e9	0.456871	0.228435	−	0.973559i	$-0.426639\pi$
$127$	1.33940e9	0.456871	0.228435	+	0.973559i	$0.426639\pi$
$128$	−3.09577e9	−1.01935
$129$	−1.30540e9	−0.415042
$130$	−2.94124e9	−0.903203
$131$	3.41422e9	1.01291	0.506455	−	0.862267i	$-0.330956\pi$
$131$	3.41422e9	1.01291	0.506455	+	0.862267i	$0.330956\pi$
$132$	−2.59115e9	−0.742864
$133$	1.58154e9	0.438276
$134$	1.25857e9	0.337214
$135$	5.22462e9	1.35379
$136$	0	0
$137$	−5.41610e9	−1.31354	−0.656771	−	0.754090i	$-0.728078\pi$
$137$	−5.41610e9	−1.31354	−0.656771	+	0.754090i	$0.728078\pi$
$138$	1.76940e9	0.415308
$139$	3.28339e9	0.746030	0.373015	−	0.927825i	$-0.378324\pi$
$139$	3.28339e9	0.746030	0.373015	+	0.927825i	$0.378324\pi$
$140$	−4.40612e9	−0.969348
$141$	3.85141e9	0.820603
$142$	5.34792e8	0.110379
$143$	1.04874e10	2.09727
$144$	−1.19363e9	−0.231334
$145$	2.34084e9	0.439760
$146$	−1.28254e9	−0.233606
$147$	−6.23903e8	−0.110202
$148$	7.68536e9	1.31670
$149$	−4.20361e8	−0.0698689	−0.0349345	−	0.999390i	$-0.511122\pi$
$149$	−4.20361e8	−0.0698689	−0.0349345	+	0.999390i	$0.511122\pi$
$150$	1.08414e9	0.174854
$151$	1.34993e8	0.0211307	0.0105653	−	0.999944i	$-0.496637\pi$
$151$	1.34993e8	0.0211307	0.0105653	+	0.999944i	$0.496637\pi$
$152$	2.31892e9	0.352362
$153$	0	0
$154$	−3.07431e9	−0.440458
$155$	−1.02111e10	−1.42095
$156$	−8.30073e9	−1.12216
$157$	−5.90561e9	−0.775740	−0.387870	−	0.921714i	$-0.626789\pi$
$157$	−5.90561e9	−0.775740	−0.387870	+	0.921714i	$0.626789\pi$
$158$	1.15706e9	0.147706
$159$	4.64976e9	0.576957
$160$	−9.97854e9	−1.20372
$161$	−1.07282e10	−1.25838
$162$	−1.35418e9	−0.154476
$163$	1.60704e10	1.78313	0.891566	−	0.452890i	$-0.149607\pi$
$163$	1.60704e10	1.78313	0.891566	+	0.452890i	$0.149607\pi$
$164$	−8.38485e9	−0.905103
$165$	−1.06076e10	−1.11414
$166$	−8.40237e8	−0.0858846
$167$	7.33291e9	0.729546	0.364773	−	0.931097i	$-0.381147\pi$
$167$	7.33291e9	0.729546	0.364773	+	0.931097i	$0.381147\pi$
$168$	5.34276e9	0.517457
$169$	2.29918e10	2.16812
$170$	0	0
$171$	2.28970e9	0.204784
$172$	5.28545e9	0.460473
$173$	1.87691e10	1.59307	0.796537	−	0.604590i	$-0.206663\pi$
$173$	1.87691e10	1.59307	0.796537	+	0.604590i	$0.206663\pi$
$174$	−1.29274e9	−0.106915
$175$	−6.57337e9	−0.529806
$176$	8.03658e9	0.631342
$177$	−6.61267e9	−0.506404
$178$	−5.08708e9	−0.379820
$179$	−2.15906e10	−1.57190	−0.785952	−	0.618287i	$-0.787827\pi$
$179$	−2.15906e10	−1.57190	−0.785952	+	0.618287i	$0.787827\pi$
$180$	−6.37903e9	−0.452927
$181$	1.14397e10	0.792249	0.396125	−	0.918197i	$-0.370355\pi$
$181$	1.14397e10	0.792249	0.396125	+	0.918197i	$0.370355\pi$
$182$	−9.84854e9	−0.665350
$183$	−1.93512e10	−1.27549
$184$	−1.57301e10	−1.01170
$185$	3.14624e10	1.97478
$186$	5.63913e9	0.345465
$187$	0	0
$188$	−1.55940e10	−0.910428
$189$	1.74943e10	0.997281
$190$	4.32357e9	0.240686
$191$	−2.88292e9	−0.156741	−0.0783705	−	0.996924i	$-0.524972\pi$
$191$	−2.88292e9	−0.156741	−0.0783705	+	0.996924i	$0.524972\pi$
$192$	−2.09495e9	−0.111254
$193$	−3.11767e10	−1.61742	−0.808709	−	0.588209i	$-0.799833\pi$
$193$	−3.11767e10	−1.61742	−0.808709	+	0.588209i	$0.799833\pi$
$194$	−6.38417e9	−0.323591
$195$	−3.39815e10	−1.68301
$196$	2.52612e9	0.122265
$197$	3.08413e9	0.145893	0.0729466	−	0.997336i	$-0.476760\pi$
$197$	3.08413e9	0.145893	0.0729466	+	0.997336i	$0.476760\pi$
$198$	−4.45088e9	−0.205803
$199$	−1.25130e10	−0.565615	−0.282808	−	0.959177i	$-0.591266\pi$
$199$	−1.25130e10	−0.565615	−0.282808	+	0.959177i	$0.591266\pi$
$200$	−9.63815e9	−0.425950
$201$	1.45409e10	0.628359
$202$	−3.51172e9	−0.148402
$203$	7.83814e9	0.323952
$204$	0	0
$205$	−3.43259e10	−1.35747
$206$	−1.34668e10	−0.521030
$207$	−1.55319e10	−0.587974
$208$	2.57452e10	0.953697
$209$	−1.54163e10	−0.558883
$210$	9.96147e9	0.353457
$211$	2.61249e9	0.0907369	0.0453684	−	0.998970i	$-0.485554\pi$
$211$	2.61249e9	0.0907369	0.0453684	+	0.998970i	$0.485554\pi$
$212$	−1.88264e10	−0.640112
$213$	6.17870e9	0.205678
$214$	4.11983e9	0.134282
$215$	2.16376e10	0.690615
$216$	2.56508e10	0.801789
$217$	−3.41911e10	−1.04675
$218$	−3.10228e9	−0.0930308
$219$	−1.48178e10	−0.435296
$220$	4.29493e10	1.23610
$221$	0	0
$222$	−1.73753e10	−0.480113
$223$	−5.19850e10	−1.40769	−0.703843	−	0.710355i	$-0.748534\pi$
$223$	−5.19850e10	−1.40769	−0.703843	+	0.710355i	$0.748534\pi$
$224$	−3.34124e10	−0.886731
$225$	−9.51670e9	−0.247551
$226$	7.46937e8	0.0190457
$227$	−6.59252e10	−1.64792	−0.823958	−	0.566650i	$-0.808239\pi$
$227$	−6.59252e10	−1.64792	−0.823958	+	0.566650i	$0.808239\pi$
$228$	1.22019e10	0.299035
$229$	−7.15519e10	−1.71934	−0.859669	−	0.510851i	$-0.829330\pi$
$229$	−7.15519e10	−1.71934	−0.859669	+	0.510851i	$0.829330\pi$
$230$	−2.93285e10	−0.691058
$231$	−3.55189e10	−0.820741
$232$	1.14926e10	0.260449
$233$	1.94101e10	0.431446	0.215723	−	0.976455i	$-0.430789\pi$
$233$	1.94101e10	0.431446	0.215723	+	0.976455i	$0.430789\pi$
$234$	−1.42584e10	−0.310884
$235$	−6.38386e10	−1.36546
$236$	2.67740e10	0.561836
