LMFDB - Embedded newform 930.2.n.f.721.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 10 x^{10} - 15 x^{9} + 61 x^{8} - 25 x^{7} + 316 x^{6} + 50 x^{5} + 1336 x^{4} + \cdots + 121 $ x^12 - 3x^11 + 10x^10 - 15x^9 + 61x^8 - 25x^7 + 316x^6 + 50x^5 + 1336x^4 - 1720x^3 + 1235x^2 - 462*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			721.3
Root			$0.145311 + 0.447222i$ of defining polynomial
Character	$\chi$	$=$	930.721
Dual form			930.2.n.f.841.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(2.67675 + 1.94477i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(2.67675 + 1.94477i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.309017 + 0.951057i) q^{10} +(2.04414 + 1.48515i) q^{11} +(-0.309017 + 0.951057i) q^{12} +(-0.0898072 - 0.276398i) q^{13} +(-2.67675 + 1.94477i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.86217 + 3.53257i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-0.921250 + 2.83532i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(1.02243 - 3.14670i) q^{21} +(-2.04414 + 1.48515i) q^{22} +(3.70901 - 2.69475i) q^{23} +(-0.809017 - 0.587785i) q^{24} +1.00000 q^{25} +0.290622 q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.02243 - 3.14670i) q^{28} +(0.594788 - 1.83057i) q^{29} +1.00000 q^{30} +(3.94316 - 3.93083i) q^{31} -1.00000 q^{32} +(0.780790 - 2.40303i) q^{33} +(-1.85718 - 5.71582i) q^{34} +(2.67675 + 1.94477i) q^{35} +1.00000 q^{36} +8.41800 q^{37} +(-2.41186 - 1.75232i) q^{38} +(-0.235118 + 0.170824i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-2.60131 + 8.00601i) q^{41} +(2.67675 + 1.94477i) q^{42} +(-3.88337 + 11.9518i) q^{43} +(-0.780790 - 2.40303i) q^{44} +(-0.809017 + 0.587785i) q^{45} +(1.41672 + 4.36020i) q^{46} +(-0.519940 - 1.60021i) q^{47} +(0.809017 - 0.587785i) q^{48} +(1.21972 + 3.75392i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(4.86217 + 3.53257i) q^{51} +(-0.0898072 + 0.276398i) q^{52} +(-2.35647 + 1.71207i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(2.04414 + 1.48515i) q^{55} +3.30864 q^{56} +2.98123 q^{57} +(1.55718 + 1.13135i) q^{58} +(-1.25881 - 3.87422i) q^{59} +(-0.309017 + 0.951057i) q^{60} +12.4598 q^{61} +(2.51994 + 4.96487i) q^{62} -3.30864 q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.0898072 - 0.276398i) q^{65} +(2.04414 + 1.48515i) q^{66} -1.95352 q^{67} +6.00997 q^{68} +(-3.70901 - 2.69475i) q^{69} +(-2.67675 + 1.94477i) q^{70} +(-2.18327 + 1.58624i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(6.06027 + 4.40304i) q^{73} +(-2.60131 + 8.00600i) q^{74} +(-0.309017 - 0.951057i) q^{75} +(2.41186 - 1.75232i) q^{76} +(2.58335 + 7.95075i) q^{77} +(-0.0898072 - 0.276398i) q^{78} +(6.45966 - 4.69321i) q^{79} +(0.309017 + 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-6.81032 - 4.94799i) q^{82} +(-1.99618 + 6.14362i) q^{83} +(-2.67675 + 1.94477i) q^{84} +(-4.86217 + 3.53257i) q^{85} +(-10.1668 - 7.38660i) q^{86} -1.92478 q^{87} +2.52669 q^{88} +(2.84090 + 2.06404i) q^{89} +(-0.309017 - 0.951057i) q^{90} +(0.297140 - 0.914502i) q^{91} -4.58459 q^{92} +(-4.95695 - 2.53548i) q^{93} +1.68256 q^{94} +(-0.921250 + 2.83532i) q^{95} +(0.309017 + 0.951057i) q^{96} +(14.0569 + 10.2130i) q^{97} -3.94710 q^{98} -2.52669 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 3 q^{15} - 3 q^{16} - 7 q^{17} + 3 q^{18} + 12 q^{19} - 3 q^{20} + q^{21} - 14 q^{22} - 6 q^{23} - 3 q^{24} + 12 q^{25} + 6 q^{26} + 3 q^{27} - q^{28} - 23 q^{29} + 12 q^{30} + 34 q^{31} - 12 q^{32} + 11 q^{33} - 3 q^{34} - q^{35} + 12 q^{36} + 22 q^{37} + 8 q^{38} + q^{39} + 3 q^{40} + 15 q^{41} - q^{42} - 17 q^{43} - 11 q^{44} - 3 q^{45} + 6 q^{46} - 2 q^{47} + 3 q^{48} - 8 q^{49} + 3 q^{50} + 7 q^{51} + 4 q^{52} - 21 q^{53} - 3 q^{54} + 14 q^{55} - 4 q^{56} + 8 q^{57} - 17 q^{58} - 15 q^{59} + 3 q^{60} + 16 q^{61} + 26 q^{62} + 4 q^{63} - 3 q^{64} + 4 q^{65} + 14 q^{66} + 24 q^{67} + 8 q^{68} + 6 q^{69} + q^{70} + 23 q^{71} + 3 q^{72} + 56 q^{73} + 8 q^{74} + 3 q^{75} - 8 q^{76} - 8 q^{77} + 4 q^{78} - 9 q^{79} - 3 q^{80} - 3 q^{81} + 15 q^{82} - 24 q^{83} + q^{84} - 7 q^{85} - 18 q^{86} - 12 q^{87} + 6 q^{88} - 27 q^{89} + 3 q^{90} - 3 q^{91} + 24 q^{92} + 11 q^{93} - 28 q^{94} + 12 q^{95} - 3 q^{96} + 38 q^{97} - 52 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 3 * q^15 - 3 * q^16 - 7 * q^17 + 3 * q^18 + 12 * q^19 - 3 * q^20 + q^21 - 14 * q^22 - 6 * q^23 - 3 * q^24 + 12 * q^25 + 6 * q^26 + 3 * q^27 - q^28 - 23 * q^29 + 12 * q^30 + 34 * q^31 - 12 * q^32 + 11 * q^33 - 3 * q^34 - q^35 + 12 * q^36 + 22 * q^37 + 8 * q^38 + q^39 + 3 * q^40 + 15 * q^41 - q^42 - 17 * q^43 - 11 * q^44 - 3 * q^45 + 6 * q^46 - 2 * q^47 + 3 * q^48 - 8 * q^49 + 3 * q^50 + 7 * q^51 + 4 * q^52 - 21 * q^53 - 3 * q^54 + 14 * q^55 - 4 * q^56 + 8 * q^57 - 17 * q^58 - 15 * q^59 + 3 * q^60 + 16 * q^61 + 26 * q^62 + 4 * q^63 - 3 * q^64 + 4 * q^65 + 14 * q^66 + 24 * q^67 + 8 * q^68 + 6 * q^69 + q^70 + 23 * q^71 + 3 * q^72 + 56 * q^73 + 8 * q^74 + 3 * q^75 - 8 * q^76 - 8 * q^77 + 4 * q^78 - 9 * q^79 - 3 * q^80 - 3 * q^81 + 15 * q^82 - 24 * q^83 + q^84 - 7 * q^85 - 18 * q^86 - 12 * q^87 + 6 * q^88 - 27 * q^89 + 3 * q^90 - 3 * q^91 + 24 * q^92 + 11 * q^93 - 28 * q^94 + 12 * q^95 - 3 * q^96 + 38 * q^97 - 52 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.00000			0.408248
$7$	2.67675	+	1.94477i	1.01172	+	0.735054i	0.964568	−	0.263834i	$-0.0849871\pi$
$7$	2.67675	+	1.94477i	1.01172	+	0.735054i	0.0471470	+	0.998888i	$0.484987\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−0.309017	+	0.951057i	−0.0977198	+	0.300750i
$11$	2.04414	+	1.48515i	0.616330	+	0.447790i	0.851638	−	0.524131i	$-0.175610\pi$
$11$	2.04414	+	1.48515i	0.616330	+	0.447790i	−0.235308	+	0.971921i	$0.575610\pi$
$12$	−0.309017	+	0.951057i	−0.0892055	+	0.274546i
$13$	−0.0898072	−	0.276398i	−0.0249080	−	0.0766591i	0.937830	−	0.347095i	$-0.112832\pi$
$13$	−0.0898072	−	0.276398i	−0.0249080	−	0.0766591i	−0.962738	+	0.270436i	$0.912832\pi$
$14$	−2.67675	+	1.94477i	−0.715391	+	0.519762i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−4.86217	+	3.53257i	−1.17925	+	0.856775i	−0.992087	−	0.125554i	$-0.959929\pi$
$17$	−4.86217	+	3.53257i	−1.17925	+	0.856775i	−0.187163	+	0.982329i	$0.559929\pi$
$18$	−0.309017	−	0.951057i	−0.0728360	−	0.224166i
$19$	−0.921250	+	2.83532i	−0.211349	+	0.650466i	0.788043	+	0.615620i	$0.211094\pi$
$19$	−0.921250	+	2.83532i	−0.211349	+	0.650466i	−0.999393	+	0.0348466i	$0.988906\pi$
$20$	−0.809017	−	0.587785i	−0.180902	−	0.131433i
$21$	1.02243	−	3.14670i	0.223112	−	0.686667i
$22$	−2.04414	+	1.48515i	−0.435811	+	0.316635i
$23$	3.70901	−	2.69475i	0.773382	−	0.561895i	−0.129603	−	0.991566i	$-0.541370\pi$
$23$	3.70901	−	2.69475i	0.773382	−	0.561895i	0.902986	+	0.429671i	$0.141370\pi$
$24$	−0.809017	−	0.587785i	−0.165140	−	0.119981i
$25$	1.00000			0.200000
$26$	0.290622			0.0569957
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−1.02243	−	3.14670i	−0.193220	−	0.594671i
$29$	0.594788	−	1.83057i	0.110449	−	0.339928i	−0.880521	−	0.474006i	$-0.842807\pi$
$29$	0.594788	−	1.83057i	0.110449	−	0.339928i	0.990971	+	0.134078i	$0.0428073\pi$
$30$	1.00000			0.182574
$31$	3.94316	−	3.93083i	0.708213	−	0.705999i
$31$	3.94316	−	3.93083i	0.708213	−	0.705999i
$32$	−1.00000			−0.176777
$33$	0.780790	−	2.40303i	0.135918	−	0.418313i
$34$	−1.85718	−	5.71582i	−0.318504	−	0.980256i
$35$	2.67675	+	1.94477i	0.452453	+	0.328726i
$36$	1.00000			0.166667
$37$	8.41800			1.38391			0.691956	−	0.721940i	$-0.256749\pi$
$37$	8.41800			1.38391			0.691956	+	0.721940i	$0.256749\pi$
$38$	−2.41186	−	1.75232i	−0.391256	−	0.284264i
$39$	−0.235118	+	0.170824i	−0.0376491	+	0.0273537i
$40$	0.809017	−	0.587785i	0.127917	−	0.0929370i
$41$	−2.60131	+	8.00601i	−0.406257	+	1.25033i	0.513585	+	0.858039i	$0.328317\pi$
$41$	−2.60131	+	8.00601i	−0.406257	+	1.25033i	−0.919841	+	0.392290i	$0.871683\pi$
$42$	2.67675	+	1.94477i	0.413031	+	0.300085i
$43$	−3.88337	+	11.9518i	−0.592208	+	1.82263i	−0.0240479	+	0.999711i	$0.507655\pi$
$43$	−3.88337	+	11.9518i	−0.592208	+	1.82263i	−0.568160	+	0.822918i	$0.692345\pi$
$44$	−0.780790	−	2.40303i	−0.117709	−	0.362270i
$45$	−0.809017	+	0.587785i	−0.120601	+	0.0876219i
$46$	1.41672	+	4.36020i	0.208883	+	0.642877i
