LMFDB - Embedded newform 36.9.d.c.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,9,Mod(19,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("36.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	36.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.6656299622$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 40x^{6} - 395x^{5} + 403x^{4} + 8998x^{3} + 74584x^{2} + 217224x + 269328 $ x^8 - 3x^7 - 40x^6 - 395x^5 + 403x^4 + 8998x^3 + 74584x^2 + 217224*x + 269328
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{10} $
Twist minimal:	no (minimal twist has level 12)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.8
Root			$-1.97054 - 1.25304i$ of defining polynomial
Character	$\chi$	$=$	36.19
Dual form			36.9.d.c.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(15.8645 + 2.07809i) q^{2} +(247.363 + 65.9356i) q^{4} +374.901 q^{5} -4472.52i q^{7} +(3787.26 + 1560.08i) q^{8} +O(q^{10})$	\(q+(15.8645 + 2.07809i) q^{2} +(247.363 + 65.9356i) q^{4} +374.901 q^{5} -4472.52i q^{7} +(3787.26 + 1560.08i) q^{8} +(5947.61 + 779.079i) q^{10} +12939.6i q^{11} +17549.0 q^{13} +(9294.30 - 70954.2i) q^{14} +(56841.0 + 32620.1i) q^{16} +99303.3 q^{17} -115642. i q^{19} +(92736.8 + 24719.4i) q^{20} +(-26889.7 + 205281. i) q^{22} +10924.8i q^{23} -250074. q^{25} +(278405. + 36468.4i) q^{26} +(294898. - 1.10634e6i) q^{28} -31214.2 q^{29} +1.20904e6i q^{31} +(833965. + 635621. i) q^{32} +(1.57539e6 + 206361. i) q^{34} -1.67675e6i q^{35} -1.24040e6 q^{37} +(240314. - 1.83459e6i) q^{38} +(1.41985e6 + 584875. i) q^{40} -2.96280e6 q^{41} -2.69350e6i q^{43} +(-853183. + 3.20079e6i) q^{44} +(-22702.7 + 173316. i) q^{46} +8.92341e6i q^{47} -1.42386e7 q^{49} +(-3.96729e6 - 519676. i) q^{50} +(4.34097e6 + 1.15710e6i) q^{52} -1.11107e7 q^{53} +4.85109e6i q^{55} +(6.97747e6 - 1.69386e7i) q^{56} +(-495196. - 64865.9i) q^{58} -6.19748e6i q^{59} -2.13656e6 q^{61} +(-2.51249e6 + 1.91807e7i) q^{62} +(1.19095e7 + 1.18169e7i) q^{64} +6.57914e6 q^{65} -2.55543e6i q^{67} +(2.45640e7 + 6.54763e6i) q^{68} +(3.48445e6 - 2.66008e7i) q^{70} -2.55352e7i q^{71} +3.32867e7 q^{73} +(-1.96783e7 - 2.57766e6i) q^{74} +(7.62490e6 - 2.86055e7i) q^{76} +5.78728e7 q^{77} +2.18934e7i q^{79} +(2.13098e7 + 1.22293e7i) q^{80} +(-4.70033e7 - 6.15697e6i) q^{82} +3.75220e7i q^{83} +3.72290e7 q^{85} +(5.59733e6 - 4.27309e7i) q^{86} +(-2.01868e7 + 4.90058e7i) q^{88} -3.61031e7 q^{89} -7.84881e7i q^{91} +(-720332. + 2.70238e6i) q^{92} +(-1.85437e7 + 1.41565e8i) q^{94} -4.33542e7i q^{95} -1.26353e7 q^{97} +(-2.25888e8 - 2.95892e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} - 52 q^{4} + 336 q^{5} + 12960 q^{8}+O(q^{10}) $ 8 * q - 6 * q^2 - 52 * q^4 + 336 * q^5 + 12960 * q^8	$ 8 q - 6 q^{2} - 52 q^{4} + 336 q^{5} + 12960 q^{8} + 36628 q^{10} - 2864 q^{13} - 52728 q^{14} + 99440 q^{16} + 193200 q^{17} - 335592 q^{20} - 556968 q^{22} - 579048 q^{25} - 21564 q^{26} - 594672 q^{28} - 2063472 q^{29} + 3602784 q^{32} + 1568476 q^{34} + 7470352 q^{37} - 3659400 q^{38} + 1749184 q^{40} + 8865456 q^{41} - 2395920 q^{44} - 13649856 q^{46} - 18923896 q^{49} - 14581842 q^{50} + 18592888 q^{52} - 8706672 q^{53} + 45565632 q^{56} - 8816444 q^{58} + 13457296 q^{61} - 80783976 q^{62} + 1268864 q^{64} - 7293408 q^{65} + 117288264 q^{68} - 60373104 q^{70} + 94738960 q^{73} - 119548428 q^{74} + 144621360 q^{76} + 56971392 q^{77} + 163857888 q^{80} - 188383460 q^{82} - 201200416 q^{85} - 240327384 q^{86} + 156323520 q^{88} - 188992272 q^{89} + 387657984 q^{92} - 38749872 q^{94} - 123291632 q^{97} - 691081830 q^{98}+O(q^{100}) $ 8 * q - 6 * q^2 - 52 * q^4 + 336 * q^5 + 12960 * q^8 + 36628 * q^10 - 2864 * q^13 - 52728 * q^14 + 99440 * q^16 + 193200 * q^17 - 335592 * q^20 - 556968 * q^22 - 579048 * q^25 - 21564 * q^26 - 594672 * q^28 - 2063472 * q^29 + 3602784 * q^32 + 1568476 * q^34 + 7470352 * q^37 - 3659400 * q^38 + 1749184 * q^40 + 8865456 * q^41 - 2395920 * q^44 - 13649856 * q^46 - 18923896 * q^49 - 14581842 * q^50 + 18592888 * q^52 - 8706672 * q^53 + 45565632 * q^56 - 8816444 * q^58 + 13457296 * q^61 - 80783976 * q^62 + 1268864 * q^64 - 7293408 * q^65 + 117288264 * q^68 - 60373104 * q^70 + 94738960 * q^73 - 119548428 * q^74 + 144621360 * q^76 + 56971392 * q^77 + 163857888 * q^80 - 188383460 * q^82 - 201200416 * q^85 - 240327384 * q^86 + 156323520 * q^88 - 188992272 * q^89 + 387657984 * q^92 - 38749872 * q^94 - 123291632 * q^97 - 691081830 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	15.8645	+	2.07809i	0.991530	+	0.129881i
$2$	15.8645	+	2.07809i	0.991530	+	0.129881i
$3$		0			0
$3$		0			0
$4$	247.363	+	65.9356i	0.966262	+	0.257561i
$5$	374.901			0.599842			0.299921	−	0.953964i	$-0.403040\pi$
$5$	374.901			0.599842			0.299921	+	0.953964i	$0.403040\pi$
$6$		0			0
$7$		−	4472.52i		−	1.86277i	−0.364031	−	0.931387i	$-0.618600\pi$
$7$		−	4472.52i		−	1.86277i	0.364031	−	0.931387i	$-0.381400\pi$
$8$	3787.26	+	1560.08i	0.924625	+	0.380878i
$9$		0			0
$10$	5947.61	+	779.079i	0.594761	+	0.0779079i
$11$			12939.6i			0.883795i	0.897066	+	0.441897i	$0.145694\pi$
$11$			12939.6i			0.883795i	−0.897066	+	0.441897i	$0.854306\pi$
$12$		0			0
$13$	17549.0			0.614438			0.307219	−	0.951639i	$-0.400602\pi$
$13$	17549.0			0.614438			0.307219	+	0.951639i	$0.400602\pi$
$14$	9294.30	−	70954.2i	0.241938	−	1.84700i
$15$		0			0
$16$	56841.0	+	32620.1i	0.867325	+	0.497743i
$17$	99303.3			1.18896			0.594481	−	0.804110i	$-0.297357\pi$
$17$	99303.3			1.18896			0.594481	+	0.804110i	$0.297357\pi$
$18$		0			0
$19$		−	115642.i		−	0.887359i	−0.896185	−	0.443680i	$-0.853673\pi$
$19$		−	115642.i		−	0.887359i	0.896185	−	0.443680i	$-0.146327\pi$
$20$	92736.8	+	24719.4i	0.579605	+	0.154496i
$21$		0			0
$22$	−26889.7	+	205281.i	−0.114788	+	0.876309i
$23$			10924.8i			0.0390392i	0.999809	+	0.0195196i	$0.00621368\pi$
$23$			10924.8i			0.0390392i	−0.999809	+	0.0195196i	$0.993786\pi$
$24$		0			0
$25$	−250074.			−0.640189
$26$	278405.	+	36468.4i	0.609234	+	0.0798037i
$27$		0			0
$28$	294898.	−	1.10634e6i	0.479778	−	1.79993i
$29$	−31214.2			−0.0441326			−0.0220663	−	0.999757i	$-0.507024\pi$
$29$	−31214.2			−0.0441326			−0.0220663	+	0.999757i	$0.507024\pi$
$30$		0			0
$31$			1.20904e6i			1.30916i	0.755993	+	0.654580i	$0.227155\pi$
$31$			1.20904e6i			1.30916i	−0.755993	+	0.654580i	$0.772845\pi$
$32$	833965.	+	635621.i	0.795331	+	0.606176i
$33$		0			0
$34$	1.57539e6	+	206361.i	1.17889	+	0.154423i
$35$		−	1.67675e6i		−	1.11737i
$36$		0			0
$37$	−1.24040e6			−0.661842			−0.330921	−	0.943659i	$-0.607359\pi$
$37$	−1.24040e6			−0.661842			−0.330921	+	0.943659i	$0.607359\pi$
$38$	240314.	−	1.83459e6i	0.115251	−	0.879843i
$39$		0			0
$40$	1.41985e6	+	584875.i	0.554629	+	0.228467i
$41$	−2.96280e6			−1.04850			−0.524249	−	0.851565i	$-0.675654\pi$
$41$	−2.96280e6			−1.04850			−0.524249	+	0.851565i	$0.675654\pi$
$42$		0			0
$43$		−	2.69350e6i		−	0.787848i	−0.919143	−	0.393924i	$-0.871117\pi$
$43$		−	2.69350e6i		−	0.787848i	0.919143	−	0.393924i	$-0.128883\pi$
$44$	−853183.	+	3.20079e6i	−0.227631	+	0.853977i
$45$		0			0
$46$	−22702.7	+	173316.i	−0.00507044	+	0.0387085i
$47$			8.92341e6i			1.82869i	0.404939	+	0.914344i	$0.367293\pi$
$47$			8.92341e6i			1.82869i	−0.404939	+	0.914344i	$0.632707\pi$
$48$		0			0
$49$	−1.42386e7			−2.46992
$50$	−3.96729e6	−	519676.i	−0.634767	−	0.0831482i
