LMFDB - Embedded newform 103.8.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [103,8,Mod(1,103)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(103, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("103.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 103 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	103.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:	$32.1756576249$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.05130 q^{2} -68.8783 q^{3} -78.2791 q^{4} +300.510 q^{5} +485.682 q^{6} -499.751 q^{7} +1454.54 q^{8} +2557.23 q^{9} +O(q^{10})$	\(q-7.05130 q^{2} -68.8783 q^{3} -78.2791 q^{4} +300.510 q^{5} +485.682 q^{6} -499.751 q^{7} +1454.54 q^{8} +2557.23 q^{9} -2118.98 q^{10} -6426.62 q^{11} +5391.74 q^{12} -9340.84 q^{13} +3523.90 q^{14} -20698.6 q^{15} -236.644 q^{16} -10258.7 q^{17} -18031.8 q^{18} -37693.4 q^{19} -23523.6 q^{20} +34422.0 q^{21} +45316.0 q^{22} -60564.0 q^{23} -100186. q^{24} +12181.1 q^{25} +65865.1 q^{26} -25500.6 q^{27} +39120.1 q^{28} +94361.3 q^{29} +145952. q^{30} -146778. q^{31} -184512. q^{32} +442655. q^{33} +72337.4 q^{34} -150180. q^{35} -200178. q^{36} +194738. q^{37} +265788. q^{38} +643382. q^{39} +437102. q^{40} +110250. q^{41} -242720. q^{42} +438842. q^{43} +503070. q^{44} +768471. q^{45} +427055. q^{46} -1.37794e6 q^{47} +16299.7 q^{48} -573792. q^{49} -85892.5 q^{50} +706604. q^{51} +731193. q^{52} -598643. q^{53} +179813. q^{54} -1.93126e6 q^{55} -726906. q^{56} +2.59626e6 q^{57} -665370. q^{58} -1.31503e6 q^{59} +1.62027e6 q^{60} +2.01398e6 q^{61} +1.03497e6 q^{62} -1.27798e6 q^{63} +1.33134e6 q^{64} -2.80701e6 q^{65} -3.12129e6 q^{66} +4.51811e6 q^{67} +803044. q^{68} +4.17155e6 q^{69} +1.05896e6 q^{70} +4.56492e6 q^{71} +3.71958e6 q^{72} -1.50986e6 q^{73} -1.37316e6 q^{74} -839013. q^{75} +2.95061e6 q^{76} +3.21171e6 q^{77} -4.53668e6 q^{78} +279539. q^{79} -71114.0 q^{80} -3.83621e6 q^{81} -777408. q^{82} -3.52544e6 q^{83} -2.69453e6 q^{84} -3.08285e6 q^{85} -3.09441e6 q^{86} -6.49945e6 q^{87} -9.34775e6 q^{88} +1.59806e6 q^{89} -5.41872e6 q^{90} +4.66810e6 q^{91} +4.74090e6 q^{92} +1.01098e7 q^{93} +9.71624e6 q^{94} -1.13272e7 q^{95} +1.27089e7 q^{96} +1.64418e7 q^{97} +4.04598e6 q^{98} -1.64343e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 39 q^{2} + 94 q^{3} + 2111 q^{4} + 945 q^{5} + 271 q^{6} + 1226 q^{7} + 8052 q^{8} + 31566 q^{9}+O(q^{10}) $ 32 * q + 39 * q^2 + 94 * q^3 + 2111 * q^4 + 945 * q^5 + 271 * q^6 + 1226 * q^7 + 8052 * q^8 + 31566 * q^9	\( 32 q + 39 q^{2} + 94 q^{3} + 2111 q^{4} + 945 q^{5} + 271 q^{6} + 1226 q^{7} + 8052 q^{8} + 31566 q^{9} + 2638 q^{10} + 8169 q^{11} + 12039 q^{12} + 14171 q^{13} + 10695 q^{14} + 10759 q^{15} + 143515 q^{16} + 120237 q^{17} + 102288 q^{18} + 45057 q^{19} + 140613 q^{20} + 115762 q^{21} + 242049 q^{22} + 203820 q^{23} + 74610 q^{24} + 686055 q^{25} - 127251 q^{26} + 132508 q^{27} - 769784 q^{28} + 310416 q^{29} - 576370 q^{30} - 101176 q^{31} + 1585740 q^{32} + 715539 q^{33} + 760438 q^{34} + 1016613 q^{35} + 4351624 q^{36} + 1548134 q^{37} + 2850210 q^{38} + 2195909 q^{39} + 4470331 q^{40} + 2031714 q^{41} + 6479435 q^{42} + 1565984 q^{43} + 4069392 q^{44} + 5790546 q^{45} + 7892113 q^{46} + 4034469 q^{47} + 7138233 q^{48} + 7627000 q^{49} + 5213658 q^{50} + 2565519 q^{51} + 8129871 q^{52} + 4799985 q^{53} + 9982795 q^{54} + 3583642 q^{55} + 4552923 q^{56} + 8733123 q^{57} + 2903090 q^{58} + 1725891 q^{59} + 7361351 q^{60} + 4299641 q^{61} + 6367509 q^{62} + 4202312 q^{63} + 13772046 q^{64} + 13614927 q^{65} + 9746103 q^{66} + 2271650 q^{67} + 17935092 q^{68} - 364650 q^{69} + 454144 q^{70} + 11201481 q^{71} + 9438726 q^{72} + 9409961 q^{73} + 8665539 q^{74} + 939165 q^{75} + 3560132 q^{76} + 14167347 q^{77} - 7436704 q^{78} + 1165551 q^{79} + 8385198 q^{80} + 29742120 q^{81} - 35007935 q^{82} + 2497407 q^{83} - 34226991 q^{84} + 607507 q^{85} - 19425795 q^{86} - 7760456 q^{87} + 29754765 q^{88} + 6604398 q^{89} - 49873976 q^{90} - 14775477 q^{91} + 27875580 q^{92} + 7773096 q^{93} - 36766264 q^{94} + 19069674 q^{95} - 40704833 q^{96} + 7841444 q^{97} - 21724491 q^{98} - 9334584 q^{99}+O(q^{100}) \) 32 * q + 39 * q^2 + 94 * q^3 + 2111 * q^4 + 945 * q^5 + 271 * q^6 + 1226 * q^7 + 8052 * q^8 + 31566 * q^9 + 2638 * q^10 + 8169 * q^11 + 12039 * q^12 + 14171 * q^13 + 10695 * q^14 + 10759 * q^15 + 143515 * q^16 + 120237 * q^17 + 102288 * q^18 + 45057 * q^19 + 140613 * q^20 + 115762 * q^21 + 242049 * q^22 + 203820 * q^23 + 74610 * q^24 + 686055 * q^25 - 127251 * q^26 + 132508 * q^27 - 769784 * q^28 + 310416 * q^29 - 576370 * q^30 - 101176 * q^31 + 1585740 * q^32 + 715539 * q^33 + 760438 * q^34 + 1016613 * q^35 + 4351624 * q^36 + 1548134 * q^37 + 2850210 * q^38 + 2195909 * q^39 + 4470331 * q^40 + 2031714 * q^41 + 6479435 * q^42 + 1565984 * q^43 + 4069392 * q^44 + 5790546 * q^45 + 7892113 * q^46 + 4034469 * q^47 + 7138233 * q^48 + 7627000 * q^49 + 5213658 * q^50 + 2565519 * q^51 + 8129871 * q^52 + 4799985 * q^53 + 9982795 * q^54 + 3583642 * q^55 + 4552923 * q^56 + 8733123 * q^57 + 2903090 * q^58 + 1725891 * q^59 + 7361351 * q^60 + 4299641 * q^61 + 6367509 * q^62 + 4202312 * q^63 + 13772046 * q^64 + 13614927 * q^65 + 9746103 * q^66 + 2271650 * q^67 + 17935092 * q^68 - 364650 * q^69 + 454144 * q^70 + 11201481 * q^71 + 9438726 * q^72 + 9409961 * q^73 + 8665539 * q^74 + 939165 * q^75 + 3560132 * q^76 + 14167347 * q^77 - 7436704 * q^78 + 1165551 * q^79 + 8385198 * q^80 + 29742120 * q^81 - 35007935 * q^82 + 2497407 * q^83 - 34226991 * q^84 + 607507 * q^85 - 19425795 * q^86 - 7760456 * q^87 + 29754765 * q^88 + 6604398 * q^89 - 49873976 * q^90 - 14775477 * q^91 + 27875580 * q^92 + 7773096 * q^93 - 36766264 * q^94 + 19069674 * q^95 - 40704833 * q^96 + 7841444 * q^97 - 21724491 * q^98 - 9334584 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−7.05130	−0.623253	−0.311626	−	0.950205i	$-0.600874\pi$
$2$	−7.05130	−0.623253	−0.311626	+	0.950205i	$0.600874\pi$
$3$	−68.8783	−1.47285	−0.736425	−	0.676520i	$-0.763487\pi$
$3$	−68.8783	−1.47285	−0.736425	+	0.676520i	$0.763487\pi$
$4$	−78.2791	−0.611556
$5$	300.510	1.07514	0.537568	−	0.843220i	$-0.319343\pi$
$5$	300.510	1.07514	0.537568	+	0.843220i	$0.319343\pi$
$6$	485.682	0.917958
$7$	−499.751	−0.550694	−0.275347	−	0.961345i	$-0.588793\pi$
$7$	−499.751	−0.550694	−0.275347	+	0.961345i	$0.588793\pi$
$8$	1454.54	1.00441
$9$	2557.23	1.16929
$10$	−2118.98	−0.670082
$11$	−6426.62	−1.45582	−0.727911	−	0.685672i	$-0.759508\pi$
$11$	−6426.62	−1.45582	−0.727911	+	0.685672i	$0.759508\pi$
$12$	5391.74	0.900730
$13$	−9340.84	−1.17919	−0.589596	−	0.807698i	$-0.700713\pi$
$13$	−9340.84	−1.17919	−0.589596	+	0.807698i	$0.700713\pi$
$14$	3523.90	0.343222
$15$	−20698.6	−1.58351
$16$	−236.644	−0.0144436
