LMFDB - Embedded newform 1890.2.t.b.1601.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(1151,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 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("1890.1151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.t (of order $6$, 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1601.5
Character	$\chi$	$=$	1890.1601
Dual form			1890.2.t.b.1151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.13731 - 1.55945i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.13731 - 1.55945i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} -0.450472i q^{11} +(4.26160 - 2.46044i) q^{13} +(-1.07124 + 2.41918i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.93285 + 6.81190i) q^{17} +(-4.75019 - 2.74252i) q^{19} +(0.500000 - 0.866025i) q^{20} +(0.225236 + 0.390121i) q^{22} -4.86229i q^{23} +1.00000 q^{25} +(-2.46044 + 4.26160i) q^{26} +(-0.281867 - 2.63069i) q^{28} +(8.05558 + 4.65089i) q^{29} +(0.497185 + 0.287050i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-6.81190 - 3.93285i) q^{34} +(2.13731 - 1.55945i) q^{35} +(-0.721812 + 1.25022i) q^{37} +5.48505 q^{38} +1.00000i q^{40} +(-0.956724 - 1.65709i) q^{41} +(-0.459119 + 0.795218i) q^{43} +(-0.390121 - 0.225236i) q^{44} +(2.43115 + 4.21087i) q^{46} +(-3.71305 - 6.43119i) q^{47} +(2.13623 - 6.66607i) q^{49} +(-0.866025 + 0.500000i) q^{50} -4.92088i q^{52} +(-8.30591 + 4.79542i) q^{53} -0.450472i q^{55} +(1.55945 + 2.13731i) q^{56} -9.30178 q^{58} +(-4.43278 + 7.67779i) q^{59} +(8.54152 - 4.93145i) q^{61} -0.574100 q^{62} -1.00000 q^{64} +(4.26160 - 2.46044i) q^{65} +(2.32102 - 4.02013i) q^{67} +7.86570 q^{68} +(-1.07124 + 2.41918i) q^{70} -3.88571i q^{71} +(4.91339 - 2.83675i) q^{73} -1.44362i q^{74} +(-4.75019 + 2.74252i) q^{76} +(-0.702489 - 0.962801i) q^{77} +(1.00320 + 1.73760i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(1.65709 + 0.956724i) q^{82} +(4.76689 - 8.25650i) q^{83} +(3.93285 + 6.81190i) q^{85} -0.918239i q^{86} +0.450472 q^{88} +(1.98445 - 3.43716i) q^{89} +(5.27146 - 11.9045i) q^{91} +(-4.21087 - 2.43115i) q^{92} +(6.43119 + 3.71305i) q^{94} +(-4.75019 - 2.74252i) q^{95} +(-8.69468 - 5.01988i) q^{97} +(1.48301 + 6.84110i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	$ 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) $ 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	2.13731	−	1.55945i	0.807829	−	0.589417i
$7$	2.13731	−	1.55945i	0.807829	−	0.589417i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$		−	0.450472i		−	0.135823i	−0.997691	−	0.0679113i	$-0.978367\pi$
$11$		−	0.450472i		−	0.135823i	0.997691	−	0.0679113i	$-0.0216335\pi$
$12$		0			0
$13$	4.26160	−	2.46044i	1.18196	−	0.682403i	0.225490	−	0.974246i	$-0.427602\pi$
$13$	4.26160	−	2.46044i	1.18196	−	0.682403i	0.956466	+	0.291843i	$0.0942684\pi$
$14$	−1.07124	+	2.41918i	−0.286302	+	0.646553i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.93285	+	6.81190i	0.953857	+	1.65213i	0.736963	+	0.675933i	$0.236259\pi$
$17$	3.93285	+	6.81190i	0.953857	+	1.65213i	0.216894	+	0.976195i	$0.430407\pi$
$18$		0			0
$19$	−4.75019	−	2.74252i	−1.08977	−	0.629178i	−0.156254	−	0.987717i	$-0.549942\pi$
$19$	−4.75019	−	2.74252i	−1.08977	−	0.629178i	−0.933515	+	0.358539i	$0.883275\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	0.225236	+	0.390121i	0.0480205	+	0.0831740i
$23$		−	4.86229i		−	1.01386i	−0.861988	−	0.506929i	$-0.830781\pi$
$23$		−	4.86229i		−	1.01386i	0.861988	−	0.506929i	$-0.169219\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−2.46044	+	4.26160i	−0.482532	+	0.835769i
$27$		0			0
$28$	−0.281867	−	2.63069i	−0.0532678	−	0.497154i
$29$	8.05558	+	4.65089i	1.49588	+	0.863648i	0.999989	−	0.00473444i	$-0.00150702\pi$
$29$	8.05558	+	4.65089i	1.49588	+	0.863648i	0.495894	+	0.868383i	$0.334840\pi$
$30$		0			0
$31$	0.497185	+	0.287050i	0.0892970	+	0.0515557i	0.543984	−	0.839096i	$-0.316915\pi$
$31$	0.497185	+	0.287050i	0.0892970	+	0.0515557i	−0.454687	+	0.890652i	$0.650249\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	−6.81190	−	3.93285i	−1.16823	−	0.674479i
$35$	2.13731	−	1.55945i	0.361272	−	0.263595i
$36$		0			0
$37$	−0.721812	+	1.25022i	−0.118665	+	0.205534i	−0.919239	−	0.393700i	$-0.871195\pi$
$37$	−0.721812	+	1.25022i	−0.118665	+	0.205534i	0.800574	+	0.599234i	$0.204528\pi$
$38$	5.48505			0.889792
$39$		0			0
$40$			1.00000i			0.158114i
$41$	−0.956724	−	1.65709i	−0.149415	−	0.258795i	0.781596	−	0.623785i	$-0.214406\pi$
$41$	−0.956724	−	1.65709i	−0.149415	−	0.258795i	−0.931011	+	0.364990i	$0.881072\pi$
$42$		0			0
$43$	−0.459119	+	0.795218i	−0.0700151	+	0.121270i	−0.898908	−	0.438138i	$-0.855638\pi$
$43$	−0.459119	+	0.795218i	−0.0700151	+	0.121270i	0.828893	+	0.559408i	$0.188971\pi$
$44$	−0.390121	−	0.225236i	−0.0588129	−	0.0339556i
$45$		0			0
$46$	2.43115	+	4.21087i	0.358453	+	0.620858i
$47$	−3.71305	−	6.43119i	−0.541604	−	0.938085i	−0.998812	−	0.0487254i	$-0.984484\pi$
$47$	−3.71305	−	6.43119i	−0.541604	−	0.938085i	0.457209	−	0.889359i	$-0.348849\pi$
$48$		0			0
$49$	2.13623	−	6.66607i	0.305175	−	0.952296i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$		0			0
$52$		−	4.92088i		−	0.682403i
$53$	−8.30591	+	4.79542i	−1.14090	+	0.658701i	−0.946654	−	0.322251i	$-0.895561\pi$
$53$	−8.30591	+	4.79542i	−1.14090	+	0.658701i	−0.194250	+	0.980952i	$0.562227\pi$
$54$		0			0
$55$		−	0.450472i		−	0.0607417i
$56$	1.55945	+	2.13731i	0.208390	+	0.285611i
$57$		0			0
$58$	−9.30178			−1.22138
$59$	−4.43278	+	7.67779i	−0.577098	+	0.999564i	0.418712	+	0.908119i	$0.362482\pi$
$59$	−4.43278	+	7.67779i	−0.577098	+	0.999564i	−0.995810	+	0.0914445i	$0.970852\pi$
$60$		0			0
$61$	8.54152	−	4.93145i	1.09363	−	0.631407i	0.159089	−	0.987264i	$-0.449144\pi$
$61$	8.54152	−	4.93145i	1.09363	−	0.631407i	0.934540	+	0.355857i	$0.115811\pi$
$62$	−0.574100			−0.0729107
$63$		0			0
$64$	−1.00000			−0.125000
$65$	4.26160	−	2.46044i	0.528587	−	0.305180i
$66$		0			0
$67$	2.32102	−	4.02013i	0.283558	−	0.491137i	−0.688700	−	0.725046i	$-0.741818\pi$
$67$	2.32102	−	4.02013i	0.283558	−	0.491137i	0.972258	+	0.233909i	$0.0751518\pi$
$68$	7.86570			0.953857
$69$		0			0
$70$	−1.07124	+	2.41918i	−0.128038	+	0.289147i
$71$		−	3.88571i		−	0.461149i	−0.973055	−	0.230575i	$-0.925939\pi$
$71$		−	3.88571i		−	0.461149i	0.973055	−	0.230575i	$-0.0740606\pi$
$72$		0			0
$73$	4.91339	−	2.83675i	0.575069	−	0.332016i	−0.184102	−	0.982907i	$-0.558938\pi$
$73$	4.91339	−	2.83675i	0.575069	−	0.332016i	0.759171	+	0.650891i	$0.225604\pi$
$74$		−	1.44362i		−	0.167818i
$75$		0			0
$76$	−4.75019	+	2.74252i	−0.544884	+	0.314589i
$77$	−0.702489	−	0.962801i	−0.0800561	−	0.109721i
$78$		0			0
$79$	1.00320	+	1.73760i	0.112869	+	0.195495i	0.916926	−	0.399058i	$-0.130663\pi$
$79$	1.00320	+	1.73760i	0.112869	+	0.195495i	−0.804057	+	0.594552i	$0.797329\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$	1.65709	+	0.956724i	0.182995	+	0.105652i
$83$	4.76689	−	8.25650i	0.523234	−	0.906268i	−0.476400	−	0.879229i	$-0.658059\pi$
$83$	4.76689	−	8.25650i	0.523234	−	0.906268i	0.999634	−	0.0270398i	$-0.00860808\pi$
$84$		0			0
$85$	3.93285	+	6.81190i	0.426578	+	0.738854i
$86$		−	0.918239i		−	0.0990162i
