LMFDB - Embedded newform 1440.2.q.p.481.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1440,2,Mod(481,1440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1440, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1440.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1440 = 2^{5} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1440.q (of order $3$, 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:	$11.4984578911$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.8528759163648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + x^{8} + 9x^{6} - 36x^{5} + 27x^{4} + 27x^{2} - 162x + 243 $ x^10 - 2x^9 + x^8 + 9x^6 - 36x^5 + 27x^4 + 27x^2 - 162x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			481.3
Root			$-1.41743 - 0.995434i$ of defining polynomial
Character	$\chi$	$=$	1440.481
Dual form			1440.2.q.p.961.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.153356 - 1.72525i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.31980 + 4.01801i) q^{7} +(-2.95296 - 0.529154i) q^{9} +O(q^{10})$	\(q+(0.153356 - 1.72525i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.31980 + 4.01801i) q^{7} +(-2.95296 - 0.529154i) q^{9} +(-2.57079 - 4.45273i) q^{11} +(-2.18664 + 3.78737i) q^{13} +(1.41743 + 0.995434i) q^{15} -1.03644 q^{17} +4.06474 q^{19} +(7.28783 - 3.38605i) q^{21} +(-3.31980 + 5.75006i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-1.36578 + 5.01345i) q^{27} +(-0.936714 - 1.62244i) q^{29} +(-4.50553 + 7.80381i) q^{31} +(-8.07632 + 3.75239i) q^{33} -4.63960 q^{35} -1.75985 q^{37} +(6.19882 + 4.35331i) q^{39} +(1.68664 - 2.92134i) q^{41} +(2.53040 + 4.38278i) q^{43} +(1.93474 - 2.29277i) q^{45} +(1.68376 + 2.91635i) q^{47} +(-7.26295 + 12.5798i) q^{49} +(-0.158945 + 1.78812i) q^{51} -8.89657 q^{53} +5.14157 q^{55} +(0.623352 - 7.01269i) q^{57} +(-5.20289 + 9.01167i) q^{59} +(-4.77625 - 8.27272i) q^{61} +(-4.72414 - 13.0926i) q^{63} +(-2.18664 - 3.78737i) q^{65} +(1.08585 - 1.88074i) q^{67} +(9.41118 + 6.60929i) q^{69} +8.47841 q^{71} -5.25606 q^{73} +(-1.57079 + 0.729814i) q^{75} +(11.9274 - 20.6589i) q^{77} +(-1.92499 - 3.33418i) q^{79} +(8.43999 + 3.12514i) q^{81} +(5.99797 + 10.3888i) q^{83} +(0.518221 - 0.897586i) q^{85} +(-2.94276 + 1.36725i) q^{87} -1.48291 q^{89} -20.2903 q^{91} +(12.7726 + 8.96992i) q^{93} +(-2.03237 + 3.52017i) q^{95} +(6.61291 + 11.4539i) q^{97} +(5.23526 + 14.5091i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} - 5 q^{5} - q^{9}+O(q^{10}) $ 10 * q + q^3 - 5 * q^5 - q^9	$ 10 q + q^{3} - 5 q^{5} - q^{9} - 9 q^{11} - 4 q^{13} - 2 q^{15} + 6 q^{17} + 14 q^{19} + 12 q^{21} - 10 q^{23} - 5 q^{25} - 2 q^{27} - 2 q^{29} - 8 q^{31} - 27 q^{33} + 16 q^{37} + 26 q^{39} - q^{41} - q^{43} - q^{45} - 10 q^{47} - q^{49} - 3 q^{51} - 20 q^{53} + 18 q^{55} - 19 q^{57} - 13 q^{59} - 14 q^{61} - 30 q^{63} - 4 q^{65} - 15 q^{67} + 8 q^{69} + 32 q^{71} - 14 q^{73} + q^{75} + 12 q^{77} - 18 q^{79} + 35 q^{81} + 8 q^{83} - 3 q^{85} - 32 q^{87} + 28 q^{89} - 36 q^{91} + 16 q^{93} - 7 q^{95} + 17 q^{97}+O(q^{100}) $ 10 * q + q^3 - 5 * q^5 - q^9 - 9 * q^11 - 4 * q^13 - 2 * q^15 + 6 * q^17 + 14 * q^19 + 12 * q^21 - 10 * q^23 - 5 * q^25 - 2 * q^27 - 2 * q^29 - 8 * q^31 - 27 * q^33 + 16 * q^37 + 26 * q^39 - q^41 - q^43 - q^45 - 10 * q^47 - q^49 - 3 * q^51 - 20 * q^53 + 18 * q^55 - 19 * q^57 - 13 * q^59 - 14 * q^61 - 30 * q^63 - 4 * q^65 - 15 * q^67 + 8 * q^69 + 32 * q^71 - 14 * q^73 + q^75 + 12 * q^77 - 18 * q^79 + 35 * q^81 + 8 * q^83 - 3 * q^85 - 32 * q^87 + 28 * q^89 - 36 * q^91 + 16 * q^93 - 7 * q^95 + 17 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.153356	−	1.72525i	0.0885400	−	0.996073i
$3$	0.153356	−	1.72525i	0.0885400	−	0.996073i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	2.31980	+	4.01801i	0.876802	+	1.51867i	0.854830	+	0.518908i	$0.173661\pi$
$7$	2.31980	+	4.01801i	0.876802	+	1.51867i	0.0219721	+	0.999759i	$0.493005\pi$
$8$		0			0
$9$	−2.95296	−	0.529154i	−0.984321	−	0.176385i
$10$		0			0
$11$	−2.57079	−	4.45273i	−0.775121	−	1.34255i	−0.934726	−	0.355369i	$-0.884355\pi$
$11$	−2.57079	−	4.45273i	−0.775121	−	1.34255i	0.159605	−	0.987181i	$-0.448978\pi$
$12$		0			0
$13$	−2.18664	+	3.78737i	−0.606464	+	1.05043i	0.385354	+	0.922769i	$0.374079\pi$
$13$	−2.18664	+	3.78737i	−0.606464	+	1.05043i	−0.991818	+	0.127658i	$0.959254\pi$
$14$		0			0
$15$	1.41743	+	0.995434i	0.365979	+	0.257020i
$16$		0			0
$17$	−1.03644			−0.251374			−0.125687	−	0.992070i	$-0.540114\pi$
$17$	−1.03644			−0.251374			−0.125687	+	0.992070i	$0.540114\pi$
$18$		0			0
$19$	4.06474			0.932516			0.466258	−	0.884649i	$-0.345602\pi$
$19$	4.06474			0.932516			0.466258	+	0.884649i	$0.345602\pi$
$20$		0			0
$21$	7.28783	−	3.38605i	1.59033	−	0.738896i
$22$		0			0
$23$	−3.31980	+	5.75006i	−0.692226	+	1.19897i	0.278880	+	0.960326i	$0.410037\pi$
$23$	−3.31980	+	5.75006i	−0.692226	+	1.19897i	−0.971107	+	0.238645i	$0.923297\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−1.36578	+	5.01345i	−0.262844	+	0.964838i
$28$		0			0
$29$	−0.936714	−	1.62244i	−0.173943	−	0.301279i	0.765852	−	0.643017i	$-0.222318\pi$
$29$	−0.936714	−	1.62244i	−0.173943	−	0.301279i	−0.939795	+	0.341738i	$0.888984\pi$
$30$		0			0
$31$	−4.50553	+	7.80381i	−0.809217	+	1.40160i	0.104190	+	0.994557i	$0.466775\pi$
$31$	−4.50553	+	7.80381i	−0.809217	+	1.40160i	−0.913407	+	0.407047i	$0.866558\pi$
$32$		0			0
$33$	−8.07632	+	3.75239i	−1.40591	+	0.653208i
$34$		0			0
$35$	−4.63960			−0.784236
$36$		0			0
$37$	−1.75985			−0.289318			−0.144659	−	0.989482i	$-0.546209\pi$
$37$	−1.75985			−0.289318			−0.144659	+	0.989482i	$0.546209\pi$
$38$		0			0
$39$	6.19882	+	4.35331i	0.992605	+	0.697087i
$40$		0			0
$41$	1.68664	−	2.92134i	0.263409	−	0.456237i	−0.703737	−	0.710461i	$-0.748487\pi$
$41$	1.68664	−	2.92134i	0.263409	−	0.456237i	0.967145	+	0.254224i	$0.0818199\pi$
$42$		0			0
$43$	2.53040	+	4.38278i	0.385883	+	0.668368i	0.991891	−	0.127090i	$-0.0405637\pi$
$43$	2.53040	+	4.38278i	0.385883	+	0.668368i	−0.606009	+	0.795458i	$0.707230\pi$
$44$		0			0
$45$	1.93474	−	2.29277i	0.288414	−	0.341785i
$46$		0			0
$47$	1.68376	+	2.91635i	0.245601	+	0.425394i	0.962300	−	0.271989i	$-0.0876813\pi$
$47$	1.68376	+	2.91635i	0.245601	+	0.425394i	−0.716699	+	0.697382i	$0.754348\pi$
$48$		0			0
$49$	−7.26295	+	12.5798i	−1.03756	+	1.79712i
$50$		0			0
$51$	−0.158945	+	1.78812i	−0.0222567	+	0.250387i
$52$		0			0
$53$	−8.89657			−1.22204			−0.611019	−	0.791616i	$-0.709240\pi$
$53$	−8.89657			−1.22204			−0.611019	+	0.791616i	$0.709240\pi$
$54$		0			0
$55$	5.14157			0.693290
$56$		0			0
$57$	0.623352	−	7.01269i	0.0825650	−	0.928854i
$58$		0			0
$59$	−5.20289	+	9.01167i	−0.677358	+	1.17322i	0.298415	+	0.954436i	$0.403542\pi$
$59$	−5.20289	+	9.01167i	−0.677358	+	1.17322i	−0.975774	+	0.218783i	$0.929791\pi$
