LMFDB - Embedded newform 105.10.a.c.1.1

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			1.1
Root			$31.8126$ 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)

$f(q)$	$=$	\(q-35.8126 q^{2} +81.0000 q^{3} +770.540 q^{4} +625.000 q^{5} -2900.82 q^{6} -2401.00 q^{7} -9258.97 q^{8} +6561.00 q^{9} -22382.9 q^{10} +84191.1 q^{11} +62413.7 q^{12} -107949. q^{13} +85986.0 q^{14} +50625.0 q^{15} -62928.9 q^{16} -534805. q^{17} -234966. q^{18} +300331. q^{19} +481587. q^{20} -194481. q^{21} -3.01510e6 q^{22} -2.04494e6 q^{23} -749977. q^{24} +390625. q^{25} +3.86592e6 q^{26} +531441. q^{27} -1.85007e6 q^{28} +1.06113e6 q^{29} -1.81301e6 q^{30} -3.40296e6 q^{31} +6.99424e6 q^{32} +6.81948e6 q^{33} +1.91527e7 q^{34} -1.50062e6 q^{35} +5.05551e6 q^{36} +1.60944e7 q^{37} -1.07556e7 q^{38} -8.74385e6 q^{39} -5.78686e6 q^{40} -2.82323e7 q^{41} +6.96486e6 q^{42} +3.41602e7 q^{43} +6.48726e7 q^{44} +4.10062e6 q^{45} +7.32347e7 q^{46} -4.39666e6 q^{47} -5.09724e6 q^{48} +5.76480e6 q^{49} -1.39893e7 q^{50} -4.33192e7 q^{51} -8.31788e7 q^{52} -4.82841e7 q^{53} -1.90323e7 q^{54} +5.26195e7 q^{55} +2.22308e7 q^{56} +2.43268e7 q^{57} -3.80016e7 q^{58} -8.28369e7 q^{59} +3.90086e7 q^{60} +1.07823e8 q^{61} +1.21869e8 q^{62} -1.57530e7 q^{63} -2.18262e8 q^{64} -6.74680e7 q^{65} -2.44223e8 q^{66} -6.09954e7 q^{67} -4.12088e8 q^{68} -1.65640e8 q^{69} +5.37412e7 q^{70} +3.45810e8 q^{71} -6.07481e7 q^{72} -4.35356e8 q^{73} -5.76383e8 q^{74} +3.16406e7 q^{75} +2.31417e8 q^{76} -2.02143e8 q^{77} +3.13140e8 q^{78} +1.56176e8 q^{79} -3.93306e7 q^{80} +4.30467e7 q^{81} +1.01107e9 q^{82} -2.28263e8 q^{83} -1.49855e8 q^{84} -3.34253e8 q^{85} -1.22336e9 q^{86} +8.59511e7 q^{87} -7.79523e8 q^{88} -1.00731e9 q^{89} -1.46854e8 q^{90} +2.59185e8 q^{91} -1.57571e9 q^{92} -2.75640e8 q^{93} +1.57456e8 q^{94} +1.87707e8 q^{95} +5.66533e8 q^{96} -1.50889e9 q^{97} -2.06452e8 q^{98} +5.52378e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−35.8126	−1.58271	−0.791353	−	0.611359i	$-0.790623\pi$
$2$	−35.8126	−1.58271	−0.791353	+	0.611359i	$0.790623\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	770.540	1.50496
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−2900.82	−0.913776
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−9258.97	−0.799204
$9$	6561.00	0.333333
$10$	−22382.9	−0.707808
$11$	84191.1	1.73380	0.866901	−	0.498481i	$-0.166109\pi$
$11$	84191.1	1.73380	0.866901	+	0.498481i	$0.166109\pi$
$12$	62413.7	0.868889
$13$	−107949.	−1.04827	−0.524134	−	0.851636i	$-0.675611\pi$
$13$	−107949.	−1.04827	−0.524134	+	0.851636i	$0.675611\pi$
$14$	85986.0	0.598207
$15$	50625.0	0.258199
$16$	−62928.9	−0.240055
$17$	−534805.	−1.55301	−0.776507	−	0.630109i	$-0.783010\pi$
$17$	−534805.	−1.55301	−0.776507	+	0.630109i	$0.783010\pi$
$18$	−234966.	−0.527569
$19$	300331.	0.528699	0.264350	−	0.964427i	$-0.414843\pi$
$19$	300331.	0.528699	0.264350	+	0.964427i	$0.414843\pi$
$20$	481587.	0.673039
$21$	−194481.	−0.218218
$22$	−3.01510e6	−2.74410
$23$	−2.04494e6	−1.52372	−0.761862	−	0.647740i	$-0.775714\pi$
$23$	−2.04494e6	−1.52372	−0.761862	+	0.647740i	$0.775714\pi$
$24$	−749977.	−0.461421
$25$	390625.	0.200000
$26$	3.86592e6	1.65910
$27$	531441.	0.192450
$28$	−1.85007e6	−0.568822
$29$	1.06113e6	0.278596	0.139298	−	0.990250i	$-0.455515\pi$
$29$	1.06113e6	0.278596	0.139298	+	0.990250i	$0.455515\pi$
$30$	−1.81301e6	−0.408653
$31$	−3.40296e6	−0.661805	−0.330902	−	0.943665i	$-0.607353\pi$
$31$	−3.40296e6	−0.661805	−0.330902	+	0.943665i	$0.607353\pi$
$32$	6.99424e6	1.17914
$33$	6.81948e6	1.00101
$34$	1.91527e7	2.45796
$35$	−1.50062e6	−0.169031
$36$	5.05551e6	0.501653
$37$	1.60944e7	1.41178	0.705892	−	0.708320i	$-0.250547\pi$
$37$	1.60944e7	1.41178	0.705892	+	0.708320i	$0.250547\pi$
$38$	−1.07556e7	−0.836776
$39$	−8.74385e6	−0.605218
$40$	−5.78686e6	−0.357415
$41$	−2.82323e7	−1.56034	−0.780169	−	0.625569i	$-0.784867\pi$
$41$	−2.82323e7	−1.56034	−0.780169	+	0.625569i	$0.784867\pi$
$42$	6.96486e6	0.345375
$43$	3.41602e7	1.52374	0.761872	−	0.647728i	$-0.224280\pi$
$43$	3.41602e7	1.52374	0.761872	+	0.647728i	$0.224280\pi$
$44$	6.48726e7	2.60930
$45$	4.10062e6	0.149071
$46$	7.32347e7	2.41161
$47$	−4.39666e6	−0.131426	−0.0657132	−	0.997839i	$-0.520932\pi$
$47$	−4.39666e6	−0.131426	−0.0657132	+	0.997839i	$0.520932\pi$
$48$	−5.09724e6	−0.138596
$49$	5.76480e6	0.142857
$50$	−1.39893e7	−0.316541
$51$	−4.33192e7	−0.896633
$52$	−8.31788e7	−1.57760
$53$	−4.82841e7	−0.840548	−0.420274	−	0.907397i	$-0.638066\pi$
$53$	−4.82841e7	−0.840548	−0.420274	+	0.907397i	$0.638066\pi$
$54$	−1.90323e7	−0.304592
$55$	5.26195e7	0.775380
$56$	2.22308e7	0.302071
$57$	2.43268e7	0.305245
$58$	−3.80016e7	−0.440936
$59$	−8.28369e7	−0.889999	−0.445000	−	0.895531i	$-0.646796\pi$
$59$	−8.28369e7	−0.889999	−0.445000	+	0.895531i	$0.646796\pi$
$60$	3.90086e7	0.388579
$61$	1.07823e8	0.997076	0.498538	−	0.866868i	$-0.333870\pi$
$61$	1.07823e8	0.997076	0.498538	+	0.866868i	$0.333870\pi$
$62$	1.21869e8	1.04744
$63$	−1.57530e7	−0.125988
$64$	−2.18262e8	−1.62618
$65$	−6.74680e7	−0.468800
$66$	−2.44223e8	−1.58431
$67$	−6.09954e7	−0.369794	−0.184897	−	0.982758i	$-0.559195\pi$
$67$	−6.09954e7	−0.369794	−0.184897	+	0.982758i	$0.559195\pi$
$68$	−4.12088e8	−2.33722
$69$	−1.65640e8	−0.879722
$70$	5.37412e7	0.267526
$71$	3.45810e8	1.61501	0.807505	−	0.589860i	$-0.200817\pi$
$71$	3.45810e8	1.61501	0.807505	+	0.589860i	$0.200817\pi$
$72$	−6.07481e7	−0.266401
$73$	−4.35356e8	−1.79428	−0.897142	−	0.441742i	$-0.854361\pi$
$73$	−4.35356e8	−1.79428	−0.897142	+	0.441742i	$0.854361\pi$
$74$	−5.76383e8	−2.23444
$75$	3.16406e7	0.115470
$76$	2.31417e8	0.795671
$77$	−2.02143e8	−0.655315
$78$	3.13140e8	0.957883
$79$	1.56176e8	0.451121	0.225560	−	0.974229i	$-0.427579\pi$
$79$	1.56176e8	0.451121	0.225560	+	0.974229i	$0.427579\pi$
$80$	−3.93306e7	−0.107356
$81$	4.30467e7	0.111111
$82$	1.01107e9	2.46956
$83$	−2.28263e8	−0.527940	−0.263970	−	0.964531i	$-0.585032\pi$
$83$	−2.28263e8	−0.527940	−0.263970	+	0.964531i	$0.585032\pi$
