LMFDB - Embedded newform 1440.2.q.o.961.3

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			961.3
Root			$-1.41743 + 0.995434i$ of defining polynomial
Character	$\chi$	$=$	1440.961
Dual form			1440.2.q.o.481.3

$q$-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 $\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times$.

$n$	$577$	$641$	$901$	$991$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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	−0.0219721	+	0.999759i	$0.506995\pi$
$7$	−2.31980	+	4.01801i	−0.876802	+	1.51867i	−0.854830	+	0.518908i	$0.826339\pi$
$8$		0			0
$9$	−2.95296	+	0.529154i	−0.984321	+	0.176385i
$10$		0			0
$11$	2.57079	−	4.45273i	0.775121	−	1.34255i	−0.159605	−	0.987181i	$-0.551022\pi$
$11$	2.57079	−	4.45273i	0.775121	−	1.34255i	0.934726	−	0.355369i	$-0.115645\pi$
$12$		0			0
$13$	−2.18664	−	3.78737i	−0.606464	−	1.05043i	−0.991818	−	0.127658i	$-0.959254\pi$
$13$	−2.18664	−	3.78737i	−0.606464	−	1.05043i	0.385354	−	0.922769i	$-0.374079\pi$
$14$		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	$-0.654398\pi$
$19$	−4.06474			−0.932516			−0.466258	+	0.884649i	$0.654398\pi$
$20$		0			0
$21$	7.28783	+	3.38605i	1.59033	+	0.738896i
$22$		0			0
$23$	3.31980	+	5.75006i	0.692226	+	1.19897i	0.971107	+	0.238645i	$0.0767034\pi$
$23$	3.31980	+	5.75006i	0.692226	+	1.19897i	−0.278880	+	0.960326i	$0.589963\pi$
$24$		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	−0.939795	−	0.341738i	$-0.888984\pi$
$29$	−0.936714	+	1.62244i	−0.173943	+	0.301279i	0.765852	+	0.643017i	$0.222318\pi$
$30$		0			0
$31$	4.50553	+	7.80381i	0.809217	+	1.40160i	0.913407	+	0.407047i	$0.133442\pi$
$31$	4.50553	+	7.80381i	0.809217	+	1.40160i	−0.104190	+	0.994557i	$0.533225\pi$
$32$		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	0.967145	−	0.254224i	$-0.0818199\pi$
$41$	1.68664	+	2.92134i	0.263409	+	0.456237i	−0.703737	+	0.710461i	$0.748487\pi$
$42$		0			0
$43$	−2.53040	+	4.38278i	−0.385883	+	0.668368i	−0.991891	−	0.127090i	$-0.959436\pi$
$43$	−2.53040	+	4.38278i	−0.385883	+	0.668368i	0.606009	+	0.795458i	$0.292770\pi$
$44$		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	$-0.912319\pi$
$47$	−1.68376	+	2.91635i	−0.245601	+	0.425394i	0.716699	+	0.697382i	$0.245652\pi$
$48$		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	0.975774	+	0.218783i	$0.0702087\pi$
$59$	5.20289	+	9.01167i	0.677358	+	1.17322i	−0.298415	+	0.954436i	$0.596458\pi$
$60$		0			0
$61$	−4.77625	+	8.27272i	−0.611537	+	1.05921i	0.379445	+	0.925214i	$0.376115\pi$
$61$	−4.77625	+	8.27272i	−0.611537	+	1.05921i	−0.990982	+	0.133998i	$0.957218\pi$
$62$		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	$-0.209018\pi$
$67$	−1.08585	−	1.88074i	−0.132657	−	0.229769i	−0.924700	+	0.380696i	$0.875684\pi$
$68$		0			0
$69$	9.41118	−	6.60929i	1.13297	−	0.795665i
$70$		0			0
$71$	−8.47841			−1.00620			−0.503101	−	0.864228i	$-0.667808\pi$
$71$	−8.47841			−1.00620			−0.503101	+	0.864228i	$0.667808\pi$
$72$		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	$-0.763844\pi$
$79$	1.92499	−	3.33418i	0.216578	−	0.375125i	0.953760	+	0.300570i	$0.0971770\pi$
$80$		0			0
$81$	8.43999	−	3.12514i	0.937777	−	0.347238i
$82$		0			0