$47$	−0.519940	−	1.60021i	−0.0758411	−	0.233415i	0.905948	−	0.423389i	$-0.139160\pi$
$47$	−0.519940	−	1.60021i	−0.0758411	−	0.233415i	−0.981789	+	0.189974i	$0.939160\pi$
$48$	0.809017	−	0.587785i	0.116772	−	0.0848395i
$49$	1.21972	+	3.75392i	0.174246	+	0.536274i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	4.86217	+	3.53257i	0.680840	+	0.494659i
$52$	−0.0898072	+	0.276398i	−0.0124540	+	0.0383295i
$53$	−2.35647	+	1.71207i	−0.323686	+	0.235171i	−0.737747	−	0.675078i	$-0.764110\pi$
$53$	−2.35647	+	1.71207i	−0.323686	+	0.235171i	0.414061	+	0.910249i	$0.364110\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	2.04414	+	1.48515i	0.275631	+	0.200258i
$56$	3.30864			0.442136
$57$	2.98123			0.394873
$58$	1.55718	+	1.13135i	0.204467	+	0.148554i
$59$	−1.25881	−	3.87422i	−0.163883	−	0.504381i	0.835069	−	0.550145i	$-0.185428\pi$
$59$	−1.25881	−	3.87422i	−0.163883	−	0.504381i	−0.998952	+	0.0457645i	$0.985428\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	12.4598			1.59531			0.797656	−	0.603113i	$-0.206073\pi$
$61$	12.4598			1.59531			0.797656	+	0.603113i	$0.206073\pi$
$62$	2.51994	+	4.96487i	0.320033	+	0.630539i
$63$	−3.30864			−0.416850
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−0.0898072	−	0.276398i	−0.0111392	−	0.0342830i
$66$	2.04414	+	1.48515i	0.251616	+	0.182809i
$67$	−1.95352			−0.238660			−0.119330	−	0.992855i	$-0.538075\pi$
$67$	−1.95352			−0.238660			−0.119330	+	0.992855i	$0.538075\pi$
$68$	6.00997			0.728816
$69$	−3.70901	−	2.69475i	−0.446512	−	0.324410i
$70$	−2.67675	+	1.94477i	−0.319932	+	0.232444i
$71$	−2.18327	+	1.58624i	−0.259106	+	0.188252i	−0.709753	−	0.704451i	$-0.751193\pi$
$71$	−2.18327	+	1.58624i	−0.259106	+	0.188252i	0.450647	+	0.892702i	$0.351193\pi$
$72$	−0.309017	+	0.951057i	−0.0364180	+	0.112083i
$73$	6.06027	+	4.40304i	0.709301	+	0.515337i	0.882948	−	0.469471i	$-0.155555\pi$
$73$	6.06027	+	4.40304i	0.709301	+	0.515337i	−0.173647	+	0.984808i	$0.555555\pi$
$74$	−2.60131	+	8.00600i	−0.302396	+	0.930678i
$75$	−0.309017	−	0.951057i	−0.0356822	−	0.109819i
$76$	2.41186	−	1.75232i	0.276660	−	0.201005i
$77$	2.58335	+	7.95075i	0.294401	+	0.906072i
$78$	−0.0898072	−	0.276398i	−0.0101687	−	0.0312959i
$79$	6.45966	−	4.69321i	0.726768	−	0.528028i	−0.161771	−	0.986828i	$-0.551721\pi$
$79$	6.45966	−	4.69321i	0.726768	−	0.528028i	0.888539	+	0.458800i	$0.151721\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−6.81032	−	4.94799i	−0.752074	−	0.546414i
$83$	−1.99618	+	6.14362i	−0.219109	+	0.674350i	0.779727	+	0.626120i	$0.215358\pi$
$83$	−1.99618	+	6.14362i	−0.219109	+	0.674350i	−0.998836	+	0.0482297i	$0.984642\pi$
$84$	−2.67675	+	1.94477i	−0.292057	+	0.212192i
$85$	−4.86217	+	3.53257i	−0.527376	+	0.383161i
$86$	−10.1668	−	7.38660i	−1.09631	−	0.796518i
$87$	−1.92478			−0.206358
$88$	2.52669			0.269346
$89$	2.84090	+	2.06404i	0.301135	+	0.218788i	0.728083	−	0.685489i	$-0.240411\pi$
$89$	2.84090	+	2.06404i	0.301135	+	0.218788i	−0.426948	+	0.904276i	$0.640411\pi$
$90$	−0.309017	−	0.951057i	−0.0325733	−	0.100250i
$91$	0.297140	−	0.914502i	0.0311487	−	0.0958659i
$92$	−4.58459			−0.477976
$93$	−4.95695	−	2.53548i	−0.514012	−	0.262917i
$94$	1.68256			0.173543
$95$	−0.921250	+	2.83532i	−0.0945183	+	0.290897i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	14.0569	+	10.2130i	1.42727	+	1.03697i	0.990518	+	0.137385i	$0.0438698\pi$
$97$	14.0569	+	10.2130i	1.42727	+	1.03697i	0.436748	+	0.899584i	$0.356130\pi$
$98$	−3.94710			−0.398718
$99$	−2.52669			−0.253942
$100$	−0.809017	−	0.587785i	−0.0809017	−	0.0587785i
$101$	9.47841	−	6.88646i	0.943137	−	0.685229i	−0.00603707	−	0.999982i	$-0.501922\pi$
$101$	9.47841	−	6.88646i	0.943137	−	0.685229i	0.949174	+	0.314753i	$0.101922\pi$
$102$	−4.86217	+	3.53257i	−0.481427	+	0.349777i
$103$	4.14500	−	12.7570i	0.408419	−	1.25699i	−0.509587	−	0.860419i	$-0.670202\pi$
$103$	4.14500	−	12.7570i	0.408419	−	1.25699i	0.918006	−	0.396566i	$-0.129798\pi$
$104$	−0.235118	−	0.170824i	−0.0230553	−	0.0167506i
$105$	1.02243	−	3.14670i	0.0997786	−	0.307087i
$106$	−0.900090	−	2.77019i	−0.0874245	−	0.269065i
$107$	−8.49251	+	6.17017i	−0.821002	+	0.596493i	−0.916999	−	0.398889i	$-0.869396\pi$
$107$	−8.49251	+	6.17017i	−0.821002	+	0.596493i	0.0959971	+	0.995382i	$0.469396\pi$
$108$	−0.309017	−	0.951057i	−0.0297352	−	0.0915155i
$109$	0.289529	+	0.891078i	0.0277318	+	0.0853498i	0.963965	−	0.266031i	$-0.0857123\pi$
$109$	0.289529	+	0.891078i	0.0277318	+	0.0853498i	−0.936233	+	0.351381i	$0.885712\pi$
$110$	−2.04414	+	1.48515i	−0.194901	+	0.141604i
$111$	−2.60131	−	8.00600i	−0.246905	−	0.759896i
$112$	−1.02243	+	3.14670i	−0.0966102	+	0.297336i
$113$	−7.65198	−	5.55949i	−0.719838	−	0.522993i	0.166495	−	0.986042i	$-0.446755\pi$
$113$	−7.65198	−	5.55949i	−0.719838	−	0.522993i	−0.886332	+	0.463050i	$0.846755\pi$
$114$	−0.921250	+	2.83532i	−0.0862830	+	0.265552i
$115$	3.70901	−	2.69475i	0.345867	−	0.251287i
$116$	−1.55718	+	1.13135i	−0.144580	+	0.105044i
$117$	0.235118	+	0.170824i	0.0217367	+	0.0157926i
$118$	4.07360			0.375005
$119$	−19.8848			−1.82284
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	−1.42637	−	4.38992i	−0.129670	−	0.399084i
$122$	−3.85028	+	11.8500i	−0.348588	+	1.07284i
$123$	8.41802			0.759027
$124$	−5.50057	+	0.862377i	−0.493966	+	0.0774438i
$125$	1.00000			0.0894427
$126$	1.02243	−	3.14670i	0.0910850	−	0.280331i
$127$	6.23878	+	19.2010i	0.553602	+	1.70381i	0.699607	+	0.714528i	$0.253359\pi$
$127$	6.23878	+	19.2010i	0.553602	+	1.70381i	−0.146005	+	0.989284i	$0.546641\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	12.5668			1.10645
$130$	0.290622			0.0254893
$131$	−17.7565	−	12.9009i	−1.55140	−	1.12716i	−0.942646	−	0.333794i	$-0.891671\pi$
$131$	−17.7565	−	12.9009i	−1.55140	−	1.12716i	−0.608750	−	0.793362i	$-0.708329\pi$
$132$	−2.04414	+	1.48515i	−0.177919	+	0.129266i
$133$	−7.97999	+	5.79781i	−0.691953	+	0.502733i
$134$	0.603671	−	1.85791i	0.0521492	−	0.160499i
$135$	0.809017	+	0.587785i	0.0696291	+	0.0505885i
$136$	−1.85718	+	5.71582i	−0.159252	+	0.490128i
$137$	−1.62999	−	5.01661i	−0.139260	−	0.428598i	0.856968	−	0.515369i	$-0.172345\pi$
$137$	−1.62999	−	5.01661i	−0.139260	−	0.428598i	−0.996228	+	0.0867712i	$0.972345\pi$
$138$	3.70901	−	2.69475i	0.315732	−	0.229393i
$139$	−6.68351	−	20.5697i	−0.566888	−	1.74470i	−0.662276	−	0.749260i	$-0.730409\pi$
$139$	−6.68351	−	20.5697i	−0.566888	−	1.74470i	0.0953881	−	0.995440i	$-0.469591\pi$
$140$	−1.02243	−	3.14670i	−0.0864108	−	0.265945i
$141$	−1.36122	+	0.988985i	−0.114635	+	0.0832876i
$142$	−0.833935	−	2.56659i	−0.0699823	−	0.215383i
$143$	0.226915	−	0.698373i	0.0189756	−	0.0584009i
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$	0.594788	−	1.83057i	0.0493945	−	0.152021i
$146$	−6.06027	+	4.40304i	−0.501552	+	0.364399i
$147$	3.19327	−	2.32005i	0.263377	−	0.191354i
$148$	−6.81031	−	4.94798i	−0.559804	−	0.406721i
$149$	−10.7148			−0.877790			−0.438895	−	0.898538i	$-0.644630\pi$
$149$	−10.7148			−0.877790			−0.438895	+	0.898538i	$0.644630\pi$
$150$	1.00000			0.0816497
$151$	−15.4734	−	11.2421i	−1.25921	−	0.914871i	−0.260493	−	0.965476i	$-0.583885\pi$
$151$	−15.4734	−	11.2421i	−1.25921	−	0.914871i	−0.998719	+	0.0506051i	$0.983885\pi$
$152$	0.921250	+	2.83532i	0.0747233	+	0.229975i
$153$	1.85718	−	5.71582i	0.150144	−	0.462097i
$154$	−8.35991			−0.673661
$155$	3.94316	−	3.93083i	0.316723	−	0.315732i
$156$	0.290622			0.0232684
$157$	5.59551	−	17.2212i	0.446570	−	1.37440i	−0.434183	−	0.900825i	$-0.642963\pi$
$157$	5.59551	−	17.2212i	0.446570	−	1.37440i	0.880753	−	0.473576i	$-0.157037\pi$
$158$	2.46737	+	7.59378i	0.196293	+	0.604129i
$159$	2.35647	+	1.71207i	0.186880	+	0.135776i
$160$	−1.00000			−0.0790569
$161$	15.1688			1.19547
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	−9.10993	+	6.61875i	−0.713545	+	0.518421i	−0.884315	−	0.466890i	$-0.845374\pi$
$163$	−9.10993	+	6.61875i	−0.713545	+	0.518421i	0.170771	+	0.985311i	$0.445374\pi$
$164$	6.81032	−	4.94799i	0.531797	−	0.386373i
$165$	0.780790	−	2.40303i	0.0607844	−	0.187075i
$166$	−5.22607	−	3.79696i	−0.405622	−	0.294702i
$167$	−1.55423	+	4.78344i	−0.120270	+	0.370153i	−0.993010	−	0.118033i	$-0.962341\pi$
$167$	−1.55423	+	4.78344i	−0.120270	+	0.370153i	0.872740	+	0.488186i	$0.162341\pi$
