LMFDB - Embedded newform 1170.2.o.b.287.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(53,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("1170.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.o (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:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 107x^{8} + 240x^{6} + 151x^{4} + 30x^{2} + 1 $ x^12 + 18x^10 + 107x^8 + 240x^6 + 151x^4 + 30*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			287.2
Root			$0.699479i$ of defining polynomial
Character	$\chi$	$=$	1170.287
Dual form			1170.2.o.b.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.28075 - 1.83294i) q^{5} +(-0.213858 - 0.213858i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.28075 - 1.83294i) q^{5} +(-0.213858 - 0.213858i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.20171 + 0.390462i) q^{10} +6.42524i q^{11} +(0.707107 - 0.707107i) q^{13} +0.302441 q^{14} -1.00000 q^{16} +(1.21578 - 1.21578i) q^{17} -5.22447i q^{19} +(-1.83294 + 1.28075i) q^{20} +(-4.54333 - 4.54333i) q^{22} +(2.51630 + 2.51630i) q^{23} +(-1.71937 + 4.69508i) q^{25} +1.00000i q^{26} +(-0.213858 + 0.213858i) q^{28} -9.43932 q^{29} +6.53992 q^{31} +(0.707107 - 0.707107i) q^{32} +1.71937i q^{34} +(-0.118092 + 0.665889i) q^{35} +(7.51904 + 7.51904i) q^{37} +(3.69426 + 3.69426i) q^{38} +(0.390462 - 2.20171i) q^{40} -0.932674i q^{41} +(7.49448 - 7.49448i) q^{43} +6.42524 q^{44} -3.55858 q^{46} +(-0.844841 + 0.844841i) q^{47} -6.90853i q^{49} +(-2.10414 - 4.53570i) q^{50} +(-0.707107 - 0.707107i) q^{52} +(8.25019 + 8.25019i) q^{53} +(11.7771 - 8.22911i) q^{55} -0.302441i q^{56} +(6.67460 - 6.67460i) q^{58} +14.4793 q^{59} +6.33002 q^{61} +(-4.62442 + 4.62442i) q^{62} +1.00000i q^{64} +(-2.20171 - 0.390462i) q^{65} +(4.61673 + 4.61673i) q^{67} +(-1.21578 - 1.21578i) q^{68} +(-0.387351 - 0.554358i) q^{70} -11.5425i q^{71} +(-6.88465 + 6.88465i) q^{73} -10.6335 q^{74} -5.22447 q^{76} +(1.37409 - 1.37409i) q^{77} +0.724996i q^{79} +(1.28075 + 1.83294i) q^{80} +(0.659500 + 0.659500i) q^{82} +(3.81300 + 3.81300i) q^{83} +(-3.78556 - 0.671348i) q^{85} +10.5988i q^{86} +(-4.54333 + 4.54333i) q^{88} +13.5989 q^{89} -0.302441 q^{91} +(2.51630 - 2.51630i) q^{92} -1.19479i q^{94} +(-9.57617 + 6.69123i) q^{95} +(10.2533 + 10.2533i) q^{97} +(4.88507 + 4.88507i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{5} - 4 q^{7}+O(q^{10}) $ 12 * q - 4 * q^5 - 4 * q^7	$ 12 q - 4 q^{5} - 4 q^{7} + 8 q^{10} - 8 q^{14} - 12 q^{16} - 8 q^{17} - 4 q^{20} - 4 q^{22} + 20 q^{23} + 8 q^{25} - 4 q^{28} + 32 q^{29} + 16 q^{31} - 28 q^{35} + 32 q^{38} + 4 q^{40} + 8 q^{43} - 16 q^{47} - 16 q^{50} + 44 q^{53} - 4 q^{55} + 4 q^{58} + 16 q^{59} + 16 q^{61} + 4 q^{62} - 8 q^{65} + 28 q^{67} + 8 q^{68} - 16 q^{70} + 24 q^{73} - 32 q^{74} + 16 q^{76} + 40 q^{77} + 4 q^{80} + 8 q^{82} + 16 q^{83} - 20 q^{85} - 4 q^{88} + 8 q^{91} + 20 q^{92} - 76 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) $ 12 * q - 4 * q^5 - 4 * q^7 + 8 * q^10 - 8 * q^14 - 12 * q^16 - 8 * q^17 - 4 * q^20 - 4 * q^22 + 20 * q^23 + 8 * q^25 - 4 * q^28 + 32 * q^29 + 16 * q^31 - 28 * q^35 + 32 * q^38 + 4 * q^40 + 8 * q^43 - 16 * q^47 - 16 * q^50 + 44 * q^53 - 4 * q^55 + 4 * q^58 + 16 * q^59 + 16 * q^61 + 4 * q^62 - 8 * q^65 + 28 * q^67 + 8 * q^68 - 16 * q^70 + 24 * q^73 - 32 * q^74 + 16 * q^76 + 40 * q^77 + 4 * q^80 + 8 * q^82 + 16 * q^83 - 20 * q^85 - 4 * q^88 + 8 * q^91 + 20 * q^92 - 76 * q^95 - 8 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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
$5$	−1.28075	−	1.83294i	−0.572768	−	0.819718i
$5$	−1.28075	−	1.83294i	−0.572768	−	0.819718i
$6$		0			0
$7$	−0.213858	−	0.213858i	−0.0808308	−	0.0808308i	0.665535	−	0.746366i	$-0.268203\pi$
$7$	−0.213858	−	0.213858i	−0.0808308	−	0.0808308i	−0.746366	+	0.665535i	$0.768203\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	2.20171	+	0.390462i	0.696243	+	0.123475i
$11$			6.42524i			1.93728i	0.248465	+	0.968641i	$0.420074\pi$
$11$			6.42524i			1.93728i	−0.248465	+	0.968641i	$0.579926\pi$
$12$		0			0
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$13$	0.707107	−	0.707107i	0.196116	−	0.196116i
$14$	0.302441			0.0808308
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.21578	−	1.21578i	0.294869	−	0.294869i	−0.544131	−	0.839000i	$-0.683141\pi$
$17$	1.21578	−	1.21578i	0.294869	−	0.294869i	0.839000	+	0.544131i	$0.183141\pi$
$18$		0			0
$19$		−	5.22447i		−	1.19858i	−0.800533	−	0.599288i	$-0.795450\pi$
$19$		−	5.22447i		−	1.19858i	0.800533	−	0.599288i	$-0.204550\pi$
$20$	−1.83294	+	1.28075i	−0.409859	+	0.286384i
$21$		0			0
$22$	−4.54333	−	4.54333i	−0.968641	−	0.968641i
$23$	2.51630	+	2.51630i	0.524685	+	0.524685i	0.918983	−	0.394298i	$-0.129012\pi$
$23$	2.51630	+	2.51630i	0.524685	+	0.524685i	−0.394298	+	0.918983i	$0.629012\pi$
$24$		0			0
$25$	−1.71937	+	4.69508i	−0.343874	+	0.939016i
$26$			1.00000i			0.196116i
$27$		0			0
$28$	−0.213858	+	0.213858i	−0.0404154	+	0.0404154i
$29$	−9.43932			−1.75284			−0.876419	−	0.481550i	$-0.840074\pi$
$29$	−9.43932			−1.75284			−0.876419	+	0.481550i	$0.840074\pi$
$30$		0			0
$31$	6.53992			1.17460			0.587302	−	0.809368i	$-0.300190\pi$
$31$	6.53992			1.17460			0.587302	+	0.809368i	$0.300190\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$			1.71937i			0.294869i
$35$	−0.118092	+	0.665889i	−0.0199611	+	0.112556i
$36$		0			0
$37$	7.51904	+	7.51904i	1.23612	+	1.23612i	0.961573	+	0.274549i	$0.0885286\pi$
$37$	7.51904	+	7.51904i	1.23612	+	1.23612i	0.274549	+	0.961573i	$0.411471\pi$
$38$	3.69426	+	3.69426i	0.599288	+	0.599288i
$39$		0			0
$40$	0.390462	−	2.20171i	0.0617374	−	0.348121i
$41$		−	0.932674i		−	0.145659i	−0.997344	−	0.0728296i	$-0.976797\pi$
$41$		−	0.932674i		−	0.145659i	0.997344	−	0.0728296i	$-0.0232029\pi$
$42$		0			0
$43$	7.49448	−	7.49448i	1.14290	−	1.14290i	0.154980	−	0.987918i	$-0.450469\pi$
$43$	7.49448	−	7.49448i	1.14290	−	1.14290i	0.987918	−	0.154980i	$-0.0495314\pi$
$44$	6.42524			0.968641
$45$		0			0
$46$	−3.55858			−0.524685
$47$	−0.844841	+	0.844841i	−0.123233	+	0.123233i	−0.766033	−	0.642801i	$-0.777772\pi$
$47$	−0.844841	+	0.844841i	−0.123233	+	0.123233i	0.642801	+	0.766033i	$0.277772\pi$
$48$		0			0
$49$		−	6.90853i		−	0.986933i
$50$	−2.10414	−	4.53570i	−0.297571	−	0.641445i
$51$		0			0
$52$	−0.707107	−	0.707107i	−0.0980581	−	0.0980581i
$53$	8.25019	+	8.25019i	1.13325	+	1.13325i	0.989633	+	0.143617i	$0.0458733\pi$
$53$	8.25019	+	8.25019i	1.13325	+	1.13325i	0.143617	+	0.989633i	$0.454127\pi$
$54$		0			0
$55$	11.7771	−	8.22911i	1.58802	−	1.10961i
$56$		−	0.302441i		−	0.0404154i
$57$		0			0
$58$	6.67460	−	6.67460i	0.876419	−	0.876419i
$59$	14.4793			1.88504			0.942522	−	0.334145i	$-0.108447\pi$
$59$	14.4793			1.88504			0.942522	+	0.334145i	$0.108447\pi$
$60$		0			0
$61$	6.33002			0.810477			0.405238	−	0.914211i	$-0.367189\pi$
$61$	6.33002			0.810477			0.405238	+	0.914211i	$0.367189\pi$
$62$	−4.62442	+	4.62442i	−0.587302	+	0.587302i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−2.20171	−	0.390462i	−0.273089	−	0.0484308i
