LMFDB - Embedded newform 210.2.m.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(13,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("210.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.m (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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1698758656.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 $ x^8 + 18x^6 + 97x^4 + 176*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.3
Root			$-0.692297i$ of defining polynomial
Character	$\chi$	$=$	210.13
Dual form			210.2.m.a.97.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.19663 - 1.88893i) q^{5} -1.00000i q^{6} +(-2.59604 - 0.510472i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.19663 - 1.88893i) q^{5} -1.00000i q^{6} +(-2.59604 - 0.510472i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(-2.18183 - 0.489528i) q^{10} +4.79881 q^{11} +(-0.707107 - 0.707107i) q^{12} +(-0.585786 + 0.585786i) q^{13} +(-2.19663 + 1.47472i) q^{14} +(-2.18183 - 0.489528i) q^{15} -1.00000 q^{16} +(4.10651 + 4.10651i) q^{17} +(-0.707107 - 0.707107i) q^{18} +2.36365 q^{19} +(-1.88893 + 1.19663i) q^{20} +(-2.19663 + 1.47472i) q^{21} +(3.39327 - 3.39327i) q^{22} +(2.97906 + 2.97906i) q^{23} -1.00000 q^{24} +(-2.13613 + 4.52072i) q^{25} +0.828427i q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.510472 + 2.59604i) q^{28} -9.94900i q^{29} +(-1.88893 + 1.19663i) q^{30} -3.02094i q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.39327 - 3.39327i) q^{33} +5.80748 q^{34} +(2.14226 + 5.51459i) q^{35} -1.00000 q^{36} +(-6.10651 + 6.10651i) q^{37} +(1.67135 - 1.67135i) q^{38} +0.828427i q^{39} +(-0.489528 + 2.18183i) q^{40} +10.9996i q^{41} +(-0.510472 + 2.59604i) q^{42} +(-5.74825 - 5.74825i) q^{43} -4.79881i q^{44} +(-1.88893 + 1.19663i) q^{45} +4.21302 q^{46} +(-0.363651 - 0.363651i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(6.47884 + 2.65041i) q^{49} +(1.68616 + 4.70711i) q^{50} +5.80748 q^{51} +(0.585786 + 0.585786i) q^{52} +(2.36365 + 2.36365i) q^{53} -1.00000 q^{54} +(-5.74242 - 9.06462i) q^{55} +(1.47472 + 2.19663i) q^{56} +(1.67135 - 1.67135i) q^{57} +(-7.03500 - 7.03500i) q^{58} +2.07912 q^{59} +(-0.489528 + 2.18183i) q^{60} +5.55573i q^{61} +(-2.13613 - 2.13613i) q^{62} +(-0.510472 + 2.59604i) q^{63} +1.00000i q^{64} +(1.80748 + 0.405538i) q^{65} -4.79881i q^{66} +(-0.979056 + 0.979056i) q^{67} +(4.10651 - 4.10651i) q^{68} +4.21302 q^{69} +(5.41421 + 2.38459i) q^{70} +5.25132 q^{71} +(-0.707107 + 0.707107i) q^{72} +(-6.11519 + 6.11519i) q^{73} +8.63591i q^{74} +(1.68616 + 4.70711i) q^{75} -2.36365i q^{76} +(-12.4579 - 2.44966i) q^{77} +(0.585786 + 0.585786i) q^{78} -5.10069i q^{79} +(1.19663 + 1.88893i) q^{80} -1.00000 q^{81} +(7.77786 + 7.77786i) q^{82} +(3.22170 - 3.22170i) q^{83} +(1.47472 + 2.19663i) q^{84} +(2.84293 - 12.6709i) q^{85} -8.12925 q^{86} +(-7.03500 - 7.03500i) q^{87} +(-3.39327 - 3.39327i) q^{88} -11.8989 q^{89} +(-0.489528 + 2.18183i) q^{90} +(1.81975 - 1.22170i) q^{91} +(2.97906 - 2.97906i) q^{92} +(-2.13613 - 2.13613i) q^{93} -0.514280 q^{94} +(-2.82843 - 4.46478i) q^{95} +1.00000i q^{96} +(-8.05595 - 8.05595i) q^{97} +(6.45535 - 2.70711i) q^{98} -4.79881i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^7	$ 8 q + 4 q^{7} - 4 q^{10} + 8 q^{11} - 16 q^{13} - 8 q^{14} - 4 q^{15} - 8 q^{16} + 12 q^{17} - 8 q^{19} + 4 q^{20} - 8 q^{21} + 8 q^{22} + 16 q^{23} - 8 q^{24} - 4 q^{25} - 8 q^{28} + 4 q^{30} + 8 q^{33} + 16 q^{34} + 8 q^{35} - 8 q^{36} - 28 q^{37} - 4 q^{38} - 8 q^{42} + 4 q^{45} - 8 q^{46} + 24 q^{47} + 4 q^{49} + 16 q^{51} + 16 q^{52} - 8 q^{53} - 8 q^{54} + 28 q^{55} + 4 q^{56} - 4 q^{57} - 12 q^{58} + 8 q^{59} - 4 q^{62} - 8 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 32 q^{70} + 8 q^{71} - 28 q^{73} - 44 q^{77} + 16 q^{78} - 8 q^{81} + 24 q^{82} - 16 q^{83} + 4 q^{84} + 28 q^{85} + 8 q^{86} - 12 q^{87} - 8 q^{88} - 64 q^{89} - 8 q^{91} + 16 q^{92} - 4 q^{93} + 8 q^{94} - 28 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 - 4 * q^10 + 8 * q^11 - 16 * q^13 - 8 * q^14 - 4 * q^15 - 8 * q^16 + 12 * q^17 - 8 * q^19 + 4 * q^20 - 8 * q^21 + 8 * q^22 + 16 * q^23 - 8 * q^24 - 4 * q^25 - 8 * q^28 + 4 * q^30 + 8 * q^33 + 16 * q^34 + 8 * q^35 - 8 * q^36 - 28 * q^37 - 4 * q^38 - 8 * q^42 + 4 * q^45 - 8 * q^46 + 24 * q^47 + 4 * q^49 + 16 * q^51 + 16 * q^52 - 8 * q^53 - 8 * q^54 + 28 * q^55 + 4 * q^56 - 4 * q^57 - 12 * q^58 + 8 * q^59 - 4 * q^62 - 8 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 32 * q^70 + 8 * q^71 - 28 * q^73 - 44 * q^77 + 16 * q^78 - 8 * q^81 + 24 * q^82 - 16 * q^83 + 4 * q^84 + 28 * q^85 + 8 * q^86 - 12 * q^87 - 8 * q^88 - 64 * q^89 - 8 * q^91 + 16 * q^92 - 4 * q^93 + 8 * q^94 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	−1.19663	−	1.88893i	−0.535151	−	0.844756i
$5$	−1.19663	−	1.88893i	−0.535151	−	0.844756i
$6$		−	1.00000i		−	0.408248i
$7$	−2.59604	−	0.510472i	−0.981211	−	0.192940i
$7$	−2.59604	−	0.510472i	−0.981211	−	0.192940i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	−2.18183	−	0.489528i	−0.689954	−	0.154802i
$11$	4.79881			1.44690			0.723448	−	0.690379i	$-0.242556\pi$
$11$	4.79881			1.44690			0.723448	+	0.690379i	$0.242556\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	−0.585786	+	0.585786i	−0.162468	+	0.162468i	−0.783659	−	0.621191i	$-0.786649\pi$
$13$	−0.585786	+	0.585786i	−0.162468	+	0.162468i	0.621191	+	0.783659i	$0.286649\pi$
$14$	−2.19663	+	1.47472i	−0.587075	+	0.394135i
$15$	−2.18183	−	0.489528i	−0.563345	−	0.126396i
$16$	−1.00000			−0.250000
$17$	4.10651	+	4.10651i	0.995975	+	0.995975i	0.999992	−	0.00401675i	$-0.00127858\pi$
$17$	4.10651	+	4.10651i	0.995975	+	0.995975i	−0.00401675	+	0.999992i	$0.501279\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	2.36365			0.542259			0.271129	−	0.962543i	$-0.412603\pi$
$19$	2.36365			0.542259			0.271129	+	0.962543i	$0.412603\pi$
$20$	−1.88893	+	1.19663i	−0.422378	+	0.267576i
$21$	−2.19663	+	1.47472i	−0.479345	+	0.321810i
$22$	3.39327	−	3.39327i	0.723448	−	0.723448i
$23$	2.97906	+	2.97906i	0.621176	+	0.621176i	0.945832	−	0.324656i	$-0.105249\pi$
$23$	2.97906	+	2.97906i	0.621176	+	0.621176i	−0.324656	+	0.945832i	$0.605249\pi$
$24$	−1.00000			−0.204124
$25$	−2.13613	+	4.52072i	−0.427226	+	0.904145i
$26$			0.828427i			0.162468i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−0.510472	+	2.59604i	−0.0964701	+	0.490605i
$29$		−	9.94900i		−	1.84748i	−0.383017	−	0.923741i	$-0.625115\pi$
$29$		−	9.94900i		−	1.84748i	0.383017	−	0.923741i	$-0.374885\pi$
$30$	−1.88893	+	1.19663i	−0.344870	+	0.218475i
$31$		−	3.02094i		−	0.542578i	−0.962498	−	0.271289i	$-0.912550\pi$
$31$		−	3.02094i		−	0.542578i	0.962498	−	0.271289i	$-0.0874498\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	3.39327	−	3.39327i	0.590692	−	0.590692i
$34$	5.80748			0.995975
$35$	2.14226	+	5.51459i	0.362109	+	0.932136i
$36$	−1.00000			−0.166667
$37$	−6.10651	+	6.10651i	−1.00390	+	1.00390i	−0.00391185	+	0.999992i	$0.501245\pi$
$37$	−6.10651	+	6.10651i	−1.00390	+	1.00390i	−0.999992	+	0.00391185i	$0.998755\pi$
$38$	1.67135	−	1.67135i	0.271129	−	0.271129i
$39$			0.828427i			0.132655i
$40$	−0.489528	+	2.18183i	−0.0774012	+	0.344977i
$41$			10.9996i			1.71784i	0.512107	+	0.858921i	$0.328865\pi$
$41$			10.9996i			1.71784i	−0.512107	+	0.858921i	$0.671135\pi$
$42$	−0.510472	+	2.59604i	−0.0787675	+	0.400578i
$43$	−5.74825	−	5.74825i	−0.876599	−	0.876599i	0.116582	−	0.993181i	$-0.462806\pi$
$43$	−5.74825	−	5.74825i	−0.876599	−	0.876599i	−0.993181	+	0.116582i	$0.962806\pi$
$44$		−	4.79881i		−	0.723448i
$45$	−1.88893	+	1.19663i	−0.281585	+	0.178384i
$46$	4.21302			0.621176
$47$	−0.363651	−	0.363651i	−0.0530439	−	0.0530439i	0.680087	−	0.733131i	$-0.261942\pi$
$47$	−0.363651	−	0.363651i	−0.0530439	−	0.0530439i	−0.733131	+	0.680087i	$0.761942\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$	6.47884	+	2.65041i	0.925548	+	0.378630i
$50$	1.68616	+	4.70711i	0.238459	+	0.665685i
$51$	5.80748			0.813210
$52$	0.585786	+	0.585786i	0.0812340	+	0.0812340i
$53$	2.36365	+	2.36365i	0.324672	+	0.324672i	0.850556	−	0.525884i	$-0.176265\pi$
$53$	2.36365	+	2.36365i	0.324672	+	0.324672i	−0.525884	+	0.850556i	$0.676265\pi$
$54$	−1.00000			−0.136083
$55$	−5.74242	−	9.06462i	−0.774308	−	1.22227i
$56$	1.47472	+	2.19663i	0.197068	+	0.293538i
$57$	1.67135	−	1.67135i	0.221376	−	0.221376i
$58$	−7.03500	−	7.03500i	−0.923741	−	0.923741i
$59$	2.07912			0.270679			0.135339	−	0.990799i	$-0.456788\pi$
$59$	2.07912			0.270679			0.135339	+	0.990799i	$0.456788\pi$
$60$	−0.489528	+	2.18183i	−0.0631978	+	0.281672i
$61$			5.55573i			0.711338i	0.934612	+	0.355669i	$0.115747\pi$
$61$			5.55573i			0.711338i	−0.934612	+	0.355669i	$0.884253\pi$