$83$	−5.99797	+	10.3888i	−0.658363	+	1.14032i	0.322677	+	0.946509i	$0.395417\pi$
$83$	−5.99797	+	10.3888i	−0.658363	+	1.14032i	−0.981039	+	0.193808i	$0.937916\pi$
$84$		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	−0.306057	−	0.952013i	$-0.599010\pi$
$97$	6.61291	−	11.4539i	0.671439	−	1.16297i	0.977496	−	0.210954i	$-0.0676570\pi$
$98$		0			0
$99$	−5.23526	+	14.5091i	−0.526163	+	1.45822i
$100$		0			0
$101$	6.40790	−	11.0988i	0.637610	−	1.10437i	−0.348346	−	0.937366i	$-0.613257\pi$
$101$	6.40790	−	11.0988i	0.637610	−	1.10437i	0.985956	−	0.167007i	$-0.0534101\pi$
$102$		0			0
$103$	8.60854	+	14.9104i	0.848224	+	1.46917i	0.882791	+	0.469765i	$0.155661\pi$
$103$	8.60854	+	14.9104i	0.848224	+	1.46917i	−0.0345670	+	0.999402i	$0.511005\pi$
$104$		0			0
$105$	−0.711510	−	8.00447i	−0.0694363	−	0.781156i
$106$		0			0
$107$	−13.4323			−1.29855			−0.649273	−	0.760556i	$-0.724927\pi$
$107$	−13.4323			−1.29855			−0.649273	+	0.760556i	$0.724927\pi$
$108$		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	0.999986	+	0.00521530i	$0.00166009\pi$
$113$	5.36301	+	9.28901i	0.504510	+	0.873837i	−0.495477	+	0.868621i	$0.665007\pi$
$114$		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	$-0.489185\pi$
$127$	0.765616			0.0679374			0.0339687	+	0.999423i	$0.489185\pi$
$128$		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	$-0.193437\pi$
$131$	−0.961434	−	1.66525i	−0.0840009	−	0.145494i	−0.904965	+	0.425486i	$0.860103\pi$
$132$		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	−0.920911	−	0.389773i	$-0.872553\pi$
$137$	−1.43853	+	2.49161i	−0.122902	+	0.212873i	0.798009	+	0.602646i	$0.205887\pi$
$138$		0			0
$139$	−7.67948	−	13.3012i	−0.651365	−	1.12820i	−0.982792	−	0.184716i	$-0.940864\pi$
$139$	−7.67948	−	13.3012i	−0.651365	−	1.12820i	0.331427	−	0.943481i	$-0.392470\pi$
$140$		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	0.737863	−	0.674950i	$-0.235835\pi$
$149$	−2.63164	−	4.55814i	−0.215593	−	0.373418i	−0.953456	+	0.301533i	$0.902502\pi$
$150$		0			0
$151$	6.80830	−	11.7923i	0.554051	−	0.959645i	−0.443925	−	0.896064i	$-0.646414\pi$
$151$	6.80830	−	11.7923i	0.554051	−	0.959645i	0.997977	−	0.0635814i	$-0.0202523\pi$
$152$		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	0.994111	+	0.108362i	$0.0345606\pi$
$157$	7.40396	+	12.8240i	0.590900	+	1.02347i	−0.403211	+	0.915107i	$0.632106\pi$
$158$		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	$-0.742199\pi$
$163$	−17.6076			−1.37913			−0.689567	+	0.724222i	$0.742199\pi$
$164$		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	$-0.186110\pi$
$167$	−0.788888	−	1.36639i	−0.0610459	−	0.105735i	−0.894933	+	0.446200i	$0.852777\pi$
$168$		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	0.0941297	+	0.995560i	$0.469993\pi$
$173$	−10.7212	+	18.5696i	−0.815115	+	1.41182i	−0.909245	+	0.416261i	$0.863340\pi$
$174$		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	$-0.275369\pi$
$179$	17.3544			1.29713			0.648566	+	0.761158i	$0.275369\pi$
$180$		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	$-0.767644\pi$
$191$	2.83186	−	4.90493i	0.204906	−	0.354908i	0.950103	+	0.311937i	$0.100978\pi$
$192$		0			0
$193$	3.09520	+	5.36105i	0.222797	+	0.385897i	0.955656	−	0.294484i	$-0.0951478\pi$