$87$		0			0
$88$	0.450472			0.0480205
$89$	1.98445	−	3.43716i	0.210351	−	0.364339i	−0.741473	−	0.670982i	$-0.765873\pi$
$89$	1.98445	−	3.43716i	0.210351	−	0.364339i	0.951824	+	0.306644i	$0.0992060\pi$
$90$		0			0
$91$	5.27146	−	11.9045i	0.552599	−	1.24793i
$92$	−4.21087	−	2.43115i	−0.439013	−	0.253464i
$93$		0			0
$94$	6.43119	+	3.71305i	0.663326	+	0.382972i
$95$	−4.75019	−	2.74252i	−0.487359	−	0.281377i
$96$		0			0
$97$	−8.69468	−	5.01988i	−0.882811	−	0.509691i	−0.0112270	−	0.999937i	$-0.503574\pi$
$97$	−8.69468	−	5.01988i	−0.882811	−	0.509691i	−0.871584	+	0.490246i	$0.836907\pi$
$98$	1.48301	+	6.84110i	0.149807	+	0.691056i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	5.49909			0.547180			0.273590	−	0.961846i	$-0.411789\pi$
$101$	5.49909			0.547180			0.273590	+	0.961846i	$0.411789\pi$
$102$		0			0
$103$			15.5075i			1.52800i	0.645216	+	0.764000i	$0.276767\pi$
$103$			15.5075i			1.52800i	−0.645216	+	0.764000i	$0.723233\pi$
$104$	2.46044	+	4.26160i	0.241266	+	0.417885i
$105$		0			0
$106$	4.79542	−	8.30591i	0.465772	−	0.806741i
$107$	−8.60043	−	4.96546i	−0.831435	−	0.480029i	0.0229088	−	0.999738i	$-0.492707\pi$
$107$	−8.60043	−	4.96546i	−0.831435	−	0.480029i	−0.854344	+	0.519708i	$0.826041\pi$
$108$		0			0
$109$	2.22823	+	3.85941i	0.213426	+	0.369665i	0.952784	−	0.303647i	$-0.0982045\pi$
$109$	2.22823	+	3.85941i	0.213426	+	0.369665i	−0.739359	+	0.673312i	$0.764871\pi$
$110$	0.225236	+	0.390121i	0.0214754	+	0.0371965i
$111$		0			0
$112$	−2.41918	−	1.07124i	−0.228591	−	0.101223i
$113$	−17.4964	+	10.1015i	−1.64592	+	0.950271i	−0.667247	+	0.744836i	$0.732528\pi$
$113$	−17.4964	+	10.1015i	−1.64592	+	0.950271i	−0.978671	+	0.205435i	$0.934139\pi$
$114$		0			0
$115$		−	4.86229i		−	0.453411i
$116$	8.05558	−	4.65089i	0.747942	−	0.431824i
$117$		0			0
$118$		−	8.86555i		−	0.816140i
$119$	19.0286	+	8.42608i	1.74435	+	0.772418i
$120$		0			0
$121$	10.7971			0.981552
$122$	−4.93145	+	8.54152i	−0.446472	+	0.773313i
$123$		0			0
$124$	0.497185	−	0.287050i	0.0446485	−	0.0257778i
$125$	1.00000			0.0894427
$126$		0			0
$127$	3.08808			0.274023			0.137012	−	0.990569i	$-0.456250\pi$
$127$	3.08808			0.274023			0.137012	+	0.990569i	$0.456250\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−2.46044	+	4.26160i	−0.215795	+	0.373767i
$131$	15.7084			1.37245			0.686227	−	0.727388i	$-0.259266\pi$
$131$	15.7084			1.37245			0.686227	+	0.727388i	$0.259266\pi$
$132$		0			0
$133$	−14.4295	+	1.54605i	−1.25120	+	0.134060i
$134$			4.64204i			0.401012i
$135$		0			0
$136$	−6.81190	+	3.93285i	−0.584116	+	0.337239i
$137$		−	13.0632i		−	1.11606i	−0.829821	−	0.558030i	$-0.811557\pi$
$137$		−	13.0632i		−	1.11606i	0.829821	−	0.558030i	$-0.188443\pi$
$138$		0			0
$139$	−0.567606	+	0.327707i	−0.0481437	+	0.0277958i	−0.523879	−	0.851793i	$-0.675515\pi$
$139$	−0.567606	+	0.327707i	−0.0481437	+	0.0277958i	0.475735	+	0.879589i	$0.342182\pi$
$140$	−0.281867	−	2.63069i	−0.0238221	−	0.222334i
$141$		0			0
$142$	1.94286	+	3.36513i	0.163041	+	0.282395i
$143$	−1.10836	−	1.91973i	−0.0926857	−	0.160536i
$144$		0			0
$145$	8.05558	+	4.65089i	0.668979	+	0.386235i
$146$	−2.83675	+	4.91339i	−0.234771	+	0.406635i
$147$		0			0
$148$	0.721812	+	1.25022i	0.0593326	+	0.102767i
$149$		−	4.62313i		−	0.378741i	−0.981906	−	0.189371i	$-0.939355\pi$
$149$		−	4.62313i		−	0.378741i	0.981906	−	0.189371i	$-0.0606448\pi$
$150$		0			0
$151$	12.3019			1.00112			0.500559	−	0.865703i	$-0.333128\pi$
$151$	12.3019			1.00112			0.500559	+	0.865703i	$0.333128\pi$
$152$	2.74252	−	4.75019i	0.222448	−	0.385291i
$153$		0			0
$154$	1.08977	+	0.482566i	0.0878165	+	0.0388862i
$155$	0.497185	+	0.287050i	0.0399349	+	0.0230564i
$156$		0			0
$157$	16.6593	+	9.61826i	1.32956	+	0.767620i	0.985231	−	0.171230i	$-0.0547740\pi$
$157$	16.6593	+	9.61826i	1.32956	+	0.767620i	0.344326	+	0.938850i	$0.388107\pi$
$158$	−1.73760	−	1.00320i	−0.138236	−	0.0798104i
$159$		0			0
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	−7.58250	−	10.3922i	−0.597585	−	0.819024i
$162$		0			0
$163$	3.11468	−	5.39478i	0.243960	−	0.422551i	−0.717879	−	0.696168i	$-0.754887\pi$
$163$	3.11468	−	5.39478i	0.243960	−	0.422551i	0.961839	+	0.273617i	$0.0882200\pi$
$164$	−1.91345			−0.149415
$165$		0			0
$166$			9.53378i			0.739965i
$167$	3.60660	+	6.24681i	0.279087	+	0.483393i	0.971158	−	0.238437i	$-0.0766349\pi$
$167$	3.60660	+	6.24681i	0.279087	+	0.483393i	−0.692071	+	0.721829i	$0.743302\pi$
$168$		0			0
$169$	5.60751	−	9.71249i	0.431347	−	0.747114i
$170$	−6.81190	−	3.93285i	−0.522449	−	0.301636i
$171$		0			0
$172$	0.459119	+	0.795218i	0.0350075	+	0.0606348i
$173$	−7.80001	−	13.5100i	−0.593024	−	1.02715i	−0.993822	−	0.110982i	$-0.964601\pi$
$173$	−7.80001	−	13.5100i	−0.593024	−	1.02715i	0.400798	−	0.916166i	$-0.368733\pi$
$174$		0			0
$175$	2.13731	−	1.55945i	0.161566	−	0.117883i
$176$	−0.390121	+	0.225236i	−0.0294064	+	0.0169778i
$177$		0			0
$178$			3.96890i			0.297481i
$179$	3.30274	−	1.90684i	0.246858	−	0.142524i	−0.371466	−	0.928446i	$-0.621145\pi$
$179$	3.30274	−	1.90684i	0.246858	−	0.142524i	0.618325	+	0.785923i	$0.287812\pi$
$180$		0			0
$181$			4.59480i			0.341529i	0.985312	+	0.170764i	$0.0546237\pi$
$181$			4.59480i			0.341529i	−0.985312	+	0.170764i	$0.945376\pi$
$182$	1.38703	+	12.9453i	0.102814	+	0.959571i
$183$		0			0
$184$	4.86229			0.358453
$185$	−0.721812	+	1.25022i	−0.0530687	+	0.0919177i
$186$		0			0
$187$	3.06857	−	1.77164i	0.224396	−	0.129555i
$188$	−7.42609			−0.541604
$189$		0			0
$190$	5.48505			0.397927
$191$	21.7317	−	12.5468i	1.57245	−	0.907855i	0.576583	−	0.817039i	$-0.304386\pi$
$191$	21.7317	−	12.5468i	1.57245	−	0.907855i	0.995868	−	0.0908162i	$-0.0289476\pi$
$192$		0			0
$193$	8.95240	−	15.5060i	0.644408	−	1.11615i	−0.340030	−	0.940415i	$-0.610437\pi$
$193$	8.95240	−	15.5060i	0.644408	−	1.11615i	0.984438	−	0.175733i	$-0.0562295\pi$
$194$	10.0398			0.720812
$195$		0			0
$196$	−4.70487	−	5.18306i	−0.336062	−	0.370219i
$197$			12.6523i			0.901439i	0.892666	+	0.450720i	$0.148833\pi$
$197$			12.6523i			0.901439i	−0.892666	+	0.450720i	$0.851167\pi$
$198$		0			0
$199$	−18.2922	+	10.5610i	−1.29670	+	0.748648i	−0.979832	−	0.199823i	$-0.935963\pi$
$199$	−18.2922	+	10.5610i	−1.29670	+	0.748648i	−0.316865	+	0.948471i	$0.602630\pi$
$200$			1.00000i			0.0707107i
$201$		0			0
$202$	−4.76235	+	2.74955i	−0.335078	+	0.193457i
$203$	24.4701	−	2.62186i	1.71747	−	0.184019i
$204$		0			0
$205$	−0.956724	−	1.65709i	−0.0668205	−	0.115736i
$206$	−7.75376	−	13.4299i	−0.540230	−	0.935705i
$207$		0			0
$208$	−4.26160	−	2.46044i	−0.295489	−	0.170601i
$209$	−1.23543	+	2.13983i	−0.0854566	+	0.148015i
$210$		0			0
$211$	10.0132	+	17.3434i	0.689338	+	1.19397i	0.972052	+	0.234764i	$0.0754318\pi$
$211$	10.0132	+	17.3434i	0.689338	+	1.19397i	−0.282714	+	0.959204i	$0.591235\pi$
$212$			9.59084i			0.658701i
$213$		0			0
$214$	9.93092			0.678864
$215$	−0.459119	+	0.795218i	−0.0313117	+	0.0542334i
$216$		0			0
$217$	1.51028	−	0.161819i	0.102525	−	0.0109850i
$218$	−3.85941	−	2.22823i	−0.261392	−	0.150915i
$219$		0			0
$220$	−0.390121	−	0.225236i	−0.0263019	−	0.0151854i
$221$	33.5205	+	19.3531i	2.25483	+	1.30183i
$222$		0			0
