LMFDB - Embedded newform 37.10.b.a.36.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,10,Mod(36,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("37.36");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	37.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$19.0563259381$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			36.12
Character	$\chi$	$=$	37.36
Dual form			37.10.b.a.36.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.6764i q^{2} +115.620 q^{3} +398.015 q^{4} -1685.85i q^{5} -1234.40i q^{6} -9624.92 q^{7} -9715.67i q^{8} -6315.04 q^{9} +O(q^{10})$	\(q-10.6764i q^{2} +115.620 q^{3} +398.015 q^{4} -1685.85i q^{5} -1234.40i q^{6} -9624.92 q^{7} -9715.67i q^{8} -6315.04 q^{9} -17998.7 q^{10} -16164.1 q^{11} +46018.4 q^{12} -24672.3i q^{13} +102759. i q^{14} -194917. i q^{15} +100055. q^{16} -147281. i q^{17} +67421.8i q^{18} -230280. i q^{19} -670991. i q^{20} -1.11283e6 q^{21} +172575. i q^{22} +1.76570e6i q^{23} -1.12332e6i q^{24} -888949. q^{25} -263411. q^{26} -3.00589e6 q^{27} -3.83086e6 q^{28} +890190. i q^{29} -2.08101e6 q^{30} -8.56024e6i q^{31} -6.04265e6i q^{32} -1.86890e6 q^{33} -1.57242e6 q^{34} +1.62261e7i q^{35} -2.51348e6 q^{36} +(1.01662e7 - 5.15847e6i) q^{37} -2.45856e6 q^{38} -2.85261e6i q^{39} -1.63791e7 q^{40} +1.71308e6 q^{41} +1.18810e7i q^{42} -3.12746e7i q^{43} -6.43357e6 q^{44} +1.06462e7i q^{45} +1.88513e7 q^{46} -364635. q^{47} +1.15684e7 q^{48} +5.22855e7 q^{49} +9.49077e6i q^{50} -1.70286e7i q^{51} -9.81995e6i q^{52} +3.78264e7 q^{53} +3.20921e7i q^{54} +2.72502e7i q^{55} +9.35126e7i q^{56} -2.66250e7i q^{57} +9.50401e6 q^{58} -5.36210e7i q^{59} -7.75799e7i q^{60} +1.73097e8i q^{61} -9.13925e7 q^{62} +6.07818e7 q^{63} -1.32854e7 q^{64} -4.15937e7 q^{65} +1.99531e7i q^{66} +2.21851e8 q^{67} -5.86198e7i q^{68} +2.04150e8i q^{69} +1.73236e8 q^{70} -2.59349e7 q^{71} +6.13548e7i q^{72} +8.14841e7 q^{73} +(-5.50739e7 - 1.08538e8i) q^{74} -1.02780e8 q^{75} -9.16549e7i q^{76} +1.55579e8 q^{77} -3.04556e7 q^{78} -5.33481e8i q^{79} -1.68678e8i q^{80} -2.23242e8 q^{81} -1.82895e7i q^{82} -4.93765e8 q^{83} -4.42924e8 q^{84} -2.48292e8 q^{85} -3.33899e8 q^{86} +1.02924e8i q^{87} +1.57046e8i q^{88} -2.88383e8i q^{89} +1.13663e8 q^{90} +2.37469e8i q^{91} +7.02775e8i q^{92} -9.89734e8i q^{93} +3.89299e6i q^{94} -3.88217e8 q^{95} -6.98651e8i q^{96} +7.11545e8i q^{97} -5.58221e8i q^{98} +1.02077e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 150 q^{3} - 7340 q^{4} + 5940 q^{7} + 203834 q^{9}+O(q^{10}) $ 28 * q - 150 * q^3 - 7340 * q^4 + 5940 * q^7 + 203834 * q^9	$ 28 q - 150 q^{3} - 7340 q^{4} + 5940 q^{7} + 203834 q^{9} - 37794 q^{10} + 64218 q^{11} + 127066 q^{12} + 1640020 q^{16} - 40760 q^{21} - 19052702 q^{25} - 6123570 q^{26} - 1640160 q^{27} + 7625000 q^{28} - 19333840 q^{30} + 15698940 q^{33} + 708476 q^{34} - 51365130 q^{36} + 16215912 q^{37} - 28583988 q^{38} + 105594566 q^{40} - 7076754 q^{41} - 103376142 q^{44} + 77028630 q^{46} + 227172960 q^{47} - 65810002 q^{48} + 204785368 q^{49} + 50216184 q^{53} - 535678486 q^{58} - 438751290 q^{62} + 78365380 q^{63} + 177466492 q^{64} - 778712844 q^{65} + 631746366 q^{67} - 160866964 q^{70} + 1006626660 q^{71} - 83180574 q^{73} - 1466328336 q^{74} - 381338576 q^{75} + 408926592 q^{77} + 2562172434 q^{78} + 2121646388 q^{81} + 2834717148 q^{83} - 2459748244 q^{84} - 1400055912 q^{85} - 1148298888 q^{86} - 1425076412 q^{90} - 3422824284 q^{95} - 2703697668 q^{99}+O(q^{100}) $ 28 * q - 150 * q^3 - 7340 * q^4 + 5940 * q^7 + 203834 * q^9 - 37794 * q^10 + 64218 * q^11 + 127066 * q^12 + 1640020 * q^16 - 40760 * q^21 - 19052702 * q^25 - 6123570 * q^26 - 1640160 * q^27 + 7625000 * q^28 - 19333840 * q^30 + 15698940 * q^33 + 708476 * q^34 - 51365130 * q^36 + 16215912 * q^37 - 28583988 * q^38 + 105594566 * q^40 - 7076754 * q^41 - 103376142 * q^44 + 77028630 * q^46 + 227172960 * q^47 - 65810002 * q^48 + 204785368 * q^49 + 50216184 * q^53 - 535678486 * q^58 - 438751290 * q^62 + 78365380 * q^63 + 177466492 * q^64 - 778712844 * q^65 + 631746366 * q^67 - 160866964 * q^70 + 1006626660 * q^71 - 83180574 * q^73 - 1466328336 * q^74 - 381338576 * q^75 + 408926592 * q^77 + 2562172434 * q^78 + 2121646388 * q^81 + 2834717148 * q^83 - 2459748244 * q^84 - 1400055912 * q^85 - 1148298888 * q^86 - 1425076412 * q^90 - 3422824284 * q^95 - 2703697668 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	10.6764i		−	0.471834i	−0.971773	−	0.235917i	$-0.924191\pi$
$2$		−	10.6764i		−	0.471834i	0.971773	−	0.235917i	$-0.0758094\pi$
$3$	115.620			0.824113			0.412057	−	0.911158i	$-0.364811\pi$
$3$	115.620			0.824113			0.412057	+	0.911158i	$0.364811\pi$
$4$	398.015			0.777372
$5$		−	1685.85i		−	1.20629i	−0.797631	−	0.603146i	$-0.793914\pi$
$5$		−	1685.85i		−	1.20629i	0.797631	−	0.603146i	$-0.206086\pi$
$6$		−	1234.40i		−	0.388845i
$7$	−9624.92			−1.51515			−0.757576	−	0.652747i	$-0.773616\pi$
$7$	−9624.92			−1.51515			−0.757576	+	0.652747i	$0.773616\pi$
$8$		−	9715.67i		−	0.838625i
$9$	−6315.04			−0.320837
$10$	−17998.7			−0.569170
$11$	−16164.1			−0.332878			−0.166439	−	0.986052i	$-0.553227\pi$
$11$	−16164.1			−0.332878			−0.166439	+	0.986052i	$0.553227\pi$
$12$	46018.4			0.640643
$13$		−	24672.3i		−	0.239588i	−0.992799	−	0.119794i	$-0.961777\pi$
$13$		−	24672.3i		−	0.239588i	0.992799	−	0.119794i	$-0.0382234\pi$
$14$			102759.i			0.714900i
$15$		−	194917.i		−	0.994122i
$16$	100055.			0.381680
$17$		−	147281.i		−	0.427686i	−0.976868	−	0.213843i	$-0.931402\pi$
$17$		−	147281.i		−	0.427686i	0.976868	−	0.213843i	$-0.0685982\pi$
$18$			67421.8i			0.151382i
$19$		−	230280.i		−	0.405383i	−0.979243	−	0.202691i	$-0.935031\pi$
$19$		−	230280.i		−	0.405383i	0.979243	−	0.202691i	$-0.0649688\pi$
$20$		−	670991.i		−	0.937739i
$21$	−1.11283e6			−1.24866
$22$			172575.i			0.157063i
$23$			1.76570e6i			1.31565i	0.753169	+	0.657827i	$0.228524\pi$
$23$			1.76570e6i			1.31565i	−0.753169	+	0.657827i	$0.771476\pi$
$24$		−	1.12332e6i		−	0.691122i
$25$	−888949.			−0.455142
$26$	−263411.			−0.113046
$27$	−3.00589e6			−1.08852
$28$	−3.83086e6			−1.17784
$29$			890190.i			0.233718i	0.993149	+	0.116859i	$0.0372825\pi$
$29$			890190.i			0.233718i	−0.993149	+	0.116859i	$0.962717\pi$
$30$	−2.08101e6			−0.469061
$31$		−	8.56024e6i		−	1.66479i	−0.554186	−	0.832393i	$-0.686970\pi$
$31$		−	8.56024e6i		−	1.66479i	0.554186	−	0.832393i	$-0.313030\pi$
$32$		−	6.04265e6i		−	1.01872i
$33$	−1.86890e6			−0.274330
$34$	−1.57242e6			−0.201797
$35$			1.62261e7i			1.82772i
$36$	−2.51348e6			−0.249410
$37$	1.01662e7	−	5.15847e6i	0.891767	−	0.452495i
$37$	1.01662e7	−	5.15847e6i	0.891767	−	0.452495i
$38$	−2.45856e6			−0.191273
$39$		−	2.85261e6i		−	0.197448i
$40$	−1.63791e7			−1.01163
$41$	1.71308e6			0.0946781			0.0473391	−	0.998879i	$-0.484926\pi$
$41$	1.71308e6			0.0946781			0.0473391	+	0.998879i	$0.484926\pi$
$42$			1.18810e7i			0.589159i
$43$		−	3.12746e7i		−	1.39503i	−0.716571	−	0.697514i	$-0.754289\pi$
$43$		−	3.12746e7i		−	1.39503i	0.716571	−	0.697514i	$-0.245711\pi$
$44$	−6.43357e6			−0.258771
$45$			1.06462e7i			0.387024i
$46$	1.88513e7			0.620771
$47$	−364635.			−0.0108998			−0.00544990	−	0.999985i	$-0.501735\pi$
$47$	−364635.			−0.0108998			−0.00544990	+	0.999985i	$0.501735\pi$
$48$	1.15684e7			0.314548
