LMFDB - Embedded newform 100.11.b.e.51.2

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			51.2
Root			$-103.213i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.11.b.e.51.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-30.9316 + 8.19968i) q^{2} -206.425i q^{3} +(889.530 - 507.259i) q^{4} +(1692.62 + 6385.07i) q^{6} -1527.38i q^{7} +(-23355.3 + 22984.2i) q^{8} +16437.6 q^{9} +O(q^{10})$	\(q+(-30.9316 + 8.19968i) q^{2} -206.425i q^{3} +(889.530 - 507.259i) q^{4} +(1692.62 + 6385.07i) q^{6} -1527.38i q^{7} +(-23355.3 + 22984.2i) q^{8} +16437.6 q^{9} +294294. i q^{11} +(-104711. - 183622. i) q^{12} -198131. q^{13} +(12524.1 + 47244.5i) q^{14} +(533953. - 902445. i) q^{16} -367959. q^{17} +(-508442. + 134783. i) q^{18} -919311. i q^{19} -315291. q^{21} +(-2.41311e6 - 9.10298e6i) q^{22} +2.57690e6i q^{23} +(4.74452e6 + 4.82111e6i) q^{24} +(6.12851e6 - 1.62461e6i) q^{26} -1.55823e7i q^{27} +(-774779. - 1.35865e6i) q^{28} -1.40898e7 q^{29} -4.90356e7i q^{31} +(-9.11626e6 + 3.22923e7i) q^{32} +6.07497e7 q^{33} +(1.13816e7 - 3.01715e6i) q^{34} +(1.46218e7 - 8.33812e6i) q^{36} +1.21502e8 q^{37} +(7.53806e6 + 2.84358e7i) q^{38} +4.08993e7i q^{39} -1.48908e8 q^{41} +(9.75245e6 - 2.58528e6i) q^{42} +1.41368e8i q^{43} +(1.49283e8 + 2.61783e8i) q^{44} +(-2.11297e7 - 7.97076e7i) q^{46} +3.99006e7i q^{47} +(-1.86287e8 - 1.10221e8i) q^{48} +2.80142e8 q^{49} +7.59561e7i q^{51} +(-1.76244e8 + 1.00504e8i) q^{52} -1.03715e8 q^{53} +(1.27770e8 + 4.81987e8i) q^{54} +(3.51057e7 + 3.56724e7i) q^{56} -1.89769e8 q^{57} +(4.35820e8 - 1.15532e8i) q^{58} -4.38769e8i q^{59} -2.83067e8 q^{61} +(4.02077e8 + 1.51675e9i) q^{62} -2.51065e7i q^{63} +(1.71940e7 - 1.07360e9i) q^{64} +(-1.87909e9 + 4.98128e8i) q^{66} -2.00990e9i q^{67} +(-3.27311e8 + 1.86651e8i) q^{68} +5.31936e8 q^{69} -1.54881e9i q^{71} +(-3.83905e8 + 3.77805e8i) q^{72} -3.44009e9 q^{73} +(-3.75824e9 + 9.96274e8i) q^{74} +(-4.66329e8 - 8.17756e8i) q^{76} +4.49499e8 q^{77} +(-3.35361e8 - 1.26508e9i) q^{78} -2.88212e9i q^{79} -2.24597e9 q^{81} +(4.60595e9 - 1.22100e9i) q^{82} -3.41069e9i q^{83} +(-2.80461e8 + 1.59934e8i) q^{84} +(-1.15917e9 - 4.37273e9i) q^{86} +2.90849e9i q^{87} +(-6.76411e9 - 6.87330e9i) q^{88} -2.47857e9 q^{89} +3.02622e8i q^{91} +(1.30715e9 + 2.29223e9i) q^{92} -1.01222e10 q^{93} +(-3.27173e8 - 1.23419e9i) q^{94} +(6.66595e9 + 1.88183e9i) q^{96} +2.70022e9 q^{97} +(-8.66526e9 + 2.29708e9i) q^{98} +4.83748e9i 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 $

$2$	−30.9316	+	8.19968i	−0.966613	+	0.256240i
$2$	−30.9316	+	8.19968i	−0.966613	+	0.256240i
$3$		−	206.425i		−	0.849487i	−0.905314	−	0.424743i	$-0.860364\pi$
$3$		−	206.425i		−	0.849487i	0.905314	−	0.424743i	$-0.139636\pi$
$4$	889.530	−	507.259i	0.868682	−	0.495370i
$5$		0			0
$5$		0			0
$6$	1692.62	+	6385.07i	0.217673	+	0.821125i
$7$		−	1527.38i		−	0.0908778i	−0.998967	−	0.0454389i	$-0.985531\pi$
$7$		−	1527.38i		−	0.0908778i	0.998967	−	0.0454389i	$-0.0144686\pi$
$8$	−23355.3	+	22984.2i	−0.712746	+	0.701422i
$9$	16437.6			0.278372
$10$		0			0
$11$			294294.i			1.82733i	0.406465	+	0.913666i	$0.366761\pi$
$11$			294294.i			1.82733i	−0.406465	+	0.913666i	$0.633239\pi$
$12$	−104711.	−	183622.i	−0.420810	−	0.737934i
$13$	−198131.			−0.533625			−0.266812	−	0.963749i	$-0.585970\pi$
$13$	−198131.			−0.533625			−0.266812	+	0.963749i	$0.585970\pi$
$14$	12524.1	+	47244.5i	0.0232865	+	0.0878437i
$15$		0			0
$16$	533953.	−	902445.i	0.509217	−	0.860638i
$17$	−367959.			−0.259152			−0.129576	−	0.991569i	$-0.541362\pi$
$17$	−367959.			−0.259152			−0.129576	+	0.991569i	$0.541362\pi$
$18$	−508442.	+	134783.i	−0.269078	+	0.0713302i
$19$		−	919311.i		−	0.371274i	−0.982618	−	0.185637i	$-0.940565\pi$
$19$		−	919311.i		−	0.371274i	0.982618	−	0.185637i	$-0.0594349\pi$
$20$		0			0
$21$	−315291.			−0.0771995
$22$	−2.41311e6	−	9.10298e6i	−0.468236	−	1.76632i
$23$			2.57690e6i			0.400366i	0.979758	+	0.200183i	$0.0641537\pi$
$23$			2.57690e6i			0.400366i	−0.979758	+	0.200183i	$0.935846\pi$
$24$	4.74452e6	+	4.82111e6i	0.595849	+	0.605468i
$25$		0			0
$26$	6.12851e6	−	1.62461e6i	0.515808	−	0.136736i
$27$		−	1.55823e7i		−	1.08596i
$28$	−774779.	−	1.35865e6i	−0.0450182	−	0.0789440i
$29$	−1.40898e7			−0.686934			−0.343467	−	0.939165i	$-0.611601\pi$
$29$	−1.40898e7			−0.686934			−0.343467	+	0.939165i	$0.611601\pi$
$30$		0			0
$31$		−	4.90356e7i		−	1.71279i	−0.516324	−	0.856393i	$-0.672700\pi$
$31$		−	4.90356e7i		−	1.71279i	0.516324	−	0.856393i	$-0.327300\pi$
$32$	−9.11626e6	+	3.22923e7i	−0.271686	+	0.962386i
$33$	6.07497e7			1.55229
$34$	1.13816e7	−	3.01715e6i	0.250500	−	0.0664052i
$35$		0			0
$36$	1.46218e7	−	8.33812e6i	0.241817	−	0.137897i
$37$	1.21502e8			1.75216			0.876079	−	0.482168i	$-0.160150\pi$
$37$	1.21502e8			1.75216			0.876079	+	0.482168i	$0.160150\pi$
$38$	7.53806e6	+	2.84358e7i	0.0951353	+	0.358878i
$39$			4.08993e7i			0.453307i
$40$		0			0
$41$	−1.48908e8			−1.28528			−0.642640	−	0.766168i	$-0.722161\pi$
$41$	−1.48908e8			−1.28528			−0.642640	+	0.766168i	$0.722161\pi$
$42$	9.75245e6	−	2.58528e6i	0.0746221	−	0.0197816i
$43$			1.41368e8i			0.961630i	0.876822	+	0.480815i	$0.159659\pi$
$43$			1.41368e8i			0.961630i	−0.876822	+	0.480815i	$0.840341\pi$
$44$	1.49283e8	+	2.61783e8i	0.905206	+	1.58737i
$45$		0			0
$46$	−2.11297e7	−	7.97076e7i	−0.102590	−	0.386999i
$47$			3.99006e7i			0.173976i	0.996209	+	0.0869882i	$0.0277243\pi$
$47$			3.99006e7i			0.173976i	−0.996209	+	0.0869882i	$0.972276\pi$
$48$	−1.86287e8	−	1.10221e8i	−0.731101	−	0.432573i
$49$	2.80142e8			0.991741
$50$		0			0
$51$			7.59561e7i			0.220146i
$52$	−1.76244e8	+	1.00504e8i	−0.463550	+	0.264342i
$53$	−1.03715e8			−0.248005			−0.124003	−	0.992282i	$-0.539573\pi$
$53$	−1.03715e8			−0.248005			−0.124003	+	0.992282i	$0.539573\pi$
$54$	1.27770e8	+	4.81987e8i	0.278267	+	1.04970i
$55$		0			0
$56$	3.51057e7	+	3.56724e7i	0.0637438	+	0.0647728i
$57$	−1.89769e8			−0.315392
$58$	4.35820e8	−	1.15532e8i	0.663999	−	0.176020i
$59$		−	4.38769e8i		−	0.613728i	−0.951753	−	0.306864i	$-0.900720\pi$
$59$		−	4.38769e8i		−	0.613728i	0.951753	−	0.306864i	$-0.0992797\pi$
$60$		0			0
$61$	−2.83067e8			−0.335151			−0.167575	−	0.985859i	$-0.553594\pi$
$61$	−2.83067e8			−0.335151			−0.167575	+	0.985859i	$0.553594\pi$
$62$	4.02077e8	+	1.51675e9i	0.438885	+	1.65560i
$63$		−	2.51065e7i		−	0.0252979i
$64$	1.71940e7	−	1.07360e9i	0.0160132	−	0.999872i
$65$		0			0
$66$	−1.87909e9	+	4.98128e8i	−1.50047	+	0.397760i
$67$		−	2.00990e9i		−	1.48868i	−0.667801	−	0.744340i	$-0.732764\pi$
$67$		−	2.00990e9i		−	1.48868i	0.667801	−	0.744340i	$-0.267236\pi$
$68$	−3.27311e8	+	1.86651e8i	−0.225121	+	0.128376i
$69$	5.31936e8			0.340106
$70$		0			0
$71$		−	1.54881e9i		−	0.858434i	−0.903201	−	0.429217i	$-0.858790\pi$
$71$		−	1.54881e9i		−	0.858434i	0.903201	−	0.429217i	$-0.141210\pi$
$72$	−3.83905e8	+	3.77805e8i	−0.198409	+	0.195257i
$73$	−3.44009e9			−1.65942			−0.829709	−	0.558196i	$-0.811494\pi$
$73$	−3.44009e9			−1.65942			−0.829709	+	0.558196i	$0.811494\pi$
$74$	−3.75824e9	+	9.96274e8i	−1.69366	+	0.448973i
$75$		0			0
$76$	−4.66329e8	−	8.17756e8i	−0.183918	−	0.322519i
$77$	4.49499e8			0.166064
$78$	−3.35361e8	−	1.26508e9i	−0.116155	−	0.438172i
$79$		−	2.88212e9i		−	0.936649i	−0.883556	−	0.468325i	$-0.844858\pi$
$79$		−	2.88212e9i		−	0.936649i	0.883556	−	0.468325i	$-0.155142\pi$
$80$		0			0
$81$	−2.24597e9			−0.644137
$82$	4.60595e9	−	1.22100e9i	1.24237	−	0.329340i
$83$		−	3.41069e9i		−	0.865868i	−0.901426	−	0.432934i	$-0.857478\pi$
