LMFDB - Embedded newform 29.18.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,18,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	29.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:	$53.1344053299$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+616.905 q^{2} +17761.1 q^{3} +249500. q^{4} +768235. q^{5} +1.09569e7 q^{6} +1.64486e6 q^{7} +7.30585e7 q^{8} +1.86316e8 q^{9} +O(q^{10})$	\(q+616.905 q^{2} +17761.1 q^{3} +249500. q^{4} +768235. q^{5} +1.09569e7 q^{6} +1.64486e6 q^{7} +7.30585e7 q^{8} +1.86316e8 q^{9} +4.73928e8 q^{10} -6.23226e8 q^{11} +4.43138e9 q^{12} +1.86416e9 q^{13} +1.01472e9 q^{14} +1.36447e10 q^{15} +1.23678e10 q^{16} -1.09640e10 q^{17} +1.14939e11 q^{18} -3.02142e10 q^{19} +1.91674e11 q^{20} +2.92144e10 q^{21} -3.84471e11 q^{22} +2.62133e11 q^{23} +1.29760e12 q^{24} -1.72754e11 q^{25} +1.15001e12 q^{26} +1.01550e12 q^{27} +4.10391e11 q^{28} +5.00246e11 q^{29} +8.41747e12 q^{30} -4.65989e12 q^{31} -1.94620e12 q^{32} -1.10692e13 q^{33} -6.76375e12 q^{34} +1.26364e12 q^{35} +4.64857e13 q^{36} +2.56925e13 q^{37} -1.86393e13 q^{38} +3.31094e13 q^{39} +5.61262e13 q^{40} +4.31933e13 q^{41} +1.80225e13 q^{42} -6.43816e13 q^{43} -1.55495e14 q^{44} +1.43134e14 q^{45} +1.61711e14 q^{46} -1.91076e14 q^{47} +2.19665e14 q^{48} -2.29925e14 q^{49} -1.06573e14 q^{50} -1.94733e14 q^{51} +4.65107e14 q^{52} -7.46298e14 q^{53} +6.26465e14 q^{54} -4.78784e14 q^{55} +1.20171e14 q^{56} -5.36637e14 q^{57} +3.08604e14 q^{58} +2.00465e15 q^{59} +3.40434e15 q^{60} +1.38827e15 q^{61} -2.87471e15 q^{62} +3.06463e14 q^{63} -2.82169e15 q^{64} +1.43211e15 q^{65} -6.82862e15 q^{66} -2.66642e15 q^{67} -2.73551e15 q^{68} +4.65576e15 q^{69} +7.79545e14 q^{70} +6.06764e15 q^{71} +1.36119e16 q^{72} +7.52337e15 q^{73} +1.58498e16 q^{74} -3.06829e15 q^{75} -7.53843e15 q^{76} -1.02512e15 q^{77} +2.04254e16 q^{78} +2.43578e16 q^{79} +9.50135e15 q^{80} -6.02451e15 q^{81} +2.66462e16 q^{82} +1.12492e16 q^{83} +7.28899e15 q^{84} -8.42294e15 q^{85} -3.97173e16 q^{86} +8.88491e15 q^{87} -4.55320e16 q^{88} +3.40745e16 q^{89} +8.83002e16 q^{90} +3.06628e15 q^{91} +6.54020e16 q^{92} -8.27646e16 q^{93} -1.17876e17 q^{94} -2.32116e16 q^{95} -3.45666e16 q^{96} -7.90652e16 q^{97} -1.41842e17 q^{98} -1.16117e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) $ 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9} - 224469478 q^{10} + 1203139534 q^{11} - 5164251122 q^{12} + 3854339312 q^{13} + 25262272904 q^{14} + 28324474306 q^{15} + 196520815922 q^{16} + 76444714794 q^{17} + 75758949126 q^{18} + 246497292428 q^{19} - 46900976670 q^{20} + 360937126704 q^{21} - 275001533522 q^{22} + 213498528140 q^{23} - 451123453870 q^{24} + 3898884886997 q^{25} - 3609347694206 q^{26} - 2718903745978 q^{27} - 5946174617200 q^{28} + 10505174672181 q^{29} - 20237658929454 q^{30} + 16670029895798 q^{31} - 42141001912046 q^{32} - 7157109761394 q^{33} + 12785761151136 q^{34} + 46677934312888 q^{35} + 132137824374868 q^{36} + 53445659988410 q^{37} + 76581637956388 q^{38} + 79233849032530 q^{39} + 193617444734146 q^{40} - 20814769309298 q^{41} + 76690667258352 q^{42} + 185498647364454 q^{43} + 315429066899678 q^{44} - 486270821438526 q^{45} + 261474367677132 q^{46} + 389503471719450 q^{47} - 101509672247630 q^{48} + 730079062141437 q^{49} + 14\!\cdots\!54 q^{50}+ \cdots - 95\!\cdots\!64 q^{99}+O(q^{100}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9 - 224469478 * q^10 + 1203139534 * q^11 - 5164251122 * q^12 + 3854339312 * q^13 + 25262272904 * q^14 + 28324474306 * q^15 + 196520815922 * q^16 + 76444714794 * q^17 + 75758949126 * q^18 + 246497292428 * q^19 - 46900976670 * q^20 + 360937126704 * q^21 - 275001533522 * q^22 + 213498528140 * q^23 - 451123453870 * q^24 + 3898884886997 * q^25 - 3609347694206 * q^26 - 2718903745978 * q^27 - 5946174617200 * q^28 + 10505174672181 * q^29 - 20237658929454 * q^30 + 16670029895798 * q^31 - 42141001912046 * q^32 - 7157109761394 * q^33 + 12785761151136 * q^34 + 46677934312888 * q^35 + 132137824374868 * q^36 + 53445659988410 * q^37 + 76581637956388 * q^38 + 79233849032530 * q^39 + 193617444734146 * q^40 - 20814769309298 * q^41 + 76690667258352 * q^42 + 185498647364454 * q^43 + 315429066899678 * q^44 - 486270821438526 * q^45 + 261474367677132 * q^46 + 389503471719450 * q^47 - 101509672247630 * q^48 + 730079062141437 * q^49 + 1482269666368354 * q^50 + 718238208473988 * q^51 + 1966802817157170 * q^52 + 747441265526156 * q^53 + 5692893333117030 * q^54 + 1639109418219546 * q^55 + 5657219329125240 * q^56 + 4694352396864932 * q^57 + 128063081718016 * q^58 + 5280258638332960 * q^59 + 15251367906033378 * q^60 + 5813675353074254 * q^61 + 6242066590947250 * q^62 + 10947760075450368 * q^63 + 24583792057508902 * q^64 + 19190799243789974 * q^65 + 41877805444482390 * q^66 + 13420580230958268 * q^67 + 24771837384165388 * q^68 + 30973047049935252 * q^69 + 8505088080182440 * q^70 + 4824462822979508 * q^71 + 1180071997284592 * q^72 + 11228916281304662 * q^73 - 89132715356772 * q^74 + 59161419576630296 * q^75 + 57466858643173460 * q^76 + 58741564492720064 * q^77 + 142050530910210210 * q^78 + 71718598015696758 * q^79 + 48350023652407550 * q^80 + 75805931446703569 * q^81 + 188661890754420812 * q^82 + 50769377111735608 * q^83 + 198832046985593048 * q^84 + 53422044849490784 * q^85 + 35014892323844118 * q^86 + 11988905533023326 * q^87 + 37459283979085258 * q^88 - 70981414576978018 * q^89 + 57211029866143724 * q^90 + 112933943315157320 * q^91 - 103019729095759724 * q^92 - 350358290646906646 * q^93 - 150286322409612578 * q^94 - 102561321856584476 * q^95 - 213770098354021866 * q^96 - 130930167251505210 * q^97 - 537387515497557296 * q^98 - 95267700931431064 * 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 $

$2$	616.905	1.70397	0.851987	−	0.523562i	$-0.175397\pi$
$2$	616.905	1.70397	0.851987	+	0.523562i	$0.175397\pi$
$3$	17761.1	1.56293	0.781463	−	0.623951i	$-0.214474\pi$
$3$	17761.1	1.56293	0.781463	+	0.623951i	$0.214474\pi$
$4$	249500.	1.90353
$5$	768235.	0.879527	0.439764	−	0.898114i	$-0.355062\pi$
$5$	768235.	0.879527	0.439764	+	0.898114i	$0.355062\pi$
$6$	1.09569e7	2.66319
$7$	1.64486e6	0.107844	0.0539219	−	0.998545i	$-0.482828\pi$
$7$	1.64486e6	0.107844	0.0539219	+	0.998545i	$0.482828\pi$
$8$	7.30585e7	1.53959
$9$	1.86316e8	1.44274
$10$	4.73928e8	1.49869
$11$	−6.23226e8	−0.876612	−0.438306	−	0.898826i	$-0.644421\pi$
$11$	−6.23226e8	−0.876612	−0.438306	+	0.898826i	$0.644421\pi$
$12$	4.43138e9	2.97508
$13$	1.86416e9	0.633817	0.316909	−	0.948456i	$-0.397355\pi$
$13$	1.86416e9	0.633817	0.316909	+	0.948456i	$0.397355\pi$
$14$	1.01472e9	0.183763
$15$	1.36447e10	1.37464
$16$	1.23678e10	0.719898
$17$	−1.09640e10	−0.381200	−0.190600	−	0.981668i	$-0.561043\pi$
$17$	−1.09640e10	−0.381200	−0.190600	+	0.981668i	$0.561043\pi$
$18$	1.14939e11	2.45839
$19$	−3.02142e10	−0.408137	−0.204068	−	0.978957i	$-0.565416\pi$
