LMFDB - Embedded newform 210.2.m.b.97.4

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			97.4
Root			$0.692297i$ of defining polynomial
Character	$\chi$	$=$	210.97
Dual form			210.2.m.b.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.19663 - 1.88893i) q^{5} -1.00000i q^{6} +(0.510472 - 2.59604i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(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} +(0.510472 - 2.59604i) 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} +(2.59604 + 0.510472i) 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} +(-4.29289 - 4.07076i) 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} +(-2.59604 - 0.510472i) 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} +(2.59604 + 0.510472i) 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} +(-0.157074 - 5.91399i) 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} +(2.44966 - 12.4579i) 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} +(-2.70711 - 6.45535i) q^{98} +4.79881i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{7}+O(q^{10}) $ 8 * q + 8 * q^7	$ 8 q + 8 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} - 4 q^{28} + 4 q^{30} - 8 q^{33} - 16 q^{34} - 40 q^{35} - 8 q^{36} - 28 q^{37} + 4 q^{38} + 4 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} - 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} + 4 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} - 16 q^{98}+O(q^{100}) $ 8 * q + 8 * 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 - 4 * q^28 + 4 * q^30 - 8 * q^33 - 16 * q^34 - 40 * q^35 - 8 * q^36 - 28 * q^37 + 4 * q^38 + 4 * 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 - 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 + 4 * 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 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	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
$7$	0.510472	−	2.59604i	0.192940	−	0.981211i
$7$	0.510472	−	2.59604i	0.192940	−	0.981211i
$8$	−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	$-0.213351\pi$
$13$	0.585786	+	0.585786i	0.162468	+	0.162468i	−0.621191	+	0.783659i	$0.713351\pi$
$14$	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	$-0.998721\pi$
$17$	−4.10651	+	4.10651i	−0.995975	+	0.995975i	0.00401675	+	0.999992i	$0.498721\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−2.36365			−0.542259			−0.271129	−	0.962543i	$-0.587397\pi$
$19$	−2.36365			−0.542259			−0.271129	+	0.962543i	$0.587397\pi$
$20$	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	−0.324656	−	0.945832i	$-0.605249\pi$
$23$	2.97906	−	2.97906i	0.621176	−	0.621176i	0.945832	+	0.324656i	$0.105249\pi$
$24$	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
$28$	2.59604	+	0.510472i	0.490605	+	0.0964701i
$29$			9.94900i			1.84748i	0.383017	+	0.923741i	$0.374885\pi$
$29$			9.94900i			1.84748i	−0.383017	+	0.923741i	$0.625115\pi$
$30$	−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
$35$	−4.29289	−	4.07076i	−0.725631	−	0.688084i
$36$	−1.00000			−0.166667
$37$	−6.10651	−	6.10651i	−1.00390	−	1.00390i	−0.999992	−	0.00391185i	$-0.998755\pi$
$37$	−6.10651	−	6.10651i	−1.00390	−	1.00390i	−0.00391185	−	0.999992i	$-0.501245\pi$
$38$	−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	$0.671135\pi$
$42$	−2.59604	−	0.510472i	−0.400578	−	0.0787675i
$43$	−5.74825	+	5.74825i	−0.876599	+	0.876599i	−0.993181	−	0.116582i	$-0.962806\pi$
$43$	−5.74825	+	5.74825i	−0.876599	+	0.876599i	0.116582	+	0.993181i	$0.462806\pi$
$44$			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	$-0.738058\pi$
$47$	0.363651	−	0.363651i	0.0530439	−	0.0530439i	0.733131	+	0.680087i	$0.238058\pi$
$48$	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	−0.525884	−	0.850556i	$-0.676265\pi$
$53$	2.36365	−	2.36365i	0.324672	−	0.324672i	0.850556	+	0.525884i	$0.176265\pi$
$54$	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	$-0.543212\pi$
$59$	−2.07912			−0.270679			−0.135339	+	0.990799i	$0.543212\pi$
$60$	−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
$63$	2.59604	+	0.510472i	0.327070	+	0.0643134i
$64$		−	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	0.644768	−	0.764379i	$-0.276954\pi$
$67$	−0.979056	−	0.979056i	−0.119611	−	0.119611i	−0.764379	+	0.644768i	$0.776954\pi$
$68$	−4.10651	−	4.10651i	−0.497988	−	0.497988i
$69$	−4.21302			−0.507188
$70$	−0.157074	−	5.91399i	−0.0187739	−	0.706858i
