LMFDB - Embedded newform 1197.2.j.m.856.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1197,2,Mod(172,1197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1197, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1197.172");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1197 = 3^{2} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1197.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.55809312195$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 13 x^{14} - 2 x^{13} + 118 x^{12} - 16 x^{11} + 534 x^{10} - 21 x^{9} + 1743 x^{8} - 101 x^{7} + \cdots + 256 $ x^16 + 13x^14 - 2x^13 + 118x^12 - 16x^11 + 534x^10 - 21x^9 + 1743x^8 - 101x^7 + 2902x^6 - 401x^5 + 3427x^4 - 294x^3 + 1076x^2 + 96x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 399)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			856.5
Root			$0.323314 - 0.559997i$ of defining polynomial
Character	$\chi$	$=$	1197.856
Dual form			1197.2.j.m.172.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.323314 - 0.559997i) q^{2} +(0.790936 + 1.36994i) q^{4} +(-2.12692 + 3.68394i) q^{5} +(-0.107079 + 2.64358i) q^{7} +2.31614 q^{8} +O(q^{10})$	\(q+(0.323314 - 0.559997i) q^{2} +(0.790936 + 1.36994i) q^{4} +(-2.12692 + 3.68394i) q^{5} +(-0.107079 + 2.64358i) q^{7} +2.31614 q^{8} +(1.37533 + 2.38214i) q^{10} +(-0.155724 - 0.269722i) q^{11} +5.14716 q^{13} +(1.44578 + 0.914672i) q^{14} +(-0.833031 + 1.44285i) q^{16} +(0.513554 + 0.889502i) q^{17} +(0.500000 - 0.866025i) q^{19} -6.72904 q^{20} -0.201391 q^{22} +(1.32111 - 2.28822i) q^{23} +(-6.54760 - 11.3408i) q^{25} +(1.66415 - 2.88239i) q^{26} +(-3.70625 + 1.94421i) q^{28} -5.32830 q^{29} +(2.39910 + 4.15537i) q^{31} +(2.85480 + 4.94466i) q^{32} +0.664158 q^{34} +(-9.51105 - 6.01717i) q^{35} +(-3.12491 + 5.41251i) q^{37} +(-0.323314 - 0.559997i) q^{38} +(-4.92625 + 8.53251i) q^{40} +8.94237 q^{41} -6.50987 q^{43} +(0.246336 - 0.426666i) q^{44} +(-0.854264 - 1.47963i) q^{46} +(-4.33575 + 7.50974i) q^{47} +(-6.97707 - 0.566142i) q^{49} -8.46772 q^{50} +(4.07108 + 7.05131i) q^{52} +(0.251532 + 0.435666i) q^{53} +1.32485 q^{55} +(-0.248009 + 6.12291i) q^{56} +(-1.72272 + 2.98383i) q^{58} +(-4.14554 - 7.18028i) q^{59} +(2.74943 - 4.76214i) q^{61} +3.10266 q^{62} +0.359867 q^{64} +(-10.9476 + 18.9618i) q^{65} +(-3.46463 - 6.00092i) q^{67} +(-0.812377 + 1.40708i) q^{68} +(-6.44465 + 3.38072i) q^{70} -2.94259 q^{71} +(-7.46436 - 12.9287i) q^{73} +(2.02066 + 3.49988i) q^{74} +1.58187 q^{76} +(0.729708 - 0.382788i) q^{77} +(7.45744 - 12.9167i) q^{79} +(-3.54358 - 6.13767i) q^{80} +(2.89119 - 5.00769i) q^{82} +13.4789 q^{83} -4.36916 q^{85} +(-2.10473 + 3.64550i) q^{86} +(-0.360679 - 0.624714i) q^{88} +(-0.0485645 + 0.0841162i) q^{89} +(-0.551151 + 13.6070i) q^{91} +4.17964 q^{92} +(2.80362 + 4.85601i) q^{94} +(2.12692 + 3.68394i) q^{95} +13.4801 q^{97} +(-2.57282 + 3.72409i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 10 q^{4} - 5 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) $ 16 * q - 10 * q^4 - 5 * q^5 + q^7 + 6 * q^8	$ 16 q - 10 q^{4} - 5 q^{5} + q^{7} + 6 q^{8} + 3 q^{10} - 7 q^{11} - 12 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{19} + 32 q^{20} + 36 q^{22} - 9 q^{23} - 15 q^{25} - 12 q^{26} - 40 q^{28} - 8 q^{29} + 11 q^{31} - 26 q^{32} - 32 q^{34} + 7 q^{35} - 17 q^{37} + 3 q^{40} + 34 q^{41} + 16 q^{43} - 31 q^{44} - q^{46} - 29 q^{47} + q^{49} - 60 q^{50} + 25 q^{52} - 6 q^{53} - 42 q^{55} + 54 q^{56} + 37 q^{58} - 7 q^{59} + 2 q^{61} + 78 q^{62} + 58 q^{64} - 13 q^{65} - 13 q^{67} + 14 q^{68} - 81 q^{70} - 36 q^{71} + 20 q^{73} - 26 q^{74} - 20 q^{76} - 19 q^{77} + 3 q^{79} - 35 q^{80} + 5 q^{82} + 72 q^{83} + 10 q^{85} - 51 q^{86} - 53 q^{88} - q^{89} - 9 q^{91} - 30 q^{92} + 30 q^{94} + 5 q^{95} + 6 q^{97} + 75 q^{98}+O(q^{100}) $ 16 * q - 10 * q^4 - 5 * q^5 + q^7 + 6 * q^8 + 3 * q^10 - 7 * q^11 - 12 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^19 + 32 * q^20 + 36 * q^22 - 9 * q^23 - 15 * q^25 - 12 * q^26 - 40 * q^28 - 8 * q^29 + 11 * q^31 - 26 * q^32 - 32 * q^34 + 7 * q^35 - 17 * q^37 + 3 * q^40 + 34 * q^41 + 16 * q^43 - 31 * q^44 - q^46 - 29 * q^47 + q^49 - 60 * q^50 + 25 * q^52 - 6 * q^53 - 42 * q^55 + 54 * q^56 + 37 * q^58 - 7 * q^59 + 2 * q^61 + 78 * q^62 + 58 * q^64 - 13 * q^65 - 13 * q^67 + 14 * q^68 - 81 * q^70 - 36 * q^71 + 20 * q^73 - 26 * q^74 - 20 * q^76 - 19 * q^77 + 3 * q^79 - 35 * q^80 + 5 * q^82 + 72 * q^83 + 10 * q^85 - 51 * q^86 - 53 * q^88 - q^89 - 9 * q^91 - 30 * q^92 + 30 * q^94 + 5 * q^95 + 6 * q^97 + 75 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1197\mathbb{Z}\right)^\times$.

$n$	$514$	$533$	$1009$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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 $

$2$	0.323314	−	0.559997i	0.228618	−	0.395977i	−0.728781	−	0.684747i	$-0.759913\pi$
$2$	0.323314	−	0.559997i	0.228618	−	0.395977i	0.957399	+	0.288769i	$0.0932461\pi$
$3$		0			0
$3$		0			0
$4$	0.790936	+	1.36994i	0.395468	+	0.684971i
$5$	−2.12692	+	3.68394i	−0.951188	+	1.64751i	−0.208330	+	0.978059i	$0.566803\pi$
$5$	−2.12692	+	3.68394i	−0.951188	+	1.64751i	−0.742859	+	0.669448i	$0.766531\pi$
$6$		0			0
$7$	−0.107079	+	2.64358i	−0.0404719	+	0.999181i
$7$	−0.107079	+	2.64358i	−0.0404719	+	0.999181i
$8$	2.31614			0.818879
$9$		0			0
$10$	1.37533	+	2.38214i	0.434917	+	0.753298i
$11$	−0.155724	−	0.269722i	−0.0469526	−	0.0813243i	0.841594	−	0.540111i	$-0.181618\pi$
$11$	−0.155724	−	0.269722i	−0.0469526	−	0.0813243i	−0.888547	+	0.458786i	$0.848284\pi$
$12$		0			0
$13$	5.14716			1.42757			0.713783	−	0.700367i	$-0.246980\pi$
$13$	5.14716			1.42757			0.713783	+	0.700367i	$0.246980\pi$
$14$	1.44578	+	0.914672i	0.386400	+	0.244456i
$15$		0			0
$16$	−0.833031	+	1.44285i	−0.208258	+	0.360713i
$17$	0.513554	+	0.889502i	0.124555	+	0.215736i	0.921559	−	0.388238i	$-0.126916\pi$
$17$	0.513554	+	0.889502i	0.124555	+	0.215736i	−0.797004	+	0.603974i	$0.793583\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$20$	−6.72904			−1.50466
$21$		0			0
$22$	−0.201391			−0.0429368
$23$	1.32111	−	2.28822i	0.275470	−	0.477127i	−0.694784	−	0.719219i	$-0.744500\pi$
$23$	1.32111	−	2.28822i	0.275470	−	0.477127i	0.970253	+	0.242091i	$0.0778333\pi$
$24$		0			0
$25$	−6.54760	−	11.3408i	−1.30952	−	2.26815i
$26$	1.66415	−	2.88239i	0.326367	−	0.565284i
$27$		0			0
$28$	−3.70625	+	1.94421i	−0.700415	+	0.367422i
$29$	−5.32830			−0.989441			−0.494720	−	0.869052i	$-0.664730\pi$
$29$	−5.32830			−0.989441			−0.494720	+	0.869052i	$0.664730\pi$
$30$		0			0
$31$	2.39910	+	4.15537i	0.430892	+	0.746327i	0.996950	−	0.0780384i	$-0.0248657\pi$
$31$	2.39910	+	4.15537i	0.430892	+	0.746327i	−0.566058	+	0.824365i	$0.691532\pi$
$32$	2.85480	+	4.94466i	0.504662	+	0.874101i
$33$		0			0
$34$	0.664158			0.113902
$35$	−9.51105	−	6.01717i	−1.60766	−	1.01709i
$36$		0			0
$37$	−3.12491	+	5.41251i	−0.513732	+	0.889810i	0.486141	+	0.873880i	$0.338404\pi$
$37$	−3.12491	+	5.41251i	−0.513732	+	0.889810i	−0.999873	+	0.0159299i	$0.994929\pi$
$38$	−0.323314	−	0.559997i	−0.0524485	−	0.0908434i
$39$		0			0
$40$	−4.92625	+	8.53251i	−0.778908	+	1.34911i
$41$	8.94237			1.39656			0.698282	−	0.715823i	$-0.253948\pi$
$41$	8.94237			1.39656			0.698282	+	0.715823i	$0.253948\pi$
$42$		0			0
$43$	−6.50987			−0.992746			−0.496373	−	0.868109i	$-0.665335\pi$
$43$	−6.50987			−0.992746			−0.496373	+	0.868109i	$0.665335\pi$
$44$	0.246336	−	0.426666i	0.0371365	−	0.0643223i
$45$		0			0
$46$	−0.854264	−	1.47963i	−0.125954	−	0.218159i
$47$	−4.33575	+	7.50974i	−0.632434	+	1.09541i	0.354618	+	0.935011i	$0.384611\pi$