$223$	2.43988	+	1.40867i	0.163387	+	0.0943313i	0.579464	−	0.814998i	$-0.303262\pi$
$223$	2.43988	+	1.40867i	0.163387	+	0.0943313i	−0.416077	+	0.909329i	$0.636595\pi$
$224$	2.63069	−	0.281867i	0.175771	−	0.0188330i
$225$		0			0
$226$	10.1015	−	17.4964i	0.671943	−	1.16384i
$227$	2.59017			0.171915			0.0859577	−	0.996299i	$-0.472605\pi$
$227$	2.59017			0.171915			0.0859577	+	0.996299i	$0.472605\pi$
$228$		0			0
$229$		−	21.5183i		−	1.42197i	−0.703206	−	0.710986i	$-0.748249\pi$
$229$		−	21.5183i		−	1.42197i	0.703206	−	0.710986i	$-0.251751\pi$
$230$	2.43115	+	4.21087i	0.160305	+	0.277656i
$231$		0			0
$232$	−4.65089	+	8.05558i	−0.305346	+	0.528875i
$233$	2.79452	+	1.61342i	0.183075	+	0.105699i	0.588737	−	0.808325i	$-0.299625\pi$
$233$	2.79452	+	1.61342i	0.183075	+	0.105699i	−0.405661	+	0.914023i	$0.632959\pi$
$234$		0			0
$235$	−3.71305	−	6.43119i	−0.242212	−	0.419524i
$236$	4.43278	+	7.67779i	0.288549	+	0.499782i
$237$		0			0
$238$	−20.6923	+	2.21708i	−1.34128	+	0.143712i
$239$	−13.9417	+	8.04923i	−0.901812	+	0.520661i	−0.877788	−	0.479050i	$-0.840981\pi$
$239$	−13.9417	+	8.04923i	−0.901812	+	0.520661i	−0.0240242	+	0.999711i	$0.507648\pi$
$240$		0			0
$241$			25.6376i			1.65147i	0.564061	+	0.825733i	$0.309238\pi$
$241$			25.6376i			1.65147i	−0.564061	+	0.825733i	$0.690762\pi$
$242$	−9.35054	+	5.39854i	−0.601076	+	0.347031i
$243$		0			0
$244$		−	9.86290i		−	0.631407i
$245$	2.13623	−	6.66607i	0.136479	−	0.425880i
$246$		0			0
$247$	−26.9912			−1.71741
$248$	−0.287050	+	0.497185i	−0.0182277	+	0.0315713i
$249$		0			0
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	−12.7547			−0.805068			−0.402534	−	0.915405i	$-0.631871\pi$
$251$	−12.7547			−0.805068			−0.402534	+	0.915405i	$0.631871\pi$
$252$		0			0
$253$	−2.19033			−0.137705
$254$	−2.67436	+	1.54404i	−0.167804	+	0.0968818i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−27.0776			−1.68906			−0.844528	−	0.535512i	$-0.820119\pi$
$257$	−27.0776			−1.68906			−0.844528	+	0.535512i	$0.820119\pi$
$258$		0			0
$259$	0.406909	+	3.79773i	0.0252841	+	0.235980i
$260$		−	4.92088i		−	0.305180i
$261$		0			0
$262$	−13.6039	+	7.85422i	−0.840453	+	0.485235i
$263$			13.3334i			0.822172i	0.911597	+	0.411086i	$0.134850\pi$
$263$			13.3334i			0.822172i	−0.911597	+	0.411086i	$0.865150\pi$
$264$		0			0
$265$	−8.30591	+	4.79542i	−0.510228	+	0.294580i
$266$	11.7233	−	8.55366i	0.718800	−	0.524459i
$267$		0			0
$268$	−2.32102	−	4.02013i	−0.141779	−	0.245568i
$269$	7.58415	+	13.1361i	0.462414	+	0.800924i	0.999081	−	0.0428702i	$-0.0136502\pi$
$269$	7.58415	+	13.1361i	0.462414	+	0.800924i	−0.536667	+	0.843794i	$0.680317\pi$
$270$		0			0
$271$	22.7711	+	13.1469i	1.38325	+	0.798617i	0.992542	−	0.121900i	$-0.0388986\pi$
$271$	22.7711	+	13.1469i	1.38325	+	0.798617i	0.390703	+	0.920517i	$0.372232\pi$
$272$	3.93285	−	6.81190i	0.238464	−	0.413032i
$273$		0			0
$274$	6.53158	+	11.3130i	0.394587	+	0.683445i
$275$		−	0.450472i		−	0.0271645i
$276$		0			0
$277$	23.2800			1.39876			0.699381	−	0.714749i	$-0.253459\pi$
$277$	23.2800			1.39876			0.699381	+	0.714749i	$0.253459\pi$
$278$	0.327707	−	0.567606i	0.0196546	−	0.0340427i
$279$		0			0
$280$	1.55945	+	2.13731i	0.0931950	+	0.127729i
$281$	3.40387	+	1.96523i	0.203058	+	0.117236i	0.598081	−	0.801436i	$-0.295930\pi$
$281$	3.40387	+	1.96523i	0.203058	+	0.117236i	−0.395023	+	0.918671i	$0.629263\pi$
$282$		0			0
$283$	−25.0227	−	14.4469i	−1.48745	−	0.858778i	−0.487550	−	0.873095i	$-0.662109\pi$
$283$	−25.0227	−	14.4469i	−1.48745	−	0.858778i	−0.999898	+	0.0143172i	$0.995443\pi$
$284$	−3.36513	−	1.94286i	−0.199683	−	0.115287i
$285$		0			0
$286$	1.91973	+	1.10836i	0.113516	+	0.0655387i
$287$	−4.62898	−	2.04977i	−0.273240	−	0.120994i
$288$		0			0
$289$	−22.4347	+	38.8580i	−1.31969	+	2.28576i
$290$	−9.30178			−0.546219
$291$		0			0
$292$		−	5.67350i		−	0.332016i
$293$	−2.16359	−	3.74744i	−0.126398	−	0.218928i	0.795880	−	0.605454i	$-0.207008\pi$
$293$	−2.16359	−	3.74744i	−0.126398	−	0.218928i	−0.922279	+	0.386526i	$0.873675\pi$
$294$		0			0
$295$	−4.43278	+	7.67779i	−0.258086	+	0.447018i
$296$	−1.25022	−	0.721812i	−0.0726673	−	0.0419545i
$297$		0			0
$298$	2.31156	+	4.00375i	0.133905	+	0.231931i
$299$	−11.9634	−	20.7212i	−0.691859	−	1.19834i
$300$		0			0
$301$	0.258821	+	2.41561i	0.0149182	+	0.139233i
$302$	−10.6538	+	6.15097i	−0.613057	+	0.353948i
$303$		0			0
$304$			5.48505i			0.314589i
$305$	8.54152	−	4.93145i	0.489086	−	0.282374i
$306$		0			0
$307$			0.419882i			0.0239639i	0.999928	+	0.0119820i	$0.00381407\pi$
$307$			0.419882i			0.0239639i	−0.999928	+	0.0119820i	$0.996186\pi$
$308$	−1.18506	+	0.126973i	−0.0675248	+	0.00723496i
$309$		0			0
$310$	−0.574100			−0.0326067
$311$	3.14218	−	5.44241i	0.178177	−	0.308611i	−0.763079	−	0.646305i	$-0.776314\pi$
$311$	3.14218	−	5.44241i	0.178177	−	0.308611i	0.941256	+	0.337694i	$0.109647\pi$
$312$		0			0
$313$	−4.92258	+	2.84206i	−0.278241	+	0.160642i	−0.632627	−	0.774457i	$-0.718023\pi$
$313$	−4.92258	+	2.84206i	−0.278241	+	0.160642i	0.354386	+	0.935099i	$0.384690\pi$
$314$	−19.2365			−1.08558
$315$		0			0
$316$	2.00640			0.112869
$317$	8.68744	−	5.01570i	0.487935	−	0.281710i	−0.235782	−	0.971806i	$-0.575765\pi$
$317$	8.68744	−	5.01570i	0.487935	−	0.281710i	0.723718	+	0.690096i	$0.242432\pi$
$318$		0			0
$319$	2.09510	−	3.62881i	0.117303	−	0.203175i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	11.7628	+	5.20870i	0.655513	+	0.290269i
$323$		−	43.1438i		−	2.40058i
$324$		0			0
$325$	4.26160	−	2.46044i	0.236391	−	0.136481i
$326$			6.22935i			0.345012i
$327$		0			0
$328$	1.65709	−	0.956724i	0.0914977	−	0.0528262i
$329$	−17.9651	−	7.95515i	−0.990446	−	0.438582i
$330$		0			0
$331$	−15.8516	−	27.4558i	−0.871282	−	1.50910i	−0.860671	−	0.509161i	$-0.829956\pi$
$331$	−15.8516	−	27.4558i	−0.871282	−	1.50910i	−0.0106106	−	0.999944i	$-0.503378\pi$
$332$	−4.76689	−	8.25650i	−0.261617	−	0.453134i
$333$		0			0
$334$	−6.24681	−	3.60660i	−0.341810	−	0.197344i
$335$	2.32102	−	4.02013i	0.126811	−	0.219643i
$336$		0			0
$337$	−7.09612	−	12.2908i	−0.386550	−	0.669525i	0.605433	−	0.795897i	$-0.293000\pi$
$337$	−7.09612	−	12.2908i	−0.386550	−	0.669525i	−0.991983	+	0.126372i	$0.959667\pi$
$338$			11.2150i			0.610016i
$339$		0			0
$340$	7.86570			0.426578
$341$	0.129308	−	0.223968i	0.00700242	−	0.0121286i
$342$		0			0
$343$	−5.82962	−	17.5788i	−0.314770	−	0.949168i
$344$	−0.795218	−	0.459119i	−0.0428753	−	0.0247541i
$345$		0			0
$346$	13.5100	+	7.80001i	0.726303	+	0.419331i
$347$	−0.634656	−	0.366419i	−0.0340701	−	0.0196704i	0.482868	−	0.875693i	$-0.339595\pi$
$347$	−0.634656	−	0.366419i	−0.0340701	−	0.0196704i	−0.516938	+	0.856023i	$0.672928\pi$
$348$		0			0
$349$	−23.1243	−	13.3508i	−1.23782	−	0.714653i	−0.269169	−	0.963093i	$-0.586749\pi$
$349$	−23.1243	−	13.3508i	−1.23782	−	0.714653i	−0.968647	+	0.248440i	$0.920082\pi$
$350$	−1.07124	+	2.41918i	−0.0572604	+	0.129311i
$351$		0			0
$352$	0.225236	−	0.390121i	0.0120051	−	0.0207935i
$353$	−6.00317			−0.319516			−0.159758	−	0.987156i	$-0.551071\pi$
$353$	−6.00317			−0.319516			−0.159758	+	0.987156i	$0.551071\pi$
$354$		0			0
$355$		−	3.88571i		−	0.206232i
$356$	−1.98445	−	3.43716i	−0.105176	−	0.182169i
$357$		0			0
$358$	−1.90684	+	3.30274i	−0.100780	+	0.174555i
