LMFDB - Embedded newform 900.2.i.c.601.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(301,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("900.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.i (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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.954288.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 2x^{4} + 3x^{3} - 6x^{2} - 9x + 27 $ x^6 - x^5 - 2x^4 + 3x^3 - 6x^2 - 9x + 27
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			601.3
Root			$1.71903 + 0.211943i$ of defining polynomial
Character	$\chi$	$=$	900.601
Dual form			900.2.i.c.301.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71903 - 0.211943i) q^{3} +(1.36710 - 2.36788i) q^{7} +(2.91016 - 0.728674i) q^{9} +(-2.76210 + 4.78410i) q^{11} +(-1.76210 - 3.05205i) q^{13} +5.52420 q^{17} +7.52420 q^{19} +(1.84823 - 4.36021i) q^{21} +(0.367095 + 0.635828i) q^{23} +(4.84823 - 1.86940i) q^{27} +(2.23419 - 3.86973i) q^{29} +(-3.76210 - 6.51615i) q^{31} +(-3.73419 + 8.80944i) q^{33} -6.05582 q^{37} +(-3.67597 - 4.87311i) q^{39} +(0.527909 + 0.914365i) q^{41} +(-1.76210 + 3.05205i) q^{43} +(0.604996 - 1.04788i) q^{47} +(-0.237900 - 0.412055i) q^{49} +(9.49629 - 1.17081i) q^{51} -1.46838 q^{53} +(12.9344 - 1.59470i) q^{57} +(0.734191 + 1.27166i) q^{59} +(-4.52791 + 7.84257i) q^{61} +(2.25306 - 7.88707i) q^{63} +(-2.12920 - 3.68787i) q^{67} +(0.765809 + 1.01521i) q^{69} +10.0558 q^{71} -8.00000 q^{73} +(7.55211 + 13.0806i) q^{77} +(-1.00000 + 1.73205i) q^{79} +(7.93807 - 4.24111i) q^{81} +(-2.63290 + 4.56032i) q^{83} +(3.02049 - 7.12572i) q^{87} -3.00000 q^{89} -9.63583 q^{91} +(-7.84823 - 10.4041i) q^{93} +(4.73419 - 8.19986i) q^{97} +(-4.55211 + 15.9352i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 3 q^{7} + 5 q^{9} + 6 q^{13} + 12 q^{19} - 20 q^{21} - 3 q^{23} - 2 q^{27} + 3 q^{29} - 6 q^{31} - 12 q^{33} - 24 q^{37} - 20 q^{39} - 3 q^{41} + 6 q^{43} + 15 q^{47} - 18 q^{49} + 30 q^{51}+ \cdots + 12 q^{99}+O(q^{100}) $ 6 * q + q^3 + 3 * q^7 + 5 * q^9 + 6 * q^13 + 12 * q^19 - 20 * q^21 - 3 * q^23 - 2 * q^27 + 3 * q^29 - 6 * q^31 - 12 * q^33 - 24 * q^37 - 20 * q^39 - 3 * q^41 + 6 * q^43 + 15 * q^47 - 18 * q^49 + 30 * q^51 + 12 * q^53 + 32 * q^57 - 6 * q^59 - 21 * q^61 + 29 * q^63 + 9 * q^67 + 15 * q^69 + 48 * q^71 - 48 * q^73 + 6 * q^77 - 6 * q^79 + 29 * q^81 - 21 * q^83 - 42 * q^87 - 18 * q^89 - 16 * q^93 + 18 * q^97 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	1.71903	−	0.211943i	0.992485	−	0.122365i
$3$	1.71903	−	0.211943i	0.992485	−	0.122365i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.36710	−	2.36788i	0.516714	−	0.894974i	−0.483098	−	0.875566i	$-0.660489\pi$
$7$	1.36710	−	2.36788i	0.516714	−	0.894974i	0.999812	−	0.0194079i	$-0.00617810\pi$
$8$		0			0
$9$	2.91016	−	0.728674i	0.970054	−	0.242891i
$10$		0			0
$11$	−2.76210	+	4.78410i	−0.832804	+	1.44246i	0.0630012	+	0.998013i	$0.479933\pi$
$11$	−2.76210	+	4.78410i	−0.832804	+	1.44246i	−0.895806	+	0.444446i	$0.853401\pi$
$12$		0			0
$13$	−1.76210	−	3.05205i	−0.488719	−	0.846485i	0.511197	−	0.859463i	$-0.329202\pi$
$13$	−1.76210	−	3.05205i	−0.488719	−	0.846485i	−0.999916	+	0.0129781i	$0.995869\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.52420			1.33982			0.669908	−	0.742444i	$-0.266334\pi$
$17$	5.52420			1.33982			0.669908	+	0.742444i	$0.266334\pi$
$18$		0			0
$19$	7.52420			1.72617			0.863085	−	0.505059i	$-0.168529\pi$
$19$	7.52420			1.72617			0.863085	+	0.505059i	$0.168529\pi$
$20$		0			0
$21$	1.84823	−	4.36021i	0.403317	−	0.951476i
$22$		0			0
$23$	0.367095	+	0.635828i	0.0765447	+	0.132579i	0.901757	−	0.432243i	$-0.142278\pi$
$23$	0.367095	+	0.635828i	0.0765447	+	0.132579i	−0.825212	+	0.564823i	$0.808945\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	4.84823	−	1.86940i	0.933042	−	0.359767i
$28$		0			0
$29$	2.23419	−	3.86973i	0.414879	−	0.718591i	−0.580537	−	0.814234i	$-0.697157\pi$
$29$	2.23419	−	3.86973i	0.414879	−	0.718591i	0.995416	+	0.0956427i	$0.0304906\pi$
$30$		0			0
$31$	−3.76210	−	6.51615i	−0.675693	−	1.17033i	−0.976266	−	0.216576i	$-0.930511\pi$
$31$	−3.76210	−	6.51615i	−0.675693	−	1.17033i	0.300573	−	0.953759i	$-0.402822\pi$
$32$		0			0
$33$	−3.73419	+	8.80944i	−0.650039	+	1.53353i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.05582			−0.995570			−0.497785	−	0.867300i	$-0.665853\pi$
$37$	−6.05582			−0.995570			−0.497785	+	0.867300i	$0.665853\pi$
$38$		0			0
$39$	−3.67597	−	4.87311i	−0.588626	−	0.780322i
$40$		0			0
$41$	0.527909	+	0.914365i	0.0824455	+	0.142800i	0.904300	−	0.426898i	$-0.140394\pi$
$41$	0.527909	+	0.914365i	0.0824455	+	0.142800i	−0.821854	+	0.569698i	$0.807060\pi$
$42$		0			0
$43$	−1.76210	+	3.05205i	−0.268718	+	0.465433i	−0.968531	−	0.248893i	$-0.919933\pi$
$43$	−1.76210	+	3.05205i	−0.268718	+	0.465433i	0.699813	+	0.714326i	$0.253267\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.604996	−	1.04788i	0.0882477	−	0.152849i	−0.818523	−	0.574474i	$-0.805207\pi$
$47$	0.604996	−	1.04788i	0.0882477	−	0.152849i	0.906771	+	0.421625i	$0.138540\pi$
$48$		0			0
$49$	−0.237900	−	0.412055i	−0.0339857	−	0.0588650i
$50$		0			0
$51$	9.49629	−	1.17081i	1.32975	−	0.163947i
$52$		0			0
$53$	−1.46838			−0.201698			−0.100849	−	0.994902i	$-0.532156\pi$
$53$	−1.46838			−0.201698			−0.100849	+	0.994902i	$0.532156\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	12.9344	−	1.59470i	1.71320	−	0.211223i
$58$		0			0
$59$	0.734191	+	1.27166i	0.0955835	+	0.165556i	0.909852	−	0.414933i	$-0.136195\pi$
$59$	0.734191	+	1.27166i	0.0955835	+	0.165556i	−0.814268	+	0.580488i	$0.802862\pi$
$60$		0			0
$61$	−4.52791	+	7.84257i	−0.579739	+	1.00414i	0.415770	+	0.909470i	$0.363512\pi$
$61$	−4.52791	+	7.84257i	−0.579739	+	1.00414i	−0.995509	+	0.0946680i	$0.969821\pi$
$62$		0			0
$63$	2.25306	−	7.88707i	0.283858	−	0.993678i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.12920	−	3.68787i	−0.260123	−	0.450546i	0.706152	−	0.708061i	$-0.250430\pi$
$67$	−2.12920	−	3.68787i	−0.260123	−	0.450546i	−0.966274	+	0.257515i	$0.917096\pi$
$68$		0			0
$69$	0.765809	+	1.01521i	0.0921926	+	0.122217i
$70$		0			0
$71$	10.0558			1.19341			0.596703	−	0.802462i	$-0.296477\pi$
$71$	10.0558			1.19341			0.596703	+	0.802462i	$0.296477\pi$
$72$		0			0
$73$	−8.00000			−0.936329			−0.468165	−	0.883641i	$-0.655085\pi$