$71$	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	$-0.0810880\pi$
$73$	6.11519	+	6.11519i	0.715728	+	0.715728i	−0.251999	+	0.967727i	$0.581088\pi$
$74$		−	8.63591i		−	1.00390i
$75$	−1.68616	+	4.70711i	−0.194701	+	0.543530i
$76$		−	2.36365i		−	0.271129i
$77$	2.44966	−	12.4579i	0.279164	−	1.41971i
$78$	0.585786	−	0.585786i	0.0663273	−	0.0663273i
$79$			5.10069i			0.573872i	0.957950	+	0.286936i	$0.0926367\pi$
$79$			5.10069i			0.573872i	−0.957950	+	0.286936i	$0.907363\pi$
$80$	−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	$-0.330448\pi$
$83$	−3.22170	−	3.22170i	−0.353627	−	0.353627i	−0.861457	+	0.507830i	$0.830448\pi$
$84$	−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	$-0.282793\pi$
$89$	11.8989			1.26128			0.630639	+	0.776076i	$0.282793\pi$
$90$	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	$-0.553684\pi$
$97$	8.05595	−	8.05595i	0.817958	−	0.817958i	0.985812	+	0.167854i	$0.0536838\pi$
$98$	−2.70711	−	6.45535i	−0.273459	−	0.652089i
$99$			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	$-0.226367\pi$
$103$	1.06462	+	1.06462i	0.104900	+	0.104900i	−0.652709	+	0.757609i	$0.726367\pi$
$104$	−0.828427			−0.0812340
$105$	0.157074	+	5.91399i	0.0153288	+	0.577147i
$106$	3.34271			0.324672
$107$	2.15063	+	2.15063i	0.207909	+	0.207909i	0.803378	−	0.595469i	$-0.203034\pi$
$107$	2.15063	+	2.15063i	0.207909	+	0.207909i	−0.595469	+	0.803378i	$0.703034\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$		−	12.8984i		−	1.23545i	−0.786396	−	0.617723i	$-0.788055\pi$
$109$		−	12.8984i		−	1.23545i	0.786396	−	0.617723i	$-0.211945\pi$
$110$	10.4702	−	2.34915i	0.998291	−	0.223983i
$111$			8.63591i			0.819684i
$112$	−0.510472	+	2.59604i	−0.0482351	+	0.245303i
$113$	−11.5853	+	11.5853i	−1.08986	+	1.08986i	−0.0943155	+	0.995542i	$0.530066\pi$
$113$	−11.5853	+	11.5853i	−1.08986	+	1.08986i	−0.995542	+	0.0943155i	$0.969934\pi$
$114$			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	0.724619	−	0.689150i	$-0.242016\pi$
$127$	0.399714	+	0.399714i	0.0354689	+	0.0354689i	−0.689150	+	0.724619i	$0.742016\pi$
$128$	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
$133$	−1.20658	+	6.13613i	−0.104624	+	0.532070i
$134$		−	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	0.406947	−	0.913452i	$-0.366594\pi$
$137$	−5.92849	−	5.92849i	−0.506505	−	0.506505i	−0.913452	+	0.406947i	$0.866594\pi$
$138$	−2.97906	−	2.97906i	−0.253594	−	0.253594i
$139$	−8.46478			−0.717973			−0.358986	−	0.933343i	$-0.616878\pi$
$139$	−8.46478			−0.717973			−0.358986	+	0.933343i	$0.616878\pi$
$140$	4.07076	−	4.29289i	0.344042	−	0.362816i
$141$	−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
$147$	2.70711	+	6.45535i	0.223278	+	0.532428i
$148$	6.10651	−	6.10651i	0.501952	−	0.501952i
$149$		−	4.43516i		−	0.363342i	−0.983359	−	0.181671i	$-0.941849\pi$
$149$		−	4.43516i		−	0.363342i	0.983359	−	0.181671i	$-0.0581506\pi$
$150$	−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	$-0.865736\pi$
$157$	−6.30188	+	6.30188i	−0.502945	+	0.502945i	0.409407	+	0.912352i	$0.365736\pi$
$158$	−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	−0.140348	−	0.990102i	$-0.544822\pi$
$163$	10.8489	−	10.8489i	0.849754	−	0.849754i	0.990102	+	0.140348i	$0.0448222\pi$
$164$	−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	$-0.650204\pi$
$167$	5.63635	−	5.63635i	0.436154	−	0.436154i	0.890715	+	0.454562i	$0.150204\pi$
$168$	0.510472	−	2.59604i	0.0393838	−	0.200289i
$169$		−	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	$-0.489039\pi$
$173$	−12.6923	−	12.6923i	−0.964977	−	0.964977i	−0.999407	+	0.0344296i	$0.989039\pi$
$174$	9.94900			0.754232
$175$	−12.8264	+	3.23777i	−0.969586	+	0.244753i
$176$	−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	$-0.931325\pi$
$179$		−	5.72836i		−	0.428158i	0.976816	−	0.214079i	$-0.0686750\pi$
$180$	−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	$0.892540\pi$
$182$	2.15063	+	0.422889i	0.159415	+	0.0313466i
$183$	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	−0.852945	−	0.522001i	$-0.825186\pi$
$193$	−4.59762	+	4.59762i	−0.330944	+	0.330944i	0.522001	+	0.852945i	$0.325186\pi$
$194$	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	0.494842	−	0.868983i	$-0.335226\pi$
$197$	−5.25132	−	5.25132i	−0.374141	−	0.374141i	−0.868983	+	0.494842i	$0.835226\pi$
$198$	−3.39327	+	3.39327i	−0.241149	+	0.241149i