$66$		0			0
$67$	4.61673	+	4.61673i	0.564023	+	0.564023i	0.930448	−	0.366424i	$-0.119418\pi$
$67$	4.61673	+	4.61673i	0.564023	+	0.564023i	−0.366424	+	0.930448i	$0.619418\pi$
$68$	−1.21578	−	1.21578i	−0.147435	−	0.147435i
$69$		0			0
$70$	−0.387351	−	0.554358i	−0.0462973	−	0.0662584i
$71$		−	11.5425i		−	1.36984i	−0.728617	−	0.684922i	$-0.759836\pi$
$71$		−	11.5425i		−	1.36984i	0.728617	−	0.684922i	$-0.240164\pi$
$72$		0			0
$73$	−6.88465	+	6.88465i	−0.805787	+	0.805787i	−0.983993	−	0.178206i	$-0.942971\pi$
$73$	−6.88465	+	6.88465i	−0.805787	+	0.805787i	0.178206	+	0.983993i	$0.442971\pi$
$74$	−10.6335			−1.23612
$75$		0			0
$76$	−5.22447			−0.599288
$77$	1.37409	−	1.37409i	0.156592	−	0.156592i
$78$		0			0
$79$			0.724996i			0.0815684i	0.999168	+	0.0407842i	$0.0129856\pi$
$79$			0.724996i			0.0815684i	−0.999168	+	0.0407842i	$0.987014\pi$
$80$	1.28075	+	1.83294i	0.143192	+	0.204929i
$81$		0			0
$82$	0.659500	+	0.659500i	0.0728296	+	0.0728296i
$83$	3.81300	+	3.81300i	0.418532	+	0.418532i	0.884697	−	0.466166i	$-0.154365\pi$
$83$	3.81300	+	3.81300i	0.418532	+	0.418532i	−0.466166	+	0.884697i	$0.654365\pi$
$84$		0			0
$85$	−3.78556	−	0.671348i	−0.410601	−	0.0728179i
$86$			10.5988i			1.14290i
$87$		0			0
$88$	−4.54333	+	4.54333i	−0.484320	+	0.484320i
$89$	13.5989			1.44149			0.720743	−	0.693203i	$-0.243801\pi$
$89$	13.5989			1.44149			0.720743	+	0.693203i	$0.243801\pi$
$90$		0			0
$91$	−0.302441			−0.0317045
$92$	2.51630	−	2.51630i	0.262342	−	0.262342i
$93$		0			0
$94$		−	1.19479i		−	0.123233i
$95$	−9.57617	+	6.69123i	−0.982494	+	0.686506i
$96$		0			0
$97$	10.2533	+	10.2533i	1.04106	+	1.04106i	0.999120	+	0.0419403i	$0.0133539\pi$
$97$	10.2533	+	10.2533i	1.04106	+	1.04106i	0.0419403	+	0.999120i	$0.486646\pi$
$98$	4.88507	+	4.88507i	0.493466	+	0.493466i
$99$		0			0
$100$	4.69508	+	1.71937i	0.469508	+	0.171937i
$101$			2.01831i			0.200830i	0.994946	+	0.100415i	$0.0320170\pi$
$101$			2.01831i			0.200830i	−0.994946	+	0.100415i	$0.967983\pi$
$102$		0			0
$103$	−12.2048	+	12.2048i	−1.20258	+	1.20258i	−0.229196	+	0.973380i	$0.573610\pi$
$103$	−12.2048	+	12.2048i	−1.20258	+	1.20258i	−0.973380	+	0.229196i	$0.926390\pi$
$104$	1.00000			0.0980581
$105$		0			0
$106$	−11.6675			−1.13325
$107$	2.66248	−	2.66248i	0.257392	−	0.257392i	−0.566601	−	0.823992i	$-0.691742\pi$
$107$	2.66248	−	2.66248i	0.257392	−	0.257392i	0.823992	+	0.566601i	$0.191742\pi$
$108$		0			0
$109$		−	10.6094i		−	1.01620i	−0.861299	−	0.508098i	$-0.830349\pi$
$109$		−	10.6094i		−	1.01620i	0.861299	−	0.508098i	$-0.169651\pi$
$110$	−2.50881	+	14.1465i	−0.239206	+	1.34882i
$111$		0			0
$112$	0.213858	+	0.213858i	0.0202077	+	0.0202077i
$113$	−4.62751	−	4.62751i	−0.435320	−	0.435320i	0.455114	−	0.890433i	$-0.349599\pi$
$113$	−4.62751	−	4.62751i	−0.435320	−	0.435320i	−0.890433	+	0.455114i	$0.849599\pi$
$114$		0			0
$115$	1.38949	−	7.83498i	0.129571	−	0.730616i
$116$			9.43932i			0.876419i
$117$		0			0
$118$	−10.2384	+	10.2384i	−0.942522	+	0.942522i
$119$	−0.520008			−0.0476691
$120$		0			0
$121$	−30.2837			−2.75306
$122$	−4.47600	+	4.47600i	−0.405238	+	0.405238i
$123$		0			0
$124$		−	6.53992i		−	0.587302i
$125$	10.8079	−	2.86170i	0.966688	−	0.255959i
$126$		0			0
$127$	3.06468	+	3.06468i	0.271946	+	0.271946i	0.829883	−	0.557937i	$-0.188407\pi$
$127$	3.06468	+	3.06468i	0.271946	+	0.271946i	−0.557937	+	0.829883i	$0.688407\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	1.83294	−	1.28075i	0.160760	−	0.112329i
$131$		−	9.33333i		−	0.815457i	−0.913103	−	0.407729i	$-0.866321\pi$
$131$		−	9.33333i		−	0.815457i	0.913103	−	0.407729i	$-0.133679\pi$
$132$		0			0
$133$	−1.11730	+	1.11730i	−0.0968819	+	0.0968819i
$134$	−6.52904			−0.564023
$135$		0			0
$136$	1.71937			0.147435
$137$	0.324017	−	0.324017i	0.0276826	−	0.0276826i	−0.693130	−	0.720813i	$-0.743769\pi$
$137$	0.324017	−	0.324017i	0.0276826	−	0.0276826i	0.720813	+	0.693130i	$0.243769\pi$
$138$		0			0
$139$		−	7.22530i		−	0.612842i	−0.951896	−	0.306421i	$-0.900869\pi$
$139$		−	7.22530i		−	0.612842i	0.951896	−	0.306421i	$-0.0991315\pi$
$140$	0.665889	+	0.118092i	0.0562779	+	0.00998057i
$141$		0			0
$142$	8.16178	+	8.16178i	0.684922	+	0.684922i
$143$	4.54333	+	4.54333i	0.379932	+	0.379932i
$144$		0			0
$145$	12.0894	+	17.3017i	1.00397	+	1.43683i
$146$		−	9.73636i		−	0.805787i
$147$		0			0
$148$	7.51904	−	7.51904i	0.618061	−	0.618061i
$149$	0.602445			0.0493542			0.0246771	−	0.999695i	$-0.492144\pi$
$149$	0.602445			0.0493542			0.0246771	+	0.999695i	$0.492144\pi$
$150$		0			0
$151$	1.01112			0.0822838			0.0411419	−	0.999153i	$-0.486900\pi$
$151$	1.01112			0.0822838			0.0411419	+	0.999153i	$0.486900\pi$
$152$	3.69426	−	3.69426i	0.299644	−	0.299644i
$153$		0			0
$154$			1.94326i			0.156592i
$155$	−8.37599	−	11.9873i	−0.672776	−	0.962844i
$156$		0			0
$157$	6.81281	+	6.81281i	0.543721	+	0.543721i	0.924618	−	0.380896i	$-0.124385\pi$
$157$	6.81281	+	6.81281i	0.543721	+	0.543721i	−0.380896	+	0.924618i	$0.624385\pi$
$158$	−0.512649	−	0.512649i	−0.0407842	−	0.0407842i
$159$		0			0
$160$	−2.20171	−	0.390462i	−0.174061	−	0.0308687i
$161$		−	1.07626i		−	0.0848214i
$162$		0			0
$163$	4.52097	−	4.52097i	0.354110	−	0.354110i	−0.507526	−	0.861636i	$-0.669440\pi$
$163$	4.52097	−	4.52097i	0.354110	−	0.354110i	0.861636	+	0.507526i	$0.169440\pi$
$164$	−0.932674			−0.0728296
$165$		0			0
$166$	−5.39240			−0.418532
$167$	−6.70971	+	6.70971i	−0.519213	+	0.519213i	−0.917333	−	0.398120i	$-0.869663\pi$
$167$	−6.70971	+	6.70971i	−0.519213	+	0.519213i	0.398120	+	0.917333i	$0.369663\pi$
$168$		0			0
$169$		−	1.00000i		−	0.0769231i
$170$	3.15151	−	2.20208i	0.241710	−	0.168892i
$171$		0			0
$172$	−7.49448	−	7.49448i	−0.571449	−	0.571449i
$173$	3.89442	+	3.89442i	0.296087	+	0.296087i	0.839479	−	0.543392i	$-0.182860\pi$
$173$	3.89442	+	3.89442i	0.296087	+	0.296087i	−0.543392	+	0.839479i	$0.682860\pi$
$174$		0			0
$175$	1.37178	−	0.636380i	0.103697	−	0.0481058i
$176$		−	6.42524i		−	0.484320i
$177$		0			0
$178$	−9.61591	+	9.61591i	−0.720743	+	0.720743i
$179$	−21.7807			−1.62797			−0.813984	−	0.580887i	$-0.802706\pi$
$179$	−21.7807			−1.62797			−0.813984	+	0.580887i	$0.802706\pi$
$180$		0			0
$181$	1.89023			0.140500			0.0702500	−	0.997529i	$-0.477620\pi$
$181$	1.89023			0.140500			0.0702500	+	0.997529i	$0.477620\pi$
$182$	0.213858	−	0.213858i	0.0158522	−	0.0158522i
$183$		0			0
$184$			3.55858i			0.262342i
$185$	4.15199	−	23.4120i	0.305260	−	1.72128i
$186$		0			0
$187$	7.81166	+	7.81166i	0.571245	+	0.571245i
$188$	0.844841	+	0.844841i	0.0616164	+	0.0616164i
$189$		0			0
$190$	2.03996	−	11.5028i	0.147994	−	0.834500i
$191$			16.7639i			1.21299i	0.795086	+	0.606497i	$0.207426\pi$
$191$			16.7639i			1.21299i	−0.795086	+	0.606497i	$0.792574\pi$
$192$		0			0
$193$	6.10616	−	6.10616i	0.439531	−	0.439531i	−0.452323	−	0.891854i	$-0.649405\pi$
$193$	6.10616	−	6.10616i	0.439531	−	0.439531i	0.891854	+	0.452323i	$0.149405\pi$
$194$	−14.5003			−1.04106
$195$		0			0
$196$	−6.90853			−0.493466
$197$	−7.17231	+	7.17231i	−0.511006	+	0.511006i	−0.914835	−	0.403829i	$-0.867679\pi$
