LMFDB - Embedded newform 60.7.k.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(13,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("60.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.k (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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 66x^{10} + 1601x^{8} + 17520x^{6} + 84208x^{4} + 136704x^{2} + 14400 $ x^12 + 66x^10 + 1601x^8 + 17520x^6 + 84208x^4 + 136704*x^2 + 14400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{19}\cdot 3^{10}\cdot 5^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.3
Root			$1.70867i$ of defining polynomial
Character	$\chi$	$=$	60.13
Dual form			60.7.k.a.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.0227 - 11.0227i) q^{3} +(123.592 - 18.7066i) q^{5} +(-26.9845 + 26.9845i) q^{7} +243.000i q^{9} +O(q^{10})$	\(q+(-11.0227 - 11.0227i) q^{3} +(123.592 - 18.7066i) q^{5} +(-26.9845 + 26.9845i) q^{7} +243.000i q^{9} +307.790 q^{11} +(-195.251 - 195.251i) q^{13} +(-1568.52 - 1156.12i) q^{15} +(6501.62 - 6501.62i) q^{17} -10040.9i q^{19} +594.884 q^{21} +(-6827.82 - 6827.82i) q^{23} +(14925.1 - 4623.99i) q^{25} +(2678.52 - 2678.52i) q^{27} -1771.39i q^{29} +4118.74 q^{31} +(-3392.68 - 3392.68i) q^{33} +(-2830.29 + 3839.86i) q^{35} +(54046.2 - 54046.2i) q^{37} +4304.38i q^{39} -56328.0 q^{41} +(2576.35 + 2576.35i) q^{43} +(4545.71 + 30032.9i) q^{45} +(-48200.0 + 48200.0i) q^{47} +116193. i q^{49} -143331. q^{51} +(42413.8 + 42413.8i) q^{53} +(38040.5 - 5757.71i) q^{55} +(-110678. + 110678. i) q^{57} +255171. i q^{59} +128835. q^{61} +(-6557.23 - 6557.23i) q^{63} +(-27784.0 - 20479.0i) q^{65} +(185918. - 185918. i) q^{67} +150522. i q^{69} -550828. q^{71} +(438496. + 438496. i) q^{73} +(-215484. - 113546. i) q^{75} +(-8305.55 + 8305.55i) q^{77} -626890. i q^{79} -59049.0 q^{81} +(-99263.9 - 99263.9i) q^{83} +(681927. - 925173. i) q^{85} +(-19525.5 + 19525.5i) q^{87} +180438. i q^{89} +10537.5 q^{91} +(-45399.7 - 45399.7i) q^{93} +(-187831. - 1.24098e6i) q^{95} +(938737. - 938737. i) q^{97} +74792.9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 312 q^{5} + 120 q^{7}+O(q^{10}) $ 12 * q + 312 * q^5 + 120 * q^7	$ 12 q + 312 q^{5} + 120 q^{7} - 3248 q^{11} - 2100 q^{13} + 4536 q^{15} - 5540 q^{17} - 15552 q^{21} - 23840 q^{23} + 10044 q^{25} - 127152 q^{31} - 35640 q^{33} + 102976 q^{35} + 282900 q^{37} - 320720 q^{41} - 62880 q^{43} - 10692 q^{45} + 381600 q^{47} - 145152 q^{51} - 400300 q^{53} + 502152 q^{55} - 38880 q^{57} + 807024 q^{61} + 29160 q^{63} + 124500 q^{65} + 752160 q^{67} + 202400 q^{71} - 322020 q^{73} - 645408 q^{75} - 2448400 q^{77} - 708588 q^{81} + 1894560 q^{83} - 857124 q^{85} - 1007640 q^{87} + 2294400 q^{91} + 835920 q^{93} - 2620000 q^{95} - 3161700 q^{97}+O(q^{100}) $ 12 * q + 312 * q^5 + 120 * q^7 - 3248 * q^11 - 2100 * q^13 + 4536 * q^15 - 5540 * q^17 - 15552 * q^21 - 23840 * q^23 + 10044 * q^25 - 127152 * q^31 - 35640 * q^33 + 102976 * q^35 + 282900 * q^37 - 320720 * q^41 - 62880 * q^43 - 10692 * q^45 + 381600 * q^47 - 145152 * q^51 - 400300 * q^53 + 502152 * q^55 - 38880 * q^57 + 807024 * q^61 + 29160 * q^63 + 124500 * q^65 + 752160 * q^67 + 202400 * q^71 - 322020 * q^73 - 645408 * q^75 - 2448400 * q^77 - 708588 * q^81 + 1894560 * q^83 - 857124 * q^85 - 1007640 * q^87 + 2294400 * q^91 + 835920 * q^93 - 2620000 * q^95 - 3161700 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−11.0227	−	11.0227i	−0.408248	−	0.408248i
$3$	−11.0227	−	11.0227i	−0.408248	−	0.408248i
$4$		0			0
$5$	123.592	−	18.7066i	0.988739	−	0.149653i
$5$	123.592	−	18.7066i	0.988739	−	0.149653i
$6$		0			0
$7$	−26.9845	+	26.9845i	−0.0786720	+	0.0786720i	−0.745348	−	0.666676i	$-0.767717\pi$
$7$	−26.9845	+	26.9845i	−0.0786720	+	0.0786720i	0.666676	+	0.745348i	$0.267717\pi$
$8$		0			0
$9$			243.000i			0.333333i
$10$		0			0
$11$	307.790			0.231247			0.115624	−	0.993293i	$-0.463113\pi$
$11$	307.790			0.231247			0.115624	+	0.993293i	$0.463113\pi$
$12$		0			0
$13$	−195.251	−	195.251i	−0.0888715	−	0.0888715i	0.661273	−	0.750145i	$-0.270016\pi$
$13$	−195.251	−	195.251i	−0.0888715	−	0.0888715i	−0.750145	+	0.661273i	$0.770016\pi$
$14$		0			0
$15$	−1568.52	−	1156.12i	−0.464746	−	0.342555i
$16$		0			0
$17$	6501.62	−	6501.62i	1.32335	−	1.32335i	0.412302	−	0.911047i	$-0.364725\pi$
$17$	6501.62	−	6501.62i	1.32335	−	1.32335i	0.911047	−	0.412302i	$-0.135275\pi$
$18$		0			0
$19$		−	10040.9i		−	1.46390i	−0.681359	−	0.731950i	$-0.738611\pi$
$19$		−	10040.9i		−	1.46390i	0.681359	−	0.731950i	$-0.261389\pi$
$20$		0			0
$21$	594.884			0.0642354
$22$		0			0
$23$	−6827.82	−	6827.82i	−0.561175	−	0.561175i	0.368466	−	0.929641i	$-0.379883\pi$
$23$	−6827.82	−	6827.82i	−0.561175	−	0.561175i	−0.929641	+	0.368466i	$0.879883\pi$
$24$		0			0
$25$	14925.1	−	4623.99i	0.955208	−	0.295935i
$26$		0			0
$27$	2678.52	−	2678.52i	0.136083	−	0.136083i
$28$		0			0
$29$		−	1771.39i		−	0.0726305i	−0.999340	−	0.0363153i	$-0.988438\pi$
$29$		−	1771.39i		−	0.0726305i	0.999340	−	0.0363153i	$-0.0115621\pi$
$30$		0			0
$31$	4118.74			0.138255			0.0691273	−	0.997608i	$-0.477979\pi$
$31$	4118.74			0.138255			0.0691273	+	0.997608i	$0.477979\pi$
$32$		0			0
$33$	−3392.68	−	3392.68i	−0.0944062	−	0.0944062i
$34$		0			0
$35$	−2830.29	+	3839.86i	−0.0660125	+	0.0895595i
$36$		0			0
$37$	54046.2	−	54046.2i	1.06699	−	1.06699i	0.0693993	−	0.997589i	$-0.477892\pi$
$37$	54046.2	−	54046.2i	1.06699	−	1.06699i	0.997589	−	0.0693993i	$-0.0221082\pi$
$38$		0			0
$39$			4304.38i			0.0725633i
$40$		0			0
$41$	−56328.0			−0.817284			−0.408642	−	0.912695i	$-0.633998\pi$
$41$	−56328.0			−0.817284			−0.408642	+	0.912695i	$0.633998\pi$
$42$		0			0
$43$	2576.35	+	2576.35i	0.0324040	+	0.0324040i	0.723123	−	0.690719i	$-0.242706\pi$
$43$	2576.35	+	2576.35i	0.0324040	+	0.0324040i	−0.690719	+	0.723123i	$0.742706\pi$
$44$		0			0
$45$	4545.71	+	30032.9i	0.0498843	+	0.329580i
$46$		0			0
$47$	−48200.0	+	48200.0i	−0.464252	+	0.464252i	−0.900046	−	0.435794i	$-0.856467\pi$
$47$	−48200.0	+	48200.0i	−0.464252	+	0.464252i	0.435794	+	0.900046i	$0.356467\pi$
$48$		0			0
$49$			116193.i			0.987621i
$50$		0			0
$51$	−143331.			−1.08051
$52$		0			0
$53$	42413.8	+	42413.8i	0.284891	+	0.284891i	0.835056	−	0.550165i	$-0.185435\pi$
$53$	42413.8	+	42413.8i	0.284891	+	0.284891i	−0.550165	+	0.835056i	$0.685435\pi$
$54$		0			0
$55$	38040.5	−	5757.71i	0.228643	−	0.0346068i
$56$		0			0
$57$	−110678.	+	110678.i	−0.597634	+	0.597634i
$58$		0			0
$59$			255171.i			1.24244i	0.783637	+	0.621219i	$0.213362\pi$
$59$			255171.i			1.24244i	−0.783637	+	0.621219i	$0.786638\pi$
$60$		0			0
$61$	128835.			0.567603			0.283801	−	0.958883i	$-0.408404\pi$
$61$	128835.			0.567603			0.283801	+	0.958883i	$0.408404\pi$
$62$		0			0
