LMFDB - Embedded newform 99.8.j.a.62.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,8,Mod(8,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 3]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("99.8");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	99.j (of order $10$, degree $4$, 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:	$30.9261175229$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			62.4
Character	$\chi$	$=$	99.62
Dual form			99.8.j.a.8.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-14.7879 - 10.7440i) q^{2} +(63.6930 + 196.027i) q^{4} +(194.917 + 268.280i) q^{5} +(-72.5991 + 23.5889i) q^{7} +(441.228 - 1357.96i) q^{8} -6061.48i q^{10} +(4373.83 + 597.324i) q^{11} +(5506.28 - 7578.75i) q^{13} +(1327.03 + 431.177i) q^{14} +(229.262 - 166.569i) q^{16} +(-9949.29 + 7228.58i) q^{17} +(-20612.9 - 6697.54i) q^{19} +(-40175.3 + 55296.5i) q^{20} +(-58261.9 - 55825.6i) q^{22} +88301.0i q^{23} +(-9839.67 + 30283.4i) q^{25} +(-162852. + 52913.9i) q^{26} +(-9248.11 - 12728.9i) q^{28} +(21088.6 + 64904.1i) q^{29} +(39589.7 + 28763.6i) q^{31} -187944. q^{32} +224793. q^{34} +(-20479.2 - 14879.0i) q^{35} +(12353.9 + 38021.3i) q^{37} +(232862. + 320508. i) q^{38} +(450317. - 146317. i) q^{40} +(129634. - 398974. i) q^{41} -273270. i q^{43} +(161491. + 895433. i) q^{44} +(948707. - 1.30578e6i) q^{46} +(1.12068e6 + 364132. i) q^{47} +(-661546. + 480641. i) q^{49} +(470873. - 342109. i) q^{50} +(1.83635e6 + 596666. i) q^{52} +(431286. - 593614. i) q^{53} +(692283. + 1.28984e6i) q^{55} +108995. i q^{56} +(385475. - 1.18637e6i) q^{58} +(-1.86916e6 + 607326. i) q^{59} +(1.39569e6 + 1.92100e6i) q^{61} +(-276411. - 850705. i) q^{62} +(2.74995e6 + 1.99795e6i) q^{64} +3.10649e6 q^{65} -369220. q^{67} +(-2.05070e6 - 1.48992e6i) q^{68} +(142984. + 440058. i) q^{70} +(2.08693e6 + 2.87241e6i) q^{71} +(-1.18339e6 + 384506. i) q^{73} +(225814. - 694984. i) q^{74} -4.46727e6i q^{76} +(-331626. + 59808.5i) q^{77} +(2.54246e6 - 3.49939e6i) q^{79} +(89374.2 + 29039.4i) q^{80} +(-6.20360e6 + 4.50718e6i) q^{82} +(-2.09707e6 + 1.52361e6i) q^{83} +(-3.87857e6 - 1.26022e6i) q^{85} +(-2.93601e6 + 4.04107e6i) q^{86} +(2.74100e6 - 5.67593e6i) q^{88} +6.18536e6i q^{89} +(-220977. + 680097. i) q^{91} +(-1.73094e7 + 5.62416e6i) q^{92} +(-1.26603e7 - 1.74254e7i) q^{94} +(-2.22099e6 - 6.83550e6i) q^{95} +(-7.39031e6 - 5.36938e6i) q^{97} +1.49469e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 1792 q^{4} - 134096 q^{16} + 401484 q^{22} - 68552 q^{25} + 1493020 q^{28} - 398144 q^{31} - 729944 q^{34} + 685476 q^{37} - 399360 q^{40} - 1410880 q^{46} + 2923872 q^{49} + 6472520 q^{52} + 1445488 q^{55}+ \cdots - 27695460 q^{97}+O(q^{100}) $ 112 * q - 1792 * q^4 - 134096 * q^16 + 401484 * q^22 - 68552 * q^25 + 1493020 * q^28 - 398144 * q^31 - 729944 * q^34 + 685476 * q^37 - 399360 * q^40 - 1410880 * q^46 + 2923872 * q^49 + 6472520 * q^52 + 1445488 * q^55 + 13215936 * q^58 - 7843440 * q^61 - 12806712 * q^64 + 1864032 * q^67 - 1233728 * q^70 + 53841940 * q^73 - 53845440 * q^79 - 36360204 * q^82 + 41703500 * q^85 + 21474024 * q^88 + 27611736 * q^91 - 94707560 * q^94 - 27695460 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	−14.7879	−	10.7440i	−1.30708	−	0.949646i	−0.307077	−	0.951685i	$-0.599351\pi$
$2$	−14.7879	−	10.7440i	−1.30708	−	0.949646i	−0.999998	+	0.00203905i	$0.999351\pi$
$3$		0			0
$3$		0			0
$4$	63.6930	+	196.027i	0.497601	+	1.53146i
$5$	194.917	+	268.280i	0.697356	+	0.959828i	0.999977	+	0.00671741i	$0.00213823\pi$
$5$	194.917	+	268.280i	0.697356	+	0.959828i	−0.302621	+	0.953111i	$0.597862\pi$
$6$		0			0
$7$	−72.5991	+	23.5889i	−0.0799997	+	0.0259935i	−0.348743	−	0.937218i	$-0.613392\pi$
$7$	−72.5991	+	23.5889i	−0.0799997	+	0.0259935i	0.268744	+	0.963212i	$0.413392\pi$
$8$	441.228	−	1357.96i	0.304683	−	0.937719i
$9$		0			0
$10$		−	6061.48i		−	1.91681i
$11$	4373.83	+	597.324i	0.990803	+	0.135312i
$11$	4373.83	+	597.324i	0.990803	+	0.135312i
$12$		0			0
$13$	5506.28	−	7578.75i	0.695115	−	0.956744i	−0.304876	−	0.952392i	$-0.598615\pi$
$13$	5506.28	−	7578.75i	0.695115	−	0.956744i	0.999991	−	0.00435150i	$-0.00138513\pi$
$14$	1327.03	+	431.177i	0.129250	+	0.0419959i
$15$		0			0
$16$	229.262	−	166.569i	0.0139931	−	0.0101665i
$17$	−9949.29	+	7228.58i	−0.491157	+	0.356847i	−0.805629	−	0.592420i	$-0.798173\pi$
$17$	−9949.29	+	7228.58i	−0.491157	+	0.356847i	0.314472	+	0.949267i	$0.398173\pi$
$18$		0			0
$19$	−20612.9	−	6697.54i	−0.689448	−	0.224015i	−0.0567209	−	0.998390i	$-0.518065\pi$
$19$	−20612.9	−	6697.54i	−0.689448	−	0.224015i	−0.632727	+	0.774375i	$0.718065\pi$
$20$	−40175.3	+	55296.5i	−1.12293	+	1.54558i
$21$		0			0
$22$	−58261.9	−	55825.6i	−1.16656	−	1.11777i
$23$			88301.0i			1.51328i	0.653834	+	0.756638i	$0.273160\pi$
$23$			88301.0i			1.51328i	−0.653834	+	0.756638i	$0.726840\pi$
$24$		0			0
$25$	−9839.67	+	30283.4i	−0.125948	+	0.387628i
$26$	−162852.	+	52913.9i	−1.81713	+	0.590423i
$27$		0			0
$28$	−9248.11	−	12728.9i	−0.0796159	−	0.109582i
$29$	21088.6	+	64904.1i	0.160567	+	0.494173i	0.998682	−	0.0513193i	$-0.0163426\pi$
$29$	21088.6	+	64904.1i	0.160567	+	0.494173i	−0.838116	+	0.545493i	$0.816343\pi$
$30$		0			0
$31$	39589.7	+	28763.6i	0.238680	+	0.173411i	0.700695	−	0.713461i	$-0.252873\pi$
$31$	39589.7	+	28763.6i	0.238680	+	0.173411i	−0.462015	+	0.886872i	$0.652873\pi$
$32$	−187944.			−1.01392
$33$		0			0
$34$	224793.			0.980858
$35$	−20479.2	−	14879.0i	−0.0807375	−	0.0586592i
$36$		0			0
$37$	12353.9	+	38021.3i	0.0400956	+	0.123402i	0.969101	−	0.246665i	$-0.0793348\pi$
$37$	12353.9	+	38021.3i	0.0400956	+	0.123402i	−0.929005	+	0.370067i	$0.879335\pi$
$38$	232862.	+	320508.i	0.688425	+	0.947536i
$39$		0			0
$40$	450317.	−	146317.i	1.11252	−	0.361480i
$41$	129634.	−	398974.i	0.293749	−	0.904067i	−0.689889	−	0.723915i	$-0.742341\pi$
$41$	129634.	−	398974.i	0.293749	−	0.904067i	0.983639	−	0.180153i	$-0.0576592\pi$
$42$		0			0
$43$		−	273270.i		−	0.524145i	−0.965048	−	0.262073i	$-0.915594\pi$
$43$		−	273270.i		−	0.524145i	0.965048	−	0.262073i	$-0.0844060\pi$
$44$	161491.	+	895433.i	0.285800	+	1.58471i
$45$		0			0
$46$	948707.	−	1.30578e6i	1.43708	−	1.97797i
$47$	1.12068e6	+	364132.i	1.57449	+	0.511583i	0.960630	−	0.277832i	$-0.0896158\pi$
$47$	1.12068e6	+	364132.i	1.57449	+	0.511583i	0.613860	+	0.789415i	$0.289616\pi$
$48$		0			0
$49$	−661546.	+	480641.i	−0.803293	+	0.583626i
$50$	470873.	−	342109.i	0.532732	−	0.387053i
$51$		0			0
$52$	1.83635e6	+	596666.i	1.81110	+	0.588464i
$53$	431286.	−	593614.i	0.397924	−	0.547695i	−0.562298	−	0.826935i	$-0.690082\pi$
$53$	431286.	−	593614.i	0.397924	−	0.547695i	0.960221	+	0.279240i	$0.0900825\pi$
$54$		0			0
$55$	692283.	+	1.28984e6i	0.561066	+	1.04536i
$56$			108995.i			0.0829370i
$57$		0			0
$58$	385475.	−	1.18637e6i	0.259417	−	0.798403i
$59$	−1.86916e6	+	607326.i	−1.18485	+	0.384982i	−0.834167	−	0.551512i	$-0.814051\pi$
$59$	−1.86916e6	+	607326.i	−1.18485	+	0.384982i	−0.350684	+	0.936494i	$0.614051\pi$
$60$		0			0
$61$	1.39569e6	+	1.92100e6i	0.787288	+	1.08361i	0.994440	+	0.105300i	$0.0335804\pi$
$61$	1.39569e6	+	1.92100e6i	0.787288	+	1.08361i	−0.207152	+	0.978309i	$0.566420\pi$
$62$	−276411.	−	850705.i	−0.147294	−	0.453323i
$63$		0			0
$64$	2.74995e6	+	1.99795e6i	1.31128	+	0.952698i
$65$	3.10649e6			1.40305
$66$		0			0
$67$	−369220.			−0.149977			−0.0749884	−	0.997184i	$-0.523892\pi$
$67$	−369220.			−0.149977			−0.0749884	+	0.997184i	$0.523892\pi$
$68$	−2.05070e6	−	1.48992e6i	−0.790897	−	0.574620i
$69$		0			0
$70$	142984.	+	440058.i	0.0498245	+	0.153344i
$71$	2.08693e6	+	2.87241e6i	0.691995	+	0.952449i	0.999999	+	0.00106427i	$0.000338768\pi$
$71$	2.08693e6	+	2.87241e6i	0.691995	+	0.952449i	−0.308005	+	0.951385i	$0.599661\pi$
$72$		0			0
$73$	−1.18339e6	+	384506.i	−0.356039	+	0.115684i	−0.481575	−	0.876405i	$-0.659935\pi$
