LMFDB - Embedded newform 37.8.a.a.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,Mod(1,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, 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("37.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	37.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:	$11.5582459429$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4 x^{9} - 905 x^{8} + 4018 x^{7} + 291290 x^{6} - 1367036 x^{5} - 39566544 x^{4} + \cdots - 45399525376 $ x^10 - 4x^9 - 905x^8 + 4018x^7 + 291290x^6 - 1367036x^5 - 39566544x^4 + 175732512x^3 + 2143908736x^2 - 5929608704*x - 45399525376
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-18.2140$ of defining polynomial
Character	$\chi$	$=$	37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+16.2140 q^{2} -32.8739 q^{3} +134.894 q^{4} -220.871 q^{5} -533.017 q^{6} -808.413 q^{7} +111.778 q^{8} -1106.31 q^{9} +O(q^{10})$	\(q+16.2140 q^{2} -32.8739 q^{3} +134.894 q^{4} -220.871 q^{5} -533.017 q^{6} -808.413 q^{7} +111.778 q^{8} -1106.31 q^{9} -3581.21 q^{10} +6075.11 q^{11} -4434.48 q^{12} -12100.6 q^{13} -13107.6 q^{14} +7260.90 q^{15} -15454.1 q^{16} +18283.6 q^{17} -17937.7 q^{18} -35170.4 q^{19} -29794.2 q^{20} +26575.7 q^{21} +98501.9 q^{22} +102709. q^{23} -3674.57 q^{24} -29340.8 q^{25} -196199. q^{26} +108264. q^{27} -109050. q^{28} -72006.9 q^{29} +117728. q^{30} -112519. q^{31} -264880. q^{32} -199712. q^{33} +296450. q^{34} +178555. q^{35} -149234. q^{36} +50653.0 q^{37} -570253. q^{38} +397794. q^{39} -24688.5 q^{40} +430792. q^{41} +430898. q^{42} +342869. q^{43} +819496. q^{44} +244352. q^{45} +1.66533e6 q^{46} -523067. q^{47} +508034. q^{48} -170011. q^{49} -475732. q^{50} -601051. q^{51} -1.63230e6 q^{52} +43080.5 q^{53} +1.75539e6 q^{54} -1.34182e6 q^{55} -90362.7 q^{56} +1.15619e6 q^{57} -1.16752e6 q^{58} -2.41890e6 q^{59} +979451. q^{60} -17287.9 q^{61} -1.82438e6 q^{62} +894355. q^{63} -2.31664e6 q^{64} +2.67268e6 q^{65} -3.23814e6 q^{66} -3.97944e6 q^{67} +2.46634e6 q^{68} -3.37645e6 q^{69} +2.89510e6 q^{70} +2.20119e6 q^{71} -123661. q^{72} -2.86846e6 q^{73} +821288. q^{74} +964546. q^{75} -4.74428e6 q^{76} -4.91120e6 q^{77} +6.44983e6 q^{78} -2.56218e6 q^{79} +3.41336e6 q^{80} -1.13955e6 q^{81} +6.98486e6 q^{82} -3.64318e6 q^{83} +3.58489e6 q^{84} -4.03831e6 q^{85} +5.55927e6 q^{86} +2.36715e6 q^{87} +679063. q^{88} -6.04689e6 q^{89} +3.96192e6 q^{90} +9.78229e6 q^{91} +1.38548e7 q^{92} +3.69892e6 q^{93} -8.48100e6 q^{94} +7.76814e6 q^{95} +8.70762e6 q^{96} -1.03736e7 q^{97} -2.75657e6 q^{98} -6.72095e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9}+O(q^{10}) $ 10 * q - 24 * q^2 - 95 * q^3 + 602 * q^4 - 624 * q^5 - 777 * q^6 - 501 * q^7 - 3810 * q^8 + 6181 * q^9	\( 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9} + 8595 q^{10} - 8325 q^{11} - 19645 q^{12} - 17108 q^{13} - 65418 q^{14} - 55756 q^{15} - 56998 q^{16} - 72924 q^{17} - 156165 q^{18} - 47786 q^{19} - 226209 q^{20} - 65313 q^{21} - 138973 q^{22} - 148086 q^{23} - 68031 q^{24} + 108736 q^{25} - 60237 q^{26} - 87329 q^{27} + 219974 q^{28} - 164154 q^{29} + 78864 q^{30} - 189560 q^{31} - 30114 q^{32} - 179737 q^{33} + 532624 q^{34} - 705156 q^{35} + 1923693 q^{36} + 506530 q^{37} + 1256412 q^{38} + 1322800 q^{39} + 2936777 q^{40} + 814263 q^{41} + 3415826 q^{42} - 590572 q^{43} + 610311 q^{44} - 250574 q^{45} + 2903897 q^{46} - 1534185 q^{47} + 2082419 q^{48} - 214337 q^{49} - 2313525 q^{50} + 722138 q^{51} + 149159 q^{52} - 2518209 q^{53} + 1095990 q^{54} - 3482468 q^{55} - 3645834 q^{56} - 9225638 q^{57} + 5626023 q^{58} - 5894748 q^{59} - 1289832 q^{60} - 2569480 q^{61} - 863697 q^{62} - 2836574 q^{63} - 4093742 q^{64} - 6774600 q^{65} + 17251556 q^{66} - 6983232 q^{67} - 8114412 q^{68} - 11557564 q^{69} + 8982748 q^{70} - 5013963 q^{71} - 7567137 q^{72} - 11678449 q^{73} - 1215672 q^{74} - 6586901 q^{75} + 4912252 q^{76} + 1333113 q^{77} - 7352119 q^{78} - 3853378 q^{79} - 11975661 q^{80} - 7381718 q^{81} + 564093 q^{82} - 15677895 q^{83} + 4781738 q^{84} + 11909320 q^{85} + 34274010 q^{86} - 12611710 q^{87} + 14448317 q^{88} - 25836 q^{89} + 64591590 q^{90} + 12335744 q^{91} + 7579845 q^{92} + 4592632 q^{93} + 26251718 q^{94} + 11723664 q^{95} + 42299113 q^{96} + 4648834 q^{97} + 15230184 q^{98} - 16904018 q^{99}+O(q^{100}) \) 10 * q - 24 * q^2 - 95 * q^3 + 602 * q^4 - 624 * q^5 - 777 * q^6 - 501 * q^7 - 3810 * q^8 + 6181 * q^9 + 8595 * q^10 - 8325 * q^11 - 19645 * q^12 - 17108 * q^13 - 65418 * q^14 - 55756 * q^15 - 56998 * q^16 - 72924 * q^17 - 156165 * q^18 - 47786 * q^19 - 226209 * q^20 - 65313 * q^21 - 138973 * q^22 - 148086 * q^23 - 68031 * q^24 + 108736 * q^25 - 60237 * q^26 - 87329 * q^27 + 219974 * q^28 - 164154 * q^29 + 78864 * q^30 - 189560 * q^31 - 30114 * q^32 - 179737 * q^33 + 532624 * q^34 - 705156 * q^35 + 1923693 * q^36 + 506530 * q^37 + 1256412 * q^38 + 1322800 * q^39 + 2936777 * q^40 + 814263 * q^41 + 3415826 * q^42 - 590572 * q^43 + 610311 * q^44 - 250574 * q^45 + 2903897 * q^46 - 1534185 * q^47 + 2082419 * q^48 - 214337 * q^49 - 2313525 * q^50 + 722138 * q^51 + 149159 * q^52 - 2518209 * q^53 + 1095990 * q^54 - 3482468 * q^55 - 3645834 * q^56 - 9225638 * q^57 + 5626023 * q^58 - 5894748 * q^59 - 1289832 * q^60 - 2569480 * q^61 - 863697 * q^62 - 2836574 * q^63 - 4093742 * q^64 - 6774600 * q^65 + 17251556 * q^66 - 6983232 * q^67 - 8114412 * q^68 - 11557564 * q^69 + 8982748 * q^70 - 5013963 * q^71 - 7567137 * q^72 - 11678449 * q^73 - 1215672 * q^74 - 6586901 * q^75 + 4912252 * q^76 + 1333113 * q^77 - 7352119 * q^78 - 3853378 * q^79 - 11975661 * q^80 - 7381718 * q^81 + 564093 * q^82 - 15677895 * q^83 + 4781738 * q^84 + 11909320 * q^85 + 34274010 * q^86 - 12611710 * q^87 + 14448317 * q^88 - 25836 * q^89 + 64591590 * q^90 + 12335744 * q^91 + 7579845 * q^92 + 4592632 * q^93 + 26251718 * q^94 + 11723664 * q^95 + 42299113 * q^96 + 4648834 * q^97 + 15230184 * q^98 - 16904018 * 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 $

$2$	16.2140	1.43313	0.716564	−	0.697521i	$-0.245714\pi$
$2$	16.2140	1.43313	0.716564	+	0.697521i	$0.245714\pi$
$3$	−32.8739	−0.702953	−0.351477	−	0.936197i	$-0.614320\pi$
$3$	−32.8739	−0.702953	−0.351477	+	0.936197i	$0.614320\pi$
$4$	134.894	1.05386
$5$	−220.871	−0.790214	−0.395107	−	0.918635i	$-0.629292\pi$
$5$	−220.871	−0.790214	−0.395107	+	0.918635i	$0.629292\pi$
$6$	−533.017	−1.00742
$7$	−808.413	−0.890820	−0.445410	−	0.895327i	$-0.646942\pi$
$7$	−808.413	−0.890820	−0.445410	+	0.895327i	$0.646942\pi$
$8$	111.778	0.0771864
$9$	−1106.31	−0.505857
$10$	−3581.21	−1.13248
$11$	6075.11	1.37619	0.688097	−	0.725618i	$-0.258446\pi$
$11$	6075.11	1.37619	0.688097	+	0.725618i	$0.258446\pi$
$12$	−4434.48	−0.740813
$13$	−12100.6	−1.52759	−0.763793	−	0.645461i	$-0.776665\pi$