$49$	5.22855e7			1.29568
$50$			9.49077e6i			0.214751i
$51$		−	1.70286e7i		−	0.352462i
$52$		−	9.81995e6i		−	0.186249i
$53$	3.78264e7			0.658498			0.329249	−	0.944243i	$-0.393205\pi$
$53$	3.78264e7			0.658498			0.329249	+	0.944243i	$0.393205\pi$
$54$			3.20921e7i			0.513601i
$55$			2.72502e7i			0.401549i
$56$			9.35126e7i			1.27064i
$57$		−	2.66250e7i		−	0.334081i
$58$	9.50401e6			0.110276
$59$		−	5.36210e7i		−	0.576104i	−0.957615	−	0.288052i	$-0.906992\pi$
$59$		−	5.36210e7i		−	0.576104i	0.957615	−	0.288052i	$-0.0930076\pi$
$60$		−	7.75799e7i		−	0.772803i
$61$			1.73097e8i			1.60068i	0.599545	+	0.800341i	$0.295348\pi$
$61$			1.73097e8i			1.60068i	−0.599545	+	0.800341i	$0.704652\pi$
$62$	−9.13925e7			−0.785503
$63$	6.07818e7			0.486117
$64$	−1.32854e7			−0.0989841
$65$	−4.15937e7			−0.289013
$66$			1.99531e7i			0.129438i
$67$	2.21851e8			1.34501			0.672504	−	0.740094i	$-0.265219\pi$
$67$	2.21851e8			1.34501			0.672504	+	0.740094i	$0.265219\pi$
$68$		−	5.86198e7i		−	0.332472i
$69$			2.04150e8i			1.08425i
$70$	1.73236e8			0.862379
$71$	−2.59349e7			−0.121122			−0.0605608	−	0.998165i	$-0.519289\pi$
$71$	−2.59349e7			−0.121122			−0.0605608	+	0.998165i	$0.519289\pi$
$72$			6.13548e7i			0.269062i
$73$	8.14841e7			0.335830			0.167915	−	0.985801i	$-0.446297\pi$
$73$	8.14841e7			0.335830			0.167915	+	0.985801i	$0.446297\pi$
$74$	−5.50739e7	−	1.08538e8i	−0.213502	−	0.420766i
$75$	−1.02780e8			−0.375088
$76$		−	9.16549e7i		−	0.315133i
$77$	1.55579e8			0.504361
$78$	−3.04556e7			−0.0931626
$79$		−	5.33481e8i		−	1.54098i	−0.637452	−	0.770490i	$-0.720012\pi$
$79$		−	5.33481e8i		−	1.54098i	0.637452	−	0.770490i	$-0.279988\pi$
$80$		−	1.68678e8i		−	0.460418i
$81$	−2.23242e8			−0.576226
$82$		−	1.82895e7i		−	0.0446724i
$83$	−4.93765e8			−1.14201			−0.571004	−	0.820947i	$-0.693446\pi$
$83$	−4.93765e8			−1.14201			−0.571004	+	0.820947i	$0.693446\pi$
$84$	−4.42924e8			−0.970671
$85$	−2.48292e8			−0.515915
$86$	−3.33899e8			−0.658222
$87$			1.02924e8i			0.192610i
$88$			1.57046e8i			0.279160i
$89$		−	2.88383e8i		−	0.487208i	−0.969875	−	0.243604i	$-0.921670\pi$
$89$		−	2.88383e8i		−	0.487208i	0.969875	−	0.243604i	$-0.0783296\pi$
$90$	1.13663e8			0.182611
$91$			2.37469e8i			0.363012i
$92$			7.02775e8i			1.02275i
$93$		−	9.89734e8i		−	1.37197i
$94$			3.89299e6i			0.00514290i
$95$	−3.88217e8			−0.489010
$96$		−	6.98651e8i		−	0.839537i
$97$			7.11545e8i			0.816074i	0.912965	+	0.408037i	$0.133787\pi$
$97$			7.11545e8i			0.816074i	−0.912965	+	0.408037i	$0.866213\pi$
$98$		−	5.58221e8i		−	0.611348i
$99$	1.02077e8			0.106800
$100$	−3.53815e8			−0.353815
$101$	6.50117e8			0.621649			0.310824	−	0.950467i	$-0.399395\pi$
$101$	6.50117e8			0.621649			0.310824	+	0.950467i	$0.399395\pi$
$102$	−1.81804e8			−0.166304
$103$		−	4.95305e8i		−	0.433616i	−0.976214	−	0.216808i	$-0.930435\pi$
$103$		−	4.95305e8i		−	0.433616i	0.976214	−	0.216808i	$-0.0695645\pi$
$104$	−2.39708e8			−0.200925
$105$			1.87606e9i			1.50625i
$106$		−	4.03850e8i		−	0.310702i
$107$	2.43701e9			1.79734			0.898671	−	0.438624i	$-0.144534\pi$
$107$	2.43701e9			1.79734			0.898671	+	0.438624i	$0.144534\pi$
$108$	−1.19639e9			−0.846185
$109$			1.19477e9i			0.810707i	0.914160	+	0.405353i	$0.132852\pi$
$109$			1.19477e9i			0.810707i	−0.914160	+	0.405353i	$0.867148\pi$
$110$	2.90934e8			0.189464
$111$	1.17542e9	−	5.96422e8i	0.734917	−	0.372907i
$112$	−9.63024e8			−0.578304
$113$			1.89525e9i			1.09349i	0.837300	+	0.546744i	$0.184133\pi$
$113$			1.89525e9i			1.09349i	−0.837300	+	0.546744i	$0.815867\pi$
$114$	−2.84259e8			−0.157631
$115$	2.97670e9			1.58706
$116$			3.54309e8i			0.181686i
$117$			1.55807e8i			0.0768688i
$118$	−5.72479e8			−0.271826
$119$			1.41756e9i			0.648010i
$120$	−1.89375e9			−0.833696
$121$	−2.09667e9			−0.889192
$122$	1.84805e9			0.755257
$123$	1.98066e8			0.0780255
$124$		−	3.40710e9i		−	1.29416i
$125$		−	1.79404e9i		−	0.657258i
$126$		−	6.48930e8i		−	0.229367i
$127$	4.73617e9			1.61551			0.807756	−	0.589517i	$-0.200682\pi$
$127$	4.73617e9			1.61551			0.807756	+	0.589517i	$0.200682\pi$
$128$		−	2.95200e9i		−	0.972011i
$129$		−	3.61596e9i		−	1.14966i
$130$			4.44071e8i			0.136366i
$131$			3.94559e9i			1.17055i	0.810834	+	0.585277i	$0.199014\pi$
$131$			3.94559e9i			1.17055i	−0.810834	+	0.585277i	$0.800986\pi$
$132$	−7.43848e8			−0.213256
$133$			2.21643e9i			0.614216i
$134$		−	2.36857e9i		−	0.634620i
$135$			5.06747e9i			1.31307i
$136$	−1.43093e9			−0.358669
$137$	4.10595e9			0.995799			0.497899	−	0.867235i	$-0.334105\pi$
$137$	4.10595e9			0.995799			0.497899	+	0.867235i	$0.334105\pi$
$138$	2.17959e9			0.511585
$139$	8.60144e8			0.195436			0.0977179	−	0.995214i	$-0.468846\pi$
$139$	8.60144e8			0.195436			0.0977179	+	0.995214i	$0.468846\pi$
$140$			6.45824e9i			1.42082i
$141$	−4.21591e7			−0.00898267
$142$			2.76891e8i			0.0571493i
$143$			3.98807e8i			0.0797537i
$144$	−6.31853e8			−0.122457
$145$	1.50072e9			0.281932
$146$		−	8.69956e8i		−	0.158456i
$147$	6.04525e9			1.06779
$148$	4.04630e9	−	2.05315e9i	0.693235	−	0.351757i
$149$	−1.09266e10			−1.81613			−0.908065	−	0.418829i	$-0.862441\pi$
$149$	−1.09266e10			−1.81613			−0.908065	+	0.418829i	$0.862441\pi$
$150$			1.09732e9i			0.176980i
$151$	−2.86959e9			−0.449184			−0.224592	−	0.974453i	$-0.572105\pi$
$151$	−2.86959e9			−0.449184			−0.224592	+	0.974453i	$0.572105\pi$
$152$	−2.23733e9			−0.339964
$153$			9.30083e8i			0.137218i
$154$		−	1.66102e9i		−	0.237975i
$155$	−1.44312e10			−2.00822
$156$		−	1.13538e9i		−	0.153490i
$157$	−4.96979e9			−0.652815			−0.326407	−	0.945229i	$-0.605838\pi$
$157$	−4.96979e9			−0.652815			−0.326407	+	0.945229i	$0.605838\pi$
$158$	−5.69565e9			−0.727087
$159$	4.37349e9			0.542677
$160$	−1.01870e10			−1.22887
$161$		−	1.69947e10i		−	1.99342i
$162$			2.38342e9i			0.271883i
$163$		−	1.66773e10i		−	1.85047i	−0.379392	−	0.925236i	$-0.623867\pi$
$163$		−	1.66773e10i		−	1.85047i	0.379392	−	0.925236i	$-0.376133\pi$
$164$	6.81830e8			0.0736002
$165$			3.15067e9i			0.330922i
$166$			5.27163e9i			0.538838i
$167$		−	4.95826e8i		−	0.0493293i	−0.999696	−	0.0246646i	$-0.992148\pi$
$167$		−	4.95826e8i		−	0.0493293i	0.999696	−	0.0246646i	$-0.00785180\pi$
$168$			1.08119e10i			1.04715i
$169$	9.99578e9			0.942598
$170$			2.65087e9i			0.243426i
$171$			1.45423e9i			0.130062i
$172$		−	1.24477e10i		−	1.08446i
$173$	−1.57436e10			−1.33628			−0.668138	−	0.744038i	$-0.732908\pi$
$173$	−1.57436e10			−1.33628			−0.668138	+	0.744038i	$0.732908\pi$
$174$	1.09885e9			0.0908799
$175$	8.55607e9			0.689609
$176$	−1.61731e9			−0.127053
$177$		−	6.19966e9i		−	0.474775i
$178$	−3.07888e9			−0.229881
$179$			1.17479e10i			0.855307i	0.903943	+	0.427654i	$0.140660\pi$
$179$			1.17479e10i			0.855307i	−0.903943	+	0.427654i	$0.859340\pi$
$180$			4.23734e9i			0.300861i
$181$	2.78914e9			0.193160			0.0965799	−	0.995325i	$-0.469210\pi$
$181$	2.78914e9			0.193160			0.0965799	+	0.995325i	$0.469210\pi$
$182$	2.53532e9			0.171282
$183$			2.00135e10i			1.31914i
$184$	1.71550e10			1.10334
$185$	−8.69639e9	−	1.71387e10i	−0.545841	−	1.07573i
$186$	−1.05668e10			−0.647344
$187$			2.38067e9i			0.142368i
$188$	−1.45130e8			−0.00847320
$189$	2.89315e10			1.64927
$190$			4.14475e9i			0.230732i
$191$		−	1.59119e10i		−	0.865113i	−0.901607	−	0.432557i	$-0.857612\pi$