$60$		0			0
$61$	−4.77625	−	8.27272i	−0.611537	−	1.05921i	−0.990982	−	0.133998i	$-0.957218\pi$
$61$	−4.77625	−	8.27272i	−0.611537	−	1.05921i	0.379445	−	0.925214i	$-0.376115\pi$
$62$		0			0
$63$	−4.72414	−	13.0926i	−0.595186	−	1.64951i
$64$		0			0
$65$	−2.18664	−	3.78737i	−0.271219	−	0.469765i
$66$		0			0
$67$	1.08585	−	1.88074i	0.132657	−	0.229769i	−0.792043	−	0.610466i	$-0.790982\pi$
$67$	1.08585	−	1.88074i	0.132657	−	0.229769i	0.924700	+	0.380696i	$0.124316\pi$
$68$		0			0
$69$	9.41118	+	6.60929i	1.13297	+	0.795665i
$70$		0			0
$71$	8.47841			1.00620			0.503101	−	0.864228i	$-0.332192\pi$
$71$	8.47841			1.00620			0.503101	+	0.864228i	$0.332192\pi$
$72$		0			0
$73$	−5.25606			−0.615176			−0.307588	−	0.951520i	$-0.599522\pi$
$73$	−5.25606			−0.615176			−0.307588	+	0.951520i	$0.599522\pi$
$74$		0			0
$75$	−1.57079	+	0.729814i	−0.181379	+	0.0842717i
$76$		0			0
$77$	11.9274	−	20.6589i	1.35926	−	2.35430i
$78$		0			0
$79$	−1.92499	−	3.33418i	−0.216578	−	0.375125i	0.737181	−	0.675695i	$-0.236156\pi$
$79$	−1.92499	−	3.33418i	−0.216578	−	0.375125i	−0.953760	+	0.300570i	$0.902823\pi$
$80$		0			0
$81$	8.43999	+	3.12514i	0.937777	+	0.347238i
$82$		0			0
$83$	5.99797	+	10.3888i	0.658363	+	1.14032i	0.981039	+	0.193808i	$0.0620840\pi$
$83$	5.99797	+	10.3888i	0.658363	+	1.14032i	−0.322677	+	0.946509i	$0.604583\pi$
$84$		0			0
$85$	0.518221	−	0.897586i	0.0562090	−	0.0973569i
$86$		0			0
$87$	−2.94276	+	1.36725i	−0.315497	+	0.146585i
$88$		0			0
$89$	−1.48291			−0.157188			−0.0785940	−	0.996907i	$-0.525043\pi$
$89$	−1.48291			−0.157188			−0.0785940	+	0.996907i	$0.525043\pi$
$90$		0			0
$91$	−20.2903			−2.12700
$92$		0			0
$93$	12.7726	+	8.96992i	1.32445	+	0.930137i
$94$		0			0
$95$	−2.03237	+	3.52017i	−0.208517	+	0.361162i
$96$		0			0
$97$	6.61291	+	11.4539i	0.671439	+	1.16297i	0.977496	+	0.210954i	$0.0676570\pi$
$97$	6.61291	+	11.4539i	0.671439	+	1.16297i	−0.306057	+	0.952013i	$0.599010\pi$
$98$		0			0
$99$	5.23526	+	14.5091i	0.526163	+	1.45822i
$100$		0			0
$101$	6.40790	+	11.0988i	0.637610	+	1.10437i	0.985956	+	0.167007i	$0.0534101\pi$
$101$	6.40790	+	11.0988i	0.637610	+	1.10437i	−0.348346	+	0.937366i	$0.613257\pi$
$102$		0			0
$103$	−8.60854	+	14.9104i	−0.848224	+	1.46917i	0.0345670	+	0.999402i	$0.488995\pi$
$103$	−8.60854	+	14.9104i	−0.848224	+	1.46917i	−0.882791	+	0.469765i	$0.844339\pi$
$104$		0			0
$105$	−0.711510	+	8.00447i	−0.0694363	+	0.781156i
$106$		0			0
$107$	13.4323			1.29855			0.649273	−	0.760556i	$-0.275073\pi$
$107$	13.4323			1.29855			0.649273	+	0.760556i	$0.275073\pi$
$108$		0			0
$109$	7.64592			0.732347			0.366173	−	0.930547i	$-0.380668\pi$
$109$	7.64592			0.732347			0.366173	+	0.930547i	$0.380668\pi$
$110$		0			0
$111$	−0.269884	+	3.03618i	−0.0256162	+	0.288182i
$112$		0			0
$113$	5.36301	−	9.28901i	0.504510	−	0.873837i	−0.495477	−	0.868621i	$-0.665007\pi$
$113$	5.36301	−	9.28901i	0.504510	−	0.873837i	0.999986	−	0.00521530i	$-0.00166009\pi$
$114$		0			0
$115$	−3.31980	−	5.75006i	−0.309573	−	0.536196i
$116$		0			0
$117$	8.46116	−	10.0269i	0.782235	−	0.926987i
$118$		0			0
$119$	−2.40434	−	4.16444i	−0.220406	−	0.381754i
$120$		0			0
$121$	−7.71789	+	13.3678i	−0.701626	+	1.21525i
$122$		0			0
$123$	−4.78139	−	3.35787i	−0.431123	−	0.302769i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−0.765616			−0.0679374			−0.0339687	−	0.999423i	$-0.510815\pi$
$127$	−0.765616			−0.0679374			−0.0339687	+	0.999423i	$0.510815\pi$
$128$		0			0
$129$	7.94944	−	3.69345i	0.699909	−	0.325190i
$130$		0			0
$131$	0.961434	−	1.66525i	0.0840009	−	0.145494i	−0.820964	−	0.570980i	$-0.806563\pi$
$131$	0.961434	−	1.66525i	0.0840009	−	0.145494i	0.904965	+	0.425486i	$0.139897\pi$
$132$		0			0
$133$	9.42940	+	16.3322i	0.817633	+	1.41618i
$134$		0			0
$135$	−3.65889	−	3.68952i	−0.314907	−	0.317543i
$136$		0			0
$137$	−1.43853	−	2.49161i	−0.122902	−	0.212873i	0.798009	−	0.602646i	$-0.205887\pi$
$137$	−1.43853	−	2.49161i	−0.122902	−	0.212873i	−0.920911	+	0.389773i	$0.872553\pi$
$138$		0			0
$139$	7.67948	−	13.3012i	0.651365	−	1.12820i	−0.331427	−	0.943481i	$-0.607530\pi$
$139$	7.67948	−	13.3012i	0.651365	−	1.12820i	0.982792	−	0.184716i	$-0.0591365\pi$
$140$		0			0
$141$	5.28965	−	2.45766i	0.445469	−	0.206972i
$142$		0			0
$143$	22.4855			1.88033
$144$		0			0
$145$	1.87343			0.155580
$146$		0			0
$147$	20.5895	+	14.4596i	1.69819	+	1.19261i
$148$		0			0
$149$	−2.63164	+	4.55814i	−0.215593	+	0.373418i	−0.953456	−	0.301533i	$-0.902502\pi$
$149$	−2.63164	+	4.55814i	−0.215593	+	0.373418i	0.737863	+	0.674950i	$0.235835\pi$
$150$		0			0
$151$	−6.80830	−	11.7923i	−0.554051	−	0.959645i	−0.997977	−	0.0635814i	$-0.979748\pi$
$151$	−6.80830	−	11.7923i	−0.554051	−	0.959645i	0.443925	−	0.896064i	$-0.353586\pi$
$152$		0			0
$153$	3.06058	+	0.548438i	0.247433	+	0.0443386i
$154$		0			0
$155$	−4.50553	−	7.80381i	−0.361893	−	0.626817i
$156$		0			0
$157$	7.40396	−	12.8240i	0.590900	−	1.02347i	−0.403211	−	0.915107i	$-0.632106\pi$
$157$	7.40396	−	12.8240i	0.590900	−	1.02347i	0.994111	−	0.108362i	$-0.0345606\pi$
$158$		0			0
$159$	−1.36434	+	15.3488i	−0.108199	+	1.21724i
$160$		0			0
$161$	−30.8051			−2.42778
$162$		0			0
$163$	17.6076			1.37913			0.689567	−	0.724222i	$-0.257801\pi$
$163$	17.6076			1.37913			0.689567	+	0.724222i	$0.257801\pi$
$164$		0			0
$165$	0.788490	−	8.87049i	0.0613839	−	0.690567i
$166$		0			0
$167$	0.788888	−	1.36639i	0.0610459	−	0.105735i	−0.833887	−	0.551935i	$-0.813890\pi$
$167$	0.788888	−	1.36639i	0.0610459	−	0.105735i	0.894933	+	0.446200i	$0.147223\pi$
$168$		0			0
$169$	−3.06277	−	5.30488i	−0.235598	−	0.408068i
$170$		0			0
$171$	−12.0030	−	2.15087i	−0.917896	−	0.164481i
$172$		0			0
$173$	−10.7212	−	18.5696i	−0.815115	−	1.41182i	−0.909245	−	0.416261i	$-0.863340\pi$
$173$	−10.7212	−	18.5696i	−0.815115	−	1.41182i	0.0941297	−	0.995560i	$-0.469993\pi$
$174$		0			0
$175$	2.31980	−	4.01801i	0.175360	−	0.303733i
$176$		0			0
$177$	14.7495	+	10.3583i	1.10864	+	0.778575i
$178$		0			0
$179$	−17.3544			−1.29713			−0.648566	−	0.761158i	$-0.724631\pi$
$179$	−17.3544			−1.29713			−0.648566	+	0.761158i	$0.724631\pi$
$180$		0			0
$181$	−24.0323			−1.78631			−0.893154	−	0.449751i	$-0.851513\pi$
$181$	−24.0323			−1.78631			−0.893154	+	0.449751i	$0.851513\pi$
$182$		0			0
$183$	−15.0050	+	6.97156i	−1.10920	+	0.515352i
$184$		0			0
$185$	0.879927	−	1.52408i	0.0646935	−	0.112052i
$186$		0			0
$187$	2.66447	+	4.61500i	0.194846	+	0.337483i
$188$		0			0
$189$	−23.3124	+	6.14250i	−1.69573	+	0.446801i
$190$		0			0
$191$	−2.83186	−	4.90493i	−0.204906	−	0.354908i	0.745197	−	0.666845i	$-0.232356\pi$
$191$	−2.83186	−	4.90493i	−0.204906	−	0.354908i	−0.950103	+	0.311937i	$0.899022\pi$
$192$		0			0
$193$	3.09520	−	5.36105i	0.222797	−	0.385897i	−0.732859	−	0.680381i	$-0.761814\pi$