$17$	−10258.7	−0.506433	−0.253217	−	0.967410i	$-0.581489\pi$
$17$	−10258.7	−0.506433	−0.253217	+	0.967410i	$0.581489\pi$
$18$	−18031.8	−0.728760
$19$	−37693.4	−1.26075	−0.630374	−	0.776292i	$-0.717098\pi$
$19$	−37693.4	−1.26075	−0.630374	+	0.776292i	$0.717098\pi$
$20$	−23523.6	−0.657506
$21$	34422.0	0.811090
$22$	45316.0	0.907345
$23$	−60564.0	−1.03793	−0.518964	−	0.854796i	$-0.673682\pi$
$23$	−60564.0	−1.03793	−0.518964	+	0.854796i	$0.673682\pi$
$24$	−100186.	−1.47934
$25$	12181.1	0.155918
$26$	65865.1	0.734935
$27$	−25500.6	−0.249332
$28$	39120.1	0.336780
$29$	94361.3	0.718457	0.359229	−	0.933250i	$-0.383040\pi$
$29$	94361.3	0.718457	0.359229	+	0.933250i	$0.383040\pi$
$30$	145952.	0.986929
$31$	−146778.	−0.884900	−0.442450	−	0.896793i	$-0.645891\pi$
$31$	−146778.	−0.884900	−0.442450	+	0.896793i	$0.645891\pi$
$32$	−184512.	−0.995405
$33$	442655.	2.14421
$34$	72337.4	0.315636
$35$	−150180.	−0.592071
$36$	−200178.	−0.715083
$37$	194738.	0.632042	0.316021	−	0.948752i	$-0.397653\pi$
$37$	194738.	0.632042	0.316021	+	0.948752i	$0.397653\pi$
$38$	265788.	0.785765
$39$	643382.	1.73677
$40$	437102.	1.07987
$41$	110250.	0.249825	0.124913	−	0.992168i	$-0.460135\pi$
$41$	110250.	0.249825	0.124913	+	0.992168i	$0.460135\pi$
$42$	−242720.	−0.505514
$43$	438842.	0.841722	0.420861	−	0.907125i	$-0.361728\pi$
$43$	438842.	0.841722	0.420861	+	0.907125i	$0.361728\pi$
$44$	503070.	0.890316
$45$	768471.	1.25714
$46$	427055.	0.646891
$47$	−1.37794e6	−1.93592	−0.967958	−	0.251112i	$-0.919204\pi$
$47$	−1.37794e6	−1.93592	−0.967958	+	0.251112i	$0.919204\pi$
$48$	16299.7	0.0212733
$49$	−573792.	−0.696736
$50$	−85892.5	−0.0971762
$51$	706604.	0.745900
$52$	731193.	0.721142
$53$	−598643.	−0.552335	−0.276168	−	0.961110i	$-0.589064\pi$
$53$	−598643.	−0.552335	−0.276168	+	0.961110i	$0.589064\pi$
$54$	179813.	0.155397
$55$	−1.93126e6	−1.56521
$56$	−726906.	−0.553121
$57$	2.59626e6	1.85689
$58$	−665370.	−0.447780
$59$	−1.31503e6	−0.833589	−0.416795	−	0.909001i	$-0.636847\pi$
$59$	−1.31503e6	−0.833589	−0.416795	+	0.909001i	$0.636847\pi$
$60$	1.62027e6	0.968407
$61$	2.01398e6	1.13606	0.568030	−	0.823008i	$-0.307706\pi$
$61$	2.01398e6	1.13606	0.568030	+	0.823008i	$0.307706\pi$
$62$	1.03497e6	0.551516
$63$	−1.27798e6	−0.643919
$64$	1.33134e6	0.634833
$65$	−2.80701e6	−1.26779
$66$	−3.12129e6	−1.33638
$67$	4.51811e6	1.83525	0.917625	−	0.397448i	$-0.130104\pi$
$67$	4.51811e6	1.83525	0.917625	+	0.397448i	$0.130104\pi$
$68$	803044.	0.309712
$69$	4.17155e6	1.52871
$70$	1.05896e6	0.369010
$71$	4.56492e6	1.51366	0.756831	−	0.653611i	$-0.226747\pi$
$71$	4.56492e6	1.51366	0.756831	+	0.653611i	$0.226747\pi$
$72$	3.71958e6	1.17444
$73$	−1.50986e6	−0.454261	−0.227130	−	0.973864i	$-0.572934\pi$
$73$	−1.50986e6	−0.454261	−0.227130	+	0.973864i	$0.572934\pi$
$74$	−1.37316e6	−0.393922
$75$	−839013.	−0.229643
$76$	2.95061e6	0.771018
$77$	3.21171e6	0.801712
$78$	−4.53668e6	−1.08245
$79$	279539.	0.0637892	0.0318946	−	0.999491i	$-0.489846\pi$
$79$	279539.	0.0637892	0.0318946	+	0.999491i	$0.489846\pi$
$80$	−71114.0	−0.0155289
$81$	−3.83621e6	−0.802057
$82$	−777408.	−0.155704
$83$	−3.52544e6	−0.676768	−0.338384	−	0.941008i	$-0.609880\pi$
$83$	−3.52544e6	−0.676768	−0.338384	+	0.941008i	$0.609880\pi$
$84$	−2.69453e6	−0.496027
$85$	−3.08285e6	−0.544485
$86$	−3.09441e6	−0.524606
$87$	−6.49945e6	−1.05818
$88$	−9.34775e6	−1.46224
$89$	1.59806e6	0.240285	0.120143	−	0.992757i	$-0.461665\pi$
$89$	1.59806e6	0.240285	0.120143	+	0.992757i	$0.461665\pi$
$90$	−5.41872e6	−0.783517
$91$	4.66810e6	0.649374
$92$	4.74090e6	0.634750
$93$	1.01098e7	1.30332
$94$	9.71624e6	1.20657
$95$	−1.13272e7	−1.35548
$96$	1.27089e7	1.46608
$97$	1.64418e7	1.82914	0.914572	−	0.404423i	$-0.132528\pi$
$97$	1.64418e7	1.82914	0.914572	+	0.404423i	$0.132528\pi$
$98$	4.04598e6	0.434243
$99$	−1.64343e7	−1.70227
$100$	−953524.	−0.0953524
$101$	−1.64547e7	−1.58915	−0.794575	−	0.607166i	$-0.792306\pi$
$101$	−1.64547e7	−1.58915	−0.794575	+	0.607166i	$0.792306\pi$
$102$	−4.98248e6	−0.464884
$103$	−1.09273e6	−0.0985329
$103$	−1.09273e6	−0.0985329
$104$	−1.35866e7	−1.18439
$105$	1.03442e7	0.872032
$106$	4.22121e6	0.344244
$107$	−8.85954e6	−0.699146	−0.349573	−	0.936909i	$-0.613673\pi$
$107$	−8.85954e6	−0.699146	−0.349573	+	0.936909i	$0.613673\pi$
$108$	1.99617e6	0.152480
$109$	−7.92226e6	−0.585944	−0.292972	−	0.956121i	$-0.594644\pi$
$109$	−7.92226e6	−0.585944	−0.292972	+	0.956121i	$0.594644\pi$
$110$	1.36179e7	0.975519
$111$	−1.34133e7	−0.930902
$112$	118263.	0.00795403
$113$	2.44317e7	1.59286	0.796432	−	0.604729i	$-0.206718\pi$
$113$	2.44317e7	1.59286	0.796432	+	0.604729i	$0.206718\pi$
$114$	−1.83070e7	−1.15731
$115$	−1.82001e7	−1.11591
$116$	−7.38652e6	−0.439377
$117$	−2.38867e7	−1.37881
$118$	9.27264e6	0.519537
$119$	5.12681e6	0.278890
$120$	−3.01069e7	−1.59049
$121$	2.18142e7	1.11942
$122$	−1.42012e7	−0.708053
$123$	−7.59386e6	−0.367955
$124$	1.14896e7	0.541166
$125$	−1.98168e7	−0.907503
$126$	9.01140e6	0.401324
$127$	−8.09878e6	−0.350838	−0.175419	−	0.984494i	$-0.556128\pi$
$127$	−8.09878e6	−0.350838	−0.175419	+	0.984494i	$0.556128\pi$
$128$	1.42299e7	0.599744
$129$	−3.02267e7	−1.23973
$130$	1.97931e7	0.790155
$131$	4.01644e7	1.56096	0.780481	−	0.625180i	$-0.214974\pi$
$131$	4.01644e7	1.56096	0.780481	+	0.625180i	$0.214974\pi$
$132$	−3.46506e7	−1.31130
$133$	1.88373e7	0.694287
$134$	−3.18586e7	−1.14382
$135$	−7.66318e6	−0.268066
$136$	−1.49217e7	−0.508665
$137$	−8.55816e6	−0.284353	−0.142177	−	0.989841i	$-0.545410\pi$
$137$	−8.55816e6	−0.284353	−0.142177	+	0.989841i	$0.545410\pi$
$138$	−2.94148e7	−0.952773
$139$	−3.19816e7	−1.01006	−0.505032	−	0.863101i	$-0.668519\pi$
$139$	−3.19816e7	−1.01006	−0.505032	+	0.863101i	$0.668519\pi$
$140$	1.17560e7	0.362085
$141$	9.49100e7	2.85131
$142$	−3.21886e7	−0.943394
$143$	6.00300e7	1.71669
$144$	−605154.	−0.0168887
$145$	2.83565e7	0.772439
$146$	1.06464e7	0.283119
$147$	3.95218e7	1.02619
$148$	−1.52440e7	−0.386529
$149$	7.23799e7	1.79253	0.896264	−	0.443521i	$-0.146271\pi$
$149$	7.23799e7	1.79253	0.896264	+	0.443521i	$0.146271\pi$
$150$	5.91613e6	0.143126
$151$	−720703.	−0.0170348	−0.00851740	−	0.999964i	$-0.502711\pi$
$151$	−720703.	−0.0170348	−0.00851740	+	0.999964i	$0.502711\pi$
$152$	−5.48265e7	−1.26630
$153$	−2.62339e7	−0.592165
$154$	−2.26467e7	−0.499670
$155$	−4.41081e7	−0.951388
$156$	−5.03634e7	−1.06213
$157$	−2.11197e7	−0.435552	−0.217776	−	0.975999i	$-0.569880\pi$
$157$	−2.11197e7	−0.435552	−0.217776	+	0.975999i	$0.569880\pi$
$158$	−1.97111e6	−0.0397568
$159$	4.12336e7	0.813506
$160$	−5.54477e7	−1.07020
$161$	3.02669e7	0.571581
$162$	2.70503e7	0.499884
$163$	1.91974e7	0.347204	0.173602	−	0.984816i	$-0.444459\pi$
$163$	1.91974e7	0.347204	0.173602	+	0.984816i	$0.444459\pi$
$164$	−8.63030e6	−0.152782
$165$	1.33022e8	2.30531
