LMFDB - Embedded newform 99.12.f.a.91.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [99,12,Mod(37,99)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("99.37"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(99, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,-11] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$76.0659748754$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.7
Character	$\chi$	$=$	99.91
Dual form			99.12.f.a.37.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(32.2868 - 23.4578i) q^{2} +(-140.693 + 433.009i) q^{4} +(5225.04 + 3796.22i) q^{5} +(-10421.9 + 32075.4i) q^{7} +(30871.8 + 95013.6i) q^{8} +257751. q^{10} +(-534118. + 5398.75i) q^{11} +(1.51212e6 - 1.09862e6i) q^{13} +(415926. + 1.28009e6i) q^{14} +(2.47120e6 + 1.79543e6i) q^{16} +(7.07508e6 + 5.14035e6i) q^{17} +(1.12278e6 + 3.45556e6i) q^{19} +(-2.37892e6 + 1.72839e6i) q^{20} +(-1.71184e7 + 1.27035e7i) q^{22} -3.57846e6 q^{23} +(-2.19890e6 - 6.76752e6i) q^{25} +(2.30504e7 - 7.09417e7i) q^{26} +(-1.24227e7 - 9.02559e6i) q^{28} +(-4.87068e7 + 1.49904e8i) q^{29} +(-7.75532e7 + 5.63457e7i) q^{31} -8.26977e7 q^{32} +3.49013e8 q^{34} +(-1.76220e8 + 1.28032e8i) q^{35} +(1.22645e8 - 3.77462e8i) q^{37} +(1.17311e8 + 8.52313e7i) q^{38} +(-1.99386e8 + 6.13646e8i) q^{40} +(-1.29621e8 - 3.98933e8i) q^{41} -1.37574e9 q^{43} +(7.28091e7 - 2.32038e8i) q^{44} +(-1.15537e8 + 8.39426e7i) q^{46} +(-1.45109e7 - 4.46598e7i) q^{47} +(6.79475e8 + 4.93667e8i) q^{49} +(-2.29746e8 - 1.66921e8i) q^{50} +(2.62967e8 + 8.09328e8i) q^{52} +(-3.26331e9 + 2.37093e9i) q^{53} +(-2.81129e9 - 1.99942e9i) q^{55} -3.36935e9 q^{56} +(1.94383e9 + 5.98248e9i) q^{58} +(-3.07095e9 + 9.45140e9i) q^{59} +(-3.60357e9 - 2.61815e9i) q^{61} +(-1.18220e9 + 3.63845e9i) q^{62} +(-7.73107e9 + 5.61695e9i) q^{64} +1.20715e10 q^{65} +1.31058e10 q^{67} +(-3.22123e9 + 2.34036e9i) q^{68} +(-2.68626e9 + 8.26747e9i) q^{70} +(-2.21873e9 - 1.61200e9i) q^{71} +(-1.15544e9 + 3.55607e9i) q^{73} +(-4.89460e9 - 1.50640e10i) q^{74} -1.65426e9 q^{76} +(5.39338e9 - 1.71883e10i) q^{77} +(-1.17002e10 + 8.50068e9i) q^{79} +(6.09628e9 + 1.87624e10i) q^{80} +(-1.35431e10 - 9.83966e9i) q^{82} +(9.56204e9 + 6.94723e9i) q^{83} +(1.74537e10 + 5.37171e10i) q^{85} +(-4.44183e10 + 3.22718e10i) q^{86} +(-1.70022e10 - 5.05819e10i) q^{88} -3.19799e10 q^{89} +(1.94794e10 + 5.99515e10i) q^{91} +(5.03464e8 - 1.54950e9i) q^{92} +(-1.51613e9 - 1.10153e9i) q^{94} +(-7.25149e9 + 2.23178e10i) q^{95} +(2.68932e10 - 1.95390e10i) q^{97} +3.35184e10 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 11 q^{2} - 6137 q^{4} - 6038 q^{5} + 55440 q^{7} + 347809 q^{8} + 782320 q^{10} + 288860 q^{11} - 794178 q^{13} - 9181256 q^{14} - 10033697 q^{16} - 11803154 q^{17} - 33326568 q^{19} - 34173582 q^{20}+ \cdots - 1187521497580 q^{98}+O(q^{100}) $ 40 * q - 11 * q^2 - 6137 * q^4 - 6038 * q^5 + 55440 * q^7 + 347809 * q^8 + 782320 * q^10 + 288860 * q^11 - 794178 * q^13 - 9181256 * q^14 - 10033697 * q^16 - 11803154 * q^17 - 33326568 * q^19 - 34173582 * q^20 + 77957825 * q^22 - 75694752 * q^23 - 118409216 * q^25 - 605949712 * q^26 - 546845442 * q^28 + 400113538 * q^29 + 514005960 * q^31 + 84440796 * q^32 - 899802542 * q^34 + 1820315508 * q^35 + 1207982934 * q^37 - 1815036992 * q^38 - 1263004028 * q^40 + 3269102782 * q^41 + 2749122728 * q^43 - 5968984648 * q^44 - 1240862964 * q^46 + 2081937184 * q^47 - 2514603052 * q^49 - 7217881803 * q^50 + 23226253050 * q^52 + 7132071266 * q^53 - 9211291408 * q^55 - 33017775912 * q^56 - 34218647932 * q^58 + 12866186432 * q^59 + 2702502990 * q^61 + 18405787180 * q^62 + 28267347551 * q^64 - 28056414980 * q^65 - 549542392 * q^67 + 17332191778 * q^68 - 90854725304 * q^70 + 37002489528 * q^71 - 41936764254 * q^73 - 118297253448 * q^74 + 136670345702 * q^76 - 85397422330 * q^77 - 140458240296 * q^79 + 257276697596 * q^80 - 94584428059 * q^82 + 238929577568 * q^83 + 48160626338 * q^85 - 176827923479 * q^86 + 742233436703 * q^88 - 311499953960 * q^89 - 410566597652 * q^91 - 77316479782 * q^92 - 508753213738 * q^94 + 524637979272 * q^95 + 474017921070 * q^97 - 1187521497580 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	32.2868	−	23.4578i	0.713445	−	0.518348i	−0.170838	−	0.985299i	$-0.554647\pi$
$2$	32.2868	−	23.4578i	0.713445	−	0.518348i	0.884283	+	0.466951i	$0.154647\pi$
$3$		0			0
$3$		0			0
$4$	−140.693	+	433.009i	−0.0686979	+	0.211430i
$5$	5225.04	+	3796.22i	0.747747	+	0.543270i	0.895128	−	0.445810i	$-0.147084\pi$
$5$	5225.04	+	3796.22i	0.747747	+	0.543270i	−0.147380	+	0.989080i	$0.547084\pi$
$6$		0			0
$7$	−10421.9	+	32075.4i	−0.234374	+	0.721329i	0.762830	+	0.646599i	$0.223809\pi$
$7$	−10421.9	+	32075.4i	−0.234374	+	0.721329i	−0.997204	+	0.0747296i	$0.976191\pi$
$8$	30871.8	+	95013.6i	0.333094	+	1.02516i
$9$		0			0
$10$	257751.			0.815080
$11$	−534118.	+	5398.75i	−0.999949	+	0.0101073i
$11$	−534118.	+	5398.75i	−0.999949	+	0.0101073i
$12$		0			0
$13$	1.51212e6	−	1.09862e6i	1.12953	−	0.820649i	0.143901	−	0.989592i	$-0.454035\pi$
$13$	1.51212e6	−	1.09862e6i	1.12953	−	0.820649i	0.985626	+	0.168943i	$0.0540353\pi$
$14$	415926.	+	1.28009e6i	0.206687	+	0.636116i
$15$		0			0
$16$	2.47120e6	+	1.79543e6i	0.589180	+	0.428065i
$17$	7.07508e6	+	5.14035e6i	1.20854	+	0.878058i	0.995098	−	0.0988967i	$-0.0315313\pi$
$17$	7.07508e6	+	5.14035e6i	1.20854	+	0.878058i	0.213446	+	0.976955i	$0.431531\pi$
$18$		0			0
$19$	1.12278e6	+	3.45556e6i	0.104028	+	0.320165i	0.989501	−	0.144525i	$-0.0461656\pi$
$19$	1.12278e6	+	3.45556e6i	0.104028	+	0.320165i	−0.885473	+	0.464691i	$0.846166\pi$
$20$	−2.37892e6	+	1.72839e6i	−0.166232	+	0.120775i
$21$		0			0
$22$	−1.71184e7	+	1.27035e7i	−0.708170	+	0.525533i
$23$	−3.57846e6			−0.115929			−0.0579646	−	0.998319i	$-0.518461\pi$
$23$	−3.57846e6			−0.115929			−0.0579646	+	0.998319i	$0.518461\pi$
$24$		0			0
$25$	−2.19890e6	−	6.76752e6i	−0.0450335	−	0.138599i
$26$	2.30504e7	−	7.09417e7i	0.380473	−	1.17098i
$27$		0			0
$28$	−1.24227e7	−	9.02559e6i	−0.136410	−	0.0991075i
$29$	−4.87068e7	+	1.49904e8i	−0.440961	+	1.35714i	0.445892	+	0.895087i	$0.352887\pi$
$29$	−4.87068e7	+	1.49904e8i	−0.440961	+	1.35714i	−0.886853	+	0.462052i	$0.847113\pi$
$30$		0			0
$31$	−7.75532e7	+	5.63457e7i	−0.486531	+	0.353486i	−0.803849	−	0.594834i	$-0.797218\pi$
$31$	−7.75532e7	+	5.63457e7i	−0.486531	+	0.353486i	0.317318	+	0.948319i	$0.397218\pi$
$32$	−8.26977e7			−0.435681
$33$		0			0
$34$	3.49013e8			1.31737
$35$	−1.76220e8	+	1.28032e8i	−0.567129	+	0.412043i
$36$		0			0
$37$	1.22645e8	−	3.77462e8i	0.290763	−	0.894877i	−0.693849	−	0.720121i	$-0.744086\pi$
$37$	1.22645e8	−	3.77462e8i	0.290763	−	0.894877i	0.984612	−	0.174756i	$-0.0559137\pi$
$38$	1.17311e8	+	8.52313e7i	0.240175	+	0.174498i
$39$		0			0
$40$	−1.99386e8	+	6.13646e8i	−0.307868	+	0.947520i
$41$	−1.29621e8	−	3.98933e8i	−0.174729	−	0.537760i	0.824892	−	0.565290i	$-0.191236\pi$
$41$	−1.29621e8	−	3.98933e8i	−0.174729	−	0.537760i	−0.999621	+	0.0275300i	$0.991236\pi$
$42$		0			0
$43$	−1.37574e9			−1.42712			−0.713559	−	0.700595i	$-0.752918\pi$
$43$	−1.37574e9			−1.42712			−0.713559	+	0.700595i	$0.752918\pi$
$44$	7.28091e7	−	2.32038e8i	0.0665574	−	0.212114i
$45$		0			0
$46$	−1.15537e8	+	8.39426e7i	−0.0827091	+	0.0600917i
$47$	−1.45109e7	−	4.46598e7i	−0.00922901	−	0.0284040i	0.946336	−	0.323185i	$-0.104753\pi$
$47$	−1.45109e7	−	4.46598e7i	−0.00922901	−	0.0284040i	−0.955565	+	0.294781i	$0.904753\pi$
$48$		0			0
$49$	6.79475e8	+	4.93667e8i	0.343633	+	0.249664i
$50$	−2.29746e8	−	1.66921e8i	−0.103971	−	0.0755396i
$51$		0			0
$52$	2.62967e8	+	8.09328e8i	0.0959140	+	0.295193i
$53$	−3.26331e9	+	2.37093e9i	−1.07187	+	0.778757i	−0.976247	−	0.216660i	$-0.930484\pi$
$53$	−3.26331e9	+	2.37093e9i	−1.07187	+	0.778757i	−0.0956206	+	0.995418i	$0.530484\pi$
$54$		0			0
$55$	−2.81129e9	−	1.99942e9i	−0.753200	−	0.535685i
$56$	−3.36935e9			−0.817545
$57$		0			0
$58$	1.94383e9	+	5.98248e9i	0.388869	+	1.19682i
$59$	−3.07095e9	+	9.45140e9i	−0.559224	+	1.72112i	0.125294	+	0.992120i	$0.460013\pi$
$59$	−3.07095e9	+	9.45140e9i	−0.559224	+	1.72112i	−0.684518	+	0.728996i	$0.739987\pi$
$60$		0			0
$61$	−3.60357e9	−	2.61815e9i	−0.546284	−	0.396899i	0.280129	−	0.959962i	$-0.409623\pi$
$61$	−3.60357e9	−	2.61815e9i	−0.546284	−	0.396899i	−0.826414	+	0.563063i	$0.809623\pi$
