LMFDB - Embedded newform 1638.2.x.a.811.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(307,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("1638.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.x (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.836829184.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 $ x^8 + 14x^6 + 61x^4 + 84*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			811.4
Root			$-1.65222i$ of defining polynomial
Character	$\chi$	$=$	1638.811
Dual form			1638.2.x.a.307.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.461191 + 0.461191i) q^{5} +(-0.292893 - 2.62949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.461191 + 0.461191i) q^{5} +(-0.292893 - 2.62949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.652223 q^{10} +(-1.60525 - 1.60525i) q^{11} +(-2.51608 - 2.58251i) q^{13} +(-2.06644 - 1.65222i) q^{14} -1.00000 q^{16} +6.40303 q^{17} +(-2.52763 - 2.52763i) q^{19} +(0.461191 - 0.461191i) q^{20} -2.27016 q^{22} +8.51280i q^{23} -4.57461i q^{25} +(-3.60525 - 0.0469777i) q^{26} +(-2.62949 + 0.292893i) q^{28} -7.91120 q^{29} +(-0.922382 - 0.922382i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.52763 - 4.52763i) q^{34} +(1.07762 - 1.34778i) q^{35} +(-0.953022 - 0.953022i) q^{37} -3.57461 q^{38} -0.652223i q^{40} +(-3.89486 - 3.89486i) q^{41} +4.17620i q^{43} +(-1.60525 + 1.60525i) q^{44} +(6.01946 + 6.01946i) q^{46} +(1.41421 - 1.41421i) q^{47} +(-6.82843 + 1.54032i) q^{49} +(-3.23473 - 3.23473i) q^{50} +(-2.58251 + 2.51608i) q^{52} -9.10072 q^{53} -1.48065i q^{55} +(-1.65222 + 2.06644i) q^{56} +(-5.59406 + 5.59406i) q^{58} +(1.17834 - 1.17834i) q^{59} -14.4874i q^{61} -1.30445 q^{62} +1.00000i q^{64} +(0.0306399 - 2.35142i) q^{65} +(3.47602 - 3.47602i) q^{67} -6.40303i q^{68} +(-0.191032 - 1.71501i) q^{70} +(8.29326 - 8.29326i) q^{71} +(5.89851 - 5.89851i) q^{73} -1.34778 q^{74} +(-2.52763 + 2.52763i) q^{76} +(-3.75081 + 4.69114i) q^{77} -9.18813 q^{79} +(-0.461191 - 0.461191i) q^{80} -5.50817 q^{82} +(9.98882 + 9.98882i) q^{83} +(2.95302 + 2.95302i) q^{85} +(2.95302 + 2.95302i) q^{86} +2.27016i q^{88} +(8.54709 - 8.54709i) q^{89} +(-6.05374 + 7.37239i) q^{91} +8.51280 q^{92} -2.00000i q^{94} -2.33144i q^{95} +(-0.272296 - 0.272296i) q^{97} +(-3.73926 + 5.91760i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} - 8 q^{7}+O(q^{10}) $ 8 * q - 4 * q^5 - 8 * q^7	$ 8 q - 4 q^{5} - 8 q^{7} - 4 q^{10} - 16 q^{13} + 4 q^{14} - 8 q^{16} + 4 q^{17} + 8 q^{19} - 4 q^{20} - 12 q^{22} - 16 q^{26} - 12 q^{29} + 8 q^{31} + 8 q^{34} + 24 q^{35} - 4 q^{37} - 4 q^{38} + 12 q^{41} + 24 q^{46} - 32 q^{49} + 8 q^{50} + 4 q^{52} - 40 q^{53} - 4 q^{56} + 4 q^{58} - 8 q^{59} + 8 q^{62} + 12 q^{65} + 32 q^{67} + 12 q^{71} - 20 q^{73} - 20 q^{74} + 8 q^{76} + 8 q^{77} + 24 q^{79} + 4 q^{80} - 40 q^{82} + 44 q^{83} + 20 q^{85} + 20 q^{86} + 16 q^{89} - 12 q^{91} + 28 q^{92} + 8 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q - 4 * q^5 - 8 * q^7 - 4 * q^10 - 16 * q^13 + 4 * q^14 - 8 * q^16 + 4 * q^17 + 8 * q^19 - 4 * q^20 - 12 * q^22 - 16 * q^26 - 12 * q^29 + 8 * q^31 + 8 * q^34 + 24 * q^35 - 4 * q^37 - 4 * q^38 + 12 * q^41 + 24 * q^46 - 32 * q^49 + 8 * q^50 + 4 * q^52 - 40 * q^53 - 4 * q^56 + 4 * q^58 - 8 * q^59 + 8 * q^62 + 12 * q^65 + 32 * q^67 + 12 * q^71 - 20 * q^73 - 20 * q^74 + 8 * q^76 + 8 * q^77 + 24 * q^79 + 4 * q^80 - 40 * q^82 + 44 * q^83 + 20 * q^85 + 20 * q^86 + 16 * q^89 - 12 * q^91 + 28 * q^92 + 8 * q^97 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	0.461191	+	0.461191i	0.206251	+	0.206251i	0.802672	−	0.596421i	$-0.203411\pi$
$5$	0.461191	+	0.461191i	0.206251	+	0.206251i	−0.596421	+	0.802672i	$0.703411\pi$
$6$		0			0
$7$	−0.292893	−	2.62949i	−0.110703	−	0.993854i
$7$	−0.292893	−	2.62949i	−0.110703	−	0.993854i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	0.652223			0.206251
$11$	−1.60525	−	1.60525i	−0.484000	−	0.484000i	0.422407	−	0.906406i	$-0.361185\pi$
$11$	−1.60525	−	1.60525i	−0.484000	−	0.484000i	−0.906406	+	0.422407i	$0.861185\pi$
$12$		0			0
$13$	−2.51608	−	2.58251i	−0.697834	−	0.716260i
$13$	−2.51608	−	2.58251i	−0.697834	−	0.716260i
$14$	−2.06644	−	1.65222i	−0.552278	−	0.441575i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	6.40303			1.55296			0.776482	−	0.630140i	$-0.217002\pi$
$17$	6.40303			1.55296			0.776482	+	0.630140i	$0.217002\pi$
$18$		0			0
$19$	−2.52763	−	2.52763i	−0.579878	−	0.579878i	0.354992	−	0.934869i	$-0.384484\pi$
$19$	−2.52763	−	2.52763i	−0.579878	−	0.579878i	−0.934869	+	0.354992i	$0.884484\pi$
$20$	0.461191	−	0.461191i	0.103125	−	0.103125i
$21$		0			0
$22$	−2.27016			−0.484000
$23$			8.51280i			1.77504i	0.460768	+	0.887521i	$0.347574\pi$
$23$			8.51280i			1.77504i	−0.460768	+	0.887521i	$0.652426\pi$
$24$		0			0
$25$		−	4.57461i		−	0.914921i
$26$	−3.60525	−	0.0469777i	−0.707047	−	0.00921308i
$27$		0			0
$28$	−2.62949	+	0.292893i	−0.496927	+	0.0553516i
$29$	−7.91120			−1.46907			−0.734537	−	0.678569i	$-0.762600\pi$
$29$	−7.91120			−1.46907			−0.734537	+	0.678569i	$0.762600\pi$
$30$		0			0
$31$	−0.922382	−	0.922382i	−0.165665	−	0.165665i	0.619406	−	0.785071i	$-0.287373\pi$
$31$	−0.922382	−	0.922382i	−0.165665	−	0.165665i	−0.785071	+	0.619406i	$0.787373\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$	4.52763	−	4.52763i	0.776482	−	0.776482i
$35$	1.07762	−	1.34778i	0.182151	−	0.227816i
$36$		0			0
$37$	−0.953022	−	0.953022i	−0.156676	−	0.156676i	0.624416	−	0.781092i	$-0.285337\pi$
$37$	−0.953022	−	0.953022i	−0.156676	−	0.156676i	−0.781092	+	0.624416i	$0.785337\pi$
$38$	−3.57461			−0.579878
$39$		0			0
$40$		−	0.652223i		−	0.103125i
$41$	−3.89486	−	3.89486i	−0.608275	−	0.608275i	0.334220	−	0.942495i	$-0.391527\pi$
$41$	−3.89486	−	3.89486i	−0.608275	−	0.608275i	−0.942495	+	0.334220i	$0.891527\pi$
$42$		0			0
$43$			4.17620i			0.636865i	0.947946	+	0.318433i	$0.103156\pi$
$43$			4.17620i			0.636865i	−0.947946	+	0.318433i	$0.896844\pi$
$44$	−1.60525	+	1.60525i	−0.242000	+	0.242000i
$45$		0			0
$46$	6.01946	+	6.01946i	0.887521	+	0.887521i
$47$	1.41421	−	1.41421i	0.206284	−	0.206284i	−0.596402	−	0.802686i	$-0.703403\pi$
$47$	1.41421	−	1.41421i	0.206284	−	0.206284i	0.802686	+	0.596402i	$0.203403\pi$
$48$		0			0
$49$	−6.82843	+	1.54032i	−0.975490	+	0.220046i
$50$	−3.23473	−	3.23473i	−0.457461	−	0.457461i
$51$		0			0
$52$	−2.58251	+	2.51608i	−0.358130	+	0.348917i
$53$	−9.10072			−1.25008			−0.625040	−	0.780593i	$-0.714917\pi$
$53$	−9.10072			−1.25008			−0.625040	+	0.780593i	$0.714917\pi$
$54$		0			0
$55$		−	1.48065i		−	0.199651i
$56$	−1.65222	+	2.06644i	−0.220788	+	0.276139i
$57$		0			0
$58$	−5.59406	+	5.59406i	−0.734537	+	0.734537i
$59$	1.17834	−	1.17834i	0.153407	−	0.153407i	−0.626231	−	0.779638i	$-0.715403\pi$
$59$	1.17834	−	1.17834i	0.153407	−	0.153407i	0.779638	+	0.626231i	$0.215403\pi$
$60$		0			0
$61$		−	14.4874i		−	1.85492i	−0.373918	−	0.927462i	$-0.621986\pi$
$61$		−	14.4874i		−	1.85492i	0.373918	−	0.927462i	$-0.378014\pi$
$62$	−1.30445			−0.165665
$63$		0			0
$64$			1.00000i			0.125000i
$65$	0.0306399	−	2.35142i	0.00380041	−	0.291658i
