LMFDB - Embedded newform 656.2.u.h.305.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(305,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("656.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.u (of order $5$, degree $4$, not 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:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 7 x^{18} - 6 x^{17} + 60 x^{16} - 92 x^{15} + 603 x^{14} - 690 x^{13} + 2935 x^{12} + \cdots + 4096 $ x^20 - 2x^19 + 7x^18 - 6x^17 + 60x^16 - 92x^15 + 603x^14 - 690x^13 + 2935x^12 - 3168x^11 + 7811x^10 - 7928x^9 + 15482x^8 - 24314x^7 + 44829x^6 - 45930x^5 + 53273x^4 - 47528x^3 + 33216x^2 - 12800*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 328)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			305.3
Root			$0.165728 + 0.510060i$ of defining polynomial
Character	$\chi$	$=$	656.305
Dual form			656.2.u.h.385.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.536309 q^{3} +(1.18977 - 0.864417i) q^{5} +(-1.04717 + 3.22286i) q^{7} -2.71237 q^{9} +O(q^{10})$	\(q-0.536309 q^{3} +(1.18977 - 0.864417i) q^{5} +(-1.04717 + 3.22286i) q^{7} -2.71237 q^{9} +(-4.18339 - 3.03941i) q^{11} +(-1.60660 - 4.94461i) q^{13} +(-0.638082 + 0.463594i) q^{15} +(0.00992776 + 0.00721294i) q^{17} +(-0.532049 + 1.63748i) q^{19} +(0.561606 - 1.72845i) q^{21} +(-1.34950 - 4.15334i) q^{23} +(-0.876755 + 2.69837i) q^{25} +3.06359 q^{27} +(6.38144 - 4.63638i) q^{29} +(-6.47869 - 4.70704i) q^{31} +(2.24359 + 1.63006i) q^{33} +(1.54000 + 4.73964i) q^{35} +(-6.51439 + 4.73298i) q^{37} +(0.861634 + 2.65184i) q^{39} +(-0.865824 - 6.34432i) q^{41} +(-1.75493 - 5.40113i) q^{43} +(-3.22709 + 2.34462i) q^{45} +(2.40280 + 7.39507i) q^{47} +(-3.62712 - 2.63526i) q^{49} +(-0.00532435 - 0.00386836i) q^{51} +(-10.6132 + 7.71091i) q^{53} -7.60459 q^{55} +(0.285342 - 0.878193i) q^{57} +(0.308516 + 0.949516i) q^{59} +(-2.41802 + 7.44191i) q^{61} +(2.84031 - 8.74159i) q^{63} +(-6.18568 - 4.49416i) q^{65} +(12.4686 - 9.05897i) q^{67} +(0.723750 + 2.22747i) q^{69} +(-10.9227 - 7.93581i) q^{71} -2.99847 q^{73} +(0.470211 - 1.44716i) q^{75} +(14.1763 - 10.2997i) q^{77} +0.897185 q^{79} +6.49409 q^{81} +6.26216 q^{83} +0.0180467 q^{85} +(-3.42242 + 2.48653i) q^{87} +(-2.00520 + 6.17138i) q^{89} +17.6181 q^{91} +(3.47458 + 2.52443i) q^{93} +(0.782449 + 2.40813i) q^{95} +(-3.71453 + 2.69876i) q^{97} +(11.3469 + 8.24403i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.536309			−0.309638			−0.154819	−	0.987943i	$-0.549479\pi$
$3$	−0.536309			−0.309638			−0.154819	+	0.987943i	$0.549479\pi$
$4$		0			0
$5$	1.18977	−	0.864417i	0.532080	−	0.386579i	−0.289055	−	0.957312i	$-0.593341\pi$
$5$	1.18977	−	0.864417i	0.532080	−	0.386579i	0.821135	+	0.570734i	$0.193341\pi$
$6$		0			0
$7$	−1.04717	+	3.22286i	−0.395793	+	1.21813i	0.532549	+	0.846399i	$0.321234\pi$
$7$	−1.04717	+	3.22286i	−0.395793	+	1.21813i	−0.928342	+	0.371726i	$0.878766\pi$
$8$		0			0
$9$	−2.71237			−0.904124
$10$		0			0
$11$	−4.18339	−	3.03941i	−1.26134	−	0.916418i	−0.262518	−	0.964927i	$-0.584553\pi$
$11$	−4.18339	−	3.03941i	−1.26134	−	0.916418i	−0.998823	+	0.0485092i	$0.984553\pi$
$12$		0			0
$13$	−1.60660	−	4.94461i	−0.445591	−	1.37139i	−0.881834	−	0.471559i	$-0.843691\pi$
$13$	−1.60660	−	4.94461i	−0.445591	−	1.37139i	0.436244	−	0.899829i	$-0.356309\pi$
$14$		0			0
$15$	−0.638082	+	0.463594i	−0.164752	+	0.119699i
$16$		0			0
$17$	0.00992776	+	0.00721294i	0.00240784	+	0.00174940i	0.588989	−	0.808141i	$-0.299526\pi$
$17$	0.00992776	+	0.00721294i	0.00240784	+	0.00174940i	−0.586581	+	0.809891i	$0.699526\pi$
$18$		0			0
$19$	−0.532049	+	1.63748i	−0.122060	+	0.375663i	−0.993354	−	0.115099i	$-0.963282\pi$
$19$	−0.532049	+	1.63748i	−0.122060	+	0.375663i	0.871294	+	0.490762i	$0.163282\pi$
$20$		0			0
$21$	0.561606	−	1.72845i	0.122552	−	0.377178i
$22$		0			0
$23$	−1.34950	−	4.15334i	−0.281391	−	0.866031i	−0.987457	−	0.157886i	$-0.949532\pi$
$23$	−1.34950	−	4.15334i	−0.281391	−	0.866031i	0.706067	−	0.708145i	$-0.250468\pi$
$24$		0			0
$25$	−0.876755	+	2.69837i	−0.175351	+	0.539675i
$26$		0			0
$27$	3.06359			0.589589
$28$		0			0
$29$	6.38144	−	4.63638i	1.18500	−	0.860955i	0.192276	−	0.981341i	$-0.438413\pi$
$29$	6.38144	−	4.63638i	1.18500	−	0.860955i	0.992727	+	0.120386i	$0.0384132\pi$
$30$		0			0
$31$	−6.47869	−	4.70704i	−1.16361	−	0.845410i	−0.173377	−	0.984855i	$-0.555468\pi$
$31$	−6.47869	−	4.70704i	−1.16361	−	0.845410i	−0.990230	+	0.139445i	$0.955468\pi$
$32$		0			0
$33$	2.24359	+	1.63006i	0.390559	+	0.283758i
$34$		0			0
$35$	1.54000	+	4.73964i	0.260308	+	0.801145i
$36$		0			0
$37$	−6.51439	+	4.73298i	−1.07096	+	0.778097i	−0.976084	−	0.217392i	$-0.930245\pi$
$37$	−6.51439	+	4.73298i	−1.07096	+	0.778097i	−0.0948746	+	0.995489i	$0.530245\pi$
$38$		0			0
$39$	0.861634	+	2.65184i	0.137972	+	0.424634i
$40$		0			0
$41$	−0.865824	−	6.34432i	−0.135219	−	0.990816i
$41$	−0.865824	−	6.34432i	−0.135219	−	0.990816i
$42$		0			0
$43$	−1.75493	−	5.40113i	−0.267625	−	0.823664i	−0.991077	−	0.133290i	$-0.957446\pi$
$43$	−1.75493	−	5.40113i	−0.267625	−	0.823664i	0.723452	−	0.690374i	$-0.242554\pi$
$44$		0			0
$45$	−3.22709	+	2.34462i	−0.481067	+	0.349515i
$46$		0			0
$47$	2.40280	+	7.39507i	0.350485	+	1.07868i	0.958581	+	0.284818i	$0.0919333\pi$
$47$	2.40280	+	7.39507i	0.350485	+	1.07868i	−0.608097	+	0.793863i	$0.708067\pi$
$48$		0			0
$49$	−3.62712	−	2.63526i	−0.518160	−	0.376465i
$50$		0			0
$51$	−0.00532435	−	0.00386836i	−0.000745557	−	0.000541679i
$52$		0			0
$53$	−10.6132	+	7.71091i	−1.45783	+	1.05917i	−0.473907	+	0.880575i	$0.657157\pi$
$53$	−10.6132	+	7.71091i	−1.45783	+	1.05917i	−0.983922	+	0.178599i	$0.942843\pi$
$54$		0			0
$55$	−7.60459			−1.02540
$56$		0			0
$57$	0.285342	−	0.878193i	0.0377945	−	0.116320i
$58$		0			0
$59$	0.308516	+	0.949516i	0.0401654	+	0.123616i	0.969129	−	0.246556i	$-0.0792988\pi$
$59$	0.308516	+	0.949516i	0.0401654	+	0.123616i	−0.928963	+	0.370172i	$0.879299\pi$
$60$		0			0
$61$	−2.41802	+	7.44191i	−0.309596	+	0.952839i	0.668326	+	0.743869i	$0.267011\pi$
$61$	−2.41802	+	7.44191i	−0.309596	+	0.952839i	−0.977922	+	0.208970i	$0.932989\pi$
$62$		0			0
$63$	2.84031	−	8.74159i	0.357846	−	1.10134i
$64$		0			0
$65$	−6.18568	−	4.49416i	−0.767240	−	0.557432i
$66$		0			0
$67$	12.4686	−	9.05897i	1.52328	−	1.10673i	0.563451	−	0.826149i	$-0.309473\pi$
$67$	12.4686	−	9.05897i	1.52328	−	1.10673i	0.959831	−	0.280580i	$-0.0905267\pi$
$68$		0			0
$69$	0.723750	+	2.22747i	0.0871292	+	0.268156i
$70$		0			0
$71$	−10.9227	−	7.93581i	−1.29629	−	0.941808i	−0.296375	−	0.955072i	$-0.595778\pi$
