LMFDB - Embedded newform 2100.2.ce.e.493.1

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			493.1
Character	$\chi$	$=$	2100.493
Dual form			2100.2.ce.e.1657.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{3} +(-1.94431 - 1.79435i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{3} +(-1.94431 - 1.79435i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(-2.81503 + 4.87578i) q^{11} +(0.322009 - 0.322009i) q^{13} +(0.182069 - 0.0487852i) q^{17} +(0.531552 + 0.920676i) q^{19} +(-1.22998 + 2.34247i) q^{21} +(1.48218 - 5.53156i) q^{23} +(0.707107 + 0.707107i) q^{27} +0.319426i q^{29} +(4.60261 + 2.65732i) q^{31} +(5.43823 + 1.45717i) q^{33} +(9.91946 + 2.65791i) q^{37} +(-0.394379 - 0.227695i) q^{39} +5.68139i q^{41} +(0.844231 + 0.844231i) q^{43} +(-3.23771 + 12.0833i) q^{47} +(0.560652 + 6.97751i) q^{49} +(-0.0942458 - 0.163239i) q^{51} +(0.320712 - 0.0859345i) q^{53} +(0.751729 - 0.751729i) q^{57} +(4.47674 - 7.75395i) q^{59} +(8.80767 - 5.08511i) q^{61} +(2.58099 + 0.581795i) q^{63} +(-2.16933 - 8.09607i) q^{67} -5.72669 q^{69} +0.489937 q^{71} +(-0.678524 - 2.53229i) q^{73} +(14.2221 - 4.42887i) q^{77} +(12.2025 - 7.04514i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-4.75762 + 4.75762i) q^{83} +(0.308542 - 0.0826735i) q^{87} +(1.63014 + 2.82349i) q^{89} +(-1.20388 + 0.0482888i) q^{91} +(1.37553 - 5.13354i) q^{93} +(10.1827 + 10.1827i) q^{97} -5.63007i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.94431	−	1.79435i	−0.734879	−	0.678199i
$7$	−1.94431	−	1.79435i	−0.734879	−	0.678199i
$8$		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	$-0.729885\pi$
$13$	0.322009	−	0.322009i	0.0893093	−	0.0893093i	0.750350	+	0.661041i	$0.229885\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.182069	−	0.0487852i	0.0441582	−	0.0118322i	−0.236672	−	0.971590i	$-0.576057\pi$
$17$	0.182069	−	0.0487852i	0.0441582	−	0.0118322i	0.280831	+	0.959757i	$0.409390\pi$
$18$		0			0
$19$	0.531552	+	0.920676i	0.121946	+	0.211217i	0.920535	−	0.390660i	$-0.127753\pi$
$19$	0.531552	+	0.920676i	0.121946	+	0.211217i	−0.798589	+	0.601877i	$0.794420\pi$
$20$		0			0
$21$	−1.22998	+	2.34247i	−0.268404	+	0.511168i
$22$		0			0
$23$	1.48218	−	5.53156i	0.309055	−	1.15341i	−0.620343	−	0.784331i	$-0.713007\pi$
$23$	1.48218	−	5.53156i	0.309055	−	1.15341i	0.929398	−	0.369079i	$-0.120327\pi$
$24$		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	$0.00944181\pi$
$29$			0.319426i			0.0593159i	−0.999560	+	0.0296580i	$0.990558\pi$
$30$		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
$33$	5.43823	+	1.45717i	0.946674	+	0.253660i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	9.91946	+	2.65791i	1.63075	+	0.436958i	0.954134	−	0.299380i	$-0.0967797\pi$
$37$	9.91946	+	2.65791i	1.63075	+	0.436958i	0.676614	+	0.736337i	$0.263446\pi$
$38$		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	0.768543	−	0.639799i	$-0.220982\pi$
$43$	0.844231	+	0.844231i	0.128744	+	0.128744i	−0.639799	+	0.768543i	$0.720982\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.23771	+	12.0833i	−0.472268	+	1.76253i	0.159322	+	0.987227i	$0.449069\pi$
$47$	−3.23771	+	12.0833i	−0.472268	+	1.76253i	−0.631590	+	0.775302i	$0.717598\pi$
$48$		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
$53$	0.320712	−	0.0859345i	0.0440532	−	0.0118040i	−0.236725	−	0.971577i	$-0.576074\pi$
$53$	0.320712	−	0.0859345i	0.0440532	−	0.0118040i	0.280778	+	0.959773i	$0.409407\pi$
$54$		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	$-0.635282\pi$
$59$	4.47674	−	7.75395i	0.582823	−	1.00948i	0.995143	−	0.0984394i	$-0.0313850\pi$
$60$		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
$63$	2.58099	+	0.581795i	0.325174	+	0.0732993i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.16933	−	8.09607i	−0.265026	−	0.989092i	−0.962234	−	0.272223i	$-0.912241\pi$
$67$	−2.16933	−	8.09607i	−0.265026	−	0.989092i	0.697208	−	0.716869i	$-0.254425\pi$
$68$		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
$73$	−0.678524	−	2.53229i	−0.0794153	−	0.296382i	0.914783	−	0.403946i	$-0.132362\pi$
$73$	−0.678524	−	2.53229i	−0.0794153	−	0.296382i	−0.994198	+	0.107564i	$0.965695\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	14.2221	−	4.42887i	1.62076	−	0.504716i
$78$		0			0
$79$	12.2025	−	7.04514i	1.37289	−	0.792640i	0.381602	−	0.924327i	$-0.375373\pi$
$79$	12.2025	−	7.04514i	1.37289	−	0.792640i	0.991291	+	0.131687i	$0.0420393\pi$
$80$		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	$-0.870390\pi$
$83$	−4.75762	+	4.75762i	−0.522217	+	0.522217i	0.396024	+	0.918240i	$0.370390\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.308542	−	0.0826735i	0.0330792	−	0.00886353i