$193$	3.09520	+	5.36105i	0.222797	+	0.385897i	−0.732859	+	0.680381i	$0.761814\pi$
$194$		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	$-0.696214\pi$
$199$	−16.3108			−1.15624			−0.578121	+	0.815951i	$0.696214\pi$
$200$		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	−0.916659	−	0.399670i	$-0.869125\pi$
$211$	−11.6854	−	20.2396i	−0.804454	−	1.39335i	0.112205	−	0.993685i	$-0.464209\pi$
$212$		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	$-0.857250\pi$
$223$	−1.12098	+	1.94160i	−0.0750666	+	0.130019i	0.826049	+	0.563599i	$0.190584\pi$
$224$		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	$-0.864839\pi$
$227$	−1.48880	+	2.57867i	−0.0988150	+	0.171153i	0.812379	+	0.583129i	$0.198172\pi$
$228$		0			0
$229$	−13.5205	−	23.4182i	−0.893460	−	1.54752i	−0.835699	−	0.549188i	$-0.814937\pi$
$229$	−13.5205	−	23.4182i	−0.893460	−	1.54752i	−0.0577615	−	0.998330i	$-0.518396\pi$
$230$		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	$-0.273415\pi$
$239$	−5.08789	−	8.81248i	−0.329108	−	0.570032i	−0.982335	+	0.187130i	$0.940081\pi$
$240$		0			0
$241$	6.56639	−	11.3733i	0.422978	−	0.732620i	−0.573251	−	0.819380i	$-0.694318\pi$
$241$	6.56639	−	11.3733i	0.422978	−	0.732620i	0.996229	+	0.0867601i	$0.0276514\pi$
$242$		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	$-0.307939\pi$
$251$	17.9795			1.13486			0.567428	+	0.823423i	$0.307939\pi$
$252$		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	−0.802888	−	0.596130i	$-0.796704\pi$
$257$	−14.7120	−	25.4819i	−0.917708	−	1.58952i	−0.114820	−	0.993386i	$-0.536629\pi$
$258$		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	−0.344963	−	0.938616i	$-0.612109\pi$
$263$	10.3853	−	17.9878i	0.640384	−	1.10918i	0.985347	−	0.170561i	$-0.0545580\pi$
$264$		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	$-0.373423\pi$
$271$	12.7500			0.774509			0.387255	+	0.921973i	$0.373423\pi$
$272$		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	−0.797179	−	0.603742i	$-0.793676\pi$
$277$	2.06821	−	3.58224i	0.124267	−	0.215236i	0.921446	+	0.388506i	$0.127009\pi$
$278$		0			0
$279$	−17.4341	−	20.6602i	−1.04375	−	1.23690i
$280$		0			0
$281$	−0.784699	+	1.35914i	−0.0468112	+	0.0810794i	−0.888482	−	0.458912i	$-0.848239\pi$
$281$	−0.784699	+	1.35914i	−0.0468112	+	0.0810794i	0.841670	+	0.539992i	$0.181573\pi$
$282$		0			0
$283$	1.78533	+	3.09228i	0.106127	+	0.183817i	0.914198	−	0.405268i	$-0.132822\pi$
$283$	1.78533	+	3.09228i	0.106127	+	0.183817i	−0.808071	+	0.589085i	$0.799488\pi$
$284$		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	0.982690	+	0.185260i	$0.0593127\pi$
$293$	11.1568	+	19.3241i	0.651784	+	1.12892i	−0.330905	+	0.943664i	$0.607354\pi$
$294$		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	$-0.662830\pi$
$307$	−17.1543			−0.979050			−0.489525	+	0.871989i	$0.662830\pi$
$308$		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	$-0.0705938\pi$
$311$	5.24224	+	9.07983i	0.297260	+	0.514870i	−0.678248	+	0.734833i	$0.737260\pi$
$312$		0			0
$313$	−8.49522	+	14.7141i	−0.480178	+	0.831693i	−0.999741	−	0.0227392i	$-0.992761\pi$
$313$	−8.49522	+	14.7141i	−0.480178	+	0.831693i	0.519563	+	0.854432i	$0.326095\pi$
$314$		0			0
$315$	−13.7006	+	2.45506i	−0.771940	+	0.138327i
$316$		0			0