$71$	−10.9227	−	7.93581i	−1.29629	−	0.941808i	−0.999912	+	0.0132636i	$0.995778\pi$
$72$		0			0
$73$	−2.99847			−0.350944			−0.175472	−	0.984484i	$-0.556145\pi$
$73$	−2.99847			−0.350944			−0.175472	+	0.984484i	$0.556145\pi$
$74$		0			0
$75$	0.470211	−	1.44716i	0.0542953	−	0.167104i
$76$		0			0
$77$	14.1763	−	10.2997i	1.61554	−	1.17376i
$78$		0			0
$79$	0.897185			0.100941			0.0504706	−	0.998726i	$-0.483928\pi$
$79$	0.897185			0.100941			0.0504706	+	0.998726i	$0.483928\pi$
$80$		0			0
$81$	6.49409			0.721565
$82$		0			0
$83$	6.26216			0.687362			0.343681	−	0.939087i	$-0.388326\pi$
$83$	6.26216			0.687362			0.343681	+	0.939087i	$0.388326\pi$
$84$		0			0
$85$	0.0180467			0.00195744
$86$		0			0
$87$	−3.42242	+	2.48653i	−0.366922	+	0.266584i
$88$		0			0
$89$	−2.00520	+	6.17138i	−0.212551	+	0.654165i	0.786767	+	0.617250i	$0.211753\pi$
$89$	−2.00520	+	6.17138i	−0.212551	+	0.654165i	−0.999318	+	0.0369152i	$0.988247\pi$
$90$		0			0
$91$	17.6181			1.84688
$92$		0			0
$93$	3.47458	+	2.52443i	0.360297	+	0.261771i
$94$		0			0
$95$	0.782449	+	2.40813i	0.0802776	+	0.247069i
$96$		0			0
$97$	−3.71453	+	2.69876i	−0.377153	+	0.274018i	−0.760171	−	0.649723i	$-0.774885\pi$
$97$	−3.71453	+	2.69876i	−0.377153	+	0.274018i	0.383018	+	0.923741i	$0.374885\pi$
$98$		0			0
$99$	11.3469	+	8.24403i	1.14041	+	0.828556i
$100$		0			0
$101$	1.46185	−	4.49910i	0.145459	−	0.447677i	−0.851611	−	0.524175i	$-0.824374\pi$
$101$	1.46185	−	4.49910i	0.145459	−	0.447677i	0.997070	+	0.0764978i	$0.0243738\pi$
$102$		0			0
$103$	−2.23371	+	6.87465i	−0.220094	+	0.677379i	0.778659	+	0.627448i	$0.215900\pi$
$103$	−2.23371	+	6.87465i	−0.220094	+	0.677379i	−0.998753	+	0.0499315i	$0.984100\pi$
$104$		0			0
$105$	−0.825917	−	2.54191i	−0.0806012	−	0.248065i
$106$		0			0
$107$	0.811952	−	2.49893i	0.0784944	−	0.241581i	−0.904108	−	0.427305i	$-0.859463\pi$
$107$	0.811952	−	2.49893i	0.0784944	−	0.241581i	0.982602	+	0.185724i	$0.0594631\pi$
$108$		0			0
$109$	−0.907645			−0.0869366			−0.0434683	−	0.999055i	$-0.513841\pi$
$109$	−0.907645			−0.0869366			−0.0434683	+	0.999055i	$0.513841\pi$
$110$		0			0
$111$	3.49372	−	2.53834i	0.331609	−	0.240928i
$112$		0			0
$113$	−0.938120	−	0.681584i	−0.0882509	−	0.0641181i	0.542785	−	0.839872i	$-0.317370\pi$
$113$	−0.938120	−	0.681584i	−0.0882509	−	0.0641181i	−0.631036	+	0.775754i	$0.717370\pi$
$114$		0			0
$115$	−5.19581	−	3.77498i	−0.484512	−	0.352018i
$116$		0			0
$117$	4.35770	+	13.4116i	0.402870	+	1.23991i
$118$		0			0
$119$	−0.0336423	+	0.0244426i	−0.00308399	+	0.00224065i
$120$		0			0
$121$	4.86357	+	14.9685i	0.442142	+	1.36077i
$122$		0			0
$123$	0.464349	+	3.40251i	0.0418689	+	0.306794i
$124$		0			0
$125$	3.56164	+	10.9616i	0.318563	+	0.980435i
$126$		0			0
$127$	−10.4551	+	7.59607i	−0.927739	+	0.674042i	−0.945438	−	0.325802i	$-0.894366\pi$
$127$	−10.4551	+	7.59607i	−0.927739	+	0.674042i	0.0176992	+	0.999843i	$0.494366\pi$
$128$		0			0
$129$	0.941185	+	2.89667i	0.0828667	+	0.255038i
$130$		0			0
$131$	7.06156	+	5.13052i	0.616971	+	0.448256i	0.851862	−	0.523766i	$-0.175473\pi$
$131$	7.06156	+	5.13052i	0.616971	+	0.448256i	−0.234891	+	0.972022i	$0.575473\pi$
$132$		0			0
$133$	−4.72021	−	3.42943i	−0.409294	−	0.297370i
$134$		0			0
$135$	3.64497	−	2.64822i	0.313709	−	0.227923i
$136$		0			0
$137$	14.4218			1.23214			0.616068	−	0.787693i	$-0.288724\pi$
$137$	14.4218			1.23214			0.616068	+	0.787693i	$0.288724\pi$
$138$		0			0
$139$	−2.54121	+	7.82103i	−0.215542	+	0.663371i	0.783572	+	0.621301i	$0.213395\pi$
$139$	−2.54121	+	7.82103i	−0.215542	+	0.663371i	−0.999115	+	0.0420704i	$0.986605\pi$
$140$		0			0
$141$	−1.28864	−	3.96604i	−0.108523	−	0.334001i
$142$		0			0
$143$	−8.30767	+	25.5684i	−0.694722	+	2.13814i
$144$		0			0
$145$	3.58466	−	11.0324i	0.297690	−	0.916194i
$146$		0			0
$147$	1.94526	+	1.41331i	0.160442	+	0.116568i
$148$		0			0
$149$	6.47421	−	4.70379i	0.530388	−	0.385350i	−0.290115	−	0.956992i	$-0.593693\pi$
$149$	6.47421	−	4.70379i	0.530388	−	0.385350i	0.820503	+	0.571642i	$0.193693\pi$
$150$		0			0
$151$	−1.50888	−	4.64386i	−0.122791	−	0.377912i	0.870701	−	0.491812i	$-0.163665\pi$
$151$	−1.50888	−	4.64386i	−0.122791	−	0.377912i	−0.993492	+	0.113901i	$0.963665\pi$
$152$		0			0
$153$	−0.0269278	−	0.0195642i	−0.00217698	−	0.00158167i
$154$		0			0
$155$	−11.7770			−0.945950
$156$		0			0
$157$	6.33293	−	19.4908i	0.505423	−	1.55553i	−0.294636	−	0.955610i	$-0.595198\pi$
$157$	6.33293	−	19.4908i	0.505423	−	1.55553i	0.800058	−	0.599922i	$-0.204802\pi$
$158$		0			0
$159$	5.69192	−	4.13543i	0.451399	−	0.327961i
$160$		0			0
$161$	14.7988			1.16631
$162$		0			0
$163$	11.9723			0.937740			0.468870	−	0.883267i	$-0.344661\pi$
$163$	11.9723			0.937740			0.468870	+	0.883267i	$0.344661\pi$
$164$		0			0
$165$	4.07841			0.317503
$166$		0			0
$167$	12.9084			0.998881			0.499440	−	0.866348i	$-0.333539\pi$
$167$	12.9084			0.998881			0.499440	+	0.866348i	$0.333539\pi$
$168$		0			0
$169$	−11.3508	+	8.24682i	−0.873136	+	0.634371i
$170$		0			0
$171$	1.44312	−	4.44145i	0.110358	−	0.339646i
$172$		0			0
$173$	12.4230			0.944500			0.472250	−	0.881465i	$-0.343442\pi$
$173$	12.4230			0.944500			0.472250	+	0.881465i	$0.343442\pi$
$174$		0			0
$175$	−7.77836	−	5.65131i	−0.587989	−	0.427199i
$176$		0			0
$177$	−0.165460	−	0.509234i	−0.0124367	−	0.0382763i
$178$		0			0
$179$	−12.5860	+	9.14428i	−0.940723	+	0.683476i	−0.948595	−	0.316493i	$-0.897494\pi$
$179$	−12.5860	+	9.14428i	−0.940723	+	0.683476i	0.00787122	+	0.999969i	$0.497494\pi$
$180$		0			0
$181$	−14.8005	−	10.7532i	−1.10011	−	0.799277i	−0.119033	−	0.992890i	$-0.537979\pi$
$181$	−14.8005	−	10.7532i	−1.10011	−	0.799277i	−0.981078	+	0.193613i	$0.937979\pi$
$182$		0			0
$183$	1.29681	−	3.99116i	0.0958627	−	0.295035i
$184$		0			0
$185$	−3.65934	+	11.2623i	−0.269040	+	0.828020i
$186$		0			0
$187$	−0.0196086	−	0.0603492i	−0.00143393	−	0.00441317i
$188$		0			0
$189$	−3.20810	+	9.87353i	−0.233355	+	0.718193i
$190$		0			0
$191$	−11.6699			−0.844405			−0.422203	−	0.906501i	$-0.638743\pi$
$191$	−11.6699			−0.844405			−0.422203	+	0.906501i	$0.638743\pi$
$192$		0			0
$193$	16.9084	−	12.2847i	1.21709	−	0.884270i	0.221238	−	0.975220i	$-0.428990\pi$
$193$	16.9084	−	12.2847i	1.21709	−	0.884270i	0.995855	+	0.0909498i	$0.0289903\pi$
$194$		0			0
$195$	3.31744	+	2.41026i	0.237566	+	0.172602i
$196$		0			0
$197$	0.468208	+	0.340173i	0.0333584	+	0.0242363i	0.604340	−	0.796727i	$-0.293437\pi$
$197$	0.468208	+	0.340173i	0.0333584	+	0.0242363i	−0.570981	+	0.820963i	$0.693437\pi$
$198$		0			0
$199$	−3.59686	−	11.0700i	−0.254975	−	0.784731i	−0.993835	−	0.110872i	$-0.964636\pi$