$88$		0			0
$89$	1.63014	+	2.82349i	0.172795	+	0.299289i	0.939396	−	0.342834i	$-0.111387\pi$
$89$	1.63014	+	2.82349i	0.172795	+	0.299289i	−0.766601	+	0.642124i	$0.778054\pi$
$90$		0			0
$91$	−1.20388	+	0.0482888i	−0.126201	+	0.00506205i
$92$		0			0
$93$	1.37553	−	5.13354i	0.142636	−	0.532323i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	10.1827	+	10.1827i	1.03390	+	1.03390i	0.999405	+	0.0344908i	$0.0109810\pi$
$97$	10.1827	+	10.1827i	1.03390	+	1.03390i	0.0344908	+	0.999405i	$0.489019\pi$
$98$		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
$103$	−15.9587	−	4.27612i	−1.57246	−	0.421339i	−0.635877	−	0.771790i	$-0.719362\pi$
$103$	−15.9587	−	4.27612i	−1.57246	−	0.421339i	−0.936581	+	0.350451i	$0.886028\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	11.4019	+	3.05513i	1.10226	+	0.295350i	0.763685	−	0.645589i	$-0.223388\pi$
$107$	11.4019	+	3.05513i	1.10226	+	0.295350i	0.338577	+	0.940939i	$0.390055\pi$
$108$		0			0
$109$	3.30183	+	1.90631i	0.316258	+	0.182592i	0.649723	−	0.760171i	$-0.274885\pi$
$109$	3.30183	+	1.90631i	0.316258	+	0.182592i	−0.333465	+	0.942762i	$0.608218\pi$
$110$		0			0
$111$		−	10.2694i		−	0.974726i
$112$		0			0
$113$	−0.939611	−	0.939611i	−0.0883912	−	0.0883912i	0.661529	−	0.749920i	$-0.269908\pi$
$113$	−0.939611	−	0.939611i	−0.0883912	−	0.0883912i	−0.749920	+	0.661529i	$0.769908\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.117864	+	0.439873i	−0.0108965	+	0.0406663i
$118$		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
$123$	5.48780	−	1.47045i	0.494819	−	0.132586i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−9.08221	+	9.08221i	−0.805916	+	0.805916i	−0.984013	−	0.178097i	$-0.943006\pi$
$127$	−9.08221	+	9.08221i	−0.805916	+	0.805916i	0.178097	+	0.984013i	$0.443006\pi$
$128$		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
$133$	0.618509	−	2.74386i	0.0536316	−	0.237923i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.165947	+	0.619321i	0.0141778	+	0.0529122i	0.972652	−	0.232266i	$-0.0746139\pi$
$137$	0.165947	+	0.619321i	0.0141778	+	0.0529122i	−0.958475	+	0.285178i	$0.907947\pi$
$138$		0			0
$139$	−13.3321			−1.13082			−0.565408	−	0.824812i	$-0.691281\pi$
$139$	−13.3321			−1.13082			−0.565408	+	0.824812i	$0.691281\pi$
$140$		0			0
$141$	12.5095			1.05349
$142$		0			0
$143$	0.663580	+	2.47651i	0.0554913	+	0.207096i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.59465	−	2.34746i	0.543918	−	0.193615i
$148$		0			0
$149$	15.1864	−	8.76789i	1.24412	−	0.718293i	0.274190	−	0.961676i	$-0.411590\pi$
$149$	15.1864	−	8.76789i	1.24412	−	0.718293i	0.969930	+	0.243382i	$0.0782569\pi$
$150$		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
$157$	6.50881	−	1.74403i	0.519459	−	0.139189i	0.0104428	−	0.999945i	$-0.496676\pi$
$157$	6.50881	−	1.74403i	0.519459	−	0.139189i	0.509016	+	0.860757i	$0.330009\pi$
$158$		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
$163$	3.27191	−	12.2109i	0.256276	−	0.956434i	−0.711101	−	0.703090i	$-0.751803\pi$
$163$	3.27191	−	12.2109i	0.256276	−	0.956434i	0.967376	−	0.253344i	$-0.0815303\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.45171	+	8.45171i	0.654013	+	0.654013i	0.953957	−	0.299944i	$-0.0969679\pi$
$167$	8.45171	+	8.45171i	0.654013	+	0.654013i	−0.299944	+	0.953957i	$0.596968\pi$
$168$		0			0
$169$			12.7926i			0.984048i
$170$		0			0
$171$	−0.920676	−	0.531552i	−0.0704058	−	0.0406488i
$172$		0			0
$173$	2.46758	+	0.661185i	0.187606	+	0.0502690i	0.351399	−	0.936226i	$-0.385706\pi$
$173$	2.46758	+	0.661185i	0.187606	+	0.0502690i	−0.163793	+	0.986495i	$0.552373\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−8.64841	−	2.31733i	−0.650054	−	0.174181i
$178$		0			0
$179$	17.9708	+	10.3754i	1.34320	+	0.775496i	0.987275	−	0.159019i	$-0.0508332\pi$
$179$	17.9708	+	10.3754i	1.34320	+	0.775496i	0.355923	+	0.934515i	$0.384167\pi$
$180$		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
$187$	−0.274664	+	1.02506i	−0.0200854	+	0.0749598i
$188$		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
$193$	24.3595	−	6.52710i	1.75343	−	0.469831i	0.768079	−	0.640355i	$-0.221213\pi$
$193$	24.3595	−	6.52710i	1.75343	−	0.469831i	0.985354	+	0.170524i	$0.0545460\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.12836	−	5.12836i	0.365380	−	0.365380i	−0.500409	−	0.865789i	$-0.666817\pi$
$197$	5.12836	−	5.12836i	0.365380	−	0.365380i	0.865789	+	0.500409i	$0.166817\pi$
$198$		0			0
$199$	6.55338	−	11.3508i	0.464557	−	0.804636i	−0.534625	−	0.845090i	$-0.679547\pi$
$199$	6.55338	−	11.3508i	0.464557	−	0.804636i	0.999181	+	0.0404537i	$0.0128803\pi$
$200$		0			0
