LMFDB - Embedded newform 289.10.a.g.1.35

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:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.35
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)

$f(q)$	$=$	$q+40.9577 q^{2} +105.034 q^{3} +1165.53 q^{4} -2072.52 q^{5} +4301.96 q^{6} -5180.84 q^{7} +26767.1 q^{8} -8650.78 q^{9} +O(q^{10})$	\(q+40.9577 q^{2} +105.034 q^{3} +1165.53 q^{4} -2072.52 q^{5} +4301.96 q^{6} -5180.84 q^{7} +26767.1 q^{8} -8650.78 q^{9} -84885.6 q^{10} +83913.5 q^{11} +122421. q^{12} -38456.2 q^{13} -212195. q^{14} -217686. q^{15} +499564. q^{16} -354316. q^{18} +727879. q^{19} -2.41558e6 q^{20} -544167. q^{21} +3.43690e6 q^{22} -2.28425e6 q^{23} +2.81146e6 q^{24} +2.34222e6 q^{25} -1.57508e6 q^{26} -2.97602e6 q^{27} -6.03843e6 q^{28} -2.05994e6 q^{29} -8.91591e6 q^{30} -2.10705e6 q^{31} +6.75626e6 q^{32} +8.81380e6 q^{33} +1.07374e7 q^{35} -1.00827e7 q^{36} -1.39359e7 q^{37} +2.98122e7 q^{38} -4.03923e6 q^{39} -5.54753e7 q^{40} -2.53391e7 q^{41} -2.22878e7 q^{42} -2.22102e7 q^{43} +9.78037e7 q^{44} +1.79289e7 q^{45} -9.35575e7 q^{46} +1.95036e7 q^{47} +5.24714e7 q^{48} -1.35125e7 q^{49} +9.59317e7 q^{50} -4.48219e7 q^{52} -3.74339e6 q^{53} -1.21891e8 q^{54} -1.73912e8 q^{55} -1.38676e8 q^{56} +7.64523e7 q^{57} -8.43705e7 q^{58} -7.17696e7 q^{59} -2.53719e8 q^{60} +1.17343e7 q^{61} -8.63000e7 q^{62} +4.48183e7 q^{63} +2.09436e7 q^{64} +7.97013e7 q^{65} +3.60993e8 q^{66} +3.00544e8 q^{67} -2.39925e8 q^{69} +4.39779e8 q^{70} -1.31667e8 q^{71} -2.31556e8 q^{72} -3.21930e8 q^{73} -5.70782e8 q^{74} +2.46013e8 q^{75} +8.48364e8 q^{76} -4.34743e8 q^{77} -1.65437e8 q^{78} -3.05655e8 q^{79} -1.03536e9 q^{80} -1.42311e8 q^{81} -1.03783e9 q^{82} -4.83143e8 q^{83} -6.34243e8 q^{84} -9.09678e8 q^{86} -2.16365e8 q^{87} +2.24612e9 q^{88} +1.76273e8 q^{89} +7.34326e8 q^{90} +1.99236e8 q^{91} -2.66236e9 q^{92} -2.21313e8 q^{93} +7.98822e8 q^{94} -1.50854e9 q^{95} +7.09640e8 q^{96} +8.15034e8 q^{97} -5.53439e8 q^{98} -7.25917e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) $ 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9} - 60000 q^{10} - 76902 q^{11} - 373248 q^{12} + 54216 q^{13} - 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} - 6439479 q^{20} - 138102 q^{21} - 267324 q^{22} - 4041462 q^{23} - 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} - 13281612 q^{27} - 18614784 q^{28} - 4005936 q^{29} + 22471686 q^{30} - 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} - 22076682 q^{37} - 27401376 q^{38} - 62736162 q^{39} + 12231630 q^{40} - 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} + 49578936 q^{44} - 129308238 q^{45} - 140524827 q^{46} - 118557912 q^{47} - 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} - 209848575 q^{54} - 365439924 q^{55} - 203095059 q^{56} + 4614108 q^{57} + 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} - 175597116 q^{61} - 720602571 q^{62} - 587415936 q^{63} + 853082511 q^{64} - 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} - 1308709542 q^{71} - 275337849 q^{72} - 494841342 q^{73} - 1545361890 q^{74} - 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} - 2270624538 q^{78} - 1980107868 q^{79} - 2897000199 q^{80} + 1598298840 q^{81} - 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} + 2705904618 q^{88} + 148394658 q^{89} - 117916215 q^{90} - 636340896 q^{91} + 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} - 4878626298 q^{95} + 8390096634 q^{96} + 891786822 q^{97} + 4285627647 q^{98} + 1476187998 q^{99}+O(q^{100}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9 - 60000 * q^10 - 76902 * q^11 - 373248 * q^12 + 54216 * q^13 - 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 - 6439479 * q^20 - 138102 * q^21 - 267324 * q^22 - 4041462 * q^23 - 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 - 13281612 * q^27 - 18614784 * q^28 - 4005936 * q^29 + 22471686 * q^30 - 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 - 22076682 * q^37 - 27401376 * q^38 - 62736162 * q^39 + 12231630 * q^40 - 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 + 49578936 * q^44 - 129308238 * q^45 - 140524827 * q^46 - 118557912 * q^47 - 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 - 209848575 * q^54 - 365439924 * q^55 - 203095059 * q^56 + 4614108 * q^57 + 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 - 175597116 * q^61 - 720602571 * q^62 - 587415936 * q^63 + 853082511 * q^64 - 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 - 1308709542 * q^71 - 275337849 * q^72 - 494841342 * q^73 - 1545361890 * q^74 - 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 - 2270624538 * q^78 - 1980107868 * q^79 - 2897000199 * q^80 + 1598298840 * q^81 - 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 + 2705904618 * q^88 + 148394658 * q^89 - 117916215 * q^90 - 636340896 * q^91 + 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 - 4878626298 * q^95 + 8390096634 * q^96 + 891786822 * q^97 + 4285627647 * q^98 + 1476187998 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	40.9577	1.81009	0.905045	−	0.425316i	$-0.139837\pi$
$2$	40.9577	1.81009	0.905045	+	0.425316i	$0.139837\pi$
$3$	105.034	0.748662	0.374331	−	0.927295i	$-0.377872\pi$
$3$	105.034	0.748662	0.374331	+	0.927295i	$0.377872\pi$
$4$	1165.53	2.27643
$5$	−2072.52	−1.48297	−0.741487	−	0.670967i	$-0.765879\pi$
$5$	−2072.52	−1.48297	−0.741487	+	0.670967i	$0.765879\pi$
$6$	4301.96	1.35515
$7$	−5180.84	−0.815566	−0.407783	−	0.913079i	$-0.633698\pi$
$7$	−5180.84	−0.815566	−0.407783	+	0.913079i	$0.633698\pi$
$8$	26767.1	2.31044
$9$	−8650.78	−0.439505
$10$	−84885.6	−2.68432
$11$	83913.5	1.72808	0.864042	−	0.503420i	$-0.167925\pi$
$11$	83913.5	1.72808	0.864042	+	0.503420i	$0.167925\pi$
$12$	122421.	1.70427
$13$	−38456.2	−0.373441	−0.186720	−	0.982413i	$-0.559786\pi$
$13$	−38456.2	−0.373441	−0.186720	+	0.982413i	$0.559786\pi$
$14$	−212195.	−1.47625
$15$	−217686.	−1.11025
$16$	499564.	1.90569
$17$	0	0
$17$	0	0
$18$	−354316.	−0.795544
$19$	727879.	1.28135	0.640675	−	0.767812i	$-0.278655\pi$
$19$	727879.	1.28135	0.640675	+	0.767812i	$0.278655\pi$
$20$	−2.41558e6	−3.37588
$21$	−544167.	−0.610584
$22$	3.43690e6	3.12799
$23$	−2.28425e6	−1.70203	−0.851017	−	0.525139i	$-0.824013\pi$
$23$	−2.28425e6	−1.70203	−0.851017	+	0.525139i	$0.824013\pi$
$24$	2.81146e6	1.72974
$25$	2.34222e6	1.19921
$26$	−1.57508e6	−0.675961
$27$	−2.97602e6	−1.07770
$28$	−6.03843e6	−1.85658
$29$	−2.05994e6	−0.540834	−0.270417	−	0.962743i	$-0.587162\pi$
$29$	−2.05994e6	−0.540834	−0.270417	+	0.962743i	$0.587162\pi$