$199$	−3.59686	−	11.0700i	−0.254975	−	0.784731i	0.738860	−	0.673859i	$-0.235364\pi$
$200$		0			0
$201$	−6.68702	+	4.85840i	−0.471666	+	0.342685i
$202$		0			0
$203$	8.25996	+	25.4215i	0.579735	+	1.78424i
$204$		0			0
$205$	−6.51426	−	6.79983i	−0.454976	−	0.474921i
$206$		0			0
$207$	3.66035	+	11.2654i	0.254412	+	0.783000i
$208$		0			0
$209$	7.20274	−	5.23310i	0.498224	−	0.361981i
$210$		0			0
$211$	−4.54377	−	13.9843i	−0.312806	−	0.962718i	−0.976648	−	0.214845i	$-0.931075\pi$
$211$	−4.54377	−	13.9843i	−0.312806	−	0.962718i	0.663842	−	0.747873i	$-0.268925\pi$
$212$		0			0
$213$	5.85794	+	4.25605i	0.401380	+	0.291619i
$214$		0			0
$215$	−6.75679	−	4.90909i	−0.460809	−	0.334797i
$216$		0			0
$217$	21.9544	−	15.9508i	1.49036	−	1.08281i
$218$		0			0
$219$	1.60810			0.108666
$220$		0			0
$221$	0.0197152	−	0.0606772i	0.00132619	−	0.00408159i
$222$		0			0
$223$	−5.32387	−	16.3852i	−0.356513	−	1.09723i	−0.955127	−	0.296197i	$-0.904282\pi$
$223$	−5.32387	−	16.3852i	−0.356513	−	1.09723i	0.598614	−	0.801038i	$-0.295718\pi$
$224$		0			0
$225$	2.37809	−	7.31899i	0.158539	−	0.487933i
$226$		0			0
$227$	5.13209	−	15.7949i	0.340629	−	1.04835i	−0.623254	−	0.782019i	$-0.714190\pi$
$227$	5.13209	−	15.7949i	0.340629	−	1.04835i	0.963883	−	0.266327i	$-0.0858102\pi$
$228$		0			0
$229$	−8.70970	−	6.32797i	−0.575553	−	0.418164i	0.261565	−	0.965186i	$-0.415761\pi$
$229$	−8.70970	−	6.32797i	−0.575553	−	0.418164i	−0.837118	+	0.547022i	$0.815761\pi$
$230$		0			0
$231$	−7.60288	+	5.52382i	−0.500233	+	0.363440i
$232$		0			0
$233$	−3.68794	−	11.3503i	−0.241605	−	0.743585i	−0.996176	−	0.0873662i	$-0.972155\pi$
$233$	−3.68794	−	11.3503i	−0.241605	−	0.743585i	0.754571	−	0.656218i	$-0.227845\pi$
$234$		0			0
$235$	9.25120	+	6.72139i	0.603482	+	0.438455i
$236$		0			0
$237$	−0.481168			−0.0312552
$238$		0			0
$239$	−3.60319	+	11.0895i	−0.233071	+	0.717318i	0.764301	+	0.644860i	$0.223084\pi$
$239$	−3.60319	+	11.0895i	−0.233071	+	0.717318i	−0.997371	+	0.0724582i	$0.976916\pi$
$240$		0			0
$241$	−22.0825	+	16.0439i	−1.42246	+	1.03348i	−0.431097	+	0.902305i	$0.641873\pi$
$241$	−22.0825	+	16.0439i	−1.42246	+	1.03348i	−0.991360	+	0.131170i	$0.958127\pi$
$242$		0			0
$243$	−12.6736			−0.813013
$244$		0			0
$245$	−6.59339			−0.421236
$246$		0			0
$247$	8.95148			0.569569
$248$		0			0
$249$	−3.35845			−0.212833
$250$		0			0
$251$	1.75058	−	1.27187i	0.110496	−	0.0802799i	−0.531165	−	0.847268i	$-0.678246\pi$
$251$	1.75058	−	1.27187i	0.110496	−	0.0802799i	0.641661	+	0.766988i	$0.278246\pi$
$252$		0			0
$253$	−6.97822	+	21.4768i	−0.438717	+	1.35023i
$254$		0			0
$255$	−0.00967861			−0.000606098
$256$		0			0
$257$	14.0484	+	10.2067i	0.876314	+	0.636679i	0.932274	−	0.361754i	$-0.117822\pi$
$257$	14.0484	+	10.2067i	0.876314	+	0.636679i	−0.0559600	+	0.998433i	$0.517822\pi$
$258$		0			0
$259$	−8.43205	−	25.9512i	−0.523942	−	1.61253i
$260$		0			0
$261$	−17.3088	+	12.5756i	−1.07139	+	0.778410i
$262$		0			0
$263$	0.643703	+	0.467678i	0.0396924	+	0.0288382i	0.607455	−	0.794354i	$-0.292191\pi$
$263$	0.643703	+	0.467678i	0.0396924	+	0.0288382i	−0.567762	+	0.823193i	$0.692191\pi$
$264$		0			0
$265$	−5.96175	+	18.3484i	−0.366227	+	1.12713i
$266$		0			0
$267$	1.07541	−	3.30976i	0.0658139	−	0.202554i
$268$		0			0
$269$	−0.0295506	−	0.0909474i	−0.00180173	−	0.00554516i	0.950152	−	0.311788i	$-0.100928\pi$
$269$	−0.0295506	−	0.0909474i	−0.00180173	−	0.00554516i	−0.951953	+	0.306243i	$0.900928\pi$
$270$		0			0
$271$	0.814651	−	2.50724i	0.0494865	−	0.152304i	−0.923260	−	0.384177i	$-0.874485\pi$
$271$	0.814651	−	2.50724i	0.0494865	−	0.152304i	0.972746	+	0.231873i	$0.0744853\pi$
$272$		0			0
$273$	−9.44876			−0.571865
$274$		0			0
$275$	11.8693	−	8.62354i	0.715745	−	0.520019i
$276$		0			0
$277$	−18.8841	−	13.7201i	−1.13464	−	0.824361i	−0.148272	−	0.988947i	$-0.547371\pi$
$277$	−18.8841	−	13.7201i	−1.13464	−	0.824361i	−0.986363	+	0.164586i	$0.947371\pi$
$278$		0			0
$279$	17.5726	+	12.7673i	1.05205	+	0.764356i
$280$		0			0
$281$	3.12914	+	9.63049i	0.186669	+	0.574507i	0.999973	−	0.00733142i	$-0.00233369\pi$
$281$	3.12914	+	9.63049i	0.186669	+	0.574507i	−0.813305	+	0.581838i	$0.802334\pi$
$282$		0			0
$283$	1.68807	−	1.22645i	0.100345	−	0.0729049i	−0.536481	−	0.843912i	$-0.680247\pi$
$283$	1.68807	−	1.22645i	0.100345	−	0.0729049i	0.636826	+	0.771007i	$0.280247\pi$
$284$		0			0
$285$	−0.419634	−	1.29150i	−0.0248570	−	0.0765019i
$286$		0			0
$287$	21.3535	+	3.85315i	1.26046	+	0.227444i
$288$		0			0
$289$	−5.25324	−	16.1678i	−0.309014	−	0.951048i
$290$		0			0
$291$	1.99213	−	1.44737i	0.116781	−	0.0848464i
$292$		0			0
$293$	1.64566	+	5.06481i	0.0961403	+	0.295890i	0.987549	−	0.157310i	$-0.0502823\pi$
$293$	1.64566	+	5.06481i	0.0961403	+	0.295890i	−0.891409	+	0.453200i	$0.850282\pi$
$294$		0			0
$295$	1.18784	+	0.863016i	0.0691587	+	0.0502468i
$296$		0			0
$297$	−12.8162	−	9.31153i	−0.743673	−	0.540310i
$298$		0			0
$299$	−18.3685	+	13.3455i	−1.06228	+	0.771791i
$300$		0			0
$301$	19.2448			1.10925
$302$		0			0
$303$	−0.784000	+	2.41290i	−0.0450396	+	0.138618i
$304$		0			0
$305$	3.55603	+	10.9443i	0.203617	+	0.626670i
$306$		0			0
$307$	−1.59193	+	4.89945i	−0.0908561	+	0.279626i	−0.986152	−	0.165846i	$-0.946964\pi$
$307$	−1.59193	+	4.89945i	−0.0908561	+	0.279626i	0.895295	+	0.445473i	$0.146964\pi$
$308$		0			0
$309$	1.19796	−	3.68693i	0.0681494	−	0.209742i
$310$		0			0
$311$	4.14700	+	3.01297i	0.235155	+	0.170850i	0.699122	−	0.715003i	$-0.253574\pi$
$311$	4.14700	+	3.01297i	0.235155	+	0.170850i	−0.463967	+	0.885852i	$0.653574\pi$
$312$		0			0
$313$	3.61294	−	2.62495i	0.204215	−	0.148371i	−0.480977	−	0.876733i	$-0.659718\pi$
$313$	3.61294	−	2.62495i	0.204215	−	0.148371i	0.685193	+	0.728362i	$0.259718\pi$
$314$		0			0
$315$	−4.17706	−	12.8557i	−0.235351	−	0.724335i
$316$		0			0
$317$	−19.8307	−	14.4078i	−1.11380	−	0.809225i	−0.130545	−	0.991442i	$-0.541673\pi$
$317$	−19.8307	−	14.4078i	−1.11380	−	0.809225i	−0.983258	+	0.182217i	$0.941673\pi$
$318$		0			0
$319$	−40.7880			−2.28369
$320$		0			0
$321$	−0.435457	+	1.34020i	−0.0243048	+	0.0748026i
$322$		0			0
$323$	−0.0170931	+	0.0124189i	−0.000951085	+	0.000691004i
$324$		0			0
$325$	14.7510			0.818238
$326$		0			0
$327$	0.486778			0.0269189
$328$		0			0
$329$	−26.3494			−1.45269
$330$		0			0
$331$	6.12261			0.336529			0.168265	−	0.985742i	$-0.446184\pi$
$331$	6.12261			0.336529			0.168265	+	0.985742i	$0.446184\pi$
$332$		0			0
$333$	17.6695	−	12.8376i	0.968280	−	0.703497i
$334$		0			0
$335$	7.00401	−	21.5561i	0.382670	−	1.17774i
$336$		0			0
$337$	−33.5383			−1.82694			−0.913472	−	0.406901i	$-0.866610\pi$