$63$	−6557.23	−	6557.23i	−0.0262240	−	0.0262240i
$64$		0			0
$65$	−27784.0	−	20479.0i	−0.101171	−	0.0745708i
$66$		0			0
$67$	185918.	−	185918.i	0.618154	−	0.618154i	−0.326903	−	0.945058i	$-0.606005\pi$
$67$	185918.	−	185918.i	0.618154	−	0.618154i	0.945058	+	0.326903i	$0.106005\pi$
$68$		0			0
$69$			150522.i			0.458198i
$70$		0			0
$71$	−550828.			−1.53901			−0.769504	−	0.638642i	$-0.779497\pi$
$71$	−550828.			−1.53901			−0.769504	+	0.638642i	$0.779497\pi$
$72$		0			0
$73$	438496.	+	438496.i	1.12719	+	1.12719i	0.990632	+	0.136558i	$0.0436039\pi$
$73$	438496.	+	438496.i	1.12719	+	1.12719i	0.136558	+	0.990632i	$0.456396\pi$
$74$		0			0
$75$	−215484.	−	113546.i	−0.510777	−	0.269147i
$76$		0			0
$77$	−8305.55	+	8305.55i	−0.0181927	+	0.0181927i
$78$		0			0
$79$		−	626890.i		−	1.27148i	−0.771903	−	0.635740i	$-0.780695\pi$
$79$		−	626890.i		−	1.27148i	0.771903	−	0.635740i	$-0.219305\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	−99263.9	−	99263.9i	−0.173603	−	0.173603i	0.614957	−	0.788560i	$-0.289173\pi$
$83$	−99263.9	−	99263.9i	−0.173603	−	0.173603i	−0.788560	+	0.614957i	$0.789173\pi$
$84$		0			0
$85$	681927.	−	925173.i	1.11040	−	1.50649i
$86$		0			0
$87$	−19525.5	+	19525.5i	−0.0296513	+	0.0296513i
$88$		0			0
$89$			180438.i			0.255952i	0.991777	+	0.127976i	$0.0408481\pi$
$89$			180438.i			0.255952i	−0.991777	+	0.127976i	$0.959152\pi$
$90$		0			0
$91$	10537.5			0.0139834
$92$		0			0
$93$	−45399.7	−	45399.7i	−0.0564422	−	0.0564422i
$94$		0			0
$95$	−187831.	−	1.24098e6i	−0.219077	−	1.44741i
$96$		0			0
$97$	938737.	−	938737.i	1.02856	−	1.02856i	0.0289774	−	0.999580i	$-0.490775\pi$
$97$	938737.	−	938737.i	1.02856	−	1.02856i	0.999580	−	0.0289774i	$-0.00922508\pi$
$98$		0			0
$99$			74792.9i			0.0770824i
$100$		0			0
$101$	−16806.0			−0.0163118			−0.00815588	−	0.999967i	$-0.502596\pi$
$101$	−16806.0			−0.0163118			−0.00815588	+	0.999967i	$0.502596\pi$
$102$		0			0
$103$	456492.	+	456492.i	0.417754	+	0.417754i	0.884429	−	0.466675i	$-0.154548\pi$
$103$	456492.	+	456492.i	0.417754	+	0.417754i	−0.466675	+	0.884429i	$0.654548\pi$
$104$		0			0
$105$	73523.1	−	11128.3i	0.0635120	−	0.00961302i
$106$		0			0
$107$	−14152.1	+	14152.1i	−0.0115523	+	0.0115523i	−0.712859	−	0.701307i	$-0.752600\pi$
$107$	−14152.1	+	14152.1i	−0.0115523	+	0.0115523i	0.701307	+	0.712859i	$0.252600\pi$
$108$		0			0
$109$			1.15380e6i			0.890949i	0.895295	+	0.445474i	$0.146965\pi$
$109$			1.15380e6i			0.890949i	−0.895295	+	0.445474i	$0.853035\pi$
$110$		0			0
$111$	−1.19147e6			−0.871192
$112$		0			0
$113$	1.25927e6	+	1.25927e6i	0.872734	+	0.872734i	0.992770	−	0.120036i	$-0.0383009\pi$
$113$	1.25927e6	+	1.25927e6i	0.872734	+	0.872734i	−0.120036	+	0.992770i	$0.538301\pi$
$114$		0			0
$115$	−971592.	−	716141.i	−0.638837	−	0.470874i
$116$		0			0
$117$	47445.9	−	47445.9i	0.0296238	−	0.0296238i
$118$		0			0
$119$			350885.i			0.208221i
$120$		0			0
$121$	−1.67683e6			−0.946525
$122$		0			0
$123$	620887.	+	620887.i	0.333655	+	0.333655i
$124$		0			0
$125$	1.75813e6	−	850688.i	0.900163	−	0.435552i
$126$		0			0
$127$	−404592.	+	404592.i	−0.197518	+	0.197518i	−0.798935	−	0.601417i	$-0.794603\pi$
$127$	−404592.	+	404592.i	−0.197518	+	0.197518i	0.601417	+	0.798935i	$0.294603\pi$
$128$		0			0
$129$		−	56796.6i		−	0.0264578i
$130$		0			0
$131$	−3.43393e6			−1.52749			−0.763743	−	0.645520i	$-0.776641\pi$
$131$	−3.43393e6			−1.52749			−0.763743	+	0.645520i	$0.776641\pi$
$132$		0			0
$133$	270948.	+	270948.i	0.115168	+	0.115168i
$134$		0			0
$135$	280938.	−	381150.i	0.114185	−	0.154915i
$136$		0			0
$137$	−12503.2	+	12503.2i	−0.00486250	+	0.00486250i	−0.709534	−	0.704671i	$-0.751094\pi$
$137$	−12503.2	+	12503.2i	−0.00486250	+	0.00486250i	0.704671	+	0.709534i	$0.251094\pi$
$138$		0			0
$139$			4.30496e6i			1.60297i	0.598016	+	0.801484i	$0.295956\pi$
$139$			4.30496e6i			1.60297i	−0.598016	+	0.801484i	$0.704044\pi$
$140$		0			0
$141$	1.06259e6			0.379060
$142$		0			0
$143$	−60096.2	−	60096.2i	−0.0205513	−	0.0205513i
$144$		0			0
$145$	−33136.6	−	218930.i	−0.0108694	−	0.0718126i
$146$		0			0
$147$	1.28076e6	−	1.28076e6i	0.403195	−	0.403195i
$148$		0			0
$149$			5.77835e6i			1.74681i	0.486996	+	0.873404i	$0.338093\pi$
$149$			5.77835e6i			1.74681i	−0.486996	+	0.873404i	$0.661907\pi$
$150$		0			0
$151$	−6.61742e6			−1.92202			−0.961010	−	0.276514i	$-0.910821\pi$
$151$	−6.61742e6			−1.92202			−0.961010	+	0.276514i	$0.910821\pi$
$152$		0			0
$153$	1.57989e6	+	1.57989e6i	0.441116	+	0.441116i
$154$		0			0
$155$	509045.	−	77047.7i	0.136698	−	0.0206902i
$156$		0			0
$157$	−2.12605e6	+	2.12605e6i	−0.549382	+	0.549382i	−0.926262	−	0.376880i	$-0.876997\pi$
$157$	−2.12605e6	+	2.12605e6i	−0.549382	+	0.549382i	0.376880	+	0.926262i	$0.376997\pi$
$158$		0			0
$159$		−	935029.i		−	0.232613i
$160$		0			0
$161$	368490.			0.0882975
$162$		0			0
$163$	2.99274e6	+	2.99274e6i	0.691044	+	0.691044i	0.962462	−	0.271417i	$-0.0874924\pi$
$163$	2.99274e6	+	2.99274e6i	0.691044	+	0.691044i	−0.271417	+	0.962462i	$0.587492\pi$
$164$		0			0
$165$	−482774.	−	355843.i	−0.107471	−	0.0792149i
$166$		0			0
$167$	4.92029e6	−	4.92029e6i	1.05643	−	1.05643i	0.0581209	−	0.998310i	$-0.481489\pi$
$167$	4.92029e6	−	4.92029e6i	1.05643	−	1.05643i	0.998310	−	0.0581209i	$-0.0185109\pi$
$168$		0			0
$169$		−	4.75056e6i		−	0.984204i
$170$		0			0
$171$	2.43994e6			0.487966
$172$		0			0
$173$	−2.26890e6	−	2.26890e6i	−0.438204	−	0.438204i	0.453203	−	0.891407i	$-0.350281\pi$
$173$	−2.26890e6	−	2.26890e6i	−0.438204	−	0.438204i	−0.891407	+	0.453203i	$0.850281\pi$
$174$		0			0
$175$	−277971.	+	527523.i	−0.0518663	+	0.0984299i
$176$		0			0
$177$	2.81267e6	−	2.81267e6i	0.507223	−	0.507223i
$178$		0			0
$179$		−	3.32550e6i		−	0.579827i	−0.957053	−	0.289913i	$-0.906374\pi$
$179$		−	3.32550e6i		−	0.579827i	0.957053	−	0.289913i	$-0.0936265\pi$
$180$		0			0
$181$	−7.03508e6			−1.18641			−0.593203	−	0.805053i	$-0.702137\pi$
$181$	−7.03508e6			−1.18641			−0.593203	+	0.805053i	$0.702137\pi$
$182$		0			0
$183$	−1.42011e6	−	1.42011e6i	−0.231723	−	0.231723i
$184$		0			0
$185$	5.66867e6	−	7.69071e6i	0.895294	−	1.21465i
$186$		0			0
$187$	2.00113e6	−	2.00113e6i	0.306021	−	0.306021i
$188$		0			0
$189$			144557.i			0.0214118i
$190$		0			0
$191$	1.13949e7			1.63534			0.817672	−	0.575684i	$-0.195264\pi$
$191$	1.13949e7			1.63534			0.817672	+	0.575684i	$0.195264\pi$
$192$		0			0
$193$	−6.94705e6	−	6.94705e6i	−0.966337	−	0.966337i	0.0331146	−	0.999452i	$-0.489457\pi$
$193$	−6.94705e6	−	6.94705e6i	−0.966337	−	0.966337i	−0.999452	+	0.0331146i	$0.989457\pi$
$194$		0			0
$195$	80520.4	+	531988.i	0.0108593	+	0.0717461i
$196$		0			0
$197$	−3.18121e6	+	3.18121e6i	−0.416096	+	0.416096i	−0.883856	−	0.467760i	$-0.845061\pi$