$66$		0			0
$67$	3.47602	−	3.47602i	0.424663	−	0.424663i	−0.462142	−	0.886806i	$-0.652919\pi$
$67$	3.47602	−	3.47602i	0.424663	−	0.424663i	0.886806	+	0.462142i	$0.152919\pi$
$68$		−	6.40303i		−	0.776482i
$69$		0			0
$70$	−0.191032	−	1.71501i	−0.0228327	−	0.204983i
$71$	8.29326	−	8.29326i	0.984229	−	0.984229i	−0.0156481	−	0.999878i	$-0.504981\pi$
$71$	8.29326	−	8.29326i	0.984229	−	0.984229i	0.999878	+	0.0156481i	$0.00498116\pi$
$72$		0			0
$73$	5.89851	−	5.89851i	0.690368	−	0.690368i	−0.271945	−	0.962313i	$-0.587667\pi$
$73$	5.89851	−	5.89851i	0.690368	−	0.690368i	0.962313	+	0.271945i	$0.0876667\pi$
$74$	−1.34778			−0.156676
$75$		0			0
$76$	−2.52763	+	2.52763i	−0.289939	+	0.289939i
$77$	−3.75081	+	4.69114i	−0.427444	+	0.534605i
$78$		0			0
$79$	−9.18813			−1.03375			−0.516873	−	0.856062i	$-0.672904\pi$
$79$	−9.18813			−1.03375			−0.516873	+	0.856062i	$0.672904\pi$
$80$	−0.461191	−	0.461191i	−0.0515627	−	0.0515627i
$81$		0			0
$82$	−5.50817			−0.608275
$83$	9.98882	+	9.98882i	1.09642	+	1.09642i	0.994826	+	0.101589i	$0.0323926\pi$
$83$	9.98882	+	9.98882i	1.09642	+	1.09642i	0.101589	+	0.994826i	$0.467607\pi$
$84$		0			0
$85$	2.95302	+	2.95302i	0.320300	+	0.320300i
$86$	2.95302	+	2.95302i	0.318433	+	0.318433i
$87$		0			0
$88$			2.27016i			0.242000i
$89$	8.54709	−	8.54709i	0.905989	−	0.905989i	−0.0899564	−	0.995946i	$-0.528673\pi$
$89$	8.54709	−	8.54709i	0.905989	−	0.905989i	0.995946	+	0.0899564i	$0.0286728\pi$
$90$		0			0
$91$	−6.05374	+	7.37239i	−0.634605	+	0.772837i
$92$	8.51280			0.887521
$93$		0			0
$94$		−	2.00000i		−	0.206284i
$95$		−	2.33144i		−	0.239201i
$96$		0			0
$97$	−0.272296	−	0.272296i	−0.0276474	−	0.0276474i	0.693148	−	0.720795i	$-0.256223\pi$
$97$	−0.272296	−	0.272296i	−0.0276474	−	0.0276474i	−0.720795	+	0.693148i	$0.756223\pi$
$98$	−3.73926	+	5.91760i	−0.377722	+	0.597768i
$99$		0			0
$100$	−4.57461			−0.457461
$101$	−8.03892			−0.799902			−0.399951	−	0.916536i	$-0.630973\pi$
$101$	−8.03892			−0.799902			−0.399951	+	0.916536i	$0.630973\pi$
$102$		0			0
$103$	7.62934			0.751741			0.375870	−	0.926672i	$-0.377344\pi$
$103$	7.62934			0.751741			0.375870	+	0.926672i	$0.377344\pi$
$104$	−0.0469777	+	3.60525i	−0.00460654	+	0.353523i
$105$		0			0
$106$	−6.43518	+	6.43518i	−0.625040	+	0.625040i
$107$	14.3986			1.39197			0.695984	−	0.718058i	$-0.254969\pi$
$107$	14.3986			1.39197			0.695984	+	0.718058i	$0.254969\pi$
$108$		0			0
$109$	−10.6815	+	10.6815i	−1.02310	+	1.02310i	−0.0233724	+	0.999727i	$0.507440\pi$
$109$	−10.6815	+	10.6815i	−1.02310	+	1.02310i	−0.999727	+	0.0233724i	$0.992560\pi$
$110$	−1.04698	−	1.04698i	−0.0998254	−	0.0998254i
$111$		0			0
$112$	0.292893	+	2.62949i	0.0276758	+	0.248463i
$113$	−15.0256			−1.41349			−0.706745	−	0.707469i	$-0.749837\pi$
$113$	−15.0256			−1.41349			−0.706745	+	0.707469i	$0.749837\pi$
$114$		0			0
$115$	−3.92603	+	3.92603i	−0.366104	+	0.366104i
$116$			7.91120i			0.734537i
$117$		0			0
$118$		−	1.66642i		−	0.153407i
$119$	−1.87540	−	16.8367i	−0.171918	−	1.54342i
$120$		0			0
$121$		−	5.84638i		−	0.531489i
$122$	−10.2442	−	10.2442i	−0.927462	−	0.927462i
$123$		0			0
$124$	−0.922382	+	0.922382i	−0.0828324	+	0.0828324i
$125$	4.41572	−	4.41572i	0.394954	−	0.394954i
$126$		0			0
$127$		−	15.7970i		−	1.40176i	−0.713280	−	0.700879i	$-0.752791\pi$
$127$		−	15.7970i		−	1.40176i	0.713280	−	0.700879i	$-0.247209\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−1.64104	−	1.68437i	−0.143929	−	0.147729i
$131$			1.75522i			0.153355i	0.997056	+	0.0766773i	$0.0244311\pi$
$131$			1.75522i			0.153355i	−0.997056	+	0.0766773i	$0.975569\pi$
$132$		0			0
$133$	−5.90604	+	7.38669i	−0.512119	+	0.640508i
$134$		−	4.91583i		−	0.424663i
$135$		0			0
$136$	−4.52763	−	4.52763i	−0.388241	−	0.388241i
$137$	1.82994	+	1.82994i	0.156342	+	0.156342i	0.780944	−	0.624602i	$-0.214739\pi$
$137$	1.82994	+	1.82994i	0.156342	+	0.156342i	−0.624602	+	0.780944i	$0.714739\pi$
$138$		0			0
$139$			13.8448i			1.17430i	0.809479	+	0.587149i	$0.199750\pi$
$139$			13.8448i			1.17430i	−0.809479	+	0.587149i	$0.800250\pi$
$140$	−1.34778	−	1.07762i	−0.113908	−	0.0910753i
$141$		0			0
$142$		−	11.7284i		−	0.984229i
$143$	−0.106647	+	8.18448i	−0.00891825	+	0.684421i
$144$		0			0
$145$	−3.64858	−	3.64858i	−0.302998	−	0.302998i
$146$		−	8.34175i		−	0.690368i
$147$		0			0
$148$	−0.953022	+	0.953022i	−0.0783380	+	0.0783380i
$149$	3.12824	−	3.12824i	0.256276	−	0.256276i	−0.567262	−	0.823537i	$-0.691997\pi$
$149$	3.12824	−	3.12824i	0.256276	−	0.256276i	0.823537	+	0.567262i	$0.191997\pi$
$150$		0			0
$151$	11.5502	+	11.5502i	0.939943	+	0.939943i	0.998296	−	0.0583534i	$-0.0185850\pi$
$151$	11.5502	+	11.5502i	0.939943	+	0.939943i	−0.0583534	+	0.998296i	$0.518585\pi$
$152$			3.57461i			0.289939i
$153$		0			0
$154$	0.664914	+	5.96936i	0.0535803	+	0.481025i
$155$		−	0.850789i		−	0.0683370i
$156$		0			0
$157$			18.5294i			1.47880i	0.673264	+	0.739402i	$0.264892\pi$
$157$			18.5294i			1.47880i	−0.673264	+	0.739402i	$0.735108\pi$
$158$	−6.49699	+	6.49699i	−0.516873	+	0.516873i
$159$		0			0
$160$	−0.652223			−0.0515627
$161$	22.3843	−	2.49334i	1.76413	−	0.196503i
$162$		0			0
$163$	−13.1032	−	13.1032i	−1.02632	−	1.02632i	−0.999644	−	0.0266792i	$-0.991507\pi$
$163$	−13.1032	−	13.1032i	−1.02632	−	1.02632i	−0.0266792	−	0.999644i	$-0.508493\pi$
$164$	−3.89486	+	3.89486i	−0.304138	+	0.304138i
$165$		0			0
$166$	14.1263			1.09642
$167$	9.82552	−	9.82552i	0.760322	−	0.760322i	−0.216059	−	0.976380i	$-0.569320\pi$
$167$	9.82552	−	9.82552i	0.760322	−	0.760322i	0.976380	+	0.216059i	$0.0693202\pi$
$168$		0			0
$169$	−0.338732	+	12.9956i	−0.0260563	+	0.999660i
$170$	4.17620			0.320300
$171$		0			0
$172$	4.17620			0.318433
$173$	−10.9940			−0.835856			−0.417928	−	0.908480i	$-0.637244\pi$
$173$	−10.9940			−0.835856			−0.417928	+	0.908480i	$0.637244\pi$
$174$		0			0
$175$	−12.0289	+	1.33987i	−0.909298	+	0.101285i
$176$	1.60525	+	1.60525i	0.121000	+	0.121000i
$177$		0			0
$178$		−	12.0874i		−	0.905989i
$179$		−	2.54656i		−	0.190339i	−0.995461	−	0.0951695i	$-0.969661\pi$
$179$		−	2.54656i		−	0.190339i	0.995461	−	0.0951695i	$-0.0303393\pi$
$180$		0			0
$181$	13.8933			1.03268			0.516339	−	0.856384i	$-0.327295\pi$
$181$	13.8933			1.03268			0.516339	+	0.856384i	$0.327295\pi$
$182$	0.932425	+	9.49371i	0.0691159	+	0.703721i
$183$		0			0
$184$	6.01946	−	6.01946i	0.443760	−	0.443760i
$185$		−	0.879051i		−	0.0646291i
$186$		0			0
$187$	−10.2784	−	10.2784i	−0.751634	−	0.751634i
$188$	−1.41421	−	1.41421i	−0.103142	−	0.103142i
$189$		0			0
$190$	−1.64858	−	1.64858i	−0.119600	−	0.119600i
$191$	10.2290			0.740142			0.370071	−	0.929004i	$-0.379333\pi$
$191$	10.2290			0.740142			0.370071	+	0.929004i	$0.379333\pi$
$192$		0			0
$193$	12.3940	+	12.3940i	0.892139	+	0.892139i	0.994724	−	0.102585i	$-0.0327115\pi$
$193$	12.3940	+	12.3940i	0.892139	+	0.892139i	−0.102585	+	0.994724i	$0.532712\pi$
$194$	−0.385084			−0.0276474
$195$		0			0
$196$	1.54032	+	6.82843i	0.110023	+	0.487745i
$197$	−8.84638	+	8.84638i	−0.630278	+	0.630278i	−0.948138	−	0.317860i	$-0.897036\pi$
$197$	−8.84638	+	8.84638i	−0.630278	+	0.630278i	0.317860	+	0.948138i	$0.397036\pi$
