LMFDB - Embedded newform 100.11.b.e.51.18

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			51.18
Root			$68.5823i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.11.b.e.51.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(29.9163 + 11.3585i) q^{2} +137.165i q^{3} +(765.971 + 679.606i) q^{4} +(-1557.98 + 4103.46i) q^{6} +24910.8i q^{7} +(15195.7 + 29031.6i) q^{8} +40234.9 q^{9} +O(q^{10})$	\(q+(29.9163 + 11.3585i) q^{2} +137.165i q^{3} +(765.971 + 679.606i) q^{4} +(-1557.98 + 4103.46i) q^{6} +24910.8i q^{7} +(15195.7 + 29031.6i) q^{8} +40234.9 q^{9} +11312.4i q^{11} +(-93217.9 + 105064. i) q^{12} +407265. q^{13} +(-282948. + 745239. i) q^{14} +(124847. + 1.04112e6i) q^{16} +1.49997e6 q^{17} +(1.20368e6 + 457006. i) q^{18} +2.09616e6i q^{19} -3.41688e6 q^{21} +(-128491. + 338425. i) q^{22} -1.00854e7i q^{23} +(-3.98210e6 + 2.08432e6i) q^{24} +(1.21839e7 + 4.62590e6i) q^{26} +1.36182e7i q^{27} +(-1.69295e7 + 1.90809e7i) q^{28} -2.68271e7 q^{29} -9.47015e6i q^{31} +(-8.09054e6 + 3.25644e7i) q^{32} -1.55166e6 q^{33} +(4.48735e7 + 1.70373e7i) q^{34} +(3.08187e7 + 2.73439e7i) q^{36} +6.03238e7 q^{37} +(-2.38091e7 + 6.27094e7i) q^{38} +5.58623e7i q^{39} -3.12967e7 q^{41} +(-1.02220e8 - 3.88105e7i) q^{42} +2.55575e8i q^{43} +(-7.68797e6 + 8.66496e6i) q^{44} +(1.14555e8 - 3.01719e8i) q^{46} -3.78083e8i q^{47} +(-1.42804e8 + 1.71245e7i) q^{48} -3.38072e8 q^{49} +2.05743e8i q^{51} +(3.11953e8 + 2.76780e8i) q^{52} -7.29570e6 q^{53} +(-1.54682e8 + 4.07407e8i) q^{54} +(-7.23199e8 + 3.78538e8i) q^{56} -2.87519e8 q^{57} +(-8.02566e8 - 3.04714e8i) q^{58} +2.59793e8i q^{59} -3.30862e8 q^{61} +(1.07566e8 - 2.83312e8i) q^{62} +1.00228e9i q^{63} +(-6.11921e8 + 8.82312e8i) q^{64} +(-4.64199e7 - 1.76244e7i) q^{66} +7.94046e7i q^{67} +(1.14893e9 + 1.01939e9i) q^{68} +1.38336e9 q^{69} -1.16126e9i q^{71} +(6.11399e8 + 1.16808e9i) q^{72} -3.86449e9 q^{73} +(1.80467e9 + 6.85185e8i) q^{74} +(-1.42456e9 + 1.60560e9i) q^{76} -2.81800e8 q^{77} +(-6.34510e8 + 1.67120e9i) q^{78} -3.82600e9i q^{79} +5.07889e8 q^{81} +(-9.36280e8 - 3.55482e8i) q^{82} -9.01358e8i q^{83} +(-2.61723e9 - 2.32213e9i) q^{84} +(-2.90294e9 + 7.64586e9i) q^{86} -3.67972e9i q^{87} +(-3.28416e8 + 1.71900e8i) q^{88} -4.02278e9 q^{89} +1.01453e10i q^{91} +(6.85412e9 - 7.72515e9i) q^{92} +1.29897e9 q^{93} +(4.29444e9 - 1.13108e10i) q^{94} +(-4.46669e9 - 1.10974e9i) q^{96} +1.37620e10 q^{97} +(-1.01139e10 - 3.83998e9i) q^{98} +4.55152e8i 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 $

$2$	29.9163	+	11.3585i	0.934885	+	0.354952i
$2$	29.9163	+	11.3585i	0.934885	+	0.354952i
$3$			137.165i			0.564463i	0.959346	+	0.282232i	$0.0910747\pi$
$3$			137.165i			0.564463i	−0.959346	+	0.282232i	$0.908925\pi$
$4$	765.971	+	679.606i	0.748018	+	0.663678i
$5$		0			0
$5$		0			0
$6$	−1557.98	+	4103.46i	−0.200357	+	0.527708i
$7$			24910.8i			1.48217i	0.671413	+	0.741084i	$0.265688\pi$
$7$			24910.8i			1.48217i	−0.671413	+	0.741084i	$0.734312\pi$
$8$	15195.7	+	29031.6i	0.463737	+	0.885973i
$9$	40234.9			0.681381
$10$		0			0
$11$			11312.4i			0.0702410i	0.999383	+	0.0351205i	$0.0111815\pi$
$11$			11312.4i			0.0702410i	−0.999383	+	0.0351205i	$0.988818\pi$
$12$	−93217.9	+	105064.i	−0.374622	+	0.422229i
$13$	407265.			1.09688			0.548442	−	0.836189i	$-0.315221\pi$
$13$	407265.			1.09688			0.548442	+	0.836189i	$0.315221\pi$
$14$	−282948.	+	745239.i	−0.526098	+	1.38566i
$15$		0			0
$16$	124847.	+	1.04112e6i	0.119063	+	0.992887i
$17$	1.49997e6			1.05642			0.528211	−	0.849113i	$-0.322863\pi$
$17$	1.49997e6			1.05642			0.528211	+	0.849113i	$0.322863\pi$
$18$	1.20368e6	+	457006.i	0.637013	+	0.241857i
$19$			2.09616e6i			0.846557i	0.906000	+	0.423279i	$0.139121\pi$
$19$			2.09616e6i			0.846557i	−0.906000	+	0.423279i	$0.860879\pi$
$20$		0			0
$21$	−3.41688e6			−0.836629
$22$	−128491.	+	338425.i	−0.0249322	+	0.0656672i
$23$		−	1.00854e7i		−	1.56695i	−0.621423	−	0.783476i	$-0.713445\pi$
$23$		−	1.00854e7i		−	1.56695i	0.621423	−	0.783476i	$-0.286555\pi$
$24$	−3.98210e6	+	2.08432e6i	−0.500099	+	0.261763i
$25$		0			0
$26$	1.21839e7	+	4.62590e6i	1.02546	+	0.389341i
$27$			1.36182e7i			0.949078i
$28$	−1.69295e7	+	1.90809e7i	−0.983682	+	1.10869i
$29$	−2.68271e7			−1.30793			−0.653963	−	0.756527i	$-0.726895\pi$
$29$	−2.68271e7			−1.30793			−0.653963	+	0.756527i	$0.726895\pi$
$30$		0			0
$31$		−	9.47015e6i		−	0.330787i	−0.986228	−	0.165393i	$-0.947111\pi$
$31$		−	9.47015e6i		−	0.330787i	0.986228	−	0.165393i	$-0.0528894\pi$
$32$	−8.09054e6	+	3.25644e7i	−0.241117	+	0.970496i
$33$	−1.55166e6			−0.0396485
$34$	4.48735e7	+	1.70373e7i	0.987633	+	0.374979i
$35$		0			0
$36$	3.08187e7	+	2.73439e7i	0.509686	+	0.452218i
$37$	6.03238e7			0.869922			0.434961	−	0.900449i	$-0.356762\pi$
$37$	6.03238e7			0.869922			0.434961	+	0.900449i	$0.356762\pi$
$38$	−2.38091e7	+	6.27094e7i	−0.300487	+	0.791433i
$39$			5.58623e7i			0.619150i
$40$		0			0
$41$	−3.12967e7			−0.270134			−0.135067	−	0.990836i	$-0.543125\pi$
$41$	−3.12967e7			−0.270134			−0.135067	+	0.990836i	$0.543125\pi$
$42$	−1.02220e8	−	3.88105e7i	−0.782152	−	0.296963i
$43$			2.55575e8i			1.73851i	0.494367	+	0.869253i	$0.335400\pi$
$43$			2.55575e8i			1.73851i	−0.494367	+	0.869253i	$0.664600\pi$
$44$	−7.68797e6	+	8.66496e6i	−0.0466174	+	0.0525416i
$45$		0			0
$46$	1.14555e8	−	3.01719e8i	0.556192	−	1.46492i
$47$		−	3.78083e8i		−	1.64853i	−0.566202	−	0.824267i	$-0.691588\pi$
$47$		−	3.78083e8i		−	1.64853i	0.566202	−	0.824267i	$-0.308412\pi$
$48$	−1.42804e8	+	1.71245e7i	−0.560448	+	0.0672067i
$49$	−3.38072e8			−1.19682
$50$		0			0
$51$			2.05743e8i			0.596312i
$52$	3.11953e8	+	2.76780e8i	0.820489	+	0.727977i
$53$	−7.29570e6			−0.0174457			−0.00872283	−	0.999962i	$-0.502777\pi$
$53$	−7.29570e6			−0.0174457			−0.00872283	+	0.999962i	$0.502777\pi$
$54$	−1.54682e8	+	4.07407e8i	−0.336877	+	0.887278i
$55$		0			0
$56$	−7.23199e8	+	3.78538e8i	−1.31316	+	0.687336i
$57$	−2.87519e8			−0.477851
$58$	−8.02566e8	−	3.04714e8i	−1.22276	−	0.464251i
$59$			2.59793e8i			0.363386i	0.983355	+	0.181693i	$0.0581577\pi$
$59$			2.59793e8i			0.363386i	−0.983355	+	0.181693i	$0.941842\pi$
$60$		0			0
$61$	−3.30862e8			−0.391740			−0.195870	−	0.980630i	$-0.562753\pi$
$61$	−3.30862e8			−0.391740			−0.195870	+	0.980630i	$0.562753\pi$
$62$	1.07566e8	−	2.83312e8i	0.117413	−	0.309248i
$63$			1.00228e9i			1.00992i
$64$	−6.11921e8	+	8.82312e8i	−0.569896	+	0.821717i
$65$		0			0
$66$	−4.64199e7	−	1.76244e7i	−0.0370667	−	0.0140733i
$67$			7.94046e7i			0.0588128i	0.999568	+	0.0294064i	$0.00936169\pi$
$67$			7.94046e7i			0.0588128i	−0.999568	+	0.0294064i	$0.990638\pi$
$68$	1.14893e9	+	1.01939e9i	0.790223	+	0.701124i
$69$	1.38336e9			0.884487
$70$		0			0
$71$		−	1.16126e9i		−	0.643630i	−0.946803	−	0.321815i	$-0.895707\pi$
$71$		−	1.16126e9i		−	0.643630i	0.946803	−	0.321815i	$-0.104293\pi$
$72$	6.11399e8	+	1.16808e9i	0.315982	+	0.603685i
$73$	−3.86449e9			−1.86414			−0.932069	−	0.362280i	$-0.881998\pi$
$73$	−3.86449e9			−1.86414			−0.932069	+	0.362280i	$0.881998\pi$
$74$	1.80467e9	+	6.85185e8i	0.813276	+	0.308780i
$75$		0			0
$76$	−1.42456e9	+	1.60560e9i	−0.561841	+	0.633240i
$77$	−2.81800e8			−0.104109
$78$	−6.34510e8	+	1.67120e9i	−0.219769	+	0.578834i
$79$		−	3.82600e9i		−	1.24340i	−0.783257	−	0.621698i	$-0.786443\pi$
$79$		−	3.82600e9i		−	1.24340i	0.783257	−	0.621698i	$-0.213557\pi$
$80$		0			0
$81$	5.07889e8			0.145661
$82$	−9.36280e8	−	3.55482e8i	−0.252544	−	0.0958844i
$83$		−	9.01358e8i		−	0.228827i	−0.993433	−	0.114413i	$-0.963501\pi$
