LMFDB - Embedded newform 810.2.f.c.323.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(323,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("810.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.f (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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.3
Root			$0.500000 - 1.00333i$ of defining polynomial
Character	$\chi$	$=$	810.323
Dual form			810.2.f.c.647.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.86274 + 1.23701i) q^{5} +(-1.70010 + 1.70010i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.86274 + 1.23701i) q^{5} +(-1.70010 + 1.70010i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.442462 - 2.19185i) q^{10} +1.14518i q^{11} +(-1.74939 - 1.74939i) q^{13} +2.40430 q^{14} -1.00000 q^{16} +(4.99855 + 4.99855i) q^{17} -2.78390i q^{19} +(-1.23701 + 1.86274i) q^{20} +(0.809767 - 0.809767i) q^{22} +(-4.36116 + 4.36116i) q^{23} +(1.93963 + 4.60845i) q^{25} +2.47401i q^{26} +(-1.70010 - 1.70010i) q^{28} +1.34450 q^{29} -2.50446 q^{31} +(0.707107 + 0.707107i) q^{32} -7.06902i q^{34} +(-5.26988 + 1.06381i) q^{35} +(-8.16761 + 8.16761i) q^{37} +(-1.96852 + 1.96852i) q^{38} +(2.19185 - 0.442462i) q^{40} +1.97253i q^{41} +(-6.35785 - 6.35785i) q^{43} -1.14518 q^{44} +6.16761 q^{46} +(8.72003 + 8.72003i) q^{47} +1.21934i q^{49} +(1.88715 - 4.63019i) q^{50} +(1.74939 - 1.74939i) q^{52} +(-1.84828 + 1.84828i) q^{53} +(-1.41660 + 2.13318i) q^{55} +2.40430i q^{56} +(-0.950705 - 0.950705i) q^{58} +2.62911 q^{59} +7.08551 q^{61} +(1.77092 + 1.77092i) q^{62} -1.00000i q^{64} +(-1.09466 - 5.42268i) q^{65} +(-0.0399176 + 0.0399176i) q^{67} +(-4.99855 + 4.99855i) q^{68} +(4.47860 + 2.97414i) q^{70} -9.10005i q^{71} +(7.82779 + 7.82779i) q^{73} +11.5507 q^{74} +2.78390 q^{76} +(-1.94692 - 1.94692i) q^{77} +9.77309i q^{79} +(-1.86274 - 1.23701i) q^{80} +(1.39479 - 1.39479i) q^{82} +(-1.98017 + 1.98017i) q^{83} +(3.12778 + 15.4943i) q^{85} +8.99135i q^{86} +(0.809767 + 0.809767i) q^{88} +4.87832 q^{89} +5.94827 q^{91} +(-4.36116 - 4.36116i) q^{92} -12.3320i q^{94} +(3.44371 - 5.18570i) q^{95} +(5.70947 - 5.70947i) q^{97} +(0.862203 - 0.862203i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{7}+O(q^{10}) $ 16 * q - 16 * q^7	$ 16 q - 16 q^{7} - 8 q^{10} - 16 q^{16} - 16 q^{22} + 32 q^{25} - 16 q^{28} + 16 q^{31} + 8 q^{40} - 32 q^{46} + 24 q^{55} - 32 q^{58} + 48 q^{61} + 32 q^{67} - 32 q^{70} + 16 q^{73} - 32 q^{76} - 16 q^{82} + 8 q^{85} - 16 q^{88} + 96 q^{97}+O(q^{100}) $ 16 * q - 16 * q^7 - 8 * q^10 - 16 * q^16 - 16 * q^22 + 32 * q^25 - 16 * q^28 + 16 * q^31 + 8 * q^40 - 32 * q^46 + 24 * q^55 - 32 * q^58 + 48 * q^61 + 32 * q^67 - 32 * q^70 + 16 * q^73 - 32 * q^76 - 16 * q^82 + 8 * q^85 - 16 * q^88 + 96 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.707107	−	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
$5$	1.86274	+	1.23701i	0.833044	+	0.553206i
$5$	1.86274	+	1.23701i	0.833044	+	0.553206i
$6$		0			0
$7$	−1.70010	+	1.70010i	−0.642576	+	0.642576i	−0.951188	−	0.308612i	$-0.900136\pi$
$7$	−1.70010	+	1.70010i	−0.642576	+	0.642576i	0.308612	+	0.951188i	$0.400136\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−0.442462	−	2.19185i	−0.139919	−	0.693125i
$11$			1.14518i			0.345286i	0.984984	+	0.172643i	$0.0552306\pi$
$11$			1.14518i			0.345286i	−0.984984	+	0.172643i	$0.944769\pi$
$12$		0			0
$13$	−1.74939	−	1.74939i	−0.485194	−	0.485194i	0.421592	−	0.906786i	$-0.361472\pi$
$13$	−1.74939	−	1.74939i	−0.485194	−	0.485194i	−0.906786	+	0.421592i	$0.861472\pi$
$14$	2.40430			0.642576
$15$		0			0
$16$	−1.00000			−0.250000
$17$	4.99855	+	4.99855i	1.21233	+	1.21233i	0.970259	+	0.242068i	$0.0778258\pi$
$17$	4.99855	+	4.99855i	1.21233	+	1.21233i	0.242068	+	0.970259i	$0.422174\pi$
$18$		0			0
$19$		−	2.78390i		−	0.638671i	−0.947642	−	0.319336i	$-0.896540\pi$
$19$		−	2.78390i		−	0.638671i	0.947642	−	0.319336i	$-0.103460\pi$
$20$	−1.23701	+	1.86274i	−0.276603	+	0.416522i
$21$		0			0
$22$	0.809767	−	0.809767i	0.172643	−	0.172643i
$23$	−4.36116	+	4.36116i	−0.909365	+	0.909365i	−0.996221	−	0.0868559i	$-0.972318\pi$
$23$	−4.36116	+	4.36116i	−0.909365	+	0.909365i	0.0868559	+	0.996221i	$0.472318\pi$
$24$		0			0
$25$	1.93963	+	4.60845i	0.387925	+	0.921691i
$26$			2.47401i			0.485194i
$27$		0			0
$28$	−1.70010	−	1.70010i	−0.321288	−	0.321288i
$29$	1.34450			0.249667			0.124834	−	0.992178i	$-0.460160\pi$
$29$	1.34450			0.249667			0.124834	+	0.992178i	$0.460160\pi$
$30$		0			0
$31$	−2.50446			−0.449814			−0.224907	−	0.974380i	$-0.572208\pi$
$31$	−2.50446			−0.449814			−0.224907	+	0.974380i	$0.572208\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$		−	7.06902i		−	1.21233i
$35$	−5.26988	+	1.06381i	−0.890772	+	0.179817i
$36$		0			0
$37$	−8.16761	+	8.16761i	−1.34275	+	1.34275i	−0.449434	+	0.893314i	$0.648374\pi$
$37$	−8.16761	+	8.16761i	−1.34275	+	1.34275i	−0.893314	+	0.449434i	$0.851626\pi$
$38$	−1.96852	+	1.96852i	−0.319336	+	0.319336i
$39$		0			0
$40$	2.19185	−	0.442462i	0.346563	−	0.0699594i
$41$			1.97253i			0.308057i	0.988066	+	0.154029i	$0.0492248\pi$
$41$			1.97253i			0.308057i	−0.988066	+	0.154029i	$0.950775\pi$
$42$		0			0
$43$	−6.35785	−	6.35785i	−0.969563	−	0.969563i	0.0299877	−	0.999550i	$-0.490453\pi$
$43$	−6.35785	−	6.35785i	−0.969563	−	0.969563i	−0.999550	+	0.0299877i	$0.990453\pi$
$44$	−1.14518			−0.172643
$45$		0			0
$46$	6.16761			0.909365
$47$	8.72003	+	8.72003i	1.27195	+	1.27195i	0.945065	+	0.326882i	$0.105998\pi$
$47$	8.72003	+	8.72003i	1.27195	+	1.27195i	0.326882	+	0.945065i	$0.394002\pi$
$48$		0			0
$49$			1.21934i			0.174191i
$50$	1.88715	−	4.63019i	0.266883	−	0.654808i
$51$		0			0
$52$	1.74939	−	1.74939i	0.242597	−	0.242597i
$53$	−1.84828	+	1.84828i	−0.253881	+	0.253881i	−0.822560	−	0.568679i	$-0.807455\pi$
$53$	−1.84828	+	1.84828i	−0.253881	+	0.253881i	0.568679	+	0.822560i	$0.307455\pi$
$54$		0			0
$55$	−1.41660	+	2.13318i	−0.191014	+	0.287638i
$56$			2.40430i			0.321288i
$57$		0			0
$58$	−0.950705	−	0.950705i	−0.124834	−	0.124834i
$59$	2.62911			0.342281			0.171141	−	0.985247i	$-0.445255\pi$
$59$	2.62911			0.342281			0.171141	+	0.985247i	$0.445255\pi$
$60$		0			0
$61$	7.08551			0.907206			0.453603	−	0.891204i	$-0.350138\pi$
$61$	7.08551			0.907206			0.453603	+	0.891204i	$0.350138\pi$
$62$	1.77092	+	1.77092i	0.224907	+	0.224907i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−1.09466	−	5.42268i	−0.135776	−	0.672601i
$66$		0			0
$67$	−0.0399176	+	0.0399176i	−0.00487672	+	0.00487672i	−0.709541	−	0.704664i	$-0.751098\pi$
$67$	−0.0399176	+	0.0399176i	−0.00487672	+	0.00487672i	0.704664	+	0.709541i	$0.251098\pi$
$68$	−4.99855	+	4.99855i	−0.606164	+	0.606164i
$69$		0			0
$70$	4.47860	+	2.97414i	0.535294	+	0.355477i
$71$		−	9.10005i		−	1.07998i	−0.841672	−	0.539989i	$-0.818429\pi$
$71$		−	9.10005i		−	1.07998i	0.841672	−	0.539989i	$-0.181571\pi$
$72$		0			0
$73$	7.82779	+	7.82779i	0.916174	+	0.916174i	0.996749	−	0.0805747i	$-0.0256756\pi$
$73$	7.82779	+	7.82779i	0.916174	+	0.916174i	−0.0805747	+	0.996749i	$0.525676\pi$
$74$	11.5507			1.34275
$75$		0			0
$76$	2.78390			0.319336