$166$	2.48589e7	0.421798
$167$	7.13554e7	1.18555	0.592774	−	0.805369i	$-0.298033\pi$
$167$	7.13554e7	1.18555	0.592774	+	0.805369i	$0.298033\pi$
$168$	5.00681e7	0.814664
$169$	2.45029e7	0.390493
$170$	2.17381e7	0.339352
$171$	−9.63907e7	−1.47417
$172$	−3.43522e7	−0.514760
$173$	4.80428e7	0.705450	0.352725	−	0.935727i	$-0.385255\pi$
$173$	4.80428e7	0.705450	0.352725	+	0.935727i	$0.385255\pi$
$174$	4.58296e7	0.659513
$175$	−6.08751e6	−0.0858631
$176$	1.52082e6	0.0210273
$177$	9.05768e7	1.22775
$178$	−1.12684e7	−0.149759
$179$	4.94648e7	0.644631	0.322315	−	0.946632i	$-0.395539\pi$
$179$	4.94648e7	0.644631	0.322315	+	0.946632i	$0.395539\pi$
$180$	−6.01553e7	−0.768812
$181$	−8.21488e6	−0.102974	−0.0514868	−	0.998674i	$-0.516396\pi$
$181$	−8.21488e6	−0.102974	−0.0514868	+	0.998674i	$0.516396\pi$
$182$	−3.29162e7	−0.404724
$183$	−1.38720e8	−1.67325
$184$	−8.80925e7	−1.04250
$185$	5.85208e7	0.679531
$186$	−7.12873e7	−0.812300
$187$	6.59289e7	0.737276
$188$	1.07864e8	1.18392
$189$	1.27440e7	0.137306
$190$	7.98718e7	0.844804
$191$	−9.16369e7	−0.951598	−0.475799	−	0.879554i	$-0.657841\pi$
$191$	−9.16369e7	−0.951598	−0.475799	+	0.879554i	$0.657841\pi$
$192$	−9.17005e7	−0.935013
$193$	2.26657e7	0.226944	0.113472	−	0.993541i	$-0.463803\pi$
$193$	2.26657e7	0.226944	0.113472	+	0.993541i	$0.463803\pi$
$194$	−1.15936e8	−1.14002
$195$	1.93343e8	1.86727
$196$	4.49159e7	0.426093
$197$	−2.92274e7	−0.272370	−0.136185	−	0.990683i	$-0.543484\pi$
$197$	−2.92274e7	−0.272370	−0.136185	+	0.990683i	$0.543484\pi$
$198$	1.15883e8	1.06094
$199$	5.27973e7	0.474926	0.237463	−	0.971397i	$-0.423684\pi$
$199$	5.27973e7	0.474926	0.237463	+	0.971397i	$0.423684\pi$
$200$	1.77178e7	0.156605
$201$	−3.11200e8	−2.70305
$202$	1.16027e8	0.990442
$203$	−4.71572e7	−0.395650
$204$	−5.53124e7	−0.456160
$205$	3.31313e7	0.268596
$206$	7.70515e6	0.0614109
$207$	−1.54876e8	−1.21363
$208$	2.21046e6	0.0170318
$209$	2.42241e8	1.83542
$210$	−7.29397e7	−0.543496
$211$	−1.65753e8	−1.21471	−0.607354	−	0.794431i	$-0.707769\pi$
$211$	−1.65753e8	−1.21471	−0.607354	+	0.794431i	$0.707769\pi$
$212$	4.68613e7	0.337784
$213$	−3.14424e8	−2.22940
$214$	6.24713e7	0.435745
$215$	1.31876e8	0.904966
$216$	−3.70916e7	−0.250430
$217$	7.33523e7	0.487309
$218$	5.58622e7	0.365191
$219$	1.03996e8	0.669058
$220$	1.51177e8	0.957211
$221$	9.58252e7	0.597182
$222$	9.45810e7	0.580187
$223$	−1.81232e7	−0.109438	−0.0547188	−	0.998502i	$-0.517426\pi$
$223$	−1.81232e7	−0.109438	−0.0547188	+	0.998502i	$0.517426\pi$
$224$	9.22101e7	0.548164
$225$	3.11498e7	0.182312
$226$	−1.72275e8	−0.992757
$227$	5.90745e7	0.335204	0.167602	−	0.985855i	$-0.446398\pi$
$227$	5.90745e7	0.335204	0.167602	+	0.985855i	$0.446398\pi$
$228$	−2.03233e8	−1.13559
$229$	−2.75691e8	−1.51705	−0.758524	−	0.651646i	$-0.774079\pi$
$229$	−2.75691e8	−1.51705	−0.758524	+	0.651646i	$0.774079\pi$
$230$	1.28334e8	0.695496
$231$	−2.21217e8	−1.18080
$232$	1.37252e8	0.721623
$233$	2.15286e8	1.11499	0.557494	−	0.830181i	$-0.311763\pi$
$233$	2.15286e8	1.11499	0.557494	+	0.830181i	$0.311763\pi$
$234$	1.68432e8	0.859348
$235$	−4.14083e8	−2.08137
$236$	1.02939e8	0.509786
$237$	−1.92542e7	−0.0939519
$238$	−3.61507e7	−0.173819
$239$	−6.87155e7	−0.325583	−0.162792	−	0.986660i	$-0.552050\pi$
$239$	−6.87155e7	−0.325583	−0.162792	+	0.986660i	$0.552050\pi$
$240$	4.89821e6	0.0228717
$241$	7.04297e7	0.324113	0.162056	−	0.986782i	$-0.448187\pi$
$241$	7.04297e7	0.324113	0.162056	+	0.986782i	$0.448187\pi$
$242$	−1.53819e8	−0.697679
$243$	3.20002e8	1.43064
$244$	−1.57653e8	−0.694765
$245$	−1.72430e8	−0.749086
$246$	5.35466e7	0.229329
$247$	3.52089e8	1.48666
$248$	−2.13493e8	−0.888799
$249$	2.42826e8	0.996777
$250$	1.39734e8	0.565604
$251$	1.53976e8	0.614604	0.307302	−	0.951612i	$-0.400574\pi$
$251$	1.53976e8	0.614604	0.307302	+	0.951612i	$0.400574\pi$
$252$	1.00039e8	0.393792
$253$	3.89221e8	1.51104
$254$	5.71070e7	0.218661
$255$	2.12341e8	0.801944
$256$	−2.70751e8	−1.00862
$257$	2.57229e7	0.0945266	0.0472633	−	0.998882i	$-0.484950\pi$
$257$	2.57229e7	0.0945266	0.0472633	+	0.998882i	$0.484950\pi$
$258$	2.13138e8	0.772665
$259$	−9.73208e7	−0.348062
$260$	2.19731e8	0.775325
$261$	2.41303e8	0.840081
$262$	−2.83212e8	−0.972874
$263$	−3.04551e8	−1.03232	−0.516160	−	0.856492i	$-0.672639\pi$
$263$	−3.04551e8	−1.03232	−0.516160	+	0.856492i	$0.672639\pi$
$264$	6.43857e8	2.15365
$265$	−1.79898e8	−0.593835
$266$	−1.32828e8	−0.432716
$267$	−1.10072e8	−0.353904
$268$	−3.53674e8	−1.12236
$269$	−1.92774e8	−0.603830	−0.301915	−	0.953335i	$-0.597626\pi$
$269$	−1.92774e8	−0.603830	−0.301915	+	0.953335i	$0.597626\pi$
$270$	5.40354e7	0.167073
$271$	−4.67431e8	−1.42667	−0.713337	−	0.700821i	$-0.752817\pi$
$271$	−4.67431e8	−1.42667	−0.713337	+	0.700821i	$0.752817\pi$
$272$	2.42767e6	0.00731474
$273$	−3.21531e8	−0.956430
$274$	6.03462e7	0.177224
$275$	−7.82831e7	−0.226988
$276$	−3.26545e8	−0.934892
$277$	2.47336e8	0.699211	0.349606	−	0.936897i	$-0.386316\pi$
$277$	2.47336e8	0.699211	0.349606	+	0.936897i	$0.386316\pi$
$278$	2.25512e8	0.629525
$279$	−3.75344e8	−1.03470
$280$	−2.18442e8	−0.594681
$281$	−3.58083e7	−0.0962746	−0.0481373	−	0.998841i	$-0.515329\pi$
$281$	−3.58083e7	−0.0962746	−0.0481373	+	0.998841i	$0.515329\pi$
$282$	−6.69239e8	−1.77709
$283$	−2.92218e8	−0.766399	−0.383199	−	0.923666i	$-0.625178\pi$
$283$	−2.92218e8	−0.766399	−0.383199	+	0.923666i	$0.625178\pi$
$284$	−3.57338e8	−0.925689
$285$	7.80202e8	1.99641
$286$	−4.23290e8	−1.06993
$287$	−5.50977e7	−0.137577
$288$	−4.71839e8	−1.16391
$289$	−3.05097e8	−0.743525
$290$	−1.99950e8	−0.481425
$291$	−1.13248e9	−2.69405
$292$	1.18190e8	0.277806
$293$	−4.37633e8	−1.01642	−0.508210	−	0.861233i	$-0.669693\pi$
$293$	−4.37633e8	−1.01642	−0.508210	+	0.861233i	$0.669693\pi$
$294$	−2.78680e8	−0.639574
$295$	−3.95178e8	−0.896222
$296$	2.83254e8	0.634827
$297$	1.63883e8	0.362982
$298$	−5.10372e8	−1.11720
$299$	5.65719e8	1.22392
$300$	6.56772e7	0.140440
$301$	−2.19312e8	−0.463532
$302$	5.08190e6	0.0106170
$303$	1.13337e9	2.34058
$304$	8.91994e6	0.0182098
$305$	6.05222e8	1.22142
$306$	1.84983e8	0.369069
$307$	−3.18830e8	−0.628891	−0.314446	−	0.949275i	$-0.601819\pi$
$307$	−3.18830e8	−0.628891	−0.314446	+	0.949275i	$0.601819\pi$
$308$	−2.51410e8	−0.490292
$309$	7.52652e7	0.145124
$310$	3.11020e8	0.592955
$311$	−8.68269e8	−1.63679	−0.818394	−	0.574657i	$-0.805136\pi$
$311$	−8.68269e8	−1.63679	−0.818394	+	0.574657i	$0.805136\pi$
$312$	9.35823e8	1.74443
$313$	3.11209e8	0.573650	0.286825	−	0.957983i	$-0.407400\pi$
$313$	3.11209e8	0.573650	0.286825	+	0.957983i	$0.407400\pi$
$314$	1.48922e8	0.271459
$315$	−3.84044e8	−0.692300
$316$	−2.18821e7	−0.0390107
$317$	−2.14834e8	−0.378788	−0.189394	−	0.981901i	$-0.560652\pi$
$317$	−2.14834e8	−0.378788	−0.189394	+	0.981901i	$0.560652\pi$