$83$		−	9.01358e8i		−	0.228827i	0.993433	−	0.114413i	$-0.0364988\pi$
$84$	−2.61723e9	−	2.32213e9i	−0.625814	−	0.555252i
$85$		0			0
$86$	−2.90294e9	+	7.64586e9i	−0.617086	+	1.62530i
$87$		−	3.67972e9i		−	0.738276i
$88$	−3.28416e8	+	1.71900e8i	−0.0622316	+	0.0325734i
$89$	−4.02278e9			−0.720404			−0.360202	−	0.932874i	$-0.617292\pi$
$89$	−4.02278e9			−0.720404			−0.360202	+	0.932874i	$0.617292\pi$
$90$		0			0
$91$			1.01453e10i			1.62576i
$92$	6.85412e9	−	7.72515e9i	1.03995	−	1.17211i
$93$	1.29897e9			0.186717
$94$	4.29444e9	−	1.13108e10i	0.585150	−	1.54119i
$95$		0			0
$96$	−4.46669e9	−	1.10974e9i	−0.547810	−	0.136102i
$97$	1.37620e10			1.60259			0.801296	−	0.598268i	$-0.204144\pi$
$97$	1.37620e10			1.60259			0.801296	+	0.598268i	$0.204144\pi$
$98$	−1.01139e10	−	3.83998e9i	−1.11889	−	0.424813i
$99$			4.55152e8i			0.0478609i
$100$		0			0
$101$	−1.30862e10			−1.24511			−0.622555	−	0.782576i	$-0.713905\pi$
$101$	−1.30862e10			−1.24511			−0.622555	+	0.782576i	$0.713905\pi$
$102$	−2.33692e9	+	6.15506e9i	−0.211662	+	0.557482i
$103$			1.33473e10i			1.15135i	0.817678	+	0.575675i	$0.195261\pi$
$103$			1.33473e10i			1.15135i	−0.817678	+	0.575675i	$0.804739\pi$
$104$	6.18869e9	+	1.18235e10i	0.508665	+	0.971809i
$105$		0			0
$106$	−2.18260e8	−	8.28679e7i	−0.0163097	−	0.00619237i
$107$		−	8.37635e9i		−	0.597222i	−0.954375	−	0.298611i	$-0.903477\pi$
$107$		−	8.37635e9i		−	0.597222i	0.954375	−	0.298611i	$-0.0965234\pi$
$108$	−9.25504e9	+	1.04312e10i	−0.629882	+	0.709928i
$109$	2.51755e9			0.163623			0.0818117	−	0.996648i	$-0.473929\pi$
$109$	2.51755e9			0.163623			0.0818117	+	0.996648i	$0.473929\pi$
$110$		0			0
$111$			8.27429e9i			0.491039i
$112$	−2.59350e10	+	3.11003e9i	−1.47162	+	0.176471i
$113$	−1.47892e9			−0.0802698			−0.0401349	−	0.999194i	$-0.512779\pi$
$113$	−1.47892e9			−0.0802698			−0.0401349	+	0.999194i	$0.512779\pi$
$114$	−8.60150e9	−	3.26577e9i	−0.446735	−	0.169614i
$115$		0			0
$116$	−2.05487e10	−	1.82318e10i	−0.978352	−	0.868041i
$117$	1.63863e10			0.747395
$118$	−2.95085e9	+	7.77205e9i	−0.128984	+	0.339724i
$119$			3.73654e10i			1.56579i
$120$		0			0
$121$	2.58095e10			0.995066
$122$	−9.89817e9	−	3.75808e9i	−0.366232	−	0.139049i
$123$		−	4.29279e9i		−	0.152481i
$124$	6.43597e9	−	7.25386e9i	0.219536	−	0.247435i
$125$		0			0
$126$	−1.13844e10	+	2.99846e10i	−0.358473	+	0.944159i
$127$			3.20677e10i			0.970621i	0.874342	+	0.485311i	$0.161293\pi$
$127$			3.20677e10i			0.970621i	−0.874342	+	0.485311i	$0.838707\pi$
$128$	−2.83281e10	+	1.94450e10i	−0.824457	+	0.565925i
$129$	−3.50559e10			−0.981323
$130$		0			0
$131$		−	4.86920e10i		−	1.26212i	−0.775733	−	0.631061i	$-0.782620\pi$
$131$		−	4.86920e10i		−	1.26212i	0.775733	−	0.631061i	$-0.217380\pi$
$132$	−1.18853e9	−	1.05452e9i	−0.0296578	−	0.0263138i
$133$	−5.22170e10			−1.25474
$134$	−9.01914e8	+	2.37549e9i	−0.0208757	+	0.0549831i
$135$		0			0
$136$	2.27931e10	+	4.35464e10i	0.489902	+	0.935961i
$137$	3.90738e9			0.0809623			0.0404812	−	0.999180i	$-0.487111\pi$
$137$	3.90738e9			0.0809623			0.0404812	+	0.999180i	$0.487111\pi$
$138$	4.13852e10	+	1.57129e10i	0.826893	+	0.313950i
$139$			3.40878e9i			0.0656938i	0.999460	+	0.0328469i	$0.0104574\pi$
$139$			3.40878e9i			0.0656938i	−0.999460	+	0.0328469i	$0.989543\pi$
$140$		0			0
$141$	5.18596e10			0.930537
$142$	1.31901e10	−	3.47405e10i	0.228458	−	0.601720i
$143$			4.60714e9i			0.0770462i
$144$	5.02319e9	+	4.18892e10i	0.0811273	+	0.676534i
$145$		0			0
$146$	−1.15611e11	−	4.38947e10i	−1.74275	−	0.661679i
$147$		−	4.63715e10i		−	0.675561i
$148$	4.62063e10	+	4.09964e10i	0.650717	+	0.577348i
$149$	2.39565e9			0.0326207			0.0163103	−	0.999867i	$-0.494808\pi$
$149$	2.39565e9			0.0326207			0.0163103	+	0.999867i	$0.494808\pi$
$150$		0			0
$151$		−	8.19556e10i		−	1.04398i	−0.852950	−	0.521992i	$-0.825189\pi$
$151$		−	8.19556e10i		−	1.04398i	0.852950	−	0.521992i	$-0.174811\pi$
$152$	−6.08548e10	+	3.18527e10i	−0.750027	+	0.392580i
$153$	6.03510e10			0.719826
$154$	−8.43042e9	−	3.20082e9i	−0.0973298	−	0.0369536i
$155$		0			0
$156$	−3.79644e10	+	4.27889e10i	−0.410916	+	0.463136i
$157$	1.18679e11			1.24416			0.622082	−	0.782952i	$-0.286287\pi$
$157$	1.18679e11			1.24416			0.622082	+	0.782952i	$0.286287\pi$
$158$	4.34575e10	−	1.14460e11i	0.441346	−	1.16243i
$159$		−	1.00071e9i		−	0.00984744i
$160$		0			0
$161$	2.51236e11			2.32248
$162$	1.51942e10	+	5.76884e9i	0.136176	+	0.0517027i
$163$		−	5.39517e10i		−	0.468886i	−0.972130	−	0.234443i	$-0.924673\pi$
$163$		−	5.39517e10i		−	0.468886i	0.972130	−	0.234443i	$-0.0753266\pi$
$164$	−2.39723e10	−	2.12694e10i	−0.202065	−	0.179282i
$165$		0			0
$166$	1.02380e10	−	2.69653e10i	0.0812224	−	0.213927i
$167$		−	8.18493e10i		−	0.630133i	−0.949070	−	0.315067i	$-0.897973\pi$
$167$		−	8.18493e10i		−	0.630133i	0.949070	−	0.315067i	$-0.102027\pi$
$168$	−5.19220e10	−	9.91973e10i	−0.387976	−	0.741231i
$169$	2.80063e10			0.203153
$170$		0			0
$171$			8.43387e10i			0.576828i
$172$	−1.73690e11	+	1.95763e11i	−1.15381	+	1.30043i
$173$	2.43804e11			1.57330			0.786649	−	0.617400i	$-0.211814\pi$
$173$	2.43804e11			1.57330			0.786649	+	0.617400i	$0.211814\pi$
$174$	4.17960e10	−	1.10084e11i	0.262052	−	0.690203i
$175$		0			0
$176$	−1.17775e10	+	1.41231e9i	−0.0697414	+	0.00836311i
$177$	−3.56344e10			−0.205118
$178$	−1.20347e11	−	4.56926e10i	−0.673495	−	0.255709i
$179$		−	3.02221e11i		−	1.64460i	−0.569056	−	0.822299i	$-0.692691\pi$
$179$		−	3.02221e11i		−	1.64460i	0.569056	−	0.822299i	$-0.307309\pi$
$180$		0			0
$181$	2.83369e11			1.45868			0.729340	−	0.684152i	$-0.239827\pi$
$181$	2.83369e11			1.45868			0.729340	+	0.684152i	$0.239827\pi$
$182$	−1.15235e11	+	3.03510e11i	−0.577068	+	1.51990i
$183$		−	4.53826e10i		−	0.221123i
$184$	2.92796e11	−	1.53256e11i	1.38828	−	0.726653i
$185$		0			0
$186$	3.88604e10	+	1.47543e10i	0.174559	+	0.0662756i
$187$			1.69682e10i			0.0742041i
$188$	2.56948e11	−	2.89600e11i	1.09410	−	1.23313i
$189$	−3.39241e11			−1.40669
$190$		0			0
$191$		−	3.63631e11i		−	1.43052i	−0.698859	−	0.715260i	$-0.746308\pi$
$191$		−	3.63631e11i		−	1.43052i	0.698859	−	0.715260i	$-0.253692\pi$
$192$	−1.21022e11	−	8.39339e10i	−0.463829	−	0.321685i
$193$	2.05085e11			0.765857			0.382929	−	0.923778i	$-0.374916\pi$
$193$	2.05085e11			0.765857			0.382929	+	0.923778i	$0.374916\pi$
$194$	4.11708e11	+	1.56315e11i	1.49824	+	0.568843i
$195$		0			0
$196$	−2.58953e11	−	2.29756e11i	−0.895243	−	0.794303i
$197$	4.83954e11			1.63107			0.815536	−	0.578706i	$-0.196442\pi$
$197$	4.83954e11			1.63107			0.815536	+	0.578706i	$0.196442\pi$
$198$	−5.16983e9	+	1.36165e10i	−0.0169883	+	0.0447444i
$199$			5.61971e11i			1.80073i	0.435137	+	0.900364i	$0.356700\pi$
$199$			5.61971e11i			1.80073i	−0.435137	+	0.900364i	$0.643300\pi$
$200$		0			0
$201$	−1.08915e10			−0.0331977
$202$	−3.91492e11	−	1.48640e11i	−1.16403	−	0.441954i
$203$		−	6.68283e11i		−	1.93856i
$204$	−1.39824e11	+	1.57593e11i	−0.395759	+	0.446052i
$205$		0			0
$206$	−1.51605e11	+	3.99302e11i	−0.408674	+	1.07638i
$207$		−	4.05786e11i		−	1.06769i
$208$	5.08457e10	+	4.24011e11i	0.130598	+	1.08908i
$209$	−2.37126e10			−0.0594630
$210$		0			0
$211$		−	3.25143e11i		−	0.777432i	−0.921358	−	0.388716i	$-0.872919\pi$
$211$		−	3.25143e11i		−	0.777432i	0.921358	−	0.388716i	$-0.127081\pi$
$212$	−5.58829e9	−	4.95820e9i	−0.0130497	−	0.0115783i
$213$	1.59283e11			0.363306
$214$	9.51425e10	−	2.50590e11i	0.211985	−	0.558334i
$215$		0			0
$216$	−3.95359e11	+	2.06939e11i	−0.840857	+	0.440123i
$217$	2.35909e11			0.490281