$30$	−8.91591e6	−2.00965
$31$	−2.10705e6	−0.409778	−0.204889	−	0.978785i	$-0.565683\pi$
$31$	−2.10705e6	−0.409778	−0.204889	+	0.978785i	$0.565683\pi$
$32$	6.75626e6	1.13902
$33$	8.81380e6	1.29375
$34$	0	0
$35$	1.07374e7	1.20946
$36$	−1.00827e7	−1.00050
$37$	−1.39359e7	−1.22244	−0.611220	−	0.791461i	$-0.709321\pi$
$37$	−1.39359e7	−1.22244	−0.611220	+	0.791461i	$0.709321\pi$
$38$	2.98122e7	2.31936
$39$	−4.03923e6	−0.279581
$40$	−5.54753e7	−3.42633
$41$	−2.53391e7	−1.40044	−0.700220	−	0.713927i	$-0.746915\pi$
$41$	−2.53391e7	−1.40044	−0.700220	+	0.713927i	$0.746915\pi$
$42$	−2.22878e7	−1.10521
$43$	−2.22102e7	−0.990706	−0.495353	−	0.868692i	$-0.664961\pi$
$43$	−2.22102e7	−0.990706	−0.495353	+	0.868692i	$0.664961\pi$
$44$	9.78037e7	3.93385
$45$	1.79289e7	0.651775
$46$	−9.35575e7	−3.08083
$47$	1.95036e7	0.583008	0.291504	−	0.956570i	$-0.405844\pi$
$47$	1.95036e7	0.583008	0.291504	+	0.956570i	$0.405844\pi$
$48$	5.24714e7	1.42672
$49$	−1.35125e7	−0.334851
$50$	9.59317e7	2.17069
$51$	0	0
$52$	−4.48219e7	−0.850110
$53$	−3.74339e6	−0.0651663	−0.0325832	−	0.999469i	$-0.510373\pi$
$53$	−3.74339e6	−0.0651663	−0.0325832	+	0.999469i	$0.510373\pi$
$54$	−1.21891e8	−1.95074
$55$	−1.73912e8	−2.56271
$56$	−1.38676e8	−1.88432
$57$	7.64523e7	0.959298
$58$	−8.43705e7	−0.978959
$59$	−7.17696e7	−0.771092	−0.385546	−	0.922689i	$-0.625987\pi$
$59$	−7.17696e7	−0.771092	−0.385546	+	0.922689i	$0.625987\pi$
$60$	−2.53719e8	−2.52739
$61$	1.17343e7	0.108511	0.0542554	−	0.998527i	$-0.482721\pi$
$61$	1.17343e7	0.108511	0.0542554	+	0.998527i	$0.482721\pi$
$62$	−8.63000e7	−0.741734
$63$	4.48183e7	0.358446
$64$	2.09436e7	0.156042
$65$	7.97013e7	0.553803
$66$	3.60993e8	2.34181
$67$	3.00544e8	1.82209	0.911047	−	0.412302i	$-0.135275\pi$
$67$	3.00544e8	1.82209	0.911047	+	0.412302i	$0.135275\pi$
$68$	0	0
$69$	−2.39925e8	−1.27425
$70$	4.39779e8	2.18924
$71$	−1.31667e8	−0.614913	−0.307457	−	0.951562i	$-0.599478\pi$
$71$	−1.31667e8	−0.614913	−0.307457	+	0.951562i	$0.599478\pi$
$72$	−2.31556e8	−1.01545
$73$	−3.21930e8	−1.32681	−0.663406	−	0.748260i	$-0.730890\pi$
$73$	−3.21930e8	−1.32681	−0.663406	+	0.748260i	$0.730890\pi$
$74$	−5.70782e8	−2.21273
$75$	2.46013e8	0.897807
$76$	8.48364e8	2.91690
$77$	−4.34743e8	−1.40937
$78$	−1.65437e8	−0.506066
$79$	−3.05655e8	−0.882895	−0.441448	−	0.897287i	$-0.645535\pi$
$79$	−3.05655e8	−0.882895	−0.441448	+	0.897287i	$0.645535\pi$
$80$	−1.03536e9	−2.82609
$81$	−1.42311e8	−0.367330
$82$	−1.03783e9	−2.53492
$83$	−4.83143e8	−1.11744	−0.558720	−	0.829356i	$-0.688707\pi$
$83$	−4.83143e8	−1.11744	−0.558720	+	0.829356i	$0.688707\pi$
$84$	−6.34243e8	−1.38995
$85$	0	0
$86$	−9.09678e8	−1.79327
$87$	−2.16365e8	−0.404902
$88$	2.24612e9	3.99264
$89$	1.76273e8	0.297803	0.148902	−	0.988852i	$-0.452426\pi$
$89$	1.76273e8	0.297803	0.148902	+	0.988852i	$0.452426\pi$
$90$	7.34326e8	1.17977
$91$	1.99236e8	0.304566
$92$	−2.66236e9	−3.87455
$93$	−2.21313e8	−0.306785
$94$	7.98822e8	1.05530
$95$	−1.50854e9	−1.90021
$96$	7.09640e8	0.852741
$97$	8.15034e8	0.934766	0.467383	−	0.884055i	$-0.345197\pi$
$97$	8.15034e8	0.934766	0.467383	+	0.884055i	$0.345197\pi$
$98$	−5.53439e8	−0.606111
$99$	−7.25917e8	−0.759502
$100$	2.72992e9	2.72992
$101$	2.53858e8	0.242742	0.121371	−	0.992607i	$-0.461271\pi$
$101$	2.53858e8	0.242742	0.121371	+	0.992607i	$0.461271\pi$
$102$	0	0
$103$	−1.52399e9	−1.33418	−0.667090	−	0.744977i	$-0.732460\pi$
$103$	−1.52399e9	−1.33418	−0.667090	+	0.744977i	$0.732460\pi$
$104$	−1.02936e9	−0.862814
$105$	1.12780e9	0.905480
$106$	−1.53320e8	−0.117957
$107$	1.73003e9	1.27593	0.637966	−	0.770064i	$-0.279776\pi$
$107$	1.73003e9	1.27593	0.637966	+	0.770064i	$0.279776\pi$
$108$	−3.46864e9	−2.45331
$109$	3.58188e8	0.243048	0.121524	−	0.992589i	$-0.461222\pi$
$109$	3.58188e8	0.243048	0.121524	+	0.992589i	$0.461222\pi$
$110$	−7.12305e9	−4.63873
$111$	−1.46375e9	−0.915195
$112$	−2.58817e9	−1.55421
$113$	7.59574e8	0.438245	0.219123	−	0.975697i	$-0.429681\pi$
$113$	7.59574e8	0.438245	0.219123	+	0.975697i	$0.429681\pi$
$114$	3.13131e9	1.73642
$115$	4.73415e9	2.52407
$116$	−2.40093e9	−1.23117
$117$	3.32676e8	0.164129
$118$	−2.93951e9	−1.39575
$119$	0	0
$120$	−5.82681e9	−2.56516
$121$	4.68353e9	1.98627
$122$	4.80610e8	0.196414
$123$	−2.66148e9	−1.04846
$124$	−2.45583e9	−0.932828
$125$	−8.06399e8	−0.295430
$126$	1.83565e9	0.648819
$127$	3.23828e9	1.10458	0.552291	−	0.833651i	$-0.313754\pi$
$127$	3.23828e9	1.10458	0.552291	+	0.833651i	$0.313754\pi$
$128$	−2.60140e9	−0.856570
$129$	−2.33284e9	−0.741704
$130$	3.26438e9	1.00243
$131$	2.74138e9	0.813294	0.406647	−	0.913585i	$-0.366698\pi$
$131$	2.74138e9	0.813294	0.406647	+	0.913585i	$0.366698\pi$
$132$	1.02728e10	2.94513
$133$	−3.77103e9	−1.04503
$134$	1.23096e10	3.29815
$135$	6.16786e9	1.59821
$136$	0	0
$137$	6.82540e9	1.65533	0.827667	−	0.561220i	$-0.189668\pi$
$137$	6.82540e9	1.65533	0.827667	+	0.561220i	$0.189668\pi$
$138$	−9.82675e9	−2.30650
$139$	2.21726e9	0.503789	0.251895	−	0.967755i	$-0.418946\pi$
$139$	2.21726e9	0.503789	0.251895	+	0.967755i	$0.418946\pi$
$140$	1.25148e10	2.75326
$141$	2.04855e9	0.436476
$142$	−5.39277e9	−1.11305
$143$	−3.22700e9	−0.645337
$144$	−4.32162e9	−0.837559
$145$	4.26928e9	0.802044
$146$	−1.31855e10	−2.40165
$147$	−1.41927e9	−0.250690
$148$	−1.62427e10	−2.78279
$149$	−4.15025e9	−0.689821	−0.344910	−	0.938636i	$-0.612091\pi$
$149$	−4.15025e9	−0.689821	−0.344910	+	0.938636i	$0.612091\pi$
$150$	1.00761e10	1.62511
$151$	4.22098e8	0.0660719	0.0330359	−	0.999454i	$-0.489482\pi$
$151$	4.22098e8	0.0660719	0.0330359	+	0.999454i	$0.489482\pi$
$152$	1.94832e10	2.96049
$153$	0	0
$154$	−1.78061e10	−2.55108
$155$	4.36691e9	0.607690
$156$	−4.70784e9	−0.636445
$157$	1.77965e9	0.233769	0.116885	−	0.993146i	$-0.462709\pi$
$157$	1.77965e9	0.233769	0.116885	+	0.993146i	$0.462709\pi$
$158$	−1.25189e10	−1.59812
$159$	−3.93184e8	−0.0487876
$160$	−1.40025e10	−1.68914
$161$	1.18343e10	1.38812
$162$	−5.82874e9	−0.664901
$163$	6.54651e9	0.726383	0.363192	−	0.931714i	$-0.381687\pi$
$163$	6.54651e9	0.726383	0.363192	+	0.931714i	$0.381687\pi$
$164$	−2.95335e10	−3.18800
$165$	−1.82668e10	−1.91860
$166$	−1.97884e10	−2.02267
$167$	−1.94448e9	−0.193454	−0.0967271	−	0.995311i	$-0.530837\pi$
$167$	−1.94448e9	−0.193454	−0.0967271	+	0.995311i	$0.530837\pi$
$168$	−1.45657e10	−1.41072
$169$	−9.12562e9	−0.860542
$170$	0	0
$171$	−6.29672e9	−0.563160
$172$	−2.58867e10	−2.25527
$173$	−1.57301e10	−1.33513	−0.667567	−	0.744550i	$-0.732664\pi$
$173$	−1.57301e10	−1.33513	−0.667567	+	0.744550i	$0.732664\pi$
$174$	−8.86180e9	−0.732909
