LMFDB - Embedded newform 702.2.j.b.161.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [702,2,Mod(161,702)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(702, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("702.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			161.6
Character	$\chi$	$=$	702.161
Dual form			702.2.j.b.593.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(3.09035 + 3.09035i) q^{5} +(2.51306 + 2.51306i) q^{7} +(0.707107 - 0.707107i) q^{8} -4.37041i q^{10} +(1.30078 - 1.30078i) q^{11} +(3.38281 + 1.24764i) q^{13} -3.55400i q^{14} -1.00000 q^{16} -7.96266 q^{17} +(1.81357 - 1.81357i) q^{19} +(-3.09035 + 3.09035i) q^{20} -1.83958 q^{22} -4.57533 q^{23} +14.1005i q^{25} +(-1.50979 - 3.27422i) q^{26} +(-2.51306 + 2.51306i) q^{28} -2.20171i q^{29} +(1.85735 - 1.85735i) q^{31} +(0.707107 + 0.707107i) q^{32} +(5.63045 + 5.63045i) q^{34} +15.5324i q^{35} +(-2.39642 - 2.39642i) q^{37} -2.56477 q^{38} +4.37041 q^{40} +(-2.35810 - 2.35810i) q^{41} -6.20999i q^{43} +(1.30078 + 1.30078i) q^{44} +(3.23524 + 3.23524i) q^{46} +(-2.43756 + 2.43756i) q^{47} +5.63091i q^{49} +(9.97054 - 9.97054i) q^{50} +(-1.24764 + 3.38281i) q^{52} -8.05668i q^{53} +8.03972 q^{55} +3.55400 q^{56} +(-1.55684 + 1.55684i) q^{58} +(9.17514 - 9.17514i) q^{59} -6.76562 q^{61} -2.62669 q^{62} -1.00000i q^{64} +(6.59840 + 14.3097i) q^{65} +(4.76607 - 4.76607i) q^{67} -7.96266i q^{68} +(10.9831 - 10.9831i) q^{70} +(7.32632 + 7.32632i) q^{71} +(5.48780 + 5.48780i) q^{73} +3.38905i q^{74} +(1.81357 + 1.81357i) q^{76} +6.53787 q^{77} -2.87513 q^{79} +(-3.09035 - 3.09035i) q^{80} +3.33486i q^{82} +(7.25822 + 7.25822i) q^{83} +(-24.6074 - 24.6074i) q^{85} +(-4.39113 + 4.39113i) q^{86} -1.83958i q^{88} +(4.33187 - 4.33187i) q^{89} +(5.36579 + 11.6366i) q^{91} -4.57533i q^{92} +3.44723 q^{94} +11.2091 q^{95} +(3.13933 - 3.13933i) q^{97} +(3.98165 - 3.98165i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{16} - 24 q^{19} + 24 q^{34} + 24 q^{37} + 24 q^{46} + 48 q^{70} - 24 q^{73} - 24 q^{76} - 24 q^{79} - 24 q^{91} + 72 q^{94} + 96 q^{97}+O(q^{100}) $ 24 * q - 24 * q^16 - 24 * q^19 + 24 * q^34 + 24 * q^37 + 24 * q^46 + 48 * q^70 - 24 * q^73 - 24 * q^76 - 24 * q^79 - 24 * q^91 + 72 * q^94 + 96 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	3.09035	+	3.09035i	1.38204	+	1.38204i	0.840982	+	0.541062i	$0.181978\pi$
$5$	3.09035	+	3.09035i	1.38204	+	1.38204i	0.541062	+	0.840982i	$0.318022\pi$
$6$		0			0
$7$	2.51306	+	2.51306i	0.949846	+	0.949846i	0.998801	−	0.0489549i	$-0.0155891\pi$
$7$	2.51306	+	2.51306i	0.949846	+	0.949846i	−0.0489549	+	0.998801i	$0.515589\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$		−	4.37041i		−	1.38204i
$11$	1.30078	−	1.30078i	0.392200	−	0.392200i	−0.483271	−	0.875471i	$-0.660551\pi$
$11$	1.30078	−	1.30078i	0.392200	−	0.392200i	0.875471	+	0.483271i	$0.160551\pi$
$12$		0			0
$13$	3.38281	+	1.24764i	0.938222	+	0.346034i
$13$	3.38281	+	1.24764i	0.938222	+	0.346034i
$14$		−	3.55400i		−	0.949846i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−7.96266			−1.93123			−0.965614	−	0.259979i	$-0.916284\pi$
$17$	−7.96266			−1.93123			−0.965614	+	0.259979i	$0.916284\pi$
$18$		0			0
$19$	1.81357	−	1.81357i	0.416061	−	0.416061i	−0.467783	−	0.883844i	$-0.654947\pi$
$19$	1.81357	−	1.81357i	0.416061	−	0.416061i	0.883844	+	0.467783i	$0.154947\pi$
$20$	−3.09035	+	3.09035i	−0.691022	+	0.691022i
$21$		0			0
$22$	−1.83958			−0.392200
$23$	−4.57533			−0.954021			−0.477011	−	0.878898i	$-0.658280\pi$
$23$	−4.57533			−0.954021			−0.477011	+	0.878898i	$0.658280\pi$
$24$		0			0
$25$			14.1005i			2.82010i
$26$	−1.50979	−	3.27422i	−0.296094	−	0.642128i
$27$		0			0
$28$	−2.51306	+	2.51306i	−0.474923	+	0.474923i
$29$		−	2.20171i		−	0.408847i	−0.978883	−	0.204423i	$-0.934468\pi$
$29$		−	2.20171i		−	0.408847i	0.978883	−	0.204423i	$-0.0655319\pi$
$30$		0			0
$31$	1.85735	−	1.85735i	0.333590	−	0.333590i	−0.520358	−	0.853948i	$-0.674201\pi$
$31$	1.85735	−	1.85735i	0.333590	−	0.333590i	0.853948	+	0.520358i	$0.174201\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	5.63045	+	5.63045i	0.965614	+	0.965614i
$35$			15.5324i			2.62546i
$36$		0			0
$37$	−2.39642	−	2.39642i	−0.393969	−	0.393969i	0.482130	−	0.876100i	$-0.339863\pi$
$37$	−2.39642	−	2.39642i	−0.393969	−	0.393969i	−0.876100	+	0.482130i	$0.839863\pi$
$38$	−2.56477			−0.416061
$39$		0			0
$40$	4.37041			0.691022
$41$	−2.35810	−	2.35810i	−0.368274	−	0.368274i	0.498573	−	0.866847i	$-0.333857\pi$
$41$	−2.35810	−	2.35810i	−0.368274	−	0.368274i	−0.866847	+	0.498573i	$0.833857\pi$
$42$		0			0
$43$		−	6.20999i		−	0.947015i	−0.880790	−	0.473507i	$-0.842988\pi$
$43$		−	6.20999i		−	0.947015i	0.880790	−	0.473507i	$-0.157012\pi$
$44$	1.30078	+	1.30078i	0.196100	+	0.196100i
$45$		0			0
$46$	3.23524	+	3.23524i	0.477011	+	0.477011i
$47$	−2.43756	+	2.43756i	−0.355555	+	0.355555i	−0.862171	−	0.506617i	$-0.830896\pi$
$47$	−2.43756	+	2.43756i	−0.355555	+	0.355555i	0.506617	+	0.862171i	$0.330896\pi$
$48$		0			0
$49$			5.63091i			0.804415i
$50$	9.97054	−	9.97054i	1.41005	−	1.41005i
$51$		0			0
$52$	−1.24764	+	3.38281i	−0.173017	+	0.469111i
$53$		−	8.05668i		−	1.10667i	−0.832959	−	0.553335i	$-0.813355\pi$
$53$		−	8.05668i		−	1.10667i	0.832959	−	0.553335i	$-0.186645\pi$
$54$		0			0
$55$	8.03972			1.08408
$56$	3.55400			0.474923
$57$		0			0
$58$	−1.55684	+	1.55684i	−0.204423	+	0.204423i
$59$	9.17514	−	9.17514i	1.19450	−	1.19450i	0.218712	−	0.975789i	$-0.429815\pi$
$59$	9.17514	−	9.17514i	1.19450	−	1.19450i	0.975789	−	0.218712i	$-0.0701855\pi$
$60$		0			0
$61$	−6.76562			−0.866248			−0.433124	−	0.901334i	$-0.642589\pi$
$61$	−6.76562			−0.866248			−0.433124	+	0.901334i	$0.642589\pi$
$62$	−2.62669			−0.333590
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	6.59840	+	14.3097i	0.818431	+	1.77490i
$66$		0			0
$67$	4.76607	−	4.76607i	0.582268	−	0.582268i	−0.353258	−	0.935526i	$-0.614926\pi$
$67$	4.76607	−	4.76607i	0.582268	−	0.582268i	0.935526	+	0.353258i	$0.114926\pi$
$68$		−	7.96266i		−	0.965614i
$69$		0			0
$70$	10.9831	−	10.9831i	1.31273	−	1.31273i
$71$	7.32632	+	7.32632i	0.869474	+	0.869474i	0.992414	−	0.122940i	$-0.0392323\pi$
$71$	7.32632	+	7.32632i	0.869474	+	0.869474i	−0.122940	+	0.992414i	$0.539232\pi$
$72$		0			0
$73$	5.48780	+	5.48780i	0.642299	+	0.642299i	0.951120	−	0.308821i	$-0.0999345\pi$
$73$	5.48780	+	5.48780i	0.642299	+	0.642299i	−0.308821	+	0.951120i	$0.599935\pi$
$74$			3.38905i			0.393969i
$75$		0			0
$76$	1.81357	+	1.81357i	0.208031	+	0.208031i
$77$	6.53787			0.745059
$78$		0			0
$79$	−2.87513			−0.323477			−0.161738	−	0.986834i	$-0.551710\pi$
$79$	−2.87513			−0.323477			−0.161738	+	0.986834i	$0.551710\pi$