$197$	−3.18121e6	+	3.18121e6i	−0.416096	+	0.416096i	0.467760	+	0.883856i	$0.345061\pi$
$198$		0			0
$199$			2.65517e6i			0.336925i	0.985708	+	0.168462i	$0.0538801\pi$
$199$			2.65517e6i			0.336925i	−0.985708	+	0.168462i	$0.946120\pi$
$200$		0			0
$201$	−4.09864e6			−0.504721
$202$		0			0
$203$	47799.9	+	47799.9i	0.00571399	+	0.00571399i
$204$		0			0
$205$	−6.96171e6	+	1.05371e6i	−0.808080	+	0.122309i
$206$		0			0
$207$	1.65916e6	−	1.65916e6i	0.187058	−	0.187058i
$208$		0			0
$209$		−	3.09048e6i		−	0.338523i
$210$		0			0
$211$	1.09828e7			1.16914			0.584569	−	0.811344i	$-0.301263\pi$
$211$	1.09828e7			1.16914			0.584569	+	0.811344i	$0.301263\pi$
$212$		0			0
$213$	6.07162e6	+	6.07162e6i	0.628298	+	0.628298i
$214$		0			0
$215$	366611.	+	270222.i	0.0368885	+	0.0271898i
$216$		0			0
$217$	−111142.	+	111142.i	−0.0108768	+	0.0108768i
$218$		0			0
$219$		−	9.66682e6i		−	0.920347i
$220$		0			0
$221$	−2.53889e6			−0.235216
$222$		0			0
$223$	1.07233e7	+	1.07233e7i	0.966972	+	0.966972i	0.999472	−	0.0324997i	$-0.0103468\pi$
$223$	1.07233e7	+	1.07233e7i	0.966972	+	0.966972i	−0.0324997	+	0.999472i	$0.510347\pi$
$224$		0			0
$225$	1.12363e6	+	3.62681e6i	0.0986451	+	0.318403i
$226$		0			0
$227$	−1.12056e7	+	1.12056e7i	−0.957985	+	0.957985i	−0.999152	−	0.0411672i	$-0.986892\pi$
$227$	−1.12056e7	+	1.12056e7i	−0.957985	+	0.957985i	0.0411672	+	0.999152i	$0.486892\pi$
$228$		0			0
$229$		−	1.07033e7i		−	0.891274i	−0.895214	−	0.445637i	$-0.852977\pi$
$229$		−	1.07033e7i		−	0.891274i	0.895214	−	0.445637i	$-0.147023\pi$
$230$		0			0
$231$	183099.			0.0148542
$232$		0			0
$233$	−1.08666e7	−	1.08666e7i	−0.859068	−	0.859068i	0.132161	−	0.991228i	$-0.457809\pi$
$233$	−1.08666e7	−	1.08666e7i	−0.859068	−	0.859068i	−0.991228	+	0.132161i	$0.957809\pi$
$234$		0			0
$235$	−5.05549e6	+	6.85881e6i	−0.389547	+	0.528500i
$236$		0			0
$237$	−6.91002e6	+	6.91002e6i	−0.519080	+	0.519080i
$238$		0			0
$239$			1.58235e7i			1.15907i	0.814948	+	0.579534i	$0.196765\pi$
$239$			1.58235e7i			1.15907i	−0.814948	+	0.579534i	$0.803235\pi$
$240$		0			0
$241$	8.96144e6			0.640216			0.320108	−	0.947381i	$-0.396281\pi$
$241$	8.96144e6			0.640216			0.320108	+	0.947381i	$0.396281\pi$
$242$		0			0
$243$	650880.	+	650880.i	0.0453609	+	0.0453609i
$244$		0			0
$245$	2.17357e6	+	1.43605e7i	0.147800	+	0.976499i
$246$		0			0
$247$	−1.96049e6	+	1.96049e6i	−0.130099	+	0.130099i
$248$		0			0
$249$			2.18831e6i			0.141746i
$250$		0			0
$251$	9.04761e6			0.572154			0.286077	−	0.958207i	$-0.407649\pi$
$251$	9.04761e6			0.572154			0.286077	+	0.958207i	$0.407649\pi$
$252$		0			0
$253$	−2.10153e6	−	2.10153e6i	−0.129770	−	0.129770i
$254$		0			0
$255$	−1.77146e7	+	2.68123e6i	−1.06834	+	0.161702i
$256$		0			0
$257$	−1.77613e7	+	1.77613e7i	−1.04635	+	1.04635i	−0.0474756	+	0.998872i	$0.515118\pi$
$257$	−1.77613e7	+	1.77613e7i	−1.04635	+	1.04635i	−0.998872	+	0.0474756i	$0.984882\pi$
$258$		0			0
$259$			2.91682e6i			0.167884i
$260$		0			0
$261$	430447.			0.0242102
$262$		0			0
$263$	−2.23195e7	−	2.23195e7i	−1.22692	−	1.22692i	−0.965122	−	0.261800i	$-0.915684\pi$
$263$	−2.23195e7	−	2.23195e7i	−1.22692	−	1.22692i	−0.261800	−	0.965122i	$-0.584316\pi$
$264$		0			0
$265$	6.03544e6	+	4.44860e6i	0.324318	+	0.239048i
$266$		0			0
$267$	1.98892e6	−	1.98892e6i	0.104492	−	0.104492i
$268$		0			0
$269$			5.22760e6i			0.268563i	0.990943	+	0.134281i	$0.0428726\pi$
$269$			5.22760e6i			0.268563i	−0.990943	+	0.134281i	$0.957127\pi$
$270$		0			0
$271$	2.46355e7			1.23781			0.618904	−	0.785467i	$-0.287577\pi$
$271$	2.46355e7			1.23781			0.618904	+	0.785467i	$0.287577\pi$
$272$		0			0
$273$	−116151.	−	116151.i	−0.00570870	−	0.00570870i
$274$		0			0
$275$	4.59380e6	−	1.42322e6i	0.220889	−	0.0684342i
$276$		0			0
$277$	4.03213e6	−	4.03213e6i	0.189712	−	0.189712i	−0.605860	−	0.795572i	$-0.707171\pi$
$277$	4.03213e6	−	4.03213e6i	0.189712	−	0.189712i	0.795572	+	0.605860i	$0.207171\pi$
$278$		0			0
$279$			1.00085e6i			0.0460848i
$280$		0			0
$281$	2.15050e7			0.969214			0.484607	−	0.874732i	$-0.338963\pi$
$281$	2.15050e7			0.969214			0.484607	+	0.874732i	$0.338963\pi$
$282$		0			0
$283$	7.37561e6	+	7.37561e6i	0.325416	+	0.325416i	0.850840	−	0.525425i	$-0.176093\pi$
$283$	7.37561e6	+	7.37561e6i	0.325416	+	0.325416i	−0.525425	+	0.850840i	$0.676093\pi$
$284$		0			0
$285$	−1.16085e7	+	1.57493e7i	−0.501466	+	0.680342i
$286$		0			0
$287$	1.51998e6	−	1.51998e6i	0.0642973	−	0.0642973i
$288$		0			0
$289$		−	6.04045e7i		−	2.50251i
$290$		0			0
$291$	−2.06948e7			−0.839814
$292$		0			0
$293$	−3.20942e6	−	3.20942e6i	−0.127592	−	0.127592i	0.640427	−	0.768019i	$-0.278757\pi$
$293$	−3.20942e6	−	3.20942e6i	−0.127592	−	0.127592i	−0.768019	+	0.640427i	$0.778757\pi$
$294$		0			0
$295$	4.77338e6	+	3.15371e7i	0.185934	+	1.22845i
$296$		0			0
$297$	824421.	−	824421.i	0.0314687	−	0.0314687i
$298$		0			0
$299$			2.66627e6i			0.0997450i
$300$		0			0
$301$	−139043.			−0.00509858
$302$		0			0
$303$	185248.	+	185248.i	0.00665924	+	0.00665924i
$304$		0			0
$305$	1.59230e7	−	2.41007e6i	0.561211	−	0.0849434i
$306$		0			0
$307$	2.80417e7	−	2.80417e7i	0.969147	−	0.969147i	−0.0303912	−	0.999538i	$-0.509675\pi$
$307$	2.80417e7	−	2.80417e7i	0.969147	−	0.969147i	0.999538	+	0.0303912i	$0.00967532\pi$
$308$		0			0
$309$		−	1.00635e7i		−	0.341095i
$310$		0			0
$311$	2.07079e7			0.688423			0.344212	−	0.938892i	$-0.388146\pi$
$311$	2.07079e7			0.688423			0.344212	+	0.938892i	$0.388146\pi$
$312$		0			0
$313$	−7.78636e6	−	7.78636e6i	−0.253923	−	0.253923i	0.568654	−	0.822577i	$-0.307464\pi$
$313$	−7.78636e6	−	7.78636e6i	−0.253923	−	0.253923i	−0.822577	+	0.568654i	$0.807464\pi$
$314$		0			0
$315$	−933087.	−	687760.i	−0.0298532	−	0.0220042i
$316$		0			0
$317$	−2.05933e7	+	2.05933e7i	−0.646471	+	0.646471i	−0.952138	−	0.305668i	$-0.901120\pi$
$317$	−2.05933e7	+	2.05933e7i	−0.646471	+	0.646471i	0.305668	+	0.952138i	$0.401120\pi$
$318$		0			0
$319$		−	545215.i		−	0.0167956i
$320$		0			0
$321$	311989.			0.00943244
$322$		0			0
$323$	−6.52820e7	−	6.52820e7i	−1.93725	−	1.93725i
$324$		0			0
$325$	−3.81698e6	−	2.01130e6i	−0.111191	−	0.0585906i
$326$		0			0
$327$	1.27180e7	−	1.27180e7i	0.363728	−	0.363728i
$328$		0			0
$329$		−	2.60130e6i		−	0.0730472i
$330$		0			0
$331$	4.26207e7			1.17527			0.587634	−	0.809127i	$-0.300060\pi$
$331$	4.26207e7			1.17527			0.587634	+	0.809127i	$0.300060\pi$
$332$		0			0
$333$	1.31332e7	+	1.31332e7i	0.355663	+	0.355663i
$334$		0			0
$335$	1.95001e7	−	2.64559e7i	0.518684	−	0.703702i
$336$		0			0
$337$	3.66357e7	−	3.66357e7i	0.957227	−	0.957227i	−0.0418955	−	0.999122i	$-0.513340\pi$
$337$	3.66357e7	−	3.66357e7i	0.957227	−	0.957227i	0.999122	+	0.0418955i	$0.0133396\pi$
$338$		0			0
$339$		−	2.77610e7i		−	0.712584i
$340$		0			0
$341$	1.26771e6			0.0319710
