LMFDB - Embedded newform 180.2.i.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,2,Mod(61,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("180.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.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:	$1.43730723638$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$1.71903 + 0.211943i$ of defining polynomial
Character	$\chi$	$=$	180.121
Dual form			180.2.i.b.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71903 - 0.211943i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.36710 - 2.36788i) q^{7} +(2.91016 + 0.728674i) q^{9} +O(q^{10})$	\(q+(-1.71903 - 0.211943i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.36710 - 2.36788i) q^{7} +(2.91016 + 0.728674i) q^{9} +(-2.76210 - 4.78410i) q^{11} +(1.76210 - 3.05205i) q^{13} +(-1.04307 + 1.38276i) q^{15} -5.52420 q^{17} +7.52420 q^{19} +(1.84823 + 4.36021i) q^{21} +(-0.367095 + 0.635828i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-4.84823 - 1.86940i) q^{27} +(2.23419 + 3.86973i) q^{29} +(-3.76210 + 6.51615i) q^{31} +(3.73419 + 8.80944i) q^{33} -2.73419 q^{35} +6.05582 q^{37} +(-3.67597 + 4.87311i) q^{39} +(0.527909 - 0.914365i) q^{41} +(1.76210 + 3.05205i) q^{43} +(2.08613 - 2.15594i) q^{45} +(-0.604996 - 1.04788i) q^{47} +(-0.237900 + 0.412055i) q^{49} +(9.49629 + 1.17081i) q^{51} +1.46838 q^{53} -5.52420 q^{55} +(-12.9344 - 1.59470i) q^{57} +(0.734191 - 1.27166i) q^{59} +(-4.52791 - 7.84257i) q^{61} +(-2.25306 - 7.88707i) q^{63} +(-1.76210 - 3.05205i) q^{65} +(2.12920 - 3.68787i) q^{67} +(0.765809 - 1.01521i) q^{69} +10.0558 q^{71} +8.00000 q^{73} +(0.675970 + 1.59470i) q^{75} +(-7.55211 + 13.0806i) q^{77} +(-1.00000 - 1.73205i) q^{79} +(7.93807 + 4.24111i) q^{81} +(2.63290 + 4.56032i) q^{83} +(-2.76210 + 4.78410i) q^{85} +(-3.02049 - 7.12572i) q^{87} -3.00000 q^{89} -9.63583 q^{91} +(7.84823 - 10.4041i) q^{93} +(3.76210 - 6.51615i) q^{95} +(-4.73419 - 8.19986i) q^{97} +(-4.55211 - 15.9352i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 3 q^{5} - 3 q^{7} + 5 q^{9}+O(q^{10}) $ 6 * q - q^3 + 3 * q^5 - 3 * q^7 + 5 * q^9	$ 6 q - q^{3} + 3 q^{5} - 3 q^{7} + 5 q^{9} - 6 q^{13} + q^{15} + 12 q^{19} - 20 q^{21} + 3 q^{23} - 3 q^{25} + 2 q^{27} + 3 q^{29} - 6 q^{31} + 12 q^{33} - 6 q^{35} + 24 q^{37} - 20 q^{39} - 3 q^{41} - 6 q^{43} - 2 q^{45} - 15 q^{47} - 18 q^{49} + 30 q^{51} - 12 q^{53} - 32 q^{57} - 6 q^{59} - 21 q^{61} - 29 q^{63} + 6 q^{65} - 9 q^{67} + 15 q^{69} + 48 q^{71} + 48 q^{73} + 2 q^{75} - 6 q^{77} - 6 q^{79} + 29 q^{81} + 21 q^{83} + 42 q^{87} - 18 q^{89} + 16 q^{93} + 6 q^{95} - 18 q^{97} + 12 q^{99}+O(q^{100}) $ 6 * q - q^3 + 3 * q^5 - 3 * q^7 + 5 * q^9 - 6 * q^13 + q^15 + 12 * q^19 - 20 * q^21 + 3 * q^23 - 3 * q^25 + 2 * q^27 + 3 * q^29 - 6 * q^31 + 12 * q^33 - 6 * q^35 + 24 * q^37 - 20 * q^39 - 3 * q^41 - 6 * q^43 - 2 * q^45 - 15 * q^47 - 18 * q^49 + 30 * q^51 - 12 * q^53 - 32 * q^57 - 6 * q^59 - 21 * q^61 - 29 * q^63 + 6 * q^65 - 9 * q^67 + 15 * q^69 + 48 * q^71 + 48 * q^73 + 2 * q^75 - 6 * q^77 - 6 * q^79 + 29 * q^81 + 21 * q^83 + 42 * q^87 - 18 * q^89 + 16 * q^93 + 6 * q^95 - 18 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−1.36710	−	2.36788i	−0.516714	−	0.894974i	−0.999812	−	0.0194079i	$-0.993822\pi$
$7$	−1.36710	−	2.36788i	−0.516714	−	0.894974i	0.483098	−	0.875566i	$-0.339511\pi$
$8$		0			0
$9$	2.91016	+	0.728674i	0.970054	+	0.242891i
$10$		0			0
$11$	−2.76210	−	4.78410i	−0.832804	−	1.44246i	−0.895806	−	0.444446i	$-0.853401\pi$
$11$	−2.76210	−	4.78410i	−0.832804	−	1.44246i	0.0630012	−	0.998013i	$-0.479933\pi$
$12$		0			0
$13$	1.76210	−	3.05205i	0.488719	−	0.846485i	−0.511197	−	0.859463i	$-0.670798\pi$
$13$	1.76210	−	3.05205i	0.488719	−	0.846485i	0.999916	+	0.0129781i	$0.00413116\pi$
$14$		0			0
$15$	−1.04307	+	1.38276i	−0.269318	+	0.357026i
$16$		0			0
$17$	−5.52420			−1.33982			−0.669908	−	0.742444i	$-0.733666\pi$
$17$	−5.52420			−1.33982			−0.669908	+	0.742444i	$0.733666\pi$
$18$		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	$-0.857722\pi$
$23$	−0.367095	+	0.635828i	−0.0765447	+	0.132579i	0.825212	+	0.564823i	$0.191055\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−4.84823	−	1.86940i	−0.933042	−	0.359767i
$28$		0			0
$29$	2.23419	+	3.86973i	0.414879	+	0.718591i	0.995416	−	0.0956427i	$-0.0304906\pi$
$29$	2.23419	+	3.86973i	0.414879	+	0.718591i	−0.580537	+	0.814234i	$0.697157\pi$
$30$		0			0
$31$	−3.76210	+	6.51615i	−0.675693	+	1.17033i	0.300573	+	0.953759i	$0.402822\pi$
$31$	−3.76210	+	6.51615i	−0.675693	+	1.17033i	−0.976266	+	0.216576i	$0.930511\pi$
$32$		0			0
$33$	3.73419	+	8.80944i	0.650039	+	1.53353i
$34$		0			0
$35$	−2.73419			−0.462163
$36$		0			0
$37$	6.05582			0.995570			0.497785	−	0.867300i	$-0.334147\pi$
$37$	6.05582			0.995570			0.497785	+	0.867300i	$0.334147\pi$
$38$		0			0
$39$	−3.67597	+	4.87311i	−0.588626	+	0.780322i
$40$		0			0
$41$	0.527909	−	0.914365i	0.0824455	−	0.142800i	−0.821854	−	0.569698i	$-0.807060\pi$
$41$	0.527909	−	0.914365i	0.0824455	−	0.142800i	0.904300	+	0.426898i	$0.140394\pi$
$42$		0			0
$43$	1.76210	+	3.05205i	0.268718	+	0.465433i	0.968531	−	0.248893i	$-0.0800668\pi$
$43$	1.76210	+	3.05205i	0.268718	+	0.465433i	−0.699813	+	0.714326i	$0.746733\pi$
$44$		0			0
$45$	2.08613	−	2.15594i	0.310982	−	0.321388i
$46$		0			0