$359$	−25.3873	−	14.6574i	−1.33989	−	0.773587i	−0.353101	−	0.935585i	$-0.614873\pi$
$359$	−25.3873	−	14.6574i	−1.33989	−	0.773587i	−0.986791	+	0.161998i	$0.948206\pi$
$360$		0			0
$361$	5.54288	+	9.60055i	0.291730	+	0.505292i
$362$	−2.29740	−	3.97921i	−0.120749	−	0.209143i
$363$		0			0
$364$	−7.67386	−	10.5175i	−0.402220	−	0.551265i
$365$	4.91339	−	2.83675i	0.257179	−	0.148482i
$366$		0			0
$367$			20.0340i			1.04576i	0.852405	+	0.522882i	$0.175143\pi$
$367$			20.0340i			1.04576i	−0.852405	+	0.522882i	$0.824857\pi$
$368$	−4.21087	+	2.43115i	−0.219507	+	0.126732i
$369$		0			0
$370$		−	1.44362i		−	0.0750505i
$371$	−10.2741	+	23.2020i	−0.533406	+	1.20459i
$372$		0			0
$373$	−6.86717			−0.355568			−0.177784	−	0.984069i	$-0.556893\pi$
$373$	−6.86717			−0.355568			−0.177784	+	0.984069i	$0.556893\pi$
$374$	−1.77164	+	3.06857i	−0.0916094	+	0.158672i
$375$		0			0
$376$	6.43119	−	3.71305i	0.331663	−	0.191486i
$377$	45.7729			2.35742
$378$		0			0
$379$	0.682216			0.0350431			0.0175216	−	0.999846i	$-0.494422\pi$
$379$	0.682216			0.0350431			0.0175216	+	0.999846i	$0.494422\pi$
$380$	−4.75019	+	2.74252i	−0.243680	+	0.140689i
$381$		0			0
$382$	−12.5468	+	21.7317i	−0.641950	+	1.11189i
$383$	−31.6323			−1.61634			−0.808168	−	0.588952i	$-0.799541\pi$
$383$	−31.6323			−1.61634			−0.808168	+	0.588952i	$0.799541\pi$
$384$		0			0
$385$	−0.702489	−	0.962801i	−0.0358022	−	0.0490689i
$386$			17.9048i			0.911331i
$387$		0			0
$388$	−8.69468	+	5.01988i	−0.441406	+	0.254846i
$389$			28.0321i			1.42128i	0.703554	+	0.710641i	$0.251595\pi$
$389$			28.0321i			1.42128i	−0.703554	+	0.710641i	$0.748405\pi$
$390$		0			0
$391$	33.1214	−	19.1227i	1.67502	−	0.967075i
$392$	6.66607	+	2.13623i	0.336688	+	0.107896i
$393$		0			0
$394$	−6.32615	−	10.9572i	−0.318707	−	0.552017i
$395$	1.00320	+	1.73760i	0.0504765	+	0.0874279i
$396$		0			0
$397$	−25.3210	−	14.6191i	−1.27083	−	0.733711i	−0.295682	−	0.955286i	$-0.595547\pi$
$397$	−25.3210	−	14.6191i	−1.27083	−	0.733711i	−0.975143	+	0.221575i	$0.928880\pi$
$398$	10.5610	−	18.2922i	0.529374	−	0.916903i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$			11.5694i			0.577750i	0.957367	+	0.288875i	$0.0932812\pi$
$401$			11.5694i			0.577750i	−0.957367	+	0.288875i	$0.906719\pi$
$402$		0			0
$403$	2.82507			0.140727
$404$	2.74955	−	4.76235i	0.136795	−	0.236936i
$405$		0			0
$406$	−19.8808	+	14.5057i	−0.986669	+	0.719904i
$407$	0.563188	+	0.325157i	0.0279162	+	0.0161174i
$408$		0			0
$409$	−1.79921	−	1.03878i	−0.0889653	−	0.0513641i	0.454857	−	0.890564i	$-0.349690\pi$
$409$	−1.79921	−	1.03878i	−0.0889653	−	0.0513641i	−0.543823	+	0.839200i	$0.683024\pi$
$410$	1.65709	+	0.956724i	0.0818380	+	0.0472492i
$411$		0			0
$412$	13.4299	+	7.75376i	0.661644	+	0.382000i
$413$	2.49890	+	23.3226i	0.122963	+	1.14763i
$414$		0			0
$415$	4.76689	−	8.25650i	0.233998	−	0.405296i
$416$	4.92088			0.241266
$417$		0			0
$418$		−	2.47086i		−	0.120854i
$419$	3.15211	+	5.45962i	0.153991	+	0.266720i	0.932691	−	0.360676i	$-0.117454\pi$
$419$	3.15211	+	5.45962i	0.153991	+	0.266720i	−0.778700	+	0.627396i	$0.784121\pi$
$420$		0			0
$421$	−1.30121	+	2.25376i	−0.0634172	+	0.109842i	−0.895991	−	0.444073i	$-0.853533\pi$
$421$	−1.30121	+	2.25376i	−0.0634172	+	0.109842i	0.832574	+	0.553914i	$0.186867\pi$
$422$	−17.3434	−	10.0132i	−0.844263	−	0.487436i
$423$		0			0
$424$	−4.79542	−	8.30591i	−0.232886	−	0.403371i
$425$	3.93285	+	6.81190i	0.190771	+	0.330426i
$426$		0			0
$427$	10.5656	−	23.8601i	0.511303	−	1.15467i
$428$	−8.60043	+	4.96546i	−0.415717	+	0.240015i
$429$		0			0
$430$		−	0.918239i		−	0.0442814i
$431$	8.46126	−	4.88511i	0.407564	−	0.235307i	−0.282178	−	0.959362i	$-0.591057\pi$
$431$	8.46126	−	4.88511i	0.407564	−	0.235307i	0.689743	+	0.724055i	$0.257724\pi$
$432$		0			0
$433$			34.4543i			1.65577i	0.560898	+	0.827885i	$0.310456\pi$
$433$			34.4543i			1.65577i	−0.560898	+	0.827885i	$0.689544\pi$
$434$	−1.22703	+	0.895280i	−0.0588994	+	0.0429748i
$435$		0			0
$436$	4.45646			0.213426
$437$	−13.3349	+	23.0968i	−0.637897	+	1.10487i
$438$		0			0
$439$	−17.9508	+	10.3639i	−0.856745	+	0.494642i	−0.862921	−	0.505339i	$-0.831367\pi$
$439$	−17.9508	+	10.3639i	−0.856745	+	0.494642i	0.00617595	+	0.999981i	$0.498034\pi$
$440$	0.450472			0.0214754
$441$		0			0
$442$	−38.7061			−1.84106
$443$	−8.25856	+	4.76808i	−0.392376	+	0.226538i	−0.683189	−	0.730241i	$-0.739408\pi$
$443$	−8.25856	+	4.76808i	−0.392376	+	0.226538i	0.290813	+	0.956780i	$0.406074\pi$
$444$		0			0
$445$	1.98445	−	3.43716i	0.0940719	−	0.162937i
$446$	−2.81733			−0.133405
$447$		0			0
$448$	−2.13731	+	1.55945i	−0.100979	+	0.0736771i
$449$		−	2.23000i		−	0.105240i	−0.998615	−	0.0526200i	$-0.983243\pi$
$449$		−	2.23000i		−	0.105240i	0.998615	−	0.0526200i	$-0.0167572\pi$
$450$		0			0
$451$	−0.746475	+	0.430978i	−0.0351501	+	0.0202939i
$452$			20.2030i			0.950271i
$453$		0			0
$454$	−2.24315	+	1.29508i	−0.105276	+	0.0607813i
$455$	5.27146	−	11.9045i	0.247130	−	0.558091i
$456$		0			0
$457$	−6.43820	−	11.1513i	−0.301166	−	0.521635i	0.675234	−	0.737603i	$-0.264043\pi$
$457$	−6.43820	−	11.1513i	−0.301166	−	0.521635i	−0.976400	+	0.215968i	$0.930709\pi$
$458$	10.7592	+	18.6354i	0.502743	+	0.870776i
$459$		0			0
$460$	−4.21087	−	2.43115i	−0.196333	−	0.113353i
$461$	−1.56738	+	2.71478i	−0.0730000	+	0.126440i	−0.900215	−	0.435446i	$-0.856591\pi$
$461$	−1.56738	+	2.71478i	−0.0730000	+	0.126440i	0.827215	+	0.561886i	$0.189924\pi$
$462$		0			0
$463$	−7.25355	−	12.5635i	−0.337101	−	0.583877i	0.646785	−	0.762672i	$-0.276113\pi$
$463$	−7.25355	−	12.5635i	−0.337101	−	0.583877i	−0.983886	+	0.178796i	$0.942780\pi$
$464$		−	9.30178i		−	0.431824i
$465$		0			0
$466$	−3.22684			−0.149480
$467$	−4.83041	+	8.36651i	−0.223525	+	0.387156i	−0.955876	−	0.293771i	$-0.905090\pi$
$467$	−4.83041	+	8.36651i	−0.223525	+	0.387156i	0.732351	+	0.680927i	$0.238423\pi$
$468$		0			0
$469$	−1.30844	−	12.2118i	−0.0604180	−	0.563888i
$470$	6.43119	+	3.71305i	0.296648	+	0.171270i
$471$		0			0
$472$	−7.67779	−	4.43278i	−0.353399	−	0.204035i
$473$	0.358224	+	0.206821i	0.0164711	+	0.00950962i
$474$		0			0
$475$	−4.75019	−	2.74252i	−0.217954	−	0.125836i
$476$	16.8115	−	12.2662i	0.770553	−	0.562219i
$477$		0			0
$478$	8.04923	−	13.9417i	0.368163	−	0.637677i
$479$	−35.7357			−1.63280			−0.816402	−	0.577483i	$-0.804035\pi$
$479$	−35.7357			−1.63280			−0.816402	+	0.577483i	$0.804035\pi$
$480$		0			0
$481$			7.10390i			0.323910i
$482$	−12.8188	−	22.2029i	−0.583881	−	1.01131i
$483$		0			0
$484$	5.39854	−	9.35054i	0.245388	−	0.425025i
$485$	−8.69468	−	5.01988i	−0.394805	−	0.227941i
$486$		0			0
$487$	−9.42060	−	16.3170i	−0.426888	−	0.739392i	0.569707	−	0.821848i	$-0.307057\pi$
$487$	−9.42060	−	16.3170i	−0.426888	−	0.739392i	−0.996595	+	0.0824564i	$0.973723\pi$
$488$	4.93145	+	8.54152i	0.223236	+	0.386656i
$489$		0			0
$490$	1.48301	+	6.84110i	0.0669955	+	0.309050i
$491$	13.9486	−	8.05323i	0.629492	−	0.363437i	−0.151064	−	0.988524i	$-0.548270\pi$
$491$	13.9486	−	8.05323i	0.629492	−	0.363437i	0.780555	+	0.625087i	$0.214936\pi$
$492$		0			0
$493$			73.1650i			3.29519i
$494$	23.3751	−	13.4956i	1.05170	−	0.607197i
$495$		0			0
$496$		−	0.574100i		−	0.0257778i