$83$		−	3.41069e9i		−	0.865868i	0.901426	−	0.432934i	$-0.142522\pi$
$84$	−2.80461e8	+	1.59934e8i	−0.0670618	+	0.0382423i
$85$		0			0
$86$	−1.15917e9	−	4.37273e9i	−0.246408	−	0.929525i
$87$			2.90849e9i			0.583541i
$88$	−6.76411e9	−	6.87330e9i	−1.28173	−	1.30242i
$89$	−2.47857e9			−0.443865			−0.221932	−	0.975062i	$-0.571236\pi$
$89$	−2.47857e9			−0.443865			−0.221932	+	0.975062i	$0.571236\pi$
$90$		0			0
$91$			3.02622e8i			0.0484946i
$92$	1.30715e9	+	2.29223e9i	0.198330	+	0.347791i
$93$	−1.01222e10			−1.45499
$94$	−3.27173e8	−	1.23419e9i	−0.0445798	−	0.168168i
$95$		0			0
$96$	6.66595e9	+	1.88183e9i	0.817534	+	0.230793i
$97$	2.70022e9			0.314442			0.157221	−	0.987563i	$-0.449746\pi$
$97$	2.70022e9			0.314442			0.157221	+	0.987563i	$0.449746\pi$
$98$	−8.66526e9	+	2.29708e9i	−0.958630	+	0.254124i
$99$			4.83748e9i			0.508679i
$100$		0			0
$101$	−1.16539e10			−1.10883			−0.554413	−	0.832242i	$-0.687057\pi$
$101$	−1.16539e10			−1.10883			−0.554413	+	0.832242i	$0.687057\pi$
$102$	−6.22816e8	−	2.34944e9i	−0.0564103	−	0.212796i
$103$		−	1.62063e10i		−	1.39797i	−0.715136	−	0.698986i	$-0.753635\pi$
$103$		−	1.62063e10i		−	1.39797i	0.715136	−	0.698986i	$-0.246365\pi$
$104$	4.62740e9	−	4.55389e9i	0.380339	−	0.374296i
$105$		0			0
$106$	3.20806e9	−	8.50427e8i	0.239725	−	0.0635488i
$107$			1.62492e9i			0.115854i	0.998321	+	0.0579271i	$0.0184491\pi$
$107$			1.62492e9i			0.115854i	−0.998321	+	0.0579271i	$0.981551\pi$
$108$	−7.90428e9	−	1.38610e10i	−0.537952	−	0.943354i
$109$	−1.11266e10			−0.723152			−0.361576	−	0.932343i	$-0.617761\pi$
$109$	−1.11266e10			−0.723152			−0.361576	+	0.932343i	$0.617761\pi$
$110$		0			0
$111$		−	2.50810e10i		−	1.48843i
$112$	−1.37838e9	−	8.15551e8i	−0.0782129	−	0.0462765i
$113$	3.01321e9			0.163545			0.0817724	−	0.996651i	$-0.473942\pi$
$113$	3.01321e9			0.163545			0.0817724	+	0.996651i	$0.473942\pi$
$114$	5.86987e9	−	1.55605e9i	0.304862	−	0.0808162i
$115$		0			0
$116$	−1.25333e10	+	7.14718e9i	−0.596727	+	0.340286i
$117$	−3.25680e9			−0.148546
$118$	3.59777e9	+	1.35718e10i	0.157262	+	0.593238i
$119$			5.62015e8i			0.0235512i
$120$		0			0
$121$	−6.06714e10			−2.33914
$122$	8.75572e9	−	2.32106e9i	0.323961	−	0.0858790i
$123$			3.07383e10i			1.09183i
$124$	−2.48738e10	−	4.36187e10i	−0.848463	−	1.48787i
$125$		0			0
$126$	2.05866e8	+	7.76586e8i	0.00648233	+	0.0244533i
$127$			4.21591e10i			1.27607i	0.770009	+	0.638033i	$0.220252\pi$
$127$			4.21591e10i			1.27607i	−0.770009	+	0.638033i	$0.779748\pi$
$128$	8.27137e9	+	3.33493e10i	0.240729	+	0.970592i
$129$	2.91819e10			0.816892
$130$		0			0
$131$			4.76933e10i			1.23623i	0.786086	+	0.618117i	$0.212104\pi$
$131$			4.76933e10i			1.23623i	−0.786086	+	0.618117i	$0.787896\pi$
$132$	5.40387e10	−	3.08158e10i	1.34845	−	0.768960i
$133$	−1.40414e9			−0.0337406
$134$	1.64806e10	+	6.21696e10i	0.381459	+	1.43898i
$135$		0			0
$136$	8.59378e9	−	8.45725e9i	0.184710	−	0.181775i
$137$	−8.32695e10			−1.72537			−0.862687	−	0.505738i	$-0.831220\pi$
$137$	−8.32695e10			−1.72537			−0.862687	+	0.505738i	$0.831220\pi$
$138$	−1.64537e10	+	4.36171e9i	−0.328751	+	0.0871488i
$139$			6.32987e10i			1.21989i	0.792444	+	0.609945i	$0.208809\pi$
$139$			6.32987e10i			1.21989i	−0.792444	+	0.609945i	$0.791191\pi$
$140$		0			0
$141$	8.23650e9			0.147791
$142$	1.26998e10	+	4.79073e10i	0.219965	+	0.829774i
$143$		−	5.83087e10i		−	0.975109i
$144$	8.77690e9	−	1.48340e10i	0.141752	−	0.239578i
$145$		0			0
$146$	1.06408e11	−	2.82077e10i	1.60401	−	0.425209i
$147$		−	5.78285e10i		−	0.842471i
$148$	1.08079e11	−	6.16328e10i	1.52207	−	0.867967i
$149$	1.38919e11			1.89161			0.945805	−	0.324735i	$-0.105275\pi$
$149$	1.38919e11			1.89161			0.945805	+	0.324735i	$0.105275\pi$
$150$		0			0
$151$		−	1.00714e11i		−	1.28294i	−0.767149	−	0.641469i	$-0.778325\pi$
$151$		−	1.00714e11i		−	1.28294i	0.767149	−	0.641469i	$-0.221675\pi$
$152$	2.11296e10	+	2.14708e10i	0.260420	+	0.264624i
$153$	−6.04837e9			−0.0721408
$154$	−1.39037e10	+	3.68575e9i	−0.160520	+	0.0425523i
$155$		0			0
$156$	2.07465e10	+	3.63811e10i	0.224555	+	0.393780i
$157$	−8.15950e10			−0.855393			−0.427696	−	0.903922i	$-0.640675\pi$
$157$	−8.15950e10			−0.855393			−0.427696	+	0.903922i	$0.640675\pi$
$158$	2.36325e10	+	8.91487e10i	0.240007	+	0.905378i
$159$			2.14093e10i			0.210677i
$160$		0			0
$161$	3.93591e9			0.0363844
$162$	6.94713e10	−	1.84162e10i	0.622631	−	0.165054i
$163$			1.23455e11i			1.07293i	0.843924	+	0.536463i	$0.180240\pi$
$163$			1.23455e11i			1.07293i	−0.843924	+	0.536463i	$0.819760\pi$
$164$	−1.32458e11	+	7.55347e10i	−1.11650	+	0.636689i
$165$		0			0
$166$	2.79666e10	+	1.05498e11i	0.221870	+	0.836959i
$167$		−	1.93005e11i		−	1.48589i	−0.669354	−	0.742943i	$-0.733429\pi$
$167$		−	1.93005e11i		−	1.48589i	0.669354	−	0.742943i	$-0.266571\pi$
$168$	7.36369e9	−	7.24671e9i	0.0550236	−	0.0541495i
$169$	−9.86026e10			−0.715245
$170$		0			0
$171$		−	1.51113e10i		−	0.103352i
$172$	7.17101e10	+	1.25751e11i	0.476363	+	0.835351i
$173$	5.57217e10			0.359579			0.179789	−	0.983705i	$-0.442458\pi$
$173$	5.57217e10			0.359579			0.179789	+	0.983705i	$0.442458\pi$
$174$	−2.38487e10	−	8.99643e10i	−0.149527	−	0.564058i
$175$		0			0
$176$	2.65584e11	+	1.57139e11i	1.57267	+	0.930509i
$177$	−9.05731e10			−0.521354
$178$	7.66661e10	−	2.03235e10i	0.429046	−	0.113736i
$179$		−	2.93214e11i		−	1.59558i	−0.602933	−	0.797792i	$-0.706001\pi$
$179$		−	2.93214e11i		−	1.59558i	0.602933	−	0.797792i	$-0.293999\pi$
$180$		0			0
$181$	−2.72240e11			−1.40139			−0.700695	−	0.713461i	$-0.747127\pi$
$181$	−2.72240e11			−1.40139			−0.700695	+	0.713461i	$0.747127\pi$
$182$	−2.48141e9	−	9.36059e9i	−0.0124263	−	0.0468756i
$183$			5.84322e10i			0.284706i
$184$	−5.92279e10	−	6.01840e10i	−0.280826	−	0.285359i
$185$		0			0
$186$	3.13096e11	−	8.29988e10i	1.40641	−	0.372827i
$187$		−	1.08288e11i		−	0.473557i
$188$	2.02400e10	+	3.54928e10i	0.0861827	+	0.151130i
$189$	−2.38002e10			−0.0986897
$190$		0			0
$191$			2.99399e11i			1.17783i	0.808195	+	0.588916i	$0.200445\pi$
$191$			2.99399e11i			1.17783i	−0.808195	+	0.588916i	$0.799555\pi$
$192$	−2.21619e11	−	3.54928e9i	−0.849378	−	0.0136030i
$193$	3.18585e11			1.18970			0.594852	−	0.803835i	$-0.297211\pi$
$193$	3.18585e11			1.18970			0.594852	+	0.803835i	$0.297211\pi$
$194$	−8.35223e10	+	2.21410e10i	−0.303944	+	0.0805727i
$195$		0			0
$196$	2.49195e11	−	1.42105e11i	0.861508	−	0.491279i
$197$	−4.95289e11			−1.66927			−0.834637	−	0.550801i	$-0.814322\pi$
$197$	−4.95289e11			−1.66927			−0.834637	+	0.550801i	$0.814322\pi$
$198$	−3.96658e10	−	1.49631e11i	−0.130344	−	0.491696i
$199$		−	1.49165e11i		−	0.477972i	−0.971023	−	0.238986i	$-0.923185\pi$
$199$		−	1.49165e11i		−	0.477972i	0.971023	−	0.238986i	$-0.0768150\pi$
$200$		0			0
$201$	−4.14895e11			−1.26461
$202$	3.60473e11	−	9.55581e10i	1.07181	−	0.284126i
$203$			2.15205e10i			0.0624270i
$204$	3.85294e10	+	6.75652e10i	0.109054	+	0.191237i
$205$		0			0
$206$	1.32887e11	+	5.01288e11i	0.358216	+	1.35130i
$207$			4.23580e10i			0.111451i
$208$	−1.05793e11	+	1.78802e11i	−0.271731	+	0.459258i
$209$	2.70548e11			0.678441
$210$		0			0
$211$		−	4.40130e11i		−	1.05237i	−0.850370	−	0.526186i	$-0.823622\pi$
$211$		−	4.40130e11i		−	1.05237i	0.850370	−	0.526186i	$-0.176378\pi$
$212$	−9.22573e10	+	5.26102e10i	−0.215438	+	0.122854i
$213$	−3.19714e11			−0.729228
$214$	−1.33238e10	−	5.02613e10i	−0.0296865	−	0.111986i
$215$		0			0
$216$	3.58148e11	+	3.63930e11i	0.761717	+	0.774014i
$217$	−7.48962e10			−0.155654