$73$	−1.18339e6	+	384506.i	−0.356039	+	0.115684i	0.125536	+	0.992089i	$0.459935\pi$
$74$	225814.	−	694984.i	0.0647799	−	0.199372i
$75$		0			0
$76$		−	4.46727e6i		−	1.16733i
$77$	−331626.	+	59808.5i	−0.0827811	+	0.0149295i
$78$		0			0
$79$	2.54246e6	−	3.49939e6i	0.580174	−	0.798542i	−0.413540	−	0.910486i	$-0.635708\pi$
$79$	2.54246e6	−	3.49939e6i	0.580174	−	0.798542i	0.993714	+	0.111944i	$0.0357078\pi$
$80$	89374.2	+	29039.4i	0.0195163	+	0.00634122i
$81$		0			0
$82$	−6.20360e6	+	4.50718e6i	−1.24250	+	0.902726i
$83$	−2.09707e6	+	1.52361e6i	−0.402569	+	0.292484i	−0.770587	−	0.637335i	$-0.780037\pi$
$83$	−2.09707e6	+	1.52361e6i	−0.402569	+	0.292484i	0.368017	+	0.929819i	$0.380037\pi$
$84$		0			0
$85$	−3.87857e6	−	1.26022e6i	−0.685023	−	0.222578i
$86$	−2.93601e6	+	4.04107e6i	−0.497752	+	0.685097i
$87$		0			0
$88$	2.74100e6	−	5.67593e6i	0.428765	−	0.887867i
$89$			6.18536e6i			0.930037i	0.885301	+	0.465018i	$0.153952\pi$
$89$			6.18536e6i			0.930037i	−0.885301	+	0.465018i	$0.846048\pi$
$90$		0			0
$91$	−220977.	+	680097.i	−0.0307399	+	0.0946076i
$92$	−1.73094e7	+	5.62416e6i	−2.31752	+	0.753009i
$93$		0			0
$94$	−1.26603e7	−	1.74254e7i	−1.57215	−	2.16388i
$95$	−2.22099e6	−	6.83550e6i	−0.265775	−	0.817970i
$96$		0			0
$97$	−7.39031e6	−	5.36938e6i	−0.822170	−	0.597342i	0.0951629	−	0.995462i	$-0.469663\pi$
$97$	−7.39031e6	−	5.36938e6i	−0.822170	−	0.597342i	−0.917333	+	0.398120i	$0.869663\pi$
$98$	1.49469e7			1.60420
$99$		0			0
$100$	−6.56308e6			−0.656308
$101$	8.99227e6	+	6.53326e6i	0.868449	+	0.630965i	0.930170	−	0.367128i	$-0.119659\pi$
$101$	8.99227e6	+	6.53326e6i	0.868449	+	0.630965i	−0.0617212	+	0.998093i	$0.519659\pi$
$102$		0			0
$103$	3.84333e6	+	1.18286e7i	0.346559	+	1.06660i	0.960744	+	0.277437i	$0.0894850\pi$
$103$	3.84333e6	+	1.18286e7i	0.346559	+	1.06660i	−0.614185	+	0.789162i	$0.710515\pi$
$104$	−7.86212e6	−	1.08213e7i	−0.685367	−	0.943326i
$105$		0			0
$106$	−1.27556e7	+	4.14455e6i	−1.04023	+	0.337992i
$107$	−470632.	+	1.44846e6i	−0.0371397	+	0.114304i	−0.967908	−	0.251306i	$-0.919140\pi$
$107$	−470632.	+	1.44846e6i	−0.0371397	+	0.114304i	0.930768	+	0.365611i	$0.119140\pi$
$108$		0			0
$109$			2.42278e7i			1.79193i	0.444121	+	0.895967i	$0.353516\pi$
$109$			2.42278e7i			1.79193i	−0.444121	+	0.895967i	$0.646484\pi$
$110$	3.62067e6	−	2.65119e7i	0.259367	−	1.89918i
$111$		0			0
$112$	−12715.1	+	17500.8i	−0.000855176	+	0.00117705i
$113$	−1.43236e7	−	4.65400e6i	−0.933848	−	0.303426i	−0.197713	−	0.980260i	$-0.563351\pi$
$113$	−1.43236e7	−	4.65400e6i	−0.933848	−	0.303426i	−0.736135	+	0.676834i	$0.763351\pi$
$114$		0			0
$115$	−2.36894e7	+	1.72114e7i	−1.45249	+	1.05529i
$116$	−1.13798e7	+	8.26787e6i	−0.676908	+	0.491803i
$117$		0			0
$118$	3.41660e7	+	1.11012e7i	1.91429	+	0.621989i
$119$	551795.	−	759481.i	0.0300168	−	0.0413145i
$120$		0			0
$121$	1.87736e7	+	5.22519e6i	0.963381	+	0.268135i
$122$		−	4.34028e7i		−	2.16400i
$123$		0			0
$124$	−3.11685e6	+	9.59268e6i	−0.146805	+	0.451819i
$125$	1.45969e7	−	4.74281e6i	0.668459	−	0.217196i
$126$		0			0
$127$	−469790.	−	646611.i	−0.0203512	−	0.0280111i	0.798720	−	0.601703i	$-0.205511\pi$
$127$	−469790.	−	646611.i	−0.0203512	−	0.0280111i	−0.819071	+	0.573692i	$0.805511\pi$
$128$	−1.17658e7	−	3.62115e7i	−0.495893	−	1.52620i
$129$		0			0
$130$	−4.59384e7	−	3.33762e7i	−1.83389	−	1.33240i
$131$	4.37657e7			1.70092			0.850460	−	0.526039i	$-0.176324\pi$
$131$	4.37657e7			1.70092			0.850460	+	0.526039i	$0.176324\pi$
$132$		0			0
$133$	1.65447e6			0.0609786
$134$	5.45998e6	+	3.96691e6i	0.196031	+	0.142425i
$135$		0			0
$136$	5.42623e6	+	1.67002e7i	0.184974	+	0.569293i
$137$	3.35338e7	+	4.61553e7i	1.11419	+	1.53355i	0.815091	+	0.579333i	$0.196687\pi$
$137$	3.35338e7	+	4.61553e7i	1.11419	+	1.53355i	0.299102	+	0.954221i	$0.403313\pi$
$138$		0			0
$139$	2.50224e7	−	8.13027e6i	0.790273	−	0.256775i	0.114053	−	0.993475i	$-0.463617\pi$
$139$	2.50224e7	−	8.13027e6i	0.790273	−	0.256775i	0.676220	+	0.736699i	$0.263617\pi$
$140$	1.61231e6	−	4.96217e6i	0.0496592	−	0.152835i
$141$		0			0
$142$		−	6.48987e7i		−	1.90207i
$143$	2.86105e7	−	2.98591e7i	0.818181	−	0.853887i
$144$		0			0
$145$	−1.33020e7	+	1.83086e7i	−0.362349	+	0.498731i
$146$	2.16309e7	+	7.02832e6i	0.575229	+	0.186903i
$147$		0			0
$148$	−6.66634e6	+	4.84338e6i	−0.169033	+	0.122810i
$149$	−4.90229e7	+	3.56172e7i	−1.21408	+	0.882081i	−0.995595	−	0.0937595i	$-0.970112\pi$
$149$	−4.90229e7	+	3.56172e7i	−1.21408	+	0.882081i	−0.218485	+	0.975840i	$0.570112\pi$
$150$		0			0
$151$	6.61252e7	+	2.14854e7i	1.56296	+	0.507837i	0.957597	−	0.288112i	$-0.0930276\pi$
$151$	6.61252e7	+	2.14854e7i	1.56296	+	0.507837i	0.605364	+	0.795949i	$0.293028\pi$
$152$	−1.81900e7	+	2.50364e7i	−0.420127	+	0.578255i
$153$		0			0
$154$	5.54663e6	+	2.67856e6i	0.122379	+	0.0590988i
$155$			1.62276e7i			0.350021i
$156$		0			0
$157$	−9.68557e6	+	2.98091e7i	−0.199745	+	0.614752i	0.800143	+	0.599809i	$0.204757\pi$
$157$	−9.68557e6	+	2.98091e7i	−0.199745	+	0.614752i	−0.999888	+	0.0149434i	$0.995243\pi$
$158$	−7.51950e7	+	2.44323e7i	−1.51666	+	0.492794i
$159$		0			0
$160$	−3.66335e7	−	5.04217e7i	−0.707063	−	0.973189i
$161$	−2.08292e6	−	6.41058e6i	−0.0393353	−	0.121062i
$162$		0			0
$163$	3.21683e6	+	2.33717e6i	0.0581797	+	0.0422701i	0.616495	−	0.787359i	$-0.288552\pi$
$163$	3.21683e6	+	2.33717e6i	0.0581797	+	0.0422701i	−0.558315	+	0.829629i	$0.688552\pi$
$164$	8.64664e7			1.53071
$165$		0			0
$166$	4.73810e7			0.803944
$167$	−8.53648e7	−	6.20211e7i	−1.41831	−	1.03046i	−0.992048	−	0.125862i	$-0.959830\pi$
$167$	−8.53648e7	−	6.20211e7i	−1.41831	−	1.03046i	−0.426262	−	0.904600i	$-0.640170\pi$
$168$		0			0
$169$	−7.72790e6	−	2.37840e7i	−0.123157	−	0.379037i
$170$	4.38159e7	+	6.03074e7i	0.684007	+	0.941455i
$171$		0			0
$172$	5.35682e7	−	1.74054e7i	0.802707	−	0.260815i
$173$	−2.78623e7	+	8.57512e7i	−0.409124	+	1.25915i	0.508278	+	0.861193i	$0.330282\pi$
$173$	−2.78623e7	+	8.57512e7i	−0.409124	+	1.25915i	−0.917402	+	0.397961i	$0.869718\pi$
$174$		0			0
$175$		−	2.43066e6i		−	0.0342839i
$176$	1.10225e6	−	591599.i	0.0152400	−	0.00817962i
$177$		0			0
$178$	6.64556e7	−	9.14683e7i	0.883205	−	1.21563i
$179$	−1.14626e8	−	3.72441e7i	−1.49381	−	0.485369i	−0.555606	−	0.831446i	$-0.687514\pi$
$179$	−1.14626e8	−	3.72441e7i	−1.49381	−	0.485369i	−0.938206	+	0.346077i	$0.887514\pi$
$180$		0			0
$181$	−9.53899e7	+	6.93048e7i	−1.19571	+	0.868737i	−0.993856	−	0.110677i	$-0.964698\pi$
$181$	−9.53899e7	+	6.93048e7i	−1.19571	+	0.868737i	−0.201858	+	0.979415i	$0.564698\pi$
$182$	1.05748e7	−	7.68301e6i	0.130023	−	0.0944673i
$183$		0			0
$184$	1.19909e8	+	3.89609e7i	1.41903	+	0.461070i
$185$	−7.79239e6	+	1.07253e7i	−0.0904835	+	0.124540i
$186$		0			0
$187$	−4.78343e7	+	2.56736e7i	−0.534926	+	0.287106i
$188$			2.42876e8i			2.66583i
$189$		0			0
$190$	−4.05970e7	+	1.24945e8i	−0.429394	+	1.32154i
$191$	−9.64312e7	+	3.13324e7i	−1.00138	+	0.325370i	−0.763419	−	0.645904i	$-0.776481\pi$
$191$	−9.64312e7	+	3.13324e7i	−1.00138	+	0.325370i	−0.237966	+	0.971274i	$0.576481\pi$
$192$		0			0
$193$	−1.02374e7	−	1.40906e7i	−0.102504	−	0.141084i	0.754684	−	0.656089i	$-0.227790\pi$
$193$	−1.02374e7	−	1.40906e7i	−0.102504	−	0.141084i	−0.857188	+	0.515004i	$0.827790\pi$
$194$	5.15983e7	+	1.58803e8i	0.507375	+	1.56154i
$195$		0			0
$196$	−1.36354e8	−	9.90673e7i	−1.29352	−	0.939797i
$197$	1.27719e6			0.0119021			0.00595105	−	0.999982i	$-0.498106\pi$
$197$	1.27719e6			0.0119021			0.00595105	+	0.999982i	$0.498106\pi$
$198$		0			0
$199$	1.89402e8			1.70372			0.851861	−	0.523768i	$-0.175474\pi$
$199$	1.89402e8			1.70372			0.851861	+	0.523768i	$0.175474\pi$
$200$	3.67822e7	+	2.67238e7i	0.325111	+	0.236207i
$201$		0			0
$202$	−6.27830e7	−	1.93226e8i	−0.535935	−	1.64944i
$203$	−3.06203e6	−	4.21452e6i	−0.0256906	−	0.0353600i
$204$		0			0
$205$	1.32305e8	−	4.29884e7i	1.07260	−	0.348508i