$198$		0			0
$199$	7.40980			0.525267			0.262633	−	0.964896i	$-0.415409\pi$
$199$	7.40980			0.525267			0.262633	+	0.964896i	$0.415409\pi$
$200$	−3.23473	+	3.23473i	−0.228730	+	0.228730i
$201$		0			0
$202$	−5.68437	+	5.68437i	−0.399951	+	0.399951i
$203$	2.31714	+	20.8024i	0.162631	+	1.46004i
$204$		0			0
$205$		−	3.59255i		−	0.250915i
$206$	5.39475	−	5.39475i	0.375870	−	0.375870i
$207$		0			0
$208$	2.51608	+	2.58251i	0.174458	+	0.179065i
$209$			8.11492i			0.561321i
$210$		0			0
$211$	14.6299			1.00716			0.503581	−	0.863948i	$-0.332016\pi$
$211$	14.6299			1.00716			0.503581	+	0.863948i	$0.332016\pi$
$212$			9.10072i			0.625040i
$213$		0			0
$214$	10.1814	−	10.1814i	0.695984	−	0.695984i
$215$	−1.92603	+	1.92603i	−0.131354	+	0.131354i
$216$		0			0
$217$	−2.15524	+	2.69555i	−0.146307	+	0.182986i
$218$			15.1059i			1.02310i
$219$		0			0
$220$	−1.48065			−0.0998254
$221$	−16.1105	−	16.5359i	−1.08371	−	1.11233i
$222$		0			0
$223$	11.0574	+	11.0574i	0.740458	+	0.740458i	0.972666	−	0.232208i	$-0.0745951\pi$
$223$	11.0574	+	11.0574i	0.740458	+	0.740458i	−0.232208	+	0.972666i	$0.574595\pi$
$224$	2.06644	+	1.65222i	0.138070	+	0.110394i
$225$		0			0
$226$	−10.6247	+	10.6247i	−0.706745	+	0.706745i
$227$	9.31423	+	9.31423i	0.618207	+	0.618207i	0.945071	−	0.326864i	$-0.105992\pi$
$227$	9.31423	+	9.31423i	0.618207	+	0.618207i	−0.326864	+	0.945071i	$0.605992\pi$
$228$		0			0
$229$	15.5860	−	15.5860i	1.02995	−	1.02995i	0.0304148	−	0.999537i	$-0.490317\pi$
$229$	15.5860	−	15.5860i	1.02995	−	1.02995i	0.999537	−	0.0304148i	$-0.00968282\pi$
$230$			5.55224i			0.366104i
$231$		0			0
$232$	5.59406	+	5.59406i	0.367268	+	0.367268i
$233$		−	14.4240i		−	0.944948i	−0.881345	−	0.472474i	$-0.843361\pi$
$233$		−	14.4240i		−	0.944948i	0.881345	−	0.472474i	$-0.156639\pi$
$234$		0			0
$235$	1.30445			0.0850927
$236$	−1.17834	−	1.17834i	−0.0767034	−	0.0767034i
$237$		0			0
$238$	−13.2315	−	10.5792i	−0.857668	−	0.685750i
$239$	−3.83747	+	3.83747i	−0.248225	+	0.248225i	−0.820242	−	0.572017i	$-0.806161\pi$
$239$	−3.83747	+	3.83747i	−0.248225	+	0.248225i	0.572017	+	0.820242i	$0.306161\pi$
$240$		0			0
$241$	14.2110	−	14.2110i	0.915412	−	0.915412i	−0.0812794	−	0.996691i	$-0.525901\pi$
$241$	14.2110	−	14.2110i	0.915412	−	0.915412i	0.996691	+	0.0812794i	$0.0259006\pi$
$242$	−4.13401	−	4.13401i	−0.265744	−	0.265744i
$243$		0			0
$244$	−14.4874			−0.927462
$245$	−3.85959	−	2.43883i	−0.246580	−	0.155811i
$246$		0			0
$247$	−0.167927	+	12.8873i	−0.0106849	+	0.820001i
$248$			1.30445i			0.0828324i
$249$		0			0
$250$		−	6.24478i		−	0.394954i
$251$	−5.39399			−0.340465			−0.170233	−	0.985404i	$-0.554452\pi$
$251$	−5.39399			−0.340465			−0.170233	+	0.985404i	$0.554452\pi$
$252$		0			0
$253$	13.6651	−	13.6651i	0.859119	−	0.859119i
$254$	−11.1702	−	11.1702i	−0.700879	−	0.700879i
$255$		0			0
$256$	1.00000			0.0625000
$257$	4.38508			0.273534			0.136767	−	0.990603i	$-0.456329\pi$
$257$	4.38508			0.273534			0.136767	+	0.990603i	$0.456329\pi$
$258$		0			0
$259$	−2.22683	+	2.78510i	−0.138368	+	0.173057i
$260$	−2.35142	−	0.0306399i	−0.145829	−	0.00190021i
$261$		0			0
$262$	1.24113	+	1.24113i	0.0766773	+	0.0766773i
$263$	12.4336			0.766687			0.383343	−	0.923606i	$-0.374773\pi$
$263$	12.4336			0.766687			0.383343	+	0.923606i	$0.374773\pi$
$264$		0			0
$265$	−4.19717	−	4.19717i	−0.257830	−	0.257830i
$266$	1.04698	+	9.39939i	0.0641943	+	0.576313i
$267$		0			0
$268$	−3.47602	−	3.47602i	−0.212332	−	0.212332i
$269$			29.7839i			1.81596i	0.419016	+	0.907979i	$0.362375\pi$
$269$			29.7839i			1.81596i	−0.419016	+	0.907979i	$0.637625\pi$
$270$		0			0
$271$	−14.7173	+	14.7173i	−0.894010	+	0.894010i	−0.994898	−	0.100888i	$-0.967832\pi$
$271$	−14.7173	+	14.7173i	−0.894010	+	0.894010i	0.100888	+	0.994898i	$0.467832\pi$
$272$	−6.40303			−0.388241
$273$		0			0
$274$	2.58792			0.156342
$275$	−7.34336	+	7.34336i	−0.442821	+	0.442821i
$276$		0			0
$277$		−	24.1271i		−	1.44965i	−0.688930	−	0.724827i	$-0.741919\pi$
$277$		−	24.1271i		−	1.44965i	0.688930	−	0.724827i	$-0.258081\pi$
$278$	9.78973	+	9.78973i	0.587149	+	0.587149i
$279$		0			0
$280$	−1.71501	+	0.191032i	−0.102492	+	0.0114163i
$281$	7.70534	+	7.70534i	0.459662	+	0.459662i	0.898545	−	0.438882i	$-0.144626\pi$
$281$	7.70534	+	7.70534i	0.459662	+	0.459662i	−0.438882	+	0.898545i	$0.644626\pi$
$282$		0			0
$283$	6.39133			0.379925			0.189962	−	0.981791i	$-0.439163\pi$
$283$	6.39133			0.379925			0.189962	+	0.981791i	$0.439163\pi$
$284$	−8.29326	−	8.29326i	−0.492115	−	0.492115i
$285$		0			0
$286$	5.71189	+	5.86271i	0.337751	+	0.346670i
$287$	−9.10072	+	11.3823i	−0.537199	+	0.671875i
$288$		0			0
$289$	23.9988			1.41170
$290$	−5.15987			−0.302998
$291$		0			0
$292$	−5.89851	−	5.89851i	−0.345184	−	0.345184i
$293$	8.93819	−	8.93819i	0.522175	−	0.522175i	−0.396053	−	0.918228i	$-0.629620\pi$
$293$	8.93819	−	8.93819i	0.522175	−	0.522175i	0.918228	+	0.396053i	$0.129620\pi$
$294$		0			0
$295$	1.08688			0.0632806
$296$			1.34778i			0.0783380i
$297$		0			0
$298$		−	4.42400i		−	0.256276i
$299$	21.9844	−	21.4188i	1.27139	−	1.23868i
$300$		0			0
$301$	10.9813	−	1.22318i	0.632951	−	0.0705030i
$302$	16.3345			0.939943
$303$		0			0
$304$	2.52763	+	2.52763i	0.144969	+	0.144969i
$305$	6.68147	−	6.68147i	0.382580	−	0.382580i
$306$		0			0
$307$	−1.27177	+	1.27177i	−0.0725838	+	0.0725838i	−0.742467	−	0.669883i	$-0.766344\pi$
$307$	−1.27177	+	1.27177i	−0.0725838	+	0.0725838i	0.669883	+	0.742467i	$0.266344\pi$
$308$	4.69114	+	3.75081i	0.267303	+	0.213722i
$309$		0			0
$310$	−0.601599	−	0.601599i	−0.0341685	−	0.0341685i
$311$	−1.52201			−0.0863053			−0.0431527	−	0.999068i	$-0.513740\pi$
$311$	−1.52201			−0.0863053			−0.0431527	+	0.999068i	$0.513740\pi$
$312$		0			0
$313$		−	3.48506i		−	0.196987i	−0.995138	−	0.0984937i	$-0.968598\pi$
$313$		−	3.48506i		−	0.196987i	0.995138	−	0.0984937i	$-0.0314024\pi$
$314$	13.1022	+	13.1022i	0.739402	+	0.739402i
$315$		0			0
$316$			9.18813i			0.516873i
$317$	−3.61566	+	3.61566i	−0.203076	+	0.203076i	−0.801316	−	0.598241i	$-0.795867\pi$
$317$	−3.61566	+	3.61566i	−0.203076	+	0.203076i	0.598241	+	0.801316i	$0.295867\pi$
$318$		0			0
$319$	12.6994	+	12.6994i	0.711031	+	0.711031i
$320$	−0.461191	+	0.461191i	−0.0257814	+	0.0257814i
$321$		0			0
$322$	14.0650	−	17.5912i	0.783814	−	0.980317i
$323$	−16.1845	−	16.1845i	−0.900529	−	0.900529i
$324$		0			0
$325$	−11.8140	+	11.5101i	−0.655321	+	0.638463i
$326$	−18.5307			−1.02632
$327$		0			0
$328$			5.50817i			0.304138i
$329$	−4.13287	−	3.30445i	−0.227853	−	0.182180i
$330$		0			0
$331$	4.50162	−	4.50162i	0.247431	−	0.247431i	−0.572484	−	0.819916i	$-0.694020\pi$
$331$	4.50162	−	4.50162i	0.247431	−	0.247431i	0.819916	+	0.572484i	$0.194020\pi$
$332$	9.98882	−	9.98882i	0.548208	−	0.548208i
$333$		0			0
$334$		−	13.8954i		−	0.760322i
$335$	3.20622			0.175174
$336$		0			0
$337$		−	20.7331i		−	1.12940i	−0.825295	−	0.564701i	$-0.808991\pi$
$337$		−	20.7331i		−	1.12940i	0.825295	−	0.564701i	$-0.191009\pi$
$338$	8.94975	+	9.42879i	0.486802	+	0.512858i
$339$		0			0
$340$	2.95302	−	2.95302i	0.160150	−	0.160150i