$218$	7.53158e10	+	2.85955e10i	0.152969	+	0.0580784i
$219$		−	5.30072e11i		−	1.05224i
$220$		0			0
$221$	6.10885e11			1.15877
$222$	−9.39832e10	+	2.47536e11i	−0.174295	+	0.459065i
$223$			5.08960e11i			0.922910i	0.887164	+	0.461455i	$0.152672\pi$
$223$			5.08960e11i			0.922910i	−0.887164	+	0.461455i	$0.847328\pi$
$224$	−8.11206e11	−	2.01542e11i	−1.43844	−	0.357375i
$225$		0			0
$226$	−4.42438e10	−	1.67982e10i	−0.0750430	−	0.0284919i
$227$			1.00059e11i			0.166008i	0.996549	+	0.0830038i	$0.0264514\pi$
$227$			1.00059e11i			0.166008i	−0.996549	+	0.0830038i	$0.973549\pi$
$228$	−2.20231e11	−	1.95400e11i	−0.357441	−	0.317139i
$229$	−5.09987e10			−0.0809808			−0.0404904	−	0.999180i	$-0.512892\pi$
$229$	−5.09987e10			−0.0809808			−0.0404904	+	0.999180i	$0.512892\pi$
$230$		0			0
$231$		−	3.86530e10i		−	0.0587657i
$232$	−4.07657e11	−	7.78831e11i	−0.606534	−	1.15879i
$233$	−1.13041e12			−1.64610			−0.823051	−	0.567968i	$-0.807730\pi$
$233$	−1.13041e12			−1.64610			−0.823051	+	0.567968i	$0.807730\pi$
$234$	4.90216e11	+	1.86123e11i	0.698728	+	0.265289i
$235$		0			0
$236$	−1.76557e11	+	1.98994e11i	−0.241171	+	0.271819i
$237$	5.24792e11			0.701852
$238$	−4.24413e11	+	1.11783e12i	−0.555781	+	1.46384i
$239$			6.47347e11i			0.830133i	0.909791	+	0.415067i	$0.136242\pi$
$239$			6.47347e11i			0.830133i	−0.909791	+	0.415067i	$0.863758\pi$
$240$		0			0
$241$	1.18012e12			1.45158			0.725788	−	0.687919i	$-0.241475\pi$
$241$	1.18012e12			1.45158			0.725788	+	0.687919i	$0.241475\pi$
$242$	7.72124e11	+	2.93156e11i	0.930272	+	0.353201i
$243$			8.73807e11i			1.03130i
$244$	−2.53431e11	−	2.24856e11i	−0.293029	−	0.259989i
$245$		0			0
$246$	4.87595e10	−	1.28425e11i	0.0541233	−	0.142552i
$247$			8.53693e11i			0.928574i
$248$	2.74933e11	−	1.43906e11i	0.293068	−	0.153398i
$249$	1.23634e11			0.129164
$250$		0			0
$251$			6.64973e11i			0.667476i	0.942666	+	0.333738i	$0.108310\pi$
$251$			6.64973e11i			0.667476i	−0.942666	+	0.333738i	$0.891690\pi$
$252$	−6.81157e11	+	7.67719e11i	−0.670262	+	0.755439i
$253$	1.14090e11			0.110064
$254$	−3.64240e11	+	9.59348e11i	−0.344524	+	0.907419i
$255$		0			0
$256$	−1.06834e12	+	2.59960e11i	−0.971648	+	0.236432i
$257$	−1.03129e12			−0.919844			−0.459922	−	0.887959i	$-0.652123\pi$
$257$	−1.03129e12			−0.919844			−0.459922	+	0.887959i	$0.652123\pi$
$258$	−1.04874e12	−	3.98181e11i	−0.917424	−	0.348323i
$259$			1.50271e12i			1.28937i
$260$		0			0
$261$	−1.07938e12			−0.891196
$262$	5.53066e11	−	1.45668e12i	0.447992	−	1.17994i
$263$			1.84871e12i			1.46923i	0.678485	+	0.734615i	$0.262637\pi$
$263$			1.84871e12i			1.46923i	−0.678485	+	0.734615i	$0.737363\pi$
$264$	−2.35786e10	−	4.50471e10i	−0.0183865	−	0.0351275i
$265$		0			0
$266$	−1.56214e12	−	5.93104e11i	−1.17304	−	0.445372i
$267$		−	5.51783e11i		−	0.406642i
$268$	−5.39639e10	+	6.08216e10i	−0.0390327	+	0.0439930i
$269$	−5.02760e11			−0.356943			−0.178472	−	0.983945i	$-0.557115\pi$
$269$	−5.02760e11			−0.356943			−0.178472	+	0.983945i	$0.557115\pi$
$270$		0			0
$271$			4.51814e11i			0.309110i	0.987984	+	0.154555i	$0.0493944\pi$
$271$			4.51814e11i			0.309110i	−0.987984	+	0.154555i	$0.950606\pi$
$272$	1.87266e11	+	1.56164e12i	0.125781	+	1.04891i
$273$	−1.39157e12			−0.917684
$274$	1.16894e11	+	4.43818e10i	0.0756904	+	0.0287377i
$275$		0			0
$276$	1.05962e12	+	9.40143e11i	0.661612	+	0.587014i
$277$	2.53984e12			1.55742			0.778712	−	0.627381i	$-0.215873\pi$
$277$	2.53984e12			1.55742			0.778712	+	0.627381i	$0.215873\pi$
$278$	−3.87185e10	+	1.01978e11i	−0.0233181	+	0.0614161i
$279$		−	3.81030e11i		−	0.225392i
$280$		0			0
$281$	−7.11997e11			−0.406393			−0.203197	−	0.979138i	$-0.565133\pi$
$281$	−7.11997e11			−0.406393			−0.203197	+	0.979138i	$0.565133\pi$
$282$	1.55145e12	+	5.89045e11i	0.869945	+	0.330296i
$283$		−	2.47422e12i		−	1.36303i	−0.731804	−	0.681515i	$-0.761322\pi$
$283$		−	2.47422e12i		−	1.36303i	0.731804	−	0.681515i	$-0.238678\pi$
$284$	7.89197e11	−	8.89488e11i	0.427163	−	0.481447i
$285$		0			0
$286$	−5.23300e10	+	1.37829e11i	−0.0273477	+	0.0720293i
$287$		−	7.79624e11i		−	0.400383i
$288$	−3.25522e11	+	1.31023e12i	−0.164292	+	0.661278i
$289$	2.33911e11			0.116027
$290$		0			0
$291$			1.88766e12i			0.904604i
$292$	−2.96009e12	−	2.62633e12i	−1.39441	−	1.23719i
$293$	6.83082e11			0.316326			0.158163	−	0.987413i	$-0.449443\pi$
$293$	6.83082e11			0.316326			0.158163	+	0.987413i	$0.449443\pi$
$294$	5.26709e11	−	1.38726e12i	0.239792	−	0.631571i
$295$		0			0
$296$	9.16665e11	+	1.75129e12i	0.403415	+	0.770727i
$297$	−1.54055e11			−0.0666642
$298$	7.16691e10	+	2.72109e10i	0.0304965	+	0.0115788i
$299$		−	4.10744e12i		−	1.71876i
$300$		0			0
$301$	−6.36658e12			−2.57676
$302$	9.30889e11	−	2.45181e12i	0.370564	−	0.976005i
$303$		−	1.79497e12i		−	0.702819i
$304$	−2.18235e12	+	2.61698e11i	−0.840536	+	0.100794i
$305$		0			0
$306$	1.80548e12	+	6.85495e11i	0.672954	+	0.255504i
$307$		−	1.64841e12i		−	0.604467i	−0.953234	−	0.302234i	$-0.902268\pi$
$307$		−	1.64841e12i		−	0.604467i	0.953234	−	0.302234i	$-0.0977323\pi$
$308$	−2.15851e11	−	1.91513e11i	−0.0778754	−	0.0690948i
$309$	−1.83078e12			−0.649895
$310$		0			0
$311$		−	2.37457e12i		−	0.816174i	−0.912943	−	0.408087i	$-0.866196\pi$
$311$		−	2.37457e12i		−	0.816174i	0.912943	−	0.408087i	$-0.133804\pi$
$312$	−1.62177e12	+	8.48870e11i	−0.548550	+	0.287123i
$313$	1.22906e12			0.409122			0.204561	−	0.978854i	$-0.434423\pi$
$313$	1.22906e12			0.409122			0.204561	+	0.978854i	$0.434423\pi$
$314$	3.55045e12	+	1.34802e12i	1.16315	+	0.441618i
$315$		0			0
$316$	2.60018e12	−	2.93061e12i	0.825215	−	0.930084i
$317$	−6.24013e12			−1.94938			−0.974692	−	0.223551i	$-0.928235\pi$
$317$	−6.24013e12			−1.94938			−0.974692	+	0.223551i	$0.928235\pi$
$318$	1.13665e10	−	2.99376e10i	0.00349537	−	0.00920622i
$319$		−	3.03478e11i		−	0.0918700i
$320$		0			0
$321$	1.14894e12			0.337110
$322$	7.51606e12	+	2.85365e12i	2.17125	+	0.824370i
$323$			3.14417e12i			0.894322i
$324$	3.89028e11	+	3.45165e11i	0.108957	+	0.0966722i
$325$		0			0
$326$	6.12809e11	−	1.61404e12i	0.166432	−	0.438354i
$327$			3.45319e11i			0.0923594i
$328$	−4.75576e11	−	9.08591e11i	−0.125271	−	0.239331i
$329$	9.41834e12			2.44340
$330$		0			0
$331$			6.89984e11i			0.173660i	0.996223	+	0.0868299i	$0.0276737\pi$
$331$			6.89984e11i			0.173660i	−0.996223	+	0.0868299i	$0.972326\pi$
$332$	6.12568e11	−	6.90414e11i	0.151867	−	0.171167i
$333$	2.42712e12			0.592748
$334$	9.29682e11	−	2.44863e12i	0.223667	−	0.589102i
$335$		0			0
$336$	−4.26586e11	−	3.55737e12i	−0.0996116	−	0.830678i
$337$	−1.19316e12			−0.274503			−0.137252	−	0.990536i	$-0.543827\pi$
$337$	−1.19316e12			−0.274503			−0.137252	+	0.990536i	$0.543827\pi$
$338$	8.37845e11	+	3.18108e11i	0.189924	+	0.0721094i
$339$		−	2.02855e11i		−	0.0453093i
$340$		0			0
$341$	1.07130e11			0.0232348
$342$	−9.57958e11	+	2.52310e12i	−0.204746	+	0.539268i
$343$		−	1.38496e12i		−	0.291719i
$344$	−7.41974e12	+	3.88365e12i	−1.54027	+	0.806210i
$345$		0			0
$346$	7.29373e12	+	2.76924e12i	1.47085	+	0.558445i
$347$			7.68368e12i			1.52729i	0.645635	+	0.763646i	$0.276593\pi$
$347$			7.68368e12i			1.52729i	−0.645635	+	0.763646i	$0.723407\pi$
$348$	2.50076e12	−	2.81856e12i	0.489978	−	0.552244i
$349$	−5.29768e12			−1.02320			−0.511598	−	0.859225i	$-0.670946\pi$
$349$	−5.29768e12			−1.02320			−0.511598	+	0.859225i	$0.670946\pi$
$350$		0			0
$351$			5.54623e12i			1.04103i
$352$	−3.68381e11	−	9.15232e10i	−0.0681686	−	0.0169363i
$353$	−6.78784e12			−1.23839			−0.619196	−	0.785237i	$-0.712541\pi$