$175$	−1.21347e10	−0.978039
$176$	4.19202e10	3.29319
$177$	−7.53828e9	−0.577288
$178$	7.21971e9	0.539051
$179$	4.51445e9	0.328674	0.164337	−	0.986404i	$-0.447451\pi$
$179$	4.51445e9	0.328674	0.164337	+	0.986404i	$0.447451\pi$
$180$	2.08967e10	1.48372
$181$	2.26434e10	1.56815	0.784076	−	0.620665i	$-0.213137\pi$
$181$	2.26434e10	1.56815	0.784076	+	0.620665i	$0.213137\pi$
$182$	8.16023e9	0.551291
$183$	1.23251e9	0.0812380
$184$	−6.11426e10	−3.93245
$185$	2.88825e10	1.81285
$186$	−9.06447e9	−0.555308
$187$	0	0
$188$	2.27320e10	1.32717
$189$	1.54183e10	0.878938
$190$	−6.17864e10	−3.43955
$191$	−7.88641e9	−0.428775	−0.214387	−	0.976749i	$-0.568776\pi$
$191$	−7.88641e9	−0.428775	−0.214387	+	0.976749i	$0.568776\pi$
$192$	2.19980e9	0.116823
$193$	1.42449e10	0.739012	0.369506	−	0.929228i	$-0.379527\pi$
$193$	1.42449e10	0.739012	0.369506	+	0.929228i	$0.379527\pi$
$194$	3.33819e10	1.69201
$195$	8.37138e9	0.414611
$196$	−1.57492e10	−0.762264
$197$	−3.25891e9	−0.154161	−0.0770805	−	0.997025i	$-0.524560\pi$
$197$	−3.25891e9	−0.154161	−0.0770805	+	0.997025i	$0.524560\pi$
$198$	−2.97319e10	−1.37477
$199$	7.31449e9	0.330632	0.165316	−	0.986241i	$-0.447136\pi$
$199$	7.31449e9	0.330632	0.165316	+	0.986241i	$0.447136\pi$
$200$	6.26942e10	2.77072
$201$	3.15674e10	1.36413
$202$	1.03974e10	0.439385
$203$	1.06722e10	0.441086
$204$	0	0
$205$	5.25159e10	2.07682
$206$	−6.24190e10	−2.41499
$207$	1.97605e10	0.748052
$208$	−1.92114e10	−0.711661
$209$	6.10789e10	2.21428
$210$	4.61919e10	1.63900
$211$	−8.04733e8	−0.0279499	−0.0139750	−	0.999902i	$-0.504449\pi$
$211$	−8.04733e8	−0.0279499	−0.0139750	+	0.999902i	$0.504449\pi$
$212$	−4.36303e9	−0.148346
$213$	−1.38295e10	−0.460362
$214$	7.08581e10	2.30955
$215$	4.60311e10	1.46919
$216$	−7.96593e10	−2.48997
$217$	1.09163e10	0.334201
$218$	1.46705e10	0.439938
$219$	−3.38138e10	−0.993333
$220$	−2.02700e11	−5.83381
$221$	0	0
$222$	−5.99518e10	−1.65658
$223$	2.06904e10	0.560268	0.280134	−	0.959961i	$-0.409621\pi$
$223$	2.06904e10	0.560268	0.280134	+	0.959961i	$0.409621\pi$
$224$	−3.50031e10	−0.928947
$225$	−2.02620e10	−0.527061
$226$	3.11104e10	0.793264
$227$	3.22296e10	0.805636	0.402818	−	0.915280i	$-0.368031\pi$
$227$	3.22296e10	0.805636	0.402818	+	0.915280i	$0.368031\pi$
$228$	8.91074e10	2.18377
$229$	−1.46098e10	−0.351064	−0.175532	−	0.984474i	$-0.556165\pi$
$229$	−1.46098e10	−0.351064	−0.175532	+	0.984474i	$0.556165\pi$
$230$	1.93900e11	4.56880
$231$	−4.56630e10	−1.05514
$232$	−5.51386e10	−1.24957
$233$	−1.40255e10	−0.311758	−0.155879	−	0.987776i	$-0.549821\pi$
$233$	−1.40255e10	−0.311758	−0.155879	+	0.987776i	$0.549821\pi$
$234$	1.36256e10	0.297088
$235$	−4.04216e10	−0.864587
$236$	−8.36496e10	−1.75533
$237$	−3.21043e10	−0.660990
$238$	0	0
$239$	−4.43516e9	−0.0879264	−0.0439632	−	0.999033i	$-0.513998\pi$
$239$	−4.43516e9	−0.0879264	−0.0439632	+	0.999033i	$0.513998\pi$
$240$	−1.08748e11	−2.11578
$241$	−1.91454e10	−0.365584	−0.182792	−	0.983152i	$-0.558513\pi$
$241$	−1.91454e10	−0.365584	−0.182792	+	0.983152i	$0.558513\pi$
$242$	1.91826e11	3.59533
$243$	4.36294e10	0.802697
$244$	1.36767e10	0.247017
$245$	2.80048e10	0.496576
$246$	−1.09008e11	−1.89780
$247$	−2.79915e10	−0.478508
$248$	−5.63996e10	−0.946768
$249$	−5.07467e10	−0.836585
$250$	−3.30282e10	−0.534755
$251$	−8.63881e9	−0.137380	−0.0686898	−	0.997638i	$-0.521882\pi$
$251$	−8.63881e9	−0.137380	−0.0686898	+	0.997638i	$0.521882\pi$
$252$	5.22371e10	0.815975
$253$	−1.91679e11	−2.94126
$254$	1.32633e11	1.99939
$255$	0	0
$256$	−1.17271e11	−1.70651
$257$	−1.14783e11	−1.64127	−0.820634	−	0.571455i	$-0.806379\pi$
$257$	−1.14783e11	−1.64127	−0.820634	+	0.571455i	$0.806379\pi$
$258$	−9.55475e10	−1.34255
$259$	7.21998e10	0.996981
$260$	9.28942e10	1.26069
$261$	1.78201e10	0.237699
$262$	1.12280e11	1.47214
$263$	3.42476e10	0.441397	0.220699	−	0.975342i	$-0.429166\pi$
$263$	3.42476e10	0.441397	0.220699	+	0.975342i	$0.429166\pi$
$264$	2.35920e11	2.98914
$265$	7.75825e9	0.0966400
$266$	−1.54452e11	−1.89159
$267$	1.85147e10	0.222954
$268$	3.50293e11	4.14786
$269$	−6.94696e10	−0.808927	−0.404464	−	0.914554i	$-0.632542\pi$
$269$	−6.94696e10	−0.808927	−0.404464	+	0.914554i	$0.632542\pi$
$270$	2.52621e11	2.89290
$271$	−1.06575e9	−0.0120031	−0.00600154	−	0.999982i	$-0.501910\pi$
$271$	−1.06575e9	−0.0120031	−0.00600154	+	0.999982i	$0.501910\pi$
$272$	0	0
$273$	2.09266e10	0.228017
$274$	2.79552e11	2.99630
$275$	1.96544e11	2.07234
$276$	−2.79639e11	−2.90073
$277$	−9.88531e10	−1.00886	−0.504431	−	0.863452i	$-0.668298\pi$
$277$	−9.88531e10	−1.00886	−0.504431	+	0.863452i	$0.668298\pi$
$278$	9.08136e10	0.911904
$279$	1.82277e10	0.180099
$280$	2.87409e11	2.79440
$281$	−1.79379e11	−1.71630	−0.858151	−	0.513398i	$-0.828386\pi$
$281$	−1.79379e11	−1.71630	−0.858151	+	0.513398i	$0.828386\pi$
$282$	8.39038e10	0.790061
$283$	−3.09384e10	−0.286720	−0.143360	−	0.989671i	$-0.545791\pi$
$283$	−3.09384e10	−0.286720	−0.143360	+	0.989671i	$0.545791\pi$
$284$	−1.53462e11	−1.39980
$285$	−1.58449e11	−1.42262
$286$	−1.32170e11	−1.16812
$287$	1.31278e11	1.14215
$288$	−5.84469e10	−0.500605
$289$	0	0
$290$	1.74860e11	1.45177
$291$	8.56066e10	0.699824
$292$	−3.75219e11	−3.02039
$293$	1.72026e10	0.136361	0.0681803	−	0.997673i	$-0.478281\pi$
$293$	1.72026e10	0.136361	0.0681803	+	0.997673i	$0.478281\pi$
$294$	−5.81301e10	−0.453772
$295$	1.48744e11	1.14351
$296$	−3.73023e11	−2.82438
$297$	−2.49728e11	−1.86236
$298$	−1.69985e11	−1.24864
$299$	8.78436e10	0.635608
$300$	2.86736e11	2.04379
$301$	1.15068e11	0.807986
$302$	1.72881e10	0.119596
$303$	2.66638e10	0.181732
$304$	3.63622e11	2.44185
$305$	−2.43196e10	−0.160919
$306$	0	0
$307$	−1.84456e11	−1.18514	−0.592570	−	0.805519i	$-0.701887\pi$
$307$	−1.84456e11	−1.18514	−0.592570	+	0.805519i	$0.701887\pi$
$308$	−5.06706e11	−3.20832
$309$	−1.60071e11	−0.998850
$310$	1.78859e11	1.09997
$311$	−1.97872e11	−1.19939	−0.599697	−	0.800227i	$-0.704712\pi$
$311$	−1.97872e11	−1.19939	−0.599697	+	0.800227i	$0.704712\pi$
$312$	−1.08118e11	−0.645956
$313$	8.05381e10	0.474299	0.237149	−	0.971473i	$-0.423787\pi$
$313$	8.05381e10	0.474299	0.237149	+	0.971473i	$0.423787\pi$
$314$	7.28905e10	0.423143
$315$	−9.28869e10	−0.531566
$316$	−3.56250e11	−2.00985
$317$	1.37985e11	0.767475	0.383738	−	0.923442i	$-0.374637\pi$
$317$	1.37985e11	0.767475	0.383738	+	0.923442i	$0.374637\pi$
$318$	−1.61039e10	−0.0883099
$319$	−1.72857e11	−0.934607
$320$	−4.34061e10	−0.231407
$321$	1.81713e11	0.955242
$322$	4.84707e11	2.51262
$323$	0	0
$324$	−1.65868e11	−0.836200
$325$	−9.00728e10	−0.447835