$317$	−6.28206	+	10.8809i	−0.352836	+	0.611130i	−0.986745	−	0.162278i	$-0.948116\pi$
$317$	−6.28206	+	10.8809i	−0.352836	+	0.611130i	0.633909	+	0.773407i	$0.281449\pi$
$318$		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	0.279509	+	0.960143i	$0.409828\pi$
$331$	−12.5854	+	21.7985i	−0.691754	+	1.19815i	−0.971263	+	0.238010i	$0.923505\pi$
$332$		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	0.746509	−	0.665376i	$-0.231729\pi$
$337$	−3.72618	−	6.45394i	−0.202978	−	0.351568i	−0.949487	+	0.313807i	$0.898395\pi$
$338$		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	0.999308	+	0.0371987i	$0.0118434\pi$
$347$	9.90762	+	17.1605i	0.531869	+	0.921224i	−0.467439	+	0.884025i	$0.654823\pi$
$348$		0			0
$349$	−3.25642	+	5.64029i	−0.174312	+	0.301918i	−0.939923	−	0.341386i	$-0.889104\pi$
$349$	−3.25642	+	5.64029i	−0.174312	+	0.301918i	0.765611	+	0.643304i	$0.222437\pi$
$350$		0			0
$351$	16.0013	−	16.1353i	0.854087	−	0.861238i
$352$		0			0
$353$	−10.5162	+	18.2145i	−0.559719	+	0.969461i	0.437801	+	0.899072i	$0.355757\pi$
$353$	−10.5162	+	18.2145i	−0.559719	+	0.969461i	−0.997520	+	0.0703891i	$0.977576\pi$
$354$		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	$-0.861237\pi$
$359$	−34.3505			−1.81295			−0.906475	+	0.422259i	$0.861237\pi$
$360$		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	$-0.997769\pi$
$367$	−9.46211	+	16.3889i	−0.493918	+	0.855491i	0.506057	+	0.862500i	$0.331102\pi$
$368$		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	−0.935007	−	0.354628i	$-0.884608\pi$
$373$	−14.9604	−	25.9122i	−0.774621	−	1.34168i	0.160387	−	0.987054i	$-0.448726\pi$
$374$		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	$-0.680610\pi$
$379$	−20.9258			−1.07489			−0.537443	+	0.843300i	$0.680610\pi$
$380$		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	$-0.0924688\pi$
$383$	4.52065	+	7.82999i	0.230994	+	0.400094i	−0.727107	+	0.686525i	$0.759135\pi$
$384$		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	−0.937335	−	0.348431i	$-0.886715\pi$
$389$	−3.29213	+	5.70214i	−0.166918	+	0.289110i	0.770417	+	0.637540i	$0.220048\pi$
$390$		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	0.939166	−	0.343464i	$-0.111601\pi$
$401$	3.44698	+	5.97034i	0.172134	+	0.298145i	−0.767032	+	0.641609i	$0.778267\pi$
$402$		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	0.674906	+	0.737904i	$0.264184\pi$
$409$	19.7484	+	34.2053i	0.976496	+	1.69134i	0.301591	+	0.953437i	$0.402482\pi$
$410$		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	0.803460	+	0.595359i	$0.202990\pi$
$419$	18.7772	+	32.5231i	0.917326	+	1.58886i	0.113866	+	0.993496i	$0.463676\pi$
$420$		0			0
$421$	−11.5064	+	19.9297i	−0.560788	+	0.971313i	0.436640	+	0.899636i	$0.356168\pi$
$421$	−11.5064	+	19.9297i	−0.560788	+	0.971313i	−0.997428	+	0.0716768i	$0.977165\pi$
$422$		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	$-0.416949\pi$
$431$	10.7109			0.515924			0.257962	+	0.966155i	$0.416949\pi$
$432$		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	$-0.982464\pi$
$439$	−9.46116	+	16.3872i	−0.451557	+	0.782119i	0.546926	+	0.837181i	$0.315798\pi$
$440$		0			0
$441$	28.1039	+	33.3045i	1.33828	+	1.58593i
$442$		0			0
