LMFDB - Embedded newform 11.17.b.b.10.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,17,Mod(10,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("11.10");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	11.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$17.8556998242$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 762654 x^{12} + 222057901680 x^{10} + \cdots + 52\!\cdots\!00 $ x^14 + 762654x^12 + 222057901680x^10 + 31126553561629440x^8 + 2178288986643965767680x^6 + 68943354209834930932285440x^4 + 663241956553385810373220761600x^2 + 526534944269351107365521326080000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{34}\cdot 3^{10}\cdot 5\cdot 11^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.14
Root			$500.336i$ of defining polynomial
Character	$\chi$	$=$	11.10
Dual form			11.17.b.b.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+500.336i q^{2} +6314.33 q^{3} -184800. q^{4} -411618. q^{5} +3.15929e6i q^{6} +5.61072e6i q^{7} -5.96719e7i q^{8} -3.17591e6 q^{9} +O(q^{10})$	\(q+500.336i q^{2} +6314.33 q^{3} -184800. q^{4} -411618. q^{5} +3.15929e6i q^{6} +5.61072e6i q^{7} -5.96719e7i q^{8} -3.17591e6 q^{9} -2.05947e8i q^{10} +(1.57603e8 + 1.45296e8i) q^{11} -1.16689e9 q^{12} -9.84738e8i q^{13} -2.80724e9 q^{14} -2.59909e9 q^{15} +1.77449e10 q^{16} -3.91109e9i q^{17} -1.58902e9i q^{18} -6.54178e9i q^{19} +7.60669e10 q^{20} +3.54279e10i q^{21} +(-7.26968e10 + 7.88545e10i) q^{22} -5.18551e9 q^{23} -3.76788e11i q^{24} +1.68413e10 q^{25} +4.92700e11 q^{26} -2.91865e11 q^{27} -1.03686e12i q^{28} +4.23938e11i q^{29} -1.30042e12i q^{30} -9.55801e11 q^{31} +4.96777e12i q^{32} +(9.95159e11 + 9.17448e11i) q^{33} +1.95686e12 q^{34} -2.30947e12i q^{35} +5.86908e11 q^{36} -6.48209e12 q^{37} +3.27308e12 q^{38} -6.21797e12i q^{39} +2.45620e13i q^{40} -6.13562e12i q^{41} -1.77259e13 q^{42} -2.61059e12i q^{43} +(-2.91250e13 - 2.68507e13i) q^{44} +1.30726e12 q^{45} -2.59449e12i q^{46} -4.60944e12 q^{47} +1.12047e14 q^{48} +1.75278e12 q^{49} +8.42632e12i q^{50} -2.46959e13i q^{51} +1.81979e14i q^{52} -5.01201e13 q^{53} -1.46031e14i q^{54} +(-6.48723e13 - 5.98065e13i) q^{55} +3.34802e14 q^{56} -4.13070e13i q^{57} -2.12111e14 q^{58} -1.49324e14 q^{59} +4.80312e14 q^{60} -4.31237e13i q^{61} -4.78221e14i q^{62} -1.78191e13i q^{63} -1.32262e15 q^{64} +4.05336e14i q^{65} +(-4.59032e14 + 4.97914e14i) q^{66} +4.66203e14 q^{67} +7.22768e14i q^{68} -3.27430e13 q^{69} +1.15551e15 q^{70} +3.68204e14 q^{71} +1.89513e14i q^{72} +1.30177e15i q^{73} -3.24322e15i q^{74} +1.06342e14 q^{75} +1.20892e15i q^{76} +(-8.15215e14 + 8.84267e14i) q^{77} +3.11107e15 q^{78} +1.29483e14i q^{79} -7.30413e15 q^{80} -1.70622e15 q^{81} +3.06987e15 q^{82} -3.00771e14i q^{83} -6.54707e15i q^{84} +1.60987e15i q^{85} +1.30617e15 q^{86} +2.67689e15i q^{87} +(8.67010e15 - 9.40448e15i) q^{88} -4.02920e14 q^{89} +6.54070e14i q^{90} +5.52509e15 q^{91} +9.58281e14 q^{92} -6.03525e15 q^{93} -2.30627e15i q^{94} +2.69271e15i q^{95} +3.13682e16i q^{96} -2.36411e15 q^{97} +8.76981e14i q^{98} +(-5.00534e14 - 4.61448e14i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 498 q^{3} - 607804 q^{4} - 535618 q^{5} + 273235356 q^{9}+O(q^{10}) $ 14 * q + 498 * q^3 - 607804 * q^4 - 535618 * q^5 + 273235356 * q^9	$ 14 q + 498 q^{3} - 607804 q^{4} - 535618 q^{5} + 273235356 q^{9} + 160637170 q^{11} + 643691748 q^{12} - 3197599848 q^{14} - 10873685706 q^{15} + 35292427592 q^{16} - 99612496468 q^{20} + 127643346840 q^{22} - 305748171262 q^{23} + 289695273612 q^{25} + 1506094012008 q^{26} - 104606894394 q^{27} - 2810074524110 q^{31} + 2285298776958 q^{33} - 4903464738408 q^{34} - 9716494869936 q^{36} + 1225852399438 q^{37} + 19938057531240 q^{38} - 24118470534600 q^{42} - 84053621084948 q^{44} + 129684654333576 q^{45} + 54334138546628 q^{47} - 8779129089432 q^{48} - 17095708773634 q^{49} - 314109617965972 q^{53} - 244204596500798 q^{55} + 506018447074416 q^{56} - 811982470463040 q^{58} + 487958802125282 q^{59} + 23\!\cdots\!24 q^{60}+ \cdots + 16\!\cdots\!60 q^{99}+O(q^{100}) $ 14 * q + 498 * q^3 - 607804 * q^4 - 535618 * q^5 + 273235356 * q^9 + 160637170 * q^11 + 643691748 * q^12 - 3197599848 * q^14 - 10873685706 * q^15 + 35292427592 * q^16 - 99612496468 * q^20 + 127643346840 * q^22 - 305748171262 * q^23 + 289695273612 * q^25 + 1506094012008 * q^26 - 104606894394 * q^27 - 2810074524110 * q^31 + 2285298776958 * q^33 - 4903464738408 * q^34 - 9716494869936 * q^36 + 1225852399438 * q^37 + 19938057531240 * q^38 - 24118470534600 * q^42 - 84053621084948 * q^44 + 129684654333576 * q^45 + 54334138546628 * q^47 - 8779129089432 * q^48 - 17095708773634 * q^49 - 314109617965972 * q^53 - 244204596500798 * q^55 + 506018447074416 * q^56 - 811982470463040 * q^58 + 487958802125282 * q^59 + 2319336599734524 * q^60 - 3058743051134512 * q^64 - 1714489234815960 * q^66 + 951784823334898 * q^67 - 663392073940710 * q^69 + 2102378909371560 * q^70 + 2066090774899778 * q^71 - 4477364985559896 * q^75 - 2087904685537200 * q^77 + 6639282395859240 * q^78 - 5159446405219528 * q^80 - 7813295278584966 * q^81 + 10456916101015560 * q^82 + 11739026032493808 * q^86 + 2795712403748880 * q^88 + 8630276341635710 * q^89 + 7159890945002448 * q^91 - 13184625175008892 * q^92 - 30650238109292214 * q^93 + 10852702786337998 * q^97 + 16903336262615460 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$			500.336i			1.95444i	0.212238	+	0.977218i	$0.431925\pi$
$2$			500.336i			1.95444i	−0.212238	+	0.977218i	$0.568075\pi$
$3$	6314.33			0.962404			0.481202	−	0.876610i	$-0.340200\pi$
$3$	6314.33			0.962404			0.481202	+	0.876610i	$0.340200\pi$
$4$	−184800.			−2.81982
$5$	−411618.			−1.05374			−0.526871	−	0.849945i	$-0.676635\pi$
$5$	−411618.			−1.05374			−0.526871	+	0.849945i	$0.676635\pi$
$6$			3.15929e6i			1.88096i
$7$			5.61072e6i			0.973272i	0.873605	+	0.486636i	$0.161776\pi$
$7$			5.61072e6i			0.973272i	−0.873605	+	0.486636i	$0.838224\pi$
$8$		−	5.96719e7i		−	3.55672i
$9$	−3.17591e6			−0.0737782
$10$		−	2.05947e8i		−	2.05947i
$11$	1.57603e8	+	1.45296e8i	0.735231	+	0.677817i
$11$	1.57603e8	+	1.45296e8i	0.735231	+	0.677817i
$12$	−1.16689e9			−2.71381
$13$		−	9.84738e8i		−	1.20719i	−0.797293	−	0.603593i	$-0.793735\pi$
$13$		−	9.84738e8i		−	1.20719i	0.797293	−	0.603593i	$-0.206265\pi$
$14$	−2.80724e9			−1.90220
$15$	−2.59909e9			−1.01413
$16$	1.77449e10			4.13157
$17$		−	3.91109e9i		−	0.560669i	−0.959902	−	0.280334i	$-0.909555\pi$
$17$		−	3.91109e9i		−	0.560669i	0.959902	−	0.280334i	$-0.0904453\pi$
$18$		−	1.58902e9i		−	0.144195i
$19$		−	6.54178e9i		−	0.385183i	−0.981279	−	0.192591i	$-0.938311\pi$
$19$		−	6.54178e9i		−	0.385183i	0.981279	−	0.192591i	$-0.0616892\pi$
$20$	7.60669e10			2.97136
$21$			3.54279e10i			0.936681i
$22$	−7.26968e10	+	7.88545e10i	−1.32475	+	1.43696i
$23$	−5.18551e9			−0.0662169			−0.0331084	−	0.999452i	$-0.510541\pi$
$23$	−5.18551e9			−0.0662169			−0.0331084	+	0.999452i	$0.510541\pi$
$24$		−	3.76788e11i		−	3.42300i
$25$	1.68413e10			0.110371
$26$	4.92700e11			2.35937
$27$	−2.91865e11			−1.03341
$28$		−	1.03686e12i		−	2.74445i
$29$			4.23938e11i			0.847459i	0.905789	+	0.423730i	$0.139279\pi$
$29$			4.23938e11i			0.847459i	−0.905789	+	0.423730i	$0.860721\pi$
$30$		−	1.30042e12i		−	1.98204i
$31$	−9.55801e11			−1.12066			−0.560330	−	0.828269i	$-0.689326\pi$
$31$	−9.55801e11			−1.12066			−0.560330	+	0.828269i	$0.689326\pi$
$32$			4.96777e12i			4.51816i
$33$	9.95159e11	+	9.17448e11i	0.707589	+	0.652334i
$34$	1.95686e12			1.09579
$35$		−	2.30947e12i		−	1.02558i
$36$	5.86908e11			0.208041
$37$	−6.48209e12			−1.84544			−0.922722	−	0.385465i	$-0.874041\pi$
