LMFDB - Embedded newform 15.22.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,22,Mod(1,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("15.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	15.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:	$41.9216016431$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 157936x - 9799664 $ x^3 - x^2 - 157936*x - 9799664
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{4}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$425.878$ of defining polynomial
Character	$\chi$	$=$	15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2787.27 q^{2} -59049.0 q^{3} +5.67172e6 q^{4} -9.76562e6 q^{5} -1.64586e8 q^{6} -1.37938e9 q^{7} +9.96329e9 q^{8} +3.48678e9 q^{9} +O(q^{10})$	\(q+2787.27 q^{2} -59049.0 q^{3} +5.67172e6 q^{4} -9.76562e6 q^{5} -1.64586e8 q^{6} -1.37938e9 q^{7} +9.96329e9 q^{8} +3.48678e9 q^{9} -2.72194e10 q^{10} +2.99797e10 q^{11} -3.34910e11 q^{12} -7.63100e11 q^{13} -3.84470e12 q^{14} +5.76650e11 q^{15} +1.58759e13 q^{16} -1.14939e13 q^{17} +9.71861e12 q^{18} -5.19898e12 q^{19} -5.53879e13 q^{20} +8.14510e13 q^{21} +8.35614e13 q^{22} -8.03048e13 q^{23} -5.88322e14 q^{24} +9.53674e13 q^{25} -2.12696e15 q^{26} -2.05891e14 q^{27} -7.82346e15 q^{28} -2.01015e14 q^{29} +1.60728e15 q^{30} +1.53535e15 q^{31} +2.33559e16 q^{32} -1.77027e15 q^{33} -3.20366e16 q^{34} +1.34705e16 q^{35} +1.97761e16 q^{36} +1.53969e16 q^{37} -1.44910e16 q^{38} +4.50603e16 q^{39} -9.72978e16 q^{40} -7.88656e16 q^{41} +2.27026e17 q^{42} -1.61914e17 q^{43} +1.70036e17 q^{44} -3.40506e16 q^{45} -2.23831e17 q^{46} -3.76922e17 q^{47} -9.37457e17 q^{48} +1.34414e18 q^{49} +2.65815e17 q^{50} +6.78704e17 q^{51} -4.32809e18 q^{52} +3.24880e17 q^{53} -5.73874e17 q^{54} -2.92770e17 q^{55} -1.37432e19 q^{56} +3.06994e17 q^{57} -5.60284e17 q^{58} -9.88461e17 q^{59} +3.27060e18 q^{60} +1.01280e19 q^{61} +4.27945e18 q^{62} -4.80960e18 q^{63} +3.18051e19 q^{64} +7.45214e18 q^{65} -4.93422e18 q^{66} -1.02596e19 q^{67} -6.51902e19 q^{68} +4.74192e18 q^{69} +3.75459e19 q^{70} +3.23535e19 q^{71} +3.47399e19 q^{72} -2.89708e19 q^{73} +4.29154e19 q^{74} -5.63135e18 q^{75} -2.94872e19 q^{76} -4.13533e19 q^{77} +1.25595e20 q^{78} +3.51920e19 q^{79} -1.55038e20 q^{80} +1.21577e19 q^{81} -2.19820e20 q^{82} +2.86096e19 q^{83} +4.61967e20 q^{84} +1.12245e20 q^{85} -4.51299e20 q^{86} +1.18698e19 q^{87} +2.98696e20 q^{88} +5.20282e19 q^{89} -9.49083e19 q^{90} +1.05260e21 q^{91} -4.55467e20 q^{92} -9.06611e19 q^{93} -1.05058e21 q^{94} +5.07713e19 q^{95} -1.37915e21 q^{96} +7.90419e20 q^{97} +3.74649e21 q^{98} +1.04533e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 702 q^{2} - 177147 q^{3} + 5244228 q^{4} - 29296875 q^{5} - 41452398 q^{6} - 2072418204 q^{7} + 11461067832 q^{8} + 10460353203 q^{9}+O(q^{10}) $ 3 * q + 702 * q^2 - 177147 * q^3 + 5244228 * q^4 - 29296875 * q^5 - 41452398 * q^6 - 2072418204 * q^7 + 11461067832 * q^8 + 10460353203 * q^9	$ 3 q + 702 q^{2} - 177147 q^{3} + 5244228 q^{4} - 29296875 q^{5} - 41452398 q^{6} - 2072418204 q^{7} + 11461067832 q^{8} + 10460353203 q^{9} - 6855468750 q^{10} - 8467600440 q^{11} - 309666419172 q^{12} - 469447548570 q^{13} - 2389270234872 q^{14} + 1729951171875 q^{15} + 14993057845776 q^{16} - 6865096035486 q^{17} + 2447722649502 q^{18} + 33215593555044 q^{19} - 51213164062500 q^{20} + 122374222527996 q^{21} + 301288671211728 q^{22} + 48760125154728 q^{23} - 676764594411768 q^{24} + 286102294921875 q^{25} - 21\!\cdots\!24 q^{26}+ \cdots - 29\!\cdots\!40 q^{99}+O(q^{100}) $ 3 * q + 702 * q^2 - 177147 * q^3 + 5244228 * q^4 - 29296875 * q^5 - 41452398 * q^6 - 2072418204 * q^7 + 11461067832 * q^8 + 10460353203 * q^9 - 6855468750 * q^10 - 8467600440 * q^11 - 309666419172 * q^12 - 469447548570 * q^13 - 2389270234872 * q^14 + 1729951171875 * q^15 + 14993057845776 * q^16 - 6865096035486 * q^17 + 2447722649502 * q^18 + 33215593555044 * q^19 - 51213164062500 * q^20 + 122374222527996 * q^21 + 301288671211728 * q^22 + 48760125154728 * q^23 - 676764594411768 * q^24 + 286102294921875 * q^25 - 2164287288914724 * q^26 - 617673396283947 * q^27 - 9203502520938768 * q^28 + 2622046450702398 * q^29 + 404808574218750 * q^30 + 6533642328115464 * q^31 + 29519917545774816 * q^32 + 500003338381560 * q^33 - 45081813673901004 * q^34 + 20238459023437500 * q^35 + 18285492385687428 * q^36 - 21354228159481914 * q^37 - 108063021361090296 * q^38 + 27720408295509930 * q^39 - 111924490546875000 * q^40 - 63794855315977266 * q^41 + 141084018098956728 * q^42 - 332824264211549796 * q^43 - 192174659345792928 * q^44 - 102151886748046875 * q^45 - 431524141843343376 * q^46 - 1028504160073809912 * q^47 - 885325072735227024 * q^48 + 804417891162197307 * q^49 + 66947937011718750 * q^50 + 405377055799412814 * q^51 - 4951478317146373176 * q^52 + 811321254325423998 * q^53 - 144535574730443598 * q^54 + 82691410546875000 * q^55 - 14362364751613106400 * q^56 - 1961347583831793156 * q^57 - 5682617216112818772 * q^58 - 526619402549960904 * q^59 + 3024086124726562500 * q^60 + 826732383760533522 * q^61 - 3494141388054166608 * q^62 - 7226075466055635804 * q^63 + 18241430414481738816 * q^64 + 4584448716503906250 * q^65 - 17790794746381326672 * q^66 - 9384022533389399076 * q^67 - 49040734788483425256 * q^68 - 2879236630261533672 * q^69 + 23332717137421875000 * q^70 + 60019641798452716896 * q^71 + 39962272535420488632 * q^72 - 17009842434251898522 * q^73 + 135690473789754431388 * q^74 - 16894054412841796875 * q^75 + 73904848422041181936 * q^76 + 53710247923965432672 * q^77 + 127799000123125537476 * q^78 + 192112433593115883000 * q^79 - 146416580525156250000 * q^80 + 36472996377170786403 * q^81 - 367171610825203944948 * q^82 + 284198623110184688316 * q^83 + 543457620358913311632 * q^84 + 67041953471542968750 * q^85 - 75848580157311095400 * q^86 - 154829220867525899502 * q^87 + 245615805643415437632 * q^88 + 132940763694174535254 * q^89 - 23903541499042968750 * q^90 + 1074557595270409043784 * q^91 - 330567977024321701344 * q^92 - 385805045832890033736 * q^93 - 712373552658444529680 * q^94 - 324371030810976562500 * q^95 - 1743121611160457109984 * q^96 - 985976190327562940826 * q^97 + 3801329211782343852270 * q^98 - 29524697128092736440 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2787.27	1.92470	0.962352	−	0.271805i	$-0.0876206\pi$
$2$	2787.27	1.92470	0.962352	+	0.271805i	$0.0876206\pi$
$3$	−59049.0	−0.577350
$3$	−59049.0	−0.577350
$4$	5.67172e6	2.70449
$5$	−9.76562e6	−0.447214
$5$	−9.76562e6	−0.447214
$6$	−1.64586e8	−1.11123
$7$	−1.37938e9	−1.84567	−0.922836	−	0.385194i	$-0.874134\pi$
$7$	−1.37938e9	−1.84567	−0.922836	+	0.385194i	$0.874134\pi$
$8$	9.96329e9	3.28064
$9$	3.48678e9	0.333333
$10$	−2.72194e10	−0.860754
$11$	2.99797e10	0.348501	0.174250	−	0.984701i	$-0.444250\pi$
$11$	2.99797e10	0.348501	0.174250	+	0.984701i	$0.444250\pi$
$12$	−3.34910e11	−1.56144
$13$	−7.63100e11	−1.53524	−0.767619	−	0.640906i	$-0.778559\pi$
$13$	−7.63100e11	−1.53524	−0.767619	+	0.640906i	$0.778559\pi$