$19$	−3.02142e10	−0.408137	−0.204068	+	0.978957i	$0.565416\pi$
$20$	1.91674e11	1.67421
$21$	2.92144e10	0.168552
$22$	−3.84471e11	−1.49373
$23$	2.62133e11	0.697966	0.348983	−	0.937129i	$-0.386527\pi$
$23$	2.62133e11	0.697966	0.348983	+	0.937129i	$0.386527\pi$
$24$	1.29760e12	2.40627
$25$	−1.72754e11	−0.226432
$26$	1.15001e12	1.08001
$27$	1.01550e12	0.691969
$28$	4.10391e11	0.205284
$29$	5.00246e11	0.185695
$29$	5.00246e11	0.185695
$30$	8.41747e12	2.34235
$31$	−4.65989e12	−0.981299	−0.490649	−	0.871357i	$-0.663240\pi$
$31$	−4.65989e12	−0.981299	−0.490649	+	0.871357i	$0.663240\pi$
$32$	−1.94620e12	−0.312905
$33$	−1.10692e13	−1.37008
$34$	−6.76375e12	−0.649556
$35$	1.26364e12	0.0948516
$36$	4.64857e13	2.74630
$37$	2.56925e13	1.20252	0.601258	−	0.799055i	$-0.294666\pi$
$37$	2.56925e13	1.20252	0.601258	+	0.799055i	$0.294666\pi$
$38$	−1.86393e13	−0.695455
$39$	3.31094e13	0.990610
$40$	5.61262e13	1.35411
$41$	4.31933e13	0.844800	0.422400	−	0.906410i	$-0.361188\pi$
$41$	4.31933e13	0.844800	0.422400	+	0.906410i	$0.361188\pi$
$42$	1.80225e13	0.287208
$43$	−6.43816e13	−0.840002	−0.420001	−	0.907524i	$-0.637970\pi$
$43$	−6.43816e13	−0.840002	−0.420001	+	0.907524i	$0.637970\pi$
$44$	−1.55495e14	−1.66866
$45$	1.43134e14	1.26893
$46$	1.61711e14	1.18932
$47$	−1.91076e14	−1.17051	−0.585255	−	0.810849i	$-0.699006\pi$
$47$	−1.91076e14	−1.17051	−0.585255	+	0.810849i	$0.699006\pi$
$48$	2.19665e14	1.12515
$49$	−2.29925e14	−0.988370
$50$	−1.06573e14	−0.385834
$51$	−1.94733e14	−0.595788
$52$	4.65107e14	1.20649
$53$	−7.46298e14	−1.64652	−0.823260	−	0.567664i	$-0.807847\pi$
$53$	−7.46298e14	−1.64652	−0.823260	+	0.567664i	$0.807847\pi$
$54$	6.26465e14	1.17910
$55$	−4.78784e14	−0.771004
$56$	1.20171e14	0.166036
$57$	−5.36637e14	−0.637888
$58$	3.08604e14	0.316420
$59$	2.00465e15	1.77744	0.888721	−	0.458448i	$-0.151594\pi$
$59$	2.00465e15	1.77744	0.888721	+	0.458448i	$0.151594\pi$
$60$	3.40434e15	2.61666
$61$	1.38827e15	0.927193	0.463597	−	0.886046i	$-0.346559\pi$
$61$	1.38827e15	0.927193	0.463597	+	0.886046i	$0.346559\pi$
$62$	−2.87471e15	−1.67211
$63$	3.06463e14	0.155590
$64$	−2.82169e15	−1.25308
$65$	1.43211e15	0.557460
$66$	−6.82862e15	−2.33458
$67$	−2.66642e15	−0.802219	−0.401110	−	0.916030i	$-0.631375\pi$
$67$	−2.66642e15	−0.802219	−0.401110	+	0.916030i	$0.631375\pi$
$68$	−2.73551e15	−0.725627
$69$	4.65576e15	1.09087
$70$	7.79545e14	0.161625
$71$	6.06764e15	1.11513	0.557563	−	0.830135i	$-0.311737\pi$
$71$	6.06764e15	1.11513	0.557563	+	0.830135i	$0.311737\pi$
$72$	1.36119e16	2.22123
$73$	7.52337e15	1.09186	0.545931	−	0.837830i	$-0.316176\pi$
$73$	7.52337e15	1.09186	0.545931	+	0.837830i	$0.316176\pi$
$74$	1.58498e16	2.04906
$75$	−3.06829e15	−0.353896
$76$	−7.53843e15	−0.776901
$77$	−1.02512e15	−0.0945372
$78$	2.04254e16	1.68797
$79$	2.43578e16	1.80637	0.903186	−	0.429250i	$-0.141222\pi$
$79$	2.43578e16	1.80637	0.903186	+	0.429250i	$0.141222\pi$
$80$	9.50135e15	0.633170
$81$	−6.02451e15	−0.361243
$82$	2.66462e16	1.43952
$83$	1.12492e16	0.548223	0.274111	−	0.961698i	$-0.411616\pi$
$83$	1.12492e16	0.548223	0.274111	+	0.961698i	$0.411616\pi$
$84$	7.28899e15	0.320844
$85$	−8.42294e15	−0.335276
$86$	−3.97173e16	−1.43134
$87$	8.88491e15	0.290228
$88$	−4.55320e16	−1.34963
$89$	3.40745e16	0.917518	0.458759	−	0.888561i	$-0.348294\pi$
$89$	3.40745e16	0.917518	0.458759	+	0.888561i	$0.348294\pi$
$90$	8.83002e16	2.16222
$91$	3.06628e15	0.0683533
$92$	6.54020e16	1.32860
$93$	−8.27646e16	−1.53370
$94$	−1.17876e17	−1.99452
$95$	−2.32116e16	−0.358967
$96$	−3.45666e16	−0.489048
$97$	−7.90652e16	−1.02430	−0.512148	−	0.858897i	$-0.671150\pi$
$97$	−7.90652e16	−1.02430	−0.512148	+	0.858897i	$0.671150\pi$
$98$	−1.41842e17	−1.68416
$99$	−1.16117e17	−1.26472
$100$	−4.31020e16	−0.431020
$101$	−6.86893e16	−0.631186	−0.315593	−	0.948895i	$-0.602203\pi$
$101$	−6.86893e16	−0.631186	−0.315593	+	0.948895i	$0.602203\pi$
$102$	−1.20131e17	−1.01521
$103$	1.98925e16	0.154730	0.0773648	−	0.997003i	$-0.475349\pi$
$103$	1.98925e16	0.154730	0.0773648	+	0.997003i	$0.475349\pi$
$104$	1.36193e17	0.975821
$105$	2.24436e16	0.148246
$106$	−4.60395e17	−2.80563
$107$	2.76501e16	0.155573	0.0777865	−	0.996970i	$-0.475215\pi$
$107$	2.76501e16	0.155573	0.0777865	+	0.996970i	$0.475215\pi$
$108$	2.53366e17	1.31718
$109$	−4.89888e16	−0.235490	−0.117745	−	0.993044i	$-0.537566\pi$
$109$	−4.89888e16	−0.235490	−0.117745	+	0.993044i	$0.537566\pi$
$110$	−2.95364e17	−1.31377
$111$	4.56326e17	1.87944
$112$	2.03432e16	0.0776365
$113$	−3.83273e17	−1.35626	−0.678128	−	0.734944i	$-0.737208\pi$
$113$	−3.83273e17	−1.35626	−0.678128	+	0.734944i	$0.737208\pi$
$114$	−3.31054e17	−1.08694
$115$	2.01380e17	0.613880
$116$	1.24811e17	0.353477
$117$	3.47322e17	0.914433
$118$	1.23668e18	3.02872
$119$	−1.80342e16	−0.0411101
$120$	9.96861e17	2.11638
$121$	−1.17037e17	−0.231551
$122$	8.56430e17	1.57991
$123$	7.67160e17	1.32036
$124$	−1.16264e18	−1.86793
$125$	−7.18833e17	−1.07868
$126$	1.89058e17	0.265122
$127$	5.70520e17	0.748065	0.374032	−	0.927416i	$-0.377975\pi$
$127$	5.70520e17	0.748065	0.374032	+	0.927416i	$0.377975\pi$
$128$	−1.48562e18	−1.82231
$129$	−1.14349e18	−1.31286
$130$	8.83477e17	0.949897
$131$	−1.50293e18	−1.51403	−0.757014	−	0.653399i	$-0.773343\pi$
$131$	−1.50293e18	−1.51403	−0.757014	+	0.653399i	$0.773343\pi$
$132$	−2.76175e18	−2.60799
$133$	−4.96981e16	−0.0440150
$134$	−1.64493e18	−1.36696
$135$	7.80141e17	0.608606
$136$	−8.01014e17	−0.586894
$137$	−7.83173e17	−0.539179	−0.269589	−	0.962975i	$-0.586888\pi$
$137$	−7.83173e17	−0.539179	−0.269589	+	0.962975i	$0.586888\pi$
$138$	2.87216e18	1.85882
$139$	−1.16884e18	−0.711425	−0.355713	−	0.934595i	$-0.615762\pi$
$139$	−1.16884e18	−0.711425	−0.355713	+	0.934595i	$0.615762\pi$
$140$	3.15277e17	0.180553
$141$	−3.39372e18	−1.82942
$142$	3.74316e18	1.90015
$143$	−1.16179e18	−0.555612
$144$	2.30431e18	1.03863
$145$	3.84307e17	0.163324
$146$	4.64120e18	1.86051
$147$	−4.08371e18	−1.54475
$148$	6.41025e18	2.28903
$149$	4.95807e18	1.67197	0.835987	−	0.548749i	$-0.184896\pi$
$149$	4.95807e18	1.67197	0.835987	+	0.548749i	$0.184896\pi$
$150$	−1.89284e18	−0.603030
$151$	4.70660e18	1.41711	0.708555	−	0.705656i	$-0.249348\pi$
$151$	4.70660e18	1.41711	0.708555	+	0.705656i	$0.249348\pi$
$152$	−2.20741e18	−0.628364
$153$	−2.04277e18	−0.549973
$154$	−6.32400e17	−0.161089
$155$	−3.57989e18	−0.863079
$156$	8.26079e18	1.88566
$157$	−1.05313e18	−0.227686	−0.113843	−	0.993499i	$-0.536316\pi$
$157$	−1.05313e18	−0.227686	−0.113843	+	0.993499i	$0.536316\pi$
$158$	1.50264e19	3.07801
$159$	−1.32550e19	−2.57339
$160$	−1.49514e18	−0.275209
$161$	4.31171e17	0.0752713
$162$	−3.71655e18	−0.615548
$163$	2.80001e18	0.440113	0.220057	−	0.975487i	$-0.429376\pi$
$163$	2.80001e18	0.440113	0.220057	+	0.975487i	$0.429376\pi$
$164$	1.07767e19	1.60810
$165$	−8.50372e18	−1.20502
$166$	6.93967e18	0.934158
$167$	−5.93390e18	−0.759015	−0.379508	−	0.925189i	$-0.623907\pi$