$326$	2.68130e11	1.31482
$327$	3.76220e10	0.181961
$328$	−6.78254e11	−3.23564
$329$	−1.01045e11	−0.475482
$330$	−7.48165e11	−3.47284
$331$	−1.12292e11	−0.514189	−0.257095	−	0.966386i	$-0.582765\pi$
$331$	−1.12292e11	−0.514189	−0.257095	+	0.966386i	$0.582765\pi$
$332$	−5.63118e11	−2.54377
$333$	1.20556e11	0.537269
$334$	−7.96412e10	−0.350170
$335$	−6.22883e11	−2.70212
$336$	−2.71846e11	−1.16358
$337$	−2.22819e11	−0.941063	−0.470531	−	0.882383i	$-0.655938\pi$
$337$	−2.22819e11	−0.941063	−0.470531	+	0.882383i	$0.655938\pi$
$338$	−3.73764e11	−1.55766
$339$	7.97814e10	0.328098
$340$	0	0
$341$	−1.76810e11	−0.708130
$342$	−2.57899e11	−1.01937
$343$	2.79072e11	1.08866
$344$	−5.94502e11	−2.28897
$345$	4.97249e11	1.88968
$346$	−6.44269e11	−2.41671
$347$	−8.77169e10	−0.324788	−0.162394	−	0.986726i	$-0.551922\pi$
$347$	−8.77169e10	−0.324788	−0.162394	+	0.986726i	$0.551922\pi$
$348$	−2.52180e11	−0.921730
$349$	−3.18539e11	−1.14934	−0.574669	−	0.818386i	$-0.694869\pi$
$349$	−3.18539e11	−1.14934	−0.574669	+	0.818386i	$0.694869\pi$
$350$	−4.97007e11	−1.77034
$351$	1.14447e11	0.402458
$352$	5.66942e11	1.96832
$353$	−5.28579e11	−1.81186	−0.905928	−	0.423432i	$-0.860825\pi$
$353$	−5.28579e11	−1.81186	−0.905928	+	0.423432i	$0.860825\pi$
$354$	−3.08750e11	−1.04494
$355$	2.72882e11	0.911901
$356$	2.05451e11	0.677927
$357$	0	0
$358$	1.84901e11	0.594930
$359$	4.14566e11	1.31725	0.658625	−	0.752471i	$-0.271138\pi$
$359$	4.14566e11	1.31725	0.658625	+	0.752471i	$0.271138\pi$
$360$	4.79904e11	1.50589
$361$	2.07120e11	0.641858
$362$	9.27421e11	2.83850
$363$	4.91932e11	1.48705
$364$	2.32215e11	0.693321
$365$	6.67207e11	1.96763
$366$	5.04805e10	0.147048
$367$	−2.91075e11	−0.837543	−0.418771	−	0.908092i	$-0.637539\pi$
$367$	−2.91075e11	−0.837543	−0.418771	+	0.908092i	$0.637539\pi$
$368$	−1.14113e12	−3.24354
$369$	2.19203e11	0.615500
$370$	1.18296e12	3.28142
$371$	1.93939e10	0.0531475
$372$	−2.57947e11	−0.698373
$373$	−8.23127e10	−0.220180	−0.110090	−	0.993922i	$-0.535114\pi$
$373$	−8.23127e10	−0.220180	−0.110090	+	0.993922i	$0.535114\pi$
$374$	0	0
$375$	−8.46997e10	−0.221177
$376$	5.22054e11	1.34701
$377$	7.92176e10	0.201970
$378$	6.31498e11	1.59096
$379$	−5.54877e11	−1.38140	−0.690701	−	0.723140i	$-0.742698\pi$
$379$	−5.54877e11	−1.38140	−0.690701	+	0.723140i	$0.742698\pi$
$380$	−1.75825e12	−4.32569
$381$	3.40131e11	0.826959
$382$	−3.23009e11	−0.776121
$383$	5.79022e11	1.37499	0.687496	−	0.726188i	$-0.258710\pi$
$383$	5.79022e11	1.37499	0.687496	+	0.726188i	$0.258710\pi$
$384$	−2.73237e11	−0.641282
$385$	9.01014e11	2.09006
$386$	5.83438e11	1.33768
$387$	1.92136e11	0.435420
$388$	9.49946e11	2.12792
$389$	5.29321e11	1.17205	0.586025	−	0.810293i	$-0.300692\pi$
$389$	5.29321e11	1.17205	0.586025	+	0.810293i	$0.300692\pi$
$390$	3.42872e11	0.750484
$391$	0	0
$392$	−3.61689e11	−0.773655
$393$	2.87939e11	0.608883
$394$	−1.33477e11	−0.279045
$395$	6.33476e11	1.30931
$396$	−8.46078e11	−1.72895
$397$	4.75199e10	0.0960105	0.0480052	−	0.998847i	$-0.484714\pi$
$397$	4.75199e10	0.0960105	0.0480052	+	0.998847i	$0.484714\pi$
$398$	2.99584e11	0.598474
$399$	−3.96087e11	−0.782372
$400$	1.17009e12	2.28533
$401$	−5.62820e11	−1.08697	−0.543487	−	0.839417i	$-0.682896\pi$
$401$	−5.62820e11	−1.08697	−0.543487	+	0.839417i	$0.682896\pi$
$402$	1.29293e12	2.46920
$403$	8.10293e10	0.153028
$404$	2.95879e11	0.552584
$405$	2.94943e11	0.544742
$406$	4.37110e11	0.798406
$407$	−1.16941e12	−2.11248
$408$	0	0
$409$	−1.86774e11	−0.330037	−0.165018	−	0.986290i	$-0.552768\pi$
$409$	−1.86774e11	−0.330037	−0.165018	+	0.986290i	$0.552768\pi$
$410$	2.15093e12	3.75923
$411$	7.16902e11	1.23929
$412$	−1.77626e12	−3.03716
$413$	3.71827e11	0.628877
$414$	8.09345e11	1.35404
$415$	1.00132e12	1.65714
$416$	−2.59820e11	−0.425356
$417$	2.32888e11	0.377168
$418$	2.50165e12	4.00805
$419$	−5.54170e11	−0.878375	−0.439187	−	0.898395i	$-0.644734\pi$
$419$	−5.54170e11	−0.878375	−0.439187	+	0.898395i	$0.644734\pi$
$420$	1.31448e12	2.06126
$421$	−4.58096e11	−0.710701	−0.355351	−	0.934733i	$-0.615639\pi$
$421$	−4.58096e11	−0.710701	−0.355351	+	0.934733i	$0.615639\pi$
$422$	−3.29600e10	−0.0505919
$423$	−1.68721e11	−0.256235
$424$	−1.00199e11	−0.150563
$425$	0	0
$426$	−5.66426e11	−0.833297
$427$	−6.07936e10	−0.0884978
$428$	2.01641e12	2.90456
$429$	−3.38946e11	−0.483139
$430$	1.88533e12	2.65937
$431$	3.33640e11	0.465726	0.232863	−	0.972510i	$-0.425191\pi$
$431$	3.33640e11	0.465726	0.232863	+	0.972510i	$0.425191\pi$
$432$	−1.48671e12	−2.05376
$433$	−7.14343e11	−0.976588	−0.488294	−	0.872679i	$-0.662381\pi$
$433$	−7.14343e11	−0.976588	−0.488294	+	0.872679i	$0.662381\pi$
$434$	4.47107e11	0.604934
$435$	4.48421e11	0.600460
$436$	4.17478e11	0.553280
$437$	−1.66266e12	−2.18090
$438$	−1.38493e12	−1.79802
$439$	5.11066e11	0.656729	0.328365	−	0.944551i	$-0.393503\pi$
$439$	5.11066e11	0.656729	0.328365	+	0.944551i	$0.393503\pi$
$440$	−4.65512e12	−5.92099
$441$	1.16893e11	0.147169
$442$	0	0
$443$	5.01063e11	0.618124	0.309062	−	0.951042i	$-0.399985\pi$
$443$	5.01063e11	0.618124	0.309062	+	0.951042i	$0.399985\pi$
$444$	−1.70604e12	−2.08337
$445$	−3.65328e11	−0.441635
$446$	8.47428e11	1.01414
$447$	−4.35919e11	−0.516443
$448$	−1.08506e11	−0.127263
$449$	1.40379e12	1.63002	0.815011	−	0.579445i	$-0.196731\pi$
$449$	1.40379e12	1.63002	0.815011	+	0.579445i	$0.196731\pi$
$450$	−8.29884e11	−0.954028
$451$	−2.12630e12	−2.42008
$452$	8.85307e11	0.997633
$453$	4.43348e10	0.0494655
$454$	1.32005e12	1.45827
$455$	−4.12920e11	−0.451663
$456$	2.04640e12	2.21641
$457$	1.21248e12	1.30032	0.650161	−	0.759797i	$-0.274702\pi$
$457$	1.21248e12	1.30032	0.650161	+	0.759797i	$0.274702\pi$
$458$	−5.98385e11	−0.635457
$459$	0	0
$460$	5.51779e12	5.74586
$461$	9.45438e10	0.0974942	0.0487471	−	0.998811i	$-0.484477\pi$
$461$	9.45438e10	0.0974942	0.0487471	+	0.998811i	$0.484477\pi$
$462$	−1.87025e12	−1.90990
$463$	6.27192e11	0.634287	0.317144	−	0.948378i	$-0.397276\pi$
$463$	6.27192e11	0.634287	0.317144	+	0.948378i	$0.397276\pi$
$464$	−1.02907e12	−1.03066
$465$	4.58676e11	0.454954
$466$	−5.74453e11	−0.564310
$467$	1.46476e12	1.42508	0.712542	−	0.701630i	$-0.247544\pi$
$467$	1.46476e12	1.42508	0.712542	+	0.701630i	$0.247544\pi$
$468$	3.87744e11	0.373627
$469$	−1.55707e12	−1.48604
$470$	−1.65558e12	−1.56498
$471$	1.86925e11	0.175014
$472$	−1.92106e12	−1.78157
$473$	−1.86374e12	−1.71202
$474$	−1.31492e12	−1.19645
$475$	1.70485e12	1.53661
$476$	0	0
$477$	3.23832e10	0.0286409
$478$	−1.81654e11	−0.159155
$479$	−1.19999e12	−1.04152	−0.520761	−	0.853703i	$-0.674352\pi$