$206$	7.02515e7	−	2.16212e8i	0.559913	−	1.72323i
$207$		0			0
$208$		−	2.65469e6i		−	0.0204547i
$209$	−8.61567e7	−	4.16065e7i	−0.652795	−	0.315245i
$210$		0			0
$211$	9.01787e7	−	1.24120e8i	0.660869	−	0.909608i	−0.338641	−	0.940916i	$-0.609967\pi$
$211$	9.01787e7	−	1.24120e8i	0.660869	−	0.909608i	0.999510	+	0.0313077i	$0.00996719\pi$
$212$	1.43834e8	+	4.67346e7i	1.03678	+	0.336870i
$213$		0			0
$214$	2.25219e7	−	1.63631e7i	0.157093	−	0.114135i
$215$	7.33128e7	−	5.32649e7i	0.503089	−	0.365516i
$216$		0			0
$217$	−3.55268e6	−	1.15434e6i	−0.0236019	−	0.00766872i
$218$	2.60304e8	−	3.58278e8i	1.70170	−	2.34219i
$219$		0			0
$220$	−2.08750e8	+	2.17860e8i	−1.32174	+	1.37942i
$221$			1.15206e8i			0.717961i
$222$		0			0
$223$	4.53676e7	−	1.39627e8i	0.273955	−	0.843145i	−0.715540	−	0.698572i	$-0.753819\pi$
$223$	4.53676e7	−	1.39627e8i	0.273955	−	0.843145i	0.989494	−	0.144573i	$-0.0461809\pi$
$224$	1.36446e7	−	4.43339e6i	0.0811133	−	0.0263553i
$225$		0			0
$226$	1.61812e8	+	2.22715e8i	0.932463	+	1.28342i
$227$	−2.81273e7	−	8.65669e7i	−0.159602	−	0.491203i	0.838996	−	0.544137i	$-0.183143\pi$
$227$	−2.81273e7	−	8.65669e7i	−0.159602	−	0.491203i	−0.998598	+	0.0529337i	$0.983143\pi$
$228$		0			0
$229$	5.17047e7	+	3.75657e7i	0.284515	+	0.206713i	0.720885	−	0.693055i	$-0.243736\pi$
$229$	5.17047e7	+	3.75657e7i	0.284515	+	0.206713i	−0.436369	+	0.899768i	$0.643736\pi$
$230$	5.35235e8			2.90066
$231$		0			0
$232$	9.74422e7			0.512317
$233$	−1.95276e8	−	1.41876e8i	−1.01135	−	0.734792i	−0.0468612	−	0.998901i	$-0.514922\pi$
$233$	−1.95276e8	−	1.41876e8i	−1.01135	−	0.734792i	−0.964493	+	0.264110i	$0.914922\pi$
$234$		0			0
$235$	1.20751e8	+	3.71632e8i	0.606948	+	1.86800i
$236$	−2.38104e8	−	3.27723e8i	−1.17917	−	1.62298i
$237$		0			0
$238$	−1.63198e7	+	5.30261e6i	−0.0784683	+	0.0254959i
$239$	−6.81816e7	+	2.09841e8i	−0.323054	+	0.994257i	0.649258	+	0.760568i	$0.275080\pi$
$239$	−6.81816e7	+	2.09841e8i	−0.323054	+	0.994257i	−0.972311	+	0.233689i	$0.924920\pi$
$240$		0			0
$241$		−	3.16216e8i		−	1.45521i	−0.685998	−	0.727603i	$-0.740634\pi$
$241$		−	3.16216e8i		−	1.45521i	0.685998	−	0.727603i	$-0.259366\pi$
$242$	−2.21482e8	−	2.78973e8i	−1.00458	−	1.26534i
$243$		0			0
$244$	−2.87672e8	+	3.95946e8i	−1.26775	+	1.74491i
$245$	−2.57893e8	−	8.37945e7i	−1.12036	−	0.364028i
$246$		0			0
$247$	−1.64259e8	+	1.19341e8i	−0.693571	+	0.503909i
$248$	5.65280e7	−	4.10700e7i	0.235333	−	0.170979i
$249$		0			0
$250$	−2.66814e8	−	8.66930e7i	−1.07999	−	0.350909i
$251$	−849631.	+	1.16942e6i	−0.00339135	+	0.00466779i	−0.810709	−	0.585449i	$-0.800918\pi$
$251$	−849631.	+	1.16942e6i	−0.00339135	+	0.00466779i	0.807318	+	0.590117i	$0.200918\pi$
$252$		0			0
$253$	−5.27443e7	+	3.86214e8i	−0.204764	+	1.49936i
$254$			1.46094e7i			0.0559391i
$255$		0			0
$256$	−8.06160e7	+	2.48110e8i	−0.300318	+	0.924283i
$257$	2.83614e8	−	9.21519e7i	1.04223	−	0.338640i	0.262613	−	0.964901i	$-0.415416\pi$
$257$	2.83614e8	−	9.21519e7i	1.04223	−	0.338640i	0.779613	+	0.626261i	$0.215416\pi$
$258$		0			0
$259$	−1.79376e6	−	2.46890e6i	−0.00641528	−	0.00882987i
$260$	1.97862e8	+	6.08956e8i	0.698161	+	2.14872i
$261$		0			0
$262$	−6.47201e8	−	4.70219e8i	−2.22323	−	1.61527i
$263$	−3.08584e8			−1.04599			−0.522996	−	0.852335i	$-0.675186\pi$
$263$	−3.08584e8			−1.04599			−0.522996	+	0.852335i	$0.675186\pi$
$264$		0			0
$265$	2.43320e8			0.803188
$266$	−2.44660e7	−	1.77756e7i	−0.0797035	−	0.0579080i
$267$		0			0
$268$	−2.35167e7	−	7.23771e7i	−0.0746286	−	0.229683i
$269$	−2.57083e8	−	3.53845e8i	−0.805269	−	1.10836i	−0.992036	−	0.125954i	$-0.959801\pi$
$269$	−2.57083e8	−	3.53845e8i	−0.805269	−	1.10836i	0.186767	−	0.982404i	$-0.440199\pi$
$270$		0			0
$271$	9.85469e7	−	3.20198e7i	0.300781	−	0.0977296i	−0.154739	−	0.987955i	$-0.549454\pi$
$271$	9.85469e7	−	3.20198e7i	0.300781	−	0.0977296i	0.455519	+	0.890226i	$0.349454\pi$
$272$	−1.07694e6	+	3.31448e6i	−0.00324489	+	0.00998675i
$273$		0			0
$274$		−	1.04282e9i		−	3.06256i
$275$	−6.11261e7	+	1.26577e8i	−0.177240	+	0.367020i
$276$		0			0
$277$	−7.39417e7	+	1.01772e8i	−0.209031	+	0.287706i	−0.900640	−	0.434566i	$-0.856902\pi$
$277$	−7.39417e7	+	1.01772e8i	−0.209031	+	0.287706i	0.691609	+	0.722272i	$0.256902\pi$
$278$	−4.57380e8	−	1.48612e8i	−1.27679	−	0.414855i
$279$		0			0
$280$	−2.92412e7	+	2.12450e7i	−0.0796052	+	0.0578366i
$281$	1.30972e8	−	9.51567e7i	0.352133	−	0.255839i	−0.397630	−	0.917546i	$-0.630167\pi$
$281$	1.30972e8	−	9.51567e7i	0.352133	−	0.255839i	0.749763	+	0.661706i	$0.230167\pi$
$282$		0			0
$283$	−2.04333e8	−	6.63917e7i	−0.535901	−	0.174125i	0.0285482	−	0.999592i	$-0.490912\pi$
$283$	−2.04333e8	−	6.63917e7i	−0.535901	−	0.174125i	−0.564450	+	0.825467i	$0.690912\pi$
$284$	−4.30146e8	+	5.92046e8i	−1.11430	+	1.53370i
$285$		0			0
$286$	−7.43895e8	+	1.34161e8i	−1.88031	+	0.339113i
$287$			3.20231e7i			0.0799607i
$288$		0			0
$289$	−8.00657e7	+	2.46417e8i	−0.195121	+	0.600521i
$290$	3.93415e8	−	1.27828e8i	0.947236	−	0.307775i
$291$		0			0
$292$	−1.50747e8	−	2.07486e8i	−0.354331	−	0.487695i
$293$	1.77785e8	+	5.47165e8i	0.412912	+	1.27081i	0.914105	+	0.405478i	$0.132895\pi$
$293$	1.77785e8	+	5.47165e8i	0.412912	+	1.27081i	−0.501193	+	0.865336i	$0.667105\pi$
$294$		0			0
$295$	−5.27264e8	−	3.83080e8i	−1.19578	−	0.868785i
$296$	5.70824e7			0.127933
$297$		0			0
$298$	1.10762e9			2.42456
$299$	6.69211e8	+	4.86210e8i	1.44782	+	1.05190i
$300$		0			0
$301$	6.44612e6	+	1.98391e7i	0.0136244	+	0.0419315i
$302$	−7.47012e8	−	1.02817e9i	−1.56064	−	2.14804i
$303$		0			0
$304$	−5.84136e6	+	1.89797e6i	−0.0119249	+	0.00387465i
$305$	−2.43323e8	+	7.48870e8i	−0.491059	+	1.51132i
$306$		0			0
$307$		−	1.06336e8i		−	0.209746i	−0.994486	−	0.104873i	$-0.966556\pi$
$307$		−	1.06336e8i		−	0.209746i	0.994486	−	0.104873i	$-0.0334436\pi$
$308$	−3.28463e7	−	6.11983e7i	−0.0640560	−	0.119347i
$309$		0			0
$310$	1.74350e8	−	2.39972e8i	0.332396	−	0.457504i
$311$	−2.88639e8	−	9.37846e7i	−0.544119	−	0.176795i	0.0240440	−	0.999711i	$-0.492346\pi$
$311$	−2.88639e8	−	9.37846e7i	−0.544119	−	0.176795i	−0.568163	+	0.822916i	$0.692346\pi$
$312$		0			0
$313$	6.64300e7	−	4.82642e7i	0.122450	−	0.0889652i	−0.524875	−	0.851180i	$-0.675888\pi$
$313$	6.64300e7	−	4.82642e7i	0.122450	−	0.0889652i	0.647325	+	0.762214i	$0.275888\pi$
$314$	4.63498e8	−	3.36751e8i	0.844879	−	0.613840i
$315$		0			0
$316$	8.47911e8	+	2.75503e8i	1.51163	+	0.491158i
$317$	6.54888e8	−	9.01376e8i	1.15467	−	1.58927i	0.425477	−	0.904969i	$-0.360106\pi$
$317$	6.54888e8	−	9.01376e8i	1.15467	−	1.58927i	0.729197	−	0.684303i	$-0.239894\pi$
$318$		0			0
$319$	5.34692e7	+	2.96476e8i	0.0922224	+	0.511355i
$320$			1.12719e9i			1.92297i
$321$		0			0
$322$	−3.80733e7	+	1.17178e8i	−0.0635514	+	0.195591i
$323$	2.53497e8	−	8.23663e7i	0.418567	−	0.136001i
$324$		0			0
$325$	1.75330e8	+	2.41321e8i	0.283312	+	0.389946i
$326$	−2.24595e7	−	6.91234e7i	−0.0359037	−	0.110500i
$327$		0			0
$328$	−4.84593e8	−	3.52077e8i	−0.758260	−	0.550908i
$329$	−8.99500e7			−0.139256
$330$		0			0
$331$	5.26497e8			0.797991			0.398996	−	0.916953i	$-0.369359\pi$
$331$	5.26497e8			0.797991			0.398996	+	0.916953i	$0.369359\pi$
$332$	−4.32238e8	−	3.14039e8i	−0.648246	−	0.470978i
$333$		0			0
$334$	5.96007e8	+	1.83432e9i	0.875263	+	2.69378i
$335$	−7.19673e7	−	9.90545e7i	−0.104587	−	0.143952i
$336$		0			0
$337$	−5.61134e8	+	1.82324e8i	−0.798661	+	0.259501i	−0.679788	−	0.733409i	$-0.737928\pi$
$337$	−5.61134e8	+	1.82324e8i	−0.798661	+	0.259501i	−0.118873	+	0.992909i	$0.537928\pi$
$338$	−1.41257e8	+	4.34744e8i	−0.198976	+	0.612385i
$339$		0			0
$340$		−	8.40571e8i		−	1.15984i
$341$	1.55977e8	+	1.49455e8i	0.213020	+	0.204113i
$342$		0			0
$343$	7.36412e7	−	1.01358e8i	0.0985352	−	0.135622i
$344$	−3.71090e8	−	1.20574e8i	−0.491501	−	0.159698i
$345$		0			0
$346$	1.33334e9	−	9.68725e8i	1.73051	−	1.25729i
$347$	5.28779e8	−	3.84180e8i	0.679393	−	0.493608i	−0.193763	−	0.981048i	$-0.562069\pi$