$62$	−2.13613	−	2.13613i	−0.271289	−	0.271289i
$63$	−0.510472	+	2.59604i	−0.0643134	+	0.327070i
$64$			1.00000i			0.125000i
$65$	1.80748	+	0.405538i	0.224191	+	0.0503008i
$66$		−	4.79881i		−	0.590692i
$67$	−0.979056	+	0.979056i	−0.119611	+	0.119611i	−0.764379	−	0.644768i	$-0.776954\pi$
$67$	−0.979056	+	0.979056i	−0.119611	+	0.119611i	0.644768	+	0.764379i	$0.276954\pi$
$68$	4.10651	−	4.10651i	0.497988	−	0.497988i
$69$	4.21302			0.507188
$70$	5.41421	+	2.38459i	0.647122	+	0.285014i
$71$	5.25132			0.623217			0.311608	−	0.950211i	$-0.399132\pi$
$71$	5.25132			0.623217			0.311608	+	0.950211i	$0.399132\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	−6.11519	+	6.11519i	−0.715728	+	0.715728i	−0.967727	−	0.251999i	$-0.918912\pi$
$73$	−6.11519	+	6.11519i	−0.715728	+	0.715728i	0.251999	+	0.967727i	$0.418912\pi$
$74$			8.63591i			1.00390i
$75$	1.68616	+	4.70711i	0.194701	+	0.543530i
$76$		−	2.36365i		−	0.271129i
$77$	−12.4579	−	2.44966i	−1.41971	−	0.279164i
$78$	0.585786	+	0.585786i	0.0663273	+	0.0663273i
$79$		−	5.10069i		−	0.573872i	−0.957950	−	0.286936i	$-0.907363\pi$
$79$		−	5.10069i		−	0.573872i	0.957950	−	0.286936i	$-0.0926367\pi$
$80$	1.19663	+	1.88893i	0.133788	+	0.211189i
$81$	−1.00000			−0.111111
$82$	7.77786	+	7.77786i	0.858921	+	0.858921i
$83$	3.22170	−	3.22170i	0.353627	−	0.353627i	−0.507830	−	0.861457i	$-0.669552\pi$
$83$	3.22170	−	3.22170i	0.353627	−	0.353627i	0.861457	+	0.507830i	$0.169552\pi$
$84$	1.47472	+	2.19663i	0.160905	+	0.239673i
$85$	2.84293	−	12.6709i	0.308359	−	1.37435i
$86$	−8.12925			−0.876599
$87$	−7.03500	−	7.03500i	−0.754232	−	0.754232i
$88$	−3.39327	−	3.39327i	−0.361724	−	0.361724i
$89$	−11.8989			−1.26128			−0.630639	−	0.776076i	$-0.717207\pi$
$89$	−11.8989			−1.26128			−0.630639	+	0.776076i	$0.717207\pi$
$90$	−0.489528	+	2.18183i	−0.0516008	+	0.229985i
$91$	1.81975	−	1.22170i	0.190762	−	0.128069i
$92$	2.97906	−	2.97906i	0.310588	−	0.310588i
$93$	−2.13613	−	2.13613i	−0.221506	−	0.221506i
$94$	−0.514280			−0.0530439
$95$	−2.82843	−	4.46478i	−0.290191	−	0.458076i
$96$			1.00000i			0.102062i
$97$	−8.05595	−	8.05595i	−0.817958	−	0.817958i	0.167854	−	0.985812i	$-0.446316\pi$
$97$	−8.05595	−	8.05595i	−0.817958	−	0.817958i	−0.985812	+	0.167854i	$0.946316\pi$
$98$	6.45535	−	2.70711i	0.652089	−	0.273459i
$99$		−	4.79881i		−	0.482298i
$100$	4.52072	+	2.13613i	0.452072	+	0.213613i
$101$			4.89020i			0.486593i	0.969952	+	0.243297i	$0.0782288\pi$
$101$			4.89020i			0.486593i	−0.969952	+	0.243297i	$0.921771\pi$
$102$	4.10651	−	4.10651i	0.406605	−	0.406605i
$103$	−1.06462	+	1.06462i	−0.104900	+	0.104900i	−0.757609	−	0.652709i	$-0.773633\pi$
$103$	−1.06462	+	1.06462i	−0.104900	+	0.104900i	0.652709	+	0.757609i	$0.273633\pi$
$104$	0.828427			0.0812340
$105$	5.41421	+	2.38459i	0.528373	+	0.232713i
$106$	3.34271			0.324672
$107$	2.15063	−	2.15063i	0.207909	−	0.207909i	−0.595469	−	0.803378i	$-0.703034\pi$
$107$	2.15063	−	2.15063i	0.207909	−	0.207909i	0.803378	+	0.595469i	$0.203034\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$			12.8984i			1.23545i	0.786396	+	0.617723i	$0.211945\pi$
$109$			12.8984i			1.23545i	−0.786396	+	0.617723i	$0.788055\pi$
$110$	−10.4702	−	2.34915i	−0.998291	−	0.223983i
$111$			8.63591i			0.819684i
$112$	2.59604	+	0.510472i	0.245303	+	0.0482351i
$113$	−11.5853	−	11.5853i	−1.08986	−	1.08986i	−0.995542	−	0.0943155i	$-0.969934\pi$
$113$	−11.5853	−	11.5853i	−1.08986	−	1.08986i	−0.0943155	−	0.995542i	$-0.530066\pi$
$114$		−	2.36365i		−	0.221376i
$115$	2.06239	−	9.19208i	0.192319	−	0.857166i
$116$	−9.94900			−0.923741
$117$	0.585786	+	0.585786i	0.0541560	+	0.0541560i
$118$	1.47016	−	1.47016i	0.135339	−	0.135339i
$119$	−8.56440	−	12.7569i	−0.785098	−	1.16943i
$120$	1.19663	+	1.88893i	0.109237	+	0.172435i
$121$	12.0286			1.09351
$122$	3.92849	+	3.92849i	0.355669	+	0.355669i
$123$	7.77786	+	7.77786i	0.701306	+	0.701306i
$124$	−3.02094			−0.271289
$125$	11.0955	−	1.37465i	0.992413	−	0.122953i
$126$	1.47472	+	2.19663i	0.131378	+	0.195692i
$127$	0.399714	−	0.399714i	0.0354689	−	0.0354689i	−0.689150	−	0.724619i	$-0.742016\pi$
$127$	0.399714	−	0.399714i	0.0354689	−	0.0354689i	0.724619	+	0.689150i	$0.242016\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−8.12925			−0.715740
$130$	1.56484	−	0.991325i	0.137246	−	0.0869449i
$131$		−	22.2039i		−	1.93996i	−0.243176	−	0.969982i	$-0.578189\pi$
$131$		−	22.2039i		−	1.93996i	0.243176	−	0.969982i	$-0.421811\pi$
$132$	−3.39327	−	3.39327i	−0.295346	−	0.295346i
$133$	−6.13613	−	1.20658i	−0.532070	−	0.104624i
$134$			1.38459i			0.119611i
$135$	−0.489528	+	2.18183i	−0.0421319	+	0.187782i
$136$		−	5.80748i		−	0.497988i
$137$	−5.92849	+	5.92849i	−0.506505	+	0.506505i	−0.913452	−	0.406947i	$-0.866594\pi$
$137$	−5.92849	+	5.92849i	−0.506505	+	0.506505i	0.406947	+	0.913452i	$0.366594\pi$
$138$	2.97906	−	2.97906i	0.253594	−	0.253594i
$139$	8.46478			0.717973			0.358986	−	0.933343i	$-0.383122\pi$
$139$	8.46478			0.717973			0.358986	+	0.933343i	$0.383122\pi$
$140$	5.51459	−	2.14226i	0.466068	−	0.181054i
$141$	−0.514280			−0.0433102
$142$	3.71324	−	3.71324i	0.311608	−	0.311608i
$143$	−2.81108	+	2.81108i	−0.235074	+	0.235074i
$144$			1.00000i			0.0833333i
$145$	−18.7930	+	11.9053i	−1.56067	+	0.988683i
$146$			8.64818i			0.715728i
$147$	6.45535	−	2.70711i	0.532428	−	0.223278i
$148$	6.10651	+	6.10651i	0.501952	+	0.501952i
$149$			4.43516i			0.363342i	0.983359	+	0.181671i	$0.0581506\pi$
$149$			4.43516i			0.363342i	−0.983359	+	0.181671i	$0.941849\pi$
$150$	4.52072	+	2.13613i	0.369116	+	0.174414i
$151$	7.61497			0.619697			0.309849	−	0.950786i	$-0.399722\pi$
$151$	7.61497			0.619697			0.309849	+	0.950786i	$0.399722\pi$
$152$	−1.67135	−	1.67135i	−0.135565	−	0.135565i
$153$	4.10651	−	4.10651i	0.331992	−	0.331992i
$154$	−10.5412	+	7.07689i	−0.849436	+	0.570272i
$155$	−5.70636	+	3.61497i	−0.458346	+	0.290361i
$156$	0.828427			0.0663273
$157$	6.30188	+	6.30188i	0.502945	+	0.502945i	0.912352	−	0.409407i	$-0.134264\pi$
$157$	6.30188	+	6.30188i	0.502945	+	0.502945i	−0.409407	+	0.912352i	$0.634264\pi$
$158$	−3.60673	−	3.60673i	−0.286936	−	0.286936i
$159$	3.34271			0.265094
$160$	2.18183	+	0.489528i	0.172488	+	0.0387006i
$161$	−6.21302	−	9.25447i	−0.489655	−	0.729354i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	10.8489	+	10.8489i	0.849754	+	0.849754i	0.990102	−	0.140348i	$-0.0448222\pi$
$163$	10.8489	+	10.8489i	0.849754	+	0.849754i	−0.140348	+	0.990102i	$0.544822\pi$
$164$	10.9996			0.858921
$165$	−10.4702	−	2.34915i	−0.815101	−	0.182881i
$166$		−	4.55617i		−	0.353627i
$167$	−5.63635	−	5.63635i	−0.436154	−	0.436154i	0.454562	−	0.890715i	$-0.349796\pi$
$167$	−5.63635	−	5.63635i	−0.436154	−	0.436154i	−0.890715	+	0.454562i	$0.849796\pi$
$168$	2.59604	+	0.510472i	0.200289	+	0.0393838i
$169$			12.3137i			0.947208i
$170$	−6.94944	−	10.9699i	−0.532998	−	0.841356i
$171$		−	2.36365i		−	0.180753i
$172$	−5.74825	+	5.74825i	−0.438300	+	0.438300i
$173$	12.6923	−	12.6923i	0.964977	−	0.964977i	−0.0344296	−	0.999407i	$-0.510961\pi$
$173$	12.6923	−	12.6923i	0.964977	−	0.964977i	0.999407	+	0.0344296i	$0.0109615\pi$
$174$	−9.94900			−0.754232
$175$	7.85318	−	10.6455i	0.593645	−	0.804727i
$176$	−4.79881			−0.361724
$177$	1.47016	−	1.47016i	0.110504	−	0.110504i
$178$	−8.41377	+	8.41377i	−0.630639	+	0.630639i
$179$			5.72836i			0.428158i	0.976816	+	0.214079i	$0.0686750\pi$
$179$			5.72836i			0.428158i	−0.976816	+	0.214079i	$0.931325\pi$
$180$	1.19663	+	1.88893i	0.0891919	+	0.140793i
$181$			8.91220i			0.662439i	0.943554	+	0.331219i	$0.107460\pi$
$181$			8.91220i			0.662439i	−0.943554	+	0.331219i	$0.892540\pi$
$182$	0.422889	−	2.15063i	0.0313466	−	0.159415i
$183$	3.92849	+	3.92849i	0.290403	+	0.290403i
$184$		−	4.21302i		−	0.310588i
$185$	18.8420	+	4.22752i	1.38530	+	0.310814i
$186$	−3.02094			−0.221506
$187$	19.7064	+	19.7064i	1.44107	+	1.44107i
$188$	−0.363651	+	0.363651i	−0.0265220	+	0.0265220i
$189$	1.47472	+	2.19663i	0.107270	+	0.159782i
$190$	−5.15707	−	1.15707i	−0.374133	−	0.0839429i
$191$	−7.67824			−0.555578			−0.277789	−	0.960642i	$-0.589602\pi$
$191$	−7.67824			−0.555578			−0.277789	+	0.960642i	$0.589602\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−4.59762	−	4.59762i	−0.330944	−	0.330944i	0.522001	−	0.852945i	$-0.325186\pi$
$193$	−4.59762	−	4.59762i	−0.330944	−	0.330944i	−0.852945	+	0.522001i	$0.825186\pi$
$194$	−11.3928			−0.817958
$195$	1.56484	−	0.991325i	0.112061	−	0.0709902i
$196$	2.65041	−	6.47884i	0.189315	−	0.462774i
$197$	−5.25132	+	5.25132i	−0.374141	+	0.374141i	−0.868983	−	0.494842i	$-0.835226\pi$
$197$	−5.25132	+	5.25132i	−0.374141	+	0.374141i	0.494842	+	0.868983i	$0.335226\pi$
$198$	−3.39327	−	3.39327i	−0.241149	−	0.241149i
$199$	−4.12163			−0.292175			−0.146087	−	0.989272i	$-0.546668\pi$
