LMFDB - Embedded newform 100.11.b.e.51.19

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			51.19
Root			$-137.813i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.11.b.e.51.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(31.5088 - 5.58516i) q^{2} -275.626i q^{3} +(961.612 - 351.964i) q^{4} +(-1539.42 - 8684.66i) q^{6} +19327.7i q^{7} +(28333.5 - 16460.7i) q^{8} -16920.9 q^{9} +O(q^{10})$	\(q+(31.5088 - 5.58516i) q^{2} -275.626i q^{3} +(961.612 - 351.964i) q^{4} +(-1539.42 - 8684.66i) q^{6} +19327.7i q^{7} +(28333.5 - 16460.7i) q^{8} -16920.9 q^{9} -171457. i q^{11} +(-97010.5 - 265046. i) q^{12} -203208. q^{13} +(107948. + 608993. i) q^{14} +(800819. - 676905. i) q^{16} -2.12800e6 q^{17} +(-533158. + 94506.1i) q^{18} -559482. i q^{19} +5.32723e6 q^{21} +(-957618. - 5.40242e6i) q^{22} -8.97100e6i q^{23} +(-4.53701e6 - 7.80946e6i) q^{24} +(-6.40286e6 + 1.13495e6i) q^{26} -1.16116e7i q^{27} +(6.80265e6 + 1.85858e7i) q^{28} -6.60179e6 q^{29} -4.19743e7i q^{31} +(2.14522e7 - 2.58012e7i) q^{32} -4.72582e7 q^{33} +(-6.70509e7 + 1.18852e7i) q^{34} +(-1.62714e7 + 5.95555e6i) q^{36} -3.19289e7 q^{37} +(-3.12480e6 - 1.76286e7i) q^{38} +5.60096e7i q^{39} +1.21675e8 q^{41} +(1.67855e8 - 2.97534e7i) q^{42} -1.35742e8i q^{43} +(-6.03468e7 - 1.64876e8i) q^{44} +(-5.01045e7 - 2.82666e8i) q^{46} +3.08719e8i q^{47} +(-1.86573e8 - 2.20727e8i) q^{48} -9.10849e7 q^{49} +5.86534e8i q^{51} +(-1.95408e8 + 7.15220e7i) q^{52} -7.27144e8 q^{53} +(-6.48527e7 - 3.65868e8i) q^{54} +(3.18148e8 + 5.47621e8i) q^{56} -1.54208e8 q^{57} +(-2.08015e8 + 3.68721e7i) q^{58} +2.51543e8i q^{59} -9.40126e8 q^{61} +(-2.34433e8 - 1.32256e9i) q^{62} -3.27043e8i q^{63} +(5.31831e8 - 9.32779e8i) q^{64} +(-1.48905e9 + 2.63945e8i) q^{66} +2.07721e9i q^{67} +(-2.04631e9 + 7.48980e8i) q^{68} -2.47264e9 q^{69} -1.90668e9i q^{71} +(-4.79429e8 + 2.78531e8i) q^{72} +1.72391e9 q^{73} +(-1.00604e9 + 1.78328e8i) q^{74} +(-1.96917e8 - 5.38004e8i) q^{76} +3.31388e9 q^{77} +(3.12823e8 + 1.76480e9i) q^{78} +2.36260e9i q^{79} -4.19963e9 q^{81} +(3.83384e9 - 6.79575e8i) q^{82} -5.22555e9i q^{83} +(5.12272e9 - 1.87499e9i) q^{84} +(-7.58139e8 - 4.27706e9i) q^{86} +1.81963e9i q^{87} +(-2.82231e9 - 4.85799e9i) q^{88} +8.10687e9 q^{89} -3.92755e9i q^{91} +(-3.15747e9 - 8.62662e9i) q^{92} -1.15692e10 q^{93} +(1.72425e9 + 9.72737e9i) q^{94} +(-7.11149e9 - 5.91280e9i) q^{96} +5.70229e9 q^{97} +(-2.86998e9 + 5.08724e8i) q^{98} +2.90122e9i 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 $

$2$	31.5088	−	5.58516i	0.984651	−	0.174536i
$2$	31.5088	−	5.58516i	0.984651	−	0.174536i
$3$		−	275.626i		−	1.13427i	−0.823627	−	0.567133i	$-0.808053\pi$
$3$		−	275.626i		−	1.13427i	0.823627	−	0.567133i	$-0.191947\pi$
$4$	961.612	−	351.964i	0.939074	−	0.343715i
$5$		0			0
$5$		0			0
$6$	−1539.42	−	8684.66i	−0.197970	−	1.11685i
$7$			19327.7i			1.14998i	0.818161	+	0.574990i	$0.194994\pi$
$7$			19327.7i			1.14998i	−0.818161	+	0.574990i	$0.805006\pi$
$8$	28333.5	−	16460.7i	0.864669	−	0.502341i
$9$	−16920.9			−0.286557
$10$		0			0
$11$		−	171457.i		−	1.06462i	−0.846551	−	0.532308i	$-0.821325\pi$
$11$		−	171457.i		−	1.06462i	0.846551	−	0.532308i	$-0.178675\pi$
$12$	−97010.5	−	265046.i	−0.389864	−	1.06516i
$13$	−203208.			−0.547299			−0.273650	−	0.961829i	$-0.588231\pi$
$13$	−203208.			−0.547299			−0.273650	+	0.961829i	$0.588231\pi$
$14$	107948.	+	608993.i	0.200713	+	1.13233i
$15$		0			0
$16$	800819.	−	676905.i	0.763720	−	0.645547i
$17$	−2.12800e6			−1.49874			−0.749372	−	0.662149i	$-0.769645\pi$
$17$	−2.12800e6			−1.49874			−0.749372	+	0.662149i	$0.769645\pi$
$18$	−533158.	+	94506.1i	−0.282159	+	0.0500147i
$19$		−	559482.i		−	0.225953i	−0.993598	−	0.112976i	$-0.963962\pi$
$19$		−	559482.i		−	0.225953i	0.993598	−	0.112976i	$-0.0360385\pi$
$20$		0			0
$21$	5.32723e6			1.30438
$22$	−957618.	−	5.40242e6i	−0.185814	−	1.04827i
$23$		−	8.97100e6i		−	1.39380i	−0.717167	−	0.696902i	$-0.754561\pi$
$23$		−	8.97100e6i		−	1.39380i	0.717167	−	0.696902i	$-0.245439\pi$
$24$	−4.53701e6	−	7.80946e6i	−0.569788	−	0.980764i
$25$		0			0
$26$	−6.40286e6	+	1.13495e6i	−0.538899	+	0.0955236i
$27$		−	1.16116e7i		−	0.809233i
$28$	6.80265e6	+	1.85858e7i	0.395265	+	1.07992i
$29$	−6.60179e6			−0.321863			−0.160932	−	0.986966i	$-0.551450\pi$
$29$	−6.60179e6			−0.321863			−0.160932	+	0.986966i	$0.551450\pi$
$30$		0			0
$31$		−	4.19743e7i		−	1.46614i	−0.680154	−	0.733069i	$-0.738087\pi$
$31$		−	4.19743e7i		−	1.46614i	0.680154	−	0.733069i	$-0.261913\pi$
$32$	2.14522e7	−	2.58012e7i	0.639326	−	0.768935i
$33$	−4.72582e7			−1.20756
$34$	−6.70509e7	+	1.18852e7i	−1.47574	+	0.261585i
$35$		0			0
$36$	−1.62714e7	+	5.95555e6i	−0.269099	+	0.0984940i
$37$	−3.19289e7			−0.460443			−0.230221	−	0.973138i	$-0.573945\pi$
$37$	−3.19289e7			−0.460443			−0.230221	+	0.973138i	$0.573945\pi$
$38$	−3.12480e6	−	1.76286e7i	−0.0394370	−	0.222485i
$39$			5.60096e7i			0.620783i
$40$		0			0
$41$	1.21675e8			1.05023			0.525113	−	0.851033i	$-0.324023\pi$
$41$	1.21675e8			1.05023			0.525113	+	0.851033i	$0.324023\pi$
$42$	1.67855e8	−	2.97534e7i	1.28436	−	0.227662i
$43$		−	1.35742e8i		−	0.923359i	−0.887047	−	0.461679i	$-0.847247\pi$
$43$		−	1.35742e8i		−	0.923359i	0.887047	−	0.461679i	$-0.152753\pi$
$44$	−6.03468e7	−	1.64876e8i	−0.365924	−	0.999753i
$45$		0			0
$46$	−5.01045e7	−	2.82666e8i	−0.243269	−	1.37241i
$47$			3.08719e8i			1.34609i	0.739602	+	0.673045i	$0.235014\pi$
$47$			3.08719e8i			1.34609i	−0.739602	+	0.673045i	$0.764986\pi$
$48$	−1.86573e8	−	2.20727e8i	−0.732222	−	0.866261i
$49$	−9.10849e7			−0.322453
$50$		0			0
$51$			5.86534e8i			1.69997i
$52$	−1.95408e8	+	7.15220e7i	−0.513955	+	0.188115i
$53$	−7.27144e8			−1.73877			−0.869383	−	0.494138i	$-0.835484\pi$
$53$	−7.27144e8			−1.73877			−0.869383	+	0.494138i	$0.835484\pi$
$54$	−6.48527e7	−	3.65868e8i	−0.141241	−	0.796812i
$55$		0			0
$56$	3.18148e8	+	5.47621e8i	0.577682	+	0.994352i
$57$	−1.54208e8			−0.256291
$58$	−2.08015e8	+	3.68721e7i	−0.316923	+	0.0561769i
$59$			2.51543e8i			0.351846i	0.984404	+	0.175923i	$0.0562910\pi$
$59$			2.51543e8i			0.351846i	−0.984404	+	0.175923i	$0.943709\pi$
$60$		0			0
$61$	−9.40126e8			−1.11311			−0.556553	−	0.830812i	$-0.687877\pi$
$61$	−9.40126e8			−1.11311			−0.556553	+	0.830812i	$0.687877\pi$
$62$	−2.34433e8	−	1.32256e9i	−0.255895	−	1.44363i
$63$		−	3.27043e8i		−	0.329535i
$64$	5.31831e8	−	9.32779e8i	0.495306	−	0.868719i
$65$		0			0
$66$	−1.48905e9	+	2.63945e8i	−1.18902	+	0.210763i
$67$			2.07721e9i			1.53853i	0.638927	+	0.769267i	$0.279379\pi$
$67$			2.07721e9i			1.53853i	−0.638927	+	0.769267i	$0.720621\pi$
$68$	−2.04631e9	+	7.48980e8i	−1.40743	+	0.515141i
$69$	−2.47264e9			−1.58094
$70$		0			0
$71$		−	1.90668e9i		−	1.05678i	−0.849000	−	0.528392i	$-0.822795\pi$
$71$		−	1.90668e9i		−	1.05678i	0.849000	−	0.528392i	$-0.177205\pi$
$72$	−4.79429e8	+	2.78531e8i	−0.247777	+	0.143950i
$73$	1.72391e9			0.831574			0.415787	−	0.909462i	$-0.363506\pi$
$73$	1.72391e9			0.831574			0.415787	+	0.909462i	$0.363506\pi$
$74$	−1.00604e9	+	1.78328e8i	−0.453375	+	0.0803640i
$75$		0			0
$76$	−1.96917e8	−	5.38004e8i	−0.0776633	−	0.212187i
$77$	3.31388e9			1.22429
$78$	3.12823e8	+	1.76480e9i	0.108349	+	0.611254i
$79$			2.36260e9i			0.767812i	0.923372	+	0.383906i	$0.125421\pi$
$79$			2.36260e9i			0.767812i	−0.923372	+	0.383906i	$0.874579\pi$
$80$		0			0
$81$	−4.19963e9			−1.20444
$82$	3.83384e9	−	6.79575e8i	1.03411	−	0.183302i
$83$		−	5.22555e9i		−	1.32660i	−0.748352	−	0.663302i	$-0.769154\pi$