$73$	−8.00000			−0.936329			−0.468165	+	0.883641i	$0.655085\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.55211	+	13.0806i	0.860643	+	1.49068i
$78$		0			0
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	−0.916781	−	0.399390i	$-0.869222\pi$
$79$	−1.00000	+	1.73205i	−0.112509	+	0.194871i	0.804272	+	0.594261i	$0.202555\pi$
$80$		0			0
$81$	7.93807	−	4.24111i	0.882008	−	0.471235i
$82$		0			0
$83$	−2.63290	+	4.56032i	−0.288999	+	0.500561i	−0.973571	−	0.228384i	$-0.926656\pi$
$83$	−2.63290	+	4.56032i	−0.288999	+	0.500561i	0.684572	+	0.728945i	$0.259989\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.02049	−	7.12572i	0.323831	−	0.763958i
$88$		0			0
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	−9.63583			−1.01011
$92$		0			0
$93$	−7.84823	−	10.4041i	−0.813824	−	1.07886i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.73419	−	8.19986i	0.480684	−	0.832570i	−0.519070	−	0.854732i	$-0.673722\pi$
$97$	4.73419	−	8.19986i	0.480684	−	0.832570i	0.999754	+	0.0221621i	$0.00705499\pi$
$98$		0			0
$99$	−4.55211	+	15.9352i	−0.457504	+	1.60154i
$100$		0			0
$101$	−6.73419	+	11.6640i	−0.670077	+	1.16061i	0.307805	+	0.951450i	$0.400406\pi$
$101$	−6.73419	+	11.6640i	−0.670077	+	1.16061i	−0.977882	+	0.209158i	$0.932928\pi$
$102$		0			0
$103$	9.28630	+	16.0843i	0.915006	+	1.58484i	0.806892	+	0.590699i	$0.201148\pi$
$103$	9.28630	+	16.0843i	0.915006	+	1.58484i	0.108114	+	0.994138i	$0.465519\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−19.2510			−1.86106			−0.930531	−	0.366213i	$-0.880654\pi$
$107$	−19.2510			−1.86106			−0.930531	+	0.366213i	$0.880654\pi$
$108$		0			0
$109$	−0.524200			−0.0502092			−0.0251046	−	0.999685i	$-0.507992\pi$
$109$	−0.524200			−0.0502092			−0.0251046	+	0.999685i	$0.507992\pi$
$110$		0			0
$111$	−10.4102	+	1.28349i	−0.988089	+	0.121823i
$112$		0			0
$113$	−3.73419	−	6.46781i	−0.351283	−	0.608440i	0.635191	−	0.772355i	$-0.280921\pi$
$113$	−3.73419	−	6.46781i	−0.351283	−	0.608440i	−0.986475	+	0.163915i	$0.947588\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−7.35194	−	7.59795i	−0.679687	−	0.702431i
$118$		0			0
$119$	7.55211	−	13.0806i	0.692301	−	1.19910i
$120$		0			0
$121$	−9.75839	−	16.9020i	−0.887126	−	1.53655i
$122$		0			0
$123$	1.10129	+	1.45994i	0.0992997	+	0.131638i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−8.25839			−0.732814			−0.366407	−	0.930455i	$-0.619412\pi$
$127$	−8.25839			−0.732814			−0.366407	+	0.930455i	$0.619412\pi$
$128$		0			0
$129$	−2.38225	+	5.62004i	−0.209746	+	0.494817i
$130$		0			0
$131$	8.04840	+	13.9402i	0.703192	+	1.21796i	0.967340	+	0.253482i	$0.0815759\pi$
$131$	8.04840	+	13.9402i	0.703192	+	1.21796i	−0.264148	+	0.964482i	$0.585091\pi$
$132$		0			0
$133$	10.2863	−	17.8164i	0.891935	−	1.54488i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.25839	+	16.0360i	−0.790998	+	1.37005i	0.134352	+	0.990934i	$0.457105\pi$
$137$	−9.25839	+	16.0360i	−0.790998	+	1.37005i	−0.925350	+	0.379115i	$0.876229\pi$
$138$		0			0
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$		0			0
$141$	0.817917	−	1.92957i	0.0688811	−	0.162499i
$142$		0			0
$143$	19.4684			1.62803
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.496291	−	0.657916i	−0.0409334	−	0.0542640i
$148$		0			0
$149$	−6.78630	−	11.7542i	−0.555955	−	0.962943i	−0.997829	−	0.0658653i	$-0.979019\pi$
$149$	−6.78630	−	11.7542i	−0.555955	−	0.962943i	0.441873	−	0.897078i	$-0.354314\pi$
$150$		0			0
$151$	6.23048	−	10.7915i	0.507029	−	0.878201i	−0.492937	−	0.870065i	$-0.664077\pi$
$151$	6.23048	−	10.7915i	0.507029	−	0.878201i	0.999967	−	0.00813598i	$-0.00258979\pi$
$152$		0			0
$153$	16.0763	−	4.02534i	1.29969	−	0.325429i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.790009	−	1.36834i	−0.0630496	−	0.109205i	0.832778	−	0.553608i	$-0.186749\pi$
$157$	−0.790009	−	1.36834i	−0.0630496	−	0.109205i	−0.895827	+	0.444403i	$0.853416\pi$
$158$		0			0
$159$	−2.52420	+	0.311213i	−0.200182	+	0.0246808i
$160$		0			0
$161$	2.00742			0.158207
$162$		0			0
$163$	4.47580			0.350572			0.175286	−	0.984518i	$-0.443915\pi$
$163$	4.47580			0.350572			0.175286	+	0.984518i	$0.443915\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.39500	+	14.5406i	0.649625	+	1.12518i	0.983212	+	0.182464i	$0.0584074\pi$
$167$	8.39500	+	14.5406i	0.649625	+	1.12518i	−0.333588	+	0.942719i	$0.608259\pi$
$168$		0			0
$169$	0.290009	−	0.502310i	0.0223084	−	0.0386392i
$170$		0			0
$171$	21.8966	−	5.48269i	1.67448	−	0.419271i
$172$		0			0
$173$	−11.5242	+	19.9605i	−0.876169	+	1.51757i	−0.0206561	+	0.999787i	$0.506576\pi$
$173$	−11.5242	+	19.9605i	−0.876169	+	1.51757i	−0.855513	+	0.517782i	$0.826758\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.53162	+	2.03041i	0.115123	+	0.152615i
$178$		0			0
$179$	12.9926			0.971111			0.485556	−	0.874206i	$-0.338617\pi$
$179$	12.9926			0.971111			0.485556	+	0.874206i	$0.338617\pi$
$180$		0			0
$181$	−24.5652			−1.82592			−0.912958	−	0.408054i	$-0.866207\pi$
$181$	−24.5652			−1.82592			−0.912958	+	0.408054i	$0.866207\pi$
$182$		0			0
$183$	−6.12146	+	14.4413i	−0.452511	+	1.06753i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−15.2584	+	26.4283i	−1.11580	+	1.93263i
$188$		0			0
$189$	2.20147	−	14.0357i	0.160134	−	1.02094i
$190$		0			0
$191$	−7.55211	+	13.0806i	−0.546451	+	0.946482i	0.452063	+	0.891986i	$0.350688\pi$
$191$	−7.55211	+	13.0806i	−0.546451	+	0.946482i	−0.998514	+	0.0544954i	$0.982645\pi$
$192$		0			0
$193$	−7.28630	−	12.6202i	−0.524479	−	0.908425i	−0.999594	−	0.0285008i	$-0.990927\pi$
$193$	−7.28630	−	12.6202i	−0.524479	−	0.908425i	0.475114	−	0.879924i	$-0.342407\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.53162			0.322864			0.161432	−	0.986884i	$-0.448389\pi$
$197$	4.53162			0.322864			0.161432	+	0.986884i	$0.448389\pi$
$198$		0			0
$199$	−7.41256			−0.525463			−0.262731	−	0.964869i	$-0.584623\pi$
$199$	−7.41256			−0.525463			−0.262731	+	0.964869i	$0.584623\pi$
$200$		0			0
$201$	−4.44178	−	5.88832i	−0.313299	−	0.415330i
$202$		0			0
$203$	−6.10870	−	10.5806i	−0.428747	−	0.742612i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.53162	+	1.58287i	0.106455	+	0.110017i
$208$		0			0
$209$	−20.7826	+	35.9965i	−1.43756	+	2.48993i
$210$		0			0
$211$	6.70628	+	11.6156i	0.461680	+	0.799652i	0.999045	−	0.0436972i	$-0.0139137\pi$
$211$	6.70628	+	11.6156i	0.461680	+	0.799652i	−0.537365	+	0.843350i	$0.680580\pi$