$14$	−3.84470e12	−3.55237
$15$	5.76650e11	0.258199
$16$	1.58759e13	3.60977
$17$	−1.14939e13	−1.38278	−0.691391	−	0.722480i	$-0.743002\pi$
$17$	−1.14939e13	−1.38278	−0.691391	+	0.722480i	$0.743002\pi$
$18$	9.71861e12	0.641568
$19$	−5.19898e12	−0.194538	−0.0972692	−	0.995258i	$-0.531011\pi$
$19$	−5.19898e12	−0.194538	−0.0972692	+	0.995258i	$0.531011\pi$
$20$	−5.53879e13	−1.20948
$21$	8.14510e13	1.06560
$22$	8.35614e13	0.670761
$23$	−8.03048e13	−0.404203	−0.202101	−	0.979365i	$-0.564777\pi$
$23$	−8.03048e13	−0.404203	−0.202101	+	0.979365i	$0.564777\pi$
$24$	−5.88322e14	−1.89408
$25$	9.53674e13	0.200000
$26$	−2.12696e15	−2.95488
$27$	−2.05891e14	−0.192450
$28$	−7.82346e15	−4.99159
$29$	−2.01015e14	−0.0887259	−0.0443629	−	0.999015i	$-0.514126\pi$
$29$	−2.01015e14	−0.0887259	−0.0443629	+	0.999015i	$0.514126\pi$
$30$	1.60728e15	0.496957
$31$	1.53535e15	0.336442	0.168221	−	0.985749i	$-0.446198\pi$
$31$	1.53535e15	0.336442	0.168221	+	0.985749i	$0.446198\pi$
$32$	2.33559e16	3.66710
$33$	−1.77027e15	−0.201207
$34$	−3.20366e16	−2.66145
$35$	1.34705e16	0.825409
$36$	1.97761e16	0.901496
$37$	1.53969e16	0.526401	0.263200	−	0.964741i	$-0.415222\pi$
$37$	1.53969e16	0.526401	0.263200	+	0.964741i	$0.415222\pi$
$38$	−1.44910e16	−0.374429
$39$	4.50603e16	0.886371
$40$	−9.72978e16	−1.46714
$41$	−7.88656e16	−0.917608	−0.458804	−	0.888538i	$-0.651722\pi$
$41$	−7.88656e16	−0.917608	−0.458804	+	0.888538i	$0.651722\pi$
$42$	2.27026e17	2.05096
$43$	−1.61914e17	−1.14253	−0.571264	−	0.820766i	$-0.693547\pi$
$43$	−1.61914e17	−1.14253	−0.571264	+	0.820766i	$0.693547\pi$
$44$	1.70036e17	0.942516
$45$	−3.40506e16	−0.149071
$46$	−2.23831e17	−0.777971
$47$	−3.76922e17	−1.04526	−0.522629	−	0.852560i	$-0.675049\pi$
$47$	−3.76922e17	−1.04526	−0.522629	+	0.852560i	$0.675049\pi$
$48$	−9.37457e17	−2.08410
$49$	1.34414e18	2.40650
$50$	2.65815e17	0.384941
$51$	6.78704e17	0.798350
$52$	−4.32809e18	−4.15204
$53$	3.24880e17	0.255168	0.127584	−	0.991828i	$-0.459278\pi$
$53$	3.24880e17	0.255168	0.127584	+	0.991828i	$0.459278\pi$
$54$	−5.73874e17	−0.370410
$55$	−2.92770e17	−0.155854
$56$	−1.37432e19	−6.05497
$57$	3.06994e17	0.112317
$58$	−5.60284e17	−0.170771
$59$	−9.88461e17	−0.251775	−0.125888	−	0.992044i	$-0.540178\pi$
$59$	−9.88461e17	−0.251775	−0.125888	+	0.992044i	$0.540178\pi$
$60$	3.27060e18	0.698296
$61$	1.01280e19	1.81786	0.908929	−	0.416951i	$-0.136901\pi$
$61$	1.01280e19	1.81786	0.908929	+	0.416951i	$0.136901\pi$
$62$	4.27945e18	0.647552
$63$	−4.80960e18	−0.615224
$64$	3.18051e19	3.44832
$65$	7.45214e18	0.686580
$66$	−4.93422e18	−0.387264
$67$	−1.02596e19	−0.687616	−0.343808	−	0.939040i	$-0.611717\pi$
$67$	−1.02596e19	−0.687616	−0.343808	+	0.939040i	$0.611717\pi$
$68$	−6.51902e19	−3.73972
$69$	4.74192e18	0.233367
$70$	3.75459e19	1.58867
$71$	3.23535e19	1.17953	0.589765	−	0.807575i	$-0.299220\pi$
$71$	3.23535e19	1.17953	0.589765	+	0.807575i	$0.299220\pi$
$72$	3.47399e19	1.09355
$73$	−2.89708e19	−0.788987	−0.394494	−	0.918899i	$-0.629080\pi$
$73$	−2.89708e19	−0.788987	−0.394494	+	0.918899i	$0.629080\pi$
$74$	4.29154e19	1.01317
$75$	−5.63135e18	−0.115470
$76$	−2.94872e19	−0.526126
$77$	−4.13533e19	−0.643218
$78$	1.25595e20	1.70600
$79$	3.51920e19	0.418176	0.209088	−	0.977897i	$-0.432950\pi$
$79$	3.51920e19	0.418176	0.209088	+	0.977897i	$0.432950\pi$
$80$	−1.55038e20	−1.61434
$81$	1.21577e19	0.111111
$82$	−2.19820e20	−1.76612
$83$	2.86096e19	0.202391	0.101196	−	0.994867i	$-0.467733\pi$
$83$	2.86096e19	0.202391	0.101196	+	0.994867i	$0.467733\pi$
$84$	4.61967e20	2.88190
$85$	1.12245e20	0.618399
$86$	−4.51299e20	−2.19903
$87$	1.18698e19	0.0512259
$88$	2.98696e20	1.14330
$89$	5.20282e19	0.176866	0.0884328	−	0.996082i	$-0.471814\pi$
$89$	5.20282e19	0.176866	0.0884328	+	0.996082i	$0.471814\pi$
$90$	−9.49083e19	−0.286918
$91$	1.05260e21	2.83355
$92$	−4.55467e20	−1.09316
$93$	−9.06611e19	−0.194245
$94$	−1.05058e21	−2.01181
$95$	5.07713e19	0.0870002
$96$	−1.37915e21	−2.11720
$97$	7.90419e20	1.08831	0.544157	−	0.838983i	$-0.316850\pi$
$97$	7.90419e20	1.08831	0.544157	+	0.838983i	$0.316850\pi$
$98$	3.74649e21	4.63180
$99$	1.04533e20	0.116167
$100$	5.40898e20	0.540898
$101$	−1.18585e21	−1.06821	−0.534105	−	0.845418i	$-0.679351\pi$
$101$	−1.18585e21	−1.06821	−0.534105	+	0.845418i	$0.679351\pi$
$102$	1.89173e21	1.53659
$103$	1.17111e21	0.858632	0.429316	−	0.903154i	$-0.358755\pi$
$103$	1.17111e21	0.858632	0.429316	+	0.903154i	$0.358755\pi$
$104$	−7.60298e21	−5.03656
$105$	−7.95420e20	−0.476550
$106$	9.05529e20	0.491123
$107$	1.02156e21	0.502035	0.251018	−	0.967983i	$-0.419235\pi$
$107$	1.02156e21	0.502035	0.251018	+	0.967983i	$0.419235\pi$
$108$	−1.16776e21	−0.520479
$109$	−8.82895e20	−0.357216	−0.178608	−	0.983920i	$-0.557159\pi$
$109$	−8.82895e20	−0.357216	−0.178608	+	0.983920i	$0.557159\pi$
$110$	−8.16030e20	−0.299973
$111$	−9.09174e20	−0.303917
$112$	−2.18989e22	−6.66244
$113$	3.34874e21	0.928022	0.464011	−	0.885829i	$-0.346410\pi$
$113$	3.34874e21	0.928022	0.464011	+	0.885829i	$0.346410\pi$
$114$	8.55676e20	0.216177
$115$	7.84227e20	0.180765
$116$	−1.14010e21	−0.239958
$117$	−2.66076e21	−0.511746
$118$	−2.75511e21	−0.484593
$119$	1.58545e22	2.55216
$120$	5.74534e21	0.847056
$121$	−6.50147e21	−0.878547
$122$	2.82294e22	3.49884
$123$	4.65694e21	0.529781
$124$	8.70810e21	0.909905
$125$	−9.31323e20	−0.0894427
$126$	−1.34056e22	−1.18412
$127$	1.00016e20	0.00813076	0.00406538	−	0.999992i	$-0.498706\pi$
$127$	1.00016e20	0.00813076	0.00406538	+	0.999992i	$0.498706\pi$
$128$	3.96684e22	2.96989
$129$	9.56089e21	0.659639
$130$	2.07711e22	1.32146
$131$	1.82022e21	0.106850	0.0534252	−	0.998572i	$-0.482986\pi$
$131$	1.82022e21	0.106850	0.0534252	+	0.998572i	$0.482986\pi$
$132$	−1.00405e22	−0.544162
$133$	7.17136e21	0.359054
$134$	−2.85964e22	−1.32346
$135$	2.01066e21	0.0860663
$136$	−1.14517e23	−4.53641
$137$	−3.39671e22	−1.24593	−0.622963	−	0.782251i	$-0.714071\pi$
$137$	−3.39671e22	−1.24593	−0.622963	+	0.782251i	$0.714071\pi$
$138$	1.32170e22	0.449162
$139$	5.60010e21	0.176417	0.0882085	−	0.996102i	$-0.471886\pi$
$139$	5.60010e21	0.176417	0.0882085	+	0.996102i	$0.471886\pi$
$140$	7.64009e22	2.23231
$141$	2.22568e22	0.603480
$142$	9.01780e22	2.27025
$143$	−2.28775e22	−0.535032
$144$	5.53559e22	1.20326
$145$	1.96304e21	0.0396794
$146$	−8.07494e22	−1.51857
$147$	−7.93702e22	−1.38939
$148$	8.73272e22	1.42364
$149$	−3.33164e22	−0.506060	−0.253030	−	0.967458i	$-0.581427\pi$
$149$	−3.33164e22	−0.506060	−0.253030	+	0.967458i	$0.581427\pi$
$150$	−1.56961e22	−0.222246
$151$	−8.19754e22	−1.08249	−0.541247	−	0.840863i	$-0.682048\pi$
$151$	−8.19754e22	−1.08249	−0.541247	+	0.840863i	$0.682048\pi$
$152$	−5.17989e22	−0.638209
$153$	−4.00768e22	−0.460928
$154$	−1.15263e23	−1.23800
$155$	−1.49937e22	−0.150462
$156$	2.55569e23	2.39718
$157$	−1.47933e23	−1.29754	−0.648769	−	0.760986i	$-0.724716\pi$
$157$	−1.47933e23	−1.29754	−0.648769	+	0.760986i	$0.724716\pi$
$158$	9.80896e22	0.804866
$159$	−1.91839e22	−0.147321
$160$	−2.28085e23	−1.63998
$161$	1.10771e23	0.746025
