LMFDB - Embedded newform 198.2.f.c.181.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [198,2,Mod(37,198)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(198, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("198.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	198.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,1,0,-1,-8,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$1.58103796002$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	198.181
Dual form			198.2.f.c.163.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-0.881966 + 2.71441i) q^{5} +(-3.73607 + 2.71441i) q^{7} +(0.809017 + 0.587785i) q^{8} +2.85410 q^{10} +(-1.23607 + 3.07768i) q^{11} +(-1.00000 - 3.07768i) q^{13} +(3.73607 + 2.71441i) q^{14} +(0.309017 - 0.951057i) q^{16} +(0.763932 - 2.35114i) q^{17} +(2.61803 + 1.90211i) q^{19} +(-0.881966 - 2.71441i) q^{20} +(3.30902 + 0.224514i) q^{22} +3.23607 q^{23} +(-2.54508 - 1.84911i) q^{25} +(-2.61803 + 1.90211i) q^{26} +(1.42705 - 4.39201i) q^{28} +(-0.309017 + 0.224514i) q^{29} +(2.66312 + 8.19624i) q^{31} -1.00000 q^{32} -2.47214 q^{34} +(-4.07295 - 12.5352i) q^{35} +(-1.23607 + 0.898056i) q^{37} +(1.00000 - 3.07768i) q^{38} +(-2.30902 + 1.67760i) q^{40} +(-2.61803 - 1.90211i) q^{41} -3.23607 q^{43} +(-0.809017 - 3.21644i) q^{44} +(-1.00000 - 3.07768i) q^{46} +(2.00000 + 1.45309i) q^{47} +(4.42705 - 13.6251i) q^{49} +(-0.972136 + 2.99193i) q^{50} +(2.61803 + 1.90211i) q^{52} +(1.19098 + 3.66547i) q^{53} +(-7.26393 - 6.06961i) q^{55} -4.61803 q^{56} +(0.309017 + 0.224514i) q^{58} +(-3.11803 + 2.26538i) q^{59} +(-2.09017 + 6.43288i) q^{61} +(6.97214 - 5.06555i) q^{62} +(0.309017 + 0.951057i) q^{64} +9.23607 q^{65} +4.00000 q^{67} +(0.763932 + 2.35114i) q^{68} +(-10.6631 + 7.74721i) q^{70} +(-3.85410 + 11.8617i) q^{71} +(9.16312 - 6.65740i) q^{73} +(1.23607 + 0.898056i) q^{74} -3.23607 q^{76} +(-3.73607 - 14.8536i) q^{77} +(-2.88197 - 8.86978i) q^{79} +(2.30902 + 1.67760i) q^{80} +(-1.00000 + 3.07768i) q^{82} +(0.208204 - 0.640786i) q^{83} +(5.70820 + 4.14725i) q^{85} +(1.00000 + 3.07768i) q^{86} +(-2.80902 + 1.76336i) q^{88} +11.7082 q^{89} +(12.0902 + 8.78402i) q^{91} +(-2.61803 + 1.90211i) q^{92} +(0.763932 - 2.35114i) q^{94} +(-7.47214 + 5.42882i) q^{95} +(3.50000 + 10.7719i) q^{97} -14.3262 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{4} - 8 q^{5} - 6 q^{7} + q^{8} - 2 q^{10} + 4 q^{11} - 4 q^{13} + 6 q^{14} - q^{16} + 12 q^{17} + 6 q^{19} - 8 q^{20} + 11 q^{22} + 4 q^{23} + q^{25} - 6 q^{26} - q^{28} + q^{29}+ \cdots - 26 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^4 - 8 * q^5 - 6 * q^7 + q^8 - 2 * q^10 + 4 * q^11 - 4 * q^13 + 6 * q^14 - q^16 + 12 * q^17 + 6 * q^19 - 8 * q^20 + 11 * q^22 + 4 * q^23 + q^25 - 6 * q^26 - q^28 + q^29 - 5 * q^31 - 4 * q^32 + 8 * q^34 - 23 * q^35 + 4 * q^37 + 4 * q^38 - 7 * q^40 - 6 * q^41 - 4 * q^43 - q^44 - 4 * q^46 + 8 * q^47 + 11 * q^49 + 14 * q^50 + 6 * q^52 + 7 * q^53 - 38 * q^55 - 14 * q^56 - q^58 - 8 * q^59 + 14 * q^61 + 10 * q^62 - q^64 + 28 * q^65 + 16 * q^67 + 12 * q^68 - 27 * q^70 - 2 * q^71 + 21 * q^73 - 4 * q^74 - 4 * q^76 - 6 * q^77 - 16 * q^79 + 7 * q^80 - 4 * q^82 - 26 * q^83 - 4 * q^85 + 4 * q^86 - 9 * q^88 + 20 * q^89 + 26 * q^91 - 6 * q^92 + 12 * q^94 - 12 * q^95 + 14 * q^97 - 26 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−0.881966	+	2.71441i	−0.394427	+	1.21392i	0.534980	+	0.844865i	$0.320319\pi$
$5$	−0.881966	+	2.71441i	−0.394427	+	1.21392i	−0.929407	+	0.369057i	$0.879681\pi$
$6$		0			0
$7$	−3.73607	+	2.71441i	−1.41210	+	1.02595i	−0.419088	+	0.907946i	$0.637650\pi$
$7$	−3.73607	+	2.71441i	−1.41210	+	1.02595i	−0.993013	+	0.118006i	$0.962350\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$		0			0
$10$	2.85410			0.902546
$11$	−1.23607	+	3.07768i	−0.372689	+	0.927957i
$11$	−1.23607	+	3.07768i	−0.372689	+	0.927957i
$12$		0			0
$13$	−1.00000	−	3.07768i	−0.277350	−	0.853596i	−0.988588	−	0.150644i	$-0.951865\pi$
$13$	−1.00000	−	3.07768i	−0.277350	−	0.853596i	0.711238	−	0.702951i	$-0.248135\pi$
$14$	3.73607	+	2.71441i	0.998506	+	0.725457i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	0.763932	−	2.35114i	0.185281	−	0.570235i	−0.814672	−	0.579922i	$-0.803083\pi$
$17$	0.763932	−	2.35114i	0.185281	−	0.570235i	0.999953	+	0.00968605i	$0.00308321\pi$
$18$		0			0
$19$	2.61803	+	1.90211i	0.600618	+	0.436375i	0.846098	−	0.533027i	$-0.178946\pi$
$19$	2.61803	+	1.90211i	0.600618	+	0.436375i	−0.245480	+	0.969402i	$0.578946\pi$
$20$	−0.881966	−	2.71441i	−0.197214	−	0.606961i
$21$		0			0
$22$	3.30902	+	0.224514i	0.705485	+	0.0478665i
$23$	3.23607			0.674767			0.337383	−	0.941367i	$-0.390458\pi$
$23$	3.23607			0.674767			0.337383	+	0.941367i	$0.390458\pi$
$24$		0			0
$25$	−2.54508	−	1.84911i	−0.509017	−	0.369822i
$26$	−2.61803	+	1.90211i	−0.513439	+	0.373035i
$27$		0			0
$28$	1.42705	−	4.39201i	0.269687	−	0.830012i
$29$	−0.309017	+	0.224514i	−0.0573830	+	0.0416912i	−0.616107	−	0.787662i	$-0.711291\pi$
$29$	−0.309017	+	0.224514i	−0.0573830	+	0.0416912i	0.558724	+	0.829354i	$0.311291\pi$
$30$		0			0
$31$	2.66312	+	8.19624i	0.478310	+	1.47209i	0.841441	+	0.540349i	$0.181708\pi$
$31$	2.66312	+	8.19624i	0.478310	+	1.47209i	−0.363130	+	0.931738i	$0.618292\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−2.47214			−0.423968
$35$	−4.07295	−	12.5352i	−0.688454	−	2.11884i
$36$		0			0
$37$	−1.23607	+	0.898056i	−0.203208	+	0.147639i	−0.684735	−	0.728792i	$-0.740082\pi$
$37$	−1.23607	+	0.898056i	−0.203208	+	0.147639i	0.481527	+	0.876431i	$0.340082\pi$
$38$	1.00000	−	3.07768i	0.162221	−	0.499266i
$39$		0			0
$40$	−2.30902	+	1.67760i	−0.365088	+	0.265252i
$41$	−2.61803	−	1.90211i	−0.408868	−	0.297060i	0.364275	−	0.931291i	$-0.381317\pi$
$41$	−2.61803	−	1.90211i	−0.408868	−	0.297060i	−0.773143	+	0.634231i	$0.781317\pi$
$42$		0			0
$43$	−3.23607			−0.493496			−0.246748	−	0.969080i	$-0.579362\pi$
$43$	−3.23607			−0.493496			−0.246748	+	0.969080i	$0.579362\pi$
$44$	−0.809017	−	3.21644i	−0.121964	−	0.484897i
$45$		0			0
$46$	−1.00000	−	3.07768i	−0.147442	−	0.453780i
$47$	2.00000	+	1.45309i	0.291730	+	0.211954i	0.724018	−	0.689782i	$-0.242293\pi$
$47$	2.00000	+	1.45309i	0.291730	+	0.211954i	−0.432288	+	0.901736i	$0.642293\pi$
$48$		0			0
$49$	4.42705	−	13.6251i	0.632436	−	1.94644i
$50$	−0.972136	+	2.99193i	−0.137481	+	0.423122i
$51$		0			0
$52$	2.61803	+	1.90211i	0.363056	+	0.263776i
$53$	1.19098	+	3.66547i	0.163594	+	0.503491i	0.998930	−	0.0462491i	$-0.0147268\pi$
$53$	1.19098	+	3.66547i	0.163594	+	0.503491i	−0.835336	+	0.549740i	$0.814727\pi$
$54$		0			0
$55$	−7.26393	−	6.06961i	−0.979468	−	0.818426i
$56$	−4.61803			−0.617111
$57$		0			0
$58$	0.309017	+	0.224514i	0.0405759	+	0.0294801i
$59$	−3.11803	+	2.26538i	−0.405933	+	0.294928i	−0.771953	−	0.635679i	$-0.780720\pi$
$59$	−3.11803	+	2.26538i	−0.405933	+	0.294928i	0.366020	+	0.930607i	$0.380720\pi$
$60$		0			0
$61$	−2.09017	+	6.43288i	−0.267619	+	0.823646i	0.723460	+	0.690367i	$0.242551\pi$
$61$	−2.09017	+	6.43288i	−0.267619	+	0.823646i	−0.991078	+	0.133279i	$0.957449\pi$
$62$	6.97214	−	5.06555i	0.885462	−	0.643326i
$63$		0			0
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	9.23607			1.14559
$66$		0			0
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	0.763932	+	2.35114i	0.0926404	+	0.285118i
$69$		0			0
$70$	−10.6631	+	7.74721i	−1.27449	+	0.925969i
$71$	−3.85410	+	11.8617i	−0.457398	+	1.40773i	0.410899	+	0.911681i	$0.365215\pi$
$71$	−3.85410	+	11.8617i	−0.457398	+	1.40773i	−0.868297	+	0.496045i	$0.834785\pi$
$72$		0			0