$193$	3.09520	−	5.36105i	0.222797	−	0.385897i	0.955656	+	0.294484i	$0.0951478\pi$
$194$		0			0
$195$	−6.86949	+	3.19168i	−0.491934	+	0.228561i
$196$		0			0
$197$	−7.28709			−0.519184			−0.259592	−	0.965718i	$-0.583588\pi$
$197$	−7.28709			−0.519184			−0.259592	+	0.965718i	$0.583588\pi$
$198$		0			0
$199$	16.3108			1.15624			0.578121	−	0.815951i	$-0.303786\pi$
$199$	16.3108			1.15624			0.578121	+	0.815951i	$0.303786\pi$
$200$		0			0
$201$	−3.07823	−	2.16178i	−0.217122	−	0.152480i
$202$		0			0
$203$	4.34598	−	7.52746i	0.305028	−	0.528324i
$204$		0			0
$205$	1.68664	+	2.92134i	0.117800	+	0.204035i
$206$		0			0
$207$	12.8459	−	15.2230i	0.892853	−	1.05807i
$208$		0			0
$209$	−10.4496	−	18.0992i	−0.722813	−	1.25195i
$210$		0			0
$211$	11.6854	−	20.2396i	0.804454	−	1.39335i	−0.112205	−	0.993685i	$-0.535791\pi$
$211$	11.6854	−	20.2396i	0.804454	−	1.39335i	0.916659	−	0.399670i	$-0.130875\pi$
$212$		0			0
$213$	1.30021	−	14.6274i	0.0890891	−	1.00225i
$214$		0			0
$215$	−5.06080			−0.345144
$216$		0			0
$217$	−41.8077			−2.83809
$218$		0			0
$219$	−0.806048	+	9.06801i	−0.0544676	+	0.612759i
$220$		0			0
$221$	2.26633	−	3.92539i	0.152450	−	0.264050i
$222$		0			0
$223$	1.12098	+	1.94160i	0.0750666	+	0.130019i	0.901115	−	0.433580i	$-0.142750\pi$
$223$	1.12098	+	1.94160i	0.0750666	+	0.130019i	−0.826049	+	0.563599i	$0.809416\pi$
$224$		0			0
$225$	1.01822	+	2.82192i	0.0678814	+	0.188128i
$226$		0			0
$227$	1.48880	+	2.57867i	0.0988150	+	0.171153i	0.911194	−	0.411977i	$-0.135161\pi$
$227$	1.48880	+	2.57867i	0.0988150	+	0.171153i	−0.812379	+	0.583129i	$0.801828\pi$
$228$		0			0
$229$	−13.5205	+	23.4182i	−0.893460	+	1.54752i	−0.0577615	+	0.998330i	$0.518396\pi$
$229$	−13.5205	+	23.4182i	−0.893460	+	1.54752i	−0.835699	+	0.549188i	$0.814937\pi$
$230$		0			0
$231$	−33.8126	−	23.7459i	−2.22471	−	1.56237i
$232$		0			0
$233$	0.913026			0.0598143			0.0299072	−	0.999553i	$-0.490479\pi$
$233$	0.913026			0.0598143			0.0299072	+	0.999553i	$0.490479\pi$
$234$		0			0
$235$	−3.36751			−0.219672
$236$		0			0
$237$	−6.04750	+	2.80977i	−0.392827	+	0.182514i
$238$		0			0
$239$	5.08789	−	8.81248i	0.329108	−	0.570032i	−0.653227	−	0.757162i	$-0.726585\pi$
$239$	5.08789	−	8.81248i	0.329108	−	0.570032i	0.982335	+	0.187130i	$0.0599186\pi$
$240$		0			0
$241$	6.56639	+	11.3733i	0.422978	+	0.732620i	0.996229	−	0.0867601i	$-0.0276514\pi$
$241$	6.56639	+	11.3733i	0.422978	+	0.732620i	−0.573251	+	0.819380i	$0.694318\pi$
$242$		0			0
$243$	6.68597	−	14.0818i	0.428905	−	0.903349i
$244$		0			0
$245$	−7.26295	−	12.5798i	−0.464013	−	0.803694i
$246$		0			0
$247$	−8.88813	+	15.3947i	−0.565538	+	0.979540i
$248$		0			0
$249$	18.8431	−	8.75481i	1.19413	−	0.554813i
$250$		0			0
$251$	−17.9795			−1.13486			−0.567428	−	0.823423i	$-0.692061\pi$
$251$	−17.9795			−1.13486			−0.567428	+	0.823423i	$0.692061\pi$
$252$		0			0
$253$	34.1380			2.14624
$254$		0			0
$255$	−1.46909	−	1.03171i	−0.0919978	−	0.0646082i
$256$		0			0
$257$	−14.7120	+	25.4819i	−0.917708	+	1.58952i	−0.114820	+	0.993386i	$0.536629\pi$
$257$	−14.7120	+	25.4819i	−0.917708	+	1.58952i	−0.802888	+	0.596130i	$0.796704\pi$
$258$		0			0
$259$	−4.08251	−	7.07111i	−0.253675	−	0.439378i
$260$		0			0
$261$	1.90756	+	5.28666i	0.118075	+	0.327236i
$262$		0			0
$263$	−10.3853	−	17.9878i	−0.640384	−	1.10918i	−0.985347	−	0.170561i	$-0.945442\pi$
$263$	−10.3853	−	17.9878i	−0.640384	−	1.10918i	0.344963	−	0.938616i	$-0.387891\pi$
$264$		0			0
$265$	4.44829	−	7.70466i	0.273256	−	0.473293i
$266$		0			0
$267$	−0.227413	+	2.55839i	−0.0139174	+	0.156571i
$268$		0			0
$269$	8.16593			0.497886			0.248943	−	0.968518i	$-0.419917\pi$
$269$	8.16593			0.497886			0.248943	+	0.968518i	$0.419917\pi$
$270$		0			0
$271$	−12.7500			−0.774509			−0.387255	−	0.921973i	$-0.626577\pi$
$271$	−12.7500			−0.774509			−0.387255	+	0.921973i	$0.626577\pi$
$272$		0			0
$273$	−3.11163	+	35.0057i	−0.188324	+	2.11864i
$274$		0			0
$275$	−2.57079	+	4.45273i	−0.155024	+	0.268510i
$276$		0			0
$277$	2.06821	+	3.58224i	0.124267	+	0.215236i	0.921446	−	0.388506i	$-0.127009\pi$
$277$	2.06821	+	3.58224i	0.124267	+	0.215236i	−0.797179	+	0.603742i	$0.793676\pi$
$278$		0			0
$279$	17.4341	−	20.6602i	1.04375	−	1.23690i
$280$		0			0
$281$	−0.784699	−	1.35914i	−0.0468112	−	0.0810794i	0.841670	−	0.539992i	$-0.181573\pi$
$281$	−0.784699	−	1.35914i	−0.0468112	−	0.0810794i	−0.888482	+	0.458912i	$0.848239\pi$
$282$		0			0
$283$	−1.78533	+	3.09228i	−0.106127	+	0.183817i	−0.914198	−	0.405268i	$-0.867178\pi$
$283$	−1.78533	+	3.09228i	−0.106127	+	0.183817i	0.808071	+	0.589085i	$0.200512\pi$
$284$		0			0
$285$	5.76150	+	4.04619i	0.341282	+	0.239675i
$286$		0			0
$287$	15.6507			0.923829
$288$		0			0
$289$	−15.9258			−0.936811
$290$		0			0
$291$	20.7749	−	9.65239i	1.21785	−	0.565833i
$292$		0			0
$293$	11.1568	−	19.3241i	0.651784	−	1.12892i	−0.330905	−	0.943664i	$-0.607354\pi$
$293$	11.1568	−	19.3241i	0.651784	−	1.12892i	0.982690	−	0.185260i	$-0.0593127\pi$
$294$		0			0
$295$	−5.20289	−	9.01167i	−0.302924	−	0.524680i
$296$		0			0
$297$	25.8347	−	6.80707i	1.49908	−	0.394986i
$298$		0			0
$299$	−14.5184	−	25.1466i	−0.839621	−	1.45427i
$300$		0			0
$301$	−11.7401	+	20.3344i	−0.676685	+	1.17205i
$302$		0			0
$303$	20.1309	−	9.35315i	1.15649	−	0.537325i
$304$		0			0
$305$	9.55251			0.546975
$306$		0			0
$307$	17.1543			0.979050			0.489525	−	0.871989i	$-0.337170\pi$
$307$	17.1543			0.979050			0.489525	+	0.871989i	$0.337170\pi$
$308$		0			0
$309$	24.4040	+	17.1385i	1.38830	+	0.974973i
$310$		0			0
$311$	−5.24224	+	9.07983i	−0.297260	+	0.514870i	−0.975508	−	0.219963i	$-0.929406\pi$
$311$	−5.24224	+	9.07983i	−0.297260	+	0.514870i	0.678248	+	0.734833i	$0.262740\pi$
$312$		0			0
$313$	−8.49522	−	14.7141i	−0.480178	−	0.831693i	0.519563	−	0.854432i	$-0.326095\pi$
$313$	−8.49522	−	14.7141i	−0.480178	−	0.831693i	−0.999741	+	0.0227392i	$0.992761\pi$
$314$		0			0
$315$	13.7006	+	2.45506i	0.771940	+	0.138327i
$316$		0			0
$317$	−6.28206	−	10.8809i	−0.352836	−	0.611130i	0.633909	−	0.773407i	$-0.281449\pi$
$317$	−6.28206	−	10.8809i	−0.352836	−	0.611130i	−0.986745	+	0.162278i	$0.948116\pi$
$318$		0			0
$319$	−4.81618	+	8.34188i	−0.269655	+	0.467055i
$320$		0			0
$321$	2.05991	−	23.1740i	0.114973	−	1.29345i
$322$		0			0
$323$	−4.21288			−0.234411
$324$		0			0
$325$	4.37328			0.242586
$326$		0			0
$327$	1.17255	−	13.1911i	0.0648420	−	0.729470i
$328$		0			0
$329$	−7.81196	+	13.5307i	−0.430687	+	0.745972i
$330$		0			0
$331$	12.5854	+	21.7985i	0.691754	+	1.19815i	0.971263	+	0.238010i	$0.0764950\pi$
$331$	12.5854	+	21.7985i	0.691754	+	1.19815i	−0.279509	+	0.960143i	$0.590172\pi$
$332$		0			0
$333$	5.19678	+	0.931233i	0.284782	+	0.0510312i
$334$		0			0
$335$	1.08585	+	1.88074i	0.0593262	+	0.102756i
