LMFDB - Embedded newform 105.10.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,10,Mod(1,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("105.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	105.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:	$54.0787627972$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 1462x^{2} + 568x + 469504 $ x^4 - x^3 - 1462x^2 + 568x + 469504
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-21.7320$ of defining polynomial
Character	$\chi$	$=$	105.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+17.7320 q^{2} +81.0000 q^{3} -197.578 q^{4} +625.000 q^{5} +1436.29 q^{6} -2401.00 q^{7} -12582.2 q^{8} +6561.00 q^{9} +11082.5 q^{10} -11869.9 q^{11} -16003.8 q^{12} +175503. q^{13} -42574.4 q^{14} +50625.0 q^{15} -121947. q^{16} -581422. q^{17} +116339. q^{18} -38838.5 q^{19} -123486. q^{20} -194481. q^{21} -210477. q^{22} -1.55065e6 q^{23} -1.01916e6 q^{24} +390625. q^{25} +3.11201e6 q^{26} +531441. q^{27} +474385. q^{28} -6.49890e6 q^{29} +897680. q^{30} +3.23767e6 q^{31} +4.27973e6 q^{32} -961463. q^{33} -1.03098e7 q^{34} -1.50062e6 q^{35} -1.29631e6 q^{36} -1.88645e7 q^{37} -688682. q^{38} +1.42157e7 q^{39} -7.86388e6 q^{40} -1.94238e7 q^{41} -3.44853e6 q^{42} -2.00447e6 q^{43} +2.34523e6 q^{44} +4.10062e6 q^{45} -2.74960e7 q^{46} -3.63900e6 q^{47} -9.87771e6 q^{48} +5.76480e6 q^{49} +6.92654e6 q^{50} -4.70952e7 q^{51} -3.46755e7 q^{52} -6.43457e7 q^{53} +9.42349e6 q^{54} -7.41869e6 q^{55} +3.02099e7 q^{56} -3.14592e6 q^{57} -1.15238e8 q^{58} +1.26038e8 q^{59} -1.00024e7 q^{60} +1.56864e8 q^{61} +5.74102e7 q^{62} -1.57530e7 q^{63} +1.38325e8 q^{64} +1.09689e8 q^{65} -1.70486e7 q^{66} -2.27636e8 q^{67} +1.14876e8 q^{68} -1.25603e8 q^{69} -2.66090e7 q^{70} -3.55345e8 q^{71} -8.25518e7 q^{72} -1.59247e8 q^{73} -3.34504e8 q^{74} +3.16406e7 q^{75} +7.67363e6 q^{76} +2.84997e7 q^{77} +2.52073e8 q^{78} -1.49712e8 q^{79} -7.62169e7 q^{80} +4.30467e7 q^{81} -3.44421e8 q^{82} +1.83947e8 q^{83} +3.84252e7 q^{84} -3.63389e8 q^{85} -3.55432e7 q^{86} -5.26411e8 q^{87} +1.49350e8 q^{88} -4.22798e8 q^{89} +7.27121e7 q^{90} -4.21383e8 q^{91} +3.06374e8 q^{92} +2.62251e8 q^{93} -6.45266e7 q^{94} -2.42740e7 q^{95} +3.46658e8 q^{96} +7.23133e8 q^{97} +1.02221e8 q^{98} -7.78785e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 17 q^{2} + 324 q^{3} + 949 q^{4} + 2500 q^{5} - 1377 q^{6} - 9604 q^{7} - 20679 q^{8} + 26244 q^{9} - 10625 q^{10} + 16382 q^{11} + 76869 q^{12} - 84914 q^{13} + 40817 q^{14} + 202500 q^{15} - 829359 q^{16}+ \cdots + 107482302 q^{99}+O(q^{100}) $ 4 * q - 17 * q^2 + 324 * q^3 + 949 * q^4 + 2500 * q^5 - 1377 * q^6 - 9604 * q^7 - 20679 * q^8 + 26244 * q^9 - 10625 * q^10 + 16382 * q^11 + 76869 * q^12 - 84914 * q^13 + 40817 * q^14 + 202500 * q^15 - 829359 * q^16 - 451528 * q^17 - 111537 * q^18 - 1031478 * q^19 + 593125 * q^20 - 777924 * q^21 - 2609948 * q^22 - 5459068 * q^23 - 1674999 * q^24 + 1562500 * q^25 + 169794 * q^26 + 2125764 * q^27 - 2278549 * q^28 - 4867288 * q^29 - 860625 * q^30 + 1098642 * q^31 + 10125105 * q^32 + 1326942 * q^33 + 10466142 * q^34 - 6002500 * q^35 + 6226389 * q^36 + 2110068 * q^37 - 1633028 * q^38 - 6878034 * q^39 - 12924375 * q^40 + 1104700 * q^41 + 3306177 * q^42 - 15322648 * q^43 + 57398124 * q^44 + 16402500 * q^45 + 4904680 * q^46 - 5033968 * q^47 - 67178079 * q^48 + 23059204 * q^49 - 6640625 * q^50 - 36573768 * q^51 - 153789226 * q^52 - 149234422 * q^53 - 9034497 * q^54 + 10238750 * q^55 + 49650279 * q^56 - 83549718 * q^57 + 7850594 * q^58 - 141913876 * q^59 + 48043125 * q^60 + 235578792 * q^61 + 60170880 * q^62 - 63011844 * q^63 + 30064673 * q^64 - 53071250 * q^65 - 211405788 * q^66 - 401097064 * q^67 - 170870006 * q^68 - 442184508 * q^69 + 25510625 * q^70 - 126532750 * q^71 - 135674919 * q^72 - 653180926 * q^73 - 1130189382 * q^74 + 126562500 * q^75 + 7344404 * q^76 - 39333182 * q^77 + 13753314 * q^78 - 624551664 * q^79 - 518349375 * q^80 + 172186884 * q^81 + 193533606 * q^82 - 702347048 * q^83 - 184562469 * q^84 - 282205000 * q^85 - 2076482652 * q^86 - 394250328 * q^87 - 871546276 * q^88 - 1510406712 * q^89 - 69710625 * q^90 + 203878514 * q^91 - 1662743304 * q^92 + 88990002 * q^93 - 852748960 * q^94 - 644673750 * q^95 + 820133505 * q^96 - 717560562 * q^97 - 98001617 * q^98 + 107482302 * q^99

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 $

$2$	17.7320	0.783649	0.391824	−	0.920040i	$-0.371844\pi$
$2$	17.7320	0.783649	0.391824	+	0.920040i	$0.371844\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	−197.578	−0.385894
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	1436.29	0.452440
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−12582.2	−1.08605
$9$	6561.00	0.333333
$10$	11082.5	0.350458
$11$	−11869.9	−0.244445	−0.122222	−	0.992503i	$-0.539002\pi$
$11$	−11869.9	−0.244445	−0.122222	+	0.992503i	$0.539002\pi$
$12$	−16003.8	−0.222796
$13$	175503.	1.70427	0.852137	−	0.523319i	$-0.175306\pi$
$13$	175503.	1.70427	0.852137	+	0.523319i	$0.175306\pi$
$14$	−42574.4	−0.296191
$15$	50625.0	0.258199
$16$	−121947.	−0.465191
$17$	−581422.	−1.68839	−0.844193	−	0.536040i	$-0.819920\pi$
$17$	−581422.	−1.68839	−0.844193	+	0.536040i	$0.819920\pi$
$18$	116339.	0.261216
$19$	−38838.5	−0.0683709	−0.0341854	−	0.999416i	$-0.510884\pi$
$19$	−38838.5	−0.0683709	−0.0341854	+	0.999416i	$0.510884\pi$
$20$	−123486.	−0.172577
$21$	−194481.	−0.218218
$22$	−210477.	−0.191559
$23$	−1.55065e6	−1.15542	−0.577708	−	0.816244i	$-0.696053\pi$
$23$	−1.55065e6	−1.15542	−0.577708	+	0.816244i	$0.696053\pi$
$24$	−1.01916e6	−0.627034
$25$	390625.	0.200000
$26$	3.11201e6	1.33555
$27$	531441.	0.192450
$28$	474385.	0.145854
$29$	−6.49890e6	−1.70627	−0.853137	−	0.521687i	$-0.825303\pi$
$29$	−6.49890e6	−1.70627	−0.853137	+	0.521687i	$0.825303\pi$
$30$	897680.	0.202337
$31$	3.23767e6	0.629658	0.314829	−	0.949148i	$-0.398053\pi$
$31$	3.23767e6	0.629658	0.314829	+	0.949148i	$0.398053\pi$
$32$	4.27973e6	0.721508
$33$	−961463.	−0.141130
$34$	−1.03098e7	−1.32310
$35$	−1.50062e6	−0.169031
$36$	−1.29631e6	−0.128631
$37$	−1.88645e7	−1.65477	−0.827383	−	0.561638i	$-0.810171\pi$
$37$	−1.88645e7	−1.65477	−0.827383	+	0.561638i	$0.810171\pi$
$38$	−688682.	−0.0535787
$39$	1.42157e7	0.983963
$40$	−7.86388e6	−0.485698
$41$	−1.94238e7	−1.07351	−0.536755	−	0.843738i	$-0.680350\pi$
$41$	−1.94238e7	−1.07351	−0.536755	+	0.843738i	$0.680350\pi$
$42$	−3.44853e6	−0.171006
$43$	−2.00447e6	−0.0894113	−0.0447056	−	0.999000i	$-0.514235\pi$