$341$			2.96130i			0.160363i
$342$		0			0
$343$	6.05025	+	17.5041i	0.326683	+	0.945134i
$344$	2.95302	−	2.95302i	0.159216	−	0.159216i
$345$		0			0
$346$	−7.77391	+	7.77391i	−0.417928	+	0.417928i
$347$	−0.161276			−0.00865778			−0.00432889	−	0.999991i	$-0.501378\pi$
$347$	−0.161276			−0.00865778			−0.00432889	+	0.999991i	$0.501378\pi$
$348$		0			0
$349$	−7.17995	+	7.17995i	−0.384334	+	0.384334i	−0.872661	−	0.488327i	$-0.837607\pi$
$349$	−7.17995	+	7.17995i	−0.384334	+	0.384334i	0.488327	+	0.872661i	$0.337607\pi$
$350$	−7.55827	+	9.45313i	−0.404006	+	0.505291i
$351$		0			0
$352$	2.27016			0.121000
$353$	−9.44711	−	9.44711i	−0.502819	−	0.502819i	0.409494	−	0.912313i	$-0.365705\pi$
$353$	−9.44711	−	9.44711i	−0.502819	−	0.502819i	−0.912313	+	0.409494i	$0.865705\pi$
$354$		0			0
$355$	7.64956			0.405997
$356$	−8.54709	−	8.54709i	−0.452995	−	0.452995i
$357$		0			0
$358$	−1.80069	−	1.80069i	−0.0951695	−	0.0951695i
$359$	19.1933	+	19.1933i	1.01298	+	1.01298i	0.999915	+	0.0130682i	$0.00415986\pi$
$359$	19.1933	+	19.1933i	1.01298	+	1.01298i	0.0130682	+	0.999915i	$0.495840\pi$
$360$		0			0
$361$		−	6.22220i		−	0.327484i
$362$	9.82401	−	9.82401i	0.516339	−	0.516339i
$363$		0			0
$364$	7.37239	+	6.05374i	0.386418	+	0.317302i
$365$	5.44068			0.284778
$366$		0			0
$367$		−	24.3142i		−	1.26919i	−0.772844	−	0.634596i	$-0.781166\pi$
$367$		−	24.3142i		−	1.26919i	0.772844	−	0.634596i	$-0.218834\pi$
$368$		−	8.51280i		−	0.443760i
$369$		0			0
$370$	−0.621583	−	0.621583i	−0.0323146	−	0.0323146i
$371$	2.66554	+	23.9303i	0.138388	+	1.24240i
$372$		0			0
$373$	9.74654			0.504657			0.252328	−	0.967642i	$-0.418804\pi$
$373$	9.74654			0.504657			0.252328	+	0.967642i	$0.418804\pi$
$374$	−14.5359			−0.751634
$375$		0			0
$376$	−2.00000			−0.103142
$377$	19.9052	+	20.4308i	1.02517	+	1.05224i
$378$		0			0
$379$	14.5776	−	14.5776i	0.748802	−	0.748802i	−0.225452	−	0.974254i	$-0.572386\pi$
$379$	14.5776	−	14.5776i	0.748802	−	0.748802i	0.974254	+	0.225452i	$0.0723859\pi$
$380$	−2.33144			−0.119600
$381$		0			0
$382$	7.23297	−	7.23297i	0.370071	−	0.370071i
$383$	−20.8642	−	20.8642i	−1.06611	−	1.06611i	−0.997654	−	0.0684580i	$-0.978192\pi$
$383$	−20.8642	−	20.8642i	−1.06611	−	1.06611i	−0.0684580	−	0.997654i	$-0.521808\pi$
$384$		0			0
$385$	−3.89335	+	0.433672i	−0.198424	+	0.0221020i
$386$	17.5277			0.892139
$387$		0			0
$388$	−0.272296	+	0.272296i	−0.0138237	+	0.0138237i
$389$			6.09321i			0.308938i	0.987998	+	0.154469i	$0.0493667\pi$
$389$			6.09321i			0.308938i	−0.987998	+	0.154469i	$0.950633\pi$
$390$		0			0
$391$			54.5077i			2.75657i
$392$	5.91760	+	3.73926i	0.298884	+	0.188861i
$393$		0			0
$394$			12.5107i			0.630278i
$395$	−4.23748	−	4.23748i	−0.213211	−	0.213211i
$396$		0			0
$397$	26.9792	−	26.9792i	1.35405	−	1.35405i	0.472972	−	0.881077i	$-0.343181\pi$
$397$	26.9792	−	26.9792i	1.35405	−	1.35405i	0.881077	−	0.472972i	$-0.156819\pi$
$398$	5.23952	−	5.23952i	0.262633	−	0.262633i
$399$		0			0
$400$			4.57461i			0.228730i
$401$	−21.4604	−	21.4604i	−1.07168	−	1.07168i	−0.997224	−	0.0744583i	$-0.976277\pi$
$401$	−21.4604	−	21.4604i	−1.07168	−	1.07168i	−0.0744583	−	0.997224i	$-0.523723\pi$
$402$		0			0
$403$	−0.0612798	+	4.70285i	−0.00305256	+	0.234265i
$404$			8.03892i			0.399951i
$405$		0			0
$406$	16.3480	+	13.0711i	0.811337	+	0.648706i
$407$			3.05967i			0.151662i
$408$		0			0
$409$	−4.20898	−	4.20898i	−0.208121	−	0.208121i	0.595348	−	0.803468i	$-0.297014\pi$
$409$	−4.20898	−	4.20898i	−0.208121	−	0.208121i	−0.803468	+	0.595348i	$0.797014\pi$
$410$	−2.54032	−	2.54032i	−0.125457	−	0.125457i
$411$		0			0
$412$		−	7.62934i		−	0.375870i
$413$	−3.44356	−	2.75330i	−0.169447	−	0.135481i
$414$		0			0
$415$			9.21351i			0.452273i
$416$	3.60525	+	0.0469777i	0.176762	+	0.00230327i
$417$		0			0
$418$	5.73812	+	5.73812i	0.280661	+	0.280661i
$419$			3.78685i			0.185000i	0.995713	+	0.0924998i	$0.0294858\pi$
$419$			3.78685i			0.185000i	−0.995713	+	0.0924998i	$0.970514\pi$
$420$		0			0
$421$	−16.2730	+	16.2730i	−0.793099	+	0.793099i	−0.981997	−	0.188897i	$-0.939509\pi$
$421$	−16.2730	+	16.2730i	−0.793099	+	0.793099i	0.188897	+	0.981997i	$0.439509\pi$
$422$	10.3449	−	10.3449i	0.503581	−	0.503581i
$423$		0			0
$424$	6.43518	+	6.43518i	0.312520	+	0.312520i
$425$		−	29.2913i		−	1.42084i
$426$		0			0
$427$	−38.0945	+	4.24327i	−1.84352	+	0.205346i
$428$		−	14.3986i		−	0.695984i
$429$		0			0
$430$			2.72382i			0.131354i
$431$	17.7084	−	17.7084i	0.852982	−	0.852982i	−0.137518	−	0.990499i	$-0.543912\pi$
$431$	17.7084	−	17.7084i	0.852982	−	0.852982i	0.990499	+	0.137518i	$0.0439123\pi$
$432$		0			0
$433$	13.2092			0.634796			0.317398	−	0.948292i	$-0.397191\pi$
$433$	13.2092			0.634796			0.317398	+	0.948292i	$0.397191\pi$
$434$	0.382063	+	3.43003i	0.0183396	+	0.164647i
$435$		0			0
$436$	10.6815	+	10.6815i	0.511550	+	0.511550i
$437$	21.5172	−	21.5172i	1.02931	−	1.02931i
$438$		0			0
$439$	27.2638			1.30123			0.650616	−	0.759407i	$-0.274511\pi$
$439$	27.2638			1.30123			0.650616	+	0.759407i	$0.274511\pi$
$440$	−1.04698	+	1.04698i	−0.0499127	+	0.0499127i
$441$		0			0
$442$	−23.0845	−	0.300799i	−1.09802	−	0.0143076i
$443$	−22.3627			−1.06248			−0.531242	−	0.847220i	$-0.678275\pi$
$443$	−22.3627			−1.06248			−0.531242	+	0.847220i	$0.678275\pi$
$444$		0			0
$445$	7.88368			0.373722
$446$	15.6375			0.740458
$447$		0			0
$448$	2.62949	−	0.292893i	0.124232	−	0.0138379i
$449$	−3.36702	−	3.36702i	−0.158899	−	0.158899i	0.623179	−	0.782079i	$-0.285841\pi$
$449$	−3.36702	−	3.36702i	−0.158899	−	0.158899i	−0.782079	+	0.623179i	$0.785841\pi$
$450$		0			0
$451$			12.5044i			0.588810i
$452$			15.0256i			0.706745i
$453$		0			0
$454$	13.1723			0.618207
$455$	−6.19202	+	0.608149i	−0.290286	+	0.0285104i
$456$		0			0
$457$	−12.5030	+	12.5030i	−0.584866	+	0.584866i	−0.936237	−	0.351370i	$-0.885716\pi$
$457$	−12.5030	+	12.5030i	−0.584866	+	0.584866i	0.351370	+	0.936237i	$0.385716\pi$
$458$		−	22.0419i		−	1.02995i
$459$		0			0
$460$	3.92603	+	3.92603i	0.183052	+	0.183052i
$461$	4.03719	+	4.03719i	0.188031	+	0.188031i	0.794844	−	0.606814i	$-0.207553\pi$
$461$	4.03719	+	4.03719i	0.188031	+	0.188031i	−0.606814	+	0.794844i	$0.707553\pi$
$462$		0			0
$463$	−12.8250	−	12.8250i	−0.596028	−	0.596028i	0.343225	−	0.939253i	$-0.388481\pi$
$463$	−12.8250	−	12.8250i	−0.596028	−	0.596028i	−0.939253	+	0.343225i	$0.888481\pi$
$464$	7.91120			0.367268
$465$		0			0
$466$	−10.1993	−	10.1993i	−0.472474	−	0.472474i
$467$	17.0280			0.787964			0.393982	−	0.919118i	$-0.371097\pi$
$467$	17.0280			0.787964			0.393982	+	0.919118i	$0.371097\pi$
$468$		0			0
$469$	−10.1583	−	8.12205i	−0.469065	−	0.375041i
$470$	0.922382	−	0.922382i	0.0425463	−	0.0425463i
$471$		0			0
$472$	−1.66642			−0.0767034
$473$	6.70383	−	6.70383i	0.308243	−	0.308243i
$474$		0			0
$475$	−11.5629	+	11.5629i	−0.530542	+	0.530542i
$476$	−16.8367	+	1.87540i	−0.771709	+	0.0859590i
$477$		0			0
$478$			5.42701i			0.248225i
$479$	−22.7406	+	22.7406i	−1.03905	+	1.03905i	−0.0398390	+	0.999206i	$0.512685\pi$
$479$	−22.7406	+	22.7406i	−1.03905	+	1.03905i	−0.999206	+	0.0398390i	$0.987315\pi$
$480$		0			0