$443$	12.9593	−	22.4461i	0.615714	−	1.06645i	−0.374545	−	0.927209i	$-0.622201\pi$
$443$	12.9593	−	22.4461i	0.615714	−	1.06645i	0.990259	−	0.139239i	$-0.0444656\pi$
$444$		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	0.235484	−	0.971878i	$-0.424332\pi$
$457$	20.5099	−	35.5242i	0.959413	−	1.66175i	0.723929	−	0.689874i	$-0.242334\pi$
$458$		0			0
$459$	−1.41555	−	5.19615i	−0.0660721	−	0.242536i
$460$		0			0
$461$	0.378678	−	0.655890i	0.0176368	−	0.0305478i	−0.857072	−	0.515196i	$-0.827719\pi$
$461$	0.378678	−	0.655890i	0.0176368	−	0.0305478i	0.874709	+	0.484648i	$0.161052\pi$
$462$		0			0
$463$	−15.1949	−	26.3183i	−0.706166	−	1.22311i	−0.966269	−	0.257534i	$-0.917090\pi$
$463$	−15.1949	−	26.3183i	−0.706166	−	1.22311i	0.260103	−	0.965581i	$-0.416243\pi$
$464$		0			0
$465$	−14.1545	−	6.57640i	−0.656397	−	0.304973i
$466$		0			0
$467$	−2.41191			−0.111610			−0.0558049	−	0.998442i	$-0.517772\pi$
$467$	−2.41191			−0.111610			−0.0558049	+	0.998442i	$0.517772\pi$
$468$		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	0.142436	+	0.989804i	$0.454506\pi$
$479$	−17.2020	+	29.7947i	−0.785977	+	1.36135i	−0.928413	+	0.371549i	$0.878827\pi$
$480$		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	$-0.625266\pi$
$487$	−16.9242			−0.766909			−0.383455	+	0.923560i	$0.625266\pi$
$488$		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	$-0.0731482\pi$
$491$	6.41686	+	11.1143i	0.289589	+	0.501582i	−0.684123	+	0.729367i	$0.739815\pi$
$492$		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	$-0.0295511\pi$
$499$	9.32764	+	16.1559i	0.417563	+	0.723240i	−0.578131	+	0.815944i	$0.696218\pi$
$500$		0			0
$501$	−2.23639	+	1.57057i	−0.0999144	+	0.0701679i
$502$		0			0
$503$	−25.4535			−1.13492			−0.567458	−	0.823402i	$-0.692073\pi$
$503$	−25.4535			−1.13492			−0.567458	+	0.823402i	$0.692073\pi$
$504$		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	0.713199	−	0.700961i	$-0.247245\pi$
$509$	−5.65042	−	9.78681i	−0.250450	−	0.433793i	−0.963650	+	0.267168i	$0.913912\pi$
$510$		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	$-0.476003\pi$
$523$	3.44488			0.150634			0.0753171	+	0.997160i	$0.476003\pi$
$524$		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	$-0.812197\pi$
$547$	1.55190	−	2.68797i	0.0663544	−	0.114929i	0.897294	+	0.441434i	$0.145530\pi$
$548$		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	$-0.137435\pi$
$563$	2.17598	+	3.76890i	0.0917065	+	0.158840i	−0.816523	+	0.577313i	$0.804101\pi$
$564$		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	0.445928	+	0.895069i	$0.352874\pi$
$569$	−13.1717	+	22.8141i	−0.552188	+	0.956418i	−0.998116	+	0.0613492i	$0.980460\pi$
$570$		0			0
$571$	−1.85712	−	3.21662i	−0.0777180	−	0.134612i	0.824547	−	0.565793i	$-0.191430\pi$
$571$	−1.85712	−	3.21662i	−0.0777180	−	0.134612i	−0.902265	+	0.431182i	$0.858097\pi$
$572$		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	$-0.744707\pi$
$587$	6.65897	−	11.5337i	0.274845	−	0.476045i	0.970096	+	0.242722i	$0.0780401\pi$
$588$		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	$-0.229623\pi$
$599$	−4.80917	−	8.32974i	−0.196498	−	0.340344i	−0.947390	+	0.320080i	$0.896290\pi$
$600$		0			0
$601$	−2.33420	+	4.04295i	−0.0952139	+	0.164915i	−0.909698	−	0.415271i	$-0.863687\pi$