$62$	−1.18220e9	+	3.63845e9i	−0.163885	+	0.504385i
$63$		0			0
$64$	−7.73107e9	+	5.61695e9i	−0.900015	+	0.653899i
$65$	1.20715e10			1.29044
$66$		0			0
$67$	1.31058e10			1.18591			0.592954	−	0.805237i	$-0.297962\pi$
$67$	1.31058e10			1.18591			0.592954	+	0.805237i	$0.297962\pi$
$68$	−3.22123e9	+	2.34036e9i	−0.268672	+	0.195202i
$69$		0			0
$70$	−2.68626e9	+	8.26747e9i	−0.191033	+	0.587941i
$71$	−2.21873e9	−	1.61200e9i	−0.145943	−	0.106034i	0.512418	−	0.858736i	$-0.328750\pi$
$71$	−2.21873e9	−	1.61200e9i	−0.145943	−	0.106034i	−0.658361	+	0.752702i	$0.728750\pi$
$72$		0			0
$73$	−1.15544e9	+	3.55607e9i	−0.0652335	+	0.200768i	−0.978361	−	0.206907i	$-0.933660\pi$
$73$	−1.15544e9	+	3.55607e9i	−0.0652335	+	0.200768i	0.913127	+	0.407675i	$0.133660\pi$
$74$	−4.89460e9	−	1.50640e10i	−0.256414	−	0.789162i
$75$		0			0
$76$	−1.65426e9			−0.0748391
$77$	5.39338e9	−	1.71883e10i	0.227071	−	0.723661i
$78$		0			0
$79$	−1.17002e10	+	8.50068e9i	−0.427803	+	0.310817i	−0.780770	−	0.624819i	$-0.785173\pi$
$79$	−1.17002e10	+	8.50068e9i	−0.427803	+	0.310817i	0.352967	+	0.935636i	$0.385173\pi$
$80$	6.09628e9	+	1.87624e10i	0.208003	+	0.640168i
$81$		0			0
$82$	−1.35431e10	−	9.83966e9i	−0.403407	−	0.293092i
$83$	9.56204e9	+	6.94723e9i	0.266453	+	0.193590i	0.712987	−	0.701177i	$-0.247342\pi$
$83$	9.56204e9	+	6.94723e9i	0.266453	+	0.193590i	−0.446534	+	0.894767i	$0.647342\pi$
$84$		0			0
$85$	1.74537e10	+	5.37171e10i	0.426662	+	1.31313i
$86$	−4.44183e10	+	3.22718e10i	−1.01817	+	0.739744i
$87$		0			0
$88$	−1.70022e10	−	5.05819e10i	−0.343439	−	1.02174i
$89$	−3.19799e10			−0.607061			−0.303531	−	0.952822i	$-0.598166\pi$
$89$	−3.19799e10			−0.607061			−0.303531	+	0.952822i	$0.598166\pi$
$90$		0			0
$91$	1.94794e10	+	5.99515e10i	0.327226	+	1.00710i
$92$	5.03464e8	−	1.54950e9i	0.00796408	−	0.0245109i
$93$		0			0
$94$	−1.51613e9	−	1.10153e9i	−0.0213075	−	0.0154808i
$95$	−7.25149e9	+	2.23178e10i	−0.0961496	+	0.295918i
$96$		0			0
$97$	2.68932e10	−	1.95390e10i	0.317978	−	0.231025i	−0.417334	−	0.908753i	$-0.637036\pi$
$97$	2.68932e10	−	1.95390e10i	0.317978	−	0.231025i	0.735312	+	0.677728i	$0.237036\pi$
$98$	3.35184e10			0.374576
$99$		0			0
$100$	3.23977e9			0.0323977
$101$	1.58750e11	−	1.15339e11i	1.50295	−	1.09196i	0.533769	−	0.845630i	$-0.320775\pi$
$101$	1.58750e11	−	1.15339e11i	1.50295	−	1.09196i	0.969186	−	0.246330i	$-0.0792247\pi$
$102$		0			0
$103$	−4.74085e10	+	1.45908e11i	−0.402950	+	1.24015i	0.519644	+	0.854383i	$0.326065\pi$
$103$	−4.74085e10	+	1.45908e11i	−0.402950	+	1.24015i	−0.922595	+	0.385771i	$0.873935\pi$
$104$	1.51065e11	+	1.09755e11i	1.21753	+	0.884591i
$105$		0			0
$106$	−4.97452e10	+	1.53100e11i	−0.361051	+	1.11120i
$107$	−7.50123e9	−	2.30864e10i	−0.0517037	−	0.159128i	0.921871	−	0.387498i	$-0.126660\pi$
$107$	−7.50123e9	−	2.30864e10i	−0.0517037	−	0.159128i	−0.973574	+	0.228370i	$0.926660\pi$
$108$		0			0
$109$	−2.78393e10			−0.173305			−0.0866526	−	0.996239i	$-0.527617\pi$
$109$	−2.78393e10			−0.173305			−0.0866526	+	0.996239i	$0.527617\pi$
$110$	−1.37670e11	+	1.39153e9i	−0.815038	+	0.00823823i
$111$		0			0
$112$	−8.33440e10	+	6.05530e10i	−0.446864	+	0.324666i
$113$	7.24263e10	+	2.22905e11i	0.369798	+	1.13812i	0.946921	+	0.321465i	$0.104175\pi$
$113$	7.24263e10	+	2.22905e11i	0.369798	+	1.13812i	−0.577123	+	0.816657i	$0.695825\pi$
$114$		0			0
$115$	−1.86976e10	−	1.35846e10i	−0.0866857	−	0.0629808i
$116$	−5.80571e10	−	4.21809e10i	−0.256647	−	0.186465i
$117$		0			0
$118$	1.22558e11	+	3.77193e11i	0.493161	+	1.51779i
$119$	−2.38615e11	+	1.73364e11i	−0.916620	+	0.665963i
$120$		0			0
$121$	2.85253e11	−	5.76715e9i	0.999796	−	0.0202135i
$122$	−1.77764e11			−0.595476
$123$		0			0
$124$	−1.34870e10	−	4.15087e10i	−0.0413139	−	0.127151i
$125$	1.11652e11	−	3.43630e11i	0.327237	−	1.00713i
$126$		0			0
$127$	−5.22299e11	−	3.79472e11i	−1.40281	−	1.01920i	−0.994319	−	0.106437i	$-0.966056\pi$
$127$	−5.22299e11	−	3.79472e11i	−1.40281	−	1.01920i	−0.408489	−	0.912763i	$-0.633944\pi$
$128$	−6.55141e10	+	2.01632e11i	−0.168531	+	0.518685i
$129$		0			0
$130$	3.89749e11	−	2.83169e11i	0.920655	−	0.668895i
$131$	−4.54488e11			−1.02927			−0.514636	−	0.857409i	$-0.672073\pi$
$131$	−4.54488e11			−1.02927			−0.514636	+	0.857409i	$0.672073\pi$
$132$		0			0
$133$	−1.22540e11			−0.255326
$134$	4.23144e11	−	3.07432e11i	0.846080	−	0.614713i
$135$		0			0
$136$	−2.69983e11	+	8.30921e11i	−0.497590	+	1.53142i
$137$	6.88994e11	+	5.00583e11i	1.21970	+	0.886162i	0.996075	−	0.0885140i	$-0.0282118\pi$
$137$	6.88994e11	+	5.00583e11i	1.21970	+	0.886162i	0.223622	+	0.974676i	$0.428212\pi$
$138$		0			0
$139$	−1.32242e11	+	4.07001e11i	−0.216167	+	0.665294i	0.782902	+	0.622146i	$0.213739\pi$
$139$	−1.32242e11	+	4.07001e11i	−0.216167	+	0.665294i	−0.999069	+	0.0431484i	$0.986261\pi$
$140$	−3.06458e10	−	9.43182e10i	−0.0481579	−	0.148215i
$141$		0			0
$142$	−1.09450e11			−0.159085
$143$	−8.01718e11	+	5.94955e11i	−1.12117	+	0.832024i
$144$		0			0
$145$	−8.23563e11	+	5.98353e11i	−1.06702	+	0.775236i
$146$	4.61121e10	+	1.41918e11i	0.0575273	+	0.177051i
$147$		0			0
$148$	1.46189e11	+	1.06213e11i	0.169229	+	0.122952i
$149$	−4.34949e10	−	3.16009e10i	−0.0485192	−	0.0352513i	0.563261	−	0.826279i	$-0.309546\pi$
$149$	−4.34949e10	−	3.16009e10i	−0.0485192	−	0.0352513i	−0.611781	+	0.791028i	$0.709546\pi$
$150$		0			0
$151$	3.39345e11	+	1.04440e12i	0.351777	+	1.08266i	0.957855	+	0.287253i	$0.0927422\pi$
$151$	3.39345e11	+	1.04440e12i	0.351777	+	1.08266i	−0.606077	+	0.795406i	$0.707258\pi$
$152$	−2.93663e11	+	2.13359e11i	−0.293569	+	0.213290i
$153$		0			0
$154$	−2.29065e11	−	6.81474e11i	−0.213105	−	0.633994i
$155$	−6.19120e11			−0.555840
$156$		0			0
$157$	−5.82806e10	−	1.79369e11i	−0.0487614	−	0.150072i	0.923711	−	0.383090i	$-0.125140\pi$
$157$	−5.82806e10	−	1.79369e11i	−0.0487614	−	0.150072i	−0.972473	+	0.233018i	$0.925140\pi$
$158$	−1.78355e11	+	5.48920e11i	−0.144102	+	0.443501i
$159$		0			0
$160$	−4.32099e11	−	3.13938e11i	−0.325779	−	0.236693i
$161$	3.72944e10	−	1.14780e11i	0.0271708	−	0.0836230i
$162$		0			0
$163$	1.41616e12	−	1.02890e12i	0.964010	−	0.700394i	0.00993162	−	0.999951i	$-0.496839\pi$
$163$	1.41616e12	−	1.02890e12i	0.964010	−	0.700394i	0.954079	+	0.299556i	$0.0968386\pi$
$164$	1.90978e11			0.125702
$165$		0			0
$166$	4.71695e11			0.290447
$167$	−9.71654e11	+	7.05948e11i	−0.578856	+	0.420564i	−0.838312	−	0.545191i	$-0.816457\pi$
$167$	−9.71654e11	+	7.05948e11i	−0.578856	+	0.420564i	0.259455	+	0.965755i	$0.416457\pi$
$168$		0			0
$169$	5.25728e11	−	1.61803e12i	0.293349	−	0.902835i
$170$	1.82361e12	+	1.32493e12i	0.985060	+	0.715688i
$171$		0			0
$172$	1.93557e11	−	5.95708e11i	0.0980399	−	0.301736i
$173$	−8.03234e11	−	2.47210e12i	−0.394084	−	1.21287i	−0.929673	−	0.368386i	$-0.879910\pi$
$173$	−8.03234e11	−	2.47210e12i	−0.394084	−	1.21287i	0.535589	−	0.844479i	$-0.320090\pi$
$174$		0			0
$175$	2.39988e11			0.110530
$176$	−1.32961e12	−	9.45632e11i	−0.593477	−	0.422088i
$177$		0			0
$178$	−1.03253e12	+	7.50178e11i	−0.433105	+	0.314669i
$179$	−5.26435e11	−	1.62020e12i	−0.214118	−	0.658988i	−0.999215	−	0.0396147i	$-0.987387\pi$
$179$	−5.26435e11	−	1.62020e12i	−0.214118	−	0.658988i	0.785097	−	0.619373i	$-0.212613\pi$
$180$		0			0
$181$	1.32508e12	+	9.62724e11i	0.507001	+	0.368357i	0.811685	−	0.584096i	$-0.198551\pi$
$181$	1.32508e12	+	9.62724e11i	0.507001	+	0.368357i	−0.304684	+	0.952453i	$0.598551\pi$
$182$	2.03526e12	+	1.47870e12i	0.755486	+	0.548893i
$183$		0			0
$184$	−1.10473e11	−	3.40002e11i	−0.0386153	−	0.118846i
$185$	2.07375e12	−	1.50667e12i	0.703577	−	0.511179i
$186$		0			0
$187$	−3.80668e12	−	2.70736e12i	−1.21736	−	0.865798i
$188$	2.13797e10			0.00663947
$189$		0			0
$190$	2.89398e11	+	8.90675e11i	0.0847911	+	0.260960i
$191$	1.35230e12	−	4.16195e12i	0.384937	−	1.18471i	−0.551589	−	0.834116i	$-0.685978\pi$
$191$	1.35230e12	−	4.16195e12i	0.384937	−	1.18471i	0.936526	−	0.350598i	$-0.114022\pi$
$192$		0			0
$193$	−3.07992e12	−	2.23769e12i	−0.827893	−	0.601500i	0.0910691	−	0.995845i	$-0.470972\pi$
$193$	−3.07992e12	−	2.23769e12i	−0.827893	−	0.601500i	−0.918963	+	0.394345i	$0.870972\pi$
$194$	4.09953e11	−	1.26171e12i	0.107109	−	0.329647i
$195$		0			0
$196$	−3.09360e11	+	2.24763e11i	−0.0763934	+	0.0555030i
