LMFDB - Embedded newform 2100.2.ce.e.157.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(157,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("2100.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.ce (of order $12$, degree $4$, 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.2
Character	$\chi$	$=$	2100.157
Dual form			2100.2.ce.e.1993.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{3} +(1.79435 - 1.94431i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{3} +(1.79435 - 1.94431i) q^{7} +(0.866025 - 0.500000i) q^{9} +(-2.81503 + 4.87578i) q^{11} +(-0.322009 - 0.322009i) q^{13} +(0.0487852 + 0.182069i) q^{17} +(-0.531552 - 0.920676i) q^{19} +(-1.22998 + 2.34247i) q^{21} +(-5.53156 - 1.48218i) q^{23} +(-0.707107 + 0.707107i) q^{27} -0.319426i q^{29} +(4.60261 + 2.65732i) q^{31} +(1.45717 - 5.43823i) q^{33} +(-2.65791 + 9.91946i) q^{37} +(0.394379 + 0.227695i) q^{39} +5.68139i q^{41} +(0.844231 - 0.844231i) q^{43} +(-12.0833 - 3.23771i) q^{47} +(-0.560652 - 6.97751i) q^{49} +(-0.0942458 - 0.163239i) q^{51} +(-0.0859345 - 0.320712i) q^{53} +(0.751729 + 0.751729i) q^{57} +(-4.47674 + 7.75395i) q^{59} +(8.80767 - 5.08511i) q^{61} +(0.581795 - 2.58099i) q^{63} +(8.09607 - 2.16933i) q^{67} +5.72669 q^{69} +0.489937 q^{71} +(-2.53229 + 0.678524i) q^{73} +(4.42887 + 14.2221i) q^{77} +(-12.2025 + 7.04514i) q^{79} +(0.500000 - 0.866025i) q^{81} +(4.75762 + 4.75762i) q^{83} +(0.0826735 + 0.308542i) q^{87} +(-1.63014 - 2.82349i) q^{89} +(-1.20388 + 0.0482888i) q^{91} +(-5.13354 - 1.37553i) q^{93} +(-10.1827 + 10.1827i) q^{97} +5.63007i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 8 q^{11} - 8 q^{21} - 16 q^{23} + 24 q^{31} - 12 q^{33} - 20 q^{37} + 24 q^{43} - 12 q^{47} - 8 q^{51} - 40 q^{53} + 16 q^{57} - 24 q^{61} + 12 q^{63} - 16 q^{71} + 60 q^{73} + 84 q^{77} + 16 q^{81} + 48 q^{87} + 40 q^{91} - 8 q^{93}+O(q^{100}) $ 32 * q + 8 * q^11 - 8 * q^21 - 16 * q^23 + 24 * q^31 - 12 * q^33 - 20 * q^37 + 24 * q^43 - 12 * q^47 - 8 * q^51 - 40 * q^53 + 16 * q^57 - 24 * q^61 + 12 * q^63 - 16 * q^71 + 60 * q^73 + 84 * q^77 + 16 * q^81 + 48 * q^87 + 40 * q^91 - 8 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.79435	−	1.94431i	0.678199	−	0.734879i
$7$	1.79435	−	1.94431i	0.678199	−	0.734879i
$8$		0			0
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	−2.81503	+	4.87578i	−0.848764	+	1.47010i	0.0335471	+	0.999437i	$0.489320\pi$
$11$	−2.81503	+	4.87578i	−0.848764	+	1.47010i	−0.882311	+	0.470666i	$0.844014\pi$
$12$		0			0
$13$	−0.322009	−	0.322009i	−0.0893093	−	0.0893093i	0.661041	−	0.750350i	$-0.270115\pi$
$13$	−0.322009	−	0.322009i	−0.0893093	−	0.0893093i	−0.750350	+	0.661041i	$0.770115\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.0487852	+	0.182069i	0.0118322	+	0.0441582i	0.971590	−	0.236672i	$-0.0760568\pi$
$17$	0.0487852	+	0.182069i	0.0118322	+	0.0441582i	−0.959757	+	0.280831i	$0.909390\pi$
$18$		0			0
$19$	−0.531552	−	0.920676i	−0.121946	−	0.211217i	0.798589	−	0.601877i	$-0.205580\pi$
$19$	−0.531552	−	0.920676i	−0.121946	−	0.211217i	−0.920535	+	0.390660i	$0.872247\pi$
$20$		0			0
$21$	−1.22998	+	2.34247i	−0.268404	+	0.511168i
$22$		0			0
$23$	−5.53156	−	1.48218i	−1.15341	−	0.309055i	−0.369079	−	0.929398i	$-0.620327\pi$
$23$	−5.53156	−	1.48218i	−1.15341	−	0.309055i	−0.784331	+	0.620343i	$0.786993\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	0.319426i		−	0.0593159i	−0.999560	−	0.0296580i	$-0.990558\pi$
$29$		−	0.319426i		−	0.0593159i	0.999560	−	0.0296580i	$-0.00944181\pi$
$30$		0			0
$31$	4.60261	+	2.65732i	0.826653	+	0.477268i	0.852705	−	0.522393i	$-0.174960\pi$
$31$	4.60261	+	2.65732i	0.826653	+	0.477268i	−0.0260526	+	0.999661i	$0.508294\pi$
$32$		0			0
$33$	1.45717	−	5.43823i	0.253660	−	0.946674i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.65791	+	9.91946i	−0.436958	+	1.63075i	0.299380	+	0.954134i	$0.403220\pi$
$37$	−2.65791	+	9.91946i	−0.436958	+	1.63075i	−0.736337	+	0.676614i	$0.763446\pi$
$38$		0			0
$39$	0.394379	+	0.227695i	0.0631512	+	0.0364604i
$40$		0			0
$41$			5.68139i			0.887284i	0.896204	+	0.443642i	$0.146314\pi$
$41$			5.68139i			0.887284i	−0.896204	+	0.443642i	$0.853686\pi$
$42$		0			0
$43$	0.844231	−	0.844231i	0.128744	−	0.128744i	−0.639799	−	0.768543i	$-0.720982\pi$
$43$	0.844231	−	0.844231i	0.128744	−	0.128744i	0.768543	+	0.639799i	$0.220982\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−12.0833	−	3.23771i	−1.76253	−	0.472268i	−0.775302	−	0.631590i	$-0.782402\pi$
$47$	−12.0833	−	3.23771i	−1.76253	−	0.472268i	−0.987227	+	0.159322i	$0.949069\pi$
$48$		0			0
$49$	−0.560652	−	6.97751i	−0.0800931	−	0.996787i
$50$		0			0
$51$	−0.0942458	−	0.163239i	−0.0131971	−	0.0228580i
$52$		0			0
$53$	−0.0859345	−	0.320712i	−0.0118040	−	0.0440532i	0.959773	−	0.280778i	$-0.0905926\pi$
$53$	−0.0859345	−	0.320712i	−0.0118040	−	0.0440532i	−0.971577	+	0.236725i	$0.923926\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.751729	+	0.751729i	0.0995689	+	0.0995689i
$58$		0			0
$59$	−4.47674	+	7.75395i	−0.582823	+	1.00948i	0.412321	+	0.911039i	$0.364718\pi$
$59$	−4.47674	+	7.75395i	−0.582823	+	1.00948i	−0.995143	+	0.0984394i	$0.968615\pi$
$60$		0			0
$61$	8.80767	−	5.08511i	1.12771	−	0.651082i	0.184349	−	0.982861i	$-0.440982\pi$
$61$	8.80767	−	5.08511i	1.12771	−	0.651082i	0.943357	+	0.331779i	$0.107649\pi$
$62$		0			0
$63$	0.581795	−	2.58099i	0.0732993	−	0.325174i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	8.09607	−	2.16933i	0.989092	−	0.265026i	0.272223	−	0.962234i	$-0.412241\pi$
$67$	8.09607	−	2.16933i	0.989092	−	0.265026i	0.716869	+	0.697208i	$0.245575\pi$
$68$		0			0
$69$	5.72669			0.689412
$70$		0			0
$71$	0.489937			0.0581449			0.0290724	−	0.999577i	$-0.490745\pi$
$71$	0.489937			0.0581449			0.0290724	+	0.999577i	$0.490745\pi$
$72$		0			0
$73$	−2.53229	+	0.678524i	−0.296382	+	0.0794153i	−0.403946	−	0.914783i	$-0.632362\pi$
$73$	−2.53229	+	0.678524i	−0.296382	+	0.0794153i	0.107564	+	0.994198i	$0.465695\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.42887	+	14.2221i	0.504716	+	1.62076i
$78$		0			0
$79$	−12.2025	+	7.04514i	−1.37289	+	0.792640i	−0.991291	−	0.131687i	$-0.957961\pi$
$79$	−12.2025	+	7.04514i	−1.37289	+	0.792640i	−0.381602	+	0.924327i	$0.624627\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	4.75762	+	4.75762i	0.522217	+	0.522217i	0.918240	−	0.396024i	$-0.129610\pi$
