LMFDB - Embedded newform 136.2.n.c.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(9,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("136.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.n (of order $8$, degree $4$, 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:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 28x^{10} + 258x^{8} + 880x^{6} + 1033x^{4} + 132x^{2} + 4 $ x^12 + 28x^10 + 258x^8 + 880x^6 + 1033x^4 + 132*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			121.3
Root			$3.49562i$ of defining polynomial
Character	$\chi$	$=$	136.121
Dual form			136.2.n.c.9.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.47178 - 1.02384i) q^{3} +(-0.392531 - 0.947653i) q^{5} +(-0.893542 + 2.15720i) q^{7} +(2.94010 - 2.94010i) q^{9} +(-4.81196 - 1.99318i) q^{11} +4.35777i q^{13} +(-1.94050 - 1.94050i) q^{15} +(3.77648 + 1.65476i) q^{17} +(-1.89281 - 1.89281i) q^{19} +6.24696i q^{21} +(3.79373 + 1.57141i) q^{23} +(2.79157 - 2.79157i) q^{25} +(1.18554 - 2.86215i) q^{27} +(-1.46962 - 3.54797i) q^{29} +(-10.1411 + 4.20057i) q^{31} -13.9348 q^{33} +2.39502 q^{35} +(1.02168 - 0.423195i) q^{37} +(4.46167 + 10.7714i) q^{39} +(-1.00448 + 2.42504i) q^{41} +(-2.86647 + 2.86647i) q^{43} +(-3.94028 - 1.63212i) q^{45} -10.4047i q^{47} +(1.09465 + 1.09465i) q^{49} +(11.0288 + 0.223677i) q^{51} +(-5.49867 - 5.49867i) q^{53} +5.34245i q^{55} +(-6.61654 - 2.74066i) q^{57} +(7.69489 - 7.69489i) q^{59} +(3.04576 - 7.35311i) q^{61} +(3.71528 + 8.96949i) q^{63} +(4.12965 - 1.71056i) q^{65} +6.44882 q^{67} +10.9861 q^{69} +(1.73561 - 0.718913i) q^{71} +(5.05217 + 12.1970i) q^{73} +(4.04200 - 9.75826i) q^{75} +(8.59937 - 8.59937i) q^{77} +(2.31129 + 0.957366i) q^{79} +4.18540i q^{81} +(0.0232879 + 0.0232879i) q^{83} +(0.0857556 - 4.22833i) q^{85} +(-7.26512 - 7.26512i) q^{87} +7.34936i q^{89} +(-9.40057 - 3.89384i) q^{91} +(-20.7657 + 20.7657i) q^{93} +(-1.05074 + 2.53671i) q^{95} +(-6.98779 - 16.8700i) q^{97} +(-20.0078 + 8.28750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{5} - 8 q^{9} - 12 q^{11} + 20 q^{15} + 4 q^{17} - 4 q^{19} - 8 q^{23} - 16 q^{25} + 24 q^{27} + 8 q^{29} - 32 q^{31} - 24 q^{33} - 32 q^{35} + 4 q^{37} - 8 q^{39} + 16 q^{41} + 8 q^{43} - 64 q^{45}+ \cdots - 68 q^{99}+O(q^{100}) $ 12 * q + 4 * q^5 - 8 * q^9 - 12 * q^11 + 20 * q^15 + 4 * q^17 - 4 * q^19 - 8 * q^23 - 16 * q^25 + 24 * q^27 + 8 * q^29 - 32 * q^31 - 24 * q^33 - 32 * q^35 + 4 * q^37 - 8 * q^39 + 16 * q^41 + 8 * q^43 - 64 * q^45 + 44 * q^49 - 8 * q^51 - 8 * q^53 - 12 * q^57 + 16 * q^59 + 44 * q^61 + 100 * q^63 - 20 * q^65 - 40 * q^67 + 56 * q^69 + 32 * q^71 + 8 * q^73 + 92 * q^75 - 12 * q^77 - 8 * q^79 + 40 * q^83 + 40 * q^85 - 84 * q^87 - 40 * q^91 - 76 * q^93 + 28 * q^95 - 16 * q^97 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.47178	−	1.02384i	1.42708	−	0.591116i	0.470452	−	0.882426i	$-0.344091\pi$
$3$	2.47178	−	1.02384i	1.42708	−	0.591116i	0.956629	+	0.291310i	$0.0940910\pi$
$4$		0			0
$5$	−0.392531	−	0.947653i	−0.175545	−	0.423803i	0.811478	−	0.584383i	$-0.198664\pi$
$5$	−0.392531	−	0.947653i	−0.175545	−	0.423803i	−0.987023	+	0.160580i	$0.948664\pi$
$6$		0			0
$7$	−0.893542	+	2.15720i	−0.337727	+	0.815345i	0.660206	+	0.751084i	$0.270469\pi$
$7$	−0.893542	+	2.15720i	−0.337727	+	0.815345i	−0.997933	+	0.0642606i	$0.979531\pi$
$8$		0			0
$9$	2.94010	−	2.94010i	0.980034	−	0.980034i
$10$		0			0
$11$	−4.81196	−	1.99318i	−1.45086	−	0.600966i	−0.488457	−	0.872588i	$-0.662440\pi$
$11$	−4.81196	−	1.99318i	−1.45086	−	0.600966i	−0.962404	+	0.271622i	$0.912440\pi$
$12$		0			0
$13$			4.35777i			1.20863i	0.796747	+	0.604313i	$0.206552\pi$
$13$			4.35777i			1.20863i	−0.796747	+	0.604313i	$0.793448\pi$
$14$		0			0
$15$	−1.94050	−	1.94050i	−0.501034	−	0.501034i
$16$		0			0
$17$	3.77648	+	1.65476i	0.915930	+	0.401338i
$17$	3.77648	+	1.65476i	0.915930	+	0.401338i
$18$		0			0
$19$	−1.89281	−	1.89281i	−0.434240	−	0.434240i	0.455828	−	0.890068i	$-0.349343\pi$
$19$	−1.89281	−	1.89281i	−0.434240	−	0.434240i	−0.890068	+	0.455828i	$0.849343\pi$
$20$		0			0
$21$			6.24696i			1.36320i
$22$		0			0
$23$	3.79373	+	1.57141i	0.791047	+	0.327662i	0.741364	−	0.671103i	$-0.234179\pi$
$23$	3.79373	+	1.57141i	0.791047	+	0.327662i	0.0496826	+	0.998765i	$0.484179\pi$
$24$		0			0
$25$	2.79157	−	2.79157i	0.558314	−	0.558314i
$26$		0			0
$27$	1.18554	−	2.86215i	0.228157	−	0.550820i
$28$		0			0
$29$	−1.46962	−	3.54797i	−0.272901	−	0.658841i	0.726704	−	0.686951i	$-0.241051\pi$
$29$	−1.46962	−	3.54797i	−0.272901	−	0.658841i	−0.999605	+	0.0281099i	$0.991051\pi$
$30$		0			0
$31$	−10.1411	+	4.20057i	−1.82139	+	0.754444i	−0.846272	+	0.532751i	$0.821158\pi$
$31$	−10.1411	+	4.20057i	−1.82139	+	0.754444i	−0.975117	+	0.221693i	$0.928842\pi$
$32$		0			0
$33$	−13.9348			−2.42574
$34$		0			0
$35$	2.39502			0.404832
$36$		0			0
$37$	1.02168	−	0.423195i	0.167964	−	0.0695728i	−0.297117	−	0.954841i	$-0.596025\pi$
$37$	1.02168	−	0.423195i	0.167964	−	0.0695728i	0.465081	+	0.885268i	$0.346025\pi$
$38$		0			0
$39$	4.46167	+	10.7714i	0.714439	+	1.72481i
$40$		0			0
$41$	−1.00448	+	2.42504i	−0.156874	+	0.378728i	−0.982702	−	0.185195i	$-0.940708\pi$
$41$	−1.00448	+	2.42504i	−0.156874	+	0.378728i	0.825828	+	0.563923i	$0.190708\pi$
$42$		0			0
$43$	−2.86647	+	2.86647i	−0.437132	+	0.437132i	−0.891046	−	0.453914i	$-0.850027\pi$
$43$	−2.86647	+	2.86647i	−0.437132	+	0.437132i	0.453914	+	0.891046i	$0.350027\pi$
$44$		0			0
$45$	−3.94028	−	1.63212i	−0.587382	−	0.243302i
$46$		0			0
$47$		−	10.4047i		−	1.51768i	−0.651280	−	0.758838i	$-0.725767\pi$
$47$		−	10.4047i		−	1.51768i	0.651280	−	0.758838i	$-0.274233\pi$
$48$		0			0
$49$	1.09465	+	1.09465i	0.156379	+	0.156379i
$50$		0			0
$51$	11.0288	+	0.223677i	1.54434	+	0.0313211i
$52$		0			0
$53$	−5.49867	−	5.49867i	−0.755301	−	0.755301i	0.220162	−	0.975463i	$-0.429341\pi$
$53$	−5.49867	−	5.49867i	−0.755301	−	0.755301i	−0.975463	+	0.220162i	$0.929341\pi$
$54$		0			0
$55$			5.34245i			0.720376i
$56$		0			0
$57$	−6.61654	−	2.74066i	−0.876383	−	0.363010i
$58$		0			0
$59$	7.69489	−	7.69489i	1.00179	−	1.00179i	0.00179152	−	0.999998i	$-0.499430\pi$
$59$	7.69489	−	7.69489i	1.00179	−	1.00179i	0.999998	−	0.00179152i	$-0.000570259\pi$
$60$		0			0
$61$	3.04576	−	7.35311i	0.389969	−	0.941469i	−0.599976	−	0.800018i	$-0.704823\pi$
$61$	3.04576	−	7.35311i	0.389969	−	0.941469i	0.989945	−	0.141451i	$-0.0451767\pi$
$62$		0			0
$63$	3.71528	+	8.96949i	0.468082	+	1.13005i
$64$		0			0
$65$	4.12965	−	1.71056i	0.512220	−	0.212169i
$66$		0			0
$67$	6.44882			0.787848			0.393924	−	0.919143i	$-0.371117\pi$
$67$	6.44882			0.787848			0.393924	+	0.919143i	$0.371117\pi$
$68$		0			0
$69$	10.9861			1.32257
$70$		0			0