$481$	−0.0633154	+	4.85907i	−0.00288693	+	0.221554i
$482$		−	20.0974i		−	0.915412i
$483$		0			0
$484$	−5.84638			−0.265744
$485$		−	0.251161i		−	0.0114046i
$486$		0			0
$487$	−8.40745	+	8.40745i	−0.380978	+	0.380978i	−0.871454	−	0.490477i	$-0.836823\pi$
$487$	−8.40745	+	8.40745i	−0.380978	+	0.380978i	0.490477	+	0.871454i	$0.336823\pi$
$488$	−10.2442	+	10.2442i	−0.463731	+	0.463731i
$489$		0			0
$490$	−4.45366	+	1.00463i	−0.201196	+	0.0453846i
$491$			12.3150i			0.555767i	0.960615	+	0.277884i	$0.0896329\pi$
$491$			12.3150i			0.555767i	−0.960615	+	0.277884i	$0.910367\pi$
$492$		0			0
$493$	−50.6557			−2.28142
$494$	8.99398	+	9.23146i	0.404658	+	0.415343i
$495$		0			0
$496$	0.922382	+	0.922382i	0.0414162	+	0.0414162i
$497$	−24.2361	−	19.3780i	−1.08714	−	0.869222i
$498$		0			0
$499$	4.13266	−	4.13266i	0.185003	−	0.185003i	−0.608529	−	0.793532i	$-0.708240\pi$
$499$	4.13266	−	4.13266i	0.185003	−	0.185003i	0.793532	+	0.608529i	$0.208240\pi$
$500$	−4.41572	−	4.41572i	−0.197477	−	0.197477i
$501$		0			0
$502$	−3.81412	+	3.81412i	−0.170233	+	0.170233i
$503$			32.1557i			1.43375i	0.697201	+	0.716875i	$0.254428\pi$
$503$			32.1557i			1.43375i	−0.697201	+	0.716875i	$0.745572\pi$
$504$		0			0
$505$	−3.70748	−	3.70748i	−0.164981	−	0.164981i
$506$		−	19.3254i		−	0.859119i
$507$		0			0
$508$	−15.7970			−0.700879
$509$	−25.9435	−	25.9435i	−1.14992	−	1.14992i	−0.986567	−	0.163357i	$-0.947768\pi$
$509$	−25.9435	−	25.9435i	−1.14992	−	1.14992i	−0.163357	−	0.986567i	$-0.552232\pi$
$510$		0			0
$511$	−17.2377	−	13.7824i	−0.762551	−	0.609699i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	3.10072	−	3.10072i	0.136767	−	0.136767i
$515$	3.51858	+	3.51858i	0.155047	+	0.155047i
$516$		0			0
$517$	−4.54032			−0.199683
$518$	0.394755	+	3.54397i	0.0173445	+	0.155713i
$519$		0			0
$520$	−1.68437	+	1.64104i	−0.0738646	+	0.0719644i
$521$			3.85949i			0.169087i	0.996420	+	0.0845437i	$0.0269433\pi$
$521$			3.85949i			0.169087i	−0.996420	+	0.0845437i	$0.973057\pi$
$522$		0			0
$523$		−	36.3670i		−	1.59022i	−0.606467	−	0.795109i	$-0.707414\pi$
$523$		−	36.3670i		−	1.59022i	0.606467	−	0.795109i	$-0.292586\pi$
$524$	1.75522			0.0766773
$525$		0			0
$526$	8.79186	−	8.79186i	0.383343	−	0.383343i
$527$	−5.90604	−	5.90604i	−0.257271	−	0.257271i
$528$		0			0
$529$	−49.4678			−2.15077
$530$	−5.93570			−0.257830
$531$		0			0
$532$	7.38669	+	5.90604i	0.320254	+	0.256060i
$533$	−0.258761	+	19.8583i	−0.0112082	+	0.860158i
$534$		0			0
$535$	6.64052	+	6.64052i	0.287095	+	0.287095i
$536$	−4.91583			−0.212332
$537$		0			0
$538$	21.0604	+	21.0604i	0.907979	+	0.907979i
$539$	13.4339	+	8.48871i	0.578639	+	0.365635i
$540$		0			0
$541$	18.4800	+	18.4800i	0.794518	+	0.794518i	0.982225	−	0.187707i	$-0.0601055\pi$
$541$	18.4800	+	18.4800i	0.794518	+	0.794518i	−0.187707	+	0.982225i	$0.560105\pi$
$542$			20.8134i			0.894010i
$543$		0			0
$544$	−4.52763	+	4.52763i	−0.194120	+	0.194120i
$545$	−9.85240			−0.422030
$546$		0			0
$547$	3.22661			0.137960			0.0689800	−	0.997618i	$-0.478026\pi$
$547$	3.22661			0.137960			0.0689800	+	0.997618i	$0.478026\pi$
$548$	1.82994	−	1.82994i	0.0781711	−	0.0781711i
$549$		0			0
$550$			10.3851i			0.442821i
$551$	19.9966	+	19.9966i	0.851883	+	0.851883i
$552$		0			0
$553$	2.69114	+	24.1601i	0.114439	+	1.02739i
$554$	−17.0604	−	17.0604i	−0.724827	−	0.724827i
$555$		0			0
$556$	13.8448			0.587149
$557$	27.1310	+	27.1310i	1.14958	+	1.14958i	0.986636	+	0.162939i	$0.0520975\pi$
$557$	27.1310	+	27.1310i	1.14958	+	1.14958i	0.162939	+	0.986636i	$0.447903\pi$
$558$		0			0
$559$	10.7851	−	10.5076i	0.456161	−	0.444426i
$560$	−1.07762	+	1.34778i	−0.0455377	+	0.0569540i
$561$		0			0
$562$	10.8970			0.459662
$563$	2.30304			0.0970614			0.0485307	−	0.998822i	$-0.484546\pi$
$563$	2.30304			0.0970614			0.0485307	+	0.998822i	$0.484546\pi$
$564$		0			0
$565$	−6.92968	−	6.92968i	−0.291534	−	0.291534i
$566$	4.51935	−	4.51935i	0.189962	−	0.189962i
$567$		0			0
$568$	−11.7284			−0.492115
$569$		−	5.19115i		−	0.217624i	−0.994062	−	0.108812i	$-0.965295\pi$
$569$		−	5.19115i		−	0.217624i	0.994062	−	0.108812i	$-0.0347047\pi$
$570$		0			0
$571$			11.8508i			0.495941i	0.968768	+	0.247970i	$0.0797636\pi$
$571$			11.8508i			0.495941i	−0.968768	+	0.247970i	$0.920236\pi$
$572$	8.18448	+	0.106647i	0.342210	+	0.00445913i
$573$		0			0
$574$	1.61331	+	14.4837i	0.0673381	+	0.604537i
$575$	38.9427			1.62402
$576$		0			0
$577$	29.5340	+	29.5340i	1.22952	+	1.22952i	0.964147	+	0.265369i	$0.0854938\pi$
$577$	29.5340	+	29.5340i	1.22952	+	1.22952i	0.265369	+	0.964147i	$0.414506\pi$
$578$	16.9697	−	16.9697i	0.705848	−	0.705848i
$579$		0			0
$580$	−3.64858	+	3.64858i	−0.151499	+	0.151499i
$581$	23.3398	−	29.1911i	0.968299	−	1.21105i
$582$		0			0
$583$	14.6089	+	14.6089i	0.605038	+	0.605038i
$584$	−8.34175			−0.345184
$585$		0			0
$586$		−	12.6405i		−	0.522175i
$587$	−11.2384	−	11.2384i	−0.463857	−	0.463857i	0.436060	−	0.899917i	$-0.356373\pi$
$587$	−11.2384	−	11.2384i	−0.463857	−	0.463857i	−0.899917	+	0.436060i	$0.856373\pi$
$588$		0			0
$589$			4.66288i			0.192131i
$590$	0.768540	−	0.768540i	0.0316403	−	0.0316403i
$591$		0			0
$592$	0.953022	+	0.953022i	0.0391690	+	0.0391690i
$593$	7.99323	−	7.99323i	0.328243	−	0.328243i	−0.523675	−	0.851918i	$-0.675439\pi$
$593$	7.99323	−	7.99323i	0.328243	−	0.328243i	0.851918	+	0.523675i	$0.175439\pi$
$594$		0			0
$595$	6.90002	−	8.62986i	0.282873	−	0.353790i
$596$	−3.12824	−	3.12824i	−0.128138	−	0.128138i
$597$		0			0
$598$	0.399911	−	30.6907i	0.0163536	−	1.25504i
$599$	−25.0503			−1.02353			−0.511764	−	0.859126i	$-0.671008\pi$
$599$	−25.0503			−1.02353			−0.511764	+	0.859126i	$0.671008\pi$
$600$		0			0
$601$		−	11.5478i		−	0.471046i	−0.971869	−	0.235523i	$-0.924320\pi$
$601$		−	11.5478i		−	0.471046i	0.971869	−	0.235523i	$-0.0756803\pi$
$602$	6.90002	−	8.62986i	0.281224	−	0.351727i
$603$		0			0
$604$	11.5502	−	11.5502i	0.469971	−	0.469971i
$605$	2.69630	−	2.69630i	0.109620	−	0.109620i
$606$		0			0
$607$		−	15.2350i		−	0.618369i	−0.951002	−	0.309185i	$-0.899944\pi$
$607$		−	15.2350i		−	0.618369i	0.951002	−	0.309185i	$-0.100056\pi$
$608$	3.57461			0.144969
$609$		0			0
$610$		−	9.44903i		−	0.382580i
$611$	−7.21049	−	0.0939553i	−0.291705	−	0.00380103i
$612$		0			0
$613$	11.5903	−	11.5903i	0.468129	−	0.468129i	−0.433179	−	0.901308i	$-0.642608\pi$
$613$	11.5903	−	11.5903i	0.468129	−	0.468129i	0.901308	+	0.433179i	$0.142608\pi$
$614$			1.79855i			0.0725838i
$615$		0			0
$616$	5.96936	−	0.664914i	0.240512	−	0.0267902i
$617$	−14.5420	+	14.5420i	−0.585441	+	0.585441i	−0.936393	−	0.350952i	$-0.885858\pi$
$617$	−14.5420	+	14.5420i	−0.585441	+	0.585441i	0.350952	+	0.936393i	$0.385858\pi$
$618$		0			0
$619$	7.62482	−	7.62482i	0.306467	−	0.306467i	−0.537070	−	0.843538i	$-0.680469\pi$
$619$	7.62482	−	7.62482i	0.306467	−	0.306467i	0.843538	+	0.537070i	$0.180469\pi$
$620$	−0.850789			−0.0341685
$621$		0			0
$622$	−1.07622	+	1.07622i	−0.0431527	+	0.0431527i
$623$	−24.9779	−	19.9711i	−1.00072	−	0.800125i
$624$		0			0
$625$	−18.8000			−0.752002
$626$	−2.46431	−	2.46431i	−0.0984937	−	0.0984937i
$627$		0			0
$628$	18.5294			0.739402