$43$	−2.00447e6	−0.0894113	−0.0447056	+	0.999000i	$0.514235\pi$
$44$	2.34523e6	0.0943298
$45$	4.10062e6	0.149071
$46$	−2.74960e7	−0.905440
$47$	−3.63900e6	−0.108778	−0.0543891	−	0.998520i	$-0.517321\pi$
$47$	−3.63900e6	−0.108778	−0.0543891	+	0.998520i	$0.517321\pi$
$48$	−9.87771e6	−0.268578
$49$	5.76480e6	0.142857
$50$	6.92654e6	0.156730
$51$	−4.70952e7	−0.974790
$52$	−3.46755e7	−0.657670
$53$	−6.43457e7	−1.12015	−0.560077	−	0.828441i	$-0.689228\pi$
$53$	−6.43457e7	−1.12015	−0.560077	+	0.828441i	$0.689228\pi$
$54$	9.42349e6	0.150813
$55$	−7.41869e6	−0.109319
$56$	3.02099e7	0.410490
$57$	−3.14592e6	−0.0394739
$58$	−1.15238e8	−1.33712
$59$	1.26038e8	1.35415	0.677076	−	0.735913i	$-0.263247\pi$
$59$	1.26038e8	1.35415	0.677076	+	0.735913i	$0.263247\pi$
$60$	−1.00024e7	−0.0996375
$61$	1.56864e8	1.45057	0.725286	−	0.688448i	$-0.241708\pi$
$61$	1.56864e8	1.45057	0.725286	+	0.688448i	$0.241708\pi$
$62$	5.74102e7	0.493431
$63$	−1.57530e7	−0.125988
$64$	1.38325e8	1.03060
$65$	1.09689e8	0.762175
$66$	−1.70486e7	−0.110596
$67$	−2.27636e8	−1.38008	−0.690041	−	0.723771i	$-0.742407\pi$
$67$	−2.27636e8	−1.38008	−0.690041	+	0.723771i	$0.742407\pi$
$68$	1.14876e8	0.651539
$69$	−1.25603e8	−0.667079
$70$	−2.66090e7	−0.132461
$71$	−3.55345e8	−1.65954	−0.829769	−	0.558106i	$-0.811528\pi$
$71$	−3.55345e8	−1.65954	−0.829769	+	0.558106i	$0.811528\pi$
$72$	−8.25518e7	−0.362018
$73$	−1.59247e8	−0.656326	−0.328163	−	0.944621i	$-0.606429\pi$
$73$	−1.59247e8	−0.656326	−0.328163	+	0.944621i	$0.606429\pi$
$74$	−3.34504e8	−1.29676
$75$	3.16406e7	0.115470
$76$	7.67363e6	0.0263839
$77$	2.84997e7	0.0923913
$78$	2.52073e8	0.771082
$79$	−1.49712e8	−0.432449	−0.216225	−	0.976344i	$-0.569374\pi$
$79$	−1.49712e8	−0.432449	−0.216225	+	0.976344i	$0.569374\pi$
$80$	−7.62169e7	−0.208040
$81$	4.30467e7	0.111111
$82$	−3.44421e8	−0.841254
$83$	1.83947e8	0.425444	0.212722	−	0.977113i	$-0.431767\pi$
$83$	1.83947e8	0.425444	0.212722	+	0.977113i	$0.431767\pi$
$84$	3.84252e7	0.0842091
$85$	−3.63389e8	−0.755069
$86$	−3.55432e7	−0.0700670
$87$	−5.26411e8	−0.985118
$88$	1.49350e8	0.265480
$89$	−4.22798e8	−0.714295	−0.357148	−	0.934048i	$-0.616251\pi$
$89$	−4.22798e8	−0.714295	−0.357148	+	0.934048i	$0.616251\pi$
$90$	7.27121e7	0.116819
$91$	−4.21383e8	−0.644155
$92$	3.06374e8	0.445868
$93$	2.62251e8	0.363533
$94$	−6.45266e7	−0.0852439
$95$	−2.42740e7	−0.0305764
$96$	3.46658e8	0.416563
$97$	7.23133e8	0.829364	0.414682	−	0.909966i	$-0.363893\pi$
$97$	7.23133e8	0.829364	0.414682	+	0.909966i	$0.363893\pi$
$98$	1.02221e8	0.111950
$99$	−7.78785e7	−0.0814815
$100$	−7.71789e7	−0.0771789
$101$	−1.43279e8	−0.137005	−0.0685024	−	0.997651i	$-0.521822\pi$
$101$	−1.43279e8	−0.137005	−0.0685024	+	0.997651i	$0.521822\pi$
$102$	−8.35090e8	−0.763893
$103$	1.03828e9	0.908963	0.454482	−	0.890756i	$-0.349825\pi$
$103$	1.03828e9	0.908963	0.454482	+	0.890756i	$0.349825\pi$
$104$	−2.20821e9	−1.85093
$105$	−1.21551e8	−0.0975900
$106$	−1.14097e9	−0.877808
$107$	3.54295e8	0.261300	0.130650	−	0.991429i	$-0.458294\pi$
$107$	3.54295e8	0.261300	0.130650	+	0.991429i	$0.458294\pi$
$108$	−1.05001e8	−0.0742654
$109$	−3.28928e8	−0.223193	−0.111597	−	0.993754i	$-0.535596\pi$
$109$	−3.28928e8	−0.223193	−0.111597	+	0.993754i	$0.535596\pi$
$110$	−1.31548e8	−0.0856676
$111$	−1.52802e9	−0.955380
$112$	2.92795e8	0.175826
$113$	1.18479e8	0.0683581	0.0341790	−	0.999416i	$-0.489118\pi$
$113$	1.18479e8	0.0683581	0.0341790	+	0.999416i	$0.489118\pi$
$114$	−5.57832e7	−0.0309337
$115$	−9.69155e8	−0.516718
$116$	1.28404e9	0.658442
$117$	1.15148e9	0.568091
$118$	2.23490e9	1.06118
$119$	1.39600e9	0.638150
$120$	−6.36974e8	−0.280418
$121$	−2.21705e9	−0.940247
$122$	2.78151e9	1.13674
$123$	−1.57332e9	−0.619791
$124$	−6.39692e8	−0.242982
$125$	2.44141e8	0.0894427
$126$	−2.79331e8	−0.0987305
$127$	−2.89100e9	−0.986123	−0.493062	−	0.869994i	$-0.664122\pi$
$127$	−2.89100e9	−0.986123	−0.493062	+	0.869994i	$0.664122\pi$
$128$	2.61548e8	0.0861207
$129$	−1.62362e8	−0.0516216
$130$	1.94501e9	0.597277
$131$	1.72561e8	0.0511944	0.0255972	−	0.999672i	$-0.491851\pi$
$131$	1.72561e8	0.0511944	0.0255972	+	0.999672i	$0.491851\pi$
$132$	1.89964e8	0.0544613
$133$	9.32512e7	0.0258418
$134$	−4.03643e9	−1.08150
$135$	3.32151e8	0.0860663
$136$	7.31557e9	1.83368
$137$	3.53468e9	0.857251	0.428625	−	0.903482i	$-0.358998\pi$
$137$	3.53468e9	0.857251	0.428625	+	0.903482i	$0.358998\pi$
$138$	−2.22718e9	−0.522756
$139$	2.53144e9	0.575177	0.287588	−	0.957754i	$-0.407147\pi$
$139$	2.53144e9	0.575177	0.287588	+	0.957754i	$0.407147\pi$
$140$	2.96490e8	0.0652281
$141$	−2.94759e8	−0.0628031
$142$	−6.30096e9	−1.30050
$143$	−2.08320e9	−0.416600
$144$	−8.00095e8	−0.155064
$145$	−4.06181e9	−0.763069
$146$	−2.82377e9	−0.514329
$147$	4.66949e8	0.0824786
$148$	3.72720e9	0.638565
$149$	1.16796e10	1.94129	0.970645	−	0.240518i	$-0.0773172\pi$
$149$	1.16796e10	1.94129	0.970645	+	0.240518i	$0.0773172\pi$
$150$	5.61050e8	0.0904880
$151$	−1.04789e10	−1.64029	−0.820144	−	0.572157i	$-0.806107\pi$
$151$	−1.04789e10	−1.64029	−0.820144	+	0.572157i	$0.806107\pi$
$152$	4.88674e8	0.0742545
$153$	−3.81471e9	−0.562795
$154$	5.05354e8	0.0724024
$155$	2.02354e9	0.281592
$156$	−2.80872e9	−0.379706
$157$	1.26126e10	1.65675	0.828375	−	0.560174i	$-0.189266\pi$
$157$	1.26126e10	1.65675	0.828375	+	0.560174i	$0.189266\pi$
$158$	−2.65469e9	−0.338889
$159$	−5.21200e9	−0.646721
$160$	2.67483e9	0.322668
$161$	3.72311e9	0.436706
$162$	7.63302e8	0.0870721
$163$	1.42138e10	1.57713	0.788564	−	0.614952i	$-0.210825\pi$
$163$	1.42138e10	1.57713	0.788564	+	0.614952i	$0.210825\pi$
$164$	3.83770e9	0.414261
$165$	−6.00914e8	−0.0631153
$166$	3.26175e9	0.333399
$167$	1.13747e10	1.13166	0.565829	−	0.824523i	$-0.308556\pi$
$167$	1.13747e10	1.13166	0.565829	+	0.824523i	$0.308556\pi$
$168$	2.44700e9	0.236997
$169$	2.01968e10	1.90455
$170$	−6.44360e9	−0.591709
$171$	−2.54819e8	−0.0227903
$172$	3.96040e8	0.0345033
$173$	1.28185e10	1.08800	0.544000	−	0.839085i	$-0.316909\pi$
$173$	1.28185e10	1.08800	0.544000	+	0.839085i	$0.316909\pi$
$174$	−9.33429e9	−0.771987
$175$	−9.37891e8	−0.0755929
$176$	1.44750e9	0.113713
$177$	1.02091e10	0.781820
$178$	−7.49703e9	−0.559757
$179$	−1.99262e10	−1.45073	−0.725363	−	0.688366i	$-0.758328\pi$
$179$	−1.99262e10	−1.45073	−0.725363	+	0.688366i	$0.758328\pi$
$180$	−8.10193e8	−0.0575257
$181$	3.73456e9	0.258634	0.129317	−	0.991603i	$-0.458721\pi$
$181$	3.73456e9	0.258634	0.129317	+	0.991603i	$0.458721\pi$
$182$	−7.47194e9	−0.504791
$183$	1.27060e10	0.837488
$184$	1.95106e10	1.25484