$51$		0			0
$52$	4.34097e6	+	1.15710e6i	0.593708	+	0.158255i
$53$	−1.11107e7			−1.40811			−0.704055	−	0.710146i	$-0.748629\pi$
$53$	−1.11107e7			−1.40811			−0.704055	+	0.710146i	$0.748629\pi$
$54$		0			0
$55$			4.85109e6i			0.530137i
$56$	6.97747e6	−	1.69386e7i	0.709490	−	1.72237i
$57$		0			0
$58$	−495196.	−	64865.9i	−0.0437588	−	0.00573197i
$59$		−	6.19748e6i		−	0.511454i	−0.966749	−	0.255727i	$-0.917685\pi$
$59$		−	6.19748e6i		−	0.511454i	0.966749	−	0.255727i	$-0.0823149\pi$
$60$		0			0
$61$	−2.13656e6			−0.154310			−0.0771552	−	0.997019i	$-0.524584\pi$
$61$	−2.13656e6			−0.154310			−0.0771552	+	0.997019i	$0.524584\pi$
$62$	−2.51249e6	+	1.91807e7i	−0.170035	+	1.29807i
$63$		0			0
$64$	1.19095e7	+	1.18169e7i	0.709864	+	0.704339i
$65$	6.57914e6			0.368566
$66$		0			0
$67$		−	2.55543e6i		−	0.126813i	−0.997988	−	0.0634067i	$-0.979803\pi$
$67$		−	2.55543e6i		−	0.126813i	0.997988	−	0.0634067i	$-0.0201965\pi$
$68$	2.45640e7	+	6.54763e6i	1.14885	+	0.306230i
$69$		0			0
$70$	3.48445e6	−	2.66008e7i	0.145125	−	1.10791i
$71$		−	2.55352e7i		−	1.00486i	−0.864618	−	0.502431i	$-0.832439\pi$
$71$		−	2.55352e7i		−	1.00486i	0.864618	−	0.502431i	$-0.167561\pi$
$72$		0			0
$73$	3.32867e7			1.17214			0.586070	−	0.810260i	$-0.300674\pi$
$73$	3.32867e7			1.17214			0.586070	+	0.810260i	$0.300674\pi$
$74$	−1.96783e7	−	2.57766e6i	−0.656236	−	0.0859604i
$75$		0			0
$76$	7.62490e6	−	2.86055e7i	0.228549	−	0.857422i
$77$	5.78728e7			1.64631
$78$		0			0
$79$			2.18934e7i			0.562088i	0.959695	+	0.281044i	$0.0906807\pi$
$79$			2.18934e7i			0.562088i	−0.959695	+	0.281044i	$0.909319\pi$
$80$	2.13098e7	+	1.22293e7i	0.520258	+	0.298567i
$81$		0			0
$82$	−4.70033e7	−	6.15697e6i	−1.03962	−	0.136180i
$83$			3.75220e7i			0.790630i	0.918546	+	0.395315i	$0.129364\pi$
$83$			3.75220e7i			0.790630i	−0.918546	+	0.395315i	$0.870636\pi$
$84$		0			0
$85$	3.72290e7			0.713190
$86$	5.59733e6	−	4.27309e7i	0.102326	−	0.781175i
$87$		0			0
$88$	−2.01868e7	+	4.90058e7i	−0.336618	+	0.817179i
$89$	−3.61031e7			−0.575420			−0.287710	−	0.957718i	$-0.592894\pi$
$89$	−3.61031e7			−0.575420			−0.287710	+	0.957718i	$0.592894\pi$
$90$		0			0
$91$		−	7.84881e7i		−	1.14456i
$92$	−720332.	+	2.70238e6i	−0.0100550	+	0.0377221i
$93$		0			0
$94$	−1.85437e7	+	1.41565e8i	−0.237511	+	1.81320i
$95$		−	4.33542e7i		−	0.532276i
$96$		0			0
$97$	−1.26353e7			−0.142724			−0.0713621	−	0.997450i	$-0.522735\pi$
$97$	−1.26353e7			−0.142724			−0.0713621	+	0.997450i	$0.522735\pi$
$98$	−2.25888e8	−	2.95892e7i	−2.44900	−	0.320795i
$99$		0			0
$100$	−6.18591e7	−	1.64888e7i	−0.618591	−	0.164888i
$101$	−6.19037e6			−0.0594882			−0.0297441	−	0.999558i	$-0.509469\pi$
$101$	−6.19037e6			−0.0594882			−0.0297441	+	0.999558i	$0.509469\pi$
$102$		0			0
$103$			1.93155e7i			0.171616i	0.996312	+	0.0858079i	$0.0273471\pi$
$103$			1.93155e7i			0.171616i	−0.996312	+	0.0858079i	$0.972653\pi$
$104$	6.64626e7	+	2.73778e7i	0.568125	+	0.234026i
$105$		0			0
$106$	−1.76265e8	−	2.30890e7i	−1.39618	−	0.182886i
$107$			2.27863e8i			1.73836i	0.494498	+	0.869179i	$0.335352\pi$
$107$			2.27863e8i			1.73836i	−0.494498	+	0.869179i	$0.664648\pi$
$108$		0			0
$109$	1.49887e8			1.06184			0.530920	−	0.847422i	$-0.321846\pi$
$109$	1.49887e8			1.06184			0.530920	+	0.847422i	$0.321846\pi$
$110$	−1.00810e7	+	7.69600e7i	−0.0688546	+	0.525647i
$111$		0			0
$112$	1.45894e8	−	2.54222e8i	0.927182	−	1.61563i
$113$	9.43384e7			0.578595			0.289298	−	0.957239i	$-0.406578\pi$
$113$	9.43384e7			0.578595			0.289298	+	0.957239i	$0.406578\pi$
$114$		0			0
$115$			4.09571e6i			0.0234174i
$116$	−7.72123e6	−	2.05813e6i	−0.0426437	−	0.0113668i
$117$		0			0
$118$	1.28789e7	−	9.83197e7i	0.0664280	−	0.507122i
$119$		−	4.44136e8i		−	2.21477i
$120$		0			0
$121$	4.69246e7			0.218907
$122$	−3.38954e7	−	4.43996e6i	−0.153003	−	0.0200419i
$123$		0			0
$124$	−7.97186e7	+	2.99071e8i	−0.337189	+	1.26499i
$125$	−2.40199e8			−0.983855
$126$		0			0
$127$			2.82897e8i			1.08746i	0.839260	+	0.543731i	$0.182989\pi$
$127$			2.82897e8i			1.08746i	−0.839260	+	0.543731i	$0.817011\pi$
$128$	1.64382e8	+	2.12217e8i	0.612371	+	0.790571i
$129$		0			0
$130$	1.04375e8	+	1.36720e7i	0.365444	+	0.0478696i
$131$			9.98571e7i			0.339073i	0.985524	+	0.169537i	$0.0542271\pi$
$131$			9.98571e7i			0.339073i	−0.985524	+	0.169537i	$0.945773\pi$
$132$		0			0
$133$	−5.17209e8			−1.65295
$134$	5.31042e6	−	4.05406e7i	0.0164706	−	0.125739i
$135$		0			0
$136$	3.76088e8	+	1.54921e8i	1.09934	+	0.452850i
$137$	1.18390e8			0.336074			0.168037	−	0.985781i	$-0.446257\pi$
$137$	1.18390e8			0.336074			0.168037	+	0.985781i	$0.446257\pi$
$138$		0			0
$139$		−	2.90295e8i		−	0.777642i	−0.921313	−	0.388821i	$-0.872882\pi$
$139$		−	2.90295e8i		−	0.777642i	0.921313	−	0.388821i	$-0.127118\pi$
$140$	1.10558e8	−	4.14767e8i	0.287791	−	1.07967i
$141$		0			0
$142$	5.30645e7	−	4.05103e8i	0.130512	−	0.996350i
$143$			2.27077e8i			0.543037i
$144$		0			0
$145$	−1.17022e7			−0.0264726
$146$	5.28076e8	+	6.91728e7i	1.16221	+	0.152238i
$147$		0			0
$148$	−3.06829e8	−	8.17864e7i	−0.639512	−	0.170465i
$149$	1.78016e8			0.361173			0.180586	−	0.983559i	$-0.442200\pi$
$149$	1.78016e8			0.361173			0.180586	+	0.983559i	$0.442200\pi$
$150$		0			0
$151$			9.14545e6i			0.0175913i	0.999961	+	0.00879563i	$0.00279977\pi$
$151$			9.14545e6i			0.0175913i	−0.999961	+	0.00879563i	$0.997200\pi$
$152$	1.80410e8	−	4.37965e8i	0.337976	−	0.820475i
$153$		0			0
$154$	9.18121e8	+	1.20265e8i	1.63236	+	0.213824i
$155$			4.53270e8i			0.785290i
$156$		0			0
$157$	−2.24414e8			−0.369361			−0.184681	−	0.982799i	$-0.559125\pi$
$157$	−2.24414e8			−0.369361			−0.184681	+	0.982799i	$0.559125\pi$
$158$	−4.54964e7	+	3.47327e8i	−0.0730044	+	0.557327i
$159$		0			0
$160$	3.12655e8	+	2.38295e8i	0.477073	+	0.363610i
$161$	4.88612e7			0.0727212
$162$		0			0
$163$		−	7.18722e8i		−	1.01815i	−0.860723	−	0.509074i	$-0.829988\pi$
$163$		−	7.18722e8i		−	1.01815i	0.860723	−	0.509074i	$-0.170012\pi$
$164$	−7.32888e8	−	1.95354e8i	−1.01312	−	0.270052i
$165$		0			0
$166$	−7.79740e7	+	5.95266e8i	−0.102688	+	0.783933i
$167$		−	2.91809e8i		−	0.375174i	−0.982248	−	0.187587i	$-0.939933\pi$
$167$		−	2.91809e8i		−	0.375174i	0.982248	−	0.187587i	$-0.0600667\pi$
$168$		0			0
$169$	−5.07764e8			−0.622465
$170$	5.90618e8	+	7.73651e7i	0.707149	+	0.0926296i
$171$		0			0
$172$	1.77597e8	−	6.66271e8i	0.202919	−	0.761268i
$173$	−1.20998e9			−1.35080			−0.675402	−	0.737450i	$-0.736030\pi$
$173$	−1.20998e9			−1.35080			−0.675402	+	0.737450i	$0.736030\pi$
$174$		0			0
$175$			1.11846e9i			1.19253i
$176$	−4.22092e8	+	7.35502e8i	−0.439903	+	0.766537i
$177$		0			0
$178$	−5.72757e8	−	7.50255e7i	−0.570546	−	0.0747359i
$179$		−	1.45368e9i		−	1.41598i	−0.706223	−	0.707990i	$-0.749602\pi$
$179$		−	1.45368e9i		−	1.41598i	0.706223	−	0.707990i	$-0.250398\pi$
$180$		0			0
$181$	2.11074e8			0.196662			0.0983311	−	0.995154i	$-0.468650\pi$
$181$	2.11074e8			0.196662			0.0983311	+	0.995154i	$0.468650\pi$
$182$	1.63105e8	−	1.24517e9i	0.148656	−	1.13486i
$183$		0			0
$184$	−1.70435e7	+	4.13750e7i	−0.0148692	+	0.0360966i
$185$	−4.65027e8			−0.397001
$186$		0			0
$187$			1.28495e9i			1.05080i
$188$	−5.88371e8	+	2.20732e9i	−0.470999	+	1.76699i
$189$		0			0
$190$	9.00939e7	−	6.87791e8i	0.0691323	−	0.527767i
$191$			1.66532e9i			1.25130i	0.780102	+	0.625652i	$0.215167\pi$