$237$	1.33681e10	0.275233
$238$	0	0
$239$	−9.93587e8	−0.0196977	−0.00984885	−	0.999951i	$-0.503135\pi$
$239$	−9.93587e8	−0.0196977	−0.00984885	+	0.999951i	$0.503135\pi$
$240$	−2.60404e10	−0.506637
$241$	−7.36838e9	−0.140700	−0.0703502	−	0.997522i	$-0.522412\pi$
$241$	−7.36838e9	−0.140700	−0.0703502	+	0.997522i	$0.522412\pi$
$242$	8.38297e9	0.157119
$243$	4.30176e10	0.791440
$244$	7.83510e10	1.41511
$245$	1.03414e10	0.183372
$246$	1.89567e10	0.330031
$247$	−4.93860e10	−0.844243
$248$	−5.01324e10	−0.841562
$249$	−9.70765e9	−0.160036
$250$	1.33710e10	0.216488
$251$	−1.14806e11	−1.82571	−0.912855	−	0.408283i	$-0.866128\pi$
$251$	−1.14806e11	−1.82571	−0.912855	+	0.408283i	$0.866128\pi$
$252$	−2.13597e10	−0.333651
$253$	1.04575e11	1.60466
$254$	1.22607e10	0.184826
$255$	0	0
$256$	−1.81962e10	−0.264790
$257$	3.12571e10	0.446940	0.223470	−	0.974711i	$-0.428262\pi$
$257$	3.12571e10	0.446940	0.223470	+	0.974711i	$0.428262\pi$
$258$	−1.19495e10	−0.167904
$259$	1.05349e11	1.45473
$260$	1.37588e11	1.86724
$261$	1.13478e10	0.151366
$262$	3.12533e10	0.409770
$263$	−1.77723e10	−0.229057	−0.114529	−	0.993420i	$-0.536536\pi$
$263$	−1.77723e10	−0.229057	−0.114529	+	0.993420i	$0.536536\pi$
$264$	−5.20794e10	−0.659855
$265$	−7.70716e10	−0.960037
$266$	1.44772e10	0.177303
$267$	−5.87734e10	−0.707750
$268$	−5.88745e10	−0.697141
$269$	7.34859e10	0.855694	0.427847	−	0.903851i	$-0.359272\pi$
$269$	7.34859e10	0.855694	0.427847	+	0.903851i	$0.359272\pi$
$270$	4.78254e10	0.547674
$271$	1.05771e11	1.19125	0.595625	−	0.803263i	$-0.296904\pi$
$271$	1.05771e11	1.19125	0.595625	+	0.803263i	$0.296904\pi$
$272$	0	0
$273$	−1.13785e11	−1.23980
$274$	−4.95782e10	−0.531389
$275$	6.40749e10	0.675602
$276$	−8.27704e10	−0.858587
$277$	−1.55982e11	−1.59190	−0.795952	−	0.605360i	$-0.793029\pi$
$277$	−1.55982e11	−1.59190	−0.795952	+	0.605360i	$0.793029\pi$
$278$	3.00557e10	0.301804
$279$	−4.95007e10	−0.489094
$280$	−8.85585e10	−0.861031
$281$	1.55794e10	0.149064	0.0745320	−	0.997219i	$-0.476254\pi$
$281$	1.55794e10	0.149064	0.0745320	+	0.997219i	$0.476254\pi$
$282$	3.52552e10	0.331973
$283$	1.55832e10	0.144416	0.0722082	−	0.997390i	$-0.476995\pi$
$283$	1.55832e10	0.144416	0.0722082	+	0.997390i	$0.476995\pi$
$284$	−2.50169e10	−0.228193
$285$	4.99523e10	0.448491
$286$	9.60001e10	0.848447
$287$	−1.14938e11	−0.999988
$288$	−4.83734e10	−0.414324
$289$	0	0
$290$	2.14277e10	0.177904
$291$	−7.37593e10	−0.602974
$292$	5.99958e10	0.482945
$293$	−1.00556e11	−0.797081	−0.398541	−	0.917151i	$-0.630483\pi$
$293$	−1.00556e11	−0.797081	−0.398541	+	0.917151i	$0.630483\pi$
$294$	−5.71112e9	−0.0445819
$295$	1.09608e11	0.842639
$296$	1.54468e11	1.16957
$297$	−1.70528e11	−1.27172
$298$	−3.84792e9	−0.0282653
$299$	3.35004e11	2.42399
$300$	−5.07150e10	−0.361485
$301$	7.24520e10	0.508746
$302$	1.23570e9	0.00854836
$303$	−4.05725e10	−0.276529
$304$	−3.78449e10	−0.254142
$305$	3.20754e11	2.12238
$306$	0	0
$307$	−1.89792e11	−1.21942	−0.609712	−	0.792623i	$-0.708715\pi$
$307$	−1.89792e11	−1.21942	−0.609712	+	0.792623i	$0.708715\pi$
$308$	1.43813e11	0.910581
$309$	−1.55589e11	−0.970877
$310$	−9.34708e10	−0.574842
$311$	1.73614e10	0.105236	0.0526179	−	0.998615i	$-0.483243\pi$
$311$	1.73614e10	0.105236	0.0526179	+	0.998615i	$0.483243\pi$
$312$	−1.66836e11	−0.996769
$313$	−2.56822e11	−1.51245	−0.756227	−	0.654309i	$-0.772960\pi$
$313$	−2.56822e11	−1.51245	−0.756227	+	0.654309i	$0.772960\pi$
$314$	−5.40591e10	−0.313823
$315$	−8.74425e10	−0.500409
$316$	−5.41259e10	−0.305361
$317$	−1.00545e11	−0.559232	−0.279616	−	0.960112i	$-0.590207\pi$
$317$	−1.00545e11	−0.559232	−0.279616	+	0.960112i	$0.590207\pi$
$318$	4.25632e10	0.233406
$319$	−7.64034e10	−0.413100
$320$	3.47245e10	0.185124
$321$	4.75984e10	0.250219
$322$	−9.82044e10	−0.509072
$323$	0	0
$324$	6.33472e10	0.319356
$325$	2.05264e11	1.02056
$326$	1.47107e11	0.721361
$327$	−3.58421e10	−0.173352
$328$	−1.68527e11	−0.803965
$329$	−2.13759e11	−1.00587
$330$	−9.71009e10	−0.450724
$331$	3.48086e11	1.59390	0.796950	−	0.604046i	$-0.206446\pi$
$331$	3.48086e11	1.59390	0.796950	+	0.604046i	$0.206446\pi$
$332$	3.93053e10	0.177554
$333$	1.52521e11	0.679722
$334$	6.71244e10	0.295136
$335$	−2.41020e11	−1.04557
$336$	−8.71943e10	−0.373217
$337$	2.40170e10	0.101434	0.0507171	−	0.998713i	$-0.483849\pi$
$337$	2.40170e10	0.101434	0.0507171	+	0.998713i	$0.483849\pi$
$338$	2.10464e11	0.877106
$339$	8.62971e9	0.0354893
$340$	0	0
$341$	3.33283e11	1.33481
$342$	2.09596e10	0.0828447
$343$	2.71494e11	1.05910
$344$	1.06232e11	0.409019
$345$	−3.38846e11	−1.28770
$346$	1.71810e11	0.644474
$347$	−9.10819e10	−0.337248	−0.168624	−	0.985680i	$-0.553932\pi$
$347$	−9.10819e10	−0.337248	−0.168624	+	0.985680i	$0.553932\pi$
$348$	6.04730e10	0.221032
$349$	−1.89982e10	−0.0685485	−0.0342743	−	0.999412i	$-0.510912\pi$
$349$	−1.89982e10	−0.0685485	−0.0342743	+	0.999412i	$0.510912\pi$
$350$	−6.01717e10	−0.214331
$351$	−5.46286e11	−1.92105