$185$	−1.17903e10	−0.740034
$186$	4.65023e9	0.284883
$187$	6.90143e9	0.412717
$188$	7.18986e8	0.0419769
$189$	−1.27599e9	−0.0727393
$190$	−4.30426e8	−0.0239611
$191$	1.77074e10	0.962733	0.481366	−	0.876520i	$-0.340141\pi$
$191$	1.77074e10	0.962733	0.481366	+	0.876520i	$0.340141\pi$
$192$	1.12043e10	0.595017
$193$	2.72962e10	1.41610	0.708051	−	0.706161i	$-0.249575\pi$
$193$	2.72962e10	1.41610	0.708051	+	0.706161i	$0.249575\pi$
$194$	1.28226e10	0.649931
$195$	8.88484e9	0.440042
$196$	−1.13900e9	−0.0551278
$197$	−2.38043e10	−1.12605	−0.563024	−	0.826441i	$-0.690362\pi$
$197$	−2.38043e10	−1.12605	−0.563024	+	0.826441i	$0.690362\pi$
$198$	−1.38094e9	−0.0638529
$199$	−1.02232e10	−0.462111	−0.231056	−	0.972941i	$-0.574218\pi$
$199$	−1.02232e10	−0.462111	−0.231056	+	0.972941i	$0.574218\pi$
$200$	−4.91492e9	−0.217211
$201$	−1.84385e10	−0.796790
$202$	−2.54061e9	−0.107364
$203$	1.56039e10	0.644911
$204$	9.30498e9	0.376166
$205$	−1.21398e10	−0.480088
$206$	1.84107e10	0.712308
$207$	−1.01738e10	−0.385138
$208$	−2.14021e10	−0.792813
$209$	4.61009e8	0.0167129
$210$	−2.15533e9	−0.0764763
$211$	1.71955e9	0.0597233	0.0298617	−	0.999554i	$-0.490493\pi$
$211$	1.71955e9	0.0597233	0.0298617	+	0.999554i	$0.490493\pi$
$212$	1.27133e10	0.432261
$213$	−2.87829e10	−0.958135
$214$	6.28235e9	0.204767
$215$	−1.25280e9	−0.0399859
$216$	−6.68670e9	−0.209011
$217$	−7.77365e9	−0.237989
$218$	−5.83253e9	−0.174905
$219$	−1.28990e10	−0.378930
$220$	1.46577e9	0.0421856
$221$	−1.02041e11	−2.87747
$222$	−2.70948e10	−0.748682
$223$	−2.29518e10	−0.621505	−0.310753	−	0.950491i	$-0.600581\pi$
$223$	−2.29518e10	−0.621505	−0.310753	+	0.950491i	$0.600581\pi$
$224$	−1.02756e10	−0.272704
$225$	2.56289e9	0.0666667
$226$	2.10087e9	0.0535687
$227$	−3.03913e10	−0.759684	−0.379842	−	0.925051i	$-0.624022\pi$
$227$	−3.03913e10	−0.759684	−0.379842	+	0.925051i	$0.624022\pi$
$228$	6.21564e8	0.0152328
$229$	3.73975e10	0.898634	0.449317	−	0.893372i	$-0.351667\pi$
$229$	3.73975e10	0.898634	0.449317	+	0.893372i	$0.351667\pi$
$230$	−1.71850e10	−0.404925
$231$	2.30847e9	0.0533422
$232$	8.17705e10	1.85311
$233$	−7.70456e10	−1.71256	−0.856281	−	0.516510i	$-0.827231\pi$
$233$	−7.70456e10	−1.71256	−0.856281	+	0.516510i	$0.827231\pi$
$234$	2.04179e10	0.445184
$235$	−2.27437e9	−0.0486471
$236$	−2.49023e10	−0.522560
$237$	−1.21267e10	−0.249675
$238$	2.47537e10	0.500085
$239$	2.31989e10	0.459914	0.229957	−	0.973201i	$-0.426141\pi$
$239$	2.31989e10	0.459914	0.229957	+	0.973201i	$0.426141\pi$
$240$	−6.17357e9	−0.120112
$241$	5.44449e10	1.03963	0.519817	−	0.854278i	$-0.326000\pi$
$241$	5.44449e10	1.03963	0.519817	+	0.854278i	$0.326000\pi$
$242$	−3.93127e10	−0.736823
$243$	3.48678e9	0.0641500
$244$	−3.09929e10	−0.559768
$245$	3.60300e9	0.0638877
$246$	−2.78981e10	−0.485698
$247$	−6.81627e9	−0.116523
$248$	−4.07370e10	−0.683843
$249$	1.48997e10	0.245630
$250$	4.32909e9	0.0700917
$251$	−1.03598e11	−1.64748	−0.823741	−	0.566966i	$-0.808117\pi$
$251$	−1.03598e11	−1.64748	−0.823741	+	0.566966i	$0.808117\pi$
$252$	3.11244e9	0.0486181
$253$	1.84061e10	0.282435
$254$	−5.12630e10	−0.772774
$255$	−2.94345e10	−0.435939
$256$	−6.61845e10	−0.963112
$257$	−4.69338e10	−0.671099	−0.335550	−	0.942023i	$-0.608922\pi$
$257$	−4.69338e10	−0.671099	−0.335550	+	0.942023i	$0.608922\pi$
$258$	−2.87900e9	−0.0404532
$259$	4.52936e10	0.625443
$260$	−2.16722e10	−0.294119
$261$	−4.26393e10	−0.568758
$262$	3.05985e9	0.0401184
$263$	6.03960e10	0.778409	0.389204	−	0.921151i	$-0.372750\pi$
$263$	6.03960e10	0.778409	0.389204	+	0.921151i	$0.372750\pi$
$264$	1.20973e10	0.153275
$265$	−4.02160e10	−0.500948
$266$	1.65353e9	0.0202509
$267$	−3.42466e10	−0.412399
$268$	4.49759e10	0.532566
$269$	3.92688e10	0.457259	0.228630	−	0.973513i	$-0.426576\pi$
$269$	3.92688e10	0.457259	0.228630	+	0.973513i	$0.426576\pi$
$270$	5.88968e9	0.0674458
$271$	4.64368e10	0.522999	0.261500	−	0.965204i	$-0.415783\pi$
$271$	4.64368e10	0.522999	0.261500	+	0.965204i	$0.415783\pi$
$272$	7.09028e10	0.785422
$273$	−3.41320e10	−0.371903
$274$	6.26768e10	0.671784
$275$	−4.63668e9	−0.0488889
$276$	2.48163e10	0.257422
$277$	−4.14668e10	−0.423196	−0.211598	−	0.977357i	$-0.567867\pi$
$277$	−4.14668e10	−0.423196	−0.211598	+	0.977357i	$0.567867\pi$
$278$	4.48874e10	0.450736
$279$	2.12424e10	0.209886
$280$	1.88812e10	0.183577
$281$	−8.02095e10	−0.767445	−0.383723	−	0.923448i	$-0.625358\pi$
$281$	−8.02095e10	−0.767445	−0.383723	+	0.923448i	$0.625358\pi$
$282$	−5.22665e9	−0.0492156
$283$	−2.02123e10	−0.187317	−0.0936585	−	0.995604i	$-0.529856\pi$
$283$	−2.02123e10	−0.187317	−0.0936585	+	0.995604i	$0.529856\pi$
$284$	7.02083e10	0.640407
$285$	−1.96620e9	−0.0176533
$286$	−3.69393e10	−0.326469
$287$	4.66364e10	0.405748
$288$	2.80793e10	0.240503
$289$	2.19464e11	1.85065
$290$	−7.20239e10	−0.597978
$291$	5.85738e10	0.478834
$292$	3.14638e10	0.253272
$293$	−1.90018e11	−1.50623	−0.753115	−	0.657889i	$-0.771450\pi$
$293$	−1.90018e11	−1.50623	−0.753115	+	0.657889i	$0.771450\pi$
$294$	8.27991e9	0.0646343
$295$	7.87737e10	0.605595
$296$	2.37356e11	1.79717
$297$	−6.30816e9	−0.0470434
$298$	2.07102e11	1.52129
$299$	−2.72144e11	−1.96914
$300$	−6.25149e9	−0.0445592
$301$	4.81274e9	0.0337943
$302$	−1.85812e11	−1.28541
$303$	−1.16056e10	−0.0790997
$304$	4.73624e9	0.0318055
$305$	9.80401e10	0.648716
$306$	−6.76423e10	−0.441034
$307$	−2.54830e11	−1.63730	−0.818651	−	0.574292i	$-0.805278\pi$
$307$	−2.54830e11	−1.63730	−0.818651	+	0.574292i	$0.805278\pi$
$308$	−5.63090e9	−0.0356533
$309$	8.41006e10	0.524790
$310$	3.58814e10	0.220669
$311$	−3.61990e10	−0.219419	−0.109710	−	0.993964i	$-0.534992\pi$
$311$	−3.61990e10	−0.219419	−0.109710	+	0.993964i	$0.534992\pi$
$312$	−1.78865e11	−1.06864
$313$	−6.67555e10	−0.393131	−0.196566	−	0.980491i	$-0.562979\pi$
$313$	−6.67555e10	−0.393131	−0.196566	+	0.980491i	$0.562979\pi$
$314$	2.23646e11	1.29831
$315$	−9.84560e9	−0.0563436
$316$	2.95798e10	0.166880
$317$	1.49501e11	0.831529	0.415765	−	0.909472i	$-0.363514\pi$
$317$	1.49501e11	0.831529	0.415765	+	0.909472i	$0.363514\pi$
$318$	−9.24189e10	−0.506802
$319$	7.71414e10	0.417089
$320$	8.64530e10	0.460898
$321$	2.86979e10	0.150861
$322$	6.60180e10	0.342224
$323$	2.25816e10	0.115436
$324$	−8.50508e9	−0.0428772
$325$	6.85559e10	0.340855
$326$	2.52039e11	1.23592
$327$	−2.66431e10	−0.128861
$328$	2.44394e11	1.16589
$329$	8.73724e9	0.0411143
$330$	−1.06554e10	−0.0494602
$331$	−3.03930e11	−1.39171	−0.695854	−	0.718183i	$-0.744974\pi$
$331$	−3.03930e11	−1.39171	−0.695854	+	0.718183i	$0.744974\pi$
