LMFDB - Embedded newform 850.2.h.l.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [850,2,Mod(251,850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(850, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("850.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 850 = 2 \cdot 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	850.h (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:	$6.78728417181$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.17572153600.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 18x^{6} - 40x^{5} + 80x^{4} - 98x^{3} + 93x^{2} - 50x + 10 $ x^8 - 4x^7 + 18x^6 - 40x^5 + 80x^4 - 98x^3 + 93x^2 - 50*x + 10
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.2
Root			$0.500000 - 1.25081i$ of defining polynomial
Character	$\chi$	$=$	850.251
Dual form			850.2.h.l.701.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.750811 - 0.750811i) q^{3} -1.00000 q^{4} +(-0.750811 + 0.750811i) q^{6} +(-1.70459 + 1.70459i) q^{7} +1.00000i q^{8} -1.87256i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.750811 - 0.750811i) q^{3} -1.00000 q^{4} +(-0.750811 + 0.750811i) q^{6} +(-1.70459 + 1.70459i) q^{7} +1.00000i q^{8} -1.87256i q^{9} +(3.64088 - 3.64088i) q^{11} +(0.750811 + 0.750811i) q^{12} +5.59791 q^{13} +(1.70459 + 1.70459i) q^{14} +1.00000 q^{16} +(-3.02902 - 2.79733i) q^{17} -1.87256 q^{18} -2.18547i q^{19} +2.55966 q^{21} +(-3.64088 - 3.64088i) q^{22} +(-5.72534 + 5.72534i) q^{23} +(0.750811 - 0.750811i) q^{24} -5.59791i q^{26} +(-3.65838 + 3.65838i) q^{27} +(1.70459 - 1.70459i) q^{28} +(-6.78338 - 6.78338i) q^{29} +(-0.519124 - 0.519124i) q^{31} -1.00000i q^{32} -5.46722 q^{33} +(-2.79733 + 3.02902i) q^{34} +1.87256i q^{36} +(-5.87256 - 5.87256i) q^{37} -2.18547 q^{38} +(-4.20297 - 4.20297i) q^{39} +(-2.95703 + 2.95703i) q^{41} -2.55966i q^{42} -5.00325i q^{43} +(-3.64088 + 3.64088i) q^{44} +(5.72534 + 5.72534i) q^{46} +1.03825 q^{47} +(-0.750811 - 0.750811i) q^{48} +1.18872i q^{49} +(0.173954 + 4.37449i) q^{51} -5.59791 q^{52} -8.18872i q^{53} +(3.65838 + 3.65838i) q^{54} +(-1.70459 - 1.70459i) q^{56} +(-1.64088 + 1.64088i) q^{57} +(-6.78338 + 6.78338i) q^{58} +10.1926i q^{59} +(8.09628 - 8.09628i) q^{61} +(-0.519124 + 0.519124i) q^{62} +(3.19196 + 3.19196i) q^{63} -1.00000 q^{64} +5.46722i q^{66} +4.50547 q^{67} +(3.02902 + 2.79733i) q^{68} +8.59730 q^{69} +(0.422841 + 0.422841i) q^{71} +1.87256 q^{72} +(-0.455406 - 0.455406i) q^{73} +(-5.87256 + 5.87256i) q^{74} +2.18547i q^{76} +12.4124i q^{77} +(-4.20297 + 4.20297i) q^{78} +(7.07878 - 7.07878i) q^{79} -0.124190 q^{81} +(2.95703 + 2.95703i) q^{82} -14.2506i q^{83} -2.55966 q^{84} -5.00325 q^{86} +10.1861i q^{87} +(3.64088 + 3.64088i) q^{88} -15.5087 q^{89} +(-9.54216 + 9.54216i) q^{91} +(5.72534 - 5.72534i) q^{92} +0.779528i q^{93} -1.03825i q^{94} +(-0.750811 + 0.750811i) q^{96} +(-2.96885 - 2.96885i) q^{97} +1.18872 q^{98} +(-6.81778 - 6.81778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 2 q^{7}+O(q^{10}) $ 8 * q - 8 * q^4 - 2 * q^7	$ 8 q - 8 q^{4} - 2 q^{7} + 2 q^{11} - 12 q^{13} + 2 q^{14} + 8 q^{16} - 4 q^{17} + 16 q^{18} - 32 q^{21} - 2 q^{22} - 20 q^{23} - 12 q^{27} + 2 q^{28} + 12 q^{29} - 2 q^{31} + 20 q^{33} - 6 q^{34} - 16 q^{37} - 8 q^{38} - 34 q^{39} + 6 q^{41} - 2 q^{44} + 20 q^{46} + 4 q^{47} + 22 q^{51} + 12 q^{52} + 12 q^{54} - 2 q^{56} + 14 q^{57} + 12 q^{58} + 20 q^{61} - 2 q^{62} - 32 q^{63} - 8 q^{64} - 32 q^{67} + 4 q^{68} + 44 q^{69} + 46 q^{71} - 16 q^{72} + 14 q^{73} - 16 q^{74} - 34 q^{78} + 2 q^{79} - 56 q^{81} - 6 q^{82} + 32 q^{84} - 16 q^{86} + 2 q^{88} - 32 q^{89} - 14 q^{91} + 20 q^{92} + 52 q^{97} - 24 q^{98} - 40 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 2 * q^7 + 2 * q^11 - 12 * q^13 + 2 * q^14 + 8 * q^16 - 4 * q^17 + 16 * q^18 - 32 * q^21 - 2 * q^22 - 20 * q^23 - 12 * q^27 + 2 * q^28 + 12 * q^29 - 2 * q^31 + 20 * q^33 - 6 * q^34 - 16 * q^37 - 8 * q^38 - 34 * q^39 + 6 * q^41 - 2 * q^44 + 20 * q^46 + 4 * q^47 + 22 * q^51 + 12 * q^52 + 12 * q^54 - 2 * q^56 + 14 * q^57 + 12 * q^58 + 20 * q^61 - 2 * q^62 - 32 * q^63 - 8 * q^64 - 32 * q^67 + 4 * q^68 + 44 * q^69 + 46 * q^71 - 16 * q^72 + 14 * q^73 - 16 * q^74 - 34 * q^78 + 2 * q^79 - 56 * q^81 - 6 * q^82 + 32 * q^84 - 16 * q^86 + 2 * q^88 - 32 * q^89 - 14 * q^91 + 20 * q^92 + 52 * q^97 - 24 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/850\mathbb{Z}\right)^\times$.

$n$	$477$	$751$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.750811	−	0.750811i	−0.433481	−	0.433481i	0.456330	−	0.889811i	$-0.349164\pi$
$3$	−0.750811	−	0.750811i	−0.433481	−	0.433481i	−0.889811	+	0.456330i	$0.849164\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−0.750811	+	0.750811i	−0.306517	+	0.306517i
$7$	−1.70459	+	1.70459i	−0.644276	+	0.644276i	−0.951604	−	0.307328i	$-0.900565\pi$
$7$	−1.70459	+	1.70459i	−0.644276	+	0.644276i	0.307328	+	0.951604i	$0.400565\pi$
$8$			1.00000i			0.353553i
$9$		−	1.87256i		−	0.624188i
$10$		0			0
$11$	3.64088	−	3.64088i	1.09777	−	1.09777i	0.103094	−	0.994672i	$-0.467126\pi$
$11$	3.64088	−	3.64088i	1.09777	−	1.09777i	0.994672	−	0.103094i	$-0.0328742\pi$
$12$	0.750811	+	0.750811i	0.216741	+	0.216741i
$13$	5.59791			1.55258			0.776290	−	0.630376i	$-0.217099\pi$
$13$	5.59791			1.55258			0.776290	+	0.630376i	$0.217099\pi$
$14$	1.70459	+	1.70459i	0.455572	+	0.455572i
$15$		0			0
$16$	1.00000			0.250000
$17$	−3.02902	−	2.79733i	−0.734645	−	0.678452i
$17$	−3.02902	−	2.79733i	−0.734645	−	0.678452i
$18$	−1.87256			−0.441368
$19$		−	2.18547i		−	0.501381i	−0.968067	−	0.250691i	$-0.919342\pi$
$19$		−	2.18547i		−	0.501381i	0.968067	−	0.250691i	$-0.0806577\pi$
$20$		0			0
$21$	2.55966			0.558563
$22$	−3.64088	−	3.64088i	−0.776237	−	0.776237i
$23$	−5.72534	+	5.72534i	−1.19382	+	1.19382i	−0.217829	+	0.975987i	$0.569898\pi$
$23$	−5.72534	+	5.72534i	−1.19382	+	1.19382i	−0.975987	+	0.217829i	$0.930102\pi$
$24$	0.750811	−	0.750811i	0.153259	−	0.153259i
$25$		0			0
$26$		−	5.59791i		−	1.09784i
$27$	−3.65838	+	3.65838i	−0.704055	+	0.704055i
$28$	1.70459	−	1.70459i	0.322138	−	0.322138i
$29$	−6.78338	−	6.78338i	−1.25964	−	1.25964i	−0.951264	−	0.308377i	$-0.900214\pi$
$29$	−6.78338	−	6.78338i	−1.25964	−	1.25964i	−0.308377	−	0.951264i	$-0.599786\pi$
$30$		0			0
$31$	−0.519124	−	0.519124i	−0.0932374	−	0.0932374i	0.658950	−	0.752187i	$-0.271001\pi$
$31$	−0.519124	−	0.519124i	−0.0932374	−	0.0932374i	−0.752187	+	0.658950i	$0.771001\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−5.46722			−0.951721
$34$	−2.79733	+	3.02902i	−0.479738	+	0.519472i
$35$		0			0
$36$			1.87256i			0.312094i
$37$	−5.87256	−	5.87256i	−0.965444	−	0.965444i	0.0339789	−	0.999423i	$-0.489182\pi$
$37$	−5.87256	−	5.87256i	−0.965444	−	0.965444i	−0.999423	+	0.0339789i	$0.989182\pi$
$38$	−2.18547			−0.354530
$39$	−4.20297	−	4.20297i	−0.673014	−	0.673014i
$40$		0			0
$41$	−2.95703	+	2.95703i	−0.461810	+	0.461810i	−0.899248	−	0.437438i	$-0.855886\pi$
$41$	−2.95703	+	2.95703i	−0.461810	+	0.461810i	0.437438	+	0.899248i	$0.355886\pi$
$42$		−	2.55966i		−	0.394964i
$43$		−	5.00325i		−	0.762988i	−0.924371	−	0.381494i	$-0.875410\pi$
$43$		−	5.00325i		−	0.762988i	0.924371	−	0.381494i	$-0.124590\pi$
$44$	−3.64088	+	3.64088i	−0.548883	+	0.548883i
$45$		0			0
$46$	5.72534	+	5.72534i	0.844155	+	0.844155i
$47$	1.03825			0.151444			0.0757220	−	0.997129i	$-0.475874\pi$
$47$	1.03825			0.151444			0.0757220	+	0.997129i	$0.475874\pi$
$48$	−0.750811	−	0.750811i	−0.108370	−	0.108370i
$49$			1.18872i			0.169817i
$50$		0			0
$51$	0.173954	+	4.37449i	0.0243584	+	0.612551i
$52$	−5.59791			−0.776290
$53$		−	8.18872i		−	1.12481i	−0.826863	−	0.562403i	$-0.809877\pi$
