LMFDB - Embedded newform 100.11.b.e.51.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,11,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	100.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:	$63.5357252674$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 199481 x^{18} + 16413464051 x^{16} + 725560177607766 x^{14} + \cdots + 21\!\cdots\!25 $ x^20 + 199481x^18 + 16413464051x^16 + 725560177607766x^14 + 18834574233849489621x^12 + 294503164498899790078095x^10 + 2731275057520962661290869385x^8 + 14154171070179138865031966998950x^6 + 35770310815174676049504613026680775x^4 + 31929367165777304447910767061760715625*x^2 + 2155644618924695638814066662020965503125
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{97}\cdot 3^{4}\cdot 5^{29} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.7
Root			$-165.390i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.11.b.e.51.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.98863 - 30.4011i) q^{2} -330.781i q^{3} +(-824.454 + 607.331i) q^{4} +(-10056.1 + 3304.05i) q^{6} -29449.0i q^{7} +(26698.7 + 18997.9i) q^{8} -50366.8 q^{9} +O(q^{10})$	\(q+(-9.98863 - 30.4011i) q^{2} -330.781i q^{3} +(-824.454 + 607.331i) q^{4} +(-10056.1 + 3304.05i) q^{6} -29449.0i q^{7} +(26698.7 + 18997.9i) q^{8} -50366.8 q^{9} -122442. i q^{11} +(200893. + 272713. i) q^{12} -449354. q^{13} +(-895281. + 294155. i) q^{14} +(310874. - 1.00143e6i) q^{16} +132144. q^{17} +(503095. + 1.53120e6i) q^{18} -3.03458e6i q^{19} -9.74114e6 q^{21} +(-3.72238e6 + 1.22303e6i) q^{22} -4.11212e6i q^{23} +(6.28414e6 - 8.83141e6i) q^{24} +(4.48843e6 + 1.36609e7i) q^{26} -2.87192e6i q^{27} +(1.78853e7 + 2.42793e7i) q^{28} -2.05671e7 q^{29} +4.65842e7i q^{31} +(-3.35499e7 + 552041. i) q^{32} -4.05016e7 q^{33} +(-1.31994e6 - 4.01731e6i) q^{34} +(4.15251e7 - 3.05893e7i) q^{36} -7.43988e7 q^{37} +(-9.22546e7 + 3.03113e7i) q^{38} +1.48637e8i q^{39} +1.29152e7 q^{41} +(9.73007e7 + 2.96141e8i) q^{42} +4.13136e7i q^{43} +(7.43631e7 + 1.00948e8i) q^{44} +(-1.25013e8 + 4.10744e7i) q^{46} -1.40161e8i q^{47} +(-3.31255e8 - 1.02831e8i) q^{48} -5.84766e8 q^{49} -4.37106e7i q^{51} +(3.70472e8 - 2.72906e8i) q^{52} +7.63529e8 q^{53} +(-8.73095e7 + 2.86865e7i) q^{54} +(5.59469e8 - 7.86249e8i) q^{56} -1.00378e9 q^{57} +(2.05437e8 + 6.25262e8i) q^{58} -3.73192e8i q^{59} +1.40526e9 q^{61} +(1.41621e9 - 4.65313e8i) q^{62} +1.48325e9i q^{63} +(3.51900e8 + 1.01444e9i) q^{64} +(4.04555e8 + 1.23129e9i) q^{66} -1.39456e9i q^{67} +(-1.08946e8 + 8.02550e7i) q^{68} -1.36021e9 q^{69} -7.53953e8i q^{71} +(-1.34473e9 - 9.56863e8i) q^{72} -1.69785e8 q^{73} +(7.43142e8 + 2.26181e9i) q^{74} +(1.84300e9 + 2.50187e9i) q^{76} -3.60580e9 q^{77} +(4.51874e9 - 1.48469e9i) q^{78} -3.47862e9i q^{79} -3.92408e9 q^{81} +(-1.29005e8 - 3.92637e8i) q^{82} +8.27276e8i q^{83} +(8.03113e9 - 5.91610e9i) q^{84} +(1.25598e9 - 4.12667e8i) q^{86} +6.80319e9i q^{87} +(2.32615e9 - 3.26905e9i) q^{88} +6.94167e9 q^{89} +1.32330e10i q^{91} +(2.49742e9 + 3.39025e9i) q^{92} +1.54092e10 q^{93} +(-4.26106e9 + 1.40002e9i) q^{94} +(1.82605e8 + 1.10977e10i) q^{96} -1.99530e8 q^{97} +(5.84101e9 + 1.77775e10i) q^{98} +6.16703e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9}+O(q^{10}) $ 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9} - 1329640 q^{12} + 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} + 1921656 q^{17} + 3556082 q^{18} + 4157512 q^{21} + 5811280 q^{22} - 19112144 q^{24} + 25066884 q^{26} + 87415400 q^{28} - 66014888 q^{29} + 33171328 q^{32} - 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} + 153620656 q^{37} - 250352720 q^{38} + 477406160 q^{41} + 570662040 q^{42} + 339141040 q^{44} - 897549304 q^{46} + 479727360 q^{48} + 333772012 q^{49} + 110465096 q^{52} + 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} - 3973032960 q^{57} - 2075027916 q^{58} - 4283166080 q^{61} - 1664032240 q^{62} + 340459456 q^{64} + 1884031760 q^{66} - 3042411896 q^{68} - 5321669928 q^{69} - 1632326712 q^{72} - 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} - 410885040 q^{77} + 19914223760 q^{78} + 9939722652 q^{81} + 3197757116 q^{82} + 2383099552 q^{84} + 19648321456 q^{86} - 2774318240 q^{88} + 3011851592 q^{89} + 27349072440 q^{92} + 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} + 39984502056 q^{97} - 38416891998 q^{98}+O(q^{100}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9 - 1329640 * q^12 + 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 + 1921656 * q^17 + 3556082 * q^18 + 4157512 * q^21 + 5811280 * q^22 - 19112144 * q^24 + 25066884 * q^26 + 87415400 * q^28 - 66014888 * q^29 + 33171328 * q^32 - 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 + 153620656 * q^37 - 250352720 * q^38 + 477406160 * q^41 + 570662040 * q^42 + 339141040 * q^44 - 897549304 * q^46 + 479727360 * q^48 + 333772012 * q^49 + 110465096 * q^52 + 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 - 3973032960 * q^57 - 2075027916 * q^58 - 4283166080 * q^61 - 1664032240 * q^62 + 340459456 * q^64 + 1884031760 * q^66 - 3042411896 * q^68 - 5321669928 * q^69 - 1632326712 * q^72 - 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 - 410885040 * q^77 + 19914223760 * q^78 + 9939722652 * q^81 + 3197757116 * q^82 + 2383099552 * q^84 + 19648321456 * q^86 - 2774318240 * q^88 + 3011851592 * q^89 + 27349072440 * q^92 + 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 + 39984502056 * q^97 - 38416891998 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−9.98863	−	30.4011i	−0.312145	−	0.950035i
$2$	−9.98863	−	30.4011i	−0.312145	−	0.950035i
$3$		−	330.781i		−	1.36124i	−0.732638	−	0.680618i	$-0.761711\pi$
$3$		−	330.781i		−	1.36124i	0.732638	−	0.680618i	$-0.238289\pi$
$4$	−824.454	+	607.331i	−0.805131	+	0.593097i
$5$		0			0
$5$		0			0
$6$	−10056.1	+	3304.05i	−1.29322	+	0.424903i
$7$		−	29449.0i		−	1.75218i	−0.482144	−	0.876092i	$-0.660142\pi$
$7$		−	29449.0i		−	1.75218i	0.482144	−	0.876092i	$-0.339858\pi$
$8$	26698.7	+	18997.9i	0.814780	+	0.579770i
$9$	−50366.8			−0.852965
$10$		0			0
$11$		−	122442.i		−	0.760271i	−0.924931	−	0.380136i	$-0.875877\pi$
$11$		−	122442.i		−	0.760271i	0.924931	−	0.380136i	$-0.124123\pi$
$12$	200893.	+	272713.i	0.807345	+	1.09597i
$13$	−449354.			−1.21024			−0.605120	−	0.796134i	$-0.706875\pi$
$13$	−449354.			−1.21024			−0.605120	+	0.796134i	$0.706875\pi$
$14$	−895281.	+	294155.i	−1.66464	+	0.546935i
$15$		0			0
$16$	310874.	−	1.00143e6i	0.296473	−	0.955041i
$17$	132144.			0.0930683			0.0465342	−	0.998917i	$-0.485182\pi$
$17$	132144.			0.0930683			0.0465342	+	0.998917i	$0.485182\pi$
$18$	503095.	+	1.53120e6i	0.266249	+	0.810347i
$19$		−	3.03458e6i		−	1.22555i	−0.790258	−	0.612775i	$-0.790053\pi$
$19$		−	3.03458e6i		−	1.22555i	0.790258	−	0.612775i	$-0.209947\pi$
$20$		0			0
$21$	−9.74114e6			−2.38514
$22$	−3.72238e6	+	1.22303e6i	−0.722284	+	0.237315i
$23$		−	4.11212e6i		−	0.638890i	−0.947605	−	0.319445i	$-0.896503\pi$
$23$		−	4.11212e6i		−	0.638890i	0.947605	−	0.319445i	$-0.103497\pi$
$24$	6.28414e6	−	8.83141e6i	0.789205	−	1.10911i
$25$		0			0
$26$	4.48843e6	+	1.36609e7i	0.377770	+	1.14977i
$27$		−	2.87192e6i		−	0.200149i
$28$	1.78853e7	+	2.42793e7i	1.03921	+	1.41074i
$29$	−2.05671e7			−1.00273			−0.501363	−	0.865237i	$-0.667168\pi$
$29$	−2.05671e7			−1.00273			−0.501363	+	0.865237i	$0.667168\pi$
$30$		0			0
$31$			4.65842e7i			1.62716i	0.581452	+	0.813581i	$0.302485\pi$
$31$			4.65842e7i			1.62716i	−0.581452	+	0.813581i	$0.697515\pi$
$32$	−3.35499e7	+	552041.i	−0.999865	+	0.0164521i
$33$	−4.05016e7			−1.03491
$34$	−1.31994e6	−	4.01731e6i	−0.0290508	−	0.0884181i
$35$		0			0
$36$	4.15251e7	−	3.05893e7i	0.686749	−	0.505891i
$37$	−7.43988e7			−1.07290			−0.536448	−	0.843934i	$-0.680234\pi$
$37$	−7.43988e7			−1.07290			−0.536448	+	0.843934i	$0.680234\pi$
$38$	−9.22546e7	+	3.03113e7i	−1.16431	+	0.382549i
$39$			1.48637e8i			1.64742i
$40$		0			0
$41$	1.29152e7			0.111476			0.0557382	−	0.998445i	$-0.482249\pi$
$41$	1.29152e7			0.111476			0.0557382	+	0.998445i	$0.482249\pi$
$42$	9.73007e7	+	2.96141e8i	0.744508	+	2.26596i
$43$			4.13136e7i			0.281029i	0.990079	+	0.140515i	$0.0448757\pi$