$353$	−6.78784e12			−1.23839			−0.619196	+	0.785237i	$0.712541\pi$
$354$	−1.06605e12	−	4.04752e11i	−0.191762	−	0.0728070i
$355$		0			0
$356$	−3.08133e12	−	2.73391e12i	−0.538875	−	0.478116i
$357$	−5.12521e12			−0.883833
$358$	3.43277e12	−	9.04134e12i	0.583753	−	1.53751i
$359$		−	1.68781e11i		−	0.0283042i	−0.999900	−	0.0141521i	$-0.995495\pi$
$359$		−	1.68781e11i		−	0.0283042i	0.999900	−	0.0141521i	$-0.00450491\pi$
$360$		0			0
$361$	1.73718e12			0.283341
$362$	8.47736e12	+	3.21864e12i	1.36370	+	0.517761i
$363$			3.54014e12i			0.561678i
$364$	−6.89480e12	+	7.77100e12i	−1.07898	+	1.21610i
$365$		0			0
$366$	5.15476e11	−	1.35768e12i	0.0784879	−	0.206724i
$367$		−	2.20336e12i		−	0.330945i	−0.986214	−	0.165472i	$-0.947085\pi$
$367$		−	2.20336e12i		−	0.330945i	0.986214	−	0.165472i	$-0.0529148\pi$
$368$	1.05001e13	−	1.25913e12i	1.55580	−	0.186566i
$369$	−1.25922e12			−0.184064
$370$		0			0
$371$		−	1.81742e11i		−	0.0258574i
$372$	9.94972e11	+	8.82788e11i	0.139668	+	0.123920i
$373$	5.85726e12			0.811241			0.405621	−	0.914042i	$-0.367055\pi$
$373$	5.85726e12			0.811241			0.405621	+	0.914042i	$0.367055\pi$
$374$	−1.92733e11	+	5.07626e11i	−0.0263389	+	0.0693723i
$375$		0			0
$376$	1.09763e13	−	5.74525e12i	1.46056	−	0.764486i
$377$	−1.09257e13			−1.43464
$378$	−1.01488e13	−	3.85325e12i	−1.31509	−	0.499308i
$379$			1.01146e13i			1.29347i	0.762717	+	0.646733i	$0.223865\pi$
$379$			1.01146e13i			1.29347i	−0.762717	+	0.646733i	$0.776135\pi$
$380$		0			0
$381$	−4.39856e12			−0.547880
$382$	4.13029e12	−	1.08785e13i	0.507766	−	1.33737i
$383$		−	5.61682e12i		−	0.681549i	−0.940145	−	0.340774i	$-0.889311\pi$
$383$		−	5.61682e12i		−	0.681549i	0.940145	−	0.340774i	$-0.110689\pi$
$384$	−2.66717e12	−	3.88561e12i	−0.319444	−	0.465376i
$385$		0			0
$386$	6.13539e12	+	2.32945e12i	0.715988	+	0.271842i
$387$			1.02830e13i			1.18459i
$388$	1.05413e13	+	9.35274e12i	1.19877	+	1.06361i
$389$	1.05262e13			1.18175			0.590875	−	0.806763i	$-0.298783\pi$
$389$	1.05262e13			1.18175			0.590875	+	0.806763i	$0.298783\pi$
$390$		0			0
$391$		−	1.51278e13i		−	1.65536i
$392$	−5.13725e12	−	9.81475e12i	−0.555010	−	1.06035i
$393$	6.67882e12			0.712421
$394$	1.44781e13	+	5.49698e12i	1.52486	+	0.578952i
$395$		0			0
$396$	−3.09324e11	+	3.48633e11i	−0.0317642	+	0.0358008i
$397$	1.84913e12			0.187506			0.0937531	−	0.995595i	$-0.470114\pi$
$397$	1.84913e12			0.187506			0.0937531	+	0.995595i	$0.470114\pi$
$398$	−6.38312e12	+	1.68121e13i	−0.639172	+	1.68347i
$399$		−	7.16232e12i		−	0.708254i
$400$		0			0
$401$	−8.10185e12			−0.781380			−0.390690	−	0.920522i	$-0.627764\pi$
$401$	−8.10185e12			−0.781380			−0.390690	+	0.920522i	$0.627764\pi$
$402$	−3.25833e11	−	1.23711e11i	−0.0310360	−	0.0117836i
$403$		−	3.85686e12i		−	0.362835i
$404$	−1.00237e13	−	8.89349e12i	−0.931366	−	0.826353i
$405$		0			0
$406$	7.59066e12	−	1.99926e13i	0.688097	−	1.81233i
$407$			6.82406e11i			0.0611042i
$408$	−5.97303e12	+	3.12641e12i	−0.528316	+	0.276532i
$409$	9.35378e11			0.0817280			0.0408640	−	0.999165i	$-0.486989\pi$
$409$	9.35378e11			0.0817280			0.0408640	+	0.999165i	$0.486989\pi$
$410$		0			0
$411$			5.35954e11i			0.0457003i
$412$	−9.07091e12	+	1.02236e13i	−0.764126	+	0.861231i
$413$	−6.47165e12			−0.538598
$414$	4.60911e12	−	1.21396e13i	0.378979	−	0.998168i
$415$		0			0
$416$	−3.29499e12	+	1.32624e13i	−0.264477	+	1.06452i
$417$	−4.67564e11			−0.0370818
$418$	−7.09392e11	−	2.69338e11i	−0.0555911	−	0.0211065i
$419$			4.25922e11i			0.0329807i	0.999864	+	0.0164903i	$0.00524927\pi$
$419$			4.25922e11i			0.0329807i	−0.999864	+	0.0164903i	$0.994751\pi$
$420$		0			0
$421$	−7.58379e12			−0.573424			−0.286712	−	0.958017i	$-0.592562\pi$
$421$	−7.58379e12			−0.573424			−0.286712	+	0.958017i	$0.592562\pi$
$422$	3.69313e12	−	9.72709e12i	0.275951	−	0.726810i
$423$		−	1.52121e13i		−	1.12328i
$424$	−1.10864e11	−	2.11806e11i	−0.00809020	−	0.0154564i
$425$		0			0
$426$	4.76517e12	+	1.80921e12i	0.339649	+	0.128956i
$427$		−	8.24203e12i		−	0.580624i
$428$	5.69262e12	−	6.41604e12i	0.396363	−	0.446733i
$429$	−6.31936e11			−0.0434897
$430$		0			0
$431$			2.23217e13i			1.50086i	0.660949	+	0.750431i	$0.270154\pi$
$431$			2.23217e13i			1.50086i	−0.660949	+	0.750431i	$0.729846\pi$
$432$	−1.41782e13	+	1.70019e12i	−0.942327	+	0.113000i
$433$	−2.91087e12			−0.191242			−0.0956209	−	0.995418i	$-0.530484\pi$
$433$	−2.91087e12			−0.191242			−0.0956209	+	0.995418i	$0.530484\pi$
$434$	7.05752e12	+	2.67956e12i	0.458357	+	0.174026i
$435$		0			0
$436$	1.92837e12	+	1.71094e12i	0.122393	+	0.108593i
$437$	2.11407e13			1.32651
$438$	6.02080e12	−	1.58578e13i	0.373494	−	0.983721i
$439$		−	1.34336e13i		−	0.823891i	−0.911208	−	0.411946i	$-0.864849\pi$
$439$		−	1.34336e13i		−	0.823891i	0.911208	−	0.411946i	$-0.135151\pi$
$440$		0			0
$441$	−1.36023e13			−0.815490
$442$	1.82754e13	+	6.93871e12i	1.08332	+	0.411308i
$443$			1.25121e13i			0.733348i	0.930350	+	0.366674i	$0.119504\pi$
$443$			1.25121e13i			0.733348i	−0.930350	+	0.366674i	$0.880496\pi$
$444$	−5.62326e12	+	6.33787e12i	−0.325892	+	0.367306i
$445$		0			0
$446$	−5.78100e12	+	1.52262e13i	−0.327589	+	0.862814i
$447$			3.28599e11i			0.0184132i
$448$	−2.19791e13	−	1.52434e13i	−1.21792	−	0.844681i
$449$	−1.25344e13			−0.686865			−0.343433	−	0.939177i	$-0.611590\pi$
$449$	−1.25344e13			−0.686865			−0.343433	+	0.939177i	$0.611590\pi$
$450$		0			0
$451$		−	3.54040e11i		−	0.0189745i
$452$	−1.13281e12	−	1.00508e12i	−0.0600433	−	0.0532733i
$453$	1.12414e13			0.589291
$454$	−1.13652e12	+	2.99340e12i	−0.0589247	+	0.155198i
$455$		0			0
$456$	−4.36906e12	−	8.34712e12i	−0.221597	−	0.423363i
$457$	−9.29846e12			−0.466477			−0.233238	−	0.972420i	$-0.574932\pi$
$457$	−9.29846e12			−0.466477			−0.233238	+	0.972420i	$0.574932\pi$
$458$	−1.52569e12	−	5.79267e11i	−0.0757077	−	0.0287443i
$459$			2.04269e13i			1.00263i
$460$		0			0
$461$	2.01065e13			0.965675			0.482837	−	0.875710i	$-0.339606\pi$
$461$	2.01065e13			0.965675			0.482837	+	0.875710i	$0.339606\pi$
$462$	4.39039e11	−	1.15636e12i	0.0208590	−	0.0549391i
$463$			1.04776e13i			0.492442i	0.969214	+	0.246221i	$0.0791889\pi$
$463$			1.04776e13i			0.492442i	−0.969214	+	0.246221i	$0.920811\pi$
$464$	−3.34927e12	−	2.79301e13i	−0.155726	−	1.29862i
$465$		0			0
$466$	−3.38177e13	−	1.28397e13i	−1.53891	−	0.584287i
$467$			5.13372e12i			0.231125i	0.993300	+	0.115563i	$0.0368671\pi$
$467$			5.13372e12i			0.231125i	−0.993300	+	0.115563i	$0.963133\pi$
$468$	1.25514e13	+	1.11362e13i	0.559066	+	0.496030i
$469$	−1.97803e12			−0.0871703
$470$		0			0
$471$			1.62786e13i			0.702285i
$472$	−7.54220e12	+	3.94775e12i	−0.321950	+	0.168515i
$473$	−2.89116e12			−0.122114
$474$	1.56998e13	+	5.96083e12i	0.656151	+	0.249124i
$475$		0			0
$476$	−2.53937e13	+	2.86208e13i	−1.03918	+	1.17124i
$477$	−2.93542e11			−0.0118871
$478$	−7.35287e12	+	1.93662e13i	−0.294657	+	0.776079i
$479$		−	1.62966e12i		−	0.0646279i	−0.999478	−	0.0323139i	$-0.989712\pi$
$479$		−	1.62966e12i		−	0.0646279i	0.999478	−	0.0323139i	$-0.0102876\pi$
$480$		0			0
$481$	2.45678e13			0.954202
$482$	3.53047e13	+	1.34043e13i	1.35706	+	0.515239i
$483$			3.44607e13i			1.31096i
$484$	1.97693e13	+	1.75403e13i	0.744328	+	0.660404i
$485$		0			0
$486$	−9.92511e12	+	2.61411e13i	−0.366061	+	0.964145i
$487$		−	4.02012e13i		−	1.46756i	−0.679390	−	0.733778i	$-0.737755\pi$
$487$		−	4.02012e13i		−	1.46756i	0.679390	−	0.733778i	$-0.262245\pi$
$488$	−5.02769e12	−	9.60544e12i	−0.181664	−	0.347071i
$489$	7.40027e12			0.264669
$490$		0			0
$491$			2.15779e13i			0.756140i	0.925777	+	0.378070i	$0.123412\pi$
