LMFDB - Embedded newform 75.9.f.e.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,9,Mod(7,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("75.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	75.f (of order $4$, degree $2$, 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:	$30.5533957546$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4140 x^{13} + 1109893 x^{12} - 3063780 x^{11} + 8569800 x^{10} - 2336277960 x^{9} + \cdots + 66\!\cdots\!00 $ x^16 - 4140x^13 + 1109893x^12 - 3063780x^11 + 8569800x^10 - 2336277960x^9 + 311176823556x^8 - 1727244961920x^7 + 4854003667200x^6 - 30001722912000x^5 + 6803138028400000x^4 - 35113381084800000x^3 + 91055220768000000x^2 - 110364533280000000*x + 66884304400000000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{20}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Root			$19.6124 - 19.6124i$ of defining polynomial
Character	$\chi$	$=$	75.43
Dual form			75.9.f.e.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-17.1630 + 17.1630i) q^{2} +(-33.0681 - 33.0681i) q^{3} -333.134i q^{4} +1135.09 q^{6} +(-1268.31 + 1268.31i) q^{7} +(1323.85 + 1323.85i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(-17.1630 + 17.1630i) q^{2} +(-33.0681 - 33.0681i) q^{3} -333.134i q^{4} +1135.09 q^{6} +(-1268.31 + 1268.31i) q^{7} +(1323.85 + 1323.85i) q^{8} +2187.00i q^{9} -19228.7 q^{11} +(-11016.1 + 11016.1i) q^{12} +(-29969.0 - 29969.0i) q^{13} -43536.0i q^{14} +39840.0 q^{16} +(42622.5 - 42622.5i) q^{17} +(-37535.4 - 37535.4i) q^{18} +86450.9i q^{19} +83881.4 q^{21} +(330022. - 330022. i) q^{22} +(-213387. - 213387. i) q^{23} -87554.3i q^{24} +1.02871e6 q^{26} +(72320.0 - 72320.0i) q^{27} +(422518. + 422518. i) q^{28} -625320. i q^{29} +84417.0 q^{31} +(-1.02268e6 + 1.02268e6i) q^{32} +(635858. + 635858. i) q^{33} +1.46306e6i q^{34} +728564. q^{36} +(1.16375e6 - 1.16375e6i) q^{37} +(-1.48375e6 - 1.48375e6i) q^{38} +1.98204e6i q^{39} -4.76142e6 q^{41} +(-1.43965e6 + 1.43965e6i) q^{42} +(2.56935e6 + 2.56935e6i) q^{43} +6.40574e6i q^{44} +7.32470e6 q^{46} +(-5.81734e6 + 5.81734e6i) q^{47} +(-1.31743e6 - 1.31743e6i) q^{48} +2.54757e6i q^{49} -2.81889e6 q^{51} +(-9.98369e6 + 9.98369e6i) q^{52} +(7.04666e6 + 7.04666e6i) q^{53} +2.48245e6i q^{54} -3.35811e6 q^{56} +(2.85877e6 - 2.85877e6i) q^{57} +(1.07323e7 + 1.07323e7i) q^{58} +6.85603e6i q^{59} +2.17390e7 q^{61} +(-1.44885e6 + 1.44885e6i) q^{62} +(-2.77380e6 - 2.77380e6i) q^{63} -2.49053e7i q^{64} -2.18264e7 q^{66} +(3.01457e6 - 3.01457e6i) q^{67} +(-1.41990e7 - 1.41990e7i) q^{68} +1.41126e7i q^{69} +1.55981e7 q^{71} +(-2.89526e6 + 2.89526e6i) q^{72} +(-4.88183e6 - 4.88183e6i) q^{73} +3.99467e7i q^{74} +2.87997e7 q^{76} +(2.43880e7 - 2.43880e7i) q^{77} +(-3.40176e7 - 3.40176e7i) q^{78} -2.98436e6i q^{79} -4.78297e6 q^{81} +(8.17200e7 - 8.17200e7i) q^{82} +(3.64832e7 + 3.64832e7i) q^{83} -2.79438e7i q^{84} -8.81951e7 q^{86} +(-2.06781e7 + 2.06781e7i) q^{87} +(-2.54559e7 - 2.54559e7i) q^{88} -4.15909e7i q^{89} +7.60201e7 q^{91} +(-7.10865e7 + 7.10865e7i) q^{92} +(-2.79151e6 - 2.79151e6i) q^{93} -1.99685e8i q^{94} +6.76360e7 q^{96} +(3.41937e7 - 3.41937e7i) q^{97} +(-4.37238e7 - 4.37238e7i) q^{98} -4.20532e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) $ 16 * q - 2268 * q^6 - 4540 * q^7 - 17460 * q^8	$ 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8} - 23616 q^{11} - 22680 q^{12} - 133420 q^{13} - 471380 q^{16} - 573300 q^{17} + 163944 q^{21} + 234700 q^{22} - 651480 q^{23} - 448848 q^{26} + 3567940 q^{28} + 1311776 q^{31} - 641460 q^{32} + 3815100 q^{33} + 5519988 q^{36} + 3607340 q^{37} - 8139840 q^{38} - 14740104 q^{41} + 9643860 q^{42} + 4805480 q^{43} + 14024216 q^{46} - 26529600 q^{47} - 3661200 q^{48} - 6168312 q^{51} + 15861080 q^{52} - 16612140 q^{53} + 10752000 q^{56} - 4714200 q^{57} - 63562980 q^{58} - 12550600 q^{61} + 35190840 q^{62} - 9928980 q^{63} + 46958616 q^{66} - 46836760 q^{67} + 197811840 q^{68} - 85681968 q^{71} + 38185020 q^{72} + 50835800 q^{73} + 101166648 q^{76} - 97175880 q^{77} - 131709240 q^{78} - 76527504 q^{81} + 181542400 q^{82} + 208234800 q^{83} - 187512576 q^{86} + 74298060 q^{87} - 138207420 q^{88} + 38623856 q^{91} - 652331400 q^{92} - 159787080 q^{93} + 531512604 q^{96} + 138370520 q^{97} + 50186520 q^{98}+O(q^{100}) $ 16 * q - 2268 * q^6 - 4540 * q^7 - 17460 * q^8 - 23616 * q^11 - 22680 * q^12 - 133420 * q^13 - 471380 * q^16 - 573300 * q^17 + 163944 * q^21 + 234700 * q^22 - 651480 * q^23 - 448848 * q^26 + 3567940 * q^28 + 1311776 * q^31 - 641460 * q^32 + 3815100 * q^33 + 5519988 * q^36 + 3607340 * q^37 - 8139840 * q^38 - 14740104 * q^41 + 9643860 * q^42 + 4805480 * q^43 + 14024216 * q^46 - 26529600 * q^47 - 3661200 * q^48 - 6168312 * q^51 + 15861080 * q^52 - 16612140 * q^53 + 10752000 * q^56 - 4714200 * q^57 - 63562980 * q^58 - 12550600 * q^61 + 35190840 * q^62 - 9928980 * q^63 + 46958616 * q^66 - 46836760 * q^67 + 197811840 * q^68 - 85681968 * q^71 + 38185020 * q^72 + 50835800 * q^73 + 101166648 * q^76 - 97175880 * q^77 - 131709240 * q^78 - 76527504 * q^81 + 181542400 * q^82 + 208234800 * q^83 - 187512576 * q^86 + 74298060 * q^87 - 138207420 * q^88 + 38623856 * q^91 - 652331400 * q^92 - 159787080 * q^93 + 531512604 * q^96 + 138370520 * q^97 + 50186520 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−17.1630	+	17.1630i	−1.07268	+	1.07268i	−0.0755421	+	0.997143i	$0.524069\pi$
$2$	−17.1630	+	17.1630i	−1.07268	+	1.07268i	−0.997143	+	0.0755421i	$0.975931\pi$
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$4$		−	333.134i		−	1.30130i
$5$		0			0
$5$		0			0
$6$	1135.09			0.875843
$7$	−1268.31	+	1268.31i	−0.528244	+	0.528244i	−0.920048	−	0.391805i	$-0.871851\pi$
$7$	−1268.31	+	1268.31i	−0.528244	+	0.528244i	0.391805	+	0.920048i	$0.371851\pi$
$8$	1323.85	+	1323.85i	0.323205	+	0.323205i
$9$			2187.00i			0.333333i
$10$		0			0
$11$	−19228.7			−1.31335			−0.656674	−	0.754175i	$-0.728037\pi$
$11$	−19228.7			−1.31335			−0.656674	+	0.754175i	$0.728037\pi$
$12$	−11016.1	+	11016.1i	−0.531255	+	0.531255i
$13$	−29969.0	−	29969.0i	−1.04930	−	1.04930i	−0.998720	−	0.0505774i	$-0.983894\pi$
$13$	−29969.0	−	29969.0i	−1.04930	−	1.04930i	−0.0505774	−	0.998720i	$-0.516106\pi$
$14$		−	43536.0i		−	1.13328i
$15$		0			0
$16$	39840.0			0.607911
$17$	42622.5	−	42622.5i	0.510321	−	0.510321i	−0.404304	−	0.914625i	$-0.632486\pi$
$17$	42622.5	−	42622.5i	0.510321	−	0.510321i	0.914625	+	0.404304i	$0.132486\pi$
$18$	−37535.4	−	37535.4i	−0.357562	−	0.357562i
$19$			86450.9i			0.663369i	0.943390	+	0.331684i	$0.107617\pi$
$19$			86450.9i			0.663369i	−0.943390	+	0.331684i	$0.892383\pi$
$20$		0			0
$21$	83881.4			0.431309
$22$	330022.	−	330022.i	1.40881	−	1.40881i
$23$	−213387.	−	213387.i	−0.762529	−	0.762529i	0.214249	−	0.976779i	$-0.431269\pi$
$23$	−213387.	−	213387.i	−0.762529	−	0.762529i	−0.976779	+	0.214249i	$0.931269\pi$
$24$		−	87554.3i		−	0.263896i
$25$		0			0
$26$	1.02871e6			2.25113
$27$	72320.0	−	72320.0i	0.136083	−	0.136083i
$28$	422518.	+	422518.i	0.687406	+	0.687406i
$29$		−	625320.i		−	0.884118i	−0.896986	−	0.442059i	$-0.854248\pi$
$29$		−	625320.i		−	0.884118i	0.896986	−	0.442059i	$-0.145752\pi$
$30$		0			0
$31$	84417.0			0.0914078			0.0457039	−	0.998955i	$-0.485447\pi$
$31$	84417.0			0.0914078			0.0457039	+	0.998955i	$0.485447\pi$
$32$	−1.02268e6	+	1.02268e6i	−0.975301	+	0.975301i
$33$	635858.	+	635858.i	0.536172	+	0.536172i
$34$			1.46306e6i			1.09483i
$35$		0			0
$36$	728564.			0.433768
$37$	1.16375e6	−	1.16375e6i	0.620944	−	0.620944i	−0.324829	−	0.945773i	$-0.605307\pi$
$37$	1.16375e6	−	1.16375e6i	0.620944	−	0.620944i	0.945773	+	0.324829i	$0.105307\pi$
$38$	−1.48375e6	−	1.48375e6i	−0.711585	−	0.711585i
$39$			1.98204e6i			0.856748i
$40$		0			0
$41$	−4.76142e6			−1.68500			−0.842502	−	0.538694i	$-0.818918\pi$
$41$	−4.76142e6			−1.68500			−0.842502	+	0.538694i	$0.818918\pi$
$42$	−1.43965e6	+	1.43965e6i	−0.462659	+	0.462659i
$43$	2.56935e6	+	2.56935e6i	0.751534	+	0.751534i	0.974765	−	0.223231i	$-0.0716606\pi$
$43$	2.56935e6	+	2.56935e6i	0.751534	+	0.751534i	−0.223231	+	0.974765i	$0.571661\pi$
$44$			6.40574e6i			1.70907i
$45$		0			0
$46$	7.32470e6			1.63591