$479$	−1.19999e12	−1.04152	−0.520761	+	0.853703i	$0.674352\pi$
$480$	−1.47074e12	−1.26459
$481$	5.35922e11	0.456509
$482$	−7.84149e11	−0.661740
$483$	1.24301e12	1.03923
$484$	5.45879e12	4.52160
$485$	−1.68917e12	−1.38623
$486$	1.78696e12	1.45295
$487$	−2.37860e11	−0.191620	−0.0958100	−	0.995400i	$-0.530544\pi$
$487$	−2.37860e11	−0.191620	−0.0958100	+	0.995400i	$0.530544\pi$
$488$	3.14093e11	0.250708
$489$	6.87609e11	0.543816
$490$	1.14701e12	0.898847
$491$	−2.34046e12	−1.81734	−0.908668	−	0.417520i	$-0.862899\pi$
$491$	−2.34046e12	−1.81734	−0.908668	+	0.417520i	$0.862899\pi$
$492$	−3.10204e12	−2.38673
$493$	0	0
$494$	−1.14646e12	−0.866143
$495$	1.50448e12	1.12632
$496$	−1.05261e12	−0.780908
$497$	6.82146e11	0.501503
$498$	−2.07846e12	−1.51429
$499$	1.92746e12	1.39166	0.695829	−	0.718207i	$-0.255037\pi$
$499$	1.92746e12	1.39166	0.695829	+	0.718207i	$0.255037\pi$
$500$	−9.39882e11	−0.672525
$501$	−2.04237e11	−0.144832
$502$	−3.53825e11	−0.248669
$503$	5.96651e11	0.415589	0.207795	−	0.978172i	$-0.433371\pi$
$503$	5.96651e11	0.415589	0.207795	+	0.978172i	$0.433371\pi$
$504$	1.19965e12	0.828169
$505$	−5.26126e11	−0.359980
$506$	−7.85074e12	−5.32394
$507$	−9.58504e11	−0.644255
$508$	3.77432e12	2.51450
$509$	1.05883e12	0.699190	0.349595	−	0.936901i	$-0.386319\pi$
$509$	1.05883e12	0.699190	0.349595	+	0.936901i	$0.386319\pi$
$510$	0	0
$511$	1.66787e12	1.08210
$512$	−3.47121e12	−2.23237
$513$	−2.16618e12	−1.38091
$514$	−4.70125e12	−2.97084
$515$	3.15850e12	1.97856
$516$	−2.71899e12	−1.68843
$517$	1.63662e12	1.00749
$518$	2.95713e12	1.80463
$519$	−1.65220e12	−0.999564
$520$	2.13337e12	1.27953
$521$	3.10824e12	1.84818	0.924091	−	0.382172i	$-0.124824\pi$
$521$	3.10824e12	1.84818	0.924091	+	0.382172i	$0.124824\pi$
$522$	7.29870e11	0.430257
$523$	1.18130e12	0.690400	0.345200	−	0.938529i	$-0.387811\pi$
$523$	1.18130e12	0.690400	0.345200	+	0.938529i	$0.387811\pi$
$524$	3.19516e12	1.85140
$525$	−1.27456e12	−0.732221
$526$	1.40270e12	0.798968
$527$	0	0
$528$	4.40306e12	2.46548
$529$	3.41664e12	1.89692
$530$	3.17760e11	0.174927
$531$	6.20863e11	0.338899
$532$	−4.39524e12	−2.37892
$533$	9.74447e11	0.522981
$534$	7.58318e11	0.403567
$535$	−3.58553e12	−1.89218
$536$	8.04467e12	4.20985
$537$	4.74172e11	0.246066
$538$	−2.84531e12	−1.46423
$539$	−1.13388e12	−0.578651
$540$	7.18883e12	3.63820
$541$	3.43819e12	1.72561	0.862803	−	0.505540i	$-0.168707\pi$
$541$	3.43819e12	1.72561	0.862803	+	0.505540i	$0.168707\pi$
$542$	−4.36506e10	−0.0217267
$543$	2.37834e12	1.17402
$544$	0	0
$545$	−7.42351e11	−0.360433
$546$	8.57104e11	0.412731
$547$	1.60640e12	0.767201	0.383601	−	0.923499i	$-0.374684\pi$
$547$	1.60640e12	0.767201	0.383601	+	0.923499i	$0.374684\pi$
$548$	7.95521e12	3.76824
$549$	−1.01511e11	−0.0476911
$550$	8.04997e12	3.75113
$551$	−1.49939e12	−0.692998
$552$	−6.42207e12	−2.94408
$553$	1.58355e12	0.720060
$554$	−4.04879e12	−1.82613
$555$	3.03365e12	1.35721
$556$	2.58428e12	1.14684
$557$	−1.82680e12	−0.804160	−0.402080	−	0.915604i	$-0.631713\pi$
$557$	−1.82680e12	−0.804160	−0.402080	+	0.915604i	$0.631713\pi$
$558$	7.46562e11	0.325996
$559$	8.54121e11	0.369970
$560$	5.36403e12	2.30486
$561$	0	0
$562$	−7.34695e12	−3.10666
$563$	−2.07582e12	−0.870768	−0.435384	−	0.900245i	$-0.643387\pi$
$563$	−2.07582e12	−0.870768	−0.435384	+	0.900245i	$0.643387\pi$
$564$	2.38765e12	0.993606
$565$	−1.57423e12	−0.649907
$566$	−1.26716e12	−0.518989
$567$	7.37293e11	0.299582
$568$	−3.52433e12	−1.42072
$569$	−2.00630e12	−0.802398	−0.401199	−	0.915991i	$-0.631406\pi$
$569$	−2.00630e12	−0.802398	−0.401199	+	0.915991i	$0.631406\pi$
$570$	−6.48970e12	−2.57506
$571$	4.13921e12	1.62950	0.814750	−	0.579812i	$-0.196874\pi$
$571$	4.13921e12	1.62950	0.814750	+	0.579812i	$0.196874\pi$
$572$	−3.76116e12	−1.46906
$573$	−8.28345e11	−0.321008
$574$	5.37684e12	2.06740
$575$	−5.35020e12	−2.04110
$576$	−1.81179e11	−0.0685814
$577$	−1.32648e12	−0.498207	−0.249103	−	0.968477i	$-0.580136\pi$
$577$	−1.32648e12	−0.498207	−0.249103	+	0.968477i	$0.580136\pi$
$578$	0	0
$579$	1.49620e12	0.553270
$580$	4.97597e12	1.82579
$581$	2.50309e12	0.911347
$582$	3.50624e12	1.26674
$583$	−3.14121e11	−0.112613
$584$	−8.61713e12	−3.06552
$585$	−6.89478e11	−0.243399
$586$	7.04576e11	0.246825
$587$	1.74995e12	0.608350	0.304175	−	0.952616i	$-0.401619\pi$
$587$	1.74995e12	0.608350	0.304175	+	0.952616i	$0.401619\pi$
$588$	−1.65420e12	−0.570678
$589$	−1.53368e12	−0.525068
$590$	6.09220e12	2.06986
$591$	−3.42298e11	−0.115415
$592$	−6.96189e12	−2.32959
$593$	1.45962e12	0.484723	0.242361	−	0.970186i	$-0.422078\pi$
$593$	1.45962e12	0.484723	0.242361	+	0.970186i	$0.422078\pi$
$594$	−1.02283e13	−3.37104
$595$	0	0
$596$	−4.83724e12	−1.57033
$597$	7.68272e11	0.247532
$598$	3.59787e12	1.15051
$599$	5.09467e12	1.61695	0.808473	−	0.588534i	$-0.200295\pi$
$599$	5.09467e12	1.61695	0.808473	+	0.588534i	$0.200295\pi$
$600$	6.58505e12	2.07433
$601$	−3.21832e12	−1.00622	−0.503111	−	0.864222i	$-0.667811\pi$
$601$	−3.21832e12	−1.00622	−0.503111	+	0.864222i	$0.667811\pi$
$602$	4.71290e12	1.46253
$603$	−2.59994e12	−0.800820
$604$	4.91968e11	0.150408
$605$	−9.70671e12	−2.94559
$606$	1.09209e12	0.328951
$607$	−6.15206e12	−1.83938	−0.919690	−	0.392645i	$-0.871560\pi$
$607$	−6.15206e12	−1.83938	−0.919690	+	0.392645i	$0.871560\pi$
$608$	4.91774e12	1.45948
$609$	1.12095e12	0.330225
$610$	−9.96073e11	−0.291278
$611$	−7.50035e11	−0.217719
$612$	0	0
$613$	−4.67903e12	−1.33839	−0.669196	−	0.743086i	$-0.733361\pi$
$613$	−4.67903e12	−1.33839	−0.669196	+	0.743086i	$0.733361\pi$
$614$	−7.55488e12	−2.14521
$615$	5.51597e12	1.55483
$616$	−1.16368e13	−3.25627
$617$	1.42170e12	0.394933	0.197467	−	0.980310i	$-0.436729\pi$
$617$	1.42170e12	0.394933	0.197467	+	0.980310i	$0.436729\pi$
$618$	−6.55615e12	−1.80801
$619$	2.99905e12	0.821061	0.410531	−	0.911847i	$-0.365344\pi$
$619$	2.99905e12	0.821061	0.410531	+	0.911847i	$0.365344\pi$
$620$	5.08977e12	1.38336
$621$	6.79797e12	1.83429
$622$	−8.10436e12	−2.17101
$623$	−9.13240e11	−0.242878
$624$	−2.01785e12	−0.532794
$625$	−2.90336e12	−0.761099
$626$	3.29865e12	0.858523
$627$	6.41538e12	1.65775
$628$	2.07424e12	0.532158
$629$	0	0
$630$	−3.80443e12	−0.962182
$631$	−3.26952e12	−0.821017	−0.410508	−	0.911857i	$-0.634649\pi$
$631$	−3.26952e12	−0.821017	−0.410508	+	0.911857i	$0.634649\pi$
$632$	−8.18148e12	−2.03988
$633$	−8.45246e10	−0.0209251
$634$	5.65153e12	1.38920
$635$	−6.71141e12	−1.63807
$636$	−4.58268e11	−0.111061
$637$	5.19638e11	0.125047
$638$	−7.07982e12	−1.69172
$639$	1.13902e12	0.270258
$640$	5.39146e12	1.27027
$641$	2.29784e12	0.537598	0.268799	−	0.963196i	$-0.413373\pi$