$47$	−4.33575	+	7.50974i	−0.632434	+	1.09541i	−0.987053	+	0.160397i	$0.948723\pi$
$48$		0			0
$49$	−6.97707	−	0.566142i	−0.996724	−	0.0808774i
$50$	−8.46772			−1.19752
$51$		0			0
$52$	4.07108	+	7.05131i	0.564557	+	0.977841i
$53$	0.251532	+	0.435666i	0.0345506	+	0.0598434i	0.882784	−	0.469780i	$-0.155667\pi$
$53$	0.251532	+	0.435666i	0.0345506	+	0.0598434i	−0.848233	+	0.529623i	$0.822333\pi$
$54$		0			0
$55$	1.32485			0.178643
$56$	−0.248009	+	6.12291i	−0.0331416	+	0.818208i
$57$		0			0
$58$	−1.72272	+	2.98383i	−0.226204	+	0.391796i
$59$	−4.14554	−	7.18028i	−0.539703	−	0.934793i	−0.998920	−	0.0464684i	$-0.985203\pi$
$59$	−4.14554	−	7.18028i	−0.539703	−	0.934793i	0.459217	−	0.888324i	$-0.348130\pi$
$60$		0			0
$61$	2.74943	−	4.76214i	0.352028	−	0.609730i	−0.634577	−	0.772860i	$-0.718826\pi$
$61$	2.74943	−	4.76214i	0.352028	−	0.609730i	0.986605	+	0.163130i	$0.0521589\pi$
$62$	3.10266			0.394038
$63$		0			0
$64$	0.359867			0.0449833
$65$	−10.9476	+	18.9618i	−1.35788	+	2.35193i
$66$		0			0
$67$	−3.46463	−	6.00092i	−0.423272	−	0.733129i	0.572985	−	0.819566i	$-0.305785\pi$
$67$	−3.46463	−	6.00092i	−0.423272	−	0.733129i	−0.996257	+	0.0864367i	$0.972452\pi$
$68$	−0.812377	+	1.40708i	−0.0985152	+	0.170633i
$69$		0			0
$70$	−6.44465	+	3.38072i	−0.770283	+	0.404073i
$71$	−2.94259			−0.349221			−0.174610	−	0.984638i	$-0.555867\pi$
$71$	−2.94259			−0.349221			−0.174610	+	0.984638i	$0.555867\pi$
$72$		0			0
$73$	−7.46436	−	12.9287i	−0.873638	−	1.51318i	−0.858207	−	0.513304i	$-0.828421\pi$
$73$	−7.46436	−	12.9287i	−0.873638	−	1.51318i	−0.0154306	−	0.999881i	$-0.504912\pi$
$74$	2.02066	+	3.49988i	0.234897	+	0.406853i
$75$		0			0
$76$	1.58187			0.181453
$77$	0.729708	−	0.382788i	0.0831579	−	0.0436228i
$78$		0			0
$79$	7.45744	−	12.9167i	0.839027	−	1.45324i	−0.0516812	−	0.998664i	$-0.516458\pi$
$79$	7.45744	−	12.9167i	0.839027	−	1.45324i	0.890709	−	0.454575i	$-0.150209\pi$
$80$	−3.54358	−	6.13767i	−0.396185	−	0.686212i
$81$		0			0
$82$	2.89119	−	5.00769i	0.319279	−	0.553007i
$83$	13.4789			1.47951			0.739753	−	0.672878i	$-0.234942\pi$
$83$	13.4789			1.47951			0.739753	+	0.672878i	$0.234942\pi$
$84$		0			0
$85$	−4.36916			−0.473902
$86$	−2.10473	+	3.64550i	−0.226959	+	0.393105i
$87$		0			0
$88$	−0.360679	−	0.624714i	−0.0384485	−	0.0665948i
$89$	−0.0485645	+	0.0841162i	−0.00514782	+	0.00891629i	−0.868588	−	0.495535i	$-0.834972\pi$
$89$	−0.0485645	+	0.0841162i	−0.00514782	+	0.00891629i	0.863440	+	0.504452i	$0.168305\pi$
$90$		0			0
$91$	−0.551151	+	13.6070i	−0.0577763	+	1.42640i
$92$	4.17964			0.435758
$93$		0			0
$94$	2.80362	+	4.85601i	0.289171	+	0.500859i
$95$	2.12692	+	3.68394i	0.218218	+	0.377964i
$96$		0			0
$97$	13.4801			1.36869			0.684347	−	0.729156i	$-0.260087\pi$
$97$	13.4801			1.36869			0.684347	+	0.729156i	$0.260087\pi$
$98$	−2.57282	+	3.72409i	−0.259894	+	0.376190i
$99$		0			0
$100$	10.3575	−	17.9396i	1.03575	−	1.79396i
$101$	8.78925	+	15.2234i	0.874563	+	1.51479i	0.857227	+	0.514938i	$0.172185\pi$
$101$	8.78925	+	15.2234i	0.874563	+	1.51479i	0.0173356	+	0.999850i	$0.494482\pi$
$102$		0			0
$103$	−5.80562	+	10.0556i	−0.572045	+	0.990811i	0.424311	+	0.905517i	$0.360516\pi$
$103$	−5.80562	+	10.0556i	−0.572045	+	0.990811i	−0.996356	+	0.0852943i	$0.972817\pi$
$104$	11.9216			1.16900
$105$		0			0
$106$	0.325296			0.0315955
$107$	2.70695	−	4.68858i	0.261691	−	0.453262i	−0.705000	−	0.709207i	$-0.749053\pi$
$107$	2.70695	−	4.68858i	0.261691	−	0.453262i	0.966691	+	0.255945i	$0.0823865\pi$
$108$		0			0
$109$	−0.547197	−	0.947773i	−0.0524119	−	0.0907801i	0.838629	−	0.544703i	$-0.183358\pi$
$109$	−0.547197	−	0.947773i	−0.0524119	−	0.0907801i	−0.891041	+	0.453923i	$0.850024\pi$
$110$	0.428344	−	0.741913i	0.0408410	−	0.0707386i
$111$		0			0
$112$	−3.72510	−	2.35669i	−0.351989	−	0.222686i
$113$	1.76812			0.166331			0.0831655	−	0.996536i	$-0.473497\pi$
$113$	1.76812			0.166331			0.0831655	+	0.996536i	$0.473497\pi$
$114$		0			0
$115$	5.61978	+	9.73374i	0.524047	+	0.907676i
$116$	−4.21435	−	7.29946i	−0.391292	−	0.677738i
$117$		0			0
$118$	−5.36124			−0.493542
$119$	−2.40646	+	1.26238i	−0.220600	+	0.115722i
$120$		0			0
$121$	5.45150	−	9.44227i	0.495591	−	0.858389i
$122$	−1.77786	−	3.07934i	−0.160960	−	0.278790i
$123$		0			0
$124$	−3.79508	+	6.57326i	−0.340808	+	0.590297i
$125$	34.4357			3.08002
$126$		0			0
$127$	3.57134			0.316905			0.158453	−	0.987367i	$-0.449349\pi$
$127$	3.57134			0.316905			0.158453	+	0.987367i	$0.449349\pi$
$128$	−5.59325	+	9.68780i	−0.494378	+	0.856288i
$129$		0			0
$130$	7.07904	+	12.2613i	0.620873	+	1.07538i
$131$	−0.784647	+	1.35905i	−0.0685549	+	0.118741i	−0.898265	−	0.439453i	$-0.855172\pi$
$131$	−0.784647	+	1.35905i	−0.0685549	+	0.118741i	0.829710	+	0.558194i	$0.188505\pi$
$132$		0			0
$133$	2.23587	+	1.41452i	0.193875	+	0.122655i
$134$	−4.48066			−0.387070
$135$		0			0
$136$	1.18946	+	2.06021i	0.101996	+	0.176662i
$137$	−3.92105	−	6.79145i	−0.334998	−	0.580233i	0.648487	−	0.761226i	$-0.275402\pi$
$137$	−3.92105	−	6.79145i	−0.334998	−	0.580233i	−0.983484	+	0.180993i	$0.942069\pi$
$138$		0			0
$139$	4.96849			0.421422			0.210711	−	0.977548i	$-0.432422\pi$
$139$	4.96849			0.421422			0.210711	+	0.977548i	$0.432422\pi$
$140$	0.720535	−	17.7888i	0.0608963	−	1.50343i
$141$		0			0
$142$	−0.951380	+	1.64784i	−0.0798380	+	0.138284i
$143$	−0.801538	−	1.38830i	−0.0670280	−	0.116096i
$144$		0			0
$145$	11.3329	−	19.6291i	0.941145	−	1.63011i
$146$	−9.65334			−0.798916
$147$		0			0
$148$	−9.88642			−0.812659
$149$	−4.15022	+	7.18840i	−0.340000	+	0.588897i	−0.984432	−	0.175765i	$-0.943760\pi$
$149$	−4.15022	+	7.18840i	−0.340000	+	0.588897i	0.644433	+	0.764661i	$0.277094\pi$
$150$		0			0
$151$	4.33385	+	7.50645i	0.352684	+	0.610866i	0.986719	−	0.162438i	$-0.0519358\pi$
$151$	4.33385	+	7.50645i	0.352684	+	0.610866i	−0.634035	+	0.773304i	$0.718602\pi$
$152$	1.15807	−	2.00584i	0.0939319	−	0.162695i
$153$		0			0
$154$	0.0215647	−	0.532395i	0.00173773	−	0.0429016i
$155$	−20.4108			−1.63944
$156$		0			0
$157$	3.08201	+	5.33819i	0.245971	+	0.426034i	0.962404	−	0.271621i	$-0.0875599\pi$
$157$	3.08201	+	5.33819i	0.245971	+	0.426034i	−0.716433	+	0.697656i	$0.754227\pi$
$158$	−4.82219	−	8.35228i	−0.383633	−	0.664472i
$159$		0			0
$160$	−24.2878			−1.92012
$161$	5.90764	+	3.73747i	0.465588	+	0.294554i
$162$		0			0
$163$	−2.96209	+	5.13049i	−0.232009	+	0.401851i	−0.958399	−	0.285431i	$-0.907863\pi$
$163$	−2.96209	+	5.13049i	−0.232009	+	0.401851i	0.726390	+	0.687282i	$0.241197\pi$
$164$	7.07284	+	12.2505i	0.552296	+	0.956605i
$165$		0			0
$166$	4.35793	−	7.54816i	0.338241	−	0.585851i
$167$	8.63948			0.668543			0.334271	−	0.942477i	$-0.391510\pi$
$167$	8.63948			0.668543			0.334271	+	0.942477i	$0.391510\pi$
$168$		0			0
$169$	13.4933			1.03795
$170$	−1.41261	+	2.44671i	−0.108342	+	0.187654i
$171$		0			0
$172$	−5.14889	−	8.91814i	−0.392599	−	0.680002i
$173$	4.00263	−	6.93275i	0.304314	−	0.527087i	−0.672794	−	0.739830i	$-0.734906\pi$
$173$	4.00263	−	6.93275i	0.304314	−	0.527087i	0.977108	+	0.212742i	$0.0682394\pi$
$174$		0			0
$175$	30.6814	−	16.0948i	2.31929	−	1.21665i
$176$	0.518892			0.0391130
$177$		0			0
$178$	0.0314032	+	0.0543919i	0.00235377	+	0.00407684i
$179$	5.04642	+	8.74065i	0.377187	+	0.653307i	0.990652	−	0.136415i	$-0.0435581\pi$
$179$	5.04642	+	8.74065i	0.377187	+	0.653307i	−0.613465	+	0.789722i	$0.710225\pi$
$180$		0			0
$181$	8.89534			0.661185			0.330593	−	0.943774i	$-0.392751\pi$
$181$	8.89534			0.661185			0.330593	+	0.943774i	$0.392751\pi$
$182$	7.44166	+	4.70797i	0.551612	+	0.348978i