$47$	−5.81734e6	+	5.81734e6i	−1.19216	+	1.19216i	−0.215695	+	0.976461i	$0.569202\pi$
$47$	−5.81734e6	+	5.81734e6i	−1.19216	+	1.19216i	−0.976461	+	0.215695i	$0.930798\pi$
$48$	−1.31743e6	−	1.31743e6i	−0.248178	−	0.248178i
$49$			2.54757e6i			0.441917i
$50$		0			0
$51$	−2.81889e6			−0.416675
$52$	−9.98369e6	+	9.98369e6i	−1.36546	+	1.36546i
$53$	7.04666e6	+	7.04666e6i	0.893058	+	0.893058i	0.994810	−	0.101752i	$-0.0324447\pi$
$53$	7.04666e6	+	7.04666e6i	0.893058	+	0.893058i	−0.101752	+	0.994810i	$0.532445\pi$
$54$			2.48245e6i			0.291948i
$55$		0			0
$56$	−3.35811e6			−0.341462
$57$	2.85877e6	−	2.85877e6i	0.270819	−	0.270819i
$58$	1.07323e7	+	1.07323e7i	0.948379	+	0.948379i
$59$			6.85603e6i			0.565803i	0.959149	+	0.282901i	$0.0912969\pi$
$59$			6.85603e6i			0.565803i	−0.959149	+	0.282901i	$0.908703\pi$
$60$		0			0
$61$	2.17390e7			1.57008			0.785038	−	0.619447i	$-0.212643\pi$
$61$	2.17390e7			1.57008			0.785038	+	0.619447i	$0.212643\pi$
$62$	−1.44885e6	+	1.44885e6i	−0.0980518	+	0.0980518i
$63$	−2.77380e6	−	2.77380e6i	−0.176081	−	0.176081i
$64$		−	2.49053e7i		−	1.48447i
$65$		0			0
$66$	−2.18264e7			−1.15029
$67$	3.01457e6	−	3.01457e6i	0.149598	−	0.149598i	−0.628340	−	0.777939i	$-0.716265\pi$
$67$	3.01457e6	−	3.01457e6i	0.149598	−	0.149598i	0.777939	+	0.628340i	$0.216265\pi$
$68$	−1.41990e7	−	1.41990e7i	−0.664083	−	0.664083i
$69$			1.41126e7i			0.622603i
$70$		0			0
$71$	1.55981e7			0.613816			0.306908	−	0.951739i	$-0.400706\pi$
$71$	1.55981e7			0.613816			0.306908	+	0.951739i	$0.400706\pi$
$72$	−2.89526e6	+	2.89526e6i	−0.107735	+	0.107735i
$73$	−4.88183e6	−	4.88183e6i	−0.171906	−	0.171906i	0.615910	−	0.787816i	$-0.288788\pi$
$73$	−4.88183e6	−	4.88183e6i	−0.171906	−	0.171906i	−0.787816	+	0.615910i	$0.788788\pi$
$74$			3.99467e7i			1.33215i
$75$		0			0
$76$	2.87997e7			0.863245
$77$	2.43880e7	−	2.43880e7i	0.693768	−	0.693768i
$78$	−3.40176e7	−	3.40176e7i	−0.919020	−	0.919020i
$79$		−	2.98436e6i		−	0.0766202i	−0.999266	−	0.0383101i	$-0.987803\pi$
$79$		−	2.98436e6i		−	0.0766202i	0.999266	−	0.0383101i	$-0.0121975\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$	8.17200e7	−	8.17200e7i	1.80748	−	1.80748i
$83$	3.64832e7	+	3.64832e7i	0.768742	+	0.768742i	0.977885	−	0.209143i	$-0.0670673\pi$
$83$	3.64832e7	+	3.64832e7i	0.768742	+	0.768742i	−0.209143	+	0.977885i	$0.567067\pi$
$84$		−	2.79438e7i		−	0.561265i
$85$		0			0
$86$	−8.81951e7			−1.61232
$87$	−2.06781e7	+	2.06781e7i	−0.360940	+	0.360940i
$88$	−2.54559e7	−	2.54559e7i	−0.424481	−	0.424481i
$89$		−	4.15909e7i		−	0.662885i	−0.943475	−	0.331443i	$-0.892465\pi$
$89$		−	4.15909e7i		−	0.662885i	0.943475	−	0.331443i	$-0.107535\pi$
$90$		0			0
$91$	7.60201e7			1.10857
$92$	−7.10865e7	+	7.10865e7i	−0.992283	+	0.992283i
$93$	−2.79151e6	−	2.79151e6i	−0.0373171	−	0.0373171i
$94$		−	1.99685e8i		−	2.55761i
$95$		0			0
$96$	6.76360e7			0.796330
$97$	3.41937e7	−	3.41937e7i	0.386242	−	0.386242i	−0.487103	−	0.873345i	$-0.661946\pi$
$97$	3.41937e7	−	3.41937e7i	0.386242	−	0.386242i	0.873345	+	0.487103i	$0.161946\pi$
$98$	−4.37238e7	−	4.37238e7i	−0.474038	−	0.474038i
$99$		−	4.20532e7i		−	0.437783i
$100$		0			0
$101$	−6.66598e7			−0.640588			−0.320294	−	0.947318i	$-0.603782\pi$
$101$	−6.66598e7			−0.640588			−0.320294	+	0.947318i	$0.603782\pi$
$102$	4.83805e7	−	4.83805e7i	0.446961	−	0.446961i
$103$	1.02131e8	+	1.02131e8i	0.907418	+	0.907418i	0.996063	−	0.0886456i	$-0.0282538\pi$
$103$	1.02131e8	+	1.02131e8i	0.907418	+	0.907418i	−0.0886456	+	0.996063i	$0.528254\pi$
$104$		−	7.93488e7i		−	0.678277i
$105$		0			0
$106$	−2.41883e8			−1.91594
$107$	−2.07056e7	+	2.07056e7i	−0.157962	+	0.157962i	−0.781663	−	0.623701i	$-0.785628\pi$
$107$	−2.07056e7	+	2.07056e7i	−0.157962	+	0.157962i	0.623701	+	0.781663i	$0.285628\pi$
$108$	−2.40922e7	−	2.40922e7i	−0.177085	−	0.177085i
$109$			2.67676e8i			1.89628i	0.317848	+	0.948142i	$0.397040\pi$
$109$			2.67676e8i			1.89628i	−0.317848	+	0.948142i	$0.602960\pi$
$110$		0			0
$111$	−7.69659e7			−0.506998
$112$	−5.05296e7	+	5.05296e7i	−0.321125	+	0.321125i
$113$	−4.77124e7	−	4.77124e7i	−0.292629	−	0.292629i	0.545489	−	0.838118i	$-0.316344\pi$
$113$	−4.77124e7	−	4.77124e7i	−0.292629	−	0.292629i	−0.838118	+	0.545489i	$0.816344\pi$
$114$			9.81298e7i			0.581007i
$115$		0			0
$116$	−2.08315e8			−1.15051
$117$	6.55422e7	−	6.55422e7i	0.349766	−	0.349766i
$118$	−1.17670e8	−	1.17670e8i	−0.606928	−	0.606928i
$119$			1.08117e8i			0.539147i
$120$		0			0
$121$	1.55385e8			0.724883
$122$	−3.73106e8	+	3.73106e8i	−1.68420	+	1.68420i
$123$	1.57451e8	+	1.57451e8i	0.687900	+	0.687900i
$124$		−	2.81222e7i		−	0.118949i
$125$		0			0
$126$	9.52132e7			0.377759
$127$	1.27669e8	−	1.27669e8i	0.490761	−	0.490761i	−0.417785	−	0.908546i	$-0.637193\pi$
$127$	1.27669e8	−	1.27669e8i	0.490761	−	0.490761i	0.908546	+	0.417785i	$0.137193\pi$
$128$	1.65643e8	+	1.65643e8i	0.617068	+	0.617068i
$129$		−	1.69927e8i		−	0.613625i
$130$		0			0
$131$	1.02793e7			0.0349042			0.0174521	−	0.999848i	$-0.494445\pi$
$131$	1.02793e7			0.0349042			0.0174521	+	0.999848i	$0.494445\pi$
$132$	2.11826e8	−	2.11826e8i	0.697723	−	0.697723i
$133$	−1.09647e8	−	1.09647e8i	−0.350420	−	0.350420i
$134$			1.03478e8i			0.320943i
$135$		0			0
$136$	1.12851e8			0.329876
$137$	3.36375e8	−	3.36375e8i	0.954865	−	0.954865i	−0.0441598	−	0.999024i	$-0.514061\pi$
$137$	3.36375e8	−	3.36375e8i	0.954865	−	0.954865i	0.999024	+	0.0441598i	$0.0140611\pi$
$138$	−2.42214e8	−	2.42214e8i	−0.667856	−	0.667856i
$139$		−	4.39953e8i		−	1.17855i	−0.807934	−	0.589274i	$-0.799414\pi$
$139$		−	4.39953e8i		−	1.17855i	0.807934	−	0.589274i	$-0.200586\pi$
$140$		0			0
$141$	3.84737e8			0.973391
$142$	−2.67709e8	+	2.67709e8i	−0.658431	+	0.658431i
$143$	5.76265e8	+	5.76265e8i	1.37809	+	1.37809i
$144$			8.71301e7i			0.202637i
$145$		0			0
$146$	1.67573e8			0.368802
$147$	8.42432e7	−	8.42432e7i	0.180412	−	0.180412i
$148$	−3.87684e8	−	3.87684e8i	−0.808037	−	0.808037i
$149$		−	1.50853e8i		−	0.306061i	−0.988221	−	0.153030i	$-0.951097\pi$
$149$		−	1.50853e8i		−	0.306061i	0.988221	−	0.153030i	$-0.0489032\pi$
$150$		0			0
$151$	3.76976e8			0.725113			0.362556	−	0.931962i	$-0.381904\pi$
$151$	3.76976e8			0.725113			0.362556	+	0.931962i	$0.381904\pi$
$152$	−1.14448e8	+	1.14448e8i	−0.214404	+	0.214404i
$153$	9.32154e7	+	9.32154e7i	0.170107	+	0.170107i
$154$			8.37142e8i			1.48839i
$155$		0			0
$156$	6.60284e8			1.11489
$157$	−1.52190e8	+	1.52190e8i	−0.250488	+	0.250488i	−0.821171	−	0.570682i	$-0.806679\pi$
$157$	−1.52190e8	+	1.52190e8i	−0.250488	+	0.250488i	0.570682	+	0.821171i	$0.306679\pi$
$158$	5.12205e7	+	5.12205e7i	0.0821893	+	0.0821893i
$159$		−	4.66039e8i		−	0.729179i
$160$		0			0
$161$	5.41283e8			0.805603
$162$	8.20899e7	−	8.20899e7i	0.119187	−	0.119187i
$163$	−5.90397e8	−	5.90397e8i	−0.836362	−	0.836362i	0.152016	−	0.988378i	$-0.451423\pi$
$163$	−5.90397e8	−	5.90397e8i	−0.836362	−	0.836362i	−0.988378	+	0.152016i	$0.951423\pi$
$164$			1.58619e9i			2.19270i
$165$		0			0
$166$	−1.25232e9			−1.64924
$167$	−6.43590e8	+	6.43590e8i	−0.827453	+	0.827453i	−0.987164	−	0.159711i	$-0.948944\pi$
$167$	−6.43590e8	+	6.43590e8i	−0.827453	+	0.827453i	0.159711	+	0.987164i	$0.448944\pi$
$168$	1.11046e8	+	1.11046e8i	0.139401	+	0.139401i
$169$			9.80550e8i			1.20205i
$170$		0			0
$171$	−1.89068e8			−0.221123
$172$	8.55936e8	−	8.55936e8i	0.977975	−	0.977975i
$173$	−2.81559e8	−	2.81559e8i	−0.314330	−	0.314330i	0.532255	−	0.846584i	$-0.321345\pi$
$173$	−2.81559e8	−	2.81559e8i	−0.314330	−	0.314330i	−0.846584	+	0.532255i	$0.821345\pi$
$174$		−	7.09796e8i		−	0.774349i
$175$		0			0
$176$	−7.66073e8			−0.798398
$177$	2.26716e8	−	2.26716e8i	0.230988	−	0.230988i
$178$	7.13823e8	+	7.13823e8i	0.711067	+	0.711067i
$179$		−	8.23090e8i		−	0.801743i	−0.916134	−	0.400872i	$-0.868707\pi$
$179$		−	8.23090e8i		−	0.801743i	0.916134	−	0.400872i	$-0.131293\pi$
$180$		0			0
$181$	−5.98881e8			−0.557990			−0.278995	−	0.960293i	$-0.590001\pi$
$181$	−5.98881e8			−0.557990			−0.278995	+	0.960293i	$0.590001\pi$
$182$	−1.30473e9	+	1.30473e9i	−1.18915	+	1.18915i
$183$	−7.18869e8	−	7.18869e8i	−0.640981	−	0.640981i
$184$		−	5.64984e8i		−	0.492907i
$185$		0			0
$186$	9.58212e7			0.0800589
$187$	−8.19576e8	+	8.19576e8i	−0.670229	+	0.670229i
$188$	1.93795e9	+	1.93795e9i	1.55136	+	1.55136i