$84$	−1.49855e8	−0.328409
$85$	−3.34253e8	−0.694529
$86$	−1.22336e9	−2.41164
$87$	8.59511e7	0.160848
$88$	−7.79523e8	−1.38566
$89$	−1.00731e9	−1.70181	−0.850903	−	0.525323i	$-0.823945\pi$
$89$	−1.00731e9	−1.70181	−0.850903	+	0.525323i	$0.823945\pi$
$90$	−1.46854e8	−0.235936
$91$	2.59185e8	0.396208
$92$	−1.57571e9	−2.29314
$93$	−2.75640e8	−0.382093
$94$	1.57456e8	0.208009
$95$	1.87707e8	0.236441
$96$	5.66533e8	0.680777
$97$	−1.50889e9	−1.73055	−0.865274	−	0.501300i	$-0.832855\pi$
$97$	−1.50889e9	−1.73055	−0.865274	+	0.501300i	$0.832855\pi$
$98$	−2.06452e8	−0.226101
$99$	5.52378e8	0.577934
$100$	3.00992e8	0.300992
$101$	−6.12709e8	−0.585880	−0.292940	−	0.956131i	$-0.594634\pi$
$101$	−6.12709e8	−0.585880	−0.292940	+	0.956131i	$0.594634\pi$
$102$	1.55137e9	1.41911
$103$	−9.19459e8	−0.804942	−0.402471	−	0.915433i	$-0.631849\pi$
$103$	−9.19459e8	−0.804942	−0.402471	+	0.915433i	$0.631849\pi$
$104$	9.99495e8	0.837781
$105$	−1.21551e8	−0.0975900
$106$	1.72918e9	1.33034
$107$	1.17064e9	0.863368	0.431684	−	0.902025i	$-0.357919\pi$
$107$	1.17064e9	0.863368	0.431684	+	0.902025i	$0.357919\pi$
$108$	4.09496e8	0.289630
$109$	−1.15522e9	−0.783872	−0.391936	−	0.919993i	$-0.628194\pi$
$109$	−1.15522e9	−0.783872	−0.391936	+	0.919993i	$0.628194\pi$
$110$	−1.88444e9	−1.22720
$111$	1.30365e9	0.815094
$112$	1.51092e8	0.0907322
$113$	−1.00961e9	−0.582505	−0.291253	−	0.956646i	$-0.594072\pi$
$113$	−1.00961e9	−0.582505	−0.291253	+	0.956646i	$0.594072\pi$
$114$	−8.71205e8	−0.483113
$115$	−1.27809e9	−0.681430
$116$	8.17639e8	0.419277
$117$	−7.08252e8	−0.349423
$118$	2.96660e9	1.40861
$119$	1.28407e9	0.586984
$120$	−4.68735e8	−0.206354
$121$	4.73020e9	2.00607
$122$	−3.86143e9	−1.57808
$123$	−2.28681e9	−0.900861
$124$	−2.62212e9	−0.995990
$125$	2.44141e8	0.0894427
$126$	5.64154e8	0.199402
$127$	2.17464e8	0.0741773	0.0370887	−	0.999312i	$-0.488192\pi$
$127$	2.17464e8	0.0741773	0.0370887	+	0.999312i	$0.488192\pi$
$128$	4.23547e9	1.39462
$129$	2.76697e9	0.879734
$130$	2.41620e9	0.741973
$131$	−1.77259e9	−0.525880	−0.262940	−	0.964812i	$-0.584692\pi$
$131$	−1.77259e9	−0.525880	−0.262940	+	0.964812i	$0.584692\pi$
$132$	5.25468e9	1.50648
$133$	−7.21094e8	−0.199830
$134$	2.18440e9	0.585276
$135$	3.32151e8	0.0860663
$136$	4.95174e9	1.24117
$137$	3.14137e9	0.761861	0.380931	−	0.924604i	$-0.375604\pi$
$137$	3.14137e9	0.761861	0.380931	+	0.924604i	$0.375604\pi$
$138$	5.93201e9	1.39234
$139$	3.25429e9	0.739417	0.369709	−	0.929148i	$-0.379457\pi$
$139$	3.25429e9	0.739417	0.369709	+	0.929148i	$0.379457\pi$
$140$	−1.15629e9	−0.254385
$141$	−3.56130e8	−0.0758791
$142$	−1.23844e10	−2.55609
$143$	−9.08833e9	−1.81749
$144$	−4.12877e8	−0.0800182
$145$	6.63203e8	0.124592
$146$	1.55912e10	2.83983
$147$	4.66949e8	0.0824786
$148$	1.24014e10	2.12468
$149$	−6.61484e9	−1.09946	−0.549732	−	0.835341i	$-0.685270\pi$
$149$	−6.61484e9	−1.09946	−0.549732	+	0.835341i	$0.685270\pi$
$150$	−1.13313e9	−0.182755
$151$	6.35305e9	0.994457	0.497228	−	0.867620i	$-0.334351\pi$
$151$	6.35305e9	0.994457	0.497228	+	0.867620i	$0.334351\pi$
$152$	−2.78075e9	−0.422539
$153$	−3.50885e9	−0.517671
$154$	7.23926e9	1.03717
$155$	−2.12685e9	−0.295968
$156$	−6.73749e9	−0.910830
$157$	−8.89146e9	−1.16795	−0.583976	−	0.811771i	$-0.698504\pi$
$157$	−8.89146e9	−1.16795	−0.583976	+	0.811771i	$0.698504\pi$
$158$	−5.59307e9	−0.713991
$159$	−3.91101e9	−0.485291
$160$	4.37140e9	0.527328
$161$	4.90991e9	0.575913
$162$	−1.54161e9	−0.175856
$163$	−1.03493e10	−1.14833	−0.574163	−	0.818741i	$-0.694672\pi$
$163$	−1.03493e10	−1.14833	−0.574163	+	0.818741i	$0.694672\pi$
$164$	−2.17541e10	−2.34825
$165$	4.26218e9	0.447666
$166$	8.17469e9	0.835574
$167$	8.18502e8	0.0814321	0.0407161	−	0.999171i	$-0.487036\pi$
$167$	8.18502e8	0.0814321	0.0407161	+	0.999171i	$0.487036\pi$
$168$	1.80069e9	0.174401
$169$	1.04844e9	0.0988678
$170$	1.19705e10	1.09924
$171$	1.97047e9	0.176233
$172$	2.63218e10	2.29317
$173$	−1.96017e10	−1.66374	−0.831872	−	0.554968i	$-0.812731\pi$
$173$	−1.96017e10	−1.66374	−0.831872	+	0.554968i	$0.812731\pi$
$174$	−3.07813e9	−0.254575
$175$	−9.37891e8	−0.0755929
$176$	−5.29806e9	−0.416207
$177$	−6.70979e9	−0.513841
$178$	3.60745e10	2.69346
$179$	−1.77307e10	−1.29089	−0.645443	−	0.763809i	$-0.723327\pi$
$179$	−1.77307e10	−1.29089	−0.645443	+	0.763809i	$0.723327\pi$
$180$	3.15969e9	0.224346
$181$	−5.76852e9	−0.399494	−0.199747	−	0.979847i	$-0.564012\pi$
$181$	−5.76852e9	−0.399494	−0.199747	+	0.979847i	$0.564012\pi$
$182$	−9.28208e9	−0.627082
$183$	8.73369e9	0.575662
$184$	1.89341e10	1.21777
$185$	1.00590e10	0.631369
$186$	9.87138e9	0.604741
$187$	−4.50258e10	−2.69262
$188$	−3.38780e9	−0.197792
$189$	−1.27599e9	−0.0727393
$190$	−6.72226e9	−0.374218
$191$	−2.73585e10	−1.48745	−0.743724	−	0.668487i	$-0.766942\pi$
$191$	−2.73585e10	−1.48745	−0.743724	+	0.668487i	$0.766942\pi$
$192$	−1.76792e10	−0.938875
$193$	3.19892e10	1.65957	0.829785	−	0.558084i	$-0.188463\pi$
$193$	3.19892e10	1.65957	0.829785	+	0.558084i	$0.188463\pi$
$194$	5.40371e10	2.73895
$195$	−5.46491e9	−0.270662
$196$	4.44201e9	0.214994
$197$	−2.39420e10	−1.13256	−0.566281	−	0.824212i	$-0.691618\pi$
$197$	−2.39420e10	−1.13256	−0.566281	+	0.824212i	$0.691618\pi$
$198$	−1.97821e10	−0.914700
$199$	−2.39019e10	−1.08042	−0.540212	−	0.841529i	$-0.681656\pi$
$199$	−2.39019e10	−1.08042	−0.540212	+	0.841529i	$0.681656\pi$
$200$	−3.61678e9	−0.159841
$201$	−4.94062e9	−0.213501
$202$	2.19427e10	0.927275
$203$	−2.54776e9	−0.105300
$204$	−3.33792e10	−1.34940
$205$	−1.76452e10	−0.697804
$206$	3.29282e10	1.27399
$207$	−1.34169e10	−0.507908
$208$	6.79310e9	0.251642
$209$	2.52852e10	0.916659
$210$	4.35304e9	0.154456
$211$	4.63597e10	1.61016	0.805081	−	0.593165i	$-0.202122\pi$
$211$	4.63597e10	1.61016	0.805081	+	0.593165i	$0.202122\pi$
$212$	−3.72048e10	−1.26499
$213$	2.80106e10	0.932427
$214$	−4.19236e10	−1.36646
$215$	2.13501e10	0.681439
$216$	−4.92060e9	−0.153807
$217$	8.17052e9	0.250139
$218$	4.13713e10	1.24064