$352$	3.25693e11	1.13075
$353$	8.47880e10	0.290635	0.145318	−	0.989385i	$-0.453580\pi$
$353$	8.47880e10	0.290635	0.145318	+	0.989385i	$0.453580\pi$
$354$	−6.05314e10	−0.204864
$355$	−1.02414e11	−0.342242
$356$	2.37968e11	0.785222
$357$	0	0
$358$	−1.97637e11	−0.635909
$359$	−3.40209e11	−1.08099	−0.540494	−	0.841348i	$-0.681763\pi$
$359$	−3.40209e11	−1.08099	−0.540494	+	0.841348i	$0.681763\pi$
$360$	−1.28212e11	−0.402316
$361$	−2.50091e11	−0.775025
$362$	1.04718e11	0.320502
$363$	9.68524e10	0.292773
$364$	4.60703e11	1.37551
$365$	2.45611e11	0.724319
$366$	−1.77138e11	−0.515997
$367$	−1.38234e11	−0.397758	−0.198879	−	0.980024i	$-0.563730\pi$
$367$	−1.38234e11	−0.397758	−0.198879	+	0.980024i	$0.563730\pi$
$368$	2.56717e11	0.729692
$369$	−1.66403e11	−0.467243
$370$	2.88002e11	0.798891
$371$	−2.58069e11	−0.707217
$372$	−2.63792e11	−0.714197
$373$	−5.31263e11	−1.42108	−0.710542	−	0.703655i	$-0.751550\pi$
$373$	−5.31263e11	−1.42108	−0.710542	+	0.703655i	$0.751550\pi$
$374$	0	0
$375$	1.54482e11	0.403401
$376$	−3.13422e11	−0.808695
$377$	−2.44758e11	−0.624024
$378$	1.60140e11	0.403447
$379$	5.46410e11	1.36032	0.680162	−	0.733062i	$-0.261909\pi$
$379$	5.46410e11	1.36032	0.680162	+	0.733062i	$0.261909\pi$
$380$	−2.02252e11	−0.497583
$381$	1.41653e11	0.344401
$382$	−2.63898e10	−0.0634091
$383$	3.55500e11	0.844200	0.422100	−	0.906549i	$-0.361293\pi$
$383$	3.55500e11	0.844200	0.422100	+	0.906549i	$0.361293\pi$
$384$	−3.27405e11	−0.768414
$385$	5.88741e11	1.36569
$386$	−2.85387e11	−0.654322
$387$	1.04894e11	0.237711
$388$	2.98644e11	0.668976
$389$	−6.89360e11	−1.52642	−0.763208	−	0.646153i	$-0.776377\pi$
$389$	−6.89360e11	−1.52642	−0.763208	+	0.646153i	$0.776377\pi$
$390$	−3.11062e11	−0.680858
$391$	0	0
$392$	5.07725e10	0.108603
$393$	3.61084e11	0.763557
$394$	2.82317e10	0.0590207
$395$	−2.21581e11	−0.457979
$396$	2.08207e11	0.425468
$397$	8.59801e11	1.73716	0.868582	−	0.495546i	$-0.165032\pi$
$397$	8.59801e11	1.73716	0.868582	+	0.495546i	$0.165032\pi$
$398$	−1.14542e11	−0.228818
$399$	1.67262e11	0.330383
$400$	1.57295e11	0.307217
$401$	−2.49159e11	−0.481202	−0.240601	−	0.970624i	$-0.577344\pi$
$401$	−2.49159e11	−0.481202	−0.240601	+	0.970624i	$0.577344\pi$
$402$	1.33105e11	0.254201
$403$	1.06767e12	2.01634
$404$	1.64274e11	0.306798
$405$	2.59331e11	0.478968
$406$	7.17492e10	0.131054
$407$	−1.02691e12	−1.85506
$408$	0	0
$409$	2.46410e11	0.435416	0.217708	−	0.976014i	$-0.430142\pi$
$409$	2.46410e11	0.435416	0.217708	+	0.976014i	$0.430142\pi$
$410$	−3.14215e11	−0.549160
$411$	−5.72800e11	−0.990181
$412$	6.29962e11	1.07715
$413$	3.67013e11	0.620735
$414$	−1.42177e11	−0.237863
$415$	1.60908e11	0.266294
$416$	1.04336e12	1.70810
$417$	3.47248e11	0.562377
$418$	−1.41118e11	−0.226095
$419$	8.92561e10	0.141473	0.0707367	−	0.997495i	$-0.477465\pi$
$419$	8.92561e10	0.141473	0.0707367	+	0.997495i	$0.477465\pi$
$420$	−4.65986e11	−0.730720
$421$	1.44866e11	0.224749	0.112374	−	0.993666i	$-0.464154\pi$
$421$	1.44866e11	0.224749	0.112374	+	0.993666i	$0.464154\pi$
$422$	2.39144e10	0.0367074
$423$	−3.09473e11	−0.469993
$424$	−3.78392e11	−0.568585
$425$	0	0
$426$	5.65589e10	0.0832067
$427$	1.07402e12	1.56346
$428$	−1.92721e11	−0.277608
$429$	1.10913e12	1.58098
$430$	1.98068e11	0.279386
$431$	−7.07364e11	−0.987405	−0.493702	−	0.869631i	$-0.664357\pi$
$431$	−7.07364e11	−0.987405	−0.493702	+	0.869631i	$0.664357\pi$
$432$	−4.18624e11	−0.578292
$433$	2.33937e10	0.0319818	0.0159909	−	0.999872i	$-0.494910\pi$
$433$	2.33937e10	0.0319818	0.0159909	+	0.999872i	$0.494910\pi$
$434$	−3.12980e11	−0.423461
$435$	2.47565e11	0.331503
$436$	1.45121e11	0.192327
$437$	−4.92451e11	−0.645946
$438$	−1.35640e11	−0.176098
$439$	−1.22303e12	−1.57161	−0.785806	−	0.618474i	$-0.787751\pi$
$439$	−1.22303e12	−1.57161	−0.785806	+	0.618474i	$0.787751\pi$
$440$	8.63237e11	1.09798
$441$	5.01327e10	0.0631171
$442$	0	0
$443$	1.01038e12	1.24643	0.623215	−	0.782050i	$-0.285826\pi$
$443$	1.01038e12	1.24643	0.623215	+	0.782050i	$0.285826\pi$
$444$	8.12795e11	0.992562
$445$	9.74192e11	1.17767
$446$	−4.75863e11	−0.569476
$447$	−4.44569e10	−0.0526690
$448$	1.16273e11	0.136372
$449$	4.77607e10	0.0554578	0.0277289	−	0.999615i	$-0.491172\pi$
$449$	4.77607e10	0.0554578	0.0277289	+	0.999615i	$0.491172\pi$
$450$	−8.71145e10	−0.100146
$451$	1.12037e12	1.27517
$452$	−3.49408e10	−0.0393741
$453$	1.42767e10	0.0159289
$454$	−6.03470e11	−0.666660
$455$	1.88603e12	2.06299
$456$	2.45246e11	0.265620
$457$	−1.47001e12	−1.57651	−0.788255	−	0.615349i	$-0.789015\pi$
$457$	−1.47001e12	−1.57651	−0.788255	+	0.615349i	$0.789015\pi$
$458$	−6.54976e11	−0.695553
$459$	0	0
$460$	1.37195e12	1.42866
$461$	−1.65629e12	−1.70797	−0.853986	−	0.520295i	$-0.825822\pi$
$461$	−1.65629e12	−1.70797	−0.853986	+	0.520295i	$0.825822\pi$
$462$	−3.25135e11	−0.332029
$463$	−1.55332e11	−0.157089	−0.0785444	−	0.996911i	$-0.525027\pi$
$463$	−1.55332e11	−0.157089	−0.0785444	+	0.996911i	$0.525027\pi$