$347$	5.28779e8	−	3.84180e8i	0.679393	−	0.493608i	0.873156	+	0.487440i	$0.162069\pi$
$348$		0			0
$349$	1.50436e9	+	4.88797e8i	1.89437	+	0.615517i	0.975045	+	0.222009i	$0.0712615\pi$
$349$	1.50436e9	+	4.88797e8i	1.89437	+	0.615517i	0.919321	+	0.393508i	$0.128739\pi$
$350$	−2.61150e7	+	3.59442e7i	−0.0325576	+	0.0448116i
$351$		0			0
$352$	−8.22035e8	−	1.12264e8i	−1.00460	−	0.137195i
$353$		−	3.80307e8i		−	0.460175i	−0.973170	−	0.230088i	$-0.926099\pi$
$353$		−	3.80307e8i		−	0.460175i	0.973170	−	0.230088i	$-0.0739012\pi$
$354$		0			0
$355$	−3.63833e8	+	1.11976e9i	−0.431621	+	1.32839i
$356$	−1.21250e9	+	3.93964e8i	−1.42431	+	0.462787i
$357$		0			0
$358$	1.29492e9	+	1.78230e9i	1.49160	+	2.05301i
$359$	4.32632e8	+	1.33150e9i	0.493501	+	1.51884i	0.819280	+	0.573394i	$0.194374\pi$
$359$	4.32632e8	+	1.33150e9i	0.493501	+	1.51884i	−0.325779	+	0.945446i	$0.605626\pi$
$360$		0			0
$361$	−3.43123e8	−	2.49293e8i	−0.383861	−	0.278892i
$362$	2.15523e9			2.38788
$363$		0			0
$364$	−1.47392e8			−0.160184
$365$	−3.33818e8	−	2.42533e8i	−0.359323	−	0.261063i
$366$		0			0
$367$	−2.45330e8	−	7.55048e8i	−0.259071	−	0.797340i	−0.993000	−	0.118113i	$-0.962315\pi$
$367$	−2.45330e8	−	7.55048e8i	−0.259071	−	0.797340i	0.733929	−	0.679226i	$-0.237685\pi$
$368$	1.47082e7	+	2.02441e7i	0.0153848	+	0.0211754i
$369$		0			0
$370$	2.30465e8	−	7.48828e7i	0.236537	−	0.0768557i
$371$	−1.73083e7	+	5.32694e7i	−0.0175973	+	0.0541589i
$372$		0			0
$373$		−	1.12986e9i		−	1.12731i	−0.826010	−	0.563655i	$-0.809395\pi$
$373$		−	1.12986e9i		−	1.12731i	0.826010	−	0.563655i	$-0.190605\pi$
$374$	9.83205e8	+	1.34274e8i	0.971837	+	0.132722i
$375$		0			0
$376$	9.88954e8	−	1.36118e9i	0.959441	−	1.32056i
$377$	6.08012e8	+	1.97555e8i	0.584409	+	0.189886i
$378$		0			0
$379$	−2.95684e8	+	2.14827e8i	−0.278991	+	0.202699i	−0.718477	−	0.695551i	$-0.755161\pi$
$379$	−2.95684e8	+	2.14827e8i	−0.278991	+	0.202699i	0.439486	+	0.898249i	$0.355161\pi$
$380$	1.19848e9	−	8.70746e8i	1.12044	−	0.814046i
$381$		0			0
$382$	1.76265e9	+	5.72719e8i	1.61787	+	0.525678i
$383$	4.78842e8	−	6.59069e8i	0.435508	−	0.599426i	−0.533698	−	0.845675i	$-0.679198\pi$
$383$	4.78842e8	−	6.59069e8i	0.435508	−	0.599426i	0.969207	+	0.246249i	$0.0791982\pi$
$384$		0			0
$385$	−8.06850e7	−	7.73111e7i	−0.0720577	−	0.0690445i
$386$			3.18361e8i			0.281750i
$387$		0			0
$388$	5.81831e8	−	1.79069e9i	0.505692	−	1.55636i
$389$	−4.48316e7	+	1.45667e7i	−0.0386154	+	0.0125469i	−0.328261	−	0.944587i	$-0.606463\pi$
$389$	−4.48316e7	+	1.45667e7i	−0.0386154	+	0.0125469i	0.289646	+	0.957134i	$0.406463\pi$
$390$		0			0
$391$	−6.38291e8	−	8.78532e8i	−0.540008	−	0.743257i
$392$	3.60800e8	+	1.11043e9i	0.302527	+	0.931084i
$393$		0			0
$394$	−1.88869e7	−	1.37222e7i	−0.0155570	−	0.0113028i
$395$	1.43438e9			1.17105
$396$		0			0
$397$	−1.78256e9			−1.42980			−0.714902	−	0.699224i	$-0.753529\pi$
$397$	−1.78256e9			−1.42980			−0.714902	+	0.699224i	$0.753529\pi$
$398$	−2.80085e9	−	2.03494e9i	−2.22689	−	1.61793i
$399$		0			0
$400$	2.78840e6	+	8.58182e6i	0.00217844	+	0.00670455i
$401$	−8.77578e8	−	1.20788e9i	−0.679643	−	0.935448i	0.320287	−	0.947321i	$-0.396221\pi$
$401$	−8.77578e8	−	1.20788e9i	−0.679643	−	0.935448i	−0.999930	+	0.0118727i	$0.996221\pi$
$402$		0			0
$403$	4.35984e8	−	1.41660e8i	0.331820	−	0.107815i
$404$	−7.07951e8	+	2.17885e9i	−0.534156	+	1.64396i
$405$		0			0
$406$			9.52223e7i			0.0706151i
$407$	3.13227e7	+	1.73678e8i	0.0230292	+	0.127692i
$408$		0			0
$409$	7.90411e7	−	1.08791e8i	0.0571244	−	0.0786250i	−0.779499	−	0.626403i	$-0.784526\pi$
$409$	7.90411e7	−	1.08791e8i	0.0571244	−	0.0786250i	0.836623	+	0.547778i	$0.184526\pi$
$410$	−2.41837e9	−	7.85777e8i	−1.73292	−	0.563061i
$411$		0			0
$412$	−2.07392e9	+	1.50679e9i	−1.46101	+	1.06148i
$413$	1.21373e8	−	8.81827e7i	0.0847807	−	0.0615968i
$414$		0			0
$415$	−8.17511e8	−	2.65625e8i	−0.561468	−	0.182432i
$416$	−1.03487e9	+	1.42438e9i	−0.704791	+	0.970062i
$417$		0			0
$418$	8.27053e8	+	1.54094e9i	0.553881	+	1.03197i
$419$			2.46822e9i			1.63921i	0.572930	+	0.819604i	$0.305807\pi$
$419$			2.46822e9i			1.63921i	−0.572930	+	0.819604i	$0.694193\pi$
$420$		0			0
$421$	−2.15144e8	+	6.62146e8i	−0.140521	+	0.432480i	−0.996408	−	0.0846833i	$-0.973012\pi$
$421$	−2.15144e8	+	6.62146e8i	−0.140521	+	0.432480i	0.855887	+	0.517164i	$0.173012\pi$
$422$	−2.66710e9	+	8.66593e8i	−1.72761	+	0.561335i
$423$		0			0
$424$	−6.15810e8	−	8.47590e8i	−0.392343	−	0.540014i
$425$	−1.21008e8	−	3.72425e8i	−0.0764634	−	0.235330i
$426$		0			0
$427$	−1.46640e8	−	1.06540e8i	−0.0911496	−	0.0662240i
$428$	−3.13913e8			−0.193533
$429$		0			0
$430$	−1.65642e9			−1.00469
$431$	4.45542e8	+	3.23706e8i	0.268052	+	0.194751i	0.713689	−	0.700463i	$-0.247023\pi$
$431$	4.45542e8	+	3.23706e8i	0.268052	+	0.194751i	−0.445637	+	0.895214i	$0.647023\pi$
$432$		0			0
$433$	−3.42794e8	−	1.05501e9i	−0.202920	−	0.624524i	−0.999792	−	0.0203762i	$-0.993514\pi$
$433$	−3.42794e8	−	1.05501e9i	−0.202920	−	0.624524i	0.796872	−	0.604148i	$-0.206486\pi$
$434$	4.01344e7	+	5.52402e7i	0.0235669	+	0.0324370i
$435$		0			0
$436$	−4.74931e9	+	1.54314e9i	−2.74427	+	0.891669i
$437$	5.91399e8	−	1.82014e9i	0.338997	−	1.04333i
$438$		0			0
$439$			1.80506e9i			1.01828i	0.860684	+	0.509139i	$0.170036\pi$
$439$			1.80506e9i			1.01828i	−0.860684	+	0.509139i	$0.829964\pi$
$440$	2.05701e9	−	3.70980e8i	1.15120	−	0.207618i
$441$		0			0
$442$	1.23777e9	−	1.70365e9i	0.681809	−	0.938429i
$443$	1.17482e8	+	3.81722e7i	0.0642034	+	0.0208609i	0.340943	−	0.940084i	$-0.389254\pi$
$443$	1.17482e8	+	3.81722e7i	0.0642034	+	0.0208609i	−0.276739	+	0.960945i	$0.589254\pi$
$444$		0			0
$445$	−1.65941e9	+	1.20563e9i	−0.892675	+	0.648567i
$446$	−2.17104e9	+	1.57736e9i	−1.15877	+	0.841895i
$447$		0			0
$448$	−2.46773e8	−	8.01815e7i	−0.129666	−	0.0421309i
$449$	−1.68117e9	+	2.31393e9i	−0.876494	+	1.20639i	0.100886	+	0.994898i	$0.467832\pi$
$449$	−1.68117e9	+	2.31393e9i	−0.876494	+	1.20639i	−0.977380	+	0.211492i	$0.932168\pi$
$450$		0			0
$451$	8.05315e8	−	1.66761e9i	0.413379	−	0.856005i
$452$		−	3.10423e9i		−	1.58114i
$453$		0			0
$454$	−5.14133e8	+	1.58234e9i	−0.257858	+	0.793604i
$455$	−2.25529e8	+	7.32787e7i	−0.112244	+	0.0364702i
$456$		0			0
$457$	−1.49764e9	−	2.06132e9i	−0.734007	−	1.01027i	−0.998941	−	0.0460069i	$-0.985350\pi$
$457$	−1.49764e9	−	2.06132e9i	−0.734007	−	1.01027i	0.264935	−	0.964266i	$-0.414650\pi$
$458$	−3.60996e8	−	1.11103e9i	−0.175579	−	0.540378i
$459$		0			0
$460$	−4.88274e9	−	3.54752e9i	−2.33890	−	1.69931i
$461$	1.43615e9			0.682726			0.341363	−	0.939932i	$-0.389112\pi$
$461$	1.43615e9			0.682726			0.341363	+	0.939932i	$0.389112\pi$
$462$		0			0
$463$	3.63234e9			1.70080			0.850399	−	0.526138i	$-0.176360\pi$
$463$	3.63234e9			1.70080			0.850399	+	0.526138i	$0.176360\pi$
$464$	1.56458e7	+	1.13674e7i	0.00727085	+	0.00528258i
$465$		0			0
$466$	1.36339e9	+	4.19610e9i	0.624124	+	1.92086i
$467$	1.00506e8	+	1.38334e8i	0.0456648	+	0.0628521i	0.831239	−	0.555916i	$-0.187632\pi$
$467$	1.00506e8	+	1.38334e8i	0.0456648	+	0.0628521i	−0.785574	+	0.618768i	$0.787632\pi$
$468$		0			0
$469$	2.68051e7	−	8.70950e6i	0.0119981	−	0.00389842i
$470$	2.20718e9	−	6.79299e9i	0.980606	−	3.01800i
$471$		0			0
$472$			2.80621e9i			1.22835i
$473$	1.63231e8	−	1.19523e9i	0.0709230	−	0.519325i
$474$		0			0
$475$	4.05648e8	−	5.58327e8i	0.173669	−	0.239035i
$476$	1.84024e8	+	5.97931e7i	0.0782079	+	0.0254113i
$477$		0			0
$478$	3.26280e9	−	2.37056e9i	1.36645	−	0.992782i
$479$	1.95205e9	−	1.41825e9i	0.811551	−	0.589626i	−0.102729	−	0.994709i	$-0.532757\pi$
$479$	1.95205e9	−	1.41825e9i	0.811551	−	0.589626i	0.914280	+	0.405083i	$0.132757\pi$
$480$		0			0
$481$	3.56178e8	+	1.15729e8i	0.145935	+	0.0474171i
$482$	−3.39743e9	+	4.67616e9i	−1.38193	+	1.90206i
$483$		0			0
$484$	1.71468e8	+	4.01293e9i	0.0687425	+	1.60880i
