LMFDB - Embedded newform 396.2.c.a.287.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [396,2,Mod(287,396)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(396, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("396.287");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 396 = 2^{2} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	396.c (of order $2$, degree $1$, 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:	$3.16207592004$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.5236158660608.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{8} - 4x^{7} + 3x^{6} + 8x^{5} + 6x^{4} - 16x^{3} - 16x^{2} + 32 $ x^10 - 2x^8 - 4x^7 + 3x^6 + 8x^5 + 6x^4 - 16x^3 - 16*x^2 + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			287.2
Root			$1.40857 - 0.126175i$ of defining polynomial
Character	$\chi$	$=$	396.287
Dual form			396.2.c.a.287.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40857 + 0.126175i) q^{2} +(1.96816 - 0.355453i) q^{4} +0.450958i q^{5} -4.60354i q^{7} +(-2.72745 + 0.749014i) q^{8} +(-0.0568995 - 0.635207i) q^{10} -1.00000 q^{11} -5.39122 q^{13} +(0.580851 + 6.48443i) q^{14} +(3.74731 - 1.39918i) q^{16} -5.39826i q^{17} +4.38126i q^{19} +(0.160294 + 0.887557i) q^{20} +(1.40857 - 0.126175i) q^{22} -6.03971 q^{23} +4.79664 q^{25} +(7.59393 - 0.680236i) q^{26} +(-1.63634 - 9.06050i) q^{28} -3.31081i q^{29} -4.57881i q^{31} +(-5.10182 + 2.44366i) q^{32} +(0.681125 + 7.60385i) q^{34} +2.07600 q^{35} -6.27205 q^{37} +(-0.552805 - 6.17133i) q^{38} +(-0.337774 - 1.22996i) q^{40} -11.2722i q^{41} -0.650922i q^{43} +(-1.96816 + 0.355453i) q^{44} +(8.50738 - 0.762060i) q^{46} +5.79062 q^{47} -14.1926 q^{49} +(-6.75642 + 0.605215i) q^{50} +(-10.6108 + 1.91633i) q^{52} -1.46036i q^{53} -0.450958i q^{55} +(3.44812 + 12.5559i) q^{56} +(0.417741 + 4.66353i) q^{58} +4.71375 q^{59} +1.28023 q^{61} +(0.577730 + 6.44958i) q^{62} +(6.87796 - 4.08580i) q^{64} -2.43121i q^{65} -6.54628i q^{67} +(-1.91883 - 10.6246i) q^{68} +(-2.92420 + 0.261939i) q^{70} +4.27806 q^{71} +9.86189 q^{73} +(8.83464 - 0.791374i) q^{74} +(1.55733 + 8.62303i) q^{76} +4.60354i q^{77} +8.84129i q^{79} +(0.630970 + 1.68988i) q^{80} +(1.42227 + 15.8777i) q^{82} -0.627004 q^{83} +2.43439 q^{85} +(0.0821299 + 0.916871i) q^{86} +(2.72745 - 0.749014i) q^{88} +10.6365i q^{89} +24.8187i q^{91} +(-11.8871 + 2.14684i) q^{92} +(-8.15652 + 0.730631i) q^{94} -1.97576 q^{95} +1.59931 q^{97} +(19.9913 - 1.79075i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{4} - 12 q^{8} + 4 q^{10} - 10 q^{11} + 8 q^{13} + 8 q^{14} - 4 q^{16} - 24 q^{20} - 8 q^{23} - 10 q^{25} + 16 q^{26} + 16 q^{28} + 8 q^{34} + 16 q^{35} - 4 q^{37} + 32 q^{38} - 4 q^{44} + 20 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) $ 10 * q + 4 * q^4 - 12 * q^8 + 4 * q^10 - 10 * q^11 + 8 * q^13 + 8 * q^14 - 4 * q^16 - 24 * q^20 - 8 * q^23 - 10 * q^25 + 16 * q^26 + 16 * q^28 + 8 * q^34 + 16 * q^35 - 4 * q^37 + 32 * q^38 - 4 * q^44 + 20 * q^46 - 34 * q^49 + 12 * q^50 - 20 * q^52 - 32 * q^56 - 28 * q^58 + 40 * q^59 + 20 * q^61 + 28 * q^62 - 8 * q^64 - 20 * q^68 - 36 * q^70 - 16 * q^71 + 24 * q^73 + 28 * q^74 - 12 * q^76 - 32 * q^80 - 8 * q^82 + 8 * q^83 - 36 * q^85 - 24 * q^86 + 12 * q^88 - 24 * q^92 - 20 * q^94 - 96 * q^95 + 24 * q^97 + 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/396\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.40857	+	0.126175i	−0.996012	+	0.0892191i
$2$	−1.40857	+	0.126175i	−0.996012	+	0.0892191i
$3$		0			0
$3$		0			0
$4$	1.96816	−	0.355453i	0.984080	−	0.177727i
$5$			0.450958i			0.201674i	0.994903	+	0.100837i	$0.0321521\pi$
$5$			0.450958i			0.201674i	−0.994903	+	0.100837i	$0.967848\pi$
$6$		0			0
$7$		−	4.60354i		−	1.73997i	−0.493074	−	0.869987i	$-0.664127\pi$
$7$		−	4.60354i		−	1.73997i	0.493074	−	0.869987i	$-0.335873\pi$
$8$	−2.72745	+	0.749014i	−0.964299	+	0.264816i
$9$		0			0
$10$	−0.0568995	−	0.635207i	−0.0179932	−	0.200870i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		0			0
$13$	−5.39122			−1.49525			−0.747627	−	0.664118i	$-0.768807\pi$
$13$	−5.39122			−1.49525			−0.747627	+	0.664118i	$0.768807\pi$
$14$	0.580851	+	6.48443i	0.155239	+	1.73304i
$15$		0			0
$16$	3.74731	−	1.39918i	0.936827	−	0.349794i
$17$		−	5.39826i		−	1.30927i	−0.755945	−	0.654635i	$-0.772822\pi$
$17$		−	5.39826i		−	1.30927i	0.755945	−	0.654635i	$-0.227178\pi$
$18$		0			0
$19$			4.38126i			1.00513i	0.864539	+	0.502565i	$0.167610\pi$
$19$			4.38126i			1.00513i	−0.864539	+	0.502565i	$0.832390\pi$
$20$	0.160294	+	0.887557i	0.0358429	+	0.198464i
$21$		0			0
$22$	1.40857	−	0.126175i	0.300309	−	0.0269006i
$23$	−6.03971			−1.25937			−0.629684	−	0.776852i	$-0.716816\pi$
$23$	−6.03971			−1.25937			−0.629684	+	0.776852i	$0.716816\pi$
$24$		0			0
$25$	4.79664			0.959327
$26$	7.59393	−	0.680236i	1.48929	−	0.133405i
$27$		0			0
$28$	−1.63634	−	9.06050i	−0.309240	−	1.71227i
$29$		−	3.31081i		−	0.614803i	−0.951580	−	0.307401i	$-0.900541\pi$
$29$		−	3.31081i		−	0.614803i	0.951580	−	0.307401i	$-0.0994594\pi$
$30$		0			0
$31$		−	4.57881i		−	0.822378i	−0.911550	−	0.411189i	$-0.865114\pi$
$31$		−	4.57881i		−	0.822378i	0.911550	−	0.411189i	$-0.134886\pi$
$32$	−5.10182	+	2.44366i	−0.901882	+	0.431982i
$33$		0			0
$34$	0.681125	+	7.60385i	0.116812	+	1.30405i
$35$	2.07600			0.350908
$36$		0			0
$37$	−6.27205			−1.03112			−0.515559	−	0.856854i	$-0.672416\pi$
$37$	−6.27205			−1.03112			−0.515559	+	0.856854i	$0.672416\pi$
$38$	−0.552805	−	6.17133i	−0.0896769	−	1.00112i
$39$		0			0
$40$	−0.337774	−	1.22996i	−0.0534067	−	0.194474i
$41$		−	11.2722i		−	1.76042i	−0.474580	−	0.880212i	$-0.657400\pi$
$41$		−	11.2722i		−	1.76042i	0.474580	−	0.880212i	$-0.342600\pi$
$42$		0			0
$43$		−	0.650922i		−	0.0992646i	−0.998768	−	0.0496323i	$-0.984195\pi$
$43$		−	0.650922i		−	0.0992646i	0.998768	−	0.0496323i	$-0.0158049\pi$
$44$	−1.96816	+	0.355453i	−0.296711	+	0.0535866i
$45$		0			0
$46$	8.50738	−	0.762060i	1.25435	−	0.112360i
$47$	5.79062			0.844649			0.422325	−	0.906445i	$-0.361214\pi$
$47$	5.79062			0.844649			0.422325	+	0.906445i	$0.361214\pi$
$48$		0			0
$49$	−14.1926			−2.02751
$50$	−6.75642	+	0.605215i	−0.955502	+	0.0855903i
$51$		0			0
$52$	−10.6108	+	1.91633i	−1.47145	+	0.265746i
$53$		−	1.46036i		−	0.200595i	−0.994957	−	0.100298i	$-0.968020\pi$
$53$		−	1.46036i		−	0.200595i	0.994957	−	0.100298i	$-0.0319795\pi$
$54$		0			0
$55$		−	0.450958i		−	0.0608071i
$56$	3.44812	+	12.5559i	0.460774	+	1.67786i
$57$		0			0
$58$	0.417741	+	4.66353i	0.0548521	+	0.612351i
$59$	4.71375			0.613678			0.306839	−	0.951761i	$-0.400729\pi$
$59$	4.71375			0.613678			0.306839	+	0.951761i	$0.400729\pi$
$60$		0			0
$61$	1.28023			0.163917			0.0819586	−	0.996636i	$-0.473882\pi$