$162$	3.38867e22	0.213856
$163$	5.52958e22	0.327132	0.163566	−	0.986532i	$-0.447700\pi$
$163$	5.52958e22	0.327132	0.163566	+	0.986532i	$0.447700\pi$
$164$	−4.47304e23	−2.48166
$165$	1.72878e22	0.0899825
$166$	7.97426e22	0.389543
$167$	−4.62356e22	−0.212058	−0.106029	−	0.994363i	$-0.533814\pi$
$167$	−4.62356e22	−0.212058	−0.106029	+	0.994363i	$0.533814\pi$
$168$	8.11520e23	3.49584
$169$	3.35256e23	1.35696
$170$	3.12858e23	1.19024
$171$	−1.81277e22	−0.0648461
$172$	−9.18334e23	−3.08995
$173$	−4.87339e23	−1.54293	−0.771466	−	0.636270i	$-0.780476\pi$
$173$	−4.87339e23	−1.54293	−0.771466	+	0.636270i	$0.780476\pi$
$174$	3.30842e22	0.0985947
$175$	−1.31548e23	−0.369134
$176$	4.75955e23	1.25801
$177$	5.83676e22	0.145363
$178$	1.45017e23	0.340414
$179$	−4.33940e23	−0.960446	−0.480223	−	0.877146i	$-0.659444\pi$
$179$	−4.33940e23	−0.960446	−0.480223	+	0.877146i	$0.659444\pi$
$180$	−1.93126e23	−0.403161
$181$	−7.08757e23	−1.39596	−0.697979	−	0.716118i	$-0.745917\pi$
$181$	−7.08757e23	−1.39596	−0.697979	+	0.716118i	$0.745917\pi$
$182$	2.93389e24	5.45374
$183$	−5.98048e23	−1.04954
$184$	−8.00100e23	−1.32604
$185$	−1.50361e23	−0.235413
$186$	−2.52697e23	−0.373865
$187$	−3.44583e23	−0.481901
$188$	−2.13779e24	−2.82689
$189$	2.84002e23	0.355200
$190$	1.41513e23	0.167450
$191$	−1.37779e24	−1.54289	−0.771443	−	0.636299i	$-0.780464\pi$
$191$	−1.37779e24	−1.54289	−0.771443	+	0.636299i	$0.780464\pi$
$192$	−1.87806e24	−1.99089
$193$	4.06115e23	0.407659	0.203829	−	0.979006i	$-0.434661\pi$
$193$	4.06115e23	0.407659	0.203829	+	0.979006i	$0.434661\pi$
$194$	2.20311e24	2.09468
$195$	−4.40042e23	−0.396397
$196$	7.62360e24	6.50835
$197$	1.19621e24	0.968083	0.484041	−	0.875045i	$-0.339168\pi$
$197$	1.19621e24	0.968083	0.484041	+	0.875045i	$0.339168\pi$
$198$	2.91361e23	0.223587
$199$	1.89020e24	1.37579	0.687894	−	0.725811i	$-0.258535\pi$
$199$	1.89020e24	1.37579	0.687894	+	0.725811i	$0.258535\pi$
$200$	9.50174e23	0.656127
$201$	6.05821e23	0.396995
$202$	−3.30529e24	−2.05599
$203$	2.77276e23	0.163759
$204$	3.84942e24	2.15913
$205$	7.70172e23	0.410367
$206$	3.26420e24	1.65261
$207$	−2.80006e23	−0.134734
$208$	−1.21149e25	−5.54185
$209$	−1.55864e23	−0.0677967
$210$	−2.21705e24	−0.917218
$211$	−3.61070e24	−1.42110	−0.710552	−	0.703645i	$-0.751555\pi$
$211$	−3.61070e24	−1.42110	−0.710552	+	0.703645i	$0.751555\pi$
$212$	1.84263e24	0.690099
$213$	−1.91044e24	−0.681002
$214$	2.84736e24	0.966270
$215$	1.58120e24	0.510954
$216$	−2.05135e24	−0.631359
$217$	−2.11784e24	−0.620962
$218$	−2.46087e24	−0.687535
$219$	1.71070e24	0.455522
$220$	−1.66051e24	−0.421506
$221$	8.77099e24	2.12290
$222$	−2.53411e24	−0.584951
$223$	2.51046e24	0.552780	0.276390	−	0.961046i	$-0.410862\pi$
$223$	2.51046e24	0.552780	0.276390	+	0.961046i	$0.410862\pi$
$224$	−3.22167e25	−6.76826
$225$	3.32526e23	0.0666667
$226$	9.33385e24	1.78617
$227$	9.57954e24	1.75014	0.875071	−	0.483995i	$-0.160815\pi$
$227$	9.57954e24	1.75014	0.875071	+	0.483995i	$0.160815\pi$
$228$	1.74119e24	0.303759
$229$	−9.71373e24	−1.61850	−0.809251	−	0.587463i	$-0.800127\pi$
$229$	−9.71373e24	−1.61850	−0.809251	+	0.587463i	$0.800127\pi$
$230$	2.18585e24	0.347919
$231$	2.44187e24	0.371362
$232$	−2.00277e24	−0.291077
$233$	−9.68019e24	−1.34477	−0.672383	−	0.740204i	$-0.734729\pi$
$233$	−9.68019e24	−1.34477	−0.672383	+	0.740204i	$0.734729\pi$
$234$	−7.41627e24	−0.984961
$235$	3.68087e24	0.467454
$236$	−5.60628e24	−0.680924
$237$	−2.07805e24	−0.241434
$238$	4.41907e25	4.91216
$239$	−1.36780e25	−1.45494	−0.727471	−	0.686138i	$-0.759305\pi$
$239$	−1.36780e25	−1.45494	−0.727471	+	0.686138i	$0.759305\pi$
$240$	9.15486e24	0.932038
$241$	−1.69789e25	−1.65474	−0.827372	−	0.561654i	$-0.810165\pi$
$241$	−1.69789e25	−1.65474	−0.827372	+	0.561654i	$0.810165\pi$
$242$	−1.81214e25	−1.69094
$243$	−7.17898e23	−0.0641500
$244$	5.74432e25	4.91638
$245$	−1.31264e25	−1.07622
$246$	1.29801e25	1.01967
$247$	3.96734e24	0.298663
$248$	1.52972e25	1.10375
$249$	−1.68937e24	−0.116851
$250$	−2.59585e24	−0.172151
$251$	1.20909e25	0.768929	0.384465	−	0.923140i	$-0.374386\pi$
$251$	1.20909e25	0.768929	0.384465	+	0.923140i	$0.374386\pi$
$252$	−2.72787e25	−1.66386
$253$	−2.40751e24	−0.140865
$254$	2.78772e23	0.0156493
$255$	−6.62797e24	−0.357033
$256$	4.38665e25	2.26785
$257$	−1.47338e25	−0.731167	−0.365584	−	0.930779i	$-0.619131\pi$
$257$	−1.47338e25	−0.731167	−0.365584	+	0.930779i	$0.619131\pi$
$258$	2.66488e25	1.26961
$259$	−2.12382e25	−0.971562
$260$	4.22665e25	1.85685
$261$	−7.00897e23	−0.0295753
$262$	5.07346e24	0.205656
$263$	3.43475e25	1.33770	0.668852	−	0.743396i	$-0.266786\pi$
$263$	3.43475e25	1.33770	0.668852	+	0.743396i	$0.266786\pi$
$264$	−1.76377e25	−0.660087
$265$	−3.17266e24	−0.114115
$266$	1.99885e25	0.691072
$267$	−3.07221e24	−0.102113
$268$	−5.81898e25	−1.85965
$269$	3.49311e25	1.07353	0.536764	−	0.843733i	$-0.319647\pi$
$269$	3.49311e25	1.07353	0.536764	+	0.843733i	$0.319647\pi$
$270$	5.60424e24	0.165652
$271$	−5.04797e25	−1.43529	−0.717644	−	0.696410i	$-0.754779\pi$
$271$	−5.04797e25	−1.43529	−0.717644	+	0.696410i	$0.754779\pi$
$272$	−1.82476e26	−4.99152
$273$	−6.21552e25	−1.63595
$274$	−9.46755e25	−2.39804
$275$	2.85908e24	0.0697001
$276$	2.68949e25	0.631137
$277$	−3.43914e24	−0.0776985	−0.0388492	−	0.999245i	$-0.512369\pi$
$277$	−3.43914e24	−0.0776985	−0.0388492	+	0.999245i	$0.512369\pi$
$278$	1.56090e25	0.339551
$279$	5.35345e24	0.112147
$280$	1.34211e26	2.70787
$281$	−8.07634e25	−1.56963	−0.784817	−	0.619727i	$-0.787243\pi$
$281$	−8.07634e25	−1.56963	−0.784817	+	0.619727i	$0.787243\pi$
$282$	6.20358e25	1.16152
$283$	−2.52971e25	−0.456366	−0.228183	−	0.973618i	$-0.573278\pi$
$283$	−2.52971e25	−0.456366	−0.228183	+	0.973618i	$0.573278\pi$
$284$	1.83500e26	3.19002
$285$	−2.99799e24	−0.0502296
$286$	−6.37657e25	−1.02978
$287$	1.08786e26	1.69360
$288$	8.14371e25	1.22237
$289$	6.30180e25	0.912088
$290$	5.47152e24	0.0763712
$291$	−4.66735e25	−0.628338
$292$	−1.64314e26	−2.13381
$293$	1.39891e26	1.75259	0.876295	−	0.481775i	$-0.160008\pi$
$293$	1.39891e26	1.75259	0.876295	+	0.481775i	$0.160008\pi$
$294$	−2.21226e26	−2.67417
$295$	9.65294e24	0.112597
$296$	1.53404e26	1.72693
$297$	−6.17255e24	−0.0670690
$298$	−9.28617e25	−0.974016
$299$	6.12806e25	0.620548
$300$	−3.19395e25	−0.312287
$301$	2.23341e26	2.10873
$302$	−2.28488e26	−2.08348
$303$	7.00235e25	0.616731
$304$	−8.25386e25	−0.702238
$305$	−9.89062e25	−0.812971
$306$	−1.11705e26	−0.887150
$307$	−1.66063e26	−1.27444	−0.637222	−	0.770681i	$-0.719916\pi$
$307$	−1.66063e26	−1.27444	−0.637222	+	0.770681i	$0.719916\pi$
$308$	−2.34545e26	−1.73957
$309$	−6.91529e25	−0.495732
$310$	−4.17915e25	−0.289594
$311$	2.85915e26	1.91537	0.957685	−	0.287819i	$-0.0929302\pi$
$311$	2.85915e26	1.91537	0.957685	+	0.287819i	$0.0929302\pi$
$312$	4.48949e26	2.90786
$313$	6.78268e25	0.424801	0.212401	−	0.977183i	$-0.431872\pi$
$313$	6.78268e25	0.424801	0.212401	+	0.977183i	$0.431872\pi$
$314$	−4.12330e26	−2.49738
$315$	4.69687e25	0.275136
$316$	1.99599e26	1.13095