$485$		−	3.02926e9i		−	1.20570i
$486$		0			0
$487$	1.16512e9	−	3.58586e9i	0.457107	−	1.40683i	−0.411538	−	0.911393i	$-0.635008\pi$
$487$	1.16512e9	−	3.58586e9i	0.457107	−	1.40683i	0.868644	−	0.495436i	$-0.164992\pi$
$488$	3.22446e9	−	1.04769e9i	1.25599	−	0.408097i
$489$		0			0
$490$	2.91340e9	+	4.00995e9i	1.11870	+	1.53976i
$491$	−1.15909e9	−	3.56732e9i	−0.441909	−	1.36006i	−0.885838	−	0.463994i	$-0.846416\pi$
$491$	−1.15909e9	−	3.56732e9i	−0.441909	−	1.36006i	0.443929	−	0.896062i	$-0.353584\pi$
$492$		0			0
$493$	−6.78981e8	−	4.93309e8i	−0.255208	−	0.185419i
$494$	3.71125e9			1.38508
$495$		0			0
$496$	1.38675e7			0.00510286
$497$	−2.19266e8	−	1.59306e8i	−0.0801168	−	0.0582083i
$498$		0			0
$499$	−1.50366e9	−	4.62778e9i	−0.541748	−	1.66733i	−0.728600	−	0.684940i	$-0.759828\pi$
$499$	−1.50366e9	−	4.62778e9i	−0.541748	−	1.66733i	0.186852	−	0.982388i	$-0.440172\pi$
$500$	1.85944e9	+	2.55930e9i	0.665253	+	0.915642i
$501$		0			0
$502$	2.51285e7	−	8.16473e6i	0.00886549	−	0.00288057i
$503$	9.71261e8	−	2.98923e9i	0.340289	−	1.04730i	−0.623769	−	0.781609i	$-0.714399\pi$
$503$	9.71261e8	−	2.98923e9i	0.340289	−	1.04730i	0.964058	−	0.265693i	$-0.0856007\pi$
$504$		0			0
$505$			3.68589e9i			1.27357i
$506$	4.92946e9	−	5.14459e9i	1.69150	−	1.76532i
$507$		0			0
$508$	9.68307e7	−	1.33276e8i	0.0327710	−	0.0451055i
$509$	3.07026e9	+	9.97588e8i	1.03196	+	0.335304i	0.775565	−	0.631268i	$-0.217465\pi$
$509$	3.07026e9	+	9.97588e8i	1.03196	+	0.335304i	0.256395	+	0.966572i	$0.417465\pi$
$510$		0			0
$511$	7.68429e7	−	5.58297e7i	0.0254760	−	0.0185094i
$512$	−8.49894e7	+	6.17484e7i	−0.0279847	+	0.0203320i
$513$		0			0
$514$	−5.18413e9	−	1.68443e9i	−1.68386	−	0.547118i
$515$	−2.42424e9	+	3.33667e9i	−0.782077	+	1.07644i
$516$		0			0
$517$	4.68417e9	+	2.26206e9i	1.49079	+	0.719925i
$518$			5.57820e7i			0.0176335i
$519$		0			0
$520$	1.37067e9	−	4.21850e9i	0.427487	−	1.31567i
$521$	−1.64022e7	+	5.32940e6i	−0.00508125	+	0.00165100i	−0.311557	−	0.950228i	$-0.600850\pi$
$521$	−1.64022e7	+	5.32940e6i	−0.00508125	+	0.00165100i	0.306475	+	0.951879i	$0.400850\pi$
$522$		0			0
$523$	−2.28534e9	−	3.14550e9i	−0.698546	−	0.961466i	−0.999968	−	0.00797495i	$-0.997461\pi$
$523$	−2.28534e9	−	3.14550e9i	−0.698546	−	0.961466i	0.301423	−	0.953491i	$-0.402539\pi$
$524$	2.78757e9	+	8.57924e9i	0.846380	+	2.60489i
$525$		0			0
$526$	4.56330e9	+	3.31543e9i	1.36719	+	0.993321i
$527$	−6.01809e8			−0.179111
$528$		0			0
$529$	−4.39225e9			−1.29001
$530$	−3.59818e9	−	2.61423e9i	−1.04983	−	0.762744i
$531$		0			0
$532$	1.05378e8	+	3.24320e8i	0.0303430	+	0.0933862i
$533$	−2.30992e9	−	3.17933e9i	−0.660771	−	0.909474i
$534$		0			0
$535$	−4.80327e8	+	1.56068e8i	−0.135612	+	0.0440630i
$536$	−1.62911e8	+	5.01387e8i	−0.0456954	+	0.140636i
$537$		0			0
$538$			7.99472e9i			2.21343i
$539$	−3.18059e9	+	1.70709e9i	−0.874876	+	0.469564i
$540$		0			0
$541$	−1.06024e8	+	1.45930e8i	−0.0287882	+	0.0396236i	−0.823168	−	0.567797i	$-0.807796\pi$
$541$	−1.06024e8	+	1.45930e8i	−0.0287882	+	0.0396236i	0.794380	+	0.607421i	$0.207796\pi$
$542$	−1.80132e9	−	5.85284e8i	−0.485952	−	0.157895i
$543$		0			0
$544$	1.86991e9	−	1.35857e9i	0.497995	−	0.361814i
$545$	−6.49985e9	+	4.72242e9i	−1.71995	+	1.24962i
$546$		0			0
$547$	4.64326e9	+	1.50869e9i	1.21302	+	0.394134i	0.844535	−	0.535501i	$-0.179877\pi$
$547$	4.64326e9	+	1.50869e9i	1.21302	+	0.394134i	0.368484	+	0.929634i	$0.379877\pi$
$548$	−6.91180e9	+	9.51328e9i	−1.79415	+	2.46944i
$549$		0			0
$550$	2.26387e9	−	1.21506e9i	0.580205	−	0.311408i
$551$		−	1.47910e9i		−	0.376676i
$552$		0			0
$553$	−1.02033e8	+	3.14026e8i	−0.0256569	+	0.0789638i
$554$	2.18688e9	−	7.10560e8i	0.546438	−	0.177548i
$555$		0			0
$556$	3.18750e9	+	4.38722e9i	0.786482	+	1.08250i
$557$	−1.37870e8	−	4.24321e8i	−0.0338047	−	0.104040i	0.932730	−	0.360575i	$-0.117419\pi$
$557$	−1.37870e8	−	4.24321e8i	−0.0338047	−	0.104040i	−0.966535	+	0.256534i	$0.917419\pi$
$558$		0			0
$559$	−2.07104e9	−	1.50470e9i	−0.501473	−	0.364341i
$560$	−7.17349e6			−0.00172613
$561$		0			0
$562$	−2.95916e9			−0.703221
$563$	−1.07591e9	−	7.81691e8i	−0.254094	−	0.184610i	0.453445	−	0.891284i	$-0.350195\pi$
$563$	−1.07591e9	−	7.81691e8i	−0.254094	−	0.184610i	−0.707539	+	0.706674i	$0.750195\pi$
$564$		0			0
$565$	−1.54333e9	−	4.74987e9i	−0.359988	−	1.10793i
$566$	2.30833e9	+	3.17714e9i	0.535106	+	0.736511i
$567$		0			0
$568$	4.82143e9	−	1.56658e9i	1.10397	−	0.358701i
$569$	5.16896e8	−	1.59084e9i	0.117628	−	0.362021i	−0.874858	−	0.484379i	$-0.839046\pi$
$569$	5.16896e8	−	1.59084e9i	0.117628	−	0.362021i	0.992486	+	0.122358i	$0.0390455\pi$
$570$		0			0
$571$			1.64546e9i			0.369881i	0.982750	+	0.184940i	$0.0592092\pi$
$571$			1.64546e9i			0.369881i	−0.982750	+	0.184940i	$0.940791\pi$
$572$	7.67547e9	+	3.70661e9i	1.71482	+	0.828115i
$573$		0			0
$574$	3.44056e8	−	4.73553e8i	0.0759343	−	0.104515i
$575$	−2.67406e9	−	8.68853e8i	−0.586588	−	0.190594i
$576$		0			0
$577$	1.48214e9	−	1.07684e9i	0.321200	−	0.233365i	−0.415488	−	0.909599i	$-0.636389\pi$
$577$	1.48214e9	−	1.07684e9i	0.321200	−	0.233365i	0.736687	+	0.676234i	$0.236389\pi$
$578$	3.83151e9	−	2.78375e9i	0.825319	−	0.599630i
$579$		0			0
$580$	−4.43621e9	−	1.44141e9i	−0.944092	−	0.306754i
$581$	1.16305e8	−	1.60081e8i	0.0246027	−	0.0338628i
$582$		0			0
$583$	2.24095e9	−	2.33875e9i	0.468374	−	0.488814i
$584$			1.77665e9i			0.369111i
$585$		0			0
$586$	3.24969e9	−	1.00015e10i	0.667115	−	2.05317i
$587$	−5.54757e8	+	1.80251e8i	−0.113206	+	0.0367828i	−0.365072	−	0.930979i	$-0.618956\pi$
$587$	−5.54757e8	+	1.80251e8i	−0.113206	+	0.0367828i	0.251866	+	0.967762i	$0.418956\pi$
$588$		0			0
$589$	−6.23413e8	−	8.58055e8i	−0.125711	−	0.173026i
$590$	3.68130e9	+	1.13299e10i	0.737936	+	2.27113i
$591$		0			0
$592$	9.16544e6	+	6.65908e6i	0.00181563	+	0.00131913i
$593$	−6.34419e9			−1.24935			−0.624676	−	0.780884i	$-0.714769\pi$
$593$	−6.34419e9			−1.24935			−0.624676	+	0.780884i	$0.714769\pi$
$594$		0			0
$595$	3.11308e8			0.0605872
$596$	−1.01044e10	−	7.34124e9i	−1.95500	−	1.42039i
$597$		0			0
$598$	−4.67235e9	−	1.43800e10i	−0.893473	−	2.74983i
$599$	4.39871e9	+	6.05430e9i	0.836241	+	1.15099i	0.986729	+	0.162375i	$0.0519155\pi$
$599$	4.39871e9	+	6.05430e9i	0.836241	+	1.15099i	−0.150488	+	0.988612i	$0.548085\pi$
$600$		0			0
$601$	−2.91754e9	+	9.47966e8i	−0.548222	+	0.178128i	−0.570015	−	0.821634i	$-0.693063\pi$
$601$	−2.91754e9	+	9.47966e8i	−0.548222	+	0.178128i	0.0217930	+	0.999763i	$0.493063\pi$
$602$	1.17827e8	−	3.62636e8i	0.0220120	−	0.0677459i
$603$		0			0
$604$			1.43308e10i			2.64631i
$605$	2.25747e9	+	6.05506e9i	0.414457	+	1.11167i
$606$		0			0
$607$	2.70175e9	−	3.71864e9i	0.490325	−	0.674875i	−0.490123	−	0.871653i	$-0.663048\pi$
$607$	2.70175e9	−	3.71864e9i	0.490325	−	0.674875i	0.980448	+	0.196779i	$0.0630480\pi$
$608$	3.87407e9	+	1.25876e9i	0.699045	+	0.227134i
$609$		0			0
$610$	1.16441e10	−	8.45993e9i	2.07707	−	1.50908i
$611$	8.93045e9	−	6.48835e9i	1.58391	−	1.15077i
$612$		0			0
$613$	−2.67774e9	−	8.70050e8i	−0.469522	−	0.152557i	0.0646934	−	0.997905i	$-0.479393\pi$
$613$	−2.67774e9	−	8.70050e8i	−0.469522	−	0.152557i	−0.534216	+	0.845348i	$0.679393\pi$
$614$	−1.14247e9	+	1.57248e9i	−0.199185	+	0.274154i
$615$		0			0
$616$	−6.51053e7	+	4.76725e8i	−0.0112223	+	0.0821742i
$617$			7.32574e9i			1.25561i	0.778373	+	0.627803i	$0.216046\pi$
$617$			7.32574e9i			1.25561i	−0.778373	+	0.627803i	$0.783954\pi$
$618$		0			0
$619$	−1.50954e8	+	4.64590e8i	−0.0255816	+	0.0787322i	−0.963032	−	0.269386i	$-0.913179\pi$
$619$	−1.50954e8	+	4.64590e8i	−0.0255816	+	0.0787322i	0.937451	+	0.348118i	$0.113179\pi$
$620$	−3.18105e9	+	1.03359e9i	−0.536044	+	0.174171i
$621$		0			0
$622$	3.26074e9	+	4.48802e9i	0.543312	+	0.747805i
$623$	−1.45906e8	−	4.49052e8i	−0.0241749	−	0.0744026i
$624$		0			0
$625$	6.13013e9	+	4.45380e9i	1.00436	+	0.729711i
$626$	−1.50091e9			−0.244537
