LMFDB - Embedded newform 297.2.e.d.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(100,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("297.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	297.100
Dual form			297.2.e.d.199.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.939693 + 1.62760i) q^{2} +(-0.766044 - 1.32683i) q^{4} +(1.43969 + 2.49362i) q^{5} +(0.326352 - 0.565258i) q^{7} -0.879385 q^{8} -5.41147 q^{10} +(-0.500000 + 0.866025i) q^{11} +(3.37939 + 5.85327i) q^{13} +(0.613341 + 1.06234i) q^{14} +(2.35844 - 4.08494i) q^{16} -0.184793 q^{17} -5.22668 q^{19} +(2.20574 - 3.82045i) q^{20} +(-0.939693 - 1.62760i) q^{22} +(-1.59240 - 2.75811i) q^{23} +(-1.64543 + 2.84997i) q^{25} -12.7023 q^{26} -1.00000 q^{28} +(-2.01114 + 3.48340i) q^{29} +(-0.553033 - 0.957882i) q^{31} +(3.55303 + 6.15403i) q^{32} +(0.173648 - 0.300767i) q^{34} +1.87939 q^{35} +0.106067 q^{37} +(4.91147 - 8.50692i) q^{38} +(-1.26604 - 2.19285i) q^{40} +(-2.80793 - 4.86348i) q^{41} +(-1.92989 + 3.34267i) q^{43} +1.53209 q^{44} +5.98545 q^{46} +(6.00387 - 10.3990i) q^{47} +(3.28699 + 5.69323i) q^{49} +(-3.09240 - 5.35619i) q^{50} +(5.17752 - 8.96773i) q^{52} +10.0719 q^{53} -2.87939 q^{55} +(-0.286989 + 0.497079i) q^{56} +(-3.77972 - 6.54666i) q^{58} +(5.27719 + 9.14036i) q^{59} +(3.67365 - 6.36295i) q^{61} +2.07873 q^{62} -3.92127 q^{64} +(-9.73055 + 16.8538i) q^{65} +(5.90420 + 10.2264i) q^{67} +(0.141559 + 0.245188i) q^{68} +(-1.76604 + 3.05888i) q^{70} +2.47565 q^{71} +10.4611 q^{73} +(-0.0996702 + 0.172634i) q^{74} +(4.00387 + 6.93491i) q^{76} +(0.326352 + 0.565258i) q^{77} +(0.733956 - 1.27125i) q^{79} +13.5817 q^{80} +10.5544 q^{82} +(-0.520945 + 0.902302i) q^{83} +(-0.266044 - 0.460802i) q^{85} +(-3.62701 - 6.28217i) q^{86} +(0.439693 - 0.761570i) q^{88} +3.01960 q^{89} +4.41147 q^{91} +(-2.43969 + 4.22567i) q^{92} +(11.2836 + 19.5437i) q^{94} +(-7.52481 - 13.0334i) q^{95} +(2.86959 - 4.97027i) q^{97} -12.3550 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7} + 6 q^{8} - 12 q^{10} - 3 q^{11} + 9 q^{13} - 3 q^{14} + 6 q^{16} + 6 q^{17} - 18 q^{19} + 3 q^{20} - 6 q^{23} + 6 q^{25} - 24 q^{26} - 6 q^{28} - 6 q^{29} + 9 q^{31} + 9 q^{32}+ \cdots - 24 q^{98}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 + 6 * q^8 - 12 * q^10 - 3 * q^11 + 9 * q^13 - 3 * q^14 + 6 * q^16 + 6 * q^17 - 18 * q^19 + 3 * q^20 - 6 * q^23 + 6 * q^25 - 24 * q^26 - 6 * q^28 - 6 * q^29 + 9 * q^31 + 9 * q^32 - 24 * q^37 + 9 * q^38 - 3 * q^40 - 6 * q^41 - 3 * q^43 + 12 * q^47 + 12 * q^49 - 15 * q^50 + 6 * q^52 - 6 * q^53 - 6 * q^55 + 6 * q^56 + 3 * q^58 + 21 * q^59 + 21 * q^61 + 30 * q^62 - 6 * q^64 - 21 * q^65 - 3 * q^67 + 9 * q^68 - 6 * q^70 - 24 * q^71 - 12 * q^73 - 15 * q^74 + 3 * q^77 + 9 * q^79 + 18 * q^80 + 42 * q^82 + 3 * q^85 + 6 * q^86 - 3 * q^88 + 24 * q^89 + 6 * q^91 - 9 * q^92 + 18 * q^94 - 18 * q^95 + 3 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.939693	+	1.62760i	−0.664463	+	1.15088i	0.314968	+	0.949102i	$0.398006\pi$
$2$	−0.939693	+	1.62760i	−0.664463	+	1.15088i	−0.979431	+	0.201781i	$0.935327\pi$
$3$		0			0
$3$		0			0
$4$	−0.766044	−	1.32683i	−0.383022	−	0.663414i
$5$	1.43969	+	2.49362i	0.643850	+	1.11518i	0.984566	+	0.175015i	$0.0559973\pi$
$5$	1.43969	+	2.49362i	0.643850	+	1.11518i	−0.340716	+	0.940166i	$0.610669\pi$
$6$		0			0
$7$	0.326352	−	0.565258i	0.123349	−	0.213647i	−0.797737	−	0.603005i	$-0.793970\pi$
$7$	0.326352	−	0.565258i	0.123349	−	0.213647i	0.921087	+	0.389358i	$0.127303\pi$
$8$	−0.879385			−0.310910
$9$		0			0
$10$	−5.41147			−1.71126
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	3.37939	+	5.85327i	0.937273	+	1.62340i	0.770530	+	0.637404i	$0.219992\pi$
$13$	3.37939	+	5.85327i	0.937273	+	1.62340i	0.166743	+	0.986000i	$0.446675\pi$
$14$	0.613341	+	1.06234i	0.163922	+	0.283922i
$15$		0			0
$16$	2.35844	−	4.08494i	0.589610	−	1.02123i
$17$	−0.184793			−0.0448188			−0.0224094	−	0.999749i	$-0.507134\pi$
$17$	−0.184793			−0.0448188			−0.0224094	+	0.999749i	$0.507134\pi$
$18$		0			0
$19$	−5.22668			−1.19908			−0.599541	−	0.800344i	$-0.704650\pi$
$19$	−5.22668			−1.19908			−0.599541	+	0.800344i	$0.704650\pi$
$20$	2.20574	−	3.82045i	0.493218	−	0.854278i
$21$		0			0
$22$	−0.939693	−	1.62760i	−0.200343	−	0.347004i
$23$	−1.59240	−	2.75811i	−0.332038	−	0.575106i	0.650874	−	0.759186i	$-0.274403\pi$
$23$	−1.59240	−	2.75811i	−0.332038	−	0.575106i	−0.982911	+	0.184080i	$0.941069\pi$
$24$		0			0
$25$	−1.64543	+	2.84997i	−0.329086	+	0.569994i
$26$	−12.7023			−2.49113
$27$		0			0
$28$	−1.00000			−0.188982
$29$	−2.01114	+	3.48340i	−0.373460	+	0.646852i	−0.990095	−	0.140397i	$-0.955162\pi$
$29$	−2.01114	+	3.48340i	−0.373460	+	0.646852i	0.616635	+	0.787249i	$0.288495\pi$
$30$		0			0
$31$	−0.553033	−	0.957882i	−0.0993277	−	0.172041i	0.812079	−	0.583548i	$-0.198336\pi$
$31$	−0.553033	−	0.957882i	−0.0993277	−	0.172041i	−0.911407	+	0.411507i	$0.865003\pi$
$32$	3.55303	+	6.15403i	0.628094	+	1.08789i
$33$		0			0
$34$	0.173648	−	0.300767i	0.0297804	−	0.0515812i
$35$	1.87939			0.317674
$36$		0			0
$37$	0.106067			0.0174373			0.00871864	−	0.999962i	$-0.497225\pi$
$37$	0.106067			0.0174373			0.00871864	+	0.999962i	$0.497225\pi$
$38$	4.91147	−	8.50692i	0.796746	−	1.38001i
$39$		0			0
$40$	−1.26604	−	2.19285i	−0.200179	−	0.346721i
$41$	−2.80793	−	4.86348i	−0.438526	−	0.759549i	0.559050	−	0.829134i	$-0.311166\pi$
$41$	−2.80793	−	4.86348i	−0.438526	−	0.759549i	−0.997576	+	0.0695851i	$0.977832\pi$
$42$		0			0
$43$	−1.92989	+	3.34267i	−0.294306	+	0.509753i	−0.974823	−	0.222979i	$-0.928422\pi$
$43$	−1.92989	+	3.34267i	−0.294306	+	0.509753i	0.680517	+	0.732732i	$0.261755\pi$
$44$	1.53209			0.230971
$45$		0			0
$46$	5.98545			0.882507
$47$	6.00387	−	10.3990i	0.875755	−	1.51685i	0.0197977	−	0.999804i	$-0.493698\pi$
$47$	6.00387	−	10.3990i	0.875755	−	1.51685i	0.855957	−	0.517047i	$-0.172969\pi$
$48$		0			0
$49$	3.28699	+	5.69323i	0.469570	+	0.813319i
$50$	−3.09240	−	5.35619i	−0.437331	−	0.757479i
$51$		0			0
$52$	5.17752	−	8.96773i	0.717993	−	1.24360i
$53$	10.0719			1.38348			0.691742	−	0.722145i	$-0.256843\pi$
$53$	10.0719			1.38348			0.691742	+	0.722145i	$0.256843\pi$
$54$		0			0
$55$	−2.87939			−0.388256
$56$	−0.286989	+	0.497079i	−0.0383505	+	0.0664250i
$57$		0			0
$58$	−3.77972	−	6.54666i	−0.496301	−	0.859618i
$59$	5.27719	+	9.14036i	0.687031	+	1.18997i	0.972794	+	0.231673i	$0.0744199\pi$
$59$	5.27719	+	9.14036i	0.687031	+	1.18997i	−0.285762	+	0.958301i	$0.592247\pi$
$60$		0			0
$61$	3.67365	−	6.36295i	0.470362	−	0.814692i	−0.529063	−	0.848582i	$-0.677457\pi$
$61$	3.67365	−	6.36295i	0.470362	−	0.814692i	0.999426	+	0.0338908i	$0.0107899\pi$
$62$	2.07873			0.263998
$63$		0			0
$64$	−3.92127			−0.490159
$65$	−9.73055	+	16.8538i	−1.20693	+	2.09046i
$66$		0			0
$67$	5.90420	+	10.2264i	0.721313	+	1.24935i	0.960474	+	0.278371i	$0.0897943\pi$
$67$	5.90420	+	10.2264i	0.721313	+	1.24935i	−0.239161	+	0.970980i	$0.576872\pi$
$68$	0.141559	+	0.245188i	0.0171666	+	0.0297334i
$69$		0			0
$70$	−1.76604	+	3.05888i	−0.211083	+	0.365606i
$71$	2.47565			0.293806			0.146903	−	0.989151i	$-0.453070\pi$