$197$	−7.17231	+	7.17231i	−0.511006	+	0.511006i	0.403829	+	0.914835i	$0.367679\pi$
$198$		0			0
$199$			16.8682i			1.19575i	0.801588	+	0.597876i	$0.203989\pi$
$199$			16.8682i			1.19575i	−0.801588	+	0.597876i	$0.796011\pi$
$200$	−4.53570	+	2.10414i	−0.320722	+	0.148785i
$201$		0			0
$202$	−1.42716	−	1.42716i	−0.100415	−	0.100415i
$203$	2.01868	+	2.01868i	0.141683	+	0.141683i
$204$		0			0
$205$	−1.70954	+	1.19452i	−0.119399	+	0.0834289i
$206$		−	17.2602i		−	1.20258i
$207$		0			0
$208$	−0.707107	+	0.707107i	−0.0490290	+	0.0490290i
$209$	33.5685			2.32198
$210$		0			0
$211$	−3.20670			−0.220758			−0.110379	−	0.993890i	$-0.535207\pi$
$211$	−3.20670			−0.220758			−0.110379	+	0.993890i	$0.535207\pi$
$212$	8.25019	−	8.25019i	0.566625	−	0.566625i
$213$		0			0
$214$			3.76532i			0.257392i
$215$	−23.3355	−	4.13843i	−1.59147	−	0.282238i
$216$		0			0
$217$	−1.39862	−	1.39862i	−0.0949442	−	0.0949442i
$218$	7.50197	+	7.50197i	0.508098	+	0.508098i
$219$		0			0
$220$	−8.22911	−	11.7771i	−0.554806	−	0.794012i
$221$		−	1.71937i		−	0.115657i
$222$		0			0
$223$	−7.45886	+	7.45886i	−0.499482	+	0.499482i	−0.911277	−	0.411794i	$-0.864902\pi$
$223$	−7.45886	+	7.45886i	−0.499482	+	0.499482i	0.411794	+	0.911277i	$0.364902\pi$
$224$	−0.302441			−0.0202077
$225$		0			0
$226$	6.54429			0.435320
$227$	17.6094	−	17.6094i	1.16878	−	1.16878i	0.186279	−	0.982497i	$-0.440357\pi$
$227$	17.6094	−	17.6094i	1.16878	−	1.16878i	0.982497	−	0.186279i	$-0.0596427\pi$
$228$		0			0
$229$			9.79092i			0.647002i	0.946228	+	0.323501i	$0.104860\pi$
$229$			9.79092i			0.647002i	−0.946228	+	0.323501i	$0.895140\pi$
$230$	4.55765	+	6.52269i	0.300523	+	0.430093i
$231$		0			0
$232$	−6.67460	−	6.67460i	−0.438209	−	0.438209i
$233$	−17.7966	−	17.7966i	−1.16589	−	1.16589i	−0.983163	−	0.182732i	$-0.941506\pi$
$233$	−17.7966	−	17.7966i	−1.16589	−	1.16589i	−0.182732	−	0.983163i	$-0.558494\pi$
$234$		0			0
$235$	2.63057	+	0.466518i	0.171600	+	0.0304323i
$236$		−	14.4793i		−	0.942522i
$237$		0			0
$238$	0.367701	−	0.367701i	0.0238345	−	0.0238345i
$239$	−3.84377			−0.248633			−0.124317	−	0.992243i	$-0.539674\pi$
$239$	−3.84377			−0.248633			−0.124317	+	0.992243i	$0.539674\pi$
$240$		0			0
$241$	−11.1993			−0.721412			−0.360706	−	0.932680i	$-0.617464\pi$
$241$	−11.1993			−0.721412			−0.360706	+	0.932680i	$0.617464\pi$
$242$	21.4138	−	21.4138i	1.37653	−	1.37653i
$243$		0			0
$244$		−	6.33002i		−	0.405238i
$245$	−12.6629	+	8.84808i	−0.809006	+	0.565283i
$246$		0			0
$247$	−3.69426	−	3.69426i	−0.235060	−	0.235060i
$248$	4.62442	+	4.62442i	0.293651	+	0.293651i
$249$		0			0
$250$	−5.61881	+	9.66587i	−0.355365	+	0.611323i
$251$		−	20.1828i		−	1.27393i	−0.770894	−	0.636964i	$-0.780190\pi$
$251$		−	20.1828i		−	1.27393i	0.770894	−	0.636964i	$-0.219810\pi$
$252$		0			0
$253$	−16.1678	+	16.1678i	−1.01646	+	1.01646i
$254$	−4.33411			−0.271946
$255$		0			0
$256$	1.00000			0.0625000
$257$	11.1789	−	11.1789i	0.697323	−	0.697323i	−0.266509	−	0.963832i	$-0.585870\pi$
$257$	11.1789	−	11.1789i	0.697323	−	0.697323i	0.963832	+	0.266509i	$0.0858702\pi$
$258$		0			0
$259$		−	3.21602i		−	0.199834i
$260$	−0.390462	+	2.20171i	−0.0242154	+	0.136544i
$261$		0			0
$262$	6.59966	+	6.59966i	0.407729	+	0.407729i
$263$	−13.3898	−	13.3898i	−0.825647	−	0.825647i	0.161264	−	0.986911i	$-0.448443\pi$
$263$	−13.3898	−	13.3898i	−0.825647	−	0.825647i	−0.986911	+	0.161264i	$0.948443\pi$
$264$		0			0
$265$	4.55572	−	25.6885i	0.279856	−	1.57803i
$266$		−	1.58010i		−	0.0968819i
$267$		0			0
$268$	4.61673	−	4.61673i	0.282012	−	0.282012i
$269$	−10.7429			−0.655008			−0.327504	−	0.944850i	$-0.606208\pi$
$269$	−10.7429			−0.655008			−0.327504	+	0.944850i	$0.606208\pi$
$270$		0			0
$271$	−6.60628			−0.401303			−0.200652	−	0.979663i	$-0.564306\pi$
$271$	−6.60628			−0.401303			−0.200652	+	0.979663i	$0.564306\pi$
$272$	−1.21578	+	1.21578i	−0.0737174	+	0.0737174i
$273$		0			0
$274$			0.458229i			0.0276826i
$275$	−30.1670	−	11.0474i	−1.81914	−	0.666181i
$276$		0			0
$277$	12.5302	+	12.5302i	0.752870	+	0.752870i	0.975014	−	0.222144i	$-0.0713056\pi$
$277$	12.5302	+	12.5302i	0.752870	+	0.752870i	−0.222144	+	0.975014i	$0.571306\pi$
$278$	5.10906	+	5.10906i	0.306421	+	0.306421i
$279$		0			0
$280$	−0.554358	+	0.387351i	−0.0331292	+	0.0231486i
$281$			33.3200i			1.98770i	0.110714	+	0.993852i	$0.464686\pi$
$281$			33.3200i			1.98770i	−0.110714	+	0.993852i	$0.535314\pi$
$282$		0			0
$283$	10.8541	−	10.8541i	0.645212	−	0.645212i	−0.306620	−	0.951832i	$-0.599198\pi$
$283$	10.8541	−	10.8541i	0.645212	−	0.645212i	0.951832	+	0.306620i	$0.0991982\pi$
$284$	−11.5425			−0.684922
$285$		0			0
$286$	−6.42524			−0.379932
$287$	−0.199460	+	0.199460i	−0.0117738	+	0.0117738i
$288$		0			0
$289$			14.0438i			0.826104i
$290$	−20.7827	−	3.68569i	−1.22040	−	0.216431i
$291$		0			0
$292$	6.88465	+	6.88465i	0.402893	+	0.402893i
$293$	2.59262	+	2.59262i	0.151462	+	0.151462i	0.778771	−	0.627308i	$-0.215843\pi$
$293$	2.59262	+	2.59262i	0.151462	+	0.151462i	−0.627308	+	0.778771i	$0.715843\pi$
$294$		0			0
$295$	−18.5443	−	26.5397i	−1.07969	−	1.54520i
$296$			10.6335i			0.618061i
$297$		0			0
$298$	−0.425993	+	0.425993i	−0.0246771	+	0.0246771i
$299$	3.55858			0.205798
$300$		0			0
$301$	−3.20551			−0.184763
$302$	−0.714970	+	0.714970i	−0.0411419	+	0.0411419i
$303$		0			0
$304$			5.22447i			0.299644i
$305$	−8.10716	−	11.6026i	−0.464215	−	0.664362i
$306$		0			0
$307$	−5.46512	−	5.46512i	−0.311911	−	0.311911i	0.533739	−	0.845649i	$-0.320787\pi$
$307$	−5.46512	−	5.46512i	−0.311911	−	0.311911i	−0.845649	+	0.533739i	$0.820787\pi$
$308$	−1.37409	−	1.37409i	−0.0782960	−	0.0782960i
$309$		0			0
$310$	14.3990	+	2.55359i	0.817810	+	0.145034i
$311$		−	11.1956i		−	0.634847i	−0.948284	−	0.317423i	$-0.897182\pi$
$311$		−	11.1956i		−	0.634847i	0.948284	−	0.317423i	$-0.102818\pi$
$312$		0			0
$313$	6.99883	−	6.99883i	0.395597	−	0.395597i	−0.481080	−	0.876677i	$-0.659755\pi$
$313$	6.99883	−	6.99883i	0.395597	−	0.395597i	0.876677	+	0.481080i	$0.159755\pi$
$314$	−9.63477			−0.543721
$315$		0			0
$316$	0.724996			0.0407842
$317$	16.3733	−	16.3733i	0.919615	−	0.919615i	−0.0773860	−	0.997001i	$-0.524657\pi$
$317$	16.3733	−	16.3733i	0.919615	−	0.919615i	0.997001	+	0.0773860i	$0.0246574\pi$
$318$		0			0
$319$		−	60.6498i		−	3.39574i
$320$	1.83294	−	1.28075i	0.102465	−	0.0715960i
$321$		0			0
$322$	0.761033	+	0.761033i	0.0424107	+	0.0424107i
$323$	−6.35180	−	6.35180i	−0.353424	−	0.353424i
$324$		0			0
$325$	2.10414	+	4.53570i	0.116717	+	0.251595i
$326$			6.39362i			0.354110i
$327$		0			0
$328$	0.659500	−	0.659500i	0.0364148	−	0.0364148i
$329$	0.361352			0.0199220
$330$		0			0
$331$	−16.9423			−0.931234			−0.465617	−	0.884986i	$-0.654168\pi$
$331$	−16.9423			−0.931234			−0.465617	+	0.884986i	$0.654168\pi$
$332$	3.81300	−	3.81300i	0.209266	−	0.209266i
$333$		0			0
$334$		−	9.48896i		−	0.519213i
$335$	2.54934	−	14.3751i	0.139285	−	0.785394i
$336$		0			0
$337$	−9.48022	−	9.48022i	−0.516420	−	0.516420i	0.400066	−	0.916486i	$-0.368987\pi$
$337$	−9.48022	−	9.48022i	−0.516420	−	0.516420i	−0.916486	+	0.400066i	$0.868987\pi$