$199$	−4.12163			−0.292175			−0.146087	+	0.989272i	$0.546668\pi$
$200$	4.70711	−	1.68616i	0.332843	−	0.119230i
$201$			1.38459i			0.0976618i
$202$	3.45789	+	3.45789i	0.243297	+	0.243297i
$203$	−5.07868	+	25.8280i	−0.356454	+	1.81277i
$204$		−	5.80748i		−	0.406605i
$205$	20.7774	−	13.1625i	1.45116	−	0.919306i
$206$			1.50560i			0.104900i
$207$	2.97906	−	2.97906i	0.207059	−	0.207059i
$208$	0.585786	−	0.585786i	0.0406170	−	0.0406170i
$209$	11.3427			0.784591
$210$	5.51459	−	2.14226i	0.380543	−	0.147830i
$211$	−27.6560			−1.90392			−0.951958	−	0.306229i	$-0.900933\pi$
$211$	−27.6560			−1.90392			−0.951958	+	0.306229i	$0.900933\pi$
$212$	2.36365	−	2.36365i	0.162336	−	0.162336i
$213$	3.71324	−	3.71324i	0.254427	−	0.254427i
$214$		−	3.04145i		−	0.207909i
$215$	−3.97949	+	17.7366i	−0.271399	+	1.20963i
$216$			1.00000i			0.0680414i
$217$	−1.54211	+	7.84249i	−0.104685	+	0.532383i
$218$	9.12057	+	9.12057i	0.617723	+	0.617723i
$219$			8.64818i			0.584390i
$220$	−9.06462	+	5.74242i	−0.611137	+	0.387154i
$221$	−4.81108			−0.323628
$222$	6.10651	+	6.10651i	0.409842	+	0.409842i
$223$	−15.3271	+	15.3271i	−1.02638	+	1.02638i	−0.0267394	+	0.999642i	$0.508512\pi$
$223$	−15.3271	+	15.3271i	−1.02638	+	1.02638i	−0.999642	+	0.0267394i	$0.991488\pi$
$224$	2.19663	−	1.47472i	0.146769	−	0.0985338i
$225$	4.52072	+	2.13613i	0.301382	+	0.142409i
$226$	−16.3842			−1.08986
$227$	18.8984	+	18.8984i	1.25433	+	1.25433i	0.953758	+	0.300575i	$0.0971786\pi$
$227$	18.8984	+	18.8984i	1.25433	+	1.25433i	0.300575	+	0.953758i	$0.402821\pi$
$228$	−1.67135	−	1.67135i	−0.110688	−	0.110688i
$229$	13.3137			0.879795			0.439897	−	0.898048i	$-0.355015\pi$
$229$	13.3137			0.879795			0.439897	+	0.898048i	$0.355015\pi$
$230$	−5.04145	−	7.95811i	−0.332423	−	0.524742i
$231$	−10.5412	+	7.07689i	−0.693562	+	0.465625i
$232$	−7.03500	+	7.03500i	−0.461871	+	0.461871i
$233$	7.35498	+	7.35498i	0.481840	+	0.481840i	0.905719	−	0.423879i	$-0.139332\pi$
$233$	7.35498	+	7.35498i	0.481840	+	0.481840i	−0.423879	+	0.905719i	$0.639332\pi$
$234$	0.828427			0.0541560
$235$	−0.251755	+	1.12207i	−0.0164227	+	0.0731957i
$236$		−	2.07912i		−	0.135339i
$237$	−3.60673	−	3.60673i	−0.234282	−	0.234282i
$238$	−15.0765	−	2.96456i	−0.977261	−	0.192164i
$239$			13.0491i			0.844074i	0.906579	+	0.422037i	$0.138685\pi$
$239$			13.0491i			0.844074i	−0.906579	+	0.422037i	$0.861315\pi$
$240$	2.18183	+	0.489528i	0.140836	+	0.0315989i
$241$		−	24.4542i		−	1.57523i	−0.616167	−	0.787616i	$-0.711315\pi$
$241$		−	24.4542i		−	1.57523i	0.616167	−	0.787616i	$-0.288685\pi$
$242$	8.50548	−	8.50548i	0.546753	−	0.546753i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	5.55573			0.355669
$245$	−2.74636	−	15.4097i	−0.175458	−	0.984487i
$246$	10.9996			0.701306
$247$	−1.38459	+	1.38459i	−0.0880996	+	0.0880996i
$248$	−2.13613	+	2.13613i	−0.135644	+	0.135644i
$249$		−	4.55617i		−	0.288735i
$250$	6.87368	−	8.81774i	0.434730	−	0.557683i
$251$			4.32326i			0.272882i	0.990648	+	0.136441i	$0.0435664\pi$
$251$			4.32326i			0.272882i	−0.990648	+	0.136441i	$0.956434\pi$
$252$	2.59604	+	0.510472i	0.163535	+	0.0321567i
$253$	14.2959	+	14.2959i	0.898777	+	0.898777i
$254$		−	0.565281i		−	0.0354689i
$255$	−6.94944	−	10.9699i	−0.435191	−	0.686964i
$256$	1.00000			0.0625000
$257$	−5.06418	−	5.06418i	−0.315895	−	0.315895i	0.531293	−	0.847188i	$-0.321706\pi$
$257$	−5.06418	−	5.06418i	−0.315895	−	0.315895i	−0.847188	+	0.531293i	$0.821706\pi$
$258$	−5.74825	+	5.74825i	−0.357870	+	0.357870i
$259$	18.9699	−	12.7355i	1.17873	−	0.791348i
$260$	0.405538	−	1.80748i	0.0251504	−	0.112095i
$261$	−9.94900			−0.615828
$262$	−15.7005	−	15.7005i	−0.969982	−	0.969982i
$263$	−4.17113	−	4.17113i	−0.257203	−	0.257203i	0.566712	−	0.823916i	$-0.308215\pi$
$263$	−4.17113	−	4.17113i	−0.257203	−	0.257203i	−0.823916	+	0.566712i	$0.808215\pi$
$264$	−4.79881			−0.295346
$265$	1.63635	−	7.29320i	0.100520	−	0.448018i
$266$	−5.19208	+	3.48572i	−0.318347	+	0.213723i
$267$	−8.41377	+	8.41377i	−0.514915	+	0.514915i
$268$	0.979056	+	0.979056i	0.0598054	+	0.0598054i
$269$	−24.7484			−1.50894			−0.754469	−	0.656336i	$-0.772106\pi$
$269$	−24.7484			−1.50894			−0.754469	+	0.656336i	$0.772106\pi$
$270$	1.19663	+	1.88893i	0.0728249	+	0.114957i
$271$		−	21.9960i		−	1.33616i	−0.744089	−	0.668080i	$-0.767116\pi$
$271$		−	21.9960i		−	1.33616i	0.744089	−	0.668080i	$-0.232884\pi$
$272$	−4.10651	−	4.10651i	−0.248994	−	0.248994i
$273$	0.422889	−	2.15063i	0.0255944	−	0.130162i
$274$			8.38416i			0.506505i
$275$	−10.2509	+	21.6941i	−0.618151	+	1.30820i
$276$		−	4.21302i		−	0.253594i
$277$	12.0646	−	12.0646i	0.724893	−	0.724893i	−0.244705	−	0.969598i	$-0.578691\pi$
$277$	12.0646	−	12.0646i	0.724893	−	0.724893i	0.969598	+	0.244705i	$0.0786910\pi$
$278$	5.98550	−	5.98550i	0.358986	−	0.358986i
$279$	−3.02094			−0.180859
$280$	2.38459	−	5.41421i	0.142507	−	0.323561i
$281$	14.3668			0.857052			0.428526	−	0.903530i	$-0.359033\pi$
$281$	14.3668			0.857052			0.428526	+	0.903530i	$0.359033\pi$
$282$	−0.363651	+	0.363651i	−0.0216551	+	0.0216551i
$283$	11.0833	−	11.0833i	0.658836	−	0.658836i	−0.296269	−	0.955105i	$-0.595742\pi$
$283$	11.0833	−	11.0833i	0.658836	−	0.658836i	0.955105	+	0.296269i	$0.0957424\pi$
$284$		−	5.25132i		−	0.311608i
$285$	−5.15707	−	1.15707i	−0.305479	−	0.0685391i
$286$			3.97546i			0.235074i
$287$	5.61497	−	28.5553i	0.331441	−	1.68557i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$			16.7269i			0.983933i
$290$	−4.87031	+	21.7070i	−0.285995	+	1.27468i
$291$	−11.3928			−0.667860
$292$	6.11519	+	6.11519i	0.357864	+	0.357864i
$293$	−6.35827	+	6.35827i	−0.371454	+	0.371454i	−0.868007	−	0.496553i	$-0.834599\pi$
$293$	−6.35827	+	6.35827i	−0.371454	+	0.371454i	0.496553	+	0.868007i	$0.334599\pi$
$294$	2.65041	−	6.47884i	0.154575	−	0.377853i
$295$	−2.48795	−	3.92732i	−0.144854	−	0.228658i
$296$	8.63591			0.501952
$297$	−3.39327	−	3.39327i	−0.196897	−	0.196897i
$298$	3.13613	+	3.13613i	0.181671	+	0.181671i
$299$	−3.49018			−0.201842
$300$	4.70711	−	1.68616i	0.271765	−	0.0973507i
$301$	11.9884	+	17.8570i	0.690997	+	1.02926i
$302$	5.38459	−	5.38459i	0.309849	−	0.309849i
$303$	3.45789	+	3.45789i	0.198651	+	0.198651i
$304$	−2.36365			−0.135565
$305$	10.4944	−	6.64818i	0.600907	−	0.380674i
$306$		−	5.80748i		−	0.331992i
$307$	−16.8663	−	16.8663i	−0.962610	−	0.962610i	0.0367161	−	0.999326i	$-0.488310\pi$
$307$	−16.8663	−	16.8663i	−0.962610	−	0.962610i	−0.999326	+	0.0367161i	$0.988310\pi$
$308$	−2.44966	+	12.4579i	−0.139582	+	0.709854i
$309$			1.50560i			0.0856509i
$310$	−1.47884	+	6.59117i	−0.0839923	+	0.374353i
$311$			0.0592379i			0.00335907i	0.999999	+	0.00167954i	$0.000534613\pi$
$311$			0.0592379i			0.00335907i	−0.999999	+	0.00167954i	$0.999465\pi$
$312$	0.585786	−	0.585786i	0.0331636	−	0.0331636i
$313$	0.458332	−	0.458332i	0.0259064	−	0.0259064i	−0.694035	−	0.719941i	$-0.744169\pi$
$313$	0.458332	−	0.458332i	0.0259064	−	0.0259064i	0.719941	+	0.694035i	$0.244169\pi$
$314$	8.91220			0.502945
$315$	5.51459	−	2.14226i	0.310712	−	0.120703i
$316$	−5.10069			−0.286936
$317$	13.1130	−	13.1130i	0.736497	−	0.736497i	−0.235401	−	0.971898i	$-0.575640\pi$
$317$	13.1130	−	13.1130i	0.736497	−	0.736497i	0.971898	+	0.235401i	$0.0756404\pi$
$318$	2.36365	−	2.36365i	0.132547	−	0.132547i
$319$		−	47.7433i		−	2.67311i
$320$	1.88893	−	1.19663i	0.105595	−	0.0668939i
$321$		−	3.04145i		−	0.169757i
$322$	−10.9372	−	2.15063i	−0.609505	−	0.119850i
$323$	9.70636	+	9.70636i	0.540076	+	0.540076i
$324$			1.00000i			0.0555556i
$325$	−1.39686	−	3.89949i	−0.0774840	−	0.216305i
$326$	15.3427			0.849754
$327$	9.12057	+	9.12057i	0.504369	+	0.504369i
$328$	7.77786	−	7.77786i	0.429461	−	0.429461i
$329$	0.758418	+	1.12969i	0.0418130	+	0.0622816i
$330$	−9.06462	+	5.74242i	−0.498991	+	0.316110i
$331$	−25.1288			−1.38120			−0.690602	−	0.723235i	$-0.742654\pi$
$331$	−25.1288			−1.38120			−0.690602	+	0.723235i	$0.742654\pi$
$332$	−3.22170	−	3.22170i	−0.176814	−	0.176814i
$333$	6.10651	+	6.10651i	0.334635	+	0.334635i
$334$	−7.97100			−0.436154
$335$	3.02094	+	0.677798i	0.165052	+	0.0370321i
$336$	2.19663	−	1.47472i	0.119836	−	0.0804525i
$337$	16.5976	−	16.5976i	0.904130	−	0.904130i	−0.0916605	−	0.995790i	$-0.529217\pi$
$337$	16.5976	−	16.5976i	0.904130	−	0.904130i	0.995790	+	0.0916605i	$0.0292175\pi$
$338$	8.70711	+	8.70711i	0.473604	+	0.473604i
$339$	−16.3842			−0.889865
$340$	−12.6709	−	2.84293i	−0.687177	−	0.154179i
$341$		−	14.4969i		−	0.785053i
$342$	−1.67135	−	1.67135i	−0.0903764	−	0.0903764i
$343$	−15.4664	−	10.1878i	−0.835105	−	0.550091i
$344$			8.12925i			0.438300i
$345$	−5.04145	−	7.95811i	−0.271422	−	0.428450i
$346$		−	17.9496i		−	0.964977i
$347$	14.4214	−	14.4214i	0.774181	−	0.774181i	−0.204654	−	0.978834i	$-0.565607\pi$