$491$			2.15779e13i			0.756140i	−0.925777	+	0.378070i	$0.876588\pi$
$492$	2.91741e12	−	3.28815e12i	0.101198	−	0.114058i
$493$	−4.02397e13			−1.38172
$494$	−9.69663e12	+	2.55393e13i	−0.329599	+	0.868110i
$495$		0			0
$496$	9.85953e12	−	1.18232e12i	0.328434	−	0.0393845i
$497$	2.89278e13			0.953967
$498$	3.69868e12	+	1.40430e12i	0.120754	+	0.0458471i
$499$		−	4.38721e13i		−	1.41803i	−0.705194	−	0.709015i	$-0.749140\pi$
$499$		−	4.38721e13i		−	1.41803i	0.705194	−	0.709015i	$-0.250860\pi$
$500$		0			0
$501$	1.12268e13			0.355687
$502$	−7.55307e12	+	1.98935e13i	−0.236922	+	0.624013i
$503$			5.52162e12i			0.171485i	0.996317	+	0.0857426i	$0.0273263\pi$
$503$			5.52162e12i			0.171485i	−0.996317	+	0.0857426i	$0.972674\pi$
$504$	−2.90978e13	+	1.52304e13i	−0.894762	+	0.468338i
$505$		0			0
$506$	3.41316e12	+	1.29589e12i	0.102897	+	0.0390675i
$507$			3.84147e12i			0.114672i
$508$	−2.17934e13	+	2.45629e13i	−0.644180	+	0.726042i
$509$	1.28339e13			0.375639			0.187819	−	0.982204i	$-0.439858\pi$
$509$	1.28339e13			0.375639			0.187819	+	0.982204i	$0.439858\pi$
$510$		0			0
$511$		−	9.62675e13i		−	2.76296i
$512$	−3.49135e13	−	4.35763e12i	−0.992301	−	0.123851i
$513$	−2.85460e13			−0.803449
$514$	−3.08523e13	−	1.17138e13i	−0.859948	−	0.326500i
$515$		0			0
$516$	−2.68518e13	−	2.38242e13i	−0.734048	−	0.651283i
$517$	4.27702e12			0.115795
$518$	−1.70685e13	+	4.49556e13i	−0.457664	+	1.20541i
$519$			3.34413e13i			0.888069i
$520$		0			0
$521$	−1.10526e13			−0.287922			−0.143961	−	0.989583i	$-0.545984\pi$
$521$	−1.10526e13			−0.287922			−0.143961	+	0.989583i	$0.545984\pi$
$522$	−3.22912e13	−	1.22601e13i	−0.833165	−	0.316332i
$523$		−	2.47975e13i		−	0.633723i	−0.948472	−	0.316861i	$-0.897371\pi$
$523$		−	2.47975e13i		−	0.633723i	0.948472	−	0.316861i	$-0.102629\pi$
$524$	3.30914e13	−	3.72967e13i	0.837642	−	0.944090i
$525$		0			0
$526$	−2.09985e13	+	5.53065e13i	−0.521506	+	1.37356i
$527$		−	1.42049e13i		−	0.349451i
$528$	−1.93719e11	−	1.61546e12i	−0.00472067	−	0.0393664i
$529$	−6.02895e13			−1.45534
$530$		0			0
$531$			1.04527e13i			0.247604i
$532$	−3.99967e13	−	3.54870e13i	−0.938568	−	0.832743i
$533$	−1.27460e13			−0.296305
$534$	6.26740e12	−	1.65073e13i	0.144338	−	0.380163i
$535$		0			0
$536$	−2.30524e12	+	1.20661e12i	−0.0521065	+	0.0272737i
$537$	4.14540e13			0.928315
$538$	−1.50407e13	−	5.71058e12i	−0.333701	−	0.126698i
$539$		−	3.82440e12i		−	0.0840658i
$540$		0			0
$541$	7.51994e13			1.62266			0.811331	−	0.584588i	$-0.198744\pi$
$541$	7.51994e13			1.62266			0.811331	+	0.584588i	$0.198744\pi$
$542$	−5.13191e12	+	1.35166e13i	−0.109719	+	0.288983i
$543$			3.88682e13i			0.823371i
$544$	−1.21355e13	+	4.88456e13i	−0.254721	+	1.02525i
$545$		0			0
$546$	−4.16308e13	−	1.58061e13i	−0.857929	−	0.325734i
$547$		−	2.15841e13i		−	0.440755i	−0.975415	−	0.220378i	$-0.929271\pi$
$547$		−	2.15841e13i		−	0.440755i	0.975415	−	0.220378i	$-0.0707289\pi$
$548$	2.99294e12	+	2.65548e12i	0.0605613	+	0.0537329i
$549$	−1.33122e13			−0.266924
$550$		0			0
$551$		−	5.62338e13i		−	1.10723i
$552$	2.10212e13	+	4.01612e13i	0.410169	+	0.783631i
$553$	9.53087e13			1.84292
$554$	7.59825e13	+	2.88486e13i	1.45601	+	0.552811i
$555$		0			0
$556$	−2.31663e12	+	2.61102e12i	−0.0435995	+	0.0491402i
$557$	2.33738e13			0.435966			0.217983	−	0.975953i	$-0.430052\pi$
$557$	2.33738e13			0.435966			0.217983	+	0.975953i	$0.430052\pi$
$558$	4.32792e12	−	1.13990e13i	0.0800033	−	0.210715i
$559$			1.04087e14i			1.90694i
$560$		0			0
$561$	−2.32744e12			−0.0418855
$562$	−2.13003e13	−	8.08719e12i	−0.379931	−	0.144250i
$563$		−	7.94427e13i		−	1.40447i	−0.711946	−	0.702235i	$-0.752186\pi$
$563$		−	7.94427e13i		−	1.40447i	0.711946	−	0.702235i	$-0.247814\pi$
$564$	3.97229e13	+	3.52441e13i	0.696059	+	0.617577i
$565$		0			0
$566$	2.81033e13	−	7.40194e13i	0.483810	−	1.27428i
$567$			1.26519e13i			0.215894i
$568$	3.37131e13	−	1.76461e13i	0.570239	−	0.298475i
$569$	−6.17162e13			−1.03476			−0.517378	−	0.855757i	$-0.673092\pi$
$569$	−6.17162e13			−1.03476			−0.517378	+	0.855757i	$0.673092\pi$
$570$		0			0
$571$			7.52115e13i			1.23909i	0.784960	+	0.619546i	$0.212683\pi$
$571$			7.52115e13i			1.23909i	−0.784960	+	0.619546i	$0.787317\pi$
$572$	−3.13104e12	+	3.52893e12i	−0.0511338	+	0.0576319i
$573$	4.98773e13			0.807476
$574$	8.85533e12	−	2.33235e13i	0.142117	−	0.374312i
$575$		0			0
$576$	−2.46206e13	+	3.54997e13i	−0.388316	+	0.559902i
$577$	6.39211e13			0.999459			0.499730	−	0.866182i	$-0.333433\pi$
$577$	6.39211e13			0.999459			0.499730	+	0.866182i	$0.333433\pi$
$578$	6.99774e12	+	2.65686e12i	0.108472	+	0.0411841i
$579$			2.81304e13i			0.432298i
$580$		0			0
$581$	2.24535e13			0.339159
$582$	−2.14409e13	+	5.64718e13i	−0.321091	+	0.845701i
$583$		−	8.25317e10i		−	0.00122540i
$584$	−5.87238e13	−	1.12192e14i	−0.864470	−	1.65158i
$585$		0			0
$586$	2.04353e13	+	7.75876e12i	0.295728	+	0.112280i
$587$			2.79751e13i			0.401404i	0.979652	+	0.200702i	$0.0643223\pi$
$587$			2.79751e13i			0.401404i	−0.979652	+	0.200702i	$0.935678\pi$
$588$	3.15144e13	−	3.55192e13i	0.448355	−	0.505332i
$589$	1.98509e13			0.280030
$590$		0			0
$591$			6.63814e13i			0.920681i
$592$	7.53122e12	+	6.28042e13i	0.103576	+	0.863734i
$593$	4.39437e13			0.599270			0.299635	−	0.954054i	$-0.403135\pi$
$593$	4.39437e13			0.599270			0.299635	+	0.954054i	$0.403135\pi$
$594$	−4.60875e12	−	1.74982e12i	−0.0623233	−	0.0236626i
$595$		0			0
$596$	1.83500e12	+	1.62810e12i	0.0244008	+	0.0216496i
$597$	−7.70825e13			−1.01645
$598$	4.66542e13	−	1.22880e14i	0.610078	−	1.60684i
$599$		−	7.69712e13i		−	0.998146i	−0.866560	−	0.499073i	$-0.833674\pi$
$599$		−	7.69712e13i		−	0.998146i	0.866560	−	0.499073i	$-0.166326\pi$
$600$		0			0
$601$	6.71438e13			0.856315			0.428157	−	0.903704i	$-0.359163\pi$
$601$	6.71438e13			0.856315			0.428157	+	0.903704i	$0.359163\pi$
$602$	−1.90464e14	−	7.23145e13i	−2.40897	−	0.914625i
$603$			3.19483e12i			0.0400739i
$604$	5.56975e13	−	6.27756e13i	0.692869	−	0.780919i
$605$		0			0
$606$	2.03881e13	−	5.36988e13i	0.249467	−	0.657055i
$607$			7.52005e13i			0.912594i	0.889828	+	0.456297i	$0.150824\pi$
$607$			7.52005e13i			0.912594i	−0.889828	+	0.456297i	$0.849176\pi$
$608$	−6.82603e13	−	1.69591e13i	−0.821581	−	0.204119i
$609$	9.16648e13			1.09425
$610$		0			0
$611$		−	1.53980e14i		−	1.80825i
$612$	4.62271e13	+	4.10149e13i	0.538443	+	0.477733i
$613$	−5.79122e13			−0.669064			−0.334532	−	0.942384i	$-0.608578\pi$
$613$	−5.79122e13			−0.669064			−0.334532	+	0.942384i	$0.608578\pi$
$614$	1.87234e13	−	4.93143e13i	0.214557	−	0.565107i
$615$		0			0
$616$	−4.28216e12	−	8.18110e12i	−0.0482792	−	0.0922377i
$617$	1.25223e14			1.40042			0.700210	−	0.713937i	$-0.253090\pi$
$617$	1.25223e14			1.40042			0.700210	+	0.713937i	$0.253090\pi$
$618$	−5.47701e13	−	2.07948e13i	−0.607577	−	0.230681i
$619$		−	1.33820e14i		−	1.47254i	−0.676687	−	0.736271i	$-0.736585\pi$
$619$		−	1.33820e14i		−	1.47254i	0.676687	−	0.736271i	$-0.263415\pi$
$620$		0			0
$621$	1.37346e14			1.48716
$622$	2.69714e13	−	7.10383e13i	0.289702	−	0.763028i
$623$		−	1.00211e14i		−	1.06776i
$624$	−5.81592e13	+	6.97423e12i	−0.614746	+	0.0737179i
$625$		0			0
$626$	3.67691e13	+	1.39603e13i	0.382482	+	0.145219i
$627$		−	3.25252e12i		−	0.0335647i
$628$	9.09050e13	+	8.06553e13i	0.930657	+	0.825724i
$629$	9.04838e13			0.919004
$630$		0			0
$631$		−	4.09639e13i		−	0.409501i	−0.978814	−	0.204750i	$-0.934362\pi$
$631$		−	4.09639e13i		−	0.409501i	0.978814	−	0.204750i	$-0.0656382\pi$