$641$	2.29784e12	0.537598	0.268799	+	0.963196i	$0.413373\pi$
$642$	7.44254e12	1.72907
$643$	1.34089e12	0.309345	0.154673	−	0.987966i	$-0.450568\pi$
$643$	1.34089e12	0.309345	0.154673	+	0.987966i	$0.450568\pi$
$644$	1.37933e13	3.15995
$645$	4.83485e12	1.09993
$646$	0	0
$647$	6.20336e12	1.39174	0.695869	−	0.718168i	$-0.255019\pi$
$647$	6.20336e12	1.39174	0.695869	+	0.718168i	$0.255019\pi$
$648$	−3.80925e12	−0.848696
$649$	−6.02244e12	−1.33251
$650$	−3.68917e12	−0.810622
$651$	1.14659e12	0.250203
$652$	7.63016e12	1.65356
$653$	−5.36324e11	−0.115430	−0.0577149	−	0.998333i	$-0.518381\pi$
$653$	−5.36324e11	−0.115430	−0.0577149	+	0.998333i	$0.518381\pi$
$654$	1.54091e12	0.329365
$655$	−5.68156e12	−1.20610
$656$	−1.26585e13	−2.66880
$657$	2.78495e12	0.583140
$658$	−4.13857e12	−0.860665
$659$	3.60641e11	0.0744887	0.0372443	−	0.999306i	$-0.488142\pi$
$659$	3.60641e11	0.0744887	0.0372443	+	0.999306i	$0.488142\pi$
$660$	−2.12905e13	−4.36755
$661$	−6.10771e12	−1.24443	−0.622216	−	0.782845i	$-0.713768\pi$
$661$	−6.10771e12	−1.24443	−0.622216	+	0.782845i	$0.713768\pi$
$662$	−4.59922e12	−0.930729
$663$	0	0
$664$	−1.29323e13	−2.58178
$665$	7.81553e12	1.54975
$666$	4.93771e12	0.972504
$667$	4.70542e12	0.920518
$668$	−2.26634e12	−0.440384
$669$	2.17320e12	0.419452
$670$	−2.55118e13	−4.89108
$671$	9.84667e11	0.187516
$672$	−3.67653e12	−0.695467
$673$	5.35107e12	1.00548	0.502739	−	0.864438i	$-0.332326\pi$
$673$	5.35107e12	1.00548	0.502739	+	0.864438i	$0.332326\pi$
$674$	−9.12616e12	−1.70341
$675$	−6.97048e12	−1.29240
$676$	−1.06362e13	−1.95896
$677$	−2.46559e12	−0.451099	−0.225550	−	0.974232i	$-0.572418\pi$
$677$	−2.46559e12	−0.451099	−0.225550	+	0.974232i	$0.572418\pi$
$678$	3.26766e12	0.593886
$679$	−4.22256e12	−0.762364
$680$	0	0
$681$	3.38522e12	0.603149
$682$	−7.24174e12	−1.28178
$683$	8.41114e12	1.47898	0.739489	−	0.673169i	$-0.235067\pi$
$683$	8.41114e12	1.47898	0.739489	+	0.673169i	$0.235067\pi$
$684$	−7.33901e12	−1.28199
$685$	−1.41458e13	−2.45482
$686$	1.14301e13	1.97057
$687$	−1.53454e12	−0.262828
$688$	−1.10954e13	−1.88797
$689$	1.43957e11	0.0243358
$690$	2.03661e13	3.42049
$691$	3.08875e12	0.515384	0.257692	−	0.966227i	$-0.417038\pi$
$691$	3.08875e12	0.515384	0.257692	+	0.966227i	$0.417038\pi$
$692$	−1.83339e13	−3.03933
$693$	3.76086e12	0.619424
$694$	−3.59268e12	−0.587896
$695$	−4.59531e12	−0.747107
$696$	−5.79145e12	−0.935504
$697$	0	0
$698$	−1.30466e13	−2.08040
$699$	−1.47316e12	−0.233401
$700$	−1.41433e13	−2.22643
$701$	−9.89703e12	−1.54801	−0.774005	−	0.633180i	$-0.781749\pi$
$701$	−9.89703e12	−1.54801	−0.774005	+	0.633180i	$0.781749\pi$
$702$	4.68746e12	0.728485
$703$	−1.01437e13	−1.56637
$704$	1.75745e12	0.269654
$705$	−4.24566e12	−0.647283
$706$	−2.16494e13	−3.27962
$707$	−1.31520e12	−0.197972
$708$	−8.78608e12	−1.31415
$709$	−6.74854e12	−1.00300	−0.501501	−	0.865157i	$-0.667219\pi$
$709$	−6.74854e12	−1.00300	−0.501501	+	0.865157i	$0.667219\pi$
$710$	1.11766e13	1.65062
$711$	2.64415e12	0.388037
$712$	4.71830e12	0.688058
$713$	4.81304e12	0.697455
$714$	0	0
$715$	6.68802e12	0.957018
$716$	5.26172e12	0.748203
$717$	−4.65845e11	−0.0658272
$718$	1.69796e13	2.38434
$719$	−8.19160e12	−1.14311	−0.571556	−	0.820563i	$-0.693660\pi$
$719$	−8.19160e12	−1.14311	−0.571556	+	0.820563i	$0.693660\pi$
$720$	8.95665e12	1.24208
$721$	7.89555e12	1.08811
$722$	8.48314e12	1.16182
$723$	−2.01092e12	−0.273699
$724$	2.63916e13	3.56978
$725$	−4.82483e12	−0.648577
$726$	2.01484e13	2.69169
$727$	5.33262e12	0.708004	0.354002	−	0.935245i	$-0.384821\pi$
$727$	5.33262e12	0.708004	0.354002	+	0.935245i	$0.384821\pi$
$728$	5.33295e12	0.703682
$729$	7.38370e12	0.968279
$730$	2.73272e13	3.56158
$731$	0	0
$732$	1.43652e12	0.184932
$733$	−7.95146e12	−1.01737	−0.508685	−	0.860953i	$-0.669868\pi$
$733$	−7.95146e12	−1.01737	−0.508685	+	0.860953i	$0.669868\pi$
$734$	−1.19217e13	−1.51603
$735$	2.94147e12	0.371768
$736$	−1.54330e13	−1.93865
$737$	2.52197e13	3.14873
$738$	8.97805e12	1.11411
$739$	−2.28266e11	−0.0281541	−0.0140770	−	0.999901i	$-0.504481\pi$
$739$	−2.28266e11	−0.0281541	−0.0140770	+	0.999901i	$0.504481\pi$
$740$	3.36634e13	4.12681
$741$	−2.94007e12	−0.358241
$742$	7.94329e11	0.0962017
$743$	8.49426e12	1.02253	0.511265	−	0.859423i	$-0.329177\pi$
$743$	8.49426e12	1.02253	0.511265	+	0.859423i	$0.329177\pi$
$744$	−5.92390e12	−0.708810
$745$	8.60148e12	1.02299
$746$	−3.37134e12	−0.398545
$747$	4.17956e12	0.491121
$748$	0	0
$749$	−8.96304e12	−1.04061
$750$	−3.46910e12	−0.400351
$751$	−7.62165e12	−0.874318	−0.437159	−	0.899384i	$-0.644015\pi$
$751$	−7.62165e12	−0.874318	−0.437159	+	0.899384i	$0.644015\pi$
$752$	9.74331e12	1.11103
$753$	−9.07372e11	−0.102851
$754$	3.24457e12	0.365583
$755$	−8.74806e11	−0.0979830
$756$	1.79705e13	2.00084
$757$	1.21708e13	1.34706	0.673532	−	0.739158i	$-0.264776\pi$
$757$	1.21708e13	1.34706	0.673532	+	0.739158i	$0.264776\pi$
$758$	−2.27265e13	−2.50046
$759$	−2.01329e13	−2.20201
$760$	−4.03793e13	−4.39033
$761$	−1.72056e13	−1.85968	−0.929840	−	0.367964i	$-0.880055\pi$
$761$	−1.72056e13	−1.85968	−0.929840	+	0.367964i	$0.880055\pi$
$762$	1.39310e13	1.49687
$763$	−1.85571e12	−0.198221
$764$	−9.19185e12	−0.976074
$765$	0	0
$766$	2.37154e13	2.48886
$767$	2.75999e12	0.287957
$768$	−1.23174e13	−1.27760
$769$	−1.42533e13	−1.46976	−0.734879	−	0.678198i	$-0.762761\pi$
$769$	−1.42533e13	−1.46976	−0.734879	+	0.678198i	$0.762761\pi$
$770$	3.69034e13	3.78319
$771$	−1.20562e13	−1.22875
$772$	1.66029e13	1.68231
$773$	−3.75655e12	−0.378426	−0.189213	−	0.981936i	$-0.560594\pi$
$773$	−3.75655e12	−0.378426	−0.189213	+	0.981936i	$0.560594\pi$
$774$	7.86942e12	0.788150
$775$	−4.93518e12	−0.491411
$776$	2.18160e13	2.15972
$777$	7.58346e12	0.746402
$778$	2.16798e13	2.12152
$779$	−1.84438e13	−1.79445
$780$	9.75709e12	0.943832
$781$	−1.10486e13	−1.06262
$782$	0	0
$783$	6.13044e12	0.582859
$784$	−6.75034e12	−0.638122
$785$	−3.68837e12	−0.346674
$786$	1.17933e13	1.10213
$787$	−1.53858e13	−1.42967	−0.714833	−	0.699296i	$-0.753497\pi$
$787$	−1.53858e13	−1.42967	−0.714833	+	0.699296i	$0.753497\pi$
$788$	−3.79836e12	−0.350936
$789$	3.59718e12	0.330457
$790$	2.59457e13	2.36997
$791$	−3.93524e12	−0.357418
$792$	−1.94307e13	−1.75479
$793$	−4.51257e11	−0.0405224
$794$	1.94631e12	0.173788
$795$	8.14883e11	0.0723507
$796$	8.52525e12	0.752659
$797$	−1.86441e13	−1.63674	−0.818370	−	0.574692i	$-0.805122\pi$
$797$	−1.86441e13	−1.63674	−0.818370	+	0.574692i	$0.805122\pi$
$798$	−1.62228e13	−1.41616
$799$	0	0
$800$	1.58246e13	1.36593
$801$	−1.52489e12	−0.130886