$37$	−6.48209e12			−1.84544			−0.922722	+	0.385465i	$0.874041\pi$
$38$	3.27308e12			0.752815
$39$		−	6.21797e12i		−	1.16180i
$40$			2.45620e13i			3.74787i
$41$		−	6.13562e12i		−	0.768401i	−0.923250	−	0.384200i	$-0.874477\pi$
$41$		−	6.13562e12i		−	0.768401i	0.923250	−	0.384200i	$-0.125523\pi$
$42$	−1.77259e13			−1.83068
$43$		−	2.61059e12i		−	0.223353i	−0.993745	−	0.111676i	$-0.964378\pi$
$43$		−	2.61059e12i		−	0.223353i	0.993745	−	0.111676i	$-0.0356220\pi$
$44$	−2.91250e13	−	2.68507e13i	−2.07322	−	1.91132i
$45$	1.30726e12			0.0777432
$46$		−	2.59449e12i		−	0.129417i
$47$	−4.60944e12			−0.193582			−0.0967910	−	0.995305i	$-0.530858\pi$
$47$	−4.60944e12			−0.193582			−0.0967910	+	0.995305i	$0.530858\pi$
$48$	1.12047e14			3.97624
$49$	1.75278e12			0.0527424
$50$			8.42632e12i			0.215714i
$51$		−	2.46959e13i		−	0.539590i
$52$			1.81979e14i			3.40405i
$53$	−5.01201e13			−0.805017			−0.402509	−	0.915416i	$-0.631862\pi$
$53$	−5.01201e13			−0.805017			−0.402509	+	0.915416i	$0.631862\pi$
$54$		−	1.46031e14i		−	2.01973i
$55$	−6.48723e13	−	5.98065e13i	−0.774743	−	0.714244i
$56$	3.34802e14			3.46166
$57$		−	4.13070e13i		−	0.370702i
$58$	−2.12111e14			−1.65630
$59$	−1.49324e14			−1.01698			−0.508492	−	0.861067i	$-0.669797\pi$
$59$	−1.49324e14			−1.01698			−0.508492	+	0.861067i	$0.669797\pi$
$60$	4.80312e14			2.85965
$61$		−	4.31237e13i		−	0.224946i	−0.993655	−	0.112473i	$-0.964123\pi$
$61$		−	4.31237e13i		−	0.224946i	0.993655	−	0.112473i	$-0.0358771\pi$
$62$		−	4.78221e14i		−	2.19026i
$63$		−	1.78191e13i		−	0.0718063i
$64$	−1.32262e15			−4.69889
$65$			4.05336e14i			1.27206i
$66$	−4.59032e14	+	4.97914e14i	−1.27495	+	1.38294i
$67$	4.66203e14			1.14809			0.574046	−	0.818823i	$-0.305373\pi$
$67$	4.66203e14			1.14809			0.574046	+	0.818823i	$0.305373\pi$
$68$			7.22768e14i			1.58098i
$69$	−3.27430e13			−0.0637274
$70$	1.15551e15			2.00442
$71$	3.68204e14			0.570193			0.285096	−	0.958499i	$-0.407974\pi$
$71$	3.68204e14			0.570193			0.285096	+	0.958499i	$0.407974\pi$
$72$			1.89513e14i			0.262409i
$73$			1.30177e15i			1.61418i	0.590428	+	0.807090i	$0.298959\pi$
$73$			1.30177e15i			1.61418i	−0.590428	+	0.807090i	$0.701041\pi$
$74$		−	3.24322e15i		−	3.60680i
$75$	1.06342e14			0.106222
$76$			1.20892e15i			1.08615i
$77$	−8.15215e14	+	8.84267e14i	−0.659700	+	0.715579i
$78$	3.11107e15			2.27066
$79$			1.29483e14i			0.0853486i	0.999089	+	0.0426743i	$0.0135878\pi$
$79$			1.29483e14i			0.0853486i	−0.999089	+	0.0426743i	$0.986412\pi$
$80$	−7.30413e15			−4.35360
$81$	−1.70622e15			−0.920779
$82$	3.06987e15			1.50179
$83$		−	3.00771e14i		−	0.133540i	−0.997768	−	0.0667699i	$-0.978731\pi$
$83$		−	3.00771e14i		−	0.133540i	0.997768	−	0.0667699i	$-0.0212693\pi$
$84$		−	6.54707e15i		−	2.64127i
$85$			1.60987e15i			0.590800i
$86$	1.30617e15			0.436529
$87$			2.67689e15i			0.815598i
$88$	8.67010e15	−	9.40448e15i	2.41081	−	2.61501i
$89$	−4.02920e14			−0.102353			−0.0511763	−	0.998690i	$-0.516297\pi$
$89$	−4.02920e14			−0.102353			−0.0511763	+	0.998690i	$0.516297\pi$
$90$			6.54070e14i			0.151944i
$91$	5.52509e15			1.17492
$92$	9.58281e14			0.186720
$93$	−6.03525e15			−1.07853
$94$		−	2.30627e15i		−	0.378344i
$95$			2.69271e15i			0.405883i
$96$			3.13682e16i			4.34830i
$97$	−2.36411e15			−0.301643			−0.150821	−	0.988561i	$-0.548192\pi$
$97$	−2.36411e15			−0.301643			−0.150821	+	0.988561i	$0.548192\pi$
$98$			8.76981e14i			0.103082i
$99$	−5.00534e14	−	4.61448e14i	−0.0542440	−	0.0500082i
$100$	−3.11227e15			−0.311227
$101$		−	3.30959e15i		−	0.305635i	−0.988254	−	0.152817i	$-0.951165\pi$
$101$		−	3.30959e15i		−	0.305635i	0.988254	−	0.152817i	$-0.0488346\pi$
$102$	1.23562e16			1.05459
$103$	−6.33861e15			−0.500376			−0.250188	−	0.968197i	$-0.580492\pi$
$103$	−6.33861e15			−0.500376			−0.250188	+	0.968197i	$0.580492\pi$
$104$	−5.87612e16			−4.29362
$105$		−	1.45828e16i		−	0.987019i
$106$		−	2.50769e16i		−	1.57335i
$107$		−	2.28964e16i		−	1.33259i	−0.745688	−	0.666295i	$-0.767879\pi$
$107$		−	2.28964e16i		−	1.33259i	0.745688	−	0.666295i	$-0.232121\pi$
$108$	5.39366e16			2.91403
$109$			3.31402e16i			1.66319i	0.555380	+	0.831597i	$0.312573\pi$
$109$			3.31402e16i			1.66319i	−0.555380	+	0.831597i	$0.687427\pi$
$110$	2.99233e16	−	3.24579e16i	1.39594	−	1.51419i
$111$	−4.09301e16			−1.77606
$112$			9.95619e16i			4.02114i
$113$	−4.99360e16			−1.87839			−0.939197	−	0.343379i	$-0.888428\pi$
$113$	−4.99360e16			−1.87839			−0.939197	+	0.343379i	$0.888428\pi$
$114$	2.06673e16			0.724513
$115$	2.13445e15			0.0697755
$116$		−	7.83437e16i		−	2.38968i
$117$			3.12744e15i			0.0890640i
$118$		−	7.47122e16i		−	1.98763i
$119$	2.19440e16			0.545683
$120$			1.55093e17i			3.60696i
$121$	3.72781e15	+	4.57983e16i	0.0811281	+	0.996704i
$122$	2.15763e16			0.439642
$123$		−	3.87424e16i		−	0.739512i
$124$	1.76632e17			3.16006
$125$	5.58757e16			0.937439
$126$	8.91555e15			0.140341
$127$			6.13858e16i			0.907064i	0.891240	+	0.453532i	$0.149836\pi$
$127$			6.13858e16i			0.907064i	−0.891240	+	0.453532i	$0.850164\pi$
$128$		−	3.36186e17i		−	4.66552i
$129$		−	1.64841e16i		−	0.214956i
$130$	−2.02804e17			−2.48616
$131$			7.75100e16i			0.893691i	0.894611	+	0.446846i	$0.147453\pi$
$131$			7.75100e16i			0.893691i	−0.894611	+	0.446846i	$0.852547\pi$
$132$	−1.83905e17	−	1.69544e17i	−1.99527	−	1.83946i
$133$	3.67041e16			0.374888
$134$			2.33258e17i			2.24387i
$135$	1.20137e17			1.08895
$136$	−2.33382e17			−1.99414
$137$	4.82056e16			0.388448			0.194224	−	0.980957i	$-0.437781\pi$
$137$	4.82056e16			0.388448			0.194224	+	0.980957i	$0.437781\pi$
$138$		−	1.63825e16i		−	0.124551i
$139$		−	1.65872e17i		−	1.19029i	−0.803617	−	0.595146i	$-0.797094\pi$
$139$		−	1.65872e17i		−	1.19029i	0.803617	−	0.595146i	$-0.202906\pi$
$140$			4.26790e17i			2.89194i
$141$	−2.91055e16			−0.186304
$142$			1.84226e17i			1.11441i
$143$	1.43079e17	−	1.55198e17i	0.818251	−	0.887560i
$144$	−5.63564e16			−0.304820
$145$		−	1.74501e17i		−	0.893003i
$146$	−6.51323e17			−3.15481
$147$	1.10677e16			0.0507595
$148$	1.19789e18			5.20382
$149$			2.96036e17i			1.21858i	0.792947	+	0.609291i	$0.208546\pi$
$149$			2.96036e17i			1.21858i	−0.792947	+	0.609291i	$0.791454\pi$
$150$			5.32066e16i			0.207604i
$151$			2.26939e17i			0.839641i	0.907607	+	0.419821i	$0.137907\pi$
$151$			2.26939e17i			0.839641i	−0.907607	+	0.419821i	$0.862093\pi$
$152$	−3.90360e17			−1.36999
$153$			1.24213e16i			0.0413651i
$154$	−4.42430e17	−	4.07881e17i	−1.39855	−	1.28934i
$155$	3.93425e17			1.18089
$156$			1.14908e18i			3.27607i
$157$	1.66032e16			0.0449774			0.0224887	−	0.999747i	$-0.492841\pi$
$157$	1.66032e16			0.0449774			0.0224887	+	0.999747i	$0.492841\pi$
$158$	−6.47850e16			−0.166808
$159$	−3.16475e17			−0.774752
$160$		−	2.04482e18i		−	4.76097i
$161$		−	2.90944e16i		−	0.0644470i
$162$		−	8.53683e17i		−	1.79960i
$163$	1.94866e17			0.391052			0.195526	−	0.980699i	$-0.437359\pi$
$163$	1.94866e17			0.391052			0.195526	+	0.980699i	$0.437359\pi$
$164$			1.13386e18i			2.16675i
$165$	−4.09625e17	−	3.77638e17i	−0.745616	−	0.687391i
$166$	1.50486e17			0.260995
$167$		−	9.20482e17i		−	1.52154i	−0.649021	−	0.760770i	$-0.724821\pi$
$167$		−	9.20482e17i		−	1.52154i	0.649021	−	0.760770i	$-0.275179\pi$
$168$	2.11405e18			3.33151
$169$	−3.04293e17			−0.457296
$170$	−8.05477e17			−1.15468
$171$			2.07761e16i			0.0284181i
$172$			4.82437e17i			0.629815i
$173$		−	4.34148e17i		−	0.541089i	−0.962707	−	0.270545i	$-0.912796\pi$
$173$		−	4.34148e17i		−	0.541089i	0.962707	−	0.270545i	$-0.0872037\pi$
$174$	−1.33934e18			−1.59403
$175$			9.44919e16i			0.107421i
$176$	2.79666e18	+	2.57827e18i	3.03765	+	2.80045i
$177$	−9.42883e17			−0.978749
$178$		−	2.01595e17i		−	0.200042i