$464$	−1.87560e11	−0.187850
$465$	−1.07991e12	−1.07115
$466$	1.77678e11	0.174540
$467$	5.17128e11	0.503120	0.251560	−	0.967842i	$-0.419056\pi$
$467$	5.17128e11	0.503120	0.251560	+	0.967842i	$0.419056\pi$
$468$	6.66990e11	0.642707
$469$	−8.07040e11	−0.770224
$470$	−5.84369e11	−0.552392
$471$	−6.24570e11	−0.584773
$472$	5.38130e11	0.499055
$473$	−7.06237e11	−0.648747
$474$	1.22369e11	0.111345
$475$	−3.01734e11	−0.271959
$476$	0	0
$477$	−3.73623e11	−0.330447
$478$	−9.09515e9	−0.00796865
$479$	−4.57403e11	−0.396998	−0.198499	−	0.980101i	$-0.563607\pi$
$479$	−4.57403e11	−0.396998	−0.198499	+	0.980101i	$0.563607\pi$
$480$	−1.05532e12	−0.907399
$481$	−3.28970e12	−2.80223
$482$	−6.74491e10	−0.0569200
$483$	−1.13460e12	−0.948596
$484$	−3.92146e11	−0.324820
$485$	1.22259e12	1.00333
$486$	3.93777e11	0.320175
$487$	1.79433e11	0.144552	0.0722758	−	0.997385i	$-0.476974\pi$
$487$	1.79433e11	0.144552	0.0722758	+	0.997385i	$0.476974\pi$
$488$	1.57478e12	1.25698
$489$	1.69959e12	1.34417
$490$	9.46641e10	0.0741828
$491$	2.26673e12	1.76009	0.880043	−	0.474895i	$-0.157514\pi$
$491$	2.26673e12	1.76009	0.880043	+	0.474895i	$0.157514\pi$
$492$	−8.86772e11	−0.682290
$493$	0	0
$494$	−4.52072e11	−0.341536
$495$	8.52359e11	0.638115
$496$	8.18165e11	0.606978
$497$	−3.42927e11	−0.252115
$498$	−8.88625e10	−0.0647420
$499$	−1.09096e12	−0.787690	−0.393845	−	0.919177i	$-0.628855\pi$
$499$	−1.09096e12	−0.787690	−0.393845	+	0.919177i	$0.628855\pi$
$500$	−6.25481e11	−0.447558
$501$	7.75520e11	0.549950
$502$	−1.05092e12	−0.738586
$503$	2.02678e12	1.41173	0.705863	−	0.708348i	$-0.250559\pi$
$503$	2.02678e12	1.41173	0.705863	+	0.708348i	$0.250559\pi$
$504$	−4.29309e11	−0.296369
$505$	6.72506e11	0.460135
$506$	9.57262e11	0.649162
$507$	2.43159e12	1.63438
$508$	−5.73540e11	−0.382100
$509$	−2.14859e11	−0.141881	−0.0709405	−	0.997481i	$-0.522600\pi$
$509$	−2.14859e11	−0.141881	−0.0709405	+	0.997481i	$0.522600\pi$
$510$	0	0
$511$	8.22411e11	0.533574
$512$	1.41847e12	0.912232
$513$	8.03030e11	0.511922
$514$	2.86123e11	0.180808
$515$	2.57894e12	1.61551
$516$	5.58983e11	0.347116
$517$	2.08365e12	1.28268
$518$	9.64354e11	0.588508
$519$	1.98500e12	1.20090
$520$	2.76538e12	1.65859
$521$	−1.53683e12	−0.913810	−0.456905	−	0.889515i	$-0.651042\pi$
$521$	−1.53683e12	−0.913810	−0.456905	+	0.889515i	$0.651042\pi$
$522$	1.03876e11	0.0612348
$523$	8.69337e11	0.508078	0.254039	−	0.967194i	$-0.418241\pi$
$523$	8.69337e11	0.508078	0.254039	+	0.967194i	$0.418241\pi$
$524$	−1.46199e12	−0.847138
$525$	−6.95192e11	−0.399381
$526$	−1.62685e11	−0.0926644
$527$	0	0
$528$	8.49940e11	0.475922
$529$	1.53933e12	0.854638
$530$	−7.05503e11	−0.388380
$531$	5.31349e11	0.290038
$532$	−6.77225e11	−0.366548
$533$	3.58912e12	1.92626
$534$	−5.38003e11	−0.286318
$535$	−7.88962e11	−0.416355
$536$	−1.18332e12	−0.619240
$537$	−2.28340e12	−1.18494
$538$	6.72679e11	0.346169
$539$	−3.37538e11	−0.172255
$540$	−2.23722e12	−1.13223
$541$	2.22560e12	1.11702	0.558509	−	0.829499i	$-0.311374\pi$
$541$	2.22560e12	1.11702	0.558509	+	0.829499i	$0.311374\pi$
$542$	9.68209e11	0.481917
$543$	1.20985e12	0.597218
$544$	0	0
$545$	5.94097e11	0.288452
$546$	−1.04157e12	−0.501558
$547$	1.01266e12	0.483638	0.241819	−	0.970321i	$-0.422256\pi$
$547$	1.01266e12	0.483638	0.241819	+	0.970321i	$0.422256\pi$
$548$	2.31921e12	1.09857
$549$	1.55493e12	0.730526
$550$	5.86532e11	0.273313
$551$	3.59790e11	0.166290
$552$	−1.66360e12	−0.762647
$553$	−7.41948e11	−0.337373
$554$	−1.42784e12	−0.644000
$555$	3.32742e12	1.48864
$556$	−1.40597e12	−0.623936
$557$	−1.24117e12	−0.546364	−0.273182	−	0.961962i	$-0.588076\pi$
$557$	−1.24117e12	−0.546364	−0.273182	+	0.961962i	$0.588076\pi$
$558$	−4.53122e11	−0.197862
$559$	−2.26243e12	−0.979989
$560$	1.44528e12	0.621021
$561$	0	0
$562$	1.42612e11	0.0603035
$563$	−1.01943e12	−0.427632	−0.213816	−	0.976874i	$-0.568589\pi$
$563$	−1.01943e12	−0.427632	−0.213816	+	0.976874i	$0.568589\pi$
$564$	−1.64920e12	−0.686305
$565$	−1.43041e11	−0.0590530
$566$	1.42646e11	0.0584233
$567$	8.68351e11	0.352835
$568$	−5.02815e11	−0.202694
$569$	1.48027e12	0.592021	0.296011	−	0.955185i	$-0.404344\pi$
$569$	1.48027e12	0.592021	0.296011	+	0.955185i	$0.404344\pi$
$570$	4.57256e11	0.181436
$571$	−7.76183e11	−0.305563	−0.152782	−	0.988260i	$-0.548823\pi$
$571$	−7.76183e11	−0.305563	−0.152782	+	0.988260i	$0.548823\pi$
$572$	−4.49077e12	−1.75404
$573$	−3.04894e11	−0.118155
$574$	−1.05213e12	−0.404542
$575$	2.04678e12	0.780846
$576$	1.68336e11	0.0637199
$577$	−4.47042e12	−1.67903	−0.839513	−	0.543339i	$-0.817160\pi$
$577$	−4.47042e12	−1.67903	−0.839513	+	0.543339i	$0.817160\pi$
$578$	0	0
$579$	−3.29721e12	−1.21925
$580$	−1.00236e12	−0.367790
$581$	5.38790e11	0.196167
$582$	−6.75182e11	−0.243931
$583$	2.51556e12	0.901835
$584$	1.20585e12	0.428980
$585$	2.73053e12	0.963929
$586$	−9.20473e11	−0.322457
$587$	−4.82640e11	−0.167784	−0.0838922	−	0.996475i	$-0.526735\pi$