$338$	0.707107	+	0.707107i	0.0384615	+	0.0384615i
$339$		0			0
$340$	−0.671348	+	3.78556i	−0.0364090	+	0.205301i
$341$			42.0205i			2.27554i
$342$		0			0
$343$	−2.97445	+	2.97445i	−0.160605	+	0.160605i
$344$	10.5988			0.571449
$345$		0			0
$346$	−5.50754			−0.296087
$347$	12.4255	−	12.4255i	0.667034	−	0.667034i	−0.289994	−	0.957028i	$-0.593653\pi$
$347$	12.4255	−	12.4255i	0.667034	−	0.667034i	0.957028	+	0.289994i	$0.0936534\pi$
$348$		0			0
$349$			8.54562i			0.457437i	0.973493	+	0.228718i	$0.0734535\pi$
$349$			8.54562i			0.457437i	−0.973493	+	0.228718i	$0.926547\pi$
$350$	−0.520008	+	1.41999i	−0.0277956	+	0.0759014i
$351$		0			0
$352$	4.54333	+	4.54333i	0.242160	+	0.242160i
$353$	−12.7379	−	12.7379i	−0.677969	−	0.677969i	0.281571	−	0.959540i	$-0.409144\pi$
$353$	−12.7379	−	12.7379i	−0.677969	−	0.677969i	−0.959540	+	0.281571i	$0.909144\pi$
$354$		0			0
$355$	−21.1568	+	14.7830i	−1.12288	+	0.784602i
$356$		−	13.5989i		−	0.720743i
$357$		0			0
$358$	15.4013	−	15.4013i	0.813984	−	0.813984i
$359$	7.48611			0.395102			0.197551	−	0.980293i	$-0.436701\pi$
$359$	7.48611			0.395102			0.197551	+	0.980293i	$0.436701\pi$
$360$		0			0
$361$	−8.29512			−0.436585
$362$	−1.33660	+	1.33660i	−0.0702500	+	0.0702500i
$363$		0			0
$364$			0.302441i			0.0158522i
$365$	21.4367	+	3.80168i	1.12205	+	0.198989i
$366$		0			0
$367$	13.1558	+	13.1558i	0.686727	+	0.686727i	0.961507	−	0.274780i	$-0.0886049\pi$
$367$	13.1558	+	13.1558i	0.686727	+	0.686727i	−0.274780	+	0.961507i	$0.588605\pi$
$368$	−2.51630	−	2.51630i	−0.131171	−	0.131171i
$369$		0			0
$370$	13.6189	+	19.4907i	0.708011	+	1.01327i
$371$		−	3.52874i		−	0.183203i
$372$		0			0
$373$	−22.3706	+	22.3706i	−1.15830	+	1.15830i	−0.173464	+	0.984840i	$0.555496\pi$
$373$	−22.3706	+	22.3706i	−1.15830	+	1.15830i	−0.984840	+	0.173464i	$0.944504\pi$
$374$	−11.0474			−0.571245
$375$		0			0
$376$	−1.19479			−0.0616164
$377$	−6.67460	+	6.67460i	−0.343760	+	0.343760i
$378$		0			0
$379$			9.42313i			0.484034i	0.970272	+	0.242017i	$0.0778089\pi$
$379$			9.42313i			0.484034i	−0.970272	+	0.242017i	$0.922191\pi$
$380$	6.69123	+	9.57617i	0.343253	+	0.491247i
$381$		0			0
$382$	−11.8539	−	11.8539i	−0.606497	−	0.606497i
$383$	18.1809	+	18.1809i	0.929001	+	0.929001i	0.997641	−	0.0686409i	$-0.0218663\pi$
$383$	18.1809	+	18.1809i	0.929001	+	0.929001i	−0.0686409	+	0.997641i	$0.521866\pi$
$384$		0			0
$385$	−4.27849	−	0.758767i	−0.218052	−	0.0386704i
$386$			8.63542i			0.439531i
$387$		0			0
$388$	10.2533	−	10.2533i	0.520530	−	0.520530i
$389$	−12.8842			−0.653253			−0.326627	−	0.945153i	$-0.605912\pi$
$389$	−12.8842			−0.653253			−0.326627	+	0.945153i	$0.605912\pi$
$390$		0			0
$391$	6.11852			0.309427
$392$	4.88507	−	4.88507i	0.246733	−	0.246733i
$393$		0			0
$394$		−	10.1432i		−	0.511006i
$395$	1.32888	−	0.928537i	0.0668631	−	0.0467198i
$396$		0			0
$397$	−0.370404	−	0.370404i	−0.0185900	−	0.0185900i	0.697751	−	0.716341i	$-0.254184\pi$
$397$	−0.370404	−	0.370404i	−0.0185900	−	0.0185900i	−0.716341	+	0.697751i	$0.754184\pi$
$398$	−11.9276	−	11.9276i	−0.597876	−	0.597876i
$399$		0			0
$400$	1.71937	−	4.69508i	0.0859685	−	0.234754i
$401$			17.0021i			0.849046i	0.905417	+	0.424523i	$0.139558\pi$
$401$			17.0021i			0.849046i	−0.905417	+	0.424523i	$0.860442\pi$
$402$		0			0
$403$	4.62442	−	4.62442i	0.230359	−	0.230359i
$404$	2.01831			0.100415
$405$		0			0
$406$	−2.85484			−0.141683
$407$	−48.3116	+	48.3116i	−2.39472	+	2.39472i
$408$		0			0
$409$		−	6.16823i		−	0.304999i	−0.988304	−	0.152500i	$-0.951268\pi$
$409$		−	6.16823i		−	0.304999i	0.988304	−	0.152500i	$-0.0487323\pi$
$410$	0.364174	−	2.05348i	0.0179853	−	0.101414i
$411$		0			0
$412$	12.2048	+	12.2048i	0.601288	+	0.601288i
$413$	−3.09652	−	3.09652i	−0.152370	−	0.152370i
$414$		0			0
$415$	2.10553	−	11.8725i	0.103356	−	0.582799i
$416$		−	1.00000i		−	0.0490290i
$417$		0			0
$418$	−23.7365	+	23.7365i	−1.16099	+	1.16099i
$419$	−1.73982			−0.0849958			−0.0424979	−	0.999097i	$-0.513532\pi$
$419$	−1.73982			−0.0849958			−0.0424979	+	0.999097i	$0.513532\pi$
$420$		0			0
$421$	−10.1670			−0.495509			−0.247755	−	0.968823i	$-0.579693\pi$
$421$	−10.1670			−0.495509			−0.247755	+	0.968823i	$0.579693\pi$
$422$	2.26748	−	2.26748i	0.110379	−	0.110379i
$423$		0			0
$424$			11.6675i			0.566625i
$425$	3.61780	+	7.79855i	0.175489	+	0.378285i
$426$		0			0
$427$	−1.35373	−	1.35373i	−0.0655115	−	0.0655115i
$428$	−2.66248	−	2.66248i	−0.128696	−	0.128696i
$429$		0			0
$430$	19.4270	−	13.5744i	0.936853	−	0.654615i
$431$		−	13.7840i		−	0.663950i	−0.943288	−	0.331975i	$-0.892285\pi$
$431$		−	13.7840i		−	0.663950i	0.943288	−	0.331975i	$-0.107715\pi$
$432$		0			0
$433$	−24.3771	+	24.3771i	−1.17149	+	1.17149i	−0.189633	+	0.981855i	$0.560730\pi$
$433$	−24.3771	+	24.3771i	−1.17149	+	1.17149i	−0.981855	+	0.189633i	$0.939270\pi$
$434$	1.97794			0.0949442
$435$		0			0
$436$	−10.6094			−0.508098
$437$	13.1463	−	13.1463i	0.628875	−	0.628875i
$438$		0			0
$439$		−	12.2646i		−	0.585356i	−0.956211	−	0.292678i	$-0.905454\pi$
$439$		−	12.2646i		−	0.585356i	0.956211	−	0.292678i	$-0.0945463\pi$
$440$	14.1465	+	2.50881i	0.674409	+	0.119603i
$441$		0			0
$442$	1.21578	+	1.21578i	0.0578287	+	0.0578287i
$443$	−0.734528	−	0.734528i	−0.0348985	−	0.0348985i	0.689442	−	0.724341i	$-0.257856\pi$
$443$	−0.734528	−	0.734528i	−0.0348985	−	0.0348985i	−0.724341	+	0.689442i	$0.757856\pi$
$444$		0			0
$445$	−17.4168	−	24.9261i	−0.825636	−	1.18161i
$446$		−	10.5484i		−	0.499482i
$447$		0			0
$448$	0.213858	−	0.213858i	0.0101039	−	0.0101039i
$449$	−9.19292			−0.433841			−0.216920	−	0.976189i	$-0.569601\pi$
$449$	−9.19292			−0.433841			−0.216920	+	0.976189i	$0.569601\pi$
$450$		0			0
$451$	5.99265			0.282183
$452$	−4.62751	+	4.62751i	−0.217660	+	0.217660i
$453$		0			0
$454$			24.9034i			1.16878i
$455$	0.387351	+	0.554358i	0.0181593	+	0.0259887i
$456$		0			0
$457$	24.4549	+	24.4549i	1.14395	+	1.14395i	0.987720	+	0.156234i	$0.0499354\pi$
$457$	24.4549	+	24.4549i	1.14395	+	1.14395i	0.156234	+	0.987720i	$0.450065\pi$
$458$	−6.92322	−	6.92322i	−0.323501	−	0.323501i
$459$		0			0
$460$	−7.83498	−	1.38949i	−0.365308	−	0.0647854i
$461$			18.8260i			0.876814i	0.898777	+	0.438407i	$0.144457\pi$
$461$			18.8260i			0.876814i	−0.898777	+	0.438407i	$0.855543\pi$
$462$		0			0
$463$	23.3387	−	23.3387i	1.08464	−	1.08464i	0.0885727	−	0.996070i	$-0.471769\pi$
$463$	23.3387	−	23.3387i	1.08464	−	1.08464i	0.996070	−	0.0885727i	$-0.0282306\pi$
$464$	9.43932			0.438209
$465$		0			0
$466$	25.1682			1.16589
$467$	−18.3416	+	18.3416i	−0.848750	+	0.848750i	−0.989977	−	0.141227i	$-0.954895\pi$
$467$	−18.3416	+	18.3416i	−0.848750	+	0.848750i	0.141227	+	0.989977i	$0.454895\pi$
$468$		0			0
$469$		−	1.97465i		−	0.0911809i
$470$	−2.18998	+	1.53022i	−0.101016	+	0.0705837i
$471$		0			0
$472$	10.2384	+	10.2384i	0.471261	+	0.471261i
$473$	48.1538	+	48.1538i	2.21412	+	2.21412i
$474$		0			0
$475$	24.5293	+	8.98280i	1.12548	+	0.412159i
$476$			0.520008i			0.0238345i
$477$		0			0
$478$	2.71796	−	2.71796i	0.124317	−	0.124317i
$479$	10.9169			0.498804			0.249402	−	0.968400i	$-0.419766\pi$