$191$		−	1.59119e10i		−	0.865113i	0.901607	−	0.432557i	$-0.142388\pi$
$192$	−1.53606e9			−0.0815741
$193$		−	2.37920e9i		−	0.123431i	−0.998094	−	0.0617154i	$-0.980343\pi$
$193$		−	2.37920e9i		−	0.123431i	0.998094	−	0.0617154i	$-0.0196571\pi$
$194$	7.59673e9			0.385051
$195$	−4.80906e9			−0.238180
$196$	2.08104e10			1.00723
$197$	−4.09579e9			−0.193749			−0.0968745	−	0.995297i	$-0.530885\pi$
$197$	−4.09579e9			−0.193749			−0.0968745	+	0.995297i	$0.530885\pi$
$198$		−	1.08982e9i		−	0.0503918i
$199$			3.64147e10i			1.64603i	0.568021	+	0.823014i	$0.307709\pi$
$199$			3.64147e10i			1.64603i	−0.568021	+	0.823014i	$0.692291\pi$
$200$			8.63674e9i			0.381693i
$201$	2.56504e10			1.10844
$202$		−	6.94090e9i		−	0.293315i
$203$		−	8.56801e9i		−	0.354118i
$204$		−	6.77762e9i		−	0.273994i
$205$		−	2.88798e9i		−	0.114210i
$206$	−5.28807e9			−0.204595
$207$		−	1.11505e10i		−	0.422111i
$208$		−	2.46860e9i		−	0.0914461i
$209$			3.72228e9i			0.134943i
$210$	2.00296e10			0.710698
$211$	−2.30030e10			−0.798937			−0.399469	−	0.916747i	$-0.630805\pi$
$211$	−2.30030e10			−0.798937			−0.399469	+	0.916747i	$0.630805\pi$
$212$	1.50555e10			0.511898
$213$	−2.99859e9			−0.0998179
$214$		−	2.60185e10i		−	0.848047i
$215$	−5.27241e10			−1.68281
$216$			2.92042e10i			0.912860i
$217$			8.23917e10i			2.52240i
$218$	1.27558e10			0.382519
$219$	9.42118e9			0.276762
$220$			1.08460e10i			0.312153i
$221$	−3.63376e9			−0.102469
$222$	−6.36764e9	−	1.25492e10i	−0.175950	−	0.346759i
$223$	−1.22759e10			−0.332416			−0.166208	−	0.986091i	$-0.553152\pi$
$223$	−1.22759e10			−0.332416			−0.166208	+	0.986091i	$0.553152\pi$
$224$			5.81601e10i			1.54351i
$225$	5.61375e9			0.146026
$226$	2.02345e10			0.515945
$227$		−	4.46746e10i		−	1.11672i	−0.829599	−	0.558360i	$-0.811431\pi$
$227$		−	4.46746e10i		−	1.11672i	0.829599	−	0.558360i	$-0.188569\pi$
$228$		−	1.05971e10i		−	0.259706i
$229$	−6.91514e9			−0.166166			−0.0830828	−	0.996543i	$-0.526477\pi$
$229$	−6.91514e9			−0.166166			−0.0830828	+	0.996543i	$0.526477\pi$
$230$		−	3.17804e10i		−	0.748831i
$231$	1.79880e10			0.415651
$232$	8.64879e9			0.196001
$233$	1.97668e10			0.439374			0.219687	−	0.975570i	$-0.429496\pi$
$233$	1.97668e10			0.439374			0.219687	+	0.975570i	$0.429496\pi$
$234$	1.66345e9			0.0362693
$235$			6.14719e8i			0.0131483i
$236$		−	2.13420e10i		−	0.447847i
$237$		−	6.16810e10i		−	1.26994i
$238$	1.51345e10			0.305753
$239$		−	3.96171e10i		−	0.785402i	−0.919666	−	0.392701i	$-0.871541\pi$
$239$		−	3.96171e10i		−	0.785402i	0.919666	−	0.392701i	$-0.128459\pi$
$240$		−	1.95025e10i		−	0.379437i
$241$			5.37515e10i			1.02639i	0.858271	+	0.513197i	$0.171539\pi$
$241$			5.37515e10i			1.02639i	−0.858271	+	0.513197i	$0.828461\pi$
$242$			2.23848e10i			0.419551i
$243$	3.33537e10			0.613644
$244$			6.88951e10i			1.24433i
$245$		−	8.81453e10i		−	1.56297i
$246$		−	2.11463e9i		−	0.0368151i
$247$	−5.68155e9			−0.0971249
$248$	−8.31685e10			−1.39613
$249$	−5.70891e10			−0.941144
$250$	−1.91538e10			−0.310117
$251$		−	5.46783e10i		−	0.869528i	−0.900544	−	0.434764i	$-0.856832\pi$
$251$		−	5.46783e10i		−	0.869528i	0.900544	−	0.434764i	$-0.143168\pi$
$252$	2.41920e10			0.377894
$253$		−	2.85410e10i		−	0.437953i
$254$		−	5.05652e10i		−	0.762254i
$255$	−2.87075e10			−0.425172
$256$	−3.83188e10			−0.557612
$257$			1.00641e11i			1.43904i	0.694470	+	0.719522i	$0.255639\pi$
$257$			1.00641e11i			1.43904i	−0.694470	+	0.719522i	$0.744361\pi$
$258$	−3.86054e10			−0.542450
$259$	−9.78490e10	+	4.96499e10i	−1.35116	+	0.685598i
$260$	−1.65549e10			−0.224671
$261$		−	5.62158e9i		−	0.0749853i
$262$	4.21247e10			0.552307
$263$	−1.22367e11			−1.57711			−0.788556	−	0.614963i	$-0.789171\pi$
$263$	−1.22367e11			−1.57711			−0.788556	+	0.614963i	$0.789171\pi$
$264$			1.81576e10i			0.230060i
$265$		−	6.37695e10i		−	0.794341i
$266$	2.36635e10			0.289808
$267$		−	3.33428e10i		−	0.401514i
$268$	8.82999e10			1.04557
$269$	−1.07814e11			−1.25542			−0.627712	−	0.778445i	$-0.716009\pi$
$269$	−1.07814e11			−1.25542			−0.627712	+	0.778445i	$0.716009\pi$
$270$	5.41022e10			0.619553
$271$	1.00479e11			1.13166			0.565829	−	0.824522i	$-0.308556\pi$
$271$	1.00479e11			1.13166			0.565829	+	0.824522i	$0.308556\pi$
$272$		−	1.47362e10i		−	0.163240i
$273$			2.74562e10i			0.299163i
$274$		−	4.38368e10i		−	0.469852i
$275$	1.43691e10			0.151507
$276$			8.12547e10i			0.842865i
$277$		−	2.90794e10i		−	0.296774i	−0.988929	−	0.148387i	$-0.952592\pi$
$277$		−	2.90794e10i		−	0.296774i	0.988929	−	0.148387i	$-0.0474081\pi$
$278$		−	9.18323e9i		−	0.0922133i
$279$			5.40583e10i			0.534125i
$280$	1.57648e11			1.53277
$281$			1.02968e11i			0.985203i	0.870255	+	0.492602i	$0.163954\pi$
$281$			1.02968e11i			0.985203i	−0.870255	+	0.492602i	$0.836046\pi$
$282$			4.50107e8i			0.00423833i
$283$		−	1.60431e11i		−	1.48679i	−0.668853	−	0.743395i	$-0.733214\pi$
$283$		−	1.60431e11i		−	1.48679i	0.668853	−	0.743395i	$-0.266786\pi$
$284$	−1.03225e10			−0.0941566
$285$	−4.48856e10			−0.403000
$286$	4.25782e9			0.0376305
$287$	−1.64882e10			−0.143452
$288$			3.81596e10i			0.326842i
$289$	9.68963e10			0.817084
$290$		−	1.60223e10i		−	0.133025i
$291$			8.22687e10i			0.672537i
$292$	3.24319e10			0.261065
$293$	−1.84405e11			−1.46173			−0.730866	−	0.682520i	$-0.760884\pi$
$293$	−1.84405e11			−1.46173			−0.730866	+	0.682520i	$0.760884\pi$
$294$		−	6.45414e10i		−	0.503820i
$295$	−9.03967e10			−0.694950
$296$	−5.01180e10	−	9.87716e10i	−0.379473	−	0.747858i
$297$	4.85877e10			0.362345
$298$			1.16657e11i			0.856912i
$299$	4.35640e10			0.315215
$300$	−4.09080e10			−0.291583
$301$			3.01015e11i			2.11368i
$302$			3.06369e10i			0.211940i
$303$	7.51664e10			0.512309
$304$		−	2.30407e10i		−	0.154727i
$305$	2.91815e11			1.93089
$306$	9.92992e9			0.0647440
$307$	1.71467e11			1.10169			0.550844	−	0.834608i	$-0.314306\pi$
$307$	1.71467e11			1.10169			0.550844	+	0.834608i	$0.314306\pi$
$308$	6.19226e10			0.392077
$309$		−	5.72671e10i		−	0.357349i
$310$			1.54074e11i			0.947546i
$311$			1.07057e11i			0.648925i	0.945898	+	0.324463i	$0.105183\pi$
$311$			1.07057e11i			0.648925i	−0.945898	+	0.324463i	$0.894817\pi$
$312$	−2.77151e10			−0.165585
$313$		−	6.35488e10i		−	0.374247i	−0.982336	−	0.187123i	$-0.940084\pi$
$313$		−	6.35488e10i		−	0.374247i	0.982336	−	0.187123i	$-0.0599164\pi$
$314$			5.30594e10i			0.308020i
$315$		−	1.02469e11i		−	0.586399i
$316$		−	2.12333e11i		−	1.19792i
$317$	2.89454e11			1.60995			0.804975	−	0.593309i	$-0.202179\pi$
$317$	2.89454e11			1.60995			0.804975	+	0.593309i	$0.202179\pi$
$318$		−	4.66931e10i		−	0.256053i
$319$		−	1.43892e10i		−	0.0777996i
$320$			2.23972e10i			0.119404i
$321$	2.81767e11			1.48121
$322$	−1.81442e11			−0.940562
$323$	−3.39158e10			−0.173377
$324$	−8.88535e10			−0.447942
$325$			2.19325e10i			0.109047i
$326$	−1.78054e11			−0.873116
$327$			1.38139e11i			0.668114i
$328$		−	1.66437e10i		−	0.0793995i
$329$	3.50959e9			0.0165148
$330$	3.36378e10			0.156140
$331$		−	2.57773e11i		−	1.18035i	−0.807275	−	0.590176i	$-0.799059\pi$
$331$		−	2.57773e11i		−	1.18035i	0.807275	−	0.590176i	$-0.200941\pi$
$332$	−1.96526e11			−0.887765
$333$	−6.42000e10	+	3.25760e10i	−0.286112	+	0.145177i
$334$	−5.29363e9			−0.0232752
$335$		−	3.74006e11i		−	1.62247i
$336$	−1.11345e11			−0.476588