$53$		−	8.18872i		−	1.12481i	0.826863	−	0.562403i	$-0.190123\pi$
$54$	3.65838	+	3.65838i	0.497842	+	0.497842i
$55$		0			0
$56$	−1.70459	−	1.70459i	−0.227786	−	0.227786i
$57$	−1.64088	+	1.64088i	−0.217339	+	0.217339i
$58$	−6.78338	+	6.78338i	−0.890701	+	0.890701i
$59$			10.1926i			1.32696i	0.748195	+	0.663479i	$0.230921\pi$
$59$			10.1926i			1.32696i	−0.748195	+	0.663479i	$0.769079\pi$
$60$		0			0
$61$	8.09628	−	8.09628i	1.03662	−	1.03662i	0.0373193	−	0.999303i	$-0.488118\pi$
$61$	8.09628	−	8.09628i	1.03662	−	1.03662i	0.999303	−	0.0373193i	$-0.0118819\pi$
$62$	−0.519124	+	0.519124i	−0.0659288	+	0.0659288i
$63$	3.19196	+	3.19196i	0.402149	+	0.402149i
$64$	−1.00000			−0.125000
$65$		0			0
$66$			5.46722i			0.672969i
$67$	4.50547			0.550431			0.275215	−	0.961383i	$-0.411251\pi$
$67$	4.50547			0.550431			0.275215	+	0.961383i	$0.411251\pi$
$68$	3.02902	+	2.79733i	0.367322	+	0.339226i
$69$	8.59730			1.03499
$70$		0			0
$71$	0.422841	+	0.422841i	0.0501820	+	0.0501820i	0.731752	−	0.681570i	$-0.238703\pi$
$71$	0.422841	+	0.422841i	0.0501820	+	0.0501820i	−0.681570	+	0.731752i	$0.738703\pi$
$72$	1.87256			0.220684
$73$	−0.455406	−	0.455406i	−0.0533012	−	0.0533012i	0.679954	−	0.733255i	$-0.262000\pi$
$73$	−0.455406	−	0.455406i	−0.0533012	−	0.0533012i	−0.733255	+	0.679954i	$0.762000\pi$
$74$	−5.87256	+	5.87256i	−0.682672	+	0.682672i
$75$		0			0
$76$			2.18547i			0.250691i
$77$			12.4124i			1.41453i
$78$	−4.20297	+	4.20297i	−0.475893	+	0.475893i
$79$	7.07878	−	7.07878i	0.796425	−	0.796425i	−0.186105	−	0.982530i	$-0.559586\pi$
$79$	7.07878	−	7.07878i	0.796425	−	0.796425i	0.982530	+	0.186105i	$0.0595864\pi$
$80$		0			0
$81$	−0.124190			−0.0137989
$82$	2.95703	+	2.95703i	0.326549	+	0.326549i
$83$		−	14.2506i		−	1.56421i	−0.623149	−	0.782103i	$-0.714147\pi$
$83$		−	14.2506i		−	1.56421i	0.623149	−	0.782103i	$-0.285853\pi$
$84$	−2.55966			−0.279282
$85$		0			0
$86$	−5.00325			−0.539514
$87$			10.1861i			1.09206i
$88$	3.64088	+	3.64088i	0.388119	+	0.388119i
$89$	−15.5087			−1.64392			−0.821960	−	0.569545i	$-0.807120\pi$
$89$	−15.5087			−1.64392			−0.821960	+	0.569545i	$0.807120\pi$
$90$		0			0
$91$	−9.54216	+	9.54216i	−1.00029	+	1.00029i
$92$	5.72534	−	5.72534i	0.596908	−	0.596908i
$93$			0.779528i			0.0808333i
$94$		−	1.03825i		−	0.107087i
$95$		0			0
$96$	−0.750811	+	0.750811i	−0.0766294	+	0.0766294i
$97$	−2.96885	−	2.96885i	−0.301441	−	0.301441i	0.540137	−	0.841577i	$-0.318373\pi$
$97$	−2.96885	−	2.96885i	−0.301441	−	0.301441i	−0.841577	+	0.540137i	$0.818373\pi$
$98$	1.18872			0.120079
$99$	−6.81778	−	6.81778i	−0.685212	−	0.685212i
$100$		0			0
$101$	4.77953			0.475581			0.237790	−	0.971316i	$-0.423577\pi$
$101$	4.77953			0.475581			0.237790	+	0.971316i	$0.423577\pi$
$102$	4.37449	−	0.173954i	0.433139	−	0.0172240i
$103$	−1.67055			−0.164604			−0.0823022	−	0.996607i	$-0.526227\pi$
$103$	−1.67055			−0.164604			−0.0823022	+	0.996607i	$0.526227\pi$
$104$			5.59791i			0.548920i
$105$		0			0
$106$	−8.18872			−0.795358
$107$	−3.37987	−	3.37987i	−0.326744	−	0.326744i	0.524603	−	0.851347i	$-0.324214\pi$
$107$	−3.37987	−	3.37987i	−0.326744	−	0.326744i	−0.851347	+	0.524603i	$0.824214\pi$
$108$	3.65838	−	3.65838i	0.352028	−	0.352028i
$109$	8.27851	−	8.27851i	0.792937	−	0.792937i	−0.189033	−	0.981971i	$-0.560535\pi$
$109$	8.27851	−	8.27851i	0.792937	−	0.792937i	0.981971	+	0.189033i	$0.0605355\pi$
$110$		0			0
$111$			8.81838i			0.837003i
$112$	−1.70459	+	1.70459i	−0.161069	+	0.161069i
$113$	−3.45865	+	3.45865i	−0.325363	+	0.325363i	−0.850820	−	0.525457i	$-0.823894\pi$
$113$	−3.45865	+	3.45865i	−0.325363	+	0.325363i	0.525457	+	0.850820i	$0.323894\pi$
$114$	1.64088	+	1.64088i	0.153682	+	0.153682i
$115$		0			0
$116$	6.78338	+	6.78338i	0.629821	+	0.629821i
$117$		−	10.4824i		−	0.969102i
$118$	10.1926			0.938302
$119$	9.93156	−	0.394934i	0.910424	−	0.0362035i
$120$		0			0
$121$		−	15.5120i		−	1.41018i
$122$	−8.09628	−	8.09628i	−0.733003	−	0.733003i
$123$	4.44034			0.400372
$124$	0.519124	+	0.519124i	0.0466187	+	0.0466187i
$125$		0			0
$126$	3.19196	−	3.19196i	0.284363	−	0.284363i
$127$			13.7451i			1.21968i	0.792523	+	0.609841i	$0.208767\pi$
$127$			13.7451i			1.21968i	−0.792523	+	0.609841i	$0.791233\pi$
$128$			1.00000i			0.0883883i
$129$	−3.75649	+	3.75649i	−0.330741	+	0.330741i
$130$		0			0
$131$	−5.07554	−	5.07554i	−0.443452	−	0.443452i	0.449719	−	0.893170i	$-0.351524\pi$
$131$	−5.07554	−	5.07554i	−0.443452	−	0.443452i	−0.893170	+	0.449719i	$0.851524\pi$
$132$	5.46722			0.475861
$133$	3.72534	+	3.72534i	0.323028	+	0.323028i
$134$		−	4.50547i		−	0.389213i
$135$		0			0
$136$	2.79733	−	3.02902i	0.239869	−	0.259736i
$137$	0.958507			0.0818908			0.0409454	−	0.999161i	$-0.486963\pi$
$137$	0.958507			0.0818908			0.0409454	+	0.999161i	$0.486963\pi$
$138$		−	8.59730i		−	0.731851i
$139$	2.02547	+	2.02547i	0.171798	+	0.171798i	0.787769	−	0.615971i	$-0.211236\pi$
$139$	2.02547	+	2.02547i	0.171798	+	0.171798i	−0.615971	+	0.787769i	$0.711236\pi$
$140$		0			0
$141$	−0.779528	−	0.779528i	−0.0656481	−	0.0656481i
$142$	0.422841	−	0.422841i	0.0354841	−	0.0354841i
$143$	20.3813	−	20.3813i	1.70437	−	1.70437i
$144$		−	1.87256i		−	0.156047i
$145$		0			0
$146$	−0.455406	+	0.455406i	−0.0376896	+	0.0376896i
$147$	0.892502	−	0.892502i	0.0736123	−	0.0736123i
$148$	5.87256	+	5.87256i	0.482722	+	0.482722i
$149$	13.4545			1.10224			0.551119	−	0.834427i	$-0.314201\pi$
$149$	13.4545			1.10224			0.551119	+	0.834427i	$0.314201\pi$
$150$		0			0
$151$			9.40919i			0.765709i	0.923809	+	0.382854i	$0.125059\pi$
$151$			9.40919i			0.765709i	−0.923809	+	0.382854i	$0.874941\pi$
$152$	2.18547			0.177265
$153$	−5.23818	+	5.67203i	−0.423482	+	0.458556i
$154$	12.4124			1.00022
$155$		0			0
$156$	4.20297	+	4.20297i	0.336507	+	0.336507i
$157$	23.3845			1.86629			0.933144	−	0.359502i	$-0.117054\pi$
$157$	23.3845			1.86629			0.933144	+	0.359502i	$0.117054\pi$
$158$	−7.07878	−	7.07878i	−0.563158	−	0.563158i
$159$	−6.14818	+	6.14818i	−0.487583	+	0.487583i
$160$		0			0
$161$		−	19.5188i		−	1.53829i
$162$			0.124190i			0.00975728i
$163$	−5.74757	+	5.74757i	−0.450184	+	0.450184i	−0.895416	−	0.445231i	$-0.853121\pi$
$163$	−5.74757	+	5.74757i	−0.450184	+	0.450184i	0.445231	+	0.895416i	$0.353121\pi$
$164$	2.95703	−	2.95703i	0.230905	−	0.230905i
$165$		0			0
$166$	−14.2506			−1.10606
$167$	12.1887	+	12.1887i	0.943191	+	0.943191i	0.998471	−	0.0552797i	$-0.0176051\pi$
$167$	12.1887	+	12.1887i	0.943191	+	0.943191i	−0.0552797	+	0.998471i	$0.517605\pi$
$168$			2.55966i			0.197482i
$169$	18.3365			1.41050
$170$		0			0
$171$	−4.09243			−0.312956
$172$			5.00325i			0.381494i
$173$	2.55966	+	2.55966i	0.194607	+	0.194607i	0.797683	−	0.603076i	$-0.206059\pi$
$173$	2.55966	+	2.55966i	0.194607	+	0.194607i	−0.603076	+	0.797683i	$0.706059\pi$
$174$	10.1861			0.772204
$175$		0			0
$176$	3.64088	−	3.64088i	0.274441	−	0.274441i
$177$	7.65269	−	7.65269i	0.575212	−	0.575212i
$178$			15.5087i			1.16243i
$179$			17.3813i			1.29914i	0.760303	+	0.649569i	$0.225051\pi$
$179$			17.3813i			1.29914i	−0.760303	+	0.649569i	$0.774949\pi$
$180$		0			0
$181$	−8.13778	+	8.13778i	−0.604876	+	0.604876i	−0.941603	−	0.336726i	$-0.890680\pi$
$181$	−8.13778	+	8.13778i	−0.604876	+	0.604876i	0.336726	+	0.941603i	$0.390680\pi$
$182$	9.54216	+	9.54216i	0.707312	+	0.707312i
$183$	−12.1576			−0.898713
$184$	−5.72534	−	5.72534i	−0.422078	−	0.422078i
$185$		0			0
$186$	0.779528			0.0571578
$187$	−21.2130	+	0.843547i	−1.55125	+	0.0616863i
$188$	−1.03825			−0.0757220
$189$		−	12.4721i		−	0.907212i
$190$		0			0
$191$	−11.1478			−0.806628			−0.403314	−	0.915062i	$-0.632142\pi$