$83$		−	5.22555e9i		−	1.32660i	0.748352	−	0.663302i	$-0.230846\pi$
$84$	5.12272e9	−	1.87499e9i	1.22491	−	0.448335i
$85$		0			0
$86$	−7.58139e8	−	4.27706e9i	−0.161160	−	0.909186i
$87$			1.81963e9i			0.365078i
$88$	−2.82231e9	−	4.85799e9i	−0.534801	−	0.920541i
$89$	8.10687e9			1.45179			0.725894	−	0.687806i	$-0.241426\pi$
$89$	8.10687e9			1.45179			0.725894	+	0.687806i	$0.241426\pi$
$90$		0			0
$91$		−	3.92755e9i		−	0.629383i
$92$	−3.15747e9	−	8.62662e9i	−0.479071	−	1.30888i
$93$	−1.15692e10			−1.66299
$94$	1.72425e9	+	9.72737e9i	0.234942	+	1.32543i
$95$		0			0
$96$	−7.11149e9	−	5.91280e9i	−0.872177	−	0.725166i
$97$	5.70229e9			0.664034			0.332017	−	0.943273i	$-0.392271\pi$
$97$	5.70229e9			0.664034			0.332017	+	0.943273i	$0.392271\pi$
$98$	−2.86998e9	+	5.08724e8i	−0.317503	+	0.0562797i
$99$			2.90122e9i			0.305073i
$100$		0			0
$101$	6.05972e9			0.576561			0.288281	−	0.957546i	$-0.406916\pi$
$101$	6.05972e9			0.576561			0.288281	+	0.957546i	$0.406916\pi$
$102$	3.27589e9	+	1.84810e10i	0.296707	+	1.67388i
$103$			1.67947e10i			1.44872i	0.689421	+	0.724361i	$0.257865\pi$
$103$			1.67947e10i			1.44872i	−0.689421	+	0.724361i	$0.742135\pi$
$104$	−5.75760e9	+	3.34496e9i	−0.473233	+	0.274931i
$105$		0			0
$106$	−2.29115e10	+	4.06122e9i	−1.71208	+	0.303478i
$107$		−	1.90759e10i		−	1.36009i	−0.733172	−	0.680043i	$-0.761961\pi$
$107$		−	1.90759e10i		−	1.36009i	0.733172	−	0.680043i	$-0.238039\pi$
$108$	−4.08687e9	−	1.11659e10i	−0.278145	−	0.759930i
$109$	−5.30524e9			−0.344804			−0.172402	−	0.985027i	$-0.555153\pi$
$109$	−5.30524e9			−0.344804			−0.172402	+	0.985027i	$0.555153\pi$
$110$		0			0
$111$			8.80046e9i			0.522264i
$112$	1.30830e10	+	1.54780e10i	0.742366	+	0.878263i
$113$	−1.91431e10			−1.03901			−0.519506	−	0.854467i	$-0.673884\pi$
$113$	−1.91431e10			−1.03901			−0.519506	+	0.854467i	$0.673884\pi$
$114$	−4.85891e9	+	8.61277e8i	−0.252357	+	0.0447320i
$115$		0			0
$116$	−6.34836e9	+	2.32359e9i	−0.302254	+	0.110629i
$117$	3.43847e9			0.156833
$118$	1.40491e9	+	7.92583e9i	0.0614099	+	0.346445i
$119$		−	4.11294e10i		−	1.72353i
$120$		0			0
$121$	−3.46023e9			−0.133407
$122$	−2.96223e10	+	5.25076e9i	−1.09602	+	0.194278i
$123$		−	3.35369e10i		−	1.19123i
$124$	−1.47734e10	−	4.03630e10i	−0.503933	−	1.37681i
$125$		0			0
$126$	−1.82659e9	−	1.03047e10i	−0.0575158	−	0.324477i
$127$			6.78978e9i			0.205512i	0.994707	+	0.102756i	$0.0327661\pi$
$127$			6.78978e9i			0.205512i	−0.994707	+	0.102756i	$0.967234\pi$
$128$	1.15476e10	−	3.23611e10i	0.336081	−	0.941833i
$129$	−3.74140e10			−1.04733
$130$		0			0
$131$			9.35522e8i			0.0242492i	0.999926	+	0.0121246i	$0.00385947\pi$
$131$			9.35522e8i			0.0242492i	−0.999926	+	0.0121246i	$0.996141\pi$
$132$	−4.54440e10	+	1.66332e10i	−1.13399	+	0.415055i
$133$	1.08135e10			0.259841
$134$	1.16016e10	+	6.54506e10i	0.268530	+	1.51492i
$135$		0			0
$136$	−6.02937e10	+	3.50285e10i	−1.29592	+	0.752882i
$137$	6.46143e10			1.33883			0.669416	−	0.742888i	$-0.266545\pi$
$137$	6.46143e10			1.33883			0.669416	+	0.742888i	$0.266545\pi$
$138$	−7.79101e10	+	1.38101e10i	−1.55668	+	0.275932i
$139$		−	4.60447e10i		−	0.887371i	−0.896183	−	0.443686i	$-0.853671\pi$
$139$		−	4.60447e10i		−	0.887371i	0.896183	−	0.443686i	$-0.146329\pi$
$140$		0			0
$141$	8.50911e10			1.52682
$142$	−1.06491e10	−	6.00773e10i	−0.184447	−	1.04056i
$143$			3.48416e10i			0.582664i
$144$	−1.35506e10	+	1.14539e10i	−0.218850	+	0.184986i
$145$		0			0
$146$	5.43185e10	−	9.62833e9i	0.818810	−	0.145140i
$147$			2.51054e10i			0.365747i
$148$	−3.07032e10	+	1.12378e10i	−0.432390	+	0.158261i
$149$	−3.73082e10			−0.508010			−0.254005	−	0.967203i	$-0.581748\pi$
$149$	−3.73082e10			−0.508010			−0.254005	+	0.967203i	$0.581748\pi$
$150$		0			0
$151$			8.54915e9i			0.108903i	0.998516	+	0.0544513i	$0.0173410\pi$
$151$			8.54915e9i			0.108903i	−0.998516	+	0.0544513i	$0.982659\pi$
$152$	−9.20948e9	−	1.58521e10i	−0.113506	−	0.195375i
$153$	3.60078e10			0.429476
$154$	1.04416e11	−	1.85086e10i	1.20549	−	0.213682i
$155$		0			0
$156$	1.97134e10	+	5.38595e10i	0.213372	+	0.582961i
$157$	1.01524e11			1.06431			0.532155	−	0.846647i	$-0.321382\pi$
$157$	1.01524e11			1.06431			0.532155	+	0.846647i	$0.321382\pi$
$158$	1.31955e10	+	7.44428e10i	0.134011	+	0.756027i
$159$			2.00420e11i			1.97222i
$160$		0			0
$161$	1.73389e11			1.60285
$162$	−1.32325e11	+	2.34556e10i	−1.18595	+	0.210219i
$163$		−	4.50348e10i		−	0.391390i	−0.980665	−	0.195695i	$-0.937304\pi$
$163$		−	4.50348e10i		−	0.391390i	0.980665	−	0.195695i	$-0.0626963\pi$
$164$	1.17004e11	−	4.28252e10i	0.986239	−	0.360978i
$165$		0			0
$166$	−2.91855e10	−	1.64651e11i	−0.231541	−	1.30624i
$167$		−	4.14775e10i		−	0.319323i	−0.987172	−	0.159662i	$-0.948960\pi$
$167$		−	4.14775e10i		−	0.319323i	0.987172	−	0.159662i	$-0.0510403\pi$
$168$	1.50939e11	−	8.76900e10i	1.12786	−	0.655245i
$169$	−9.65648e10			−0.700463
$170$		0			0
$171$			9.46695e9i			0.0647485i
$172$	−4.77761e10	−	1.30531e11i	−0.317372	−	0.867102i
$173$	2.75222e11			1.77604			0.888020	−	0.459805i	$-0.152081\pi$
$173$	2.75222e11			1.77604			0.888020	+	0.459805i	$0.152081\pi$
$174$	1.01629e10	+	5.73343e10i	0.0637194	+	0.359475i
$175$		0			0
$176$	−1.16060e11	−	1.37306e11i	−0.687260	−	0.813069i
$177$	6.93320e10			0.399087
$178$	2.55438e11	−	4.52782e10i	1.42950	−	0.253390i
$179$		−	1.07239e11i		−	0.583561i	−0.956485	−	0.291781i	$-0.905752\pi$
$179$		−	1.07239e11i		−	0.583561i	0.956485	−	0.291781i	$-0.0942477\pi$
$180$		0			0
$181$	3.21432e11			1.65461			0.827306	−	0.561752i	$-0.189872\pi$
$181$	3.21432e11			1.65461			0.827306	+	0.561752i	$0.189872\pi$
$182$	−2.19360e10	−	1.23753e11i	−0.109850	−	0.619722i
$183$			2.59124e11i			1.26256i
$184$	−1.47669e11	−	2.54180e11i	−0.700165	−	1.20518i
$185$		0			0
$186$	−3.64533e11	+	6.46160e10i	−1.63746	+	0.290252i
$187$			3.64862e11i			1.59559i
$188$	1.08658e11	+	2.96868e11i	0.462671	+	1.26408i
$189$	2.24426e11			0.930601
$190$		0			0
$191$			3.39617e11i			1.33605i	0.744139	+	0.668025i	$0.232860\pi$
$191$			3.39617e11i			1.33605i	−0.744139	+	0.668025i	$0.767140\pi$
$192$	−2.57099e11	−	1.46587e11i	−0.985357	−	0.561808i
$193$	2.40211e11			0.897029			0.448515	−	0.893776i	$-0.351953\pi$
$193$	2.40211e11			0.897029			0.448515	+	0.893776i	$0.351953\pi$
$194$	1.79672e11	−	3.18482e10i	0.653842	−	0.115898i
$195$		0			0
$196$	−8.75883e10	+	3.20586e10i	−0.302807	+	0.110832i
$197$	−1.72524e11			−0.581457			−0.290728	−	0.956806i	$-0.593898\pi$
$197$	−1.72524e11			−0.581457			−0.290728	+	0.956806i	$0.593898\pi$
$198$	1.62038e10	+	9.14140e10i	0.0532464	+	0.300391i
$199$			3.69172e11i			1.18294i	0.806326	+	0.591472i	$0.201453\pi$
$199$			3.69172e11i			1.18294i	−0.806326	+	0.591472i	$0.798547\pi$
$200$		0			0
$201$	5.72535e11			1.74511
$202$	1.90935e11	−	3.38445e10i	0.567711	−	0.100631i
$203$		−	1.27597e11i		−	0.370136i
$204$	2.06439e11	+	5.64018e11i	0.584306	+	1.59640i
$205$		0			0
$206$	9.38009e10	+	5.29180e11i	0.252855	+	1.42649i
$207$			1.51798e11i			0.399405i
$208$	−1.62733e11	+	1.37553e11i	−0.417984	+	0.353308i
$209$	−9.59273e10			−0.240553
$210$		0			0
$211$			1.80217e11i			0.430908i	0.976514	+	0.215454i	$0.0691231\pi$
$211$			1.80217e11i			0.430908i	−0.976514	+	0.215454i	$0.930877\pi$
$212$	−6.99231e11	+	2.55929e11i	−1.63283	+	0.597640i
$213$	−5.25532e11			−1.19867
$214$	−1.06542e11	−	6.01060e11i	−0.237385	−	1.33921i
$215$		0			0
$216$	−1.91136e11	−	3.28997e11i	−0.406511	−	0.699719i
$217$	8.11267e11			1.68603