$627$		0			0
$628$	−6.46029e9			−1.04086
$629$	−3.97752e8	−	2.88984e8i	−0.0637288	−	0.0463017i
$630$		0			0
$631$	1.30938e9	+	4.02987e9i	0.207474	+	0.638539i	0.999603	+	0.0281853i	$0.00897286\pi$
$631$	1.30938e9	+	4.02987e9i	0.207474	+	0.638539i	−0.792129	+	0.610354i	$0.791027\pi$
$632$	−3.63023e9	−	4.99659e9i	−0.572038	−	0.787343i
$633$		0			0
$634$	−1.93688e10	+	6.29330e9i	−3.01849	+	0.980767i
$635$	8.19028e7	−	2.52071e8i	0.0126938	−	0.0390674i
$636$		0			0
$637$			7.66024e9i			1.17423i
$638$	2.39465e9	−	4.95872e9i	0.365064	−	0.755958i
$639$		0			0
$640$	7.42147e9	−	1.02148e10i	1.11908	−	1.54028i
$641$	−9.19294e9	−	2.98697e9i	−1.37864	−	0.447948i	−0.476418	−	0.879219i	$-0.658065\pi$
$641$	−9.19294e9	−	2.98697e9i	−1.37864	−	0.447948i	−0.902222	+	0.431271i	$0.858065\pi$
$642$		0			0
$643$	1.04351e10	−	7.58156e9i	1.54796	−	1.12466i	0.602871	−	0.797839i	$-0.294023\pi$
$643$	1.04351e10	−	7.58156e9i	1.54796	−	1.12466i	0.945087	−	0.326818i	$-0.105977\pi$
$644$	1.12398e9	−	8.16617e8i	0.165828	−	0.120481i
$645$		0			0
$646$	−4.63363e9	−	1.50556e9i	−0.676250	−	0.219727i
$647$	−9.00612e8	+	1.23959e9i	−0.130729	+	0.179933i	−0.869364	−	0.494173i	$-0.835471\pi$
$647$	−9.00612e8	+	1.23959e9i	−0.130729	+	0.179933i	0.738634	+	0.674106i	$0.235471\pi$
$648$		0			0
$649$	−8.53814e9	+	1.53985e9i	−1.22605	+	0.221117i
$650$		−	5.45238e9i		−	0.778734i
$651$		0			0
$652$	−2.53257e8	+	7.79446e8i	−0.0357846	+	0.110134i
$653$	1.09247e10	−	3.54965e9i	1.53537	−	0.498872i	0.585276	−	0.810834i	$-0.300986\pi$
$653$	1.09247e10	−	3.54965e9i	1.53537	−	0.498872i	0.950094	+	0.311963i	$0.100986\pi$
$654$		0			0
$655$	8.53067e9	+	1.17415e10i	1.18615	+	1.63259i
$656$	−3.67363e7	−	1.13063e8i	−0.00508080	−	0.0156371i
$657$		0			0
$658$	1.33017e9	+	9.66424e8i	0.182019	+	0.132244i
$659$	1.09359e7			0.00148852			0.000744262	−	1.00000i	$-0.499763\pi$
$659$	1.09359e7			0.00148852			0.000744262		1.00000i	$0.499763\pi$
$660$		0			0
$661$	−3.76410e9			−0.506939			−0.253469	−	0.967343i	$-0.581572\pi$
$661$	−3.76410e9			−0.506939			−0.253469	+	0.967343i	$0.581572\pi$
$662$	−7.78577e9	−	5.65669e9i	−1.04303	−	0.757809i
$663$		0			0
$664$	1.14372e9	+	3.52001e9i	0.151611	+	0.466612i
$665$	3.22483e8	+	4.43860e8i	0.0425238	+	0.0585289i
$666$		0			0
$667$	−5.73110e9	+	1.86215e9i	−0.747821	+	0.242982i
$668$	6.72067e9	−	2.06841e10i	0.872358	−	2.68484i
$669$		0			0
$670$			2.23802e9i			0.287477i
$671$	4.95704e9	+	9.23580e9i	0.633422	+	1.18017i
$672$		0			0
$673$	−3.59607e9	+	4.94957e9i	−0.454753	+	0.625914i	−0.973410	−	0.229068i	$-0.926432\pi$
$673$	−3.59607e9	+	4.94957e9i	−0.454753	+	0.625914i	0.518657	+	0.854982i	$0.326432\pi$
$674$	1.02569e10	+	3.33266e9i	1.29034	+	0.419258i
$675$		0			0
$676$	4.17009e9	−	3.02975e9i	0.519197	−	0.377219i
$677$	6.01956e9	−	4.37347e9i	0.745597	−	0.541708i	−0.148862	−	0.988858i	$-0.547561\pi$
$677$	6.01956e9	−	4.37347e9i	0.745597	−	0.541708i	0.894459	+	0.447150i	$0.147561\pi$
$678$		0			0
$679$	6.63188e8	+	2.15483e8i	0.0813004	+	0.0264161i
$680$	−3.42267e9	+	4.71090e9i	−0.417430	+	0.574543i
$681$		0			0
$682$	−7.00827e8	−	3.88594e9i	−0.0845990	−	0.469085i
$683$		−	6.55957e9i		−	0.787777i	−0.919158	−	0.393888i	$-0.871130\pi$
$683$		−	6.55957e9i		−	0.787777i	0.919158	−	0.393888i	$-0.128870\pi$
$684$		0			0
$685$	−5.84624e9	+	1.79929e10i	−0.694960	+	2.13887i
$686$	−2.17799e9	+	7.07673e8i	−0.257586	+	0.0836947i
$687$		0			0
$688$	−4.55182e7	−	6.26504e7i	−0.00532875	−	0.00733439i
$689$	−2.12407e9	−	6.53722e9i	−0.247401	−	0.761422i
$690$		0			0
$691$	3.46227e9	+	2.51548e9i	0.399197	+	0.290034i	0.769214	−	0.638992i	$-0.220648\pi$
$691$	3.46227e9	+	2.51548e9i	0.399197	+	0.290034i	−0.370017	+	0.929025i	$0.620648\pi$
$692$	−1.85842e10			−2.13192
$693$		0			0
$694$	−1.19472e10			−1.35677
$695$	7.05848e9	+	5.12829e9i	0.797562	+	0.579463i
$696$		0			0
$697$	1.59424e9	+	4.90658e9i	0.178336	+	0.548863i
$698$	−1.69947e10	−	2.33912e10i	−1.89156	−	2.60350i
$699$		0			0
$700$	4.76474e8	−	1.54816e8i	0.0525044	−	0.0170597i
$701$	−1.74200e9	+	5.36131e9i	−0.191000	+	0.587838i	0.809000	+	0.587809i	$0.200009\pi$
$701$	−1.74200e9	+	5.36131e9i	−0.191000	+	0.587838i	−1.00000		2.93357e-5i	$0.999991\pi$
$702$		0			0
$703$		−	8.66470e8i		−	0.0940611i
$704$	1.08344e10	+	1.03813e10i	1.17031	+	1.12137i
$705$		0			0
$706$	−4.08603e9	+	5.62393e9i	−0.437003	+	0.601483i
$707$	−8.06943e8	−	2.62192e8i	−0.0858766	−	0.0279030i
$708$		0			0
$709$	−7.18831e9	+	5.22261e9i	−0.757469	+	0.550334i	−0.898133	−	0.439724i	$-0.855076\pi$
$709$	−7.18831e9	+	5.22261e9i	−0.757469	+	0.550334i	0.140664	+	0.990057i	$0.455076\pi$
$710$	1.74110e10	−	1.26499e10i	1.82566	−	1.32642i
$711$		0			0
$712$	8.39948e9	+	2.72916e9i	0.872113	+	0.283367i
$713$	−2.53986e9	+	3.49581e9i	−0.262419	+	0.361189i
$714$		0			0
$715$	1.35873e10	+	1.85558e9i	1.39015	+	0.189850i
$716$		−	2.48419e10i		−	2.52923i
$717$		0			0
$718$	7.90800e9	−	2.43383e10i	0.797317	−	2.45389i
$719$	1.28303e10	−	4.16881e9i	1.28732	−	0.418274i	0.416164	−	0.909289i	$-0.363374\pi$
$719$	1.28303e10	−	4.16881e9i	1.28732	−	0.418274i	0.871151	+	0.491015i	$0.163374\pi$
$720$		0			0
$721$	−5.58045e8	−	7.68083e8i	−0.0554492	−	0.0763193i
$722$	2.39564e9	+	7.37303e9i	0.236887	+	0.729064i
$723$		0			0
$724$	−1.96613e10	−	1.42848e10i	−1.92543	−	1.39890i
$725$	−2.17302e9			−0.211778
$726$		0			0
$727$	−3.88356e9			−0.374852			−0.187426	−	0.982279i	$-0.560014\pi$
$727$	−3.88356e9			−0.374852			−0.187426	+	0.982279i	$0.560014\pi$
$728$	8.26045e8	+	6.00157e8i	0.0793494	+	0.0576507i
$729$		0			0
$730$	2.33068e9	+	7.17309e9i	0.221744	+	0.682459i
$731$	1.97535e9	+	2.71884e9i	0.187040	+	0.257438i
$732$		0			0
$733$	−6.86357e9	+	2.23011e9i	−0.643704	+	0.209152i	−0.612636	−	0.790365i	$-0.709891\pi$
$733$	−6.86357e9	+	2.23011e9i	−0.643704	+	0.209152i	−0.0310677	+	0.999517i	$0.509891\pi$
$734$	−4.48434e9	+	1.38014e10i	−0.418564	+	1.28821i
$735$		0			0
$736$		−	1.65957e10i		−	1.53434i
$737$	−1.61491e9	−	2.20544e8i	−0.148597	−	0.0202936i
$738$		0			0
$739$	−1.29510e9	+	1.78255e9i	−0.118045	+	0.162475i	−0.863950	−	0.503577i	$-0.832017\pi$
$739$	−1.29510e9	+	1.78255e9i	−0.118045	+	0.162475i	0.745905	+	0.666052i	$0.232017\pi$
$740$	−2.59877e9	−	8.44390e8i	−0.235752	−	0.0766006i
$741$		0			0
$742$	8.28280e8	−	6.01781e8i	0.0744327	−	0.0540785i
$743$	−6.12290e9	+	4.44855e9i	−0.547641	+	0.397885i	−0.826915	−	0.562327i	$-0.809906\pi$
$743$	−6.12290e9	+	4.44855e9i	−0.547641	+	0.397885i	0.279274	+	0.960212i	$0.409906\pi$
$744$		0			0
$745$	−1.91108e10	−	6.20947e9i	−1.69329	−	0.550184i
$746$	−1.21392e10	+	1.67082e10i	−1.07055	+	1.47348i
$747$		0			0
$748$	−8.07943e9	−	7.74157e9i	−0.705870	−	0.676353i
$749$		−	1.16258e8i		−	0.0101097i
$750$		0			0
$751$	5.75420e9	−	1.77096e10i	0.495730	−	1.52570i	−0.320086	−	0.947389i	$-0.603712\pi$
$751$	5.75420e9	−	1.77096e10i	0.495730	−	1.52570i	0.815816	−	0.578312i	$-0.196288\pi$
$752$	3.17583e8	−	1.03189e8i	0.0272330	−	0.00884852i
$753$		0			0
$754$	−6.86866e9	−	9.45390e9i	−0.583542	−	0.803177i
$755$	7.12483e9	+	2.19280e10i	0.602504	+	1.85432i
$756$		0			0
$757$	1.80582e10	+	1.31200e10i	1.51300	+	1.09926i	0.964825	+	0.262894i	$0.0846770\pi$
$757$	1.80582e10	+	1.31200e10i	1.51300	+	1.09926i	0.548174	+	0.836364i	$0.315323\pi$
$758$	6.68063e9			0.557154
$759$		0			0
$760$	−1.02623e10			−0.848003
$761$	−1.01033e10	−	7.34046e9i	−0.831029	−	0.603778i	0.0888215	−	0.996048i	$-0.471690\pi$
$761$	−1.01033e10	−	7.34046e9i	−0.831029	−	0.603778i	−0.919850	+	0.392270i	$0.871690\pi$
$762$		0			0
$763$	−5.71508e8	−	1.75892e9i	−0.0465786	−	0.143354i
$764$	−1.22840e10	−	1.69074e10i	−0.996581	−	1.37168i
$765$		0			0
$766$	−1.41621e10	+	4.60154e9i	−1.13848	+	0.369916i
$767$	−5.68934e9	+	1.75100e10i	−0.455279	+	1.40121i
$768$		0			0
$769$		−	1.17360e10i		−	0.930630i	−0.885145	−	0.465315i	$-0.845941\pi$
$769$		−	1.17360e10i		−	0.930630i	0.885145	−	0.465315i	$-0.154059\pi$