$71$	2.47565			0.293806			0.146903	+	0.989151i	$0.453070\pi$
$72$		0			0
$73$	10.4611			1.22438			0.612190	−	0.790711i	$-0.290289\pi$
$73$	10.4611			1.22438			0.612190	+	0.790711i	$0.290289\pi$
$74$	−0.0996702	+	0.172634i	−0.0115864	+	0.0200683i
$75$		0			0
$76$	4.00387	+	6.93491i	0.459275	+	0.795488i
$77$	0.326352	+	0.565258i	0.0371912	+	0.0644171i
$78$		0			0
$79$	0.733956	−	1.27125i	0.0825765	−	0.143027i	−0.821779	−	0.569806i	$-0.807018\pi$
$79$	0.733956	−	1.27125i	0.0825765	−	0.143027i	0.904356	+	0.426779i	$0.140352\pi$
$80$	13.5817			1.51848
$81$		0			0
$82$	10.5544			1.16554
$83$	−0.520945	+	0.902302i	−0.0571811	+	0.0990406i	−0.893199	−	0.449662i	$-0.851545\pi$
$83$	−0.520945	+	0.902302i	−0.0571811	+	0.0990406i	0.836018	+	0.548702i	$0.184878\pi$
$84$		0			0
$85$	−0.266044	−	0.460802i	−0.0288566	−	0.0499810i
$86$	−3.62701	−	6.28217i	−0.391111	−	0.677424i
$87$		0			0
$88$	0.439693	−	0.761570i	0.0468714	−	0.0811836i
$89$	3.01960			0.320077			0.160038	−	0.987111i	$-0.448838\pi$
$89$	3.01960			0.320077			0.160038	+	0.987111i	$0.448838\pi$
$90$		0			0
$91$	4.41147			0.462448
$92$	−2.43969	+	4.22567i	−0.254356	+	0.440557i
$93$		0			0
$94$	11.2836	+	19.5437i	1.16381	+	2.01578i
$95$	−7.52481	−	13.0334i	−0.772030	−	1.33719i
$96$		0			0
$97$	2.86959	−	4.97027i	0.291362	−	0.504654i	−0.682770	−	0.730633i	$-0.739225\pi$
$97$	2.86959	−	4.97027i	0.291362	−	0.504654i	0.974132	+	0.225979i	$0.0725582\pi$
$98$	−12.3550			−1.24805
$99$		0			0
$100$	5.04189			0.504189
$101$	−2.20961	+	3.82715i	−0.219864	+	0.380816i	−0.954766	−	0.297357i	$-0.903895\pi$
$101$	−2.20961	+	3.82715i	−0.219864	+	0.380816i	0.734902	+	0.678173i	$0.237228\pi$
$102$		0			0
$103$	−5.21941	−	9.04028i	−0.514284	−	0.890765i	−0.999863	−	0.0165725i	$-0.994725\pi$
$103$	−5.21941	−	9.04028i	−0.514284	−	0.890765i	0.485579	−	0.874193i	$-0.338609\pi$
$104$	−2.97178	−	5.14728i	−0.291407	−	0.504732i
$105$		0			0
$106$	−9.46451	+	16.3930i	−0.919274	+	1.59223i
$107$	8.31315			0.803662			0.401831	−	0.915714i	$-0.368374\pi$
$107$	8.31315			0.803662			0.401831	+	0.915714i	$0.368374\pi$
$108$		0			0
$109$	−15.9881			−1.53139			−0.765693	−	0.643206i	$-0.777604\pi$
$109$	−15.9881			−1.53139			−0.765693	+	0.643206i	$0.777604\pi$
$110$	2.70574	−	4.68647i	0.257982	−	0.446838i
$111$		0			0
$112$	−1.53936	−	2.66625i	−0.145456	−	0.251937i
$113$	−2.53209	−	4.38571i	−0.238199	−	0.412573i	0.721999	−	0.691894i	$-0.243224\pi$
$113$	−2.53209	−	4.38571i	−0.238199	−	0.412573i	−0.960198	+	0.279322i	$0.909890\pi$
$114$		0			0
$115$	4.58512	−	7.94166i	0.427565	−	0.740564i
$116$	6.16250			0.572174
$117$		0			0
$118$	−19.8357			−1.82603
$119$	−0.0603074	+	0.104455i	−0.00552837	+	0.00957541i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	6.90420	+	11.9584i	0.625077	+	1.08266i
$123$		0			0
$124$	−0.847296	+	1.46756i	−0.0760895	+	0.131791i
$125$	4.92127			0.440172
$126$		0			0
$127$	7.80066			0.692197			0.346098	−	0.938198i	$-0.387506\pi$
$127$	7.80066			0.692197			0.346098	+	0.938198i	$0.387506\pi$
$128$	−3.42127	+	5.92582i	−0.302401	+	0.523774i
$129$		0			0
$130$	−18.2875	−	31.6748i	−1.60392	−	2.77806i
$131$	−6.24897	−	10.8235i	−0.545975	−	0.945657i	−0.998545	−	0.0539276i	$-0.982826\pi$
$131$	−6.24897	−	10.8235i	−0.545975	−	0.945657i	0.452570	−	0.891729i	$-0.350507\pi$
$132$		0			0
$133$	−1.70574	+	2.95442i	−0.147906	+	0.256181i
$134$	−22.1925			−1.91714
$135$		0			0
$136$	0.162504			0.0139346
$137$	7.61334	−	13.1867i	0.650452	−	1.12662i	−0.332562	−	0.943081i	$-0.607913\pi$
$137$	7.61334	−	13.1867i	0.650452	−	1.12662i	0.983013	−	0.183534i	$-0.0587537\pi$
$138$		0			0
$139$	−7.25150	−	12.5600i	−0.615064	−	1.06532i	−0.990373	−	0.138422i	$-0.955797\pi$
$139$	−7.25150	−	12.5600i	−0.615064	−	1.06532i	0.375309	−	0.926900i	$-0.377536\pi$
$140$	−1.43969	−	2.49362i	−0.121676	−	0.210749i
$141$		0			0
$142$	−2.32635	+	4.02936i	−0.195223	+	0.338136i
$143$	−6.75877			−0.565197
$144$		0			0
$145$	−11.5817			−0.961809
$146$	−9.83022	+	17.0264i	−0.813555	+	1.40912i
$147$		0			0
$148$	−0.0812519	−	0.140732i	−0.00667887	−	0.0115681i
$149$	7.30453	+	12.6518i	0.598410	+	1.03648i	0.993056	+	0.117644i	$0.0375341\pi$
$149$	7.30453	+	12.6518i	0.598410	+	1.03648i	−0.394645	+	0.918833i	$0.629133\pi$
$150$		0			0
$151$	10.5535	−	18.2792i	0.858832	−	1.48754i	−0.0142125	−	0.999899i	$-0.504524\pi$
$151$	10.5535	−	18.2792i	0.858832	−	1.48754i	0.873044	−	0.487641i	$-0.162143\pi$
$152$	4.59627			0.372806
$153$		0			0
$154$	−1.22668			−0.0988488
$155$	1.59240	−	2.75811i	0.127904	−	0.221537i
$156$		0			0
$157$	2.21554	+	3.83742i	0.176819	+	0.306260i	0.940789	−	0.338992i	$-0.110086\pi$
$157$	2.21554	+	3.83742i	0.176819	+	0.306260i	−0.763970	+	0.645252i	$0.776753\pi$
$158$	1.37939	+	2.38917i	0.109738	+	0.190072i
$159$		0			0
$160$	−10.2306	+	17.7198i	−0.808796	+	1.40088i
$161$	−2.07873			−0.163827
$162$		0			0
$163$	−2.12567			−0.166495			−0.0832476	−	0.996529i	$-0.526529\pi$
$163$	−2.12567			−0.166495			−0.0832476	+	0.996529i	$0.526529\pi$
$164$	−4.30200	+	7.45129i	−0.335930	+	0.581848i
$165$		0			0
$166$	−0.979055	−	1.69577i	−0.0759894	−	0.131618i
$167$	6.21554	+	10.7656i	0.480973	+	0.833069i	0.999762	−	0.0218332i	$-0.00695027\pi$
$167$	6.21554	+	10.7656i	0.480973	+	0.833069i	−0.518789	+	0.854902i	$0.673617\pi$
$168$		0			0
$169$	−16.3405	+	28.3026i	−1.25696	+	2.17712i
$170$	1.00000			0.0766965
$171$		0			0
$172$	5.91353			0.450903
$173$	1.80200	−	3.12116i	0.137004	−	0.237298i	−0.789357	−	0.613934i	$-0.789586\pi$
$173$	1.80200	−	3.12116i	0.137004	−	0.237298i	0.926361	+	0.376636i	$0.122919\pi$
$174$		0			0
$175$	1.07398	+	1.86018i	0.0811851	+	0.140617i
$176$	2.35844	+	4.08494i	0.177774	+	0.307914i
$177$		0			0
$178$	−2.83750	+	4.91469i	−0.212679	+	0.368371i
$179$	−12.8726			−0.962142			−0.481071	−	0.876682i	$-0.659752\pi$
$179$	−12.8726			−0.962142			−0.481071	+	0.876682i	$0.659752\pi$
$180$		0			0
$181$	−24.3405			−1.80921			−0.904607	−	0.426246i	$-0.859836\pi$
$181$	−24.3405			−1.80921			−0.904607	+	0.426246i	$0.859836\pi$
$182$	−4.14543	+	7.18009i	−0.307280	+	0.532224i
$183$		0			0
$184$	1.40033	+	2.42544i	0.103234	+	0.178806i
$185$	0.152704	+	0.264490i	0.0112270	+	0.0194457i
$186$		0			0
$187$	0.0923963	−	0.160035i	0.00675668	−	0.0117029i
$188$	−18.3969			−1.34173
$189$		0			0
$190$	28.2841			2.05194
$191$	2.97906	−	5.15988i	0.215557	−	0.373355i	−0.737888	−	0.674923i	$-0.764177\pi$
$191$	2.97906	−	5.15988i	0.215557	−	0.373355i	0.953445	+	0.301568i	$0.0975100\pi$
$192$		0			0
$193$	−5.41147	−	9.37295i	−0.389526	−	0.674680i	0.602859	−	0.797847i	$-0.294028\pi$
$193$	−5.41147	−	9.37295i	−0.389526	−	0.674680i	−0.992386	+	0.123168i	$0.960695\pi$
$194$	5.39306	+	9.34105i	0.387199	+	0.670648i
$195$		0			0
$196$	5.03596	−	8.72254i	0.359711	−	0.623038i
$197$	−3.07192			−0.218865			−0.109433	−	0.993994i	$-0.534903\pi$
$197$	−3.07192			−0.218865			−0.109433	+	0.993994i	$0.534903\pi$
$198$		0			0
$199$	1.54664			0.109638			0.0548191	−	0.998496i	$-0.482542\pi$
$199$	1.54664			0.109638			0.0548191	+	0.998496i	$0.482542\pi$
$200$	1.44697	−	2.50622i	0.102316	−	0.177216i
$201$		0			0
$202$	−4.15270	−	7.19269i	−0.292183	−	0.506076i