$497$	−6.05958	−	8.30499i	−0.271809	−	0.372530i
$498$		0			0
$499$	1.35262			0.0605518			0.0302759	−	0.999542i	$-0.490361\pi$
$499$	1.35262			0.0605518			0.0302759	+	0.999542i	$0.490361\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		0			0
$502$	11.0459	−	6.37734i	0.493002	−	0.284635i
$503$	−39.9065			−1.77934			−0.889671	−	0.456603i	$-0.849066\pi$
$503$	−39.9065			−1.77934			−0.889671	+	0.456603i	$0.849066\pi$
$504$		0			0
$505$	5.49909			0.244706
$506$	1.89688	−	1.09516i	0.0843266	−	0.0486860i
$507$		0			0
$508$	1.54404	−	2.67436i	0.0685058	−	0.118656i
$509$	10.8798			0.482240			0.241120	−	0.970495i	$-0.422485\pi$
$509$	10.8798			0.482240			0.241120	+	0.970495i	$0.422485\pi$
$510$		0			0
$511$	6.07770	−	13.7252i	0.268861	−	0.607168i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	23.4499	−	13.5388i	1.03433	−	0.597171i
$515$			15.5075i			0.683343i
$516$		0			0
$517$	−2.89707	+	1.67263i	−0.127413	+	0.0735620i
$518$	−2.25126	−	3.08548i	−0.0989147	−	0.135568i
$519$		0			0
$520$	2.46044	+	4.26160i	0.107897	+	0.186884i
$521$	−19.6042	−	33.9555i	−0.858877	−	1.48762i	−0.873001	−	0.487718i	$-0.837829\pi$
$521$	−19.6042	−	33.9555i	−0.858877	−	1.48762i	0.0141243	−	0.999900i	$-0.495504\pi$
$522$		0			0
$523$	13.7286	+	7.92622i	0.600310	+	0.346589i	0.769164	−	0.639052i	$-0.220673\pi$
$523$	13.7286	+	7.92622i	0.600310	+	0.346589i	−0.168853	+	0.985641i	$0.554006\pi$
$524$	7.85422	−	13.6039i	0.343113	−	0.594290i
$525$		0			0
$526$	−6.66669	−	11.5471i	−0.290682	−	0.503475i
$527$			4.51570i			0.196707i
$528$		0			0
$529$	−0.641865			−0.0279072
$530$	4.79542	−	8.30591i	0.208300	−	0.360786i
$531$		0			0
$532$	−5.87582	+	13.2693i	−0.254749	+	0.575298i
$533$	−8.15435	−	4.70792i	−0.353204	−	0.203923i
$534$		0			0
$535$	−8.60043	−	4.96546i	−0.371829	−	0.214676i
$536$	4.02013	+	2.32102i	0.173643	+	0.100253i
$537$		0			0
$538$	−13.1361	−	7.58415i	−0.566339	−	0.326976i
$539$	−3.00288	−	0.962312i	−0.129343	−	0.0414497i
$540$		0			0
$541$	−8.42008	+	14.5840i	−0.362007	+	0.627015i	−0.988291	−	0.152580i	$-0.951242\pi$
$541$	−8.42008	+	14.5840i	−0.362007	+	0.627015i	0.626284	+	0.779595i	$0.284575\pi$
$542$	−26.2938			−1.12942
$543$		0			0
$544$			7.86570i			0.337239i
$545$	2.22823	+	3.85941i	0.0954470	+	0.165319i
$546$		0			0
$547$	−13.5255	+	23.4268i	−0.578307	+	1.00166i	0.417366	+	0.908738i	$0.362953\pi$
$547$	−13.5255	+	23.4268i	−0.578307	+	1.00166i	−0.995674	+	0.0929192i	$0.970380\pi$
$548$	−11.3130	−	6.53158i	−0.483268	−	0.279015i
$549$		0			0
$550$	0.225236	+	0.390121i	0.00960410	+	0.0166348i
$551$	−25.5104	−	44.1852i	−1.08678	−	1.88235i
$552$		0			0
$553$	4.85385	+	2.14935i	0.206407	+	0.0913995i
$554$	−20.1611	+	11.6400i	−0.856563	+	0.494537i
$555$		0			0
$556$			0.655415i			0.0277958i
$557$	−31.3474	+	18.0984i	−1.32823	+	0.766854i	−0.985026	−	0.172406i	$-0.944846\pi$
$557$	−31.3474	+	18.0984i	−1.32823	+	0.766854i	−0.343205	+	0.939261i	$0.611513\pi$
$558$		0			0
$559$			4.51854i			0.191114i
$560$	−2.41918	−	1.07124i	−0.102229	−	0.0452683i
$561$		0			0
$562$	−3.93045			−0.165796
$563$	−7.00932	+	12.1405i	−0.295408	+	0.511661i	−0.975080	−	0.221855i	$-0.928789\pi$
$563$	−7.00932	+	12.1405i	−0.295408	+	0.511661i	0.679672	+	0.733516i	$0.262122\pi$
$564$		0			0
$565$	−17.4964	+	10.1015i	−0.736077	+	0.424974i
$566$	28.8938			1.21450
$567$		0			0
$568$	3.88571			0.163041
$569$	22.2561	−	12.8496i	0.933024	−	0.538682i	0.0452575	−	0.998975i	$-0.485589\pi$
$569$	22.2561	−	12.8496i	0.933024	−	0.538682i	0.887767	+	0.460294i	$0.152256\pi$
$570$		0			0
$571$	−7.82510	+	13.5535i	−0.327470	+	0.567195i	−0.982009	−	0.188833i	$-0.939530\pi$
$571$	−7.82510	+	13.5535i	−0.327470	+	0.567195i	0.654539	+	0.756028i	$0.272863\pi$
$572$	−2.21672			−0.0926857
$573$		0			0
$574$	5.03369	−	0.539337i	0.210102	−	0.0225115i
$575$		−	4.86229i		−	0.202772i
$576$		0			0
$577$	−26.9592	+	15.5649i	−1.12233	+	0.647976i	−0.941994	−	0.335629i	$-0.891051\pi$
$577$	−26.9592	+	15.5649i	−1.12233	+	0.647976i	−0.180334	+	0.983605i	$0.557718\pi$
$578$		−	44.8693i		−	1.86632i
$579$		0			0
$580$	8.05558	−	4.65089i	0.334490	−	0.193118i
$581$	−2.68725	−	25.0805i	−0.111486	−	1.04051i
$582$		0			0
$583$	2.16020	+	3.74158i	0.0894665	+	0.154961i
$584$	2.83675	+	4.91339i	0.117385	+	0.203318i
$585$		0			0
$586$	3.74744	+	2.16359i	0.154805	+	0.0893770i
$587$	2.19821	−	3.80741i	0.0907299	−	0.157149i	−0.817089	−	0.576512i	$-0.804413\pi$
$587$	2.19821	−	3.80741i	0.0907299	−	0.157149i	0.907818	+	0.419363i	$0.137747\pi$
$588$		0			0
$589$	−1.57448	−	2.72708i	−0.0648754	−	0.112368i
$590$		−	8.86555i		−	0.364989i
$591$		0			0
$592$	1.44362			0.0593326
$593$	−8.99345	+	15.5771i	−0.369317	+	0.639675i	−0.989459	−	0.144814i	$-0.953742\pi$
$593$	−8.99345	+	15.5771i	−0.369317	+	0.639675i	0.620142	+	0.784489i	$0.287075\pi$
$594$		0			0
$595$	19.0286	+	8.42608i	0.780095	+	0.345436i
$596$	−4.00375	−	2.31156i	−0.164000	−	0.0946853i
$597$		0			0
$598$	20.7212	+	11.9634i	0.847351	+	0.489218i
$599$	1.19486	+	0.689852i	0.0488206	+	0.0281866i	0.524212	−	0.851588i	$-0.324360\pi$
$599$	1.19486	+	0.689852i	0.0488206	+	0.0281866i	−0.475391	+	0.879775i	$0.657693\pi$
$600$		0			0
$601$	−40.5777	−	23.4275i	−1.65520	−	0.955630i	−0.974885	−	0.222709i	$-0.928510\pi$
$601$	−40.5777	−	23.4275i	−1.65520	−	0.955630i	−0.680314	−	0.732921i	$-0.738157\pi$
$602$	−1.43195	−	1.96257i	−0.0583618	−	0.0799882i
$603$		0			0
$604$	6.15097	−	10.6538i	0.250279	−	0.433496i
$605$	10.7971			0.438964
$606$		0			0
$607$		−	22.5955i		−	0.917121i	−0.888663	−	0.458561i	$-0.848365\pi$
$607$		−	22.5955i		−	0.917121i	0.888663	−	0.458561i	$-0.151635\pi$
$608$	−2.74252	−	4.75019i	−0.111224	−	0.192646i
$609$		0			0
$610$	−4.93145	+	8.54152i	−0.199668	+	0.345836i
$611$	−31.6471	−	18.2714i	−1.28030	−	0.739183i
$612$		0			0
$613$	10.4551	+	18.1088i	0.422279	+	0.731409i	0.996162	−	0.0875282i	$-0.0278968\pi$
$613$	10.4551	+	18.1088i	0.422279	+	0.731409i	−0.573883	+	0.818938i	$0.694563\pi$
$614$	−0.209941	−	0.363629i	−0.00847253	−	0.0146749i
$615$		0			0
$616$	0.962801	−	0.702489i	0.0387924	−	0.0283041i
$617$	8.43544	−	4.87020i	0.339598	−	0.196067i	−0.320496	−	0.947250i	$-0.603850\pi$
$617$	8.43544	−	4.87020i	0.339598	−	0.196067i	0.660094	+	0.751183i	$0.270516\pi$
$618$		0			0
$619$			18.2795i			0.734715i	0.930080	+	0.367358i	$0.119737\pi$
$619$			18.2795i			0.734715i	−0.930080	+	0.367358i	$0.880263\pi$
$620$	0.497185	−	0.287050i	0.0199674	−	0.0115282i
$621$		0			0
$622$			6.28435i			0.251980i
$623$	−1.11870	−	10.4410i	−0.0448197	−	0.418308i
$624$		0			0
$625$	1.00000			0.0400000
$626$	2.84206	−	4.92258i	0.113591	−	0.196746i
$627$		0			0
$628$	16.6593	−	9.61826i	0.664779	−	0.383810i
$629$	−11.3551			−0.452758
$630$		0			0
$631$	23.4168			0.932209			0.466104	−	0.884730i	$-0.345657\pi$
$631$	23.4168			0.932209			0.466104	+	0.884730i	$0.345657\pi$
$632$	−1.73760	+	1.00320i	−0.0691178	+	0.0399052i
$633$		0			0
$634$	−5.01570	+	8.68744i	−0.199199	+	0.345022i
$635$	3.08808			0.122547
$636$		0			0
$637$	−7.29770	−	33.6642i	−0.289146	−	1.33382i
$638$			4.19019i			0.165891i
$639$		0			0
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$		−	3.99917i		−	0.157958i	−0.996876	−	0.0789788i	$-0.974834\pi$