$77$	−1.94692	−	1.94692i	−0.221872	−	0.221872i
$78$		0			0
$79$			9.77309i			1.09956i	0.835310	+	0.549779i	$0.185288\pi$
$79$			9.77309i			1.09956i	−0.835310	+	0.549779i	$0.814712\pi$
$80$	−1.86274	−	1.23701i	−0.208261	−	0.138302i
$81$		0			0
$82$	1.39479	−	1.39479i	0.154029	−	0.154029i
$83$	−1.98017	+	1.98017i	−0.217352	+	0.217352i	−0.807382	−	0.590029i	$-0.799116\pi$
$83$	−1.98017	+	1.98017i	−0.217352	+	0.217352i	0.590029	+	0.807382i	$0.299116\pi$
$84$		0			0
$85$	3.12778	+	15.4943i	0.339255	+	1.68059i
$86$			8.99135i			0.969563i
$87$		0			0
$88$	0.809767	+	0.809767i	0.0863214	+	0.0863214i
$89$	4.87832			0.517100			0.258550	−	0.965998i	$-0.416755\pi$
$89$	4.87832			0.517100			0.258550	+	0.965998i	$0.416755\pi$
$90$		0			0
$91$	5.94827			0.623549
$92$	−4.36116	−	4.36116i	−0.454682	−	0.454682i
$93$		0			0
$94$		−	12.3320i		−	1.27195i
$95$	3.44371	−	5.18570i	0.353317	−	0.532041i
$96$		0			0
$97$	5.70947	−	5.70947i	0.579709	−	0.579709i	−0.355114	−	0.934823i	$-0.615558\pi$
$97$	5.70947	−	5.70947i	0.579709	−	0.579709i	0.934823	+	0.355114i	$0.115558\pi$
$98$	0.862203	−	0.862203i	0.0870956	−	0.0870956i
$99$		0			0
$100$	−4.60845	+	1.93963i	−0.460845	+	0.193963i
$101$		−	0.728702i		−	0.0725085i	−0.999343	−	0.0362543i	$-0.988457\pi$
$101$		−	0.728702i		−	0.0725085i	0.999343	−	0.0362543i	$-0.0115426\pi$
$102$		0			0
$103$	0.965489	+	0.965489i	0.0951324	+	0.0951324i	0.753071	−	0.657939i	$-0.228572\pi$
$103$	0.965489	+	0.965489i	0.0951324	+	0.0951324i	−0.657939	+	0.753071i	$0.728572\pi$
$104$	−2.47401			−0.242597
$105$		0			0
$106$	2.61386			0.253881
$107$	0.399208	+	0.399208i	0.0385929	+	0.0385929i	0.726140	−	0.687547i	$-0.241312\pi$
$107$	0.399208	+	0.399208i	0.0385929	+	0.0385929i	−0.687547	+	0.726140i	$0.741312\pi$
$108$		0			0
$109$		−	13.5974i		−	1.30239i	−0.758909	−	0.651196i	$-0.774268\pi$
$109$		−	13.5974i		−	1.30239i	0.758909	−	0.651196i	$-0.225732\pi$
$110$	2.51007	−	0.506700i	0.239326	−	0.0483120i
$111$		0			0
$112$	1.70010	−	1.70010i	0.160644	−	0.160644i
$113$	3.61920	−	3.61920i	0.340465	−	0.340465i	−0.516077	−	0.856542i	$-0.672608\pi$
$113$	3.61920	−	3.61920i	0.340465	−	0.340465i	0.856542	+	0.516077i	$0.172608\pi$
$114$		0			0
$115$	−13.5185	+	2.72894i	−1.26061	+	0.254475i
$116$			1.34450i			0.124834i
$117$		0			0
$118$	−1.85906	−	1.85906i	−0.171141	−	0.171141i
$119$	−16.9961			−1.55803
$120$		0			0
$121$	9.68856			0.880778
$122$	−5.01021	−	5.01021i	−0.453603	−	0.453603i
$123$		0			0
$124$		−	2.50446i		−	0.224907i
$125$	−2.08767	+	10.9837i	−0.186727	+	0.982412i
$126$		0			0
$127$	−4.88817	+	4.88817i	−0.433755	+	0.433755i	−0.889904	−	0.456149i	$-0.849228\pi$
$127$	−4.88817	+	4.88817i	−0.433755	+	0.433755i	0.456149	+	0.889904i	$0.349228\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−3.06037	+	4.60845i	−0.268413	+	0.404188i
$131$		−	5.75447i		−	0.502770i	−0.967887	−	0.251385i	$-0.919114\pi$
$131$		−	5.75447i		−	0.502770i	0.967887	−	0.251385i	$-0.0808861\pi$
$132$		0			0
$133$	4.73291	+	4.73291i	0.410395	+	0.410395i
$134$	0.0564521			0.00487672
$135$		0			0
$136$	7.06902			0.606164
$137$	−7.35405	−	7.35405i	−0.628299	−	0.628299i	0.319341	−	0.947640i	$-0.396538\pi$
$137$	−7.35405	−	7.35405i	−0.628299	−	0.628299i	−0.947640	+	0.319341i	$0.896538\pi$
$138$		0			0
$139$		−	2.53500i		−	0.215016i	−0.994204	−	0.107508i	$-0.965713\pi$
$139$		−	2.53500i		−	0.215016i	0.994204	−	0.107508i	$-0.0342871\pi$
$140$	−1.06381	−	5.26988i	−0.0899085	−	0.445386i
$141$		0			0
$142$	−6.43471	+	6.43471i	−0.539989	+	0.539989i
$143$	2.00337	−	2.00337i	0.167531	−	0.167531i
$144$		0			0
$145$	2.50446	+	1.66316i	0.207984	+	0.138118i
$146$		−	11.0702i		−	0.916174i
$147$		0			0
$148$	−8.16761	−	8.16761i	−0.671374	−	0.671374i
$149$	12.9859			1.06384			0.531922	−	0.846793i	$-0.321470\pi$
$149$	12.9859			1.06384			0.531922	+	0.846793i	$0.321470\pi$
$150$		0			0
$151$	−3.17004			−0.257974			−0.128987	−	0.991646i	$-0.541173\pi$
$151$	−3.17004			−0.257974			−0.128987	+	0.991646i	$0.541173\pi$
$152$	−1.96852	−	1.96852i	−0.159668	−	0.159668i
$153$		0			0
$154$			2.75336i			0.221872i
$155$	−4.66516	−	3.09803i	−0.374715	−	0.248840i
$156$		0			0
$157$	−7.55375	+	7.55375i	−0.602855	+	0.602855i	−0.941069	−	0.338214i	$-0.890177\pi$
$157$	−7.55375	+	7.55375i	−0.602855	+	0.602855i	0.338214	+	0.941069i	$0.390177\pi$
$158$	6.91062	−	6.91062i	0.549779	−	0.549779i
$159$		0			0
$160$	0.442462	+	2.19185i	0.0349797	+	0.173281i
$161$		−	14.8288i		−	1.16867i
$162$		0			0
$163$	−15.7354	−	15.7354i	−1.23249	−	1.23249i	−0.963003	−	0.269490i	$-0.913145\pi$
$163$	−15.7354	−	15.7354i	−1.23249	−	1.23249i	−0.269490	−	0.963003i	$-0.586855\pi$
$164$	−1.97253			−0.154029
$165$		0			0
$166$	2.80039			0.217352
$167$	2.87494	+	2.87494i	0.222470	+	0.222470i	0.809538	−	0.587068i	$-0.199718\pi$
$167$	2.87494	+	2.87494i	0.222470	+	0.222470i	−0.587068	+	0.809538i	$0.699718\pi$
$168$		0			0
$169$		−	6.87925i		−	0.529173i
$170$	8.74443	−	13.1678i	0.670667	−	1.00992i
$171$		0			0
$172$	6.35785	−	6.35785i	0.484781	−	0.484781i
$173$	3.93703	−	3.93703i	0.299327	−	0.299327i	−0.541423	−	0.840750i	$-0.682114\pi$
$173$	3.93703	−	3.93703i	0.299327	−	0.299327i	0.840750	+	0.541423i	$0.182114\pi$
$174$		0			0
$175$	−11.1324	−	4.53727i	−0.841528	−	0.342985i
$176$		−	1.14518i		−	0.0863214i
$177$		0			0
$178$	−3.44949	−	3.44949i	−0.258550	−	0.258550i
$179$	0.310192			0.0231848			0.0115924	−	0.999933i	$-0.496310\pi$
$179$	0.310192			0.0231848			0.0115924	+	0.999933i	$0.496310\pi$
$180$		0			0
$181$	3.07416			0.228501			0.114250	−	0.993452i	$-0.463553\pi$
$181$	3.07416			0.228501			0.114250	+	0.993452i	$0.463553\pi$
$182$	−4.20607	−	4.20607i	−0.311774	−	0.311774i
$183$		0			0
$184$			6.16761i			0.454682i
$185$	−25.3176	+	5.11077i	−1.86138	+	0.375751i
$186$		0			0
$187$	−5.72426	+	5.72426i	−0.418599	+	0.418599i
$188$	−8.72003	+	8.72003i	−0.635974	+	0.635974i
$189$		0			0
$190$	−6.10191	+	1.23177i	−0.442679	+	0.0893622i
$191$		−	14.2652i		−	1.03220i	−0.856529	−	0.516098i	$-0.827384\pi$
$191$		−	14.2652i		−	1.03220i	0.856529	−	0.516098i	$-0.172616\pi$
$192$		0			0
$193$	−6.78931	−	6.78931i	−0.488705	−	0.488705i	0.419192	−	0.907897i	$-0.362313\pi$
$193$	−6.78931	−	6.78931i	−0.488705	−	0.488705i	−0.907897	+	0.419192i	$0.862313\pi$
$194$	−8.07442			−0.579709
$195$		0			0
$196$	−1.21934			−0.0870956
$197$	−4.62495	−	4.62495i	−0.329514	−	0.329514i	0.522887	−	0.852402i	$-0.324855\pi$
$197$	−4.62495	−	4.62495i	−0.329514	−	0.329514i	−0.852402	+	0.522887i	$0.824855\pi$
$198$		0			0
$199$		−	4.07227i		−	0.288675i	−0.989528	−	0.144338i	$-0.953895\pi$
$199$		−	4.07227i		−	0.288675i	0.989528	−	0.144338i	$-0.0461051\pi$
$200$	4.63019	+	1.88715i	0.327404	+	0.133441i
$201$		0			0
$202$	−0.515270	+	0.515270i	−0.0362543	+	0.0362543i
$203$	−2.28578	+	2.28578i	−0.160430	+	0.160430i
$204$		0			0
$205$	−2.44003	+	3.67431i	−0.170419	+	0.256625i
$206$		−	1.36541i		−	0.0951324i
$207$		0			0
$208$	1.74939	+	1.74939i	0.121299	+	0.121299i
$209$	3.18808			0.220524
$210$		0			0
$211$	15.1760			1.04476			0.522379	−	0.852713i	$-0.325045\pi$