$587$	−4.82640e11	−0.167784	−0.0838922	+	0.996475i	$0.526735\pi$
$588$	2.67160e11	0.0921665
$589$	−1.56946e12	−0.537316
$590$	1.00333e12	0.340887
$591$	3.26174e11	0.109978
$592$	−2.52093e12	−0.843553
$593$	−2.96619e12	−0.985036	−0.492518	−	0.870302i	$-0.663923\pi$
$593$	−2.96619e12	−0.985036	−0.492518	+	0.870302i	$0.663923\pi$
$594$	−1.56099e12	−0.514471
$595$	0	0
$596$	1.80001e11	0.0584343
$597$	−1.32336e12	−0.426375
$598$	3.06658e12	0.980617
$599$	−4.35994e12	−1.38376	−0.691878	−	0.722015i	$-0.743216\pi$
$599$	−4.35994e12	−1.38376	−0.691878	+	0.722015i	$0.743216\pi$
$600$	−1.01932e12	−0.321092
$601$	−6.75122e11	−0.211080	−0.105540	−	0.994415i	$-0.533657\pi$
$601$	−6.75122e11	−0.211080	−0.105540	+	0.994415i	$0.533657\pi$
$602$	6.63215e11	0.205812
$603$	−1.16840e12	−0.359886
$604$	−5.78048e10	−0.0176725
$605$	−1.60537e12	−0.487164
$606$	−3.71395e11	−0.111869
$607$	8.01007e11	0.239490	0.119745	−	0.992805i	$-0.461792\pi$
$607$	8.01007e11	0.239490	0.119745	+	0.992805i	$0.461792\pi$
$608$	−1.53371e12	−0.455175
$609$	8.28953e11	0.244204
$610$	2.93613e12	0.858602
$611$	6.67495e12	1.93759
$612$	0	0
$613$	−4.78001e12	−1.36728	−0.683639	−	0.729820i	$-0.739604\pi$
$613$	−4.78001e12	−1.36728	−0.683639	+	0.729820i	$0.739604\pi$
$614$	−1.73733e12	−0.493314
$615$	−3.63027e12	−1.02330
$616$	2.89049e12	0.808831
$617$	−2.09791e12	−0.582778	−0.291389	−	0.956605i	$-0.594117\pi$
$617$	−2.09791e12	−0.582778	−0.291389	+	0.956605i	$0.594117\pi$
$618$	−1.42424e12	−0.392766
$619$	−2.32970e12	−0.637812	−0.318906	−	0.947786i	$-0.603315\pi$
$619$	−2.32970e12	−0.637812	−0.318906	+	0.947786i	$0.603315\pi$
$620$	4.37246e12	1.18840
$621$	−5.44727e12	−1.46983
$622$	1.58924e11	0.0425728
$623$	3.26201e12	0.867540
$624$	2.72278e12	0.718922
$625$	−4.74784e12	−1.24462
$626$	−2.35091e12	−0.611859
$627$	−1.63041e12	−0.421301
$628$	2.52882e12	0.648784
$629$	0	0
$630$	−8.00436e11	−0.202439
$631$	−2.59453e12	−0.651519	−0.325760	−	0.945453i	$-0.605620\pi$
$631$	−2.59453e12	−0.651519	−0.325760	+	0.945453i	$0.605620\pi$
$632$	−1.08788e12	−0.271239
$633$	2.76294e11	0.0683998
$634$	−9.20371e11	−0.226236
$635$	−2.34796e12	−0.573071
$636$	−1.99106e12	−0.482533
$637$	−1.08130e12	−0.260207
$638$	−6.99386e11	−0.167118
$639$	−4.96479e11	−0.117800
$640$	5.42688e12	1.27862
$641$	1.33545e12	0.312440	0.156220	−	0.987722i	$-0.450069\pi$
$641$	1.33545e12	0.312440	0.156220	+	0.987722i	$0.450069\pi$
$642$	4.35709e11	0.101225
$643$	−3.82970e12	−0.883518	−0.441759	−	0.897134i	$-0.645645\pi$
$643$	−3.82970e12	−0.883518	−0.441759	+	0.897134i	$0.645645\pi$
$644$	4.59389e12	1.05243
$645$	2.28837e12	0.520604
$646$	0	0
$647$	3.08395e12	0.691891	0.345945	−	0.938255i	$-0.387558\pi$
$647$	3.08395e12	0.691891	0.345945	+	0.938255i	$0.387558\pi$
$648$	1.27321e12	0.283670
$649$	−3.57752e12	−0.791554
$650$	1.87895e12	0.412863
$651$	−3.61601e12	−0.789069
$652$	−6.88147e12	−1.49131
$653$	2.77681e12	0.597636	0.298818	−	0.954310i	$-0.403408\pi$
$653$	2.77681e12	0.597636	0.298818	+	0.954310i	$0.403408\pi$
$654$	−3.28094e11	−0.0701290
$655$	−5.98511e12	−1.27053
$656$	2.75037e12	0.579861
$657$	1.19066e12	0.249312
$658$	−1.95672e12	−0.406923
$659$	−4.83603e12	−0.998861	−0.499430	−	0.866354i	$-0.666457\pi$
$659$	−4.83603e12	−0.998861	−0.499430	+	0.866354i	$0.666457\pi$
$660$	4.54227e12	0.931805
$661$	2.72225e12	0.554653	0.277327	−	0.960776i	$-0.410552\pi$
$661$	2.72225e12	0.554653	0.277327	+	0.960776i	$0.410552\pi$
$662$	3.18633e12	0.644808
$663$	0	0
$664$	7.89996e11	0.157713
$665$	−2.77243e12	−0.549747
$666$	1.39616e12	0.274980
$667$	−2.44060e12	−0.477452
$668$	−3.14000e12	−0.610149
$669$	−5.49787e12	−1.06115
$670$	−2.20627e12	−0.422982
$671$	−1.04692e13	−1.99371
$672$	−3.53366e12	−0.668441
$673$	1.85594e12	0.348735	0.174368	−	0.984681i	$-0.444212\pi$
$673$	1.85594e12	0.348735	0.174368	+	0.984681i	$0.444212\pi$
$674$	2.19848e11	0.0410349
$675$	−3.33765e12	−0.618833
$676$	−9.84525e12	−1.81329
$677$	−6.23311e12	−1.14040	−0.570198	−	0.821507i	$-0.693133\pi$
$677$	−6.23311e12	−1.14040	−0.570198	+	0.821507i	$0.693133\pi$
$678$	7.89952e10	0.0143571
$679$	4.09375e12	0.739108
$680$	0	0
$681$	−6.97218e12	−1.24224
$682$	3.05082e12	0.539992
$683$	3.80694e12	0.669395	0.334697	−	0.942326i	$-0.391366\pi$
$683$	3.80694e12	0.669395	0.334697	+	0.942326i	$0.391366\pi$
$684$	−9.80464e11	−0.171269
$685$	9.49439e12	1.64763
$686$	2.48522e12	0.428456
$687$	−7.56724e12	−1.29608
$688$	−1.73372e12	−0.295006
$689$	8.05860e12	1.36230
$690$	−3.10175e12	−0.520937
$691$	−6.26370e12	−1.04515	−0.522576	−	0.852592i	$-0.675029\pi$
$691$	−6.26370e12	−1.04515	−0.522576	+	0.852592i	$0.675029\pi$
$692$	−8.03706e12	−1.33235
$693$	2.85406e12	0.470072
$694$	−8.33751e11	−0.136433
$695$	−5.75577e12	−0.935776
$696$	1.21545e12	0.196333
$697$	0	0
$698$	−1.73907e11	−0.0277311
$699$	2.05279e12	0.325236
$700$	2.81476e12	0.443099
$701$	−8.90825e12	−1.39335	−0.696677	−	0.717385i	$-0.745339\pi$