$199$	4.12163			0.292175			0.146087	−	0.989272i	$-0.453332\pi$
$199$	4.12163			0.292175			0.146087	+	0.989272i	$0.453332\pi$
$200$	4.70711	+	1.68616i	0.332843	+	0.119230i
$201$			1.38459i			0.0976618i
$202$	−3.45789	+	3.45789i	−0.243297	+	0.243297i
$203$	25.8280	+	5.07868i	1.81277	+	0.356454i
$204$			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
$210$	−4.07076	+	4.29289i	−0.280909	+	0.296238i
$211$	−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
$217$	−7.84249	−	1.54211i	−0.532383	−	0.104685i
$218$	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	0.999642	+	0.0267394i	$0.00851242\pi$
$223$	15.3271	+	15.3271i	1.02638	+	1.02638i	0.0267394	+	0.999642i	$0.491488\pi$
$224$	−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	−0.300575	+	0.953758i	$0.597179\pi$
$227$	−18.8984	+	18.8984i	−1.25433	+	1.25433i	−0.953758	+	0.300575i	$0.902821\pi$
$228$	−1.67135	+	1.67135i	−0.110688	+	0.110688i
$229$	−13.3137			−0.879795			−0.439897	−	0.898048i	$-0.644985\pi$
$229$	−13.3137			−0.879795			−0.439897	+	0.898048i	$0.644985\pi$
$230$	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	−0.423879	−	0.905719i	$-0.639332\pi$
$233$	7.35498	−	7.35498i	0.481840	−	0.481840i	0.905719	+	0.423879i	$0.139332\pi$
$234$	−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
$238$	−2.96456	+	15.0765i	−0.192164	+	0.977261i
$239$		−	13.0491i		−	0.844074i	−0.906579	−	0.422037i	$-0.861315\pi$
$239$		−	13.0491i		−	0.844074i	0.906579	−	0.422037i	$-0.138685\pi$
$240$	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
$245$	−12.7592	+	9.06651i	−0.815158	+	0.579238i
$246$	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	$0.956434\pi$
$252$	−0.510472	+	2.59604i	−0.0321567	+	0.163535i
$253$	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	$-0.678294\pi$
$257$	5.06418	−	5.06418i	0.315895	−	0.315895i	0.847188	+	0.531293i	$0.178294\pi$
$258$	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	−0.823916	−	0.566712i	$-0.808215\pi$
$263$	−4.17113	+	4.17113i	−0.257203	+	0.257203i	0.566712	+	0.823916i	$0.308215\pi$
$264$	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	$-0.227894\pi$
$269$	24.7484			1.50894			0.754469	+	0.656336i	$0.227894\pi$
$270$	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
$273$	−2.15063	−	0.422889i	−0.130162	−	0.0255944i
$274$		−	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	0.969598	−	0.244705i	$-0.0786910\pi$
$277$	12.0646	+	12.0646i	0.724893	+	0.724893i	−0.244705	+	0.969598i	$0.578691\pi$
$278$	−5.98550	−	5.98550i	−0.358986	−	0.358986i
$279$	3.02094			0.180859
$280$	5.91399	−	0.157074i	0.353429	−	0.00938694i
$281$	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	$-0.404258\pi$
$283$	−11.0833	−	11.0833i	−0.658836	−	0.658836i	−0.955105	+	0.296269i	$0.904258\pi$
$284$			5.25132i			0.311608i
$285$	5.15707	−	1.15707i	0.305479	−	0.0685391i
$286$			3.97546i			0.235074i
$287$	28.5553	+	5.61497i	1.68557	+	0.331441i
$288$	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	$-0.165401\pi$
$293$	6.35827	+	6.35827i	0.371454	+	0.371454i	−0.496553	+	0.868007i	$0.665401\pi$
$294$	−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	$-0.511690\pi$
$307$	16.8663	−	16.8663i	0.962610	−	0.962610i	0.999326	+	0.0367161i	$0.0116897\pi$
$308$	12.4579	+	2.44966i	0.709854	+	0.139582i
$309$		−	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	$-0.255831\pi$
$313$	−0.458332	−	0.458332i	−0.0259064	−	0.0259064i	−0.719941	+	0.694035i	$0.755831\pi$
$314$	−8.91220			−0.502945
$315$	4.07076	−	4.29289i	0.229361	−	0.241877i
$316$	−5.10069			−0.286936
$317$	13.1130	+	13.1130i	0.736497	+	0.736497i	0.971898	−	0.235401i	$-0.0756404\pi$
$317$	13.1130	+	13.1130i	0.736497	+	0.736497i	−0.235401	+	0.971898i	$0.575640\pi$
$318$	−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
$322$	2.15063	−	10.9372i	0.119850	−	0.609505i
$323$	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	0.995790	−	0.0916605i	$-0.0292175\pi$
$337$	16.5976	+	16.5976i	0.904130	+	0.904130i	−0.0916605	+	0.995790i	$0.529217\pi$
$338$	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
$343$	−10.1878	+	15.4664i	−0.550091	+	0.835105i
$344$		−	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	0.978834	−	0.204654i	$-0.0656068\pi$
$347$	14.4214	+	14.4214i	0.774181	+	0.774181i	−0.204654	+	0.978834i	$0.565607\pi$
$348$	7.03500	+	7.03500i	0.377116	+	0.377116i