$219$	−3.52638e10	−1.03593
$220$	4.05454e10	1.16692
$221$	5.77315e10	1.62798
$222$	−4.66870e10	−1.29005
$223$	4.21324e10	1.14089	0.570446	−	0.821335i	$-0.306770\pi$
$223$	4.21324e10	1.14089	0.570446	+	0.821335i	$0.306770\pi$
$224$	−1.67932e10	−0.445673
$225$	2.56289e9	0.0666667
$226$	3.61567e10	0.921935
$227$	5.31913e10	1.32961	0.664805	−	0.747017i	$-0.268515\pi$
$227$	5.31913e10	1.32961	0.664805	+	0.747017i	$0.268515\pi$
$228$	1.87448e10	0.459381
$229$	1.07297e10	0.257826	0.128913	−	0.991656i	$-0.458851\pi$
$229$	1.07297e10	0.257826	0.128913	+	0.991656i	$0.458851\pi$
$230$	4.57717e10	1.07850
$231$	−1.63736e10	−0.378346
$232$	−9.82492e9	−0.222655
$233$	9.09223e9	0.202101	0.101051	−	0.994881i	$-0.467780\pi$
$233$	9.09223e9	0.202101	0.101051	+	0.994881i	$0.467780\pi$
$234$	2.53643e10	0.553034
$235$	−2.74791e9	−0.0587757
$236$	−6.38291e10	−1.33941
$237$	1.26503e10	0.260455
$238$	−4.59857e10	−0.929023
$239$	−3.87663e10	−0.768536	−0.384268	−	0.923222i	$-0.625546\pi$
$239$	−3.87663e10	−0.768536	−0.384268	+	0.923222i	$0.625546\pi$
$240$	−3.18578e9	−0.0619819
$241$	−2.43486e10	−0.464941	−0.232471	−	0.972603i	$-0.574681\pi$
$241$	−2.43486e10	−0.464941	−0.232471	+	0.972603i	$0.574681\pi$
$242$	−1.69401e11	−3.17502
$243$	3.48678e9	0.0641500
$244$	8.30822e10	1.50056
$245$	3.60300e9	0.0638877
$246$	8.18967e10	1.42580
$247$	−3.24204e10	−0.554219
$248$	3.15079e10	0.528917
$249$	−1.84893e10	−0.304806
$250$	−8.74330e9	−0.141562
$251$	7.45034e10	1.18480	0.592399	−	0.805644i	$-0.298181\pi$
$251$	7.45034e10	1.18480	0.592399	+	0.805644i	$0.298181\pi$
$252$	−1.21383e10	−0.189607
$253$	−1.72166e11	−2.64183
$254$	−7.78795e9	−0.117401
$255$	−2.70745e10	−0.400986
$256$	−3.99330e10	−0.581101
$257$	−5.48723e10	−0.784610	−0.392305	−	0.919835i	$-0.628322\pi$
$257$	−5.48723e10	−0.784610	−0.392305	+	0.919835i	$0.628322\pi$
$258$	−9.90924e10	−1.39236
$259$	−3.86427e10	−0.533604
$260$	−5.19868e10	−0.705526
$261$	6.96204e9	0.0928655
$262$	6.34808e10	0.832313
$263$	−2.49569e9	−0.0321655	−0.0160827	−	0.999871i	$-0.505120\pi$
$263$	−2.49569e9	−0.0321655	−0.0160827	+	0.999871i	$0.505120\pi$
$264$	−6.31414e10	−0.800012
$265$	−3.01776e10	−0.375905
$266$	2.58242e10	0.316272
$267$	−8.15925e10	−0.982538
$268$	−4.69993e10	−0.556526
$269$	1.01620e11	1.18329	0.591647	−	0.806197i	$-0.298478\pi$
$269$	1.01620e11	1.18329	0.591647	+	0.806197i	$0.298478\pi$
$270$	−1.18952e10	−0.136218
$271$	−2.26977e10	−0.255635	−0.127817	−	0.991798i	$-0.540797\pi$
$271$	−2.26977e10	−0.255635	−0.127817	+	0.991798i	$0.540797\pi$
$272$	3.36547e10	0.372808
$273$	2.09940e10	0.228751
$274$	−1.12500e11	−1.20580
$275$	3.28872e10	0.346760
$276$	−1.27633e11	−1.32395
$277$	2.71976e10	0.277570	0.138785	−	0.990323i	$-0.455680\pi$
$277$	2.71976e10	0.277570	0.138785	+	0.990323i	$0.455680\pi$
$278$	−1.16544e11	−1.17028
$279$	−2.23268e10	−0.220602
$280$	1.38942e10	0.135090
$281$	−1.24340e11	−1.18968	−0.594842	−	0.803842i	$-0.702786\pi$
$281$	−1.24340e11	−1.18968	−0.594842	+	0.803842i	$0.702786\pi$
$282$	1.27539e10	0.120094
$283$	−2.18159e10	−0.202179	−0.101089	−	0.994877i	$-0.532233\pi$
$283$	−2.18159e10	−0.202179	−0.101089	+	0.994877i	$0.532233\pi$
$284$	2.66461e11	2.43053
$285$	1.52042e10	0.136510
$286$	3.25477e11	2.87655
$287$	6.77857e10	0.589752
$288$	4.58892e10	0.393047
$289$	1.67428e11	1.41185
$290$	−2.37510e10	−0.197193
$291$	−1.22220e11	−0.999132
$292$	−3.35459e11	−2.70033
$293$	−1.84628e11	−1.46350	−0.731750	−	0.681573i	$-0.761296\pi$
$293$	−1.84628e11	−1.46350	−0.731750	+	0.681573i	$0.761296\pi$
$294$	−1.67226e10	−0.130539
$295$	−5.17730e10	−0.398020
$296$	−1.49018e11	−1.12830
$297$	4.47426e10	0.333670
$298$	2.36894e11	1.74013
$299$	2.20749e11	1.59727
$300$	2.43804e10	0.173778
$301$	−8.20186e10	−0.575921
$302$	−2.27519e11	−1.57393
$303$	−4.96295e10	−0.338258
$304$	−1.88995e10	−0.126917
$305$	6.73896e10	0.445906
$306$	1.25661e11	0.819321
$307$	−1.05117e10	−0.0675386	−0.0337693	−	0.999430i	$-0.510751\pi$
$307$	−1.05117e10	−0.0675386	−0.0337693	+	0.999430i	$0.510751\pi$
$308$	−1.55759e11	−0.986224
$309$	−7.44762e10	−0.464734
$310$	7.61680e10	0.468431
$311$	2.19914e11	1.33300	0.666500	−	0.745505i	$-0.267791\pi$
$311$	2.19914e11	1.33300	0.666500	+	0.745505i	$0.267791\pi$
$312$	8.09591e10	0.483693
$313$	−9.45697e9	−0.0556932	−0.0278466	−	0.999612i	$-0.508865\pi$
$313$	−9.45697e9	−0.0556932	−0.0278466	+	0.999612i	$0.508865\pi$
$314$	3.18426e11	1.84852
$315$	−9.84560e9	−0.0563436
$316$	1.20340e11	0.678918
$317$	−1.44675e11	−0.804689	−0.402344	−	0.915488i	$-0.631805\pi$
$317$	−1.44675e11	−0.804689	−0.402344	+	0.915488i	$0.631805\pi$
$318$	1.40063e11	0.768073
$319$	8.93373e10	0.483031
$320$	−1.36414e11	−0.727249
$321$	9.48218e10	0.498466
$322$	−1.75836e11	−0.911502
$323$	−1.60618e11	−0.821077
$324$	3.31692e10	0.167218
$325$	−4.21675e10	−0.209654
$326$	3.70633e11	1.81746
$327$	−9.35727e10	−0.452569
$328$	2.61402e11	1.24703
$329$	1.05564e10	0.0496745
$330$	−1.52639e11	−0.708523
$331$	−1.44951e10	−0.0663734	−0.0331867	−	0.999449i	$-0.510566\pi$
$331$	−1.44951e10	−0.0663734	−0.0331867	+	0.999449i	$0.510566\pi$
$332$	−1.75886e11	−0.794529
$333$	1.05596e11	0.470594
$334$	−2.93127e10	−0.128883
$335$	−3.81221e10	−0.165377
$336$	1.22385e10	0.0523842
$337$	4.48099e11	1.89252	0.946258	−	0.323412i	$-0.104830\pi$
$337$	4.48099e11	1.89252	0.946258	+	0.323412i	$0.104830\pi$
$338$	−3.75474e10	−0.156479
$339$	−8.17783e10	−0.336310
$340$	−2.57555e11	−1.04524
$341$	−2.86499e11	−1.14744
$342$	−7.05676e10	−0.278925
$343$	−1.38413e10	−0.0539949
$344$	−3.16288e11	−1.21778
$345$	−1.03525e11	−0.393424
$346$	7.01987e11	2.63322
$347$	−9.24776e10	−0.342416	−0.171208	−	0.985235i	$-0.554767\pi$
$347$	−9.24776e10	−0.342416	−0.171208	+	0.985235i	$0.554767\pi$
$348$	6.62288e10	0.242069
$349$	3.15231e11	1.13740	0.568702	−	0.822543i	$-0.307446\pi$
$349$	3.15231e11	1.13740	0.568702	+	0.822543i	$0.307446\pi$
$350$	3.35883e10	0.119641
$351$	−5.73684e10	−0.201739
$352$	5.88853e11	2.04440