$61$	1.28023			0.163917			0.0819586	+	0.996636i	$0.473882\pi$
$62$	0.577730	+	6.44958i	0.0733718	+	0.819098i
$63$		0			0
$64$	6.87796	−	4.08580i	0.859744	−	0.510724i
$65$		−	2.43121i		−	0.301555i
$66$		0			0
$67$		−	6.54628i		−	0.799756i	−0.916568	−	0.399878i	$-0.869053\pi$
$67$		−	6.54628i		−	0.799756i	0.916568	−	0.399878i	$-0.130947\pi$
$68$	−1.91883	−	10.6246i	−0.232692	−	1.28843i
$69$		0			0
$70$	−2.92420	+	0.261939i	−0.349509	+	0.0313077i
$71$	4.27806			0.507712			0.253856	−	0.967242i	$-0.418301\pi$
$71$	4.27806			0.507712			0.253856	+	0.967242i	$0.418301\pi$
$72$		0			0
$73$	9.86189			1.15425			0.577124	−	0.816657i	$-0.304175\pi$
$73$	9.86189			1.15425			0.577124	+	0.816657i	$0.304175\pi$
$74$	8.83464	−	0.791374i	1.02701	−	0.0919954i
$75$		0			0
$76$	1.55733	+	8.62303i	0.178638	+	0.989129i
$77$			4.60354i			0.524622i
$78$		0			0
$79$			8.84129i			0.994723i	0.867543	+	0.497362i	$0.165698\pi$
$79$			8.84129i			0.994723i	−0.867543	+	0.497362i	$0.834302\pi$
$80$	0.630970	+	1.68988i	0.0705446	+	0.188934i
$81$		0			0
$82$	1.42227	+	15.8777i	0.157063	+	1.75340i
$83$	−0.627004			−0.0688226			−0.0344113	−	0.999408i	$-0.510956\pi$
$83$	−0.627004			−0.0688226			−0.0344113	+	0.999408i	$0.510956\pi$
$84$		0			0
$85$	2.43439			0.264046
$86$	0.0821299	+	0.916871i	0.00885630	+	0.0988688i
$87$		0			0
$88$	2.72745	−	0.749014i	0.290747	−	0.0798452i
$89$			10.6365i			1.12747i	0.825957	+	0.563733i	$0.190635\pi$
$89$			10.6365i			1.12747i	−0.825957	+	0.563733i	$0.809365\pi$
$90$		0			0
$91$			24.8187i			2.60171i
$92$	−11.8871	+	2.14684i	−1.23932	+	0.223823i
$93$		0			0
$94$	−8.15652	+	0.730631i	−0.841281	+	0.0753588i
$95$	−1.97576			−0.202709
$96$		0			0
$97$	1.59931			0.162386			0.0811928	−	0.996698i	$-0.474127\pi$
$97$	1.59931			0.162386			0.0811928	+	0.996698i	$0.474127\pi$
$98$	19.9913	−	1.79075i	2.01943	−	0.180893i
$99$		0			0
$100$	9.44055	−	1.70498i	0.944055	−	0.170498i
$101$			5.90296i			0.587367i	0.955903	+	0.293683i	$0.0948811\pi$
$101$			5.90296i			0.587367i	−0.955903	+	0.293683i	$0.905119\pi$
$102$		0			0
$103$			7.11963i			0.701518i	0.936466	+	0.350759i	$0.114076\pi$
$103$			7.11963i			0.701518i	−0.936466	+	0.350759i	$0.885924\pi$
$104$	14.7043	−	4.03810i	1.44187	−	0.395968i
$105$		0			0
$106$	0.184260	+	2.05702i	0.0178969	+	0.199795i
$107$	12.9205			1.24908			0.624538	−	0.780994i	$-0.285287\pi$
$107$	12.9205			1.24908			0.624538	+	0.780994i	$0.285287\pi$
$108$		0			0
$109$	−7.40196			−0.708980			−0.354490	−	0.935060i	$-0.615345\pi$
$109$	−7.40196			−0.708980			−0.354490	+	0.935060i	$0.615345\pi$
$110$	0.0568995	+	0.635207i	0.00542516	+	0.0605646i
$111$		0			0
$112$	−6.44117	−	17.2509i	−0.608633	−	1.63005i
$113$			13.2201i			1.24365i	0.783158	+	0.621823i	$0.213608\pi$
$113$			13.2201i			1.24365i	−0.783158	+	0.621823i	$0.786392\pi$
$114$		0			0
$115$		−	2.72366i		−	0.253982i
$116$	−1.17684	−	6.51621i	−0.109267	−	0.605015i
$117$		0			0
$118$	−6.63967	+	0.594757i	−0.611231	+	0.0547518i
$119$	−24.8511			−2.27810
$120$		0			0
$121$	1.00000			0.0909091
$122$	−1.80330	+	0.161533i	−0.163263	+	0.0146245i
$123$		0			0
$124$	−1.62755	−	9.01182i	−0.146158	−	0.809285i
$125$			4.41787i			0.395146i
$126$		0			0
$127$		−	14.9079i		−	1.32286i	−0.750008	−	0.661429i	$-0.769950\pi$
$127$		−	14.9079i		−	1.32286i	0.750008	−	0.661429i	$-0.230050\pi$
$128$	−9.17258	+	6.62297i	−0.810749	+	0.585393i
$129$		0			0
$130$	0.306758	+	3.42454i	0.0269044	+	0.300352i
$131$	−5.69955			−0.497972			−0.248986	−	0.968507i	$-0.580097\pi$
$131$	−5.69955			−0.497972			−0.248986	+	0.968507i	$0.580097\pi$
$132$		0			0
$133$	20.1693			1.74890
$134$	0.825976	+	9.22092i	0.0713535	+	0.796566i
$135$		0			0
$136$	4.04337	+	14.7235i	0.346716	+	1.26253i
$137$		−	3.67780i		−	0.314215i	−0.987581	−	0.157108i	$-0.949783\pi$
$137$		−	3.67780i		−	0.314215i	0.987581	−	0.157108i	$-0.0502170\pi$
$138$		0			0
$139$			11.3998i			0.966917i	0.875367	+	0.483459i	$0.160620\pi$
$139$			11.3998i			0.966917i	−0.875367	+	0.483459i	$0.839380\pi$
$140$	4.08590	−	0.737921i	0.345322	−	0.0623657i
$141$		0			0
$142$	−6.02596	+	0.539783i	−0.505687	+	0.0452976i
$143$	5.39122			0.450836
$144$		0			0
$145$	1.49304			0.123990
$146$	−13.8912	+	1.24432i	−1.14964	+	0.102981i
$147$		0			0
$148$	−12.3444	+	2.22942i	−1.01470	+	0.183257i
$149$		−	19.7575i		−	1.61860i	−0.587397	−	0.809299i	$-0.699847\pi$
$149$		−	19.7575i		−	1.61860i	0.587397	−	0.809299i	$-0.300153\pi$
$150$		0			0
$151$		−	4.51126i		−	0.367121i	−0.983008	−	0.183560i	$-0.941238\pi$
$151$		−	4.51126i		−	0.367121i	0.983008	−	0.183560i	$-0.0587623\pi$
$152$	−3.28163	−	11.9497i	−0.266175	−	0.969247i
$153$		0			0
$154$	−0.580851	−	6.48443i	−0.0468063	−	0.522530i
$155$	2.06485			0.165853
$156$		0			0
$157$	−2.46466			−0.196701			−0.0983507	−	0.995152i	$-0.531357\pi$
$157$	−2.46466			−0.196701			−0.0983507	+	0.995152i	$0.531357\pi$
$158$	−1.11555	−	12.4536i	−0.0887483	−	0.990756i
$159$		0			0
$160$	−1.10199	−	2.30070i	−0.0871197	−	0.181887i
$161$			27.8041i			2.19127i
$162$		0			0
$163$		−	22.2074i		−	1.73941i	−0.493568	−	0.869707i	$-0.664307\pi$
$163$		−	22.2074i		−	1.73941i	0.493568	−	0.869707i	$-0.335693\pi$
$164$	−4.00674	−	22.1855i	−0.312874	−	1.73240i
$165$		0			0
$166$	0.883181	−	0.0791121i	0.0685482	−	0.00614029i
$167$	11.8748			0.918898			0.459449	−	0.888204i	$-0.348047\pi$
$167$	11.8748			0.918898			0.459449	+	0.888204i	$0.348047\pi$
$168$		0			0
$169$	16.0652			1.23579
$170$	−3.42901	+	0.307158i	−0.262993	+	0.0235580i
$171$		0			0
$172$	−0.231372	−	1.28112i	−0.0176420	−	0.0976843i
$173$			12.9026i			0.980968i	0.871450	+	0.490484i	$0.163180\pi$
$173$			12.9026i			0.980968i	−0.871450	+	0.490484i	$0.836820\pi$
$174$		0			0
$175$		−	22.0815i		−	1.66921i
$176$	−3.74731	+	1.39918i	−0.282464	+	0.105467i
$177$		0			0
$178$	−1.34206	−	14.9823i	−0.100591	−	1.12297i
$179$	14.2207			1.06290			0.531452	−	0.847088i	$-0.321647\pi$
$179$	14.2207			1.06290			0.531452	+	0.847088i	$0.321647\pi$
$180$		0			0
$181$	15.1818			1.12846			0.564229	−	0.825619i	$-0.309174\pi$
$181$	15.1818			1.12846			0.564229	+	0.825619i	$0.309174\pi$
$182$	−3.13149	−	34.9590i	−0.232122	−	2.59133i
$183$		0			0
$184$	16.4730	−	4.52383i	1.21441	−	0.333501i
$185$		−	2.82843i		−	0.207950i
$186$		0			0
$187$			5.39826i			0.394760i
$188$	11.3969	−	2.05830i	0.831202	−	0.150117i
$189$		0			0
$190$	2.78301	−	0.249292i	0.201901	−	0.0180855i
$191$	−13.7056			−0.991700			−0.495850	−	0.868408i	$-0.665143\pi$
$191$	−13.7056			−0.991700			−0.495850	+	0.868408i	$0.665143\pi$
$192$		0			0
$193$	−15.7345			−1.13260			−0.566298	−	0.824200i	$-0.691625\pi$
$193$	−15.7345			−1.13260			−0.566298	+	0.824200i	$0.691625\pi$
$194$	−2.25275	+	0.201793i	−0.161738	+	0.0144879i