$191$	−11.1478			−0.806628			−0.403314	+	0.915062i	$0.632142\pi$
$192$	0.750811	+	0.750811i	0.0541852	+	0.0541852i
$193$	−9.19669	+	9.19669i	−0.661992	+	0.661992i	−0.955849	−	0.293857i	$-0.905061\pi$
$193$	−9.19669	+	9.19669i	−0.661992	+	0.661992i	0.293857	+	0.955849i	$0.405061\pi$
$194$	−2.96885	+	2.96885i	−0.213151	+	0.213151i
$195$		0			0
$196$		−	1.18872i		−	0.0849083i
$197$	10.0963	−	10.0963i	0.719330	−	0.719330i	−0.249138	−	0.968468i	$-0.580147\pi$
$197$	10.0963	−	10.0963i	0.719330	−	0.719330i	0.968468	+	0.249138i	$0.0801472\pi$
$198$	−6.81778	+	6.81778i	−0.484518	+	0.484518i
$199$	7.55641	+	7.55641i	0.535660	+	0.535660i	0.922251	−	0.386591i	$-0.126348\pi$
$199$	7.55641	+	7.55641i	0.535660	+	0.535660i	−0.386591	+	0.922251i	$0.626348\pi$
$200$		0			0
$201$	−3.38276	−	3.38276i	−0.238601	−	0.238601i
$202$		−	4.77953i		−	0.336286i
$203$	23.1258			1.62311
$204$	−0.173954	−	4.37449i	−0.0121792	−	0.306275i
$205$		0			0
$206$			1.67055i			0.116393i
$207$	10.7211	+	10.7211i	0.745166	+	0.745166i
$208$	5.59791			0.388145
$209$	−7.95703	−	7.95703i	−0.550399	−	0.550399i
$210$		0			0
$211$	−0.214187	+	0.214187i	−0.0147453	+	0.0147453i	−0.714441	−	0.699696i	$-0.753319\pi$
$211$	−0.214187	+	0.214187i	−0.0147453	+	0.0147453i	0.699696	+	0.714441i	$0.253319\pi$
$212$			8.18872i			0.562403i
$213$		−	0.634948i		−	0.0435059i
$214$	−3.37987	+	3.37987i	−0.231043	+	0.231043i
$215$		0			0
$216$	−3.65838	−	3.65838i	−0.248921	−	0.248921i
$217$	1.76979			0.120141
$218$	−8.27851	−	8.27851i	−0.560691	−	0.560691i
$219$			0.683848i			0.0462101i
$220$		0			0
$221$	−16.9562	−	15.6592i	−1.14059	−	1.05335i
$222$	8.81838			0.591851
$223$		−	14.4124i		−	0.965128i	−0.875861	−	0.482564i	$-0.839706\pi$
$223$		−	14.4124i		−	0.965128i	0.875861	−	0.482564i	$-0.160294\pi$
$224$	1.70459	+	1.70459i	0.113893	+	0.113893i
$225$		0			0
$226$	3.45865	+	3.45865i	0.230066	+	0.230066i
$227$	16.0476	−	16.0476i	1.06512	−	1.06512i	0.0673919	−	0.997727i	$-0.478532\pi$
$227$	16.0476	−	16.0476i	1.06512	−	1.06512i	0.997727	−	0.0673919i	$-0.0214678\pi$
$228$	1.64088	−	1.64088i	0.108670	−	0.108670i
$229$		−	22.2379i		−	1.46952i	−0.678326	−	0.734761i	$-0.737294\pi$
$229$		−	22.2379i		−	1.46952i	0.678326	−	0.734761i	$-0.262706\pi$
$230$		0			0
$231$	9.31940	−	9.31940i	0.613171	−	0.613171i
$232$	6.78338	−	6.78338i	0.445350	−	0.445350i
$233$	−9.37479	−	9.37479i	−0.614163	−	0.614163i	0.329865	−	0.944028i	$-0.392997\pi$
$233$	−9.37479	−	9.37479i	−0.614163	−	0.614163i	−0.944028	+	0.329865i	$0.892997\pi$
$234$	−10.4824			−0.685258
$235$		0			0
$236$		−	10.1926i		−	0.663479i
$237$	−10.6297			−0.690471
$238$	−0.394934	−	9.93156i	−0.0255998	−	0.643767i
$239$	19.0032			1.22922			0.614609	−	0.788832i	$-0.289314\pi$
$239$	19.0032			1.22922			0.614609	+	0.788832i	$0.289314\pi$
$240$		0			0
$241$	14.3893	+	14.3893i	0.926893	+	0.926893i	0.997504	−	0.0706108i	$-0.0224948\pi$
$241$	14.3893	+	14.3893i	0.926893	+	0.926893i	−0.0706108	+	0.997504i	$0.522495\pi$
$242$	−15.5120			−0.997147
$243$	11.0684	+	11.0684i	0.710037	+	0.710037i
$244$	−8.09628	+	8.09628i	−0.518311	+	0.518311i
$245$		0			0
$246$		−	4.44034i		−	0.283106i
$247$		−	12.2341i		−	0.778434i
$248$	0.519124	−	0.519124i	0.0329644	−	0.0329644i
$249$	−10.6995	+	10.6995i	−0.678054	+	0.678054i
$250$		0			0
$251$	−5.68709			−0.358966			−0.179483	−	0.983761i	$-0.557443\pi$
$251$	−5.68709			−0.358966			−0.179483	+	0.983761i	$0.557443\pi$
$252$	−3.19196	−	3.19196i	−0.201075	−	0.201075i
$253$			41.6905i			2.62106i
$254$	13.7451			0.862446
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	18.5738i		−	1.15860i	−0.815113	−	0.579302i	$-0.803325\pi$
$257$		−	18.5738i		−	1.15860i	0.815113	−	0.579302i	$-0.196675\pi$
$258$	3.75649	+	3.75649i	0.233869	+	0.233869i
$259$	20.0207			1.24402
$260$		0			0
$261$	−12.7023	+	12.7023i	−0.786253	+	0.786253i
$262$	−5.07554	+	5.07554i	−0.313568	+	0.313568i
$263$			4.45393i			0.274641i	0.990527	+	0.137320i	$0.0438490\pi$
$263$			4.45393i			0.274641i	−0.990527	+	0.137320i	$0.956151\pi$
$264$		−	5.46722i		−	0.336484i
$265$		0			0
$266$	3.72534	−	3.72534i	0.228415	−	0.228415i
$267$	11.6441	+	11.6441i	0.712609	+	0.712609i
$268$	−4.50547			−0.275215
$269$	−5.77628	−	5.77628i	−0.352186	−	0.352186i	0.508736	−	0.860922i	$-0.330113\pi$
$269$	−5.77628	−	5.77628i	−0.352186	−	0.352186i	−0.860922	+	0.508736i	$0.830113\pi$
$270$		0			0
$271$	15.0382			0.913508			0.456754	−	0.889593i	$-0.349012\pi$
$271$	15.0382			0.913508			0.456754	+	0.889593i	$0.349012\pi$
$272$	−3.02902	−	2.79733i	−0.183661	−	0.169613i
$273$	14.3287			0.867214
$274$		−	0.958507i		−	0.0579055i
$275$		0			0
$276$	−8.59730			−0.517497
$277$	−6.81453	−	6.81453i	−0.409445	−	0.409445i	0.472100	−	0.881545i	$-0.343496\pi$
$277$	−6.81453	−	6.81453i	−0.409445	−	0.409445i	−0.881545	+	0.472100i	$0.843496\pi$
$278$	2.02547	−	2.02547i	0.121480	−	0.121480i
$279$	−0.972092	+	0.972092i	−0.0581976	+	0.0581976i
$280$		0			0
$281$		−	23.0486i		−	1.37496i	−0.726202	−	0.687482i	$-0.758716\pi$
$281$		−	23.0486i		−	1.37496i	0.726202	−	0.687482i	$-0.241284\pi$
$282$	−0.779528	+	0.779528i	−0.0464202	+	0.0464202i
$283$	−10.2038	+	10.2038i	−0.606552	+	0.606552i	−0.942043	−	0.335491i	$-0.891098\pi$
$283$	−10.2038	+	10.2038i	−0.606552	+	0.606552i	0.335491	+	0.942043i	$0.391098\pi$
$284$	−0.422841	−	0.422841i	−0.0250910	−	0.0250910i
$285$		0			0
$286$	−20.3813	−	20.3813i	−1.20517	−	1.20517i
$287$		−	10.0811i		−	0.595067i
$288$	−1.87256			−0.110342
$289$	1.34989	+	16.9463i	0.0794055	+	0.996842i
$290$		0			0
$291$			4.45809i			0.261338i
$292$	0.455406	+	0.455406i	0.0266506	+	0.0266506i
$293$	0.665388			0.0388724			0.0194362	−	0.999811i	$-0.493813\pi$
$293$	0.665388			0.0388724			0.0194362	+	0.999811i	$0.493813\pi$
$294$	−0.892502	−	0.892502i	−0.0520518	−	0.0520518i
$295$		0			0
$296$	5.87256	−	5.87256i	0.341336	−	0.341336i
$297$			26.6394i			1.54577i
$298$		−	13.4545i		−	0.779400i
$299$	−32.0499	+	32.0499i	−1.85349	+	1.85349i
$300$		0			0
$301$	8.52850	+	8.52850i	0.491575	+	0.491575i
$302$	9.40919			0.541438
$303$	−3.58852	−	3.58852i	−0.206155	−	0.206155i
$304$		−	2.18547i		−	0.125345i
$305$		0			0
$306$	5.67203	+	5.23818i	0.324248	+	0.299447i
$307$	23.4163			1.33644			0.668219	−	0.743965i	$-0.267057\pi$
$307$	23.4163			1.33644			0.668219	+	0.743965i	$0.267057\pi$
$308$		−	12.4124i		−	0.707264i
$309$	1.25427	+	1.25427i	0.0713529	+	0.0713529i
$310$		0			0
$311$	4.67019	+	4.67019i	0.264822	+	0.264822i	0.827010	−	0.562187i	$-0.190040\pi$
$311$	4.67019	+	4.67019i	0.264822	+	0.264822i	−0.562187	+	0.827010i	$0.690040\pi$
$312$	4.20297	−	4.20297i	0.237946	−	0.237946i
$313$	3.59730	−	3.59730i	0.203332	−	0.203332i	−0.598094	−	0.801426i	$-0.704075\pi$
$313$	3.59730	−	3.59730i	0.203332	−	0.203332i	0.801426	+	0.598094i	$0.204075\pi$
$314$		−	23.3845i		−	1.31967i
$315$		0			0
$316$	−7.07878	+	7.07878i	−0.398213	+	0.398213i
$317$	4.51816	−	4.51816i	0.253765	−	0.253765i	−0.568747	−	0.822512i	$-0.692572\pi$
$317$	4.51816	−	4.51816i	0.253765	−	0.253765i	0.822512	+	0.568747i	$0.192572\pi$
$318$	6.14818	+	6.14818i	0.344773	+	0.344773i
$319$	−49.3949			−2.76558
$320$		0			0
$321$			5.07529i			0.283275i
$322$	−19.5188			−1.08774
$323$	−6.11348	+	6.61983i	−0.340163	+	0.368337i
$324$	0.124190			0.00689944
$325$		0			0
$326$	5.74757	+	5.74757i	0.318328	+	0.318328i
$327$	−12.4312			−0.687447
$328$	−2.95703	−	2.95703i	−0.163275	−	0.163275i
$329$	−1.76979	+	1.76979i	−0.0975717	+	0.0975717i
$330$		0			0
$331$			23.0340i			1.26606i	0.774127	+	0.633031i	$0.218189\pi$
$331$			23.0340i			1.26606i	−0.774127	+	0.633031i	$0.781811\pi$
$332$			14.2506i			0.782103i
$333$	−10.9968	+	10.9968i	−0.602618	+	0.602618i