$349$	28.6672			1.53452			0.767260	−	0.641337i	$-0.221620\pi$
$349$	28.6672			1.53452			0.767260	+	0.641337i	$0.221620\pi$
$350$	−11.3591	−	6.78019i	−0.607169	−	0.362416i
$351$	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	$-0.311052\pi$
$353$	−5.06506	−	5.06506i	−0.269586	−	0.269586i	−0.828933	+	0.559347i	$0.811052\pi$
$354$			2.07912i			0.110504i
$355$	6.28391	−	9.91938i	0.333515	−	0.526466i
$356$			11.8989i			0.630639i
$357$	2.96456	−	15.0765i	0.156901	−	0.797931i
$358$	4.05056	−	4.05056i	0.214079	−	0.214079i
$359$			8.46478i			0.446754i	0.974732	+	0.223377i	$0.0717081\pi$
$359$			8.46478i			0.446754i	−0.974732	+	0.223377i	$0.928292\pi$
$360$	−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	$-0.983968\pi$
$367$	−18.1685	+	18.1685i	−0.948386	+	0.948386i	0.0503457	+	0.998732i	$0.483968\pi$
$368$	−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	−0.983084	−	0.183154i	$-0.941369\pi$
$373$	−15.4492	+	15.4492i	−0.799930	+	0.799930i	0.183154	+	0.983084i	$0.441369\pi$
$374$	−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
$378$	0.510472	−	2.59604i	0.0262558	−	0.133526i
$379$		−	32.3833i		−	1.66342i	−0.555212	−	0.831709i	$-0.687363\pi$
$379$		−	32.3833i		−	1.66342i	0.555212	−	0.831709i	$-0.312637\pi$
$380$	−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	$-0.0510836\pi$
$383$	16.1916	+	16.1916i	0.827354	+	0.827354i	−0.159796	+	0.987150i	$0.551084\pi$
$384$	−1.00000			−0.0510310
$385$	−20.6008	−	19.5348i	−1.04991	−	0.995585i
$386$	−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	$-0.901530\pi$
$389$		−	12.0091i		−	0.608886i	0.952531	−	0.304443i	$-0.0984704\pi$
$390$	−0.405538	−	1.80748i	−0.0205352	−	0.0915255i
$391$			24.4671i			1.23735i
$392$	6.45535	−	2.70711i	0.326045	−	0.136730i
$393$	−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	$-0.720284\pi$
$397$	2.62680	−	2.62680i	0.131835	−	0.131835i	0.769945	+	0.638110i	$0.220284\pi$
$398$	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	$-0.375800\pi$
$409$	15.3846			0.760719			0.380360	+	0.924839i	$0.375800\pi$
$410$	5.38459	+	23.9991i	0.265926	+	1.18523i
$411$			8.38416i			0.413560i
$412$	−1.06462	+	1.06462i	−0.0524502	+	0.0524502i
$413$	−1.06133	+	5.39748i	−0.0522248	+	0.265593i
$414$			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	$-0.740572\pi$
$419$	−28.0782			−1.37171			−0.685856	+	0.727737i	$0.740572\pi$
$420$	−5.91399	+	0.157074i	−0.288573	+	0.00766441i
$421$	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
$427$	14.4229	+	2.83604i	0.697973	+	0.137246i
$428$	−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	$-0.303396\pi$
$433$	−4.91337	−	4.91337i	−0.236122	−	0.236122i	−0.815242	+	0.579120i	$0.803396\pi$
$434$	−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	$-0.317124\pi$
$439$	22.7723			1.08686			0.543432	+	0.839453i	$0.317124\pi$
$440$	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	−0.261484	+	0.965208i	$0.584212\pi$
$443$	−25.8189	+	25.8189i	−1.22669	+	1.22669i	−0.965208	+	0.261484i	$0.915788\pi$
$444$	−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
$448$	−2.59604	−	0.510472i	−0.122651	−	0.0241175i
$449$			9.55573i			0.450963i	0.974247	+	0.225481i	$0.0723955\pi$
$449$			9.55573i			0.450963i	−0.974247	+	0.225481i	$0.927605\pi$
$450$	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
$455$	−0.130124	−	4.89931i	−0.00610031	−	0.229683i
$456$	−2.36365			−0.110688
$457$	−16.6569	−	16.6569i	−0.779175	−	0.779175i	0.200516	−	0.979690i	$-0.435738\pi$
$457$	−16.6569	−	16.6569i	−0.779175	−	0.779175i	−0.979690	+	0.200516i	$0.935738\pi$
$458$	−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	$-0.193051\pi$
$462$	−12.4579	−	2.44966i	−0.579594	−	0.113968i
$463$	6.83022	−	6.83022i	0.317427	−	0.317427i	−0.530351	−	0.847778i	$-0.677940\pi$
$463$	6.83022	−	6.83022i	0.317427	−	0.317427i	0.847778	+	0.530351i	$0.177940\pi$
$464$		−	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	$-0.980551\pi$
$467$	−20.2503	+	20.2503i	−0.937070	+	0.937070i	0.0610637	+	0.998134i	$0.480551\pi$
$468$	−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	$-0.450140\pi$
$479$	6.82843			0.311999			0.155999	+	0.987757i	$0.450140\pi$
$480$	1.88893	+	1.19663i	0.0862176	+	0.0546187i
$481$		−	7.15422i		−	0.326204i
$482$	17.2917	−	17.2917i	0.787616	−	0.787616i
$483$	−2.15063	+	10.9372i	−0.0978570	+	0.497658i
$484$			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	0.714490	−	0.699646i	$-0.246659\pi$