$189$			1.83449e8i			0.143770i
$190$		0			0
$191$	9.82848e8			0.738504			0.369252	−	0.929329i	$-0.379614\pi$
$191$	9.82848e8			0.738504			0.369252	+	0.929329i	$0.379614\pi$
$192$	−8.23571e8	+	8.23571e8i	−0.606033	+	0.606033i
$193$	3.07858e8	+	3.07858e8i	0.221881	+	0.221881i	0.809290	−	0.587409i	$-0.199852\pi$
$193$	3.07858e8	+	3.07858e8i	0.221881	+	0.221881i	−0.587409	+	0.809290i	$0.699852\pi$
$194$			1.17373e9i			0.828631i
$195$		0			0
$196$	8.48681e8			0.575069
$197$	−3.09428e8	+	3.09428e8i	−0.205444	+	0.205444i	−0.802328	−	0.596884i	$-0.796405\pi$
$197$	−3.09428e8	+	3.09428e8i	−0.205444	+	0.205444i	0.596884	+	0.802328i	$0.296405\pi$
$198$	7.21758e8	+	7.21758e8i	0.469603	+	0.469603i
$199$		−	8.67221e8i		−	0.552990i	−0.961015	−	0.276495i	$-0.910827\pi$
$199$		−	8.67221e8i		−	0.552990i	0.961015	−	0.276495i	$-0.0891729\pi$
$200$		0			0
$201$	−1.99372e8			−0.122146
$202$	1.14408e9	−	1.14408e9i	0.687148	−	0.687148i
$203$	7.93101e8	+	7.93101e8i	0.467029	+	0.467029i
$204$			9.39068e8i			0.542221i
$205$		0			0
$206$	−3.50573e9			−1.94675
$207$	4.66677e8	−	4.66677e8i	0.254176	−	0.254176i
$208$	−1.19397e9	−	1.19397e9i	−0.637879	−	0.637879i
$209$		−	1.66234e9i		−	0.871234i
$210$		0			0
$211$	1.80030e9			0.908269			0.454134	−	0.890933i	$-0.349949\pi$
$211$	1.80030e9			0.908269			0.454134	+	0.890933i	$0.349949\pi$
$212$	2.34748e9	−	2.34748e9i	1.16214	−	1.16214i
$213$	−5.15799e8	−	5.15799e8i	−0.250589	−	0.250589i
$214$		−	7.10737e8i		−	0.338886i
$215$		0			0
$216$	1.91481e8			0.0879653
$217$	−1.07067e8	+	1.07067e8i	−0.0482856	+	0.0482856i
$218$	−4.59411e9	−	4.59411e9i	−2.03411	−	2.03411i
$219$			3.22866e8i			0.140361i
$220$		0			0
$221$	−2.55471e9			−1.07096
$222$	1.32096e9	−	1.32096e9i	0.543849	−	0.543849i
$223$	2.69534e9	+	2.69534e9i	1.08992	+	1.08992i	0.995536	+	0.0943825i	$0.0300877\pi$
$223$	2.69534e9	+	2.69534e9i	1.08992	+	1.08992i	0.0943825	+	0.995536i	$0.469912\pi$
$224$		−	2.59415e9i		−	1.03039i
$225$		0			0
$226$	1.63777e9			0.627798
$227$	8.98568e8	−	8.98568e8i	0.338414	−	0.338414i	−0.517356	−	0.855770i	$-0.673084\pi$
$227$	8.98568e8	−	8.98568e8i	0.338414	−	0.338414i	0.855770	+	0.517356i	$0.173084\pi$
$228$	−9.52353e8	−	9.52353e8i	−0.352418	−	0.352418i
$229$		−	2.69759e9i		−	0.980922i	−0.871463	−	0.490461i	$-0.836828\pi$
$229$		−	2.69759e9i		−	0.980922i	0.871463	−	0.490461i	$-0.163172\pi$
$230$		0			0
$231$	−1.61293e9			−0.566459
$232$	8.27828e8	−	8.27828e8i	0.285751	−	0.285751i
$233$	−2.99952e9	−	2.99952e9i	−1.01772	−	1.01772i	−0.999840	−	0.0178787i	$-0.994309\pi$
$233$	−2.99952e9	−	2.99952e9i	−1.01772	−	1.01772i	−0.0178787	−	0.999840i	$-0.505691\pi$
$234$			2.24979e9i			0.750377i
$235$		0			0
$236$	2.28398e9			0.736282
$237$	−9.86872e7	+	9.86872e7i	−0.0312801	+	0.0312801i
$238$	−1.85561e9	−	1.85561e9i	−0.578335	−	0.578335i
$239$		−	5.76374e8i		−	0.176650i	−0.996092	−	0.0883249i	$-0.971849\pi$
$239$		−	5.76374e8i		−	0.176650i	0.996092	−	0.0883249i	$-0.0281514\pi$
$240$		0			0
$241$	1.87192e9			0.554905			0.277453	−	0.960739i	$-0.410510\pi$
$241$	1.87192e9			0.554905			0.277453	+	0.960739i	$0.410510\pi$
$242$	−2.66687e9	+	2.66687e9i	−0.777571	+	0.777571i
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$		−	7.24201e9i		−	2.04315i
$245$		0			0
$246$	−5.40465e9			−1.47580
$247$	2.59084e9	−	2.59084e9i	0.696071	−	0.696071i
$248$	1.11755e8	+	1.11755e8i	0.0295435	+	0.0295435i
$249$		−	2.41286e9i		−	0.627675i
$250$		0			0
$251$	−3.69308e8			−0.0930451			−0.0465226	−	0.998917i	$-0.514814\pi$
$251$	−3.69308e8			−0.0930451			−0.0465226	+	0.998917i	$0.514814\pi$
$252$	−9.24047e8	+	9.24047e8i	−0.229135	+	0.229135i
$253$	4.10316e9	+	4.10316e9i	1.00147	+	1.00147i
$254$			4.38235e9i			1.05286i
$255$		0			0
$256$	6.89910e8			0.160632
$257$	2.91119e9	−	2.91119e9i	0.667326	−	0.667326i	−0.289770	−	0.957096i	$-0.593579\pi$
$257$	2.91119e9	−	2.91119e9i	0.667326	−	0.667326i	0.957096	+	0.289770i	$0.0935789\pi$
$258$	2.91645e9	+	2.91645e9i	0.658226	+	0.658226i
$259$			2.95199e9i			0.656019i
$260$		0			0
$261$	1.36757e9			0.294706
$262$	−1.76423e8	+	1.76423e8i	−0.0374412	+	0.0374412i
$263$	−9.28381e8	−	9.28381e8i	−0.194045	−	0.194045i	0.603396	−	0.797442i	$-0.293814\pi$
$263$	−9.28381e8	−	9.28381e8i	−0.194045	−	0.194045i	−0.797442	+	0.603396i	$0.793814\pi$
$264$			1.68356e9i			0.346587i
$265$		0			0
$266$	3.76372e9			0.751781
$267$	−1.37533e9	+	1.37533e9i	−0.270622	+	0.270622i
$268$	−1.00426e9	−	1.00426e9i	−0.194673	−	0.194673i
$269$		−	1.13620e8i		−	0.0216993i	−0.999941	−	0.0108496i	$-0.996546\pi$
$269$		−	1.13620e8i		−	0.0216993i	0.999941	−	0.0108496i	$-0.00345361\pi$
$270$		0			0
$271$	7.17873e9			1.33098			0.665488	−	0.746408i	$-0.268223\pi$
$271$	7.17873e9			1.33098			0.665488	+	0.746408i	$0.268223\pi$
$272$	1.69808e9	−	1.69808e9i	0.310229	−	0.310229i
$273$	−2.51384e9	−	2.51384e9i	−0.452572	−	0.452572i
$274$			1.15464e10i			2.04854i
$275$		0			0
$276$	4.70139e9			0.810196
$277$	−6.39462e9	+	6.39462e9i	−1.08616	+	1.08616i	−0.0902452	+	0.995920i	$0.528765\pi$
$277$	−6.39462e9	+	6.39462e9i	−1.08616	+	1.08616i	−0.995920	+	0.0902452i	$0.971235\pi$
$278$	7.55089e9	+	7.55089e9i	1.26421	+	1.26421i
$279$			1.84620e8i			0.0304693i
$280$		0			0
$281$	2.91550e9			0.467615			0.233807	−	0.972283i	$-0.424881\pi$
$281$	2.91550e9			0.467615			0.233807	+	0.972283i	$0.424881\pi$
$282$	−6.60322e9	+	6.60322e9i	−1.04414	+	1.04414i
$283$	1.14766e9	+	1.14766e9i	0.178923	+	0.178923i	0.790886	−	0.611963i	$-0.209620\pi$
$283$	1.14766e9	+	1.14766e9i	0.178923	+	0.178923i	−0.611963	+	0.790886i	$0.709620\pi$
$284$		−	5.19625e9i		−	0.798761i
$285$		0			0
$286$	−1.97808e10			−2.95652
$287$	6.03897e9	−	6.03897e9i	0.890092	−	0.890092i
$288$	−2.23660e9	−	2.23660e9i	−0.325100	−	0.325100i
$289$			3.34240e9i			0.479146i
$290$		0			0
$291$	−2.26144e9			−0.315365
$292$	−1.62630e9	+	1.62630e9i	−0.223702	+	0.223702i
$293$	3.61978e9	+	3.61978e9i	0.491147	+	0.491147i	0.908667	−	0.417521i	$-0.137101\pi$
$293$	3.61978e9	+	3.61978e9i	0.491147	+	0.491147i	−0.417521	+	0.908667i	$0.637101\pi$
$294$			2.89172e9i			0.387050i
$295$		0			0
$296$	3.08125e9			0.401384
$297$	−1.39062e9	+	1.39062e9i	−0.178724	+	0.178724i
$298$	2.58908e9	+	2.58908e9i	0.328307	+	0.328307i
$299$			1.27900e10i			1.60024i
$300$		0			0
$301$	−6.51747e9			−0.793986
$302$	−6.47002e9	+	6.47002e9i	−0.777818	+	0.777818i
$303$	2.20431e9	+	2.20431e9i	0.261519	+	0.261519i
$304$			3.44420e9i			0.403269i
$305$		0			0
$306$	−3.19970e9			−0.364942
$307$	−6.49422e9	+	6.49422e9i	−0.731095	+	0.731095i	−0.970837	−	0.239742i	$-0.922937\pi$
$307$	−6.49422e9	+	6.49422e9i	−0.731095	+	0.731095i	0.239742	+	0.970837i	$0.422937\pi$
$308$	−8.12449e9	−	8.12449e9i	−0.902803	−	0.902803i
$309$		−	6.75454e9i		−	0.740903i
$310$		0			0
$311$	9.27270e9			0.991208			0.495604	−	0.868549i	$-0.334947\pi$
$311$	9.27270e9			0.991208			0.495604	+	0.868549i	$0.334947\pi$
$312$	−2.62391e9	+	2.62391e9i	−0.276905	+	0.276905i
$313$	−2.56422e9	−	2.56422e9i	−0.267164	−	0.267164i	0.560793	−	0.827956i	$-0.310496\pi$
$313$	−2.56422e9	−	2.56422e9i	−0.267164	−	0.267164i	−0.827956	+	0.560793i	$0.810496\pi$
$314$		−	5.22406e9i		−	0.537390i
$315$		0			0
$316$	−9.94193e8			−0.0997062
$317$	−4.30226e9	+	4.30226e9i	−0.426049	+	0.426049i	−0.887280	−	0.461231i	$-0.847408\pi$
$317$	−4.30226e9	+	4.30226e9i	−0.426049	+	0.426049i	0.461231	+	0.887280i	$0.347408\pi$
$318$	7.99861e9	+	7.99861e9i	0.782179	+	0.782179i
$319$			1.20241e10i			1.16115i
$320$		0			0
$321$	1.36939e9			0.128975
$322$	−9.29002e9	+	9.29002e9i	−0.864158	+	0.864158i
$323$	3.68475e9	+	3.68475e9i	0.338531	+	0.338531i
$324$			1.59337e9i			0.144589i
$325$		0			0
$326$	2.02659e10			1.79430
$327$	8.85153e9	−	8.85153e9i	0.774154	−	0.774154i
$328$	−6.30339e9	−	6.30339e9i	−0.544602	−	0.544602i
$329$		−	1.47564e10i		−	1.25950i
$330$		0			0
$331$	−3.54491e9			−0.295320			−0.147660	−	0.989038i	$-0.547174\pi$
$331$	−3.54491e9			−0.295320			−0.147660	+	0.989038i	$0.547174\pi$
$332$	1.21538e10	−	1.21538e10i	1.00037	−	1.00037i
$333$	2.54512e9	+	2.54512e9i	0.206981	+	0.206981i
$334$		−	2.20918e10i		−	1.77519i
$335$		0			0
$336$	3.34184e9			0.262197
$337$	6.56998e9	−	6.56998e9i	0.509383	−	0.509383i	−0.404954	−	0.914337i	$-0.632712\pi$