$334$	12.1887	−	12.1887i	0.666937	−	0.666937i
$335$		0			0
$336$	2.55966			0.139641
$337$	1.64412	+	1.64412i	0.0895610	+	0.0895610i	0.750468	−	0.660907i	$-0.229828\pi$
$337$	1.64412	+	1.64412i	0.0895610	+	0.0895610i	−0.660907	+	0.750468i	$0.729828\pi$
$338$		−	18.3365i		−	0.997376i
$339$	5.19359			0.282077
$340$		0			0
$341$	−3.78013			−0.204706
$342$			4.09243i			0.221294i
$343$	−13.9584	−	13.9584i	−0.753685	−	0.753685i
$344$	5.00325			0.269757
$345$		0			0
$346$	2.55966	−	2.55966i	0.137608	−	0.137608i
$347$	−11.8159	+	11.8159i	−0.634313	+	0.634313i	−0.949147	−	0.314834i	$-0.898051\pi$
$347$	−11.8159	+	11.8159i	−0.634313	+	0.634313i	0.314834	+	0.949147i	$0.398051\pi$
$348$		−	10.1861i		−	0.546031i
$349$			28.0038i			1.49901i	0.661998	+	0.749506i	$0.269709\pi$
$349$			28.0038i			1.49901i	−0.661998	+	0.749506i	$0.730291\pi$
$350$		0			0
$351$	−20.4792	+	20.4792i	−1.09310	+	1.09310i
$352$	−3.64088	−	3.64088i	−0.194059	−	0.194059i
$353$	4.60115			0.244895			0.122447	−	0.992475i	$-0.460926\pi$
$353$	4.60115			0.244895			0.122447	+	0.992475i	$0.460926\pi$
$354$	−7.65269	−	7.65269i	−0.406736	−	0.406736i
$355$		0			0
$356$	15.5087			0.821960
$357$	−7.75325	−	7.16021i	−0.410345	−	0.378958i
$358$	17.3813			0.918629
$359$		−	35.9027i		−	1.89487i	−0.319946	−	0.947436i	$-0.603665\pi$
$359$		−	35.9027i		−	1.89487i	0.319946	−	0.947436i	$-0.396335\pi$
$360$		0			0
$361$	14.2237			0.748617
$362$	8.13778	+	8.13778i	0.427712	+	0.427712i
$363$	−11.6466	+	11.6466i	−0.611286	+	0.611286i
$364$	9.54216	−	9.54216i	0.500145	−	0.500145i
$365$		0			0
$366$			12.1576i			0.635486i
$367$	−5.97925	+	5.97925i	−0.312114	+	0.312114i	−0.845728	−	0.533614i	$-0.820834\pi$
$367$	−5.97925	+	5.97925i	−0.312114	+	0.312114i	0.533614	+	0.845728i	$0.320834\pi$
$368$	−5.72534	+	5.72534i	−0.298454	+	0.298454i
$369$	5.53723	+	5.53723i	0.288256	+	0.288256i
$370$		0			0
$371$	13.9584	+	13.9584i	0.724686	+	0.724686i
$372$		−	0.779528i		−	0.0404166i
$373$	28.0453			1.45213			0.726066	−	0.687625i	$-0.241347\pi$
$373$	28.0453			1.45213			0.726066	+	0.687625i	$0.241347\pi$
$374$	0.843547	+	21.2130i	0.0436188	+	1.09690i
$375$		0			0
$376$			1.03825i			0.0535435i
$377$	−37.9727	−	37.9727i	−1.95569	−	1.95569i
$378$	−12.4721			−0.641495
$379$	2.34932	+	2.34932i	0.120676	+	0.120676i	0.764866	−	0.644190i	$-0.222805\pi$
$379$	2.34932	+	2.34932i	0.120676	+	0.120676i	−0.644190	+	0.764866i	$0.722805\pi$
$380$		0			0
$381$	10.3200	−	10.3200i	0.528710	−	0.528710i
$382$			11.1478i			0.570372i
$383$		−	16.2671i		−	0.831212i	−0.909545	−	0.415606i	$-0.863570\pi$
$383$		−	16.2671i		−	0.831212i	0.909545	−	0.415606i	$-0.136430\pi$
$384$	0.750811	−	0.750811i	0.0383147	−	0.0383147i
$385$		0			0
$386$	9.19669	+	9.19669i	0.468099	+	0.468099i
$387$	−9.36890			−0.476248
$388$	2.96885	+	2.96885i	0.150720	+	0.150720i
$389$			16.0842i			0.815501i	0.913093	+	0.407750i	$0.133687\pi$
$389$			16.0842i			0.815501i	−0.913093	+	0.407750i	$0.866313\pi$
$390$		0			0
$391$	33.3578	−	1.32649i	1.68698	−	0.0670836i
$392$	−1.18872			−0.0600393
$393$			7.62154i			0.384456i
$394$	−10.0963	−	10.0963i	−0.508643	−	0.508643i
$395$		0			0
$396$	6.81778	+	6.81778i	0.342606	+	0.342606i
$397$	1.17513	−	1.17513i	0.0589781	−	0.0589781i	−0.677003	−	0.735981i	$-0.736721\pi$
$397$	1.17513	−	1.17513i	0.0589781	−	0.0589781i	0.735981	+	0.677003i	$0.236721\pi$
$398$	7.55641	−	7.55641i	0.378769	−	0.378769i
$399$		−	5.59406i		−	0.280053i
$400$		0			0
$401$	−6.92263	+	6.92263i	−0.345700	+	0.345700i	−0.858505	−	0.512805i	$-0.828606\pi$
$401$	−6.92263	+	6.92263i	−0.345700	+	0.345700i	0.512805	+	0.858505i	$0.328606\pi$
$402$	−3.38276	+	3.38276i	−0.168717	+	0.168717i
$403$	−2.90600	−	2.90600i	−0.144758	−	0.144758i
$404$	−4.77953			−0.237790
$405$		0			0
$406$		−	23.1258i		−	1.14771i
$407$	−42.7626			−2.11966
$408$	−4.37449	+	0.173954i	−0.216569	+	0.00861200i
$409$	23.0236			1.13845			0.569223	−	0.822183i	$-0.307244\pi$
$409$	23.0236			1.13845			0.569223	+	0.822183i	$0.307244\pi$
$410$		0			0
$411$	−0.719658	−	0.719658i	−0.0354981	−	0.0354981i
$412$	1.67055			0.0823022
$413$	−17.3742	−	17.3742i	−0.854928	−	0.854928i
$414$	10.7211	−	10.7211i	0.526912	−	0.526912i
$415$		0			0
$416$		−	5.59791i		−	0.274460i
$417$		−	3.04149i		−	0.148943i
$418$	−7.95703	+	7.95703i	−0.389191	+	0.389191i
$419$	−13.5128	+	13.5128i	−0.660145	+	0.660145i	−0.955414	−	0.295269i	$-0.904591\pi$
$419$	−13.5128	+	13.5128i	−0.660145	+	0.660145i	0.295269	+	0.955414i	$0.404591\pi$
$420$		0			0
$421$	12.4163			0.605133			0.302566	−	0.953128i	$-0.402157\pi$
$421$	12.4163			0.605133			0.302566	+	0.953128i	$0.402157\pi$
$422$	0.214187	+	0.214187i	0.0104265	+	0.0104265i
$423$		−	1.94418i		−	0.0945295i
$424$	8.18872			0.397679
$425$		0			0
$426$	−0.634948			−0.0307633
$427$			27.6018i			1.33574i
$428$	3.37987	+	3.37987i	0.163372	+	0.163372i
$429$	−30.6050			−1.47762
$430$		0			0
$431$	−4.73899	+	4.73899i	−0.228269	+	0.228269i	−0.811969	−	0.583700i	$-0.801604\pi$
$431$	−4.73899	+	4.73899i	−0.228269	+	0.228269i	0.583700	+	0.811969i	$0.301604\pi$
$432$	−3.65838	+	3.65838i	−0.176014	+	0.176014i
$433$		−	17.9721i		−	0.863684i	−0.901949	−	0.431842i	$-0.857864\pi$
$433$		−	17.9721i		−	0.863684i	0.901949	−	0.431842i	$-0.142136\pi$
$434$		−	1.76979i		−	0.0849527i
$435$		0			0
$436$	−8.27851	+	8.27851i	−0.396469	+	0.396469i
$437$	12.5126	+	12.5126i	0.598557	+	0.598557i
$438$	0.683848			0.0326755
$439$	−11.3158	−	11.3158i	−0.540073	−	0.540073i	0.383477	−	0.923550i	$-0.374727\pi$
$439$	−11.3158	−	11.3158i	−0.540073	−	0.540073i	−0.923550	+	0.383477i	$0.874727\pi$
$440$		0			0
$441$	2.22595			0.105998
$442$	−15.6592	+	16.9562i	−0.744832	+	0.806522i
$443$	−2.55346			−0.121318			−0.0606592	−	0.998159i	$-0.519320\pi$
$443$	−2.55346			−0.121318			−0.0606592	+	0.998159i	$0.519320\pi$
$444$		−	8.81838i		−	0.418502i
$445$		0			0
$446$	−14.4124			−0.682449
$447$	−10.1018	−	10.1018i	−0.477799	−	0.477799i
$448$	1.70459	−	1.70459i	0.0805345	−	0.0805345i
$449$	12.5549	−	12.5549i	0.592504	−	0.592504i	−0.345803	−	0.938307i	$-0.612393\pi$
$449$	12.5549	−	12.5549i	0.592504	−	0.592504i	0.938307	+	0.345803i	$0.112393\pi$
$450$		0			0
$451$			21.5324i			1.01392i
$452$	3.45865	−	3.45865i	0.162681	−	0.162681i
$453$	7.06453	−	7.06453i	0.331920	−	0.331920i
$454$	−16.0476	−	16.0476i	−0.753153	−	0.753153i
$455$		0			0
$456$	−1.64088	−	1.64088i	−0.0768411	−	0.0768411i
$457$			26.2450i			1.22769i	0.789427	+	0.613845i	$0.210378\pi$
$457$			26.2450i			1.22769i	−0.789427	+	0.613845i	$0.789622\pi$
$458$	−22.2379			−1.03911
$459$	21.3150	−	0.847602i	0.994898	−	0.0395627i
$460$		0			0
$461$		−	16.9344i		−	0.788716i	−0.918957	−	0.394358i	$-0.870967\pi$
$461$		−	16.9344i		−	0.788716i	0.918957	−	0.394358i	$-0.129033\pi$
$462$	−9.31940	−	9.31940i	−0.433578	−	0.433578i
$463$	14.4539			0.671731			0.335865	−	0.941910i	$-0.390971\pi$
$463$	14.4539			0.671731			0.335865	+	0.941910i	$0.390971\pi$
$464$	−6.78338	−	6.78338i	−0.314910	−	0.314910i
$465$		0			0
$466$	−9.37479	+	9.37479i	−0.434279	+	0.434279i
$467$		−	16.7911i		−	0.776998i	−0.921449	−	0.388499i	$-0.872994\pi$
$467$		−	16.7911i		−	0.776998i	0.921449	−	0.388499i	$-0.127006\pi$
$468$			10.4824i			0.484551i
$469$	−7.68000	+	7.68000i	−0.354629	+	0.354629i
$470$		0			0
$471$	−17.5574	−	17.5574i	−0.809001	−	0.809001i
$472$	−10.1926			−0.469151
$473$	−18.2162	−	18.2162i	−0.837582	−	0.837582i
$474$			10.6297i			0.488236i
$475$		0			0
$476$	−9.93156	+	0.394934i	−0.455212	+	0.0181018i
$477$	−15.3339			−0.702091
$478$		−	19.0032i		−	0.869188i
$479$	27.6215	+	27.6215i	1.26206	+	1.26206i	0.950093	+	0.311968i	$0.100988\pi$