$317$	−3.05982e25	−0.167716	−0.0838579	−	0.996478i	$-0.526724\pi$
$317$	−3.05982e25	−0.167716	−0.0838579	+	0.996478i	$0.526724\pi$
$318$	−5.34706e25	−0.283550
$319$	−6.02637e24	−0.0309210
$320$	−3.10597e26	−1.54213
$321$	−6.03221e25	−0.289850
$322$	3.08748e26	1.43588
$323$	5.97566e25	0.269004
$324$	6.89549e25	0.300499
$325$	−7.27748e25	−0.307048
$326$	1.54124e26	0.629632
$327$	5.21341e25	0.206239
$328$	−7.85761e26	−3.01034
$329$	5.19918e26	1.92920
$330$	4.81857e25	0.173190
$331$	2.97902e26	1.03724	0.518620	−	0.855005i	$-0.326446\pi$
$331$	2.97902e26	1.03724	0.518620	+	0.855005i	$0.326446\pi$
$332$	1.62266e26	0.547364
$333$	5.36858e25	0.175467
$334$	−1.28871e26	−0.408148
$335$	1.00192e26	0.307511
$336$	1.29311e27	3.84656
$337$	1.35212e26	0.389852	0.194926	−	0.980818i	$-0.437553\pi$
$337$	1.35212e26	0.389852	0.194926	+	0.980818i	$0.437553\pi$
$338$	9.34450e26	2.61174
$339$	−1.97740e26	−0.535794
$340$	6.36623e26	1.67245
$341$	4.60294e25	0.117250
$342$	−5.05268e25	−0.124810
$343$	−1.08363e27	−2.59594
$344$	−1.61320e27	−3.74822
$345$	−4.63078e25	−0.104365
$346$	−1.35834e27	−2.96969
$347$	2.89431e26	0.613884	0.306942	−	0.951728i	$-0.400694\pi$
$347$	2.89431e26	0.613884	0.306942	+	0.951728i	$0.400694\pi$
$348$	6.73220e25	0.138540
$349$	5.89250e26	1.17661	0.588306	−	0.808639i	$-0.299795\pi$
$349$	5.89250e26	1.17661	0.588306	+	0.808639i	$0.299795\pi$
$350$	−3.66659e26	−0.710474
$351$	1.57115e26	0.295457
$352$	7.00203e26	1.27799
$353$	6.63803e25	0.117599	0.0587996	−	0.998270i	$-0.481273\pi$
$353$	6.63803e25	0.117599	0.0587996	+	0.998270i	$0.481273\pi$
$354$	1.62686e26	0.279780
$355$	−3.15952e26	−0.527502
$356$	2.95089e26	0.478331
$357$	−9.36190e26	−1.47349
$358$	−1.20951e27	−1.84858
$359$	9.35962e26	1.38921	0.694603	−	0.719393i	$-0.255580\pi$
$359$	9.35962e26	1.38921	0.694603	+	0.719393i	$0.255580\pi$
$360$	−3.39256e26	−0.489048
$361$	−6.87180e26	−0.962155
$362$	−1.97550e27	−2.68681
$363$	3.83905e26	0.507230
$364$	5.97008e27	7.66329
$365$	2.82918e26	0.352846
$366$	−1.66692e27	−2.02006
$367$	1.41202e27	1.66282	0.831411	−	0.555658i	$-0.187534\pi$
$367$	1.41202e27	1.66282	0.831411	+	0.555658i	$0.187534\pi$
$368$	−1.27491e27	−1.45908
$369$	−2.74987e26	−0.305869
$370$	−4.19096e26	−0.453101
$371$	−4.48133e26	−0.470957
$372$	−5.14205e26	−0.525334
$373$	−4.21905e26	−0.419056	−0.209528	−	0.977803i	$-0.567193\pi$
$373$	−4.21905e26	−0.419056	−0.209528	+	0.977803i	$0.567193\pi$
$374$	−9.60447e26	−0.927517
$375$	5.49937e25	0.0516398
$376$	−3.75538e27	−3.42911
$377$	1.53395e26	0.136215
$378$	7.91590e26	0.683654
$379$	−1.82216e27	−1.53065	−0.765325	−	0.643644i	$-0.777422\pi$
$379$	−1.82216e27	−1.53065	−0.765325	+	0.643644i	$0.777422\pi$
$380$	2.87961e26	0.235291
$381$	−5.90586e24	−0.00469430
$382$	−3.84028e27	−2.96960
$383$	−3.47058e26	−0.261105	−0.130552	−	0.991441i	$-0.541675\pi$
$383$	−3.47058e26	−0.261105	−0.130552	+	0.991441i	$0.541675\pi$
$384$	−2.34238e27	−1.71467
$385$	4.03841e26	0.287656
$386$	1.13195e27	0.784623
$387$	−5.64561e26	−0.380843
$388$	4.48304e27	2.94333
$389$	−1.66189e27	−1.06202	−0.531009	−	0.847366i	$-0.678187\pi$
$389$	−1.66189e27	−1.06202	−0.531009	+	0.847366i	$0.678187\pi$
$390$	−1.22651e27	−0.762947
$391$	9.23016e26	0.558925
$392$	1.33921e28	7.89485
$393$	−1.07482e26	−0.0616902
$394$	3.33416e27	1.86327
$395$	−3.43672e26	−0.187014
$396$	5.92880e26	0.314172
$397$	−3.53949e27	−1.82659	−0.913293	−	0.407304i	$-0.866469\pi$
$397$	−3.53949e27	−1.82659	−0.913293	+	0.407304i	$0.866469\pi$
$398$	5.26851e27	2.64798
$399$	−4.23462e26	−0.207300
$400$	1.51405e27	0.721953
$401$	−1.58374e27	−0.735644	−0.367822	−	0.929896i	$-0.619896\pi$
$401$	−1.58374e27	−0.735644	−0.367822	+	0.929896i	$0.619896\pi$
$402$	1.68859e27	0.764099
$403$	−1.17163e27	−0.516520
$404$	−6.72583e27	−2.88896
$405$	−1.18727e26	−0.0496904
$406$	7.72844e26	0.315187
$407$	4.61595e26	0.183451
$408$	6.76212e27	2.61910
$409$	2.05726e27	0.776596	0.388298	−	0.921534i	$-0.373063\pi$
$409$	2.05726e27	0.776596	0.388298	+	0.921534i	$0.373063\pi$
$410$	2.14668e27	0.789835
$411$	2.00572e27	0.719336
$412$	6.64222e27	2.32216
$413$	1.36346e27	0.464695
$414$	−7.80451e26	−0.259324
$415$	−2.79390e26	−0.0905120
$416$	−1.78229e28	−5.62987
$417$	−3.30680e26	−0.101854
$418$	−4.34434e26	−0.130489
$419$	1.53990e27	0.451071	0.225536	−	0.974235i	$-0.427587\pi$
$419$	1.53990e27	0.451071	0.225536	+	0.974235i	$0.427587\pi$
$420$	−4.51140e27	−1.28882
$421$	3.15043e27	0.877824	0.438912	−	0.898530i	$-0.355364\pi$
$421$	3.15043e27	0.877824	0.438912	+	0.898530i	$0.355364\pi$
$422$	−1.00640e28	−2.73521
$423$	−1.31424e27	−0.348419
$424$	3.23688e27	0.837114
$425$	−1.09614e27	−0.276557
$426$	−5.32492e27	−1.31073
$427$	−1.39703e28	−3.35517
$428$	5.79400e27	1.35775
$429$	1.35089e27	0.308901
$430$	4.40722e27	0.983436
$431$	1.98201e27	0.431614	0.215807	−	0.976436i	$-0.430762\pi$
$431$	1.98201e27	0.431614	0.215807	+	0.976436i	$0.430762\pi$
$432$	−3.26871e27	−0.694700
$433$	5.59999e27	1.16162	0.580810	−	0.814039i	$-0.302736\pi$
$433$	5.59999e27	1.16162	0.580810	+	0.814039i	$0.302736\pi$
$434$	−5.90298e27	−1.19517
$435$	−1.15916e26	−0.0229089
$436$	−5.00754e27	−0.966087
$437$	4.17503e26	0.0786329
$438$	4.76817e27	0.876746
$439$	1.53894e27	0.276277	0.138138	−	0.990413i	$-0.455888\pi$
$439$	1.53894e27	0.276277	0.138138	+	0.990413i	$0.455888\pi$
$440$	−2.91695e27	−0.511301
$441$	4.68673e27	0.802167
$442$	2.44471e28	4.08596
$443$	−3.27390e27	−0.534351	−0.267175	−	0.963648i	$-0.586090\pi$
$443$	−3.27390e27	−0.534351	−0.267175	+	0.963648i	$0.586090\pi$
$444$	−5.15658e27	−0.821941
$445$	−5.08087e26	−0.0790967
$446$	6.99733e27	1.06394
$447$	1.96730e27	0.292174
$448$	−4.38713e28	−6.36446
$449$	3.04397e27	0.431374	0.215687	−	0.976463i	$-0.430801\pi$
$449$	3.04397e27	0.431374	0.215687	+	0.976463i	$0.430801\pi$
$450$	9.26839e26	0.128314
$451$	−2.36436e27	−0.319787
$452$	1.89931e28	2.50982
$453$	4.84057e27	0.624979
$454$	2.67008e28	3.36850
$455$	−1.02793e28	−1.26720
$456$	3.05868e27	0.368470
$457$	−4.76153e26	−0.0560566	−0.0280283	−	0.999607i	$-0.508923\pi$
$457$	−4.76153e26	−0.0560566	−0.0280283	+	0.999607i	$0.508923\pi$
$458$	−2.70748e28	−3.11514
$459$	2.36649e27	0.266117
$460$	4.44792e27	0.488877
$461$	−9.99698e27	−1.07401	−0.537006	−	0.843578i	$-0.680445\pi$
$461$	−9.99698e27	−1.07401	−0.537006	+	0.843578i	$0.680445\pi$
$462$	6.80616e27	0.714762
$463$	1.40995e28	1.44745	0.723723	−	0.690090i	$-0.242429\pi$
$463$	1.40995e28	1.44745	0.723723	+	0.690090i	$0.242429\pi$
$464$	−3.19130e27	−0.320280
$465$	8.85363e26	0.0868691
$466$	−2.69813e28	−2.58828
$467$	3.82873e25	0.00359110	0.00179555	−	0.999998i	$-0.499428\pi$
$467$	3.82873e25	0.00359110	0.00179555	+	0.999998i	$0.499428\pi$
$468$	−1.50911e28	−1.38401
$469$	1.41519e28	1.26911
$470$	1.02596e28	0.899710
$471$	8.73532e27	0.749133
$472$	−9.84832e27	−0.825983
$473$	−4.85414e27	−0.398172
$474$	−5.79209e27	−0.464690
$475$	−4.95813e26	−0.0389077
$476$	8.99221e28	6.90229
$477$	1.13279e27	0.0850561
$478$	−3.81244e28	−2.80033
$479$	9.30936e27	0.668955	0.334477	−	0.942404i	$-0.391440\pi$