$318$	−2.90750e8	−0.507020
$319$	−6.06424e8	−1.04595
$320$	4.00081e8	0.682531
$321$	6.10230e8	1.02974
$322$	−2.13421e8	−0.356239
$323$	3.86687e8	0.638485
$324$	3.00296e8	0.490503
$325$	−1.13782e8	−0.183857
$326$	−1.35366e8	−0.216396
$327$	5.45672e8	0.863007
$328$	1.60363e8	0.250926
$329$	6.88625e8	1.06610
$330$	−9.37979e8	−1.43679
$331$	−4.54873e8	−0.689433	−0.344717	−	0.938707i	$-0.612025\pi$
$331$	−4.54873e8	−0.689433	−0.344717	+	0.938707i	$0.612025\pi$
$332$	2.75968e8	0.413881
$333$	4.97990e8	0.739037
$334$	−5.03148e8	−0.738896
$335$	1.35774e9	1.97314
$336$	−8.14578e6	−0.0117151
$337$	8.88532e8	1.26464	0.632322	−	0.774705i	$-0.282102\pi$
$337$	8.88532e8	1.26464	0.632322	+	0.774705i	$0.282102\pi$
$338$	−1.72777e8	−0.243376
$339$	−1.68281e9	−2.34605
$340$	2.41323e8	0.332983
$341$	9.43284e8	1.28826
$342$	6.79680e8	0.918783
$343$	6.98320e8	0.934383
$344$	6.38312e8	0.845431
$345$	1.25359e9	1.64357
$346$	−3.38764e8	−0.439674
$347$	3.96578e8	0.509537	0.254769	−	0.967002i	$-0.418001\pi$
$347$	3.96578e8	0.509537	0.254769	+	0.967002i	$0.418001\pi$
$348$	5.08771e8	0.647136
$349$	−8.81996e8	−1.11065	−0.555326	−	0.831633i	$-0.687406\pi$
$349$	−8.81996e8	−1.11065	−0.555326	+	0.831633i	$0.687406\pi$
$350$	4.29249e7	0.0535144
$351$	2.38197e8	0.294010
$352$	1.18579e9	1.44913
$353$	−2.37161e8	−0.286967	−0.143484	−	0.989653i	$-0.545830\pi$
$353$	−2.37161e8	−0.286967	−0.143484	+	0.989653i	$0.545830\pi$
$354$	−6.38684e8	−0.765200
$355$	1.37180e9	1.62739
$356$	−1.25095e8	−0.146948
$357$	−3.53126e8	−0.410763
$358$	−3.48791e8	−0.401768
$359$	9.00772e8	1.02751	0.513753	−	0.857938i	$-0.328255\pi$
$359$	9.00772e8	1.02751	0.513753	+	0.857938i	$0.328255\pi$
$360$	1.11777e9	1.26268
$361$	5.26924e8	0.589484
$362$	5.79256e7	0.0641786
$363$	−1.50253e9	−1.64873
$364$	−3.65415e8	−0.397129
$365$	−4.53726e8	−0.488392
$366$	9.78156e8	1.04286
$367$	1.74058e9	1.83807	0.919035	−	0.394175i	$-0.128970\pi$
$367$	1.74058e9	1.83807	0.919035	+	0.394175i	$0.128970\pi$
$368$	1.43321e7	0.0149914
$369$	2.81935e8	0.292117
$370$	−4.12648e8	−0.423520
$371$	2.99173e8	0.304168
$372$	−7.91387e8	−0.797055
$373$	−1.70329e9	−1.69945	−0.849723	−	0.527229i	$-0.823231\pi$
$373$	−1.70329e9	−1.69945	−0.849723	+	0.527229i	$0.823231\pi$
$374$	−4.64885e8	−0.459510
$375$	1.36495e9	1.33662
$376$	−2.00426e9	−1.94445
$377$	−8.81414e8	−0.847199
$378$	−8.98615e7	−0.0855761
$379$	8.31732e8	0.784777	0.392388	−	0.919800i	$-0.371649\pi$
$379$	8.31732e8	0.784777	0.392388	+	0.919800i	$0.371649\pi$
$380$	8.86687e8	0.828949
$381$	5.57831e8	0.516732
$382$	6.46159e8	0.593086
$383$	−2.08279e9	−1.89430	−0.947150	−	0.320791i	$-0.896051\pi$
$383$	−2.08279e9	−1.89430	−0.947150	+	0.320791i	$0.896051\pi$
$384$	−9.80129e8	−0.883332
$385$	9.65150e8	0.861950
$386$	−1.59823e8	−0.141444
$387$	1.12222e9	0.984213
$388$	−1.28705e9	−1.11862
$389$	−3.64267e8	−0.313759	−0.156879	−	0.987618i	$-0.550143\pi$
$389$	−3.64267e8	−0.313759	−0.156879	+	0.987618i	$0.550143\pi$
$390$	−1.36332e9	−1.16378
$391$	6.21309e8	0.525641
$392$	−8.34601e8	−0.699806
$393$	−2.76646e9	−2.29906
$394$	2.06091e8	0.169755
$395$	8.40041e7	0.0685821
$396$	1.28646e9	1.04103
$397$	2.30470e9	1.84862	0.924308	−	0.381646i	$-0.124643\pi$
$397$	2.30470e9	1.84862	0.924308	+	0.381646i	$0.124643\pi$
$398$	−3.72290e8	−0.295999
$399$	−1.29748e9	−1.02258
$400$	−2.88259e6	−0.00225202
$401$	5.94239e8	0.460210	0.230105	−	0.973166i	$-0.426093\pi$
$401$	5.94239e8	0.460210	0.230105	+	0.973166i	$0.426093\pi$
$402$	2.19436e9	1.68468
$403$	1.37103e9	1.04347
$404$	1.28806e9	0.971854
$405$	−1.15282e9	−0.862321
$406$	3.32519e8	0.246590
$407$	−1.25151e9	−0.920140
$408$	1.02778e9	0.749187
$409$	1.75725e9	1.26999	0.634996	−	0.772516i	$-0.281002\pi$
$409$	1.75725e9	1.26999	0.634996	+	0.772516i	$0.281002\pi$
$410$	−2.33619e8	−0.167403
$411$	5.89472e8	0.418810
$412$	8.55377e7	0.0602584
$413$	6.57185e8	0.459053
$414$	1.09208e9	0.756400
$415$	−1.05943e9	−0.727618
$416$	1.72350e9	1.17377
$417$	2.20284e9	1.48767
$418$	−1.70812e9	−1.14393
$419$	−2.60177e9	−1.72790	−0.863952	−	0.503573i	$-0.832018\pi$
$419$	−2.60177e9	−1.72790	−0.863952	+	0.503573i	$0.832018\pi$
$420$	−8.09732e8	−0.533296
$421$	−8.17528e8	−0.533968	−0.266984	−	0.963701i	$-0.586027\pi$
$421$	−8.17528e8	−0.533968	−0.266984	+	0.963701i	$0.586027\pi$
$422$	1.16877e9	0.757070
$423$	−3.52369e9	−2.26364
$424$	−8.70749e8	−0.554769
$425$	−1.24962e8	−0.0789620
$426$	2.21710e9	1.38948
$427$	−1.00649e9	−0.625622
$428$	6.93517e8	0.427567
$429$	−4.13477e9	−2.52843
$430$	−9.29900e8	−0.564023
$431$	−1.84279e9	−1.10868	−0.554338	−	0.832292i	$-0.687028\pi$
$431$	−1.84279e9	−1.10868	−0.554338	+	0.832292i	$0.687028\pi$
$432$	6.03458e6	0.00360126
$433$	1.00522e9	0.595052	0.297526	−	0.954714i	$-0.403839\pi$
$433$	1.00522e9	0.595052	0.297526	+	0.954714i	$0.403839\pi$
$434$	−5.17229e8	−0.303717
$435$	−1.95315e9	−1.13769
$436$	6.20148e8	0.358338
$437$	2.28286e9	1.30856
$438$	−7.33310e8	−0.416992
$439$	1.63682e9	0.923368	0.461684	−	0.887044i	$-0.347245\pi$
$439$	1.63682e9	0.923368	0.461684	+	0.887044i	$0.347245\pi$
$440$	−2.80909e9	−1.57210
$441$	−1.46732e9	−0.814683
$442$	−6.75692e8	−0.372195
$443$	8.74009e8	0.477643	0.238821	−	0.971064i	$-0.423239\pi$
$443$	8.74009e8	0.477643	0.238821	+	0.971064i	$0.423239\pi$
$444$	1.04998e9	0.569299
$445$	4.80232e8	0.258339
$446$	1.27792e8	0.0682073
$447$	−4.98541e9	−2.64012
$448$	−6.65339e8	−0.349599
$449$	5.04596e8	0.263076	0.131538	−	0.991311i	$-0.458008\pi$
$449$	5.04596e8	0.263076	0.131538	+	0.991311i	$0.458008\pi$
$450$	−2.19647e8	−0.113627
$451$	−7.08536e8	−0.363701
$452$	−1.91249e9	−0.974125
$453$	4.96409e7	0.0250897
$454$	−4.16552e8	−0.208917
$455$	1.40281e9	0.698166
$456$	3.77636e9	1.86507
$457$	−3.44707e9	−1.68944	−0.844722	−	0.535206i	$-0.820234\pi$
$457$	−3.44707e9	−1.68944	−0.844722	+	0.535206i	$0.820234\pi$
$458$	1.94398e9	0.945504
$459$	2.61604e8	0.126270
$460$	1.42469e9	0.682443
$461$	−2.93893e9	−1.39713	−0.698564	−	0.715548i	$-0.746177\pi$
$461$	−2.93893e9	−1.39713	−0.698564	+	0.715548i	$0.746177\pi$
$462$	1.55987e9	0.735938
$463$	2.03500e9	0.952863	0.476431	−	0.879212i	$-0.341930\pi$
$463$	2.03500e9	0.952863	0.476431	+	0.879212i	$0.341930\pi$
$464$	−2.23301e7	−0.0103771
$465$	3.03809e9	1.40125
$466$	−1.51805e9	−0.694919
$467$	2.56017e9	1.16321	0.581607	−	0.813470i	$-0.302424\pi$
$467$	2.56017e9	1.16321	0.581607	+	0.813470i	$0.302424\pi$
$468$	1.86983e9	0.843220
$469$	−2.25793e9	−1.01066
$470$	2.91982e9	1.29722
$471$	1.45469e9	0.641502
$472$	−1.91275e9	−0.837263
$473$	−2.82027e9	−1.22540
$474$	1.35767e8	0.0585558
$475$	−4.59147e8	−0.196573
$476$	−4.01322e8	−0.170557
$477$	−1.53087e9	−0.645837
$478$	4.84534e8	0.202921
$479$	2.93513e9	1.22026	0.610131	−	0.792300i	$-0.291117\pi$
$479$	2.93513e9	1.22026	0.610131	+	0.792300i	$0.291117\pi$