$80$	−3.09035	−	3.09035i	−0.345511	−	0.345511i
$81$		0			0
$82$			3.33486i			0.368274i
$83$	7.25822	+	7.25822i	0.796693	+	0.796693i	0.982573	−	0.185880i	$-0.0595134\pi$
$83$	7.25822	+	7.25822i	0.796693	+	0.796693i	−0.185880	+	0.982573i	$0.559513\pi$
$84$		0			0
$85$	−24.6074	−	24.6074i	−2.66904	−	2.66904i
$86$	−4.39113	+	4.39113i	−0.473507	+	0.473507i
$87$		0			0
$88$		−	1.83958i		−	0.196100i
$89$	4.33187	−	4.33187i	0.459177	−	0.459177i	−0.439208	−	0.898385i	$-0.644741\pi$
$89$	4.33187	−	4.33187i	0.459177	−	0.459177i	0.898385	+	0.439208i	$0.144741\pi$
$90$		0			0
$91$	5.36579	+	11.6366i	0.562488	+	1.21985i
$92$		−	4.57533i		−	0.477011i
$93$		0			0
$94$	3.44723			0.355555
$95$	11.2091			1.15003
$96$		0			0
$97$	3.13933	−	3.13933i	0.318751	−	0.318751i	−0.529536	−	0.848287i	$-0.677634\pi$
$97$	3.13933	−	3.13933i	0.318751	−	0.318751i	0.848287	+	0.529536i	$0.177634\pi$
$98$	3.98165	−	3.98165i	0.402208	−	0.402208i
$99$		0			0
$100$	−14.1005			−1.41005
$101$	−4.88116			−0.485693			−0.242847	−	0.970065i	$-0.578081\pi$
$101$	−4.88116			−0.485693			−0.242847	+	0.970065i	$0.578081\pi$
$102$		0			0
$103$			7.58040i			0.746919i	0.927646	+	0.373459i	$0.121829\pi$
$103$			7.58040i			0.746919i	−0.927646	+	0.373459i	$0.878171\pi$
$104$	3.27422	−	1.50979i	0.321064	−	0.148047i
$105$		0			0
$106$	−5.69693	+	5.69693i	−0.553335	+	0.553335i
$107$			4.74027i			0.458259i	0.973396	+	0.229130i	$0.0735880\pi$
$107$			4.74027i			0.458259i	−0.973396	+	0.229130i	$0.926412\pi$
$108$		0			0
$109$	−7.39311	+	7.39311i	−0.708131	+	0.708131i	−0.966142	−	0.258011i	$-0.916933\pi$
$109$	−7.39311	+	7.39311i	−0.708131	+	0.708131i	0.258011	+	0.966142i	$0.416933\pi$
$110$	−5.68494	−	5.68494i	−0.542038	−	0.542038i
$111$		0			0
$112$	−2.51306	−	2.51306i	−0.237462	−	0.237462i
$113$		−	1.11846i		−	0.105216i	−0.998615	−	0.0526079i	$-0.983247\pi$
$113$		−	1.11846i		−	0.105216i	0.998615	−	0.0526079i	$-0.0167533\pi$
$114$		0			0
$115$	−14.1393	−	14.1393i	−1.31850	−	1.31850i
$116$	2.20171			0.204423
$117$		0			0
$118$	−12.9756			−1.19450
$119$	−20.0106	−	20.0106i	−1.83437	−	1.83437i
$120$		0			0
$121$			7.61594i			0.692359i
$122$	4.78401	+	4.78401i	0.433124	+	0.433124i
$123$		0			0
$124$	1.85735	+	1.85735i	0.166795	+	0.166795i
$125$	−28.1236	+	28.1236i	−2.51545	+	2.51545i
$126$		0			0
$127$		−	16.8438i		−	1.49464i	−0.664464	−	0.747321i	$-0.731340\pi$
$127$		−	16.8438i		−	1.49464i	0.664464	−	0.747321i	$-0.268660\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	5.45271	−	14.7843i	0.478234	−	1.29667i
$131$		−	7.04715i		−	0.615712i	−0.951433	−	0.307856i	$-0.900388\pi$
$131$		−	7.04715i		−	0.615712i	0.951433	−	0.307856i	$-0.0996115\pi$
$132$		0			0
$133$	9.11520			0.790388
$134$	−6.74024			−0.582268
$135$		0			0
$136$	−5.63045	+	5.63045i	−0.482807	+	0.482807i
$137$	−9.76774	+	9.76774i	−0.834514	+	0.834514i	−0.988131	−	0.153616i	$-0.950908\pi$
$137$	−9.76774	+	9.76774i	−0.834514	+	0.834514i	0.153616	+	0.988131i	$0.450908\pi$
$138$		0			0
$139$	17.2006			1.45893			0.729466	−	0.684017i	$-0.239769\pi$
$139$	17.2006			1.45893			0.729466	+	0.684017i	$0.239769\pi$
$140$	−15.5324			−1.31273
$141$		0			0
$142$		−	10.3610i		−	0.869474i
$143$	6.02319	−	2.77738i	0.503685	−	0.232256i
$144$		0			0
$145$	6.80403	−	6.80403i	0.565044	−	0.565044i
$146$		−	7.76093i		−	0.642299i
$147$		0			0
$148$	2.39642	−	2.39642i	0.196985	−	0.196985i
$149$	3.57725	+	3.57725i	0.293060	+	0.293060i	0.838288	−	0.545228i	$-0.183557\pi$
$149$	3.57725	+	3.57725i	0.293060	+	0.293060i	−0.545228	+	0.838288i	$0.683557\pi$
$150$		0			0
$151$	−12.6135	−	12.6135i	−1.02648	−	1.02648i	−0.999640	−	0.0268352i	$-0.991457\pi$
$151$	−12.6135	−	12.6135i	−1.02648	−	1.02648i	−0.0268352	−	0.999640i	$-0.508543\pi$
$152$		−	2.56477i		−	0.208031i
$153$		0			0
$154$	−4.62297	−	4.62297i	−0.372529	−	0.372529i
$155$	11.4797			0.922074
$156$		0			0
$157$	4.22074			0.336852			0.168426	−	0.985714i	$-0.446132\pi$
$157$	4.22074			0.336852			0.168426	+	0.985714i	$0.446132\pi$
$158$	2.03302	+	2.03302i	0.161738	+	0.161738i
$159$		0			0
$160$			4.37041i			0.345511i
$161$	−11.4981	−	11.4981i	−0.906173	−	0.906173i
$162$		0			0
$163$	8.05910	+	8.05910i	0.631238	+	0.631238i	0.948378	−	0.317141i	$-0.102723\pi$
$163$	8.05910	+	8.05910i	0.631238	+	0.631238i	−0.317141	+	0.948378i	$0.602723\pi$
$164$	2.35810	−	2.35810i	0.184137	−	0.184137i
$165$		0			0
$166$		−	10.2647i		−	0.796693i
$167$	1.49165	−	1.49165i	0.115427	−	0.115427i	−0.647034	−	0.762461i	$-0.723991\pi$
$167$	1.49165	−	1.49165i	0.115427	−	0.115427i	0.762461	+	0.647034i	$0.223991\pi$
$168$		0			0
$169$	9.88678	+	8.44107i	0.760522	+	0.649313i
$170$			34.8001i			2.66904i
$171$		0			0
$172$	6.20999			0.473507
$173$	−9.13714			−0.694684			−0.347342	−	0.937739i	$-0.612916\pi$
$173$	−9.13714			−0.694684			−0.347342	+	0.937739i	$0.612916\pi$
$174$		0			0
$175$	−35.4353	+	35.4353i	−2.67866	+	2.67866i
$176$	−1.30078	+	1.30078i	−0.0980499	+	0.0980499i
$177$		0			0
$178$	−6.12619			−0.459177
$179$	10.5948			0.791895			0.395947	−	0.918273i	$-0.370416\pi$
$179$	10.5948			0.791895			0.395947	+	0.918273i	$0.370416\pi$
$180$		0			0
$181$		−	16.5929i		−	1.23334i	−0.787221	−	0.616671i	$-0.788481\pi$
$181$		−	16.5929i		−	1.23334i	0.787221	−	0.616671i	$-0.211519\pi$
$182$	4.43412	−	12.0225i	0.328679	−	0.891167i
$183$		0			0
$184$	−3.23524	+	3.23524i	−0.238505	+	0.238505i
$185$		−	14.8115i		−	1.08897i
$186$		0			0
$187$	−10.3577	+	10.3577i	−0.757427	+	0.757427i
$188$	−2.43756	−	2.43756i	−0.177777	−	0.177777i
$189$		0			0
$190$	−7.92604	−	7.92604i	−0.575015	−	0.575015i
$191$			9.37809i			0.678575i	0.940683	+	0.339287i	$0.110186\pi$
$191$			9.37809i			0.678575i	−0.940683	+	0.339287i	$0.889814\pi$
$192$		0			0
$193$	−4.25587	−	4.25587i	−0.306344	−	0.306344i	0.537145	−	0.843490i	$-0.319503\pi$
$193$	−4.25587	−	4.25587i	−0.306344	−	0.306344i	−0.843490	+	0.537145i	$0.819503\pi$
$194$	−4.43969			−0.318751
$195$		0			0
$196$	−5.63091			−0.402208
$197$	−3.88777	−	3.88777i	−0.276992	−	0.276992i	0.554915	−	0.831907i	$-0.312751\pi$
$197$	−3.88777	−	3.88777i	−0.276992	−	0.276992i	−0.831907	+	0.554915i	$0.812751\pi$
$198$		0			0
$199$		−	20.6546i		−	1.46416i	−0.681217	−	0.732082i	$-0.738549\pi$
$199$		−	20.6546i		−	1.46416i	0.681217	−	0.732082i	$-0.261451\pi$
$200$	9.97054	+	9.97054i	0.705024	+	0.705024i
$201$		0			0
$202$	3.45150	+	3.45150i	0.242847	+	0.242847i
$203$	5.53301	−	5.53301i	0.388341	−	0.388341i
$204$		0			0
$205$		−	14.5747i		−	1.01794i
$206$	5.36015	−	5.36015i	0.373459	−	0.373459i
$207$		0			0
$208$	−3.38281	−	1.24764i	−0.234556	−	0.0865084i
$209$		−	4.71810i		−	0.326358i
$210$		0			0