$487$	0.327587	+	0.327587i	0.0148444	+	0.0148444i	−0.699646	+	0.714490i	$0.746659\pi$
$488$	−3.92849	−	3.92849i	−0.177835	−	0.177835i
$489$	−15.3427			−0.693821
$490$	−15.4331	−	2.61116i	−0.697198	−	0.117960i
$491$	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
$497$	2.68065	−	13.6326i	0.120244	−	0.611507i
$498$	−3.22170	+	3.22170i	−0.144368	+	0.144368i
$499$		−	4.17771i		−	0.187020i	−0.995618	−	0.0935101i	$-0.970191\pi$
$499$		−	4.17771i		−	0.187020i	0.995618	−	0.0935101i	$-0.0298087\pi$
$500$	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	$-0.162841\pi$
$503$	8.57667	+	8.57667i	0.382415	+	0.382415i	−0.489557	+	0.871972i	$0.662841\pi$
$504$	−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	$-0.523288\pi$
$509$	−3.29829			−0.146194			−0.0730970	+	0.997325i	$0.523288\pi$
$510$	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
$518$	−22.4192	−	4.40839i	−0.985041	−	0.193694i
$519$			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	−0.993748	−	0.111644i	$-0.964388\pi$
$523$	−25.2794	−	25.2794i	−1.10539	−	1.10539i	−0.111644	−	0.993748i	$-0.535612\pi$
$524$	22.2039			0.969982
$525$	11.3591	+	6.78019i	0.495752	+	0.295912i
$526$	−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
$532$	−6.13613	−	1.20658i	−0.266035	−	0.0523118i
$533$	−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	0.741576	−	0.670869i	$-0.234079\pi$
$547$	1.65370	+	1.65370i	0.0707071	+	0.0707071i	−0.670869	+	0.741576i	$0.734079\pi$
$548$	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
$553$	13.2416	+	2.60376i	0.563089	+	0.110723i
$554$			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	−0.981874	−	0.189535i	$-0.939302\pi$
$557$	−27.6462	−	27.6462i	−1.17141	−	1.17141i	−0.189535	−	0.981874i	$-0.560698\pi$
$558$	2.13613	+	2.13613i	0.0904296	+	0.0904296i
$559$	−6.73449			−0.284839
$560$	4.29289	+	4.07076i	0.181408	+	0.172021i
$561$	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	$-0.280920\pi$
$563$	−3.25447	−	3.25447i	−0.137160	−	0.137160i	−0.772353	+	0.635193i	$0.780920\pi$
$564$		−	0.514280i		−	0.0216551i
$565$	8.02051	+	35.7474i	0.337425	+	1.50390i
$566$		−	15.6742i		−	0.658836i
$567$	−0.510472	+	2.59604i	−0.0214378	+	0.109023i
$568$	−3.71324	+	3.71324i	−0.155804	+	0.155804i
$569$			24.2411i			1.01624i	0.861286	+	0.508121i	$0.169660\pi$
$569$			24.2411i			1.01624i	−0.861286	+	0.508121i	$0.830340\pi$
$570$	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	$-0.515841\pi$
$577$	22.7961	−	22.7961i	0.949016	−	0.949016i	0.998762	+	0.0497462i	$0.0158413\pi$
$578$	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	$-0.743589\pi$
$587$	0.690067	−	0.690067i	0.0284821	−	0.0284821i	0.721204	+	0.692722i	$0.243589\pi$
$588$	−6.45535	+	2.70711i	−0.266214	+	0.111639i
$589$			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	$-0.404286\pi$
$593$	−16.0464	−	16.0464i	−0.658946	−	0.658946i	−0.955131	+	0.296184i	$0.904286\pi$
$594$	4.79881			0.196897
$595$	34.3454	−	0.912202i	1.40803	−	0.0373966i
$596$	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	$-0.998293\pi$
$599$		−	0.262525i		−	0.0107265i	0.999986	−	0.00536325i	$-0.00170718\pi$
$600$	−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	$0.958604\pi$
$602$	−4.14975	+	21.1038i	−0.169131	+	0.860128i
$603$	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	$-0.525856\pi$
$607$	22.5571	−	22.5571i	0.915564	−	0.915564i	0.996703	+	0.0811391i	$0.0258558\pi$
$608$	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	−0.786440	−	0.617667i	$-0.788078\pi$
$613$	−4.17864	+	4.17864i	−0.168774	+	0.168774i	0.617667	+	0.786440i	$0.288078\pi$
$614$	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	0.891819	−	0.452391i	$-0.149429\pi$
$617$	10.9152	+	10.9152i	0.439428	+	0.439428i	−0.452391	+	0.891819i	$0.649429\pi$
$618$	1.06462	−	1.06462i	0.0428254	−	0.0428254i
$619$	−2.48720			−0.0999688			−0.0499844	−	0.998750i	$-0.515917\pi$
$619$	−2.48720			−0.0999688			−0.0499844	+	0.998750i	$0.515917\pi$
$620$	3.61497	−	5.70636i	0.145181	−	0.229173i
$621$		−	4.21302i		−	0.169063i
$622$	−0.0418875	+	0.0418875i	−0.00167954	+	0.00167954i
$623$	6.07404	−	30.8899i	0.243351	−	1.23758i
$624$			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
$630$	5.91399	−	0.157074i	0.235619	−	0.00625796i
$631$	−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
$637$	−2.24264	−	5.34779i	−0.0888567	−	0.211887i