$353$	1.59837e10	0.0547886	0.0273943	−	0.999625i	$-0.491279\pi$
$353$	1.59837e10	0.0547886	0.0273943	+	0.999625i	$0.491279\pi$
$354$	2.40295e11	0.813260
$355$	2.16131e11	0.722255
$356$	−7.76176e11	−2.56115
$357$	1.04009e11	0.338895
$358$	6.34982e11	2.04309
$359$	−1.43936e11	−0.457346	−0.228673	−	0.973503i	$-0.573439\pi$
$359$	−1.43936e11	−0.457346	−0.228673	+	0.973503i	$0.573439\pi$
$360$	−3.79676e10	−0.119138
$361$	−2.32489e11	−0.720477
$362$	2.06585e11	0.632282
$363$	3.83146e11	1.15820
$364$	1.99712e11	0.596278
$365$	−2.72097e11	−0.802428
$366$	−3.12776e11	−0.911105
$367$	−2.20156e11	−0.633481	−0.316740	−	0.948512i	$-0.602588\pi$
$367$	−2.20156e11	−0.633481	−0.316740	+	0.948512i	$0.602588\pi$
$368$	1.28686e11	0.365777
$369$	−1.85232e11	−0.520113
$370$	−3.60239e11	−0.999271
$371$	1.15930e11	0.317697
$372$	−2.12392e11	−0.575035
$373$	1.12990e10	0.0302238	0.0151119	−	0.999886i	$-0.495190\pi$
$373$	1.12990e10	0.0302238	0.0151119	+	0.999886i	$0.495190\pi$
$374$	1.61249e12	4.26162
$375$	1.97754e10	0.0516398
$376$	4.07086e10	0.105037
$377$	−1.14547e11	−0.292044
$378$	4.56965e10	0.115125
$379$	−5.70052e11	−1.41918	−0.709590	−	0.704614i	$-0.751120\pi$
$379$	−5.70052e11	−1.41918	−0.709590	+	0.704614i	$0.751120\pi$
$380$	1.44636e11	0.355835
$381$	1.76146e10	0.0428263
$382$	9.79777e11	2.35419
$383$	1.52007e11	0.360968	0.180484	−	0.983578i	$-0.442234\pi$
$383$	1.52007e11	0.360968	0.180484	+	0.983578i	$0.442234\pi$
$384$	3.43073e11	0.805186
$385$	−1.26339e11	−0.293066
$386$	−1.14561e12	−2.62661
$387$	2.24125e11	0.507915
$388$	−1.16266e12	−2.60441
$389$	−6.06438e11	−1.34281	−0.671403	−	0.741092i	$-0.734308\pi$
$389$	−6.06438e11	−1.34281	−0.671403	+	0.741092i	$0.734308\pi$
$390$	1.95712e11	0.428378
$391$	1.09365e12	2.36636
$392$	−5.33761e10	−0.114172
$393$	−1.43579e11	−0.303617
$394$	8.57424e11	1.79251
$395$	9.76100e10	0.201747
$396$	4.25629e11	0.869767
$397$	−1.84846e11	−0.373467	−0.186734	−	0.982411i	$-0.559790\pi$
$397$	−1.84846e11	−0.373467	−0.186734	+	0.982411i	$0.559790\pi$
$398$	8.55990e11	1.70999
$399$	−5.84086e10	−0.115372
$400$	−2.45816e10	−0.0480109
$401$	−9.11060e10	−0.175953	−0.0879766	−	0.996123i	$-0.528040\pi$
$401$	−9.11060e10	−0.175953	−0.0879766	+	0.996123i	$0.528040\pi$
$402$	1.76936e11	0.337909
$403$	3.67346e11	0.693749
$404$	−4.72117e11	−0.881725
$405$	2.69042e10	0.0496904
$406$	9.12419e10	0.166658
$407$	1.35501e12	2.44775
$408$	4.01091e11	0.716592
$409$	−5.88759e11	−1.04036	−0.520179	−	0.854057i	$-0.674135\pi$
$409$	−5.88759e11	−1.04036	−0.520179	+	0.854057i	$0.674135\pi$
$410$	6.31919e11	1.10442
$411$	2.54451e11	0.439861
$412$	−7.08480e11	−1.21141
$413$	1.98891e11	0.336388
$414$	4.80493e11	0.803869
$415$	−1.42665e11	−0.236102
$416$	−7.55020e11	−1.23606
$417$	2.63597e11	0.426903
$418$	−9.05528e11	−1.45080
$419$	8.87719e10	0.140706	0.0703529	−	0.997522i	$-0.477587\pi$
$419$	8.87719e10	0.140706	0.0703529	+	0.997522i	$0.477587\pi$
$420$	−9.36596e10	−0.146869
$421$	−6.81644e11	−1.05752	−0.528760	−	0.848772i	$-0.677343\pi$
$421$	−6.81644e11	−1.05752	−0.528760	+	0.848772i	$0.677343\pi$
$422$	−1.66026e12	−2.54841
$423$	−2.88465e10	−0.0438088
$424$	4.47061e11	0.671770
$425$	−2.08908e11	−0.310603
$426$	−1.00313e12	−1.47576
$427$	−2.58884e11	−0.376859
$428$	9.02024e11	1.29934
$429$	−7.36155e11	−1.04933
$430$	−7.64602e11	−1.07852
$431$	−8.67770e11	−1.21131	−0.605657	−	0.795726i	$-0.707090\pi$
$431$	−8.67770e11	−1.21131	−0.605657	+	0.795726i	$0.707090\pi$
$432$	−3.34430e10	−0.0461986
$433$	5.63267e10	0.0770050	0.0385025	−	0.999259i	$-0.487741\pi$
$433$	5.63267e10	0.0770050	0.0385025	+	0.999259i	$0.487741\pi$
$434$	−2.92607e11	−0.395896
$435$	5.37195e10	0.0719333
$436$	−8.90142e11	−1.17970
$437$	−6.14160e11	−0.805592
$438$	1.26289e12	1.63957
$439$	2.74363e11	0.352562	0.176281	−	0.984340i	$-0.443593\pi$
$439$	2.74363e11	0.352562	0.176281	+	0.984340i	$0.443593\pi$
$440$	−4.87202e11	−0.619686
$441$	3.78229e10	0.0476190
$442$	−2.06751e12	−2.57661
$443$	−2.04299e11	−0.252028	−0.126014	−	0.992028i	$-0.540218\pi$
$443$	−2.04299e11	−0.252028	−0.126014	+	0.992028i	$0.540218\pi$
$444$	1.00451e12	1.22668
$445$	−6.29572e11	−0.761071
$446$	−1.50887e12	−1.80570
$447$	−5.35802e11	−0.634776
$448$	5.24047e11	0.614638
$449$	1.50425e12	1.74668	0.873338	−	0.487114i	$-0.161951\pi$
$449$	1.50425e12	1.74668	0.873338	+	0.487114i	$0.161951\pi$
$450$	−9.17837e10	−0.105514
$451$	−2.37691e12	−2.70532
$452$	−7.77943e11	−0.876648
$453$	5.14597e11	0.574150
$454$	−1.90492e12	−2.10438
$455$	1.61991e11	0.177190
$456$	−2.25241e11	−0.243953
$457$	4.80154e10	0.0514941	0.0257470	−	0.999668i	$-0.491804\pi$
$457$	4.80154e10	0.0514941	0.0257470	+	0.999668i	$0.491804\pi$
$458$	−3.84258e11	−0.408064
$459$	−2.84217e11	−0.298878
$460$	−9.84819e11	−1.02552
$461$	9.97395e11	1.02852	0.514260	−	0.857634i	$-0.328067\pi$
$461$	9.97395e11	1.02852	0.514260	+	0.857634i	$0.328067\pi$
$462$	5.86380e11	0.598811
$463$	−1.62897e12	−1.64740	−0.823699	−	0.567027i	$-0.808093\pi$
$463$	−1.62897e12	−1.64740	−0.823699	+	0.567027i	$0.808093\pi$
$464$	−6.67754e10	−0.0668784
$465$	−1.72275e11	−0.170877
$466$	−3.25616e11	−0.319867
$467$	2.32981e11	0.226670	0.113335	−	0.993557i	$-0.463847\pi$
$467$	2.32981e11	0.226670	0.113335	+	0.993557i	$0.463847\pi$
$468$	−5.45736e11	−0.525868
$469$	1.46450e11	0.139769
$470$	9.84098e10	0.0930247
$471$	−7.20209e11	−0.674317
$472$	7.66984e11	0.711291
$473$	2.87598e12	2.64187
$474$	−4.53038e11	−0.412223
$475$	1.17317e11	0.105740
$476$	9.89424e11	0.883387
$477$	−3.16792e11	−0.280183
$478$	1.38832e12	1.21637
$479$	5.50909e11	0.478157	0.239078	−	0.971000i	$-0.423155\pi$
$479$	5.50909e11	0.478157	0.239078	+	0.971000i	$0.423155\pi$
$480$	3.54083e11	0.304453
$481$	−1.73738e12	−1.47993
$482$	8.71988e11	0.735866
$483$	3.97703e11	0.332504
$484$	3.64481e12	3.01905
$485$	−9.43053e11	−0.773924
$486$	−1.24871e11	−0.101531
$487$	−8.41488e11	−0.677903	−0.338952	−	0.940804i	$-0.610072\pi$
$487$	−8.41488e11	−0.677903	−0.338952	+	0.940804i	$0.610072\pi$