$203$	1.31268	+	2.27363i	0.0921322	+	0.159578i
$204$		0			0
$205$	8.08512	−	14.0038i	0.564689	−	0.978071i
$206$	19.6186			1.36689
$207$		0			0
$208$	31.8803			2.21050
$209$	2.61334	−	4.52644i	0.180769	−	0.313100i
$210$		0			0
$211$	7.92649	+	13.7291i	0.545682	+	0.945149i	0.998564	+	0.0535783i	$0.0170627\pi$
$211$	7.92649	+	13.7291i	0.545682	+	0.945149i	−0.452882	+	0.891571i	$0.649604\pi$
$212$	−7.71554	−	13.3637i	−0.529905	−	0.917823i
$213$		0			0
$214$	−7.81180	+	13.5304i	−0.534004	+	0.924922i
$215$	−11.1138			−0.757955
$216$		0			0
$217$	−0.721934			−0.0490081
$218$	15.0239	−	26.0222i	1.01755	−	1.76245i
$219$		0			0
$220$	2.20574	+	3.82045i	0.148711	+	0.257575i
$221$	−0.624485	−	1.08164i	−0.0420074	−	0.0727590i
$222$		0			0
$223$	−3.12314	+	5.40944i	−0.209141	+	0.362243i	−0.951444	−	0.307821i	$-0.900400\pi$
$223$	−3.12314	+	5.40944i	−0.209141	+	0.362243i	0.742303	+	0.670064i	$0.233733\pi$
$224$	4.63816			0.309900
$225$		0			0
$226$	9.51754			0.633097
$227$	1.63088	−	2.82477i	0.108245	−	0.187487i	−0.806814	−	0.590805i	$-0.798810\pi$
$227$	1.63088	−	2.82477i	0.108245	−	0.187487i	0.915060	+	0.403319i	$0.132143\pi$
$228$		0			0
$229$	5.40760	+	9.36624i	0.357345	+	0.618939i	0.987516	−	0.157517i	$-0.0503489\pi$
$229$	5.40760	+	9.36624i	0.357345	+	0.618939i	−0.630172	+	0.776456i	$0.717016\pi$
$230$	8.61721	+	14.9254i	0.568202	+	0.984155i
$231$		0			0
$232$	1.76857	−	3.06325i	0.116112	−	0.201112i
$233$	3.71688			0.243501			0.121750	−	0.992561i	$-0.461149\pi$
$233$	3.71688			0.243501			0.121750	+	0.992561i	$0.461149\pi$
$234$		0			0
$235$	34.5749			2.25542
$236$	8.08512	−	14.0038i	0.526297	−	0.911573i
$237$		0			0
$238$	−0.113341	−	0.196312i	−0.00734679	−	0.0127250i
$239$	4.02869	+	6.97789i	0.260594	+	0.451362i	0.966400	−	0.257043i	$-0.0827483\pi$
$239$	4.02869	+	6.97789i	0.260594	+	0.451362i	−0.705806	+	0.708405i	$0.749415\pi$
$240$		0			0
$241$	2.15998	−	3.74119i	0.139136	−	0.240991i	−0.788034	−	0.615632i	$-0.788901\pi$
$241$	2.15998	−	3.74119i	0.139136	−	0.240991i	0.927170	+	0.374641i	$0.122234\pi$
$242$	1.87939			0.120811
$243$		0			0
$244$	−11.2567			−0.720637
$245$	−9.46451	+	16.3930i	−0.604665	+	1.04731i
$246$		0			0
$247$	−17.6630	−	30.5932i	−1.12387	−	1.94660i
$248$	0.486329	+	0.842347i	0.0308819	+	0.0534891i
$249$		0			0
$250$	−4.62449	+	8.00984i	−0.292478	+	0.506587i
$251$	−14.1753			−0.894737			−0.447368	−	0.894350i	$-0.647639\pi$
$251$	−14.1753			−0.894737			−0.447368	+	0.894350i	$0.647639\pi$
$252$		0			0
$253$	3.18479			0.200226
$254$	−7.33022	+	12.6963i	−0.459939	+	0.796638i
$255$		0			0
$256$	−10.3512	−	17.9287i	−0.646948	−	1.12055i
$257$	−4.31655	−	7.47649i	−0.269259	−	0.466370i	0.699412	−	0.714719i	$-0.253445\pi$
$257$	−4.31655	−	7.47649i	−0.269259	−	0.466370i	−0.968671	+	0.248349i	$0.920112\pi$
$258$		0			0
$259$	0.0346151	−	0.0599551i	0.00215088	−	0.00372543i
$260$	29.8161			1.84912
$261$		0			0
$262$	23.4884			1.45112
$263$	0.599670	−	1.03866i	0.0369773	−	0.0640465i	−0.846945	−	0.531681i	$-0.821560\pi$
$263$	0.599670	−	1.03866i	0.0369773	−	0.0640465i	0.883922	+	0.467635i	$0.154894\pi$
$264$		0			0
$265$	14.5005	+	25.1155i	0.890757	+	1.54284i
$266$	−3.20574	−	5.55250i	−0.196556	−	0.340446i
$267$		0			0
$268$	9.04576	−	15.6677i	0.552558	−	0.957058i
$269$	−27.9213			−1.70239			−0.851195	−	0.524849i	$-0.824122\pi$
$269$	−27.9213			−1.70239			−0.851195	+	0.524849i	$0.824122\pi$
$270$		0			0
$271$	−13.4311			−0.815880			−0.407940	−	0.913009i	$-0.633753\pi$
$271$	−13.4311			−0.815880			−0.407940	+	0.913009i	$0.633753\pi$
$272$	−0.435822	+	0.754866i	−0.0264256	+	0.0457705i
$273$		0			0
$274$	14.3084	+	24.7829i	0.864402	+	1.49719i
$275$	−1.64543	−	2.84997i	−0.0992231	−	0.171860i
$276$		0			0
$277$	4.24035	−	7.34451i	0.254778	−	0.441289i	−0.710057	−	0.704144i	$-0.751331\pi$
$277$	4.24035	−	7.34451i	0.254778	−	0.441289i	0.964835	+	0.262855i	$0.0846642\pi$
$278$	27.2567			1.63475
$279$		0			0
$280$	−1.65270			−0.0987679
$281$	−1.26945	+	2.19875i	−0.0757289	+	0.131166i	−0.901403	−	0.432981i	$-0.857462\pi$
$281$	−1.26945	+	2.19875i	−0.0757289	+	0.131166i	0.825674	+	0.564147i	$0.190795\pi$
$282$		0			0
$283$	2.33750	+	4.04866i	0.138950	+	0.240668i	0.927099	−	0.374816i	$-0.122294\pi$
$283$	2.33750	+	4.04866i	0.138950	+	0.240668i	−0.788150	+	0.615484i	$0.788961\pi$
$284$	−1.89646	−	3.28476i	−0.112534	−	0.194915i
$285$		0			0
$286$	6.35117	−	11.0005i	0.375552	−	0.650476i
$287$	−3.66550			−0.216367
$288$		0			0
$289$	−16.9659			−0.997991
$290$	10.8833	−	18.8504i	0.639087	−	1.10693i
$291$		0			0
$292$	−8.01367	−	13.8801i	−0.468965	−	0.812271i
$293$	3.92262	+	6.79417i	0.229162	+	0.396920i	0.957560	−	0.288234i	$-0.0930682\pi$
$293$	3.92262	+	6.79417i	0.229162	+	0.396920i	−0.728398	+	0.685154i	$0.759735\pi$
$294$		0			0
$295$	−15.1951	+	26.3186i	−0.884691	+	1.53233i
$296$	−0.0932736			−0.00542142
$297$		0			0
$298$	−27.4561			−1.59049
$299$	10.7626	−	18.6414i	0.622420	−	1.07806i
$300$		0			0
$301$	1.25965	+	2.18177i	0.0726049	+	0.125755i
$302$	19.8341	+	34.3537i	1.14132	+	1.97683i
$303$		0			0
$304$	−12.3268	+	21.3507i	−0.706992	+	1.22455i
$305$	21.1557			1.21137
$306$		0			0
$307$	26.4047			1.50699			0.753497	−	0.657451i	$-0.228365\pi$
$307$	26.4047			1.50699			0.753497	+	0.657451i	$0.228365\pi$
$308$	0.500000	−	0.866025i	0.0284901	−	0.0493464i
$309$		0			0
$310$	2.99273	+	5.18355i	0.169975	+	0.294406i
$311$	−9.57057	−	16.5767i	−0.542697	−	0.939980i	−0.998748	−	0.0500257i	$-0.984070\pi$
$311$	−9.57057	−	16.5767i	−0.542697	−	0.939980i	0.456050	−	0.889954i	$-0.349264\pi$
$312$		0			0
$313$	4.48545	−	7.76903i	0.253533	−	0.439132i	−0.710963	−	0.703229i	$-0.751741\pi$
$313$	4.48545	−	7.76903i	0.253533	−	0.439132i	0.964496	+	0.264098i	$0.0850741\pi$
$314$	−8.32770			−0.469959
$315$		0			0
$316$	−2.24897			−0.126514
$317$	3.13903	−	5.43696i	0.176306	−	0.305370i	−0.764307	−	0.644853i	$-0.776919\pi$
$317$	3.13903	−	5.43696i	0.176306	−	0.305370i	0.940612	+	0.339483i	$0.110252\pi$
$318$		0			0
$319$	−2.01114	−	3.48340i	−0.112602	−	0.195033i
$320$	−5.64543	−	9.77817i	−0.315589	−	0.546616i
$321$		0			0
$322$	1.95336	−	3.38332i	0.108857	−	0.188545i
$323$	0.965852			0.0537414
$324$		0			0
$325$	−22.2422			−1.23377
$326$	1.99747	−	3.45973i	0.110630	−	0.191617i
$327$		0			0
$328$	2.46926	+	4.27688i	0.136342	+	0.236151i
$329$	−3.91875	−	6.78747i	−0.216048	−	0.374205i
$330$		0			0
$331$	5.93629	−	10.2820i	0.326288	−	0.565147i	−0.655484	−	0.755209i	$-0.727535\pi$
$331$	5.93629	−	10.2820i	0.326288	−	0.565147i	0.981772	+	0.190062i	$0.0608688\pi$
$332$	1.59627			0.0876065
$333$		0			0
$334$	−23.3628			−1.27835
$335$	−17.0005	+	29.4457i	−0.928835	+	1.60879i
$336$		0			0
$337$	−4.52094	−	7.83051i	−0.246272	−	0.426555i	0.716217	−	0.697878i	$-0.245872\pi$
$337$	−4.52094	−	7.83051i	−0.246272	−	0.426555i	−0.962488	+	0.271323i	$0.912539\pi$
$338$	−30.7101	−	53.1914i	−1.67041	−	2.89323i
$339$		0			0
$340$	−0.407604	+	0.705990i	−0.0221054	+	0.0382877i
$341$	1.10607			0.0598969
$342$		0			0
$343$	8.85978			0.478383
$344$	1.69712	−	2.93950i	0.0915025	−	0.158487i
$345$		0			0
$346$	3.38666	+	5.86587i	0.182068	+	0.315351i