$337$	6.56998e9	−	6.56998e9i	0.509383	−	0.509383i	0.914337	+	0.404954i	$0.132712\pi$
$338$	−1.68291e10	−	1.68291e10i	−1.28942	−	1.28942i
$339$			3.15552e9i			0.238931i
$340$		0			0
$341$	−1.62323e9			−0.120050
$342$	3.24497e9	−	3.24497e9i	0.237195	−	0.237195i
$343$	−1.05427e10	−	1.05427e10i	−0.761684	−	0.761684i
$344$			6.80285e9i			0.485799i
$345$		0			0
$346$	9.66477e9			0.674353
$347$	1.98801e10	−	1.98801e10i	1.37120	−	1.37120i	0.512533	−	0.858667i	$-0.328707\pi$
$347$	1.98801e10	−	1.98801e10i	1.37120	−	1.37120i	0.858667	−	0.512533i	$-0.171293\pi$
$348$	6.88859e9	+	6.88859e9i	0.469692	+	0.469692i
$349$			2.14289e10i			1.44443i	0.691667	+	0.722216i	$0.256877\pi$
$349$			2.14289e10i			1.44443i	−0.691667	+	0.722216i	$0.743123\pi$
$350$		0			0
$351$	−4.33471e9			−0.285583
$352$	1.96648e10	−	1.96648e10i	1.28091	−	1.28091i
$353$	5.07173e9	+	5.07173e9i	0.326631	+	0.326631i	0.851304	−	0.524673i	$-0.175812\pi$
$353$	5.07173e9	+	5.07173e9i	0.326631	+	0.326631i	−0.524673	+	0.851304i	$0.675812\pi$
$354$			7.78224e9i			0.495554i
$355$		0			0
$356$	−1.38553e10			−0.862615
$357$	3.57524e9	−	3.57524e9i	0.220106	−	0.220106i
$358$	1.41267e10	+	1.41267e10i	0.860018	+	0.860018i
$359$		−	1.91616e10i		−	1.15360i	−0.816886	−	0.576799i	$-0.804302\pi$
$359$		−	1.91616e10i		−	1.15360i	0.816886	−	0.576799i	$-0.195698\pi$
$360$		0			0
$361$	9.50981e9			0.559942
$362$	1.02786e10	−	1.02786e10i	0.598547	−	0.598547i
$363$	−5.13829e9	−	5.13829e9i	−0.295932	−	0.295932i
$364$		−	2.53249e10i		−	1.44259i
$365$		0			0
$366$	2.46758e10			1.37514
$367$	−2.28450e10	+	2.28450e10i	−1.25930	+	1.25930i	−0.307866	+	0.951430i	$0.599615\pi$
$367$	−2.28450e10	+	2.28450e10i	−1.25930	+	1.25930i	−0.951430	+	0.307866i	$0.900385\pi$
$368$	−8.50134e9	−	8.50134e9i	−0.463550	−	0.463550i
$369$		−	1.04132e10i		−	0.561668i
$370$		0			0
$371$	−1.78747e10			−0.943505
$372$	−9.29948e8	+	9.29948e8i	−0.0485609	+	0.0485609i
$373$	−6.40647e8	−	6.40647e8i	−0.0330966	−	0.0330966i	0.690365	−	0.723461i	$-0.257450\pi$
$373$	−6.40647e8	−	6.40647e8i	−0.0330966	−	0.0330966i	−0.723461	+	0.690365i	$0.757450\pi$
$374$		−	2.81327e10i		−	1.43789i
$375$		0			0
$376$	−1.54025e10			−0.770622
$377$	−1.87402e10	+	1.87402e10i	−0.927702	+	0.927702i
$378$	−3.14852e9	−	3.14852e9i	−0.154220	−	0.154220i
$379$			2.55013e10i			1.23596i	0.786193	+	0.617982i	$0.212049\pi$
$379$			2.55013e10i			1.23596i	−0.786193	+	0.617982i	$0.787951\pi$
$380$		0			0
$381$	−8.44353e9			−0.400705
$382$	−1.68686e10	+	1.68686e10i	−0.792182	+	0.792182i
$383$	5.42375e9	+	5.42375e9i	0.252060	+	0.252060i	0.821815	−	0.569755i	$-0.192962\pi$
$383$	5.42375e9	+	5.42375e9i	0.252060	+	0.252060i	−0.569755	+	0.821815i	$0.692962\pi$
$384$		−	1.09550e10i		−	0.503834i
$385$		0			0
$386$	−1.05675e10			−0.476017
$387$	−5.61916e9	+	5.61916e9i	−0.250511	+	0.250511i
$388$	−1.13911e10	−	1.13911e10i	−0.502618	−	0.502618i
$389$			1.22528e10i			0.535104i	0.963543	+	0.267552i	$0.0862146\pi$
$389$			1.22528e10i			0.535104i	−0.963543	+	0.267552i	$0.913785\pi$
$390$		0			0
$391$	−1.81902e10			−0.778269
$392$	−3.37259e9	+	3.37259e9i	−0.142830	+	0.142830i
$393$	−3.39916e8	−	3.39916e8i	−0.0142496	−	0.0142496i
$394$		−	1.06214e10i		−	0.440754i
$395$		0			0
$396$	−1.40094e10			−0.569689
$397$	3.10306e10	−	3.10306e10i	1.24919	−	1.24919i	0.293111	−	0.956078i	$-0.405309\pi$
$397$	3.10306e10	−	3.10306e10i	1.24919	−	1.24919i	0.956078	−	0.293111i	$-0.0946906\pi$
$398$	1.48841e10	+	1.48841e10i	0.593184	+	0.593184i
$399$			7.25162e9i			0.286117i
$400$		0			0
$401$	−1.38357e10			−0.535085			−0.267542	−	0.963546i	$-0.586212\pi$
$401$	−1.38357e10			−0.535085			−0.267542	+	0.963546i	$0.586212\pi$
$402$	3.42182e9	−	3.42182e9i	0.131025	−	0.131025i
$403$	−2.52989e9	−	2.52989e9i	−0.0959140	−	0.0959140i
$404$			2.22066e10i			0.833600i
$405$		0			0
$406$	−2.72239e10			−1.00195
$407$	−2.23774e10	+	2.23774e10i	−0.815515	+	0.815515i
$408$	−3.73178e9	−	3.73178e9i	−0.134672	−	0.134672i
$409$		−	3.64124e10i		−	1.30124i	−0.759405	−	0.650618i	$-0.774510\pi$
$409$		−	3.64124e10i		−	1.30124i	0.759405	−	0.650618i	$-0.225490\pi$
$410$		0			0
$411$	−2.22466e10			−0.779644
$412$	3.40232e10	−	3.40232e10i	1.18083	−	1.18083i
$413$	−8.69560e9	−	8.69560e9i	−0.298882	−	0.298882i
$414$			1.60191e10i			0.545302i
$415$		0			0
$416$	6.12972e10			2.04676
$417$	−1.45484e10	+	1.45484e10i	−0.481140	+	0.481140i
$418$	2.85307e10	+	2.85307e10i	0.934559	+	0.934559i
$419$			2.41251e10i			0.782732i	0.920235	+	0.391366i	$0.127997\pi$
$419$			2.41251e10i			0.782732i	−0.920235	+	0.391366i	$0.872003\pi$
$420$		0			0
$421$	−2.43539e10			−0.775247			−0.387623	−	0.921818i	$-0.626704\pi$
$421$	−2.43539e10			−0.775247			−0.387623	+	0.921818i	$0.626704\pi$
$422$	−3.08984e10	+	3.08984e10i	−0.974286	+	0.974286i
$423$	−1.27225e10	−	1.27225e10i	−0.397385	−	0.397385i
$424$			1.86574e10i			0.577282i
$425$		0			0
$426$	1.77053e10			0.537606
$427$	−2.75719e10	+	2.75719e10i	−0.829383	+	0.829383i
$428$	6.89772e9	+	6.89772e9i	0.205556	+	0.205556i
$429$		−	3.81120e10i		−	1.12521i
$430$		0			0
$431$	−1.77334e10			−0.513906			−0.256953	−	0.966424i	$-0.582719\pi$
$431$	−1.77334e10			−0.513906			−0.256953	+	0.966424i	$0.582719\pi$
$432$	2.88123e9	−	2.88123e9i	0.0827261	−	0.0827261i
$433$	−2.86488e10	−	2.86488e10i	−0.814994	−	0.814994i	0.170384	−	0.985378i	$-0.445499\pi$
$433$	−2.86488e10	−	2.86488e10i	−0.814994	−	0.814994i	−0.985378	+	0.170384i	$0.945499\pi$
$434$		−	3.67518e9i		−	0.103590i
$435$		0			0
$436$	8.91719e10			2.46764
$437$	1.84475e10	−	1.84475e10i	0.505838	−	0.505838i
$438$	−5.54133e9	−	5.54133e9i	−0.150563	−	0.150563i
$439$		−	4.43850e10i		−	1.19503i	−0.801859	−	0.597513i	$-0.796155\pi$
$439$		−	4.43850e10i		−	1.19503i	0.801859	−	0.597513i	$-0.203845\pi$
$440$		0			0
$441$	−5.57153e9			−0.147306
$442$	4.38463e10	−	4.38463e10i	1.14880	−	1.14880i
$443$	1.52964e10	+	1.52964e10i	0.397168	+	0.397168i	0.877233	−	0.480065i	$-0.159387\pi$
$443$	1.52964e10	+	1.52964e10i	0.397168	+	0.397168i	−0.480065	+	0.877233i	$0.659387\pi$
$444$			2.56400e10i			0.659759i
$445$		0			0
$446$	−9.25200e10			−2.33828
$447$	−4.98841e9	+	4.98841e9i	−0.124949	+	0.124949i
$448$	3.15877e10	+	3.15877e10i	0.784162	+	0.784162i
$449$			5.79660e10i			1.42623i	0.701049	+	0.713113i	$0.252715\pi$
$449$			5.79660e10i			1.42623i	−0.701049	+	0.713113i	$0.747285\pi$
$450$		0			0
$451$	9.15560e10			2.21300
$452$	−1.58946e10	+	1.58946e10i	−0.380800	+	0.380800i
$453$	−1.24659e10	−	1.24659e10i	−0.296026	−	0.296026i
$454$			3.08442e10i			0.726022i
$455$		0			0
$456$	7.56915e9			0.175060
$457$	−5.08408e9	+	5.08408e9i	−0.116560	+	0.116560i	−0.762981	−	0.646421i	$-0.776265\pi$
$457$	−5.08408e9	+	5.08408e9i	−0.116560	+	0.116560i	0.646421	+	0.762981i	$0.276265\pi$
$458$	4.62987e10	+	4.62987e10i	1.05222	+	1.05222i
$459$		−	6.16491e9i		−	0.138892i
$460$		0			0
$461$	−1.46027e10			−0.323318			−0.161659	−	0.986847i	$-0.551685\pi$
$461$	−1.46027e10			−0.323318			−0.161659	+	0.986847i	$0.551685\pi$
$462$	2.76827e10	−	2.76827e10i	0.607632	−	0.607632i
$463$	7.72764e9	+	7.72764e9i	0.168160	+	0.168160i	0.786170	−	0.618010i	$-0.212061\pi$
$463$	7.72764e9	+	7.72764e9i	0.168160	+	0.168160i	−0.618010	+	0.786170i	$0.712061\pi$
$464$		−	2.49128e10i		−	0.537464i
$465$		0			0
$466$	1.02961e11			2.18338
$467$	2.02567e10	−	2.02567e10i	0.425894	−	0.425894i	−0.461333	−	0.887227i	$-0.652629\pi$
$467$	2.02567e10	−	2.02567e10i	0.425894	−	0.425894i	0.887227	+	0.461333i	$0.152629\pi$
$468$	−2.18343e10	−	2.18343e10i	−0.455152	−	0.455152i
$469$			7.64684e9i			0.158049i
$470$		0			0
$471$	1.00653e10			0.204523
$472$	−9.07635e9	+	9.07635e9i	−0.182870	+	0.182870i
$473$	−4.94052e10	−	4.94052e10i	−0.987026	−	0.987026i
$474$		−	3.38753e9i		−	0.0671073i
$475$		0			0
$476$	3.60176e10			0.701595
$477$	−1.54110e10	+	1.54110e10i	−0.297686	+	0.297686i
$478$	9.89228e9	+	9.89228e9i	0.189489	+	0.189489i
$479$			5.82622e10i			1.10674i	0.832936	+	0.553369i	$0.186658\pi$
$479$			5.82622e10i			1.10674i	−0.832936	+	0.553369i	$0.813342\pi$
$480$		0			0
$481$	−6.97527e10			−1.30311
$482$	−3.21277e10	+	3.21277e10i	−0.595239	+	0.595239i
$483$	−1.78992e10	−	1.78992e10i	−0.328886	−	0.328886i
$484$		−	5.17641e10i		−	0.943294i
$485$		0			0