$479$	27.6215	+	27.6215i	1.26206	+	1.26206i	0.311968	+	0.950093i	$0.399012\pi$
$480$		0			0
$481$	−32.8741	−	32.8741i	−1.49893	−	1.49893i
$482$	14.3893	−	14.3893i	0.655412	−	0.655412i
$483$	−14.6549	+	14.6549i	−0.666822	+	0.666822i
$484$			15.5120i			0.705089i
$485$		0			0
$486$	11.0684	−	11.0684i	0.502072	−	0.502072i
$487$	6.76359	−	6.76359i	0.306487	−	0.306487i	−0.537058	−	0.843545i	$-0.680464\pi$
$487$	6.76359	−	6.76359i	0.306487	−	0.306487i	0.843545	+	0.537058i	$0.180464\pi$
$488$	8.09628	+	8.09628i	0.366501	+	0.366501i
$489$	8.63068			0.390293
$490$		0			0
$491$			31.5603i			1.42429i	0.702030	+	0.712147i	$0.252277\pi$
$491$			31.5603i			1.42429i	−0.702030	+	0.712147i	$0.747723\pi$
$492$	−4.44034			−0.200186
$493$	1.57163	+	39.5223i	0.0707825	+	1.77999i
$494$	−12.2341			−0.550436
$495$		0			0
$496$	−0.519124	−	0.519124i	−0.0233093	−	0.0233093i
$497$	−1.44155			−0.0646622
$498$	10.6995	+	10.6995i	0.479457	+	0.479457i
$499$	−24.4121	+	24.4121i	−1.09283	+	1.09283i	−0.0976099	+	0.995225i	$0.531120\pi$
$499$	−24.4121	+	24.4121i	−1.09283	+	1.09283i	−0.995225	+	0.0976099i	$0.968880\pi$
$500$		0			0
$501$		−	18.3029i		−	0.817711i
$502$			5.68709i			0.253827i
$503$	14.7457	−	14.7457i	0.657480	−	0.657480i	−0.297303	−	0.954783i	$-0.596087\pi$
$503$	14.7457	−	14.7457i	0.657480	−	0.657480i	0.954783	+	0.297303i	$0.0960873\pi$
$504$	−3.19196	+	3.19196i	−0.142181	+	0.142181i
$505$		0			0
$506$	41.6905			1.85337
$507$	−13.7673	−	13.7673i	−0.611427	−	0.611427i
$508$		−	13.7451i		−	0.609841i
$509$	−14.2029			−0.629533			−0.314766	−	0.949169i	$-0.601926\pi$
$509$	−14.2029			−0.629533			−0.314766	+	0.949169i	$0.601926\pi$
$510$		0			0
$511$	1.55256			0.0686814
$512$		−	1.00000i		−	0.0441942i
$513$	7.99528	+	7.99528i	0.353000	+	0.353000i
$514$	−18.5738			−0.819257
$515$		0			0
$516$	3.75649	−	3.75649i	0.165370	−	0.165370i
$517$	3.78013	−	3.78013i	0.166250	−	0.166250i
$518$		−	20.0207i		−	0.879658i
$519$		−	3.84364i		−	0.168717i
$520$		0			0
$521$	18.4473	−	18.4473i	0.808190	−	0.808190i	−0.176170	−	0.984360i	$-0.556371\pi$
$521$	18.4473	−	18.4473i	0.808190	−	0.808190i	0.984360	+	0.176170i	$0.0563707\pi$
$522$	12.7023	+	12.7023i	0.555965	+	0.555965i
$523$	−32.5055			−1.42136			−0.710682	−	0.703513i	$-0.751614\pi$
$523$	−32.5055			−1.42136			−0.710682	+	0.703513i	$0.751614\pi$
$524$	5.07554	+	5.07554i	0.221726	+	0.221726i
$525$		0			0
$526$	4.45393			0.194200
$527$	0.120275	+	3.02459i	0.00523925	+	0.131753i
$528$	−5.46722			−0.237930
$529$		−	42.5591i		−	1.85039i
$530$		0			0
$531$	19.0862			0.828272
$532$	−3.72534	−	3.72534i	−0.161514	−	0.161514i
$533$	−16.5532	+	16.5532i	−0.716997	+	0.716997i
$534$	11.6441	−	11.6441i	0.503890	−	0.503890i
$535$		0			0
$536$			4.50547i			0.194607i
$537$	13.0501	−	13.0501i	0.563152	−	0.563152i
$538$	−5.77628	+	5.77628i	−0.249033	+	0.249033i
$539$	4.32797	+	4.32797i	0.186419	+	0.186419i
$540$		0			0
$541$	13.8216	+	13.8216i	0.594238	+	0.594238i	0.938773	−	0.344535i	$-0.111964\pi$
$541$	13.8216	+	13.8216i	0.594238	+	0.594238i	−0.344535	+	0.938773i	$0.611964\pi$
$542$		−	15.0382i		−	0.645948i
$543$	12.2199			0.524405
$544$	−2.79733	+	3.02902i	−0.119935	+	0.129868i
$545$		0			0
$546$		−	14.3287i		−	0.613213i
$547$	−31.9670	−	31.9670i	−1.36681	−	1.36681i	−0.864946	−	0.501864i	$-0.832648\pi$
$547$	−31.9670	−	31.9670i	−1.36681	−	1.36681i	−0.501864	−	0.864946i	$-0.667352\pi$
$548$	−0.958507			−0.0409454
$549$	−15.1608	−	15.1608i	−0.647048	−	0.647048i
$550$		0			0
$551$	−14.8249	+	14.8249i	−0.631561	+	0.631561i
$552$			8.59730i			0.365926i
$553$			24.1329i			1.02624i
$554$	−6.81453	+	6.81453i	−0.289522	+	0.289522i
$555$		0			0
$556$	−2.02547	−	2.02547i	−0.0858991	−	0.0858991i
$557$	20.6407			0.874576			0.437288	−	0.899322i	$-0.355939\pi$
$557$	20.6407			0.874576			0.437288	+	0.899322i	$0.355939\pi$
$558$	0.972092	+	0.972092i	0.0411520	+	0.0411520i
$559$		−	28.0077i		−	1.18460i
$560$		0			0
$561$	16.5603	+	15.2936i	0.699177	+	0.645697i
$562$	−23.0486			−0.972246
$563$		−	10.5985i		−	0.446674i	−0.974741	−	0.223337i	$-0.928305\pi$
$563$		−	10.5985i		−	0.446674i	0.974741	−	0.223337i	$-0.0716950\pi$
$564$	0.779528	+	0.779528i	0.0328240	+	0.0328240i
$565$		0			0
$566$	10.2038	+	10.2038i	0.428897	+	0.428897i
$567$	0.211693	−	0.211693i	0.00889028	−	0.00889028i
$568$	−0.422841	+	0.422841i	−0.0177420	+	0.0177420i
$569$			36.9671i			1.54974i	0.632120	+	0.774871i	$0.282185\pi$
$569$			36.9671i			1.54974i	−0.632120	+	0.774871i	$0.717815\pi$
$570$		0			0
$571$	−25.3822	+	25.3822i	−1.06221	+	1.06221i	−0.0642819	+	0.997932i	$0.520476\pi$
$571$	−25.3822	+	25.3822i	−1.06221	+	1.06221i	−0.997932	+	0.0642819i	$0.979524\pi$
$572$	−20.3813	+	20.3813i	−0.852184	+	0.852184i
$573$	8.36992	+	8.36992i	0.349658	+	0.349658i
$574$	−10.0811			−0.420776
$575$		0			0
$576$			1.87256i			0.0780235i
$577$	8.04210			0.334797			0.167398	−	0.985889i	$-0.446463\pi$
$577$	8.04210			0.334797			0.167398	+	0.985889i	$0.446463\pi$
$578$	16.9463	−	1.34989i	0.704874	−	0.0561482i
$579$	13.8100			0.573922
$580$		0			0
$581$	24.2915	+	24.2915i	1.00778	+	1.00778i
$582$	4.45809			0.184794
$583$	−29.8141	−	29.8141i	−1.23477	−	1.23477i
$584$	0.455406	−	0.455406i	0.0188448	−	0.0188448i
$585$		0			0
$586$		−	0.665388i		−	0.0274869i
$587$		−	17.6342i		−	0.727843i	−0.931430	−	0.363921i	$-0.881438\pi$
$587$		−	17.6342i		−	0.727843i	0.931430	−	0.363921i	$-0.118562\pi$
$588$	−0.892502	+	0.892502i	−0.0368062	+	0.0368062i
$589$	−1.13453	+	1.13453i	−0.0467475	+	0.0467475i
$590$		0			0
$591$	−15.1608			−0.623632
$592$	−5.87256	−	5.87256i	−0.241361	−	0.241361i
$593$		−	3.06055i		−	0.125682i	−0.998024	−	0.0628410i	$-0.979984\pi$
$593$		−	3.06055i		−	0.125682i	0.998024	−	0.0628410i	$-0.0200161\pi$
$594$	26.6394			1.09303
$595$		0			0
$596$	−13.4545			−0.551119
$597$		−	11.3469i		−	0.464397i
$598$	32.0499	+	32.0499i	1.31062	+	1.31062i
$599$	−25.7528			−1.05223			−0.526116	−	0.850413i	$-0.676352\pi$
$599$	−25.7528			−1.05223			−0.526116	+	0.850413i	$0.676352\pi$
$600$		0			0
$601$	11.3153	−	11.3153i	0.461560	−	0.461560i	−0.437607	−	0.899166i	$-0.644174\pi$
$601$	11.3153	−	11.3153i	0.461560	−	0.461560i	0.899166	+	0.437607i	$0.144174\pi$
$602$	8.52850	−	8.52850i	0.347596	−	0.347596i
$603$		−	8.43678i		−	0.343572i
$604$		−	9.40919i		−	0.382854i
$605$		0			0
$606$	−3.58852	+	3.58852i	−0.145774	+	0.145774i
$607$	4.08883	+	4.08883i	0.165961	+	0.165961i	0.785201	−	0.619241i	$-0.212559\pi$
$607$	4.08883	+	4.08883i	0.165961	+	0.165961i	−0.619241	+	0.785201i	$0.712559\pi$
$608$	−2.18547			−0.0886325
$609$	−17.3631	−	17.3631i	−0.703589	−	0.703589i
$610$		0			0
$611$	5.81201			0.235129
$612$	5.23818	−	5.67203i	0.211741	−	0.229278i
$613$	−35.5771			−1.43695			−0.718473	−	0.695555i	$-0.755158\pi$
$613$	−35.5771			−1.43695			−0.718473	+	0.695555i	$0.755158\pi$
$614$		−	23.4163i		−	0.945004i
$615$		0			0
$616$	−12.4124			−0.500111
$617$	8.18547	+	8.18547i	0.329535	+	0.329535i	0.852409	−	0.522875i	$-0.175140\pi$
$617$	8.18547	+	8.18547i	0.329535	+	0.329535i	−0.522875	+	0.852409i	$0.675140\pi$
$618$	1.25427	−	1.25427i	0.0504541	−	0.0504541i
$619$	15.5049	−	15.5049i	0.623193	−	0.623193i	−0.323153	−	0.946347i	$-0.604743\pi$
$619$	15.5049	−	15.5049i	0.623193	−	0.623193i	0.946347	+	0.323153i	$0.104743\pi$
$620$		0			0
$621$		−	41.8909i		−	1.68102i
$622$	4.67019	−	4.67019i	0.187258	−	0.187258i
$623$	26.4361	−	26.4361i	1.05914	−	1.05914i
$624$	−4.20297	−	4.20297i	−0.168254	−	0.168254i
$625$		0			0
$626$	−3.59730	−	3.59730i	−0.143777	−	0.143777i
$627$			11.9485i			0.477175i
$628$	−23.3845			−0.933144
$629$	1.36060	+	34.2156i	0.0542507	+	1.36427i
$630$		0			0
$631$			5.64325i			0.224654i	0.993671	+	0.112327i	$0.0358304\pi$