$211$	15.1760			1.04476			0.522379	+	0.852713i	$0.325045\pi$
$212$	−1.84828	−	1.84828i	−0.126940	−	0.126940i
$213$		0			0
$214$		−	0.564565i		−	0.0385929i
$215$	−3.97833	−	19.7077i	−0.271320	−	1.34406i
$216$		0			0
$217$	4.25782	−	4.25782i	0.289040	−	0.289040i
$218$	−9.61480	+	9.61480i	−0.651196	+	0.651196i
$219$		0			0
$220$	−2.13318	−	1.41660i	−0.143819	−	0.0955071i
$221$		−	17.4889i		−	1.17643i
$222$		0			0
$223$	−6.01730	−	6.01730i	−0.402948	−	0.402948i	0.476323	−	0.879271i	$-0.341969\pi$
$223$	−6.01730	−	6.01730i	−0.402948	−	0.402948i	−0.879271	+	0.476323i	$0.841969\pi$
$224$	−2.40430			−0.160644
$225$		0			0
$226$	−5.11832			−0.340465
$227$	14.3985	+	14.3985i	0.955661	+	0.955661i	0.999058	−	0.0433973i	$-0.0138181\pi$
$227$	14.3985	+	14.3985i	0.955661	+	0.955661i	−0.0433973	+	0.999058i	$0.513818\pi$
$228$		0			0
$229$		−	14.0910i		−	0.931161i	−0.885006	−	0.465580i	$-0.845846\pi$
$229$		−	14.0910i		−	0.931161i	0.885006	−	0.465580i	$-0.154154\pi$
$230$	11.4887	+	7.62938i	0.757541	+	0.503067i
$231$		0			0
$232$	0.950705	−	0.950705i	0.0624168	−	0.0624168i
$233$	−0.643009	+	0.643009i	−0.0421249	+	0.0421249i	−0.727855	−	0.685731i	$-0.759483\pi$
$233$	−0.643009	+	0.643009i	−0.0421249	+	0.0421249i	0.685731	+	0.727855i	$0.259483\pi$
$234$		0			0
$235$	5.45644	+	27.0299i	0.355939	+	1.76324i
$236$			2.62911i			0.171141i
$237$		0			0
$238$	12.0180	+	12.0180i	0.779013	+	0.779013i
$239$	−10.6826			−0.691001			−0.345501	−	0.938419i	$-0.612291\pi$
$239$	−10.6826			−0.691001			−0.345501	+	0.938419i	$0.612291\pi$
$240$		0			0
$241$	21.1332			1.36131			0.680654	−	0.732605i	$-0.261696\pi$
$241$	21.1332			1.36131			0.680654	+	0.732605i	$0.261696\pi$
$242$	−6.85084	−	6.85084i	−0.440389	−	0.440389i
$243$		0			0
$244$			7.08551i			0.453603i
$245$	−1.50833	+	2.27132i	−0.0963637	+	0.145109i
$246$		0			0
$247$	−4.87014	+	4.87014i	−0.309880	+	0.309880i
$248$	−1.77092	+	1.77092i	−0.112453	+	0.112453i
$249$		0			0
$250$	9.24285	−	6.29045i	0.584569	−	0.397843i
$251$			24.6952i			1.55874i	0.626561	+	0.779372i	$0.284462\pi$
$251$			24.6952i			1.55874i	−0.626561	+	0.779372i	$0.715538\pi$
$252$		0			0
$253$	−4.99433	−	4.99433i	−0.313991	−	0.313991i
$254$	6.91291			0.433755
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.71612	+	3.71612i	0.231805	+	0.231805i	0.813446	−	0.581641i	$-0.197589\pi$
$257$	3.71612	+	3.71612i	0.231805	+	0.231805i	−0.581641	+	0.813446i	$0.697589\pi$
$258$		0			0
$259$		−	27.7715i		−	1.72564i
$260$	5.42268	−	1.09466i	0.336300	−	0.0678878i
$261$		0			0
$262$	−4.06902	+	4.06902i	−0.251385	+	0.251385i
$263$	10.5608	−	10.5608i	0.651205	−	0.651205i	−0.302078	−	0.953283i	$-0.597680\pi$
$263$	10.5608	−	10.5608i	0.651205	−	0.651205i	0.953283	+	0.302078i	$0.0976803\pi$
$264$		0			0
$265$	−5.72920	+	1.15653i	−0.351942	+	0.0710454i
$266$		−	6.69334i		−	0.410395i
$267$		0			0
$268$	−0.0399176	−	0.0399176i	−0.00243836	−	0.00243836i
$269$	−20.0071			−1.21985			−0.609927	−	0.792457i	$-0.708801\pi$
$269$	−20.0071			−1.21985			−0.609927	+	0.792457i	$0.708801\pi$
$270$		0			0
$271$	−3.02714			−0.183886			−0.0919428	−	0.995764i	$-0.529308\pi$
$271$	−3.02714			−0.183886			−0.0919428	+	0.995764i	$0.529308\pi$
$272$	−4.99855	−	4.99855i	−0.303082	−	0.303082i
$273$		0			0
$274$			10.4002i			0.628299i
$275$	−5.27752	+	2.22123i	−0.318247	+	0.133945i
$276$		0			0
$277$	−1.97784	+	1.97784i	−0.118837	+	0.118837i	−0.764024	−	0.645187i	$-0.776779\pi$
$277$	−1.97784	+	1.97784i	−0.118837	+	0.118837i	0.645187	+	0.764024i	$0.276779\pi$
$278$	−1.79251	+	1.79251i	−0.107508	+	0.107508i
$279$		0			0
$280$	−2.97414	+	4.47860i	−0.177739	+	0.267647i
$281$			15.1264i			0.902364i	0.892432	+	0.451182i	$0.148998\pi$
$281$			15.1264i			0.902364i	−0.892432	+	0.451182i	$0.851002\pi$
$282$		0			0
$283$	−16.9976	−	16.9976i	−1.01040	−	1.01040i	−0.999945	−	0.0104553i	$-0.996672\pi$
$283$	−16.9976	−	16.9976i	−1.01040	−	1.01040i	−0.0104553	−	0.999945i	$-0.503328\pi$
$284$	9.10005			0.539989
$285$		0			0
$286$	−2.83320			−0.167531
$287$	−3.35349	−	3.35349i	−0.197950	−	0.197950i
$288$		0			0
$289$			32.9711i			1.93948i
$290$	−0.594890	−	2.94695i	−0.0349332	−	0.173051i
$291$		0			0
$292$	−7.82779	+	7.82779i	−0.458087	+	0.458087i
$293$	10.6770	−	10.6770i	0.623757	−	0.623757i	−0.322733	−	0.946490i	$-0.604602\pi$
$293$	10.6770	−	10.6770i	0.623757	−	0.623757i	0.946490	+	0.322733i	$0.104602\pi$
$294$		0			0
$295$	4.89736	+	3.25223i	0.285135	+	0.189352i
$296$			11.5507i			0.671374i
$297$		0			0
$298$	−9.18240	−	9.18240i	−0.531922	−	0.531922i
$299$	15.2588			0.882437
$300$		0			0
$301$	21.6179			1.24604
$302$	2.24156	+	2.24156i	0.128987	+	0.128987i
$303$		0			0
$304$			2.78390i			0.159668i
$305$	13.1985	+	8.76483i	0.755743	+	0.501872i
$306$		0			0
$307$	8.29531	−	8.29531i	0.473438	−	0.473438i	−0.429587	−	0.903025i	$-0.641341\pi$
$307$	8.29531	−	8.29531i	0.473438	−	0.473438i	0.903025	+	0.429587i	$0.141341\pi$
$308$	1.94692	−	1.94692i	0.110936	−	0.110936i
$309$		0			0
$310$	1.10813	+	5.48941i	0.0629374	+	0.311777i
$311$		−	12.5698i		−	0.712766i	−0.934340	−	0.356383i	$-0.884010\pi$
$311$		−	12.5698i		−	0.712766i	0.934340	−	0.356383i	$-0.115990\pi$
$312$		0			0
$313$	−8.44084	−	8.44084i	−0.477105	−	0.477105i	0.427100	−	0.904204i	$-0.359535\pi$
$313$	−8.44084	−	8.44084i	−0.477105	−	0.477105i	−0.904204	+	0.427100i	$0.859535\pi$
$314$	10.6826			0.602855
$315$		0			0
$316$	−9.77309			−0.549779
$317$	−1.37294	−	1.37294i	−0.0771120	−	0.0771120i	0.667499	−	0.744611i	$-0.267365\pi$
$317$	−1.37294	−	1.37294i	−0.0771120	−	0.0771120i	−0.744611	+	0.667499i	$0.767365\pi$
$318$		0			0
$319$			1.53970i			0.0862065i
$320$	1.23701	−	1.86274i	0.0691508	−	0.104131i
$321$		0			0
$322$	−10.4855	+	10.4855i	−0.584336	+	0.584336i
$323$	13.9155	−	13.9155i	0.774279	−	0.774279i
$324$		0			0
$325$	4.66883	−	11.4552i	0.258980	−	0.635418i
$326$			22.2532i			1.23249i
$327$		0			0
$328$	1.39479	+	1.39479i	0.0770143	+	0.0770143i
$329$	−29.6498			−1.63465
$330$		0			0
$331$	21.9622			1.20715			0.603575	−	0.797306i	$-0.293742\pi$
$331$	21.9622			1.20715			0.603575	+	0.797306i	$0.293742\pi$
$332$	−1.98017	−	1.98017i	−0.108676	−	0.108676i
$333$		0			0
$334$		−	4.06578i		−	0.222470i
$335$	−0.123735	+	0.0249779i	−0.00676035	+	0.00136469i
$336$		0			0
$337$	18.9485	−	18.9485i	1.03219	−	1.03219i	0.0327285	−	0.999464i	$-0.489580\pi$
$337$	18.9485	−	18.9485i	1.03219	−	1.03219i	0.999464	−	0.0327285i	$-0.0104197\pi$
$338$	−4.86437	+	4.86437i	−0.264587	+	0.264587i
$339$		0			0
$340$	−15.4943	+	3.12778i	−0.840295	+	0.169627i
$341$		−	2.86806i		−	0.155314i
$342$		0			0
$343$	−13.9737	−	13.9737i	−0.754508	−	0.754508i
$344$	−8.99135			−0.484781
$345$		0			0
$346$	−5.56781			−0.299327
$347$	21.2748	+	21.2748i	1.14209	+	1.14209i	0.988067	+	0.154025i	$0.0492236\pi$
$347$	21.2748	+	21.2748i	1.14209	+	1.14209i	0.154025	+	0.988067i	$0.450776\pi$
$348$		0			0
$349$			25.7320i			1.37740i	0.725045	+	0.688702i	$0.241819\pi$
$349$			25.7320i			1.37740i	−0.725045	+	0.688702i	$0.758181\pi$
$350$	4.66344	+	11.0801i	0.249272	+	0.592257i
$351$		0			0
$352$	−0.809767	+	0.809767i	−0.0431607	+	0.0431607i