$337$	1.45260e11			0.613495			0.306747	−	0.951791i	$-0.400759\pi$
$337$	1.45260e11			0.613495			0.306747	+	0.951791i	$0.400759\pi$
$338$		−	1.06719e11i		−	0.444750i
$339$			2.19129e11i			0.901158i
$340$	−9.88240e10			−0.401058
$341$			1.38369e11i			0.554171i
$342$	1.55259e10			0.0613676
$343$	−1.14844e11			−0.448007
$344$	−3.03853e11			−1.16991
$345$	3.44165e11			1.30792
$346$			1.68085e11i			0.630500i
$347$		−	3.87660e11i		−	1.43538i	−0.696361	−	0.717692i	$-0.745199\pi$
$347$		−	3.87660e11i		−	1.43538i	0.696361	−	0.717692i	$-0.254801\pi$
$348$			4.09651e10i			0.149730i
$349$	−2.14206e11			−0.772888			−0.386444	−	0.922313i	$-0.626297\pi$
$349$	−2.14206e11			−0.772888			−0.386444	+	0.922313i	$0.626297\pi$
$350$		−	9.13479e10i		−	0.325381i
$351$			7.41624e10i			0.260796i
$352$			9.76743e10i			0.339108i
$353$			3.23659e11i			1.10943i	0.832039	+	0.554717i	$0.187173\pi$
$353$			3.23659e11i			1.10943i	−0.832039	+	0.554717i	$0.812827\pi$
$354$	−6.61899e10			−0.224015
$355$			4.37222e10i			0.146108i
$356$		−	1.14781e11i		−	0.378742i
$357$			1.63899e11i			0.534033i
$358$	1.25425e11			0.403563
$359$	−4.30563e11			−1.36808			−0.684040	−	0.729444i	$-0.739779\pi$
$359$	−4.30563e11			−1.36808			−0.684040	+	0.729444i	$0.739779\pi$
$360$	1.03435e11			0.324568
$361$	2.69659e11			0.835665
$362$		−	2.97779e10i		−	0.0911394i
$363$	−2.42417e11			−0.732795
$364$			9.45163e10i			0.282196i
$365$		−	1.37370e11i		−	0.405110i
$366$	2.13671e11			0.622417
$367$	−5.01163e11			−1.44206			−0.721028	−	0.692906i	$-0.756330\pi$
$367$	−5.01163e11			−1.44206			−0.721028	+	0.692906i	$0.756330\pi$
$368$			1.76668e11i			0.502160i
$369$	−1.08182e10			−0.0303763
$370$	−1.82979e11	+	9.28460e10i	−0.507567	+	0.257546i
$371$	−3.64077e11			−0.997724
$372$		−	3.93929e11i		−	1.06653i
$373$	3.31574e10			0.0886933			0.0443466	−	0.999016i	$-0.485879\pi$
$373$	3.31574e10			0.0886933			0.0443466	+	0.999016i	$0.485879\pi$
$374$	2.54169e10			0.0671739
$375$		−	2.07426e11i		−	0.541655i
$376$			3.54268e9i			0.00914085i
$377$	2.19631e10			0.0559960
$378$		−	3.08884e11i		−	0.778183i
$379$	2.61045e11			0.649888			0.324944	−	0.945733i	$-0.394654\pi$
$379$	2.61045e11			0.649888			0.324944	+	0.945733i	$0.394654\pi$
$380$	−1.54516e11			−0.380143
$381$	5.47595e11			1.33136
$382$	−1.69882e11			−0.408190
$383$			4.44790e11i			1.05624i	0.849171	+	0.528118i	$0.177102\pi$
$383$			4.44790e11i			1.05624i	−0.849171	+	0.528118i	$0.822898\pi$
$384$		−	3.41310e11i		−	0.801047i
$385$		−	2.62282e11i		−	0.608407i
$386$	−2.54013e10			−0.0582388
$387$			1.97500e11i			0.447577i
$388$			2.83205e11i			0.634393i
$389$		−	3.81235e11i		−	0.844150i	−0.906561	−	0.422075i	$-0.861302\pi$
$389$		−	3.81235e11i		−	0.844150i	0.906561	−	0.422075i	$-0.138698\pi$
$390$			5.13434e10i			0.112381i
$391$	2.60053e11			0.562687
$392$		−	5.07989e11i		−	1.08659i
$393$			4.56189e11i			0.964669i
$394$			4.37282e10i			0.0914174i
$395$	−8.99366e11			−1.85887
$396$	4.06282e10			0.0830232
$397$	6.93446e11			1.40106			0.700528	−	0.713625i	$-0.252948\pi$
$397$	6.93446e11			1.40106			0.700528	+	0.713625i	$0.252948\pi$
$398$	3.88777e11			0.776652
$399$			2.56263e11i			0.506184i
$400$	−8.89440e10			−0.173719
$401$		−	5.41091e11i		−	1.04501i	−0.852636	−	0.522506i	$-0.824997\pi$
$401$		−	5.41091e11i		−	1.04501i	0.852636	−	0.522506i	$-0.175003\pi$
$402$		−	2.73853e11i		−	0.522999i
$403$	−2.11201e11			−0.398863
$404$	2.58756e11			0.483253
$405$			3.76351e11i			0.695097i
$406$	−9.14754e10			−0.167085
$407$	−1.64328e11	+	8.33823e10i	−0.296850	+	0.150626i
$408$	−1.65444e11			−0.295584
$409$		−	1.15251e8i		−	0.000203652i	−1.00000		0.000101826i	$-0.999968\pi$
$409$		−	1.15251e8i		−	0.000203652i	1.00000		0.000101826i	$-3.24122e-5\pi$
$410$	−3.08332e10			−0.0538880
$411$	4.74730e11			0.820651
$412$		−	1.97139e11i		−	0.337081i
$413$			5.16098e11i			0.872885i
$414$	−1.19047e11			−0.199166
$415$			8.32412e11i			1.37760i
$416$	−1.49086e11			−0.244072
$417$	9.94497e10			0.161061
$418$	3.97405e10			0.0636708
$419$	−1.10931e11			−0.175829			−0.0879146	−	0.996128i	$-0.528020\pi$
$419$	−1.10931e11			−0.175829			−0.0879146	+	0.996128i	$0.528020\pi$
$420$			7.46701e11i			1.17091i
$421$		−	9.56394e11i		−	1.48377i	−0.670526	−	0.741886i	$-0.733931\pi$
$421$		−	9.56394e11i		−	1.48377i	0.670526	−	0.741886i	$-0.266069\pi$
$422$			2.45589e11i			0.376966i
$423$	2.30269e9			0.00349706
$424$		−	3.67509e11i		−	0.552233i
$425$			1.30925e11i			0.194658i
$426$			3.20141e10i			0.0470975i
$427$		−	1.66605e12i		−	2.42528i
$428$	9.69966e11			1.39720
$429$			4.61101e10i			0.0657261i
$430$			5.62903e11i			0.794009i
$431$			1.07470e12i			1.50017i	0.661340	+	0.750086i	$0.269988\pi$
$431$			1.07470e12i			1.50017i	−0.661340	+	0.750086i	$0.730012\pi$
$432$	−3.00755e11			−0.415467
$433$	1.02600e12			1.40266			0.701330	−	0.712836i	$-0.252590\pi$
$433$	1.02600e12			1.40266			0.701330	+	0.712836i	$0.252590\pi$
$434$	8.79646e11			1.19016
$435$	1.73513e11			0.232344
$436$			4.75535e11i			0.630221i
$437$	4.06606e11			0.533344
$438$		−	1.00584e11i		−	0.130586i
$439$		−	1.52864e11i		−	0.196433i	−0.995165	−	0.0982164i	$-0.968686\pi$
$439$		−	1.52864e11i		−	0.196433i	0.995165	−	0.0982164i	$-0.0313137\pi$
$440$	2.64754e11			0.336749
$441$	−3.30185e11			−0.415704
$442$			3.87954e10i			0.0483482i
$443$	1.42971e12			1.76373			0.881865	−	0.471502i	$-0.156288\pi$
$443$	1.42971e12			1.76373			0.881865	+	0.471502i	$0.156288\pi$
$444$	4.67833e11	−	2.37385e11i	0.571304	−	0.289888i
$445$	−4.86168e11			−0.587715
$446$			1.31062e11i			0.156845i
$447$	−1.26333e12			−1.49670
$448$	1.27871e11			0.149976
$449$			1.20619e12i			1.40058i	0.713857	+	0.700291i	$0.246947\pi$
$449$			1.20619e12i			1.40058i	−0.713857	+	0.700291i	$0.753053\pi$
$450$		−	5.99346e10i		−	0.0689003i
$451$	−2.76904e10			−0.0315163
$452$			7.54339e11i			0.850048i
$453$	−3.31782e11			−0.370178
$454$	−4.76964e11			−0.526907
$455$	4.00337e11			0.437899
$456$	−2.58679e11			−0.280169
$457$		−	2.85197e9i		−	0.00305860i	−0.999999	−	0.00152930i	$-0.999513\pi$
$457$		−	2.85197e9i		−	0.00305860i	0.999999	−	0.00152930i	$-0.000486791\pi$
$458$			7.38287e10i			0.0784026i
$459$			4.42709e11i			0.465545i
$460$	1.18477e12			1.23374
$461$			3.33099e11i			0.343494i	0.985141	+	0.171747i	$0.0549411\pi$
$461$			3.33099e11i			0.343494i	−0.985141	+	0.171747i	$0.945059\pi$
$462$		−	1.92047e11i		−	0.196118i
$463$		−	1.47908e12i		−	1.49581i	−0.663806	−	0.747905i	$-0.731060\pi$
$463$		−	1.47908e12i		−	1.49581i	0.663806	−	0.747905i	$-0.268940\pi$
$464$			8.90681e10i			0.0892055i
$465$	−1.66854e12			−1.65500
$466$		−	2.11038e11i		−	0.207312i
$467$		−	8.68555e11i		−	0.845028i	−0.906356	−	0.422514i	$-0.861148\pi$
$467$		−	8.68555e11i		−	0.845028i	0.906356	−	0.422514i	$-0.138852\pi$
$468$			6.20134e10i			0.0597557i
$469$	−2.13530e12			−2.03789
$470$	6.56298e9			0.00620384
$471$	−5.74607e11			−0.537993
$472$	−5.20964e11			−0.483135
$473$			5.05527e11i			0.464375i
$474$	−6.58531e11			−0.599202
$475$			2.04707e11i			0.184507i
$476$			5.64212e11i			0.503745i
$477$	−2.38876e11			−0.211271
$478$	−4.22968e11			−0.370580
$479$		−	1.66206e12i		−	1.44257i	−0.692638	−	0.721286i	$-0.743551\pi$
$479$		−	1.66206e12i		−	1.44257i	0.692638	−	0.721286i	$-0.256449\pi$
$480$	−1.17782e12			−1.01273