$480$	3.81914e9	1.57624
$481$	−1.81902e9	−0.745298
$482$	−4.96621e8	−0.202004
$483$	−2.08473e9	−0.841852
$484$	−1.70760e9	−0.684585
$485$	4.94092e9	1.96658
$486$	−2.25643e9	−0.891651
$487$	1.00837e9	0.395612	0.197806	−	0.980241i	$-0.436618\pi$
$487$	1.00837e9	0.395612	0.197806	+	0.980241i	$0.436618\pi$
$488$	2.92941e9	1.14107
$489$	−1.32228e9	−0.511379
$490$	1.21586e9	0.466870
$491$	4.38881e9	1.67325	0.836626	−	0.547775i	$-0.184525\pi$
$491$	4.38881e9	1.67325	0.836626	+	0.547775i	$0.184525\pi$
$492$	5.94441e8	0.225025
$493$	−9.68027e8	−0.363851
$494$	−2.48268e9	−0.926567
$495$	−4.93867e9	−1.83017
$496$	3.47341e7	0.0127812
$497$	−2.28132e9	−0.833565
$498$	−1.71224e9	−0.621244
$499$	−3.15354e9	−1.13618	−0.568089	−	0.822967i	$-0.692317\pi$
$499$	−3.15354e9	−1.13618	−0.568089	+	0.822967i	$0.692317\pi$
$500$	1.55124e9	0.554989
$501$	−4.91484e9	−1.74613
$502$	−1.08573e9	−0.383054
$503$	4.88887e9	1.71285	0.856427	−	0.516268i	$-0.172679\pi$
$503$	4.88887e9	1.71285	0.856427	+	0.516268i	$0.172679\pi$
$504$	−1.85886e9	−0.646756
$505$	−4.94479e9	−1.70855
$506$	−2.74452e9	−0.941758
$507$	−1.68772e9	−0.575138
$508$	6.33966e8	0.214557
$509$	2.98861e9	1.00452	0.502258	−	0.864718i	$-0.332503\pi$
$509$	2.98861e9	1.00452	0.502258	+	0.864718i	$0.332503\pi$
$510$	−1.49728e9	−0.499814
$511$	7.54552e8	0.250159
$512$	8.77224e7	0.0288845
$513$	9.61206e8	0.314344
$514$	−1.81380e8	−0.0589139
$515$	−3.28375e8	−0.105936
$516$	2.36612e9	0.758164
$517$	8.85547e9	2.81835
$518$	6.86238e8	0.216931
$519$	−3.30911e9	−1.03902
$520$	−4.08290e9	−1.27338
$521$	−1.56808e9	−0.485776	−0.242888	−	0.970054i	$-0.578095\pi$
$521$	−1.56808e9	−0.485776	−0.242888	+	0.970054i	$0.578095\pi$
$522$	−1.70150e9	−0.523583
$523$	3.71095e9	1.13430	0.567152	−	0.823613i	$-0.308045\pi$
$523$	3.71095e9	1.13430	0.567152	+	0.823613i	$0.308045\pi$
$524$	−3.14404e9	−0.954615
$525$	4.19297e8	0.126463
$526$	2.14748e9	0.643396
$527$	1.50575e9	0.448143
$528$	−1.04752e8	−0.0309701
$529$	2.63169e8	0.0772930
$530$	1.26852e9	0.370110
$531$	−3.36282e9	−0.974704
$532$	−1.47457e9	−0.424595
$533$	−1.02983e9	−0.294592
$534$	7.76147e8	0.220572
$535$	−2.66238e9	−0.751677
$536$	6.57176e9	1.84334
$537$	−3.40706e9	−0.949444
$538$	1.35930e9	0.376339
$539$	3.68754e9	1.01432
$540$	5.99867e8	0.163937
$541$	−3.88909e9	−1.05598	−0.527992	−	0.849249i	$-0.677055\pi$
$541$	−3.88909e9	−1.05598	−0.527992	+	0.849249i	$0.677055\pi$
$542$	3.29600e9	0.889179
$543$	5.65827e8	0.151665
$544$	1.89286e9	0.504106
$545$	−2.38072e9	−0.629970
$546$	2.26721e9	0.596098
$547$	−5.01533e9	−1.31022	−0.655109	−	0.755534i	$-0.727377\pi$
$547$	−5.01533e9	−1.31022	−0.655109	+	0.755534i	$0.727377\pi$
$548$	6.69926e8	0.173898
$549$	5.15021e9	1.32838
$550$	5.51998e8	0.141471
$551$	−3.55680e9	−0.905793
$552$	6.06767e9	1.53545
$553$	−1.39700e8	−0.0351284
$554$	−1.74404e9	−0.435786
$555$	−4.03082e9	−1.00085
$556$	2.50349e9	0.617710
$557$	2.62787e8	0.0644333	0.0322166	−	0.999481i	$-0.489743\pi$
$557$	2.62787e8	0.0644333	0.0322166	+	0.999481i	$0.489743\pi$
$558$	2.64666e9	0.644880
$559$	−4.09916e9	−0.992552
$560$	3.55393e7	0.00855166
$561$	−4.54107e9	−1.08590
$562$	2.52495e8	0.0600034
$563$	−4.14418e9	−0.978722	−0.489361	−	0.872081i	$-0.662770\pi$
$563$	−4.14418e9	−0.978722	−0.489361	+	0.872081i	$0.662770\pi$
$564$	−7.42947e9	−1.74374
$565$	7.34195e9	1.71254
$566$	2.06052e9	0.477660
$567$	1.91715e9	0.441688
$568$	6.63984e9	1.52033
$569$	5.06424e9	1.15245	0.576225	−	0.817291i	$-0.304525\pi$
$569$	5.06424e9	1.15245	0.576225	+	0.817291i	$0.304525\pi$
$570$	−5.50144e9	−1.24427
$571$	−6.84834e9	−1.53943	−0.769713	−	0.638390i	$-0.779601\pi$
$571$	−6.84834e9	−1.53943	−0.769713	+	0.638390i	$0.779601\pi$
$572$	−4.69910e9	−1.04985
$573$	6.31180e9	1.40156
$574$	3.88511e8	0.0857455
$575$	−7.37735e8	−0.161831
$576$	3.40454e9	0.742300
$577$	4.44804e9	0.963947	0.481974	−	0.876186i	$-0.339920\pi$
$577$	4.44804e9	0.963947	0.481974	+	0.876186i	$0.339920\pi$
$578$	2.15133e9	0.463404
$579$	−1.56118e9	−0.334255
$580$	−2.21972e9	−0.472390
$581$	1.76184e9	0.372692
$582$	7.98548e9	1.67908
$583$	3.84725e9	0.804101
$584$	−2.19614e9	−0.456263
$585$	−7.17817e9	−1.48241
$586$	3.08588e9	0.633487
$587$	9.20633e8	0.187868	0.0939341	−	0.995578i	$-0.470056\pi$
$587$	9.20633e8	0.187868	0.0939341	+	0.995578i	$0.470056\pi$
$588$	−3.09374e9	−0.627571
$589$	5.53255e9	1.11564
$590$	2.78652e9	0.558573
$591$	2.01314e9	0.401160
$592$	−4.60838e7	−0.00912898
$593$	−3.80511e9	−0.749335	−0.374667	−	0.927159i	$-0.622243\pi$
$593$	−3.80511e9	−0.749335	−0.374667	+	0.927159i	$0.622243\pi$
$594$	−1.15559e9	−0.226230
$595$	1.54066e9	0.299845
$596$	−5.66584e9	−1.09623
$597$	−3.63659e9	−0.699495
$598$	−3.98905e9	−0.762809
$599$	−3.41795e9	−0.649789	−0.324895	−	0.945750i	$-0.605329\pi$
$599$	−3.41795e9	−0.649789	−0.324895	+	0.945750i	$0.605329\pi$
$600$	−1.22037e9	−0.230655
$601$	1.26832e9	0.238325	0.119162	−	0.992875i	$-0.461979\pi$
$601$	1.26832e9	0.238325	0.119162	+	0.992875i	$0.461979\pi$
$602$	1.54643e9	0.288897
$603$	1.15538e10	2.14593
$604$	5.64160e7	0.0104177
$605$	6.55539e9	1.20352
$606$	−7.99175e9	−1.45877
$607$	8.33038e9	1.51184	0.755918	−	0.654667i	$-0.227191\pi$
$607$	8.33038e9	1.51184	0.755918	+	0.654667i	$0.227191\pi$
$608$	6.95489e9	1.25495
$609$	3.24811e9	0.582733
$610$	−4.26760e9	−0.761254
$611$	1.28711e10	2.28282
$612$	2.05357e9	0.362142
$613$	6.17230e9	1.08227	0.541135	−	0.840936i	$-0.317995\pi$
$613$	6.17230e9	1.08227	0.541135	+	0.840936i	$0.317995\pi$
$614$	2.24817e9	0.391958
$615$	−2.28203e9	−0.395602
$616$	4.67155e9	0.805245
$617$	3.51460e9	0.602391	0.301195	−	0.953562i	$-0.402614\pi$
$617$	3.51460e9	0.602391	0.301195	+	0.953562i	$0.402614\pi$
$618$	−5.30718e8	−0.0904491
$619$	−2.03691e9	−0.345188	−0.172594	−	0.984993i	$-0.555215\pi$
$619$	−2.03691e9	−0.345188	−0.172594	+	0.984993i	$0.555215\pi$
$620$	3.45275e9	0.581827
$621$	1.54442e9	0.258788
$622$	6.12242e9	1.02013
$623$	−7.98631e8	−0.132324
$624$	−1.52253e8	−0.0250853
$625$	−6.90678e9	−1.13161
$626$	−2.19443e9	−0.357529
$627$	−1.66852e10	−2.70330
$628$	1.65323e9	0.266364
$629$	−1.99777e9	−0.320087
$630$	2.70801e9	0.431478
$631$	−7.65857e9	−1.21351	−0.606757	−	0.794887i	$-0.707530\pi$
$631$	−7.65857e9	−1.21351	−0.606757	+	0.794887i	$0.707530\pi$
$632$	4.06599e8	0.0640703
$633$	1.14168e10	1.78908
$634$	1.51486e9	0.236080
$635$	−2.43376e9	−0.377199
$636$	−3.22773e9	−0.497505
$637$	5.35970e9	0.821585
$638$	4.27608e9	0.651888
$639$	1.16735e10	1.76990
$640$	4.27621e9	0.644806
$641$	−9.75679e9	−1.46320	−0.731600	−	0.681734i	$-0.761226\pi$
$641$	−9.75679e9	−1.46320	−0.731600	+	0.681734i	$0.761226\pi$
$642$	−4.30292e9	−0.641787
$643$	−7.34589e9	−1.08970	−0.544849	−	0.838534i	$-0.683413\pi$
$643$	−7.34589e9	−1.08970	−0.544849	+	0.838534i	$0.683413\pi$
$644$	−2.36927e9	−0.349554