$83$	4.75762	+	4.75762i	0.522217	+	0.522217i	−0.396024	+	0.918240i	$0.629610\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.0826735	+	0.308542i	0.00886353	+	0.0330792i
$88$		0			0
$89$	−1.63014	−	2.82349i	−0.172795	−	0.299289i	0.766601	−	0.642124i	$-0.221946\pi$
$89$	−1.63014	−	2.82349i	−0.172795	−	0.299289i	−0.939396	+	0.342834i	$0.888613\pi$
$90$		0			0
$91$	−1.20388	+	0.0482888i	−0.126201	+	0.00506205i
$92$		0			0
$93$	−5.13354	−	1.37553i	−0.532323	−	0.142636i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−10.1827	+	10.1827i	−1.03390	+	1.03390i	−0.0344908	+	0.999405i	$0.510981\pi$
$97$	−10.1827	+	10.1827i	−1.03390	+	1.03390i	−0.999405	+	0.0344908i	$0.989019\pi$
$98$		0			0
$99$			5.63007i			0.565843i
$100$		0			0
$101$	12.7539	+	7.36347i	1.26906	+	0.732693i	0.974810	−	0.223035i	$-0.0715965\pi$
$101$	12.7539	+	7.36347i	1.26906	+	0.732693i	0.294251	+	0.955728i	$0.404930\pi$
$102$		0			0
$103$	−4.27612	+	15.9587i	−0.421339	+	1.57246i	0.350451	+	0.936581i	$0.386028\pi$
$103$	−4.27612	+	15.9587i	−0.421339	+	1.57246i	−0.771790	+	0.635877i	$0.780638\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.05513	+	11.4019i	−0.295350	+	1.10226i	0.645589	+	0.763685i	$0.276612\pi$
$107$	−3.05513	+	11.4019i	−0.295350	+	1.10226i	−0.940939	+	0.338577i	$0.890055\pi$
$108$		0			0
$109$	−3.30183	−	1.90631i	−0.316258	−	0.182592i	0.333465	−	0.942762i	$-0.391782\pi$
$109$	−3.30183	−	1.90631i	−0.316258	−	0.182592i	−0.649723	+	0.760171i	$0.725115\pi$
$110$		0			0
$111$		−	10.2694i		−	0.974726i
$112$		0			0
$113$	−0.939611	+	0.939611i	−0.0883912	+	0.0883912i	−0.749920	−	0.661529i	$-0.769908\pi$
$113$	−0.939611	+	0.939611i	−0.0883912	+	0.0883912i	0.661529	+	0.749920i	$0.269908\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.439873	−	0.117864i	−0.0406663	−	0.0108965i
$118$		0			0
$119$	0.441535	+	0.231841i	0.0404755	+	0.0212528i
$120$		0			0
$121$	−10.3488	−	17.9247i	−0.940802	−	1.62952i
$122$		0			0
$123$	−1.47045	−	5.48780i	−0.132586	−	0.494819i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−9.08221	−	9.08221i	−0.805916	−	0.805916i	0.178097	−	0.984013i	$-0.443006\pi$
$127$	−9.08221	−	9.08221i	−0.805916	−	0.805916i	−0.984013	+	0.178097i	$0.943006\pi$
$128$		0			0
$129$	−0.596961	+	1.03397i	−0.0525595	+	0.0910358i
$130$		0			0
$131$	−9.52939	+	5.50179i	−0.832586	+	0.480694i	−0.854737	−	0.519061i	$-0.826282\pi$
$131$	−9.52939	+	5.50179i	−0.832586	+	0.480694i	0.0221510	+	0.999755i	$0.492949\pi$
$132$		0			0
$133$	−2.74386	−	0.618509i	−0.237923	−	0.0536316i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.619321	+	0.165947i	−0.0529122	+	0.0141778i	−0.285178	−	0.958475i	$-0.592053\pi$
$137$	−0.619321	+	0.165947i	−0.0529122	+	0.0141778i	0.232266	+	0.972652i	$0.425386\pi$
$138$		0			0
$139$	13.3321			1.13082			0.565408	−	0.824812i	$-0.308719\pi$
$139$	13.3321			1.13082			0.565408	+	0.824812i	$0.308719\pi$
$140$		0			0
$141$	12.5095			1.05349
$142$		0			0
$143$	2.47651	−	0.663580i	0.207096	−	0.0554913i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.34746	+	6.59465i	0.193615	+	0.543918i
$148$		0			0
$149$	−15.1864	+	8.76789i	−1.24412	+	0.718293i	−0.969930	−	0.243382i	$-0.921743\pi$
$149$	−15.1864	+	8.76789i	−1.24412	+	0.718293i	−0.274190	+	0.961676i	$0.588410\pi$
$150$		0			0
$151$	−9.15912	+	15.8641i	−0.745359	+	1.29100i	0.204668	+	0.978831i	$0.434389\pi$
$151$	−9.15912	+	15.8641i	−0.745359	+	1.29100i	−0.950027	+	0.312168i	$0.898945\pi$
$152$		0			0
$153$	0.133284	+	0.133284i	0.0107753	+	0.0107753i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.74403	+	6.50881i	0.139189	+	0.519459i	0.999945	+	0.0104428i	$0.00332410\pi$
$157$	1.74403	+	6.50881i	0.139189	+	0.519459i	−0.860757	+	0.509016i	$0.830009\pi$
$158$		0			0
$159$	0.166013	+	0.287542i	0.0131657	+	0.0228036i
$160$		0			0
$161$	−12.8073	+	8.09550i	−1.00936	+	0.638015i
$162$		0			0
$163$	−12.2109	−	3.27191i	−0.956434	−	0.256276i	−0.253344	−	0.967376i	$-0.581530\pi$
$163$	−12.2109	−	3.27191i	−0.956434	−	0.256276i	−0.703090	+	0.711101i	$0.748197\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.45171	+	8.45171i	−0.654013	+	0.654013i	−0.953957	−	0.299944i	$-0.903032\pi$
$167$	−8.45171	+	8.45171i	−0.654013	+	0.654013i	0.299944	+	0.953957i	$0.403032\pi$
$168$		0			0
$169$		−	12.7926i		−	0.984048i
$170$		0			0
$171$	−0.920676	−	0.531552i	−0.0704058	−	0.0406488i
$172$		0			0
$173$	0.661185	−	2.46758i	0.0502690	−	0.187606i	−0.936226	−	0.351399i	$-0.885706\pi$
$173$	0.661185	−	2.46758i	0.0502690	−	0.187606i	0.986495	+	0.163793i	$0.0523728\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.31733	−	8.64841i	0.174181	−	0.650054i
$178$		0			0
$179$	−17.9708	−	10.3754i	−1.34320	−	0.775496i	−0.355923	−	0.934515i	$-0.615833\pi$
$179$	−17.9708	−	10.3754i	−1.34320	−	0.775496i	−0.987275	+	0.159019i	$0.949167\pi$
$180$		0			0
$181$			11.3534i			0.843894i	0.906620	+	0.421947i	$0.138653\pi$
$181$			11.3534i			0.843894i	−0.906620	+	0.421947i	$0.861347\pi$
$182$		0			0
$183$	−7.19143	+	7.19143i	−0.531606	+	0.531606i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.02506	−	0.274664i	−0.0749598	−	0.0200854i
$188$		0			0
$189$	0.106038	+	2.64363i	0.00771316	+	0.192295i
$190$		0			0
$191$	10.7996	+	18.7054i	0.781430	+	1.35348i	0.931109	+	0.364742i	$0.118843\pi$
$191$	10.7996	+	18.7054i	0.781430	+	1.35348i	−0.149679	+	0.988735i	$0.547824\pi$
$192$		0			0
$193$	−6.52710	−	24.3595i	−0.469831	−	1.75343i	−0.640355	−	0.768079i	$-0.721213\pi$
$193$	−6.52710	−	24.3595i	−0.469831	−	1.75343i	0.170524	−	0.985354i	$-0.445454\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.12836	+	5.12836i	0.365380	+	0.365380i	0.865789	−	0.500409i	$-0.166817\pi$
$197$	5.12836	+	5.12836i	0.365380	+	0.365380i	−0.500409	+	0.865789i	$0.666817\pi$
$198$		0			0
$199$	−6.55338	+	11.3508i	−0.464557	+	0.804636i	−0.999181	−	0.0404537i	$-0.987120\pi$
$199$	−6.55338	+	11.3508i	−0.464557	+	0.804636i	0.534625	+	0.845090i	$0.320453\pi$
$200$		0			0
$201$	−7.25873	+	4.19083i	−0.511992	+	0.295598i
$202$		0			0
$203$	−0.621062	−	0.573160i	−0.0435900	−	0.0402280i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−5.53156	+	1.48218i	−0.384470	+	0.103018i
$208$		0			0
$209$	5.98535			0.414015
$210$		0			0
$211$	−9.05363			−0.623278			−0.311639	−	0.950201i	$-0.600878\pi$
$211$	−9.05363			−0.623278			−0.311639	+	0.950201i	$0.600878\pi$
$212$		0			0
$213$	−0.473243	+	0.126805i	−0.0324261	+	0.00868854i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	13.4253	−	4.18073i	0.911369	−	0.283807i