$168$	−1.02243	−	3.14670i	−0.0788819	−	0.242773i
$169$	10.4489	−	7.59156i	0.803761	−	0.583966i
$170$	−1.85718	−	5.71582i	−0.142440	−	0.438384i
$171$	−0.921250	−	2.83532i	−0.0704498	−	0.216822i
$172$	10.1668	−	7.38660i	0.775210	−	0.563223i
$173$	−0.488263	−	1.50272i	−0.0371220	−	0.114250i	0.930778	−	0.365584i	$-0.119131\pi$
$173$	−0.488263	−	1.50272i	−0.0371220	−	0.114250i	−0.967900	+	0.251334i	$0.919131\pi$
$174$	0.594788	−	1.83057i	0.0450908	−	0.138775i
$175$	2.67675	+	1.94477i	0.202343	+	0.147011i
$176$	−0.780790	+	2.40303i	−0.0588543	+	0.181135i
$177$	−3.29561	+	2.39440i	−0.247713	+	0.179974i
$178$	−2.84090	+	2.06404i	−0.212935	+	0.154706i
$179$	4.68921	+	3.40691i	0.350488	+	0.254645i	0.749074	−	0.662486i	$-0.230499\pi$
$179$	4.68921	+	3.40691i	0.350488	+	0.254645i	−0.398586	+	0.917131i	$0.630499\pi$
$180$	1.00000			0.0745356
$181$	−7.50082			−0.557532			−0.278766	−	0.960359i	$-0.589925\pi$
$181$	−7.50082			−0.557532			−0.278766	+	0.960359i	$0.589925\pi$
$182$	0.777922	+	0.565194i	0.0576634	+	0.0418949i
$183$	−3.85028	−	11.8500i	−0.284621	−	0.875974i
$184$	1.41672	−	4.36020i	0.104442	−	0.321438i
$185$	8.41800			0.618904
$186$	3.94316	−	3.93083i	0.289127	−	0.288223i
$187$	−15.1853			−1.11046
$188$	−0.519940	+	1.60021i	−0.0379205	+	0.116707i
$189$	1.02243	+	3.14670i	0.0743706	+	0.228889i
$190$	−2.41186	−	1.75232i	−0.174975	−	0.127127i
$191$	−0.520043			−0.0376290			−0.0188145	−	0.999823i	$-0.505989\pi$
$191$	−0.520043			−0.0376290			−0.0188145	+	0.999823i	$0.505989\pi$
$192$	−1.00000			−0.0721688
$193$	−2.96903	−	2.15712i	−0.213715	−	0.155273i	0.475778	−	0.879565i	$-0.342167\pi$
$193$	−2.96903	−	2.15712i	−0.213715	−	0.155273i	−0.689493	+	0.724292i	$0.742167\pi$
$194$	−14.0569	+	10.2130i	−1.00923	+	0.733248i
$195$	−0.235118	+	0.170824i	−0.0168372	+	0.0122329i
$196$	1.21972	−	3.75392i	0.0871230	−	0.268137i
$197$	7.91413	+	5.74995i	0.563859	+	0.409667i	0.832869	−	0.553470i	$-0.186697\pi$
$197$	7.91413	+	5.74995i	0.563859	+	0.409667i	−0.269011	+	0.963137i	$0.586697\pi$
$198$	0.780790	−	2.40303i	0.0554883	−	0.170776i
$199$	−3.99449	−	12.2938i	−0.283162	−	0.871483i	−0.986944	−	0.161067i	$-0.948507\pi$
$199$	−3.99449	−	12.2938i	−0.283162	−	0.871483i	0.703781	−	0.710417i	$-0.251493\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$	0.603671	+	1.85791i	0.0425797	+	0.131047i
$202$	3.62043	+	11.1425i	0.254732	+	0.783986i
$203$	5.15214	−	3.74325i	0.361609	−	0.262724i
$204$	−1.85718	−	5.71582i	−0.130029	−	0.400188i
$205$	−2.60131	+	8.00601i	−0.181683	+	0.559164i
$206$	10.8518	+	7.88427i	0.756078	+	0.549323i
$207$	−1.41672	+	4.36020i	−0.0984686	+	0.303055i
$208$	0.235118	−	0.170824i	0.0163025	−	0.0118445i
$209$	−6.09404	+	4.42758i	−0.421533	+	0.306262i
$210$	2.67675	+	1.94477i	0.184713	+	0.134202i
$211$	−4.98244			−0.343005			−0.171503	−	0.985184i	$-0.554862\pi$
$211$	−4.98244			−0.343005			−0.171503	+	0.985184i	$0.554862\pi$
$212$	2.91275			0.200049
$213$	2.18327	+	1.58624i	0.149595	+	0.108687i
$214$	−3.24385	−	9.98355i	−0.221745	−	0.682461i
$215$	−3.88337	+	11.9518i	−0.264843	+	0.815104i
$216$	1.00000			0.0680414
$217$	18.1994	−	2.85330i	1.23546	−	0.193694i
$218$	−0.936935			−0.0634573
$219$	2.31482	−	7.12428i	0.156421	−	0.481414i
$220$	−0.780790	−	2.40303i	−0.0526409	−	0.162012i
$221$	1.41306	+	1.02664i	0.0950524	+	0.0690596i
$222$	8.41800			0.564979
$223$	−0.982235			−0.0657753			−0.0328877	−	0.999459i	$-0.510470\pi$
$223$	−0.982235			−0.0657753			−0.0328877	+	0.999459i	$0.510470\pi$
$224$	−2.67675	−	1.94477i	−0.178848	−	0.129940i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	7.65198	−	5.55949i	0.509002	−	0.369812i
$227$	−4.13203	+	12.7171i	−0.274252	+	0.844062i	0.715164	+	0.698957i	$0.246352\pi$
$227$	−4.13203	+	12.7171i	−0.274252	+	0.844062i	−0.989416	+	0.145105i	$0.953648\pi$
$228$	−2.41186	−	1.75232i	−0.159730	−	0.116050i
$229$	4.31137	−	13.2690i	0.284903	−	0.876843i	−0.701524	−	0.712646i	$-0.747497\pi$
$229$	4.31137	−	13.2690i	0.284903	−	0.876843i	0.986428	−	0.164197i	$-0.0525033\pi$
$230$	1.41672	+	4.36020i	0.0934155	+	0.287503i
$231$	6.76331	−	4.91383i	0.444993	−	0.323306i
$232$	−0.594788	−	1.83057i	−0.0390498	−	0.120183i
$233$	−2.52654	−	7.77588i	−0.165519	−	0.509415i	0.833555	−	0.552436i	$-0.186302\pi$
$233$	−2.52654	−	7.77588i	−0.165519	−	0.509415i	−0.999074	+	0.0430211i	$0.986302\pi$
$234$	−0.235118	+	0.170824i	−0.0153702	+	0.0111671i
$235$	−0.519940	−	1.60021i	−0.0339172	−	0.104386i
$236$	−1.25881	+	3.87422i	−0.0819416	+	0.252190i
$237$	−6.45966	−	4.69321i	−0.419600	−	0.304857i
$238$	6.14475	−	18.9116i	0.398305	−	1.22586i
$239$	9.75786	−	7.08950i	0.631184	−	0.458582i	−0.225626	−	0.974214i	$-0.572443\pi$
$239$	9.75786	−	7.08950i	0.631184	−	0.458582i	0.856810	+	0.515632i	$0.172443\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	14.8007	+	10.7533i	0.953395	+	0.692682i	0.951607	−	0.307316i	$-0.0994309\pi$
$241$	14.8007	+	10.7533i	0.953395	+	0.692682i	0.00178784	+	0.999998i	$0.499431\pi$
$242$	4.61584			0.296717
$243$	−1.00000			−0.0641500
$244$	−10.0802	−	7.32368i	−0.645317	−	0.468850i
$245$	1.21972	+	3.75392i	0.0779252	+	0.239829i
$246$	−2.60131	+	8.00601i	−0.165854	+	0.510445i
$247$	0.866412			0.0551285
$248$	0.879601	−	5.49785i	0.0558547	−	0.349114i
$249$	6.45978			0.409372
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−9.44435	−	29.0667i	−0.596122	−	1.83467i	−0.549060	−	0.835783i	$-0.685014\pi$
$251$	−9.44435	−	29.0667i	−0.596122	−	1.83467i	−0.0470615	−	0.998892i	$-0.514986\pi$
$252$	2.67675	+	1.94477i	0.168619	+	0.122509i
$253$	11.5838			0.728270
$254$	−20.1891			−1.26678
$255$	4.86217	+	3.53257i	0.304481	+	0.221218i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−3.72624	+	2.70728i	−0.232437	+	0.168875i	−0.697907	−	0.716188i	$-0.745885\pi$
$257$	−3.72624	+	2.70728i	−0.232437	+	0.168875i	0.465470	+	0.885063i	$0.345885\pi$
$258$	−3.88337	+	11.9518i	−0.241768	+	0.744085i
$259$	22.5329	+	16.3711i	1.40012	+	1.01725i
$260$	−0.0898072	+	0.276398i	−0.00556961	+	0.0171415i
$261$	0.594788	+	1.83057i	0.0368165	+	0.113309i
$262$	17.7565	−	12.9009i	1.09700	−	0.797019i
$263$	3.29392	+	10.1377i	0.203112	+	0.625114i	0.999786	+	0.0207047i	$0.00659099\pi$
$263$	3.29392	+	10.1377i	0.203112	+	0.625114i	−0.796674	+	0.604410i	$0.793409\pi$
$264$	−0.780790	−	2.40303i	−0.0480543	−	0.147896i
$265$	−2.35647	+	1.71207i	−0.144757	+	0.105172i
$266$	−3.04809	−	9.38105i	−0.186890	−	0.575189i
$267$	1.08513	−	3.33968i	0.0664088	−	0.204385i
$268$	1.58043	+	1.14825i	0.0965402	+	0.0701405i
$269$	5.68004	−	17.4814i	0.346318	−	1.06586i	−0.614556	−	0.788873i	$-0.710665\pi$
$269$	5.68004	−	17.4814i	0.346318	−	1.06586i	0.960874	−	0.276985i	$-0.0893353\pi$
$270$	−0.809017	+	0.587785i	−0.0492352	+	0.0357715i
$271$	−17.0473	+	12.3856i	−1.03555	+	0.752373i	−0.969412	−	0.245438i	$-0.921068\pi$
$271$	−17.0473	+	12.3856i	−1.03555	+	0.752373i	−0.0661397	+	0.997810i	$0.521068\pi$
$272$	−4.86217	−	3.53257i	−0.294812	−	0.214194i
$273$	−0.961565			−0.0581965
$274$	5.27477			0.318661
$275$	2.04414	+	1.48515i	0.123266	+	0.0895580i
$276$	1.41672	+	4.36020i	0.0852763	+	0.262453i
$277$	−1.52646	+	4.69797i	−0.0917163	+	0.282274i	−0.986384	−	0.164459i	$-0.947412\pi$
$277$	−1.52646	+	4.69797i	−0.0917163	+	0.282274i	0.894668	+	0.446732i	$0.147412\pi$
$278$	21.6283			1.29718
$279$	−0.879601	+	5.49785i	−0.0526603	+	0.329147i
$280$	3.30864			0.197729
$281$	4.87178	−	14.9938i	0.290626	−	0.894455i	−0.694030	−	0.719946i	$-0.744166\pi$
$281$	4.87178	−	14.9938i	0.290626	−	0.894455i	0.984656	−	0.174508i	$-0.0558336\pi$
$282$	−0.519940	−	1.60021i	−0.0309620	−	0.0952912i
$283$	−16.3127	−	11.8519i	−0.969688	−	0.704519i	−0.0143074	−	0.999898i	$-0.504554\pi$
$283$	−16.3127	−	11.8519i	−0.969688	−	0.704519i	−0.955380	+	0.295378i	$0.904554\pi$
$284$	2.69867			0.160137
$285$	2.98123			0.176593
$286$	0.594071	+	0.431618i	0.0351282	+	0.0255221i
$287$	−22.5329	+	16.3711i	−1.33008	+	0.966356i
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	5.90834	−	18.1840i	0.347549	−	1.06965i
$290$	1.55718	+	1.13135i	0.0914405	+	0.0664354i
$291$	5.36927	−	16.5249i	0.314752	−	0.968708i
$292$	−2.31482	−	7.12428i	−0.135464	−	0.416917i
$293$	−15.2550	+	11.0834i	−0.891208	+	0.647501i	−0.936193	−	0.351487i	$-0.885676\pi$