$201$	−7.25873	+	4.19083i	−0.511992	+	0.295598i
$202$		0			0
$203$	0.573160	−	0.621062i	0.0402280	−	0.0435900i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.48218	+	5.53156i	0.103018	+	0.384470i
$208$		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
$213$	−0.126805	−	0.473243i	−0.00868854	−	0.0324261i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−4.18073	−	13.4253i	−0.283807	−	0.911369i
$218$		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	$-0.557904\pi$
$223$	11.9852	−	11.9852i	0.802591	−	0.802591i	0.983500	+	0.180909i	$0.0579039\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−15.6308	+	4.18826i	−1.03745	+	0.277985i	−0.737057	−	0.675830i	$-0.763785\pi$
$227$	−15.6308	+	4.18826i	−1.03745	+	0.277985i	−0.300395	+	0.953815i	$0.597119\pi$
$228$		0			0
$229$	−12.5466	−	21.7313i	−0.829102	−	1.43605i	−0.898744	−	0.438474i	$-0.855519\pi$
$229$	−12.5466	−	21.7313i	−0.829102	−	1.43605i	0.0696420	−	0.997572i	$-0.477814\pi$
$230$		0			0
$231$	−7.95891	−	12.5912i	−0.523658	−	0.828442i
$232$		0			0
$233$	−1.62271	+	6.05603i	−0.106307	+	0.396743i	−0.998490	−	0.0549305i	$-0.982506\pi$
$233$	−1.62271	+	6.05603i	−0.106307	+	0.396743i	0.892183	+	0.451674i	$0.149173\pi$
$234$		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	$0.233102\pi$
$239$			20.6723i			1.33718i	−0.743632	+	0.668589i	$0.766898\pi$
$240$		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
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.467631	+	0.125301i	0.0297546	+	0.00797273i
$248$		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
$257$	−0.118451	+	0.442064i	−0.00738875	+	0.0275752i	−0.969522	−	0.245005i	$-0.921210\pi$
$257$	−0.118451	+	0.442064i	−0.00738875	+	0.0275752i	0.962133	+	0.272580i	$0.0878770\pi$
$258$		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
$263$	−28.0662	+	7.52032i	−1.73064	+	0.463723i	−0.980330	−	0.197367i	$-0.936761\pi$
$263$	−28.0662	+	7.52032i	−1.73064	+	0.463723i	−0.750307	+	0.661089i	$0.770094\pi$
$264$		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	−0.997889	−	0.0649371i	$-0.979315\pi$
$269$	−7.26094	+	12.5763i	−0.442707	+	0.766792i	0.555182	+	0.831729i	$0.312649\pi$
$270$		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
$273$	0.358231	+	1.15036i	0.0216811	+	0.0696230i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.84685	−	6.89254i	−0.110966	−	0.414133i	0.887987	−	0.459868i	$-0.152103\pi$
$277$	−1.84685	−	6.89254i	−0.110966	−	0.414133i	−0.998954	+	0.0457358i	$0.985437\pi$
$278$		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
$283$	−0.213991	−	0.798624i	−0.0127204	−	0.0474733i	0.959274	−	0.282478i	$-0.0911563\pi$
$283$	−0.213991	−	0.798624i	−0.0127204	−	0.0474733i	−0.971994	+	0.235004i	$0.924490\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10.1944	−	11.0464i	0.601755	−	0.652046i
$288$		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	$-0.978819\pi$
$293$	−15.9412	+	15.9412i	−0.931294	+	0.931294i	0.0664928	+	0.997787i	$0.478819\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−5.43823	+	1.45717i	−0.315558	+	0.0845535i
$298$		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
$303$	3.81161	−	14.2251i	0.218971	−	0.817213i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−15.0084	−	15.0084i	−0.856572	−	0.856572i	0.134360	−	0.990933i	$-0.457102\pi$
$307$	−15.0084	−	15.0084i	−0.856572	−	0.856572i	−0.990933	+	0.134360i	$0.957102\pi$
$308$		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
$313$	−0.904959	−	0.242483i	−0.0511513	−	0.0137060i	0.233153	−	0.972440i	$-0.425096\pi$
$313$	−0.904959	−	0.242483i	−0.0511513	−	0.0137060i	−0.284304	+	0.958734i	$0.591762\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−12.9422	−	3.46785i	−0.726905	−	0.194774i	−0.123655	−	0.992325i	$-0.539461\pi$
$317$	−12.9422	−	3.46785i	−0.726905	−	0.194774i	−0.603251	+	0.797552i	$0.706128\pi$
$318$		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
$327$	0.986780	−	3.68271i	0.0545691	−	0.203655i
$328$		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
$333$	−9.91946	+	2.65791i	−0.543583	+	0.145653i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−6.15002	+	6.15002i	−0.335013	+	0.335013i	−0.854487	−	0.519473i	$-0.826128\pi$
$337$	−6.15002	+	6.15002i	−0.335013	+	0.335013i	0.519473	+	0.854487i	$0.326128\pi$
$338$		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
$343$	11.4300	−	14.5724i	0.617161	−	0.786837i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.871773	+	3.25350i	0.0467992	+	0.174657i	0.985370	−	0.170431i	$-0.0545159\pi$
$347$	0.871773	+	3.25350i	0.0467992	+	0.174657i	−0.938570	+	0.345088i	$0.887849\pi$