$629$	−6.10223	−	6.10223i	−0.243312	−	0.243312i
$630$		0			0
$631$	28.8742	+	28.8742i	1.14946	+	1.14946i	0.986658	+	0.162807i	$0.0520548\pi$
$631$	28.8742	+	28.8742i	1.14946	+	1.14946i	0.162807	+	0.986658i	$0.447945\pi$
$632$	6.49699	+	6.49699i	0.258436	+	0.258436i
$633$		0			0
$634$			5.11331i			0.203076i
$635$	7.28545	−	7.28545i	0.289114	−	0.289114i
$636$		0			0
$637$	21.1587	+	13.7589i	0.838339	+	0.545149i
$638$	17.9597			0.711031
$639$		0			0
$640$			0.652223i			0.0257814i
$641$			13.9110i			0.549453i	0.961522	+	0.274726i	$0.0885873\pi$
$641$			13.9110i			0.549453i	−0.961522	+	0.274726i	$0.911413\pi$
$642$		0			0
$643$	−31.6768	−	31.6768i	−1.24921	−	1.24921i	−0.956068	−	0.293144i	$-0.905298\pi$
$643$	−31.6768	−	31.6768i	−1.24921	−	1.24921i	−0.293144	−	0.956068i	$-0.594702\pi$
$644$	−2.49334	−	22.3843i	−0.0982514	−	0.882066i
$645$		0			0
$646$	−22.8883			−0.900529
$647$	2.61086			0.102644			0.0513218	−	0.998682i	$-0.483657\pi$
$647$	2.61086			0.102644			0.0513218	+	0.998682i	$0.483657\pi$
$648$		0			0
$649$	−3.78305			−0.148498
$650$	−0.214904	+	16.4926i	−0.00842924	+	0.646892i
$651$		0			0
$652$	−13.1032	+	13.1032i	−0.513162	+	0.513162i
$653$	−2.35132			−0.0920144			−0.0460072	−	0.998941i	$-0.514650\pi$
$653$	−2.35132			−0.0920144			−0.0460072	+	0.998941i	$0.514650\pi$
$654$		0			0
$655$	−0.809494	+	0.809494i	−0.0316295	+	0.0316295i
$656$	3.89486	+	3.89486i	0.152069	+	0.152069i
$657$		0			0
$658$	−5.25898	+	0.585786i	−0.205016	+	0.0228363i
$659$	−13.1002			−0.510312			−0.255156	−	0.966900i	$-0.582127\pi$
$659$	−13.1002			−0.510312			−0.255156	+	0.966900i	$0.582127\pi$
$660$		0			0
$661$	12.5885	−	12.5885i	0.489636	−	0.489636i	−0.418555	−	0.908191i	$-0.637463\pi$
$661$	12.5885	−	12.5885i	0.489636	−	0.489636i	0.908191	+	0.418555i	$0.137463\pi$
$662$		−	6.36625i		−	0.247431i
$663$		0			0
$664$		−	14.1263i		−	0.548208i
$665$	−6.13049	+	0.682863i	−0.237730	+	0.0264803i
$666$		0			0
$667$		−	67.3465i		−	2.60767i
$668$	−9.82552	−	9.82552i	−0.380161	−	0.380161i
$669$		0			0
$670$	2.26714	−	2.26714i	0.0875872	−	0.0875872i
$671$	−23.2559	+	23.2559i	−0.897782	+	0.897782i
$672$		0			0
$673$		−	7.32134i		−	0.282217i	−0.989994	−	0.141109i	$-0.954933\pi$
$673$		−	7.32134i		−	0.282217i	0.989994	−	0.141109i	$-0.0450667\pi$
$674$	−14.6605	−	14.6605i	−0.564701	−	0.564701i
$675$		0			0
$676$	12.9956	+	0.338732i	0.499830	+	0.0130282i
$677$		−	27.2432i		−	1.04704i	−0.852013	−	0.523520i	$-0.824619\pi$
$677$		−	27.2432i		−	1.04704i	0.852013	−	0.523520i	$-0.175381\pi$
$678$		0			0
$679$	−0.636245	+	0.795752i	−0.0244168	+	0.0305381i
$680$		−	4.17620i		−	0.160150i
$681$		0			0
$682$	2.09396	+	2.09396i	0.0801817	+	0.0801817i
$683$	3.89033	+	3.89033i	0.148859	+	0.148859i	0.777608	−	0.628749i	$-0.216433\pi$
$683$	3.89033	+	3.89033i	0.148859	+	0.148859i	−0.628749	+	0.777608i	$0.716433\pi$
$684$		0			0
$685$			1.68790i			0.0644914i
$686$	16.6555	+	8.09911i	0.635908	+	0.309226i
$687$		0			0
$688$		−	4.17620i		−	0.159216i
$689$	22.8981	+	23.5027i	0.872348	+	0.895382i
$690$		0			0
$691$	−7.75081	−	7.75081i	−0.294855	−	0.294855i	0.544140	−	0.838995i	$-0.316856\pi$
$691$	−7.75081	−	7.75081i	−0.294855	−	0.294855i	−0.838995	+	0.544140i	$0.816856\pi$
$692$			10.9940i			0.417928i
$693$		0			0
$694$	−0.114040	+	0.114040i	−0.00432889	+	0.00432889i
$695$	−6.38508	+	6.38508i	−0.242200	+	0.242200i
$696$		0			0
$697$	−24.9389	−	24.9389i	−0.944630	−	0.944630i
$698$			10.1540i			0.384334i
$699$		0			0
$700$	1.33987	+	12.0289i	0.0506424	+	0.454649i
$701$			5.02289i			0.189712i	0.995491	+	0.0948559i	$0.0302390\pi$
$701$			5.02289i			0.189712i	−0.995491	+	0.0948559i	$0.969761\pi$
$702$		0			0
$703$			4.81777i			0.181706i
$704$	1.60525	−	1.60525i	0.0605000	−	0.0605000i
$705$		0			0
$706$	−13.3602			−0.502819
$707$	2.35454	+	21.1382i	0.0885518	+	0.794986i
$708$		0			0
$709$	4.80002	+	4.80002i	0.180269	+	0.180269i	0.791473	−	0.611204i	$-0.209315\pi$
$709$	4.80002	+	4.80002i	0.180269	+	0.180269i	−0.611204	+	0.791473i	$0.709315\pi$
$710$	5.40906	−	5.40906i	0.202998	−	0.202998i
$711$		0			0
$712$	−12.0874			−0.452995
$713$	7.85206	−	7.85206i	0.294062	−	0.294062i
$714$		0			0
$715$	−3.82380	+	3.72543i	−0.143002	+	0.139323i
$716$	−2.54656			−0.0951695
$717$		0			0
$718$	27.1434			1.01298
$719$	−23.2670			−0.867713			−0.433857	−	0.900982i	$-0.642848\pi$
$719$	−23.2670			−0.867713			−0.433857	+	0.900982i	$0.642848\pi$
$720$		0			0
$721$	−2.23458	−	20.0613i	−0.0832201	−	0.747120i
$722$	−4.39976	−	4.39976i	−0.163742	−	0.163742i
$723$		0			0
$724$		−	13.8933i		−	0.516339i
$725$			36.1906i			1.34409i
$726$		0			0
$727$	−29.8368			−1.10659			−0.553293	−	0.832987i	$-0.686629\pi$
$727$	−29.8368			−1.10659			−0.553293	+	0.832987i	$0.686629\pi$
$728$	9.49371	−	0.932425i	0.351860	−	0.0345580i
$729$		0			0
$730$	3.84714	−	3.84714i	0.142389	−	0.142389i
$731$			26.7404i			0.989028i
$732$		0			0
$733$	−11.7443	−	11.7443i	−0.433784	−	0.433784i	0.456129	−	0.889913i	$-0.349235\pi$
$733$	−11.7443	−	11.7443i	−0.433784	−	0.433784i	−0.889913	+	0.456129i	$0.849235\pi$
$734$	−17.1928	−	17.1928i	−0.634596	−	0.634596i
$735$		0			0
$736$	−6.01946	−	6.01946i	−0.221880	−	0.221880i
$737$	−11.1597			−0.411074
$738$		0			0
$739$	−21.9136	−	21.9136i	−0.806103	−	0.806103i	0.177938	−	0.984042i	$-0.443057\pi$
$739$	−21.9136	−	21.9136i	−0.806103	−	0.806103i	−0.984042	+	0.177938i	$0.943057\pi$
$740$	−0.879051			−0.0323146
$741$		0			0
$742$	18.8061	+	15.0364i	0.690392	+	0.552004i
$743$	−8.70770	+	8.70770i	−0.319454	+	0.319454i	−0.848558	−	0.529103i	$-0.822528\pi$
$743$	−8.70770	+	8.70770i	−0.319454	+	0.319454i	0.529103	+	0.848558i	$0.322528\pi$
$744$		0			0
$745$	2.88544			0.105714
$746$	6.89184	−	6.89184i	0.252328	−	0.252328i
$747$		0			0
$748$	−10.2784	+	10.2784i	−0.375817	+	0.375817i
$749$	−4.21726	−	37.8610i	−0.154095	−	1.38341i
$750$		0			0
$751$			34.2765i			1.25077i	0.780318	+	0.625384i	$0.215057\pi$
$751$			34.2765i			1.25077i	−0.780318	+	0.625384i	$0.784943\pi$
$752$	−1.41421	+	1.41421i	−0.0515711	+	0.0515711i
$753$		0			0
$754$	28.5218	+	0.371650i	1.03870	+	0.0135347i
$755$			10.6537i			0.387728i
$756$		0			0
$757$	−28.0153			−1.01823			−0.509117	−	0.860697i	$-0.670028\pi$
$757$	−28.0153			−1.01823			−0.509117	+	0.860697i	$0.670028\pi$
$758$		−	20.6159i		−	0.748802i
$759$		0			0
$760$	−1.64858	+	1.64858i	−0.0598002	+	0.0598002i
$761$	−24.7400	+	24.7400i	−0.896824	+	0.896824i	−0.995154	−	0.0983300i	$-0.968650\pi$
$761$	−24.7400	+	24.7400i	−0.896824	+	0.896824i	0.0983300	+	0.995154i	$0.468650\pi$
$762$		0			0
$763$	31.2153	+	24.9583i	1.13007	+	0.903550i
$764$		−	10.2290i		−	0.370071i
$765$		0			0
$766$	−29.5065			−1.06611
$767$	−6.00787	−	0.0782847i	−0.216932	−	0.00282670i
$768$		0			0
$769$	24.3745	+	24.3745i	0.878968	+	0.878968i	0.993428	−	0.114460i	$-0.0365137\pi$
$769$	24.3745	+	24.3745i	0.878968	+	0.878968i	−0.114460	+	0.993428i	$0.536514\pi$
$770$	−2.44636	+	3.05967i	−0.0881608	+	0.110263i
$771$		0			0
$772$	12.3940	−	12.3940i	0.446069	−	0.446069i
$773$	−21.0774	−	21.0774i	−0.758100	−	0.758100i	0.217876	−	0.975976i	$-0.430087\pi$