$13$	−12100.6	−1.52759	−0.763793	+	0.645461i	$0.776665\pi$
$14$	−13107.6	−1.27666
$15$	7260.90	0.555483
$16$	−15454.1	−0.943241
$17$	18283.6	0.902588	0.451294	−	0.892375i	$-0.350963\pi$
$17$	18283.6	0.902588	0.451294	+	0.892375i	$0.350963\pi$
$18$	−17937.7	−0.724958
$19$	−35170.4	−1.17636	−0.588180	−	0.808730i	$-0.700155\pi$
$19$	−35170.4	−1.17636	−0.588180	+	0.808730i	$0.700155\pi$
$20$	−29794.2	−0.832773
$21$	26575.7	0.626205
$22$	98501.9	1.97226
$23$	102709.	1.76020	0.880099	−	0.474790i	$-0.157476\pi$
$23$	102709.	1.76020	0.880099	+	0.474790i	$0.157476\pi$
$24$	−3674.57	−0.0542584
$25$	−29340.8	−0.375562
$26$	−196199.	−2.18923
$27$	108264.	1.05855
$28$	−109050.	−0.938799
$29$	−72006.9	−0.548253	−0.274127	−	0.961694i	$-0.588389\pi$
$29$	−72006.9	−0.548253	−0.274127	+	0.961694i	$0.588389\pi$
$30$	117728.	0.796079
$31$	−112519.	−0.678357	−0.339178	−	0.940722i	$-0.610149\pi$
$31$	−112519.	−0.678357	−0.339178	+	0.940722i	$0.610149\pi$
$32$	−264880.	−1.42897
$33$	−199712.	−0.967401
$34$	296450.	1.29352
$35$	178555.	0.703938
$36$	−149234.	−0.533102
$37$	50653.0	0.164399
$37$	50653.0	0.164399
$38$	−570253.	−1.68587
$39$	397794.	1.07382
$40$	−24688.5	−0.0609937
$41$	430792.	0.976166	0.488083	−	0.872797i	$-0.337696\pi$
$41$	430792.	0.976166	0.488083	+	0.872797i	$0.337696\pi$
$42$	430898.	0.897433
$43$	342869.	0.657640	0.328820	−	0.944393i	$-0.393349\pi$
$43$	342869.	0.657640	0.328820	+	0.944393i	$0.393349\pi$
$44$	819496.	1.45031
$45$	244352.	0.399735
$46$	1.66533e6	2.52259
$47$	−523067.	−0.734877	−0.367438	−	0.930048i	$-0.619765\pi$
$47$	−523067.	−0.734877	−0.367438	+	0.930048i	$0.619765\pi$
$48$	508034.	0.663054
$49$	−170011.	−0.206439
$50$	−475732.	−0.538229
$51$	−601051.	−0.634477
$52$	−1.63230e6	−1.60986
$53$	43080.5	0.0397480	0.0198740	−	0.999802i	$-0.493673\pi$
$53$	43080.5	0.0397480	0.0198740	+	0.999802i	$0.493673\pi$
$54$	1.75539e6	1.51703
$55$	−1.34182e6	−1.08749
$56$	−90362.7	−0.0687592
$57$	1.15619e6	0.826926
$58$	−1.16752e6	−0.785717
$59$	−2.41890e6	−1.53333	−0.766667	−	0.642045i	$-0.778086\pi$
$59$	−2.41890e6	−1.53333	−0.766667	+	0.642045i	$0.778086\pi$
$60$	979451.	0.585401
$61$	−17287.9	−0.00975185	−0.00487592	−	0.999988i	$-0.501552\pi$
$61$	−17287.9	−0.00975185	−0.00487592	+	0.999988i	$0.501552\pi$
$62$	−1.82438e6	−0.972172
$63$	894355.	0.450628
$64$	−2.31664e6	−1.10466
$65$	2.67268e6	1.20712
$66$	−3.23814e6	−1.38641
$67$	−3.97944e6	−1.61644	−0.808222	−	0.588878i	$-0.799570\pi$
$67$	−3.97944e6	−1.61644	−0.808222	+	0.588878i	$0.799570\pi$
$68$	2.46634e6	0.951200
$69$	−3.37645e6	−1.23734
$70$	2.89510e6	1.00883
$71$	2.20119e6	0.729884	0.364942	−	0.931030i	$-0.381089\pi$
$71$	2.20119e6	0.729884	0.364942	+	0.931030i	$0.381089\pi$
$72$	−123661.	−0.0390453
$73$	−2.86846e6	−0.863016	−0.431508	−	0.902109i	$-0.642018\pi$
$73$	−2.86846e6	−0.863016	−0.431508	+	0.902109i	$0.642018\pi$
$74$	821288.	0.235605
$75$	964546.	0.264003
$76$	−4.74428e6	−1.23972
$77$	−4.91120e6	−1.22594
$78$	6.44983e6	1.53892
$79$	−2.56218e6	−0.584675	−0.292338	−	0.956315i	$-0.594433\pi$
$79$	−2.56218e6	−0.584675	−0.292338	+	0.956315i	$0.594433\pi$
$80$	3.41336e6	0.745362
$81$	−1.13955e6	−0.238252
$82$	6.98486e6	1.39897
$83$	−3.64318e6	−0.699370	−0.349685	−	0.936867i	$-0.613711\pi$
$83$	−3.64318e6	−0.699370	−0.349685	+	0.936867i	$0.613711\pi$
$84$	3.58489e6	0.659932
$85$	−4.03831e6	−0.713237
$86$	5.55927e6	0.942483
$87$	2.36715e6	0.385396
$88$	679063.	0.106224
$89$	−6.04689e6	−0.909216	−0.454608	−	0.890692i	$-0.650221\pi$
$89$	−6.04689e6	−0.909216	−0.454608	+	0.890692i	$0.650221\pi$
$90$	3.96192e6	0.572872
$91$	9.78229e6	1.36080
$92$	1.38548e7	1.85500
$93$	3.69892e6	0.476853
$94$	−8.48100e6	−1.05317
$95$	7.76814e6	0.929575
$96$	8.70762e6	1.00450
$97$	−1.03736e7	−1.15406	−0.577029	−	0.816724i	$-0.695788\pi$
$97$	−1.03736e7	−1.15406	−0.577029	+	0.816724i	$0.695788\pi$
$98$	−2.75657e6	−0.295854
$99$	−6.72095e6	−0.696158
$100$	−3.95790e6	−0.395790
$101$	1.94709e7	1.88045	0.940223	−	0.340559i	$-0.110616\pi$
$101$	1.94709e7	1.88045	0.940223	+	0.340559i	$0.110616\pi$
$102$	−9.74545e6	−0.909287
$103$	−4.09866e6	−0.369583	−0.184791	−	0.982778i	$-0.559161\pi$
$103$	−4.09866e6	−0.369583	−0.184791	+	0.982778i	$0.559161\pi$
$104$	−1.35258e6	−0.117909
$105$	−5.86980e6	−0.494836
$106$	698507.	0.0569640
$107$	−1.37489e7	−1.08499	−0.542493	−	0.840060i	$-0.682519\pi$
$107$	−1.37489e7	−1.08499	−0.542493	+	0.840060i	$0.682519\pi$
$108$	1.46041e7	1.11556
$109$	−506179.	−0.0374379	−0.0187189	−	0.999825i	$-0.505959\pi$
$109$	−506179.	−0.0374379	−0.0187189	+	0.999825i	$0.505959\pi$
$110$	−2.17563e7	−1.55851
$111$	−1.66516e6	−0.115565
$112$	1.24933e7	0.840258
$113$	1.24772e7	0.813469	0.406735	−	0.913546i	$-0.366667\pi$
$113$	1.24772e7	0.813469	0.406735	+	0.913546i	$0.366667\pi$
$114$	1.87464e7	1.18509
$115$	−2.26855e7	−1.39093
$116$	−9.71329e6	−0.577781
$117$	1.33870e7	0.772740
$118$	−3.92201e7	−2.19746
$119$	−1.47807e7	−0.804044
$120$	811607.	0.0428757
$121$	1.74198e7	0.893913
$122$	−280305.	−0.0139757
$123$	−1.41618e7	−0.686199
$124$	−1.51781e7	−0.714892
$125$	2.37361e7	1.08699
$126$	1.45011e7	0.645807
$127$	4.46620e7	1.93475	0.967376	−	0.253344i	$-0.0815305\pi$
$127$	4.46620e7	1.93475	0.967376	+	0.253344i	$0.0815305\pi$
$128$	−3.65742e6	−0.154149
$129$	−1.12714e7	−0.462290
$130$	4.33348e7	1.72996
$131$	4.24214e6	0.164868	0.0824338	−	0.996597i	$-0.473731\pi$
$131$	4.24214e6	0.164868	0.0824338	+	0.996597i	$0.473731\pi$
$132$	−2.69400e7	−1.01950
$133$	2.84322e7	1.04792
$134$	−6.45227e7	−2.31657
$135$	−2.39124e7	−0.836478
$136$	2.04370e6	0.0696675
$137$	−3.61646e7	−1.20160	−0.600802	−	0.799398i	$-0.705152\pi$
$137$	−3.61646e7	−1.20160	−0.600802	+	0.799398i	$0.705152\pi$
$138$	−5.47457e7	−1.77326
$139$	2.83379e7	0.894984	0.447492	−	0.894288i	$-0.352317\pi$
$139$	2.83379e7	0.894984	0.447492	+	0.894288i	$0.352317\pi$
$140$	2.40860e7	0.741852
$141$	1.71952e7	0.516584
$142$	3.56902e7	1.04602
$143$	−7.35126e7	−2.10226
$144$	1.70970e7	0.477145
$145$	1.59043e7	0.433237
$146$	−4.65092e7	−1.23681
$147$	5.58893e6	0.145117
$148$	6.83278e6	0.173253
$149$	6.74607e7	1.67070	0.835351	−	0.549716i	$-0.185264\pi$
$149$	6.74607e7	1.67070	0.835351	+	0.549716i	$0.185264\pi$
$150$	1.56392e7	0.378350
$151$	4.87003e7	1.15110	0.575549	−	0.817767i	$-0.304788\pi$
$151$	4.87003e7	1.15110	0.575549	+	0.817767i	$0.304788\pi$
$152$	−3.93127e6	−0.0907989
$153$	−2.02273e7	−0.456580
$154$	−7.96302e7	−1.75693
$155$	2.48521e7	0.536047
$156$	5.36600e7	1.13166
$157$	−1.49296e7	−0.307894	−0.153947	−	0.988079i	$-0.549198\pi$
$157$	−1.49296e7	−0.307894	−0.153947	+	0.988079i	$0.549198\pi$
$158$	−4.15432e7	−0.837915
$159$	−1.41622e6	−0.0279410
$160$	5.85043e7	1.12919
$161$	−8.30314e7	−1.56802
$162$	−1.84767e7	−0.341446
$163$	−6.86558e7	−1.24171	−0.620855	−	0.783925i	$-0.713215\pi$