$348$		0			0
$349$	−21.6071			−1.15660			−0.578301	−	0.815824i	$-0.696284\pi$
$349$	−21.6071			−1.15660			−0.578301	+	0.815824i	$0.696284\pi$
$350$		0			0
$351$	0.455390			0.0243069
$352$		0			0
$353$	4.14414	+	15.4661i	0.220570	+	0.823179i	0.984131	+	0.177443i	$0.0567827\pi$
$353$	4.14414	+	15.4661i	0.220570	+	0.823179i	−0.763561	+	0.645736i	$0.776551\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.109664	+	0.486495i	−0.00580401	+	0.0257481i
$358$		0			0
$359$	−2.16163	+	1.24802i	−0.114086	+	0.0658678i	−0.555957	−	0.831211i	$-0.687648\pi$
$359$	−2.16163	+	1.24802i	−0.114086	+	0.0658678i	0.441871	+	0.897079i	$0.354315\pi$
$360$		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
$367$	6.95927	−	1.86473i	0.363271	−	0.0973382i	−0.0725664	−	0.997364i	$-0.523119\pi$
$367$	6.95927	−	1.86473i	0.363271	−	0.0973382i	0.435837	+	0.900025i	$0.356452\pi$
$368$		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
$373$	−8.82585	+	32.9385i	−0.456985	+	1.70549i	0.225200	+	0.974312i	$0.427696\pi$
$373$	−8.82585	+	32.9385i	−0.456985	+	1.70549i	−0.682185	+	0.731179i	$0.738970\pi$
$374$		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	$0.114946\pi$
$379$			13.7567i			0.706632i	−0.935504	+	0.353316i	$0.885054\pi$
$380$		0			0
$381$	11.1234	+	6.42209i	0.569869	+	0.329014i
$382$		0			0
$383$	−14.1114	−	3.78113i	−0.721057	−	0.193207i	−0.120413	−	0.992724i	$-0.538422\pi$
$383$	−14.1114	−	3.78113i	−0.721057	−	0.193207i	−0.600643	+	0.799517i	$0.705089\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.15324	−	0.309010i	−0.0586225	−	0.0157079i
$388$		0			0
$389$	6.89800	+	3.98256i	0.349742	+	0.201924i	0.664572	−	0.747224i	$-0.268614\pi$
$389$	6.89800	+	3.98256i	0.349742	+	0.201924i	−0.314829	+	0.949148i	$0.601947\pi$
$390$		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
$397$	−4.89845	+	18.2812i	−0.245846	+	0.917510i	0.727110	+	0.686521i	$0.240863\pi$
$397$	−4.89845	+	18.2812i	−0.245846	+	0.917510i	−0.972956	+	0.230989i	$0.925804\pi$
$398$		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
$403$	2.33776	−	0.626402i	0.116452	−	0.0312033i
$404$		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	−0.934302	−	0.356481i	$-0.883976\pi$
$409$	−3.20404	+	5.54955i	−0.158429	+	0.274408i	0.775873	+	0.630889i	$0.217310\pi$
$410$		0			0
$411$	0.555268	−	0.320584i	0.0273893	−	0.0158132i
$412$		0			0
$413$	−22.6174	+	7.04323i	−1.11293	+	0.346574i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	3.45061	+	12.8778i	0.168977	+	0.630630i
$418$		0			0
$419$	−11.0491			−0.539785			−0.269893	−	0.962890i	$-0.586988\pi$
$419$	−11.0491			−0.539785			−0.269893	+	0.962890i	$0.586988\pi$
$420$		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
$423$	−3.23771	−	12.0833i	−0.157423	−	0.587510i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−26.2492	−	5.91699i	−1.27029	−	0.286343i
$428$		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	$-0.950333\pi$
$433$	−17.3222	+	17.3222i	−0.832450	+	0.832450i	0.155402	+	0.987851i	$0.450333\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.88062	−	1.57571i	0.281308	−	0.0753763i
$438$		0			0
$439$	11.4540	+	19.8389i	0.546670	+	0.946860i	0.998500	+	0.0547558i	$0.0174380\pi$
$439$	11.4540	+	19.8389i	0.546670	+	0.946860i	−0.451830	+	0.892104i	$0.649229\pi$
$440$		0			0
$441$	−3.97429	−	5.76238i	−0.189252	−	0.274399i
$442$		0			0
$443$	4.23331	−	15.7989i	0.201131	−	0.750629i	−0.789464	−	0.613797i	$-0.789641\pi$
$443$	4.23331	−	15.7989i	0.201131	−	0.750629i	0.990594	−	0.136832i	$-0.0436921\pi$
$444$		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	$0.0891532\pi$
$449$			11.7151i			0.552871i	−0.961032	+	0.276436i	$0.910847\pi$
$450$		0			0
$451$	−27.7012	−	15.9933i	−1.30440	−	0.753095i
$452$		0			0
$453$	17.6941	+	4.74111i	0.831340	+	0.222757i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.59999	+	0.964614i	0.168400	+	0.0451228i	0.342034	−	0.939688i	$-0.388884\pi$
$457$	3.59999	+	0.964614i	0.168400	+	0.0451228i	−0.173634	+	0.984810i	$0.555551\pi$
$458$		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	0.858124	−	0.513442i	$-0.171630\pi$
$463$	7.41668	+	7.41668i	0.344682	+	0.344682i	−0.513442	+	0.858124i	$0.671630\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.05853	−	22.6108i	0.280356	−	1.04630i	−0.671811	−	0.740722i	$-0.734483\pi$
$467$	6.05853	−	22.6108i	0.280356	−	1.04630i	0.952167	−	0.305579i	$-0.0988499\pi$
$468$		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
$473$	−6.49282	+	1.73975i	−0.298540	+	0.0799936i
$474$		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	−0.902288	−	0.431133i	$-0.858114\pi$