$218$		0			0
$219$	2.27039	−	1.31081i	0.153419	−	0.0885762i
$220$		0			0
$221$	0.0429186	−	0.0743372i	0.00288702	−	0.00500046i
$222$		0			0
$223$	−11.9852	−	11.9852i	−0.802591	−	0.802591i	0.180909	−	0.983500i	$-0.442096\pi$
$223$	−11.9852	−	11.9852i	−0.802591	−	0.802591i	−0.983500	+	0.180909i	$0.942096\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.18826	−	15.6308i	−0.277985	−	1.03745i	−0.953815	−	0.300395i	$-0.902881\pi$
$227$	−4.18826	−	15.6308i	−0.277985	−	1.03745i	0.675830	−	0.737057i	$-0.263785\pi$
$228$		0			0
$229$	12.5466	+	21.7313i	0.829102	+	1.43605i	0.898744	+	0.438474i	$0.144481\pi$
$229$	12.5466	+	21.7313i	0.829102	+	1.43605i	−0.0696420	+	0.997572i	$0.522186\pi$
$230$		0			0
$231$	−7.95891	−	12.5912i	−0.523658	−	0.828442i
$232$		0			0
$233$	6.05603	+	1.62271i	0.396743	+	0.106307i	0.451674	−	0.892183i	$-0.350827\pi$
$233$	6.05603	+	1.62271i	0.396743	+	0.106307i	−0.0549305	+	0.998490i	$0.517494\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	9.96333	−	9.96333i	0.647188	−	0.647188i
$238$		0			0
$239$		−	20.6723i		−	1.33718i	−0.743632	−	0.668589i	$-0.766898\pi$
$239$		−	20.6723i		−	1.33718i	0.743632	−	0.668589i	$-0.233102\pi$
$240$		0			0
$241$	7.23827	+	4.17901i	0.466258	+	0.269194i	0.714672	−	0.699460i	$-0.246576\pi$
$241$	7.23827	+	4.17901i	0.466258	+	0.269194i	−0.248414	+	0.968654i	$0.579909\pi$
$242$		0			0
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.125301	+	0.467631i	−0.00797273	+	0.0297546i
$248$		0			0
$249$	−5.82687	−	3.36415i	−0.369263	−	0.213194i
$250$		0			0
$251$			10.5554i			0.666251i	0.942882	+	0.333126i	$0.108103\pi$
$251$			10.5554i			0.666251i	−0.942882	+	0.333126i	$0.891897\pi$
$252$		0			0
$253$	22.7983	−	22.7983i	1.43332	−	1.43332i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.442064	−	0.118451i	−0.0275752	−	0.00738875i	0.245005	−	0.969522i	$-0.421210\pi$
$257$	−0.442064	−	0.118451i	−0.0275752	−	0.00738875i	−0.272580	+	0.962133i	$0.587877\pi$
$258$		0			0
$259$	14.5172	+	22.9667i	0.902058	+	1.42708i
$260$		0			0
$261$	−0.159713	−	0.276631i	−0.00988599	−	0.0171230i
$262$		0			0
$263$	7.52032	+	28.0662i	0.463723	+	1.73064i	0.661089	+	0.750307i	$0.270094\pi$
$263$	7.52032	+	28.0662i	0.463723	+	1.73064i	−0.197367	+	0.980330i	$0.563239\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	2.30537	+	2.30537i	0.141086	+	0.141086i
$268$		0			0
$269$	7.26094	−	12.5763i	0.442707	−	0.766792i	−0.555182	−	0.831729i	$-0.687351\pi$
$269$	7.26094	−	12.5763i	0.442707	−	0.766792i	0.997889	+	0.0649371i	$0.0206847\pi$
$270$		0			0
$271$	25.9039	−	14.9556i	1.57355	−	0.908489i	0.577820	−	0.816164i	$-0.303904\pi$
$271$	25.9039	−	14.9556i	1.57355	−	0.908489i	0.995729	−	0.0923244i	$-0.0294297\pi$
$272$		0			0
$273$	1.15036	−	0.358231i	0.0696230	−	0.0216811i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	6.89254	−	1.84685i	0.414133	−	0.110966i	−0.0457358	−	0.998954i	$-0.514563\pi$
$277$	6.89254	−	1.84685i	0.414133	−	0.110966i	0.459868	+	0.887987i	$0.347897\pi$
$278$		0			0
$279$	5.31463			0.318179
$280$		0			0
$281$	29.7558			1.77508			0.887541	−	0.460728i	$-0.152412\pi$
$281$	29.7558			1.77508			0.887541	+	0.460728i	$0.152412\pi$
$282$		0			0
$283$	−0.798624	+	0.213991i	−0.0474733	+	0.0127204i	−0.282478	−	0.959274i	$-0.591156\pi$
$283$	−0.798624	+	0.213991i	−0.0474733	+	0.0127204i	0.235004	+	0.971994i	$0.424490\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	11.0464	+	10.1944i	0.652046	+	0.601755i
$288$		0			0
$289$	14.6917	−	8.48224i	0.864215	−	0.498955i
$290$		0			0
$291$	7.20025	−	12.4712i	0.422086	−	0.731075i
$292$		0			0
$293$	15.9412	+	15.9412i	0.931294	+	0.931294i	0.997787	−	0.0664928i	$-0.0211809\pi$
$293$	15.9412	+	15.9412i	0.931294	+	0.931294i	−0.0664928	+	0.997787i	$0.521181\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.45717	−	5.43823i	−0.0845535	−	0.315558i
$298$		0			0
$299$	1.30394	+	2.25849i	0.0754087	+	0.130612i
$300$		0			0
$301$	−0.126602	−	3.15628i	−0.00729720	−	0.181925i
$302$		0			0
$303$	−14.2251	−	3.81161i	−0.817213	−	0.218971i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	15.0084	−	15.0084i	0.856572	−	0.856572i	−0.134360	−	0.990933i	$-0.542898\pi$
$307$	15.0084	−	15.0084i	0.856572	−	0.856572i	0.990933	+	0.134360i	$0.0428979\pi$
$308$		0			0
$309$		−	16.5217i		−	0.939885i
$310$		0			0
$311$	−21.6718	−	12.5122i	−1.22889	−	0.709503i	−0.262096	−	0.965042i	$-0.584414\pi$
$311$	−21.6718	−	12.5122i	−1.22889	−	0.709503i	−0.966799	+	0.255539i	$0.917747\pi$
$312$		0			0
$313$	−0.242483	+	0.904959i	−0.0137060	+	0.0511513i	−0.972440	−	0.233153i	$-0.925096\pi$
$313$	−0.242483	+	0.904959i	−0.0137060	+	0.0511513i	0.958734	+	0.284304i	$0.0917625\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.46785	−	12.9422i	0.194774	−	0.726905i	−0.797552	−	0.603251i	$-0.793872\pi$
$317$	3.46785	−	12.9422i	0.194774	−	0.726905i	0.992325	−	0.123655i	$-0.0394615\pi$
$318$		0			0
$319$	1.55745	+	0.899195i	0.0872005	+	0.0503452i
$320$		0			0
$321$		−	11.8041i		−	0.658841i
$322$		0			0
$323$	0.141695	−	0.141695i	0.00788409	−	0.00788409i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	3.68271	+	0.986780i	0.203655	+	0.0545691i
$328$		0			0
$329$	−27.9767	+	17.6840i	−1.54240	+	0.974953i
$330$		0			0
$331$	−11.1822	−	19.3681i	−0.614627	−	1.06457i	−0.990450	−	0.137874i	$-0.955973\pi$
$331$	−11.1822	−	19.3681i	−0.614627	−	1.06457i	0.375823	−	0.926692i	$-0.377360\pi$
$332$		0			0
$333$	2.65791	+	9.91946i	0.145653	+	0.543583i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−6.15002	−	6.15002i	−0.335013	−	0.335013i	0.519473	−	0.854487i	$-0.326128\pi$
$337$	−6.15002	−	6.15002i	−0.335013	−	0.335013i	−0.854487	+	0.519473i	$0.826128\pi$
$338$		0			0
$339$	0.664405	−	1.15078i	0.0360856	−	0.0625020i
$340$		0			0
$341$	−25.9130	+	14.9609i	−1.40327	+	0.810176i
$342$		0			0
$343$	−14.5724	−	11.4300i	−0.786837	−	0.617161i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.25350	+	0.871773i	−0.174657	+	0.0467992i	−0.345088	−	0.938570i	$-0.612151\pi$
$347$	−3.25350	+	0.871773i	−0.174657	+	0.0467992i	0.170431	+	0.985370i	$0.445484\pi$
$348$		0			0
$349$	21.6071			1.15660			0.578301	−	0.815824i	$-0.303716\pi$
$349$	21.6071			1.15660			0.578301	+	0.815824i	$0.303716\pi$
$350$		0			0
$351$	0.455390			0.0243069
$352$		0			0
$353$	15.4661	−	4.14414i	0.823179	−	0.220570i	0.177443	−	0.984131i	$-0.443217\pi$