$293$	−15.2550	+	11.0834i	−0.891208	+	0.647501i	0.0449844	+	0.998988i	$0.485676\pi$
$294$	1.21972	+	3.75392i	0.0711356	+	0.218933i
$295$	−1.25881	−	3.87422i	−0.0732908	−	0.225566i
$296$	6.81031	−	4.94798i	0.395841	−	0.287595i
$297$	0.780790	+	2.40303i	0.0453060	+	0.139438i
$298$	3.31105	−	10.1904i	0.191804	−	0.590312i
$299$	−1.07792	−	0.783156i	−0.0623378	−	0.0452911i
$300$	−0.309017	+	0.951057i	−0.0178411	+	0.0549093i
$301$	−33.6382	+	24.4396i	−1.93888	+	1.40868i
$302$	15.4734	−	11.2421i	0.890397	−	0.646911i
$303$	−9.47841	−	6.88646i	−0.544520	−	0.395617i
$304$	−2.98123			−0.170985
$305$	12.4598			0.713445
$306$	4.86217	+	3.53257i	0.277952	+	0.201944i
$307$	−5.04309	−	15.5210i	−0.287824	−	0.885832i	−0.985538	−	0.169455i	$-0.945799\pi$
$307$	−5.04309	−	15.5210i	−0.287824	−	0.885832i	0.697714	−	0.716377i	$-0.254201\pi$
$308$	2.58335	−	7.95075i	0.147200	−	0.453036i
$309$	−13.4135			−0.763068
$310$	2.51994	+	4.96487i	0.143123	+	0.281985i
$311$	−5.33516			−0.302529			−0.151265	−	0.988493i	$-0.548335\pi$
$311$	−5.33516			−0.302529			−0.151265	+	0.988493i	$0.548335\pi$
$312$	−0.0898072	+	0.276398i	−0.00508433	+	0.0156480i
$313$	−1.19032	−	3.66343i	−0.0672809	−	0.207069i	0.911764	−	0.410715i	$-0.134721\pi$
$313$	−1.19032	−	3.66343i	−0.0672809	−	0.207069i	−0.979045	+	0.203646i	$0.934721\pi$
$314$	14.6492	+	10.6433i	0.826703	+	0.600635i
$315$	−3.30864			−0.186421
$316$	−7.98457			−0.449167
$317$	−5.22861	−	3.79881i	−0.293668	−	0.213362i	0.431189	−	0.902262i	$-0.358094\pi$
$317$	−5.22861	−	3.79881i	−0.293668	−	0.213362i	−0.724857	+	0.688899i	$0.758094\pi$
$318$	−2.35647	+	1.71207i	−0.132144	+	0.0960083i
$319$	3.93450	−	2.85858i	0.220290	−	0.160050i
$320$	0.309017	−	0.951057i	0.0172746	−	0.0531657i
$321$	8.49251	+	6.17017i	0.474006	+	0.344385i
$322$	−4.68740	+	14.4263i	−0.261219	+	0.803949i
$323$	−5.53669	−	17.0402i	−0.308070	−	0.948141i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	−0.0898072	−	0.276398i	−0.00498161	−	0.0153318i
$326$	−3.47968	−	10.7094i	−0.192722	−	0.593137i
$327$	0.757997	−	0.550717i	0.0419173	−	0.0304547i
$328$	2.60131	+	8.00601i	0.143633	+	0.442058i
$329$	1.72029	−	5.29452i	0.0948429	−	0.291897i
$330$	2.04414	+	1.48515i	0.112526	+	0.0817549i
$331$	−8.28171	+	25.4885i	−0.455204	+	1.40097i	0.415691	+	0.909506i	$0.363540\pi$
$331$	−8.28171	+	25.4885i	−0.455204	+	1.40097i	−0.870895	+	0.491469i	$0.836460\pi$
$332$	5.22607	−	3.79696i	0.286818	−	0.208386i
$333$	−6.81031	+	4.94798i	−0.373203	+	0.271148i
$334$	−4.06903	−	2.95633i	−0.222648	−	0.161763i
$335$	−1.95352			−0.106732
$336$	3.30864			0.180501
$337$	−1.73439	−	1.26011i	−0.0944781	−	0.0686423i	0.539543	−	0.841958i	$-0.318597\pi$
$337$	−1.73439	−	1.26011i	−0.0944781	−	0.0686423i	−0.634021	+	0.773315i	$0.718597\pi$
$338$	3.99112	+	12.2834i	0.217088	+	0.668129i
$339$	−2.92280	+	8.99544i	−0.158744	+	0.488565i
$340$	6.00997			0.325937
$341$	13.8982	−	2.17896i	0.752632	−	0.117997i
$342$	2.98123			0.161206
$343$	3.12136	−	9.60657i	0.168538	−	0.518706i
$344$	3.88337	+	11.9518i	0.209377	+	0.644397i
$345$	−3.70901	−	2.69475i	−0.199686	−	0.145081i
$346$	1.58005			0.0849442
$347$	−10.6820			−0.573438			−0.286719	−	0.958015i	$-0.592565\pi$
$347$	−10.6820			−0.573438			−0.286719	+	0.958015i	$0.592565\pi$
$348$	1.55718	+	1.13135i	0.0834734	+	0.0606470i
$349$	−19.9831	+	14.5185i	−1.06967	+	0.777160i	−0.975853	−	0.218430i	$-0.929907\pi$
$349$	−19.9831	+	14.5185i	−1.06967	+	0.777160i	−0.0938160	+	0.995590i	$0.529907\pi$
$350$	−2.67675	+	1.94477i	−0.143078	+	0.103952i
$351$	0.0898072	−	0.276398i	0.00479356	−	0.0147530i
$352$	−2.04414	−	1.48515i	−0.108953	−	0.0791588i
$353$	−3.16917	+	9.75371i	−0.168678	+	0.519138i	−0.999288	−	0.0377162i	$-0.987992\pi$
$353$	−3.16917	+	9.75371i	−0.168678	+	0.519138i	0.830610	+	0.556854i	$0.187992\pi$
$354$	−1.25881	−	3.87422i	−0.0669050	−	0.205913i
$355$	−2.18327	+	1.58624i	−0.115876	+	0.0841888i
$356$	−1.08513	−	3.33968i	−0.0575117	−	0.177003i
$357$	6.14475	+	18.9116i	0.325215	+	1.00091i
$358$	−4.68921	+	3.40691i	−0.247833	+	0.180061i
$359$	−10.3754	−	31.9323i	−0.547595	−	1.68532i	−0.714739	−	0.699391i	$-0.753455\pi$
$359$	−10.3754	−	31.9323i	−0.547595	−	1.68532i	0.167144	−	0.985932i	$-0.446545\pi$
$360$	−0.309017	+	0.951057i	−0.0162866	+	0.0501251i
$361$	8.18100	+	5.94385i	0.430579	+	0.312834i
$362$	2.31788	−	7.13371i	0.121825	−	0.374939i
$363$	−3.73429	+	2.71312i	−0.195999	+	0.142402i
$364$	−0.777922	+	0.565194i	−0.0407742	+	0.0296242i
$365$	6.06027	+	4.40304i	0.317209	+	0.230466i
$366$	12.4598			0.651283
$367$	−15.9616			−0.833187			−0.416594	−	0.909093i	$-0.636776\pi$
$367$	−15.9616			−0.833187			−0.416594	+	0.909093i	$0.636776\pi$
$368$	3.70901	+	2.69475i	0.193346	+	0.140474i
$369$	−2.60131	−	8.00601i	−0.135419	−	0.416776i
$370$	−2.60131	+	8.00600i	−0.135235	+	0.416212i
$371$	−9.63725			−0.500341
$372$	2.51994	+	4.96487i	0.130653	+	0.257416i
$373$	−17.6743			−0.915140			−0.457570	−	0.889174i	$-0.651280\pi$
$373$	−17.6743			−0.915140			−0.457570	+	0.889174i	$0.651280\pi$
$374$	4.69253	−	14.4421i	0.242645	−	0.746784i
$375$	−0.309017	−	0.951057i	−0.0159576	−	0.0491123i
$376$	−1.36122	−	0.988985i	−0.0701996	−	0.0510030i
$377$	−0.559383			−0.0288097
$378$	−3.30864			−0.170178
$379$	26.8816	+	19.5306i	1.38081	+	1.00322i	0.996804	+	0.0798918i	$0.0254575\pi$
$379$	26.8816	+	19.5306i	1.38081	+	1.00322i	0.384011	+	0.923329i	$0.374543\pi$
$380$	2.41186	−	1.75232i	0.123726	−	0.0898922i
$381$	16.3333	−	11.8669i	0.836782	−	0.607958i
$382$	0.160702	−	0.494591i	0.00822224	−	0.0253055i
$383$	20.2141	+	14.6864i	1.03289	+	0.750439i	0.968885	−	0.247510i	$-0.0796124\pi$
$383$	20.2141	+	14.6864i	1.03289	+	0.750439i	0.0640058	+	0.997950i	$0.479612\pi$
$384$	0.309017	−	0.951057i	0.0157695	−	0.0485334i
$385$	2.58335	+	7.95075i	0.131660	+	0.405208i
$386$	2.96903	−	2.15712i	0.151119	−	0.109795i
$387$	−3.88337	−	11.9518i	−0.197403	−	0.607543i
$388$	−5.36927	−	16.5249i	−0.272583	−	0.838926i
$389$	17.7119	−	12.8684i	0.898028	−	0.652456i	−0.0399305	−	0.999202i	$-0.512714\pi$
$389$	17.7119	−	12.8684i	0.898028	−	0.652456i	0.937959	+	0.346747i	$0.112714\pi$
$390$	−0.0898072	−	0.276398i	−0.00454757	−	0.0139960i
$391$	−8.51442	+	26.2047i	−0.430593	+	1.32523i
$392$	3.19327	+	2.32005i	0.161285	+	0.117180i
$393$	−6.78240	+	20.8741i	−0.342127	+	1.05296i
$394$	−7.91413	+	5.74995i	−0.398708	+	0.289678i
$395$	6.45966	−	4.69321i	0.325021	−	0.236141i
$396$	2.04414	+	1.48515i	0.102722	+	0.0746317i
$397$	−4.74520			−0.238155			−0.119077	−	0.992885i	$-0.537994\pi$
$397$	−4.74520			−0.238155			−0.119077	+	0.992885i	$0.537994\pi$
$398$	12.9265			0.647944
$399$	7.97999	+	5.79781i	0.399499	+	0.290253i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−4.19483	+	12.9104i	−0.209480	+	0.644712i	0.790020	+	0.613081i	$0.210070\pi$
$401$	−4.19483	+	12.9104i	−0.209480	+	0.644712i	−0.999500	+	0.0316311i	$0.989930\pi$
$402$	−1.95352			−0.0974327
$403$	−1.44060	−	0.736866i	−0.0717614	−	0.0367059i
$404$	−11.7160			−0.582890
$405$	0.309017	−	0.951057i	0.0153552	−	0.0472584i
$406$	1.96794	+	6.05670i	0.0976673	+	0.300589i
$407$	17.2075	+	12.5020i	0.852946	+	0.619701i
$408$	6.00997			0.297538
$409$	19.6588			0.972068			0.486034	−	0.873940i	$-0.338443\pi$
$409$	19.6588			0.972068			0.486034	+	0.873940i	$0.338443\pi$
$410$	−6.81032	−	4.94799i	−0.336338	−	0.244364i
$411$	−4.26738	+	3.10043i	−0.210494	+	0.152933i
$412$	−10.8518	+	7.88427i	−0.534628	+	0.388430i
$413$	4.16495	−	12.8184i	0.204944	−	0.630752i
$414$	−3.70901	−	2.69475i	−0.182288	−	0.132440i
$415$	−1.99618	+	6.14362i	−0.0979887	+	0.301578i
$416$	0.0898072	+	0.276398i	0.00440316	+	0.0135515i
$417$	−17.4976	+	12.7128i	−0.856863	+	0.622548i
$418$	−2.32771	−	7.16397i	−0.113852	−	0.350401i
$419$	−2.51277	−	7.73352i	−0.122757	−	0.377807i	0.870729	−	0.491763i	$-0.163648\pi$
$419$	−2.51277	−	7.73352i	−0.122757	−	0.377807i	−0.993486	+	0.113957i	$0.963648\pi$
$420$	−2.67675	+	1.94477i	−0.130612	+	0.0948951i
$421$	2.43129	+	7.48275i	0.118494	+	0.364687i	0.992660	−	0.120941i	$-0.0385911\pi$
$421$	2.43129	+	7.48275i	0.118494	+	0.364687i	−0.874166	+	0.485628i	$0.838591\pi$
$422$	1.53966	−	4.73858i	0.0749493	−	0.230670i
$423$	1.36122	+	0.988985i	0.0661848	+	0.0480861i
$424$	−0.900090	+	2.77019i	−0.0437122	+	0.134532i