$211$	−8.78470			−0.604764			−0.302382	−	0.953187i	$-0.597782\pi$
$211$	−8.78470			−0.604764			−0.302382	+	0.953187i	$0.597782\pi$
$212$	8.05668			0.553335
$213$		0			0
$214$	3.35188	−	3.35188i	0.229130	−	0.229130i
$215$	19.1910	−	19.1910i	1.30882	−	1.30882i
$216$		0			0
$217$	9.33527			0.633719
$218$	10.4554			0.708131
$219$		0			0
$220$			8.03972i			0.542038i
$221$	−26.9361	−	9.93455i	−1.81192	−	0.668270i
$222$		0			0
$223$	−16.8918	+	16.8918i	−1.13116	+	1.13116i	−0.141174	+	0.989985i	$0.545088\pi$
$223$	−16.8918	+	16.8918i	−1.13116	+	1.13116i	−0.989985	+	0.141174i	$0.954912\pi$
$224$			3.55400i			0.237462i
$225$		0			0
$226$	−0.790870	+	0.790870i	−0.0526079	+	0.0526079i
$227$	2.59459	+	2.59459i	0.172209	+	0.172209i	0.787949	−	0.615740i	$-0.211143\pi$
$227$	2.59459	+	2.59459i	0.172209	+	0.172209i	−0.615740	+	0.787949i	$0.711143\pi$
$228$		0			0
$229$	−5.71471	−	5.71471i	−0.377638	−	0.377638i	0.492611	−	0.870250i	$-0.336043\pi$
$229$	−5.71471	−	5.71471i	−0.377638	−	0.377638i	−0.870250	+	0.492611i	$0.836043\pi$
$230$			19.9960i			1.31850i
$231$		0			0
$232$	−1.55684	−	1.55684i	−0.102212	−	0.102212i
$233$	−5.51719			−0.361443			−0.180721	−	0.983534i	$-0.557843\pi$
$233$	−5.51719			−0.361443			−0.180721	+	0.983534i	$0.557843\pi$
$234$		0			0
$235$	−15.0658			−0.982785
$236$	9.17514	+	9.17514i	0.597251	+	0.597251i
$237$		0			0
$238$			28.2993i			1.83437i
$239$	0.973712	+	0.973712i	0.0629842	+	0.0629842i	0.737897	−	0.674913i	$-0.235819\pi$
$239$	0.973712	+	0.973712i	0.0629842	+	0.0629842i	−0.674913	+	0.737897i	$0.735819\pi$
$240$		0			0
$241$	−10.2868	−	10.2868i	−0.662632	−	0.662632i	0.293368	−	0.956000i	$-0.405224\pi$
$241$	−10.2868	−	10.2868i	−0.662632	−	0.662632i	−0.956000	+	0.293368i	$0.905224\pi$
$242$	5.38529	−	5.38529i	0.346179	−	0.346179i
$243$		0			0
$244$		−	6.76562i		−	0.433124i
$245$	−17.4015	+	17.4015i	−1.11174	+	1.11174i
$246$		0			0
$247$	8.39764	−	3.87227i	0.534329	−	0.246387i
$248$		−	2.62669i		−	0.166795i
$249$		0			0
$250$	39.7728			2.51545
$251$	19.2774			1.21678			0.608391	−	0.793638i	$-0.291815\pi$
$251$	19.2774			1.21678			0.608391	+	0.793638i	$0.291815\pi$
$252$		0			0
$253$	−5.95149	+	5.95149i	−0.374167	+	0.374167i
$254$	−11.9103	+	11.9103i	−0.747321	+	0.747321i
$255$		0			0
$256$	1.00000			0.0625000
$257$	13.1347			0.819323			0.409662	−	0.912238i	$-0.365647\pi$
$257$	13.1347			0.819323			0.409662	+	0.912238i	$0.365647\pi$
$258$		0			0
$259$		−	12.0447i		−	0.748420i
$260$	−14.3097	+	6.59840i	−0.887450	+	0.409216i
$261$		0			0
$262$	−4.98309	+	4.98309i	−0.307856	+	0.307856i
$263$		−	12.9572i		−	0.798976i	−0.916738	−	0.399488i	$-0.869188\pi$
$263$		−	12.9572i		−	0.798976i	0.916738	−	0.399488i	$-0.130812\pi$
$264$		0			0
$265$	24.8979	−	24.8979i	1.52947	−	1.52947i
$266$	−6.44542	−	6.44542i	−0.395194	−	0.395194i
$267$		0			0
$268$	4.76607	+	4.76607i	0.291134	+	0.291134i
$269$		−	6.46246i		−	0.394023i	−0.980401	−	0.197012i	$-0.936876\pi$
$269$		−	6.46246i		−	0.394023i	0.980401	−	0.197012i	$-0.0631237\pi$
$270$		0			0
$271$	1.66930	+	1.66930i	0.101403	+	0.101403i	0.755988	−	0.654585i	$-0.227157\pi$
$271$	1.66930	+	1.66930i	0.101403	+	0.101403i	−0.654585	+	0.755988i	$0.727157\pi$
$272$	7.96266			0.482807
$273$		0			0
$274$	13.8137			0.834514
$275$	18.3416	+	18.3416i	1.10604	+	1.10604i
$276$		0			0
$277$			5.19050i			0.311867i	0.987768	+	0.155934i	$0.0498386\pi$
$277$			5.19050i			0.311867i	−0.987768	+	0.155934i	$0.950161\pi$
$278$	−12.1626	−	12.1626i	−0.729466	−	0.729466i
$279$		0			0
$280$	10.9831	+	10.9831i	0.656365	+	0.656365i
$281$	9.69297	−	9.69297i	0.578234	−	0.578234i	−0.356182	−	0.934416i	$-0.615922\pi$
$281$	9.69297	−	9.69297i	0.578234	−	0.578234i	0.934416	+	0.356182i	$0.115922\pi$
$282$		0			0
$283$			11.8852i			0.706502i	0.935529	+	0.353251i	$0.114924\pi$
$283$			11.8852i			0.706502i	−0.935529	+	0.353251i	$0.885076\pi$
$284$	−7.32632	+	7.32632i	−0.434737	+	0.434737i
$285$		0			0
$286$	−6.22295	−	2.29514i	−0.367971	−	0.135714i
$287$		−	11.8521i		−	0.699607i
$288$		0			0
$289$	46.4039			2.72964
$290$	−9.62236			−0.565044
$291$		0			0
$292$	−5.48780	+	5.48780i	−0.321149	+	0.321149i
$293$	2.46536	−	2.46536i	0.144028	−	0.144028i	−0.631416	−	0.775444i	$-0.717526\pi$
$293$	2.46536	−	2.46536i	0.144028	−	0.144028i	0.775444	+	0.631416i	$0.217526\pi$
$294$		0			0
$295$	56.7087			3.30171
$296$	−3.38905			−0.196985
$297$		0			0
$298$		−	5.05900i		−	0.293060i
$299$	−15.4774	−	5.70837i	−0.895084	−	0.330123i
$300$		0			0
$301$	15.6061	−	15.6061i	0.899518	−	0.899518i
$302$			17.8382i			1.02648i
$303$		0			0
$304$	−1.81357	+	1.81357i	−0.104015	+	0.104015i
$305$	−20.9081	−	20.9081i	−1.19719	−	1.19719i
$306$		0			0
$307$	−5.84034	−	5.84034i	−0.333326	−	0.333326i	0.520522	−	0.853848i	$-0.325737\pi$
$307$	−5.84034	−	5.84034i	−0.333326	−	0.333326i	−0.853848	+	0.520522i	$0.825737\pi$
$308$			6.53787i			0.372529i
$309$		0			0
$310$	−8.11739	−	8.11739i	−0.461037	−	0.461037i
$311$	−20.8091			−1.17998			−0.589988	−	0.807412i	$-0.700867\pi$
$311$	−20.8091			−1.17998			−0.589988	+	0.807412i	$0.700867\pi$
$312$		0			0
$313$	−30.9223			−1.74783			−0.873916	−	0.486078i	$-0.838427\pi$
$313$	−30.9223			−1.74783			−0.873916	+	0.486078i	$0.838427\pi$
$314$	−2.98451	−	2.98451i	−0.168426	−	0.168426i
$315$		0			0
$316$		−	2.87513i		−	0.161738i
$317$	22.5211	+	22.5211i	1.26491	+	1.26491i	0.948684	+	0.316226i	$0.102416\pi$
$317$	22.5211	+	22.5211i	1.26491	+	1.26491i	0.316226	+	0.948684i	$0.397584\pi$
$318$		0			0
$319$	−2.86393	−	2.86393i	−0.160350	−	0.160350i
$320$	3.09035	−	3.09035i	0.172756	−	0.172756i
$321$		0			0
$322$			16.2607i			0.906173i
$323$	−14.4408	+	14.4408i	−0.803509	+	0.803509i
$324$		0			0
$325$	−17.5923	+	47.6992i	−0.975848	+	2.64588i
$326$		−	11.3973i		−	0.631238i
$327$		0			0
$328$	−3.33486			−0.184137
$329$	−12.2515			−0.675444
$330$		0			0
$331$	−19.1783	+	19.1783i	−1.05413	+	1.05413i	−0.0556841	+	0.998448i	$0.517734\pi$
$331$	−19.1783	+	19.1783i	−1.05413	+	1.05413i	−0.998448	+	0.0556841i	$0.982266\pi$
$332$	−7.25822	+	7.25822i	−0.398346	+	0.398346i
$333$		0			0
$334$	−2.10951			−0.115427
$335$	29.4576			1.60944
$336$		0			0
$337$			15.5870i			0.849079i	0.905409	+	0.424540i	$0.139564\pi$
$337$			15.5870i			0.849079i	−0.905409	+	0.424540i	$0.860436\pi$
$338$	−1.02227	−	12.9597i	−0.0556044	−	0.704917i
$339$		0			0
$340$	24.6074	−	24.6074i	1.33452	−	1.33452i
$341$		−	4.83201i		−	0.261668i
$342$		0			0
$343$	3.44061	−	3.44061i	0.185775	−	0.185775i
$344$	−4.39113	−	4.39113i	−0.236754	−	0.236754i
$345$		0			0
$346$	6.46093	+	6.46093i	0.347342	+	0.347342i
$347$		−	13.4196i		−	0.720404i	−0.932874	−	0.360202i	$-0.882708\pi$