$179$	−4.45391e17			−0.422588			−0.211294	−	0.977423i	$-0.567768\pi$
$179$	−4.45391e17			−0.422588			−0.211294	+	0.977423i	$0.567768\pi$
$180$	−2.41582e17			−0.219222
$181$	−3.68362e17			−0.319776			−0.159888	−	0.987135i	$-0.551113\pi$
$181$	−3.68362e17			−0.319776			−0.159888	+	0.987135i	$0.551113\pi$
$182$			2.76440e18i			2.29630i
$183$		−	2.72298e17i		−	0.216489i
$184$			3.09429e17i			0.235515i
$185$	2.66814e18			1.94462
$186$		−	3.01965e18i		−	2.10791i
$187$	5.68266e17	−	6.16400e17i	0.380031	−	0.412221i
$188$	8.51823e17			0.545867
$189$		−	1.63757e18i		−	1.00579i
$190$	−1.34726e18			−0.793273
$191$	−3.38006e17			−0.190835			−0.0954174	−	0.995437i	$-0.530419\pi$
$191$	−3.38006e17			−0.190835			−0.0954174	+	0.995437i	$0.530419\pi$
$192$	−8.35146e18			−4.52223
$193$			2.67800e18i			1.39108i	0.718488	+	0.695539i	$0.244835\pi$
$193$			2.67800e18i			1.39108i	−0.718488	+	0.695539i	$0.755165\pi$
$194$		−	1.18285e18i		−	0.589542i
$195$			2.55943e18i			1.22424i
$196$	−3.23914e17			−0.148724
$197$			2.41073e17i			0.106272i	0.998587	+	0.0531361i	$0.0169217\pi$
$197$			2.41073e17i			0.106272i	−0.998587	+	0.0531361i	$0.983078\pi$
$198$	2.30879e17	−	2.50435e17i	0.0977377	−	0.106016i
$199$	−1.94330e18			−0.790160			−0.395080	−	0.918647i	$-0.629283\pi$
$199$	−1.94330e18			−0.790160			−0.395080	+	0.918647i	$0.629283\pi$
$200$		−	1.00495e18i		−	0.392560i
$201$	2.94376e18			1.10493
$202$	1.65590e18			0.597344
$203$	−2.37860e18			−0.824808
$204$			4.56380e18i			1.52155i
$205$			2.52553e18i			0.809696i
$206$		−	3.17143e18i		−	0.977953i
$207$	1.64687e16			0.00488536
$208$		−	1.74741e19i		−	4.98757i
$209$	9.50495e17	−	1.03101e18i	0.261084	−	0.283198i
$210$	7.29628e18			1.92907
$211$			3.80400e18i			0.968236i	0.875003	+	0.484118i	$0.160860\pi$
$211$			3.80400e18i			0.968236i	−0.875003	+	0.484118i	$0.839140\pi$
$212$	9.26219e18			2.27000
$213$	2.32496e18			0.548756
$214$	1.14559e19			2.60446
$215$			1.07457e18i			0.235356i
$216$			1.74161e19i			3.67555i
$217$		−	5.36273e18i		−	1.09071i
$218$	−1.65812e19			−3.25061
$219$			8.21983e18i			1.55349i
$220$	1.19884e19	+	1.10522e19i	2.18464	+	2.01404i
$221$	−3.85140e18			−0.676831
$222$		−	2.04788e19i		−	3.47120i
$223$	−8.22763e18			−1.34535			−0.672676	−	0.739937i	$-0.734855\pi$
$223$	−8.22763e18			−1.34535			−0.672676	+	0.739937i	$0.734855\pi$
$224$	−2.78727e19			−4.39740
$225$	−5.34866e16			−0.00814300
$226$		−	2.49848e19i		−	3.67120i
$227$			3.90486e18i			0.553858i	0.960890	+	0.276929i	$0.0893166\pi$
$227$			3.90486e18i			0.553858i	−0.960890	+	0.276929i	$0.910683\pi$
$228$			7.63352e18i			1.04531i
$229$	2.06368e18			0.272871			0.136436	−	0.990649i	$-0.456435\pi$
$229$	2.06368e18			0.272871			0.136436	+	0.990649i	$0.456435\pi$
$230$			1.06794e18i			0.136372i
$231$	−5.14754e18	+	5.58356e18i	−0.634898	+	0.688676i
$232$	2.52972e19			3.01418
$233$		−	4.77541e18i		−	0.549747i	−0.961480	−	0.274874i	$-0.911364\pi$
$233$		−	4.77541e18i		−	0.549747i	0.961480	−	0.274874i	$-0.0886360\pi$
$234$	−1.56477e18			−0.174070
$235$	1.89733e18			0.203985
$236$	2.75951e19			2.86771
$237$			8.17600e17i			0.0821398i
$238$			1.09794e19i			1.06650i
$239$		−	1.32045e19i		−	1.24034i	−0.784468	−	0.620169i	$-0.787064\pi$
$239$		−	1.32045e19i		−	1.24034i	0.784468	−	0.620169i	$-0.212936\pi$
$240$	−4.61207e19			−4.18993
$241$		−	1.06699e19i		−	0.937616i	−0.883300	−	0.468808i	$-0.844684\pi$
$241$		−	1.06699e19i		−	0.937616i	0.883300	−	0.468808i	$-0.155316\pi$
$242$	−2.29145e19	+	1.86516e18i	−1.94799	+	0.158560i
$243$	1.79019e18			0.147248
$244$			7.96926e18i			0.634307i
$245$	−7.21477e17			−0.0555769
$246$	1.93842e19			1.44533
$247$	−6.44194e18			−0.464987
$248$			5.70345e19i			3.98588i
$249$		−	1.89917e18i		−	0.128519i
$250$			2.79566e19i			1.83216i
$251$	1.37299e19			0.871522			0.435761	−	0.900062i	$-0.356479\pi$
$251$	1.37299e19			0.871522			0.435761	+	0.900062i	$0.356479\pi$
$252$			3.29297e18i			0.202481i
$253$	−8.17253e17	−	7.53434e17i	−0.0486847	−	0.0448829i
$254$	−3.07135e19			−1.77280
$255$			1.01653e19i			0.568588i
$256$	8.15266e19			4.41957
$257$	−1.52600e19			−0.801841			−0.400921	−	0.916113i	$-0.631310\pi$
$257$	−1.52600e19			−0.801841			−0.400921	+	0.916113i	$0.631310\pi$
$258$	8.24761e18			0.420117
$259$		−	3.63692e19i		−	1.79612i
$260$		−	7.49059e19i		−	3.58698i
$261$		−	1.34639e18i		−	0.0625240i
$262$	−3.87810e19			−1.74666
$263$		−	1.73585e19i		−	0.758344i	−0.925326	−	0.379172i	$-0.876209\pi$
$263$		−	1.73585e19i		−	0.758344i	0.925326	−	0.379172i	$-0.123791\pi$
$264$	5.47459e19	−	5.93830e19i	2.32017	−	2.51670i
$265$	2.06303e19			0.848280
$266$			1.83644e19i			0.732694i
$267$	−2.54417e18			−0.0985046
$268$	−8.61542e19			−3.23741
$269$	−9.43228e18			−0.344032			−0.172016	−	0.985094i	$-0.555028\pi$
$269$	−9.43228e18			−0.344032			−0.172016	+	0.985094i	$0.555028\pi$
$270$			6.01088e19i			2.12827i
$271$			1.45307e18i			0.0499498i	0.999688	+	0.0249749i	$0.00795058\pi$
$271$			1.45307e18i			0.0499498i	−0.999688	+	0.0249749i	$0.992049\pi$
$272$		−	6.94020e19i		−	2.31644i
$273$	3.48872e19			1.13075
$274$			2.41190e19i			0.759197i
$275$	2.65425e18	+	2.44698e18i	0.0811484	+	0.0748116i
$276$	6.05090e18			0.179700
$277$			4.27073e19i			1.23215i	0.787687	+	0.616076i	$0.211279\pi$
$277$			4.27073e19i			1.23215i	−0.787687	+	0.616076i	$0.788721\pi$
$278$	8.29915e19			2.32635
$279$	3.03554e18			0.0826803
$280$	−1.37811e20			−3.64769
$281$		−	1.91119e19i		−	0.491647i	−0.969315	−	0.245824i	$-0.920942\pi$
$281$		−	1.91119e19i		−	0.491647i	0.969315	−	0.245824i	$-0.0790584\pi$
$282$		−	1.45625e19i		−	0.364120i
$283$			7.03706e19i			1.71041i	0.518291	+	0.855204i	$0.326568\pi$
$283$			7.03706e19i			1.71041i	−0.518291	+	0.855204i	$0.673432\pi$
$284$	−6.80440e19			−1.60784
$285$			1.70027e19i			0.390624i
$286$	7.76510e19	+	7.15873e19i	1.73468	+	1.59922i
$287$	3.44252e19			0.747863
$288$		−	1.57772e19i		−	0.333342i
$289$	3.33646e19			0.685651
$290$	8.73089e19			1.74532
$291$	−1.49278e19			−0.290302
$292$		−	2.40567e20i		−	4.55170i
$293$			5.19146e18i			0.0955759i	0.998858	+	0.0477880i	$0.0152172\pi$
$293$			5.19146e18i			0.0955759i	−0.998858	+	0.0477880i	$0.984783\pi$
$294$			5.53755e18i			0.0992062i
$295$	6.14645e19			1.07164
$296$			3.86798e20i			6.56373i
$297$	−4.59989e19	−	4.24069e19i	−0.759794	−	0.700462i
$298$	−1.48117e20			−2.38164
$299$			5.10637e18i			0.0799360i
$300$	−1.96519e19			−0.299526
$301$	1.46473e19			0.217383
$302$	−1.13546e20			−1.64103
$303$		−	2.08978e19i		−	0.294144i
$304$		−	1.16083e20i		−	1.59141i
$305$			1.77505e19i			0.237035i
$306$	−6.21480e18			−0.0808455
$307$		−	9.82920e19i		−	1.24569i	−0.782344	−	0.622847i	$-0.785976\pi$
$307$		−	9.82920e19i		−	1.24569i	0.782344	−	0.622847i	$-0.214024\pi$
$308$	1.50652e20	−	1.63412e20i	1.86024	−	2.01780i
$309$	−4.00241e19			−0.481564
$310$			1.96844e20i			2.30797i
$311$	−1.07883e20			−1.23273			−0.616366	−	0.787460i	$-0.711396\pi$
$311$	−1.07883e20			−1.23273			−0.616366	+	0.787460i	$0.711396\pi$
$312$	−3.71038e20			−4.13220
$313$	1.51186e20			1.64119			0.820593	−	0.571513i	$-0.193643\pi$
$313$	1.51186e20			1.64119			0.820593	+	0.571513i	$0.193643\pi$
$314$			8.30717e18i			0.0879055i
$315$			7.33468e18i			0.0756653i
$316$		−	2.39284e19i		−	0.240668i
$317$	−2.91666e18			−0.0286030			−0.0143015	−	0.999898i	$-0.504552\pi$
$317$	−2.91666e18			−0.0286030			−0.0143015	+	0.999898i	$0.504552\pi$
$318$		−	1.58344e20i		−	1.51420i
$319$	−6.15966e19	+	6.68140e19i	−0.574422	+	0.623078i
$320$	5.44414e20			4.95141
$321$		−	1.44575e20i		−	1.28249i
$322$	1.45570e19			0.125958
$323$	−2.55855e19			−0.215960
$324$	3.15309e20			2.59643
$325$		−	1.65843e19i		−	0.133239i