$601$	−2.33420	+	4.04295i	−0.0952139	+	0.164915i	0.814484	+	0.580186i	$0.197020\pi$
$602$		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	$-0.124917\pi$
$607$	3.22217	+	5.58096i	0.130784	+	0.226524i	−0.793195	+	0.608968i	$0.791584\pi$
$608$		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	0.917938	−	0.396725i	$-0.129853\pi$
$617$	2.86636	+	4.96468i	0.115395	+	0.199870i	−0.802542	+	0.596595i	$0.796520\pi$
$618$		0			0
$619$	9.08484	−	15.7354i	0.365151	−	0.632459i	−0.623650	−	0.781704i	$-0.714351\pi$
$619$	9.08484	−	15.7354i	0.365151	−	0.632459i	0.988800	+	0.149244i	$0.0476841\pi$
$620$		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	$-0.638589\pi$
$631$	−21.1892			−0.843528			−0.421764	+	0.906706i	$0.638589\pi$
$632$		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	0.0851952	−	0.996364i	$-0.472849\pi$
$641$	22.9248	−	39.7069i	0.905474	−	1.56833i	0.820279	−	0.571963i	$-0.193818\pi$
$642$		0			0
$643$	−14.2494	−	24.6807i	−0.561942	−	0.973311i	−0.997327	−	0.0730672i	$-0.976721\pi$
$643$	−14.2494	−	24.6807i	−0.561942	−	0.973311i	0.435385	−	0.900244i	$-0.356612\pi$
$644$		0			0
$645$	−0.776103	−	8.73114i	−0.0305590	−	0.343788i
$646$		0			0
$647$	−32.9396			−1.29499			−0.647494	−	0.762070i	$-0.724183\pi$
$647$	−32.9396			−1.29499			−0.647494	+	0.762070i	$0.724183\pi$
$648$		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	0.808816	−	0.588062i	$-0.200109\pi$
$653$	−2.67981	−	4.64157i	−0.104869	−	0.181639i	−0.913685	+	0.406424i	$0.866776\pi$
$654$		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	$-0.928625\pi$
$659$	−7.57080	+	13.1130i	−0.294916	+	0.510810i	0.680049	+	0.733167i	$0.261958\pi$
$660$		0			0
$661$	−2.15422	−	3.73121i	−0.0837893	−	0.145127i	0.821085	−	0.570805i	$-0.193369\pi$
$661$	−2.15422	−	3.73121i	−0.0837893	−	0.145127i	−0.904875	+	0.425678i	$0.860036\pi$
$662$		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	−0.605618	−	0.795756i	$-0.707074\pi$
$673$	10.0224	−	17.3593i	0.386336	−	0.669153i	0.991954	+	0.126603i	$0.0404073\pi$
$674$		0			0
$675$	−5.02466	−	1.32393i	−0.193399	−	0.0509580i
$676$		0			0
$677$	13.3326	−	23.0928i	0.512415	−	0.887529i	−0.487481	−	0.873134i	$-0.662084\pi$
$677$	13.3326	−	23.0928i	0.512415	−	0.887529i	0.999896	−	0.0143957i	$-0.00458245\pi$
$678$		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	$-0.339850\pi$
$683$	25.2021			0.964331			0.482166	+	0.876080i	$0.339850\pi$
$684$		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	$-0.744105\pi$
$691$	7.27258	−	12.5965i	0.276662	−	0.479193i	0.970553	+	0.240887i	$0.0774384\pi$
$692$		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	0.410215	+	0.911989i	$0.365454\pi$
$709$	−15.5688	+	26.9659i	−0.584698	+	1.01273i	−0.994913	+	0.100738i	$0.967880\pi$
$710$		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	$-0.304408\pi$
$719$	30.9181			1.15305			0.576525	+	0.817080i	$0.304408\pi$
$720$		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	$-0.938640\pi$
$727$	−8.75834	+	15.1699i	−0.324829	+	0.562620i	0.656649	+	0.754197i	$0.271973\pi$
$728$		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	0.991163	+	0.132652i	$0.0423492\pi$
$733$	16.5276	+	28.6267i	0.610461	+	1.05735i	−0.380701	+	0.924698i	$0.624317\pi$