$486$	−5.42911e9			−0.0973159
$487$	−5.54456e10	+	5.54456e10i	−0.985714	+	0.985714i	−0.999899	−	0.0141852i	$-0.995485\pi$
$487$	−5.54456e10	+	5.54456e10i	−0.985714	+	0.985714i	0.0141852	+	0.999899i	$0.495485\pi$
$488$	2.87792e10	+	2.87792e10i	0.507457	+	0.507457i
$489$			3.90467e10i			0.682886i
$490$		0			0
$491$	2.06600e10			0.355472			0.177736	−	0.984078i	$-0.443123\pi$
$491$	2.06600e10			0.355472			0.177736	+	0.984078i	$0.443123\pi$
$492$	5.24523e10	−	5.24523e10i	0.895167	−	0.895167i
$493$	−2.66527e10	−	2.66527e10i	−0.451184	−	0.451184i
$494$			8.89331e10i			1.49333i
$495$		0			0
$496$	3.36318e9			0.0555678
$497$	−1.97833e10	+	1.97833e10i	−0.324244	+	0.324244i
$498$	4.14118e10	+	4.14118e10i	0.673298	+	0.673298i
$499$		−	4.68529e10i		−	0.755673i	−0.925872	−	0.377837i	$-0.876668\pi$
$499$		−	4.68529e10i		−	0.755673i	0.925872	−	0.377837i	$-0.123332\pi$
$500$		0			0
$501$	4.25646e10			0.675612
$502$	6.33841e9	−	6.33841e9i	0.0998081	−	0.0998081i
$503$	−2.89023e10	−	2.89023e10i	−0.451504	−	0.451504i	0.444350	−	0.895853i	$-0.353435\pi$
$503$	−2.89023e10	−	2.89023e10i	−0.451504	−	0.451504i	−0.895853	+	0.444350i	$0.853435\pi$
$504$		−	7.34418e9i		−	0.113821i
$505$		0			0
$506$	−1.40845e11			−2.14852
$507$	3.24249e10	−	3.24249e10i	0.490735	−	0.490735i
$508$	−4.25308e10	−	4.25308e10i	−0.638629	−	0.638629i
$509$		−	8.29321e10i		−	1.23553i	−0.786365	−	0.617763i	$-0.788039\pi$
$509$		−	8.29321e10i		−	1.23553i	0.786365	−	0.617763i	$-0.211961\pi$
$510$		0			0
$511$	1.23834e10			0.181617
$512$	−5.42455e10	+	5.42455e10i	−0.789376	+	0.789376i
$513$	6.25212e9	+	6.25212e9i	0.0902730	+	0.0902730i
$514$			9.99292e10i			1.43166i
$515$		0			0
$516$	−5.66084e10			−0.798513
$517$	1.11860e11	−	1.11860e11i	1.56572	−	1.56572i
$518$	−5.06649e10	−	5.06649e10i	−0.703701	−	0.703701i
$519$			1.86213e10i			0.256649i
$520$		0			0
$521$	9.15715e10			1.24282			0.621412	−	0.783484i	$-0.286560\pi$
$521$	9.15715e10			1.24282			0.621412	+	0.783484i	$0.286560\pi$
$522$	−2.34716e10	+	2.34716e10i	−0.316126	+	0.316126i
$523$	4.34006e10	+	4.34006e10i	0.580082	+	0.580082i	0.934926	−	0.354844i	$-0.115466\pi$
$523$	4.34006e10	+	4.34006e10i	0.580082	+	0.580082i	−0.354844	+	0.934926i	$0.615466\pi$
$524$		−	3.42438e9i		−	0.0454209i
$525$		0			0
$526$	3.18675e10			0.416299
$527$	3.59806e9	−	3.59806e9i	0.0466473	−	0.0466473i
$528$	2.53326e10	+	2.53326e10i	0.325945	+	0.325945i
$529$			1.27570e10i			0.162902i
$530$		0			0
$531$	−1.49941e10			−0.188601
$532$	−3.65271e10	+	3.65271e10i	−0.456004	+	0.456004i
$533$	1.42695e11	+	1.42695e11i	1.76807	+	1.76807i
$534$		−	4.72095e10i		−	0.580583i
$535$		0			0
$536$	7.98167e9			0.0967018
$537$	−2.72180e10	+	2.72180e10i	−0.327310	+	0.327310i
$538$	1.95005e9	+	1.95005e9i	0.0232765	+	0.0232765i
$539$		−	4.89865e10i		−	0.580391i
$540$		0			0
$541$	−1.31119e11			−1.53066			−0.765329	−	0.643640i	$-0.777424\pi$
$541$	−1.31119e11			−1.53066			−0.765329	+	0.643640i	$0.777424\pi$
$542$	−1.23208e11	+	1.23208e11i	−1.42772	+	1.42772i
$543$	1.98039e10	+	1.98039e10i	0.227798	+	0.227798i
$544$			8.71781e10i			0.995433i
$545$		0			0
$546$	8.62899e10			0.970933
$547$	−3.75422e10	+	3.75422e10i	−0.419344	+	0.419344i	−0.884978	−	0.465634i	$-0.845827\pi$
$547$	−3.75422e10	+	3.75422e10i	−0.419344	+	0.419344i	0.465634	+	0.884978i	$0.345827\pi$
$548$	−1.12058e11	−	1.12058e11i	−1.24257	−	1.24257i
$549$			4.75432e10i			0.523359i
$550$		0			0
$551$	5.40594e10			0.586496
$552$	−1.86830e10	+	1.86830e10i	−0.201228	+	0.201228i
$553$	3.78511e9	+	3.78511e9i	0.0404741	+	0.0404741i
$554$		−	2.19501e11i		−	2.33022i
$555$		0			0
$556$	−1.46563e11			−1.53365
$557$	6.21073e10	−	6.21073e10i	0.645241	−	0.645241i	−0.306598	−	0.951839i	$-0.599191\pi$
$557$	6.21073e10	−	6.21073e10i	0.645241	−	0.645241i	0.951839	+	0.306598i	$0.0991907\pi$
$558$	−3.16863e9	−	3.16863e9i	−0.0326839	−	0.0326839i
$559$		−	1.54001e11i		−	1.57717i
$560$		0			0
$561$	5.42037e10			0.547239
$562$	−5.00387e10	+	5.00387e10i	−0.501603	+	0.501603i
$563$	1.14631e11	+	1.14631e11i	1.14096	+	1.14096i	0.988275	+	0.152684i	$0.0487918\pi$
$563$	1.14631e11	+	1.14631e11i	1.14096	+	1.14096i	0.152684	+	0.988275i	$0.451208\pi$
$564$		−	1.28169e11i		−	1.26668i
$565$		0			0
$566$	−3.93943e10			−0.383856
$567$	6.06630e9	−	6.06630e9i	0.0586937	−	0.0586937i
$568$	2.06495e10	+	2.06495e10i	0.198388	+	0.198388i
$569$			8.63822e10i			0.824091i	0.911163	+	0.412045i	$0.135186\pi$
$569$			8.63822e10i			0.824091i	−0.911163	+	0.412045i	$0.864814\pi$
$570$		0			0
$571$	−1.75762e11			−1.65341			−0.826703	−	0.562639i	$-0.809786\pi$
$571$	−1.75762e11			−1.65341			−0.826703	+	0.562639i	$0.809786\pi$
$572$	1.91974e11	−	1.91974e11i	1.79332	−	1.79332i
$573$	−3.25009e10	−	3.25009e10i	−0.301493	−	0.301493i
$574$			2.07293e11i			1.90958i
$575$		0			0
$576$	5.44679e10			0.494824
$577$	2.15084e10	−	2.15084e10i	0.194046	−	0.194046i	−0.603396	−	0.797442i	$-0.706186\pi$
$577$	2.15084e10	−	2.15084e10i	0.194046	−	0.194046i	0.797442	+	0.603396i	$0.206186\pi$
$578$	−5.73655e10	−	5.73655e10i	−0.513972	−	0.513972i
$579$		−	2.03605e10i		−	0.181165i
$580$		0			0
$581$	−9.25443e10			−0.812166
$582$	3.88130e10	−	3.88130e10i	0.338287	−	0.338287i
$583$	−1.35498e11	−	1.35498e11i	−1.17290	−	1.17290i
$584$		−	1.29256e10i		−	0.111122i
$585$		0			0
$586$	−1.24252e11			−1.05369
$587$	−3.42847e10	+	3.42847e10i	−0.288767	+	0.288767i	−0.836593	−	0.547826i	$-0.815456\pi$
$587$	−3.42847e10	+	3.42847e10i	−0.288767	+	0.288767i	0.547826	+	0.836593i	$0.315456\pi$
$588$	−2.80643e10	−	2.80643e10i	−0.234771	−	0.234771i
$589$			7.29793e9i			0.0606371i
$590$		0			0
$591$	2.04644e10			0.167745
$592$	4.63638e10	−	4.63638e10i	0.377478	−	0.377478i
$593$	7.32380e10	+	7.32380e10i	0.592267	+	0.592267i	0.938243	−	0.345976i	$-0.112452\pi$
$593$	7.32380e10	+	7.32380e10i	0.592267	+	0.592267i	−0.345976	+	0.938243i	$0.612452\pi$
$594$		−	4.77343e10i		−	0.383429i
$595$		0			0
$596$	−5.02541e10			−0.398278
$597$	−2.86774e10	+	2.86774e10i	−0.225757	+	0.225757i
$598$	−2.19514e11	−	2.19514e11i	−1.71655	−	1.71655i
$599$			2.17395e11i			1.68866i	0.535821	+	0.844331i	$0.320002\pi$
$599$			2.17395e11i			1.68866i	−0.535821	+	0.844331i	$0.679998\pi$
$600$		0			0
$601$	1.56619e11			1.20046			0.600229	−	0.799828i	$-0.295076\pi$
$601$	1.56619e11			1.20046			0.600229	+	0.799828i	$0.295076\pi$
$602$	1.11859e11	−	1.11859e11i	0.851697	−	0.851697i
$603$	6.59287e9	+	6.59287e9i	0.0498661	+	0.0498661i
$604$		−	1.25583e11i		−	0.943593i
$605$		0			0
$606$	−7.56651e10			−0.561054
$607$	1.03509e11	−	1.03509e11i	0.762470	−	0.762470i	−0.214299	−	0.976768i	$-0.568747\pi$
$607$	1.03509e11	−	1.03509e11i	0.762470	−	0.762470i	0.976768	+	0.214299i	$0.0687465\pi$
$608$	−8.84114e10	−	8.84114e10i	−0.646984	−	0.646984i
$609$		−	5.24527e10i		−	0.381328i
$610$		0			0
$611$	3.48680e11			2.50185
$612$	3.10532e10	−	3.10532e10i	0.221361	−	0.221361i
$613$	1.06340e11	+	1.06340e11i	0.753107	+	0.753107i	0.975058	−	0.221951i	$-0.0712425\pi$
$613$	1.06340e11	+	1.06340e11i	0.753107	+	0.753107i	−0.221951	+	0.975058i	$0.571242\pi$
$614$		−	2.22920e11i		−	1.56847i
$615$		0			0
$616$	6.45721e10			0.448458
$617$	1.72024e11	−	1.72024e11i	1.18699	−	1.18699i	0.209099	−	0.977895i	$-0.432947\pi$
$617$	1.72024e11	−	1.72024e11i	1.18699	−	1.18699i	0.977895	−	0.209099i	$-0.0670530\pi$
$618$	1.15928e11	+	1.15928e11i	0.794756	+	0.794756i
$619$			9.12403e9i			0.0621476i	0.999517	+	0.0310738i	$0.00989268\pi$
$619$			9.12403e9i			0.0621476i	−0.999517	+	0.0310738i	$0.990107\pi$
$620$		0			0
$621$	−3.08643e10			−0.207534
$622$	−1.59147e11	+	1.59147e11i	−1.06325	+	1.06325i
$623$	5.27503e10	+	5.27503e10i	0.350165	+	0.350165i
$624$			7.89643e10i			0.520826i
$625$		0			0
$626$	8.80190e10			0.573165
$627$	−5.49705e10	+	5.49705e10i	−0.355680	+	0.355680i
$628$	5.06997e10	+	5.06997e10i	0.325962	+	0.325962i
$629$		−	9.92037e10i		−	0.633761i
$630$		0			0
$631$	1.60100e11			1.00989			0.504944	−	0.863152i	$-0.331513\pi$
$631$	1.60100e11			1.00989			0.504944	+	0.863152i	$0.331513\pi$
$632$	3.95084e9	−	3.95084e9i	0.0247640	−	0.0247640i
$633$	−5.95324e10	−	5.95324e10i	−0.370799	−	0.370799i
$634$		−	1.47679e11i		−	0.914032i
$635$		0			0
$636$	−1.55254e11			−0.948884