$342$		0			0
$343$	−6.31010e6	−	6.31010e6i	−0.156370	−	0.156370i
$344$		0			0
$345$	2.81576e6	+	1.86034e7i	0.0685707	+	0.453038i
$346$		0			0
$347$	−1.89995e7	+	1.89995e7i	−0.454731	+	0.454731i	−0.896921	−	0.442190i	$-0.854202\pi$
$347$	−1.89995e7	+	1.89995e7i	−0.454731	+	0.454731i	0.442190	+	0.896921i	$0.354202\pi$
$348$		0			0
$349$		−	5.04916e6i		−	0.118780i	−0.998235	−	0.0593900i	$-0.981084\pi$
$349$		−	5.04916e6i		−	0.118780i	0.998235	−	0.0593900i	$-0.0189155\pi$
$350$		0			0
$351$	−1.04596e6			−0.0241878
$352$		0			0
$353$	1.01330e7	+	1.01330e7i	0.230363	+	0.230363i	0.812844	−	0.582481i	$-0.197918\pi$
$353$	1.01330e7	+	1.01330e7i	0.230363	+	0.230363i	−0.582481	+	0.812844i	$0.697918\pi$
$354$		0			0
$355$	−6.80781e7	+	1.03041e7i	−1.52168	+	0.230317i
$356$		0			0
$357$	3.86771e6	−	3.86771e6i	0.0850059	−	0.0850059i
$358$		0			0
$359$			2.43745e7i			0.526809i	0.964685	+	0.263405i	$0.0848454\pi$
$359$			2.43745e7i			0.526809i	−0.964685	+	0.263405i	$0.915155\pi$
$360$		0			0
$361$	−5.37735e7			−1.14300
$362$		0			0
$363$	1.84832e7	+	1.84832e7i	0.386417	+	0.386417i
$364$		0			0
$365$	6.23975e7	+	4.59920e7i	1.28318	+	0.945809i
$366$		0			0
$367$	−4.17799e7	+	4.17799e7i	−0.845218	+	0.845218i	−0.989532	−	0.144314i	$-0.953903\pi$
$367$	−4.17799e7	+	4.17799e7i	−0.845218	+	0.845218i	0.144314	+	0.989532i	$0.453903\pi$
$368$		0			0
$369$		−	1.36877e7i		−	0.272428i
$370$		0			0
$371$	−2.28903e6			−0.0448259
$372$		0			0
$373$	5.77466e7	+	5.77466e7i	1.11276	+	1.11276i	0.992776	+	0.119980i	$0.0382829\pi$
$373$	5.77466e7	+	5.77466e7i	1.11276	+	1.11276i	0.119980	+	0.992776i	$0.461717\pi$
$374$		0			0
$375$	−2.87562e7	−	1.00025e7i	−0.545304	−	0.189677i
$376$		0			0
$377$	−345864.	+	345864.i	−0.00645479	+	0.00645479i
$378$		0			0
$379$			7.43599e7i			1.36591i	0.730462	+	0.682953i	$0.239305\pi$
$379$			7.43599e7i			1.36591i	−0.730462	+	0.682953i	$0.760695\pi$
$380$		0			0
$381$	8.91939e6			0.161273
$382$		0			0
$383$	−2.30040e7	−	2.30040e7i	−0.409456	−	0.409456i	0.472093	−	0.881549i	$-0.343499\pi$
$383$	−2.30040e7	−	2.30040e7i	−0.409456	−	0.409456i	−0.881549	+	0.472093i	$0.843499\pi$
$384$		0			0
$385$	−871134.	+	1.18187e6i	−0.0152652	+	0.0207104i
$386$		0			0
$387$	−626052.	+	626052.i	−0.0108013	+	0.0108013i
$388$		0			0
$389$			8.20207e7i			1.39340i	0.717365	+	0.696698i	$0.245348\pi$
$389$			8.20207e7i			1.39340i	−0.717365	+	0.696698i	$0.754652\pi$
$390$		0			0
$391$	−8.87837e7			−1.48526
$392$		0			0
$393$	3.78512e7	+	3.78512e7i	0.623594	+	0.623594i
$394$		0			0
$395$	−1.17270e7	−	7.74787e7i	−0.190281	−	1.25716i
$396$		0			0
$397$	−7.33075e7	+	7.33075e7i	−1.17159	+	1.17159i	−0.189764	+	0.981830i	$0.560772\pi$
$397$	−7.33075e7	+	7.33075e7i	−1.17159	+	1.17159i	−0.981830	+	0.189764i	$0.939228\pi$
$398$		0			0
$399$		−	5.97316e6i		−	0.0940341i
$400$		0			0
$401$	8.91142e7			1.38202			0.691009	−	0.722846i	$-0.257166\pi$
$401$	8.91142e7			1.38202			0.691009	+	0.722846i	$0.257166\pi$
$402$		0			0
$403$	−804187.	−	804187.i	−0.0122869	−	0.0122869i
$404$		0			0
$405$	−7.29800e6	+	1.10461e6i	−0.109860	+	0.0166281i
$406$		0			0
$407$	1.66349e7	−	1.66349e7i	0.246738	−	0.246738i
$408$		0			0
$409$		−	7.65934e7i		−	1.11949i	−0.828664	−	0.559747i	$-0.810898\pi$
$409$		−	7.65934e7i		−	1.11949i	0.828664	−	0.559747i	$-0.189102\pi$
$410$		0			0
$411$	275638.			0.00397021
$412$		0			0
$413$	−6.88564e6	−	6.88564e6i	−0.0977450	−	0.0977450i
$414$		0			0
$415$	−1.41251e7	−	1.04114e7i	−0.197628	−	0.145668i
$416$		0			0
$417$	4.74523e7	−	4.74523e7i	0.654409	−	0.654409i
$418$		0			0
$419$			1.10908e8i			1.50772i	0.657035	+	0.753860i	$0.271811\pi$
$419$			1.10908e8i			1.50772i	−0.657035	+	0.753860i	$0.728189\pi$
$420$		0			0
$421$	−1.05627e8			−1.41557			−0.707784	−	0.706429i	$-0.750305\pi$
$421$	−1.05627e8			−1.41557			−0.707784	+	0.706429i	$0.750305\pi$
$422$		0			0
$423$	−1.17126e7	−	1.17126e7i	−0.154751	−	0.154751i
$424$		0			0
$425$	6.69740e7	−	1.27101e8i	0.872448	−	1.65570i
$426$		0			0
$427$	−3.47655e6	+	3.47655e6i	−0.0446544	+	0.0446544i
$428$		0			0
$429$			1.32484e6i			0.0167800i
$430$		0			0
$431$	−1.07787e7			−0.134627			−0.0673137	−	0.997732i	$-0.521443\pi$
$431$	−1.07787e7			−0.134627			−0.0673137	+	0.997732i	$0.521443\pi$
$432$		0			0
$433$	3.99558e7	+	3.99558e7i	0.492171	+	0.492171i	0.908990	−	0.416819i	$-0.136855\pi$
$433$	3.99558e7	+	3.99558e7i	0.492171	+	0.492171i	−0.416819	+	0.908990i	$0.636855\pi$
$434$		0			0
$435$	−2.04794e6	+	2.77845e6i	−0.0248800	+	0.0337548i
$436$		0			0
$437$	−6.85574e7	+	6.85574e7i	−0.821504	+	0.821504i
$438$		0			0
$439$			2.72322e7i			0.321877i	0.986964	+	0.160938i	$0.0514520\pi$
$439$			2.72322e7i			0.321877i	−0.986964	+	0.160938i	$0.948548\pi$
$440$		0			0
$441$	−2.82348e7			−0.329207
$442$		0			0
$443$	2.19002e7	+	2.19002e7i	0.251905	+	0.251905i	0.821751	−	0.569846i	$-0.192997\pi$
$443$	2.19002e7	+	2.19002e7i	0.251905	+	0.251905i	−0.569846	+	0.821751i	$0.692997\pi$
$444$		0			0
$445$	3.37539e6	+	2.23008e7i	0.0383040	+	0.253070i
$446$		0			0
$447$	6.36931e7	−	6.36931e7i	0.713132	−	0.713132i
$448$		0			0
$449$		−	1.41180e8i		−	1.55967i	−0.625984	−	0.779836i	$-0.715303\pi$
$449$		−	1.41180e8i		−	1.55967i	0.625984	−	0.779836i	$-0.284697\pi$
$450$		0			0
$451$	−1.73372e7			−0.188995
$452$		0			0
$453$	7.29419e7	+	7.29419e7i	0.784661	+	0.784661i
$454$		0			0
$455$	1.30235e6	−	197121.i	0.0138259	−	0.00209266i
$456$		0			0
$457$	6.67208e7	−	6.67208e7i	0.699057	−	0.699057i	−0.265150	−	0.964207i	$-0.585422\pi$
$457$	6.67208e7	−	6.67208e7i	0.699057	−	0.699057i	0.964207	+	0.265150i	$0.0854216\pi$
$458$		0			0
$459$		−	3.48294e7i		−	0.360170i
$460$		0			0
$461$	−1.12338e8			−1.14663			−0.573314	−	0.819336i	$-0.694342\pi$
$461$	−1.12338e8			−1.14663			−0.573314	+	0.819336i	$0.694342\pi$
$462$		0			0
$463$	2.04097e7	+	2.04097e7i	0.205633	+	0.205633i	0.802408	−	0.596775i	$-0.203552\pi$
$463$	2.04097e7	+	2.04097e7i	0.205633	+	0.205633i	−0.596775	+	0.802408i	$0.703552\pi$
$464$		0			0
$465$	−6.46032e6	−	4.76177e6i	−0.0642533	−	0.0473598i
$466$		0			0
$467$	6.59499e7	−	6.59499e7i	0.647536	−	0.647536i	−0.304861	−	0.952397i	$-0.598610\pi$
$467$	6.59499e7	−	6.59499e7i	0.647536	−	0.647536i	0.952397	+	0.304861i	$0.0986101\pi$
$468$		0			0
$469$			1.00338e7i			0.0972628i
$470$		0			0
$471$	4.68696e7			0.448568
$472$		0			0
$473$	792973.	+	792973.i	0.00749334	+	0.00749334i
$474$		0			0
$475$	−4.64289e7	−	1.49861e8i	−0.433219	−	1.39833i
$476$		0			0
$477$	−1.03065e7	+	1.03065e7i	−0.0949638	+	0.0949638i
$478$		0			0
$479$			1.25222e8i			1.13939i	0.821855	+	0.569697i	$0.192939\pi$
$479$			1.25222e8i			1.13939i	−0.821855	+	0.569697i	$0.807061\pi$
$480$		0			0
$481$	−2.11051e7			−0.189650
$482$		0			0