$71$	1.73561	−	0.718913i	0.205979	−	0.0853193i	−0.277309	−	0.960781i	$-0.589442\pi$
$71$	1.73561	−	0.718913i	0.205979	−	0.0853193i	0.483288	+	0.875462i	$0.339442\pi$
$72$		0			0
$73$	5.05217	+	12.1970i	0.591312	+	1.42755i	0.882236	+	0.470807i	$0.156037\pi$
$73$	5.05217	+	12.1970i	0.591312	+	1.42755i	−0.290924	+	0.956746i	$0.593963\pi$
$74$		0			0
$75$	4.04200	−	9.75826i	0.466730	−	1.12679i
$76$		0			0
$77$	8.59937	−	8.59937i	0.979989	−	0.979989i
$78$		0			0
$79$	2.31129	+	0.957366i	0.260040	+	0.107712i	0.508895	−	0.860829i	$-0.330054\pi$
$79$	2.31129	+	0.957366i	0.260040	+	0.107712i	−0.248855	+	0.968541i	$0.580054\pi$
$80$		0			0
$81$			4.18540i			0.465045i
$82$		0			0
$83$	0.0232879	+	0.0232879i	0.00255618	+	0.00255618i	0.708384	−	0.705828i	$-0.249425\pi$
$83$	0.0232879	+	0.0232879i	0.00255618	+	0.00255618i	−0.705828	+	0.708384i	$0.749425\pi$
$84$		0			0
$85$	0.0857556	−	4.22833i	0.00930150	−	0.458627i
$86$		0			0
$87$	−7.26512	−	7.26512i	−0.778903	−	0.778903i
$88$		0			0
$89$			7.34936i			0.779030i	0.921020	+	0.389515i	$0.127357\pi$
$89$			7.34936i			0.779030i	−0.921020	+	0.389515i	$0.872643\pi$
$90$		0			0
$91$	−9.40057	−	3.89384i	−0.985448	−	0.408186i
$92$		0			0
$93$	−20.7657	+	20.7657i	−2.15330	+	2.15330i
$94$		0			0
$95$	−1.05074	+	2.53671i	−0.107804	+	0.260261i
$96$		0			0
$97$	−6.98779	−	16.8700i	−0.709502	−	1.71289i	−0.701241	−	0.712924i	$-0.747370\pi$
$97$	−6.98779	−	16.8700i	−0.709502	−	1.71289i	−0.00826130	−	0.999966i	$-0.502630\pi$
$98$		0			0
$99$	−20.0078	+	8.28750i	−2.01086	+	0.832925i
$100$		0			0
$101$	9.20094			0.915528			0.457764	−	0.889074i	$-0.348650\pi$
$101$	9.20094			0.915528			0.457764	+	0.889074i	$0.348650\pi$
$102$		0			0
$103$	7.88599			0.777029			0.388515	−	0.921443i	$-0.372988\pi$
$103$	7.88599			0.777029			0.388515	+	0.921443i	$0.372988\pi$
$104$		0			0
$105$	5.91995	−	2.45213i	0.577728	−	0.239303i
$106$		0			0
$107$	−1.67810	−	4.05130i	−0.162228	−	0.391654i	0.821773	−	0.569815i	$-0.192985\pi$
$107$	−1.67810	−	4.05130i	−0.162228	−	0.391654i	−0.984001	+	0.178161i	$0.942985\pi$
$108$		0			0
$109$	2.32974	−	5.62449i	0.223149	−	0.538729i	−0.772166	−	0.635421i	$-0.780826\pi$
$109$	2.32974	−	5.62449i	0.223149	−	0.538729i	0.995314	+	0.0966928i	$0.0308264\pi$
$110$		0			0
$111$	2.09209	−	2.09209i	0.198572	−	0.198572i
$112$		0			0
$113$	−16.8902	−	6.99617i	−1.58890	−	0.658144i	−0.599109	−	0.800667i	$-0.704478\pi$
$113$	−16.8902	−	6.99617i	−1.58890	−	0.658144i	−0.989791	+	0.142523i	$0.954478\pi$
$114$		0			0
$115$		−	4.21197i		−	0.392768i
$116$		0			0
$117$	12.8123	+	12.8123i	1.18449	+	1.18449i
$118$		0			0
$119$	−6.94409	+	6.66802i	−0.636563	+	0.611256i
$120$		0			0
$121$	11.4040	+	11.4040i	1.03673	+	1.03673i
$122$		0			0
$123$			7.02259i			0.633206i
$124$		0			0
$125$	−8.47948	−	3.51232i	−0.758428	−	0.314151i
$126$		0			0
$127$	−6.83989	+	6.83989i	−0.606942	+	0.606942i	−0.942146	−	0.335203i	$-0.891195\pi$
$127$	−6.83989	+	6.83989i	−0.606942	+	0.606942i	0.335203	+	0.942146i	$0.391195\pi$
$128$		0			0
$129$	−4.15045	+	10.0201i	−0.365427	+	0.882219i
$130$		0			0
$131$	3.79494	+	9.16179i	0.331565	+	0.800469i	0.998468	+	0.0553249i	$0.0176195\pi$
$131$	3.79494	+	9.16179i	0.331565	+	0.800469i	−0.666903	+	0.745144i	$0.732381\pi$
$132$		0			0
$133$	5.77448	−	2.39187i	0.500711	−	0.207401i
$134$		0			0
$135$	−3.17768			−0.273491
$136$		0			0
$137$	2.40322			0.205321			0.102661	−	0.994716i	$-0.467264\pi$
$137$	2.40322			0.205321			0.102661	+	0.994716i	$0.467264\pi$
$138$		0			0
$139$	−8.03405	+	3.32781i	−0.681439	+	0.282261i	−0.696428	−	0.717626i	$-0.745229\pi$
$139$	−8.03405	+	3.32781i	−0.681439	+	0.282261i	0.0149893	+	0.999888i	$0.495229\pi$
$140$		0			0
$141$	−10.6527	−	25.7180i	−0.897123	−	2.16585i
$142$		0			0
$143$	8.68581	−	20.9694i	0.726344	−	1.75355i
$144$		0			0
$145$	−2.78537	+	2.78537i	−0.231313	+	0.231313i
$146$		0			0
$147$	3.82649	+	1.58498i	0.315603	+	0.130727i
$148$		0			0
$149$			3.90029i			0.319524i	0.987156	+	0.159762i	$0.0510727\pi$
$149$			3.90029i			0.319524i	−0.987156	+	0.159762i	$0.948927\pi$
$150$		0			0
$151$	2.53060	+	2.53060i	0.205938	+	0.205938i	0.802538	−	0.596601i	$-0.203482\pi$
$151$	2.53060	+	2.53060i	0.205938	+	0.205938i	−0.596601	+	0.802538i	$0.703482\pi$
$152$		0			0
$153$	15.9684	−	6.23806i	1.29097	−	0.504317i
$154$		0			0
$155$	7.96136	+	7.96136i	0.639472	+	0.639472i
$156$		0			0
$157$			13.5186i			1.07890i	0.842018	+	0.539449i	$0.181367\pi$
$157$			13.5186i			1.07890i	−0.842018	+	0.539449i	$0.818633\pi$
$158$		0			0
$159$	−19.2213	−	7.96171i	−1.52435	−	0.631405i
$160$		0			0
$161$	−6.77971	+	6.77971i	−0.534316	+	0.534316i
$162$		0			0
$163$	0.517312	−	1.24890i	0.0405190	−	0.0978216i	−0.902324	−	0.431058i	$-0.858141\pi$
$163$	0.517312	−	1.24890i	0.0405190	−	0.0978216i	0.942843	+	0.333236i	$0.108141\pi$
$164$		0			0
$165$	5.46984	+	13.2053i	0.425826	+	1.02804i
$166$		0			0
$167$	2.52757	−	1.04696i	0.195589	−	0.0810158i	−0.282739	−	0.959197i	$-0.591243\pi$
$167$	2.52757	−	1.04696i	0.195589	−	0.0810158i	0.478328	+	0.878181i	$0.341243\pi$
$168$		0			0
$169$	−5.99012			−0.460778
$170$		0			0
$171$	−11.1301			−0.851141
$172$		0			0
$173$	−3.58906	+	1.48664i	−0.272871	+	0.113027i	−0.514923	−	0.857236i	$-0.672180\pi$
$173$	−3.58906	+	1.48664i	−0.272871	+	0.113027i	0.242052	+	0.970263i	$0.422180\pi$
$174$		0			0
$175$	3.52759	+	8.51635i	0.266661	+	0.643776i
$176$		0			0
$177$	11.1417	−	26.8984i	0.837461	−	2.02181i
$178$		0			0
$179$	−5.91821	+	5.91821i	−0.442348	+	0.442348i	−0.892800	−	0.450452i	$-0.851263\pi$
$179$	−5.91821	+	5.91821i	−0.442348	+	0.442348i	0.450452	+	0.892800i	$0.351263\pi$
$180$		0			0
$181$	−6.48711	−	2.68705i	−0.482183	−	0.199727i	0.128332	−	0.991731i	$-0.459038\pi$
$181$	−6.48711	−	2.68705i	−0.482183	−	0.199727i	−0.610515	+	0.792004i	$0.709038\pi$
$182$		0			0
$183$		−	21.2936i		−	1.57407i
$184$		0			0
$185$	−0.802084	−	0.802084i	−0.0589704	−	0.0589704i
$186$		0			0
$187$	−14.8740	−	15.4898i	−1.08770	−	1.13273i
$188$		0			0
$189$	5.11489	+	5.11489i	0.372054	+	0.372054i
$190$		0			0
$191$			12.6238i			0.913427i	0.889614	+	0.456713i	$0.150973\pi$
$191$			12.6238i			0.913427i	−0.889614	+	0.456713i	$0.849027\pi$
$192$		0			0
$193$	17.3393	+	7.18217i	1.24811	+	0.516984i	0.906240	−	0.422764i	$-0.138940\pi$
$193$	17.3393	+	7.18217i	1.24811	+	0.516984i	0.341869	+	0.939748i	$0.388940\pi$
$194$		0			0
$195$	8.45623	−	8.45623i	0.605563	−	0.605563i
$196$		0			0
$197$	−5.51876	+	13.3235i	−0.393196	+	0.949258i	0.596044	+	0.802952i	$0.296739\pi$
$197$	−5.51876	+	13.3235i	−0.393196	+	0.949258i	−0.989239	+	0.146306i	$0.953261\pi$
$198$		0			0
$199$	−3.66350	−	8.84447i	−0.259699	−	0.626968i	0.739220	−	0.673464i	$-0.235194\pi$