$218$	3.44164e11	−	9.12346e10i	0.699009	−	0.185301i
$219$			7.10122e11i			1.40965i
$220$		0			0
$221$	7.29041e10			0.138290
$222$	2.05656e11	+	7.75796e11i	0.381397	+	1.43874i
$223$		−	9.51115e10i		−	0.172468i	−0.996275	−	0.0862340i	$-0.972517\pi$
$223$		−	9.51115e10i		−	0.172468i	0.996275	−	0.0862340i	$-0.0274833\pi$
$224$	4.93228e10	+	1.39240e10i	0.0874596	+	0.0246902i
$225$		0			0
$226$	−9.32034e10	+	2.47073e10i	−0.158085	+	0.0419067i
$227$			1.42996e11i			0.237244i	0.992940	+	0.118622i	$0.0378476\pi$
$227$			1.42996e11i			0.237244i	−0.992940	+	0.118622i	$0.962152\pi$
$228$	−1.68805e11	+	9.62621e10i	−0.273976	+	0.156236i
$229$	8.22920e11			1.30671			0.653356	−	0.757050i	$-0.273360\pi$
$229$	8.22920e11			1.30671			0.653356	+	0.757050i	$0.273360\pi$
$230$		0			0
$231$		−	9.27880e10i		−	0.141069i
$232$	3.29071e11	−	3.23843e11i	0.489609	−	0.481831i
$233$	−1.15258e11			−0.167838			−0.0839192	−	0.996473i	$-0.526744\pi$
$233$	−1.15258e11			−0.167838			−0.0839192	+	0.996473i	$0.526744\pi$
$234$	1.00738e11	−	2.67047e10i	0.143587	−	0.0380635i
$235$		0			0
$236$	−2.22570e11	−	3.90299e11i	−0.304023	−	0.533135i
$237$	−5.94943e11			−0.795671
$238$	−4.60834e9	−	1.73840e10i	−0.00603476	−	0.0227649i
$239$			7.84274e11i			1.00572i	0.864367	+	0.502862i	$0.167719\pi$
$239$			7.84274e11i			1.00572i	−0.864367	+	0.502862i	$0.832281\pi$
$240$		0			0
$241$	−1.28221e12			−1.57715			−0.788576	−	0.614938i	$-0.789181\pi$
$241$	−1.28221e12			−1.57715			−0.788576	+	0.614938i	$0.789181\pi$
$242$	1.87666e12	−	4.97486e11i	2.26105	−	0.599382i
$243$		−	4.56498e11i		−	0.538775i
$244$	−2.51797e11	+	1.43588e11i	−0.291139	+	0.166024i
$245$		0			0
$246$	−2.52044e11	−	9.50785e11i	−0.279770	−	1.05538i
$247$			1.82144e11i			0.198121i
$248$	1.12704e12	+	1.14524e12i	1.20139	+	1.22078i
$249$	−7.04052e11			−0.735543
$250$		0			0
$251$		−	6.60746e11i		−	0.663233i	−0.943414	−	0.331616i	$-0.892406\pi$
$251$		−	6.60746e11i		−	0.663233i	0.943414	−	0.331616i	$-0.107594\pi$
$252$	−1.27355e10	−	2.23330e10i	−0.0125318	−	0.0219758i
$253$	−7.58364e11			−0.731602
$254$	−3.45692e11	−	1.30405e12i	−0.326979	−	1.23346i
$255$		0			0
$256$	−5.29301e11	−	9.63725e11i	−0.481396	−	0.876503i
$257$	1.79592e10			0.0160185			0.00800924	−	0.999968i	$-0.497451\pi$
$257$	1.79592e10			0.0160185			0.00800924	+	0.999968i	$0.497451\pi$
$258$	−9.02643e11	+	2.39282e11i	−0.789619	+	0.209321i
$259$		−	1.85580e11i		−	0.159232i
$260$		0			0
$261$	−2.31603e11			−0.191223
$262$	−3.91070e11	−	1.47523e12i	−0.316773	−	1.19496i
$263$			6.81244e11i			0.541407i	0.962663	+	0.270703i	$0.0872563\pi$
$263$			6.81244e11i			0.541407i	−0.962663	+	0.270703i	$0.912744\pi$
$264$	−1.41882e12	+	1.39628e12i	−1.10639	+	1.08881i
$265$		0			0
$266$	4.34324e10	−	1.15135e10i	0.0326141	−	0.00864569i
$267$			5.11639e11i			0.377057i
$268$	−1.01954e12	−	1.78787e12i	−0.737447	−	1.29319i
$269$	9.92471e11			0.704622			0.352311	−	0.935883i	$-0.385396\pi$
$269$	9.92471e11			0.704622			0.352311	+	0.935883i	$0.385396\pi$
$270$		0			0
$271$			7.25450e10i			0.0496319i	0.999692	+	0.0248160i	$0.00789998\pi$
$271$			7.25450e10i			0.0496319i	−0.999692	+	0.0248160i	$0.992100\pi$
$272$	−1.96473e11	+	3.32063e11i	−0.131965	+	0.223036i
$273$	6.24689e10			0.0411956
$274$	2.57566e12	−	6.82784e11i	1.66777	−	0.442110i
$275$		0			0
$276$	4.73174e11	−	2.69829e11i	0.295444	−	0.168478i
$277$	−3.65227e11			−0.223957			−0.111978	−	0.993711i	$-0.535719\pi$
$277$	−3.65227e11			−0.223957			−0.111978	+	0.993711i	$0.535719\pi$
$278$	−5.19029e11	−	1.95793e12i	−0.312585	−	1.17916i
$279$		−	8.06028e11i		−	0.476792i
$280$		0			0
$281$	−2.08767e11			−0.119160			−0.0595799	−	0.998224i	$-0.518976\pi$
$281$	−2.08767e11			−0.119160			−0.0595799	+	0.998224i	$0.518976\pi$
$282$	−2.54768e11	+	6.75367e10i	−0.142856	+	0.0378699i
$283$		−	3.26659e12i		−	1.79954i	−0.436363	−	0.899771i	$-0.643734\pi$
$283$		−	3.26659e12i		−	1.79954i	0.436363	−	0.899771i	$-0.356266\pi$
$284$	−7.85649e11	−	1.37772e12i	−0.425243	−	0.745706i
$285$		0			0
$286$	4.78113e11	+	1.80358e12i	0.249862	+	0.942553i
$287$			2.27439e11i			0.116803i
$288$	−1.49850e11	+	5.30808e11i	−0.0756298	+	0.267902i
$289$	−1.88060e12			−0.932840
$290$		0			0
$291$		−	5.57394e11i		−	0.267115i
$292$	−3.06007e12	+	1.74502e12i	−1.44151	+	0.822026i
$293$	−2.68734e12			−1.24447			−0.622235	−	0.782830i	$-0.713775\pi$
$293$	−2.68734e12			−1.24447			−0.622235	+	0.782830i	$0.713775\pi$
$294$	4.74175e11	+	1.78873e12i	0.215875	+	0.814344i
$295$		0			0
$296$	−2.83770e12	+	2.79262e12i	−1.24884	+	1.22900i
$297$	4.58579e12			1.98441
$298$	−4.29700e12	+	1.13909e12i	−1.82845	+	0.484706i
$299$		−	5.10563e11i		−	0.213645i
$300$		0			0
$301$	2.15923e11			0.0873909
$302$	8.25824e11	+	3.11525e12i	0.328740	+	1.24011i
$303$			2.40565e12i			0.941933i
$304$	−8.29628e11	−	4.90869e11i	−0.319533	−	0.189059i
$305$		0			0
$306$	1.87086e11	−	4.95947e10i	0.0697323	−	0.0184854i
$307$		−	1.34058e12i		−	0.491588i	−0.969322	−	0.245794i	$-0.920951\pi$
$307$		−	1.34058e12i		−	0.491588i	0.969322	−	0.245794i	$-0.0790487\pi$
$308$	3.99843e11	−	2.28013e11i	0.144257	−	0.0822631i
$309$	−3.34539e12			−1.18756
$310$		0			0
$311$			2.65376e12i			0.912138i	0.889945	+	0.456069i	$0.150743\pi$
$311$			2.65376e12i			0.912138i	−0.889945	+	0.456069i	$0.849257\pi$
$312$	−9.40037e11	−	9.55213e11i	−0.317960	−	0.323093i
$313$	2.02340e12			0.673536			0.336768	−	0.941588i	$-0.390666\pi$
$313$	2.02340e12			0.673536			0.336768	+	0.941588i	$0.390666\pi$
$314$	2.52387e12	−	6.69053e11i	0.826834	−	0.219186i
$315$		0			0
$316$	−1.46198e12	−	2.56374e12i	−0.463988	−	0.813650i
$317$	9.05864e11			0.282987			0.141494	−	0.989939i	$-0.454810\pi$
$317$	9.05864e11			0.282987			0.141494	+	0.989939i	$0.454810\pi$
$318$	−1.75550e11	−	6.62225e11i	−0.0539839	−	0.203643i
$319$		−	4.14654e12i		−	1.25526i
$320$		0			0
$321$	3.35424e11			0.0984167
$322$	−1.21744e11	+	3.22732e10i	−0.0351697	+	0.00932315i
$323$			3.38269e11i			0.0962165i
$324$	−1.99785e12	+	1.13929e12i	−0.559550	+	0.319086i
$325$		0			0
$326$	−1.01229e12	−	3.81866e12i	−0.274927	−	1.03710i
$327$			2.29681e12i			0.614308i
$328$	3.47778e12	−	3.42252e12i	0.916078	−	0.901524i
$329$	6.09436e10			0.0158106
$330$		0			0
$331$		−	5.36141e11i		−	0.134940i	−0.997721	−	0.0674698i	$-0.978507\pi$
$331$		−	5.36141e11i		−	0.134940i	0.997721	−	0.0674698i	$-0.0214926\pi$
$332$	−1.73010e12	−	3.03391e12i	−0.428925	−	0.752164i
$333$	1.99720e12			0.487752
$334$	1.58258e12	+	5.96995e12i	0.380744	+	1.43628i
$335$		0			0
$336$	−1.68350e11	+	2.84532e11i	−0.0393113	+	0.0664409i
$337$	1.54118e12			0.354572			0.177286	−	0.984159i	$-0.443268\pi$
$337$	1.54118e12			0.354572			0.177286	+	0.984159i	$0.443268\pi$
$338$	3.04994e12	−	8.08510e11i	0.691365	−	0.183274i
$339$		−	6.22002e11i		−	0.138929i
$340$		0			0
$341$	1.44309e13			3.12983
$342$	1.23908e11	+	4.67416e11i	0.0264830	+	0.0999018i
$343$		−	8.59333e11i		−	0.181005i
$344$	−3.24923e12	−	3.30168e12i	−0.674509	−	0.685398i
$345$		0			0
$346$	−1.72356e12	+	4.56900e11i	−0.347573	+	0.0921384i
$347$		−	4.01330e12i		−	0.797728i	−0.917010	−	0.398864i	$-0.869405\pi$
$347$		−	4.01330e12i		−	0.797728i	0.917010	−	0.398864i	$-0.130595\pi$
$348$	1.47536e12	+	2.58719e12i	0.289069	+	0.506912i
$349$	5.09569e12			0.984183			0.492091	−	0.870544i	$-0.336233\pi$
$349$	5.09569e12			0.984183			0.492091	+	0.870544i	$0.336233\pi$
$350$		0			0
$351$			3.08735e12i			0.579495i
$352$	−9.50342e12	−	2.68286e12i	−1.75860	−	0.496460i
$353$	1.98418e12			0.362000			0.181000	−	0.983483i	$-0.442067\pi$