$191$			1.66532e9i			1.25130i	−0.780102	+	0.625652i	$0.784833\pi$
$192$		0			0
$193$	7.57046e8			0.545624			0.272812	−	0.962067i	$-0.412046\pi$
$193$	7.57046e8			0.545624			0.272812	+	0.962067i	$0.412046\pi$
$194$	−2.00452e8	−	2.62572e7i	−0.141515	−	0.0185371i
$195$		0			0
$196$	−3.52211e9	−	9.38833e8i	−2.38659	−	0.636156i
$197$	7.31378e8			0.485598			0.242799	−	0.970077i	$-0.421934\pi$
$197$	7.31378e8			0.485598			0.242799	+	0.970077i	$0.421934\pi$
$198$		0			0
$199$		−	1.02039e9i		−	0.650663i	−0.945600	−	0.325331i	$-0.894524\pi$
$199$		−	1.02039e9i		−	0.650663i	0.945600	−	0.325331i	$-0.105476\pi$
$200$	−9.47096e8	−	3.90135e8i	−0.591935	−	0.243834i
$201$		0			0
$202$	−9.82069e7	−	1.28641e7i	−0.0589843	−	0.00772637i
$203$			1.39606e8i			0.0822091i
$204$		0			0
$205$	−1.11076e9			−0.628933
$206$	−4.01394e7	+	3.06430e8i	−0.0222896	+	0.170162i
$207$		0			0
$208$	9.97501e8	+	5.72449e8i	0.532918	+	0.305832i
$209$	1.49636e9			0.784244
$210$		0			0
$211$		−	1.81728e9i		−	0.916834i	−0.888737	−	0.458417i	$-0.848417\pi$
$211$		−	1.81728e9i		−	0.916834i	0.888737	−	0.458417i	$-0.151583\pi$
$212$	−2.74837e9	−	7.32589e8i	−1.36060	−	0.362674i
$213$		0			0
$214$	−4.73520e8	+	3.61493e9i	−0.225779	+	1.72363i
$215$		−	1.00980e9i		−	0.472584i
$216$		0			0
$217$	5.40744e9			2.43867
$218$	2.37789e9	+	3.11480e8i	1.05285	+	0.137913i
$219$		0			0
$220$	−3.19860e8	+	1.19998e9i	−0.136543	+	0.512252i
$221$	1.74267e9			0.730544
$222$		0			0
$223$		−	2.10749e9i		−	0.852207i	−0.904674	−	0.426104i	$-0.859886\pi$
$223$		−	2.10749e9i		−	0.852207i	0.904674	−	0.426104i	$-0.140114\pi$
$224$	2.84283e9	−	3.72992e9i	1.12917	−	1.48152i
$225$		0			0
$226$	1.49663e9	+	1.96044e8i	0.573694	+	0.0751483i
$227$		−	9.20581e7i		−	0.0346704i	−0.999850	−	0.0173352i	$-0.994482\pi$
$227$		−	9.20581e7i		−	0.0346704i	0.999850	−	0.0173352i	$-0.00551824\pi$
$228$		0			0
$229$	3.72077e9			1.35298			0.676490	−	0.736452i	$-0.263500\pi$
$229$	3.72077e9			1.35298			0.676490	+	0.736452i	$0.263500\pi$
$230$	−8.51126e6	+	6.49763e7i	−0.00304146	+	0.0232190i
$231$		0			0
$232$	−1.18216e8	−	4.86965e7i	−0.0408061	−	0.0168092i
$233$	4.16272e9			1.41239			0.706193	−	0.708020i	$-0.250411\pi$
$233$	4.16272e9			1.41239			0.706193	+	0.708020i	$0.250411\pi$
$234$		0			0
$235$			3.34540e9i			1.09692i
$236$	4.08634e8	−	1.53303e9i	0.131731	−	0.494199i
$237$		0			0
$238$	9.22955e8	−	7.04598e9i	0.287655	−	2.19601i
$239$			1.41116e9i			0.432499i	0.976338	+	0.216250i	$0.0693825\pi$
$239$			1.41116e9i			0.432499i	−0.976338	+	0.216250i	$0.930618\pi$
$240$		0			0
$241$	−5.52118e9			−1.63668			−0.818339	−	0.574736i	$-0.805105\pi$
$241$	−5.52118e9			−1.63668			−0.818339	+	0.574736i	$0.805105\pi$
$242$	7.44434e8	+	9.75136e7i	0.217053	+	0.0284318i
$243$		0			0
$244$	−5.28506e8	−	1.40875e8i	−0.149104	−	0.0397444i
$245$	−5.33808e9			−1.48157
$246$		0			0
$247$		−	2.02939e9i		−	0.545228i
$248$	−1.88619e9	+	4.57894e9i	−0.498631	+	1.21048i
$249$		0			0
$250$	−3.81063e9	−	4.99155e8i	−0.975521	−	0.127784i
$251$			6.67446e8i			0.168159i	0.996459	+	0.0840797i	$0.0267950\pi$
$251$			6.67446e8i			0.168159i	−0.996459	+	0.0840797i	$0.973205\pi$
$252$		0			0
$253$	−1.41363e8			−0.0345026
$254$	−5.87886e8	+	4.48802e9i	−0.141240	+	1.07825i
$255$		0			0
$256$	2.16683e9	+	3.70832e9i	0.504504	+	0.863409i
$257$	1.30371e9			0.298846			0.149423	−	0.988773i	$-0.452258\pi$
$257$	1.30371e9			0.298846			0.149423	+	0.988773i	$0.452258\pi$
$258$		0			0
$259$			5.54770e9i			1.23286i
$260$	1.62744e9	+	4.33799e8i	0.356131	+	0.0949283i
$261$		0			0
$262$	−2.07512e8	+	1.58418e9i	−0.0440391	+	0.336201i
$263$		−	5.57666e9i		−	1.16560i	−0.812614	−	0.582802i	$-0.801956\pi$
$263$		−	5.57666e9i		−	1.16560i	0.812614	−	0.582802i	$-0.198044\pi$
$264$		0			0
$265$	−4.16540e9			−0.844644
$266$	−8.20525e9	−	1.07481e9i	−1.63895	−	0.214686i
$267$		0			0
$268$	1.68494e8	−	6.32119e8i	0.0326622	−	0.122535i
$269$	−7.68316e9			−1.46734			−0.733670	−	0.679506i	$-0.762194\pi$
$269$	−7.68316e9			−1.46734			−0.733670	+	0.679506i	$0.762194\pi$
$270$		0			0
$271$		−	3.30747e9i		−	0.613224i	−0.951835	−	0.306612i	$-0.900805\pi$
$271$		−	3.30747e9i		−	0.613224i	0.951835	−	0.306612i	$-0.0991954\pi$
$272$	5.64450e9	+	3.23928e9i	1.03122	+	0.591798i
$273$		0			0
$274$	1.87820e9	+	2.46026e8i	0.333227	+	0.0436495i
$275$		−	3.23587e9i		−	0.565796i
$276$		0			0
$277$	−6.82083e9			−1.15856			−0.579280	−	0.815129i	$-0.696666\pi$
$277$	−6.82083e9			−1.15856			−0.579280	+	0.815129i	$0.696666\pi$
$278$	6.03258e8	−	4.60537e9i	0.101001	−	0.771055i
$279$		0			0
$280$	2.61586e9	−	6.35031e9i	0.425582	−	1.03315i
$281$	−4.59488e9			−0.736969			−0.368484	−	0.929634i	$-0.620123\pi$
$281$	−4.59488e9			−0.736969			−0.368484	+	0.929634i	$0.620123\pi$
$282$		0			0
$283$			6.87759e9i			1.07224i	0.844143	+	0.536118i	$0.180110\pi$
$283$			6.87759e9i			1.07224i	−0.844143	+	0.536118i	$0.819890\pi$
$284$	1.68368e9	−	6.31647e9i	0.258813	−	0.970959i
$285$		0			0
$286$	−4.71887e8	+	3.60246e9i	−0.0705301	+	0.538438i
$287$			1.32512e10i			1.95311i
$288$		0			0
$289$	2.88539e9			0.413631
$290$	−1.85650e8	−	2.43183e7i	−0.0262484	−	0.00343828i
$291$		0			0
$292$	8.23390e9	+	2.19478e9i	1.13259	+	0.301898i
$293$	3.84587e9			0.521825			0.260912	−	0.965363i	$-0.415977\pi$
$293$	3.84587e9			0.521825			0.260912	+	0.965363i	$0.415977\pi$
$294$		0			0
$295$		−	2.32344e9i		−	0.306792i
$296$	−4.69772e9	−	1.93512e9i	−0.611955	−	0.252081i
$297$		0			0
$298$	2.82414e9	+	3.69934e8i	0.358114	+	0.0469094i
$299$			1.91718e8i			0.0239872i
$300$		0			0
$301$	−1.20467e10			−1.46758
$302$	−1.90051e7	+	1.45088e8i	−0.00228477	+	0.0174423i
$303$		0			0
$304$	3.77224e9	−	6.57318e9i	0.441677	−	0.769629i
$305$	−8.00999e8			−0.0925619
$306$		0			0
$307$		−	1.59131e10i		−	1.79144i	−0.444621	−	0.895719i	$-0.646662\pi$
$307$		−	1.59131e10i		−	1.79144i	0.444621	−	0.895719i	$-0.353338\pi$
$308$	1.43156e10	+	3.81588e9i	1.59077	+	0.424025i
$309$		0			0
$310$	−9.41936e8	+	7.19089e9i	−0.101994	+	0.778638i
$311$			4.82439e9i			0.515704i	0.966184	+	0.257852i	$0.0830147\pi$
$311$			4.82439e9i			0.515704i	−0.966184	+	0.257852i	$0.916985\pi$
$312$		0			0
$313$	9.94627e9			1.03629			0.518147	−	0.855292i	$-0.326622\pi$
$313$	9.94627e9			1.03629			0.518147	+	0.855292i	$0.326622\pi$
$314$	−3.56021e9	−	4.66353e8i	−0.366233	−	0.0479729i
$315$		0			0
$316$	−1.44355e9	+	5.41561e9i	−0.144772	+	0.543124i
$317$	−1.13655e10			−1.12552			−0.562760	−	0.826621i	$-0.690260\pi$
$317$	−1.13655e10			−1.12552			−0.562760	+	0.826621i	$0.690260\pi$
$318$		0			0
$319$		−	4.03900e8i		−	0.0390042i
$320$	4.46490e9	+	4.43015e9i	0.425806	+	0.422492i
$321$		0			0
$322$	7.75158e8	+	1.01538e8i	0.0721052	+	0.00944508i
$323$		−	1.14836e10i		−	1.05504i
$324$		0			0
$325$	−4.38854e9			−0.393357
$326$	1.49357e9	−	1.14022e10i	0.132238	−	1.00952i
$327$		0			0
$328$	−1.12209e10	−	4.62220e9i	−0.969467	−	0.399350i
$329$	3.99101e10			3.40643
$330$		0			0
$331$			3.51927e9i			0.293185i	0.989197	+	0.146592i	$0.0468305\pi$
$331$			3.51927e9i			0.293185i	−0.989197	+	0.146592i	$0.953169\pi$
$332$	−2.47403e9	+	9.28155e9i	−0.203635	+	0.763955i
$333$		0			0
$334$	6.06406e8	−	4.62940e9i	0.0487279	−	0.371996i
$335$		−	9.58035e8i		−	0.0760680i
$336$		0			0
$337$	1.46645e10			1.13697			0.568484	−	0.822695i	$-0.307530\pi$