$212$		0			0
$213$	17.2863	−	2.13126i	1.18444	−	0.146031i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−20.5726			−1.39656
$218$		0			0
$219$	−13.7523	+	1.69554i	−0.929293	+	0.114574i
$220$		0			0
$221$	−9.73419	−	16.8601i	−0.654793	−	1.13413i
$222$		0			0
$223$	−4.39500	+	7.61237i	−0.294311	+	0.509762i	−0.974824	−	0.222974i	$-0.928424\pi$
$223$	−4.39500	+	7.61237i	−0.294311	+	0.509762i	0.680513	+	0.732736i	$0.261757\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.02791	−	3.51244i	0.134597	−	0.233129i	−0.790846	−	0.612015i	$-0.790359\pi$
$227$	2.02791	−	3.51244i	0.134597	−	0.233129i	0.925443	+	0.378886i	$0.123693\pi$
$228$		0			0
$229$	−1.29001	−	2.23436i	−0.0852462	−	0.147651i	0.820250	−	0.572005i	$-0.193834\pi$
$229$	−1.29001	−	2.23436i	−0.0852462	−	0.147651i	−0.905496	+	0.424355i	$0.860501\pi$
$230$		0			0
$231$	15.7547	+	20.8855i	1.03658	+	1.37416i
$232$		0			0
$233$	1.94418			0.127368			0.0636838	−	0.997970i	$-0.479715\pi$
$233$	1.94418			0.127368			0.0636838	+	0.997970i	$0.479715\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.35194	+	3.18940i	−0.0878179	+	0.207174i
$238$		0			0
$239$	−3.73419	−	6.46781i	−0.241545	−	0.418368i	0.719610	−	0.694379i	$-0.244321\pi$
$239$	−3.73419	−	6.46781i	−0.241545	−	0.418368i	−0.961154	+	0.276011i	$0.910987\pi$
$240$		0			0
$241$	−1.20628	+	2.08934i	−0.0777035	+	0.134586i	−0.902259	−	0.431195i	$-0.858092\pi$
$241$	−1.20628	+	2.08934i	−0.0777035	+	0.134586i	0.824555	+	0.565781i	$0.191425\pi$
$242$		0			0
$243$	12.7469	−	8.97304i	0.817717	−	0.575621i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.2584	−	22.9642i	−0.843611	−	1.46118i
$248$		0			0
$249$	−3.55953	+	8.39738i	−0.225576	+	0.532162i
$250$		0			0
$251$	−6.99258			−0.441368			−0.220684	−	0.975345i	$-0.570829\pi$
$251$	−6.99258			−0.441368			−0.220684	+	0.975345i	$0.570829\pi$
$252$		0			0
$253$	−4.05582			−0.254987
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.0484	−	24.3325i	−0.876315	−	1.51782i	−0.855355	−	0.518042i	$-0.826661\pi$
$257$	−14.0484	−	24.3325i	−0.876315	−	1.51782i	−0.0209598	−	0.999780i	$-0.506672\pi$
$258$		0			0
$259$	−8.27888	+	14.3394i	−0.514425	+	0.891010i
$260$		0			0
$261$	3.68208	−	12.8895i	0.227915	−	0.797842i
$262$		0			0
$263$	3.81792	−	6.61283i	0.235423	−	0.407764i	−0.723973	−	0.689829i	$-0.757686\pi$
$263$	3.81792	−	6.61283i	0.235423	−	0.407764i	0.959395	+	0.282064i	$0.0910192\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.15710	+	0.635828i	−0.315610	+	0.0389120i
$268$		0			0
$269$	−18.6210			−1.13534			−0.567671	−	0.823255i	$-0.692155\pi$
$269$	−18.6210			−1.13534			−0.567671	+	0.823255i	$0.692155\pi$
$270$		0			0
$271$	6.57260			0.399257			0.199628	−	0.979872i	$-0.436026\pi$
$271$	6.57260			0.399257			0.199628	+	0.979872i	$0.436026\pi$
$272$		0			0
$273$	−16.5643	+	2.04224i	−1.00252	+	0.123602i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	0.762100	−	1.32000i	0.0457901	−	0.0793108i	−0.842222	−	0.539131i	$-0.818753\pi$
$277$	0.762100	−	1.32000i	0.0457901	−	0.0793108i	0.888012	+	0.459820i	$0.152086\pi$
$278$		0			0
$279$	−15.6965	−	16.2217i	−0.939722	−	0.971167i
$280$		0			0
$281$	−7.26210	+	12.5783i	−0.433221	+	0.750360i	−0.997149	−	0.0754640i	$-0.975956\pi$
$281$	−7.26210	+	12.5783i	−0.433221	+	0.750360i	0.563928	+	0.825824i	$0.309290\pi$
$282$		0			0
$283$	−8.36710	−	14.4922i	−0.497372	−	0.861474i	0.502623	−	0.864506i	$-0.332368\pi$
$283$	−8.36710	−	14.4922i	−0.497372	−	0.861474i	−0.999995	+	0.00303167i	$0.999035\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.88681			0.170403
$288$		0			0
$289$	13.5168			0.795105
$290$		0			0
$291$	6.40034	−	15.0992i	0.375194	−	0.885132i
$292$		0			0
$293$	−10.2305	−	17.7197i	−0.597671	−	1.03520i	−0.993164	−	0.116728i	$-0.962760\pi$
$293$	−10.2305	−	17.7197i	−0.597671	−	1.03520i	0.395493	−	0.918469i	$-0.370574\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.44789	+	28.3579i	−0.258093	+	1.64549i
$298$		0			0
$299$	1.29372	−	2.24078i	0.0748176	−	0.129588i
$300$		0			0
$301$	4.81792	+	8.34488i	0.277700	+	0.480991i
$302$		0			0
$303$	−9.10422	+	21.4780i	−0.523024	+	1.23388i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	18.2026			1.03888			0.519438	−	0.854508i	$-0.326141\pi$
$307$	18.2026			1.03888			0.519438	+	0.854508i	$0.326141\pi$
$308$		0			0
$309$	19.3724	+	25.6814i	1.10206	+	1.46096i
$310$		0			0
$311$	−1.55211	−	2.68833i	−0.0880120	−	0.152441i	0.818659	−	0.574280i	$-0.194718\pi$
$311$	−1.55211	−	2.68833i	−0.0880120	−	0.152441i	−0.906671	+	0.421839i	$0.861385\pi$
$312$		0			0
$313$	−9.55211	+	16.5447i	−0.539917	+	0.935164i	0.458991	+	0.888441i	$0.348211\pi$
$313$	−9.55211	+	16.5447i	−0.539917	+	0.935164i	−0.998908	+	0.0467228i	$0.985122\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.50371	−	4.33655i	0.140622	−	0.243565i	−0.787109	−	0.616814i	$-0.788423\pi$
$317$	2.50371	−	4.33655i	0.140622	−	0.243565i	0.927731	+	0.373249i	$0.121756\pi$
$318$		0			0
$319$	12.3421	+	21.3772i	0.691026	+	1.19689i
$320$		0			0
$321$	−33.0931	+	4.08010i	−1.84708	+	0.227729i
$322$		0			0
$323$	41.5652			2.31275
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.901117	+	0.111100i	−0.0498319	+	0.00614386i
$328$		0			0
$329$	−1.65417	−	2.86511i	−0.0911976	−	0.157959i
$330$		0			0
$331$	1.74161	−	3.01656i	0.0957275	−	0.165805i	−0.814184	−	0.580606i	$-0.802816\pi$
$331$	1.74161	−	3.01656i	0.0957275	−	0.165805i	0.909912	+	0.414801i	$0.136149\pi$
$332$		0			0
$333$	−17.6234	+	4.41271i	−0.965756	+	0.241815i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	5.79001	+	10.0286i	0.315402	+	0.546292i	0.979523	−	0.201333i	$-0.0645274\pi$
$337$	5.79001	+	10.0286i	0.315402	+	0.546292i	−0.664121	+	0.747625i	$0.731194\pi$
$338$		0			0
$339$	−7.79001	−	10.3270i	−0.423095	−	0.560883i
$340$		0			0
$341$	41.5652			2.25088
$342$		0			0
$343$	17.8384			0.963183
$344$		0			0
$345$		0			0
$346$		0			0
$347$	13.2305	+	22.9159i	0.710249	+	1.23019i	0.964763	+	0.263119i	$0.0847512\pi$
$347$	13.2305	+	22.9159i	0.710249	+	1.23019i	−0.254514	+	0.967069i	$0.581915\pi$
$348$		0			0
$349$	13.0168	−	22.5457i	0.696772	−	1.20685i	−0.272807	−	0.962069i	$-0.587952\pi$
$349$	13.0168	−	22.5457i	0.696772	−	1.20685i	0.969580	−	0.244776i	$-0.0787145\pi$
$350$		0			0
$351$	−14.2486	−	11.5029i	−0.760532	−	0.613982i