$195$		0			0
$196$	−27.9333	+	5.04480i	−1.99523	+	0.360343i
$197$		−	12.5112i		−	0.891386i	−0.895186	−	0.445693i	$-0.852957\pi$
$197$		−	12.5112i		−	0.891386i	0.895186	−	0.445693i	$-0.147043\pi$
$198$		0			0
$199$		−	11.9736i		−	0.848783i	−0.905479	−	0.424391i	$-0.860488\pi$
$199$		−	11.9736i		−	0.848783i	0.905479	−	0.424391i	$-0.139512\pi$
$200$	−13.0826	+	3.59275i	−0.925078	+	0.254046i
$201$		0			0
$202$	−0.744805	−	8.31476i	−0.0524043	−	0.585024i
$203$	−15.2415			−1.06974
$204$		0			0
$205$	5.08329			0.355033
$206$	−0.898319	−	10.0285i	−0.0625888	−	0.698721i
$207$		0			0
$208$	−20.2025	+	7.54327i	−1.40079	+	0.523032i
$209$		−	4.38126i		−	0.303058i
$210$		0			0
$211$			22.8088i			1.57022i	0.619354	+	0.785112i	$0.287395\pi$
$211$			22.8088i			1.57022i	−0.619354	+	0.785112i	$0.712605\pi$
$212$	−0.519088	−	2.87421i	−0.0356511	−	0.197402i
$213$		0			0
$214$	−18.1995	+	1.63025i	−1.24409	+	0.111441i
$215$	0.293538			0.0200191
$216$		0			0
$217$	−21.0787			−1.43092
$218$	10.4262	−	0.933942i	0.706152	−	0.0632545i
$219$		0			0
$220$	−0.160294	−	0.887557i	−0.0108070	−	0.0598391i
$221$			29.1032i			1.95769i
$222$		0			0
$223$			7.05369i			0.472350i	0.971710	+	0.236175i	$0.0758939\pi$
$223$			7.05369i			0.472350i	−0.971710	+	0.236175i	$0.924106\pi$
$224$	11.2495	+	23.4864i	0.751638	+	1.56925i
$225$		0			0
$226$	−1.66805	−	18.6215i	−0.110957	−	1.23869i
$227$	−17.1425			−1.13779			−0.568894	−	0.822411i	$-0.692629\pi$
$227$	−17.1425			−1.13779			−0.568894	+	0.822411i	$0.692629\pi$
$228$		0			0
$229$	−0.206790			−0.0136650			−0.00683252	−	0.999977i	$-0.502175\pi$
$229$	−0.206790			−0.0136650			−0.00683252	+	0.999977i	$0.502175\pi$
$230$	0.343657	+	3.83647i	0.0226601	+	0.252969i
$231$		0			0
$232$	2.47985	+	9.03008i	0.162810	+	0.592854i
$233$		−	7.61451i		−	0.498843i	−0.968395	−	0.249421i	$-0.919760\pi$
$233$		−	7.61451i		−	0.498843i	0.968395	−	0.249421i	$-0.0802404\pi$
$234$		0			0
$235$			2.61133i			0.170344i
$236$	9.27742	−	1.67552i	0.603909	−	0.109067i
$237$		0			0
$238$	35.0046	−	3.13559i	2.26901	−	0.203250i
$239$	−11.7859			−0.762366			−0.381183	−	0.924500i	$-0.624483\pi$
$239$	−11.7859			−0.762366			−0.381183	+	0.924500i	$0.624483\pi$
$240$		0			0
$241$	5.78630			0.372728			0.186364	−	0.982481i	$-0.440330\pi$
$241$	5.78630			0.372728			0.186364	+	0.982481i	$0.440330\pi$
$242$	−1.40857	+	0.126175i	−0.0905465	+	0.00811083i
$243$		0			0
$244$	2.51970	−	0.455063i	0.161308	−	0.0291324i
$245$		−	6.40026i		−	0.408897i
$246$		0			0
$247$		−	23.6203i		−	1.50293i
$248$	3.42959	+	12.4885i	0.217779	+	0.793018i
$249$		0			0
$250$	−0.557424	−	6.22289i	−0.0352546	−	0.393570i
$251$	22.0592			1.39237			0.696183	−	0.717865i	$-0.254880\pi$
$251$	22.0592			1.39237			0.696183	+	0.717865i	$0.254880\pi$
$252$		0			0
$253$	6.03971			0.379714
$254$	1.88100	+	20.9988i	0.118024	+	1.31758i
$255$		0			0
$256$	12.0846	−	10.4863i	0.755288	−	0.655393i
$257$			8.51467i			0.531130i	0.964093	+	0.265565i	$0.0855586\pi$
$257$			8.51467i			0.531130i	−0.964093	+	0.265565i	$0.914441\pi$
$258$		0			0
$259$			28.8736i			1.79412i
$260$	−0.864182	−	4.78501i	−0.0535943	−	0.296754i
$261$		0			0
$262$	8.02824	−	0.719140i	0.495986	−	0.0444286i
$263$	−5.07086			−0.312682			−0.156341	−	0.987703i	$-0.549970\pi$
$263$	−5.07086			−0.312682			−0.156341	+	0.987703i	$0.549970\pi$
$264$		0			0
$265$	0.658559			0.0404550
$266$	−28.4100	+	2.54486i	−1.74193	+	0.156035i
$267$		0			0
$268$	−2.32690	−	12.8841i	−0.142138	−	0.787024i
$269$		−	25.5790i		−	1.55958i	−0.626040	−	0.779791i	$-0.715326\pi$
$269$		−	25.5790i		−	1.55958i	0.626040	−	0.779791i	$-0.284674\pi$
$270$		0			0
$271$		−	29.2394i		−	1.77617i	−0.459682	−	0.888084i	$-0.652037\pi$
$271$		−	29.2394i		−	1.77617i	0.459682	−	0.888084i	$-0.347963\pi$
$272$	−7.55312	−	20.2289i	−0.457975	−	1.22656i
$273$		0			0
$274$	0.464045	+	5.18045i	0.0280340	+	0.312962i
$275$	−4.79664			−0.289248
$276$		0			0
$277$	32.1011			1.92877			0.964383	−	0.264508i	$-0.0852097\pi$
$277$	32.1011			1.92877			0.964383	+	0.264508i	$0.0852097\pi$
$278$	−1.43837	−	16.0574i	−0.0862675	−	0.963061i
$279$		0			0
$280$	−5.66219	+	1.55495i	−0.338381	+	0.0929263i
$281$			19.4654i			1.16121i	0.814186	+	0.580604i	$0.197183\pi$
$281$			19.4654i			1.16121i	−0.814186	+	0.580604i	$0.802817\pi$
$282$		0			0
$283$			14.3357i			0.852169i	0.904683	+	0.426084i	$0.140107\pi$
$283$			14.3357i			0.852169i	−0.904683	+	0.426084i	$0.859893\pi$
$284$	8.41990	−	1.52065i	0.499629	−	0.0902339i
$285$		0			0
$286$	−7.59393	+	0.680236i	−0.449038	+	0.0402232i
$287$	−51.8921			−3.06309
$288$		0			0
$289$	−12.1412			−0.714190
$290$	−2.10305	+	0.188384i	−0.123496	+	0.0110623i
$291$		0			0
$292$	19.4098	−	3.50544i	1.13587	−	0.205140i
$293$			21.2956i			1.24410i	0.782976	+	0.622052i	$0.213701\pi$
$293$			21.2956i			1.24410i	−0.782976	+	0.622052i	$0.786299\pi$
$294$		0			0
$295$			2.12570i			0.123763i
$296$	17.1067	−	4.69785i	0.994306	−	0.273057i
$297$		0			0
$298$	2.49290	+	27.8299i	0.144410	+	1.61214i
$299$	32.5614			1.88308
$300$		0			0
$301$	−2.99654			−0.172718
$302$	0.569207	+	6.35444i	0.0327542	+	0.365657i
$303$		0			0
$304$	6.13016	+	16.4179i	0.351589	+	0.941633i
$305$			0.577331i			0.0330579i
$306$		0			0
$307$		−	2.34785i		−	0.133999i	−0.997753	−	0.0669993i	$-0.978657\pi$
$307$		−	2.34785i		−	0.133999i	0.997753	−	0.0669993i	$-0.0213425\pi$
$308$	1.63634	+	9.06050i	0.0932393	+	0.516270i
$309$		0			0
$310$	−2.90849	+	0.260532i	−0.165191	+	0.0147972i
$311$	12.9742			0.735697			0.367848	−	0.929886i	$-0.380095\pi$
$311$	12.9742			0.735697			0.367848	+	0.929886i	$0.380095\pi$
$312$		0			0
$313$	8.66454			0.489749			0.244874	−	0.969555i	$-0.421253\pi$
$313$	8.66454			0.489749			0.244874	+	0.969555i	$0.421253\pi$
$314$	3.47166	−	0.310978i	0.195917	−	0.0175495i
$315$		0			0
$316$	3.14267	+	17.4011i	0.176789	+	0.978887i
$317$		−	7.51714i		−	0.422205i	−0.977464	−	0.211102i	$-0.932295\pi$
$317$		−	7.51714i		−	0.422205i	0.977464	−	0.211102i	$-0.0677053\pi$
$318$		0			0
$319$			3.31081i			0.185370i
$320$	1.84252	+	3.10167i	0.103000	+	0.173388i
$321$		0			0
$322$	−3.50817	−	39.1641i	−0.195503	−	2.18253i
$323$	23.6512			1.31599
$324$		0			0
$325$	−25.8597			−1.43444
$326$	2.80201	+	31.2807i	0.155189	+	1.73248i
$327$		0			0
$328$	8.44305	+	30.7444i	0.466189	+	1.69758i
$329$		−	26.6574i		−	1.46967i
$330$		0			0
$331$		−	26.1423i		−	1.43691i	−0.695572	−	0.718456i	$-0.744849\pi$
$331$		−	26.1423i		−	1.43691i	0.695572	−	0.718456i	$-0.255151\pi$
$332$	−1.23404	+	0.222871i	−0.0677270	+	0.0122316i
$333$		0			0
$334$	−16.7265	+	1.49830i	−0.915234	+	0.0819833i
$335$	2.95210			0.161290
$336$		0			0
$337$	7.72064			0.420570			0.210285	−	0.977640i	$-0.432561\pi$