$637$	7.63480e10	−	7.63480e10i	0.463703	−	0.463703i
$638$	−2.06369e11	−	2.06369e11i	−1.24555	−	1.24555i
$639$			3.41130e10i			0.204605i
$640$		0			0
$641$	3.05431e11			1.80918			0.904588	−	0.426287i	$-0.140179\pi$
$641$	3.05431e11			1.80918			0.904588	+	0.426287i	$0.140179\pi$
$642$	−2.35027e10	+	2.35027e10i	−0.138350	+	0.138350i
$643$	5.66348e10	+	5.66348e10i	0.331314	+	0.331314i	0.853085	−	0.521772i	$-0.174729\pi$
$643$	5.66348e10	+	5.66348e10i	0.331314	+	0.331314i	−0.521772	+	0.853085i	$0.674729\pi$
$644$		−	1.80320e11i		−	1.04833i
$645$		0			0
$646$	−1.26482e11			−0.726273
$647$	−9.92301e10	+	9.92301e10i	−0.566273	+	0.566273i	−0.931082	−	0.364809i	$-0.881134\pi$
$647$	−9.92301e10	+	9.92301e10i	−0.566273	+	0.566273i	0.364809	+	0.931082i	$0.381134\pi$
$648$	−6.33192e9	−	6.33192e9i	−0.0359117	−	0.0359117i
$649$		−	1.31833e11i		−	0.743096i
$650$		0			0
$651$	7.08102e9			0.0394250
$652$	−1.96681e11	+	1.96681e11i	−1.08836	+	1.08836i
$653$	−9.46204e10	−	9.46204e10i	−0.520394	−	0.520394i	0.397297	−	0.917690i	$-0.369948\pi$
$653$	−9.46204e10	−	9.46204e10i	−0.520394	−	0.520394i	−0.917690	+	0.397297i	$0.869948\pi$
$654$			3.03837e11i			1.66085i
$655$		0			0
$656$	−1.89695e11			−1.02433
$657$	1.06766e10	−	1.06766e10i	0.0573020	−	0.0573020i
$658$	2.53264e11	+	2.53264e11i	1.35104	+	1.35104i
$659$			3.38192e11i			1.79317i	0.442872	+	0.896585i	$0.353960\pi$
$659$			3.38192e11i			1.79317i	−0.442872	+	0.896585i	$0.646040\pi$
$660$		0			0
$661$	−1.18923e11			−0.622962			−0.311481	−	0.950252i	$-0.600825\pi$
$661$	−1.18923e11			−0.622962			−0.311481	+	0.950252i	$0.600825\pi$
$662$	6.08411e10	−	6.08411e10i	0.316785	−	0.316785i
$663$	8.44793e10	+	8.44793e10i	0.437216	+	0.437216i
$664$			9.65965e10i			0.496923i
$665$		0			0
$666$	−8.73635e10			−0.444051
$667$	−1.33435e11	+	1.33435e11i	−0.674166	+	0.674166i
$668$	2.14402e11	+	2.14402e11i	1.07677	+	1.07677i
$669$		−	1.78260e11i		−	0.889915i
$670$		0			0
$671$	−4.18014e11			−2.06206
$672$	−8.57837e10	+	8.57837e10i	−0.420656	+	0.420656i
$673$	−1.70179e11	−	1.70179e11i	−0.829557	−	0.829557i	0.157898	−	0.987455i	$-0.449528\pi$
$673$	−1.70179e11	−	1.70179e11i	−0.829557	−	0.829557i	−0.987455	+	0.157898i	$0.949528\pi$
$674$			2.25521e11i			1.09281i
$675$		0			0
$676$	3.26654e11			1.56423
$677$	−2.63270e10	+	2.63270e10i	−0.125328	+	0.125328i	−0.766988	−	0.641661i	$-0.778246\pi$
$677$	−2.63270e10	+	2.63270e10i	−0.125328	+	0.125328i	0.641661	+	0.766988i	$0.278246\pi$
$678$	−5.41581e10	−	5.41581e10i	−0.256297	−	0.256297i
$679$			8.67366e10i			0.408059i
$680$		0			0
$681$	−5.94279e10			−0.276313
$682$	2.78595e10	−	2.78595e10i	0.128776	−	0.128776i
$683$	1.26414e11	+	1.26414e11i	0.580913	+	0.580913i	0.935154	−	0.354241i	$-0.115261\pi$
$683$	1.26414e11	+	1.26414e11i	0.580913	+	0.580913i	−0.354241	+	0.935154i	$0.615261\pi$
$684$			6.29850e10i			0.287748i
$685$		0			0
$686$	3.61887e11			1.63409
$687$	−8.92043e10	+	8.92043e10i	−0.400460	+	0.400460i
$688$	1.02363e11	+	1.02363e11i	0.456865	+	0.456865i
$689$		−	4.22362e11i		−	1.87417i
$690$		0			0
$691$	2.31709e11			1.01632			0.508159	−	0.861263i	$-0.330326\pi$
$691$	2.31709e11			1.01632			0.508159	+	0.861263i	$0.330326\pi$
$692$	−9.37969e10	+	9.37969e10i	−0.409039	+	0.409039i
$693$	5.33367e10	+	5.33367e10i	0.231256	+	0.231256i
$694$			6.82403e11i			2.94173i
$695$		0			0
$696$	−5.47494e10			−0.233315
$697$	−2.02943e11	+	2.02943e11i	−0.859892	+	0.859892i
$698$	−3.67783e11	−	3.67783e11i	−1.54942	−	1.54942i
$699$			1.98377e11i			0.830964i
$700$		0			0
$701$	−1.76797e11			−0.732155			−0.366077	−	0.930584i	$-0.619299\pi$
$701$	−1.76797e11			−0.732155			−0.366077	+	0.930584i	$0.619299\pi$
$702$	7.43965e10	−	7.43965e10i	0.306340	−	0.306340i
$703$	1.00607e11	+	1.00607e11i	0.411915	+	0.411915i
$704$			4.78897e11i			1.94963i
$705$		0			0
$706$	−1.74092e11			−0.700744
$707$	8.45455e10	−	8.45455e10i	0.338386	−	0.338386i
$708$	−7.55269e10	−	7.55269e10i	−0.300586	−	0.300586i
$709$		−	4.27410e11i		−	1.69145i	−0.533619	−	0.845725i	$-0.679168\pi$
$709$		−	4.27410e11i		−	1.69145i	0.533619	−	0.845725i	$-0.320832\pi$
$710$		0			0
$711$	6.52680e9			0.0255401
$712$	5.50600e10	−	5.50600e10i	0.214248	−	0.214248i
$713$	−1.80135e10	−	1.80135e10i	−0.0697012	−	0.0697012i
$714$			1.22723e11i			0.472209i
$715$		0			0
$716$	−2.74199e11			−1.04331
$717$	−1.90596e10	+	1.90596e10i	−0.0721169	+	0.0721169i
$718$	3.28870e11	+	3.28870e11i	1.23745	+	1.23745i
$719$			4.10573e11i			1.53630i	0.640273	+	0.768148i	$0.278821\pi$
$719$			4.10573e11i			1.53630i	−0.640273	+	0.768148i	$0.721179\pi$
$720$		0			0
$721$	−2.59067e11			−0.958675
$722$	−1.63216e11	+	1.63216e11i	−0.600641	+	0.600641i
$723$	−6.19008e10	−	6.19008e10i	−0.226539	−	0.226539i
$724$			1.99508e11i			0.726115i
$725$		0			0
$726$	1.76377e11			0.634884
$727$	1.64242e11	−	1.64242e11i	0.587957	−	0.587957i	−0.349121	−	0.937078i	$-0.613520\pi$
$727$	1.64242e11	−	1.64242e11i	0.587957	−	0.587957i	0.937078	+	0.349121i	$0.113520\pi$
$728$	1.00639e11	+	1.00639e11i	0.358295	+	0.358295i
$729$		−	1.04604e10i		−	0.0370370i
$730$		0			0
$731$	2.19024e11			0.767047
$732$	−2.39480e11	+	2.39480e11i	−0.834112	+	0.834112i
$733$	1.10142e11	+	1.10142e11i	0.381536	+	0.381536i	0.871655	−	0.490119i	$-0.163047\pi$
$733$	1.10142e11	+	1.10142e11i	0.381536	+	0.381536i	−0.490119	+	0.871655i	$0.663047\pi$
$734$		−	7.84177e11i		−	2.70165i
$735$		0			0
$736$	4.36452e11			1.48739
$737$	−5.79664e10	+	5.79664e10i	−0.196474	+	0.196474i
$738$	1.78722e11	+	1.78722e11i	0.602493	+	0.602493i
$739$			2.64286e11i			0.886127i	0.896490	+	0.443064i	$0.146108\pi$
$739$			2.64286e11i			0.886127i	−0.896490	+	0.443064i	$0.853892\pi$
$740$		0			0
$741$	−1.71349e11			−0.568340
$742$	3.06783e11	−	3.06783e11i	1.01208	−	1.01208i
$743$	−1.02658e11	−	1.02658e11i	−0.336851	−	0.336851i	0.518330	−	0.855181i	$-0.326554\pi$
$743$	−1.02658e11	−	1.02658e11i	−0.336851	−	0.336851i	−0.855181	+	0.518330i	$0.826554\pi$
$744$		−	7.39108e9i		−	0.0241221i
$745$		0			0
$746$	2.19908e10			0.0710044
$747$	−7.97888e10	+	7.97888e10i	−0.256247	+	0.256247i
$748$	2.73029e11	+	2.73029e11i	0.872172	+	0.872172i
$749$		−	5.25222e10i		−	0.166884i
$750$		0			0
$751$	4.48613e11			1.41030			0.705151	−	0.709057i	$-0.250879\pi$
$751$	4.48613e11			1.41030			0.705151	+	0.709057i	$0.250879\pi$
$752$	−2.31763e11	+	2.31763e11i	−0.724724	+	0.724724i
$753$	1.22123e10	+	1.22123e10i	0.0379855	+	0.0379855i
$754$		−	6.43274e11i		−	1.99026i
$755$		0			0
$756$	6.11130e10			0.187088
$757$	2.01768e11	−	2.01768e11i	0.614425	−	0.614425i	−0.329671	−	0.944096i	$-0.606938\pi$
$757$	2.01768e11	−	2.01768e11i	0.614425	−	0.614425i	0.944096	+	0.329671i	$0.106938\pi$
$758$	−4.37678e11	−	4.37678e11i	−1.32580	−	1.32580i
$759$		−	2.71368e11i		−	0.817694i
$760$		0			0
$761$	2.07019e11			0.617265			0.308632	−	0.951181i	$-0.400129\pi$
$761$	2.07019e11			0.617265			0.308632	+	0.951181i	$0.400129\pi$
$762$	1.44916e11	−	1.44916e11i	0.429830	−	0.429830i
$763$	−3.39497e11	−	3.39497e11i	−1.00170	−	1.00170i
$764$		−	3.27420e11i		−	0.961019i
$765$		0			0
$766$	−1.86175e11			−0.540762
$767$	2.05468e11	−	2.05468e11i	0.593695	−	0.593695i
$768$	−2.28140e10	−	2.28140e10i	−0.0655778	−	0.0655778i
$769$		−	5.81261e11i		−	1.66213i	−0.556172	−	0.831067i	$-0.687730\pi$
$769$		−	5.81261e11i		−	1.66213i	0.556172	−	0.831067i	$-0.312270\pi$
$770$		0			0
$771$	−1.92535e11			−0.544869
$772$	1.02558e11	−	1.02558e11i	0.288735	−	0.288735i
$773$	7.04229e10	+	7.04229e10i	0.197240	+	0.197240i	0.798816	−	0.601576i	$-0.205460\pi$
$773$	7.04229e10	+	7.04229e10i	0.197240	+	0.197240i	−0.601576	+	0.798816i	$0.705460\pi$
$774$		−	1.92883e11i		−	0.537439i
$775$		0			0
$776$	9.05345e10			0.249671
$777$	9.76169e10	−	9.76169e10i	0.267819	−	0.267819i
$778$	−2.10295e11	−	2.10295e11i	−0.573997	−	0.573997i
$779$		−	4.11629e11i		−	1.11778i
$780$		0			0
$781$	−2.99931e11			−0.806153
$782$	3.12197e11	−	3.12197e11i	0.834837	−	0.834837i
$783$	−4.52231e10	−	4.52231e10i	−0.120313	−	0.120313i
$784$			1.01495e11i			0.268646i
$785$		0			0
$786$	1.16679e10			0.0305706
$787$	−8.91512e10	+	8.91512e10i	−0.232396	+	0.232396i	−0.813692	−	0.581296i	$-0.802546\pi$
$787$	−8.91512e10	+	8.91512e10i	−0.232396	+	0.232396i	0.581296	+	0.813692i	$0.302546\pi$