$199$	−3.66350	−	8.84447i	−0.259699	−	0.626968i	−0.998918	+	0.0464963i	$0.985194\pi$
$200$		0			0
$201$	15.9400	−	6.60258i	1.12432	−	0.465710i
$202$		0			0
$203$	8.96683			0.629348
$204$		0			0
$205$	2.69239			0.188045
$206$		0			0
$207$	15.7741	−	6.53383i	1.09637	−	0.454133i
$208$		0			0
$209$	5.33542	+	12.8808i	0.369059	+	0.890986i
$210$		0			0
$211$	0.615646	−	1.48630i	0.0423828	−	0.102321i	−0.901270	−	0.433257i	$-0.857364\pi$
$211$	0.615646	−	1.48630i	0.0423828	−	0.102321i	0.943653	+	0.330936i	$0.107364\pi$
$212$		0			0
$213$	3.55399	−	3.55399i	0.243515	−	0.243515i
$214$		0			0
$215$	3.84159	+	1.59124i	0.261995	+	0.108522i
$216$		0			0
$217$		−	25.6297i		−	1.73986i
$218$		0			0
$219$	24.9757	+	24.9757i	1.68770	+	1.68770i
$220$		0			0
$221$	−7.21106	+	16.4570i	−0.485068	+	1.10702i
$222$		0			0
$223$	6.70407	+	6.70407i	0.448937	+	0.448937i	0.895001	−	0.446064i	$-0.147175\pi$
$223$	6.70407	+	6.70407i	0.448937	+	0.448937i	−0.446064	+	0.895001i	$0.647175\pi$
$224$		0			0
$225$		−	16.4150i		−	1.09433i
$226$		0			0
$227$	2.41865	+	1.00184i	0.160531	+	0.0664943i	0.461502	−	0.887139i	$-0.347311\pi$
$227$	2.41865	+	1.00184i	0.160531	+	0.0664943i	−0.300971	+	0.953633i	$0.597311\pi$
$228$		0			0
$229$	3.48993	−	3.48993i	0.230621	−	0.230621i	−0.582331	−	0.812952i	$-0.697859\pi$
$229$	3.48993	−	3.48993i	0.230621	−	0.230621i	0.812952	+	0.582331i	$0.197859\pi$
$230$		0			0
$231$	12.4513	−	30.0601i	0.819236	−	1.97781i
$232$		0			0
$233$	−0.873453	−	2.10870i	−0.0572218	−	0.138146i	0.892683	−	0.450685i	$-0.148820\pi$
$233$	−0.873453	−	2.10870i	−0.0572218	−	0.138146i	−0.949905	+	0.312540i	$0.898820\pi$
$234$		0			0
$235$	−9.86001	+	4.08415i	−0.643196	+	0.266421i
$236$		0			0
$237$	6.69317			0.434768
$238$		0			0
$239$	−12.1821			−0.787995			−0.393997	−	0.919112i	$-0.628908\pi$
$239$	−12.1821			−0.787995			−0.393997	+	0.919112i	$0.628908\pi$
$240$		0			0
$241$	−13.3105	+	5.51338i	−0.857404	+	0.355148i	−0.767692	−	0.640820i	$-0.778595\pi$
$241$	−13.3105	+	5.51338i	−0.857404	+	0.355148i	−0.0897121	+	0.995968i	$0.528595\pi$
$242$		0			0
$243$	7.84181	+	18.9318i	0.503053	+	1.21448i
$244$		0			0
$245$	0.607666	−	1.46704i	0.0388223	−	0.0937254i
$246$		0			0
$247$	8.24842	−	8.24842i	0.524835	−	0.524835i
$248$		0			0
$249$	0.0814055	+	0.0337193i	0.00515887	+	0.00213687i
$250$		0			0
$251$			17.8445i			1.12634i	0.826342	+	0.563168i	$0.190418\pi$
$251$			17.8445i			1.12634i	−0.826342	+	0.563168i	$0.809582\pi$
$252$		0			0
$253$	−15.1232	−	15.1232i	−0.950785	−	0.950785i
$254$		0			0
$255$	−4.11718	−	10.5393i	−0.257828	−	0.659996i
$256$		0			0
$257$	−3.82080	−	3.82080i	−0.238335	−	0.238335i	0.577825	−	0.816160i	$-0.303901\pi$
$257$	−3.82080	−	3.82080i	−0.238335	−	0.238335i	−0.816160	+	0.577825i	$0.803901\pi$
$258$		0			0
$259$			2.58212i			0.160445i
$260$		0			0
$261$	−14.7522	−	6.11056i	−0.913138	−	0.378234i
$262$		0			0
$263$	6.98795	−	6.98795i	0.430896	−	0.430896i	−0.458037	−	0.888933i	$-0.651447\pi$
$263$	6.98795	−	6.98795i	0.430896	−	0.430896i	0.888933	+	0.458037i	$0.151447\pi$
$264$		0			0
$265$	−3.05244	+	7.36924i	−0.187510	+	0.452689i
$266$		0			0
$267$	7.52459	+	18.1660i	0.460497	+	1.11174i
$268$		0			0
$269$	−24.7296	+	10.2433i	−1.50779	+	0.624546i	−0.975100	−	0.221765i	$-0.928818\pi$
$269$	−24.7296	+	10.2433i	−1.50779	+	0.624546i	−0.532688	+	0.846312i	$0.678818\pi$
$270$		0			0
$271$	26.6483			1.61877			0.809384	−	0.587280i	$-0.199801\pi$
$271$	26.6483			1.61877			0.809384	+	0.587280i	$0.199801\pi$
$272$		0			0
$273$	−27.2228			−1.64760
$274$		0			0
$275$	−18.9970	+	7.86882i	−1.14556	+	0.474508i
$276$		0			0
$277$	−10.7366	−	25.9204i	−0.645097	−	1.55740i	−0.819718	−	0.572767i	$-0.805870\pi$
$277$	−10.7366	−	25.9204i	−0.645097	−	1.55740i	0.174621	−	0.984636i	$-0.444130\pi$
$278$		0			0
$279$	−17.4657	+	42.1658i	−1.04564	+	2.52440i
$280$		0			0
$281$	−14.9649	+	14.9649i	−0.892731	+	0.892731i	−0.994779	−	0.102049i	$-0.967460\pi$
$281$	−14.9649	+	14.9649i	−0.892731	+	0.892731i	0.102049	+	0.994779i	$0.467460\pi$
$282$		0			0
$283$	4.05293	+	1.67878i	0.240922	+	0.0997931i	0.499877	−	0.866096i	$-0.333378\pi$
$283$	4.05293	+	1.67878i	0.240922	+	0.0997931i	−0.258956	+	0.965889i	$0.583378\pi$
$284$		0			0
$285$			7.34598i			0.435139i
$286$		0			0
$287$	−4.33375	−	4.33375i	−0.255813	−	0.255813i
$288$		0			0
$289$	11.5235	+	12.4983i	0.677855	+	0.735195i
$290$		0			0
$291$	−34.5445	−	34.5445i	−2.02503	−	2.02503i
$292$		0			0
$293$		−	11.8892i		−	0.694573i	−0.937759	−	0.347286i	$-0.887103\pi$
$293$		−	11.8892i		−	0.694573i	0.937759	−	0.347286i	$-0.112897\pi$
$294$		0			0
$295$	−10.3126	−	4.27161i	−0.600421	−	0.248703i
$296$		0			0
$297$	−11.4095	+	11.4095i	−0.662049	+	0.662049i
$298$		0			0
$299$	−6.84785	+	16.5322i	−0.396022	+	0.956080i
$300$		0			0
$301$	−3.62224	−	8.74485i	−0.208782	−	0.504045i
$302$		0			0
$303$	22.7427	−	9.42032i	1.30653	−	0.541183i
$304$		0			0
$305$	−8.16375			−0.467455
$306$		0			0
$307$	20.9185			1.19388			0.596941	−	0.802285i	$-0.296383\pi$
$307$	20.9185			1.19388			0.596941	+	0.802285i	$0.296383\pi$
$308$		0			0
$309$	19.4924	−	8.07401i	1.10888	−	0.459315i
$310$		0			0
$311$	2.34082	+	5.65124i	0.132736	+	0.320453i	0.976248	−	0.216658i	$-0.0695157\pi$
$311$	2.34082	+	5.65124i	0.132736	+	0.320453i	−0.843512	+	0.537111i	$0.819516\pi$
$312$		0			0
$313$	−10.9736	+	26.4926i	−0.620264	+	1.49745i	0.231130	+	0.972923i	$0.425758\pi$
$313$	−10.9736	+	26.4926i	−0.620264	+	1.49745i	−0.851394	+	0.524527i	$0.824242\pi$
$314$		0			0
$315$	7.04160	−	7.04160i	0.396749	−	0.396749i
$316$		0			0
$317$	5.79187	+	2.39907i	0.325304	+	0.134745i	0.539358	−	0.842077i	$-0.318667\pi$
$317$	5.79187	+	2.39907i	0.325304	+	0.134745i	−0.214054	+	0.976822i	$0.568667\pi$
$318$		0			0
$319$			20.0019i			1.11989i
$320$		0			0
$321$	−8.29578	−	8.29578i	−0.463026	−	0.463026i
$322$		0			0
$323$	−4.01601	−	10.2803i	−0.223457	−	0.572011i
$324$		0			0
$325$	12.1650	+	12.1650i	0.674793	+	0.674793i
$326$		0			0
$327$		−	16.2878i		−	0.900716i
$328$		0			0
$329$	22.4449	+	9.29700i	1.23743	+	0.512560i
$330$		0			0
$331$	6.76610	−	6.76610i	0.371899	−	0.371899i	−0.496270	−	0.868168i	$-0.665297\pi$
$331$	6.76610	−	6.76610i	0.371899	−	0.371899i	0.868168	+	0.496270i	$0.165297\pi$
$332$		0			0
$333$	1.75961	−	4.24809i	0.0964263	−	0.232794i
$334$		0			0
$335$	−2.53136	−	6.11124i	−0.138303	−	0.333893i
$336$		0			0
$337$	−2.11552	+	0.876277i	−0.115240	+	0.0477339i	−0.439558	−	0.898214i	$-0.644865\pi$
$337$	−2.11552	+	0.876277i	−0.115240	+	0.0477339i	0.324319	+	0.945948i	$0.394865\pi$
$338$		0			0
$339$	−48.9119			−2.65653
$340$		0			0
$341$	57.1709			3.09598
$342$		0			0
$343$	−18.4399	+	7.63806i	−0.995661	+	0.412416i
$344$		0			0