$197$	4.63372e12			1.11267			0.556334	−	0.830959i	$-0.312208\pi$
$197$	4.63372e12			1.11267			0.556334	+	0.830959i	$0.312208\pi$
$198$		0			0
$199$	7.75820e12			1.76226			0.881128	−	0.472878i	$-0.156785\pi$
$199$	7.75820e12			1.76226			0.881128	+	0.472878i	$0.156785\pi$
$200$	5.75123e11	−	4.17851e11i	0.127085	−	0.0923329i
$201$		0			0
$202$	2.41995e12	−	7.44784e12i	0.506260	−	1.55811i
$203$	−4.30062e12	−	3.12458e12i	−0.875593	−	0.636156i
$204$		0			0
$205$	8.37160e11	−	2.57651e12i	0.161496	−	0.497034i
$206$	1.89201e12	+	5.82302e12i	0.355349	+	1.09365i
$207$		0			0
$208$	5.70924e12			1.01679
$209$	−6.18354e11	−	1.83962e12i	−0.107259	−	0.319097i
$210$		0			0
$211$	4.42269e12	−	3.21327e12i	0.728003	−	0.528925i	−0.160928	−	0.986966i	$-0.551449\pi$
$211$	4.42269e12	−	3.21327e12i	0.728003	−	0.528925i	0.888931	+	0.458041i	$0.151449\pi$
$212$	−5.67510e11	−	1.74662e12i	−0.0910179	−	0.280124i
$213$		0			0
$214$	−7.83747e11	−	5.69426e11i	−0.119371	−	0.0867284i
$215$	−7.18830e12	−	5.22261e12i	−1.06712	−	0.775311i
$216$		0			0
$217$	−9.99058e11	−	3.07478e12i	−0.140949	−	0.433797i
$218$	−8.98842e11	+	6.53047e11i	−0.123644	+	0.0898325i
$219$		0			0
$220$	1.26130e12	−	9.36008e11i	0.165003	−	0.122449i
$221$	1.63456e13			2.08566
$222$		0			0
$223$	−2.89041e12	−	8.89576e12i	−0.350980	−	1.08021i	−0.958304	−	0.285751i	$-0.907757\pi$
$223$	−2.89041e12	−	8.89576e12i	−0.350980	−	1.08021i	0.607324	−	0.794454i	$-0.292243\pi$
$224$	8.61870e11	−	2.65256e12i	0.102112	−	0.314269i
$225$		0			0
$226$	7.56728e12	+	5.49795e12i	0.853775	+	0.620304i
$227$	−1.03461e12	+	3.18421e12i	−0.113929	+	0.350639i	−0.991722	−	0.128402i	$-0.959015\pi$
$227$	−1.03461e12	+	3.18421e12i	−0.113929	+	0.350639i	0.877793	+	0.479041i	$0.159015\pi$
$228$		0			0
$229$	−1.17357e13	+	8.52647e12i	−1.23144	+	0.894693i	−0.996997	−	0.0774368i	$-0.975326\pi$
$229$	−1.17357e13	+	8.52647e12i	−1.23144	+	0.894693i	−0.234442	+	0.972130i	$0.575326\pi$
$230$	−9.22350e11			−0.0944915
$231$		0			0
$232$	−1.57466e13			−1.53816
$233$	−3.64575e12	+	2.64879e12i	−0.347800	+	0.252691i	−0.747945	−	0.663760i	$-0.768960\pi$
$233$	−3.64575e12	+	2.64879e12i	−0.347800	+	0.252691i	0.400146	+	0.916452i	$0.368960\pi$
$234$		0			0
$235$	9.37185e10	−	2.88436e11i	0.00853006	−	0.0262528i
$236$	−3.66048e12	−	2.65950e12i	−0.325478	−	0.236474i
$237$		0			0
$238$	−3.63739e12	+	1.11947e13i	−0.308757	+	0.950257i
$239$	4.98185e12	+	1.53326e13i	0.413240	+	1.27182i	0.913816	+	0.406129i	$0.133122\pi$
$239$	4.98185e12	+	1.53326e13i	0.413240	+	1.27182i	−0.500576	+	0.865693i	$0.666878\pi$
$240$		0			0
$241$	1.21575e13			0.963276			0.481638	−	0.876370i	$-0.340042\pi$
$241$	1.21575e13			0.963276			0.481638	+	0.876370i	$0.340042\pi$
$242$	9.07465e12	−	6.87761e12i	0.702822	−	0.532664i
$243$		0			0
$244$	1.64068e12	−	1.19202e12i	0.121445	−	0.0882350i
$245$	1.67622e12	+	5.15887e12i	0.121316	+	0.373371i
$246$		0			0
$247$	5.49411e12	+	3.99171e12i	0.380246	+	0.276265i
$248$	−7.74782e12	−	5.62912e12i	−0.524439	−	0.381027i
$249$		0			0
$250$	−4.45590e12	−	1.37139e13i	−0.288579	−	0.888156i
$251$	1.19796e10	−	8.70367e9i	0.000758989	−	0.000551438i	−0.587406	−	0.809293i	$-0.699851\pi$
$251$	1.19796e10	−	8.70367e9i	0.000758989	−	0.000551438i	0.588165	+	0.808741i	$0.299851\pi$
$252$		0			0
$253$	1.91132e12	−	1.93192e10i	0.115923	−	0.00117173i
$254$	−2.57649e13			−1.52913
$255$		0			0
$256$	−3.43317e12	−	1.05662e13i	−0.195153	−	0.600620i
$257$	1.65034e12	−	5.07922e12i	0.0918208	−	0.282595i	−0.894591	−	0.446885i	$-0.852533\pi$
$257$	1.65034e12	−	5.07922e12i	0.0918208	−	0.282595i	0.986412	+	0.164290i	$0.0525333\pi$
$258$		0			0
$259$	1.08290e13	+	7.86776e12i	0.577353	+	0.419472i
$260$	−1.69837e12	+	5.22705e12i	−0.0886501	+	0.272837i
$261$		0			0
$262$	−1.46740e13	+	1.06613e13i	−0.734330	+	0.533522i
$263$	−7.78786e12			−0.381646			−0.190823	−	0.981624i	$-0.561116\pi$
$263$	−7.78786e12			−0.381646			−0.190823	+	0.981624i	$0.561116\pi$
$264$		0			0
$265$	−2.60515e13			−1.22456
$266$	−3.95644e12	+	2.87452e12i	−0.182161	+	0.132348i
$267$		0			0
$268$	−1.84389e12	+	5.67491e12i	−0.0814693	+	0.250737i
$269$	−3.45430e13	−	2.50969e13i	−1.49528	−	1.08638i	−0.972215	−	0.234089i	$-0.924789\pi$
$269$	−3.45430e13	−	2.50969e13i	−1.49528	−	1.08638i	−0.523063	−	0.852294i	$-0.675211\pi$
$270$		0			0
$271$	3.04802e12	−	9.38084e12i	0.126674	−	0.389862i	−0.867529	−	0.497387i	$-0.834293\pi$
$271$	3.04802e12	−	9.38084e12i	0.126674	−	0.389862i	0.994202	+	0.107526i	$0.0342928\pi$
$272$	8.25480e12	+	2.54057e13i	0.336184	+	1.03467i
$273$		0			0
$274$	3.39880e13			1.32953
$275$	1.21101e12	+	3.60279e12i	0.0464320	+	0.138137i
$276$		0			0
$277$	3.76426e12	−	2.73490e12i	0.138689	−	0.100763i	−0.516278	−	0.856421i	$-0.672683\pi$
$277$	3.76426e12	−	2.73490e12i	0.138689	−	0.100763i	0.654966	+	0.755658i	$0.272683\pi$
$278$	5.27763e12	+	1.62429e13i	0.190631	+	0.586701i
$279$		0			0
$280$	−1.76050e13	−	1.27908e13i	−0.611317	−	0.444148i
$281$	1.50837e13	+	1.09589e13i	0.513597	+	0.373150i	0.814186	−	0.580604i	$-0.197183\pi$
$281$	1.50837e13	+	1.09589e13i	0.513597	+	0.373150i	−0.300590	+	0.953754i	$0.597183\pi$
$282$		0			0
$283$	1.56903e13	+	4.82898e13i	0.513814	+	1.58136i	0.785429	+	0.618951i	$0.212442\pi$
$283$	1.56903e13	+	4.82898e13i	0.513814	+	1.58136i	−0.271615	+	0.962406i	$0.587558\pi$
$284$	1.01017e12	−	7.33932e11i	0.0324447	−	0.0235725i
$285$		0			0
$286$	−1.19286e13	+	3.80157e13i	−0.368619	+	1.17476i
$287$	1.41469e13			0.428854
$288$		0			0
$289$	1.30430e13	+	4.01422e13i	0.380574	+	1.17129i
$290$	−1.25542e13	+	3.86379e13i	−0.359419	+	1.10618i
$291$		0			0
$292$	−1.37725e12	−	1.00063e12i	−0.0379671	−	0.0275847i
$293$	2.52620e12	−	7.77484e12i	0.0683432	−	0.210339i	−0.911052	−	0.412291i	$-0.864729\pi$
$293$	2.52620e12	−	7.77484e12i	0.0683432	−	0.210339i	0.979395	+	0.201952i	$0.0647286\pi$
$294$		0			0
$295$	−5.19254e13	+	3.77260e13i	−1.35319	+	0.983150i
$296$	3.96503e13			1.01424
$297$		0			0
$298$	−2.14560e12			−0.0528883
$299$	−5.41104e12	+	3.93135e12i	−0.130945	+	0.0951372i
$300$		0			0
$301$	1.43379e13	−	4.41274e13i	0.334479	−	1.02942i
$302$	3.54555e13	+	2.57600e13i	0.812168	+	0.590075i
$303$		0			0
$304$	−3.42961e12	+	1.05553e13i	−0.0757601	+	0.233166i
$305$	−8.88976e12	−	2.73599e13i	−0.192859	−	0.593560i
$306$		0			0
$307$	−5.89564e13			−1.23387			−0.616936	−	0.787014i	$-0.711626\pi$
$307$	−5.89564e13			−1.23387			−0.616936	+	0.787014i	$0.711626\pi$
$308$	6.68390e12	+	4.75367e12i	0.137404	+	0.0977237i
$309$		0			0
$310$	−1.99894e13	+	1.45232e13i	−0.396562	+	0.288119i
$311$	−7.17564e12	−	2.20843e13i	−0.139855	−	0.430430i	0.856458	−	0.516216i	$-0.172660\pi$
$311$	−7.17564e12	−	2.20843e13i	−0.139855	−	0.430430i	−0.996314	+	0.0857862i	$0.972660\pi$
$312$		0			0
$313$	6.36764e13	+	4.62636e13i	1.19808	+	0.870454i	0.994094	−	0.108521i	$-0.0346114\pi$
$313$	6.36764e13	+	4.62636e13i	1.19808	+	0.870454i	0.203982	+	0.978975i	$0.434611\pi$
$314$	−6.08930e12	−	4.42414e12i	−0.112578	−	0.0817929i
$315$		0			0
$316$	−2.03474e12	−	6.26227e12i	−0.0363269	−	0.111803i
$317$	−3.55309e13	+	2.58147e13i	−0.623419	+	0.452941i	−0.854114	−	0.520085i	$-0.825900\pi$
$317$	−3.55309e13	+	2.58147e13i	−0.623419	+	0.452941i	0.230695	+	0.973026i	$0.425900\pi$
$318$		0			0
$319$	2.52059e13	−	8.03294e13i	0.427222	−	1.36153i
$320$	−6.17183e13			−1.02823
$321$		0			0
$322$	−1.48837e12	−	4.58074e12i	−0.0239610	−	0.0737443i
$323$	−9.81903e12	+	3.02199e13i	−0.155401	+	0.478276i
$324$		0			0
$325$	−1.07599e13	−	7.81752e12i	−0.164608	−	0.119594i
$326$	2.15877e13	−	6.64401e13i	0.324720	−	0.999386i
$327$		0			0
$328$	3.39024e13	−	2.46316e13i	0.493088	−	0.358250i
$329$	1.58372e12			0.0226516
$330$		0			0
$331$	8.95166e13			1.23837			0.619184	−	0.785246i	$-0.287464\pi$
$331$	8.95166e13			1.23837			0.619184	+	0.785246i	$0.287464\pi$
$332$	−4.35353e12	+	3.16302e12i	−0.0592355	+	0.0430371i
$333$		0			0
$334$	−1.48117e13	+	4.55856e13i	−0.194984	+	0.600099i
$335$	6.84782e13	+	4.97523e13i	0.886759	+	0.644268i
$336$		0			0
$337$	3.88505e12	−	1.19570e13i	0.0486892	−	0.149850i	−0.923756	−	0.382981i	$-0.874897\pi$
$337$	3.88505e12	−	1.19570e13i	0.0486892	−	0.149850i	0.972445	+	0.233132i	$0.0748973\pi$
$338$	−2.09811e13	−	6.45733e13i	−0.258695	−	0.796180i
$339$		0			0