$163$	−6.86558e7	−1.24171	−0.620855	+	0.783925i	$0.713215\pi$
$164$	5.81112e7	1.02874
$165$	4.41108e7	0.764453
$166$	−5.90705e7	−1.00229
$167$	−4.24027e7	−0.704508	−0.352254	−	0.935904i	$-0.614585\pi$
$167$	−4.24027e7	−0.704508	−0.352254	+	0.935904i	$0.614585\pi$
$168$	2.97057e6	0.0483345
$169$	8.36763e7	1.33352
$170$	−6.54773e7	−1.02216
$171$	3.89094e7	0.595069
$172$	4.62509e7	0.693060
$173$	6.20517e7	0.911155	0.455577	−	0.890196i	$-0.349433\pi$
$173$	6.20517e7	0.911155	0.455577	+	0.890196i	$0.349433\pi$
$174$	3.83809e7	0.552323
$175$	2.37195e7	0.334559
$176$	−9.38851e7	−1.29808
$177$	7.95187e7	1.07786
$178$	−9.80443e7	−1.30302
$179$	2.93140e7	0.382023	0.191011	−	0.981588i	$-0.438823\pi$
$179$	2.93140e7	0.382023	0.191011	+	0.981588i	$0.438823\pi$
$180$	3.29616e7	0.421264
$181$	8.46538e7	1.06114	0.530569	−	0.847642i	$-0.321978\pi$
$181$	8.46538e7	1.06114	0.530569	+	0.847642i	$0.321978\pi$
$182$	1.58610e8	1.95021
$183$	568319.	0.00685509
$184$	1.14806e7	0.135863
$185$	−1.11878e7	−0.129910
$186$	5.99743e7	0.683392
$187$	1.11075e8	1.24214
$188$	−7.05585e7	−0.774456
$189$	−8.75219e7	−0.942975
$190$	1.25953e8	1.33220
$191$	3.78588e7	0.393143	0.196572	−	0.980489i	$-0.437019\pi$
$191$	3.78588e7	0.393143	0.196572	+	0.980489i	$0.437019\pi$
$192$	7.61569e7	0.776524
$193$	−1.55153e7	−0.155349	−0.0776747	−	0.996979i	$-0.524750\pi$
$193$	−1.55153e7	−0.155349	−0.0776747	+	0.996979i	$0.524750\pi$
$194$	−1.68197e8	−1.65391
$195$	−8.78613e7	−0.848548
$196$	−2.29335e7	−0.217558
$197$	−1.42254e8	−1.32566	−0.662829	−	0.748771i	$-0.730644\pi$
$197$	−1.42254e8	−1.32566	−0.662829	+	0.748771i	$0.730644\pi$
$198$	−1.08974e8	−0.997684
$199$	−1.86991e7	−0.168203	−0.0841015	−	0.996457i	$-0.526802\pi$
$199$	−1.86991e7	−0.168203	−0.0841015	+	0.996457i	$0.526802\pi$
$200$	−3.27965e6	−0.0289883
$201$	1.30820e8	1.13628
$202$	3.15701e8	2.69492
$203$	5.82113e7	0.488395
$204$	−8.10781e7	−0.668649
$205$	−9.51496e7	−0.771380
$206$	−6.64557e7	−0.529660
$207$	−1.13628e8	−0.890408
$208$	1.87004e8	1.44088
$209$	−2.13664e8	−1.61890
$210$	−9.51730e7	−0.709163
$211$	−1.92361e8	−1.40970	−0.704852	−	0.709354i	$-0.748987\pi$
$211$	−1.92361e8	−1.40970	−0.704852	+	0.709354i	$0.748987\pi$
$212$	5.81130e6	0.0418888
$213$	−7.23617e7	−0.513074
$214$	−2.22924e8	−1.55492
$215$	−7.57299e7	−0.519676
$216$	1.21015e7	0.0817054
$217$	9.09614e7	0.604294
$218$	−8.20719e6	−0.0536533
$219$	9.42974e7	0.606660
$220$	−1.81003e8	−1.14606
$221$	−2.21242e8	−1.37878
$222$	−2.69989e7	−0.165619
$223$	−7.93186e7	−0.478970	−0.239485	−	0.970900i	$-0.576979\pi$
$223$	−7.93186e7	−0.478970	−0.239485	+	0.970900i	$0.576979\pi$
$224$	2.14132e8	1.27296
$225$	3.24600e7	0.189981
$226$	2.02305e8	1.16581
$227$	−8.15000e7	−0.462452	−0.231226	−	0.972900i	$-0.574274\pi$
$227$	−8.15000e7	−0.462452	−0.231226	+	0.972900i	$0.574274\pi$
$228$	1.55963e8	0.871463
$229$	−3.16591e8	−1.74210	−0.871052	−	0.491191i	$-0.836562\pi$
$229$	−3.16591e8	−1.74210	−0.871052	+	0.491191i	$0.836562\pi$
$230$	−3.67823e8	−1.99339
$231$	1.61450e8	0.861780
$232$	−8.04878e6	−0.0423177
$233$	2.48583e8	1.28744	0.643719	−	0.765262i	$-0.277391\pi$
$233$	2.48583e8	1.28744	0.643719	+	0.765262i	$0.277391\pi$
$234$	2.17057e8	1.10744
$235$	1.15530e8	0.580710
$236$	−3.26295e8	−1.61592
$237$	8.42287e7	0.410999
$238$	−2.39654e8	−1.15230
$239$	1.00643e8	0.476858	0.238429	−	0.971160i	$-0.423368\pi$
$239$	1.00643e8	0.476858	0.238429	+	0.971160i	$0.423368\pi$
$240$	−1.12210e8	−0.523954
$241$	6.25745e7	0.287964	0.143982	−	0.989580i	$-0.454009\pi$
$241$	6.25745e7	0.287964	0.143982	+	0.989580i	$0.454009\pi$
$242$	2.82445e8	1.28109
$243$	−1.99311e8	−0.891067
$244$	−2.33203e6	−0.0102771
$245$	3.75507e7	0.163131
$246$	−2.29619e8	−0.983412
$247$	4.25584e8	1.79699
$248$	−1.25771e7	−0.0523599
$249$	1.19765e8	0.491625
$250$	3.84858e8	1.55779
$251$	−1.44632e8	−0.577306	−0.288653	−	0.957434i	$-0.593207\pi$
$251$	−1.44632e8	−0.577306	−0.288653	+	0.957434i	$0.593207\pi$
$252$	1.20643e8	0.474898
$253$	6.23969e8	2.42238
$254$	7.24150e8	2.77275
$255$	1.32755e8	0.501372
$256$	2.37229e8	0.883745
$257$	−3.89613e7	−0.143175	−0.0715876	−	0.997434i	$-0.522807\pi$
$257$	−3.89613e7	−0.143175	−0.0715876	+	0.997434i	$0.522807\pi$
$258$	−1.82755e8	−0.662521
$259$	−4.09485e7	−0.146450
$260$	3.60528e8	1.27213
$261$	7.96619e7	0.277338
$262$	6.87820e7	0.236276
$263$	−4.49018e8	−1.52202	−0.761008	−	0.648743i	$-0.775295\pi$
$263$	−4.49018e8	−1.52202	−0.761008	+	0.648743i	$0.775295\pi$
$264$	−2.23234e7	−0.0746702
$265$	−9.51525e6	−0.0314094
$266$	4.61000e8	1.50181
$267$	1.98785e8	0.639136
$268$	−5.36803e8	−1.70350
$269$	−5.87303e7	−0.183962	−0.0919812	−	0.995761i	$-0.529320\pi$
$269$	−5.87303e7	−0.183962	−0.0919812	+	0.995761i	$0.529320\pi$
$270$	−3.87715e8	−1.19878
$271$	−2.00540e8	−0.612081	−0.306040	−	0.952019i	$-0.599004\pi$
$271$	−2.00540e8	−0.612081	−0.306040	+	0.952019i	$0.599004\pi$
$272$	−2.82555e8	−0.851357
$273$	−3.21582e8	−0.956582
$274$	−5.86373e8	−1.72205
$275$	−1.78249e8	−0.516847
$276$	−4.55462e8	−1.30398
$277$	2.66768e8	0.754146	0.377073	−	0.926184i	$-0.376931\pi$
$277$	2.66768e8	0.754146	0.377073	+	0.926184i	$0.376931\pi$
$278$	4.59470e8	1.28263
$279$	1.24480e8	0.343151
$280$	1.99585e7	0.0543345
$281$	4.90428e8	1.31857	0.659285	−	0.751893i	$-0.270859\pi$
$281$	4.90428e8	1.31857	0.659285	+	0.751893i	$0.270859\pi$
$282$	2.78803e8	0.740331
$283$	−6.83285e8	−1.79205	−0.896023	−	0.444007i	$-0.853557\pi$
$283$	−6.83285e8	−1.79205	−0.896023	+	0.444007i	$0.853557\pi$
$284$	2.96928e8	0.769195
$285$	−2.55369e8	−0.653448
$286$	−1.19193e9	−3.01280
$287$	−3.48258e8	−0.869589
$288$	2.93039e8	0.722855
$289$	−7.60503e7	−0.185335
$290$	2.57872e8	0.620885
$291$	3.41020e8	0.811249
$292$	−3.86938e8	−0.909497
$293$	−7.00506e7	−0.162695	−0.0813476	−	0.996686i	$-0.525922\pi$
$293$	−7.00506e7	−0.162695	−0.0813476	+	0.996686i	$0.525922\pi$
$294$	9.06190e7	0.207971
$295$	5.34267e8	1.21166
$296$	5.66188e6	0.0126894
$297$	6.57715e8	1.45677
$298$	1.09381e9	2.39433
$299$	−1.24284e9	−2.68885
$300$	1.30111e8	0.278222
$301$	−2.77179e8	−0.585839
$302$	7.89627e8	1.64967
$303$	−6.40083e8	−1.32187
$304$	5.43526e8	1.10959
$305$	3.81839e6	0.00770604
$306$	−3.27965e8	−0.654338
$307$	−5.90082e8	−1.16393	−0.581967	−	0.813212i	$-0.697717\pi$
$307$	−5.90082e8	−1.16393	−0.581967	+	0.813212i	$0.697717\pi$
$308$	−6.62491e8	−1.29197
$309$	1.34739e8	0.259799
$310$	4.02952e8	0.768224
$311$	7.52682e8	1.41889	0.709447	−	0.704758i	$-0.248945\pi$
$311$	7.52682e8	1.41889	0.709447	+	0.704758i	$0.248945\pi$
$312$	4.44645e7	0.0828844
$313$	−2.68461e8	−0.494853	−0.247426	−	0.968907i	$-0.579585\pi$
$313$	−2.68461e8	−0.494853	−0.247426	+	0.968907i	$0.579585\pi$
$314$	−2.42069e8	−0.441251
$315$	−1.97537e8	−0.356092
$316$	−3.45622e8	−0.616165