$183$		0			0
$184$	3.05987	−	5.29984i	0.225576	−	0.390710i
$185$	−13.2929	−	23.0240i	−0.977312	−	1.69275i
$186$		0			0
$187$	0.159946	−	0.277034i	0.0116964	−	0.0202587i
$188$	−13.7172			−1.00043
$189$		0			0
$190$	2.75066			0.199554
$191$	−8.33161	+	14.4308i	−0.602854	+	1.04417i	0.389533	+	0.921013i	$0.372637\pi$
$191$	−8.33161	+	14.4308i	−0.602854	+	1.04417i	−0.992387	+	0.123161i	$0.960697\pi$
$192$		0			0
$193$	9.34217	+	16.1811i	0.672464	+	1.16474i	0.977203	+	0.212306i	$0.0680974\pi$
$193$	9.34217	+	16.1811i	0.672464	+	1.16474i	−0.304739	+	0.952436i	$0.598569\pi$
$194$	4.35830	−	7.54880i	0.312908	−	0.541972i
$195$		0			0
$196$	−4.74283	−	10.0060i	−0.338774	−	0.714711i
$197$	20.0674			1.42974			0.714870	−	0.699258i	$-0.246486\pi$
$197$	20.0674			1.42974			0.714870	+	0.699258i	$0.246486\pi$
$198$		0			0
$199$	4.99089	+	8.64447i	0.353795	+	0.612791i	0.986911	−	0.161266i	$-0.0515578\pi$
$199$	4.99089	+	8.64447i	0.353795	+	0.612791i	−0.633116	+	0.774057i	$0.718224\pi$
$200$	−15.1651	−	26.2668i	−1.07234	−	1.85734i
$201$		0			0
$202$	11.3668			0.799762
$203$	0.570547	−	14.0858i	0.0400445	−	0.988630i
$204$		0			0
$205$	−19.0197	+	32.9431i	−1.32839	+	2.30085i
$206$	3.75408	+	6.50226i	0.261559	+	0.453034i
$207$		0			0
$208$	−4.28775	+	7.42660i	−0.297302	+	0.514942i
$209$	−0.311448			−0.0215433
$210$		0			0
$211$	−17.7191			−1.21983			−0.609917	−	0.792466i	$-0.708797\pi$
$211$	−17.7191			−1.21983			−0.609917	+	0.792466i	$0.708797\pi$
$212$	−0.397891	+	0.689168i	−0.0273273	+	0.0473323i
$213$		0			0
$214$	−1.75039	−	3.03177i	−0.119654	−	0.207248i
$215$	13.8460	−	23.9819i	0.944288	−	1.63556i
$216$		0			0
$217$	−11.2420	+	5.89728i	−0.763154	+	0.400334i
$218$	−0.707666			−0.0479292
$219$		0			0
$220$	1.04787	+	1.81497i	0.0706476	+	0.122365i
$221$	2.64335	+	4.57841i	0.177811	+	0.307977i
$222$		0			0
$223$	−23.9838			−1.60607			−0.803035	−	0.595931i	$-0.796783\pi$
$223$	−23.9838			−1.60607			−0.803035	+	0.595931i	$0.796783\pi$
$224$	−13.3773	+	7.01744i	−0.893809	+	0.468872i
$225$		0			0
$226$	0.571659	−	0.990143i	0.0380262	−	0.0658633i
$227$	−5.10576	−	8.84344i	−0.338881	−	0.586959i	0.645341	−	0.763894i	$-0.276715\pi$
$227$	−5.10576	−	8.84344i	−0.338881	−	0.586959i	−0.984223	+	0.176935i	$0.943382\pi$
$228$		0			0
$229$	−11.6950	+	20.2563i	−0.772826	+	1.33857i	0.163182	+	0.986596i	$0.447824\pi$
$229$	−11.6950	+	20.2563i	−0.772826	+	1.33857i	−0.936008	+	0.351978i	$0.885509\pi$
$230$	7.26782			0.479226
$231$		0			0
$232$	−12.3411			−0.810232
$233$	13.5165	−	23.4113i	0.885497	−	1.53373i	0.0403541	−	0.999185i	$-0.487151\pi$
$233$	13.5165	−	23.4113i	0.885497	−	1.53373i	0.845143	−	0.534540i	$-0.179515\pi$
$234$		0			0
$235$	−18.4436	−	31.9453i	−1.20313	−	2.08388i
$236$	6.55771	−	11.3583i	0.426870	−	0.739361i
$237$		0			0
$238$	−0.0711170	+	1.75576i	−0.00460983	+	0.113809i
$239$	10.4948			0.678851			0.339426	−	0.940633i	$-0.389767\pi$
$239$	10.4948			0.678851			0.339426	+	0.940633i	$0.389767\pi$
$240$		0			0
$241$	11.3093	+	19.5882i	0.728493	+	1.26179i	0.957520	+	0.288367i	$0.0931125\pi$
$241$	11.3093	+	19.5882i	0.728493	+	1.26179i	−0.229026	+	0.973420i	$0.573554\pi$
$242$	−3.52509	−	6.10564i	−0.226602	−	0.392486i
$243$		0			0
$244$	8.69848			0.556863
$245$	16.9253	−	24.4989i	1.08132	−	1.56518i
$246$		0			0
$247$	2.57358	−	4.45758i	0.163753	−	0.283629i
$248$	5.55666	+	9.62442i	0.352848	+	0.611151i
$249$		0			0
$250$	11.1335	−	19.2839i	0.704147	−	1.21962i
$251$	−21.8173			−1.37710			−0.688548	−	0.725191i	$-0.741752\pi$
$251$	−21.8173			−1.37710			−0.688548	+	0.725191i	$0.741752\pi$
$252$		0			0
$253$	−0.822912			−0.0517361
$254$	1.15467	−	1.99994i	0.0724502	−	0.125487i
$255$		0			0
$256$	3.97662	+	6.88771i	0.248539	+	0.430482i
$257$	−13.4644	+	23.3211i	−0.839888	+	1.45473i	0.0500989	+	0.998744i	$0.484046\pi$
$257$	−13.4644	+	23.3211i	−0.839888	+	1.45473i	−0.889987	+	0.455985i	$0.849287\pi$
$258$		0			0
$259$	−13.9738	−	8.84053i	−0.868290	−	0.549324i
$260$	−34.6355			−2.14800
$261$		0			0
$262$	0.507375	+	0.878799i	0.0313457	+	0.0542924i
$263$	7.56739	+	13.1071i	0.466625	+	0.808218i	0.999273	−	0.0381185i	$-0.0121364\pi$
$263$	7.56739	+	13.1071i	0.466625	+	0.808218i	−0.532648	+	0.846337i	$0.678803\pi$
$264$		0			0
$265$	−2.13996			−0.131456
$266$	1.51502	−	0.794744i	0.0928917	−	0.0487289i
$267$		0			0
$268$	5.48061	−	9.49269i	0.334781	−	0.579858i
$269$	−11.8885	−	20.5915i	−0.724854	−	1.25548i	−0.959034	−	0.283291i	$-0.908574\pi$
$269$	−11.8885	−	20.5915i	−0.724854	−	1.25548i	0.234180	−	0.972193i	$-0.424760\pi$
$270$		0			0
$271$	−6.47450	+	11.2142i	−0.393298	+	0.681212i	−0.992882	−	0.119099i	$-0.961999\pi$
$271$	−6.47450	+	11.2142i	−0.393298	+	0.681212i	0.599584	+	0.800312i	$0.295333\pi$
$272$	−1.71123			−0.103758
$273$		0			0
$274$	−5.07092			−0.306345
$275$	−2.03924	+	3.53206i	−0.122971	+	0.212991i
$276$		0			0
$277$	0.187553	+	0.324851i	0.0112690	+	0.0195184i	0.871605	−	0.490209i	$-0.163080\pi$
$277$	0.187553	+	0.324851i	0.0112690	+	0.0195184i	−0.860336	+	0.509727i	$0.829746\pi$
$278$	1.60638	−	2.78234i	0.0963444	−	0.166873i
$279$		0			0
$280$	−22.0289	−	13.9366i	−1.31648	−	0.832871i
$281$	16.5698			0.988469			0.494235	−	0.869329i	$-0.335448\pi$
$281$	16.5698			0.988469			0.494235	+	0.869329i	$0.335448\pi$
$282$		0			0
$283$	9.76351	+	16.9109i	0.580380	+	1.00525i	0.995434	+	0.0954512i	$0.0304294\pi$
$283$	9.76351	+	16.9109i	0.580380	+	1.00525i	−0.415054	+	0.909797i	$0.636237\pi$
$284$	−2.32740	−	4.03117i	−0.138106	−	0.239206i
$285$		0			0
$286$	−1.03659			−0.0612951
$287$	−0.957535	+	23.6399i	−0.0565215	+	1.39542i
$288$		0			0
$289$	7.97252	−	13.8088i	0.468972	−	0.812283i
$290$	−7.32816	−	12.6928i	−0.430325	−	0.745344i
$291$		0			0
$292$	11.8077	−	20.4515i	0.690991	−	1.19683i
$293$	9.80487			0.572807			0.286403	−	0.958109i	$-0.407540\pi$
$293$	9.80487			0.572807			0.286403	+	0.958109i	$0.407540\pi$
$294$		0			0
$295$	35.2689			2.05344
$296$	−7.23773	+	12.5361i	−0.420685	+	0.728647i
$297$		0			0
$298$	2.68365	+	4.64822i	0.155460	+	0.269264i
$299$	6.79995	−	11.7779i	0.393251	−	0.681131i
$300$		0			0
$301$	0.697067	−	17.2094i	0.0401783	−	0.991932i
$302$	5.60478			0.322519
$303$		0			0
$304$	0.833031	+	1.44285i	0.0477776	+	0.0827532i
$305$	11.6956	+	20.2574i	0.669690	+	1.15994i
$306$		0			0
$307$	17.0506			0.973132			0.486566	−	0.873644i	$-0.338249\pi$
$307$	17.0506			0.973132			0.486566	+	0.873644i	$0.338249\pi$
$308$	1.10155	+	0.696896i	0.0627666	+	0.0397093i
$309$		0			0
$310$	−6.59911	+	11.4300i	−0.374804	+	0.649180i
$311$	−5.21233	−	9.02802i	−0.295564	−	0.511932i	0.679552	−	0.733627i	$-0.262174\pi$
$311$	−5.21233	−	9.02802i	−0.295564	−	0.511932i	−0.975116	+	0.221696i	$0.928841\pi$
$312$		0			0
$313$	−2.43406	+	4.21592i	−0.137581	+	0.238298i	−0.926581	−	0.376096i	$-0.877266\pi$
$313$	−2.43406	+	4.21592i	−0.137581	+	0.238298i	0.788999	+	0.614394i	$0.210600\pi$
$314$	3.98583			0.224933
$315$		0			0
$316$	23.5934			1.32723
$317$	−1.86081	+	3.22302i	−0.104514	+	0.181023i	−0.913539	−	0.406750i	$-0.866662\pi$
$317$	−1.86081	+	3.22302i	−0.104514	+	0.181023i	0.809026	+	0.587773i	$0.199995\pi$
$318$		0			0
$319$	0.829746	+	1.43716i	0.0464568	+	0.0804656i
$320$	−0.765408	+	1.32573i	−0.0427876	+	0.0741103i
$321$		0			0
$322$	4.00300	−	2.09988i	0.223078	−	0.117022i
$323$	1.02711			0.0571499
$324$		0			0
$325$	−33.7015	−	58.3728i	−1.86943	−	3.23794i
$326$	1.91537	+	3.31752i	0.106083	+	0.183741i
$327$		0			0
$328$	20.7118			1.14362
$329$	−19.3884	−	12.2661i	−1.06891	−	0.676249i
$330$		0			0