$701$	−8.90825e12	−1.39335	−0.696677	+	0.717385i	$0.745339\pi$
$702$	−5.00062e12	−0.777154
$703$	4.83580e12	0.746740
$704$	−1.13339e12	−0.173900
$705$	−6.75149e12	−1.02932
$706$	7.76137e11	0.117576
$707$	2.25184e12	0.338961
$708$	2.83159e12	0.423527
$709$	−4.27216e12	−0.634950	−0.317475	−	0.948267i	$-0.602835\pi$
$709$	−4.27216e12	−0.634950	−0.317475	+	0.948267i	$0.602835\pi$
$710$	−9.37487e11	−0.138453
$711$	−1.07417e12	−0.157637
$712$	4.78290e12	0.697480
$713$	1.06462e13	1.54274
$714$	0	0
$715$	−1.83843e13	−2.63070
$716$	9.24524e12	1.31465
$717$	−1.05081e11	−0.0148486
$718$	−3.11423e12	−0.437311
$719$	3.94871e12	0.551030	0.275515	−	0.961297i	$-0.411152\pi$
$719$	3.94871e12	0.551030	0.275515	+	0.961297i	$0.411152\pi$
$720$	2.09243e12	0.290171
$721$	8.63540e12	1.19007
$722$	−2.28930e12	−0.313534
$723$	−7.79271e11	−0.106064
$724$	−4.89857e12	−0.662591
$725$	−1.49540e12	−0.201019
$726$	8.86573e11	0.118440
$727$	8.36118e12	1.11010	0.555051	−	0.831817i	$-0.312699\pi$
$727$	8.36118e12	1.11010	0.555051	+	0.831817i	$0.312699\pi$
$728$	9.25966e12	1.22181
$729$	7.46132e12	0.978457
$730$	2.24829e12	0.293021
$731$	0	0
$732$	8.28631e12	1.06675
$733$	−7.60099e12	−0.972529	−0.486264	−	0.873812i	$-0.661641\pi$
$733$	−7.60099e12	−0.972529	−0.486264	+	0.873812i	$0.661641\pi$
$734$	−1.26538e12	−0.160912
$735$	1.09370e12	0.138231
$736$	1.04038e13	1.30690
$737$	7.86674e12	0.982180
$738$	−1.52323e12	−0.189022
$739$	3.28352e12	0.404986	0.202493	−	0.979284i	$-0.435096\pi$
$739$	3.28352e12	0.404986	0.202493	+	0.979284i	$0.435096\pi$
$740$	−1.34724e13	−1.65159
$741$	−5.22300e12	−0.636412
$742$	−2.36233e12	−0.286103
$743$	1.32835e13	1.59905	0.799524	−	0.600634i	$-0.205085\pi$
$743$	1.32835e13	1.59905	0.799524	+	0.600634i	$0.205085\pi$
$744$	−5.30195e12	−0.634391
$745$	7.36890e11	0.0876395
$746$	−4.86310e12	−0.574895
$747$	7.80041e11	0.0916589
$748$	0	0
$749$	−2.64178e12	−0.306711
$750$	1.41410e12	0.163195
$751$	−8.12330e12	−0.931865	−0.465932	−	0.884820i	$-0.654281\pi$
$751$	−8.12330e12	−0.931865	−0.465932	+	0.884820i	$0.654281\pi$
$752$	5.11508e12	0.583273
$753$	−1.21417e13	−1.37627
$754$	−2.24048e12	−0.252447
$755$	−2.36641e11	−0.0265051
$756$	−7.49117e12	−0.834068
$757$	3.70809e12	0.410410	0.205205	−	0.978719i	$-0.434214\pi$
$757$	3.70809e12	0.410410	0.205205	+	0.978719i	$0.434214\pi$
$758$	5.00176e12	0.550315
$759$	1.10597e13	1.20964
$760$	−4.06505e12	−0.441982
$761$	−4.47551e11	−0.0483739	−0.0241870	−	0.999707i	$-0.507700\pi$
$761$	−4.47551e11	−0.0483739	−0.0241870	+	0.999707i	$0.507700\pi$
$762$	1.29667e12	0.139326
$763$	1.98929e12	0.212490
$764$	1.23449e12	0.131089
$765$	0	0
$766$	3.25420e12	0.341519
$767$	−1.14606e13	−1.19571
$768$	−1.92441e12	−0.199605
$769$	8.98580e12	0.926592	0.463296	−	0.886204i	$-0.346667\pi$
$769$	8.98580e12	0.926592	0.463296	+	0.886204i	$0.346667\pi$
$770$	5.38925e12	0.552484
$771$	3.30571e12	0.336915
$772$	1.33501e13	1.35271
$773$	−4.99734e12	−0.503421	−0.251710	−	0.967803i	$-0.580993\pi$
$773$	−4.99734e12	−0.503421	−0.251710	+	0.967803i	$0.580993\pi$
$774$	9.60180e11	0.0961653
$775$	6.52315e12	0.649530
$776$	6.00244e12	0.594224
$777$	1.11416e13	1.09662
$778$	−6.31030e12	−0.617507
$779$	−5.27594e12	−0.513311
$780$	1.45511e13	1.40757
$781$	3.34274e12	0.321494
$782$	0	0
$783$	3.97984e12	0.378388
$784$	−8.28610e11	−0.0783300
$785$	1.03525e13	0.973043
$786$	3.30531e12	0.308895
$787$	6.77515e12	0.629554	0.314777	−	0.949166i	$-0.398070\pi$
$787$	6.77515e12	0.629554	0.314777	+	0.949166i	$0.398070\pi$
$788$	−1.32065e12	−0.122017
$789$	−1.87958e12	−0.172669
$790$	−2.02832e12	−0.185274
$791$	−4.78962e11	−0.0435018
$792$	4.18475e12	0.377925
$793$	−3.35380e13	−3.01167
$794$	7.87050e12	0.702765
$795$	−8.15100e12	−0.723701
$796$	5.35813e12	0.473047
$797$	1.23826e13	1.08705	0.543524	−	0.839394i	$-0.317090\pi$
$797$	1.23826e13	1.08705	0.543524	+	0.839394i	$0.317090\pi$
$798$	1.53109e12	0.133656
$799$	0	0
$800$	6.37459e12	0.550234
$801$	4.72263e12	0.405357
$802$	−2.28077e12	−0.194669
$803$	−8.01657e12	−0.680407
$804$	−6.22649e12	−0.525523
$805$	1.88065e13	1.57843
$806$	9.77330e12	0.815705
$807$	7.77178e12	0.645044
$808$	3.30174e12	0.272516
$809$	−1.06631e13	−0.875219	−0.437610	−	0.899165i	$-0.644175\pi$
$809$	−1.06631e13	−0.875219	−0.437610	+	0.899165i	$0.644175\pi$
$810$	2.37388e12	0.193765
$811$	8.22083e12	0.667301	0.333651	−	0.942697i	$-0.391719\pi$
$811$	8.22083e12	0.667301	0.333651	+	0.942697i	$0.391719\pi$
$812$	−3.35635e12	−0.270935
$813$	1.11862e13	0.897995
$814$	−9.40018e12	−0.750458
$815$	−2.81714e13	−2.23666
$816$	0	0
$817$	3.32573e12	0.261148
$818$	2.25560e12	0.176146
$819$	9.14298e12	0.710085
$820$	1.46986e13	1.13531
$821$	−1.44361e13	−1.10894	−0.554469	−	0.832205i	$-0.687079\pi$
$821$	−1.44361e13	−1.10894	−0.554469	+	0.832205i	$0.687079\pi$
$822$	−5.24333e12	−0.400575
$823$	−7.07329e12	−0.537430	−0.268715	−	0.963220i	$-0.586599\pi$