$773$	−21.0774	−	21.0774i	−0.758100	−	0.758100i	−0.975976	+	0.217876i	$0.930087\pi$
$774$		0			0
$775$	−4.21954	+	4.21954i	−0.151570	+	0.151570i
$776$			0.385084i			0.0138237i
$777$		0			0
$778$	4.30855	+	4.30855i	0.154469	+	0.154469i
$779$			19.6895i			0.705451i
$780$		0			0
$781$	−26.6254			−0.952733
$782$	38.5428	+	38.5428i	1.37829	+	1.37829i
$783$		0			0
$784$	6.82843	−	1.54032i	0.243872	−	0.0550114i
$785$	−8.54558	+	8.54558i	−0.305005	+	0.305005i
$786$		0			0
$787$	−5.03100	+	5.03100i	−0.179336	+	0.179336i	−0.791066	−	0.611730i	$-0.790474\pi$
$787$	−5.03100	+	5.03100i	−0.179336	+	0.179336i	0.611730	+	0.791066i	$0.290474\pi$
$788$	8.84638	+	8.84638i	0.315139	+	0.315139i
$789$		0			0
$790$	−5.99271			−0.213211
$791$	4.40090	+	39.5097i	0.156478	+	1.40480i
$792$		0			0
$793$	−37.4139	+	36.4514i	−1.32861	+	1.29443i
$794$		−	38.1544i		−	1.35405i
$795$		0			0
$796$		−	7.40980i		−	0.262633i
$797$	−35.6777			−1.26377			−0.631884	−	0.775063i	$-0.717718\pi$
$797$	−35.6777			−1.26377			−0.631884	+	0.775063i	$0.717718\pi$
$798$		0			0
$799$	9.05526	−	9.05526i	0.320352	−	0.320352i
$800$	3.23473	+	3.23473i	0.114365	+	0.114365i
$801$		0			0
$802$	−30.3496			−1.07168
$803$	−18.9371			−0.668276
$804$		0			0
$805$	11.4734	+	9.17354i	0.404383	+	0.323325i
$806$	3.28208	+	3.36875i	0.115606	+	0.118659i
$807$		0			0
$808$	5.68437	+	5.68437i	0.199976	+	0.199976i
$809$	24.7540			0.870306			0.435153	−	0.900357i	$-0.356694\pi$
$809$	24.7540			0.870306			0.435153	+	0.900357i	$0.356694\pi$
$810$		0			0
$811$	−19.5605	−	19.5605i	−0.686863	−	0.686863i	0.274674	−	0.961537i	$-0.411430\pi$
$811$	−19.5605	−	19.5605i	−0.686863	−	0.686863i	−0.961537	+	0.274674i	$0.911430\pi$
$812$	20.8024	−	2.31714i	0.730022	−	0.0813156i
$813$		0			0
$814$	2.16351	+	2.16351i	0.0758311	+	0.0758311i
$815$		−	12.0862i		−	0.423360i
$816$		0			0
$817$	10.5559	−	10.5559i	0.369304	−	0.369304i
$818$	−5.95240			−0.208121
$819$		0			0
$820$	−3.59255			−0.125457
$821$	−8.90959	+	8.90959i	−0.310947	+	0.310947i	−0.845276	−	0.534329i	$-0.820564\pi$
$821$	−8.90959	+	8.90959i	−0.310947	+	0.310947i	0.534329	+	0.845276i	$0.320564\pi$
$822$		0			0
$823$			6.11934i			0.213307i	0.994296	+	0.106653i	$0.0340135\pi$
$823$			6.11934i			0.213307i	−0.994296	+	0.106653i	$0.965986\pi$
$824$	−5.39475	−	5.39475i	−0.187935	−	0.187935i
$825$		0			0
$826$	−4.38185	+	0.488084i	−0.152464	+	0.0169826i
$827$	26.8873	+	26.8873i	0.934964	+	0.934964i	0.998011	−	0.0630466i	$-0.0200817\pi$
$827$	26.8873	+	26.8873i	0.934964	+	0.934964i	−0.0630466	+	0.998011i	$0.520082\pi$
$828$		0			0
$829$	−31.1247			−1.08101			−0.540503	−	0.841342i	$-0.681766\pi$
$829$	−31.1247			−1.08101			−0.540503	+	0.841342i	$0.681766\pi$
$830$	6.51494	+	6.51494i	0.226137	+	0.226137i
$831$		0			0
$832$	2.58251	−	2.51608i	0.0895325	−	0.0872292i
$833$	−43.7226	+	9.86271i	−1.51490	+	0.341723i
$834$		0			0
$835$	9.06289			0.313634
$836$	8.11492			0.280661
$837$		0			0
$838$	2.67771	+	2.67771i	0.0924998	+	0.0924998i
$839$	−9.22932	+	9.22932i	−0.318632	+	0.318632i	−0.848241	−	0.529610i	$-0.822338\pi$
$839$	−9.22932	+	9.22932i	−0.318632	+	0.318632i	0.529610	+	0.848241i	$0.322338\pi$
$840$		0			0
$841$	33.5871			1.15818
$842$			23.0136i			0.793099i
$843$		0			0
$844$		−	14.6299i		−	0.503581i
$845$	−6.14967	+	5.83723i	−0.211555	+	0.200807i
$846$		0			0
$847$	−15.3730	+	1.71236i	−0.528222	+	0.0588375i
$848$	9.10072			0.312520
$849$		0			0
$850$	−20.7121	−	20.7121i	−0.710419	−	0.710419i
$851$	8.11289	−	8.11289i	0.278106	−	0.278106i
$852$		0			0
$853$	−9.34638	+	9.34638i	−0.320014	+	0.320014i	−0.848772	−	0.528758i	$-0.822658\pi$
$853$	−9.34638	+	9.34638i	−0.320014	+	0.320014i	0.528758	+	0.848772i	$0.322658\pi$
$854$	−23.9364	+	29.9373i	−0.819088	+	1.02443i
$855$		0			0
$856$	−10.1814	−	10.1814i	−0.347992	−	0.347992i
$857$	55.3845			1.89190			0.945949	−	0.324315i	$-0.105134\pi$
$857$	55.3845			1.89190			0.945949	+	0.324315i	$0.105134\pi$
$858$		0			0
$859$		−	42.0994i		−	1.43641i	−0.695830	−	0.718206i	$-0.744963\pi$
$859$		−	42.0994i		−	1.43641i	0.695830	−	0.718206i	$-0.255037\pi$
$860$	1.92603	+	1.92603i	0.0656770	+	0.0656770i
$861$		0			0
$862$		−	25.0434i		−	0.852982i
$863$	3.47410	−	3.47410i	0.118260	−	0.118260i	−0.645500	−	0.763760i	$-0.723351\pi$
$863$	3.47410	−	3.47410i	0.118260	−	0.118260i	0.763760	+	0.645500i	$0.223351\pi$
$864$		0			0
$865$	−5.07032	−	5.07032i	−0.172396	−	0.172396i
$866$	9.34034	−	9.34034i	0.317398	−	0.317398i
$867$		0			0
$868$	2.69555	+	2.15524i	0.0914931	+	0.0731534i
$869$	14.7492	+	14.7492i	0.500332	+	0.500332i
$870$		0			0
$871$	−17.7228	−	0.230934i	−0.600514	−	0.00782491i
$872$	15.1059			0.511550
$873$		0			0
$874$		−	30.4299i		−	1.02931i
$875$	−12.9044	−	10.3178i	−0.436249	−	0.348804i
$876$		0			0
$877$	16.8673	−	16.8673i	0.569570	−	0.569570i	−0.362438	−	0.932008i	$-0.618056\pi$
$877$	16.8673	−	16.8673i	0.569570	−	0.569570i	0.932008	+	0.362438i	$0.118056\pi$
$878$	19.2784	−	19.2784i	0.650616	−	0.650616i
$879$		0			0
$880$			1.48065i			0.0499127i
$881$	28.2254			0.950939			0.475470	−	0.879732i	$-0.342278\pi$
$881$	28.2254			0.950939			0.475470	+	0.879732i	$0.342278\pi$
$882$		0			0
$883$			42.1795i			1.41945i	0.704478	+	0.709726i	$0.251181\pi$
$883$			42.1795i			1.41945i	−0.704478	+	0.709726i	$0.748819\pi$
$884$	−16.5359	+	16.1105i	−0.556163	+	0.541855i
$885$		0			0
$886$	−15.8128	+	15.8128i	−0.531242	+	0.531242i
$887$		−	57.2398i		−	1.92192i	−0.276682	−	0.960962i	$-0.589235\pi$
$887$		−	57.2398i		−	1.92192i	0.276682	−	0.960962i	$-0.410765\pi$
$888$		0			0
$889$	−41.5381	+	4.62684i	−1.39314	+	0.155179i
$890$	5.57461	−	5.57461i	0.186861	−	0.186861i
$891$		0			0
$892$	11.0574	−	11.0574i	0.370229	−	0.370229i
$893$	−7.14921			−0.239239
$894$		0			0
$895$	1.17445	−	1.17445i	0.0392576	−	0.0392576i
$896$	1.65222	−	2.06644i	0.0551969	−	0.0690348i
$897$		0			0
$898$	−4.76168			−0.158899
$899$	7.29715	+	7.29715i	0.243374	+	0.243374i
$900$		0			0
$901$	−58.2722			−1.94133
$902$	8.84196	+	8.84196i	0.294405	+	0.294405i
$903$		0			0
$904$	10.6247	+	10.6247i	0.353372	+	0.353372i
$905$	6.40745	+	6.40745i	0.212991	+	0.212991i
$906$		0			0
$907$			28.7641i			0.955097i	0.878605	+	0.477549i	$0.158475\pi$
$907$			28.7641i			0.955097i	−0.878605	+	0.477549i	$0.841525\pi$
$908$	9.31423	−	9.31423i	0.309104	−	0.309104i
$909$		0			0
$910$	−3.94839	+	4.80844i	−0.130888	+	0.159398i
$911$	−27.0639			−0.896666			−0.448333	−	0.893867i	$-0.647982\pi$
$911$	−27.0639			−0.896666			−0.448333	+	0.893867i	$0.647982\pi$
$912$		0			0
$913$		−	32.0690i		−	1.06133i
$914$			17.6819i			0.584866i
$915$		0			0
$916$	−15.5860	−	15.5860i	−0.514976	−	0.514976i
$917$	4.61534	−	0.514093i	0.152412	−	0.0169768i
$918$		0			0
$919$	38.1464			1.25833			0.629167	−	0.777270i	$-0.283396\pi$
$919$	38.1464			1.25833			0.629167	+	0.777270i	$0.283396\pi$
$920$	5.55224			0.183052
$921$		0			0
$922$	5.70945			0.188031
$923$	−42.2839	−	0.550975i	−1.39179	−	0.0181356i
$924$		0			0
$925$	−4.35970	+	4.35970i	−0.143346	+	0.143346i
$926$	−18.1373			−0.596028
$927$		0			0
$928$	5.59406	−	5.59406i	0.183634	−	0.183634i