$347$	14.4214	−	14.4214i	0.774181	−	0.774181i	0.978834	+	0.204654i	$0.0656068\pi$
$348$	−7.03500	+	7.03500i	−0.377116	+	0.377116i
$349$	−28.6672			−1.53452			−0.767260	−	0.641337i	$-0.778380\pi$
$349$	−28.6672			−1.53452			−0.767260	+	0.641337i	$0.778380\pi$
$350$	−1.97450	−	13.0806i	−0.105541	−	0.699186i
$351$	0.828427			0.0442182
$352$	−3.39327	+	3.39327i	−0.180862	+	0.180862i
$353$	5.06506	−	5.06506i	0.269586	−	0.269586i	−0.559347	−	0.828933i	$-0.688948\pi$
$353$	5.06506	−	5.06506i	0.269586	−	0.269586i	0.828933	+	0.559347i	$0.188948\pi$
$354$		−	2.07912i		−	0.110504i
$355$	−6.28391	−	9.91938i	−0.333515	−	0.526466i
$356$			11.8989i			0.630639i
$357$	−15.0765	−	2.96456i	−0.797931	−	0.156901i
$358$	4.05056	+	4.05056i	0.214079	+	0.214079i
$359$		−	8.46478i		−	0.446754i	−0.974732	−	0.223377i	$-0.928292\pi$
$359$		−	8.46478i		−	0.446754i	0.974732	−	0.223377i	$-0.0717081\pi$
$360$	2.18183	+	0.489528i	0.114992	+	0.0258004i
$361$	−13.4132			−0.705956
$362$	6.30188	+	6.30188i	0.331219	+	0.331219i
$363$	8.50548	−	8.50548i	0.446422	−	0.446422i
$364$	−1.22170	−	1.81975i	−0.0640343	−	0.0953809i
$365$	18.8688	+	4.23353i	0.987639	+	0.221593i
$366$	5.55573			0.290403
$367$	18.1685	+	18.1685i	0.948386	+	0.948386i	0.998732	−	0.0503457i	$-0.0160323\pi$
$367$	18.1685	+	18.1685i	0.948386	+	0.948386i	−0.0503457	+	0.998732i	$0.516032\pi$
$368$	−2.97906	−	2.97906i	−0.155294	−	0.155294i
$369$	10.9996			0.572614
$370$	16.3126	−	10.3340i	0.848054	−	0.537241i
$371$	−4.92955	−	7.34271i	−0.255930	−	0.381214i
$372$	−2.13613	+	2.13613i	−0.110753	+	0.110753i
$373$	−15.4492	−	15.4492i	−0.799930	−	0.799930i	0.183154	−	0.983084i	$-0.441369\pi$
$373$	−15.4492	−	15.4492i	−0.799930	−	0.799930i	−0.983084	+	0.183154i	$0.941369\pi$
$374$	27.8690			1.44107
$375$	6.87368	−	8.81774i	0.354956	−	0.455346i
$376$			0.514280i			0.0265220i
$377$	5.82799	+	5.82799i	0.300157	+	0.300157i
$378$	2.59604	+	0.510472i	0.133526	+	0.0262558i
$379$			32.3833i			1.66342i	0.555212	+	0.831709i	$0.312637\pi$
$379$			32.3833i			1.66342i	−0.555212	+	0.831709i	$0.687363\pi$
$380$	−4.46478	+	2.82843i	−0.229038	+	0.145095i
$381$		−	0.565281i		−	0.0289602i
$382$	−5.42933	+	5.42933i	−0.277789	+	0.277789i
$383$	−16.1916	+	16.1916i	−0.827354	+	0.827354i	−0.987150	−	0.159796i	$-0.948916\pi$
$383$	−16.1916	+	16.1916i	−0.827354	+	0.827354i	0.159796	+	0.987150i	$0.448916\pi$
$384$	1.00000			0.0510310
$385$	10.2803	+	26.4635i	0.523933	+	1.34870i
$386$	−6.50201			−0.330944
$387$	−5.74825	+	5.74825i	−0.292200	+	0.292200i
$388$	−8.05595	+	8.05595i	−0.408979	+	0.408979i
$389$			12.0091i			0.608886i	0.952531	+	0.304443i	$0.0984704\pi$
$389$			12.0091i			0.608886i	−0.952531	+	0.304443i	$0.901530\pi$
$390$	0.405538	−	1.80748i	0.0205352	−	0.0915255i
$391$			24.4671i			1.23735i
$392$	−2.70711	−	6.45535i	−0.136730	−	0.326045i
$393$	−15.7005	−	15.7005i	−0.791987	−	0.791987i
$394$			7.42648i			0.374141i
$395$	−9.63485	+	6.10366i	−0.484782	+	0.307108i
$396$	−4.79881			−0.241149
$397$	−2.62680	−	2.62680i	−0.131835	−	0.131835i	0.638110	−	0.769945i	$-0.279716\pi$
$397$	−2.62680	−	2.62680i	−0.131835	−	0.131835i	−0.769945	+	0.638110i	$0.779716\pi$
$398$	−2.91443	+	2.91443i	−0.146087	+	0.146087i
$399$	−5.19208	+	3.48572i	−0.259929	+	0.174504i
$400$	2.13613	−	4.52072i	0.106806	−	0.226036i
$401$	19.7571			0.986623			0.493311	−	0.869853i	$-0.335786\pi$
$401$	19.7571			0.986623			0.493311	+	0.869853i	$0.335786\pi$
$402$	0.979056	+	0.979056i	0.0488309	+	0.0488309i
$403$	1.76963	+	1.76963i	0.0881514	+	0.0881514i
$404$	4.89020			0.243297
$405$	1.19663	+	1.88893i	0.0594613	+	0.0938618i
$406$	14.6720	+	21.8543i	0.728158	+	1.08461i
$407$	−29.3040	+	29.3040i	−1.45254	+	1.45254i
$408$	−4.10651	−	4.10651i	−0.203303	−	0.203303i
$409$	−15.3846			−0.760719			−0.380360	−	0.924839i	$-0.624200\pi$
$409$	−15.3846			−0.760719			−0.380360	+	0.924839i	$0.624200\pi$
$410$	5.38459	−	23.9991i	0.265926	−	1.18523i
$411$			8.38416i			0.413560i
$412$	1.06462	+	1.06462i	0.0524502	+	0.0524502i
$413$	−5.39748	−	1.06133i	−0.265593	−	0.0522248i
$414$		−	4.21302i		−	0.207059i
$415$	−9.94076	−	2.23037i	−0.487973	−	0.109485i
$416$		−	0.828427i		−	0.0406170i
$417$	5.98550	−	5.98550i	0.293111	−	0.293111i
$418$	8.02051	−	8.02051i	0.392296	−	0.392296i
$419$	28.0782			1.37171			0.685856	−	0.727737i	$-0.259428\pi$
$419$	28.0782			1.37171			0.685856	+	0.727737i	$0.259428\pi$
$420$	2.38459	−	5.41421i	0.116356	−	0.264187i
$421$	11.4836			0.559677			0.279838	−	0.960047i	$-0.409719\pi$
$421$	11.4836			0.559677			0.279838	+	0.960047i	$0.409719\pi$
$422$	−19.5557	+	19.5557i	−0.951958	+	0.951958i
$423$	−0.363651	+	0.363651i	−0.0176813	+	0.0176813i
$424$		−	3.34271i		−	0.162336i
$425$	−27.3364	+	9.79236i	−1.32601	+	0.474999i
$426$		−	5.25132i		−	0.254427i
$427$	2.83604	−	14.4229i	0.137246	−	0.697973i
$428$	−2.15063	−	2.15063i	−0.103955	−	0.103955i
$429$			3.97546i			0.191937i
$430$	9.72774	+	15.3556i	0.469113	+	0.740513i
$431$	11.3330			0.545890			0.272945	−	0.962030i	$-0.412002\pi$
$431$	11.3330			0.545890			0.272945	+	0.962030i	$0.412002\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	4.91337	−	4.91337i	0.236122	−	0.236122i	−0.579120	−	0.815242i	$-0.696604\pi$
$433$	4.91337	−	4.91337i	0.236122	−	0.236122i	0.815242	+	0.579120i	$0.196604\pi$
$434$	4.45504	+	6.63591i	0.213849	+	0.318534i
$435$	−4.87031	+	21.7070i	−0.233514	+	1.04077i
$436$	12.8984			0.617723
$437$	7.04145	+	7.04145i	0.336838	+	0.336838i
$438$	6.11519	+	6.11519i	0.292195	+	0.292195i
$439$	−22.7723			−1.08686			−0.543432	−	0.839453i	$-0.682876\pi$
$439$	−22.7723			−1.08686			−0.543432	+	0.839453i	$0.682876\pi$
$440$	−2.34915	+	10.4702i	−0.111991	+	0.499145i
$441$	2.65041	−	6.47884i	0.126210	−	0.308516i
$442$	−3.40194	+	3.40194i	−0.161814	+	0.161814i
$443$	−25.8189	−	25.8189i	−1.22669	−	1.22669i	−0.965208	−	0.261484i	$-0.915788\pi$
$443$	−25.8189	−	25.8189i	−1.22669	−	1.22669i	−0.261484	−	0.965208i	$-0.584212\pi$
$444$	8.63591			0.409842
$445$	14.2386	+	22.4762i	0.674975	+	1.06547i
$446$			21.6759i			1.02638i
$447$	3.13613	+	3.13613i	0.148334	+	0.148334i
$448$	0.510472	−	2.59604i	0.0241175	−	0.122651i
$449$		−	9.55573i		−	0.450963i	−0.974247	−	0.225481i	$-0.927605\pi$
$449$		−	9.55573i		−	0.450963i	0.974247	−	0.225481i	$-0.0723955\pi$
$450$	4.70711	−	1.68616i	0.221895	−	0.0794865i
$451$			52.7848i			2.48554i
$452$	−11.5853	+	11.5853i	−0.544929	+	0.544929i
$453$	5.38459	−	5.38459i	0.252990	−	0.252990i
$454$	26.7264			1.25433
$455$	−4.48528	−	1.97546i	−0.210273	−	0.0926111i
$456$	−2.36365			−0.110688
$457$	−16.6569	+	16.6569i	−0.779175	+	0.779175i	−0.979690	−	0.200516i	$-0.935738\pi$
$457$	−16.6569	+	16.6569i	−0.779175	+	0.779175i	0.200516	+	0.979690i	$0.435738\pi$
$458$	9.41421	−	9.41421i	0.439897	−	0.439897i
$459$		−	5.80748i		−	0.271070i
$460$	−9.19208	−	2.06239i	−0.428583	−	0.0961596i
$461$		−	24.4762i		−	1.13997i	−0.821656	−	0.569984i	$-0.806949\pi$
$461$		−	24.4762i		−	1.13997i	0.821656	−	0.569984i	$-0.193051\pi$
$462$	−2.44966	+	12.4579i	−0.113968	+	0.579594i
$463$	6.83022	+	6.83022i	0.317427	+	0.317427i	0.847778	−	0.530351i	$-0.177940\pi$
$463$	6.83022	+	6.83022i	0.317427	+	0.317427i	−0.530351	+	0.847778i	$0.677940\pi$
$464$			9.94900i			0.461871i
$465$	−1.47884	+	6.59117i	−0.0685794	+	0.305658i
$466$	10.4015			0.481840
$467$	20.2503	+	20.2503i	0.937070	+	0.937070i	0.998134	−	0.0610637i	$-0.0194493\pi$
$467$	20.2503	+	20.2503i	0.937070	+	0.937070i	−0.0610637	+	0.998134i	$0.519449\pi$
$468$	0.585786	−	0.585786i	0.0270780	−	0.0270780i
$469$	3.04145	−	2.04189i	0.140441	−	0.0942856i
$470$	0.615405	+	0.971440i	0.0283865	+	0.0448092i
$471$	8.91220			0.410653
$472$	−1.47016	−	1.47016i	−0.0676697	−	0.0676697i
$473$	−27.5847	−	27.5847i	−1.26835	−	1.26835i
$474$	−5.10069			−0.234282
$475$	−5.04907	+	10.6854i	−0.231667	+	0.490280i
$476$	−12.7569	+	8.56440i	−0.584713	+	0.392549i
$477$	2.36365	−	2.36365i	0.108224	−	0.108224i
$478$	9.22708	+	9.22708i	0.422037	+	0.422037i
$479$	−6.82843			−0.311999			−0.155999	−	0.987757i	$-0.549860\pi$
$479$	−6.82843			−0.311999			−0.155999	+	0.987757i	$0.549860\pi$
$480$	1.88893	−	1.19663i	0.0862176	−	0.0546187i
$481$		−	7.15422i		−	0.326204i
$482$	−17.2917	−	17.2917i	−0.787616	−	0.787616i
$483$	−10.9372	−	2.15063i	−0.497658	−	0.0978570i
$484$		−	12.0286i		−	0.546753i
$485$	−5.57711	+	24.8572i	−0.253244	+	1.12871i
$486$			1.00000i			0.0453609i
$487$	0.327587	−	0.327587i	0.0148444	−	0.0148444i	−0.699646	−	0.714490i	$-0.746659\pi$
$487$	0.327587	−	0.327587i	0.0148444	−	0.0148444i	0.714490	+	0.699646i	$0.246659\pi$
$488$	3.92849	−	3.92849i	0.177835	−	0.177835i
$489$	15.3427			0.693821
$490$	−12.8382	−	8.95430i	−0.579973	−	0.404514i
$491$	3.38521			0.152773			0.0763863	−	0.997078i	$-0.475662\pi$