$479$	9.30936e27	0.668955	0.334477	+	0.942404i	$0.391440\pi$
$480$	1.34682e28	0.946841
$481$	−1.17494e28	−0.808151
$482$	−4.73248e28	−3.18490
$483$	−6.54091e27	−0.430718
$484$	−3.68745e28	−2.37602
$485$	−7.71894e27	−0.486709
$486$	−2.00098e27	−0.123470
$487$	−1.33180e28	−0.804239	−0.402119	−	0.915587i	$-0.631726\pi$
$487$	−1.33180e28	−0.804239	−0.402119	+	0.915587i	$0.631726\pi$
$488$	1.00908e29	5.96373
$489$	−3.26516e27	−0.188869
$490$	−3.65868e28	−2.07141
$491$	−5.75994e27	−0.319199	−0.159600	−	0.987182i	$-0.551020\pi$
$491$	−5.75994e27	−0.319199	−0.159600	+	0.987182i	$0.551020\pi$
$492$	2.64128e28	1.43279
$493$	2.31045e27	0.122689
$494$	1.10580e28	0.574838
$495$	−1.02083e27	−0.0519514
$496$	2.43752e28	1.21448
$497$	−4.46278e28	−2.17702
$498$	−4.70872e27	−0.224903
$499$	1.10496e28	0.516763	0.258382	−	0.966043i	$-0.416811\pi$
$499$	1.10496e28	0.516763	0.258382	+	0.966043i	$0.416811\pi$
$500$	−5.28220e27	−0.241897
$501$	2.73017e27	0.122432
$502$	3.37007e28	1.47996
$503$	2.38869e28	1.02730	0.513649	−	0.858001i	$-0.328294\pi$
$503$	2.38869e28	1.02730	0.513649	+	0.858001i	$0.328294\pi$
$504$	−4.79194e28	−2.01832
$505$	1.15806e28	0.477718
$506$	−6.71039e27	−0.271123
$507$	−1.97966e28	−0.783440
$508$	5.67264e26	0.0219896
$509$	7.62092e27	0.289381	0.144691	−	0.989477i	$-0.453781\pi$
$509$	7.62092e27	0.289381	0.144691	+	0.989477i	$0.453781\pi$
$510$	−1.84739e28	−0.687183
$511$	3.99617e28	1.45621
$512$	3.90771e28	1.39504
$513$	1.07042e27	0.0374389
$514$	−4.10671e28	−1.40728
$515$	−1.14366e28	−0.383992
$516$	5.42267e28	1.78399
$517$	−1.13000e28	−0.364273
$518$	−5.91967e28	−1.86997
$519$	2.87769e28	0.890813
$520$	7.42479e28	2.25242
$521$	−2.68092e28	−0.797055	−0.398527	−	0.917156i	$-0.630479\pi$
$521$	−2.68092e28	−0.797055	−0.398527	+	0.917156i	$0.630479\pi$
$522$	−1.95359e27	−0.0569237
$523$	−1.54301e28	−0.440657	−0.220328	−	0.975426i	$-0.570713\pi$
$523$	−1.54301e28	−0.440657	−0.220328	+	0.975426i	$0.570713\pi$
$524$	1.03238e28	0.288976
$525$	7.76777e27	0.213120
$526$	9.57358e28	2.57469
$527$	−1.76472e28	−0.465227
$528$	−2.81047e28	−0.726310
$529$	−3.30227e28	−0.836620
$530$	−8.84306e27	−0.219637
$531$	−3.44655e27	−0.0839251
$532$	4.06740e28	0.971056
$533$	6.01823e28	1.40875
$534$	−8.56308e27	−0.196538
$535$	−9.97617e27	−0.224517
$536$	−1.02220e29	−2.25582
$537$	2.56237e28	0.554514
$538$	9.73623e28	2.06622
$539$	4.02969e28	0.838667
$540$	1.14039e28	0.232765
$541$	−5.53635e28	−1.10829	−0.554143	−	0.832421i	$-0.686954\pi$
$541$	−5.53635e28	−1.10829	−0.554143	+	0.832421i	$0.686954\pi$
$542$	−1.40700e29	−2.76250
$543$	4.18514e28	0.805957
$544$	−2.68451e29	−5.07080
$545$	8.62203e27	0.159752
$546$	−1.73243e29	−3.14872
$547$	−3.14951e28	−0.561535	−0.280767	−	0.959776i	$-0.590589\pi$
$547$	−3.14951e28	−0.561535	−0.280767	+	0.959776i	$0.590589\pi$
$548$	−1.92652e29	−3.36959
$549$	3.53141e28	0.605953
$550$	7.96904e27	0.134152
$551$	1.04507e27	0.0172606
$552$	4.72451e28	0.765591
$553$	−4.85431e28	−0.771816
$554$	−9.58581e27	−0.149547
$555$	8.87865e27	0.135916
$556$	3.17622e28	0.477118
$557$	4.25159e28	0.626717	0.313358	−	0.949635i	$-0.398546\pi$
$557$	4.25159e28	0.626717	0.313358	+	0.949635i	$0.398546\pi$
$558$	1.49215e28	0.215851
$559$	1.23557e29	1.75405
$560$	2.13857e29	2.97953
$561$	2.03473e28	0.278226
$562$	−2.25110e29	−3.02108
$563$	−7.19780e28	−0.948116	−0.474058	−	0.880494i	$-0.657211\pi$
$563$	−7.19780e28	−0.948116	−0.474058	+	0.880494i	$0.657211\pi$
$564$	1.26235e29	1.63210
$565$	−3.27026e28	−0.415024
$566$	−7.05098e28	−0.878369
$567$	−1.67700e28	−0.205075
$568$	3.22348e29	3.86961
$569$	1.32568e29	1.56228	0.781142	−	0.624353i	$-0.214637\pi$
$569$	1.32568e29	1.56228	0.781142	+	0.624353i	$0.214637\pi$
$570$	−8.35621e27	−0.0966771
$571$	5.77857e28	0.656359	0.328179	−	0.944615i	$-0.393565\pi$
$571$	5.77857e28	0.656359	0.328179	+	0.944615i	$0.393565\pi$
$572$	−1.29755e29	−1.44699
$573$	8.13573e28	0.890785
$574$	3.03215e29	3.25968
$575$	−7.65847e27	−0.0808406
$576$	1.10898e29	1.14944
$577$	−1.02641e29	−1.04466	−0.522332	−	0.852742i	$-0.674938\pi$
$577$	−1.02641e29	−1.04466	−0.522332	+	0.852742i	$0.674938\pi$
$578$	1.75648e29	1.75550
$579$	−2.39807e28	−0.235362
$580$	1.11338e28	0.107312
$581$	−3.94635e28	−0.373547
$582$	−1.30092e29	−1.20937
$583$	9.73980e27	0.0889263
$584$	−2.88644e29	−2.58838
$585$	2.59840e28	0.228860
$586$	3.89914e29	3.37322
$587$	1.42995e29	1.21512	0.607562	−	0.794272i	$-0.292148\pi$
$587$	1.42995e29	1.21512	0.607562	+	0.794272i	$0.292148\pi$
$588$	−4.50166e29	−3.75760
$589$	−7.98227e27	−0.0654510
$590$	2.69053e28	0.216717
$591$	−7.06351e28	−0.558923
$592$	2.44441e29	1.90018
$593$	1.90982e29	1.45854	0.729270	−	0.684226i	$-0.239860\pi$
$593$	1.90982e29	1.45854	0.729270	+	0.684226i	$0.239860\pi$
$594$	−1.72046e28	−0.129088
$595$	−1.54829e29	−1.14136
$596$	−1.88961e29	−1.36863
$597$	−1.11615e29	−0.794311
$598$	1.70806e29	1.19437
$599$	1.17313e29	0.806053	0.403027	−	0.915188i	$-0.367958\pi$
$599$	1.17313e29	0.806053	0.403027	+	0.915188i	$0.367958\pi$
$600$	−5.61068e28	−0.378815
$601$	−2.19161e29	−1.45405	−0.727027	−	0.686609i	$-0.759099\pi$
$601$	−2.19161e29	−1.45405	−0.727027	+	0.686609i	$0.759099\pi$
$602$	6.22513e29	4.05868
$603$	−3.57731e28	−0.229205
$604$	−4.64942e29	−2.92759
$605$	6.34909e28	0.392898
$606$	1.95174e29	1.18703
$607$	1.48966e29	0.890445	0.445222	−	0.895420i	$-0.353125\pi$
$607$	1.48966e29	0.890445	0.445222	+	0.895420i	$0.353125\pi$
$608$	−1.21427e29	−0.713391
$609$	−1.63729e28	−0.0945462
$610$	−2.75678e29	−1.56473
$611$	2.87629e29	1.60472
$612$	−2.27304e29	−1.24657
$613$	2.26313e29	1.22004	0.610022	−	0.792385i	$-0.291161\pi$
$613$	2.26313e29	1.22004	0.610022	+	0.792385i	$0.291161\pi$
$614$	−4.62863e29	−2.45293
$615$	−4.54779e28	−0.236925
$616$	−4.12015e29	−2.11016
$617$	−3.85893e29	−1.94300	−0.971500	−	0.237040i	$-0.923823\pi$
$617$	−3.85893e29	−1.94300	−0.971500	+	0.237040i	$0.923823\pi$
$618$	−1.92748e29	−0.954137
$619$	−1.80368e29	−0.877823	−0.438912	−	0.898530i	$-0.644636\pi$
$619$	−1.80368e29	−0.877823	−0.438912	+	0.898530i	$0.644636\pi$
$620$	−8.50401e28	−0.406922
$621$	1.65341e28	0.0777889
$622$	7.96922e29	3.68652
$623$	−7.17666e28	−0.326436
$624$	7.15373e29	3.19959
$625$	9.09495e27	0.0400000
$626$	1.89052e29	0.817617
$627$	9.20359e27	0.0391425
$628$	−8.39037e29	−3.50917
$629$	−1.76971e29	−0.727898
$630$	1.30915e29	0.529556
$631$	2.76208e29	1.09882	0.549411	−	0.835552i	$-0.314852\pi$
$631$	2.76208e29	1.09882	0.549411	+	0.835552i	$0.314852\pi$
$632$	3.50628e29	1.37188
$633$	2.13208e29	0.820475
$634$	−8.52855e28	−0.322803
$635$	−9.76721e26	−0.00363619
$636$	−1.08805e29	−0.398429
$637$	−1.02571e30	−3.69455
$638$	−1.67971e28	−0.0595138
$639$	1.12810e29	0.393177
$640$	−3.87387e29	−1.32818
$641$	1.28643e29	0.433889	0.216944	−	0.976184i	$-0.430391\pi$
$641$	1.28643e29	0.433889	0.216944	+	0.976184i	$0.430391\pi$
$642$	−1.68134e29	−0.557876
$643$	−3.99417e29	−1.30380	−0.651900	−	0.758305i	$-0.726028\pi$
$643$	−3.99417e29	−1.30380	−0.651900	+	0.758305i	$0.726028\pi$