$353$	15.4661	−	4.14414i	0.823179	−	0.220570i	0.645736	+	0.763561i	$0.276551\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.486495	−	0.109664i	−0.0257481	−	0.00580401i
$358$		0			0
$359$	2.16163	−	1.24802i	0.114086	−	0.0658678i	−0.441871	−	0.897079i	$-0.645685\pi$
$359$	2.16163	−	1.24802i	0.114086	−	0.0658678i	0.555957	+	0.831211i	$0.312352\pi$
$360$		0			0
$361$	8.93490	−	15.4757i	0.470258	−	0.814511i
$362$		0			0
$363$	14.6354	+	14.6354i	0.768162	+	0.768162i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.86473	+	6.95927i	0.0973382	+	0.363271i	0.997364	−	0.0725664i	$-0.0231189\pi$
$367$	1.86473	+	6.95927i	0.0973382	+	0.363271i	−0.900025	+	0.435837i	$0.856452\pi$
$368$		0			0
$369$	2.84070	+	4.92023i	0.147881	+	0.256137i
$370$		0			0
$371$	−0.777758	−	0.408385i	−0.0403792	−	0.0212023i
$372$		0			0
$373$	32.9385	+	8.82585i	1.70549	+	0.456985i	0.974312	−	0.225200i	$-0.0723037\pi$
$373$	32.9385	+	8.82585i	1.70549	+	0.456985i	0.731179	+	0.682185i	$0.238970\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.102858	+	0.102858i	−0.00529746	+	0.00529746i
$378$		0			0
$379$		−	13.7567i		−	0.706632i	−0.935504	−	0.353316i	$-0.885054\pi$
$379$		−	13.7567i		−	0.706632i	0.935504	−	0.353316i	$-0.114946\pi$
$380$		0			0
$381$	11.1234	+	6.42209i	0.569869	+	0.329014i
$382$		0			0
$383$	−3.78113	+	14.1114i	−0.193207	+	0.721057i	0.799517	+	0.600643i	$0.205089\pi$
$383$	−3.78113	+	14.1114i	−0.193207	+	0.721057i	−0.992724	+	0.120413i	$0.961578\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.309010	−	1.15324i	0.0157079	−	0.0586225i
$388$		0			0
$389$	−6.89800	−	3.98256i	−0.349742	−	0.201924i	0.314829	−	0.949148i	$-0.398053\pi$
$389$	−6.89800	−	3.98256i	−0.349742	−	0.201924i	−0.664572	+	0.747224i	$0.731386\pi$
$390$		0			0
$391$		−	1.07943i		−	0.0545893i
$392$		0			0
$393$	7.78071	−	7.78071i	0.392485	−	0.392485i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−18.2812	−	4.89845i	−0.917510	−	0.245846i	−0.230989	−	0.972956i	$-0.574196\pi$
$397$	−18.2812	−	4.89845i	−0.917510	−	0.245846i	−0.686521	+	0.727110i	$0.740863\pi$
$398$		0			0
$399$	2.81045	−	0.112730i	0.140699	−	0.00564356i
$400$		0			0
$401$	−7.05926	−	12.2270i	−0.352523	−	0.610587i	0.634168	−	0.773195i	$-0.281343\pi$
$401$	−7.05926	−	12.2270i	−0.352523	−	0.610587i	−0.986691	+	0.162608i	$0.948009\pi$
$402$		0			0
$403$	−0.626402	−	2.33776i	−0.0312033	−	0.116452i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−40.8830	−	40.8830i	−2.02649	−	2.02649i
$408$		0			0
$409$	3.20404	−	5.54955i	0.158429	−	0.274408i	−0.775873	−	0.630889i	$-0.782690\pi$
$409$	3.20404	−	5.54955i	0.158429	−	0.274408i	0.934302	+	0.356481i	$0.116024\pi$
$410$		0			0
$411$	0.555268	−	0.320584i	0.0273893	−	0.0158132i
$412$		0			0
$413$	7.04323	+	22.6174i	0.346574	+	1.11293i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−12.8778	+	3.45061i	−0.630630	+	0.168977i
$418$		0			0
$419$	11.0491			0.539785			0.269893	−	0.962890i	$-0.413012\pi$
$419$	11.0491			0.539785			0.269893	+	0.962890i	$0.413012\pi$
$420$		0			0
$421$	−0.571065			−0.0278320			−0.0139160	−	0.999903i	$-0.504430\pi$
$421$	−0.571065			−0.0278320			−0.0139160	+	0.999903i	$0.504430\pi$
$422$		0			0
$423$	−12.0833	+	3.23771i	−0.587510	+	0.157423i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	5.91699	−	26.2492i	0.286343	−	1.27029i
$428$		0			0
$429$	−2.22038	+	1.28194i	−0.107201	+	0.0618925i
$430$		0			0
$431$	7.04843	−	12.2082i	0.339511	−	0.588050i	−0.644830	−	0.764326i	$-0.723072\pi$
$431$	7.04843	−	12.2082i	0.339511	−	0.588050i	0.984341	+	0.176276i	$0.0564051\pi$
$432$		0			0
$433$	17.3222	+	17.3222i	0.832450	+	0.832450i	0.987851	−	0.155402i	$-0.0496671\pi$
$433$	17.3222	+	17.3222i	0.832450	+	0.832450i	−0.155402	+	0.987851i	$0.549667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.57571	+	5.88062i	0.0753763	+	0.281308i
$438$		0			0
$439$	−11.4540	−	19.8389i	−0.546670	−	0.946860i	−0.998500	−	0.0547558i	$-0.982562\pi$
$439$	−11.4540	−	19.8389i	−0.546670	−	0.946860i	0.451830	−	0.892104i	$-0.350771\pi$
$440$		0			0
$441$	−3.97429	−	5.76238i	−0.189252	−	0.274399i
$442$		0			0
$443$	−15.7989	−	4.23331i	−0.750629	−	0.201131i	−0.136832	−	0.990594i	$-0.543692\pi$
$443$	−15.7989	−	4.23331i	−0.750629	−	0.201131i	−0.613797	+	0.789464i	$0.710359\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	12.3997	−	12.3997i	0.586484	−	0.586484i
$448$		0			0
$449$		−	11.7151i		−	0.552871i	−0.961032	−	0.276436i	$-0.910847\pi$
$449$		−	11.7151i		−	0.552871i	0.961032	−	0.276436i	$-0.0891532\pi$
$450$		0			0
$451$	−27.7012	−	15.9933i	−1.30440	−	0.753095i
$452$		0			0
$453$	4.74111	−	17.6941i	0.222757	−	0.831340i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.964614	+	3.59999i	−0.0451228	+	0.168400i	−0.984810	−	0.173634i	$-0.944449\pi$
$457$	−0.964614	+	3.59999i	−0.0451228	+	0.168400i	0.939688	+	0.342034i	$0.111116\pi$
$458$		0			0
$459$	−0.163239	−	0.0942458i	−0.00761932	−	0.00439902i
$460$		0			0
$461$			16.7937i			0.782163i	0.920356	+	0.391081i	$0.127899\pi$
$461$			16.7937i			0.782163i	−0.920356	+	0.391081i	$0.872101\pi$
$462$		0			0
$463$	7.41668	−	7.41668i	0.344682	−	0.344682i	−0.513442	−	0.858124i	$-0.671630\pi$
$463$	7.41668	−	7.41668i	0.344682	−	0.344682i	0.858124	+	0.513442i	$0.171630\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	22.6108	+	6.05853i	1.04630	+	0.280356i	0.740722	−	0.671811i	$-0.234483\pi$
$467$	22.6108	+	6.05853i	1.04630	+	0.280356i	0.305579	+	0.952167i	$0.401150\pi$
$468$		0			0
$469$	10.3093	−	19.6338i	0.476039	−	0.906603i
$470$		0			0
$471$	−3.36921	−	5.83564i	−0.155245	−	0.268892i
$472$		0			0
$473$	1.73975	+	6.49282i	0.0799936	+	0.298540i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.234777	−	0.234777i	−0.0107497	−	0.0107497i
$478$		0			0
$479$	1.70212	−	2.94816i	0.0777719	−	0.134705i	−0.824516	−	0.565838i	$-0.808553\pi$
$479$	1.70212	−	2.94816i	0.0777719	−	0.134705i	0.902288	+	0.431133i	$0.141886\pi$
$480$		0			0
$481$	4.05003	−	2.33829i	0.184665	−	0.106617i
$482$		0			0
$483$	10.2757	−	11.1344i	0.467558	−	0.506634i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−28.5061	+	7.63817i	−1.29173	+	0.346119i	−0.838318	−	0.545181i	$-0.816461\pi$
$487$	−28.5061	+	7.63817i	−1.29173	+	0.346119i	−0.453414	+	0.891300i	$0.649794\pi$
$488$		0			0
$489$	12.6417			0.571677
$490$		0			0
$491$	5.14807			0.232329			0.116164	−	0.993230i	$-0.462940\pi$
$491$	5.14807			0.232329			0.116164	+	0.993230i	$0.462940\pi$