$481$	−1.27272e11	−	2.50824e11i	−0.108412	−	0.213657i
$482$	5.73872e11			0.484287
$483$		−	1.96493e12i		−	1.64280i
$484$	−8.34505e11			−0.691233
$485$	1.19955e12			0.984424
$486$		−	3.56098e11i		−	0.289538i
$487$			7.94277e11i			0.639870i	0.947440	+	0.319935i	$0.103661\pi$
$487$			7.94277e11i			0.639870i	−0.947440	+	0.319935i	$0.896339\pi$
$488$	1.68175e12			1.34237
$489$		−	1.92823e12i		−	1.52500i
$490$	−9.41074e11			−0.737465
$491$	−4.56186e11			−0.354222			−0.177111	−	0.984191i	$-0.556675\pi$
$491$	−4.56186e11			−0.354222			−0.177111	+	0.984191i	$0.556675\pi$
$492$	7.88331e10			0.0606549
$493$	1.31108e11			0.0999578
$494$			6.06584e10i			0.0458268i
$495$		−	1.72086e11i		−	0.128832i
$496$		−	8.56497e11i		−	0.635416i
$497$	2.49621e11			0.183518
$498$			6.09505e11i			0.444064i
$499$			2.21578e12i			1.59983i	0.600114	+	0.799914i	$0.295122\pi$
$499$			2.21578e12i			1.59983i	−0.600114	+	0.799914i	$0.704878\pi$
$500$		−	7.14053e11i		−	0.510935i
$501$		−	5.73273e10i		−	0.0406529i
$502$	−5.83767e11			−0.410273
$503$			2.03088e12i			1.41458i	0.706922	+	0.707291i	$0.250083\pi$
$503$			2.03088e12i			1.41458i	−0.706922	+	0.707291i	$0.749917\pi$
$504$		−	5.90536e11i		−	0.407670i
$505$		−	1.09600e12i		−	0.749890i
$506$	−3.04715e11			−0.206641
$507$	1.15571e12			0.776807
$508$	1.88506e12			1.25585
$509$	8.83617e11			0.583491			0.291746	−	0.956496i	$-0.405764\pi$
$509$	8.83617e11			0.583491			0.291746	+	0.956496i	$0.405764\pi$
$510$			3.06493e11i			0.200611i
$511$	−7.84278e11			−0.508834
$512$		−	1.10232e12i		−	0.708910i
$513$			6.92197e11i			0.441267i
$514$	1.07448e12			0.678990
$515$	−8.35007e11			−0.523067
$516$		−	1.43921e12i		−	0.893716i
$517$	5.89402e9			0.00362831
$518$	5.30082e11	+	1.04467e12i	0.323489	+	0.637525i
$519$	−1.82027e12			−1.10124
$520$			4.04111e11i			0.242374i
$521$	2.98537e11			0.177512			0.0887560	−	0.996053i	$-0.471711\pi$
$521$	2.98537e11			0.177512			0.0887560	+	0.996053i	$0.471711\pi$
$522$	−6.00182e10			−0.0353806
$523$		−	6.23136e11i		−	0.364188i	−0.983281	−	0.182094i	$-0.941713\pi$
$523$		−	6.23136e11i		−	0.364188i	0.983281	−	0.182094i	$-0.0582875\pi$
$524$			1.57040e12i			0.909956i
$525$	9.89251e11			0.568316
$526$			1.30643e12i			0.744135i
$527$	−1.26076e12			−0.712006
$528$	−1.86993e11			−0.104706
$529$	−1.31655e12			−0.730946
$530$	−6.80828e11			−0.374797
$531$			3.38619e11i			0.184836i
$532$			8.82171e11i			0.477475i
$533$		−	4.22656e10i		−	0.0226838i
$534$	−3.55980e11			−0.189448
$535$		−	4.10842e12i		−	2.16812i
$536$		−	2.15543e12i		−	1.12796i
$537$			1.35829e12i			0.704870i
$538$			1.15107e12i			0.592352i
$539$	−8.45151e11			−0.431305
$540$			2.01693e12i			1.02075i
$541$			1.22542e12i			0.615033i	0.951543	+	0.307517i	$0.0994980\pi$
$541$			1.22542e12i			0.615033i	−0.951543	+	0.307517i	$0.900502\pi$
$542$		−	1.07276e12i		−	0.533955i
$543$	3.22480e11			0.159186
$544$	−8.89965e11			−0.435691
$545$	2.01419e12			0.977950
$546$	2.93133e11			0.141155
$547$			7.03370e11i			0.335924i	0.985793	+	0.167962i	$0.0537186\pi$
$547$			7.03370e11i			0.335924i	−0.985793	+	0.167962i	$0.946281\pi$
$548$	1.63423e12			0.774106
$549$		−	1.09311e12i		−	0.513559i
$550$		−	1.53410e11i		−	0.0714861i
$551$	2.04993e11			0.0947451
$552$	1.98346e12			0.909278
$553$			5.13471e12i			2.33482i
$554$	−3.10463e11			−0.140028
$555$	−1.00548e12	−	1.98157e12i	−0.449835	−	0.886525i
$556$	3.42350e11			0.151926
$557$			1.53756e12i			0.676835i	0.940996	+	0.338418i	$0.109892\pi$
$557$			1.53756e12i			0.676835i	−0.940996	+	0.338418i	$0.890108\pi$
$558$	5.77147e11			0.252019
$559$	−7.71617e11			−0.334232
$560$			1.62351e12i			0.697604i
$561$			2.75252e11i			0.117327i
$562$	1.09933e12			0.464853
$563$		−	3.44352e12i		−	1.44449i	−0.691637	−	0.722245i	$-0.743110\pi$
$563$		−	3.44352e12i		−	1.44449i	0.691637	−	0.722245i	$-0.256890\pi$
$564$	−1.67799e10			−0.00698288
$565$	3.19510e12			1.31907
$566$	−1.71283e12			−0.701518
$567$	2.14869e12			0.873070
$568$			2.51975e11i			0.101576i
$569$		−	6.66708e11i		−	0.266643i	−0.991073	−	0.133321i	$-0.957436\pi$
$569$		−	6.66708e11i		−	0.266643i	0.991073	−	0.133321i	$-0.0425643\pi$
$570$			4.79216e11i			0.190149i
$571$	−3.30011e12			−1.29917			−0.649586	−	0.760289i	$-0.725058\pi$
$571$	−3.30011e12			−1.29917			−0.649586	+	0.760289i	$0.725058\pi$
$572$			1.58731e11i			0.0619983i
$573$		−	1.83974e12i		−	0.712951i
$574$			1.76035e11i			0.0676854i
$575$		−	1.56962e12i		−	0.598809i
$576$	8.38979e10			0.0317578
$577$		−	3.34404e11i		−	0.125597i	−0.998026	−	0.0627987i	$-0.979997\pi$
$577$		−	3.34404e11i		−	0.125597i	0.998026	−	0.0627987i	$-0.0200026\pi$
$578$		−	1.03450e12i		−	0.385528i
$579$		−	2.75083e11i		−	0.101721i
$580$	5.97309e11			0.219166
$581$	4.75245e12			1.73032
$582$	8.78333e11			0.317326
$583$	−6.11432e11			−0.219200
$584$		−	7.91673e11i		−	0.281636i
$585$	2.62666e11			0.0927262
$586$			1.96878e12i			0.689696i
$587$			4.93550e12i			1.71577i	0.513841	+	0.857885i	$0.328222\pi$
$587$			4.93550e12i			1.71577i	−0.513841	+	0.857885i	$0.671778\pi$
$588$	2.40610e12			0.830071
$589$	−1.97125e12			−0.674876
$590$			9.65111e11i			0.327901i
$591$	−4.73555e11			−0.159671
$592$	1.01718e12	−	5.16132e11i	0.340370	−	0.172708i
$593$	3.44361e12			1.14358			0.571791	−	0.820399i	$-0.306249\pi$
$593$	3.44361e12			1.14358			0.571791	+	0.820399i	$0.306249\pi$
$594$		−	5.18741e11i		−	0.170967i
$595$	2.38979e12			0.781689
$596$	−4.34895e12			−1.41181
$597$			4.21026e12i			1.35651i
$598$		−	4.65106e11i		−	0.148729i
$599$	−6.66166e10			−0.0211428			−0.0105714	−	0.999944i	$-0.503365\pi$
$599$	−6.66166e10			−0.0211428			−0.0105714	+	0.999944i	$0.503365\pi$
$600$			9.98579e11i			0.314559i
$601$	3.97296e11			0.124217			0.0621083	−	0.998069i	$-0.480218\pi$
$601$	3.97296e11			0.124217			0.0621083	+	0.998069i	$0.480218\pi$
$602$	3.21376e12			0.997307
$603$	−1.40100e12			−0.431528
$604$	−1.14214e12			−0.349183
$605$			3.53466e12i			1.07263i
$606$		−	8.02506e11i		−	0.241725i
$607$		−	2.65373e12i		−	0.793429i	−0.917942	−	0.396715i	$-0.870150\pi$
$607$		−	2.65373e12i		−	0.793429i	0.917942	−	0.396715i	$-0.129850\pi$
$608$	−1.39150e12			−0.412970
$609$		−	9.90632e11i		−	0.291833i
$610$		−	3.11553e12i		−	0.911061i
$611$			8.99641e9i			0.00261146i
$612$			3.70187e11i			0.106669i
$613$	1.43446e12			0.410314			0.205157	−	0.978729i	$-0.434230\pi$
$613$	1.43446e12			0.410314			0.205157	+	0.978729i	$0.434230\pi$
$614$		−	1.83065e12i		−	0.519814i
$615$		−	3.33908e11i		−	0.0941216i
$616$		−	1.51155e12i		−	0.422970i
$617$	4.38127e12			1.21707			0.608537	−	0.793525i	$-0.291757\pi$
$617$	4.38127e12			1.21707			0.608537	+	0.793525i	$0.291757\pi$
$618$	−6.11406e11			−0.168609
$619$	−5.95175e12			−1.62943			−0.814717	−	0.579859i	$-0.803107\pi$
$619$	−5.95175e12			−1.62943			−0.814717	+	0.579859i	$0.803107\pi$
$620$	−5.74385e12			−1.56113
$621$		−	5.30750e12i		−	1.43212i
$622$	1.14299e12			0.306185
$623$			2.77566e12i			0.738193i
$624$		−	2.85419e11i		−	0.0753620i
$625$	−4.76070e12			−1.24799
$626$	−6.78472e11			−0.176582
$627$			4.30370e11i			0.111208i
$628$	−1.97805e12			−0.507480
$629$	−7.59743e11	−	1.49729e12i	−0.193526	−	0.381397i
$630$	−1.09400e12			−0.276683
$631$			7.20462e11i			0.180917i	0.995900	+	0.0904584i	$0.0288332\pi$
$631$			7.20462e11i			0.180917i	−0.995900	+	0.0904584i	$0.971167\pi$