$483$	−4.06176e6	−	4.06176e6i	−0.0360473	−	0.0360473i
$484$		0			0
$485$	9.84601e7	−	1.33581e8i	0.863048	−	1.17090i
$486$		0			0
$487$	1.42869e8	−	1.42869e8i	1.23695	−	1.23695i	0.275702	−	0.961243i	$-0.411090\pi$
$487$	1.42869e8	−	1.42869e8i	1.23695	−	1.23695i	0.961243	−	0.275702i	$-0.0889103\pi$
$488$		0			0
$489$		−	6.59761e7i		−	0.564235i
$490$		0			0
$491$	1.12699e8			0.952083			0.476042	−	0.879423i	$-0.342071\pi$
$491$	1.12699e8			0.952083			0.476042	+	0.879423i	$0.342071\pi$
$492$		0			0
$493$	−1.15169e7	−	1.15169e7i	−0.0961156	−	0.0961156i
$494$		0			0
$495$	1.39912e6	+	9.24383e6i	0.0115356	+	0.0762143i
$496$		0			0
$497$	1.48638e7	−	1.48638e7i	0.121077	−	0.121077i
$498$		0			0
$499$			8.10892e7i			0.652622i	0.945262	+	0.326311i	$0.105806\pi$
$499$			8.10892e7i			0.652622i	−0.945262	+	0.326311i	$0.894194\pi$
$500$		0			0
$501$	−1.08470e8			−0.862572
$502$		0			0
$503$	−1.18247e8	−	1.18247e8i	−0.929149	−	0.929149i	0.0685017	−	0.997651i	$-0.478178\pi$
$503$	−1.18247e8	−	1.18247e8i	−0.929149	−	0.929149i	−0.997651	+	0.0685017i	$0.978178\pi$
$504$		0			0
$505$	−2.07709e6	+	314384.i	−0.0161281	+	0.00244110i
$506$		0			0
$507$	−5.23641e7	+	5.23641e7i	−0.401799	+	0.401799i
$508$		0			0
$509$			9.74725e7i			0.739143i	0.929202	+	0.369572i	$0.120496\pi$
$509$			9.74725e7i			0.739143i	−0.929202	+	0.369572i	$0.879504\pi$
$510$		0			0
$511$	−2.36652e7			−0.177356
$512$		0			0
$513$	−2.68947e7	−	2.68947e7i	−0.199211	−	0.199211i
$514$		0			0
$515$	6.49583e7	+	4.78794e7i	0.475568	+	0.350532i
$516$		0			0
$517$	−1.48355e7	+	1.48355e7i	−0.107357	+	0.107357i
$518$		0			0
$519$			5.00188e7i			0.357792i
$520$		0			0
$521$	−2.46713e8			−1.74453			−0.872267	−	0.489030i	$-0.837351\pi$
$521$	−2.46713e8			−1.74453			−0.872267	+	0.489030i	$0.837351\pi$
$522$		0			0
$523$	1.16274e8	+	1.16274e8i	0.812790	+	0.812790i	0.985051	−	0.172261i	$-0.0551072\pi$
$523$	1.16274e8	+	1.16274e8i	0.812790	+	0.812790i	−0.172261	+	0.985051i	$0.555107\pi$
$524$		0			0
$525$	8.87872e6	−	2.75074e6i	0.0613582	−	0.0190095i
$526$		0			0
$527$	2.67785e7	−	2.67785e7i	0.182959	−	0.182959i
$528$		0			0
$529$		−	5.47976e7i		−	0.370164i
$530$		0			0
$531$	−6.20064e7			−0.414146
$532$		0			0
$533$	1.09981e7	+	1.09981e7i	0.0726333	+	0.0726333i
$534$		0			0
$535$	−1.48435e6	+	2.01383e6i	−0.00969340	+	0.0131511i
$536$		0			0
$537$	−3.66560e7	+	3.66560e7i	−0.236713	+	0.236713i
$538$		0			0
$539$			3.57629e7i			0.228385i
$540$		0			0
$541$	−3.51137e7			−0.221761			−0.110880	−	0.993834i	$-0.535367\pi$
$541$	−3.51137e7			−0.221761			−0.110880	+	0.993834i	$0.535367\pi$
$542$		0			0
$543$	7.75457e7	+	7.75457e7i	0.484349	+	0.484349i
$544$		0			0
$545$	2.15838e7	+	1.42601e8i	0.133333	+	0.880916i
$546$		0			0
$547$	7.31352e7	−	7.31352e7i	0.446853	−	0.446853i	−0.447454	−	0.894307i	$-0.647669\pi$
$547$	7.31352e7	−	7.31352e7i	0.446853	−	0.446853i	0.894307	+	0.447454i	$0.147669\pi$
$548$		0			0
$549$			3.13069e7i			0.189201i
$550$		0			0
$551$	−1.77863e7			−0.106324
$552$		0			0
$553$	1.69163e7	+	1.69163e7i	0.100030	+	0.100030i
$554$		0			0
$555$	−1.47256e8	+	2.22884e7i	−0.861381	+	0.130376i
$556$		0			0
$557$	−1.36802e8	+	1.36802e8i	−0.791639	+	0.791639i	−0.981761	−	0.190121i	$-0.939112\pi$
$557$	−1.36802e8	+	1.36802e8i	−0.791639	+	0.791639i	0.190121	+	0.981761i	$0.439112\pi$
$558$		0			0
$559$		−	1.00607e6i		−	0.00575959i
$560$		0			0
$561$	−4.41158e7			−0.249865
$562$		0			0
$563$	1.31424e8	+	1.31424e8i	0.736459	+	0.736459i	0.971891	−	0.235432i	$-0.0756504\pi$
$563$	1.31424e8	+	1.31424e8i	0.736459	+	0.736459i	−0.235432	+	0.971891i	$0.575650\pi$
$564$		0			0
$565$	1.79192e8	+	1.32079e8i	0.993513	+	0.732298i
$566$		0			0
$567$	1.59341e6	−	1.59341e6i	0.00874133	−	0.00874133i
$568$		0			0
$569$			3.72311e7i			0.202101i	0.994881	+	0.101051i	$0.0322204\pi$
$569$			3.72311e7i			0.202101i	−0.994881	+	0.101051i	$0.967780\pi$
$570$		0			0
$571$	2.11887e8			1.13814			0.569070	−	0.822289i	$-0.307304\pi$
$571$	2.11887e8			1.13814			0.569070	+	0.822289i	$0.307304\pi$
$572$		0			0
$573$	−1.25602e8	−	1.25602e8i	−0.667627	−	0.667627i
$574$		0			0
$575$	−1.33478e8	−	7.03343e7i	−0.702111	−	0.369968i
$576$		0			0
$577$	−7.72403e7	+	7.72403e7i	−0.402084	+	0.402084i	−0.878967	−	0.476883i	$-0.841767\pi$
$577$	−7.72403e7	+	7.72403e7i	−0.402084	+	0.402084i	0.476883	+	0.878967i	$0.341767\pi$
$578$		0			0
$579$			1.53151e8i			0.789011i
$580$		0			0
$581$	5.35717e6			0.0273154
$582$		0			0
$583$	1.30545e7	+	1.30545e7i	0.0658803	+	0.0658803i
$584$		0			0
$585$	4.97640e6	−	6.75150e6i	0.0248569	−	0.0337235i
$586$		0			0
$587$	−1.09847e8	+	1.09847e8i	−0.543091	+	0.543091i	−0.924434	−	0.381343i	$-0.875462\pi$
$587$	−1.09847e8	+	1.09847e8i	−0.543091	+	0.543091i	0.381343	+	0.924434i	$0.375462\pi$
$588$		0			0
$589$		−	4.13558e7i		−	0.202391i
$590$		0			0
$591$	7.01310e7			0.339741
$592$		0			0
$593$	−2.02470e8	−	2.02470e8i	−0.970952	−	0.970952i	0.0286381	−	0.999590i	$-0.490883\pi$
$593$	−2.02470e8	−	2.02470e8i	−0.970952	−	0.970952i	−0.999590	+	0.0286381i	$0.990883\pi$
$594$		0			0
$595$	6.56388e6	+	4.33668e7i	0.0311609	+	0.205876i
$596$		0			0
$597$	2.92671e7	−	2.92671e7i	0.137549	−	0.137549i
$598$		0			0
$599$			3.15157e8i			1.46638i	0.680024	+	0.733190i	$0.261969\pi$
$599$			3.15157e8i			1.46638i	−0.680024	+	0.733190i	$0.738031\pi$
$600$		0			0
$601$	6.38999e7			0.294358			0.147179	−	0.989110i	$-0.452981\pi$
$601$	6.38999e7			0.294358			0.147179	+	0.989110i	$0.452981\pi$
$602$		0			0
$603$	4.51781e7	+	4.51781e7i	0.206051	+	0.206051i
$604$		0			0
$605$	−2.07243e8	+	3.13678e7i	−0.935866	+	0.141650i
$606$		0			0
$607$	6.49112e7	−	6.49112e7i	0.290238	−	0.290238i	−0.546936	−	0.837174i	$-0.684206\pi$
$607$	6.49112e7	−	6.49112e7i	0.290238	−	0.290238i	0.837174	+	0.546936i	$0.184206\pi$
$608$		0			0
$609$		−	1.05377e6i		−	0.00466545i
$610$		0			0
$611$	1.88222e7			0.0825175
$612$		0			0
$613$	2.92180e6	+	2.92180e6i	0.0126844	+	0.0126844i	0.713421	−	0.700736i	$-0.247145\pi$
$613$	2.92180e6	+	2.92180e6i	0.0126844	+	0.0126844i	−0.700736	+	0.713421i	$0.747145\pi$
$614$		0			0
$615$	8.83516e7	+	6.51222e7i	0.379830	+	0.279965i
$616$		0			0
$617$	−1.29053e8	+	1.29053e8i	−0.549432	+	0.549432i	−0.926277	−	0.376844i	$-0.877009\pi$
$617$	−1.29053e8	+	1.29053e8i	−0.549432	+	0.549432i	0.376844	+	0.926277i	$0.377009\pi$
$618$		0			0
$619$		−	3.11757e8i		−	1.31445i	−0.753694	−	0.657226i	$-0.771730\pi$
$619$		−	3.11757e8i		−	1.31445i	0.753694	−	0.657226i	$-0.228270\pi$
$620$		0			0
$621$	−3.65769e7			−0.152733
$622$		0			0
$623$	−4.86904e6	−	4.86904e6i	−0.0201363	−	0.0201363i
$624$		0			0
$625$	2.01378e8	−	1.38027e8i	0.824845	−	0.565360i
$626$		0			0
$627$	−3.40655e7	+	3.40655e7i	−0.138201	+	0.138201i
$628$		0			0
$629$		−	7.02775e8i		−	2.82400i