$479$	10.9169			0.498804			0.249402	+	0.968400i	$0.419766\pi$
$480$		0			0
$481$	10.6335			0.484847
$482$	7.91912	−	7.91912i	0.360706	−	0.360706i
$483$		0			0
$484$			30.2837i			1.37653i
$485$	5.66181	−	31.9255i	0.257090	−	1.44966i
$486$		0			0
$487$	7.78498	+	7.78498i	0.352771	+	0.352771i	0.861140	−	0.508369i	$-0.169751\pi$
$487$	7.78498	+	7.78498i	0.352771	+	0.352771i	−0.508369	+	0.861140i	$0.669751\pi$
$488$	4.47600	+	4.47600i	0.202619	+	0.202619i
$489$		0			0
$490$	2.69752	−	15.2106i	0.121861	−	0.687145i
$491$			3.81065i			0.171972i	0.996296	+	0.0859860i	$0.0274040\pi$
$491$			3.81065i			0.171972i	−0.996296	+	0.0859860i	$0.972596\pi$
$492$		0			0
$493$	−11.4761	+	11.4761i	−0.516858	+	0.516858i
$494$	5.22447			0.235060
$495$		0			0
$496$	−6.53992			−0.293651
$497$	−2.46846	+	2.46846i	−0.110726	+	0.110726i
$498$		0			0
$499$		−	20.2063i		−	0.904558i	−0.891877	−	0.452279i	$-0.850611\pi$
$499$		−	20.2063i		−	0.904558i	0.891877	−	0.452279i	$-0.149389\pi$
$500$	−2.86170	−	10.8079i	−0.127979	−	0.483344i
$501$		0			0
$502$	14.2714	+	14.2714i	0.636964	+	0.636964i
$503$	−24.2379	−	24.2379i	−1.08071	−	1.08071i	−0.996443	−	0.0842709i	$-0.973144\pi$
$503$	−24.2379	−	24.2379i	−1.08071	−	1.08071i	−0.0842709	−	0.996443i	$-0.526856\pi$
$504$		0			0
$505$	3.69946	−	2.58495i	0.164624	−	0.115029i
$506$		−	22.8647i		−	1.01646i
$507$		0			0
$508$	3.06468	−	3.06468i	0.135973	−	0.135973i
$509$	−22.8610			−1.01329			−0.506647	−	0.862153i	$-0.669115\pi$
$509$	−22.8610			−1.01329			−0.506647	+	0.862153i	$0.669115\pi$
$510$		0			0
$511$	2.94468			0.130265
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$			15.8094i			0.697323i
$515$	38.0020	+	6.73946i	1.67457	+	0.296976i
$516$		0			0
$517$	−5.42830	−	5.42830i	−0.238737	−	0.238737i
$518$	2.27407	+	2.27407i	0.0999168	+	0.0999168i
$519$		0			0
$520$	−1.28075	−	1.83294i	−0.0561645	−	0.0803799i
$521$		−	6.36289i		−	0.278763i	−0.990239	−	0.139382i	$-0.955489\pi$
$521$		−	6.36289i		−	0.278763i	0.990239	−	0.139382i	$-0.0445115\pi$
$522$		0			0
$523$	−7.70410	+	7.70410i	−0.336877	+	0.336877i	−0.855190	−	0.518314i	$-0.826560\pi$
$523$	−7.70410	+	7.70410i	−0.336877	+	0.336877i	0.518314	+	0.855190i	$0.326560\pi$
$524$	−9.33333			−0.407729
$525$		0			0
$526$	18.9360			0.825647
$527$	7.95109	−	7.95109i	0.346355	−	0.346355i
$528$		0			0
$529$		−	10.3365i		−	0.449412i
$530$	14.9432	+	21.3859i	0.649089	+	0.928945i
$531$		0			0
$532$	1.11730	+	1.11730i	0.0484409	+	0.0484409i
$533$	−0.659500	−	0.659500i	−0.0285661	−	0.0285661i
$534$		0			0
$535$	−8.29014	−	1.47021i	−0.358414	−	0.0635628i
$536$			6.52904i			0.282012i
$537$		0			0
$538$	7.59640	−	7.59640i	0.327504	−	0.327504i
$539$	44.3889			1.91197
$540$		0			0
$541$	28.4253			1.22210			0.611050	−	0.791592i	$-0.290747\pi$
$541$	28.4253			1.22210			0.611050	+	0.791592i	$0.290747\pi$
$542$	4.67135	−	4.67135i	0.200652	−	0.200652i
$543$		0			0
$544$		−	1.71937i		−	0.0737174i
$545$	−19.4464	+	13.5880i	−0.832993	+	0.582044i
$546$		0			0
$547$	7.98666	+	7.98666i	0.341485	+	0.341485i	0.856925	−	0.515441i	$-0.172372\pi$
$547$	7.98666	+	7.98666i	0.341485	+	0.341485i	−0.515441	+	0.856925i	$0.672372\pi$
$548$	−0.324017	−	0.324017i	−0.0138413	−	0.0138413i
$549$		0			0
$550$	29.1429	−	13.5196i	1.24266	−	0.576479i
$551$			49.3155i			2.10091i
$552$		0			0
$553$	0.155046	−	0.155046i	0.00659324	−	0.00659324i
$554$	−17.7204			−0.752870
$555$		0			0
$556$	−7.22530			−0.306421
$557$	10.8652	−	10.8652i	0.460373	−	0.460373i	−0.438405	−	0.898778i	$-0.644456\pi$
$557$	10.8652	−	10.8652i	0.460373	−	0.460373i	0.898778	+	0.438405i	$0.144456\pi$
$558$		0			0
$559$		−	10.5988i		−	0.448281i
$560$	0.118092	−	0.665889i	0.00499029	−	0.0281389i
$561$		0			0
$562$	−23.5608	−	23.5608i	−0.993852	−	0.993852i
$563$	0.306520	+	0.306520i	0.0129183	+	0.0129183i	0.713536	−	0.700618i	$-0.247092\pi$
$563$	0.306520	+	0.306520i	0.0129183	+	0.0129183i	−0.700618	+	0.713536i	$0.747092\pi$
$564$		0			0
$565$	−2.55530	+	14.4086i	−0.107502	+	0.606176i
$566$			15.3501i			0.645212i
$567$		0			0
$568$	8.16178	−	8.16178i	0.342461	−	0.342461i
$569$	18.0114			0.755079			0.377540	−	0.925993i	$-0.376770\pi$
$569$	18.0114			0.755079			0.377540	+	0.925993i	$0.376770\pi$
$570$		0			0
$571$	28.6290			1.19808			0.599042	−	0.800717i	$-0.295548\pi$
$571$	28.6290			1.19808			0.599042	+	0.800717i	$0.295548\pi$
$572$	4.54333	−	4.54333i	0.189966	−	0.189966i
$573$		0			0
$574$		−	0.282079i		−	0.0117738i
$575$	−16.1407	+	7.48778i	−0.673113	+	0.312262i
$576$		0			0
$577$	5.00919	+	5.00919i	0.208535	+	0.208535i	0.803645	−	0.595109i	$-0.202891\pi$
$577$	5.00919	+	5.00919i	0.208535	+	0.208535i	−0.595109	+	0.803645i	$0.702891\pi$
$578$	−9.93044	−	9.93044i	−0.413052	−	0.413052i
$579$		0			0
$580$	17.3017	−	12.0894i	0.718416	−	0.501984i
$581$		−	1.63088i		−	0.0676605i
$582$		0			0
$583$	−53.0094	+	53.0094i	−2.19543	+	2.19543i
$584$	−9.73636			−0.402893
$585$		0			0
$586$	−3.66652			−0.151462
$587$	9.73220	−	9.73220i	0.401691	−	0.401691i	−0.477138	−	0.878829i	$-0.658326\pi$
$587$	9.73220	−	9.73220i	0.401691	−	0.401691i	0.878829	+	0.477138i	$0.158326\pi$
$588$		0			0
$589$		−	34.1676i		−	1.40785i
$590$	31.8792	+	5.65361i	1.31245	+	0.232756i
$591$		0			0
$592$	−7.51904	−	7.51904i	−0.309031	−	0.309031i
$593$	−3.93343	−	3.93343i	−0.161527	−	0.161527i	0.621716	−	0.783243i	$-0.286436\pi$
$593$	−3.93343	−	3.93343i	−0.161527	−	0.161527i	−0.783243	+	0.621716i	$0.786436\pi$
$594$		0			0
$595$	0.665999	+	0.953146i	0.0273033	+	0.0390752i
$596$		−	0.602445i		−	0.0246771i
$597$		0			0
$598$	−2.51630	+	2.51630i	−0.102899	+	0.102899i
$599$	1.59388			0.0651244			0.0325622	−	0.999470i	$-0.489633\pi$
$599$	1.59388			0.0651244			0.0325622	+	0.999470i	$0.489633\pi$
$600$		0			0
$601$	6.12625			0.249895			0.124948	−	0.992163i	$-0.460124\pi$
$601$	6.12625			0.249895			0.124948	+	0.992163i	$0.460124\pi$
$602$	2.26664	−	2.26664i	0.0923814	−	0.0923814i
$603$		0			0
$604$		−	1.01112i		−	0.0411419i
$605$	38.7857	+	55.5083i	1.57686	+	2.25673i
$606$		0			0
$607$	−1.98025	−	1.98025i	−0.0803761	−	0.0803761i	0.665776	−	0.746152i	$-0.268101\pi$
$607$	−1.98025	−	1.98025i	−0.0803761	−	0.0803761i	−0.746152	+	0.665776i	$0.768101\pi$
$608$	−3.69426	−	3.69426i	−0.149822	−	0.149822i
$609$		0			0
$610$	13.9369	+	2.47163i	0.564288	+	0.100073i
$611$			1.19479i			0.0483359i
$612$		0			0
$613$	−2.52355	+	2.52355i	−0.101925	+	0.101925i	−0.756230	−	0.654305i	$-0.772961\pi$
$613$	−2.52355	+	2.52355i	−0.101925	+	0.101925i	0.654305	+	0.756230i	$0.272961\pi$
$614$	7.72884			0.311911
$615$		0			0
$616$	1.94326			0.0782960
$617$	−21.7246	+	21.7246i	−0.874601	+	0.874601i	−0.992970	−	0.118369i	$-0.962233\pi$
$617$	−21.7246	+	21.7246i	−0.874601	+	0.874601i	0.118369	+	0.992970i	$0.462233\pi$
$618$		0			0
$619$		−	40.5807i		−	1.63108i	−0.578703	−	0.815538i	$-0.696441\pi$
$619$		−	40.5807i		−	1.63108i	0.578703	−	0.815538i	$-0.303559\pi$
$620$	−11.9873	+	8.37599i	−0.481422	+	0.336388i
$621$		0			0
$622$	7.91652	+	7.91652i	0.317423	+	0.317423i
$623$	−2.90825	−	2.90825i	−0.116516	−	0.116516i
$624$		0			0