$770$	3.62528e8	+	2.01015e9i	0.0286170	+	0.158676i
$771$		0			0
$772$	2.11008e9	−	2.90428e9i	0.165059	−	0.227184i
$773$	−4.38016e9	−	1.42320e9i	−0.341084	−	0.110825i	0.133466	−	0.991053i	$-0.457389\pi$
$773$	−4.38016e9	−	1.42320e9i	−0.341084	−	0.110825i	−0.474550	+	0.880228i	$0.657389\pi$
$774$		0			0
$775$	−1.26061e9	+	9.15887e8i	−0.0972803	+	0.0706782i
$776$	−1.05522e10	+	7.66664e9i	−0.810640	+	0.588965i
$777$		0			0
$778$	8.19468e8	+	2.66261e8i	0.0623883	+	0.0202712i
$779$	−5.34428e9	+	7.35578e9i	−0.405050	+	0.557503i
$780$		0			0
$781$	7.41210e9	+	1.38100e10i	0.556753	+	1.03732i
$782$			1.98494e10i			1.48431i
$783$		0			0
$784$	−7.16077e7	+	2.20386e8i	−0.00530705	+	0.0163334i
$785$	−9.88507e9	+	3.21186e9i	−0.729350	+	0.236980i
$786$		0			0
$787$	−1.26764e9	−	1.74476e9i	−0.0927012	−	0.127592i	0.760147	−	0.649751i	$-0.225127\pi$
$787$	−1.26764e9	−	1.74476e9i	−0.0927012	−	0.127592i	−0.852848	+	0.522159i	$0.825127\pi$
$788$	8.13481e7	+	2.50364e8i	0.00592251	+	0.0182276i
$789$		0			0
$790$	−2.12115e10	−	1.54110e10i	−1.53065	−	1.11208i
$791$	1.14966e9			0.0825946
$792$		0			0
$793$	2.22438e10			1.58399
$794$	2.63602e10	+	1.91518e10i	1.86886	+	1.35781i
$795$		0			0
$796$	1.20636e10	+	3.71279e10i	0.847774	+	2.60918i
$797$	−1.18068e10	−	1.62507e10i	−0.826092	−	1.13702i	−0.988638	−	0.150317i	$-0.951971\pi$
$797$	−1.18068e10	−	1.62507e10i	−0.826092	−	1.13702i	0.162546	−	0.986701i	$-0.448029\pi$
$798$		0			0
$799$	−1.37821e10	+	4.47809e9i	−0.955879	+	0.310584i
$800$	1.84931e9	−	5.69159e9i	0.127701	−	0.393023i
$801$		0			0
$802$			2.72907e10i			1.86812i
$803$	−5.40562e9	+	9.74898e8i	−0.368418	+	0.0664439i
$804$		0			0
$805$	1.31383e9	−	1.80834e9i	0.0887677	−	0.122178i
$806$	−7.96927e9	−	2.58937e9i	−0.536100	−	0.174189i
$807$		0			0
$808$	1.28396e10	−	9.32849e9i	0.856270	−	0.622116i
$809$	1.26505e9	−	9.19111e8i	0.0840015	−	0.0610307i	−0.544992	−	0.838441i	$-0.683467\pi$
$809$	1.26505e9	−	9.19111e8i	0.0840015	−	0.0610307i	0.628993	+	0.777411i	$0.283467\pi$
$810$		0			0
$811$	−3.66932e9	−	1.19223e9i	−0.241553	−	0.0784854i	0.185739	−	0.982599i	$-0.440532\pi$
$811$	−3.66932e9	−	1.19223e9i	−0.241553	−	0.0784854i	−0.427292	+	0.904114i	$0.640532\pi$
$812$	6.31130e8	−	8.68676e8i	0.0413688	−	0.0569392i
$813$		0			0
$814$	1.40280e9	−	2.90486e9i	0.0911615	−	0.188773i
$815$			1.31857e9i			0.0853198i
$816$		0			0
$817$	−1.83023e9	+	5.63288e9i	−0.117417	+	0.361371i
$818$	−2.33770e9	+	7.59565e8i	−0.149332	+	0.0485208i
$819$		0			0
$820$	1.68538e10	+	2.31972e10i	1.06745	+	1.46922i
$821$	−5.97105e9	−	1.83770e10i	−0.376573	−	1.15897i	−0.942411	−	0.334457i	$-0.891447\pi$
$821$	−5.97105e9	−	1.83770e10i	−0.376573	−	1.15897i	0.565838	−	0.824517i	$-0.308553\pi$
$822$		0			0
$823$	1.08113e10	+	7.85490e9i	0.676052	+	0.491181i	0.872046	−	0.489424i	$-0.162793\pi$
$823$	1.08113e10	+	7.85490e9i	0.676052	+	0.491181i	−0.195993	+	0.980605i	$0.562793\pi$
$824$	1.77585e10			1.10576
$825$		0			0
$826$	−2.74228e9			−0.169310
$827$	1.12248e9	+	8.15533e8i	0.0690098	+	0.0501386i	0.621755	−	0.783212i	$-0.286420\pi$
$827$	1.12248e9	+	8.15533e8i	0.0690098	+	0.0501386i	−0.552745	+	0.833350i	$0.686420\pi$
$828$		0			0
$829$	3.34208e9	+	1.02859e10i	0.203740	+	0.627046i	0.999763	+	0.0217801i	$0.00693337\pi$
$829$	3.34208e9	+	1.02859e10i	0.203740	+	0.627046i	−0.796023	+	0.605266i	$0.793067\pi$
$830$	9.23536e9	+	1.27114e10i	0.560635	+	0.771648i
$831$		0			0
$832$	3.02840e10	−	9.83986e9i	1.82298	−	0.592321i
$833$	3.10756e9	−	9.56408e9i	0.186278	−	0.573305i
$834$		0			0
$835$		−	3.49906e10i		−	2.07993i
$836$	2.66841e9	−	1.95391e10i	0.157954	−	1.15660i
$837$		0			0
$838$	2.65186e10	−	3.64997e10i	1.55667	−	2.14257i
$839$	−5.93024e9	−	1.92685e9i	−0.346662	−	0.112637i	0.130511	−	0.991447i	$-0.458338\pi$
$839$	−5.93024e9	−	1.92685e9i	−0.346662	−	0.112637i	−0.477172	+	0.878810i	$0.658338\pi$
$840$		0			0
$841$	1.01876e10	−	7.40175e9i	0.590591	−	0.429090i
$842$	1.02956e10	−	7.48021e9i	0.594375	−	0.431839i
$843$		0			0
$844$	3.00747e10	+	9.77185e9i	1.72188	+	0.559472i
$845$	4.87448e9	−	6.70915e9i	0.277927	−	0.382533i
$846$		0			0
$847$	−1.48620e9	+	6.35039e7i	−0.0840400	+	0.00359094i
$848$		−	2.07932e8i		−	0.0117094i
$849$		0			0
$850$	−2.21189e9	+	6.80749e9i	−0.123537	+	0.380207i
$851$	−3.35732e9	+	1.09086e9i	−0.186741	+	0.0606758i
$852$		0			0
$853$	−9.05184e9	−	1.24588e10i	−0.499362	−	0.687312i	0.482719	−	0.875775i	$-0.339649\pi$
$853$	−9.05184e9	−	1.24588e10i	−0.499362	−	0.687312i	−0.982080	+	0.188463i	$0.939649\pi$
$854$	1.02382e9	+	3.15100e9i	0.0562500	+	0.173120i
$855$		0			0
$856$	1.75929e9	+	1.27820e9i	0.0958694	+	0.0696532i
$857$	1.19814e10			0.650243			0.325121	−	0.945672i	$-0.394595\pi$
$857$	1.19814e10			0.650243			0.325121	+	0.945672i	$0.394595\pi$
$858$		0			0
$859$	2.41476e10			1.29987			0.649933	−	0.759992i	$-0.274797\pi$
$859$	2.41476e10			1.29987			0.649933	+	0.759992i	$0.274797\pi$
$860$	1.51109e10	+	1.09787e10i	0.810111	+	0.588580i
$861$		0			0
$862$	−3.11073e9	−	9.57383e9i	−0.165419	−	0.509108i
$863$	1.27344e10	+	1.75273e10i	0.674434	+	0.928278i	0.999850	−	0.0172924i	$-0.00550463\pi$
$863$	1.27344e10	+	1.75273e10i	0.674434	+	0.928278i	−0.325417	+	0.945571i	$0.605505\pi$
$864$		0			0
$865$	−2.84362e10	+	9.23947e9i	−1.49388	+	0.485390i
$866$	−6.26586e9	+	1.92843e10i	−0.327845	+	1.00900i
$867$		0			0
$868$		−	7.69944e8i		−	0.0399613i
$869$	1.32105e10	−	1.37871e10i	0.682891	−	0.712693i
$870$		0			0
$871$	−2.03303e9	+	2.79823e9i	−0.104251	+	0.143489i
$872$	3.29005e10	+	1.06900e10i	1.68033	+	0.545972i
$873$		0			0
$874$	−2.83011e10	+	2.05620e10i	−1.43388	+	1.04178i
$875$	−9.47843e8	+	6.88648e8i	−0.0478309	+	0.0347512i
$876$		0			0
$877$	1.94812e10	+	6.32983e9i	0.975254	+	0.316879i	0.752935	−	0.658095i	$-0.228637\pi$
$877$	1.94812e10	+	6.32983e9i	0.975254	+	0.316879i	0.222319	+	0.974974i	$0.428637\pi$
$878$	1.93936e10	−	2.66930e10i	0.967003	−	1.33097i
$879$		0			0
$880$	3.73561e8	+	1.80399e8i	0.0184787	+	0.00892369i
$881$			1.62086e10i			0.798602i	0.916820	+	0.399301i	$0.130747\pi$
$881$			1.62086e10i			0.798602i	−0.916820	+	0.399301i	$0.869253\pi$
$882$		0			0
$883$	−5.47591e9	+	1.68531e10i	−0.267667	+	0.823793i	0.723400	+	0.690429i	$0.242578\pi$
$883$	−5.47591e9	+	1.68531e10i	−0.267667	+	0.823793i	−0.991067	+	0.133364i	$0.957422\pi$
$884$	−2.25834e10	+	7.33780e9i	−1.09953	+	0.357259i
$885$		0			0
$886$	−1.32718e9	−	1.82671e9i	−0.0641081	−	0.0882373i
$887$	−2.49531e9	−	7.67977e9i	−0.120058	−	0.369501i	0.872910	−	0.487881i	$-0.162230\pi$
$887$	−2.49531e9	−	7.67977e9i	−0.120058	−	0.369501i	−0.992968	+	0.118380i	$0.962230\pi$
$888$		0			0
$889$	4.93592e7	+	3.58615e7i	0.00235620	+	0.00171188i
$890$	3.74924e10			1.78270
$891$		0			0
$892$	3.02602e10			1.42756
$893$	−2.06617e10	−	1.50116e10i	−0.970927	−	0.705419i
$894$		0			0
$895$	−1.23506e10	−	3.80113e10i	−0.575848	−	1.77228i
$896$	1.70838e9	+	2.35138e9i	0.0793425	+	0.109206i
$897$		0			0
$898$	4.97218e10	−	1.61556e10i	2.29129	−	0.744484i
$899$	−1.03198e9	+	3.17612e9i	−0.0473712	+	0.145793i
$900$		0			0
$901$			9.02363e9i			0.411002i
$902$	−2.98257e10	+	1.60081e10i	−1.35322	+	0.726300i
$903$		0			0
$904$	−1.26399e10	+	1.73974e10i	−0.569056	+	0.783238i
$905$	−3.71862e10	−	1.20825e10i	−1.66768	−	0.541861i
$906$		0			0
$907$	−2.67369e8	+	1.94255e8i	−0.0118983	+	0.00864463i	−0.593719	−	0.804673i	$-0.702341\pi$
$907$	−2.67369e8	+	1.94255e8i	−0.0118983	+	0.00864463i	0.581820	+	0.813317i	$0.302341\pi$
$908$	1.51779e10	−	1.10274e10i	0.672840	−	0.488847i
$909$		0			0
$910$	4.12240e9	+	1.33945e9i	0.181345	+	0.0589225i
$911$	1.58619e10	−	2.18321e10i	0.695092	−	0.956711i	−0.304899	−	0.952385i	$-0.598623\pi$
$911$	1.58619e10	−	2.18321e10i	0.695092	−	0.956711i	0.999991	−	0.00432681i	$-0.00137727\pi$
$912$		0			0
$913$	−1.00823e10	+	5.41139e9i	−0.438443	+	0.235321i