$353$	1.98418e12			0.362000			0.181000	+	0.983483i	$0.442067\pi$
$354$	2.80157e12	−	7.42670e11i	0.503948	−	0.133592i
$355$		0			0
$356$	−2.20476e12	+	1.25728e12i	−0.385577	+	0.219877i
$357$	1.16014e11			0.0200064
$358$	2.40426e12	+	9.06958e12i	0.408852	+	1.54231i
$359$			3.86028e12i			0.647362i	0.946166	+	0.323681i	$0.104920\pi$
$359$			3.86028e12i			0.647362i	−0.946166	+	0.323681i	$0.895080\pi$
$360$		0			0
$361$	5.28593e12			0.862156
$362$	8.42083e12	−	2.23228e12i	1.35460	−	0.359092i
$363$			1.25241e13i			1.98707i
$364$	1.53508e11	+	2.69192e11i	0.0240228	+	0.0421264i
$365$		0			0
$366$	−4.79125e11	−	1.80740e12i	−0.0729531	−	0.275201i
$367$		−	5.05920e12i		−	0.759892i	−0.925009	−	0.379946i	$-0.875943\pi$
$367$		−	5.05920e12i		−	0.759892i	0.925009	−	0.379946i	$-0.124057\pi$
$368$	2.32551e12	+	1.37594e12i	0.344571	+	0.203873i
$369$	−2.44769e12			−0.357786
$370$		0			0
$371$			1.58412e11i			0.0225382i
$372$	−9.00400e12	+	5.13457e12i	−1.26392	+	0.720758i
$373$	4.20322e12			0.582154			0.291077	−	0.956700i	$-0.405986\pi$
$373$	4.20322e12			0.582154			0.291077	+	0.956700i	$0.405986\pi$
$374$	8.87928e11	+	3.34952e12i	0.121344	+	0.457747i
$375$		0			0
$376$	−9.17085e11	−	9.31890e11i	−0.122031	−	0.124001i
$377$	2.79163e12			0.366565
$378$	7.36179e11	−	1.95154e11i	0.0953948	−	0.0252883i
$379$			1.01261e13i			1.29493i	0.762094	+	0.647466i	$0.224171\pi$
$379$			1.01261e13i			1.29493i	−0.762094	+	0.647466i	$0.775829\pi$
$380$		0			0
$381$	8.70271e12			1.08400
$382$	−2.45497e12	−	9.26089e12i	−0.301808	−	1.13851i
$383$		−	1.15938e13i		−	1.40680i	−0.710796	−	0.703399i	$-0.751665\pi$
$383$		−	1.15938e13i		−	1.40680i	0.710796	−	0.703399i	$-0.248335\pi$
$384$	6.88414e12	−	1.70742e12i	0.824505	−	0.204496i
$385$		0			0
$386$	−9.85436e12	+	2.61230e12i	−1.14998	+	0.304850i
$387$			2.32375e12i			0.267691i
$388$	2.40193e12	−	1.36971e12i	0.273150	−	0.155765i
$389$	3.83589e12			0.430643			0.215322	−	0.976543i	$-0.430920\pi$
$389$	3.83589e12			0.430643			0.215322	+	0.976543i	$0.430920\pi$
$390$		0			0
$391$		−	9.48192e11i		−	0.103756i
$392$	−6.54280e12	+	6.43885e12i	−0.706859	+	0.695630i
$393$	9.84510e12			1.05016
$394$	1.53201e13	−	4.06121e12i	1.61354	−	0.427735i
$395$		0			0
$396$	2.45386e12	+	4.30309e12i	0.251984	+	0.441880i
$397$	4.57753e11			0.0464171			0.0232086	−	0.999731i	$-0.492612\pi$
$397$	4.57753e11			0.0464171			0.0232086	+	0.999731i	$0.492612\pi$
$398$	1.22311e12	+	4.61393e12i	0.122476	+	0.462014i
$399$			2.89850e11i			0.0286622i
$400$		0			0
$401$	2.67792e12			0.258271			0.129136	−	0.991627i	$-0.458780\pi$
$401$	2.67792e12			0.258271			0.129136	+	0.991627i	$0.458780\pi$
$402$	1.28334e13	−	3.40201e12i	1.22239	−	0.324045i
$403$			9.71548e12i			0.913985i
$404$	−1.03665e13	+	5.91153e12i	−0.963218	+	0.549279i
$405$		0			0
$406$	−1.76462e11	−	6.65665e11i	−0.0159963	−	0.0603428i
$407$			3.57571e13i			3.20177i
$408$	−1.74579e12	−	1.77397e12i	−0.154416	−	0.156908i
$409$	−1.32601e13			−1.15859			−0.579297	−	0.815117i	$-0.696673\pi$
$409$	−1.32601e13			−1.15859			−0.579297	+	0.815117i	$0.696673\pi$
$410$		0			0
$411$			1.71889e13i			1.46568i
$412$	−8.22080e12	−	1.44160e13i	−0.692513	−	1.21439i
$413$	−6.70169e11			−0.0557743
$414$	−3.47322e11	−	1.31020e12i	−0.0285582	−	0.107730i
$415$		0			0
$416$	1.80621e12	−	6.39811e12i	0.144978	−	0.513553i
$417$	1.30665e13			1.03628
$418$	−8.36847e12	+	2.21840e12i	−0.655790	+	0.173844i
$419$		−	1.44719e13i		−	1.12061i	−0.828286	−	0.560306i	$-0.810684\pi$
$419$		−	1.44719e13i		−	1.12061i	0.828286	−	0.560306i	$-0.189316\pi$
$420$		0			0
$421$	−1.64597e13			−1.24455			−0.622274	−	0.782800i	$-0.713791\pi$
$421$	−1.64597e13			−1.24455			−0.622274	+	0.782800i	$0.713791\pi$
$422$	3.60893e12	+	1.36139e13i	0.269660	+	1.01724i
$423$			6.55871e11i			0.0484302i
$424$	2.42228e12	−	2.38380e12i	0.176765	−	0.173956i
$425$		0			0
$426$	9.88927e12	−	2.62155e12i	0.704882	−	0.186858i
$427$			4.32352e11i			0.0304578i
$428$	8.24253e11	+	1.44541e12i	0.0573907	+	0.100641i
$429$	−1.20364e13			−0.828342
$430$		0			0
$431$			5.96650e12i			0.401174i	0.979676	+	0.200587i	$0.0642850\pi$
$431$			5.96650e12i			0.401174i	−0.979676	+	0.200587i	$0.935715\pi$
$432$	−1.40622e13	−	8.32023e12i	−0.934619	−	0.552989i
$433$	2.04949e12			0.134650			0.0673250	−	0.997731i	$-0.478554\pi$
$433$	2.04949e12			0.134650			0.0673250	+	0.997731i	$0.478554\pi$
$434$	2.31666e12	−	6.14125e11i	0.150458	−	0.0398849i
$435$		0			0
$436$	−9.89745e12	+	5.64407e12i	−0.628190	+	0.358228i
$437$	2.36897e12			0.148646
$438$	−5.82277e12	−	2.19652e13i	−0.361210	−	1.36259i
$439$			1.83908e12i			0.112792i	0.998408	+	0.0563958i	$0.0179609\pi$
$439$			1.83908e12i			0.112792i	−0.998408	+	0.0563958i	$0.982039\pi$
$440$		0			0
$441$	4.60487e12			0.276073
$442$	−2.25504e12	+	5.97791e11i	−0.133673	+	0.0354354i
$443$		−	2.87837e13i		−	1.68705i	−0.537091	−	0.843524i	$-0.680477\pi$
$443$		−	2.87837e13i		−	1.68705i	0.537091	−	0.843524i	$-0.319523\pi$
$444$	−1.27226e13	−	2.23103e13i	−0.737326	−	1.29298i
$445$		0			0
$446$	7.79884e11	+	2.94195e12i	0.0441932	+	0.166710i
$447$		−	2.86765e13i		−	1.60690i
$448$	−1.63981e12	−	2.62619e10i	−0.0908662	−	0.00145524i
$449$	6.38160e12			0.349702			0.174851	−	0.984595i	$-0.444056\pi$
$449$	6.38160e12			0.349702			0.174851	+	0.984595i	$0.444056\pi$
$450$		0			0
$451$		−	4.38226e13i		−	2.34863i
$452$	2.68034e12	−	1.52848e12i	0.142068	−	0.0810152i
$453$	−2.07900e13			−1.08984
$454$	−1.17252e12	−	4.42310e12i	−0.0607913	−	0.229323i
$455$		0			0
$456$	4.43211e12	−	4.36169e12i	0.224795	−	0.221223i
$457$	−2.02709e13			−1.01693			−0.508465	−	0.861082i	$-0.669787\pi$
$457$	−2.02709e13			−1.01693			−0.508465	+	0.861082i	$0.669787\pi$
$458$	−2.54542e13	+	6.74768e12i	−1.26309	+	0.334832i
$459$			5.73367e12i			0.281429i
$460$		0			0
$461$	3.93541e11			0.0189010			0.00945052	−	0.999955i	$-0.496992\pi$
$461$	3.93541e11			0.0189010			0.00945052	+	0.999955i	$0.496992\pi$
$462$	7.60833e11	+	2.87008e12i	0.0361476	+	0.136359i
$463$			7.03622e12i			0.330700i	0.986235	+	0.165350i	$0.0528754\pi$
$463$			7.03622e12i			0.330700i	−0.986235	+	0.165350i	$0.947125\pi$
$464$	−7.52329e12	+	1.27153e13i	−0.349798	+	0.591201i
$465$		0			0
$466$	3.56511e12	−	9.45078e11i	0.162235	−	0.0430069i
$467$		−	3.74030e13i		−	1.68392i	−0.539538	−	0.841961i	$-0.681401\pi$
$467$		−	3.74030e13i		−	1.68392i	0.539538	−	0.841961i	$-0.318599\pi$
$468$	−2.89702e12	+	1.65204e12i	−0.129039	+	0.0735854i
$469$	−3.06990e12			−0.135288
$470$		0			0
$471$			1.68433e13i			0.726645i
$472$	1.00848e13	+	1.02476e13i	0.430483	+	0.437432i
$473$	−4.16036e13			−1.75722
$474$	1.84026e13	−	4.87834e12i	0.769106	−	0.203883i
$475$		0			0
$476$	2.85087e11	+	4.99929e11i	0.0116666	+	0.0204585i
$477$	−1.70482e12			−0.0690377
$478$	−6.43080e12	−	2.42589e13i	−0.257707	−	0.972145i
$479$		−	2.13984e13i		−	0.848600i	−0.905522	−	0.424300i	$-0.860520\pi$
$479$		−	2.13984e13i		−	0.848600i	0.905522	−	0.424300i	$-0.139480\pi$
$480$		0			0
$481$	−2.40732e13			−0.934994
$482$	3.96608e13	−	1.05137e13i	1.52450	−	0.404129i
$483$		−	8.12471e11i		−	0.0309081i
$484$	−5.39690e13	+	3.07761e13i	−2.03197	+	1.15874i
$485$		0			0
$486$	3.74314e12	+	1.41202e13i	0.138056	+	0.520787i
$487$			1.54715e13i			0.564790i	0.959298	+	0.282395i	$0.0911289\pi$
$487$			1.54715e13i			0.564790i	−0.959298	+	0.282395i	$0.908871\pi$
$488$	6.61110e12	−	6.50607e12i	0.238877	−	0.235082i
$489$	2.54842e13			0.911436
$490$		0			0
$491$		−	2.70952e13i		−	0.949477i	−0.880127	−	0.474739i	$-0.842543\pi$