$317$	8.41802e8	1.48423	0.742117	−	0.670270i	$-0.233822\pi$
$317$	8.41802e8	1.48423	0.742117	+	0.670270i	$0.233822\pi$
$318$	−2.29626e7	−0.0400430
$319$	−4.37450e8	−0.754503
$320$	5.11680e8	0.872918
$321$	4.51979e8	0.762694
$322$	−1.34627e9	−2.24718
$323$	−6.43040e8	−1.06177
$324$	−1.53719e8	−0.251084
$325$	3.55042e8	0.573704
$326$	−1.11319e9	−1.77953
$327$	1.66401e7	0.0263171
$328$	4.81530e7	0.0753468
$329$	4.22854e8	0.654643
$330$	7.15212e8	1.09556
$331$	−9.38014e7	−0.142171	−0.0710855	−	0.997470i	$-0.522646\pi$
$331$	−9.38014e7	−0.142171	−0.0710855	+	0.997470i	$0.522646\pi$
$332$	−4.91443e8	−0.737037
$333$	−5.60379e7	−0.0831624
$334$	−6.87518e8	−1.00965
$335$	8.78946e8	1.27734
$336$	−4.10702e8	−0.590662
$337$	−1.59375e8	−0.226838	−0.113419	−	0.993547i	$-0.536180\pi$
$337$	−1.59375e8	−0.226838	−0.113419	+	0.993547i	$0.536180\pi$
$338$	1.35673e9	1.91110
$339$	−4.10172e8	−0.571831
$340$	−5.44744e8	−0.751651
$341$	−6.83563e8	−0.933551
$342$	6.30876e8	0.852811
$343$	8.03202e8	1.07472
$344$	3.83251e7	0.0507609
$345$	7.45760e8	0.977760
$346$	1.00611e9	1.30580
$347$	1.98414e8	0.254929	0.127465	−	0.991843i	$-0.459316\pi$
$347$	1.98414e8	0.254929	0.127465	+	0.991843i	$0.459316\pi$
$348$	3.19313e8	0.406153
$349$	−6.50218e8	−0.818785	−0.409393	−	0.912358i	$-0.634259\pi$
$349$	−6.50218e8	−0.818785	−0.409393	+	0.912358i	$0.634259\pi$
$350$	3.84588e8	0.479466
$351$	−1.31006e9	−1.61702
$352$	−1.60917e9	−1.96654
$353$	6.80595e8	0.823526	0.411763	−	0.911291i	$-0.364913\pi$
$353$	6.80595e8	0.823526	0.411763	+	0.911291i	$0.364913\pi$
$354$	1.28932e9	1.54471
$355$	−4.86181e8	−0.576765
$356$	−8.15689e8	−0.958185
$357$	4.85898e8	0.565205
$358$	4.75297e8	0.547488
$359$	−1.28215e9	−1.46254	−0.731268	−	0.682090i	$-0.761071\pi$
$359$	−1.28215e9	−1.46254	−0.731268	+	0.682090i	$0.761071\pi$
$360$	2.73131e7	0.0308541
$361$	3.43087e8	0.383821
$362$	1.37258e9	1.52075
$363$	−5.72657e8	−0.628379
$364$	1.31957e9	1.43410
$365$	6.33561e8	0.681967
$366$	9.21472e6	0.00982423
$367$	1.56952e8	0.165743	0.0828714	−	0.996560i	$-0.473591\pi$
$367$	1.56952e8	0.165743	0.0828714	+	0.996560i	$0.473591\pi$
$368$	−1.58727e9	−1.66029
$369$	−4.76589e8	−0.493800
$370$	−1.81399e8	−0.186178
$371$	−3.48268e7	−0.0354083
$372$	4.98962e8	0.502536
$373$	−6.19222e8	−0.617825	−0.308913	−	0.951090i	$-0.599965\pi$
$373$	−6.19222e8	−0.617825	−0.308913	+	0.951090i	$0.599965\pi$
$374$	1.80097e9	1.78014
$375$	−7.80298e8	−0.764102
$376$	−5.84673e7	−0.0567225
$377$	8.71328e8	0.837504
$378$	−1.41908e9	−1.35140
$379$	1.56036e9	1.47227	0.736135	−	0.676835i	$-0.236649\pi$
$379$	1.56036e9	1.47227	0.736135	+	0.676835i	$0.236649\pi$
$380$	1.04788e9	0.979641
$381$	−1.46821e9	−1.36004
$382$	6.13843e8	0.563425
$383$	−7.16484e8	−0.651645	−0.325822	−	0.945431i	$-0.605641\pi$
$383$	−7.16484e8	−0.651645	−0.325822	+	0.945431i	$0.605641\pi$
$384$	1.20234e8	0.108359
$385$	1.08474e9	0.968756
$386$	−2.51565e8	−0.222636
$387$	−3.79319e8	−0.332672
$388$	−1.39933e9	−1.21621
$389$	2.01742e9	1.73769	0.868844	−	0.495085i	$-0.164863\pi$
$389$	2.01742e9	1.73769	0.868844	+	0.495085i	$0.164863\pi$
$390$	−1.42458e9	−1.21608
$391$	1.87789e9	1.58873
$392$	−1.90035e7	−0.0159343
$393$	−1.39455e8	−0.115894
$394$	−2.30650e9	−1.89984
$395$	5.65912e8	0.462018
$396$	−9.06615e8	−0.733652
$397$	−1.80163e9	−1.44510	−0.722552	−	0.691316i	$-0.757031\pi$
$397$	−1.80163e9	−1.44510	−0.722552	+	0.691316i	$0.757031\pi$
$398$	−3.03187e8	−0.241057
$399$	−9.34677e8	−0.736642
$400$	4.53435e8	0.354246
$401$	−3.65348e8	−0.282945	−0.141472	−	0.989942i	$-0.545184\pi$
$401$	−3.65348e8	−0.282945	−0.141472	+	0.989942i	$0.545184\pi$
$402$	2.12111e9	1.62844
$403$	1.36154e9	1.03625
$404$	2.62650e9	1.98172
$405$	2.51694e8	0.188270
$406$	9.43838e8	0.699933
$407$	3.07723e8	0.226245
$408$	−6.71842e7	−0.0489730
$409$	1.37446e9	0.993349	0.496674	−	0.867937i	$-0.334554\pi$
$409$	1.37446e9	0.993349	0.496674	+	0.867937i	$0.334554\pi$
$410$	−1.54276e9	−1.10549
$411$	1.18887e9	0.844672
$412$	−5.52884e8	−0.389488
$413$	1.95547e9	1.36592
$414$	−1.84236e9	−1.27607
$415$	8.04674e8	0.552652
$416$	3.20521e9	2.18288
$417$	−9.31575e8	−0.629132
$418$	−3.46435e9	−2.32009
$419$	1.35141e9	0.897506	0.448753	−	0.893656i	$-0.351868\pi$
$419$	1.35141e9	0.897506	0.448753	+	0.893656i	$0.351868\pi$
$420$	−7.91801e8	−0.521487
$421$	−2.59236e8	−0.169320	−0.0846600	−	0.996410i	$-0.526980\pi$
$421$	−2.59236e8	−0.169320	−0.0846600	+	0.996410i	$0.526980\pi$
$422$	−3.11894e9	−2.02029
$423$	5.78673e8	0.371742
$424$	4.81545e6	0.00306800
$425$	−5.36454e8	−0.338978
$426$	−1.17327e9	−0.735302
$427$	1.39757e7	0.00868714
$428$	−1.85464e9	−1.14342
$429$	2.41664e9	1.47779
$430$	−1.22788e9	−0.744763
$431$	−3.04822e8	−0.183390	−0.0916951	−	0.995787i	$-0.529229\pi$
$431$	−3.04822e8	−0.183390	−0.0916951	+	0.995787i	$0.529229\pi$
$432$	−1.67311e9	−0.998464
$433$	3.03101e9	1.79424	0.897119	−	0.441789i	$-0.145656\pi$
$433$	3.03101e9	1.79424	0.897119	+	0.441789i	$0.145656\pi$
$434$	1.47485e9	0.866031
$435$	−5.22835e8	−0.304545
$436$	−6.82805e7	−0.0394542
$437$	−3.61232e9	−2.07063
$438$	1.52894e9	0.869422
$439$	1.45030e9	0.818151	0.409075	−	0.912501i	$-0.365851\pi$
$439$	1.45030e9	0.818151	0.409075	+	0.912501i	$0.365851\pi$
$440$	−1.49986e8	−0.0839393
$441$	1.88085e8	0.104429
$442$	−3.58722e9	−1.97597
$443$	−2.89689e9	−1.58314	−0.791570	−	0.611078i	$-0.790736\pi$
$443$	−2.89689e9	−1.58314	−0.791570	+	0.611078i	$0.790736\pi$
$444$	−2.24620e8	−0.121789
$445$	1.33559e9	0.718475
$446$	−1.28607e9	−0.686425
$447$	−2.21770e9	−1.17443
$448$	1.87280e9	0.984054
$449$	−4.55030e8	−0.237234	−0.118617	−	0.992940i	$-0.537846\pi$
$449$	−4.55030e8	−0.237234	−0.118617	+	0.992940i	$0.537846\pi$
$450$	5.26307e8	0.272267
$451$	2.61711e9	1.34340
$452$	1.68309e9	0.857282
$453$	−1.60097e9	−0.809168
$454$	−1.32144e9	−0.662754
$455$	−2.16063e9	−1.07533
$456$	1.29236e8	0.0638274
$457$	−1.79001e9	−0.877300	−0.438650	−	0.898658i	$-0.644543\pi$
$457$	−1.79001e9	−0.877300	−0.438650	+	0.898658i	$0.644543\pi$
$458$	−5.13320e9	−2.49666
$459$	1.97945e9	0.955431
$460$	−3.06014e9	−1.46585
$461$	−2.95013e9	−1.40245	−0.701225	−	0.712940i	$-0.747363\pi$
$461$	−2.95013e9	−1.40245	−0.701225	+	0.712940i	$0.747363\pi$
$462$	2.61775e9	1.23504
$463$	−3.02642e9	−1.41708	−0.708542	−	0.705669i	$-0.750647\pi$
$463$	−3.02642e9	−1.41708	−0.708542	+	0.705669i	$0.750647\pi$
$464$	1.11280e9	0.517135
$465$	−8.16985e8	−0.376816
$466$	4.03053e9	1.84506
$467$	−2.94423e9	−1.33771	−0.668857	−	0.743391i	$-0.733216\pi$
$467$	−2.94423e9	−1.33771	−0.668857	+	0.743391i	$0.733216\pi$
$468$	1.80583e9	0.814359
$469$	3.21703e9	1.43996
$470$	1.87321e9	0.832232
$471$	4.90795e8	0.216435
$472$	−2.70380e8	−0.118352
$473$	2.08297e9	0.905041
$474$	1.36568e9	0.589015
$475$	1.03193e9	0.441796
$476$	−1.99382e9	−0.847348
$477$	−4.76603e7	−0.0201068