$644$	6.28261e29	2.01762
$645$	−9.33680e28	−0.294999
$646$	1.66558e29	0.517754
$647$	−2.80444e29	−0.857730	−0.428865	−	0.903368i	$-0.641086\pi$
$647$	−2.80444e29	−0.857730	−0.428865	+	0.903368i	$0.641086\pi$
$648$	1.21130e29	0.364515
$649$	−2.96337e28	−0.0877439
$650$	−2.02843e29	−0.590976
$651$	1.25056e29	0.358513
$652$	3.13623e29	0.884723
$653$	−1.79013e29	−0.496931	−0.248466	−	0.968641i	$-0.579926\pi$
$653$	−1.79013e29	−0.496931	−0.248466	+	0.968641i	$0.579926\pi$
$654$	1.45312e29	0.396949
$655$	−1.77756e28	−0.0477850
$656$	−1.25206e30	−3.31235
$657$	−1.01015e29	−0.262996
$658$	1.44915e30	3.71314
$659$	7.33826e29	1.85053	0.925265	−	0.379320i	$-0.123842\pi$
$659$	7.33826e29	1.85053	0.925265	+	0.379320i	$0.123842\pi$
$660$	9.80515e28	0.243357
$661$	−5.96638e29	−1.45746	−0.728728	−	0.684803i	$-0.759888\pi$
$661$	−5.96638e29	−1.45746	−0.728728	+	0.684803i	$0.759888\pi$
$662$	8.30333e29	1.99638
$663$	−5.17918e29	−1.22566
$664$	2.85046e29	0.663971
$665$	−7.00328e28	−0.160574
$666$	1.49637e29	0.337722
$667$	1.61425e28	0.0358632
$668$	−2.62236e29	−0.573507
$669$	−1.48240e29	−0.319148
$670$	2.79261e29	0.591868
$671$	3.03634e29	0.633525
$672$	1.90236e30	3.90766
$673$	−1.89245e28	−0.0382706	−0.0191353	−	0.999817i	$-0.506091\pi$
$673$	−1.89245e28	−0.0382706	−0.0191353	+	0.999817i	$0.506091\pi$
$674$	3.76871e29	0.750350
$675$	−1.96353e28	−0.0384900
$676$	1.90148e30	3.66988
$677$	−2.47018e28	−0.0469405	−0.0234703	−	0.999725i	$-0.507471\pi$
$677$	−2.47018e28	−0.0469405	−0.0234703	+	0.999725i	$0.507471\pi$
$678$	−5.51155e29	−1.03124
$679$	−1.09029e30	−2.00867
$680$	1.11833e30	2.02874
$681$	−5.65662e29	−1.01044
$682$	1.28296e29	0.225672
$683$	−2.88518e29	−0.499752	−0.249876	−	0.968278i	$-0.580390\pi$
$683$	−2.88518e29	−0.499752	−0.249876	+	0.968278i	$0.580390\pi$
$684$	−1.02815e29	−0.175375
$685$	3.31710e29	0.557195
$686$	−3.02038e30	−4.99642
$687$	5.73586e29	0.934443
$688$	−2.57054e30	−4.12426
$689$	−2.47916e29	−0.391744
$690$	−1.29072e29	−0.200871
$691$	−3.59152e29	−0.550502	−0.275251	−	0.961372i	$-0.588761\pi$
$691$	−3.59152e29	−0.550502	−0.275251	+	0.961372i	$0.588761\pi$
$692$	−2.76405e30	−4.17284
$693$	−1.44190e29	−0.214406
$694$	8.06723e29	1.18154
$695$	−5.46885e28	−0.0788961
$696$	1.18262e29	0.168054
$697$	9.06474e29	1.26885
$698$	1.64240e30	2.26463
$699$	5.71605e29	0.776401
$700$	−7.46103e29	−0.998319
$701$	1.21736e30	1.60465	0.802327	−	0.596885i	$-0.203595\pi$
$701$	1.21736e30	1.60465	0.802327	+	0.596885i	$0.203595\pi$
$702$	4.37923e29	0.568667
$703$	−8.00483e28	−0.102405
$704$	9.53506e29	1.20174
$705$	−2.17352e29	−0.269884
$706$	1.85020e29	0.226344
$707$	1.63574e30	1.97156
$708$	3.31045e29	0.393131
$709$	1.19822e30	1.40202	0.701008	−	0.713154i	$-0.252734\pi$
$709$	1.19822e30	1.40202	0.701008	+	0.713154i	$0.252734\pi$
$710$	−8.80644e29	−1.01528
$711$	1.22707e29	0.139392
$712$	5.18372e29	0.580232
$713$	−1.23296e29	−0.135991
$714$	−2.60941e30	−2.83604
$715$	2.23413e29	0.239273
$716$	−2.46119e30	−2.59752
$717$	8.07674e29	0.840011
$718$	2.60878e30	2.67381
$719$	−2.33520e29	−0.235869	−0.117935	−	0.993021i	$-0.537627\pi$
$719$	−2.33520e29	−0.235869	−0.117935	+	0.993021i	$0.537627\pi$
$720$	−5.40585e29	−0.538112
$721$	−1.61541e30	−1.58475
$722$	−1.91536e30	−1.85186
$723$	1.00259e30	0.955367
$724$	−4.01987e30	−3.77535
$725$	−1.91703e28	−0.0177452
$726$	1.07005e30	0.976267
$727$	−5.30551e29	−0.477107	−0.238554	−	0.971129i	$-0.576673\pi$
$727$	−5.30551e29	−0.477107	−0.238554	+	0.971129i	$0.576673\pi$
$728$	1.04874e31	9.29583
$729$	4.23912e28	0.0370370
$730$	7.88568e29	0.679124
$731$	1.86103e30	1.57987
$732$	−3.39196e30	−2.83847
$733$	4.20011e28	0.0346473	0.0173236	−	0.999850i	$-0.494485\pi$
$733$	4.20011e28	0.0346473	0.0173236	+	0.999850i	$0.494485\pi$
$734$	3.93567e30	3.20044
$735$	7.75100e29	0.621356
$736$	−1.87559e30	−1.48225
$737$	−3.07580e29	−0.239635
$738$	−7.66464e29	−0.588708
$739$	−8.41533e28	−0.0637243	−0.0318621	−	0.999492i	$-0.510144\pi$
$739$	−8.41533e28	−0.0637243	−0.0318621	+	0.999492i	$0.510144\pi$
$740$	−8.52804e29	−0.636673
$741$	−2.34267e29	−0.172433
$742$	−1.24907e30	−0.906452
$743$	−1.91121e30	−1.36749	−0.683746	−	0.729720i	$-0.739650\pi$
$743$	−1.91121e30	−1.36749	−0.683746	+	0.729720i	$0.739650\pi$
$744$	−9.03283e29	−0.637248
$745$	3.25355e29	0.226317
$746$	−1.17596e30	−0.806559
$747$	9.97554e28	0.0674637
$748$	−1.95438e30	−1.30329
$749$	−1.40912e30	−0.926592
$750$	1.53282e29	0.0993913
$751$	−1.07482e29	−0.0687250	−0.0343625	−	0.999409i	$-0.510940\pi$
$751$	−1.07482e29	−0.0687250	−0.0343625	+	0.999409i	$0.510940\pi$
$752$	−5.98398e30	−3.77314
$753$	−7.13958e29	−0.443941
$754$	4.27553e29	0.262174
$755$	8.00541e29	0.484106
$756$	1.61078e30	0.960633
$757$	3.00991e30	1.77030	0.885149	−	0.465307i	$-0.154056\pi$
$757$	3.00991e30	1.77030	0.885149	+	0.465307i	$0.154056\pi$
$758$	−5.07887e30	−2.94605
$759$	1.42161e29	0.0813284
$760$	5.05849e29	0.285416
$761$	−1.13756e29	−0.0633049	−0.0316524	−	0.999499i	$-0.510077\pi$
$761$	−1.13756e29	−0.0633049	−0.0316524	+	0.999499i	$0.510077\pi$
$762$	−1.64612e28	−0.00903514
$763$	1.21785e30	0.659303
$764$	−7.81446e30	−4.17271
$765$	3.91375e29	0.206133
$766$	−9.67344e29	−0.502549
$767$	7.54294e29	0.386535
$768$	−2.59027e30	−1.30934
$769$	2.78880e29	0.139056	0.0695281	−	0.997580i	$-0.477851\pi$
$769$	2.78880e29	0.139056	0.0695281	+	0.997580i	$0.477851\pi$
$770$	1.12561e30	0.553652
$771$	8.70016e29	0.422140
$772$	2.30337e30	1.10251
$773$	1.53967e30	0.727012	0.363506	−	0.931592i	$-0.381580\pi$
$773$	1.53967e30	0.727012	0.363506	+	0.931592i	$0.381580\pi$
$774$	−1.57358e30	−0.733010
$775$	1.46423e29	0.0672885
$776$	7.87518e30	3.57036
$777$	1.25410e30	0.560932
$778$	−4.63214e30	−2.04407
$779$	4.10021e29	0.178510
$780$	−2.49579e30	−1.07205
$781$	9.69948e29	0.411067
$782$	2.57270e30	1.07577
$783$	4.13873e28	0.0170753
$784$	2.13395e31	8.68691
$785$	1.44466e30	0.580276
$786$	−2.99583e29	−0.118735
$787$	7.03087e29	0.274963	0.137482	−	0.990504i	$-0.456099\pi$
$787$	7.03087e29	0.274963	0.137482	+	0.990504i	$0.456099\pi$
$788$	6.78458e30	2.61817
$789$	−2.02819e30	−0.772324
$790$	−9.57906e29	−0.359947
$791$	−4.61919e30	−1.71282
$792$	1.04149e30	0.381101
$793$	−7.72867e30	−2.79085
$794$	−9.86551e30	−3.51564
$795$	1.87342e29	0.0658842
$796$	1.07207e31	3.72080
$797$	−2.01448e30	−0.690001	−0.345001	−	0.938602i	$-0.612121\pi$
$797$	−2.01448e30	−0.690001	−0.345001	+	0.938602i	$0.612121\pi$
$798$	−1.18030e30	−0.398991
$799$	4.33230e30	1.44536
$800$	2.22740e30	0.733420
$801$	1.81411e29	0.0589552
$802$	−4.41431e30	−1.41590
$803$	−8.68534e29	−0.274963
$804$	3.43605e30	1.07367
$805$	−1.08175e30	−0.333633
$806$	−3.26564e30	−0.994148
$807$	−2.06264e30	−0.619801
$808$	−1.18150e31	−3.50441
$809$	−5.38496e30	−1.57660	−0.788302	−	0.615288i	$-0.789040\pi$
$809$	−5.38496e30	−1.57660	−0.788302	+	0.615288i	$0.789040\pi$
$810$	−3.30925e29	−0.0956393
$811$	1.66080e30	0.473804	0.236902	−	0.971534i	$-0.423868\pi$
$811$	1.66080e30	0.473804	0.236902	+	0.971534i	$0.423868\pi$