$352$		0			0
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	10.2100	−	24.0867i	0.540370	−	1.27480i
$358$		0			0
$359$	6.04098			0.318831			0.159415	−	0.987212i	$-0.449039\pi$
$359$	6.04098			0.318831			0.159415	+	0.987212i	$0.449039\pi$
$360$		0			0
$361$	37.6136			1.97966
$362$		0			0
$363$	−20.3573	−	26.9870i	−1.06848	−	1.41645i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	11.2305	−	19.4518i	0.586226	−	1.01537i	−0.408495	−	0.912761i	$-0.633946\pi$
$367$	11.2305	−	19.4518i	0.586226	−	1.01537i	0.994721	−	0.102613i	$-0.0327204\pi$
$368$		0			0
$369$	2.20257	+	2.27628i	0.114661	+	0.118498i
$370$		0			0
$371$	−2.00742	+	3.47695i	−0.104220	+	0.180514i
$372$		0			0
$373$	−1.26581	−	2.19245i	−0.0655411	−	0.113521i	0.831393	−	0.555685i	$-0.187544\pi$
$373$	−1.26581	−	2.19245i	−0.0655411	−	0.113521i	−0.896934	+	0.442165i	$0.854211\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−15.7475			−0.811036
$378$		0			0
$379$	−21.0484			−1.08118			−0.540592	−	0.841285i	$-0.681800\pi$
$379$	−21.0484			−1.08118			−0.540592	+	0.841285i	$0.681800\pi$
$380$		0			0
$381$	−14.1965	+	1.75031i	−0.727307	+	0.0896709i
$382$		0			0
$383$	−3.81792	−	6.61283i	−0.195086	−	0.337900i	0.751842	−	0.659343i	$-0.229165\pi$
$383$	−3.81792	−	6.61283i	−0.195086	−	0.337900i	−0.946929	+	0.321443i	$0.895832\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.90405	+	10.1659i	−0.147621	+	0.516764i
$388$		0			0
$389$	9.46467	−	16.3933i	0.479878	−	0.831173i	−0.519856	−	0.854254i	$-0.674014\pi$
$389$	9.46467	−	16.3933i	0.479878	−	0.831173i	0.999734	+	0.0230811i	$0.00734760\pi$
$390$		0			0
$391$	2.02791	+	3.51244i	0.102556	+	0.177632i
$392$		0			0
$393$	16.7900	+	22.2580i	0.846944	+	1.12277i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	29.1600			1.46350			0.731750	−	0.681573i	$-0.238704\pi$
$397$	29.1600			1.46350			0.731750	+	0.681573i	$0.238704\pi$
$398$		0			0
$399$	13.9065	−	32.8071i	0.696193	−	1.64241i
$400$		0			0
$401$	−16.3142	−	28.2570i	−0.814693	−	1.41109i	−0.909548	−	0.415598i	$-0.863572\pi$
$401$	−16.3142	−	28.2570i	−0.814693	−	1.41109i	0.0948557	−	0.995491i	$-0.469761\pi$
$402$		0			0
$403$	−13.2584	+	22.9642i	−0.660447	+	1.14393i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	16.7268	−	28.9716i	0.829115	−	1.43607i
$408$		0			0
$409$	−16.1042	−	27.8933i	−0.796302	−	1.37924i	−0.922009	−	0.387169i	$-0.873453\pi$
$409$	−16.1042	−	27.8933i	−0.796302	−	1.37924i	0.125707	−	0.992067i	$-0.459880\pi$
$410$		0			0
$411$	−12.5168	+	29.5287i	−0.617407	+	1.45654i
$412$		0			0
$413$	4.01484			0.197557
$414$		0			0
$415$		0			0
$416$		0			0
$417$	4.17226	+	5.53103i	0.204316	+	0.270855i
$418$		0			0
$419$	10.7063	+	18.5438i	0.523036	+	0.905925i	0.999641	+	0.0268073i	$0.00853405\pi$
$419$	10.7063	+	18.5438i	0.523036	+	0.905925i	−0.476605	+	0.879118i	$0.658133\pi$
$420$		0			0
$421$	0.944182	−	1.63537i	0.0460166	−	0.0797031i	−0.842100	−	0.539322i	$-0.818681\pi$
$421$	0.944182	−	1.63537i	0.0460166	−	0.0797031i	0.888116	+	0.459619i	$0.152014\pi$
$422$		0			0
$423$	0.997070	−	3.49035i	0.0484792	−	0.169707i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	12.3802	+	21.4431i	0.599118	+	1.03770i
$428$		0			0
$429$	33.4668	−	4.12618i	1.61579	−	0.199214i
$430$		0			0
$431$	−2.11164			−0.101714			−0.0508569	−	0.998706i	$-0.516195\pi$
$431$	−2.11164			−0.101714			−0.0508569	+	0.998706i	$0.516195\pi$
$432$		0			0
$433$	9.52420			0.457704			0.228852	−	0.973461i	$-0.426503\pi$
$433$	9.52420			0.457704			0.228852	+	0.973461i	$0.426503\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.76210	+	4.78410i	0.132129	+	0.228854i
$438$		0			0
$439$	7.20257	−	12.4752i	0.343760	−	0.595410i	−0.641368	−	0.767234i	$-0.721633\pi$
$439$	7.20257	−	12.4752i	0.343760	−	0.595410i	0.985128	+	0.171824i	$0.0549660\pi$
$440$		0			0
$441$	−0.992582	−	1.02580i	−0.0472658	−	0.0488474i
$442$		0			0
$443$	−9.60500	+	16.6363i	−0.456347	+	0.790416i	−0.998765	−	0.0496927i	$-0.984176\pi$
$443$	−9.60500	+	16.6363i	−0.456347	+	0.790416i	0.542417	+	0.840109i	$0.317509\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−14.1571	−	18.7676i	−0.669608	−	0.887677i
$448$		0			0
$449$	33.5800			1.58474			0.792369	−	0.610041i	$-0.208847\pi$
$449$	33.5800			1.58474			0.792369	+	0.610041i	$0.208847\pi$
$450$		0			0
$451$	−5.83255			−0.274644
$452$		0			0
$453$	8.42323	−	19.8715i	0.395758	−	0.933644i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.08373	−	1.87707i	0.0506946	−	0.0878056i	−0.839565	−	0.543260i	$-0.817190\pi$
$457$	1.08373	−	1.87707i	0.0506946	−	0.0878056i	0.890259	+	0.455454i	$0.150523\pi$
$458$		0			0
$459$	26.7826	−	10.3270i	1.25010	−	0.482021i
$460$		0			0
$461$	12.8700	−	22.2915i	0.599417	−	1.03822i	−0.393490	−	0.919329i	$-0.628733\pi$
$461$	12.8700	−	22.2915i	0.599417	−	1.03822i	0.992907	−	0.118892i	$-0.0379341\pi$
$462$		0			0
$463$	6.02791	+	10.4406i	0.280141	+	0.485218i	0.971419	−	0.237371i	$-0.0762855\pi$
$463$	6.02791	+	10.4406i	0.280141	+	0.485218i	−0.691279	+	0.722588i	$0.742952\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.4610			0.669174			0.334587	−	0.942365i	$-0.391403\pi$
$467$	14.4610			0.669174			0.334587	+	0.942365i	$0.391403\pi$
$468$		0			0
$469$	−11.6433			−0.537635
$470$		0			0
$471$	−1.64806	−	2.18478i	−0.0759386	−	0.100669i
$472$		0			0
$473$	−9.73419	−	16.8601i	−0.447579	−	0.775229i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−4.27323	+	1.06997i	−0.195658	+	0.0489906i
$478$		0			0
$479$	9.99258	−	17.3077i	0.456573	−	0.790807i	−0.542204	−	0.840247i	$-0.682410\pi$
$479$	9.99258	−	17.3077i	0.456573	−	0.790807i	0.998777	+	0.0494395i	$0.0157435\pi$
$480$		0			0
$481$	10.6710	+	18.4826i	0.486554	+	0.842736i
$482$		0			0
$483$	3.45082	−	0.425458i	0.157018	−	0.0193590i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	18.1526			0.822574			0.411287	−	0.911506i	$-0.365079\pi$
$487$	18.1526			0.822574			0.411287	+	0.911506i	$0.365079\pi$
$488$		0			0
$489$	7.69406	−	0.948613i	0.347937	−	0.0428978i
$490$		0			0
$491$	−19.7900	−	34.2773i	−0.893111	−	1.54691i	−0.836126	−	0.548538i	$-0.815185\pi$
$491$	−19.7900	−	34.2773i	−0.893111	−	1.54691i	−0.0569849	−	0.998375i	$-0.518149\pi$
$492$		0			0
$493$	12.3421	−	21.3772i	0.555861	−	0.962779i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	13.7473	−	23.8110i	0.616649	−	1.06807i