$347$	−9.48158	−	16.4226i	−0.508998	−	0.881610i	−0.999946	−	0.0104213i	$-0.996683\pi$
$347$	−9.48158	−	16.4226i	−0.508998	−	0.881610i	0.490948	−	0.871189i	$-0.336651\pi$
$348$		0			0
$349$	11.0642	−	19.1637i	0.592252	−	1.02581i	−0.401677	−	0.915782i	$-0.631572\pi$
$349$	11.0642	−	19.1637i	0.592252	−	1.02581i	0.993928	−	0.110029i	$-0.0350943\pi$
$350$	−4.03684			−0.215778
$351$		0			0
$352$	−7.10607			−0.378755
$353$	−12.2208	+	21.1670i	−0.650445	+	1.12660i	0.332570	+	0.943079i	$0.392084\pi$
$353$	−12.2208	+	21.1670i	−0.650445	+	1.12660i	−0.983015	+	0.183525i	$0.941249\pi$
$354$		0			0
$355$	3.56418	+	6.17334i	0.189167	+	0.327647i
$356$	−2.31315	−	4.00649i	−0.122597	−	0.212344i
$357$		0			0
$358$	12.0963	−	20.9513i	0.639308	−	1.10731i
$359$	4.68685			0.247363			0.123681	−	0.992322i	$-0.460530\pi$
$359$	4.68685			0.247363			0.123681	+	0.992322i	$0.460530\pi$
$360$		0			0
$361$	8.31820			0.437800
$362$	22.8726	−	39.6165i	1.20216	−	2.08220i
$363$		0			0
$364$	−3.37939	−	5.85327i	−0.177128	−	0.306795i
$365$	15.0608	+	26.0860i	0.788317	+	1.36541i
$366$		0			0
$367$	4.50134	−	7.79656i	0.234968	−	0.406977i	−0.724295	−	0.689490i	$-0.757835\pi$
$367$	4.50134	−	7.79656i	0.234968	−	0.406977i	0.959263	+	0.282513i	$0.0911680\pi$
$368$	−15.0223			−0.783091
$369$		0			0
$370$	−0.573978			−0.0298397
$371$	3.28699	−	5.69323i	0.170652	−	0.295578i
$372$		0			0
$373$	−5.13950	−	8.90187i	−0.266113	−	0.460922i	0.701741	−	0.712432i	$-0.252406\pi$
$373$	−5.13950	−	8.90187i	−0.266113	−	0.460922i	−0.967855	+	0.251510i	$0.919073\pi$
$374$	0.173648	+	0.300767i	0.00897913	+	0.0155523i
$375$		0			0
$376$	−5.27972	+	9.14473i	−0.272281	+	0.471604i
$377$	−27.1857			−1.40014
$378$		0			0
$379$	14.2540			0.732180			0.366090	−	0.930579i	$-0.380696\pi$
$379$	14.2540			0.732180			0.366090	+	0.930579i	$0.380696\pi$
$380$	−11.5287	+	19.9683i	−0.591409	+	1.02435i
$381$		0			0
$382$	5.59879	+	9.69739i	0.286459	+	0.496162i
$383$	7.41740	+	12.8473i	0.379012	+	0.656467i	0.990919	−	0.134462i	$-0.0429307\pi$
$383$	7.41740	+	12.8473i	0.379012	+	0.656467i	−0.611907	+	0.790930i	$0.709597\pi$
$384$		0			0
$385$	−0.939693	+	1.62760i	−0.0478912	+	0.0829499i
$386$	20.3405			1.03530
$387$		0			0
$388$	−8.79292			−0.446393
$389$	5.46064	−	9.45810i	0.276865	−	0.479545i	−0.693739	−	0.720227i	$-0.744038\pi$
$389$	5.46064	−	9.45810i	0.276865	−	0.479545i	0.970604	+	0.240682i	$0.0773711\pi$
$390$		0			0
$391$	0.294263	+	0.509678i	0.0148815	+	0.0257755i
$392$	−2.89053	−	5.00654i	−0.145994	−	0.252869i
$393$		0			0
$394$	2.88666	−	4.99984i	0.145428	−	0.251888i
$395$	4.22668			0.212667
$396$		0			0
$397$	−34.5945			−1.73625			−0.868124	−	0.496347i	$-0.834674\pi$
$397$	−34.5945			−1.73625			−0.868124	+	0.496347i	$0.834674\pi$
$398$	−1.45336	+	2.51730i	−0.0728505	+	0.126181i
$399$		0			0
$400$	7.76130	+	13.4430i	0.388065	+	0.672148i
$401$	8.62061	+	14.9313i	0.430493	+	0.745636i	0.996916	−	0.0784791i	$-0.0250064\pi$
$401$	8.62061	+	14.9313i	0.430493	+	0.745636i	−0.566423	+	0.824115i	$0.691673\pi$
$402$		0			0
$403$	3.73783	−	6.47410i	0.186194	−	0.322498i
$404$	6.77063			0.336851
$405$		0			0
$406$	−4.93407			−0.244874
$407$	−0.0530334	+	0.0918566i	−0.00262877	+	0.00455316i
$408$		0			0
$409$	2.21167	+	3.83072i	0.109360	+	0.189417i	0.915511	−	0.402293i	$-0.131787\pi$
$409$	2.21167	+	3.83072i	0.109360	+	0.189417i	−0.806151	+	0.591710i	$0.798453\pi$
$410$	15.1951	+	26.3186i	0.750431	+	1.29978i
$411$		0			0
$412$	−7.99660	+	13.8505i	−0.393964	+	0.682366i
$413$	6.88888			0.338980
$414$		0			0
$415$	−3.00000			−0.147264
$416$	−24.0141	+	41.5937i	−1.17739	+	2.03930i
$417$		0			0
$418$	4.91147	+	8.50692i	0.240228	+	0.416087i
$419$	−8.75877	−	15.1706i	−0.427894	−	0.741134i	0.568792	−	0.822481i	$-0.307411\pi$
$419$	−8.75877	−	15.1706i	−0.427894	−	0.741134i	−0.996686	+	0.0813475i	$0.974078\pi$
$420$		0			0
$421$	−4.95858	+	8.58851i	−0.241666	+	0.418578i	−0.961189	−	0.275891i	$-0.911027\pi$
$421$	−4.95858	+	8.58851i	−0.241666	+	0.418578i	0.719523	+	0.694469i	$0.244361\pi$
$422$	−29.7939			−1.45034
$423$		0			0
$424$	−8.85710			−0.430139
$425$	0.304063	−	0.526653i	0.0147492	−	0.0255464i
$426$		0			0
$427$	−2.39780	−	4.15312i	−0.116038	−	0.200983i
$428$	−6.36824	−	11.0301i	−0.307821	−	0.533161i
$429$		0			0
$430$	10.4436	−	18.0888i	0.503633	−	0.872319i
$431$	2.38238			0.114755			0.0573776	−	0.998353i	$-0.481726\pi$
$431$	2.38238			0.114755			0.0573776	+	0.998353i	$0.481726\pi$
$432$		0			0
$433$	31.1661			1.49775			0.748874	−	0.662712i	$-0.230595\pi$
$433$	31.1661			1.49775			0.748874	+	0.662712i	$0.230595\pi$
$434$	0.678396	−	1.17502i	0.0325640	−	0.0564026i
$435$		0			0
$436$	12.2476	+	21.2135i	0.586555	+	1.01594i
$437$	8.32295	+	14.4158i	0.398141	+	0.689600i
$438$		0			0
$439$	−4.02734	+	6.97556i	−0.192215	+	0.332925i	−0.945984	−	0.324214i	$-0.894900\pi$
$439$	−4.02734	+	6.97556i	−0.192215	+	0.332925i	0.753769	+	0.657139i	$0.228234\pi$
$440$	2.53209			0.120713
$441$		0			0
$442$	2.34730			0.111650
$443$	−5.81773	+	10.0766i	−0.276409	+	0.478754i	−0.970490	−	0.241143i	$-0.922478\pi$
$443$	−5.81773	+	10.0766i	−0.276409	+	0.478754i	0.694081	+	0.719897i	$0.255811\pi$
$444$		0			0
$445$	4.34730	+	7.52974i	0.206082	+	0.356944i
$446$	−5.86959	−	10.1664i	−0.277933	−	0.481394i
$447$		0			0
$448$	−1.27972	+	2.21653i	−0.0604609	+	0.104721i
$449$	25.7442			1.21494			0.607472	−	0.794341i	$-0.292183\pi$
$449$	25.7442			1.21494			0.607472	+	0.794341i	$0.292183\pi$
$450$		0			0
$451$	5.61587			0.264441
$452$	−3.87939	+	6.71929i	−0.182471	+	0.316049i
$453$		0			0
$454$	3.06506	+	5.30883i	0.143850	+	0.249156i
$455$	6.35117	+	11.0005i	0.297747	+	0.515713i
$456$		0			0
$457$	−19.2160	+	33.2831i	−0.898887	+	1.55692i	−0.0699675	+	0.997549i	$0.522290\pi$
$457$	−19.2160	+	33.2831i	−0.898887	+	1.55692i	−0.828919	+	0.559368i	$0.811044\pi$
$458$	−20.3259			−0.949769
$459$		0			0
$460$	−14.0496			−0.655067
$461$	2.79948	−	4.84884i	0.130385	−	0.225833i	−0.793440	−	0.608648i	$-0.791712\pi$
$461$	2.79948	−	4.84884i	0.130385	−	0.225833i	0.923825	+	0.382815i	$0.125045\pi$
$462$		0			0
$463$	−4.64677	−	8.04845i	−0.215954	−	0.374043i	0.737613	−	0.675223i	$-0.235953\pi$
$463$	−4.64677	−	8.04845i	−0.215954	−	0.374043i	−0.953567	+	0.301180i	$0.902619\pi$
$464$	9.48633	+	16.4308i	0.440392	+	0.762781i
$465$		0			0
$466$	−3.49273	+	6.04958i	−0.161797	+	0.280241i
$467$	−17.0642			−0.789636			−0.394818	−	0.918759i	$-0.629192\pi$
$467$	−17.0642			−0.789636			−0.394818	+	0.918759i	$0.629192\pi$
$468$		0			0
$469$	7.70739			0.355894
$470$	−32.4898	+	56.2740i	−1.49864	+	2.59572i
$471$		0			0
$472$	−4.64068	−	8.03790i	−0.213605	−	0.369974i
$473$	−1.92989	−	3.34267i	−0.0887365	−	0.153696i
$474$		0			0
$475$	8.60014	−	14.8959i	0.394601	−	0.683470i
$476$	0.184793			0.00846995
$477$		0			0
$478$	−15.1429			−0.692620
$479$	−19.7101	+	34.1389i	−0.900576	+	1.55984i	−0.0738286	+	0.997271i	$0.523522\pi$
$479$	−19.7101	+	34.1389i	−0.900576	+	1.55984i	−0.826748	+	0.562573i	$0.809812\pi$
$480$		0			0
$481$	0.358441	+	0.620838i	0.0163435	+	0.0283078i
$482$	4.05943	+	7.03114i	0.184902	+	0.320260i
$483$		0			0