$43$			4.13136e7i			0.281029i	−0.990079	+	0.140515i	$0.955124\pi$
$44$	7.43631e7	+	1.00948e8i	0.450914	+	0.612118i
$45$		0			0
$46$	−1.25013e8	+	4.10744e7i	−0.606968	+	0.199426i
$47$		−	1.40161e8i		−	0.611138i	−0.952170	−	0.305569i	$-0.901153\pi$
$47$		−	1.40161e8i		−	0.611138i	0.952170	−	0.305569i	$-0.0988467\pi$
$48$	−3.31255e8	−	1.02831e8i	−1.30004	−	0.403569i
$49$	−5.84766e8			−2.07015
$50$		0			0
$51$		−	4.37106e7i		−	0.126688i
$52$	3.70472e8	−	2.72906e8i	0.974402	−	0.717790i
$53$	7.63529e8			1.82577			0.912885	−	0.408216i	$-0.133849\pi$
$53$	7.63529e8			1.82577			0.912885	+	0.408216i	$0.133849\pi$
$54$	−8.73095e7	+	2.86865e7i	−0.190148	+	0.0624755i
$55$		0			0
$56$	5.59469e8	−	7.86249e8i	1.01586	−	1.42764i
$57$	−1.00378e9			−1.66826
$58$	2.05437e8	+	6.25262e8i	0.312996	+	0.952625i
$59$		−	3.73192e8i		−	0.522002i	−0.965338	−	0.261001i	$-0.915947\pi$
$59$		−	3.73192e8i		−	0.522002i	0.965338	−	0.261001i	$-0.0840527\pi$
$60$		0			0
$61$	1.40526e9			1.66383			0.831913	−	0.554906i	$-0.187246\pi$
$61$	1.40526e9			1.66383			0.831913	+	0.554906i	$0.187246\pi$
$62$	1.41621e9	−	4.65313e8i	1.54586	−	0.507910i
$63$			1.48325e9i			1.49455i
$64$	3.51900e8	+	1.01444e9i	0.327733	+	0.944771i
$65$		0			0
$66$	4.04555e8	+	1.23129e9i	0.323041	+	0.983199i
$67$		−	1.39456e9i		−	1.03291i	−0.856314	−	0.516456i	$-0.827251\pi$
$67$		−	1.39456e9i		−	1.03291i	0.856314	−	0.516456i	$-0.172749\pi$
$68$	−1.08946e8	+	8.02550e7i	−0.0749322	+	0.0551985i
$69$	−1.36021e9			−0.869681
$70$		0			0
$71$		−	7.53953e8i		−	0.417881i	−0.977928	−	0.208941i	$-0.932998\pi$
$71$		−	7.53953e8i		−	0.417881i	0.977928	−	0.208941i	$-0.0670015\pi$
$72$	−1.34473e9	−	9.56863e8i	−0.694979	−	0.494524i
$73$	−1.69785e8			−0.0819002			−0.0409501	−	0.999161i	$-0.513038\pi$
$73$	−1.69785e8			−0.0819002			−0.0409501	+	0.999161i	$0.513038\pi$
$74$	7.43142e8	+	2.26181e9i	0.334899	+	1.01929i
$75$		0			0
$76$	1.84300e9	+	2.50187e9i	0.726869	+	0.986728i
$77$	−3.60580e9			−1.33213
$78$	4.51874e9	−	1.48469e9i	1.56511	−	0.514235i
$79$		−	3.47862e9i		−	1.13050i	−0.824919	−	0.565251i	$-0.808779\pi$
$79$		−	3.47862e9i		−	1.13050i	0.824919	−	0.565251i	$-0.191221\pi$
$80$		0			0
$81$	−3.92408e9			−1.12542
$82$	−1.29005e8	−	3.92637e8i	−0.0347968	−	0.105906i
$83$			8.27276e8i			0.210020i	0.994471	+	0.105010i	$0.0334874\pi$
$83$			8.27276e8i			0.210020i	−0.994471	+	0.105010i	$0.966513\pi$
$84$	8.03113e9	−	5.91610e9i	1.92035	−	1.41462i
$85$		0			0
$86$	1.25598e9	−	4.12667e8i	0.266987	−	0.0877218i
$87$			6.80319e9i			1.36495i
$88$	2.32615e9	−	3.26905e9i	0.440783	−	0.619454i
$89$	6.94167e9			1.24312			0.621561	−	0.783365i	$-0.286499\pi$
$89$	6.94167e9			1.24312			0.621561	+	0.783365i	$0.286499\pi$
$90$		0			0
$91$			1.32330e10i			2.12056i
$92$	2.49742e9	+	3.39025e9i	0.378924	+	0.514391i
$93$	1.54092e10			2.21495
$94$	−4.26106e9	+	1.40002e9i	−0.580602	+	0.190764i
$95$		0			0
$96$	1.82605e8	+	1.10977e10i	0.0223952	+	1.36105i
$97$	−1.99530e8			−0.0232354			−0.0116177	−	0.999933i	$-0.503698\pi$
$97$	−1.99530e8			−0.0232354			−0.0116177	+	0.999933i	$0.503698\pi$
$98$	5.84101e9	+	1.77775e10i	0.646186	+	1.96671i
$99$			6.16703e9i			0.648485i
$100$		0			0
$101$	1.55739e10			1.48180			0.740900	−	0.671615i	$-0.234399\pi$
$101$	1.55739e10			1.48180			0.740900	+	0.671615i	$0.234399\pi$
$102$	−1.32885e9	+	4.36609e8i	−0.120358	+	0.0395450i
$103$			5.68607e9i			0.490486i	0.969462	+	0.245243i	$0.0788677\pi$
$103$			5.68607e9i			0.490486i	−0.969462	+	0.245243i	$0.921132\pi$
$104$	−1.19972e10	−	8.53678e9i	−0.986080	−	0.701661i
$105$		0			0
$106$	−7.62661e9	−	2.32121e10i	−0.569905	−	1.73454i
$107$		−	1.17015e10i		−	0.834300i	−0.908838	−	0.417150i	$-0.863029\pi$
$107$		−	1.17015e10i		−	0.834300i	0.908838	−	0.417150i	$-0.136971\pi$
$108$	1.74421e9	+	2.36777e9i	0.118708	+	0.161146i
$109$	8.01843e9			0.521143			0.260571	−	0.965455i	$-0.416089\pi$
$109$	8.01843e9			0.521143			0.260571	+	0.965455i	$0.416089\pi$
$110$		0			0
$111$			2.46097e10i			1.46046i
$112$	−2.94912e10	−	9.15491e9i	−1.67341	−	0.519474i
$113$	1.16116e10			0.630231			0.315116	−	0.949053i	$-0.397957\pi$
$113$	1.16116e10			0.630231			0.315116	+	0.949053i	$0.397957\pi$
$114$	1.00264e10	+	3.05160e10i	0.520739	+	1.58491i
$115$		0			0
$116$	1.69566e10	−	1.24910e10i	0.807327	−	0.594714i
$117$	2.26325e10			1.03229
$118$	−1.13455e10	+	3.72768e9i	−0.495920	+	0.162940i
$119$		−	3.89149e9i		−	0.163073i
$120$		0			0
$121$	1.09453e10			0.421988
$122$	−1.40366e10	−	4.27215e10i	−0.519355	−	1.58069i
$123$		−	4.27210e9i		−	0.151746i
$124$	−2.82921e10	−	3.84066e10i	−0.965064	−	1.31008i
$125$		0			0
$126$	4.50924e10	−	1.48156e10i	1.41988	−	0.466517i
$127$			1.28991e10i			0.390428i	0.980761	+	0.195214i	$0.0625401\pi$
$127$			1.28991e10i			0.390428i	−0.980761	+	0.195214i	$0.937460\pi$
$128$	2.73251e10	−	2.08310e10i	0.795265	−	0.606263i
$129$	1.36657e10			0.382547
$130$		0			0
$131$		−	2.97636e10i		−	0.771488i	−0.922606	−	0.385744i	$-0.873945\pi$
$131$		−	2.97636e10i		−	0.771488i	0.922606	−	0.385744i	$-0.126055\pi$
$132$	3.33917e10	−	2.45979e10i	0.833237	−	0.613801i
$133$	−8.93652e10			−2.14739
$134$	−4.23962e10	+	1.39297e10i	−0.981302	+	0.322418i
$135$		0			0
$136$	3.52807e9	+	2.51045e9i	0.0758302	+	0.0539582i
$137$	1.43872e10			0.298107			0.149053	−	0.988829i	$-0.452377\pi$
$137$	1.43872e10			0.298107			0.149053	+	0.988829i	$0.452377\pi$
$138$	1.35866e10	+	4.13518e10i	0.271466	+	0.826227i
$139$			4.79542e10i			0.924172i	0.886835	+	0.462086i	$0.152899\pi$
$139$			4.79542e10i			0.924172i	−0.886835	+	0.462086i	$0.847101\pi$
$140$		0			0
$141$	−4.63627e10			−0.831904
$142$	−2.29210e10	+	7.53096e9i	−0.397001	+	0.130439i
$143$			5.50200e10i			0.920111i
$144$	−1.56577e10	+	5.04390e10i	−0.252881	+	0.814617i
$145$		0			0
$146$	1.69592e9	+	5.16165e9i	0.0255647	+	0.0778080i
$147$			1.93429e11i			2.81796i
$148$	6.13384e10	−	4.51847e10i	0.863821	−	0.636331i
$149$	−4.81786e10			−0.656029			−0.328014	−	0.944673i	$-0.606379\pi$
$149$	−4.81786e10			−0.656029			−0.328014	+	0.944673i	$0.606379\pi$
$150$		0			0
$151$			1.16695e11i			1.48651i	0.669009	+	0.743254i	$0.266719\pi$
$151$			1.16695e11i			1.48651i	−0.669009	+	0.743254i	$0.733281\pi$
$152$	5.76507e10	−	8.10194e10i	0.710537	−	0.998553i
$153$	−6.65565e9			−0.0793840
$154$	3.60170e10	+	1.09620e11i	0.415819	+	1.26557i
$155$		0			0
$156$	−9.02722e10	−	1.22545e11i	−0.977082	−	1.32639i
$157$	−1.19475e11			−1.25250			−0.626251	−	0.779621i	$-0.715412\pi$
$157$	−1.19475e11			−1.25250			−0.626251	+	0.779621i	$0.715412\pi$
$158$	−1.05754e11	+	3.47466e10i	−1.07402	+	0.352880i
$159$		−	2.52561e11i		−	2.48531i
$160$		0			0
$161$	−1.21098e11			−1.11945
$162$	3.91962e10	+	1.19296e11i	0.351293	+	1.06918i
$163$			2.89533e9i			0.0251629i	0.999921	+	0.0125814i	$0.00400490\pi$
$163$			2.89533e9i			0.0251629i	−0.999921	+	0.0125814i	$0.995995\pi$
$164$	−1.06480e10	+	7.84382e9i	−0.0897531	+	0.0661163i
$165$		0			0
$166$	2.51501e10	−	8.26336e9i	0.199526	−	0.0655566i
$167$			3.31302e10i			0.255060i	0.991835	+	0.127530i	$0.0407048\pi$
$167$			3.31302e10i			0.255060i	−0.991835	+	0.127530i	$0.959295\pi$
$168$	−2.60076e11	−	1.85061e11i	−1.94336	−	1.38283i
$169$	6.40603e10			0.464682
$170$		0			0
$171$			1.52842e11i			1.04535i
$172$	−2.50911e10	−	3.40612e10i	−0.166677	−	0.226265i
$173$	1.42255e11			0.917988			0.458994	−	0.888439i	$-0.348210\pi$
$173$	1.42255e11			0.917988			0.458994	+	0.888439i	$0.348210\pi$
$174$	2.06824e11	−	6.79546e10i	1.29675	−	0.426062i
$175$		0			0
$176$	−1.22618e11	−	3.80642e10i	−0.726090	−	0.225399i
$177$	−1.23445e11			−0.710569
$178$	−6.93378e10	−	2.11034e11i	−0.388034	−	1.18101i
$179$		−	3.52295e10i		−	0.191708i	−0.995395	−	0.0958542i	$-0.969442\pi$
$179$		−	3.52295e10i		−	0.191708i	0.995395	−	0.0958542i	$-0.0305583\pi$
$180$		0			0
$181$	−8.52774e10			−0.438977			−0.219488	−	0.975615i	$-0.570439\pi$
$181$	−8.52774e10			−0.438977			−0.219488	+	0.975615i	$0.570439\pi$
$182$	4.02298e11	−	1.32180e11i	2.01461	−	0.661923i
$183$		−	4.64833e11i		−	2.26486i
$184$	7.81217e10	−	1.09788e11i	0.370410	−	0.520555i
$185$		0			0
$186$	−1.53916e11	−	4.68455e11i	−0.691386	−	2.10428i