$491$		−	2.70952e13i		−	0.949477i	0.880127	−	0.474739i	$-0.157457\pi$
$492$	1.55923e13	+	2.73427e13i	0.540859	+	0.948451i
$493$	5.18447e12			0.178020
$494$	−1.49352e12	−	5.63401e12i	−0.0507665	−	0.191506i
$495$		0			0
$496$	−4.42519e13	−	2.61827e13i	−1.47409	−	0.872180i
$497$	−2.36563e12			−0.0780127
$498$	2.17775e13	−	5.77301e12i	0.710986	−	0.188476i
$499$			4.37577e12i			0.141433i	0.997496	+	0.0707167i	$0.0225286\pi$
$499$			4.37577e12i			0.141433i	−0.997496	+	0.0707167i	$0.977471\pi$
$500$		0			0
$501$	−3.98411e13			−1.26224
$502$	5.41791e12	+	2.04380e13i	0.169947	+	0.641090i
$503$			1.22895e13i			0.381676i	0.981622	+	0.190838i	$0.0611205\pi$
$503$			1.22895e13i			0.381676i	−0.981622	+	0.190838i	$0.938879\pi$
$504$	5.77054e11	+	5.86370e11i	0.0177445	+	0.0180310i
$505$		0			0
$506$	2.34574e13	−	6.21834e12i	0.707177	−	0.187466i
$507$			2.03541e13i			0.607591i
$508$	2.13856e13	+	3.75018e13i	0.632125	+	1.10850i
$509$	2.55728e13			0.748497			0.374249	−	0.927328i	$-0.377901\pi$
$509$	2.55728e13			0.748497			0.374249	+	0.927328i	$0.377901\pi$
$510$		0			0
$511$			5.25434e12i			0.150804i
$512$	2.42744e13	+	2.54695e13i	0.689919	+	0.723886i
$513$	−1.43250e13			−0.403189
$514$	−5.55507e11	+	1.47260e11i	−0.0154837	+	0.00410458i
$515$		0			0
$516$	2.59582e13	−	1.48028e13i	0.709620	−	0.404664i
$517$	−1.17425e13			−0.317913
$518$	1.52169e12	+	5.74028e12i	0.0408017	+	0.153916i
$519$		−	1.15024e13i		−	0.305457i
$520$		0			0
$521$	−2.48387e13			−0.647055			−0.323527	−	0.946219i	$-0.604869\pi$
$521$	−2.48387e13			−0.647055			−0.323527	+	0.946219i	$0.604869\pi$
$522$	7.16384e12	−	1.89907e12i	0.184839	−	0.0489991i
$523$		−	4.31081e13i		−	1.10167i	−0.834615	−	0.550834i	$-0.814310\pi$
$523$		−	4.31081e13i		−	1.10167i	0.834615	−	0.550834i	$-0.185690\pi$
$524$	2.41928e13	+	4.24246e13i	0.612393	+	1.07389i
$525$		0			0
$526$	−5.58598e12	−	2.10720e13i	−0.138730	−	0.523331i
$527$			1.80431e13i			0.443872i
$528$	3.24374e13	−	5.48232e13i	0.790455	−	1.33596i
$529$	3.47861e13			0.839707
$530$		0			0
$531$		−	7.21232e12i		−	0.170845i
$532$	−1.24903e12	+	7.12263e11i	−0.0293098	+	0.0167141i
$533$	2.95032e13			0.685857
$534$	−4.19528e12	−	1.58258e13i	−0.0966172	−	0.364469i
$535$		0			0
$536$	4.61961e13	+	4.69418e13i	1.04419	+	1.06105i
$537$	−6.05268e13			−1.35543
$538$	−3.06987e13	+	8.13795e12i	−0.681097	+	0.180553i
$539$			8.24441e13i			1.81224i
$540$		0			0
$541$	−6.39742e13			−1.38044			−0.690221	−	0.723598i	$-0.742487\pi$
$541$	−6.39742e13			−1.38044			−0.690221	+	0.723598i	$0.742487\pi$
$542$	−5.94846e11	−	2.24394e12i	−0.0127177	−	0.0479749i
$543$			5.61972e13i			1.19046i
$544$	3.35441e12	−	1.18823e13i	0.0704080	−	0.249404i
$545$		0			0
$546$	−1.93226e12	+	5.12225e11i	−0.0398202	+	0.0105560i
$547$		−	7.77019e13i		−	1.58670i	−0.608765	−	0.793350i	$-0.708335\pi$
$547$		−	7.77019e13i		−	1.58670i	0.608765	−	0.793350i	$-0.291665\pi$
$548$	−7.40708e13	+	4.22392e13i	−1.49880	+	0.854699i
$549$	−4.65295e12			−0.0932967
$550$		0			0
$551$			1.29529e13i			0.255041i
$552$	−1.24235e13	+	1.22261e13i	−0.242409	+	0.238558i
$553$	−4.40211e12			−0.0851207
$554$	1.12971e13	−	2.99474e12i	0.216479	−	0.0573867i
$555$		0			0
$556$	3.21088e13	+	5.63061e13i	0.604297	+	1.05970i
$557$	2.51347e13			0.468810			0.234405	−	0.972139i	$-0.424686\pi$
$557$	2.51347e13			0.468810			0.234405	+	0.972139i	$0.424686\pi$
$558$	6.60918e12	+	2.49318e13i	0.122173	+	0.460874i
$559$		−	2.80093e13i		−	0.513150i
$560$		0			0
$561$	−2.23534e13			−0.402281
$562$	6.45749e12	−	1.71182e12i	0.115181	−	0.0305335i
$563$			3.40287e13i			0.601593i	0.953688	+	0.300797i	$0.0972525\pi$
$563$			3.40287e13i			0.601593i	−0.953688	+	0.300797i	$0.902747\pi$
$564$	7.32662e12	−	4.17804e12i	0.128383	−	0.0732111i
$565$		0			0
$566$	2.67850e13	+	1.01041e14i	0.461115	+	1.73946i
$567$			3.43045e12i			0.0585377i
$568$	3.55982e13	+	3.61729e13i	0.602125	+	0.611845i
$569$	−1.44547e13			−0.242352			−0.121176	−	0.992631i	$-0.538667\pi$
$569$	−1.44547e13			−0.242352			−0.121176	+	0.992631i	$0.538667\pi$
$570$		0			0
$571$		−	7.83937e13i		−	1.29152i	−0.763541	−	0.645759i	$-0.776541\pi$
$571$		−	7.83937e13i		−	1.29152i	0.763541	−	0.645759i	$-0.223459\pi$
$572$	−2.95776e13	−	5.18674e13i	−0.483040	−	0.847060i
$573$	6.18035e13			1.00055
$574$	−1.86493e12	−	7.03506e12i	−0.0299297	−	0.112904i
$575$		0			0
$576$	2.82629e11	−	1.76475e13i	0.00445763	−	0.278337i
$577$	−8.39202e13			−1.31216			−0.656081	−	0.754691i	$-0.727787\pi$
$577$	−8.39202e13			−1.31216			−0.656081	+	0.754691i	$0.727787\pi$
$578$	5.81700e13	−	1.54203e13i	0.901696	−	0.239031i
$579$		−	6.57640e13i		−	1.01064i
$580$		0			0
$581$	−5.20943e12			−0.0786882
$582$	4.57046e12	+	1.72411e13i	0.0684455	+	0.258196i
$583$		−	3.05225e13i		−	0.453188i
$584$	8.03442e13	−	7.90678e13i	1.18274	−	1.16395i
$585$		0			0
$586$	8.31238e13	−	2.20353e13i	1.20292	−	0.318883i
$587$			6.78604e13i			0.973702i	0.873485	+	0.486851i	$0.161855\pi$
$587$			6.78604e13i			0.973702i	−0.873485	+	0.486851i	$0.838145\pi$
$588$	−2.93340e13	−	5.14402e13i	−0.417335	−	0.731839i
$589$	−4.50790e13			−0.635913
$590$		0			0
$591$			1.02240e14i			1.41803i
$592$	6.48761e13	−	1.09648e14i	0.892229	−	1.50797i
$593$	4.32732e13			0.590127			0.295064	−	0.955478i	$-0.404659\pi$
$593$	4.32732e13			0.590127			0.295064	+	0.955478i	$0.404659\pi$
$594$	−1.41846e14	+	3.76020e13i	−1.91816	+	0.508485i
$595$		0			0
$596$	1.23573e14	−	7.04681e13i	1.64321	−	0.937047i
$597$	−3.07915e13			−0.406031
$598$	4.18645e12	+	1.57925e13i	0.0547445	+	0.206512i
$599$			9.37963e13i			1.21633i	0.793811	+	0.608165i	$0.208094\pi$
$599$			9.37963e13i			1.21633i	−0.793811	+	0.608165i	$0.791906\pi$
$600$		0			0
$601$	6.78423e13			0.865224			0.432612	−	0.901580i	$-0.357592\pi$
$601$	6.78423e13			0.865224			0.432612	+	0.901580i	$0.357592\pi$
$602$	−6.67884e12	+	1.77050e12i	−0.0844732	+	0.0223931i
$603$		−	3.30380e13i		−	0.414407i
$604$	−5.10882e13	−	8.95883e13i	−0.635530	−	1.11447i
$605$		0			0
$606$	−1.97256e13	−	7.44108e13i	−0.241361	−	0.910485i
$607$			1.53821e13i			0.186668i	0.995635	+	0.0933342i	$0.0297525\pi$
$607$			1.53821e13i			0.186668i	−0.995635	+	0.0933342i	$0.970247\pi$
$608$	2.96867e13	+	8.38068e12i	0.357309	+	0.100870i
$609$	4.44238e12			0.0530309
$610$		0			0
$611$		−	7.90556e12i		−	0.0928381i
$612$	−5.38021e12	+	3.06809e12i	−0.0626674	+	0.0357364i
$613$	1.01243e13			0.116966			0.0584831	−	0.998288i	$-0.481374\pi$
$613$	1.01243e13			0.116966			0.0584831	+	0.998288i	$0.481374\pi$
$614$	1.09923e13	+	4.14664e13i	0.125965	+	0.475176i
$615$		0			0
$616$	−1.04982e13	+	1.03314e13i	−0.118361	+	0.116481i
$617$	5.97536e13			0.668249			0.334125	−	0.942529i	$-0.391559\pi$
$617$	5.97536e13			0.668249			0.334125	+	0.942529i	$0.391559\pi$
$618$	1.03478e14	−	2.74312e13i	1.14791	−	0.304300i
$619$			1.02486e13i			0.112775i	0.998409	+	0.0563875i	$0.0179582\pi$
$619$			1.02486e13i			0.112775i	−0.998409	+	0.0563875i	$0.982042\pi$
$620$		0			0
$621$	4.01541e13			0.434782
$622$	−2.17600e13	−	8.20852e13i	−0.233726	−	0.881684i
$623$			3.78572e12i			0.0403375i
$624$	3.69093e13	+	2.18383e13i	0.390133	+	0.230832i
$625$		0			0
$626$	−6.25872e13	+	1.65913e13i	−0.651049	+	0.172587i
$627$		−	5.58479e13i		−	0.576327i
$628$	−7.25813e13	+	4.13898e13i	−0.743064	+	0.423736i
$629$	−4.47076e13			−0.454076
$630$		0			0
$631$			4.39320e13i			0.439172i	0.975593	+	0.219586i	$0.0704706\pi$
$631$			4.39320e13i			0.439172i	−0.975593	+	0.219586i	$0.929529\pi$
$632$	6.62433e13	+	6.73127e13i	0.656987	+	0.667593i