$491$	3.38521			0.152773			0.0763863	+	0.997078i	$0.475662\pi$
$492$	7.77786	−	7.77786i	0.350653	−	0.350653i
$493$	40.8557	−	40.8557i	1.84005	−	1.84005i
$494$			1.95811i			0.0880996i
$495$	−9.06462	+	5.74242i	−0.407425	+	0.258103i
$496$			3.02094i			0.135644i
$497$	−13.6326	−	2.68065i	−0.611507	−	0.120244i
$498$	−3.22170	−	3.22170i	−0.144368	−	0.144368i
$499$			4.17771i			0.187020i	0.995618	+	0.0935101i	$0.0298087\pi$
$499$			4.17771i			0.187020i	−0.995618	+	0.0935101i	$0.970191\pi$
$500$	−1.37465	−	11.0955i	−0.0614763	−	0.496206i
$501$	−7.97100			−0.356118
$502$	3.05701	+	3.05701i	0.136441	+	0.136441i
$503$	−8.57667	+	8.57667i	−0.382415	+	0.382415i	−0.871972	−	0.489557i	$-0.837159\pi$
$503$	−8.57667	+	8.57667i	−0.382415	+	0.382415i	0.489557	+	0.871972i	$0.337159\pi$
$504$	2.19663	−	1.47472i	0.0978459	−	0.0656892i
$505$	9.23726	−	5.85178i	0.411052	−	0.260401i
$506$	20.2175			0.898777
$507$	8.70711	+	8.70711i	0.386696	+	0.386696i
$508$	−0.399714	−	0.399714i	−0.0177345	−	0.0177345i
$509$	3.29829			0.146194			0.0730970	−	0.997325i	$-0.476712\pi$
$509$	3.29829			0.146194			0.0730970	+	0.997325i	$0.476712\pi$
$510$	−12.6709	−	2.84293i	−0.561078	−	0.125887i
$511$	18.9969	−	12.7536i	0.840373	−	0.564187i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.67135	−	1.67135i	−0.0737921	−	0.0737921i
$514$	−7.16184			−0.315895
$515$	3.28497	+	0.737036i	0.144753	+	0.0324777i
$516$			8.12925i			0.357870i
$517$	−1.74509	−	1.74509i	−0.0767490	−	0.0767490i
$518$	4.40839	−	22.4192i	0.193694	−	0.985041i
$519$		−	17.9496i		−	0.787901i
$520$	−0.991325	−	1.56484i	−0.0434725	−	0.0686229i
$521$			15.6386i			0.685141i	0.939492	+	0.342570i	$0.111298\pi$
$521$			15.6386i			0.685141i	−0.939492	+	0.342570i	$0.888702\pi$
$522$	−7.03500	+	7.03500i	−0.307914	+	0.307914i
$523$	25.2794	−	25.2794i	1.10539	−	1.10539i	0.111644	−	0.993748i	$-0.464388\pi$
$523$	25.2794	−	25.2794i	1.10539	−	1.10539i	0.993748	−	0.111644i	$-0.0356118\pi$
$524$	−22.2039			−0.969982
$525$	−1.97450	−	13.0806i	−0.0861742	−	0.570883i
$526$	−5.89887			−0.257203
$527$	12.4055	−	12.4055i	0.540394	−	0.540394i
$528$	−3.39327	+	3.39327i	−0.147673	+	0.147673i
$529$		−	5.25045i		−	0.228280i
$530$	−4.00000	−	6.31415i	−0.173749	−	0.274269i
$531$		−	2.07912i		−	0.0902262i
$532$	−1.20658	+	6.13613i	−0.0523118	+	0.266035i
$533$	−6.44339	−	6.44339i	−0.279094	−	0.279094i
$534$			11.8989i			0.514915i
$535$	−6.63591	−	1.48887i	−0.286895	−	0.0643697i
$536$	1.38459			0.0598054
$537$	4.05056	+	4.05056i	0.174795	+	0.174795i
$538$	−17.4998	+	17.4998i	−0.754469	+	0.754469i
$539$	31.0907	+	12.7188i	1.33917	+	0.547838i
$540$	2.18183	+	0.489528i	0.0938908	+	0.0210659i
$541$	−2.70276			−0.116201			−0.0581005	−	0.998311i	$-0.518504\pi$
$541$	−2.70276			−0.116201			−0.0581005	+	0.998311i	$0.518504\pi$
$542$	−15.5535	−	15.5535i	−0.668080	−	0.668080i
$543$	6.30188	+	6.30188i	0.270439	+	0.270439i
$544$	−5.80748			−0.248994
$545$	24.3643	−	15.4347i	1.04365	−	0.661151i
$546$	−1.22170	−	1.81975i	−0.0522838	−	0.0778782i
$547$	1.65370	−	1.65370i	0.0707071	−	0.0707071i	−0.670869	−	0.741576i	$-0.734079\pi$
$547$	1.65370	−	1.65370i	0.0707071	−	0.0707071i	0.741576	+	0.670869i	$0.234079\pi$
$548$	5.92849	+	5.92849i	0.253253	+	0.253253i
$549$	5.55573			0.237113
$550$	8.09157	+	22.5885i	0.345026	+	0.963177i
$551$		−	23.5160i		−	1.00181i
$552$	−2.97906	−	2.97906i	−0.126797	−	0.126797i
$553$	−2.60376	+	13.2416i	−0.110723	+	0.563089i
$554$		−	17.0620i		−	0.724893i
$555$	16.3126	−	10.3340i	0.692433	−	0.438655i
$556$		−	8.46478i		−	0.358986i
$557$	−27.6462	+	27.6462i	−1.17141	+	1.17141i	−0.189535	+	0.981874i	$0.560698\pi$
$557$	−27.6462	+	27.6462i	−1.17141	+	1.17141i	−0.981874	+	0.189535i	$0.939302\pi$
$558$	−2.13613	+	2.13613i	−0.0904296	+	0.0904296i
$559$	6.73449			0.284839
$560$	−2.14226	−	5.51459i	−0.0905272	−	0.233034i
$561$	27.8690			1.17663
$562$	10.1589	−	10.1589i	0.428526	−	0.428526i
$563$	3.25447	−	3.25447i	0.137160	−	0.137160i	−0.635193	−	0.772353i	$-0.719080\pi$
$563$	3.25447	−	3.25447i	0.137160	−	0.137160i	0.772353	+	0.635193i	$0.219080\pi$
$564$			0.514280i			0.0216551i
$565$	−8.02051	+	35.7474i	−0.337425	+	1.50390i
$566$		−	15.6742i		−	0.658836i
$567$	2.59604	+	0.510472i	0.109023	+	0.0214378i
$568$	−3.71324	−	3.71324i	−0.155804	−	0.155804i
$569$		−	24.2411i		−	1.01624i	−0.861286	−	0.508121i	$-0.830340\pi$
$569$		−	24.2411i		−	1.01624i	0.861286	−	0.508121i	$-0.169660\pi$
$570$	−4.46478	+	2.82843i	−0.187009	+	0.118470i
$571$	17.3801			0.727336			0.363668	−	0.931529i	$-0.381524\pi$
$571$	17.3801			0.727336			0.363668	+	0.931529i	$0.381524\pi$
$572$	2.81108	+	2.81108i	0.117537	+	0.117537i
$573$	−5.42933	+	5.42933i	−0.226814	+	0.226814i
$574$	−16.2213	−	24.1620i	−0.677062	−	1.00850i
$575$	−19.8311	+	7.10384i	−0.827016	+	0.296251i
$576$	1.00000			0.0416667
$577$	−22.7961	−	22.7961i	−0.949016	−	0.949016i	0.0497462	−	0.998762i	$-0.484159\pi$
$577$	−22.7961	−	22.7961i	−0.949016	−	0.949016i	−0.998762	+	0.0497462i	$0.984159\pi$
$578$	11.8277	+	11.8277i	0.491967	+	0.491967i
$579$	−6.50201			−0.270214
$580$	11.9053	+	18.7930i	0.494341	+	0.780336i
$581$	−10.0082	+	6.71907i	−0.415212	+	0.278754i
$582$	−8.05595	+	8.05595i	−0.333930	+	0.333930i
$583$	11.3427	+	11.3427i	0.469767	+	0.469767i
$584$	8.64818			0.357864
$585$	0.405538	−	1.80748i	0.0167669	−	0.0747302i
$586$			8.99195i			0.371454i
$587$	−0.690067	−	0.690067i	−0.0284821	−	0.0284821i	0.692722	−	0.721204i	$-0.256411\pi$
$587$	−0.690067	−	0.690067i	−0.0284821	−	0.0284821i	−0.721204	+	0.692722i	$0.756411\pi$
$588$	−2.70711	−	6.45535i	−0.111639	−	0.266214i
$589$		−	7.14046i		−	0.294217i
$590$	−4.53628	−	1.01779i	−0.186756	−	0.0419017i
$591$			7.42648i			0.305485i
$592$	6.10651	−	6.10651i	0.250976	−	0.250976i
$593$	16.0464	−	16.0464i	0.658946	−	0.658946i	−0.296184	−	0.955131i	$-0.595714\pi$
$593$	16.0464	−	16.0464i	0.658946	−	0.658946i	0.955131	+	0.296184i	$0.0957143\pi$
$594$	−4.79881			−0.196897
$595$	−13.8485	+	31.4430i	−0.567733	+	1.28904i
$596$	4.43516			0.181671
$597$	−2.91443	+	2.91443i	−0.119280	+	0.119280i
$598$	−2.46793	+	2.46793i	−0.100921	+	0.100921i
$599$			0.262525i			0.0107265i	0.999986	+	0.00536325i	$0.00170718\pi$
$599$			0.262525i			0.0107265i	−0.999986	+	0.00536325i	$0.998293\pi$
$600$	2.13613	−	4.52072i	0.0872071	−	0.184558i
$601$			6.35838i			0.259364i	0.991556	+	0.129682i	$0.0413956\pi$
$601$			6.35838i			0.259364i	−0.991556	+	0.129682i	$0.958604\pi$
$602$	21.1038	+	4.14975i	0.860128	+	0.169131i
$603$	0.979056	+	0.979056i	0.0398703	+	0.0398703i
$604$		−	7.61497i		−	0.309849i
$605$	−14.3938	−	22.7211i	−0.585191	−	0.923745i
$606$	4.89020			0.198651
$607$	−22.5571	−	22.5571i	−0.915564	−	0.915564i	0.0811391	−	0.996703i	$-0.474144\pi$
$607$	−22.5571	−	22.5571i	−0.915564	−	0.915564i	−0.996703	+	0.0811391i	$0.974144\pi$
$608$	−1.67135	+	1.67135i	−0.0677823	+	0.0677823i
$609$	14.6720	+	21.8543i	0.594538	+	0.885582i
$610$	2.71969	−	12.1216i	0.110117	−	0.490790i
$611$	0.426043			0.0172359
$612$	−4.10651	−	4.10651i	−0.165996	−	0.165996i
$613$	−4.17864	−	4.17864i	−0.168774	−	0.168774i	0.617667	−	0.786440i	$-0.288078\pi$
$613$	−4.17864	−	4.17864i	−0.168774	−	0.168774i	−0.786440	+	0.617667i	$0.788078\pi$
$614$	−23.8525			−0.962610
$615$	5.38459	−	23.9991i	0.217128	−	0.967738i
$616$	7.07689	+	10.5412i	0.285136	+	0.424718i
$617$	10.9152	−	10.9152i	0.439428	−	0.439428i	−0.452391	−	0.891819i	$-0.649429\pi$
$617$	10.9152	−	10.9152i	0.439428	−	0.439428i	0.891819	+	0.452391i	$0.149429\pi$
$618$	1.06462	+	1.06462i	0.0428254	+	0.0428254i
$619$	2.48720			0.0999688			0.0499844	−	0.998750i	$-0.484083\pi$
$619$	2.48720			0.0999688			0.0499844	+	0.998750i	$0.484083\pi$
$620$	3.61497	+	5.70636i	0.145181	+	0.229173i
$621$		−	4.21302i		−	0.169063i
$622$	0.0418875	+	0.0418875i	0.00167954	+	0.00167954i
$623$	30.8899	+	6.07404i	1.23758	+	0.243351i
$624$		−	0.828427i		−	0.0331636i
$625$	−15.8739	−	19.3137i	−0.634956	−	0.772548i
$626$		−	0.648179i		−	0.0259064i
$627$	8.02051	−	8.02051i	0.320308	−	0.320308i
$628$	6.30188	−	6.30188i	0.251472	−	0.251472i
$629$	−50.1529			−1.99973
$630$	2.38459	−	5.41421i	0.0950045	−	0.215707i
$631$	−34.6801			−1.38059			−0.690296	−	0.723527i	$-0.742520\pi$
$631$	−34.6801			−1.38059			−0.690296	+	0.723527i	$0.742520\pi$
$632$	−3.60673	+	3.60673i	−0.143468	+	0.143468i
$633$	−19.5557	+	19.5557i	−0.777270	+	0.777270i
$634$		−	18.5445i		−	0.736497i
$635$	−1.23335	−	0.276721i	−0.0489438	−	0.0109813i
$636$		−	3.34271i		−	0.132547i
$637$	−5.34779	+	2.24264i	−0.211887	+	0.0888567i
$638$	−33.7596	−	33.7596i	−1.33656	−	1.33656i
$639$		−	5.25132i		−	0.207739i
$640$	0.489528	−	2.18183i	0.0193503	−	0.0862442i
$641$	−17.9572			−0.709268			−0.354634	−	0.935005i	$-0.615395\pi$