$345$	−4.31239	−	10.4110i	−0.232171	−	0.560512i
$346$		0			0
$347$	−1.53048	+	3.69490i	−0.0821603	+	0.198353i	−0.959621	−	0.281296i	$-0.909236\pi$
$347$	−1.53048	+	3.69490i	−0.0821603	+	0.198353i	0.877461	+	0.479648i	$0.159236\pi$
$348$		0			0
$349$	18.7738	−	18.7738i	1.00494	−	1.00494i	0.00495064	−	0.999988i	$-0.498424\pi$
$349$	18.7738	−	18.7738i	1.00494	−	1.00494i	0.999988	−	0.00495064i	$-0.00157584\pi$
$350$		0			0
$351$	12.4726	+	5.16630i	0.665736	+	0.275757i
$352$		0			0
$353$		−	1.75320i		−	0.0933134i	−0.998911	−	0.0466567i	$-0.985143\pi$
$353$		−	1.75320i		−	0.0933134i	0.998911	−	0.0466567i	$-0.0148567\pi$
$354$		0			0
$355$	−1.36256	−	1.36256i	−0.0723172	−	0.0723172i
$356$		0			0
$357$	−10.3372	+	23.5915i	−0.547104	+	1.24859i
$358$		0			0
$359$	−14.0466	−	14.0466i	−0.741353	−	0.741353i	0.231486	−	0.972838i	$-0.425641\pi$
$359$	−14.0466	−	14.0466i	−0.741353	−	0.741353i	−0.972838	+	0.231486i	$0.925641\pi$
$360$		0			0
$361$		−	11.8345i		−	0.622870i
$362$		0			0
$363$	39.8641	+	16.5123i	2.09232	+	0.866669i
$364$		0			0
$365$	9.57541	−	9.57541i	0.501200	−	0.501200i
$366$		0			0
$367$	6.63148	−	16.0098i	0.346160	−	0.835705i	−0.650906	−	0.759159i	$-0.725611\pi$
$367$	6.63148	−	16.0098i	0.346160	−	0.835705i	0.997066	−	0.0765462i	$-0.0243893\pi$
$368$		0			0
$369$	4.17658	+	10.0832i	0.217424	+	0.524908i
$370$		0			0
$371$	16.7750	−	6.94845i	0.870916	−	0.360745i
$372$		0			0
$373$	0.854460			0.0442423			0.0221211	−	0.999755i	$-0.492958\pi$
$373$	0.854460			0.0442423			0.0221211	+	0.999755i	$0.492958\pi$
$374$		0			0
$375$	−24.5554			−1.26804
$376$		0			0
$377$	15.4612	−	6.40424i	0.796292	−	0.329835i
$378$		0			0
$379$	−11.4441	−	27.6284i	−0.587843	−	1.41918i	−0.885561	−	0.464524i	$-0.846226\pi$
$379$	−11.4441	−	27.6284i	−0.587843	−	1.41918i	0.297718	−	0.954654i	$-0.403774\pi$
$380$		0			0
$381$	−9.90370	+	23.9097i	−0.507382	+	1.22493i
$382$		0			0
$383$	−19.5522	+	19.5522i	−0.999073	+	0.999073i	−1.00000		0.000926910i	$-0.999705\pi$
$383$	−19.5522	+	19.5522i	−0.999073	+	0.999073i	0.000926910		1.00000i	$0.499705\pi$
$384$		0			0
$385$	−11.5247	−	4.77370i	−0.587355	−	0.243291i
$386$		0			0
$387$			16.8554i			0.856809i
$388$		0			0
$389$	−20.7260	−	20.7260i	−1.05085	−	1.05085i	−0.998636	−	0.0522161i	$-0.983372\pi$
$389$	−20.7260	−	20.7260i	−1.05085	−	1.05085i	−0.0522161	−	0.998636i	$-0.516628\pi$
$390$		0			0
$391$	11.7266	+	12.2121i	0.593040	+	0.617593i
$392$		0			0
$393$	18.7605	+	18.7605i	0.946341	+	0.946341i
$394$		0			0
$395$		−	2.56609i		−	0.129114i
$396$		0			0
$397$	17.1844	+	7.11800i	0.862458	+	0.357242i	0.769668	−	0.638444i	$-0.220422\pi$
$397$	17.1844	+	7.11800i	0.862458	+	0.357242i	0.0927899	+	0.995686i	$0.470422\pi$
$398$		0			0
$399$	11.8243	−	11.8243i	0.591956	−	0.591956i
$400$		0			0
$401$	3.03684	−	7.33159i	0.151653	−	0.366122i	−0.829735	−	0.558157i	$-0.811509\pi$
$401$	3.03684	−	7.33159i	0.151653	−	0.366122i	0.981388	+	0.192035i	$0.0615087\pi$
$402$		0			0
$403$	−18.3051	−	44.1924i	−0.911841	−	2.20138i
$404$		0			0
$405$	3.96631	−	1.64290i	0.197088	−	0.0816363i
$406$		0			0
$407$	−5.75980			−0.285503
$408$		0			0
$409$	−6.93345			−0.342837			−0.171418	−	0.985198i	$-0.554835\pi$
$409$	−6.93345			−0.342837			−0.171418	+	0.985198i	$0.554835\pi$
$410$		0			0
$411$	5.94023	−	2.46052i	0.293010	−	0.121369i
$412$		0			0
$413$	9.72372	+	23.4751i	0.478473	+	1.15514i
$414$		0			0
$415$	0.0129276	−	0.0312100i	0.000634592	−	0.00153204i
$416$		0			0
$417$	−16.4512	+	16.4512i	−0.805619	+	0.805619i
$418$		0			0
$419$	23.6912	+	9.81323i	1.15739	+	0.479407i	0.877006	−	0.480480i	$-0.159537\pi$
$419$	23.6912	+	9.81323i	1.15739	+	0.479407i	0.280386	+	0.959887i	$0.409537\pi$
$420$		0			0
$421$			34.5518i			1.68395i	0.539513	+	0.841977i	$0.318608\pi$
$421$			34.5518i			1.68395i	−0.539513	+	0.841977i	$0.681392\pi$
$422$		0			0
$423$	−30.5908	−	30.5908i	−1.48737	−	1.48737i
$424$		0			0
$425$	15.1617	−	5.92291i	0.735449	−	0.287303i
$426$		0			0
$427$	13.1406	+	13.1406i	0.635919	+	0.635919i
$428$		0			0
$429$		−	60.7245i		−	2.93181i
$430$		0			0
$431$	−2.65090	−	1.09804i	−0.127689	−	0.0528907i	0.317924	−	0.948116i	$-0.397014\pi$
$431$	−2.65090	−	1.09804i	−0.127689	−	0.0528907i	−0.445613	+	0.895226i	$0.647014\pi$
$432$		0			0
$433$	11.9564	−	11.9564i	0.574586	−	0.574586i	−0.358820	−	0.933407i	$-0.616821\pi$
$433$	11.9564	−	11.9564i	0.574586	−	0.574586i	0.933407	+	0.358820i	$0.116821\pi$
$434$		0			0
$435$	−4.03303	+	9.73660i	−0.193369	+	0.466834i
$436$		0			0
$437$	−4.20642	−	10.1552i	−0.201220	−	0.485789i
$438$		0			0
$439$	19.2330	−	7.96657i	0.917941	−	0.380223i	0.126850	−	0.991922i	$-0.459513\pi$
$439$	19.2330	−	7.96657i	0.917941	−	0.380223i	0.791091	+	0.611698i	$0.209513\pi$
$440$		0			0
$441$	6.43678			0.306513
$442$		0			0
$443$	−23.5157			−1.11726			−0.558632	−	0.829416i	$-0.688673\pi$
$443$	−23.5157			−1.11726			−0.558632	+	0.829416i	$0.688673\pi$
$444$		0			0
$445$	6.96464	−	2.88485i	0.330156	−	0.136755i
$446$		0			0
$447$	3.99328	+	9.64063i	0.188876	+	0.455986i
$448$		0			0
$449$	3.67748	−	8.87821i	0.173551	−	0.418989i	−0.813039	−	0.582210i	$-0.802188\pi$
$449$	3.67748	−	8.87821i	0.173551	−	0.418989i	0.986590	+	0.163221i	$0.0521883\pi$
$450$		0			0
$451$	9.66708	−	9.66708i	0.455205	−	0.455205i
$452$		0			0
$453$	8.84603	+	3.66414i	0.415623	+	0.172157i
$454$		0			0
$455$			10.4369i			0.489291i
$456$		0			0
$457$	−12.1391	−	12.1391i	−0.567843	−	0.567843i	0.363681	−	0.931524i	$-0.381520\pi$
$457$	−12.1391	−	12.1391i	−0.567843	−	0.567843i	−0.931524	+	0.363681i	$0.881520\pi$
$458$		0			0
$459$	9.21333	−	8.84704i	0.430041	−	0.412945i
$460$		0			0
$461$	−21.3878	−	21.3878i	−0.996131	−	0.996131i	0.00386124	−	0.999993i	$-0.498771\pi$
$461$	−21.3878	−	21.3878i	−0.996131	−	0.996131i	−0.999993	+	0.00386124i	$0.998771\pi$
$462$		0			0
$463$			33.1695i			1.54152i	0.637128	+	0.770758i	$0.280122\pi$
$463$			33.1695i			1.54152i	−0.637128	+	0.770758i	$0.719878\pi$
$464$		0			0
$465$	27.8299	+	11.5275i	1.29058	+	0.534576i
$466$		0			0
$467$	3.94231	−	3.94231i	0.182428	−	0.182428i	−0.609985	−	0.792413i	$-0.708824\pi$
$467$	3.94231	−	3.94231i	0.182428	−	0.182428i	0.792413	+	0.609985i	$0.208824\pi$
$468$		0			0
$469$	−5.76229	+	13.9114i	−0.266078	+	0.642368i
$470$		0			0
$471$	13.8409	+	33.4148i	0.637754	+	1.53967i
$472$		0			0
$473$	19.5067	−	8.07994i	0.896919	−	0.371516i
$474$		0			0
$475$	−10.5678			−0.484885
$476$		0			0
$477$	−32.3333			−1.48044
$478$		0			0
$479$	21.3489	−	8.84301i	0.975457	−	0.404047i	0.162716	−	0.986673i	$-0.447975\pi$
$479$	21.3489	−	8.84301i	0.975457	−	0.404047i	0.812741	+	0.582626i	$0.197975\pi$
$480$		0			0
$481$	1.84418	+	4.45225i	0.0840875	+	0.203005i
$482$		0			0