$337$	−33.5383			−1.82694			−0.913472	+	0.406901i	$0.866610\pi$
$338$		0			0
$339$	0.503122	+	0.365540i	0.0273258	+	0.0198534i
$340$		0			0
$341$	12.7963	+	39.3828i	0.692956	+	2.13270i
$342$		0			0
$343$	−6.89941	+	5.01271i	−0.372533	+	0.270661i
$344$		0			0
$345$	2.78656	+	2.02455i	0.150023	+	0.108998i
$346$		0			0
$347$	4.06478	−	12.5101i	0.218209	−	0.671577i	−0.780702	−	0.624904i	$-0.785138\pi$
$347$	4.06478	−	12.5101i	0.218209	−	0.671577i	0.998910	−	0.0466730i	$-0.0148619\pi$
$348$		0			0
$349$	−0.961393	+	2.95886i	−0.0514622	+	0.158384i	−0.973485	−	0.228752i	$-0.926536\pi$
$349$	−0.961393	+	2.95886i	−0.0514622	+	0.158384i	0.922023	+	0.387136i	$0.126536\pi$
$350$		0			0
$351$	−4.92197	−	15.1483i	−0.262716	−	0.808555i
$352$		0			0
$353$	7.85621	−	24.1789i	0.418144	−	1.28691i	−0.491265	−	0.871010i	$-0.663465\pi$
$353$	7.85621	−	24.1789i	0.418144	−	1.28691i	0.909409	−	0.415904i	$-0.136535\pi$
$354$		0			0
$355$	−19.8553			−1.05381
$356$		0			0
$357$	0.0180427	−	0.0131088i	0.000954919	−	0.000693790i
$358$		0			0
$359$	13.8239	+	10.0436i	0.729597	+	0.530083i	0.889436	−	0.457060i	$-0.151098\pi$
$359$	13.8239	+	10.0436i	0.729597	+	0.530083i	−0.159839	+	0.987143i	$0.551098\pi$
$360$		0			0
$361$	12.9731	+	9.42548i	0.682793	+	0.496078i
$362$		0			0
$363$	−2.60837	−	8.02774i	−0.136904	−	0.421347i
$364$		0			0
$365$	−3.56748	+	2.59192i	−0.186730	+	0.135667i
$366$		0			0
$367$	−6.43731	−	19.8120i	−0.336025	−	1.03418i	−0.966215	−	0.257738i	$-0.917023\pi$
$367$	−6.43731	−	19.8120i	−0.336025	−	1.03418i	0.630190	−	0.776441i	$-0.282977\pi$
$368$		0			0
$369$	2.34844	+	17.2082i	0.122255	+	0.895821i
$370$		0			0
$371$	−13.7374	−	42.2793i	−0.713209	−	2.19503i
$372$		0			0
$373$	−14.4832	+	10.5226i	−0.749910	+	0.544842i	−0.895799	−	0.444459i	$-0.853396\pi$
$373$	−14.4832	+	10.5226i	−0.749910	+	0.544842i	0.145889	+	0.989301i	$0.453396\pi$
$374$		0			0
$375$	−1.91014	−	5.87880i	−0.0986391	−	0.303580i
$376$		0			0
$377$	−33.1775	−	24.1049i	−1.70873	−	1.24146i
$378$		0			0
$379$	18.8584	+	13.7014i	0.968692	+	0.703796i	0.955153	−	0.296113i	$-0.0956904\pi$
$379$	18.8584	+	13.7014i	0.968692	+	0.703796i	0.0135387	+	0.999908i	$0.495690\pi$
$380$		0			0
$381$	5.60715	−	4.07383i	0.287263	−	0.208709i
$382$		0			0
$383$	16.1270			0.824051			0.412026	−	0.911172i	$-0.364821\pi$
$383$	16.1270			0.824051			0.412026	+	0.911172i	$0.364821\pi$
$384$		0			0
$385$	7.96329	−	24.5085i	0.405847	−	1.24907i
$386$		0			0
$387$	4.76003	+	14.6499i	0.241966	+	0.744695i
$388$		0			0
$389$	0.171436	−	0.527626i	0.00869216	−	0.0267517i	−0.946616	−	0.322362i	$-0.895523\pi$
$389$	0.171436	−	0.527626i	0.00869216	−	0.0267517i	0.955309	+	0.295611i	$0.0955231\pi$
$390$		0			0
$391$	0.0165603	−	0.0509673i	0.000837489	−	0.00257753i
$392$		0			0
$393$	−3.78717	−	2.75154i	−0.191038	−	0.138797i
$394$		0			0
$395$	1.06744	−	0.775542i	0.0537088	−	0.0390217i
$396$		0			0
$397$	−8.58528	−	26.4228i	−0.430883	−	1.32612i	−0.897247	−	0.441529i	$-0.854436\pi$
$397$	−8.58528	−	26.4228i	−0.430883	−	1.32612i	0.466364	−	0.884593i	$-0.345564\pi$
$398$		0			0
$399$	2.53149	+	1.83923i	0.126733	+	0.0920769i
$400$		0			0
$401$	21.6172			1.07951			0.539756	−	0.841822i	$-0.318517\pi$
$401$	21.6172			1.07951			0.539756	+	0.841822i	$0.318517\pi$
$402$		0			0
$403$	−12.8658	+	39.5969i	−0.640892	+	1.97246i
$404$		0			0
$405$	7.72645	−	5.61360i	0.383931	−	0.278942i
$406$		0			0
$407$	41.6378			2.06391
$408$		0			0
$409$	−38.5588			−1.90661			−0.953306	−	0.302007i	$-0.902343\pi$
$409$	−38.5588			−1.90661			−0.953306	+	0.302007i	$0.902343\pi$
$410$		0			0
$411$	−7.73453			−0.381516
$412$		0			0
$413$	−3.38322			−0.166477
$414$		0			0
$415$	7.45052	−	5.41312i	0.365731	−	0.265719i
$416$		0			0
$417$	1.36287	−	4.19448i	0.0667401	−	0.205405i
$418$		0			0
$419$	−17.3204			−0.846155			−0.423077	−	0.906094i	$-0.639050\pi$
$419$	−17.3204			−0.846155			−0.423077	+	0.906094i	$0.639050\pi$
$420$		0			0
$421$	−6.19204	−	4.49878i	−0.301782	−	0.219257i	0.426580	−	0.904450i	$-0.359718\pi$
$421$	−6.19204	−	4.49878i	−0.301782	−	0.219257i	−0.728362	+	0.685192i	$0.759718\pi$
$422$		0			0
$423$	−6.51730	−	20.0582i	−0.316882	−	0.975262i
$424$		0			0
$425$	−0.0281674	+	0.0204648i	−0.00136632	+	0.000992690i
$426$		0			0
$427$	−21.4521	−	15.5859i	−1.03814	−	0.754254i
$428$		0			0
$429$	4.45547	−	13.7125i	0.215112	−	0.662048i
$430$		0			0
$431$	−2.27642	+	7.00610i	−0.109651	+	0.337472i	−0.990794	−	0.135378i	$-0.956775\pi$
$431$	−2.27642	+	7.00610i	−0.109651	+	0.337472i	0.881143	+	0.472851i	$0.156775\pi$
$432$		0			0
$433$	−1.93618	−	5.95894i	−0.0930467	−	0.286368i	0.893693	−	0.448679i	$-0.148105\pi$
$433$	−1.93618	−	5.95894i	−0.0930467	−	0.286368i	−0.986740	+	0.162311i	$0.948105\pi$
$434$		0			0
$435$	−1.92248	+	5.91679i	−0.0921760	+	0.283688i
$436$		0			0
$437$	7.51901			0.359683
$438$		0			0
$439$	−31.2592	+	22.7111i	−1.49192	+	1.08394i	−0.518457	+	0.855104i	$0.673493\pi$
$439$	−31.2592	+	22.7111i	−1.49192	+	1.08394i	−0.973464	+	0.228840i	$0.926507\pi$
$440$		0			0
$441$	9.83811	+	7.14780i	0.468481	+	0.340372i
$442$		0			0
$443$	−10.8720	−	7.89896i	−0.516543	−	0.375291i	0.298757	−	0.954329i	$-0.403428\pi$
$443$	−10.8720	−	7.89896i	−0.516543	−	0.375291i	−0.815300	+	0.579038i	$0.803428\pi$
$444$		0			0
$445$	2.94892	+	9.07584i	0.139792	+	0.430236i
$446$		0			0
$447$	−3.47218	+	2.52268i	−0.164228	+	0.119319i
$448$		0			0
$449$	1.12377	+	3.45861i	0.0530339	+	0.163222i	0.974065	−	0.226266i	$-0.0726520\pi$
$449$	1.12377	+	3.45861i	0.0530339	+	0.163222i	−0.921032	+	0.389488i	$0.872652\pi$
$450$		0			0
$451$	−15.6609	+	29.1724i	−0.737444	+	1.37367i
$452$		0			0
$453$	0.809226	+	2.49054i	0.0380207	+	0.117016i
$454$		0			0
$455$	20.9615	−	15.2294i	0.982690	−	0.713966i
$456$		0			0
$457$	1.41606	+	4.35820i	0.0662407	+	0.203868i	0.978698	−	0.205303i	$-0.0658180\pi$
$457$	1.41606	+	4.35820i	0.0662407	+	0.203868i	−0.912458	+	0.409171i	$0.865818\pi$
$458$		0			0
$459$	0.0304146	+	0.0220975i	0.00141963	+	0.00103142i
$460$		0			0
$461$	−15.5266	−	11.2807i	−0.723145	−	0.525396i	0.164242	−	0.986420i	$-0.447482\pi$
$461$	−15.5266	−	11.2807i	−0.723145	−	0.525396i	−0.887388	+	0.461024i	$0.847482\pi$
$462$		0			0
$463$	20.7458	−	15.0727i	0.964137	−	0.700487i	0.0100295	−	0.999950i	$-0.496807\pi$
$463$	20.7458	−	15.0727i	0.964137	−	0.700487i	0.954108	+	0.299463i	$0.0968075\pi$
$464$		0			0
$465$	6.31610			0.292902
$466$		0			0
$467$	−9.11407	+	28.0502i	−0.421749	+	1.29801i	0.484325	+	0.874888i	$0.339065\pi$
$467$	−9.11407	+	28.0502i	−0.421749	+	1.29801i	−0.906073	+	0.423121i	$0.860935\pi$