$788$	1.03081e11	+	1.03081e11i	0.267346	+	0.267346i
$789$			6.13996e10i			0.158437i
$790$		0			0
$791$	1.21029e11			0.309159
$792$	5.56721e10	−	5.56721e10i	0.141494	−	0.141494i
$793$	−6.51497e11	−	6.51497e11i	−1.64748	−	1.64748i
$794$			1.06515e12i			2.67997i
$795$		0			0
$796$	−2.88901e11			−0.719609
$797$	2.83454e11	−	2.83454e11i	0.702506	−	0.702506i	−0.262442	−	0.964948i	$-0.584528\pi$
$797$	2.83454e11	−	2.83454e11i	0.702506	−	0.702506i	0.964948	+	0.262442i	$0.0845278\pi$
$798$	−1.24459e11	−	1.24459e11i	−0.306913	−	0.306913i
$799$			4.95899e11i			1.21676i
$800$		0			0
$801$	9.09593e10			0.220962
$802$	2.37461e11	−	2.37461e11i	0.573977	−	0.573977i
$803$	9.38714e10	+	9.38714e10i	0.225772	+	0.225772i
$804$			6.64177e10i			0.158950i
$805$		0			0
$806$	8.68409e10			0.205771
$807$	−3.75719e9	+	3.75719e9i	−0.00885869	+	0.00885869i
$808$	−8.82474e10	−	8.82474e10i	−0.207041	−	0.207041i
$809$			6.86525e10i			0.160274i	0.996784	+	0.0801369i	$0.0255357\pi$
$809$			6.86525e10i			0.160274i	−0.996784	+	0.0801369i	$0.974464\pi$
$810$		0			0
$811$	−5.32627e11			−1.23123			−0.615615	−	0.788047i	$-0.711092\pi$
$811$	−5.32627e11			−1.23123			−0.615615	+	0.788047i	$0.711092\pi$
$812$	2.64209e11	−	2.64209e11i	0.607748	−	0.607748i
$813$	−2.37387e11	−	2.37387e11i	−0.543369	−	0.543369i
$814$		−	7.68125e11i		−	1.74958i
$815$		0			0
$816$	−1.12305e11			−0.253301
$817$	−2.22122e11	+	2.22122e11i	−0.498544	+	0.498544i
$818$	6.24944e11	+	6.24944e11i	1.39582	+	1.39582i
$819$			1.66256e11i			0.369523i
$820$		0			0
$821$	−6.21242e11			−1.36738			−0.683688	−	0.729774i	$-0.739625\pi$
$821$	−6.21242e11			−1.36738			−0.683688	+	0.729774i	$0.739625\pi$
$822$	3.81817e11	−	3.81817e11i	0.836312	−	0.836312i
$823$	5.17826e10	+	5.17826e10i	0.112872	+	0.112872i	0.761287	−	0.648415i	$-0.224568\pi$
$823$	5.17826e10	+	5.17826e10i	0.112872	+	0.112872i	−0.648415	+	0.761287i	$0.724568\pi$
$824$			2.70411e11i			0.586564i
$825$		0			0
$826$	2.98484e11			0.641211
$827$	−4.94342e11	+	4.94342e11i	−1.05683	+	1.05683i	−0.0585456	+	0.998285i	$0.518646\pi$
$827$	−4.94342e11	+	4.94342e11i	−1.05683	+	1.05683i	−0.998285	+	0.0585456i	$0.981354\pi$
$828$	−1.55466e11	−	1.55466e11i	−0.330761	−	0.330761i
$829$			3.10698e11i			0.657839i	0.944358	+	0.328920i	$0.106685\pi$
$829$			3.10698e11i			0.657839i	−0.944358	+	0.328920i	$0.893315\pi$
$830$		0			0
$831$	4.22916e11			0.886850
$832$	−7.46386e11	+	7.46386e11i	−1.55765	+	1.55765i
$833$	1.08584e11	+	1.08584e11i	0.225520	+	0.225520i
$834$		−	4.99387e11i		−	1.03222i
$835$		0			0
$836$	−5.53782e11			−1.13374
$837$	6.10504e9	−	6.10504e9i	0.0124390	−	0.0124390i
$838$	−4.14058e11	−	4.14058e11i	−0.839625	−	0.839625i
$839$		−	2.97303e11i		−	0.600000i	−0.953939	−	0.300000i	$-0.903013\pi$
$839$		−	2.97303e11i		−	0.600000i	0.953939	−	0.300000i	$-0.0969867\pi$
$840$		0			0
$841$	1.09222e11			0.218336
$842$	4.17985e11	−	4.17985e11i	0.831595	−	0.831595i
$843$	−9.64102e10	−	9.64102e10i	−0.190903	−	0.190903i
$844$		−	5.99740e11i		−	1.18193i
$845$		0			0
$846$	4.36712e11			0.852538
$847$	−1.97077e11	+	1.97077e11i	−0.382915	+	0.382915i
$848$	2.80739e11	+	2.80739e11i	0.542900	+	0.542900i
$849$		−	7.59016e10i		−	0.146090i
$850$		0			0
$851$	−4.96657e11			−0.946976
$852$	−1.71830e11	+	1.71830e11i	−0.326093	+	0.326093i
$853$	3.68635e11	+	3.68635e11i	0.696306	+	0.696306i	0.963612	−	0.267306i	$-0.0861335\pi$
$853$	3.68635e11	+	3.68635e11i	0.696306	+	0.696306i	−0.267306	+	0.963612i	$0.586133\pi$
$854$		−	9.46430e11i		−	1.77933i
$855$		0			0
$856$	−5.48220e10			−0.102108
$857$	−3.48994e11	+	3.48994e11i	−0.646986	+	0.646986i	−0.952263	−	0.305277i	$-0.901251\pi$
$857$	−3.48994e11	+	3.48994e11i	−0.646986	+	0.646986i	0.305277	+	0.952263i	$0.401251\pi$
$858$	6.54115e11	+	6.54115e11i	1.20699	+	1.20699i
$859$			5.94590e11i			1.09206i	0.837767	+	0.546028i	$0.183861\pi$
$859$			5.94590e11i			1.09206i	−0.837767	+	0.546028i	$0.816139\pi$
$860$		0			0
$861$	−3.99394e11			−0.726757
$862$	3.04358e11	−	3.04358e11i	0.551259	−	0.551259i
$863$	−2.31589e10	−	2.31589e10i	−0.0417518	−	0.0417518i	0.685923	−	0.727674i	$-0.259399\pi$
$863$	−2.31589e10	−	2.31589e10i	−0.0417518	−	0.0417518i	−0.727674	+	0.685923i	$0.759399\pi$
$864$			1.47920e11i			0.265443i
$865$		0			0
$866$	9.83395e11			1.74846
$867$	1.10527e11	−	1.10527e11i	0.195610	−	0.195610i
$868$	3.56677e10	+	3.56677e10i	0.0628343	+	0.0628343i
$869$			5.73855e10i			0.100629i
$870$		0			0
$871$	−1.80687e11			−0.313946
$872$	−3.54362e11	+	3.54362e11i	−0.612888	+	0.612888i
$873$	7.47816e10	+	7.47816e10i	0.128747	+	0.128747i
$874$			6.33227e11i			1.08521i
$875$		0			0
$876$	1.07558e11			0.182652
$877$	−4.04264e11	+	4.04264e11i	−0.683387	+	0.683387i	−0.960762	−	0.277375i	$-0.910536\pi$
$877$	−4.04264e11	+	4.04264e11i	−0.683387	+	0.683387i	0.277375	+	0.960762i	$0.410536\pi$
$878$	7.61777e11	+	7.61777e11i	1.28189	+	1.28189i
$879$		−	2.39398e11i		−	0.401020i
$880$		0			0
$881$	−2.39280e11			−0.397193			−0.198597	−	0.980081i	$-0.563638\pi$
$881$	−2.39280e11			−0.397193			−0.198597	+	0.980081i	$0.563638\pi$
$882$	9.56239e10	−	9.56239e10i	0.158013	−	0.158013i
$883$	7.09135e11	+	7.09135e11i	1.16650	+	1.16650i	0.983023	+	0.183481i	$0.0587365\pi$
$883$	7.09135e11	+	7.09135e11i	1.16650	+	1.16650i	0.183481	+	0.983023i	$0.441264\pi$
$884$			8.51059e11i			1.39364i
$885$		0			0
$886$	−5.25063e11			−0.852073
$887$	1.67605e11	−	1.67605e11i	0.270765	−	0.270765i	−0.558643	−	0.829408i	$-0.688678\pi$
$887$	1.67605e11	−	1.67605e11i	0.270765	−	0.270765i	0.829408	+	0.558643i	$0.188678\pi$
$888$	−1.01891e11	−	1.01891e11i	−0.163864	−	0.163864i
$889$			3.23848e11i			0.518483i
$890$		0			0
$891$	9.19704e10			0.145928
$892$	8.97909e11	−	8.97909e11i	1.41832	−	1.41832i
$893$	−5.02914e11	−	5.02914e11i	−0.790839	−	0.790839i
$894$		−	1.71232e11i		−	0.268061i
$895$		0			0
$896$	−4.20174e11			−0.651925
$897$	4.22941e11	−	4.22941e11i	0.653295	−	0.653295i
$898$	−9.94869e11	−	9.94869e11i	−1.52989	−	1.52989i
$899$		−	5.27876e10i		−	0.0808153i
$900$		0			0
$901$	6.00692e11			0.911492
$902$	−1.57137e12	+	1.57137e12i	−2.37385	+	2.37385i
$903$	2.15520e11	+	2.15520e11i	0.324143	+	0.324143i
$904$		−	1.26328e11i		−	0.189159i
$905$		0			0
$906$	4.27903e11			0.635085
$907$	−2.52036e11	+	2.52036e11i	−0.372420	+	0.372420i	−0.868358	−	0.495938i	$-0.834824\pi$
$907$	−2.52036e11	+	2.52036e11i	−0.372420	+	0.372420i	0.495938	+	0.868358i	$0.334824\pi$
$908$	−2.99344e11	−	2.99344e11i	−0.440379	−	0.440379i
$909$		−	1.45785e11i		−	0.213529i
$910$		0			0
$911$	1.03269e12			1.49933			0.749665	−	0.661817i	$-0.230215\pi$
$911$	1.03269e12			1.49933			0.749665	+	0.661817i	$0.230215\pi$
$912$	1.13893e11	−	1.13893e11i	0.164634	−	0.164634i
$913$	−7.01526e11	−	7.01526e11i	−1.00963	−	1.00963i
$914$		−	1.74516e11i		−	0.250063i
$915$		0			0
$916$	−8.98660e11			−1.27648
$917$	−1.30373e10	+	1.30373e10i	−0.0184379	+	0.0184379i
$918$	1.05808e11	+	1.05808e11i	0.148987	+	0.148987i
$919$			1.22516e11i			0.171764i	0.996305	+	0.0858820i	$0.0273708\pi$
$919$			1.22516e11i			0.171764i	−0.996305	+	0.0858820i	$0.972629\pi$
$920$		0			0
$921$	4.29503e11			0.596936
$922$	2.50626e11	−	2.50626e11i	0.346819	−	0.346819i
$923$	−4.67459e11	−	4.67459e11i	−0.644075	−	0.644075i
$924$			5.37323e11i			0.737136i
$925$		0			0
$926$	−2.65258e11			−0.360766
$927$	−2.23360e11	+	2.23360e11i	−0.302473	+	0.302473i
$928$	6.39500e11	+	6.39500e11i	0.862281	+	0.862281i
$929$			9.37399e11i			1.25852i	0.777193	+	0.629262i	$0.216643\pi$
$929$			9.37399e11i			1.25852i	−0.777193	+	0.629262i	$0.783357\pi$
$930$		0			0
$931$	−2.20239e11			−0.293154
$932$	−9.99242e11	+	9.99242e11i	−1.32436	+	1.32436i
$933$	−3.06631e11	−	3.06631e11i	−0.404659	−	0.404659i
$934$			6.95330e11i			0.913700i
$935$		0			0
$936$	1.73536e11			0.226092
$937$	6.80284e11	−	6.80284e11i	0.882535	−	0.882535i	−0.111257	−	0.993792i	$-0.535488\pi$
$937$	6.80284e11	−	6.80284e11i	0.882535	−	0.882535i	0.993792	+	0.111257i	$0.0354876\pi$
$938$	−1.31242e11	−	1.31242e11i	−0.169536	−	0.169536i
$939$			1.69588e11i			0.218138i
$940$		0			0
$941$	−7.92920e11			−1.01128			−0.505640	−	0.862745i	$-0.668743\pi$
$941$	−7.92920e11			−1.01128			−0.505640	+	0.862745i	$0.668743\pi$
$942$	−1.72750e11	+	1.72750e11i	−0.219389	+	0.219389i