$336$		0			0
$337$	−3.72618	+	6.45394i	−0.202978	+	0.351568i	−0.949487	−	0.313807i	$-0.898395\pi$
$337$	−3.72618	+	6.45394i	−0.202978	+	0.351568i	0.746509	+	0.665376i	$0.231729\pi$
$338$		0			0
$339$	−15.2034	−	10.6771i	−0.825735	−	0.579898i
$340$		0			0
$341$	46.3310			2.50897
$342$		0			0
$343$	−34.9172			−1.88535
$344$		0			0
$345$	−10.4294	+	4.84568i	−0.561500	+	0.260882i
$346$		0			0
$347$	−9.90762	+	17.1605i	−0.531869	+	0.921224i	0.467439	+	0.884025i	$0.345177\pi$
$347$	−9.90762	+	17.1605i	−0.531869	+	0.921224i	−0.999308	+	0.0371987i	$0.988157\pi$
$348$		0			0
$349$	−3.25642	−	5.64029i	−0.174312	−	0.301918i	0.765611	−	0.643304i	$-0.222437\pi$
$349$	−3.25642	−	5.64029i	−0.174312	−	0.301918i	−0.939923	+	0.341386i	$0.889104\pi$
$350$		0			0
$351$	−16.0013	−	16.1353i	−0.854087	−	0.861238i
$352$		0			0
$353$	−10.5162	−	18.2145i	−0.559719	−	0.969461i	−0.997520	−	0.0703891i	$-0.977576\pi$
$353$	−10.5162	−	18.2145i	−0.559719	−	0.969461i	0.437801	−	0.899072i	$-0.355757\pi$
$354$		0			0
$355$	−4.23920	+	7.34252i	−0.224994	+	0.389700i
$356$		0			0
$357$	−7.55342	+	3.50945i	−0.399769	+	0.185740i
$358$		0			0
$359$	34.3505			1.81295			0.906475	−	0.422259i	$-0.138763\pi$
$359$	34.3505			1.81295			0.906475	+	0.422259i	$0.138763\pi$
$360$		0			0
$361$	−2.47785			−0.130413
$362$		0			0
$363$	21.8792	+	15.3653i	1.14836	+	0.806469i
$364$		0			0
$365$	2.62803	−	4.55188i	0.137557	−	0.238256i
$366$		0			0
$367$	9.46211	+	16.3889i	0.493918	+	0.855491i	0.999975	−	0.00700874i	$-0.00223097\pi$
$367$	9.46211	+	16.3889i	0.493918	+	0.855491i	−0.506057	+	0.862500i	$0.668898\pi$
$368$		0			0
$369$	−6.52642	+	7.73413i	−0.339752	+	0.402623i
$370$		0			0
$371$	−20.6383	−	35.7465i	−1.07149	−	1.85587i
$372$		0			0
$373$	−14.9604	+	25.9122i	−0.774621	+	1.34168i	0.160387	+	0.987054i	$0.448726\pi$
$373$	−14.9604	+	25.9122i	−0.774621	+	1.34168i	−0.935007	+	0.354628i	$0.884608\pi$
$374$		0			0
$375$	0.153356	−	1.72525i	0.00791926	−	0.0890914i
$376$		0			0
$377$	8.19302			0.421962
$378$		0			0
$379$	20.9258			1.07489			0.537443	−	0.843300i	$-0.319390\pi$
$379$	20.9258			1.07489			0.537443	+	0.843300i	$0.319390\pi$
$380$		0			0
$381$	−0.117412	+	1.32088i	−0.00601518	+	0.0676706i
$382$		0			0
$383$	−4.52065	+	7.82999i	−0.230994	+	0.400094i	−0.958101	−	0.286431i	$-0.907531\pi$
$383$	−4.52065	+	7.82999i	−0.230994	+	0.400094i	0.727107	+	0.686525i	$0.240865\pi$
$384$		0			0
$385$	11.9274	+	20.6589i	0.607878	+	1.05288i
$386$		0			0
$387$	−5.15302	−	14.2812i	−0.261943	−	0.725953i
$388$		0			0
$389$	−3.29213	−	5.70214i	−0.166918	−	0.289110i	0.770417	−	0.637540i	$-0.220048\pi$
$389$	−3.29213	−	5.70214i	−0.166918	−	0.289110i	−0.937335	+	0.348431i	$0.886715\pi$
$390$		0			0
$391$	3.44078	−	5.95961i	0.174008	−	0.301391i
$392$		0			0
$393$	−2.72553	−	1.91409i	−0.137485	−	0.0965530i
$394$		0			0
$395$	3.84998			0.193714
$396$		0			0
$397$	−26.7100			−1.34054			−0.670269	−	0.742119i	$-0.733821\pi$
$397$	−26.7100			−1.34054			−0.670269	+	0.742119i	$0.733821\pi$
$398$		0			0
$399$	29.6232	−	13.7634i	1.48301	−	0.689033i
$400$		0			0
$401$	3.44698	−	5.97034i	0.172134	−	0.298145i	−0.767032	−	0.641609i	$-0.778267\pi$
$401$	3.44698	−	5.97034i	0.172134	−	0.298145i	0.939166	+	0.343464i	$0.111601\pi$
$402$		0			0
$403$	−19.7039	−	34.1282i	−0.981522	−	1.70005i
$404$		0			0
$405$	−6.92645	+	5.74668i	−0.344178	+	0.285555i
$406$		0			0
$407$	4.52421	+	7.83616i	0.224257	+	0.388424i
$408$		0			0
$409$	19.7484	−	34.2053i	0.976496	−	1.69134i	0.301591	−	0.953437i	$-0.402482\pi$
$409$	19.7484	−	34.2053i	0.976496	−	1.69134i	0.674906	−	0.737904i	$-0.264184\pi$
$410$		0			0
$411$	−4.51926	+	2.09972i	−0.222919	+	0.103572i
$412$		0			0
$413$	−48.2787			−2.37564
$414$		0			0
$415$	−11.9959			−0.588857
$416$		0			0
$417$	−21.7703	−	15.2888i	−1.06609	−	0.748697i
$418$		0			0
$419$	−18.7772	+	32.5231i	−0.917326	+	1.58886i	−0.113866	+	0.993496i	$0.536324\pi$
$419$	−18.7772	+	32.5231i	−0.917326	+	1.58886i	−0.803460	+	0.595359i	$0.797010\pi$
$420$		0			0
$421$	−11.5064	−	19.9297i	−0.560788	−	0.971313i	−0.997428	−	0.0716768i	$-0.977165\pi$
$421$	−11.5064	−	19.9297i	−0.560788	−	0.971313i	0.436640	−	0.899636i	$-0.356168\pi$
$422$		0			0
$423$	−3.42887	−	9.50285i	−0.166718	−	0.462044i
$424$		0			0
$425$	0.518221	+	0.897586i	0.0251374	+	0.0435393i
$426$		0			0
$427$	22.1599	−	38.3821i	1.07239	−	1.85744i
$428$		0			0
$429$	3.44829	−	38.7931i	0.166485	−	1.87295i
$430$		0			0
$431$	−10.7109			−0.515924			−0.257962	−	0.966155i	$-0.583051\pi$
$431$	−10.7109			−0.515924			−0.257962	+	0.966155i	$0.583051\pi$
$432$		0			0
$433$	32.1104			1.54313			0.771563	−	0.636153i	$-0.219475\pi$
$433$	32.1104			1.54313			0.771563	+	0.636153i	$0.219475\pi$
$434$		0			0
$435$	0.287301	−	3.23213i	0.0137750	−	0.154969i
$436$		0			0
$437$	−13.4941	+	23.3725i	−0.645512	+	1.11806i
$438$		0			0
$439$	9.46116	+	16.3872i	0.451557	+	0.782119i	0.998483	−	0.0550616i	$-0.0175355\pi$
$439$	9.46116	+	16.3872i	0.451557	+	0.782119i	−0.546926	+	0.837181i	$0.684202\pi$
$440$		0			0
$441$	28.1039	−	33.3045i	1.33828	−	1.58593i
$442$		0			0
$443$	−12.9593	−	22.4461i	−0.615714	−	1.06645i	−0.990259	−	0.139239i	$-0.955534\pi$
$443$	−12.9593	−	22.4461i	−0.615714	−	1.06645i	0.374545	−	0.927209i	$-0.377799\pi$
$444$		0			0
$445$	0.741454	−	1.28424i	0.0351483	−	0.0608786i
$446$		0			0
$447$	7.46035	+	5.23926i	0.352862	+	0.247808i
$448$		0			0
$449$	32.4821			1.53292			0.766462	−	0.642290i	$-0.222016\pi$
$449$	32.4821			1.53292			0.766462	+	0.642290i	$0.222016\pi$
$450$		0			0
$451$	−17.3439			−0.816695
$452$		0			0
$453$	−21.3888	+	9.93758i	−1.00493	+	0.466908i
$454$		0			0
$455$	10.1451	−	17.5719i	0.475611	−	0.823783i
$456$		0			0
$457$	20.5099	+	35.5242i	0.959413	+	1.66175i	0.723929	+	0.689874i	$0.242334\pi$
$457$	20.5099	+	35.5242i	0.959413	+	1.66175i	0.235484	+	0.971878i	$0.424332\pi$
$458$		0			0
$459$	1.41555	−	5.19615i	0.0660721	−	0.242536i
$460$		0			0
$461$	0.378678	+	0.655890i	0.0176368	+	0.0305478i	0.874709	−	0.484648i	$-0.161052\pi$
$461$	0.378678	+	0.655890i	0.0176368	+	0.0305478i	−0.857072	+	0.515196i	$0.827719\pi$
$462$		0			0
$463$	15.1949	−	26.3183i	0.706166	−	1.22311i	−0.260103	−	0.965581i	$-0.583757\pi$
$463$	15.1949	−	26.3183i	0.706166	−	1.22311i	0.966269	−	0.257534i	$-0.0829100\pi$
$464$		0			0
$465$	−14.1545	+	6.57640i	−0.656397	+	0.304973i
$466$		0			0
$467$	2.41191			0.111610			0.0558049	−	0.998442i	$-0.482228\pi$
$467$	2.41191			0.111610			0.0558049	+	0.998442i	$0.482228\pi$
$468$		0			0
$469$	10.0758			0.465257
$470$		0			0
$471$	−20.9892	−	14.7403i	−0.967131	−	0.679197i
$472$		0			0
$473$	13.0102	−	22.5344i	0.598212	−	1.03613i
$474$		0			0
$475$	−2.03237	−	3.52017i	−0.0932516	−	0.161517i
$476$		0			0
$477$	26.2713	+	4.70765i	1.20288	+	0.215549i