$353$	11.0273	−	11.0273i	0.586924	−	0.586924i	−0.349873	−	0.936797i	$-0.613775\pi$
$353$	11.0273	−	11.0273i	0.586924	−	0.586924i	0.936797	+	0.349873i	$0.113775\pi$
$354$		0			0
$355$	11.2568	−	16.9511i	0.597450	−	0.899669i
$356$			4.87832i			0.258550i
$357$		0			0
$358$	−0.219339	−	0.219339i	−0.0115924	−	0.0115924i
$359$	22.9830			1.21300			0.606498	−	0.795085i	$-0.292574\pi$
$359$	22.9830			1.21300			0.606498	+	0.795085i	$0.292574\pi$
$360$		0			0
$361$	11.2499			0.592099
$362$	−2.17376	−	2.17376i	−0.114250	−	0.114250i
$363$		0			0
$364$			5.94827i			0.311774i
$365$	4.89813	+	24.2642i	0.256380	+	1.27005i
$366$		0			0
$367$	−2.46354	+	2.46354i	−0.128596	+	0.128596i	−0.768475	−	0.639879i	$-0.778984\pi$
$367$	−2.46354	+	2.46354i	−0.128596	+	0.128596i	0.639879	+	0.768475i	$0.278984\pi$
$368$	4.36116	−	4.36116i	0.227341	−	0.227341i
$369$		0			0
$370$	21.5161	+	14.2884i	1.11857	+	0.742817i
$371$		−	6.28451i		−	0.326275i
$372$		0			0
$373$	16.1709	+	16.1709i	0.837295	+	0.837295i	0.988502	−	0.151207i	$-0.0483160\pi$
$373$	16.1709	+	16.1709i	0.837295	+	0.837295i	−0.151207	+	0.988502i	$0.548316\pi$
$374$	8.09532			0.418599
$375$		0			0
$376$	12.3320			0.635974
$377$	−2.35206	−	2.35206i	−0.121137	−	0.121137i
$378$		0			0
$379$		−	36.3113i		−	1.86519i	−0.360927	−	0.932594i	$-0.617540\pi$
$379$		−	36.3113i		−	1.86519i	0.360927	−	0.932594i	$-0.382460\pi$
$380$	5.18570	+	3.44371i	0.266021	+	0.176659i
$381$		0			0
$382$	−10.0870	+	10.0870i	−0.516098	+	0.516098i
$383$	11.7378	−	11.7378i	0.599775	−	0.599775i	−0.340477	−	0.940253i	$-0.610589\pi$
$383$	11.7378	−	11.7378i	0.599775	−	0.599775i	0.940253	+	0.340477i	$0.110589\pi$
$384$		0			0
$385$	−1.21826	−	6.03497i	−0.0620883	−	0.307571i
$386$			9.60153i			0.488705i
$387$		0			0
$388$	5.70947	+	5.70947i	0.289855	+	0.289855i
$389$	−23.5757			−1.19533			−0.597667	−	0.801744i	$-0.703906\pi$
$389$	−23.5757			−1.19533			−0.597667	+	0.801744i	$0.703906\pi$
$390$		0			0
$391$	−43.5990			−2.20490
$392$	0.862203	+	0.862203i	0.0435478	+	0.0435478i
$393$		0			0
$394$			6.54067i			0.329514i
$395$	−12.0894	+	18.2048i	−0.608283	+	0.915981i
$396$		0			0
$397$	27.6509	−	27.6509i	1.38776	−	1.38776i	0.557748	−	0.830011i	$-0.311666\pi$
$397$	27.6509	−	27.6509i	1.38776	−	1.38776i	0.830011	−	0.557748i	$-0.188334\pi$
$398$	−2.87953	+	2.87953i	−0.144338	+	0.144338i
$399$		0			0
$400$	−1.93963	−	4.60845i	−0.0969813	−	0.230423i
$401$			30.5601i			1.52610i	0.646340	+	0.763050i	$0.276299\pi$
$401$			30.5601i			1.52610i	−0.646340	+	0.763050i	$0.723701\pi$
$402$		0			0
$403$	4.38128	+	4.38128i	0.218247	+	0.218247i
$404$	0.728702			0.0362543
$405$		0			0
$406$	3.23258			0.160430
$407$	−9.35341	−	9.35341i	−0.463631	−	0.463631i
$408$		0			0
$409$		−	2.81363i		−	0.139125i	−0.997578	−	0.0695626i	$-0.977840\pi$
$409$		−	2.81363i		−	0.139125i	0.997578	−	0.0695626i	$-0.0221603\pi$
$410$	4.32350	−	0.872769i	0.213522	−	0.0431030i
$411$		0			0
$412$	−0.965489	+	0.965489i	−0.0475662	+	0.0475662i
$413$	−4.46974	+	4.46974i	−0.219942	+	0.219942i
$414$		0			0
$415$	−6.13805	+	1.23907i	−0.301305	+	0.0608234i
$416$		−	2.47401i		−	0.121299i
$417$		0			0
$418$	−2.25431	−	2.25431i	−0.110262	−	0.110262i
$419$	−4.47625			−0.218679			−0.109339	−	0.994004i	$-0.534874\pi$
$419$	−4.47625			−0.218679			−0.109339	+	0.994004i	$0.534874\pi$
$420$		0			0
$421$	−5.70354			−0.277973			−0.138987	−	0.990294i	$-0.544385\pi$
$421$	−5.70354			−0.277973			−0.138987	+	0.990294i	$0.544385\pi$
$422$	−10.7310	−	10.7310i	−0.522379	−	0.522379i
$423$		0			0
$424$			2.61386i			0.126940i
$425$	−13.3403	+	32.7309i	−0.647099	+	1.58768i
$426$		0			0
$427$	−12.0461	+	12.0461i	−0.582949	+	0.582949i
$428$	−0.399208	+	0.399208i	−0.0192964	+	0.0192964i
$429$		0			0
$430$	−11.1224	+	16.7486i	−0.536368	+	0.807688i
$431$			28.4120i			1.36856i	0.729221	+	0.684278i	$0.239883\pi$
$431$			28.4120i			1.36856i	−0.729221	+	0.684278i	$0.760117\pi$
$432$		0			0
$433$	20.2290	+	20.2290i	0.972142	+	0.972142i	0.999622	−	0.0274806i	$-0.00874844\pi$
$433$	20.2290	+	20.2290i	0.972142	+	0.972142i	−0.0274806	+	0.999622i	$0.508748\pi$
$434$	−6.02147			−0.289040
$435$		0			0
$436$	13.5974			0.651196
$437$	12.1411	+	12.1411i	0.580785	+	0.580785i
$438$		0			0
$439$		−	14.4089i		−	0.687702i	−0.939024	−	0.343851i	$-0.888269\pi$
$439$		−	14.4089i		−	0.687702i	0.939024	−	0.343851i	$-0.111731\pi$
$440$	0.506700	+	2.51007i	0.0241560	+	0.119663i
$441$		0			0
$442$	−12.3665	+	12.3665i	−0.588214	+	0.588214i
$443$	−18.9744	+	18.9744i	−0.901501	+	0.901501i	−0.995566	−	0.0940652i	$-0.970014\pi$
$443$	−18.9744	+	18.9744i	−0.901501	+	0.901501i	0.0940652	+	0.995566i	$0.470014\pi$
$444$		0			0
$445$	9.08705	+	6.03451i	0.430767	+	0.286063i
$446$			8.50974i			0.402948i
$447$		0			0
$448$	1.70010	+	1.70010i	0.0803220	+	0.0803220i
$449$	1.72288			0.0813077			0.0406538	−	0.999173i	$-0.487056\pi$
$449$	1.72288			0.0813077			0.0406538	+	0.999173i	$0.487056\pi$
$450$		0			0
$451$	−2.25891			−0.106368
$452$	3.61920	+	3.61920i	0.170233	+	0.170233i
$453$		0			0
$454$		−	20.3625i		−	0.955661i
$455$	11.0801	+	7.35806i	0.519444	+	0.344951i
$456$		0			0
$457$	−9.01999	+	9.01999i	−0.421938	+	0.421938i	−0.885870	−	0.463933i	$-0.846438\pi$
$457$	−9.01999	+	9.01999i	−0.421938	+	0.421938i	0.463933	+	0.885870i	$0.346438\pi$
$458$	−9.96386	+	9.96386i	−0.465580	+	0.465580i
$459$		0			0
$460$	−2.72894	−	13.5185i	−0.127237	−	0.630304i
$461$			10.0738i			0.469184i	0.972094	+	0.234592i	$0.0753755\pi$
$461$			10.0738i			0.469184i	−0.972094	+	0.234592i	$0.924625\pi$
$462$		0			0
$463$	27.0666	+	27.0666i	1.25789	+	1.25789i	0.952098	+	0.305793i	$0.0989217\pi$
$463$	27.0666	+	27.0666i	1.25789	+	1.25789i	0.305793	+	0.952098i	$0.401078\pi$
$464$	−1.34450			−0.0624168
$465$		0			0
$466$	0.909352			0.0421249
$467$	14.5094	+	14.5094i	0.671413	+	0.671413i	0.958042	−	0.286629i	$-0.0925347\pi$
$467$	14.5094	+	14.5094i	0.671413	+	0.671413i	−0.286629	+	0.958042i	$0.592535\pi$
$468$		0			0
$469$		−	0.135728i		−	0.00626733i
$470$	15.2548	−	22.9713i	0.703649	−	1.05959i
$471$		0			0
$472$	1.85906	−	1.85906i	0.0855703	−	0.0855703i
$473$	7.28090	−	7.28090i	0.334776	−	0.334776i
$474$		0			0
$475$	12.8295	−	5.39973i	0.588658	−	0.247757i
$476$		−	16.9961i		−	0.779013i
$477$		0			0
$478$	7.55375	+	7.55375i	0.345501	+	0.345501i
$479$	4.55627			0.208181			0.104091	−	0.994568i	$-0.466807\pi$
$479$	4.55627			0.208181			0.104091	+	0.994568i	$0.466807\pi$
$480$		0			0
$481$	28.5767			1.30299
$482$	−14.9434	−	14.9434i	−0.680654	−	0.680654i
$483$		0			0
$484$			9.68856i			0.440389i
$485$	17.6979	−	3.57262i	0.803622	−	0.162225i
$486$		0			0
$487$	−18.4889	+	18.4889i	−0.837814	+	0.837814i	−0.988571	−	0.150757i	$-0.951829\pi$
$487$	−18.4889	+	18.4889i	−0.837814	+	0.837814i	0.150757	+	0.988571i	$0.451829\pi$
$488$	5.01021	−	5.01021i	0.226802	−	0.226802i
$489$		0			0
$490$	2.67261	−	0.539511i	0.120736	−	0.0243726i
$491$			0.843014i			0.0380447i	0.999819	+	0.0190223i	$0.00605536\pi$
$491$			0.843014i			0.0380447i	−0.999819	+	0.0190223i	$0.993945\pi$
$492$		0			0
$493$	6.72055	+	6.72055i	0.302679	+	0.302679i