$478$	1.63182e9	0.683399
$479$	1.49589e9	0.621907	0.310953	−	0.950425i	$-0.399352\pi$
$479$	1.49589e9	0.621907	0.310953	+	0.950425i	$0.399352\pi$
$480$	−1.92326e9	−0.793770
$481$	−6.12932e8	−0.251134
$482$	1.01458e9	0.412689
$483$	2.72956e9	1.10224
$484$	2.34983e9	0.942057
$485$	2.29123e9	0.911953
$486$	−3.23164e9	−1.27701
$487$	2.97901e9	1.16875	0.584374	−	0.811484i	$-0.301340\pi$
$487$	2.97901e9	1.16875	0.584374	+	0.811484i	$0.301340\pi$
$488$	−1.93240e6	−0.000752710 0
$489$	2.25698e9	0.872865
$490$	6.08847e8	0.233788
$491$	−2.24499e9	−0.855913	−0.427956	−	0.903799i	$-0.640766\pi$
$491$	−2.24499e9	−0.855913	−0.427956	+	0.903799i	$0.640766\pi$
$492$	−1.91034e9	−0.723157
$493$	−1.31654e9	−0.494847
$494$	6.90042e9	2.57532
$495$	1.48447e9	0.550113
$496$	1.73887e9	0.639853
$497$	−1.77947e9	−0.650196
$498$	1.94188e9	0.704561
$499$	−3.17101e9	−1.14247	−0.571235	−	0.820786i	$-0.693536\pi$
$499$	−3.17101e9	−1.14247	−0.571235	+	0.820786i	$0.693536\pi$
$500$	3.20186e9	1.14553
$501$	1.39394e9	0.495236
$502$	−2.34506e9	−0.827354
$503$	−4.20686e9	−1.47391	−0.736954	−	0.675943i	$-0.763737\pi$
$503$	−4.20686e9	−1.47391	−0.736954	+	0.675943i	$0.763737\pi$
$504$	9.99690e7	0.0347823
$505$	−4.30056e9	−1.48595
$506$	1.01170e10	3.47158
$507$	−2.75076e9	−0.937401
$508$	6.02464e9	2.03896
$509$	−2.31176e9	−0.777018	−0.388509	−	0.921445i	$-0.627010\pi$
$509$	−2.31176e9	−0.777018	−0.388509	+	0.921445i	$0.627010\pi$
$510$	2.15249e9	0.718531
$511$	2.31890e9	0.768792
$512$	4.31457e9	1.42067
$513$	−3.80768e9	−1.24523
$514$	−6.31719e8	−0.205188
$515$	9.05277e8	0.292049
$516$	−1.52045e9	−0.487188
$517$	−3.17769e9	−1.01133
$518$	−6.63940e8	−0.209882
$519$	−2.03988e9	−0.640499
$520$	2.98746e8	0.0931732
$521$	−5.90286e7	−0.0182865	−0.00914324	−	0.999958i	$-0.502910\pi$
$521$	−5.90286e7	−0.0182865	−0.00914324	+	0.999958i	$0.502910\pi$
$522$	1.29164e9	0.397461
$523$	1.79049e9	0.547287	0.273644	−	0.961831i	$-0.411771\pi$
$523$	1.79049e9	0.547287	0.273644	+	0.961831i	$0.411771\pi$
$524$	5.72238e8	0.173747
$525$	−7.79752e8	−0.235179
$526$	−7.28039e9	−2.18124
$527$	−2.05724e9	−0.612276
$528$	3.08637e9	0.912491
$529$	7.14433e9	2.09830
$530$	−1.54280e8	−0.0450137
$531$	2.67605e9	0.775647
$532$	3.83533e9	1.10436
$533$	−5.21284e9	−1.49118
$534$	3.22310e9	0.915965
$535$	3.03673e9	0.857371
$536$	−4.44814e8	−0.124767
$537$	−9.63664e8	−0.268544
$538$	−9.52253e8	−0.263642
$539$	−1.03284e9	−0.284100
$540$	−3.22563e9	−0.881530
$541$	−2.58849e9	−0.702840	−0.351420	−	0.936218i	$-0.614301\pi$
$541$	−2.58849e9	−0.702840	−0.351420	+	0.936218i	$0.614301\pi$
$542$	−3.25156e9	−0.877190
$543$	−2.78290e9	−0.745930
$544$	−4.84294e9	−1.28977
$545$	1.11800e8	0.0295839
$546$	−5.21413e9	−1.37091
$547$	7.42290e8	0.193918	0.0969589	−	0.995288i	$-0.469088\pi$
$547$	7.42290e8	0.193918	0.0969589	+	0.995288i	$0.469088\pi$
$548$	−4.87838e9	−1.26632
$549$	1.91257e7	0.00493304
$550$	−2.89013e9	−0.740709
$551$	2.53251e9	0.644943
$552$	−3.77412e8	−0.0955056
$553$	2.07130e9	0.520841
$554$	4.32538e9	1.08079
$555$	3.67786e8	0.0913209
$556$	3.82261e9	0.943187
$557$	−2.00353e9	−0.491250	−0.245625	−	0.969365i	$-0.578993\pi$
$557$	−2.00353e9	−0.491250	−0.245625	+	0.969365i	$0.578993\pi$
$558$	2.01832e9	0.491780
$559$	−4.14892e9	−1.00460
$560$	−2.75940e9	−0.663983
$561$	−3.65145e9	−0.873164
$562$	7.95181e9	1.88968
$563$	−1.54197e8	−0.0364164	−0.0182082	−	0.999834i	$-0.505796\pi$
$563$	−1.54197e8	−0.0364164	−0.0182082	+	0.999834i	$0.505796\pi$
$564$	2.31953e9	0.544406
$565$	−2.75585e9	−0.642814
$566$	−1.10788e10	−2.56823
$567$	9.21228e8	0.212240
$568$	2.46045e8	0.0563371
$569$	5.62458e9	1.27996	0.639981	−	0.768391i	$-0.278942\pi$
$569$	5.62458e9	1.27996	0.639981	+	0.768391i	$0.278942\pi$
$570$	−4.14055e9	−0.936475
$571$	−5.99373e9	−1.34732	−0.673660	−	0.739041i	$-0.735279\pi$
$571$	−5.99373e9	−1.34732	−0.673660	+	0.739041i	$0.735279\pi$
$572$	−9.91640e9	−2.21548
$573$	−1.24457e9	−0.276361
$574$	−5.64665e9	−1.24623
$575$	−3.01357e9	−0.661064
$576$	2.56292e9	0.558800
$577$	−1.13647e9	−0.246287	−0.123144	−	0.992389i	$-0.539298\pi$
$577$	−1.13647e9	−0.246287	−0.123144	+	0.992389i	$0.539298\pi$
$578$	−1.23308e9	−0.265609
$579$	5.10048e8	0.109203
$580$	2.14539e9	0.456571
$581$	2.94519e9	0.623013
$582$	5.52930e9	1.16262
$583$	2.61719e8	0.0547010
$584$	−3.20630e8	−0.0666131
$585$	−2.95681e9	−0.610630
$586$	−1.13580e9	−0.233163
$587$	2.96518e9	0.605086	0.302543	−	0.953136i	$-0.402164\pi$
$587$	2.96518e9	0.605086	0.302543	+	0.953136i	$0.402164\pi$
$588$	7.53913e8	0.152933
$589$	3.95732e9	0.797991
$590$	8.66260e9	1.73647
$591$	4.67643e9	0.931876
$592$	−7.82794e8	−0.155068
$593$	4.68286e9	0.922189	0.461095	−	0.887351i	$-0.347457\pi$
$593$	4.68286e9	0.922189	0.461095	+	0.887351i	$0.347457\pi$
$594$	1.06642e10	2.08773
$595$	3.26463e9	0.635366
$596$	9.10004e9	1.76068
$597$	6.14710e8	0.118239
$598$	−2.01515e10	−3.85347
$599$	2.66405e9	0.506464	0.253232	−	0.967406i	$-0.418506\pi$
$599$	2.66405e9	0.506464	0.253232	+	0.967406i	$0.418506\pi$
$600$	1.07815e8	0.0203774
$601$	−4.31587e9	−0.810975	−0.405487	−	0.914101i	$-0.632898\pi$
$601$	−4.31587e9	−0.810975	−0.405487	+	0.914101i	$0.632898\pi$
$602$	−4.49419e9	−0.839583
$603$	4.40250e9	0.817689
$604$	6.56938e9	1.21310
$605$	−3.84754e9	−0.706382
$606$	−1.03783e10	−1.89440
$607$	1.89044e9	0.343085	0.171542	−	0.985177i	$-0.445125\pi$
$607$	1.89044e9	0.343085	0.171542	+	0.985177i	$0.445125\pi$
$608$	9.31593e9	1.68098
$609$	−1.91363e9	−0.343319
$610$	6.19115e7	0.0110438
$611$	6.32943e9	1.12259
$612$	−2.72853e9	−0.481171
$613$	−9.24200e9	−1.62052	−0.810260	−	0.586071i	$-0.800674\pi$
$613$	−9.24200e9	−1.62052	−0.810260	+	0.586071i	$0.800674\pi$
$614$	−9.56760e9	−1.66807
$615$	3.12793e9	0.542244
$616$	−5.48963e8	−0.0946261
$617$	−3.73822e9	−0.640718	−0.320359	−	0.947296i	$-0.603804\pi$
$617$	−3.73822e9	−0.640718	−0.320359	+	0.947296i	$0.603804\pi$
$618$	2.18466e9	0.372326
$619$	9.69271e9	1.64259	0.821293	−	0.570507i	$-0.193253\pi$
$619$	9.69271e9	1.64259	0.821293	+	0.570507i	$0.193253\pi$
$620$	3.35240e9	0.564917
$621$	1.11197e10	1.86325
$622$	1.22040e10	2.03346
$623$	4.88839e9	0.809948
$624$	−6.14753e9	−1.01287
$625$	−2.95038e9	−0.483390
$626$	−4.35283e9	−0.709188
$627$	7.02397e9	1.13801
$628$	−2.01392e9	−0.324476
$629$	9.26117e8	0.148385
$630$	−3.20287e9	−0.510326
$631$	−1.02717e9	−0.162757	−0.0813787	−	0.996683i	$-0.525932\pi$
$631$	−1.02717e9	−0.162757	−0.0813787	+	0.996683i	$0.525932\pi$
$632$	−2.86395e8	−0.0451290
$633$	6.32364e9	0.990956
$634$	1.36490e10	2.12710
$635$	−9.86456e9	−1.52887
$636$	−1.91040e8	−0.0294458
$637$	2.05724e9	0.315353
$638$	−7.09282e9	−1.08130
$639$	−2.43520e9	−0.369217
$640$	8.07820e8	0.121811
$641$	2.77233e9	0.415760	0.207880	−	0.978154i	$-0.433344\pi$
$641$	2.77233e9	0.415760	0.207880	+	0.978154i	$0.433344\pi$