$488$	−9.98333e11	−0.796868
$489$	−8.38290e11	−0.662986
$490$	−1.29033e11	−0.101115
$491$	5.68127e10	0.0441143	0.0220571	−	0.999757i	$-0.492978\pi$
$491$	5.68127e10	0.0441143	0.0220571	+	0.999757i	$0.492978\pi$
$492$	−1.76208e12	−1.35576
$493$	−5.67495e11	−0.432664
$494$	1.16106e12	0.877166
$495$	3.45236e11	0.258460
$496$	2.14145e11	0.158869
$497$	−8.30291e11	−0.610417
$498$	6.62150e11	0.482419
$499$	1.59993e12	1.15518	0.577589	−	0.816328i	$-0.303994\pi$
$499$	1.59993e12	1.15518	0.577589	+	0.816328i	$0.303994\pi$
$500$	1.88120e11	0.134608
$501$	6.62987e10	0.0470149
$502$	−2.66816e12	−1.87519
$503$	−2.13568e12	−1.48758	−0.743790	−	0.668413i	$-0.766974\pi$
$503$	−2.13568e12	−1.48758	−0.743790	+	0.668413i	$0.766974\pi$
$504$	1.45856e11	0.100690
$505$	−3.82943e11	−0.262013
$506$	6.16571e12	4.18125
$507$	8.49239e10	0.0570813
$508$	1.67565e11	0.111634
$509$	−2.64888e11	−0.174917	−0.0874585	−	0.996168i	$-0.527875\pi$
$509$	−2.64888e11	−0.174917	−0.0874585	+	0.996168i	$0.527875\pi$
$510$	9.69607e11	0.634644
$511$	1.04529e12	0.678176
$512$	−7.38460e11	−0.474911
$513$	1.59608e11	0.101748
$514$	1.96512e12	1.24181
$515$	−5.74662e11	−0.359981
$516$	2.13206e12	1.32396
$517$	−3.70160e11	−0.227867
$518$	1.38390e12	0.844539
$519$	−1.58774e12	−0.960563
$520$	6.24684e11	0.374667
$521$	6.57232e11	0.390795	0.195398	−	0.980724i	$-0.437400\pi$
$521$	6.57232e11	0.390795	0.195398	+	0.980724i	$0.437400\pi$
$522$	−2.49329e11	−0.146979
$523$	−7.78872e11	−0.455207	−0.227603	−	0.973754i	$-0.573089\pi$
$523$	−7.78872e11	−0.455207	−0.227603	+	0.973754i	$0.573089\pi$
$524$	−1.36585e12	−0.791428
$525$	−7.59691e10	−0.0436436
$526$	8.93771e10	0.0509085
$527$	1.81992e12	1.02779
$528$	−4.29143e11	−0.240297
$529$	2.38064e12	1.32173
$530$	1.08074e12	0.594947
$531$	−5.43493e11	−0.296666
$532$	−5.55632e11	−0.300736
$533$	3.04764e12	1.63565
$534$	2.92204e12	1.55507
$535$	7.31650e11	0.386110
$536$	5.64754e11	0.295541
$537$	−1.43619e12	−0.745293
$538$	−3.63926e12	−1.87281
$539$	4.85345e11	0.247686
$540$	2.55935e11	0.129526
$541$	3.65316e12	1.83350	0.916749	−	0.399463i	$-0.130803\pi$
$541$	3.65316e12	1.83350	0.916749	+	0.399463i	$0.130803\pi$
$542$	8.12863e11	0.404595
$543$	−4.67250e11	−0.230648
$544$	−3.74055e12	−1.83122
$545$	−7.22012e11	−0.350558
$546$	−7.51849e11	−0.362046
$547$	3.95047e12	1.88671	0.943357	−	0.331780i	$-0.107649\pi$
$547$	3.95047e12	1.88671	0.943357	+	0.331780i	$0.107649\pi$
$548$	2.42055e12	1.14657
$549$	7.07429e11	0.332359
$550$	−1.17777e12	−0.548820
$551$	3.18689e11	0.147294
$552$	1.53366e12	0.703078
$553$	−3.74979e11	−0.170508
$554$	−9.74017e11	−0.439312
$555$	8.14781e11	0.364521
$556$	2.50756e12	1.11279
$557$	−2.64871e12	−1.16597	−0.582983	−	0.812485i	$-0.698114\pi$
$557$	−2.64871e12	−1.16597	−0.582983	+	0.812485i	$0.698114\pi$
$558$	7.99582e11	0.349147
$559$	−3.68755e12	−1.59729
$560$	9.44327e10	0.0405767
$561$	−3.64709e12	−1.55458
$562$	4.45293e12	1.88292
$563$	4.22760e12	1.77340	0.886700	−	0.462346i	$-0.152992\pi$
$563$	4.22760e12	1.77340	0.886700	+	0.462346i	$0.152992\pi$
$564$	−2.74412e11	−0.114195
$565$	−6.31005e11	−0.260504
$566$	7.81285e11	0.319989
$567$	−1.03355e11	−0.0419961
$568$	−3.20185e12	−1.29072
$569$	−2.22544e11	−0.0890040	−0.0445020	−	0.999009i	$-0.514170\pi$
$569$	−2.22544e11	−0.0890040	−0.0445020	+	0.999009i	$0.514170\pi$
$570$	−5.44503e11	−0.216055
$571$	−2.23366e11	−0.0879336	−0.0439668	−	0.999033i	$-0.514000\pi$
$571$	−2.23366e11	−0.0879336	−0.0439668	+	0.999033i	$0.514000\pi$
$572$	−7.00292e12	−2.73525
$573$	−2.21604e12	−0.858778
$574$	−2.42758e12	−0.933405
$575$	−7.98806e11	−0.304745
$576$	−1.43202e12	−0.542059
$577$	9.14770e11	0.343574	0.171787	−	0.985134i	$-0.445046\pi$
$577$	9.14770e11	0.343574	0.171787	+	0.985134i	$0.445046\pi$
$578$	−5.99604e12	−2.23454
$579$	2.59112e12	0.958153
$580$	5.11024e11	0.187506
$581$	5.48060e11	0.199543
$582$	4.37700e12	1.58133
$583$	−4.06509e12	−1.45734
$584$	4.03094e12	1.43400
$585$	−4.42658e11	−0.156267
$586$	6.61200e12	2.31629
$587$	−8.90998e10	−0.0309746	−0.0154873	−	0.999880i	$-0.504930\pi$
$587$	−8.90998e10	−0.0309746	−0.0154873	+	0.999880i	$0.504930\pi$
$588$	3.59803e11	0.124127
$589$	−1.02202e12	−0.349896
$590$	1.85413e12	0.629948
$591$	−1.93930e12	−0.653885
$592$	−1.01281e12	−0.338905
$593$	4.43657e12	1.47333	0.736667	−	0.676255i	$-0.236398\pi$
$593$	4.43657e12	1.47333	0.736667	+	0.676255i	$0.236398\pi$
$594$	−1.60235e12	−0.528102
$595$	8.02541e11	0.262507
$596$	−5.09700e12	−1.65465
$597$	−1.93606e12	−0.623783
$598$	−7.90560e12	−2.52801
$599$	−2.96966e12	−0.942510	−0.471255	−	0.881997i	$-0.656199\pi$
$599$	−2.96966e12	−0.942510	−0.471255	+	0.881997i	$0.656199\pi$
$600$	−2.92960e11	−0.0922841
$601$	4.15976e12	1.30057	0.650284	−	0.759691i	$-0.274650\pi$
$601$	4.15976e12	1.30057	0.650284	+	0.759691i	$0.274650\pi$
$602$	2.93730e12	0.911514
$603$	−4.00191e11	−0.123265
$604$	4.89527e12	1.49662
$605$	2.95638e12	0.897141
$606$	1.77736e12	0.535363
$607$	1.72840e12	0.516767	0.258383	−	0.966042i	$-0.416810\pi$
$607$	1.72840e12	0.516767	0.258383	+	0.966042i	$0.416810\pi$
$608$	2.10059e12	0.623411
$609$	−2.06369e11	−0.0607947
$610$	−2.41339e12	−0.705739
$611$	4.74614e11	0.137770
$612$	−2.70371e12	−0.779074
$613$	−3.80459e12	−1.08827	−0.544134	−	0.838998i	$-0.683142\pi$
$613$	−3.80459e12	−1.08827	−0.544134	+	0.838998i	$0.683142\pi$
$614$	3.76453e11	0.106894
$615$	−1.42926e12	−0.402877
$616$	1.87164e12	0.523731
$617$	3.47525e12	0.965390	0.482695	−	0.875788i	$-0.339658\pi$
$617$	3.47525e12	0.965390	0.482695	+	0.875788i	$0.339658\pi$
$618$	2.66718e12	0.735537
$619$	5.88125e11	0.161013	0.0805067	−	0.996754i	$-0.474346\pi$
$619$	5.88125e11	0.161013	0.0805067	+	0.996754i	$0.474346\pi$
$620$	−1.63882e12	−0.445420
$621$	−1.08677e12	−0.293241
$622$	−7.87567e12	−2.10975
$623$	2.41856e12	0.643222
$624$	5.50241e11	0.145286
$625$	1.52588e11	0.0400000
$626$	3.38678e11	0.0881460
$627$	2.04810e12	0.529234
$628$	−6.85123e12	−1.75772
$629$	−8.60738e12	−2.19252