$641$	−17.9572			−0.709268			−0.354634	+	0.935005i	$0.615395\pi$
$642$	−2.15063	−	2.15063i	−0.0848786	−	0.0848786i
$643$	3.76560	−	3.76560i	0.148501	−	0.148501i	−0.628947	−	0.777448i	$-0.716514\pi$
$643$	3.76560	−	3.76560i	0.148501	−	0.148501i	0.777448	+	0.628947i	$0.216514\pi$
$644$	−9.25447	+	6.21302i	−0.364677	+	0.244827i
$645$	9.72774	+	15.3556i	0.383029	+	0.604626i
$646$	13.7269			0.540076
$647$	−24.7759	−	24.7759i	−0.974042	−	0.974042i	0.0256293	−	0.999672i	$-0.491841\pi$
$647$	−24.7759	−	24.7759i	−0.974042	−	0.974042i	−0.999672	+	0.0256293i	$0.991841\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	9.97731			0.391644
$650$	−3.74509	−	1.76963i	−0.146895	−	0.0694105i
$651$	4.45504	+	6.63591i	0.174607	+	0.260082i
$652$	10.8489	−	10.8489i	0.424877	−	0.424877i
$653$	−15.9566	−	15.9566i	−0.624431	−	0.624431i	0.322231	−	0.946661i	$-0.395567\pi$
$653$	−15.9566	−	15.9566i	−0.624431	−	0.624431i	−0.946661	+	0.322231i	$0.895567\pi$
$654$	12.8984			0.504369
$655$	−41.9417	+	26.5700i	−1.63880	+	1.03817i
$656$		−	10.9996i		−	0.429461i
$657$	6.11519	+	6.11519i	0.238576	+	0.238576i
$658$	1.33509	+	0.262525i	0.0520473	+	0.0102343i
$659$		−	15.8705i		−	0.618227i	−0.951025	−	0.309113i	$-0.899968\pi$
$659$		−	15.8705i		−	0.618227i	0.951025	−	0.309113i	$-0.100032\pi$
$660$	−2.34915	+	10.4702i	−0.0914406	+	0.407550i
$661$			15.8409i			0.616139i	0.951364	+	0.308069i	$0.0996829\pi$
$661$			15.8409i			0.616139i	−0.951364	+	0.308069i	$0.900317\pi$
$662$	−17.7688	+	17.7688i	−0.690602	+	0.690602i
$663$	−3.40194	+	3.40194i	−0.132121	+	0.132121i
$664$	−4.55617			−0.176814
$665$	5.06356	+	13.0346i	0.196357	+	0.505459i
$666$	8.63591			0.334635
$667$	29.6386	−	29.6386i	1.14761	−	1.14761i
$668$	−5.63635	+	5.63635i	−0.218077	+	0.218077i
$669$			21.6759i			0.838037i
$670$	2.61541	−	1.65685i	0.101042	−	0.0640099i
$671$			26.6609i			1.02923i
$672$	0.510472	−	2.59604i	0.0196919	−	0.100144i
$673$	4.25535	+	4.25535i	0.164032	+	0.164032i	0.784350	−	0.620318i	$-0.212997\pi$
$673$	4.25535	+	4.25535i	0.164032	+	0.164032i	−0.620318	+	0.784350i	$0.712997\pi$
$674$		−	23.4726i		−	0.904130i
$675$	4.70711	−	1.68616i	0.181177	−	0.0649004i
$676$	12.3137			0.473604
$677$	34.7614	+	34.7614i	1.33599	+	1.33599i	0.899906	+	0.436085i	$0.143635\pi$
$677$	34.7614	+	34.7614i	1.33599	+	1.33599i	0.436085	+	0.899906i	$0.356365\pi$
$678$	−11.5853	+	11.5853i	−0.444933	+	0.444933i
$679$	16.8012	+	25.0259i	0.644772	+	0.960406i
$680$	−10.9699	+	6.94944i	−0.420678	+	0.266499i
$681$	26.7264			1.02416
$682$	−10.2509	−	10.2509i	−0.392526	−	0.392526i
$683$	8.10025	+	8.10025i	0.309947	+	0.309947i	0.844889	−	0.534942i	$-0.179666\pi$
$683$	8.10025	+	8.10025i	0.309947	+	0.309947i	−0.534942	+	0.844889i	$0.679666\pi$
$684$	−2.36365			−0.0903764
$685$	18.2928	+	4.10428i	0.698931	+	0.156816i
$686$	−18.1402	+	3.73248i	−0.692598	+	0.142507i
$687$	9.41421	−	9.41421i	0.359175	−	0.359175i
$688$	5.74825	+	5.74825i	0.219150	+	0.219150i
$689$	−2.76919			−0.105498
$690$	−9.19208	−	2.06239i	−0.349936	−	0.0785139i
$691$		−	39.2567i		−	1.49340i	−0.665163	−	0.746699i	$-0.731638\pi$
$691$		−	39.2567i		−	1.49340i	0.665163	−	0.746699i	$-0.268362\pi$
$692$	−12.6923	−	12.6923i	−0.482489	−	0.482489i
$693$	−2.44966	+	12.4579i	−0.0930548	+	0.473236i
$694$		−	20.3949i		−	0.774181i
$695$	−10.1292	−	15.9894i	−0.384224	−	0.606512i
$696$			9.94900i			0.377116i
$697$	−45.1698	+	45.1698i	−1.71093	+	1.71093i
$698$	−20.2708	+	20.2708i	−0.767260	+	0.767260i
$699$	10.4015			0.393421
$700$	−10.6455	−	7.85318i	−0.402364	−	0.296822i
$701$	27.9663			1.05627			0.528137	−	0.849159i	$-0.322891\pi$
$701$	27.9663			1.05627			0.528137	+	0.849159i	$0.322891\pi$
$702$	0.585786	−	0.585786i	0.0221091	−	0.0221091i
$703$	−14.4337	+	14.4337i	−0.544376	+	0.544376i
$704$			4.79881i			0.180862i
$705$	0.615405	+	0.971440i	0.0231775	+	0.0365865i
$706$		−	7.16308i		−	0.269586i
$707$	2.49631	−	12.6951i	0.0938834	−	0.477450i
$708$	−1.47016	−	1.47016i	−0.0552521	−	0.0552521i
$709$		−	23.3998i		−	0.878799i	−0.898292	−	0.439399i	$-0.855191\pi$
$709$		−	23.3998i		−	0.878799i	0.898292	−	0.439399i	$-0.144809\pi$
$710$	−11.4575	−	2.57067i	−0.429991	−	0.0964754i
$711$	−5.10069			−0.191291
$712$	8.41377	+	8.41377i	0.315320	+	0.315320i
$713$	8.99956	−	8.99956i	0.337036	−	0.337036i
$714$	−12.7569	+	8.56440i	−0.477416	+	0.320515i
$715$	8.67377	+	1.94610i	0.324380	+	0.0727800i
$716$	5.72836			0.214079
$717$	9.22708	+	9.22708i	0.344592	+	0.344592i
$718$	−5.98550	−	5.98550i	−0.223377	−	0.223377i
$719$	50.8254			1.89547			0.947734	−	0.319060i	$-0.103367\pi$
$719$	50.8254			1.89547			0.947734	+	0.319060i	$0.103367\pi$
$720$	1.88893	−	1.19663i	0.0703963	−	0.0445959i
$721$	3.30726	−	2.22034i	0.123169	−	0.0826899i
$722$	−9.48453	+	9.48453i	−0.352978	+	0.352978i
$723$	−17.2917	−	17.2917i	−0.643085	−	0.643085i
$724$	8.91220			0.331219
$725$	44.9767	+	21.2524i	1.67039	+	0.789293i
$726$		−	12.0286i		−	0.446422i
$727$	5.10248	+	5.10248i	0.189240	+	0.189240i	0.795368	−	0.606127i	$-0.207278\pi$
$727$	5.10248	+	5.10248i	0.189240	+	0.189240i	−0.606127	+	0.795368i	$0.707278\pi$
$728$	−2.15063	−	0.422889i	−0.0797076	−	0.0156733i
$729$			1.00000i			0.0370370i
$730$	16.3358	−	10.3487i	0.604616	−	0.383023i
$731$		−	47.2105i		−	1.74614i
$732$	3.92849	−	3.92849i	0.145201	−	0.145201i
$733$	1.79925	−	1.79925i	0.0664567	−	0.0664567i	−0.673097	−	0.739554i	$-0.735036\pi$
$733$	1.79925	−	1.79925i	0.0664567	−	0.0664567i	0.739554	+	0.673097i	$0.235036\pi$
$734$	25.6941			0.948386
$735$	−12.8382	−	8.95430i	−0.473546	−	0.330284i
$736$	−4.21302			−0.155294
$737$	−4.69830	+	4.69830i	−0.173064	+	0.173064i
$738$	7.77786	−	7.77786i	0.286307	−	0.286307i
$739$		−	10.9122i		−	0.401412i	−0.979652	−	0.200706i	$-0.935676\pi$
$739$		−	10.9122i		−	0.401412i	0.979652	−	0.200706i	$-0.0643236\pi$
$740$	4.22752	−	18.8420i	0.155407	−	0.692648i
$741$			1.95811i			0.0719331i
$742$	−8.67780	−	1.70636i	−0.318572	−	0.0626424i
$743$	−12.3076	−	12.3076i	−0.451521	−	0.451521i	0.444338	−	0.895859i	$-0.353439\pi$
$743$	−12.3076	−	12.3076i	−0.451521	−	0.451521i	−0.895859	+	0.444338i	$0.853439\pi$
$744$			3.02094i			0.110753i
$745$	8.37771	−	5.30726i	0.306936	−	0.194443i
$746$	−21.8485			−0.799930
$747$	−3.22170	−	3.22170i	−0.117876	−	0.117876i
$748$	19.7064	−	19.7064i	0.720536	−	0.720536i
$749$	−6.68095	+	4.48528i	−0.244117	+	0.163889i
$750$	−1.37465	−	11.0955i	−0.0501952	−	0.405151i
$751$	−12.4787			−0.455354			−0.227677	−	0.973737i	$-0.573113\pi$
$751$	−12.4787			−0.455354			−0.227677	+	0.973737i	$0.573113\pi$
$752$	0.363651	+	0.363651i	0.0132610	+	0.0132610i
$753$	3.05701	+	3.05701i	0.111404	+	0.111404i
$754$	8.24202			0.300157
$755$	−9.11233	−	14.3842i	−0.331632	−	0.523493i
$756$	2.19663	−	1.47472i	0.0798908	−	0.0536350i
$757$	30.1930	−	30.1930i	1.09738	−	1.09738i	0.102667	−	0.994716i	$-0.467262\pi$
$757$	30.1930	−	30.1930i	1.09738	−	1.09738i	0.994716	−	0.102667i	$-0.0327377\pi$
$758$	22.8984	+	22.8984i	0.831709	+	0.831709i
$759$	20.2175			0.733848
$760$	−1.15707	+	5.15707i	−0.0419715	+	0.187067i
$761$			33.4920i			1.21409i	0.794669	+	0.607043i	$0.207644\pi$
$761$			33.4920i			1.21409i	−0.794669	+	0.607043i	$0.792356\pi$
$762$	−0.399714	−	0.399714i	−0.0144801	−	0.0144801i
$763$	6.58429	−	33.4848i	0.238367	−	1.21223i
$764$			7.67824i			0.277789i
$765$	−12.6709	−	2.84293i	−0.458118	−	0.102786i
$766$			22.8984i			0.827354i
$767$	−1.21792	+	1.21792i	−0.0439766	+	0.0439766i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−31.8992			−1.15032			−0.575158	−	0.818042i	$-0.695059\pi$
$769$	−31.8992			−1.15032			−0.575158	+	0.818042i	$0.695059\pi$
$770$	25.9818	+	11.4432i	0.936318	+	0.412385i
$771$	−7.16184			−0.257927
$772$	−4.59762	+	4.59762i	−0.165472	+	0.165472i
$773$	−11.0809	+	11.0809i	−0.398553	+	0.398553i	−0.877722	−	0.479170i	$-0.840938\pi$
$773$	−11.0809	+	11.0809i	−0.398553	+	0.398553i	0.479170	+	0.877722i	$0.340938\pi$
$774$			8.12925i			0.292200i
$775$	13.6569	+	6.45313i	0.490569	+	0.231803i
$776$			11.3928i			0.408979i
$777$	4.40839	−	22.4192i	0.158150	−	0.804283i
$778$	8.49173	+	8.49173i	0.304443	+	0.304443i
$779$			25.9991i			0.931515i
$780$	−0.991325	−	1.56484i	−0.0354951	−	0.0560304i
$781$	25.2001			0.901729
$782$	17.3008	+	17.3008i	0.618676	+	0.618676i
$783$	−7.03500	+	7.03500i	−0.251411	+	0.251411i
$784$	−6.47884	−	2.65041i	−0.231387	−	0.0946575i
$785$	4.36277	−	19.4449i	0.155714	−	0.694017i
$786$	−22.2039			−0.791987
$787$	27.9894	+	27.9894i	0.997714	+	0.997714i	0.999997	−	0.00228344i	$-0.000726843\pi$
$787$	27.9894	+	27.9894i	0.997714	+	0.997714i	−0.00228344	+	0.999997i	$0.500727\pi$
$788$	5.25132	+	5.25132i	0.187070	+	0.187070i
$789$	−5.89887			−0.210005
$790$	−2.49693	+	11.1288i	−0.0888368	+	0.395945i