$633$	−9.08540e13			−0.893975
$634$	−2.80198e13	+	7.42780e12i	−0.273539	+	0.0725126i
$635$		0			0
$636$	1.08601e13	+	1.90442e13i	0.104363	+	0.183011i
$637$	−5.55049e13			−0.529217
$638$	3.40003e13	+	1.28259e14i	0.321647	+	1.21335i
$639$		−	2.54588e13i		−	0.238964i
$640$		0			0
$641$	4.97085e13			0.459347			0.229673	−	0.973268i	$-0.426234\pi$
$641$	4.97085e13			0.459347			0.229673	+	0.973268i	$0.426234\pi$
$642$	−1.03752e13	+	2.75037e12i	−0.0951308	+	0.0252183i
$643$		−	6.71533e12i		−	0.0610960i	−0.999533	−	0.0305480i	$-0.990275\pi$
$643$		−	6.71533e12i		−	0.0610960i	0.999533	−	0.0305480i	$-0.00972524\pi$
$644$	3.50111e12	−	1.99652e12i	0.0316065	−	0.0180238i
$645$		0			0
$646$	−2.77370e12	−	1.04632e13i	−0.0246545	−	0.0930042i
$647$			6.66499e13i			0.587866i	0.955826	+	0.293933i	$0.0949642\pi$
$647$			6.66499e13i			0.587866i	−0.955826	+	0.293933i	$0.905036\pi$
$648$	5.24551e13	−	5.16217e13i	0.459106	−	0.451812i
$649$	1.29127e14			1.12149
$650$		0			0
$651$			1.54605e13i			0.132226i
$652$	6.26235e13	+	1.09817e14i	0.531495	+	0.932032i
$653$	7.03440e13			0.592463			0.296231	−	0.955116i	$-0.404270\pi$
$653$	7.03440e13			0.592463			0.296231	+	0.955116i	$0.404270\pi$
$654$	−1.88331e13	−	7.10441e13i	−0.157410	−	0.593799i
$655$		0			0
$656$	−7.95096e13	+	1.34381e14i	−0.654486	+	1.10616i
$657$	−5.65469e13			−0.461936
$658$	−1.88508e12	+	4.99718e11i	−0.0152827	+	0.00405131i
$659$		−	2.63637e13i		−	0.212119i	−0.994360	−	0.106060i	$-0.966177\pi$
$659$		−	2.63637e13i		−	0.212119i	0.994360	−	0.106060i	$-0.0338234\pi$
$660$		0			0
$661$	1.68700e14			1.33693			0.668463	−	0.743745i	$-0.266952\pi$
$661$	1.68700e14			1.33693			0.668463	+	0.743745i	$0.266952\pi$
$662$	4.39619e12	+	1.65837e13i	0.0345769	+	0.130434i
$663$		−	1.50493e13i		−	0.117476i
$664$	7.83920e13	+	7.96575e13i	0.607339	+	0.617144i
$665$		0			0
$666$	−6.17765e13	+	1.63764e13i	−0.471468	+	0.124982i
$667$		−	3.63079e13i		−	0.275025i
$668$	−9.79034e13	−	1.71684e14i	−0.736064	−	1.29076i
$669$	−1.96334e13			−0.146509
$670$		0			0
$671$		−	8.33048e13i		−	0.612432i
$672$	2.87427e12	−	1.01815e13i	0.0209740	−	0.0742957i
$673$	−1.04637e14			−0.757900			−0.378950	−	0.925417i	$-0.623715\pi$
$673$	−1.04637e14			−0.757900			−0.378950	+	0.925417i	$0.623715\pi$
$674$	−4.76713e13	+	1.26372e13i	−0.342734	+	0.0908556i
$675$		0			0
$676$	−8.77100e13	+	5.00170e13i	−0.621320	+	0.354311i
$677$	1.48361e14			1.04322			0.521612	−	0.853183i	$-0.325331\pi$
$677$	1.48361e14			1.04322			0.521612	+	0.853183i	$0.325331\pi$
$678$	5.10022e12	+	1.92395e13i	0.0355992	+	0.134291i
$679$		−	4.12428e12i		−	0.0285758i
$680$		0			0
$681$	2.95180e13			0.201535
$682$	−4.46370e14	+	1.18329e14i	−3.02533	+	0.801988i
$683$			1.62332e14i			1.09220i	0.837722	+	0.546098i	$0.183887\pi$
$683$			1.62332e14i			1.09220i	−0.837722	+	0.546098i	$0.816113\pi$
$684$	−7.66533e12	−	1.34419e13i	−0.0511977	−	0.0897804i
$685$		0			0
$686$	7.04626e12	+	2.65806e13i	0.0463808	+	0.174962i
$687$		−	1.69871e14i		−	1.11004i
$688$	1.27577e14	+	7.54837e13i	0.827616	+	0.489678i
$689$	2.05491e13			0.132342
$690$		0			0
$691$			1.49548e14i			0.949269i	0.880183	+	0.474635i	$0.157420\pi$
$691$			1.49548e14i			0.949269i	−0.880183	+	0.474635i	$0.842580\pi$
$692$	4.95661e13	−	2.82653e13i	0.312359	−	0.178124i
$693$	7.38870e12			0.0462276
$694$	3.29078e13	+	1.24138e14i	0.204410	+	0.771094i
$695$		0			0
$696$	−6.68494e13	−	6.79285e13i	−0.409309	−	0.415916i
$697$	5.47919e13			0.333083
$698$	−1.57618e14	+	4.17830e13i	−0.951324	+	0.252187i
$699$			2.37921e13i			0.142576i
$700$		0			0
$701$	−1.48453e14			−0.876997			−0.438498	−	0.898732i	$-0.644489\pi$
$701$	−1.48453e14			−0.876997			−0.438498	+	0.898732i	$0.644489\pi$
$702$	−2.53153e13	−	9.54966e13i	−0.148490	−	0.560148i
$703$		−	1.11698e14i		−	0.650531i
$704$	3.15955e14	+	5.06010e12i	1.82710	+	0.0292614i
$705$		0			0
$706$	−6.13740e13	+	1.62697e13i	−0.349914	+	0.0927589i
$707$			1.77999e13i			0.100768i
$708$	−8.05675e13	+	4.59440e13i	−0.452891	+	0.258263i
$709$	−2.32221e13			−0.129619			−0.0648097	−	0.997898i	$-0.520644\pi$
$709$	−2.32221e13			−0.129619			−0.0648097	+	0.997898i	$0.520644\pi$
$710$		0			0
$711$		−	4.73752e13i		−	0.260737i
$712$	5.78876e13	−	5.69679e13i	0.316363	−	0.311337i
$713$	1.26360e14			0.685742
$714$	−3.58850e12	+	9.51279e11i	−0.0193385	+	0.00512645i
$715$		0			0
$716$	−1.48735e14	−	2.60823e14i	−0.790404	−	1.38605i
$717$	1.61894e14			0.854348
$718$	−3.16531e13	−	1.19405e14i	−0.165880	−	0.625748i
$719$		−	2.66908e14i		−	1.38905i	−0.719470	−	0.694523i	$-0.755615\pi$
$719$		−	2.66908e14i		−	1.38905i	0.719470	−	0.694523i	$-0.244385\pi$
$720$		0			0
$721$	−2.47533e13			−0.127045
$722$	−1.63502e14	+	4.33430e13i	−0.833371	+	0.220919i
$723$			2.64680e14i			1.33977i
$724$	−2.42166e14	+	1.38096e14i	−1.21736	+	0.694207i
$725$		0			0
$726$	−1.02694e14	−	3.87391e14i	−0.509167	−	1.92073i
$727$			2.88697e14i			1.42157i	0.703407	+	0.710787i	$0.251661\pi$
$727$			2.88697e14i			1.42157i	−0.703407	+	0.710787i	$0.748339\pi$
$728$	−6.95553e12	−	7.06782e12i	−0.0340152	−	0.0345644i
$729$	−2.26855e14			−1.10182
$730$		0			0
$731$		−	5.20176e13i		−	0.249209i
$732$	2.96403e13	+	5.19772e13i	0.141035	+	0.247319i
$733$	1.34165e14			0.634043			0.317022	−	0.948418i	$-0.397317\pi$
$733$	1.34165e14			0.634043			0.317022	+	0.948418i	$0.397317\pi$
$734$	4.14839e13	+	1.56489e14i	0.194715	+	0.734522i
$735$		0			0
$736$	−8.32139e13	−	2.34917e13i	−0.385307	−	0.108774i
$737$	5.91502e14			2.72031
$738$	7.57109e13	−	2.00702e13i	0.345841	−	0.0916792i
$739$		−	4.06753e10i		−	0.000184548i	−1.00000		9.22738e-5i	$-0.999971\pi$
$739$		−	4.06753e10i		−	0.000184548i	1.00000		9.22738e-5i	$-2.93717e-5\pi$
$740$		0			0
$741$	3.75992e13			0.168301
$742$	−1.29893e12	−	4.89994e12i	−0.00577518	−	0.0217857i
$743$		−	3.43972e14i		−	1.51907i	−0.650465	−	0.759536i	$-0.725426\pi$
$743$		−	3.43972e14i		−	1.51907i	0.650465	−	0.759536i	$-0.274574\pi$
$744$	2.36406e14	−	2.32651e14i	1.03704	−	1.02056i
$745$		0			0
$746$	−1.30012e14	+	3.44651e13i	−0.562718	+	0.149171i
$747$		−	5.60636e13i		−	0.241034i
$748$	−5.49301e13	−	9.63255e13i	−0.234586	−	0.411371i
$749$	2.48187e12			0.0105286
$750$		0			0
$751$		−	1.75584e14i		−	0.734996i	−0.930024	−	0.367498i	$-0.880214\pi$
$751$		−	1.75584e14i		−	0.734996i	0.930024	−	0.367498i	$-0.119786\pi$
$752$	3.60081e13	+	2.13051e13i	0.149731	+	0.0885918i
$753$	−1.36395e14			−0.563408
$754$	−8.63495e13	+	2.28905e13i	−0.354326	+	0.0939286i
$755$		0			0
$756$	−2.11710e13	+	1.20729e13i	−0.0857300	+	0.0488879i
$757$	1.35481e13			0.0545005			0.0272502	−	0.999629i	$-0.491325\pi$
$757$	1.35481e13			0.0545005			0.0272502	+	0.999629i	$0.491325\pi$
$758$	−8.30310e13	−	3.13217e14i	−0.331814	−	1.25170i
$759$			1.56546e14i			0.621487i
$760$		0			0
$761$	7.63675e13			0.299216			0.149608	−	0.988745i	$-0.452199\pi$
$761$	7.63675e13			0.299216			0.149608	+	0.988745i	$0.452199\pi$
$762$	−2.69189e14	+	7.13595e13i	−1.04781	+	0.277765i
$763$			1.69946e13i			0.0657185i
$764$	1.51873e14	+	2.66324e14i	0.583462	+	1.02316i
$765$		0			0
$766$	9.50654e13	+	3.58615e14i	0.360478	+	1.35983i
$767$			8.69338e13i			0.327500i
$768$	−1.98937e14	+	1.09261e14i	−0.744578	+	0.408940i
$769$	−3.71137e14			−1.38008			−0.690038	−	0.723773i	$-0.742406\pi$
$769$	−3.71137e14			−1.38008			−0.690038	+	0.723773i	$0.742406\pi$
$770$		0			0
$771$		−	3.70723e12i		−	0.0136075i
$772$	2.83391e14	−	1.61605e14i	1.03347	−	0.589344i
$773$	−5.41146e14			−1.96072			−0.980362	−	0.197205i	$-0.936814\pi$