$632$	−5.18313e12			−1.29230
$633$	−2.65960e12			−0.658415
$634$		−	3.09032e12i		−	0.759629i
$635$		−	7.98444e12i		−	1.94878i
$636$	1.74071e12			0.421862
$637$		−	1.29001e12i		−	0.310431i
$638$	−1.53624e11			−0.0367085
$639$	1.63780e11			0.0388603
$640$	−4.97661e12			−1.17253
$641$	6.90851e12			1.61630			0.808152	−	0.588974i	$-0.200468\pi$
$641$	6.90851e12			1.61630			0.808152	+	0.588974i	$0.200468\pi$
$642$		−	3.00825e12i		−	0.698887i
$643$			2.16123e12i			0.498600i	0.968426	+	0.249300i	$0.0802006\pi$
$643$			2.16123e12i			0.498600i	−0.968426	+	0.249300i	$0.919799\pi$
$644$		−	6.76415e12i		−	1.54963i
$645$	−6.09595e12			−1.38683
$646$			3.62098e11i			0.0818050i
$647$			7.44236e12i			1.66971i	0.550468	+	0.834856i	$0.314449\pi$
$647$			7.44236e12i			1.66971i	−0.550468	+	0.834856i	$0.685551\pi$
$648$			2.16894e12i			0.483238i
$649$			8.66738e11i			0.191773i
$650$	2.34159e11			0.0514519
$651$			9.52612e12i			2.07875i
$652$		−	6.63783e12i		−	1.43851i
$653$			3.51296e12i			0.756074i	0.925791	+	0.378037i	$0.123401\pi$
$653$			3.51296e12i			0.756074i	−0.925791	+	0.378037i	$0.876599\pi$
$654$	1.47482e12			0.315239
$655$	6.65165e12			1.41203
$656$	1.71402e11			0.0361368
$657$	−5.14575e11			−0.107747
$658$		−	3.74697e10i		−	0.00779227i
$659$	−7.33215e12			−1.51442			−0.757211	−	0.653170i	$-0.773439\pi$
$659$	−7.33215e12			−1.51442			−0.757211	+	0.653170i	$0.773439\pi$
$660$			1.25401e12i			0.257249i
$661$			5.89973e12i			1.20206i	0.799227	+	0.601029i	$0.205242\pi$
$661$			5.89973e12i			1.20206i	−0.799227	+	0.601029i	$0.794758\pi$
$662$	−2.75208e12			−0.556930
$663$	−4.20135e11			−0.0844457
$664$			4.79726e12i			0.957716i
$665$	3.73656e12			0.740925
$666$	3.47794e11	+	6.85424e11i	0.0684995	+	0.134997i
$667$	−1.57181e12			−0.307492
$668$		−	1.97346e11i		−	0.0383472i
$669$	−1.41934e12			−0.273948
$670$	−3.99304e12			−0.765538
$671$		−	2.79796e12i		−	0.532833i
$672$			6.72446e12i			1.27203i
$673$	4.51059e12			0.847550			0.423775	−	0.905768i	$-0.360705\pi$
$673$	4.51059e12			0.847550			0.423775	+	0.905768i	$0.360705\pi$
$674$		−	1.55085e12i		−	0.289468i
$675$	2.67208e12			0.495431
$676$	3.97847e12			0.732749
$677$	3.07670e12			0.562906			0.281453	−	0.959575i	$-0.409184\pi$
$677$	3.07670e12			0.562906			0.281453	+	0.959575i	$0.409184\pi$
$678$	2.33951e12			0.425197
$679$		−	6.84856e12i		−	1.23648i
$680$			2.41233e12i			0.432659i
$681$		−	5.16527e12i		−	0.920304i
$682$	1.47728e12			0.261477
$683$			6.31154e12i			1.10979i	0.831919	+	0.554897i	$0.187242\pi$
$683$			6.31154e12i			1.10979i	−0.831919	+	0.554897i	$0.812758\pi$
$684$			5.78804e11i			0.101107i
$685$		−	6.92200e12i		−	1.20122i
$686$			1.22612e12i			0.211385i
$687$	−7.99527e11			−0.136939
$688$		−	3.12918e12i		−	0.532455i
$689$		−	9.33267e11i		−	0.157768i
$690$		−	3.67444e12i		−	0.617122i
$691$	9.99594e12			1.66791			0.833955	−	0.551833i	$-0.186071\pi$
$691$	9.99594e12			1.66791			0.833955	+	0.551833i	$0.186071\pi$
$692$	−6.26618e12			−1.03878
$693$	−9.82485e11			−0.161818
$694$	−4.13881e12			−0.677263
$695$		−	1.45007e12i		−	0.235753i
$696$	9.99972e11			0.161527
$697$		−	2.52303e11i		−	0.0404925i
$698$			2.28694e12i			0.364675i
$699$	2.28543e12			0.362094
$700$	3.40544e12			0.536083
$701$		−	2.05074e12i		−	0.320760i	−0.987055	−	0.160380i	$-0.948728\pi$
$701$		−	2.05074e12i		−	0.320760i	0.987055	−	0.160380i	$-0.0512719\pi$
$702$	7.91786e11			0.123053
$703$	−1.18789e12	−	2.34108e12i	−0.183434	−	0.361507i
$704$	2.14747e11			0.0329497
$705$			7.10737e10i			0.0108357i
$706$	3.45551e12			0.523469
$707$	−6.25732e12			−0.941892
$708$		−	2.46755e12i		−	0.369077i
$709$		−	2.76523e12i		−	0.410983i	−0.978659	−	0.205491i	$-0.934121\pi$
$709$		−	2.76523e12i		−	0.410983i	0.978659	−	0.205491i	$-0.0658793\pi$
$710$	4.66795e11			0.0689388
$711$			3.36895e12i			0.494404i
$712$	−2.80183e12			−0.408584
$713$	1.51148e13			2.19028
$714$	1.74985e12			0.251975
$715$	6.72327e11			0.0962063
$716$			4.67584e12i			0.664893i
$717$		−	4.58053e12i		−	0.647261i
$718$			4.59686e12i			0.645507i
$719$	−2.70430e12			−0.377376			−0.188688	−	0.982037i	$-0.560423\pi$
$719$	−2.70430e12			−0.377376			−0.188688	+	0.982037i	$0.560423\pi$
$720$			1.06521e12i			0.147719i
$721$			4.76727e12i			0.656994i
$722$		−	2.87898e12i		−	0.394295i
$723$			6.21474e12i			0.845864i
$724$	1.11012e12			0.150157
$725$		−	7.91333e11i		−	0.106375i
$726$			2.58813e12i			0.345758i
$727$			3.11123e12i			0.413074i	0.978439	+	0.206537i	$0.0662194\pi$
$727$			3.11123e12i			0.413074i	−0.978439	+	0.206537i	$0.933781\pi$
$728$	2.30717e12			0.304431
$729$	8.25043e12			1.08194
$730$	−1.46661e12			−0.191145
$731$	−4.60614e12			−0.596635
$732$			7.96565e12i			1.02547i
$733$	−5.41565e12			−0.692920			−0.346460	−	0.938065i	$-0.612616\pi$
$733$	−5.41565e12			−0.692920			−0.346460	+	0.938065i	$0.612616\pi$
$734$			5.35061e12i			0.680411i
$735$		−	1.01914e13i		−	1.28807i
$736$	1.06695e13			1.34028
$737$	−3.58603e12			−0.447724
$738$			1.15499e11i			0.0143326i
$739$	1.03962e13			1.28225			0.641127	−	0.767435i	$-0.278467\pi$
$739$	1.03962e13			1.28225			0.641127	+	0.767435i	$0.278467\pi$
$740$	−3.46129e12	−	6.82144e12i	−0.424322	−	0.836245i
$741$	−6.56900e11			−0.0800419
$742$			3.88702e12i			0.470760i
$743$	1.24097e13			1.49387			0.746935	−	0.664898i	$-0.231525\pi$
$743$	1.24097e13			1.49387			0.746935	+	0.664898i	$0.231525\pi$
$744$	−9.61593e12			−1.15057
$745$			1.84206e13i			2.19078i
$746$		−	3.54001e11i		−	0.0418485i
$747$	3.11815e12			0.366399
$748$			9.47540e11i			0.110673i
$749$	−2.34560e13			−2.72324
$750$	−2.21456e12			−0.255572
$751$	1.80317e12			0.206851			0.103425	−	0.994637i	$-0.467020\pi$
$751$	1.80317e12			0.206851			0.103425	+	0.994637i	$0.467020\pi$
$752$	−3.64837e10			−0.00416024
$753$		−	6.32190e12i		−	0.716589i
$754$		−	2.34486e11i		−	0.0264208i
$755$			4.83769e12i			0.541847i
$756$	1.15151e13			1.28210
$757$		−	8.21800e12i		−	0.909568i	−0.890602	−	0.454784i	$-0.849717\pi$
$757$		−	8.21800e12i		−	0.909568i	0.890602	−	0.454784i	$-0.150283\pi$
$758$		−	2.78702e12i		−	0.306640i
$759$		−	3.29991e12i		−	0.360923i
$760$			3.77179e12i			0.410096i
$761$	−5.36207e12			−0.579565			−0.289782	−	0.957093i	$-0.593583\pi$
$761$	−5.36207e12			−0.579565			−0.289782	+	0.957093i	$0.593583\pi$
$762$		−	5.84634e12i		−	0.628183i
$763$		−	1.14995e13i		−	1.22834i
$764$		−	6.33319e12i		−	0.672515i
$765$	1.56798e12			0.165525
$766$	4.74875e12			0.498368
$767$	−1.32296e12			−0.138028
$768$	−4.43042e12			−0.459536
$769$		−	2.61553e12i		−	0.269706i	−0.990866	−	0.134853i	$-0.956944\pi$
$769$		−	2.61553e12i		−	0.269706i	0.990866	−	0.134853i	$-0.0430563\pi$
$770$	−2.80022e12			−0.287067
$771$			1.16361e13i			1.18594i
$772$		−	9.46957e11i		−	0.0959517i
$773$	2.50175e11			0.0252021			0.0126010	−	0.999921i	$-0.495989\pi$
$773$	2.50175e11			0.0252021			0.0126010	+	0.999921i	$0.495989\pi$
$774$	2.10859e12			0.211182
$775$			7.60962e12i			0.757714i
$776$	6.91313e12			0.684380
$777$	−1.13133e13	+	5.74052e12i	−1.11351	+	0.565011i
$778$	−4.07021e12			−0.398299
$779$		−	3.94488e11i		−	0.0383809i
$780$	−1.91408e12			−0.185154
$781$	4.19215e11			0.0403188
$782$		−	2.77643e12i		−	0.265495i
$783$		−	2.67581e12i		−	0.254406i
$784$	5.23144e12			0.494538
$785$			8.37830e12i			0.787486i