$734$		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	$-0.405431\pi$
$739$	15.9164			0.585493			0.292747	+	0.956190i	$0.405431\pi$
$740$		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	$-0.0721056\pi$
$743$	7.97902	+	13.8201i	0.292722	+	0.507009i	−0.681730	+	0.731604i	$0.738772\pi$
$744$		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	$-0.259367\pi$
$751$	−7.86854	−	13.6287i	−0.287127	−	0.497319i	−0.973123	+	0.230287i	$0.926034\pi$
$752$		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	0.697830	−	0.716263i	$-0.254149\pi$
$761$	−7.48654	−	12.9671i	−0.271387	−	0.470056i	−0.969217	+	0.246207i	$0.920816\pi$
$762$		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	0.854517	−	0.519424i	$-0.173854\pi$
$769$	−0.626060	−	1.08437i	−0.0225763	−	0.0391033i	−0.877093	+	0.480321i	$0.840520\pi$
$770$		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	$-0.178201\pi$
$787$	−1.01630	−	1.76028i	−0.0362272	−	0.0627473i	−0.883571	+	0.468298i	$0.844867\pi$
$788$		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	0.953684	−	0.300810i	$-0.0972571\pi$
$797$	6.10733	+	10.5782i	0.216333	+	0.374699i	−0.737351	+	0.675510i	$0.763924\pi$
$798$		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	$-0.551881\pi$
$811$	−9.24210			−0.324534			−0.162267	+	0.986747i	$0.551881\pi$
$812$		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	−0.686179	−	0.727433i	$-0.740713\pi$
$821$	8.22018	−	14.2378i	0.286886	−	0.496901i	0.973065	+	0.230532i	$0.0740465\pi$
$822$		0			0
$823$	−20.8503	−	36.1138i	−0.726796	−	1.25885i	−0.958231	−	0.285996i	$-0.907675\pi$
$823$	−20.8503	−	36.1138i	−0.726796	−	1.25885i	0.231435	−	0.972850i	$-0.425658\pi$
$824$		0			0
$825$	7.28783	−	5.11810i	0.253730	−	0.178189i
$826$		0			0
$827$	−6.03875			−0.209988			−0.104994	−	0.994473i	$-0.533482\pi$
$827$	−6.03875			−0.209988			−0.104994	+	0.994473i	$0.533482\pi$
$828$		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	$-0.801558\pi$
$839$	2.88669	−	4.99990i	0.0996597	−	0.172616i	0.911544	+	0.411203i	$0.134891\pi$
$840$		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	−0.928774	−	0.370646i	$-0.879136\pi$
$853$	−4.18810	+	7.25401i	−0.143398	+	0.248372i	0.785376	+	0.619019i	$0.212470\pi$
$854$		0			0
$855$	−7.86423	−	9.31950i	−0.268951	−	0.318720i
$856$		0			0
$857$	4.04677	−	7.00920i	0.138235	−	0.239430i	−0.788594	−	0.614915i	$-0.789190\pi$
$857$	4.04677	−	7.00920i	0.138235	−	0.239430i	0.926829	+	0.375485i	$0.122524\pi$
$858$		0			0
$859$	19.8503	+	34.3817i	0.677283	+	1.17309i	0.975796	+	0.218683i	$0.0701762\pi$
$859$	19.8503	+	34.3817i	0.677283	+	1.17309i	−0.298513	+	0.954406i	$0.596490\pi$
$860$		0			0
$861$	2.40012	+	27.0013i	0.0817959	+	0.920201i
$862$		0			0
$863$	34.2524			1.16597			0.582983	−	0.812484i	$-0.301885\pi$
$863$	34.2524			1.16597			0.582983	+	0.812484i	$0.301885\pi$
$864$		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	−0.960589	−	0.277972i	$-0.910338\pi$
$877$	−21.3526	−	36.9837i	−0.721025	−	1.24885i	0.239564	−	0.970881i	$-0.422995\pi$
$878$		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	$-0.590081\pi$
$883$	−16.5952			−0.558472			−0.279236	+	0.960223i	$0.590081\pi$