$494$	6.88742			0.309880
$495$		0			0
$496$	2.50446			0.112453
$497$	15.4710	+	15.4710i	0.693968	+	0.693968i
$498$		0			0
$499$		−	9.76726i		−	0.437243i	−0.975810	−	0.218621i	$-0.929844\pi$
$499$		−	9.76726i		−	0.437243i	0.975810	−	0.218621i	$-0.0701559\pi$
$500$	−10.9837	−	2.08767i	−0.491206	−	0.0933633i
$501$		0			0
$502$	17.4621	−	17.4621i	0.779372	−	0.779372i
$503$	−22.3161	+	22.3161i	−0.995025	+	0.995025i	−0.999988	−	0.00496279i	$-0.998420\pi$
$503$	−22.3161	+	22.3161i	−0.995025	+	0.995025i	0.00496279	+	0.999988i	$0.498420\pi$
$504$		0			0
$505$	0.901410	−	1.35738i	0.0401122	−	0.0604028i
$506$			7.06305i			0.313991i
$507$		0			0
$508$	−4.88817	−	4.88817i	−0.216877	−	0.216877i
$509$	7.67295			0.340098			0.170049	−	0.985436i	$-0.445607\pi$
$509$	7.67295			0.340098			0.170049	+	0.985436i	$0.445607\pi$
$510$		0			0
$511$	−26.6160			−1.17742
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	5.25539i		−	0.231805i
$515$	0.604141	+	2.99277i	0.0266216	+	0.131877i
$516$		0			0
$517$	−9.98603	+	9.98603i	−0.439185	+	0.439185i
$518$	−19.6374	+	19.6374i	−0.862818	+	0.862818i
$519$		0			0
$520$	−4.60845	−	3.06037i	−0.202094	−	0.134206i
$521$		−	23.2333i		−	1.01787i	−0.860805	−	0.508934i	$-0.830040\pi$
$521$		−	23.2333i		−	1.01787i	0.860805	−	0.508934i	$-0.169960\pi$
$522$		0			0
$523$	−3.86103	−	3.86103i	−0.168831	−	0.168831i	0.617634	−	0.786465i	$-0.288091\pi$
$523$	−3.86103	−	3.86103i	−0.168831	−	0.168831i	−0.786465	+	0.617634i	$0.788091\pi$
$524$	5.75447			0.251385
$525$		0			0
$526$	−14.9352			−0.651205
$527$	−12.5187	−	12.5187i	−0.545322	−	0.545322i
$528$		0			0
$529$		−	15.0395i		−	0.653889i
$530$	4.86895	+	3.23336i	0.211494	+	0.140448i
$531$		0			0
$532$	−4.73291	+	4.73291i	−0.205198	+	0.205198i
$533$	3.45073	−	3.45073i	0.149468	−	0.149468i
$534$		0			0
$535$	0.249799	+	1.23745i	0.0107997	+	0.0534994i
$536$			0.0564521i			0.00243836i
$537$		0			0
$538$	14.1472	+	14.1472i	0.609927	+	0.609927i
$539$	−1.39637			−0.0601457
$540$		0			0
$541$	−21.3692			−0.918732			−0.459366	−	0.888247i	$-0.651923\pi$
$541$	−21.3692			−0.918732			−0.459366	+	0.888247i	$0.651923\pi$
$542$	2.14051	+	2.14051i	0.0919428	+	0.0919428i
$543$		0			0
$544$			7.06902i			0.303082i
$545$	16.8201	−	25.3284i	0.720492	−	1.08495i
$546$		0			0
$547$	19.4244	−	19.4244i	0.830529	−	0.830529i	−0.157060	−	0.987589i	$-0.550202\pi$
$547$	19.4244	−	19.4244i	0.830529	−	0.830529i	0.987589	+	0.157060i	$0.0502016\pi$
$548$	7.35405	−	7.35405i	0.314149	−	0.314149i
$549$		0			0
$550$	5.30242	+	2.16113i	0.226096	+	0.0921508i
$551$		−	3.74296i		−	0.159455i
$552$		0			0
$553$	−16.6152	−	16.6152i	−0.706550	−	0.706550i
$554$	2.79709			0.118837
$555$		0			0
$556$	2.53500			0.107508
$557$	13.7347	+	13.7347i	0.581958	+	0.581958i	0.935441	−	0.353483i	$-0.115003\pi$
$557$	13.7347	+	13.7347i	0.581958	+	0.581958i	−0.353483	+	0.935441i	$0.615003\pi$
$558$		0			0
$559$			22.2447i			0.940852i
$560$	5.26988	−	1.06381i	0.222693	−	0.0449543i
$561$		0			0
$562$	10.6960	−	10.6960i	0.451182	−	0.451182i
$563$	−10.5239	+	10.5239i	−0.443529	+	0.443529i	−0.893196	−	0.449667i	$-0.851543\pi$
$563$	−10.5239	+	10.5239i	−0.443529	+	0.443529i	0.449667	+	0.893196i	$0.351543\pi$
$564$		0			0
$565$	11.2186	−	2.26466i	0.471970	−	0.0952751i
$566$			24.0382i			1.01040i
$567$		0			0
$568$	−6.43471	−	6.43471i	−0.269994	−	0.269994i
$569$	29.4163			1.23320			0.616599	−	0.787278i	$-0.288510\pi$
$569$	29.4163			1.23320			0.616599	+	0.787278i	$0.288510\pi$
$570$		0			0
$571$	−30.5819			−1.27981			−0.639906	−	0.768454i	$-0.721027\pi$
$571$	−30.5819			−1.27981			−0.639906	+	0.768454i	$0.721027\pi$
$572$	2.00337	+	2.00337i	0.0837653	+	0.0837653i
$573$		0			0
$574$			4.74255i			0.197950i
$575$	−28.5572	−	11.6392i	−1.19092	−	0.485388i
$576$		0			0
$577$	−2.75877	+	2.75877i	−0.114849	+	0.114849i	−0.762196	−	0.647347i	$-0.775879\pi$
$577$	−2.75877	+	2.75877i	−0.114849	+	0.114849i	0.647347	+	0.762196i	$0.275879\pi$
$578$	23.3141	−	23.3141i	0.969738	−	0.969738i
$579$		0			0
$580$	−1.66316	+	2.50446i	−0.0690588	+	0.103992i
$581$		−	6.73298i		−	0.279331i
$582$		0			0
$583$	−2.11662	−	2.11662i	−0.0876613	−	0.0876613i
$584$	11.0702			0.458087
$585$		0			0
$586$	−15.0996			−0.623757
$587$	−11.3822	−	11.3822i	−0.469793	−	0.469793i	0.432054	−	0.901848i	$-0.357789\pi$
$587$	−11.3822	−	11.3822i	−0.469793	−	0.469793i	−0.901848	+	0.432054i	$0.857789\pi$
$588$		0			0
$589$			6.97217i			0.287283i
$590$	−1.16328	−	5.76263i	−0.0478916	−	0.237244i
$591$		0			0
$592$	8.16761	−	8.16761i	0.335687	−	0.335687i
$593$	31.4829	−	31.4829i	1.29285	−	1.29285i	0.359830	−	0.933018i	$-0.382835\pi$
$593$	31.4829	−	31.4829i	1.29285	−	1.29285i	0.933018	−	0.359830i	$-0.117165\pi$
$594$		0			0
$595$	−31.6593	−	21.0242i	−1.29790	−	0.861910i
$596$			12.9859i			0.531922i
$597$		0			0
$598$	−10.7896	−	10.7896i	−0.441219	−	0.441219i
$599$	−0.141715			−0.00579033			−0.00289517	−	0.999996i	$-0.500922\pi$
$599$	−0.141715			−0.00579033			−0.00289517	+	0.999996i	$0.500922\pi$
$600$		0			0
$601$	−43.8849			−1.79010			−0.895052	−	0.445962i	$-0.852862\pi$
$601$	−43.8849			−1.79010			−0.895052	+	0.445962i	$0.852862\pi$
$602$	−15.2862	−	15.2862i	−0.623018	−	0.623018i
$603$		0			0
$604$		−	3.17004i		−	0.128987i
$605$	18.0473	+	11.9848i	0.733727	+	0.487252i
$606$		0			0
$607$	23.6336	−	23.6336i	0.959258	−	0.959258i	−0.0399442	−	0.999202i	$-0.512718\pi$
$607$	23.6336	−	23.6336i	0.959258	−	0.959258i	0.999202	+	0.0399442i	$0.0127180\pi$
$608$	1.96852	−	1.96852i	0.0798339	−	0.0798339i
$609$		0			0
$610$	−3.13507	−	15.5304i	−0.126935	−	0.628808i
$611$		−	30.5095i		−	1.23428i
$612$		0			0
$613$	6.75021	+	6.75021i	0.272638	+	0.272638i	0.830161	−	0.557523i	$-0.188248\pi$
$613$	6.75021	+	6.75021i	0.272638	+	0.272638i	−0.557523	+	0.830161i	$0.688248\pi$
$614$	−11.7313			−0.473438
$615$		0			0
$616$	−2.75336			−0.110936
$617$	−23.3304	−	23.3304i	−0.939248	−	0.939248i	0.0590095	−	0.998257i	$-0.481206\pi$
$617$	−23.3304	−	23.3304i	−0.939248	−	0.939248i	−0.998257	+	0.0590095i	$0.981206\pi$
$618$		0			0
$619$		−	15.2837i		−	0.614302i	−0.951661	−	0.307151i	$-0.900624\pi$
$619$		−	15.2837i		−	0.614302i	0.951661	−	0.307151i	$-0.0993757\pi$
$620$	3.09803	−	4.66516i	0.124420	−	0.187357i
$621$		0			0
$622$	−8.88817	+	8.88817i	−0.356383	+	0.356383i
$623$	−8.29361	+	8.29361i	−0.332276	+	0.332276i
$624$		0			0
$625$	−17.4757	+	17.8774i	−0.699028	+	0.715094i
$626$			11.9372i			0.477105i
$627$		0			0
$628$	−7.55375	−	7.55375i	−0.301428	−	0.301428i
$629$	−81.6525			−3.25570
$630$		0			0
$631$	10.8347			0.431321			0.215660	−	0.976468i	$-0.430810\pi$
$631$	10.8347			0.431321			0.215660	+	0.976468i	$0.430810\pi$
$632$	6.91062	+	6.91062i	0.274890	+	0.274890i
$633$		0			0
$634$			1.94163i			0.0771120i
$635$	−15.1521	+	3.05870i	−0.601293	+	0.121381i
$636$		0			0
$637$	2.13310	−	2.13310i	0.0845166	−	0.0845166i
$638$	1.08873	−	1.08873i	0.0431033	−	0.0431033i
$639$		0			0
$640$	−2.19185	+	0.442462i	−0.0866407	+	0.0174899i
$641$		−	26.6472i		−	1.05250i	−0.850330	−	0.526250i	$-0.823598\pi$
$641$		−	26.6472i		−	1.05250i	0.850330	−	0.526250i	$-0.176402\pi$