$187$		−	1.61800e10i		−	0.0707571i
$188$	8.51244e10	+	1.15557e11i	0.362464	+	0.492046i
$189$	−8.45750e10			−0.350698
$190$		0			0
$191$			3.50495e11i			1.37884i	0.724360	+	0.689422i	$0.242135\pi$
$191$			3.50495e11i			1.37884i	−0.724360	+	0.689422i	$0.757865\pi$
$192$	3.35557e11	−	1.16402e11i	1.28606	−	0.446122i
$193$	−1.57930e11			−0.589765			−0.294883	−	0.955533i	$-0.595281\pi$
$193$	−1.57930e11			−0.589765			−0.294883	+	0.955533i	$0.595281\pi$
$194$	1.99303e9	+	6.06593e9i	0.00725280	+	0.0220744i
$195$		0			0
$196$	4.82113e11	−	3.55147e11i	1.66674	−	1.22780i
$197$	−3.95179e11			−1.33187			−0.665936	−	0.746009i	$-0.731968\pi$
$197$	−3.95179e11			−1.33187			−0.665936	+	0.746009i	$0.731968\pi$
$198$	1.87484e11	−	6.16002e10i	0.616083	−	0.202421i
$199$		−	2.13388e10i		−	0.0683763i	−0.999415	−	0.0341881i	$-0.989115\pi$
$199$		−	2.13388e10i		−	0.0683763i	0.999415	−	0.0341881i	$-0.0108845\pi$
$200$		0			0
$201$	−4.61293e11			−1.40604
$202$	−1.55562e11	−	4.73463e11i	−0.462536	−	1.40776i
$203$			6.05679e11i			1.75696i
$204$	2.65468e10	+	3.60374e10i	0.0751382	+	0.102000i
$205$		0			0
$206$	1.72863e11	−	5.67961e10i	0.465978	−	0.153103i
$207$			2.07114e11i			0.544951i
$208$	−1.39692e11	+	4.49998e11i	−0.358803	+	1.15583i
$209$	−3.71561e11			−0.931749
$210$		0			0
$211$		−	2.89532e11i		−	0.692283i	−0.938182	−	0.346141i	$-0.887492\pi$
$211$		−	2.89532e11i		−	0.692283i	0.938182	−	0.346141i	$-0.112508\pi$
$212$	−6.29495e11	+	4.63715e11i	−1.46998	+	1.08286i
$213$	−2.49393e11			−0.568835
$214$	−3.55738e11	+	1.16882e11i	−0.792614	+	0.260422i
$215$		0			0
$216$	5.45605e10	−	7.66765e10i	0.116040	−	0.163077i
$217$	1.37186e12			2.85109
$218$	−8.00932e10	−	2.43769e11i	−0.162672	−	0.495104i
$219$			5.61616e10i			0.111486i
$220$		0			0
$221$	−5.93793e10			−0.112635
$222$	7.48161e11	−	2.45817e11i	1.38749	−	0.455876i
$223$		−	7.87602e11i		−	1.42818i	−0.700055	−	0.714089i	$-0.746841\pi$
$223$		−	7.87602e11i		−	1.42818i	0.700055	−	0.714089i	$-0.253159\pi$
$224$	1.62570e10	+	9.88009e11i	0.0288271	+	1.75195i
$225$		0			0
$226$	−1.15984e11	−	3.53005e11i	−0.196723	−	0.598741i
$227$			1.02226e12i			1.69602i	0.529982	+	0.848009i	$0.322199\pi$
$227$			1.02226e12i			1.69602i	−0.529982	+	0.848009i	$0.677801\pi$
$228$	8.27571e11	−	6.09627e11i	1.34317	−	0.989441i
$229$	1.03140e12			1.63775			0.818877	−	0.573970i	$-0.194597\pi$
$229$	1.03140e12			1.63775			0.818877	+	0.573970i	$0.194597\pi$
$230$		0			0
$231$			1.19273e12i			1.81335i
$232$	−5.49115e11	−	3.90732e11i	−0.817002	−	0.581351i
$233$	−2.15652e11			−0.314032			−0.157016	−	0.987596i	$-0.550187\pi$
$233$	−2.15652e11			−0.314032			−0.157016	+	0.987596i	$0.550187\pi$
$234$	−2.26068e11	−	6.88053e11i	−0.322225	−	0.980714i
$235$		0			0
$236$	2.26651e11	+	3.07680e11i	0.309598	+	0.420280i
$237$	−1.15066e12			−1.53888
$238$	−1.18306e11	+	3.88707e10i	−0.154925	+	0.0509023i
$239$		−	1.01800e12i		−	1.30545i	−0.757597	−	0.652723i	$-0.773627\pi$
$239$		−	1.01800e12i		−	1.30545i	0.757597	−	0.652723i	$-0.226373\pi$
$240$		0			0
$241$	7.81848e11			0.961694			0.480847	−	0.876804i	$-0.340329\pi$
$241$	7.81848e11			0.961694			0.480847	+	0.876804i	$0.340329\pi$
$242$	−1.09328e11	−	3.32749e11i	−0.131721	−	0.400903i
$243$			1.12843e12i			1.33181i
$244$	−1.15857e12	+	8.53459e11i	−1.33960	+	0.986810i
$245$		0			0
$246$	−1.29877e11	+	4.26725e10i	−0.144164	+	0.0473666i
$247$			1.36360e12i			1.48321i
$248$	−8.85003e11	+	1.24374e12i	−0.943380	+	1.32578i
$249$	2.73647e11			0.285887
$250$		0			0
$251$			6.23828e11i			0.626176i	0.949724	+	0.313088i	$0.101363\pi$
$251$			6.23828e11i			0.626176i	−0.949724	+	0.313088i	$0.898637\pi$
$252$	−9.00823e11	−	1.22287e12i	−0.886414	−	1.20331i
$253$	−5.03498e11			−0.485730
$254$	3.92147e11	−	1.28844e11i	0.370920	−	0.121870i
$255$		0			0
$256$	−9.06226e11	−	6.22639e11i	−0.824208	−	0.566287i
$257$	−1.04389e12			−0.931086			−0.465543	−	0.885025i	$-0.654141\pi$
$257$	−1.04389e12			−0.931086			−0.465543	+	0.885025i	$0.654141\pi$
$258$	−1.36502e11	−	4.15454e11i	−0.119410	−	0.363433i
$259$			2.19097e12i			1.87991i
$260$		0			0
$261$	1.03590e12			0.855291
$262$	−9.04847e11	+	2.97298e11i	−0.732940	+	0.240816i
$263$			2.25563e12i			1.79262i	0.443423	+	0.896312i	$0.353764\pi$
$263$			2.25563e12i			1.79262i	−0.443423	+	0.896312i	$0.646236\pi$
$264$	−1.08134e12	−	7.69445e11i	−0.843223	−	0.600009i
$265$		0			0
$266$	8.92637e11	+	2.71680e12i	0.670296	+	2.04009i
$267$		−	2.29617e12i		−	1.69218i
$268$	8.46959e11	+	1.14975e12i	0.612616	+	0.831629i
$269$	4.57791e11			0.325017			0.162509	−	0.986707i	$-0.448042\pi$
$269$	4.57791e11			0.325017			0.162509	+	0.986707i	$0.448042\pi$
$270$		0			0
$271$		−	7.07347e10i		−	0.0483934i	−0.999707	−	0.0241967i	$-0.992297\pi$
$271$		−	7.07347e10i		−	0.0483934i	0.999707	−	0.0241967i	$-0.00770280\pi$
$272$	4.10800e10	−	1.32333e11i	0.0275922	−	0.0888841i
$273$	4.37722e12			2.88659
$274$	−1.43708e11	−	4.37385e11i	−0.0930525	−	0.283212i
$275$		0			0
$276$	1.12143e12	−	8.26097e11i	0.700207	−	0.515805i
$277$	2.83728e12			1.73982			0.869908	−	0.493214i	$-0.164178\pi$
$277$	2.83728e12			1.73982			0.869908	+	0.493214i	$0.164178\pi$
$278$	1.45786e12	−	4.78997e11i	0.877995	−	0.288475i
$279$		−	2.34630e12i		−	1.38791i
$280$		0			0
$281$	−4.75819e11			−0.271588			−0.135794	−	0.990737i	$-0.543358\pi$
$281$	−4.75819e11			−0.271588			−0.135794	+	0.990737i	$0.543358\pi$
$282$	4.63100e11	+	1.40948e12i	0.259674	+	0.790337i
$283$		−	9.46174e11i		−	0.521241i	−0.965441	−	0.260621i	$-0.916073\pi$
$283$		−	9.46174e11i		−	0.521241i	0.965441	−	0.260621i	$-0.0839272\pi$
$284$	4.57899e11	+	6.21600e11i	0.247844	+	0.336449i
$285$		0			0
$286$	1.67267e12	−	5.49574e11i	0.874137	−	0.287208i
$287$		−	3.80340e11i		−	0.195327i
$288$	1.68980e12	−	2.78045e10i	0.852850	−	0.0140331i
$289$	−1.99853e12			−0.991338
$290$		0			0
$291$			6.60006e10i			0.0316288i
$292$	1.39980e11	−	1.03116e11i	0.0659404	−	0.0485748i
$293$	−2.37212e12			−1.09849			−0.549247	−	0.835660i	$-0.685085\pi$
$293$	−2.37212e12			−1.09849			−0.549247	+	0.835660i	$0.685085\pi$
$294$	5.88046e12	−	1.93209e12i	2.67716	−	0.879613i
$295$		0			0
$296$	−1.98635e12	−	1.41342e12i	−0.874173	−	0.622033i
$297$	−3.51645e11			−0.152167
$298$	4.81238e11	+	1.46468e12i	0.204776	+	0.623250i
$299$			1.84780e12i			0.773211i
$300$		0			0
$301$	1.21664e12			0.492415
$302$	3.54766e12	−	1.16562e12i	1.41223	−	0.464006i
$303$		−	5.15153e12i		−	2.01708i
$304$	−3.03893e12	−	9.43372e11i	−1.17045	−	0.363342i
$305$		0			0
$306$	6.64808e10	+	2.02339e11i	0.0247793	+	0.0754176i
$307$		−	3.27142e12i		−	1.19962i	−0.800142	−	0.599811i	$-0.795243\pi$
$307$		−	3.27142e12i		−	1.19962i	0.800142	−	0.599811i	$-0.204757\pi$
$308$	2.97282e12	−	2.18992e12i	1.07254	−	0.790085i
$309$	1.88084e12			0.667667
$310$		0			0
$311$		−	2.94681e12i		−	1.01286i	−0.862280	−	0.506431i	$-0.830964\pi$
$311$		−	2.94681e12i		−	1.01286i	0.862280	−	0.506431i	$-0.169036\pi$
$312$	−2.82380e12	+	3.96843e12i	−0.955127	+	1.34229i
$313$	3.18034e11			0.105865			0.0529324	−	0.998598i	$-0.483143\pi$
$313$	3.18034e11			0.105865			0.0529324	+	0.998598i	$0.483143\pi$
$314$	1.19339e12	+	3.63217e12i	0.390962	+	1.18992i
$315$		0			0
$316$	2.11267e12	+	2.86796e12i	0.670497	+	0.910202i
$317$	−3.80109e12			−1.18744			−0.593720	−	0.804672i	$-0.702341\pi$
$317$	−3.80109e12			−1.18744			−0.593720	+	0.804672i	$0.702341\pi$
$318$	−7.67812e12	+	2.52273e12i	−2.36113	+	0.775775i
$319$			2.51828e12i			0.762344i
$320$		0			0
$321$	−3.87063e12			−1.13568
$322$	1.20960e12	+	3.68150e12i	0.349432	+	1.06352i
$323$		−	4.01001e11i		−	0.114060i
$324$	3.23523e12	−	2.38322e12i	0.906107	−	0.667480i
$325$		0			0
$326$	8.80213e10	−	2.89204e10i	0.0239056	−	0.00785447i
$327$		−	2.65234e12i		−	0.709399i
$328$	3.44820e11	+	2.45362e11i	0.0908287	+	0.0646307i
$329$	−4.12761e12			−1.07083
$330$		0			0
$331$		−	4.34328e12i		−	1.09315i	−0.837411	−	0.546573i	$-0.815932\pi$
$331$		−	4.34328e12i		−	1.09315i	0.837411	−	0.546573i	$-0.184068\pi$
$332$	−5.02431e11	−	6.82051e11i	−0.124562	−	0.169093i
$333$	3.74723e12			0.915142
$334$	1.00719e12	−	3.30925e11i	0.242315	−	0.0796155i
$335$		0			0
$336$	−3.02827e12	+	9.75511e12i	−0.707128	+	2.27790i