$73$	9.16312	−	6.65740i	1.07246	−	0.779189i	0.0961088	−	0.995371i	$-0.469360\pi$
$73$	9.16312	−	6.65740i	1.07246	−	0.779189i	0.976353	+	0.216182i	$0.0693603\pi$
$74$	1.23607	+	0.898056i	0.143690	+	0.104397i
$75$		0			0
$76$	−3.23607			−0.371202
$77$	−3.73607	−	14.8536i	−0.425764	−	1.69273i
$78$		0			0
$79$	−2.88197	−	8.86978i	−0.324247	−	0.997928i	−0.971780	−	0.235891i	$-0.924199\pi$
$79$	−2.88197	−	8.86978i	−0.324247	−	0.997928i	0.647533	−	0.762037i	$-0.275801\pi$
$80$	2.30902	+	1.67760i	0.258156	+	0.187561i
$81$		0			0
$82$	−1.00000	+	3.07768i	−0.110432	+	0.339873i
$83$	0.208204	−	0.640786i	0.0228534	−	0.0703354i	−0.938979	−	0.343973i	$-0.888227\pi$
$83$	0.208204	−	0.640786i	0.0228534	−	0.0703354i	0.961833	+	0.273638i	$0.0882270\pi$
$84$		0			0
$85$	5.70820	+	4.14725i	0.619142	+	0.449833i
$86$	1.00000	+	3.07768i	0.107833	+	0.331875i
$87$		0			0
$88$	−2.80902	+	1.76336i	−0.299442	+	0.187974i
$89$	11.7082			1.24107			0.620534	−	0.784180i	$-0.286916\pi$
$89$	11.7082			1.24107			0.620534	+	0.784180i	$0.286916\pi$
$90$		0			0
$91$	12.0902	+	8.78402i	1.26739	+	0.920816i
$92$	−2.61803	+	1.90211i	−0.272949	+	0.198309i
$93$		0			0
$94$	0.763932	−	2.35114i	0.0787936	−	0.242502i
$95$	−7.47214	+	5.42882i	−0.766625	+	0.556986i
$96$		0			0
$97$	3.50000	+	10.7719i	0.355371	+	1.09372i	0.955794	+	0.294037i	$0.0949990\pi$
$97$	3.50000	+	10.7719i	0.355371	+	1.09372i	−0.600423	+	0.799683i	$0.705001\pi$
$98$	−14.3262			−1.44717
$99$		0			0
$100$	3.14590			0.314590
$101$	3.82624	+	11.7759i	0.380725	+	1.17175i	0.939534	+	0.342455i	$0.111258\pi$
$101$	3.82624	+	11.7759i	0.380725	+	1.17175i	−0.558809	+	0.829296i	$0.688742\pi$
$102$		0			0
$103$	−9.73607	+	7.07367i	−0.959323	+	0.696989i	−0.952993	−	0.302991i	$-0.902015\pi$
$103$	−9.73607	+	7.07367i	−0.959323	+	0.696989i	−0.00632980	+	0.999980i	$0.502015\pi$
$104$	1.00000	−	3.07768i	0.0980581	−	0.301792i
$105$		0			0
$106$	3.11803	−	2.26538i	0.302850	−	0.220034i
$107$	4.35410	+	3.16344i	0.420927	+	0.305821i	0.778011	−	0.628251i	$-0.216229\pi$
$107$	4.35410	+	3.16344i	0.420927	+	0.305821i	−0.357084	+	0.934072i	$0.616229\pi$
$108$		0			0
$109$	17.4164			1.66819			0.834095	−	0.551621i	$-0.185991\pi$
$109$	17.4164			1.66819			0.834095	+	0.551621i	$0.185991\pi$
$110$	−3.52786	+	8.78402i	−0.336369	+	0.837524i
$111$		0			0
$112$	1.42705	+	4.39201i	0.134844	+	0.415006i
$113$	−10.0902	−	7.33094i	−0.949203	−	0.689637i	0.00141497	−	0.999999i	$-0.499550\pi$
$113$	−10.0902	−	7.33094i	−0.949203	−	0.689637i	−0.950618	+	0.310362i	$0.899550\pi$
$114$		0			0
$115$	−2.85410	+	8.78402i	−0.266146	+	0.819114i
$116$	0.118034	−	0.363271i	0.0109592	−	0.0337289i
$117$		0			0
$118$	3.11803	+	2.26538i	0.287038	+	0.208546i
$119$	3.52786	+	10.8576i	0.323399	+	0.995319i
$120$		0			0
$121$	−7.94427	−	7.60845i	−0.722207	−	0.691677i
$122$	6.76393			0.612378
$123$		0			0
$124$	−6.97214	−	5.06555i	−0.626116	−	0.454900i
$125$	−4.28115	+	3.11044i	−0.382918	+	0.278206i
$126$		0			0
$127$	3.70820	−	11.4127i	0.329050	−	1.01271i	−0.640529	−	0.767934i	$-0.721285\pi$
$127$	3.70820	−	11.4127i	0.329050	−	1.01271i	0.969579	−	0.244778i	$-0.0787150\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$		0			0
$130$	−2.85410	−	8.78402i	−0.250321	−	0.770410i
$131$	15.2705			1.33419			0.667095	−	0.744972i	$-0.267537\pi$
$131$	15.2705			1.33419			0.667095	+	0.744972i	$0.267537\pi$
$132$		0			0
$133$	−14.9443			−1.29583
$134$	−1.23607	−	3.80423i	−0.106780	−	0.328635i
$135$		0			0
$136$	2.00000	−	1.45309i	0.171499	−	0.124601i
$137$	7.14590	−	21.9928i	0.610515	−	1.87897i	0.157360	−	0.987541i	$-0.449702\pi$
$137$	7.14590	−	21.9928i	0.610515	−	1.87897i	0.453156	−	0.891431i	$-0.350298\pi$
$138$		0			0
$139$	−10.7082	+	7.77997i	−0.908258	+	0.659888i	−0.940574	−	0.339590i	$-0.889712\pi$
$139$	−10.7082	+	7.77997i	−0.908258	+	0.659888i	0.0323157	+	0.999478i	$0.489712\pi$
$140$	10.6631	+	7.74721i	0.901198	+	0.654759i
$141$		0			0
$142$	12.4721			1.04664
$143$	10.7082	+	0.726543i	0.895465	+	0.0607565i
$144$		0			0
$145$	−0.336881	−	1.03681i	−0.0279764	−	0.0861027i
$146$	−9.16312	−	6.65740i	−0.758345	−	0.550970i
$147$		0			0
$148$	0.472136	−	1.45309i	0.0388093	−	0.119443i
$149$	−0.427051	+	1.31433i	−0.0349854	+	0.107674i	−0.967024	−	0.254685i	$-0.918028\pi$
$149$	−0.427051	+	1.31433i	−0.0349854	+	0.107674i	0.932039	+	0.362358i	$0.118028\pi$
$150$		0			0
$151$	−7.54508	−	5.48183i	−0.614010	−	0.446105i	0.236814	−	0.971555i	$-0.423897\pi$
$151$	−7.54508	−	5.48183i	−0.614010	−	0.446105i	−0.850824	+	0.525450i	$0.823897\pi$
$152$	1.00000	+	3.07768i	0.0811107	+	0.249633i
$153$		0			0
$154$	−12.9721	+	8.14324i	−1.04532	+	0.656201i
$155$	−24.5967			−1.97566
$156$		0			0
$157$	−3.61803	−	2.62866i	−0.288751	−	0.209790i	0.433975	−	0.900925i	$-0.357111\pi$
$157$	−3.61803	−	2.62866i	−0.288751	−	0.209790i	−0.722725	+	0.691136i	$0.757111\pi$
$158$	−7.54508	+	5.48183i	−0.600255	+	0.436111i
$159$		0			0
$160$	0.881966	−	2.71441i	0.0697255	−	0.214593i
$161$	−12.0902	+	8.78402i	−0.952839	+	0.692278i
$162$		0			0
$163$	−4.14590	−	12.7598i	−0.324732	−	0.999422i	−0.971562	−	0.236787i	$-0.923906\pi$
$163$	−4.14590	−	12.7598i	−0.324732	−	0.999422i	0.646830	−	0.762634i	$-0.276094\pi$
$164$	3.23607			0.252694
$165$		0			0
$166$	−0.673762			−0.0522941
$167$	−2.23607	−	6.88191i	−0.173032	−	0.532538i	0.826506	−	0.562928i	$-0.190325\pi$
$167$	−2.23607	−	6.88191i	−0.173032	−	0.532538i	−0.999538	+	0.0303898i	$0.990325\pi$
$168$		0			0
$169$	2.04508	−	1.48584i	0.157314	−	0.114295i
$170$	2.18034	−	6.71040i	0.167224	−	0.514664i
$171$		0			0
$172$	2.61803	−	1.90211i	0.199623	−	0.145035i
$173$	−3.35410	−	2.43690i	−0.255008	−	0.185274i	0.452936	−	0.891543i	$-0.350377\pi$
$173$	−3.35410	−	2.43690i	−0.255008	−	0.185274i	−0.707943	+	0.706269i	$0.750377\pi$
$174$		0			0
$175$	14.5279			1.09820
$176$	2.54508	+	2.12663i	0.191843	+	0.160301i
$177$		0			0
$178$	−3.61803	−	11.1352i	−0.271183	−	0.834616i
$179$	−5.16312	−	3.75123i	−0.385910	−	0.280380i	0.377868	−	0.925860i	$-0.376657\pi$
$179$	−5.16312	−	3.75123i	−0.385910	−	0.280380i	−0.763777	+	0.645480i	$0.776657\pi$
$180$		0			0
$181$	−5.09017	+	15.6659i	−0.378349	+	1.16444i	0.562842	+	0.826565i	$0.309708\pi$
$181$	−5.09017	+	15.6659i	−0.378349	+	1.16444i	−0.941191	+	0.337875i	$0.890292\pi$
$182$	4.61803	−	14.2128i	0.342311	−	1.05353i
$183$		0			0
$184$	2.61803	+	1.90211i	0.193004	+	0.140226i
$185$	−1.34752	−	4.14725i	−0.0990719	−	0.304912i
$186$		0			0
$187$	6.29180	+	5.25731i	0.460102	+	0.384453i
$188$	−2.47214			−0.180299
$189$		0			0
$190$	7.47214	+	5.42882i	0.542086	+	0.393848i
$191$	18.1803	−	13.2088i	1.31548	−	0.955755i	0.315507	−	0.948923i	$-0.397826\pi$
$191$	18.1803	−	13.2088i	1.31548	−	0.955755i	0.999977	−	0.00683111i	$-0.00217443\pi$
$192$		0			0
$193$	0.100813	−	0.310271i	0.00725668	−	0.0223338i	−0.947363	−	0.320163i	$-0.896262\pi$
$193$	0.100813	−	0.310271i	0.00725668	−	0.0223338i	0.954619	+	0.297829i	$0.0962625\pi$
$194$	9.16312	−	6.65740i	0.657874	−	0.477973i
$195$		0			0
$196$	4.42705	+	13.6251i	0.316218	+	0.973219i
$197$	−6.09017			−0.433907			−0.216953	−	0.976182i	$-0.569612\pi$
$197$	−6.09017			−0.433907			−0.216953	+	0.976182i	$0.569612\pi$
$198$		0			0
$199$	13.1459			0.931888			0.465944	−	0.884814i	$-0.345715\pi$
$199$	13.1459			0.931888			0.465944	+	0.884814i	$0.345715\pi$
$200$	−0.972136	−	2.99193i	−0.0687404	−	0.211561i
$201$		0			0
$202$	10.0172	−	7.27794i	0.704809	−	0.512074i
$203$	0.545085	−	1.67760i	0.0382575	−	0.117744i
$204$		0			0
$205$	7.47214	−	5.42882i	0.521877	−	0.379166i