$479$	−1.70212	+	2.94816i	−0.0777719	+	0.134705i	0.824516	+	0.565838i	$0.191447\pi$
$480$		0			0
$481$	4.05003	−	2.33829i	0.184665	−	0.106617i
$482$		0			0
$483$	11.1344	+	10.2757i	0.506634	+	0.467558i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	7.63817	+	28.5061i	0.346119	+	1.29173i	0.891300	+	0.453414i	$0.149794\pi$
$487$	7.63817	+	28.5061i	0.346119	+	1.29173i	−0.545181	+	0.838318i	$0.683539\pi$
$488$		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
$493$	0.0155833	+	0.0581576i	0.000701835	+	0.00261928i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.952588	−	0.879116i	−0.0427294	−	0.0394338i
$498$		0			0
$499$	23.8743	−	13.7838i	1.06876	−	0.617049i	0.140918	−	0.990021i	$-0.454995\pi$
$499$	23.8743	−	13.7838i	1.06876	−	0.617049i	0.927843	+	0.372972i	$0.121661\pi$
$500$		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	$-0.829687\pi$
$503$	−7.85759	+	7.85759i	−0.350353	+	0.350353i	0.509888	+	0.860241i	$0.329687\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	12.3567	−	3.31097i	0.548781	−	0.147046i
$508$		0			0
$509$	4.04153	+	7.00013i	0.179138	+	0.310275i	0.941585	−	0.336774i	$-0.109336\pi$
$509$	4.04153	+	7.00013i	0.179138	+	0.310275i	−0.762448	+	0.647050i	$0.776003\pi$
$510$		0			0
$511$	−3.22454	+	6.14105i	−0.142645	+	0.271664i
$512$		0			0
$513$	−0.275152	+	1.02688i	−0.0121482	+	0.0453379i
$514$		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
$523$	−33.0608	−	8.85863i	−1.44565	−	0.387361i	−0.551141	−	0.834412i	$-0.685807\pi$
$523$	−33.0608	−	8.85863i	−1.44565	−	0.387361i	−0.894508	+	0.447051i	$0.852474\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.967629	+	0.259276i	0.0421506	+	0.0112942i
$528$		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
$537$	5.37072	−	20.0438i	0.231764	−	0.864953i
$538$		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
$543$	10.9666	−	2.93848i	0.470621	−	0.126102i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	16.1296	−	16.1296i	0.689650	−	0.689650i	−0.272504	−	0.962155i	$-0.587852\pi$
$547$	16.1296	−	16.1296i	0.689650	−	0.689650i	0.962155	+	0.272504i	$0.0878518\pi$
$548$		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
$553$	−36.3669	−	8.19766i	−1.54648	−	0.348600i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.183735	−	0.685709i	−0.00778511	−	0.0290544i	0.961924	−	0.273317i	$-0.0881208\pi$
$557$	−0.183735	−	0.685709i	−0.00778511	−	0.0290544i	−0.969709	+	0.244263i	$0.921454\pi$
$558$		0			0
$559$	0.543700			0.0229961
$560$		0			0
$561$	1.06122			0.0448048
$562$		0			0
$563$	3.52961	+	13.1727i	0.148755	+	0.555163i	0.999559	+	0.0296797i	$0.00944872\pi$
$563$	3.52961	+	13.1727i	0.148755	+	0.555163i	−0.850804	+	0.525483i	$0.823885\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.52610	+	0.786646i	−0.106086	+	0.0330360i
$568$		0			0
$569$	37.7464	−	21.7929i	1.58241	−	0.913607i	0.587907	−	0.808928i	$-0.299952\pi$
$569$	37.7464	−	21.7929i	1.58241	−	0.913607i	0.994506	−	0.104678i	$-0.0333813\pi$
$570$		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
$577$	17.2864	−	4.63188i	0.719643	−	0.192828i	0.119631	−	0.992818i	$-0.461829\pi$
$577$	17.2864	−	4.63188i	0.719643	−	0.192828i	0.600012	+	0.799991i	$0.295162\pi$
$578$		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
$583$	−0.483817	+	1.80563i	−0.0200377	+	0.0747815i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−22.1491	−	22.1491i	−0.914190	−	0.914190i	0.0824083	−	0.996599i	$-0.473739\pi$
$587$	−22.1491	−	22.1491i	−0.914190	−	0.914190i	−0.996599	+	0.0824083i	$0.973739\pi$
$588$		0			0
$589$			5.65001i			0.232805i
$590$		0			0
$591$	−6.28093	−	3.62630i	−0.258363	−	0.149166i
$592$		0			0
$593$	42.5732	+	11.4075i	1.74827	+	0.468448i	0.984256	−	0.176749i	$-0.0565579\pi$
$593$	42.5732	+	11.4075i	1.74827	+	0.468448i	0.764016	+	0.645197i	$0.223225\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.6602	−	3.39228i	−0.518146	−	0.138837i
$598$		0			0
$599$	−36.0256	−	20.7994i	−1.47196	−	0.849839i	−0.472461	−	0.881352i	$-0.656634\pi$
$599$	−36.0256	−	20.7994i	−1.47196	−	0.849839i	−0.999503	+	0.0315126i	$0.989968\pi$
$600$		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
$607$	0.0297122	−	0.110887i	0.00120598	−	0.00450078i	−0.965320	−	0.261069i	$-0.915925\pi$
$607$	0.0297122	−	0.110887i	0.00120598	−	0.00450078i	0.966526	+	0.256568i	$0.0825917\pi$
$608$		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
$613$	30.6918	−	8.22384i	1.23963	−	0.332158i	0.421308	−	0.906918i	$-0.361571\pi$
$613$	30.6918	−	8.22384i	1.23963	−	0.332158i	0.818322	+	0.574760i	$0.194905\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.62323	−	4.62323i	0.186124	−	0.186124i	−0.607894	−	0.794018i	$-0.707985\pi$