$337$	7.72064			0.420570			0.210285	+	0.977640i	$0.432561\pi$
$338$	−22.6291	+	2.02703i	−1.23086	+	0.110256i
$339$		0			0
$340$	4.79126	−	0.865311i	0.259843	−	0.0469281i
$341$			4.57881i			0.247956i
$342$		0			0
$343$			33.1114i			1.78785i
$344$	0.487550	+	1.77536i	0.0262869	+	0.0957208i
$345$		0			0
$346$	−1.62799	−	18.1743i	−0.0875211	−	0.977056i
$347$	30.6201			1.64377			0.821886	−	0.569651i	$-0.192922\pi$
$347$	30.6201			1.64377			0.821886	+	0.569651i	$0.192922\pi$
$348$		0			0
$349$	−19.2853			−1.03232			−0.516161	−	0.856492i	$-0.672639\pi$
$349$	−19.2853			−1.03232			−0.516161	+	0.856492i	$0.672639\pi$
$350$	2.78613	+	31.1034i	0.148925	+	1.66255i
$351$		0			0
$352$	5.10182	−	2.44366i	0.271928	−	0.130248i
$353$		−	24.5083i		−	1.30444i	−0.758028	−	0.652222i	$-0.773837\pi$
$353$		−	24.5083i		−	1.30444i	0.758028	−	0.652222i	$-0.226163\pi$
$354$		0			0
$355$			1.92922i			0.102393i
$356$	3.78077	+	20.9343i	0.200381	+	1.10952i
$357$		0			0
$358$	−20.0309	+	1.79429i	−1.05867	+	0.0948313i
$359$	21.6374			1.14198			0.570990	−	0.820957i	$-0.306559\pi$
$359$	21.6374			1.14198			0.570990	+	0.820957i	$0.306559\pi$
$360$		0			0
$361$	−0.195476			−0.0102882
$362$	−21.3847	+	1.91557i	−1.12396	+	0.100680i
$363$		0			0
$364$	8.82188	+	48.8471i	0.462392	+	2.56029i
$365$			4.44730i			0.232782i
$366$		0			0
$367$		−	11.3739i		−	0.593710i	−0.954923	−	0.296855i	$-0.904062\pi$
$367$		−	11.3739i		−	0.593710i	0.954923	−	0.296855i	$-0.0959379\pi$
$368$	−22.6327	+	8.45063i	−1.17981	+	0.440520i
$369$		0			0
$370$	0.356876	+	3.98405i	0.0185531	+	0.207121i
$371$	−6.72281			−0.349031
$372$		0			0
$373$	−22.0678			−1.14263			−0.571313	−	0.820732i	$-0.693566\pi$
$373$	−22.0678			−1.14263			−0.571313	+	0.820732i	$0.693566\pi$
$374$	−0.681125	−	7.60385i	−0.0352201	−	0.393186i
$375$		0			0
$376$	−15.7936	+	4.33726i	−0.814494	+	0.223677i
$377$			17.8493i			0.919287i
$378$		0			0
$379$			11.5928i			0.595480i	0.954647	+	0.297740i	$0.0962329\pi$
$379$			11.5928i			0.595480i	−0.954647	+	0.297740i	$0.903767\pi$
$380$	−3.88862	+	0.702292i	−0.199482	+	0.0360268i
$381$		0			0
$382$	19.3053	−	1.72930i	0.987745	−	0.0884785i
$383$	−8.35063			−0.426697			−0.213349	−	0.976976i	$-0.568437\pi$
$383$	−8.35063			−0.426697			−0.213349	+	0.976976i	$0.568437\pi$
$384$		0			0
$385$	−2.07600			−0.105803
$386$	22.1632	−	1.98530i	1.12808	−	0.101049i
$387$		0			0
$388$	3.14770	−	0.568481i	0.159800	−	0.0288602i
$389$		−	21.1897i		−	1.07436i	−0.843467	−	0.537181i	$-0.819489\pi$
$389$		−	21.1897i		−	1.07436i	0.843467	−	0.537181i	$-0.180511\pi$
$390$		0			0
$391$			32.6040i			1.64885i
$392$	38.7096	−	10.6304i	1.95513	−	0.536919i
$393$		0			0
$394$	1.57860	+	17.6230i	0.0795287	+	0.887831i
$395$	−3.98705			−0.200610
$396$		0			0
$397$	−5.63389			−0.282757			−0.141378	−	0.989956i	$-0.545153\pi$
$397$	−5.63389			−0.282757			−0.141378	+	0.989956i	$0.545153\pi$
$398$	1.51076	+	16.8656i	0.0757276	+	0.845398i
$399$		0			0
$400$	17.9745	−	6.71134i	0.898723	−	0.335567i
$401$		−	27.1670i		−	1.35665i	−0.734761	−	0.678327i	$-0.762705\pi$
$401$		−	27.1670i		−	1.35665i	0.734761	−	0.678327i	$-0.237295\pi$
$402$		0			0
$403$			24.6853i			1.22966i
$404$	2.09823	+	11.6180i	0.104391	+	0.578016i
$405$		0			0
$406$	21.4687	−	1.92309i	1.06548	−	0.0954413i
$407$	6.27205			0.310894
$408$		0			0
$409$	−35.1236			−1.73675			−0.868374	−	0.495909i	$-0.834835\pi$
$409$	−35.1236			−1.73675			−0.868374	+	0.495909i	$0.834835\pi$
$410$	−7.16019	+	0.641384i	−0.353617	+	0.0316757i
$411$		0			0
$412$	2.53070	+	14.0126i	0.124678	+	0.690350i
$413$		−	21.7000i		−	1.06778i
$414$		0			0
$415$		−	0.282752i		−	0.0138798i
$416$	27.5050	−	13.1743i	1.34854	−	0.645923i
$417$		0			0
$418$	0.552805	+	6.17133i	0.0270386	+	0.301850i
$419$	5.90419			0.288439			0.144219	−	0.989546i	$-0.453933\pi$
$419$	5.90419			0.288439			0.144219	+	0.989546i	$0.453933\pi$
$420$		0			0
$421$	−4.05579			−0.197667			−0.0988336	−	0.995104i	$-0.531511\pi$
$421$	−4.05579			−0.197667			−0.0988336	+	0.995104i	$0.531511\pi$
$422$	−2.87790	−	32.1279i	−0.140094	−	1.56396i
$423$		0			0
$424$	1.09383	+	3.98305i	0.0531210	+	0.193434i
$425$		−	25.8935i		−	1.25602i
$426$		0			0
$427$		−	5.89361i		−	0.285212i
$428$	25.4297	−	4.59265i	1.22919	−	0.221994i
$429$		0			0
$430$	−0.413470	+	0.0370371i	−0.0199393	+	0.00178609i
$431$	−12.5967			−0.606763			−0.303382	−	0.952869i	$-0.598116\pi$
$431$	−12.5967			−0.606763			−0.303382	+	0.952869i	$0.598116\pi$
$432$		0			0
$433$	7.12665			0.342485			0.171242	−	0.985229i	$-0.445222\pi$
$433$	7.12665			0.342485			0.171242	+	0.985229i	$0.445222\pi$
$434$	29.6909	−	2.65960i	1.42521	−	0.127665i
$435$		0			0
$436$	−14.5682	+	2.63105i	−0.697693	+	0.126004i
$437$		−	26.4616i		−	1.26583i
$438$		0			0
$439$		−	14.7602i		−	0.704466i	−0.935912	−	0.352233i	$-0.885422\pi$
$439$		−	14.7602i		−	0.704466i	0.935912	−	0.352233i	$-0.114578\pi$
$440$	0.337774	+	1.22996i	0.0161027	+	0.0586362i
$441$		0			0
$442$	−3.67209	−	40.9940i	−0.174664	−	1.94989i
$443$	0.00946572			0.000449730			0.000224865	−	1.00000i	$-0.499928\pi$
$443$	0.00946572			0.000449730			0.000224865		1.00000i	$0.499928\pi$
$444$		0			0
$445$	−4.79661			−0.227381
$446$	−0.889999	−	9.93565i	−0.0421427	−	0.470467i
$447$		0			0
$448$	−18.8091	−	31.6629i	−0.888648	−	1.49593i
$449$			3.11056i			0.146796i	0.997303	+	0.0733982i	$0.0233844\pi$
$449$			3.11056i			0.146796i	−0.997303	+	0.0733982i	$0.976616\pi$
$450$		0			0
$451$			11.2722i			0.530788i
$452$	4.69914	+	26.0193i	0.221029	+	1.22385i
$453$		0			0
$454$	24.1465	−	2.16295i	1.13325	−	0.101512i
$455$	−11.1922			−0.524697
$456$		0			0
$457$	7.09532			0.331905			0.165953	−	0.986134i	$-0.446930\pi$
$457$	7.09532			0.331905			0.165953	+	0.986134i	$0.446930\pi$
$458$	0.291278	−	0.0260916i	0.0136105	−	0.00121918i
$459$		0			0
$460$	−0.968132	−	5.36059i	−0.0451394	−	0.249939i
$461$			30.5522i			1.42296i	0.702708	+	0.711478i	$0.251974\pi$
$461$			30.5522i			1.42296i	−0.702708	+	0.711478i	$0.748026\pi$
$462$		0			0
$463$		−	25.8995i		−	1.20365i	−0.798628	−	0.601825i	$-0.794441\pi$
$463$		−	25.8995i		−	1.20365i	0.798628	−	0.601825i	$-0.205559\pi$
$464$	−4.63241	−	12.4066i	−0.215054	−	0.575963i
$465$		0			0
$466$	0.960759	+	10.7256i	0.0445063	+	0.496854i
$467$	−30.1266			−1.39409			−0.697047	−	0.717026i	$-0.745503\pi$
$467$	−30.1266			−1.39409			−0.697047	+	0.717026i	$0.745503\pi$
$468$		0			0
$469$	−30.1361			−1.39156
$470$	−0.329484	−	3.67825i	−0.0151979	−	0.169665i
$471$		0			0
$472$	−12.8565	+	3.53067i	−0.591769	+	0.162512i
$473$			0.650922i			0.0299294i
$474$		0			0
$475$			21.0153i			0.964250i
$476$	−48.9110	+	8.83341i	−2.24183	+	0.404879i
$477$		0			0
$478$	16.6013	−	1.48708i	0.759326	−	0.0680176i