$326$			9.74982e19i			0.764286i
$327$			2.09258e20i			1.60066i
$328$	−3.66124e20			−2.73299
$329$		−	2.58623e19i		−	0.188408i
$330$	1.88946e20	−	2.04950e20i	1.34346	−	1.45726i
$331$	1.51698e19			0.105282			0.0526411	−	0.998613i	$-0.483236\pi$
$331$	1.51698e19			0.105282			0.0526411	+	0.998613i	$0.483236\pi$
$332$			5.55823e19i			0.376558i
$333$	2.05865e19			0.136154
$334$	4.60550e20			2.97375
$335$	−1.91898e20			−1.20979
$336$			6.28667e20i			3.86996i
$337$		−	9.06345e19i		−	0.544821i	−0.962181	−	0.272411i	$-0.912179\pi$
$337$		−	9.06345e19i		−	0.544821i	0.962181	−	0.272411i	$-0.0878209\pi$
$338$		−	1.52248e20i		−	0.893757i
$339$	−3.15313e20			−1.80777
$340$		−	2.97504e20i		−	1.66595i
$341$	−1.50637e20	−	1.38874e20i	−0.823944	−	0.759603i
$342$	−1.03950e19			−0.0555414
$343$			1.96295e20i			1.02460i
$344$	−1.55779e20			−0.794404
$345$	1.34776e19			0.0671522
$346$	2.17220e20			1.05752
$347$		−	6.22199e19i		−	0.296001i	−0.988987	−	0.148001i	$-0.952716\pi$
$347$		−	6.22199e19i		−	0.296001i	0.988987	−	0.148001i	$-0.0472838\pi$
$348$		−	4.94688e20i		−	2.29984i
$349$		−	1.54128e20i		−	0.700290i	−0.936695	−	0.350145i	$-0.886132\pi$
$349$		−	1.54128e20i		−	0.700290i	0.936695	−	0.350145i	$-0.113868\pi$
$350$	−4.72777e19			−0.209948
$351$			2.87411e20i			1.24752i
$352$	−7.21798e20	+	7.82936e20i	−3.06249	+	3.32189i
$353$	2.82167e20			1.17033			0.585165	−	0.810915i	$-0.301030\pi$
$353$	2.82167e20			1.17033			0.585165	+	0.810915i	$0.301030\pi$
$354$		−	4.71758e20i		−	1.91290i
$355$	−1.51559e20			−0.600836
$356$	7.44595e19			0.288616
$357$	1.38562e20			0.525167
$358$		−	2.22845e20i		−	0.825921i
$359$			3.47881e20i			1.26089i	0.776236	+	0.630443i	$0.217127\pi$
$359$			3.47881e20i			1.26089i	−0.776236	+	0.630443i	$0.782873\pi$
$360$		−	7.80068e19i		−	0.276511i
$361$	2.45647e20			0.851634
$362$		−	1.84305e20i		−	0.624982i
$363$	2.35387e19	+	2.89186e20i	0.0780780	+	0.959232i
$364$	−1.02103e21			−3.31306
$365$		−	5.35833e20i		−	1.70093i
$366$	1.36240e20			0.423113
$367$	−6.23518e20			−1.89461			−0.947306	−	0.320330i	$-0.896206\pi$
$367$	−6.23518e20			−1.89461			−0.947306	+	0.320330i	$0.896206\pi$
$368$	−9.20165e19			−0.273579
$369$			1.94862e19i			0.0566913i
$370$			1.33497e21i			3.80064i
$371$		−	2.81210e20i		−	0.783501i
$372$	1.11531e21			3.04126
$373$			5.08124e20i			1.35612i	0.735005	+	0.678062i	$0.237180\pi$
$373$			5.08124e20i			1.35612i	−0.735005	+	0.678062i	$0.762820\pi$
$374$	3.08407e20	+	2.84324e20i	0.805659	+	0.742746i
$375$	3.52818e20			0.902195
$376$			2.75054e20i			0.688518i
$377$	4.17468e20			1.02304
$378$	8.19336e20			1.96575
$379$	1.08912e20			0.255836			0.127918	−	0.991785i	$-0.459171\pi$
$379$	1.08912e20			0.255836			0.127918	+	0.991785i	$0.459171\pi$
$380$		−	4.97613e20i		−	1.14452i
$381$			3.87610e20i			0.872962i
$382$		−	1.69116e20i		−	0.372974i
$383$	−3.22650e19			−0.0696853			−0.0348427	−	0.999393i	$-0.511093\pi$
$383$	−3.22650e19			−0.0696853			−0.0348427	+	0.999393i	$0.511093\pi$
$384$		−	2.12279e21i		−	4.49011i
$385$	3.35557e20	−	3.63980e20i	0.695153	−	0.754035i
$386$	−1.33990e21			−2.71877
$387$			8.29101e18i			0.0164786i
$388$	4.36886e20			0.850579
$389$	−6.86982e19			−0.131023			−0.0655117	−	0.997852i	$-0.520868\pi$
$389$	−6.86982e19			−0.131023			−0.0655117	+	0.997852i	$0.520868\pi$
$390$	−1.28057e21			−2.39269
$391$			2.02810e19i			0.0371257i
$392$		−	1.04592e20i		−	0.187590i
$393$			4.89424e20i			0.860092i
$394$	−1.20618e20			−0.207702
$395$		−	5.32976e19i		−	0.0899354i
$396$	9.24985e19	+	8.52754e19i	0.152958	+	0.141014i
$397$	8.83048e20			1.43107			0.715534	−	0.698578i	$-0.246184\pi$
$397$	8.83048e20			1.43107			0.715534	+	0.698578i	$0.246184\pi$
$398$		−	9.72301e20i		−	1.54432i
$399$	2.31762e20			0.360793
$400$	2.98848e20			0.456007
$401$	−7.58837e20			−1.13499			−0.567497	−	0.823376i	$-0.692088\pi$
$401$	−7.58837e20			−1.13499			−0.567497	+	0.823376i	$0.692088\pi$
$402$			1.47287e21i			2.15951i
$403$			9.41214e20i			1.35284i
$404$			6.11611e20i			0.861835i
$405$	7.02311e20			0.970263
$406$		−	1.19010e21i		−	1.61203i
$407$	−1.02160e21	−	9.41822e20i	−1.35683	−	1.25087i
$408$	−1.47365e21			−1.91917
$409$		−	1.18529e21i		−	1.51370i	−0.653590	−	0.756848i	$-0.726738\pi$
$409$		−	1.18529e21i		−	1.51370i	0.653590	−	0.756848i	$-0.273262\pi$
$410$	−1.26361e21			−1.58250
$411$	3.04386e20			0.373844
$412$	1.17137e21			1.41097
$413$		−	8.37816e20i		−	0.989801i
$414$			8.23988e18i			0.00954813i
$415$			1.23803e20i			0.140716i
$416$	4.89195e21			5.45426
$417$		−	1.04737e21i		−	1.14554i
$418$	5.15849e20	+	4.75566e20i	0.553493	+	0.510271i
$419$	−9.73230e20			−1.02448			−0.512240	−	0.858843i	$-0.671184\pi$
$419$	−9.73230e20			−1.02448			−0.512240	+	0.858843i	$0.671184\pi$
$420$			2.69489e21i			2.78322i
$421$	−4.34103e20			−0.439882			−0.219941	−	0.975513i	$-0.570587\pi$
$421$	−4.34103e20			−0.439882			−0.219941	+	0.975513i	$0.570587\pi$
$422$	−1.90328e21			−1.89236
$423$	1.46392e19			0.0142821
$424$			2.99076e21i			2.86322i
$425$		−	6.58679e19i		−	0.0618817i
$426$			1.16326e21i			1.07251i
$427$	2.41955e20			0.218933
$428$			4.23125e21i			3.75767i
$429$	9.03446e20	−	9.79971e20i	0.787488	−	0.854191i
$430$	−5.37644e20			−0.459988
$431$		−	4.83403e20i		−	0.405968i	−0.979182	−	0.202984i	$-0.934936\pi$
$431$		−	4.83403e20i		−	0.405968i	0.979182	−	0.202984i	$-0.0650639\pi$
$432$	−5.17913e21			−4.26960
$433$	6.58830e19			0.0533175			0.0266588	−	0.999645i	$-0.491513\pi$
$433$	6.58830e19			0.0533175			0.0266588	+	0.999645i	$0.491513\pi$
$434$	2.68316e21			2.13172
$435$		−	1.10185e21i		−	0.859430i
$436$		−	6.12430e21i		−	4.68991i
$437$			3.39224e19i			0.0255056i
$438$	−4.11267e21			−3.03621
$439$			2.38322e21i			1.72762i	0.503818	+	0.863810i	$0.331928\pi$
$439$			2.38322e21i			1.72762i	−0.503818	+	0.863810i	$0.668072\pi$
$440$	−3.56877e21	+	3.87105e21i	−2.54037	+	2.75555i
$441$	−5.56669e18			−0.00389124
$442$		−	1.92699e21i		−	1.32282i
$443$	1.06614e21			0.718762			0.359381	−	0.933191i	$-0.382988\pi$
$443$	1.06614e21			0.718762			0.359381	+	0.933191i	$0.382988\pi$
$444$	7.56386e21			5.00818
$445$	1.65849e20			0.107853
$446$		−	4.11658e21i		−	2.62940i
$447$			1.86927e21i			1.17277i
$448$		−	7.42084e21i		−	4.57329i
$449$	−2.31949e21			−1.40418			−0.702089	−	0.712089i	$-0.747749\pi$
$449$	−2.31949e21			−1.40418			−0.702089	+	0.712089i	$0.747749\pi$
$450$		−	2.67612e19i		−	0.0159150i
$451$	8.91482e20	−	9.66994e20i	0.520835	−	0.564952i
$452$	9.22817e21			5.29673
$453$			1.43297e21i			0.808074i
$454$	−1.95374e21			−1.08248
$455$	−2.27422e21			−1.23806
$456$	−2.46487e21			−1.31848
$457$			1.51542e20i			0.0796532i	0.999207	+	0.0398266i	$0.0126806\pi$
$457$			1.51542e20i			0.0796532i	−0.999207	+	0.0398266i	$0.987319\pi$
$458$			1.03253e21i			0.533309i
$459$			1.14151e21i			0.579400i
$460$	−3.94445e20			−0.196754
$461$		−	3.23095e21i		−	1.58388i	−0.610599	−	0.791940i	$-0.709071\pi$
$461$		−	3.23095e21i		−	1.58388i	0.610599	−	0.791940i	$-0.290929\pi$
$462$	−2.79365e21	−	2.57550e21i	−1.34597	−	1.24087i
$463$	−1.31527e21			−0.622827			−0.311414	−	0.950274i	$-0.600802\pi$
$463$	−1.31527e21			−0.622827			−0.311414	+	0.950274i	$0.600802\pi$
$464$			7.52276e21i			3.50133i
$465$	2.48422e21			1.13649
$466$	2.38931e21			1.07445
$467$	3.55146e20			0.156990			0.0784950	−	0.996915i	$-0.474989\pi$
$467$	3.55146e20			0.156990			0.0784950	+	0.996915i	$0.474989\pi$
$468$		−	5.77950e20i		−	0.251145i
$469$			2.61573e21i			1.11741i
$470$			9.49300e20i			0.398677i
$471$	1.04838e20			0.0432865
$472$			8.91046e21i			3.61713i
$473$	3.79309e20	−	4.11438e20i	0.151392	−	0.164216i
$474$	−4.09074e20			−0.160537
$475$		−	1.10172e20i		−	0.0425131i