$218$	−1.67162e11	+	2.96306e10i	−0.339511	+	0.0601808i
$219$		−	4.75156e11i		−	0.943226i
$220$		0			0
$221$	4.32428e11			0.820262
$222$	4.91520e10	+	2.77292e11i	0.0911541	+	0.514248i
$223$		−	4.75342e11i		−	0.861949i	−0.902364	−	0.430974i	$-0.858170\pi$
$223$		−	4.75342e11i		−	0.861949i	0.902364	−	0.430974i	$-0.141830\pi$
$224$	4.98678e11	+	4.14622e11i	0.884260	+	0.735212i
$225$		0			0
$226$	−6.03178e11	+	1.06918e11i	−1.02306	+	0.181345i
$227$		−	7.08678e11i		−	1.17576i	−0.808947	−	0.587881i	$-0.799962\pi$
$227$		−	7.08678e11i		−	1.17576i	0.808947	−	0.587881i	$-0.200038\pi$
$228$	−1.48288e11	+	5.42756e10i	−0.240676	+	0.0880908i
$229$	−5.93281e11			−0.942070			−0.471035	−	0.882114i	$-0.656119\pi$
$229$	−5.93281e11			−0.942070			−0.471035	+	0.882114i	$0.656119\pi$
$230$		0			0
$231$		−	9.13393e11i		−	1.38867i
$232$	−1.87052e11	+	1.08670e11i	−0.278305	+	0.161685i
$233$	7.00437e11			1.01997			0.509987	−	0.860182i	$-0.329650\pi$
$233$	7.00437e11			1.01997			0.509987	+	0.860182i	$0.329650\pi$
$234$	1.08342e11	−	1.92044e10i	0.154425	−	0.0273730i
$235$		0			0
$236$	8.85341e10	+	2.41887e11i	0.120935	+	0.330410i
$237$	6.51195e11			0.870902
$238$	−2.29715e11	−	1.29594e12i	−0.300818	−	1.69707i
$239$		−	7.62902e11i		−	0.978316i	−0.872195	−	0.489158i	$-0.837304\pi$
$239$		−	7.62902e11i		−	0.978316i	0.872195	−	0.489158i	$-0.162696\pi$
$240$		0			0
$241$	−4.19010e11			−0.515393			−0.257697	−	0.966226i	$-0.582964\pi$
$241$	−4.19010e11			−0.515393			−0.257697	+	0.966226i	$0.582964\pi$
$242$	−1.09028e11	+	1.93260e10i	−0.131359	+	0.0232843i
$243$			4.71875e11i			0.556924i
$244$	−9.04036e11	+	3.30890e11i	−1.04529	+	0.382591i
$245$		0			0
$246$	−1.87309e11	−	1.05671e12i	−0.207914	−	1.17295i
$247$			1.13691e11i			0.123664i
$248$	−6.90928e11	−	1.18928e12i	−0.736502	−	1.26773i
$249$	−1.44030e12			−1.50472
$250$		0			0
$251$			4.01811e11i			0.403323i	0.979455	+	0.201662i	$0.0646341\pi$
$251$			4.01811e11i			0.403323i	−0.979455	+	0.201662i	$0.935366\pi$
$252$	−1.15107e11	−	3.14488e11i	−0.113266	−	0.309458i
$253$	−1.53814e12			−1.48387
$254$	3.79220e10	+	2.13938e11i	0.0358693	+	0.202357i
$255$		0			0
$256$	1.83110e11	−	1.08416e12i	0.166538	−	0.986035i
$257$	1.60741e12			1.43370			0.716852	−	0.697225i	$-0.245582\pi$
$257$	1.60741e12			1.43370			0.716852	+	0.697225i	$0.245582\pi$
$258$	−1.17887e12	+	2.08963e11i	−1.03126	+	0.182798i
$259$		−	6.17113e11i		−	0.529500i
$260$		0			0
$261$	1.11708e11			0.0922323
$262$	5.22504e9	+	2.94772e10i	0.00423237	+	0.0238770i
$263$			1.21331e12i			0.964257i	0.876100	+	0.482129i	$0.160136\pi$
$263$			1.21331e12i			0.964257i	−0.876100	+	0.482129i	$0.839864\pi$
$264$	−1.33899e12	+	7.77904e11i	−1.04414	+	0.606606i
$265$		0			0
$266$	3.40721e11	−	6.03952e10i	0.255853	−	0.0453517i
$267$		−	2.23447e12i		−	1.64671i
$268$	7.31104e11	+	1.99747e12i	0.528817	+	1.44480i
$269$	5.14295e11			0.365133			0.182566	−	0.983194i	$-0.441560\pi$
$269$	5.14295e11			0.365133			0.182566	+	0.983194i	$0.441560\pi$
$270$		0			0
$271$			5.73434e11i			0.392317i	0.980572	+	0.196158i	$0.0628467\pi$
$271$			5.73434e11i			0.392317i	−0.980572	+	0.196158i	$0.937153\pi$
$272$	−1.70415e12	+	1.44046e12i	−1.14462	+	0.967510i
$273$	−1.08254e12			−0.713887
$274$	2.03592e12	−	3.60881e11i	1.31828	−	0.233675i
$275$		0			0
$276$	−2.37772e12	+	8.70281e11i	−1.48462	+	0.543393i
$277$	−2.21093e12			−1.35574			−0.677868	−	0.735183i	$-0.737096\pi$
$277$	−2.21093e12			−1.35574			−0.677868	+	0.735183i	$0.737096\pi$
$278$	−2.57167e11	−	1.45081e12i	−0.154878	−	0.873751i
$279$			7.10244e11i			0.420133i
$280$		0			0
$281$	−3.10629e12			−1.77301			−0.886503	−	0.462724i	$-0.846872\pi$
$281$	−3.10629e12			−1.77301			−0.886503	+	0.462724i	$0.846872\pi$
$282$	2.68112e12	−	4.75248e11i	1.50339	−	0.266486i
$283$		−	2.35766e12i		−	1.29882i	−0.760438	−	0.649411i	$-0.775016\pi$
$283$		−	2.35766e12i		−	1.29882i	0.760438	−	0.649411i	$-0.224984\pi$
$284$	−6.71083e11	−	1.83349e12i	−0.363232	−	0.992399i
$285$		0			0
$286$	1.94596e11	+	1.09782e12i	0.101696	+	0.573720i
$287$			2.35170e12i			1.20774i
$288$	−3.62992e11	+	4.36580e11i	−0.183204	+	0.220344i
$289$	2.51240e12			1.24624
$290$		0			0
$291$		−	1.57170e12i		−	0.753191i
$292$	1.65774e12	−	6.06755e11i	0.780910	−	0.285824i
$293$	−3.63068e11			−0.168132			−0.0840660	−	0.996460i	$-0.526791\pi$
$293$	−3.63068e11			−0.168132			−0.0840660	+	0.996460i	$0.526791\pi$
$294$	1.40218e11	+	7.91042e11i	0.0638361	+	0.360133i
$295$		0			0
$296$	−9.04658e11	+	5.25573e11i	−0.398131	+	0.231300i
$297$	−1.99090e12			−0.861522
$298$	−1.17554e12	+	2.08372e11i	−0.500213	+	0.0886663i
$299$			1.82298e12i			0.762828i
$300$		0			0
$301$	2.62357e12			1.06184
$302$	4.77484e10	+	2.69374e11i	0.0190075	+	0.107231i
$303$		−	1.67022e12i		−	0.653973i
$304$	−3.78716e11	−	4.48044e11i	−0.145863	−	0.172565i
$305$		0			0
$306$	1.13456e12	−	2.01109e11i	0.422884	−	0.0749592i
$307$			4.23605e12i			1.55335i	0.629903	+	0.776674i	$0.283095\pi$
$307$			4.23605e12i			1.55335i	−0.629903	+	0.776674i	$0.716905\pi$
$308$	3.18667e12	−	1.16637e12i	1.14970	−	0.420805i
$309$	4.62905e12			1.64324
$310$		0			0
$311$		−	8.64139e11i		−	0.297017i	−0.988911	−	0.148509i	$-0.952553\pi$
$311$		−	8.64139e11i		−	0.297017i	0.988911	−	0.148509i	$-0.0474473\pi$
$312$	9.21959e11	+	1.58695e12i	0.311845	+	0.536772i
$313$	7.86801e11			0.261905			0.130952	−	0.991389i	$-0.458197\pi$
$313$	7.86801e11			0.261905			0.130952	+	0.991389i	$0.458197\pi$
$314$	3.19889e12	−	5.67026e11i	1.04797	−	0.185761i
$315$		0			0
$316$	8.31550e11	+	2.27190e12i	0.263908	+	0.721032i
$317$	5.00461e11			0.156341			0.0781706	−	0.996940i	$-0.475092\pi$
$317$	5.00461e11			0.156341			0.0781706	+	0.996940i	$0.475092\pi$
$318$	1.11938e12	+	6.31500e12i	0.344224	+	1.94195i
$319$			1.13193e12i			0.342661i
$320$		0			0
$321$	−5.25783e12			−1.54270
$322$	5.46328e12	−	9.68405e11i	1.57824	−	0.279755i
$323$			1.19058e12i			0.338646i
$324$	−4.03841e12	+	1.47812e12i	−1.13106	+	0.413984i
$325$		0			0
$326$	−2.51527e11	−	1.41899e12i	−0.0683119	−	0.385383i
$327$			1.46226e12i			0.391099i
$328$	3.44748e12	−	2.00286e12i	0.908098	−	0.527572i
$329$	−5.96683e12			−1.54798
$330$		0			0
$331$			2.47212e12i			0.622200i	0.950377	+	0.311100i	$0.100697\pi$
$331$			2.47212e12i			0.622200i	−0.950377	+	0.311100i	$0.899303\pi$
$332$	−1.83920e12	−	5.02495e12i	−0.455973	−	1.24578i
$333$	5.40267e11			0.131943
$334$	−2.31659e11	−	1.30691e12i	−0.0557335	−	0.314422i
$335$		0			0
$336$	4.26614e12	−	3.60603e12i	0.996183	−	0.842040i
$337$	−2.80886e12			−0.646220			−0.323110	−	0.946361i	$-0.604728\pi$
$337$	−2.80886e12			−0.646220			−0.323110	+	0.946361i	$0.604728\pi$
$338$	−3.04264e12	+	5.39330e11i	−0.689712	+	0.122256i
$339$			5.27635e12i			1.17852i
$340$		0			0
$341$	−7.19681e12			−1.56087
$342$	5.28745e10	+	2.98292e11i	0.0113010	+	0.0637546i
$343$			3.69914e12i			0.779165i
$344$	−2.23440e12	−	3.84603e12i	−0.463841	−	0.798400i
$345$		0			0
$346$	8.67192e12	−	1.53716e12i	1.74878	−	0.309983i
$347$		−	7.32954e12i		−	1.45690i	−0.685099	−	0.728450i	$-0.740241\pi$
$347$		−	7.32954e12i		−	1.45690i	0.685099	−	0.728450i	$-0.259759\pi$
$348$	6.40443e11	+	1.74977e12i	0.125483	+	0.342836i
$349$	1.98931e12			0.384216			0.192108	−	0.981374i	$-0.438468\pi$
$349$	1.98931e12			0.384216			0.192108	+	0.981374i	$0.438468\pi$
$350$		0			0
$351$			2.35958e12i			0.442893i
$352$	−4.42381e12	−	3.67815e12i	−0.818621	−	0.680637i
$353$	7.20531e12			1.31456			0.657278	−	0.753648i	$-0.271708\pi$