$167$	−5.93390e18	−0.759015	−0.379508	+	0.925189i	$0.623907\pi$
$168$	2.13436e18	0.259501
$169$	−5.17533e18	−0.598275
$170$	−5.19615e18	−0.571302
$171$	−5.62938e18	−0.588835
$172$	−1.60632e19	−1.59897
$173$	−1.40993e19	−1.33599	−0.667997	−	0.744164i	$-0.732848\pi$
$173$	−1.40993e19	−1.33599	−0.667997	+	0.744164i	$0.732848\pi$
$174$	5.48115e18	0.494542
$175$	−2.84155e17	−0.0244193
$176$	−7.70790e18	−0.631071
$177$	3.56047e19	2.77801
$178$	2.10207e19	1.56343
$179$	3.92554e18	0.278387	0.139193	−	0.990265i	$-0.455549\pi$
$179$	3.92554e18	0.278387	0.139193	+	0.990265i	$0.455549\pi$
$180$	3.57119e19	2.41544
$181$	1.71539e18	0.110687	0.0553433	−	0.998467i	$-0.482375\pi$
$181$	1.71539e18	0.110687	0.0553433	+	0.998467i	$0.482375\pi$
$182$	1.89160e18	0.116472
$183$	2.46572e19	1.44913
$184$	1.91510e19	1.07458
$185$	1.97379e19	1.05765
$186$	−5.10579e19	−2.61338
$187$	6.83305e18	0.334165
$188$	−4.76735e19	−2.22810
$189$	1.67035e18	0.0746246
$190$	−1.43194e19	−0.611671
$191$	−2.17453e18	−0.0888345	−0.0444172	−	0.999013i	$-0.514143\pi$
$191$	−2.17453e18	−0.0888345	−0.0444172	+	0.999013i	$0.514143\pi$
$192$	−5.01162e19	−1.95847
$193$	−3.43554e19	−1.28457	−0.642286	−	0.766465i	$-0.722014\pi$
$193$	−3.43554e19	−1.28457	−0.642286	+	0.766465i	$0.722014\pi$
$194$	−4.87757e19	−1.74537
$195$	2.54358e19	0.871269
$196$	−5.73662e19	−1.88139
$197$	5.01100e19	1.57384	0.786922	−	0.617053i	$-0.211674\pi$
$197$	5.01100e19	1.57384	0.786922	+	0.617053i	$0.211674\pi$
$198$	−7.16329e19	−2.15506
$199$	4.41185e19	1.27166	0.635828	−	0.771831i	$-0.280659\pi$
$199$	4.41185e19	1.27166	0.635828	+	0.771831i	$0.280659\pi$
$200$	−1.26211e19	−0.348613
$201$	−4.73585e19	−1.25381
$202$	−4.23747e19	−1.07552
$203$	8.22834e17	0.0200261
$204$	−4.85857e19	−1.13410
$205$	3.31826e19	0.743024
$206$	1.22718e19	0.263655
$207$	4.88394e19	1.00698
$208$	2.30554e19	0.456284
$209$	1.88303e19	0.357778
$210$	1.38455e19	0.252607
$211$	3.20402e19	0.561428	0.280714	−	0.959791i	$-0.409429\pi$
$211$	3.20402e19	0.561428	0.280714	+	0.959791i	$0.409429\pi$
$212$	−1.86201e20	−3.13420
$213$	1.07768e20	1.74286
$214$	1.70575e19	0.265093
$215$	−4.94602e19	−0.738804
$216$	7.41907e19	1.06535
$217$	−7.66486e18	−0.105827
$218$	−3.02214e19	−0.401268
$219$	1.33623e20	1.70650
$220$	−1.19456e20	−1.46763
$221$	−2.04386e19	−0.241611
$222$	2.81509e20	3.20253
$223$	−2.15691e19	−0.236179	−0.118089	−	0.993003i	$-0.537677\pi$
$223$	−2.15691e19	−0.236179	−0.118089	+	0.993003i	$0.537677\pi$
$224$	−3.20123e18	−0.0337449
$225$	−3.21867e19	−0.326682
$226$	−2.36443e20	−2.31103
$227$	2.49194e19	0.234595	0.117297	−	0.993097i	$-0.462577\pi$
$227$	2.49194e19	0.234595	0.117297	+	0.993097i	$0.462577\pi$
$228$	−1.33891e20	−1.21424
$229$	1.43336e19	0.125243	0.0626215	−	0.998037i	$-0.480054\pi$
$229$	1.43336e19	0.125243	0.0626215	+	0.998037i	$0.480054\pi$
$230$	1.24232e20	1.04604
$231$	−1.82072e19	−0.147755
$232$	3.65473e19	0.285895
$233$	−2.07402e20	−1.56418	−0.782090	−	0.623165i	$-0.785847\pi$
$233$	−2.07402e20	−1.56418	−0.782090	+	0.623165i	$0.785847\pi$
$234$	2.14264e20	1.55817
$235$	−1.46792e20	−1.02950
$236$	5.00158e20	3.38342
$237$	4.32620e20	2.82323
$238$	−1.11254e19	−0.0700506
$239$	2.86450e20	1.74047	0.870237	−	0.492634i	$-0.163966\pi$
$239$	2.86450e20	1.74047	0.870237	+	0.492634i	$0.163966\pi$
$240$	1.68754e20	0.989598
$241$	1.88925e19	0.106941	0.0534706	−	0.998569i	$-0.482972\pi$
$241$	1.88925e19	0.106941	0.0534706	+	0.998569i	$0.482972\pi$
$242$	−7.22005e19	−0.394557
$243$	−2.38143e20	−1.25656
$244$	3.46373e20	1.76494
$245$	−1.76637e20	−0.869298
$246$	4.73265e20	2.24986
$247$	−5.63240e19	−0.258684
$248$	−3.40445e20	−1.51080
$249$	1.99797e20	0.856832
$250$	−4.43451e20	−1.83804
$251$	1.59121e20	0.637530	0.318765	−	0.947834i	$-0.396732\pi$
$251$	1.59121e20	0.637530	0.318765	+	0.947834i	$0.396732\pi$
$252$	7.64623e19	0.296171
$253$	−1.63368e20	−0.611846
$254$	3.51957e20	1.27468
$255$	−1.49600e20	−0.524012
$256$	−5.46642e20	−1.85209
$257$	−3.68683e19	−0.120843	−0.0604215	−	0.998173i	$-0.519244\pi$
$257$	−3.68683e19	−0.120843	−0.0604215	+	0.998173i	$0.519244\pi$
$258$	−7.05423e20	−2.23708
$259$	4.22604e19	0.129684
$260$	3.57311e20	1.06114
$261$	9.32037e19	0.267910
$262$	−9.27167e20	−2.57987
$263$	6.68560e20	1.80101	0.900506	−	0.434844i	$-0.143197\pi$
$263$	6.68560e20	1.80101	0.900506	+	0.434844i	$0.143197\pi$
$264$	−8.08697e20	−2.10937
$265$	−5.73332e20	−1.44816
$266$	−3.06590e19	−0.0750005
$267$	6.05200e20	1.43401
$268$	−6.65271e20	−1.52705
$269$	8.52453e20	1.89573	0.947864	−	0.318674i	$-0.103237\pi$
$269$	8.52453e20	1.89573	0.947864	+	0.318674i	$0.103237\pi$
$270$	4.81273e20	1.03705
$271$	2.06618e19	0.0431448	0.0215724	−	0.999767i	$-0.493133\pi$
$271$	2.06618e19	0.0431448	0.0215724	+	0.999767i	$0.493133\pi$
$272$	−1.35600e20	−0.274425
$273$	5.44603e19	0.106831
$274$	−4.83143e20	−0.918747
$275$	1.07665e20	0.198493
$276$	1.16161e21	2.07650
$277$	4.95320e20	0.858633	0.429316	−	0.903154i	$-0.358755\pi$
$277$	4.95320e20	0.858633	0.429316	+	0.903154i	$0.358755\pi$
$278$	−7.21063e20	−1.21225
$279$	−8.68210e20	−1.41576
$280$	9.23196e19	0.146033
$281$	6.31720e20	0.969441	0.484720	−	0.874669i	$-0.338921\pi$
$281$	6.31720e20	0.969441	0.484720	+	0.874669i	$0.338921\pi$
$282$	−2.09360e21	−3.11729
$283$	−7.12915e20	−1.03004	−0.515019	−	0.857179i	$-0.672215\pi$
$283$	−7.12915e20	−1.03004	−0.515019	+	0.857179i	$0.672215\pi$
$284$	1.51387e21	2.12268
$285$	−4.12263e20	−0.561040
$286$	−7.16715e20	−0.946749
$287$	7.10469e19	0.0911064
$288$	−3.62608e20	−0.451441
$289$	−7.07031e20	−0.854686
$290$	2.37081e20	0.278300
$291$	−1.40428e21	−1.60090
$292$	1.87708e21	2.07839
$293$	3.49413e20	0.375806	0.187903	−	0.982188i	$-0.439831\pi$
$293$	3.49413e20	0.375806	0.187903	+	0.982188i	$0.439831\pi$
$294$	−2.51926e21	−2.63221
$295$	1.54004e21	1.56331
$296$	1.87705e21	1.85139
$297$	−6.32884e20	−0.606589
$298$	3.05866e21	2.84900
$299$	4.88657e20	0.442383
$300$	−7.65537e20	−0.673652
$301$	−1.05899e20	−0.0905889
$302$	2.90352e21	2.41472
$303$	−1.21999e21	−0.986497
$304$	−3.73682e20	−0.293817
$305$	1.06652e21	0.815492
$306$	−1.26019e21	−0.937140
$307$	−4.85152e20	−0.350915	−0.175457	−	0.984487i	$-0.556140\pi$
$307$	−4.85152e20	−0.350915	−0.175457	+	0.984487i	$0.556140\pi$
$308$	−2.55766e20	−0.179954
$309$	3.53313e20	0.241831
$310$	−2.20845e21	−1.47066
$311$	8.15051e19	0.0528106	0.0264053	−	0.999651i	$-0.491594\pi$
$311$	8.15051e19	0.0528106	0.0264053	+	0.999651i	$0.491594\pi$
$312$	2.41893e21	1.52514
$313$	−6.96402e20	−0.427300	−0.213650	−	0.976910i	$-0.568535\pi$
$313$	−6.96402e20	−0.427300	−0.213650	+	0.976910i	$0.568535\pi$
$314$	−6.49684e20	−0.387972
$315$	2.35436e20	0.136846
$316$	6.07725e21	3.43848
$317$	−1.74073e20	−0.0958798	−0.0479399	−	0.998850i	$-0.515266\pi$
$317$	−1.74073e20	−0.0958798	−0.0479399	+	0.998850i	$0.515266\pi$
$318$	−8.17710e21	−4.38499
$319$	−3.11766e20	−0.162783
$320$	−2.16772e21	−1.10212
$321$	4.91095e20	0.243149