$331$	4.75839	−	8.24177i	0.261545	−	0.453009i	−0.705108	−	0.709100i	$-0.749101\pi$
$331$	4.75839	−	8.24177i	0.261545	−	0.453009i	0.966653	+	0.256091i	$0.0824348\pi$
$332$	10.6610	+	18.4654i	0.585097	+	1.01342i
$333$		0			0
$334$	2.79326	−	4.83808i	0.152841	−	0.264728i
$335$	29.4760			1.61045
$336$		0			0
$337$	−7.24860			−0.394856			−0.197428	−	0.980317i	$-0.563259\pi$
$337$	−7.24860			−0.394856			−0.197428	+	0.980317i	$0.563259\pi$
$338$	4.36258	−	7.55620i	0.237293	−	0.411003i
$339$		0			0
$340$	−3.45573	−	5.98549i	−0.187413	−	0.324609i
$341$	0.747197	−	1.29418i	0.0404630	−	0.0700840i
$342$		0			0
$343$	2.24374	−	18.3838i	0.121150	−	0.992634i
$344$	−15.0778			−0.812939
$345$		0			0
$346$	−2.58821	−	4.48291i	−0.139143	−	0.241003i
$347$	−7.37754	−	12.7783i	−0.396047	−	0.685974i	0.597187	−	0.802102i	$-0.296285\pi$
$347$	−7.37754	−	12.7783i	−0.396047	−	0.685974i	−0.993234	+	0.116128i	$0.962952\pi$
$348$		0			0
$349$	−3.64447			−0.195084			−0.0975419	−	0.995231i	$-0.531098\pi$
$349$	−3.64447			−0.195084			−0.0975419	+	0.995231i	$0.531098\pi$
$350$	0.906711	−	22.3851i	0.0484657	−	1.19654i
$351$		0			0
$352$	0.889123	−	1.54001i	0.0473904	−	0.0820826i
$353$	−0.862486	−	1.49387i	−0.0459055	−	0.0795106i	0.842160	−	0.539228i	$-0.181284\pi$
$353$	−0.862486	−	1.49387i	−0.0459055	−	0.0795106i	−0.888065	+	0.459718i	$0.847951\pi$
$354$		0			0
$355$	6.25865	−	10.8403i	0.332175	−	0.575344i
$356$	−0.153646			−0.00814320
$357$		0			0
$358$	6.52631			0.344926
$359$	−3.65089	+	6.32353i	−0.192687	+	0.333743i	−0.946140	−	0.323759i	$-0.895053\pi$
$359$	−3.65089	+	6.32353i	−0.192687	+	0.333743i	0.753453	+	0.657502i	$0.228387\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	2.87599	−	4.98136i	0.151159	−	0.261814i
$363$		0			0
$364$	−19.0767	+	10.0072i	−0.999889	+	0.524519i
$365$	63.5045			3.32398
$366$		0			0
$367$	−3.54851	−	6.14619i	−0.185230	−	0.320829i	0.758424	−	0.651762i	$-0.225970\pi$
$367$	−3.54851	−	6.14619i	−0.185230	−	0.320829i	−0.943654	+	0.330933i	$0.892636\pi$
$368$	2.20104	+	3.81232i	0.114737	+	0.198731i
$369$		0			0
$370$	−17.1911			−0.893723
$371$	−1.17865	+	0.618296i	−0.0611927	+	0.0321003i
$372$		0			0
$373$	−14.5281	+	25.1635i	−0.752239	+	1.30292i	0.194497	+	0.980903i	$0.437693\pi$
$373$	−14.5281	+	25.1635i	−0.752239	+	1.30292i	−0.946735	+	0.322012i	$0.895641\pi$
$374$	−0.103425	−	0.179138i	−0.00534800	−	0.00926301i
$375$		0			0
$376$	−10.0422	+	17.3936i	−0.517887	+	0.897007i
$377$	−27.4256			−1.41249
$378$		0			0
$379$	−14.1658			−0.727650			−0.363825	−	0.931467i	$-0.618529\pi$
$379$	−14.1658			−0.727650			−0.363825	+	0.931467i	$0.618529\pi$
$380$	−3.36452	+	5.82752i	−0.172596	+	0.298945i
$381$		0			0
$382$	5.38745	+	9.33135i	0.275646	+	0.477433i
$383$	9.03032	−	15.6410i	0.461428	−	0.799216i	−0.537605	−	0.843197i	$-0.680671\pi$
$383$	9.03032	−	15.6410i	0.461428	−	0.799216i	0.999032	+	0.0439807i	$0.0140040\pi$
$384$		0			0
$385$	−0.141863	+	3.50236i	−0.00723002	+	0.178497i
$386$	12.0818			0.614949
$387$		0			0
$388$	10.6619	+	18.4669i	0.541275	+	0.937516i
$389$	−15.8576	−	27.4662i	−0.804014	−	1.39259i	−0.916955	−	0.398991i	$-0.869360\pi$
$389$	−15.8576	−	27.4662i	−0.804014	−	1.39259i	0.112941	−	0.993602i	$-0.463973\pi$
$390$		0			0
$391$	2.71384			0.137245
$392$	−16.1599	−	1.31126i	−0.816196	−	0.0662288i
$393$		0			0
$394$	6.48806	−	11.2376i	0.326864	−	0.566144i
$395$	31.7228	+	54.9455i	1.59615	+	2.76461i
$396$		0			0
$397$	11.5742	−	20.0470i	0.580890	−	1.00613i	−0.414484	−	0.910057i	$-0.636038\pi$
$397$	11.5742	−	20.0470i	0.580890	−	1.00613i	0.995374	−	0.0960745i	$-0.0306287\pi$
$398$	6.45450			0.323535
$399$		0			0
$400$	21.8174			1.09087
$401$	−0.768226	+	1.33061i	−0.0383634	+	0.0664473i	−0.884570	−	0.466408i	$-0.845548\pi$
$401$	−0.768226	+	1.33061i	−0.0383634	+	0.0664473i	0.846206	+	0.532856i	$0.178881\pi$
$402$		0			0
$403$	12.3486	+	21.3884i	0.615127	+	1.06543i
$404$	−13.9035	+	24.0815i	−0.691723	+	1.19810i
$405$		0			0
$406$	−7.70354	−	4.87365i	−0.382320	−	0.241875i
$407$	1.94650			0.0964843
$408$		0			0
$409$	4.78687	+	8.29110i	0.236695	+	0.409968i	0.959764	−	0.280808i	$-0.0906024\pi$
$409$	4.78687	+	8.29110i	0.236695	+	0.409968i	−0.723069	+	0.690776i	$0.757269\pi$
$410$	12.2987	+	21.3020i	0.607389	+	1.05203i
$411$		0			0
$412$	−18.3675			−0.904902
$413$	19.4256	−	10.1902i	0.955869	−	0.501428i
$414$		0			0
$415$	−28.6687	+	49.6556i	−1.40729	+	2.43750i
$416$	14.6941	+	25.4510i	0.720439	+	1.24784i
$417$		0			0
$418$	−0.100696	+	0.174410i	−0.00492519	+	0.00853067i
$419$	−28.8346			−1.40866			−0.704332	−	0.709870i	$-0.748753\pi$
$419$	−28.8346			−1.40866			−0.704332	+	0.709870i	$0.748753\pi$
$420$		0			0
$421$	15.6465			0.762566			0.381283	−	0.924458i	$-0.375482\pi$
$421$	15.6465			0.762566			0.381283	+	0.924458i	$0.375482\pi$
$422$	−5.72884	+	9.92264i	−0.278875	+	0.483026i
$423$		0			0
$424$	0.582583	+	1.00906i	0.0282928	+	0.0490045i
$425$	6.72509	−	11.6482i	0.326215	−	0.565021i
$426$		0			0
$427$	12.2947	+	7.77826i	0.594983	+	0.376416i
$428$	8.56411			0.413962
$429$		0			0
$430$	−8.95321	−	15.5074i	−0.431762	−	0.747834i
$431$	−4.56954	−	7.91467i	−0.220107	−	0.381236i	0.734733	−	0.678356i	$-0.237307\pi$
$431$	−4.56954	−	7.91467i	−0.220107	−	0.381236i	−0.954840	+	0.297120i	$0.903974\pi$
$432$		0			0
$433$	11.9528			0.574414			0.287207	−	0.957869i	$-0.407273\pi$
$433$	11.9528			0.574414			0.287207	+	0.957869i	$0.407273\pi$
$434$	−0.332228	+	8.20214i	−0.0159475	+	0.393715i
$435$		0			0
$436$	0.865595	−	1.49925i	0.0414545	−	0.0718013i
$437$	−1.32111	−	2.28822i	−0.0631971	−	0.109461i
$438$		0			0
$439$	10.8669	−	18.8220i	0.518649	−	0.898326i	−0.481116	−	0.876657i	$-0.659769\pi$
$439$	10.8669	−	18.8220i	0.518649	−	0.898326i	0.999765	−	0.0216694i	$-0.00689814\pi$
$440$	3.06854			0.146287
$441$		0			0
$442$	3.41853			0.162603
$443$	10.4040	−	18.0202i	0.494308	−	0.856166i	−0.505671	−	0.862727i	$-0.668755\pi$
$443$	10.4040	−	18.0202i	0.494308	−	0.856166i	0.999978	+	0.00656028i	$0.00208822\pi$
$444$		0			0
$445$	−0.206586	−	0.357817i	−0.00979310	−	0.0169622i
$446$	−7.75429	+	13.4308i	−0.367176	+	0.635968i
$447$		0			0
$448$	−0.0385340	+	0.951338i	−0.00182056	+	0.0449465i
$449$	10.5978			0.500141			0.250070	−	0.968228i	$-0.419546\pi$
$449$	10.5978			0.500141			0.250070	+	0.968228i	$0.419546\pi$
$450$		0			0
$451$	−1.39254	−	2.41195i	−0.0655723	−	0.113575i
$452$	1.39847	+	2.42222i	0.0657786	+	0.113932i
$453$		0			0
$454$	−6.60306			−0.309897
$455$	−48.9549	−	30.9713i	−2.29504	−	1.45196i
$456$		0			0
$457$	2.14329	−	3.71229i	0.100259	−	0.173654i	−0.811532	−	0.584307i	$-0.801366\pi$
$457$	2.14329	−	3.71229i	0.100259	−	0.173654i	0.911791	+	0.410654i	$0.134700\pi$
$458$	7.56231	+	13.0983i	0.353363	+	0.612043i
$459$		0			0
$460$	−8.88977	+	15.3975i	−0.414488	+	0.717914i
$461$	−36.6892			−1.70879			−0.854394	−	0.519625i	$-0.826072\pi$
$461$	−36.6892			−1.70879			−0.854394	+	0.519625i	$0.826072\pi$
$462$		0			0
$463$	4.80965			0.223523			0.111762	−	0.993735i	$-0.464351\pi$
$463$	4.80965			0.223523			0.111762	+	0.993735i	$0.464351\pi$
$464$	4.43864	−	7.68795i	0.206059	−	0.356904i
$465$		0			0
$466$	−8.74017	−	15.1384i	−0.404880	−	0.701274i
$467$	−0.305731	+	0.529541i	−0.0141475	+	0.0245042i	−0.873012	−	0.487698i	$-0.837837\pi$
$467$	−0.305731	+	0.529541i	−0.0141475	+	0.0245042i	0.858865	+	0.512202i	$0.171170\pi$
$468$		0			0
$469$	16.2349	−	8.51648i	0.749659	−	0.393254i
$470$	−23.8523			−1.10023
$471$		0			0
$472$	−9.60164	−	16.6305i	−0.441951	−	0.765482i
$473$	1.01374	+	1.75586i	0.0466120	+	0.0807344i
$474$		0			0
$475$	−13.0952			−0.600849