$206$	9.73607	+	7.07367i	0.678344	+	0.492846i
$207$		0			0
$208$	−3.23607			−0.224381
$209$	−9.09017	+	5.70634i	−0.628780	+	0.394716i
$210$		0			0
$211$	−1.43769	−	4.42477i	−0.0989749	−	0.304614i	0.889294	−	0.457335i	$-0.151196\pi$
$211$	−1.43769	−	4.42477i	−0.0989749	−	0.304614i	−0.988269	+	0.152722i	$0.951196\pi$
$212$	−3.11803	−	2.26538i	−0.214147	−	0.155587i
$213$		0			0
$214$	1.66312	−	5.11855i	0.113688	−	0.349897i
$215$	2.85410	−	8.78402i	0.194648	−	0.599065i
$216$		0			0
$217$	−32.1976	−	23.3929i	−2.18571	−	1.58801i
$218$	−5.38197	−	16.5640i	−0.364513	−	1.12185i
$219$		0			0
$220$	9.44427	+	0.640786i	0.636733	+	0.0432018i
$221$	−8.00000			−0.538138
$222$		0			0
$223$	1.54508	+	1.12257i	0.103467	+	0.0751728i	0.638316	−	0.769775i	$-0.279632\pi$
$223$	1.54508	+	1.12257i	0.103467	+	0.0751728i	−0.534849	+	0.844948i	$0.679632\pi$
$224$	3.73607	−	2.71441i	0.249627	−	0.181364i
$225$		0			0
$226$	−3.85410	+	11.8617i	−0.256371	+	0.789029i
$227$	−5.78115	+	4.20025i	−0.383709	+	0.278781i	−0.762873	−	0.646549i	$-0.776212\pi$
$227$	−5.78115	+	4.20025i	−0.383709	+	0.278781i	0.379164	+	0.925330i	$0.376212\pi$
$228$		0			0
$229$	7.09017	+	21.8213i	0.468532	+	1.44199i	0.854486	+	0.519474i	$0.173872\pi$
$229$	7.09017	+	21.8213i	0.468532	+	1.44199i	−0.385954	+	0.922518i	$0.626128\pi$
$230$	9.23607			0.609008
$231$		0			0
$232$	−0.381966			−0.0250773
$233$	2.76393	+	8.50651i	0.181071	+	0.557280i	0.999859	−	0.0168170i	$-0.00535327\pi$
$233$	2.76393	+	8.50651i	0.181071	+	0.557280i	−0.818787	+	0.574097i	$0.805353\pi$
$234$		0			0
$235$	−5.70820	+	4.14725i	−0.372362	+	0.270537i
$236$	1.19098	−	3.66547i	0.0775264	−	0.238602i
$237$		0			0
$238$	9.23607	−	6.71040i	0.598685	−	0.434970i
$239$	−13.3262	−	9.68208i	−0.862003	−	0.626282i	0.0664264	−	0.997791i	$-0.478840\pi$
$239$	−13.3262	−	9.68208i	−0.862003	−	0.626282i	−0.928429	+	0.371510i	$0.878840\pi$
$240$		0			0
$241$	−2.43769			−0.157026			−0.0785128	−	0.996913i	$-0.525017\pi$
$241$	−2.43769			−0.157026			−0.0785128	+	0.996913i	$0.525017\pi$
$242$	−4.78115	+	9.90659i	−0.307344	+	0.636820i
$243$		0			0
$244$	−2.09017	−	6.43288i	−0.133809	−	0.411823i
$245$	33.0795	+	24.0337i	2.11337	+	1.53546i
$246$		0			0
$247$	3.23607	−	9.95959i	0.205906	−	0.633714i
$248$	−2.66312	+	8.19624i	−0.169108	+	0.520462i
$249$		0			0
$250$	4.28115	+	3.11044i	0.270764	+	0.196721i
$251$	5.97214	+	18.3803i	0.376958	+	1.16016i	0.942148	+	0.335197i	$0.108803\pi$
$251$	5.97214	+	18.3803i	0.376958	+	1.16016i	−0.565190	+	0.824961i	$0.691197\pi$
$252$		0			0
$253$	−4.00000	+	9.95959i	−0.251478	+	0.626154i
$254$	−12.0000			−0.752947
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.47214	+	1.06957i	−0.0918293	+	0.0667179i	−0.632753	−	0.774354i	$-0.718075\pi$
$257$	−1.47214	+	1.06957i	−0.0918293	+	0.0667179i	0.540923	+	0.841072i	$0.318075\pi$
$258$		0			0
$259$	2.18034	−	6.71040i	0.135480	−	0.416964i
$260$	−7.47214	+	5.42882i	−0.463402	+	0.336681i
$261$		0			0
$262$	−4.71885	−	14.5231i	−0.291531	−	0.897241i
$263$	−7.70820			−0.475308			−0.237654	−	0.971350i	$-0.576378\pi$
$263$	−7.70820			−0.475308			−0.237654	+	0.971350i	$0.576378\pi$
$264$		0			0
$265$	−11.0000			−0.675725
$266$	4.61803	+	14.2128i	0.283150	+	0.871446i
$267$		0			0
$268$	−3.23607	+	2.35114i	−0.197674	+	0.143619i
$269$	0.909830	−	2.80017i	0.0554733	−	0.170729i	−0.919481	−	0.393134i	$-0.871391\pi$
$269$	0.909830	−	2.80017i	0.0554733	−	0.170729i	0.974954	+	0.222405i	$0.0713907\pi$
$270$		0			0
$271$	−18.9443	+	13.7638i	−1.15078	+	0.836092i	−0.988585	−	0.150666i	$-0.951858\pi$
$271$	−18.9443	+	13.7638i	−1.15078	+	0.836092i	−0.162198	+	0.986758i	$0.551858\pi$
$272$	−2.00000	−	1.45309i	−0.121268	−	0.0881062i
$273$		0			0
$274$	−23.1246			−1.39701
$275$	8.83688	−	5.54734i	0.532884	−	0.334517i
$276$		0			0
$277$	3.43769	+	10.5801i	0.206551	+	0.635699i	0.999646	+	0.0266009i	$0.00846832\pi$
$277$	3.43769	+	10.5801i	0.206551	+	0.635699i	−0.793095	+	0.609098i	$0.791532\pi$
$278$	10.7082	+	7.77997i	0.642235	+	0.466611i
$279$		0			0
$280$	4.07295	−	12.5352i	0.243405	−	0.749124i
$281$	−7.14590	+	21.9928i	−0.426289	+	1.31198i	0.475467	+	0.879734i	$0.342279\pi$
$281$	−7.14590	+	21.9928i	−0.426289	+	1.31198i	−0.901755	+	0.432247i	$0.857721\pi$
$282$		0			0
$283$	19.3262	+	14.0413i	1.14883	+	0.834671i	0.988324	−	0.152365i	$-0.0486889\pi$
$283$	19.3262	+	14.0413i	1.14883	+	0.834671i	0.160501	+	0.987036i	$0.448689\pi$
$284$	−3.85410	−	11.8617i	−0.228699	−	0.703863i
$285$		0			0
$286$	−2.61803	−	10.4086i	−0.154808	−	0.615475i
$287$	14.9443			0.882132
$288$		0			0
$289$	8.80902	+	6.40013i	0.518177	+	0.376478i
$290$	−0.881966	+	0.640786i	−0.0517908	+	0.0376282i
$291$		0			0
$292$	−3.50000	+	10.7719i	−0.204822	+	0.630377i
$293$	18.5902	−	13.5065i	1.08605	−	0.789061i	0.107322	−	0.994224i	$-0.465773\pi$
$293$	18.5902	−	13.5065i	1.08605	−	0.789061i	0.978728	+	0.205163i	$0.0657726\pi$
$294$		0			0
$295$	−3.39919	−	10.4616i	−0.197908	−	0.609099i
$296$	−1.52786			−0.0888053
$297$		0			0
$298$	1.38197			0.0800551
$299$	−3.23607	−	9.95959i	−0.187147	−	0.575978i
$300$		0			0
$301$	12.0902	−	8.78402i	0.696866	−	0.506303i
$302$	−2.88197	+	8.86978i	−0.165839	+	0.510398i
$303$		0			0
$304$	2.61803	−	1.90211i	0.150155	−	0.109094i
$305$	−15.6180	−	11.3472i	−0.894286	−	0.649737i
$306$		0			0
$307$	−16.6525			−0.950407			−0.475203	−	0.879876i	$-0.657626\pi$
$307$	−16.6525			−0.950407			−0.475203	+	0.879876i	$0.657626\pi$
$308$	11.7533	+	9.82084i	0.669706	+	0.559594i
$309$		0			0
$310$	7.60081	+	23.3929i	0.431697	+	1.32863i
$311$	−19.3262	−	14.0413i	−1.09589	−	0.796211i	−0.115506	−	0.993307i	$-0.536849\pi$
$311$	−19.3262	−	14.0413i	−1.09589	−	0.796211i	−0.980384	+	0.197096i	$0.936849\pi$
$312$		0			0
$313$	4.68034	−	14.4046i	0.264548	−	0.814196i	−0.727249	−	0.686374i	$-0.759201\pi$
$313$	4.68034	−	14.4046i	0.264548	−	0.814196i	0.991797	−	0.127822i	$-0.0407987\pi$
$314$	−1.38197	+	4.25325i	−0.0779889	+	0.240025i
$315$		0			0
$316$	7.54508	+	5.48183i	0.424444	+	0.308377i
$317$	6.14590	+	18.9151i	0.345188	+	1.06238i	0.961483	+	0.274864i	$0.0886329\pi$
$317$	6.14590	+	18.9151i	0.345188	+	1.06238i	−0.616295	+	0.787515i	$0.711367\pi$
$318$		0			0
$319$	−0.309017	−	1.22857i	−0.0173016	−	0.0687868i
$320$	−2.85410			−0.159549
$321$		0			0
$322$	12.0902	+	8.78402i	0.673759	+	0.489514i
$323$	6.47214	−	4.70228i	0.360119	−	0.261642i
$324$		0			0
$325$	−3.14590	+	9.68208i	−0.174503	+	0.537065i
$326$	−10.8541	+	7.88597i	−0.601153	+	0.436763i
$327$		0			0
$328$	−1.00000	−	3.07768i	−0.0552158	−	0.169937i
$329$	−11.4164			−0.629407
$330$		0			0
$331$	8.94427			0.491622			0.245811	−	0.969318i	$-0.420946\pi$
$331$	8.94427			0.491622			0.245811	+	0.969318i	$0.420946\pi$
$332$	0.208204	+	0.640786i	0.0114267	+	0.0351677i
$333$		0			0
$334$	−5.85410	+	4.25325i	−0.320322	+	0.232728i
$335$	−3.52786	+	10.8576i	−0.192748	+	0.593217i
$336$		0			0
$337$	−5.61803	+	4.08174i	−0.306034	+	0.222347i	−0.730193	−	0.683241i	$-0.760570\pi$
$337$	−5.61803	+	4.08174i	−0.306034	+	0.222347i	0.424159	+	0.905588i	$0.360570\pi$
$338$	−2.04508	−	1.48584i	−0.111238	−	0.0808191i
$339$		0			0
$340$	−7.05573			−0.382651
$341$	−28.5172	−	1.93487i	−1.54429	−	0.104779i
$342$		0			0
$343$	10.4549	+	32.1769i	0.564512	+	1.73739i
$344$	−2.61803	−	1.90211i	−0.141155	−	0.102555i
$345$		0			0
$346$	−1.28115	+	3.94298i	−0.0688752	+	0.211976i
$347$	−3.66312	+	11.2739i	−0.196647	+	0.605216i	0.803307	+	0.595565i	$0.203072\pi$
$347$	−3.66312	+	11.2739i	−0.196647	+	0.605216i	−0.999953	+	0.00965049i	$0.996928\pi$
$348$		0			0