$47$	−0.604996	−	1.04788i	−0.0882477	−	0.152849i	0.818523	−	0.574474i	$-0.194793\pi$
$47$	−0.604996	−	1.04788i	−0.0882477	−	0.152849i	−0.906771	+	0.421625i	$0.861460\pi$
$48$		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	$-0.467844\pi$
$53$	1.46838			0.201698			0.100849	+	0.994902i	$0.467844\pi$
$54$		0			0
$55$	−5.52420			−0.744883
$56$		0			0
$57$	−12.9344	−	1.59470i	−1.71320	−	0.211223i
$58$		0			0
$59$	0.734191	−	1.27166i	0.0955835	−	0.165556i	−0.814268	−	0.580488i	$-0.802862\pi$
$59$	0.734191	−	1.27166i	0.0955835	−	0.165556i	0.909852	+	0.414933i	$0.136195\pi$
$60$		0			0
$61$	−4.52791	−	7.84257i	−0.579739	−	1.00414i	−0.995509	−	0.0946680i	$-0.969821\pi$
$61$	−4.52791	−	7.84257i	−0.579739	−	1.00414i	0.415770	−	0.909470i	$-0.363512\pi$
$62$		0			0
$63$	−2.25306	−	7.88707i	−0.283858	−	0.993678i
$64$		0			0
$65$	−1.76210	−	3.05205i	−0.218562	−	0.378560i
$66$		0			0
$67$	2.12920	−	3.68787i	0.260123	−	0.450546i	−0.706152	−	0.708061i	$-0.749570\pi$
$67$	2.12920	−	3.68787i	0.260123	−	0.450546i	0.966274	+	0.257515i	$0.0829037\pi$
$68$		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	$-0.344915\pi$
$73$	8.00000			0.936329			0.468165	+	0.883641i	$0.344915\pi$
$74$		0			0
$75$	0.675970	+	1.59470i	0.0780542	+	0.184140i
$76$		0			0
$77$	−7.55211	+	13.0806i	−0.860643	+	1.49068i
$78$		0			0
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	0.804272	−	0.594261i	$-0.202555\pi$
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	−0.916781	+	0.399390i	$0.869222\pi$
$80$		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	$-0.0733443\pi$
$83$	2.63290	+	4.56032i	0.288999	+	0.500561i	−0.684572	+	0.728945i	$0.740011\pi$
$84$		0			0
$85$	−2.76210	+	4.78410i	−0.299592	+	0.518908i
$86$		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
$95$	3.76210	−	6.51615i	0.385983	−	0.668543i
$96$		0			0
$97$	−4.73419	−	8.19986i	−0.480684	−	0.832570i	0.519070	−	0.854732i	$-0.326278\pi$
$97$	−4.73419	−	8.19986i	−0.480684	−	0.832570i	−0.999754	+	0.0221621i	$0.992945\pi$
$98$		0			0
$99$	−4.55211	−	15.9352i	−0.457504	−	1.60154i
$100$		0			0
$101$	−6.73419	−	11.6640i	−0.670077	−	1.16061i	−0.977882	−	0.209158i	$-0.932928\pi$
$101$	−6.73419	−	11.6640i	−0.670077	−	1.16061i	0.307805	−	0.951450i	$-0.400406\pi$
$102$		0			0
$103$	−9.28630	+	16.0843i	−0.915006	+	1.58484i	−0.108114	+	0.994138i	$0.534481\pi$
$103$	−9.28630	+	16.0843i	−0.915006	+	1.58484i	−0.806892	+	0.590699i	$0.798852\pi$
$104$		0			0
$105$	4.70017	+	0.579492i	0.458690	+	0.0565526i
$106$		0			0
$107$	19.2510			1.86106			0.930531	−	0.366213i	$-0.119346\pi$
$107$	19.2510			1.86106			0.930531	+	0.366213i	$0.119346\pi$
$108$		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	$-0.719079\pi$
$113$	3.73419	−	6.46781i	0.351283	−	0.608440i	0.986475	+	0.163915i	$0.0524121\pi$
$114$		0			0
$115$	0.367095	+	0.635828i	0.0342318	+	0.0592913i
$116$		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
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	8.25839			0.732814			0.366407	−	0.930455i	$-0.380588\pi$
$127$	8.25839			0.732814			0.366407	+	0.930455i	$0.380588\pi$
$128$		0			0
$129$	−2.38225	−	5.62004i	−0.209746	−	0.494817i
$130$		0			0
$131$	8.04840	−	13.9402i	0.703192	−	1.21796i	−0.264148	−	0.964482i	$-0.585091\pi$
$131$	8.04840	−	13.9402i	0.703192	−	1.21796i	0.967340	−	0.253482i	$-0.0815759\pi$
$132$		0			0
$133$	−10.2863	−	17.8164i	−0.891935	−	1.54488i
$134$		0			0
$135$	−4.04307	+	3.26399i	−0.347972	+	0.280919i
$136$		0			0
$137$	9.25839	+	16.0360i	0.790998	+	1.37005i	0.925350	+	0.379115i	$0.123771\pi$
$137$	9.25839	+	16.0360i	0.790998	+	1.37005i	−0.134352	+	0.990934i	$0.542895\pi$
$138$		0			0
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$		0			0
$141$	0.817917	+	1.92957i	0.0688811	+	0.162499i
$142$		0			0
$143$	−19.4684			−1.62803
$144$		0			0
$145$	4.46838			0.371079
$146$		0			0
$147$	0.496291	−	0.657916i	0.0409334	−	0.0542640i
$148$		0			0
$149$	−6.78630	+	11.7542i	−0.555955	+	0.962943i	0.441873	+	0.897078i	$0.354314\pi$
$149$	−6.78630	+	11.7542i	−0.555955	+	0.962943i	−0.997829	+	0.0658653i	$0.979019\pi$
$150$		0			0
$151$	6.23048	+	10.7915i	0.507029	+	0.878201i	0.999967	+	0.00813598i	$0.00258979\pi$
$151$	6.23048	+	10.7915i	0.507029	+	0.878201i	−0.492937	+	0.870065i	$0.664077\pi$
$152$		0			0
$153$	−16.0763	−	4.02534i	−1.29969	−	0.325429i
$154$		0			0
$155$	3.76210	+	6.51615i	0.302179	+	0.523390i
$156$		0			0
$157$	0.790009	−	1.36834i	0.0630496	−	0.109205i	−0.832778	−	0.553608i	$-0.813251\pi$
$157$	0.790009	−	1.36834i	0.0630496	−	0.109205i	0.895827	+	0.444403i	$0.146584\pi$
$158$		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	$-0.556085\pi$
$163$	−4.47580			−0.350572			−0.175286	+	0.984518i	$0.556085\pi$
$164$		0			0
$165$	9.49629	+	1.17081i	0.739285	+	0.0911477i
$166$		0			0
$167$	−8.39500	+	14.5406i	−0.649625	+	1.12518i	0.333588	+	0.942719i	$0.391741\pi$
$167$	−8.39500	+	14.5406i	−0.649625	+	1.12518i	−0.983212	+	0.182464i	$0.941593\pi$
$168$		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	0.855513	+	0.517782i	$0.173242\pi$
$173$	11.5242	+	19.9605i	0.876169	+	1.51757i	0.0206561	+	0.999787i	$0.493424\pi$
$174$		0			0
$175$	−1.36710	+	2.36788i	−0.103343	+	0.178995i
$176$		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
$185$	3.02791	−	5.24449i	0.222616	−	0.385583i