$478$		0			0
$479$	17.2020	+	29.7947i	0.785977	+	1.36135i	0.928413	+	0.371549i	$0.121173\pi$
$479$	17.2020	+	29.7947i	0.785977	+	1.36135i	−0.142436	+	0.989804i	$0.545494\pi$
$480$		0			0
$481$	3.84816	−	6.66521i	0.175461	−	0.303908i
$482$		0			0
$483$	−4.72414	+	53.1465i	−0.214956	+	2.41825i
$484$		0			0
$485$	−13.2258			−0.600554
$486$		0			0
$487$	16.9242			0.766909			0.383455	−	0.923560i	$-0.374734\pi$
$487$	16.9242			0.766909			0.383455	+	0.923560i	$0.374734\pi$
$488$		0			0
$489$	2.70023	−	30.3775i	0.122108	−	1.37372i
$490$		0			0
$491$	−6.41686	+	11.1143i	−0.289589	+	0.501582i	−0.973712	−	0.227784i	$-0.926852\pi$
$491$	−6.41686	+	11.1143i	−0.289589	+	0.501582i	0.684123	+	0.729367i	$0.260185\pi$
$492$		0			0
$493$	0.970851	+	1.68156i	0.0437249	+	0.0757338i
$494$		0			0
$495$	−15.1829	−	2.72068i	−0.682420	−	0.122286i
$496$		0			0
$497$	19.6682	+	34.0664i	0.882240	+	1.52808i
$498$		0			0
$499$	−9.32764	+	16.1559i	−0.417563	+	0.723240i	−0.995694	−	0.0927043i	$-0.970449\pi$
$499$	−9.32764	+	16.1559i	−0.417563	+	0.723240i	0.578131	+	0.815944i	$0.303782\pi$
$500$		0			0
$501$	−2.23639	−	1.57057i	−0.0999144	−	0.0701679i
$502$		0			0
$503$	25.4535			1.13492			0.567458	−	0.823402i	$-0.307927\pi$
$503$	25.4535			1.13492			0.567458	+	0.823402i	$0.307927\pi$
$504$		0			0
$505$	−12.8158			−0.570296
$506$		0			0
$507$	−9.62193	+	4.47051i	−0.427325	+	0.198542i
$508$		0			0
$509$	−5.65042	+	9.78681i	−0.250450	+	0.433793i	−0.963650	−	0.267168i	$-0.913912\pi$
$509$	−5.65042	+	9.78681i	−0.250450	+	0.433793i	0.713199	+	0.700961i	$0.247245\pi$
$510$		0			0
$511$	−12.1930	−	21.1189i	−0.539387	−	0.934246i
$512$		0			0
$513$	−5.55153	+	20.3784i	−0.245106	+	0.899728i
$514$		0			0
$515$	−8.60854	−	14.9104i	−0.379337	−	0.657032i
$516$		0			0
$517$	8.65716	−	14.9946i	0.380741	−	0.659464i
$518$		0			0
$519$	−33.6813	+	15.6489i	−1.47845	+	0.686911i
$520$		0			0
$521$	30.8279			1.35059			0.675297	−	0.737546i	$-0.264015\pi$
$521$	30.8279			1.35059			0.675297	+	0.737546i	$0.264015\pi$
$522$		0			0
$523$	−3.44488			−0.150634			−0.0753171	−	0.997160i	$-0.523997\pi$
$523$	−3.44488			−0.150634			−0.0753171	+	0.997160i	$0.523997\pi$
$524$		0			0
$525$	−6.57632	−	4.61842i	−0.287014	−	0.201564i
$526$		0			0
$527$	4.66972	−	8.08820i	0.203416	−	0.352328i
$528$		0			0
$529$	−10.5422	−	18.2596i	−0.458355	−	0.793894i
$530$		0			0
$531$	20.1325	−	23.8580i	0.873676	−	1.03535i
$532$		0			0
$533$	7.37614	+	12.7758i	0.319496	+	0.553383i
$534$		0			0
$535$	−6.71613	+	11.6327i	−0.290364	+	0.502924i
$536$		0			0
$537$	−2.66141	+	29.9407i	−0.114848	+	1.29204i
$538$		0			0
$539$	74.6860			3.21696
$540$		0			0
$541$	12.7479			0.548074			0.274037	−	0.961719i	$-0.411641\pi$
$541$	12.7479			0.548074			0.274037	+	0.961719i	$0.411641\pi$
$542$		0			0
$543$	−3.68549	+	41.4617i	−0.158160	+	1.77929i
$544$		0			0
$545$	−3.82296	+	6.62156i	−0.163758	+	0.283637i
$546$		0			0
$547$	−1.55190	−	2.68797i	−0.0663544	−	0.114929i	0.830940	−	0.556363i	$-0.187803\pi$
$547$	−1.55190	−	2.68797i	−0.0663544	−	0.114929i	−0.897294	+	0.441434i	$0.854470\pi$
$548$		0			0
$549$	9.72657	+	26.9564i	0.415120	+	1.15047i
$550$		0			0
$551$	−3.80750	−	6.59479i	−0.162205	−	0.280947i
$552$		0			0
$553$	8.93119	−	15.4693i	0.379793	−	0.657821i
$554$		0			0
$555$	−2.49447	−	1.75182i	−0.105884	−	0.0743605i
$556$		0			0
$557$	16.5905			0.702960			0.351480	−	0.936195i	$-0.385678\pi$
$557$	16.5905			0.702960			0.351480	+	0.936195i	$0.385678\pi$
$558$		0			0
$559$	−22.1323			−0.936096
$560$		0			0
$561$	8.37064	−	3.88914i	0.353409	−	0.164200i
$562$		0			0
$563$	−2.17598	+	3.76890i	−0.0917065	+	0.158840i	−0.908229	−	0.418473i	$-0.862565\pi$
$563$	−2.17598	+	3.76890i	−0.0917065	+	0.158840i	0.816523	+	0.577313i	$0.195899\pi$
$564$		0			0
$565$	5.36301	+	9.28901i	0.225624	+	0.390792i
$566$		0			0
$567$	7.02224	+	41.1617i	0.294906	+	1.72863i
$568$		0			0
$569$	−13.1717	−	22.8141i	−0.552188	−	0.956418i	−0.998116	−	0.0613492i	$-0.980460\pi$
$569$	−13.1717	−	22.8141i	−0.552188	−	0.956418i	0.445928	−	0.895069i	$-0.352874\pi$
$570$		0			0
$571$	1.85712	−	3.21662i	0.0777180	−	0.134612i	−0.824547	−	0.565793i	$-0.808570\pi$
$571$	1.85712	−	3.21662i	0.0777180	−	0.134612i	0.902265	+	0.431182i	$0.141903\pi$
$572$		0			0
$573$	−8.89650	+	4.13347i	−0.371657	+	0.172678i
$574$		0			0
$575$	6.63960			0.276891
$576$		0			0
$577$	6.77213			0.281927			0.140964	−	0.990015i	$-0.454980\pi$
$577$	6.77213			0.281927			0.140964	+	0.990015i	$0.454980\pi$
$578$		0			0
$579$	−8.77447	−	6.16214i	−0.364655	−	0.256090i
$580$		0			0
$581$	−27.8282	+	48.1998i	−1.15451	+	1.99967i
$582$		0			0
$583$	22.8712	+	39.6141i	0.947228	+	1.64065i
$584$		0			0
$585$	4.45296	+	12.3410i	0.184107	+	0.510239i
$586$		0			0
$587$	−6.65897	−	11.5337i	−0.274845	−	0.476045i	0.695251	−	0.718767i	$-0.255293\pi$
$587$	−6.65897	−	11.5337i	−0.274845	−	0.476045i	−0.970096	+	0.242722i	$0.921960\pi$
$588$		0			0
$589$	−18.3138	+	31.7205i	−0.754608	+	1.30702i
$590$		0			0
$591$	−1.11752	+	12.5720i	−0.0459685	+	0.517145i
$592$		0			0
$593$	13.3373			0.547696			0.273848	−	0.961773i	$-0.411703\pi$
$593$	13.3373			0.547696			0.273848	+	0.961773i	$0.411703\pi$
$594$		0			0
$595$	4.80868			0.197137
$596$		0			0
$597$	2.50135	−	28.1402i	0.102374	−	1.15170i
$598$		0			0
$599$	4.80917	−	8.32974i	0.196498	−	0.340344i	−0.750893	−	0.660424i	$-0.770377\pi$
$599$	4.80917	−	8.32974i	0.196498	−	0.340344i	0.947390	+	0.320080i	$0.103710\pi$
$600$		0			0
$601$	−2.33420	−	4.04295i	−0.0952139	−	0.164915i	0.814484	−	0.580186i	$-0.197020\pi$
$601$	−2.33420	−	4.04295i	−0.0952139	−	0.164915i	−0.909698	+	0.415271i	$0.863687\pi$
$602$		0			0
$603$	−4.20167	+	4.97919i	−0.171105	+	0.202768i
$604$		0			0
$605$	−7.71789	−	13.3678i	−0.313777	−	0.543477i
$606$		0			0
$607$	−3.22217	+	5.58096i	−0.130784	+	0.226524i	−0.923979	−	0.382443i	$-0.875083\pi$
$607$	−3.22217	+	5.58096i	−0.130784	+	0.226524i	0.793195	+	0.608968i	$0.208416\pi$
$608$		0			0
$609$	−12.3203	−	8.65227i	−0.499242	−	0.350608i
$610$		0			0
$611$	−14.7271			−0.595793
$612$		0			0
$613$	20.1411			0.813493			0.406746	−	0.913541i	$-0.366663\pi$
$613$	20.1411			0.813493			0.406746	+	0.913541i	$0.366663\pi$
$614$		0			0
$615$	5.29870	−	2.46186i	0.213664	−	0.0992720i
$616$		0			0
$617$	2.86636	−	4.96468i	0.115395	−	0.199870i	−0.802542	−	0.596595i	$-0.796520\pi$
$617$	2.86636	−	4.96468i	0.115395	−	0.199870i	0.917938	+	0.396725i	$0.129853\pi$
$618$		0			0
$619$	−9.08484	−	15.7354i	−0.365151	−	0.632459i	0.623650	−	0.781704i	$-0.285649\pi$
$619$	−9.08484	−	15.7354i	−0.365151	−	0.632459i	−0.988800	+	0.149244i	$0.952316\pi$
$620$		0			0
$621$	−24.2935	−	24.4969i	−0.974866	−	0.983029i
$622$		0			0