$802$	−2.30518e13	−1.96752
$803$	−2.70143e13	−2.29284
$804$	3.67928e13	3.10535
$805$	−2.45269e13	−2.05855
$806$	3.31877e12	0.276994
$807$	−7.29670e12	−0.605613
$808$	6.79503e12	0.560842
$809$	1.03571e13	0.850099	0.425050	−	0.905170i	$-0.360257\pi$
$809$	1.03571e13	0.850099	0.425050	+	0.905170i	$0.360257\pi$
$810$	1.20802e13	0.986031
$811$	1.65829e13	1.34607	0.673035	−	0.739611i	$-0.264990\pi$
$811$	1.65829e13	1.34607	0.673035	+	0.739611i	$0.264990\pi$
$812$	1.24388e13	1.00410
$813$	−1.11940e11	−0.00898626
$814$	−4.78963e13	−3.82378
$815$	−1.35678e13	−1.07721
$816$	0	0
$817$	−1.61663e13	−1.26944
$818$	−7.64984e12	−0.597396
$819$	−1.72354e12	−0.133858
$820$	6.12088e13	4.72772
$821$	4.69704e11	0.0360811	0.0180406	−	0.999837i	$-0.494257\pi$
$821$	4.69704e11	0.0360811	0.0180406	+	0.999837i	$0.494257\pi$
$822$	2.93626e13	2.24322
$823$	9.83346e12	0.747149	0.373574	−	0.927600i	$-0.378132\pi$
$823$	9.83346e12	0.747149	0.373574	+	0.927600i	$0.378132\pi$
$824$	−4.07927e13	−3.08255
$825$	2.06438e13	1.55149
$826$	1.52292e13	1.13832
$827$	−1.86474e13	−1.38625	−0.693126	−	0.720816i	$-0.743767\pi$
$827$	−1.86474e13	−1.38625	−0.693126	+	0.720816i	$0.743767\pi$
$828$	2.30315e13	1.70289
$829$	−1.30982e13	−0.963202	−0.481601	−	0.876391i	$-0.659945\pi$
$829$	−1.30982e13	−0.963202	−0.481601	+	0.876391i	$0.659945\pi$
$830$	4.10119e13	2.99957
$831$	−1.03830e13	−0.755296
$832$	−8.05413e11	−0.0582725
$833$	0	0
$834$	9.53855e12	0.682708
$835$	4.02997e12	0.286888
$836$	7.11892e13	5.04064
$837$	6.27064e12	0.441618
$838$	−2.26975e13	−1.58994
$839$	1.02237e13	0.712325	0.356163	−	0.934424i	$-0.384085\pi$
$839$	1.02237e13	0.712325	0.356163	+	0.934424i	$0.384085\pi$
$840$	3.01878e13	2.09206
$841$	−1.02638e13	−0.707498
$842$	−1.87625e13	−1.28643
$843$	−1.88410e13	−1.28493
$844$	−9.37940e11	−0.0636259
$845$	1.89130e13	1.27616
$846$	−6.91044e12	−0.463809
$847$	−2.42646e13	−1.61994
$848$	−1.87006e12	−0.124187
$849$	−3.24959e12	−0.214657
$850$	0	0
$851$	3.18331e13	2.08063
$852$	−1.61188e13	−1.04798
$853$	−2.01132e13	−1.30080	−0.650399	−	0.759593i	$-0.725398\pi$
$853$	−2.01132e13	−1.30080	−0.650399	+	0.759593i	$0.725398\pi$
$854$	−2.48996e12	−0.160189
$855$	1.30501e13	0.835152
$856$	4.63079e13	2.94797
$857$	1.09459e13	0.693168	0.346584	−	0.938019i	$-0.387342\pi$
$857$	1.09459e13	0.693168	0.346584	+	0.938019i	$0.387342\pi$
$858$	−1.38824e13	−0.874525
$859$	2.56259e13	1.60587	0.802935	−	0.596066i	$-0.203270\pi$
$859$	2.56259e13	1.60587	0.802935	+	0.596066i	$0.203270\pi$
$860$	5.36506e13	3.34450
$861$	1.37887e13	0.855086
$862$	1.36651e13	0.843006
$863$	2.79069e13	1.71263	0.856313	−	0.516456i	$-0.172749\pi$
$863$	2.79069e13	1.71263	0.856313	+	0.516456i	$0.172749\pi$
$864$	−2.01068e13	−1.22753
$865$	3.26010e13	1.97997
$866$	−2.92578e13	−1.76771
$867$	0	0
$868$	1.27233e13	0.760783
$869$	−2.56486e13	−1.52572
$870$	1.83663e13	1.08689
$871$	−1.15578e13	−0.680444
$872$	9.58763e12	0.561548
$873$	−7.05068e12	−0.410834
$874$	−6.80985e13	−3.94763
$875$	4.17783e12	0.240943
$876$	−3.94109e13	−2.26125
$877$	−3.22173e12	−0.183904	−0.0919520	−	0.995763i	$-0.529311\pi$
$877$	−3.22173e12	−0.183904	−0.0919520	+	0.995763i	$0.529311\pi$
$878$	2.09321e13	1.18874
$879$	1.80686e12	0.102088
$880$	−8.68805e13	−4.88371
$881$	−2.98527e13	−1.66952	−0.834762	−	0.550611i	$-0.814395\pi$
$881$	−2.98527e13	−1.66952	−0.834762	+	0.550611i	$0.814395\pi$
$882$	4.78767e12	0.266389
$883$	2.33030e13	1.29000	0.644998	−	0.764184i	$-0.276858\pi$
$883$	2.33030e13	1.29000	0.644998	+	0.764184i	$0.276858\pi$
$884$	0	0
$885$	1.56232e13	0.856103
$886$	2.05224e13	1.11886
$887$	1.81953e13	0.986966	0.493483	−	0.869755i	$-0.335724\pi$
$887$	1.81953e13	0.986966	0.493483	+	0.869755i	$0.335724\pi$
$888$	−3.91803e13	−2.11451
$889$	−1.67770e13	−0.900860
$890$	−1.49630e13	−0.799399
$891$	−1.19418e13	−0.634777
$892$	2.41152e13	1.27541
$893$	1.41963e13	0.747038
$894$	−1.78542e13	−0.934807
$895$	−9.35628e12	−0.487416
$896$	1.34775e13	0.698590
$897$	9.22659e12	0.475856
$898$	5.74959e13	2.95049
$899$	4.34041e12	0.221622
$900$	−2.36160e13	−1.19981
$901$	0	0
$902$	−8.70881e13	−4.38056
$903$	1.20861e13	0.604909
$904$	2.03316e13	1.01254
$905$	−4.69289e13	−2.32553
$906$	1.81585e12	0.0895371
$907$	8.29665e12	0.407071	0.203535	−	0.979068i	$-0.434757\pi$
$907$	8.29665e12	0.407071	0.203535	+	0.979068i	$0.434757\pi$
$908$	3.75646e13	1.83397
$909$	−2.19607e12	−0.106686
$910$	−1.69122e13	−0.817551
$911$	1.97513e13	0.950089	0.475044	−	0.879962i	$-0.342432\pi$
$911$	1.97513e13	0.950089	0.475044	+	0.879962i	$0.342432\pi$
$912$	3.81929e13	1.82812
$913$	−4.05422e13	−1.93103
$914$	4.96602e13	2.35370
$915$	−2.55439e12	−0.120474
$916$	−1.70282e13	−0.799170
$917$	−1.42026e13	−0.663296
$918$	0	0
$919$	2.17107e13	1.00405	0.502023	−	0.864854i	$-0.332589\pi$
$919$	2.17107e13	1.00405	0.502023	+	0.864854i	$0.332589\pi$
$920$	1.26719e14	5.83173
$921$	−1.93742e13	−0.887270
$922$	3.87229e12	0.176473
$923$	5.06341e12	0.229634
$924$	−5.32215e13	−2.40195
$925$	−3.26409e13	−1.46597
$926$	2.56883e13	1.14812
$927$	1.31837e13	0.586379
$928$	−1.39175e13	−0.616022
$929$	2.57045e13	1.13224	0.566119	−	0.824324i	$-0.308444\pi$
$929$	2.57045e13	1.13224	0.566119	+	0.824324i	$0.308444\pi$
$930$	1.87863e13	0.823508
$931$	−9.83543e12	−0.429062
$932$	−1.63472e13	−0.709694
$933$	−2.07833e13	−0.897941
$934$	5.99931e13	2.57953
$935$	0	0
$936$	8.90476e12	0.379211
$937$	6.39027e12	0.270827	0.135413	−	0.990789i	$-0.456764\pi$
$937$	6.39027e12	0.270827	0.135413	+	0.990789i	$0.456764\pi$
$938$	−6.37739e13	−2.68986
$939$	8.45927e12	0.355089
$940$	−4.71126e13	−1.96817
$941$	−4.18227e13	−1.73884	−0.869419	−	0.494076i	$-0.835507\pi$
$941$	−4.18227e13	−1.73884	−0.869419	+	0.494076i	$0.835507\pi$
$942$	7.65600e12	0.316791
$943$	5.78809e13	2.38360
$944$	−3.58535e13	−1.46946
$945$	−3.19547e13	−1.30344
$946$	−7.63343e13	−3.09891
$947$	−2.86239e13	−1.15652	−0.578260	−	0.815852i	$-0.696268\pi$
$947$	−2.86239e13	−1.15652	−0.578260	+	0.815852i	$0.696268\pi$
$948$	−3.74185e13	−1.50470
$949$	1.23802e13	0.495485
$950$	6.98266e13	2.78141
$951$	1.44931e13	0.574580
$952$	0	0
$953$	4.18770e13	1.64459	0.822295	−	0.569062i	$-0.192693\pi$
$953$	4.18770e13	1.64459	0.822295	+	0.569062i	$0.192693\pi$
$954$	1.32634e12	0.0518427
$955$	1.63448e13	0.635862
$956$	−5.16932e12	−0.200158
$957$	−1.81559e13	−0.699705
$958$	−4.91488e13	−1.88525
$959$	−3.53613e13	−1.35003
$960$	−4.55913e12	−0.173245
$961$	−2.19999e13	−0.832082
$962$	2.19501e13	0.826322
$963$	−1.49661e13	−0.560779
$964$	−2.23145e13	−0.832224
$965$	−2.95228e13	−1.09594