$353$	7.20531e12			1.31456			0.657278	+	0.753648i	$0.271708\pi$
$354$	2.18457e12	−	3.87230e11i	0.392961	−	0.0696551i
$355$		0			0
$356$	7.79567e12	−	2.85333e12i	1.36334	−	0.499001i
$357$	−1.13364e13			−1.95494
$358$	−5.98945e11	−	3.37896e12i	−0.101853	−	0.574604i
$359$		−	6.73646e12i		−	1.12969i	−0.825197	−	0.564845i	$-0.808936\pi$
$359$		−	6.73646e12i		−	1.12969i	0.825197	−	0.564845i	$-0.191064\pi$
$360$		0			0
$361$	5.81805e12			0.948945
$362$	1.01279e13	−	1.79525e12i	1.62921	−	0.288790i
$363$			9.53731e11i			0.151319i
$364$	−1.38236e12	−	3.77678e12i	−0.216328	−	0.591037i
$365$		0			0
$366$	1.44725e12	+	8.16468e12i	0.220362	+	1.24318i
$367$		−	6.74098e12i		−	1.01249i	−0.862388	−	0.506247i	$-0.831032\pi$
$367$		−	6.74098e12i		−	1.01249i	0.862388	−	0.506247i	$-0.168968\pi$
$368$	−6.07251e12	−	7.18414e12i	−0.899766	−	1.06448i
$369$	−2.05886e12			−0.300950
$370$		0			0
$371$		−	1.40540e13i		−	1.99955i
$372$	−1.11251e13	+	4.07195e12i	−1.56167	+	0.571594i
$373$	−1.62651e12			−0.225275			−0.112637	−	0.993636i	$-0.535930\pi$
$373$	−1.62651e12			−0.225275			−0.112637	+	0.993636i	$0.535930\pi$
$374$	2.03781e12	+	1.14964e13i	0.278488	+	1.57110i
$375$		0			0
$376$	5.08174e12	+	8.74708e12i	0.676197	+	1.16392i
$377$	1.34154e12			0.176156
$378$	7.07139e12	−	1.25345e12i	0.916317	−	0.162424i
$379$		−	4.04668e12i		−	0.517491i	−0.965946	−	0.258746i	$-0.916691\pi$
$379$		−	4.04668e12i		−	0.517491i	0.965946	−	0.258746i	$-0.0833091\pi$
$380$		0			0
$381$	1.87144e12			0.233105
$382$	1.89682e12	+	1.07009e13i	0.233189	+	1.31554i
$383$		−	6.06033e12i		−	0.735364i	−0.929952	−	0.367682i	$-0.880152\pi$
$383$		−	6.06033e12i		−	0.735364i	0.929952	−	0.367682i	$-0.119848\pi$
$384$	−8.91959e12	−	3.18283e12i	−1.06829	−	0.381204i
$385$		0			0
$386$	7.56877e12	−	1.34162e12i	0.883260	−	0.156564i
$387$			2.29687e12i			0.264595i
$388$	5.48339e12	−	2.00700e12i	0.623577	−	0.228238i
$389$	4.19765e12			0.471257			0.235629	−	0.971843i	$-0.424285\pi$
$389$	4.19765e12			0.471257			0.235629	+	0.971843i	$0.424285\pi$
$390$		0			0
$391$			1.90903e13i			2.08896i
$392$	−2.58075e12	+	1.49932e12i	−0.278815	+	0.161981i
$393$	2.57854e11			0.0275050
$394$	−5.43601e12	+	9.63572e11i	−0.572532	+	0.101485i
$395$		0			0
$396$	1.02112e12	+	2.78985e12i	0.104858	+	0.286487i
$397$	−3.84548e11			−0.0389940			−0.0194970	−	0.999810i	$-0.506206\pi$
$397$	−3.84548e11			−0.0389940			−0.0194970	+	0.999810i	$0.506206\pi$
$398$	2.06189e12	+	1.16322e13i	0.206467	+	1.16479i
$399$		−	2.98049e12i		−	0.294729i
$400$		0			0
$401$	−1.65040e13			−1.59173			−0.795863	−	0.605477i	$-0.792982\pi$
$401$	−1.65040e13			−1.59173			−0.795863	+	0.605477i	$0.792982\pi$
$402$	1.80399e13	−	3.19770e12i	1.71832	−	0.304585i
$403$			8.52953e12i			0.802417i
$404$	5.82710e12	−	2.13280e12i	0.541434	−	0.198173i
$405$		0			0
$406$	−7.12652e11	−	4.02044e12i	−0.0646022	−	0.364455i
$407$			5.47445e12i			0.490195i
$408$	9.65477e12	+	1.66185e13i	0.853967	+	1.46992i
$409$	6.06231e12			0.529690			0.264845	−	0.964291i	$-0.414679\pi$
$409$	6.06231e12			0.529690			0.264845	+	0.964291i	$0.414679\pi$
$410$		0			0
$411$		−	1.78094e13i		−	1.51859i
$412$	5.91112e12	+	1.61500e13i	0.497947	+	1.36046i
$413$	−4.86175e12			−0.404616
$414$	8.47814e11	+	4.78296e12i	0.0697106	+	0.393274i
$415$		0			0
$416$	−4.35927e12	+	5.24302e12i	−0.349903	+	0.420838i
$417$	−1.26911e13			−1.00651
$418$	−3.02256e12	+	5.35770e11i	−0.236861	+	0.0419853i
$419$			4.24052e12i			0.328359i	0.986430	+	0.164180i	$0.0524977\pi$
$419$			4.24052e12i			0.328359i	−0.986430	+	0.164180i	$0.947502\pi$
$420$		0			0
$421$	7.80004e12			0.589775			0.294887	−	0.955532i	$-0.404718\pi$
$421$	7.80004e12			0.589775			0.294887	+	0.955532i	$0.404718\pi$
$422$	1.00654e12	+	5.67844e12i	0.0752091	+	0.424294i
$423$		−	5.22381e12i		−	0.385732i
$424$	−2.06025e13	+	1.19693e13i	−1.50346	+	0.873455i
$425$		0			0
$426$	−1.65589e13	+	2.93518e12i	−1.18027	+	0.209212i
$427$		−	1.81705e13i		−	1.28005i
$428$	−6.71403e12	−	1.83436e13i	−0.467482	−	1.27722i
$429$	9.60326e12			0.660895
$430$		0			0
$431$			2.58799e13i			1.74011i	0.492953	+	0.870056i	$0.335917\pi$
$431$			2.58799e13i			1.74011i	−0.492953	+	0.870056i	$0.664083\pi$
$432$	−7.85996e12	−	9.29880e12i	−0.522398	−	0.618028i
$433$	−8.44727e10			−0.00554979			−0.00277490	−	0.999996i	$-0.500883\pi$
$433$	−8.44727e10			−0.00554979			−0.00277490	+	0.999996i	$0.500883\pi$
$434$	2.55621e13	−	4.53106e12i	1.66015	−	0.294273i
$435$		0			0
$436$	−5.10158e12	+	1.86725e12i	−0.323796	+	0.118514i
$437$	−5.01911e12			−0.314934
$438$	−2.65382e12	−	1.49716e13i	−0.164627	−	0.928748i
$439$		−	1.75937e13i		−	1.07903i	−0.841975	−	0.539516i	$-0.818607\pi$
$439$		−	1.75937e13i		−	1.07903i	0.841975	−	0.539516i	$-0.181393\pi$
$440$		0			0
$441$	1.54124e12			0.0924012
$442$	1.36253e13	−	2.41518e12i	0.807672	−	0.143166i
$443$			6.58242e12i			0.385804i	0.981218	+	0.192902i	$0.0617900\pi$
$443$			6.58242e12i			0.385804i	−0.981218	+	0.192902i	$0.938210\pi$
$444$	3.09744e12	+	8.46262e12i	0.179510	+	0.490445i
$445$		0			0
$446$	−2.65486e12	−	1.49775e13i	−0.150441	−	0.848719i
$447$			1.02831e13i			0.576219i
$448$	1.80285e13	+	1.02791e13i	0.999008	+	0.569592i
$449$	1.87414e13			1.02700			0.513499	−	0.858090i	$-0.328349\pi$
$449$	1.87414e13			1.02700			0.513499	+	0.858090i	$0.328349\pi$
$450$		0			0
$451$		−	2.08621e13i		−	1.11809i
$452$	−1.84083e13	+	6.73769e12i	−0.975710	+	0.357124i
$453$	2.35637e12			0.123524
$454$	−3.95808e12	−	2.23296e13i	−0.205213	−	1.15772i
$455$		0			0
$456$	−4.36925e12	+	2.53838e12i	−0.221607	+	0.128745i
$457$	2.43734e13			1.22274			0.611372	−	0.791343i	$-0.290618\pi$
$457$	2.43734e13			1.22274			0.611372	+	0.791343i	$0.290618\pi$
$458$	−1.86936e13	+	3.31357e12i	−0.927610	+	0.164425i
$459$			2.47095e13i			1.21283i
$460$		0			0
$461$	−1.26442e13			−0.607279			−0.303639	−	0.952787i	$-0.598202\pi$
$461$	−1.26442e13			−0.607279			−0.303639	+	0.952787i	$0.598202\pi$
$462$	−5.10145e12	−	2.87799e13i	−0.242373	−	1.36735i
$463$			1.80127e13i			0.846594i	0.905991	+	0.423297i	$0.139127\pi$
$463$			1.80127e13i			0.846594i	−0.905991	+	0.423297i	$0.860873\pi$
$464$	−5.28684e12	+	4.46878e12i	−0.245814	+	0.207778i
$465$		0			0
$466$	2.20699e13	−	3.91205e12i	1.00432	−	0.178023i
$467$		−	1.09940e13i		−	0.494963i	−0.968893	−	0.247481i	$-0.920397\pi$
$467$		−	1.09940e13i		−	0.494963i	0.968893	−	0.247481i	$-0.0796029\pi$
$468$	3.30648e12	−	1.21022e12i	0.147277	−	0.0539057i
$469$	−4.01478e13			−1.76928
$470$		0			0
$471$		−	2.79826e13i		−	1.20721i
$472$	4.14059e12	+	7.12710e12i	0.176747	+	0.304230i
$473$	−2.32739e13			−0.983022
$474$	2.05184e13	−	3.63703e12i	0.857535	−	0.152004i
$475$		0			0
$476$	−1.44761e13	−	3.95505e13i	−0.592401	−	1.61852i
$477$	1.23040e13			0.498256
$478$	−4.26093e12	−	2.40381e13i	−0.170752	−	0.963299i
$479$			2.43669e13i			0.966323i	0.875531	+	0.483162i	$0.160512\pi$
$479$			2.43669e13i			0.966323i	−0.875531	+	0.483162i	$0.839488\pi$
$480$		0			0
$481$	6.48823e12			0.252000
$482$	−1.32025e13	+	2.34024e12i	−0.507483	+	0.0899549i
$483$		−	4.77905e13i		−	1.81805i
$484$	−3.32740e12	+	1.21788e12i	−0.125279	+	0.0458539i
$485$		0			0
$486$	2.63550e12	+	1.48682e13i	0.0972034	+	0.548375i
$487$			2.71201e13i			0.990026i	0.868886	+	0.495013i	$0.164837\pi$
$487$			2.71201e13i			0.990026i	−0.868886	+	0.495013i	$0.835163\pi$
$488$	−2.66370e13	+	1.54752e13i	−0.962469	+	0.559160i
$489$	−1.24128e13			−0.443941
$490$		0			0
$491$			1.59046e13i			0.557335i	0.960388	+	0.278668i	$0.0898928\pi$