$332$	−3.63440e10	−0.164176
$333$	−1.23770e11	−0.551589
$334$	2.01695e11	0.886822
$335$	−1.42273e11	−0.617191
$336$	2.37164e10	0.101513
$337$	1.68831e11	0.713046	0.356523	−	0.934286i	$-0.383962\pi$
$337$	1.68831e11	0.713046	0.356523	+	0.934286i	$0.383962\pi$
$338$	3.58129e11	1.49250
$339$	9.59683e9	0.0394665
$340$	7.17976e10	0.291377
$341$	−3.84309e10	−0.153917
$342$	−4.51844e9	−0.0178596
$343$	−1.38413e10	−0.0539949
$344$	2.52207e10	0.0971055
$345$	−7.85016e10	−0.298327
$346$	2.27297e11	0.852611
$347$	−4.83989e11	−1.79206	−0.896030	−	0.443993i	$-0.853562\pi$
$347$	−4.83989e11	−1.79206	−0.896030	+	0.443993i	$0.853562\pi$
$348$	1.04007e11	0.380151
$349$	−1.00182e11	−0.361474	−0.180737	−	0.983531i	$-0.557848\pi$
$349$	−1.00182e11	−0.361474	−0.180737	+	0.983531i	$0.557848\pi$
$350$	−1.66306e10	−0.0592383
$351$	9.32695e10	0.327988
$352$	−5.08000e10	−0.176369
$353$	2.45377e11	0.841100	0.420550	−	0.907269i	$-0.361837\pi$
$353$	2.45377e11	0.841100	0.420550	+	0.907269i	$0.361837\pi$
$354$	1.81027e11	0.612672
$355$	−2.22090e11	−0.742168
$356$	8.35355e10	0.275643
$357$	1.13076e11	0.368436
$358$	−3.53330e11	−1.13686
$359$	2.99212e11	0.950723	0.475362	−	0.879791i	$-0.342317\pi$
$359$	2.99212e11	0.950723	0.475362	+	0.879791i	$0.342317\pi$
$360$	−5.15949e10	−0.161899
$361$	−3.21179e11	−0.995325
$362$	6.62211e10	0.202679
$363$	−1.79581e11	−0.542852
$364$	8.32559e10	0.248576
$365$	−9.95296e10	−0.293518
$366$	2.25302e11	0.656297
$367$	−3.24328e11	−0.933228	−0.466614	−	0.884461i	$-0.654526\pi$
$367$	−3.24328e11	−0.933228	−0.466614	+	0.884461i	$0.654526\pi$
$368$	1.89097e11	0.537489
$369$	−1.27439e11	−0.357836
$370$	−2.09065e11	−0.579927
$371$	1.54494e11	0.423378
$372$	−5.18151e10	−0.140286
$373$	5.38766e11	1.44115	0.720577	−	0.693375i	$-0.243877\pi$
$373$	5.38766e11	1.44115	0.720577	+	0.693375i	$0.243877\pi$
$374$	1.22376e11	0.323425
$375$	1.97754e10	0.0516398
$376$	4.57866e10	0.118139
$377$	−1.14058e12	−2.90796
$378$	−2.26258e10	−0.0570021
$379$	−4.13899e11	−1.03043	−0.515214	−	0.857061i	$-0.672288\pi$
$379$	−4.13899e11	−1.03043	−0.515214	+	0.857061i	$0.672288\pi$
$380$	4.79602e9	0.0117993
$381$	−2.34171e11	−0.569338
$382$	3.13988e11	0.754444
$383$	6.72205e11	1.59627	0.798137	−	0.602476i	$-0.205819\pi$
$383$	6.72205e11	1.59627	0.798137	+	0.602476i	$0.205819\pi$
$384$	2.11854e10	0.0497218
$385$	1.78123e10	0.0413187
$386$	4.84015e11	1.10973
$387$	−1.31514e10	−0.0298038
$388$	−1.42875e11	−0.320047
$389$	1.39495e11	0.308877	0.154439	−	0.988002i	$-0.450643\pi$
$389$	1.39495e11	0.308877	0.154439	+	0.988002i	$0.450643\pi$
$390$	1.57546e11	0.344838
$391$	9.01582e11	1.95079
$392$	−7.25339e10	−0.155151
$393$	1.39775e10	0.0295571
$394$	−4.22096e11	−0.882426
$395$	−9.35701e10	−0.193397
$396$	1.53871e10	0.0314433
$397$	−8.19036e11	−1.65480	−0.827400	−	0.561613i	$-0.810181\pi$
$397$	−8.19036e11	−1.65480	−0.827400	+	0.561613i	$0.810181\pi$
$398$	−1.81277e11	−0.362133
$399$	7.55335e9	0.0149197
$400$	−4.76356e10	−0.0930382
$401$	−4.81162e11	−0.929270	−0.464635	−	0.885502i	$-0.653814\pi$
$401$	−4.81162e11	−0.929270	−0.464635	+	0.885502i	$0.653814\pi$
$402$	−3.26951e11	−0.624404
$403$	5.68221e11	1.07311
$404$	2.83087e10	0.0528694
$405$	2.69042e10	0.0496904
$406$	2.76687e11	0.505384
$407$	2.23919e11	0.404499
$408$	5.92561e11	1.05868
$409$	1.13116e11	0.199879	0.0999397	−	0.994993i	$-0.468135\pi$
$409$	1.13116e11	0.199879	0.0999397	+	0.994993i	$0.468135\pi$
$410$	−2.15263e11	−0.376220
$411$	2.86309e11	0.494934
$412$	−2.05141e11	−0.350764
$413$	−3.02617e11	−0.511821
$414$	−1.80401e11	−0.301813
$415$	1.14967e11	0.190264
$416$	7.51105e11	1.22965
$417$	2.05047e11	0.332078
$418$	8.17459e9	0.0130970
$419$	3.24356e11	0.514114	0.257057	−	0.966396i	$-0.417247\pi$
$419$	3.24356e11	0.514114	0.257057	+	0.966396i	$0.417247\pi$
$420$	2.40157e10	0.0376594
$421$	1.72118e11	0.267028	0.133514	−	0.991047i	$-0.457374\pi$
$421$	1.72118e11	0.267028	0.133514	+	0.991047i	$0.457374\pi$
$422$	3.04910e10	0.0468021
$423$	−2.38755e10	−0.0362594
$424$	8.09610e11	1.21655
$425$	−2.27118e11	−0.337677
$426$	−5.10377e11	−0.750842
$427$	−3.76631e11	−0.548265
$428$	−7.00010e10	−0.100834
$429$	−1.68740e11	−0.240524
$430$	−2.22145e10	−0.0313349
$431$	1.01287e12	1.41385	0.706927	−	0.707286i	$-0.250081\pi$
$431$	1.01287e12	1.41385	0.706927	+	0.707286i	$0.250081\pi$
$432$	−6.48077e10	−0.0895261
$433$	−8.94338e11	−1.22266	−0.611331	−	0.791375i	$-0.709365\pi$
$433$	−8.94338e11	−1.22266	−0.611331	+	0.791375i	$0.709365\pi$
$434$	−1.37842e11	−0.186499
$435$	−3.29007e11	−0.440558
$436$	6.49888e10	0.0861290
$437$	6.02248e10	0.0789967
$438$	−2.28725e11	−0.296948
$439$	4.10432e11	0.527413	0.263706	−	0.964603i	$-0.415055\pi$
$439$	4.10432e11	0.527413	0.263706	+	0.964603i	$0.415055\pi$
$440$	9.33435e10	0.118726
$441$	3.78229e10	0.0476190
$442$	−1.80939e12	−2.25493
$443$	3.71191e11	0.457911	0.228955	−	0.973437i	$-0.426469\pi$
$443$	3.71191e11	0.457911	0.228955	+	0.973437i	$0.426469\pi$
$444$	3.01903e11	0.368676
$445$	−2.64249e11	−0.319443
$446$	−4.06980e11	−0.487042
$447$	9.46049e11	1.12080
$448$	−3.32118e11	−0.389530
$449$	8.93496e11	1.03749	0.518745	−	0.854929i	$-0.326399\pi$
$449$	8.93496e11	1.03749	0.518745	+	0.854929i	$0.326399\pi$
$450$	4.54451e10	0.0522433
$451$	2.30558e11	0.262413
$452$	−2.34089e10	−0.0263790
$453$	−8.48792e11	−0.947021
$454$	−5.38897e11	−0.595325
$455$	−2.63364e11	−0.288075
$456$	3.95826e10	0.0428708
$457$	−7.44453e11	−0.798388	−0.399194	−	0.916866i	$-0.630710\pi$
$457$	−7.44453e11	−0.798388	−0.399194	+	0.916866i	$0.630710\pi$
$458$	6.63131e11	0.704214
$459$	−3.08992e11	−0.324930
$460$	1.91484e11	0.199398
$461$	3.98579e10	0.0411017	0.0205509	−	0.999789i	$-0.493458\pi$
$461$	3.98579e10	0.0411017	0.0205509	+	0.999789i	$0.493458\pi$
$462$	4.09337e10	0.0418015
$463$	−1.33184e12	−1.34691	−0.673453	−	0.739230i	$-0.735190\pi$
$463$	−1.33184e12	−1.34691	−0.673453	+	0.739230i	$0.735190\pi$
$464$	7.92522e11	0.793744
$465$	1.63907e11	0.162577
$466$	−1.36617e12	−1.34205
$467$	−1.65914e12	−1.61419	−0.807097	−	0.590419i	$-0.798963\pi$
$467$	−1.65914e12	−1.61419	−0.807097	+	0.590419i	$0.798963\pi$
$468$	−2.27506e11	−0.219223
$469$	5.46554e11	0.521622
$470$	−4.03291e10	−0.0381222
$471$	1.02162e12	0.956525
$472$	−1.58584e12	−1.47068
$473$	2.37929e10	0.0218561
$474$	−2.15030e11	−0.195657
$475$	−1.51713e10	−0.0136742
$476$	−2.75818e11	−0.246258
$477$	−4.22172e11	−0.373385
$478$	4.11361e11	0.360411
$479$	−1.70555e12	−1.48032	−0.740160	−	0.672430i	$-0.765250\pi$