$476$	−4.05525e21			−1.53873
$477$	1.59177e20			0.0593928
$478$	6.60670e21			2.42416
$479$		−	2.31150e21i		−	0.834082i	−0.908888	−	0.417041i	$-0.863067\pi$
$479$		−	2.31150e21i		−	0.834082i	0.908888	−	0.417041i	$-0.136933\pi$
$480$		−	1.29117e22i		−	4.58198i
$481$			6.38316e21i			2.22779i
$482$	5.33854e21			1.83251
$483$		−	1.83712e20i		−	0.0620241i
$484$	−6.88899e20	−	8.46351e21i	−0.228767	−	2.81053i
$485$	9.73108e20			0.317854
$486$			8.95694e20i			0.287786i
$487$	−1.62509e21			−0.513626			−0.256813	−	0.966461i	$-0.582672\pi$
$487$	−1.62509e21			−0.513626			−0.256813	+	0.966461i	$0.582672\pi$
$488$	−2.57328e21			−0.800070
$489$	1.23045e21			0.376350
$490$		−	3.60981e20i		−	0.108621i
$491$			1.05092e21i			0.311113i	0.987827	+	0.155556i	$0.0497170\pi$
$491$			1.05092e21i			0.311113i	−0.987827	+	0.155556i	$0.950283\pi$
$492$			7.15958e21i			2.08529i
$493$	1.65806e21			0.475144
$494$		−	3.22313e21i		−	0.908788i
$495$	2.06029e20	+	1.89940e20i	0.0571592	+	0.0526957i
$496$	−1.69606e22			−4.63008
$497$			2.06589e21i			0.554952i
$498$	9.50221e20			0.251183
$499$	4.89587e21			1.27358			0.636789	−	0.771038i	$-0.280262\pi$
$499$	4.89587e21			1.27358			0.636789	+	0.771038i	$0.280262\pi$
$500$	−1.03258e22			−2.64341
$501$		−	5.81223e21i		−	1.46434i
$502$			6.86957e21i			1.70333i
$503$			4.66726e21i			1.13898i	0.821997	+	0.569492i	$0.192860\pi$
$503$			4.66726e21i			1.13898i	−0.821997	+	0.569492i	$0.807140\pi$
$504$	−1.06330e21			−0.255395
$505$			1.36229e21i			0.322060i
$506$	3.76970e20	−	4.08901e20i	0.0877208	−	0.0951511i
$507$	−1.92141e21			−0.440104
$508$		−	1.13441e22i		−	2.55776i
$509$	−1.76096e21			−0.390848			−0.195424	−	0.980719i	$-0.562608\pi$
$509$	−1.76096e21			−0.390848			−0.195424	+	0.980719i	$0.562608\pi$
$510$	−5.08605e21			−1.11127
$511$	−7.30388e21			−1.57104
$512$			1.87584e22i			3.97224i
$513$			1.90932e21i			0.398051i
$514$		−	7.63510e21i		−	1.56715i
$515$	2.60909e21			0.527267
$516$			3.04627e21i			0.606136i
$517$	−7.26462e20	−	6.69733e20i	−0.142327	−	0.131213i
$518$	1.81968e22			3.51040
$519$		−	2.74135e21i		−	0.520746i
$520$	2.41872e22			4.52437
$521$	−5.65257e21			−1.04122			−0.520612	−	0.853794i	$-0.674296\pi$
$521$	−5.65257e21			−1.04122			−0.520612	+	0.853794i	$0.674296\pi$
$522$	6.73647e20			0.122199
$523$		−	8.47715e21i		−	1.51438i	−0.653192	−	0.757192i	$-0.726571\pi$
$523$		−	8.47715e21i		−	1.51438i	0.653192	−	0.757192i	$-0.273429\pi$
$524$		−	1.43238e22i		−	2.52005i
$525$			5.96654e20i			0.103383i
$526$	8.68508e21			1.48214
$527$			3.73822e21i			0.628319i
$528$	1.76590e22	+	1.62801e22i	2.92345	+	2.69516i
$529$	−6.10572e21			−0.995615
$530$			1.03221e22i			1.65791i
$531$	4.74240e20			0.0750313
$532$	−6.78290e21			−1.05712
$533$	−6.04198e21			−0.927602
$534$		−	1.27294e21i		−	0.192521i
$535$			9.42456e21i			1.40421i
$536$		−	2.78192e22i		−	4.08345i
$537$	−2.81235e21			−0.406700
$538$		−	4.71931e21i		−	0.672388i
$539$	2.76244e20	+	2.54673e20i	0.0387778	+	0.0357497i
$540$	−2.22013e22			−3.07063
$541$		−	4.10128e21i		−	0.558910i	−0.960159	−	0.279455i	$-0.909846\pi$
$541$		−	4.10128e21i		−	0.558910i	0.960159	−	0.279455i	$-0.0901538\pi$
$542$	−7.27025e20			−0.0976236
$543$	−2.32596e21			−0.307754
$544$	1.94294e22			2.53319
$545$		−	1.36411e22i		−	1.75258i
$546$			1.74553e22i			2.20997i
$547$		−	6.92437e21i		−	0.863936i	−0.901889	−	0.431968i	$-0.857819\pi$
$547$		−	6.92437e21i		−	0.863936i	0.901889	−	0.431968i	$-0.142181\pi$
$548$	−8.90839e21			−1.09535
$549$			1.36957e20i			0.0165961i
$550$	−1.22431e21	+	1.32801e21i	−0.146214	+	0.158599i
$551$	2.77331e21			0.326427
$552$			1.95384e21i			0.226661i
$553$	−7.26493e20			−0.0830674
$554$	−2.13680e22			−2.40816
$555$	1.68475e22			1.87151
$556$			3.06530e22i			3.35641i
$557$			7.72797e21i			0.834111i	0.908881	+	0.417055i	$0.136938\pi$
$557$			7.72797e21i			0.834111i	−0.908881	+	0.417055i	$0.863062\pi$
$558$			1.51879e21i			0.161593i
$559$	−2.57075e21			−0.269628
$560$		−	4.09814e22i		−	4.23724i
$561$	3.58822e21	−	3.89216e21i	0.365743	−	0.396723i
$562$	9.56237e21			0.960893
$563$		−	1.89309e22i		−	1.87545i	−0.347385	−	0.937723i	$-0.612930\pi$
$563$		−	1.89309e22i		−	1.87545i	0.347385	−	0.937723i	$-0.387070\pi$
$564$	5.37870e21			0.525344
$565$	2.05546e22			1.97934
$566$	−3.52089e22			−3.34288
$567$		−	9.57312e21i		−	0.896168i
$568$		−	2.19714e22i		−	2.02802i
$569$			1.76500e22i			1.60637i	0.595727	+	0.803187i	$0.296864\pi$
$569$			1.76500e22i			1.60637i	−0.595727	+	0.803187i	$0.703136\pi$
$570$	−8.50705e21			−0.763449
$571$			4.60911e21i			0.407876i	0.978984	+	0.203938i	$0.0653741\pi$
$571$			4.60911e21i			0.407876i	−0.978984	+	0.203938i	$0.934626\pi$
$572$	−2.64409e22	+	2.86805e22i	−2.30732	+	2.50276i
$573$	−2.13428e21			−0.183660
$574$			1.72242e22i			1.46165i
$575$	−8.73309e19			−0.00730844
$576$	4.20052e21			0.346676
$577$	1.41021e22			1.14783			0.573915	−	0.818915i	$-0.305424\pi$
$577$	1.41021e22			1.14783			0.573915	+	0.818915i	$0.305424\pi$
$578$			1.66935e22i			1.34006i
$579$			1.69098e22i			1.33878i
$580$			3.22477e22i			2.51811i
$581$	1.68754e21			0.129971
$582$		−	7.46889e21i		−	0.567377i
$583$	−7.89909e21	−	7.28226e21i	−0.591873	−	0.545654i
$584$	7.76792e22			5.74119
$585$		−	1.28731e21i		−	0.0938505i
$586$	−2.59747e21			−0.186797
$587$	1.67561e22			1.18869			0.594344	−	0.804211i	$-0.297412\pi$
$587$	1.67561e22			1.18869			0.594344	+	0.804211i	$0.297412\pi$
$588$	−2.04530e21			−0.143133
$589$			6.25264e21i			0.431659i
$590$			3.07529e22i			2.09445i
$591$			1.52222e21i			0.102277i
$592$	−1.15024e23			−7.62458
$593$		−	7.89724e21i		−	0.516461i	−0.966083	−	0.258230i	$-0.916861\pi$
$593$		−	7.89724e21i		−	0.516461i	0.966083	−	0.258230i	$-0.0831394\pi$
$594$	2.12177e22	−	2.30149e22i	1.36901	−	1.48497i
$595$	−9.03254e21			−0.575009
$596$		−	5.47074e22i		−	3.43618i
$597$	−1.22706e22			−0.760453
$598$	−2.55490e21			−0.156230
$599$	2.28169e22			1.37671			0.688355	−	0.725374i	$-0.258333\pi$
$599$	2.28169e22			1.37671			0.688355	+	0.725374i	$0.258333\pi$
$600$		−	6.34562e21i		−	0.377802i
$601$			6.22298e21i			0.365597i	0.983150	+	0.182799i	$0.0585156\pi$
$601$			6.22298e21i			0.365597i	−0.983150	+	0.182799i	$0.941484\pi$
$602$			7.32856e21i			0.424861i
$603$	−1.48062e21			−0.0847042
$604$		−	4.19383e22i		−	2.36764i
$605$	−1.53443e21	−	1.88514e22i	−0.0854880	−	1.05027i
$606$	1.04559e22			0.574886
$607$		−	8.32099e21i		−	0.451508i	−0.974184	−	0.225754i	$-0.927515\pi$
$607$		−	8.32099e21i		−	0.451508i	0.974184	−	0.225754i	$-0.0724845\pi$
$608$	3.24980e22			1.74032
$609$	−1.50193e22			−0.793798
$610$	−8.88121e21			−0.463269
$611$			4.53909e21i			0.233689i
$612$		−	2.29545e21i		−	0.116642i
$613$			2.81744e22i			1.41309i	0.707666	+	0.706547i	$0.249748\pi$
$613$			2.81744e22i			1.41309i	−0.707666	+	0.706547i	$0.750252\pi$
$614$	4.91790e22			2.43463
$615$			1.59471e22i			0.779255i
$616$	5.27659e22	+	4.86455e22i	2.54512	+	2.34637i
$617$	−1.34510e22			−0.640433			−0.320217	−	0.947344i	$-0.603756\pi$
$617$	−1.34510e22			−0.640433			−0.320217	+	0.947344i	$0.603756\pi$
$618$		−	2.00255e22i		−	0.941186i
$619$	−1.10942e22			−0.514718			−0.257359	−	0.966316i	$-0.582852\pi$
$619$	−1.10942e22			−0.514718			−0.257359	+	0.966316i	$0.582852\pi$
$620$	−7.27048e22			−3.32989
$621$	1.51347e21			0.0684291
$622$		−	5.39775e22i		−	2.40930i
$623$		−	2.26067e21i		−	0.0996169i
$624$		−	1.10337e23i		−	4.80005i
$625$	−2.55692e22			−1.09819
$626$			7.56439e22i			3.20759i
$627$	6.00174e21	−	6.51011e21i	0.251268	−	0.272551i
$628$	−3.06827e21			−0.126828
$629$			2.53520e22i			1.03468i
$630$	−3.66980e21			−0.147883
$631$	2.95288e22			1.17493			0.587464	−	0.809250i	$-0.300126\pi$