$322$	2.65991e20	0.128260
$323$	3.31269e20	0.155582
$324$	−1.50311e21	−0.687636
$325$	−3.22040e20	−0.143516
$326$	1.72734e21	0.749942
$327$	−8.70094e20	−0.368053
$328$	3.15564e21	1.30065
$329$	−3.14294e20	−0.126232
$330$	−5.24599e21	−2.05333
$331$	1.98290e21	0.756422	0.378211	−	0.925719i	$-0.376539\pi$
$331$	1.98290e21	0.756422	0.378211	+	0.925719i	$0.376539\pi$
$332$	2.80666e21	1.04356
$333$	4.78690e21	1.73492
$334$	−3.66065e21	−1.29334
$335$	−2.04844e21	−0.705574
$336$	3.61317e20	0.121340
$337$	3.36216e21	1.10094	0.550471	−	0.834854i	$-0.314448\pi$
$337$	3.36216e21	1.10094	0.550471	+	0.834854i	$0.314448\pi$
$338$	−3.19269e21	−1.01945
$339$	−6.80734e21	−2.11973
$340$	−2.10152e21	−0.638208
$341$	2.90416e21	0.860218
$342$	−3.47279e21	−1.00336
$343$	−7.60838e20	−0.214433
$344$	−4.70363e21	−1.29326
$345$	3.57672e21	0.959450
$346$	−8.69791e21	−2.27650
$347$	−6.87056e21	−1.75465	−0.877327	−	0.479894i	$-0.840675\pi$
$347$	−6.87056e21	−1.75465	−0.877327	+	0.479894i	$0.840675\pi$
$348$	2.21678e21	0.552458
$349$	5.26478e21	1.28045	0.640227	−	0.768186i	$-0.278840\pi$
$349$	5.26478e21	1.28045	0.640227	+	0.768186i	$0.278840\pi$
$350$	−1.75297e20	−0.0416098
$351$	1.89305e21	0.438582
$352$	1.21292e21	0.274297
$353$	7.61718e21	1.68155	0.840774	−	0.541387i	$-0.182101\pi$
$353$	7.61718e21	1.68155	0.840774	+	0.541387i	$0.182101\pi$
$354$	2.19647e22	4.73366
$355$	4.66137e21	0.980783
$356$	8.50157e21	1.74652
$357$	−3.20307e20	−0.0642521
$358$	2.42168e21	0.474364
$359$	6.16367e20	0.117906	0.0589531	−	0.998261i	$-0.481224\pi$
$359$	6.16367e20	0.117906	0.0589531	+	0.998261i	$0.481224\pi$
$360$	1.04572e22	1.95363
$361$	−4.56749e21	−0.833424
$362$	1.05823e21	0.188607
$363$	−2.07870e21	−0.361897
$364$	7.65034e20	0.130113
$365$	5.77972e21	0.960323
$366$	1.52111e22	2.46929
$367$	−6.11806e21	−0.970403	−0.485201	−	0.874402i	$-0.661254\pi$
$367$	−6.11806e21	−0.970403	−0.485201	+	0.874402i	$0.661254\pi$
$368$	3.24199e21	0.502464
$369$	8.04759e21	1.21883
$370$	1.21764e22	1.80220
$371$	−1.22755e21	−0.177567
$372$	−2.06497e22	−2.91944
$373$	−2.66728e21	−0.368590	−0.184295	−	0.982871i	$-0.559000\pi$
$373$	−2.66728e21	−0.368590	−0.184295	+	0.982871i	$0.559000\pi$
$374$	4.21534e21	0.569409
$375$	−1.27672e22	−1.68590
$376$	−1.39598e22	−1.80211
$377$	9.32538e20	0.117697
$378$	1.03045e21	0.127158
$379$	7.99626e21	0.964837	0.482418	−	0.875941i	$-0.339758\pi$
$379$	7.99626e21	0.964837	0.482418	+	0.875941i	$0.339758\pi$
$380$	−5.79129e21	−0.683305
$381$	1.01330e22	1.16917
$382$	−1.34148e21	−0.151372
$383$	−3.17222e21	−0.350085	−0.175043	−	0.984561i	$-0.556006\pi$
$383$	−3.17222e21	−0.350085	−0.175043	+	0.984561i	$0.556006\pi$
$384$	−2.63862e22	−2.84814
$385$	−7.87532e20	−0.0831480
$386$	−2.11940e22	−2.18888
$387$	−1.19953e22	−1.21190
$388$	−1.97267e22	−1.94978
$389$	1.28849e22	1.24598	0.622988	−	0.782231i	$-0.285919\pi$
$389$	1.28849e22	1.24598	0.622988	+	0.782231i	$0.285919\pi$
$390$	1.56915e22	1.48462
$391$	−2.87402e21	−0.266065
$392$	−1.67980e22	−1.52169
$393$	−2.66937e22	−2.36631
$394$	3.09131e22	2.68179
$395$	1.87125e22	1.58875
$396$	−2.89711e22	−2.40744
$397$	−8.69038e21	−0.706837	−0.353419	−	0.935465i	$-0.614981\pi$
$397$	−8.69038e21	−0.706837	−0.353419	+	0.935465i	$0.614981\pi$
$398$	2.72169e22	2.16687
$399$	−8.82691e20	−0.0687922
$400$	−2.13658e21	−0.163008
$401$	4.36758e20	0.0326222	0.0163111	−	0.999867i	$-0.494808\pi$
$401$	4.36758e20	0.0326222	0.0163111	+	0.999867i	$0.494808\pi$
$402$	−2.92157e22	−2.13646
$403$	−8.68677e21	−0.621964
$404$	−1.71379e22	−1.20148
$405$	−4.62824e21	−0.317723
$406$	5.07611e20	0.0341240
$407$	−1.60122e22	−1.05414
$408$	−1.42269e22	−0.917272
$409$	2.33651e22	1.47543	0.737715	−	0.675112i	$-0.235905\pi$
$409$	2.33651e22	1.47543	0.737715	+	0.675112i	$0.235905\pi$
$410$	2.04705e22	1.26610
$411$	−1.39100e22	−0.842697
$412$	4.96318e21	0.294533
$413$	3.29736e21	0.191686
$414$	3.01293e22	1.71587
$415$	8.64202e21	0.482177
$416$	−3.62803e21	−0.198325
$417$	−2.07599e22	−1.11191
$418$	1.16165e22	0.609644
$419$	1.48396e22	0.763139	0.381569	−	0.924340i	$-0.375384\pi$
$419$	1.48396e22	0.763139	0.381569	+	0.924340i	$0.375384\pi$
$420$	5.59966e21	0.282191
$421$	2.90867e22	1.43647	0.718236	−	0.695800i	$-0.244950\pi$
$421$	2.90867e22	1.43647	0.718236	+	0.695800i	$0.244950\pi$
$422$	1.97657e22	0.956659
$423$	−3.56005e22	−1.68874
$424$	−5.45234e22	−2.53497
$425$	1.89407e21	0.0863159
$426$	6.64825e22	2.96979
$427$	2.28351e21	0.0999920
$428$	6.89868e21	0.296138
$429$	−2.06347e22	−0.868381
$430$	−3.05123e22	−1.25890
$431$	−2.74838e22	−1.11178	−0.555892	−	0.831255i	$-0.687623\pi$
$431$	−2.74838e22	−1.11178	−0.555892	+	0.831255i	$0.687623\pi$
$432$	1.25594e22	0.498147
$433$	7.84182e21	0.304979	0.152489	−	0.988305i	$-0.451271\pi$
$433$	7.84182e21	0.304979	0.152489	+	0.988305i	$0.451271\pi$
$434$	−4.72849e21	−0.180326
$435$	6.82571e21	0.255264
$436$	−1.22227e22	−0.448262
$437$	−7.92013e21	−0.284866
$438$	8.24328e22	2.90784
$439$	−1.59731e22	−0.552637	−0.276319	−	0.961066i	$-0.589115\pi$
$439$	−1.59731e22	−0.552637	−0.276319	+	0.961066i	$0.589115\pi$
$440$	−3.49793e22	−1.18703
$441$	−4.28386e22	−1.42596
$442$	−1.26087e22	−0.411700
$443$	2.94720e22	0.944013	0.472007	−	0.881595i	$-0.343530\pi$
$443$	2.94720e22	0.944013	0.472007	+	0.881595i	$0.343530\pi$
$444$	1.13853e23	3.57758
$445$	2.61772e22	0.806982
$446$	−1.33061e22	−0.402443
$447$	8.80607e22	2.61317
$448$	−4.64128e21	−0.135137
$449$	6.31767e22	1.80494	0.902470	−	0.430752i	$-0.141752\pi$
$449$	6.31767e22	1.80494	0.902470	+	0.430752i	$0.141752\pi$
$450$	−1.98561e22	−0.556658
$451$	−2.69192e22	−0.740562
$452$	−9.56265e22	−2.58167
$453$	8.35943e22	2.21484
$454$	1.53729e22	0.399744
$455$	2.35562e21	0.0601186
$456$	−3.92059e22	−0.982087
$457$	−5.41927e22	−1.33246	−0.666228	−	0.745748i	$-0.732092\pi$
$457$	−5.41927e22	−1.33246	−0.666228	+	0.745748i	$0.732092\pi$
$458$	8.84246e21	0.213411
$459$	−1.11339e22	−0.263779
$460$	5.02441e22	1.16854
$461$	−6.10164e22	−1.39312	−0.696560	−	0.717499i	$-0.745287\pi$
$461$	−6.10164e22	−1.39312	−0.696560	+	0.717499i	$0.745287\pi$
$462$	−1.12321e22	−0.251770
$463$	2.32813e22	0.512351	0.256176	−	0.966630i	$-0.417537\pi$
$463$	2.32813e22	0.512351	0.256176	+	0.966630i	$0.417537\pi$
$464$	6.18692e21	0.133682
$465$	−6.35827e22	−1.34893
$466$	−1.27947e23	−2.66533
$467$	−1.94649e22	−0.398161	−0.199080	−	0.979983i	$-0.563796\pi$
$467$	−1.94649e22	−0.398161	−0.199080	+	0.979983i	$0.563796\pi$
$468$	8.66566e22	1.74065
$469$	−4.38589e21	−0.0865144
$470$	−9.05565e22	−1.75423
$471$	−1.87048e22	−0.355857
$472$	1.46457e23	2.73654
$473$	4.01243e22	0.736356
$474$	2.66885e23	4.81071
$475$	5.21962e21	0.0924151
$476$	−4.49953e21	−0.0782543
$477$	−1.39047e23	−2.37550
$478$	1.76713e23	2.96572
$479$	−3.32545e22	−0.548275	−0.274137	−	0.961691i	$-0.588392\pi$
$479$	−3.32545e22	−0.548275	−0.274137	+	0.961691i	$0.588392\pi$
$480$	−2.65553e22	−0.430131