$479$	−1.70555e12	−1.48032	−0.740160	+	0.672430i	$0.765250\pi$
$480$	2.16661e11	0.186293
$481$	−3.31077e12	−2.82018
$482$	9.65414e11	0.814708
$483$	3.01572e11	0.252132
$484$	4.38041e11	0.362836
$485$	4.51958e11	0.370903
$486$	6.18275e10	0.0502711
$487$	3.09447e11	0.249290	0.124645	−	0.992201i	$-0.460221\pi$
$487$	3.09447e11	0.249290	0.124645	+	0.992201i	$0.460221\pi$
$488$	−1.97370e12	−1.57540
$489$	1.15132e12	0.910556
$490$	6.38882e10	0.0500655
$491$	−7.75236e11	−0.601960	−0.300980	−	0.953630i	$-0.597314\pi$
$491$	−7.75236e11	−0.601960	−0.300980	+	0.953630i	$0.597314\pi$
$492$	3.10854e11	0.239174
$493$	3.77861e12	2.88085
$494$	−1.20866e11	−0.0913129
$495$	−4.86740e10	−0.0364396
$496$	−3.94824e11	−0.292912
$497$	8.53183e11	0.627247
$498$	2.64202e11	0.192488
$499$	6.93045e11	0.500391	0.250195	−	0.968195i	$-0.419505\pi$
$499$	6.93045e11	0.500391	0.250195	+	0.968195i	$0.419505\pi$
$500$	−4.82368e10	−0.0345154
$501$	9.21349e11	0.653363
$502$	−1.83700e12	−1.29105
$503$	−1.75731e12	−1.22403	−0.612016	−	0.790845i	$-0.709641\pi$
$503$	−1.75731e12	−1.22403	−0.612016	+	0.790845i	$0.709641\pi$
$504$	1.98207e11	0.136830
$505$	−8.95492e10	−0.0612704
$506$	3.26375e11	0.221330
$507$	1.63594e12	1.09959
$508$	5.71197e11	0.380539
$509$	−7.33230e11	−0.484184	−0.242092	−	0.970253i	$-0.577834\pi$
$509$	−7.33230e11	−0.484184	−0.242092	+	0.970253i	$0.577834\pi$
$510$	−5.21931e11	−0.341623
$511$	3.82353e11	0.248068
$512$	−1.30749e12	−0.840862
$513$	−2.06404e10	−0.0131580
$514$	−8.32228e11	−0.525906
$515$	6.48924e11	0.406501
$516$	3.20792e10	0.0199205
$517$	4.31946e10	0.0265902
$518$	8.03143e11	0.490128
$519$	1.03830e12	0.628158
$520$	−1.38013e12	−0.827763
$521$	1.58170e12	0.940488	0.470244	−	0.882536i	$-0.344166\pi$
$521$	1.58170e12	0.940488	0.470244	+	0.882536i	$0.344166\pi$
$522$	−7.56078e11	−0.445707
$523$	2.20359e12	1.28787	0.643937	−	0.765079i	$-0.277300\pi$
$523$	2.20359e12	1.28787	0.643937	+	0.765079i	$0.277300\pi$
$524$	−3.40943e10	−0.0197556
$525$	−7.59691e10	−0.0436436
$526$	1.07094e12	0.609999
$527$	−1.88245e12	−1.06311
$528$	1.17248e11	0.0656525
$529$	6.03359e11	0.334985
$530$	−7.13109e11	−0.392567
$531$	8.26935e11	0.451384
$532$	−1.84244e10	−0.00997219
$533$	−3.40893e12	−1.82955
$534$	−6.07260e11	−0.323176
$535$	2.21435e11	0.116857
$536$	2.86416e12	1.49884
$537$	−1.61402e12	−0.837577
$538$	6.96313e11	0.358331
$539$	−6.84277e10	−0.0349206
$540$	−6.56256e10	−0.0332125
$541$	−1.11931e12	−0.561778	−0.280889	−	0.959740i	$-0.590629\pi$
$541$	−1.11931e12	−0.561778	−0.280889	+	0.959740i	$0.590629\pi$
$542$	8.23416e11	0.409848
$543$	3.02500e11	0.149323
$544$	−2.48833e12	−1.21818
$545$	−2.05580e11	−0.0998150
$546$	−6.05227e11	−0.291441
$547$	−2.45295e12	−1.17151	−0.585755	−	0.810488i	$-0.699202\pi$
$547$	−2.45295e12	−1.17151	−0.585755	+	0.810488i	$0.699202\pi$
$548$	−6.98375e11	−0.330808
$549$	1.02919e12	0.483524
$550$	−8.22174e10	−0.0383117
$551$	2.52407e11	0.116659
$552$	1.58036e12	0.724485
$553$	3.59459e11	0.163451
$554$	−7.35286e11	−0.331637
$555$	−9.55013e11	−0.427259
$556$	−5.00157e11	−0.221957
$557$	2.09941e12	0.924163	0.462082	−	0.886837i	$-0.347103\pi$
$557$	2.09941e12	0.924163	0.462082	+	0.886837i	$0.347103\pi$
$558$	3.76668e11	0.164477
$559$	−3.51791e11	−0.152381
$560$	1.82997e11	0.0786317
$561$	5.59016e11	0.238282
$562$	−1.42227e12	−0.601408
$563$	1.19601e12	0.501702	0.250851	−	0.968026i	$-0.419290\pi$
$563$	1.19601e12	0.501702	0.250851	+	0.968026i	$0.419290\pi$
$564$	5.82379e10	0.0242354
$565$	7.40496e10	0.0305707
$566$	−3.58404e11	−0.146791
$567$	−1.03355e11	−0.0419961
$568$	4.47102e12	1.80235
$569$	4.07783e12	1.63089	0.815444	−	0.578836i	$-0.196493\pi$
$569$	4.07783e12	1.63089	0.815444	+	0.578836i	$0.196493\pi$
$570$	−3.48645e10	−0.0138340
$571$	1.37719e11	0.0542163	0.0271081	−	0.999633i	$-0.491370\pi$
$571$	1.37719e11	0.0542163	0.0271081	+	0.999633i	$0.491370\pi$
$572$	4.11595e11	0.160764
$573$	1.43430e12	0.555834
$574$	8.26955e11	0.317964
$575$	−6.05722e11	−0.231083
$576$	9.07549e11	0.343533
$577$	3.97826e12	1.49418	0.747088	−	0.664725i	$-0.231451\pi$
$577$	3.97826e12	1.49418	0.747088	+	0.664725i	$0.231451\pi$
$578$	3.89153e12	1.45026
$579$	2.21099e12	0.817587
$580$	8.02524e11	0.294464
$581$	−4.41658e11	−0.160803
$582$	1.03863e12	0.375238
$583$	7.63777e11	0.273816
$584$	2.00368e12	0.712806
$585$	7.19672e11	0.254058
$586$	−3.36940e12	−1.18036
$587$	1.37046e12	0.476427	0.238213	−	0.971213i	$-0.423438\pi$
$587$	1.37046e12	0.476427	0.238213	+	0.971213i	$0.423438\pi$
$588$	−9.22588e10	−0.0318280
$589$	−1.25746e11	−0.0430503
$590$	1.39681e12	0.474574
$591$	−1.92815e12	−0.650124
$592$	2.30047e12	0.769783
$593$	−7.50360e11	−0.249186	−0.124593	−	0.992208i	$-0.539762\pi$
$593$	−7.50360e11	−0.249186	−0.124593	+	0.992208i	$0.539762\pi$
$594$	−1.11856e11	−0.0368655
$595$	8.72497e11	0.285389
$596$	−2.30763e12	−0.749133
$597$	−8.28077e11	−0.266800
$598$	−4.82564e12	−1.54312
$599$	3.97361e12	1.26114	0.630572	−	0.776131i	$-0.282820\pi$
$599$	3.97361e12	1.26114	0.630572	+	0.776131i	$0.282820\pi$
$600$	−3.98109e11	−0.125407
$601$	−1.37812e12	−0.430876	−0.215438	−	0.976518i	$-0.569118\pi$
$601$	−1.37812e12	−0.430876	−0.215438	+	0.976518i	$0.569118\pi$
$602$	8.53393e10	0.0264829
$603$	−1.49352e12	−0.460027
$604$	2.07040e12	0.632978
$605$	−1.38566e12	−0.420491
$606$	−2.05790e11	−0.0619864
$607$	2.45767e12	0.734810	0.367405	−	0.930061i	$-0.380246\pi$
$607$	2.45767e12	0.734810	0.367405	+	0.930061i	$0.380246\pi$
$608$	−1.66218e11	−0.0493301
$609$	1.26391e12	0.372340
$610$	1.73844e12	0.508365
$611$	−6.38655e11	−0.185388
$612$	7.53703e11	0.217180
$613$	−6.52053e12	−1.86514	−0.932568	−	0.360993i	$-0.882438\pi$
$613$	−6.52053e12	−1.86514	−0.932568	+	0.360993i	$0.882438\pi$
$614$	−4.51864e12	−1.28307
$615$	−9.83327e11	−0.277179
$616$	−3.58588e11	−0.100342
$617$	−3.58985e11	−0.0997224	−0.0498612	−	0.998756i	$-0.515878\pi$
$617$	−3.58985e11	−0.0997224	−0.0498612	+	0.998756i	$0.515878\pi$
$618$	1.49127e12	0.411251
$619$	6.27430e12	1.71774	0.858870	−	0.512193i	$-0.171167\pi$
$619$	6.27430e12	1.71774	0.858870	+	0.512193i	$0.171167\pi$
$620$	−3.99808e11	−0.108665
$621$	−8.24078e11	−0.222360
$622$	−6.41879e11	−0.171948
$623$	1.01514e12	0.269978
$624$	−1.73357e12	−0.457731
$625$	1.52588e11	0.0400000
$626$	−1.18371e12	−0.308077
$627$	3.73417e10	0.00964919
$628$	−2.49198e12	−0.639330
$629$	1.09682e13	2.79388
$630$	−1.74582e11	−0.0441536
$631$	−4.37176e12	−1.09780	−0.548901	−	0.835888i	$-0.684954\pi$
$631$	−4.37176e12	−1.09780	−0.548901	+	0.835888i	$0.684954\pi$