$638$	−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	$-0.283486\pi$
$643$	−3.76560	−	3.76560i	−0.148501	−	0.148501i	−0.777448	+	0.628947i	$0.783486\pi$
$644$	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	$-0.508159\pi$
$647$	24.7759	−	24.7759i	0.974042	−	0.974042i	0.999672	+	0.0256293i	$0.00815894\pi$
$648$	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	−0.946661	−	0.322231i	$-0.895567\pi$
$653$	−15.9566	+	15.9566i	−0.624431	+	0.624431i	0.322231	+	0.946661i	$0.395567\pi$
$654$	−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
$658$	0.262525	−	1.33509i	0.0102343	−	0.0520473i
$659$			15.8705i			0.618227i	0.951025	+	0.309113i	$0.100032\pi$
$659$			15.8705i			0.618227i	−0.951025	+	0.309113i	$0.899968\pi$
$660$	−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
$665$	10.1469	+	9.62185i	0.393480	+	0.373119i
$666$	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
$672$	2.59604	+	0.510472i	0.100144	+	0.0196919i
$673$	4.25535	−	4.25535i	0.164032	−	0.164032i	−0.620318	−	0.784350i	$-0.712997\pi$
$673$	4.25535	−	4.25535i	0.164032	−	0.164032i	0.784350	+	0.620318i	$0.212997\pi$
$674$			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	−0.436085	+	0.899906i	$0.643635\pi$
$677$	−34.7614	+	34.7614i	−1.33599	+	1.33599i	−0.899906	+	0.436085i	$0.856365\pi$
$678$	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	−0.534942	−	0.844889i	$-0.679666\pi$
$683$	8.10025	−	8.10025i	0.309947	−	0.309947i	0.844889	+	0.534942i	$0.179666\pi$
$684$	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
$693$	12.4579	+	2.44966i	0.473236	+	0.0930548i
$694$			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
$700$	−3.23777	−	12.8264i	−0.122376	−	0.484793i
$701$	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
$707$	12.6951	+	2.49631i	0.477450	+	0.0938834i
$708$	−1.47016	+	1.47016i	−0.0552521	+	0.0552521i
$709$			23.3998i			0.878799i	0.898292	+	0.439399i	$0.144809\pi$
$709$			23.3998i			0.878799i	−0.898292	+	0.439399i	$0.855191\pi$
$710$	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	$-0.896633\pi$
$719$	−50.8254			−1.89547			−0.947734	+	0.319060i	$0.896633\pi$
$720$	−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	$-0.792722\pi$
$727$	−5.10248	+	5.10248i	−0.189240	+	0.189240i	0.606127	+	0.795368i	$0.292722\pi$
$728$	−0.422889	+	2.15063i	−0.0156733	+	0.0797076i
$729$		−	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	$-0.264964\pi$
$733$	−1.79925	−	1.79925i	−0.0664567	−	0.0664567i	−0.739554	+	0.673097i	$0.764964\pi$
$734$	−25.6941			−0.948386
$735$	15.4331	+	2.61116i	0.569260	+	0.0963140i
$736$	−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	$0.0643236\pi$
$739$			10.9122i			0.401412i	−0.979652	+	0.200706i	$0.935676\pi$
$740$	−4.22752	−	18.8420i	−0.155407	−	0.692648i
$741$			1.95811i			0.0719331i
$742$	1.70636	−	8.67780i	0.0626424	−	0.318572i
$743$	−12.3076	+	12.3076i	−0.451521	+	0.451521i	−0.895859	−	0.444338i	$-0.853439\pi$
$743$	−12.3076	+	12.3076i	−0.451521	+	0.451521i	0.444338	+	0.895859i	$0.353439\pi$
$744$		−	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	0.994716	+	0.102667i	$0.0327377\pi$
$757$	30.1930	+	30.1930i	1.09738	+	1.09738i	0.102667	+	0.994716i	$0.467262\pi$
$758$	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
$763$	−33.4848	−	6.58429i	−1.21223	−	0.238367i
$764$		−	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	$-0.304941\pi$
$769$	31.8992			1.15032			0.575158	+	0.818042i	$0.304941\pi$
$770$	−0.753766	−	28.3801i	−0.0271638	−	1.02275i
$771$	−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	$-0.159062\pi$
$773$	11.0809	+	11.0809i	0.398553	+	0.398553i	−0.479170	+	0.877722i	$0.659062\pi$
$774$		−	8.12925i		−	0.292200i
$775$	−13.6569	+	6.45313i	−0.490569	+	0.231803i
$776$			11.3928i			0.408979i
$777$	22.4192	+	4.40839i	0.804283	+	0.158150i
$778$	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	$-0.999273\pi$
$787$	−27.9894	+	27.9894i	−0.997714	+	0.997714i	0.00228344	+	0.999997i	$0.499273\pi$
$788$	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	$-0.801512\pi$
$797$	−6.43293	+	6.43293i	−0.227866	+	0.227866i	0.583935	+	0.811801i	$0.301512\pi$
$798$	6.13613	+	1.20658i	0.217217	+	0.0427124i
$799$			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
$805$	−24.9158	+	0.661754i	−0.878166	+	0.0233238i
$806$	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	$-0.779100\pi$