$186$		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	−0.998514	−	0.0544954i	$-0.982645\pi$
$191$	−7.55211	−	13.0806i	−0.546451	−	0.946482i	0.452063	−	0.891986i	$-0.350688\pi$
$192$		0			0
$193$	7.28630	−	12.6202i	0.524479	−	0.908425i	−0.475114	−	0.879924i	$-0.657593\pi$
$193$	7.28630	−	12.6202i	0.524479	−	0.908425i	0.999594	−	0.0285008i	$-0.00907332\pi$
$194$		0			0
$195$	2.38225	+	5.62004i	0.170597	+	0.402459i
$196$		0			0
$197$	−4.53162			−0.322864			−0.161432	−	0.986884i	$-0.551611\pi$
$197$	−4.53162			−0.322864			−0.161432	+	0.986884i	$0.551611\pi$
$198$		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
$205$	−0.527909	−	0.914365i	−0.0368708	−	0.0638620i
$206$		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	−0.537365	−	0.843350i	$-0.680580\pi$
$211$	6.70628	−	11.6156i	0.461680	−	0.799652i	0.999045	+	0.0436972i	$0.0139137\pi$
$212$		0			0
$213$	−17.2863	−	2.13126i	−1.18444	−	0.146031i
$214$		0			0
$215$	3.52420			0.240348
$216$		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	$-0.0715764\pi$
$223$	4.39500	+	7.61237i	0.294311	+	0.509762i	−0.680513	+	0.732736i	$0.738243\pi$
$224$		0			0
$225$	−0.824030	−	2.88461i	−0.0549354	−	0.192307i
$226$		0			0
$227$	−2.02791	−	3.51244i	−0.134597	−	0.233129i	0.790846	−	0.612015i	$-0.209641\pi$
$227$	−2.02791	−	3.51244i	−0.134597	−	0.233129i	−0.925443	+	0.378886i	$0.876307\pi$
$228$		0			0
$229$	−1.29001	+	2.23436i	−0.0852462	+	0.147651i	−0.905496	−	0.424355i	$-0.860501\pi$
$229$	−1.29001	+	2.23436i	−0.0852462	+	0.147651i	0.820250	+	0.572005i	$0.193834\pi$
$230$		0			0
$231$	15.7547	−	20.8855i	1.03658	−	1.37416i
$232$		0			0
$233$	−1.94418			−0.127368			−0.0636838	−	0.997970i	$-0.520285\pi$
$233$	−1.94418			−0.127368			−0.0636838	+	0.997970i	$0.520285\pi$
$234$		0			0
$235$	−1.20999			−0.0789311
$236$		0			0
$237$	1.35194	+	3.18940i	0.0878179	+	0.207174i
$238$		0			0
$239$	−3.73419	+	6.46781i	−0.241545	+	0.418368i	−0.961154	−	0.276011i	$-0.910987\pi$
$239$	−3.73419	+	6.46781i	−0.241545	+	0.418368i	0.719610	+	0.694379i	$0.244321\pi$
$240$		0			0
$241$	−1.20628	−	2.08934i	−0.0777035	−	0.134586i	0.824555	−	0.565781i	$-0.191425\pi$
$241$	−1.20628	−	2.08934i	−0.0777035	−	0.134586i	−0.902259	+	0.431195i	$0.858092\pi$
$242$		0			0
$243$	−12.7469	−	8.97304i	−0.817717	−	0.575621i
$244$		0			0
$245$	0.237900	+	0.412055i	0.0151989	+	0.0263252i
$246$		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
$255$	5.76210	−	7.63862i	0.360837	−	0.478349i
$256$		0			0
$257$	14.0484	−	24.3325i	0.876315	−	1.51782i	0.0209598	−	0.999780i	$-0.493328\pi$
$257$	14.0484	−	24.3325i	0.876315	−	1.51782i	0.855355	−	0.518042i	$-0.173339\pi$
$258$		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	$-0.242314\pi$
$263$	−3.81792	−	6.61283i	−0.235423	−	0.407764i	−0.959395	+	0.282064i	$0.908981\pi$
$264$		0			0
$265$	0.734191	−	1.27166i	0.0451010	−	0.0781172i
$266$		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
$275$	−2.76210	+	4.78410i	−0.166561	+	0.288492i
$276$		0			0
$277$	−0.762100	−	1.32000i	−0.0457901	−	0.0793108i	0.842222	−	0.539131i	$-0.181247\pi$
$277$	−0.762100	−	1.32000i	−0.0457901	−	0.0793108i	−0.888012	+	0.459820i	$0.847914\pi$
$278$		0			0
$279$	−15.6965	+	16.2217i	−0.939722	+	0.971167i
$280$		0			0
$281$	−7.26210	−	12.5783i	−0.433221	−	0.750360i	0.563928	−	0.825824i	$-0.309290\pi$
$281$	−7.26210	−	12.5783i	−0.433221	−	0.750360i	−0.997149	+	0.0754640i	$0.975956\pi$
$282$		0			0
$283$	8.36710	−	14.4922i	0.497372	−	0.861474i	−0.502623	−	0.864506i	$-0.667632\pi$
$283$	8.36710	−	14.4922i	0.497372	−	0.861474i	0.999995	+	0.00303167i	$0.000965011\pi$
$284$		0			0
$285$	−7.84823	+	10.4041i	−0.464889	+	0.616288i
$286$		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	−0.395493	−	0.918469i	$-0.629426\pi$
$293$	10.2305	−	17.7197i	0.597671	−	1.03520i	0.993164	−	0.116728i	$-0.0372405\pi$
$294$		0			0
$295$	−0.734191	−	1.27166i	−0.0427463	−	0.0740387i
$296$		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
$305$	−9.05582			−0.518535
$306$		0			0
$307$	−18.2026			−1.03888			−0.519438	−	0.854508i	$-0.673859\pi$
$307$	−18.2026			−1.03888			−0.519438	+	0.854508i	$0.673859\pi$
$308$		0			0
$309$	19.3724	−	25.6814i	1.10206	−	1.46096i
$310$		0			0
$311$	−1.55211	+	2.68833i	−0.0880120	+	0.152441i	−0.906671	−	0.421839i	$-0.861385\pi$
$311$	−1.55211	+	2.68833i	−0.0880120	+	0.152441i	0.818659	+	0.574280i	$0.194718\pi$
$312$		0			0
$313$	9.55211	+	16.5447i	0.539917	+	0.935164i	0.998908	+	0.0467228i	$0.0148777\pi$
$313$	9.55211	+	16.5447i	0.539917	+	0.935164i	−0.458991	+	0.888441i	$0.651789\pi$
$314$		0			0
$315$	−7.95693	−	1.99233i	−0.448322	−	0.112255i
$316$		0			0
$317$	−2.50371	−	4.33655i	−0.140622	−	0.243565i	0.787109	−	0.616814i	$-0.211577\pi$
$317$	−2.50371	−	4.33655i	−0.140622	−	0.243565i	−0.927731	+	0.373249i	$0.878244\pi$
$318$		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
$325$	−3.52420			−0.195487
$326$		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	0.909912	−	0.414801i	$-0.136149\pi$
$331$	1.74161	+	3.01656i	0.0957275	+	0.165805i	−0.814184	+	0.580606i	$0.802816\pi$
$332$		0			0
$333$	17.6234	+	4.41271i	0.965756	+	0.241815i
$334$		0			0
$335$	−2.12920	−	3.68787i	−0.116330	−	0.201490i
$336$		0			0
$337$	−5.79001	+	10.0286i	−0.315402	+	0.546292i	−0.979523	−	0.201333i	$-0.935473\pi$
$337$	−5.79001	+	10.0286i	−0.315402	+	0.546292i	0.664121	+	0.747625i	$0.268806\pi$