$349$	10.7082	+	7.77997i	0.573197	+	0.416452i	0.836265	−	0.548325i	$-0.184734\pi$
$349$	10.7082	+	7.77997i	0.573197	+	0.416452i	−0.263068	+	0.964777i	$0.584734\pi$
$350$	−4.48936	−	13.8168i	−0.239966	−	0.738540i
$351$		0			0
$352$	1.23607	−	3.07768i	0.0658826	−	0.164041i
$353$	21.5967			1.14948			0.574739	−	0.818336i	$-0.305103\pi$
$353$	21.5967			1.14948			0.574739	+	0.818336i	$0.305103\pi$
$354$		0			0
$355$	−28.7984	−	20.9232i	−1.52846	−	1.11049i
$356$	−9.47214	+	6.88191i	−0.502022	+	0.364740i
$357$		0			0
$358$	−1.97214	+	6.06961i	−0.104231	+	0.320789i
$359$	10.3262	−	7.50245i	0.544998	−	0.395964i	−0.280940	−	0.959725i	$-0.590646\pi$
$359$	10.3262	−	7.50245i	0.544998	−	0.395964i	0.825938	+	0.563761i	$0.190646\pi$
$360$		0			0
$361$	−2.63525	−	8.11048i	−0.138698	−	0.426867i
$362$	16.4721			0.865756
$363$		0			0
$364$	−14.9443			−0.783293
$365$	9.98936	+	30.7441i	0.522867	+	1.60922i
$366$		0			0
$367$	30.3435	−	22.0458i	1.58392	−	1.15078i	0.671888	−	0.740652i	$-0.265483\pi$
$367$	30.3435	−	22.0458i	1.58392	−	1.15078i	0.912027	−	0.410130i	$-0.134517\pi$
$368$	1.00000	−	3.07768i	0.0521286	−	0.160435i
$369$		0			0
$370$	−3.52786	+	2.56314i	−0.183405	+	0.133251i
$371$	−14.3992	−	10.4616i	−0.747569	−	0.543140i
$372$		0			0
$373$	−9.52786			−0.493334			−0.246667	−	0.969100i	$-0.579335\pi$
$373$	−9.52786			−0.493334			−0.246667	+	0.969100i	$0.579335\pi$
$374$	3.05573	−	7.60845i	0.158008	−	0.393424i
$375$		0			0
$376$	0.763932	+	2.35114i	0.0393968	+	0.121251i
$377$	1.00000	+	0.726543i	0.0515026	+	0.0374188i
$378$		0			0
$379$	1.14590	−	3.52671i	0.0588608	−	0.181155i	−0.917303	−	0.398190i	$-0.869639\pi$
$379$	1.14590	−	3.52671i	0.0588608	−	0.181155i	0.976164	+	0.217035i	$0.0696385\pi$
$380$	2.85410	−	8.78402i	0.146412	−	0.450611i
$381$		0			0
$382$	−18.1803	−	13.2088i	−0.930187	−	0.675820i
$383$	−4.09017	−	12.5882i	−0.208998	−	0.643229i	−0.999525	−	0.0308030i	$-0.990194\pi$
$383$	−4.09017	−	12.5882i	−0.208998	−	0.643229i	0.790528	−	0.612426i	$-0.209806\pi$
$384$		0			0
$385$	43.6140	+	2.95917i	2.22277	+	0.150813i
$386$	−0.326238			−0.0166051
$387$		0			0
$388$	−9.16312	−	6.65740i	−0.465187	−	0.337978i
$389$	31.5066	−	22.8909i	1.59745	−	1.16061i	0.705258	−	0.708951i	$-0.250831\pi$
$389$	31.5066	−	22.8909i	1.59745	−	1.16061i	0.892189	−	0.451662i	$-0.149169\pi$
$390$		0			0
$391$	2.47214	−	7.60845i	0.125021	−	0.384776i
$392$	11.5902	−	8.42075i	0.585392	−	0.425312i
$393$		0			0
$394$	1.88197	+	5.79210i	0.0948121	+	0.291802i
$395$	26.6180			1.33930
$396$		0			0
$397$	9.88854			0.496292			0.248146	−	0.968723i	$-0.420179\pi$
$397$	9.88854			0.496292			0.248146	+	0.968723i	$0.420179\pi$
$398$	−4.06231	−	12.5025i	−0.203625	−	0.626693i
$399$		0			0
$400$	−2.54508	+	1.84911i	−0.127254	+	0.0924556i
$401$	−3.18034	+	9.78808i	−0.158819	+	0.488793i	−0.998528	−	0.0542430i	$-0.982725\pi$
$401$	−3.18034	+	9.78808i	−0.158819	+	0.488793i	0.839709	+	0.543036i	$0.182725\pi$
$402$		0			0
$403$	22.5623	−	16.3925i	1.12391	−	0.816567i
$404$	−10.0172	−	7.27794i	−0.498375	−	0.362091i
$405$		0			0
$406$	−1.76393			−0.0875425
$407$	−1.23607	−	4.91428i	−0.0612696	−	0.243592i
$408$		0			0
$409$	−3.73607	−	11.4984i	−0.184737	−	0.568561i	0.815207	−	0.579170i	$-0.196623\pi$
$409$	−3.73607	−	11.4984i	−0.184737	−	0.568561i	−0.999944	+	0.0106086i	$0.996623\pi$
$410$	−7.47214	−	5.42882i	−0.369022	−	0.268111i
$411$		0			0
$412$	3.71885	−	11.4454i	0.183214	−	0.563876i
$413$	5.50000	−	16.9273i	0.270637	−	0.832936i
$414$		0			0
$415$	1.55573	+	1.13030i	0.0763677	+	0.0554844i
$416$	1.00000	+	3.07768i	0.0490290	+	0.150896i
$417$		0			0
$418$	8.23607	+	6.88191i	0.402839	+	0.336605i
$419$	17.9787			0.878318			0.439159	−	0.898409i	$-0.355277\pi$
$419$	17.9787			0.878318			0.439159	+	0.898409i	$0.355277\pi$
$420$		0			0
$421$	−28.4164	−	20.6457i	−1.38493	−	1.00621i	−0.996400	−	0.0847756i	$-0.972983\pi$
$421$	−28.4164	−	20.6457i	−1.38493	−	1.00621i	−0.388531	−	0.921436i	$-0.627017\pi$
$422$	−3.76393	+	2.73466i	−0.183225	+	0.133121i
$423$		0			0
$424$	−1.19098	+	3.66547i	−0.0578392	+	0.178011i
$425$	−6.29180	+	4.57126i	−0.305197	+	0.221739i
$426$		0			0
$427$	−9.65248	−	29.7073i	−0.467116	−	1.43764i
$428$	−5.38197			−0.260147
$429$		0			0
$430$	−9.23607			−0.445403
$431$	2.23607	+	6.88191i	0.107708	+	0.331490i	0.990356	−	0.138543i	$-0.0442420\pi$
$431$	2.23607	+	6.88191i	0.107708	+	0.331490i	−0.882649	+	0.470033i	$0.844242\pi$
$432$		0			0
$433$	−9.97214	+	7.24518i	−0.479230	+	0.348181i	−0.801028	−	0.598627i	$-0.795713\pi$
$433$	−9.97214	+	7.24518i	−0.479230	+	0.348181i	0.321797	+	0.946809i	$0.395713\pi$
$434$	−12.2984	+	37.8505i	−0.590341	+	1.81688i
$435$		0			0
$436$	−14.0902	+	10.2371i	−0.674797	+	0.490269i
$437$	8.47214	+	6.15537i	0.405277	+	0.294451i
$438$		0			0
$439$	16.0344			0.765282			0.382641	−	0.923897i	$-0.375015\pi$
$439$	16.0344			0.765282			0.382641	+	0.923897i	$0.375015\pi$
$440$	−2.30902	−	9.18005i	−0.110078	−	0.437642i
$441$		0			0
$442$	2.47214	+	7.60845i	0.117588	+	0.361897i
$443$	−1.35410	−	0.983813i	−0.0643353	−	0.0467424i	0.555153	−	0.831748i	$-0.312660\pi$
$443$	−1.35410	−	0.983813i	−0.0643353	−	0.0467424i	−0.619488	+	0.785006i	$0.712660\pi$
$444$		0			0
$445$	−10.3262	+	31.7809i	−0.489511	+	1.50656i
$446$	0.590170	−	1.81636i	0.0279454	−	0.0860070i
$447$		0			0
$448$	−3.73607	−	2.71441i	−0.176513	−	0.128244i
$449$	−11.0902	−	34.1320i	−0.523377	−	1.61079i	−0.767502	−	0.641046i	$-0.778501\pi$
$449$	−11.0902	−	34.1320i	−0.523377	−	1.61079i	0.244125	−	0.969744i	$-0.421499\pi$
$450$		0			0
$451$	9.09017	−	5.70634i	0.428039	−	0.268701i
$452$	12.4721			0.586640
$453$		0			0
$454$	5.78115	+	4.20025i	0.271323	+	0.197128i
$455$	−34.5066	+	25.0705i	−1.61769	+	1.17532i
$456$		0			0
$457$	−6.79180	+	20.9030i	−0.317707	+	0.977801i	0.656919	+	0.753961i	$0.271859\pi$
$457$	−6.79180	+	20.9030i	−0.317707	+	0.977801i	−0.974626	+	0.223840i	$0.928141\pi$
$458$	18.5623	−	13.4863i	0.867360	−	0.630174i
$459$		0			0
$460$	−2.85410	−	8.78402i	−0.133073	−	0.409557i
$461$	−40.8328			−1.90177			−0.950887	−	0.309538i	$-0.899825\pi$
$461$	−40.8328			−1.90177			−0.950887	+	0.309538i	$0.899825\pi$
$462$		0			0
$463$	19.0902			0.887195			0.443598	−	0.896226i	$-0.353702\pi$
$463$	19.0902			0.887195			0.443598	+	0.896226i	$0.353702\pi$
$464$	0.118034	+	0.363271i	0.00547959	+	0.0168644i
$465$		0			0
$466$	7.23607	−	5.25731i	0.335204	−	0.243540i
$467$	−6.04508	+	18.6049i	−0.279733	+	0.860930i	0.708195	+	0.706017i	$0.249510\pi$
$467$	−6.04508	+	18.6049i	−0.279733	+	0.860930i	−0.987928	+	0.154913i	$0.950490\pi$
$468$		0			0
$469$	−14.9443	+	10.8576i	−0.690062	+	0.501360i
$470$	5.70820	+	4.14725i	0.263300	+	0.191299i
$471$		0			0
$472$	−3.85410			−0.177399
$473$	4.00000	−	9.95959i	0.183920	−	0.457943i
$474$		0			0
$475$	−3.14590	−	9.68208i	−0.144344	−	0.444244i
$476$	−9.23607	−	6.71040i	−0.423334	−	0.307571i
$477$		0			0
$478$	−5.09017	+	15.6659i	−0.232819	+	0.716543i
$479$	2.23607	−	6.88191i	0.102169	−	0.314442i	−0.886887	−	0.461987i	$-0.847137\pi$
$479$	2.23607	−	6.88191i	0.102169	−	0.314442i	0.989055	+	0.147544i	$0.0471368\pi$
$480$		0			0
$481$	4.00000	+	2.90617i	0.182384	+	0.132510i
$482$	0.753289	+	2.31838i	0.0343114	+	0.105600i
$483$		0			0
$484$	10.8992	+	1.48584i	0.495418	+	0.0675382i
$485$	−32.3262			−1.46786
$486$		0			0
$487$	−20.2082	−	14.6821i	−0.915721	−	0.665310i	0.0267342	−	0.999643i	$-0.491489\pi$
$487$	−20.2082	−	14.6821i	−0.915721	−	0.665310i	−0.942455	+	0.334332i	$0.891489\pi$
$488$	−5.47214	+	3.97574i	−0.247712	+	0.179973i
$489$		0			0