$479$	35.2644			1.61127			0.805636	−	0.592411i	$-0.201824\pi$
$479$	35.2644			1.61127			0.805636	+	0.592411i	$0.201824\pi$
$480$		0			0
$481$	33.8140			1.54178
$482$	−8.15043	+	0.730085i	−0.371242	+	0.0332545i
$483$		0			0
$484$	1.96816	−	0.355453i	0.0894618	−	0.0161570i
$485$			0.721223i			0.0327490i
$486$		0			0
$487$			8.15092i			0.369354i	0.982799	+	0.184677i	$0.0591238\pi$
$487$			8.15092i			0.369354i	−0.982799	+	0.184677i	$0.940876\pi$
$488$	−3.49177	+	0.958913i	−0.158065	+	0.0434080i
$489$		0			0
$490$	0.807551	+	9.01523i	0.0364814	+	0.407267i
$491$	−35.0295			−1.58086			−0.790430	−	0.612553i	$-0.790143\pi$
$491$	−35.0295			−1.58086			−0.790430	+	0.612553i	$0.790143\pi$
$492$		0			0
$493$	−17.8726			−0.804943
$494$	2.98029	+	33.2710i	0.134090	+	1.49693i
$495$		0			0
$496$	−6.40656	−	17.1582i	−0.287663	−	0.770425i
$497$		−	19.6942i		−	0.883406i
$498$		0			0
$499$		−	25.0804i		−	1.12275i	−0.827560	−	0.561377i	$-0.810272\pi$
$499$		−	25.0804i		−	1.12275i	0.827560	−	0.561377i	$-0.189728\pi$
$500$	1.57035	+	8.69507i	0.0702280	+	0.388855i
$501$		0			0
$502$	−31.0720	+	2.78332i	−1.38681	+	0.124226i
$503$	18.9025			0.842820			0.421410	−	0.906870i	$-0.361535\pi$
$503$	18.9025			0.842820			0.421410	+	0.906870i	$0.361535\pi$
$504$		0			0
$505$	−2.66199			−0.118457
$506$	−8.50738	+	0.762060i	−0.378199	+	0.0338777i
$507$		0			0
$508$	−5.29904	−	29.3410i	−0.235107	−	1.30180i
$509$		−	10.9702i		−	0.486247i	−0.969995	−	0.243124i	$-0.921828\pi$
$509$		−	10.9702i		−	0.486247i	0.969995	−	0.243124i	$-0.0781720\pi$
$510$		0			0
$511$		−	45.3996i		−	2.00836i
$512$	−15.6990	+	16.2955i	−0.693802	+	0.720165i
$513$		0			0
$514$	−1.07434	−	11.9935i	−0.0473870	−	0.529012i
$515$	−3.21065			−0.141478
$516$		0			0
$517$	−5.79062			−0.254671
$518$	−3.64312	−	40.6706i	−0.160070	−	1.78696i
$519$		0			0
$520$	1.82101	+	6.63100i	0.0798566	+	0.290789i
$521$		−	6.21862i		−	0.272443i	−0.990678	−	0.136221i	$-0.956504\pi$
$521$		−	6.21862i		−	0.272443i	0.990678	−	0.136221i	$-0.0434959\pi$
$522$		0			0
$523$			8.06214i			0.352533i	0.984343	+	0.176266i	$0.0564020\pi$
$523$			8.06214i			0.352533i	−0.984343	+	0.176266i	$0.943598\pi$
$524$	−11.2176	+	2.02592i	−0.490044	+	0.0885029i
$525$		0			0
$526$	7.14268	−	0.639815i	0.311435	−	0.0278972i
$527$	−24.7176			−1.07672
$528$		0			0
$529$	13.4782			0.586007
$530$	−0.927629	+	0.0830936i	−0.0402936	+	0.00360935i
$531$		0			0
$532$	39.6965	−	7.16925i	1.72106	−	0.310826i
$533$			60.7710i			2.63228i
$534$		0			0
$535$			5.82662i			0.251907i
$536$	4.90326	+	17.8547i	0.211789	+	0.771204i
$537$		0			0
$538$	3.22743	+	36.0300i	0.139144	+	1.55336i
$539$	14.1926			0.611318
$540$		0			0
$541$	−15.5904			−0.670284			−0.335142	−	0.942168i	$-0.608784\pi$
$541$	−15.5904			−0.670284			−0.335142	+	0.942168i	$0.608784\pi$
$542$	3.68928	+	41.1859i	0.158468	+	1.76908i
$543$		0			0
$544$	13.1915	+	27.5409i	0.565582	+	1.18081i
$545$		−	3.33797i		−	0.142983i
$546$		0			0
$547$		−	35.1984i		−	1.50497i	−0.658607	−	0.752487i	$-0.728854\pi$
$547$		−	35.1984i		−	1.50497i	0.658607	−	0.752487i	$-0.271146\pi$
$548$	−1.30728	−	7.23849i	−0.0558444	−	0.309213i
$549$		0			0
$550$	6.75642	−	0.605215i	0.288095	−	0.0258064i
$551$	14.5055			0.617957
$552$		0			0
$553$	40.7013			1.73079
$554$	−45.2167	+	4.05035i	−1.92107	+	0.172083i
$555$		0			0
$556$	4.05209	+	22.4366i	0.171847	+	0.951524i
$557$		−	34.1280i		−	1.44605i	−0.690823	−	0.723024i	$-0.742752\pi$
$557$		−	34.1280i		−	1.44605i	0.690823	−	0.723024i	$-0.257248\pi$
$558$		0			0
$559$			3.50926i			0.148426i
$560$	7.77942	−	2.90469i	0.328740	−	0.122746i
$561$		0			0
$562$	−2.45604	−	27.4184i	−0.103602	−	1.15658i
$563$	45.8757			1.93343			0.966716	−	0.255853i	$-0.0823562\pi$
$563$	45.8757			1.93343			0.966716	+	0.255853i	$0.0823562\pi$
$564$		0			0
$565$	−5.96172			−0.250812
$566$	−1.80880	−	20.1929i	−0.0760297	−	0.848770i
$567$		0			0
$568$	−11.6682	+	3.20433i	−0.489586	+	0.134451i
$569$			6.58959i			0.276250i	0.990415	+	0.138125i	$0.0441075\pi$
$569$			6.58959i			0.276250i	−0.990415	+	0.138125i	$0.955892\pi$
$570$		0			0
$571$		−	4.44412i		−	0.185981i	−0.995667	−	0.0929904i	$-0.970357\pi$
$571$		−	4.44412i		−	0.185981i	0.995667	−	0.0929904i	$-0.0296426\pi$
$572$	10.6108	−	1.91633i	0.443659	−	0.0801256i
$573$		0			0
$574$	73.0939	−	6.54748i	3.05088	−	0.273286i
$575$	−28.9703			−1.20815
$576$		0			0
$577$	−26.8917			−1.11952			−0.559759	−	0.828656i	$-0.689106\pi$
$577$	−26.8917			−1.11952			−0.559759	+	0.828656i	$0.689106\pi$
$578$	17.1018	−	1.53192i	0.711342	−	0.0637194i
$579$		0			0
$580$	2.93854	−	0.530705i	0.122016	−	0.0220363i
$581$			2.88644i			0.119750i
$582$		0			0
$583$			1.46036i			0.0604818i
$584$	−26.8978	+	7.38670i	−1.11304	+	0.305664i
$585$		0			0
$586$	−2.68697	−	29.9965i	−0.110998	−	1.23914i
$587$	−18.6184			−0.768464			−0.384232	−	0.923237i	$-0.625534\pi$
$587$	−18.6184			−0.768464			−0.384232	+	0.923237i	$0.625534\pi$
$588$		0			0
$589$	20.0610			0.826597
$590$	−0.268210	−	2.99421i	−0.0110420	−	0.123270i
$591$		0			0
$592$	−23.5033	+	8.77570i	−0.965979	+	0.360679i
$593$			24.8200i			1.01924i	0.860401	+	0.509618i	$0.170213\pi$
$593$			24.8200i			1.01924i	−0.860401	+	0.509618i	$0.829787\pi$
$594$		0			0
$595$		−	11.2068i		−	0.459434i
$596$	−7.02286	−	38.8859i	−0.287668	−	1.59283i
$597$		0			0
$598$	−45.8652	+	4.10843i	−1.87557	+	0.168006i
$599$	−4.54608			−0.185748			−0.0928739	−	0.995678i	$-0.529605\pi$
$599$	−4.54608			−0.185748			−0.0928739	+	0.995678i	$0.529605\pi$
$600$		0			0
$601$	10.5497			0.430332			0.215166	−	0.976577i	$-0.430971\pi$
$601$	10.5497			0.430332			0.215166	+	0.976577i	$0.430971\pi$
$602$	4.22085	−	0.378088i	0.172029	−	0.0154097i
$603$		0			0
$604$	−1.60354	−	8.87887i	−0.0652471	−	0.361276i
$605$			0.450958i			0.0183340i
$606$		0			0
$607$		−	4.75119i		−	0.192845i	−0.995340	−	0.0964225i	$-0.969260\pi$
$607$		−	4.75119i		−	0.192845i	0.995340	−	0.0964225i	$-0.0307400\pi$
$608$	−10.7063	−	22.3524i	−0.434199	−	0.906510i
$609$		0			0
$610$	−0.0728447	−	0.813214i	−0.00294939	−	0.0329261i
$611$	−31.2185			−1.26297
$612$		0			0
$613$	24.6283			0.994726			0.497363	−	0.867543i	$-0.334302\pi$
$613$	24.6283			0.994726			0.497363	+	0.867543i	$0.334302\pi$
$614$	0.296239	+	3.30712i	0.0119552	+	0.133464i
$615$		0			0
$616$	−3.44812	−	12.5559i	−0.138929	−	0.505893i
$617$			14.0774i			0.566736i	0.959011	+	0.283368i	$0.0914518\pi$
$617$			14.0774i			0.566736i	−0.959011	+	0.283368i	$0.908548\pi$
$618$		0			0
$619$			16.9924i			0.682980i	0.939885	+	0.341490i	$0.110932\pi$
$619$			16.9924i			0.682980i	−0.939885	+	0.341490i	$0.889068\pi$
$620$	4.06395	−	0.733956i	0.163212	−	0.0294764i
$621$		0			0
$622$	−18.2751	+	1.63701i	−0.732763	+	0.0656382i
$623$	48.9655			1.96176