$823$	−7.07329e12	−0.537430	−0.268715	+	0.963220i	$0.586599\pi$
$824$	1.26616e13	0.956789
$825$	6.77648e12	0.509286
$826$	3.35959e12	0.251117
$827$	7.67968e12	0.570911	0.285456	−	0.958392i	$-0.407855\pi$
$827$	7.67968e12	0.570911	0.285456	+	0.958392i	$0.407855\pi$
$828$	6.65087e12	0.491747
$829$	1.96058e13	1.44174	0.720872	−	0.693068i	$-0.243741\pi$
$829$	1.96058e13	1.44174	0.720872	+	0.693068i	$0.243741\pi$
$830$	1.47293e12	0.107729
$831$	−1.64965e13	−1.20002
$832$	−3.63080e12	−0.262692
$833$	0	0
$834$	3.17866e12	0.227508
$835$	−1.28546e13	−0.915099
$836$	6.60136e12	0.467417
$837$	−1.73606e13	−1.22265
$838$	8.17038e11	0.0572327
$839$	−2.18456e13	−1.52207	−0.761035	−	0.648711i	$-0.775308\pi$
$839$	−2.18456e13	−1.52207	−0.761035	+	0.648711i	$0.775308\pi$
$840$	−9.36584e12	−0.649068
$841$	−1.27240e13	−0.877086
$842$	1.32608e12	0.0909215
$843$	1.64766e12	0.112368
$844$	−1.11869e12	−0.0758870
$845$	−4.03045e13	−2.71956
$846$	−2.83287e12	−0.190134
$847$	−5.37546e12	−0.358873
$848$	6.17538e12	0.410093
$849$	1.64806e12	0.108865
$850$	0	0
$851$	−3.28031e13	−2.14404
$852$	−2.64576e12	−0.172017
$853$	−2.71420e13	−1.75538	−0.877691	−	0.479226i	$-0.840917\pi$
$853$	−2.71420e13	−1.75538	−0.877691	+	0.479226i	$0.840917\pi$
$854$	9.83144e12	0.632494
$855$	−4.01383e12	−0.256869
$856$	−3.87350e12	−0.246588
$857$	−1.35044e13	−0.855188	−0.427594	−	0.903971i	$-0.640639\pi$
$857$	−1.35044e13	−0.855188	−0.427594	+	0.903971i	$0.640639\pi$
$858$	1.01529e13	0.639581
$859$	4.28812e12	0.268718	0.134359	−	0.990933i	$-0.457102\pi$
$859$	4.28812e12	0.268718	0.134359	+	0.990933i	$0.457102\pi$
$860$	−9.26537e12	−0.577590
$861$	−1.21557e13	−0.753817
$862$	−6.47511e12	−0.399452
$863$	1.91319e13	1.17411	0.587057	−	0.809546i	$-0.300287\pi$
$863$	1.91319e13	1.17411	0.587057	+	0.809546i	$0.300287\pi$
$864$	−1.69653e13	−1.03573
$865$	−3.29021e13	−1.99826
$866$	2.14142e11	0.0129381
$867$	0	0
$868$	1.46409e13	0.875443
$869$	7.23225e12	0.430214
$870$	2.26617e12	0.134108
$871$	2.52011e13	1.48367
$872$	2.91678e12	0.170836
$873$	5.92680e12	0.345347
$874$	−4.50782e12	−0.261316
$875$	−8.57398e12	−0.494477
$876$	6.34508e12	0.364057
$877$	2.05194e13	1.17130	0.585649	−	0.810565i	$-0.300840\pi$
$877$	2.05194e13	1.17130	0.585649	+	0.810565i	$0.300840\pi$
$878$	−1.11954e13	−0.635791
$879$	−1.06347e13	−0.600861
$880$	−1.40881e13	−0.791918
$881$	−2.26888e12	−0.126888	−0.0634439	−	0.997985i	$-0.520208\pi$
$881$	−2.26888e12	−0.126888	−0.0634439	+	0.997985i	$0.520208\pi$
$882$	4.58907e11	0.0255339
$883$	−2.33723e13	−1.29383	−0.646916	−	0.762561i	$-0.723942\pi$
$883$	−2.33723e13	−1.29383	−0.646916	+	0.762561i	$0.723942\pi$
$884$	0	0
$885$	1.15920e13	0.635203
$886$	9.24888e12	0.504240
$887$	3.36710e13	1.82642	0.913208	−	0.407494i	$-0.133597\pi$
$887$	3.36710e13	1.82642	0.913208	+	0.407494i	$0.133597\pi$
$888$	1.63363e13	0.881651
$889$	−7.86197e12	−0.422157
$890$	8.91762e12	0.476424
$891$	−8.46438e12	−0.449931
$892$	2.22603e13	1.17731
$893$	−9.81206e12	−0.516332
$894$	−4.06952e11	−0.0213071
$895$	3.78482e13	1.97170
$896$	1.81715e13	0.941900
$897$	3.54297e13	1.82726
$898$	4.37195e11	0.0224353
$899$	−7.77826e12	−0.397158
$900$	4.07512e12	0.207037
$901$	0	0
$902$	1.02558e13	0.515867
$903$	7.66244e12	0.383506
$904$	−7.02275e11	−0.0349743
$905$	−2.00538e13	−0.993751
$906$	1.30687e11	0.00644398
$907$	−1.86605e13	−0.915569	−0.457784	−	0.889063i	$-0.651357\pi$
$907$	−1.86605e13	−0.915569	−0.457784	+	0.889063i	$0.651357\pi$
$908$	2.82296e13	1.37822
$909$	3.26014e12	0.158379
$910$	1.72644e13	0.834576
$911$	3.60008e13	1.73173	0.865864	−	0.500280i	$-0.166769\pi$
$911$	3.60008e13	1.73173	0.865864	+	0.500280i	$0.166769\pi$
$912$	−4.00243e12	−0.191579
$913$	−5.25193e12	−0.250150
$914$	−1.34562e13	−0.637773
$915$	3.39225e13	1.59990
$916$	3.06390e13	1.43795
$917$	−2.00407e13	−0.935947
$918$	0	0
$919$	3.51601e13	1.62603	0.813017	−	0.582240i	$-0.197823\pi$
$919$	3.51601e13	1.62603	0.813017	+	0.582240i	$0.197823\pi$
$920$	2.75748e13	1.26902
$921$	−2.00722e13	−0.919233
$922$	−1.51614e13	−0.690956
$923$	1.07084e13	0.485645
$924$	1.52095e13	0.686420
$925$	−2.00991e13	−0.902690
$926$	−1.42188e12	−0.0635499
$927$	1.25020e13	0.556061
$928$	−7.60112e12	−0.336443
$929$	3.54580e13	1.56187	0.780933	−	0.624614i	$-0.214744\pi$
$929$	3.54580e13	1.56187	0.780933	+	0.624614i	$0.214744\pi$
$930$	−9.88536e12	−0.433331
$931$	1.58949e12	0.0693402
$932$	−8.31155e12	−0.360837
$933$	1.83612e12	0.0793295
$934$	4.73371e12	0.203536
$935$	0	0
$936$	1.34058e13	0.570890
$937$	−2.19169e13	−0.928861	−0.464431	−	0.885609i	$-0.653741\pi$
$937$	−2.19169e13	−0.928861	−0.464431	+	0.885609i	$0.653741\pi$
$938$	−7.38753e12	−0.311592
$939$	−2.71612e13	−1.14013
$940$	2.73361e13	1.14199
$941$	−3.66369e13	−1.52323	−0.761615	−	0.648029i	$-0.775593\pi$
$941$	−3.66369e13	−1.52323	−0.761615	+	0.648029i	$0.775593\pi$
$942$	−5.71723e12	−0.236568
$943$	3.57887e13	1.47382
$944$	−8.78233e12	−0.359945
$945$	−3.06674e13	−1.25093