$484$	−0.766044	+	1.32683i	−0.0348202	+	0.0603104i
$485$	16.5253			0.750374
$486$		0			0
$487$	−34.9522			−1.58384			−0.791919	−	0.610627i	$-0.790918\pi$
$487$	−34.9522			−1.58384			−0.791919	+	0.610627i	$0.790918\pi$
$488$	−3.23055	+	5.59548i	−0.146240	+	0.253295i
$489$		0			0
$490$	−17.7875	−	30.8088i	−0.803555	−	1.39180i
$491$	−12.0235	−	20.8253i	−0.542612	−	0.939831i	−0.998753	−	0.0499236i	$-0.984102\pi$
$491$	−12.0235	−	20.8253i	−0.542612	−	0.939831i	0.456141	−	0.889907i	$-0.349231\pi$
$492$		0			0
$493$	0.371644	−	0.643707i	0.0167380	−	0.0289911i
$494$	66.3911			2.98707
$495$		0			0
$496$	−5.21719			−0.234259
$497$	0.807934	−	1.39938i	0.0362408	−	0.0627709i
$498$		0			0
$499$	−13.5608	−	23.4879i	−0.607064	−	1.05147i	−0.991722	−	0.128406i	$-0.959014\pi$
$499$	−13.5608	−	23.4879i	−0.607064	−	1.05147i	0.384658	−	0.923059i	$-0.374319\pi$
$500$	−3.76991	−	6.52968i	−0.168596	−	0.292016i
$501$		0			0
$502$	13.3204	−	23.0716i	0.594520	−	1.02974i
$503$	−16.2867			−0.726190			−0.363095	−	0.931752i	$-0.618280\pi$
$503$	−16.2867			−0.726190			−0.363095	+	0.931752i	$0.618280\pi$
$504$		0			0
$505$	−12.7246			−0.566238
$506$	−2.99273	+	5.18355i	−0.133043	+	0.230437i
$507$		0			0
$508$	−5.97565	−	10.3501i	−0.265127	−	0.459213i
$509$	10.6655	+	18.4732i	0.472740	+	0.818809i	0.999513	−	0.0311963i	$-0.00993171\pi$
$509$	10.6655	+	18.4732i	0.472740	+	0.818809i	−0.526773	+	0.850006i	$0.676598\pi$
$510$		0			0
$511$	3.41400	−	5.91322i	0.151026	−	0.261586i
$512$	25.2226			1.11469
$513$		0			0
$514$	16.2249			0.715651
$515$	15.0287	−	26.0304i	0.662243	−	1.14704i
$516$		0			0
$517$	6.00387	+	10.3990i	0.264050	+	0.457348i
$518$	0.0650551	+	0.112679i	0.00285836	+	0.00495082i
$519$		0			0
$520$	8.55690	−	14.8210i	0.375245	−	0.649944i
$521$	39.4671			1.72908			0.864542	−	0.502560i	$-0.167608\pi$
$521$	39.4671			1.72908			0.864542	+	0.502560i	$0.167608\pi$
$522$		0			0
$523$	4.68779			0.204983			0.102491	−	0.994734i	$-0.467319\pi$
$523$	4.68779			0.204983			0.102491	+	0.994734i	$0.467319\pi$
$524$	−9.57398	+	16.5826i	−0.418241	+	0.724415i
$525$		0			0
$526$	1.12701	+	1.95204i	0.0491400	+	0.0851130i
$527$	0.102196	+	0.177009i	0.00445175	+	0.00771065i
$528$		0			0
$529$	6.42855	−	11.1346i	0.279502	−	0.484112i
$530$	−54.5039			−2.36750
$531$		0			0
$532$	5.22668			0.226605
$533$	18.9782	−	32.8712i	0.822036	−	1.42381i
$534$		0			0
$535$	11.9684	+	20.7298i	0.517438	+	0.896229i
$536$	−5.19207	−	8.99292i	−0.224263	−	0.388435i
$537$		0			0
$538$	26.2374	−	45.4445i	1.13118	−	1.95925i
$539$	−6.57398			−0.283161
$540$		0			0
$541$	0.200274			0.00861046			0.00430523	−	0.999991i	$-0.498630\pi$
$541$	0.200274			0.00861046			0.00430523	+	0.999991i	$0.498630\pi$
$542$	12.6211	−	21.8604i	0.542122	−	0.938983i
$543$		0			0
$544$	−0.656574	−	1.13722i	−0.0281504	−	0.0487579i
$545$	−23.0180	−	39.8684i	−0.985983	−	1.70777i
$546$		0			0
$547$	−17.9697	+	31.1245i	−0.768330	+	1.33079i	0.170138	+	0.985420i	$0.445579\pi$
$547$	−17.9697	+	31.1245i	−0.768330	+	1.33079i	−0.938468	+	0.345366i	$0.887755\pi$
$548$	−23.3286			−0.996550
$549$		0			0
$550$	6.18479			0.263720
$551$	10.5116	−	18.2066i	0.447810	−	0.775629i
$552$		0			0
$553$	−0.479055	−	0.829748i	−0.0203715	−	0.0352845i
$554$	7.96926	+	13.8032i	0.338581	+	0.586440i
$555$		0			0
$556$	−11.1099	+	19.2430i	−0.471166	+	0.816084i
$557$	−16.6186			−0.704151			−0.352075	−	0.935972i	$-0.614524\pi$
$557$	−16.6186			−0.704151			−0.352075	+	0.935972i	$0.614524\pi$
$558$		0			0
$559$	−26.0874			−1.10338
$560$	4.43242	−	7.67717i	0.187304	−	0.324420i
$561$		0			0
$562$	−2.38578	−	4.13230i	−0.100638	−	0.174310i
$563$	−6.46316	−	11.1945i	−0.272390	−	0.471793i	0.697083	−	0.716990i	$-0.254481\pi$
$563$	−6.46316	−	11.1945i	−0.272390	−	0.471793i	−0.969473	+	0.245197i	$0.921147\pi$
$564$		0			0
$565$	7.29086	−	12.6281i	0.306729	−	0.531270i
$566$	−8.78611			−0.369308
$567$		0			0
$568$	−2.17705			−0.0913471
$569$	6.73648	−	11.6679i	0.282408	−	0.489145i	−0.689569	−	0.724220i	$-0.742200\pi$
$569$	6.73648	−	11.6679i	0.282408	−	0.489145i	0.971977	+	0.235075i	$0.0755335\pi$
$570$		0			0
$571$	−0.427204	−	0.739939i	−0.0178779	−	0.0309655i	0.856948	−	0.515403i	$-0.172358\pi$
$571$	−0.427204	−	0.739939i	−0.0178779	−	0.0309655i	−0.874826	+	0.484437i	$0.839024\pi$
$572$	5.17752	+	8.96773i	0.216483	+	0.374959i
$573$		0			0
$574$	3.44444	−	5.96595i	0.143768	−	0.249014i
$575$	10.4807			0.437076
$576$		0			0
$577$	−2.22668			−0.0926980			−0.0463490	−	0.998925i	$-0.514759\pi$
$577$	−2.22668			−0.0926980			−0.0463490	+	0.998925i	$0.514759\pi$
$578$	15.9427	−	27.6135i	0.663128	−	1.14857i
$579$		0			0
$580$	8.87211	+	15.3669i	0.368394	+	0.638078i
$581$	0.340022	+	0.588936i	0.0141065	+	0.0244332i
$582$		0			0
$583$	−5.03596	+	8.72254i	−0.208568	+	0.361251i
$584$	−9.19934			−0.380671
$585$		0			0
$586$	−14.7442			−0.609078
$587$	2.41993	−	4.19144i	0.0998812	−	0.172999i	−0.811754	−	0.583999i	$-0.801487\pi$
$587$	2.41993	−	4.19144i	0.0998812	−	0.172999i	0.911635	+	0.411000i	$0.134820\pi$
$588$		0			0
$589$	2.89053	+	5.00654i	0.119102	+	0.206291i
$590$	−28.5574	−	49.4628i	−1.17569	−	2.03635i
$591$		0			0
$592$	0.250152	−	0.433277i	0.0102812	−	0.0178076i
$593$	−42.2523			−1.73509			−0.867546	−	0.497356i	$-0.834304\pi$
$593$	−42.2523			−1.73509			−0.867546	+	0.497356i	$0.834304\pi$
$594$		0			0
$595$	−0.347296			−0.0142378
$596$	11.1912	−	19.3837i	0.458409	−	0.793988i
$597$		0			0
$598$	20.2271	+	35.0344i	0.827150	+	1.43267i
$599$	−1.18227	−	2.04775i	−0.0483061	−	0.0836686i	0.840861	−	0.541251i	$-0.182049\pi$
$599$	−1.18227	−	2.04775i	−0.0483061	−	0.0836686i	−0.889167	+	0.457582i	$0.848716\pi$
$600$		0			0
$601$	6.14455	−	10.6427i	0.250642	−	0.434124i	−0.713061	−	0.701102i	$-0.752692\pi$
$601$	6.14455	−	10.6427i	0.250642	−	0.434124i	0.963703	+	0.266978i	$0.0860251\pi$
$602$	−4.73473			−0.192973
$603$		0			0
$604$	−32.3378			−1.31581
$605$	1.43969	−	2.49362i	0.0585318	−	0.101380i
$606$		0			0
$607$	−7.08765	−	12.2762i	−0.287679	−	0.498274i	0.685576	−	0.728001i	$-0.259550\pi$
$607$	−7.08765	−	12.2762i	−0.287679	−	0.498274i	−0.973255	+	0.229726i	$0.926217\pi$
$608$	−18.5706	−	32.1652i	−0.753136	−	1.30447i
$609$		0			0
$610$	−19.8799	+	34.4329i	−0.804912	+	1.39415i
$611$	81.1576			3.28328
$612$		0			0
$613$	28.5749			1.15413			0.577065	−	0.816698i	$-0.304198\pi$
$613$	28.5749			1.15413			0.577065	+	0.816698i	$0.304198\pi$
$614$	−24.8123	+	42.9761i	−1.00134	+	1.73437i
$615$		0			0
$616$	−0.286989	−	0.497079i	−0.0115631	−	0.0200279i
$617$	9.03983	+	15.6574i	0.363930	+	0.630345i	0.988604	−	0.150541i	$-0.0481015\pi$
$617$	9.03983	+	15.6574i	0.363930	+	0.630345i	−0.624674	+	0.780886i	$0.714768\pi$
$618$		0			0
$619$	−7.73190	+	13.3920i	−0.310771	+	0.538271i	−0.978530	−	0.206107i	$-0.933921\pi$
$619$	−7.73190	+	13.3920i	−0.310771	+	0.538271i	0.667758	+	0.744378i	$0.267254\pi$
$620$	−4.87939			−0.195961
$621$		0			0
$622$	35.9736			1.44241
$623$	0.985452	−	1.70685i	0.0394813	−	0.0683836i
$624$		0			0
$625$	15.3123	+	26.5216i	0.612491	+	1.06087i
$626$	8.42989	+	14.6010i	0.336926	+	0.583573i
$627$		0			0
$628$	3.39440	−	5.87927i	0.135451	−	0.234609i