$624$		0			0
$625$	21.9909			0.879637
$626$	−12.2046	+	1.09325i	−0.487796	+	0.0436949i
$627$		0			0
$628$	−4.85085	+	0.876072i	−0.193570	+	0.0349591i
$629$			33.8581i			1.35001i
$630$		0			0
$631$			11.2451i			0.447659i	0.974628	+	0.223829i	$0.0718558\pi$
$631$			11.2451i			0.447659i	−0.974628	+	0.223829i	$0.928144\pi$
$632$	−6.62225	−	24.1142i	−0.263419	−	0.959211i
$633$		0			0
$634$	0.948474	+	10.5884i	0.0376687	+	0.420521i
$635$	6.72281			0.266787
$636$		0			0
$637$	76.5153			3.03165
$638$	−0.417741	−	4.66353i	−0.0165385	−	0.184631i
$639$		0			0
$640$	−2.98668	−	4.13645i	−0.118059	−	0.163507i
$641$		−	17.6143i		−	0.695722i	−0.937546	−	0.347861i	$-0.886908\pi$
$641$		−	17.6143i		−	0.695722i	0.937546	−	0.347861i	$-0.113092\pi$
$642$		0			0
$643$		−	6.03887i		−	0.238150i	−0.992885	−	0.119075i	$-0.962007\pi$
$643$		−	6.03887i		−	0.238150i	0.992885	−	0.119075i	$-0.0379929\pi$
$644$	9.88304	+	54.7229i	0.389446	+	2.15638i
$645$		0			0
$646$	−33.3145	+	2.98419i	−1.31074	+	0.117411i
$647$	−48.1430			−1.89270			−0.946349	−	0.323146i	$-0.895260\pi$
$647$	−48.1430			−1.89270			−0.946349	+	0.323146i	$0.895260\pi$
$648$		0			0
$649$	−4.71375			−0.185031
$650$	36.4253	−	3.26285i	1.42872	−	0.127979i
$651$		0			0
$652$	−7.89368	−	43.7076i	−0.309140	−	1.71172i
$653$			20.5620i			0.804655i	0.915496	+	0.402328i	$0.131799\pi$
$653$			20.5620i			0.804655i	−0.915496	+	0.402328i	$0.868201\pi$
$654$		0			0
$655$		−	2.57026i		−	0.100428i
$656$	−15.7718	−	42.2404i	−0.615786	−	1.64921i
$657$		0			0
$658$	3.36349	+	37.5489i	0.131122	+	1.46381i
$659$	−33.8196			−1.31742			−0.658712	−	0.752395i	$-0.728898\pi$
$659$	−33.8196			−1.31742			−0.658712	+	0.752395i	$0.728898\pi$
$660$		0			0
$661$	−18.7893			−0.730821			−0.365410	−	0.930847i	$-0.619071\pi$
$661$	−18.7893			−0.730821			−0.365410	+	0.930847i	$0.619071\pi$
$662$	3.29850	+	36.8234i	0.128200	+	1.43118i
$663$		0			0
$664$	1.71012	−	0.469635i	0.0663656	−	0.0182254i
$665$			9.09551i			0.352709i
$666$		0			0
$667$			19.9964i			0.774263i
$668$	23.3715	−	4.22093i	0.904270	−	0.163313i
$669$		0			0
$670$	−4.15825	+	0.372480i	−0.160647	+	0.0143902i
$671$	−1.28023			−0.0494229
$672$		0			0
$673$	−10.8744			−0.419178			−0.209589	−	0.977790i	$-0.567213\pi$
$673$	−10.8744			−0.419178			−0.209589	+	0.977790i	$0.567213\pi$
$674$	−10.8751	+	0.974150i	−0.418893	+	0.0375228i
$675$		0			0
$676$	31.6189	−	5.71043i	1.21611	−	0.219632i
$677$			49.5233i			1.90333i	0.307133	+	0.951667i	$0.400630\pi$
$677$			49.5233i			1.90333i	−0.307133	+	0.951667i	$0.599370\pi$
$678$		0			0
$679$		−	7.36250i		−	0.282547i
$680$	−6.63967	+	1.82339i	−0.254620	+	0.0699238i
$681$		0			0
$682$	−0.577730	−	6.44958i	−0.0221224	−	0.246967i
$683$	−8.75966			−0.335179			−0.167590	−	0.985857i	$-0.553598\pi$
$683$	−8.75966			−0.335179			−0.167590	+	0.985857i	$0.553598\pi$
$684$		0			0
$685$	1.65853			0.0633692
$686$	−4.17782	−	46.6398i	−0.159510	−	1.78072i
$687$		0			0
$688$	−0.910755	−	2.43920i	−0.0347222	−	0.0929937i
$689$			7.87310i			0.299941i
$690$		0			0
$691$		−	9.60042i		−	0.365217i	−0.983186	−	0.182609i	$-0.941546\pi$
$691$		−	9.60042i		−	0.365217i	0.983186	−	0.182609i	$-0.0584541\pi$
$692$	4.58628	+	25.3944i	0.174344	+	0.965351i
$693$		0			0
$694$	−43.1307	+	3.86349i	−1.63722	+	0.146656i
$695$	−5.14082			−0.195002
$696$		0			0
$697$	−60.8504			−2.30487
$698$	27.1648	−	2.43333i	1.02820	−	0.0921027i
$699$		0			0
$700$	−7.84894	−	43.4600i	−0.296662	−	1.64263i
$701$		−	28.5860i		−	1.07968i	−0.841769	−	0.539839i	$-0.818485\pi$
$701$		−	28.5860i		−	1.07968i	0.841769	−	0.539839i	$-0.181515\pi$
$702$		0			0
$703$		−	27.4795i		−	1.03641i
$704$	−6.87796	+	4.08580i	−0.259223	+	0.153989i
$705$		0			0
$706$	3.09233	+	34.5217i	0.116381	+	1.29924i
$707$	27.1745			1.02200
$708$		0			0
$709$	−6.19988			−0.232841			−0.116421	−	0.993200i	$-0.537142\pi$
$709$	−6.19988			−0.232841			−0.116421	+	0.993200i	$0.537142\pi$
$710$	−0.243419	−	2.71745i	−0.00913537	−	0.101984i
$711$		0			0
$712$	−7.96688	−	29.0105i	−0.298572	−	1.08721i
$713$			27.6547i			1.03568i
$714$		0			0
$715$			2.43121i			0.0909221i
$716$	27.9886	−	5.05479i	1.04598	−	0.188906i
$717$		0			0
$718$	−30.4779	+	2.73010i	−1.13743	+	0.101886i
$719$	−16.1753			−0.603238			−0.301619	−	0.953428i	$-0.597527\pi$
$719$	−16.1753			−0.603238			−0.301619	+	0.953428i	$0.597527\pi$
$720$		0			0
$721$	32.7755			1.22062
$722$	0.275342	−	0.0246641i	0.0102472	−	0.000917903i
$723$		0			0
$724$	29.8803	−	5.39643i	1.11049	−	0.200557i
$725$		−	15.8808i		−	0.589797i
$726$		0			0
$727$			14.8038i			0.549042i	0.961581	+	0.274521i	$0.0885193\pi$
$727$			14.8038i			0.549042i	−0.961581	+	0.274521i	$0.911481\pi$
$728$	−18.5895	−	67.6917i	−0.688975	−	2.50882i
$729$		0			0
$730$	−0.561137	−	6.26434i	−0.0207686	−	0.231854i
$731$	−3.51385			−0.129964
$732$		0			0
$733$	4.58421			0.169322			0.0846609	−	0.996410i	$-0.473019\pi$
$733$	4.58421			0.169322			0.0846609	+	0.996410i	$0.473019\pi$
$734$	1.43509	+	16.0209i	0.0529703	+	0.591343i
$735$		0			0
$736$	30.8135	−	14.7590i	1.13580	−	0.544024i
$737$			6.54628i			0.241135i
$738$		0			0
$739$		−	1.28355i		−	0.0472163i	−0.999721	−	0.0236081i	$-0.992485\pi$
$739$		−	1.28355i		−	0.0472163i	0.999721	−	0.0236081i	$-0.00751540\pi$
$740$	−1.00537	−	5.56680i	−0.0369583	−	0.204640i
$741$		0			0
$742$	9.46957	−	0.848249i	0.347639	−	0.0311402i
$743$	−23.9767			−0.879620			−0.439810	−	0.898091i	$-0.644954\pi$
$743$	−23.9767			−0.879620			−0.439810	+	0.898091i	$0.644954\pi$
$744$		0			0
$745$	8.90980			0.326430
$746$	31.0841	−	2.78440i	1.13807	−	0.101944i
$747$		0			0
$748$	1.91883	+	10.6246i	0.0701593	+	0.388475i
$749$		−	59.4802i		−	2.17336i
$750$		0			0
$751$			37.2322i			1.35862i	0.733850	+	0.679312i	$0.237722\pi$
$751$			37.2322i			1.35862i	−0.733850	+	0.679312i	$0.762278\pi$
$752$	21.6992	−	8.10211i	0.791290	−	0.295453i
$753$		0			0
$754$	−2.25213	−	25.1421i	−0.0820179	−	0.915621i
$755$	2.03439			0.0740389
$756$		0			0
$757$	33.0955			1.20288			0.601438	−	0.798919i	$-0.294595\pi$
$757$	33.0955			1.20288			0.601438	+	0.798919i	$0.294595\pi$
$758$	−1.46272	−	16.3293i	−0.0531282	−	0.593106i
$759$		0			0
$760$	5.38880	−	1.47988i	0.195472	−	0.0536807i
$761$			14.2090i			0.515077i	0.966268	+	0.257538i	$0.0829114\pi$
$761$			14.2090i			0.515077i	−0.966268	+	0.257538i	$0.917089\pi$
$762$		0			0
$763$			34.0752i			1.23361i
$764$	−26.9747	+	4.87169i	−0.975912	+	0.176251i
$765$		0			0
$766$	11.7625	−	1.05364i	0.424996	−	0.0380696i
$767$	−25.4129			−0.917605
$768$		0			0
$769$	−29.1166			−1.04997			−0.524985	−	0.851111i	$-0.675929\pi$
$769$	−29.1166			−1.04997			−0.524985	+	0.851111i	$0.675929\pi$
$770$	2.92420	−	0.261939i	0.105381	−	0.00943963i
$771$		0			0