$481$	4.78948e22	0.762176
$482$	1.16549e22	0.182225
$483$	7.65806e21	0.117644
$484$	−2.92006e22	−0.440764
$485$	−6.07407e22	−0.900896
$486$	−1.46912e23	−2.14115
$487$	3.28210e21	0.0470063	0.0235031	−	0.999724i	$-0.492518\pi$
$487$	3.28210e21	0.0470063	0.0235031	+	0.999724i	$0.492518\pi$
$488$	1.01425e23	1.42750
$489$	4.97311e22	0.687864
$490$	−1.08968e23	−1.48126
$491$	2.84768e22	0.380450	0.190225	−	0.981740i	$-0.439078\pi$
$491$	2.84768e22	0.380450	0.190225	+	0.981740i	$0.439078\pi$
$492$	1.91406e23	2.51335
$493$	−5.48470e21	−0.0707871
$494$	−3.47466e22	−0.440791
$495$	−8.92050e22	−1.11236
$496$	−5.76323e22	−0.706435
$497$	9.98040e21	0.120259
$498$	1.23256e23	1.46002
$499$	−3.85028e22	−0.448371	−0.224186	−	0.974546i	$-0.571972\pi$
$499$	−3.85028e22	−0.448371	−0.224186	+	0.974546i	$0.571972\pi$
$500$	−1.79348e23	−2.05330
$501$	−1.05392e23	−1.18628
$502$	9.81624e22	1.08633
$503$	−8.27652e22	−0.900575	−0.450287	−	0.892884i	$-0.648678\pi$
$503$	−8.27652e22	−0.900575	−0.450287	+	0.892884i	$0.648678\pi$
$504$	2.23897e22	0.239546
$505$	−5.27695e22	−0.555145
$506$	−1.00782e23	−1.04257
$507$	−9.19194e22	−0.935061
$508$	1.42344e23	1.42396
$509$	−1.71083e22	−0.168309	−0.0841543	−	0.996453i	$-0.526819\pi$
$509$	−1.71083e22	−0.168309	−0.0841543	+	0.996453i	$0.526819\pi$
$510$	−9.22892e22	−0.892903
$511$	1.23749e22	0.117751
$512$	−1.42503e23	−1.33361
$513$	−3.06824e22	−0.282418
$514$	−2.27442e22	−0.205913
$515$	1.52821e22	0.136089
$516$	−2.85299e23	−2.49907
$517$	1.19084e23	1.02608
$518$	2.60707e22	0.220978
$519$	−2.50418e23	−2.08806
$520$	1.04628e23	0.858261
$521$	−5.27327e22	−0.425559	−0.212779	−	0.977100i	$-0.568252\pi$
$521$	−5.27327e22	−0.425559	−0.212779	+	0.977100i	$0.568252\pi$
$522$	5.74978e22	0.456512
$523$	−9.98311e22	−0.779833	−0.389916	−	0.920850i	$-0.627496\pi$
$523$	−9.98311e22	−0.779833	−0.389916	+	0.920850i	$0.627496\pi$
$524$	−3.74981e23	−2.88200
$525$	−5.04691e21	−0.0381655
$526$	4.12438e23	3.06888
$527$	5.10910e22	0.374071
$528$	−1.36901e23	−0.986318
$529$	−7.23365e22	−0.512843
$530$	−3.53691e23	−2.46763
$531$	3.73497e23	2.56439
$532$	−1.23997e22	−0.0837839
$533$	8.05192e22	0.535449
$534$	3.73351e23	2.44352
$535$	2.12418e22	0.136831
$536$	−1.94805e23	−1.23509
$537$	6.97217e22	0.435098
$538$	5.25883e23	3.23027
$539$	1.43295e23	0.866417
$540$	1.94645e23	1.15850
$541$	−1.32366e23	−0.775532	−0.387766	−	0.921758i	$-0.626753\pi$
$541$	−1.32366e23	−0.775532	−0.387766	+	0.921758i	$0.626753\pi$
$542$	1.27463e22	0.0735176
$543$	3.04672e22	0.172995
$544$	2.13382e22	0.119280
$545$	−3.76349e22	−0.207119
$546$	3.35968e22	0.182038
$547$	2.22866e23	1.18892	0.594458	−	0.804126i	$-0.297366\pi$
$547$	2.22866e23	1.18892	0.594458	+	0.804126i	$0.297366\pi$
$548$	−1.95401e23	−1.02634
$549$	2.58656e23	1.33770
$550$	6.64188e22	0.338227
$551$	−1.51145e22	−0.0757891
$552$	3.40143e23	1.67950
$553$	4.00651e22	0.194806
$554$	3.05565e23	1.46309
$555$	3.50565e23	1.65302
$556$	−2.91625e23	−1.35422
$557$	−2.46656e23	−1.12803	−0.564017	−	0.825763i	$-0.690745\pi$
$557$	−2.46656e23	−1.12803	−0.564017	+	0.825763i	$0.690745\pi$
$558$	−5.35603e23	−2.41242
$559$	−1.20018e23	−0.532408
$560$	1.56284e22	0.0682834
$561$	1.21362e23	0.522275
$562$	3.89711e23	1.65190
$563$	1.27538e23	0.532500	0.266250	−	0.963904i	$-0.414215\pi$
$563$	1.27538e23	0.532500	0.266250	+	0.963904i	$0.414215\pi$
$564$	−8.46732e23	−3.48236
$565$	−2.94444e23	−1.19286
$566$	−4.39801e23	−1.75516
$567$	−9.90946e21	−0.0389578
$568$	4.43293e23	1.71684
$569$	−9.14120e22	−0.348778	−0.174389	−	0.984677i	$-0.555795\pi$
$569$	−9.14120e22	−0.348778	−0.174389	+	0.984677i	$0.555795\pi$
$570$	−2.54327e23	−0.955997
$571$	4.57553e23	1.69447	0.847237	−	0.531215i	$-0.178264\pi$
$571$	4.57553e23	1.69447	0.847237	+	0.531215i	$0.178264\pi$
$572$	−2.89866e23	−1.05762
$573$	−3.86220e22	−0.138842
$574$	4.38292e22	0.155243
$575$	−4.52844e22	−0.158042
$576$	−5.25724e23	−1.80787
$577$	−2.90602e23	−0.984702	−0.492351	−	0.870397i	$-0.663862\pi$
$577$	−2.90602e23	−0.984702	−0.492351	+	0.870397i	$0.663862\pi$
$578$	−4.36171e23	−1.45636
$579$	−6.10190e23	−2.00769
$580$	9.58844e22	0.310892
$581$	1.85033e22	0.0591224
$582$	−8.66309e23	−2.72789
$583$	4.65112e23	1.44336
$584$	5.49646e23	1.68102
$585$	2.66825e23	0.804269
$586$	2.15554e23	0.640365
$587$	4.87166e23	1.42644	0.713219	−	0.700941i	$-0.247236\pi$
$587$	4.87166e23	1.42644	0.713219	+	0.700941i	$0.247236\pi$
$588$	−1.01888e24	−2.94048
$589$	1.40795e23	0.400504
$590$	9.50058e23	2.66384
$591$	8.90008e23	2.45980
$592$	3.17758e23	0.865689
$593$	−1.95140e23	−0.524061	−0.262031	−	0.965060i	$-0.584392\pi$
$593$	−1.95140e23	−0.524061	−0.262031	+	0.965060i	$0.584392\pi$
$594$	−3.90429e23	−1.03361
$595$	−1.38545e22	−0.0361575
$596$	1.23704e24	3.18265
$597$	7.83592e23	1.98750
$598$	3.01455e23	0.753810
$599$	−6.05879e23	−1.49368	−0.746841	−	0.665003i	$-0.768430\pi$
$599$	−6.05879e23	−1.49368	−0.746841	+	0.665003i	$0.768430\pi$
$600$	−2.24165e23	−0.544856
$601$	−3.30763e23	−0.792655	−0.396327	−	0.918109i	$-0.629715\pi$
$601$	−3.30763e23	−0.792655	−0.396327	+	0.918109i	$0.629715\pi$
$602$	−6.53294e22	−0.154361
$603$	−4.96796e23	−1.15739
$604$	1.17429e24	2.69751
$605$	−8.99117e22	−0.203655
$606$	−7.52621e23	−1.68097
$607$	−3.52469e23	−0.776277	−0.388138	−	0.921601i	$-0.626882\pi$
$607$	−3.52469e23	−0.776277	−0.388138	+	0.921601i	$0.626882\pi$
$608$	5.88029e22	0.127708
$609$	1.46144e22	0.0312993
$610$	6.57940e23	1.38958
$611$	−3.56196e23	−0.741890
$612$	−5.09669e23	−1.04689
$613$	−5.57210e22	−0.112877	−0.0564385	−	0.998406i	$-0.517974\pi$
$613$	−5.57210e22	−0.112877	−0.0564385	+	0.998406i	$0.517974\pi$
$614$	−2.99293e23	−0.597950
$615$	5.89359e23	1.16129
$616$	−7.48936e22	−0.145549
$617$	8.07897e23	1.54858	0.774288	−	0.632834i	$-0.218108\pi$
$617$	8.07897e23	1.54858	0.774288	+	0.632834i	$0.218108\pi$
$618$	2.17960e23	0.412074
$619$	8.02898e23	1.49723	0.748617	−	0.663002i	$-0.230718\pi$
$619$	8.02898e23	1.49723	0.748617	+	0.663002i	$0.230718\pi$
$620$	−8.93181e23	−1.64290
$621$	2.66195e23	0.482971
$622$	5.02809e22	0.0899880
$623$	5.60477e22	0.0989486
$624$	4.09489e23	0.713138
$625$	−4.20432e23	−0.722297
$626$	−4.29614e23	−0.728109
$627$	3.34446e23	0.559180
$628$	−2.62757e23	−0.433408
$629$	−2.81692e23	−0.458400
$630$	1.45241e23	0.233182
$631$	8.50827e23	1.34770	0.673848	−	0.738870i	$-0.264640\pi$
$631$	8.50827e23	1.34770	0.673848	+	0.738870i	$0.264640\pi$
$632$	1.77954e24	2.78108
$633$	5.69068e23	0.877471
$634$	−1.07386e23	−0.163377
$635$	4.38294e23	0.657943
$636$	−3.30713e24	−4.89853
$637$	−4.28616e23	−0.626446
$638$	−1.92330e23	−0.277378
$639$	1.13050e24	1.60884
$640$	−1.14131e24	−1.60277
$641$	5.24512e23	0.726879	0.363439	−	0.931618i	$-0.381602\pi$
$641$	5.24512e23	0.726879	0.363439	+	0.931618i	$0.381602\pi$
$642$	3.02959e23	0.414320
$643$	−4.45693e23	−0.601510	−0.300755	−	0.953701i	$-0.597239\pi$
$643$	−4.45693e23	−0.601510	−0.300755	+	0.953701i	$0.597239\pi$