$625$	−19.0875	−	16.1452i	−0.763501	−	0.645806i
$626$			9.89785i			0.395597i
$627$		0			0
$628$	6.81281	−	6.81281i	0.271861	−	0.271861i
$629$	18.2830			0.728989
$630$		0			0
$631$	−21.0227			−0.836902			−0.418451	−	0.908239i	$-0.637427\pi$
$631$	−21.0227			−0.836902			−0.418451	+	0.908239i	$0.637427\pi$
$632$	−0.512649	+	0.512649i	−0.0203921	+	0.0203921i
$633$		0			0
$634$			23.1553i			0.919615i
$635$	1.69231	−	9.54247i	0.0671571	−	0.378681i
$636$		0			0
$637$	−4.88507	−	4.88507i	−0.193553	−	0.193553i
$638$	42.8859	+	42.8859i	1.69787	+	1.69787i
$639$		0			0
$640$	−0.390462	+	2.20171i	−0.0154344	+	0.0870303i
$641$			6.69454i			0.264418i	0.991222	+	0.132209i	$0.0422071\pi$
$641$			6.69454i			0.264418i	−0.991222	+	0.132209i	$0.957793\pi$
$642$		0			0
$643$	9.44318	−	9.44318i	0.372402	−	0.372402i	−0.495949	−	0.868352i	$-0.665180\pi$
$643$	9.44318	−	9.44318i	0.372402	−	0.372402i	0.868352	+	0.495949i	$0.165180\pi$
$644$	−1.07626			−0.0424107
$645$		0			0
$646$	8.98280			0.353424
$647$	−25.1807	+	25.1807i	−0.989954	+	0.989954i	−0.999950	−	0.00999576i	$-0.996818\pi$
$647$	−25.1807	+	25.1807i	−0.989954	+	0.989954i	0.00999576	+	0.999950i	$0.496818\pi$
$648$		0			0
$649$			93.0329i			3.65186i
$650$	−4.69508	−	1.71937i	−0.184156	−	0.0674392i
$651$		0			0
$652$	−4.52097	−	4.52097i	−0.177055	−	0.177055i
$653$	5.04713	+	5.04713i	0.197510	+	0.197510i	0.798932	−	0.601422i	$-0.205399\pi$
$653$	5.04713	+	5.04713i	0.197510	+	0.197510i	−0.601422	+	0.798932i	$0.705399\pi$
$654$		0			0
$655$	−17.1075	+	11.9536i	−0.668445	+	0.467068i
$656$			0.932674i			0.0364148i
$657$		0			0
$658$	−0.255515	+	0.255515i	−0.00996100	+	0.00996100i
$659$	−9.61632			−0.374599			−0.187299	−	0.982303i	$-0.559973\pi$
$659$	−9.61632			−0.374599			−0.187299	+	0.982303i	$0.559973\pi$
$660$		0			0
$661$	−40.6349			−1.58051			−0.790257	−	0.612775i	$-0.790053\pi$
$661$	−40.6349			−1.58051			−0.790257	+	0.612775i	$0.790053\pi$
$662$	11.9800	−	11.9800i	0.465617	−	0.465617i
$663$		0			0
$664$			5.39240i			0.209266i
$665$	3.47892	+	0.616967i	0.134907	+	0.0239250i
$666$		0			0
$667$	−23.7521	−	23.7521i	−0.919687	−	0.919687i
$668$	6.70971	+	6.70971i	0.259606	+	0.259606i
$669$		0			0
$670$	8.36206	+	11.9674i	0.323054	+	0.462340i
$671$			40.6719i			1.57012i
$672$		0			0
$673$	29.7315	−	29.7315i	1.14607	−	1.14607i	0.158746	−	0.987319i	$-0.449255\pi$
$673$	29.7315	−	29.7315i	1.14607	−	1.14607i	0.987319	−	0.158746i	$-0.0507452\pi$
$674$	13.4071			0.516420
$675$		0			0
$676$	−1.00000			−0.0384615
$677$	18.8512	−	18.8512i	0.724512	−	0.724512i	−0.245009	−	0.969521i	$-0.578791\pi$
$677$	18.8512	−	18.8512i	0.724512	−	0.724512i	0.969521	+	0.245009i	$0.0787909\pi$
$678$		0			0
$679$		−	4.38549i		−	0.168300i
$680$	−2.20208	−	3.15151i	−0.0844459	−	0.120855i
$681$		0			0
$682$	−29.7130	−	29.7130i	−1.13777	−	1.13777i
$683$	18.9300	+	18.9300i	0.724334	+	0.724334i	0.969485	−	0.245151i	$-0.0788374\pi$
$683$	18.9300	+	18.9300i	0.724334	+	0.724334i	−0.245151	+	0.969485i	$0.578837\pi$
$684$		0			0
$685$	−1.00889	−	0.178921i	−0.0385477	−	0.00683622i
$686$		−	4.20651i		−	0.160605i
$687$		0			0
$688$	−7.49448	+	7.49448i	−0.285724	+	0.285724i
$689$	11.6675			0.444497
$690$		0			0
$691$	19.4444			0.739702			0.369851	−	0.929091i	$-0.379409\pi$
$691$	19.4444			0.739702			0.369851	+	0.929091i	$0.379409\pi$
$692$	3.89442	−	3.89442i	0.148044	−	0.148044i
$693$		0			0
$694$			17.5723i			0.667034i
$695$	−13.2436	+	9.25379i	−0.502357	+	0.351016i
$696$		0			0
$697$	−1.13392	−	1.13392i	−0.0429505	−	0.0429505i
$698$	−6.04267	−	6.04267i	−0.228718	−	0.228718i
$699$		0			0
$700$	−0.636380	−	1.37178i	−0.0240529	−	0.0518485i
$701$			12.2436i			0.462434i	0.972902	+	0.231217i	$0.0742708\pi$
$701$			12.2436i			0.462434i	−0.972902	+	0.231217i	$0.925729\pi$
$702$		0			0
$703$	39.2830	−	39.2830i	1.48159	−	1.48159i
$704$	−6.42524			−0.242160
$705$		0			0
$706$	18.0141			0.677969
$707$	0.431633	−	0.431633i	0.0162332	−	0.0162332i
$708$		0			0
$709$			6.40891i			0.240692i	0.992732	+	0.120346i	$0.0384003\pi$
$709$			6.40891i			0.240692i	−0.992732	+	0.120346i	$0.961600\pi$
$710$	4.50691	−	25.4133i	0.169141	−	0.953743i
$711$		0			0
$712$	9.61591	+	9.61591i	0.360371	+	0.360371i
$713$	16.4564	+	16.4564i	0.616297	+	0.616297i
$714$		0			0
$715$	2.50881	−	14.1465i	0.0938242	−	0.529050i
$716$			21.7807i			0.813984i
$717$		0			0
$718$	−5.29348	+	5.29348i	−0.197551	+	0.197551i
$719$	−41.4906			−1.54734			−0.773670	−	0.633589i	$-0.781581\pi$
$719$	−41.4906			−1.54734			−0.773670	+	0.633589i	$0.781581\pi$
$720$		0			0
$721$	5.22020			0.194410
$722$	5.86554	−	5.86554i	0.218293	−	0.218293i
$723$		0			0
$724$		−	1.89023i		−	0.0702500i
$725$	16.2297	−	44.3183i	0.602755	−	1.64594i
$726$		0			0
$727$	−17.4250	−	17.4250i	−0.646258	−	0.646258i	0.305829	−	0.952086i	$-0.401066\pi$
$727$	−17.4250	−	17.4250i	−0.646258	−	0.646258i	−0.952086	+	0.305829i	$0.901066\pi$
$728$	−0.213858	−	0.213858i	−0.00792611	−	0.00792611i
$729$		0			0
$730$	−17.8462	+	12.4698i	−0.660518	+	0.461529i
$731$		−	18.2233i		−	0.674011i
$732$		0			0
$733$	−0.823936	+	0.823936i	−0.0304328	+	0.0304328i	−0.722159	−	0.691727i	$-0.756850\pi$
$733$	−0.823936	+	0.823936i	−0.0304328	+	0.0304328i	0.691727	+	0.722159i	$0.256850\pi$
$734$	−18.6051			−0.686727
$735$		0			0
$736$	3.55858			0.131171
$737$	−29.6636	+	29.6636i	−1.09267	+	1.09267i
$738$		0			0
$739$		−	15.8752i		−	0.583978i	−0.956422	−	0.291989i	$-0.905683\pi$
$739$		−	15.8752i		−	0.583978i	0.956422	−	0.291989i	$-0.0943171\pi$
$740$	−23.4120	−	4.15199i	−0.860641	−	0.152630i
$741$		0			0
$742$	2.49520	+	2.49520i	0.0916015	+	0.0916015i
$743$	−13.2941	−	13.2941i	−0.487715	−	0.487715i	0.419870	−	0.907584i	$-0.362076\pi$
$743$	−13.2941	−	13.2941i	−0.487715	−	0.487715i	−0.907584	+	0.419870i	$0.862076\pi$
$744$		0			0
$745$	−0.771580	−	1.10425i	−0.0282685	−	0.0404565i
$746$		−	31.6368i		−	1.15830i
$747$		0			0
$748$	7.81166	−	7.81166i	0.285623	−	0.285623i
$749$	−1.13879			−0.0416104
$750$		0			0
$751$	−29.9007			−1.09109			−0.545546	−	0.838081i	$-0.683678\pi$
$751$	−29.9007			−1.09109			−0.545546	+	0.838081i	$0.683678\pi$
$752$	0.844841	−	0.844841i	0.0308082	−	0.0308082i
$753$		0			0
$754$		−	9.43932i		−	0.343760i
$755$	−1.29499	−	1.85333i	−0.0471295	−	0.0674495i
$756$		0			0
$757$	16.9651	+	16.9651i	0.616607	+	0.616607i	0.944659	−	0.328053i	$-0.106392\pi$
$757$	16.9651	+	16.9651i	0.616607	+	0.616607i	−0.328053	+	0.944659i	$0.606392\pi$
$758$	−6.66316	−	6.66316i	−0.242017	−	0.242017i
$759$		0			0
$760$	−11.5028	−	2.03996i	−0.417250	−	0.0739970i
$761$			26.0758i			0.945247i	0.881265	+	0.472623i	$0.156693\pi$
$761$			26.0758i			0.945247i	−0.881265	+	0.472623i	$0.843307\pi$
$762$		0			0
$763$	−2.26891	+	2.26891i	−0.0821399	+	0.0821399i
$764$	16.7639			0.606497
$765$		0			0
$766$	−25.7117			−0.929001
$767$	10.2384	−	10.2384i	0.369687	−	0.369687i
$768$		0			0
$769$			11.9343i			0.430364i	0.976574	+	0.215182i	$0.0690344\pi$
$769$			11.9343i			0.430364i	−0.976574	+	0.215182i	$0.930966\pi$
$770$	3.56188	−	2.48882i	0.128361	−	0.0896909i
$771$		0			0