$347$		−	13.4196i		−	0.720404i	0.932874	−	0.360202i	$-0.117292\pi$
$348$		0			0
$349$	−13.8258	−	13.8258i	−0.740080	−	0.740080i	0.232513	−	0.972593i	$-0.425305\pi$
$349$	−13.8258	−	13.8258i	−0.740080	−	0.740080i	−0.972593	+	0.232513i	$0.925305\pi$
$350$	50.1131			2.67866
$351$		0			0
$352$	1.83958			0.0980499
$353$	−9.67851	−	9.67851i	−0.515135	−	0.515135i	0.400960	−	0.916095i	$-0.368677\pi$
$353$	−9.67851	−	9.67851i	−0.515135	−	0.515135i	−0.916095	+	0.400960i	$0.868677\pi$
$354$		0			0
$355$			45.2817i			2.40330i
$356$	4.33187	+	4.33187i	0.229589	+	0.229589i
$357$		0			0
$358$	−7.49167	−	7.49167i	−0.395947	−	0.395947i
$359$	8.13457	−	8.13457i	0.429326	−	0.429326i	−0.459073	−	0.888399i	$-0.651818\pi$
$359$	8.13457	−	8.13457i	0.429326	−	0.429326i	0.888399	+	0.459073i	$0.151818\pi$
$360$		0			0
$361$			12.4219i			0.653786i
$362$	−11.7330	+	11.7330i	−0.616671	+	0.616671i
$363$		0			0
$364$	−11.6366	+	5.36579i	−0.609923	+	0.281244i
$365$			33.9184i			1.77537i
$366$		0			0
$367$	5.65303			0.295086			0.147543	−	0.989056i	$-0.452864\pi$
$367$	5.65303			0.295086			0.147543	+	0.989056i	$0.452864\pi$
$368$	4.57533			0.238505
$369$		0			0
$370$	−10.4733	+	10.4733i	−0.544483	+	0.544483i
$371$	20.2469	−	20.2469i	1.05117	−	1.05117i
$372$		0			0
$373$	−20.0334			−1.03729			−0.518644	−	0.854990i	$-0.673563\pi$
$373$	−20.0334			−1.03729			−0.518644	+	0.854990i	$0.673563\pi$
$374$	14.6479			0.757427
$375$		0			0
$376$			3.44723i			0.177777i
$377$	2.74694	−	7.44795i	0.141475	−	0.383589i
$378$		0			0
$379$	16.6434	−	16.6434i	0.854914	−	0.854914i	−0.135820	−	0.990734i	$-0.543367\pi$
$379$	16.6434	−	16.6434i	0.854914	−	0.854914i	0.990734	+	0.135820i	$0.0433668\pi$
$380$			11.2091i			0.575015i
$381$		0			0
$382$	6.63131	−	6.63131i	0.339287	−	0.339287i
$383$	2.11934	+	2.11934i	0.108293	+	0.108293i	0.759177	−	0.650884i	$-0.225602\pi$
$383$	2.11934	+	2.11934i	0.108293	+	0.108293i	−0.650884	+	0.759177i	$0.725602\pi$
$384$		0			0
$385$	20.2043	+	20.2043i	1.02970	+	1.02970i
$386$			6.01871i			0.306344i
$387$		0			0
$388$	3.13933	+	3.13933i	0.159376	+	0.159376i
$389$	26.8934			1.36355			0.681776	−	0.731561i	$-0.261208\pi$
$389$	26.8934			1.36355			0.681776	+	0.731561i	$0.261208\pi$
$390$		0			0
$391$	36.4318			1.84243
$392$	3.98165	+	3.98165i	0.201104	+	0.201104i
$393$		0			0
$394$			5.49814i			0.276992i
$395$	−8.88513	−	8.88513i	−0.447060	−	0.447060i
$396$		0			0
$397$	10.0839	+	10.0839i	0.506096	+	0.506096i	0.913326	−	0.407229i	$-0.133505\pi$
$397$	10.0839	+	10.0839i	0.506096	+	0.506096i	−0.407229	+	0.913326i	$0.633505\pi$
$398$	−14.6050	+	14.6050i	−0.732082	+	0.732082i
$399$		0			0
$400$		−	14.1005i		−	0.705024i
$401$	−21.4453	+	21.4453i	−1.07093	+	1.07093i	−0.0736421	+	0.997285i	$0.523462\pi$
$401$	−21.4453	+	21.4453i	−1.07093	+	1.07093i	−0.997285	+	0.0736421i	$0.976538\pi$
$402$		0			0
$403$	8.60038	−	3.96576i	0.428415	−	0.197548i
$404$		−	4.88116i		−	0.242847i
$405$		0			0
$406$	−7.82486			−0.388341
$407$	−6.23443			−0.309029
$408$		0			0
$409$	6.53454	−	6.53454i	0.323112	−	0.323112i	−0.526848	−	0.849960i	$-0.676626\pi$
$409$	6.53454	−	6.53454i	0.323112	−	0.323112i	0.849960	+	0.526848i	$0.176626\pi$
$410$	−10.3059	+	10.3059i	−0.508971	+	0.508971i
$411$		0			0
$412$	−7.58040			−0.373459
$413$	46.1153			2.26918
$414$		0			0
$415$			44.8608i			2.20213i
$416$	1.50979	+	3.27422i	0.0740236	+	0.160532i
$417$		0			0
$418$	−3.33620	+	3.33620i	−0.163179	+	0.163179i
$419$		−	18.9957i		−	0.927999i	−0.885835	−	0.464000i	$-0.846414\pi$
$419$		−	18.9957i		−	0.927999i	0.885835	−	0.464000i	$-0.153586\pi$
$420$		0			0
$421$	7.67992	−	7.67992i	0.374296	−	0.374296i	−0.494743	−	0.869039i	$-0.664738\pi$
$421$	7.67992	−	7.67992i	0.374296	−	0.374296i	0.869039	+	0.494743i	$0.164738\pi$
$422$	6.21172	+	6.21172i	0.302382	+	0.302382i
$423$		0			0
$424$	−5.69693	−	5.69693i	−0.276668	−	0.276668i
$425$		−	112.277i		−	5.44625i
$426$		0			0
$427$	−17.0024	−	17.0024i	−0.822803	−	0.822803i
$428$	−4.74027			−0.229130
$429$		0			0
$430$	−27.1402			−1.30882
$431$	24.3980	+	24.3980i	1.17521	+	1.17521i	0.980950	+	0.194260i	$0.0622306\pi$
$431$	24.3980	+	24.3980i	1.17521	+	1.17521i	0.194260	+	0.980950i	$0.437769\pi$
$432$		0			0
$433$			13.5640i			0.651843i	0.945397	+	0.325921i	$0.105674\pi$
$433$			13.5640i			0.651843i	−0.945397	+	0.325921i	$0.894326\pi$
$434$	−6.60103	−	6.60103i	−0.316860	−	0.316860i
$435$		0			0
$436$	−7.39311	−	7.39311i	−0.354066	−	0.354066i
$437$	−8.29766	+	8.29766i	−0.396931	+	0.396931i
$438$		0			0
$439$		−	38.0568i		−	1.81635i	−0.418590	−	0.908175i	$-0.637475\pi$
$439$		−	38.0568i		−	1.81635i	0.418590	−	0.908175i	$-0.362525\pi$
$440$	5.68494	−	5.68494i	0.271019	−	0.271019i
$441$		0			0
$442$	12.0219	+	26.0715i	0.571826	+	1.24010i
$443$			15.5746i			0.739972i	0.929037	+	0.369986i	$0.120638\pi$
$443$			15.5746i			0.739972i	−0.929037	+	0.369986i	$0.879362\pi$
$444$		0			0
$445$	26.7740			1.26921
$446$	23.8886			1.13116
$447$		0			0
$448$	2.51306	−	2.51306i	0.118731	−	0.118731i
$449$	2.64196	−	2.64196i	0.124682	−	0.124682i	−0.642012	−	0.766694i	$-0.721900\pi$
$449$	2.64196	−	2.64196i	0.124682	−	0.124682i	0.766694	+	0.642012i	$0.221900\pi$
$450$		0			0
$451$	−6.13475			−0.288874
$452$	1.11846			0.0526079
$453$		0			0
$454$		−	3.66931i		−	0.172209i
$455$	−19.3789	+	52.5432i	−0.908497	+	2.46326i
$456$		0			0
$457$	−8.84419	+	8.84419i	−0.413714	+	0.413714i	−0.883030	−	0.469316i	$-0.844500\pi$
$457$	−8.84419	+	8.84419i	−0.413714	+	0.413714i	0.469316	+	0.883030i	$0.344500\pi$
$458$			8.08181i			0.377638i
$459$		0			0
$460$	14.1393	−	14.1393i	0.659250	−	0.659250i
$461$	−5.63360	−	5.63360i	−0.262383	−	0.262383i	0.563639	−	0.826021i	$-0.309401\pi$
$461$	−5.63360	−	5.63360i	−0.262383	−	0.262383i	−0.826021	+	0.563639i	$0.809401\pi$
$462$		0			0
$463$	−20.5655	−	20.5655i	−0.955759	−	0.955759i	0.0433029	−	0.999062i	$-0.486212\pi$
$463$	−20.5655	−	20.5655i	−0.955759	−	0.955759i	−0.999062	+	0.0433029i	$0.986212\pi$
$464$			2.20171i			0.102212i
$465$		0			0
$466$	3.90124	+	3.90124i	0.180721	+	0.180721i
$467$	−35.1220			−1.62525			−0.812627	−	0.582784i	$-0.801963\pi$
$467$	−35.1220			−1.62525			−0.812627	+	0.582784i	$0.801963\pi$
$468$		0			0
$469$	23.9548			1.10613
$470$	10.6531	+	10.6531i	0.491392	+	0.491392i
$471$		0			0
$472$		−	12.9756i		−	0.597251i
$473$	−8.07783	−	8.07783i	−0.371419	−	0.371419i
$474$		0			0
$475$	25.5722	+	25.5722i	1.17333	+	1.17333i
$476$	20.0106	−	20.0106i	0.917185	−	0.917185i
$477$		0			0
$478$		−	1.37704i		−	0.0629842i
$479$	10.3373	−	10.3373i	0.472325	−	0.472325i	−0.430341	−	0.902666i	$-0.641607\pi$
$479$	10.3373	−	10.3373i	0.472325	−	0.472325i	0.902666	+	0.430341i	$0.141607\pi$