$632$	1.11075e14	−	5.81389e13i	1.10162	−	0.576609i
$633$	4.45982e13			0.438832
$634$	−1.86682e14	−	7.08783e13i	−1.82245	−	0.691938i
$635$		0			0
$636$	6.80090e11	−	7.66516e11i	0.00653553	−	0.00736607i
$637$	−1.37685e14			−1.31277
$638$	3.44704e12	−	9.07894e12i	0.0326094	−	0.0858878i
$639$		−	4.67230e13i		−	0.438557i
$640$		0			0
$641$	−5.26152e13			−0.486207			−0.243103	−	0.970000i	$-0.578165\pi$
$641$	−5.26152e13			−0.486207			−0.243103	+	0.970000i	$0.578165\pi$
$642$	3.43720e13	+	1.30502e13i	0.315159	+	0.119658i
$643$		−	1.09830e14i		−	0.999228i	−0.866248	−	0.499614i	$-0.833475\pi$
$643$		−	1.09830e14i		−	0.999228i	0.866248	−	0.499614i	$-0.166525\pi$
$644$	1.92440e14	+	1.70742e14i	1.73726	+	1.54138i
$645$		0			0
$646$	−3.57130e13	+	9.40620e13i	−0.317441	+	0.836088i
$647$		−	1.73561e14i		−	1.53084i	−0.643532	−	0.765420i	$-0.722531\pi$
$647$		−	1.73561e14i		−	1.53084i	0.643532	−	0.765420i	$-0.277469\pi$
$648$	7.71775e12	+	1.47448e13i	0.0675485	+	0.129052i
$649$	−2.93888e12			−0.0255246
$650$		0			0
$651$			3.23583e13i			0.276746i
$652$	3.66659e13	−	4.13255e13i	0.311189	−	0.350735i
$653$	6.41305e13			0.540131			0.270065	−	0.962842i	$-0.412955\pi$
$653$	6.41305e13			0.540131			0.270065	+	0.962842i	$0.412955\pi$
$654$	−3.92229e12	+	1.03307e13i	−0.0327831	+	0.0863454i
$655$		0			0
$656$	−3.90728e12	−	3.25835e13i	−0.0321629	−	0.268212i
$657$	−1.55487e14			−1.27019
$658$	2.81762e14	+	1.06978e14i	2.28430	+	0.867290i
$659$			4.28929e12i			0.0345111i	0.999851	+	0.0172555i	$0.00549288\pi$
$659$			4.28929e12i			0.0345111i	−0.999851	+	0.0172555i	$0.994507\pi$
$660$		0			0
$661$	−1.96698e14			−1.55881			−0.779403	−	0.626523i	$-0.784477\pi$
$661$	−1.96698e14			−1.55881			−0.779403	+	0.626523i	$0.784477\pi$
$662$	−7.83716e12	+	2.06418e13i	−0.0616409	+	0.162352i
$663$			8.37917e13i			0.654084i
$664$	2.61678e13	−	1.36968e13i	0.202734	−	0.106115i
$665$		0			0
$666$	7.26105e13	+	2.75683e13i	0.554151	+	0.210397i
$667$			2.70562e14i			2.04946i
$668$	5.56253e13	−	6.26942e13i	0.418206	−	0.471351i
$669$	−6.98113e13			−0.520949
$670$		0			0
$671$		−	3.74284e12i		−	0.0275162i
$672$	2.76444e13	−	1.11269e14i	0.201725	−	0.811945i
$673$	−1.92127e14			−1.39160			−0.695799	−	0.718237i	$-0.744949\pi$
$673$	−1.92127e14			−1.39160			−0.695799	+	0.718237i	$0.744949\pi$
$674$	−3.56948e13	−	1.35524e13i	−0.256629	−	0.0974354i
$675$		0			0
$676$	2.14520e13	+	1.90333e13i	0.151962	+	0.134828i
$677$	2.18777e13			0.153836			0.0769180	−	0.997037i	$-0.475492\pi$
$677$	2.18777e13			0.153836			0.0769180	+	0.997037i	$0.475492\pi$
$678$	2.30412e12	−	6.06868e12i	0.0160826	−	0.0423590i
$679$			3.42822e14i			2.37531i
$680$		0			0
$681$	−1.37246e13			−0.0937053
$682$	3.20493e12	+	1.21683e12i	0.0217219	+	0.00824724i
$683$			8.96485e13i			0.603169i	0.953439	+	0.301585i	$0.0975156\pi$
$683$			8.96485e13i			0.603169i	−0.953439	+	0.301585i	$0.902484\pi$
$684$	−5.73171e13	+	6.46010e13i	−0.382828	+	0.431478i
$685$		0			0
$686$	1.57310e13	−	4.14327e13i	0.103546	−	0.272724i
$687$		−	6.99522e12i		−	0.0457107i
$688$	−2.66084e14	+	3.19077e13i	−1.72614	+	0.206992i
$689$	−2.97128e12			−0.0191359
$690$		0			0
$691$			1.22078e14i			0.774905i	0.921890	+	0.387452i	$0.126645\pi$
$691$			1.22078e14i			0.774905i	−0.921890	+	0.387452i	$0.873355\pi$
$692$	1.86747e14	+	1.65691e14i	1.17686	+	1.04416i
$693$	−1.13382e13			−0.0709378
$694$	−8.72748e13	+	2.29867e14i	−0.542115	+	1.42784i
$695$		0			0
$696$	1.06828e14	−	5.59161e13i	0.654092	−	0.342366i
$697$	−4.69440e13			−0.285375
$698$	−1.58487e14	−	6.01735e13i	−0.956570	−	0.363185i
$699$		−	1.55052e14i		−	0.929164i
$700$		0			0
$701$	−1.05940e14			−0.625847			−0.312924	−	0.949778i	$-0.601308\pi$
$701$	−1.05940e14			−0.625847			−0.312924	+	0.949778i	$0.601308\pi$
$702$	−6.29966e13	+	1.65923e14i	−0.369515	+	0.973241i
$703$			1.26448e14i			0.736439i
$704$	−9.98105e12	−	6.92228e12i	−0.0577182	−	0.0400300i
$705$		0			0
$706$	−2.03067e14	−	7.70994e13i	−1.15775	−	0.439569i
$707$		−	3.25988e14i		−	1.84546i
$708$	−2.72949e13	−	2.42174e13i	−0.153432	−	0.136132i
$709$	−4.78197e13			−0.266916			−0.133458	−	0.991054i	$-0.542608\pi$
$709$	−4.78197e13			−0.266916			−0.133458	+	0.991054i	$0.542608\pi$
$710$		0			0
$711$		−	1.53939e14i		−	0.847227i
$712$	−6.11291e13	−	1.16788e14i	−0.334078	−	0.638258i
$713$	−9.55106e13			−0.518327
$714$	−1.53327e14	−	5.82145e13i	−0.826282	−	0.313718i
$715$		0			0
$716$	2.05391e14	−	2.31493e14i	1.09148	−	1.23019i
$717$	−8.87931e13			−0.468580
$718$	1.91709e12	−	5.04930e12i	0.0100466	−	0.0264612i
$719$		−	1.91248e14i		−	0.995295i	−0.867379	−	0.497648i	$-0.834197\pi$
$719$		−	1.91248e14i		−	0.995295i	0.867379	−	0.497648i	$-0.165803\pi$
$720$		0			0
$721$	−3.32492e14			−1.70649
$722$	5.19700e13	+	1.97317e13i	0.264891	+	0.100572i
$723$			1.61870e14i			0.819361i
$724$	2.17053e14	+	1.92579e14i	1.09112	+	0.968093i
$725$		0			0
$726$	−4.02106e13	+	1.05908e14i	−0.199369	+	0.525105i
$727$			1.45816e14i			0.718013i	0.933335	+	0.359006i	$0.116884\pi$
$727$			1.45816e14i			0.718013i	−0.933335	+	0.359006i	$0.883116\pi$
$728$	−2.94534e14	+	1.54165e14i	−1.44038	+	0.753927i
$729$	−8.98651e13			−0.436469
$730$		0			0
$731$			3.83355e14i			1.83660i
$732$	3.08423e13	−	3.47617e13i	0.146754	−	0.165404i
$733$	5.65926e13			0.267448			0.133724	−	0.991019i	$-0.457306\pi$
$733$	5.65926e13			0.267448			0.133724	+	0.991019i	$0.457306\pi$
$734$	2.50268e13	−	6.59164e13i	0.117469	−	0.309395i
$735$		0			0
$736$	3.28427e14	+	8.15966e13i	1.52072	+	0.377818i
$737$	−8.98255e11			−0.00413107
$738$	−3.76711e13	−	1.43028e13i	−0.172079	−	0.0653338i
$739$			1.97385e14i			0.895552i	0.894146	+	0.447776i	$0.147784\pi$
$739$			1.97385e14i			0.895552i	−0.894146	+	0.447776i	$0.852216\pi$
$740$		0			0
$741$	−1.17096e14			−0.524146
$742$	2.06430e12	−	5.43704e12i	0.00917813	−	0.0241737i
$743$			2.26298e14i			0.999392i	0.866201	+	0.499696i	$0.166555\pi$
$743$			2.26298e14i			0.999392i	−0.866201	+	0.499696i	$0.833445\pi$
$744$	1.97388e13	+	3.77111e13i	0.0865877	+	0.165426i
$745$		0			0
$746$	1.75227e14	+	6.65294e13i	0.758417	+	0.287952i
$747$		−	3.62660e13i		−	0.155918i
$748$	−1.15317e13	+	1.29972e13i	−0.0492477	+	0.0555061i
$749$	2.08662e14			0.885183
$750$		0			0
$751$			3.96141e14i			1.65825i	0.559063	+	0.829125i	$0.311161\pi$
$751$			3.96141e14i			1.65825i	−0.559063	+	0.829125i	$0.688839\pi$
$752$	3.93629e14	−	4.72024e13i	1.63681	−	0.196279i
$753$	−9.12108e13			−0.376766
$754$	−3.26857e14	−	1.24099e14i	−1.34122	−	0.509229i
$755$		0			0
$756$	−2.59849e14	−	2.30550e14i	−1.05223	−	0.933591i
$757$	−3.60698e13			−0.145099			−0.0725495	−	0.997365i	$-0.523114\pi$
$757$	−3.60698e13			−0.145099			−0.0725495	+	0.997365i	$0.523114\pi$
$758$	−1.14887e14	+	3.02593e14i	−0.459118	+	1.20924i
$759$			1.56492e13i			0.0621272i
$760$		0			0
$761$	−3.12974e14			−1.22627			−0.613133	−	0.789980i	$-0.710091\pi$
$761$	−3.12974e14			−1.22627			−0.613133	+	0.789980i	$0.710091\pi$
$762$	−1.31589e14	−	4.99608e13i	−0.512205	−	0.194471i
$763$			6.27141e13i			0.242517i
$764$	2.47126e14	−	2.78531e14i	0.949404	−	1.07005i
$765$		0			0
$766$	6.37985e13	−	1.68035e14i	0.241917	−	0.637170i
$767$			1.05805e14i			0.398592i
$768$	−3.56573e13	−	1.46538e14i	−0.133457	−	0.548460i
$769$	1.81483e14			0.674847			0.337423	−	0.941353i	$-0.390445\pi$
$769$	1.81483e14			0.674847			0.337423	+	0.941353i	$0.390445\pi$
$770$		0			0
$771$		−	1.41456e14i		−	0.519218i
$772$	1.57089e14	+	1.39377e14i	0.572875	+	0.508283i
$773$	3.11418e13			0.112835			0.0564177	−	0.998407i	$-0.482032\pi$