$642$		0			0
$643$	−10.0268	−	10.0268i	−0.395420	−	0.395420i	0.481194	−	0.876614i	$-0.340203\pi$
$643$	−10.0268	−	10.0268i	−0.395420	−	0.395420i	−0.876614	+	0.481194i	$0.840203\pi$
$644$	14.8288			0.584336
$645$		0			0
$646$	−19.6795			−0.774279
$647$	22.3507	+	22.3507i	0.878698	+	0.878698i	0.993400	−	0.114702i	$-0.0365912\pi$
$647$	22.3507	+	22.3507i	0.878698	+	0.878698i	−0.114702	+	0.993400i	$0.536591\pi$
$648$		0			0
$649$			3.01081i			0.118185i
$650$	−11.4014	+	4.79866i	−0.447199	+	0.188219i
$651$		0			0
$652$	15.7354	−	15.7354i	0.616247	−	0.616247i
$653$	18.0395	−	18.0395i	0.705942	−	0.705942i	−0.259738	−	0.965679i	$-0.583636\pi$
$653$	18.0395	−	18.0395i	0.705942	−	0.705942i	0.965679	+	0.259738i	$0.0836361\pi$
$654$		0			0
$655$	7.11832	−	10.7191i	0.278136	−	0.418830i
$656$		−	1.97253i		−	0.0770143i
$657$		0			0
$658$	20.9656	+	20.9656i	0.817323	+	0.817323i
$659$	−20.4692			−0.797367			−0.398684	−	0.917089i	$-0.630533\pi$
$659$	−20.4692			−0.797367			−0.398684	+	0.917089i	$0.630533\pi$
$660$		0			0
$661$	1.76645			0.0687068			0.0343534	−	0.999410i	$-0.489063\pi$
$661$	1.76645			0.0687068			0.0343534	+	0.999410i	$0.489063\pi$
$662$	−15.5296	−	15.5296i	−0.603575	−	0.603575i
$663$		0			0
$664$			2.80039i			0.108676i
$665$	2.96155	+	14.6708i	0.114844	+	0.568911i
$666$		0			0
$667$	−5.86358	+	5.86358i	−0.227039	+	0.227039i
$668$	−2.87494	+	2.87494i	−0.111235	+	0.111235i
$669$		0			0
$670$	0.105156	+	0.0698316i	0.00406252	+	0.00269783i
$671$			8.11420i			0.313245i
$672$		0			0
$673$	9.86941	+	9.86941i	0.380438	+	0.380438i	0.871260	−	0.490822i	$-0.163303\pi$
$673$	9.86941	+	9.86941i	0.380438	+	0.380438i	−0.490822	+	0.871260i	$0.663303\pi$
$674$	−26.7973			−1.03219
$675$		0			0
$676$	6.87925			0.264587
$677$	−1.25147	−	1.25147i	−0.0480980	−	0.0480980i	0.682649	−	0.730747i	$-0.260828\pi$
$677$	−1.25147	−	1.25147i	−0.0480980	−	0.0480980i	−0.730747	+	0.682649i	$0.760828\pi$
$678$		0			0
$679$			19.4133i			0.745015i
$680$	13.1678	+	8.74443i	0.504961	+	0.335334i
$681$		0			0
$682$	−2.02803	+	2.02803i	−0.0776571	+	0.0776571i
$683$	22.8964	−	22.8964i	0.876105	−	0.876105i	−0.117024	−	0.993129i	$-0.537335\pi$
$683$	22.8964	−	22.8964i	0.876105	−	0.876105i	0.993129	+	0.117024i	$0.0373354\pi$
$684$		0			0
$685$	−4.60169	−	22.7957i	−0.175822	−	0.870980i
$686$			19.7618i			0.754508i
$687$		0			0
$688$	6.35785	+	6.35785i	0.242391	+	0.242391i
$689$	6.46673			0.246363
$690$		0			0
$691$	−22.7816			−0.866654			−0.433327	−	0.901237i	$-0.642661\pi$
$691$	−22.7816			−0.866654			−0.433327	+	0.901237i	$0.642661\pi$
$692$	3.93703	+	3.93703i	0.149664	+	0.149664i
$693$		0			0
$694$		−	30.0871i		−	1.14209i
$695$	3.13581	−	4.72205i	0.118948	−	0.179118i
$696$		0			0
$697$	−9.85979	+	9.85979i	−0.373466	+	0.373466i
$698$	18.1953	−	18.1953i	0.688702	−	0.688702i
$699$		0			0
$700$	4.53727	−	11.1324i	0.171493	−	0.420764i
$701$		−	26.0321i		−	0.983220i	−0.870816	−	0.491610i	$-0.836409\pi$
$701$		−	26.0321i		−	0.983220i	0.870816	−	0.491610i	$-0.163591\pi$
$702$		0			0
$703$	22.7379	+	22.7379i	0.857574	+	0.857574i
$704$	1.14518			0.0431607
$705$		0			0
$706$	−15.5949			−0.586924
$707$	1.23886	+	1.23886i	0.0465923	+	0.0465923i
$708$		0			0
$709$			2.98206i			0.111994i	0.998431	+	0.0559968i	$0.0178337\pi$
$709$			2.98206i			0.111994i	−0.998431	+	0.0559968i	$0.982166\pi$
$710$	−19.9460	+	4.02643i	−0.748559	+	0.151109i
$711$		0			0
$712$	3.44949	−	3.44949i	0.129275	−	0.129275i
$713$	10.9223	−	10.9223i	0.409045	−	0.409045i
$714$		0			0
$715$	6.20996	−	1.25358i	0.232239	−	0.0468814i
$716$			0.310192i			0.0115924i
$717$		0			0
$718$	−16.2514	−	16.2514i	−0.606498	−	0.606498i
$719$	7.38853			0.275546			0.137773	−	0.990464i	$-0.456006\pi$
$719$	7.38853			0.275546			0.137773	+	0.990464i	$0.456006\pi$
$720$		0			0
$721$	−3.28285			−0.122260
$722$	−7.95487	−	7.95487i	−0.296049	−	0.296049i
$723$		0			0
$724$			3.07416i			0.114250i
$725$	2.60783	+	6.19606i	0.0968522	+	0.230116i
$726$		0			0
$727$	−15.2416	+	15.2416i	−0.565279	+	0.565279i	−0.930802	−	0.365523i	$-0.880890\pi$
$727$	−15.2416	+	15.2416i	−0.565279	+	0.565279i	0.365523	+	0.930802i	$0.380890\pi$
$728$	4.20607	−	4.20607i	0.155887	−	0.155887i
$729$		0			0
$730$	13.6939	−	20.6209i	0.506833	−	0.763213i
$731$		−	63.5601i		−	2.35085i
$732$		0			0
$733$	−4.77382	−	4.77382i	−0.176325	−	0.176325i	0.613427	−	0.789752i	$-0.289791\pi$
$733$	−4.77382	−	4.77382i	−0.176325	−	0.176325i	−0.789752	+	0.613427i	$0.789791\pi$
$734$	3.48398			0.128596
$735$		0			0
$736$	−6.16761			−0.227341
$737$	−0.0457130	−	0.0457130i	−0.00168386	−	0.00168386i
$738$		0			0
$739$			12.8637i			0.473200i	0.971607	+	0.236600i	$0.0760331\pi$
$739$			12.8637i			0.473200i	−0.971607	+	0.236600i	$0.923967\pi$
$740$	−5.11077	−	25.3176i	−0.187876	−	0.930692i
$741$		0			0
$742$	−4.44382	+	4.44382i	−0.163138	+	0.163138i
$743$	−23.9674	+	23.9674i	−0.879280	+	0.879280i	−0.993460	−	0.114180i	$-0.963576\pi$
$743$	−23.9674	+	23.9674i	−0.879280	+	0.879280i	0.114180	+	0.993460i	$0.463576\pi$
$744$		0			0
$745$	24.1893	+	16.0636i	0.886229	+	0.588525i
$746$		−	22.8690i		−	0.837295i
$747$		0			0
$748$	−5.72426	−	5.72426i	−0.209300	−	0.209300i
$749$	−1.35738			−0.0495978
$750$		0			0
$751$	−13.4083			−0.489276			−0.244638	−	0.969614i	$-0.578669\pi$
$751$	−13.4083			−0.489276			−0.244638	+	0.969614i	$0.578669\pi$
$752$	−8.72003	−	8.72003i	−0.317987	−	0.317987i
$753$		0			0
$754$			3.32631i			0.121137i
$755$	−5.90498	−	3.92137i	−0.214904	−	0.142713i
$756$		0			0
$757$	−1.11492	+	1.11492i	−0.0405223	+	0.0405223i	−0.727078	−	0.686555i	$-0.759122\pi$
$757$	−1.11492	+	1.11492i	−0.0405223	+	0.0405223i	0.686555	+	0.727078i	$0.259122\pi$
$758$	−25.6760	+	25.6760i	−0.932594	+	0.932594i
$759$		0			0
$760$	−1.23177	−	6.10191i	−0.0446811	−	0.221340i
$761$			34.3560i			1.24540i	0.782459	+	0.622702i	$0.213965\pi$
$761$			34.3560i			1.24540i	−0.782459	+	0.622702i	$0.786035\pi$
$762$		0			0
$763$	23.1169	+	23.1169i	0.836887	+	0.836887i
$764$	14.2652			0.516098
$765$		0			0
$766$	−16.5998			−0.599775
$767$	−4.59935	−	4.59935i	−0.166073	−	0.166073i
$768$		0			0
$769$			16.7304i			0.603315i	0.953416	+	0.301658i	$0.0975399\pi$
$769$			16.7304i			0.603315i	−0.953416	+	0.301658i	$0.902460\pi$
$770$	−3.40593	+	5.12881i	−0.122741	+	0.184829i
$771$		0			0
$772$	6.78931	−	6.78931i	0.244353	−	0.244353i
$773$	−5.20827	+	5.20827i	−0.187328	+	0.187328i	−0.794540	−	0.607212i	$-0.792288\pi$
$773$	−5.20827	+	5.20827i	−0.187328	+	0.187328i	0.607212	+	0.794540i	$0.292288\pi$
$774$		0			0
$775$	−4.85771	−	11.5417i	−0.174494	−	0.414589i
$776$		−	8.07442i		−	0.289855i
$777$		0			0
$778$	16.6705	+	16.6705i	0.597667	+	0.597667i
$779$	5.49133			0.196747
$780$		0			0
$781$	10.4212			0.372901
$782$	30.8291	+	30.8291i	1.10245	+	1.10245i
$783$		0			0
$784$		−	1.21934i		−	0.0435478i
$785$	−23.4148	+	4.72666i	−0.835708	+	0.168702i
$786$		0			0
$787$	32.7091	−	32.7091i	1.16595	−	1.16595i	0.182804	−	0.983149i	$-0.441483\pi$
$787$	32.7091	−	32.7091i	1.16595	−	1.16595i	0.983149	−	0.182804i	$-0.0585174\pi$
$788$	4.62495	−	4.62495i	0.164757	−	0.164757i