$642$	7.32839e9	1.09304
$643$	−8.30171e9	−1.23149	−0.615743	−	0.787947i	$-0.711144\pi$
$643$	−8.30171e9	−1.23149	−0.615743	+	0.787947i	$0.711144\pi$
$644$	−1.12004e10	−1.65247
$645$	2.48953e9	0.365308
$646$	−1.04263e10	−1.52165
$647$	1.13742e10	1.65104	0.825518	−	0.564376i	$-0.190883\pi$
$647$	1.13742e10	1.65104	0.825518	+	0.564376i	$0.190883\pi$
$648$	−1.27377e8	−0.0183898
$649$	−1.46951e10	−2.11017
$650$	5.75665e9	0.822192
$651$	−2.99025e9	−0.424790
$652$	−9.26125e9	−1.30859
$653$	−1.12484e10	−1.58086	−0.790430	−	0.612553i	$-0.790143\pi$
$653$	−1.12484e10	−1.58086	−0.790430	+	0.612553i	$0.790143\pi$
$654$	2.69802e8	0.0377158
$655$	−9.36967e8	−0.130281
$656$	−6.65748e9	−0.920760
$657$	3.17340e9	0.436563
$658$	6.85615e9	0.938188
$659$	7.46402e9	1.01595	0.507977	−	0.861371i	$-0.330394\pi$
$659$	7.46402e9	1.01595	0.507977	+	0.861371i	$0.330394\pi$
$660$	5.95027e9	0.805626
$661$	−2.44649e9	−0.329487	−0.164743	−	0.986336i	$-0.552680\pi$
$661$	−2.44649e9	−0.329487	−0.164743	+	0.986336i	$0.552680\pi$
$662$	−1.52090e9	−0.203750
$663$	7.27309e9	0.969218
$664$	−4.07227e8	−0.0539819
$665$	−6.27987e9	−0.828085
$666$	−9.08598e8	−0.119182
$667$	−7.39576e9	−0.965034
$668$	−5.71987e9	−0.742452
$669$	2.60751e9	0.336693
$670$	1.42512e10	1.83059
$671$	−1.05026e8	−0.0134204
$672$	−7.03935e9	−0.894829
$673$	7.31914e9	0.925566	0.462783	−	0.886472i	$-0.346851\pi$
$673$	7.31914e9	0.925566	0.462783	+	0.886472i	$0.346851\pi$
$674$	−2.58411e9	−0.325089
$675$	−3.17655e9	−0.397550
$676$	1.12874e10	1.40534
$677$	2.81914e8	0.0349185	0.0174593	−	0.999848i	$-0.494442\pi$
$677$	2.81914e8	0.0349185	0.0174593	+	0.999848i	$0.494442\pi$
$678$	−6.65054e9	−0.819507
$679$	8.38614e9	1.02806
$680$	−4.51394e8	−0.0550522
$681$	2.67922e9	0.325082
$682$	−1.10833e10	−1.33790
$683$	8.04277e9	0.965902	0.482951	−	0.875647i	$-0.339565\pi$
$683$	8.04277e9	0.965902	0.482951	+	0.875647i	$0.339565\pi$
$684$	5.24864e9	0.627119
$685$	7.98772e9	0.949524
$686$	1.30231e10	1.54021
$687$	1.04076e10	1.22462
$688$	−5.29871e9	−0.620313
$689$	−5.21301e8	−0.0607185
$690$	1.20918e10	1.40126
$691$	−1.22210e10	−1.40907	−0.704534	−	0.709670i	$-0.748844\pi$
$691$	−1.22210e10	−1.40907	−0.704534	+	0.709670i	$0.748844\pi$
$692$	8.37039e9	0.960228
$693$	5.43330e9	0.620151
$694$	3.21709e9	0.365346
$695$	−6.25902e9	−0.707229
$696$	2.64594e8	0.0297474
$697$	7.87640e9	0.881076
$698$	−1.05426e10	−1.17342
$699$	−8.17189e9	−0.905008
$700$	3.19962e9	0.352578
$701$	−2.20163e9	−0.241396	−0.120698	−	0.992689i	$-0.538513\pi$
$701$	−2.20163e9	−0.241396	−0.120698	+	0.992689i	$0.538513\pi$
$702$	−2.12413e10	−2.31740
$703$	−1.78149e9	−0.193392
$704$	−1.40739e10	−1.52023
$705$	−3.79793e9	−0.408212
$706$	1.10352e10	1.18022
$707$	−1.57405e10	−1.67514
$708$	1.07266e10	1.13591
$709$	1.15060e10	1.21244	0.606222	−	0.795295i	$-0.292684\pi$
$709$	1.15060e10	1.21244	0.606222	+	0.795295i	$0.292684\pi$
$710$	−7.88294e9	−0.826578
$711$	2.83456e9	0.295762
$712$	−6.75908e8	−0.0701791
$713$	−1.15567e10	−1.19404
$714$	7.87834e9	0.810012
$715$	1.62368e10	1.66123
$716$	3.95428e9	0.402598
$717$	−3.30851e9	−0.335209
$718$	−2.07887e10	−2.09600
$719$	3.50528e9	0.351699	0.175849	−	0.984417i	$-0.443733\pi$
$719$	3.50528e9	0.351699	0.175849	+	0.984417i	$0.443733\pi$
$720$	−3.77623e9	−0.377046
$721$	3.31341e9	0.329232
$722$	5.56282e9	0.550066
$723$	−2.05707e9	−0.202425
$724$	1.14193e10	1.11829
$725$	2.11274e9	0.205903
$726$	−9.28506e9	−0.900548
$727$	5.19370e9	0.501310	0.250655	−	0.968076i	$-0.419354\pi$
$727$	5.19370e9	0.501310	0.250655	+	0.968076i	$0.419354\pi$
$728$	1.09344e9	0.105036
$729$	9.04434e9	0.864630
$730$	1.02726e10	0.977346
$731$	6.26886e9	0.593578
$732$	7.66627e7	0.00722430
$733$	1.10000e10	1.03164	0.515822	−	0.856696i	$-0.327486\pi$
$733$	1.10000e10	1.03164	0.515822	+	0.856696i	$0.327486\pi$
$734$	2.54481e9	0.237531
$735$	−1.23444e9	−0.114673
$736$	−2.72056e10	−2.51527
$737$	−2.41756e10	−2.22454
$738$	−7.72741e9	−0.707680
$739$	−1.82910e10	−1.66717	−0.833587	−	0.552388i	$-0.813717\pi$
$739$	−1.82910e10	−1.66717	−0.833587	+	0.552388i	$0.813717\pi$
$740$	−1.50917e9	−0.136907
$741$	−1.39906e10	−1.26320
$742$	−5.64682e8	−0.0507447
$743$	1.03040e10	0.921603	0.460802	−	0.887503i	$-0.347562\pi$
$743$	1.03040e10	0.921603	0.460802	+	0.887503i	$0.347562\pi$
$744$	4.13457e8	0.0368066
$745$	−1.49002e10	−1.32021
$746$	−1.00401e10	−0.885423
$747$	4.03048e9	0.353781
$748$	1.49833e10	1.30904
$749$	1.11148e10	0.966528
$750$	−1.26518e10	−1.09506
$751$	3.20675e9	0.276264	0.138132	−	0.990414i	$-0.455890\pi$
$751$	3.20675e9	0.276264	0.138132	+	0.990414i	$0.455890\pi$
$752$	8.08350e9	0.693166
$753$	4.75461e9	0.405819
$754$	1.41277e10	1.20025
$755$	−1.07565e10	−0.909614
$756$	−1.18062e10	−0.993762
$757$	−2.05945e10	−1.72550	−0.862751	−	0.505629i	$-0.831261\pi$
$757$	−2.05945e10	−1.72550	−0.862751	+	0.505629i	$0.831261\pi$
$758$	2.52997e10	2.10995
$759$	−2.05123e10	−1.70282
$760$	8.68306e8	0.0717506
$761$	−3.40657e9	−0.280202	−0.140101	−	0.990137i	$-0.544743\pi$
$761$	−3.40657e9	−0.280202	−0.140101	+	0.990137i	$0.544743\pi$
$762$	−2.38056e10	−1.94911
$763$	4.09202e8	0.0333504
$764$	5.10693e9	0.414317
$765$	4.46762e9	0.360796
$766$	−1.16171e10	−0.933891
$767$	2.92702e10	2.34230
$768$	−7.79862e9	−0.621231
$769$	−1.13041e10	−0.896386	−0.448193	−	0.893937i	$-0.647932\pi$
$769$	−1.13041e10	−0.896386	−0.448193	+	0.893937i	$0.647932\pi$
$770$	1.75880e10	1.38835
$771$	1.28081e9	0.100645
$772$	−2.09292e9	−0.163716
$773$	−2.42454e10	−1.88800	−0.943999	−	0.329949i	$-0.892968\pi$
$773$	−2.42454e10	−1.88800	−0.943999	+	0.329949i	$0.892968\pi$
$774$	−6.15027e9	−0.476761
$775$	3.30139e9	0.254765
$776$	−1.15954e9	−0.0890776
$777$	1.34614e9	0.102947
$778$	3.27104e10	2.49033
$779$	−1.51511e10	−1.14832
$780$	−1.18520e10	−0.894250
$781$	1.33725e10	1.00446
$782$	3.04481e10	2.27686
$783$	−7.79574e9	−0.580352
$784$	2.62737e9	0.194722
$785$	3.29753e9	0.243302
$786$	−2.26113e9	−0.166091
$787$	2.52875e10	1.84924	0.924622	−	0.380886i	$-0.124381\pi$
$787$	2.52875e10	1.84924	0.924622	+	0.380886i	$0.124381\pi$
$788$	−1.91891e10	−1.39706
$789$	1.47610e10	1.06991
$790$	9.17570e9	0.662132
$791$	−1.00867e10	−0.724655
$792$	−7.51254e8	−0.0537339
$793$	2.09194e8	0.0148968
$794$	−2.92117e10	−2.07102
$795$	3.12803e8	0.0220793
$796$	−2.52239e9	−0.177262
$797$	2.20254e10	1.54106	0.770531	−	0.637403i	$-0.219991\pi$
$797$	2.20254e10	1.54106	0.770531	+	0.637403i	$0.219991\pi$
$798$	−1.51549e10	−1.05570
$799$	−9.56352e9	−0.663291
$800$	7.77179e9	0.536668
$801$	6.68973e9	0.459933
$802$	−5.92376e9	−0.405496
$803$	−1.74262e10	−1.18768
$804$	1.76468e10	1.19748
$805$	1.83393e10	1.23907
$806$	2.20761e10	1.48508
$807$	1.93069e9	0.129317
$808$	2.17641e9	0.145145
$809$	−1.56853e10	−1.04153	−0.520765	−	0.853700i	$-0.674353\pi$