$340$	−2.57156e13			−0.306946
$341$	4.11184e13	−	3.05140e13i	0.482933	−	0.358385i
$342$		0			0
$343$	−7.68674e13	+	5.58474e13i	−0.874227	+	0.635163i
$344$	−4.24716e13	−	1.30714e14i	−0.475365	−	1.46302i
$345$		0			0
$346$	−8.39238e13	−	6.09742e13i	−0.909844	−	0.661040i
$347$	1.33612e14	+	9.70746e13i	1.42571	+	1.03584i	0.990795	+	0.135373i	$0.0432234\pi$
$347$	1.33612e14	+	9.70746e13i	1.42571	+	1.03584i	0.434920	+	0.900469i	$0.356777\pi$
$348$		0			0
$349$	3.36625e13	+	1.03602e14i	0.348022	+	1.07110i	0.959946	+	0.280184i	$0.0903956\pi$
$349$	3.36625e13	+	1.03602e14i	0.348022	+	1.07110i	−0.611925	+	0.790916i	$0.709604\pi$
$350$	7.74845e12	−	5.62958e12i	0.0788571	−	0.0572930i
$351$		0			0
$352$	4.41704e13	−	4.46465e11i	0.435659	−	0.00440354i
$353$	−6.04177e12			−0.0586683			−0.0293341	−	0.999570i	$-0.509339\pi$
$353$	−6.04177e12			−0.0586683			−0.0293341	+	0.999570i	$0.509339\pi$
$354$		0			0
$355$	−5.47345e12	−	1.68455e13i	−0.0515235	−	0.158573i
$356$	4.49936e12	−	1.38476e13i	0.0417038	−	0.128351i
$357$		0			0
$358$	−5.50032e13	−	3.99622e13i	−0.494347	−	0.359164i
$359$	−9.48959e12	+	2.92060e13i	−0.0839901	+	0.258495i	−0.984228	−	0.176903i	$-0.943392\pi$
$359$	−9.48959e12	+	2.92060e13i	−0.0839901	+	0.258495i	0.900238	+	0.435398i	$0.143392\pi$
$360$		0			0
$361$	8.35623e13	−	6.07116e13i	0.717333	−	0.521173i
$362$	6.53658e13			0.552655
$363$		0			0
$364$	−2.87002e13			−0.235411
$365$	−1.95368e13	+	1.41943e13i	−0.157850	+	0.114684i
$366$		0			0
$367$	−4.34115e13	+	1.33607e14i	−0.340363	+	1.04753i	0.623657	+	0.781698i	$0.285646\pi$
$367$	−4.34115e13	+	1.33607e14i	−0.340363	+	1.04753i	−0.964020	+	0.265830i	$0.914354\pi$
$368$	−8.84308e12	−	6.42488e12i	−0.0683032	−	0.0496251i
$369$		0			0
$370$	3.16118e13	−	9.72911e13i	0.236995	−	0.729396i
$371$	−4.20387e13	−	1.29382e14i	−0.310522	−	0.955689i
$372$		0			0
$373$	1.91339e14			1.37216			0.686079	−	0.727527i	$-0.259331\pi$
$373$	1.91339e14			1.37216			0.686079	+	0.727527i	$0.259331\pi$
$374$	−1.86414e14	+	1.88424e12i	−1.31730	+	0.0133150i
$375$		0			0
$376$	3.79532e12	−	2.75746e12i	0.0260444	−	0.0189224i
$377$	9.10367e13	+	2.80182e14i	0.615658	+	1.89480i
$378$		0			0
$379$	−1.07821e14	−	7.83367e13i	−0.708253	−	0.514576i	0.174357	−	0.984683i	$-0.444215\pi$
$379$	−1.07821e14	−	7.83367e13i	−0.708253	−	0.514576i	−0.882610	+	0.470107i	$0.844215\pi$
$380$	−8.64357e12	−	6.27992e12i	−0.0559607	−	0.0406578i
$381$		0			0
$382$	−5.39686e13	−	1.66098e14i	−0.339463	−	1.04476i
$383$	−3.74400e13	+	2.72017e13i	−0.232136	+	0.168657i	−0.697773	−	0.716319i	$-0.745825\pi$
$383$	−3.74400e13	+	2.72017e13i	−0.232136	+	0.168657i	0.465637	+	0.884976i	$0.345825\pi$
$384$		0			0
$385$	9.34313e13	−	6.93354e13i	0.562935	−	0.417754i
$386$	−1.51932e14			−0.902443
$387$		0			0
$388$	4.67689e12	+	1.43940e13i	0.0270012	+	0.0831011i
$389$	3.37260e13	−	1.03798e14i	0.191974	−	0.590835i	−0.808025	−	0.589149i	$-0.799463\pi$
$389$	3.37260e13	−	1.03798e14i	0.191974	−	0.590835i	0.999999	−	0.00168643i	$-0.000536807\pi$
$390$		0			0
$391$	−2.53179e13	−	1.83945e13i	−0.140105	−	0.101793i
$392$	−2.59285e13	+	7.97998e13i	−0.141483	+	0.435440i
$393$		0			0
$394$	1.49608e14	−	1.08697e14i	0.793827	−	0.576749i
$395$	−9.34043e13			−0.488746
$396$		0			0
$397$	−4.54442e13			−0.231276			−0.115638	−	0.993291i	$-0.536891\pi$
$397$	−4.54442e13			−0.231276			−0.115638	+	0.993291i	$0.536891\pi$
$398$	2.50488e14	−	1.81990e14i	1.25727	−	0.913462i
$399$		0			0
$400$	6.71670e12	−	2.06719e13i	0.0327964	−	0.100937i
$401$	−2.31901e13	−	1.68486e13i	−0.111689	−	0.0811465i	0.530539	−	0.847661i	$-0.321990\pi$
$401$	−2.31901e13	−	1.68486e13i	−0.111689	−	0.0811465i	−0.642228	+	0.766514i	$0.721990\pi$
$402$		0			0
$403$	−5.53671e13	+	1.70403e14i	−0.259462	+	0.798543i
$404$	2.76076e13	+	8.49675e13i	0.127624	+	0.392785i
$405$		0			0
$406$	−2.12149e14			−0.954438
$407$	−6.34690e13	+	2.02271e14i	−0.281704	+	0.897770i
$408$		0			0
$409$	2.20000e14	−	1.59839e14i	0.950482	−	0.690566i	−0.000438655	−	1.00000i	$-0.500140\pi$
$409$	2.20000e14	−	1.59839e14i	0.950482	−	0.690566i	0.950921	+	0.309434i	$0.100140\pi$
$410$	−3.34100e13	−	1.02825e14i	−0.142418	−	0.438318i
$411$		0			0
$412$	−5.65096e13	−	4.10566e13i	−0.234524	−	0.170392i
$413$	−2.71152e14	−	1.97004e14i	−1.11042	−	0.806769i
$414$		0			0
$415$	2.35889e13	+	7.25992e13i	0.0940683	+	0.289512i
$416$	−1.25049e14	+	9.08531e13i	−0.492113	+	0.357541i
$417$		0			0
$418$	−6.31180e13	−	4.48903e13i	−0.241927	−	0.172061i
$419$	2.90634e14			1.09944			0.549718	−	0.835351i	$-0.314735\pi$
$419$	2.90634e14			1.09944			0.549718	+	0.835351i	$0.314735\pi$
$420$		0			0
$421$	9.87384e13	+	3.03886e14i	0.363860	+	1.11985i	0.950692	+	0.310137i	$0.100375\pi$
$421$	9.87384e13	+	3.03886e14i	0.363860	+	1.11985i	−0.586832	+	0.809709i	$0.699625\pi$
$422$	6.74185e13	−	2.07493e14i	0.245223	−	0.754718i
$423$		0			0
$424$	−3.26015e14	−	2.36864e14i	−1.15538	−	0.839435i
$425$	1.92300e13	−	5.91838e13i	0.0672729	−	0.207045i
$426$		0			0
$427$	1.21534e14	−	8.82999e13i	0.414329	−	0.301028i
$428$	1.10520e13			0.0371964
$429$		0			0
$430$	−3.54598e14			−1.16321
$431$	2.79597e14	−	2.03139e14i	0.905539	−	0.657913i	−0.0343434	−	0.999410i	$-0.510934\pi$
$431$	2.79597e14	−	2.03139e14i	0.905539	−	0.657913i	0.939883	+	0.341497i	$0.110934\pi$
$432$		0			0
$433$	5.74077e13	−	1.76683e14i	0.181254	−	0.557841i	−0.818610	−	0.574350i	$-0.805255\pi$
$433$	5.74077e13	−	1.76683e14i	0.181254	−	0.557841i	0.999864	+	0.0165084i	$0.00525503\pi$
$434$	−1.04384e14	−	7.58394e13i	−0.325417	−	0.236429i
$435$		0			0
$436$	3.91679e12	−	1.20547e13i	0.0119057	−	0.0366420i
$437$	−4.01782e12	−	1.23656e13i	−0.0120599	−	0.0371165i
$438$		0			0
$439$	3.73877e14			1.09439			0.547197	−	0.837004i	$-0.315695\pi$
$439$	3.73877e14			1.09439			0.547197	+	0.837004i	$0.315695\pi$
$440$	1.03183e14	−	3.28836e14i	0.298275	−	0.950583i
$441$		0			0
$442$	5.27748e14	−	3.83431e14i	1.48800	−	1.08110i
$443$	1.88388e14	+	5.79798e14i	0.524605	+	1.61457i	0.765095	+	0.643917i	$0.222692\pi$
$443$	1.88388e14	+	5.79798e14i	0.524605	+	1.61457i	−0.240490	+	0.970652i	$0.577308\pi$
$444$		0			0
$445$	−1.67097e14	−	1.21403e14i	−0.453929	−	0.329798i
$446$	−3.01997e14	−	2.19413e14i	−0.810327	−	0.588737i
$447$		0			0
$448$	−9.95934e13	−	3.06517e14i	−0.260736	−	0.802463i
$449$	4.71532e14	−	3.42588e14i	1.21943	−	0.885967i	0.223377	−	0.974732i	$-0.428292\pi$
$449$	4.71532e14	−	3.42588e14i	1.21943	−	0.885967i	0.996053	+	0.0887649i	$0.0282920\pi$
$450$		0			0
$451$	7.13868e13	+	2.12378e14i	0.180155	+	0.535967i
$452$	−1.06710e14			−0.266038
$453$		0			0
$454$	4.12901e13	+	1.27078e14i	0.100471	+	0.309217i
$455$	−1.25808e14	+	3.87197e14i	−0.302444	+	0.930828i
$456$		0			0
$457$	−2.02436e13	−	1.47078e13i	−0.0475060	−	0.0345151i	0.563779	−	0.825926i	$-0.309347\pi$
$457$	−2.02436e13	−	1.47078e13i	−0.0475060	−	0.0345151i	−0.611285	+	0.791411i	$0.709347\pi$
$458$	−1.78896e14	+	5.50586e14i	−0.414802	+	1.27663i
$459$		0			0
$460$	8.51287e12	−	6.18497e12i	0.0192712	−	0.0140013i
$461$	−1.22926e14			−0.274972			−0.137486	−	0.990504i	$-0.543902\pi$
$461$	−1.22926e14			−0.274972			−0.137486	+	0.990504i	$0.543902\pi$
$462$		0			0
$463$	6.08822e14			1.32983			0.664913	−	0.746921i	$-0.268469\pi$
$463$	6.08822e14			1.32983			0.664913	+	0.746921i	$0.268469\pi$
$464$	−3.89507e14	+	2.82993e14i	−0.840748	+	0.610840i
$465$		0			0
$466$	−5.55750e13	+	1.71042e14i	−0.117154	+	0.360563i
$467$	−5.71275e14	−	4.15055e14i	−1.19015	−	0.864696i	−0.196871	−	0.980429i	$-0.563078\pi$
$467$	−5.71275e14	−	4.15055e14i	−1.19015	−	0.864696i	−0.993280	+	0.115734i	$0.963078\pi$
$468$		0			0
$469$	−1.36587e14	+	4.20373e14i	−0.277946	+	0.855429i
$470$	−3.74019e12	−	1.15111e13i	−0.00752238	−	0.0231515i
$471$		0			0
$472$	−9.92818e14			−1.95069
$473$	7.34808e14	−	7.42728e12i	1.42704	−	0.0144243i
$474$		0			0
$475$	2.09167e13	−	1.51969e13i	0.0396898	−	0.0288363i
$476$	−4.14966e13	−	1.27714e14i	−0.0778350	−	0.239551i
$477$		0			0
$478$	5.20516e14	+	3.78177e14i	0.954071	+	0.693173i
$479$	5.38003e14	+	3.90882e14i	0.974853	+	0.708272i	0.956552	−	0.291560i	$-0.0941745\pi$
$479$	5.38003e14	+	3.90882e14i	0.974853	+	0.708272i	0.0183004	+	0.999833i	$0.494174\pi$
$480$		0			0
$481$	−2.29233e14	−	7.05505e14i	−0.405955	−	1.24940i