$480$		0			0
$481$	−5.11676	−	11.0965i	−0.233304	−	0.505957i
$482$			14.5477i			0.662632i
$483$		0			0
$484$	−7.61594			−0.346179
$485$	19.4033			0.881056
$486$		0			0
$487$	−2.50980	+	2.50980i	−0.113730	+	0.113730i	−0.761682	−	0.647952i	$-0.775626\pi$
$487$	−2.50980	+	2.50980i	−0.113730	+	0.113730i	0.647952	+	0.761682i	$0.275626\pi$
$488$	−4.78401	+	4.78401i	−0.216562	+	0.216562i
$489$		0			0
$490$	24.6094			1.11174
$491$	−31.6248			−1.42721			−0.713604	−	0.700550i	$-0.752938\pi$
$491$	−31.6248			−1.42721			−0.713604	+	0.700550i	$0.752938\pi$
$492$		0			0
$493$			17.5314i			0.789576i
$494$	−8.67613	−	3.19992i	−0.390358	−	0.143971i
$495$		0			0
$496$	−1.85735	+	1.85735i	−0.0833976	+	0.0833976i
$497$			36.8229i			1.65173i
$498$		0			0
$499$	23.1304	−	23.1304i	1.03546	−	1.03546i	0.0361094	−	0.999348i	$-0.488504\pi$
$499$	23.1304	−	23.1304i	1.03546	−	1.03546i	0.999348	−	0.0361094i	$-0.0114965\pi$
$500$	−28.1236	−	28.1236i	−1.25773	−	1.25773i
$501$		0			0
$502$	−13.6312	−	13.6312i	−0.608391	−	0.608391i
$503$			8.63482i			0.385008i	0.981296	+	0.192504i	$0.0616608\pi$
$503$			8.63482i			0.385008i	−0.981296	+	0.192504i	$0.938339\pi$
$504$		0			0
$505$	−15.0845	−	15.0845i	−0.671250	−	0.671250i
$506$	8.41668			0.374167
$507$		0			0
$508$	16.8438			0.747321
$509$	−14.7012	−	14.7012i	−0.651618	−	0.651618i	0.301765	−	0.953382i	$-0.402424\pi$
$509$	−14.7012	−	14.7012i	−0.651618	−	0.651618i	−0.953382	+	0.301765i	$0.902424\pi$
$510$		0			0
$511$			27.5823i			1.22017i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−9.28767	−	9.28767i	−0.409662	−	0.409662i
$515$	−23.4261	+	23.4261i	−1.03228	+	1.03228i
$516$		0			0
$517$			6.34146i			0.278897i
$518$	−8.51688	+	8.51688i	−0.374210	+	0.374210i
$519$		0			0
$520$	14.7843	+	5.45271i	0.648333	+	0.239117i
$521$		−	3.91650i		−	0.171585i	−0.996313	−	0.0857926i	$-0.972658\pi$
$521$		−	3.91650i		−	0.171585i	0.996313	−	0.0857926i	$-0.0273422\pi$
$522$		0			0
$523$	−6.87668			−0.300696			−0.150348	−	0.988633i	$-0.548039\pi$
$523$	−6.87668			−0.300696			−0.150348	+	0.988633i	$0.548039\pi$
$524$	7.04715			0.307856
$525$		0			0
$526$	−9.16214	+	9.16214i	−0.399488	+	0.399488i
$527$	−14.7895	+	14.7895i	−0.644239	+	0.644239i
$528$		0			0
$529$	−2.06640			−0.0898435
$530$	−35.2110			−1.52947
$531$		0			0
$532$			9.11520i			0.395194i
$533$	−5.03495	−	10.9191i	−0.218088	−	0.472958i
$534$		0			0
$535$	−14.6491	+	14.6491i	−0.633335	+	0.633335i
$536$		−	6.74024i		−	0.291134i
$537$		0			0
$538$	−4.56965	+	4.56965i	−0.197012	+	0.197012i
$539$	7.32457	+	7.32457i	0.315492	+	0.315492i
$540$		0			0
$541$	−24.5620	−	24.5620i	−1.05600	−	1.05600i	−0.998336	−	0.0576658i	$-0.981634\pi$
$541$	−24.5620	−	24.5620i	−1.05600	−	1.05600i	−0.0576658	−	0.998336i	$-0.518366\pi$
$542$		−	2.36075i		−	0.101403i
$543$		0			0
$544$	−5.63045	−	5.63045i	−0.241404	−	0.241404i
$545$	−45.6945			−1.95734
$546$		0			0
$547$	7.41566			0.317071			0.158535	−	0.987353i	$-0.449323\pi$
$547$	7.41566			0.317071			0.158535	+	0.987353i	$0.449323\pi$
$548$	−9.76774	−	9.76774i	−0.417257	−	0.417257i
$549$		0			0
$550$		−	25.9390i		−	1.10604i
$551$	−3.99294	−	3.99294i	−0.170105	−	0.170105i
$552$		0			0
$553$	−7.22535	−	7.22535i	−0.307253	−	0.307253i
$554$	3.67024	−	3.67024i	0.155934	−	0.155934i
$555$		0			0
$556$			17.2006i			0.729466i
$557$	−23.7606	+	23.7606i	−1.00677	+	1.00677i	−0.00679291	+	0.999977i	$0.502162\pi$
$557$	−23.7606	+	23.7606i	−1.00677	+	1.00677i	−0.999977	+	0.00679291i	$0.997838\pi$
$558$		0			0
$559$	7.74784	−	21.0072i	0.327699	−	0.888510i
$560$		−	15.5324i		−	0.656365i
$561$		0			0
$562$	−13.7079			−0.578234
$563$	38.0827			1.60499			0.802496	−	0.596657i	$-0.203505\pi$
$563$	38.0827			1.60499			0.802496	+	0.596657i	$0.203505\pi$
$564$		0			0
$565$	3.45642	−	3.45642i	0.145413	−	0.145413i
$566$	8.40411	−	8.40411i	0.353251	−	0.353251i
$567$		0			0
$568$	10.3610			0.434737
$569$	−20.6163			−0.864281			−0.432141	−	0.901806i	$-0.642242\pi$
$569$	−20.6163			−0.864281			−0.432141	+	0.901806i	$0.642242\pi$
$570$		0			0
$571$			29.2202i			1.22283i	0.791311	+	0.611414i	$0.209399\pi$
$571$			29.2202i			1.22283i	−0.791311	+	0.611414i	$0.790601\pi$
$572$	2.77738	+	6.02319i	0.116128	+	0.251842i
$573$		0			0
$574$	−8.38070	+	8.38070i	−0.349804	+	0.349804i
$575$		−	64.5143i		−	2.69043i
$576$		0			0
$577$	−8.66402	+	8.66402i	−0.360688	+	0.360688i	−0.864066	−	0.503378i	$-0.832090\pi$
$577$	−8.66402	+	8.66402i	−0.360688	+	0.360688i	0.503378	+	0.864066i	$0.332090\pi$
$578$	−32.8125	−	32.8125i	−1.36482	−	1.36482i
$579$		0			0
$580$	6.80403	+	6.80403i	0.282522	+	0.282522i
$581$			36.4806i			1.51347i
$582$		0			0
$583$	−10.4800	−	10.4800i	−0.434036	−	0.434036i
$584$	7.76093			0.321149
$585$		0			0
$586$	−3.48655			−0.144028
$587$	3.98421	+	3.98421i	0.164446	+	0.164446i	0.784533	−	0.620087i	$-0.212903\pi$
$587$	3.98421	+	3.98421i	0.164446	+	0.164446i	−0.620087	+	0.784533i	$0.712903\pi$
$588$		0			0
$589$		−	6.73687i		−	0.277588i
$590$	−40.0991	−	40.0991i	−1.65085	−	1.65085i
$591$		0			0
$592$	2.39642	+	2.39642i	0.0984923	+	0.0984923i
$593$	15.0310	−	15.0310i	0.617247	−	0.617247i	−0.327577	−	0.944824i	$-0.606232\pi$
$593$	15.0310	−	15.0310i	0.617247	−	0.617247i	0.944824	+	0.327577i	$0.106232\pi$
$594$		0			0
$595$		−	123.679i		−	5.07036i
$596$	−3.57725	+	3.57725i	−0.146530	+	0.146530i
$597$		0			0
$598$	6.90778	+	14.9806i	0.282480	+	0.612604i
$599$			30.7247i			1.25538i	0.778465	+	0.627688i	$0.215999\pi$
$599$			30.7247i			1.25538i	−0.778465	+	0.627688i	$0.784001\pi$
$600$		0			0
$601$	−2.52289			−0.102911			−0.0514553	−	0.998675i	$-0.516386\pi$
$601$	−2.52289			−0.102911			−0.0514553	+	0.998675i	$0.516386\pi$
$602$	−22.0703			−0.899518
$603$		0			0
$604$	12.6135	−	12.6135i	0.513238	−	0.513238i
$605$	−23.5359	+	23.5359i	−0.956871	+	0.956871i
$606$		0			0
$607$	−38.9224			−1.57981			−0.789907	−	0.613227i	$-0.789871\pi$
$607$	−38.9224			−1.57981			−0.789907	+	0.613227i	$0.789871\pi$
$608$	2.56477			0.104015
$609$		0			0
$610$			29.5685i			1.19719i
$611$	−11.2870	+	5.20460i	−0.456623	+	0.210555i
$612$		0			0
$613$	−9.25966	+	9.25966i	−0.373994	+	0.373994i	−0.868930	−	0.494936i	$-0.835192\pi$
$613$	−9.25966	+	9.25966i	−0.373994	+	0.373994i	0.494936	+	0.868930i	$0.335192\pi$
$614$			8.25949i			0.333326i
$615$		0			0
$616$	4.62297	−	4.62297i	0.186265	−	0.186265i
$617$	30.3934	+	30.3934i	1.22359	+	1.22359i	0.966345	+	0.257248i	$0.0828159\pi$
$617$	30.3934	+	30.3934i	1.22359	+	1.22359i	0.257248	+	0.966345i	$0.417184\pi$
$618$		0			0
$619$	−13.2648	−	13.2648i	−0.533156	−	0.533156i	0.388354	−	0.921510i	$-0.373044\pi$
$619$	−13.2648	−	13.2648i	−0.533156	−	0.533156i	−0.921510	+	0.388354i	$0.873044\pi$