$337$	1.46645e10			1.13697			0.568484	+	0.822695i	$0.307530\pi$
$338$	−8.05541e9	−	1.05518e9i	−0.617193	−	0.0808462i
$339$		0			0
$340$	9.20907e9	+	2.45471e9i	0.689128	+	0.183690i
$341$	−1.56445e10			−1.15703
$342$		0			0
$343$			3.78993e10i			2.73814i
$344$	4.20206e9	−	1.02010e10i	0.300074	−	0.728464i
$345$		0			0
$346$	−1.91956e10	−	2.51444e9i	−1.33936	−	0.175443i
$347$		−	1.68810e10i		−	1.16434i	−0.813066	−	0.582172i	$-0.802203\pi$
$347$		−	1.68810e10i		−	1.16434i	0.813066	−	0.582172i	$-0.197797\pi$
$348$		0			0
$349$	1.01348e10			0.683145			0.341572	−	0.939855i	$-0.389041\pi$
$349$	1.01348e10			0.683145			0.341572	+	0.939855i	$0.389041\pi$
$350$	−2.32426e9	+	1.77438e10i	−0.154886	+	1.18243i
$351$		0			0
$352$	−8.22471e9	+	1.07912e10i	−0.535735	+	0.702909i
$353$	−1.91125e9			−0.123089			−0.0615445	−	0.998104i	$-0.519603\pi$
$353$	−1.91125e9			−0.123089			−0.0615445	+	0.998104i	$0.519603\pi$
$354$		0			0
$355$		−	9.57319e9i		−	0.602758i
$356$	−8.93058e9	−	2.38048e9i	−0.556006	−	0.148206i
$357$		0			0
$358$	3.02088e9	−	2.30619e10i	0.183908	−	1.40399i
$359$		−	8.33129e9i		−	0.501573i	−0.968042	−	0.250787i	$-0.919311\pi$
$359$		−	8.33129e9i		−	0.501573i	0.968042	−	0.250787i	$-0.0806892\pi$
$360$		0			0
$361$	3.61059e9			0.212593
$362$	3.34858e9	+	4.38631e8i	0.194996	+	0.0255426i
$363$		0			0
$364$	5.17516e9	−	1.94151e10i	0.294794	−	1.10594i
$365$	1.24792e10			0.703099
$366$		0			0
$367$		−	2.75727e10i		−	1.51990i	−0.649981	−	0.759950i	$-0.725223\pi$
$367$		−	2.75727e10i		−	1.51990i	0.649981	−	0.759950i	$-0.274777\pi$
$368$	−3.56367e8	+	6.20975e8i	−0.0194315	+	0.0338597i
$369$		0			0
$370$	−7.37741e9	−	9.66368e8i	−0.393638	−	0.0515627i
$371$			4.96927e10i			2.62299i
$372$		0			0
$373$	1.13007e10			0.583809			0.291905	−	0.956447i	$-0.405711\pi$
$373$	1.13007e10			0.583809			0.291905	+	0.956447i	$0.405711\pi$
$374$	−2.67024e9	+	2.03850e10i	−0.136478	+	1.04190i
$375$		0			0
$376$	−1.39212e10	+	3.37953e10i	−0.696507	+	1.69085i
$377$	−5.47777e8			−0.0271168
$378$		0			0
$379$		−	2.00812e10i		−	0.973267i	−0.873606	−	0.486634i	$-0.838225\pi$
$379$		−	2.00812e10i		−	0.973267i	0.873606	−	0.486634i	$-0.161775\pi$
$380$	2.85859e9	−	1.07242e10i	0.137093	−	0.514318i
$381$		0			0
$382$	−3.46068e9	+	2.64194e10i	−0.162520	+	1.24071i
$383$		−	2.28867e10i		−	1.06363i	−0.846862	−	0.531813i	$-0.821511\pi$
$383$		−	2.28867e10i		−	1.06363i	0.846862	−	0.531813i	$-0.178489\pi$
$384$		0			0
$385$	2.16966e10			0.987526
$386$	1.20101e10	+	1.57321e9i	0.541002	+	0.0708660i
$387$		0			0
$388$	−3.12550e9	−	8.33114e8i	−0.137909	−	0.0367602i
$389$	−3.25250e10			−1.42043			−0.710214	−	0.703986i	$-0.751402\pi$
$389$	−3.25250e10			−1.42043			−0.710214	+	0.703986i	$0.751402\pi$
$390$		0			0
$391$			1.08487e9i			0.0464161i
$392$	−5.39254e10	−	2.22134e10i	−2.28375	−	0.940741i
$393$		0			0
$394$	1.16029e10	+	1.51987e9i	0.481485	+	0.0630698i
$395$			8.20786e9i			0.337164i
$396$		0			0
$397$	−3.95474e10			−1.59205			−0.796024	−	0.605264i	$-0.793067\pi$
$397$	−3.95474e10			−1.59205			−0.796024	+	0.605264i	$0.793067\pi$
$398$	2.12047e9	−	1.61880e10i	0.0845085	−	0.645151i
$399$		0			0
$400$	−1.42144e10	−	8.15743e9i	−0.555252	−	0.318650i
$401$	4.03775e10			1.56157			0.780786	−	0.624798i	$-0.214819\pi$
$401$	4.03775e10			1.56157			0.780786	+	0.624798i	$0.214819\pi$
$402$		0			0
$403$			2.12174e10i			0.804398i
$404$	−1.53127e9	−	4.08166e8i	−0.0574812	−	0.0153218i
$405$		0			0
$406$	−2.90114e8	+	2.21477e9i	−0.0106774	+	0.0815127i
$407$		−	1.60503e10i		−	0.584932i
$408$		0			0
$409$	−2.14604e9			−0.0766912			−0.0383456	−	0.999265i	$-0.512209\pi$
$409$	−2.14604e9			−0.0766912			−0.0383456	+	0.999265i	$0.512209\pi$
$410$	−1.76216e10	−	2.30826e9i	−0.623606	−	0.0816862i
$411$		0			0
$412$	−1.27358e9	+	4.77794e9i	−0.0442015	+	0.165826i
$413$	−2.77183e10			−0.952723
$414$		0			0
$415$			1.40670e10i			0.474253i
$416$	1.46352e10	+	1.11545e10i	0.488682	+	0.372458i
$417$		0			0
$418$	2.37390e10	+	3.10957e9i	0.777601	+	0.101858i
$419$			5.54260e10i			1.79828i	0.437662	+	0.899140i	$0.355807\pi$
$419$			5.54260e10i			1.79828i	−0.437662	+	0.899140i	$0.644193\pi$
$420$		0			0
$421$	7.84742e9			0.249803			0.124902	−	0.992169i	$-0.460138\pi$
$421$	7.84742e9			0.249803			0.124902	+	0.992169i	$0.460138\pi$
$422$	3.77646e9	−	2.88301e10i	0.119079	−	0.909068i
$423$		0			0
$424$	−4.20790e10	−	1.73335e10i	−1.30197	−	0.536318i
$425$	−2.48332e10			−0.761161
$426$		0			0
$427$			9.55580e9i			0.287445i
$428$	−1.50243e10	+	5.63649e10i	−0.447733	+	1.67971i
$429$		0			0
$430$	2.09845e9	−	1.60199e10i	0.0613796	−	0.468582i
$431$		−	2.02028e10i		−	0.585468i	−0.956194	−	0.292734i	$-0.905435\pi$
$431$		−	2.02028e10i		−	0.585468i	0.956194	−	0.292734i	$-0.0945651\pi$
$432$		0			0
$433$	−4.24666e10			−1.20808			−0.604040	−	0.796954i	$-0.706443\pi$
$433$	−4.24666e10			−1.20808			−0.604040	+	0.796954i	$0.706443\pi$
$434$	8.57862e10	+	1.12372e10i	2.41801	+	0.316736i
$435$		0			0
$436$	3.70766e10	+	9.88292e9i	1.02602	+	0.273489i
$437$	1.26336e9			0.0346418
$438$		0			0
$439$		−	3.13705e9i		−	0.0844624i	−0.999108	−	0.0422312i	$-0.986553\pi$
$439$		−	3.13705e9i		−	0.0844624i	0.999108	−	0.0422312i	$-0.0134466\pi$
$440$	−7.56807e9	+	1.83724e10i	−0.201918	+	0.490178i
$441$		0			0
$442$	2.76466e10	+	3.62143e9i	0.724356	+	0.0948836i
$443$		−	7.34157e10i		−	1.90623i	−0.302616	−	0.953113i	$-0.597860\pi$
$443$		−	7.34157e10i		−	1.90623i	0.302616	−	0.953113i	$-0.402140\pi$
$444$		0			0
$445$	−1.35351e10			−0.345161
$446$	4.37955e9	−	3.34342e10i	0.110685	−	0.844989i
$447$		0			0
$448$	5.28511e10	−	5.32656e10i	1.31202	−	1.32232i
$449$	6.05149e10			1.48894			0.744469	−	0.667657i	$-0.232703\pi$
$449$	6.05149e10			1.48894			0.744469	+	0.667657i	$0.232703\pi$
$450$		0			0
$451$		−	3.83376e10i		−	0.926656i
$452$	2.33358e10	+	6.22026e9i	0.559075	+	0.149024i
$453$		0			0
$454$	1.91305e8	−	1.46045e9i	0.00450301	−	0.0343767i
$455$		−	2.94253e10i		−	0.686555i
$456$		0			0
$457$	2.60402e10			0.597008			0.298504	−	0.954408i	$-0.403512\pi$
$457$	2.60402e10			0.597008			0.298504	+	0.954408i	$0.403512\pi$
$458$	5.90281e10	+	7.73210e9i	1.34152	+	0.175726i
$459$		0			0
$460$	−2.70053e8	+	1.01313e9i	−0.00603140	+	0.0226273i
$461$	−4.25451e10			−0.941990			−0.470995	−	0.882136i	$-0.656105\pi$
$461$	−4.25451e10			−0.941990			−0.470995	+	0.882136i	$0.656105\pi$
$462$		0			0
$463$			2.22263e10i			0.483663i	0.970318	+	0.241832i	$0.0777481\pi$
$463$			2.22263e10i			0.483663i	−0.970318	+	0.241832i	$0.922252\pi$
$464$	−1.77424e9	−	1.01821e9i	−0.0382773	−	0.0219667i
$465$		0			0
$466$	6.60393e10	+	8.65050e9i	1.40042	+	0.183442i
$467$			6.05685e10i			1.27344i	0.771094	+	0.636721i	$0.219710\pi$
$467$			6.05685e10i			1.27344i	−0.771094	+	0.636721i	$0.780290\pi$
$468$		0			0
$469$	−1.14292e10			−0.236225
$470$	−6.95204e9	+	5.30730e10i	−0.142469	+	1.08763i
$471$		0			0
$472$	9.66854e9	−	2.34715e10i	0.194802	−	0.472903i
$473$	3.48529e10			0.696296
$474$		0			0
$475$			2.89189e10i			0.568078i
$476$	2.92844e10	−	1.09863e11i	0.570438	−	2.14005i
$477$		0			0
$478$	−2.93252e9	+	2.23873e10i	−0.0561733	+	0.428836i
$479$			4.26641e10i			0.810439i	0.914219	+	0.405219i	$0.132805\pi$
$479$			4.26641e10i			0.810439i	−0.914219	+	0.405219i	$0.867195\pi$
$480$		0			0
$481$	−2.17677e10			−0.406661
$482$	−8.75905e10	−	1.14735e10i	−1.62282	−	0.212573i