$630$	3.52596e11	0.0891754
$631$	4.71015e12	1.18278	0.591388	−	0.806387i	$-0.298580\pi$
$631$	4.71015e12	1.18278	0.591388	+	0.806387i	$0.298580\pi$
$632$	−1.44603e12	−0.360537
$633$	3.75514e12	0.929627
$634$	5.18119e12	1.27359
$635$	1.35915e11	0.0331731
$636$	−3.01359e12	−0.730343
$637$	−6.22303e11	−0.149753
$638$	−3.19940e12	−0.764496
$639$	2.26886e12	0.538337
$640$	2.64717e12	0.623694
$641$	1.19663e12	0.279962	0.139981	−	0.990154i	$-0.455296\pi$
$641$	1.19663e12	0.279962	0.139981	+	0.990154i	$0.455296\pi$
$642$	−3.39581e12	−0.788925
$643$	1.29513e12	0.298789	0.149395	−	0.988778i	$-0.452267\pi$
$643$	1.29513e12	0.298789	0.149395	+	0.988778i	$0.452267\pi$
$644$	3.78328e12	0.866727
$645$	1.72936e12	0.393429
$646$	5.75216e12	1.29952
$647$	1.48852e11	0.0333953	0.0166977	−	0.999861i	$-0.494685\pi$
$647$	1.48852e11	0.0333953	0.0166977	+	0.999861i	$0.494685\pi$
$648$	−3.98568e11	−0.0888005
$649$	−6.97413e12	−1.54308
$650$	1.51013e12	0.331820
$651$	6.61812e11	0.144418
$652$	−7.97451e12	−1.72818
$653$	3.04475e12	0.655302	0.327651	−	0.944799i	$-0.393743\pi$
$653$	3.04475e12	0.655302	0.327651	+	0.944799i	$0.393743\pi$
$654$	3.35108e12	0.716283
$655$	−1.10787e12	−0.235181
$656$	1.77663e12	0.374566
$657$	−2.85637e12	−0.598095
$658$	−3.78051e11	−0.0786202
$659$	−1.26892e12	−0.262090	−0.131045	−	0.991376i	$-0.541833\pi$
$659$	−1.26892e12	−0.262090	−0.131045	+	0.991376i	$0.541833\pi$
$660$	3.28418e12	0.673719
$661$	5.05562e11	0.103007	0.0515036	−	0.998673i	$-0.483599\pi$
$661$	5.05562e11	0.103007	0.0515036	+	0.998673i	$0.483599\pi$
$662$	5.19106e11	0.105050
$663$	4.67625e12	0.939912
$664$	2.11348e12	0.421932
$665$	−4.50684e11	−0.0893665
$666$	−3.78165e12	−0.744813
$667$	−2.16994e12	−0.424504
$668$	6.30689e11	0.122552
$669$	3.41273e12	0.658695
$670$	1.36525e12	0.261743
$671$	9.07777e12	1.72873
$672$	−1.36025e12	−0.257310
$673$	3.83391e12	0.720401	0.360201	−	0.932875i	$-0.382708\pi$
$673$	3.83391e12	0.720401	0.360201	+	0.932875i	$0.382708\pi$
$674$	−1.60476e13	−2.99530
$675$	2.07594e11	0.0384900
$676$	8.07867e11	0.148792
$677$	−7.47732e12	−1.36803	−0.684017	−	0.729466i	$-0.739769\pi$
$677$	−7.47732e12	−1.36803	−0.684017	+	0.729466i	$0.739769\pi$
$678$	2.92869e12	0.532280
$679$	3.62283e12	0.654085
$680$	3.09484e12	0.555070
$681$	4.30849e12	0.767650
$682$	1.02603e13	1.81606
$683$	4.35616e11	0.0765969	0.0382984	−	0.999266i	$-0.487806\pi$
$683$	4.35616e11	0.0765969	0.0382984	+	0.999266i	$0.487806\pi$
$684$	1.51833e12	0.265224
$685$	1.96335e12	0.340715
$686$	4.95692e11	0.0854581
$687$	8.69105e11	0.148856
$688$	−2.14966e12	−0.365782
$689$	5.21221e12	0.881121
$690$	3.70751e12	0.622674
$691$	3.77081e12	0.629193	0.314596	−	0.949226i	$-0.398131\pi$
$691$	3.77081e12	0.629193	0.314596	+	0.949226i	$0.398131\pi$
$692$	−1.51039e13	−2.50387
$693$	−1.32626e12	−0.218438
$694$	3.31186e12	0.541944
$695$	2.03393e12	0.330678
$696$	−7.95819e11	−0.128550
$697$	1.50988e13	2.42323
$698$	−1.12892e13	−1.80018
$699$	7.36471e11	0.116683
$700$	−7.22682e11	−0.113764
$701$	−2.85631e12	−0.446760	−0.223380	−	0.974731i	$-0.571709\pi$
$701$	−2.85631e12	−0.446760	−0.223380	+	0.974731i	$0.571709\pi$
$702$	2.05451e12	0.319294
$703$	4.83366e12	0.746409
$704$	−1.83757e13	−2.81947
$705$	−2.22581e11	−0.0339342
$706$	−5.72416e11	−0.0867143
$707$	1.47112e12	0.221442
$708$	−5.17016e12	−0.773311
$709$	−3.58768e12	−0.533219	−0.266609	−	0.963805i	$-0.585903\pi$
$709$	−3.58768e12	−0.533219	−0.266609	+	0.963805i	$0.585903\pi$
$710$	−7.74022e12	−1.14312
$711$	1.02467e12	0.150374
$712$	9.32670e12	1.36009
$713$	6.95887e12	1.00841
$714$	−3.72484e12	−0.536372
$715$	−5.68021e12	−0.812806
$716$	−1.36622e13	−1.94273
$717$	−3.14007e12	−0.443715
$718$	5.15472e12	0.723844
$719$	−1.01912e13	−1.42214	−0.711072	−	0.703119i	$-0.751790\pi$
$719$	−1.01912e13	−1.42214	−0.711072	+	0.703119i	$0.751790\pi$
$720$	−2.58048e11	−0.0357852
$721$	2.20762e12	0.304240
$722$	8.32603e12	1.14030
$723$	−1.97224e12	−0.268434
$724$	−4.44487e12	−0.601223
$725$	4.14502e11	0.0557193
$726$	−1.37215e13	−1.83310
$727$	−3.99530e12	−0.530450	−0.265225	−	0.964186i	$-0.585446\pi$
$727$	−3.99530e12	−0.530450	−0.265225	+	0.964186i	$0.585446\pi$
$728$	−2.39979e12	−0.316651
$729$	2.82430e11	0.0370370
$730$	9.74450e12	1.27001
$731$	−1.82690e13	−2.36639
$732$	6.72965e12	0.866349
$733$	9.16984e12	1.17326	0.586630	−	0.809855i	$-0.300454\pi$
$733$	9.16984e12	1.17326	0.586630	+	0.809855i	$0.300454\pi$
$734$	7.88435e12	1.00261
$735$	2.91843e11	0.0368856
$736$	−1.43028e13	−1.79668
$737$	−5.13527e12	−0.641150
$738$	6.63363e12	0.823186
$739$	3.49268e12	0.430783	0.215391	−	0.976528i	$-0.430897\pi$
$739$	3.49268e12	0.430783	0.215391	+	0.976528i	$0.430897\pi$
$740$	7.75088e12	0.950185
$741$	−2.62605e12	−0.319978
$742$	−4.15175e12	−0.502822
$743$	5.84311e12	0.703387	0.351694	−	0.936115i	$-0.385606\pi$
$743$	5.84311e12	0.703387	0.351694	+	0.936115i	$0.385606\pi$
$744$	2.55214e12	0.305370
$745$	−4.13428e12	−0.491696
$746$	−4.04644e11	−0.0478353
$747$	−1.49763e12	−0.175980
$748$	−3.46942e13	−4.05228
$749$	−2.81071e12	−0.326323
$750$	−7.08207e11	−0.0817306
$751$	2.28360e12	0.261964	0.130982	−	0.991385i	$-0.458187\pi$
$751$	2.28360e12	0.261964	0.130982	+	0.991385i	$0.458187\pi$
$752$	2.76677e11	0.0315495
$753$	6.03478e12	0.684044
$754$	4.10223e12	0.462220
$755$	3.97065e12	0.444734
$756$	−9.83201e11	−0.109470
$757$	5.77803e12	0.639511	0.319755	−	0.947500i	$-0.396399\pi$
$757$	5.77803e12	0.639511	0.319755	+	0.947500i	$0.396399\pi$
$758$	2.04150e13	2.24615
$759$	−1.39455e13	−1.52526
$760$	−1.73797e12	−0.188965
$761$	1.40979e13	1.52378	0.761892	−	0.647704i	$-0.224271\pi$
$761$	1.40979e13	1.52378	0.761892	+	0.647704i	$0.224271\pi$
$762$	−6.30824e11	−0.0677815
$763$	2.77368e12	0.296276
$764$	−2.10808e13	−2.23855
$765$	−2.19303e12	−0.231510
$766$	−5.44376e12	−0.571307
$767$	8.94214e12	0.932959
$768$	−3.23457e12	−0.335499
$769$	1.16373e13	1.20000	0.600002	−	0.799999i	$-0.295167\pi$
$769$	1.16373e13	1.20000	0.600002	+	0.799999i	$0.295167\pi$