$644$	1.07577e23	0.143281
$645$	−8.78467e23	−1.15470
$646$	2.04361e23	0.265108
$647$	1.34835e24	1.72630	0.863151	−	0.504946i	$-0.168488\pi$
$647$	1.34835e24	1.72630	0.863151	+	0.504946i	$0.168488\pi$
$648$	−4.40142e23	−0.556167
$649$	−1.24935e24	−1.55813
$650$	−1.98668e23	−0.244548
$651$	−1.36136e23	−0.165400
$652$	6.98600e23	0.837769
$653$	5.92522e23	0.701363	0.350681	−	0.936495i	$-0.385950\pi$
$653$	5.92522e23	0.701363	0.350681	+	0.936495i	$0.385950\pi$
$654$	−5.36765e23	−0.627153
$655$	−1.15461e24	−1.33163
$656$	5.34204e23	0.608170
$657$	1.40172e24	1.57527
$658$	−1.93889e23	−0.215097
$659$	−5.92079e23	−0.648416	−0.324208	−	0.945986i	$-0.605098\pi$
$659$	−5.92079e23	−0.648416	−0.324208	+	0.945986i	$0.605098\pi$
$660$	−2.12167e24	−2.29380
$661$	1.59306e23	0.170028	0.0850138	−	0.996380i	$-0.472907\pi$
$661$	1.59306e23	0.170028	0.0850138	+	0.996380i	$0.472907\pi$
$662$	1.22326e24	1.28892
$663$	−3.63012e23	−0.377621
$664$	8.21848e23	0.844040
$665$	−3.81798e22	−0.0387124
$666$	2.95306e24	2.95626
$667$	1.31131e23	0.129609
$668$	−1.48051e24	−1.44481
$669$	−3.83091e23	−0.369130
$670$	−1.26369e24	−1.20228
$671$	−8.65205e23	−0.812789
$672$	−5.68572e22	−0.0527408
$673$	−1.08833e24	−0.996853	−0.498427	−	0.866932i	$-0.666089\pi$
$673$	−1.08833e24	−0.996853	−0.498427	+	0.866932i	$0.666089\pi$
$674$	2.07413e24	1.87598
$675$	−1.75431e23	−0.156684
$676$	−1.29124e24	−1.13884
$677$	−1.36486e24	−1.18873	−0.594365	−	0.804196i	$-0.702596\pi$
$677$	−1.36486e24	−1.18873	−0.594365	+	0.804196i	$0.702596\pi$
$678$	−4.19948e24	−3.61196
$679$	−1.30051e23	−0.110464
$680$	−6.15367e23	−0.516189
$681$	4.42596e23	0.366654
$682$	1.79159e24	1.46579
$683$	1.66169e24	1.34269	0.671344	−	0.741146i	$-0.265717\pi$
$683$	1.66169e24	1.34269	0.671344	+	0.741146i	$0.265717\pi$
$684$	−1.40453e24	−1.12087
$685$	−6.01661e23	−0.474222
$686$	−4.69365e23	−0.365389
$687$	2.54580e23	0.195746
$688$	−7.96256e23	−0.604715
$689$	−1.39122e24	−1.04359
$690$	2.20649e24	1.63488
$691$	−1.86577e24	−1.36551	−0.682756	−	0.730646i	$-0.739219\pi$
$691$	−1.86577e24	−1.36551	−0.682756	+	0.730646i	$0.739219\pi$
$692$	−3.51776e24	−2.54311
$693$	−1.90995e23	−0.136393
$694$	−4.23848e24	−2.98989
$695$	−8.97945e23	−0.625718
$696$	6.49119e23	0.446833
$697$	−4.73572e23	−0.322038
$698$	3.24787e24	2.18186
$699$	−3.68368e24	−2.44470
$700$	−7.08966e22	−0.0464828
$701$	−1.63544e24	−1.05933	−0.529666	−	0.848206i	$-0.677683\pi$
$701$	−1.63544e24	−1.05933	−0.529666	+	0.848206i	$0.677683\pi$
$702$	1.16783e24	0.747333
$703$	−7.76277e23	−0.490791
$704$	1.75855e24	1.09847
$705$	−2.60718e24	−1.60903
$706$	4.69907e24	2.86531
$707$	−1.12984e23	−0.0680695
$708$	8.88335e24	5.28803
$709$	5.44397e23	0.320201	0.160101	−	0.987101i	$-0.448818\pi$
$709$	5.44397e23	0.320201	0.160101	+	0.987101i	$0.448818\pi$
$710$	2.87562e24	1.67123
$711$	4.53823e24	2.60612
$712$	2.48943e24	1.41260
$713$	−1.22151e24	−0.684913
$714$	−1.97599e23	−0.109484
$715$	−8.92529e23	−0.488676
$716$	9.79420e23	0.529917
$717$	5.08767e24	2.72023
$718$	3.80240e23	0.200909
$719$	−1.75855e24	−0.918247	−0.459123	−	0.888372i	$-0.651836\pi$
$719$	−1.75855e24	−0.918247	−0.459123	+	0.888372i	$0.651836\pi$
$720$	1.77025e24	0.913499
$721$	3.27204e22	0.0166866
$722$	−2.81771e24	−1.42013
$723$	3.35551e23	0.167141
$724$	4.27989e23	0.210695
$725$	−8.64194e22	−0.0420473
$726$	−1.28236e24	−0.616663
$727$	2.90848e24	1.38237	0.691185	−	0.722678i	$-0.257089\pi$
$727$	2.90848e24	1.38237	0.691185	+	0.722678i	$0.257089\pi$
$728$	2.24018e23	0.105236
$729$	−3.45167e24	−1.60268
$730$	3.56554e24	1.63637
$731$	7.05881e23	0.320209
$732$	6.15195e24	2.75847
$733$	2.06719e24	0.916213	0.458106	−	0.888897i	$-0.348528\pi$
$733$	2.06719e24	0.916213	0.458106	+	0.888897i	$0.348528\pi$
$734$	−3.77426e24	−1.65354
$735$	−3.13725e24	−1.35865
$736$	−5.10163e23	−0.218397
$737$	1.66178e24	0.703235
$738$	4.96460e24	2.07685
$739$	−8.82599e23	−0.364994	−0.182497	−	0.983206i	$-0.558418\pi$
$739$	−8.82599e23	−0.364994	−0.182497	+	0.983206i	$0.558418\pi$
$740$	4.92459e24	2.01326
$741$	−1.00038e24	−0.404304
$742$	−7.57284e23	−0.302570
$743$	−4.67097e24	−1.84502	−0.922512	−	0.385967i	$-0.873868\pi$
$743$	−4.67097e24	−1.84502	−0.922512	+	0.385967i	$0.873868\pi$
$744$	−6.04666e24	−2.36127
$745$	3.80897e24	1.47055
$746$	−1.64546e24	−0.628068
$747$	2.09590e24	0.790942
$748$	1.70484e24	0.636093
$749$	4.54805e22	0.0167776
$750$	−7.87617e24	−2.87273
$751$	4.67198e24	1.68485	0.842426	−	0.538813i	$-0.181127\pi$
$751$	4.67198e24	1.68485	0.842426	+	0.538813i	$0.181127\pi$
$752$	−2.36319e24	−0.842648
$753$	2.82616e24	0.996412
$754$	5.75287e23	0.200553
$755$	3.61578e24	1.24639
$756$	4.16751e23	0.142050
$757$	−4.38253e24	−1.47710	−0.738550	−	0.674198i	$-0.764489\pi$
$757$	−4.38253e24	−1.47710	−0.738550	+	0.674198i	$0.764489\pi$
$758$	4.93293e24	1.64406
$759$	−2.90159e24	−0.956270
$760$	−1.69581e24	−0.552664
$761$	−2.60349e24	−0.839046	−0.419523	−	0.907745i	$-0.637803\pi$
$761$	−2.60349e24	−0.839046	−0.419523	+	0.907745i	$0.637803\pi$
$762$	6.25113e24	1.99224
$763$	−8.05796e22	−0.0253961
$764$	−5.42544e23	−0.169099
$765$	−1.56932e24	−0.483716
$766$	−1.95696e24	−0.596537
$767$	3.73698e24	1.12657
$768$	−9.70895e24	−2.89469
$769$	4.34175e24	1.28024	0.640119	−	0.768275i	$-0.278885\pi$
$769$	4.34175e24	1.28024	0.640119	+	0.768275i	$0.278885\pi$
$770$	−4.85832e23	−0.141682
$771$	−6.54821e23	−0.188869
$772$	−8.57167e24	−2.44522
$773$	−4.32285e24	−1.21968	−0.609838	−	0.792526i	$-0.708765\pi$
$773$	−4.32285e24	−1.21968	−0.609838	+	0.792526i	$0.708765\pi$
$774$	−7.39996e24	−2.06505
$775$	8.05013e23	0.222197
$776$	−5.77639e24	−1.57700
$777$	7.50591e23	0.202686
$778$	7.94876e24	2.12311
$779$	−1.30505e24	−0.344794
$780$	6.34623e24	1.65849
$781$	−3.78151e24	−0.977533
$782$	−1.77300e24	−0.453368
$783$	5.07999e23	0.128495
$784$	−2.84365e24	−0.711525
$785$	−8.09055e23	−0.200256
$786$	−1.64675e25	−4.03214
$787$	−2.56312e24	−0.620847	−0.310423	−	0.950598i	$-0.600471\pi$
$787$	−2.56312e24	−0.620847	−0.310423	+	0.950598i	$0.600471\pi$
$788$	1.25024e25	2.99586
$789$	1.18743e25	2.81485
$790$	1.15438e25	2.70720
$791$	−6.30430e23	−0.146264
$792$	−8.48331e24	−1.94716
$793$	2.58795e24	0.587671
$794$	−5.36114e24	−1.20443
$795$	−1.01830e25	−2.26337
$796$	1.10075e25	2.42063
$797$	−2.79968e24	−0.609133	−0.304567	−	0.952491i	$-0.598512\pi$
$797$	−2.79968e24	−0.609133	−0.304567	+	0.952491i	$0.598512\pi$
$798$	−5.44537e23	−0.117220
$799$	2.09496e24	0.446199
$800$	3.36214e23	0.0708517
$801$	6.34861e24	1.32374
$802$	2.69438e23	0.0555874
$803$	−4.68876e24	−0.957140
$804$	−1.18159e25	−2.38666
$805$	3.31241e23	0.0662032
$806$	−5.35891e24	−1.05981
$807$	1.51405e25	2.96289
$808$	−5.01834e24	−0.971769
$809$	−4.86003e24	−0.931272	−0.465636	−	0.884976i	$-0.654174\pi$
$809$	−4.86003e24	−0.931272	−0.465636	+	0.884976i	$0.654174\pi$
$810$	−2.85518e24	−0.541391
$811$	−1.04176e25	−1.95476	−0.977378	−	0.211502i	$-0.932165\pi$