$490$	12.6353	−	38.8873i	0.570803	−	1.75675i
$491$	34.1803	−	24.8335i	1.54254	−	1.12072i	0.593818	−	0.804600i	$-0.297620\pi$
$491$	34.1803	−	24.8335i	1.54254	−	1.12072i	0.948719	−	0.316119i	$-0.102380\pi$
$492$		0			0
$493$	0.291796	+	0.898056i	0.0131418	+	0.0404464i
$494$	−10.4721			−0.471164
$495$		0			0
$496$	8.61803			0.386961
$497$	−17.7984	−	54.7778i	−0.798366	−	2.45712i
$498$		0			0
$499$	6.00000	−	4.35926i	0.268597	−	0.195147i	−0.445332	−	0.895366i	$-0.646914\pi$
$499$	6.00000	−	4.35926i	0.268597	−	0.195147i	0.713928	+	0.700219i	$0.246914\pi$
$500$	1.63525	−	5.03280i	0.0731308	−	0.225074i
$501$		0			0
$502$	15.6353	−	11.3597i	0.697836	−	0.507007i
$503$	3.52786	+	2.56314i	0.157300	+	0.114285i	0.663651	−	0.748042i	$-0.269006\pi$
$503$	3.52786	+	2.56314i	0.157300	+	0.114285i	−0.506351	+	0.862327i	$0.669006\pi$
$504$		0			0
$505$	−35.3394			−1.57258
$506$	10.7082	+	0.726543i	0.476038	+	0.0322988i
$507$		0			0
$508$	3.70820	+	11.4127i	0.164525	+	0.506356i
$509$	2.59017	+	1.88187i	0.114807	+	0.0834124i	0.643707	−	0.765272i	$-0.277395\pi$
$509$	2.59017	+	1.88187i	0.114807	+	0.0834124i	−0.528900	+	0.848684i	$0.677395\pi$
$510$		0			0
$511$	−16.1631	+	49.7450i	−0.715014	+	2.20059i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$		0			0
$514$	1.47214	+	1.06957i	0.0649331	+	0.0471767i
$515$	−10.6140	−	32.6664i	−0.467707	−	1.43946i
$516$		0			0
$517$	−6.94427	+	4.35926i	−0.305409	+	0.191720i
$518$	−7.05573			−0.310011
$519$		0			0
$520$	7.47214	+	5.42882i	0.327675	+	0.238070i
$521$	25.4164	−	18.4661i	1.11351	−	0.809015i	0.130300	−	0.991475i	$-0.458406\pi$
$521$	25.4164	−	18.4661i	1.11351	−	0.809015i	0.983213	+	0.182460i	$0.0584060\pi$
$522$		0			0
$523$	6.05573	−	18.6376i	0.264799	−	0.814966i	−0.726941	−	0.686700i	$-0.759059\pi$
$523$	6.05573	−	18.6376i	0.264799	−	0.814966i	0.991740	−	0.128266i	$-0.0409412\pi$
$524$	−12.3541	+	8.97578i	−0.539691	+	0.392109i
$525$		0			0
$526$	2.38197	+	7.33094i	0.103859	+	0.319644i
$527$	21.3050			0.928058
$528$		0			0
$529$	−12.5279			−0.544690
$530$	3.39919	+	10.4616i	0.147651	+	0.454424i
$531$		0			0
$532$	12.0902	−	8.78402i	0.524175	−	0.380836i
$533$	−3.23607	+	9.95959i	−0.140170	+	0.431398i
$534$		0			0
$535$	−12.4271	+	9.02878i	−0.537268	+	0.390348i
$536$	3.23607	+	2.35114i	0.139777	+	0.101554i
$537$		0			0
$538$	−2.94427			−0.126937
$539$	36.4615	+	30.4666i	1.57051	+	1.31229i
$540$		0			0
$541$	2.32624	+	7.15942i	0.100013	+	0.307808i	0.988528	−	0.151040i	$-0.0482623\pi$
$541$	2.32624	+	7.15942i	0.100013	+	0.307808i	−0.888515	+	0.458848i	$0.848262\pi$
$542$	18.9443	+	13.7638i	0.813726	+	0.591207i
$543$		0			0
$544$	−0.763932	+	2.35114i	−0.0327533	+	0.100804i
$545$	−15.3607	+	47.2753i	−0.657979	+	2.02505i
$546$		0			0
$547$	−14.7082	−	10.6861i	−0.628877	−	0.456906i	0.227134	−	0.973864i	$-0.427065\pi$
$547$	−14.7082	−	10.6861i	−0.628877	−	0.456906i	−0.856011	+	0.516957i	$0.827065\pi$
$548$	7.14590	+	21.9928i	0.305258	+	0.939486i
$549$		0			0
$550$	−8.00658	−	6.69015i	−0.341402	−	0.285269i
$551$	−1.23607			−0.0526583
$552$		0			0
$553$	34.8435	+	25.3153i	1.48169	+	1.07651i
$554$	9.00000	−	6.53888i	0.382373	−	0.277811i
$555$		0			0
$556$	4.09017	−	12.5882i	0.173462	−	0.533861i
$557$	−34.0066	+	24.7072i	−1.44090	+	1.04688i	−0.453053	+	0.891484i	$0.649665\pi$
$557$	−34.0066	+	24.7072i	−1.44090	+	1.04688i	−0.987852	+	0.155395i	$0.950335\pi$
$558$		0			0
$559$	3.23607	+	9.95959i	0.136871	+	0.421246i
$560$	−13.1803			−0.556971
$561$		0			0
$562$	23.1246			0.975453
$563$	14.4721	+	44.5407i	0.609928	+	1.87716i	0.458494	+	0.888697i	$0.348389\pi$
$563$	14.4721	+	44.5407i	0.609928	+	1.87716i	0.151433	+	0.988467i	$0.451611\pi$
$564$		0			0
$565$	28.7984	−	20.9232i	1.21156	−	0.880247i
$566$	7.38197	−	22.7194i	0.310287	−	0.954966i
$567$		0			0
$568$	−10.0902	+	7.33094i	−0.423374	+	0.307599i
$569$	29.7984	+	21.6498i	1.24921	+	0.907606i	0.998176	−	0.0603713i	$-0.0192285\pi$
$569$	29.7984	+	21.6498i	1.24921	+	0.907606i	0.251037	+	0.967978i	$0.419228\pi$
$570$		0			0
$571$	9.59675			0.401611			0.200806	−	0.979631i	$-0.435644\pi$
$571$	9.59675			0.401611			0.200806	+	0.979631i	$0.435644\pi$
$572$	−9.09017	+	5.70634i	−0.380079	+	0.238594i
$573$		0			0
$574$	−4.61803	−	14.2128i	−0.192753	−	0.593233i
$575$	−8.23607	−	5.98385i	−0.343468	−	0.249544i
$576$		0			0
$577$	2.19098	−	6.74315i	0.0912118	−	0.280721i	−0.895036	−	0.445994i	$-0.852850\pi$
$577$	2.19098	−	6.74315i	0.0912118	−	0.280721i	0.986248	+	0.165273i	$0.0528504\pi$
$578$	3.36475	−	10.3556i	0.139955	−	0.430737i
$579$		0			0
$580$	0.881966	+	0.640786i	0.0366216	+	0.0266072i
$581$	0.961493	+	2.95917i	0.0398894	+	0.122767i
$582$		0			0
$583$	−12.7533	−	0.865300i	−0.528187	−	0.0358371i
$584$	11.3262			0.468683
$585$		0			0
$586$	−18.5902	−	13.5065i	−0.767953	−	0.557950i
$587$	−19.4894	+	14.1598i	−0.804412	+	0.584439i	−0.912205	−	0.409734i	$-0.865622\pi$
$587$	−19.4894	+	14.1598i	−0.804412	+	0.584439i	0.107793	+	0.994173i	$0.465622\pi$
$588$		0			0
$589$	−8.61803	+	26.5236i	−0.355100	+	1.09289i
$590$	−8.89919	+	6.46564i	−0.366374	+	0.266186i
$591$		0			0
$592$	0.472136	+	1.45309i	0.0194047	+	0.0597214i
$593$	−24.4721			−1.00495			−0.502475	−	0.864592i	$-0.667577\pi$
$593$	−24.4721			−1.00495			−0.502475	+	0.864592i	$0.667577\pi$
$594$		0			0
$595$	−32.5836			−1.33580
$596$	−0.427051	−	1.31433i	−0.0174927	−	0.0538370i
$597$		0			0
$598$	−8.47214	+	6.15537i	−0.346451	+	0.251712i
$599$	−2.58359	+	7.95148i	−0.105563	+	0.324889i	−0.989862	−	0.142032i	$-0.954637\pi$
$599$	−2.58359	+	7.95148i	−0.105563	+	0.324889i	0.884299	+	0.466920i	$0.154637\pi$
$600$		0			0
$601$	19.2082	−	13.9556i	0.783519	−	0.569260i	−0.122514	−	0.992467i	$-0.539096\pi$
$601$	19.2082	−	13.9556i	0.783519	−	0.569260i	0.906033	+	0.423207i	$0.139096\pi$
$602$	−12.0902	−	8.78402i	−0.492759	−	0.358010i
$603$		0			0
$604$	9.32624			0.379479
$605$	27.6591	−	14.8536i	1.12450	−	0.603886i
$606$		0			0
$607$	7.34752	+	22.6134i	0.298227	+	0.917848i	0.982118	+	0.188264i	$0.0602861\pi$
$607$	7.34752	+	22.6134i	0.298227	+	0.917848i	−0.683892	+	0.729584i	$0.739714\pi$
$608$	−2.61803	−	1.90211i	−0.106175	−	0.0771409i
$609$		0			0
$610$	−5.96556	+	18.3601i	−0.241538	+	0.743379i
$611$	2.47214	−	7.60845i	0.100012	−	0.307805i
$612$		0			0
$613$	11.5623	+	8.40051i	0.466997	+	0.339293i	0.796270	−	0.604942i	$-0.206804\pi$
$613$	11.5623	+	8.40051i	0.466997	+	0.339293i	−0.329273	+	0.944235i	$0.606804\pi$
$614$	5.14590	+	15.8374i	0.207672	+	0.639147i
$615$		0			0
$616$	5.70820	−	14.2128i	0.229990	−	0.572652i
$617$	30.2918			1.21950			0.609751	−	0.792593i	$-0.291269\pi$
$617$	30.2918			1.21950			0.609751	+	0.792593i	$0.291269\pi$
$618$		0			0
$619$	20.4721	+	14.8739i	0.822845	+	0.597832i	0.917526	−	0.397676i	$-0.130183\pi$
$619$	20.4721	+	14.8739i	0.822845	+	0.597832i	−0.0946813	+	0.995508i	$0.530183\pi$
$620$	19.8992	−	14.4576i	0.799171	−	0.580631i
$621$		0			0
$622$	−7.38197	+	22.7194i	−0.295990	+	0.910963i
$623$	−43.7426	+	31.7809i	−1.75251	+	1.27327i
$624$		0			0
$625$	−9.52786	−	29.3238i	−0.381115	−	1.17295i
$626$	−15.1459			−0.605352
$627$		0			0
$628$	4.47214			0.178458
$629$	1.16718	+	3.59222i	0.0465387	+	0.143231i
$630$		0			0
$631$	13.8713	−	10.0781i	0.552209	−	0.401203i	−0.276390	−	0.961045i	$-0.589138\pi$
$631$	13.8713	−	10.0781i	0.552209	−	0.401203i	0.828599	+	0.559842i	$0.189138\pi$
$632$	2.88197	−	8.86978i	0.114638	−	0.352821i
$633$		0			0
$634$	16.0902	−	11.6902i	0.639022	−	0.464277i
$635$	27.7082	+	20.1312i	1.09957	+	0.798882i
$636$		0			0
$637$	−46.3607			−1.83688