$476$	−3.63274	−	2.29825i	−0.166506	−	0.105340i
$477$		0			0
$478$	3.39311	−	5.87704i	0.155197	−	0.268810i
$479$	12.9151	+	22.3696i	0.590104	+	1.02209i	0.994218	+	0.107382i	$0.0342468\pi$
$479$	12.9151	+	22.3696i	0.590104	+	1.02209i	−0.404113	+	0.914709i	$0.632420\pi$
$480$		0			0
$481$	−16.0844	+	27.8591i	−0.733387	+	1.27026i
$482$	14.6258			0.666186
$483$		0			0
$484$	17.2471			0.783961
$485$	−28.6711	+	49.6598i	−1.30189	+	2.25493i
$486$		0			0
$487$	−6.79115	−	11.7626i	−0.307736	−	0.533015i	0.670131	−	0.742243i	$-0.266238\pi$
$487$	−6.79115	−	11.7626i	−0.307736	−	0.533015i	−0.977867	+	0.209228i	$0.932905\pi$
$488$	6.36805	−	11.0298i	0.288268	−	0.499295i
$489$		0			0
$490$	−8.24713	−	17.3990i	−0.372567	−	0.786005i
$491$	−11.9793			−0.540619			−0.270310	−	0.962773i	$-0.587126\pi$
$491$	−11.9793			−0.540619			−0.270310	+	0.962773i	$0.587126\pi$
$492$		0			0
$493$	−2.73637	−	4.73954i	−0.123240	−	0.213458i
$494$	−1.66415	−	2.88239i	−0.0748737	−	0.129685i
$495$		0			0
$496$	−7.99411			−0.358946
$497$	0.315088	−	7.77897i	0.0141336	−	0.348935i
$498$		0			0
$499$	−6.77009	+	11.7261i	−0.303071	+	0.524934i	−0.976830	−	0.214017i	$-0.931345\pi$
$499$	−6.77009	+	11.7261i	−0.303071	+	0.524934i	0.673759	+	0.738951i	$0.264679\pi$
$500$	27.2364	+	47.1749i	1.21805	+	2.10972i
$501$		0			0
$502$	−7.05385	+	12.2176i	−0.314829	+	0.545299i
$503$	21.1177			0.941592			0.470796	−	0.882242i	$-0.343967\pi$
$503$	21.1177			0.941592			0.470796	+	0.882242i	$0.343967\pi$
$504$		0			0
$505$	−74.7762			−3.32750
$506$	−0.266059	+	0.460828i	−0.0118278	+	0.0204863i
$507$		0			0
$508$	2.82470	+	4.89253i	0.125326	+	0.217071i
$509$	−14.1138	+	24.4459i	−0.625585	+	1.08354i	0.362843	+	0.931850i	$0.381806\pi$
$509$	−14.1138	+	24.4459i	−0.625585	+	1.08354i	−0.988427	+	0.151694i	$0.951527\pi$
$510$		0			0
$511$	34.9773	−	18.3483i	1.54730	−	0.811680i
$512$	−17.2302			−0.761475
$513$		0			0
$514$	8.70649	+	15.0801i	0.384027	+	0.665154i
$515$	−24.6962	−	42.7751i	−1.08825	−	1.88490i
$516$		0			0
$517$	2.70072			0.118778
$518$	−9.46859	+	4.96701i	−0.416026	+	0.218238i
$519$		0			0
$520$	−25.3562	+	43.9182i	−1.11194	+	1.92594i
$521$	2.04092	+	3.53498i	0.0894143	+	0.154870i	0.907264	−	0.420562i	$-0.138167\pi$
$521$	2.04092	+	3.53498i	0.0894143	+	0.154870i	−0.817849	+	0.575432i	$0.804834\pi$
$522$		0			0
$523$	0.310177	−	0.537242i	0.0135631	−	0.0234920i	−0.859164	−	0.511700i	$-0.829016\pi$
$523$	0.310177	−	0.537242i	0.0135631	−	0.0234920i	0.872727	+	0.488208i	$0.162349\pi$
$524$	−2.48242			−0.108445
$525$		0			0
$526$	9.78657			0.426715
$527$	−2.46414	+	4.26802i	−0.107340	+	0.185918i
$528$		0			0
$529$	8.00936	+	13.8726i	0.348233	+	0.603157i
$530$	−0.691878	+	1.19837i	−0.0300533	+	0.0520538i
$531$		0			0
$532$	−0.169384	+	4.18181i	−0.00734375	+	0.181304i
$533$	46.0278			1.99369
$534$		0			0
$535$	11.5150	+	19.9445i	0.497835	+	0.862276i
$536$	−8.02457	−	13.8990i	−0.346609	−	0.600344i
$537$		0			0
$538$	−15.3749			−0.662858
$539$	0.933797	+	1.97003i	0.0402215	+	0.0848553i
$540$		0			0
$541$	16.9291	−	29.3221i	0.727840	−	1.26066i	−0.229955	−	0.973201i	$-0.573858\pi$
$541$	16.9291	−	29.3221i	0.727840	−	1.26066i	0.957794	−	0.287454i	$-0.0928088\pi$
$542$	4.18660	+	7.25140i	0.179830	+	0.311474i
$543$		0			0
$544$	−2.93219	+	5.07870i	−0.125717	+	0.217748i
$545$	4.65538			0.199415
$546$		0			0
$547$	1.11487			0.0476684			0.0238342	−	0.999716i	$-0.492413\pi$
$547$	1.11487			0.0476684			0.0238342	+	0.999716i	$0.492413\pi$
$548$	6.20259	−	10.7432i	0.264962	−	0.458927i
$549$		0			0
$550$	1.31863	+	2.28393i	0.0562265	+	0.0973872i
$551$	−2.66415	+	4.61445i	−0.113497	+	0.196582i
$552$		0			0
$553$	33.3477	+	21.0975i	1.41809	+	0.897155i
$554$	0.242554			0.0103051
$555$		0			0
$556$	3.92976	+	6.80654i	0.166659	+	0.288661i
$557$	−4.64743	−	8.04959i	−0.196918	−	0.341072i	0.750610	−	0.660746i	$-0.229760\pi$
$557$	−4.64743	−	8.04959i	−0.196918	−	0.341072i	−0.947528	+	0.319674i	$0.896427\pi$
$558$		0			0
$559$	−33.5074			−1.41721
$560$	16.6049	−	8.71055i	0.701684	−	0.368088i
$561$		0			0
$562$	5.35724	−	9.27901i	0.225981	−	0.391411i
$563$	−10.1765	−	17.6262i	−0.428888	−	0.742855i	0.567887	−	0.823106i	$-0.307761\pi$
$563$	−10.1765	−	17.6262i	−0.428888	−	0.742855i	−0.996775	+	0.0802514i	$0.974428\pi$
$564$		0			0
$565$	−3.76066	+	6.51365i	−0.158212	+	0.274031i
$566$	12.6267			0.530741
$567$		0			0
$568$	−6.81544			−0.285970
$569$	−12.2334	+	21.1889i	−0.512852	+	0.888286i	0.487037	+	0.873382i	$0.338078\pi$
$569$	−12.2334	+	21.1889i	−0.512852	+	0.888286i	−0.999889	+	0.0149048i	$0.995255\pi$
$570$		0			0
$571$	−2.44126	−	4.22838i	−0.102163	−	0.176952i	0.810412	−	0.585860i	$-0.199243\pi$
$571$	−2.44126	−	4.22838i	−0.102163	−	0.176952i	−0.912576	+	0.408908i	$0.865910\pi$
$572$	1.26793	−	2.19612i	0.0530148	−	0.0918244i
$573$		0			0
$574$	12.9287	+	8.17933i	0.539632	+	0.341399i
$575$	−34.6003			−1.44293
$576$		0			0
$577$	9.44991	+	16.3677i	0.393405	+	0.681397i	0.992896	−	0.118984i	$-0.0379637\pi$
$577$	9.44991	+	16.3677i	0.393405	+	0.681397i	−0.599491	+	0.800381i	$0.704630\pi$
$578$	−5.15526	−	8.92917i	−0.214431	−	0.371405i
$579$		0			0
$580$	35.8543			1.48877
$581$	−1.44331	+	35.6327i	−0.0598784	+	1.47829i
$582$		0			0
$583$	0.0783393	−	0.135688i	0.00324448	−	0.00561960i
$584$	−17.2885	−	29.9446i	−0.715404	−	1.23912i
$585$		0			0
$586$	3.17005	−	5.49069i	0.130954	−	0.226819i
$587$	25.6183			1.05738			0.528690	−	0.848815i	$-0.322683\pi$
$587$	25.6183			1.05738			0.528690	+	0.848815i	$0.322683\pi$
$588$		0			0
$589$	4.79821			0.197707
$590$	11.4029	−	19.7505i	0.469452	−	0.813114i
$591$		0			0
$592$	−5.20630	−	9.01757i	−0.213977	−	0.370620i
$593$	9.23690	−	15.9988i	0.379314	−	0.656991i	−0.611649	−	0.791130i	$-0.709493\pi$
$593$	9.23690	−	15.9988i	0.379314	−	0.656991i	0.990963	+	0.134138i	$0.0428267\pi$
$594$		0			0
$595$	0.467843	−	11.5502i	0.0191797	−	0.473514i
$596$	−13.1302			−0.537836
$597$		0			0
$598$	−4.39704	−	7.61590i	−0.179808	−	0.311437i
$599$	−19.2900	−	33.4112i	−0.788167	−	1.36515i	−0.927089	−	0.374842i	$-0.877697\pi$
$599$	−19.2900	−	33.4112i	−0.788167	−	1.36515i	0.138921	−	0.990303i	$-0.455637\pi$
$600$		0			0
$601$	28.5239			1.16351			0.581757	−	0.813362i	$-0.302365\pi$
$601$	28.5239			1.16351			0.581757	+	0.813362i	$0.302365\pi$
$602$	−9.41182	−	5.95439i	−0.383597	−	0.242683i
$603$		0			0
$604$	−6.85560	+	11.8742i	−0.278950	+	0.483156i
$605$	23.1898	+	40.1660i	0.942801	+	1.63298i
$606$		0			0
$607$	23.3741	−	40.4851i	0.948725	−	1.64324i	0.200611	−	0.979671i	$-0.435707\pi$
$607$	23.3741	−	40.4851i	0.948725	−	1.64324i	0.748115	−	0.663569i	$-0.230959\pi$
$608$	5.70960			0.231555
$609$		0			0
$610$	15.1254			0.612412
$611$	−22.3168	+	38.6539i	−0.902842	+	1.56377i
$612$		0			0
$613$	1.04846	+	1.81598i	0.0423468	+	0.0733468i	0.886422	−	0.462878i	$-0.153183\pi$
$613$	1.04846	+	1.81598i	0.0423468	+	0.0733468i	−0.844075	+	0.536225i	$0.819850\pi$
$614$	5.51272	−	9.54830i	0.222475	−	0.385338i
$615$		0			0
$616$	1.69011	−	0.886592i	0.0680963	−	0.0357218i
$617$	30.5560			1.23014			0.615069	−	0.788473i	$-0.289128\pi$
$617$	30.5560			1.23014			0.615069	+	0.788473i	$0.289128\pi$
$618$		0			0
$619$	3.88711	+	6.73268i	0.156236	+	0.270609i	0.933508	−	0.358555i	$-0.116731\pi$
$619$	3.88711	+	6.73268i	0.156236	+	0.270609i	−0.777272	+	0.629164i	$0.783397\pi$
$620$	−16.1437	−	27.9616i	−0.648345	−	1.12297i
$621$		0			0
$622$	−6.74088			−0.270285
$623$	−0.217168	−	0.137391i	−0.00870065	−	0.00550447i
$624$		0			0
$625$	−40.5040	+	70.1550i	−1.62016	+	2.80620i
$626$	1.57393	+	2.72613i	0.0629071	+	0.108958i