$772$	−6.10616	−	6.10616i	−0.219766	−	0.219766i
$773$	−3.95240	−	3.95240i	−0.142158	−	0.142158i	0.632446	−	0.774604i	$-0.282051\pi$
$773$	−3.95240	−	3.95240i	−0.142158	−	0.142158i	−0.774604	+	0.632446i	$0.782051\pi$
$774$		0			0
$775$	−11.2445	+	30.7054i	−0.403916	+	1.10297i
$776$			14.5003i			0.520530i
$777$		0			0
$778$	9.11048	−	9.11048i	0.326627	−	0.326627i
$779$	−4.87273			−0.174584
$780$		0			0
$781$	74.1633			2.65377
$782$	−4.32645	+	4.32645i	−0.154714	+	0.154714i
$783$		0			0
$784$			6.90853i			0.246733i
$785$	3.76201	−	21.2130i	0.134272	−	0.757124i
$786$		0			0
$787$	11.9500	+	11.9500i	0.425973	+	0.425973i	0.887254	−	0.461281i	$-0.152610\pi$
$787$	11.9500	+	11.9500i	0.425973	+	0.425973i	−0.461281	+	0.887254i	$0.652610\pi$
$788$	7.17231	+	7.17231i	0.255503	+	0.255503i
$789$		0			0
$790$	−0.283083	+	1.59623i	−0.0100716	+	0.0567914i
$791$			1.97926i			0.0703745i
$792$		0			0
$793$	4.47600	−	4.47600i	0.158948	−	0.158948i
$794$	0.523831			0.0185900
$795$		0			0
$796$	16.8682			0.597876
$797$	−9.39074	+	9.39074i	−0.332637	+	0.332637i	−0.853587	−	0.520950i	$-0.825578\pi$
$797$	−9.39074	+	9.39074i	−0.332637	+	0.332637i	0.520950	+	0.853587i	$0.325578\pi$
$798$		0			0
$799$			2.05428i			0.0726751i
$800$	2.10414	+	4.53570i	0.0743927	+	0.160361i
$801$		0			0
$802$	−12.0223	−	12.0223i	−0.424523	−	0.424523i
$803$	−44.2355	−	44.2355i	−1.56104	−	1.56104i
$804$		0			0
$805$	−1.97273	+	1.37842i	−0.0695296	+	0.0485830i
$806$			6.53992i			0.230359i
$807$		0			0
$808$	−1.42716	+	1.42716i	−0.0502074	+	0.0502074i
$809$	−27.3703			−0.962288			−0.481144	−	0.876642i	$-0.659779\pi$
$809$	−27.3703			−0.962288			−0.481144	+	0.876642i	$0.659779\pi$
$810$		0			0
$811$	32.8419			1.15323			0.576617	−	0.817014i	$-0.304372\pi$
$811$	32.8419			1.15323			0.576617	+	0.817014i	$0.304372\pi$
$812$	2.01868	−	2.01868i	0.0708416	−	0.0708416i
$813$		0			0
$814$		−	68.3229i		−	2.39472i
$815$	−14.0769	−	2.49646i	−0.493093	−	0.0874473i
$816$		0			0
$817$	−39.1547	−	39.1547i	−1.36985	−	1.36985i
$818$	4.36160	+	4.36160i	0.152500	+	0.152500i
$819$		0			0
$820$	1.19452	+	1.70954i	0.0417145	+	0.0596997i
$821$		−	32.8399i		−	1.14612i	−0.819514	−	0.573060i	$-0.805756\pi$
$821$		−	32.8399i		−	1.14612i	0.819514	−	0.573060i	$-0.194244\pi$
$822$		0			0
$823$	9.23702	−	9.23702i	0.321982	−	0.321982i	−0.527545	−	0.849527i	$-0.676887\pi$
$823$	9.23702	−	9.23702i	0.321982	−	0.321982i	0.849527	+	0.527545i	$0.176887\pi$
$824$	−17.2602			−0.601288
$825$		0			0
$826$	4.37914			0.152370
$827$	−4.74762	+	4.74762i	−0.165091	+	0.165091i	−0.784818	−	0.619727i	$-0.787243\pi$
$827$	−4.74762	+	4.74762i	−0.165091	+	0.165091i	0.619727	+	0.784818i	$0.287243\pi$
$828$		0			0
$829$		−	11.2448i		−	0.390550i	−0.980749	−	0.195275i	$-0.937440\pi$
$829$		−	11.2448i		−	0.390550i	0.980749	−	0.195275i	$-0.0625599\pi$
$830$	6.90631	+	9.88397i	0.239721	+	0.343078i
$831$		0			0
$832$	0.707107	+	0.707107i	0.0245145	+	0.0245145i
$833$	−8.39924	−	8.39924i	−0.291016	−	0.291016i
$834$		0			0
$835$	20.8920	+	3.70508i	0.722996	+	0.128219i
$836$		−	33.5685i		−	1.16099i
$837$		0			0
$838$	1.23024	−	1.23024i	0.0424979	−	0.0424979i
$839$	40.3821			1.39414			0.697072	−	0.717001i	$-0.254486\pi$
$839$	40.3821			1.39414			0.697072	+	0.717001i	$0.254486\pi$
$840$		0			0
$841$	60.1007			2.07244
$842$	7.18916	−	7.18916i	0.247755	−	0.247755i
$843$		0			0
$844$			3.20670i			0.110379i
$845$	−1.83294	+	1.28075i	−0.0630552	+	0.0440591i
$846$		0			0
$847$	6.47641	+	6.47641i	0.222532	+	0.222532i
$848$	−8.25019	−	8.25019i	−0.283313	−	0.283313i
$849$		0			0
$850$	−8.07258	−	2.95623i	−0.276887	−	0.101398i
$851$			37.8403i			1.29715i
$852$		0			0
$853$	−12.6515	+	12.6515i	−0.433181	+	0.433181i	−0.889709	−	0.456528i	$-0.849093\pi$
$853$	−12.6515	+	12.6515i	−0.433181	+	0.433181i	0.456528	+	0.889709i	$0.349093\pi$
$854$	1.91446			0.0655115
$855$		0			0
$856$	3.76532			0.128696
$857$	17.3430	−	17.3430i	0.592425	−	0.592425i	−0.345861	−	0.938286i	$-0.612413\pi$
$857$	17.3430	−	17.3430i	0.592425	−	0.592425i	0.938286	+	0.345861i	$0.112413\pi$
$858$		0			0
$859$		−	10.6281i		−	0.362626i	−0.983425	−	0.181313i	$-0.941965\pi$
$859$		−	10.6281i		−	0.362626i	0.983425	−	0.181313i	$-0.0580347\pi$
$860$	−4.13843	+	23.3355i	−0.141119	+	0.795734i
$861$		0			0
$862$	9.74673	+	9.74673i	0.331975	+	0.331975i
$863$	24.4886	+	24.4886i	0.833601	+	0.833601i	0.988007	−	0.154406i	$-0.0493464\pi$
$863$	24.4886	+	24.4886i	0.833601	+	0.833601i	−0.154406	+	0.988007i	$0.549346\pi$
$864$		0			0
$865$	2.15048	−	12.1260i	0.0731187	−	0.412297i
$866$		−	34.4744i		−	1.17149i
$867$		0			0
$868$	−1.39862	+	1.39862i	−0.0474721	+	0.0474721i
$869$	−4.65827			−0.158021
$870$		0			0
$871$	6.52904			0.221228
$872$	7.50197	−	7.50197i	0.254049	−	0.254049i
$873$		0			0
$874$			18.5917i			0.628875i
$875$	−2.92336	−	1.69936i	−0.0988275	−	0.0574488i
$876$		0			0
$877$	−24.1224	−	24.1224i	−0.814556	−	0.814556i	0.170757	−	0.985313i	$-0.445379\pi$
$877$	−24.1224	−	24.1224i	−0.814556	−	0.814556i	−0.985313	+	0.170757i	$0.945379\pi$
$878$	8.67235	+	8.67235i	0.292678	+	0.292678i
$879$		0			0
$880$	−11.7771	+	8.22911i	−0.397006	+	0.277403i
$881$			29.5233i			0.994665i	0.867560	+	0.497333i	$0.165687\pi$
$881$			29.5233i			0.994665i	−0.867560	+	0.497333i	$0.834313\pi$
$882$		0			0
$883$	−1.84975	+	1.84975i	−0.0622490	+	0.0622490i	−0.737546	−	0.675297i	$-0.764015\pi$
$883$	−1.84975	+	1.84975i	−0.0622490	+	0.0622490i	0.675297	+	0.737546i	$0.264015\pi$
$884$	−1.71937			−0.0578287
$885$		0			0
$886$	1.03878			0.0348985
$887$	−15.0373	+	15.0373i	−0.504903	+	0.504903i	−0.912957	−	0.408055i	$-0.866207\pi$
$887$	−15.0373	+	15.0373i	−0.504903	+	0.504903i	0.408055	+	0.912957i	$0.366207\pi$
$888$		0			0
$889$		−	1.31081i		−	0.0439633i
$890$	29.9410	+	5.30987i	1.00362	+	0.177987i
$891$		0			0
$892$	7.45886	+	7.45886i	0.249741	+	0.249741i
$893$	4.41385	+	4.41385i	0.147704	+	0.147704i
$894$		0			0
$895$	27.8956	+	39.9229i	0.932448	+	1.33447i
$896$			0.302441i			0.0101039i
$897$		0			0
$898$	6.50037	−	6.50037i	0.216920	−	0.216920i
$899$	−61.7324			−2.05889
$900$		0			0
$901$	20.0608			0.668322
$902$	−4.23745	+	4.23745i	−0.141092	+	0.141092i
$903$		0			0
$904$		−	6.54429i		−	0.217660i
$905$	−2.42091	−	3.46469i	−0.0804739	−	0.115170i
$906$		0			0
$907$	20.0091	+	20.0091i	0.664391	+	0.664391i	0.956412	−	0.292021i	$-0.0943278\pi$
$907$	20.0091	+	20.0091i	0.664391	+	0.664391i	−0.292021	+	0.956412i	$0.594328\pi$
$908$	−17.6094	−	17.6094i	−0.584388	−	0.584388i
$909$		0			0
$910$	−0.665889	−	0.118092i	−0.0220740	−	0.00391470i
$911$		−	17.8678i		−	0.591987i	−0.955190	−	0.295993i	$-0.904349\pi$
$911$		−	17.8678i		−	0.591987i	0.955190	−	0.295993i	$-0.0956507\pi$
$912$		0			0
$913$	−24.4995	+	24.4995i	−0.810814	+	0.810814i
$914$	−34.5845			−1.14395
$915$		0			0
$916$	9.79092			0.323501
$917$	−1.99601	+	1.99601i	−0.0659141	+	0.0659141i
$918$		0			0
$919$			8.82184i			0.291006i	0.989358	+	0.145503i	$0.0464800\pi$
$919$			8.82184i			0.291006i	−0.989358	+	0.145503i	$0.953520\pi$
$920$	6.52269	−	4.55765i	0.215047	−	0.150261i
$921$		0			0