$482$	3.92528e14	−	2.85188e14i	0.687245	−	0.499313i
$483$		0			0
$484$	−3.76360e13	+	1.24329e14i	−0.0644101	+	0.212776i
$485$	2.14692e14			0.363276
$486$		0			0
$487$	3.30008e14	+	1.01566e15i	0.545902	+	1.68011i	0.718835	+	0.695181i	$0.244676\pi$
$487$	3.30008e14	+	1.01566e15i	0.545902	+	1.68011i	−0.172933	+	0.984934i	$0.555324\pi$
$488$	1.37511e14	−	4.23215e14i	0.224920	−	0.692233i
$489$		0			0
$490$	1.75135e14	+	1.27243e14i	0.280088	+	0.203496i
$491$	8.02394e13	−	2.46952e14i	0.126894	−	0.390538i	−0.867348	−	0.497703i	$-0.834177\pi$
$491$	8.02394e13	−	2.46952e14i	0.126894	−	0.390538i	0.994241	+	0.107164i	$0.0341771\pi$
$492$		0			0
$493$	−1.11516e15	+	8.10213e14i	−1.72457	+	1.25297i
$494$	2.71024e14			0.414486
$495$		0			0
$496$	−2.92815e14			−0.437969
$497$	7.48290e13	−	5.43665e13i	0.110690	−	0.0804213i
$498$		0			0
$499$	2.63603e14	−	8.11287e14i	0.381415	−	1.17387i	−0.557633	−	0.830087i	$-0.688290\pi$
$499$	2.63603e14	−	8.11287e14i	0.381415	−	1.17387i	0.939048	−	0.343786i	$-0.111710\pi$
$500$	1.33086e14	+	9.66929e13i	0.190458	+	0.138376i
$501$		0			0
$502$	1.82614e11	−	5.62028e11i	0.000255660	−	0.000786842i
$503$	6.48409e13	+	1.99560e14i	0.0897894	+	0.276343i	0.985861	−	0.167567i	$-0.0535909\pi$
$503$	6.48409e13	+	1.99560e14i	0.0897894	+	0.276343i	−0.896071	+	0.443910i	$0.853591\pi$
$504$		0			0
$505$	1.26733e15			1.71706
$506$	6.12573e13	−	4.54590e13i	0.0820975	−	0.0609246i
$507$		0			0
$508$	2.37799e14	−	1.72771e14i	0.311860	−	0.226579i
$509$	1.59134e14	+	4.89765e14i	0.206451	+	0.635390i	0.999651	+	0.0264285i	$0.00841343\pi$
$509$	1.59134e14	+	4.89765e14i	0.206451	+	0.635390i	−0.793200	+	0.608961i	$0.791587\pi$
$510$		0			0
$511$	−1.02021e14	−	7.41224e13i	−0.129531	−	0.0941097i
$512$	−7.09975e14	−	5.15827e14i	−0.891781	−	0.647917i
$513$		0			0
$514$	−6.58629e13	−	2.02705e14i	−0.0809737	−	0.249211i
$515$	−8.01611e14	+	5.82405e14i	−0.975044	+	0.708411i
$516$		0			0
$517$	7.99163e12	+	2.37753e13i	0.00951562	+	0.0283092i
$518$	5.34196e14			0.629342
$519$		0			0
$520$	3.72668e14	+	1.14695e15i	0.429836	+	1.32290i
$521$	−2.76262e14	+	8.50248e14i	−0.315293	+	0.970372i	0.660341	+	0.750966i	$0.270412\pi$
$521$	−2.76262e14	+	8.50248e14i	−0.315293	+	0.970372i	−0.975634	+	0.219406i	$0.929588\pi$
$522$		0			0
$523$	2.67635e14	+	1.94448e14i	0.299078	+	0.217293i	0.727196	−	0.686430i	$-0.240823\pi$
$523$	2.67635e14	+	1.94448e14i	0.299078	+	0.217293i	−0.428118	+	0.903723i	$0.640823\pi$
$524$	6.39434e13	−	1.96798e14i	0.0707088	−	0.217619i
$525$		0			0
$526$	−2.51445e14	+	1.82686e14i	−0.272284	+	0.197826i
$527$	−8.38332e14			−0.898375
$528$		0			0
$529$	−9.40004e14			−0.986560
$530$	−8.41121e14	+	6.11110e14i	−0.873658	+	0.634750i
$531$		0			0
$532$	1.72406e13	−	5.30610e13i	0.0175403	−	0.0539836i
$533$	−6.34277e14	−	4.60829e14i	−0.638674	−	0.464024i
$534$		0			0
$535$	4.84468e13	−	1.49104e14i	0.0477880	−	0.147076i
$536$	4.04598e14	+	1.24523e15i	0.395019	+	1.21574i
$537$		0			0
$538$	−1.70400e15			−1.62992
$539$	−3.65585e14	−	2.60008e14i	−0.346139	−	0.246178i
$540$		0			0
$541$	−5.82825e14	+	4.23447e14i	−0.540696	+	0.392839i	−0.824343	−	0.566090i	$-0.808455\pi$
$541$	−5.82825e14	+	4.23447e14i	−0.540696	+	0.392839i	0.283647	+	0.958929i	$0.408455\pi$
$542$	−1.21643e14	−	3.74377e14i	−0.111709	−	0.343806i
$543$		0			0
$544$	−5.85093e14	−	4.25095e14i	−0.526539	−	0.382553i
$545$	−1.45461e14	−	1.05684e14i	−0.129589	−	0.0941516i
$546$		0			0
$547$	4.82688e14	+	1.48556e15i	0.421441	+	1.29706i	0.906362	+	0.422503i	$0.138848\pi$
$547$	4.82688e14	+	1.48556e15i	0.421441	+	1.29706i	−0.484921	+	0.874558i	$0.661152\pi$
$548$	−3.13694e14	+	2.27912e14i	−0.271152	+	0.197003i
$549$		0			0
$550$	1.23613e14	+	8.79150e13i	0.104730	+	0.0744849i
$551$	−5.72690e14			−0.480381
$552$		0			0
$553$	−1.50724e14	−	4.63882e14i	−0.123935	−	0.381434i
$554$	5.73816e13	−	1.76602e14i	0.0467163	−	0.143778i
$555$		0			0
$556$	−1.57629e14	−	1.14524e14i	−0.125813	−	0.0914085i
$557$	9.72549e13	−	2.99320e14i	0.0768613	−	0.236555i	−0.905242	−	0.424895i	$-0.860311\pi$
$557$	9.72549e13	−	2.99320e14i	0.0768613	−	0.236555i	0.982104	+	0.188341i	$0.0603109\pi$
$558$		0			0
$559$	−2.08028e15	+	1.51141e15i	−1.61197	+	1.17116i
$560$	−6.65348e14			−0.510522
$561$		0			0
$562$	7.44076e14			0.559845
$563$	7.72939e14	−	5.61573e14i	0.575903	−	0.418418i	−0.261342	−	0.965246i	$-0.584165\pi$
$563$	7.72939e14	−	5.61573e14i	0.575903	−	0.418418i	0.837245	+	0.546829i	$0.184165\pi$
$564$		0			0
$565$	−4.67766e14	+	1.43964e15i	−0.341792	+	1.05193i
$566$	1.63936e15	+	1.19107e15i	1.18627	+	0.861877i
$567$		0			0
$568$	8.46659e13	−	2.60575e14i	0.0600887	−	0.184934i
$569$	2.08485e14	+	6.41650e14i	0.146540	+	0.451004i	0.997206	−	0.0747028i	$-0.0238008\pi$
$569$	2.08485e14	+	6.41650e14i	0.146540	+	0.451004i	−0.850666	+	0.525707i	$0.823801\pi$
$570$		0			0
$571$	2.55622e15			1.76238			0.881190	−	0.472762i	$-0.156743\pi$
$571$	2.55622e15			1.76238			0.881190	+	0.472762i	$0.156743\pi$
$572$	−1.44825e14	−	4.30857e14i	−0.0988927	−	0.294209i
$573$		0			0
$574$	4.56757e14	−	3.31854e14i	0.305964	−	0.222296i
$575$	7.86867e12	+	2.42173e13i	0.00522069	+	0.0160676i
$576$		0			0
$577$	−1.81188e13	−	1.31641e13i	−0.0117940	−	0.00856885i	0.581873	−	0.813280i	$-0.302320\pi$
$577$	−1.81188e13	−	1.31641e13i	−0.0117940	−	0.00856885i	−0.593667	+	0.804711i	$0.702320\pi$
$578$	1.36276e15	+	9.90106e14i	0.878653	+	0.638379i
$579$		0			0
$580$	−1.43223e14	−	4.40794e14i	−0.0906063	−	0.278857i
$581$	−3.22490e14	+	2.34303e14i	−0.202092	+	0.146828i
$582$		0			0
$583$	1.73019e15	−	1.28398e15i	1.06394	−	0.789551i
$584$	−3.73546e14			−0.227548
$585$		0			0
$586$	−1.00817e14	−	3.10284e14i	−0.0602696	−	0.185491i
$587$	6.16952e14	−	1.89878e15i	0.365378	−	1.12452i	−0.584367	−	0.811490i	$-0.698657\pi$
$587$	6.16952e14	−	1.89878e15i	0.365378	−	1.12452i	0.949744	−	0.313027i	$-0.101343\pi$
$588$		0			0
$589$	−2.81781e14	−	2.04726e14i	−0.163787	−	0.118998i
$590$	−7.91539e14	+	2.43611e15i	−0.455813	+	1.40285i
$591$		0			0
$592$	9.80787e14	−	7.12583e14i	0.554377	−	0.402778i
$593$	−5.45617e14			−0.305554			−0.152777	−	0.988261i	$-0.548822\pi$
$593$	−5.45617e14			−0.305554			−0.152777	+	0.988261i	$0.548822\pi$
$594$		0			0
$595$	−1.90490e15			−1.04720
$596$	1.98029e13	−	1.43877e13i	0.0107864	−	0.00783675i
$597$		0			0
$598$	−8.24847e13	+	2.53862e14i	−0.0441079	+	0.135750i
$599$	2.48278e14	+	1.80384e14i	0.131550	+	0.0955766i	0.651614	−	0.758550i	$-0.274092\pi$
$599$	2.48278e14	+	1.80384e14i	0.131550	+	0.0955766i	−0.520064	+	0.854127i	$0.674092\pi$
$600$		0			0
$601$	−3.42838e14	+	1.05515e15i	−0.178353	+	0.548913i	−0.999771	−	0.0214137i	$-0.993183\pi$
$601$	−3.42838e14	+	1.05515e15i	−0.178353	+	0.548913i	0.821418	+	0.570326i	$0.193183\pi$
$602$	−5.72206e14	−	1.76107e15i	−0.294966	−	0.907812i
$603$		0			0
$604$	−4.99976e14			−0.253073
$605$	1.51235e15	+	1.05275e15i	0.758576	+	0.528045i
$606$		0			0
$607$	1.73776e15	−	1.26255e15i	0.855956	−	0.621888i	−0.0708260	−	0.997489i	$-0.522564\pi$
$607$	1.73776e15	−	1.26255e15i	0.855956	−	0.621888i	0.926782	+	0.375600i	$0.122564\pi$
$608$	−9.28514e13	−	2.85767e14i	−0.0453230	−	0.139490i
$609$		0			0
$610$	−9.28823e14	−	6.74830e14i	−0.445266	−	0.323504i
$611$	−7.10062e13	−	5.15890e13i	−0.0337341	−	0.0245093i
$612$		0			0
$613$	3.68081e14	+	1.13284e15i	0.171755	+	0.528609i	0.999470	−	0.0325399i	$-0.0103596\pi$
$613$	3.68081e14	+	1.13284e15i	0.171755	+	0.528609i	−0.827715	+	0.561149i	$0.810360\pi$
$614$	−1.90352e15	+	1.38299e15i	−0.880299	+	0.639575i
$615$		0			0
$616$	1.79963e15	−	1.81903e13i	0.817503	−	0.00826314i
$617$	−2.63353e15			−1.18569			−0.592844	−	0.805317i	$-0.701995\pi$
$617$	−2.63353e15			−1.18569			−0.592844	+	0.805317i	$0.701995\pi$
$618$		0			0
$619$	−4.41352e14	−	1.35834e15i	−0.195203	−	0.600774i	−0.999974	−	0.00718827i	$-0.997712\pi$
$619$	−4.41352e14	−	1.35834e15i	−0.195203	−	0.600774i	0.804771	−	0.593585i	$-0.202288\pi$
$620$	8.71059e13	−	2.68084e14i	0.0381850	−	0.117521i
$621$		0			0
$622$	−7.49728e14	−	5.44709e14i	−0.322891	−	0.234594i
$623$	3.33293e14	−	1.02577e15i	0.142279	−	0.437891i
$624$		0			0
$625$	1.60679e15	−	1.16740e15i	0.673936	−	0.489643i
$626$	3.14115e15			1.30596
$627$		0			0
$628$	8.58682e13			0.0350796
$629$	2.80800e15	−	2.04013e15i	1.13715	−	0.826191i