$632$	1.88371e12	0.469664
$633$	1.39284e11	0.0344813
$634$	2.65095e12	0.651627
$635$	−1.80687e12	−0.441008
$636$	1.02978e12	0.249566
$637$	1.01174e12	0.243468
$638$	1.36787e12	0.326852
$639$	−2.33142e12	−0.553180
$640$	1.63468e11	0.0385143
$641$	2.65177e12	0.620405	0.310203	−	0.950670i	$-0.399603\pi$
$641$	2.65177e12	0.620405	0.310203	+	0.950670i	$0.399603\pi$
$642$	5.08870e11	0.118222
$643$	5.57601e12	1.28639	0.643197	−	0.765701i	$-0.277608\pi$
$643$	5.57601e12	1.28639	0.643197	+	0.765701i	$0.277608\pi$
$644$	−7.35604e11	−0.168522
$645$	−1.01476e11	−0.0230859
$646$	4.00415e11	0.0904616
$647$	−8.42501e11	−0.189017	−0.0945086	−	0.995524i	$-0.530128\pi$
$647$	−8.42501e11	−0.189017	−0.0945086	+	0.995524i	$0.530128\pi$
$648$	−5.41622e11	−0.120673
$649$	−1.49606e12	−0.331015
$650$	1.21563e12	0.267111
$651$	−6.29665e11	−0.137403
$652$	−2.80834e12	−0.608605
$653$	−3.14411e12	−0.676688	−0.338344	−	0.941022i	$-0.609867\pi$
$653$	−3.14411e12	−0.676688	−0.338344	+	0.941022i	$0.609867\pi$
$654$	−4.72435e11	−0.100982
$655$	1.07851e11	0.0228948
$656$	2.36867e12	0.499387
$657$	−1.04482e12	−0.218775
$658$	1.54928e11	0.0322192
$659$	−3.84118e12	−0.793378	−0.396689	−	0.917953i	$-0.629841\pi$
$659$	−3.84118e12	−0.793378	−0.396689	+	0.917953i	$0.629841\pi$
$660$	1.18727e11	0.0243558
$661$	3.86205e12	0.786885	0.393442	−	0.919349i	$-0.371284\pi$
$661$	3.86205e12	0.786885	0.393442	+	0.919349i	$0.371284\pi$
$662$	−5.38928e12	−1.09061
$663$	−8.26535e12	−1.66131
$664$	−2.31446e12	−0.462055
$665$	5.82820e10	0.0115568
$666$	−2.19468e12	−0.432252
$667$	1.00775e13	1.97146
$668$	−2.24738e12	−0.436700
$669$	−1.85910e12	−0.358826
$670$	−2.52277e12	−0.483661
$671$	−1.86196e12	−0.354584
$672$	−8.32326e11	−0.157446
$673$	9.02826e12	1.69643	0.848216	−	0.529651i	$-0.177677\pi$
$673$	9.02826e12	1.69643	0.848216	+	0.529651i	$0.177677\pi$
$674$	2.99370e12	0.558778
$675$	2.07594e11	0.0384900
$676$	−3.99044e12	−0.734955
$677$	−2.09789e12	−0.383825	−0.191913	−	0.981412i	$-0.561469\pi$
$677$	−2.09789e12	−0.383825	−0.191913	+	0.981412i	$0.561469\pi$
$678$	1.70170e11	0.0309279
$679$	−1.73624e12	−0.313470
$680$	4.57223e12	0.820046
$681$	−2.46170e12	−0.438604
$682$	−6.81454e11	−0.120617
$683$	−8.96881e11	−0.157704	−0.0788518	−	0.996886i	$-0.525125\pi$
$683$	−8.96881e11	−0.157704	−0.0788518	+	0.996886i	$0.525125\pi$
$684$	5.03467e10	0.00879464
$685$	2.20918e12	0.383374
$686$	−2.45433e11	−0.0423131
$687$	3.02920e12	0.518827
$688$	2.44440e11	0.0415933
$689$	−1.12929e13	−1.90905
$690$	−1.39199e12	−0.233784
$691$	−1.00944e13	−1.68433	−0.842166	−	0.539218i	$-0.818720\pi$
$691$	−1.00944e13	−1.68433	−0.842166	+	0.539218i	$0.818720\pi$
$692$	−2.53265e12	−0.419853
$693$	1.86986e11	0.0307971
$694$	−8.58207e12	−1.40435
$695$	1.58215e12	0.257227
$696$	6.62341e12	1.06989
$697$	1.12934e13	1.81250
$698$	−1.77643e12	−0.283269
$699$	−6.24069e12	−0.988748
$700$	1.85306e11	0.0291709
$701$	−2.93533e12	−0.459120	−0.229560	−	0.973295i	$-0.573729\pi$
$701$	−2.93533e12	−0.459120	−0.229560	+	0.973295i	$0.573729\pi$
$702$	1.65385e12	0.257027
$703$	7.32667e11	0.113138
$704$	−1.64190e12	−0.251925
$705$	−1.84224e11	−0.0280864
$706$	4.35102e12	0.659127
$707$	3.44012e11	0.0517829
$708$	−2.01709e12	−0.301700
$709$	−1.02071e13	−1.51703	−0.758514	−	0.651656i	$-0.774074\pi$
$709$	−1.02071e13	−1.51703	−0.758514	+	0.651656i	$0.774074\pi$
$710$	−3.93810e12	−0.581599
$711$	−9.82262e11	−0.144150
$712$	5.31973e12	0.775764
$713$	−5.02049e12	−0.727517
$714$	2.00505e12	0.288724
$715$	−1.30200e12	−0.186309
$716$	3.93697e12	0.559827
$717$	1.87911e12	0.265531
$718$	5.30561e12	0.745033
$719$	2.00023e12	0.279126	0.139563	−	0.990213i	$-0.455430\pi$
$719$	2.00023e12	0.279126	0.139563	+	0.990213i	$0.455430\pi$
$720$	−5.00059e11	−0.0693466
$721$	−2.49291e12	−0.343556
$722$	−5.69514e12	−0.779986
$723$	4.41004e12	0.600233
$724$	−7.37867e11	−0.0998056
$725$	−2.53863e12	−0.341255
$726$	−3.18433e12	−0.425405
$727$	−3.22295e12	−0.427907	−0.213953	−	0.976844i	$-0.568634\pi$
$727$	−3.22295e12	−0.427907	−0.213953	+	0.976844i	$0.568634\pi$
$728$	5.30192e12	0.699588
$729$	2.82430e11	0.0370370
$730$	−1.76485e12	−0.230015
$731$	1.16545e12	0.150961
$732$	−2.51042e12	−0.323182
$733$	−5.91731e12	−0.757106	−0.378553	−	0.925580i	$-0.623578\pi$
$733$	−5.91731e12	−0.757106	−0.378553	+	0.925580i	$0.623578\pi$
$734$	−5.75098e12	−0.731323
$735$	2.91843e11	0.0368856
$736$	−6.63635e12	−0.833642
$737$	2.70202e12	0.337353
$738$	−2.25975e12	−0.280418
$739$	6.71625e12	0.828374	0.414187	−	0.910192i	$-0.364066\pi$
$739$	6.71625e12	0.828374	0.414187	+	0.910192i	$0.364066\pi$
$740$	2.32950e12	0.285575
$741$	−5.52118e11	−0.0672744
$742$	2.73948e12	0.331780
$743$	−1.24230e13	−1.49546	−0.747731	−	0.664002i	$-0.768857\pi$
$743$	−1.24230e13	−1.49546	−0.747731	+	0.664002i	$0.768857\pi$
$744$	−3.29970e12	−0.394817
$745$	7.29976e12	0.868171
$746$	9.55337e12	1.12936
$747$	1.20688e12	0.141815
$748$	−1.36357e12	−0.159265
$749$	−8.50663e11	−0.0987619
$750$	3.50656e11	0.0404675
$751$	7.52055e11	0.0862720	0.0431360	−	0.999069i	$-0.486265\pi$
$751$	7.52055e11	0.0862720	0.0431360	+	0.999069i	$0.486265\pi$
$752$	4.43765e11	0.0506026
$753$	−8.39146e12	−0.951174
$754$	−2.02246e13	−2.27882
$755$	−6.54932e12	−0.733559
$756$	2.52107e11	0.0280697
$757$	2.12671e12	0.235383	0.117692	−	0.993050i	$-0.462451\pi$
$757$	2.12671e12	0.235383	0.117692	+	0.993050i	$0.462451\pi$
$758$	−7.33924e12	−0.807494
$759$	1.49089e12	0.163064
$760$	3.05421e11	0.0332076
$761$	3.97518e12	0.429661	0.214831	−	0.976651i	$-0.431080\pi$
$761$	3.97518e12	0.429661	0.214831	+	0.976651i	$0.431080\pi$
$762$	−4.15231e12	−0.446161
$763$	7.89755e11	0.0843591
$764$	−3.49860e12	−0.371513
$765$	−2.38420e12	−0.251690
$766$	1.19195e13	1.25092
$767$	2.21200e13	2.30785
$768$	−5.36095e12	−0.556053
$769$	5.74016e11	0.0591910	0.0295955	−	0.999562i	$-0.490578\pi$
$769$	5.74016e11	0.0591910	0.0295955	+	0.999562i	$0.490578\pi$
$770$	3.15847e11	0.0323793
$771$	−3.80164e12	−0.387459
$772$	−5.39313e12	−0.546466
$773$	−2.24260e12	−0.225914	−0.112957	−	0.993600i	$-0.536032\pi$
$773$	−2.24260e12	−0.225914	−0.112957	+	0.993600i	$0.536032\pi$
$774$	−2.33199e11	−0.0233557
$775$	1.26471e12	0.125932
$776$	−9.09861e12	−0.900735
$777$	3.66878e12	0.361100
$778$	2.47352e12	0.242051
$779$	7.54389e11	0.0733967
$780$	−1.75545e12	−0.169810
$781$	4.21791e12	0.405665
$782$	1.59868e13	1.52873
$783$	−3.45378e12	−0.328373
$784$	−7.03001e11	−0.0664559
$785$	7.88289e12	0.740921
$786$	2.47847e11	0.0231624