$770$	4.52454e12	0.463837
$771$	−4.44466e12	−0.452995
$772$	2.46489e13	2.49759
$773$	1.57196e13	1.58356	0.791779	−	0.610808i	$-0.209155\pi$
$773$	1.57196e13	1.58356	0.791779	+	0.610808i	$0.209155\pi$
$774$	−8.02649e12	−0.803880
$775$	−1.32928e12	−0.132361
$776$	1.39707e13	1.38306
$777$	−3.13006e12	−0.308076
$778$	2.17181e13	2.12527
$779$	−8.47902e12	−0.824949
$780$	−4.21093e12	−0.407335
$781$	2.91142e13	2.80011
$782$	−3.91663e13	−3.74526
$783$	5.63925e11	0.0536159
$784$	−3.62773e11	−0.0342935
$785$	−5.55717e12	−0.522324
$786$	5.14195e12	0.480536
$787$	8.78355e12	0.816176	0.408088	−	0.912943i	$-0.366196\pi$
$787$	8.78355e12	0.816176	0.408088	+	0.912943i	$0.366196\pi$
$788$	−1.84483e13	−1.70446
$789$	−2.02151e11	−0.0185707
$790$	−3.49567e12	−0.319307
$791$	2.42407e12	0.220166
$792$	−5.11445e12	−0.461887
$793$	−1.16394e13	−1.04520
$794$	6.61981e12	0.591089
$795$	−2.44438e12	−0.217029
$796$	−1.84174e13	−1.62600
$797$	9.70422e12	0.851919	0.425960	−	0.904742i	$-0.359937\pi$
$797$	9.70422e12	0.851919	0.425960	+	0.904742i	$0.359937\pi$
$798$	2.09176e12	0.182599
$799$	2.35136e12	0.204107
$800$	2.73212e12	0.235828
$801$	−6.60899e12	−0.567269
$802$	3.26274e12	0.278482
$803$	−3.66531e13	−3.11093
$804$	−3.80695e12	−0.321310
$805$	3.06869e12	0.257556
$806$	−1.31556e13	−1.09800
$807$	8.23119e12	0.683175
$808$	5.67306e12	0.468237
$809$	1.62305e13	1.33218	0.666090	−	0.745872i	$-0.267967\pi$
$809$	1.62305e13	1.33218	0.666090	+	0.745872i	$0.267967\pi$
$810$	−9.63508e11	−0.0786453
$811$	−5.37254e12	−0.436100	−0.218050	−	0.975938i	$-0.569970\pi$
$811$	−5.37254e12	−0.436100	−0.218050	+	0.975938i	$0.569970\pi$
$812$	−1.96315e12	−0.158472
$813$	−1.83851e12	−0.147591
$814$	−4.85264e13	−3.87407
$815$	−6.46829e12	−0.513547
$816$	2.72603e12	0.215241
$817$	1.02594e13	0.805602
$818$	2.10850e13	1.64658
$819$	1.70051e12	0.132069
$820$	−1.35963e13	−1.05017
$821$	−1.92984e13	−1.48244	−0.741221	−	0.671262i	$-0.765753\pi$
$821$	−1.92984e13	−1.48244	−0.741221	+	0.671262i	$0.765753\pi$
$822$	−9.11253e12	−0.696171
$823$	−1.24146e10	−0.000943268 0	−0.000471634	−	1.00000i	$-0.500150\pi$
$823$	−1.24146e10	−0.000943268 0	−0.000471634		1.00000i	$0.500150\pi$
$824$	8.51324e12	0.643313
$825$	2.66386e12	0.200202
$826$	−7.12281e12	−0.532404
$827$	2.23970e13	1.66500	0.832502	−	0.554022i	$-0.186908\pi$
$827$	2.23970e13	1.66500	0.832502	+	0.554022i	$0.186908\pi$
$828$	−1.03382e13	−0.764381
$829$	−1.36701e13	−1.00525	−0.502627	−	0.864504i	$-0.667633\pi$
$829$	−1.36701e13	−1.00525	−0.502627	+	0.864504i	$0.667633\pi$
$830$	5.10918e12	0.373680
$831$	2.20301e12	0.160255
$832$	2.35611e13	1.70467
$833$	−3.08304e12	−0.221859
$834$	−9.44010e12	−0.675662
$835$	5.11564e11	0.0364176
$836$	1.94832e13	1.37954
$837$	−1.80847e12	−0.127364
$838$	−3.17915e12	−0.222696
$839$	−8.86389e12	−0.617583	−0.308792	−	0.951130i	$-0.599925\pi$
$839$	−8.86389e12	−0.617583	−0.308792	+	0.951130i	$0.599925\pi$
$840$	1.12543e12	0.0779943
$841$	−1.33812e13	−0.922384
$842$	2.44114e13	1.67374
$843$	−1.00715e13	−0.686865
$844$	3.57220e13	2.42323
$845$	6.55277e11	0.0442150
$846$	1.03307e12	0.0693365
$847$	−1.13572e13	−0.758222
$848$	3.03847e12	0.201778
$849$	−1.76709e12	−0.116728
$850$	7.48154e12	0.491593
$851$	−3.29122e13	−2.15117
$852$	2.15833e13	1.40327
$853$	1.57022e11	0.0101552	0.00507762	−	0.999987i	$-0.498384\pi$
$853$	1.57022e11	0.0101552	0.00507762	+	0.999987i	$0.498384\pi$
$854$	9.27129e12	0.596458
$855$	1.23154e12	0.0788138
$856$	−1.08389e13	−0.690008
$857$	−1.86750e13	−1.18262	−0.591312	−	0.806443i	$-0.701390\pi$
$857$	−1.86750e13	−1.18262	−0.591312	+	0.806443i	$0.701390\pi$
$858$	2.63636e13	1.66078
$859$	4.59125e10	0.00287714	0.00143857	−	0.999999i	$-0.499542\pi$
$859$	4.59125e10	0.00287714	0.00143857	+	0.999999i	$0.499542\pi$
$860$	1.64511e13	1.02554
$861$	5.49064e12	0.340494
$862$	3.10771e13	1.91716
$863$	−6.27875e12	−0.385323	−0.192661	−	0.981265i	$-0.561712\pi$
$863$	−6.27875e12	−0.385323	−0.192661	+	0.981265i	$0.561712\pi$
$864$	3.71702e12	0.226926
$865$	−1.22511e13	−0.744049
$866$	−2.01720e12	−0.121876
$867$	1.35617e13	0.815132
$868$	6.29571e12	0.376449
$869$	1.31486e13	0.782153
$870$	−1.92383e12	−0.113849
$871$	6.58437e12	0.387644
$872$	1.06961e13	0.626473
$873$	−9.89980e12	−0.576849
$874$	2.19946e13	1.27502
$875$	−5.86182e11	−0.0338062
$876$	−2.71722e13	−1.55903
$877$	−1.02257e13	−0.583708	−0.291854	−	0.956463i	$-0.594272\pi$
$877$	−1.02257e13	−0.583708	−0.291854	+	0.956463i	$0.594272\pi$
$878$	−9.82564e12	−0.558002
$879$	−1.49549e13	−0.844952
$880$	−3.31129e12	−0.186134
$881$	2.72329e13	1.52301	0.761503	−	0.648161i	$-0.224462\pi$
$881$	2.72329e13	1.52301	0.761503	+	0.648161i	$0.224462\pi$
$882$	−1.35453e12	−0.0753670
$883$	−6.00194e12	−0.332253	−0.166126	−	0.986104i	$-0.553126\pi$
$883$	−6.00194e12	−0.332253	−0.166126	+	0.986104i	$0.553126\pi$
$884$	4.44844e13	2.45004
$885$	−4.19362e12	−0.229797
$886$	7.31647e12	0.398887
$887$	−3.89408e12	−0.211227	−0.105613	−	0.994407i	$-0.533681\pi$
$887$	−3.89408e12	−0.211227	−0.105613	+	0.994407i	$0.533681\pi$
$888$	−1.20705e13	−0.651426
$889$	−5.22132e11	−0.0280364
$890$	2.25466e13	1.20455
$891$	3.62415e12	0.192645
$892$	3.24647e13	1.71700
$893$	−1.32045e12	−0.0694850
$894$	1.91885e13	1.00466
$895$	−1.10817e13	−0.577302
$896$	−1.01694e13	−0.527118
$897$	1.78807e13	0.922185
$898$	−5.38712e13	−2.76448
$899$	−3.61097e12	−0.184376
$900$	1.97481e12	0.100331
$901$	2.58226e13	1.30538
$902$	8.51232e13	4.28172
$903$	−6.64351e12	−0.332508
$904$	9.34793e12	0.465541
$905$	−3.60532e12	−0.178659
$906$	−1.84290e13	−0.908711
$907$	2.08550e13	1.02324	0.511619	−	0.859212i	$-0.329046\pi$
$907$	2.08550e13	1.02324	0.511619	+	0.859212i	$0.329046\pi$
$908$	4.09860e13	2.00101
$909$	−4.01999e12	−0.195293
$910$	−5.80130e12	−0.280439
$911$	3.23594e13	1.55657	0.778283	−	0.627914i	$-0.216091\pi$
$911$	3.23594e13	1.55657	0.778283	+	0.627914i	$0.216091\pi$
$912$	−1.53086e12	−0.0732754
$913$	−1.92177e13	−0.915343