$809$	−1.56853e10	−1.04153	−0.520765	+	0.853700i	$0.674353\pi$
$810$	4.08097e9	0.269815
$811$	1.56681e10	1.03144	0.515720	−	0.856757i	$-0.327525\pi$
$811$	1.56681e10	1.03144	0.515720	+	0.856757i	$0.327525\pi$
$812$	7.85235e9	0.514699
$813$	6.59253e9	0.430264
$814$	4.98942e9	0.324238
$815$	1.51641e10	0.981217
$816$	9.28868e9	0.598464
$817$	−1.20588e10	−0.773621
$818$	2.22856e10	1.42360
$819$	−1.08222e10	−0.688372
$820$	−1.28351e10	−0.812925
$821$	1.43393e10	0.904330	0.452165	−	0.891934i	$-0.350652\pi$
$821$	1.43393e10	0.904330	0.452165	+	0.891934i	$0.350652\pi$
$822$	1.92763e10	1.21052
$823$	−3.89949e9	−0.243842	−0.121921	−	0.992540i	$-0.538905\pi$
$823$	−3.89949e9	−0.243842	−0.121921	+	0.992540i	$0.538905\pi$
$824$	−4.58139e8	−0.0285268
$825$	5.85973e9	0.363319
$826$	3.17060e10	1.95755
$827$	2.28965e9	0.140767	0.0703834	−	0.997520i	$-0.477578\pi$
$827$	2.28965e9	0.140767	0.0703834	+	0.997520i	$0.477578\pi$
$828$	−1.53277e10	−0.938364
$829$	−2.07647e10	−1.26586	−0.632929	−	0.774210i	$-0.718147\pi$
$829$	−2.07647e10	−1.26586	−0.632929	+	0.774210i	$0.718147\pi$
$830$	1.30470e10	0.792022
$831$	−8.76971e9	−0.530129
$832$	2.80328e10	1.68746
$833$	−3.10841e9	−0.186329
$834$	−1.51046e10	−0.901627
$835$	9.36555e9	0.556712
$836$	−2.88220e10	−1.70609
$837$	−1.21817e10	−0.718072
$838$	2.19117e10	1.28624
$839$	2.45666e10	1.43608	0.718039	−	0.696003i	$-0.245040\pi$
$839$	2.45666e10	1.43608	0.718039	+	0.696003i	$0.245040\pi$
$840$	−6.56114e8	−0.0381946
$841$	−1.20649e10	−0.699418
$842$	−4.20326e9	−0.242658
$843$	−1.61223e10	−0.926893
$844$	−2.59483e10	−1.48563
$845$	−1.84817e10	−1.05376
$846$	9.38261e9	0.532755
$847$	−1.40824e10	−0.796316
$848$	−6.65768e8	−0.0374919
$849$	2.24622e10	1.25972
$850$	−8.69807e9	−0.485799
$851$	5.20252e9	0.289375
$852$	−9.76116e9	−0.540708
$853$	−2.42389e10	−1.33718	−0.668592	−	0.743629i	$-0.733103\pi$
$853$	−2.42389e10	−1.33718	−0.668592	+	0.743629i	$0.733103\pi$
$854$	2.26603e8	0.0124498
$855$	−8.59397e9	−0.470232
$856$	−1.53682e9	−0.0837462
$857$	−3.73588e9	−0.202750	−0.101375	−	0.994848i	$-0.532324\pi$
$857$	−3.73588e9	−0.202750	−0.101375	+	0.994848i	$0.532324\pi$
$858$	3.91835e10	2.11786
$859$	−8.10666e9	−0.436381	−0.218190	−	0.975906i	$-0.570015\pi$
$859$	−8.10666e9	−0.436381	−0.218190	+	0.975906i	$0.570015\pi$
$860$	−1.02155e10	−0.547665
$861$	1.14486e10	0.611280
$862$	−4.94239e9	−0.262822
$863$	6.45411e9	0.341821	0.170911	−	0.985287i	$-0.445329\pi$
$863$	6.45411e9	0.341821	0.170911	+	0.985287i	$0.445329\pi$
$864$	−2.86769e10	−1.51263
$865$	−1.37054e10	−0.720007
$866$	4.91448e10	2.57137
$867$	2.50007e9	0.130282
$868$	1.22701e10	0.636840
$869$	−1.55655e10	−0.804627
$870$	−8.47724e9	−0.436453
$871$	4.81537e10	2.46926
$872$	−5.65796e7	−0.00288970
$873$	1.14764e10	0.583788
$874$	−5.85702e10	−2.96747
$875$	−1.91886e10	−0.968311
$876$	1.27201e10	0.639334
$877$	1.57677e10	0.789353	0.394676	−	0.918820i	$-0.370857\pi$
$877$	1.57677e10	0.789353	0.394676	+	0.918820i	$0.370857\pi$
$878$	2.35152e10	1.17252
$879$	2.30283e9	0.114367
$880$	2.07365e10	1.02576
$881$	3.18275e10	1.56815	0.784074	−	0.620668i	$-0.213138\pi$
$881$	3.18275e10	1.56815	0.784074	+	0.620668i	$0.213138\pi$
$882$	3.04961e9	0.149660
$883$	6.26121e9	0.306053	0.153026	−	0.988222i	$-0.451098\pi$
$883$	6.26121e9	0.306053	0.153026	+	0.988222i	$0.451098\pi$
$884$	−2.98442e10	−1.45304
$885$	−1.75634e10	−0.851741
$886$	−4.69702e10	−2.26885
$887$	2.86337e9	0.137767	0.0688834	−	0.997625i	$-0.478056\pi$
$887$	2.86337e9	0.137767	0.0688834	+	0.997625i	$0.478056\pi$
$888$	−1.86128e8	−0.00892003
$889$	−3.61054e10	−1.72352
$890$	2.16552e10	1.02967
$891$	−6.92291e9	−0.327881
$892$	−1.06996e10	−0.504766
$893$	1.83965e10	0.864479
$894$	−3.59577e10	−1.68310
$895$	−6.47462e9	−0.301879
$896$	2.95671e9	0.137319
$897$	4.08571e10	1.89014
$898$	−7.37786e9	−0.339988
$899$	8.10211e9	0.371911
$900$	4.37866e9	0.200213
$901$	7.87665e8	0.0358761
$902$	4.24338e10	1.92526
$903$	9.11196e9	0.411817
$904$	1.39467e9	0.0627888
$905$	−1.86976e10	−0.838525
$906$	−2.59581e10	−1.15964
$907$	−2.76510e10	−1.23051	−0.615256	−	0.788327i	$-0.710947\pi$
$907$	−2.76510e10	−1.23051	−0.615256	+	0.788327i	$0.710947\pi$
$908$	−1.09938e10	−0.487359
$909$	−2.15408e10	−0.951237
$910$	−3.50324e10	−1.54108
$911$	−1.91783e10	−0.840420	−0.420210	−	0.907427i	$-0.638044\pi$
$911$	−1.91783e10	−0.840420	−0.420210	+	0.907427i	$0.638044\pi$
$912$	−1.78678e10	−0.779990
$913$	−2.21327e10	−0.962470
$914$	−2.90232e10	−1.25728
$915$	−1.25525e8	−0.00541699
$916$	−4.27062e10	−1.83593
$917$	−3.42940e9	−0.146867
$918$	3.20948e10	1.36926
$919$	−3.23151e9	−0.137341	−0.0686707	−	0.997639i	$-0.521876\pi$
$919$	−3.23151e9	−0.137341	−0.0686707	+	0.997639i	$0.521876\pi$
$920$	−2.53574e9	−0.107361
$921$	1.93983e10	0.818191
$922$	−4.78334e10	−2.00989
$923$	−2.66358e10	−1.11496
$924$	2.17786e10	0.908194
$925$	−1.48620e9	−0.0617421
$926$	−4.90704e10	−2.03086
$927$	4.53438e9	0.186956
$928$	1.90732e10	0.783438
$929$	4.02784e10	1.64823	0.824114	−	0.566424i	$-0.191674\pi$
$929$	4.02784e10	1.64823	0.824114	+	0.566424i	$0.191674\pi$
$930$	−1.32466e10	−0.540025
$931$	5.97937e9	0.242846
$932$	3.35324e10	1.35678
$933$	−2.47436e10	−0.997417
$934$	−4.77378e10	−1.91712
$935$	−2.45332e10	−0.981553
$936$	1.49637e9	0.0596450
$937$	−3.51781e9	−0.139696	−0.0698479	−	0.997558i	$-0.522251\pi$
$937$	−3.51781e9	−0.139696	−0.0698479	+	0.997558i	$0.522251\pi$
$938$	5.21610e10	2.06365
$939$	8.82535e9	0.347858
$940$	1.55844e10	0.611986
$941$	−1.50436e10	−0.588557	−0.294279	−	0.955720i	$-0.595079\pi$
$941$	−1.50436e10	−0.588557	−0.294279	+	0.955720i	$0.595079\pi$
$942$	7.95775e9	0.310179
$943$	4.42462e10	1.71825
$944$	3.73819e10	1.44630
$945$	1.93311e10	0.745152
$946$	3.37732e10	1.29704
$947$	−1.64609e9	−0.0629836	−0.0314918	−	0.999504i	$-0.510026\pi$
$947$	−1.64609e9	−0.0629836	−0.0314918	+	0.999504i	$0.510026\pi$
$948$	1.13619e10	0.433135
$949$	3.47101e10	1.31833
$950$	1.67317e10	0.633151
$951$	−2.76733e10	−1.04335
$952$	−1.65215e9	−0.0620612
$953$	−4.17834e10	−1.56379	−0.781895	−	0.623410i	$-0.785747\pi$
$953$	−4.17834e10	−1.56379	−0.781895	+	0.623410i	$0.785747\pi$
$954$	−7.72765e8	−0.0288156
$955$	−8.36194e9	−0.310667
$956$	1.35761e10	0.502541
$957$	1.43807e10	0.530380
$958$	2.42544e10	0.891272
$959$	2.92359e10	1.07041
$960$	−1.68209e10	−0.613620
$961$	−1.48522e10	−0.539832
$962$	−9.93809e9	−0.359907
$963$	1.52105e10	0.548848
$964$	8.44092e9	0.303473
$965$	3.42688e9	0.122759
$966$	4.42571e10	1.57966
$967$	2.65844e10	0.945441	0.472720	−	0.881212i	$-0.343272\pi$
$967$	2.65844e10	0.945441	0.472720	+	0.881212i	$0.343272\pi$
$968$	1.94715e9	0.0689979
$969$	2.11392e10	0.746373
$970$	3.71500e10	1.30695
$971$	2.30612e9	0.0808380	0.0404190	−	0.999183i	$-0.487131\pi$
$971$	2.30612e9	0.0808380	0.0404190	+	0.999183i	$0.487131\pi$
$972$	−2.68859e10	−0.939059