$811$	−1.04176e25	−1.95476	−0.977378	+	0.211502i	$0.932165\pi$
$812$	2.05297e23	0.0381203
$813$	3.66975e23	0.0674321
$814$	−9.87800e24	−1.79623
$815$	2.15106e24	0.387091
$816$	−2.40840e24	−0.428907
$817$	1.94524e24	0.342835
$818$	1.44140e25	2.51410
$819$	5.71295e23	0.0986160
$820$	8.27905e24	1.41437
$821$	−7.25397e24	−1.22647	−0.613237	−	0.789899i	$-0.710133\pi$
$821$	−7.25397e24	−1.22647	−0.613237	+	0.789899i	$0.710133\pi$
$822$	−8.58114e24	−1.43593
$823$	8.00151e24	1.32518	0.662588	−	0.748984i	$-0.269458\pi$
$823$	8.00151e24	1.32518	0.662588	+	0.748984i	$0.269458\pi$
$824$	1.45332e24	0.238221
$825$	1.91224e24	0.310230
$826$	2.03416e24	0.326628
$827$	−3.05939e24	−0.486226	−0.243113	−	0.969998i	$-0.578169\pi$
$827$	−3.05939e24	−0.486226	−0.243113	+	0.969998i	$0.578169\pi$
$828$	1.21854e25	1.91682
$829$	8.57946e24	1.33582	0.667908	−	0.744244i	$-0.267190\pi$
$829$	8.57946e24	1.33582	0.667908	+	0.744244i	$0.267190\pi$
$830$	5.33130e24	0.821617
$831$	8.79741e24	1.34198
$832$	−5.26007e24	−0.794224
$833$	2.52090e24	0.376767
$834$	−1.28069e25	−1.89466
$835$	−4.55863e24	−0.667575
$836$	4.69814e24	0.681041
$837$	−4.73210e24	−0.679028
$838$	9.15463e24	1.30037
$839$	1.95760e24	0.275262	0.137631	−	0.990484i	$-0.456051\pi$
$839$	1.95760e24	0.275262	0.137631	+	0.990484i	$0.456051\pi$
$840$	1.63969e24	0.228239
$841$	2.50246e23	0.0344828
$842$	1.79437e25	2.44771
$843$	1.12200e25	1.51516
$844$	7.99401e24	1.06870
$845$	−3.97587e24	−0.526200
$846$	−2.19621e25	−2.87757
$847$	−1.92509e23	−0.0249713
$848$	−9.23002e24	−1.18533
$849$	−1.26621e25	−1.60987
$850$	1.16846e24	0.147080
$851$	6.73483e24	0.839316
$852$	2.68880e25	3.31759
$853$	−9.66703e24	−1.18094	−0.590468	−	0.807061i	$-0.701057\pi$
$853$	−9.66703e24	−1.18094	−0.590468	+	0.807061i	$0.701057\pi$
$854$	1.40871e24	0.170384
$855$	−4.32469e24	−0.517896
$856$	2.02007e24	0.239519
$857$	1.08428e25	1.27293	0.636465	−	0.771305i	$-0.280396\pi$
$857$	1.08428e25	1.27293	0.636465	+	0.771305i	$0.280396\pi$
$858$	−1.27296e25	−1.47970
$859$	1.74432e24	0.200764	0.100382	−	0.994949i	$-0.467994\pi$
$859$	1.74432e24	0.200764	0.100382	+	0.994949i	$0.467994\pi$
$860$	−1.23403e25	−1.40634
$861$	1.26187e24	0.142393
$862$	−1.69549e25	−1.89445
$863$	−7.07810e24	−0.783114	−0.391557	−	0.920154i	$-0.628063\pi$
$863$	−7.07810e24	−0.783114	−0.391557	+	0.920154i	$0.628063\pi$
$864$	−1.97636e24	−0.216521
$865$	−1.08316e25	−1.17504
$866$	4.83766e24	0.519676
$867$	−1.25576e25	−1.33581
$868$	−1.91238e24	−0.201445
$869$	−1.51804e25	−1.58349
$870$	4.21081e24	0.434963
$871$	−4.97063e24	−0.508460
$872$	−3.57905e24	−0.362558
$873$	−1.47311e25	−1.47779
$874$	−4.88597e24	−0.485404
$875$	−1.18238e24	−0.116329
$876$	3.33389e25	3.24838
$877$	−9.33647e24	−0.900920	−0.450460	−	0.892797i	$-0.648740\pi$
$877$	−9.33647e24	−0.900920	−0.450460	+	0.892797i	$0.648740\pi$
$878$	−9.85387e24	−0.941680
$879$	6.20595e24	0.587358
$880$	−5.92148e24	−0.555045
$881$	1.23542e25	1.14688	0.573442	−	0.819246i	$-0.305608\pi$
$881$	1.23542e25	1.14688	0.573442	+	0.819246i	$0.305608\pi$
$882$	−2.64273e25	−2.42980
$883$	−4.93699e24	−0.449568	−0.224784	−	0.974409i	$-0.572168\pi$
$883$	−4.93699e24	−0.449568	−0.224784	+	0.974409i	$0.572168\pi$
$884$	−5.09943e24	−0.459915
$885$	2.73528e25	2.44334
$886$	1.81814e25	1.60857
$887$	−1.33070e25	−1.16608	−0.583042	−	0.812442i	$-0.698138\pi$
$887$	−1.33070e25	−1.16608	−0.583042	+	0.812442i	$0.698138\pi$
$888$	3.33385e25	2.89358
$889$	9.38424e23	0.0806741
$890$	1.61489e25	1.37508
$891$	3.75463e24	0.316670
$892$	−5.38149e24	−0.449574
$893$	5.77322e24	0.477728
$894$	5.43251e25	4.45278
$895$	3.01574e24	0.244849
$896$	−2.44363e24	−0.196525
$897$	8.67906e24	0.691412
$898$	3.89740e25	3.07557
$899$	−2.33109e24	−0.182223
$900$	−8.03057e24	−0.621849
$901$	8.18241e24	0.627654
$902$	−1.66066e25	−1.26190
$903$	−1.88087e24	−0.141584
$904$	−2.80014e25	−2.08808
$905$	1.31782e24	0.0973518
$906$	5.15697e25	3.77403
$907$	−1.02480e25	−0.742977	−0.371488	−	0.928438i	$-0.621152\pi$
$907$	−1.02480e25	−0.742977	−0.371488	+	0.928438i	$0.621152\pi$
$908$	6.21739e24	0.446558
$909$	−1.27979e25	−0.910636
$910$	1.45319e24	0.102441
$911$	−3.99109e24	−0.278731	−0.139365	−	0.990241i	$-0.544506\pi$
$911$	−3.99109e24	−0.278731	−0.139365	+	0.990241i	$0.544506\pi$
$912$	−6.63699e24	−0.459214
$913$	−7.01078e24	−0.480579
$914$	−3.34317e25	−2.27047
$915$	1.89425e25	1.27455
$916$	3.57622e24	0.238404
$917$	−2.47211e24	−0.163279
$918$	−6.86857e24	−0.449473
$919$	8.49585e24	0.550839	0.275420	−	0.961324i	$-0.411183\pi$
$919$	8.49585e24	0.550839	0.275420	+	0.961324i	$0.411183\pi$
$920$	1.47125e25	0.945126
$921$	−8.61682e24	−0.548454
$922$	−3.76413e25	−2.37384
$923$	1.13110e25	0.706786
$924$	−4.54269e24	−0.281256
$925$	−4.43847e24	−0.272288
$926$	1.43623e25	0.873034
$927$	3.70629e24	0.223235
$928$	−9.73580e23	−0.0581051
$929$	−2.88104e25	−1.70379	−0.851895	−	0.523712i	$-0.824547\pi$
$929$	−2.88104e25	−1.70379	−0.851895	+	0.523712i	$0.824547\pi$
$930$	−3.92245e25	−2.29854
$931$	6.94700e24	0.403390
$932$	−5.17466e25	−2.97747
$933$	1.44762e24	0.0825392
$934$	−1.20080e25	−0.678456
$935$	5.24939e24	0.293907
$936$	2.53748e25	1.40786
$937$	1.04086e25	0.572277	0.286139	−	0.958188i	$-0.407628\pi$
$937$	1.04086e25	0.572277	0.286139	+	0.958188i	$0.407628\pi$
$938$	−2.70567e24	−0.147418
$939$	−1.23688e25	−0.667839
$940$	−3.66244e25	−1.95968
$941$	2.04560e25	1.08470	0.542349	−	0.840153i	$-0.317535\pi$
$941$	2.04560e25	1.08470	0.542349	+	0.840153i	$0.317535\pi$
$942$	−1.15391e25	−0.606371
$943$	1.13224e25	0.589642
$944$	2.47930e25	1.27958
$945$	1.28322e24	0.0656343
$946$	2.47529e25	1.25473
$947$	−3.70342e25	−1.86049	−0.930247	−	0.366934i	$-0.880408\pi$
$947$	−3.70342e25	−1.86049	−0.930247	+	0.366934i	$0.880408\pi$
$948$	1.07938e26	5.37410
$949$	1.40247e25	0.692042
$950$	3.22001e24	0.157473
$951$	−3.09172e24	−0.149853
$952$	−1.31755e24	−0.0632928
$953$	−1.70689e25	−0.812674	−0.406337	−	0.913723i	$-0.633194\pi$
$953$	−1.70689e25	−0.812674	−0.406337	+	0.913723i	$0.633194\pi$
$954$	−8.57787e25	−4.04779
$955$	−1.67055e24	−0.0781323
$956$	7.14693e25	3.31304
$957$	−5.53731e24	−0.254418
$958$	−2.05148e25	−0.934246
$959$	−1.28821e24	−0.0581471
$960$	−3.85010e25	−1.72253
$961$	−8.35555e23	−0.0370532
$962$	2.95465e25	1.29873
$963$	5.15164e24	0.224451
$964$	4.71367e24	0.203566
$965$	−2.63931e25	−1.12982
$966$	4.72429e24	0.200462
$967$	3.65492e25	1.53728	0.768641	−	0.639681i	$-0.220933\pi$
$967$	3.65492e25	1.53728	0.768641	+	0.639681i	$0.220933\pi$
$968$	−8.55052e24	−0.356494
$969$	5.88369e24	0.243163
$970$	−3.74712e25	−1.53510
$971$	3.73289e25	1.51594	0.757969	−	0.652290i	$-0.226192\pi$
$971$	3.73289e25	1.51594	0.757969	+	0.652290i	$0.226192\pi$
$972$	−5.94166e25	−2.39191
$973$	−1.92258e24	−0.0767228
$974$	2.02474e24	0.0800975
$975$	−5.71978e24	−0.224306
$976$	1.71698e25	0.667484
$977$	4.72931e25	1.82261	0.911305	−	0.411731i	$-0.135076\pi$