$623$	−3.44005	−	5.95835i	−0.137823	−	0.238716i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−32.8282	+	15.2525i	−1.31103	+	0.609127i
$628$		0			0
$629$	1.82399			0.0727271
$630$		0			0
$631$	21.1892			0.843528			0.421764	−	0.906706i	$-0.361411\pi$
$631$	21.1892			0.843528			0.421764	+	0.906706i	$0.361411\pi$
$632$		0			0
$633$	−33.1264	−	23.2640i	−1.31666	−	0.924662i
$634$		0			0
$635$	0.382808	−	0.663043i	0.0151913	−	0.0263121i
$636$		0			0
$637$	−31.7629	−	55.0150i	−1.25849	−	2.17977i
$638$		0			0
$639$	−25.0364	−	4.48638i	−0.990426	−	0.177478i
$640$		0			0
$641$	22.9248	+	39.7069i	0.905474	+	1.56833i	0.820279	+	0.571963i	$0.193818\pi$
$641$	22.9248	+	39.7069i	0.905474	+	1.56833i	0.0851952	+	0.996364i	$0.472849\pi$
$642$		0			0
$643$	14.2494	−	24.6807i	0.561942	−	0.973311i	−0.435385	−	0.900244i	$-0.643388\pi$
$643$	14.2494	−	24.6807i	0.561942	−	0.973311i	0.997327	−	0.0730672i	$-0.0232788\pi$
$644$		0			0
$645$	−0.776103	+	8.73114i	−0.0305590	+	0.343788i
$646$		0			0
$647$	32.9396			1.29499			0.647494	−	0.762070i	$-0.275817\pi$
$647$	32.9396			1.29499			0.647494	+	0.762070i	$0.275817\pi$
$648$		0			0
$649$	53.5021			2.10014
$650$		0			0
$651$	−6.41146	+	72.1287i	−0.251285	+	2.82695i
$652$		0			0
$653$	−2.67981	+	4.64157i	−0.104869	+	0.181639i	−0.913685	−	0.406424i	$-0.866776\pi$
$653$	−2.67981	+	4.64157i	−0.104869	+	0.181639i	0.808816	+	0.588062i	$0.200109\pi$
$654$		0			0
$655$	0.961434	+	1.66525i	0.0375663	+	0.0650668i
$656$		0			0
$657$	15.5210	+	2.78126i	0.605530	+	0.108507i
$658$		0			0
$659$	7.57080	+	13.1130i	0.294916	+	0.510810i	0.974965	−	0.222357i	$-0.0713749\pi$
$659$	7.57080	+	13.1130i	0.294916	+	0.510810i	−0.680049	+	0.733167i	$0.738042\pi$
$660$		0			0
$661$	−2.15422	+	3.73121i	−0.0837893	+	0.145127i	−0.904875	−	0.425678i	$-0.860036\pi$
$661$	−2.15422	+	3.73121i	−0.0837893	+	0.145127i	0.821085	+	0.570805i	$0.193369\pi$
$662$		0			0
$663$	−6.42472	−	4.51196i	−0.249515	−	0.175230i
$664$		0			0
$665$	−18.8588			−0.731313
$666$		0			0
$667$	12.4388			0.481633
$668$		0			0
$669$	3.52165	−	1.63622i	0.136155	−	0.0632599i
$670$		0			0
$671$	−24.5575	+	42.5348i	−0.948030	+	1.64204i
$672$		0			0
$673$	10.0224	+	17.3593i	0.386336	+	0.669153i	0.991954	−	0.126603i	$-0.0404073\pi$
$673$	10.0224	+	17.3593i	0.386336	+	0.669153i	−0.605618	+	0.795756i	$0.707074\pi$
$674$		0			0
$675$	5.02466	−	1.32393i	0.193399	−	0.0509580i
$676$		0			0
$677$	13.3326	+	23.0928i	0.512415	+	0.887529i	0.999896	+	0.0143957i	$0.00458245\pi$
$677$	13.3326	+	23.0928i	0.512415	+	0.887529i	−0.487481	+	0.873134i	$0.662084\pi$
$678$		0			0
$679$	−30.6813	+	53.1415i	−1.17744	+	2.03938i
$680$		0			0
$681$	4.67717	−	2.17309i	0.179230	−	0.0832731i
$682$		0			0
$683$	−25.2021			−0.964331			−0.482166	−	0.876080i	$-0.660150\pi$
$683$	−25.2021			−0.964331			−0.482166	+	0.876080i	$0.660150\pi$
$684$		0			0
$685$	2.87707			0.109927
$686$		0			0
$687$	38.3288	+	26.9176i	1.46233	+	1.02697i
$688$		0			0
$689$	19.4536	−	33.6946i	0.741122	−	1.28366i
$690$		0			0
$691$	−7.27258	−	12.5965i	−0.276662	−	0.479193i	0.693891	−	0.720080i	$-0.255895\pi$
$691$	−7.27258	−	12.5965i	−0.276662	−	0.479193i	−0.970553	+	0.240887i	$0.922562\pi$
$692$		0			0
$693$	−46.1530	+	54.6936i	−1.75321	+	2.07764i
$694$		0			0
$695$	7.67948	+	13.3012i	0.291299	+	0.504545i
$696$		0			0
$697$	−1.74810	+	3.02781i	−0.0662142	+	0.114686i
$698$		0			0
$699$	0.140018	−	1.57520i	0.00529596	−	0.0595794i
$700$		0			0
$701$	−16.0567			−0.606455			−0.303227	−	0.952918i	$-0.598064\pi$
$701$	−16.0567			−0.606455			−0.303227	+	0.952918i	$0.598064\pi$
$702$		0			0
$703$	−7.15335			−0.269794
$704$		0			0
$705$	−0.516428	+	5.80980i	−0.0194498	+	0.218810i
$706$		0			0
$707$	−29.7301	+	51.4941i	−1.11812	+	1.93663i
$708$		0			0
$709$	−15.5688	−	26.9659i	−0.584698	−	1.01273i	−0.994913	−	0.100738i	$-0.967880\pi$
$709$	−15.5688	−	26.9659i	−0.584698	−	1.01273i	0.410215	−	0.911989i	$-0.365454\pi$
$710$		0			0
$711$	3.92013	+	10.8643i	0.147017	+	0.407444i
$712$		0			0
$713$	−29.9149	−	51.8142i	−1.12032	−	1.94046i
$714$		0			0
$715$	−11.2428	+	19.4730i	−0.420455	+	0.728250i
$716$		0			0
$717$	−14.4235	−	10.1293i	−0.538654	−	0.378286i
$718$		0			0
$719$	−30.9181			−1.15305			−0.576525	−	0.817080i	$-0.695592\pi$
$719$	−30.9181			−1.15305			−0.576525	+	0.817080i	$0.695592\pi$
$720$		0			0
$721$	−79.8804			−2.97490
$722$		0			0
$723$	20.6288	−	9.58448i	0.767193	−	0.356451i
$724$		0			0
$725$	−0.936714	+	1.62244i	−0.0347887	+	0.0602558i
$726$		0			0
$727$	8.75834	+	15.1699i	0.324829	+	0.562620i	0.981478	−	0.191576i	$-0.0613599\pi$
$727$	8.75834	+	15.1699i	0.324829	+	0.562620i	−0.656649	+	0.754197i	$0.728027\pi$
$728$		0			0
$729$	−23.2693	−	13.6945i	−0.861826	−	0.507203i
$730$		0			0
$731$	−2.62262	−	4.54250i	−0.0970010	−	0.168011i
$732$		0			0
$733$	16.5276	−	28.6267i	0.610461	−	1.05735i	−0.380701	−	0.924698i	$-0.624317\pi$
$733$	16.5276	−	28.6267i	0.610461	−	1.05735i	0.991163	−	0.132652i	$-0.0423492\pi$
$734$		0			0
$735$	−22.8171	+	10.6012i	−0.841622	+	0.391032i
$736$		0			0
$737$	−11.1659			−0.411302
$738$		0			0
$739$	−15.9164			−0.585493			−0.292747	−	0.956190i	$-0.594569\pi$
$739$	−15.9164			−0.585493			−0.292747	+	0.956190i	$0.594569\pi$
$740$		0			0
$741$	25.1966	+	17.6951i	0.925621	+	0.650045i
$742$		0			0
$743$	−7.97902	+	13.8201i	−0.292722	+	0.507009i	−0.974452	−	0.224594i	$-0.927894\pi$
$743$	−7.97902	+	13.8201i	−0.292722	+	0.507009i	0.681730	+	0.731604i	$0.261228\pi$
$744$		0			0
$745$	−2.63164	−	4.55814i	−0.0964160	−	0.166997i
$746$		0			0
$747$	−12.2145	−	33.8516i	−0.446906	−	1.23856i
$748$		0			0
$749$	31.1602	+	53.9710i	1.13857	+	1.97206i
$750$		0			0
$751$	7.86854	−	13.6287i	0.287127	−	0.497319i	−0.685996	−	0.727606i	$-0.740633\pi$
$751$	7.86854	−	13.6287i	0.287127	−	0.497319i	0.973123	+	0.230287i	$0.0739664\pi$
$752$		0			0
$753$	−2.75726	+	31.0191i	−0.100480	+	1.13040i
$754$		0			0
$755$	13.6166			0.495559
$756$		0			0
$757$	−9.11012			−0.331113			−0.165556	−	0.986200i	$-0.552942\pi$
$757$	−9.11012			−0.331113			−0.165556	+	0.986200i	$0.552942\pi$
$758$		0			0
$759$	5.23526	−	58.8965i	0.190028	−	2.13781i
$760$		0			0
$761$	−7.48654	+	12.9671i	−0.271387	+	0.470056i	−0.969217	−	0.246207i	$-0.920816\pi$
$761$	−7.48654	+	12.9671i	−0.271387	+	0.470056i	0.697830	+	0.716263i	$0.254149\pi$
$762$		0			0
$763$	17.7370	+	30.7214i	0.642123	+	1.11219i
$764$		0			0
$765$	−2.00525	+	2.37632i	−0.0725000	+	0.0859160i
$766$		0			0
$767$	−22.7537	−	39.4105i	−0.821587	−	1.42303i
$768$		0			0
$769$	−0.626060	+	1.08437i	−0.0225763	+	0.0391033i	−0.877093	−	0.480321i	$-0.840520\pi$
$769$	−0.626060	+	1.08437i	−0.0225763	+	0.0391033i	0.854517	+	0.519424i	$0.173854\pi$
$770$		0			0
$771$	41.7064	+	29.2896i	1.50202	+	1.05484i
$772$		0			0
$773$	−14.5747			−0.524215			−0.262108	−	0.965039i	$-0.584418\pi$