$645$	−9.08342e9	−1.33288
$646$	−2.72664e9	−0.397937
$647$	1.08039e10	1.56825	0.784124	−	0.620605i	$-0.213113\pi$
$647$	1.08039e10	1.56825	0.784124	+	0.620605i	$0.213113\pi$
$648$	−5.57991e9	−0.805592
$649$	8.45116e9	1.21356
$650$	8.02308e8	0.114589
$651$	−5.05239e9	−0.717733
$652$	−1.50275e9	−0.212335
$653$	−8.31478e9	−1.16857	−0.584285	−	0.811549i	$-0.698625\pi$
$653$	−8.31478e9	−1.16857	−0.584285	+	0.811549i	$0.698625\pi$
$654$	−3.84770e9	−0.537872
$655$	1.20698e10	1.67825
$656$	−2.60901e7	−0.00360838
$657$	−3.86104e9	−0.531160
$658$	−4.85570e9	−0.664449
$659$	1.03570e10	1.40973	0.704863	−	0.709344i	$-0.251009\pi$
$659$	1.03570e10	1.40973	0.704863	+	0.709344i	$0.251009\pi$
$660$	−1.04129e10	−1.40983
$661$	−5.15645e9	−0.694458	−0.347229	−	0.937780i	$-0.612877\pi$
$661$	−5.15645e9	−0.694458	−0.347229	+	0.937780i	$0.612877\pi$
$662$	3.20745e9	0.429691
$663$	−6.60028e9	−0.879559
$664$	−5.12788e9	−0.679750
$665$	5.66080e9	0.746453
$666$	−3.51148e9	−0.460607
$667$	−5.71489e9	−0.745706
$668$	−5.58564e9	−0.725029
$669$	1.24829e9	0.161185
$670$	−9.57381e9	−1.22977
$671$	−1.29431e10	−1.65390
$672$	−6.35128e9	−0.807363
$673$	−4.19151e9	−0.530051	−0.265026	−	0.964241i	$-0.585380\pi$
$673$	−4.19151e9	−0.530051	−0.265026	+	0.964241i	$0.585380\pi$
$674$	−6.26531e9	−0.788194
$675$	−3.10625e8	−0.0388753
$676$	−1.91806e9	−0.238808
$677$	4.55565e9	0.564274	0.282137	−	0.959374i	$-0.408957\pi$
$677$	4.55565e9	0.564274	0.282137	+	0.959374i	$0.408957\pi$
$678$	1.18660e10	1.46218
$679$	−8.21680e9	−1.00730
$680$	−4.48411e9	−0.546884
$681$	−4.06895e9	−0.493705
$682$	−6.65138e9	−0.802909
$683$	1.39053e10	1.66996	0.834981	−	0.550279i	$-0.185479\pi$
$683$	1.39053e10	1.66996	0.834981	+	0.550279i	$0.185479\pi$
$684$	7.54538e9	0.901539
$685$	−2.57181e9	−0.305719
$686$	−4.92406e9	−0.582357
$687$	1.89892e10	2.23438
$688$	−1.03850e8	−0.0121575
$689$	5.59183e9	0.651309
$690$	−8.83944e9	−1.02436
$691$	1.97846e9	0.228116	0.114058	−	0.993474i	$-0.463615\pi$
$691$	1.97846e9	0.228116	0.114058	+	0.993474i	$0.463615\pi$
$692$	−3.76075e9	−0.431422
$693$	8.21307e9	0.937431
$694$	−2.79639e9	−0.317571
$695$	−9.61079e9	−1.08596
$696$	−9.45369e9	−1.06284
$697$	−1.13103e9	−0.126520
$698$	6.21922e9	0.692217
$699$	−1.48285e10	−1.64221
$700$	4.76525e8	0.0525101
$701$	1.61756e10	1.77357	0.886785	−	0.462182i	$-0.152933\pi$
$701$	1.61756e10	1.77357	0.886785	+	0.462182i	$0.152933\pi$
$702$	−1.67960e9	−0.183243
$703$	−7.34036e9	−0.796845
$704$	−8.55601e9	−0.924203
$705$	2.85214e10	3.06555
$706$	1.67230e9	0.178853
$707$	8.22325e9	0.875136
$708$	−7.09027e9	−0.750838
$709$	9.70866e9	1.02305	0.511526	−	0.859268i	$-0.329080\pi$
$709$	9.70866e9	1.02305	0.511526	+	0.859268i	$0.329080\pi$
$710$	−9.67299e9	−1.01428
$711$	7.14844e8	0.0745878
$712$	2.32443e9	0.241344
$713$	8.88944e9	0.918462
$714$	2.49000e9	0.256009
$715$	1.80396e10	1.84568
$716$	−3.87206e9	−0.394228
$717$	4.73301e9	0.479535
$718$	−6.35161e9	−0.640396
$719$	7.65697e9	0.768256	0.384128	−	0.923280i	$-0.374502\pi$
$719$	7.65697e9	0.768256	0.384128	+	0.923280i	$0.374502\pi$
$720$	−1.81855e8	−0.0181577
$721$	5.46092e8	0.0542615
$722$	−3.71550e9	−0.367398
$723$	−4.85108e9	−0.477369
$724$	6.43054e8	0.0629741
$725$	1.14942e9	0.112020
$726$	1.05948e10	1.02758
$727$	6.93893e9	0.669764	0.334882	−	0.942260i	$-0.391304\pi$
$727$	6.93893e9	0.669764	0.334882	+	0.942260i	$0.391304\pi$
$728$	6.78992e9	0.652236
$729$	−1.36514e10	−1.30506
$730$	3.19936e9	0.304392
$731$	−4.50196e9	−0.426276
$732$	1.08589e10	1.02328
$733$	−4.87209e9	−0.456932	−0.228466	−	0.973552i	$-0.573371\pi$
$733$	−4.87209e9	−0.456932	−0.228466	+	0.973552i	$0.573371\pi$
$734$	−1.22733e10	−1.14558
$735$	1.18767e10	1.10329
$736$	1.11748e10	1.03316
$737$	−2.90362e10	−2.67179
$738$	−1.98801e9	−0.182063
$739$	−3.91342e9	−0.356698	−0.178349	−	0.983967i	$-0.557076\pi$
$739$	−3.91342e9	−0.356698	−0.178349	+	0.983967i	$0.557076\pi$
$740$	−4.58096e9	−0.415571
$741$	−2.42513e10	−2.18963
$742$	−2.10956e9	−0.189573
$743$	1.13781e10	1.01768	0.508838	−	0.860863i	$-0.330075\pi$
$743$	1.13781e10	1.01768	0.508838	+	0.860863i	$0.330075\pi$
$744$	1.47051e10	1.30907
$745$	2.17509e10	1.92721
$746$	1.20104e10	1.05919
$747$	−9.01534e9	−0.791335
$748$	−5.16086e9	−0.450886
$749$	4.42756e9	0.385016
$750$	−9.62466e9	−0.833050
$751$	−2.09726e10	−1.80681	−0.903406	−	0.428786i	$-0.858942\pi$
$751$	−2.09726e10	−1.80681	−0.903406	+	0.428786i	$0.858942\pi$
$752$	3.26081e8	0.0279617
$753$	−1.06056e10	−0.905220
$754$	6.21512e9	0.528019
$755$	−2.16578e8	−0.0183147
$756$	−9.97586e8	−0.0839700
$757$	1.73624e10	1.45471	0.727353	−	0.686264i	$-0.240750\pi$
$757$	1.73624e10	1.45471	0.727353	+	0.686264i	$0.240750\pi$
$758$	−5.86479e9	−0.489114
$759$	−2.68089e10	−2.22553
$760$	−1.64759e10	−1.36145
$761$	−7.26917e9	−0.597914	−0.298957	−	0.954267i	$-0.596639\pi$
$761$	−7.26917e9	−0.597914	−0.298957	+	0.954267i	$0.596639\pi$
$762$	−3.93343e9	−0.322055
$763$	3.95916e9	0.322676
$764$	7.17326e9	0.581955
$765$	−7.88354e9	−0.636658
$766$	1.46863e10	1.18063
$767$	1.22834e10	0.982961
$768$	1.86489e10	1.48555
$769$	−1.09581e10	−0.868947	−0.434474	−	0.900684i	$-0.643066\pi$
$769$	−1.09581e10	−0.868947	−0.434474	+	0.900684i	$0.643066\pi$
$770$	−6.80556e9	−0.537213
$771$	−1.77175e9	−0.139223
$772$	−1.77425e9	−0.138789
$773$	−1.92589e10	−1.49969	−0.749847	−	0.661612i	$-0.769873\pi$
$773$	−1.92589e10	−1.49969	−0.749847	+	0.661612i	$0.769873\pi$
$774$	−7.91310e9	−0.613414
$775$	−1.78791e9	−0.137972
$776$	2.39152e10	1.83720
$777$	6.70329e9	0.512643
$778$	2.56855e9	0.195551
$779$	−4.15571e9	−0.314967
$780$	−1.51347e10	−1.14194
$781$	−2.93370e10	−2.20362
$782$	−4.38104e9	−0.327607
$783$	−2.40627e9	−0.179134
$784$	1.35785e8	0.0100634
$785$	−6.34668e9	−0.468277
$786$	1.95071e10	1.43290
$787$	9.34542e9	0.683419	0.341710	−	0.939806i	$-0.388994\pi$
$787$	9.34542e9	0.683419	0.341710	+	0.939806i	$0.388994\pi$
$788$	2.28790e9	0.166569
$789$	2.09769e10	1.52045
$790$	−5.92338e8	−0.0427440
$791$	−1.22098e10	−0.877181
$792$	−2.39043e10	−1.70977
$793$	−1.88123e10	−1.33963
$794$	−1.62511e10	−1.15216
$795$	1.23911e10	0.874630
$796$	−4.13293e9	−0.290444
$797$	1.28039e10	0.895854	0.447927	−	0.894070i	$-0.352162\pi$
$797$	1.28039e10	0.895854	0.447927	+	0.894070i	$0.352162\pi$
$798$	9.14896e9	0.637326
$799$	1.41359e10	0.980412
$800$	−2.24756e9	−0.155201
$801$	4.08659e9	0.280962
$802$	−4.19016e9	−0.286827
$803$	9.70326e9	0.661323
$804$	2.43605e10	1.65306
$805$	9.09550e9	0.614527
$806$	−9.66753e9	−0.650343
$807$	1.32779e10	0.889350
$808$	−2.39339e10	−1.59615
$809$	−2.79120e10	−1.85341	−0.926703	−	0.375794i	$-0.877370\pi$
$809$	−2.79120e10	−1.85341	−0.926703	+	0.375794i	$0.877370\pi$
$810$	8.12888e9	0.537444
$811$	−1.55830e10	−1.02583	−0.512917	−	0.858438i	$-0.671435\pi$