$977$	4.72931e25	1.82261	0.911305	+	0.411731i	$0.135076\pi$
$978$	3.06794e25	1.17210
$979$	−2.12361e25	−0.804307
$980$	−4.40707e25	−1.65474
$981$	−9.12738e24	−0.339750
$982$	1.75675e25	0.648278
$983$	−2.27666e25	−0.832900	−0.416450	−	0.909159i	$-0.636726\pi$
$983$	−2.27666e25	−0.832900	−0.416450	+	0.909159i	$0.636726\pi$
$984$	5.60476e25	2.03282
$985$	3.84963e25	1.38424
$986$	−3.38354e24	−0.120620
$987$	−5.58219e24	−0.197292
$988$	−1.40528e25	−0.492413
$989$	−1.68765e25	−0.586293
$990$	−5.50310e25	−1.89543
$991$	6.54550e24	0.223520	0.111760	−	0.993735i	$-0.464351\pi$
$991$	6.54550e24	0.223520	0.111760	+	0.993735i	$0.464351\pi$
$992$	9.06908e24	0.307054
$993$	3.52185e25	1.18223
$994$	6.15696e24	0.204919
$995$	3.38934e25	1.11846
$996$	4.98494e25	1.63101
$997$	3.73337e25	1.21113	0.605567	−	0.795795i	$-0.292947\pi$
$997$	3.73337e25	1.21113	0.605567	+	0.795795i	$0.292947\pi$
$998$	−2.37526e25	−0.764014
$999$	2.60906e25	0.832104

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.18.a.b.1.19	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.18.a.b.1.19	✓	21	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+616.905 q^{2} +17761.1 q^{3} +249500. q^{4} +768235. q^{5} +1.09569e7 q^{6} +1.64486e6 q^{7} +7.30585e7 q^{8} +1.86316e8 q^{9} +O(q^{10})\)	\(q+616.905 q^{2} +17761.1 q^{3} +249500. q^{4} +768235. q^{5} +1.09569e7 q^{6} +1.64486e6 q^{7} +7.30585e7 q^{8} +1.86316e8 q^{9} +4.73928e8 q^{10} -6.23226e8 q^{11} +4.43138e9 q^{12} +1.86416e9 q^{13} +1.01472e9 q^{14} +1.36447e10 q^{15} +1.23678e10 q^{16} -1.09640e10 q^{17} +1.14939e11 q^{18} -3.02142e10 q^{19} +1.91674e11 q^{20} +2.92144e10 q^{21} -3.84471e11 q^{22} +2.62133e11 q^{23} +1.29760e12 q^{24} -1.72754e11 q^{25} +1.15001e12 q^{26} +1.01550e12 q^{27} +4.10391e11 q^{28} +5.00246e11 q^{29} +8.41747e12 q^{30} -4.65989e12 q^{31} -1.94620e12 q^{32} -1.10692e13 q^{33} -6.76375e12 q^{34} +1.26364e12 q^{35} +4.64857e13 q^{36} +2.56925e13 q^{37} -1.86393e13 q^{38} +3.31094e13 q^{39} +5.61262e13 q^{40} +4.31933e13 q^{41} +1.80225e13 q^{42} -6.43816e13 q^{43} -1.55495e14 q^{44} +1.43134e14 q^{45} +1.61711e14 q^{46} -1.91076e14 q^{47} +2.19665e14 q^{48} -2.29925e14 q^{49} -1.06573e14 q^{50} -1.94733e14 q^{51} +4.65107e14 q^{52} -7.46298e14 q^{53} +6.26465e14 q^{54} -4.78784e14 q^{55} +1.20171e14 q^{56} -5.36637e14 q^{57} +3.08604e14 q^{58} +2.00465e15 q^{59} +3.40434e15 q^{60} +1.38827e15 q^{61} -2.87471e15 q^{62} +3.06463e14 q^{63} -2.82169e15 q^{64} +1.43211e15 q^{65} -6.82862e15 q^{66} -2.66642e15 q^{67} -2.73551e15 q^{68} +4.65576e15 q^{69} +7.79545e14 q^{70} +6.06764e15 q^{71} +1.36119e16 q^{72} +7.52337e15 q^{73} +1.58498e16 q^{74} -3.06829e15 q^{75} -7.53843e15 q^{76} -1.02512e15 q^{77} +2.04254e16 q^{78} +2.43578e16 q^{79} +9.50135e15 q^{80} -6.02451e15 q^{81} +2.66462e16 q^{82} +1.12492e16 q^{83} +7.28899e15 q^{84} -8.42294e15 q^{85} -3.97173e16 q^{86} +8.88491e15 q^{87} -4.55320e16 q^{88} +3.40745e16 q^{89} +8.83002e16 q^{90} +3.06628e15 q^{91} +6.54020e16 q^{92} -8.27646e16 q^{93} -1.17876e17 q^{94} -2.32116e16 q^{95} -3.45666e16 q^{96} -7.90652e16 q^{97} -1.41842e17 q^{98} -1.16117e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9}+O(q^{10}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9	\( 21 q + 256 q^{2} + 23966 q^{3} + 1452522 q^{4} + 998272 q^{5} + 3411526 q^{6} + 2193368 q^{7} - 138137226 q^{8} + 1264832799 q^{9} - 224469478 q^{10} + 1203139534 q^{11} - 5164251122 q^{12} + 3854339312 q^{13} + 25262272904 q^{14} + 28324474306 q^{15} + 196520815922 q^{16} + 76444714794 q^{17} + 75758949126 q^{18} + 246497292428 q^{19} - 46900976670 q^{20} + 360937126704 q^{21} - 275001533522 q^{22} + 213498528140 q^{23} - 451123453870 q^{24} + 3898884886997 q^{25} - 3609347694206 q^{26} - 2718903745978 q^{27} - 5946174617200 q^{28} + 10505174672181 q^{29} - 20237658929454 q^{30} + 16670029895798 q^{31} - 42141001912046 q^{32} - 7157109761394 q^{33} + 12785761151136 q^{34} + 46677934312888 q^{35} + 132137824374868 q^{36} + 53445659988410 q^{37} + 76581637956388 q^{38} + 79233849032530 q^{39} + 193617444734146 q^{40} - 20814769309298 q^{41} + 76690667258352 q^{42} + 185498647364454 q^{43} + 315429066899678 q^{44} - 486270821438526 q^{45} + 261474367677132 q^{46} + 389503471719450 q^{47} - 101509672247630 q^{48} + 730079062141437 q^{49} + 14\!\cdots\!54 q^{50}+ \cdots - 95\!\cdots\!64 q^{99}+O(q^{100}) \) 21 * q + 256 * q^2 + 23966 * q^3 + 1452522 * q^4 + 998272 * q^5 + 3411526 * q^6 + 2193368 * q^7 - 138137226 * q^8 + 1264832799 * q^9 - 224469478 * q^10 + 1203139534 * q^11 - 5164251122 * q^12 + 3854339312 * q^13 + 25262272904 * q^14 + 28324474306 * q^15 + 196520815922 * q^16 + 76444714794 * q^17 + 75758949126 * q^18 + 246497292428 * q^19 - 46900976670 * q^20 + 360937126704 * q^21 - 275001533522 * q^22 + 213498528140 * q^23 - 451123453870 * q^24 + 3898884886997 * q^25 - 3609347694206 * q^26 - 2718903745978 * q^27 - 5946174617200 * q^28 + 10505174672181 * q^29 - 20237658929454 * q^30 + 16670029895798 * q^31 - 42141001912046 * q^32 - 7157109761394 * q^33 + 12785761151136 * q^34 + 46677934312888 * q^35 + 132137824374868 * q^36 + 53445659988410 * q^37 + 76581637956388 * q^38 + 79233849032530 * q^39 + 193617444734146 * q^40 - 20814769309298 * q^41 + 76690667258352 * q^42 + 185498647364454 * q^43 + 315429066899678 * q^44 - 486270821438526 * q^45 + 261474367677132 * q^46 + 389503471719450 * q^47 - 101509672247630 * q^48 + 730079062141437 * q^49 + 1482269666368354 * q^50 + 718238208473988 * q^51 + 1966802817157170 * q^52 + 747441265526156 * q^53 + 5692893333117030 * q^54 + 1639109418219546 * q^55 + 5657219329125240 * q^56 + 4694352396864932 * q^57 + 128063081718016 * q^58 + 5280258638332960 * q^59 + 15251367906033378 * q^60 + 5813675353074254 * q^61 + 6242066590947250 * q^62 + 10947760075450368 * q^63 + 24583792057508902 * q^64 + 19190799243789974 * q^65 + 41877805444482390 * q^66 + 13420580230958268 * q^67 + 24771837384165388 * q^68 + 30973047049935252 * q^69 + 8505088080182440 * q^70 + 4824462822979508 * q^71 + 1180071997284592 * q^72 + 11228916281304662 * q^73 - 89132715356772 * q^74 + 59161419576630296 * q^75 + 57466858643173460 * q^76 + 58741564492720064 * q^77 + 142050530910210210 * q^78 + 71718598015696758 * q^79 + 48350023652407550 * q^80 + 75805931446703569 * q^81 + 188661890754420812 * q^82 + 50769377111735608 * q^83 + 198832046985593048 * q^84 + 53422044849490784 * q^85 + 35014892323844118 * q^86 + 11988905533023326 * q^87 + 37459283979085258 * q^88 - 70981414576978018 * q^89 + 57211029866143724 * q^90 + 112933943315157320 * q^91 - 103019729095759724 * q^92 - 350358290646906646 * q^93 - 150286322409612578 * q^94 - 102561321856584476 * q^95 - 213770098354021866 * q^96 - 130930167251505210 * q^97 - 537387515497557296 * q^98 - 95267700931431064 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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