$773$	−5.41146e14			−1.96072			−0.980362	+	0.197205i	$0.936814\pi$
$774$	−1.90540e13	−	7.18773e13i	−0.0685932	−	0.258754i
$775$		0			0
$776$	−6.30644e13	+	6.20625e13i	−0.224117	+	0.220557i
$777$	−3.83083e13			−0.135266
$778$	−1.18650e14	+	3.14531e13i	−0.416266	+	0.110348i
$779$			1.36892e14i			0.477191i
$780$		0			0
$781$	4.55806e14			1.56864
$782$	7.77487e12	+	2.93291e13i	0.0265864	+	0.100292i
$783$			2.19552e14i			0.745983i
$784$	1.49583e14	−	2.52813e14i	0.505011	−	0.853530i
$785$		0			0
$786$	−3.04525e14	+	8.07267e13i	−1.01510	+	0.269094i
$787$		−	4.82190e13i		−	0.159714i	−0.996806	−	0.0798572i	$-0.974554\pi$
$787$		−	4.82190e13i		−	0.159714i	0.996806	−	0.0798572i	$-0.0254464\pi$
$788$	−4.40575e14	+	2.51240e14i	−1.45007	+	0.826908i
$789$	1.40626e14			0.459918
$790$		0			0
$791$		−	4.60232e12i		−	0.0148626i
$792$	−1.11186e14	−	1.12981e14i	−0.356799	−	0.362559i
$793$	5.60844e13			0.178845
$794$	−1.41590e13	+	3.75343e12i	−0.0448674	+	0.0118939i
$795$		0			0
$796$	−7.56655e13	−	1.32687e14i	−0.236773	−	0.415206i
$797$	−1.02585e14			−0.319001			−0.159501	−	0.987198i	$-0.550988\pi$
$797$	−1.02585e14			−0.319001			−0.159501	+	0.987198i	$0.550988\pi$
$798$	−2.37668e12	−	8.96554e12i	−0.00734440	−	0.0277052i
$799$		−	1.46818e13i		−	0.0450864i
$800$		0			0
$801$	−4.07417e13			−0.123560
$802$	−8.28324e13	+	2.19581e13i	−0.249648	+	0.0661794i
$803$		−	1.01240e15i		−	3.03231i
$804$	−3.69062e14	+	2.10459e14i	−1.09855	+	0.626452i
$805$		0			0
$806$	−7.96638e13	−	3.00516e14i	−0.234200	−	0.883470i
$807$		−	2.04871e14i		−	0.598567i
$808$	2.72179e14	−	2.67855e14i	0.790311	−	0.777756i
$809$	3.39598e14			0.979991			0.489995	−	0.871725i	$-0.336998\pi$
$809$	3.39598e14			0.979991			0.489995	+	0.871725i	$0.336998\pi$
$810$		0			0
$811$			3.34618e14i			0.953773i	0.878965	+	0.476886i	$0.158235\pi$
$811$			3.34618e14i			0.953773i	−0.878965	+	0.476886i	$0.841765\pi$
$812$	1.09165e13	+	1.91432e13i	0.0309245	+	0.0542293i
$813$	1.49751e13			0.0421617
$814$	−2.93197e14	−	1.10603e15i	−0.820423	−	3.09488i
$815$		0			0
$816$	6.85461e13	+	4.05569e13i	0.189466	+	0.112102i
$817$	1.29961e14			0.357028
$818$	4.10157e14	−	1.08729e14i	1.11991	−	0.296878i
$819$			4.97438e12i			0.0134996i
$820$		0			0
$821$	3.85146e14			1.03255			0.516274	−	0.856424i	$-0.327319\pi$
$821$	3.85146e14			1.03255			0.516274	+	0.856424i	$0.327319\pi$
$822$	−1.40944e14	−	5.31682e14i	−0.375567	−	1.41675i
$823$			4.10368e14i			1.08686i	0.839454	+	0.543430i	$0.182875\pi$
$823$			4.10368e14i			1.08686i	−0.839454	+	0.543430i	$0.817125\pi$
$824$	3.72489e14	+	3.78503e14i	0.980569	+	0.996398i
$825$		0			0
$826$	2.07294e13	−	5.49517e12i	0.0539122	−	0.0142916i
$827$			5.90609e14i			1.52677i	0.645946	+	0.763383i	$0.276463\pi$
$827$			5.90609e14i			1.52677i	−0.645946	+	0.763383i	$0.723537\pi$
$828$	2.14865e13	+	3.76787e13i	0.0552095	+	0.0968154i
$829$	−1.46339e14			−0.373754			−0.186877	−	0.982383i	$-0.559837\pi$
$829$	−1.46339e14			−0.373754			−0.186877	+	0.982383i	$0.559837\pi$
$830$		0			0
$831$			7.53921e13i			0.190248i
$832$	−3.40667e12	+	2.12714e14i	−0.00854503	+	0.533556i
$833$	−1.03081e14			−0.257012
$834$	−4.04167e14	+	1.07141e14i	−1.00168	+	0.265537i
$835$		0			0
$836$	2.40660e14	−	1.37238e14i	0.589350	−	0.336079i
$837$	−7.64090e14			−1.86002
$838$	1.18665e14	+	4.47639e14i	0.287146	+	1.08320i
$839$			4.02177e13i			0.0967402i	0.998829	+	0.0483701i	$0.0154027\pi$
$839$			4.02177e13i			0.0967402i	−0.998829	+	0.0483701i	$0.984597\pi$
$840$		0			0
$841$	−2.22185e14			−0.528122
$842$	5.09125e14	−	1.34964e14i	1.20300	−	0.318903i
$843$			4.30947e13i			0.101225i
$844$	−2.23260e14	−	3.91509e14i	−0.521313	−	0.914176i
$845$		0			0
$846$	−5.37793e12	−	2.02872e13i	−0.0124098	−	0.0468133i
$847$			9.26684e13i			0.212576i
$848$	−5.53787e13	+	9.35967e13i	−0.126288	+	0.213443i
$849$	−6.74306e14			−1.52869
$850$		0			0
$851$			3.13097e14i			0.701505i
$852$	−2.84395e14	+	1.62178e14i	−0.633468	+	0.361238i
$853$	6.42197e14			1.42208			0.711038	−	0.703153i	$-0.248225\pi$
$853$	6.42197e14			1.42208			0.711038	+	0.703153i	$0.248225\pi$
$854$	−3.54515e12	−	1.33734e13i	−0.00780450	−	0.0294409i
$855$		0			0
$856$	−3.73474e13	−	3.79503e13i	−0.0812628	−	0.0825746i
$857$	−2.32290e14			−0.502489			−0.251245	−	0.967924i	$-0.580840\pi$
$857$	−2.32290e14			−0.502489			−0.251245	+	0.967924i	$0.580840\pi$
$858$	3.72305e14	−	9.86946e13i	0.800687	−	0.212255i
$859$		−	7.69555e14i		−	1.64541i	−0.568469	−	0.822704i	$-0.692464\pi$
$859$		−	7.69555e14i		−	1.64541i	0.568469	−	0.822704i	$-0.307536\pi$
$860$		0			0
$861$	4.69492e13			0.0992230
$862$	−4.89234e13	−	1.84554e14i	−0.102797	−	0.387781i
$863$			4.29835e14i			0.897942i	0.893546	+	0.448971i	$0.148209\pi$
$863$			4.29835e14i			0.897942i	−0.893546	+	0.448971i	$0.851791\pi$
$864$	5.03190e14	+	1.42053e14i	1.04511	+	0.295040i
$865$		0			0
$866$	−6.33941e13	+	1.68052e13i	−0.130155	+	0.0345027i
$867$			3.88203e14i			0.792435i
$868$	−6.66225e13	+	3.79918e13i	−0.135214	+	0.0771065i
$869$	8.48191e14			1.71157
$870$		0			0
$871$			3.98224e14i			0.794396i
$872$	2.59864e14	−	2.55736e14i	0.515424	−	0.507235i
$873$	4.43852e13			0.0875320
$874$	−7.32761e13	+	1.94248e13i	−0.143683	+	0.0380890i
$875$		0			0
$876$	3.60216e14	+	6.31675e14i	0.698300	+	1.22454i
$877$	2.99857e14			0.577985			0.288993	−	0.957331i	$-0.406680\pi$
$877$	2.99857e14			0.577985			0.288993	+	0.957331i	$0.406680\pi$
$878$	−1.50798e13	−	5.68856e13i	−0.0289017	−	0.109026i
$879$			5.54735e14i			1.05716i
$880$		0			0
$881$	−6.00394e14			−1.13125			−0.565623	−	0.824664i	$-0.691364\pi$
$881$	−6.00394e14			−1.13125			−0.565623	+	0.824664i	$0.691364\pi$
$882$	−1.42436e14	+	3.77585e13i	−0.266856	+	0.0707410i
$883$			4.85577e14i			0.904596i	0.891867	+	0.452298i	$0.149396\pi$
$883$			4.85577e14i			0.904596i	−0.891867	+	0.452298i	$0.850604\pi$
$884$	6.48504e13	−	3.69813e13i	0.120130	−	0.0685047i
$885$		0			0
$886$	2.36017e14	+	8.90325e14i	0.432289	+	1.63072i
$887$		−	8.89232e14i		−	1.61956i	−0.586734	−	0.809780i	$-0.699587\pi$
$887$		−	8.89232e14i		−	1.61956i	0.586734	−	0.809780i	$-0.300413\pi$
$888$	5.76467e14	+	5.85773e14i	1.04402	+	1.06088i
$889$	6.43932e13			0.115966
$890$		0			0
$891$		−	6.60973e14i		−	1.17705i
$892$	−4.82462e13	−	8.46046e13i	−0.0854355	−	0.149820i
$893$	3.66811e13			0.0645930
$894$	2.35138e14	+	8.87010e14i	0.411752	+	1.55325i
$895$		0			0
$896$	5.09372e13	−	1.26336e13i	0.0882054	−	0.0218769i
$897$	−1.05393e14			−0.181489
$898$	−1.97393e14	+	5.23271e13i	−0.338026	+	0.0896076i
$899$			6.90902e14i			1.17657i
$900$		0			0
$901$	3.81627e13			0.0642711
$902$	3.59331e14	+	1.35550e15i	0.601814	+	2.27022i
$903$		−	4.45719e13i		−	0.0742374i
$904$	−7.03742e13	+	6.92562e13i	−0.116566	+	0.114714i
$905$		0			0
$906$	6.43067e14	−	1.70471e14i	1.05345	−	0.279261i
$907$		−	6.65566e14i		−	1.08431i	−0.840277	−	0.542157i	$-0.817608\pi$
$907$		−	6.65566e14i		−	1.08431i	0.840277	−	0.542157i	$-0.182392\pi$
$908$	7.25360e13	+	1.27199e14i	0.117523	+	0.206089i
$909$	−1.91562e14			−0.308667
$910$		0			0
$911$		−	6.58300e14i		−	1.04914i	−0.851368	−	0.524568i	$-0.824227\pi$
$911$		−	6.58300e14i		−	1.04914i	0.851368	−	0.524568i	$-0.175773\pi$
$912$	−1.01328e14	+	1.71256e14i	−0.160603	+	0.271439i
$913$	1.00374e15			1.58223
$914$	6.27011e14	−	1.66215e14i	0.982979	−	0.260578i
$915$		0			0
$916$	7.32012e14	−	4.17434e14i	1.13512	−	0.647307i
$917$	7.28460e13			0.112346
$918$	−4.70142e13	−	1.77352e14i	−0.0721134	−	0.272033i
$919$			2.48932e14i			0.379755i	0.981808	+	0.189878i	$0.0608091\pi$