$492$		0			0
$493$	0.0581576	−	0.0155833i	0.00261928	−	0.000701835i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.879116	−	0.952588i	0.0394338	−	0.0427294i
$498$		0			0
$499$	−23.8743	+	13.7838i	−1.06876	+	0.617049i	−0.927843	−	0.372972i	$-0.878339\pi$
$499$	−23.8743	+	13.7838i	−1.06876	+	0.617049i	−0.140918	+	0.990021i	$0.545005\pi$
$500$		0			0
$501$	5.97626	−	10.3512i	0.267000	−	0.462457i
$502$		0			0
$503$	7.85759	+	7.85759i	0.350353	+	0.350353i	0.860241	−	0.509888i	$-0.170313\pi$
$503$	7.85759	+	7.85759i	0.350353	+	0.350353i	−0.509888	+	0.860241i	$0.670313\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.31097	+	12.3567i	0.147046	+	0.548781i
$508$		0			0
$509$	−4.04153	−	7.00013i	−0.179138	−	0.310275i	0.762448	−	0.647050i	$-0.223997\pi$
$509$	−4.04153	−	7.00013i	−0.179138	−	0.310275i	−0.941585	+	0.336774i	$0.890664\pi$
$510$		0			0
$511$	−3.22454	+	6.14105i	−0.142645	+	0.271664i
$512$		0			0
$513$	1.02688	+	0.275152i	0.0453379	+	0.0121482i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	49.8012	−	49.8012i	2.19025	−	2.19025i
$518$		0			0
$519$			2.55462i			0.112135i
$520$		0			0
$521$	−17.9610	−	10.3698i	−0.786887	−	0.454309i	0.0519787	−	0.998648i	$-0.483447\pi$
$521$	−17.9610	−	10.3698i	−0.786887	−	0.454309i	−0.838865	+	0.544339i	$0.816781\pi$
$522$		0			0
$523$	−8.85863	+	33.0608i	−0.387361	+	1.44565i	0.447051	+	0.894508i	$0.352474\pi$
$523$	−8.85863	+	33.0608i	−0.387361	+	1.44565i	−0.834412	+	0.551141i	$0.814193\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.259276	+	0.967629i	−0.0112942	+	0.0421506i
$528$		0			0
$529$	8.48268	+	4.89748i	0.368812	+	0.212934i
$530$		0			0
$531$			8.95349i			0.388548i
$532$		0			0
$533$	1.82946	−	1.82946i	0.0792428	−	0.0792428i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	20.0438	+	5.37072i	0.864953	+	0.231764i
$538$		0			0
$539$	35.5991	+	16.9083i	1.53336	+	0.728292i
$540$		0			0
$541$	−9.79472	−	16.9650i	−0.421108	−	0.729380i	0.574940	−	0.818195i	$-0.305025\pi$
$541$	−9.79472	−	16.9650i	−0.421108	−	0.729380i	−0.996048	+	0.0888152i	$0.971692\pi$
$542$		0			0
$543$	−2.93848	−	10.9666i	−0.126102	−	0.470621i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	16.1296	+	16.1296i	0.689650	+	0.689650i	0.962155	−	0.272504i	$-0.0878518\pi$
$547$	16.1296	+	16.1296i	0.689650	+	0.689650i	−0.272504	+	0.962155i	$0.587852\pi$
$548$		0			0
$549$	5.08511	−	8.80767i	0.217027	−	0.375902i
$550$		0			0
$551$	−0.294088	+	0.169792i	−0.0125286	+	0.00723337i
$552$		0			0
$553$	−8.19766	+	36.3669i	−0.348600	+	1.54648i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.685709	−	0.183735i	0.0290544	−	0.00778511i	−0.244263	−	0.969709i	$-0.578546\pi$
$557$	0.685709	−	0.183735i	0.0290544	−	0.00778511i	0.273317	+	0.961924i	$0.411879\pi$
$558$		0			0
$559$	−0.543700			−0.0229961
$560$		0			0
$561$	1.06122			0.0448048
$562$		0			0
$563$	13.1727	−	3.52961i	0.555163	−	0.148755i	0.0296797	−	0.999559i	$-0.490551\pi$
$563$	13.1727	−	3.52961i	0.555163	−	0.148755i	0.525483	+	0.850804i	$0.323885\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.786646	−	2.52610i	−0.0330360	−	0.106086i
$568$		0			0
$569$	−37.7464	+	21.7929i	−1.58241	+	0.913607i	−0.587907	+	0.808928i	$0.700048\pi$
$569$	−37.7464	+	21.7929i	−1.58241	+	0.913607i	−0.994506	+	0.104678i	$0.966619\pi$
$570$		0			0
$571$	−2.06742	+	3.58088i	−0.0865189	+	0.149855i	−0.906037	−	0.423198i	$-0.860908\pi$
$571$	−2.06742	+	3.58088i	−0.0865189	+	0.149855i	0.819519	+	0.573053i	$0.194241\pi$
$572$		0			0
$573$	−15.2729	−	15.2729i	−0.638035	−	0.638035i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	4.63188	+	17.2864i	0.192828	+	0.719643i	0.992818	+	0.119631i	$0.0381710\pi$
$577$	4.63188	+	17.2864i	0.192828	+	0.719643i	−0.799991	+	0.600012i	$0.795162\pi$
$578$		0			0
$579$	12.6094	+	21.8401i	0.524028	+	0.907644i
$580$		0			0
$581$	17.7871	−	0.713458i	0.737933	−	0.0295992i
$582$		0			0
$583$	1.80563	+	0.483817i	0.0747815	+	0.0200377i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	22.1491	−	22.1491i	0.914190	−	0.914190i	−0.0824083	−	0.996599i	$-0.526261\pi$
$587$	22.1491	−	22.1491i	0.914190	−	0.914190i	0.996599	+	0.0824083i	$0.0262612\pi$
$588$		0			0
$589$		−	5.65001i		−	0.232805i
$590$		0			0
$591$	−6.28093	−	3.62630i	−0.258363	−	0.149166i
$592$		0			0
$593$	11.4075	−	42.5732i	0.468448	−	1.74827i	−0.176749	−	0.984256i	$-0.556558\pi$
$593$	11.4075	−	42.5732i	0.468448	−	1.74827i	0.645197	−	0.764016i	$-0.276775\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.39228	−	12.6602i	0.138837	−	0.518146i
$598$		0			0
$599$	36.0256	+	20.7994i	1.47196	+	0.849839i	0.999503	−	0.0315126i	$-0.0100324\pi$
$599$	36.0256	+	20.7994i	1.47196	+	0.849839i	0.472461	+	0.881352i	$0.343366\pi$
$600$		0			0
$601$			13.3940i			0.546353i	0.961964	+	0.273177i	$0.0880744\pi$
$601$			13.3940i			0.546353i	−0.961964	+	0.273177i	$0.911926\pi$
$602$		0			0
$603$	5.92673	−	5.92673i	0.241355	−	0.241355i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	0.110887	+	0.0297122i	0.00450078	+	0.00120598i	0.261069	−	0.965320i	$-0.415925\pi$
$607$	0.110887	+	0.0297122i	0.00450078	+	0.00120598i	−0.256568	+	0.966526i	$0.582592\pi$
$608$		0			0
$609$	0.748245	+	0.392888i	0.0303204	+	0.0159206i
$610$		0			0
$611$	2.84836	+	4.93350i	0.115232	+	0.199588i
$612$		0			0
$613$	−8.22384	−	30.6918i	−0.332158	−	1.23963i	−0.906918	−	0.421308i	$-0.861571\pi$
$613$	−8.22384	−	30.6918i	−0.332158	−	1.23963i	0.574760	−	0.818322i	$-0.305095\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.62323	+	4.62323i	0.186124	+	0.186124i	0.794018	−	0.607894i	$-0.207985\pi$
$617$	4.62323	+	4.62323i	0.186124	+	0.186124i	−0.607894	+	0.794018i	$0.707985\pi$
$618$		0			0
$619$	3.47073	−	6.01149i	0.139501	−	0.241622i	−0.787807	−	0.615922i	$-0.788784\pi$
$619$	3.47073	−	6.01149i	0.139501	−	0.241622i	0.927308	+	0.374300i	$0.122117\pi$
$620$		0			0
$621$	4.95946	−	2.86334i	0.199016	−	0.114902i
$622$		0			0
$623$	−8.41477	−	1.89682i	−0.337130	−	0.0759944i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−5.78140	+	1.54912i	−0.230887	+	0.0618660i
$628$		0			0
$629$	−1.93569			−0.0771811
$630$		0			0
$631$	19.8796			0.791394			0.395697	−	0.918381i	$-0.370503\pi$
$631$	19.8796			0.791394			0.395697	+	0.918381i	$0.370503\pi$
$632$		0			0
$633$	8.74514	−	2.34325i	0.347588	−	0.0931359i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.06629	+	2.42736i	−0.0818693	+	0.0961755i