$468$		0			0
$469$	16.1390	+	49.6708i	0.745230	+	2.29358i
$470$		0			0
$471$	−3.39640	+	10.4531i	−0.156498	+	0.481652i
$472$		0			0
$473$	−9.07469	+	27.9290i	−0.417255	+	1.28418i
$474$		0			0
$475$	−3.95205	−	2.87133i	−0.181332	−	0.131746i
$476$		0			0
$477$	28.7868	−	20.9149i	1.31806	−	0.957625i
$478$		0			0
$479$	7.56000	+	23.2673i	0.345425	+	1.06311i	0.961356	+	0.275309i	$0.0887801\pi$
$479$	7.56000	+	23.2673i	0.345425	+	1.06311i	−0.615931	+	0.787800i	$0.711220\pi$
$480$		0			0
$481$	33.8688	+	24.6071i	1.54428	+	1.12199i
$482$		0			0
$483$	−7.93671			−0.361133
$484$		0			0
$485$	−2.08657	+	6.42180i	−0.0947463	+	0.291599i
$486$		0			0
$487$	−12.6539	+	9.19360i	−0.573403	+	0.416602i	−0.836340	−	0.548211i	$-0.815309\pi$
$487$	−12.6539	+	9.19360i	−0.573403	+	0.416602i	0.262937	+	0.964813i	$0.415309\pi$
$488$		0			0
$489$	−6.42083			−0.290360
$490$		0			0
$491$	−21.3678			−0.964314			−0.482157	−	0.876085i	$-0.660147\pi$
$491$	−21.3678			−0.964314			−0.482157	+	0.876085i	$0.660147\pi$
$492$		0			0
$493$	0.0967954			0.00435944
$494$		0			0
$495$	20.6265			0.927091
$496$		0			0
$497$	37.0139	−	26.8922i	1.66030	−	1.20628i
$498$		0			0
$499$	−2.50738	+	7.71694i	−0.112246	+	0.345458i	−0.991363	−	0.131149i	$-0.958133\pi$
$499$	−2.50738	+	7.71694i	−0.112246	+	0.345458i	0.879117	+	0.476607i	$0.158133\pi$
$500$		0			0
$501$	−6.92288			−0.309291
$502$		0			0
$503$	−22.5657	−	16.3949i	−1.00615	−	0.731013i	−0.0427540	−	0.999086i	$-0.513613\pi$
$503$	−22.5657	−	16.3949i	−1.00615	−	0.731013i	−0.963399	+	0.268073i	$0.913613\pi$
$504$		0			0
$505$	−2.14984	−	6.61652i	−0.0956666	−	0.294431i
$506$		0			0
$507$	6.08752	−	4.42284i	0.270356	−	0.196425i
$508$		0			0
$509$	−25.3743	−	18.4355i	−1.12469	−	0.817139i	−0.139781	−	0.990182i	$-0.544640\pi$
$509$	−25.3743	−	18.4355i	−1.12469	−	0.817139i	−0.984914	+	0.173044i	$0.944640\pi$
$510$		0			0
$511$	3.13990	−	9.66363i	0.138901	−	0.427494i
$512$		0			0
$513$	−1.62998	+	5.01657i	−0.0719655	+	0.221487i
$514$		0			0
$515$	3.28497	+	10.1101i	0.144753	+	0.445504i
$516$		0			0
$517$	12.4248	−	38.2396i	0.546442	−	1.68178i
$518$		0			0
$519$	−6.66254			−0.292453
$520$		0			0
$521$	25.4349	−	18.4795i	1.11432	−	0.809602i	0.130983	−	0.991385i	$-0.458187\pi$
$521$	25.4349	−	18.4795i	1.11432	−	0.809602i	0.983339	+	0.181782i	$0.0581866\pi$
$522$		0			0
$523$	6.79079	+	4.93380i	0.296941	+	0.215740i	0.726273	−	0.687407i	$-0.241251\pi$
$523$	6.79079	+	4.93380i	0.296941	+	0.215740i	−0.429332	+	0.903147i	$0.641251\pi$
$524$		0			0
$525$	4.17160	+	3.03085i	0.182064	+	0.132277i
$526$		0			0
$527$	−0.0303673	−	0.0934609i	−0.00132282	−	0.00407122i
$528$		0			0
$529$	3.17831	−	2.30918i	0.138187	−	0.100399i
$530$		0			0
$531$	−0.836812	−	2.57544i	−0.0363145	−	0.111765i
$532$		0			0
$533$	−29.9791	+	14.4739i	−1.29854	+	0.626936i
$534$		0			0
$535$	−1.19408	−	3.67501i	−0.0516248	−	0.158885i
$536$		0			0
$537$	6.74999	−	4.90416i	0.291284	−	0.211630i
$538$		0			0
$539$	7.16404	+	22.0486i	0.308577	+	0.949702i
$540$		0			0
$541$	20.0787	+	14.5880i	0.863251	+	0.627188i	0.928767	−	0.370663i	$-0.120870\pi$
$541$	20.0787	+	14.5880i	0.863251	+	0.627188i	−0.0655167	+	0.997851i	$0.520870\pi$
$542$		0			0
$543$	7.93762	+	5.76702i	0.340636	+	0.247486i
$544$		0			0
$545$	−1.07989	+	0.784583i	−0.0462572	+	0.0336078i
$546$		0			0
$547$	32.3022			1.38114			0.690572	−	0.723264i	$-0.257359\pi$
$547$	32.3022			1.38114			0.690572	+	0.723264i	$0.257359\pi$
$548$		0			0
$549$	6.55858	−	20.1852i	0.279913	−	0.861485i
$550$		0			0
$551$	4.19674	+	12.9162i	0.178787	+	0.550250i
$552$		0			0
$553$	−0.939505	+	2.89150i	−0.0399518	+	0.122959i
$554$		0			0
$555$	1.96254	−	6.04006i	0.0833050	−	0.256386i
$556$		0			0
$557$	3.75979	+	2.73165i	0.159307	+	0.115744i	0.664583	−	0.747214i	$-0.268609\pi$
$557$	3.75979	+	2.73165i	0.159307	+	0.115744i	−0.505276	+	0.862958i	$0.668609\pi$
$558$		0			0
$559$	−23.8870	+	17.3549i	−1.01031	+	0.734034i
$560$		0			0
$561$	0.0105163	+	0.0323658i	0.000443998	+	0.00136648i
$562$		0			0
$563$	−13.5531	−	9.84687i	−0.571193	−	0.414996i	0.264345	−	0.964428i	$-0.414844\pi$
$563$	−13.5531	−	9.84687i	−0.571193	−	0.414996i	−0.835539	+	0.549432i	$0.814844\pi$
$564$		0			0
$565$	−1.70532			−0.0717433
$566$		0			0
$567$	−6.80041	+	20.9295i	−0.285590	+	0.878957i
$568$		0			0
$569$	−30.9943	+	22.5187i	−1.29935	+	0.944032i	−0.999949	−	0.0100959i	$-0.996786\pi$
$569$	−30.9943	+	22.5187i	−1.29935	+	0.944032i	−0.299399	+	0.954128i	$0.596786\pi$
$570$		0			0
$571$	23.5668			0.986239			0.493119	−	0.869962i	$-0.335857\pi$
$571$	23.5668			0.986239			0.493119	+	0.869962i	$0.335857\pi$
$572$		0			0
$573$	6.25868			0.261460
$574$		0			0
$575$	12.3904			0.516717
$576$		0			0
$577$	45.4040			1.89019			0.945096	−	0.326792i	$-0.105968\pi$
$577$	45.4040			1.89019			0.945096	+	0.326792i	$0.105968\pi$
$578$		0			0
$579$	−9.06812	+	6.58838i	−0.376858	+	0.273804i
$580$		0			0
$581$	−6.55755	+	20.1821i	−0.272053	+	0.837293i
$582$		0			0
$583$	67.8356			2.80947
$584$		0			0
$585$	16.7779	+	12.1898i	0.693680	+	0.503988i
$586$		0			0
$587$	−10.2628	−	31.5856i	−0.423590	−	1.30368i	−0.904338	−	0.426817i	$-0.859635\pi$
$587$	−10.2628	−	31.5856i	−0.423590	−	1.30368i	0.480748	−	0.876859i	$-0.340365\pi$
$588$		0			0
$589$	11.1547	−	8.10434i	0.459620	−	0.333933i
$590$		0			0
$591$	−0.251104	−	0.182438i	−0.0103290	−	0.00750448i
$592$		0			0
$593$	6.01074	−	18.4991i	0.246831	−	0.759669i	−0.748498	−	0.663137i	$-0.769225\pi$
$593$	6.01074	−	18.4991i	0.246831	−	0.759669i	0.995330	−	0.0965324i	$-0.0307751\pi$
$594$		0			0
$595$	−0.0188980	+	0.0581620i	−0.000774741	+	0.00238441i
$596$		0			0
$597$	1.92903	+	5.93693i	0.0789498	+	0.242982i
$598$		0			0
$599$	7.18066	−	22.0998i	0.293394	−	0.902973i	−0.690363	−	0.723463i	$-0.742549\pi$
$599$	7.18066	−	22.0998i	0.293394	−	0.902973i	0.983756	−	0.179509i	$-0.0574510\pi$
$600$		0			0
$601$	−43.0819			−1.75735			−0.878674	−	0.477423i	$-0.841571\pi$
$601$	−43.0819			−1.75735			−0.878674	+	0.477423i	$0.841571\pi$
$602$		0			0
$603$	−33.8195	+	24.5713i	−1.37724	+	1.00062i
$604$		0			0
$605$	18.7255	+	13.6049i	0.761302	+	0.553118i
$606$		0			0
$607$	8.10697	+	5.89006i	0.329052	+	0.239070i	0.740028	−	0.672576i	$-0.234812\pi$
$607$	8.10697	+	5.89006i	0.329052	+	0.239070i	−0.410976	+	0.911646i	$0.634812\pi$
$608$		0			0
$609$	−4.42989	−	13.6338i	−0.179508	−	0.552469i
$610$		0			0
$611$	32.7054	−	23.7618i	1.32312	−	0.961301i
$612$		0			0
$613$	−5.82993	−	17.9427i	−0.235469	−	0.724698i	−0.997059	−	0.0766393i	$-0.975581\pi$