$630$		0			0
$631$	1.05806e15	−	3.25639e15i	0.421066	−	1.29591i	−0.485645	−	0.874156i	$-0.661415\pi$
$631$	1.05806e15	−	3.25639e15i	0.421066	−	1.29591i	0.906711	−	0.421752i	$-0.138585\pi$
$632$	−1.16889e15	−	8.49245e14i	−0.461135	−	0.335034i
$633$		0			0
$634$	−5.41625e14	+	1.66695e15i	−0.209995	+	0.646297i
$635$	−1.28847e15	−	3.96552e15i	−0.495245	−	1.52421i
$636$		0			0
$637$	1.56980e15			0.593029
$638$	−1.07053e15	−	3.18486e15i	−0.400946	−	1.19282i
$639$		0			0
$640$	−1.10775e15	+	8.04828e14i	−0.407805	+	0.296288i
$641$	3.80594e14	+	1.17135e15i	0.138913	+	0.427531i	0.996178	−	0.0873448i	$-0.0278382\pi$
$641$	3.80594e14	+	1.17135e15i	0.138913	+	0.427531i	−0.857265	+	0.514875i	$0.827838\pi$
$642$		0			0
$643$	−4.22211e15	−	3.06754e15i	−1.51485	−	1.10060i	−0.963968	−	0.266017i	$-0.914292\pi$
$643$	−4.22211e15	−	3.06754e15i	−1.51485	−	1.10060i	−0.550879	−	0.834585i	$-0.685708\pi$
$644$	4.44539e13	+	3.22977e13i	0.0158139	+	0.0114894i
$645$		0			0
$646$	3.91865e14	+	1.20604e15i	0.137043	+	0.421776i
$647$	2.83350e15	−	2.05866e15i	0.982540	−	0.713857i	0.0242652	−	0.999706i	$-0.492275\pi$
$647$	2.83350e15	−	2.05866e15i	0.982540	−	0.713857i	0.958275	+	0.285848i	$0.0922754\pi$
$648$		0			0
$649$	1.58922e15	−	5.06475e15i	0.541800	−	1.72668i
$650$	−5.30785e14			−0.179430
$651$		0			0
$652$	2.46280e14	+	7.57972e14i	0.0818591	+	0.251937i
$653$	1.66588e14	−	5.12705e14i	0.0549062	−	0.168984i	−0.919843	−	0.392287i	$-0.871684\pi$
$653$	1.66588e14	−	5.12705e14i	0.0549062	−	0.168984i	0.974749	+	0.223303i	$0.0716840\pi$
$654$		0			0
$655$	−2.37472e15	−	1.72534e15i	−0.769636	−	0.559173i
$656$	3.95937e14	−	1.21857e15i	0.127249	−	0.391633i
$657$		0			0
$658$	5.11332e13	−	3.71504e13i	0.0161607	−	0.0117414i
$659$	3.99623e15			1.25251			0.626254	−	0.779619i	$-0.284587\pi$
$659$	3.99623e15			1.25251			0.626254	+	0.779619i	$0.284587\pi$
$660$		0			0
$661$	−3.94254e13			−0.0121526			−0.00607629	−	0.999982i	$-0.501934\pi$
$661$	−3.94254e13			−0.0121526			−0.00607629	+	0.999982i	$0.501934\pi$
$662$	2.89021e15	−	2.09986e15i	0.883508	−	0.641906i
$663$		0			0
$664$	−3.64884e14	+	1.12300e15i	−0.109706	+	0.337640i
$665$	−6.40278e14	−	4.65189e14i	−0.190919	−	0.138711i
$666$		0			0
$667$	1.74295e14	−	5.36425e14i	0.0511202	−	0.157332i
$668$	−1.68977e14	−	5.20057e14i	−0.0491537	−	0.151280i
$669$		0			0
$670$	3.37802e15			0.966609
$671$	1.93887e15	+	1.37895e15i	0.550268	+	0.391357i
$672$		0			0
$673$	2.80265e15	−	2.03624e15i	0.782502	−	0.568521i	−0.123227	−	0.992379i	$-0.539324\pi$
$673$	2.80265e15	−	2.03624e15i	0.782502	−	0.568521i	0.905729	+	0.423858i	$0.139324\pi$
$674$	−1.55047e14	−	4.77187e14i	−0.0429373	−	0.132148i
$675$		0			0
$676$	6.26653e14	+	4.55290e14i	0.170734	+	0.124046i
$677$	1.18222e15	+	8.58935e14i	0.319493	+	0.232125i	0.735959	−	0.677026i	$-0.236731\pi$
$677$	1.18222e15	+	8.58935e14i	0.319493	+	0.232125i	−0.416466	+	0.909151i	$0.636731\pi$
$678$		0			0
$679$	3.46444e14	+	1.06624e15i	0.0921189	+	0.283513i
$680$	−4.56503e15	+	3.31669e15i	−1.20405	+	0.874793i
$681$		0			0
$682$	6.11794e14	−	1.94975e15i	0.158778	−	0.506016i
$683$	−3.32282e15			−0.855447			−0.427724	−	0.903910i	$-0.640684\pi$
$683$	−3.32282e15			−0.855447			−0.427724	+	0.903910i	$0.640684\pi$
$684$		0			0
$685$	1.69970e15	+	5.23114e15i	0.430600	+	1.32525i
$686$	−1.17175e15	+	3.60627e15i	−0.294477	+	0.906308i
$687$		0			0
$688$	−3.39973e15	−	2.47005e15i	−0.840830	−	0.610898i
$689$	−2.32976e15	+	7.17025e15i	−0.571617	+	1.75926i
$690$		0			0
$691$	−1.64511e15	+	1.19524e15i	−0.397251	+	0.288620i	−0.768420	−	0.639945i	$-0.778957\pi$
$691$	−1.64511e15	+	1.19524e15i	−0.397251	+	0.288620i	0.371169	+	0.928565i	$0.378957\pi$
$692$	1.18345e15			0.283509
$693$		0			0
$694$	6.59106e15			1.55410
$695$	−2.23603e15	+	1.62457e15i	−0.523073	+	0.380035i
$696$		0			0
$697$	1.13357e15	−	3.48878e15i	0.261017	−	0.803329i
$698$	3.51714e15	+	2.55535e15i	0.803498	+	0.583775i
$699$		0			0
$700$	−3.37647e13	+	1.03917e14i	−0.00759317	+	0.0233694i
$701$	−2.30452e15	−	7.09258e15i	−0.514199	−	1.58254i	−0.784735	−	0.619831i	$-0.787201\pi$
$701$	−2.30452e15	−	7.09258e15i	−0.514199	−	1.58254i	0.270537	−	0.962710i	$-0.412799\pi$
$702$		0			0
$703$	1.44205e15			0.316756
$704$	4.09898e15	−	3.04185e15i	0.893360	−	0.662962i
$705$		0			0
$706$	−1.95070e14	+	1.41726e14i	−0.0418566	+	0.0304106i
$707$	2.04505e15	+	6.29402e15i	0.435409	+	1.34005i
$708$		0			0
$709$	4.24603e15	+	3.08492e15i	0.890079	+	0.646680i	0.935899	−	0.352269i	$-0.114590\pi$
$709$	4.24603e15	+	3.08492e15i	0.890079	+	0.646680i	−0.0458195	+	0.998950i	$0.514590\pi$
$710$	−5.71879e14	−	4.15495e14i	−0.118955	−	0.0864260i
$711$		0			0
$712$	−9.87278e14	−	3.03853e15i	−0.202209	−	0.622334i
$713$	2.77521e14	−	2.01631e14i	0.0564031	−	0.0409793i
$714$		0			0
$715$	−6.44759e15	+	6.51708e13i	−1.29037	+	0.0130428i
$716$	7.75628e14			0.154039
$717$		0			0
$718$	3.78717e14	+	1.16557e15i	0.0740681	+	0.227958i
$719$	2.22904e15	−	6.86028e15i	0.432623	−	1.33148i	−0.462881	−	0.886421i	$-0.653184\pi$
$719$	2.22904e15	−	6.86028e15i	0.432623	−	1.33148i	0.895503	−	0.445055i	$-0.146816\pi$
$720$		0			0
$721$	−4.18599e15	−	3.04130e15i	−0.800118	−	0.581319i
$722$	1.27381e15	−	3.92037e15i	0.241629	−	0.743657i
$723$		0			0
$724$	−6.03297e14	+	4.38321e14i	−0.112712	+	0.0818899i
$725$	1.12158e15			0.207956
$726$		0			0
$727$	−7.78583e15			−1.42189			−0.710945	−	0.703248i	$-0.751732\pi$
$727$	−7.78583e15			−1.42189			−0.710945	+	0.703248i	$0.751732\pi$
$728$	−5.09484e15	+	3.70162e15i	−0.923439	+	0.670918i
$729$		0			0
$730$	−2.97815e14	+	9.16581e14i	−0.0531706	+	0.163642i
$731$	−9.73347e15	−	7.07178e15i	−1.72473	−	1.25309i
$732$		0			0
$733$	−2.00870e15	+	6.18215e15i	−0.350626	+	1.07911i	0.607877	+	0.794031i	$0.292021\pi$
$733$	−2.00870e15	+	6.18215e15i	−0.350626	+	1.07911i	−0.958503	+	0.285083i	$0.907979\pi$
$734$	1.73250e15	+	5.33209e15i	0.300154	+	0.923781i
$735$		0			0
$736$	2.95930e14			0.0505081
$737$	−7.00003e15	+	7.07548e13i	−1.18585	+	0.0119863i
$738$		0			0
$739$	−4.37127e15	+	3.17592e15i	−0.729564	+	0.530060i	−0.889426	−	0.457080i	$-0.848895\pi$
$739$	−4.37127e15	+	3.17592e15i	−0.729564	+	0.530060i	0.159861	+	0.987139i	$0.448895\pi$
$740$	3.60638e14	+	1.10993e15i	0.0597444	+	0.183874i
$741$		0			0
$742$	−4.39231e15	−	3.19120e15i	−0.716921	−	0.520873i
$743$	−1.46907e15	−	1.06734e15i	−0.238015	−	0.172928i	0.462383	−	0.886680i	$-0.346994\pi$
$743$	−1.46907e15	−	1.06734e15i	−0.238015	−	0.172928i	−0.700398	+	0.713752i	$0.746994\pi$
$744$		0			0
$745$	−1.07299e14	−	3.30232e14i	−0.0171292	−	0.0527181i
$746$	6.17772e15	−	4.48837e15i	0.978959	−	0.711255i
$747$		0			0
$748$	1.70788e15	−	1.26742e15i	0.266686	−	0.197907i
$749$	8.18684e14			0.126901
$750$		0			0
$751$	2.01220e15	+	6.19290e15i	0.307362	+	0.945964i	0.978785	+	0.204890i	$0.0656835\pi$
$751$	2.01220e15	+	6.19290e15i	0.307362	+	0.945964i	−0.671423	+	0.741075i	$0.734316\pi$
$752$	4.43245e13	−	1.36417e14i	0.00672118	−	0.0206857i
$753$		0			0
$754$	9.51174e15	+	6.91068e15i	1.42140	+	1.03271i
$755$	−2.19166e15	+	6.74524e15i	−0.325136	+	1.00067i
$756$		0			0
$757$	−1.51162e15	+	1.09826e15i	−0.221012	+	0.160575i	−0.692782	−	0.721147i	$-0.743615\pi$
$757$	−1.51162e15	+	1.09826e15i	−0.221012	+	0.160575i	0.471770	+	0.881722i	$0.343615\pi$
$758$	−5.31881e15			−0.772029
$759$		0			0
$760$	−2.34436e15			−0.335390
$761$	−5.17404e15	+	3.75916e15i	−0.734876	+	0.533919i	−0.891102	−	0.453802i	$-0.850067\pi$
$761$	−5.17404e15	+	3.75916e15i	−0.734876	+	0.533919i	0.156226	+	0.987721i	$0.450067\pi$
$762$		0			0
$763$	2.90139e14	−	8.92956e14i	0.0406182	−	0.125010i
$764$	1.61190e15	+	1.17112e15i	0.224040	+	0.162775i
$765$		0			0
$766$	−5.70727e14	+	1.75652e15i	−0.0781934	+	0.240654i
$767$	5.73984e15	+	1.76654e16i	0.780774	+	2.40297i
$768$		0			0
$769$	1.97046e15			0.264224			0.132112	−	0.991235i	$-0.457824\pi$
$769$	1.97046e15			0.264224			0.132112	+	0.991235i	$0.457824\pi$
$770$	1.39015e15	−	4.43031e15i	0.185081	−	0.589841i
$771$		0			0
$772$	1.40227e15	−	1.01881e15i	0.184050	−	0.133720i
$773$	−7.55676e14	−	2.32573e15i	−0.0984801	−	0.303090i	0.889665	−	0.456614i	$-0.150938\pi$
$773$	−7.55676e14	−	2.32573e15i	−0.0984801	−	0.303090i	−0.988145	+	0.153523i	$0.950938\pi$
$774$		0			0