$483$	−9.81656	+	23.6993i	−0.446669	+	1.07835i
$484$		0			0
$485$	−13.2440	+	13.2440i	−0.601379	+	0.601379i
$486$		0			0
$487$	13.6778	+	5.66554i	0.619801	+	0.256730i	0.670413	−	0.741988i	$-0.266117\pi$
$487$	13.6778	+	5.66554i	0.619801	+	0.256730i	−0.0506118	+	0.998718i	$0.516117\pi$
$488$		0			0
$489$		−	3.61665i		−	0.163551i
$490$		0			0
$491$	−0.370833	−	0.370833i	−0.0167355	−	0.0167355i	0.698690	−	0.715425i	$-0.253767\pi$
$491$	−0.370833	−	0.370833i	−0.0167355	−	0.0167355i	−0.715425	+	0.698690i	$0.753767\pi$
$492$		0			0
$493$	0.321065	−	15.8307i	0.0144600	−	0.712977i
$494$		0			0
$495$	15.7074	+	15.7074i	0.705993	+	0.705993i
$496$		0			0
$497$			4.38644i			0.196759i
$498$		0			0
$499$	14.9111	+	6.17637i	0.667512	+	0.276492i	0.690596	−	0.723241i	$-0.257348\pi$
$499$	14.9111	+	6.17637i	0.667512	+	0.276492i	−0.0230839	+	0.999734i	$0.507348\pi$
$500$		0			0
$501$	5.17568	−	5.17568i	0.231232	−	0.231232i
$502$		0			0
$503$	4.92666	−	11.8940i	0.219669	−	0.530328i	−0.775175	−	0.631747i	$-0.782338\pi$
$503$	4.92666	−	11.8940i	0.219669	−	0.530328i	0.994844	+	0.101419i	$0.0323382\pi$
$504$		0			0
$505$	−3.61165	−	8.71931i	−0.160717	−	0.388004i
$506$		0			0
$507$	−14.8062	+	6.13294i	−0.657568	+	0.272374i
$508$		0			0
$509$	0.684018			0.0303185			0.0151593	−	0.999885i	$-0.495174\pi$
$509$	0.684018			0.0303185			0.0151593	+	0.999885i	$0.495174\pi$
$510$		0			0
$511$	−30.8257			−1.36365
$512$		0			0
$513$	−7.66150	+	3.17350i	−0.338264	+	0.140113i
$514$		0			0
$515$	−3.09549	−	7.47318i	−0.136404	−	0.329308i
$516$		0			0
$517$	−20.7384	+	50.0668i	−0.912072	+	2.20194i
$518$		0			0
$519$	−7.34927	+	7.34927i	−0.322597	+	0.322597i
$520$		0			0
$521$	−4.38938	−	1.81814i	−0.192302	−	0.0796543i	0.284454	−	0.958690i	$-0.408188\pi$
$521$	−4.38938	−	1.81814i	−0.192302	−	0.0796543i	−0.476757	+	0.879035i	$0.658188\pi$
$522$		0			0
$523$		−	40.6707i		−	1.77840i	−0.457515	−	0.889202i	$-0.651260\pi$
$523$		−	40.6707i		−	1.77840i	0.457515	−	0.889202i	$-0.348740\pi$
$524$		0			0
$525$	17.4388	+	17.4388i	0.761092	+	0.761092i
$526$		0			0
$527$	−45.2484	−	0.917691i	−1.97105	−	0.0399753i
$528$		0			0
$529$	−4.34042	−	4.34042i	−0.188714	−	0.188714i
$530$		0			0
$531$		−	45.2475i		−	1.96358i
$532$		0			0
$533$	−10.5678	−	4.37731i	−0.457740	−	0.189602i
$534$		0			0
$535$	−3.18052	+	3.18052i	−0.137506	+	0.137506i
$536$		0			0
$537$	−8.56918	+	20.6878i	−0.369787	+	0.892745i
$538$		0			0
$539$	−3.08558	−	7.44926i	−0.132906	−	0.320862i
$540$		0			0
$541$	−31.9376	+	13.2290i	−1.37310	+	0.568759i	−0.942629	−	0.333843i	$-0.891654\pi$
$541$	−31.9376	+	13.2290i	−1.37310	+	0.568759i	−0.430476	+	0.902602i	$0.641654\pi$
$542$		0			0
$543$	−18.7858			−0.806176
$544$		0			0
$545$	−6.24456			−0.267488
$546$		0			0
$547$	−24.4795	+	10.1397i	−1.04667	+	0.433544i	−0.838701	−	0.544592i	$-0.816685\pi$
$547$	−24.4795	+	10.1397i	−1.04667	+	0.433544i	−0.207967	+	0.978136i	$0.566685\pi$
$548$		0			0
$549$	−12.6640	−	30.5737i	−0.540488	−	1.30485i
$550$		0			0
$551$	−3.93392	+	9.49733i	−0.167591	+	0.404600i
$552$		0			0
$553$	−4.13046	+	4.13046i	−0.175645	+	0.175645i
$554$		0			0
$555$	−2.80378	−	1.16136i	−0.119014	−	0.0492971i
$556$		0			0
$557$			24.1708i			1.02415i	0.858941	+	0.512075i	$0.171123\pi$
$557$			24.1708i			1.02415i	−0.858941	+	0.512075i	$0.828877\pi$
$558$		0			0
$559$	−12.4914	−	12.4914i	−0.528330	−	0.528330i
$560$		0			0
$561$	−52.6244	−	23.0587i	−2.22180	−	0.973541i
$562$		0			0
$563$	2.50308	+	2.50308i	0.105492	+	0.105492i	0.757883	−	0.652391i	$-0.226234\pi$
$563$	2.50308	+	2.50308i	0.105492	+	0.105492i	−0.652391	+	0.757883i	$0.726234\pi$
$564$		0			0
$565$			18.7523i			0.788916i
$566$		0			0
$567$	−9.02875	−	3.73983i	−0.379172	−	0.157058i
$568$		0			0
$569$	11.2348	−	11.2348i	0.470987	−	0.470987i	−0.431247	−	0.902234i	$-0.641926\pi$
$569$	11.2348	−	11.2348i	0.470987	−	0.470987i	0.902234	+	0.431247i	$0.141926\pi$
$570$		0			0
$571$	−6.56569	+	15.8510i	−0.274765	+	0.663342i	−0.999675	−	0.0255019i	$-0.991882\pi$
$571$	−6.56569	+	15.8510i	−0.274765	+	0.663342i	0.724909	+	0.688844i	$0.241882\pi$
$572$		0			0
$573$	12.9248	+	31.2032i	0.539941	+	1.30353i
$574$		0			0
$575$	14.9772	−	6.20374i	0.624591	−	0.258714i
$576$		0			0
$577$	39.0319			1.62492			0.812460	−	0.583017i	$-0.198128\pi$
$577$	39.0319			1.62492			0.812460	+	0.583017i	$0.198128\pi$
$578$		0			0
$579$	50.2122			2.08675
$580$		0			0
$581$	−0.0710453	+	0.0294279i	−0.00294745	+	0.00122088i
$582$		0			0
$583$	15.4996	+	37.4192i	0.641926	+	1.54975i
$584$		0			0
$585$	7.11238	−	17.1708i	0.294061	−	0.709925i
$586$		0			0
$587$	−11.2227	+	11.2227i	−0.463212	+	0.463212i	−0.899707	−	0.436495i	$-0.856220\pi$
$587$	−11.2227	+	11.2227i	−0.463212	+	0.463212i	0.436495	+	0.899707i	$0.356220\pi$
$588$		0			0
$589$	27.1460	+	11.2442i	1.11853	+	0.463311i
$590$		0			0
$591$			38.5830i			1.58709i
$592$		0			0
$593$	7.35714	+	7.35714i	0.302121	+	0.302121i	0.841843	−	0.539722i	$-0.181471\pi$
$593$	7.35714	+	7.35714i	0.302121	+	0.302121i	−0.539722	+	0.841843i	$0.681471\pi$
$594$		0			0
$595$	9.04474	+	3.96318i	0.370798	+	0.162475i
$596$		0			0
$597$	−18.1107	−	18.1107i	−0.741222	−	0.741222i
$598$		0			0
$599$		−	35.7297i		−	1.45988i	−0.683513	−	0.729938i	$-0.739549\pi$
$599$		−	35.7297i		−	1.45988i	0.683513	−	0.729938i	$-0.260451\pi$
$600$		0			0
$601$	−25.7150	−	10.6515i	−1.04894	−	0.434484i	−0.209425	−	0.977825i	$-0.567159\pi$
$601$	−25.7150	−	10.6515i	−1.04894	−	0.434484i	−0.839512	+	0.543341i	$0.817159\pi$
$602$		0			0
$603$	18.9602	−	18.9602i	0.772118	−	0.772118i
$604$		0			0
$605$	6.33063	−	15.2835i	0.257377	−	0.621362i
$606$		0			0
$607$	6.58165	+	15.8895i	0.267141	+	0.644935i	0.999346	−	0.0361486i	$-0.0115090\pi$
$607$	6.58165	+	15.8895i	0.267141	+	0.644935i	−0.732206	+	0.681084i	$0.761509\pi$
$608$		0			0
$609$	22.1640	−	9.18063i	0.898131	−	0.372018i
$610$		0			0
$611$	45.3411			1.83430
$612$		0			0
$613$	−44.0031			−1.77727			−0.888634	−	0.458618i	$-0.848345\pi$
$613$	−44.0031			−1.77727			−0.888634	+	0.458618i	$0.848345\pi$
$614$		0			0
$615$	6.65498	−	2.75658i	0.268355	−	0.111156i
$616$		0			0
$617$	−11.3310	−	27.3555i	−0.456169	−	1.10129i	−0.969936	−	0.243360i	$-0.921750\pi$
$617$	−11.3310	−	27.3555i	−0.456169	−	1.10129i	0.513767	−	0.857930i	$-0.328250\pi$
$618$		0			0
$619$	10.0162	−	24.1812i	0.402584	−	0.971923i	−0.584453	−	0.811428i	$-0.698691\pi$
$619$	10.0162	−	24.1812i	0.402584	−	0.971923i	0.987037	−	0.160495i	$-0.0513091\pi$
$620$		0			0
$621$	8.99523	−	8.99523i	0.360966	−	0.360966i
$622$		0			0
$623$	−15.8540	−	6.56695i	−0.635178	−	0.263099i
$624$		0			0
$625$		−	10.3251i		−	0.413003i
$626$		0			0
$627$	26.3759	+	26.3759i	1.05335	+	1.05335i
$628$		0			0