$425$	−4.86217	+	3.53257i	−0.235850	+	0.171355i
$426$	−2.18327	+	1.58624i	−0.105780	+	0.0768535i
$427$	33.3517	+	24.2314i	1.61400	+	1.17264i
$428$	10.4973			0.507407
$429$	−0.734313			−0.0354529
$430$	−10.1668	−	7.38660i	−0.490286	−	0.356214i
$431$	2.09080	+	6.43483i	0.100710	+	0.309955i	0.988700	−	0.149909i	$-0.0478981\pi$
$431$	2.09080	+	6.43483i	0.100710	+	0.309955i	−0.887989	+	0.459864i	$0.847898\pi$
$432$	−0.309017	+	0.951057i	−0.0148676	+	0.0457577i
$433$	−17.9721			−0.863686			−0.431843	−	0.901949i	$-0.642137\pi$
$433$	−17.9721			−0.863686			−0.431843	+	0.901949i	$0.642137\pi$
$434$	−2.91028	+	18.1904i	−0.139698	+	0.873167i
$435$	−1.92478			−0.0922859
$436$	0.289529	−	0.891078i	0.0138659	−	0.0426749i
$437$	4.22355	+	12.9988i	0.202040	+	0.621815i
$438$	6.06027	+	4.40304i	0.289571	+	0.210386i
$439$	−3.17231			−0.151406			−0.0757031	−	0.997130i	$-0.524120\pi$
$439$	−3.17231			−0.151406			−0.0757031	+	0.997130i	$0.524120\pi$
$440$	2.52669			0.120455
$441$	−3.19327	−	2.32005i	−0.152061	−	0.110479i
$442$	−1.41306	+	1.02664i	−0.0672122	+	0.0488325i
$443$	4.59400	−	3.33773i	0.218267	−	0.158581i	−0.473279	−	0.880913i	$-0.656930\pi$
$443$	4.59400	−	3.33773i	0.218267	−	0.158581i	0.691546	+	0.722332i	$0.256930\pi$
$444$	−2.60131	+	8.00600i	−0.123453	+	0.379948i
$445$	2.84090	+	2.06404i	0.134672	+	0.0978448i
$446$	0.303527	−	0.934161i	0.0143724	−	0.0442338i
$447$	3.31105	+	10.1904i	0.156607	+	0.481988i
$448$	2.67675	−	1.94477i	0.126464	−	0.0918818i
$449$	7.90459	+	24.3278i	0.373041	+	1.14810i	0.944791	+	0.327673i	$0.106265\pi$
$449$	7.90459	+	24.3278i	0.373041	+	1.14810i	−0.571750	+	0.820428i	$0.693735\pi$
$450$	−0.309017	−	0.951057i	−0.0145672	−	0.0448332i
$451$	−17.2076	+	12.5020i	−0.810273	+	0.588698i
$452$	2.92280	+	8.99544i	0.137477	+	0.423110i
$453$	−5.91033	+	18.1901i	−0.277692	+	0.854647i
$454$	−10.8178	−	7.85959i	−0.507704	−	0.368869i
$455$	0.297140	−	0.914502i	0.0139301	−	0.0428725i
$456$	2.41186	−	1.75232i	0.112946	−	0.0820600i
$457$	−11.0018	+	7.99329i	−0.514643	+	0.373910i	−0.814582	−	0.580048i	$-0.803034\pi$
$457$	−11.0018	+	7.99329i	−0.514643	+	0.373910i	0.299939	+	0.953958i	$0.403034\pi$
$458$	11.2873	+	8.20072i	0.527422	+	0.383194i
$459$	−6.00997			−0.280522
$460$	−4.58459			−0.213758
$461$	−28.0661	−	20.3912i	−1.30717	−	0.949714i	−0.307172	−	0.951654i	$-0.599383\pi$
$461$	−28.0661	−	20.3912i	−1.30717	−	0.949714i	−0.999998	+	0.00193968i	$0.999383\pi$
$462$	2.58335	+	7.95075i	0.120189	+	0.369902i
$463$	−1.66361	+	5.12007i	−0.0773146	+	0.237950i	−0.982243	−	0.187615i	$-0.939924\pi$
$463$	−1.66361	+	5.12007i	−0.0773146	+	0.237950i	0.904928	+	0.425564i	$0.139924\pi$
$464$	1.92478			0.0893555
$465$	−4.95695	−	2.53548i	−0.229873	−	0.117580i
$466$	8.17605			0.378748
$467$	11.5313	−	35.4897i	0.533605	−	1.64227i	−0.213039	−	0.977044i	$-0.568336\pi$
$467$	11.5313	−	35.4897i	0.533605	−	1.64227i	0.746644	−	0.665224i	$-0.231664\pi$
$468$	−0.0898072	−	0.276398i	−0.00415134	−	0.0127765i
$469$	−5.22908	−	3.79915i	−0.241456	−	0.175428i
$470$	1.68256			0.0776108
$471$	−18.1074			−0.834347
$472$	−3.29561	−	2.39440i	−0.151693	−	0.110211i
$473$	−25.6883	+	18.6637i	−1.18115	+	0.858156i
$474$	6.45966	−	4.69321i	0.296702	−	0.215566i
$475$	−0.921250	+	2.83532i	−0.0422699	+	0.130093i
$476$	16.0872	+	11.6880i	0.737354	+	0.535719i
$477$	0.900090	−	2.77019i	0.0412123	−	0.126838i
$478$	3.72717	+	11.4711i	0.170477	+	0.524674i
$479$	9.62054	−	6.98973i	0.439574	−	0.319369i	−0.345892	−	0.938274i	$-0.612424\pi$
$479$	9.62054	−	6.98973i	0.439574	−	0.319369i	0.785465	+	0.618905i	$0.212424\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	−0.755998	−	2.32672i	−0.0344705	−	0.106089i
$482$	−14.8007	+	10.7533i	−0.674152	+	0.489800i
$483$	−4.68740	−	14.4263i	−0.213284	−	0.656421i
$484$	−1.42637	+	4.38992i	−0.0648351	+	0.199542i
$485$	14.0569	+	10.2130i	0.638293	+	0.463747i
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	25.5139	−	18.5370i	1.15615	−	0.839990i	0.166861	−	0.985980i	$-0.446637\pi$
$487$	25.5139	−	18.5370i	1.15615	−	0.839990i	0.989286	+	0.145991i	$0.0466370\pi$
$488$	10.0802	−	7.32368i	0.456308	−	0.331527i
$489$	9.10993	+	6.61875i	0.411965	+	0.299310i
$490$	−3.94710			−0.178312
$491$	5.48151			0.247377			0.123689	−	0.992321i	$-0.460528\pi$
$491$	5.48151			0.247377			0.123689	+	0.992321i	$0.460528\pi$
$492$	−6.81032	−	4.94799i	−0.307033	−	0.223073i
$493$	3.57466	+	11.0017i	0.160995	+	0.495491i
$494$	−0.267736	+	0.824006i	−0.0120460	+	0.0370738i
$495$	−2.52669			−0.113566
$496$	4.95695	+	2.53548i	0.222574	+	0.113846i
$497$	−8.92893			−0.400517
$498$	−1.99618	+	6.14362i	−0.0894511	+	0.275302i
$499$	−1.21390	−	3.73601i	−0.0543417	−	0.167247i	0.920202	−	0.391443i	$-0.128024\pi$
$499$	−1.21390	−	3.73601i	−0.0543417	−	0.167247i	−0.974544	+	0.224197i	$0.928024\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	5.02960			0.224706
$502$	30.5626			1.36407
$503$	−8.49370	−	6.17104i	−0.378715	−	0.275153i	0.382100	−	0.924121i	$-0.375201\pi$
$503$	−8.49370	−	6.17104i	−0.378715	−	0.275153i	−0.760816	+	0.648968i	$0.775201\pi$
$504$	−2.67675	+	1.94477i	−0.119232	+	0.0866269i
$505$	9.47841	−	6.88646i	0.421783	−	0.306444i
$506$	−3.57960	+	11.0169i	−0.159133	+	0.489760i
$507$	−10.4489	−	7.59156i	−0.464052	−	0.337153i
$508$	6.23878	−	19.2010i	0.276801	−	0.851906i
$509$	−5.11155	−	15.7317i	−0.226566	−	0.697297i	−0.998129	−	0.0611448i	$-0.980525\pi$
$509$	−5.11155	−	15.7317i	−0.226566	−	0.697297i	0.771563	−	0.636153i	$-0.219475\pi$
$510$	−4.86217	+	3.53257i	−0.215301	+	0.156425i
$511$	7.65890	+	23.5717i	0.338810	+	1.04275i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−2.41186	+	1.75232i	−0.106486	+	0.0773669i
$514$	−1.42330	−	4.38046i	−0.0627790	−	0.193214i
$515$	4.14500	−	12.7570i	0.182651	−	0.562141i
$516$	−10.1668	−	7.38660i	−0.447568	−	0.325177i
$517$	1.31373	−	4.04324i	0.0577777	−	0.177821i
$518$	−22.5329	+	16.3711i	−0.990037	+	0.719304i
$519$	−1.27829	+	0.928732i	−0.0561107	+	0.0407668i
$520$	−0.235118	−	0.170824i	−0.0103106	−	0.00749111i
$521$	−11.9453			−0.523331			−0.261666	−	0.965159i	$-0.584272\pi$
$521$	−11.9453			−0.523331			−0.261666	+	0.965159i	$0.584272\pi$
$522$	−1.92478			−0.0842451
$523$	−28.5031	−	20.7087i	−1.24635	−	0.905528i	−0.248348	−	0.968671i	$-0.579888\pi$
$523$	−28.5031	−	20.7087i	−1.24635	−	0.905528i	−0.998005	+	0.0631428i	$0.979888\pi$
$524$	6.78240	+	20.8741i	0.296290	+	0.911888i
$525$	1.02243	−	3.14670i	0.0446223	−	0.137333i
$526$	−10.6594			−0.464770
$527$	−5.28638	+	33.0419i	−0.230278	+	1.43933i
$528$	2.52669			0.109960
$529$	−0.612331	+	1.88456i	−0.0266231	+	0.0819375i
$530$	−0.900090	−	2.77019i	−0.0390974	−	0.120329i
$531$	3.29561	+	2.39440i	0.143017	+	0.103908i
$532$	9.86382			0.427651
$533$	2.44646			0.105968
$534$	2.84090	+	2.06404i	0.122938	+	0.0893197i
$535$	−8.49251	+	6.17017i	−0.367163	+	0.266760i
$536$	−1.58043	+	1.14825i	−0.0682642	+	0.0495968i
$537$	1.79112	−	5.51250i	0.0772926	−	0.237882i
$538$	14.8705	+	10.8041i	0.641115	+	0.465797i
$539$	−3.08186	+	9.48499i	−0.132745	+	0.408547i
$540$	−0.309017	−	0.951057i	−0.0132980	−	0.0409270i
$541$	−15.1700	+	11.0217i	−0.652211	+	0.473859i	−0.864024	−	0.503451i	$-0.832063\pi$
$541$	−15.1700	+	11.0217i	−0.652211	+	0.473859i	0.211813	+	0.977310i	$0.432063\pi$
$542$	−6.51150	−	20.0403i	−0.279693	−	0.860807i
$543$	2.31788	+	7.13371i	0.0994699	+	0.306137i
$544$	4.86217	−	3.53257i	0.208464	−	0.151458i
$545$	0.289529	+	0.891078i	0.0124021	+	0.0381696i
$546$	0.297140	−	0.914502i	0.0127164	−	0.0391371i
$547$	9.02262	+	6.55532i	0.385780	+	0.280285i	0.763724	−	0.645543i	$-0.223369\pi$
$547$	9.02262	+	6.55532i	0.385780	+	0.280285i	−0.377944	+	0.925828i	$0.623369\pi$
$548$	−1.62999	+	5.01661i	−0.0696299	+	0.214299i
$549$	−10.0802	+	7.32368i	−0.430211	+	0.312567i
$550$	−2.04414	+	1.48515i	−0.0871622	+	0.0633271i
$551$	4.64230	+	3.37283i	0.197769	+	0.143687i
$552$	−4.58459			−0.195133
$553$	26.4181			1.12341
$554$	−3.99633	−	2.90350i	−0.169788	−	0.123358i
$555$	−2.60131	−	8.00600i	−0.110419	−	0.339836i
$556$	−6.68351	+	20.5697i	−0.283444	+	0.872350i
$557$	17.1905			0.728385			0.364193	−	0.931324i	$-0.381345\pi$
$557$	17.1905			0.728385			0.364193	+	0.931324i	$0.381345\pi$