$946$	−6.46479e12	−0.262449
$947$	2.85170e13	1.15220	0.576100	−	0.817379i	$-0.304574\pi$
$947$	2.85170e13	1.15220	0.576100	+	0.817379i	$0.304574\pi$
$948$	−5.72430e12	−0.230189
$949$	−2.56810e13	−1.02781
$950$	−2.76203e12	−0.110020
$951$	−1.06335e13	−0.421564
$952$	0	0
$953$	−1.49368e13	−0.586598	−0.293299	−	0.956021i	$-0.594753\pi$
$953$	−1.49368e13	−0.586598	−0.293299	+	0.956021i	$0.594753\pi$
$954$	−3.42009e12	−0.133681
$955$	5.05374e12	0.196607
$956$	4.25461e11	0.0164740
$957$	−8.08034e12	−0.311405
$958$	−4.18700e12	−0.160605
$959$	3.17913e13	1.21374
$960$	3.67243e12	0.139551
$961$	7.49025e12	0.283296
$962$	−3.01135e13	−1.13363
$963$	−3.82468e12	−0.143310
$964$	3.15519e12	0.117674
$965$	5.46526e13	2.02879
$966$	−1.03860e13	−0.383752
$967$	−4.03685e12	−0.148465	−0.0742324	−	0.997241i	$-0.523651\pi$
$967$	−4.03685e12	−0.148465	−0.0742324	+	0.997241i	$0.523651\pi$
$968$	−7.88173e12	−0.288524
$969$	0	0
$970$	1.11914e13	0.405893
$971$	1.48199e13	0.535007	0.267504	−	0.963557i	$-0.413801\pi$
$971$	1.48199e13	0.535007	0.267504	+	0.963557i	$0.413801\pi$
$972$	−1.84204e13	−0.661914
$973$	−1.92728e13	−0.689346
$974$	1.64251e12	0.0584779
$975$	2.17084e13	0.769321
$976$	−2.57005e13	−0.906602
$977$	4.73010e13	1.66091	0.830453	−	0.557089i	$-0.188082\pi$
$977$	4.73010e13	1.66091	0.830453	+	0.557089i	$0.188082\pi$
$978$	1.55578e13	0.543781
$979$	−3.17970e13	−1.10628
$980$	−4.42828e12	−0.153362
$981$	2.88003e12	0.0992856
$982$	2.07494e13	0.712038
$983$	−1.71849e13	−0.587025	−0.293512	−	0.955955i	$-0.594824\pi$
$983$	−1.71849e13	−0.587025	−0.293512	+	0.955955i	$0.594824\pi$
$984$	−1.78232e13	−0.606049
$985$	−5.40647e12	−0.183000
$986$	0	0
$987$	−2.26069e13	−0.758252
$988$	2.11474e13	0.706075
$989$	−2.25597e13	−0.749808
$990$	7.80237e12	0.258148
$991$	−6.36036e12	−0.209484	−0.104742	−	0.994499i	$-0.533402\pi$
$991$	−6.36036e12	−0.209484	−0.104742	+	0.994499i	$0.533402\pi$
$992$	3.31572e13	1.08711
$993$	3.68132e13	1.20152
$994$	−3.13911e12	−0.101992
$995$	2.19351e13	0.709474
$996$	4.15688e12	0.133845
$997$	−3.01569e13	−0.966624	−0.483312	−	0.875448i	$-0.660566\pi$
$997$	−3.01569e13	−0.966624	−0.483312	+	0.875448i	$0.660566\pi$
$998$	−9.98647e12	−0.318658
$999$	5.34915e13	1.69918

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.c.1.8		12
17.4	even	4		17.10.b.a.16.5	✓	12
17.13	even	4		17.10.b.a.16.6	yes	12
17.16	even	2	inner	289.10.a.c.1.7		12
51.38	odd	4		153.10.d.b.118.7		12
51.47	odd	4		153.10.d.b.118.8		12
68.47	odd	4		272.10.b.c.33.4		12
68.55	odd	4		272.10.b.c.33.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.b.a.16.5	✓	12	17.4	even	4
17.10.b.a.16.6	yes	12	17.13	even	4
153.10.d.b.118.7		12	51.38	odd	4
153.10.d.b.118.8		12	51.47	odd	4
272.10.b.c.33.4		12	68.47	odd	4
272.10.b.c.33.9		12	68.55	odd	4
289.10.a.c.1.7		12	17.16	even	2	inner
289.10.a.c.1.8		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)

\(f(q)\)	\(=\)	\(q+9.15386 q^{2} +105.759 q^{3} -428.207 q^{4} -1752.99 q^{5} +968.101 q^{6} -5869.78 q^{7} -8606.52 q^{8} -8498.07 q^{9} +O(q^{10})\)	\(q+9.15386 q^{2} +105.759 q^{3} -428.207 q^{4} -1752.99 q^{5} +968.101 q^{6} -5869.78 q^{7} -8606.52 q^{8} -8498.07 q^{9} -16046.7 q^{10} +57216.5 q^{11} -45286.7 q^{12} +183293. q^{13} -53731.1 q^{14} -185395. q^{15} +140459. q^{16} -77790.1 q^{18} -269437. q^{19} +750644. q^{20} -620781. q^{21} +523752. q^{22} +1.82770e6 q^{23} -910216. q^{24} +1.11987e6 q^{25} +1.67784e6 q^{26} -2.98040e6 q^{27} +2.51348e6 q^{28} -1.33534e6 q^{29} -1.69708e6 q^{30} +5.82494e6 q^{31} +5.69228e6 q^{32} +6.05116e6 q^{33} +1.02897e7 q^{35} +3.63893e6 q^{36} -1.79478e7 q^{37} -2.46639e6 q^{38} +1.93849e7 q^{39} +1.50872e7 q^{40} +1.95813e7 q^{41} -5.68254e6 q^{42} -1.23432e7 q^{43} -2.45005e7 q^{44} +1.48971e7 q^{45} +1.67305e7 q^{46} +3.64169e7 q^{47} +1.48548e7 q^{48} -5.89930e6 q^{49} +1.02511e7 q^{50} -7.84873e7 q^{52} +4.39657e7 q^{53} -2.72821e7 q^{54} -1.00300e8 q^{55} +5.05184e7 q^{56} -2.84954e7 q^{57} -1.22235e7 q^{58} -6.25259e7 q^{59} +7.93873e7 q^{60} -1.82975e8 q^{61} +5.33206e7 q^{62} +4.98818e7 q^{63} -1.98087e7 q^{64} -3.21312e8 q^{65} +5.53914e7 q^{66} +1.37491e8 q^{67} +1.93295e8 q^{69} +9.41904e7 q^{70} +5.84225e7 q^{71} +7.31388e7 q^{72} -1.40109e8 q^{73} -1.64291e8 q^{74} +1.18436e8 q^{75} +1.15375e8 q^{76} -3.35848e8 q^{77} +1.77446e8 q^{78} +1.26401e8 q^{79} -2.46224e8 q^{80} -1.47936e8 q^{81} +1.79245e8 q^{82} -9.17904e7 q^{83} +2.65823e8 q^{84} -1.12988e8 q^{86} -1.41224e8 q^{87} -4.92435e8 q^{88} -5.55730e8 q^{89} +1.36366e8 q^{90} -1.07589e9 q^{91} -7.82634e8 q^{92} +6.16038e8 q^{93} +3.33355e8 q^{94} +4.72322e8 q^{95} +6.02009e8 q^{96} -6.97429e8 q^{97} -5.40014e7 q^{98} -4.86230e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 30 q^{2} + 1874 q^{4} - 23550 q^{8} + 9184 q^{9}+O(q^{10}) \) 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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