$491$			1.59046e13i			0.557335i	−0.960388	+	0.278668i	$0.910107\pi$
$492$	−1.18038e13	−	3.22495e13i	−0.409445	−	1.11866i
$493$	1.40486e13			0.482391
$494$	6.34985e11	+	3.58228e12i	0.0215838	+	0.121766i
$495$		0			0
$496$	−2.84126e13	−	3.36138e13i	−0.946462	−	1.11972i
$497$	3.68518e13			1.21528
$498$	−4.53821e13	+	8.04431e12i	−1.48162	+	0.262629i
$499$			1.69650e13i			0.548341i	0.961681	+	0.274171i	$0.0884033\pi$
$499$			1.69650e13i			0.548341i	−0.961681	+	0.274171i	$0.911597\pi$
$500$		0			0
$501$	−1.14323e13			−0.362197
$502$	2.24418e12	+	1.26606e13i	0.0703946	+	0.397132i
$503$		−	4.21897e12i		−	0.131029i	−0.997852	−	0.0655143i	$-0.979131\pi$
$503$		−	4.21897e12i		−	0.131029i	0.997852	−	0.0655143i	$-0.0208688\pi$
$504$	−5.38336e12	−	9.26626e12i	−0.165539	−	0.284939i
$505$		0			0
$506$	−4.84651e13	+	8.59079e12i	−1.46109	+	0.258988i
$507$			2.66158e13i			0.794511i
$508$	2.38976e12	+	6.52913e12i	0.0706375	+	0.192991i
$509$	−2.81674e13			−0.824438			−0.412219	−	0.911085i	$-0.635246\pi$
$509$	−2.81674e13			−0.824438			−0.412219	+	0.911085i	$0.635246\pi$
$510$		0			0
$511$			3.33193e13i			0.956293i
$512$	−2.85606e11	−	3.51832e13i	−0.00811740	−	0.999967i
$513$	−6.49648e12			−0.182849
$514$	5.06474e13	−	8.97762e12i	1.41170	−	0.250234i
$515$		0			0
$516$	−3.59777e13	+	1.31684e13i	−0.983524	+	0.359984i
$517$	5.29321e13			1.43307
$518$	−3.44668e12	−	1.94445e13i	−0.0924170	−	0.521372i
$519$		−	7.58585e13i		−	2.01450i
$520$		0			0
$521$	4.63265e13			1.20682			0.603408	−	0.797433i	$-0.293809\pi$
$521$	4.63265e13			1.20682			0.603408	+	0.797433i	$0.293809\pi$
$522$	3.51980e12	−	6.23909e11i	0.0908166	−	0.0160979i
$523$			1.75920e13i			0.449581i	0.974407	+	0.224790i	$0.0721697\pi$
$523$			1.75920e13i			0.449581i	−0.974407	+	0.224790i	$0.927830\pi$
$524$	3.29270e11	+	8.99609e11i	0.00833480	+	0.0227718i
$525$		0			0
$526$	6.77653e12	+	3.82300e13i	0.168298	+	0.949456i
$527$			8.93215e13i			2.19737i
$528$	−3.78453e13	+	3.19893e13i	−0.922236	+	0.779535i
$529$	−3.90523e13			−0.942688
$530$		0			0
$531$		−	4.25635e12i		−	0.100824i
$532$	1.03984e13	−	3.80596e12i	0.244010	−	0.0893112i
$533$	−2.47254e13			−0.574788
$534$	−1.24799e13	−	7.04055e13i	−0.287411	−	1.62144i
$535$		0			0
$536$	3.41925e13	+	5.88547e13i	0.772870	+	1.33032i
$537$	−2.95578e13			−0.661913
$538$	1.62048e13	−	2.87242e12i	0.359528	−	0.0637289i
$539$			1.56172e13i			0.343288i
$540$		0			0
$541$	2.91304e13			0.628579			0.314290	−	0.949327i	$-0.398234\pi$
$541$	2.91304e13			0.628579			0.314290	+	0.949327i	$0.398234\pi$
$542$	3.20272e12	+	1.80682e13i	0.0684736	+	0.386295i
$543$		−	8.85951e13i		−	1.87677i
$544$	−4.56504e13	+	5.49050e13i	−0.958187	+	1.15244i
$545$		0			0
$546$	−3.41095e13	+	6.04615e12i	−0.702930	+	0.124599i
$547$		−	5.33612e13i		−	1.08965i	−0.838548	−	0.544827i	$-0.816595\pi$
$547$		−	5.33612e13i		−	1.08965i	0.838548	−	0.544827i	$-0.183405\pi$
$548$	6.21339e13	−	2.27419e13i	1.25726	−	0.460176i
$549$	1.59078e13			0.318969
$550$		0			0
$551$			3.69358e12i			0.0727260i
$552$	−7.00586e13	+	4.07015e13i	−1.36699	+	0.794173i
$553$	−4.56636e13			−0.882968
$554$	−6.96637e13	+	1.23484e13i	−1.33493	+	0.236625i
$555$		0			0
$556$	−1.62061e13	−	4.42771e13i	−0.305002	−	0.833307i
$557$	2.48436e12			0.0463382			0.0231691	−	0.999732i	$-0.492624\pi$
$557$	2.48436e12			0.0463382			0.0231691	+	0.999732i	$0.492624\pi$
$558$	3.96683e12	+	2.23790e13i	0.0733285	+	0.413684i
$559$			2.75838e13i			0.505354i
$560$		0			0
$561$	1.00566e14			1.80982
$562$	−9.78755e13	+	1.73491e13i	−1.74579	+	0.309454i
$563$			6.79910e13i			1.20201i	0.799244	+	0.601007i	$0.205233\pi$
$563$			6.79910e13i			1.20201i	−0.799244	+	0.601007i	$0.794767\pi$
$564$	8.18246e13	−	2.99490e13i	1.43380	−	0.524791i
$565$		0			0
$566$	−1.31679e13	−	7.42872e13i	−0.226692	−	1.27889i
$567$		−	8.11692e13i		−	1.38508i
$568$	−3.13854e13	−	5.40229e13i	−0.530866	−	0.913769i
$569$	7.08657e13			1.18816			0.594080	−	0.804406i	$-0.297516\pi$
$569$	7.08657e13			1.18816			0.594080	+	0.804406i	$0.297516\pi$
$570$		0			0
$571$			1.94186e13i			0.319917i	0.987124	+	0.159959i	$0.0511361\pi$
$571$			1.94186e13i			0.319917i	−0.987124	+	0.159959i	$0.948864\pi$
$572$	1.22630e13	+	3.35041e13i	0.200270	+	0.547164i
$573$	9.36074e13			1.51543
$574$	1.31346e13	+	7.40993e13i	0.210794	+	1.18920i
$575$		0			0
$576$	−8.99907e12	+	1.57835e13i	−0.141934	+	0.248938i
$577$	−5.81422e13			−0.909102			−0.454551	−	0.890721i	$-0.650200\pi$
$577$	−5.81422e13			−0.909102			−0.454551	+	0.890721i	$0.650200\pi$
$578$	7.91629e13	−	1.40322e13i	1.22711	−	0.217513i
$579$		−	6.62085e13i		−	1.01747i
$580$		0			0
$581$	1.00998e14			1.52557
$582$	−8.77821e12	−	4.95225e13i	−0.131459	−	0.741630i
$583$			1.24674e14i			1.85112i
$584$	4.88445e13	−	2.83769e13i	0.719037	−	0.417734i
$585$		0			0
$586$	−1.14399e13	+	2.02780e12i	−0.165551	+	0.0293451i
$587$		−	1.32027e14i		−	1.89440i	−0.320648	−	0.947198i	$-0.603901\pi$
$587$		−	1.32027e14i		−	1.89440i	0.320648	−	0.947198i	$-0.396099\pi$
$588$	8.83620e12	+	2.41417e13i	0.125713	+	0.343463i
$589$	−2.34839e13			−0.331278
$590$		0			0
$591$			4.75520e13i			0.659526i
$592$	−2.55693e13	+	2.16129e13i	−0.351650	+	0.297238i
$593$	3.20752e13			0.437417			0.218708	−	0.975790i	$-0.429816\pi$
$593$	3.20752e13			0.437417			0.218708	+	0.975790i	$0.429816\pi$
$594$	−6.27308e13	+	1.11195e13i	−0.848299	+	0.150367i
$595$		0			0
$596$	−3.58760e13	+	1.31311e13i	−0.477059	+	0.174611i
$597$	1.01754e14			1.34177
$598$	1.01817e13	+	5.74400e13i	0.133141	+	0.751119i
$599$			4.81788e13i			0.624772i	0.949955	+	0.312386i	$0.101128\pi$
$599$			4.81788e13i			0.624772i	−0.949955	+	0.312386i	$0.898872\pi$
$600$		0			0
$601$	−1.53390e13			−0.195625			−0.0978126	−	0.995205i	$-0.531185\pi$
$601$	−1.53390e13			−0.195625			−0.0978126	+	0.995205i	$0.531185\pi$
$602$	8.26657e13	−	1.46531e13i	1.04555	−	0.185330i
$603$		−	3.51484e13i		−	0.440879i
$604$	3.00899e12	+	8.22097e12i	0.0374314	+	0.102268i
$605$		0			0
$606$	−9.32844e12	−	5.26266e13i	−0.114142	−	0.643935i
$607$			8.18724e13i			0.993560i	0.867876	+	0.496780i	$0.165484\pi$
$607$			8.18724e13i			0.993560i	−0.867876	+	0.496780i	$0.834516\pi$
$608$	−1.44353e13	−	1.20021e13i	−0.173743	−	0.144458i
$609$	−3.51692e13			−0.419833
$610$		0			0
$611$		−	6.27343e13i		−	0.736714i
$612$	3.46255e13	−	1.26734e13i	0.403310	−	0.147617i
$613$	1.05652e14			1.22061			0.610306	−	0.792166i	$-0.291047\pi$
$613$	1.05652e14			1.22061			0.610306	+	0.792166i	$0.291047\pi$
$614$	2.36590e13	+	1.33473e14i	0.271116	+	1.52951i
$615$		0			0
$616$	9.38937e13	−	5.45489e13i	1.05860	−	0.615010i
$617$	3.26047e13			0.364632			0.182316	−	0.983240i	$-0.441641\pi$
$617$	3.26047e13			0.364632			0.182316	+	0.983240i	$0.441641\pi$
$618$	1.45856e14	−	2.58540e13i	1.61801	−	0.286804i
$619$		−	9.96103e13i		−	1.09610i	−0.836445	−	0.548051i	$-0.815370\pi$
$619$		−	9.96103e13i		−	1.09610i	0.836445	−	0.548051i	$-0.184630\pi$
$620$		0			0
$621$	−1.04168e14			−1.12791
$622$	−4.82636e12	−	2.72280e13i	−0.0518403	−	0.292458i
$623$			1.56687e14i			1.66953i
$624$	3.79132e13	+	4.48536e13i	0.400744	+	0.474104i
$625$		0			0
$626$	2.47912e13	−	4.39441e12i	0.257885	−	0.0457119i
$627$			2.64401e13i			0.272851i
$628$	9.76262e13	−	3.57326e13i	0.999467	−	0.365819i
$629$	6.79449e13			0.690086
$630$		0			0
$631$			4.90561e13i			0.490395i	0.969473	+	0.245197i	$0.0788528\pi$
$631$			4.90561e13i			0.490395i	−0.969473	+	0.245197i	$0.921147\pi$
$632$	3.88901e13	+	6.69407e13i	0.385704	+	0.663903i