$620$			11.4797i			0.461037i
$621$		0			0
$622$	14.7142	+	14.7142i	0.589988	+	0.589988i
$623$	21.7725			0.872296
$624$		0			0
$625$	−103.321			−4.13285
$626$	21.8654	+	21.8654i	0.873916	+	0.873916i
$627$		0			0
$628$			4.22074i			0.168426i
$629$	19.0819	+	19.0819i	0.760845	+	0.760845i
$630$		0			0
$631$	−27.8937	−	27.8937i	−1.11043	−	1.11043i	−0.993092	−	0.117339i	$-0.962564\pi$
$631$	−27.8937	−	27.8937i	−1.11043	−	1.11043i	−0.117339	−	0.993092i	$-0.537436\pi$
$632$	−2.03302	+	2.03302i	−0.0808692	+	0.0808692i
$633$		0			0
$634$		−	31.8496i		−	1.26491i
$635$	52.0530	−	52.0530i	2.06566	−	2.06566i
$636$		0			0
$637$	−7.02536	+	19.0483i	−0.278355	+	0.754720i
$638$			4.05021i			0.160350i
$639$		0			0
$640$	−4.37041			−0.172756
$641$	1.53862			0.0607720			0.0303860	−	0.999538i	$-0.490326\pi$
$641$	1.53862			0.0607720			0.0303860	+	0.999538i	$0.490326\pi$
$642$		0			0
$643$	21.9382	−	21.9382i	0.865157	−	0.865157i	−0.126775	−	0.991932i	$-0.540463\pi$
$643$	21.9382	−	21.9382i	0.865157	−	0.865157i	0.991932	+	0.126775i	$0.0404626\pi$
$644$	11.4981	−	11.4981i	0.453087	−	0.453087i
$645$		0			0
$646$	20.4224			0.803509
$647$	−2.31362			−0.0909579			−0.0454790	−	0.998965i	$-0.514481\pi$
$647$	−2.31362			−0.0909579			−0.0454790	+	0.998965i	$0.514481\pi$
$648$		0			0
$649$		−	23.8697i		−	0.936966i
$650$	46.1681	−	21.2888i	1.81086	−	0.835014i
$651$		0			0
$652$	−8.05910	+	8.05910i	−0.315619	+	0.315619i
$653$			8.64626i			0.338354i	0.985586	+	0.169177i	$0.0541110\pi$
$653$			8.64626i			0.338354i	−0.985586	+	0.169177i	$0.945889\pi$
$654$		0			0
$655$	21.7781	−	21.7781i	0.850942	−	0.850942i
$656$	2.35810	+	2.35810i	0.0920685	+	0.0920685i
$657$		0			0
$658$	8.66308	+	8.66308i	0.337722	+	0.337722i
$659$		−	25.6721i		−	1.00004i	−0.866013	−	0.500022i	$-0.833325\pi$
$659$		−	25.6721i		−	1.00004i	0.866013	−	0.500022i	$-0.166675\pi$
$660$		0			0
$661$	10.7953	+	10.7953i	0.419888	+	0.419888i	0.885165	−	0.465277i	$-0.154045\pi$
$661$	10.7953	+	10.7953i	0.419888	+	0.419888i	−0.465277	+	0.885165i	$0.654045\pi$
$662$	27.1222			1.05413
$663$		0			0
$664$	10.2647			0.398346
$665$	28.1691	+	28.1691i	1.09235	+	1.09235i
$666$		0			0
$667$			10.0735i			0.390048i
$668$	1.49165	+	1.49165i	0.0577136	+	0.0577136i
$669$		0			0
$670$	−20.8297	−	20.8297i	−0.804721	−	0.804721i
$671$	−8.80058	+	8.80058i	−0.339742	+	0.339742i
$672$		0			0
$673$			28.5527i			1.10063i	0.834958	+	0.550313i	$0.185492\pi$
$673$			28.5527i			1.10063i	−0.834958	+	0.550313i	$0.814508\pi$
$674$	11.0217	−	11.0217i	0.424540	−	0.424540i
$675$		0			0
$676$	−8.44107	+	9.88678i	−0.324656	+	0.380261i
$677$			16.5768i			0.637096i	0.947907	+	0.318548i	$0.103195\pi$
$677$			16.5768i			0.637096i	−0.947907	+	0.318548i	$0.896805\pi$
$678$		0			0
$679$	15.7786			0.605529
$680$	−34.8001			−1.33452
$681$		0			0
$682$	−3.41675	+	3.41675i	−0.130834	+	0.130834i
$683$	−16.5837	+	16.5837i	−0.634558	+	0.634558i	−0.949208	−	0.314650i	$-0.898113\pi$
$683$	−16.5837	+	16.5837i	−0.634558	+	0.634558i	0.314650	+	0.949208i	$0.398113\pi$
$684$		0			0
$685$	−60.3714			−2.30667
$686$	−4.86576			−0.185775
$687$		0			0
$688$			6.20999i			0.236754i
$689$	10.0519	−	27.2542i	0.382945	−	1.03830i
$690$		0			0
$691$	−15.1382	+	15.1382i	−0.575886	+	0.575886i	−0.933767	−	0.357881i	$-0.883499\pi$
$691$	−15.1382	+	15.1382i	−0.575886	+	0.575886i	0.357881	+	0.933767i	$0.383499\pi$
$692$		−	9.13714i		−	0.347342i
$693$		0			0
$694$	−9.48912	+	9.48912i	−0.360202	+	0.360202i
$695$	53.1557	+	53.1557i	2.01631	+	2.01631i
$696$		0			0
$697$	18.7768	+	18.7768i	0.711221	+	0.711221i
$698$			19.5527i			0.740080i
$699$		0			0
$700$	−35.4353	−	35.4353i	−1.33933	−	1.33933i
$701$	−21.7545			−0.821654			−0.410827	−	0.911713i	$-0.634760\pi$
$701$	−21.7545			−0.821654			−0.410827	+	0.911713i	$0.634760\pi$
$702$		0			0
$703$	−8.69215			−0.327831
$704$	−1.30078	−	1.30078i	−0.0490250	−	0.0490250i
$705$		0			0
$706$			13.6875i			0.515135i
$707$	−12.2666	−	12.2666i	−0.461334	−	0.461334i
$708$		0			0
$709$	−16.1111	−	16.1111i	−0.605066	−	0.605066i	0.336586	−	0.941653i	$-0.390728\pi$
$709$	−16.1111	−	16.1111i	−0.605066	−	0.605066i	−0.941653	+	0.336586i	$0.890728\pi$
$710$	32.0190	−	32.0190i	1.20165	−	1.20165i
$711$		0			0
$712$		−	6.12619i		−	0.229589i
$713$	−8.49799	+	8.49799i	−0.318252	+	0.318252i
$714$		0			0
$715$	27.1968	+	10.0307i	1.01710	+	0.375127i
$716$			10.5948i			0.395947i
$717$		0			0
$718$	−11.5040			−0.429326
$719$	−5.99109			−0.223430			−0.111715	−	0.993740i	$-0.535634\pi$
$719$	−5.99109			−0.223430			−0.111715	+	0.993740i	$0.535634\pi$
$720$		0			0
$721$	−19.0500	+	19.0500i	−0.709458	+	0.709458i
$722$	8.78364	−	8.78364i	0.326893	−	0.326893i
$723$		0			0
$724$	16.5929			0.616671
$725$	31.0451			1.15299
$726$		0			0
$727$		−	9.23878i		−	0.342647i	−0.985215	−	0.171324i	$-0.945196\pi$
$727$		−	9.23878i		−	0.342647i	0.985215	−	0.171324i	$-0.0548044\pi$
$728$	12.0225	+	4.43412i	0.445583	+	0.164339i
$729$		0			0
$730$	23.9839	−	23.9839i	0.887686	−	0.887686i
$731$			49.4480i			1.82890i
$732$		0			0
$733$	15.7923	−	15.7923i	0.583301	−	0.583301i	−0.352508	−	0.935809i	$-0.614671\pi$
$733$	15.7923	−	15.7923i	0.583301	−	0.583301i	0.935809	+	0.352508i	$0.114671\pi$
$734$	−3.99730	−	3.99730i	−0.147543	−	0.147543i
$735$		0			0
$736$	−3.23524	−	3.23524i	−0.119253	−	0.119253i
$737$		−	12.3992i		−	0.456731i
$738$		0			0
$739$	23.6222	+	23.6222i	0.868958	+	0.868958i	0.992357	−	0.123399i	$-0.0393796\pi$
$739$	23.6222	+	23.6222i	0.868958	+	0.868958i	−0.123399	+	0.992357i	$0.539380\pi$
$740$	14.8115			0.544483
$741$		0			0
$742$	−28.6334			−1.05117
$743$	−21.4254	−	21.4254i	−0.786022	−	0.786022i	0.194818	−	0.980839i	$-0.437589\pi$
$743$	−21.4254	−	21.4254i	−0.786022	−	0.786022i	−0.980839	+	0.194818i	$0.937589\pi$
$744$		0			0
$745$			22.1099i			0.810045i
$746$	14.1657	+	14.1657i	0.518644	+	0.518644i
$747$		0			0
$748$	−10.3577	−	10.3577i	−0.378714	−	0.378714i
$749$	−11.9126	+	11.9126i	−0.435276	+	0.435276i
$750$		0			0
$751$			5.78694i			0.211168i	0.994410	+	0.105584i	$0.0336712\pi$
$751$			5.78694i			0.211168i	−0.994410	+	0.105584i	$0.966329\pi$
$752$	2.43756	−	2.43756i	0.0888887	−	0.0888887i
$753$		0			0
$754$	−7.20888	+	3.32411i	−0.262532	+	0.121057i
$755$		−	77.9604i		−	2.83727i
$756$		0			0
$757$	40.9940			1.48995			0.744977	−	0.667091i	$-0.232461\pi$
$757$	40.9940			1.48995			0.744977	+	0.667091i	$0.232461\pi$
$758$	−23.5373			−0.854914
$759$		0			0
$760$	7.92604	−	7.92604i	0.287508	−	0.287508i
$761$	29.1856	−	29.1856i	1.05798	−	1.05798i	0.0597661	−	0.998212i	$-0.480965\pi$
$761$	29.1856	−	29.1856i	1.05798	−	1.05798i	0.998212	−	0.0597661i	$-0.0190355\pi$