$791$	24.1620	+	35.9900i	0.859103	+	1.27966i
$792$	−3.39327	+	3.39327i	−0.120575	+	0.120575i
$793$	−3.25447	−	3.25447i	−0.115570	−	0.115570i
$794$	−3.71485			−0.131835
$795$	−4.00000	−	6.31415i	−0.141865	−	0.223940i
$796$			4.12163i			0.146087i
$797$	6.43293	+	6.43293i	0.227866	+	0.227866i	0.811801	−	0.583935i	$-0.198488\pi$
$797$	6.43293	+	6.43293i	0.227866	+	0.227866i	−0.583935	+	0.811801i	$0.698488\pi$
$798$	−1.20658	+	6.13613i	−0.0427124	+	0.217217i
$799$		−	2.98667i		−	0.105661i
$800$	−1.68616	−	4.70711i	−0.0596149	−	0.166421i
$801$			11.8989i			0.420426i
$802$	13.9704	−	13.9704i	0.493311	−	0.493311i
$803$	−29.3456	+	29.3456i	−1.03558	+	1.03558i
$804$	1.38459			0.0488309
$805$	−10.0463	+	22.8102i	−0.354087	+	0.803954i
$806$	2.50263			0.0881514
$807$	−17.4998	+	17.4998i	−0.616021	+	0.616021i
$808$	3.45789	−	3.45789i	0.121648	−	0.121648i
$809$			36.3842i			1.27920i	0.768708	+	0.639599i	$0.220900\pi$
$809$			36.3842i			1.27920i	−0.768708	+	0.639599i	$0.779100\pi$
$810$	2.18183	+	0.489528i	0.0766615	+	0.0172003i
$811$		−	26.5629i		−	0.932750i	−0.884587	−	0.466375i	$-0.845560\pi$
$811$		−	26.5629i		−	0.932750i	0.884587	−	0.466375i	$-0.154440\pi$
$812$	25.8280	+	5.07868i	0.906385	+	0.178227i
$813$	−15.5535	−	15.5535i	−0.545485	−	0.545485i
$814$			41.4421i			1.45254i
$815$	7.51069	−	33.4751i	0.263088	−	1.17258i
$816$	−5.80748			−0.203303
$817$	−13.5868	−	13.5868i	−0.475344	−	0.475344i
$818$	−10.8786	+	10.8786i	−0.380360	+	0.380360i
$819$	−1.22170	−	1.81975i	−0.0426895	−	0.0635873i
$820$	−13.1625	−	20.7774i	−0.459653	−	0.725579i
$821$	−45.9655			−1.60421			−0.802103	−	0.597186i	$-0.796286\pi$
$821$	−45.9655			−1.60421			−0.802103	+	0.597186i	$0.796286\pi$
$822$	5.92849	+	5.92849i	0.206780	+	0.206780i
$823$	36.5397	+	36.5397i	1.27369	+	1.27369i	0.944134	+	0.329561i	$0.106901\pi$
$823$	36.5397	+	36.5397i	1.27369	+	1.27369i	0.329561	+	0.944134i	$0.393099\pi$
$824$	1.50560			0.0524502
$825$	8.09157	+	22.5885i	0.281712	+	0.786431i
$826$	−4.56707	+	3.06612i	−0.158909	+	0.106684i
$827$	15.7275	−	15.7275i	0.546898	−	0.546898i	−0.378644	−	0.925542i	$-0.623610\pi$
$827$	15.7275	−	15.7275i	0.546898	−	0.546898i	0.925542	+	0.378644i	$0.123610\pi$
$828$	−2.97906	−	2.97906i	−0.103529	−	0.103529i
$829$	29.2892			1.01725			0.508627	−	0.860987i	$-0.330153\pi$
$829$	29.2892			1.01725			0.508627	+	0.860987i	$0.330153\pi$
$830$	−8.60629	+	5.45207i	−0.298729	+	0.189244i
$831$		−	17.0620i		−	0.591873i
$832$	−0.585786	−	0.585786i	−0.0203085	−	0.0203085i
$833$	15.7215	+	37.4894i	0.544717	+	1.29893i
$834$		−	8.46478i		−	0.293111i
$835$	−3.90203	+	17.3913i	−0.135035	+	0.601852i
$836$		−	11.3427i		−	0.392296i
$837$	−2.13613	+	2.13613i	−0.0738354	+	0.0738354i
$838$	19.8543	−	19.8543i	0.685856	−	0.685856i
$839$	−2.41886			−0.0835082			−0.0417541	−	0.999128i	$-0.513295\pi$
$839$	−2.41886			−0.0835082			−0.0417541	+	0.999128i	$0.513295\pi$
$840$	−2.14226	−	5.51459i	−0.0739151	−	0.190271i
$841$	−69.9826			−2.41319
$842$	8.12013	−	8.12013i	0.279838	−	0.279838i
$843$	10.1589	−	10.1589i	0.349890	−	0.349890i
$844$			27.6560i			0.951958i
$845$	23.2598	−	14.7350i	0.800160	−	0.506900i
$846$			0.514280i			0.0176813i
$847$	−31.2266	−	6.14024i	−1.07296	−	0.210981i
$848$	−2.36365	−	2.36365i	−0.0811681	−	0.0811681i
$849$		−	15.6742i		−	0.537937i
$850$	−12.4055	+	26.2540i	−0.425506	+	0.900506i
$851$	−36.3833			−1.24720
$852$	−3.71324	−	3.71324i	−0.127214	−	0.127214i
$853$	−28.0222	+	28.0222i	−0.959461	+	0.959461i	−0.999210	−	0.0397491i	$-0.987344\pi$
$853$	−28.0222	+	28.0222i	−0.959461	+	0.959461i	0.0397491	+	0.999210i	$0.487344\pi$
$854$	−8.19314	−	12.2039i	−0.280363	−	0.417609i
$855$	−4.46478	+	2.82843i	−0.152692	+	0.0967302i
$856$	−3.04145			−0.103955
$857$	19.1782	+	19.1782i	0.655115	+	0.655115i	0.954220	−	0.299105i	$-0.0966882\pi$
$857$	19.1782	+	19.1782i	0.655115	+	0.655115i	−0.299105	+	0.954220i	$0.596688\pi$
$858$	2.81108	+	2.81108i	0.0959686	+	0.0959686i
$859$	−45.5754			−1.55501			−0.777506	−	0.628876i	$-0.783515\pi$
$859$	−45.5754			−1.55501			−0.777506	+	0.628876i	$0.783515\pi$
$860$	17.7366	+	3.97949i	0.604813	+	0.135700i
$861$	−16.2213	−	24.1620i	−0.552819	−	0.823439i
$862$	8.01362	−	8.01362i	0.272945	−	0.272945i
$863$	4.69515	+	4.69515i	0.159825	+	0.159825i	0.782489	−	0.622664i	$-0.213950\pi$
$863$	4.69515	+	4.69515i	0.159825	+	0.159825i	−0.622664	+	0.782489i	$0.713950\pi$
$864$	1.00000			0.0340207
$865$	−39.1629	−	8.78684i	−1.33158	−	0.298762i
$866$		−	6.94856i		−	0.236122i
$867$	11.8277	+	11.8277i	0.401689	+	0.401689i
$868$	7.84249	+	1.54211i	0.266191	+	0.0523425i
$869$		−	24.4772i		−	0.830333i
$870$	11.9053	+	18.7930i	0.403628	+	0.637142i
$871$		−	1.14704i		−	0.0388658i
$872$	9.12057	−	9.12057i	0.308862	−	0.308862i
$873$	−8.05595	+	8.05595i	−0.272653	+	0.272653i
$874$	9.95811			0.336838
$875$	−29.5061	−	2.09529i	−0.997488	−	0.0708339i
$876$	8.64818			0.292195
$877$	17.5321	−	17.5321i	0.592017	−	0.592017i	−0.346159	−	0.938176i	$-0.612514\pi$
$877$	17.5321	−	17.5321i	0.592017	−	0.592017i	0.938176	+	0.346159i	$0.112514\pi$
$878$	−16.1025	+	16.1025i	−0.543432	+	0.543432i
$879$			8.99195i			0.303291i
$880$	5.74242	+	9.06462i	0.193577	+	0.305568i
$881$		−	3.93358i		−	0.132526i	−0.997802	−	0.0662628i	$-0.978892\pi$
$881$		−	3.93358i		−	0.132526i	0.997802	−	0.0662628i	$-0.0211076\pi$
$882$	−2.70711	−	6.45535i	−0.0911530	−	0.217363i
$883$	34.7362	+	34.7362i	1.16896	+	1.16896i	0.982453	+	0.186512i	$0.0597184\pi$
$883$	34.7362	+	34.7362i	1.16896	+	1.16896i	0.186512	+	0.982453i	$0.440282\pi$
$884$			4.81108i			0.161814i
$885$	−4.53628	−	1.01779i	−0.152485	−	0.0342126i
$886$	−36.5134			−1.22669
$887$	−33.3213	−	33.3213i	−1.11882	−	1.11882i	−0.991915	−	0.126906i	$-0.959495\pi$
$887$	−33.3213	−	33.3213i	−1.11882	−	1.11882i	−0.126906	−	0.991915i	$-0.540505\pi$
$888$	6.10651	−	6.10651i	0.204921	−	0.204921i
$889$	−1.24172	+	0.833631i	−0.0416458	+	0.0279591i
$890$	25.9613	+	5.82483i	0.870224	+	0.195249i
$891$	−4.79881			−0.160766
$892$	15.3271	+	15.3271i	0.513191	+	0.513191i
$893$	−0.859544	−	0.859544i	−0.0287635	−	0.0287635i
$894$	4.43516			0.148334
$895$	10.8205	−	6.85476i	0.361689	−	0.229129i
$896$	−1.47472	−	2.19663i	−0.0492669	−	0.0733844i
$897$	−2.46793	+	2.46793i	−0.0824018	+	0.0824018i
$898$	−6.75692	−	6.75692i	−0.225481	−	0.225481i
$899$	−30.0554			−1.00240
$900$	2.13613	−	4.52072i	0.0712043	−	0.150691i
$901$			19.4127i			0.646731i
$902$	37.3245	+	37.3245i	1.24277	+	1.24277i
$903$	21.1038	+	4.14975i	0.702292	+	0.138095i
$904$			16.3842i			0.544929i
$905$	16.8345	−	10.6647i	0.559599	−	0.354505i
$906$		−	7.61497i		−	0.252990i
$907$	−0.932707	+	0.932707i	−0.0309700	+	0.0309700i	−0.722422	−	0.691452i	$-0.756971\pi$
$907$	−0.932707	+	0.932707i	−0.0309700	+	0.0309700i	0.691452	+	0.722422i	$0.256971\pi$
$908$	18.8984	−	18.8984i	0.627167	−	0.627167i
$909$	4.89020			0.162198
$910$	−4.56844	+	1.77471i	−0.151442	+	0.0588311i
$911$	45.5690			1.50977			0.754885	−	0.655857i	$-0.227693\pi$
$911$	45.5690			1.50977			0.754885	+	0.655857i	$0.227693\pi$
$912$	−1.67135	+	1.67135i	−0.0553440	+	0.0553440i
$913$	15.4603	−	15.4603i	0.511661	−	0.511661i
$914$			23.5563i			0.779175i
$915$	2.71969	−	12.1216i	0.0899100	−	0.400729i
$916$		−	13.3137i		−	0.439897i
$917$	−11.3345	+	57.6422i	−0.374297	+	1.90351i
$918$	−4.10651	−	4.10651i	−0.135535	−	0.135535i
$919$		−	20.8574i		−	0.688023i	−0.938965	−	0.344011i	$-0.888214\pi$
$919$		−	20.8574i		−	0.688023i	0.938965	−	0.344011i	$-0.111786\pi$
$920$	−7.95811	+	5.04145i	−0.262371	+	0.166212i
$921$	−23.8525			−0.785967
$922$	−17.3073	−	17.3073i	−0.569984	−	0.569984i
$923$	−3.07615	+	3.07615i	−0.101253	+	0.101253i
$924$	7.07689	+	10.5412i	0.232813	+	0.346781i
$925$	−14.5616	−	40.6502i	−0.478781	−	1.33657i
$926$	9.65939			0.317427
$927$	1.06462	+	1.06462i	0.0349668	+	0.0349668i
$928$	7.03500	+	7.03500i	0.230935	+	0.230935i
$929$	9.10069			0.298584			0.149292	−	0.988793i	$-0.452301\pi$
$929$	9.10069			0.298584			0.149292	+	0.988793i	$0.452301\pi$
$930$	3.61497	+	5.70636i	0.118539	+	0.187119i
$931$	15.3137	+	6.26464i	0.501887	+	0.205315i
$932$	7.35498	−	7.35498i	0.240920	−	0.240920i
$933$	0.0418875	+	0.0418875i	0.00137134	+	0.00137134i
$934$	28.6382			0.937070
$935$	13.6427	−	60.8053i	0.446163	−	1.98855i
$936$		−	0.828427i		−	0.0270780i
$937$	3.34154	+	3.34154i	0.109163	+	0.109163i	0.759579	−	0.650415i	$-0.225405\pi$
$937$	3.34154	+	3.34154i	0.109163	+	0.109163i	−0.650415	+	0.759579i	$0.725405\pi$
$938$	0.706797	−	3.59446i	0.0230777	−	0.117363i
$939$		−	0.648179i		−	0.0211525i
$940$	1.12207	+	0.251755i	0.0365979	+	0.00821133i
$941$			42.2862i			1.37849i	0.724528	+	0.689245i	$0.242058\pi$
$941$			42.2862i			1.37849i	−0.724528	+	0.689245i	$0.757942\pi$