$914$	−1.71955e12	−0.0815000
$915$	5.45856e12	0.257444
$916$	8.26765e12	0.388018
$917$	4.25598e12	0.198764
$918$	1.01785e13	0.473035
$919$	−2.97905e13	−1.37771	−0.688856	−	0.724898i	$-0.741887\pi$
$919$	−2.97905e13	−1.37771	−0.688856	+	0.724898i	$0.741887\pi$
$920$	1.18338e13	0.544602
$921$	−8.51451e11	−0.0389934
$922$	−3.57193e13	−1.62785
$923$	−3.73298e13	−1.69297
$924$	−1.26165e13	−0.569396
$925$	6.28689e12	0.282357
$926$	5.83376e13	2.60735
$927$	−6.03257e12	−0.268314
$928$	7.42176e12	0.328504
$929$	−1.26280e13	−0.556242	−0.278121	−	0.960546i	$-0.589712\pi$
$929$	−1.26280e13	−0.556242	−0.278121	+	0.960546i	$0.589712\pi$
$930$	6.16961e12	0.270448
$931$	1.73135e12	0.0755285
$932$	7.00593e12	0.304154
$933$	1.78130e13	0.769608
$934$	−8.34364e12	−0.358752
$935$	−2.81411e13	−1.20417
$936$	6.55768e12	0.279260
$937$	1.84687e13	0.782721	0.391361	−	0.920237i	$-0.372005\pi$
$937$	1.84687e13	0.782721	0.391361	+	0.920237i	$0.372005\pi$
$938$	−5.24474e12	−0.221213
$939$	−7.66014e11	−0.0321545
$940$	−2.11738e12	−0.0884551
$941$	1.58948e13	0.660849	0.330424	−	0.943832i	$-0.392808\pi$
$941$	1.58948e13	0.660849	0.330424	+	0.943832i	$0.392808\pi$
$942$	2.57925e13	1.06725
$943$	5.77334e13	2.37752
$944$	5.21283e12	0.213649
$945$	−7.97494e11	−0.0325300
$946$	−1.02996e14	−4.18130
$947$	−2.60534e13	−1.05266	−0.526331	−	0.850280i	$-0.676433\pi$
$947$	−2.60534e13	−1.05266	−0.526331	+	0.850280i	$0.676433\pi$
$948$	9.74753e12	0.391974
$949$	4.69961e13	1.88089
$950$	−4.20141e12	−0.167355
$951$	−1.17187e13	−0.464587
$952$	−1.18891e13	−0.469120
$953$	−6.58389e12	−0.258562	−0.129281	−	0.991608i	$-0.541267\pi$
$953$	−6.58389e12	−0.258562	−0.129281	+	0.991608i	$0.541267\pi$
$954$	1.13451e13	0.443447
$955$	−1.70990e13	−0.665207
$956$	−2.98710e13	−1.15662
$957$	7.23632e12	0.278878
$958$	−1.97295e13	−0.756782
$959$	−7.54242e12	−0.287957
$960$	−1.10495e13	−0.419877
$961$	−1.48595e13	−0.562015
$962$	6.22199e13	2.34229
$963$	7.68057e12	0.287789
$964$	−1.87616e13	−0.699718
$965$	1.99932e13	0.742182
$966$	−1.42428e13	−0.526256
$967$	−3.25082e12	−0.119557	−0.0597783	−	0.998212i	$-0.519039\pi$
$967$	−3.25082e12	−0.119557	−0.0597783	+	0.998212i	$0.519039\pi$
$968$	−4.37968e13	−1.60326
$969$	−1.30101e13	−0.474049
$970$	3.37732e13	1.22490
$971$	−4.83326e13	−1.74483	−0.872416	−	0.488764i	$-0.837448\pi$
$971$	−4.83326e13	−1.74483	−0.872416	+	0.488764i	$0.837448\pi$
$972$	2.68671e12	0.0965433
$973$	−7.81355e12	−0.279474
$974$	3.01359e13	1.07292
$975$	−3.41557e12	−0.121044
$976$	−6.78520e12	−0.239353
$977$	−4.29930e13	−1.50964	−0.754819	−	0.655933i	$-0.772275\pi$
$977$	−4.29930e13	−1.50964	−0.754819	+	0.655933i	$0.772275\pi$
$978$	3.00213e13	1.04931
$979$	−8.48070e13	−2.95059
$980$	2.77625e12	0.0961484
$981$	−7.57939e12	−0.261291
$982$	−2.03461e12	−0.0698199
$983$	−5.22942e12	−0.178634	−0.0893168	−	0.996003i	$-0.528468\pi$
$983$	−5.22942e12	−0.178634	−0.0893168	+	0.996003i	$0.528468\pi$
$984$	2.11735e13	0.719972
$985$	−1.49637e13	−0.506497
$986$	2.03234e13	0.684780
$987$	8.55067e11	0.0286796
$988$	−2.49812e13	−0.834078
$989$	−6.98557e13	−2.32176
$990$	−1.23638e13	−0.409066
$991$	−9.94933e12	−0.327690	−0.163845	−	0.986486i	$-0.552390\pi$
$991$	−9.94933e12	−0.327690	−0.163845	+	0.986486i	$0.552390\pi$
$992$	−2.38011e13	−0.780360
$993$	−1.17410e12	−0.0383207
$994$	2.97348e13	0.966111
$995$	−1.49387e13	−0.483180
$996$	−1.42468e13	−0.458721
$997$	2.90141e13	0.929997	0.464999	−	0.885311i	$-0.346055\pi$
$997$	2.90141e13	0.929997	0.464999	+	0.885311i	$0.346055\pi$
$998$	−5.72976e13	−1.82831
$999$	8.55324e12	0.271698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.10.a.c.1.1	✓	4
3.2	odd	2		315.10.a.f.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.10.a.c.1.1	✓	4	1.1	even	1	trivial
315.10.a.f.1.4		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)

\(f(q)\)	\(=\)	\(q-35.8126 q^{2} +81.0000 q^{3} +770.540 q^{4} +625.000 q^{5} -2900.82 q^{6} -2401.00 q^{7} -9258.97 q^{8} +6561.00 q^{9} -22382.9 q^{10} +84191.1 q^{11} +62413.7 q^{12} -107949. q^{13} +85986.0 q^{14} +50625.0 q^{15} -62928.9 q^{16} -534805. q^{17} -234966. q^{18} +300331. q^{19} +481587. q^{20} -194481. q^{21} -3.01510e6 q^{22} -2.04494e6 q^{23} -749977. q^{24} +390625. q^{25} +3.86592e6 q^{26} +531441. q^{27} -1.85007e6 q^{28} +1.06113e6 q^{29} -1.81301e6 q^{30} -3.40296e6 q^{31} +6.99424e6 q^{32} +6.81948e6 q^{33} +1.91527e7 q^{34} -1.50062e6 q^{35} +5.05551e6 q^{36} +1.60944e7 q^{37} -1.07556e7 q^{38} -8.74385e6 q^{39} -5.78686e6 q^{40} -2.82323e7 q^{41} +6.96486e6 q^{42} +3.41602e7 q^{43} +6.48726e7 q^{44} +4.10062e6 q^{45} +7.32347e7 q^{46} -4.39666e6 q^{47} -5.09724e6 q^{48} +5.76480e6 q^{49} -1.39893e7 q^{50} -4.33192e7 q^{51} -8.31788e7 q^{52} -4.82841e7 q^{53} -1.90323e7 q^{54} +5.26195e7 q^{55} +2.22308e7 q^{56} +2.43268e7 q^{57} -3.80016e7 q^{58} -8.28369e7 q^{59} +3.90086e7 q^{60} +1.07823e8 q^{61} +1.21869e8 q^{62} -1.57530e7 q^{63} -2.18262e8 q^{64} -6.74680e7 q^{65} -2.44223e8 q^{66} -6.09954e7 q^{67} -4.12088e8 q^{68} -1.65640e8 q^{69} +5.37412e7 q^{70} +3.45810e8 q^{71} -6.07481e7 q^{72} -4.35356e8 q^{73} -5.76383e8 q^{74} +3.16406e7 q^{75} +2.31417e8 q^{76} -2.02143e8 q^{77} +3.13140e8 q^{78} +1.56176e8 q^{79} -3.93306e7 q^{80} +4.30467e7 q^{81} +1.01107e9 q^{82} -2.28263e8 q^{83} -1.49855e8 q^{84} -3.34253e8 q^{85} -1.22336e9 q^{86} +8.59511e7 q^{87} -7.79523e8 q^{88} -1.00731e9 q^{89} -1.46854e8 q^{90} +2.59185e8 q^{91} -1.57571e9 q^{92} -2.75640e8 q^{93} +1.57456e8 q^{94} +1.87707e8 q^{95} +5.66533e8 q^{96} -1.50889e9 q^{97} -2.06452e8 q^{98} +5.52378e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 17 q^{2} + 324 q^{3} + 949 q^{4} + 2500 q^{5} - 1377 q^{6} - 9604 q^{7} - 20679 q^{8} + 26244 q^{9} - 10625 q^{10} + 16382 q^{11} + 76869 q^{12} - 84914 q^{13} + 40817 q^{14} + 202500 q^{15} - 829359 q^{16}+ \cdots + 107482302 q^{99}+O(q^{100}) \) 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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