$627$		0			0
$628$	−4.87534	+	8.44434i	−0.194547	+	0.336966i
$629$	−6.41925			−0.255952
$630$		0			0
$631$	−20.5370			−0.817564			−0.408782	−	0.912632i	$-0.634046\pi$
$631$	−20.5370			−0.817564			−0.408782	+	0.912632i	$0.634046\pi$
$632$	17.2725	−	29.9168i	0.687062	−	1.19003i
$633$		0			0
$634$	1.20325	+	2.08410i	0.0477873	+	0.0827701i
$635$	−7.59597	+	13.1566i	−0.301437	+	0.522104i
$636$		0			0
$637$	−35.9121	−	2.91403i	−1.42289	−	0.115458i
$638$	1.07307			0.0424834
$639$		0			0
$640$	−23.7928	−	41.2104i	−0.940494	−	1.62898i
$641$	4.73761	+	8.20578i	0.187124	+	0.324109i	0.944290	−	0.329114i	$-0.106750\pi$
$641$	4.73761	+	8.20578i	0.187124	+	0.324109i	−0.757166	+	0.653222i	$0.773417\pi$
$642$		0			0
$643$	30.9924			1.22222			0.611110	−	0.791546i	$-0.290723\pi$
$643$	30.9924			1.22222			0.611110	+	0.791546i	$0.290723\pi$
$644$	−0.447550	+	11.0492i	−0.0176359	+	0.435401i
$645$		0			0
$646$	0.332079	−	0.575177i	0.0130655	−	0.0226301i
$647$	−22.7654	−	39.4308i	−0.894999	−	1.55018i	−0.833806	−	0.552058i	$-0.813843\pi$
$647$	−22.7654	−	39.4308i	−0.894999	−	1.55018i	−0.0611936	−	0.998126i	$-0.519491\pi$
$648$		0			0
$649$	−1.29112	+	2.23629i	−0.0506809	+	0.0877819i
$650$	−43.5848			−1.70953
$651$		0			0
$652$	−9.37130			−0.367008
$653$	−10.9515	+	18.9685i	−0.428564	+	0.742294i	−0.996746	−	0.0806087i	$-0.974314\pi$
$653$	−10.9515	+	18.9685i	−0.428564	+	0.742294i	0.568182	+	0.822903i	$0.307647\pi$
$654$		0			0
$655$	−3.33776	−	5.78118i	−0.130417	−	0.225889i
$656$	−7.44927	+	12.9025i	−0.290845	+	0.503758i
$657$		0			0
$658$	−13.1375	+	6.89163i	−0.512152	+	0.268664i
$659$	−13.9146			−0.542037			−0.271019	−	0.962574i	$-0.587361\pi$
$659$	−13.9146			−0.542037			−0.271019	+	0.962574i	$0.587361\pi$
$660$		0			0
$661$	−3.42895	−	5.93912i	−0.133371	−	0.231005i	0.791603	−	0.611036i	$-0.209247\pi$
$661$	−3.42895	−	5.93912i	−0.133371	−	0.231005i	−0.924974	+	0.380031i	$0.875913\pi$
$662$	−3.07691	−	5.32936i	−0.119587	−	0.207132i
$663$		0			0
$664$	31.2191			1.21154
$665$	−9.96654	+	5.22823i	−0.386486	+	0.202742i
$666$		0			0
$667$	−7.03925	+	12.1923i	−0.272561	+	0.472089i
$668$	6.83327	+	11.8356i	0.264387	+	0.457932i
$669$		0			0
$670$	9.53001	−	16.5065i	0.368177	−	0.637701i
$671$	−1.71261			−0.0661145
$672$		0			0
$673$	16.8673			0.650187			0.325093	−	0.945682i	$-0.394604\pi$
$673$	16.8673			0.650187			0.325093	+	0.945682i	$0.394604\pi$
$674$	−2.34357	+	4.05919i	−0.0902711	+	0.156354i
$675$		0			0
$676$	10.6723	+	18.4850i	0.410474	+	0.710963i
$677$	−7.31695	+	12.6733i	−0.281213	+	0.487075i	−0.971684	−	0.236285i	$-0.924070\pi$
$677$	−7.31695	+	12.6733i	−0.281213	+	0.487075i	0.690471	+	0.723360i	$0.257403\pi$
$678$		0			0
$679$	−1.44343	+	35.6357i	−0.0553936	+	1.36757i
$680$	−10.1196			−0.388068
$681$		0			0
$682$	−0.483159	−	0.836856i	−0.0185011	−	0.0320449i
$683$	−8.88372	−	15.3871i	−0.339926	−	0.588769i	0.644492	−	0.764611i	$-0.277069\pi$
$683$	−8.88372	−	15.3871i	−0.339926	−	0.588769i	−0.984419	+	0.175841i	$0.943735\pi$
$684$		0			0
$685$	33.3590			1.27458
$686$	−9.56946	−	7.20024i	−0.365364	−	0.274907i
$687$		0			0
$688$	5.42292	−	9.39278i	0.206747	−	0.358096i
$689$	1.29468	+	2.24245i	0.0493233	+	0.0854304i
$690$		0			0
$691$	12.9289	−	22.3935i	0.491838	−	0.851888i	−0.508118	−	0.861288i	$-0.669659\pi$
$691$	12.9289	−	22.3935i	0.491838	−	0.851888i	0.999956	+	0.00939929i	$0.00299193\pi$
$692$	12.6633			0.481386
$693$		0			0
$694$	−9.54106			−0.362174
$695$	−10.5676	+	18.3036i	−0.400851	+	0.694295i
$696$		0			0
$697$	4.59239	+	7.95426i	0.173949	+	0.301289i
$698$	−1.17831	+	2.04089i	−0.0445996	+	0.0772488i
$699$		0			0
$700$	46.3159	+	29.3018i	1.75058	+	1.10750i
$701$	7.39233			0.279204			0.139602	−	0.990208i	$-0.455418\pi$
$701$	7.39233			0.279204			0.139602	+	0.990208i	$0.455418\pi$
$702$		0			0
$703$	3.12491	+	5.41251i	0.117858	+	0.204136i
$704$	−0.0560399	−	0.0970640i	−0.00211208	−	0.00365824i
$705$		0			0
$706$	−1.11542			−0.0419792
$707$	−41.1855	+	21.6050i	−1.54894	+	0.812540i
$708$		0			0
$709$	−9.83662	+	17.0375i	−0.369422	+	0.639858i	−0.989475	−	0.144702i	$-0.953778\pi$
$709$	−9.83662	+	17.0375i	−0.369422	+	0.639858i	0.620053	+	0.784560i	$0.287111\pi$
$710$	−4.04702	−	7.00965i	−0.151882	−	0.263067i
$711$		0			0
$712$	−0.112482	+	0.194825i	−0.00421545	+	0.00730137i
$713$	12.6779			0.474791
$714$		0			0
$715$	6.81924			0.255025
$716$	−7.98278	+	13.8266i	−0.298331	+	0.516724i
$717$		0			0
$718$	2.36077	+	4.08897i	0.0881031	+	0.152599i
$719$	15.1698	−	26.2749i	0.565739	−	0.979888i	−0.431242	−	0.902236i	$-0.641924\pi$
$719$	15.1698	−	26.2749i	0.565739	−	0.979888i	0.996981	−	0.0776516i	$-0.0247422\pi$
$720$		0			0
$721$	−25.9612	−	16.4244i	−0.966847	−	0.611676i
$722$	−0.646628			−0.0240650
$723$		0			0
$724$	7.03564	+	12.1861i	0.261478	+	0.452892i
$725$	34.8876	+	60.4270i	1.29569	+	2.24420i
$726$		0			0
$727$	−8.17506			−0.303196			−0.151598	−	0.988442i	$-0.548442\pi$
$727$	−8.17506			−0.303196			−0.151598	+	0.988442i	$0.548442\pi$
$728$	−1.27654	+	31.5156i	−0.0473118	+	1.16805i
$729$		0			0
$730$	20.5319	−	35.5623i	0.759920	−	1.31622i
$731$	−3.34317	−	5.79054i	−0.123652	−	0.214171i
$732$		0			0
$733$	−16.2040	+	28.0661i	−0.598508	+	1.03665i	0.394533	+	0.918882i	$0.370906\pi$
$733$	−16.2040	+	28.0661i	−0.598508	+	1.03665i	−0.993042	+	0.117765i	$0.962427\pi$
$734$	−4.58913			−0.169388
$735$		0			0
$736$	15.0860			0.556077
$737$	−1.07905	+	1.86898i	−0.0397475	+	0.0688446i
$738$		0			0
$739$	−22.2110	−	38.4706i	−0.817046	−	1.41517i	−0.907849	−	0.419296i	$-0.862277\pi$
$739$	−22.2110	−	38.4706i	−0.817046	−	1.41517i	0.0908036	−	0.995869i	$-0.471056\pi$
$740$	21.0276	−	36.4209i	0.772991	−	1.33886i
$741$		0			0
$742$	−0.0348322	+	0.859946i	−0.00127873	+	0.0315696i
$743$	15.1572			0.556063			0.278032	−	0.960572i	$-0.410318\pi$
$743$	15.1572			0.556063			0.278032	+	0.960572i	$0.410318\pi$
$744$		0			0
$745$	−17.6544	−	30.5783i	−0.646807	−	1.12030i
$746$	9.39431	+	16.2714i	0.343950	+	0.595739i
$747$		0			0
$748$	0.506027			0.0185022
$749$	12.1048	+	7.65811i	0.442300	+	0.279821i
$750$		0			0
$751$	−4.34122	+	7.51921i	−0.158413	+	0.274380i	−0.934297	−	0.356497i	$-0.883971\pi$
$751$	−4.34122	+	7.51921i	−0.158413	+	0.274380i	0.775883	+	0.630876i	$0.217304\pi$
$752$	−7.22363	−	12.5117i	−0.263419	−	0.456254i
$753$		0			0
$754$	−8.86710	+	15.3583i	−0.322921	+	0.559315i
$755$	−36.8711			−1.34188
$756$		0			0
$757$	6.11790			0.222359			0.111179	−	0.993800i	$-0.464537\pi$
$757$	6.11790			0.222359			0.111179	+	0.993800i	$0.464537\pi$
$758$	−4.58002	+	7.93282i	−0.166354	+	0.288133i
$759$		0			0
$760$	4.92625	+	8.53251i	0.178694	+	0.309507i
$761$	7.35563	−	12.7403i	0.266641	−	0.461836i	−0.701351	−	0.712816i	$-0.747419\pi$
$761$	7.35563	−	12.7403i	0.266641	−	0.461836i	0.967992	+	0.250980i	$0.0807527\pi$
$762$		0			0
$763$	2.56411	−	1.34507i	0.0928270	−	0.0486950i
$764$	−26.3591			−0.953638
$765$		0			0
$766$	−5.83926	−	10.1139i	−0.210981	−	0.365430i
$767$	−21.3378	−	36.9581i	−0.770462	−	1.33448i
$768$		0			0
$769$	2.60588			0.0939704			0.0469852	−	0.998896i	$-0.485039\pi$
$769$	2.60588			0.0939704			0.0469852	+	0.998896i	$0.485039\pi$
$770$	1.91544	+	1.21181i	0.0690278	+	0.0436704i
$771$		0			0
$772$	−14.7781	+	25.5965i	−0.531876	+	0.921236i
$773$	23.4470	+	40.6115i	0.843331	+	1.46069i	0.887063	+	0.461649i	$0.152742\pi$
$773$	23.4470	+	40.6115i	0.843331	+	1.46069i	−0.0437315	+	0.999043i	$0.513925\pi$
$774$		0			0
$775$	31.4167	−	54.4154i	1.12852	−	1.95466i
$776$	31.2217			1.12080
$777$		0			0
$778$	−20.5080			−0.735247