$773$	3.11418e13			0.112835			0.0564177	+	0.998407i	$0.482032\pi$
$774$	−1.16799e14	+	3.07630e14i	−0.420471	+	1.10745i
$775$		0			0
$776$	2.09124e14	+	3.99532e14i	0.743181	+	1.41985i
$777$	−2.06119e14			−0.727802
$778$	3.14907e14	+	1.19562e14i	1.10480	+	0.419464i
$779$		−	6.56028e13i		−	0.228684i
$780$		0			0
$781$	1.31366e13			0.0452092
$782$	1.71829e14	−	4.52569e14i	0.587574	−	1.54757i
$783$		−	3.65337e14i		−	1.24132i
$784$	−4.22071e13	−	3.51972e14i	−0.142497	−	1.18831i
$785$		0			0
$786$	1.99806e14	+	7.58611e13i	0.666032	+	0.252875i
$787$			1.00057e14i			0.331417i	0.986175	+	0.165709i	$0.0529911\pi$
$787$			1.00057e14i			0.331417i	−0.986175	+	0.165709i	$0.947009\pi$
$788$	3.70695e14	+	3.28898e14i	1.22007	+	1.08251i
$789$	−2.53577e14			−0.829326
$790$		0			0
$791$		−	3.68410e13i		−	0.118973i
$792$	−1.32138e13	+	6.91637e12i	−0.0424034	+	0.0221949i
$793$	−1.34749e14			−0.429693
$794$	5.53193e13	+	2.10033e13i	0.175297	+	0.0665557i
$795$		0			0
$796$	−3.81919e14	+	4.30453e14i	−1.19510	+	1.34698i
$797$	3.48016e14			1.08220			0.541100	−	0.840958i	$-0.318008\pi$
$797$	3.48016e14			1.08220			0.541100	+	0.840958i	$0.318008\pi$
$798$	8.13529e13	−	2.14270e14i	0.251396	−	0.662136i
$799$		−	5.67112e14i		−	1.74155i
$800$		0			0
$801$	−1.61856e14			−0.490870
$802$	−2.42378e14	−	9.20246e13i	−0.730501	−	0.277352i
$803$		−	4.37166e13i		−	0.130939i
$804$	−8.34257e12	−	7.40193e12i	−0.0248325	−	0.0220326i
$805$		0			0
$806$	4.38080e13	−	1.15383e14i	0.128789	−	0.339208i
$807$		−	6.89609e13i		−	0.201481i
$808$	−1.98855e14	−	3.79914e14i	−0.577404	−	1.10313i
$809$	3.13921e14			0.905896			0.452948	−	0.891537i	$-0.350372\pi$
$809$	3.13921e14			0.905896			0.452948	+	0.891537i	$0.350372\pi$
$810$		0			0
$811$		−	2.70608e14i		−	0.771323i	−0.922640	−	0.385662i	$-0.873973\pi$
$811$		−	2.70608e14i		−	0.771323i	0.922640	−	0.385662i	$-0.126027\pi$
$812$	4.54169e14	−	5.11885e14i	1.28658	−	1.45008i
$813$	−6.19729e13			−0.174481
$814$	−7.75108e12	+	2.04151e13i	−0.0216890	+	0.0571253i
$815$		0			0
$816$	−2.14202e14	+	2.56863e13i	−0.592070	+	0.0709987i
$817$	−5.35726e14			−1.47175
$818$	2.79831e13	+	1.06245e13i	0.0764062	+	0.0290095i
$819$			4.08194e14i			1.10776i
$820$		0			0
$821$	9.85577e13			0.264225			0.132113	−	0.991235i	$-0.457824\pi$
$821$	9.85577e13			0.264225			0.132113	+	0.991235i	$0.457824\pi$
$822$	−6.08762e12	+	1.60338e13i	−0.0162214	+	0.0427245i
$823$		−	6.43156e14i		−	1.70340i	−0.524027	−	0.851701i	$-0.675571\pi$
$823$		−	6.43156e14i		−	1.70340i	0.524027	−	0.851701i	$-0.324429\pi$
$824$	−3.87493e14	+	2.02822e14i	−1.02007	+	0.533924i
$825$		0			0
$826$	−1.93608e14	−	7.35080e13i	−0.503527	−	0.191176i
$827$			1.77707e14i			0.459386i	0.973263	+	0.229693i	$0.0737722\pi$
$827$			1.77707e14i			0.459386i	−0.973263	+	0.229693i	$0.926228\pi$
$828$	2.75775e14	−	3.10820e14i	0.708603	−	0.798652i
$829$	1.33310e14			0.340478			0.170239	−	0.985403i	$-0.445546\pi$
$829$	1.33310e14			0.340478			0.170239	+	0.985403i	$0.445546\pi$
$830$		0			0
$831$			3.48376e14i			0.879109i
$832$	−2.49214e14	+	3.59335e14i	−0.625109	+	0.901328i
$833$	−5.07097e14			−1.26435
$834$	−1.39878e13	−	5.31080e12i	−0.0346672	−	0.0131622i
$835$		0			0
$836$	−1.81631e13	−	1.61152e13i	−0.0444794	−	0.0394643i
$837$	1.28967e14			0.313943
$838$	−4.83781e12	+	1.27420e13i	−0.0117065	+	0.0308331i
$839$		−	1.39938e14i		−	0.336608i	−0.985735	−	0.168304i	$-0.946171\pi$
$839$		−	1.39938e14i		−	0.336608i	0.985735	−	0.168304i	$-0.0538290\pi$
$840$		0			0
$841$	2.98984e14			0.710669
$842$	−2.26879e14	−	8.61401e13i	−0.536085	−	0.203538i
$843$		−	9.76608e13i		−	0.229394i
$844$	2.20969e14	−	2.49050e14i	0.515965	−	0.581534i
$845$		0			0
$846$	1.72786e14	−	4.55090e14i	0.398710	−	1.05014i
$847$			6.42934e14i			1.47485i
$848$	−9.10844e11	−	7.59568e12i	−0.00207713	−	0.0173216i
$849$	3.39375e14			0.769380
$850$		0			0
$851$		−	6.08392e14i		−	1.36312i
$852$	1.22006e14	+	1.08250e14i	0.271759	+	0.241118i
$853$	5.04867e14			1.11797			0.558987	−	0.829176i	$-0.311190\pi$
$853$	5.04867e14			1.11797			0.558987	+	0.829176i	$0.311190\pi$
$854$	9.36168e13	−	2.46571e14i	0.206094	−	0.542816i
$855$		0			0
$856$	2.43179e14	−	1.27285e14i	0.529123	−	0.276954i
$857$	1.38544e14			0.299697			0.149848	−	0.988709i	$-0.452121\pi$
$857$	1.38544e14			0.299697			0.149848	+	0.988709i	$0.452121\pi$
$858$	−1.89052e13	−	7.17782e12i	−0.0406579	−	0.0154368i
$859$			3.87563e14i			0.828661i	0.910126	+	0.414331i	$0.135984\pi$
$859$			3.87563e14i			0.828661i	−0.910126	+	0.414331i	$0.864016\pi$
$860$		0			0
$861$	1.06937e14			0.226002
$862$	−2.53540e14	+	6.67782e14i	−0.532733	+	1.40313i
$863$			7.16581e14i			1.49696i	0.663155	+	0.748482i	$0.269217\pi$
$863$			7.16581e14i			1.49696i	−0.663155	+	0.748482i	$0.730783\pi$
$864$	−4.43470e14	−	1.10179e14i	−0.921077	−	0.228839i
$865$		0			0
$866$	−8.70824e13	−	3.30630e13i	−0.178789	−	0.0678816i
$867$			3.20843e13i			0.0654932i
$868$	1.80699e14	+	1.60325e14i	0.366740	+	0.325389i
$869$	4.32812e13			0.0873374
$870$		0			0
$871$			3.23387e13i			0.0645107i
$872$	3.82560e13	+	7.30884e13i	0.0758782	+	0.144966i
$873$	5.53712e14			1.09198
$874$	6.32451e14	+	2.40126e14i	1.24014	+	0.470849i
$875$		0			0
$876$	3.60240e14	−	4.06019e14i	0.698347	−	0.787093i
$877$	−7.36516e14			−1.41966			−0.709830	−	0.704373i	$-0.751228\pi$
$877$	−7.36516e14			−1.41966			−0.709830	+	0.704373i	$0.751228\pi$
$878$	1.52585e14	−	4.01884e14i	0.292442	−	0.770243i
$879$			9.36947e13i			0.178554i
$880$		0			0
$881$	8.86757e14			1.67080			0.835401	−	0.549641i	$-0.185236\pi$
$881$	8.86757e14			1.67080			0.835401	+	0.549641i	$0.185236\pi$
$882$	−4.06930e14	−	1.54501e14i	−0.762389	−	0.289460i
$883$			5.90422e14i			1.09991i	0.835193	+	0.549957i	$0.185356\pi$
$883$			5.90422e14i			1.09991i	−0.835193	+	0.549957i	$0.814644\pi$
$884$	4.67920e14	+	4.15161e14i	0.866782	+	0.769051i
$885$		0			0
$886$	−1.42118e14	+	3.74314e14i	−0.260303	+	0.685596i
$887$		−	9.79412e14i		−	1.78381i	−0.452227	−	0.891903i	$-0.649370\pi$
$887$		−	9.79412e14i		−	1.78381i	0.452227	−	0.891903i	$-0.350630\pi$
$888$	−2.40216e14	+	1.25734e14i	−0.435047	+	0.227713i
$889$	−7.98832e14			−1.43862
$890$		0			0
$891$			5.74544e12i			0.0102314i
$892$	−3.45892e14	+	3.89848e14i	−0.612515	+	0.690353i
$893$	7.92522e14			1.39558
$894$	−3.73238e12	+	9.83046e12i	−0.00653579	+	0.0172142i
$895$		0			0
$896$	−4.84391e14	−	7.05676e14i	−0.838796	−	1.22198i
$897$	5.63396e14			0.970178
$898$	−3.74983e14	−	1.42371e14i	−0.642140	−	0.243804i
$899$			2.54056e14i			0.432645i
$900$		0			0
$901$	−1.09433e13			−0.0184300
$902$	4.02135e12	−	1.05916e13i	0.00673502	−	0.0177389i
$903$		−	8.73269e14i		−	1.45449i
$904$	−2.24733e13	−	4.29353e13i	−0.0372241	−	0.0711168i
$905$		0			0
$906$	3.36301e14	+	1.27685e14i	0.550919	+	0.209170i
$907$		−	5.03887e14i		−	0.820912i	−0.911880	−	0.410456i	$-0.865369\pi$
$907$		−	5.03887e14i		−	0.820912i	0.911880	−	0.410456i	$-0.134631\pi$
$908$	−6.80009e13	+	7.66425e13i	−0.110176	+	0.124177i
$909$	−5.26523e14			−0.848395
$910$		0			0
$911$			1.24734e14i			0.198789i	0.995048	+	0.0993946i	$0.0316906\pi$
$911$			1.24734e14i			0.198789i	−0.995048	+	0.0993946i	$0.968309\pi$
$912$	−3.58958e13	−	2.99341e14i	−0.0568943	−	0.474452i
$913$	1.01965e13			0.0160730
$914$	−2.78176e14	−	1.05616e14i	−0.436102	−	0.165577i
$915$		0			0
$916$	−3.90636e13	−	3.46591e13i	−0.0605751	−	0.0537452i
$917$	1.21296e15			1.87067
$918$	−2.32018e14	+	6.11098e14i	−0.355884	+	0.937340i
$919$		−	5.28572e14i		−	0.806356i	−0.915122	−	0.403178i	$-0.867905\pi$