$483$		0			0
$484$	1.16074e10	+	3.09400e9i	0.211521	+	0.0563819i
$485$	−4.73698e9			−0.0856120
$486$		0			0
$487$			6.59829e10i			1.17305i	0.809932	+	0.586523i	$0.199504\pi$
$487$			6.59829e10i			1.17305i	−0.809932	+	0.586523i	$0.800496\pi$
$488$	−8.09171e9	−	3.33320e9i	−0.142679	−	0.0587735i
$489$		0			0
$490$	−8.46858e10	−	1.10930e10i	−1.46902	−	0.192427i
$491$		−	4.15778e10i		−	0.715379i	−0.933841	−	0.357689i	$-0.883565\pi$
$491$		−	4.15778e10i		−	0.715379i	0.933841	−	0.357689i	$-0.116435\pi$
$492$		0			0
$493$	−3.09967e9			−0.0524720
$494$	4.21726e9	−	3.21952e10i	0.0708145	−	0.540609i
$495$		0			0
$496$	−3.94389e10	+	6.87229e10i	−0.651625	+	1.13547i
$497$	−1.14207e11			−1.87183
$498$		0			0
$499$		−	7.89968e10i		−	1.27411i	−0.770818	−	0.637056i	$-0.780152\pi$
$499$		−	7.89968e10i		−	1.27411i	0.770818	−	0.637056i	$-0.219848\pi$
$500$	−5.94163e10	−	1.58377e10i	−0.950662	−	0.253403i
$501$		0			0
$502$	−1.38701e9	+	1.05887e10i	−0.0218407	+	0.166735i
$503$			4.75631e10i			0.743017i	0.928430	+	0.371508i	$0.121159\pi$
$503$			4.75631e10i			0.743017i	−0.928430	+	0.371508i	$0.878841\pi$
$504$		0			0
$505$	−2.32078e9			−0.0356835
$506$	−2.24264e9	−	2.93764e8i	−0.0342104	−	0.00448123i
$507$		0			0
$508$	−1.86530e10	+	6.99783e10i	−0.280088	+	1.05077i
$509$	5.08975e10			0.758272			0.379136	−	0.925341i	$-0.376221\pi$
$509$	5.08975e10			0.758272			0.379136	+	0.925341i	$0.376221\pi$
$510$		0			0
$511$		−	1.48875e11i		−	2.18343i
$512$	2.66694e10	+	6.33333e10i	0.388090	+	0.921621i
$513$		0			0
$514$	2.06826e10	+	2.70922e9i	0.296315	+	0.0388143i
$515$			7.24141e9i			0.102942i
$516$		0			0
$517$	−1.15466e11			−1.61618
$518$	−1.15286e10	+	8.80114e10i	−0.160125	+	1.22242i
$519$		0			0
$520$	2.49169e10	+	1.02640e10i	0.340785	+	0.140379i
$521$	1.88555e10			0.255910			0.127955	−	0.991780i	$-0.459159\pi$
$521$	1.88555e10			0.255910			0.127955	+	0.991780i	$0.459159\pi$
$522$		0			0
$523$			2.61334e10i			0.349293i	0.984631	+	0.174646i	$0.0558782\pi$
$523$			2.61334e10i			0.349293i	−0.984631	+	0.174646i	$0.944122\pi$
$524$	−6.58414e9	+	2.47010e10i	−0.0873321	+	0.327634i
$525$		0			0
$526$	1.15888e10	−	8.84708e10i	0.151390	−	1.15573i
$527$			1.20061e11i			1.55654i
$528$		0			0
$529$	7.81916e10			0.998476
$530$	−6.60819e10	−	8.65609e9i	−0.837489	−	0.109703i
$531$		0			0
$532$	−1.27938e11	−	3.41025e10i	−1.59718	−	0.425735i
$533$	−5.19941e10			−0.644237
$534$		0			0
$535$			8.54262e10i			1.04274i
$536$	3.98667e9	−	9.67810e9i	0.0483004	−	0.117255i
$537$		0			0
$538$	−1.21889e11	−	1.59663e10i	−1.45491	−	0.190579i
$539$		−	1.84243e11i		−	2.18291i
$540$		0			0
$541$	1.45275e11			1.69591			0.847956	−	0.530067i	$-0.177833\pi$
$541$	1.45275e11			1.69591			0.847956	+	0.530067i	$0.177833\pi$
$542$	6.87323e9	−	5.24713e10i	0.0796460	−	0.608030i
$543$		0			0
$544$	8.28155e10	+	6.31193e10i	0.945618	+	0.720720i
$545$	5.61930e10			0.636937
$546$		0			0
$547$			1.46238e11i			1.63347i	0.577015	+	0.816734i	$0.304218\pi$
$547$			1.46238e11i			1.63347i	−0.577015	+	0.816734i	$0.695782\pi$
$548$	2.92854e10	+	7.80615e9i	0.324735	+	0.0865595i
$549$		0			0
$550$	6.72442e9	−	5.13353e10i	0.0734860	−	0.561003i
$551$			3.60965e9i			0.0391615i
$552$		0			0
$553$	9.79185e10			1.04704
$554$	−1.08209e11	−	1.41743e10i	−1.14875	−	0.150474i
$555$		0			0
$556$	1.91408e10	−	7.18081e10i	0.200290	−	0.751406i
$557$	−7.17684e10			−0.745611			−0.372806	−	0.927909i	$-0.621604\pi$
$557$	−7.17684e10			−0.745611			−0.372806	+	0.927909i	$0.621604\pi$
$558$		0			0
$559$		−	4.72681e10i		−	0.484084i
$560$	5.46958e10	−	9.53083e10i	0.556163	−	0.969123i
$561$		0			0
$562$	−7.28954e10	−	9.54858e9i	−0.730726	−	0.0957180i
$563$		−	1.13670e11i		−	1.13139i	−0.824614	−	0.565696i	$-0.808608\pi$
$563$		−	1.13670e11i		−	1.13139i	0.824614	−	0.565696i	$-0.191392\pi$
$564$		0			0
$565$	3.53676e10			0.347066
$566$	−1.42923e10	+	1.09109e11i	−0.139263	+	1.06315i
$567$		0			0
$568$	3.98369e10	−	9.67086e10i	0.382730	−	0.929120i
$569$	1.57868e11			1.50607			0.753034	−	0.657982i	$-0.228590\pi$
$569$	1.57868e11			1.50607			0.753034	+	0.657982i	$0.228590\pi$
$570$		0			0
$571$			7.63897e10i			0.718606i	0.933221	+	0.359303i	$0.116985\pi$
$571$			7.63897e10i			0.718606i	−0.933221	+	0.359303i	$0.883015\pi$
$572$	−1.49725e10	+	5.61706e10i	−0.139865	+	0.524716i
$573$		0			0
$574$	−2.75372e10	+	2.10223e11i	−0.253672	+	1.93657i
$575$		−	2.73200e9i		−	0.0249925i
$576$		0			0
$577$	2.03064e10			0.183202			0.0916010	−	0.995796i	$-0.470802\pi$
$577$	2.03064e10			0.183202			0.0916010	+	0.995796i	$0.470802\pi$
$578$	4.57752e10	+	5.99611e9i	0.410128	+	0.0537227i
$579$		0			0
$580$	−2.89470e9	−	7.71594e8i	−0.0255795	−	0.00681831i
$581$	1.67818e11			1.47276
$582$		0			0
$583$		−	1.43768e11i		−	1.24448i
$584$	1.26066e11	+	5.19298e10i	1.08379	+	0.446443i
$585$		0			0
$586$	6.10128e10	+	7.99207e9i	0.517405	+	0.0677749i
$587$			1.14252e11i			0.962306i	0.876637	+	0.481153i	$0.159782\pi$
$587$			1.14252e11i			0.962306i	−0.876637	+	0.481153i	$0.840218\pi$
$588$		0			0
$589$	1.39815e11			1.16170
$590$	4.82832e9	−	3.68602e10i	0.0398463	−	0.304193i
$591$		0			0
$592$	−7.05054e10	−	4.04619e10i	−0.574032	−	0.329427i
$593$	3.24685e10			0.262569			0.131285	−	0.991345i	$-0.458090\pi$
$593$	3.24685e10			0.262569			0.131285	+	0.991345i	$0.458090\pi$
$594$		0			0
$595$		−	1.66507e11i		−	1.32851i
$596$	4.40347e10	+	1.17376e10i	0.348988	+	0.0930241i
$597$		0			0
$598$	−3.98408e8	+	3.04151e9i	−0.00311547	+	0.0237840i
$599$		−	1.02381e11i		−	0.795267i	−0.917544	−	0.397633i	$-0.869832\pi$
$599$		−	1.02381e11i		−	0.795267i	0.917544	−	0.397633i	$-0.130168\pi$
$600$		0			0
$601$	−1.86440e11			−1.42903			−0.714516	−	0.699619i	$-0.753353\pi$
$601$	−1.86440e11			−1.42903			−0.714516	+	0.699619i	$0.753353\pi$
$602$	−1.91115e11	−	2.50342e10i	−1.45515	−	0.190611i
$603$		0			0
$604$	−6.03011e8	+	2.26225e9i	−0.00453083	+	0.0169978i
$605$	1.75921e10			0.131310
$606$		0			0
$607$		−	1.44933e11i		−	1.06761i	−0.845608	−	0.533805i	$-0.820762\pi$
$607$		−	1.44933e11i		−	1.06761i	0.845608	−	0.533805i	$-0.179238\pi$
$608$	7.35042e10	−	9.64410e10i	0.537896	−	0.705744i
$609$		0			0
$610$	−1.27074e10	−	1.66455e9i	−0.0917779	−	0.0120220i
$611$			1.56597e11i			1.12362i
$612$		0			0
$613$	−1.17256e11			−0.830413			−0.415206	−	0.909727i	$-0.636291\pi$
$613$	−1.17256e11			−0.830413			−0.415206	+	0.909727i	$0.636291\pi$
$614$	3.30689e10	−	2.52453e11i	0.232673	−	1.77626i
$615$		0			0
$616$	2.19180e11	+	9.02860e10i	1.52222	+	0.627043i
$617$	−2.27194e11			−1.56768			−0.783838	−	0.620965i	$-0.786741\pi$
$617$	−2.27194e11			−1.56768			−0.783838	+	0.620965i	$0.786741\pi$
$618$		0			0
$619$			2.58584e11i			1.76132i	0.473747	+	0.880661i	$0.342901\pi$
$619$			2.58584e11i			1.76132i	−0.473747	+	0.880661i	$0.657099\pi$
$620$	−2.98866e10	+	1.12122e11i	−0.202260	+	0.758796i
$621$		0			0
$622$	−1.00255e10	+	7.65363e10i	−0.0669800	+	0.511336i
$623$			1.61472e11i			1.07188i
$624$		0			0
$625$	7.63422e9			0.0500316
$626$	1.57792e11	+	2.06692e10i	1.02752	+	0.134595i
$627$		0			0
$628$	−5.55118e10	−	1.47969e10i	−0.356900	−	0.0951331i
$629$	−1.23176e11			−0.786905
$630$		0			0
$631$			1.44941e11i			0.914268i	0.889398	+	0.457134i	$0.151124\pi$
$631$			1.44941e11i			0.914268i	−0.889398	+	0.457134i	$0.848876\pi$
$632$	−3.41553e10	+	8.29160e10i	−0.214087	+	0.519721i