$812$	1.57263e30	0.442884
$813$	2.98077e30	0.828664
$814$	1.28659e30	0.353089
$815$	−5.39998e29	−0.146298
$816$	1.07750e31	2.88186
$817$	8.41790e29	0.222265
$818$	5.73415e30	1.49472
$819$	3.67020e30	0.944515
$820$	4.36820e30	1.10983
$821$	−3.71407e30	−0.931638	−0.465819	−	0.884880i	$-0.654240\pi$
$821$	−3.71407e30	−0.931638	−0.465819	+	0.884880i	$0.654240\pi$
$822$	5.59049e30	1.38451
$823$	1.83682e30	0.449126	0.224563	−	0.974460i	$-0.427904\pi$
$823$	1.83682e30	0.449126	0.224563	+	0.974460i	$0.427904\pi$
$824$	1.16681e31	2.81686
$825$	−1.68826e29	−0.0402414
$826$	3.80034e30	0.894400
$827$	4.85542e30	1.12828	0.564142	−	0.825678i	$-0.309207\pi$
$827$	4.85542e30	1.12828	0.564142	+	0.825678i	$0.309207\pi$
$828$	−1.58811e30	−0.364387
$829$	−6.43767e30	−1.45850	−0.729249	−	0.684248i	$-0.760130\pi$
$829$	−6.43767e30	−1.45850	−0.729249	+	0.684248i	$0.760130\pi$
$830$	−7.78736e29	−0.174209
$831$	2.03078e29	0.0448592
$832$	−2.42705e31	−5.29399
$833$	−1.54494e31	−3.32767
$834$	−9.21696e29	−0.196040
$835$	4.51520e29	0.0948350
$836$	−8.84015e29	−0.183355
$837$	−3.16116e29	−0.0647484
$838$	4.29212e30	0.868179
$839$	3.48676e30	0.696500	0.348250	−	0.937402i	$-0.386776\pi$
$839$	3.48676e30	0.696500	0.348250	+	0.937402i	$0.386776\pi$
$840$	−7.92500e30	−1.56339
$841$	−5.09244e30	−0.992128
$842$	8.78109e30	1.68955
$843$	4.76900e30	0.906229
$844$	−2.04789e31	−3.84336
$845$	−3.27399e30	−0.606850
$846$	−3.66315e30	−0.670604
$847$	8.96799e30	1.62151
$848$	5.15777e30	0.921098
$849$	1.49377e30	0.263483
$850$	−3.05525e30	−0.532290
$851$	−1.23645e30	−0.212773
$852$	−1.08355e31	−1.84176
$853$	−5.20313e30	−0.873575	−0.436788	−	0.899565i	$-0.643884\pi$
$853$	−5.20313e30	−0.873575	−0.436788	+	0.899565i	$0.643884\pi$
$854$	−3.89391e31	−6.45771
$855$	1.77028e29	0.0290001
$856$	1.01781e31	1.64699
$857$	6.67513e30	1.06699	0.533496	−	0.845803i	$-0.320878\pi$
$857$	6.67513e30	1.06699	0.533496	+	0.845803i	$0.320878\pi$
$858$	3.76530e30	0.594543
$859$	7.89066e29	0.123079	0.0615397	−	0.998105i	$-0.480399\pi$
$859$	7.89066e29	0.123079	0.0615397	+	0.998105i	$0.480399\pi$
$860$	8.96810e30	1.38187
$861$	−6.42368e30	−0.977802
$862$	5.52440e30	0.830729
$863$	1.23936e31	1.84113	0.920564	−	0.390591i	$-0.127729\pi$
$863$	1.23936e31	1.84113	0.920564	+	0.390591i	$0.127729\pi$
$864$	−4.80878e30	−0.705734
$865$	4.75917e30	0.690020
$866$	1.56087e31	2.23578
$867$	−3.72115e30	−0.526594
$868$	−1.20118e31	−1.67938
$869$	1.05504e30	0.145735
$870$	−3.23088e29	−0.0440929
$871$	7.82912e30	1.05566
$872$	−8.79654e30	−1.17190
$873$	2.75602e30	0.362771
$874$	1.16369e30	0.151345
$875$	1.28465e30	0.165082
$876$	9.70259e30	1.23195
$877$	−8.03560e30	−1.00814	−0.504072	−	0.863662i	$-0.668165\pi$
$877$	−8.03560e30	−1.00814	−0.504072	+	0.863662i	$0.668165\pi$
$878$	4.28944e30	0.531751
$879$	−8.26043e30	−1.01186
$880$	−4.64800e30	−0.562597
$881$	6.43033e30	0.769106	0.384553	−	0.923103i	$-0.374356\pi$
$881$	6.43033e30	0.769106	0.384553	+	0.923103i	$0.374356\pi$
$882$	1.30632e31	1.54393
$883$	1.16447e31	1.36000	0.680002	−	0.733210i	$-0.261979\pi$
$883$	1.16447e31	1.36000	0.680002	+	0.733210i	$0.261979\pi$
$884$	4.97466e31	5.74136
$885$	−5.69996e29	−0.0650081
$886$	−9.12525e30	−1.02847
$887$	−1.24369e30	−0.138520	−0.0692601	−	0.997599i	$-0.522064\pi$
$887$	−1.24369e30	−0.138520	−0.0692601	+	0.997599i	$0.522064\pi$
$888$	−9.05837e30	−0.997043
$889$	−1.37960e29	−0.0150067
$890$	−1.41618e30	−0.152238
$891$	3.64483e29	0.0387223
$892$	1.42386e31	1.49499
$893$	1.95961e30	0.203343
$894$	5.48339e30	0.562348
$895$	4.23770e30	0.429525
$896$	−5.47178e31	−5.48144
$897$	−3.61856e30	−0.358274
$898$	8.48436e30	0.830267
$899$	−3.08630e29	−0.0298512
$900$	1.88599e30	0.180299
$901$	−3.73414e30	−0.352842
$902$	−6.59012e30	−0.615495
$903$	−1.31881e31	−1.21748
$904$	3.33645e31	3.04450
$905$	6.92146e30	0.624292
$906$	1.34920e31	1.20290
$907$	−3.37302e30	−0.297264	−0.148632	−	0.988893i	$-0.547487\pi$
$907$	−3.37302e30	−0.297264	−0.148632	+	0.988893i	$0.547487\pi$
$908$	5.43325e31	4.73324
$909$	−4.13482e30	−0.356070
$910$	−2.86513e31	−2.43899
$911$	−1.99391e31	−1.67789	−0.838945	−	0.544216i	$-0.816827\pi$
$911$	−1.99391e31	−1.67789	−0.838945	+	0.544216i	$0.816827\pi$
$912$	4.87382e30	0.405437
$913$	8.57705e29	0.0705334
$914$	−1.32717e30	−0.107892
$915$	5.84031e30	0.469369
$916$	−5.50936e31	−4.37722
$917$	−2.51078e30	−0.197211
$918$	6.59606e30	0.512196
$919$	−3.09702e30	−0.237756	−0.118878	−	0.992909i	$-0.537930\pi$
$919$	−3.09702e30	−0.237756	−0.118878	+	0.992909i	$0.537930\pi$
$920$	7.81348e30	0.593024
$921$	9.80587e30	0.735800
$922$	−2.78643e31	−2.06716
$923$	−2.46890e31	−1.81086
$924$	1.38496e31	1.00434
$925$	1.46837e30	0.105280
$926$	3.92990e31	2.78591
$927$	4.08341e30	0.286211
$928$	−4.69490e30	−0.325367
$929$	3.21440e30	0.220260	0.110130	−	0.993917i	$-0.464873\pi$
$929$	3.21440e30	0.220260	0.110130	+	0.993917i	$0.464873\pi$
$930$	2.46774e30	0.167197
$931$	−6.98816e30	−0.468157
$932$	−5.49033e31	−3.63690
$933$	−1.68830e31	−1.10584
$934$	1.06717e29	0.00691181
$935$	3.36507e30	0.215513
$936$	−2.65100e31	−1.67885
$937$	4.96558e30	0.310960	0.155480	−	0.987839i	$-0.450308\pi$
$937$	4.96558e30	0.310960	0.155480	+	0.987839i	$0.450308\pi$
$938$	3.94452e31	2.44267
$939$	−4.00511e30	−0.245259
$940$	2.08769e31	1.26422
$941$	1.65186e30	0.0989193	0.0494597	−	0.998776i	$-0.484250\pi$
$941$	1.65186e30	0.0989193	0.0494597	+	0.998776i	$0.484250\pi$
$942$	2.43477e31	1.44186
$943$	6.33329e30	0.370900
$944$	−1.56927e31	−0.908851
$945$	−2.77346e30	−0.158850
$946$	−1.35298e31	−0.766363
$947$	1.15884e31	0.649155	0.324578	−	0.945859i	$-0.394778\pi$
$947$	1.15884e31	0.649155	0.324578	+	0.945859i	$0.394778\pi$
$948$	−1.17861e31	−0.652956
$949$	2.21076e31	1.21128
$950$	−1.38197e30	−0.0748858
$951$	1.80679e30	0.0968308
$952$	1.57963e32	8.37271
$953$	−3.38294e31	−1.77345	−0.886724	−	0.462299i	$-0.847025\pi$
$953$	−3.38294e31	−1.77345	−0.886724	+	0.462299i	$0.847025\pi$
$954$	3.15738e30	0.163708
$955$	1.34550e31	0.689999
$956$	−7.75780e31	−3.93487
$957$	3.55851e29	0.0178523
$958$	2.59477e31	1.28754
$959$	4.68535e31	2.29957
$960$	1.83404e31	0.890351
$961$	−1.84682e31	−0.886806
$962$	−3.27487e31	−1.55545
$963$	3.56196e30	0.167345
$964$	−9.62997e31	−4.47524
$965$	−3.96596e30	−0.182311
$966$	−1.82313e31	−0.829005
$967$	−1.15852e30	−0.0521104	−0.0260552	−	0.999661i	$-0.508295\pi$
$967$	−1.15852e30	−0.0521104	−0.0260552	+	0.999661i	$0.508295\pi$
$968$	−6.47760e31	−2.88219
$969$	−3.52857e30	−0.155310
$970$	−2.15148e31	−0.936771
$971$	5.52187e30	0.237840	0.118920	−	0.992904i	$-0.462057\pi$
$971$	5.52187e30	0.237840	0.118920	+	0.992904i	$0.462057\pi$
$972$	−4.07172e30	−0.173493
$973$	−7.72467e30	−0.325608
$974$	−3.71209e31	−1.54792
$975$	4.29728e30	0.177274
$976$	1.60791e32	6.56204
$977$	4.51123e29	0.0182139	0.00910693	−	0.999959i	$-0.497101\pi$
$977$	4.51123e29	0.0182139	0.00910693	+	0.999959i	$0.497101\pi$
$978$	−9.10089e30	−0.363518
$979$	1.55979e30	0.0616378
$980$	−7.44492e31	−2.91062
$981$	−3.07847e30	−0.119072