$919$			2.48932e14i			0.379755i	−0.981808	+	0.189878i	$0.939191\pi$
$920$		0			0
$921$	−2.76730e14			−0.417598
$922$	−1.21729e13	+	3.22691e12i	−0.0182700	+	0.00484321i
$923$			3.06868e14i			0.458082i
$924$	−4.70676e13	−	8.25378e13i	−0.0698815	−	0.122544i
$925$		0			0
$926$	−5.76948e13	−	2.17642e14i	−0.0847387	−	0.319659i
$927$		−	2.66393e14i		−	0.389157i
$928$	1.28446e14	−	4.54992e14i	0.186630	−	0.661095i
$929$	6.78834e14			0.981036			0.490518	−	0.871431i	$-0.336808\pi$
$929$	6.78834e14			0.981036			0.490518	+	0.871431i	$0.336808\pi$
$930$		0			0
$931$		−	2.57538e14i		−	0.368208i
$932$	−1.02525e14	+	5.84656e13i	−0.145798	+	0.0831421i
$933$	5.47804e14			0.774849
$934$	3.06693e14	+	1.15694e15i	0.431488	+	1.62770i
$935$		0			0
$936$	7.60634e13	−	7.48550e13i	0.105876	−	0.104194i
$937$	−1.72850e14			−0.239315			−0.119658	−	0.992815i	$-0.538180\pi$
$937$	−1.72850e14			−0.239315			−0.119658	+	0.992815i	$0.538180\pi$
$938$	9.49568e13	−	2.51722e13i	0.130771	−	0.0346662i
$939$		−	4.17682e14i		−	0.572160i
$940$		0			0
$941$	2.67517e14			0.362580			0.181290	−	0.983430i	$-0.441973\pi$
$941$	2.67517e14			0.362580			0.181290	+	0.983430i	$0.441973\pi$
$942$	−1.38110e14	−	5.20990e14i	−0.186195	−	0.702384i
$943$		−	3.83719e14i		−	0.514583i
$944$	−3.95965e14	−	2.34282e14i	−0.528198	−	0.312521i
$945$		0			0
$946$	1.28687e15	−	3.41137e14i	1.69855	−	0.450270i
$947$			2.68497e14i			0.352525i	0.984343	+	0.176263i	$0.0564008\pi$
$947$			2.68497e14i			0.352525i	−0.984343	+	0.176263i	$0.943599\pi$
$948$	−5.29220e14	+	3.01790e14i	−0.691185	+	0.394152i
$949$	6.81589e14			0.885506
$950$		0			0
$951$		−	1.86993e14i		−	0.240394i
$952$	−1.29175e13	−	1.31260e13i	−0.0165193	−	0.0167860i
$953$	−1.13349e15			−1.44196			−0.720979	−	0.692957i	$-0.756307\pi$
$953$	−1.13349e15			−1.44196			−0.720979	+	0.692957i	$0.756307\pi$
$954$	5.27328e13	−	1.39790e13i	0.0667328	−	0.0176902i
$955$		0			0
$956$	3.97830e14	+	6.97636e14i	0.498205	+	0.873654i
$957$	−8.55950e14			−1.06632
$958$	1.75460e14	+	6.61886e14i	0.217445	+	0.820268i
$959$			1.27185e14i			0.156798i
$960$		0			0
$961$	−1.58486e15			−1.93364
$962$	7.44624e14	−	1.97393e14i	0.903778	−	0.239583i
$963$			2.67097e13i			0.0322506i
$964$	−1.14056e15	+	6.50412e14i	−1.37004	+	0.781274i
$965$		0			0
$966$	6.66200e12	+	2.51310e13i	0.00791989	+	0.0298762i
$967$		−	5.51099e14i		−	0.651775i	−0.945409	−	0.325887i	$-0.894337\pi$
$967$		−	5.51099e14i		−	0.651775i	0.945409	−	0.325887i	$-0.105663\pi$
$968$	1.41699e15	−	1.39448e15i	1.66721	−	1.64073i
$969$	6.98273e13			0.0817347
$970$		0			0
$971$			1.03297e15i			1.19672i	0.801228	+	0.598359i	$0.204180\pi$
$971$			1.03297e15i			1.19672i	−0.801228	+	0.598359i	$0.795820\pi$
$972$	−2.31563e14	−	4.06069e14i	−0.266893	−	0.468024i
$973$	9.66814e13			0.110861
$974$	−1.26861e14	−	4.78558e14i	−0.144722	−	0.545934i
$975$		0			0
$976$	−1.51144e14	+	2.55452e14i	−0.170664	+	0.288444i
$977$	1.28577e14			0.144441			0.0722205	−	0.997389i	$-0.476991\pi$
$977$	1.28577e14			0.144441			0.0722205	+	0.997389i	$0.476991\pi$
$978$	−7.88267e14	+	2.08962e14i	−0.881006	+	0.233547i
$979$		−	7.29427e14i		−	0.811089i
$980$		0			0
$981$	−1.82895e14			−0.201306
$982$	2.22172e14	+	8.38098e14i	0.243294	+	0.917777i
$983$			8.69065e14i			0.946858i	0.880832	+	0.473429i	$0.156984\pi$
$983$			8.69065e14i			0.946858i	−0.880832	+	0.473429i	$0.843016\pi$
$984$	−7.06495e14	−	7.17901e14i	−0.765833	−	0.778196i
$985$		0			0
$986$	−1.60364e14	+	4.25110e13i	−0.172077	+	0.0456160i
$987$		−	1.25803e13i		−	0.0134309i
$988$	9.23943e13	+	1.62023e14i	0.0981432	+	0.172104i
$989$	−3.64290e14			−0.385004
$990$		0			0
$991$		−	2.07745e14i		−	0.217352i	−0.994077	−	0.108676i	$-0.965339\pi$
$991$		−	2.07745e14i		−	0.217352i	0.994077	−	0.108676i	$-0.0346611\pi$
$992$	1.58347e15	+	4.47022e14i	1.64836	+	0.465340i
$993$	−1.10673e14			−0.114629
$994$	7.31728e13	−	1.93974e13i	0.0754081	−	0.0199900i
$995$		0			0
$996$	−6.26276e14	+	3.57137e14i	−0.638953	+	0.364366i
$997$	−1.72913e15			−1.75530			−0.877650	−	0.479303i	$-0.840890\pi$
$997$	−1.72913e15			−1.75530			−0.877650	+	0.479303i	$0.840890\pi$
$998$	−3.58800e13	−	1.35350e14i	−0.0362409	−	0.136711i
$999$		−	1.89328e15i		−	1.90277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.11.b.e.51.2		20
4.3	odd	2	inner	100.11.b.e.51.1		20
5.2	odd	4		100.11.d.c.99.17		40
5.3	odd	4		100.11.d.c.99.24		40
5.4	even	2		20.11.b.a.11.19	✓	20
15.14	odd	2		180.11.c.a.91.2		20
20.3	even	4		100.11.d.c.99.18		40
20.7	even	4		100.11.d.c.99.23		40
20.19	odd	2		20.11.b.a.11.20	yes	20
40.19	odd	2		320.11.b.d.191.14		20
40.29	even	2		320.11.b.d.191.7		20
60.59	even	2		180.11.c.a.91.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.b.a.11.19	✓	20	5.4	even	2
20.11.b.a.11.20	yes	20	20.19	odd	2
100.11.b.e.51.1		20	4.3	odd	2	inner
100.11.b.e.51.2		20	1.1	even	1	trivial
100.11.d.c.99.17		40	5.2	odd	4
100.11.d.c.99.18		40	20.3	even	4
100.11.d.c.99.23		40	20.7	even	4
100.11.d.c.99.24		40	5.3	odd	4
180.11.c.a.91.1		20	60.59	even	2
180.11.c.a.91.2		20	15.14	odd	2
320.11.b.d.191.7		20	40.29	even	2
320.11.b.d.191.14		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)

\(f(q)\)	\(=\)	\(q+(-30.9316 + 8.19968i) q^{2} -206.425i q^{3} +(889.530 - 507.259i) q^{4} +(1692.62 + 6385.07i) q^{6} -1527.38i q^{7} +(-23355.3 + 22984.2i) q^{8} +16437.6 q^{9} +O(q^{10})\)	\(q+(-30.9316 + 8.19968i) q^{2} -206.425i q^{3} +(889.530 - 507.259i) q^{4} +(1692.62 + 6385.07i) q^{6} -1527.38i q^{7} +(-23355.3 + 22984.2i) q^{8} +16437.6 q^{9} +294294. i q^{11} +(-104711. - 183622. i) q^{12} -198131. q^{13} +(12524.1 + 47244.5i) q^{14} +(533953. - 902445. i) q^{16} -367959. q^{17} +(-508442. + 134783. i) q^{18} -919311. i q^{19} -315291. q^{21} +(-2.41311e6 - 9.10298e6i) q^{22} +2.57690e6i q^{23} +(4.74452e6 + 4.82111e6i) q^{24} +(6.12851e6 - 1.62461e6i) q^{26} -1.55823e7i q^{27} +(-774779. - 1.35865e6i) q^{28} -1.40898e7 q^{29} -4.90356e7i q^{31} +(-9.11626e6 + 3.22923e7i) q^{32} +6.07497e7 q^{33} +(1.13816e7 - 3.01715e6i) q^{34} +(1.46218e7 - 8.33812e6i) q^{36} +1.21502e8 q^{37} +(7.53806e6 + 2.84358e7i) q^{38} +4.08993e7i q^{39} -1.48908e8 q^{41} +(9.75245e6 - 2.58528e6i) q^{42} +1.41368e8i q^{43} +(1.49283e8 + 2.61783e8i) q^{44} +(-2.11297e7 - 7.97076e7i) q^{46} +3.99006e7i q^{47} +(-1.86287e8 - 1.10221e8i) q^{48} +2.80142e8 q^{49} +7.59561e7i q^{51} +(-1.76244e8 + 1.00504e8i) q^{52} -1.03715e8 q^{53} +(1.27770e8 + 4.81987e8i) q^{54} +(3.51057e7 + 3.56724e7i) q^{56} -1.89769e8 q^{57} +(4.35820e8 - 1.15532e8i) q^{58} -4.38769e8i q^{59} -2.83067e8 q^{61} +(4.02077e8 + 1.51675e9i) q^{62} -2.51065e7i q^{63} +(1.71940e7 - 1.07360e9i) q^{64} +(-1.87909e9 + 4.98128e8i) q^{66} -2.00990e9i q^{67} +(-3.27311e8 + 1.86651e8i) q^{68} +5.31936e8 q^{69} -1.54881e9i q^{71} +(-3.83905e8 + 3.77805e8i) q^{72} -3.44009e9 q^{73} +(-3.75824e9 + 9.96274e8i) q^{74} +(-4.66329e8 - 8.17756e8i) q^{76} +4.49499e8 q^{77} +(-3.35361e8 - 1.26508e9i) q^{78} -2.88212e9i q^{79} -2.24597e9 q^{81} +(4.60595e9 - 1.22100e9i) q^{82} -3.41069e9i q^{83} +(-2.80461e8 + 1.59934e8i) q^{84} +(-1.15917e9 - 4.37273e9i) q^{86} +2.90849e9i q^{87} +(-6.76411e9 - 6.87330e9i) q^{88} -2.47857e9 q^{89} +3.02622e8i q^{91} +(1.30715e9 + 2.29223e9i) q^{92} -1.01222e10 q^{93} +(-3.27173e8 - 1.23419e9i) q^{94} +(6.66595e9 + 1.88183e9i) q^{96} +2.70022e9 q^{97} +(-8.66526e9 + 2.29708e9i) q^{98} +4.83748e9i 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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