$633$	4.96727e13			0.488764
$634$	1.57689e13	−	2.79515e12i	0.153942	−	0.0272872i
$635$		0			0
$636$	7.05407e13	+	1.92726e14i	0.677882	+	1.85206i
$637$	1.85092e13			0.176478
$638$	6.32199e12	+	3.56656e13i	0.0598068	+	0.337401i
$639$			3.22628e13i			0.302829i
$640$		0			0
$641$	5.37176e13			0.496394			0.248197	−	0.968710i	$-0.420162\pi$
$641$	5.37176e13			0.496394			0.248197	+	0.968710i	$0.420162\pi$
$642$	−1.65668e14	+	2.93658e13i	−1.51902	+	0.269257i
$643$		−	1.60947e14i		−	1.46429i	−0.681149	−	0.732145i	$-0.738520\pi$
$643$		−	1.60947e14i		−	1.46429i	0.681149	−	0.732145i	$-0.261480\pi$
$644$	1.66733e14	−	6.10266e13i	1.50519	−	0.550921i
$645$		0			0
$646$	6.64958e12	+	3.75137e13i	0.0591060	+	0.333448i
$647$		−	5.34989e13i		−	0.471871i	−0.971769	−	0.235935i	$-0.924185\pi$
$647$		−	5.34989e13i		−	0.471871i	0.971769	−	0.235935i	$-0.0758154\pi$
$648$	−1.18990e14	+	6.91290e13i	−1.04144	+	0.605041i
$649$	4.31290e13			0.374581
$650$		0			0
$651$		−	2.23607e14i		−	1.91240i
$652$	−1.58506e13	−	4.33060e13i	−0.134527	−	0.367545i
$653$	2.40402e13			0.202475			0.101238	−	0.994862i	$-0.467720\pi$
$653$	2.40402e13			0.202475			0.101238	+	0.994862i	$0.467720\pi$
$654$	8.16698e12	+	4.60742e13i	0.0682610	+	0.385096i
$655$		0			0
$656$	9.74397e13	−	8.23625e13i	0.802078	−	0.677970i
$657$	−2.91702e13			−0.238294
$658$	−1.88008e14	+	3.33257e13i	−1.52421	+	0.270178i
$659$			1.37559e14i			1.10678i	0.832923	+	0.553390i	$0.186666\pi$
$659$			1.37559e14i			1.10678i	−0.832923	+	0.553390i	$0.813334\pi$
$660$		0			0
$661$	1.72923e13			0.137039			0.0685197	−	0.997650i	$-0.478172\pi$
$661$	1.72923e13			0.137039			0.0685197	+	0.997650i	$0.478172\pi$
$662$	1.38072e13	+	7.78937e13i	0.108597	+	0.612650i
$663$		−	1.19189e14i		−	0.930395i
$664$	−8.60163e13	−	1.48058e14i	−0.666408	−	1.14707i
$665$		0			0
$666$	1.70232e13	−	3.01748e12i	0.129918	−	0.0230289i
$667$			5.92246e13i			0.448614i
$668$	−1.45986e13	−	3.98853e13i	−0.109756	−	0.299868i
$669$	−1.31017e14			−0.977679
$670$		0			0
$671$			1.61192e14i			1.18503i
$672$	1.14281e14	−	1.37449e14i	0.833926	−	1.00299i
$673$	−3.83664e13			−0.277892			−0.138946	−	0.990300i	$-0.544371\pi$
$673$	−3.83664e13			−0.277892			−0.138946	+	0.990300i	$0.544371\pi$
$674$	−8.85038e13	+	1.56879e13i	−0.636301	+	0.112789i
$675$		0			0
$676$	−9.28579e13	+	3.39873e13i	−0.657787	+	0.240760i
$677$	−1.30298e14			−0.916209			−0.458105	−	0.888898i	$-0.651472\pi$
$677$	−1.30298e14			−0.916209			−0.458105	+	0.888898i	$0.651472\pi$
$678$	2.94693e13	+	1.66252e14i	0.205694	+	1.16043i
$679$			1.10212e14i			0.763626i
$680$		0			0
$681$	−1.95330e14			−1.33363
$682$	−2.26763e14	+	4.01953e13i	−1.53692	+	0.272429i
$683$		−	9.87247e12i		−	0.0664236i	−0.999448	−	0.0332118i	$-0.989426\pi$
$683$		−	9.87247e12i		−	0.0664236i	0.999448	−	0.0332118i	$-0.0105736\pi$
$684$	3.33202e12	+	9.10353e12i	0.0222550	+	0.0608036i
$685$		0			0
$686$	2.06603e13	+	1.16555e14i	0.135993	+	0.767206i
$687$			1.63524e14i			1.06856i
$688$	−9.18842e13	−	1.08704e14i	−0.596072	−	0.705188i
$689$	1.47762e14			0.951626
$690$		0			0
$691$			6.92514e13i			0.439580i	0.975547	+	0.219790i	$0.0705373\pi$
$691$			6.92514e13i			0.439580i	−0.975547	+	0.219790i	$0.929463\pi$
$692$	2.64657e14	−	9.68682e13i	1.66783	−	0.610451i
$693$	−5.60739e13			−0.350828
$694$	−4.09367e13	−	2.30945e14i	−0.254282	−	1.43454i
$695$		0			0
$696$	2.99524e13	+	5.15564e13i	0.183394	+	0.315672i
$697$	−2.58925e14			−1.57402
$698$	6.26808e13	−	1.11106e13i	0.378318	−	0.0670596i
$699$		−	1.93059e14i		−	1.15692i
$700$		0			0
$701$	−1.42727e14			−0.843169			−0.421584	−	0.906789i	$-0.638526\pi$
$701$	−1.42727e14			−0.843169			−0.421584	+	0.906789i	$0.638526\pi$
$702$	1.31786e13	+	7.43475e13i	0.0773009	+	0.436095i
$703$			1.78637e13i			0.104038i
$704$	−1.59932e14	−	9.11864e13i	−0.924852	−	0.527311i
$705$		0			0
$706$	2.27031e14	−	4.02428e13i	1.29438	−	0.229438i
$707$			1.17120e14i			0.663034i
$708$	6.66705e13	−	2.44023e13i	0.374772	−	0.137172i
$709$	−1.37486e14			−0.767411			−0.383706	−	0.923455i	$-0.625352\pi$
$709$	−1.37486e14			−0.767411			−0.383706	+	0.923455i	$0.625352\pi$
$710$		0			0
$711$		−	3.99774e13i		−	0.220022i
$712$	2.29696e14	−	1.33445e14i	1.25532	−	0.729294i
$713$	−3.76551e14			−2.04351
$714$	−3.57195e14	+	6.33154e13i	−1.92493	+	0.341207i
$715$		0			0
$716$	−3.77441e13	−	1.03122e14i	−0.200578	−	0.548007i
$717$	−2.10276e14			−1.10967
$718$	−3.76242e13	−	2.12258e14i	−0.197172	−	1.11235i
$719$		−	2.25863e14i		−	1.17544i	−0.809065	−	0.587719i	$-0.800026\pi$
$719$		−	2.25863e14i		−	1.17544i	0.809065	−	0.587719i	$-0.199974\pi$
$720$		0			0
$721$	−3.24602e14			−1.66600
$722$	1.83320e14	−	3.24947e13i	0.934380	−	0.165625i
$723$			1.15490e14i			0.584593i
$724$	3.09093e14	−	1.13132e14i	1.55380	−	0.568714i
$725$		0			0
$726$	5.32674e12	+	3.00509e13i	0.0264106	+	0.148996i
$727$		−	1.90886e14i		−	0.939946i	−0.882681	−	0.469973i	$-0.844264\pi$
$727$		−	1.90886e14i		−	0.939946i	0.882681	−	0.469973i	$-0.155736\pi$
$728$	−6.46504e13	−	1.11281e14i	−0.316165	−	0.544208i
$729$	−1.17923e14			−0.572743
$730$		0			0
$731$			2.88858e14i			1.38388i
$732$	9.12021e13	+	2.49176e14i	0.433960	+	1.18564i
$733$	−2.63266e14			−1.24416			−0.622079	−	0.782955i	$-0.713712\pi$
$733$	−2.63266e14			−1.24416			−0.622079	+	0.782955i	$0.713712\pi$
$734$	−3.76495e13	−	2.12400e14i	−0.176717	−	0.996954i
$735$		0			0
$736$	−2.31462e14	−	1.92448e14i	−1.07174	−	0.891095i
$737$	3.56154e14			1.63795
$738$	−6.48721e13	+	1.14990e13i	−0.296330	+	0.0525267i
$739$			3.24126e14i			1.47059i	0.677746	+	0.735296i	$0.262957\pi$
$739$			3.24126e14i			1.47059i	−0.677746	+	0.735296i	$0.737043\pi$
$740$		0			0
$741$	3.13364e13			0.140268
$742$	−7.84941e13	−	4.42826e14i	−0.348993	−	1.96885i
$743$		−	2.17622e14i		−	0.961080i	−0.876973	−	0.480540i	$-0.840441\pi$
$743$		−	2.17622e14i		−	0.961080i	0.876973	−	0.480540i	$-0.159559\pi$
$744$	−3.27797e14	+	1.90438e14i	−1.43794	+	0.835389i
$745$		0			0
$746$	−5.12494e13	+	9.08432e12i	−0.221817	+	0.0393186i
$747$			8.84211e13i			0.380148i
$748$	1.28418e14	+	3.50856e14i	0.548427	+	1.49837i
$749$	3.68694e14			1.56407
$750$		0			0
$751$		−	3.34043e14i		−	1.39831i	−0.714970	−	0.699155i	$-0.753560\pi$
$751$		−	3.34043e14i		−	1.39831i	0.714970	−	0.699155i	$-0.246440\pi$
$752$	2.08973e14	+	2.47228e14i	0.868964	+	1.02804i
$753$	1.10750e14			0.457475
$754$	4.22703e13	−	7.49271e12i	0.173452	−	0.0307456i
$755$		0			0
$756$	2.15810e14	−	7.89898e13i	0.873904	−	0.319861i
$757$	−3.02313e14			−1.21612			−0.608061	−	0.793890i	$-0.708053\pi$
$757$	−3.02313e14			−1.21612			−0.608061	+	0.793890i	$0.708053\pi$
$758$	−2.26014e13	−	1.27506e14i	−0.0903210	−	0.509548i
$759$			4.23953e14i			1.68310i
$760$		0			0
$761$	−8.47976e13			−0.332246			−0.166123	−	0.986105i	$-0.553125\pi$
$761$	−8.47976e13			−0.332246			−0.166123	+	0.986105i	$0.553125\pi$
$762$	5.89669e13	−	1.04523e13i	0.229527	−	0.0406853i
$763$		−	1.02538e14i		−	0.396517i
$764$	1.19533e14	+	3.26580e14i	0.459220	+	1.25465i
$765$		0			0
$766$	−3.38479e13	−	1.90954e14i	−0.128348	−	0.724077i
$767$		−	5.11157e13i		−	0.192565i
$768$	−2.98822e14	−	5.04700e13i	−1.11843	−	0.188898i
$769$	−5.35657e13			−0.199184			−0.0995922	−	0.995028i	$-0.531754\pi$
$769$	−5.35657e13			−0.199184			−0.0995922	+	0.995028i	$0.531754\pi$
$770$		0			0
$771$		−	4.43043e14i		−	1.62620i
$772$	2.30990e14	−	8.45456e13i	0.842377	−	0.308322i
$773$	−1.44228e14			−0.522578			−0.261289	−	0.965261i	$-0.584148\pi$