$789$		0			0
$790$	21.4212	−	4.32422i	0.762132	−	0.153849i
$791$			12.3060i			0.437550i
$792$		0			0
$793$	−12.3953	−	12.3953i	−0.440171	−	0.440171i
$794$	−39.1043			−1.38776
$795$		0			0
$796$	4.07227			0.144338
$797$	−36.4289	−	36.4289i	−1.29038	−	1.29038i	−0.934553	−	0.355825i	$-0.884200\pi$
$797$	−36.4289	−	36.4289i	−1.29038	−	1.29038i	−0.355825	−	0.934553i	$-0.615800\pi$
$798$		0			0
$799$			87.1751i			3.08403i
$800$	−1.88715	+	4.63019i	−0.0667207	+	0.163702i
$801$		0			0
$802$	21.6093	−	21.6093i	0.763050	−	0.763050i
$803$	−8.96425	+	8.96425i	−0.316342	+	0.316342i
$804$		0			0
$805$	18.3433	−	27.6222i	0.646517	−	0.973556i
$806$		−	6.19606i		−	0.218247i
$807$		0			0
$808$	−0.515270	−	0.515270i	−0.0181271	−	0.0181271i
$809$	18.0260			0.633762			0.316881	−	0.948465i	$-0.397364\pi$
$809$	18.0260			0.633762			0.316881	+	0.948465i	$0.397364\pi$
$810$		0			0
$811$	46.7969			1.64326			0.821630	−	0.570021i	$-0.193065\pi$
$811$	46.7969			1.64326			0.821630	+	0.570021i	$0.193065\pi$
$812$	−2.28578	−	2.28578i	−0.0802152	−	0.0802152i
$813$		0			0
$814$			13.2277i			0.463631i
$815$	−9.84622	−	48.7759i	−0.344898	−	1.70854i
$816$		0			0
$817$	−17.6996	+	17.6996i	−0.619232	+	0.619232i
$818$	−1.98954	+	1.98954i	−0.0695626	+	0.0695626i
$819$		0			0
$820$	−3.67431	−	2.44003i	−0.128313	−	0.0852096i
$821$			6.82435i			0.238172i	0.992884	+	0.119086i	$0.0379963\pi$
$821$			6.82435i			0.238172i	−0.992884	+	0.119086i	$0.962004\pi$
$822$		0			0
$823$	14.4124	+	14.4124i	0.502383	+	0.502383i	0.912178	−	0.409795i	$-0.134400\pi$
$823$	14.4124	+	14.4124i	0.502383	+	0.502383i	−0.409795	+	0.912178i	$0.634400\pi$
$824$	1.36541			0.0475662
$825$		0			0
$826$	6.32117			0.219942
$827$	−29.8425	−	29.8425i	−1.03773	−	1.03773i	−0.999260	−	0.0384654i	$-0.987753\pi$
$827$	−29.8425	−	29.8425i	−1.03773	−	1.03773i	−0.0384654	−	0.999260i	$-0.512247\pi$
$828$		0			0
$829$			20.4152i			0.709050i	0.935047	+	0.354525i	$0.115357\pi$
$829$			20.4152i			0.709050i	−0.935047	+	0.354525i	$0.884643\pi$
$830$	5.21641	+	3.46410i	0.181064	+	0.120241i
$831$		0			0
$832$	−1.74939	+	1.74939i	−0.0606493	+	0.0606493i
$833$	−6.09493	+	6.09493i	−0.211177	+	0.211177i
$834$		0			0
$835$	1.79895	+	8.91160i	0.0622554	+	0.308399i
$836$			3.18808i			0.110262i
$837$		0			0
$838$	3.16518	+	3.16518i	0.109339	+	0.109339i
$839$	19.4052			0.669943			0.334971	−	0.942228i	$-0.391273\pi$
$839$	19.4052			0.669943			0.334971	+	0.942228i	$0.391273\pi$
$840$		0			0
$841$	−27.1923			−0.937666
$842$	4.03301	+	4.03301i	0.138987	+	0.138987i
$843$		0			0
$844$			15.1760i			0.522379i
$845$	8.50968	−	12.8143i	0.292742	−	0.440825i
$846$		0			0
$847$	−16.4715	+	16.4715i	−0.565967	+	0.565967i
$848$	1.84828	−	1.84828i	0.0634701	−	0.0634701i
$849$		0			0
$850$	32.5773	−	13.7113i	1.11739	−	0.470292i
$851$		−	71.2406i		−	2.44209i
$852$		0			0
$853$	0.363253	+	0.363253i	0.0124375	+	0.0124375i	0.713298	−	0.700861i	$-0.247201\pi$
$853$	0.363253	+	0.363253i	0.0124375	+	0.0124375i	−0.700861	+	0.713298i	$0.747201\pi$
$854$	17.0357			0.582949
$855$		0			0
$856$	0.564565			0.0192964
$857$	−31.5094	−	31.5094i	−1.07634	−	1.07634i	−0.996834	−	0.0795070i	$-0.974665\pi$
$857$	−31.5094	−	31.5094i	−1.07634	−	1.07634i	−0.0795070	−	0.996834i	$-0.525335\pi$
$858$		0			0
$859$			29.4947i			1.00635i	0.864185	+	0.503174i	$0.167834\pi$
$859$			29.4947i			1.00635i	−0.864185	+	0.503174i	$0.832166\pi$
$860$	19.7077	−	3.97833i	0.672028	−	0.135660i
$861$		0			0
$862$	20.0903	−	20.0903i	0.684278	−	0.684278i
$863$	6.17951	−	6.17951i	0.210353	−	0.210353i	−0.594064	−	0.804417i	$-0.702478\pi$
$863$	6.17951	−	6.17951i	0.210353	−	0.210353i	0.804417	+	0.594064i	$0.202478\pi$
$864$		0			0
$865$	12.2038	−	2.46354i	0.414943	−	0.0837630i
$866$		−	28.6081i		−	0.972142i
$867$		0			0
$868$	4.25782	+	4.25782i	0.144520	+	0.144520i
$869$	−11.1920			−0.379662
$870$		0			0
$871$	0.139663			0.00473231
$872$	−9.61480	−	9.61480i	−0.325598	−	0.325598i
$873$		0			0
$874$		−	17.1700i		−	0.580785i
$875$	−15.1241	−	22.2226i	−0.511289	−	0.751261i
$876$		0			0
$877$	−14.7066	+	14.7066i	−0.496606	+	0.496606i	−0.910380	−	0.413774i	$-0.864210\pi$
$877$	−14.7066	+	14.7066i	−0.496606	+	0.496606i	0.413774	+	0.910380i	$0.364210\pi$
$878$	−10.1887	+	10.1887i	−0.343851	+	0.343851i
$879$		0			0
$880$	1.41660	−	2.13318i	0.0477536	−	0.0719095i
$881$			28.3087i			0.953745i	0.878972	+	0.476873i	$0.158230\pi$
$881$			28.3087i			0.953745i	−0.878972	+	0.476873i	$0.841770\pi$
$882$		0			0
$883$	15.1647	+	15.1647i	0.510333	+	0.510333i	0.914629	−	0.404295i	$-0.132483\pi$
$883$	15.1647	+	15.1647i	0.510333	+	0.510333i	−0.404295	+	0.914629i	$0.632483\pi$
$884$	17.4889			0.588214
$885$		0			0
$886$	26.8339			0.901501
$887$	33.9701	+	33.9701i	1.14060	+	1.14060i	0.988340	+	0.152263i	$0.0486561\pi$
$887$	33.9701	+	33.9701i	1.14060	+	1.14060i	0.152263	+	0.988340i	$0.451344\pi$
$888$		0			0
$889$		−	16.6207i		−	0.557441i
$890$	−2.15847	−	10.6926i	−0.0723521	−	0.358415i
$891$		0			0
$892$	6.01730	−	6.01730i	0.201474	−	0.201474i
$893$	24.2757	−	24.2757i	0.812356	−	0.812356i
$894$		0			0
$895$	0.577808	+	0.383709i	0.0193140	+	0.0128260i
$896$		−	2.40430i		−	0.0803220i
$897$		0			0
$898$	−1.21826	−	1.21826i	−0.0406538	−	0.0406538i
$899$	−3.36724			−0.112304
$900$		0			0
$901$	−18.4774			−0.615573
$902$	1.59729	+	1.59729i	0.0531839	+	0.0531839i
$903$		0			0
$904$		−	5.11832i		−	0.170233i
$905$	5.72638	+	3.80276i	0.190351	+	0.126408i
$906$		0			0
$907$	26.3916	−	26.3916i	0.876320	−	0.876320i	−0.116832	−	0.993152i	$-0.537274\pi$
$907$	26.3916	−	26.3916i	0.876320	−	0.876320i	0.993152	+	0.116832i	$0.0372739\pi$
$908$	−14.3985	+	14.3985i	−0.477830	+	0.477830i
$909$		0			0
$910$	−2.63189	−	13.0378i	−0.0872462	−	0.432197i
$911$			53.8041i			1.78261i	0.453406	+	0.891304i	$0.350209\pi$
$911$			53.8041i			1.78261i	−0.453406	+	0.891304i	$0.649791\pi$
$912$		0			0
$913$	−2.26766	−	2.26766i	−0.0750486	−	0.0750486i
$914$	12.7562			0.421938
$915$		0			0
$916$	14.0910			0.465580
$917$	9.78315	+	9.78315i	0.323068	+	0.323068i
$918$		0			0
$919$			23.1668i			0.764203i	0.924120	+	0.382101i	$0.124799\pi$
$919$			23.1668i			0.764203i	−0.924120	+	0.382101i	$0.875201\pi$
$920$	−7.62938	+	11.4887i	−0.251533	+	0.378771i
$921$		0			0
$922$	7.12326	−	7.12326i	0.234592	−	0.234592i
$923$	−15.9196	+	15.9196i	−0.523999	+	0.523999i
$924$		0			0
$925$	−53.4822	−	21.7980i	−1.75848	−	0.716712i
$926$		−	38.2779i		−	1.25789i
$927$		0			0
$928$	0.950705	+	0.950705i	0.0312084	+	0.0312084i
$929$	−13.5670			−0.445119			−0.222559	−	0.974919i	$-0.571441\pi$
$929$	−13.5670			−0.445119			−0.222559	+	0.974919i	$0.571441\pi$
$930$		0			0
$931$	3.39452			0.111251
$932$	−0.643009	−	0.643009i	−0.0210625	−	0.0210625i
$933$		0			0
$934$		−	20.5193i		−	0.671413i
$935$	−17.7438	+	3.58188i	−0.580283	+	0.117140i
$936$		0			0
$937$	−6.94086	+	6.94086i	−0.226748	+	0.226748i	−0.811333	−	0.584585i	$-0.801258\pi$
$937$	−6.94086	+	6.94086i	−0.226748	+	0.226748i	0.584585	+	0.811333i	$0.301258\pi$
$938$	−0.0959740	+	0.0959740i	−0.00313366	+	0.00313366i
$939$		0			0