$638$		0			0
$639$	0.424298	−	0.244969i	0.0167850	−	0.00969081i
$640$		0			0
$641$	17.4485	−	30.2217i	0.689175	−	1.19369i	−0.282931	−	0.959140i	$-0.591307\pi$
$641$	17.4485	−	30.2217i	0.689175	−	1.19369i	0.972105	−	0.234545i	$-0.0753600\pi$
$642$		0			0
$643$	4.88618	+	4.88618i	0.192692	+	0.192692i	0.796858	−	0.604166i	$-0.206494\pi$
$643$	4.88618	+	4.88618i	0.192692	+	0.192692i	−0.604166	+	0.796858i	$0.706494\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.08346	−	7.77556i	−0.0819091	−	0.305689i	0.912802	−	0.408403i	$-0.133914\pi$
$647$	−2.08346	−	7.77556i	−0.0819091	−	0.305689i	−0.994711	+	0.102714i	$0.967247\pi$
$648$		0			0
$649$	−25.2044	−	43.6552i	−0.989358	−	1.71362i
$650$		0			0
$651$	−11.8858	+	7.51300i	−0.465841	+	0.294458i
$652$		0			0
$653$	−36.8883	−	9.88419i	−1.44355	−	0.386798i	−0.549775	−	0.835312i	$-0.685287\pi$
$653$	−36.8883	−	9.88419i	−1.44355	−	0.386798i	−0.893776	+	0.448514i	$0.851953\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−1.85376	+	1.85376i	−0.0723222	+	0.0723222i
$658$		0			0
$659$			13.6894i			0.533265i	0.963798	+	0.266633i	$0.0859110\pi$
$659$			13.6894i			0.533265i	−0.963798	+	0.266633i	$0.914089\pi$
$660$		0			0
$661$	−19.9368	−	11.5105i	−0.775451	−	0.447707i	0.0593648	−	0.998236i	$-0.481092\pi$
$661$	−19.9368	−	11.5105i	−0.775451	−	0.447707i	−0.834816	+	0.550530i	$0.814426\pi$
$662$		0			0
$663$	−0.0222163	+	0.0829124i	−0.000862810	+	0.00322005i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.473445	+	1.76692i	−0.0183319	+	0.0684155i
$668$		0			0
$669$	14.6789	+	8.47484i	0.567518	+	0.327656i
$670$		0			0
$671$			57.2590i			2.21046i
$672$		0			0
$673$	−23.2703	+	23.2703i	−0.897003	+	0.897003i	−0.995170	−	0.0981672i	$-0.968702\pi$
$673$	−23.2703	+	23.2703i	−0.897003	+	0.897003i	0.0981672	+	0.995170i	$0.468702\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−26.8957	−	7.20669i	−1.03369	−	0.276976i	−0.298192	−	0.954506i	$-0.596384\pi$
$677$	−26.8957	−	7.20669i	−1.03369	−	0.276976i	−0.735495	+	0.677530i	$0.763050\pi$
$678$		0			0
$679$	1.52701	+	38.0695i	0.0586012	+	1.46097i
$680$		0			0
$681$	8.09110	+	14.0142i	0.310051	+	0.537025i
$682$		0			0
$683$	4.57160	+	17.0614i	0.174927	+	0.652838i	0.996564	+	0.0828262i	$0.0263947\pi$
$683$	4.57160	+	17.0614i	0.174927	+	0.652838i	−0.821637	+	0.570012i	$0.806939\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−17.7436	−	17.7436i	−0.676959	−	0.676959i
$688$		0			0
$689$	−0.0756005	+	0.130944i	−0.00288015	+	0.00498857i
$690$		0			0
$691$	22.4671	−	12.9714i	0.854688	−	0.493455i	−0.00754165	−	0.999972i	$-0.502401\pi$
$691$	22.4671	−	12.9714i	0.854688	−	0.493455i	0.862230	+	0.506517i	$0.169067\pi$
$692$		0			0
$693$	10.9466	+	10.1023i	0.415826	+	0.383754i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.03441	+	0.277168i	−0.0391809	+	0.0104985i
$698$		0			0
$699$	−6.26966			−0.237140
$700$		0			0
$701$	−44.4364			−1.67834			−0.839171	−	0.543868i	$-0.816959\pi$
$701$	−44.4364			−1.67834			−0.839171	+	0.543868i	$0.816959\pi$
$702$		0			0
$703$	10.5454	−	2.82564i	0.397728	−	0.106571i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	37.2018	−	11.5849i	1.39912	−	0.435695i
$708$		0			0
$709$	−24.8956	+	14.3735i	−0.934975	+	0.539808i	−0.888382	−	0.459106i	$-0.848170\pi$
$709$	−24.8956	+	14.3735i	−0.934975	+	0.539808i	−0.0465938	+	0.998914i	$0.514837\pi$
$710$		0			0
$711$	−7.04514	+	12.2025i	−0.264213	+	0.457631i
$712$		0			0
$713$	−21.5210	−	21.5210i	−0.805966	−	0.805966i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	5.35038	+	19.9679i	0.199814	+	0.745714i
$718$		0			0
$719$	−22.2598	−	38.5551i	−0.830151	−	1.43786i	−0.897918	−	0.440162i	$-0.854921\pi$
$719$	−22.2598	−	38.5551i	−0.830151	−	1.43786i	0.0677672	−	0.997701i	$-0.478412\pi$
$720$		0			0
$721$	23.3558	+	36.9495i	0.869815	+	1.37607i
$722$		0			0
$723$	−8.07324	−	2.16322i	−0.300247	−	0.0804509i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	7.16817	−	7.16817i	0.265853	−	0.265853i	−0.561574	−	0.827427i	$-0.689804\pi$
$727$	7.16817	−	7.16817i	0.265853	−	0.265853i	0.827427	+	0.561574i	$0.189804\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	0.194894	+	0.112522i	0.00720842	+	0.00416178i
$732$		0			0
$733$	5.49163	−	20.4950i	0.202838	−	0.757002i	−0.787260	−	0.616622i	$-0.788501\pi$
$733$	5.49163	−	20.4950i	0.202838	−	0.757002i	0.990098	−	0.140380i	$-0.0448325\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.2135	+	45.5814i	−0.449890	+	1.67901i
$738$		0			0
$739$	−25.3345	−	14.6269i	−0.931943	−	0.538057i	−0.0445173	−	0.999009i	$-0.514175\pi$
$739$	−25.3345	−	14.6269i	−0.931943	−	0.538057i	−0.887426	+	0.460951i	$0.847508\pi$
$740$		0			0
$741$		−	0.484127i		−	0.0177849i
$742$		0			0
$743$	28.9524	−	28.9524i	1.06216	−	1.06216i	0.0642254	−	0.997935i	$-0.479542\pi$
$743$	28.9524	−	28.9524i	1.06216	−	1.06216i	0.997935	−	0.0642254i	$-0.0204577\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	6.49903	+	1.74141i	0.237787	+	0.0637149i
$748$		0			0
$749$	16.6868	+	26.3990i	0.609723	+	0.964599i
$750$		0			0
$751$	−12.5551	−	21.7461i	−0.458143	−	0.793526i	0.540720	−	0.841203i	$-0.318152\pi$
$751$	−12.5551	−	21.7461i	−0.458143	−	0.793526i	−0.998863	+	0.0476761i	$0.984818\pi$
$752$		0			0
$753$	−2.73194	−	10.1957i	−0.0995574	−	0.371553i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−7.56835	−	7.56835i	−0.275076	−	0.275076i	0.556063	−	0.831140i	$-0.312311\pi$
$757$	−7.56835	−	7.56835i	−0.275076	−	0.275076i	−0.831140	+	0.556063i	$0.812311\pi$
$758$		0			0
$759$	−16.1208	+	27.9221i	−0.585149	+	1.01351i
$760$		0			0
$761$	−22.6900	+	13.1001i	−0.822513	+	0.474878i	−0.851282	−	0.524708i	$-0.824174\pi$
$761$	−22.6900	+	13.1001i	−0.822513	+	0.474878i	0.0287696	+	0.999586i	$0.490841\pi$
$762$		0			0
$763$	−9.63108	+	2.99919i	−0.348668	+	0.108578i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.93840	−	1.05529i	0.142207	−	0.0381043i
$768$		0			0
$769$	31.5978			1.13944			0.569722	−	0.821837i	$-0.307051\pi$
$769$	31.5978			1.13944			0.569722	+	0.821837i	$0.307051\pi$
$770$		0			0
$771$	0.457658			0.0164822
$772$		0			0
$773$	−5.83759	+	1.56418i	−0.209964	+	0.0562596i	−0.362268	−	0.932074i	$-0.617997\pi$
$773$	−5.83759	+	1.56418i	−0.209964	+	0.0562596i	0.152304	+	0.988334i	$0.451331\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−19.9668	−	18.4268i	−0.716305	−	0.661058i
$778$		0			0