$629$	4.55865	+	0.0924547i	0.181765	+	0.00368641i
$630$		0			0
$631$	28.4881	+	28.4881i	1.13409	+	1.13409i	0.989490	+	0.144604i	$0.0461908\pi$
$631$	28.4881	+	28.4881i	1.13409	+	1.13409i	0.144604	+	0.989490i	$0.453809\pi$
$632$		0			0
$633$		−	4.30413i		−	0.171074i
$634$		0			0
$635$	9.16672	+	3.79698i	0.363770	+	0.150678i
$636$		0			0
$637$	−4.77024	+	4.77024i	−0.189004	+	0.189004i
$638$		0			0
$639$	2.98919	−	7.21655i	0.118251	−	0.285482i
$640$		0			0
$641$	3.02621	+	7.30593i	0.119528	+	0.288567i	0.972308	−	0.233705i	$-0.0750848\pi$
$641$	3.02621	+	7.30593i	0.119528	+	0.288567i	−0.852779	+	0.522271i	$0.825085\pi$
$642$		0			0
$643$	−5.12127	+	2.12130i	−0.201963	+	0.0836559i	−0.481372	−	0.876516i	$-0.659861\pi$
$643$	−5.12127	+	2.12130i	−0.201963	+	0.0836559i	0.279409	+	0.960172i	$0.409861\pi$
$644$		0			0
$645$	11.1247			0.438036
$646$		0			0
$647$	18.3835			0.722731			0.361366	−	0.932424i	$-0.382311\pi$
$647$	18.3835			0.722731			0.361366	+	0.932424i	$0.382311\pi$
$648$		0			0
$649$	−52.3648	+	21.6902i	−2.05550	+	0.851416i
$650$		0			0
$651$	−26.2408	−	63.3508i	−1.02846	−	2.48291i
$652$		0			0
$653$	13.5240	−	32.6499i	0.529236	−	1.27769i	−0.402789	−	0.915293i	$-0.631959\pi$
$653$	13.5240	−	32.6499i	0.529236	−	1.27769i	0.932024	−	0.362395i	$-0.118041\pi$
$654$		0			0
$655$	7.19257	−	7.19257i	0.281037	−	0.281037i
$656$		0			0
$657$	50.7144	+	21.0066i	1.97856	+	0.819545i
$658$		0			0
$659$		−	0.950773i		−	0.0370369i	−0.999829	−	0.0185184i	$-0.994105\pi$
$659$		−	0.950773i		−	0.0370369i	0.999829	−	0.0185184i	$-0.00589494\pi$
$660$		0			0
$661$	−8.16636	−	8.16636i	−0.317635	−	0.317635i	0.530223	−	0.847858i	$-0.322108\pi$
$661$	−8.16636	−	8.16636i	−0.317635	−	0.317635i	−0.847858	+	0.530223i	$0.822108\pi$
$662$		0			0
$663$	−0.974734	+	48.0610i	−0.0378555	+	1.86653i
$664$		0			0
$665$	−4.53332	−	4.53332i	−0.175795	−	0.175795i
$666$		0			0
$667$		−	15.7694i		−	0.610593i
$668$		0			0
$669$	23.4349	+	9.70704i	0.906044	+	0.375296i
$670$		0			0
$671$	−29.3121	+	29.3121i	−1.13158	+	1.13158i
$672$		0			0
$673$	4.59155	−	11.0850i	0.176991	−	0.427295i	−0.810341	−	0.585958i	$-0.800718\pi$
$673$	4.59155	−	11.0850i	0.176991	−	0.427295i	0.987333	+	0.158663i	$0.0507183\pi$
$674$		0			0
$675$	−4.68036	−	11.2994i	−0.180147	−	0.434914i
$676$		0			0
$677$	38.5010	−	15.9476i	1.47971	−	0.612917i	0.510663	−	0.859781i	$-0.329400\pi$
$677$	38.5010	−	15.9476i	1.47971	−	0.612917i	0.969050	+	0.246864i	$0.0794001\pi$
$678$		0			0
$679$	42.6359			1.63621
$680$		0			0
$681$	7.00409			0.268397
$682$		0			0
$683$	10.4611	−	4.33312i	0.400282	−	0.165802i	−0.173455	−	0.984842i	$-0.555493\pi$
$683$	10.4611	−	4.33312i	0.400282	−	0.165802i	0.573737	+	0.819039i	$0.305493\pi$
$684$		0			0
$685$	−0.943339	−	2.27742i	−0.0360431	−	0.0870158i
$686$		0			0
$687$	5.05319	−	12.1995i	0.192791	−	0.465439i
$688$		0			0
$689$	23.9619	−	23.9619i	0.912877	−	0.912877i
$690$		0			0
$691$	22.8129	+	9.44941i	0.867843	+	0.359472i	0.771770	−	0.635902i	$-0.219372\pi$
$691$	22.8129	+	9.44941i	0.867843	+	0.359472i	0.0960732	+	0.995374i	$0.469372\pi$
$692$		0			0
$693$		−	50.5661i		−	1.92085i
$694$		0			0
$695$	6.30722	+	6.30722i	0.239247	+	0.239247i
$696$		0			0
$697$	−7.80627	+	7.49592i	−0.295684	+	0.283928i
$698$		0			0
$699$	−4.31796	−	4.31796i	−0.163320	−	0.163320i
$700$		0			0
$701$			38.0011i			1.43528i	0.696413	+	0.717642i	$0.254778\pi$
$701$			38.0011i			1.43528i	−0.696413	+	0.717642i	$0.745222\pi$
$702$		0			0
$703$	−2.73488	−	1.13282i	−0.103148	−	0.0427253i
$704$		0			0
$705$	−20.1902	+	20.1902i	−0.760407	+	0.760407i
$706$		0			0
$707$	−8.22143	+	19.8483i	−0.309199	+	0.746471i
$708$		0			0
$709$	−7.48697	−	18.0752i	−0.281179	−	0.678827i	0.718685	−	0.695336i	$-0.244745\pi$
$709$	−7.48697	−	18.0752i	−0.281179	−	0.678827i	−0.999864	+	0.0165097i	$0.994745\pi$
$710$		0			0
$711$	9.61016	−	3.98066i	0.360409	−	0.149286i
$712$		0			0
$713$	−45.0733			−1.68801
$714$		0			0
$715$	−23.2812			−0.870666
$716$		0			0
$717$	−30.1114	+	12.4726i	−1.12453	+	0.465796i
$718$		0			0
$719$	−15.0002	−	36.2137i	−0.559414	−	1.35054i	−0.910231	−	0.414100i	$-0.864096\pi$
$719$	−15.0002	−	36.2137i	−0.559414	−	1.35054i	0.350818	−	0.936444i	$-0.385904\pi$
$720$		0			0
$721$	−7.04646	+	17.0116i	−0.262424	+	0.633547i
$722$		0			0
$723$	−27.2557	+	27.2557i	−1.01365	+	1.01365i
$724$		0			0
$725$	−14.0069	−	5.80186i	−0.520204	−	0.215475i
$726$		0			0
$727$		−	49.8981i		−	1.85062i	−0.379212	−	0.925310i	$-0.623805\pi$
$727$		−	49.8981i		−	1.85062i	0.379212	−	0.925310i	$-0.376195\pi$
$728$		0			0
$729$	29.8878	+	29.8878i	1.10696	+	1.10696i
$730$		0			0
$731$	−15.5685	+	6.08183i	−0.575820	+	0.224945i
$732$		0			0
$733$	19.7537	+	19.7537i	0.729620	+	0.729620i	0.970544	−	0.240924i	$-0.0774505\pi$
$733$	19.7537	+	19.7537i	0.729620	+	0.729620i	−0.240924	+	0.970544i	$0.577451\pi$
$734$		0			0
$735$		−	4.24834i		−	0.156702i
$736$		0			0
$737$	−31.0315	−	12.8536i	−1.14306	−	0.473470i
$738$		0			0
$739$	−21.3501	+	21.3501i	−0.785375	+	0.785375i	−0.980732	−	0.195357i	$-0.937413\pi$
$739$	−21.3501	+	21.3501i	−0.785375	+	0.785375i	0.195357	+	0.980732i	$0.437413\pi$
$740$		0			0
$741$	11.9432	−	28.8333i	0.438743	−	1.05922i
$742$		0			0
$743$	−2.00765	−	4.84689i	−0.0736534	−	0.177815i	0.882765	−	0.469815i	$-0.155679\pi$
$743$	−2.00765	−	4.84689i	−0.0736534	−	0.177815i	−0.956418	+	0.292000i	$0.905679\pi$
$744$		0			0
$745$	3.69612	−	1.53098i	0.135415	−	0.0560909i
$746$		0			0
$747$	0.136937			0.00501028
$748$		0			0
$749$	10.2389			0.374122
$750$		0			0
$751$	13.3168	−	5.51601i	0.485938	−	0.201282i	−0.126244	−	0.991999i	$-0.540292\pi$
$751$	13.3168	−	5.51601i	0.485938	−	0.201282i	0.612182	+	0.790717i	$0.290292\pi$
$752$		0			0
$753$	18.2700	+	44.1077i	0.665796	+	1.60737i
$754$		0			0
$755$	1.40480	−	3.39148i	0.0511257	−	0.123428i
$756$		0			0
$757$	−4.45055	+	4.45055i	−0.161758	+	0.161758i	−0.783345	−	0.621587i	$-0.786488\pi$
$757$	−4.45055	+	4.45055i	−0.161758	+	0.161758i	0.621587	+	0.783345i	$0.286488\pi$
$758$		0			0
$759$	−52.8648	−	21.8973i	−1.91887	−	0.794822i
$760$		0			0
$761$		−	6.45544i		−	0.234010i	−0.993131	−	0.117005i	$-0.962671\pi$
$761$		−	6.45544i		−	0.234010i	0.993131	−	0.117005i	$-0.0373293\pi$
$762$		0			0
$763$	10.0514	+	10.0514i	0.363886	+	0.363886i
$764$		0			0
$765$	−12.1796	−	12.6839i	−0.440354	−	0.458586i
$766$		0			0
$767$	33.5325	+	33.5325i	1.21079	+	1.21079i
$768$		0			0
$769$		−	0.665285i		−	0.0239908i	−0.999928	−	0.0119954i	$-0.996182\pi$
$769$		−	0.665285i		−	0.0239908i	0.999928	−	0.0119954i	$-0.00381835\pi$
$770$		0			0
$771$	−13.3561	−	5.53227i	−0.481007	−	0.199240i
$772$		0			0
$773$	3.09332	−	3.09332i	0.111259	−	0.111259i	−0.649286	−	0.760545i	$-0.724932\pi$