$919$		−	5.28572e14i		−	0.806356i	0.915122	−	0.403178i	$-0.132095\pi$
$920$		0			0
$921$	2.26103e14			0.341200
$922$	6.01511e14	+	2.28378e14i	0.902794	+	0.342768i
$923$		−	4.72939e14i		−	0.705987i
$924$	2.62688e13	−	2.96071e13i	0.0390015	−	0.0439578i
$925$		0			0
$926$	−1.19009e14	+	3.13450e14i	−0.174793	+	0.460376i
$927$			5.37027e14i			0.784508i
$928$	2.17045e14	−	8.73608e14i	0.315363	−	1.26934i
$929$	2.34323e14			0.338639			0.169319	−	0.985561i	$-0.445843\pi$
$929$	2.34323e14			0.338639			0.169319	+	0.985561i	$0.445843\pi$
$930$		0			0
$931$		−	7.08653e14i		−	1.01318i
$932$	−8.65861e14	−	7.68234e14i	−1.23131	−	1.09248i
$933$	3.25707e14			0.460700
$934$	−5.83111e13	+	1.53582e14i	−0.0820383	+	0.216075i
$935$		0			0
$936$	2.49001e14	+	4.75719e14i	0.346595	+	0.662172i
$937$	6.49421e14			0.899142			0.449571	−	0.893245i	$-0.351577\pi$
$937$	6.49421e14			0.899142			0.449571	+	0.893245i	$0.351577\pi$
$938$	−5.91754e13	−	2.24674e13i	−0.0814942	−	0.0309413i
$939$			1.68584e14i			0.230934i
$940$		0			0
$941$	5.81546e14			0.788199			0.394099	−	0.919068i	$-0.371057\pi$
$941$	5.81546e14			0.788199			0.394099	+	0.919068i	$0.371057\pi$
$942$	−1.84900e14	+	4.86996e14i	−0.249277	+	0.656555i
$943$			3.15640e14i			0.423286i
$944$	−2.70475e14	+	3.24343e13i	−0.360801	+	0.0432658i
$945$		0			0
$946$	−8.64929e13	−	3.28392e13i	−0.114163	−	0.0433447i
$947$		−	8.31766e14i		−	1.09207i	−0.837762	−	0.546036i	$-0.816136\pi$
$947$		−	8.31766e14i		−	1.09207i	0.837762	−	0.546036i	$-0.183864\pi$
$948$	4.01975e14	+	3.56652e14i	0.524998	+	0.465804i
$949$	−1.57387e15			−2.04474
$950$		0			0
$951$		−	8.55925e14i		−	1.10036i
$952$	−1.08478e15	+	5.67795e14i	−1.38725	+	0.726117i
$953$	−1.06960e15			−1.36068			−0.680338	−	0.732898i	$-0.738167\pi$
$953$	−1.06960e15			−1.36068			−0.680338	+	0.732898i	$0.738167\pi$
$954$	−8.78168e12	−	3.33418e12i	−0.0111131	−	0.00421937i
$955$		0			0
$956$	−4.39941e14	+	4.95849e14i	−0.550941	+	0.620955i
$957$	4.16264e13			0.0518572
$958$	1.85105e13	−	4.87535e13i	0.0229398	−	0.0604196i
$959$			9.73359e13i			0.120000i
$960$		0			0
$961$	7.29945e14			0.890580
$962$	7.34977e14	+	2.79052e14i	0.892069	+	0.338696i
$963$		−	3.37021e14i		−	0.406936i
$964$	9.03935e14	+	8.02015e14i	1.08581	+	0.963379i
$965$		0			0
$966$	−3.91420e14	+	1.03094e15i	−0.465327	+	1.22559i
$967$		−	6.55048e13i		−	0.0774713i	−0.999249	−	0.0387356i	$-0.987667\pi$
$967$		−	6.55048e13i		−	0.0774713i	0.999249	−	0.0387356i	$-0.0123330\pi$
$968$	3.92194e14	+	7.49289e14i	0.461449	+	0.881602i
$969$	−4.31269e14			−0.504812
$970$		0			0
$971$		−	1.63694e14i		−	0.189643i	−0.995494	−	0.0948213i	$-0.969772\pi$
$971$		−	1.63694e14i		−	0.189643i	0.995494	−	0.0948213i	$-0.0302280\pi$
$972$	−5.93845e14	+	6.69311e14i	−0.684450	+	0.771430i
$973$	−8.49153e13			−0.0973692
$974$	4.56624e14	−	1.20267e15i	0.520911	−	1.37199i
$975$		0			0
$976$	−4.13070e13	−	3.44466e14i	−0.0466417	−	0.388953i
$977$	−4.43613e14			−0.498347			−0.249173	−	0.968459i	$-0.580159\pi$
$977$	−4.43613e14			−0.498347			−0.249173	+	0.968459i	$0.580159\pi$
$978$	2.21389e14	+	8.40556e13i	0.247435	+	0.0939448i
$979$		−	4.55072e13i		−	0.0506019i
$980$		0			0
$981$	1.01293e14			0.111490
$982$	−2.45092e14	+	6.45532e14i	−0.268393	+	0.706904i
$983$			1.06351e14i			0.115870i	0.998320	+	0.0579352i	$0.0184517\pi$
$983$			1.06351e14i			0.115870i	−0.998320	+	0.0579352i	$0.981548\pi$
$984$	1.24626e14	−	6.52322e13i	0.135094	−	0.0707109i
$985$		0			0
$986$	−1.20382e15	−	4.57061e14i	−1.29175	−	0.490444i
$987$			1.29186e15i			1.37921i
$988$	−5.80175e14	+	6.53904e14i	−0.616274	+	0.694591i
$989$	2.57759e15			2.72415
$990$		0			0
$991$			6.83253e14i			0.714847i	0.933942	+	0.357424i	$0.116345\pi$
$991$			6.83253e14i			0.714847i	−0.933942	+	0.357424i	$0.883655\pi$
$992$	3.08390e14	+	7.66186e13i	0.321027	+	0.0797583i
$993$	−9.46414e13			−0.0980246
$994$	8.65413e14	+	3.28575e14i	0.891849	+	0.338612i
$995$		0			0
$996$	9.47003e13	+	8.40227e13i	0.0966173	+	0.0857235i
$997$	1.83065e14			0.185836			0.0929180	−	0.995674i	$-0.470381\pi$
$997$	1.83065e14			0.185836			0.0929180	+	0.995674i	$0.470381\pi$
$998$	4.98319e14	−	1.31249e15i	0.503332	−	1.32569i
$999$			8.21504e14i			0.825624i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.11.b.e.51.18		20
4.3	odd	2	inner	100.11.b.e.51.17		20
5.2	odd	4		100.11.d.c.99.14		40
5.3	odd	4		100.11.d.c.99.27		40
5.4	even	2		20.11.b.a.11.3	✓	20
15.14	odd	2		180.11.c.a.91.18		20
20.3	even	4		100.11.d.c.99.13		40
20.7	even	4		100.11.d.c.99.28		40
20.19	odd	2		20.11.b.a.11.4	yes	20
40.19	odd	2		320.11.b.d.191.8		20
40.29	even	2		320.11.b.d.191.13		20
60.59	even	2		180.11.c.a.91.17		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.b.a.11.3	✓	20	5.4	even	2
20.11.b.a.11.4	yes	20	20.19	odd	2
100.11.b.e.51.17		20	4.3	odd	2	inner
100.11.b.e.51.18		20	1.1	even	1	trivial
100.11.d.c.99.13		40	20.3	even	4
100.11.d.c.99.14		40	5.2	odd	4
100.11.d.c.99.27		40	5.3	odd	4
100.11.d.c.99.28		40	20.7	even	4
180.11.c.a.91.17		20	60.59	even	2
180.11.c.a.91.18		20	15.14	odd	2
320.11.b.d.191.8		20	40.19	odd	2
320.11.b.d.191.13		20	40.29	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(29.9163 + 11.3585i) q^{2} +137.165i q^{3} +(765.971 + 679.606i) q^{4} +(-1557.98 + 4103.46i) q^{6} +24910.8i q^{7} +(15195.7 + 29031.6i) q^{8} +40234.9 q^{9} +O(q^{10})\)	\(q+(29.9163 + 11.3585i) q^{2} +137.165i q^{3} +(765.971 + 679.606i) q^{4} +(-1557.98 + 4103.46i) q^{6} +24910.8i q^{7} +(15195.7 + 29031.6i) q^{8} +40234.9 q^{9} +11312.4i q^{11} +(-93217.9 + 105064. i) q^{12} +407265. q^{13} +(-282948. + 745239. i) q^{14} +(124847. + 1.04112e6i) q^{16} +1.49997e6 q^{17} +(1.20368e6 + 457006. i) q^{18} +2.09616e6i q^{19} -3.41688e6 q^{21} +(-128491. + 338425. i) q^{22} -1.00854e7i q^{23} +(-3.98210e6 + 2.08432e6i) q^{24} +(1.21839e7 + 4.62590e6i) q^{26} +1.36182e7i q^{27} +(-1.69295e7 + 1.90809e7i) q^{28} -2.68271e7 q^{29} -9.47015e6i q^{31} +(-8.09054e6 + 3.25644e7i) q^{32} -1.55166e6 q^{33} +(4.48735e7 + 1.70373e7i) q^{34} +(3.08187e7 + 2.73439e7i) q^{36} +6.03238e7 q^{37} +(-2.38091e7 + 6.27094e7i) q^{38} +5.58623e7i q^{39} -3.12967e7 q^{41} +(-1.02220e8 - 3.88105e7i) q^{42} +2.55575e8i q^{43} +(-7.68797e6 + 8.66496e6i) q^{44} +(1.14555e8 - 3.01719e8i) q^{46} -3.78083e8i q^{47} +(-1.42804e8 + 1.71245e7i) q^{48} -3.38072e8 q^{49} +2.05743e8i q^{51} +(3.11953e8 + 2.76780e8i) q^{52} -7.29570e6 q^{53} +(-1.54682e8 + 4.07407e8i) q^{54} +(-7.23199e8 + 3.78538e8i) q^{56} -2.87519e8 q^{57} +(-8.02566e8 - 3.04714e8i) q^{58} +2.59793e8i q^{59} -3.30862e8 q^{61} +(1.07566e8 - 2.83312e8i) q^{62} +1.00228e9i q^{63} +(-6.11921e8 + 8.82312e8i) q^{64} +(-4.64199e7 - 1.76244e7i) q^{66} +7.94046e7i q^{67} +(1.14893e9 + 1.01939e9i) q^{68} +1.38336e9 q^{69} -1.16126e9i q^{71} +(6.11399e8 + 1.16808e9i) q^{72} -3.86449e9 q^{73} +(1.80467e9 + 6.85185e8i) q^{74} +(-1.42456e9 + 1.60560e9i) q^{76} -2.81800e8 q^{77} +(-6.34510e8 + 1.67120e9i) q^{78} -3.82600e9i q^{79} +5.07889e8 q^{81} +(-9.36280e8 - 3.55482e8i) q^{82} -9.01358e8i q^{83} +(-2.61723e9 - 2.32213e9i) q^{84} +(-2.90294e9 + 7.64586e9i) q^{86} -3.67972e9i q^{87} +(-3.28416e8 + 1.71900e8i) q^{88} -4.02278e9 q^{89} +1.01453e10i q^{91} +(6.85412e9 - 7.72515e9i) q^{92} +1.29897e9 q^{93} +(4.29444e9 - 1.13108e10i) q^{94} +(-4.46669e9 - 1.10974e9i) q^{96} +1.37620e10 q^{97} +(-1.01139e10 - 3.83998e9i) q^{98} +4.55152e8i 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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