$773$	−14.5747			−0.524215			−0.262108	+	0.965039i	$0.584418\pi$
$774$		0			0
$775$	9.01106			0.323687
$776$		0			0
$777$	−12.8255	+	5.95895i	−0.460112	+	0.213776i
$778$		0			0
$779$	6.85575	−	11.8745i	0.245633	−	0.425449i
$780$		0			0
$781$	−21.7962	−	37.7521i	−0.779929	−	1.35088i
$782$		0			0
$783$	9.41334	−	2.48028i	0.336405	−	0.0886381i
$784$		0			0
$785$	7.40396	+	12.8240i	0.264259	+	0.457709i
$786$		0			0
$787$	1.01630	−	1.76028i	0.0362272	−	0.0627473i	−0.847343	−	0.531045i	$-0.821799\pi$
$787$	1.01630	−	1.76028i	0.0362272	−	0.0627473i	0.883571	+	0.468298i	$0.155133\pi$
$788$		0			0
$789$	−32.6261	+	15.1586i	−1.16152	+	0.539662i
$790$		0			0
$791$	49.7645			1.76942
$792$		0			0
$793$	41.7758			1.48350
$794$		0			0
$795$	−12.6103	−	8.85595i	−0.447240	−	0.314088i
$796$		0			0
$797$	6.10733	−	10.5782i	0.216333	−	0.374699i	−0.737351	−	0.675510i	$-0.763924\pi$
$797$	6.10733	−	10.5782i	0.216333	−	0.374699i	0.953684	+	0.300810i	$0.0972571\pi$
$798$		0			0
$799$	−1.74512	−	3.02263i	−0.0617378	−	0.106933i
$800$		0			0
$801$	4.37897	+	0.784686i	0.154723	+	0.0277255i
$802$		0			0
$803$	13.5122	+	23.4038i	0.476836	+	0.825904i
$804$		0			0
$805$	15.4026	−	26.6780i	0.542869	−	0.940276i
$806$		0			0
$807$	1.25229	−	14.0883i	0.0440828	−	0.495930i
$808$		0			0
$809$	−27.8097			−0.977737			−0.488869	−	0.872357i	$-0.662590\pi$
$809$	−27.8097			−0.977737			−0.488869	+	0.872357i	$0.662590\pi$
$810$		0			0
$811$	9.24210			0.324534			0.162267	−	0.986747i	$-0.448119\pi$
$811$	9.24210			0.324534			0.162267	+	0.986747i	$0.448119\pi$
$812$		0			0
$813$	−1.95529	+	21.9970i	−0.0685750	+	0.771467i
$814$		0			0
$815$	−8.80380	+	15.2486i	−0.308384	+	0.534136i
$816$		0			0
$817$	10.2854	+	17.8149i	0.359842	+	0.623264i
$818$		0			0
$819$	59.9164	+	10.7367i	2.09365	+	0.375170i
$820$		0			0
$821$	8.22018	+	14.2378i	0.286886	+	0.496901i	0.973065	−	0.230532i	$-0.0740465\pi$
$821$	8.22018	+	14.2378i	0.286886	+	0.496901i	−0.686179	+	0.727433i	$0.740713\pi$
$822$		0			0
$823$	20.8503	−	36.1138i	0.726796	−	1.25885i	−0.231435	−	0.972850i	$-0.574342\pi$
$823$	20.8503	−	36.1138i	0.726796	−	1.25885i	0.958231	−	0.285996i	$-0.0923246\pi$
$824$		0			0
$825$	7.28783	+	5.11810i	0.253730	+	0.178189i
$826$		0			0
$827$	6.03875			0.209988			0.104994	−	0.994473i	$-0.466518\pi$
$827$	6.03875			0.209988			0.104994	+	0.994473i	$0.466518\pi$
$828$		0			0
$829$	11.7973			0.409736			0.204868	−	0.978790i	$-0.434324\pi$
$829$	11.7973			0.409736			0.204868	+	0.978790i	$0.434324\pi$
$830$		0			0
$831$	6.49743	−	3.01881i	0.225393	−	0.104721i
$832$		0			0
$833$	7.52764	−	13.0383i	0.260817	−	0.451749i
$834$		0			0
$835$	0.788888	+	1.36639i	0.0273006	+	0.0472860i
$836$		0			0
$837$	−32.9704	−	33.2465i	−1.13962	−	1.14917i
$838$		0			0
$839$	−2.88669	−	4.99990i	−0.0996597	−	0.172616i	0.811884	−	0.583819i	$-0.198442\pi$
$839$	−2.88669	−	4.99990i	−0.0996597	−	0.172616i	−0.911544	+	0.411203i	$0.865109\pi$
$840$		0			0
$841$	12.7451	−	22.0752i	0.439487	−	0.761214i
$842$		0			0
$843$	−2.46519	+	1.14537i	−0.0849056	+	0.0394486i
$844$		0			0
$845$	6.12555			0.210725
$846$		0			0
$847$	−71.6159			−2.46075
$848$		0			0
$849$	5.06116	+	3.55436i	0.173699	+	0.121985i
$850$		0			0
$851$	5.84236	−	10.1193i	0.200274	−	0.346884i
$852$		0			0
$853$	−4.18810	−	7.25401i	−0.143398	−	0.248372i	0.785376	−	0.619019i	$-0.212470\pi$
$853$	−4.18810	−	7.25401i	−0.143398	−	0.248372i	−0.928774	+	0.370646i	$0.879136\pi$
$854$		0			0
$855$	7.86423	−	9.31950i	0.268951	−	0.318720i
$856$		0			0
$857$	4.04677	+	7.00920i	0.138235	+	0.239430i	0.926829	−	0.375485i	$-0.122524\pi$
$857$	4.04677	+	7.00920i	0.138235	+	0.239430i	−0.788594	+	0.614915i	$0.789190\pi$
$858$		0			0
$859$	−19.8503	+	34.3817i	−0.677283	+	1.17309i	0.298513	+	0.954406i	$0.403510\pi$
$859$	−19.8503	+	34.3817i	−0.677283	+	1.17309i	−0.975796	+	0.218683i	$0.929824\pi$
$860$		0			0
$861$	2.40012	−	27.0013i	0.0817959	−	0.920201i
$862$		0			0
$863$	−34.2524			−1.16597			−0.582983	−	0.812484i	$-0.698115\pi$
$863$	−34.2524			−1.16597			−0.582983	+	0.812484i	$0.698115\pi$
$864$		0			0
$865$	21.4423			0.729061
$866$		0			0
$867$	−2.44231	+	27.4759i	−0.0829452	+	0.933132i
$868$		0			0
$869$	−9.89748	+	17.1429i	−0.335749	+	0.581535i
$870$		0			0
$871$	4.74871	+	8.22501i	0.160904	+	0.278694i
$872$		0			0
$873$	−13.4668	−	37.3222i	−0.455783	−	1.26316i
$874$		0			0
$875$	2.31980	+	4.01801i	0.0784236	+	0.135834i
$876$		0			0
$877$	−21.3526	+	36.9837i	−0.721025	+	1.24885i	0.239564	+	0.970881i	$0.422995\pi$
$877$	−21.3526	+	36.9837i	−0.721025	+	1.24885i	−0.960589	+	0.277972i	$0.910338\pi$
$878$		0			0
$879$	−31.6279	−	22.2116i	−1.06678	−	0.749180i
$880$		0			0
$881$	8.80329			0.296590			0.148295	−	0.988943i	$-0.452621\pi$
$881$	8.80329			0.296590			0.148295	+	0.988943i	$0.452621\pi$
$882$		0			0
$883$	16.5952			0.558472			0.279236	−	0.960223i	$-0.409919\pi$
$883$	16.5952			0.558472			0.279236	+	0.960223i	$0.409919\pi$
$884$		0			0
$885$	−16.3453	+	7.59428i	−0.549440	+	0.255279i
$886$		0			0
$887$	−3.30159	+	5.71852i	−0.110857	+	0.192009i	−0.916116	−	0.400914i	$-0.868693\pi$
$887$	−3.30159	+	5.71852i	−0.110857	+	0.192009i	0.805259	+	0.592923i	$0.202026\pi$
$888$		0			0
$889$	−1.77608	−	3.07626i	−0.0595677	−	0.103174i
$890$		0			0
$891$	−7.78199	−	45.6151i	−0.260707	−	1.52816i
$892$		0			0
$893$	6.84404	+	11.8542i	0.229027	+	0.396687i
$894$		0			0
$895$	8.67722	−	15.0294i	0.290048	−	0.502377i
$896$		0			0
$897$	−45.6106	+	21.1915i	−1.52290	+	0.707563i
$898$		0			0
$899$	16.8816			0.563032
$900$		0			0
$901$	9.22079			0.307189
$902$		0			0
$903$	33.2814	+	23.3729i	1.10754	+	0.777802i
$904$		0			0
$905$	12.0162	−	20.8126i	0.399431	−	0.691834i
$906$		0			0
$907$	11.6423	+	20.1651i	0.386576	+	0.669570i	0.991987	−	0.126344i	$-0.0403243\pi$
$907$	11.6423	+	20.1651i	0.386576	+	0.669570i	−0.605410	+	0.795914i	$0.706991\pi$
$908$		0			0
$909$	−13.0493	−	36.1651i	−0.432819	−	1.19952i
$910$		0			0
$911$	16.1372	+	27.9505i	0.534650	+	0.926040i	0.999180	+	0.0404832i	$0.0128897\pi$
$911$	16.1372	+	27.9505i	0.534650	+	0.926040i	−0.464531	+	0.885557i	$0.653777\pi$
$912$		0			0
$913$	30.8390	−	53.4147i	1.02062	−	1.76777i
$914$		0			0
$915$	1.46493	−	16.4805i	0.0484292	−	0.544827i
$916$		0			0
$917$	8.92134			0.294609
$918$		0			0
$919$	12.2816			0.405131			0.202566	−	0.979269i	$-0.435072\pi$
$919$	12.2816			0.405131			0.202566	+	0.979269i	$0.435072\pi$
$920$		0			0
$921$	2.63072	−	29.5955i	0.0866851	−	0.975205i
$922$		0			0
$923$	−18.5392	+	32.1109i	−0.610226	+	1.05694i
$924$		0			0
$925$	0.879927	+	1.52408i	0.0289318	+	0.0501114i
$926$		0			0
$927$	33.3106	−	39.4747i	1.09406	−	1.29652i
$928$		0			0
$929$	28.5325	+	49.4197i	0.936120	+	1.62141i	0.772625	+	0.634863i	$0.218943\pi$