$338$		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
$345$	−0.496291	−	1.17081i	−0.0267194	−	0.0630345i
$346$		0			0
$347$	−13.2305	+	22.9159i	−0.710249	+	1.23019i	0.254514	+	0.967069i	$0.418085\pi$
$347$	−13.2305	+	22.9159i	−0.710249	+	1.23019i	−0.964763	+	0.263119i	$0.915249\pi$
$348$		0			0
$349$	13.0168	+	22.5457i	0.696772	+	1.20685i	0.969580	+	0.244776i	$0.0787145\pi$
$349$	13.0168	+	22.5457i	0.696772	+	1.20685i	−0.272807	+	0.962069i	$0.587952\pi$
$350$		0			0
$351$	−14.2486	+	11.5029i	−0.760532	+	0.613982i
$352$		0			0
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	0.985719	+	0.168397i	$0.0538590\pi$
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	−0.347024	+	0.937856i	$0.612808\pi$
$354$		0			0
$355$	5.02791	−	8.70859i	0.266854	−	0.462204i
$356$		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
$365$	4.00000	−	6.92820i	0.209370	−	0.362639i
$366$		0			0
$367$	−11.2305	−	19.4518i	−0.586226	−	1.01537i	−0.994721	−	0.102613i	$-0.967280\pi$
$367$	−11.2305	−	19.4518i	−0.586226	−	1.01537i	0.408495	−	0.912761i	$-0.366054\pi$
$368$		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	$-0.812456\pi$
$373$	1.26581	−	2.19245i	0.0655411	−	0.113521i	0.896934	+	0.442165i	$0.145789\pi$
$374$		0			0
$375$	1.71903	+	0.211943i	0.0887706	+	0.0109447i
$376$		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	$-0.770835\pi$
$383$	3.81792	−	6.61283i	0.195086	−	0.337900i	0.946929	+	0.321443i	$0.104168\pi$
$384$		0			0
$385$	7.55211	+	13.0806i	0.384891	+	0.666651i
$386$		0			0
$387$	2.90405	+	10.1659i	0.147621	+	0.516764i
$388$		0			0
$389$	9.46467	+	16.3933i	0.479878	+	0.831173i	0.999734	−	0.0230811i	$-0.00734760\pi$
$389$	9.46467	+	16.3933i	0.479878	+	0.831173i	−0.519856	+	0.854254i	$0.674014\pi$
$390$		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
$395$	−2.00000			−0.100631
$396$		0			0
$397$	−29.1600			−1.46350			−0.731750	−	0.681573i	$-0.761296\pi$
$397$	−29.1600			−1.46350			−0.731750	+	0.681573i	$0.761296\pi$
$398$		0			0
$399$	13.9065	+	32.8071i	0.696193	+	1.64241i
$400$		0			0
$401$	−16.3142	+	28.2570i	−0.814693	+	1.41109i	0.0948557	+	0.995491i	$0.469761\pi$
$401$	−16.3142	+	28.2570i	−0.814693	+	1.41109i	−0.909548	+	0.415598i	$0.863572\pi$
$402$		0			0
$403$	13.2584	+	22.9642i	0.660447	+	1.14393i
$404$		0			0
$405$	7.64195	−	4.75401i	0.379731	−	0.236229i
$406$		0			0
$407$	−16.7268	−	28.9716i	−0.829115	−	1.43607i
$408$		0			0
$409$	−16.1042	+	27.8933i	−0.796302	+	1.37924i	0.125707	+	0.992067i	$0.459880\pi$
$409$	−16.1042	+	27.8933i	−0.796302	+	1.37924i	−0.922009	+	0.387169i	$0.873453\pi$
$410$		0			0
$411$	−12.5168	−	29.5287i	−0.617407	−	1.45654i
$412$		0			0
$413$	−4.01484			−0.197557
$414$		0			0
$415$	5.26581			0.258488
$416$		0			0
$417$	−4.17226	+	5.53103i	−0.204316	+	0.270855i
$418$		0			0
$419$	10.7063	−	18.5438i	0.523036	−	0.905925i	−0.476605	−	0.879118i	$-0.658133\pi$
$419$	10.7063	−	18.5438i	0.523036	−	0.905925i	0.999641	−	0.0268073i	$-0.00853405\pi$
$420$		0			0
$421$	0.944182	+	1.63537i	0.0460166	+	0.0797031i	0.888116	−	0.459619i	$-0.152014\pi$
$421$	0.944182	+	1.63537i	0.0460166	+	0.0797031i	−0.842100	+	0.539322i	$0.818681\pi$
$422$		0			0
$423$	−0.997070	−	3.49035i	−0.0484792	−	0.169707i
$424$		0			0
$425$	2.76210	+	4.78410i	0.133982	+	0.232063i
$426$		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	$-0.573497\pi$
$433$	−9.52420			−0.457704			−0.228852	+	0.973461i	$0.573497\pi$
$434$		0			0
$435$	−7.68130	−	0.947041i	−0.368290	−	0.0454071i
$436$		0			0
$437$	−2.76210	+	4.78410i	−0.132129	+	0.228854i
$438$		0			0
$439$	7.20257	+	12.4752i	0.343760	+	0.595410i	0.985128	−	0.171824i	$-0.0549660\pi$
$439$	7.20257	+	12.4752i	0.343760	+	0.595410i	−0.641368	+	0.767234i	$0.721633\pi$
$440$		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	$-0.0158242\pi$
$443$	9.60500	+	16.6363i	0.456347	+	0.790416i	−0.542417	+	0.840109i	$0.682491\pi$
$444$		0			0
$445$	−1.50000	+	2.59808i	−0.0711068	+	0.123161i
$446$		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
$455$	−4.81792	+	8.34488i	−0.225867	+	0.391214i
$456$		0			0
$457$	−1.08373	−	1.87707i	−0.0506946	−	0.0878056i	0.839565	−	0.543260i	$-0.182810\pi$
$457$	−1.08373	−	1.87707i	−0.0506946	−	0.0878056i	−0.890259	+	0.455454i	$0.849477\pi$
$458$		0			0
$459$	26.7826	+	10.3270i	1.25010	+	0.482021i
$460$		0			0
$461$	12.8700	+	22.2915i	0.599417	+	1.03822i	0.992907	+	0.118892i	$0.0379341\pi$
$461$	12.8700	+	22.2915i	0.599417	+	1.03822i	−0.393490	+	0.919329i	$0.628733\pi$
$462$		0			0
$463$	−6.02791	+	10.4406i	−0.280141	+	0.485218i	−0.971419	−	0.237371i	$-0.923714\pi$
$463$	−6.02791	+	10.4406i	−0.280141	+	0.485218i	0.691279	+	0.722588i	$0.257048\pi$
$464$		0			0
$465$	−5.08613	−	11.9988i	−0.235864	−	0.556433i
$466$		0			0
$467$	−14.4610			−0.669174			−0.334587	−	0.942365i	$-0.608597\pi$
$467$	−14.4610			−0.669174			−0.334587	+	0.942365i	$0.608597\pi$
$468$		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
$475$	−3.76210	−	6.51615i	−0.172617	−	0.298981i
$476$		0			0
$477$	4.27323	+	1.06997i	0.195658	+	0.0489906i
$478$		0			0
$479$	9.99258	+	17.3077i	0.456573	+	0.790807i	0.998777	−	0.0494395i	$-0.0157435\pi$
$479$	9.99258	+	17.3077i	0.456573	+	0.790807i	−0.542204	+	0.840247i	$0.682410\pi$
$480$		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