$773$	−1.44228e14			−0.522578			−0.261289	+	0.965261i	$0.584148\pi$
$774$	1.28284e13	+	7.23717e13i	0.0461815	+	0.260534i
$775$		0			0
$776$	1.61566e14	−	9.38638e13i	0.574170	−	0.333572i
$777$	−1.70093e14			−0.600593
$778$	1.32263e14	−	2.34446e13i	0.464024	−	0.0822515i
$779$		−	6.80750e13i		−	0.237301i
$780$		0			0
$781$	−3.26915e14			−1.12507
$782$	1.06622e14	+	6.01513e14i	0.364599	+	2.05689i
$783$			7.66574e13i			0.260462i
$784$	−7.29425e13	+	6.16559e13i	−0.246264	+	0.208158i
$785$		0			0
$786$	8.12469e12	−	1.44016e12i	0.0270828	−	0.00480062i
$787$		−	4.14677e14i		−	1.37352i	−0.726882	−	0.686762i	$-0.759031\pi$
$787$		−	4.14677e14i		−	1.37352i	0.726882	−	0.686762i	$-0.240969\pi$
$788$	−1.65901e14	+	6.07220e13i	−0.546031	+	0.199855i
$789$	3.34420e14			1.09372
$790$		0			0
$791$		−	3.69993e14i		−	1.19484i
$792$	4.77562e13	+	8.22016e13i	0.153251	+	0.263788i
$793$	1.91042e14			0.609203
$794$	−1.21167e13	+	2.14776e12i	−0.0383955	+	0.00680588i
$795$		0			0
$796$	1.29935e14	+	3.55001e14i	0.406595	+	1.11087i
$797$	4.54207e14			1.41241			0.706207	−	0.708005i	$-0.250405\pi$
$797$	4.54207e14			1.41241			0.706207	+	0.708005i	$0.250405\pi$
$798$	−1.66465e13	−	9.39116e13i	−0.0514409	−	0.290205i
$799$		−	6.56955e14i		−	2.01744i
$800$		0			0
$801$	−1.37176e14			−0.416021
$802$	−5.20023e14	+	9.21777e13i	−1.56729	+	0.277814i
$803$		−	2.95578e14i		−	0.885307i
$804$	5.50557e14	−	2.01512e14i	1.63878	−	0.599819i
$805$		0			0
$806$	4.76388e13	+	2.68756e14i	0.140051	+	0.790100i
$807$		−	1.41753e14i		−	0.414157i
$808$	1.71693e14	−	9.97473e13i	0.498535	−	0.289631i
$809$	1.46024e14			0.421389			0.210694	−	0.977552i	$-0.432428\pi$
$809$	1.46024e14			0.421389			0.210694	+	0.977552i	$0.432428\pi$
$810$		0			0
$811$			2.49645e14i			0.711572i	0.934567	+	0.355786i	$0.115787\pi$
$811$			2.49645e14i			0.711572i	−0.934567	+	0.355786i	$0.884213\pi$
$812$	−4.49097e13	−	1.22699e14i	−0.127221	−	0.347585i
$813$	1.58054e14			0.444991
$814$	3.05757e13	+	1.72494e14i	0.0855568	+	0.482671i
$815$		0			0
$816$	3.97028e14	+	4.69707e14i	1.09741	+	1.29830i
$817$	−7.59449e13			−0.208636
$818$	1.91016e14	−	3.38590e13i	0.521560	−	0.0924501i
$819$			6.64578e13i			0.180354i
$820$		0			0
$821$	−4.07532e13			−0.109256			−0.0546281	−	0.998507i	$-0.517397\pi$
$821$	−4.07532e13			−0.109256			−0.0546281	+	0.998507i	$0.517397\pi$
$822$	−9.94684e13	−	5.61153e14i	−0.265049	−	1.49528i
$823$			4.29226e14i			1.13681i	0.822750	+	0.568404i	$0.192439\pi$
$823$			4.29226e14i			1.13681i	−0.822750	+	0.568404i	$0.807561\pi$
$824$	2.76452e14	+	4.75851e14i	0.727753	+	1.25267i
$825$		0			0
$826$	−1.53188e14	+	2.71537e13i	−0.398405	+	0.0706201i
$827$			4.37113e14i			1.12997i	0.825102	+	0.564984i	$0.191118\pi$
$827$			4.37113e14i			1.12997i	−0.825102	+	0.564984i	$0.808882\pi$
$828$	5.34273e13	+	1.45970e14i	0.137281	+	0.375071i
$829$	−1.41751e14			−0.362036			−0.181018	−	0.983480i	$-0.557939\pi$
$829$	−1.41751e14			−0.362036			−0.181018	+	0.983480i	$0.557939\pi$
$830$		0			0
$831$			6.09390e14i			1.53776i
$832$	−1.08072e14	+	1.89549e14i	−0.271081	+	0.475449i
$833$	1.93829e14			0.483274
$834$	−3.99882e14	+	7.08820e13i	−0.991065	+	0.175673i
$835$		0			0
$836$	−9.22449e13	+	3.37629e13i	−0.225897	+	0.0826816i
$837$	−4.87389e14			−1.18645
$838$	2.36840e13	+	1.33614e14i	0.0573106	+	0.323319i
$839$		−	3.05400e14i		−	0.734615i	−0.930100	−	0.367308i	$-0.880280\pi$
$839$		−	3.05400e14i		−	0.734615i	0.930100	−	0.367308i	$-0.119720\pi$
$840$		0			0
$841$	−3.77124e14			−0.896404
$842$	2.45770e14	−	4.35645e13i	0.580722	−	0.102937i
$843$			8.56175e14i			2.01106i
$844$	6.34300e13	+	1.73299e14i	0.148109	+	0.404654i
$845$		0			0
$846$	−2.91758e13	−	1.64596e14i	−0.0673242	−	0.379811i
$847$		−	6.68783e13i		−	0.153415i
$848$	−5.82311e14	+	4.92208e14i	−1.32793	+	1.12246i
$849$	−6.49834e14			−1.47321
$850$		0			0
$851$			2.86434e14i			0.641767i
$852$	−5.05357e14	+	1.84968e14i	−1.12564	+	0.412002i
$853$	6.26599e14			1.38754			0.693768	−	0.720198i	$-0.255949\pi$
$853$	6.26599e14			1.38754			0.693768	+	0.720198i	$0.255949\pi$
$854$	−1.01485e14	−	5.72530e14i	−0.223415	−	1.26040i
$855$		0			0
$856$	−3.14004e14	−	5.40487e14i	−0.683228	−	1.17603i
$857$	5.96728e14			1.29084			0.645419	−	0.763828i	$-0.276683\pi$
$857$	5.96728e14			1.29084			0.645419	+	0.763828i	$0.276683\pi$
$858$	3.02588e14	−	5.36358e13i	0.650751	−	0.115350i
$859$			4.03458e13i			0.0862646i	0.999069	+	0.0431323i	$0.0137337\pi$
$859$			4.03458e13i			0.0862646i	−0.999069	+	0.0431323i	$0.986266\pi$
$860$		0			0
$861$	6.48191e14			1.36989
$862$	1.44544e14	+	8.15447e14i	0.303713	+	1.71340i
$863$		−	3.61735e14i		−	0.755677i	−0.925872	−	0.377838i	$-0.876667\pi$
$863$		−	3.61735e14i		−	0.755677i	0.925872	−	0.377838i	$-0.123333\pi$
$864$	−2.99593e14	−	2.49095e14i	−0.622248	−	0.517364i
$865$		0			0
$866$	−2.66164e12	+	4.71794e11i	−0.00546461	+	0.000968641i
$867$		−	6.92485e14i		−	1.41356i
$868$	7.80124e14	−	2.85537e14i	1.58331	−	0.579513i
$869$	4.05085e14			0.817425
$870$		0			0
$871$		−	4.22107e14i		−	0.842039i
$872$	−1.50316e14	+	8.73280e13i	−0.298141	+	0.173209i
$873$	−9.64880e13			−0.190284
$874$	−1.58146e14	+	2.80325e13i	−0.310100	+	0.0549674i
$875$		0			0
$876$	−1.67238e14	−	4.56916e14i	−0.324200	−	0.885759i
$877$	−4.28251e14			−0.825469			−0.412734	−	0.910851i	$-0.635426\pi$
$877$	−4.28251e14			−0.825469			−0.412734	+	0.910851i	$0.635426\pi$
$878$	−9.82636e13	−	5.54356e14i	−0.188330	−	1.06247i
$879$			1.00071e14i			0.190706i
$880$		0			0
$881$	1.66202e14			0.313154			0.156577	−	0.987666i	$-0.449954\pi$
$881$	1.66202e14			0.313154			0.156577	+	0.987666i	$0.449954\pi$
$882$	4.85627e13	−	8.60808e12i	0.0909829	−	0.0161274i
$883$			2.05092e14i			0.382071i	0.981583	+	0.191036i	$0.0611846\pi$
$883$			2.05092e14i			0.382071i	−0.981583	+	0.191036i	$0.938815\pi$
$884$	4.15828e14	−	1.52199e14i	0.770287	−	0.281936i
$885$		0			0
$886$	3.67639e13	+	2.07404e14i	0.0673369	+	0.379882i
$887$			1.46413e14i			0.266663i	0.991072	+	0.133331i	$0.0425674\pi$
$887$			1.46413e14i			0.266663i	−0.991072	+	0.133331i	$0.957433\pi$
$888$	1.44862e14	+	2.49348e14i	0.262355	+	0.451586i
$889$	−1.31231e14			−0.236334
$890$		0			0
$891$			7.20058e14i			1.28227i
$892$	−1.67303e14	−	4.57094e14i	−0.296265	−	0.809434i
$893$	1.72723e14			0.304153
$894$	5.74329e13	+	3.24009e14i	0.100571	+	0.567374i
$895$		0			0
$896$	6.25467e14	+	2.23189e14i	1.08309	+	0.386486i
$897$	5.02462e14			0.865249
$898$	5.90519e14	−	1.04674e14i	1.01123	−	0.179249i
$899$			2.77105e14i			0.471896i
$900$		0			0
$901$	1.54737e15			2.60597
$902$	−1.16518e14	−	6.57340e14i	−0.195147	−	1.10092i
$903$		−	7.23126e14i		−	1.20441i
$904$	−5.42392e14	+	3.15110e14i	−0.898402	+	0.521939i
$905$		0			0
$906$	7.42465e13	−	1.31607e13i	0.121628	−	0.0215595i
$907$			8.70474e14i			1.41814i	0.705138	+	0.709070i	$0.250885\pi$
$907$			8.70474e14i			1.41814i	−0.705138	+	0.709070i	$0.749115\pi$
$908$	−2.49429e14	−	6.81473e14i	−0.404127	−	1.10413i
$909$	−1.02536e14			−0.165218
$910$		0			0
$911$		−	3.80445e14i		−	0.606317i	−0.952940	−	0.303158i	$-0.901959\pi$
$911$		−	3.80445e14i		−	0.606317i	0.952940	−	0.303158i	$-0.0980411\pi$
$912$	−1.23493e14	+	1.04384e14i	−0.195734	+	0.165448i
$913$	−8.95959e14			−1.41232
$914$	7.67978e14	−	1.36130e14i	1.20398	−	0.213413i
$915$		0			0
$916$	−5.70506e14	+	2.08814e14i	−0.884674	+	0.323803i
$917$	−1.80815e13			−0.0278861
$918$	1.38007e14	+	7.78569e14i	0.211684	+	1.19422i
$919$			3.25935e14i			0.497226i	0.968603	+	0.248613i	$0.0799747\pi$