$558$	−4.95695	−	2.53548i	−0.209844	−	0.107335i
$559$	3.65220			0.154472
$560$	−1.02243	+	3.14670i	−0.0432054	+	0.132973i
$561$	4.69253	+	14.4421i	0.198119	+	0.609747i
$562$	12.7545	+	9.26668i	0.538015	+	0.390891i
$563$	−29.6153			−1.24814			−0.624068	−	0.781370i	$-0.714521\pi$
$563$	−29.6153			−1.24814			−0.624068	+	0.781370i	$0.714521\pi$
$564$	1.68256			0.0708486
$565$	−7.65198	−	5.55949i	−0.321921	−	0.233889i
$566$	16.3127	−	11.8519i	0.685673	−	0.498170i
$567$	2.67675	−	1.94477i	0.112413	−	0.0816727i
$568$	−0.833935	+	2.56659i	−0.0349911	+	0.107692i
$569$	26.6353	+	19.3516i	1.11661	+	0.811263i	0.983691	−	0.179864i	$-0.0575658\pi$
$569$	26.6353	+	19.3516i	1.11661	+	0.811263i	0.132916	+	0.991127i	$0.457566\pi$
$570$	−0.921250	+	2.83532i	−0.0385869	+	0.118758i
$571$	2.17087	+	6.68124i	0.0908480	+	0.279601i	0.986149	−	0.165860i	$-0.0530398\pi$
$571$	2.17087	+	6.68124i	0.0908480	+	0.279601i	−0.895301	+	0.445461i	$0.853040\pi$
$572$	−0.594071	+	0.431618i	−0.0248394	+	0.0180469i
$573$	0.160702	+	0.494591i	0.00671343	+	0.0206618i
$574$	−8.60680	−	26.4890i	−0.359241	−	1.10563i
$575$	3.70901	−	2.69475i	0.154676	−	0.112379i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	13.4524	−	41.4023i	0.560032	−	1.72360i	−0.122237	−	0.992501i	$-0.539007\pi$
$577$	13.4524	−	41.4023i	0.560032	−	1.72360i	0.682270	−	0.731101i	$-0.260993\pi$
$578$	15.4682	+	11.2383i	0.643393	+	0.467453i
$579$	−1.13407	+	3.49030i	−0.0471302	+	0.145052i
$580$	−1.55718	+	1.13135i	−0.0646582	+	0.0469769i
$581$	−17.2912	+	12.5628i	−0.717360	+	0.521192i
$582$	14.0569	+	10.2130i	0.582679	+	0.423341i
$583$	−7.35963			−0.304805
$584$	7.49091			0.309976
$585$	0.235118	+	0.170824i	0.00972095	+	0.00706268i
$586$	−5.82690	−	17.9334i	−0.240707	−	0.740820i
$587$	12.0919	−	37.2151i	0.499087	−	1.53603i	−0.311402	−	0.950278i	$-0.600799\pi$
$587$	12.0919	−	37.2151i	0.499087	−	1.53603i	0.810489	−	0.585754i	$-0.199201\pi$
$588$	−3.94710			−0.162776
$589$	7.51252	+	14.8014i	0.309548	+	0.609881i
$590$	4.07360			0.167707
$591$	3.02293	−	9.30362i	0.124347	−	0.382700i
$592$	2.60131	+	8.00600i	0.106913	+	0.329044i
$593$	14.8697	+	10.8034i	0.610624	+	0.443644i	0.849634	−	0.527373i	$-0.176823\pi$
$593$	14.8697	+	10.8034i	0.610624	+	0.443644i	−0.239010	+	0.971017i	$0.576823\pi$
$594$	−2.52669			−0.103671
$595$	−19.8848			−0.815199
$596$	8.66845	+	6.29799i	0.355073	+	0.257976i
$597$	−10.4577	+	7.59798i	−0.428006	+	0.310965i
$598$	1.07792	−	0.783156i	0.0440795	−	0.0320256i
$599$	9.05409	−	27.8656i	0.369940	−	1.13856i	−0.576889	−	0.816822i	$-0.695734\pi$
$599$	9.05409	−	27.8656i	0.369940	−	1.13856i	0.946829	−	0.321736i	$-0.104266\pi$
$600$	−0.809017	−	0.587785i	−0.0330280	−	0.0239962i
$601$	−6.36724	+	19.5963i	−0.259725	+	0.799351i	0.733137	+	0.680081i	$0.238055\pi$
$601$	−6.36724	+	19.5963i	−0.259725	+	0.799351i	−0.992862	+	0.119270i	$0.961945\pi$
$602$	−12.8487	−	39.5441i	−0.523673	−	1.61170i
$603$	1.58043	−	1.14825i	0.0643601	−	0.0467604i
$604$	5.91033	+	18.1901i	0.240488	+	0.740146i
$605$	−1.42637	−	4.38992i	−0.0579903	−	0.178476i
$606$	9.47841	−	6.88646i	0.385034	−	0.279743i
$607$	2.99801	+	9.22692i	0.121685	+	0.374509i	0.993283	−	0.115714i	$-0.0369155\pi$
$607$	2.99801	+	9.22692i	0.121685	+	0.374509i	−0.871597	+	0.490223i	$0.836915\pi$
$608$	0.921250	−	2.83532i	0.0373616	−	0.114987i
$609$	−5.15214	−	3.74325i	−0.208775	−	0.151684i
$610$	−3.85028	+	11.8500i	−0.155893	+	0.479791i
$611$	−0.395601	+	0.287421i	−0.0160043	+	0.0116278i
$612$	−4.86217	+	3.53257i	−0.196542	+	0.142796i
$613$	4.19998	+	3.05146i	0.169635	+	0.123247i	0.669364	−	0.742935i	$-0.266567\pi$
$613$	4.19998	+	3.05146i	0.169635	+	0.123247i	−0.499728	+	0.866182i	$0.666567\pi$
$614$	16.3198			0.658613
$615$	8.41802			0.339447
$616$	6.76331	+	4.91383i	0.272501	+	0.197984i
$617$	12.6780	+	39.0189i	0.510398	+	1.57084i	0.791502	+	0.611166i	$0.209299\pi$
$617$	12.6780	+	39.0189i	0.510398	+	1.57084i	−0.281104	+	0.959677i	$0.590701\pi$
$618$	4.14500	−	12.7570i	0.166737	−	0.513162i
$619$	12.2643			0.492945			0.246473	−	0.969150i	$-0.420728\pi$
$619$	12.2643			0.492945			0.246473	+	0.969150i	$0.420728\pi$
$620$	−5.50057	+	0.862377i	−0.220908	+	0.0346339i
$621$	4.58459			0.183973
$622$	1.64865	−	5.07404i	0.0661050	−	0.203450i
$623$	3.59030	+	11.0498i	0.143842	+	0.442701i
$624$	−0.235118	−	0.170824i	−0.00941227	−	0.00683841i
$625$	1.00000			0.0400000
$626$	3.85196			0.153955
$627$	6.09404	+	4.42758i	0.243372	+	0.176820i
$628$	−14.6492	+	10.6433i	−0.584568	+	0.424713i
$629$	−40.9298	+	29.7372i	−1.63198	+	1.18570i
$630$	1.02243	−	3.14670i	0.0407344	−	0.125368i
$631$	−3.16633	−	2.30047i	−0.126050	−	0.0915804i	0.522974	−	0.852349i	$-0.324822\pi$
$631$	−3.16633	−	2.30047i	−0.126050	−	0.0915804i	−0.649024	+	0.760768i	$0.724822\pi$
$632$	2.46737	−	7.59378i	0.0981467	−	0.302064i
$633$	1.53966	+	4.73858i	0.0611959	+	0.188342i
$634$	5.22861	−	3.79881i	0.207655	−	0.150870i
$635$	6.23878	+	19.2010i	0.247578	+	0.761968i
$636$	−0.900090	−	2.77019i	−0.0356909	−	0.109845i
$637$	0.928036	−	0.674258i	0.0367701	−	0.0267151i
$638$	1.50285	+	4.62528i	0.0594982	+	0.183117i
$639$	0.833935	−	2.56659i	0.0329899	−	0.101533i
$640$	0.809017	+	0.587785i	0.0319792	+	0.0232343i
$641$	1.45374	−	4.47416i	0.0574194	−	0.176719i	−0.918233	−	0.396040i	$-0.870384\pi$
$641$	1.45374	−	4.47416i	0.0574194	−	0.176719i	0.975653	+	0.219321i	$0.0703842\pi$
$642$	−8.49251	+	6.17017i	−0.335173	+	0.243517i
$643$	20.1683	−	14.6531i	0.795361	−	0.577863i	−0.114189	−	0.993459i	$-0.536427\pi$
$643$	20.1683	−	14.6531i	0.795361	−	0.577863i	0.909549	+	0.415596i	$0.136427\pi$
$644$	−12.2718	−	8.91597i	−0.483576	−	0.351338i
$645$	12.5668			0.494819
$646$	17.9171			0.704939
$647$	2.43914	+	1.77214i	0.0958923	+	0.0696698i	0.634698	−	0.772760i	$-0.281124\pi$
$647$	2.43914	+	1.77214i	0.0958923	+	0.0696698i	−0.538806	+	0.842430i	$0.681124\pi$
$648$	−0.309017	−	0.951057i	−0.0121393	−	0.0373610i
$649$	3.18062	−	9.78896i	0.124850	−	0.384250i
$650$	0.290622			0.0113991
$651$	−8.33758	−	16.4270i	−0.326775	−	0.643823i
$652$	11.2605			0.440995
$653$	11.7570	−	36.1843i	0.460087	−	1.41600i	−0.404970	−	0.914330i	$-0.632718\pi$
$653$	11.7570	−	36.1843i	0.460087	−	1.41600i	0.865057	−	0.501673i	$-0.167282\pi$
$654$	0.289529	+	0.891078i	0.0113215	+	0.0348439i
$655$	−17.7565	−	12.9009i	−0.693806	−	0.504079i
$656$	−8.41802			−0.328668
$657$	−7.49091			−0.292248
$658$	4.50379	+	3.27220i	0.175576	+	0.127563i
$659$	20.8607	−	15.1562i	0.812618	−	0.590402i	−0.101970	−	0.994787i	$-0.532515\pi$
$659$	20.8607	−	15.1562i	0.812618	−	0.590402i	0.914588	+	0.404386i	$0.132515\pi$
$660$	−2.04414	+	1.48515i	−0.0795679	+	0.0578094i
$661$	9.81037	−	30.1932i	0.381579	−	1.17438i	−0.557352	−	0.830276i	$-0.688183\pi$
$661$	9.81037	−	30.1932i	0.381579	−	1.17438i	0.938932	−	0.344104i	$-0.111817\pi$
$662$	−21.6818	−	15.7528i	−0.842687	−	0.612248i
$663$	0.539739	−	1.66115i	0.0209617	−	0.0645136i
$664$	1.99618	+	6.14362i	0.0774669	+	0.238419i
$665$	−7.97999	+	5.79781i	−0.309451	+	0.224829i
$666$	−2.60131	−	8.00600i	−0.100799	−	0.310226i
$667$	−2.72686	−	8.39241i	−0.105584	−	0.324955i
$668$	4.06903	−	2.95633i	0.157436	−	0.114384i
$669$	0.303527	+	0.934161i	0.0117350	+	0.0361168i
$670$	0.603671	−	1.85791i	0.0233218	−	0.0717772i
$671$	25.4695	+	18.5047i	0.983238	+	0.714365i
$672$	−1.02243	+	3.14670i	−0.0394409	+	0.121387i
$673$	20.2269	−	14.6957i	0.779691	−	0.566478i	−0.125195	−	0.992132i	$-0.539956\pi$
$673$	20.2269	−	14.6957i	0.779691	−	0.566478i	0.904886	+	0.425654i	$0.139956\pi$
$674$	1.73439	−	1.26011i	0.0668061	−	0.0485375i
$675$	0.809017	+	0.587785i	0.0311391	+	0.0226239i
$676$	−12.9155			−0.496751
$677$	34.4186			1.32281			0.661407	−	0.750027i	$-0.269960\pi$
$677$	34.4186			1.32281			0.661407	+	0.750027i	$0.269960\pi$
$678$	−7.65198	−	5.55949i	−0.293872	−	0.213511i
$679$	17.7650	+	54.6750i	0.681758	+	2.09823i
$680$	−1.85718	+	5.71582i	−0.0712198	+	0.219192i
$681$	13.3715			0.512398
$682$	−2.22248	+	13.8914i	−0.0851031	+	0.531927i
$683$	28.7725			1.10095			0.550475	−	0.834852i	$-0.314447\pi$
$683$	28.7725			1.10095			0.550475	+	0.834852i	$0.314447\pi$
$684$	−0.921250	+	2.83532i	−0.0352249	+	0.108411i
$685$	−1.62999	−	5.01661i	−0.0622789	−	0.191675i
$686$	8.17183	+	5.93718i	0.312002	+	0.226683i