$629$	−0.0196004			−0.000781518
$630$		0			0
$631$	9.35235			0.372311			0.186156	−	0.982520i	$-0.440397\pi$
$631$	9.35235			0.372311			0.186156	+	0.982520i	$0.440397\pi$
$632$	−0.645430	+	1.11792i	−0.0256738	+	0.0444684i
$633$		0			0
$634$	5.89945	+	10.2182i	0.234297	+	0.405815i
$635$	11.2306	+	19.4519i	0.445671	+	0.771925i
$636$		0			0
$637$	−22.2160	+	38.4792i	−0.880230	+	1.52460i
$638$	7.55943			0.299281
$639$		0			0
$640$	−19.7023			−0.778803
$641$	0.607411	−	1.05207i	0.0239913	−	0.0415541i	−0.853780	−	0.520633i	$-0.825696\pi$
$641$	0.607411	−	1.05207i	0.0239913	−	0.0415541i	0.877772	+	0.479079i	$0.159029\pi$
$642$		0			0
$643$	15.9013	+	27.5418i	0.627085	+	1.08614i	0.988134	+	0.153596i	$0.0490853\pi$
$643$	15.9013	+	27.5418i	0.627085	+	1.08614i	−0.361049	+	0.932547i	$0.617581\pi$
$644$	1.59240	+	2.75811i	0.0627492	+	0.108685i
$645$		0			0
$646$	−0.907604	+	1.57202i	−0.0357092	+	0.0618501i
$647$	−30.6854			−1.20637			−0.603184	−	0.797602i	$-0.706102\pi$
$647$	−30.6854			−1.20637			−0.603184	+	0.797602i	$0.706102\pi$
$648$		0			0
$649$	−10.5544			−0.414296
$650$	20.9008	−	36.2012i	0.819797	−	1.41993i
$651$		0			0
$652$	1.62836	+	2.82039i	0.0637713	+	0.110455i
$653$	3.63176	+	6.29039i	0.142122	+	0.246162i	0.928295	−	0.371844i	$-0.121274\pi$
$653$	3.63176	+	6.29039i	0.142122	+	0.246162i	−0.786174	+	0.618006i	$0.787941\pi$
$654$		0			0
$655$	17.9932	−	31.1651i	0.703052	−	1.21772i
$656$	−26.4894			−1.03424
$657$		0			0
$658$	14.7297			0.574223
$659$	12.7939	−	22.1596i	0.498378	−	0.863216i	−0.501621	−	0.865088i	$-0.667263\pi$
$659$	12.7939	−	22.1596i	0.498378	−	0.863216i	0.999998	+	0.00187222i	$0.000595947\pi$
$660$		0			0
$661$	−3.87804	−	6.71696i	−0.150838	−	0.261260i	0.780698	−	0.624909i	$-0.214864\pi$
$661$	−3.87804	−	6.71696i	−0.150838	−	0.261260i	−0.931536	+	0.363649i	$0.881531\pi$
$662$	11.1566	+	19.3238i	0.433613	+	0.751039i
$663$		0			0
$664$	0.458111	−	0.793471i	0.0177782	−	0.0307927i
$665$	−9.82295			−0.380918
$666$		0			0
$667$	12.8102			0.496011
$668$	9.52276	−	16.4939i	0.368446	−	0.638168i
$669$		0			0
$670$	−31.9504	−	55.3398i	−1.23435	−	2.13796i
$671$	3.67365	+	6.36295i	0.141820	+	0.245639i
$672$		0			0
$673$	21.3025	−	36.8970i	0.821150	−	1.42227i	−0.0836766	−	0.996493i	$-0.526666\pi$
$673$	21.3025	−	36.8970i	0.821150	−	1.42227i	0.904827	−	0.425780i	$-0.140000\pi$
$674$	16.9932			0.654553
$675$		0			0
$676$	50.0702			1.92578
$677$	11.4256	−	19.7897i	0.439122	−	0.760581i	−0.558500	−	0.829504i	$-0.688623\pi$
$677$	11.4256	−	19.7897i	0.439122	−	0.760581i	0.997622	+	0.0689230i	$0.0219563\pi$
$678$		0			0
$679$	−1.87299	−	3.24411i	−0.0718787	−	0.124498i
$680$	0.233956	+	0.405223i	0.00897179	+	0.0155396i
$681$		0			0
$682$	−1.03936	+	1.80023i	−0.0397993	+	0.0689343i
$683$	12.3946			0.474265			0.237132	−	0.971477i	$-0.423792\pi$
$683$	12.3946			0.474265			0.237132	+	0.971477i	$0.423792\pi$
$684$		0			0
$685$	43.8435			1.67517
$686$	−8.32547	+	14.4201i	−0.317868	+	0.550564i
$687$		0			0
$688$	9.10307	+	15.7670i	0.347051	+	0.601111i
$689$	34.0369	+	58.9536i	1.29670	+	2.24595i
$690$		0			0
$691$	−8.21823	+	14.2344i	−0.312636	+	0.541501i	−0.978932	−	0.204186i	$-0.934545\pi$
$691$	−8.21823	+	14.2344i	−0.312636	+	0.541501i	0.666296	+	0.745687i	$0.267879\pi$
$692$	−5.52166			−0.209902
$693$		0			0
$694$	35.6391			1.35284
$695$	20.8799	−	36.1650i	0.792018	−	1.37182i
$696$		0			0
$697$	0.518885	+	0.898735i	0.0196542	+	0.0340420i
$698$	20.7939	+	36.0160i	0.787059	+	1.36323i
$699$		0			0
$700$	1.64543	−	2.84997i	0.0621914	−	0.107719i
$701$	−23.8084			−0.899231			−0.449615	−	0.893222i	$-0.648439\pi$
$701$	−23.8084			−0.899231			−0.449615	+	0.893222i	$0.648439\pi$
$702$		0			0
$703$	−0.554378			−0.0209087
$704$	1.96064	−	3.39592i	0.0738943	−	0.127989i
$705$		0			0
$706$	−22.9675	−	39.7809i	−0.864393	−	1.49717i
$707$	1.44222	+	2.49800i	0.0542402	+	0.0939468i
$708$		0			0
$709$	21.2811	−	36.8599i	0.799227	−	1.38430i	−0.120893	−	0.992666i	$-0.538576\pi$
$709$	21.2811	−	36.8599i	0.799227	−	1.38430i	0.920120	−	0.391636i	$-0.128091\pi$
$710$	−13.3969			−0.502778
$711$		0			0
$712$	−2.65539			−0.0995150
$713$	−1.76130	+	3.05066i	−0.0659611	+	0.114248i
$714$		0			0
$715$	−9.73055	−	16.8538i	−0.363902	−	0.630297i
$716$	9.86097	+	17.0797i	0.368522	+	0.638298i
$717$		0			0
$718$	−4.40420	+	7.62830i	−0.164363	+	0.284686i
$719$	−14.9391			−0.557135			−0.278568	−	0.960417i	$-0.589860\pi$
$719$	−14.9391			−0.557135			−0.278568	+	0.960417i	$0.589860\pi$
$720$		0			0
$721$	−6.81345			−0.253746
$722$	−7.81655	+	13.5387i	−0.290902	+	0.503857i
$723$		0			0
$724$	18.6459	+	32.2956i	0.692969	+	1.20026i
$725$	−6.61839	−	11.4634i	−0.245801	−	0.425740i
$726$		0			0
$727$	−22.1013	+	38.2806i	−0.819693	+	1.41975i	0.0862163	+	0.996276i	$0.472522\pi$
$727$	−22.1013	+	38.2806i	−0.819693	+	1.41975i	−0.905909	+	0.423473i	$0.860811\pi$
$728$	−3.87939			−0.143780
$729$		0			0
$730$	−56.6100			−2.09523
$731$	0.356630	−	0.617701i	0.0131904	−	0.0228465i
$732$		0			0
$733$	−13.4932	−	23.3709i	−0.498382	−	0.863224i	0.501616	−	0.865091i	$-0.332739\pi$
$733$	−13.4932	−	23.3709i	−0.498382	−	0.863224i	−0.999998	+	0.00186678i	$0.999406\pi$
$734$	8.45976	+	14.6527i	0.312255	+	0.540842i
$735$		0			0
$736$	11.3157	−	19.5993i	0.417101	−	0.722441i
$737$	−11.8084			−0.434968
$738$		0			0
$739$	10.5689			0.388784			0.194392	−	0.980924i	$-0.437727\pi$
$739$	10.5689			0.388784			0.194392	+	0.980924i	$0.437727\pi$
$740$	0.233956	−	0.405223i	0.00860038	−	0.0148963i
$741$		0			0
$742$	6.17752	+	10.6998i	0.226784	+	0.392801i
$743$	21.8803	+	37.8978i	0.802711	+	1.39034i	0.917825	+	0.396984i	$0.129943\pi$
$743$	21.8803	+	37.8978i	0.802711	+	1.39034i	−0.115114	+	0.993352i	$0.536723\pi$
$744$		0			0
$745$	−21.0326	+	36.4295i	−0.770573	+	1.33467i
$746$	19.3182			0.707290
$747$		0			0
$748$	−0.283119			−0.0103518
$749$	2.71301	−	4.69907i	0.0991313	−	0.171700i
$750$		0			0
$751$	−3.03091	−	5.24968i	−0.110599	−	0.191564i	0.805413	−	0.592714i	$-0.201944\pi$
$751$	−3.03091	−	5.24968i	−0.110599	−	0.191564i	−0.916012	+	0.401151i	$0.868610\pi$
$752$	−28.3195	−	49.0509i	−1.03271	−	1.78870i
$753$		0			0
$754$	25.5462	−	44.2474i	0.930339	−	1.61139i
$755$	60.7752			2.21184
$756$		0			0
$757$	20.7192			0.753054			0.376527	−	0.926406i	$-0.377118\pi$
$757$	20.7192			0.753054			0.376527	+	0.926406i	$0.377118\pi$
$758$	−13.3944	+	23.1998i	−0.486507	+	0.842654i
$759$		0			0
$760$	6.61721	+	11.4613i	0.240031	+	0.415747i
$761$	−23.7788	−	41.1862i	−0.861982	−	1.49300i	−0.870013	−	0.493029i	$-0.835890\pi$
$761$	−23.7788	−	41.1862i	−0.861982	−	1.49300i	0.00803057	−	0.999968i	$-0.497444\pi$
$762$		0			0
$763$	−5.21776	+	9.03742i	−0.188896	+	0.327177i
$764$	−9.12836			−0.330252
$765$		0			0
$766$	−27.8803			−1.00736
$767$	−35.6673	+	61.7776i	−1.28787	+	2.23066i
$768$		0			0
$769$	−20.8384	−	36.0932i	−0.751453	−	1.30155i	−0.947118	−	0.320884i	$-0.896020\pi$
$769$	−20.8384	−	36.0932i	−0.751453	−	1.30155i	0.195665	−	0.980671i	$-0.437313\pi$
$770$	−1.76604	−	3.05888i	−0.0636438	−	0.110234i
$771$		0			0
$772$	−8.29086	+	14.3602i	−0.298395	+	0.516835i
$773$	40.1652			1.44464			0.722321	−	0.691558i	$-0.243075\pi$