$919$			3.25935e14i			0.497226i	−0.968603	+	0.248613i	$0.920025\pi$
$920$		0			0
$921$	1.16757e15			1.76191
$922$	−3.98405e14	+	7.06201e13i	−0.597958	+	0.105992i
$923$			3.87454e14i			0.578377i
$924$	−3.21481e14	−	8.78329e14i	−0.477305	−	1.30406i
$925$		0			0
$926$	1.00604e14	+	5.67560e14i	0.147761	+	0.833599i
$927$		−	2.84181e14i		−	0.415142i
$928$	−1.41623e14	+	1.70334e14i	−0.205776	+	0.247492i
$929$	−9.65026e13			−0.139464			−0.0697318	−	0.997566i	$-0.522214\pi$
$929$	−9.65026e13			−0.139464			−0.0697318	+	0.997566i	$0.522214\pi$
$930$		0			0
$931$			5.09603e13i			0.0728591i
$932$	6.73548e14	−	2.46528e14i	0.957832	−	0.350580i
$933$	−2.38179e14			−0.336896
$934$	−6.14035e13	−	3.46409e14i	−0.0863890	−	0.487366i
$935$		0			0
$936$	9.74240e13	−	5.65998e13i	0.135608	−	0.0787835i
$937$	−2.64123e14			−0.365686			−0.182843	−	0.983142i	$-0.558530\pi$
$937$	−2.64123e14			−0.365686			−0.182843	+	0.983142i	$0.558530\pi$
$938$	−1.26501e15	+	2.24232e14i	−1.74213	+	0.308804i
$939$		−	2.16863e14i		−	0.297069i
$940$		0			0
$941$	9.75390e14			1.32200			0.660998	−	0.750388i	$-0.270133\pi$
$941$	9.75390e14			1.32200			0.660998	+	0.750388i	$0.270133\pi$
$942$	−1.56287e14	−	8.81698e14i	−0.210702	−	1.18868i
$943$		−	1.09155e15i		−	1.46381i
$944$	1.70271e14	+	2.01441e14i	0.227133	+	0.268712i
$945$		0			0
$946$	−7.33333e14	+	1.29989e14i	−0.967934	+	0.171573i
$947$			9.79557e14i			1.28611i	0.765818	+	0.643057i	$0.222334\pi$
$947$			9.79557e14i			1.28611i	−0.765818	+	0.643057i	$0.777666\pi$
$948$	6.26197e14	−	2.29197e14i	0.817842	−	0.299342i
$949$	−3.50314e14			−0.455120
$950$		0			0
$951$		−	1.37940e14i		−	0.177332i
$952$	−6.77020e14	−	1.16534e15i	−0.865798	−	1.49028i
$953$	6.53731e14			0.831638			0.415819	−	0.909447i	$-0.363495\pi$
$953$	6.53731e14			0.831638			0.415819	+	0.909447i	$0.363495\pi$
$954$	3.87683e14	−	6.87196e13i	0.490608	−	0.0869638i
$955$		0			0
$956$	−2.68514e14	−	7.33615e14i	−0.336262	−	0.918711i
$957$	3.11989e14			0.388668
$958$	1.36093e14	+	7.67772e14i	0.168659	+	0.951491i
$959$			1.24885e15i			1.53963i
$960$		0			0
$961$	−9.42214e14			−1.14956
$962$	2.04436e14	−	3.62378e13i	0.248132	−	0.0439832i
$963$			3.22782e14i			0.389743i
$964$	−4.02925e14	+	1.47476e14i	−0.483993	+	0.177148i
$965$		0			0
$966$	−2.66918e14	−	1.50582e15i	−0.317316	−	1.79015i
$967$		−	1.15253e15i		−	1.36308i	−0.731781	−	0.681540i	$-0.761311\pi$
$967$		−	1.15253e15i		−	1.36308i	0.731781	−	0.681540i	$-0.238689\pi$
$968$	−9.80404e13	+	5.69579e13i	−0.115353	+	0.0670158i
$969$	3.28155e14			0.384114
$970$		0			0
$971$			2.94848e14i			0.341588i	0.985307	+	0.170794i	$0.0546332\pi$
$971$			2.94848e14i			0.341588i	−0.985307	+	0.170794i	$0.945367\pi$
$972$	1.66083e14	+	4.53761e14i	0.191423	+	0.522993i
$973$	8.89938e14			1.02046
$974$	1.51470e14	+	8.54523e14i	0.172796	+	0.974830i
$975$		0			0
$976$	−7.52871e14	+	6.36376e14i	−0.850103	+	0.718563i
$977$	1.17717e15			1.32241			0.661206	−	0.750204i	$-0.270045\pi$
$977$	1.17717e15			1.32241			0.661206	+	0.750204i	$0.270045\pi$
$978$	−3.91112e14	+	6.93274e13i	−0.437126	+	0.0774838i
$979$		−	1.38998e15i		−	1.54560i
$980$		0			0
$981$	8.97695e13			0.0988061
$982$	8.88300e13	+	5.01137e14i	0.0972753	+	0.548781i
$983$			1.00446e14i			0.109437i	0.998502	+	0.0547187i	$0.0174262\pi$
$983$			1.00446e14i			0.109437i	−0.998502	+	0.0547187i	$0.982574\pi$
$984$	−5.52041e14	−	9.50216e14i	−0.598406	−	1.03002i
$985$		0			0
$986$	4.42656e14	−	7.84639e13i	0.474987	−	0.0841948i
$987$			1.64462e15i			1.75581i
$988$	4.00153e13	+	1.09327e14i	0.0425051	+	0.116130i
$989$	−1.21774e15			−1.28698
$990$		0			0
$991$		−	3.04540e14i		−	0.318622i	−0.987228	−	0.159311i	$-0.949073\pi$
$991$		−	3.04540e14i		−	0.318622i	0.987228	−	0.159311i	$-0.0509272\pi$
$992$	−1.08299e15	−	9.00443e14i	−1.12737	−	0.937341i
$993$	6.81383e14			0.705740
$994$	1.16116e15	−	2.05823e14i	1.19663	−	0.212111i
$995$		0			0
$996$	−1.38501e15	+	5.06933e14i	−1.41304	+	0.517195i
$997$	4.28019e14			0.434498			0.217249	−	0.976116i	$-0.430292\pi$
$997$	4.28019e14			0.434498			0.217249	+	0.976116i	$0.430292\pi$
$998$	9.47522e13	+	5.34547e14i	0.0957055	+	0.539924i
$999$			3.70746e14i			0.372606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.11.b.e.51.19		20
4.3	odd	2	inner	100.11.b.e.51.20		20
5.2	odd	4		100.11.d.c.99.22		40
5.3	odd	4		100.11.d.c.99.19		40
5.4	even	2		20.11.b.a.11.2	yes	20
15.14	odd	2		180.11.c.a.91.19		20
20.3	even	4		100.11.d.c.99.21		40
20.7	even	4		100.11.d.c.99.20		40
20.19	odd	2		20.11.b.a.11.1	✓	20
40.19	odd	2		320.11.b.d.191.16		20
40.29	even	2		320.11.b.d.191.5		20
60.59	even	2		180.11.c.a.91.20		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.b.a.11.1	✓	20	20.19	odd	2
20.11.b.a.11.2	yes	20	5.4	even	2
100.11.b.e.51.19		20	1.1	even	1	trivial
100.11.b.e.51.20		20	4.3	odd	2	inner
100.11.d.c.99.19		40	5.3	odd	4
100.11.d.c.99.20		40	20.7	even	4
100.11.d.c.99.21		40	20.3	even	4
100.11.d.c.99.22		40	5.2	odd	4
180.11.c.a.91.19		20	15.14	odd	2
180.11.c.a.91.20		20	60.59	even	2
320.11.b.d.191.5		20	40.29	even	2
320.11.b.d.191.16		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)

\(f(q)\)	\(=\)	\(q+(31.5088 - 5.58516i) q^{2} -275.626i q^{3} +(961.612 - 351.964i) q^{4} +(-1539.42 - 8684.66i) q^{6} +19327.7i q^{7} +(28333.5 - 16460.7i) q^{8} -16920.9 q^{9} +O(q^{10})\)	\(q+(31.5088 - 5.58516i) q^{2} -275.626i q^{3} +(961.612 - 351.964i) q^{4} +(-1539.42 - 8684.66i) q^{6} +19327.7i q^{7} +(28333.5 - 16460.7i) q^{8} -16920.9 q^{9} -171457. i q^{11} +(-97010.5 - 265046. i) q^{12} -203208. q^{13} +(107948. + 608993. i) q^{14} +(800819. - 676905. i) q^{16} -2.12800e6 q^{17} +(-533158. + 94506.1i) q^{18} -559482. i q^{19} +5.32723e6 q^{21} +(-957618. - 5.40242e6i) q^{22} -8.97100e6i q^{23} +(-4.53701e6 - 7.80946e6i) q^{24} +(-6.40286e6 + 1.13495e6i) q^{26} -1.16116e7i q^{27} +(6.80265e6 + 1.85858e7i) q^{28} -6.60179e6 q^{29} -4.19743e7i q^{31} +(2.14522e7 - 2.58012e7i) q^{32} -4.72582e7 q^{33} +(-6.70509e7 + 1.18852e7i) q^{34} +(-1.62714e7 + 5.95555e6i) q^{36} -3.19289e7 q^{37} +(-3.12480e6 - 1.76286e7i) q^{38} +5.60096e7i q^{39} +1.21675e8 q^{41} +(1.67855e8 - 2.97534e7i) q^{42} -1.35742e8i q^{43} +(-6.03468e7 - 1.64876e8i) q^{44} +(-5.01045e7 - 2.82666e8i) q^{46} +3.08719e8i q^{47} +(-1.86573e8 - 2.20727e8i) q^{48} -9.10849e7 q^{49} +5.86534e8i q^{51} +(-1.95408e8 + 7.15220e7i) q^{52} -7.27144e8 q^{53} +(-6.48527e7 - 3.65868e8i) q^{54} +(3.18148e8 + 5.47621e8i) q^{56} -1.54208e8 q^{57} +(-2.08015e8 + 3.68721e7i) q^{58} +2.51543e8i q^{59} -9.40126e8 q^{61} +(-2.34433e8 - 1.32256e9i) q^{62} -3.27043e8i q^{63} +(5.31831e8 - 9.32779e8i) q^{64} +(-1.48905e9 + 2.63945e8i) q^{66} +2.07721e9i q^{67} +(-2.04631e9 + 7.48980e8i) q^{68} -2.47264e9 q^{69} -1.90668e9i q^{71} +(-4.79429e8 + 2.78531e8i) q^{72} +1.72391e9 q^{73} +(-1.00604e9 + 1.78328e8i) q^{74} +(-1.96917e8 - 5.38004e8i) q^{76} +3.31388e9 q^{77} +(3.12823e8 + 1.76480e9i) q^{78} +2.36260e9i q^{79} -4.19963e9 q^{81} +(3.83384e9 - 6.79575e8i) q^{82} -5.22555e9i q^{83} +(5.12272e9 - 1.87499e9i) q^{84} +(-7.58139e8 - 4.27706e9i) q^{86} +1.81963e9i q^{87} +(-2.82231e9 - 4.85799e9i) q^{88} +8.10687e9 q^{89} -3.92755e9i q^{91} +(-3.15747e9 - 8.62662e9i) q^{92} -1.15692e10 q^{93} +(1.72425e9 + 9.72737e9i) q^{94} +(-7.11149e9 - 5.91280e9i) q^{96} +5.70229e9 q^{97} +(-2.86998e9 + 5.08724e8i) q^{98} +2.90122e9i 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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