$638$	−1.07295	+	0.673542i	−0.0424785	+	0.0266658i
$639$		0			0
$640$	0.881966	+	2.71441i	0.0348628	+	0.107297i
$641$	38.1246	+	27.6992i	1.50583	+	1.09405i	0.967985	+	0.251008i	$0.0807620\pi$
$641$	38.1246	+	27.6992i	1.50583	+	1.09405i	0.537847	+	0.843043i	$0.319238\pi$
$642$		0			0
$643$	3.38197	−	10.4086i	0.133372	−	0.410476i	−0.861961	−	0.506974i	$-0.830764\pi$
$643$	3.38197	−	10.4086i	0.133372	−	0.410476i	0.995333	+	0.0964978i	$0.0307641\pi$
$644$	4.61803	−	14.2128i	0.181976	−	0.560065i
$645$		0			0
$646$	−6.47214	−	4.70228i	−0.254643	−	0.185009i
$647$	0.888544	+	2.73466i	0.0349323	+	0.107510i	0.967002	−	0.254768i	$-0.0819990\pi$
$647$	0.888544	+	2.73466i	0.0349323	+	0.107510i	−0.932070	+	0.362278i	$0.881999\pi$
$648$		0			0
$649$	−3.11803	−	12.3965i	−0.122394	−	0.486605i
$650$	10.1803			0.399306
$651$		0			0
$652$	10.8541	+	7.88597i	0.425079	+	0.308838i
$653$	−17.1074	+	12.4292i	−0.669464	+	0.486394i	−0.869846	−	0.493324i	$-0.835782\pi$
$653$	−17.1074	+	12.4292i	−0.669464	+	0.486394i	0.200382	+	0.979718i	$0.435782\pi$
$654$		0			0
$655$	−13.4681	+	41.4505i	−0.526241	+	1.61960i
$656$	−2.61803	+	1.90211i	−0.102217	+	0.0742650i
$657$		0			0
$658$	3.52786	+	10.8576i	0.137530	+	0.423275i
$659$	−43.1459			−1.68073			−0.840363	−	0.542024i	$-0.817658\pi$
$659$	−43.1459			−1.68073			−0.840363	+	0.542024i	$0.817658\pi$
$660$		0			0
$661$	5.81966			0.226359			0.113179	−	0.993575i	$-0.463897\pi$
$661$	5.81966			0.226359			0.113179	+	0.993575i	$0.463897\pi$
$662$	−2.76393	−	8.50651i	−0.107423	−	0.330615i
$663$		0			0
$664$	0.545085	−	0.396027i	0.0211534	−	0.0153688i
$665$	13.1803	−	40.5649i	0.511112	−	1.57304i
$666$		0			0
$667$	−1.00000	+	0.726543i	−0.0387202	+	0.0281318i
$668$	5.85410	+	4.25325i	0.226502	+	0.164563i
$669$		0			0
$670$	11.4164			0.441054
$671$	−17.2148	−	14.3844i	−0.664569	−	0.555302i
$672$		0			0
$673$	−2.15248	−	6.62464i	−0.0829718	−	0.255361i	0.900961	−	0.433900i	$-0.142863\pi$
$673$	−2.15248	−	6.62464i	−0.0829718	−	0.255361i	−0.983933	+	0.178539i	$0.942863\pi$
$674$	5.61803	+	4.08174i	0.216399	+	0.157223i
$675$		0			0
$676$	−0.781153	+	2.40414i	−0.0300443	+	0.0924670i
$677$	12.5172	−	38.5240i	0.481076	−	1.48060i	−0.356509	−	0.934292i	$-0.616033\pi$
$677$	12.5172	−	38.5240i	0.481076	−	1.48060i	0.837585	−	0.546307i	$-0.183967\pi$
$678$		0			0
$679$	−42.3156	−	30.7441i	−1.62392	−	1.17985i
$680$	2.18034	+	6.71040i	0.0836122	+	0.257332i
$681$		0			0
$682$	6.97214	+	27.7194i	0.266977	+	1.06143i
$683$	−45.7426			−1.75029			−0.875147	−	0.483857i	$-0.839235\pi$
$683$	−45.7426			−1.75029			−0.875147	+	0.483857i	$0.839235\pi$
$684$		0			0
$685$	53.3951	+	38.7938i	2.04012	+	1.48224i
$686$	27.3713	−	19.8864i	1.04504	−	0.759267i
$687$		0			0
$688$	−1.00000	+	3.07768i	−0.0381246	+	0.117336i
$689$	10.0902	−	7.33094i	0.384405	−	0.279286i
$690$		0			0
$691$	−0.0901699	−	0.277515i	−0.00343023	−	0.0105572i	0.949327	−	0.314291i	$-0.101767\pi$
$691$	−0.0901699	−	0.277515i	−0.00343023	−	0.0105572i	−0.952757	+	0.303734i	$0.901767\pi$
$692$	4.14590			0.157603
$693$		0			0
$694$	11.8541			0.449976
$695$	−11.6738	−	35.9281i	−0.442811	−	1.36283i
$696$		0			0
$697$	−6.47214	+	4.70228i	−0.245150	+	0.178112i
$698$	4.09017	−	12.5882i	0.154815	−	0.476472i
$699$		0			0
$700$	−11.7533	+	8.53926i	−0.444233	+	0.322754i
$701$	0.854102	+	0.620541i	0.0322590	+	0.0234375i	0.603798	−	0.797137i	$-0.293653\pi$
$701$	0.854102	+	0.620541i	0.0322590	+	0.0234375i	−0.571539	+	0.820575i	$0.693653\pi$
$702$		0			0
$703$	−4.94427			−0.186477
$704$	−3.30902	−	0.224514i	−0.124713	−	0.00846169i
$705$		0			0
$706$	−6.67376	−	20.5397i	−0.251170	−	0.773023i
$707$	−46.2599	−	33.6098i	−1.73978	−	1.26403i
$708$		0			0
$709$	10.8197	−	33.2995i	0.406341	−	1.25059i	−0.513430	−	0.858132i	$-0.671625\pi$
$709$	10.8197	−	33.2995i	0.406341	−	1.25059i	0.919770	−	0.392457i	$-0.128375\pi$
$710$	−11.0000	+	33.8545i	−0.412823	+	1.27054i
$711$		0			0
$712$	9.47214	+	6.88191i	0.354983	+	0.257910i
$713$	8.61803	+	26.5236i	0.322748	+	0.993316i
$714$		0			0
$715$	−11.4164	+	28.4257i	−0.426949	+	1.06306i
$716$	6.38197			0.238505
$717$		0			0
$718$	−10.3262	−	7.50245i	−0.385372	−	0.279989i
$719$	8.85410	−	6.43288i	0.330202	−	0.239906i	−0.410314	−	0.911944i	$-0.634581\pi$
$719$	8.85410	−	6.43288i	0.330202	−	0.239906i	0.740516	+	0.672038i	$0.234581\pi$
$720$		0			0
$721$	17.1738	−	52.8554i	0.639584	−	1.96844i
$722$	−6.89919	+	5.01255i	−0.256761	+	0.186548i
$723$		0			0
$724$	−5.09017	−	15.6659i	−0.189175	−	0.582220i
$725$	1.20163			0.0446273
$726$		0			0
$727$	3.41641			0.126708			0.0633538	−	0.997991i	$-0.479820\pi$
$727$	3.41641			0.126708			0.0633538	+	0.997991i	$0.479820\pi$
$728$	4.61803	+	14.2128i	0.171156	+	0.526763i
$729$		0			0
$730$	26.1525	−	19.0009i	0.967947	−	0.703254i
$731$	−2.47214	+	7.60845i	−0.0914353	+	0.281409i
$732$		0			0
$733$	35.3607	−	25.6910i	1.30608	−	0.948920i	0.306081	−	0.952005i	$-0.400982\pi$
$733$	35.3607	−	25.6910i	1.30608	−	0.948920i	0.999995	+	0.00308526i	$0.000982070\pi$
$734$	−30.3435	−	22.0458i	−1.12000	−	0.813726i
$735$		0			0
$736$	−3.23607			−0.119283
$737$	−4.94427	+	12.3107i	−0.182125	+	0.453472i
$738$		0			0
$739$	4.65248	+	14.3188i	0.171144	+	0.526727i	0.999436	−	0.0335689i	$-0.0106873\pi$
$739$	4.65248	+	14.3188i	0.171144	+	0.526727i	−0.828292	+	0.560296i	$0.810687\pi$
$740$	3.52786	+	2.56314i	0.129687	+	0.0942230i
$741$		0			0
$742$	−5.50000	+	16.9273i	−0.201911	+	0.621419i
$743$	11.6738	−	35.9281i	0.428269	−	1.31808i	−0.471561	−	0.881834i	$-0.656309\pi$
$743$	11.6738	−	35.9281i	0.428269	−	1.31808i	0.899829	−	0.436242i	$-0.143691\pi$
$744$		0			0
$745$	−3.19098	−	2.31838i	−0.116909	−	0.0849390i
$746$	2.94427	+	9.06154i	0.107797	+	0.331766i
$747$		0			0
$748$	−8.18034	−	0.555029i	−0.299103	−	0.0202939i
$749$	−24.8541			−0.908149
$750$		0			0
$751$	8.18034	+	5.94336i	0.298505	+	0.216876i	0.726948	−	0.686692i	$-0.240938\pi$
$751$	8.18034	+	5.94336i	0.298505	+	0.216876i	−0.428444	+	0.903569i	$0.640938\pi$
$752$	2.00000	−	1.45309i	0.0729325	−	0.0529886i
$753$		0			0
$754$	0.381966	−	1.17557i	0.0139104	−	0.0428118i
$755$	21.5344	−	15.6457i	0.783719	−	0.569405i
$756$		0			0
$757$	−9.43769	−	29.0462i	−0.343019	−	1.05570i	−0.962636	−	0.270799i	$-0.912712\pi$
$757$	−9.43769	−	29.0462i	−0.343019	−	1.05570i	0.619617	−	0.784904i	$-0.287288\pi$
$758$	−3.70820			−0.134688
$759$		0			0
$760$	−9.23607			−0.335027
$761$	−3.18034	−	9.78808i	−0.115287	−	0.354818i	0.876720	−	0.481002i	$-0.159727\pi$
$761$	−3.18034	−	9.78808i	−0.115287	−	0.354818i	−0.992007	+	0.126184i	$0.959727\pi$
$762$		0			0
$763$	−65.0689	+	47.2753i	−2.35565	+	1.71148i
$764$	−6.94427	+	21.3723i	−0.251235	+	0.773222i
$765$		0			0
$766$	−10.7082	+	7.77997i	−0.386903	+	0.281102i
$767$	10.0902	+	7.33094i	0.364335	+	0.264705i
$768$		0			0
$769$	−4.27051			−0.153999			−0.0769993	−	0.997031i	$-0.524534\pi$
$769$	−4.27051			−0.153999			−0.0769993	+	0.997031i	$0.524534\pi$
$770$	−10.6631	−	42.3938i	−0.384272	−	1.52777i
$771$		0			0
$772$	0.100813	+	0.310271i	0.00362834	+	0.0111669i
$773$	7.69098	+	5.58783i	0.276625	+	0.200980i	0.717444	−	0.696616i	$-0.245312\pi$
$773$	7.69098	+	5.58783i	0.276625	+	0.200980i	−0.440819	+	0.897596i	$0.645312\pi$
$774$		0			0
$775$	8.37790	−	25.7845i	0.300943	−	0.926208i
$776$	−3.50000	+	10.7719i	−0.125643	+	0.386688i
$777$		0			0
$778$	−31.5066	−	22.8909i	−1.12957	−	0.820677i
$779$	−3.23607	−	9.95959i	−0.115944	−	0.356839i
$780$		0			0
$781$	−31.7426	−	26.5236i	−1.13584	−	0.949088i
$782$	−8.00000			−0.286079
$783$		0			0
$784$	−11.5902	−	8.42075i	−0.413935	−	0.300741i