$779$	4.47118	−	7.74432i	0.160197	−	0.277469i
$780$		0			0
$781$	0.458232	+	0.793681i	0.0163968	+	0.0284001i
$782$	0.877422	−	1.51974i	0.0313766	−	0.0543458i
$783$		0			0
$784$	6.62897	−	9.59526i	0.236749	−	0.342688i
$785$	−26.2208			−0.935859
$786$		0			0
$787$	−0.454311	−	0.786890i	−0.0161944	−	0.0280496i	0.857815	−	0.513959i	$-0.171822\pi$
$787$	−0.454311	−	0.786890i	−0.0161944	−	0.0280496i	−0.874009	+	0.485910i	$0.838488\pi$
$788$	15.8720	+	27.4911i	0.565416	+	0.979330i
$789$		0			0
$790$	41.0257			1.45963
$791$	−0.189328	+	4.67418i	−0.00673173	+	0.166195i
$792$		0			0
$793$	14.1517	−	24.5115i	0.502543	−	0.870430i
$794$	−7.48417	−	12.9630i	−0.265603	−	0.460039i
$795$		0			0
$796$	−7.89495	+	13.6745i	−0.279829	+	0.484678i
$797$	18.3683			0.650639			0.325320	−	0.945604i	$-0.394528\pi$
$797$	18.3683			0.650639			0.325320	+	0.945604i	$0.394528\pi$
$798$		0			0
$799$	−8.90657			−0.315092
$800$	37.3842	−	64.7513i	1.32173	−	2.28930i
$801$		0			0
$802$	0.496757	+	0.860408i	0.0175411	+	0.0303820i
$803$	−2.32476	+	4.02661i	−0.0820391	+	0.142096i
$804$		0			0
$805$	−26.3337	+	13.8141i	−0.928142	+	0.486882i
$806$	15.9699			0.562515
$807$		0			0
$808$	20.3571	+	35.2596i	0.716161	+	1.24043i
$809$	20.7585	+	35.9548i	0.729830	+	1.26410i	0.956955	+	0.290237i	$0.0937342\pi$
$809$	20.7585	+	35.9548i	0.729830	+	1.26410i	−0.227125	+	0.973866i	$0.572932\pi$
$810$		0			0
$811$	−28.2363			−0.991509			−0.495755	−	0.868463i	$-0.665108\pi$
$811$	−28.2363			−0.991509			−0.495755	+	0.868463i	$0.665108\pi$
$812$	19.7480	−	10.3594i	0.693019	−	0.363542i
$813$		0			0
$814$	0.629330	−	1.09003i	0.0220580	−	0.0382056i
$815$	−12.6003	−	21.8243i	−0.441368	−	0.764472i
$816$		0			0
$817$	−3.25493	+	5.63771i	−0.113876	+	0.197239i
$818$	6.19065			0.216451
$819$		0			0
$820$	−60.1735			−2.10135
$821$	19.3503	−	33.5157i	0.675331	−	1.16971i	−0.301041	−	0.953611i	$-0.597334\pi$
$821$	19.3503	−	33.5157i	0.675331	−	1.16971i	0.976372	−	0.216096i	$-0.0693326\pi$
$822$		0			0
$823$	−11.3413	−	19.6437i	−0.395333	−	0.684737i	0.597811	−	0.801637i	$-0.296037\pi$
$823$	−11.3413	−	19.6437i	−0.395333	−	0.684737i	−0.993144	+	0.116901i	$0.962704\pi$
$824$	−13.4466	+	23.2903i	−0.468436	+	0.811354i
$825$		0			0
$826$	0.574074	−	14.1729i	0.0199746	−	0.493138i
$827$	25.8795			0.899917			0.449959	−	0.893049i	$-0.351439\pi$
$827$	25.8795			0.899917			0.449959	+	0.893049i	$0.351439\pi$
$828$		0			0
$829$	12.3482	+	21.3877i	0.428870	+	0.742824i	0.996773	−	0.0802710i	$-0.0255786\pi$
$829$	12.3482	+	21.3877i	0.428870	+	0.742824i	−0.567903	+	0.823095i	$0.692245\pi$
$830$	18.5380	+	32.1087i	0.643462	+	1.11451i
$831$		0			0
$832$	1.85229			0.0642167
$833$	−3.07952	−	6.49686i	−0.106699	−	0.225103i
$834$		0			0
$835$	−18.3755	+	31.8273i	−0.635910	+	1.10143i
$836$	−0.246336	−	0.426666i	−0.00851970	−	0.0147566i
$837$		0			0
$838$	−9.32265	+	16.1473i	−0.322046	+	0.557799i
$839$	13.3927			0.462368			0.231184	−	0.972910i	$-0.425740\pi$
$839$	13.3927			0.462368			0.231184	+	0.972910i	$0.425740\pi$
$840$		0			0
$841$	−0.609195			−0.0210067
$842$	5.05875	−	8.76201i	0.174336	−	0.301959i
$843$		0			0
$844$	−14.0147	−	24.2741i	−0.482405	−	0.835550i
$845$	−28.6992	+	49.7085i	−0.987282	+	1.71002i
$846$		0			0
$847$	24.3777	+	15.4226i	0.837628	+	0.529925i
$848$	−0.838136			−0.0287817
$849$		0			0
$850$	−4.34864	−	7.53206i	−0.149157	−	0.258347i
$851$	8.25668	+	14.3010i	0.283035	+	0.490231i
$852$		0			0
$853$	25.6719			0.878990			0.439495	−	0.898245i	$-0.355157\pi$
$853$	25.6719			0.878990			0.439495	+	0.898245i	$0.355157\pi$
$854$	8.33086	−	4.37018i	0.285076	−	0.149545i
$855$		0			0
$856$	6.26969	−	10.8594i	0.214293	−	0.371167i
$857$	−21.8205	−	37.7942i	−0.745375	−	1.29103i	−0.950020	−	0.312190i	$-0.898937\pi$
$857$	−21.8205	−	37.7942i	−0.745375	−	1.29103i	0.204645	−	0.978836i	$-0.434396\pi$
$858$		0			0
$859$	−16.0147	+	27.7383i	−0.546416	+	0.946420i	0.452101	+	0.891967i	$0.350675\pi$
$859$	−16.0147	+	27.7383i	−0.546416	+	0.946420i	−0.998516	+	0.0544527i	$0.982659\pi$
$860$	43.8051			1.49374
$861$		0			0
$862$	−5.90958			−0.201281
$863$	26.5887	−	46.0530i	0.905090	−	1.56766i	0.0842929	−	0.996441i	$-0.473137\pi$
$863$	26.5887	−	46.0530i	0.905090	−	1.56766i	0.820797	−	0.571220i	$-0.193530\pi$
$864$		0			0
$865$	17.0266	+	29.4909i	0.578920	+	1.00272i
$866$	3.86450	−	6.69352i	0.131321	−	0.227455i
$867$		0			0
$868$	−16.9706	−	10.7365i	−0.576020	−	0.364419i
$869$	−4.64521			−0.157578
$870$		0			0
$871$	−17.8330	−	30.8877i	−0.604249	−	1.04659i
$872$	−1.26738	−	2.19517i	−0.0429190	−	0.0743380i
$873$		0			0
$874$	−1.70853			−0.0577918
$875$	−3.68732	+	91.0336i	−0.124654	+	3.07750i
$876$		0			0
$877$	5.20189	−	9.00994i	0.175655	−	0.304244i	−0.764733	−	0.644348i	$-0.777129\pi$
$877$	5.20189	−	9.00994i	0.175655	−	0.304244i	0.940388	+	0.340104i	$0.110462\pi$
$878$	−7.02685	−	12.1709i	−0.237145	−	0.410746i
$879$		0			0
$880$	−1.10364	+	1.91157i	−0.0372038	+	0.0644389i
$881$	−5.82879			−0.196377			−0.0981884	−	0.995168i	$-0.531305\pi$
$881$	−5.82879			−0.196377			−0.0981884	+	0.995168i	$0.531305\pi$
$882$		0			0
$883$	−21.3015			−0.716852			−0.358426	−	0.933558i	$-0.616686\pi$
$883$	−21.3015			−0.716852			−0.358426	+	0.933558i	$0.616686\pi$
$884$	−4.18144	+	7.24246i	−0.140637	+	0.243590i
$885$		0			0
$886$	−6.72751	−	11.6524i	−0.226015	−	0.391469i
$887$	−11.6787	+	20.2281i	−0.392133	+	0.679195i	−0.992731	−	0.120357i	$-0.961596\pi$
$887$	−11.6787	+	20.2281i	−0.392133	+	0.679195i	0.600598	+	0.799551i	$0.294929\pi$
$888$		0			0
$889$	−0.382414	+	9.44114i	−0.0128258	+	0.316646i
$890$	−0.267168			−0.00895550
$891$		0			0
$892$	−18.9696	−	32.8563i	−0.635149	−	1.10011i
$893$	4.33575	+	7.50974i	0.145090	+	0.251304i
$894$		0			0
$895$	−42.9333			−1.43510
$896$	−25.0116	−	15.8236i	−0.835578	−	0.528629i
$897$		0			0
$898$	3.42642	−	5.93473i	0.114341	−	0.198044i
$899$	−12.7832	−	22.1411i	−0.426342	−	0.738446i
$900$		0			0
$901$	−0.258351	+	0.447477i	−0.00860691	+	0.0149076i
$902$	−1.80092			−0.0599639
$903$		0			0
$904$	4.09522			0.136205
$905$	−18.9197	+	32.7699i	−0.628912	+	1.08931i
$906$		0			0
$907$	−27.1605	−	47.0433i	−0.901849	−	1.56205i	−0.825092	−	0.564998i	$-0.808877\pi$
$907$	−27.1605	−	47.0433i	−0.901849	−	1.56205i	−0.0767567	−	0.997050i	$-0.524456\pi$
$908$	8.07666	−	13.9892i	0.268033	−	0.464247i
$909$		0			0
$910$	−33.1717	+	17.4011i	−1.09963	+	0.576841i
$911$	21.1066			0.699292			0.349646	−	0.936882i	$-0.386302\pi$
$911$	21.1066			0.699292			0.349646	+	0.936882i	$0.386302\pi$
$912$		0			0
$913$	−2.09900	−	3.63557i	−0.0694667	−	0.120320i
$914$	−1.38591	−	2.40047i	−0.0458419	−	0.0794005i
$915$		0			0
$916$	−36.9999			−1.22251
$917$	−3.50874	−	2.21980i	−0.115869	−	0.0733044i
$918$		0			0
$919$	2.20926	−	3.82654i	0.0728767	−	0.126226i	−0.827284	−	0.561784i	$-0.810115\pi$
$919$	2.20926	−	3.82654i	0.0728767	−	0.126226i	0.900161	+	0.435557i	$0.143449\pi$
$920$	13.0162	+	22.5447i	0.429131	+	0.743277i
$921$		0			0
$922$	−11.8622	+	20.5458i	−0.390659	+	0.676642i
$923$	−15.1460			−0.498536
$924$		0			0
$925$	81.8426			2.69097
$926$	1.55503	−	2.69338i	0.0511013	−	0.0885101i
$927$		0			0
$928$	−15.2112	−	26.3466i	−0.499334	−	0.864871i
$929$	−26.5533	+	45.9916i	−0.871185	+	1.50894i	−0.0104121	+	0.999946i	$0.503314\pi$
$929$	−26.5533	+	45.9916i	−0.871185	+	1.50894i	−0.860772	+	0.508990i	$0.830019\pi$
$930$		0			0
$931$	−3.97883	+	5.75925i	−0.130401	+	0.188752i
$932$	42.7628			1.40074
$933$		0			0
$934$	0.197694	+	0.342416i	0.00646875	+	0.0112042i
$935$	0.680384	+	1.17846i	0.0222509	+	0.0385398i
$936$		0			0