$940$	−27.0299	+	5.45644i	−0.881619	+	0.177969i
$941$			16.8558i			0.549484i	0.961518	+	0.274742i	$0.0885925\pi$
$941$			16.8558i			0.549484i	−0.961518	+	0.274742i	$0.911408\pi$
$942$		0			0
$943$	−8.60252	−	8.60252i	−0.280136	−	0.280136i
$944$	−2.62911			−0.0855703
$945$		0			0
$946$	−10.2967			−0.334776
$947$	27.1223	+	27.1223i	0.881357	+	0.881357i	0.993673	−	0.112316i	$-0.0358269\pi$
$947$	27.1223	+	27.1223i	0.881357	+	0.881357i	−0.112316	+	0.993673i	$0.535827\pi$
$948$		0			0
$949$		−	27.3878i		−	0.889044i
$950$	−12.8900	−	5.25364i	−0.418207	−	0.170450i
$951$		0			0
$952$	−12.0180	+	12.0180i	−0.389506	+	0.389506i
$953$	−18.8861	+	18.8861i	−0.611780	+	0.611780i	−0.943410	−	0.331630i	$-0.892402\pi$
$953$	−18.8861	+	18.8861i	−0.611780	+	0.611780i	0.331630	+	0.943410i	$0.392402\pi$
$954$		0			0
$955$	17.6462	−	26.5725i	0.571018	−	0.859865i
$956$		−	10.6826i		−	0.345501i
$957$		0			0
$958$	−3.22177	−	3.22177i	−0.104091	−	0.104091i
$959$	25.0052			0.807460
$960$		0			0
$961$	−24.7277			−0.797667
$962$	−20.2068	−	20.2068i	−0.651493	−	0.651493i
$963$		0			0
$964$			21.1332i			0.680654i
$965$	−4.24832	−	21.0452i	−0.136758	−	0.677468i
$966$		0			0
$967$	−22.6566	+	22.6566i	−0.728586	+	0.728586i	−0.970338	−	0.241752i	$-0.922278\pi$
$967$	−22.6566	+	22.6566i	−0.728586	+	0.728586i	0.241752	+	0.970338i	$0.422278\pi$
$968$	6.85084	−	6.85084i	0.220194	−	0.220194i
$969$		0			0
$970$	−15.0406	−	9.98811i	−0.482923	−	0.320699i
$971$		−	29.2201i		−	0.937716i	−0.883274	−	0.468858i	$-0.844666\pi$
$971$		−	29.2201i		−	0.937716i	0.883274	−	0.468858i	$-0.155334\pi$
$972$		0			0
$973$	4.30974	+	4.30974i	0.138164	+	0.138164i
$974$	26.1473			0.837814
$975$		0			0
$976$	−7.08551			−0.226802
$977$	27.6275	+	27.6275i	0.883882	+	0.883882i	0.993927	−	0.110045i	$-0.0350994\pi$
$977$	27.6275	+	27.6275i	0.883882	+	0.883882i	−0.110045	+	0.993927i	$0.535099\pi$
$978$		0			0
$979$			5.58656i			0.178547i
$980$	−2.27132	−	1.50833i	−0.0725545	−	0.0481819i
$981$		0			0
$982$	0.596101	−	0.596101i	0.0190223	−	0.0190223i
$983$	−8.10091	+	8.10091i	−0.258379	+	0.258379i	−0.824394	−	0.566016i	$-0.808484\pi$
$983$	−8.10091	+	8.10091i	−0.258379	+	0.258379i	0.566016	+	0.824394i	$0.308484\pi$
$984$		0			0
$985$	−2.89400	−	14.3362i	−0.0922105	−	0.456789i
$986$		−	9.50430i		−	0.302679i
$987$		0			0
$988$	−4.87014	−	4.87014i	−0.154940	−	0.154940i
$989$	55.4552			1.76337
$990$		0			0
$991$	−26.7986			−0.851286			−0.425643	−	0.904891i	$-0.639952\pi$
$991$	−26.7986			−0.851286			−0.425643	+	0.904891i	$0.639952\pi$
$992$	−1.77092	−	1.77092i	−0.0562267	−	0.0562267i
$993$		0			0
$994$		−	21.8793i		−	0.693968i
$995$	5.03742	−	7.58559i	0.159697	−	0.240479i
$996$		0			0
$997$	38.8587	−	38.8587i	1.23067	−	1.23067i	0.266959	−	0.963708i	$-0.413981\pi$
$997$	38.8587	−	38.8587i	1.23067	−	1.23067i	0.963708	−	0.266959i	$-0.0860188\pi$
$998$	−6.90650	+	6.90650i	−0.218621	+	0.218621i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.f.c.323.3		16
3.2	odd	2	inner	810.2.f.c.323.6		16
5.2	odd	4	inner	810.2.f.c.647.6		16
9.2	odd	6		270.2.m.b.233.4		16
9.4	even	3		270.2.m.b.143.3		16
9.5	odd	6		90.2.l.b.83.2	yes	16
9.7	even	3		90.2.l.b.23.2	✓	16
15.2	even	4	inner	810.2.f.c.647.3		16
36.7	odd	6		720.2.cu.b.113.2		16
36.23	even	6		720.2.cu.b.353.1		16
45.2	even	12		270.2.m.b.17.3		16
45.4	even	6		1350.2.q.h.143.1		16
45.7	odd	12		90.2.l.b.77.2	yes	16
45.13	odd	12		1350.2.q.h.1007.2		16
45.14	odd	6		450.2.p.h.443.3		16
45.22	odd	12		270.2.m.b.197.4		16
45.23	even	12		450.2.p.h.407.3		16
45.29	odd	6		1350.2.q.h.1043.2		16
45.32	even	12		90.2.l.b.47.2	yes	16
45.34	even	6		450.2.p.h.293.3		16
45.38	even	12		1350.2.q.h.557.1		16
45.43	odd	12		450.2.p.h.257.3		16
180.7	even	12		720.2.cu.b.257.1		16
180.167	odd	12		720.2.cu.b.497.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.b.23.2	✓	16	9.7	even	3
90.2.l.b.47.2	yes	16	45.32	even	12
90.2.l.b.77.2	yes	16	45.7	odd	12
90.2.l.b.83.2	yes	16	9.5	odd	6
270.2.m.b.17.3		16	45.2	even	12
270.2.m.b.143.3		16	9.4	even	3
270.2.m.b.197.4		16	45.22	odd	12
270.2.m.b.233.4		16	9.2	odd	6
450.2.p.h.257.3		16	45.43	odd	12
450.2.p.h.293.3		16	45.34	even	6
450.2.p.h.407.3		16	45.23	even	12
450.2.p.h.443.3		16	45.14	odd	6
720.2.cu.b.113.2		16	36.7	odd	6
720.2.cu.b.257.1		16	180.7	even	12
720.2.cu.b.353.1		16	36.23	even	6
720.2.cu.b.497.2		16	180.167	odd	12
810.2.f.c.323.3		16	1.1	even	1	trivial
810.2.f.c.323.6		16	3.2	odd	2	inner
810.2.f.c.647.3		16	15.2	even	4	inner
810.2.f.c.647.6		16	5.2	odd	4	inner
1350.2.q.h.143.1		16	45.4	even	6
1350.2.q.h.557.1		16	45.38	even	12
1350.2.q.h.1007.2		16	45.13	odd	12
1350.2.q.h.1043.2		16	45.29	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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.86274 + 1.23701i) q^{5} +(-1.70010 + 1.70010i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +1.00000i q^{4} +(1.86274 + 1.23701i) q^{5} +(-1.70010 + 1.70010i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.442462 - 2.19185i) q^{10} +1.14518i q^{11} +(-1.74939 - 1.74939i) q^{13} +2.40430 q^{14} -1.00000 q^{16} +(4.99855 + 4.99855i) q^{17} -2.78390i q^{19} +(-1.23701 + 1.86274i) q^{20} +(0.809767 - 0.809767i) q^{22} +(-4.36116 + 4.36116i) q^{23} +(1.93963 + 4.60845i) q^{25} +2.47401i q^{26} +(-1.70010 - 1.70010i) q^{28} +1.34450 q^{29} -2.50446 q^{31} +(0.707107 + 0.707107i) q^{32} -7.06902i q^{34} +(-5.26988 + 1.06381i) q^{35} +(-8.16761 + 8.16761i) q^{37} +(-1.96852 + 1.96852i) q^{38} +(2.19185 - 0.442462i) q^{40} +1.97253i q^{41} +(-6.35785 - 6.35785i) q^{43} -1.14518 q^{44} +6.16761 q^{46} +(8.72003 + 8.72003i) q^{47} +1.21934i q^{49} +(1.88715 - 4.63019i) q^{50} +(1.74939 - 1.74939i) q^{52} +(-1.84828 + 1.84828i) q^{53} +(-1.41660 + 2.13318i) q^{55} +2.40430i q^{56} +(-0.950705 - 0.950705i) q^{58} +2.62911 q^{59} +7.08551 q^{61} +(1.77092 + 1.77092i) q^{62} -1.00000i q^{64} +(-1.09466 - 5.42268i) q^{65} +(-0.0399176 + 0.0399176i) q^{67} +(-4.99855 + 4.99855i) q^{68} +(4.47860 + 2.97414i) q^{70} -9.10005i q^{71} +(7.82779 + 7.82779i) q^{73} +11.5507 q^{74} +2.78390 q^{76} +(-1.94692 - 1.94692i) q^{77} +9.77309i q^{79} +(-1.86274 - 1.23701i) q^{80} +(1.39479 - 1.39479i) q^{82} +(-1.98017 + 1.98017i) q^{83} +(3.12778 + 15.4943i) q^{85} +8.99135i q^{86} +(0.809767 + 0.809767i) q^{88} +4.87832 q^{89} +5.94827 q^{91} +(-4.36116 - 4.36116i) q^{92} -12.3320i q^{94} +(3.44371 - 5.18570i) q^{95} +(5.70947 - 5.70947i) q^{97} +(0.862203 - 0.862203i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{7}+O(q^{10}) \) 16 * q - 16 * q^7	\( 16 q - 16 q^{7} - 8 q^{10} - 16 q^{16} - 16 q^{22} + 32 q^{25} - 16 q^{28} + 16 q^{31} + 8 q^{40} - 32 q^{46} + 24 q^{55} - 32 q^{58} + 48 q^{61} + 32 q^{67} - 32 q^{70} + 16 q^{73} - 32 q^{76} - 16 q^{82} + 8 q^{85} - 16 q^{88} + 96 q^{97}+O(q^{100}) \) 16 * q - 16 * q^7 - 8 * q^10 - 16 * q^16 - 16 * q^22 + 32 * q^25 - 16 * q^28 + 16 * q^31 + 8 * q^40 - 32 * q^46 + 24 * q^55 - 32 * q^58 + 48 * q^61 + 32 * q^67 - 32 * q^70 + 16 * q^73 - 32 * q^76 - 16 * q^82 + 8 * q^85 - 16 * q^88 + 96 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more