$785$	10.3262	−	7.50245i	0.368559	−	0.267774i
$786$		0			0
$787$	−11.5836	+	35.6506i	−0.412910	+	1.27081i	0.501196	+	0.865334i	$0.332894\pi$
$787$	−11.5836	+	35.6506i	−0.412910	+	1.27081i	−0.914107	+	0.405474i	$0.867106\pi$
$788$	4.92705	−	3.57971i	0.175519	−	0.127522i
$789$		0			0
$790$	−8.22542	−	25.3153i	−0.292647	−	0.900676i
$791$	57.5967			2.04790
$792$		0			0
$793$	21.8885			0.777285
$794$	−3.05573	−	9.40456i	−0.108444	−	0.333755i
$795$		0			0
$796$	−10.6353	+	7.72696i	−0.376957	+	0.273875i
$797$	6.98936	−	21.5110i	0.247576	−	0.761960i	−0.747626	−	0.664120i	$-0.768807\pi$
$797$	6.98936	−	21.5110i	0.247576	−	0.761960i	0.995202	−	0.0978402i	$-0.0311934\pi$
$798$		0			0
$799$	4.94427	−	3.59222i	0.174916	−	0.127084i
$800$	2.54508	+	1.84911i	0.0899823	+	0.0653760i
$801$		0			0
$802$	10.2918			0.363416
$803$	9.16312	+	36.4302i	0.323359	+	1.28559i
$804$		0			0
$805$	−13.1803	−	40.5649i	−0.464546	−	1.42973i
$806$	−22.5623	−	16.3925i	−0.794723	−	0.577400i
$807$		0			0
$808$	−3.82624	+	11.7759i	−0.134607	+	0.414276i
$809$	−9.34752	+	28.7687i	−0.328641	+	1.01145i	0.641129	+	0.767434i	$0.278467\pi$
$809$	−9.34752	+	28.7687i	−0.328641	+	1.01145i	−0.969770	+	0.244021i	$0.921533\pi$
$810$		0			0
$811$	32.9787	+	23.9604i	1.15804	+	0.841365i	0.989529	−	0.144335i	$-0.0461043\pi$
$811$	32.9787	+	23.9604i	1.15804	+	0.841365i	0.168510	+	0.985700i	$0.446104\pi$
$812$	0.545085	+	1.67760i	0.0191287	+	0.0588722i
$813$		0			0
$814$	−4.29180	+	2.69417i	−0.150427	+	0.0944305i
$815$	38.2918			1.34130
$816$		0			0
$817$	−8.47214	−	6.15537i	−0.296403	−	0.215349i
$818$	−9.78115	+	7.10642i	−0.341990	+	0.248470i
$819$		0			0
$820$	−2.85410	+	8.78402i	−0.0996696	+	0.306751i
$821$	17.0623	−	12.3965i	0.595479	−	0.432641i	−0.248793	−	0.968557i	$-0.580034\pi$
$821$	17.0623	−	12.3965i	0.595479	−	0.432641i	0.844271	+	0.535916i	$0.180034\pi$
$822$		0			0
$823$	−0.993422	−	3.05744i	−0.0346285	−	0.106576i	0.932248	−	0.361819i	$-0.117844\pi$
$823$	−0.993422	−	3.05744i	−0.0346285	−	0.106576i	−0.966877	+	0.255244i	$0.917844\pi$
$824$	−12.0344			−0.419240
$825$		0			0
$826$	−17.7984			−0.619285
$827$	−3.30244	−	10.1639i	−0.114837	−	0.353432i	0.877076	−	0.480352i	$-0.159491\pi$
$827$	−3.30244	−	10.1639i	−0.114837	−	0.353432i	−0.991913	+	0.126920i	$0.959491\pi$
$828$		0			0
$829$	−5.90983	+	4.29374i	−0.205257	+	0.149128i	−0.685665	−	0.727917i	$-0.740489\pi$
$829$	−5.90983	+	4.29374i	−0.205257	+	0.149128i	0.480408	+	0.877045i	$0.340489\pi$
$830$	0.594235	−	1.82887i	0.0206262	−	0.0634809i
$831$		0			0
$832$	2.61803	−	1.90211i	0.0907640	−	0.0659439i
$833$	−28.6525	−	20.8172i	−0.992749	−	0.721275i
$834$		0			0
$835$	20.6525			0.714708
$836$	4.00000	−	9.95959i	0.138343	−	0.344460i
$837$		0			0
$838$	−5.55573	−	17.0988i	−0.191919	−	0.590667i
$839$	−2.52786	−	1.83660i	−0.0872716	−	0.0634065i	0.543294	−	0.839543i	$-0.317177\pi$
$839$	−2.52786	−	1.83660i	−0.0872716	−	0.0634065i	−0.630565	+	0.776136i	$0.717177\pi$
$840$		0			0
$841$	−8.91641	+	27.4419i	−0.307462	+	0.946272i
$842$	−10.8541	+	33.4055i	−0.374057	+	1.15123i
$843$		0			0
$844$	3.76393	+	2.73466i	0.129560	+	0.0941308i
$845$	2.22949	+	6.86167i	0.0766968	+	0.236048i
$846$		0			0
$847$	50.3328	+	6.86167i	1.72946	+	0.235770i
$848$	3.85410			0.132350
$849$		0			0
$850$	6.29180	+	4.57126i	0.215807	+	0.156793i
$851$	−4.00000	+	2.90617i	−0.137118	+	0.0996222i
$852$		0			0
$853$	4.65248	−	14.3188i	0.159298	−	0.490268i	−0.839273	−	0.543710i	$-0.817019\pi$
$853$	4.65248	−	14.3188i	0.159298	−	0.490268i	0.998571	+	0.0534419i	$0.0170192\pi$
$854$	−25.2705	+	18.3601i	−0.864739	+	0.628270i
$855$		0			0
$856$	1.66312	+	5.11855i	0.0568442	+	0.174949i
$857$	−8.76393			−0.299370			−0.149685	−	0.988734i	$-0.547826\pi$
$857$	−8.76393			−0.299370			−0.149685	+	0.988734i	$0.547826\pi$
$858$		0			0
$859$	4.40325			0.150237			0.0751185	−	0.997175i	$-0.476066\pi$
$859$	4.40325			0.150237			0.0751185	+	0.997175i	$0.476066\pi$
$860$	2.85410	+	8.78402i	0.0973241	+	0.299533i
$861$		0			0
$862$	5.85410	−	4.25325i	0.199392	−	0.144866i
$863$	−0.854102	+	2.62866i	−0.0290740	+	0.0894805i	−0.964541	−	0.263935i	$-0.914980\pi$
$863$	−0.854102	+	2.62866i	−0.0290740	+	0.0894805i	0.935467	+	0.353415i	$0.114980\pi$
$864$		0			0
$865$	9.57295	−	6.95515i	0.325490	−	0.236482i
$866$	9.97214	+	7.24518i	0.338867	+	0.246201i
$867$		0			0
$868$	39.7984			1.35084
$869$	30.8607	+	2.09387i	1.04688	+	0.0710297i
$870$		0			0
$871$	−4.00000	−	12.3107i	−0.135535	−	0.417133i
$872$	14.0902	+	10.2371i	0.477153	+	0.346672i
$873$		0			0
$874$	3.23607	−	9.95959i	0.109462	−	0.336888i
$875$	7.55166	−	23.2416i	0.255293	−	0.785710i
$876$		0			0
$877$	24.5623	+	17.8456i	0.829410	+	0.602602i	0.919392	−	0.393342i	$-0.128681\pi$
$877$	24.5623	+	17.8456i	0.829410	+	0.602602i	−0.0899822	+	0.995943i	$0.528681\pi$
$878$	−4.95492	−	15.2497i	−0.167220	−	0.514651i
$879$		0			0
$880$	−8.01722	+	5.03280i	−0.270260	+	0.169656i
$881$	12.2918			0.414121			0.207061	−	0.978328i	$-0.433610\pi$
$881$	12.2918			0.414121			0.207061	+	0.978328i	$0.433610\pi$
$882$		0			0
$883$	−22.5066	−	16.3520i	−0.757407	−	0.550288i	0.140707	−	0.990051i	$-0.455062\pi$
$883$	−22.5066	−	16.3520i	−0.757407	−	0.550288i	−0.898114	+	0.439763i	$0.855062\pi$
$884$	6.47214	−	4.70228i	0.217681	−	0.158155i
$885$		0			0
$886$	−0.517221	+	1.59184i	−0.0173764	+	0.0534790i
$887$	−23.0902	+	16.7760i	−0.775292	+	0.563283i	−0.903562	−	0.428457i	$-0.859057\pi$
$887$	−23.0902	+	16.7760i	−0.775292	+	0.563283i	0.128270	+	0.991739i	$0.459057\pi$
$888$		0			0
$889$	17.1246	+	52.7041i	0.574341	+	1.76764i
$890$	33.4164			1.12012
$891$		0			0
$892$	−1.90983			−0.0639458
$893$	2.47214	+	7.60845i	0.0827269	+	0.254607i
$894$		0			0
$895$	14.7361	−	10.7064i	0.492572	−	0.357875i
$896$	−1.42705	+	4.39201i	−0.0476744	+	0.146727i
$897$		0			0
$898$	−29.0344	+	21.0948i	−0.968892	+	0.703941i
$899$	−2.66312	−	1.93487i	−0.0888200	−	0.0645315i
$900$		0			0
$901$	9.52786			0.317419
$902$	−8.23607	−	6.88191i	−0.274231	−	0.229143i
$903$		0			0
$904$	−3.85410	−	11.8617i	−0.128186	−	0.394514i
$905$	−38.0344	−	27.6336i	−1.26431	−	0.918573i
$906$		0			0
$907$	−2.52786	+	7.77997i	−0.0839363	+	0.258330i	−0.984213	−	0.176989i	$-0.943364\pi$
$907$	−2.52786	+	7.77997i	−0.0839363	+	0.258330i	0.900276	+	0.435319i	$0.143364\pi$
$908$	2.20820	−	6.79615i	0.0732818	−	0.225538i
$909$		0			0
$910$	34.5066	+	25.0705i	1.14388	+	0.831079i
$911$	−13.5066	−	41.5690i	−0.447493	−	1.37724i	−0.879727	−	0.475480i	$-0.842274\pi$
$911$	−13.5066	−	41.5690i	−0.447493	−	1.37724i	0.432234	−	0.901762i	$-0.357726\pi$
$912$		0			0
$913$	1.71478	+	1.43284i	0.0567510	+	0.0474201i
$914$	21.9787			0.726991
$915$		0			0
$916$	−18.5623	−	13.4863i	−0.613316	−	0.445600i
$917$	−57.0517	+	41.4505i	−1.88401	+	1.36881i
$918$		0			0
$919$	15.5344	−	47.8101i	0.512434	−	1.57711i	−0.275469	−	0.961310i	$-0.588833\pi$
$919$	15.5344	−	47.8101i	0.512434	−	1.57711i	0.787903	−	0.615800i	$-0.211167\pi$
$920$	−7.47214	+	5.42882i	−0.246349	+	0.178983i
$921$		0			0
$922$	12.6180	+	38.8343i	0.415553	+	1.27894i
$923$	40.3607			1.32849
$924$		0			0
$925$	4.80650			0.158037
$926$	−5.89919	−	18.1558i	−0.193859	−	0.596638i
$927$		0			0
$928$	0.309017	−	0.224514i	0.0101440	−	0.00737003i
$929$	7.14590	−	21.9928i	0.234449	−	0.721561i	−0.762745	−	0.646700i	$-0.776149\pi$
$929$	7.14590	−	21.9928i	0.234449	−	0.721561i	0.997194	−	0.0748610i	$-0.0238513\pi$
$930$		0			0
$931$	37.5066	−	27.2501i	1.22923	−	0.893087i
$932$	−7.23607	−	5.25731i	−0.237025	−	0.172209i
$933$		0			0