$613$	−5.82993	−	17.9427i	−0.235469	−	0.724698i	0.761590	−	0.648059i	$-0.224419\pi$
$614$		0			0
$615$	3.49365	+	3.64681i	0.140878	+	0.147053i
$616$		0			0
$617$	9.49321	+	29.2171i	0.382182	+	1.17624i	0.938504	+	0.345269i	$0.112212\pi$
$617$	9.49321	+	29.2171i	0.382182	+	1.17624i	−0.556322	+	0.830967i	$0.687788\pi$
$618$		0			0
$619$	34.6957	−	25.2079i	1.39454	−	1.01319i	0.399189	−	0.916868i	$-0.369292\pi$
$619$	34.6957	−	25.2079i	1.39454	−	1.01319i	0.995350	−	0.0963237i	$-0.0307084\pi$
$620$		0			0
$621$	−4.13433	−	12.7242i	−0.165905	−	0.510603i
$622$		0			0
$623$	−17.7897	−	12.9250i	−0.712728	−	0.517828i
$624$		0			0
$625$	2.23604	+	1.62458i	0.0894416	+	0.0649831i
$626$		0			0
$627$	−3.86289	+	2.80656i	−0.154269	+	0.112083i
$628$		0			0
$629$	−0.0988120			−0.00393989
$630$		0			0
$631$	−6.93368	+	21.3397i	−0.276025	+	0.849519i	0.712921	+	0.701245i	$0.247372\pi$
$631$	−6.93368	+	21.3397i	−0.276025	+	0.849519i	−0.988946	+	0.148274i	$0.952628\pi$
$632$		0			0
$633$	2.43686	+	7.49990i	0.0968566	+	0.298094i
$634$		0			0
$635$	−5.87296	+	18.0751i	−0.233061	+	0.717289i
$636$		0			0
$637$	−7.20298	+	22.1685i	−0.285393	+	0.878348i
$638$		0			0
$639$	29.6265	+	21.5249i	1.17201	+	0.851512i
$640$		0			0
$641$	−16.9608	+	12.3228i	−0.669912	+	0.486720i	−0.869996	−	0.493059i	$-0.835879\pi$
$641$	−16.9608	+	12.3228i	−0.669912	+	0.486720i	0.200084	+	0.979779i	$0.435879\pi$
$642$		0			0
$643$	−8.17691	−	25.1659i	−0.322466	−	0.992448i	−0.972572	−	0.232604i	$-0.925275\pi$
$643$	−8.17691	−	25.1659i	−0.322466	−	0.992448i	0.650106	−	0.759844i	$-0.274725\pi$
$644$		0			0
$645$	3.62372	+	2.63279i	0.142684	+	0.103666i
$646$		0			0
$647$	−12.2405			−0.481223			−0.240612	−	0.970621i	$-0.577348\pi$
$647$	−12.2405			−0.481223			−0.240612	+	0.970621i	$0.577348\pi$
$648$		0			0
$649$	1.59533	−	4.90991i	0.0626220	−	0.192731i
$650$		0			0
$651$	−11.7743	+	8.55456i	−0.461473	+	0.335280i
$652$		0			0
$653$	−13.1205			−0.513447			−0.256723	−	0.966485i	$-0.582643\pi$
$653$	−13.1205			−0.513447			−0.256723	+	0.966485i	$0.582643\pi$
$654$		0			0
$655$	12.8365			0.501564
$656$		0			0
$657$	8.13296			0.317297
$658$		0			0
$659$	5.71612			0.222668			0.111334	−	0.993783i	$-0.464488\pi$
$659$	5.71612			0.222668			0.111334	+	0.993783i	$0.464488\pi$
$660$		0			0
$661$	4.55953	−	3.31269i	0.177345	−	0.128849i	−0.495571	−	0.868567i	$-0.665041\pi$
$661$	4.55953	−	3.31269i	0.177345	−	0.128849i	0.672916	+	0.739718i	$0.265041\pi$
$662$		0			0
$663$	−0.0105734	+	0.0325417i	−0.000410639	+	0.00126382i
$664$		0			0
$665$	−8.58041			−0.332734
$666$		0			0
$667$	−27.8682	−	20.2475i	−1.07906	−	0.783985i
$668$		0			0
$669$	2.85524	+	8.78752i	0.110390	+	0.339745i
$670$		0			0
$671$	32.7346	−	23.7831i	1.26370	−	0.918135i
$672$		0			0
$673$	0.344917	+	0.250597i	0.0132956	+	0.00965980i	0.594413	−	0.804160i	$-0.297384\pi$
$673$	0.344917	+	0.250597i	0.0132956	+	0.00965980i	−0.581118	+	0.813820i	$0.697384\pi$
$674$		0			0
$675$	−2.68602	+	8.26672i	−0.103385	+	0.318186i
$676$		0			0
$677$	1.39310	−	4.28752i	0.0535412	−	0.164783i	−0.920710	−	0.390247i	$-0.872390\pi$
$677$	1.39310	−	4.28752i	0.0535412	−	0.164783i	0.974252	+	0.225464i	$0.0723897\pi$
$678$		0			0
$679$	−4.80799	−	14.7975i	−0.184514	−	0.567875i
$680$		0			0
$681$	−2.75238	+	8.47096i	−0.105471	+	0.324608i
$682$		0			0
$683$	16.2988			0.623655			0.311828	−	0.950139i	$-0.399059\pi$
$683$	16.2988			0.623655			0.311828	+	0.950139i	$0.399059\pi$
$684$		0			0
$685$	17.1586	−	12.4664i	0.655596	−	0.476318i
$686$		0			0
$687$	4.67109	+	3.39374i	0.178213	+	0.129479i
$688$		0			0
$689$	55.1785	+	40.0895i	2.10213	+	1.52729i
$690$		0			0
$691$	−2.57480	−	7.92441i	−0.0979499	−	0.301459i	0.890061	−	0.455841i	$-0.150661\pi$
$691$	−2.57480	−	7.92441i	−0.0979499	−	0.301459i	−0.988011	+	0.154382i	$0.950661\pi$
$692$		0			0
$693$	−38.4515	+	27.9366i	−1.46065	+	1.06122i
$694$		0			0
$695$	3.73718	+	11.5019i	0.141759	+	0.436291i
$696$		0			0
$697$	0.0371655	−	0.0692300i	0.00140774	−	0.00262227i
$698$		0			0
$699$	1.97788	+	6.08728i	0.0748102	+	0.230242i
$700$		0			0
$701$	33.6438	−	24.4436i	1.27071	−	0.923224i	0.271478	−	0.962445i	$-0.412488\pi$
$701$	33.6438	−	24.4436i	1.27071	−	0.923224i	0.999231	+	0.0392209i	$0.0124876\pi$
$702$		0			0
$703$	−4.28418	−	13.1853i	−0.161581	−	0.497295i
$704$		0			0
$705$	−4.96150	−	3.60474i	−0.186861	−	0.135762i
$706$		0			0
$707$	12.9691	+	9.42264i	0.487755	+	0.354375i
$708$		0			0
$709$	−13.9306	+	10.1212i	−0.523176	+	0.380110i	−0.817799	−	0.575504i	$-0.804806\pi$
$709$	−13.9306	+	10.1212i	−0.523176	+	0.380110i	0.294623	+	0.955614i	$0.404806\pi$
$710$		0			0
$711$	−2.43350			−0.0912634
$712$		0			0
$713$	−10.8070	+	33.2604i	−0.404724	+	1.24561i
$714$		0			0
$715$	12.2175	+	37.6017i	0.456910	+	1.40622i
$716$		0			0
$717$	1.93242	−	5.94738i	0.0721676	−	0.222109i
$718$		0			0
$719$	15.4502	−	47.5507i	0.576194	−	1.77334i	−0.0558835	−	0.998437i	$-0.517798\pi$
$719$	15.4502	−	47.5507i	0.576194	−	1.77334i	0.632077	−	0.774905i	$-0.282202\pi$
$720$		0			0
$721$	−19.8169	−	14.3978i	−0.738021	−	0.536204i
$722$		0			0
$723$	11.8430	−	8.60446i	0.440447	−	0.320003i
$724$		0			0
$725$	6.91574	+	21.2845i	0.256844	+	0.790485i
$726$		0			0
$727$	22.1375	+	16.0838i	0.821033	+	0.596515i	0.917008	−	0.398869i	$-0.130597\pi$
$727$	22.1375	+	16.0838i	0.821033	+	0.596515i	−0.0959754	+	0.995384i	$0.530597\pi$
$728$		0			0
$729$	−12.6853			−0.469826
$730$		0			0
$731$	0.0215355	−	0.0662793i	0.000796518	−	0.00245143i
$732$		0			0
$733$	6.71001	−	4.87511i	0.247840	−	0.180066i	−0.456929	−	0.889503i	$-0.651051\pi$
$733$	6.71001	−	4.87511i	0.247840	−	0.180066i	0.704769	+	0.709437i	$0.251051\pi$
$734$		0			0
$735$	3.53609			0.130431
$736$		0			0
$737$	−79.6950			−2.93560
$738$		0			0
$739$	−35.4186			−1.30290			−0.651448	−	0.758693i	$-0.725838\pi$
$739$	−35.4186			−1.30290			−0.651448	+	0.758693i	$0.725838\pi$
$740$		0			0
$741$	−4.80075			−0.176360
$742$		0			0
$743$	−15.5173	+	11.2740i	−0.569275	+	0.413602i	−0.834842	−	0.550490i	$-0.814441\pi$
$743$	−15.5173	+	11.2740i	−0.569275	+	0.413602i	0.265567	+	0.964092i	$0.414441\pi$
$744$		0			0
$745$	3.63677	−	11.1928i	0.133241	−	0.410074i
$746$		0			0
$747$	−16.9853			−0.621460
$748$		0			0
$749$	7.20345	+	5.23361i	0.263208	+	0.191232i
$750$		0			0
$751$	15.3662	+	47.2922i	0.560719	+	1.72572i	0.680339	+	0.732897i	$0.261832\pi$
$751$	15.3662	+	47.2922i	0.560719	+	1.72572i	−0.119620	+	0.992820i	$0.538168\pi$
$752$		0			0
$753$	−0.938853	+	0.682116i	−0.0342137	+	0.0248577i
$754$		0			0
$755$	−5.80945	−	4.22081i	−0.211427	−	0.153611i
$756$		0			0