$779$	5.23072	−	3.01996i	0.187410	−	0.108201i
$780$		0			0
$781$	−1.37919	+	2.38883i	−0.0493513	+	0.0854789i
$782$		0			0
$783$	0.225868	+	0.225868i	0.00807187	+	0.00807187i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	7.62300	+	28.4494i	0.271731	+	1.01411i	0.958001	+	0.286766i	$0.0925802\pi$
$787$	7.62300	+	28.4494i	0.271731	+	1.01411i	−0.686270	+	0.727347i	$0.740753\pi$
$788$		0			0
$789$	−14.5281	−	25.1635i	−0.517216	−	0.895844i
$790$		0			0
$791$	0.140905	+	3.51288i	0.00501001	+	0.124904i
$792$		0			0
$793$	−4.47360	−	1.19870i	−0.158862	−	0.0425670i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−10.2041	+	10.2041i	−0.361447	+	0.361447i	−0.864346	−	0.502898i	$-0.832267\pi$
$797$	−10.2041	+	10.2041i	−0.361447	+	0.361447i	0.502898	+	0.864346i	$0.332267\pi$
$798$		0			0
$799$		−	2.35794i		−	0.0834181i
$800$		0			0
$801$	−2.82349	−	1.63014i	−0.0997631	−	0.0575982i
$802$		0			0
$803$	3.82014	−	14.2569i	0.134810	−	0.503117i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.75854	+	14.0271i	−0.132307	+	0.493776i
$808$		0			0
$809$	9.72877	+	5.61691i	0.342045	+	0.197480i	0.661176	−	0.750231i	$-0.270058\pi$
$809$	9.72877	+	5.61691i	0.342045	+	0.197480i	−0.319131	+	0.947711i	$0.603391\pi$
$810$		0			0
$811$		−	12.2294i		−	0.429432i	−0.976677	−	0.214716i	$-0.931117\pi$
$811$		−	12.2294i		−	0.429432i	0.976677	−	0.214716i	$-0.0688826\pi$
$812$		0			0
$813$	−21.1504	+	21.1504i	−0.741778	+	0.741778i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.22602	−	0.328510i	−0.0428929	−	0.0114931i
$818$		0			0
$819$	−1.01845	+	0.643760i	−0.0355874	+	0.0224948i
$820$		0			0
$821$	−6.28223	−	10.8811i	−0.219251	−	0.379755i	0.735328	−	0.677712i	$-0.237028\pi$
$821$	−6.28223	−	10.8811i	−0.219251	−	0.379755i	−0.954579	+	0.297957i	$0.903695\pi$
$822$		0			0
$823$	8.79267	+	32.8147i	0.306493	+	1.14385i	0.931652	+	0.363351i	$0.118367\pi$
$823$	8.79267	+	32.8147i	0.306493	+	1.14385i	−0.625159	+	0.780497i	$0.714966\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−3.49196	−	3.49196i	−0.121427	−	0.121427i	0.643782	−	0.765209i	$-0.277364\pi$
$827$	−3.49196	−	3.49196i	−0.121427	−	0.121427i	−0.765209	+	0.643782i	$0.777364\pi$
$828$		0			0
$829$	−7.97255	+	13.8089i	−0.276898	+	0.479602i	−0.970612	−	0.240649i	$-0.922640\pi$
$829$	−7.97255	+	13.8089i	−0.276898	+	0.479602i	0.693714	+	0.720250i	$0.255973\pi$
$830$		0			0
$831$	−6.17968	+	3.56784i	−0.214371	+	0.123767i
$832$		0			0
$833$	1.24304	−	0.442477i	0.0430687	−	0.0153309i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−5.13354	+	1.37553i	−0.177441	+	0.0475452i
$838$		0			0
$839$	−2.87527			−0.0992654			−0.0496327	−	0.998768i	$-0.515805\pi$
$839$	−2.87527			−0.0992654			−0.0496327	+	0.998768i	$0.515805\pi$
$840$		0			0
$841$	28.8980			0.996482
$842$		0			0
$843$	−28.7419	+	7.70137i	−0.989924	+	0.265249i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−53.4204	−	12.0418i	−1.83555	−	0.413761i
$848$		0			0
$849$	0.716027	−	0.413398i	0.0245740	−	0.0141878i
$850$		0			0
$851$	29.4048	−	50.9305i	1.00798	−	1.74588i
$852$		0			0
$853$	30.0291	+	30.0291i	1.02818	+	1.02818i	0.999591	+	0.0285850i	$0.00910013\pi$
$853$	30.0291	+	30.0291i	1.02818	+	1.02818i	0.0285850	+	0.999591i	$0.490900\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.56022	+	28.2151i	0.258252	+	0.963810i	0.966252	+	0.257598i	$0.0829310\pi$
$857$	7.56022	+	28.2151i	0.258252	+	0.963810i	−0.708000	+	0.706212i	$0.750402\pi$
$858$		0			0
$859$	11.4892	+	19.8999i	0.392007	+	0.678976i	0.992714	−	0.120493i	$-0.0384475\pi$
$859$	11.4892	+	19.8999i	0.392007	+	0.678976i	−0.600707	+	0.799469i	$0.705114\pi$
$860$		0			0
$861$	−13.3085	−	6.98800i	−0.453551	−	0.238151i
$862$		0			0
$863$	16.9194	+	4.53355i	0.575944	+	0.154324i	0.535021	−	0.844838i	$-0.320304\pi$
$863$	16.9194	+	4.53355i	0.575944	+	0.154324i	0.0409229	+	0.999162i	$0.486970\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−11.9957	+	11.9957i	−0.407395	+	0.407395i
$868$		0			0
$869$		−	79.3292i		−	2.69106i
$870$		0			0
$871$	−3.30555	−	1.90846i	−0.112004	−	0.0646658i
$872$		0			0
$873$	−3.72712	+	13.9098i	−0.126144	+	0.470776i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−7.34472	+	27.4109i	−0.248014	+	0.925600i	0.723831	+	0.689977i	$0.242380\pi$
$877$	−7.34472	+	27.4109i	−0.248014	+	0.925600i	−0.971845	+	0.235622i	$0.924287\pi$
$878$		0			0
$879$	−19.5239	−	11.2721i	−0.658524	−	0.380199i
$880$		0			0
$881$		−	6.16979i		−	0.207865i	−0.994584	−	0.103933i	$-0.966857\pi$
$881$		−	6.16979i		−	0.207865i	0.994584	−	0.103933i	$-0.0331427\pi$
$882$		0			0
$883$	−0.783899	+	0.783899i	−0.0263803	+	0.0263803i	−0.720174	−	0.693794i	$-0.755938\pi$
$883$	−0.783899	+	0.783899i	−0.0263803	+	0.0263803i	0.693794	+	0.720174i	$0.255938\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.7743	−	4.49467i	−0.563227	−	0.150916i	−0.0340383	−	0.999421i	$-0.510837\pi$
$887$	−16.7743	−	4.49467i	−0.563227	−	0.150916i	−0.529188	+	0.848504i	$0.677504\pi$
$888$		0			0
$889$	−33.9552	+	1.36198i	−1.13882	+	0.0456793i
$890$		0			0
$891$	2.81503	+	4.87578i	0.0943072	+	0.163345i
$892$		0			0
$893$	3.44202	+	12.8458i	0.115183	+	0.429868i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−1.84405	−	1.84405i	−0.0615709	−	0.0615709i
$898$		0			0
$899$	0.848816	−	1.47019i	0.0283096	−	0.0490337i
$900$		0			0
$901$	0.0541994	−	0.0312920i	0.00180564	−	0.00104249i
$902$		0			0
$903$	0.939194	+	3.01597i	0.0312544	+	0.100365i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−24.7439	+	6.63012i	−0.821609	+	0.220150i	−0.645050	−	0.764140i	$-0.723163\pi$
$907$	−24.7439	+	6.63012i	−0.821609	+	0.220150i	−0.176559	+	0.984290i	$0.556497\pi$
$908$		0			0
$909$	14.7269			0.488462
$910$		0			0
$911$	11.6035			0.384441			0.192220	−	0.981352i	$-0.438431\pi$
$911$	11.6035			0.384441			0.192220	+	0.981352i	$0.438431\pi$
$912$		0			0
$913$	−36.5900	+	9.80425i	−1.21095	+	0.324473i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6.40184	+	28.4002i	−0.211407	+	0.937856i
$918$		0			0
$919$	−4.41048	+	2.54639i	−0.145488	+	0.0839977i	−0.570977	−	0.820966i	$-0.693436\pi$
$919$	−4.41048	+	2.54639i	−0.145488	+	0.0839977i	0.425489	+	0.904964i	$0.360102\pi$
$920$		0			0
$921$	−10.6125	+	18.3814i	−0.349694	+	0.605688i
$922$		0			0
$923$	−0.157764	−	0.157764i	−0.00519288	−	0.00519288i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	4.27612	+	15.9587i	0.140446	+	0.524153i
$928$		0			0