$641$		−	3.99917i		−	0.157958i	0.996876	−	0.0789788i	$-0.0251659\pi$
$642$		0			0
$643$	−14.6262	+	8.44444i	−0.576801	+	0.333016i	−0.759861	−	0.650085i	$-0.774733\pi$
$643$	−14.6262	+	8.44444i	−0.576801	+	0.333016i	0.183060	+	0.983102i	$0.441400\pi$
$644$	−12.7912	+	1.37052i	−0.504044	+	0.0540059i
$645$		0			0
$646$	21.5719	+	37.3636i	0.848734	+	1.47005i
$647$	14.0753	+	24.3792i	0.553358	+	0.958443i	0.998029	+	0.0627498i	$0.0199870\pi$
$647$	14.0753	+	24.3792i	0.553358	+	0.958443i	−0.444672	+	0.895694i	$0.646680\pi$
$648$		0			0
$649$	3.45863	+	1.99684i	0.135763	+	0.0783830i
$650$	−2.46044	+	4.26160i	−0.0965063	+	0.167154i
$651$		0			0
$652$	−3.11468	−	5.39478i	−0.121980	−	0.211276i
$653$			23.4509i			0.917704i	0.888513	+	0.458852i	$0.151739\pi$
$653$			23.4509i			0.917704i	−0.888513	+	0.458852i	$0.848261\pi$
$654$		0			0
$655$	15.7084			0.613780
$656$	−0.956724	+	1.65709i	−0.0373538	+	0.0646987i
$657$		0			0
$658$	19.5358	−	2.09317i	0.761584	−	0.0816002i
$659$	−13.7094	−	7.91513i	−0.534043	−	0.308330i	0.208618	−	0.977997i	$-0.433103\pi$
$659$	−13.7094	−	7.91513i	−0.534043	−	0.308330i	−0.742661	+	0.669667i	$0.766437\pi$
$660$		0			0
$661$	10.3009	+	5.94725i	0.400660	+	0.231321i	0.686769	−	0.726876i	$-0.259028\pi$
$661$	10.3009	+	5.94725i	0.400660	+	0.231321i	−0.286109	+	0.958197i	$0.592362\pi$
$662$	27.4558	+	15.8516i	1.06710	+	0.616089i
$663$		0			0
$664$	8.25650	+	4.76689i	0.320414	+	0.184991i
$665$	−14.4295	+	1.54605i	−0.559551	+	0.0599533i
$666$		0			0
$667$	22.6140	−	39.1686i	0.875617	−	1.51661i
$668$	7.21319			0.279087
$669$		0			0
$670$			4.64204i			0.179338i
$671$	−2.22148	−	3.84772i	−0.0857593	−	0.148540i
$672$		0			0
$673$	−2.58993	+	4.48588i	−0.0998343	+	0.172918i	−0.911616	−	0.411043i	$-0.865165\pi$
$673$	−2.58993	+	4.48588i	−0.0998343	+	0.172918i	0.811782	+	0.583961i	$0.198498\pi$
$674$	12.2908	+	7.09612i	0.473425	+	0.273332i
$675$		0			0
$676$	−5.60751	−	9.71249i	−0.215673	−	0.373557i
$677$	5.58197	+	9.66826i	0.214533	+	0.371582i	0.953128	−	0.302568i	$-0.0978438\pi$
$677$	5.58197	+	9.66826i	0.214533	+	0.371582i	−0.738595	+	0.674149i	$0.764510\pi$
$678$		0			0
$679$	−26.4115	+	2.82987i	−1.01358	+	0.108600i
$680$	−6.81190	+	3.93285i	−0.261224	+	0.150818i
$681$		0			0
$682$			0.258616i			0.00990292i
$683$	31.3199	−	18.0825i	1.19842	−	0.691909i	0.238219	−	0.971211i	$-0.423436\pi$
$683$	31.3199	−	18.0825i	1.19842	−	0.691909i	0.960203	+	0.279302i	$0.0901031\pi$
$684$		0			0
$685$		−	13.0632i		−	0.499117i
$686$	13.8380	+	12.3089i	0.528338	+	0.469956i
$687$		0			0
$688$	0.918239			0.0350075
$689$	−23.5977	+	40.8723i	−0.898999	+	1.55711i
$690$		0			0
$691$	5.80724	−	3.35281i	0.220918	−	0.127547i	−0.385457	−	0.922726i	$-0.625956\pi$
$691$	5.80724	−	3.35281i	0.220918	−	0.127547i	0.606375	+	0.795179i	$0.292623\pi$
$692$	−15.6000			−0.593024
$693$		0			0
$694$	0.732838			0.0278181
$695$	−0.567606	+	0.327707i	−0.0215305	+	0.0124306i
$696$		0			0
$697$	7.52531	−	13.0342i	0.285041	−	0.493706i
$698$	26.7017			1.01067
$699$		0			0
$700$	−0.281867	−	2.63069i	−0.0106536	−	0.0994309i
$701$		−	1.39464i		−	0.0526749i	−0.999653	−	0.0263375i	$-0.991616\pi$
$701$		−	1.39464i		−	0.0526749i	0.999653	−	0.0263375i	$-0.00838445\pi$
$702$		0			0
$703$	6.85749	−	3.95918i	0.258635	−	0.149323i
$704$			0.450472i			0.0169778i
$705$		0			0
$706$	5.19889	−	3.00158i	0.195663	−	0.112966i
$707$	11.7533	−	8.57557i	0.442028	−	0.322517i
$708$		0			0
$709$	24.8056	+	42.9645i	0.931593	+	1.61357i	0.780599	+	0.625032i	$0.214914\pi$
$709$	24.8056	+	42.9645i	0.931593	+	1.61357i	0.150994	+	0.988535i	$0.451753\pi$
$710$	1.94286	+	3.36513i	0.0729141	+	0.126291i
$711$		0			0
$712$	3.43716	+	1.98445i	0.128813	+	0.0743703i
$713$	1.39572	−	2.41746i	0.0522701	−	0.0905345i
$714$		0			0
$715$	−1.10836	−	1.91973i	−0.0414503	−	0.0717940i
$716$		−	3.81368i		−	0.142524i
$717$		0			0
$718$	29.3148			1.09402
$719$	10.4343	−	18.0727i	0.389133	−	0.673998i	−0.603200	−	0.797590i	$-0.706108\pi$
$719$	10.4343	−	18.0727i	0.389133	−	0.673998i	0.992333	+	0.123592i	$0.0394413\pi$
$720$		0			0
$721$	24.1832	+	33.1444i	0.900629	+	1.23436i
$722$	−9.60055	−	5.54288i	−0.357295	−	0.206285i
$723$		0			0
$724$	3.97921	+	2.29740i	0.147886	+	0.0853821i
$725$	8.05558	+	4.65089i	0.299177	+	0.172730i
$726$		0			0
$727$	−32.1908	−	18.5854i	−1.19389	−	0.689293i	−0.234704	−	0.972067i	$-0.575412\pi$
$727$	−32.1908	−	18.5854i	−1.19389	−	0.689293i	−0.959187	+	0.282773i	$0.908746\pi$
$728$	11.9045	+	5.27146i	0.441210	+	0.195373i
$729$		0			0
$730$	−2.83675	+	4.91339i	−0.104993	+	0.181853i
$731$	−7.22260			−0.267137
$732$		0			0
$733$			11.9964i			0.443096i	0.975149	+	0.221548i	$0.0711109\pi$
$733$			11.9964i			0.443096i	−0.975149	+	0.221548i	$0.928889\pi$
$734$	−10.0170	−	17.3499i	−0.369733	−	0.640397i
$735$		0			0
$736$	2.43115	−	4.21087i	0.0896132	−	0.155215i
$737$	−1.81096	−	1.04556i	−0.0667075	−	0.0385136i
$738$		0			0
$739$	16.6995	+	28.9243i	0.614300	+	1.06400i	0.990507	+	0.137463i	$0.0438947\pi$
$739$	16.6995	+	28.9243i	0.614300	+	1.06400i	−0.376207	+	0.926535i	$0.622772\pi$
$740$	0.721812	+	1.25022i	0.0265343	+	0.0459588i
$741$		0			0
$742$	−2.70334	−	25.2306i	−0.0992426	−	0.926243i
$743$	42.2679	−	24.4034i	1.55066	−	0.895273i	0.552570	−	0.833467i	$-0.313647\pi$
$743$	42.2679	−	24.4034i	1.55066	−	0.895273i	0.998088	−	0.0618062i	$-0.0196861\pi$
$744$		0			0
$745$		−	4.62313i		−	0.169378i
$746$	5.94714	−	3.43358i	0.217740	−	0.125712i
$747$		0			0
$748$		−	3.54328i		−	0.129555i
$749$	−26.1252	+	2.79919i	−0.954595	+	0.102280i
$750$		0			0
$751$	10.6219			0.387599			0.193799	−	0.981041i	$-0.437919\pi$
$751$	10.6219			0.387599			0.193799	+	0.981041i	$0.437919\pi$
$752$	−3.71305	+	6.43119i	−0.135401	+	0.234521i
$753$		0			0
$754$	−39.6405	+	22.8864i	−1.44362	+	0.833475i
$755$	12.3019			0.447713
$756$		0			0
$757$	−41.0132			−1.49065			−0.745326	−	0.666701i	$-0.767706\pi$
$757$	−41.0132			−1.49065			−0.745326	+	0.666701i	$0.767706\pi$
$758$	−0.590817	+	0.341108i	−0.0214594	+	0.0123896i
$759$		0			0
$760$	2.74252	−	4.75019i	0.0994818	−	0.172308i
$761$	−1.62266			−0.0588212			−0.0294106	−	0.999567i	$-0.509363\pi$
$761$	−1.62266			−0.0588212			−0.0294106	+	0.999567i	$0.509363\pi$
$762$		0			0
$763$	10.7810	+	4.77396i	0.390298	+	0.172829i
$764$		−	25.0936i		−	0.907855i
$765$		0			0
$766$	27.3944	−	15.8162i	0.989799	−	0.571461i
$767$			43.6263i			1.57525i
$768$		0			0
$769$	−15.4016	+	8.89210i	−0.555395	+	0.320657i	−0.751295	−	0.659966i	$-0.770570\pi$
$769$	−15.4016	+	8.89210i	−0.555395	+	0.320657i	0.195900	+	0.980624i	$0.437237\pi$
$770$	1.08977	+	0.482566i	0.0392727	+	0.0173905i
$771$		0			0
$772$	−8.95240	−	15.5060i	−0.322204	−	0.558074i
$773$	13.0759	+	22.6481i	0.470307	+	0.814596i	0.999423	−	0.0339536i	$-0.0108099\pi$
$773$	13.0759	+	22.6481i	0.470307	+	0.814596i	−0.529116	+	0.848549i	$0.677477\pi$
$774$		0			0
$775$	0.497185	+	0.287050i	0.0178594	+	0.0103111i
$776$	5.01988	−	8.69468i	0.180203	−	0.312121i
$777$		0			0
$778$	−14.0160	−	24.2765i	−0.502499	−	0.870355i
$779$			10.4954i			0.376035i
$780$		0			0
$781$	−1.75041			−0.0626344
$782$	−19.1227	+	33.1214i	−0.683825	+	1.18442i
$783$		0			0