$757$	−3.20186	+	9.85432i	−0.116374	+	0.358161i	−0.992231	−	0.124409i	$-0.960297\pi$
$757$	−3.20186	+	9.85432i	−0.116374	+	0.358161i	0.875857	+	0.482570i	$0.160297\pi$
$758$		0			0
$759$	3.74248	−	11.5182i	0.135843	−	0.418083i
$760$		0			0
$761$	2.09446	+	6.44607i	0.0759239	+	0.233670i	0.981815	−	0.189841i	$-0.0607974\pi$
$761$	2.09446	+	6.44607i	0.0759239	+	0.233670i	−0.905891	+	0.423511i	$0.860797\pi$
$762$		0			0
$763$	0.950458	−	2.92521i	0.0344089	−	0.105900i
$764$		0			0
$765$	−0.0489494			−0.00176977
$766$		0			0
$767$	4.19932	−	3.05099i	0.151629	−	0.110165i
$768$		0			0
$769$	−33.5087	−	24.3455i	−1.20835	−	0.877921i	−0.213274	−	0.976992i	$-0.568413\pi$
$769$	−33.5087	−	24.3455i	−1.20835	−	0.877921i	−0.995080	+	0.0990714i	$0.968413\pi$
$770$		0			0
$771$	−7.53427	−	5.47396i	−0.271340	−	0.197140i
$772$		0			0
$773$	−9.55313	−	29.4015i	−0.343602	−	1.05750i	−0.962328	−	0.271892i	$-0.912351\pi$
$773$	−9.55313	−	29.4015i	−0.343602	−	1.05750i	0.618725	−	0.785607i	$-0.287649\pi$
$774$		0			0
$775$	18.3816	−	13.3550i	0.660286	−	0.479726i
$776$		0			0
$777$	4.52218	+	13.9178i	0.162232	+	0.499300i
$778$		0			0
$779$	10.8493	+	1.95772i	0.388718	+	0.0701425i
$780$		0			0
$781$	21.5738	+	66.3973i	0.771971	+	2.37588i
$782$		0			0
$783$	19.5501	−	14.2040i	0.698665	−	0.507610i
$784$		0			0
$785$	−9.31342	−	28.6638i	−0.332410	−	1.02305i
$786$		0			0
$787$	38.8139	+	28.1999i	1.38356	+	1.00522i	0.996537	+	0.0831504i	$0.0264982\pi$
$787$	38.8139	+	28.1999i	1.38356	+	1.00522i	0.387028	+	0.922068i	$0.373502\pi$
$788$		0			0
$789$	−0.345224	−	0.250820i	−0.0122903	−	0.00892941i
$790$		0			0
$791$	3.17902	−	2.30969i	0.113033	−	0.0821232i
$792$		0			0
$793$	40.6821			1.44466
$794$		0			0
$795$	3.19734	−	9.84039i	0.113398	−	0.349003i
$796$		0			0
$797$	−0.828371	−	2.54946i	−0.0293424	−	0.0903067i	0.935313	−	0.353822i	$-0.115118\pi$
$797$	−0.828371	−	2.54946i	−0.0293424	−	0.0903067i	−0.964655	+	0.263515i	$0.915118\pi$
$798$		0			0
$799$	−0.0294857	+	0.0907478i	−0.00104313	+	0.00321043i
$800$		0			0
$801$	5.43886	−	16.7391i	0.192173	−	0.591446i
$802$		0			0
$803$	12.5438	+	9.11358i	0.442660	+	0.321611i
$804$		0			0
$805$	17.6071	−	12.7923i	0.620569	−	0.450870i
$806$		0			0
$807$	0.0158482	+	0.0487759i	0.000557884	+	0.00171699i
$808$		0			0
$809$	31.7561	+	23.0722i	1.11649	+	0.811174i	0.983673	−	0.179967i	$-0.0575990\pi$
$809$	31.7561	+	23.0722i	1.11649	+	0.811174i	0.132813	+	0.991141i	$0.457599\pi$
$810$		0			0
$811$	−53.8713			−1.89168			−0.945838	−	0.324640i	$-0.894757\pi$
$811$	−53.8713			−1.89168			−0.945838	+	0.324640i	$0.894757\pi$
$812$		0			0
$813$	−0.436904	+	1.34465i	−0.0153229	+	0.0471590i
$814$		0			0
$815$	14.2442	−	10.3490i	0.498953	−	0.362511i
$816$		0			0
$817$	9.77794			0.342087
$818$		0			0
$819$	−47.7870			−1.66981
$820$		0			0
$821$	−40.9833			−1.43033			−0.715164	−	0.698957i	$-0.753648\pi$
$821$	−40.9833			−1.43033			−0.715164	+	0.698957i	$0.753648\pi$
$822$		0			0
$823$	−16.4574			−0.573669			−0.286834	−	0.957980i	$-0.592603\pi$
$823$	−16.4574			−0.573669			−0.286834	+	0.957980i	$0.592603\pi$
$824$		0			0
$825$	−6.36560	+	4.62488i	−0.221622	+	0.161018i
$826$		0			0
$827$	8.21723	−	25.2900i	0.285741	−	0.879420i	−0.700435	−	0.713717i	$-0.747010\pi$
$827$	8.21723	−	25.2900i	0.285741	−	0.879420i	0.986176	−	0.165704i	$-0.0529896\pi$
$828$		0			0
$829$	−5.11442			−0.177631			−0.0888156	−	0.996048i	$-0.528308\pi$
$829$	−5.11442			−0.177631			−0.0888156	+	0.996048i	$0.528308\pi$
$830$		0			0
$831$	10.1277	+	7.35820i	0.351326	+	0.255253i
$832$		0			0
$833$	−0.0170012	−	0.0523244i	−0.000589058	−	0.00181293i
$834$		0			0
$835$	15.3580	−	11.1582i	0.531485	−	0.386146i
$836$		0			0
$837$	−19.8481	−	14.4205i	−0.686050	−	0.498445i
$838$		0			0
$839$	7.55467	−	23.2509i	0.260816	−	0.802710i	−0.731812	−	0.681507i	$-0.761325\pi$
$839$	7.55467	−	23.2509i	0.260816	−	0.802710i	0.992628	−	0.121203i	$-0.0386751\pi$
$840$		0			0
$841$	10.2652	−	31.5929i	0.353971	−	1.08941i
$842$		0			0
$843$	−1.67818	−	5.16491i	−0.0577997	−	0.177889i
$844$		0			0
$845$	−6.37609	+	19.6236i	−0.219344	+	0.675072i
$846$		0			0
$847$	−53.3344			−1.83259
$848$		0			0
$849$	−0.905324	+	0.657756i	−0.0310706	+	0.0225741i
$850$		0			0
$851$	28.4489	+	20.6693i	0.975215	+	0.708535i
$852$		0			0
$853$	20.4103	+	14.8289i	0.698835	+	0.507733i	0.879552	−	0.475802i	$-0.157842\pi$
$853$	20.4103	+	14.8289i	0.698835	+	0.507733i	−0.180718	+	0.983535i	$0.557842\pi$
$854$		0			0
$855$	−2.12229	−	6.53175i	−0.0725809	−	0.223381i
$856$		0			0
$857$	5.34559	−	3.88380i	0.182602	−	0.132668i	−0.492729	−	0.870183i	$-0.664001\pi$
$857$	5.34559	−	3.88380i	0.182602	−	0.132668i	0.675331	+	0.737515i	$0.264001\pi$
$858$		0			0
$859$	−4.71976	−	14.5259i	−0.161036	−	0.495618i	0.837686	−	0.546152i	$-0.183908\pi$
$859$	−4.71976	−	14.5259i	−0.161036	−	0.495618i	−0.998722	+	0.0505334i	$0.983908\pi$
$860$		0			0
$861$	−11.4521	−	2.06648i	−0.390285	−	0.0704253i
$862$		0			0
$863$	16.4328	+	50.5751i	0.559380	+	1.72160i	0.684086	+	0.729402i	$0.260201\pi$
$863$	16.4328	+	50.5751i	0.559380	+	1.72160i	−0.124705	+	0.992194i	$0.539799\pi$
$864$		0			0
$865$	14.7804	−	10.7386i	0.502550	−	0.365124i
$866$		0			0
$867$	2.81736	+	8.67094i	0.0956825	+	0.294481i
$868$		0			0
$869$	−3.75328	−	2.72692i	−0.127321	−	0.0925043i
$870$		0			0
$871$	−64.8251	−	47.0982i	−2.19652	−	1.59586i
$872$		0			0
$873$	10.0752	−	7.32006i	0.340994	−	0.247746i
$874$		0			0
$875$	−39.0573			−1.32038
$876$		0			0
$877$	9.20757	−	28.3380i	0.310918	−	0.956906i	−0.666485	−	0.745519i	$-0.732202\pi$
$877$	9.20757	−	28.3380i	0.310918	−	0.956906i	0.977402	−	0.211387i	$-0.0677981\pi$
$878$		0			0
$879$	−0.882580	−	2.71630i	−0.0297687	−	0.0916186i
$880$		0			0
$881$	10.8128	−	33.2785i	0.364294	−	1.12118i	−0.586128	−	0.810218i	$-0.699349\pi$
$881$	10.8128	−	33.2785i	0.364294	−	1.12118i	0.950422	−	0.310963i	$-0.100651\pi$
$882$		0			0
$883$	5.95880	−	18.3393i	0.200530	−	0.617167i	−0.799338	−	0.600882i	$-0.794816\pi$
$883$	5.95880	−	18.3393i	0.200530	−	0.617167i	0.999867	−	0.0162847i	$-0.00518383\pi$
$884$		0			0
$885$	−0.637049	−	0.462843i	−0.0214142	−	0.0155583i
$886$		0			0
$887$	25.4220	−	18.4702i	0.853587	−	0.620167i	−0.0725456	−	0.997365i	$-0.523112\pi$
$887$	25.4220	−	18.4702i	0.853587	−	0.620167i	0.926133	+	0.377198i	$0.123112\pi$
$888$		0			0
$889$	−13.5328	−	41.6496i	−0.453875	−	1.39688i
$890$		0			0
$891$	−27.1673	−	19.7382i	−0.910140	−	0.661255i
$892$		0			0
$893$	−13.3877			−0.448001
$894$		0			0
$895$	−7.06997	+	21.7591i	−0.236323	+	0.727328i
$896$		0			0
$897$	9.85120	−	7.15732i	0.328922	−	0.238976i