$498$		0			0
$499$	21.3142	+	36.9173i	0.954155	+	1.65264i	0.736290	+	0.676666i	$0.236576\pi$
$499$	21.3142	+	36.9173i	0.954155	+	1.65264i	0.217865	+	0.975979i	$0.430091\pi$
$500$		0			0
$501$	17.5131	+	23.2165i	0.782426	+	1.03724i
$502$		0			0
$503$	−21.1952			−0.945045			−0.472523	−	0.881319i	$-0.656657\pi$
$503$	−21.1952			−0.945045			−0.472523	+	0.881319i	$0.656657\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.392074	−	0.924953i	0.0174126	−	0.0410786i
$508$		0			0
$509$	11.0168	+	19.0816i	0.488310	+	0.845778i	0.999910	−	0.0134460i	$-0.00428012\pi$
$509$	11.0168	+	19.0816i	0.488310	+	0.845778i	−0.511599	+	0.859224i	$0.670947\pi$
$510$		0			0
$511$	−10.9368	+	18.9430i	−0.483814	+	0.837990i
$512$		0			0
$513$	36.4791	−	14.0658i	1.61059	−	0.621018i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	3.34212	+	5.78872i	0.146986	+	0.254587i
$518$		0			0
$519$	−15.5800	+	36.7553i	−0.683887	+	1.61338i
$520$		0			0
$521$	1.40515			0.0615606			0.0307803	−	0.999526i	$-0.490201\pi$
$521$	1.40515			0.0615606			0.0307803	+	0.999526i	$0.490201\pi$
$522$		0			0
$523$	11.8532			0.518306			0.259153	−	0.965836i	$-0.416557\pi$
$523$	11.8532			0.518306			0.259153	+	0.965836i	$0.416557\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−20.7826	−	35.9965i	−0.905304	−	1.56803i
$528$		0			0
$529$	11.2305	−	19.4518i	0.488282	−	0.845729i
$530$		0			0
$531$	3.06324	+	3.16574i	0.132933	+	0.137381i
$532$		0			0
$533$	1.86046	−	3.22240i	0.0805853	−	0.139578i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	22.3347	−	2.75368i	0.963813	−	0.118830i
$538$		0			0
$539$	2.62842			0.113214
$540$		0			0
$541$	−8.98516			−0.386302			−0.193151	−	0.981169i	$-0.561871\pi$
$541$	−8.98516			−0.386302			−0.193151	+	0.981169i	$0.561871\pi$
$542$		0			0
$543$	−42.2284	+	5.20641i	−1.81219	+	0.223428i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−3.10129	+	5.37159i	−0.132601	+	0.229672i	−0.924679	−	0.380749i	$-0.875666\pi$
$547$	−3.10129	+	5.37159i	−0.132601	+	0.229672i	0.792077	+	0.610421i	$0.209000\pi$
$548$		0			0
$549$	−7.46227	+	26.1225i	−0.318482	+	1.11488i
$550$		0			0
$551$	16.8105	−	29.1166i	0.716151	−	1.24041i
$552$		0			0
$553$	2.73419	+	4.73576i	0.116270	+	0.201385i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.00000			−0.254228			−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000			−0.254228			−0.127114	+	0.991888i	$0.540571\pi$
$558$		0			0
$559$	12.4200			0.525309
$560$		0			0
$561$	−20.6284	+	48.6651i	−0.870932	+	2.05464i
$562$		0			0
$563$	−2.13661	−	3.70072i	−0.0900475	−	0.155967i	0.817483	−	0.575952i	$-0.195369\pi$
$563$	−2.13661	−	3.70072i	−0.0900475	−	0.155967i	−0.907531	+	0.419985i	$0.862035\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.809653	−	24.5944i	0.0340022	−	1.03287i
$568$		0			0
$569$	−8.04840	+	13.9402i	−0.337406	+	0.584405i	−0.983944	−	0.178477i	$-0.942883\pi$
$569$	−8.04840	+	13.9402i	−0.337406	+	0.584405i	0.646538	+	0.762882i	$0.276216\pi$
$570$		0			0
$571$	−5.46838	−	9.47152i	−0.228845	−	0.396371i	0.728621	−	0.684917i	$-0.240161\pi$
$571$	−5.46838	−	9.47152i	−0.228845	−	0.396371i	−0.957466	+	0.288546i	$0.906828\pi$
$572$		0			0
$573$	−10.2100	+	24.0867i	−0.426529	+	1.00624i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	37.6620			1.56789			0.783944	−	0.620831i	$-0.213205\pi$
$577$	37.6620			1.56789			0.783944	+	0.620831i	$0.213205\pi$
$578$		0			0
$579$	−15.2002	−	20.1504i	−0.631697	−	0.837420i
$580$		0			0
$581$	7.19886	+	12.4688i	0.298659	+	0.517293i
$582$		0			0
$583$	4.05582	−	7.02488i	0.167975	−	0.290941i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	10.8987	−	18.8771i	0.449838	−	0.779142i	−0.548537	−	0.836126i	$-0.684815\pi$
$587$	10.8987	−	18.8771i	0.449838	−	0.779142i	0.998375	+	0.0569839i	$0.0181484\pi$
$588$		0			0
$589$	−28.3068	−	49.0288i	−1.16636	−	2.02020i
$590$		0			0
$591$	7.79001	−	0.960443i	0.320438	−	0.0395074i
$592$		0			0
$593$	−28.2643			−1.16067			−0.580337	−	0.814377i	$-0.697079\pi$
$593$	−28.2643			−1.16067			−0.580337	+	0.814377i	$0.697079\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.7425	+	1.57104i	−0.521514	+	0.0642983i
$598$		0			0
$599$	−7.05582	−	12.2210i	−0.288293	−	0.499338i	0.685109	−	0.728440i	$-0.259754\pi$
$599$	−7.05582	−	12.2210i	−0.288293	−	0.499338i	−0.973402	+	0.229102i	$0.926421\pi$
$600$		0			0
$601$	14.1042	−	24.4292i	0.575323	−	0.996489i	−0.420683	−	0.907207i	$-0.638210\pi$
$601$	14.1042	−	24.4292i	0.575323	−	0.996489i	0.996006	−	0.0892812i	$-0.0284570\pi$
$602$		0			0
$603$	−8.88356	−	9.18082i	−0.361766	−	0.373872i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	14.1850	+	24.5692i	0.575752	+	0.997232i	0.995959	+	0.0898036i	$0.0286239\pi$
$607$	14.1850	+	24.5692i	0.575752	+	0.997232i	−0.420208	+	0.907428i	$0.638043\pi$
$608$		0			0
$609$	−12.7436	−	16.8937i	−0.516395	−	0.684567i
$610$		0			0
$611$	−4.26425			−0.172513
$612$		0			0
$613$	−24.5726			−0.992478			−0.496239	−	0.868186i	$-0.665286\pi$
$613$	−24.5726			−0.992478			−0.496239	+	0.868186i	$0.665286\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.3142	−	23.0609i	−0.536010	−	0.928396i	−0.999114	−	0.0420923i	$-0.986598\pi$
$617$	−13.3142	−	23.0609i	−0.536010	−	0.928396i	0.463104	−	0.886304i	$-0.346736\pi$
$618$		0			0
$619$	−15.2863	+	26.4766i	−0.614408	+	1.06419i	0.376080	+	0.926587i	$0.377272\pi$
$619$	−15.2863	+	26.4766i	−0.614408	+	1.06419i	−0.990488	+	0.137599i	$0.956061\pi$
$620$		0			0
$621$	2.96838	+	2.39639i	0.119117	+	0.0961639i
$622$		0			0
$623$	−4.10129	+	7.10364i	−0.164315	+	0.284601i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−28.0968	+	66.2840i	−1.12208	+	2.64713i
$628$		0			0
$629$	−33.4535			−1.33388
$630$		0			0
$631$	27.4684			1.09350			0.546750	−	0.837296i	$-0.315865\pi$
$631$	27.4684			1.09350			0.546750	+	0.837296i	$0.315865\pi$
$632$		0			0
$633$	13.9902	+	18.5463i	0.556060	+	0.737150i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.838408	+	1.45216i	−0.0332189	+	0.0575369i
$638$		0			0
$639$	29.2640	−	7.32741i	1.15767	−	0.289868i
$640$		0			0
$641$	−6.26952	+	10.8591i	−0.247631	+	0.428910i	−0.962868	−	0.269972i	$-0.912985\pi$
$641$	−6.26952	+	10.8591i	−0.247631	+	0.428910i	0.715237	+	0.698882i	$0.246319\pi$
$642$		0			0
$643$	−5.12920	−	8.88403i	−0.202276	−	0.350352i	0.746986	−	0.664840i	$-0.231500\pi$