$485$	−9.46838			−0.429937
$486$		0			0
$487$	−18.1526			−0.822574			−0.411287	−	0.911506i	$-0.634921\pi$
$487$	−18.1526			−0.822574			−0.411287	+	0.911506i	$0.634921\pi$
$488$		0			0
$489$	7.69406	+	0.948613i	0.347937	+	0.0428978i
$490$		0			0
$491$	−19.7900	+	34.2773i	−0.893111	+	1.54691i	−0.0569849	+	0.998375i	$0.518149\pi$
$491$	−19.7900	+	34.2773i	−0.893111	+	1.54691i	−0.836126	+	0.548538i	$0.815185\pi$
$492$		0			0
$493$	−12.3421	−	21.3772i	−0.555861	−	0.962779i
$494$		0			0
$495$	−16.0763	−	4.02534i	−0.722576	−	0.180926i
$496$		0			0
$497$	−13.7473	−	23.8110i	−0.616649	−	1.06807i
$498$		0			0
$499$	21.3142	−	36.9173i	0.954155	−	1.65264i	0.217865	−	0.975979i	$-0.430091\pi$
$499$	21.3142	−	36.9173i	0.954155	−	1.65264i	0.736290	−	0.676666i	$-0.236576\pi$
$500$		0			0
$501$	17.5131	−	23.2165i	0.782426	−	1.03724i
$502$		0			0
$503$	21.1952			0.945045			0.472523	−	0.881319i	$-0.343343\pi$
$503$	21.1952			0.945045			0.472523	+	0.881319i	$0.343343\pi$
$504$		0			0
$505$	−13.4684			−0.599335
$506$		0			0
$507$	−0.392074	−	0.924953i	−0.0174126	−	0.0410786i
$508$		0			0
$509$	11.0168	−	19.0816i	0.488310	−	0.845778i	−0.511599	−	0.859224i	$-0.670947\pi$
$509$	11.0168	−	19.0816i	0.488310	−	0.845778i	0.999910	+	0.0134460i	$0.00428012\pi$
$510$		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
$515$	9.28630	+	16.0843i	0.409203	+	0.708761i
$516$		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	$-0.583443\pi$
$523$	−11.8532			−0.518306			−0.259153	+	0.965836i	$0.583443\pi$
$524$		0			0
$525$	2.85194	−	3.78072i	0.124469	−	0.165004i
$526$		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
$535$	9.62549	−	16.6718i	0.416146	−	0.720786i
$536$		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
$545$	−0.262100	+	0.453970i	−0.0112271	+	0.0194459i
$546$		0			0
$547$	3.10129	+	5.37159i	0.132601	+	0.229672i	0.924679	−	0.380749i	$-0.124334\pi$
$547$	3.10129	+	5.37159i	0.132601	+	0.229672i	−0.792077	+	0.610421i	$0.791000\pi$
$548$		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
$555$	−6.31661	+	8.37372i	−0.268125	+	0.355445i
$556$		0			0
$557$	6.00000			0.254228			0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000			0.254228			0.127114	+	0.991888i	$0.459429\pi$
$558$		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	$-0.804631\pi$
$563$	2.13661	−	3.70072i	0.0900475	−	0.155967i	0.907531	+	0.419985i	$0.137965\pi$
$564$		0			0
$565$	−3.73419	−	6.46781i	−0.157099	−	0.272103i
$566$		0			0
$567$	−0.809653	−	24.5944i	−0.0340022	−	1.03287i
$568$		0			0
$569$	−8.04840	−	13.9402i	−0.337406	−	0.584405i	0.646538	−	0.762882i	$-0.276216\pi$
$569$	−8.04840	−	13.9402i	−0.337406	−	0.584405i	−0.983944	+	0.178477i	$0.942883\pi$
$570$		0			0
$571$	−5.46838	+	9.47152i	−0.228845	+	0.396371i	−0.957466	−	0.288546i	$-0.906828\pi$
$571$	−5.46838	+	9.47152i	−0.228845	+	0.396371i	0.728621	+	0.684917i	$0.240161\pi$
$572$		0			0
$573$	10.2100	+	24.0867i	0.426529	+	1.00624i
$574$		0			0
$575$	0.734191			0.0306179
$576$		0			0
$577$	−37.6620			−1.56789			−0.783944	−	0.620831i	$-0.786795\pi$
$577$	−37.6620			−1.56789			−0.783944	+	0.620831i	$0.786795\pi$
$578$		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
$585$	−2.90405	−	10.1659i	−0.120068	−	0.420310i
$586$		0			0
$587$	−10.8987	−	18.8771i	−0.449838	−	0.779142i	0.548537	−	0.836126i	$-0.315185\pi$
$587$	−10.8987	−	18.8771i	−0.449838	−	0.779142i	−0.998375	+	0.0569839i	$0.981852\pi$
$588$		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	$-0.302921\pi$
$593$	28.2643			1.16067			0.580337	+	0.814377i	$0.302921\pi$
$594$		0			0
$595$	15.1042			0.619213
$596$		0			0
$597$	12.7425	+	1.57104i	0.521514	+	0.0642983i
$598$		0			0
$599$	−7.05582	+	12.2210i	−0.288293	+	0.499338i	−0.973402	−	0.229102i	$-0.926421\pi$
$599$	−7.05582	+	12.2210i	−0.288293	+	0.499338i	0.685109	+	0.728440i	$0.259754\pi$
$600$		0			0
$601$	14.1042	+	24.4292i	0.575323	+	0.996489i	0.996006	+	0.0892812i	$0.0284570\pi$
$601$	14.1042	+	24.4292i	0.575323	+	0.996489i	−0.420683	+	0.907207i	$0.638210\pi$
$602$		0			0
$603$	8.88356	−	9.18082i	0.361766	−	0.373872i
$604$		0			0
$605$	9.75839	+	16.9020i	0.396735	+	0.687165i
$606$		0			0
$607$	−14.1850	+	24.5692i	−0.575752	+	0.997232i	0.420208	+	0.907428i	$0.361957\pi$
$607$	−14.1850	+	24.5692i	−0.575752	+	0.997232i	−0.995959	+	0.0898036i	$0.971376\pi$
$608$		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	$-0.334714\pi$
$613$	24.5726			0.992478			0.496239	+	0.868186i	$0.334714\pi$
$614$		0			0
$615$	0.713701	+	1.68371i	0.0287792	+	0.0678938i
$616$		0			0
$617$	13.3142	−	23.0609i	0.536010	−	0.928396i	−0.463104	−	0.886304i	$-0.653264\pi$
$617$	13.3142	−	23.0609i	0.536010	−	0.928396i	0.999114	−	0.0420923i	$-0.0134023\pi$
$618$		0			0
$619$	−15.2863	−	26.4766i	−0.614408	−	1.06419i	−0.990488	−	0.137599i	$-0.956061\pi$
$619$	−15.2863	−	26.4766i	−0.614408	−	1.06419i	0.376080	−	0.926587i	$-0.377272\pi$
$620$		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
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		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
$635$	4.12920	−	7.15198i	0.163862	−	0.283818i
$636$		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	0.715237	−	0.698882i	$-0.246319\pi$
$641$	−6.26952	−	10.8591i	−0.247631	−	0.428910i	−0.962868	+	0.269972i	$0.912985\pi$