$775$	5.51853e14	+	4.00944e14i	0.0709028	+	0.0515139i
$776$	2.68671e15	+	1.95201e15i	0.342754	+	0.249025i
$777$		0			0
$778$	−1.34596e15	−	4.14245e15i	−0.169295	−	0.521038i
$779$	1.23300e15	−	8.95828e14i	0.153995	−	0.111884i
$780$		0			0
$781$	1.19377e15	+	8.49021e14i	0.147007	+	0.104553i
$782$	−1.24893e15			−0.152721
$783$		0			0
$784$	7.92772e14	+	2.43990e15i	0.0955895	+	0.294194i
$785$	3.76406e14	−	1.15846e15i	0.0450685	−	0.138707i
$786$		0			0
$787$	5.58356e15	+	4.05670e15i	0.659251	+	0.478974i	0.866410	−	0.499334i	$-0.166422\pi$
$787$	5.58356e15	+	4.05670e15i	0.659251	+	0.478974i	−0.207159	+	0.978307i	$0.566422\pi$
$788$	−6.51933e14	+	2.00644e15i	−0.0764379	+	0.235252i
$789$		0			0
$790$	−3.01573e15	+	2.19106e15i	−0.348693	+	0.253341i
$791$	−7.90461e15			−0.907631
$792$		0			0
$793$	−8.32535e15			−0.942758
$794$	−1.46725e15	+	1.06602e15i	−0.165003	+	0.119881i
$795$		0			0
$796$	−1.09153e15	+	3.35937e15i	−0.121063	+	0.372594i
$797$	3.28488e15	+	2.38661e15i	0.361825	+	0.262882i	0.753813	−	0.657089i	$-0.228212\pi$
$797$	3.28488e15	+	2.38661e15i	0.361825	+	0.262882i	−0.391988	+	0.919970i	$0.628212\pi$
$798$		0			0
$799$	1.26902e14	−	3.90563e14i	0.0137867	−	0.0424310i
$800$	1.81844e14	+	5.59658e14i	0.0196202	+	0.0603849i
$801$		0			0
$802$	−1.14397e15			−0.121746
$803$	5.97943e14	−	1.90560e15i	0.0632010	−	0.201417i
$804$		0			0
$805$	6.30597e14	−	4.58155e14i	0.0657467	−	0.0477678i
$806$	2.20963e15	+	6.80055e15i	0.228811	+	0.704208i
$807$		0			0
$808$	1.58596e16	+	1.15227e16i	1.62006	+	1.17704i
$809$	−3.89900e15	−	2.83279e15i	−0.395582	−	0.287407i	0.372157	−	0.928170i	$-0.378618\pi$
$809$	−3.89900e15	−	2.83279e15i	−0.395582	−	0.287407i	−0.767739	+	0.640763i	$0.778618\pi$
$810$		0			0
$811$	−3.04299e15	−	9.36536e15i	−0.304569	−	0.937367i	−0.979838	−	0.199795i	$-0.935972\pi$
$811$	−3.04299e15	−	9.36536e15i	−0.304569	−	0.937367i	0.675269	−	0.737572i	$-0.264028\pi$
$812$	1.95804e15	−	1.42260e15i	0.194654	−	0.141424i
$813$		0			0
$814$	2.69562e15	+	8.01954e15i	0.264378	+	0.786530i
$815$	1.13055e16			1.10134
$816$		0			0
$817$	−1.54465e15	−	4.75396e15i	−0.148460	−	0.456913i
$818$	3.35363e15	−	1.03214e16i	0.320163	−	0.985362i
$819$		0			0
$820$	9.97871e14	+	7.24996e14i	0.0939936	+	0.0682903i
$821$	7.43347e14	−	2.28779e15i	0.0695511	−	0.214056i	−0.910240	−	0.414082i	$-0.864103\pi$
$821$	7.43347e14	−	2.28779e15i	0.0695511	−	0.214056i	0.979791	+	0.200026i	$0.0641026\pi$
$822$		0			0
$823$	−4.75367e15	+	3.45375e15i	−0.438864	+	0.318854i	−0.785183	−	0.619263i	$-0.787431\pi$
$823$	−4.75367e15	+	3.45375e15i	−0.438864	+	0.318854i	0.346319	+	0.938117i	$0.387431\pi$
$824$	−1.53269e16			−1.40557
$825$		0			0
$826$	−1.33759e16			−1.21041
$827$	3.23995e15	−	2.35396e15i	0.291245	−	0.211602i	−0.432562	−	0.901604i	$-0.642390\pi$
$827$	3.23995e15	−	2.35396e15i	0.291245	−	0.211602i	0.723807	+	0.690002i	$0.242390\pi$
$828$		0			0
$829$	−1.73494e15	+	5.33960e15i	−0.153899	+	0.473651i	−0.998048	−	0.0624575i	$-0.980106\pi$
$829$	−1.73494e15	+	5.33960e15i	−0.153899	+	0.473651i	0.844149	+	0.536109i	$0.180106\pi$
$830$	2.46463e15	+	1.79065e15i	0.217181	+	0.157791i
$831$		0			0
$832$	−5.51940e15	+	1.69870e16i	−0.479969	+	1.47719i
$833$	2.26972e15	+	6.98547e15i	0.196076	+	0.603460i
$834$		0			0
$835$	−7.75686e15			−0.661318
$836$	8.83570e14	−	8.93093e12i	0.0748353	−	0.000756419i
$837$		0			0
$838$	9.38366e15	−	6.81763e15i	0.784387	−	0.569890i
$839$	4.25508e14	+	1.30958e15i	0.0353359	+	0.108753i	0.967169	−	0.254135i	$-0.0817908\pi$
$839$	4.25508e14	+	1.30958e15i	0.0353359	+	0.108753i	−0.931833	+	0.362888i	$0.881791\pi$
$840$		0			0
$841$	−1.02284e16	−	7.43139e15i	−0.838361	−	0.609105i
$842$	1.03164e16	+	7.49532e15i	0.840065	+	0.610343i
$843$		0			0
$844$	7.69134e14	+	2.36715e15i	0.0618185	+	0.190258i
$845$	8.88933e15	−	6.45847e15i	0.709834	−	0.515725i
$846$		0			0
$847$	−2.78791e15	+	9.20973e15i	−0.219745	+	0.725919i
$848$	−1.23212e16			−0.964882
$849$		0			0
$850$	−7.67445e14	−	2.36195e15i	−0.0593257	−	0.182586i
$851$	−4.38879e14	+	1.35073e15i	−0.0337079	+	0.103742i
$852$		0			0
$853$	−4.25141e15	−	3.08883e15i	−0.322340	−	0.234193i	0.414834	−	0.909897i	$-0.363840\pi$
$853$	−4.25141e15	−	3.08883e15i	−0.322340	−	0.234193i	−0.737173	+	0.675704i	$0.763840\pi$
$854$	1.85264e15	−	5.70185e15i	0.139564	−	0.429534i
$855$		0			0
$856$	1.96195e15	−	1.42544e15i	0.145909	−	0.106009i
$857$	4.10237e15			0.303138			0.151569	−	0.988447i	$-0.451567\pi$
$857$	4.10237e15			0.303138			0.151569	+	0.988447i	$0.451567\pi$
$858$		0			0
$859$	1.28203e16			0.935268			0.467634	−	0.883922i	$-0.345107\pi$
$859$	1.28203e16			0.935268			0.467634	+	0.883922i	$0.345107\pi$
$860$	3.27278e15	−	2.37781e15i	0.237233	−	0.172360i
$861$		0			0
$862$	4.26211e15	−	1.31174e16i	0.305025	−	0.938770i
$863$	−5.84746e15	−	4.24843e15i	−0.415823	−	0.302113i	0.360132	−	0.932901i	$-0.382732\pi$
$863$	−5.84746e15	−	4.24843e15i	−0.415823	−	0.302113i	−0.775955	+	0.630788i	$0.782732\pi$
$864$		0			0
$865$	5.18769e15	−	1.59661e16i	0.364238	−	1.12101i
$866$	−2.29107e15	−	7.05118e15i	−0.159842	−	0.491942i
$867$		0			0
$868$	1.47197e15			0.101401
$869$	6.20339e15	−	4.60353e15i	0.424639	−	0.315125i
$870$		0			0
$871$	1.98174e16	−	1.43982e16i	1.33951	−	0.973214i
$872$	−8.59448e14	−	2.64511e15i	−0.0577270	−	0.177665i
$873$		0			0
$874$	−4.19792e14	−	3.04996e14i	−0.0278433	−	0.0202293i
$875$	9.85846e15	+	7.16259e15i	0.649777	+	0.472091i
$876$		0			0
$877$	2.94068e15	+	9.05048e15i	0.191404	+	0.589080i	1.00000		0.000715567i	$0.000227772\pi$
$877$	2.94068e15	+	9.05048e15i	0.191404	+	0.589080i	−0.808596	+	0.588364i	$0.799772\pi$
$878$	1.20713e16	−	8.77032e15i	0.780791	−	0.567278i
$879$		0			0
$880$	−3.35743e15	−	9.98845e15i	−0.214463	−	0.638033i
$881$	−1.52374e16			−0.967261			−0.483631	−	0.875272i	$-0.660682\pi$
$881$	−1.52374e16			−0.967261			−0.483631	+	0.875272i	$0.660682\pi$
$882$		0			0
$883$	6.64114e15	+	2.04393e16i	0.416350	+	1.28139i	0.911037	+	0.412324i	$0.135283\pi$
$883$	6.64114e15	+	2.04393e16i	0.416350	+	1.28139i	−0.494687	+	0.869071i	$0.664717\pi$
$884$	−2.29972e15	+	7.07780e15i	−0.143280	+	0.440972i
$885$		0			0
$886$	1.96832e16	+	1.43007e16i	1.21119	+	0.879978i
$887$	−2.92775e15	+	9.01069e15i	−0.179042	+	0.551034i	−0.999795	−	0.0202492i	$-0.993554\pi$
$887$	−2.92775e15	+	9.01069e15i	−0.179042	+	0.551034i	0.820753	+	0.571283i	$0.193554\pi$
$888$		0			0
$889$	1.76151e16	−	1.27981e16i	1.06396	−	0.773012i
$890$	−8.24286e15			−0.494804
$891$		0			0
$892$	4.25861e15			0.252500
$893$	1.38032e14	−	1.00286e14i	0.00813389	−	0.00590961i
$894$		0			0
$895$	3.39999e15	−	1.04641e16i	0.197902	−	0.609080i
$896$	−5.78464e15	−	4.20278e15i	−0.334643	−	0.243133i
$897$		0			0
$898$	7.18794e15	−	2.21222e16i	0.410756	−	1.26418i
$899$	−4.66908e15	−	1.43700e16i	−0.265188	−	0.816163i
$900$		0			0
$901$	−3.52756e16			−1.97919
$902$	7.28676e15	+	5.18243e15i	0.406348	+	0.289000i
$903$		0			0
$904$	−1.89431e16	+	1.37630e16i	−1.04358	+	0.758204i
$905$	3.26887e15	+	1.00605e16i	0.178991	+	0.550877i
$906$		0			0
$907$	−2.12763e16	−	1.54582e16i	−1.15095	−	0.836214i	−0.162343	−	0.986734i	$-0.551905\pi$
$907$	−2.12763e16	−	1.54582e16i	−1.15095	−	0.836214i	−0.988607	+	0.150520i	$0.951905\pi$
$908$	−1.23323e15	−	8.95994e14i	−0.0663089	−	0.0481763i
$909$		0			0
$910$	5.02084e15	+	1.54525e16i	0.266716	+	0.820866i
$911$	−4.32920e15	+	3.14535e15i	−0.228589	+	0.166080i	−0.696185	−	0.717863i	$-0.745121\pi$
$911$	−4.32920e15	+	3.14535e15i	−0.228589	+	0.166080i	0.467595	+	0.883943i	$0.345121\pi$
$912$		0			0
$913$	−5.14477e15	−	3.65902e15i	−0.268396	−	0.190887i
$914$	−9.98615e14			−0.0517838
$915$		0			0
$916$	−2.04091e15	−	6.28127e15i	−0.104568	−	0.321827i
$917$	4.73665e15	−	1.45779e16i	0.241235	−	0.742444i
$918$		0			0
$919$	5.46508e15	+	3.97061e15i	0.275018	+	0.199812i	0.716742	−	0.697339i	$-0.245633\pi$
$919$	5.46508e15	+	3.97061e15i	0.275018	+	0.199812i	−0.441723	+	0.897151i	$0.645633\pi$
$920$	7.13493e14	−	2.19591e15i	0.0356908	−	0.109845i
$921$		0			0
$922$	−3.96890e15	+	2.88357e15i	−0.196178	+	0.142531i
$923$	−5.12594e15			−0.251863
$924$		0			0
$925$	−2.82416e15			−0.137123
$926$	1.96569e16	−	1.42816e16i	0.948758	−	0.689313i
$927$		0			0
$928$	4.02794e15	−	1.23967e16i	0.192118	−	0.591279i