$929$	28.5325	+	49.4197i	0.936120	+	1.62141i	0.163495	+	0.986544i	$0.447723\pi$
$930$		0			0
$931$	−29.5221	+	51.1337i	−0.967546	+	1.67584i
$932$		0			0
$933$	14.8610	+	10.4366i	0.486528	+	0.341679i
$934$		0			0
$935$	−5.32895			−0.174275
$936$		0			0
$937$	22.7487			0.743169			0.371585	−	0.928399i	$-0.378815\pi$
$937$	22.7487			0.743169			0.371585	+	0.928399i	$0.378815\pi$
$938$		0			0
$939$	−26.6883	+	12.3999i	−0.870941	+	0.404654i
$940$		0			0
$941$	−18.1264	+	31.3959i	−0.590905	+	1.02348i	0.403205	+	0.915109i	$0.367896\pi$
$941$	−18.1264	+	31.3959i	−0.590905	+	1.02348i	−0.994111	+	0.108369i	$0.965437\pi$
$942$		0			0
$943$	11.1986	+	19.3966i	0.364677	+	0.631639i
$944$		0			0
$945$	6.33666	−	23.2604i	0.206131	−	0.756661i
$946$		0			0
$947$	23.8257	+	41.2673i	0.774230	+	1.34101i	0.935226	+	0.354050i	$0.115196\pi$
$947$	23.8257	+	41.2673i	0.774230	+	1.34101i	−0.160996	+	0.986955i	$0.551471\pi$
$948$		0			0
$949$	11.4931	−	19.9066i	0.373082	−	0.646197i
$950$		0			0
$951$	−19.7356	+	9.16948i	−0.639970	+	0.297341i
$952$		0			0
$953$	−16.4521			−0.532935			−0.266468	−	0.963844i	$-0.585857\pi$
$953$	−16.4521			−0.532935			−0.266468	+	0.963844i	$0.585857\pi$
$954$		0			0
$955$	5.66372			0.183274
$956$		0			0
$957$	13.6532	+	9.58839i	0.441346	+	0.309949i
$958$		0			0
$959$	6.67423	−	11.5601i	0.215522	−	0.373295i
$960$		0			0
$961$	−25.0996	−	43.4738i	−0.809664	−	1.40238i
$962$		0			0
$963$	−39.6650	−	7.10773i	−1.27819	−	0.229043i
$964$		0			0
$965$	3.09520	+	5.36105i	0.0996381	+	0.172578i
$966$		0			0
$967$	−30.0324	+	52.0177i	−0.965777	+	1.67278i	−0.258265	+	0.966074i	$0.583151\pi$
$967$	−30.0324	+	52.0177i	−0.965777	+	1.67278i	−0.707513	+	0.706701i	$0.750183\pi$
$968$		0			0
$969$	−0.646069	+	7.26826i	−0.0207547	+	0.233490i
$970$		0			0
$971$	−21.5189			−0.690575			−0.345288	−	0.938497i	$-0.612219\pi$
$971$	−21.5189			−0.690575			−0.345288	+	0.938497i	$0.612219\pi$
$972$		0			0
$973$	71.2594			2.28447
$974$		0			0
$975$	0.670667	−	7.54499i	0.0214785	−	0.241633i
$976$		0			0
$977$	−17.9570	+	31.1025i	−0.574497	+	0.995057i	0.421600	+	0.906782i	$0.361469\pi$
$977$	−17.9570	+	31.1025i	−0.574497	+	0.995057i	−0.996096	+	0.0882751i	$0.971865\pi$
$978$		0			0
$979$	3.81224	+	6.60300i	0.121840	+	0.211033i
$980$		0			0
$981$	−22.5781	−	4.04587i	−0.720864	−	0.129175i
$982$		0			0
$983$	−11.6111	−	20.1110i	−0.370336	−	0.641441i	0.619281	−	0.785169i	$-0.287424\pi$
$983$	−11.6111	−	20.1110i	−0.370336	−	0.641441i	−0.989617	+	0.143728i	$0.954091\pi$
$984$		0			0
$985$	3.64355	−	6.31081i	0.116093	−	0.201079i
$986$		0			0
$987$	22.1458	+	15.5526i	0.704910	+	0.495044i
$988$		0			0
$989$	−33.6017			−1.06847
$990$		0			0
$991$	19.3020			0.613149			0.306575	−	0.951847i	$-0.400817\pi$
$991$	19.3020			0.613149			0.306575	+	0.951847i	$0.400817\pi$
$992$		0			0
$993$	39.5378	−	18.3699i	1.25470	−	0.582953i
$994$		0			0
$995$	−8.15540	+	14.1256i	−0.258543	+	0.447810i
$996$		0			0
$997$	16.9959	+	29.4378i	0.538267	+	0.932305i	0.998998	+	0.0447654i	$0.0142540\pi$
$997$	16.9959	+	29.4378i	0.538267	+	0.932305i	−0.460731	+	0.887540i	$0.652413\pi$
$998$		0			0
$999$	2.40356	−	8.82293i	0.0760454	−	0.279145i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1440.2.q.p.481.3	yes	10
3.2	odd	2		4320.2.q.p.1441.5		10
4.3	odd	2		1440.2.q.o.481.3	✓	10
9.2	odd	6		4320.2.q.p.2881.5		10
9.7	even	3	inner	1440.2.q.p.961.3	yes	10
12.11	even	2		4320.2.q.o.1441.1		10
36.7	odd	6		1440.2.q.o.961.3	yes	10
36.11	even	6		4320.2.q.o.2881.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1440.2.q.o.481.3	✓	10	4.3	odd	2
1440.2.q.o.961.3	yes	10	36.7	odd	6
1440.2.q.p.481.3	yes	10	1.1	even	1	trivial
1440.2.q.p.961.3	yes	10	9.7	even	3	inner
4320.2.q.o.1441.1		10	12.11	even	2
4320.2.q.o.2881.1		10	36.11	even	6
4320.2.q.p.1441.5		10	3.2	odd	2
4320.2.q.p.2881.5		10	9.2	odd	6

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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1440.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.153356 - 1.72525i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.31980 + 4.01801i) q^{7} +(-2.95296 - 0.529154i) q^{9} +O(q^{10})\)	\(q+(0.153356 - 1.72525i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(2.31980 + 4.01801i) q^{7} +(-2.95296 - 0.529154i) q^{9} +(-2.57079 - 4.45273i) q^{11} +(-2.18664 + 3.78737i) q^{13} +(1.41743 + 0.995434i) q^{15} -1.03644 q^{17} +4.06474 q^{19} +(7.28783 - 3.38605i) q^{21} +(-3.31980 + 5.75006i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-1.36578 + 5.01345i) q^{27} +(-0.936714 - 1.62244i) q^{29} +(-4.50553 + 7.80381i) q^{31} +(-8.07632 + 3.75239i) q^{33} -4.63960 q^{35} -1.75985 q^{37} +(6.19882 + 4.35331i) q^{39} +(1.68664 - 2.92134i) q^{41} +(2.53040 + 4.38278i) q^{43} +(1.93474 - 2.29277i) q^{45} +(1.68376 + 2.91635i) q^{47} +(-7.26295 + 12.5798i) q^{49} +(-0.158945 + 1.78812i) q^{51} -8.89657 q^{53} +5.14157 q^{55} +(0.623352 - 7.01269i) q^{57} +(-5.20289 + 9.01167i) q^{59} +(-4.77625 - 8.27272i) q^{61} +(-4.72414 - 13.0926i) q^{63} +(-2.18664 - 3.78737i) q^{65} +(1.08585 - 1.88074i) q^{67} +(9.41118 + 6.60929i) q^{69} +8.47841 q^{71} -5.25606 q^{73} +(-1.57079 + 0.729814i) q^{75} +(11.9274 - 20.6589i) q^{77} +(-1.92499 - 3.33418i) q^{79} +(8.43999 + 3.12514i) q^{81} +(5.99797 + 10.3888i) q^{83} +(0.518221 - 0.897586i) q^{85} +(-2.94276 + 1.36725i) q^{87} -1.48291 q^{89} -20.2903 q^{91} +(12.7726 + 8.96992i) q^{93} +(-2.03237 + 3.52017i) q^{95} +(6.61291 + 11.4539i) q^{97} +(5.23526 + 14.5091i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} - 5 q^{5} - q^{9}+O(q^{10}) \) 10 * q + q^3 - 5 * q^5 - q^9	\( 10 q + q^{3} - 5 q^{5} - q^{9} - 9 q^{11} - 4 q^{13} - 2 q^{15} + 6 q^{17} + 14 q^{19} + 12 q^{21} - 10 q^{23} - 5 q^{25} - 2 q^{27} - 2 q^{29} - 8 q^{31} - 27 q^{33} + 16 q^{37} + 26 q^{39} - q^{41} - q^{43} - q^{45} - 10 q^{47} - q^{49} - 3 q^{51} - 20 q^{53} + 18 q^{55} - 19 q^{57} - 13 q^{59} - 14 q^{61} - 30 q^{63} - 4 q^{65} - 15 q^{67} + 8 q^{69} + 32 q^{71} - 14 q^{73} + q^{75} + 12 q^{77} - 18 q^{79} + 35 q^{81} + 8 q^{83} - 3 q^{85} - 32 q^{87} + 28 q^{89} - 36 q^{91} + 16 q^{93} - 7 q^{95} + 17 q^{97}+O(q^{100}) \) 10 * q + q^3 - 5 * q^5 - q^9 - 9 * q^11 - 4 * q^13 - 2 * q^15 + 6 * q^17 + 14 * q^19 + 12 * q^21 - 10 * q^23 - 5 * q^25 - 2 * q^27 - 2 * q^29 - 8 * q^31 - 27 * q^33 + 16 * q^37 + 26 * q^39 - q^41 - q^43 - q^45 - 10 * q^47 - q^49 - 3 * q^51 - 20 * q^53 + 18 * q^55 - 19 * q^57 - 13 * q^59 - 14 * q^61 - 30 * q^63 - 4 * q^65 - 15 * q^67 + 8 * q^69 + 32 * q^71 - 14 * q^73 + q^75 + 12 * q^77 - 18 * q^79 + 35 * q^81 + 8 * q^83 - 3 * q^85 - 32 * q^87 + 28 * q^89 - 36 * q^91 + 16 * q^93 - 7 * q^95 + 17 * q^97

Introduction

L-functions

Modular forms

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