$966$	5.09109e13	1.88111
$967$	1.10971e13	0.408124	0.204062	−	0.978958i	$-0.434586\pi$
$967$	1.10971e13	0.408124	0.204062	+	0.978958i	$0.434586\pi$
$968$	1.25364e14	4.58918
$969$	0	0
$970$	−6.91846e13	−2.50921
$971$	−1.62887e12	−0.0588029	−0.0294015	−	0.999568i	$-0.509360\pi$
$971$	−1.62887e12	−0.0588029	−0.0294015	+	0.999568i	$0.509360\pi$
$972$	5.08514e13	1.82728
$973$	−1.14873e13	−0.410874
$974$	−9.74219e12	−0.346850
$975$	−9.46074e12	−0.335277
$976$	5.86204e12	0.206788
$977$	−4.55973e12	−0.160108	−0.0800541	−	0.996791i	$-0.525509\pi$
$977$	−4.55973e12	−0.160108	−0.0800541	+	0.996791i	$0.525509\pi$
$978$	2.81629e13	0.984355
$979$	1.47916e13	0.514629
$980$	3.26405e13	1.13042
$981$	−3.09860e12	−0.106821
$982$	−9.58599e13	−3.28954
$983$	−1.34574e13	−0.459694	−0.229847	−	0.973227i	$-0.573823\pi$
$983$	−1.34574e13	−0.459694	−0.229847	+	0.973227i	$0.573823\pi$
$984$	−7.12400e13	−2.42240
$985$	6.75416e12	0.228617
$986$	0	0
$987$	−1.06132e13	−0.355975
$988$	−3.26249e13	−1.08929
$989$	5.07336e13	1.68621
$990$	6.16199e13	2.03874
$991$	−1.26466e13	−0.416525	−0.208262	−	0.978073i	$-0.566781\pi$
$991$	−1.26466e13	−0.416525	−0.208262	+	0.978073i	$0.566781\pi$
$992$	−1.42358e13	−0.466745
$993$	−1.17945e13	−0.384954
$994$	2.79391e13	0.907765
$995$	−1.51594e13	−0.490319
$996$	−5.91467e13	−1.90442
$997$	−4.22854e13	−1.35538	−0.677692	−	0.735346i	$-0.737020\pi$
$997$	−4.22854e13	−1.35538	−0.677692	+	0.735346i	$0.737020\pi$
$998$	7.89442e13	2.51903
$999$	4.14736e13	1.31743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.g.1.35	✓	36
17.16	even	2		289.10.a.h.1.35	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.35	✓	36	1.1	even	1	trivial
289.10.a.h.1.35	yes	36	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+40.9577 q^{2} +105.034 q^{3} +1165.53 q^{4} -2072.52 q^{5} +4301.96 q^{6} -5180.84 q^{7} +26767.1 q^{8} -8650.78 q^{9} +O(q^{10})\)	\(q+40.9577 q^{2} +105.034 q^{3} +1165.53 q^{4} -2072.52 q^{5} +4301.96 q^{6} -5180.84 q^{7} +26767.1 q^{8} -8650.78 q^{9} -84885.6 q^{10} +83913.5 q^{11} +122421. q^{12} -38456.2 q^{13} -212195. q^{14} -217686. q^{15} +499564. q^{16} -354316. q^{18} +727879. q^{19} -2.41558e6 q^{20} -544167. q^{21} +3.43690e6 q^{22} -2.28425e6 q^{23} +2.81146e6 q^{24} +2.34222e6 q^{25} -1.57508e6 q^{26} -2.97602e6 q^{27} -6.03843e6 q^{28} -2.05994e6 q^{29} -8.91591e6 q^{30} -2.10705e6 q^{31} +6.75626e6 q^{32} +8.81380e6 q^{33} +1.07374e7 q^{35} -1.00827e7 q^{36} -1.39359e7 q^{37} +2.98122e7 q^{38} -4.03923e6 q^{39} -5.54753e7 q^{40} -2.53391e7 q^{41} -2.22878e7 q^{42} -2.22102e7 q^{43} +9.78037e7 q^{44} +1.79289e7 q^{45} -9.35575e7 q^{46} +1.95036e7 q^{47} +5.24714e7 q^{48} -1.35125e7 q^{49} +9.59317e7 q^{50} -4.48219e7 q^{52} -3.74339e6 q^{53} -1.21891e8 q^{54} -1.73912e8 q^{55} -1.38676e8 q^{56} +7.64523e7 q^{57} -8.43705e7 q^{58} -7.17696e7 q^{59} -2.53719e8 q^{60} +1.17343e7 q^{61} -8.63000e7 q^{62} +4.48183e7 q^{63} +2.09436e7 q^{64} +7.97013e7 q^{65} +3.60993e8 q^{66} +3.00544e8 q^{67} -2.39925e8 q^{69} +4.39779e8 q^{70} -1.31667e8 q^{71} -2.31556e8 q^{72} -3.21930e8 q^{73} -5.70782e8 q^{74} +2.46013e8 q^{75} +8.48364e8 q^{76} -4.34743e8 q^{77} -1.65437e8 q^{78} -3.05655e8 q^{79} -1.03536e9 q^{80} -1.42311e8 q^{81} -1.03783e9 q^{82} -4.83143e8 q^{83} -6.34243e8 q^{84} -9.09678e8 q^{86} -2.16365e8 q^{87} +2.24612e9 q^{88} +1.76273e8 q^{89} +7.34326e8 q^{90} +1.99236e8 q^{91} -2.66236e9 q^{92} -2.21313e8 q^{93} +7.98822e8 q^{94} -1.50854e9 q^{95} +7.09640e8 q^{96} +8.15034e8 q^{97} -5.53439e8 q^{98} -7.25917e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9} - 60000 q^{10} - 76902 q^{11} - 373248 q^{12} + 54216 q^{13} - 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} - 6439479 q^{20} - 138102 q^{21} - 267324 q^{22} - 4041462 q^{23} - 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} - 13281612 q^{27} - 18614784 q^{28} - 4005936 q^{29} + 22471686 q^{30} - 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} - 22076682 q^{37} - 27401376 q^{38} - 62736162 q^{39} + 12231630 q^{40} - 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} + 49578936 q^{44} - 129308238 q^{45} - 140524827 q^{46} - 118557912 q^{47} - 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} - 209848575 q^{54} - 365439924 q^{55} - 203095059 q^{56} + 4614108 q^{57} + 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} - 175597116 q^{61} - 720602571 q^{62} - 587415936 q^{63} + 853082511 q^{64} - 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} - 1308709542 q^{71} - 275337849 q^{72} - 494841342 q^{73} - 1545361890 q^{74} - 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} - 2270624538 q^{78} - 1980107868 q^{79} - 2897000199 q^{80} + 1598298840 q^{81} - 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} + 2705904618 q^{88} + 148394658 q^{89} - 117916215 q^{90} - 636340896 q^{91} + 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} - 4878626298 q^{95} + 8390096634 q^{96} + 891786822 q^{97} + 4285627647 q^{98} + 1476187998 q^{99}+O(q^{100}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9 - 60000 * q^10 - 76902 * q^11 - 373248 * q^12 + 54216 * q^13 - 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 - 6439479 * q^20 - 138102 * q^21 - 267324 * q^22 - 4041462 * q^23 - 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 - 13281612 * q^27 - 18614784 * q^28 - 4005936 * q^29 + 22471686 * q^30 - 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 - 22076682 * q^37 - 27401376 * q^38 - 62736162 * q^39 + 12231630 * q^40 - 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 + 49578936 * q^44 - 129308238 * q^45 - 140524827 * q^46 - 118557912 * q^47 - 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 - 209848575 * q^54 - 365439924 * q^55 - 203095059 * q^56 + 4614108 * q^57 + 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 - 175597116 * q^61 - 720602571 * q^62 - 587415936 * q^63 + 853082511 * q^64 - 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 - 1308709542 * q^71 - 275337849 * q^72 - 494841342 * q^73 - 1545361890 * q^74 - 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 - 2270624538 * q^78 - 1980107868 * q^79 - 2897000199 * q^80 + 1598298840 * q^81 - 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 + 2705904618 * q^88 + 148394658 * q^89 - 117916215 * q^90 - 636340896 * q^91 + 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 - 4878626298 * q^95 + 8390096634 * q^96 + 891786822 * q^97 + 4285627647 * q^98 + 1476187998 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more