$631$	2.95288e22			1.17493			0.587464	+	0.809250i	$0.300126\pi$
$632$	7.72650e21			0.303561
$633$			2.40198e22i			0.931835i
$634$		−	1.45931e21i		−	0.0559027i
$635$		−	2.52675e22i		−	0.955811i
$636$	5.84845e22			2.18466
$637$		−	1.72603e21i		−	0.0636699i
$638$	−3.34294e22	−	3.08190e22i	−1.21777	−	1.12267i
$639$	−1.16938e21			−0.0420678
$640$			1.38380e23i			4.91625i
$641$	5.17884e22			1.81706			0.908528	−	0.417824i	$-0.137207\pi$
$641$	5.17884e22			1.81706			0.908528	+	0.417824i	$0.137207\pi$
$642$	7.23362e22			2.50655
$643$	−2.68323e22			−0.918270			−0.459135	−	0.888366i	$-0.651841\pi$
$643$	−2.68323e22			−0.918270			−0.459135	+	0.888366i	$0.651841\pi$
$644$			5.37664e21i			0.181729i
$645$			6.78517e21i			0.226508i
$646$		−	1.28013e22i		−	0.422080i
$647$	2.47781e22			0.806927			0.403464	−	0.914996i	$-0.367806\pi$
$647$	2.47781e22			0.806927			0.403464	+	0.914996i	$0.367806\pi$
$648$			1.01813e23i			3.27495i
$649$	−2.35340e22	−	2.16962e22i	−0.747718	−	0.689329i
$650$	8.29772e21			0.260406
$651$		−	3.38621e22i		−	1.04970i
$652$	−3.60111e22			−1.10270
$653$	−6.09047e22			−1.84224			−0.921118	−	0.389284i	$-0.872723\pi$
$653$	−6.09047e22			−1.84224			−0.921118	+	0.389284i	$0.872723\pi$
$654$	−1.04699e23			−3.12840
$655$		−	3.19045e22i		−	0.941719i
$656$		−	1.08876e23i		−	3.17470i
$657$		−	4.13431e21i		−	0.119091i
$658$	1.29398e22			0.368231
$659$		−	2.61996e22i		−	0.736566i	−0.929714	−	0.368283i	$-0.879946\pi$
$659$		−	2.61996e22i		−	0.736566i	0.929714	−	0.368283i	$-0.120054\pi$
$660$	7.56986e22	+	6.97874e22i	2.10250	+	1.93832i
$661$	−2.98215e22			−0.818309			−0.409154	−	0.912465i	$-0.634176\pi$
$661$	−2.98215e22			−0.818309			−0.409154	+	0.912465i	$0.634176\pi$
$662$			7.58997e21i			0.205767i
$663$	−2.43190e22			−0.651385
$664$	−1.79476e22			−0.474964
$665$	−1.51080e22			−0.395035
$666$			1.03002e22i			0.266104i
$667$		−	2.19834e21i		−	0.0561161i
$668$			1.70105e23i			4.29047i
$669$	−5.19520e22			−1.29477
$670$		−	9.60132e22i		−	2.36446i
$671$	6.26571e21	−	6.79644e21i	0.152472	−	0.165387i
$672$	−1.75998e23			−4.23207
$673$		−	1.42205e22i		−	0.337905i	−0.985624	−	0.168953i	$-0.945962\pi$
$673$		−	1.42205e22i		−	0.337905i	0.985624	−	0.168953i	$-0.0540385\pi$
$674$	4.53476e22			1.06482
$675$	−4.91540e21			−0.114059
$676$	5.62332e22			1.28949
$677$			6.28102e22i			1.42338i	0.702494	+	0.711690i	$0.252070\pi$
$677$			6.28102e22i			1.42338i	−0.702494	+	0.711690i	$0.747930\pi$
$678$		−	1.57762e23i		−	3.53318i
$679$		−	1.32643e22i		−	0.293580i
$680$	9.60642e22			2.10131
$681$			2.46566e22i			0.533035i
$682$	6.94837e22	−	7.53692e22i	1.48459	−	1.61035i
$683$	6.16408e22			1.30168			0.650838	−	0.759217i	$-0.274418\pi$
$683$	6.16408e22			1.30168			0.650838	+	0.759217i	$0.274418\pi$
$684$		−	3.83942e21i		−	0.0801340i
$685$	−1.98423e22			−0.409324
$686$	−9.82134e22			−2.00252
$687$	1.30307e22			0.262612
$688$		−	4.63248e22i		−	0.922797i
$689$			4.93552e22i			0.971805i
$690$			6.74333e21i			0.131245i
$691$	9.15053e22			1.76044			0.880221	−	0.474564i	$-0.157394\pi$
$691$	9.15053e22			1.76044			0.880221	+	0.474564i	$0.157394\pi$
$692$			8.02304e22i			1.52577i
$693$	2.58905e21	−	2.80835e21i	0.0486715	−	0.0527942i
$694$	3.11308e22			0.578515
$695$			6.82757e22i			1.25426i
$696$	1.59735e23			2.90086
$697$	−2.39970e22			−0.430818
$698$	7.71157e22			1.36867
$699$		−	3.01535e22i		−	0.529079i
$700$		−	1.74621e22i		−	0.302909i
$701$			6.81408e22i			1.16859i	0.811540	+	0.584296i	$0.198629\pi$
$701$			6.81408e22i			1.16859i	−0.811540	+	0.584296i	$0.801371\pi$
$702$	−1.43802e23			−2.43819
$703$			4.24044e22i			0.710834i
$704$	−2.08449e23	−	1.92171e23i	−3.45477	−	3.18499i
$705$	1.19804e22			0.196316
$706$			1.41178e23i			2.28733i
$707$	1.85692e22			0.297466
$708$	1.74244e23			2.75990
$709$	5.87952e21			0.0920814			0.0460407	−	0.998940i	$-0.485340\pi$
$709$	5.87952e21			0.0920814			0.0460407	+	0.998940i	$0.485340\pi$
$710$		−	7.58305e22i		−	1.17429i
$711$		−	4.11227e20i		−	0.00629687i
$712$			2.40430e22i			0.364040i
$713$	4.95631e21			0.0742066
$714$			6.93274e22i			1.02641i
$715$	−5.88937e22	+	6.38822e22i	−0.862225	+	0.935258i
$716$	8.23081e22			1.19162
$717$		−	8.33779e22i		−	1.19371i
$718$	−1.74057e23			−2.46432
$719$	7.67804e22			1.07503			0.537513	−	0.843255i	$-0.319364\pi$
$719$	7.67804e22			1.07503			0.537513	+	0.843255i	$0.319364\pi$
$720$	2.31973e22			0.321201
$721$		−	3.55642e22i		−	0.487002i
$722$			1.22906e23i			1.66446i
$723$		−	6.73734e22i		−	0.902365i
$724$	6.80732e22			0.901711
$725$			7.13969e21i			0.0935352i
$726$	−1.44690e23	+	1.17772e22i	−1.87476	+	0.152598i
$727$	−1.23146e23			−1.57814			−0.789072	−	0.614301i	$-0.789438\pi$
$727$	−1.23146e23			−1.57814			−0.789072	+	0.614301i	$0.789438\pi$
$728$		−	3.29692e23i		−	4.17886i
$729$	8.47511e22			1.06249
$730$	2.68096e23			3.32436
$731$	−1.02103e22			−0.125227
$732$			5.03205e22i			0.610459i
$733$		−	3.13440e22i		−	0.376117i	−0.982158	−	0.188058i	$-0.939781\pi$
$733$		−	3.13440e22i		−	0.376117i	0.982158	−	0.188058i	$-0.0602194\pi$
$734$		−	3.11968e23i		−	3.70290i
$735$	−4.55565e21			−0.0534874
$736$		−	2.57604e22i		−	0.299178i
$737$	7.34751e22	+	6.77375e22i	0.844113	+	0.778196i
$738$	−9.74964e21			−0.110799
$739$			1.70986e23i			1.92223i	0.276151	+	0.961114i	$0.410941\pi$
$739$			1.70986e23i			1.92223i	−0.276151	+	0.961114i	$0.589059\pi$
$740$	−4.93072e23			−5.48348
$741$	−4.06765e22			−0.447506
$742$	1.40699e23			1.53130
$743$		−	1.50978e23i		−	1.62556i	−0.582569	−	0.812781i	$-0.697952\pi$
$743$		−	1.50978e23i		−	1.62556i	0.582569	−	0.812781i	$-0.302048\pi$
$744$			3.60135e23i			3.83603i
$745$		−	1.21854e23i		−	1.28407i
$746$	−2.54233e23			−2.65046
$747$			9.55221e20i			0.00985233i
$748$	−1.05015e23	+	1.13911e23i	−1.07162	+	1.16239i
$749$	1.28465e23			1.29697
$750$			1.76527e23i			1.76328i
$751$	4.15615e22			0.410745			0.205372	−	0.978684i	$-0.434159\pi$
$751$	4.15615e22			0.410745			0.205372	+	0.978684i	$0.434159\pi$
$752$	−8.17942e22			−0.799797
$753$	8.66953e22			0.838756
$754$			2.08874e23i			1.99947i
$755$		−	9.34122e22i		−	0.884765i
$756$			3.02623e23i			2.83614i
$757$	8.09591e20			0.00750756			0.00375378	−	0.999993i	$-0.498805\pi$
$757$	8.09591e20			0.00750756			0.00375378	+	0.999993i	$0.498805\pi$
$758$			5.44925e22i			0.500015i
$759$	−5.16041e21	−	4.75743e21i	−0.0468543	−	0.0431955i
$760$	1.60679e23			1.44361
$761$		−	1.27907e21i		−	0.0113715i	−0.999984	−	0.00568576i	$-0.998190\pi$
$761$		−	1.27907e21i		−	0.0113715i	0.999984	−	0.00568576i	$-0.00180984\pi$
$762$	−1.93935e23			−1.70615
$763$	−1.85940e23			−1.61874
$764$	6.24634e22			0.538120
$765$		−	5.11282e21i		−	0.0435882i
$766$		−	1.61433e22i		−	0.136195i
$767$			1.47045e23i			1.22769i
$768$	5.14786e23			4.25341
$769$		−	1.03058e23i		−	0.842698i	−0.906899	−	0.421349i	$-0.861557\pi$
$769$		−	1.03058e23i		−	0.842698i	0.906899	−	0.421349i	$-0.138443\pi$
$770$	1.82112e23	+	1.67891e23i	1.47371	+	1.35863i
$771$	−9.63565e22			−0.771696
$772$		−	4.94893e23i		−	3.92259i
$773$	1.89159e23			1.48385			0.741927	−	0.670481i	$-0.233912\pi$
$773$	1.89159e23			1.48385			0.741927	+	0.670481i	$0.233912\pi$
$774$	−4.14829e21			−0.0322063
$775$	−1.60970e22			−0.123689
$776$			1.41071e23i			1.07286i
$777$		−	2.29647e23i		−	1.72859i
$778$		−	3.43722e22i		−	0.256077i
$779$	−4.01379e22			−0.295975
$780$		−	4.72981e23i		−	3.45213i
$781$	5.80301e22	+	5.34986e22i	0.419223	+	0.386486i
$782$	−1.01473e22			−0.0725598
$783$		−	1.23733e23i		−	0.875771i
$784$	3.11031e22			0.217909
$785$	−6.83417e21			−0.0473946
$786$	−2.44876e23			−1.68099
$787$			2.49407e23i			1.69477i	0.530976	+	0.847387i	$0.321825\pi$
$787$			2.49407e23i			1.69477i	−0.530976	+	0.847387i	$0.678175\pi$