$773$	40.1652			1.44464			0.722321	+	0.691558i	$0.243075\pi$
$774$		0			0
$775$	3.63991			0.130749
$776$	−2.52347	+	4.37078i	−0.0905873	+	0.156902i
$777$		0			0
$778$	10.2626	+	17.7754i	0.367934	+	0.637280i
$779$	14.6762	+	25.4199i	0.525829	+	0.910762i
$780$		0			0
$781$	−1.23783	+	2.14398i	−0.0442929	+	0.0767175i
$782$	−1.10607			−0.0395529
$783$		0			0
$784$	31.0087			1.10745
$785$	−6.37939	+	11.0494i	−0.227690	+	0.394371i
$786$		0			0
$787$	11.2408	+	19.4697i	0.400692	+	0.694019i	0.993810	−	0.111097i	$-0.0354364\pi$
$787$	11.2408	+	19.4697i	0.400692	+	0.694019i	−0.593118	+	0.805116i	$0.702103\pi$
$788$	2.35323	+	4.07591i	0.0838302	+	0.145198i
$789$		0			0
$790$	−3.97178	+	6.87933i	−0.141310	+	0.244755i
$791$	−3.30541			−0.117527
$792$		0			0
$793$	49.6587			1.76343
$794$	32.5082	−	56.3059i	1.15367	−	1.99822i
$795$		0			0
$796$	−1.18479	−	2.05212i	−0.0419939	−	0.0727355i
$797$	−19.9688	−	34.5871i	−0.707333	−	1.22514i	−0.965843	−	0.259128i	$-0.916565\pi$
$797$	−19.9688	−	34.5871i	−0.707333	−	1.22514i	0.258510	−	0.966009i	$-0.416768\pi$
$798$		0			0
$799$	−1.10947	+	1.92166i	−0.0392502	+	0.0679834i
$800$	−23.3851			−0.826787
$801$		0			0
$802$	−32.4029			−1.14419
$803$	−5.23055	+	9.05958i	−0.184582	+	0.319706i
$804$		0			0
$805$	−2.99273	−	5.18355i	−0.105480	−	0.182696i
$806$	7.02481	+	12.1673i	0.247439	+	0.428576i
$807$		0			0
$808$	1.94310	−	3.36554i	0.0683579	−	0.118399i
$809$	−17.9240			−0.630173			−0.315086	−	0.949063i	$-0.602034\pi$
$809$	−17.9240			−0.630173			−0.315086	+	0.949063i	$0.602034\pi$
$810$		0			0
$811$	26.8972			0.944490			0.472245	−	0.881467i	$-0.343444\pi$
$811$	26.8972			0.944490			0.472245	+	0.881467i	$0.343444\pi$
$812$	2.01114	−	3.48340i	0.0705773	−	0.122244i
$813$		0			0
$814$	−0.0996702	−	0.172634i	−0.00349344	−	0.00605081i
$815$	−3.06031	−	5.30061i	−0.107198	−	0.185672i
$816$		0			0
$817$	10.0869	−	17.4711i	0.352897	−	0.611236i
$818$	−8.31315			−0.290662
$819$		0			0
$820$	−24.7743			−0.865154
$821$	−6.00387	+	10.3990i	−0.209537	+	0.362928i	−0.951569	−	0.307436i	$-0.900529\pi$
$821$	−6.00387	+	10.3990i	−0.209537	+	0.362928i	0.742032	+	0.670364i	$0.233862\pi$
$822$		0			0
$823$	6.47952	+	11.2229i	0.225862	+	0.391204i	0.956578	−	0.291477i	$-0.0941468\pi$
$823$	6.47952	+	11.2229i	0.225862	+	0.391204i	−0.730716	+	0.682682i	$0.760814\pi$
$824$	4.58987	+	7.94989i	0.159896	+	0.276947i
$825$		0			0
$826$	−6.47343	+	11.2123i	−0.225239	+	0.390126i
$827$	23.3678			0.812579			0.406290	−	0.913744i	$-0.366822\pi$
$827$	23.3678			0.812579			0.406290	+	0.913744i	$0.366822\pi$
$828$		0			0
$829$	−54.3164			−1.88649			−0.943244	−	0.332100i	$-0.892243\pi$
$829$	−54.3164			−1.88649			−0.943244	+	0.332100i	$0.892243\pi$
$830$	2.81908	−	4.88279i	0.0978516	−	0.169484i
$831$		0			0
$832$	−13.2515	−	22.9523i	−0.459413	−	0.795727i
$833$	−0.607411	−	1.05207i	−0.0210455	−	0.0364520i
$834$		0			0
$835$	−17.8969	+	30.9984i	−0.619349	+	1.07274i
$836$	−8.00774			−0.276954
$837$		0			0
$838$	32.9222			1.13728
$839$	−22.3790	+	38.7615i	−0.772608	+	1.33820i	0.163521	+	0.986540i	$0.447715\pi$
$839$	−22.3790	+	38.7615i	−0.772608	+	1.33820i	−0.936129	+	0.351656i	$0.885619\pi$
$840$		0			0
$841$	6.41060	+	11.1035i	0.221055	+	0.382879i
$842$	−9.31908	−	16.1411i	−0.321157	−	0.556260i
$843$		0			0
$844$	12.1441	−	21.0342i	0.418017	−	0.724026i
$845$	−94.1011			−3.23718
$846$		0			0
$847$	−0.652704			−0.0224272
$848$	23.7540	−	41.1432i	0.815716	−	1.41286i
$849$		0			0
$850$	0.571452	+	0.989783i	0.0196006	+	0.0339493i
$851$	−0.168900	−	0.292544i	−0.00578983	−	0.0100283i
$852$		0			0
$853$	−7.06402	+	12.2352i	−0.241867	+	0.418926i	−0.961246	−	0.275691i	$-0.911093\pi$
$853$	−7.06402	+	12.2352i	−0.241867	+	0.418926i	0.719379	+	0.694618i	$0.244427\pi$
$854$	9.01279			0.308411
$855$		0			0
$856$	−7.31046			−0.249866
$857$	−9.47906	+	16.4182i	−0.323798	+	0.560835i	−0.981268	−	0.192645i	$-0.938293\pi$
$857$	−9.47906	+	16.4182i	−0.323798	+	0.560835i	0.657470	+	0.753481i	$0.271627\pi$
$858$		0			0
$859$	−19.0587	−	33.0107i	−0.650275	−	1.12631i	−0.983056	−	0.183305i	$-0.941320\pi$
$859$	−19.0587	−	33.0107i	−0.650275	−	1.12631i	0.332781	−	0.943004i	$-0.392013\pi$
$860$	8.51367	+	14.7461i	0.290314	+	0.502838i
$861$		0			0
$862$	−2.23870	+	3.87755i	−0.0762505	+	0.132070i
$863$	37.9665			1.29239			0.646197	−	0.763171i	$-0.276359\pi$
$863$	37.9665			1.29239			0.646197	+	0.763171i	$0.276359\pi$
$864$		0			0
$865$	10.3773			0.352840
$866$	−29.2866	+	50.7258i	−0.995198	+	1.72373i
$867$		0			0
$868$	0.553033	+	0.957882i	0.0187712	+	0.0325126i
$869$	0.733956	+	1.27125i	0.0248977	+	0.0431241i
$870$		0			0
$871$	−39.9051	+	69.1177i	−1.35213	+	2.34196i
$872$	14.0597			0.476123
$873$		0			0
$874$	−31.2841			−1.05820
$875$	1.60607	−	2.78179i	0.0542950	−	0.0940416i
$876$		0			0
$877$	−12.5488	−	21.7351i	−0.423741	−	0.733941i	0.572561	−	0.819862i	$-0.305950\pi$
$877$	−12.5488	−	21.7351i	−0.423741	−	0.733941i	−0.996302	+	0.0859209i	$0.972617\pi$
$878$	−7.56893	−	13.1098i	−0.255439	−	0.442433i
$879$		0			0
$880$	−6.79086	+	11.7621i	−0.228920	+	0.396501i
$881$	7.51485			0.253182			0.126591	−	0.991955i	$-0.459596\pi$
$881$	7.51485			0.253182			0.126591	+	0.991955i	$0.459596\pi$
$882$		0			0
$883$	−28.9231			−0.973341			−0.486671	−	0.873586i	$-0.661789\pi$
$883$	−28.9231			−0.973341			−0.486671	+	0.873586i	$0.661789\pi$
$884$	−0.956767	+	1.65717i	−0.0321795	+	0.0557366i
$885$		0			0
$886$	−10.9338	−	18.9378i	−0.367327	−	0.636229i
$887$	0.825008	+	1.42896i	0.0277010	+	0.0479796i	0.879544	−	0.475818i	$-0.157848\pi$
$887$	0.825008	+	1.42896i	0.0277010	+	0.0479796i	−0.851843	+	0.523798i	$0.824515\pi$
$888$		0			0
$889$	2.54576	−	4.40938i	0.0853820	−	0.147886i
$890$	−16.3405			−0.547734
$891$		0			0
$892$	9.56986			0.320423
$893$	−31.3803	+	54.3523i	−1.05010	+	1.81883i
$894$		0			0
$895$	−18.5326	−	32.0993i	−0.619475	−	1.07296i
$896$	2.23308	+	3.86780i	0.0746019	+	0.129214i
$897$		0			0
$898$	−24.1917	+	41.9012i	−0.807286	+	1.39826i
$899$	4.44892			0.148380
$900$		0			0
$901$	−1.86122			−0.0620061
$902$	−5.27719	+	9.14036i	−0.175711	+	0.304341i
$903$		0			0
$904$	2.22668	+	3.85673i	0.0740583	+	0.128273i
$905$	−35.0428	−	60.6959i	−1.16486	−	2.01760i
$906$		0			0
$907$	−13.9213	+	24.1124i	−0.462248	+	0.800638i	−0.999073	−	0.0430565i	$-0.986290\pi$
$907$	−13.9213	+	24.1124i	−0.462248	+	0.800638i	0.536824	+	0.843694i	$0.319624\pi$
$908$	−4.99731			−0.165842
$909$		0			0
$910$	−23.8726			−0.791368
$911$	−8.52188	+	14.7603i	−0.282342	+	0.489031i	−0.971961	−	0.235141i	$-0.924445\pi$
$911$	−8.52188	+	14.7603i	−0.282342	+	0.489031i	0.689619	+	0.724173i	$0.257778\pi$
$912$		0			0
$913$	−0.520945	−	0.902302i	−0.0172407	−	0.0298619i
$914$	−36.1143	−	62.5518i	−1.19455	−	2.06903i
$915$		0			0
$916$	8.28493	−	14.3499i	0.273742	−	0.474135i
$917$	−8.15745			−0.269383
$918$		0			0
$919$	47.4638			1.56569			0.782843	−	0.622219i	$-0.213769\pi$
$919$	47.4638			1.56569			0.782843	+	0.622219i	$0.213769\pi$
$920$	−4.03209	+	6.98378i	−0.132934	+	0.230249i
$921$		0			0
$922$	5.26130	+	9.11283i	0.173272	+	0.300115i
$923$	8.36618	+	14.4907i	0.275376	+	0.476966i