$898$		0			0
$899$	−63.1670			−2.10674
$900$		0			0
$901$	−0.160983			−0.00536313
$902$		0			0
$903$	−10.3211			−0.343466
$904$		0			0
$905$	−26.9043			−0.894331
$906$		0			0
$907$	24.7964	−	18.0156i	0.823350	−	0.598199i	−0.0943199	−	0.995542i	$-0.530068\pi$
$907$	24.7964	−	18.0156i	0.823350	−	0.598199i	0.917670	+	0.397343i	$0.130068\pi$
$908$		0			0
$909$	−3.96507	+	12.2032i	−0.131513	+	0.404756i
$910$		0			0
$911$	22.9549			0.760528			0.380264	−	0.924878i	$-0.375833\pi$
$911$	22.9549			0.760528			0.380264	+	0.924878i	$0.375833\pi$
$912$		0			0
$913$	−26.1971	−	19.0333i	−0.866997	−	0.629910i
$914$		0			0
$915$	−1.90713	−	5.86953i	−0.0630477	−	0.194041i
$916$		0			0
$917$	−23.9296	+	17.3859i	−0.790225	+	0.574132i
$918$		0			0
$919$	12.3821	+	8.99609i	0.408446	+	0.296754i	0.772973	−	0.634440i	$-0.218769\pi$
$919$	12.3821	+	8.99609i	0.408446	+	0.296754i	−0.364526	+	0.931193i	$0.618769\pi$
$920$		0			0
$921$	0.853765	−	2.62762i	0.0281325	−	0.0865829i
$922$		0			0
$923$	−21.6911	+	66.7582i	−0.713970	+	2.19737i
$924$		0			0
$925$	−7.05983	−	21.7279i	−0.232126	−	0.714409i
$926$		0			0
$927$	6.05865	−	18.6466i	0.198992	−	0.612435i
$928$		0			0
$929$	21.9678			0.720739			0.360370	−	0.932810i	$-0.382651\pi$
$929$	21.9678			0.720739			0.360370	+	0.932810i	$0.382651\pi$
$930$		0			0
$931$	6.24498	−	4.53725i	0.204671	−	0.148702i
$932$		0			0
$933$	−2.22407	−	1.61588i	−0.0728128	−	0.0529016i
$934$		0			0
$935$	−0.0754965	−	0.0548515i	−0.00246900	−	0.00179383i
$936$		0			0
$937$	6.89444	+	21.2189i	0.225232	+	0.693191i	0.998268	+	0.0588299i	$0.0187369\pi$
$937$	6.89444	+	21.2189i	0.225232	+	0.693191i	−0.773036	+	0.634362i	$0.781263\pi$
$938$		0			0
$939$	−1.93765	+	1.40779i	−0.0632328	+	0.0459414i
$940$		0			0
$941$	−9.13349	−	28.1100i	−0.297743	−	0.916359i	−0.982286	−	0.187387i	$-0.939998\pi$
$941$	−9.13349	−	28.1100i	−0.297743	−	0.916359i	0.684543	−	0.728972i	$-0.260002\pi$
$942$		0			0
$943$	−25.1817	+	12.1577i	−0.820028	+	0.395910i
$944$		0			0
$945$	4.71794	+	14.5203i	0.153475	+	0.472347i
$946$		0			0
$947$	−7.46560	+	5.42407i	−0.242599	+	0.176259i	−0.702441	−	0.711742i	$-0.747906\pi$
$947$	−7.46560	+	5.42407i	−0.242599	+	0.176259i	0.459841	+	0.888001i	$0.347906\pi$
$948$		0			0
$949$	4.81734	+	14.8262i	0.156377	+	0.481280i
$950$		0			0
$951$	10.6354	+	7.72705i	0.344876	+	0.250567i
$952$		0			0
$953$	−9.88150	−	7.17933i	−0.320093	−	0.232561i	0.416122	−	0.909309i	$-0.363389\pi$
$953$	−9.88150	−	7.17933i	−0.320093	−	0.232561i	−0.736215	+	0.676747i	$0.763389\pi$
$954$		0			0
$955$	−13.8845	+	10.0877i	−0.449291	+	0.326429i
$956$		0			0
$957$	21.8749			0.707116
$958$		0			0
$959$	−15.1021	+	46.4794i	−0.487671	+	1.50090i
$960$		0			0
$961$	10.2376	+	31.5082i	0.330246	+	1.01639i
$962$		0			0
$963$	−2.20232	+	6.77804i	−0.0709687	+	0.218419i
$964$		0			0
$965$	9.49799	−	29.2318i	0.305751	−	0.941005i
$966$		0			0
$967$	−8.63700	−	6.27515i	−0.277747	−	0.201795i	0.440187	−	0.897906i	$-0.354912\pi$
$967$	−8.63700	−	6.27515i	−0.277747	−	0.201795i	−0.717934	+	0.696111i	$0.754912\pi$
$968$		0			0
$969$	0.00916717	−	0.00666034i	0.000294492	−	0.000213961i
$970$		0			0
$971$	−11.2070	−	34.4914i	−0.359648	−	1.10688i	−0.953265	−	0.302135i	$-0.902301\pi$
$971$	−11.2070	−	34.4914i	−0.359648	−	1.10688i	0.593617	−	0.804748i	$-0.297699\pi$
$972$		0			0
$973$	−22.5450	−	16.3799i	−0.722759	−	0.525115i
$974$		0			0
$975$	−7.91108			−0.253357
$976$		0			0
$977$	8.37994	−	25.7908i	0.268098	−	0.825121i	−0.722865	−	0.690989i	$-0.757175\pi$
$977$	8.37994	−	25.7908i	0.268098	−	0.825121i	0.990963	−	0.134132i	$-0.0428247\pi$
$978$		0			0
$979$	27.1459	−	19.7227i	0.867588	−	0.630339i
$980$		0			0
$981$	2.46187			0.0786015
$982$		0			0
$983$	−54.4521			−1.73675			−0.868376	−	0.495906i	$-0.834836\pi$
$983$	−54.4521			−1.73675			−0.868376	+	0.495906i	$0.834836\pi$
$984$		0			0
$985$	0.851110			0.0271186
$986$		0			0
$987$	14.1314			0.449807
$988$		0			0
$989$	−20.0644	+	14.5777i	−0.638012	+	0.463543i
$990$		0			0
$991$	−12.8072	+	39.4166i	−0.406835	+	1.25211i	0.512519	+	0.858676i	$0.328712\pi$
$991$	−12.8072	+	39.4166i	−0.406835	+	1.25211i	−0.919354	+	0.393432i	$0.871288\pi$
$992$		0			0
$993$	−3.28361			−0.104202
$994$		0			0
$995$	−13.8485	−	10.0615i	−0.439027	−	0.318972i
$996$		0			0
$997$	5.10132	+	15.7002i	0.161560	+	0.497231i	0.998766	−	0.0496561i	$-0.0158125\pi$
$997$	5.10132	+	15.7002i	0.161560	+	0.497231i	−0.837206	+	0.546888i	$0.815813\pi$
$998$		0			0
$999$	−19.9574	+	14.4999i	−0.631426	+	0.458758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.u.h.305.3		20
4.3	odd	2		328.2.m.c.305.3	yes	20
41.16	even	5	inner	656.2.u.h.385.3		20
164.139	odd	10		328.2.m.c.57.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
328.2.m.c.57.3	✓	20	164.139	odd	10
328.2.m.c.305.3	yes	20	4.3	odd	2
656.2.u.h.305.3		20	1.1	even	1	trivial
656.2.u.h.385.3		20	41.16	even	5	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:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q-0.536309 q^{3} +(1.18977 - 0.864417i) q^{5} +(-1.04717 + 3.22286i) q^{7} -2.71237 q^{9} +O(q^{10})\)	\(q-0.536309 q^{3} +(1.18977 - 0.864417i) q^{5} +(-1.04717 + 3.22286i) q^{7} -2.71237 q^{9} +(-4.18339 - 3.03941i) q^{11} +(-1.60660 - 4.94461i) q^{13} +(-0.638082 + 0.463594i) q^{15} +(0.00992776 + 0.00721294i) q^{17} +(-0.532049 + 1.63748i) q^{19} +(0.561606 - 1.72845i) q^{21} +(-1.34950 - 4.15334i) q^{23} +(-0.876755 + 2.69837i) q^{25} +3.06359 q^{27} +(6.38144 - 4.63638i) q^{29} +(-6.47869 - 4.70704i) q^{31} +(2.24359 + 1.63006i) q^{33} +(1.54000 + 4.73964i) q^{35} +(-6.51439 + 4.73298i) q^{37} +(0.861634 + 2.65184i) q^{39} +(-0.865824 - 6.34432i) q^{41} +(-1.75493 - 5.40113i) q^{43} +(-3.22709 + 2.34462i) q^{45} +(2.40280 + 7.39507i) q^{47} +(-3.62712 - 2.63526i) q^{49} +(-0.00532435 - 0.00386836i) q^{51} +(-10.6132 + 7.71091i) q^{53} -7.60459 q^{55} +(0.285342 - 0.878193i) q^{57} +(0.308516 + 0.949516i) q^{59} +(-2.41802 + 7.44191i) q^{61} +(2.84031 - 8.74159i) q^{63} +(-6.18568 - 4.49416i) q^{65} +(12.4686 - 9.05897i) q^{67} +(0.723750 + 2.22747i) q^{69} +(-10.9227 - 7.93581i) q^{71} -2.99847 q^{73} +(0.470211 - 1.44716i) q^{75} +(14.1763 - 10.2997i) q^{77} +0.897185 q^{79} +6.49409 q^{81} +6.26216 q^{83} +0.0180467 q^{85} +(-3.42242 + 2.48653i) q^{87} +(-2.00520 + 6.17138i) q^{89} +17.6181 q^{91} +(3.47458 + 2.52443i) q^{93} +(0.782449 + 2.40813i) q^{95} +(-3.71453 + 2.69876i) q^{97} +(11.3469 + 8.24403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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