$633$		0			0
$634$	−1.80308e11	−	2.36186e10i	−1.11599	−	0.146183i
$635$			1.06059e11i			0.652305i
$636$		0			0
$637$	−2.49873e11			−1.51762
$638$	8.39341e8	−	6.40766e9i	0.00506589	−	0.0386738i
$639$		0			0
$640$	6.16270e10	+	7.95605e10i	0.367326	+	0.474218i
$641$	−9.48881e10			−0.562056			−0.281028	−	0.959700i	$-0.590675\pi$
$641$	−9.48881e10			−0.562056			−0.281028	+	0.959700i	$0.590675\pi$
$642$		0			0
$643$		−	1.08538e11i		−	0.634949i	−0.948267	−	0.317475i	$-0.897165\pi$
$643$		−	1.08538e11i		−	0.634949i	0.948267	−	0.317475i	$-0.102835\pi$
$644$	1.20865e10	+	3.22170e9i	0.0702677	+	0.0187301i
$645$		0			0
$646$	2.38639e10	−	1.82181e11i	0.137029	−	1.04610i
$647$		−	2.25310e11i		−	1.28577i	−0.765963	−	0.642884i	$-0.777738\pi$
$647$		−	2.25310e11i		−	1.28577i	0.765963	−	0.642884i	$-0.222262\pi$
$648$		0			0
$649$	8.01931e10			0.452021
$650$	−6.96219e10	−	9.11979e9i	−0.390025	−	0.0510895i
$651$		0			0
$652$	4.73894e10	−	1.77785e11i	0.262235	−	0.983798i
$653$	2.14348e11			1.17887			0.589436	−	0.807815i	$-0.299350\pi$
$653$	2.14348e11			1.17887			0.589436	+	0.807815i	$0.299350\pi$
$654$		0			0
$655$			3.74366e10i			0.203390i
$656$	−1.68409e11	−	9.66468e10i	−0.909387	−	0.521882i
$657$		0			0
$658$	6.33153e11	+	8.29369e10i	3.37758	+	0.442429i
$659$		−	2.90756e11i		−	1.54165i	−0.637044	−	0.770827i	$-0.719843\pi$
$659$		−	2.90756e11i		−	1.54165i	0.637044	−	0.770827i	$-0.280157\pi$
$660$		0			0
$661$	6.50949e10			0.340990			0.170495	−	0.985359i	$-0.445463\pi$
$661$	6.50949e10			0.340990			0.170495	+	0.985359i	$0.445463\pi$
$662$	−7.31337e9	+	5.58314e10i	−0.0380790	+	0.290701i
$663$		0			0
$664$	−5.85371e10	+	1.42106e11i	−0.301134	+	0.731036i
$665$	−1.93902e11			−0.991509
$666$		0			0
$667$		−	3.41007e8i		−	0.00172290i
$668$	1.92406e10	−	7.21828e10i	0.0966302	−	0.362516i
$669$		0			0
$670$	1.99088e9	−	1.51987e10i	0.00987976	−	0.0754237i
$671$		−	2.76463e10i		−	0.136379i
$672$		0			0
$673$	−2.72275e11			−1.32724			−0.663618	−	0.748072i	$-0.730980\pi$
$673$	−2.72275e11			−1.32724			−0.663618	+	0.748072i	$0.730980\pi$
$674$	2.32645e11	+	3.04742e10i	1.12734	+	0.147670i
$675$		0			0
$676$	−1.25602e11	−	3.34798e10i	−0.601465	−	0.160323i
$677$	−1.04438e11			−0.497170			−0.248585	−	0.968610i	$-0.579966\pi$
$677$	−1.04438e11			−0.497170			−0.248585	+	0.968610i	$0.579966\pi$
$678$		0			0
$679$			5.65115e10i			0.265863i
$680$	1.40996e11	+	5.80800e10i	0.659433	+	0.271638i
$681$		0			0
$682$	−2.48192e11	−	3.25107e10i	−1.14723	−	0.150276i
$683$			3.01459e11i			1.38531i	0.721271	+	0.692653i	$0.243558\pi$
$683$			3.01459e11i			1.38531i	−0.721271	+	0.692653i	$0.756442\pi$
$684$		0			0
$685$	4.43847e10			0.201591
$686$	−7.87583e10	+	6.01253e11i	−0.355631	+	2.71494i
$687$		0			0
$688$	8.78620e10	−	1.53101e11i	0.392146	−	0.683320i
$689$	−1.94981e11			−0.865197
$690$		0			0
$691$		−	5.88076e10i		−	0.257941i	−0.991648	−	0.128971i	$-0.958833\pi$
$691$		−	5.88076e10i		−	0.257941i	0.991648	−	0.128971i	$-0.0411673\pi$
$692$	−2.99303e11	−	7.97805e10i	−1.30523	−	0.347915i
$693$		0			0
$694$	3.50803e10	−	2.67809e11i	0.151226	−	1.15448i
$695$		−	1.08832e11i		−	0.466462i
$696$		0			0
$697$	−2.94216e11			−1.24662
$698$	1.60783e11	+	2.10610e10i	0.677358	+	0.0887273i
$699$		0			0
$700$	−7.37464e10	+	2.76666e11i	−0.307149	+	1.15229i
$701$	1.04963e11			0.434676			0.217338	−	0.976096i	$-0.430263\pi$
$701$	1.04963e11			0.434676			0.217338	+	0.976096i	$0.430263\pi$
$702$		0			0
$703$			1.43442e11i			0.587291i
$704$	−1.52906e11	+	1.54105e11i	−0.622491	+	0.627374i
$705$		0			0
$706$	−3.03210e10	−	3.97176e9i	−0.122046	−	0.0159869i
$707$			2.76865e10i			0.110813i
$708$		0			0
$709$	1.19072e11			0.471219			0.235610	−	0.971848i	$-0.424291\pi$
$709$	1.19072e11			0.471219			0.235610	+	0.971848i	$0.424291\pi$
$710$	1.98939e10	−	1.51874e11i	0.0782866	−	0.597653i
$711$		0			0
$712$	−1.36732e11	−	5.63236e10i	−0.532047	−	0.219165i
$713$	−1.32085e10			−0.0511086
$714$		0			0
$715$			8.51316e10i			0.325737i
$716$	9.58494e10	−	3.59587e11i	0.364701	−	1.36821i
$717$		0			0
$718$	1.73132e10	−	1.32171e11i	0.0651447	−	0.497325i
$719$			2.89449e11i			1.08307i	0.840679	+	0.541534i	$0.182156\pi$
$719$			2.89449e11i			1.08307i	−0.840679	+	0.541534i	$0.817844\pi$
$720$		0			0
$721$	8.63889e10			0.319681
$722$	5.72801e10	+	7.50313e9i	0.210792	+	0.0276117i
$723$		0			0
$724$	5.22120e10	+	1.39173e10i	0.190027	+	0.0506525i
$725$	7.80585e9			0.0282532
$726$		0			0
$727$			5.53322e10i			0.198080i	0.995083	+	0.0990399i	$0.0315771\pi$
$727$			5.53322e10i			0.198080i	−0.995083	+	0.0990399i	$0.968423\pi$
$728$	1.22448e11	−	2.97255e11i	0.435938	−	1.05829i
$729$		0			0
$730$	1.97977e11	+	2.59330e10i	0.697144	+	0.0913190i
$731$		−	2.67473e11i		−	0.936721i
$732$		0			0
$733$	1.07487e11			0.372339			0.186170	−	0.982518i	$-0.440393\pi$
$733$	1.07487e11			0.372339			0.186170	+	0.982518i	$0.440393\pi$
$734$	5.72986e10	−	4.37426e11i	0.197406	−	1.50703i
$735$		0			0
$736$	−6.94401e9	+	9.11087e9i	−0.0236646	+	0.0310491i
$737$	3.30664e10			0.112077
$738$		0			0
$739$		−	3.18755e11i		−	1.06876i	−0.845245	−	0.534379i	$-0.820545\pi$
$739$		−	3.18755e11i		−	1.06876i	0.845245	−	0.534379i	$-0.179455\pi$
$740$	−1.15030e11	−	3.06618e10i	−0.383607	−	0.102252i
$741$		0			0
$742$	−1.03266e11	+	7.88348e11i	−0.340676	+	2.60077i
$743$			1.52531e10i			0.0500497i	0.999687	+	0.0250249i	$0.00796649\pi$
$743$			1.52531e10i			0.0500497i	−0.999687	+	0.0250249i	$0.992034\pi$
$744$		0			0
$745$	6.67386e10			0.216647
$746$	1.79280e11	+	2.34839e10i	0.578864	+	0.0758255i
$747$		0			0
$748$	−8.47239e10	+	3.17849e11i	−0.270645	+	1.01535i
$749$	1.01912e12			3.23817
$750$		0			0
$751$			8.51300e10i			0.267623i	0.991007	+	0.133811i	$0.0427216\pi$
$751$			8.51300e10i			0.267623i	−0.991007	+	0.133811i	$0.957278\pi$
$752$	−2.91082e11	+	5.07215e11i	−0.910216	+	1.58607i
$753$		0			0
$754$	−8.69019e9	−	1.13833e9i	−0.0268871	−	0.00352194i
$755$			3.42864e9i			0.0105520i
$756$		0			0
$757$	4.85502e11			1.47845			0.739226	−	0.673457i	$-0.235191\pi$
$757$	4.85502e11			1.47845			0.739226	+	0.673457i	$0.235191\pi$
$758$	4.17305e10	−	3.18577e11i	0.126409	−	0.965024i
$759$		0			0
$760$	6.76359e10	−	1.64194e11i	0.202732	−	0.492156i
$761$	−3.60091e11			−1.07368			−0.536839	−	0.843685i	$-0.680382\pi$
$761$	−3.60091e11			−1.07368			−0.536839	+	0.843685i	$0.680382\pi$
$762$		0			0
$763$		−	6.70374e11i		−	1.97797i
$764$	−1.09804e11	+	4.11938e11i	−0.322287	+	1.20909i
$765$		0			0
$766$	4.75607e10	−	3.63086e11i	0.138144	−	1.05462i
$767$		−	1.08759e11i		−	0.314257i
$768$		0			0
$769$	2.93454e11			0.839139			0.419570	−	0.907723i	$-0.362181\pi$
$769$	2.93454e11			0.839139			0.419570	+	0.907723i	$0.362181\pi$
$770$	3.44205e11	+	4.50875e10i	0.979161	+	0.128261i
$771$		0			0
$772$	1.87265e11	+	4.99163e10i	0.527215	+	0.140531i
$773$	3.89598e11			1.09118			0.545592	−	0.838051i	$-0.316305\pi$
$773$	3.89598e11			1.09118			0.545592	+	0.838051i	$0.316305\pi$
$774$		0			0
$775$		−	3.02349e11i		−	0.838111i
$776$	−4.78531e10	−	1.97120e10i	−0.131966	−	0.0543605i
$777$		0			0
$778$	−5.15992e11	−	6.75899e10i	−1.40840	−	0.184486i
$779$			3.42623e11i			0.930394i
$780$		0			0
$781$	3.30416e11			0.888091
$782$	−2.25445e9	+	1.72108e10i	−0.00602856	+	0.0460230i
$783$		0			0
$784$	−8.09337e11	−	4.64465e11i	−2.14223	−	1.22939i