$787$	−3.34267e12	−0.310604	−0.155302	−	0.987867i	$-0.549635\pi$
$787$	−3.34267e12	−0.310604	−0.155302	+	0.987867i	$0.549635\pi$
$788$	4.70320e12	0.434536
$789$	4.89208e12	0.449414
$790$	−1.65918e12	−0.151556
$791$	−2.84469e11	−0.0258369
$792$	9.79883e11	0.0884934
$793$	2.75301e13	2.47217
$794$	−1.45231e13	−1.29678
$795$	−3.25750e12	−0.289223
$796$	2.01987e12	0.178326
$797$	−1.60220e13	−1.40655	−0.703274	−	0.710919i	$-0.748279\pi$
$797$	−1.60220e13	−1.40655	−0.703274	+	0.710919i	$0.748279\pi$
$798$	1.33936e11	0.0116918
$799$	2.11580e12	0.183659
$800$	1.67177e12	0.144302
$801$	−2.77398e12	−0.238098
$802$	−8.53194e12	−0.728221
$803$	1.89025e12	0.160435
$804$	3.64305e12	0.307477
$805$	2.32694e12	0.195301
$806$	1.00757e13	0.840942
$807$	3.18077e12	0.263999
$808$	1.80276e12	0.148795
$809$	−1.45689e13	−1.19580	−0.597901	−	0.801570i	$-0.703998\pi$
$809$	−1.45689e13	−1.19580	−0.597901	+	0.801570i	$0.703998\pi$
$810$	4.77064e11	0.0389398
$811$	−9.11324e12	−0.739739	−0.369870	−	0.929084i	$-0.620598\pi$
$811$	−9.11324e12	−0.739739	−0.369870	+	0.929084i	$0.620598\pi$
$812$	−3.08298e12	−0.248868
$813$	3.76138e12	0.301954
$814$	3.97053e12	0.316985
$815$	8.88365e12	0.705314
$816$	5.74312e12	0.453464
$817$	7.78507e10	0.00611313
$818$	2.00576e12	0.156635
$819$	−2.76469e12	−0.214718
$820$	2.39857e12	0.185263
$821$	1.36915e13	1.05173	0.525867	−	0.850567i	$-0.323741\pi$
$821$	1.36915e13	1.05173	0.525867	+	0.850567i	$0.323741\pi$
$822$	5.07682e12	0.387854
$823$	−1.09486e13	−0.831878	−0.415939	−	0.909392i	$-0.636547\pi$
$823$	−1.09486e13	−0.831878	−0.415939	+	0.909392i	$0.636547\pi$
$824$	−1.30638e13	−0.987184
$825$	−3.75571e11	−0.0282260
$826$	−5.36599e12	−0.401088
$827$	−1.62709e13	−1.20959	−0.604795	−	0.796381i	$-0.706745\pi$
$827$	−1.62709e13	−1.20959	−0.604795	+	0.796381i	$0.706745\pi$
$828$	2.01012e12	0.148623
$829$	2.67132e13	1.96440	0.982201	−	0.187836i	$-0.0601472\pi$
$829$	2.67132e13	1.96440	0.982201	+	0.187836i	$0.0601472\pi$
$830$	2.03859e12	0.149100
$831$	−3.35881e12	−0.244332
$832$	2.42764e13	1.75643
$833$	−3.35178e12	−0.241198
$834$	3.63588e12	0.260233
$835$	7.10917e12	0.506092
$836$	−9.10852e10	−0.00644941
$837$	1.72063e12	0.121178
$838$	5.75147e12	0.402885
$839$	−1.97856e13	−1.37854	−0.689271	−	0.724503i	$-0.742069\pi$
$839$	−1.97856e13	−1.37854	−0.689271	+	0.724503i	$0.742069\pi$
$840$	1.52937e12	0.105988
$841$	2.77286e13	1.91137
$842$	3.05199e12	0.209256
$843$	−6.49697e12	−0.443085
$844$	−3.39745e11	−0.0230469
$845$	1.26230e13	0.851741
$846$	−4.23359e11	−0.0284146
$847$	5.32314e12	0.355380
$848$	7.84676e12	0.521086
$849$	−1.63720e12	−0.108147
$850$	−4.02725e12	−0.264620
$851$	2.92522e13	1.91194
$852$	5.68687e12	0.369739
$853$	−1.37782e13	−0.891089	−0.445544	−	0.895260i	$-0.646990\pi$
$853$	−1.37782e13	−0.891089	−0.445544	+	0.895260i	$0.646990\pi$
$854$	−6.67840e12	−0.429647
$855$	−1.59262e11	−0.0101921
$856$	−4.45782e12	−0.283786
$857$	1.86882e13	1.18346	0.591729	−	0.806137i	$-0.298445\pi$
$857$	1.86882e13	1.18346	0.591729	+	0.806137i	$0.298445\pi$
$858$	−2.99208e12	−0.188487
$859$	9.78965e12	0.613476	0.306738	−	0.951794i	$-0.400762\pi$
$859$	9.78965e12	0.613476	0.306738	+	0.951794i	$0.400762\pi$
$860$	2.47525e11	0.0154303
$861$	3.77755e12	0.234259
$862$	1.79601e13	1.10797
$863$	−1.31437e13	−0.806622	−0.403311	−	0.915063i	$-0.632141\pi$
$863$	−1.31437e13	−0.806622	−0.403311	+	0.915063i	$0.632141\pi$
$864$	2.27442e12	0.138854
$865$	8.01155e12	0.486569
$866$	−1.58584e13	−0.958137
$867$	1.77766e13	1.06847
$868$	1.53590e12	0.0918384
$869$	1.77707e12	0.105710
$870$	−5.83393e12	−0.345243
$871$	−3.99508e13	−2.35204
$872$	4.13863e12	0.242400
$873$	4.74448e12	0.276455
$874$	1.06790e12	0.0619057
$875$	−5.86182e11	−0.0338062
$876$	2.54857e12	0.146227
$877$	−1.13031e13	−0.645206	−0.322603	−	0.946534i	$-0.604558\pi$
$877$	−1.13031e13	−0.645206	−0.322603	+	0.946534i	$0.604558\pi$
$878$	7.27775e12	0.413306
$879$	−1.53915e13	−0.869622
$880$	9.04688e11	0.0508542
$881$	1.10676e13	0.618960	0.309480	−	0.950906i	$-0.399845\pi$
$881$	1.10676e13	0.618960	0.309480	+	0.950906i	$0.399845\pi$
$882$	6.70673e11	0.0373166
$883$	6.03115e12	0.333870	0.166935	−	0.985968i	$-0.446613\pi$
$883$	6.03115e12	0.333870	0.166935	+	0.985968i	$0.446613\pi$
$884$	2.01611e13	1.11040
$885$	6.38067e12	0.349641
$886$	6.58194e12	0.358841
$887$	−1.50209e13	−0.814778	−0.407389	−	0.913255i	$-0.633561\pi$
$887$	−1.50209e13	−0.814778	−0.407389	+	0.913255i	$0.633561\pi$
$888$	1.92259e13	1.03759
$889$	6.94129e12	0.372719
$890$	−4.68564e12	−0.250331
$891$	−5.10961e11	−0.0271605
$892$	4.53477e12	0.239835
$893$	1.41333e11	0.00743725
$894$	1.67753e13	0.878317
$895$	−1.24539e13	−0.648785
$896$	−6.27978e11	−0.0325506
$897$	−2.20436e13	−1.13689
$898$	1.58434e13	0.813029
$899$	−2.10413e13	−1.07437
$900$	−5.06371e11	−0.0257263
$901$	3.74120e13	1.89125
$902$	4.08825e12	0.205640
$903$	3.89832e11	0.0195111
$904$	−1.49073e12	−0.0742406
$905$	2.33410e12	0.115665
$906$	−1.50507e13	−0.742132
$907$	−2.38542e13	−1.17039	−0.585196	−	0.810892i	$-0.698982\pi$
$907$	−2.38542e13	−1.17039	−0.585196	+	0.810892i	$0.698982\pi$
$908$	6.00465e12	0.293158
$909$	−9.40052e11	−0.0456683
$910$	−4.66996e12	−0.225750
$911$	−4.97188e12	−0.239159	−0.119580	−	0.992825i	$-0.538155\pi$
$911$	−4.97188e12	−0.239159	−0.119580	+	0.992825i	$0.538155\pi$
$912$	3.83635e11	0.0183629
$913$	−2.18344e12	−0.103997
$914$	−1.32006e13	−0.625656
$915$	7.94124e12	0.374536
$916$	−7.38892e12	−0.346778
$917$	−4.14319e11	−0.0193496
$918$	−5.47903e12	−0.254631
$919$	2.44969e13	1.13290	0.566449	−	0.824097i	$-0.308317\pi$
$919$	2.44969e13	1.13290	0.566449	+	0.824097i	$0.308317\pi$
$920$	1.21941e13	0.561183
$921$	−2.06413e13	−0.945297
$922$	7.06758e11	0.0322093
$923$	−6.23641e13	−2.82831
$924$	−4.56103e11	−0.0205844
$925$	−7.36893e12	−0.330953
$926$	−2.36161e13	−1.05550
$927$	6.81215e12	0.302988
$928$	−2.78135e13	−1.23109
$929$	1.28522e13	0.566118	0.283059	−	0.959102i	$-0.408651\pi$
$929$	1.28522e13	0.566118	0.283059	+	0.959102i	$0.408651\pi$
$930$	2.90639e12	0.127403
$931$	−2.23896e11	−0.00976726
$932$	1.52225e13	0.660868
$933$	−2.93212e12	−0.126682
$934$	−2.94197e13	−1.26496
$935$	4.31339e12	0.184572
$936$	−1.44881e13	−0.616978
$937$	5.82676e12	0.246944	0.123472	−	0.992348i	$-0.460597\pi$
$937$	5.82676e12	0.246944	0.123472	+	0.992348i	$0.460597\pi$
$938$	9.69148e12	0.408768
$939$	−5.40720e12	−0.226975
$940$	4.49366e11	0.0187726
$941$	1.27027e13	0.528131	0.264066	−	0.964505i	$-0.414936\pi$
$941$	1.27027e13	0.528131	0.264066	+	0.964505i	$0.414936\pi$