$630$		0			0
$631$	2.16066e8			0.860001			0.430001	−	0.902829i	$-0.358513\pi$
$631$	2.16066e8			0.860001			0.430001	+	0.902829i	$0.358513\pi$
$632$		0			0
$633$	−1.21060e8	−	1.21060e8i	−0.477299	−	0.477299i
$634$		0			0
$635$	−4.24359e7	+	5.75730e7i	−0.165734	+	0.224852i
$636$		0			0
$637$	2.26867e7	−	2.26867e7i	0.0877714	−	0.0877714i
$638$		0			0
$639$		−	1.33851e8i		−	0.513003i
$640$		0			0
$641$	3.66592e8			1.39190			0.695951	−	0.718089i	$-0.254983\pi$
$641$	3.66592e8			1.39190			0.695951	+	0.718089i	$0.254983\pi$
$642$		0			0
$643$	−2.64305e8	−	2.64305e8i	−0.994198	−	0.994198i	0.00578569	−	0.999983i	$-0.498158\pi$
$643$	−2.64305e8	−	2.64305e8i	−0.994198	−	0.994198i	−0.999983	+	0.00578569i	$0.998158\pi$
$644$		0			0
$645$	−1.06247e6	−	7.01963e6i	−0.00395948	−	0.0261598i
$646$		0			0
$647$	2.97439e8	−	2.97439e8i	1.09821	−	1.09821i	0.103588	−	0.994620i	$-0.466968\pi$
$647$	2.97439e8	−	2.97439e8i	1.09821	−	1.09821i	0.994620	−	0.103588i	$-0.0330324\pi$
$648$		0			0
$649$			7.85389e7i			0.287310i
$650$		0			0
$651$	2.45017e6			0.00888083
$652$		0			0
$653$	2.81052e8	+	2.81052e8i	1.00936	+	1.00936i	0.999956	+	0.00940637i	$0.00299418\pi$
$653$	2.81052e8	+	2.81052e8i	1.00936	+	1.00936i	0.00940637	+	0.999956i	$0.497006\pi$
$654$		0			0
$655$	−4.24407e8	+	6.42372e7i	−1.51028	+	0.228593i
$656$		0			0
$657$	−1.06555e8	+	1.06555e8i	−0.375730	+	0.375730i
$658$		0			0
$659$		−	2.77113e8i		−	0.968279i	−0.874991	−	0.484139i	$-0.839133\pi$
$659$		−	2.77113e8i		−	0.968279i	0.874991	−	0.484139i	$-0.160867\pi$
$660$		0			0
$661$	1.74794e8			0.605233			0.302616	−	0.953112i	$-0.402140\pi$
$661$	1.74794e8			0.605233			0.302616	+	0.953112i	$0.402140\pi$
$662$		0			0
$663$	2.79854e7	+	2.79854e7i	0.0960266	+	0.0960266i
$664$		0			0
$665$	3.85556e7	+	2.84186e7i	0.131106	+	0.0966357i
$666$		0			0
$667$	−1.20947e7	+	1.20947e7i	−0.0407585	+	0.0407585i
$668$		0			0
$669$		−	2.36400e8i		−	0.789529i
$670$		0			0
$671$	3.96541e7			0.131257
$672$		0			0
$673$	7.65952e7	+	7.65952e7i	0.251279	+	0.251279i	0.821495	−	0.570216i	$-0.193140\pi$
$673$	7.65952e7	+	7.65952e7i	0.251279	+	0.251279i	−0.570216	+	0.821495i	$0.693140\pi$
$674$		0			0
$675$	2.75918e7	−	5.23626e7i	0.0897157	−	0.170259i
$676$		0			0
$677$	9.08594e7	−	9.08594e7i	0.292822	−	0.292822i	−0.545372	−	0.838194i	$-0.683612\pi$
$677$	9.08594e7	−	9.08594e7i	0.292822	−	0.292822i	0.838194	+	0.545372i	$0.183612\pi$
$678$		0			0
$679$			5.06626e7i			0.161837i
$680$		0			0
$681$	2.47033e8			0.782192
$682$		0			0
$683$	−2.07323e8	−	2.07323e8i	−0.650705	−	0.650705i	0.302457	−	0.953163i	$-0.402193\pi$
$683$	−2.07323e8	−	2.07323e8i	−0.650705	−	0.650705i	−0.953163	+	0.302457i	$0.902193\pi$
$684$		0			0
$685$	−1.31141e6	+	1.77919e6i	−0.00408005	+	0.00553542i
$686$		0			0
$687$	−1.17979e8	+	1.17979e8i	−0.363861	+	0.363861i
$688$		0			0
$689$		−	1.65626e7i		−	0.0506375i
$690$		0			0
$691$	2.75862e8			0.836100			0.418050	−	0.908424i	$-0.362714\pi$
$691$	2.75862e8			0.836100			0.418050	+	0.908424i	$0.362714\pi$
$692$		0			0
$693$	−2.01825e6	−	2.01825e6i	−0.00606422	−	0.00606422i
$694$		0			0
$695$	8.05313e7	+	5.32060e8i	0.239889	+	1.58492i
$696$		0			0
$697$	−3.66223e8	+	3.66223e8i	−1.08155	+	1.08155i
$698$		0			0
$699$			2.39559e8i			0.701426i
$700$		0			0
$701$	1.02702e8			0.298143			0.149072	−	0.988826i	$-0.452371\pi$
$701$	1.02702e8			0.298143			0.149072	+	0.988826i	$0.452371\pi$
$702$		0			0
$703$	−5.42671e8	−	5.42671e8i	−1.56196	−	1.56196i
$704$		0			0
$705$	1.31328e8	−	1.98774e7i	0.374791	−	0.0567274i
$706$		0			0
$707$	453502.	−	453502.i	0.00128328	−	0.00128328i
$708$		0			0
$709$			2.72444e8i			0.764432i	0.924073	+	0.382216i	$0.124839\pi$
$709$			2.72444e8i			0.764432i	−0.924073	+	0.382216i	$0.875161\pi$
$710$		0			0
$711$	1.52334e8			0.423827
$712$		0			0
$713$	−2.81220e7	−	2.81220e7i	−0.0775850	−	0.0775850i
$714$		0			0
$715$	−8.55162e6	−	6.30323e6i	−0.0233954	−	0.0172443i
$716$		0			0
$717$	1.74418e8	−	1.74418e8i	0.473187	−	0.473187i
$718$		0			0
$719$		−	3.89952e8i		−	1.04912i	−0.851374	−	0.524559i	$-0.824230\pi$
$719$		−	3.89952e8i		−	1.04912i	0.851374	−	0.524559i	$-0.175770\pi$
$720$		0			0
$721$	−2.46364e7			−0.0657311
$722$		0			0
$723$	−9.87793e7	−	9.87793e7i	−0.261367	−	0.261367i
$724$		0			0
$725$	−8.19087e6	−	2.64382e7i	−0.0214939	−	0.0693773i
$726$		0			0
$727$	−3.84044e8	+	3.84044e8i	−0.999490	+	0.999490i	−1.00000		0.000510289i	$-0.999838\pi$
$727$	−3.84044e8	+	3.84044e8i	−0.999490	+	0.999490i	0.000510289		1.00000i	$0.499838\pi$
$728$		0			0
$729$		−	1.43489e7i		−	0.0370370i
$730$		0			0
$731$	3.35008e7			0.0857637
$732$		0			0
$733$	4.46987e7	+	4.46987e7i	0.113497	+	0.113497i	0.761574	−	0.648078i	$-0.224427\pi$
$733$	4.46987e7	+	4.46987e7i	0.113497	+	0.113497i	−0.648078	+	0.761574i	$0.724427\pi$
$734$		0			0
$735$	1.34333e8	−	1.82250e8i	0.338315	−	0.458994i
$736$		0			0
$737$	5.72237e7	−	5.72237e7i	0.142946	−	0.142946i
$738$		0			0
$739$		−	4.34859e8i		−	1.07750i	−0.842467	−	0.538748i	$-0.818898\pi$
$739$		−	4.34859e8i		−	1.07750i	0.842467	−	0.538748i	$-0.181102\pi$
$740$		0			0
$741$	4.32198e7			0.106225
$742$		0			0
$743$	4.75782e8	+	4.75782e8i	1.15996	+	1.15996i	0.984485	+	0.175471i	$0.0561448\pi$
$743$	4.75782e8	+	4.75782e8i	1.15996	+	1.15996i	0.175471	+	0.984485i	$0.443855\pi$
$744$		0			0
$745$	1.08093e8	+	7.14160e8i	0.261415	+	1.72714i
$746$		0			0
$747$	2.41211e7	−	2.41211e7i	0.0578677	−	0.0578677i
$748$		0			0
$749$		−	763774.i		−	0.00181769i
$750$		0			0
$751$	−6.21544e8			−1.46741			−0.733706	−	0.679467i	$-0.762211\pi$
$751$	−6.21544e8			−1.46741			−0.733706	+	0.679467i	$0.762211\pi$
$752$		0			0
$753$	−9.97292e7	−	9.97292e7i	−0.233581	−	0.233581i
$754$		0			0
$755$	−8.17862e8	+	1.23790e8i	−1.90038	+	0.287636i
$756$		0			0
$757$	−7.71113e7	+	7.71113e7i	−0.177759	+	0.177759i	−0.790378	−	0.612619i	$-0.790116\pi$
$757$	−7.71113e7	+	7.71113e7i	−0.177759	+	0.177759i	0.612619	+	0.790378i	$0.290116\pi$
$758$		0			0
$759$			4.63292e7i			0.105957i
$760$		0			0
$761$	−4.87199e7			−0.110548			−0.0552742	−	0.998471i	$-0.517603\pi$
$761$	−4.87199e7			−0.110548			−0.0552742	+	0.998471i	$0.517603\pi$
$762$		0			0
$763$	−3.11348e7	−	3.11348e7i	−0.0700927	−	0.0700927i
$764$		0			0
$765$	2.24817e8	+	1.65708e8i	0.502163	+	0.370135i
$766$		0			0
$767$	4.98222e7	−	4.98222e7i	0.110417	−	0.110417i
$768$		0			0
$769$			4.05766e8i			0.892272i	0.894965	+	0.446136i	$0.147200\pi$
$769$			4.05766e8i			0.892272i	−0.894965	+	0.446136i	$0.852800\pi$
$770$		0			0
$771$	3.91556e8			0.854340
$772$		0			0
$773$	−6.00879e7	−	6.00879e7i	−0.130091	−	0.130091i	0.639063	−	0.769154i	$-0.279322\pi$
$773$	−6.00879e7	−	6.00879e7i	−0.130091	−	0.130091i	−0.769154	+	0.639063i	$0.779322\pi$
$774$		0			0