$642$		0			0
$643$	5.12920	−	8.88403i	0.202276	−	0.350352i	−0.746986	−	0.664840i	$-0.768500\pi$
$643$	5.12920	−	8.88403i	0.202276	−	0.350352i	0.949261	+	0.314488i	$0.101833\pi$
$644$		0			0
$645$	−6.05822	−	0.746928i	−0.238542	−	0.0294103i
$646$		0			0
$647$	16.7900			0.660083			0.330042	−	0.943966i	$-0.392937\pi$
$647$	16.7900			0.660083			0.330042	+	0.943966i	$0.392937\pi$
$648$		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	−0.312194	+	0.950018i	$0.601064\pi$
$653$	−25.0131	+	43.3239i	−0.978837	+	1.69540i	−0.666643	+	0.745377i	$0.732269\pi$
$654$		0			0
$655$	−8.04840	−	13.9402i	−0.314477	−	0.544690i
$656$		0			0
$657$	23.2813	+	5.82939i	0.908289	+	0.227426i
$658$		0			0
$659$	−2.78259	−	4.81959i	−0.108394	−	0.187744i	0.806726	−	0.590926i	$-0.201238\pi$
$659$	−2.78259	−	4.81959i	−0.108394	−	0.187744i	−0.915120	+	0.403182i	$0.867904\pi$
$660$		0			0
$661$	19.6284	−	33.9974i	0.763457	−	1.32235i	−0.177602	−	0.984102i	$-0.556834\pi$
$661$	19.6284	−	33.9974i	0.763457	−	1.32235i	0.941059	−	0.338244i	$-0.109833\pi$
$662$		0			0
$663$	20.3068	−	26.9200i	0.788650	−	1.04549i
$664$		0			0
$665$	−20.5726			−0.797771
$666$		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	$-0.266093\pi$
$673$	−7.97209	−	13.8081i	−0.307302	−	0.532262i	−0.977771	+	0.209675i	$0.932759\pi$
$674$		0			0
$675$	0.805165	+	5.13339i	0.0309908	+	0.197584i
$676$		0			0
$677$	10.4479	+	18.0963i	0.401545	+	0.695497i	0.993913	−	0.110171i	$-0.0351400\pi$
$677$	10.4479	+	18.0963i	0.401545	+	0.695497i	−0.592368	+	0.805668i	$0.701807\pi$
$678$		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	$-0.622588\pi$
$683$	−19.6358			−0.751344			−0.375672	+	0.926753i	$0.622588\pi$
$684$		0			0
$685$	18.5168			0.707490
$686$		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	0.905191	+	0.425005i	$0.139728\pi$
$691$	21.5726	+	37.3648i	0.820660	+	1.42143i	−0.0845309	+	0.996421i	$0.526939\pi$
$692$		0			0
$693$	−31.5094	+	32.5637i	−1.19694	+	1.23699i
$694$		0			0
$695$	−2.00000	−	3.46410i	−0.0758643	−	0.131401i
$696$		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
$705$	2.08002	+	0.256449i	0.0783380	+	0.00965842i
$706$		0			0
$707$	−18.4126	+	31.8915i	−0.692476	+	1.19940i
$708$		0			0
$709$	−21.7510	−	37.6738i	−0.816875	−	1.41487i	−0.907974	−	0.419027i	$-0.862371\pi$
$709$	−21.7510	−	37.6738i	−0.816875	−	1.41487i	0.0910989	−	0.995842i	$-0.470962\pi$
$710$		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
$715$	−9.73419	+	16.8601i	−0.364038	+	0.630532i
$716$		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
$725$	2.23419	−	3.86973i	0.0829758	−	0.143718i
$726$		0			0
$727$	−6.24083	−	10.8094i	−0.231460	−	0.400900i	0.726778	−	0.686872i	$-0.241017\pi$
$727$	−6.24083	−	10.8094i	−0.231460	−	0.400900i	−0.958238	+	0.285972i	$0.907683\pi$
$728$		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	0.239783	+	0.970826i	$0.422924\pi$
$733$	−19.5168	+	33.8041i	−0.720869	+	1.24858i	−0.960652	+	0.277755i	$0.910410\pi$
$734$		0			0
$735$	−0.321627	−	0.758758i	−0.0118634	−	0.0279872i
$736$		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	−0.199344	−	0.979930i	$-0.563881\pi$
$743$	20.4155	−	35.3607i	0.748972	−	1.29726i	0.948316	−	0.317328i	$-0.102786\pi$
$744$		0			0
$745$	6.78630	+	11.7542i	0.248631	+	0.430641i
$746$		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	−0.694904	−	0.719103i	$-0.744553\pi$
$751$	7.54469	−	13.0678i	0.275310	−	0.476850i	0.970213	+	0.242253i	$0.0778863\pi$
$752$		0			0
$753$	12.0205	+	1.48203i	0.438051	+	0.0540080i
$754$		0			0
$755$	12.4610			0.453501
$756$		0			0
$757$	34.4610			1.25251			0.626253	−	0.779620i	$-0.284588\pi$
$757$	34.4610			1.25251			0.626253	+	0.779620i	$0.284588\pi$
$758$		0			0
$759$	−6.97209	−	0.859601i	−0.253071	−	0.0312015i
$760$		0			0
$761$	4.17837	−	7.23716i	0.151466	−	0.262347i	−0.780301	−	0.625405i	$-0.784934\pi$
$761$	4.17837	−	7.23716i	0.151466	−	0.262347i	0.931767	+	0.363058i	$0.118267\pi$
$762$		0			0
$763$	0.716631	+	1.24124i	0.0259438	+	0.0449359i
$764$		0			0
$765$	−11.5242	+	11.9098i	−0.416658	+	0.430601i
$766$		0			0
$767$	−2.58744	−	4.48157i	−0.0934269	−	0.161820i
$768$		0			0
$769$	9.17837	−	15.8974i	0.330981	−	0.573275i	−0.651724	−	0.758456i	$-0.725954\pi$
$769$	9.17837	−	15.8974i	0.330981	−	0.573275i	0.982704	+	0.185181i	$0.0592872\pi$
$770$		0			0
$771$	−29.3068	+	38.8510i	−1.05546	+	1.39919i
$772$		0			0
$773$	−10.0968			−0.363157			−0.181578	−	0.983376i	$-0.558121\pi$
$773$	−10.0968			−0.363157			−0.181578	+	0.983376i	$0.558121\pi$
$774$		0			0
$775$	7.52420			0.270277
$776$		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
$785$	−0.790009	−	1.36834i	−0.0281966	−	0.0488380i
$786$		0			0
$787$	7.28630	−	12.6202i	0.259729	−	0.449863i	−0.706441	−	0.707772i	$-0.749700\pi$
$787$	7.28630	−	12.6202i	0.259729	−	0.449863i	0.966169	+	0.257909i	$0.0830336\pi$
$788$		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
$795$	−1.53162	+	2.03041i	−0.0543209	+	0.0720114i
$796$		0			0
$797$	1.03533	−	1.79324i	0.0366732	−	0.0635198i	−0.847106	−	0.531424i	$-0.821657\pi$
$797$	1.03533	−	1.79324i	0.0366732	−	0.0635198i	0.883779	+	0.467904i	$0.154991\pi$
$798$		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
$805$	1.00371	−	1.73848i	0.0353761	−	0.0612732i
$806$		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