$643$	−5.12920	−	8.88403i	−0.202276	−	0.350352i	−0.949261	+	0.314488i	$0.898167\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−16.7900			−0.660083			−0.330042	−	0.943966i	$-0.607063\pi$
$647$	−16.7900			−0.660083			−0.330042	+	0.943966i	$0.607063\pi$
$648$		0			0
$649$	−8.11164			−0.318410
$650$		0			0
$651$	−35.3650	+	4.36021i	−1.38606	+	0.170890i
$652$		0			0
$653$	25.0131	+	43.3239i	0.978837	+	1.69540i	0.666643	+	0.745377i	$0.267731\pi$
$653$	25.0131	+	43.3239i	0.978837	+	1.69540i	0.312194	+	0.950018i	$0.398936\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−23.2813	+	5.82939i	−0.908289	+	0.227426i
$658$		0			0
$659$	−2.78259	+	4.81959i	−0.108394	+	0.187744i	−0.915120	−	0.403182i	$-0.867904\pi$
$659$	−2.78259	+	4.81959i	−0.108394	+	0.187744i	0.806726	+	0.590926i	$0.201238\pi$
$660$		0			0
$661$	19.6284	+	33.9974i	0.763457	+	1.32235i	0.941059	+	0.338244i	$0.109833\pi$
$661$	19.6284	+	33.9974i	0.763457	+	1.32235i	−0.177602	+	0.984102i	$0.556834\pi$
$662$		0			0
$663$	−20.3068	−	26.9200i	−0.788650	−	1.04549i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.28065			0.127027
$668$		0			0
$669$	−5.94178	+	14.0174i	−0.229722	+	0.541945i
$670$		0			0
$671$	−25.0131	−	43.3239i	−0.965619	−	1.67250i
$672$		0			0
$673$	7.97209	−	13.8081i	0.307302	−	0.532262i	−0.670470	−	0.741937i	$-0.733907\pi$
$673$	7.97209	−	13.8081i	0.307302	−	0.532262i	0.977771	+	0.209675i	$0.0672406\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−10.4479	+	18.0963i	−0.401545	+	0.695497i	−0.993913	−	0.110171i	$-0.964860\pi$
$677$	−10.4479	+	18.0963i	−0.401545	+	0.695497i	0.592368	+	0.805668i	$0.298193\pi$
$678$		0			0
$679$	−12.9442	−	22.4200i	−0.496752	−	0.860400i
$680$		0			0
$681$	2.74161	−	6.46781i	0.105059	−	0.247847i
$682$		0			0
$683$	19.6358			0.751344			0.375672	−	0.926753i	$-0.377412\pi$
$683$	19.6358			0.751344			0.375672	+	0.926753i	$0.377412\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−2.69113	−	3.56754i	−0.102673	−	0.136110i
$688$		0			0
$689$	2.58744	+	4.48157i	0.0985734	+	0.170734i
$690$		0			0
$691$	21.5726	−	37.3648i	0.820660	−	1.42143i	−0.0845309	−	0.996421i	$-0.526939\pi$
$691$	21.5726	−	37.3648i	0.820660	−	1.42143i	0.905191	−	0.425005i	$-0.139728\pi$
$692$		0			0
$693$	31.5094	+	32.5637i	1.19694	+	1.23699i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	2.91627	+	5.05113i	0.110462	+	0.191325i
$698$		0			0
$699$	3.34212	−	0.412055i	0.126410	−	0.0155854i
$700$		0			0
$701$	27.0410			1.02132			0.510662	−	0.859782i	$-0.329400\pi$
$701$	27.0410			1.02132			0.510662	+	0.859782i	$0.329400\pi$
$702$		0			0
$703$	−45.5652			−1.71852
$704$		0			0
$705$		0			0
$706$		0			0
$707$	18.4126	+	31.8915i	0.692476	+	1.19940i
$708$		0			0
$709$	−21.7510	+	37.6738i	−0.816875	+	1.41487i	0.0910989	+	0.995842i	$0.470962\pi$
$709$	−21.7510	+	37.6738i	−0.816875	+	1.41487i	−0.907974	+	0.419027i	$0.862371\pi$
$710$		0			0
$711$	−1.64806	+	5.76922i	−0.0618071	+	0.216363i
$712$		0			0
$713$	2.76210	−	4.78410i	0.103441	−	0.179166i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−7.79001	−	10.3270i	−0.290923	−	0.385667i
$718$		0			0
$719$	−4.40515			−0.164284			−0.0821421	−	0.996621i	$-0.526176\pi$
$719$	−4.40515			−0.164284			−0.0821421	+	0.996621i	$0.526176\pi$
$720$		0			0
$721$	50.7810			1.89118
$722$		0			0
$723$	−1.63082	+	3.84731i	−0.0606509	+	0.143083i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	6.24083	−	10.8094i	0.231460	−	0.400900i	−0.726778	−	0.686872i	$-0.758983\pi$
$727$	6.24083	−	10.8094i	0.231460	−	0.400900i	0.958238	+	0.285972i	$0.0923166\pi$
$728$		0			0
$729$	20.0107	−	18.1266i	0.741136	−	0.671355i
$730$		0			0
$731$	−9.73419	+	16.8601i	−0.360032	+	0.623594i
$732$		0			0
$733$	19.5168	+	33.8041i	0.720869	+	1.24858i	0.960652	+	0.277755i	$0.0895903\pi$
$733$	19.5168	+	33.8041i	0.720869	+	1.24858i	−0.239783	+	0.970826i	$0.577076\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	23.5242			0.866525
$738$		0			0
$739$	−12.2935			−0.452224			−0.226112	−	0.974101i	$-0.572602\pi$
$739$	−12.2935			−0.452224			−0.226112	+	0.974101i	$0.572602\pi$
$740$		0			0
$741$	−27.6587	−	36.6662i	−1.01607	−	1.34697i
$742$		0			0
$743$	−20.4155	−	35.3607i	−0.748972	−	1.29726i	−0.948316	−	0.317328i	$-0.897214\pi$
$743$	−20.4155	−	35.3607i	−0.748972	−	1.29726i	0.199344	−	0.979930i	$-0.436119\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.33919	+	15.1898i	−0.158763	+	0.555766i
$748$		0			0
$749$	−26.3179	+	45.5840i	−0.961636	+	1.66560i
$750$		0			0
$751$	7.54469	+	13.0678i	0.275310	+	0.476850i	0.970213	−	0.242253i	$-0.0778863\pi$
$751$	7.54469	+	13.0678i	0.275310	+	0.476850i	−0.694904	+	0.719103i	$0.744553\pi$
$752$		0			0
$753$	−12.0205	+	1.48203i	−0.438051	+	0.0540080i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−34.4610			−1.25251			−0.626253	−	0.779620i	$-0.715412\pi$
$757$	−34.4610			−1.25251			−0.626253	+	0.779620i	$0.715412\pi$
$758$		0			0
$759$	−6.97209	+	0.859601i	−0.253071	+	0.0312015i
$760$		0			0
$761$	4.17837	+	7.23716i	0.151466	+	0.262347i	0.931767	−	0.363058i	$-0.118267\pi$
$761$	4.17837	+	7.23716i	0.151466	+	0.262347i	−0.780301	+	0.625405i	$0.784934\pi$
$762$		0			0
$763$	−0.716631	+	1.24124i	−0.0259438	+	0.0449359i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.58744	−	4.48157i	0.0934269	−	0.161820i
$768$		0			0
$769$	9.17837	+	15.8974i	0.330981	+	0.573275i	0.982704	−	0.185181i	$-0.0592872\pi$
$769$	9.17837	+	15.8974i	0.330981	+	0.573275i	−0.651724	+	0.758456i	$0.725954\pi$
$770$		0			0
$771$	−29.3068	−	38.8510i	−1.05546	−	1.39919i
$772$		0			0
$773$	10.0968			0.363157			0.181578	−	0.983376i	$-0.441879\pi$
$773$	10.0968			0.363157			0.181578	+	0.983376i	$0.441879\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−11.1925	+	26.4046i	−0.401530	+	0.947261i
$778$		0			0
$779$	3.97209	+	6.87986i	0.142315	+	0.246497i
$780$		0			0
$781$	−27.7752	+	48.1080i	−0.993874	+	1.72144i
$782$		0			0
$783$	3.59778	−	22.9380i	0.128574	−	0.819736i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−7.28630	−	12.6202i	−0.259729	−	0.449863i	0.706441	−	0.707772i	$-0.250300\pi$
$787$	−7.28630	−	12.6202i	−0.259729	−	0.449863i	−0.966169	+	0.257909i	$0.916966\pi$
$788$		0			0
$789$	5.16159	−	12.1769i	0.183758	−	0.433508i
$790$		0			0
$791$	−20.4200			−0.726051
$792$		0			0
$793$	31.9145			1.13332