$784$	−6.84110	+	1.48301i	−0.244325	+	0.0529646i
$785$	16.6593	+	9.61826i	0.594596	+	0.343290i
$786$		0			0
$787$	19.8282	+	11.4478i	0.706800	+	0.408071i	0.809875	−	0.586603i	$-0.199535\pi$
$787$	19.8282	+	11.4478i	0.706800	+	0.408071i	−0.103075	+	0.994674i	$0.532868\pi$
$788$	10.9572	+	6.32615i	0.390335	+	0.225360i
$789$		0			0
$790$	−1.73760	−	1.00320i	−0.0618209	−	0.0356923i
$791$	−21.6424	+	48.8748i	−0.769514	+	1.73779i
$792$		0			0
$793$	24.2670	−	42.0317i	0.861748	−	1.49259i
$794$	29.2382			1.03762
$795$		0			0
$796$			21.1220i			0.748648i
$797$	8.74751	+	15.1511i	0.309853	+	0.536681i	0.978330	−	0.207052i	$-0.0663869\pi$
$797$	8.74751	+	15.1511i	0.309853	+	0.536681i	−0.668477	+	0.743733i	$0.733054\pi$
$798$		0			0
$799$	29.2057	−	50.5858i	1.03322	−	1.78960i
$800$	0.866025	+	0.500000i	0.0306186	+	0.0176777i
$801$		0			0
$802$	−5.78471	−	10.0194i	−0.204265	−	0.353798i
$803$	−1.27788	−	2.21335i	−0.0450953	−	0.0781073i
$804$		0			0
$805$	−7.58250	−	10.3922i	−0.267248	−	0.366278i
$806$	−2.44658	+	1.41254i	−0.0861773	+	0.0497545i
$807$		0			0
$808$			5.49909i			0.193457i
$809$	3.79610	−	2.19168i	0.133464	−	0.0770553i	−0.431782	−	0.901978i	$-0.642115\pi$
$809$	3.79610	−	2.19168i	0.133464	−	0.0770553i	0.565245	+	0.824923i	$0.308782\pi$
$810$		0			0
$811$			55.5831i			1.95179i	0.218247	+	0.975893i	$0.429966\pi$
$811$			55.5831i			1.95179i	−0.218247	+	0.975893i	$0.570034\pi$
$812$	9.96447	−	22.5027i	0.349684	−	0.789690i
$813$		0			0
$814$	−0.650313			−0.0227935
$815$	3.11468	−	5.39478i	0.109102	−	0.188971i
$816$		0			0
$817$	4.36181	−	2.51829i	0.152600	−	0.0881039i
$818$	2.07755			0.0726398
$819$		0			0
$820$	−1.91345			−0.0668205
$821$	13.1066	−	7.56707i	0.457422	−	0.264093i	−0.253538	−	0.967325i	$-0.581594\pi$
$821$	13.1066	−	7.56707i	0.457422	−	0.264093i	0.710960	+	0.703233i	$0.248261\pi$
$822$		0			0
$823$	18.1011	−	31.3520i	0.630964	−	1.09286i	−0.356391	−	0.934337i	$-0.615993\pi$
$823$	18.1011	−	31.3520i	0.630964	−	1.09286i	0.987355	−	0.158525i	$-0.0506739\pi$
$824$	−15.5075			−0.540230
$825$		0			0
$826$	−13.8254	−	18.9485i	−0.481047	−	0.659302i
$827$			3.78131i			0.131489i	0.997836	+	0.0657446i	$0.0209422\pi$
$827$			3.78131i			0.131489i	−0.997836	+	0.0657446i	$0.979058\pi$
$828$		0			0
$829$	24.5988	−	14.2021i	0.854352	−	0.493260i	−0.00776491	−	0.999970i	$-0.502472\pi$
$829$	24.5988	−	14.2021i	0.854352	−	0.493260i	0.862117	+	0.506710i	$0.169138\pi$
$830$			9.53378i			0.330922i
$831$		0			0
$832$	−4.26160	+	2.46044i	−0.147745	+	0.0853003i
$833$	53.8101	−	11.6649i	1.86441	−	0.404165i
$834$		0			0
$835$	3.60660	+	6.24681i	0.124811	+	0.216180i
$836$	1.23543	+	2.13983i	0.0427283	+	0.0740076i
$837$		0			0
$838$	−5.45962	−	3.15211i	−0.188600	−	0.108888i
$839$	−13.6621	+	23.6634i	−0.471667	+	0.816951i	−0.999475	−	0.0324131i	$-0.989681\pi$
$839$	−13.6621	+	23.6634i	−0.471667	+	0.816951i	0.527808	+	0.849364i	$0.323014\pi$
$840$		0			0
$841$	28.7615	+	49.8165i	0.991777	+	1.71781i
$842$		−	2.60242i		−	0.0896854i
$843$		0			0
$844$	20.0264			0.689338
$845$	5.60751	−	9.71249i	0.192904	−	0.334120i
$846$		0			0
$847$	23.0767	−	16.8375i	0.792926	−	0.578544i
$848$	8.30591	+	4.79542i	0.285226	+	0.164675i
$849$		0			0
$850$	−6.81190	−	3.93285i	−0.233646	−	0.134896i
$851$	6.07891	+	3.50966i	0.208382	+	0.120310i
$852$		0			0
$853$	−7.91557	−	4.57006i	−0.271024	−	0.156476i	0.358329	−	0.933595i	$-0.383347\pi$
$853$	−7.91557	−	4.57006i	−0.271024	−	0.156476i	−0.629353	+	0.777120i	$0.716680\pi$
$854$	2.78002	+	25.9463i	0.0951303	+	0.887863i
$855$		0			0
$856$	4.96546	−	8.60043i	0.169716	−	0.293957i
$857$	−0.951997			−0.0325196			−0.0162598	−	0.999868i	$-0.505176\pi$
$857$	−0.951997			−0.0325196			−0.0162598	+	0.999868i	$0.505176\pi$
$858$		0			0
$859$			35.4135i			1.20829i	0.796873	+	0.604147i	$0.206486\pi$
$859$			35.4135i			1.20829i	−0.796873	+	0.604147i	$0.793514\pi$
$860$	0.459119	+	0.795218i	0.0156558	+	0.0271167i
$861$		0			0
$862$	−4.88511	+	8.46126i	−0.166388	+	0.288192i
$863$	22.9444	+	13.2469i	0.781036	+	0.450931i	0.836797	−	0.547513i	$-0.184425\pi$
$863$	22.9444	+	13.2469i	0.781036	+	0.450931i	−0.0557615	+	0.998444i	$0.517759\pi$
$864$		0			0
$865$	−7.80001	−	13.5100i	−0.265208	−	0.459354i
$866$	−17.2272	−	29.8383i	−0.585403	−	1.01395i
$867$		0			0
$868$	0.615001	−	1.38885i	0.0208745	−	0.0471407i
$869$	0.782739	−	0.451915i	0.0265526	−	0.0153301i
$870$		0			0
$871$		−	22.8429i		−	0.774003i
$872$	−3.85941	+	2.22823i	−0.130696	+	0.0754575i
$873$		0			0
$874$		−	26.6699i		−	0.902123i
$875$	2.13731	−	1.55945i	0.0722544	−	0.0527191i
$876$		0			0
$877$	12.5178			0.422697			0.211349	−	0.977411i	$-0.432214\pi$
$877$	12.5178			0.422697			0.211349	+	0.977411i	$0.432214\pi$
$878$	10.3639	−	17.9508i	0.349765	−	0.605810i
$879$		0			0
$880$	−0.390121	+	0.225236i	−0.0131510	+	0.00759271i
$881$	32.3516			1.08995			0.544977	−	0.838451i	$-0.316538\pi$
$881$	32.3516			1.08995			0.544977	+	0.838451i	$0.316538\pi$
$882$		0			0
$883$	24.9749			0.840473			0.420237	−	0.907415i	$-0.361947\pi$
$883$	24.9749			0.840473			0.420237	+	0.907415i	$0.361947\pi$
$884$	33.5205	−	19.3531i	1.12742	−	0.650914i
$885$		0			0
$886$	4.76808	−	8.25856i	0.160187	−	0.277452i
$887$	0.411815			0.0138274			0.00691370	−	0.999976i	$-0.497799\pi$
$887$	0.411815			0.0138274			0.00691370	+	0.999976i	$0.497799\pi$
$888$		0			0
$889$	6.60021	−	4.81572i	0.221364	−	0.161514i
$890$			3.96890i			0.133038i
$891$		0			0
$892$	2.43988	−	1.40867i	0.0816933	−	0.0471657i
$893$			40.7325i			1.36306i
$894$		0			0
$895$	3.30274	−	1.90684i	0.110398	−	0.0637386i
$896$	1.07124	−	2.41918i	0.0357877	−	0.0808192i
$897$		0			0
$898$	1.11500	+	1.93123i	0.0372080	+	0.0644461i
$899$	2.67007	+	4.62470i	0.0890520	+	0.154243i
$900$		0			0
$901$	−65.3318	−	37.7193i	−2.17652	−	1.25661i
$902$	0.430978	−	0.746475i	0.0143500	−	0.0248549i
$903$		0			0
$904$	−10.1015	−	17.4964i	−0.335972	−	0.581920i
$905$			4.59480i			0.152736i
$906$		0			0
$907$	−40.4316			−1.34251			−0.671254	−	0.741227i	$-0.734244\pi$
$907$	−40.4316			−1.34251			−0.671254	+	0.741227i	$0.734244\pi$
$908$	1.29508	−	2.24315i	0.0429789	−	0.0744416i
$909$		0			0
$910$	1.38703	+	12.9453i	0.0459796	+	0.429133i
$911$	24.9849	+	14.4250i	0.827786	+	0.477923i	0.853094	−	0.521757i	$-0.174723\pi$
$911$	24.9849	+	14.4250i	0.827786	+	0.477923i	−0.0253077	+	0.999680i	$0.508057\pi$
$912$		0			0
$913$	−3.71932	−	2.14735i	−0.123092	−	0.0710670i
$914$	11.1513	+	6.43820i	0.368852	+	0.212957i
$915$		0			0
$916$	−18.6354	−	10.7592i	−0.615732	−	0.355493i
$917$	33.5739	−	24.4965i	1.10871	−	0.808947i
$918$		0			0
$919$	1.99289	−	3.45179i	0.0657394	−	0.113864i	−0.831282	−	0.555850i	$-0.812393\pi$
$919$	1.99289	−	3.45179i	0.0657394	−	0.113864i	0.897022	+	0.441986i	$0.145726\pi$
$920$	4.86229			0.160305
$921$		0			0
$922$		−	3.13475i		−	0.103238i
$923$	−9.56055	−	16.5594i	−0.314689	−	0.545058i
$924$		0			0
$925$	−0.721812	+	1.25022i	−0.0237330	+	0.0411068i
$926$	12.5635	+	7.25355i	0.412863	+	0.238367i
$927$		0			0
$928$	4.65089	+	8.05558i	0.152673	+	0.264437i
$929$	21.0976	+	36.5422i	0.692191	+	1.19891i	0.971118	+	0.238598i	$0.0766878\pi$
$929$	21.0976	+	36.5422i	0.692191	+	1.19891i	−0.278927	+	0.960312i	$0.589979\pi$