$943$	1.01602e12	+	1.01602e12i	1.28486	+	1.28486i
$944$			2.73145e11i			0.343957i
$945$		0			0
$946$	1.69588e12			2.11753
$947$	−6.17340e10	+	6.17340e10i	−0.0767582	+	0.0767582i	−0.744444	−	0.667685i	$-0.767285\pi$
$947$	−6.17340e10	+	6.17340e10i	−0.0767582	+	0.0767582i	0.667685	+	0.744444i	$0.267285\pi$
$948$	3.28761e10	+	3.28761e10i	0.0407049	+	0.0407049i
$949$			2.92607e11i			0.360761i
$950$		0			0
$951$	2.84535e11			0.347867
$952$	−1.43131e11	+	1.43131e11i	−0.174255	+	0.174255i
$953$	1.30190e11	+	1.30190e11i	0.157836	+	0.157836i	0.781607	−	0.623771i	$-0.214400\pi$
$953$	1.30190e11	+	1.30190e11i	0.157836	+	0.157836i	−0.623771	+	0.781607i	$0.714400\pi$
$954$		−	5.28998e11i		−	0.638647i
$955$		0			0
$956$	−1.92010e11			−0.229875
$957$	3.97614e11	−	3.97614e11i	0.474039	−	0.474039i
$958$	−9.99951e11	−	9.99951e11i	−1.18718	−	1.18718i
$959$			8.53258e11i			1.00880i
$960$		0			0
$961$	−8.45765e11			−0.991645
$962$	1.19716e12	−	1.19716e12i	1.39783	−	1.39783i
$963$	−4.52830e10	−	4.52830e10i	−0.0526539	−	0.0526539i
$964$		−	6.23600e11i		−	0.722101i
$965$		0			0
$966$	6.14407e11			0.705582
$967$	9.46462e10	−	9.46462e10i	0.108242	−	0.108242i	−0.650911	−	0.759154i	$-0.725613\pi$
$967$	9.46462e10	−	9.46462e10i	0.108242	−	0.108242i	0.759154	+	0.650911i	$0.225613\pi$
$968$	2.05706e11	+	2.05706e11i	0.234286	+	0.234286i
$969$		−	2.43696e11i		−	0.276409i
$970$		0			0
$971$	6.63532e11			0.746422			0.373211	−	0.927746i	$-0.378257\pi$
$971$	6.63532e11			0.746422			0.373211	+	0.927746i	$0.378257\pi$
$972$	5.26897e10	−	5.26897e10i	0.0590284	−	0.0590284i
$973$	5.57998e11	+	5.57998e11i	0.622560	+	0.622560i
$974$		−	1.90322e12i		−	2.11472i
$975$		0			0
$976$	8.66083e11			0.954466
$977$	9.40069e11	−	9.40069e11i	1.03177	−	1.03177i	0.0322882	−	0.999479i	$-0.489721\pi$
$977$	9.40069e11	−	9.40069e11i	1.03177	−	1.03177i	0.999479	−	0.0322882i	$-0.0102794\pi$
$978$	−6.70156e11	−	6.70156e11i	−0.732522	−	0.732522i
$979$			7.99740e11i			0.870599i
$980$		0			0
$981$	−5.85407e11			−0.632094
$982$	−3.54587e11	+	3.54587e11i	−0.381309	+	0.381309i
$983$	5.12791e11	+	5.12791e11i	0.549195	+	0.549195i	0.926208	−	0.377013i	$-0.123049\pi$
$983$	5.12791e11	+	5.12791e11i	0.549195	+	0.549195i	−0.377013	+	0.926208i	$0.623049\pi$
$984$			4.16883e11i			0.444665i
$985$		0			0
$986$	9.14878e11			0.967955
$987$	−4.87967e11	+	4.87967e11i	−0.514188	+	0.514188i
$988$	−8.63099e11	−	8.63099e11i	−0.905801	−	0.905801i
$989$		−	1.09653e12i		−	1.14613i
$990$		0			0
$991$	8.09985e11			0.839812			0.419906	−	0.907568i	$-0.362063\pi$
$991$	8.09985e11			0.839812			0.419906	+	0.907568i	$0.362063\pi$
$992$	−8.63314e10	+	8.63314e10i	−0.0891502	+	0.0891502i
$993$	1.17223e11	+	1.17223e11i	0.120564	+	0.120564i
$994$		−	6.79078e11i		−	0.695623i
$995$		0			0
$996$	−8.03807e11			−0.816797
$997$	−2.59023e11	+	2.59023e11i	−0.262155	+	0.262155i	−0.825929	−	0.563774i	$-0.809349\pi$
$997$	−2.59023e11	+	2.59023e11i	−0.262155	+	0.262155i	0.563774	+	0.825929i	$0.309349\pi$
$998$	8.04134e11	+	8.04134e11i	0.810599	+	0.810599i
$999$		−	1.68324e11i		−	0.168999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.9.f.e.43.2		16
5.2	odd	4	inner	75.9.f.e.7.2		16
5.3	odd	4		15.9.f.a.7.7	✓	16
5.4	even	2		15.9.f.a.13.7	yes	16
15.8	even	4		45.9.g.c.37.2		16
15.14	odd	2		45.9.g.c.28.2		16
20.3	even	4		240.9.bg.d.97.3		16
20.19	odd	2		240.9.bg.d.193.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.f.a.7.7	✓	16	5.3	odd	4
15.9.f.a.13.7	yes	16	5.4	even	2
45.9.g.c.28.2		16	15.14	odd	2
45.9.g.c.37.2		16	15.8	even	4
75.9.f.e.7.2		16	5.2	odd	4	inner
75.9.f.e.43.2		16	1.1	even	1	trivial
240.9.bg.d.97.3		16	20.3	even	4
240.9.bg.d.193.3		16	20.19	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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	75.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-17.1630 + 17.1630i) q^{2} +(-33.0681 - 33.0681i) q^{3} -333.134i q^{4} +1135.09 q^{6} +(-1268.31 + 1268.31i) q^{7} +(1323.85 + 1323.85i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(-17.1630 + 17.1630i) q^{2} +(-33.0681 - 33.0681i) q^{3} -333.134i q^{4} +1135.09 q^{6} +(-1268.31 + 1268.31i) q^{7} +(1323.85 + 1323.85i) q^{8} +2187.00i q^{9} -19228.7 q^{11} +(-11016.1 + 11016.1i) q^{12} +(-29969.0 - 29969.0i) q^{13} -43536.0i q^{14} +39840.0 q^{16} +(42622.5 - 42622.5i) q^{17} +(-37535.4 - 37535.4i) q^{18} +86450.9i q^{19} +83881.4 q^{21} +(330022. - 330022. i) q^{22} +(-213387. - 213387. i) q^{23} -87554.3i q^{24} +1.02871e6 q^{26} +(72320.0 - 72320.0i) q^{27} +(422518. + 422518. i) q^{28} -625320. i q^{29} +84417.0 q^{31} +(-1.02268e6 + 1.02268e6i) q^{32} +(635858. + 635858. i) q^{33} +1.46306e6i q^{34} +728564. q^{36} +(1.16375e6 - 1.16375e6i) q^{37} +(-1.48375e6 - 1.48375e6i) q^{38} +1.98204e6i q^{39} -4.76142e6 q^{41} +(-1.43965e6 + 1.43965e6i) q^{42} +(2.56935e6 + 2.56935e6i) q^{43} +6.40574e6i q^{44} +7.32470e6 q^{46} +(-5.81734e6 + 5.81734e6i) q^{47} +(-1.31743e6 - 1.31743e6i) q^{48} +2.54757e6i q^{49} -2.81889e6 q^{51} +(-9.98369e6 + 9.98369e6i) q^{52} +(7.04666e6 + 7.04666e6i) q^{53} +2.48245e6i q^{54} -3.35811e6 q^{56} +(2.85877e6 - 2.85877e6i) q^{57} +(1.07323e7 + 1.07323e7i) q^{58} +6.85603e6i q^{59} +2.17390e7 q^{61} +(-1.44885e6 + 1.44885e6i) q^{62} +(-2.77380e6 - 2.77380e6i) q^{63} -2.49053e7i q^{64} -2.18264e7 q^{66} +(3.01457e6 - 3.01457e6i) q^{67} +(-1.41990e7 - 1.41990e7i) q^{68} +1.41126e7i q^{69} +1.55981e7 q^{71} +(-2.89526e6 + 2.89526e6i) q^{72} +(-4.88183e6 - 4.88183e6i) q^{73} +3.99467e7i q^{74} +2.87997e7 q^{76} +(2.43880e7 - 2.43880e7i) q^{77} +(-3.40176e7 - 3.40176e7i) q^{78} -2.98436e6i q^{79} -4.78297e6 q^{81} +(8.17200e7 - 8.17200e7i) q^{82} +(3.64832e7 + 3.64832e7i) q^{83} -2.79438e7i q^{84} -8.81951e7 q^{86} +(-2.06781e7 + 2.06781e7i) q^{87} +(-2.54559e7 - 2.54559e7i) q^{88} -4.15909e7i q^{89} +7.60201e7 q^{91} +(-7.10865e7 + 7.10865e7i) q^{92} +(-2.79151e6 - 2.79151e6i) q^{93} -1.99685e8i q^{94} +6.76360e7 q^{96} +(3.41937e7 - 3.41937e7i) q^{97} +(-4.37238e7 - 4.37238e7i) q^{98} -4.20532e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) \) 16 * q - 2268 * q^6 - 4540 * q^7 - 17460 * q^8	\( 16 q - 2268 q^{6} - 4540 q^{7} - 17460 q^{8} - 23616 q^{11} - 22680 q^{12} - 133420 q^{13} - 471380 q^{16} - 573300 q^{17} + 163944 q^{21} + 234700 q^{22} - 651480 q^{23} - 448848 q^{26} + 3567940 q^{28} + 1311776 q^{31} - 641460 q^{32} + 3815100 q^{33} + 5519988 q^{36} + 3607340 q^{37} - 8139840 q^{38} - 14740104 q^{41} + 9643860 q^{42} + 4805480 q^{43} + 14024216 q^{46} - 26529600 q^{47} - 3661200 q^{48} - 6168312 q^{51} + 15861080 q^{52} - 16612140 q^{53} + 10752000 q^{56} - 4714200 q^{57} - 63562980 q^{58} - 12550600 q^{61} + 35190840 q^{62} - 9928980 q^{63} + 46958616 q^{66} - 46836760 q^{67} + 197811840 q^{68} - 85681968 q^{71} + 38185020 q^{72} + 50835800 q^{73} + 101166648 q^{76} - 97175880 q^{77} - 131709240 q^{78} - 76527504 q^{81} + 181542400 q^{82} + 208234800 q^{83} - 187512576 q^{86} + 74298060 q^{87} - 138207420 q^{88} + 38623856 q^{91} - 652331400 q^{92} - 159787080 q^{93} + 531512604 q^{96} + 138370520 q^{97} + 50186520 q^{98}+O(q^{100}) \) 16 * q - 2268 * q^6 - 4540 * q^7 - 17460 * q^8 - 23616 * q^11 - 22680 * q^12 - 133420 * q^13 - 471380 * q^16 - 573300 * q^17 + 163944 * q^21 + 234700 * q^22 - 651480 * q^23 - 448848 * q^26 + 3567940 * q^28 + 1311776 * q^31 - 641460 * q^32 + 3815100 * q^33 + 5519988 * q^36 + 3607340 * q^37 - 8139840 * q^38 - 14740104 * q^41 + 9643860 * q^42 + 4805480 * q^43 + 14024216 * q^46 - 26529600 * q^47 - 3661200 * q^48 - 6168312 * q^51 + 15861080 * q^52 - 16612140 * q^53 + 10752000 * q^56 - 4714200 * q^57 - 63562980 * q^58 - 12550600 * q^61 + 35190840 * q^62 - 9928980 * q^63 + 46958616 * q^66 - 46836760 * q^67 + 197811840 * q^68 - 85681968 * q^71 + 38185020 * q^72 + 50835800 * q^73 + 101166648 * q^76 - 97175880 * q^77 - 131709240 * q^78 - 76527504 * q^81 + 181542400 * q^82 + 208234800 * q^83 - 187512576 * q^86 + 74298060 * q^87 - 138207420 * q^88 + 38623856 * q^91 - 652331400 * q^92 - 159787080 * q^93 + 531512604 * q^96 + 138370520 * q^97 + 50186520 * q^98

Introduction

L-functions

Modular forms

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