$786$	4.87045e12			0.455164
$787$	6.45966e12			0.600238			0.300119	−	0.953902i	$-0.402974\pi$
$787$	6.45966e12			0.600238			0.300119	+	0.953902i	$0.402974\pi$
$788$	−1.63018e12			−0.150615
$789$	−1.41480e13			−1.29972
$790$			9.60199e12i			0.877080i
$791$		−	1.82417e13i		−	1.65680i
$792$		−	9.91749e11i		−	0.0895650i
$793$	4.27071e12			0.383504
$794$		−	7.40350e12i		−	0.661066i
$795$		−	7.37303e12i		−	0.654627i
$796$			1.44936e13i			1.27958i
$797$		−	1.75688e12i		−	0.154234i	−0.997022	−	0.0771168i	$-0.975429\pi$
$797$		−	1.75688e12i		−	0.154234i	0.997022	−	0.0771168i	$-0.0245714\pi$
$798$	2.73597e12			0.238835
$799$			5.37037e10i			0.00466170i
$800$			5.37161e12i			0.463660i
$801$			1.82115e12i			0.156314i
$802$	−5.77690e12			−0.493072
$803$	−1.31712e12			−0.111791
$804$	1.02092e13			0.861669
$805$	−2.86505e13			−2.40464
$806$			2.25487e12i			0.188197i
$807$	−1.24655e13			−1.03461
$808$		−	6.31632e12i		−	0.521330i
$809$		−	1.36499e13i		−	1.12037i	−0.828368	−	0.560184i	$-0.810730\pi$
$809$		−	1.36499e13i		−	1.12037i	0.828368	−	0.560184i	$-0.189270\pi$
$810$	4.01807e12			0.327971
$811$	−2.56854e12			−0.208493			−0.104247	−	0.994551i	$-0.533243\pi$
$811$	−2.56854e12			−0.208493			−0.104247	+	0.994551i	$0.533243\pi$
$812$		−	3.41019e12i		−	0.275281i
$813$	1.16174e13			0.932615
$814$	8.90222e11	+	1.75443e12i	0.0710704	+	0.140064i
$815$	−2.81154e13			−2.23221
$816$		−	1.70380e12i		−	0.134528i
$817$	−7.20191e12			−0.565521
$818$	−1.23046e9			−9.60900e−5
$819$		−	1.49963e12i		−	0.116468i
$820$		−	1.14946e12i		−	0.0887834i
$821$	−9.62363e12			−0.739256			−0.369628	−	0.929180i	$-0.620515\pi$
$821$	−9.62363e12			−0.739256			−0.369628	+	0.929180i	$0.620515\pi$
$822$		−	5.06840e12i		−	0.387211i
$823$	1.12898e12			0.0857803			0.0428901	−	0.999080i	$-0.486343\pi$
$823$	1.12898e12			0.0857803			0.0428901	+	0.999080i	$0.486343\pi$
$824$	−4.81222e12			−0.363641
$825$	1.66135e12			0.124859
$826$	5.51006e12			0.411857
$827$		−	7.83837e12i		−	0.582708i	−0.956615	−	0.291354i	$-0.905894\pi$
$827$		−	7.83837e12i		−	0.582708i	0.956615	−	0.291354i	$-0.0941057\pi$
$828$		−	4.43805e12i		−	0.328137i
$829$			3.00307e12i			0.220836i	0.993885	+	0.110418i	$0.0352190\pi$
$829$			3.00307e12i			0.220836i	−0.993885	+	0.110418i	$0.964781\pi$
$830$	8.88715e12			0.649997
$831$		−	3.36215e12i		−	0.244575i
$832$			3.27782e11i			0.0237154i
$833$		−	7.70065e12i		−	0.554147i
$834$		−	1.06176e12i		−	0.0759942i
$835$	−8.35885e11			−0.0595056
$836$			1.48152e12i			0.104901i
$837$			2.57312e13i			1.81215i
$838$			1.18435e12i			0.0829622i
$839$	−4.45665e12			−0.310513			−0.155256	−	0.987874i	$-0.549620\pi$
$839$	−4.45665e12			−0.310513			−0.155256	+	0.987874i	$0.549620\pi$
$840$	1.82272e13			1.26318
$841$	1.37147e13			0.945376
$842$	−1.02108e13			−0.700095
$843$			1.19052e13i			0.811919i
$844$	−9.15552e12			−0.621072
$845$		−	1.68513e13i		−	1.13705i
$846$		−	2.45844e10i		−	0.00165003i
$847$	2.01803e13			1.34726
$848$	3.78473e12			0.251336
$849$		−	1.85490e13i		−	1.22528i
$850$	1.39781e12			0.0918463
$851$	9.10832e12	+	1.79505e13i	0.595327	+	1.17326i
$852$	−1.19348e12			−0.0775957
$853$		−	2.86713e13i		−	1.85429i	−0.374705	−	0.927144i	$-0.622256\pi$
$853$		−	2.86713e13i		−	1.85429i	0.374705	−	0.927144i	$-0.377744\pi$
$854$	−1.77873e13			−1.14433
$855$	2.45160e12			0.156893
$856$		−	2.36772e13i		−	1.50730i
$857$			1.59528e13i			1.01024i	0.863050	+	0.505118i	$0.168551\pi$
$857$			1.59528e13i			1.01024i	−0.863050	+	0.505118i	$0.831449\pi$
$858$	4.92289e11			0.0310118
$859$		−	2.23959e13i		−	1.40346i	−0.712445	−	0.701728i	$-0.752412\pi$
$859$		−	2.23959e13i		−	1.40346i	0.712445	−	0.701728i	$-0.247588\pi$
$860$	−2.09850e13			−1.30817
$861$	−1.90637e12			−0.118220
$862$	1.14740e13			0.707833
$863$	2.39027e13			1.46690			0.733448	−	0.679746i	$-0.237910\pi$
$863$	2.39027e13			1.46690			0.733448	+	0.679746i	$0.237910\pi$
$864$			1.81636e13i			1.10889i
$865$			2.65412e13i			1.61194i
$866$		−	1.09540e13i		−	0.661823i
$867$	1.12031e13			0.673370
$868$			3.27931e13i			1.96085i
$869$			8.62327e12i			0.512959i
$870$		−	1.85250e12i		−	0.109628i
$871$		−	5.47358e12i		−	0.322248i
$872$	1.16080e13			0.679879
$873$		−	4.49343e12i		−	0.261827i
$874$		−	4.34108e12i		−	0.251650i
$875$			1.72675e13i			0.995846i
$876$	3.74977e12			0.215147
$877$	2.13329e13			1.21773			0.608866	−	0.793273i	$-0.291625\pi$
$877$	2.13329e13			1.21773			0.608866	+	0.793273i	$0.291625\pi$
$878$	−1.63203e12			−0.0926837
$879$	−2.13209e13			−1.20463
$880$			2.72653e12i			0.153263i
$881$	−7.25536e12			−0.405758			−0.202879	−	0.979204i	$-0.565030\pi$
$881$	−7.25536e12			−0.405758			−0.202879	+	0.979204i	$0.565030\pi$
$882$			3.52519e12i			0.196143i
$883$			2.52446e13i			1.39748i	0.715377	+	0.698739i	$0.246255\pi$
$883$			2.52446e13i			1.39748i	−0.715377	+	0.698739i	$0.753745\pi$
$884$	−1.44629e12			−0.0796562
$885$	−1.04517e13			−0.572718
$886$		−	1.52642e13i		−	0.832188i
$887$	2.64882e13			1.43680			0.718400	−	0.695631i	$-0.244875\pi$
$887$	2.64882e13			1.43680			0.718400	+	0.695631i	$0.244875\pi$
$888$	−5.79464e12	−	1.14200e13i	−0.312729	−	0.616320i
$889$	−4.55852e13			−2.44775
$890$			5.19052e12i			0.277304i
$891$	3.60851e12			0.191813
$892$	−4.88599e12			−0.258411
$893$			8.39683e10i			0.00441859i
$894$			1.34878e13i			0.706193i
$895$	1.98052e13			1.03175
$896$			2.84128e13i			1.47274i
$897$	5.03686e12			0.259773
$898$	1.28778e13			0.660843
$899$	7.62024e12			0.389090
$900$	2.23435e12			0.113517
$901$		−	5.57110e12i		−	0.281630i
$902$			2.95634e11i			0.0148705i
$903$			3.48034e13i			1.74191i
$904$	1.84137e13			0.917027
$905$		−	4.70206e12i		−	0.233007i
$906$			3.54223e12i			0.174663i
$907$			2.02945e13i			0.995737i	0.867252	+	0.497869i	$0.165884\pi$
$907$			2.02945e13i			0.995737i	−0.867252	+	0.497869i	$0.834116\pi$
$908$		−	1.77812e13i		−	0.868108i
$909$	−4.10551e12			−0.199448
$910$		−	4.27415e12i		−	0.206616i
$911$			2.04758e13i			0.984936i	0.870331	+	0.492468i	$0.163905\pi$
$911$			2.04758e13i			0.984936i	−0.870331	+	0.492468i	$0.836095\pi$
$912$		−	2.66397e12i		−	0.127512i
$913$	7.98129e12			0.380150
$914$	−3.04488e10			−0.00144315
$915$	3.37396e13			1.59127
$916$	−2.75233e12			−0.129173
$917$		−	3.79760e13i		−	1.77357i
$918$	4.72654e12			0.219660
$919$		−	2.34202e13i		−	1.08311i	−0.840667	−	0.541553i	$-0.817837\pi$
$919$		−	2.34202e13i		−	1.08311i	0.840667	−	0.541553i	$-0.182163\pi$
$920$		−	2.89206e13i		−	1.33095i
$921$	1.98250e13			0.907915
$922$	3.55629e12			0.162072
$923$			6.39874e11i			0.0290193i
$924$	7.15948e12			0.323116
$925$	−9.03724e12	+	4.58562e12i	−0.405881	+	0.205949i
$926$	−1.57912e13			−0.705774
$927$			3.12787e12i			0.139120i
$928$	5.37911e12			0.238092
$929$	−9.52404e12			−0.419518			−0.209759	−	0.977753i	$-0.567268\pi$
$929$	−9.52404e12			−0.419518			−0.209759	+	0.977753i	$0.567268\pi$
$930$			1.78140e13i			0.780886i
$931$		−	1.20403e13i		−	0.525248i
$932$	7.86746e12			0.341557
$933$			1.23780e13i			0.534788i
$934$	−9.27303e12			−0.398713
$935$	4.01343e12			0.171737
$936$	1.51377e12			0.0644641
$937$	−2.17483e12			−0.0921716			−0.0460858	−	0.998937i	$-0.514675\pi$
$937$	−2.17483e12			−0.0921716			−0.0460858	+	0.998937i	$0.514675\pi$
$938$			2.27973e13i			0.961546i
$939$		−	7.34751e12i		−	0.308422i