$924$		0			0
$925$	−0.174526	+	0.302287i	−0.00573836	+	0.00993914i
$926$	17.4662			0.573974
$927$		0			0
$928$	−28.5827			−0.938272
$929$	14.4561	−	25.0386i	0.474288	−	0.821490i	−0.525279	−	0.850930i	$-0.676039\pi$
$929$	14.4561	−	25.0386i	0.474288	−	0.821490i	0.999567	+	0.0294398i	$0.00937233\pi$
$930$		0			0
$931$	−17.1800	−	29.7567i	−0.563053	−	0.975237i
$932$	−2.84730	−	4.93166i	−0.0932663	−	0.161542i
$933$		0			0
$934$	16.0351	−	27.7736i	0.524684	−	0.908779i
$935$	0.532089			0.0174012
$936$		0			0
$937$	−4.87258			−0.159180			−0.0795901	−	0.996828i	$-0.525361\pi$
$937$	−4.87258			−0.159180			−0.0795901	+	0.996828i	$0.525361\pi$
$938$	−7.24257	+	12.5445i	−0.236478	+	0.409593i
$939$		0			0
$940$	−26.4859	−	45.8750i	−0.863875	−	1.49628i
$941$	−27.1391	−	47.0063i	−0.884709	−	1.53236i	−0.846047	−	0.533109i	$-0.821024\pi$
$941$	−27.1391	−	47.0063i	−0.884709	−	1.53236i	−0.0386622	−	0.999252i	$-0.512310\pi$
$942$		0			0
$943$	−8.94269	+	15.4892i	−0.291214	+	0.504397i
$944$	49.7837			1.62032
$945$		0			0
$946$	7.25402			0.235849
$947$	−10.7253	+	18.5768i	−0.348527	+	0.603666i	−0.985988	−	0.166817i	$-0.946651\pi$
$947$	−10.7253	+	18.5768i	−0.348527	+	0.603666i	0.637461	+	0.770482i	$0.279985\pi$
$948$		0			0
$949$	35.3521	+	61.2316i	1.14758	+	1.98766i
$950$	16.1630	+	27.9951i	0.524396	+	0.908281i
$951$		0			0
$952$	0.0530334	−	0.0918566i	0.00171882	−	0.00297709i
$953$	13.0601			0.423057			0.211528	−	0.977372i	$-0.432156\pi$
$953$	13.0601			0.423057			0.211528	+	0.977372i	$0.432156\pi$
$954$		0			0
$955$	17.1557			0.555145
$956$	6.17230	−	10.6907i	0.199627	−	0.345763i
$957$		0			0
$958$	−37.0428	−	64.1601i	−1.19680	−	2.07292i
$959$	−4.96926	−	8.60700i	−0.160466	−	0.277935i
$960$		0			0
$961$	14.8883	−	25.7873i	0.480268	−	0.831849i
$962$	−1.34730			−0.0434386
$963$		0			0
$964$	−6.61856			−0.213169
$965$	15.5817	−	26.9883i	0.501593	−	0.868785i
$966$		0			0
$967$	−5.59240	−	9.68631i	−0.179839	−	0.311491i	0.761986	−	0.647593i	$-0.224224\pi$
$967$	−5.59240	−	9.68631i	−0.179839	−	0.311491i	−0.941825	+	0.336103i	$0.890891\pi$
$968$	0.439693	+	0.761570i	0.0141323	+	0.0244778i
$969$		0			0
$970$	−15.5287	+	26.8965i	−0.498596	+	0.863594i
$971$	−28.4935			−0.914400			−0.457200	−	0.889364i	$-0.651148\pi$
$971$	−28.4935			−0.914400			−0.457200	+	0.889364i	$0.651148\pi$
$972$		0			0
$973$	−9.46616			−0.303471
$974$	32.8444	−	56.8881i	1.05240	−	1.82281i
$975$		0			0
$976$	−17.3282	−	30.0133i	−0.554661	−	0.960701i
$977$	−9.96363	−	17.2575i	−0.318765	−	0.552117i	0.661466	−	0.749975i	$-0.269935\pi$
$977$	−9.96363	−	17.2575i	−0.318765	−	0.552117i	−0.980231	+	0.197859i	$0.936601\pi$
$978$		0			0
$979$	−1.50980	+	2.61505i	−0.0482534	+	0.0835774i
$980$	29.0009			0.926401
$981$		0			0
$982$	45.1935			1.44218
$983$	−21.5141	+	37.2636i	−0.686194	+	1.18852i	0.286865	+	0.957971i	$0.407387\pi$
$983$	−21.5141	+	37.2636i	−0.686194	+	1.18852i	−0.973060	+	0.230553i	$0.925947\pi$
$984$		0			0
$985$	−4.42262	−	7.66020i	−0.140916	−	0.244074i
$986$	0.698463	+	1.20977i	0.0222436	+	0.0385270i
$987$		0			0
$988$	−27.0612	+	46.8714i	−0.860933	+	1.49118i
$989$	12.2926			0.390882
$990$		0			0
$991$	−21.1516			−0.671902			−0.335951	−	0.941879i	$-0.609058\pi$
$991$	−21.1516			−0.671902			−0.335951	+	0.941879i	$0.609058\pi$
$992$	3.92989	−	6.80677i	0.124774	−	0.216115i
$993$		0			0
$994$	1.51842	+	2.62998i	0.0481613	+	0.0834178i
$995$	2.22668	+	3.85673i	0.0705906	+	0.122266i
$996$		0			0
$997$	13.4204	−	23.2448i	0.425028	−	0.736170i	−0.571395	−	0.820675i	$-0.693597\pi$
$997$	13.4204	−	23.2448i	0.425028	−	0.736170i	0.996423	+	0.0845048i	$0.0269308\pi$
$998$	50.9718			1.61349
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.e.d.100.1		6
3.2	odd	2		99.2.e.d.34.3	✓	6
9.2	odd	6		891.2.a.l.1.1		3
9.4	even	3	inner	297.2.e.d.199.1		6
9.5	odd	6		99.2.e.d.67.3	yes	6
9.7	even	3		891.2.a.k.1.3		3
33.32	even	2		1089.2.e.h.727.1		6
99.32	even	6		1089.2.e.h.364.1		6
99.43	odd	6		9801.2.a.bd.1.1		3
99.65	even	6		9801.2.a.be.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.d.34.3	✓	6	3.2	odd	2
99.2.e.d.67.3	yes	6	9.5	odd	6
297.2.e.d.100.1		6	1.1	even	1	trivial
297.2.e.d.199.1		6	9.4	even	3	inner
891.2.a.k.1.3		3	9.7	even	3
891.2.a.l.1.1		3	9.2	odd	6
1089.2.e.h.364.1		6	99.32	even	6
1089.2.e.h.727.1		6	33.32	even	2
9801.2.a.bd.1.1		3	99.43	odd	6
9801.2.a.be.1.3		3	99.65	even	6

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 1.62760i) q^{2} +(-0.766044 - 1.32683i) q^{4} +(1.43969 + 2.49362i) q^{5} +(0.326352 - 0.565258i) q^{7} -0.879385 q^{8} -5.41147 q^{10} +(-0.500000 + 0.866025i) q^{11} +(3.37939 + 5.85327i) q^{13} +(0.613341 + 1.06234i) q^{14} +(2.35844 - 4.08494i) q^{16} -0.184793 q^{17} -5.22668 q^{19} +(2.20574 - 3.82045i) q^{20} +(-0.939693 - 1.62760i) q^{22} +(-1.59240 - 2.75811i) q^{23} +(-1.64543 + 2.84997i) q^{25} -12.7023 q^{26} -1.00000 q^{28} +(-2.01114 + 3.48340i) q^{29} +(-0.553033 - 0.957882i) q^{31} +(3.55303 + 6.15403i) q^{32} +(0.173648 - 0.300767i) q^{34} +1.87939 q^{35} +0.106067 q^{37} +(4.91147 - 8.50692i) q^{38} +(-1.26604 - 2.19285i) q^{40} +(-2.80793 - 4.86348i) q^{41} +(-1.92989 + 3.34267i) q^{43} +1.53209 q^{44} +5.98545 q^{46} +(6.00387 - 10.3990i) q^{47} +(3.28699 + 5.69323i) q^{49} +(-3.09240 - 5.35619i) q^{50} +(5.17752 - 8.96773i) q^{52} +10.0719 q^{53} -2.87939 q^{55} +(-0.286989 + 0.497079i) q^{56} +(-3.77972 - 6.54666i) q^{58} +(5.27719 + 9.14036i) q^{59} +(3.67365 - 6.36295i) q^{61} +2.07873 q^{62} -3.92127 q^{64} +(-9.73055 + 16.8538i) q^{65} +(5.90420 + 10.2264i) q^{67} +(0.141559 + 0.245188i) q^{68} +(-1.76604 + 3.05888i) q^{70} +2.47565 q^{71} +10.4611 q^{73} +(-0.0996702 + 0.172634i) q^{74} +(4.00387 + 6.93491i) q^{76} +(0.326352 + 0.565258i) q^{77} +(0.733956 - 1.27125i) q^{79} +13.5817 q^{80} +10.5544 q^{82} +(-0.520945 + 0.902302i) q^{83} +(-0.266044 - 0.460802i) q^{85} +(-3.62701 - 6.28217i) q^{86} +(0.439693 - 0.761570i) q^{88} +3.01960 q^{89} +4.41147 q^{91} +(-2.43969 + 4.22567i) q^{92} +(11.2836 + 19.5437i) q^{94} +(-7.52481 - 13.0334i) q^{95} +(2.86959 - 4.97027i) q^{97} -12.3550 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7} + 6 q^{8} - 12 q^{10} - 3 q^{11} + 9 q^{13} - 3 q^{14} + 6 q^{16} + 6 q^{17} - 18 q^{19} + 3 q^{20} - 6 q^{23} + 6 q^{25} - 24 q^{26} - 6 q^{28} - 6 q^{29} + 9 q^{31} + 9 q^{32}+ \cdots - 24 q^{98}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 + 6 * q^8 - 12 * q^10 - 3 * q^11 + 9 * q^13 - 3 * q^14 + 6 * q^16 + 6 * q^17 - 18 * q^19 + 3 * q^20 - 6 * q^23 + 6 * q^25 - 24 * q^26 - 6 * q^28 - 6 * q^29 + 9 * q^31 + 9 * q^32 - 24 * q^37 + 9 * q^38 - 3 * q^40 - 6 * q^41 - 3 * q^43 + 12 * q^47 + 12 * q^49 - 15 * q^50 + 6 * q^52 - 6 * q^53 - 6 * q^55 + 6 * q^56 + 3 * q^58 + 21 * q^59 + 21 * q^61 + 30 * q^62 - 6 * q^64 - 21 * q^65 - 3 * q^67 + 9 * q^68 - 6 * q^70 - 24 * q^71 - 12 * q^73 - 15 * q^74 + 3 * q^77 + 9 * q^79 + 18 * q^80 + 42 * q^82 + 3 * q^85 + 6 * q^86 - 3 * q^88 + 24 * q^89 + 6 * q^91 - 9 * q^92 + 18 * q^94 - 18 * q^95 + 3 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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