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.03533	−	1.79324i	−0.0366732	−	0.0635198i	0.847106	−	0.531424i	$-0.178343\pi$
$797$	−1.03533	−	1.79324i	−0.0366732	−	0.0635198i	−0.883779	+	0.467904i	$0.845009\pi$
$798$		0			0
$799$	3.34212	−	5.78872i	0.118236	−	0.204790i
$800$		0			0
$801$	−8.73048	+	2.18602i	−0.308476	+	0.0772393i
$802$		0			0
$803$	22.0968	−	38.2728i	0.779779	−	1.35062i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−32.0101	+	3.94658i	−1.12681	+	0.138926i
$808$		0			0
$809$	3.37158			0.118539			0.0592693	−	0.998242i	$-0.481123\pi$
$809$	3.37158			0.118539			0.0592693	+	0.998242i	$0.481123\pi$
$810$		0			0
$811$	−12.9368			−0.454271			−0.227136	−	0.973863i	$-0.572936\pi$
$811$	−12.9368			−0.454271			−0.227136	+	0.973863i	$0.572936\pi$
$812$		0			0
$813$	11.2985	−	1.39301i	0.396257	−	0.0488551i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−13.2584	+	22.9642i	−0.463852	+	0.803416i
$818$		0			0
$819$	−28.0418	+	7.02138i	−0.979861	+	0.245347i
$820$		0			0
$821$	10.9963	−	19.0461i	0.383773	−	0.664715i	−0.607825	−	0.794071i	$-0.707958\pi$
$821$	10.9963	−	19.0461i	0.383773	−	0.664715i	0.991598	+	0.129356i	$0.0412911\pi$
$822$		0			0
$823$	7.45082	+	12.9052i	0.259719	+	0.449847i	0.966167	−	0.257919i	$-0.0830366\pi$
$823$	7.45082	+	12.9052i	0.259719	+	0.449847i	−0.706447	+	0.707766i	$0.749703\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−56.5785			−1.96743			−0.983713	−	0.179747i	$-0.942472\pi$
$827$	−56.5785			−1.96743			−0.983713	+	0.179747i	$0.942472\pi$
$828$		0			0
$829$	27.0558			0.939687			0.469844	−	0.882750i	$-0.344310\pi$
$829$	27.0558			0.939687			0.469844	+	0.882750i	$0.344310\pi$
$830$		0			0
$831$	1.03031	−	2.43064i	0.0357411	−	0.0843180i
$832$		0			0
$833$	−1.31421	−	2.27628i	−0.0455346	−	0.0788683i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−30.4208	−	24.5589i	−1.05150	−	0.848880i
$838$		0			0
$839$	17.2863	−	29.9407i	0.596789	−	1.03367i	−0.396502	−	0.918034i	$-0.629776\pi$
$839$	17.2863	−	29.9407i	0.596789	−	1.03367i	0.993292	−	0.115636i	$-0.0368905\pi$
$840$		0			0
$841$	4.51678	+	7.82329i	0.155751	+	0.269769i
$842$		0			0
$843$	−9.81792	+	23.1617i	−0.338147	+	0.797732i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−53.3626			−1.83356
$848$		0			0
$849$	−17.4549	−	23.1393i	−0.599049	−	0.794139i
$850$		0			0
$851$	−2.22306	−	3.85046i	−0.0762056	−	0.131992i
$852$		0			0
$853$	8.48887	−	14.7032i	0.290653	−	0.503427i	−0.683311	−	0.730127i	$-0.739461\pi$
$853$	8.48887	−	14.7032i	0.290653	−	0.503427i	0.973964	+	0.226701i	$0.0727940\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.70628	−	2.95537i	0.0582855	−	0.100953i	−0.835410	−	0.549627i	$-0.814770\pi$
$857$	1.70628	−	2.95537i	0.0582855	−	0.100953i	0.893696	+	0.448673i	$0.148103\pi$
$858$		0			0
$859$	4.91627	+	8.51524i	0.167741	+	0.290536i	0.937625	−	0.347647i	$-0.113019\pi$
$859$	4.91627	+	8.51524i	0.167741	+	0.290536i	−0.769884	+	0.638184i	$0.779686\pi$
$860$		0			0
$861$	4.96252	−	0.611838i	0.169122	−	0.0208514i
$862$		0			0
$863$	48.9836			1.66742			0.833711	−	0.552202i	$-0.186212\pi$
$863$	48.9836			1.66742			0.833711	+	0.552202i	$0.186212\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	23.2358	−	2.86478i	0.789130	−	0.0972931i
$868$		0			0
$869$	−5.52420	−	9.56819i	−0.187396	−	0.324579i
$870$		0			0
$871$	−7.50371	+	12.9968i	−0.254253	+	0.440380i
$872$		0			0
$873$	7.80223	−	27.3126i	0.264066	−	0.924391i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−6.33470	−	10.9720i	−0.213908	−	0.370499i	0.739027	−	0.673676i	$-0.235286\pi$
$877$	−6.33470	−	10.9720i	−0.213908	−	0.370499i	−0.952934	+	0.303178i	$0.901952\pi$
$878$		0			0
$879$	−21.3421	−	28.2925i	−0.719852	−	0.954283i
$880$		0			0
$881$	−26.0894			−0.878974			−0.439487	−	0.898249i	$-0.644840\pi$
$881$	−26.0894			−0.878974			−0.439487	+	0.898249i	$0.644840\pi$
$882$		0			0
$883$	−2.69321			−0.0906337			−0.0453169	−	0.998973i	$-0.514430\pi$
$883$	−2.69321			−0.0906337			−0.0453169	+	0.998973i	$0.514430\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.2789	−	21.2676i	−0.412284	−	0.714098i	0.582855	−	0.812576i	$-0.301936\pi$
$887$	−12.2789	−	21.2676i	−0.412284	−	0.714098i	−0.995139	+	0.0984788i	$0.968602\pi$
$888$		0			0
$889$	−11.2900	+	19.5549i	−0.378655	+	0.655849i
$890$		0			0
$891$	−1.63583	+	49.6909i	−0.0548025	+	1.66471i
$892$		0			0
$893$	4.55211	−	7.88448i	0.152330	−	0.263844i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.74903	−	4.12618i	0.0583983	−	0.137769i
$898$		0			0
$899$	−33.6210			−1.12132
$900$		0			0
$901$	−8.11164			−0.270238
$902$		0			0
$903$	10.0508	+	13.3240i	0.334470	+	0.443395i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	17.1850	−	29.7653i	0.570619	−	0.988341i	−0.425884	−	0.904778i	$-0.640037\pi$
$907$	17.1850	−	29.7653i	0.570619	−	0.988341i	0.996502	−	0.0835631i	$-0.0266300\pi$
$908$		0			0
$909$	−11.0984	+	38.8510i	−0.368109	+	1.28861i
$910$		0			0
$911$	−18.7752	+	32.5196i	−0.622049	+	1.07742i	0.367054	+	0.930199i	$0.380366\pi$
$911$	−18.7752	+	32.5196i	−0.622049	+	1.07742i	−0.989104	+	0.147221i	$0.952967\pi$
$912$		0			0
$913$	−14.5447	−	25.1921i	−0.481359	−	0.833738i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	44.0117			1.45340
$918$		0			0
$919$	10.1116			0.333552			0.166776	−	0.985995i	$-0.446664\pi$
$919$	10.1116			0.333552			0.166776	+	0.985995i	$0.446664\pi$
$920$		0			0
$921$	31.2909	−	3.85790i	1.03107	−	0.127122i
$922$		0			0
$923$	−17.7194	−	30.6908i	−0.583240	−	1.01020i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	38.7449	+	40.0413i	1.27255	+	1.31513i
$928$		0			0
$929$	−12.4126	+	21.4992i	−0.407243	+	0.705366i	−0.994580	−	0.103977i	$-0.966843\pi$
$929$	−12.4126	+	21.4992i	−0.407243	+	0.705366i	0.587337	+	0.809343i	$0.300176\pi$
$930$		0			0
$931$	−1.79001	−	3.10039i	−0.0586652	−	0.101611i
$932$		0			0
$933$	−3.23790	−	4.29238i	−0.106004	−	0.140526i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−1.56518			−0.0511322			−0.0255661	−	0.999673i	$-0.508139\pi$
$937$	−1.56518			−0.0511322			−0.0255661	+	0.999673i	$0.508139\pi$
$938$		0			0
$939$	−12.9139	+	30.4655i	−0.421428	+	0.994203i
$940$		0			0
$941$	5.23419	+	9.06588i	0.170630	+	0.295539i	0.938640	−	0.344898i	$-0.112086\pi$
$941$	5.23419	+	9.06588i	0.170630	+	0.295539i	−0.768010	+	0.640437i	$0.778753\pi$
$942$		0			0