$762$		0			0
$763$	−37.1586			−1.34523
$764$	−9.37809			−0.339287
$765$		0			0
$766$		−	2.99719i		−	0.108293i
$767$	42.4850	−	19.5904i	1.53405	−	0.707370i
$768$		0			0
$769$	27.5194	−	27.5194i	0.992375	−	0.992375i	−0.00759602	−	0.999971i	$-0.502418\pi$
$769$	27.5194	−	27.5194i	0.992375	−	0.992375i	0.999971	+	0.00759602i	$0.00241791\pi$
$770$		−	28.5731i		−	1.02970i
$771$		0			0
$772$	4.25587	−	4.25587i	0.153172	−	0.153172i
$773$	19.4578	+	19.4578i	0.699848	+	0.699848i	0.964378	−	0.264529i	$-0.0852166\pi$
$773$	19.4578	+	19.4578i	0.699848	+	0.699848i	−0.264529	+	0.964378i	$0.585217\pi$
$774$		0			0
$775$	26.1896	+	26.1896i	0.940757	+	0.940757i
$776$		−	4.43969i		−	0.159376i
$777$		0			0
$778$	−19.0165	−	19.0165i	−0.681776	−	0.681776i
$779$	−8.55317			−0.306449
$780$		0			0
$781$	19.0598			0.682015
$782$	−25.7611	−	25.7611i	−0.921216	−	0.921216i
$783$		0			0
$784$		−	5.63091i		−	0.201104i
$785$	13.0435	+	13.0435i	0.465544	+	0.465544i
$786$		0			0
$787$	26.8883	+	26.8883i	0.958465	+	0.958465i	0.999171	−	0.0407063i	$-0.0129608\pi$
$787$	26.8883	+	26.8883i	0.958465	+	0.958465i	−0.0407063	+	0.999171i	$0.512961\pi$
$788$	3.88777	−	3.88777i	0.138496	−	0.138496i
$789$		0			0
$790$			12.5655i			0.447060i
$791$	2.81075	−	2.81075i	0.0999388	−	0.0999388i
$792$		0			0
$793$	−22.8868	−	8.44107i	−0.812733	−	0.299751i
$794$		−	14.2608i		−	0.506096i
$795$		0			0
$796$	20.6546			0.732082
$797$	−14.6118			−0.517577			−0.258789	−	0.965934i	$-0.583323\pi$
$797$	−14.6118			−0.517577			−0.258789	+	0.965934i	$0.583323\pi$
$798$		0			0
$799$	19.4095	−	19.4095i	0.686657	−	0.686657i
$800$	−9.97054	+	9.97054i	−0.352512	+	0.352512i
$801$		0			0
$802$	30.3282			1.07093
$803$	14.2768			0.503819
$804$		0			0
$805$		−	71.0659i		−	2.50474i
$806$	−8.88560	−	3.27717i	−0.312982	−	0.115433i
$807$		0			0
$808$	−3.45150	+	3.45150i	−0.121423	+	0.121423i
$809$			32.4946i			1.14245i	0.820794	+	0.571224i	$0.193531\pi$
$809$			32.4946i			1.14245i	−0.820794	+	0.571224i	$0.806469\pi$
$810$		0			0
$811$	−11.9664	+	11.9664i	−0.420198	+	0.420198i	−0.885272	−	0.465074i	$-0.846028\pi$
$811$	−11.9664	+	11.9664i	−0.420198	+	0.420198i	0.465074	+	0.885272i	$0.346028\pi$
$812$	5.53301	+	5.53301i	0.194171	+	0.194171i
$813$		0			0
$814$	4.40841	+	4.40841i	0.154515	+	0.154515i
$815$			49.8108i			1.74480i
$816$		0			0
$817$	−11.2622	−	11.2622i	−0.394016	−	0.394016i
$818$	−9.24124			−0.323112
$819$		0			0
$820$	14.5747			0.508971
$821$	−22.3655	−	22.3655i	−0.780561	−	0.780561i	0.199365	−	0.979925i	$-0.436112\pi$
$821$	−22.3655	−	22.3655i	−0.780561	−	0.780561i	−0.979925	+	0.199365i	$0.936112\pi$
$822$		0			0
$823$		−	21.8009i		−	0.759933i	−0.925000	−	0.379966i	$-0.875936\pi$
$823$		−	21.8009i		−	0.759933i	0.925000	−	0.379966i	$-0.124064\pi$
$824$	5.36015	+	5.36015i	0.186730	+	0.186730i
$825$		0			0
$826$	−32.6084	−	32.6084i	−1.13459	−	1.13459i
$827$	−13.4359	+	13.4359i	−0.467212	+	0.467212i	−0.901010	−	0.433798i	$-0.857173\pi$
$827$	−13.4359	+	13.4359i	−0.467212	+	0.467212i	0.433798	+	0.901010i	$0.357173\pi$
$828$		0			0
$829$			52.1118i			1.80992i	0.425498	+	0.904959i	$0.360099\pi$
$829$			52.1118i			1.80992i	−0.425498	+	0.904959i	$0.639901\pi$
$830$	31.7214	−	31.7214i	1.10107	−	1.10107i
$831$		0			0
$832$	1.24764	−	3.38281i	0.0432542	−	0.117278i
$833$		−	44.8370i		−	1.55351i
$834$		0			0
$835$	9.21942			0.319051
$836$	4.71810			0.163179
$837$		0			0
$838$	−13.4320	+	13.4320i	−0.464000	+	0.464000i
$839$	−14.6711	+	14.6711i	−0.506503	+	0.506503i	−0.913451	−	0.406949i	$-0.866593\pi$
$839$	−14.6711	+	14.6711i	−0.506503	+	0.506503i	0.406949	+	0.913451i	$0.366593\pi$
$840$		0			0
$841$	24.1525			0.832844
$842$	−10.8610			−0.374296
$843$		0			0
$844$		−	8.78470i		−	0.302382i
$845$	4.46776	+	56.6394i	0.153695	+	1.94845i
$846$		0			0
$847$	−19.1393	+	19.1393i	−0.657634	+	0.657634i
$848$			8.05668i			0.276668i
$849$		0			0
$850$	−79.3920	+	79.3920i	−2.72312	+	2.72312i
$851$	10.9644	+	10.9644i	0.375855	+	0.375855i
$852$		0			0
$853$	7.09109	+	7.09109i	0.242794	+	0.242794i	0.818005	−	0.575211i	$-0.195080\pi$
$853$	7.09109	+	7.09109i	0.242794	+	0.242794i	−0.575211	+	0.818005i	$0.695080\pi$
$854$			24.0450i			0.822803i
$855$		0			0
$856$	3.35188	+	3.35188i	0.114565	+	0.114565i
$857$	−28.2594			−0.965323			−0.482661	−	0.875807i	$-0.660330\pi$
$857$	−28.2594			−0.965323			−0.482661	+	0.875807i	$0.660330\pi$
$858$		0			0
$859$	−52.5654			−1.79351			−0.896754	−	0.442529i	$-0.854081\pi$
$859$	−52.5654			−1.79351			−0.896754	+	0.442529i	$0.854081\pi$
$860$	19.1910	+	19.1910i	0.654408	+	0.654408i
$861$		0			0
$862$		−	34.5040i		−	1.17521i
$863$	0.667264	+	0.667264i	0.0227139	+	0.0227139i	0.718373	−	0.695659i	$-0.244887\pi$
$863$	0.667264	+	0.667264i	0.0227139	+	0.0227139i	−0.695659	+	0.718373i	$0.744887\pi$
$864$		0			0
$865$	−28.2369	−	28.2369i	−0.960084	−	0.960084i
$866$	9.59118	−	9.59118i	0.325921	−	0.325921i
$867$		0			0
$868$			9.33527i			0.316860i
$869$	−3.73990	+	3.73990i	−0.126868	+	0.126868i
$870$		0			0
$871$	22.0691	−	10.1764i	0.747782	−	0.344813i
$872$			10.4554i			0.354066i
$873$		0			0
$874$	11.7347			0.396931
$875$	−141.353			−4.77859
$876$		0			0
$877$	−0.845550	+	0.845550i	−0.0285522	+	0.0285522i	−0.721239	−	0.692687i	$-0.756427\pi$
$877$	−0.845550	+	0.845550i	−0.0285522	+	0.0285522i	0.692687	+	0.721239i	$0.256427\pi$
$878$	−26.9102	+	26.9102i	−0.908175	+	0.908175i
$879$		0			0
$880$	−8.03972			−0.271019
$881$	−28.4766			−0.959402			−0.479701	−	0.877432i	$-0.659255\pi$
$881$	−28.4766			−0.959402			−0.479701	+	0.877432i	$0.659255\pi$
$882$		0			0
$883$			1.46786i			0.0493973i	0.999695	+	0.0246987i	$0.00786263\pi$
$883$			1.46786i			0.0493973i	−0.999695	+	0.0246987i	$0.992137\pi$
$884$	9.93455	−	26.9361i	0.334135	−	0.905961i
$885$		0			0
$886$	11.0129	−	11.0129i	0.369986	−	0.369986i
$887$			18.3816i			0.617194i	0.951193	+	0.308597i	$0.0998594\pi$
$887$			18.3816i			0.617194i	−0.951193	+	0.308597i	$0.900141\pi$
$888$		0			0
$889$	42.3293	−	42.3293i	1.41968	−	1.41968i
$890$	−18.9320	−	18.9320i	−0.634604	−	0.634604i
$891$		0			0
$892$	−16.8918	−	16.8918i	−0.565580	−	0.565580i
$893$			8.84136i			0.295865i
$894$		0			0
$895$	32.7417	+	32.7417i	1.09443	+	1.09443i
$896$	−3.55400			−0.118731
$897$		0			0
$898$	−3.73629			−0.124682
$899$	−4.08935	−	4.08935i	−0.136387	−	0.136387i
$900$		0			0
$901$			64.1526i			2.13723i
$902$	4.33792	+	4.33792i	0.144437	+	0.144437i
$903$		0			0
$904$	−0.790870	−	0.790870i	−0.0263039	−	0.0263039i
$905$	51.2778	−	51.2778i	1.70453	−	1.70453i
$906$		0			0
$907$		−	28.2736i		−	0.938808i	−0.882983	−	0.469404i	$-0.844469\pi$
$907$		−	28.2736i		−	0.938808i	0.882983	−	0.469404i	$-0.155531\pi$