$785$	−8.41332e10			−0.221559
$786$		0			0
$787$			1.71711e11i			0.447609i	0.974634	+	0.223805i	$0.0718477\pi$
$787$			1.71711e11i			0.447609i	−0.974634	+	0.223805i	$0.928152\pi$
$788$	1.80916e11	+	4.82239e10i	0.469215	+	0.125071i
$789$		0			0
$790$	−1.70567e10	+	1.30213e11i	−0.0437911	+	0.334308i
$791$		−	4.21930e11i		−	1.07779i
$792$		0			0
$793$	−3.74944e10			−0.0948143
$794$	−6.27399e11	−	8.21832e10i	−1.57856	−	0.206776i
$795$		0			0
$796$	6.72804e10	−	2.52408e11i	0.167585	−	0.628711i
$797$	−5.13006e11			−1.27142			−0.635710	−	0.771928i	$-0.719293\pi$
$797$	−5.13006e11			−1.27142			−0.635710	+	0.771928i	$0.719293\pi$
$798$		0			0
$799$			8.86124e11i			2.17424i
$800$	−2.08553e11	−	1.58952e11i	−0.509162	−	0.388067i
$801$		0			0
$802$	6.40568e11	+	8.39081e10i	1.54835	+	0.202818i
$803$			4.30718e11i			1.03593i
$804$		0			0
$805$	1.83181e10			0.0436212
$806$	−4.40916e10	+	3.36602e11i	−0.104476	+	0.797585i
$807$		0			0
$808$	−2.34446e10	−	9.65745e9i	−0.0550043	−	0.0226578i
$809$	6.85342e11			1.59997			0.799987	−	0.600017i	$-0.204839\pi$
$809$	6.85342e11			1.59997			0.799987	+	0.600017i	$0.204839\pi$
$810$		0			0
$811$			4.87378e11i			1.12663i	0.826241	+	0.563317i	$0.190475\pi$
$811$			4.87378e11i			1.12663i	−0.826241	+	0.563317i	$0.809525\pi$
$812$	−9.20501e9	+	3.45334e10i	−0.0211739	+	0.0794355i
$813$		0			0
$814$	3.33540e10	−	2.54630e11i	0.0759714	−	0.579978i
$815$		−	2.69450e11i		−	0.610728i
$816$		0			0
$817$	−3.11480e11			−0.699104
$818$	−3.40459e10	−	4.45967e9i	−0.0760416	−	0.00996070i
$819$		0			0
$820$	−2.74761e11	−	7.32386e10i	−0.607714	−	0.161989i
$821$	−9.57797e10			−0.210815			−0.105407	−	0.994429i	$-0.533615\pi$
$821$	−9.57797e10			−0.210815			−0.105407	+	0.994429i	$0.533615\pi$
$822$		0			0
$823$		−	6.07905e9i		−	0.0132506i	−0.999978	−	0.00662531i	$-0.997891\pi$
$823$		−	6.07905e9i		−	0.0132506i	0.999978	−	0.00662531i	$-0.00210892\pi$
$824$	−3.01337e10	+	7.31529e10i	−0.0653647	+	0.158680i
$825$		0			0
$826$	−4.39737e11	−	5.76012e10i	−0.944653	−	0.123740i
$827$		−	7.37214e11i		−	1.57605i	−0.615640	−	0.788027i	$-0.711103\pi$
$827$		−	7.37214e11i		−	1.57605i	0.615640	−	0.788027i	$-0.288897\pi$
$828$		0			0
$829$	2.05577e11			0.435269			0.217634	−	0.976030i	$-0.430166\pi$
$829$	2.05577e11			0.435269			0.217634	+	0.976030i	$0.430166\pi$
$830$	−2.92326e10	+	2.23166e11i	−0.0615963	+	0.470236i
$831$		0			0
$832$	2.09000e11	+	2.07374e11i	0.436167	+	0.432773i
$833$	−1.41394e12			−2.93665
$834$		0			0
$835$		−	1.09400e11i		−	0.225045i
$836$	3.70144e11	+	9.86635e10i	0.757785	+	0.201991i
$837$		0			0
$838$	−1.15180e11	+	8.79304e11i	−0.233562	+	1.78305i
$839$			3.05355e11i			0.616250i	0.951346	+	0.308125i	$0.0997015\pi$
$839$			3.05355e11i			0.616250i	−0.951346	+	0.308125i	$0.900298\pi$
$840$		0			0
$841$	−4.99272e11			−0.998052
$842$	1.24495e11	+	1.63077e10i	0.247688	+	0.0324446i
$843$		0			0
$844$	1.19823e11	−	4.49527e11i	0.236141	−	0.885902i
$845$	−1.90362e11			−0.373381
$846$		0			0
$847$		−	2.09871e11i		−	0.407774i
$848$	−6.31541e11	−	3.62431e11i	−1.22129	−	0.700877i
$849$		0			0
$850$	−3.93965e11	−	5.16056e10i	−0.754714	−	0.0988601i
$851$		−	1.35511e10i		−	0.0258378i
$852$		0			0
$853$	−6.05342e11			−1.14342			−0.571709	−	0.820457i	$-0.693719\pi$
$853$	−6.05342e11			−1.14342			−0.571709	+	0.820457i	$0.693719\pi$
$854$	−1.98578e10	+	1.51598e11i	−0.0373336	+	0.285011i
$855$		0			0
$856$	−3.55484e11	+	8.62978e11i	−0.662102	+	1.60733i
$857$	4.98335e11			0.923843			0.461921	−	0.886921i	$-0.347160\pi$
$857$	4.98335e11			0.923843			0.461921	+	0.886921i	$0.347160\pi$
$858$		0			0
$859$		−	7.49759e11i		−	1.37705i	−0.725214	−	0.688524i	$-0.758259\pi$
$859$		−	7.49759e11i		−	1.37705i	0.725214	−	0.688524i	$-0.241741\pi$
$860$	6.65815e10	−	2.49786e11i	0.121719	−	0.456640i
$861$		0			0
$862$	4.19833e10	−	3.20507e11i	0.0760410	−	0.580509i
$863$		−	3.32171e10i		−	0.0598850i	−0.999552	−	0.0299425i	$-0.990468\pi$
$863$		−	3.32171e10i		−	0.0598850i	0.999552	−	0.0299425i	$-0.00953242\pi$
$864$		0			0
$865$	−4.53622e11			−0.810269
$866$	−6.73710e11	−	8.82494e10i	−1.19785	−	0.156906i
$867$		0			0
$868$	1.33760e12	+	3.56543e11i	2.35639	+	0.628106i
$869$	−2.83292e11			−0.496770
$870$		0			0
$871$		−	4.48452e10i		−	0.0779190i
$872$	5.67663e11	+	2.33836e11i	0.981804	+	0.404432i
$873$		0			0
$874$	2.00425e10	+	2.62537e9i	0.0343484	+	0.00449930i
$875$			1.07429e12i			1.83270i
$876$		0			0
$877$	1.59141e10			0.0269020			0.0134510	−	0.999910i	$-0.495718\pi$
$877$	1.59141e10			0.0269020			0.0134510	+	0.999910i	$0.495718\pi$
$878$	6.51907e9	−	4.97676e10i	0.0109700	−	0.0837469i
$879$		0			0
$880$	−1.58243e11	+	2.75741e11i	−0.263872	+	0.459801i
$881$	−1.50297e11			−0.249486			−0.124743	−	0.992189i	$-0.539811\pi$
$881$	−1.50297e11			−0.249486			−0.124743	+	0.992189i	$0.539811\pi$
$882$		0			0
$883$			8.12117e11i			1.33591i	0.744203	+	0.667953i	$0.232829\pi$
$883$			8.12117e11i			1.33591i	−0.744203	+	0.667953i	$0.767171\pi$
$884$	4.31073e11	+	1.14904e11i	0.705897	+	0.188160i
$885$		0			0
$886$	1.52565e11	−	1.16470e12i	0.247582	−	1.89008i
$887$			8.54543e11i			1.38051i	0.723566	+	0.690255i	$0.242502\pi$
$887$			8.54543e11i			1.38051i	−0.723566	+	0.690255i	$0.757498\pi$
$888$		0			0
$889$	1.26526e12			2.02569
$890$	−2.14727e11	−	2.81272e10i	−0.342237	−	0.0448297i
$891$		0			0
$892$	1.38958e11	−	5.21314e11i	0.219495	−	0.823456i
$893$	1.03192e12			1.62270
$894$		0			0
$895$		−	5.44987e11i		−	0.849365i
$896$	9.49146e11	−	7.35202e11i	1.47265	−	1.14071i
$897$		0			0
$898$	9.60036e11	+	1.25755e11i	1.47633	+	0.193384i
$899$		−	3.77391e10i		−	0.0577767i
$900$		0			0
$901$	−1.10333e12			−1.67419
$902$	7.96690e10	−	6.08206e11i	0.120355	−	0.918807i
$903$		0			0
$904$	3.57285e11	+	1.47175e11i	0.534984	+	0.220374i
$905$	7.91320e10			0.117966
$906$		0			0
$907$		−	3.08390e11i		−	0.455692i	−0.973697	−	0.227846i	$-0.926832\pi$
$907$		−	3.08390e11i		−	0.455692i	0.973697	−	0.227846i	$-0.0731683\pi$
$908$	6.06991e9	−	2.27718e10i	0.00892974	−	0.0335007i
$909$		0			0
$910$	6.11485e10	−	4.66817e11i	0.0891702	−	0.680740i
$911$		−	1.27670e12i		−	1.85360i	−0.375555	−	0.926800i	$-0.622548\pi$
$911$		−	1.27670e12i		−	1.85360i	0.375555	−	0.926800i	$-0.377452\pi$
$912$		0			0
$913$	−4.85521e11			−0.698754
$914$	4.13115e11	+	5.41140e10i	0.591951	+	0.0775398i
$915$		0			0
$916$	9.20382e11	+	2.45332e11i	1.30733	+	0.348475i
$917$	4.46613e11			0.631617
$918$		0			0
$919$		−	9.02035e11i		−	1.26462i	−0.774714	−	0.632312i	$-0.782106\pi$
$919$		−	9.02035e11i		−	1.26462i	0.774714	−	0.632312i	$-0.217894\pi$
$920$	−6.38962e9	+	1.55115e10i	−0.00891916	+	0.0216523i
$921$		0			0
$922$	−6.74956e11	−	8.84127e10i	−0.934011	−	0.122346i
$923$		−	4.48117e11i		−	0.617425i
$924$		0			0
$925$	3.10191e11			0.423704
$926$	−4.61882e10	+	3.52608e11i	−0.0628185	+	0.479566i
$927$		0			0
$928$	−2.60315e10	−	1.98404e10i	−0.0351000	−	0.0267521i
$929$	−4.51064e11			−0.605585			−0.302793	−	0.953056i	$-0.597919\pi$
$929$	−4.51064e11			−0.605585			−0.302793	+	0.953056i	$0.597919\pi$
$930$		0			0
$931$			1.64658e12i			2.19171i
$932$	1.02970e12	+	2.74471e11i	1.36473	+	0.363775i
$933$		0			0
$934$	−1.25867e11	+	9.60888e11i	−0.165396	+	1.26266i
$935$			4.81729e11i			0.630313i
$936$		0			0
$937$	−1.78546e10			−0.0231628			−0.0115814	−	0.999933i	$-0.503687\pi$