$942$	1.81154e13	0.749580
$943$	3.01194e13	1.24035
$944$	−1.53700e13	−0.629940
$945$	−7.97494e11	−0.0325300
$946$	4.21895e11	0.0171275
$947$	−3.27679e13	−1.32396	−0.661978	−	0.749523i	$-0.730283\pi$
$947$	−3.27679e13	−1.32396	−0.661978	+	0.749523i	$0.730283\pi$
$948$	2.39597e12	0.0963481
$949$	−2.79484e13	−1.11856
$950$	−2.69016e11	−0.0107157
$951$	1.21096e13	0.480084
$952$	−1.75647e13	−0.693066
$953$	6.00774e11	0.0235935	0.0117968	−	0.999930i	$-0.496245\pi$
$953$	6.00774e11	0.0235935	0.0117968	+	0.999930i	$0.496245\pi$
$954$	−7.48593e12	−0.292603
$955$	1.10672e13	0.430547
$956$	−4.58359e12	−0.177478
$957$	6.24845e12	0.240807
$958$	−3.02428e13	−1.16005
$959$	−8.48677e12	−0.324010
$960$	7.00269e12	0.266100
$961$	−1.59571e13	−0.603530
$962$	−5.87064e13	−2.21003
$963$	2.32453e12	0.0870998
$964$	−1.07571e13	−0.401189
$965$	1.70601e13	0.633300
$966$	5.34746e12	0.197583
$967$	3.80320e13	1.39872	0.699359	−	0.714770i	$-0.253469\pi$
$967$	3.80320e13	1.39872	0.699359	+	0.714770i	$0.253469\pi$
$968$	2.78954e13	1.02116
$969$	1.82911e12	0.0666472
$970$	8.01410e12	0.290658
$971$	3.54296e13	1.27903	0.639513	−	0.768780i	$-0.279136\pi$
$971$	3.54296e13	1.27903	0.639513	+	0.768780i	$0.279136\pi$
$972$	−6.88912e11	−0.0247551
$973$	−6.07799e12	−0.217396
$974$	5.48709e12	0.195356
$975$	5.55302e12	0.196793
$976$	−1.91291e13	−0.674793
$977$	2.15681e13	0.757332	0.378666	−	0.925533i	$-0.376383\pi$
$977$	2.15681e13	0.757332	0.378666	+	0.925533i	$0.376383\pi$
$978$	2.04152e13	0.713556
$979$	5.01857e12	0.174606
$980$	−7.11873e11	−0.0246539
$981$	−2.15809e12	−0.0743977
$982$	−1.37465e13	−0.471725
$983$	−1.64997e13	−0.563618	−0.281809	−	0.959471i	$-0.590934\pi$
$983$	−1.64997e13	−0.563618	−0.281809	+	0.959471i	$0.590934\pi$
$984$	1.97959e13	0.673127
$985$	−1.48777e13	−0.503584
$986$	6.70021e13	2.25757
$987$	7.07716e11	0.0237373
$988$	1.34674e12	0.0449654
$989$	3.10823e12	0.103307
$990$	−8.63086e11	−0.0285559
$991$	−1.53016e13	−0.503971	−0.251985	−	0.967731i	$-0.581084\pi$
$991$	−1.53016e13	−0.503971	−0.251985	+	0.967731i	$0.581084\pi$
$992$	1.38563e13	0.454304
$993$	−2.46184e13	−0.803503
$994$	1.51286e13	0.491541
$995$	−6.38948e12	−0.206663
$996$	−2.94386e12	−0.0947873
$997$	3.02444e13	0.969431	0.484715	−	0.874672i	$-0.338923\pi$
$997$	3.02444e13	0.969431	0.484715	+	0.874672i	$0.338923\pi$
$998$	1.22890e13	0.392131
$999$	−1.00253e13	−0.318460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.10.a.c.1.3	✓	4
3.2	odd	2		315.10.a.f.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.10.a.c.1.3	✓	4	1.1	even	1	trivial
315.10.a.f.1.2		4	3.2	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	105.a (trivial)

\(f(q)\)	\(=\)	\(q+17.7320 q^{2} +81.0000 q^{3} -197.578 q^{4} +625.000 q^{5} +1436.29 q^{6} -2401.00 q^{7} -12582.2 q^{8} +6561.00 q^{9} +11082.5 q^{10} -11869.9 q^{11} -16003.8 q^{12} +175503. q^{13} -42574.4 q^{14} +50625.0 q^{15} -121947. q^{16} -581422. q^{17} +116339. q^{18} -38838.5 q^{19} -123486. q^{20} -194481. q^{21} -210477. q^{22} -1.55065e6 q^{23} -1.01916e6 q^{24} +390625. q^{25} +3.11201e6 q^{26} +531441. q^{27} +474385. q^{28} -6.49890e6 q^{29} +897680. q^{30} +3.23767e6 q^{31} +4.27973e6 q^{32} -961463. q^{33} -1.03098e7 q^{34} -1.50062e6 q^{35} -1.29631e6 q^{36} -1.88645e7 q^{37} -688682. q^{38} +1.42157e7 q^{39} -7.86388e6 q^{40} -1.94238e7 q^{41} -3.44853e6 q^{42} -2.00447e6 q^{43} +2.34523e6 q^{44} +4.10062e6 q^{45} -2.74960e7 q^{46} -3.63900e6 q^{47} -9.87771e6 q^{48} +5.76480e6 q^{49} +6.92654e6 q^{50} -4.70952e7 q^{51} -3.46755e7 q^{52} -6.43457e7 q^{53} +9.42349e6 q^{54} -7.41869e6 q^{55} +3.02099e7 q^{56} -3.14592e6 q^{57} -1.15238e8 q^{58} +1.26038e8 q^{59} -1.00024e7 q^{60} +1.56864e8 q^{61} +5.74102e7 q^{62} -1.57530e7 q^{63} +1.38325e8 q^{64} +1.09689e8 q^{65} -1.70486e7 q^{66} -2.27636e8 q^{67} +1.14876e8 q^{68} -1.25603e8 q^{69} -2.66090e7 q^{70} -3.55345e8 q^{71} -8.25518e7 q^{72} -1.59247e8 q^{73} -3.34504e8 q^{74} +3.16406e7 q^{75} +7.67363e6 q^{76} +2.84997e7 q^{77} +2.52073e8 q^{78} -1.49712e8 q^{79} -7.62169e7 q^{80} +4.30467e7 q^{81} -3.44421e8 q^{82} +1.83947e8 q^{83} +3.84252e7 q^{84} -3.63389e8 q^{85} -3.55432e7 q^{86} -5.26411e8 q^{87} +1.49350e8 q^{88} -4.22798e8 q^{89} +7.27121e7 q^{90} -4.21383e8 q^{91} +3.06374e8 q^{92} +2.62251e8 q^{93} -6.45266e7 q^{94} -2.42740e7 q^{95} +3.46658e8 q^{96} +7.23133e8 q^{97} +1.02221e8 q^{98} -7.78785e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 17 q^{2} + 324 q^{3} + 949 q^{4} + 2500 q^{5} - 1377 q^{6} - 9604 q^{7} - 20679 q^{8} + 26244 q^{9} - 10625 q^{10} + 16382 q^{11} + 76869 q^{12} - 84914 q^{13} + 40817 q^{14} + 202500 q^{15} - 829359 q^{16}+ \cdots + 107482302 q^{99}+O(q^{100}) \) 4 * q - 17 * q^2 + 324 * q^3 + 949 * q^4 + 2500 * q^5 - 1377 * q^6 - 9604 * q^7 - 20679 * q^8 + 26244 * q^9 - 10625 * q^10 + 16382 * q^11 + 76869 * q^12 - 84914 * q^13 + 40817 * q^14 + 202500 * q^15 - 829359 * q^16 - 451528 * q^17 - 111537 * q^18 - 1031478 * q^19 + 593125 * q^20 - 777924 * q^21 - 2609948 * q^22 - 5459068 * q^23 - 1674999 * q^24 + 1562500 * q^25 + 169794 * q^26 + 2125764 * q^27 - 2278549 * q^28 - 4867288 * q^29 - 860625 * q^30 + 1098642 * q^31 + 10125105 * q^32 + 1326942 * q^33 + 10466142 * q^34 - 6002500 * q^35 + 6226389 * q^36 + 2110068 * q^37 - 1633028 * q^38 - 6878034 * q^39 - 12924375 * q^40 + 1104700 * q^41 + 3306177 * q^42 - 15322648 * q^43 + 57398124 * q^44 + 16402500 * q^45 + 4904680 * q^46 - 5033968 * q^47 - 67178079 * q^48 + 23059204 * q^49 - 6640625 * q^50 - 36573768 * q^51 - 153789226 * q^52 - 149234422 * q^53 - 9034497 * q^54 + 10238750 * q^55 + 49650279 * q^56 - 83549718 * q^57 + 7850594 * q^58 - 141913876 * q^59 + 48043125 * q^60 + 235578792 * q^61 + 60170880 * q^62 - 63011844 * q^63 + 30064673 * q^64 - 53071250 * q^65 - 211405788 * q^66 - 401097064 * q^67 - 170870006 * q^68 - 442184508 * q^69 + 25510625 * q^70 - 126532750 * q^71 - 135674919 * q^72 - 653180926 * q^73 - 1130189382 * q^74 + 126562500 * q^75 + 7344404 * q^76 - 39333182 * q^77 + 13753314 * q^78 - 624551664 * q^79 - 518349375 * q^80 + 172186884 * q^81 + 193533606 * q^82 - 702347048 * q^83 - 184562469 * q^84 - 282205000 * q^85 - 2076482652 * q^86 - 394250328 * q^87 - 871546276 * q^88 - 1510406712 * q^89 - 69710625 * q^90 + 203878514 * q^91 - 1662743304 * q^92 + 88990002 * q^93 - 852748960 * q^94 - 644673750 * q^95 + 820133505 * q^96 - 717560562 * q^97 - 98001617 * q^98 + 107482302 * q^99

Introduction

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