$815$	−2.23790	+	3.87616i	−0.0783902	+	0.135776i
$816$		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	0.991598	−	0.129356i	$-0.0412911\pi$
$821$	10.9963	+	19.0461i	0.383773	+	0.664715i	−0.607825	+	0.794071i	$0.707958\pi$
$822$		0			0
$823$	−7.45082	+	12.9052i	−0.259719	+	0.449847i	−0.966167	−	0.257919i	$-0.916963\pi$
$823$	−7.45082	+	12.9052i	−0.259719	+	0.449847i	0.706447	+	0.707766i	$0.250297\pi$
$824$		0			0
$825$	5.76210	−	7.63862i	0.200611	−	0.265943i
$826$		0			0
$827$	56.5785			1.96743			0.983713	−	0.179747i	$-0.0575279\pi$
$827$	56.5785			1.96743			0.983713	+	0.179747i	$0.0575279\pi$
$828$		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
$835$	8.39500	+	14.5406i	0.290521	+	0.503197i
$836$		0			0
$837$	30.4208	−	24.5589i	1.05150	−	0.848880i
$838$		0			0
$839$	17.2863	+	29.9407i	0.596789	+	1.03367i	0.993292	+	0.115636i	$0.0368905\pi$
$839$	17.2863	+	29.9407i	0.596789	+	1.03367i	−0.396502	+	0.918034i	$0.629776\pi$
$840$		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
$845$	0.580017			0.0199532
$846$		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	$-0.260539\pi$
$853$	−8.48887	−	14.7032i	−0.290653	−	0.503427i	−0.973964	+	0.226701i	$0.927206\pi$
$854$		0			0
$855$	15.6965	−	16.2217i	0.536808	−	0.554770i
$856$		0			0
$857$	−1.70628	−	2.95537i	−0.0582855	−	0.100953i	0.835410	−	0.549627i	$-0.185230\pi$
$857$	−1.70628	−	2.95537i	−0.0582855	−	0.100953i	−0.893696	+	0.448673i	$0.851897\pi$
$858$		0			0
$859$	4.91627	−	8.51524i	0.167741	−	0.290536i	−0.769884	−	0.638184i	$-0.779686\pi$
$859$	4.91627	−	8.51524i	0.167741	−	0.290536i	0.937625	+	0.347647i	$0.113019\pi$
$860$		0			0
$861$	4.96252	+	0.611838i	0.169122	+	0.0208514i
$862$		0			0
$863$	−48.9836			−1.66742			−0.833711	−	0.552202i	$-0.813788\pi$
$863$	−48.9836			−1.66742			−0.833711	+	0.552202i	$0.813788\pi$
$864$		0			0
$865$	23.0484			0.783669
$866$		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
$875$	1.36710	+	2.36788i	0.0462163	+	0.0800489i
$876$		0			0
$877$	6.33470	−	10.9720i	0.213908	−	0.370499i	−0.739027	−	0.673676i	$-0.764714\pi$
$877$	6.33470	−	10.9720i	0.213908	−	0.370499i	0.952934	+	0.303178i	$0.0980475\pi$
$878$		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	$-0.485570\pi$
$883$	2.69321			0.0906337			0.0453169	+	0.998973i	$0.485570\pi$
$884$		0			0
$885$	0.992582	+	2.34163i	0.0333653	+	0.0787129i
$886$		0			0
$887$	12.2789	−	21.2676i	0.412284	−	0.714098i	−0.582855	−	0.812576i	$-0.698064\pi$
$887$	12.2789	−	21.2676i	0.412284	−	0.714098i	0.995139	+	0.0984788i	$0.0313977\pi$
$888$		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
$895$	6.49629	−	11.2519i	0.217147	−	0.376110i
$896$		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
$905$	−12.2826	+	21.2741i	−0.408287	+	0.707174i
$906$		0			0
$907$	−17.1850	−	29.7653i	−0.570619	−	0.988341i	−0.996502	−	0.0835631i	$-0.973370\pi$
$907$	−17.1850	−	29.7653i	−0.570619	−	0.988341i	0.425884	−	0.904778i	$-0.359963\pi$
$908$		0			0
$909$	−11.0984	−	38.8510i	−0.368109	−	1.28861i
$910$		0			0
$911$	−18.7752	−	32.5196i	−0.622049	−	1.07742i	−0.989104	−	0.147221i	$-0.952967\pi$
$911$	−18.7752	−	32.5196i	−0.622049	−	1.07742i	0.367054	−	0.930199i	$-0.380366\pi$
$912$		0			0
$913$	14.5447	−	25.1921i	0.481359	−	0.833738i
$914$		0			0
$915$	15.5673	+	1.91931i	0.514638	+	0.0634506i
$916$		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
$925$	−3.02791	−	5.24449i	−0.0995570	−	0.172438i
$926$		0			0
$927$	−38.7449	+	40.0413i	−1.27255	+	1.31513i
$928$		0			0
$929$	−12.4126	−	21.4992i	−0.407243	−	0.705366i	0.587337	−	0.809343i	$-0.300176\pi$
$929$	−12.4126	−	21.4992i	−0.407243	−	0.705366i	−0.994580	+	0.103977i	$0.966843\pi$
$930$		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
$935$	30.5168			0.998005
$936$		0			0
$937$	1.56518			0.0511322			0.0255661	−	0.999673i	$-0.491861\pi$
$937$	1.56518			0.0511322			0.0255661	+	0.999673i	$0.491861\pi$
$938$		0			0
$939$	−12.9139	−	30.4655i	−0.421428	−	0.994203i
$940$		0			0
$941$	5.23419	−	9.06588i	0.170630	−	0.295539i	−0.768010	−	0.640437i	$-0.778753\pi$
$941$	5.23419	−	9.06588i	0.170630	−	0.295539i	0.938640	+	0.344898i	$0.112086\pi$
$942$		0			0
$943$	0.387586	+	0.671318i	0.0126215	+	0.0218611i
$944$		0			0
$945$	13.2560	+	5.11130i	0.431217	+	0.166271i
$946$		0			0
$947$	1.59758	+	2.76709i	0.0519143	+	0.0899182i	0.890815	−	0.454367i	$-0.150134\pi$
$947$	1.59758	+	2.76709i	0.0519143	+	0.0899182i	−0.838900	+	0.544285i	$0.816801\pi$
$948$		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	$-0.685197\pi$
$953$	−33.9293			−1.09908			−0.549540	+	0.835468i	$0.685197\pi$
$954$		0			0
$955$	−15.1042			−0.488761
$956$		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
$965$	−7.28630	−	12.6202i	−0.234554	−	0.406260i
$966$		0			0
$967$	−19.2129	+	33.2778i	−0.617846	+	1.07014i	0.372032	+	0.928220i	$0.378661\pi$
$967$	−19.2129	+	33.2778i	−0.617846	+	1.07014i	−0.989878	+	0.141921i	$0.954672\pi$
$968$		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
$975$	6.05822	+	0.746928i	0.194018	+	0.0239209i
$976$		0			0
$977$	16.4889	−	28.5596i	0.527526	−	0.913701i	−0.471960	−	0.881620i	$-0.656453\pi$
$977$	16.4889	−	28.5596i	0.527526	−	0.913701i	0.999485	−	0.0320812i	$-0.0102135\pi$
$978$		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	$-0.129130\pi$