$631$			5.64325i			0.224654i	−0.993671	+	0.112327i	$0.964170\pi$
$632$	7.07878	+	7.07878i	0.281579	+	0.281579i
$633$	0.321628			0.0127836
$634$	−4.51816	−	4.51816i	−0.179439	−	0.179439i
$635$		0			0
$636$	6.14818	−	6.14818i	0.243791	−	0.243791i
$637$			6.65432i			0.263654i
$638$			49.3949i			1.95556i
$639$	0.791798	−	0.791798i	0.0313230	−	0.0313230i
$640$		0			0
$641$	−14.1155	−	14.1155i	−0.557527	−	0.557527i	0.371075	−	0.928603i	$-0.378989\pi$
$641$	−14.1155	−	14.1155i	−0.557527	−	0.557527i	−0.928603	+	0.371075i	$0.878989\pi$
$642$	5.07529			0.200306
$643$	17.1170	+	17.1170i	0.675030	+	0.675030i	0.958871	−	0.283841i	$-0.0916090\pi$
$643$	17.1170	+	17.1170i	0.675030	+	0.675030i	−0.283841	+	0.958871i	$0.591609\pi$
$644$			19.5188i			0.769147i
$645$		0			0
$646$	6.61983	+	6.11348i	0.260454	+	0.240532i
$647$	11.0109			0.432885			0.216442	−	0.976295i	$-0.430555\pi$
$647$	11.0109			0.432885			0.216442	+	0.976295i	$0.430555\pi$
$648$		−	0.124190i		−	0.00487864i
$649$	37.1099	+	37.1099i	1.45669	+	1.45669i
$650$		0			0
$651$	−1.32878	−	1.32878i	−0.0520790	−	0.0520790i
$652$	5.74757	−	5.74757i	0.225092	−	0.225092i
$653$	22.4011	−	22.4011i	0.876622	−	0.876622i	−0.116562	−	0.993183i	$-0.537187\pi$
$653$	22.4011	−	22.4011i	0.876622	−	0.876622i	0.993183	+	0.116562i	$0.0371873\pi$
$654$			12.4312i			0.486098i
$655$		0			0
$656$	−2.95703	+	2.95703i	−0.115453	+	0.115453i
$657$	−0.852777	+	0.852777i	−0.0332700	+	0.0332700i
$658$	1.76979	+	1.76979i	0.0689936	+	0.0689936i
$659$	−28.6601			−1.11644			−0.558219	−	0.829694i	$-0.688515\pi$
$659$	−28.6601			−1.11644			−0.558219	+	0.829694i	$0.688515\pi$
$660$		0			0
$661$		−	9.15239i		−	0.355987i	−0.984032	−	0.177993i	$-0.943039\pi$
$661$		−	9.15239i		−	0.355987i	0.984032	−	0.177993i	$-0.0569605\pi$
$662$	23.0340			0.895241
$663$	0.973777	+	24.4880i	0.0378184	+	0.951034i
$664$	14.2506			0.553031
$665$		0			0
$666$	10.9968	+	10.9968i	0.426116	+	0.426116i
$667$	77.6743			3.00756
$668$	−12.1887	−	12.1887i	−0.471596	−	0.471596i
$669$	−10.8210	+	10.8210i	−0.418365	+	0.418365i
$670$		0			0
$671$		−	58.9551i		−	2.27594i
$672$		−	2.55966i		−	0.0987409i
$673$	−14.2704	+	14.2704i	−0.550083	+	0.550083i	−0.926465	−	0.376382i	$-0.877168\pi$
$673$	−14.2704	+	14.2704i	−0.550083	+	0.550083i	0.376382	+	0.926465i	$0.377168\pi$
$674$	1.64412	−	1.64412i	0.0633292	−	0.0633292i
$675$		0			0
$676$	−18.3365			−0.705252
$677$	15.7801	+	15.7801i	0.606480	+	0.606480i	0.942024	−	0.335545i	$-0.108920\pi$
$677$	15.7801	+	15.7801i	0.606480	+	0.606480i	−0.335545	+	0.942024i	$0.608920\pi$
$678$		−	5.19359i		−	0.199459i
$679$	10.1214			0.388422
$680$		0			0
$681$	−24.0975			−0.923418
$682$			3.78013i			0.144749i
$683$	16.9407	+	16.9407i	0.648219	+	0.648219i	0.952562	−	0.304343i	$-0.0984370\pi$
$683$	16.9407	+	16.9407i	0.648219	+	0.648219i	−0.304343	+	0.952562i	$0.598437\pi$
$684$	4.09243			0.156478
$685$		0			0
$686$	−13.9584	+	13.9584i	−0.532936	+	0.532936i
$687$	−16.6965	+	16.6965i	−0.637010	+	0.637010i
$688$		−	5.00325i		−	0.190747i
$689$		−	45.8397i		−	1.74635i
$690$		0			0
$691$	27.8995	−	27.8995i	1.06135	−	1.06135i	0.0633572	−	0.997991i	$-0.479819\pi$
$691$	27.8995	−	27.8995i	1.06135	−	1.06135i	0.997991	−	0.0633572i	$-0.0201807\pi$
$692$	−2.55966	−	2.55966i	−0.0973036	−	0.0973036i
$693$	23.2431			0.882932
$694$	11.8159	+	11.8159i	0.448527	+	0.448527i
$695$		0			0
$696$	−10.1861			−0.386102
$697$	17.2287	−	0.685108i	0.652583	−	0.0259503i
$698$	28.0038			1.05996
$699$			14.0774i			0.532456i
$700$		0			0
$701$	−2.44094			−0.0921932			−0.0460966	−	0.998937i	$-0.514678\pi$
$701$	−2.44094			−0.0921932			−0.0460966	+	0.998937i	$0.514678\pi$
$702$	20.4792	+	20.4792i	0.772939	+	0.772939i
$703$	−12.8343	+	12.8343i	−0.484055	+	0.484055i
$704$	−3.64088	+	3.64088i	−0.137221	+	0.137221i
$705$		0			0
$706$		−	4.60115i		−	0.173167i
$707$	−8.14716	+	8.14716i	−0.306405	+	0.306405i
$708$	−7.65269	+	7.65269i	−0.287606	+	0.287606i
$709$	−12.4163	−	12.4163i	−0.466303	−	0.466303i	0.434411	−	0.900715i	$-0.356956\pi$
$709$	−12.4163	−	12.4163i	−0.466303	−	0.466303i	−0.900715	+	0.434411i	$0.856956\pi$
$710$		0			0
$711$	−13.2555	−	13.2555i	−0.497119	−	0.497119i
$712$		−	15.5087i		−	0.581214i
$713$	5.94432			0.222617
$714$	−7.16021	+	7.75325i	−0.267964	+	0.290158i
$715$		0			0
$716$		−	17.3813i		−	0.649569i
$717$	−14.2679	−	14.2679i	−0.532843	−	0.532843i
$718$	−35.9027			−1.33988
$719$	13.6799	+	13.6799i	0.510175	+	0.510175i	0.914580	−	0.404405i	$-0.132521\pi$
$719$	13.6799	+	13.6799i	0.510175	+	0.510175i	−0.404405	+	0.914580i	$0.632521\pi$
$720$		0			0
$721$	2.84761	−	2.84761i	0.106051	−	0.106051i
$722$		−	14.2237i		−	0.529352i
$723$		−	21.6072i		−	0.803581i
$724$	8.13778	−	8.13778i	0.302438	−	0.302438i
$725$		0			0
$726$	11.6466	+	11.6466i	0.432244	+	0.432244i
$727$	8.40594			0.311759			0.155880	−	0.987776i	$-0.450179\pi$
$727$	8.40594			0.311759			0.155880	+	0.987776i	$0.450179\pi$
$728$	−9.54216	−	9.54216i	−0.353656	−	0.353656i
$729$		−	16.2480i		−	0.601776i
$730$		0			0
$731$	−13.9957	+	15.1549i	−0.517651	+	0.560525i
$732$	12.1576			0.449356
$733$		−	12.2218i		−	0.451422i	−0.974194	−	0.225711i	$-0.927529\pi$
$733$		−	12.2218i		−	0.451422i	0.974194	−	0.225711i	$-0.0724706\pi$
$734$	5.97925	+	5.97925i	0.220698	+	0.220698i
$735$		0			0
$736$	5.72534	+	5.72534i	0.211039	+	0.211039i
$737$	16.4039	−	16.4039i	0.604244	−	0.604244i
$738$	5.53723	−	5.53723i	0.203828	−	0.203828i
$739$		−	35.1750i		−	1.29393i	−0.762518	−	0.646967i	$-0.776037\pi$
$739$		−	35.1750i		−	1.29393i	0.762518	−	0.646967i	$-0.223963\pi$
$740$		0			0
$741$	−9.18547	+	9.18547i	−0.337437	+	0.337437i
$742$	13.9584	−	13.9584i	0.512430	−	0.512430i
$743$	−5.15143	−	5.15143i	−0.188988	−	0.188988i	0.606271	−	0.795258i	$-0.292665\pi$
$743$	−5.15143	−	5.15143i	−0.188988	−	0.188988i	−0.795258	+	0.606271i	$0.792665\pi$
$744$	−0.779528			−0.0285789
$745$		0			0
$746$		−	28.0453i		−	1.02681i
$747$	−26.6852			−0.976359
$748$	21.2130	−	0.843547i	0.775624	−	0.0308431i
$749$	11.5226			0.421027
$750$		0			0
$751$	−8.36709	−	8.36709i	−0.305320	−	0.305320i	0.537771	−	0.843091i	$-0.319266\pi$
$751$	−8.36709	−	8.36709i	−0.305320	−	0.305320i	−0.843091	+	0.537771i	$0.819266\pi$
$752$	1.03825			0.0378610
$753$	4.26994	+	4.26994i	0.155605	+	0.155605i
$754$	−37.9727	+	37.9727i	−1.38288	+	1.38288i
$755$		0			0
$756$			12.4721i			0.453606i
$757$			32.5000i			1.18123i	0.806953	+	0.590616i	$0.201115\pi$
$757$			32.5000i			1.18123i	−0.806953	+	0.590616i	$0.798885\pi$
$758$	2.34932	−	2.34932i	0.0853311	−	0.0853311i
$759$	31.3017	−	31.3017i	1.13618	−	1.13618i
$760$		0			0
$761$	−36.1685			−1.31111			−0.655554	−	0.755149i	$-0.727565\pi$
$761$	−36.1685			−1.31111			−0.655554	+	0.755149i	$0.727565\pi$
$762$	−10.3200	−	10.3200i	−0.373854	−	0.373854i
$763$			28.2230i			1.02174i
$764$	11.1478			0.403314
$765$		0			0
$766$	−16.2671			−0.587756
$767$			57.0570i			2.06021i
$768$	−0.750811	−	0.750811i	−0.0270926	−	0.0270926i
$769$	29.4343			1.06143			0.530714	−	0.847551i	$-0.321924\pi$
$769$	29.4343			1.06143			0.530714	+	0.847551i	$0.321924\pi$
$770$		0			0
$771$	−13.9455	+	13.9455i	−0.502233	+	0.502233i
$772$	9.19669	−	9.19669i	0.330996	−	0.330996i
$773$			15.1647i			0.545435i	0.962094	+	0.272717i	$0.0879224\pi$
$773$			15.1647i			0.545435i	−0.962094	+	0.272717i	$0.912078\pi$
$774$			9.36890i			0.336758i
$775$		0			0
$776$	2.96885	−	2.96885i	0.106575	−	0.106575i
$777$	−15.0318	−	15.0318i	−0.539261	−	0.539261i
$778$	16.0842			0.576646
$779$	6.46250	+	6.46250i	0.231543	+	0.231543i
$780$		0			0
$781$	3.07903			0.110176
$782$	−1.32649	−	33.3578i	−0.0474353	−	1.19287i