$788$		−	4.45503e22i		−	0.299668i
$789$		−	1.09607e23i		−	0.729834i
$790$	2.66667e22			0.175773
$791$		−	2.80177e23i		−	1.82819i
$792$	−2.75355e22	+	2.98678e22i	−0.177865	+	0.192931i
$793$	−4.24656e22			−0.271551
$794$			4.41820e23i			2.79693i
$795$	1.30267e23			0.816388
$796$	3.59121e23			2.22811
$797$	−1.82879e23			−1.12330			−0.561651	−	0.827374i	$-0.689834\pi$
$797$	−1.82879e23			−1.12330			−0.561651	+	0.827374i	$0.689834\pi$
$798$			1.15959e23i			0.705147i
$799$			1.80279e22i			0.108535i
$800$			8.36638e22i			0.498675i
$801$	1.27964e21			0.00755140
$802$		−	3.79673e23i		−	2.21827i
$803$	−1.89142e23	+	2.05164e23i	−1.09412	+	1.18680i
$804$	−5.44006e23			−3.11570
$805$			1.19758e22i			0.0679105i
$806$	−4.70923e23			−2.64405
$807$	−5.95586e22			−0.331098
$808$	−1.97489e23			−1.08706
$809$			7.00865e22i			0.381985i	0.981592	+	0.190992i	$0.0611706\pi$
$809$			7.00865e22i			0.381985i	−0.981592	+	0.190992i	$0.938829\pi$
$810$			3.51391e23i			1.89632i
$811$		−	5.32593e22i		−	0.284596i	−0.989824	−	0.142298i	$-0.954551\pi$
$811$		−	5.32593e22i		−	0.284596i	0.989824	−	0.142298i	$-0.0454491\pi$
$812$	4.39564e23			2.32581
$813$			9.17519e21i			0.0480719i
$814$	4.71227e23	−	5.11142e23i	2.44475	−	2.65183i
$815$	−8.02102e22			−0.412068
$816$		−	4.38228e23i		−	2.22935i
$817$	−1.70779e22			−0.0860317
$818$	5.93044e23			2.95842
$819$	−1.75472e22			−0.0866835
$820$		−	4.66718e23i		−	2.28320i
$821$		−	3.42502e23i		−	1.65927i	−0.558306	−	0.829635i	$-0.688548\pi$
$821$		−	3.42502e23i		−	1.65927i	0.558306	−	0.829635i	$-0.311452\pi$
$822$			1.52295e23i			0.730655i
$823$	1.94150e23			0.922443			0.461222	−	0.887285i	$-0.347411\pi$
$823$	1.94150e23			0.922443			0.461222	+	0.887285i	$0.347411\pi$
$824$			3.78237e23i			1.77970i
$825$	1.67598e22	+	1.54510e22i	0.0780975	+	0.0719990i
$826$	4.19189e23			1.93450
$827$			2.77645e23i			1.26896i	0.772941	+	0.634478i	$0.218785\pi$
$827$			2.77645e23i			1.26896i	−0.772941	+	0.634478i	$0.781215\pi$
$828$	−3.04341e21			−0.0137758
$829$	−2.92660e23			−1.31198			−0.655989	−	0.754770i	$-0.727748\pi$
$829$	−2.92660e23			−1.31198			−0.655989	+	0.754770i	$0.727748\pi$
$830$	−6.19428e22			−0.275021
$831$			2.69668e23i			1.18583i
$832$			1.30243e24i			5.67243i
$833$		−	6.85530e21i		−	0.0295710i
$834$	5.24036e23			2.23889
$835$			3.78887e23i			1.60331i
$836$	−1.75651e23	+	1.90529e23i	−0.736209	+	0.798568i
$837$	2.78965e23			1.15810
$838$		−	4.86941e23i		−	2.00228i
$839$	5.74494e22			0.233986			0.116993	−	0.993133i	$-0.462674\pi$
$839$	5.74494e22			0.233986			0.116993	+	0.993133i	$0.462674\pi$
$840$	−8.70182e23			−3.51055
$841$	7.05228e22			0.281813
$842$		−	2.17197e23i		−	0.859721i
$843$		−	1.20679e23i		−	0.473163i
$844$		−	7.02979e23i		−	2.73025i
$845$	1.25252e23			0.481872
$846$			7.32450e21i			0.0279135i
$847$	−2.56961e23	+	2.09157e22i	−0.970063	+	0.0789596i
$848$	−8.89379e23			−3.32598
$849$			4.44343e23i			1.64610i
$850$	3.29561e22			0.120944
$851$	3.36129e22			0.122200
$852$	−4.29652e23			−1.54739
$853$			3.93963e23i			1.40561i	0.711385	+	0.702803i	$0.248068\pi$
$853$			3.93963e23i			1.40561i	−0.711385	+	0.702803i	$0.751932\pi$
$854$			1.21059e23i			0.427891i
$855$		−	8.55182e21i		−	0.0299454i
$856$	−1.36627e24			−4.73965
$857$		−	2.20341e23i		−	0.757268i	−0.925547	−	0.378634i	$-0.876394\pi$
$857$		−	2.20341e23i		−	0.757268i	0.925547	−	0.378634i	$-0.123606\pi$
$858$	4.90315e23	+	4.52026e23i	1.66946	+	1.53909i
$859$	−1.61946e23			−0.546292			−0.273146	−	0.961973i	$-0.588064\pi$
$859$	−1.61946e23			−0.546292			−0.273146	+	0.961973i	$0.588064\pi$
$860$		−	1.98580e23i		−	0.663662i
$861$	2.17372e23			0.719746
$862$	2.41864e23			0.793438
$863$	2.98151e23			0.969058			0.484529	−	0.874775i	$-0.338991\pi$
$863$	2.98151e23			0.969058			0.484529	+	0.874775i	$0.338991\pi$
$864$		−	1.44992e24i		−	4.66911i
$865$			1.78703e23i			0.570168i
$866$			3.29636e22i			0.104206i
$867$	2.10675e23			0.659873
$868$			9.91031e23i			3.07560i
$869$	−1.88134e22	+	2.04070e22i	−0.0578507	+	0.0627509i
$870$	5.51297e23			1.67970
$871$		−	4.59088e23i		−	1.38596i
$872$	1.97754e24			5.91552
$873$	7.50819e21			0.0222547
$874$	−1.69726e22			−0.0498491
$875$			3.13503e23i			0.912382i
$876$		−	1.51902e24i		−	4.38058i
$877$		−	2.56841e23i		−	0.733951i	−0.930231	−	0.366975i	$-0.880393\pi$
$877$		−	2.56841e23i		−	0.733951i	0.930231	−	0.366975i	$-0.119607\pi$
$878$	−1.19241e24			−3.37652
$879$			3.27806e22i			0.0919827i
$880$	−1.15116e24	−	1.06126e24i	−3.20090	−	2.95095i
$881$	−3.07105e23			−0.846214			−0.423107	−	0.906080i	$-0.639060\pi$
$881$	−3.07105e23			−0.846214			−0.423107	+	0.906080i	$0.639060\pi$
$882$		−	2.78521e21i		−	0.00760518i
$883$	−5.18355e23			−1.40262			−0.701312	−	0.712854i	$-0.747402\pi$
$883$	−5.18355e23			−1.40262			−0.701312	+	0.712854i	$0.747402\pi$
$884$	7.11737e23			1.90854
$885$	3.88107e23			1.03135
$886$			5.33429e23i			1.40477i
$887$		−	3.53002e23i		−	0.921273i	−0.887589	−	0.460636i	$-0.847621\pi$
$887$		−	3.53002e23i		−	0.921273i	0.887589	−	0.460636i	$-0.152379\pi$
$888$			2.44237e24i			6.31697i
$889$	−3.44418e23			−0.882820
$890$			8.29802e22i			0.210792i
$891$	−2.68906e23	−	2.47907e23i	−0.676985	−	0.624119i
$892$	1.52046e24			3.79365
$893$			3.01539e22i			0.0745645i
$894$	−9.35263e23			−2.29210
$895$	1.83331e23			0.445298
$896$	1.88624e24			4.54082
$897$			3.22433e22i			0.0769308i
$898$		−	1.16052e24i		−	2.74438i
$899$		−	4.05201e23i		−	0.949714i
$900$	9.88431e21			0.0229618
$901$			1.96024e23i			0.451348i
$902$	4.83822e23	+	4.46040e23i	1.10416	+	1.01794i
$903$	9.24879e22			0.209210
$904$			2.97978e24i			6.68092i
$905$	1.51624e23			0.336961
$906$	−7.16966e23			−1.57933
$907$	−1.59953e23			−0.349247			−0.174624	−	0.984635i	$-0.555871\pi$
$907$	−1.59953e23			−0.349247			−0.174624	+	0.984635i	$0.555871\pi$
$908$		−	7.21616e23i		−	1.56178i
$909$			1.05110e22i			0.0225492i
$910$		−	1.13788e24i		−	2.41971i
$911$	−2.32299e23			−0.489666			−0.244833	−	0.969565i	$-0.578733\pi$
$911$	−2.32299e23			−0.489666			−0.244833	+	0.969565i	$0.578733\pi$
$912$		−	7.32990e23i		−	1.53158i
$913$	4.37008e22	−	4.74024e22i	0.0905156	−	0.0981826i
$914$	−7.58218e22			−0.155677
$915$			1.12083e23i			0.228123i
$916$	−3.81367e23			−0.769448
$917$	−4.34887e23			−0.869804
$918$	−5.71138e23			−1.13240
$919$			9.00965e23i			1.77086i	0.464773	+	0.885430i	$0.346136\pi$
$919$			9.00965e23i			1.77086i	−0.464773	+	0.885430i	$0.653864\pi$
$920$		−	1.27367e23i		−	0.248172i
$921$		−	6.20649e23i		−	1.19886i
$922$	1.61656e24			3.09559
$923$		−	3.62584e23i		−	0.688328i
$924$	9.51264e23	−	1.03184e24i	1.79030	−	1.94194i
$925$	−1.09167e23			−0.203684
$926$		−	6.58078e23i		−	1.21728i
$927$	2.01309e22			0.0369169
$928$	−2.10603e24			−3.82896
$929$	7.43974e23			1.34101			0.670505	−	0.741905i	$-0.266078\pi$
$929$	7.43974e23			1.34101			0.670505	+	0.741905i	$0.266078\pi$
$930$			1.24294e24i			2.22120i
$931$		−	1.14663e22i		−	0.0203155i
$932$			8.82494e23i			1.55019i
$933$	−6.81207e23			−1.18639
$934$			1.77692e23i			0.306827i
$935$	−2.33908e23	+	2.53721e23i	−0.400454	+	0.434374i
$936$	1.86620e23			0.316776
$937$		−	2.83967e23i		−	0.477915i	−0.971030	−	0.238958i	$-0.923194\pi$
$937$		−	2.83967e23i		−	0.477915i	0.971030	−	0.238958i	$-0.0768057\pi$
$938$	−1.30874e24			−2.18390
$939$	9.54641e23			1.57948
$940$	−3.50626e23			−0.575202
$941$		−	1.09046e24i		−	1.77375i	−0.462011	−	0.886874i	$-0.652872\pi$
$941$		−	1.09046e24i		−	1.77375i	0.462011	−	0.886874i	$-0.347128\pi$
$942$			5.24543e22i			0.0846006i
$943$			3.18163e22i			0.0508811i
$944$	−2.64975e24			−4.20174
$945$			6.74054e23i			1.05984i
$946$	2.05857e23	+	1.89782e23i	0.320949	+	0.295887i