$811$	−1.55830e10	−1.02583	−0.512917	+	0.858438i	$0.671435\pi$
$812$	3.69142e9	0.241962
$813$	3.21959e10	2.10128
$814$	8.82477e9	0.573480
$815$	5.76899e9	0.373292
$816$	−1.67214e8	−0.0107735
$817$	−1.65415e10	−1.06120
$818$	−1.23909e10	−0.791526
$819$	1.19374e10	0.759304
$820$	−2.59349e9	−0.164262
$821$	7.08253e9	0.446671	0.223335	−	0.974742i	$-0.428306\pi$
$821$	7.08253e9	0.446671	0.223335	+	0.974742i	$0.428306\pi$
$822$	−4.15655e9	−0.261024
$823$	−2.57949e10	−1.61300	−0.806500	−	0.591235i	$-0.798641\pi$
$823$	−2.57949e10	−1.61300	−0.806500	+	0.591235i	$0.798641\pi$
$824$	−1.58941e9	−0.0989671
$825$	5.39201e9	0.334320
$826$	−4.63401e9	−0.286106
$827$	−1.79203e10	−1.10173	−0.550867	−	0.834593i	$-0.685703\pi$
$827$	−1.79203e10	−1.10173	−0.550867	+	0.834593i	$0.685703\pi$
$828$	1.21235e10	0.742204
$829$	2.47043e10	1.50602	0.753012	−	0.658007i	$-0.228600\pi$
$829$	2.47043e10	1.50602	0.753012	+	0.658007i	$0.228600\pi$
$830$	7.47035e9	0.453490
$831$	−1.70361e10	−1.02983
$832$	−1.24358e10	−0.748589
$833$	5.88637e9	0.352850
$834$	−1.55329e10	−0.927195
$835$	2.14430e10	1.27463
$836$	−1.89624e10	−1.12246
$837$	3.74292e9	0.220634
$838$	1.83459e10	1.07692
$839$	−3.48291e9	−0.203599	−0.101799	−	0.994805i	$-0.532460\pi$
$839$	−3.48291e9	−0.203599	−0.101799	+	0.994805i	$0.532460\pi$
$840$	1.50459e10	0.875875
$841$	−8.34582e9	−0.483819
$842$	5.76464e9	0.332797
$843$	2.46642e9	0.141798
$844$	1.29750e10	0.742862
$845$	7.36335e9	0.419833
$846$	2.48466e10	1.41082
$847$	−1.09017e10	−0.616456
$848$	1.41666e8	0.00797773
$849$	2.01275e10	1.12879
$850$	8.81147e8	0.0492133
$851$	−1.17941e10	−0.656013
$852$	2.46129e10	1.36340
$853$	−3.01145e10	−1.66132	−0.830662	−	0.556777i	$-0.812038\pi$
$853$	−3.01145e10	−1.66132	−0.830662	+	0.556777i	$0.812038\pi$
$854$	7.09707e9	0.389921
$855$	−2.89663e10	−1.58494
$856$	−1.28865e10	−0.702227
$857$	3.07697e9	0.166990	0.0834949	−	0.996508i	$-0.473392\pi$
$857$	3.07697e9	0.166990	0.0834949	+	0.996508i	$0.473392\pi$
$858$	2.91555e10	1.57585
$859$	−6.28540e9	−0.338343	−0.169171	−	0.985587i	$-0.554109\pi$
$859$	−6.28540e9	−0.338343	−0.169171	+	0.985587i	$0.554109\pi$
$860$	−1.03232e10	−0.553437
$861$	3.79504e9	0.202631
$862$	1.29940e10	0.690985
$863$	4.61677e9	0.244512	0.122256	−	0.992499i	$-0.460987\pi$
$863$	4.61677e9	0.244512	0.122256	+	0.992499i	$0.460987\pi$
$864$	4.70517e9	0.248186
$865$	1.44373e10	0.758455
$866$	−7.08813e9	−0.370868
$867$	2.10146e10	1.09510
$868$	−5.74196e9	−0.298017
$869$	−1.79649e9	−0.0928657
$870$	1.37722e10	0.709066
$871$	−4.22030e10	−2.16411
$872$	−1.15232e10	−0.588526
$873$	4.20454e10	2.13879
$874$	−1.60972e10	−0.815566
$875$	9.90346e9	0.499757
$876$	−8.14074e9	−0.409166
$877$	1.42928e10	0.715517	0.357759	−	0.933814i	$-0.383541\pi$
$877$	1.42928e10	0.715517	0.357759	+	0.933814i	$0.383541\pi$
$878$	−1.15417e10	−0.575492
$879$	3.01434e10	1.49703
$880$	4.57022e8	0.0226073
$881$	−9.98882e8	−0.0492151	−0.0246076	−	0.999697i	$-0.507834\pi$
$881$	−9.98882e8	−0.0492151	−0.0246076	+	0.999697i	$0.507834\pi$
$882$	1.03465e10	0.507753
$883$	−1.79293e10	−0.876399	−0.438200	−	0.898878i	$-0.644384\pi$
$883$	−1.79293e10	−0.876399	−0.438200	+	0.898878i	$0.644384\pi$
$884$	−7.50111e9	−0.365210
$885$	2.72192e10	1.32000
$886$	−6.16290e9	−0.297692
$887$	−2.78654e10	−1.34070	−0.670351	−	0.742044i	$-0.733856\pi$
$887$	−2.78654e10	−1.34070	−0.670351	+	0.742044i	$0.733856\pi$
$888$	−1.95101e10	−0.935004
$889$	4.04738e9	0.193205
$890$	−3.38626e9	−0.161011
$891$	2.46539e10	1.16765
$892$	1.41866e9	0.0669272
$893$	5.19391e10	2.44070
$894$	3.51536e10	1.64546
$895$	1.48647e10	0.693066
$896$	−7.11139e9	−0.330275
$897$	−3.89658e10	−1.80264
$898$	−3.55806e9	−0.163963
$899$	−1.38501e10	−0.635763
$900$	−2.43838e9	−0.111494
$901$	6.14132e9	0.279721
$902$	4.99610e9	0.226678
$903$	1.51058e10	0.682712
$904$	3.55367e10	1.59988
$905$	−2.46865e9	−0.110711
$906$	−3.50033e8	−0.0156372
$907$	−9.56159e9	−0.425505	−0.212752	−	0.977106i	$-0.568243\pi$
$907$	−9.56159e9	−0.425505	−0.212752	+	0.977106i	$0.568243\pi$
$908$	−4.62430e9	−0.204996
$909$	−4.20784e10	−1.85817
$910$	−9.89163e9	−0.435134
$911$	4.55452e10	1.99585	0.997927	−	0.0643564i	$-0.0204995\pi$
$911$	4.55452e10	1.99585	0.997927	+	0.0643564i	$0.0204995\pi$
$912$	−6.14391e8	−0.0268203
$913$	2.26566e10	0.985253
$914$	2.43063e10	1.05295
$915$	−4.16867e10	−1.79897
$916$	2.15809e10	0.927759
$917$	−2.00722e10	−0.859613
$918$	−1.84465e9	−0.0786981
$919$	1.23944e10	0.526772	0.263386	−	0.964691i	$-0.415161\pi$
$919$	1.23944e10	0.526772	0.263386	+	0.964691i	$0.415161\pi$
$920$	−2.64727e10	−1.12083
$921$	2.19605e10	0.926262
$922$	2.07233e10	0.870764
$923$	−4.26402e10	−1.78490
$924$	1.73167e10	0.722126
$925$	2.37212e9	0.0985466
$926$	−1.43494e10	−0.593874
$927$	−2.79435e9	−0.115213
$928$	−1.74108e10	−0.715156
$929$	3.82453e10	1.56503	0.782515	−	0.622632i	$-0.213937\pi$
$929$	3.82453e10	1.56503	0.782515	+	0.622632i	$0.213937\pi$
$930$	−2.14225e10	−0.873334
$931$	2.16282e10	0.878408
$932$	−1.68524e10	−0.681877
$933$	5.98049e10	2.41074
$934$	−1.80525e10	−0.724977
$935$	1.98123e10	0.792672
$936$	−3.47440e10	−1.38489
$937$	−1.19363e10	−0.474003	−0.237002	−	0.971509i	$-0.576165\pi$
$937$	−1.19363e10	−0.474003	−0.237002	+	0.971509i	$0.576165\pi$
$938$	1.59213e10	0.629898
$939$	−2.14356e10	−0.844901
$940$	3.24141e10	1.27288
$941$	1.21635e10	0.475877	0.237938	−	0.971280i	$-0.423528\pi$
$941$	1.21635e10	0.475877	0.237938	+	0.971280i	$0.423528\pi$
$942$	−1.02575e10	−0.399818
$943$	−6.67720e9	−0.259300
$944$	3.11193e8	0.0120401
$945$	3.82968e9	0.147622
$946$	1.98866e10	0.763732
$947$	−3.62407e10	−1.38667	−0.693333	−	0.720617i	$-0.743858\pi$
$947$	−3.62407e10	−1.38667	−0.693333	+	0.720617i	$0.743858\pi$
$948$	1.50720e9	0.0574568
$949$	1.41033e10	0.535661
$950$	3.23758e9	0.122515
$951$	1.47974e10	0.557897
$952$	7.45713e9	0.280119
$953$	3.91838e10	1.46650	0.733249	−	0.679960i	$-0.238003\pi$
$953$	3.91838e10	1.46650	0.733249	+	0.679960i	$0.238003\pi$
$954$	1.07946e10	0.402520
$955$	−2.75378e10	−1.02310
$956$	5.37899e9	0.199112
$957$	4.17695e10	1.54052
$958$	−2.06965e10	−0.760532
$959$	4.27695e9	0.156592
$960$	−2.75569e10	−1.00527
$961$	−5.96893e9	−0.216952
$962$	1.28265e10	0.464509
$963$	−2.26559e10	−0.817501
$964$	−5.51317e9	−0.198213
$965$	6.81127e9	0.243996
$966$	1.47001e10	0.524687
$967$	5.15908e9	0.183476	0.0917381	−	0.995783i	$-0.470758\pi$
$967$	5.15908e9	0.183476	0.0917381	+	0.995783i	$0.470758\pi$
$968$	3.17296e10	1.12435
$969$	−2.66343e10	−0.940392
$970$	−3.48399e10	−1.22568
$971$	−3.39336e10	−1.18950	−0.594748	−	0.803912i	$-0.702748\pi$
$971$	−3.39336e10	−1.18950	−0.594748	+	0.803912i	$0.702748\pi$
$972$	−2.50495e10	−0.874917
$973$	1.59828e10	0.556236
$974$	−7.11034e9	−0.246567
$975$	7.83709e9	0.270794
$976$	−4.76598e8	−0.0164088