$983$	3.68872	+	6.38905i	0.117652	+	0.203779i	−0.801185	+	0.598417i	$0.795797\pi$
$984$		0			0
$985$	−2.26581	+	3.92450i	−0.0721947	+	0.125045i
$986$		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
$995$	−3.70628	+	6.41947i	−0.117497	+	0.203511i
$996$		0			0
$997$	24.3142	+	42.1134i	0.770039	+	1.33375i	0.937541	+	0.347874i	$0.113096\pi$
$997$	24.3142	+	42.1134i	0.770039	+	1.33375i	−0.167502	+	0.985872i	$0.553570\pi$
$998$		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	180.2.i.b.121.1	yes	6
3.2	odd	2		540.2.i.b.361.2		6
4.3	odd	2		720.2.q.k.481.3		6
5.2	odd	4		900.2.s.c.49.3		12
5.3	odd	4		900.2.s.c.49.4		12
5.4	even	2		900.2.i.c.301.3		6
9.2	odd	6		540.2.i.b.181.2		6
9.4	even	3		1620.2.a.i.1.2		3
9.5	odd	6		1620.2.a.j.1.2		3
9.7	even	3	inner	180.2.i.b.61.1	✓	6
12.11	even	2		2160.2.q.i.1441.2		6
15.2	even	4		2700.2.s.c.1549.4		12
15.8	even	4		2700.2.s.c.1549.3		12
15.14	odd	2		2700.2.i.c.901.2		6
36.7	odd	6		720.2.q.k.241.3		6
36.11	even	6		2160.2.q.i.721.2		6
36.23	even	6		6480.2.a.bw.1.2		3
36.31	odd	6		6480.2.a.bt.1.2		3
45.2	even	12		2700.2.s.c.2449.3		12
45.4	even	6		8100.2.a.v.1.2		3
45.7	odd	12		900.2.s.c.349.4		12
45.13	odd	12		8100.2.d.p.649.3		6
45.14	odd	6		8100.2.a.u.1.2		3
45.22	odd	12		8100.2.d.p.649.4		6
45.23	even	12		8100.2.d.o.649.3		6
45.29	odd	6		2700.2.i.c.1801.2		6
45.32	even	12		8100.2.d.o.649.4		6
45.34	even	6		900.2.i.c.601.3		6
45.38	even	12		2700.2.s.c.2449.4		12
45.43	odd	12		900.2.s.c.349.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.i.b.61.1	✓	6	9.7	even	3	inner
180.2.i.b.121.1	yes	6	1.1	even	1	trivial
540.2.i.b.181.2		6	9.2	odd	6
540.2.i.b.361.2		6	3.2	odd	2
720.2.q.k.241.3		6	36.7	odd	6
720.2.q.k.481.3		6	4.3	odd	2
900.2.i.c.301.3		6	5.4	even	2
900.2.i.c.601.3		6	45.34	even	6
900.2.s.c.49.3		12	5.2	odd	4
900.2.s.c.49.4		12	5.3	odd	4
900.2.s.c.349.3		12	45.43	odd	12
900.2.s.c.349.4		12	45.7	odd	12
1620.2.a.i.1.2		3	9.4	even	3
1620.2.a.j.1.2		3	9.5	odd	6
2160.2.q.i.721.2		6	36.11	even	6
2160.2.q.i.1441.2		6	12.11	even	2
2700.2.i.c.901.2		6	15.14	odd	2
2700.2.i.c.1801.2		6	45.29	odd	6
2700.2.s.c.1549.3		12	15.8	even	4
2700.2.s.c.1549.4		12	15.2	even	4
2700.2.s.c.2449.3		12	45.2	even	12
2700.2.s.c.2449.4		12	45.38	even	12
6480.2.a.bt.1.2		3	36.31	odd	6
6480.2.a.bw.1.2		3	36.23	even	6
8100.2.a.u.1.2		3	45.14	odd	6
8100.2.a.v.1.2		3	45.4	even	6
8100.2.d.o.649.3		6	45.23	even	12
8100.2.d.o.649.4		6	45.32	even	12
8100.2.d.p.649.3		6	45.13	odd	12
8100.2.d.p.649.4		6	45.22	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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.71903 - 0.211943i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.36710 - 2.36788i) q^{7} +(2.91016 + 0.728674i) q^{9} +O(q^{10})\)	\(q+(-1.71903 - 0.211943i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.36710 - 2.36788i) q^{7} +(2.91016 + 0.728674i) q^{9} +(-2.76210 - 4.78410i) q^{11} +(1.76210 - 3.05205i) q^{13} +(-1.04307 + 1.38276i) q^{15} -5.52420 q^{17} +7.52420 q^{19} +(1.84823 + 4.36021i) q^{21} +(-0.367095 + 0.635828i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-4.84823 - 1.86940i) q^{27} +(2.23419 + 3.86973i) q^{29} +(-3.76210 + 6.51615i) q^{31} +(3.73419 + 8.80944i) q^{33} -2.73419 q^{35} +6.05582 q^{37} +(-3.67597 + 4.87311i) q^{39} +(0.527909 - 0.914365i) q^{41} +(1.76210 + 3.05205i) q^{43} +(2.08613 - 2.15594i) q^{45} +(-0.604996 - 1.04788i) q^{47} +(-0.237900 + 0.412055i) q^{49} +(9.49629 + 1.17081i) q^{51} +1.46838 q^{53} -5.52420 q^{55} +(-12.9344 - 1.59470i) q^{57} +(0.734191 - 1.27166i) q^{59} +(-4.52791 - 7.84257i) q^{61} +(-2.25306 - 7.88707i) q^{63} +(-1.76210 - 3.05205i) q^{65} +(2.12920 - 3.68787i) q^{67} +(0.765809 - 1.01521i) q^{69} +10.0558 q^{71} +8.00000 q^{73} +(0.675970 + 1.59470i) q^{75} +(-7.55211 + 13.0806i) q^{77} +(-1.00000 - 1.73205i) q^{79} +(7.93807 + 4.24111i) q^{81} +(2.63290 + 4.56032i) q^{83} +(-2.76210 + 4.78410i) q^{85} +(-3.02049 - 7.12572i) q^{87} -3.00000 q^{89} -9.63583 q^{91} +(7.84823 - 10.4041i) q^{93} +(3.76210 - 6.51615i) q^{95} +(-4.73419 - 8.19986i) q^{97} +(-4.55211 - 15.9352i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 3 q^{5} - 3 q^{7} + 5 q^{9}+O(q^{10}) \) 6 * q - q^3 + 3 * q^5 - 3 * q^7 + 5 * q^9	\( 6 q - q^{3} + 3 q^{5} - 3 q^{7} + 5 q^{9} - 6 q^{13} + q^{15} + 12 q^{19} - 20 q^{21} + 3 q^{23} - 3 q^{25} + 2 q^{27} + 3 q^{29} - 6 q^{31} + 12 q^{33} - 6 q^{35} + 24 q^{37} - 20 q^{39} - 3 q^{41} - 6 q^{43} - 2 q^{45} - 15 q^{47} - 18 q^{49} + 30 q^{51} - 12 q^{53} - 32 q^{57} - 6 q^{59} - 21 q^{61} - 29 q^{63} + 6 q^{65} - 9 q^{67} + 15 q^{69} + 48 q^{71} + 48 q^{73} + 2 q^{75} - 6 q^{77} - 6 q^{79} + 29 q^{81} + 21 q^{83} + 42 q^{87} - 18 q^{89} + 16 q^{93} + 6 q^{95} - 18 q^{97} + 12 q^{99}+O(q^{100}) \) 6 * q - q^3 + 3 * q^5 - 3 * q^7 + 5 * q^9 - 6 * q^13 + q^15 + 12 * q^19 - 20 * q^21 + 3 * q^23 - 3 * q^25 + 2 * q^27 + 3 * q^29 - 6 * q^31 + 12 * q^33 - 6 * q^35 + 24 * q^37 - 20 * q^39 - 3 * q^41 - 6 * q^43 - 2 * q^45 - 15 * q^47 - 18 * q^49 + 30 * q^51 - 12 * q^53 - 32 * q^57 - 6 * q^59 - 21 * q^61 - 29 * q^63 + 6 * q^65 - 9 * q^67 + 15 * q^69 + 48 * q^71 + 48 * q^73 + 2 * q^75 - 6 * q^77 - 6 * q^79 + 29 * q^81 + 21 * q^83 + 42 * q^87 - 18 * q^89 + 16 * q^93 + 6 * q^95 - 18 * q^97 + 12 * q^99

Introduction

L-functions

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