$934$	19.5623			0.640098
$935$	−19.8197	+	12.4418i	−0.648172	+	0.406889i
$936$		0			0
$937$	8.48278	+	26.1073i	0.277120	+	0.852889i	0.988651	+	0.150233i	$0.0480024\pi$
$937$	8.48278	+	26.1073i	0.277120	+	0.852889i	−0.711530	+	0.702655i	$0.751998\pi$
$938$	14.9443	+	10.8576i	0.487948	+	0.354515i
$939$		0			0
$940$	2.18034	−	6.71040i	0.0711148	−	0.218869i
$941$	2.72949	−	8.40051i	0.0889788	−	0.273849i	−0.896659	−	0.442722i	$-0.854013\pi$
$941$	2.72949	−	8.40051i	0.0889788	−	0.273849i	0.985638	+	0.168873i	$0.0540129\pi$
$942$		0			0
$943$	−8.47214	−	6.15537i	−0.275891	−	0.200446i
$944$	1.19098	+	3.66547i	0.0387632	+	0.119301i
$945$		0			0
$946$	−10.7082	−	0.726543i	−0.348154	−	0.0236219i
$947$	−2.32624			−0.0755926			−0.0377963	−	0.999285i	$-0.512034\pi$
$947$	−2.32624			−0.0755926			−0.0377963	+	0.999285i	$0.512034\pi$
$948$		0			0
$949$	−29.6525	−	21.5438i	−0.962560	−	0.699341i
$950$	−8.23607	+	5.98385i	−0.267213	+	0.194142i
$951$		0			0
$952$	−3.52786	+	10.8576i	−0.114339	+	0.351898i
$953$	39.4164	−	28.6377i	1.27682	−	0.927666i	0.277371	−	0.960763i	$-0.410537\pi$
$953$	39.4164	−	28.6377i	1.27682	−	0.927666i	0.999452	+	0.0330970i	$0.0105370\pi$
$954$		0			0
$955$	19.8197	+	60.9986i	0.641349	+	1.97387i
$956$	16.4721			0.532747
$957$		0			0
$958$	−7.23607			−0.233787
$959$	33.0000	+	101.564i	1.06563	+	3.27966i
$960$		0			0
$961$	−35.0066	+	25.4338i	−1.12924	+	0.820444i
$962$	1.52786	−	4.70228i	0.0492603	−	0.151608i
$963$		0			0
$964$	1.97214	−	1.43284i	0.0635182	−	0.0461487i
$965$	0.753289	+	0.547296i	0.0242492	+	0.0176181i
$966$		0			0
$967$	13.6869			0.440142			0.220071	−	0.975484i	$-0.429371\pi$
$967$	13.6869			0.440142			0.220071	+	0.975484i	$0.429371\pi$
$968$	−1.95492	−	10.8249i	−0.0628333	−	0.347925i
$969$		0			0
$970$	9.98936	+	30.7441i	0.320739	+	0.987133i
$971$	−7.52786	−	5.46931i	−0.241581	−	0.175519i	0.460407	−	0.887708i	$-0.347704\pi$
$971$	−7.52786	−	5.46931i	−0.241581	−	0.175519i	−0.701987	+	0.712190i	$0.747704\pi$
$972$		0			0
$973$	18.8885	−	58.1330i	0.605539	−	1.86366i
$974$	−7.71885	+	23.7562i	−0.247328	+	0.761197i
$975$		0			0
$976$	5.47214	+	3.97574i	0.175159	+	0.127260i
$977$	11.3607	+	34.9646i	0.363460	+	1.11862i	0.950940	+	0.309377i	$0.100120\pi$
$977$	11.3607	+	34.9646i	0.363460	+	1.11862i	−0.587479	+	0.809239i	$0.699880\pi$
$978$		0			0
$979$	−14.4721	+	36.0341i	−0.462531	+	1.15166i
$980$	−40.8885			−1.30614
$981$		0			0
$982$	−34.1803	−	24.8335i	−1.09074	−	0.792468i
$983$	−7.38197	+	5.36331i	−0.235448	+	0.171063i	−0.699253	−	0.714874i	$-0.746484\pi$
$983$	−7.38197	+	5.36331i	−0.235448	+	0.171063i	0.463805	+	0.885937i	$0.346484\pi$
$984$		0			0
$985$	5.37132	−	16.5312i	0.171145	−	0.526729i
$986$	0.763932	−	0.555029i	0.0243286	−	0.0176757i
$987$		0			0
$988$	3.23607	+	9.95959i	0.102953	+	0.316857i
$989$	−10.4721			−0.332995
$990$		0			0
$991$	−45.6869			−1.45129			−0.725646	−	0.688068i	$-0.758459\pi$
$991$	−45.6869			−1.45129			−0.725646	+	0.688068i	$0.758459\pi$
$992$	−2.66312	−	8.19624i	−0.0845541	−	0.260231i
$993$		0			0
$994$	−46.5967	+	33.8545i	−1.47796	+	1.07380i
$995$	−11.5942	+	35.6834i	−0.367562	+	1.13124i
$996$		0			0
$997$	−46.8885	+	34.0665i	−1.48498	+	1.07890i	−0.509064	+	0.860729i	$0.670008\pi$
$997$	−46.8885	+	34.0665i	−1.48498	+	1.07890i	−0.975911	+	0.218169i	$0.929992\pi$
$998$	−6.00000	−	4.35926i	−0.189927	−	0.137990i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.2.f.c.181.1		4
3.2	odd	2		66.2.e.a.49.1	yes	4
11.3	even	5		2178.2.a.t.1.1		2
11.8	odd	10		2178.2.a.bb.1.1		2
11.9	even	5	inner	198.2.f.c.163.1		4
12.11	even	2		528.2.y.d.49.1		4
33.2	even	10		726.2.e.r.493.1		4
33.5	odd	10		726.2.e.f.565.1		4
33.8	even	10		726.2.a.j.1.2		2
33.14	odd	10		726.2.a.l.1.2		2
33.17	even	10		726.2.e.n.565.1		4
33.20	odd	10		66.2.e.a.31.1	✓	4
33.26	odd	10		726.2.e.f.487.1		4
33.29	even	10		726.2.e.n.487.1		4
33.32	even	2		726.2.e.r.511.1		4
132.47	even	10		5808.2.a.cb.1.2		2
132.107	odd	10		5808.2.a.cg.1.2		2
132.119	even	10		528.2.y.d.97.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.a.31.1	✓	4	33.20	odd	10
66.2.e.a.49.1	yes	4	3.2	odd	2
198.2.f.c.163.1		4	11.9	even	5	inner
198.2.f.c.181.1		4	1.1	even	1	trivial
528.2.y.d.49.1		4	12.11	even	2
528.2.y.d.97.1		4	132.119	even	10
726.2.a.j.1.2		2	33.8	even	10
726.2.a.l.1.2		2	33.14	odd	10
726.2.e.f.487.1		4	33.26	odd	10
726.2.e.f.565.1		4	33.5	odd	10
726.2.e.n.487.1		4	33.29	even	10
726.2.e.n.565.1		4	33.17	even	10
726.2.e.r.493.1		4	33.2	even	10
726.2.e.r.511.1		4	33.32	even	2
2178.2.a.t.1.1		2	11.3	even	5
2178.2.a.bb.1.1		2	11.8	odd	10
5808.2.a.cb.1.2		2	132.47	even	10
5808.2.a.cg.1.2		2	132.107	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	198.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(-0.881966 + 2.71441i) q^{5} +(-3.73607 + 2.71441i) q^{7} +(0.809017 + 0.587785i) q^{8} +2.85410 q^{10} +(-1.23607 + 3.07768i) q^{11} +(-1.00000 - 3.07768i) q^{13} +(3.73607 + 2.71441i) q^{14} +(0.309017 - 0.951057i) q^{16} +(0.763932 - 2.35114i) q^{17} +(2.61803 + 1.90211i) q^{19} +(-0.881966 - 2.71441i) q^{20} +(3.30902 + 0.224514i) q^{22} +3.23607 q^{23} +(-2.54508 - 1.84911i) q^{25} +(-2.61803 + 1.90211i) q^{26} +(1.42705 - 4.39201i) q^{28} +(-0.309017 + 0.224514i) q^{29} +(2.66312 + 8.19624i) q^{31} -1.00000 q^{32} -2.47214 q^{34} +(-4.07295 - 12.5352i) q^{35} +(-1.23607 + 0.898056i) q^{37} +(1.00000 - 3.07768i) q^{38} +(-2.30902 + 1.67760i) q^{40} +(-2.61803 - 1.90211i) q^{41} -3.23607 q^{43} +(-0.809017 - 3.21644i) q^{44} +(-1.00000 - 3.07768i) q^{46} +(2.00000 + 1.45309i) q^{47} +(4.42705 - 13.6251i) q^{49} +(-0.972136 + 2.99193i) q^{50} +(2.61803 + 1.90211i) q^{52} +(1.19098 + 3.66547i) q^{53} +(-7.26393 - 6.06961i) q^{55} -4.61803 q^{56} +(0.309017 + 0.224514i) q^{58} +(-3.11803 + 2.26538i) q^{59} +(-2.09017 + 6.43288i) q^{61} +(6.97214 - 5.06555i) q^{62} +(0.309017 + 0.951057i) q^{64} +9.23607 q^{65} +4.00000 q^{67} +(0.763932 + 2.35114i) q^{68} +(-10.6631 + 7.74721i) q^{70} +(-3.85410 + 11.8617i) q^{71} +(9.16312 - 6.65740i) q^{73} +(1.23607 + 0.898056i) q^{74} -3.23607 q^{76} +(-3.73607 - 14.8536i) q^{77} +(-2.88197 - 8.86978i) q^{79} +(2.30902 + 1.67760i) q^{80} +(-1.00000 + 3.07768i) q^{82} +(0.208204 - 0.640786i) q^{83} +(5.70820 + 4.14725i) q^{85} +(1.00000 + 3.07768i) q^{86} +(-2.80902 + 1.76336i) q^{88} +11.7082 q^{89} +(12.0902 + 8.78402i) q^{91} +(-2.61803 + 1.90211i) q^{92} +(0.763932 - 2.35114i) q^{94} +(-7.47214 + 5.42882i) q^{95} +(3.50000 + 10.7719i) q^{97} -14.3262 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{4} - 8 q^{5} - 6 q^{7} + q^{8} - 2 q^{10} + 4 q^{11} - 4 q^{13} + 6 q^{14} - q^{16} + 12 q^{17} + 6 q^{19} - 8 q^{20} + 11 q^{22} + 4 q^{23} + q^{25} - 6 q^{26} - q^{28} + q^{29}+ \cdots - 26 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^4 - 8 * q^5 - 6 * q^7 + q^8 - 2 * q^10 + 4 * q^11 - 4 * q^13 + 6 * q^14 - q^16 + 12 * q^17 + 6 * q^19 - 8 * q^20 + 11 * q^22 + 4 * q^23 + q^25 - 6 * q^26 - q^28 + q^29 - 5 * q^31 - 4 * q^32 + 8 * q^34 - 23 * q^35 + 4 * q^37 + 4 * q^38 - 7 * q^40 - 6 * q^41 - 4 * q^43 - q^44 - 4 * q^46 + 8 * q^47 + 11 * q^49 + 14 * q^50 + 6 * q^52 + 7 * q^53 - 38 * q^55 - 14 * q^56 - q^58 - 8 * q^59 + 14 * q^61 + 10 * q^62 - q^64 + 28 * q^65 + 16 * q^67 + 12 * q^68 - 27 * q^70 - 2 * q^71 + 21 * q^73 - 4 * q^74 - 4 * q^76 - 6 * q^77 - 16 * q^79 + 7 * q^80 - 4 * q^82 - 26 * q^83 - 4 * q^85 + 4 * q^86 - 9 * q^88 + 20 * q^89 + 26 * q^91 - 6 * q^92 + 12 * q^94 - 12 * q^95 + 14 * q^97 - 26 * q^98

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