$922$	−13.3120	−	13.3120i	−0.438407	−	0.438407i
$923$	−8.16178	−	8.16178i	−0.268648	−	0.268648i
$924$		0			0
$925$	−48.2305	+	22.3745i	−1.58581	+	0.735668i
$926$			33.0059i			1.08464i
$927$		0			0
$928$	−6.67460	+	6.67460i	−0.219105	+	0.219105i
$929$	−3.87775			−0.127225			−0.0636125	−	0.997975i	$-0.520262\pi$
$929$	−3.87775			−0.127225			−0.0636125	+	0.997975i	$0.520262\pi$
$930$		0			0
$931$	−36.0934			−1.18291
$932$	−17.7966	+	17.7966i	−0.582947	+	0.582947i
$933$		0			0
$934$		−	25.9390i		−	0.848750i
$935$	4.31357	−	24.3231i	0.141069	−	0.795451i
$936$		0			0
$937$	−28.3716	−	28.3716i	−0.926861	−	0.926861i	0.0706413	−	0.997502i	$-0.477495\pi$
$937$	−28.3716	−	28.3716i	−0.926861	−	0.926861i	−0.997502	+	0.0706413i	$0.977495\pi$
$938$	1.39629	+	1.39629i	0.0455905	+	0.0455905i
$939$		0			0
$940$	0.466518	−	2.63057i	0.0152161	−	0.0857999i
$941$		−	39.5974i		−	1.29084i	−0.763829	−	0.645419i	$-0.776683\pi$
$941$		−	39.5974i		−	1.29084i	0.763829	−	0.645419i	$-0.223317\pi$
$942$		0			0
$943$	2.34689	−	2.34689i	0.0764252	−	0.0764252i
$944$	−14.4793			−0.471261
$945$		0			0
$946$	−68.0998			−2.21412
$947$	12.8598	−	12.8598i	0.417888	−	0.417888i	−0.466587	−	0.884475i	$-0.654517\pi$
$947$	12.8598	−	12.8598i	0.417888	−	0.417888i	0.884475	+	0.466587i	$0.154517\pi$
$948$		0			0
$949$			9.73636i			0.316056i
$950$	−23.6966	+	10.9930i	−0.768821	+	0.356661i
$951$		0			0
$952$	−0.367701	−	0.367701i	−0.0119173	−	0.0119173i
$953$	3.40154	+	3.40154i	0.110187	+	0.110187i	0.760051	−	0.649864i	$-0.225174\pi$
$953$	3.40154	+	3.40154i	0.110187	+	0.110187i	−0.649864	+	0.760051i	$0.725174\pi$
$954$		0			0
$955$	30.7273	−	21.4704i	0.994313	−	0.694764i
$956$			3.84377i			0.124317i
$957$		0			0
$958$	−7.71938	+	7.71938i	−0.249402	+	0.249402i
$959$	−0.138587			−0.00447522
$960$		0			0
$961$	11.7706			0.379695
$962$	−7.51904	+	7.51904i	−0.242424	+	0.242424i
$963$		0			0
$964$			11.1993i			0.360706i
$965$	−19.0127	−	3.37180i	−0.612041	−	0.108542i
$966$		0			0
$967$	−17.8300	−	17.8300i	−0.573374	−	0.573374i	0.359696	−	0.933070i	$-0.382881\pi$
$967$	−17.8300	−	17.8300i	−0.573374	−	0.573374i	−0.933070	+	0.359696i	$0.882881\pi$
$968$	−21.4138	−	21.4138i	−0.688265	−	0.688265i
$969$		0			0
$970$	18.5712	+	26.5782i	0.596286	+	0.853376i
$971$		−	59.6120i		−	1.91304i	−0.291666	−	0.956520i	$-0.594210\pi$
$971$		−	59.6120i		−	1.91304i	0.291666	−	0.956520i	$-0.405790\pi$
$972$		0			0
$973$	−1.54519	+	1.54519i	−0.0495365	+	0.0495365i
$974$	−11.0096			−0.352771
$975$		0			0
$976$	−6.33002			−0.202619
$977$	1.28556	−	1.28556i	0.0411288	−	0.0411288i	−0.686243	−	0.727372i	$-0.740741\pi$
$977$	1.28556	−	1.28556i	0.0411288	−	0.0411288i	0.727372	+	0.686243i	$0.240741\pi$
$978$		0			0
$979$			87.3764i			2.79256i
$980$	8.84808	+	12.6629i	0.282642	+	0.404503i
$981$		0			0
$982$	−2.69453	−	2.69453i	−0.0859860	−	0.0859860i
$983$	10.8377	+	10.8377i	0.345670	+	0.345670i	0.858494	−	0.512824i	$-0.171401\pi$
$983$	10.8377	+	10.8377i	0.345670	+	0.345670i	−0.512824	+	0.858494i	$0.671401\pi$
$984$		0			0
$985$	22.3324	+	3.96052i	0.711568	+	0.126193i
$986$		−	16.2297i		−	0.516858i
$987$		0			0
$988$	−3.69426	+	3.69426i	−0.117530	+	0.117530i
$989$	37.7167			1.19932
$990$		0			0
$991$	−60.8006			−1.93139			−0.965697	−	0.259671i	$-0.916386\pi$
$991$	−60.8006			−1.93139			−0.965697	+	0.259671i	$0.916386\pi$
$992$	4.62442	−	4.62442i	0.146826	−	0.146826i
$993$		0			0
$994$		−	3.49093i		−	0.110726i
$995$	30.9184	−	21.6039i	0.980180	−	0.684889i
$996$		0			0
$997$	−30.8315	−	30.8315i	−0.976443	−	0.976443i	0.0232857	−	0.999729i	$-0.492587\pi$
$997$	−30.8315	−	30.8315i	−0.976443	−	0.976443i	−0.999729	+	0.0232857i	$0.992587\pi$
$998$	14.2880	+	14.2880i	0.452279	+	0.452279i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.o.b.287.2	yes	12
3.2	odd	2		1170.2.o.d.287.5	yes	12
5.3	odd	4		1170.2.o.d.53.5	yes	12
15.8	even	4	inner	1170.2.o.b.53.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.o.b.53.2	✓	12	15.8	even	4	inner
1170.2.o.b.287.2	yes	12	1.1	even	1	trivial
1170.2.o.d.53.5	yes	12	5.3	odd	4
1170.2.o.d.287.5	yes	12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.28075 - 1.83294i) q^{5} +(-0.213858 - 0.213858i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-1.28075 - 1.83294i) q^{5} +(-0.213858 - 0.213858i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.20171 + 0.390462i) q^{10} +6.42524i q^{11} +(0.707107 - 0.707107i) q^{13} +0.302441 q^{14} -1.00000 q^{16} +(1.21578 - 1.21578i) q^{17} -5.22447i q^{19} +(-1.83294 + 1.28075i) q^{20} +(-4.54333 - 4.54333i) q^{22} +(2.51630 + 2.51630i) q^{23} +(-1.71937 + 4.69508i) q^{25} +1.00000i q^{26} +(-0.213858 + 0.213858i) q^{28} -9.43932 q^{29} +6.53992 q^{31} +(0.707107 - 0.707107i) q^{32} +1.71937i q^{34} +(-0.118092 + 0.665889i) q^{35} +(7.51904 + 7.51904i) q^{37} +(3.69426 + 3.69426i) q^{38} +(0.390462 - 2.20171i) q^{40} -0.932674i q^{41} +(7.49448 - 7.49448i) q^{43} +6.42524 q^{44} -3.55858 q^{46} +(-0.844841 + 0.844841i) q^{47} -6.90853i q^{49} +(-2.10414 - 4.53570i) q^{50} +(-0.707107 - 0.707107i) q^{52} +(8.25019 + 8.25019i) q^{53} +(11.7771 - 8.22911i) q^{55} -0.302441i q^{56} +(6.67460 - 6.67460i) q^{58} +14.4793 q^{59} +6.33002 q^{61} +(-4.62442 + 4.62442i) q^{62} +1.00000i q^{64} +(-2.20171 - 0.390462i) q^{65} +(4.61673 + 4.61673i) q^{67} +(-1.21578 - 1.21578i) q^{68} +(-0.387351 - 0.554358i) q^{70} -11.5425i q^{71} +(-6.88465 + 6.88465i) q^{73} -10.6335 q^{74} -5.22447 q^{76} +(1.37409 - 1.37409i) q^{77} +0.724996i q^{79} +(1.28075 + 1.83294i) q^{80} +(0.659500 + 0.659500i) q^{82} +(3.81300 + 3.81300i) q^{83} +(-3.78556 - 0.671348i) q^{85} +10.5988i q^{86} +(-4.54333 + 4.54333i) q^{88} +13.5989 q^{89} -0.302441 q^{91} +(2.51630 - 2.51630i) q^{92} -1.19479i q^{94} +(-9.57617 + 6.69123i) q^{95} +(10.2533 + 10.2533i) q^{97} +(4.88507 + 4.88507i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{5} - 4 q^{7}+O(q^{10}) \) 12 * q - 4 * q^5 - 4 * q^7	\( 12 q - 4 q^{5} - 4 q^{7} + 8 q^{10} - 8 q^{14} - 12 q^{16} - 8 q^{17} - 4 q^{20} - 4 q^{22} + 20 q^{23} + 8 q^{25} - 4 q^{28} + 32 q^{29} + 16 q^{31} - 28 q^{35} + 32 q^{38} + 4 q^{40} + 8 q^{43} - 16 q^{47} - 16 q^{50} + 44 q^{53} - 4 q^{55} + 4 q^{58} + 16 q^{59} + 16 q^{61} + 4 q^{62} - 8 q^{65} + 28 q^{67} + 8 q^{68} - 16 q^{70} + 24 q^{73} - 32 q^{74} + 16 q^{76} + 40 q^{77} + 4 q^{80} + 8 q^{82} + 16 q^{83} - 20 q^{85} - 4 q^{88} + 8 q^{91} + 20 q^{92} - 76 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) \) 12 * q - 4 * q^5 - 4 * q^7 + 8 * q^10 - 8 * q^14 - 12 * q^16 - 8 * q^17 - 4 * q^20 - 4 * q^22 + 20 * q^23 + 8 * q^25 - 4 * q^28 + 32 * q^29 + 16 * q^31 - 28 * q^35 + 32 * q^38 + 4 * q^40 + 8 * q^43 - 16 * q^47 - 16 * q^50 + 44 * q^53 - 4 * q^55 + 4 * q^58 + 16 * q^59 + 16 * q^61 + 4 * q^62 - 8 * q^65 + 28 * q^67 + 8 * q^68 - 16 * q^70 + 24 * q^73 - 32 * q^74 + 16 * q^76 + 40 * q^77 + 4 * q^80 + 8 * q^82 + 16 * q^83 - 20 * q^85 - 4 * q^88 + 8 * q^91 + 20 * q^92 - 76 * q^95 - 8 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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