$617$	4.62323	−	4.62323i	0.186124	−	0.186124i	0.794018	+	0.607894i	$0.207985\pi$
$618$		0			0
$619$	−3.47073	+	6.01149i	−0.139501	+	0.241622i	−0.927308	−	0.374300i	$-0.877883\pi$
$619$	−3.47073	+	6.01149i	−0.139501	+	0.241622i	0.787807	+	0.615922i	$0.211216\pi$
$620$		0			0
$621$	4.95946	−	2.86334i	0.199016	−	0.114902i
$622$		0			0
$623$	1.89682	−	8.41477i	0.0759944	−	0.337130i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.54912	+	5.78140i	0.0618660	+	0.230887i
$628$		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
$633$	2.34325	+	8.74514i	0.0931359	+	0.347588i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	2.42736	+	2.06629i	0.0961755	+	0.0818693i
$638$		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	$-0.793506\pi$
$643$	−4.88618	+	4.88618i	−0.192692	+	0.192692i	0.604166	+	0.796858i	$0.293506\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.77556	+	2.08346i	−0.305689	+	0.0819091i	−0.408403	−	0.912802i	$-0.633914\pi$
$647$	−7.77556	+	2.08346i	−0.305689	+	0.0819091i	0.102714	+	0.994711i	$0.467247\pi$
$648$		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
$653$	9.88419	−	36.8883i	0.386798	−	1.44355i	−0.448514	−	0.893776i	$-0.648047\pi$
$653$	9.88419	−	36.8883i	0.386798	−	1.44355i	0.835312	−	0.549775i	$-0.185287\pi$
$654$		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	$-0.914089\pi$
$659$		−	13.6894i		−	0.533265i	0.963798	−	0.266633i	$-0.0859110\pi$
$660$		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
$663$	−0.0829124	−	0.0222163i	−0.00322005	−	0.000862810i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.76692	+	0.473445i	0.0684155	+	0.0183319i
$668$		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	0.0981672	−	0.995170i	$-0.468702\pi$
$673$	−23.2703	−	23.2703i	−0.897003	−	0.897003i	−0.995170	+	0.0981672i	$0.968702\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.20669	+	26.8957i	−0.276976	+	1.03369i	0.677530	+	0.735495i	$0.263050\pi$
$677$	−7.20669	+	26.8957i	−0.276976	+	1.03369i	−0.954506	+	0.298192i	$0.903616\pi$
$678$		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
$683$	−17.0614	+	4.57160i	−0.652838	+	0.174927i	−0.570012	−	0.821637i	$-0.693061\pi$
$683$	−17.0614	+	4.57160i	−0.652838	+	0.174927i	−0.0828262	+	0.996564i	$0.526395\pi$
$684$		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
$693$	−10.1023	+	10.9466i	−0.383754	+	0.415826i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.277168	+	1.03441i	0.0104985	+	0.0391809i
$698$		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
$703$	2.82564	+	10.5454i	0.106571	+	0.397728i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−11.5849	−	37.2018i	−0.435695	−	1.39912i
$708$		0			0
$709$	24.8956	−	14.3735i	0.934975	−	0.539808i	0.0465938	−	0.998914i	$-0.485163\pi$
$709$	24.8956	−	14.3735i	0.934975	−	0.539808i	0.888382	+	0.459106i	$0.151830\pi$
$710$		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
$717$	19.9679	−	5.35038i	0.745714	−	0.199814i
$718$		0			0
$719$	22.2598	+	38.5551i	0.830151	+	1.43786i	0.897918	+	0.440162i	$0.145079\pi$
$719$	22.2598	+	38.5551i	0.830151	+	1.43786i	−0.0677672	+	0.997701i	$0.521588\pi$
$720$		0			0
$721$	23.3558	+	36.9495i	0.869815	+	1.37607i
$722$		0			0
$723$	2.16322	−	8.07324i	0.0804509	−	0.300247i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−7.16817	−	7.16817i	−0.265853	−	0.265853i	0.561574	−	0.827427i	$-0.310196\pi$
$727$	−7.16817	−	7.16817i	−0.265853	−	0.265853i	−0.827427	+	0.561574i	$0.810196\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	0.194894	+	0.112522i	0.00720842	+	0.00416178i
$732$		0			0
$733$	20.4950	+	5.49163i	0.757002	+	0.202838i	0.616622	−	0.787260i	$-0.288501\pi$
$733$	20.4950	+	5.49163i	0.757002	+	0.202838i	0.140380	+	0.990098i	$0.455168\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	45.5814	+	12.2135i	1.67901	+	0.449890i
$738$		0			0
$739$	25.3345	+	14.6269i	0.931943	+	0.538057i	0.887426	−	0.460951i	$-0.152492\pi$
$739$	25.3345	+	14.6269i	0.931943	+	0.538057i	0.0445173	+	0.999009i	$0.485825\pi$
$740$		0			0
$741$		−	0.484127i		−	0.0177849i
$742$		0			0
$743$	28.9524	+	28.9524i	1.06216	+	1.06216i	0.997935	+	0.0642254i	$0.0204577\pi$
$743$	28.9524	+	28.9524i	1.06216	+	1.06216i	0.0642254	+	0.997935i	$0.479542\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.74141	−	6.49903i	0.0637149	−	0.237787i
$748$		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
$753$	10.1957	−	2.73194i	0.371553	−	0.0995574i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−7.56835	+	7.56835i	−0.275076	+	0.275076i	−0.831140	−	0.556063i	$-0.812311\pi$