$929$	17.2264	+	29.8370i	0.565180	+	0.978921i	0.997033	+	0.0769766i	$0.0245267\pi$
$929$	17.2264	+	29.8370i	0.565180	+	0.978921i	−0.431853	+	0.901944i	$0.642140\pi$
$930$		0			0
$931$	−6.12601	+	4.22509i	−0.200772	+	0.138472i
$932$		0			0
$933$	24.1717	+	6.47680i	0.791347	+	0.212041i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	24.2281	−	24.2281i	0.791498	−	0.791498i	−0.190240	−	0.981738i	$-0.560927\pi$
$937$	24.2281	−	24.2281i	0.791498	−	0.791498i	0.981738	+	0.190240i	$0.0609266\pi$
$938$		0			0
$939$		−	0.936883i		−	0.0305740i
$940$		0			0
$941$	−6.74532	−	3.89441i	−0.219891	−	0.126954i	0.386009	−	0.922495i	$-0.373853\pi$
$941$	−6.74532	−	3.89441i	−0.219891	−	0.126954i	−0.605900	+	0.795541i	$0.707187\pi$
$942$		0			0
$943$	8.42082	−	31.4269i	0.274220	−	1.02340i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.67540	+	9.98473i	−0.0869389	+	0.324460i	−0.995674	−	0.0929124i	$-0.970382\pi$
$947$	−2.67540	+	9.98473i	−0.0869389	+	0.324460i	0.908735	+	0.417373i	$0.137049\pi$
$948$		0			0
$949$	1.03391	+	0.596929i	0.0335622	+	0.0193771i
$950$		0			0
$951$			13.3987i			0.434484i
$952$		0			0
$953$	−6.51038	+	6.51038i	−0.210892	+	0.210892i	−0.804646	−	0.593754i	$-0.797645\pi$
$953$	−6.51038	+	6.51038i	−0.210892	+	0.210892i	0.593754	+	0.804646i	$0.297645\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.73711	−	0.465457i	−0.0561528	−	0.0150461i
$958$		0			0
$959$	−0.788625	+	1.50191i	−0.0254660	+	0.0484994i
$960$		0			0
$961$	−1.37734	−	2.38563i	−0.0444304	−	0.0769557i
$962$		0			0
$963$	3.05513	+	11.4019i	0.0984501	+	0.367421i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	28.7098	+	28.7098i	0.923246	+	0.923246i	0.997257	−	0.0740109i	$-0.0235800\pi$
$967$	28.7098	+	28.7098i	0.923246	+	0.923246i	−0.0740109	+	0.997257i	$0.523580\pi$
$968$		0			0
$969$	−0.100193	+	0.173540i	−0.00321867	+	0.00557490i
$970$		0			0
$971$	53.3528	−	30.8032i	1.71217	−	0.988523i	0.780550	−	0.625093i	$-0.214939\pi$
$971$	53.3528	−	30.8032i	1.71217	−	0.988523i	0.931622	−	0.363430i	$-0.118394\pi$
$972$		0			0
$973$	23.9224	−	25.9217i	0.766918	−	0.831012i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.10179	−	1.36702i	0.163221	−	0.0437349i	−0.176283	−	0.984339i	$-0.556407\pi$
$977$	5.10179	−	1.36702i	0.163221	−	0.0437349i	0.339504	+	0.940605i	$0.389741\pi$
$978$		0			0
$979$	18.3556			0.586648
$980$		0			0
$981$	−3.81263			−0.121728
$982$		0			0
$983$	−29.8546	+	7.99952i	−0.952215	+	0.255145i	−0.701302	−	0.712864i	$-0.747397\pi$
$983$	−29.8546	+	7.99952i	−0.952215	+	0.255145i	−0.250913	+	0.968010i	$0.580731\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	22.4464	−	24.3224i	0.714478	−	0.774190i
$988$		0			0
$989$	−5.92121	+	3.41861i	−0.188283	+	0.108706i
$990$		0			0
$991$	−13.1694	+	22.8100i	−0.418339	+	0.724584i	−0.995773	−	0.0918537i	$-0.970721\pi$
$991$	−13.1694	+	22.8100i	−0.418339	+	0.724584i	0.577434	+	0.816437i	$0.304054\pi$
$992$		0			0
$993$	15.8140	+	15.8140i	0.501841	+	0.501841i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−2.84044	−	10.6007i	−0.0899575	−	0.335726i	0.906249	−	0.422744i	$-0.138933\pi$
$997$	−2.84044	−	10.6007i	−0.0899575	−	0.335726i	−0.996207	+	0.0870178i	$0.972266\pi$
$998$		0			0
$999$	−5.13469	−	8.89354i	−0.162454	−	0.281379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.e.157.2		32
5.2	odd	4		420.2.bo.a.73.5	✓	32
5.3	odd	4	inner	2100.2.ce.e.493.1		32
5.4	even	2		420.2.bo.a.157.6	yes	32
7.5	odd	6	inner	2100.2.ce.e.1657.1		32
15.2	even	4		1260.2.dq.c.73.7		32
15.14	odd	2		1260.2.dq.c.577.4		32
35.4	even	6		2940.2.x.c.97.3		32
35.12	even	12		420.2.bo.a.313.6	yes	32
35.17	even	12		2940.2.x.c.1273.3		32
35.19	odd	6		420.2.bo.a.397.5	yes	32
35.24	odd	6		2940.2.x.c.97.10		32
35.32	odd	12		2940.2.x.c.1273.10		32
35.33	even	12	inner	2100.2.ce.e.1993.2		32
105.47	odd	12		1260.2.dq.c.1153.4		32
105.89	even	6		1260.2.dq.c.397.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bo.a.73.5	✓	32	5.2	odd	4
420.2.bo.a.157.6	yes	32	5.4	even	2
420.2.bo.a.313.6	yes	32	35.12	even	12
420.2.bo.a.397.5	yes	32	35.19	odd	6
1260.2.dq.c.73.7		32	15.2	even	4
1260.2.dq.c.397.7		32	105.89	even	6
1260.2.dq.c.577.4		32	15.14	odd	2
1260.2.dq.c.1153.4		32	105.47	odd	12
2100.2.ce.e.157.2		32	1.1	even	1	trivial
2100.2.ce.e.493.1		32	5.3	odd	4	inner
2100.2.ce.e.1657.1		32	7.5	odd	6	inner
2100.2.ce.e.1993.2		32	35.33	even	12	inner
2940.2.x.c.97.3		32	35.4	even	6
2940.2.x.c.97.10		32	35.24	odd	6
2940.2.x.c.1273.3		32	35.17	even	12
2940.2.x.c.1273.10		32	35.32	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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{3} +(1.79435 - 1.94431i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{3} +(1.79435 - 1.94431i) q^{7} +(0.866025 - 0.500000i) q^{9} +(-2.81503 + 4.87578i) q^{11} +(-0.322009 - 0.322009i) q^{13} +(0.0487852 + 0.182069i) q^{17} +(-0.531552 - 0.920676i) q^{19} +(-1.22998 + 2.34247i) q^{21} +(-5.53156 - 1.48218i) q^{23} +(-0.707107 + 0.707107i) q^{27} -0.319426i q^{29} +(4.60261 + 2.65732i) q^{31} +(1.45717 - 5.43823i) q^{33} +(-2.65791 + 9.91946i) q^{37} +(0.394379 + 0.227695i) q^{39} +5.68139i q^{41} +(0.844231 - 0.844231i) q^{43} +(-12.0833 - 3.23771i) q^{47} +(-0.560652 - 6.97751i) q^{49} +(-0.0942458 - 0.163239i) q^{51} +(-0.0859345 - 0.320712i) q^{53} +(0.751729 + 0.751729i) q^{57} +(-4.47674 + 7.75395i) q^{59} +(8.80767 - 5.08511i) q^{61} +(0.581795 - 2.58099i) q^{63} +(8.09607 - 2.16933i) q^{67} +5.72669 q^{69} +0.489937 q^{71} +(-2.53229 + 0.678524i) q^{73} +(4.42887 + 14.2221i) q^{77} +(-12.2025 + 7.04514i) q^{79} +(0.500000 - 0.866025i) q^{81} +(4.75762 + 4.75762i) q^{83} +(0.0826735 + 0.308542i) q^{87} +(-1.63014 - 2.82349i) q^{89} +(-1.20388 + 0.0482888i) q^{91} +(-5.13354 - 1.37553i) q^{93} +(-10.1827 + 10.1827i) q^{97} +5.63007i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 8 q^{11} - 8 q^{21} - 16 q^{23} + 24 q^{31} - 12 q^{33} - 20 q^{37} + 24 q^{43} - 12 q^{47} - 8 q^{51} - 40 q^{53} + 16 q^{57} - 24 q^{61} + 12 q^{63} - 16 q^{71} + 60 q^{73} + 84 q^{77} + 16 q^{81} + 48 q^{87} + 40 q^{91} - 8 q^{93}+O(q^{100}) \) 32 * q + 8 * q^11 - 8 * q^21 - 16 * q^23 + 24 * q^31 - 12 * q^33 - 20 * q^37 + 24 * q^43 - 12 * q^47 - 8 * q^51 - 40 * q^53 + 16 * q^57 - 24 * q^61 + 12 * q^63 - 16 * q^71 + 60 * q^73 + 84 * q^77 + 16 * q^81 + 48 * q^87 + 40 * q^91 - 8 * q^93

Introduction

L-functions

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