$982$	−1.60545e31	−0.614365
$983$	4.25669e31	1.61161	0.805805	−	0.592180i	$-0.201733\pi$
$983$	4.25669e31	1.61161	0.805805	+	0.592180i	$0.201733\pi$
$984$	4.63984e31	1.73802
$985$	−1.16818e31	−0.432940
$986$	6.43985e30	0.236139
$987$	−3.07006e31	−1.11383
$988$	2.25016e31	0.807730
$989$	1.30025e31	0.461813
$990$	−2.84532e30	−0.0999911
$991$	3.26274e30	0.113451	0.0567256	−	0.998390i	$-0.481934\pi$
$991$	3.26274e30	0.113451	0.0567256	+	0.998390i	$0.481934\pi$
$992$	3.58596e31	1.23377
$993$	−1.75908e31	−0.598851
$994$	−1.24390e32	−4.19013
$995$	−1.84590e31	−0.615271
$996$	−9.58162e30	−0.316021
$997$	−3.92458e31	−1.28084	−0.640419	−	0.768026i	$-0.721239\pi$
$997$	−3.92458e31	−1.28084	−0.640419	+	0.768026i	$0.721239\pi$
$998$	3.07983e31	0.994617
$999$	−3.17009e30	−0.101306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.22.a.c.1.3	✓	3
3.2	odd	2		45.22.a.c.1.1		3
5.2	odd	4		75.22.b.f.49.6		6
5.3	odd	4		75.22.b.f.49.1		6
5.4	even	2		75.22.a.f.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.22.a.c.1.3	✓	3	1.1	even	1	trivial
45.22.a.c.1.1		3	3.2	odd	2
75.22.a.f.1.1		3	5.4	even	2
75.22.b.f.49.1		6	5.3	odd	4
75.22.b.f.49.6		6	5.2	odd	4

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	15.a (trivial)

\(f(q)\)	\(=\)	\(q+2787.27 q^{2} -59049.0 q^{3} +5.67172e6 q^{4} -9.76562e6 q^{5} -1.64586e8 q^{6} -1.37938e9 q^{7} +9.96329e9 q^{8} +3.48678e9 q^{9} +O(q^{10})\)	\(q+2787.27 q^{2} -59049.0 q^{3} +5.67172e6 q^{4} -9.76562e6 q^{5} -1.64586e8 q^{6} -1.37938e9 q^{7} +9.96329e9 q^{8} +3.48678e9 q^{9} -2.72194e10 q^{10} +2.99797e10 q^{11} -3.34910e11 q^{12} -7.63100e11 q^{13} -3.84470e12 q^{14} +5.76650e11 q^{15} +1.58759e13 q^{16} -1.14939e13 q^{17} +9.71861e12 q^{18} -5.19898e12 q^{19} -5.53879e13 q^{20} +8.14510e13 q^{21} +8.35614e13 q^{22} -8.03048e13 q^{23} -5.88322e14 q^{24} +9.53674e13 q^{25} -2.12696e15 q^{26} -2.05891e14 q^{27} -7.82346e15 q^{28} -2.01015e14 q^{29} +1.60728e15 q^{30} +1.53535e15 q^{31} +2.33559e16 q^{32} -1.77027e15 q^{33} -3.20366e16 q^{34} +1.34705e16 q^{35} +1.97761e16 q^{36} +1.53969e16 q^{37} -1.44910e16 q^{38} +4.50603e16 q^{39} -9.72978e16 q^{40} -7.88656e16 q^{41} +2.27026e17 q^{42} -1.61914e17 q^{43} +1.70036e17 q^{44} -3.40506e16 q^{45} -2.23831e17 q^{46} -3.76922e17 q^{47} -9.37457e17 q^{48} +1.34414e18 q^{49} +2.65815e17 q^{50} +6.78704e17 q^{51} -4.32809e18 q^{52} +3.24880e17 q^{53} -5.73874e17 q^{54} -2.92770e17 q^{55} -1.37432e19 q^{56} +3.06994e17 q^{57} -5.60284e17 q^{58} -9.88461e17 q^{59} +3.27060e18 q^{60} +1.01280e19 q^{61} +4.27945e18 q^{62} -4.80960e18 q^{63} +3.18051e19 q^{64} +7.45214e18 q^{65} -4.93422e18 q^{66} -1.02596e19 q^{67} -6.51902e19 q^{68} +4.74192e18 q^{69} +3.75459e19 q^{70} +3.23535e19 q^{71} +3.47399e19 q^{72} -2.89708e19 q^{73} +4.29154e19 q^{74} -5.63135e18 q^{75} -2.94872e19 q^{76} -4.13533e19 q^{77} +1.25595e20 q^{78} +3.51920e19 q^{79} -1.55038e20 q^{80} +1.21577e19 q^{81} -2.19820e20 q^{82} +2.86096e19 q^{83} +4.61967e20 q^{84} +1.12245e20 q^{85} -4.51299e20 q^{86} +1.18698e19 q^{87} +2.98696e20 q^{88} +5.20282e19 q^{89} -9.49083e19 q^{90} +1.05260e21 q^{91} -4.55467e20 q^{92} -9.06611e19 q^{93} -1.05058e21 q^{94} +5.07713e19 q^{95} -1.37915e21 q^{96} +7.90419e20 q^{97} +3.74649e21 q^{98} +1.04533e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 702 q^{2} - 177147 q^{3} + 5244228 q^{4} - 29296875 q^{5} - 41452398 q^{6} - 2072418204 q^{7} + 11461067832 q^{8} + 10460353203 q^{9}+O(q^{10}) \) 3 * q + 702 * q^2 - 177147 * q^3 + 5244228 * q^4 - 29296875 * q^5 - 41452398 * q^6 - 2072418204 * q^7 + 11461067832 * q^8 + 10460353203 * q^9	\( 3 q + 702 q^{2} - 177147 q^{3} + 5244228 q^{4} - 29296875 q^{5} - 41452398 q^{6} - 2072418204 q^{7} + 11461067832 q^{8} + 10460353203 q^{9} - 6855468750 q^{10} - 8467600440 q^{11} - 309666419172 q^{12} - 469447548570 q^{13} - 2389270234872 q^{14} + 1729951171875 q^{15} + 14993057845776 q^{16} - 6865096035486 q^{17} + 2447722649502 q^{18} + 33215593555044 q^{19} - 51213164062500 q^{20} + 122374222527996 q^{21} + 301288671211728 q^{22} + 48760125154728 q^{23} - 676764594411768 q^{24} + 286102294921875 q^{25} - 21\!\cdots\!24 q^{26}+ \cdots - 29\!\cdots\!40 q^{99}+O(q^{100}) \) 3 * q + 702 * q^2 - 177147 * q^3 + 5244228 * q^4 - 29296875 * q^5 - 41452398 * q^6 - 2072418204 * q^7 + 11461067832 * q^8 + 10460353203 * q^9 - 6855468750 * q^10 - 8467600440 * q^11 - 309666419172 * q^12 - 469447548570 * q^13 - 2389270234872 * q^14 + 1729951171875 * q^15 + 14993057845776 * q^16 - 6865096035486 * q^17 + 2447722649502 * q^18 + 33215593555044 * q^19 - 51213164062500 * q^20 + 122374222527996 * q^21 + 301288671211728 * q^22 + 48760125154728 * q^23 - 676764594411768 * q^24 + 286102294921875 * q^25 - 2164287288914724 * q^26 - 617673396283947 * q^27 - 9203502520938768 * q^28 + 2622046450702398 * q^29 + 404808574218750 * q^30 + 6533642328115464 * q^31 + 29519917545774816 * q^32 + 500003338381560 * q^33 - 45081813673901004 * q^34 + 20238459023437500 * q^35 + 18285492385687428 * q^36 - 21354228159481914 * q^37 - 108063021361090296 * q^38 + 27720408295509930 * q^39 - 111924490546875000 * q^40 - 63794855315977266 * q^41 + 141084018098956728 * q^42 - 332824264211549796 * q^43 - 192174659345792928 * q^44 - 102151886748046875 * q^45 - 431524141843343376 * q^46 - 1028504160073809912 * q^47 - 885325072735227024 * q^48 + 804417891162197307 * q^49 + 66947937011718750 * q^50 + 405377055799412814 * q^51 - 4951478317146373176 * q^52 + 811321254325423998 * q^53 - 144535574730443598 * q^54 + 82691410546875000 * q^55 - 14362364751613106400 * q^56 - 1961347583831793156 * q^57 - 5682617216112818772 * q^58 - 526619402549960904 * q^59 + 3024086124726562500 * q^60 + 826732383760533522 * q^61 - 3494141388054166608 * q^62 - 7226075466055635804 * q^63 + 18241430414481738816 * q^64 + 4584448716503906250 * q^65 - 17790794746381326672 * q^66 - 9384022533389399076 * q^67 - 49040734788483425256 * q^68 - 2879236630261533672 * q^69 + 23332717137421875000 * q^70 + 60019641798452716896 * q^71 + 39962272535420488632 * q^72 - 17009842434251898522 * q^73 + 135690473789754431388 * q^74 - 16894054412841796875 * q^75 + 73904848422041181936 * q^76 + 53710247923965432672 * q^77 + 127799000123125537476 * q^78 + 192112433593115883000 * q^79 - 146416580525156250000 * q^80 + 36472996377170786403 * q^81 - 367171610825203944948 * q^82 + 284198623110184688316 * q^83 + 543457620358913311632 * q^84 + 67041953471542968750 * q^85 - 75848580157311095400 * q^86 - 154829220867525899502 * q^87 + 245615805643415437632 * q^88 + 132940763694174535254 * q^89 - 23903541499042968750 * q^90 + 1074557595270409043784 * q^91 - 330567977024321701344 * q^92 - 385805045832890033736 * q^93 - 712373552658444529680 * q^94 - 324371030810976562500 * q^95 - 1743121611160457109984 * q^96 - 985976190327562940826 * q^97 + 3801329211782343852270 * q^98 - 29524697128092736440 * q^99

Introduction

L-functions

Modular forms

Varieties

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