$687$	−13.9519			−0.532298
$688$	−12.5668			−0.479106
$689$	0.684842	+	0.497567i	0.0260904	+	0.0189558i
$690$	3.70901	−	2.69475i	0.141200	−	0.102588i
$691$	−40.2222	+	29.2232i	−1.53013	+	1.11170i	−0.573958	+	0.818885i	$0.694593\pi$
$691$	−40.2222	+	29.2232i	−1.53013	+	1.11170i	−0.956168	+	0.292817i	$0.905407\pi$
$692$	−0.488263	+	1.50272i	−0.0185610	+	0.0571248i
$693$	−6.76331	−	4.91383i	−0.256917	−	0.186661i
$694$	3.30091	−	10.1591i	0.125301	−	0.385636i
$695$	−6.68351	−	20.5697i	−0.253520	−	0.780254i
$696$	−1.55718	+	1.13135i	−0.0590246	+	0.0428839i
$697$	−15.6338	−	48.1159i	−0.592173	−	1.82252i
$698$	−7.63285	−	23.4915i	−0.288908	−	0.889166i
$699$	−6.61456	+	4.80576i	−0.250186	+	0.181771i
$700$	−1.02243	−	3.14670i	−0.0386441	−	0.118934i
$701$	−8.32999	+	25.6371i	−0.314619	+	0.968299i	0.661291	+	0.750129i	$0.270009\pi$
$701$	−8.32999	+	25.6371i	−0.314619	+	0.968299i	−0.975911	+	0.218170i	$0.929991\pi$
$702$	0.235118	+	0.170824i	0.00887397	+	0.00644732i
$703$	−7.75509	+	23.8677i	−0.292489	+	0.900188i
$704$	2.04414	−	1.48515i	0.0770413	−	0.0559737i
$705$	−1.36122	+	0.988985i	−0.0512665	+	0.0372473i
$706$	−8.29700	−	6.02813i	−0.312262	−	0.226872i
$707$	38.7639			1.45787
$708$	4.07360			0.153095
$709$	−5.15363	−	3.74433i	−0.193549	−	0.140621i	0.486790	−	0.873519i	$-0.338168\pi$
$709$	−5.15363	−	3.74433i	−0.193549	−	0.140621i	−0.680339	+	0.732897i	$0.738168\pi$
$710$	−0.833935	−	2.56659i	−0.0312970	−	0.0963223i
$711$	−2.46737	+	7.59378i	−0.0925336	+	0.284789i
$712$	3.51155			0.131601
$713$	4.03261	−	25.2054i	0.151022	−	0.943948i
$714$	−19.8848			−0.744171
$715$	0.226915	−	0.698373i	0.00848614	−	0.0261177i
$716$	−1.79112	−	5.51250i	−0.0669373	−	0.206012i
$717$	−9.75786	−	7.08950i	−0.364414	−	0.264762i
$718$	33.5756			1.25303
$719$	32.7939			1.22301			0.611503	−	0.791242i	$-0.290565\pi$
$719$	32.7939			1.22301			0.611503	+	0.791242i	$0.290565\pi$
$720$	−0.809017	−	0.587785i	−0.0301503	−	0.0219055i
$721$	35.9046	−	26.0862i	1.33716	−	0.971501i
$722$	−8.18100	+	5.94385i	−0.304465	+	0.221207i
$723$	5.65335	−	17.3992i	0.210251	−	0.647085i
$724$	6.06829	+	4.40887i	0.225526	+	0.163855i
$725$	0.594788	−	1.83057i	0.0220899	−	0.0679857i
$726$	−1.42637	−	4.38992i	−0.0529376	−	0.162925i
$727$	20.5688	−	14.9441i	0.762854	−	0.554246i	−0.136930	−	0.990581i	$-0.543724\pi$
$727$	20.5688	−	14.9441i	0.762854	−	0.554246i	0.899784	+	0.436335i	$0.143724\pi$
$728$	−0.297140	−	0.914502i	−0.0110127	−	0.0338937i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−6.06027	+	4.40304i	−0.224301	+	0.162964i
$731$	−23.3389	−	71.8299i	−0.863222	−	2.65672i
$732$	−3.85028	+	11.8500i	−0.142311	+	0.437987i
$733$	5.22555	+	3.79659i	0.193010	+	0.140230i	0.680093	−	0.733125i	$-0.261939\pi$
$733$	5.22555	+	3.79659i	0.193010	+	0.140230i	−0.487083	+	0.873356i	$0.661939\pi$
$734$	4.93240	−	15.1804i	0.182058	−	0.560317i
$735$	3.19327	−	2.32005i	0.117786	−	0.0855763i
$736$	−3.70901	+	2.69475i	−0.136716	+	0.0993299i
$737$	−3.99326	−	2.90127i	−0.147094	−	0.106870i
$738$	8.41802			0.309872
$739$	19.1674			0.705084			0.352542	−	0.935796i	$-0.385317\pi$
$739$	19.1674			0.705084			0.352542	+	0.935796i	$0.385317\pi$
$740$	−6.81031	−	4.94798i	−0.250352	−	0.181891i
$741$	−0.267736	−	0.824006i	−0.00983552	−	0.0302706i
$742$	2.97808	−	9.16557i	0.109329	−	0.336479i
$743$	−21.1261			−0.775040			−0.387520	−	0.921861i	$-0.626668\pi$
$743$	−21.1261			−0.775040			−0.387520	+	0.921861i	$0.626668\pi$
$744$	−5.50057	+	0.862377i	−0.201661	+	0.0316163i
$745$	−10.7148			−0.392559
$746$	5.46165	−	16.8092i	0.199965	−	0.615430i
$747$	−1.99618	−	6.14362i	−0.0730365	−	0.224783i
$748$	12.2852	+	8.92572i	0.449191	+	0.326357i
$749$	−34.7319			−1.26908
$750$	1.00000			0.0365148
$751$	−31.9105	−	23.1843i	−1.16443	−	0.846008i	−0.174099	−	0.984728i	$-0.555701\pi$
$751$	−31.9105	−	23.1843i	−1.16443	−	0.846008i	−0.990332	+	0.138720i	$0.955701\pi$
$752$	1.36122	−	0.988985i	0.0496386	−	0.0360646i
$753$	−24.7256	+	17.9642i	−0.901052	+	0.654652i
$754$	0.172859	−	0.532005i	0.00629514	−	0.0193745i
$755$	−15.4734	−	11.2421i	−0.563136	−	0.409143i
$756$	1.02243	−	3.14670i	0.0371853	−	0.114445i
$757$	−9.81272	−	30.2004i	−0.356649	−	1.09765i	−0.955047	−	0.296455i	$-0.904196\pi$
$757$	−9.81272	−	30.2004i	−0.356649	−	1.09765i	0.598398	−	0.801199i	$-0.295804\pi$
$758$	−26.8816	+	19.5306i	−0.976383	+	0.709384i
$759$	−3.57960	−	11.0169i	−0.129931	−	0.399888i
$760$	0.921250	+	2.83532i	0.0334173	+	0.102848i
$761$	30.7464	−	22.3386i	1.11456	−	0.809773i	0.131182	−	0.991358i	$-0.458123\pi$
$761$	30.7464	−	22.3386i	1.11456	−	0.809773i	0.983375	+	0.181585i	$0.0581229\pi$
$762$	6.23878	+	19.2010i	0.226007	+	0.695578i
$763$	−0.957947	+	2.94826i	−0.0346800	+	0.106734i
$764$	0.420724	+	0.305674i	0.0152213	+	0.0110589i
$765$	1.85718	−	5.71582i	0.0671466	−	0.206656i
$766$	−20.2141	+	14.6864i	−0.730364	+	0.530641i
$767$	−0.957777	+	0.695866i	−0.0345833	+	0.0251263i
$768$	0.809017	+	0.587785i	0.0291929	+	0.0212099i
$769$	−17.7069			−0.638527			−0.319264	−	0.947666i	$-0.603436\pi$
$769$	−17.7069			−0.638527			−0.319264	+	0.947666i	$0.603436\pi$
$770$	−8.35991			−0.301270
$771$	3.72624	+	2.70728i	0.134197	+	0.0975001i
$772$	1.13407	+	3.49030i	0.0408160	+	0.125619i
$773$	1.91516	−	5.89426i	0.0688836	−	0.212002i	−0.910689	−	0.413093i	$-0.864449\pi$
$773$	1.91516	−	5.89426i	0.0688836	−	0.212002i	0.979573	+	0.201091i	$0.0644486\pi$
$774$	12.5668			0.451706
$775$	3.94316	−	3.93083i	0.141643	−	0.141200i
$776$	17.3753			0.623738
$777$	8.60679	−	26.4890i	0.308767	−	0.950286i
$778$	6.76534	+	20.8216i	0.242549	+	0.746490i
$779$	−20.3031	−	14.7511i	−0.727435	−	0.528512i
$780$	0.290622			0.0104059
$781$	−6.81870			−0.243992
$782$	−22.2911	−	16.1954i	−0.797126	−	0.579146i
$783$	1.55718	−	1.13135i	0.0556489	−	0.0404313i
$784$	−3.19327	+	2.32005i	−0.114045	+	0.0828589i
$785$	5.59551	−	17.2212i	0.199712	−	0.614651i
$786$	−17.7565	−	12.9009i	−0.633355	−	0.460159i
$787$	−8.14050	+	25.0539i	−0.290177	+	0.893074i	0.694621	+	0.719375i	$0.255572\pi$
$787$	−8.14050	+	25.0539i	−0.290177	+	0.893074i	−0.984799	+	0.173699i	$0.944428\pi$
$788$	−3.02293	−	9.30362i	−0.107687	−	0.331428i
$789$	8.62360	−	6.26541i	0.307008	−	0.223055i
$790$	2.46737	+	7.59378i	0.0877850	+	0.270175i
$791$	−9.67048	−	29.7627i	−0.343843	−	1.05824i
$792$	−2.04414	+	1.48515i	−0.0726352	+	0.0527726i
$793$	−1.11898	−	3.44386i	−0.0397361	−	0.122295i
$794$	1.46635	−	4.51296i	0.0520387	−	0.160159i
$795$	2.35647	+	1.71207i	0.0835753	+	0.0607210i
$796$	−3.99449	+	12.2938i	−0.141581	+	0.435742i
$797$	−6.17246	+	4.48456i	−0.218640	+	0.158851i	−0.691714	−	0.722171i	$-0.743144\pi$
$797$	−6.17246	+	4.48456i	−0.218640	+	0.158851i	0.473074	+	0.881023i	$0.343144\pi$
$798$	−7.97999	+	5.79781i	−0.282489	+	0.205240i
$799$	8.18090	+	5.94377i	0.289419	+	0.210276i
$800$	−1.00000			−0.0353553
$801$	−3.51155			−0.124075
$802$	−10.9822	−	7.97904i	−0.387795	−	0.281750i
$803$	5.84883	+	18.0008i	0.206401	+	0.635236i
$804$	0.603671	−	1.85791i	0.0212898	−	0.0655234i
$805$	15.1688			0.534628
$806$	1.14597	−	1.14239i	0.0403651	−	0.0402389i
$807$	−18.3810			−0.647042
$808$	3.62043	−	11.1425i	0.127366	−	0.391993i
$809$	9.65586	+	29.7177i	0.339482	+	1.04482i	0.964472	+	0.264185i	$0.0851031\pi$
$809$	9.65586	+	29.7177i	0.339482	+	1.04482i	−0.624990	+	0.780633i	$0.714897\pi$
$810$	0.809017	+	0.587785i	0.0284260	+	0.0206527i
$811$	−12.9359			−0.454241			−0.227120	−	0.973867i	$-0.572931\pi$
$811$	−12.9359			−0.454241			−0.227120	+	0.973867i	$0.572931\pi$
$812$	−6.36839			−0.223487
$813$	17.0473	+	12.3856i	0.597876	+	0.434383i
$814$	−17.2075	+	12.5020i	−0.603124	+	0.438195i
$815$	−9.10993	+	6.61875i	−0.319107	+	0.231845i
$816$	−1.85718	+	5.71582i	−0.0650144	+	0.200094i
$817$	−30.3095	−	22.0212i	−1.06040	−	0.770423i
$818$	−6.07492	+	18.6967i	−0.212405	+	0.653714i
$819$	0.297140	+	0.914502i	0.0103829	+	0.0319553i
$820$	6.81032	−	4.94799i	0.237827	−	0.172791i
$821$	12.7080	+	39.1112i	0.443512	+	1.36499i	0.884107	+	0.467284i	$0.154767\pi$
$821$	12.7080	+	39.1112i	0.443512	+	1.36499i	−0.440595	+	0.897706i	$0.645233\pi$
$822$	−1.62999	−	5.01661i	−0.0568526	−	0.174974i
$823$	16.8504	−	12.2425i	0.587368	−	0.426748i	−0.254005	−	0.967203i	$-0.581748\pi$