$775$	6.14727e7	−	1.90450e7i	0.132062	−	0.0409144i
$776$		0			0
$777$	3.21512e7	−	3.21512e7i	0.0685384	−	0.0685384i
$778$		0			0
$779$			5.65583e8i			1.19642i
$780$		0			0
$781$	−1.69539e8			−0.355891
$782$		0			0
$783$	−4.74469e6	−	4.74469e6i	−0.00988376	−	0.00988376i
$784$		0			0
$785$	−2.22992e8	+	3.02535e8i	−0.460978	+	0.625412i
$786$		0			0
$787$	−2.06797e8	+	2.06797e8i	−0.424248	+	0.424248i	−0.886663	−	0.462415i	$-0.846983\pi$
$787$	−2.06797e8	+	2.06797e8i	−0.424248	+	0.424248i	0.462415	+	0.886663i	$0.346983\pi$
$788$		0			0
$789$			4.92042e8i			1.00178i
$790$		0			0
$791$	−6.79612e7			−0.137319
$792$		0			0
$793$	−2.51551e7	−	2.51551e7i	−0.0504437	−	0.0504437i
$794$		0			0
$795$	−1.74912e7	−	1.15562e8i	−0.0348112	−	0.229993i
$796$		0			0
$797$	1.55969e8	−	1.55969e8i	0.308080	−	0.308080i	−0.536084	−	0.844164i	$-0.680097\pi$
$797$	1.55969e8	−	1.55969e8i	0.308080	−	0.308080i	0.844164	+	0.536084i	$0.180097\pi$
$798$		0			0
$799$			6.26756e8i			1.22873i
$800$		0			0
$801$	−4.38465e7			−0.0853174
$802$		0			0
$803$	1.34965e8	+	1.34965e8i	0.260659	+	0.260659i
$804$		0			0
$805$	4.55426e7	−	6.89321e6i	0.0873032	−	0.0132140i
$806$		0			0
$807$	5.76223e7	−	5.76223e7i	0.109640	−	0.109640i
$808$		0			0
$809$		−	6.31535e8i		−	1.19276i	−0.802704	−	0.596378i	$-0.796606\pi$
$809$		−	6.31535e8i		−	1.19276i	0.802704	−	0.596378i	$-0.203394\pi$
$810$		0			0
$811$	−3.19473e8			−0.598923			−0.299462	−	0.954108i	$-0.596807\pi$
$811$	−3.19473e8			−0.598923			−0.299462	+	0.954108i	$0.596807\pi$
$812$		0			0
$813$	−2.71549e8	−	2.71549e8i	−0.505333	−	0.505333i
$814$		0			0
$815$	4.25863e8	+	3.13895e8i	0.786679	+	0.579845i
$816$		0			0
$817$	2.58688e7	−	2.58688e7i	0.0474362	−	0.0474362i
$818$		0			0
$819$			2.56061e6i			0.00466113i
$820$		0			0
$821$	2.10607e8			0.380578			0.190289	−	0.981728i	$-0.439057\pi$
$821$	2.10607e8			0.380578			0.190289	+	0.981728i	$0.439057\pi$
$822$		0			0
$823$	−2.93271e8	−	2.93271e8i	−0.526102	−	0.526102i	0.393305	−	0.919408i	$-0.371331\pi$
$823$	−2.93271e8	−	2.93271e8i	−0.526102	−	0.526102i	−0.919408	+	0.393305i	$0.871331\pi$
$824$		0			0
$825$	−6.63238e7	−	3.49484e7i	−0.118116	−	0.0622395i
$826$		0			0
$827$	3.44328e8	−	3.44328e8i	0.608774	−	0.608774i	−0.333852	−	0.942626i	$-0.608349\pi$
$827$	3.44328e8	−	3.44328e8i	0.608774	−	0.608774i	0.942626	+	0.333852i	$0.108349\pi$
$828$		0			0
$829$			1.37116e8i			0.240672i	0.992733	+	0.120336i	$0.0383971\pi$
$829$			1.37116e8i			0.240672i	−0.992733	+	0.120336i	$0.961603\pi$
$830$		0			0
$831$	−8.88898e7			−0.154899
$832$		0			0
$833$	7.55440e8	+	7.55440e8i	1.30697	+	1.30697i
$834$		0			0
$835$	5.16068e8	−	7.00151e8i	0.886436	−	1.20263i
$836$		0			0
$837$	1.10321e7	−	1.10321e7i	0.0188141	−	0.0188141i
$838$		0			0
$839$		−	8.54921e8i		−	1.44757i	−0.690025	−	0.723786i	$-0.742400\pi$
$839$		−	8.54921e8i		−	1.44757i	0.690025	−	0.723786i	$-0.257600\pi$
$840$		0			0
$841$	5.91686e8			0.994725
$842$		0			0
$843$	−2.37043e8	−	2.37043e8i	−0.395680	−	0.395680i
$844$		0			0
$845$	−8.88670e7	−	5.87133e8i	−0.147289	−	0.973120i
$846$		0			0
$847$	4.52483e7	−	4.52483e7i	0.0744650	−	0.0744650i
$848$		0			0
$849$		−	1.62598e8i		−	0.265701i
$850$		0			0
$851$	−7.38035e8			−1.19754
$852$		0			0
$853$	−3.46147e8	−	3.46147e8i	−0.557716	−	0.557716i	0.370940	−	0.928657i	$-0.379035\pi$
$853$	−3.46147e8	−	3.46147e8i	−0.557716	−	0.557716i	−0.928657	+	0.370940i	$0.879035\pi$
$854$		0			0
$855$	3.01557e8	−	4.56429e7i	0.482471	−	0.0730256i
$856$		0			0
$857$	2.08860e8	−	2.08860e8i	0.331828	−	0.331828i	−0.521452	−	0.853281i	$-0.674609\pi$
$857$	2.08860e8	−	2.08860e8i	0.331828	−	0.331828i	0.853281	+	0.521452i	$0.174609\pi$
$858$		0			0
$859$		−	3.97179e8i		−	0.626623i	−0.949650	−	0.313311i	$-0.898562\pi$
$859$		−	3.97179e8i		−	0.626623i	0.949650	−	0.313311i	$-0.101438\pi$
$860$		0			0
$861$	−3.35086e7			−0.0524986
$862$		0			0
$863$	−1.53979e8	−	1.53979e8i	−0.239568	−	0.239568i	0.577103	−	0.816671i	$-0.304183\pi$
$863$	−1.53979e8	−	1.53979e8i	−0.239568	−	0.239568i	−0.816671	+	0.577103i	$0.804183\pi$
$864$		0			0
$865$	−3.22862e8	−	2.37975e8i	−0.498848	−	0.367691i
$866$		0			0
$867$	−6.65820e8	+	6.65820e8i	−1.02164	+	1.02164i
$868$		0			0
$869$		−	1.92950e8i		−	0.294026i
$870$		0			0
$871$	−7.26012e7			−0.109873
$872$		0			0
$873$	2.28113e8	+	2.28113e8i	0.342852	+	0.342852i
$874$		0			0
$875$	−2.44869e7	+	7.03977e7i	−0.0365519	+	0.105083i
$876$		0			0
$877$	7.40984e8	−	7.40984e8i	1.09853	−	1.09853i	0.103942	−	0.994583i	$-0.466854\pi$
$877$	7.40984e8	−	7.40984e8i	1.09853	−	1.09853i	0.994583	−	0.103942i	$-0.0331458\pi$
$878$		0			0
$879$			7.07529e7i			0.104178i
$880$		0			0
$881$	−6.42211e8			−0.939183			−0.469591	−	0.882884i	$-0.655599\pi$
$881$	−6.42211e8			−0.939183			−0.469591	+	0.882884i	$0.655599\pi$
$882$		0			0
$883$	5.11389e8	+	5.11389e8i	0.742795	+	0.742795i	0.973115	−	0.230320i	$-0.0739771\pi$
$883$	5.11389e8	+	5.11389e8i	0.742795	+	0.742795i	−0.230320	+	0.973115i	$0.573977\pi$
$884$		0			0
$885$	2.95009e8	−	4.00240e8i	0.425603	−	0.577418i
$886$		0			0
$887$	5.21141e8	−	5.21141e8i	0.746766	−	0.746766i	−0.227104	−	0.973870i	$-0.572926\pi$
$887$	5.21141e8	−	5.21141e8i	0.746766	−	0.746766i	0.973870	+	0.227104i	$0.0729258\pi$
$888$		0			0
$889$		−	2.18354e7i		−	0.0310782i
$890$		0			0
$891$	−1.81747e7			−0.0256941
$892$		0			0
$893$	4.83971e8	+	4.83971e8i	0.679618	+	0.679618i
$894$		0			0
$895$	−6.22089e7	−	4.11007e8i	−0.0867728	−	0.573297i
$896$		0			0
$897$	2.93895e7	−	2.93895e7i	0.0407207	−	0.0407207i
$898$		0			0
$899$		−	7.29588e6i		−	0.0100415i
$900$		0			0
$901$	5.51516e8			0.754022
$902$		0			0
$903$	1.53263e6	+	1.53263e6i	0.00208148	+	0.00208148i
$904$		0			0
$905$	−8.69482e8	+	1.31603e8i	−1.17305	+	0.177549i
$906$		0			0
$907$	3.08091e8	−	3.08091e8i	0.412911	−	0.412911i	−0.469840	−	0.882752i	$-0.655688\pi$
$907$	3.08091e8	−	3.08091e8i	0.412911	−	0.412911i	0.882752	+	0.469840i	$0.155688\pi$
$908$		0			0
$909$		−	4.08386e6i		−	0.00543725i
$910$		0			0
$911$	−9.16815e8			−1.21263			−0.606313	−	0.795226i	$-0.707352\pi$
$911$	−9.16815e8			−1.21263			−0.606313	+	0.795226i	$0.707352\pi$
$912$		0			0
$913$	−3.05524e7	−	3.05524e7i	−0.0401452	−	0.0401452i
$914$		0			0
$915$	−2.02080e8	−	1.48949e8i	−0.263791	−	0.194435i
$916$		0			0
$917$	9.26628e7	−	9.26628e7i	0.120170	−	0.120170i
$918$		0			0
$919$			7.74874e8i			0.998354i	0.866500	+	0.499177i	$0.166364\pi$
$919$			7.74874e8i			0.998354i	−0.866500	+	0.499177i	$0.833636\pi$
$920$		0			0
$921$	−6.18191e8			−0.791305
$922$		0			0
$923$	1.07550e8	+	1.07550e8i	0.136774	+	0.136774i
$924$		0			0
$925$	5.56737e8	−	1.05655e9i	0.703436	−	1.33496i
$926$		0			0
$927$	−1.10927e8	+	1.10927e8i	−0.139251	+	0.139251i
$928$		0			0