$942$	6.30188	−	6.30188i	0.205326	−	0.205326i
$943$	−32.7683	+	32.7683i	−1.06708	+	1.06708i
$944$	−2.07912			−0.0676697
$945$	2.38459	−	5.41421i	0.0775709	−	0.176124i
$946$	−39.0107			−1.26835
$947$	−0.00253441	+	0.00253441i	−8.23572e−5	+	8.23572e-5i	−0.707148	−	0.707066i	$-0.750019\pi$
$947$	−0.00253441	+	0.00253441i	−8.23572e−5	+	8.23572e-5i	0.707066	+	0.707148i	$0.250019\pi$
$948$	−3.60673	+	3.60673i	−0.117141	+	0.117141i
$949$		−	7.16439i		−	0.232566i
$950$	3.98550	+	11.1260i	0.129307	+	0.360974i
$951$		−	18.5445i		−	0.601347i
$952$	−2.96456	+	15.0765i	−0.0960818	+	0.488631i
$953$	14.4673	+	14.4673i	0.468642	+	0.468642i	0.901474	−	0.432832i	$-0.142486\pi$
$953$	14.4673	+	14.4673i	0.468642	+	0.468642i	−0.432832	+	0.901474i	$0.642486\pi$
$954$		−	3.34271i		−	0.108224i
$955$	9.18805	+	14.5037i	0.297318	+	0.469328i
$956$	13.0491			0.422037
$957$	−33.7596	−	33.7596i	−1.09129	−	1.09129i
$958$	−4.82843	+	4.82843i	−0.155999	+	0.155999i
$959$	18.4169	−	12.3643i	0.594714	−	0.399263i
$960$	0.489528	−	2.18183i	0.0157995	−	0.0704181i
$961$	21.8739			0.705610
$962$	−5.05880	−	5.05880i	−0.163102	−	0.163102i
$963$	−2.15063	−	2.15063i	−0.0693031	−	0.0693031i
$964$	−24.4542			−0.787616
$965$	−3.18292	+	14.1863i	−0.102462	+	0.456672i
$966$	−9.25447	+	6.21302i	−0.297758	+	0.199901i
$967$	−4.38595	+	4.38595i	−0.141043	+	0.141043i	−0.774103	−	0.633060i	$-0.781799\pi$
$967$	−4.38595	+	4.38595i	−0.141043	+	0.141043i	0.633060	+	0.774103i	$0.281799\pi$
$968$	−8.50548	−	8.50548i	−0.273376	−	0.273376i
$969$	13.7269			0.440970
$970$	13.6331	+	21.5203i	0.437731	+	0.690975i
$971$			24.3630i			0.781847i	0.920423	+	0.390923i	$0.127844\pi$
$971$			24.3630i			0.781847i	−0.920423	+	0.390923i	$0.872156\pi$
$972$	0.707107	+	0.707107i	0.0226805	+	0.0226805i
$973$	−21.9749	−	4.32103i	−0.704483	−	0.138526i
$974$		−	0.463279i		−	0.0148444i
$975$	−3.74509	−	1.76963i	−0.119939	−	0.0566734i
$976$		−	5.55573i		−	0.177835i
$977$	38.9763	−	38.9763i	1.24696	−	1.24696i	0.289905	−	0.957055i	$-0.406376\pi$
$977$	38.9763	−	38.9763i	1.24696	−	1.24696i	0.957055	−	0.289905i	$-0.0936239\pi$
$978$	10.8489	−	10.8489i	0.346911	−	0.346911i
$979$	−57.1004			−1.82494
$980$	−15.4097	+	2.74636i	−0.492243	+	0.0877292i
$981$	12.8984			0.411815
$982$	2.39371	−	2.39371i	0.0763863	−	0.0763863i
$983$	14.5896	−	14.5896i	0.465335	−	0.465335i	−0.435065	−	0.900399i	$-0.643274\pi$
$983$	14.5896	−	14.5896i	0.465335	−	0.465335i	0.900399	+	0.435065i	$0.143274\pi$
$984$		−	10.9996i		−	0.350653i
$985$	16.2033	+	3.63547i	0.516280	+	0.115836i
$986$		−	57.7786i		−	1.84005i
$987$	1.33509	+	0.262525i	0.0424964	+	0.00835628i
$988$	1.38459	+	1.38459i	0.0440498	+	0.0440498i
$989$		−	34.2487i		−	1.08905i
$990$	−2.34915	+	10.4702i	−0.0746609	+	0.332764i
$991$	47.6560			1.51384			0.756921	−	0.653506i	$-0.226703\pi$
$991$	47.6560			1.51384			0.756921	+	0.653506i	$0.226703\pi$
$992$	2.13613	+	2.13613i	0.0678222	+	0.0678222i
$993$	−17.7688	+	17.7688i	−0.563874	+	0.563874i
$994$	−11.5352	+	7.74421i	−0.365875	+	0.245632i
$995$	4.93209	+	7.78548i	0.156358	+	0.246816i
$996$	−4.55617			−0.144368
$997$	−0.631258	−	0.631258i	−0.0199921	−	0.0199921i	0.697040	−	0.717032i	$-0.254500\pi$
$997$	−0.631258	−	0.631258i	−0.0199921	−	0.0199921i	−0.717032	+	0.697040i	$0.754500\pi$
$998$	2.95409	+	2.95409i	0.0935101	+	0.0935101i
$999$	8.63591			0.273228

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.m.a.13.3	✓	8
3.2	odd	2		630.2.p.b.433.2		8
4.3	odd	2		1680.2.cz.b.433.1		8
5.2	odd	4		210.2.m.b.97.4	yes	8
5.3	odd	4		1050.2.m.a.307.2		8
5.4	even	2		1050.2.m.b.643.2		8
7.6	odd	2		210.2.m.b.13.4	yes	8
15.2	even	4		630.2.p.c.307.1		8
20.7	even	4		1680.2.cz.a.97.4		8
21.20	even	2		630.2.p.c.433.1		8
28.27	even	2		1680.2.cz.a.433.4		8
35.13	even	4		1050.2.m.b.307.2		8
35.27	even	4	inner	210.2.m.a.97.3	yes	8
35.34	odd	2		1050.2.m.a.643.2		8
105.62	odd	4		630.2.p.b.307.2		8
140.27	odd	4		1680.2.cz.b.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.m.a.13.3	✓	8	1.1	even	1	trivial
210.2.m.a.97.3	yes	8	35.27	even	4	inner
210.2.m.b.13.4	yes	8	7.6	odd	2
210.2.m.b.97.4	yes	8	5.2	odd	4
630.2.p.b.307.2		8	105.62	odd	4
630.2.p.b.433.2		8	3.2	odd	2
630.2.p.c.307.1		8	15.2	even	4
630.2.p.c.433.1		8	21.20	even	2
1050.2.m.a.307.2		8	5.3	odd	4
1050.2.m.a.643.2		8	35.34	odd	2
1050.2.m.b.307.2		8	35.13	even	4
1050.2.m.b.643.2		8	5.4	even	2
1680.2.cz.a.97.4		8	20.7	even	4
1680.2.cz.a.433.4		8	28.27	even	2
1680.2.cz.b.97.1		8	140.27	odd	4
1680.2.cz.b.433.1		8	4.3	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.19663 - 1.88893i) q^{5} -1.00000i q^{6} +(-2.59604 - 0.510472i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} -1.00000i q^{4} +(-1.19663 - 1.88893i) q^{5} -1.00000i q^{6} +(-2.59604 - 0.510472i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(-2.18183 - 0.489528i) q^{10} +4.79881 q^{11} +(-0.707107 - 0.707107i) q^{12} +(-0.585786 + 0.585786i) q^{13} +(-2.19663 + 1.47472i) q^{14} +(-2.18183 - 0.489528i) q^{15} -1.00000 q^{16} +(4.10651 + 4.10651i) q^{17} +(-0.707107 - 0.707107i) q^{18} +2.36365 q^{19} +(-1.88893 + 1.19663i) q^{20} +(-2.19663 + 1.47472i) q^{21} +(3.39327 - 3.39327i) q^{22} +(2.97906 + 2.97906i) q^{23} -1.00000 q^{24} +(-2.13613 + 4.52072i) q^{25} +0.828427i q^{26} +(-0.707107 - 0.707107i) q^{27} +(-0.510472 + 2.59604i) q^{28} -9.94900i q^{29} +(-1.88893 + 1.19663i) q^{30} -3.02094i q^{31} +(-0.707107 + 0.707107i) q^{32} +(3.39327 - 3.39327i) q^{33} +5.80748 q^{34} +(2.14226 + 5.51459i) q^{35} -1.00000 q^{36} +(-6.10651 + 6.10651i) q^{37} +(1.67135 - 1.67135i) q^{38} +0.828427i q^{39} +(-0.489528 + 2.18183i) q^{40} +10.9996i q^{41} +(-0.510472 + 2.59604i) q^{42} +(-5.74825 - 5.74825i) q^{43} -4.79881i q^{44} +(-1.88893 + 1.19663i) q^{45} +4.21302 q^{46} +(-0.363651 - 0.363651i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(6.47884 + 2.65041i) q^{49} +(1.68616 + 4.70711i) q^{50} +5.80748 q^{51} +(0.585786 + 0.585786i) q^{52} +(2.36365 + 2.36365i) q^{53} -1.00000 q^{54} +(-5.74242 - 9.06462i) q^{55} +(1.47472 + 2.19663i) q^{56} +(1.67135 - 1.67135i) q^{57} +(-7.03500 - 7.03500i) q^{58} +2.07912 q^{59} +(-0.489528 + 2.18183i) q^{60} +5.55573i q^{61} +(-2.13613 - 2.13613i) q^{62} +(-0.510472 + 2.59604i) q^{63} +1.00000i q^{64} +(1.80748 + 0.405538i) q^{65} -4.79881i q^{66} +(-0.979056 + 0.979056i) q^{67} +(4.10651 - 4.10651i) q^{68} +4.21302 q^{69} +(5.41421 + 2.38459i) q^{70} +5.25132 q^{71} +(-0.707107 + 0.707107i) q^{72} +(-6.11519 + 6.11519i) q^{73} +8.63591i q^{74} +(1.68616 + 4.70711i) q^{75} -2.36365i q^{76} +(-12.4579 - 2.44966i) q^{77} +(0.585786 + 0.585786i) q^{78} -5.10069i q^{79} +(1.19663 + 1.88893i) q^{80} -1.00000 q^{81} +(7.77786 + 7.77786i) q^{82} +(3.22170 - 3.22170i) q^{83} +(1.47472 + 2.19663i) q^{84} +(2.84293 - 12.6709i) q^{85} -8.12925 q^{86} +(-7.03500 - 7.03500i) q^{87} +(-3.39327 - 3.39327i) q^{88} -11.8989 q^{89} +(-0.489528 + 2.18183i) q^{90} +(1.81975 - 1.22170i) q^{91} +(2.97906 - 2.97906i) q^{92} +(-2.13613 - 2.13613i) q^{93} -0.514280 q^{94} +(-2.82843 - 4.46478i) q^{95} +1.00000i q^{96} +(-8.05595 - 8.05595i) q^{97} +(6.45535 - 2.70711i) q^{98} -4.79881i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^7	\( 8 q + 4 q^{7} - 4 q^{10} + 8 q^{11} - 16 q^{13} - 8 q^{14} - 4 q^{15} - 8 q^{16} + 12 q^{17} - 8 q^{19} + 4 q^{20} - 8 q^{21} + 8 q^{22} + 16 q^{23} - 8 q^{24} - 4 q^{25} - 8 q^{28} + 4 q^{30} + 8 q^{33} + 16 q^{34} + 8 q^{35} - 8 q^{36} - 28 q^{37} - 4 q^{38} - 8 q^{42} + 4 q^{45} - 8 q^{46} + 24 q^{47} + 4 q^{49} + 16 q^{51} + 16 q^{52} - 8 q^{53} - 8 q^{54} + 28 q^{55} + 4 q^{56} - 4 q^{57} - 12 q^{58} + 8 q^{59} - 4 q^{62} - 8 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 32 q^{70} + 8 q^{71} - 28 q^{73} - 44 q^{77} + 16 q^{78} - 8 q^{81} + 24 q^{82} - 16 q^{83} + 4 q^{84} + 28 q^{85} + 8 q^{86} - 12 q^{87} - 8 q^{88} - 64 q^{89} - 8 q^{91} + 16 q^{92} - 4 q^{93} + 8 q^{94} - 28 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 - 4 * q^10 + 8 * q^11 - 16 * q^13 - 8 * q^14 - 4 * q^15 - 8 * q^16 + 12 * q^17 - 8 * q^19 + 4 * q^20 - 8 * q^21 + 8 * q^22 + 16 * q^23 - 8 * q^24 - 4 * q^25 - 8 * q^28 + 4 * q^30 + 8 * q^33 + 16 * q^34 + 8 * q^35 - 8 * q^36 - 28 * q^37 - 4 * q^38 - 8 * q^42 + 4 * q^45 - 8 * q^46 + 24 * q^47 + 4 * q^49 + 16 * q^51 + 16 * q^52 - 8 * q^53 - 8 * q^54 + 28 * q^55 + 4 * q^56 - 4 * q^57 - 12 * q^58 + 8 * q^59 - 4 * q^62 - 8 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 32 * q^70 + 8 * q^71 - 28 * q^73 - 44 * q^77 + 16 * q^78 - 8 * q^81 + 24 * q^82 - 16 * q^83 + 4 * q^84 + 28 * q^85 + 8 * q^86 - 12 * q^87 - 8 * q^88 - 64 * q^89 - 8 * q^91 + 16 * q^92 - 4 * q^93 + 8 * q^94 - 28 * q^97

Introduction

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