$772$	−30.9681	+	5.59289i	−1.11457	+	0.201292i
$773$		−	6.64019i		−	0.238831i	−0.992844	−	0.119416i	$-0.961898\pi$
$773$		−	6.64019i		−	0.238831i	0.992844	−	0.119416i	$-0.0381021\pi$
$774$		0			0
$775$		−	21.9629i		−	0.788929i
$776$	−4.36205	+	1.19791i	−0.156588	+	0.0430024i
$777$		0			0
$778$	2.67361	+	29.8473i	0.0958537	+	1.07008i
$779$	49.3866			1.76946
$780$		0			0
$781$	−4.27806			−0.153081
$782$	−4.11380	−	45.9251i	−0.147109	−	1.64228i
$783$		0			0
$784$	−53.1840	+	19.8579i	−1.89943	+	0.709212i
$785$		−	1.11146i		−	0.0396696i
$786$		0			0
$787$		−	5.12622i		−	0.182730i	−0.995817	−	0.0913651i	$-0.970877\pi$
$787$		−	5.12622i		−	0.182730i	0.995817	−	0.0913651i	$-0.0291230\pi$
$788$	−4.44715	−	24.6240i	−0.158423	−	0.877195i
$789$		0			0
$790$	5.61605	−	0.503065i	0.199810	−	0.0178983i
$791$	60.8594			2.16391
$792$		0			0
$793$	−6.90202			−0.245098
$794$	7.93574	−	0.710855i	0.281629	−	0.0252273i
$795$		0			0
$796$	−4.25604	−	23.5659i	−0.150851	−	0.835270i
$797$			25.6924i			0.910072i	0.890473	+	0.455036i	$0.150374\pi$
$797$			25.6924i			0.910072i	−0.890473	+	0.455036i	$0.849626\pi$
$798$		0			0
$799$		−	31.2593i		−	1.10587i
$800$	−24.4716	+	11.7213i	−0.865200	+	0.414412i
$801$		0			0
$802$	3.42779	+	38.2667i	0.121039	+	1.35124i
$803$	−9.86189			−0.348019
$804$		0			0
$805$	−12.5385			−0.441923
$806$	−3.11467	−	34.7711i	−0.109709	−	1.22476i
$807$		0			0
$808$	−4.42140	−	16.1000i	−0.155544	−	0.566397i
$809$			11.1617i			0.392424i	0.980561	+	0.196212i	$0.0628641\pi$
$809$			11.1617i			0.392424i	−0.980561	+	0.196212i	$0.937136\pi$
$810$		0			0
$811$			25.6391i			0.900309i	0.892951	+	0.450154i	$0.148631\pi$
$811$			25.6391i			0.900309i	−0.892951	+	0.450154i	$0.851369\pi$
$812$	−29.9976	+	5.41763i	−1.05271	+	0.190121i
$813$		0			0
$814$	−8.83464	+	0.791374i	−0.309654	+	0.0277377i
$815$	10.0146			0.350795
$816$		0			0
$817$	2.85186			0.0997739
$818$	49.4741	−	4.43171i	1.72982	−	0.154951i
$819$		0			0
$820$	10.0047	−	1.80687i	0.349380	−	0.0630987i
$821$		−	32.3388i		−	1.12863i	−0.825559	−	0.564316i	$-0.809140\pi$
$821$		−	32.3388i		−	1.12863i	0.825559	−	0.564316i	$-0.190860\pi$
$822$		0			0
$823$			10.1239i			0.352896i	0.984310	+	0.176448i	$0.0564607\pi$
$823$			10.1239i			0.352896i	−0.984310	+	0.176448i	$0.943539\pi$
$824$	−5.33271	−	19.4184i	−0.185774	−	0.676473i
$825$		0			0
$826$	2.73799	+	30.5660i	0.0952668	+	1.06353i
$827$	5.77199			0.200712			0.100356	−	0.994952i	$-0.468002\pi$
$827$	5.77199			0.200712			0.100356	+	0.994952i	$0.468002\pi$
$828$		0			0
$829$	46.2848			1.60754			0.803769	−	0.594942i	$-0.202825\pi$
$829$	46.2848			1.60754			0.803769	+	0.594942i	$0.202825\pi$
$830$	0.0356762	+	0.398277i	0.00123834	+	0.0138244i
$831$		0			0
$832$	−37.0806	+	22.0274i	−1.28554	+	0.763663i
$833$			76.6153i			2.65456i
$834$		0			0
$835$			5.35503i			0.185318i
$836$	−1.55733	−	8.62303i	−0.0538615	−	0.298234i
$837$		0			0
$838$	−8.31649	+	0.744961i	−0.287288	+	0.0257342i
$839$	48.0233			1.65795			0.828975	−	0.559286i	$-0.188925\pi$
$839$	48.0233			1.65795			0.828975	+	0.559286i	$0.188925\pi$
$840$		0			0
$841$	18.0385			0.622018
$842$	5.71288	−	0.511739i	0.196879	−	0.0176357i
$843$		0			0
$844$	8.10746	+	44.8914i	0.279070	+	1.54523i
$845$			7.24474i			0.249227i
$846$		0			0
$847$		−	4.60354i		−	0.158180i
$848$	−2.04330	−	5.47240i	−0.0701671	−	0.187923i
$849$		0			0
$850$	3.26711	+	36.4729i	0.112061	+	1.25101i
$851$	37.8814			1.29856
$852$		0			0
$853$	33.6945			1.15368			0.576839	−	0.816858i	$-0.304286\pi$
$853$	33.6945			1.15368			0.576839	+	0.816858i	$0.304286\pi$
$854$	0.743625	+	8.30158i	0.0254463	+	0.284074i
$855$		0			0
$856$	−35.2401	+	9.67767i	−1.20448	+	0.330776i
$857$			27.0979i			0.925646i	0.886451	+	0.462823i	$0.153164\pi$
$857$			27.0979i			0.925646i	−0.886451	+	0.462823i	$0.846836\pi$
$858$		0			0
$859$			3.07528i			0.104927i	0.998623	+	0.0524636i	$0.0167073\pi$
$859$			3.07528i			0.104927i	−0.998623	+	0.0524636i	$0.983293\pi$
$860$	0.577730	−	0.104339i	0.0197004	−	0.00355793i
$861$		0			0
$862$	17.7434	−	1.58939i	0.604343	−	0.0541348i
$863$	−4.36829			−0.148698			−0.0743492	−	0.997232i	$-0.523688\pi$
$863$	−4.36829			−0.148698			−0.0743492	+	0.997232i	$0.523688\pi$
$864$		0			0
$865$	−5.81854			−0.197836
$866$	−10.0384	+	0.899204i	−0.341119	+	0.0305562i
$867$		0			0
$868$	−41.4863	+	7.49249i	−1.40814	+	0.254312i
$869$		−	8.84129i		−	0.299920i
$870$		0			0
$871$			35.2924i			1.19584i
$872$	20.1885	−	5.54418i	0.683668	−	0.187749i
$873$		0			0
$874$	3.33879	+	37.2731i	0.112936	+	1.26078i
$875$	20.3378			0.687544
$876$		0			0
$877$	5.50220			0.185796			0.0928981	−	0.995676i	$-0.470387\pi$
$877$	5.50220			0.185796			0.0928981	+	0.995676i	$0.470387\pi$
$878$	1.86237	+	20.7908i	0.0628518	+	0.701656i
$879$		0			0
$880$	−0.630970	−	1.68988i	−0.0212700	−	0.0569657i
$881$		−	24.1682i		−	0.814247i	−0.913373	−	0.407124i	$-0.866532\pi$
$881$		−	24.1682i		−	0.814247i	0.913373	−	0.407124i	$-0.133468\pi$
$882$		0			0
$883$		−	51.0030i		−	1.71639i	−0.513326	−	0.858194i	$-0.671587\pi$
$883$		−	51.0030i		−	1.71639i	0.513326	−	0.858194i	$-0.328413\pi$
$884$	10.3448	+	57.2798i	0.347934	+	1.92653i
$885$		0			0
$886$	−0.0133332	+	0.00119434i	−0.000447936	+	4.01245e-5i
$887$	−27.1324			−0.911015			−0.455508	−	0.890232i	$-0.650542\pi$
$887$	−27.1324			−0.911015			−0.455508	+	0.890232i	$0.650542\pi$
$888$		0			0
$889$	−68.6289			−2.30174
$890$	6.75638	−	0.605211i	0.226474	−	0.0202867i
$891$		0			0
$892$	2.50726	+	13.8828i	0.0839492	+	0.464830i
$893$			25.3703i			0.848983i
$894$		0			0
$895$			6.41293i			0.214361i
$896$	30.4891	+	42.2264i	1.01857	+	1.41068i
$897$		0			0
$898$	−0.392475	−	4.38145i	−0.0130970	−	0.146211i
$899$	−15.1596			−0.505600
$900$		0			0
$901$	−7.88339			−0.262634
$902$	−1.42227	−	15.8777i	−0.0473564	−	0.528671i
$903$		0			0
$904$	−9.90207	−	36.0572i	−0.329338	−	1.19925i
$905$			6.84637i			0.227581i
$906$		0			0
$907$			53.1849i			1.76598i	0.469396	+	0.882988i	$0.344472\pi$
$907$			53.1849i			1.76598i	−0.469396	+	0.882988i	$0.655528\pi$
$908$	−33.7392	+	6.09336i	−1.11967	+	0.202215i
$909$		0			0
$910$	15.7650	−	1.41217i	0.522605	−	0.0468130i
$911$	29.2194			0.968082			0.484041	−	0.875045i	$-0.339169\pi$
$911$	29.2194			0.968082			0.484041	+	0.875045i	$0.339169\pi$
$912$		0			0
$913$	0.627004			0.0207508
$914$	−9.99428	+	0.895251i	−0.330581	+	0.0296123i
$915$		0			0
$916$	−0.406995	+	0.0735040i	−0.0134475	+	0.00242864i
$917$			26.2381i			0.866459i
$918$		0			0
$919$			37.4675i			1.23594i	0.786202	+	0.617969i	$0.212044\pi$
$919$			37.4675i			1.23594i	−0.786202	+	0.617969i	$0.787956\pi$
$920$	2.04006	+	7.42863i	0.0672587	+	0.244915i
$921$		0			0
$922$	−3.85492	−	43.0350i	−0.126955	−	1.41728i