$337$	−7.56835e11			−0.174121			−0.0870606	−	0.996203i	$-0.527747\pi$
$337$	−7.56835e11			−0.174121			−0.0870606	+	0.996203i	$0.527747\pi$
$338$	−6.39875e11	−	1.94750e12i	−0.145048	−	0.441464i
$339$		−	3.84089e12i		−	0.857894i
$340$		0			0
$341$	5.70389e12			1.23708
$342$	4.64657e12	−	1.52668e12i	0.993119	−	0.326301i
$343$			8.90215e12i			1.87510i
$344$	−7.84873e11	+	1.10302e12i	−0.162932	+	0.228977i
$345$		0			0
$346$	−1.42093e12	−	4.32471e12i	−0.286545	−	0.872120i
$347$		−	4.88633e11i		−	0.0971260i	−0.998820	−	0.0485630i	$-0.984536\pi$
$347$		−	4.88633e11i		−	0.0971260i	0.998820	−	0.0485630i	$-0.0154642\pi$
$348$	−4.13179e12	−	5.60892e12i	−0.809547	−	1.09896i
$349$	−2.32017e12			−0.448118			−0.224059	−	0.974576i	$-0.571931\pi$
$349$	−2.32017e12			−0.448118			−0.224059	+	0.974576i	$0.571931\pi$
$350$		0			0
$351$			1.29051e12i			0.242228i
$352$	6.75933e10	+	4.10793e12i	0.0125081	+	0.760168i
$353$	−2.85311e12			−0.520529			−0.260265	−	0.965537i	$-0.583810\pi$
$353$	−2.85311e12			−0.520529			−0.260265	+	0.965537i	$0.583810\pi$
$354$	1.23304e12	+	3.75286e12i	0.221800	+	0.675065i
$355$		0			0
$356$	−5.72309e12	+	4.21589e12i	−1.00088	+	0.737292i
$357$	−1.28723e12			−0.221981
$358$	−1.07102e12	+	3.51894e11i	−0.182130	+	0.0598408i
$359$		−	1.59682e12i		−	0.267783i	−0.990996	−	0.133892i	$-0.957253\pi$
$359$		−	1.59682e12i		−	0.267783i	0.990996	−	0.133892i	$-0.0427474\pi$
$360$		0			0
$361$	−3.07761e12			−0.501971
$362$	8.51805e11	+	2.59253e12i	0.137024	+	0.417043i
$363$		−	3.62049e12i		−	0.574425i
$364$	−8.03681e12	−	1.09100e13i	−1.25770	−	1.70733i
$365$		0			0
$366$	−1.41314e13	+	4.64305e12i	−2.15170	+	0.706965i
$367$		−	2.96640e11i		−	0.0445553i	−0.999752	−	0.0222777i	$-0.992908\pi$
$367$		−	2.96640e11i		−	0.0445553i	0.999752	−	0.0222777i	$-0.00709178\pi$
$368$	−4.11801e12	−	1.27835e12i	−0.610167	−	0.189413i
$369$	−6.50498e11			−0.0950855
$370$		0			0
$371$		−	2.24851e13i		−	3.19909i
$372$	−1.27041e13	+	9.35846e12i	−1.78333	+	1.31368i
$373$	−9.87929e12			−1.36830			−0.684151	−	0.729341i	$-0.739827\pi$
$373$	−9.87929e12			−1.36830			−0.684151	+	0.729341i	$0.739827\pi$
$374$	−4.91890e11	+	1.61616e11i	−0.0672217	+	0.0220865i
$375$		0			0
$376$	2.66278e12	−	3.74213e12i	0.354320	−	0.497943i
$377$	9.24190e12			1.21354
$378$	8.44789e11	+	2.57117e12i	0.109468	+	0.333175i
$379$			2.68525e12i			0.343391i	0.985150	+	0.171696i	$0.0549246\pi$
$379$			2.68525e12i			0.343391i	−0.985150	+	0.171696i	$0.945075\pi$
$380$		0			0
$381$	4.26677e12			0.531464
$382$	1.06554e13	−	3.50097e12i	1.30995	−	0.430399i
$383$		−	2.79218e12i		−	0.338805i	−0.985547	−	0.169403i	$-0.945816\pi$
$383$		−	2.79218e12i		−	0.338805i	0.985547	−	0.169403i	$-0.0541838\pi$
$384$	−6.89050e12	−	9.03860e12i	−0.825267	−	1.08254i
$385$		0			0
$386$	1.57751e12	+	4.80126e12i	0.184092	+	0.560297i
$387$		−	2.08083e12i		−	0.239708i
$388$	1.64503e11	−	1.21181e11i	0.0187075	−	0.0137808i
$389$	4.54004e12			0.509697			0.254848	−	0.966981i	$-0.417974\pi$
$389$	4.54004e12			0.509697			0.254848	+	0.966981i	$0.417974\pi$
$390$		0			0
$391$		−	5.43390e11i		−	0.0594604i
$392$	−1.56125e13	−	1.11093e13i	−1.68672	−	1.20021i
$393$	−9.84523e12			−1.05018
$394$	3.94730e12	+	1.20139e13i	0.415737	+	1.26533i
$395$		0			0
$396$	−3.74543e12	−	5.08443e12i	−0.384614	−	0.522115i
$397$	1.56339e13			1.58532			0.792659	−	0.609666i	$-0.208696\pi$
$397$	1.56339e13			1.58532			0.792659	+	0.609666i	$0.208696\pi$
$398$	−6.48724e11	+	2.13146e11i	−0.0649598	+	0.0213433i
$399$			2.95603e13i			2.92310i
$400$		0			0
$401$	−9.95481e12			−0.960088			−0.480044	−	0.877244i	$-0.659379\pi$
$401$	−9.95481e12			−0.960088			−0.480044	+	0.877244i	$0.659379\pi$
$402$	4.60769e12	+	1.40238e13i	0.438887	+	1.33578i
$403$		−	2.09328e13i		−	1.96926i
$404$	−1.28399e13	+	9.45850e12i	−1.19304	+	0.878851i
$405$		0			0
$406$	1.84133e13	−	6.04991e12i	1.66917	−	0.548427i
$407$			9.10957e12i			0.815691i
$408$	8.30409e11	−	1.16702e12i	0.0734499	−	0.103223i
$409$	−3.95071e12			−0.345191			−0.172595	−	0.984993i	$-0.555215\pi$
$409$	−3.95071e12			−0.345191			−0.172595	+	0.984993i	$0.555215\pi$
$410$		0			0
$411$		−	4.75899e12i		−	0.405794i
$412$	−3.45333e12	−	4.68791e12i	−0.290905	−	0.394905i
$413$	−1.09901e13			−0.914644
$414$	6.29649e12	−	2.06879e12i	0.517723	−	0.170104i
$415$		0			0
$416$	1.50758e13	−	2.48062e11i	1.21008	−	0.0199110i
$417$	1.58623e13			1.25802
$418$	3.71139e12	+	1.12959e13i	0.290841	+	0.885194i
$419$		−	1.57517e13i		−	1.21971i	−0.792513	−	0.609856i	$-0.791227\pi$
$419$		−	1.57517e13i		−	1.21971i	0.792513	−	0.609856i	$-0.208773\pi$
$420$		0			0
$421$	1.89265e12			0.143107			0.0715534	−	0.997437i	$-0.477204\pi$
$421$	1.89265e12			0.143107			0.0715534	+	0.997437i	$0.477204\pi$
$422$	−8.80208e12	+	2.89202e12i	−0.657693	+	0.216093i
$423$			7.05948e12i			0.521280i
$424$	2.03852e13	+	1.45055e13i	1.48760	+	1.05853i
$425$		0			0
$426$	2.49110e12	+	7.58182e12i	0.177559	+	0.540413i
$427$		−	4.13835e13i		−	2.91533i
$428$	7.10668e12	+	9.64735e12i	0.494821	+	0.671721i
$429$	1.81995e13			1.25249
$430$		0			0
$431$			1.61299e13i			1.08454i	0.840204	+	0.542271i	$0.182435\pi$
$431$			1.61299e13i			1.08454i	−0.840204	+	0.542271i	$0.817565\pi$
$432$	−2.87604e12	−	8.92805e11i	−0.191151	−	0.0593387i
$433$	2.27857e13			1.49700			0.748501	−	0.663134i	$-0.230774\pi$
$433$	2.27857e13			1.49700			0.748501	+	0.663134i	$0.230774\pi$
$434$	−1.37030e13	−	4.17060e13i	−0.889952	−	2.70863i
$435$		0			0
$436$	−6.61083e12	+	4.86984e12i	−0.419588	+	0.309088i
$437$	−1.24786e13			−0.782991
$438$	1.70737e12	−	5.60977e11i	0.105915	−	0.0347997i
$439$		−	7.33847e12i		−	0.450073i	−0.974350	−	0.225036i	$-0.927750\pi$
$439$		−	7.33847e12i		−	0.450073i	0.974350	−	0.225036i	$-0.0722501\pi$
$440$		0			0
$441$	2.94528e13			1.76577
$442$	5.93118e11	+	1.80520e12i	0.0351584	+	0.107007i
$443$		−	3.68107e11i		−	0.0215753i	−0.999942	−	0.0107876i	$-0.996566\pi$
$443$		−	3.68107e11i		−	0.0215753i	0.999942	−	0.0107876i	$-0.00343388\pi$
$444$	−1.49462e13	−	2.02896e13i	−0.866197	−	1.17587i
$445$		0			0
$446$	−2.39440e13	+	7.86707e12i	−1.35682	+	0.445799i
$447$			1.59365e13i			0.893010i
$448$	2.98742e13	−	1.03631e13i	1.65541	−	0.574248i
$449$	1.73670e13			0.951687			0.475844	−	0.879530i	$-0.342143\pi$
$449$	1.73670e13			0.951687			0.475844	+	0.879530i	$0.342143\pi$
$450$		0			0
$451$		−	1.58137e12i		−	0.0847522i
$452$	−9.57323e12	+	7.05209e12i	−0.507419	+	0.373788i
$453$	3.86004e13			2.02349
$454$	3.10777e13	−	1.02109e13i	1.61128	−	0.529403i
$455$		0			0
$456$	−2.67996e13	−	1.90697e13i	−1.35927	−	0.967209i
$457$	−1.79800e13			−0.902005			−0.451003	−	0.892523i	$-0.648933\pi$
$457$	−1.79800e13			−0.902005			−0.451003	+	0.892523i	$0.648933\pi$
$458$	−1.03022e13	−	3.13556e13i	−0.511216	−	1.55592i
$459$		−	3.79506e11i		−	0.0186275i
$460$		0			0
$461$	−4.09031e13			−1.96450			−0.982249	−	0.187580i	$-0.939936\pi$
$461$	−4.09031e13			−1.96450			−0.982249	+	0.187580i	$0.939936\pi$
$462$	3.62603e13	−	1.19137e13i	1.72275	−	0.566028i
$463$			1.70952e13i			0.803469i	0.915756	+	0.401735i	$0.131593\pi$
$463$			1.70952e13i			0.803469i	−0.915756	+	0.401735i	$0.868407\pi$
$464$	−6.39377e12	+	2.05966e13i	−0.297281	+	0.957646i
$465$		0			0
$466$	2.15407e12	+	6.55607e12i	0.0980236	+	0.298342i
$467$			2.45776e13i			1.10651i	0.833012	+	0.553255i	$0.186614\pi$
$467$			2.45776e13i			1.10651i	−0.833012	+	0.553255i	$0.813386\pi$
$468$	−1.86595e13	+	1.37454e13i	−0.831131	+	0.612250i
$469$	−4.10683e13			−1.80985
$470$		0			0
$471$			3.95200e13i			1.70495i
$472$	7.08987e12	−	9.96375e12i	0.302642	−	0.425317i
$473$	5.05854e12			0.213658
$474$	1.14935e13	+	3.49813e13i	0.480353	+	1.46199i
$475$		0			0
$476$	2.36343e12	+	3.20836e12i	0.0967180	+	0.131295i
$477$	−3.84565e13			−1.55732
$478$	−3.09484e13	+	1.01684e13i	−1.24022	+	0.407488i
$479$		−	3.22393e13i		−	1.27852i	−0.768990	−	0.639261i	$-0.779240\pi$
$479$		−	3.22393e13i		−	1.27852i	0.768990	−	0.639261i	$-0.220760\pi$
$480$		0			0
$481$	3.34314e13			1.29846
$482$	−7.80959e12	−	2.37690e13i	−0.300188	−	0.913643i
$483$			4.00567e13i			1.52384i
$484$	−9.02388e12	+	6.64741e12i	−0.339756	+	0.250280i
$485$		0			0