$943$	−0.387586	+	0.671318i	−0.0126215	+	0.0218611i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.59758	+	2.76709i	−0.0519143	+	0.0899182i	−0.890815	−	0.454367i	$-0.849866\pi$
$947$	−1.59758	+	2.76709i	−0.0519143	+	0.0899182i	0.838900	+	0.544285i	$0.183199\pi$
$948$		0			0
$949$	14.0968	+	24.4164i	0.457601	+	0.792589i
$950$		0			0
$951$	3.38486	−	7.98533i	0.109762	−	0.258942i
$952$		0			0
$953$	33.9293			1.09908			0.549540	−	0.835468i	$-0.314803\pi$
$953$	33.9293			1.09908			0.549540	+	0.835468i	$0.314803\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	25.7473	+	34.1323i	0.832291	+	1.10334i
$958$		0			0
$959$	25.3142	+	43.8455i	0.817438	+	1.41584i
$960$		0			0
$961$	−12.8068	+	22.1820i	−0.413122	+	0.715549i
$962$		0			0
$963$	−56.0234	+	14.0277i	−1.80533	+	0.452036i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	19.2129	+	33.2778i	0.617846	+	1.07014i	0.989878	+	0.141921i	$0.0453278\pi$
$967$	19.2129	+	33.2778i	0.617846	+	1.07014i	−0.372032	+	0.928220i	$0.621339\pi$
$968$		0			0
$969$	71.4520	−	8.80944i	2.29537	−	0.283000i
$970$		0			0
$971$	29.7326			0.954166			0.477083	−	0.878858i	$-0.341694\pi$
$971$	29.7326			0.954166			0.477083	+	0.878858i	$0.341694\pi$
$972$		0			0
$973$	10.9368			0.350617
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−16.4889	−	28.5596i	−0.527526	−	0.913701i	−0.999485	−	0.0320812i	$-0.989786\pi$
$977$	−16.4889	−	28.5596i	−0.527526	−	0.913701i	0.471960	−	0.881620i	$-0.343547\pi$
$978$		0			0
$979$	8.28630	−	14.3523i	0.264831	−	0.458701i
$980$		0			0
$981$	−1.52551	+	0.381970i	−0.0487056	+	0.0121954i
$982$		0			0
$983$	−3.68872	+	6.38905i	−0.117652	+	0.203779i	−0.918837	−	0.394638i	$-0.870870\pi$
$983$	−3.68872	+	6.38905i	−0.117652	+	0.203779i	0.801185	+	0.598417i	$0.204203\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−3.45082	−	4.57464i	−0.109841	−	0.145612i
$988$		0			0
$989$	−2.58744			−0.0822757
$990$		0			0
$991$	−4.51678			−0.143480			−0.0717401	−	0.997423i	$-0.522855\pi$
$991$	−4.51678			−0.143480			−0.0717401	+	0.997423i	$0.522855\pi$
$992$		0			0
$993$	2.35455	−	5.55469i	0.0747194	−	0.176273i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−24.3142	+	42.1134i	−0.770039	+	1.33375i	0.167502	+	0.985872i	$0.446430\pi$
$997$	−24.3142	+	42.1134i	−0.770039	+	1.33375i	−0.937541	+	0.347874i	$0.886904\pi$
$998$		0			0
$999$	−29.3600	+	11.3208i	−0.928909	+	0.358173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.i.c.601.3		6
3.2	odd	2		2700.2.i.c.1801.2		6
5.2	odd	4		900.2.s.c.349.3		12
5.3	odd	4		900.2.s.c.349.4		12
5.4	even	2		180.2.i.b.61.1	✓	6
9.2	odd	6		8100.2.a.u.1.2		3
9.4	even	3	inner	900.2.i.c.301.3		6
9.5	odd	6		2700.2.i.c.901.2		6
9.7	even	3		8100.2.a.v.1.2		3
15.2	even	4		2700.2.s.c.2449.4		12
15.8	even	4		2700.2.s.c.2449.3		12
15.14	odd	2		540.2.i.b.181.2		6
20.19	odd	2		720.2.q.k.241.3		6
45.2	even	12		8100.2.d.o.649.3		6
45.4	even	6		180.2.i.b.121.1	yes	6
45.7	odd	12		8100.2.d.p.649.3		6
45.13	odd	12		900.2.s.c.49.3		12
45.14	odd	6		540.2.i.b.361.2		6
45.22	odd	12		900.2.s.c.49.4		12
45.23	even	12		2700.2.s.c.1549.4		12
45.29	odd	6		1620.2.a.j.1.2		3
45.32	even	12		2700.2.s.c.1549.3		12
45.34	even	6		1620.2.a.i.1.2		3
45.38	even	12		8100.2.d.o.649.4		6
45.43	odd	12		8100.2.d.p.649.4		6
60.59	even	2		2160.2.q.i.721.2		6
180.59	even	6		2160.2.q.i.1441.2		6
180.79	odd	6		6480.2.a.bt.1.2		3
180.119	even	6		6480.2.a.bw.1.2		3
180.139	odd	6		720.2.q.k.481.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.i.b.61.1	✓	6	5.4	even	2
180.2.i.b.121.1	yes	6	45.4	even	6
540.2.i.b.181.2		6	15.14	odd	2
540.2.i.b.361.2		6	45.14	odd	6
720.2.q.k.241.3		6	20.19	odd	2
720.2.q.k.481.3		6	180.139	odd	6
900.2.i.c.301.3		6	9.4	even	3	inner
900.2.i.c.601.3		6	1.1	even	1	trivial
900.2.s.c.49.3		12	45.13	odd	12
900.2.s.c.49.4		12	45.22	odd	12
900.2.s.c.349.3		12	5.2	odd	4
900.2.s.c.349.4		12	5.3	odd	4
1620.2.a.i.1.2		3	45.34	even	6
1620.2.a.j.1.2		3	45.29	odd	6
2160.2.q.i.721.2		6	60.59	even	2
2160.2.q.i.1441.2		6	180.59	even	6
2700.2.i.c.901.2		6	9.5	odd	6
2700.2.i.c.1801.2		6	3.2	odd	2
2700.2.s.c.1549.3		12	45.32	even	12
2700.2.s.c.1549.4		12	45.23	even	12
2700.2.s.c.2449.3		12	15.8	even	4
2700.2.s.c.2449.4		12	15.2	even	4
6480.2.a.bt.1.2		3	180.79	odd	6
6480.2.a.bw.1.2		3	180.119	even	6
8100.2.a.u.1.2		3	9.2	odd	6
8100.2.a.v.1.2		3	9.7	even	3
8100.2.d.o.649.3		6	45.2	even	12
8100.2.d.o.649.4		6	45.38	even	12
8100.2.d.p.649.3		6	45.7	odd	12
8100.2.d.p.649.4		6	45.43	odd	12

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.71903 - 0.211943i) q^{3} +(1.36710 - 2.36788i) q^{7} +(2.91016 - 0.728674i) q^{9} +(-2.76210 + 4.78410i) q^{11} +(-1.76210 - 3.05205i) q^{13} +5.52420 q^{17} +7.52420 q^{19} +(1.84823 - 4.36021i) q^{21} +(0.367095 + 0.635828i) q^{23} +(4.84823 - 1.86940i) q^{27} +(2.23419 - 3.86973i) q^{29} +(-3.76210 - 6.51615i) q^{31} +(-3.73419 + 8.80944i) q^{33} -6.05582 q^{37} +(-3.67597 - 4.87311i) q^{39} +(0.527909 + 0.914365i) q^{41} +(-1.76210 + 3.05205i) q^{43} +(0.604996 - 1.04788i) q^{47} +(-0.237900 - 0.412055i) q^{49} +(9.49629 - 1.17081i) q^{51} -1.46838 q^{53} +(12.9344 - 1.59470i) q^{57} +(0.734191 + 1.27166i) q^{59} +(-4.52791 + 7.84257i) q^{61} +(2.25306 - 7.88707i) q^{63} +(-2.12920 - 3.68787i) q^{67} +(0.765809 + 1.01521i) q^{69} +10.0558 q^{71} -8.00000 q^{73} +(7.55211 + 13.0806i) q^{77} +(-1.00000 + 1.73205i) q^{79} +(7.93807 - 4.24111i) q^{81} +(-2.63290 + 4.56032i) q^{83} +(3.02049 - 7.12572i) q^{87} -3.00000 q^{89} -9.63583 q^{91} +(-7.84823 - 10.4041i) q^{93} +(4.73419 - 8.19986i) q^{97} +(-4.55211 + 15.9352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 3 q^{7} + 5 q^{9} + 6 q^{13} + 12 q^{19} - 20 q^{21} - 3 q^{23} - 2 q^{27} + 3 q^{29} - 6 q^{31} - 12 q^{33} - 24 q^{37} - 20 q^{39} - 3 q^{41} + 6 q^{43} + 15 q^{47} - 18 q^{49} + 30 q^{51}+ \cdots + 12 q^{99}+O(q^{100}) \) 6 * q + q^3 + 3 * q^7 + 5 * q^9 + 6 * q^13 + 12 * q^19 - 20 * q^21 - 3 * q^23 - 2 * q^27 + 3 * q^29 - 6 * q^31 - 12 * q^33 - 24 * q^37 - 20 * q^39 - 3 * q^41 + 6 * q^43 + 15 * q^47 - 18 * q^49 + 30 * q^51 + 12 * q^53 + 32 * q^57 - 6 * q^59 - 21 * q^61 + 29 * q^63 + 9 * q^67 + 15 * q^69 + 48 * q^71 - 48 * q^73 + 6 * q^77 - 6 * q^79 + 29 * q^81 - 21 * q^83 - 42 * q^87 - 18 * q^89 - 16 * q^93 + 18 * q^97 + 12 * q^99

Introduction

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