$757$	−7.56835	+	7.56835i	−0.275076	+	0.275076i	0.556063	+	0.831140i	$0.312311\pi$
$758$		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
$763$	−2.99919	−	9.63108i	−0.108578	−	0.348668i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.05529	−	3.93840i	−0.0381043	−	0.142207i
$768$		0			0
$769$	−31.5978			−1.13944			−0.569722	−	0.821837i	$-0.692949\pi$
$769$	−31.5978			−1.13944			−0.569722	+	0.821837i	$0.692949\pi$
$770$		0			0
$771$	0.457658			0.0164822
$772$		0			0
$773$	−1.56418	−	5.83759i	−0.0562596	−	0.209964i	0.932074	−	0.362268i	$-0.117997\pi$
$773$	−1.56418	−	5.83759i	−0.0562596	−	0.209964i	−0.988334	+	0.152304i	$0.951331\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−18.4268	+	19.9668i	−0.661058	+	0.716305i
$778$		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
$787$	28.4494	−	7.62300i	1.01411	−	0.271731i	0.286766	−	0.958001i	$-0.407420\pi$
$787$	28.4494	−	7.62300i	1.01411	−	0.271731i	0.727347	+	0.686270i	$0.240753\pi$
$788$		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
$793$	1.19870	−	4.47360i	0.0425670	−	0.158862i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	10.2041	+	10.2041i	0.361447	+	0.361447i	0.864346	−	0.502898i	$-0.167733\pi$
$797$	10.2041	+	10.2041i	0.361447	+	0.361447i	−0.502898	+	0.864346i	$0.667733\pi$
$798$		0			0
$799$			2.35794i			0.0834181i
$800$		0			0
$801$	−2.82349	−	1.63014i	−0.0997631	−	0.0575982i
$802$		0			0
$803$	14.2569	+	3.82014i	0.503117	+	0.134810i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	14.0271	+	3.75854i	0.493776	+	0.132307i
$808$		0			0
$809$	−9.72877	−	5.61691i	−0.342045	−	0.197480i	0.319131	−	0.947711i	$-0.396609\pi$
$809$	−9.72877	−	5.61691i	−0.342045	−	0.197480i	−0.661176	+	0.750231i	$0.729942\pi$
$810$		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
$817$	−0.328510	+	1.22602i	−0.0114931	+	0.0428929i
$818$		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
$823$	−32.8147	+	8.79267i	−1.14385	+	0.306493i	−0.780497	−	0.625159i	$-0.785034\pi$
$823$	−32.8147	+	8.79267i	−1.14385	+	0.306493i	−0.363351	+	0.931652i	$0.618367\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−3.49196	+	3.49196i	−0.121427	+	0.121427i	−0.765209	−	0.643782i	$-0.777364\pi$
$827$	−3.49196	+	3.49196i	−0.121427	+	0.121427i	0.643782	+	0.765209i	$0.277364\pi$
$828$		0			0
$829$	7.97255	−	13.8089i	0.276898	−	0.479602i	−0.693714	−	0.720250i	$-0.744027\pi$
$829$	7.97255	−	13.8089i	0.276898	−	0.479602i	0.970612	+	0.240649i	$0.0773602\pi$
$830$		0			0
$831$	−6.17968	+	3.56784i	−0.214371	+	0.123767i
$832$		0			0
$833$	0.442477	+	1.24304i	0.0153309	+	0.0430687i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1.37553	+	5.13354i	0.0475452	+	0.177441i
$838$		0			0
$839$	2.87527			0.0992654			0.0496327	−	0.998768i	$-0.484195\pi$
$839$	2.87527			0.0992654			0.0496327	+	0.998768i	$0.484195\pi$
$840$		0			0
$841$	28.8980			0.996482
$842$		0			0
$843$	−7.70137	−	28.7419i	−0.265249	−	0.989924i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−12.0418	+	53.4204i	−0.413761	+	1.83555i
$848$		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	−0.0285850	+	0.999591i	$0.509100\pi$
$853$	−30.0291	+	30.0291i	−1.02818	+	1.02818i	−0.999591	+	0.0285850i	$0.990900\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28.2151	−	7.56022i	0.963810	−	0.258252i	0.257598	−	0.966252i	$-0.417069\pi$
$857$	28.2151	−	7.56022i	0.963810	−	0.258252i	0.706212	+	0.708000i	$0.250402\pi$
$858$		0			0
$859$	−11.4892	−	19.8999i	−0.392007	−	0.678976i	0.600707	−	0.799469i	$-0.294886\pi$
$859$	−11.4892	−	19.8999i	−0.392007	−	0.678976i	−0.992714	+	0.120493i	$0.961553\pi$
$860$		0			0
$861$	−13.3085	−	6.98800i	−0.453551	−	0.238151i
$862$		0			0
$863$	−4.53355	+	16.9194i	−0.154324	+	0.575944i	0.844838	+	0.535021i	$0.179696\pi$
$863$	−4.53355	+	16.9194i	−0.154324	+	0.575944i	−0.999162	+	0.0409229i	$0.986970\pi$
$864$		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
$873$	−13.9098	−	3.72712i	−0.470776	−	0.126144i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	27.4109	+	7.34472i	0.925600	+	0.248014i	0.689977	−	0.723831i	$-0.257620\pi$
$877$	27.4109	+	7.34472i	0.925600	+	0.248014i	0.235622	+	0.971845i	$0.424287\pi$
$878$		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	0.693794	−	0.720174i	$-0.255938\pi$
$883$	−0.783899	−	0.783899i	−0.0263803	−	0.0263803i	−0.720174	+	0.693794i	$0.755938\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.49467	+	16.7743i	−0.150916	+	0.563227i	0.848504	+	0.529188i	$0.177504\pi$
$887$	−4.49467	+	16.7743i	−0.150916	+	0.563227i	−0.999421	+	0.0340383i	$0.989163\pi$
$888$		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