$930$		0			0
$931$	−28.4294	+	25.8065i	−0.931735	+	0.845773i
$932$	2.79452	−	1.61342i	0.0915377	−	0.0528493i
$933$		0			0
$934$		−	9.66081i		−	0.316111i
$935$	3.06857	−	1.77164i	0.100353	−	0.0579389i
$936$		0			0
$937$			41.8456i			1.36704i	0.729933	+	0.683519i	$0.239551\pi$
$937$			41.8456i			1.36704i	−0.729933	+	0.683519i	$0.760449\pi$
$938$	7.23904	+	9.92151i	0.236363	+	0.323949i
$939$		0			0
$940$	−7.42609			−0.242212
$941$	17.1592	−	29.7207i	0.559375	−	0.968866i	−0.438174	−	0.898890i	$-0.644374\pi$
$941$	17.1592	−	29.7207i	0.559375	−	0.968866i	0.997549	−	0.0699758i	$-0.0222922\pi$
$942$		0			0
$943$	−8.05727	+	4.65187i	−0.262381	+	0.151486i
$944$	8.86555			0.288549
$945$		0			0
$946$	−0.413641			−0.0134486
$947$	21.0886	−	12.1755i	0.685289	−	0.395652i	−0.116556	−	0.993184i	$-0.537185\pi$
$947$	21.0886	−	12.1755i	0.685289	−	0.395652i	0.801845	+	0.597532i	$0.203852\pi$
$948$		0			0
$949$	13.9593	−	24.1782i	0.453138	−	0.784857i
$950$	5.48505			0.177958
$951$		0			0
$952$	−8.42608	+	19.0286i	−0.273091	+	0.616719i
$953$			39.1967i			1.26970i	0.772634	+	0.634852i	$0.218939\pi$
$953$			39.1967i			1.26970i	−0.772634	+	0.634852i	$0.781061\pi$
$954$		0			0
$955$	21.7317	−	12.5468i	0.703221	−	0.406005i
$956$			16.0985i			0.520661i
$957$		0			0
$958$	30.9480	−	17.8678i	0.999885	−	0.577284i
$959$	−20.3713	−	27.9201i	−0.657825	−	0.901586i
$960$		0			0
$961$	−15.3352	−	26.5614i	−0.494684	−	0.856818i
$962$	−3.55195	−	6.15215i	−0.114519	−	0.198353i
$963$		0			0
$964$	22.2029	+	12.8188i	0.715106	+	0.412867i
$965$	8.95240	−	15.5060i	0.288188	−	0.499156i
$966$		0			0
$967$	7.42308	+	12.8572i	0.238710	+	0.413458i	0.960344	−	0.278816i	$-0.0899421\pi$
$967$	7.42308	+	12.8572i	0.238710	+	0.413458i	−0.721634	+	0.692275i	$0.756609\pi$
$968$			10.7971i			0.347031i
$969$		0			0
$970$	10.0398			0.322357
$971$	−21.8681	+	37.8766i	−0.701780	+	1.21552i	0.266061	+	0.963956i	$0.414278\pi$
$971$	−21.8681	+	37.8766i	−0.701780	+	1.21552i	−0.967841	+	0.251562i	$0.919056\pi$
$972$		0			0
$973$	−0.702109	+	1.58557i	−0.0225086	+	0.0508309i
$974$	16.3170	+	9.42060i	0.522829	+	0.301855i
$975$		0			0
$976$	−8.54152	−	4.93145i	−0.273407	−	0.157852i
$977$	−36.7089	−	21.1939i	−1.17442	−	0.678052i	−0.219704	−	0.975567i	$-0.570509\pi$
$977$	−36.7089	−	21.1939i	−1.17442	−	0.678052i	−0.954717	+	0.297514i	$0.903842\pi$
$978$		0			0
$979$	−1.54835	−	0.893939i	−0.0494854	−	0.0285704i
$980$	−4.70487	−	5.18306i	−0.150292	−	0.165567i
$981$		0			0
$982$	−8.05323	+	13.9486i	−0.256989	+	0.445118i
$983$	−57.2841			−1.82708			−0.913540	−	0.406748i	$-0.866663\pi$
$983$	−57.2841			−1.82708			−0.913540	+	0.406748i	$0.866663\pi$
$984$		0			0
$985$			12.6523i			0.403136i
$986$	−36.5825	−	63.3628i	−1.16502	−	2.01788i
$987$		0			0
$988$	−13.4956	+	23.3751i	−0.429353	+	0.743661i
$989$	3.86658	+	2.23237i	0.122950	+	0.0709853i
$990$		0			0
$991$	−13.4576	−	23.3093i	−0.427496	−	0.740445i	0.569154	−	0.822231i	$-0.307271\pi$
$991$	−13.4576	−	23.3093i	−0.427496	−	0.740445i	−0.996650	+	0.0817862i	$0.973938\pi$
$992$	0.287050	+	0.497185i	0.00911384	+	0.0157856i
$993$		0			0
$994$	9.40024	+	4.16254i	0.298158	+	0.132028i
$995$	−18.2922	+	10.5610i	−0.579900	+	0.334806i
$996$		0			0
$997$		−	59.1431i		−	1.87308i	−0.350561	−	0.936540i	$-0.614009\pi$
$997$		−	59.1431i		−	1.87308i	0.350561	−	0.936540i	$-0.385991\pi$
$998$	−1.17141	+	0.676312i	−0.0370802	+	0.0214083i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.t.b.1601.5		28
3.2	odd	2		630.2.t.b.551.8	yes	28
7.3	odd	6		1890.2.bk.b.521.9		28
9.4	even	3		630.2.bk.b.131.3	yes	28
9.5	odd	6		1890.2.bk.b.341.9		28
21.17	even	6		630.2.bk.b.101.10	yes	28
63.31	odd	6		630.2.t.b.311.8	✓	28
63.59	even	6	inner	1890.2.t.b.1151.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.8	✓	28	63.31	odd	6
630.2.t.b.551.8	yes	28	3.2	odd	2
630.2.bk.b.101.10	yes	28	21.17	even	6
630.2.bk.b.131.3	yes	28	9.4	even	3
1890.2.t.b.1151.5		28	63.59	even	6	inner
1890.2.t.b.1601.5		28	1.1	even	1	trivial
1890.2.bk.b.341.9		28	9.5	odd	6
1890.2.bk.b.521.9		28	7.3	odd	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.13731 - 1.55945i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{5} +(2.13731 - 1.55945i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} -0.450472i q^{11} +(4.26160 - 2.46044i) q^{13} +(-1.07124 + 2.41918i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.93285 + 6.81190i) q^{17} +(-4.75019 - 2.74252i) q^{19} +(0.500000 - 0.866025i) q^{20} +(0.225236 + 0.390121i) q^{22} -4.86229i q^{23} +1.00000 q^{25} +(-2.46044 + 4.26160i) q^{26} +(-0.281867 - 2.63069i) q^{28} +(8.05558 + 4.65089i) q^{29} +(0.497185 + 0.287050i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-6.81190 - 3.93285i) q^{34} +(2.13731 - 1.55945i) q^{35} +(-0.721812 + 1.25022i) q^{37} +5.48505 q^{38} +1.00000i q^{40} +(-0.956724 - 1.65709i) q^{41} +(-0.459119 + 0.795218i) q^{43} +(-0.390121 - 0.225236i) q^{44} +(2.43115 + 4.21087i) q^{46} +(-3.71305 - 6.43119i) q^{47} +(2.13623 - 6.66607i) q^{49} +(-0.866025 + 0.500000i) q^{50} -4.92088i q^{52} +(-8.30591 + 4.79542i) q^{53} -0.450472i q^{55} +(1.55945 + 2.13731i) q^{56} -9.30178 q^{58} +(-4.43278 + 7.67779i) q^{59} +(8.54152 - 4.93145i) q^{61} -0.574100 q^{62} -1.00000 q^{64} +(4.26160 - 2.46044i) q^{65} +(2.32102 - 4.02013i) q^{67} +7.86570 q^{68} +(-1.07124 + 2.41918i) q^{70} -3.88571i q^{71} +(4.91339 - 2.83675i) q^{73} -1.44362i q^{74} +(-4.75019 + 2.74252i) q^{76} +(-0.702489 - 0.962801i) q^{77} +(1.00320 + 1.73760i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(1.65709 + 0.956724i) q^{82} +(4.76689 - 8.25650i) q^{83} +(3.93285 + 6.81190i) q^{85} -0.918239i q^{86} +0.450472 q^{88} +(1.98445 - 3.43716i) q^{89} +(5.27146 - 11.9045i) q^{91} +(-4.21087 - 2.43115i) q^{92} +(6.43119 + 3.71305i) q^{94} +(-4.75019 - 2.74252i) q^{95} +(-8.69468 - 5.01988i) q^{97} +(1.48301 + 6.84110i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7}+O(q^{10}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7	\( 28 q + 14 q^{4} + 28 q^{5} - 4 q^{7} - 6 q^{14} - 14 q^{16} + 6 q^{17} - 6 q^{19} + 14 q^{20} - 6 q^{22} + 28 q^{25} - 12 q^{26} - 8 q^{28} - 12 q^{31} - 4 q^{35} + 4 q^{37} + 12 q^{38} - 18 q^{41} + 28 q^{43} - 18 q^{46} - 30 q^{47} - 14 q^{49} + 42 q^{53} - 6 q^{56} - 12 q^{58} + 24 q^{59} + 24 q^{61} + 12 q^{62} - 28 q^{64} - 40 q^{67} + 12 q^{68} - 6 q^{70} + 6 q^{73} - 6 q^{76} + 24 q^{77} + 2 q^{79} - 14 q^{80} + 24 q^{82} + 18 q^{83} + 6 q^{85} - 12 q^{88} - 6 q^{89} + 66 q^{91} + 30 q^{92} + 42 q^{94} - 6 q^{95} - 72 q^{97} + 24 q^{98}+O(q^{100}) \) 28 * q + 14 * q^4 + 28 * q^5 - 4 * q^7 - 6 * q^14 - 14 * q^16 + 6 * q^17 - 6 * q^19 + 14 * q^20 - 6 * q^22 + 28 * q^25 - 12 * q^26 - 8 * q^28 - 12 * q^31 - 4 * q^35 + 4 * q^37 + 12 * q^38 - 18 * q^41 + 28 * q^43 - 18 * q^46 - 30 * q^47 - 14 * q^49 + 42 * q^53 - 6 * q^56 - 12 * q^58 + 24 * q^59 + 24 * q^61 + 12 * q^62 - 28 * q^64 - 40 * q^67 + 12 * q^68 - 6 * q^70 + 6 * q^73 - 6 * q^76 + 24 * q^77 + 2 * q^79 - 14 * q^80 + 24 * q^82 + 18 * q^83 + 6 * q^85 - 12 * q^88 - 6 * q^89 + 66 * q^91 + 30 * q^92 + 42 * q^94 - 6 * q^95 - 72 * q^97 + 24 * q^98

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