$929$			9.05772e8i			1.12972i	0.825186	+	0.564861i	$0.191070\pi$
$929$			9.05772e8i			1.12972i	−0.825186	+	0.564861i	$0.808930\pi$
$930$		0			0
$931$	1.16668e9			1.44578
$932$		0			0
$933$	−2.28257e8	−	2.28257e8i	−0.281048	−	0.281048i
$934$		0			0
$935$	2.09890e8	−	2.84759e8i	0.256778	−	0.348371i
$936$		0			0
$937$	−8.96097e7	+	8.96097e7i	−0.108927	+	0.108927i	−0.759470	−	0.650543i	$-0.774542\pi$
$937$	−8.96097e7	+	8.96097e7i	−0.108927	+	0.108927i	0.650543	+	0.759470i	$0.274542\pi$
$938$		0			0
$939$			1.71654e8i			0.207327i
$940$		0			0
$941$	−4.03639e8			−0.484423			−0.242211	−	0.970224i	$-0.577873\pi$
$941$	−4.03639e8			−0.484423			−0.242211	+	0.970224i	$0.577873\pi$
$942$		0			0
$943$	3.84598e8	+	3.84598e8i	0.458640	+	0.458640i
$944$		0			0
$945$	2.70417e6	+	1.78661e7i	0.00320434	+	0.0211707i
$946$		0			0
$947$	−4.43540e8	+	4.43540e8i	−0.522255	+	0.522255i	−0.918252	−	0.395997i	$-0.870399\pi$
$947$	−4.43540e8	+	4.43540e8i	−0.522255	+	0.522255i	0.395997	+	0.918252i	$0.370399\pi$
$948$		0			0
$949$		−	1.71233e8i		−	0.200350i
$950$		0			0
$951$	4.53988e8			0.527841
$952$		0			0
$953$	5.59950e8	+	5.59950e8i	0.646950	+	0.646950i	0.952255	−	0.305305i	$-0.0987584\pi$
$953$	5.59950e8	+	5.59950e8i	0.646950	+	0.646950i	−0.305305	+	0.952255i	$0.598758\pi$
$954$		0			0
$955$	1.40832e9	−	2.13160e8i	1.61693	−	0.244734i
$956$		0			0
$957$	−6.00974e6	+	6.00974e6i	−0.00685678	+	0.00685678i
$958$		0			0
$959$		−	674784.i		−	0.000765084i
$960$		0			0
$961$	−8.70540e8			−0.980886
$962$		0			0
$963$	−3.43896e6	−	3.43896e6i	−0.00385078	−	0.00385078i
$964$		0			0
$965$	−9.88558e8	−	7.28646e8i	−1.10007	−	0.810839i
$966$		0			0
$967$	−5.66380e8	+	5.66380e8i	−0.626367	+	0.626367i	−0.947152	−	0.320785i	$-0.896053\pi$
$967$	−5.66380e8	+	5.66380e8i	−0.626367	+	0.626367i	0.320785	+	0.947152i	$0.396053\pi$
$968$		0			0
$969$			1.43917e9i			1.58176i
$970$		0			0
$971$	−7.53430e8			−0.822972			−0.411486	−	0.911416i	$-0.634990\pi$
$971$	−7.53430e8			−0.822972			−0.411486	+	0.911416i	$0.634990\pi$
$972$		0			0
$973$	−1.16167e8	−	1.16167e8i	−0.126109	−	0.126109i
$974$		0			0
$975$	1.99034e7	+	6.42434e7i	0.0214740	+	0.0693130i
$976$		0			0
$977$	−9.64013e8	+	9.64013e8i	−1.03371	+	1.03371i	−0.0342995	+	0.999412i	$0.510920\pi$
$977$	−9.64013e8	+	9.64013e8i	−1.03371	+	1.03371i	−0.999412	+	0.0342995i	$0.989080\pi$
$978$		0			0
$979$			5.55371e7i			0.0591882i
$980$		0			0
$981$	−2.80375e8			−0.296983
$982$		0			0
$983$	6.57085e8	+	6.57085e8i	0.691769	+	0.691769i	0.962621	−	0.270852i	$-0.0873055\pi$
$983$	6.57085e8	+	6.57085e8i	0.691769	+	0.691769i	−0.270852	+	0.962621i	$0.587305\pi$
$984$		0			0
$985$	−3.33663e8	+	4.52683e8i	−0.349140	+	0.473680i
$986$		0			0
$987$	−2.86734e7	+	2.86734e7i	−0.0298214	+	0.0298214i
$988$		0			0
$989$		−	3.51817e7i		−	0.0363687i
$990$		0			0
$991$	−6.32668e8			−0.650062			−0.325031	−	0.945703i	$-0.605375\pi$
$991$	−6.32668e8			−0.650062			−0.325031	+	0.945703i	$0.605375\pi$
$992$		0			0
$993$	−4.69796e8	−	4.69796e8i	−0.479801	−	0.479801i
$994$		0			0
$995$	4.96692e7	+	3.28158e8i	0.0504217	+	0.333130i
$996$		0			0
$997$	6.82805e8	−	6.82805e8i	0.688987	−	0.688987i	−0.273021	−	0.962008i	$-0.588023\pi$
$997$	6.82805e8	−	6.82805e8i	0.688987	−	0.688987i	0.962008	+	0.273021i	$0.0880228\pi$
$998$		0			0
$999$		−	2.89527e8i		−	0.290397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.k.a.13.3	✓	12
3.2	odd	2		180.7.l.b.73.2		12
4.3	odd	2		240.7.bg.d.193.6		12
5.2	odd	4	inner	60.7.k.a.37.3	yes	12
5.3	odd	4		300.7.k.d.157.5		12
5.4	even	2		300.7.k.d.193.5		12
15.2	even	4		180.7.l.b.37.2		12
20.7	even	4		240.7.bg.d.97.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.k.a.13.3	✓	12	1.1	even	1	trivial
60.7.k.a.37.3	yes	12	5.2	odd	4	inner
180.7.l.b.37.2		12	15.2	even	4
180.7.l.b.73.2		12	3.2	odd	2
240.7.bg.d.97.6		12	20.7	even	4
240.7.bg.d.193.6		12	4.3	odd	2
300.7.k.d.157.5		12	5.3	odd	4
300.7.k.d.193.5		12	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-11.0227 - 11.0227i) q^{3} +(123.592 - 18.7066i) q^{5} +(-26.9845 + 26.9845i) q^{7} +243.000i q^{9} +O(q^{10})\)	\(q+(-11.0227 - 11.0227i) q^{3} +(123.592 - 18.7066i) q^{5} +(-26.9845 + 26.9845i) q^{7} +243.000i q^{9} +307.790 q^{11} +(-195.251 - 195.251i) q^{13} +(-1568.52 - 1156.12i) q^{15} +(6501.62 - 6501.62i) q^{17} -10040.9i q^{19} +594.884 q^{21} +(-6827.82 - 6827.82i) q^{23} +(14925.1 - 4623.99i) q^{25} +(2678.52 - 2678.52i) q^{27} -1771.39i q^{29} +4118.74 q^{31} +(-3392.68 - 3392.68i) q^{33} +(-2830.29 + 3839.86i) q^{35} +(54046.2 - 54046.2i) q^{37} +4304.38i q^{39} -56328.0 q^{41} +(2576.35 + 2576.35i) q^{43} +(4545.71 + 30032.9i) q^{45} +(-48200.0 + 48200.0i) q^{47} +116193. i q^{49} -143331. q^{51} +(42413.8 + 42413.8i) q^{53} +(38040.5 - 5757.71i) q^{55} +(-110678. + 110678. i) q^{57} +255171. i q^{59} +128835. q^{61} +(-6557.23 - 6557.23i) q^{63} +(-27784.0 - 20479.0i) q^{65} +(185918. - 185918. i) q^{67} +150522. i q^{69} -550828. q^{71} +(438496. + 438496. i) q^{73} +(-215484. - 113546. i) q^{75} +(-8305.55 + 8305.55i) q^{77} -626890. i q^{79} -59049.0 q^{81} +(-99263.9 - 99263.9i) q^{83} +(681927. - 925173. i) q^{85} +(-19525.5 + 19525.5i) q^{87} +180438. i q^{89} +10537.5 q^{91} +(-45399.7 - 45399.7i) q^{93} +(-187831. - 1.24098e6i) q^{95} +(938737. - 938737. i) q^{97} +74792.9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 312 q^{5} + 120 q^{7}+O(q^{10}) \) 12 * q + 312 * q^5 + 120 * q^7	\( 12 q + 312 q^{5} + 120 q^{7} - 3248 q^{11} - 2100 q^{13} + 4536 q^{15} - 5540 q^{17} - 15552 q^{21} - 23840 q^{23} + 10044 q^{25} - 127152 q^{31} - 35640 q^{33} + 102976 q^{35} + 282900 q^{37} - 320720 q^{41} - 62880 q^{43} - 10692 q^{45} + 381600 q^{47} - 145152 q^{51} - 400300 q^{53} + 502152 q^{55} - 38880 q^{57} + 807024 q^{61} + 29160 q^{63} + 124500 q^{65} + 752160 q^{67} + 202400 q^{71} - 322020 q^{73} - 645408 q^{75} - 2448400 q^{77} - 708588 q^{81} + 1894560 q^{83} - 857124 q^{85} - 1007640 q^{87} + 2294400 q^{91} + 835920 q^{93} - 2620000 q^{95} - 3161700 q^{97}+O(q^{100}) \) 12 * q + 312 * q^5 + 120 * q^7 - 3248 * q^11 - 2100 * q^13 + 4536 * q^15 - 5540 * q^17 - 15552 * q^21 - 23840 * q^23 + 10044 * q^25 - 127152 * q^31 - 35640 * q^33 + 102976 * q^35 + 282900 * q^37 - 320720 * q^41 - 62880 * q^43 - 10692 * q^45 + 381600 * q^47 - 145152 * q^51 - 400300 * q^53 + 502152 * q^55 - 38880 * q^57 + 807024 * q^61 + 29160 * q^63 + 124500 * q^65 + 752160 * q^67 + 202400 * q^71 - 322020 * q^73 - 645408 * q^75 - 2448400 * q^77 - 708588 * q^81 + 1894560 * q^83 - 857124 * q^85 - 1007640 * q^87 + 2294400 * q^91 + 835920 * q^93 - 2620000 * q^95 - 3161700 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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