$914$			4.65732e10i			2.01755i
$915$		0			0
$916$	−4.07065e9	+	1.25282e10i	−0.174997	+	0.538584i
$917$	−3.17735e9	+	1.03238e9i	−0.136073	+	0.0442128i
$918$		0			0
$919$	−9.92907e9	−	1.36662e10i	−0.421992	−	0.580822i	0.544100	−	0.839021i	$-0.316871\pi$
$919$	−9.92907e9	−	1.36662e10i	−0.421992	−	0.580822i	−0.966092	+	0.258198i	$0.916871\pi$
$920$	1.29199e10	+	3.97635e10i	0.547019	+	1.68355i
$921$		0			0
$922$	−2.12376e10	−	1.54300e10i	−0.892374	−	0.648347i
$923$	3.32604e10			1.39227
$924$		0			0
$925$	−1.27297e9			−0.0528839
$926$	−5.37146e10	−	3.90259e10i	−2.22307	−	1.61516i
$927$		0			0
$928$	−3.96348e9	−	1.21983e10i	−0.162802	−	0.501052i
$929$	1.09518e10	+	1.50739e10i	0.448158	+	0.616836i	0.972000	−	0.234979i	$-0.0755021\pi$
$929$	1.09518e10	+	1.50739e10i	0.448158	+	0.616836i	−0.523843	+	0.851815i	$0.675502\pi$
$930$		0			0
$931$	1.68555e10	−	5.47668e9i	0.684570	−	0.222430i
$932$	1.53739e10	−	4.73159e10i	0.622052	−	1.91448i
$933$		0			0
$934$		−	3.12550e9i		−	0.125518i
$935$	−1.62114e10	−	7.82876e9i	−0.648606	−	0.313222i
$936$		0			0
$937$	−1.01045e9	+	1.39076e9i	−0.0401258	+	0.0552285i	−0.828608	−	0.559829i	$-0.810867\pi$
$937$	−1.01045e9	+	1.39076e9i	−0.0401258	+	0.0552285i	0.788483	+	0.615057i	$0.210867\pi$
$938$	−4.89965e8	−	1.59199e8i	−0.0193845	−	0.00629841i
$939$		0			0
$940$	−6.51589e10	+	4.73407e10i	−2.55874	+	1.85903i
$941$	−2.17714e10	+	1.58178e10i	−0.851770	+	0.618847i	−0.925634	−	0.378421i	$-0.876467\pi$
$941$	−2.17714e10	+	1.58178e10i	−0.851770	+	0.618847i	0.0738634	+	0.997268i	$0.476467\pi$
$942$		0			0
$943$	3.52298e10	+	1.14469e10i	1.36810	+	0.444524i
$944$	−3.27366e8	+	4.50580e8i	−0.0126658	+	0.0174329i
$945$		0			0
$946$	−1.52554e10	+	1.59212e10i	−0.585876	+	0.611445i
$947$			9.04420e9i			0.346055i	0.984917	+	0.173028i	$0.0553550\pi$
$947$			9.04420e9i			0.346055i	−0.984917	+	0.173028i	$0.944645\pi$
$948$		0			0
$949$	−3.60200e9	+	1.10858e10i	−0.136808	+	0.421052i
$950$	−1.19974e10	+	3.89818e9i	−0.453997	+	0.147512i
$951$		0			0
$952$	−7.87879e8	−	1.08442e9i	−0.0295958	−	0.0407351i
$953$	−1.26592e10	−	3.89609e10i	−0.473784	−	1.45816i	−0.847591	−	0.530650i	$-0.821948\pi$
$953$	−1.26592e10	−	3.89609e10i	−0.473784	−	1.45816i	0.373808	−	0.927506i	$-0.378052\pi$
$954$		0			0
$955$	−2.72019e10	−	1.97634e10i	−1.01062	−	0.734259i
$956$	−4.54772e10			−1.68342
$957$		0			0
$958$	−4.41043e10			−1.62069
$959$	−3.52327e9	−	2.55981e9i	−0.128997	−	0.0937221i
$960$		0			0
$961$	−7.76187e9	−	2.38886e10i	−0.282120	−	0.868277i
$962$	−4.02371e9	−	5.53817e9i	−0.145718	−	0.200564i
$963$		0			0
$964$	6.19869e10	−	2.01408e10i	2.22859	−	0.724113i
$965$	1.78478e9	−	5.49299e9i	0.0639351	−	0.196772i
$966$		0			0
$967$		−	4.69073e10i		−	1.66820i	−0.551615	−	0.834099i	$-0.685988\pi$
$967$		−	4.69073e10i		−	1.66820i	0.551615	−	0.834099i	$-0.314012\pi$
$968$	1.53790e10	−	2.31883e10i	0.544961	−	0.821685i
$969$		0			0
$970$	−3.25464e10	+	4.47963e10i	−1.14499	+	1.57594i
$971$	2.39702e9	+	7.78839e8i	0.0840242	+	0.0273011i	0.350727	−	0.936478i	$-0.385934\pi$
$971$	2.39702e9	+	7.78839e8i	0.0840242	+	0.0273011i	−0.266703	+	0.963779i	$0.585934\pi$
$972$		0			0
$973$	−1.62482e9	+	1.18050e9i	−0.0565471	+	0.0410839i
$974$	−5.57560e10	+	4.05091e10i	−1.93346	+	1.40474i
$975$		0			0
$976$	6.39957e8	+	2.07935e8i	0.0220331	+	0.00715900i
$977$	−1.00014e10	+	1.37657e10i	−0.343107	+	0.472246i	−0.945346	−	0.326070i	$-0.894276\pi$
$977$	−1.00014e10	+	1.37657e10i	−0.343107	+	0.472246i	0.602239	+	0.798316i	$0.294276\pi$
$978$		0			0
$979$	−3.69466e9	+	2.70537e10i	−0.125845	+	0.921483i
$980$		−	5.58911e10i		−	1.89693i
$981$		0			0
$982$	−2.11868e10	+	6.52064e10i	−0.713963	+	2.19735i
$983$	−1.43943e10	+	4.67700e9i	−0.483342	+	0.157047i	−0.540545	−	0.841315i	$-0.681782\pi$
$983$	−1.43943e10	+	4.67700e9i	−0.483342	+	0.157047i	0.0572029	+	0.998363i	$0.481782\pi$
$984$		0			0
$985$	2.48946e8	+	3.42645e8i	0.00830001	+	0.0114240i
$986$	4.74057e9	+	1.45900e10i	0.157493	+	0.484714i
$987$		0			0
$988$	−3.38563e10	−	2.45980e10i	−1.11684	−	0.811430i
$989$	2.41300e10			0.793177
$990$		0			0
$991$	4.77104e10			1.55724			0.778619	−	0.627497i	$-0.215921\pi$
$991$	4.77104e10			1.55724			0.778619	+	0.627497i	$0.215921\pi$
$992$	−7.44065e9	−	5.40595e9i	−0.242003	−	0.175825i
$993$		0			0
$994$	1.53089e9	+	4.71159e9i	0.0494415	+	0.152165i
$995$	3.69176e10	+	5.08128e10i	1.18810	+	1.63528i
$996$		0			0
$997$	−3.85321e10	+	1.25198e10i	−1.23137	+	0.400098i	−0.851212	−	0.524822i	$-0.824132\pi$
$997$	−3.85321e10	+	1.25198e10i	−1.23137	+	0.400098i	−0.380162	+	0.924920i	$0.624132\pi$
$998$	−2.74851e10	+	8.45904e10i	−0.875266	+	2.69379i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.8.j.a.62.4	yes	112
3.2	odd	2	inner	99.8.j.a.62.25	yes	112
11.8	odd	10	inner	99.8.j.a.8.25	yes	112
33.8	even	10	inner	99.8.j.a.8.4	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.8.j.a.8.4	✓	112	33.8	even	10	inner
99.8.j.a.8.25	yes	112	11.8	odd	10	inner
99.8.j.a.62.4	yes	112	1.1	even	1	trivial
99.8.j.a.62.25	yes	112	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	99.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.7879 - 10.7440i) q^{2} +(63.6930 + 196.027i) q^{4} +(194.917 + 268.280i) q^{5} +(-72.5991 + 23.5889i) q^{7} +(441.228 - 1357.96i) q^{8} -6061.48i q^{10} +(4373.83 + 597.324i) q^{11} +(5506.28 - 7578.75i) q^{13} +(1327.03 + 431.177i) q^{14} +(229.262 - 166.569i) q^{16} +(-9949.29 + 7228.58i) q^{17} +(-20612.9 - 6697.54i) q^{19} +(-40175.3 + 55296.5i) q^{20} +(-58261.9 - 55825.6i) q^{22} +88301.0i q^{23} +(-9839.67 + 30283.4i) q^{25} +(-162852. + 52913.9i) q^{26} +(-9248.11 - 12728.9i) q^{28} +(21088.6 + 64904.1i) q^{29} +(39589.7 + 28763.6i) q^{31} -187944. q^{32} +224793. q^{34} +(-20479.2 - 14879.0i) q^{35} +(12353.9 + 38021.3i) q^{37} +(232862. + 320508. i) q^{38} +(450317. - 146317. i) q^{40} +(129634. - 398974. i) q^{41} -273270. i q^{43} +(161491. + 895433. i) q^{44} +(948707. - 1.30578e6i) q^{46} +(1.12068e6 + 364132. i) q^{47} +(-661546. + 480641. i) q^{49} +(470873. - 342109. i) q^{50} +(1.83635e6 + 596666. i) q^{52} +(431286. - 593614. i) q^{53} +(692283. + 1.28984e6i) q^{55} +108995. i q^{56} +(385475. - 1.18637e6i) q^{58} +(-1.86916e6 + 607326. i) q^{59} +(1.39569e6 + 1.92100e6i) q^{61} +(-276411. - 850705. i) q^{62} +(2.74995e6 + 1.99795e6i) q^{64} +3.10649e6 q^{65} -369220. q^{67} +(-2.05070e6 - 1.48992e6i) q^{68} +(142984. + 440058. i) q^{70} +(2.08693e6 + 2.87241e6i) q^{71} +(-1.18339e6 + 384506. i) q^{73} +(225814. - 694984. i) q^{74} -4.46727e6i q^{76} +(-331626. + 59808.5i) q^{77} +(2.54246e6 - 3.49939e6i) q^{79} +(89374.2 + 29039.4i) q^{80} +(-6.20360e6 + 4.50718e6i) q^{82} +(-2.09707e6 + 1.52361e6i) q^{83} +(-3.87857e6 - 1.26022e6i) q^{85} +(-2.93601e6 + 4.04107e6i) q^{86} +(2.74100e6 - 5.67593e6i) q^{88} +6.18536e6i q^{89} +(-220977. + 680097. i) q^{91} +(-1.73094e7 + 5.62416e6i) q^{92} +(-1.26603e7 - 1.74254e7i) q^{94} +(-2.22099e6 - 6.83550e6i) q^{95} +(-7.39031e6 - 5.36938e6i) q^{97} +1.49469e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 1792 q^{4} - 134096 q^{16} + 401484 q^{22} - 68552 q^{25} + 1493020 q^{28} - 398144 q^{31} - 729944 q^{34} + 685476 q^{37} - 399360 q^{40} - 1410880 q^{46} + 2923872 q^{49} + 6472520 q^{52} + 1445488 q^{55}+ \cdots - 27695460 q^{97}+O(q^{100}) \) 112 * q - 1792 * q^4 - 134096 * q^16 + 401484 * q^22 - 68552 * q^25 + 1493020 * q^28 - 398144 * q^31 - 729944 * q^34 + 685476 * q^37 - 399360 * q^40 - 1410880 * q^46 + 2923872 * q^49 + 6472520 * q^52 + 1445488 * q^55 + 13215936 * q^58 - 7843440 * q^61 - 12806712 * q^64 + 1864032 * q^67 - 1233728 * q^70 + 53841940 * q^73 - 53845440 * q^79 - 36360204 * q^82 + 41703500 * q^85 + 21474024 * q^88 + 27611736 * q^91 - 94707560 * q^94 - 27695460 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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