$940$			2.44667e11i			0.0102212i
$941$	−3.97025e13			−1.65069			−0.825344	−	0.564630i	$-0.809019\pi$
$941$	−3.97025e13			−1.65069			−0.825344	+	0.564630i	$0.809019\pi$
$942$			6.13473e12i			0.253844i
$943$			3.02478e12i			0.124564i
$944$		−	5.36506e12i		−	0.219888i
$945$		−	4.87740e13i		−	1.98950i
$946$	5.39720e12			0.219108
$947$		−	1.85795e13i		−	0.750685i	−0.926886	−	0.375343i	$-0.877525\pi$
$947$		−	1.85795e13i		−	0.750685i	0.926886	−	0.375343i	$-0.122475\pi$
$948$		−	2.45500e13i		−	0.987218i
$949$		−	2.01040e12i		−	0.0804610i
$950$	2.18553e12			0.0870566
$951$	3.34666e13			1.32678
$952$	1.37726e13			0.543437
$953$	2.18023e12			0.0856217			0.0428108	−	0.999083i	$-0.486369\pi$
$953$	2.18023e12			0.0856217			0.0428108	+	0.999083i	$0.486369\pi$
$954$			2.55033e12i			0.0996847i
$955$	−2.68251e13			−1.04358
$956$		−	1.57682e13i		−	0.610550i
$957$		−	1.66367e12i		−	0.0641157i
$958$	−1.77448e13			−0.680655
$959$	−3.95195e13			−1.50879
$960$			2.58956e12i			0.0984022i
$961$	−4.68381e13			−1.77151
$962$	−2.67790e12	+	1.35880e12i	−0.100811	+	0.0511526i
$963$	−1.53898e13			−0.576654
$964$			2.13939e13i			0.797890i
$965$	−4.01097e12			−0.148894
$966$	−2.09783e13			−0.775129
$967$		−	1.41452e12i		−	0.0520225i	−0.999662	−	0.0260113i	$-0.991719\pi$
$967$		−	1.41452e12i		−	0.0520225i	0.999662	−	0.0260113i	$-0.00828058\pi$
$968$			2.03705e13i			0.745699i
$969$	−3.92134e12			−0.142882
$970$		−	1.28069e13i		−	0.464485i
$971$	−7.66184e12			−0.276596			−0.138298	−	0.990391i	$-0.544163\pi$
$971$	−7.66184e12			−0.276596			−0.138298	+	0.990391i	$0.544163\pi$
$972$	1.32753e13			0.477030
$973$	−8.27882e12			−0.296115
$974$	8.48001e12			0.301912
$975$			2.53583e12i			0.0898667i
$976$			1.73193e13i			0.610949i
$977$			4.47513e13i			1.57138i	0.618623	+	0.785688i	$0.287691\pi$
$977$			4.47513e13i			1.57138i	−0.618623	+	0.785688i	$0.712309\pi$
$978$	−2.05866e13			−0.719547
$979$			4.66146e12i			0.162181i
$980$		−	3.50831e13i		−	1.21501i
$981$		−	7.54500e12i		−	0.260105i
$982$			4.87042e12i			0.167134i
$983$	5.21169e13			1.78028			0.890138	−	0.455691i	$-0.150608\pi$
$983$	5.21169e13			1.78028			0.890138	+	0.455691i	$0.150608\pi$
$984$		−	1.92434e12i		−	0.0654342i
$985$			6.90487e12i			0.233718i
$986$		−	1.39976e12i		−	0.0471635i
$987$	4.05778e11			0.0136101
$988$	−2.26134e12			−0.0755022
$989$	5.52215e13			1.83538
$990$	−1.83726e12			−0.0607872
$991$			1.54987e13i			0.510462i	0.966880	+	0.255231i	$0.0821515\pi$
$991$			1.54987e13i			0.510462i	−0.966880	+	0.255231i	$0.917848\pi$
$992$	−5.17266e13			−1.69594
$993$		−	2.98037e13i		−	0.972743i
$994$		−	2.66505e12i		−	0.0865899i
$995$	6.13895e13			1.98559
$996$	−2.27223e13			−0.731619
$997$		−	8.99091e12i		−	0.288188i	−0.989564	−	0.144094i	$-0.953973\pi$
$997$		−	8.99091e12i		−	0.288188i	0.989564	−	0.144094i	$-0.0460267\pi$
$998$	2.36565e13			0.754854
$999$	−3.05585e13	+	1.55058e13i	−0.970706	+	0.492549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.10.b.a.36.12	✓	28
37.36	even	2	inner	37.10.b.a.36.17	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.10.b.a.36.12	✓	28	1.1	even	1	trivial
37.10.b.a.36.17	yes	28	37.36	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	37.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-10.6764i q^{2} +115.620 q^{3} +398.015 q^{4} -1685.85i q^{5} -1234.40i q^{6} -9624.92 q^{7} -9715.67i q^{8} -6315.04 q^{9} +O(q^{10})\)	\(q-10.6764i q^{2} +115.620 q^{3} +398.015 q^{4} -1685.85i q^{5} -1234.40i q^{6} -9624.92 q^{7} -9715.67i q^{8} -6315.04 q^{9} -17998.7 q^{10} -16164.1 q^{11} +46018.4 q^{12} -24672.3i q^{13} +102759. i q^{14} -194917. i q^{15} +100055. q^{16} -147281. i q^{17} +67421.8i q^{18} -230280. i q^{19} -670991. i q^{20} -1.11283e6 q^{21} +172575. i q^{22} +1.76570e6i q^{23} -1.12332e6i q^{24} -888949. q^{25} -263411. q^{26} -3.00589e6 q^{27} -3.83086e6 q^{28} +890190. i q^{29} -2.08101e6 q^{30} -8.56024e6i q^{31} -6.04265e6i q^{32} -1.86890e6 q^{33} -1.57242e6 q^{34} +1.62261e7i q^{35} -2.51348e6 q^{36} +(1.01662e7 - 5.15847e6i) q^{37} -2.45856e6 q^{38} -2.85261e6i q^{39} -1.63791e7 q^{40} +1.71308e6 q^{41} +1.18810e7i q^{42} -3.12746e7i q^{43} -6.43357e6 q^{44} +1.06462e7i q^{45} +1.88513e7 q^{46} -364635. q^{47} +1.15684e7 q^{48} +5.22855e7 q^{49} +9.49077e6i q^{50} -1.70286e7i q^{51} -9.81995e6i q^{52} +3.78264e7 q^{53} +3.20921e7i q^{54} +2.72502e7i q^{55} +9.35126e7i q^{56} -2.66250e7i q^{57} +9.50401e6 q^{58} -5.36210e7i q^{59} -7.75799e7i q^{60} +1.73097e8i q^{61} -9.13925e7 q^{62} +6.07818e7 q^{63} -1.32854e7 q^{64} -4.15937e7 q^{65} +1.99531e7i q^{66} +2.21851e8 q^{67} -5.86198e7i q^{68} +2.04150e8i q^{69} +1.73236e8 q^{70} -2.59349e7 q^{71} +6.13548e7i q^{72} +8.14841e7 q^{73} +(-5.50739e7 - 1.08538e8i) q^{74} -1.02780e8 q^{75} -9.16549e7i q^{76} +1.55579e8 q^{77} -3.04556e7 q^{78} -5.33481e8i q^{79} -1.68678e8i q^{80} -2.23242e8 q^{81} -1.82895e7i q^{82} -4.93765e8 q^{83} -4.42924e8 q^{84} -2.48292e8 q^{85} -3.33899e8 q^{86} +1.02924e8i q^{87} +1.57046e8i q^{88} -2.88383e8i q^{89} +1.13663e8 q^{90} +2.37469e8i q^{91} +7.02775e8i q^{92} -9.89734e8i q^{93} +3.89299e6i q^{94} -3.88217e8 q^{95} -6.98651e8i q^{96} +7.11545e8i q^{97} -5.58221e8i q^{98} +1.02077e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 150 q^{3} - 7340 q^{4} + 5940 q^{7} + 203834 q^{9}+O(q^{10}) \) 28 * q - 150 * q^3 - 7340 * q^4 + 5940 * q^7 + 203834 * q^9	\( 28 q - 150 q^{3} - 7340 q^{4} + 5940 q^{7} + 203834 q^{9} - 37794 q^{10} + 64218 q^{11} + 127066 q^{12} + 1640020 q^{16} - 40760 q^{21} - 19052702 q^{25} - 6123570 q^{26} - 1640160 q^{27} + 7625000 q^{28} - 19333840 q^{30} + 15698940 q^{33} + 708476 q^{34} - 51365130 q^{36} + 16215912 q^{37} - 28583988 q^{38} + 105594566 q^{40} - 7076754 q^{41} - 103376142 q^{44} + 77028630 q^{46} + 227172960 q^{47} - 65810002 q^{48} + 204785368 q^{49} + 50216184 q^{53} - 535678486 q^{58} - 438751290 q^{62} + 78365380 q^{63} + 177466492 q^{64} - 778712844 q^{65} + 631746366 q^{67} - 160866964 q^{70} + 1006626660 q^{71} - 83180574 q^{73} - 1466328336 q^{74} - 381338576 q^{75} + 408926592 q^{77} + 2562172434 q^{78} + 2121646388 q^{81} + 2834717148 q^{83} - 2459748244 q^{84} - 1400055912 q^{85} - 1148298888 q^{86} - 1425076412 q^{90} - 3422824284 q^{95} - 2703697668 q^{99}+O(q^{100}) \) 28 * q - 150 * q^3 - 7340 * q^4 + 5940 * q^7 + 203834 * q^9 - 37794 * q^10 + 64218 * q^11 + 127066 * q^12 + 1640020 * q^16 - 40760 * q^21 - 19052702 * q^25 - 6123570 * q^26 - 1640160 * q^27 + 7625000 * q^28 - 19333840 * q^30 + 15698940 * q^33 + 708476 * q^34 - 51365130 * q^36 + 16215912 * q^37 - 28583988 * q^38 + 105594566 * q^40 - 7076754 * q^41 - 103376142 * q^44 + 77028630 * q^46 + 227172960 * q^47 - 65810002 * q^48 + 204785368 * q^49 + 50216184 * q^53 - 535678486 * q^58 - 438751290 * q^62 + 78365380 * q^63 + 177466492 * q^64 - 778712844 * q^65 + 631746366 * q^67 - 160866964 * q^70 + 1006626660 * q^71 - 83180574 * q^73 - 1466328336 * q^74 - 381338576 * q^75 + 408926592 * q^77 + 2562172434 * q^78 + 2121646388 * q^81 + 2834717148 * q^83 - 2459748244 * q^84 - 1400055912 * q^85 - 1148298888 * q^86 - 1425076412 * q^90 - 3422824284 * q^95 - 2703697668 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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