$929$	8.97426e15	+	6.52018e15i	0.425513	+	0.309153i	0.779852	−	0.625964i	$-0.215294\pi$
$929$	8.97426e15	+	6.52018e15i	0.425513	+	0.309153i	−0.354339	+	0.935117i	$0.615294\pi$
$930$		0			0
$931$	−9.42997e14	+	2.90225e15i	−0.0441863	+	0.135991i
$932$	−6.34019e14	−	1.95131e15i	−0.0295335	−	0.0908947i
$933$		0			0
$934$	−2.81809e16			−1.29732
$935$	−9.61237e15	−	2.85970e16i	−0.439913	−	1.30875i
$936$		0			0
$937$	−4.54857e15	+	3.30473e15i	−0.205735	+	0.149475i	−0.685882	−	0.727713i	$-0.740583\pi$
$937$	−4.54857e15	+	3.30473e15i	−0.205735	+	0.149475i	0.480147	+	0.877188i	$0.340583\pi$
$938$	5.45103e15	+	1.67765e16i	0.245111	+	0.754374i
$939$		0			0
$940$	1.11710e14	+	8.11620e13i	0.00496465	+	0.00360703i
$941$	2.91770e16	+	2.11983e16i	1.28913	+	0.936610i	0.999788	−	0.0206142i	$-0.00656217\pi$
$941$	2.91770e16	+	2.11983e16i	1.28913	+	0.936610i	0.289346	+	0.957225i	$0.406562\pi$
$942$		0			0
$943$	4.63844e14	+	1.42756e15i	0.0202562	+	0.0623421i
$944$	−2.45583e16	+	1.78426e16i	−1.06623	+	0.774663i
$945$		0			0
$946$	2.35504e16	−	1.74768e16i	1.01064	−	0.749997i
$947$	−3.78479e16			−1.61479			−0.807397	−	0.590008i	$-0.799125\pi$
$947$	−3.78479e16			−1.61479			−0.807397	+	0.590008i	$0.799125\pi$
$948$		0			0
$949$	2.15960e15	+	6.64658e15i	0.0910773	+	0.280307i
$950$	3.18850e14	−	9.81318e14i	0.0133692	−	0.0411462i
$951$		0			0
$952$	−2.38384e16	−	1.73196e16i	−0.988039	−	0.717852i
$953$	6.60895e15	−	2.03402e16i	0.272346	−	0.838195i	−0.717563	−	0.696493i	$-0.754743\pi$
$953$	6.60895e15	−	2.03402e16i	0.272346	−	0.838195i	0.989909	−	0.141702i	$-0.0452575\pi$
$954$		0			0
$955$	2.28655e16	−	1.66128e16i	0.931456	−	0.676742i
$956$	−7.34005e15			−0.297290
$957$		0			0
$958$	2.65396e16			1.06264
$959$	−2.32371e16	+	1.68827e16i	−0.925079	+	0.672109i
$960$		0			0
$961$	−5.01199e15	+	1.54253e16i	−0.197257	+	0.607093i
$962$	−2.39508e16	−	1.74013e16i	−0.937253	−	0.680954i
$963$		0			0
$964$	−1.71048e15	+	5.26431e15i	−0.0661750	+	0.203666i
$965$	−7.59795e15	−	2.33841e16i	−0.292278	−	0.899540i
$966$		0			0
$967$	2.66634e15			0.101407			0.0507036	−	0.998714i	$-0.483854\pi$
$967$	2.66634e15			0.101407			0.0507036	+	0.998714i	$0.483854\pi$
$968$	9.35424e15	+	2.69249e16i	0.353748	+	1.01822i
$969$		0			0
$970$	6.93174e15	−	5.03620e15i	0.259178	−	0.188304i
$971$	−5.95153e14	−	1.83169e15i	−0.0221270	−	0.0681000i	0.939383	−	0.342869i	$-0.111399\pi$
$971$	−5.95153e14	−	1.83169e15i	−0.0221270	−	0.0681000i	−0.961510	+	0.274769i	$0.911399\pi$
$972$		0			0
$973$	−1.16765e16	−	8.48347e15i	−0.429232	−	0.311855i
$974$	3.44800e16	+	2.50512e16i	1.26036	+	0.915702i
$975$		0			0
$976$	−4.20444e15	−	1.29399e16i	−0.151962	−	0.467690i
$977$	−6.71235e15	+	4.87681e15i	−0.241243	+	0.175273i	−0.701837	−	0.712338i	$-0.747636\pi$
$977$	−6.71235e15	+	4.87681e15i	−0.241243	+	0.175273i	0.460594	+	0.887611i	$0.347636\pi$
$978$		0			0
$979$	1.70811e16	−	1.72652e14i	0.607030	−	0.00613573i
$980$	−2.46967e15			−0.0872761
$981$		0			0
$982$	−3.20225e15	−	9.85552e15i	−0.111903	−	0.344403i
$983$	5.66368e15	−	1.74310e16i	0.196813	−	0.605729i	−0.803137	−	0.595794i	$-0.796838\pi$
$983$	5.66368e15	−	1.74310e16i	0.196813	−	0.605729i	0.999951	−	0.00993502i	$-0.00316247\pi$
$984$		0			0
$985$	2.42114e16	+	1.75906e16i	0.831994	+	0.604479i
$986$	−1.69993e16	+	5.23184e16i	−0.580909	+	1.78785i
$987$		0			0
$988$	−2.50143e15	+	1.81740e15i	−0.0845328	+	0.0614167i
$989$	4.92302e15			0.165444
$990$		0			0
$991$	−3.53602e15			−0.117520			−0.0587598	−	0.998272i	$-0.518715\pi$
$991$	−3.53602e15			−0.117520			−0.0587598	+	0.998272i	$0.518715\pi$
$992$	6.41347e15	−	4.65966e15i	0.211972	−	0.154007i
$993$		0			0
$994$	1.14068e15	−	3.51064e15i	0.0372853	−	0.114752i
$995$	4.05369e16	+	2.94518e16i	1.31772	+	0.957381i
$996$		0			0
$997$	8.95544e15	−	2.75620e16i	0.287915	−	0.886110i	−0.697595	−	0.716492i	$-0.745747\pi$
$997$	8.95544e15	−	2.75620e16i	0.287915	−	0.886110i	0.985510	−	0.169618i	$-0.0542534\pi$
$998$	−1.05201e16	−	3.23774e16i	−0.336357	−	1.03520i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.12.f.a.91.7		40
3.2	odd	2		11.12.c.a.3.4	✓	40
11.4	even	5	inner	99.12.f.a.37.7		40
33.2	even	10		121.12.a.h.1.8		20
33.20	odd	10		121.12.a.j.1.13		20
33.26	odd	10		11.12.c.a.4.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.12.c.a.3.4	✓	40	3.2	odd	2
11.12.c.a.4.4	yes	40	33.26	odd	10
99.12.f.a.37.7		40	11.4	even	5	inner
99.12.f.a.91.7		40	1.1	even	1	trivial
121.12.a.h.1.8		20	33.2	even	10
121.12.a.j.1.13		20	33.20	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(32.2868 - 23.4578i) q^{2} +(-140.693 + 433.009i) q^{4} +(5225.04 + 3796.22i) q^{5} +(-10421.9 + 32075.4i) q^{7} +(30871.8 + 95013.6i) q^{8} +257751. q^{10} +(-534118. + 5398.75i) q^{11} +(1.51212e6 - 1.09862e6i) q^{13} +(415926. + 1.28009e6i) q^{14} +(2.47120e6 + 1.79543e6i) q^{16} +(7.07508e6 + 5.14035e6i) q^{17} +(1.12278e6 + 3.45556e6i) q^{19} +(-2.37892e6 + 1.72839e6i) q^{20} +(-1.71184e7 + 1.27035e7i) q^{22} -3.57846e6 q^{23} +(-2.19890e6 - 6.76752e6i) q^{25} +(2.30504e7 - 7.09417e7i) q^{26} +(-1.24227e7 - 9.02559e6i) q^{28} +(-4.87068e7 + 1.49904e8i) q^{29} +(-7.75532e7 + 5.63457e7i) q^{31} -8.26977e7 q^{32} +3.49013e8 q^{34} +(-1.76220e8 + 1.28032e8i) q^{35} +(1.22645e8 - 3.77462e8i) q^{37} +(1.17311e8 + 8.52313e7i) q^{38} +(-1.99386e8 + 6.13646e8i) q^{40} +(-1.29621e8 - 3.98933e8i) q^{41} -1.37574e9 q^{43} +(7.28091e7 - 2.32038e8i) q^{44} +(-1.15537e8 + 8.39426e7i) q^{46} +(-1.45109e7 - 4.46598e7i) q^{47} +(6.79475e8 + 4.93667e8i) q^{49} +(-2.29746e8 - 1.66921e8i) q^{50} +(2.62967e8 + 8.09328e8i) q^{52} +(-3.26331e9 + 2.37093e9i) q^{53} +(-2.81129e9 - 1.99942e9i) q^{55} -3.36935e9 q^{56} +(1.94383e9 + 5.98248e9i) q^{58} +(-3.07095e9 + 9.45140e9i) q^{59} +(-3.60357e9 - 2.61815e9i) q^{61} +(-1.18220e9 + 3.63845e9i) q^{62} +(-7.73107e9 + 5.61695e9i) q^{64} +1.20715e10 q^{65} +1.31058e10 q^{67} +(-3.22123e9 + 2.34036e9i) q^{68} +(-2.68626e9 + 8.26747e9i) q^{70} +(-2.21873e9 - 1.61200e9i) q^{71} +(-1.15544e9 + 3.55607e9i) q^{73} +(-4.89460e9 - 1.50640e10i) q^{74} -1.65426e9 q^{76} +(5.39338e9 - 1.71883e10i) q^{77} +(-1.17002e10 + 8.50068e9i) q^{79} +(6.09628e9 + 1.87624e10i) q^{80} +(-1.35431e10 - 9.83966e9i) q^{82} +(9.56204e9 + 6.94723e9i) q^{83} +(1.74537e10 + 5.37171e10i) q^{85} +(-4.44183e10 + 3.22718e10i) q^{86} +(-1.70022e10 - 5.05819e10i) q^{88} -3.19799e10 q^{89} +(1.94794e10 + 5.99515e10i) q^{91} +(5.03464e8 - 1.54950e9i) q^{92} +(-1.51613e9 - 1.10153e9i) q^{94} +(-7.25149e9 + 2.23178e10i) q^{95} +(2.68932e10 - 1.95390e10i) q^{97} +3.35184e10 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 11 q^{2} - 6137 q^{4} - 6038 q^{5} + 55440 q^{7} + 347809 q^{8} + 782320 q^{10} + 288860 q^{11} - 794178 q^{13} - 9181256 q^{14} - 10033697 q^{16} - 11803154 q^{17} - 33326568 q^{19} - 34173582 q^{20}+ \cdots - 1187521497580 q^{98}+O(q^{100}) \) 40 * q - 11 * q^2 - 6137 * q^4 - 6038 * q^5 + 55440 * q^7 + 347809 * q^8 + 782320 * q^10 + 288860 * q^11 - 794178 * q^13 - 9181256 * q^14 - 10033697 * q^16 - 11803154 * q^17 - 33326568 * q^19 - 34173582 * q^20 + 77957825 * q^22 - 75694752 * q^23 - 118409216 * q^25 - 605949712 * q^26 - 546845442 * q^28 + 400113538 * q^29 + 514005960 * q^31 + 84440796 * q^32 - 899802542 * q^34 + 1820315508 * q^35 + 1207982934 * q^37 - 1815036992 * q^38 - 1263004028 * q^40 + 3269102782 * q^41 + 2749122728 * q^43 - 5968984648 * q^44 - 1240862964 * q^46 + 2081937184 * q^47 - 2514603052 * q^49 - 7217881803 * q^50 + 23226253050 * q^52 + 7132071266 * q^53 - 9211291408 * q^55 - 33017775912 * q^56 - 34218647932 * q^58 + 12866186432 * q^59 + 2702502990 * q^61 + 18405787180 * q^62 + 28267347551 * q^64 - 28056414980 * q^65 - 549542392 * q^67 + 17332191778 * q^68 - 90854725304 * q^70 + 37002489528 * q^71 - 41936764254 * q^73 - 118297253448 * q^74 + 136670345702 * q^76 - 85397422330 * q^77 - 140458240296 * q^79 + 257276697596 * q^80 - 94584428059 * q^82 + 238929577568 * q^83 + 48160626338 * q^85 - 176827923479 * q^86 + 742233436703 * q^88 - 311499953960 * q^89 - 410566597652 * q^91 - 77316479782 * q^92 - 508753213738 * q^94 + 524637979272 * q^95 + 474017921070 * q^97 - 1187521497580 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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