$486$	3.43054e13	−	1.12714e13i	1.26526	−	0.415717i
$487$			3.24299e13i			1.18386i	0.805990	+	0.591930i	$0.201634\pi$
$487$			3.24299e13i			1.18386i	−0.805990	+	0.591930i	$0.798366\pi$
$488$	3.75187e13	+	2.66970e13i	1.35565	+	0.964637i
$489$	9.57720e11			0.0342527
$490$		0			0
$491$			1.26956e13i			0.444882i	0.974946	+	0.222441i	$0.0714025\pi$
$491$			1.26956e13i			0.444882i	−0.974946	+	0.222441i	$0.928597\pi$
$492$	2.59458e12	+	3.52216e12i	0.0899999	+	0.122175i
$493$	−2.71781e12			−0.0933221
$494$	4.14550e13	−	1.36205e13i	1.40910	−	0.462976i
$495$		0			0
$496$	4.66510e13	+	1.44818e13i	1.55401	+	0.482409i
$497$	−2.22031e13			−0.732205
$498$	−2.73336e12	−	8.31917e12i	−0.0892380	−	0.271602i
$499$			1.08543e13i			0.350832i	0.984494	+	0.175416i	$0.0561270\pi$
$499$			1.08543e13i			0.350832i	−0.984494	+	0.175416i	$0.943873\pi$
$500$		0			0
$501$	1.09588e13			0.347196
$502$	1.89651e13	−	6.23119e12i	0.594889	−	0.195458i
$503$			1.24893e13i			0.387881i	0.981013	+	0.193940i	$0.0621269\pi$
$503$			1.24893e13i			0.387881i	−0.981013	+	0.193940i	$0.937873\pi$
$504$	−2.81786e13	+	3.96008e13i	−0.866497	+	1.21773i
$505$		0			0
$506$	5.02925e12	+	1.53069e13i	0.151618	+	0.461460i
$507$		−	2.11899e13i		−	0.632542i
$508$	−7.83402e12	−	1.06347e13i	−0.231561	−	0.314345i
$509$	−4.73601e12			−0.138619			−0.0693097	−	0.997595i	$-0.522080\pi$
$509$	−4.73601e12			−0.138619			−0.0693097	+	0.997595i	$0.522080\pi$
$510$		0			0
$511$			4.99999e12i			0.143504i
$512$	−9.87695e12	+	3.37696e13i	−0.280720	+	0.959790i
$513$	−8.71507e12			−0.245292
$514$	1.04270e13	+	3.17354e13i	0.290634	+	0.884564i
$515$		0			0
$516$	−1.12668e13	+	8.29963e12i	−0.308001	+	0.226887i
$517$	−1.71617e13			−0.464631
$518$	6.66078e13	−	2.18848e13i	1.78598	−	0.586804i
$519$		−	4.70552e13i		−	1.24960i
$520$		0			0
$521$	−3.60036e13			−0.937902			−0.468951	−	0.883224i	$-0.655368\pi$
$521$	−3.60036e13			−0.937902			−0.468951	+	0.883224i	$0.655368\pi$
$522$	−1.03472e13	−	3.14924e13i	−0.266975	−	0.812556i
$523$		−	4.44220e13i		−	1.13525i	−0.823289	−	0.567623i	$-0.807863\pi$
$523$		−	4.44220e13i		−	1.13525i	0.823289	−	0.567623i	$-0.192137\pi$
$524$	1.80764e13	+	2.45387e13i	0.457567	+	0.621149i
$525$		0			0
$526$	6.85737e13	−	2.25307e13i	1.70306	−	0.559559i
$527$			6.15581e12i			0.151437i
$528$	−1.25909e13	+	4.05596e13i	−0.306822	+	0.988381i
$529$	2.45170e13			0.591819
$530$		0			0
$531$			1.87965e13i			0.445250i
$532$	7.36776e13	−	5.42743e13i	1.72893	−	1.27361i
$533$	−5.80350e12			−0.134913
$534$	−6.98061e13	+	2.29356e13i	−1.60763	+	0.528207i
$535$		0			0
$536$	2.64937e13	−	3.72329e13i	0.598851	−	0.841596i
$537$	−1.16532e13			−0.260960
$538$	−4.57271e12	−	1.39174e13i	−0.101452	−	0.308777i
$539$			7.16001e13i			1.57387i
$540$		0			0
$541$	−8.68078e12			−0.187315			−0.0936575	−	0.995604i	$-0.529856\pi$
$541$	−8.68078e12			−0.187315			−0.0936575	+	0.995604i	$0.529856\pi$
$542$	−2.15041e12	+	7.06543e11i	−0.0459754	+	0.0151058i
$543$			2.82081e13i			0.597551i
$544$	−4.43341e12	+	7.29488e10i	−0.0930557	+	0.00153117i
$545$		0			0
$546$	−4.37224e13	−	1.33072e14i	−0.901034	−	2.74236i
$547$			1.93160e13i			0.394439i	0.980359	+	0.197220i	$0.0631912\pi$
$547$			1.93160e13i			0.394439i	−0.980359	+	0.197220i	$0.936809\pi$
$548$	−1.18616e13	+	8.73777e12i	−0.240015	+	0.176806i
$549$	−7.07784e13			−1.41919
$550$		0			0
$551$			6.24125e13i			1.22889i
$552$	−3.63158e13	−	2.58411e13i	−0.708599	−	0.504215i
$553$	−1.02442e14			−1.98085
$554$	−2.83406e13	−	8.62565e13i	−0.543075	−	1.65289i
$555$		0			0
$556$	−2.91241e13	−	3.95360e13i	−0.548123	−	0.744079i
$557$	9.40071e13			1.75341			0.876707	−	0.481024i	$-0.159735\pi$
$557$	9.40071e13			1.75341			0.876707	+	0.481024i	$0.159735\pi$
$558$	−7.13300e13	+	2.34363e13i	−1.31856	+	0.433230i
$559$		−	1.85644e13i		−	0.340113i
$560$		0			0
$561$	−5.35203e12			−0.0963172
$562$	4.75278e12	+	1.44654e13i	0.0847747	+	0.258018i
$563$			1.01341e13i			0.179162i	0.995980	+	0.0895808i	$0.0285527\pi$
$563$			1.01341e13i			0.179162i	−0.995980	+	0.0895808i	$0.971447\pi$
$564$	3.82239e13	−	2.81575e13i	0.669792	−	0.493399i
$565$		0			0
$566$	−2.87647e13	+	9.45099e12i	−0.495197	+	0.162703i
$567$			1.15560e14i			1.97194i
$568$	1.43235e13	−	2.01296e13i	0.242275	−	0.340481i
$569$	−4.06690e13			−0.681871			−0.340936	−	0.940087i	$-0.610744\pi$
$569$	−4.06690e13			−0.681871			−0.340936	+	0.940087i	$0.610744\pi$
$570$		0			0
$571$		−	8.31022e13i		−	1.36909i	−0.728970	−	0.684545i	$-0.760001\pi$
$571$		−	8.31022e13i		−	1.36909i	0.728970	−	0.684545i	$-0.239999\pi$
$572$	−3.34153e13	−	4.53614e13i	−0.545715	−	0.740810i
$573$	1.15937e14			1.87693
$574$	−1.15628e13	+	3.79908e12i	−0.185567	+	0.0609703i
$575$		0			0
$576$	−1.77241e13	−	5.10940e13i	−0.279545	−	0.805857i
$577$	4.07454e13			0.637089			0.318544	−	0.947908i	$-0.396806\pi$
$577$	4.07454e13			0.637089			0.318544	+	0.947908i	$0.396806\pi$
$578$	1.99626e13	+	6.07576e13i	0.309441	+	0.941806i
$579$			5.22403e13i			0.802810i
$580$		0			0
$581$	2.43624e13			0.367993
$582$	2.00649e12	−	6.59256e11i	0.0300485	−	0.00987278i
$583$		−	9.34883e13i		−	1.38808i
$584$	−4.53304e12	−	3.22556e12i	−0.0667307	−	0.0474833i
$585$		0			0
$586$	2.36942e13	+	7.21149e13i	0.342889	+	1.04361i
$587$		−	1.26918e14i		−	1.82109i	−0.413408	−	0.910546i	$-0.635662\pi$
$587$		−	1.26918e14i		−	1.82109i	0.413408	−	0.910546i	$-0.364338\pi$
$588$	−1.17476e14	−	1.59474e14i	−1.67132	−	2.26883i
$589$	1.41364e14			1.99417
$590$		0			0
$591$			1.30718e14i			1.81299i
$592$	−2.31286e13	+	7.45054e13i	−0.318084	+	1.02466i
$593$	−1.08224e13			−0.147588			−0.0737941	−	0.997273i	$-0.523511\pi$
$593$	−1.08224e13			−0.147588			−0.0737941	+	0.997273i	$0.523511\pi$
$594$	3.51245e12	+	1.06904e13i	0.0474983	+	0.144564i
$595$		0			0
$596$	3.97211e13	−	2.92604e13i	0.528189	−	0.389088i
$597$	−7.05847e12			−0.0930763
$598$	5.61750e13	−	1.84570e13i	0.734577	−	0.241354i
$599$		−	1.11833e14i		−	1.45023i	−0.688630	−	0.725113i	$-0.741788\pi$
$599$		−	1.11833e14i		−	1.45023i	0.688630	−	0.725113i	$-0.258212\pi$
$600$		0			0
$601$	−1.24369e14			−1.58613			−0.793067	−	0.609134i	$-0.791517\pi$
$601$	−1.24369e14			−1.58613			−0.793067	+	0.609134i	$0.791517\pi$
$602$	−1.21526e13	−	3.69873e13i	−0.153705	−	0.467811i
$603$			7.02394e13i			0.881038i
$604$	−7.08725e13	−	9.62097e13i	−0.881643	−	1.19683i
$605$		0			0
$606$	−1.56612e14	+	5.14568e13i	−1.91630	+	0.629622i
$607$			1.04683e14i			1.27038i	0.772355	+	0.635192i	$0.219079\pi$
$607$			1.04683e14i			1.27038i	−0.772355	+	0.635192i	$0.780921\pi$
$608$	1.67521e12	+	1.01810e14i	0.0201629	+	1.22538i
$609$	2.00347e14			2.39164
$610$		0			0
$611$			6.29821e13i			0.739624i
$612$	5.48728e12	−	4.04218e12i	0.0639146	−	0.0470824i
$613$	−6.83052e13			−0.789135			−0.394567	−	0.918867i	$-0.629106\pi$
$613$	−6.83052e13			−0.789135			−0.394567	+	0.918867i	$0.629106\pi$
$614$	−9.94547e13	+	3.26770e13i	−1.13968	+	0.374456i
$615$		0			0
$616$	−9.62702e13	−	6.85027e13i	−1.08540	−	0.772332i
$617$	−1.45376e14			−1.62580			−0.812899	−	0.582405i	$-0.802112\pi$
$617$	−1.45376e14			−1.62580			−0.812899	+	0.582405i	$0.802112\pi$
$618$	−1.87870e13	−	5.71797e13i	−0.208409	−	0.634307i
$619$		−	8.38798e13i		−	0.923005i	−0.887139	−	0.461503i	$-0.847310\pi$
$619$		−	8.38798e13i		−	0.923005i	0.887139	−	0.461503i	$-0.152690\pi$
$620$		0			0
$621$	−1.18097e13			−0.127873
$622$	−8.95863e13	+	2.94346e13i	−0.962254	+	0.316160i
$623$		−	2.04425e14i		−	2.17818i
$624$	1.48851e14	+	4.62075e13i	1.57336	+	0.488416i
$625$		0			0
$626$	−3.17672e12	−	9.66858e12i	−0.0330451	−	0.100575i
$627$			1.22905e14i			1.26833i
$628$	9.85017e13	−	7.25609e13i	1.00843	−	0.742855i
$629$	−9.83133e12			−0.0998525
$630$		0			0
$631$			8.77540e13i			0.877244i	0.898672	+	0.438622i	$0.144533\pi$
$631$			8.77540e13i			0.877244i	−0.898672	+	0.438622i	$0.855467\pi$
$632$	6.60865e13	−	9.28746e13i	0.655431	−	0.921110i
$633$	−9.57714e13			−0.942361
$634$	3.79677e13	+	1.15557e14i	0.370653	+	1.12811i
$635$		0			0
$636$	1.53388e14	+	2.08225e14i	1.47403	+	2.00100i
$637$	2.62767e14			2.50538
$638$	7.65586e13	−	2.51542e13i	0.724253	−	0.237962i
$639$			3.79742e13i			0.356438i
$640$		0			0