$908$	−2.59459	+	2.59459i	−0.0861046	+	0.0861046i
$909$		0			0
$910$	50.8566	−	23.4507i	1.68588	−	0.777384i
$911$		−	5.98117i		−	0.198165i	−0.995079	−	0.0990825i	$-0.968409\pi$
$911$		−	5.98117i		−	0.198165i	0.995079	−	0.0990825i	$-0.0315908\pi$
$912$		0			0
$913$	18.8827			0.624926
$914$	12.5076			0.413714
$915$		0			0
$916$	5.71471	−	5.71471i	0.188819	−	0.188819i
$917$	17.7099	−	17.7099i	0.584832	−	0.584832i
$918$		0			0
$919$	−25.5705			−0.843494			−0.421747	−	0.906714i	$-0.638583\pi$
$919$	−25.5705			−0.843494			−0.421747	+	0.906714i	$0.638583\pi$
$920$	−19.9960			−0.659250
$921$		0			0
$922$			7.96711i			0.262383i
$923$	15.6429	+	33.9241i	0.514892	+	1.11663i
$924$		0			0
$925$	33.7907	−	33.7907i	1.11103	−	1.11103i
$926$			29.0840i			0.955759i
$927$		0			0
$928$	1.55684	−	1.55684i	0.0511058	−	0.0511058i
$929$	27.0373	+	27.0373i	0.887066	+	0.887066i	0.994240	−	0.107174i	$-0.0341803\pi$
$929$	27.0373	+	27.0373i	0.887066	+	0.887066i	−0.107174	+	0.994240i	$0.534180\pi$
$930$		0			0
$931$	10.2120	+	10.2120i	0.334686	+	0.334686i
$932$		−	5.51719i		−	0.180721i
$933$		0			0
$934$	24.8350	+	24.8350i	0.812627	+	0.812627i
$935$	−64.0175			−2.09360
$936$		0			0
$937$	15.7883			0.515781			0.257891	−	0.966174i	$-0.416973\pi$
$937$	15.7883			0.515781			0.257891	+	0.966174i	$0.416973\pi$
$938$	−16.9386	−	16.9386i	−0.553065	−	0.553065i
$939$		0			0
$940$		−	15.0658i		−	0.491392i
$941$	−14.2176	−	14.2176i	−0.463480	−	0.463480i	0.436314	−	0.899794i	$-0.356284\pi$
$941$	−14.2176	−	14.2176i	−0.463480	−	0.463480i	−0.899794	+	0.436314i	$0.856284\pi$
$942$		0			0
$943$	10.7891	+	10.7891i	0.351341	+	0.351341i
$944$	−9.17514	+	9.17514i	−0.298625	+	0.298625i
$945$		0			0
$946$			11.4238i			0.371419i
$947$	14.9707	−	14.9707i	0.486484	−	0.486484i	−0.420711	−	0.907195i	$-0.638219\pi$
$947$	14.9707	−	14.9707i	0.486484	−	0.486484i	0.907195	+	0.420711i	$0.138219\pi$
$948$		0			0
$949$	11.7174	+	25.4110i	0.380362	+	0.824876i
$950$		−	36.1645i		−	1.17333i
$951$		0			0
$952$	−28.2993			−0.917185
$953$	58.3291			1.88947			0.944733	−	0.327842i	$-0.106321\pi$
$953$	58.3291			1.88947			0.944733	+	0.327842i	$0.106321\pi$
$954$		0			0
$955$	−28.9815	+	28.9815i	−0.937821	+	0.937821i
$956$	−0.973712	+	0.973712i	−0.0314921	+	0.0314921i
$957$		0			0
$958$	−14.6192			−0.472325
$959$	−49.0938			−1.58532
$960$		0			0
$961$			24.1005i			0.777435i
$962$	−4.22832	+	11.4645i	−0.136327	+	0.369631i
$963$		0			0
$964$	10.2868	−	10.2868i	0.331316	−	0.331316i
$965$		−	26.3042i		−	0.846763i
$966$		0			0
$967$	−27.8650	+	27.8650i	−0.896077	+	0.896077i	−0.995086	−	0.0990097i	$-0.968433\pi$
$967$	−27.8650	+	27.8650i	−0.896077	+	0.896077i	0.0990097	+	0.995086i	$0.468433\pi$
$968$	5.38529	+	5.38529i	0.173090	+	0.173090i
$969$		0			0
$970$	−13.7202	−	13.7202i	−0.440528	−	0.440528i
$971$			31.6062i			1.01429i	0.861860	+	0.507146i	$0.169300\pi$
$971$			31.6062i			1.01429i	−0.861860	+	0.507146i	$0.830700\pi$
$972$		0			0
$973$	43.2260	+	43.2260i	1.38576	+	1.38576i
$974$	3.54940			0.113730
$975$		0			0
$976$	6.76562			0.216562
$977$	7.48118	+	7.48118i	0.239344	+	0.239344i	0.816578	−	0.577234i	$-0.195868\pi$
$977$	7.48118	+	7.48118i	0.239344	+	0.239344i	−0.577234	+	0.816578i	$0.695868\pi$
$978$		0			0
$979$		−	11.2696i		−	0.360179i
$980$	−17.4015	−	17.4015i	−0.555869	−	0.555869i
$981$		0			0
$982$	22.3621	+	22.3621i	0.713604	+	0.713604i
$983$	3.23414	−	3.23414i	0.103153	−	0.103153i	−0.653647	−	0.756800i	$-0.726762\pi$
$983$	3.23414	−	3.23414i	0.103153	−	0.103153i	0.756800	+	0.653647i	$0.226762\pi$
$984$		0			0
$985$		−	24.0291i		−	0.765632i
$986$	12.3966	−	12.3966i	0.394788	−	0.394788i
$987$		0			0
$988$	3.87227	+	8.39764i	0.123193	+	0.267164i
$989$			28.4127i			0.903472i
$990$		0			0
$991$	−43.3659			−1.37756			−0.688782	−	0.724968i	$-0.741854\pi$
$991$	−43.3659			−1.37756			−0.688782	+	0.724968i	$0.741854\pi$
$992$	2.62669			0.0833976
$993$		0			0
$994$	26.0377	−	26.0377i	0.825866	−	0.825866i
$995$	63.8298	−	63.8298i	2.02354	−	2.02354i
$996$		0			0
$997$	29.4750			0.933482			0.466741	−	0.884394i	$-0.345428\pi$
$997$	29.4750			0.933482			0.466741	+	0.884394i	$0.345428\pi$
$998$	−32.7113			−1.03546
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.j.b.161.6	✓	24
3.2	odd	2	inner	702.2.j.b.161.7	yes	24
13.8	odd	4	inner	702.2.j.b.593.7	yes	24
39.8	even	4	inner	702.2.j.b.593.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
702.2.j.b.161.6	✓	24	1.1	even	1	trivial
702.2.j.b.161.7	yes	24	3.2	odd	2	inner
702.2.j.b.593.6	yes	24	39.8	even	4	inner
702.2.j.b.593.7	yes	24	13.8	odd	4	inner

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:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(3.09035 + 3.09035i) q^{5} +(2.51306 + 2.51306i) q^{7} +(0.707107 - 0.707107i) q^{8} -4.37041i q^{10} +(1.30078 - 1.30078i) q^{11} +(3.38281 + 1.24764i) q^{13} -3.55400i q^{14} -1.00000 q^{16} -7.96266 q^{17} +(1.81357 - 1.81357i) q^{19} +(-3.09035 + 3.09035i) q^{20} -1.83958 q^{22} -4.57533 q^{23} +14.1005i q^{25} +(-1.50979 - 3.27422i) q^{26} +(-2.51306 + 2.51306i) q^{28} -2.20171i q^{29} +(1.85735 - 1.85735i) q^{31} +(0.707107 + 0.707107i) q^{32} +(5.63045 + 5.63045i) q^{34} +15.5324i q^{35} +(-2.39642 - 2.39642i) q^{37} -2.56477 q^{38} +4.37041 q^{40} +(-2.35810 - 2.35810i) q^{41} -6.20999i q^{43} +(1.30078 + 1.30078i) q^{44} +(3.23524 + 3.23524i) q^{46} +(-2.43756 + 2.43756i) q^{47} +5.63091i q^{49} +(9.97054 - 9.97054i) q^{50} +(-1.24764 + 3.38281i) q^{52} -8.05668i q^{53} +8.03972 q^{55} +3.55400 q^{56} +(-1.55684 + 1.55684i) q^{58} +(9.17514 - 9.17514i) q^{59} -6.76562 q^{61} -2.62669 q^{62} -1.00000i q^{64} +(6.59840 + 14.3097i) q^{65} +(4.76607 - 4.76607i) q^{67} -7.96266i q^{68} +(10.9831 - 10.9831i) q^{70} +(7.32632 + 7.32632i) q^{71} +(5.48780 + 5.48780i) q^{73} +3.38905i q^{74} +(1.81357 + 1.81357i) q^{76} +6.53787 q^{77} -2.87513 q^{79} +(-3.09035 - 3.09035i) q^{80} +3.33486i q^{82} +(7.25822 + 7.25822i) q^{83} +(-24.6074 - 24.6074i) q^{85} +(-4.39113 + 4.39113i) q^{86} -1.83958i q^{88} +(4.33187 - 4.33187i) q^{89} +(5.36579 + 11.6366i) q^{91} -4.57533i q^{92} +3.44723 q^{94} +11.2091 q^{95} +(3.13933 - 3.13933i) q^{97} +(3.98165 - 3.98165i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{16} - 24 q^{19} + 24 q^{34} + 24 q^{37} + 24 q^{46} + 48 q^{70} - 24 q^{73} - 24 q^{76} - 24 q^{79} - 24 q^{91} + 72 q^{94} + 96 q^{97}+O(q^{100}) \) 24 * q - 24 * q^16 - 24 * q^19 + 24 * q^34 + 24 * q^37 + 24 * q^46 + 48 * q^70 - 24 * q^73 - 24 * q^76 - 24 * q^79 - 24 * q^91 + 72 * q^94 + 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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