$884$		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	$-0.131307\pi$
$887$	3.30159	+	5.71852i	0.110857	+	0.192009i	−0.805259	+	0.592923i	$0.797974\pi$
$888$		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	$-0.959676\pi$
$907$	−11.6423	+	20.1651i	−0.386576	+	0.669570i	0.605410	+	0.795914i	$0.293009\pi$
$908$		0			0
$909$	−13.0493	+	36.1651i	−0.432819	+	1.19952i
$910$		0			0
$911$	−16.1372	+	27.9505i	−0.534650	+	0.926040i	0.464531	+	0.885557i	$0.346223\pi$
$911$	−16.1372	+	27.9505i	−0.534650	+	0.926040i	−0.999180	+	0.0404832i	$0.987110\pi$
$912$		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	$-0.564928\pi$
$919$	−12.2816			−0.405131			−0.202566	+	0.979269i	$0.564928\pi$
$920$		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	0.163495	−	0.986544i	$-0.447723\pi$
$929$	28.5325	−	49.4197i	0.936120	−	1.62141i	0.772625	−	0.634863i	$-0.218943\pi$
$930$		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	−0.994111	−	0.108369i	$-0.965437\pi$
$941$	−18.1264	−	31.3959i	−0.590905	−	1.02348i	0.403205	−	0.915109i	$-0.367896\pi$
$942$		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	0.160996	+	0.986955i	$0.448529\pi$
$947$	−23.8257	+	41.2673i	−0.774230	+	1.34101i	−0.935226	+	0.354050i	$0.884804\pi$
$948$		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	0.707513	+	0.706701i	$0.249817\pi$
$967$	30.0324	+	52.0177i	0.965777	+	1.67278i	0.258265	+	0.966074i	$0.416849\pi$
$968$		0			0
$969$	−0.646069	−	7.26826i	−0.0207547	−	0.233490i
$970$		0			0
$971$	21.5189			0.690575			0.345288	−	0.938497i	$-0.387781\pi$
$971$	21.5189			0.690575			0.345288	+	0.938497i	$0.387781\pi$
$972$		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	−0.996096	−	0.0882751i	$-0.971865\pi$
$977$	−17.9570	−	31.1025i	−0.574497	−	0.995057i	0.421600	−	0.906782i	$-0.361469\pi$
$978$		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	$-0.712576\pi$
$983$	11.6111	−	20.1110i	0.370336	−	0.641441i	0.989617	+	0.143728i	$0.0459091\pi$
$984$		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	$-0.599183\pi$
$991$	−19.3020			−0.613149			−0.306575	+	0.951847i	$0.599183\pi$
$992$		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	−0.460731	−	0.887540i	$-0.652413\pi$
$997$	16.9959	−	29.4378i	0.538267	−	0.932305i	0.998998	−	0.0447654i	$-0.0142540\pi$
$998$		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.o.961.3	yes	10
3.2	odd	2		4320.2.q.o.2881.1		10
4.3	odd	2		1440.2.q.p.961.3	yes	10
9.4	even	3	inner	1440.2.q.o.481.3	✓	10
9.5	odd	6		4320.2.q.o.1441.1		10
12.11	even	2		4320.2.q.p.2881.5		10
36.23	even	6		4320.2.q.p.1441.5		10
36.31	odd	6		1440.2.q.p.481.3	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1440.2.q.o.481.3	✓	10	9.4	even	3	inner
1440.2.q.o.961.3	yes	10	1.1	even	1	trivial
1440.2.q.p.481.3	yes	10	36.31	odd	6
1440.2.q.p.961.3	yes	10	4.3	odd	2
4320.2.q.o.1441.1		10	9.5	odd	6
4320.2.q.o.2881.1		10	3.2	odd	2
4320.2.q.p.1441.5		10	36.23	even	6
4320.2.q.p.2881.5		10	12.11	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:	\( N \)	\(=\)	\( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
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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Database

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