$977$	−1.57557e10	−0.540513	−0.270257	−	0.962788i	$-0.587109\pi$
$977$	−1.57557e10	−0.540513	−0.270257	+	0.962788i	$0.587109\pi$
$978$	9.32381e9	0.318719
$979$	−1.02701e10	−0.349812
$980$	1.34977e10	0.458108
$981$	−2.02590e10	−0.685136
$982$	−3.09468e10	−1.04286
$983$	−6.36716e9	−0.213800	−0.106900	−	0.994270i	$-0.534093\pi$
$983$	−6.36716e9	−0.213800	−0.106900	+	0.994270i	$0.534093\pi$
$984$	−1.10455e10	−0.369576
$985$	−8.78313e9	−0.292835
$986$	6.82585e9	0.226771
$987$	−4.74314e10	−1.57020
$988$	−2.75612e10	−0.909177
$989$	−2.65780e10	−0.873646
$990$	3.48241e10	1.14066
$991$	3.98274e10	1.29994	0.649971	−	0.759959i	$-0.274781\pi$
$991$	3.98274e10	1.29994	0.649971	+	0.759959i	$0.274781\pi$
$992$	2.70822e10	0.880833
$993$	3.13309e10	1.01543
$994$	1.60863e10	0.519522
$995$	1.58661e10	0.510610
$996$	−1.90082e10	−0.609585
$997$	2.53569e10	0.810333	0.405166	−	0.914243i	$-0.367214\pi$
$997$	2.53569e10	0.810333	0.405166	+	0.914243i	$0.367214\pi$
$998$	2.22366e10	0.708126
$999$	−4.96595e9	−0.157588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	103.8.a.b.1.11	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
103.8.a.b.1.11	✓	32	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:	\( N \)	\(=\)	\( 103 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	103.a (trivial)

\(f(q)\)	\(=\)	\(q-7.05130 q^{2} -68.8783 q^{3} -78.2791 q^{4} +300.510 q^{5} +485.682 q^{6} -499.751 q^{7} +1454.54 q^{8} +2557.23 q^{9} +O(q^{10})\)	\(q-7.05130 q^{2} -68.8783 q^{3} -78.2791 q^{4} +300.510 q^{5} +485.682 q^{6} -499.751 q^{7} +1454.54 q^{8} +2557.23 q^{9} -2118.98 q^{10} -6426.62 q^{11} +5391.74 q^{12} -9340.84 q^{13} +3523.90 q^{14} -20698.6 q^{15} -236.644 q^{16} -10258.7 q^{17} -18031.8 q^{18} -37693.4 q^{19} -23523.6 q^{20} +34422.0 q^{21} +45316.0 q^{22} -60564.0 q^{23} -100186. q^{24} +12181.1 q^{25} +65865.1 q^{26} -25500.6 q^{27} +39120.1 q^{28} +94361.3 q^{29} +145952. q^{30} -146778. q^{31} -184512. q^{32} +442655. q^{33} +72337.4 q^{34} -150180. q^{35} -200178. q^{36} +194738. q^{37} +265788. q^{38} +643382. q^{39} +437102. q^{40} +110250. q^{41} -242720. q^{42} +438842. q^{43} +503070. q^{44} +768471. q^{45} +427055. q^{46} -1.37794e6 q^{47} +16299.7 q^{48} -573792. q^{49} -85892.5 q^{50} +706604. q^{51} +731193. q^{52} -598643. q^{53} +179813. q^{54} -1.93126e6 q^{55} -726906. q^{56} +2.59626e6 q^{57} -665370. q^{58} -1.31503e6 q^{59} +1.62027e6 q^{60} +2.01398e6 q^{61} +1.03497e6 q^{62} -1.27798e6 q^{63} +1.33134e6 q^{64} -2.80701e6 q^{65} -3.12129e6 q^{66} +4.51811e6 q^{67} +803044. q^{68} +4.17155e6 q^{69} +1.05896e6 q^{70} +4.56492e6 q^{71} +3.71958e6 q^{72} -1.50986e6 q^{73} -1.37316e6 q^{74} -839013. q^{75} +2.95061e6 q^{76} +3.21171e6 q^{77} -4.53668e6 q^{78} +279539. q^{79} -71114.0 q^{80} -3.83621e6 q^{81} -777408. q^{82} -3.52544e6 q^{83} -2.69453e6 q^{84} -3.08285e6 q^{85} -3.09441e6 q^{86} -6.49945e6 q^{87} -9.34775e6 q^{88} +1.59806e6 q^{89} -5.41872e6 q^{90} +4.66810e6 q^{91} +4.74090e6 q^{92} +1.01098e7 q^{93} +9.71624e6 q^{94} -1.13272e7 q^{95} +1.27089e7 q^{96} +1.64418e7 q^{97} +4.04598e6 q^{98} -1.64343e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 39 q^{2} + 94 q^{3} + 2111 q^{4} + 945 q^{5} + 271 q^{6} + 1226 q^{7} + 8052 q^{8} + 31566 q^{9}+O(q^{10}) \) 32 * q + 39 * q^2 + 94 * q^3 + 2111 * q^4 + 945 * q^5 + 271 * q^6 + 1226 * q^7 + 8052 * q^8 + 31566 * q^9	\( 32 q + 39 q^{2} + 94 q^{3} + 2111 q^{4} + 945 q^{5} + 271 q^{6} + 1226 q^{7} + 8052 q^{8} + 31566 q^{9} + 2638 q^{10} + 8169 q^{11} + 12039 q^{12} + 14171 q^{13} + 10695 q^{14} + 10759 q^{15} + 143515 q^{16} + 120237 q^{17} + 102288 q^{18} + 45057 q^{19} + 140613 q^{20} + 115762 q^{21} + 242049 q^{22} + 203820 q^{23} + 74610 q^{24} + 686055 q^{25} - 127251 q^{26} + 132508 q^{27} - 769784 q^{28} + 310416 q^{29} - 576370 q^{30} - 101176 q^{31} + 1585740 q^{32} + 715539 q^{33} + 760438 q^{34} + 1016613 q^{35} + 4351624 q^{36} + 1548134 q^{37} + 2850210 q^{38} + 2195909 q^{39} + 4470331 q^{40} + 2031714 q^{41} + 6479435 q^{42} + 1565984 q^{43} + 4069392 q^{44} + 5790546 q^{45} + 7892113 q^{46} + 4034469 q^{47} + 7138233 q^{48} + 7627000 q^{49} + 5213658 q^{50} + 2565519 q^{51} + 8129871 q^{52} + 4799985 q^{53} + 9982795 q^{54} + 3583642 q^{55} + 4552923 q^{56} + 8733123 q^{57} + 2903090 q^{58} + 1725891 q^{59} + 7361351 q^{60} + 4299641 q^{61} + 6367509 q^{62} + 4202312 q^{63} + 13772046 q^{64} + 13614927 q^{65} + 9746103 q^{66} + 2271650 q^{67} + 17935092 q^{68} - 364650 q^{69} + 454144 q^{70} + 11201481 q^{71} + 9438726 q^{72} + 9409961 q^{73} + 8665539 q^{74} + 939165 q^{75} + 3560132 q^{76} + 14167347 q^{77} - 7436704 q^{78} + 1165551 q^{79} + 8385198 q^{80} + 29742120 q^{81} - 35007935 q^{82} + 2497407 q^{83} - 34226991 q^{84} + 607507 q^{85} - 19425795 q^{86} - 7760456 q^{87} + 29754765 q^{88} + 6604398 q^{89} - 49873976 q^{90} - 14775477 q^{91} + 27875580 q^{92} + 7773096 q^{93} - 36766264 q^{94} + 19069674 q^{95} - 40704833 q^{96} + 7841444 q^{97} - 21724491 q^{98} - 9334584 q^{99}+O(q^{100}) \) 32 * q + 39 * q^2 + 94 * q^3 + 2111 * q^4 + 945 * q^5 + 271 * q^6 + 1226 * q^7 + 8052 * q^8 + 31566 * q^9 + 2638 * q^10 + 8169 * q^11 + 12039 * q^12 + 14171 * q^13 + 10695 * q^14 + 10759 * q^15 + 143515 * q^16 + 120237 * q^17 + 102288 * q^18 + 45057 * q^19 + 140613 * q^20 + 115762 * q^21 + 242049 * q^22 + 203820 * q^23 + 74610 * q^24 + 686055 * q^25 - 127251 * q^26 + 132508 * q^27 - 769784 * q^28 + 310416 * q^29 - 576370 * q^30 - 101176 * q^31 + 1585740 * q^32 + 715539 * q^33 + 760438 * q^34 + 1016613 * q^35 + 4351624 * q^36 + 1548134 * q^37 + 2850210 * q^38 + 2195909 * q^39 + 4470331 * q^40 + 2031714 * q^41 + 6479435 * q^42 + 1565984 * q^43 + 4069392 * q^44 + 5790546 * q^45 + 7892113 * q^46 + 4034469 * q^47 + 7138233 * q^48 + 7627000 * q^49 + 5213658 * q^50 + 2565519 * q^51 + 8129871 * q^52 + 4799985 * q^53 + 9982795 * q^54 + 3583642 * q^55 + 4552923 * q^56 + 8733123 * q^57 + 2903090 * q^58 + 1725891 * q^59 + 7361351 * q^60 + 4299641 * q^61 + 6367509 * q^62 + 4202312 * q^63 + 13772046 * q^64 + 13614927 * q^65 + 9746103 * q^66 + 2271650 * q^67 + 17935092 * q^68 - 364650 * q^69 + 454144 * q^70 + 11201481 * q^71 + 9438726 * q^72 + 9409961 * q^73 + 8665539 * q^74 + 939165 * q^75 + 3560132 * q^76 + 14167347 * q^77 - 7436704 * q^78 + 1165551 * q^79 + 8385198 * q^80 + 29742120 * q^81 - 35007935 * q^82 + 2497407 * q^83 - 34226991 * q^84 + 607507 * q^85 - 19425795 * q^86 - 7760456 * q^87 + 29754765 * q^88 + 6604398 * q^89 - 49873976 * q^90 - 14775477 * q^91 + 27875580 * q^92 + 7773096 * q^93 - 36766264 * q^94 + 19069674 * q^95 - 40704833 * q^96 + 7841444 * q^97 - 21724491 * q^98 - 9334584 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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