$893$	−12.8458	+	3.44202i	−0.429868	+	0.115183i
$894$		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
$903$	−3.01597	+	0.939194i	−0.100365	+	0.0312544i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	6.63012	+	24.7439i	0.220150	+	0.821609i	0.984290	+	0.176559i	$0.0564967\pi$
$907$	6.63012	+	24.7439i	0.220150	+	0.821609i	−0.764140	+	0.645050i	$0.776837\pi$
$908$		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
$913$	−9.80425	−	36.5900i	−0.324473	−	1.21095i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	28.4002	+	6.40184i	0.937856	+	0.211407i
$918$		0			0
$919$	4.41048	−	2.54639i	0.145488	−	0.0839977i	−0.425489	−	0.904964i	$-0.639898\pi$
$919$	4.41048	−	2.54639i	0.145488	−	0.0839977i	0.570977	+	0.820966i	$0.306564\pi$
$920$		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
$927$	15.9587	−	4.27612i	0.524153	−	0.140446i
$928$		0			0
$929$	−17.2264	−	29.8370i	−0.565180	−	0.978921i	−0.997033	−	0.0769766i	$-0.975473\pi$
$929$	−17.2264	−	29.8370i	−0.565180	−	0.978921i	0.431853	−	0.901944i	$-0.357860\pi$
$930$		0			0
$931$	−6.12601	+	4.22509i	−0.200772	+	0.138472i
$932$		0			0
$933$	−6.47680	+	24.1717i	−0.212041	+	0.791347i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−24.2281	−	24.2281i	−0.791498	−	0.791498i	0.190240	−	0.981738i	$-0.439073\pi$
$937$	−24.2281	−	24.2281i	−0.791498	−	0.791498i	−0.981738	+	0.190240i	$0.939073\pi$
$938$		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
$943$	31.4269	+	8.42082i	1.02340	+	0.274220i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.98473	+	2.67540i	0.324460	+	0.0869389i	0.417373	−	0.908735i	$-0.362951\pi$
$947$	9.98473	+	2.67540i	0.324460	+	0.0869389i	−0.0929124	+	0.995674i	$0.529618\pi$
$948$		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	0.593754	−	0.804646i	$-0.297645\pi$
$953$	−6.51038	−	6.51038i	−0.210892	−	0.210892i	−0.804646	+	0.593754i	$0.797645\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−0.465457	+	1.73711i	−0.0150461	+	0.0561528i
$958$		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
$963$	−11.4019	+	3.05513i	−0.367421	+	0.0984501i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	28.7098	−	28.7098i	0.923246	−	0.923246i	−0.0740109	−	0.997257i	$-0.523580\pi$
$967$	28.7098	−	28.7098i	0.923246	−	0.923246i	0.997257	+	0.0740109i	$0.0235800\pi$
$968$		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
$973$	25.9217	+	23.9224i	0.831012	+	0.766918i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.36702	−	5.10179i	−0.0437349	−	0.163221i	0.940605	−	0.339504i	$-0.110259\pi$
$977$	−1.36702	−	5.10179i	−0.0437349	−	0.163221i	−0.984339	+	0.176283i	$0.943593\pi$
$978$		0			0
$979$	−18.3556			−0.586648
$980$		0			0
$981$	−3.81263			−0.121728
$982$		0			0
$983$	−7.99952	−	29.8546i	−0.255145	−	0.952215i	−0.968010	−	0.250913i	$-0.919269\pi$
$983$	−7.99952	−	29.8546i	−0.255145	−	0.952215i	0.712864	−	0.701302i	$-0.247397\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−24.3224	−	22.4464i	−0.774190	−	0.714478i
$988$		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
$997$	−10.6007	+	2.84044i	−0.335726	+	0.0899575i	−0.422744	−	0.906249i	$-0.638933\pi$
$997$	−10.6007	+	2.84044i	−0.335726	+	0.0899575i	0.0870178	+	0.996207i	$0.472266\pi$
$998$		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.493.1		32
5.2	odd	4	inner	2100.2.ce.e.157.2		32
5.3	odd	4		420.2.bo.a.157.6	yes	32
5.4	even	2		420.2.bo.a.73.5	✓	32
7.5	odd	6	inner	2100.2.ce.e.1993.2		32
15.8	even	4		1260.2.dq.c.577.4		32
15.14	odd	2		1260.2.dq.c.73.7		32
35.3	even	12		2940.2.x.c.97.10		32
35.4	even	6		2940.2.x.c.1273.10		32
35.12	even	12	inner	2100.2.ce.e.1657.1		32
35.18	odd	12		2940.2.x.c.97.3		32
35.19	odd	6		420.2.bo.a.313.6	yes	32
35.24	odd	6		2940.2.x.c.1273.3		32
35.33	even	12		420.2.bo.a.397.5	yes	32
105.68	odd	12		1260.2.dq.c.397.7		32
105.89	even	6		1260.2.dq.c.1153.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bo.a.73.5	✓	32	5.4	even	2
420.2.bo.a.157.6	yes	32	5.3	odd	4
420.2.bo.a.313.6	yes	32	35.19	odd	6
420.2.bo.a.397.5	yes	32	35.33	even	12
1260.2.dq.c.73.7		32	15.14	odd	2
1260.2.dq.c.397.7		32	105.68	odd	12
1260.2.dq.c.577.4		32	15.8	even	4
1260.2.dq.c.1153.4		32	105.89	even	6
2100.2.ce.e.157.2		32	5.2	odd	4	inner
2100.2.ce.e.493.1		32	1.1	even	1	trivial
2100.2.ce.e.1657.1		32	35.12	even	12	inner
2100.2.ce.e.1993.2		32	7.5	odd	6	inner
2940.2.x.c.97.3		32	35.18	odd	12
2940.2.x.c.97.10		32	35.3	even	12
2940.2.x.c.1273.3		32	35.24	odd	6
2940.2.x.c.1273.10		32	35.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.ce (of order \(12\), degree \(4\), minimal)

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