$923$	−23.0639			−0.759159
$924$		0			0
$925$	−30.0847			−0.989180
$926$	3.26786	+	36.4813i	0.107389	+	1.19885i
$927$		0			0
$928$	8.09050	+	16.8912i	0.265584	+	0.554480i
$929$		−	7.31585i		−	0.240025i	−0.992772	−	0.120013i	$-0.961706\pi$
$929$		−	7.31585i		−	0.240025i	0.992772	−	0.120013i	$-0.0382935\pi$
$930$		0			0
$931$		−	62.1815i		−	2.03792i
$932$	−2.70660	−	14.9866i	−0.0886576	−	0.490901i
$933$		0			0
$934$	42.4356	−	3.80122i	1.38853	−	0.124380i
$935$	−2.43439			−0.0796130
$936$		0			0
$937$	35.3106			1.15355			0.576774	−	0.816904i	$-0.304311\pi$
$937$	35.3106			1.15355			0.576774	+	0.816904i	$0.304311\pi$
$938$	42.4489	−	3.80242i	1.38601	−	0.124153i
$939$		0			0
$940$	0.928204	+	5.13951i	0.0302747	+	0.167632i
$941$			3.59895i			0.117323i	0.998278	+	0.0586613i	$0.0186832\pi$
$941$			3.59895i			0.117323i	−0.998278	+	0.0586613i	$0.981317\pi$
$942$		0			0
$943$			68.0810i			2.21702i
$944$	17.6639	−	6.59537i	0.574910	−	0.214661i
$945$		0			0
$946$	−0.0821299	−	0.916871i	−0.00267027	−	0.0298101i
$947$	−43.7091			−1.42036			−0.710178	−	0.704022i	$-0.751386\pi$
$947$	−43.7091			−1.42036			−0.710178	+	0.704022i	$0.751386\pi$
$948$		0			0
$949$	−53.1676			−1.72589
$950$	−2.65161	−	29.6016i	−0.0860295	−	0.960404i
$951$		0			0
$952$	67.7802	−	18.6138i	2.19677	−	0.603278i
$953$			7.81428i			0.253129i	0.991958	+	0.126565i	$0.0403951\pi$
$953$			7.81428i			0.253129i	−0.991958	+	0.126565i	$0.959605\pi$
$954$		0			0
$955$		−	6.18063i		−	0.200000i
$956$	−23.1965	+	4.18933i	−0.750229	+	0.135493i
$957$		0			0
$958$	−49.6725	+	4.44948i	−1.60485	+	0.143756i
$959$	−16.9309			−0.546727
$960$		0			0
$961$	10.0345			0.323695
$962$	−47.6295	+	4.26647i	−1.53564	+	0.137557i
$963$		0			0
$964$	11.3884	−	2.05676i	0.366794	−	0.0662437i
$965$		−	7.09561i		−	0.228416i
$966$		0			0
$967$			40.7961i			1.31191i	0.754798	+	0.655957i	$0.227735\pi$
$967$			40.7961i			1.31191i	−0.754798	+	0.655957i	$0.772265\pi$
$968$	−2.72745	+	0.749014i	−0.0876635	+	0.0240742i
$969$		0			0
$970$	−0.0910001	−	1.01590i	−0.00292184	−	0.0326184i
$971$	−17.8775			−0.573717			−0.286859	−	0.957973i	$-0.592611\pi$
$971$	−17.8775			−0.573717			−0.286859	+	0.957973i	$0.592611\pi$
$972$		0			0
$973$	52.4794			1.68241
$974$	−1.02844	−	11.4812i	−0.0329534	−	0.367881i
$975$		0			0
$976$	4.79743	−	1.79127i	0.153562	−	0.0573373i
$977$		−	26.9702i		−	0.862854i	−0.902148	−	0.431427i	$-0.858010\pi$
$977$		−	26.9702i		−	0.862854i	0.902148	−	0.431427i	$-0.141990\pi$
$978$		0			0
$979$		−	10.6365i		−	0.339944i
$980$	−2.27499	−	12.5967i	−0.0726719	−	0.402388i
$981$		0			0
$982$	49.3416	−	4.41984i	1.57455	−	0.141043i
$983$	21.5536			0.687452			0.343726	−	0.939070i	$-0.388311\pi$
$983$	21.5536			0.687452			0.343726	+	0.939070i	$0.388311\pi$
$984$		0			0
$985$	5.64202			0.179770
$986$	25.1749	−	2.25508i	0.801733	−	0.0718163i
$987$		0			0
$988$	−8.39593	−	46.4886i	−0.267110	−	1.47900i
$989$			3.93138i			0.125011i
$990$		0			0
$991$		−	0.996115i		−	0.0316426i	−0.999875	−	0.0158213i	$-0.994964\pi$
$991$		−	0.996115i		−	0.0316426i	0.999875	−	0.0158213i	$-0.00503629\pi$
$992$	11.1890	+	23.3602i	0.355252	+	0.741688i
$993$		0			0
$994$	2.48491	+	27.7408i	0.0788167	+	0.879883i
$995$	5.39957			0.171178
$996$		0			0
$997$	−17.8333			−0.564787			−0.282394	−	0.959299i	$-0.591128\pi$
$997$	−17.8333			−0.564787			−0.282394	+	0.959299i	$0.591128\pi$
$998$	3.16452	+	35.3276i	0.100171	+	1.11828i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	396.2.c.a.287.2	yes	10
3.2	odd	2		396.2.c.b.287.9	yes	10
4.3	odd	2		396.2.c.b.287.10	yes	10
8.3	odd	2		6336.2.d.g.3455.5		10
8.5	even	2		6336.2.d.h.3455.5		10
12.11	even	2	inner	396.2.c.a.287.1	✓	10
24.5	odd	2		6336.2.d.g.3455.6		10
24.11	even	2		6336.2.d.h.3455.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
396.2.c.a.287.1	✓	10	12.11	even	2	inner
396.2.c.a.287.2	yes	10	1.1	even	1	trivial
396.2.c.b.287.9	yes	10	3.2	odd	2
396.2.c.b.287.10	yes	10	4.3	odd	2
6336.2.d.g.3455.5		10	8.3	odd	2
6336.2.d.g.3455.6		10	24.5	odd	2
6336.2.d.h.3455.5		10	8.5	even	2
6336.2.d.h.3455.6		10	24.11	even	2

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:	\( N \)	\(=\)	\( 396 = 2^{2} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	396.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40857 + 0.126175i) q^{2} +(1.96816 - 0.355453i) q^{4} +0.450958i q^{5} -4.60354i q^{7} +(-2.72745 + 0.749014i) q^{8} +(-0.0568995 - 0.635207i) q^{10} -1.00000 q^{11} -5.39122 q^{13} +(0.580851 + 6.48443i) q^{14} +(3.74731 - 1.39918i) q^{16} -5.39826i q^{17} +4.38126i q^{19} +(0.160294 + 0.887557i) q^{20} +(1.40857 - 0.126175i) q^{22} -6.03971 q^{23} +4.79664 q^{25} +(7.59393 - 0.680236i) q^{26} +(-1.63634 - 9.06050i) q^{28} -3.31081i q^{29} -4.57881i q^{31} +(-5.10182 + 2.44366i) q^{32} +(0.681125 + 7.60385i) q^{34} +2.07600 q^{35} -6.27205 q^{37} +(-0.552805 - 6.17133i) q^{38} +(-0.337774 - 1.22996i) q^{40} -11.2722i q^{41} -0.650922i q^{43} +(-1.96816 + 0.355453i) q^{44} +(8.50738 - 0.762060i) q^{46} +5.79062 q^{47} -14.1926 q^{49} +(-6.75642 + 0.605215i) q^{50} +(-10.6108 + 1.91633i) q^{52} -1.46036i q^{53} -0.450958i q^{55} +(3.44812 + 12.5559i) q^{56} +(0.417741 + 4.66353i) q^{58} +4.71375 q^{59} +1.28023 q^{61} +(0.577730 + 6.44958i) q^{62} +(6.87796 - 4.08580i) q^{64} -2.43121i q^{65} -6.54628i q^{67} +(-1.91883 - 10.6246i) q^{68} +(-2.92420 + 0.261939i) q^{70} +4.27806 q^{71} +9.86189 q^{73} +(8.83464 - 0.791374i) q^{74} +(1.55733 + 8.62303i) q^{76} +4.60354i q^{77} +8.84129i q^{79} +(0.630970 + 1.68988i) q^{80} +(1.42227 + 15.8777i) q^{82} -0.627004 q^{83} +2.43439 q^{85} +(0.0821299 + 0.916871i) q^{86} +(2.72745 - 0.749014i) q^{88} +10.6365i q^{89} +24.8187i q^{91} +(-11.8871 + 2.14684i) q^{92} +(-8.15652 + 0.730631i) q^{94} -1.97576 q^{95} +1.59931 q^{97} +(19.9913 - 1.79075i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{4} - 12 q^{8} + 4 q^{10} - 10 q^{11} + 8 q^{13} + 8 q^{14} - 4 q^{16} - 24 q^{20} - 8 q^{23} - 10 q^{25} + 16 q^{26} + 16 q^{28} + 8 q^{34} + 16 q^{35} - 4 q^{37} + 32 q^{38} - 4 q^{44} + 20 q^{46}+ \cdots + 60 q^{98}+O(q^{100}) \) 10 * q + 4 * q^4 - 12 * q^8 + 4 * q^10 - 10 * q^11 + 8 * q^13 + 8 * q^14 - 4 * q^16 - 24 * q^20 - 8 * q^23 - 10 * q^25 + 16 * q^26 + 16 * q^28 + 8 * q^34 + 16 * q^35 - 4 * q^37 + 32 * q^38 - 4 * q^44 + 20 * q^46 - 34 * q^49 + 12 * q^50 - 20 * q^52 - 32 * q^56 - 28 * q^58 + 40 * q^59 + 20 * q^61 + 28 * q^62 - 8 * q^64 - 20 * q^68 - 36 * q^70 - 16 * q^71 + 24 * q^73 + 28 * q^74 - 12 * q^76 - 32 * q^80 - 8 * q^82 + 8 * q^83 - 36 * q^85 - 24 * q^86 + 12 * q^88 - 24 * q^92 - 20 * q^94 - 96 * q^95 + 24 * q^97 + 60 * q^98

Introduction

L-functions

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