$641$	−7.91930e12			−0.0731807			−0.0365903	−	0.999330i	$-0.511650\pi$
$641$	−7.91930e12			−0.0731807			−0.0365903	+	0.999330i	$0.511650\pi$
$642$	3.86623e13	+	1.17671e14i	0.354497	+	1.07894i
$643$			6.97979e13i			0.635020i	0.948255	+	0.317510i	$0.102847\pi$
$643$			6.97979e13i			0.635020i	−0.948255	+	0.317510i	$0.897153\pi$
$644$	9.98394e13	−	7.35463e13i	0.901307	−	0.663944i
$645$		0			0
$646$	−1.21909e13	+	4.00545e12i	−0.108361	+	0.0356032i
$647$		−	3.64847e13i		−	0.321803i	−0.986970	−	0.160901i	$-0.948560\pi$
$647$		−	3.64847e13i		−	0.321803i	0.986970	−	0.160901i	$-0.0514401\pi$
$648$	−1.04768e14	−	7.45494e13i	−0.916966	−	0.652483i
$649$	−4.56946e13			−0.396863
$650$		0			0
$651$		−	4.53784e14i		−	3.88100i
$652$	−1.75843e12	−	2.38707e12i	−0.0149240	−	0.0202594i
$653$	−1.18590e14			−0.998811			−0.499406	−	0.866368i	$-0.666448\pi$
$653$	−1.18590e14			−0.998811			−0.499406	+	0.866368i	$0.666448\pi$
$654$	−8.06341e13	+	2.64933e13i	−0.673953	+	0.221435i
$655$		0			0
$656$	4.01501e12	−	1.29337e13i	0.0330497	−	0.106465i
$657$	8.55152e12			0.0698581
$658$	4.12292e13	+	1.25484e14i	0.334253	+	1.01732i
$659$			8.68704e13i			0.698948i	0.936946	+	0.349474i	$0.113640\pi$
$659$			8.68704e13i			0.698948i	−0.936946	+	0.349474i	$0.886360\pi$
$660$		0			0
$661$	−1.41387e14			−1.12048			−0.560238	−	0.828332i	$-0.689290\pi$
$661$	−1.41387e14			−1.12048			−0.560238	+	0.828332i	$0.689290\pi$
$662$	−1.32041e14	+	4.33835e13i	−1.03853	+	0.341220i
$663$			1.96415e13i			0.153323i
$664$	−1.57165e13	+	2.20872e13i	−0.121763	+	0.171120i
$665$		0			0
$666$	−3.74297e13	−	1.13920e14i	−0.285657	−	0.869417i
$667$			8.45743e13i			0.640633i
$668$	−2.01210e13	−	2.73143e13i	−0.151275	−	0.205356i
$669$	−2.60523e14			−1.94409
$670$		0			0
$671$		−	1.72064e14i		−	1.26496i
$672$	3.26814e14	−	5.37751e12i	2.38481	−	0.0392406i
$673$	8.61618e13			0.624079			0.312039	−	0.950069i	$-0.398988\pi$
$673$	8.61618e13			0.624079			0.312039	+	0.950069i	$0.398988\pi$
$674$	7.55975e12	+	2.30086e13i	0.0543510	+	0.165421i
$675$		0			0
$676$	−5.28148e13	+	3.89058e13i	−0.374130	+	0.275601i
$677$	−1.26787e14			−0.891520			−0.445760	−	0.895152i	$-0.647067\pi$
$677$	−1.26787e14			−0.891520			−0.445760	+	0.895152i	$0.647067\pi$
$678$	−1.16767e14	+	3.83653e13i	−0.815029	+	0.267787i
$679$			5.87595e12i			0.0407126i
$680$		0			0
$681$	3.38142e14			2.30868
$682$	−5.69740e13	−	1.73404e14i	−0.386149	−	1.17527i
$683$			1.04109e14i			0.700461i	0.936664	+	0.350230i	$0.113897\pi$
$683$			1.04109e14i			0.700461i	−0.936664	+	0.350230i	$0.886103\pi$
$684$	−9.28257e13	−	1.26011e14i	−0.619994	−	0.841645i
$685$		0			0
$686$	2.70635e14	−	8.89203e13i	1.78141	−	0.585302i
$687$		−	3.41166e14i		−	2.22937i
$688$	4.13729e13	+	1.28433e13i	0.268394	+	0.0833174i
$689$	−3.43095e14			−2.20962
$690$		0			0
$691$			3.73752e13i			0.237243i	0.992940	+	0.118621i	$0.0378475\pi$
$691$			3.73752e13i			0.237243i	−0.992940	+	0.118621i	$0.962153\pi$
$692$	−1.17283e14	+	8.63959e13i	−0.739101	+	0.544456i
$693$	1.81613e14			1.13626
$694$	−1.48550e13	+	4.88078e12i	−0.0922730	+	0.0303174i
$695$		0			0
$696$	−1.29246e14	+	1.81636e14i	−0.791357	+	1.11213i
$697$	1.70667e12			0.0103749
$698$	2.31753e13	+	7.05357e13i	0.139878	+	0.425727i
$699$			7.13336e13i			0.427472i
$700$		0			0
$701$	−1.57586e13			−0.0930950			−0.0465475	−	0.998916i	$-0.514822\pi$
$701$	−1.57586e13			−0.0930950			−0.0465475	+	0.998916i	$0.514822\pi$
$702$	3.92328e13	−	1.28904e13i	0.230125	−	0.0756103i
$703$			2.25769e14i			1.31489i
$704$	1.24210e14	−	4.30875e13i	0.718282	−	0.249166i
$705$		0			0
$706$	2.84987e13	+	8.67377e13i	0.162481	+	0.494521i
$707$		−	4.58634e14i		−	2.59639i
$708$	1.01775e14	−	7.49718e13i	0.572101	−	0.421436i
$709$	2.52712e14			1.41057			0.705285	−	0.708924i	$-0.250819\pi$
$709$	2.52712e14			1.41057			0.705285	+	0.708924i	$0.250819\pi$
$710$		0			0
$711$			1.75207e14i			0.964278i
$712$	1.85334e14	+	1.31877e14i	1.01287	+	0.720726i
$713$	1.91560e14			1.03958
$714$	1.28577e13	+	3.91332e13i	0.0692901	+	0.210889i
$715$		0			0
$716$	2.13960e13	+	2.90451e13i	0.113702	+	0.154350i
$717$	−3.36735e14			−1.77702
$718$	−4.85450e13	+	1.59500e13i	−0.254403	+	0.0835871i
$719$			1.11740e13i			0.0581517i	0.999577	+	0.0290759i	$0.00925644\pi$
$719$			1.11740e13i			0.0581517i	−0.999577	+	0.0290759i	$0.990744\pi$
$720$		0			0
$721$	1.67449e14			0.859421
$722$	3.07412e13	+	9.35629e13i	0.156688	+	0.476889i
$723$		−	2.58620e14i		−	1.30909i
$724$	7.03074e13	−	5.17916e13i	0.353434	−	0.260356i
$725$		0			0
$726$	−1.10067e14	+	3.61637e13i	−0.545724	+	0.179304i
$727$		−	1.13819e14i		−	0.560455i	−0.959934	−	0.280228i	$-0.909590\pi$
$727$		−	1.13819e14i		−	0.560455i	0.959934	−	0.280228i	$-0.0904100\pi$
$728$	−2.51399e14	+	3.53304e14i	−1.22944	+	1.72779i
$729$	1.41548e14			0.687490
$730$		0			0
$731$			5.45934e12i			0.0261549i
$732$	2.82308e14	+	3.83234e14i	1.34328	+	1.82351i
$733$	−3.18416e12			−0.0150479			−0.00752393	−	0.999972i	$-0.502395\pi$
$733$	−3.18416e12			−0.0150479			−0.00752393	+	0.999972i	$0.502395\pi$
$734$	−9.01819e12	+	2.96303e12i	−0.0423291	+	0.0139077i
$735$		0			0
$736$	2.27006e12	+	1.37961e14i	0.0105111	+	0.638804i
$737$	−1.70753e14			−0.785293
$738$	6.49759e12	+	1.97759e13i	0.0296804	+	0.0903345i
$739$			1.84171e14i			0.835599i	0.908539	+	0.417800i	$0.137199\pi$
$739$			1.84171e14i			0.835599i	−0.908539	+	0.417800i	$0.862801\pi$
$740$		0			0
$741$	4.51052e14			2.01900
$742$	−6.83573e14	+	2.24596e14i	−3.03924	+	0.998578i
$743$			2.17569e14i			0.960844i	0.877037	+	0.480422i	$0.159517\pi$
$743$			2.17569e14i			0.960844i	−0.877037	+	0.480422i	$0.840483\pi$
$744$	4.11405e14	+	2.92742e14i	1.80470	+	1.28416i
$745$		0			0
$746$	9.86807e13	+	3.00341e14i	0.427108	+	1.29993i
$747$		−	4.16672e13i		−	0.179140i
$748$	9.82661e12	+	1.33397e13i	0.0419658	+	0.0569688i
$749$	−3.44597e14			−1.46185
$750$		0			0
$751$		−	2.81405e14i		−	1.17797i	−0.808146	−	0.588983i	$-0.799529\pi$
$751$		−	2.81405e14i		−	1.17797i	0.808146	−	0.588983i	$-0.200471\pi$
$752$	−1.40362e14	−	4.35725e13i	−0.583662	−	0.181186i
$753$	2.06350e14			0.852374
$754$	−9.23139e13	−	2.80964e14i	−0.378800	−	1.15291i
$755$		0			0
$756$	6.97282e13	−	5.13650e13i	0.282358	−	0.207998i
$757$	8.77891e13			0.353152			0.176576	−	0.984287i	$-0.443498\pi$
$757$	8.77891e13			0.353152			0.176576	+	0.984287i	$0.443498\pi$
$758$	8.16347e13	−	2.68220e13i	0.326234	−	0.107188i
$759$			1.66547e14i			0.661193i
$760$		0			0
$761$	−3.64374e14			−1.42766			−0.713829	−	0.700320i	$-0.753041\pi$
$761$	−3.64374e14			−1.42766			−0.713829	+	0.700320i	$0.753041\pi$
$762$	−4.26192e13	−	1.29714e14i	−0.165894	−	0.504909i
$763$		−	2.36134e14i		−	0.913138i
$764$	−2.12867e14	−	2.88967e14i	−0.817788	−	1.11015i
$765$		0			0
$766$	−8.48855e13	+	2.78901e13i	−0.321877	+	0.105756i
$767$			1.67695e14i			0.631748i
$768$	−2.05957e14	+	2.99762e14i	−0.770851	+	1.12194i
$769$	−2.27454e14			−0.845790			−0.422895	−	0.906179i	$-0.638986\pi$
$769$	−2.27454e14			−0.845790			−0.422895	+	0.906179i	$0.638986\pi$
$770$		0			0
$771$			3.45299e14i			1.26743i
$772$	1.30206e14	−	9.59161e13i	0.474839	−	0.349788i
$773$	2.31980e14			0.840531			0.420265	−	0.907401i	$-0.361937\pi$
$773$	2.31980e14			0.840531			0.420265	+	0.907401i	$0.361937\pi$
$774$	−6.32596e13	+	2.07847e13i	−0.227731	+	0.0748236i
$775$		0			0
$776$	−5.32719e12	−	3.79065e12i	−0.0189317	−	0.0134712i
$777$	7.24729e14			2.55900
$778$	−4.53488e13	−	1.38022e14i	−0.159099	−	0.484230i
$779$		−	3.91923e13i		−	0.136620i
$780$		0			0
$781$	−9.23159e13			−0.317703
$782$	−1.65197e13	+	5.42773e12i	−0.0564895	+	0.0185603i
$783$			5.90670e13i			0.200695i
$784$	−1.81788e14	+	5.85604e14i	−0.613742	+	1.97708i
$785$		0			0
$786$	9.83404e13	+	2.99306e14i	0.327808	+	0.997705i
$787$			4.63128e14i			1.53401i	0.641644	+	0.767003i	$0.278253\pi$
$787$			4.63128e14i			1.53401i	−0.641644	+	0.767003i	$0.721747\pi$
$788$	3.25807e14	−	2.40004e14i	1.07233	−	0.789929i
$789$	7.46119e14			2.44019
$790$		0			0
$791$		−	3.41950e14i		−	1.10428i
$792$	−1.17161e14	+	1.64652e14i	−0.375972	+	0.528372i
$793$	−6.31459e14			−2.01363
$794$	−1.56162e14	−	4.75289e14i	−0.494849	−	1.50611i
$795$		0			0