$809$		−	36.3842i		−	1.27920i	0.768708	−	0.639599i	$-0.220900\pi$
$810$	−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	$-0.154440\pi$
$812$	−5.07868	+	25.8280i	−0.178227	+	0.906385i
$813$	−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	0.329561	−	0.944134i	$-0.393099\pi$
$823$	36.5397	−	36.5397i	1.27369	−	1.27369i	0.944134	−	0.329561i	$-0.106901\pi$
$824$	−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	0.925542	−	0.378644i	$-0.123610\pi$
$827$	15.7275	+	15.7275i	0.546898	+	0.546898i	−0.378644	+	0.925542i	$0.623610\pi$
$828$	−2.97906	+	2.97906i	−0.103529	+	0.103529i
$829$	−29.2892			−1.01725			−0.508627	−	0.860987i	$-0.669847\pi$
$829$	−29.2892			−1.01725			−0.508627	+	0.860987i	$0.669847\pi$
$830$	−8.60629	−	5.45207i	−0.298729	−	0.189244i
$831$		−	17.0620i		−	0.591873i
$832$	0.585786	−	0.585786i	0.0203085	−	0.0203085i
$833$	37.4894	−	15.7215i	1.29893	−	0.544717i
$834$			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	$-0.486705\pi$
$839$	2.41886			0.0835082			0.0417541	+	0.999128i	$0.486705\pi$
$840$	−4.29289	−	4.07076i	−0.148119	−	0.140454i
$841$	−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
$847$	6.14024	−	31.2266i	0.210981	−	1.07296i
$848$	−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	$-0.0126559\pi$
$853$	28.0222	+	28.0222i	0.959461	+	0.959461i	−0.0397491	+	0.999210i	$0.512656\pi$
$854$	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	$-0.903312\pi$
$857$	−19.1782	+	19.1782i	−0.655115	+	0.655115i	0.299105	+	0.954220i	$0.403312\pi$
$858$	2.81108	−	2.81108i	0.0959686	−	0.0959686i
$859$	45.5754			1.55501			0.777506	−	0.628876i	$-0.216485\pi$
$859$	45.5754			1.55501			0.777506	+	0.628876i	$0.216485\pi$
$860$	−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	−0.622664	−	0.782489i	$-0.713950\pi$
$863$	4.69515	−	4.69515i	0.159825	−	0.159825i	0.782489	+	0.622664i	$0.213950\pi$
$864$	−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
$868$	1.54211	−	7.84249i	0.0523425	−	0.266191i
$869$			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
$875$	−9.23260	+	28.1027i	−0.312119	+	0.950043i
$876$	8.64818			0.292195
$877$	17.5321	+	17.5321i	0.592017	+	0.592017i	0.938176	−	0.346159i	$-0.112514\pi$
$877$	17.5321	+	17.5321i	0.592017	+	0.592017i	−0.346159	+	0.938176i	$0.612514\pi$
$878$	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	$-0.0211076\pi$
$882$	6.45535	−	2.70711i	0.217363	−	0.0911530i
$883$	34.7362	−	34.7362i	1.16896	−	1.16896i	0.186512	−	0.982453i	$-0.440282\pi$
$883$	34.7362	−	34.7362i	1.16896	−	1.16896i	0.982453	−	0.186512i	$-0.0597184\pi$
$884$		−	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	0.126906	−	0.991915i	$-0.459495\pi$
$887$	33.3213	−	33.3213i	1.11882	−	1.11882i	0.991915	−	0.126906i	$-0.0405046\pi$
$888$	−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
$903$	4.14975	−	21.1038i	0.138095	−	0.702292i
$904$		−	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	0.691452	−	0.722422i	$-0.256971\pi$
$907$	−0.932707	−	0.932707i	−0.0309700	−	0.0309700i	−0.722422	+	0.691452i	$0.756971\pi$
$908$	−18.8984	−	18.8984i	−0.627167	−	0.627167i
$909$	−4.89020			−0.162198
$910$	3.37233	−	3.55635i	0.111792	−	0.117892i
$911$	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
$917$	−57.6422	−	11.3345i	−1.90351	−	0.374297i
$918$	−4.10651	+	4.10651i	−0.135535	+	0.135535i
$919$			20.8574i			0.688023i	0.938965	+	0.344011i	$0.111786\pi$
$919$			20.8574i			0.688023i	−0.938965	+	0.344011i	$0.888214\pi$
$920$	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	$-0.547699\pi$
$929$	−9.10069			−0.298584			−0.149292	+	0.988793i	$0.547699\pi$
$930$	−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	$-0.774595\pi$
$937$	−3.34154	+	3.34154i	−0.109163	+	0.109163i	0.650415	+	0.759579i	$0.274595\pi$
$938$	−3.59446	−	0.706797i	−0.117363	−	0.0230777i
$939$			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
$945$	−5.91399	+	0.157074i	−0.192382	+	0.00510960i
$946$	−39.0107			−1.26835
$947$	−0.00253441	−	0.00253441i	−8.23572e−5	−	8.23572e-5i	0.707066	−	0.707148i	$-0.250019\pi$
$947$	−0.00253441	−	0.00253441i	−8.23572e−5	−	8.23572e-5i	−0.707148	+	0.707066i	$0.750019\pi$
$948$	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
$952$	−15.0765	−	2.96456i	−0.488631	−	0.0960818i
$953$	14.4673	−	14.4673i	0.468642	−	0.468642i	−0.432832	−	0.901474i	$-0.642486\pi$