$773$	3.09332	−	3.09332i	0.111259	−	0.111259i	0.760545	+	0.649286i	$0.224932\pi$
$774$		0			0
$775$	−16.5833	+	40.0356i	−0.595690	+	1.43812i
$776$		0			0
$777$	2.64368	+	6.38241i	0.0948416	+	0.228968i
$778$		0			0
$779$	6.49144	−	2.68884i	0.232580	−	0.0963378i
$780$		0			0
$781$	−9.78461			−0.350121
$782$		0			0
$783$	−11.8971			−0.425167
$784$		0			0
$785$	12.8109	−	5.30645i	0.457241	−	0.189395i
$786$		0			0
$787$	−2.82833	−	6.82819i	−0.100819	−	0.243399i	0.865419	−	0.501048i	$-0.167052\pi$
$787$	−2.82833	−	6.82819i	−0.100819	−	0.243399i	−0.966238	+	0.257649i	$0.917052\pi$
$788$		0			0
$789$	10.1181	−	24.4272i	0.360213	−	0.869632i
$790$		0			0
$791$	30.1843	−	30.1843i	1.07323	−	1.07323i
$792$		0			0
$793$	32.0431	+	13.2727i	1.13788	+	0.471327i
$794$		0			0
$795$			21.3403i			0.756863i
$796$		0			0
$797$	15.9635	+	15.9635i	0.565458	+	0.565458i	0.930853	−	0.365395i	$-0.119066\pi$
$797$	15.9635	+	15.9635i	0.565458	+	0.565458i	−0.365395	+	0.930853i	$0.619066\pi$
$798$		0			0
$799$	17.2172	−	39.2930i	0.609101	−	1.39008i
$800$		0			0
$801$	21.6078	+	21.6078i	0.763476	+	0.763476i
$802$		0			0
$803$		−	68.7615i		−	2.42654i
$804$		0			0
$805$	9.08606	+	3.76357i	0.320241	+	0.132648i
$806$		0			0
$807$	−50.6384	+	50.6384i	−1.78256	+	1.78256i
$808$		0			0
$809$	1.68152	−	4.05955i	0.0591191	−	0.142726i	−0.891560	−	0.452903i	$-0.850388\pi$
$809$	1.68152	−	4.05955i	0.0591191	−	0.142726i	0.950679	+	0.310177i	$0.100388\pi$
$810$		0			0
$811$	4.35027	+	10.5025i	0.152759	+	0.368792i	0.981670	−	0.190588i	$-0.0610394\pi$
$811$	4.35027	+	10.5025i	0.152759	+	0.368792i	−0.828912	+	0.559380i	$0.811039\pi$
$812$		0			0
$813$	65.8686	−	27.2837i	2.31011	−	0.956880i
$814$		0			0
$815$	−1.38659			−0.0485700
$816$		0			0
$817$	10.8514			0.379641
$818$		0			0
$819$	−39.0869	+	16.1903i	−1.36581	+	0.565736i
$820$		0			0
$821$	17.2551	+	41.6575i	0.602207	+	1.45386i	0.871304	+	0.490743i	$0.163275\pi$
$821$	17.2551	+	41.6575i	0.602207	+	1.45386i	−0.269097	+	0.963113i	$0.586725\pi$
$822$		0			0
$823$	4.09403	−	9.88385i	0.142709	−	0.344529i	−0.836323	−	0.548237i	$-0.815299\pi$
$823$	4.09403	−	9.88385i	0.142709	−	0.344529i	0.979032	+	0.203708i	$0.0652992\pi$
$824$		0			0
$825$	−38.8999	+	38.8999i	−1.35432	+	1.35432i
$826$		0			0
$827$	−46.9906	−	19.4641i	−1.63402	−	0.676834i	−0.638348	−	0.769748i	$-0.720382\pi$
$827$	−46.9906	−	19.4641i	−1.63402	−	0.676834i	−0.995674	+	0.0929138i	$0.970382\pi$
$828$		0			0
$829$			6.52156i			0.226503i	0.993566	+	0.113252i	$0.0361266\pi$
$829$			6.52156i			0.226503i	−0.993566	+	0.113252i	$0.963873\pi$
$830$		0			0
$831$	−53.0767	−	53.0767i	−1.84121	−	1.84121i
$832$		0			0
$833$	2.32254	+	5.94531i	0.0804712	+	0.205993i
$834$		0			0
$835$	−1.98430	−	1.98430i	−0.0686696	−	0.0686696i
$836$		0			0
$837$			34.0051i			1.17539i
$838$		0			0
$839$	7.72808	+	3.20108i	0.266803	+	0.110513i	0.512075	−	0.858941i	$-0.328877\pi$
$839$	7.72808	+	3.20108i	0.266803	+	0.110513i	−0.245272	+	0.969454i	$0.578877\pi$
$840$		0			0
$841$	10.0778	−	10.0778i	0.347511	−	0.347511i
$842$		0			0
$843$	−21.6682	+	52.3116i	−0.746291	+	1.80171i
$844$		0			0
$845$	2.35131	+	5.67656i	0.0808874	+	0.195279i
$846$		0			0
$847$	−34.7907	+	14.4108i	−1.19542	+	0.495161i
$848$		0			0
$849$	11.7367			0.402804
$850$		0			0
$851$	4.54100			0.155663
$852$		0			0
$853$	−2.86110	+	1.18511i	−0.0979622	+	0.0405773i	−0.431126	−	0.902292i	$-0.641884\pi$
$853$	−2.86110	+	1.18511i	−0.0979622	+	0.0405773i	0.333164	+	0.942869i	$0.391884\pi$
$854$		0			0
$855$	4.36891	+	10.5475i	0.149414	+	0.360716i
$856$		0			0
$857$	3.14145	−	7.58414i	0.107310	−	0.259069i	−0.861099	−	0.508438i	$-0.830223\pi$
$857$	3.14145	−	7.58414i	0.107310	−	0.259069i	0.968409	+	0.249369i	$0.0802231\pi$
$858$		0			0
$859$	−7.93014	+	7.93014i	−0.270573	+	0.270573i	−0.829331	−	0.558758i	$-0.811278\pi$
$859$	−7.93014	+	7.93014i	−0.270573	+	0.270573i	0.558758	+	0.829331i	$0.311278\pi$
$860$		0			0
$861$	−15.1491	−	6.27498i	−0.516281	−	0.213851i
$862$		0			0
$863$		−	34.8722i		−	1.18706i	−0.804811	−	0.593532i	$-0.797733\pi$
$863$		−	34.8722i		−	1.18706i	0.804811	−	0.593532i	$-0.202267\pi$
$864$		0			0
$865$	2.81763	+	2.81763i	0.0958024	+	0.0958024i
$866$		0			0
$867$	41.2799	+	19.0948i	1.40194	+	0.648492i
$868$		0			0
$869$	−9.21361	−	9.21361i	−0.312550	−	0.312550i
$870$		0			0
$871$			28.1024i			0.952215i
$872$		0			0
$873$	−70.1443	−	29.0547i	−2.37403	−	0.983354i
$874$		0			0
$875$	15.1535	−	15.1535i	0.512283	−	0.512283i
$876$		0			0
$877$	4.71367	−	11.3798i	0.159169	−	0.384269i	−0.824095	−	0.566451i	$-0.808316\pi$
$877$	4.71367	−	11.3798i	0.159169	−	0.384269i	0.983265	+	0.182182i	$0.0583160\pi$
$878$		0			0
$879$	−12.1726	−	29.3874i	−0.410573	−	0.991211i
$880$		0			0
$881$	−38.7338	+	16.0441i	−1.30498	+	0.540538i	−0.923414	−	0.383805i	$-0.874613\pi$
$881$	−38.7338	+	16.0441i	−1.30498	+	0.540538i	−0.381561	+	0.924344i	$0.624613\pi$
$882$		0			0
$883$	14.6148			0.491828			0.245914	−	0.969292i	$-0.420912\pi$
$883$	14.6148			0.491828			0.245914	+	0.969292i	$0.420912\pi$
$884$		0			0
$885$	−29.8638			−1.00386
$886$		0			0
$887$	−5.37765	+	2.22750i	−0.180564	+	0.0747920i	−0.471134	−	0.882062i	$-0.656155\pi$
$887$	−5.37765	+	2.22750i	−0.180564	+	0.0747920i	0.290570	+	0.956854i	$0.406155\pi$
$888$		0			0
$889$	−8.64329	−	20.8667i	−0.289887	−	0.699848i
$890$		0			0
$891$	8.34226	−	20.1400i	0.279476	−	0.674715i
$892$		0			0
$893$	−19.6941	+	19.6941i	−0.659036	+	0.659036i
$894$		0			0
$895$	7.93150	+	3.28533i	0.265121	+	0.109817i
$896$		0			0
$897$			47.8750i			1.59850i
$898$		0			0
$899$	29.8069	+	29.8069i	0.994117	+	0.994117i
$900$		0			0
$901$	−11.6666	−	29.8646i	−0.388672	−	0.994934i
$902$		0			0
$903$	−17.9067	−	17.9067i	−0.595898	−	0.595898i
$904$		0			0
$905$			7.20228i			0.239412i
$906$		0			0
$907$	−2.22827	−	0.922978i	−0.0739884	−	0.0306470i	0.345382	−	0.938462i	$-0.387749\pi$
$907$	−2.22827	−	0.922978i	−0.0739884	−	0.0306470i	−0.419371	+	0.907815i	$0.637749\pi$
$908$		0			0
$909$	27.0517	−	27.0517i	0.897249	−	0.897249i
$910$		0			0
$911$	−7.59570	+	18.3377i	−0.251657	+	0.607553i	−0.998338	−	0.0576286i	$-0.981646\pi$
$911$	−7.59570	+	18.3377i	−0.251657	+	0.607553i	0.746681	+	0.665182i	$0.231646\pi$
$912$		0			0
$913$	−0.0656434	−	0.158477i	−0.00217248	−	0.00524483i
$914$		0			0
$915$	−20.1790	+	8.35840i	−0.667096	+	0.276320i
$916$		0			0
$917$	−23.1547			−0.764637
$918$		0			0
$919$	16.7830			0.553619			0.276810	−	0.960925i	$-0.410723\pi$
$919$	16.7830			0.553619			0.276810	+	0.960925i	$0.410723\pi$
$920$		0			0
$921$	51.7058	−	21.4173i	1.70377	−	0.705723i
$922$		0			0
$923$	3.13286	+	7.56338i	0.103119	+	0.248952i
$924$		0			0
$925$	1.67072	−	4.03347i	0.0549329	−	0.132620i