$796$	1.29597e13	+	1.75929e13i	0.0405537	+	0.0550519i
$797$	−5.47068e13			−0.170118			−0.0850588	−	0.996376i	$-0.527108\pi$
$797$	−5.47068e13			−0.170118			−0.0850588	+	0.996376i	$0.527108\pi$
$798$	8.98665e14	−	2.95267e14i	2.77705	−	0.912431i
$799$		−	1.85215e13i		−	0.0568776i
$800$		0			0
$801$	−3.49629e14			−1.06034
$802$	9.94350e13	+	3.02637e14i	0.299687	+	0.912117i
$803$			2.07889e13i			0.0622664i
$804$	3.80315e14	−	2.80158e14i	1.13204	−	0.833916i
$805$		0			0
$806$	−6.36380e14	+	2.09090e14i	−1.87086	+	0.614693i
$807$		−	1.51428e14i		−	0.442425i
$808$	4.15802e14	+	2.95871e14i	1.20734	+	0.859104i
$809$	3.59793e14			1.03827			0.519135	−	0.854692i	$-0.326254\pi$
$809$	3.59793e14			1.03827			0.519135	+	0.854692i	$0.326254\pi$
$810$		0			0
$811$		−	4.03312e13i		−	0.114957i	−0.998347	−	0.0574787i	$-0.981694\pi$
$811$		−	4.03312e13i		−	0.114957i	0.998347	−	0.0574787i	$-0.0183061\pi$
$812$	−3.67848e14	−	4.99355e14i	−1.04205	−	1.41459i
$813$	−2.33977e13			−0.0658749
$814$	2.76941e14	−	9.09921e13i	0.774935	−	0.254614i
$815$		0			0
$816$	−4.37732e13	−	1.35885e13i	−0.120992	−	0.0375595i
$817$	1.25370e14			0.344415
$818$	3.94622e13	+	1.20106e14i	0.107749	+	0.327943i
$819$		−	6.66503e14i		−	1.80877i
$820$		0			0
$821$	6.29121e14			1.68662			0.843312	−	0.537424i	$-0.180602\pi$
$821$	6.29121e14			1.68662			0.843312	+	0.537424i	$0.180602\pi$
$822$	−1.44679e14	+	4.75358e13i	−0.385518	+	0.126667i
$823$		−	3.91664e13i		−	0.103732i	−0.998654	−	0.0518662i	$-0.983483\pi$
$823$		−	3.91664e13i		−	0.103732i	0.998654	−	0.0518662i	$-0.0165169\pi$
$824$	−1.08024e14	+	1.51811e14i	−0.284369	+	0.399638i
$825$		0			0
$826$	1.09776e14	+	3.34112e14i	0.285502	+	0.868944i
$827$		−	5.12246e14i		−	1.32419i	−0.749419	−	0.662096i	$-0.769667\pi$
$827$		−	5.12246e14i		−	1.32419i	0.749419	−	0.662096i	$-0.230333\pi$
$828$	−1.25787e14	−	1.70756e14i	−0.323209	−	0.438757i
$829$	2.87121e14			0.733317			0.366658	−	0.930356i	$-0.380502\pi$
$829$	2.87121e14			0.733317			0.366658	+	0.930356i	$0.380502\pi$
$830$		0			0
$831$		−	9.38517e14i		−	2.36830i
$832$	−1.58128e14	−	4.55842e14i	−0.396635	−	1.14340i
$833$	−7.72731e13			−0.192665
$834$	−1.58443e14	−	4.82232e14i	−0.392683	−	1.19516i
$835$		0			0
$836$	3.06335e14	−	2.25661e14i	0.750181	−	0.552618i
$837$	1.33786e14			0.325675
$838$	−4.78869e14	+	1.57338e14i	−1.15877	+	0.380727i
$839$			2.95325e14i			0.710379i	0.934794	+	0.355190i	$0.115584\pi$
$839$			2.95325e14i			0.710379i	−0.934794	+	0.355190i	$0.884416\pi$
$840$		0			0
$841$	2.29764e12			0.00546136
$842$	−1.89050e13	−	5.75387e13i	−0.0446700	−	0.135956i
$843$			1.57392e14i			0.369695i
$844$	1.75841e14	+	2.38706e14i	0.410591	+	0.557379i
$845$		0			0
$846$	2.14616e14	−	7.05145e13i	0.495234	−	0.162715i
$847$		−	3.22327e14i		−	0.739401i
$848$	2.37361e14	−	7.64623e14i	0.541291	−	1.74369i
$849$	−3.12976e14			−0.709533
$850$		0			0
$851$			3.05937e14i			0.685462i
$852$	2.05613e14	−	1.51464e14i	0.457987	−	0.337374i
$853$	1.08283e14			0.239780			0.119890	−	0.992787i	$-0.461746\pi$
$853$	1.08283e14			0.239780			0.119890	+	0.992787i	$0.461746\pi$
$854$	−1.25810e15	+	4.13364e14i	−2.76966	+	0.910005i
$855$		0			0
$856$	2.22304e14	−	3.12415e14i	0.483702	−	0.679771i
$857$	3.60461e14			0.779748			0.389874	−	0.920868i	$-0.372519\pi$
$857$	3.60461e14			0.779748			0.389874	+	0.920868i	$0.372519\pi$
$858$	−1.81788e14	−	5.53286e14i	−0.390958	−	1.18991i
$859$			6.06012e13i			0.129573i	0.997899	+	0.0647866i	$0.0206367\pi$
$859$			6.06012e13i			0.129573i	−0.997899	+	0.0647866i	$0.979363\pi$
$860$		0			0
$861$	−1.25809e14			−0.265886
$862$	4.90368e14	−	1.61116e14i	1.03035	−	0.338534i
$863$		−	1.17507e13i		−	0.0245476i	−0.999925	−	0.0122738i	$-0.996093\pi$
$863$		−	1.17507e13i		−	0.0245476i	0.999925	−	0.0122738i	$-0.00390698\pi$
$864$	1.58542e12	+	9.63525e13i	0.00329287	+	0.200122i
$865$		0			0
$866$	−2.27598e14	−	6.92709e14i	−0.467281	−	1.42220i
$867$			6.61075e14i			1.34945i
$868$	−1.13103e15	+	8.33172e14i	−2.29550	+	1.69097i
$869$	−4.25930e14			−0.859487
$870$		0			0
$871$			6.26651e14i			1.25007i
$872$	2.14082e14	+	1.52333e14i	0.424617	+	0.302143i
$873$	1.00497e13			0.0198190
$874$	1.24644e14	+	3.79362e14i	0.244407	+	0.743869i
$875$		0			0
$876$	−3.41087e13	−	4.63027e13i	−0.0661217	−	0.0897605i
$877$	−6.85003e14			−1.32037			−0.660183	−	0.751104i	$-0.729521\pi$
$877$	−6.85003e14			−1.32037			−0.660183	+	0.751104i	$0.729521\pi$
$878$	−2.23098e14	+	7.33013e13i	−0.427585	+	0.140488i
$879$			7.84650e14i			1.49531i
$880$		0			0
$881$	−2.09299e14			−0.394355			−0.197177	−	0.980368i	$-0.563177\pi$
$881$	−2.09299e14			−0.394355			−0.197177	+	0.980368i	$0.563177\pi$
$882$	−2.94193e14	−	8.95396e14i	−0.551175	−	1.67754i
$883$		−	6.25256e14i		−	1.16481i	−0.812899	−	0.582404i	$-0.802112\pi$
$883$		−	6.25256e14i		−	1.16481i	0.812899	−	0.582404i	$-0.197888\pi$
$884$	4.89555e13	−	3.60629e13i	0.0906860	−	0.0668035i
$885$		0			0
$886$	−1.11909e13	+	3.67689e12i	−0.0204972	+	0.00673460i
$887$			7.59597e14i			1.38346i	0.722158	+	0.691728i	$0.243150\pi$
$887$			7.59597e14i			1.38346i	−0.722158	+	0.691728i	$0.756850\pi$
$888$	−4.67532e14	+	6.57046e14i	−0.846734	+	1.18996i
$889$	3.79865e14			0.684101
$890$		0			0
$891$			4.80474e14i			0.855621i
$892$	4.78335e14	+	6.49342e14i	0.847048	+	1.14987i
$893$	−4.25331e14			−0.748980
$894$	4.84488e14	−	1.59184e14i	0.848391	−	0.278749i
$895$		0			0
$896$	−6.13452e14	−	8.04695e14i	−1.06228	−	1.39345i
$897$	6.11215e14			1.05252
$898$	−1.73473e14	−	5.27977e14i	−0.297064	−	0.904136i
$899$		−	9.58102e14i		−	1.63160i
$900$		0			0
$901$	1.00896e14			0.169921
$902$	−4.80754e13	+	1.57957e13i	−0.0805175	+	0.0264550i
$903$		−	4.02442e14i		−	0.670293i
$904$	3.10015e14	+	2.20596e14i	0.513500	+	0.365389i
$905$		0			0
$906$	−3.85566e14	−	1.17350e15i	−0.631622	−	1.92239i
$907$			6.72197e13i			0.109512i	0.998500	+	0.0547558i	$0.0174380\pi$
$907$			6.72197e13i			0.109512i	−0.998500	+	0.0547558i	$0.982562\pi$
$908$	−6.20848e14	−	8.42804e14i	−1.00590	−	1.36552i
$909$	−7.84405e14			−1.26392
$910$		0			0
$911$		−	9.95355e14i		−	1.58630i	−0.609025	−	0.793151i	$-0.708439\pi$
$911$		−	9.95355e14i		−	1.58630i	0.609025	−	0.793151i	$-0.291561\pi$
$912$	−3.12049e14	+	1.00522e15i	−0.494594	+	1.59326i
$913$	1.01294e14			0.159672
$914$	1.79596e14	+	5.46612e14i	0.281556	+	0.856936i
$915$		0			0
$916$	−8.50340e14	+	6.26399e14i	−1.31861	+	0.971346i
$917$	−8.76508e14			−1.35179
$918$	−1.15374e13	+	3.79075e12i	−0.0176968	+	0.00581448i
$919$			3.20262e14i			0.488572i	0.969703	+	0.244286i	$0.0785535\pi$
$919$			3.20262e14i			0.488572i	−0.969703	+	0.244286i	$0.921447\pi$
$920$		0			0
$921$	−1.08212e15			−1.63297
$922$	4.08566e14	+	1.24350e15i	0.613208	+	1.86634i
$923$			3.38792e14i			0.505736i
$924$	−7.24381e14	−	9.83351e14i	−1.07549	−	1.45999i
$925$		0			0
$926$	5.19713e14	−	1.70758e14i	0.763324	−	0.250799i
$927$		−	2.86389e14i		−	0.418367i
$928$	6.90023e14	−	1.13539e13i	1.00259	−	0.0164970i
$929$	−6.44525e14			−0.931454			−0.465727	−	0.884929i	$-0.654207\pi$
$929$	−6.44525e14			−0.931454			−0.465727	+	0.884929i	$0.654207\pi$
$930$		0			0
$931$			1.77452e15i			2.53707i
$932$	1.77795e14	−	1.30972e14i	0.252837	−	0.186252i
$933$	−9.74748e14			−1.37875
$934$	7.47186e14	−	2.45497e14i	1.05122	−	0.345391i
$935$		0			0
$936$	6.04258e14	+	4.29970e14i	0.841092	+	0.598493i
$937$	−1.17565e15			−1.62772			−0.813860	−	0.581061i	$-0.802638\pi$
$937$	−1.17565e15			−1.62772			−0.813860	+	0.581061i	$0.802638\pi$
$938$	4.10217e14	+	1.24852e15i	0.564936	+	1.71942i
$939$		−	1.05199e14i		−	0.144107i
$940$		0			0
$941$	−1.07542e14			−0.145757			−0.0728787	−	0.997341i	$-0.523219\pi$
$941$	−1.07542e14			−0.145757			−0.0728787	+	0.997341i	$0.523219\pi$
$942$	1.20145e15	−	3.94751e14i	1.61976	−	0.532192i
$943$		−	5.31089e13i		−	0.0712212i
$944$	−3.73727e14	−	1.16016e14i	−0.498534	−	0.154759i
$945$		0			0
$946$	−5.05279e13	−	1.53785e14i	−0.0666923	−	0.202983i
$947$			9.03973e14i			1.18688i	0.804880	+	0.593438i	$0.202230\pi$
$947$			9.03973e14i			1.18688i	−0.804880	+	0.593438i	$0.797770\pi$
$948$	9.48665e14	−	6.98831e14i	1.23900	−	0.912705i
$949$	7.62935e13			0.0991190
$950$		0			0
$951$			1.25733e15i			1.61639i