$953$	14.4673	−	14.4673i	0.468642	−	0.468642i	0.901474	+	0.432832i	$0.142486\pi$
$954$			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	0.633060	−	0.774103i	$-0.281799\pi$
$967$	−4.38595	−	4.38595i	−0.141043	−	0.141043i	−0.774103	+	0.633060i	$0.781799\pi$
$968$	−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
$973$	−4.32103	+	21.9749i	−0.138526	+	0.704483i
$974$			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	0.957055	+	0.289905i	$0.0936239\pi$
$977$	38.9763	+	38.9763i	1.24696	+	1.24696i	0.289905	+	0.957055i	$0.406376\pi$
$978$	−10.8489	−	10.8489i	−0.346911	−	0.346911i
$979$	57.1004			1.82494
$980$	−9.06651	−	12.7592i	−0.289619	−	0.407579i
$981$	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	$-0.356726\pi$
$983$	−14.5896	−	14.5896i	−0.465335	−	0.465335i	−0.900399	+	0.435065i	$0.856726\pi$
$984$			10.9996i			0.350653i
$985$	−16.2033	+	3.63547i	−0.516280	+	0.115836i
$986$		−	57.7786i		−	1.84005i
$987$	−0.262525	+	1.33509i	−0.00835628	+	0.0424964i
$988$	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	$-0.745500\pi$
$997$	0.631258	−	0.631258i	0.0199921	−	0.0199921i	0.717032	+	0.697040i	$0.245500\pi$
$998$	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.b.97.4	yes	8
3.2	odd	2		630.2.p.c.307.1		8
4.3	odd	2		1680.2.cz.a.97.4		8
5.2	odd	4		1050.2.m.b.643.2		8
5.3	odd	4		210.2.m.a.13.3	✓	8
5.4	even	2		1050.2.m.a.307.2		8
7.6	odd	2		210.2.m.a.97.3	yes	8
15.8	even	4		630.2.p.b.433.2		8
20.3	even	4		1680.2.cz.b.433.1		8
21.20	even	2		630.2.p.b.307.2		8
28.27	even	2		1680.2.cz.b.97.1		8
35.13	even	4	inner	210.2.m.b.13.4	yes	8
35.27	even	4		1050.2.m.a.643.2		8
35.34	odd	2		1050.2.m.b.307.2		8
105.83	odd	4		630.2.p.c.433.1		8
140.83	odd	4		1680.2.cz.a.433.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.m.a.13.3	✓	8	5.3	odd	4
210.2.m.a.97.3	yes	8	7.6	odd	2
210.2.m.b.13.4	yes	8	35.13	even	4	inner
210.2.m.b.97.4	yes	8	1.1	even	1	trivial
630.2.p.b.307.2		8	21.20	even	2
630.2.p.b.433.2		8	15.8	even	4
630.2.p.c.307.1		8	3.2	odd	2
630.2.p.c.433.1		8	105.83	odd	4
1050.2.m.a.307.2		8	5.4	even	2
1050.2.m.a.643.2		8	35.27	even	4
1050.2.m.b.307.2		8	35.34	odd	2
1050.2.m.b.643.2		8	5.2	odd	4
1680.2.cz.a.97.4		8	4.3	odd	2
1680.2.cz.a.433.4		8	140.83	odd	4
1680.2.cz.b.97.1		8	28.27	even	2
1680.2.cz.b.433.1		8	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.19663 - 1.88893i) q^{5} -1.00000i q^{6} +(0.510472 - 2.59604i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(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} +(0.510472 - 2.59604i) 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} +(2.59604 + 0.510472i) 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} +(-4.29289 - 4.07076i) 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} +(-2.59604 - 0.510472i) 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} +(2.59604 + 0.510472i) 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} +(-0.157074 - 5.91399i) 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} +(2.44966 - 12.4579i) 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} +(-2.70711 - 6.45535i) q^{98} +4.79881i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{7}+O(q^{10}) \) 8 * q + 8 * q^7	\( 8 q + 8 q^{7} + 4 q^{10} + 8 q^{11} + 16 q^{13} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 12 q^{17} + 8 q^{19} - 4 q^{20} - 8 q^{21} + 8 q^{22} + 16 q^{23} + 8 q^{24} - 4 q^{25} - 4 q^{28} + 4 q^{30} - 8 q^{33} - 16 q^{34} - 40 q^{35} - 8 q^{36} - 28 q^{37} + 4 q^{38} + 4 q^{42} - 4 q^{45} - 8 q^{46} - 24 q^{47} - 4 q^{49} + 16 q^{51} - 16 q^{52} - 8 q^{53} + 8 q^{54} - 28 q^{55} + 4 q^{56} - 4 q^{57} - 12 q^{58} - 8 q^{59} + 4 q^{62} - 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} + 4 q^{70} + 8 q^{71} + 28 q^{73} + 44 q^{77} + 16 q^{78} - 8 q^{81} - 24 q^{82} + 16 q^{83} - 4 q^{84} + 28 q^{85} + 8 q^{86} + 12 q^{87} - 8 q^{88} + 64 q^{89} - 8 q^{91} + 16 q^{92} - 4 q^{93} - 8 q^{94} + 28 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q + 8 * 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 - 4 * q^28 + 4 * q^30 - 8 * q^33 - 16 * q^34 - 40 * q^35 - 8 * q^36 - 28 * q^37 + 4 * q^38 + 4 * 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 - 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 + 4 * 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 - 16 * q^98

Introduction

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