$926$		0			0
$927$	23.1856	−	23.1856i	0.761515	−	0.761515i
$928$		0			0
$929$	−21.5034	−	8.90700i	−0.705504	−	0.292229i	0.000938752	−	1.00000i	$-0.499701\pi$
$929$	−21.5034	−	8.90700i	−0.705504	−	0.292229i	−0.706443	+	0.707770i	$0.749701\pi$
$930$		0			0
$931$		−	4.14394i		−	0.135812i
$932$		0			0
$933$	11.5720	+	11.5720i	0.378849	+	0.378849i
$934$		0			0
$935$	−8.84048	+	20.1756i	−0.289115	+	0.659814i
$936$		0			0
$937$	−28.1329	−	28.1329i	−0.919062	−	0.919062i	0.0778997	−	0.996961i	$-0.475179\pi$
$937$	−28.1329	−	28.1329i	−0.919062	−	0.919062i	−0.996961	+	0.0778997i	$0.975179\pi$
$938$		0			0
$939$			76.7190i			2.50363i
$940$		0			0
$941$	26.4136	+	10.9409i	0.861059	+	0.356662i	0.769122	−	0.639102i	$-0.220694\pi$
$941$	26.4136	+	10.9409i	0.861059	+	0.356662i	0.0919374	+	0.995765i	$0.470694\pi$
$942$		0			0
$943$	−7.62148	+	7.62148i	−0.248190	+	0.248190i
$944$		0			0
$945$	2.83939	−	6.85490i	0.0923654	−	0.222990i
$946$		0			0
$947$	16.3787	+	39.5418i	0.532238	+	1.28494i	0.930038	+	0.367463i	$0.119774\pi$
$947$	16.3787	+	39.5418i	0.532238	+	1.28494i	−0.397801	+	0.917472i	$0.630226\pi$
$948$		0			0
$949$	−53.1517	+	22.0162i	−1.72538	+	0.714675i
$950$		0			0
$951$	16.7725			0.543885
$952$		0			0
$953$	−41.2093			−1.33490			−0.667451	−	0.744654i	$-0.732614\pi$
$953$	−41.2093			−1.33490			−0.667451	+	0.744654i	$0.732614\pi$
$954$		0			0
$955$	11.9630	−	4.95523i	0.387113	−	0.160348i
$956$		0			0
$957$	20.4788	+	49.4402i	0.661985	+	1.59817i
$958$		0			0
$959$	−2.14738	+	5.18423i	−0.0693425	+	0.167408i
$960$		0			0
$961$	63.2761	−	63.2761i	2.04116	−	2.04116i
$962$		0			0
$963$	−16.8450	−	6.97743i	−0.542823	−	0.224845i
$964$		0			0
$965$		−	19.2509i		−	0.619707i
$966$		0			0
$967$	−21.3856	−	21.3856i	−0.687714	−	0.687714i	0.274013	−	0.961726i	$-0.411649\pi$
$967$	−21.3856	−	21.3856i	−0.687714	−	0.687714i	−0.961726	+	0.274013i	$0.911649\pi$
$968$		0			0
$969$	−20.4521	−	21.2988i	−0.657015	−	0.684217i
$970$		0			0
$971$	−26.4835	−	26.4835i	−0.849896	−	0.849896i	0.140224	−	0.990120i	$-0.455218\pi$
$971$	−26.4835	−	26.4835i	−0.849896	−	0.849896i	−0.990120	+	0.140224i	$0.955218\pi$
$972$		0			0
$973$		−	20.3046i		−	0.650935i
$974$		0			0
$975$	42.5242	+	17.6141i	1.36186	+	0.564103i
$976$		0			0
$977$	26.9082	−	26.9082i	0.860868	−	0.860868i	−0.130571	−	0.991439i	$-0.541681\pi$
$977$	26.9082	−	26.9082i	0.860868	−	0.860868i	0.991439	+	0.130571i	$0.0416810\pi$
$978$		0			0
$979$	14.6486	−	35.3648i	0.468171	−	1.13026i
$980$		0			0
$981$	−9.68690	−	23.3862i	−0.309279	−	0.746665i
$982$		0			0
$983$	45.3329	−	18.7775i	1.44590	−	0.598909i	0.484676	−	0.874694i	$-0.338938\pi$
$983$	45.3329	−	18.7775i	1.44590	−	0.598909i	0.961219	+	0.275785i	$0.0889376\pi$
$984$		0			0
$985$	14.7923			0.471323
$986$		0			0
$987$	64.9975			2.06889
$988$		0			0
$989$	−15.3790	+	6.37019i	−0.489024	+	0.202560i
$990$		0			0
$991$	−12.8773	−	31.0886i	−0.409062	−	0.987563i	−0.985385	−	0.170341i	$-0.945513\pi$
$991$	−12.8773	−	31.0886i	−0.409062	−	0.987563i	0.576323	−	0.817222i	$-0.304487\pi$
$992$		0			0
$993$	9.79686	−	23.6517i	0.310894	−	0.750565i
$994$		0			0
$995$	−6.94345	+	6.94345i	−0.220122	+	0.220122i
$996$		0			0
$997$	35.8385	+	14.8448i	1.13502	+	0.470139i	0.869483	−	0.493963i	$-0.164452\pi$
$997$	35.8385	+	14.8448i	1.13502	+	0.470139i	0.265533	+	0.964102i	$0.414452\pi$
$998$		0			0
$999$		−	3.42592i		−	0.108391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.n.c.121.3	yes	12
3.2	odd	2		1224.2.bq.c.937.2		12
4.3	odd	2		272.2.v.f.257.1		12
17.3	odd	16		2312.2.a.w.1.10		12
17.5	odd	16		2312.2.b.n.577.10		12
17.9	even	8	inner	136.2.n.c.9.3	✓	12
17.12	odd	16		2312.2.b.n.577.3		12
17.14	odd	16		2312.2.a.w.1.3		12
51.26	odd	8		1224.2.bq.c.145.2		12
68.3	even	16		4624.2.a.bt.1.3		12
68.31	even	16		4624.2.a.bt.1.10		12
68.43	odd	8		272.2.v.f.145.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.n.c.9.3	✓	12	17.9	even	8	inner
136.2.n.c.121.3	yes	12	1.1	even	1	trivial
272.2.v.f.145.1		12	68.43	odd	8
272.2.v.f.257.1		12	4.3	odd	2
1224.2.bq.c.145.2		12	51.26	odd	8
1224.2.bq.c.937.2		12	3.2	odd	2
2312.2.a.w.1.3		12	17.14	odd	16
2312.2.a.w.1.10		12	17.3	odd	16
2312.2.b.n.577.3		12	17.12	odd	16
2312.2.b.n.577.10		12	17.5	odd	16
4624.2.a.bt.1.3		12	68.3	even	16
4624.2.a.bt.1.10		12	68.31	even	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.47178 - 1.02384i) q^{3} +(-0.392531 - 0.947653i) q^{5} +(-0.893542 + 2.15720i) q^{7} +(2.94010 - 2.94010i) q^{9} +(-4.81196 - 1.99318i) q^{11} +4.35777i q^{13} +(-1.94050 - 1.94050i) q^{15} +(3.77648 + 1.65476i) q^{17} +(-1.89281 - 1.89281i) q^{19} +6.24696i q^{21} +(3.79373 + 1.57141i) q^{23} +(2.79157 - 2.79157i) q^{25} +(1.18554 - 2.86215i) q^{27} +(-1.46962 - 3.54797i) q^{29} +(-10.1411 + 4.20057i) q^{31} -13.9348 q^{33} +2.39502 q^{35} +(1.02168 - 0.423195i) q^{37} +(4.46167 + 10.7714i) q^{39} +(-1.00448 + 2.42504i) q^{41} +(-2.86647 + 2.86647i) q^{43} +(-3.94028 - 1.63212i) q^{45} -10.4047i q^{47} +(1.09465 + 1.09465i) q^{49} +(11.0288 + 0.223677i) q^{51} +(-5.49867 - 5.49867i) q^{53} +5.34245i q^{55} +(-6.61654 - 2.74066i) q^{57} +(7.69489 - 7.69489i) q^{59} +(3.04576 - 7.35311i) q^{61} +(3.71528 + 8.96949i) q^{63} +(4.12965 - 1.71056i) q^{65} +6.44882 q^{67} +10.9861 q^{69} +(1.73561 - 0.718913i) q^{71} +(5.05217 + 12.1970i) q^{73} +(4.04200 - 9.75826i) q^{75} +(8.59937 - 8.59937i) q^{77} +(2.31129 + 0.957366i) q^{79} +4.18540i q^{81} +(0.0232879 + 0.0232879i) q^{83} +(0.0857556 - 4.22833i) q^{85} +(-7.26512 - 7.26512i) q^{87} +7.34936i q^{89} +(-9.40057 - 3.89384i) q^{91} +(-20.7657 + 20.7657i) q^{93} +(-1.05074 + 2.53671i) q^{95} +(-6.98779 - 16.8700i) q^{97} +(-20.0078 + 8.28750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{5} - 8 q^{9} - 12 q^{11} + 20 q^{15} + 4 q^{17} - 4 q^{19} - 8 q^{23} - 16 q^{25} + 24 q^{27} + 8 q^{29} - 32 q^{31} - 24 q^{33} - 32 q^{35} + 4 q^{37} - 8 q^{39} + 16 q^{41} + 8 q^{43} - 64 q^{45}+ \cdots - 68 q^{99}+O(q^{100}) \) 12 * q + 4 * q^5 - 8 * q^9 - 12 * q^11 + 20 * q^15 + 4 * q^17 - 4 * q^19 - 8 * q^23 - 16 * q^25 + 24 * q^27 + 8 * q^29 - 32 * q^31 - 24 * q^33 - 32 * q^35 + 4 * q^37 - 8 * q^39 + 16 * q^41 + 8 * q^43 - 64 * q^45 + 44 * q^49 - 8 * q^51 - 8 * q^53 - 12 * q^57 + 16 * q^59 + 44 * q^61 + 100 * q^63 - 20 * q^65 - 40 * q^67 + 56 * q^69 + 32 * q^71 + 8 * q^73 + 92 * q^75 - 12 * q^77 - 8 * q^79 + 40 * q^83 + 40 * q^85 - 84 * q^87 - 40 * q^91 - 76 * q^93 + 28 * q^95 - 16 * q^97 - 68 * q^99

Introduction

L-functions

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Varieties

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Representations

Groups

Database

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