$929$	−11.1005	−	11.1005i	−0.364196	−	0.364196i	0.501159	−	0.865355i	$-0.332907\pi$
$929$	−11.1005	−	11.1005i	−0.364196	−	0.364196i	−0.865355	+	0.501159i	$0.832907\pi$
$930$		0			0
$931$	21.1531	+	13.3664i	0.693264	+	0.438065i
$932$	−14.4240			−0.472474
$933$		0			0
$934$	12.0406	−	12.0406i	0.393982	−	0.393982i
$935$		−	9.48065i		−	0.310050i
$936$		0			0
$937$			47.2311i			1.54297i	0.636245	+	0.771487i	$0.280487\pi$
$937$			47.2311i			1.54297i	−0.636245	+	0.771487i	$0.719513\pi$
$938$	−12.9261	+	1.43981i	−0.422053	+	0.0470116i
$939$		0			0
$940$		−	1.30445i		−	0.0425463i
$941$	−27.0580	−	27.0580i	−0.882065	−	0.882065i	0.111680	−	0.993744i	$-0.464377\pi$
$941$	−27.0580	−	27.0580i	−0.882065	−	0.882065i	−0.993744	+	0.111680i	$0.964377\pi$
$942$		0			0
$943$	33.1562	−	33.1562i	1.07971	−	1.07971i
$944$	−1.17834	+	1.17834i	−0.0383517	+	0.0383517i
$945$		0			0
$946$		−	9.48065i		−	0.308243i
$947$	14.2815	+	14.2815i	0.464085	+	0.464085i	0.899992	−	0.435907i	$-0.143572\pi$
$947$	14.2815	+	14.2815i	0.464085	+	0.464085i	−0.435907	+	0.899992i	$0.643572\pi$
$948$		0			0
$949$	−30.0741	−	0.391876i	−0.976245	−	0.0127208i
$950$			16.3524i			0.530542i
$951$		0			0
$952$	−10.5792	+	13.2315i	−0.342875	+	0.428834i
$953$		−	6.01656i		−	0.194895i	−0.995241	−	0.0974477i	$-0.968932\pi$
$953$		−	6.01656i		−	0.194895i	0.995241	−	0.0974477i	$-0.0310679\pi$
$954$		0			0
$955$	4.71751	+	4.71751i	0.152655	+	0.152655i
$956$	3.83747	+	3.83747i	0.124113	+	0.124113i
$957$		0			0
$958$			32.1601i			1.03905i
$959$	4.27582	−	5.34778i	0.138074	−	0.172689i
$960$		0			0
$961$		−	29.2984i		−	0.945110i
$962$	3.39111	+	3.48065i	0.109334	+	0.112221i
$963$		0			0
$964$	−14.2110	−	14.2110i	−0.457706	−	0.457706i
$965$			11.4320i			0.368009i
$966$		0			0
$967$	−29.0413	+	29.0413i	−0.933906	+	0.933906i	−0.997947	−	0.0640416i	$-0.979601\pi$
$967$	−29.0413	+	29.0413i	−0.933906	+	0.933906i	0.0640416	+	0.997947i	$0.479601\pi$
$968$	−4.13401	+	4.13401i	−0.132872	+	0.132872i
$969$		0			0
$970$	−0.177597	−	0.177597i	−0.00570231	−	0.00570231i
$971$			37.3180i			1.19759i	0.800902	+	0.598795i	$0.204354\pi$
$971$			37.3180i			1.19759i	−0.800902	+	0.598795i	$0.795646\pi$
$972$		0			0
$973$	36.4047	−	4.05504i	1.16708	−	0.129999i
$974$			11.8899i			0.380978i
$975$		0			0
$976$			14.4874i			0.463731i
$977$	4.00859	−	4.00859i	0.128246	−	0.128246i	−0.640070	−	0.768316i	$-0.721095\pi$
$977$	4.00859	−	4.00859i	0.128246	−	0.128246i	0.768316	+	0.640070i	$0.221095\pi$
$978$		0			0
$979$	−27.4403			−0.876997
$980$	−2.43883	+	3.85959i	−0.0779055	+	0.123290i
$981$		0			0
$982$	8.70800	+	8.70800i	0.277884	+	0.277884i
$983$	−20.0717	+	20.0717i	−0.640188	+	0.640188i	−0.950601	−	0.310414i	$-0.899532\pi$
$983$	−20.0717	+	20.0717i	−0.640188	+	0.640188i	0.310414	+	0.950601i	$0.399532\pi$
$984$		0			0
$985$	−8.15974			−0.259991
$986$	−35.8190	+	35.8190i	−1.14071	+	1.14071i
$987$		0			0
$988$	12.8873	+	0.167927i	0.410001	+	0.00534246i
$989$	−35.5512			−1.13046
$990$		0			0
$991$	−16.1309			−0.512415			−0.256208	−	0.966622i	$-0.582473\pi$
$991$	−16.1309			−0.512415			−0.256208	+	0.966622i	$0.582473\pi$
$992$	1.30445			0.0414162
$993$		0			0
$994$	−30.8398	+	3.43518i	−0.978180	+	0.108957i
$995$	3.41733	+	3.41733i	0.108337	+	0.108337i
$996$		0			0
$997$		−	32.1324i		−	1.01764i	−0.860872	−	0.508821i	$-0.830081\pi$
$997$		−	32.1324i		−	1.01764i	0.860872	−	0.508821i	$-0.169919\pi$
$998$		−	5.84446i		−	0.185003i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.x.a.811.4		8
3.2	odd	2		546.2.o.c.265.1	yes	8
7.6	odd	2		1638.2.x.c.811.3		8
13.8	odd	4		1638.2.x.c.307.3		8
21.20	even	2		546.2.o.b.265.2	✓	8
39.8	even	4		546.2.o.b.307.2	yes	8
91.34	even	4	inner	1638.2.x.a.307.4		8
273.125	odd	4		546.2.o.c.307.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.b.265.2	✓	8	21.20	even	2
546.2.o.b.307.2	yes	8	39.8	even	4
546.2.o.c.265.1	yes	8	3.2	odd	2
546.2.o.c.307.1	yes	8	273.125	odd	4
1638.2.x.a.307.4		8	91.34	even	4	inner
1638.2.x.a.811.4		8	1.1	even	1	trivial
1638.2.x.c.307.3		8	13.8	odd	4
1638.2.x.c.811.3		8	7.6	odd	2

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.461191 + 0.461191i) q^{5} +(-0.292893 - 2.62949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(0.461191 + 0.461191i) q^{5} +(-0.292893 - 2.62949i) q^{7} +(-0.707107 - 0.707107i) q^{8} +0.652223 q^{10} +(-1.60525 - 1.60525i) q^{11} +(-2.51608 - 2.58251i) q^{13} +(-2.06644 - 1.65222i) q^{14} -1.00000 q^{16} +6.40303 q^{17} +(-2.52763 - 2.52763i) q^{19} +(0.461191 - 0.461191i) q^{20} -2.27016 q^{22} +8.51280i q^{23} -4.57461i q^{25} +(-3.60525 - 0.0469777i) q^{26} +(-2.62949 + 0.292893i) q^{28} -7.91120 q^{29} +(-0.922382 - 0.922382i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(4.52763 - 4.52763i) q^{34} +(1.07762 - 1.34778i) q^{35} +(-0.953022 - 0.953022i) q^{37} -3.57461 q^{38} -0.652223i q^{40} +(-3.89486 - 3.89486i) q^{41} +4.17620i q^{43} +(-1.60525 + 1.60525i) q^{44} +(6.01946 + 6.01946i) q^{46} +(1.41421 - 1.41421i) q^{47} +(-6.82843 + 1.54032i) q^{49} +(-3.23473 - 3.23473i) q^{50} +(-2.58251 + 2.51608i) q^{52} -9.10072 q^{53} -1.48065i q^{55} +(-1.65222 + 2.06644i) q^{56} +(-5.59406 + 5.59406i) q^{58} +(1.17834 - 1.17834i) q^{59} -14.4874i q^{61} -1.30445 q^{62} +1.00000i q^{64} +(0.0306399 - 2.35142i) q^{65} +(3.47602 - 3.47602i) q^{67} -6.40303i q^{68} +(-0.191032 - 1.71501i) q^{70} +(8.29326 - 8.29326i) q^{71} +(5.89851 - 5.89851i) q^{73} -1.34778 q^{74} +(-2.52763 + 2.52763i) q^{76} +(-3.75081 + 4.69114i) q^{77} -9.18813 q^{79} +(-0.461191 - 0.461191i) q^{80} -5.50817 q^{82} +(9.98882 + 9.98882i) q^{83} +(2.95302 + 2.95302i) q^{85} +(2.95302 + 2.95302i) q^{86} +2.27016i q^{88} +(8.54709 - 8.54709i) q^{89} +(-6.05374 + 7.37239i) q^{91} +8.51280 q^{92} -2.00000i q^{94} -2.33144i q^{95} +(-0.272296 - 0.272296i) q^{97} +(-3.73926 + 5.91760i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - 8 q^{7}+O(q^{10}) \) 8 * q - 4 * q^5 - 8 * q^7	\( 8 q - 4 q^{5} - 8 q^{7} - 4 q^{10} - 16 q^{13} + 4 q^{14} - 8 q^{16} + 4 q^{17} + 8 q^{19} - 4 q^{20} - 12 q^{22} - 16 q^{26} - 12 q^{29} + 8 q^{31} + 8 q^{34} + 24 q^{35} - 4 q^{37} - 4 q^{38} + 12 q^{41} + 24 q^{46} - 32 q^{49} + 8 q^{50} + 4 q^{52} - 40 q^{53} - 4 q^{56} + 4 q^{58} - 8 q^{59} + 8 q^{62} + 12 q^{65} + 32 q^{67} + 12 q^{71} - 20 q^{73} - 20 q^{74} + 8 q^{76} + 8 q^{77} + 24 q^{79} + 4 q^{80} - 40 q^{82} + 44 q^{83} + 20 q^{85} + 20 q^{86} + 16 q^{89} - 12 q^{91} + 28 q^{92} + 8 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q - 4 * q^5 - 8 * q^7 - 4 * q^10 - 16 * q^13 + 4 * q^14 - 8 * q^16 + 4 * q^17 + 8 * q^19 - 4 * q^20 - 12 * q^22 - 16 * q^26 - 12 * q^29 + 8 * q^31 + 8 * q^34 + 24 * q^35 - 4 * q^37 - 4 * q^38 + 12 * q^41 + 24 * q^46 - 32 * q^49 + 8 * q^50 + 4 * q^52 - 40 * q^53 - 4 * q^56 + 4 * q^58 - 8 * q^59 + 8 * q^62 + 12 * q^65 + 32 * q^67 + 12 * q^71 - 20 * q^73 - 20 * q^74 + 8 * q^76 + 8 * q^77 + 24 * q^79 + 4 * q^80 - 40 * q^82 + 44 * q^83 + 20 * q^85 + 20 * q^86 + 16 * q^89 - 12 * q^91 + 28 * q^92 + 8 * q^97 - 16 * q^98

Introduction

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