$947$	−1.28339e24			−1.98407			−0.992036	−	0.125957i	$-0.959800\pi$
$947$	−1.28339e24			−1.98407			−0.992036	+	0.125957i	$0.959800\pi$
$948$		−	1.51092e23i		−	0.231620i
$949$	1.28191e24			1.94862
$950$	5.51231e22			0.0830892
$951$	−1.84167e22			−0.0275276
$952$		−	1.30944e24i		−	1.94084i
$953$		−	8.44805e23i		−	1.24169i	−0.783933	−	0.620845i	$-0.786789\pi$
$953$		−	8.44805e23i		−	1.24169i	0.783933	−	0.620845i	$-0.213211\pi$
$954$			7.96420e22i			0.116079i
$955$	1.39129e23			0.201091
$956$			2.44020e24i			3.49753i
$957$	−3.88941e23	+	4.21886e23i	−0.552826	+	0.599653i
$958$	1.15652e24			1.63016
$959$			2.70468e23i			0.378066i
$960$	3.43761e24			4.76526
$961$	1.86133e23			0.255879
$962$	−3.19372e24			−4.35408
$963$			7.27169e22i			0.0983162i
$964$			1.97180e24i			2.64391i
$965$		−	1.10231e24i		−	1.46584i
$966$	9.19176e22			0.121222
$967$			3.88234e23i			0.507787i	0.967232	+	0.253893i	$0.0817112\pi$
$967$			3.88234e23i			0.507787i	−0.967232	+	0.253893i	$0.918289\pi$
$968$	2.73287e24	−	2.22446e23i	3.54500	−	0.288550i
$969$	−1.61555e23			−0.207841
$970$			4.86881e23i			0.621225i
$971$	−2.31749e22			−0.0293267			−0.0146633	−	0.999892i	$-0.504668\pi$
$971$	−2.31749e22			−0.0293267			−0.0146633	+	0.999892i	$0.504668\pi$
$972$	−3.30826e23			−0.415212
$973$	9.30659e23			1.15848
$974$		−	8.13093e23i		−	1.00385i
$975$		−	1.04719e23i		−	0.128229i
$976$		−	7.65228e23i		−	0.929378i
$977$	7.20804e23			0.868282			0.434141	−	0.900845i	$-0.357052\pi$
$977$	7.20804e23			0.868282			0.434141	+	0.900845i	$0.357052\pi$
$978$			6.15636e23i			0.735552i
$979$	−6.35015e22	−	5.85427e22i	−0.0752528	−	0.0693763i
$980$	1.33329e23			0.156717
$981$		−	1.05250e23i		−	0.122708i
$982$	−5.25813e23			−0.608050
$983$	1.09197e23			0.125251			0.0626257	−	0.998037i	$-0.480053\pi$
$983$	1.09197e23			0.125251			0.0626257	+	0.998037i	$0.480053\pi$
$984$	−2.31183e24			−2.63024
$985$		−	9.92301e22i		−	0.111983i
$986$			8.29587e23i			0.928638i
$987$		−	1.63303e23i		−	0.181325i
$988$	1.19047e24			1.31118
$989$			1.35372e22i			0.0147897i
$990$	−9.50338e22	+	1.03083e23i	−0.102990	+	0.111714i
$991$	−4.53458e23			−0.487470			−0.243735	−	0.969842i	$-0.578373\pi$
$991$	−4.53458e23			−0.487470			−0.243735	+	0.969842i	$0.578373\pi$
$992$		−	4.74820e24i		−	5.06332i
$993$	9.57869e22			0.101324
$994$	−1.03364e24			−1.08462
$995$	7.99896e23			0.832624
$996$			3.50965e23i			0.362401i
$997$			1.09961e24i			1.12636i	0.826333	+	0.563182i	$0.190423\pi$
$997$			1.09961e24i			1.12636i	−0.826333	+	0.563182i	$0.809577\pi$
$998$			2.44958e24i			2.48913i
$999$	1.89189e24			1.90710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.17.b.b.10.14	yes	14
3.2	odd	2		99.17.c.b.10.1		14
11.10	odd	2	inner	11.17.b.b.10.1	✓	14
33.32	even	2		99.17.c.b.10.14		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.17.b.b.10.1	✓	14	11.10	odd	2	inner
11.17.b.b.10.14	yes	14	1.1	even	1	trivial
99.17.c.b.10.1		14	3.2	odd	2
99.17.c.b.10.14		14	33.32	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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	11.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+500.336i q^{2} +6314.33 q^{3} -184800. q^{4} -411618. q^{5} +3.15929e6i q^{6} +5.61072e6i q^{7} -5.96719e7i q^{8} -3.17591e6 q^{9} +O(q^{10})\)	\(q+500.336i q^{2} +6314.33 q^{3} -184800. q^{4} -411618. q^{5} +3.15929e6i q^{6} +5.61072e6i q^{7} -5.96719e7i q^{8} -3.17591e6 q^{9} -2.05947e8i q^{10} +(1.57603e8 + 1.45296e8i) q^{11} -1.16689e9 q^{12} -9.84738e8i q^{13} -2.80724e9 q^{14} -2.59909e9 q^{15} +1.77449e10 q^{16} -3.91109e9i q^{17} -1.58902e9i q^{18} -6.54178e9i q^{19} +7.60669e10 q^{20} +3.54279e10i q^{21} +(-7.26968e10 + 7.88545e10i) q^{22} -5.18551e9 q^{23} -3.76788e11i q^{24} +1.68413e10 q^{25} +4.92700e11 q^{26} -2.91865e11 q^{27} -1.03686e12i q^{28} +4.23938e11i q^{29} -1.30042e12i q^{30} -9.55801e11 q^{31} +4.96777e12i q^{32} +(9.95159e11 + 9.17448e11i) q^{33} +1.95686e12 q^{34} -2.30947e12i q^{35} +5.86908e11 q^{36} -6.48209e12 q^{37} +3.27308e12 q^{38} -6.21797e12i q^{39} +2.45620e13i q^{40} -6.13562e12i q^{41} -1.77259e13 q^{42} -2.61059e12i q^{43} +(-2.91250e13 - 2.68507e13i) q^{44} +1.30726e12 q^{45} -2.59449e12i q^{46} -4.60944e12 q^{47} +1.12047e14 q^{48} +1.75278e12 q^{49} +8.42632e12i q^{50} -2.46959e13i q^{51} +1.81979e14i q^{52} -5.01201e13 q^{53} -1.46031e14i q^{54} +(-6.48723e13 - 5.98065e13i) q^{55} +3.34802e14 q^{56} -4.13070e13i q^{57} -2.12111e14 q^{58} -1.49324e14 q^{59} +4.80312e14 q^{60} -4.31237e13i q^{61} -4.78221e14i q^{62} -1.78191e13i q^{63} -1.32262e15 q^{64} +4.05336e14i q^{65} +(-4.59032e14 + 4.97914e14i) q^{66} +4.66203e14 q^{67} +7.22768e14i q^{68} -3.27430e13 q^{69} +1.15551e15 q^{70} +3.68204e14 q^{71} +1.89513e14i q^{72} +1.30177e15i q^{73} -3.24322e15i q^{74} +1.06342e14 q^{75} +1.20892e15i q^{76} +(-8.15215e14 + 8.84267e14i) q^{77} +3.11107e15 q^{78} +1.29483e14i q^{79} -7.30413e15 q^{80} -1.70622e15 q^{81} +3.06987e15 q^{82} -3.00771e14i q^{83} -6.54707e15i q^{84} +1.60987e15i q^{85} +1.30617e15 q^{86} +2.67689e15i q^{87} +(8.67010e15 - 9.40448e15i) q^{88} -4.02920e14 q^{89} +6.54070e14i q^{90} +5.52509e15 q^{91} +9.58281e14 q^{92} -6.03525e15 q^{93} -2.30627e15i q^{94} +2.69271e15i q^{95} +3.13682e16i q^{96} -2.36411e15 q^{97} +8.76981e14i q^{98} +(-5.00534e14 - 4.61448e14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 498 q^{3} - 607804 q^{4} - 535618 q^{5} + 273235356 q^{9}+O(q^{10}) \) 14 * q + 498 * q^3 - 607804 * q^4 - 535618 * q^5 + 273235356 * q^9	\( 14 q + 498 q^{3} - 607804 q^{4} - 535618 q^{5} + 273235356 q^{9} + 160637170 q^{11} + 643691748 q^{12} - 3197599848 q^{14} - 10873685706 q^{15} + 35292427592 q^{16} - 99612496468 q^{20} + 127643346840 q^{22} - 305748171262 q^{23} + 289695273612 q^{25} + 1506094012008 q^{26} - 104606894394 q^{27} - 2810074524110 q^{31} + 2285298776958 q^{33} - 4903464738408 q^{34} - 9716494869936 q^{36} + 1225852399438 q^{37} + 19938057531240 q^{38} - 24118470534600 q^{42} - 84053621084948 q^{44} + 129684654333576 q^{45} + 54334138546628 q^{47} - 8779129089432 q^{48} - 17095708773634 q^{49} - 314109617965972 q^{53} - 244204596500798 q^{55} + 506018447074416 q^{56} - 811982470463040 q^{58} + 487958802125282 q^{59} + 23\!\cdots\!24 q^{60}+ \cdots + 16\!\cdots\!60 q^{99}+O(q^{100}) \) 14 * q + 498 * q^3 - 607804 * q^4 - 535618 * q^5 + 273235356 * q^9 + 160637170 * q^11 + 643691748 * q^12 - 3197599848 * q^14 - 10873685706 * q^15 + 35292427592 * q^16 - 99612496468 * q^20 + 127643346840 * q^22 - 305748171262 * q^23 + 289695273612 * q^25 + 1506094012008 * q^26 - 104606894394 * q^27 - 2810074524110 * q^31 + 2285298776958 * q^33 - 4903464738408 * q^34 - 9716494869936 * q^36 + 1225852399438 * q^37 + 19938057531240 * q^38 - 24118470534600 * q^42 - 84053621084948 * q^44 + 129684654333576 * q^45 + 54334138546628 * q^47 - 8779129089432 * q^48 - 17095708773634 * q^49 - 314109617965972 * q^53 - 244204596500798 * q^55 + 506018447074416 * q^56 - 811982470463040 * q^58 + 487958802125282 * q^59 + 2319336599734524 * q^60 - 3058743051134512 * q^64 - 1714489234815960 * q^66 + 951784823334898 * q^67 - 663392073940710 * q^69 + 2102378909371560 * q^70 + 2066090774899778 * q^71 - 4477364985559896 * q^75 - 2087904685537200 * q^77 + 6639282395859240 * q^78 - 5159446405219528 * q^80 - 7813295278584966 * q^81 + 10456916101015560 * q^82 + 11739026032493808 * q^86 + 2795712403748880 * q^88 + 8630276341635710 * q^89 + 7159890945002448 * q^91 - 13184625175008892 * q^92 - 30650238109292214 * q^93 + 10852702786337998 * q^97 + 16903336262615460 * q^99

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