$973$	−2.29087e10	−0.797270
$974$	4.83017e10	1.67497
$975$	−1.16716e10	−0.403287
$976$	2.67168e8	0.00919834
$977$	1.76151e10	0.604303	0.302152	−	0.953260i	$-0.402295\pi$
$977$	1.76151e10	0.604303	0.302152	+	0.953260i	$0.402295\pi$
$978$	3.65947e10	1.25093
$979$	−3.67355e10	−1.25126
$980$	5.06536e9	0.171917
$981$	5.59990e8	0.0189382
$982$	−3.64003e10	−1.22663
$983$	−2.51186e10	−0.843448	−0.421724	−	0.906724i	$-0.638575\pi$
$983$	−2.51186e10	−0.843448	−0.421724	+	0.906724i	$0.638575\pi$
$984$	−1.58297e9	−0.0529652
$985$	3.14198e10	1.04755
$986$	−2.13464e10	−0.709179
$987$	−1.39008e10	−0.460183
$988$	5.74087e10	1.89377
$989$	3.52157e10	1.15758
$990$	2.40691e10	0.788383
$991$	−6.00729e9	−0.196074	−0.0980372	−	0.995183i	$-0.531256\pi$
$991$	−6.00729e9	−0.196074	−0.0980372	+	0.995183i	$0.531256\pi$
$992$	2.98039e10	0.969352
$993$	3.08361e9	0.0999396
$994$	−2.88524e10	−0.931815
$995$	4.13009e9	0.132916
$996$	1.61556e10	0.518103
$997$	2.55789e10	0.817426	0.408713	−	0.912663i	$-0.365978\pi$
$997$	2.55789e10	0.817426	0.408713	+	0.912663i	$0.365978\pi$
$998$	−5.14147e10	−1.63731
$999$	5.48389e9	0.174024

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.a.a.1.10	✓	10
3.2	odd	2		333.8.a.c.1.1		10
4.3	odd	2		592.8.a.f.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.a.a.1.10	✓	10	1.1	even	1	trivial
333.8.a.c.1.1		10	3.2	odd	2
592.8.a.f.1.7		10	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.a (trivial)

\(f(q)\)	\(=\)	\(q+16.2140 q^{2} -32.8739 q^{3} +134.894 q^{4} -220.871 q^{5} -533.017 q^{6} -808.413 q^{7} +111.778 q^{8} -1106.31 q^{9} +O(q^{10})\)	\(q+16.2140 q^{2} -32.8739 q^{3} +134.894 q^{4} -220.871 q^{5} -533.017 q^{6} -808.413 q^{7} +111.778 q^{8} -1106.31 q^{9} -3581.21 q^{10} +6075.11 q^{11} -4434.48 q^{12} -12100.6 q^{13} -13107.6 q^{14} +7260.90 q^{15} -15454.1 q^{16} +18283.6 q^{17} -17937.7 q^{18} -35170.4 q^{19} -29794.2 q^{20} +26575.7 q^{21} +98501.9 q^{22} +102709. q^{23} -3674.57 q^{24} -29340.8 q^{25} -196199. q^{26} +108264. q^{27} -109050. q^{28} -72006.9 q^{29} +117728. q^{30} -112519. q^{31} -264880. q^{32} -199712. q^{33} +296450. q^{34} +178555. q^{35} -149234. q^{36} +50653.0 q^{37} -570253. q^{38} +397794. q^{39} -24688.5 q^{40} +430792. q^{41} +430898. q^{42} +342869. q^{43} +819496. q^{44} +244352. q^{45} +1.66533e6 q^{46} -523067. q^{47} +508034. q^{48} -170011. q^{49} -475732. q^{50} -601051. q^{51} -1.63230e6 q^{52} +43080.5 q^{53} +1.75539e6 q^{54} -1.34182e6 q^{55} -90362.7 q^{56} +1.15619e6 q^{57} -1.16752e6 q^{58} -2.41890e6 q^{59} +979451. q^{60} -17287.9 q^{61} -1.82438e6 q^{62} +894355. q^{63} -2.31664e6 q^{64} +2.67268e6 q^{65} -3.23814e6 q^{66} -3.97944e6 q^{67} +2.46634e6 q^{68} -3.37645e6 q^{69} +2.89510e6 q^{70} +2.20119e6 q^{71} -123661. q^{72} -2.86846e6 q^{73} +821288. q^{74} +964546. q^{75} -4.74428e6 q^{76} -4.91120e6 q^{77} +6.44983e6 q^{78} -2.56218e6 q^{79} +3.41336e6 q^{80} -1.13955e6 q^{81} +6.98486e6 q^{82} -3.64318e6 q^{83} +3.58489e6 q^{84} -4.03831e6 q^{85} +5.55927e6 q^{86} +2.36715e6 q^{87} +679063. q^{88} -6.04689e6 q^{89} +3.96192e6 q^{90} +9.78229e6 q^{91} +1.38548e7 q^{92} +3.69892e6 q^{93} -8.48100e6 q^{94} +7.76814e6 q^{95} +8.70762e6 q^{96} -1.03736e7 q^{97} -2.75657e6 q^{98} -6.72095e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9}+O(q^{10}) \) 10 * q - 24 * q^2 - 95 * q^3 + 602 * q^4 - 624 * q^5 - 777 * q^6 - 501 * q^7 - 3810 * q^8 + 6181 * q^9	\( 10 q - 24 q^{2} - 95 q^{3} + 602 q^{4} - 624 q^{5} - 777 q^{6} - 501 q^{7} - 3810 q^{8} + 6181 q^{9} + 8595 q^{10} - 8325 q^{11} - 19645 q^{12} - 17108 q^{13} - 65418 q^{14} - 55756 q^{15} - 56998 q^{16} - 72924 q^{17} - 156165 q^{18} - 47786 q^{19} - 226209 q^{20} - 65313 q^{21} - 138973 q^{22} - 148086 q^{23} - 68031 q^{24} + 108736 q^{25} - 60237 q^{26} - 87329 q^{27} + 219974 q^{28} - 164154 q^{29} + 78864 q^{30} - 189560 q^{31} - 30114 q^{32} - 179737 q^{33} + 532624 q^{34} - 705156 q^{35} + 1923693 q^{36} + 506530 q^{37} + 1256412 q^{38} + 1322800 q^{39} + 2936777 q^{40} + 814263 q^{41} + 3415826 q^{42} - 590572 q^{43} + 610311 q^{44} - 250574 q^{45} + 2903897 q^{46} - 1534185 q^{47} + 2082419 q^{48} - 214337 q^{49} - 2313525 q^{50} + 722138 q^{51} + 149159 q^{52} - 2518209 q^{53} + 1095990 q^{54} - 3482468 q^{55} - 3645834 q^{56} - 9225638 q^{57} + 5626023 q^{58} - 5894748 q^{59} - 1289832 q^{60} - 2569480 q^{61} - 863697 q^{62} - 2836574 q^{63} - 4093742 q^{64} - 6774600 q^{65} + 17251556 q^{66} - 6983232 q^{67} - 8114412 q^{68} - 11557564 q^{69} + 8982748 q^{70} - 5013963 q^{71} - 7567137 q^{72} - 11678449 q^{73} - 1215672 q^{74} - 6586901 q^{75} + 4912252 q^{76} + 1333113 q^{77} - 7352119 q^{78} - 3853378 q^{79} - 11975661 q^{80} - 7381718 q^{81} + 564093 q^{82} - 15677895 q^{83} + 4781738 q^{84} + 11909320 q^{85} + 34274010 q^{86} - 12611710 q^{87} + 14448317 q^{88} - 25836 q^{89} + 64591590 q^{90} + 12335744 q^{91} + 7579845 q^{92} + 4592632 q^{93} + 26251718 q^{94} + 11723664 q^{95} + 42299113 q^{96} + 4648834 q^{97} + 15230184 q^{98} - 16904018 q^{99}+O(q^{100}) \) 10 * q - 24 * q^2 - 95 * q^3 + 602 * q^4 - 624 * q^5 - 777 * q^6 - 501 * q^7 - 3810 * q^8 + 6181 * q^9 + 8595 * q^10 - 8325 * q^11 - 19645 * q^12 - 17108 * q^13 - 65418 * q^14 - 55756 * q^15 - 56998 * q^16 - 72924 * q^17 - 156165 * q^18 - 47786 * q^19 - 226209 * q^20 - 65313 * q^21 - 138973 * q^22 - 148086 * q^23 - 68031 * q^24 + 108736 * q^25 - 60237 * q^26 - 87329 * q^27 + 219974 * q^28 - 164154 * q^29 + 78864 * q^30 - 189560 * q^31 - 30114 * q^32 - 179737 * q^33 + 532624 * q^34 - 705156 * q^35 + 1923693 * q^36 + 506530 * q^37 + 1256412 * q^38 + 1322800 * q^39 + 2936777 * q^40 + 814263 * q^41 + 3415826 * q^42 - 590572 * q^43 + 610311 * q^44 - 250574 * q^45 + 2903897 * q^46 - 1534185 * q^47 + 2082419 * q^48 - 214337 * q^49 - 2313525 * q^50 + 722138 * q^51 + 149159 * q^52 - 2518209 * q^53 + 1095990 * q^54 - 3482468 * q^55 - 3645834 * q^56 - 9225638 * q^57 + 5626023 * q^58 - 5894748 * q^59 - 1289832 * q^60 - 2569480 * q^61 - 863697 * q^62 - 2836574 * q^63 - 4093742 * q^64 - 6774600 * q^65 + 17251556 * q^66 - 6983232 * q^67 - 8114412 * q^68 - 11557564 * q^69 + 8982748 * q^70 - 5013963 * q^71 - 7567137 * q^72 - 11678449 * q^73 - 1215672 * q^74 - 6586901 * q^75 + 4912252 * q^76 + 1333113 * q^77 - 7352119 * q^78 - 3853378 * q^79 - 11975661 * q^80 - 7381718 * q^81 + 564093 * q^82 - 15677895 * q^83 + 4781738 * q^84 + 11909320 * q^85 + 34274010 * q^86 - 12611710 * q^87 + 14448317 * q^88 - 25836 * q^89 + 64591590 * q^90 + 12335744 * q^91 + 7579845 * q^92 + 4592632 * q^93 + 26251718 * q^94 + 11723664 * q^95 + 42299113 * q^96 + 4648834 * q^97 + 15230184 * q^98 - 16904018 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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