$952$	7.39303e13	−	1.03898e14i	0.0945448	−	0.132868i
$953$	6.08081e13			0.0773565			0.0386783	−	0.999252i	$-0.487685\pi$
$953$	6.08081e13			0.0773565			0.0386783	+	0.999252i	$0.487685\pi$
$954$	3.84128e14	+	1.16912e15i	0.486109	+	1.47951i
$955$		0			0
$956$	6.18264e14	+	8.39296e14i	0.774256	+	1.05106i
$957$	8.32999e14			1.03773
$958$	−9.80111e14	+	3.22027e14i	−1.21464	+	0.399084i
$959$		−	4.23687e14i		−	0.522338i
$960$		0			0
$961$	−1.35046e15			−1.64765
$962$	−3.33934e14	−	1.01635e15i	−0.405308	−	1.23358i
$963$			5.89366e14i			0.711629i
$964$	−6.44598e14	+	4.74841e14i	−0.774290	+	0.570378i
$965$		0			0
$966$	1.21777e15	−	4.00112e14i	1.44770	−	0.475659i
$967$		−	2.41545e13i		−	0.0285671i	−0.999898	−	0.0142836i	$-0.995453\pi$
$967$		−	2.41545e13i		−	0.0285671i	0.999898	−	0.0142836i	$-0.00454675\pi$
$968$	2.92225e14	+	2.07938e14i	0.343827	+	0.244656i
$969$	−1.32643e14			−0.155262
$970$		0			0
$971$		−	4.34211e14i		−	0.503042i	−0.967852	−	0.251521i	$-0.919069\pi$
$971$		−	4.34211e14i		−	0.503042i	0.967852	−	0.251521i	$-0.0809308\pi$
$972$	−6.85328e14	−	9.30335e14i	−0.789891	−	1.07228i
$973$	1.41220e15			1.61932
$974$	9.85903e14	−	3.23930e14i	1.12471	−	0.369536i
$975$		0			0
$976$	4.36859e14	−	1.40728e15i	0.493279	−	1.58902i
$977$	−8.83322e14			−0.992308			−0.496154	−	0.868235i	$-0.665255\pi$
$977$	−8.83322e14			−0.992308			−0.496154	+	0.868235i	$0.665255\pi$
$978$	−9.56631e12	−	2.91157e13i	−0.0106918	−	0.0325412i
$979$		−	8.49955e14i		−	0.945110i
$980$		0			0
$981$	−4.03862e14			−0.444517
$982$	3.85960e14	−	1.26812e14i	0.422654	−	0.138868i
$983$			9.46697e14i			1.03144i	0.856758	+	0.515719i	$0.172475\pi$
$983$			9.46697e14i			1.03144i	−0.856758	+	0.515719i	$0.827525\pi$
$984$	8.11611e13	−	1.14060e14i	0.0879776	−	0.123639i
$985$		0			0
$986$	2.71472e13	+	8.26244e13i	0.0291300	+	0.0886592i
$987$			1.36533e15i			1.45765i
$988$	−8.28157e14	−	1.12423e15i	−0.879686	−	1.19418i
$989$	1.69887e14			0.179547
$990$		0			0
$991$		−	6.43587e14i		−	0.673347i	−0.941621	−	0.336674i	$-0.890698\pi$
$991$		−	6.43587e14i		−	0.673347i	0.941621	−	0.336674i	$-0.109302\pi$
$992$	−2.57164e13	−	1.56290e15i	−0.0267702	−	1.62694i
$993$	−1.43667e15			−1.48803
$994$	2.21779e14	+	6.75000e14i	0.228554	+	0.695620i
$995$		0			0
$996$	−2.25609e14	+	1.66194e14i	−0.230176	+	0.169558i
$997$	−3.34658e14			−0.339723			−0.169862	−	0.985468i	$-0.554332\pi$
$997$	−3.34658e14			−0.339723			−0.169862	+	0.985468i	$0.554332\pi$
$998$	3.29983e14	−	1.08420e14i	0.333303	−	0.109510i
$999$			2.13667e14i			0.214739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.11.b.e.51.7		20
4.3	odd	2	inner	100.11.b.e.51.8		20
5.2	odd	4		100.11.d.c.99.35		40
5.3	odd	4		100.11.d.c.99.6		40
5.4	even	2		20.11.b.a.11.14	yes	20
15.14	odd	2		180.11.c.a.91.7		20
20.3	even	4		100.11.d.c.99.36		40
20.7	even	4		100.11.d.c.99.5		40
20.19	odd	2		20.11.b.a.11.13	✓	20
40.19	odd	2		320.11.b.d.191.18		20
40.29	even	2		320.11.b.d.191.3		20
60.59	even	2		180.11.c.a.91.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.b.a.11.13	✓	20	20.19	odd	2
20.11.b.a.11.14	yes	20	5.4	even	2
100.11.b.e.51.7		20	1.1	even	1	trivial
100.11.b.e.51.8		20	4.3	odd	2	inner
100.11.d.c.99.5		40	20.7	even	4
100.11.d.c.99.6		40	5.3	odd	4
100.11.d.c.99.35		40	5.2	odd	4
100.11.d.c.99.36		40	20.3	even	4
180.11.c.a.91.7		20	15.14	odd	2
180.11.c.a.91.8		20	60.59	even	2
320.11.b.d.191.3		20	40.29	even	2
320.11.b.d.191.18		20	40.19	odd	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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.98863 - 30.4011i) q^{2} -330.781i q^{3} +(-824.454 + 607.331i) q^{4} +(-10056.1 + 3304.05i) q^{6} -29449.0i q^{7} +(26698.7 + 18997.9i) q^{8} -50366.8 q^{9} +O(q^{10})\)	\(q+(-9.98863 - 30.4011i) q^{2} -330.781i q^{3} +(-824.454 + 607.331i) q^{4} +(-10056.1 + 3304.05i) q^{6} -29449.0i q^{7} +(26698.7 + 18997.9i) q^{8} -50366.8 q^{9} -122442. i q^{11} +(200893. + 272713. i) q^{12} -449354. q^{13} +(-895281. + 294155. i) q^{14} +(310874. - 1.00143e6i) q^{16} +132144. q^{17} +(503095. + 1.53120e6i) q^{18} -3.03458e6i q^{19} -9.74114e6 q^{21} +(-3.72238e6 + 1.22303e6i) q^{22} -4.11212e6i q^{23} +(6.28414e6 - 8.83141e6i) q^{24} +(4.48843e6 + 1.36609e7i) q^{26} -2.87192e6i q^{27} +(1.78853e7 + 2.42793e7i) q^{28} -2.05671e7 q^{29} +4.65842e7i q^{31} +(-3.35499e7 + 552041. i) q^{32} -4.05016e7 q^{33} +(-1.31994e6 - 4.01731e6i) q^{34} +(4.15251e7 - 3.05893e7i) q^{36} -7.43988e7 q^{37} +(-9.22546e7 + 3.03113e7i) q^{38} +1.48637e8i q^{39} +1.29152e7 q^{41} +(9.73007e7 + 2.96141e8i) q^{42} +4.13136e7i q^{43} +(7.43631e7 + 1.00948e8i) q^{44} +(-1.25013e8 + 4.10744e7i) q^{46} -1.40161e8i q^{47} +(-3.31255e8 - 1.02831e8i) q^{48} -5.84766e8 q^{49} -4.37106e7i q^{51} +(3.70472e8 - 2.72906e8i) q^{52} +7.63529e8 q^{53} +(-8.73095e7 + 2.86865e7i) q^{54} +(5.59469e8 - 7.86249e8i) q^{56} -1.00378e9 q^{57} +(2.05437e8 + 6.25262e8i) q^{58} -3.73192e8i q^{59} +1.40526e9 q^{61} +(1.41621e9 - 4.65313e8i) q^{62} +1.48325e9i q^{63} +(3.51900e8 + 1.01444e9i) q^{64} +(4.04555e8 + 1.23129e9i) q^{66} -1.39456e9i q^{67} +(-1.08946e8 + 8.02550e7i) q^{68} -1.36021e9 q^{69} -7.53953e8i q^{71} +(-1.34473e9 - 9.56863e8i) q^{72} -1.69785e8 q^{73} +(7.43142e8 + 2.26181e9i) q^{74} +(1.84300e9 + 2.50187e9i) q^{76} -3.60580e9 q^{77} +(4.51874e9 - 1.48469e9i) q^{78} -3.47862e9i q^{79} -3.92408e9 q^{81} +(-1.29005e8 - 3.92637e8i) q^{82} +8.27276e8i q^{83} +(8.03113e9 - 5.91610e9i) q^{84} +(1.25598e9 - 4.12667e8i) q^{86} +6.80319e9i q^{87} +(2.32615e9 - 3.26905e9i) q^{88} +6.94167e9 q^{89} +1.32330e10i q^{91} +(2.49742e9 + 3.39025e9i) q^{92} +1.54092e10 q^{93} +(-4.26106e9 + 1.40002e9i) q^{94} +(1.82605e8 + 1.10977e10i) q^{96} -1.99530e8 q^{97} +(5.84101e9 + 1.77775e10i) q^{98} +6.16703e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9}+O(q^{10}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9} - 1329640 q^{12} + 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} + 1921656 q^{17} + 3556082 q^{18} + 4157512 q^{21} + 5811280 q^{22} - 19112144 q^{24} + 25066884 q^{26} + 87415400 q^{28} - 66014888 q^{29} + 33171328 q^{32} - 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} + 153620656 q^{37} - 250352720 q^{38} + 477406160 q^{41} + 570662040 q^{42} + 339141040 q^{44} - 897549304 q^{46} + 479727360 q^{48} + 333772012 q^{49} + 110465096 q^{52} + 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} - 3973032960 q^{57} - 2075027916 q^{58} - 4283166080 q^{61} - 1664032240 q^{62} + 340459456 q^{64} + 1884031760 q^{66} - 3042411896 q^{68} - 5321669928 q^{69} - 1632326712 q^{72} - 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} - 410885040 q^{77} + 19914223760 q^{78} + 9939722652 q^{81} + 3197757116 q^{82} + 2383099552 q^{84} + 19648321456 q^{86} - 2774318240 q^{88} + 3011851592 q^{89} + 27349072440 q^{92} + 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} + 39984502056 q^{97} - 38416891998 q^{98}+O(q^{100}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9 - 1329640 * q^12 + 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 + 1921656 * q^17 + 3556082 * q^18 + 4157512 * q^21 + 5811280 * q^22 - 19112144 * q^24 + 25066884 * q^26 + 87415400 * q^28 - 66014888 * q^29 + 33171328 * q^32 - 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 + 153620656 * q^37 - 250352720 * q^38 + 477406160 * q^41 + 570662040 * q^42 + 339141040 * q^44 - 897549304 * q^46 + 479727360 * q^48 + 333772012 * q^49 + 110465096 * q^52 + 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 - 3973032960 * q^57 - 2075027916 * q^58 - 4283166080 * q^61 - 1664032240 * q^62 + 340459456 * q^64 + 1884031760 * q^66 - 3042411896 * q^68 - 5321669928 * q^69 - 1632326712 * q^72 - 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 - 410885040 * q^77 + 19914223760 * q^78 + 9939722652 * q^81 + 3197757116 * q^82 + 2383099552 * q^84 + 19648321456 * q^86 - 2774318240 * q^88 + 3011851592 * q^89 + 27349072440 * q^92 + 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 + 39984502056 * q^97 - 38416891998 * q^98

Introduction

L-functions

Modular forms

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