$937$	−1.78546e10			−0.0231628			−0.0115814	+	0.999933i	$0.503687\pi$
$938$	−1.81318e11	−	2.37509e10i	−0.234224	−	0.0306810i
$939$		0			0
$940$	−2.20581e11	+	8.27528e11i	−0.282525	+	1.05992i
$941$	−4.03037e11			−0.514028			−0.257014	−	0.966408i	$-0.582739\pi$
$941$	−4.03037e11			−0.514028			−0.257014	+	0.966408i	$0.582739\pi$
$942$		0			0
$943$		−	3.23679e10i		−	0.0409325i
$944$	2.02162e11	−	3.52271e11i	0.254573	−	0.443597i
$945$		0			0
$946$	5.52922e11	+	7.24274e10i	0.690398	+	0.0904354i
$947$		−	1.09600e12i		−	1.36273i	−0.731942	−	0.681367i	$-0.761386\pi$
$947$		−	1.09600e12i		−	1.36273i	0.731942	−	0.681367i	$-0.238614\pi$
$948$		0			0
$949$	5.84148e11			0.720208
$950$	−6.00962e10	+	4.58784e11i	−0.0737824	+	0.563266i
$951$		0			0
$952$	6.92886e11	−	1.68206e12i	0.843557	−	2.04783i
$953$	−1.08909e12			−1.32036			−0.660179	−	0.751108i	$-0.729520\pi$
$953$	−1.08909e12			−1.32036			−0.660179	+	0.751108i	$0.729520\pi$
$954$		0			0
$955$			6.24329e11i			0.750586i
$956$	−9.30458e10	+	3.49069e11i	−0.111395	+	0.417907i
$957$		0			0
$958$	−8.86598e10	+	6.76843e11i	−0.105260	+	0.803574i
$959$		−	5.29503e11i		−	0.626029i
$960$		0			0
$961$	−6.08880e11			−0.713901
$962$	−3.45333e11	−	4.52353e10i	−0.403216	−	0.0528174i
$963$		0			0
$964$	−1.36573e12	−	3.64042e11i	−1.58146	−	0.421545i
$965$	2.83818e11			0.327288
$966$		0			0
$967$			3.98199e11i			0.455402i	0.973731	+	0.227701i	$0.0731208\pi$
$967$			3.98199e11i			0.455402i	−0.973731	+	0.227701i	$0.926879\pi$
$968$	1.77716e11	+	7.32060e10i	0.202407	+	0.0833768i
$969$		0			0
$970$	−7.51497e10	−	9.84387e9i	−0.0848868	−	0.0111193i
$971$			6.52799e11i			0.734349i	0.930152	+	0.367175i	$0.119675\pi$
$971$			6.52799e11i			0.734349i	−0.930152	+	0.367175i	$0.880325\pi$
$972$		0			0
$973$	−1.29835e12			−1.44857
$974$	−1.37118e11	+	1.04678e12i	−0.152356	+	1.16311i
$975$		0			0
$976$	−1.21444e11	−	6.96947e10i	−0.133837	−	0.0768070i
$977$	7.17862e11			0.787885			0.393943	−	0.919135i	$-0.371111\pi$
$977$	7.17862e11			0.787885			0.393943	+	0.919135i	$0.371111\pi$
$978$		0			0
$979$		−	4.67161e11i		−	0.508553i
$980$	−1.32044e12	−	3.51970e11i	−1.43158	−	0.381594i
$981$		0			0
$982$	8.64025e10	−	6.59611e11i	0.0929139	−	0.709319i
$983$			9.40181e11i			1.00693i	0.864017	+	0.503463i	$0.167941\pi$
$983$			9.40181e11i			1.00693i	−0.864017	+	0.503463i	$0.832059\pi$
$984$		0			0
$985$	2.74195e11			0.291282
$986$	−4.91746e10	−	6.44140e9i	−0.0520276	−	0.00681510i
$987$		0			0
$988$	1.33809e11	−	5.01996e11i	0.140429	−	0.526833i
$989$	2.94258e10			0.0307570
$990$		0			0
$991$		−	8.13083e10i		−	0.0843025i	−0.999111	−	0.0421512i	$-0.986579\pi$
$991$		−	8.13083e10i		−	0.0843025i	0.999111	−	0.0421512i	$-0.0134211\pi$
$992$	−7.68490e11	+	1.00829e12i	−0.793581	+	1.04122i
$993$		0			0
$994$	−1.81183e12	−	2.37332e11i	−1.85597	−	0.243114i
$995$		−	3.82547e11i		−	0.390295i
$996$		0			0
$997$	1.94960e12			1.97318			0.986588	−	0.163232i	$-0.0521919\pi$
$997$	1.94960e12			1.97318			0.986588	+	0.163232i	$0.0521919\pi$
$998$	1.64163e11	−	1.25324e12i	0.165482	−	1.26332i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.9.d.c.19.8		8
3.2	odd	2		12.9.d.a.7.1	✓	8
4.3	odd	2	inner	36.9.d.c.19.7		8
12.11	even	2		12.9.d.a.7.2	yes	8
24.5	odd	2		192.9.g.e.127.3		8
24.11	even	2		192.9.g.e.127.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.9.d.a.7.1	✓	8	3.2	odd	2
12.9.d.a.7.2	yes	8	12.11	even	2
36.9.d.c.19.7		8	4.3	odd	2	inner
36.9.d.c.19.8		8	1.1	even	1	trivial
192.9.g.e.127.3		8	24.5	odd	2
192.9.g.e.127.7		8	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	36.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(15.8645 + 2.07809i) q^{2} +(247.363 + 65.9356i) q^{4} +374.901 q^{5} -4472.52i q^{7} +(3787.26 + 1560.08i) q^{8} +O(q^{10})\)	\(q+(15.8645 + 2.07809i) q^{2} +(247.363 + 65.9356i) q^{4} +374.901 q^{5} -4472.52i q^{7} +(3787.26 + 1560.08i) q^{8} +(5947.61 + 779.079i) q^{10} +12939.6i q^{11} +17549.0 q^{13} +(9294.30 - 70954.2i) q^{14} +(56841.0 + 32620.1i) q^{16} +99303.3 q^{17} -115642. i q^{19} +(92736.8 + 24719.4i) q^{20} +(-26889.7 + 205281. i) q^{22} +10924.8i q^{23} -250074. q^{25} +(278405. + 36468.4i) q^{26} +(294898. - 1.10634e6i) q^{28} -31214.2 q^{29} +1.20904e6i q^{31} +(833965. + 635621. i) q^{32} +(1.57539e6 + 206361. i) q^{34} -1.67675e6i q^{35} -1.24040e6 q^{37} +(240314. - 1.83459e6i) q^{38} +(1.41985e6 + 584875. i) q^{40} -2.96280e6 q^{41} -2.69350e6i q^{43} +(-853183. + 3.20079e6i) q^{44} +(-22702.7 + 173316. i) q^{46} +8.92341e6i q^{47} -1.42386e7 q^{49} +(-3.96729e6 - 519676. i) q^{50} +(4.34097e6 + 1.15710e6i) q^{52} -1.11107e7 q^{53} +4.85109e6i q^{55} +(6.97747e6 - 1.69386e7i) q^{56} +(-495196. - 64865.9i) q^{58} -6.19748e6i q^{59} -2.13656e6 q^{61} +(-2.51249e6 + 1.91807e7i) q^{62} +(1.19095e7 + 1.18169e7i) q^{64} +6.57914e6 q^{65} -2.55543e6i q^{67} +(2.45640e7 + 6.54763e6i) q^{68} +(3.48445e6 - 2.66008e7i) q^{70} -2.55352e7i q^{71} +3.32867e7 q^{73} +(-1.96783e7 - 2.57766e6i) q^{74} +(7.62490e6 - 2.86055e7i) q^{76} +5.78728e7 q^{77} +2.18934e7i q^{79} +(2.13098e7 + 1.22293e7i) q^{80} +(-4.70033e7 - 6.15697e6i) q^{82} +3.75220e7i q^{83} +3.72290e7 q^{85} +(5.59733e6 - 4.27309e7i) q^{86} +(-2.01868e7 + 4.90058e7i) q^{88} -3.61031e7 q^{89} -7.84881e7i q^{91} +(-720332. + 2.70238e6i) q^{92} +(-1.85437e7 + 1.41565e8i) q^{94} -4.33542e7i q^{95} -1.26353e7 q^{97} +(-2.25888e8 - 2.95892e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 52 q^{4} + 336 q^{5} + 12960 q^{8}+O(q^{10}) \) 8 * q - 6 * q^2 - 52 * q^4 + 336 * q^5 + 12960 * q^8	\( 8 q - 6 q^{2} - 52 q^{4} + 336 q^{5} + 12960 q^{8} + 36628 q^{10} - 2864 q^{13} - 52728 q^{14} + 99440 q^{16} + 193200 q^{17} - 335592 q^{20} - 556968 q^{22} - 579048 q^{25} - 21564 q^{26} - 594672 q^{28} - 2063472 q^{29} + 3602784 q^{32} + 1568476 q^{34} + 7470352 q^{37} - 3659400 q^{38} + 1749184 q^{40} + 8865456 q^{41} - 2395920 q^{44} - 13649856 q^{46} - 18923896 q^{49} - 14581842 q^{50} + 18592888 q^{52} - 8706672 q^{53} + 45565632 q^{56} - 8816444 q^{58} + 13457296 q^{61} - 80783976 q^{62} + 1268864 q^{64} - 7293408 q^{65} + 117288264 q^{68} - 60373104 q^{70} + 94738960 q^{73} - 119548428 q^{74} + 144621360 q^{76} + 56971392 q^{77} + 163857888 q^{80} - 188383460 q^{82} - 201200416 q^{85} - 240327384 q^{86} + 156323520 q^{88} - 188992272 q^{89} + 387657984 q^{92} - 38749872 q^{94} - 123291632 q^{97} - 691081830 q^{98}+O(q^{100}) \) 8 * q - 6 * q^2 - 52 * q^4 + 336 * q^5 + 12960 * q^8 + 36628 * q^10 - 2864 * q^13 - 52728 * q^14 + 99440 * q^16 + 193200 * q^17 - 335592 * q^20 - 556968 * q^22 - 579048 * q^25 - 21564 * q^26 - 594672 * q^28 - 2063472 * q^29 + 3602784 * q^32 + 1568476 * q^34 + 7470352 * q^37 - 3659400 * q^38 + 1749184 * q^40 + 8865456 * q^41 - 2395920 * q^44 - 13649856 * q^46 - 18923896 * q^49 - 14581842 * q^50 + 18592888 * q^52 - 8706672 * q^53 + 45565632 * q^56 - 8816444 * q^58 + 13457296 * q^61 - 80783976 * q^62 + 1268864 * q^64 - 7293408 * q^65 + 117288264 * q^68 - 60373104 * q^70 + 94738960 * q^73 - 119548428 * q^74 + 144621360 * q^76 + 56971392 * q^77 + 163857888 * q^80 - 188383460 * q^82 - 201200416 * q^85 - 240327384 * q^86 + 156323520 * q^88 - 188992272 * q^89 + 387657984 * q^92 - 38749872 * q^94 - 123291632 * q^97 - 691081830 * q^98

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