$783$	49.6323			1.77371
$784$			1.18872i			0.0424542i
$785$		0			0
$786$	7.62154			0.271851
$787$	−2.96981	−	2.96981i	−0.105862	−	0.105862i	0.652192	−	0.758054i	$-0.273850\pi$
$787$	−2.96981	−	2.96981i	−0.105862	−	0.105862i	−0.758054	+	0.652192i	$0.773850\pi$
$788$	−10.0963	+	10.0963i	−0.359665	+	0.359665i
$789$	3.34406	−	3.34406i	0.119052	−	0.119052i
$790$		0			0
$791$		−	11.7912i		−	0.419247i
$792$	6.81778	−	6.81778i	0.242259	−	0.242259i
$793$	45.3222	−	45.3222i	1.60944	−	1.60944i
$794$	−1.17513	−	1.17513i	−0.0417038	−	0.0417038i
$795$		0			0
$796$	−7.55641	−	7.55641i	−0.267830	−	0.267830i
$797$		−	6.15563i		−	0.218044i	−0.994039	−	0.109022i	$-0.965228\pi$
$797$		−	6.15563i		−	0.218044i	0.994039	−	0.109022i	$-0.0347718\pi$
$798$	−5.59406			−0.198027
$799$	−3.14487	−	2.90432i	−0.111257	−	0.102747i
$800$		0			0
$801$			29.0411i			1.02612i
$802$	6.92263	+	6.92263i	0.244447	+	0.244447i
$803$	−3.31615			−0.117024
$804$	3.38276	+	3.38276i	0.119301	+	0.119301i
$805$		0			0
$806$	−2.90600	+	2.90600i	−0.102360	+	0.102360i
$807$			8.67380i			0.305332i
$808$			4.77953i			0.168143i
$809$	15.1641	−	15.1641i	0.533140	−	0.533140i	−0.388366	−	0.921505i	$-0.626960\pi$
$809$	15.1641	−	15.1641i	0.533140	−	0.533140i	0.921505	+	0.388366i	$0.126960\pi$
$810$		0			0
$811$	−29.5729	−	29.5729i	−1.03844	−	1.03844i	−0.999231	−	0.0392136i	$-0.987515\pi$
$811$	−29.5729	−	29.5729i	−1.03844	−	1.03844i	−0.0392136	−	0.999231i	$-0.512485\pi$
$812$	−23.1258			−0.811557
$813$	−11.2909	−	11.2909i	−0.395989	−	0.395989i
$814$			42.7626i			1.49883i
$815$		0			0
$816$	0.173954	+	4.37449i	0.00608960	+	0.153138i
$817$	−10.9344			−0.382548
$818$		−	23.0236i		−	0.805003i
$819$	17.8683	+	17.8683i	0.624369	+	0.624369i
$820$		0			0
$821$	12.5852	+	12.5852i	0.439227	+	0.439227i	0.891752	−	0.452525i	$-0.149477\pi$
$821$	12.5852	+	12.5852i	0.439227	+	0.439227i	−0.452525	+	0.891752i	$0.649477\pi$
$822$	−0.719658	+	0.719658i	−0.0251010	+	0.0251010i
$823$	−3.05635	+	3.05635i	−0.106538	+	0.106538i	−0.758366	−	0.651829i	$-0.774002\pi$
$823$	−3.05635	+	3.05635i	−0.106538	+	0.106538i	0.651829	+	0.758366i	$0.274002\pi$
$824$		−	1.67055i		−	0.0581964i
$825$		0			0
$826$	−17.3742	+	17.3742i	−0.604525	+	0.604525i
$827$	6.05271	−	6.05271i	0.210473	−	0.210473i	−0.593995	−	0.804469i	$-0.702450\pi$
$827$	6.05271	−	6.05271i	0.210473	−	0.210473i	0.804469	+	0.593995i	$0.202450\pi$
$828$	−10.7211	−	10.7211i	−0.372583	−	0.372583i
$829$	22.3190			0.775170			0.387585	−	0.921834i	$-0.373309\pi$
$829$	22.3190			0.775170			0.387585	+	0.921834i	$0.373309\pi$
$830$		0			0
$831$			10.2329i			0.354974i
$832$	−5.59791			−0.194072
$833$	3.32523	−	3.60064i	0.115212	−	0.124755i
$834$	−3.04149			−0.105318
$835$		0			0
$836$	7.95703	+	7.95703i	0.275200	+	0.275200i
$837$	3.79830			0.131288
$838$	13.5128	+	13.5128i	0.466793	+	0.466793i
$839$	22.6193	−	22.6193i	0.780903	−	0.780903i	−0.199080	−	0.979983i	$-0.563795\pi$
$839$	22.6193	−	22.6193i	0.780903	−	0.780903i	0.979983	+	0.199080i	$0.0637953\pi$
$840$		0			0
$841$			63.0284i			2.17339i
$842$		−	12.4163i		−	0.427893i
$843$	−17.3051	+	17.3051i	−0.596021	+	0.596021i
$844$	0.214187	−	0.214187i	0.00737263	−	0.00737263i
$845$		0			0
$846$	−1.94418			−0.0668424
$847$	26.4416	+	26.4416i	0.908544	+	0.908544i
$848$		−	8.18872i		−	0.281202i
$849$	15.3222			0.525858
$850$		0			0
$851$	67.2449			2.30512
$852$			0.634948i			0.0217530i
$853$	−10.9497	−	10.9497i	−0.374909	−	0.374909i	0.494352	−	0.869262i	$-0.335405\pi$
$853$	−10.9497	−	10.9497i	−0.374909	−	0.374909i	−0.869262	+	0.494352i	$0.835405\pi$
$854$	27.6018			0.944513
$855$		0			0
$856$	3.37987	−	3.37987i	0.115522	−	0.115522i
$857$	−31.9220	+	31.9220i	−1.09044	+	1.09044i	−0.0949540	+	0.995482i	$0.530270\pi$
$857$	−31.9220	+	31.9220i	−1.09044	+	1.09044i	−0.995482	+	0.0949540i	$0.969730\pi$
$858$			30.6050i			1.04484i
$859$			5.68252i			0.193885i	0.995290	+	0.0969425i	$0.0309063\pi$
$859$			5.68252i			0.193885i	−0.995290	+	0.0969425i	$0.969094\pi$
$860$		0			0
$861$	−7.56898	+	7.56898i	−0.257950	+	0.257950i
$862$	4.73899	+	4.73899i	0.161411	+	0.161411i
$863$	−28.9474			−0.985382			−0.492691	−	0.870204i	$-0.663987\pi$
$863$	−28.9474			−0.985382			−0.492691	+	0.870204i	$0.663987\pi$
$864$	3.65838	+	3.65838i	0.124461	+	0.124461i
$865$		0			0
$866$	−17.9721			−0.610717
$867$	11.7100	−	13.7370i	0.397692	−	0.466533i
$868$	−1.76979			−0.0600706
$869$		−	51.5459i		−	1.74858i
$870$		0			0
$871$	25.2212			0.854588
$872$	8.27851	+	8.27851i	0.280346	+	0.280346i
$873$	−5.55936	+	5.55936i	−0.188156	+	0.188156i
$874$	12.5126	−	12.5126i	0.423244	−	0.423244i
$875$		0			0
$876$		−	0.683848i		−	0.0231051i
$877$	4.77688	−	4.77688i	0.161304	−	0.161304i	−0.621840	−	0.783144i	$-0.713615\pi$
$877$	4.77688	−	4.77688i	0.161304	−	0.161304i	0.783144	+	0.621840i	$0.213615\pi$
$878$	−11.3158	+	11.3158i	−0.381890	+	0.381890i
$879$	−0.499581	−	0.499581i	−0.0168505	−	0.0168505i
$880$		0			0
$881$	−19.6115	−	19.6115i	−0.660728	−	0.660728i	0.294824	−	0.955552i	$-0.404739\pi$
$881$	−19.6115	−	19.6115i	−0.660728	−	0.660728i	−0.955552	+	0.294824i	$0.904739\pi$
$882$		−	2.22595i		−	0.0749516i
$883$	43.4891			1.46352			0.731762	−	0.681560i	$-0.238698\pi$
$883$	43.4891			1.46352			0.731762	+	0.681560i	$0.238698\pi$
$884$	16.9562	+	15.6592i	0.570297	+	0.526675i
$885$		0			0
$886$			2.55346i			0.0857850i
$887$	29.0797	+	29.0797i	0.976400	+	0.976400i	0.999728	−	0.0233280i	$-0.00742621\pi$
$887$	29.0797	+	29.0797i	0.976400	+	0.976400i	−0.0233280	+	0.999728i	$0.507426\pi$
$888$	−8.81838			−0.295925
$889$	−23.4299	−	23.4299i	−0.785813	−	0.785813i
$890$		0			0
$891$	−0.452160	+	0.452160i	−0.0151479	+	0.0151479i
$892$			14.4124i			0.482564i
$893$		−	2.26906i		−	0.0759312i
$894$	−10.1018	+	10.1018i	−0.337855	+	0.337855i
$895$		0			0
$896$	−1.70459	−	1.70459i	−0.0569465	−	0.0569465i
$897$	48.1269			1.60691
$898$	−12.5549	−	12.5549i	−0.418964	−	0.418964i
$899$			7.04282i			0.234891i
$900$		0			0
$901$	−22.9065	+	24.8038i	−0.763127	+	0.826333i
$902$	21.5324			0.716949
$903$		−	12.8066i		−	0.426177i
$904$	−3.45865	−	3.45865i	−0.115033	−	0.115033i
$905$		0			0
$906$	−7.06453	−	7.06453i	−0.234703	−	0.234703i
$907$	15.8823	−	15.8823i	0.527363	−	0.527363i	−0.392422	−	0.919785i	$-0.628363\pi$
$907$	15.8823	−	15.8823i	0.527363	−	0.527363i	0.919785	+	0.392422i	$0.128363\pi$
$908$	−16.0476	+	16.0476i	−0.532559	+	0.532559i
$909$		−	8.94997i		−	0.296852i
$910$		0			0
$911$	19.2139	−	19.2139i	0.636585	−	0.636585i	−0.313126	−	0.949712i	$-0.601376\pi$
$911$	19.2139	−	19.2139i	0.636585	−	0.636585i	0.949712	+	0.313126i	$0.101376\pi$
$912$	−1.64088	+	1.64088i	−0.0543348	+	0.0543348i
$913$	−51.8847	−	51.8847i	−1.71713	−	1.71713i
$914$	26.2450			0.868107
$915$		0			0
$916$			22.2379i			0.734761i
$917$	17.3035			0.571411
$918$	−0.847602	−	21.3150i	−0.0279750	−	0.703499i
$919$	−25.8488			−0.852673			−0.426337	−	0.904565i	$-0.640196\pi$
$919$	−25.8488			−0.852673			−0.426337	+	0.904565i	$0.640196\pi$
$920$		0			0
$921$	−17.5812	−	17.5812i	−0.579321	−	0.579321i
$922$	−16.9344			−0.557706
$923$	2.36703	+	2.36703i	0.0779116	+	0.0779116i
$924$	−9.31940	+	9.31940i	−0.306586	+	0.306586i
$925$		0			0
$926$		−	14.4539i		−	0.474986i
$927$			3.12822i			0.102744i
$928$	−6.78338	+	6.78338i	−0.222675	+	0.222675i
$929$	−17.5247	+	17.5247i	−0.574965	+	0.574965i	−0.933512	−	0.358547i	$-0.883272\pi$
$929$	−17.5247	+	17.5247i	−0.574965	+	0.574965i	0.358547	+	0.933512i	$0.383272\pi$
$930$		0			0
$931$	2.59791			0.0851429
$932$	9.37479	+	9.37479i	0.307081	+	0.307081i
$933$		−	7.01287i		−	0.229591i
$934$	−16.7911			−0.549421
$935$		0			0
$936$	10.4824			0.342629