$937$	23.9110			0.781137			0.390568	−	0.920574i	$-0.372278\pi$
$937$	23.9110			0.781137			0.390568	+	0.920574i	$0.372278\pi$
$938$	0.479782	−	11.8450i	0.0156655	−	0.386753i
$939$		0			0
$940$	29.1754	−	50.5333i	0.951597	−	1.64821i
$941$	15.9145	+	27.5646i	0.518796	+	0.898582i	0.999761	+	0.0218420i	$0.00695306\pi$
$941$	15.9145	+	27.5646i	0.518796	+	0.898582i	−0.480965	+	0.876740i	$0.659714\pi$
$942$		0			0
$943$	11.8138	−	20.4621i	0.384711	−	0.666338i
$944$	13.8134			0.449589
$945$		0			0
$946$	1.31103			0.0426253
$947$	−12.9604	+	22.4480i	−0.421155	+	0.729462i	−0.996053	−	0.0887633i	$-0.971709\pi$
$947$	−12.9604	+	22.4480i	−0.421155	+	0.729462i	0.574898	+	0.818225i	$0.305042\pi$
$948$		0			0
$949$	−38.4203	−	66.5459i	−1.24718	−	2.16017i
$950$	−4.23386	+	7.33326i	−0.137365	+	0.237922i
$951$		0			0
$952$	−5.57371	+	2.92384i	−0.180645	+	0.0947623i
$953$	13.4538			0.435811			0.217906	−	0.975970i	$-0.430078\pi$
$953$	13.4538			0.435811			0.217906	+	0.975970i	$0.430078\pi$
$954$		0			0
$955$	−35.4414	−	61.3863i	−1.14686	−	1.98641i
$956$	8.30070	+	14.3772i	0.268464	+	0.464993i
$957$		0			0
$958$	16.7025			0.539633
$959$	18.3736	−	9.63839i	0.593315	−	0.311240i
$960$		0			0
$961$	3.98859	−	6.90845i	0.128664	−	0.222853i
$962$	10.4006	+	18.0145i	0.335330	+	0.580809i
$963$		0			0
$964$	−17.8898	+	30.9860i	−0.576192	+	0.997993i
$965$	−79.4803			−2.55856
$966$		0			0
$967$	−0.611077			−0.0196509			−0.00982546	−	0.999952i	$-0.503128\pi$
$967$	−0.611077			−0.0196509			−0.00982546	+	0.999952i	$0.503128\pi$
$968$	12.6264	−	21.8696i	0.405829	−	0.702916i
$969$		0			0
$970$	18.5395	+	32.1114i	0.595268	+	1.03104i
$971$	−5.29247	+	9.16682i	−0.169843	+	0.294177i	−0.938365	−	0.345647i	$-0.887660\pi$
$971$	−5.29247	+	9.16682i	−0.169843	+	0.294177i	0.768521	+	0.639824i	$0.220993\pi$
$972$		0			0
$973$	−0.532018	+	13.1346i	−0.0170557	+	0.421076i
$974$	−8.78270			−0.281416
$975$		0			0
$976$	4.58071	+	7.93403i	0.146625	+	0.253962i
$977$	−10.3174	−	17.8703i	−0.330083	−	0.571720i	0.652445	−	0.757836i	$-0.273743\pi$
$977$	−10.3174	−	17.8703i	−0.330083	−	0.571720i	−0.982528	+	0.186116i	$0.940410\pi$
$978$		0			0
$979$	0.0302507			0.000966815
$980$	46.9489	+	3.80959i	1.49973	+	0.121693i
$981$		0			0
$982$	−3.87308	+	6.70838i	−0.123595	+	0.214073i
$983$	−7.39675	−	12.8115i	−0.235920	−	0.408625i	0.723620	−	0.690199i	$-0.242477\pi$
$983$	−7.39675	−	12.8115i	−0.235920	−	0.408625i	−0.959540	+	0.281574i	$0.909144\pi$
$984$		0			0
$985$	−42.6817	+	73.9269i	−1.35995	+	2.35551i
$986$	−3.53883			−0.112699
$987$		0			0
$988$	8.14215			0.259036
$989$	−8.60023	+	14.8960i	−0.273471	+	0.473666i
$990$		0			0
$991$	26.1847	+	45.3533i	0.831785	+	1.44069i	0.896621	+	0.442798i	$0.146014\pi$
$991$	26.1847	+	45.3533i	0.831785	+	1.44069i	−0.0648362	+	0.997896i	$0.520653\pi$
$992$	−13.6979	+	23.7255i	−0.434910	+	0.753286i
$993$		0			0
$994$	−4.25433	−	2.69150i	−0.134939	−	0.0853692i
$995$	−42.4609			−1.34610
$996$		0			0
$997$	−2.60930	−	4.51944i	−0.0826373	−	0.143132i	0.821745	−	0.569856i	$-0.193001\pi$
$997$	−2.60930	−	4.51944i	−0.0826373	−	0.143132i	−0.904382	+	0.426724i	$0.859668\pi$
$998$	4.37773	+	7.58246i	0.138575	+	0.240018i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1197.2.j.m.856.5		16
3.2	odd	2		399.2.j.g.58.4	✓	16
7.2	even	3		8379.2.a.cr.1.4		8
7.4	even	3	inner	1197.2.j.m.172.5		16
7.5	odd	6		8379.2.a.cq.1.4		8
21.2	odd	6		2793.2.a.bm.1.5		8
21.5	even	6		2793.2.a.bn.1.5		8
21.11	odd	6		399.2.j.g.172.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.g.58.4	✓	16	3.2	odd	2
399.2.j.g.172.4	yes	16	21.11	odd	6
1197.2.j.m.172.5		16	7.4	even	3	inner
1197.2.j.m.856.5		16	1.1	even	1	trivial
2793.2.a.bm.1.5		8	21.2	odd	6
2793.2.a.bn.1.5		8	21.5	even	6
8379.2.a.cq.1.4		8	7.5	odd	6
8379.2.a.cr.1.4		8	7.2	even	3

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:	\( N \)	\(=\)	\( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1197.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.323314 - 0.559997i) q^{2} +(0.790936 + 1.36994i) q^{4} +(-2.12692 + 3.68394i) q^{5} +(-0.107079 + 2.64358i) q^{7} +2.31614 q^{8} +O(q^{10})\)	\(q+(0.323314 - 0.559997i) q^{2} +(0.790936 + 1.36994i) q^{4} +(-2.12692 + 3.68394i) q^{5} +(-0.107079 + 2.64358i) q^{7} +2.31614 q^{8} +(1.37533 + 2.38214i) q^{10} +(-0.155724 - 0.269722i) q^{11} +5.14716 q^{13} +(1.44578 + 0.914672i) q^{14} +(-0.833031 + 1.44285i) q^{16} +(0.513554 + 0.889502i) q^{17} +(0.500000 - 0.866025i) q^{19} -6.72904 q^{20} -0.201391 q^{22} +(1.32111 - 2.28822i) q^{23} +(-6.54760 - 11.3408i) q^{25} +(1.66415 - 2.88239i) q^{26} +(-3.70625 + 1.94421i) q^{28} -5.32830 q^{29} +(2.39910 + 4.15537i) q^{31} +(2.85480 + 4.94466i) q^{32} +0.664158 q^{34} +(-9.51105 - 6.01717i) q^{35} +(-3.12491 + 5.41251i) q^{37} +(-0.323314 - 0.559997i) q^{38} +(-4.92625 + 8.53251i) q^{40} +8.94237 q^{41} -6.50987 q^{43} +(0.246336 - 0.426666i) q^{44} +(-0.854264 - 1.47963i) q^{46} +(-4.33575 + 7.50974i) q^{47} +(-6.97707 - 0.566142i) q^{49} -8.46772 q^{50} +(4.07108 + 7.05131i) q^{52} +(0.251532 + 0.435666i) q^{53} +1.32485 q^{55} +(-0.248009 + 6.12291i) q^{56} +(-1.72272 + 2.98383i) q^{58} +(-4.14554 - 7.18028i) q^{59} +(2.74943 - 4.76214i) q^{61} +3.10266 q^{62} +0.359867 q^{64} +(-10.9476 + 18.9618i) q^{65} +(-3.46463 - 6.00092i) q^{67} +(-0.812377 + 1.40708i) q^{68} +(-6.44465 + 3.38072i) q^{70} -2.94259 q^{71} +(-7.46436 - 12.9287i) q^{73} +(2.02066 + 3.49988i) q^{74} +1.58187 q^{76} +(0.729708 - 0.382788i) q^{77} +(7.45744 - 12.9167i) q^{79} +(-3.54358 - 6.13767i) q^{80} +(2.89119 - 5.00769i) q^{82} +13.4789 q^{83} -4.36916 q^{85} +(-2.10473 + 3.64550i) q^{86} +(-0.360679 - 0.624714i) q^{88} +(-0.0485645 + 0.0841162i) q^{89} +(-0.551151 + 13.6070i) q^{91} +4.17964 q^{92} +(2.80362 + 4.85601i) q^{94} +(2.12692 + 3.68394i) q^{95} +13.4801 q^{97} +(-2.57282 + 3.72409i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 10 q^{4} - 5 q^{5} + q^{7} + 6 q^{8}+O(q^{10}) \) 16 * q - 10 * q^4 - 5 * q^5 + q^7 + 6 * q^8	\( 16 q - 10 q^{4} - 5 q^{5} + q^{7} + 6 q^{8} + 3 q^{10} - 7 q^{11} - 12 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{19} + 32 q^{20} + 36 q^{22} - 9 q^{23} - 15 q^{25} - 12 q^{26} - 40 q^{28} - 8 q^{29} + 11 q^{31} - 26 q^{32} - 32 q^{34} + 7 q^{35} - 17 q^{37} + 3 q^{40} + 34 q^{41} + 16 q^{43} - 31 q^{44} - q^{46} - 29 q^{47} + q^{49} - 60 q^{50} + 25 q^{52} - 6 q^{53} - 42 q^{55} + 54 q^{56} + 37 q^{58} - 7 q^{59} + 2 q^{61} + 78 q^{62} + 58 q^{64} - 13 q^{65} - 13 q^{67} + 14 q^{68} - 81 q^{70} - 36 q^{71} + 20 q^{73} - 26 q^{74} - 20 q^{76} - 19 q^{77} + 3 q^{79} - 35 q^{80} + 5 q^{82} + 72 q^{83} + 10 q^{85} - 51 q^{86} - 53 q^{88} - q^{89} - 9 q^{91} - 30 q^{92} + 30 q^{94} + 5 q^{95} + 6 q^{97} + 75 q^{98}+O(q^{100}) \) 16 * q - 10 * q^4 - 5 * q^5 + q^7 + 6 * q^8 + 3 * q^10 - 7 * q^11 - 12 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^19 + 32 * q^20 + 36 * q^22 - 9 * q^23 - 15 * q^25 - 12 * q^26 - 40 * q^28 - 8 * q^29 + 11 * q^31 - 26 * q^32 - 32 * q^34 + 7 * q^35 - 17 * q^37 + 3 * q^40 + 34 * q^41 + 16 * q^43 - 31 * q^44 - q^46 - 29 * q^47 + q^49 - 60 * q^50 + 25 * q^52 - 6 * q^53 - 42 * q^55 + 54 * q^56 + 37 * q^58 - 7 * q^59 + 2 * q^61 + 78 * q^62 + 58 * q^64 - 13 * q^65 - 13 * q^67 + 14 * q^68 - 81 * q^70 - 36 * q^71 + 20 * q^73 - 26 * q^74 - 20 * q^76 - 19 * q^77 + 3 * q^79 - 35 * q^80 + 5 * q^82 + 72 * q^83 + 10 * q^85 - 51 * q^86 - 53 * q^88 - q^89 - 9 * q^91 - 30 * q^92 + 30 * q^94 + 5 * q^95 + 6 * q^97 + 75 * q^98

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