$937$			27.6096i			0.901965i	0.892533	+	0.450983i	$0.148926\pi$
$937$			27.6096i			0.901965i	−0.892533	+	0.450983i	$0.851074\pi$
$938$	7.68000	+	7.68000i	0.250761	+	0.250761i
$939$	−5.40179			−0.176281
$940$		0			0
$941$	−41.1297	+	41.1297i	−1.34079	+	1.34079i	−0.445513	+	0.895275i	$0.646979\pi$
$941$	−41.1297	+	41.1297i	−1.34079	+	1.34079i	−0.895275	+	0.445513i	$0.853021\pi$
$942$	−17.5574	+	17.5574i	−0.572050	+	0.572050i
$943$		−	33.8600i		−	1.10263i
$944$			10.1926i			0.331740i
$945$		0			0
$946$	−18.2162	+	18.2162i	−0.592260	+	0.592260i
$947$	−23.6351	−	23.6351i	−0.768038	−	0.768038i	0.209723	−	0.977761i	$-0.432744\pi$
$947$	−23.6351	−	23.6351i	−0.768038	−	0.768038i	−0.977761	+	0.209723i	$0.932744\pi$
$948$	10.6297			0.345235
$949$	−2.54932	−	2.54932i	−0.0827544	−	0.0827544i
$950$		0			0
$951$	−6.78458			−0.220005
$952$	0.394934	+	9.93156i	0.0127999	+	0.321884i
$953$	58.7914			1.90444			0.952219	−	0.305415i	$-0.0987950\pi$
$953$	58.7914			1.90444			0.952219	+	0.305415i	$0.0987950\pi$
$954$			15.3339i			0.496453i
$955$		0			0
$956$	−19.0032			−0.614609
$957$	37.0862	+	37.0862i	1.19883	+	1.19883i
$958$	27.6215	−	27.6215i	0.892411	−	0.892411i
$959$	−1.63387	+	1.63387i	−0.0527603	+	0.0527603i
$960$		0			0
$961$		−	30.4610i		−	0.982614i
$962$	−32.8741	+	32.8741i	−1.05990	+	1.05990i
$963$	−6.32902	+	6.32902i	−0.203950	+	0.203950i
$964$	−14.3893	−	14.3893i	−0.463447	−	0.463447i
$965$		0			0
$966$	14.6549	+	14.6549i	0.471514	+	0.471514i
$967$			9.59863i			0.308671i	0.988018	+	0.154336i	$0.0493237\pi$
$967$			9.59863i			0.308671i	−0.988018	+	0.154336i	$0.950676\pi$
$968$	15.5120			0.498573
$969$	9.56032	−	0.380171i	0.307122	−	0.0122129i
$970$		0			0
$971$		−	45.7025i		−	1.46666i	−0.679871	−	0.733331i	$-0.737964\pi$
$971$		−	45.7025i		−	1.46666i	0.679871	−	0.733331i	$-0.262036\pi$
$972$	−11.0684	−	11.0684i	−0.355018	−	0.355018i
$973$	−6.90521			−0.221371
$974$	−6.76359	−	6.76359i	−0.216719	−	0.216719i
$975$		0			0
$976$	8.09628	−	8.09628i	0.259156	−	0.259156i
$977$		−	16.9270i		−	0.541544i	−0.962644	−	0.270772i	$-0.912721\pi$
$977$		−	16.9270i		−	0.541544i	0.962644	−	0.270772i	$-0.0872789\pi$
$978$		−	8.63068i		−	0.275979i
$979$	−56.4653	+	56.4653i	−1.80464	+	1.80464i
$980$		0			0
$981$	−15.5020	−	15.5020i	−0.494942	−	0.494942i
$982$	31.5603			1.00713
$983$	22.3842	+	22.3842i	0.713944	+	0.713944i	0.967358	−	0.253414i	$-0.0815534\pi$
$983$	22.3842	+	22.3842i	0.713944	+	0.713944i	−0.253414	+	0.967358i	$0.581553\pi$
$984$			4.44034i			0.141553i
$985$		0			0
$986$	39.5223	−	1.57163i	1.25865	−	0.0500508i
$987$	2.65756			0.0845910
$988$			12.2341i			0.389217i
$989$	28.6453	+	28.6453i	0.910867	+	0.910867i
$990$		0			0
$991$	27.9140	+	27.9140i	0.886717	+	0.886717i	0.994206	−	0.107489i	$-0.0342811\pi$
$991$	27.9140	+	27.9140i	0.886717	+	0.886717i	−0.107489	+	0.994206i	$0.534281\pi$
$992$	−0.519124	+	0.519124i	−0.0164822	+	0.0164822i
$993$	17.2942	−	17.2942i	0.548814	−	0.548814i
$994$			1.44155i			0.0457231i
$995$		0			0
$996$	10.6995	−	10.6995i	0.339027	−	0.339027i
$997$	−20.9759	+	20.9759i	−0.664315	+	0.664315i	−0.956394	−	0.292079i	$-0.905653\pi$
$997$	−20.9759	+	20.9759i	−0.664315	+	0.664315i	0.292079	+	0.956394i	$0.405653\pi$
$998$	24.4121	+	24.4121i	0.772751	+	0.772751i
$999$	42.9681			1.35945

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	850.2.h.l.251.2	✓	8
5.2	odd	4		850.2.g.k.149.2		8
5.3	odd	4		850.2.g.j.149.3		8
5.4	even	2		850.2.h.m.251.3	yes	8
17.4	even	4	inner	850.2.h.l.701.2	yes	8
85.4	even	4		850.2.h.m.701.3	yes	8
85.38	odd	4		850.2.g.k.599.2		8
85.72	odd	4		850.2.g.j.599.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
850.2.g.j.149.3		8	5.3	odd	4
850.2.g.j.599.3		8	85.72	odd	4
850.2.g.k.149.2		8	5.2	odd	4
850.2.g.k.599.2		8	85.38	odd	4
850.2.h.l.251.2	✓	8	1.1	even	1	trivial
850.2.h.l.701.2	yes	8	17.4	even	4	inner
850.2.h.m.251.3	yes	8	5.4	even	2
850.2.h.m.701.3	yes	8	85.4	even	4

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:	\( N \)	\(=\)	\( 850 = 2 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	850.h (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.750811 - 0.750811i) q^{3} -1.00000 q^{4} +(-0.750811 + 0.750811i) q^{6} +(-1.70459 + 1.70459i) q^{7} +1.00000i q^{8} -1.87256i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.750811 - 0.750811i) q^{3} -1.00000 q^{4} +(-0.750811 + 0.750811i) q^{6} +(-1.70459 + 1.70459i) q^{7} +1.00000i q^{8} -1.87256i q^{9} +(3.64088 - 3.64088i) q^{11} +(0.750811 + 0.750811i) q^{12} +5.59791 q^{13} +(1.70459 + 1.70459i) q^{14} +1.00000 q^{16} +(-3.02902 - 2.79733i) q^{17} -1.87256 q^{18} -2.18547i q^{19} +2.55966 q^{21} +(-3.64088 - 3.64088i) q^{22} +(-5.72534 + 5.72534i) q^{23} +(0.750811 - 0.750811i) q^{24} -5.59791i q^{26} +(-3.65838 + 3.65838i) q^{27} +(1.70459 - 1.70459i) q^{28} +(-6.78338 - 6.78338i) q^{29} +(-0.519124 - 0.519124i) q^{31} -1.00000i q^{32} -5.46722 q^{33} +(-2.79733 + 3.02902i) q^{34} +1.87256i q^{36} +(-5.87256 - 5.87256i) q^{37} -2.18547 q^{38} +(-4.20297 - 4.20297i) q^{39} +(-2.95703 + 2.95703i) q^{41} -2.55966i q^{42} -5.00325i q^{43} +(-3.64088 + 3.64088i) q^{44} +(5.72534 + 5.72534i) q^{46} +1.03825 q^{47} +(-0.750811 - 0.750811i) q^{48} +1.18872i q^{49} +(0.173954 + 4.37449i) q^{51} -5.59791 q^{52} -8.18872i q^{53} +(3.65838 + 3.65838i) q^{54} +(-1.70459 - 1.70459i) q^{56} +(-1.64088 + 1.64088i) q^{57} +(-6.78338 + 6.78338i) q^{58} +10.1926i q^{59} +(8.09628 - 8.09628i) q^{61} +(-0.519124 + 0.519124i) q^{62} +(3.19196 + 3.19196i) q^{63} -1.00000 q^{64} +5.46722i q^{66} +4.50547 q^{67} +(3.02902 + 2.79733i) q^{68} +8.59730 q^{69} +(0.422841 + 0.422841i) q^{71} +1.87256 q^{72} +(-0.455406 - 0.455406i) q^{73} +(-5.87256 + 5.87256i) q^{74} +2.18547i q^{76} +12.4124i q^{77} +(-4.20297 + 4.20297i) q^{78} +(7.07878 - 7.07878i) q^{79} -0.124190 q^{81} +(2.95703 + 2.95703i) q^{82} -14.2506i q^{83} -2.55966 q^{84} -5.00325 q^{86} +10.1861i q^{87} +(3.64088 + 3.64088i) q^{88} -15.5087 q^{89} +(-9.54216 + 9.54216i) q^{91} +(5.72534 - 5.72534i) q^{92} +0.779528i q^{93} -1.03825i q^{94} +(-0.750811 + 0.750811i) q^{96} +(-2.96885 - 2.96885i) q^{97} +1.18872 q^{98} +(-6.81778 - 6.81778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 2 q^{7}+O(q^{10}) \) 8 * q - 8 * q^4 - 2 * q^7	\( 8 q - 8 q^{4} - 2 q^{7} + 2 q^{11} - 12 q^{13} + 2 q^{14} + 8 q^{16} - 4 q^{17} + 16 q^{18} - 32 q^{21} - 2 q^{22} - 20 q^{23} - 12 q^{27} + 2 q^{28} + 12 q^{29} - 2 q^{31} + 20 q^{33} - 6 q^{34} - 16 q^{37} - 8 q^{38} - 34 q^{39} + 6 q^{41} - 2 q^{44} + 20 q^{46} + 4 q^{47} + 22 q^{51} + 12 q^{52} + 12 q^{54} - 2 q^{56} + 14 q^{57} + 12 q^{58} + 20 q^{61} - 2 q^{62} - 32 q^{63} - 8 q^{64} - 32 q^{67} + 4 q^{68} + 44 q^{69} + 46 q^{71} - 16 q^{72} + 14 q^{73} - 16 q^{74} - 34 q^{78} + 2 q^{79} - 56 q^{81} - 6 q^{82} + 32 q^{84} - 16 q^{86} + 2 q^{88} - 32 q^{89} - 14 q^{91} + 20 q^{92} + 52 q^{97} - 24 q^{98} - 40 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 2 * q^7 + 2 * q^11 - 12 * q^13 + 2 * q^14 + 8 * q^16 - 4 * q^17 + 16 * q^18 - 32 * q^21 - 2 * q^22 - 20 * q^23 - 12 * q^27 + 2 * q^28 + 12 * q^29 - 2 * q^31 + 20 * q^33 - 6 * q^34 - 16 * q^37 - 8 * q^38 - 34 * q^39 + 6 * q^41 - 2 * q^44 + 20 * q^46 + 4 * q^47 + 22 * q^51 + 12 * q^52 + 12 * q^54 - 2 * q^56 + 14 * q^57 + 12 * q^58 + 20 * q^61 - 2 * q^62 - 32 * q^63 - 8 * q^64 - 32 * q^67 + 4 * q^68 + 44 * q^69 + 46 * q^71 - 16 * q^72 + 14 * q^73 - 16 * q^74 - 34 * q^78 + 2 * q^79 - 56 * q^81 - 6 * q^82 + 32 * q^84 - 16 * q^86 + 2 * q^88 - 32 * q^89 - 14 * q^91 + 20 * q^92 + 52 * q^97 - 24 * q^98 - 40 * q^99

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