$823$	16.8504	−	12.2425i	0.587368	−	0.426748i	0.841373	+	0.540455i	$0.181748\pi$
$824$	−4.14500	−	12.7570i	−0.144398	−	0.444411i
$825$	0.780790	−	2.40303i	0.0271836	−	0.0836626i
$826$	10.9040	+	7.92221i	0.379398	+	0.275649i
$827$	−2.18709	+	6.73118i	−0.0760527	+	0.234066i	−0.981855	−	0.189635i	$-0.939269\pi$
$827$	−2.18709	+	6.73118i	−0.0760527	+	0.234066i	0.905802	+	0.423701i	$0.139269\pi$
$828$	3.70901	−	2.69475i	0.128897	−	0.0936492i
$829$	27.1906	−	19.7551i	0.944368	−	0.686124i	−0.00509974	−	0.999987i	$-0.501623\pi$
$829$	27.1906	−	19.7551i	0.944368	−	0.686124i	0.949468	+	0.313863i	$0.101623\pi$
$830$	−5.22607	−	3.79696i	−0.181400	−	0.131795i
$831$	4.93974			0.171358
$832$	−0.290622			−0.0100755
$833$	−19.1915	−	13.9434i	−0.664946	−	0.483111i
$834$	−6.68351	−	20.5697i	−0.231431	−	0.712271i
$835$	−1.55423	+	4.78344i	−0.0537864	+	0.165538i
$836$	7.53264			0.260522
$837$	5.50057	−	0.862377i	0.190128	−	0.0298081i
$838$	8.13150			0.280898
$839$	0.723587	−	2.22697i	0.0249810	−	0.0768836i	−0.937789	−	0.347206i	$-0.887130\pi$
$839$	0.723587	−	2.22697i	0.0249810	−	0.0768836i	0.962770	+	0.270323i	$0.0871304\pi$
$840$	−1.02243	−	3.14670i	−0.0352771	−	0.108572i
$841$	20.4643	+	14.8682i	0.705665	+	0.512695i
$842$	−7.86783			−0.271143
$843$	−15.7654			−0.542990
$844$	4.03088	+	2.92860i	0.138748	+	0.100807i
$845$	10.4489	−	7.59156i	0.359453	−	0.261158i
$846$	−1.36122	+	0.988985i	−0.0467997	+	0.0340020i
$847$	4.71935	−	14.5247i	0.162159	−	0.499074i
$848$	−2.35647	−	1.71207i	−0.0809214	−	0.0587928i
$849$	−6.23089	+	19.1767i	−0.213843	+	0.658143i
$850$	−1.85718	−	5.71582i	−0.0637009	−	0.196051i
$851$	31.2225	−	22.6844i	1.07029	−	0.777613i
$852$	−0.833935	−	2.56659i	−0.0285701	−	0.0879298i
$853$	10.0421	+	30.9064i	0.343834	+	1.05821i	0.962205	+	0.272327i	$0.0877931\pi$
$853$	10.0421	+	30.9064i	0.343834	+	1.05821i	−0.618370	+	0.785887i	$0.712207\pi$
$854$	−33.3517	+	24.2314i	−1.14127	+	0.829182i
$855$	−0.921250	−	2.83532i	−0.0315061	−	0.0969658i
$856$	−3.24385	+	9.98355i	−0.110873	+	0.341231i
$857$	−27.1294	−	19.7107i	−0.926724	−	0.673304i	0.0184647	−	0.999830i	$-0.494122\pi$
$857$	−27.1294	−	19.7107i	−0.926724	−	0.673304i	−0.945188	+	0.326525i	$0.894122\pi$
$858$	0.226915	−	0.698373i	0.00774675	−	0.0238421i
$859$	−46.0305	+	33.4431i	−1.57054	+	1.14107i	−0.643906	+	0.765105i	$0.722687\pi$
$859$	−46.0305	+	33.4431i	−1.57054	+	1.14107i	−0.926636	+	0.375960i	$0.877313\pi$
$860$	10.1668	−	7.38660i	0.346685	−	0.251881i
$861$	22.5329	+	16.3711i	0.767919	+	0.557926i
$862$	−6.76598			−0.230450
$863$	35.8354			1.21985			0.609926	−	0.792458i	$-0.291199\pi$
$863$	35.8354			1.21985			0.609926	+	0.792458i	$0.291199\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−0.488263	−	1.50272i	−0.0166014	−	0.0510940i
$866$	5.55370	−	17.0925i	0.188722	−	0.580828i
$867$	−19.1198			−0.649342
$868$	−16.4008	−	8.38899i	−0.556678	−	0.284741i
$869$	20.1745			0.684375
$870$	0.594788	−	1.83057i	0.0201652	−	0.0620621i
$871$	0.175440	+	0.539949i	0.00594456	+	0.0182955i
$872$	0.757997	+	0.550717i	0.0256690	+	0.0186496i
$873$	−17.3753			−0.588066
$874$	−13.6677			−0.462317
$875$	2.67675	+	1.94477i	0.0904905	+	0.0657452i
$876$	−6.06027	+	4.40304i	−0.204758	+	0.148765i
$877$	18.3050	−	13.2994i	0.618117	−	0.449088i	−0.234146	−	0.972201i	$-0.575229\pi$
$877$	18.3050	−	13.2994i	0.618117	−	0.449088i	0.852263	+	0.523113i	$0.175229\pi$
$878$	0.980299	−	3.01705i	0.0330835	−	0.101820i
$879$	15.2550	+	11.0834i	0.514539	+	0.373835i
$880$	−0.780790	+	2.40303i	−0.0263204	+	0.0810060i
$881$	10.0612	+	30.9653i	0.338972	+	1.04325i	0.964732	+	0.263232i	$0.0847886\pi$
$881$	10.0612	+	30.9653i	0.338972	+	1.04325i	−0.625761	+	0.780015i	$0.715211\pi$
$882$	3.19327	−	2.32005i	0.107523	−	0.0781201i
$883$	−13.3900	−	41.2101i	−0.450609	−	1.38683i	−0.876214	−	0.481922i	$-0.839939\pi$
$883$	−13.3900	−	41.2101i	−0.450609	−	1.38683i	0.425605	−	0.904909i	$-0.360061\pi$
$884$	−0.539739	−	1.66115i	−0.0181534	−	0.0558704i
$885$	−3.29561	+	2.39440i	−0.110781	+	0.0804869i
$886$	1.75475	+	5.40057i	0.0589520	+	0.181436i
$887$	11.0807	−	34.1029i	0.372054	−	1.14506i	−0.573391	−	0.819282i	$-0.694372\pi$
$887$	11.0807	−	34.1029i	0.372054	−	1.14506i	0.945445	−	0.325782i	$-0.105628\pi$
$888$	−6.81031	−	4.94798i	−0.228539	−	0.166043i
$889$	−20.6419	+	63.5292i	−0.692306	+	2.13070i
$890$	−2.84090	+	2.06404i	−0.0952273	+	0.0691867i
$891$	2.04414	−	1.48515i	0.0684811	−	0.0497544i
$892$	0.794645	+	0.577343i	0.0266067	+	0.0193309i
$893$	5.01610			0.167857
$894$	−10.7148			−0.358356
$895$	4.68921	+	3.40691i	0.156743	+	0.113881i
$896$	1.02243	+	3.14670i	0.0341569	+	0.105124i
$897$	−0.411729	+	1.26717i	−0.0137472	+	0.0423097i
$898$	−25.5798			−0.853609
$899$	−4.85032	−	9.55625i	−0.161767	−	0.318719i
$900$	1.00000			0.0333333
$901$	5.40952	−	16.6488i	0.180217	−	0.554651i
$902$	−6.57271	−	20.2287i	−0.218847	−	0.673543i
$903$	33.6382	+	24.4396i	1.11941	+	0.813300i
$904$	−9.45837			−0.314581
$905$	−7.50082			−0.249336
$906$	−15.4734	−	11.2421i	−0.514071	−	0.373494i
$907$	−15.9270	+	11.5717i	−0.528848	+	0.384231i	−0.819927	−	0.572468i	$-0.805986\pi$
$907$	−15.9270	+	11.5717i	−0.528848	+	0.384231i	0.291079	+	0.956699i	$0.405986\pi$
$908$	10.8178	−	7.85959i	0.359001	−	0.260830i
$909$	−3.62043	+	11.1425i	−0.120082	+	0.369575i
$910$	0.777922	+	0.565194i	0.0257879	+	0.0187360i
$911$	−12.2021	+	37.5543i	−0.404275	+	1.24423i	0.517225	+	0.855849i	$0.326965\pi$
$911$	−12.2021	+	37.5543i	−0.404275	+	1.24423i	−0.921499	+	0.388380i	$0.873035\pi$
$912$	0.921250	+	2.83532i	0.0305056	+	0.0938867i
$913$	−13.2047	+	9.59375i	−0.437011	+	0.317507i
$914$	−4.20232	−	12.9334i	−0.139000	−	0.427799i
$915$	−3.85028	−	11.8500i	−0.127286	−	0.391747i
$916$	−11.2873	+	8.20072i	−0.372943	+	0.270959i
$917$	−22.4405	−	69.0648i	−0.741051	−	2.28072i
$918$	1.85718	−	5.71582i	0.0612962	−	0.188650i
$919$	−8.15419	−	5.92437i	−0.268982	−	0.195427i	0.445115	−	0.895473i	$-0.353163\pi$
$919$	−8.15419	−	5.92437i	−0.268982	−	0.195427i	−0.714097	+	0.700046i	$0.753163\pi$
$920$	1.41672	−	4.36020i	0.0467077	−	0.143752i
$921$	−13.2030	+	9.59252i	−0.435053	+	0.316084i
$922$	28.0661	−	20.3912i	0.924309	−	0.671550i
$923$	0.634507	+	0.460996i	0.0208850	+	0.0151739i
$924$	−8.35991			−0.275021
$925$	8.41800			0.276782
$926$	−4.35539	−	3.16438i	−0.143127	−	0.103988i
$927$	4.14500	+	12.7570i	0.136140	+	0.418995i
$928$	−0.594788	+	1.83057i	−0.0195249	+	0.0600914i
$929$	22.3855			0.734445			0.367223	−	0.930133i	$-0.380309\pi$
$929$	22.3855			0.734445			0.367223	+	0.930133i	$0.380309\pi$
$930$	3.94316	−	3.93083i	0.129301	−	0.128897i
$931$	−11.7672			−0.385655
$932$	−2.52654	+	7.77588i	−0.0827595	+	0.254708i
$933$	1.64865	+	5.07404i	0.0539745	+	0.166117i
$934$	30.1893	+	21.9338i	0.987825	+	0.717697i
$935$	−15.1853			−0.496614
$936$	0.290622			0.00949929
$937$	−31.0997	−	22.5953i	−1.01598	−	0.738155i	−0.0505280	−	0.998723i	$-0.516090\pi$
$937$	−31.0997	−	22.5953i	−1.01598	−	0.738155i	−0.965456	+	0.260567i	$0.916090\pi$
$938$	5.22908	−	3.79915i	0.170735	−	0.124047i
$939$	−3.11630	+	2.26413i	−0.101697	+	0.0738869i
$940$	−0.519940	+	1.60021i	−0.0169586	+	0.0521931i
$941$	28.5777	+	20.7629i	0.931605	+	0.676851i	0.946385	−	0.323040i	$-0.104705\pi$
$941$	28.5777	+	20.7629i	0.931605	+	0.676851i	−0.0147803	+	0.999891i	$0.504705\pi$
$942$	5.59551	−	17.2212i	0.182311	−	0.561097i
$943$	11.9259	+	36.7043i	0.388362	+	1.19526i
$944$	3.29561	−	2.39440i	0.107263	−	0.0779311i
$945$	1.02243	+	3.14670i	0.0332595	+	0.102362i
$946$	−9.81207	−	30.1984i	−0.319018	−	0.981836i
$947$	−41.4931	+	30.1465i	−1.34835	+	0.979630i	−0.349253	+	0.937028i	$0.613565\pi$
$947$	−41.4931	+	30.1465i	−1.34835	+	0.979630i	−0.999092	+	0.0426016i	$0.986435\pi$
$948$	2.46737	+	7.59378i	0.0801364	+	0.246635i
$949$	0.672738	−	2.07047i	0.0218380	−	0.0672104i
$950$	−2.41186	−	1.75232i	−0.0782512	−	0.0568528i
$951$	−1.99715	+	6.14660i	−0.0647620	+	0.199317i
$952$	−16.0872	+	11.6880i	−0.521388	+	0.378811i
$953$	11.2289	−	8.15824i	0.363738	−	0.264271i	−0.390871	−	0.920445i	$-0.627826\pi$
$953$	11.2289	−	8.15824i	0.363738	−	0.264271i	0.754610	+	0.656174i	$0.227826\pi$
$954$	2.35647	+	1.71207i	0.0762934	+	0.0554304i
$955$	−0.520043			−0.0168282
$956$	−12.0614			−0.390093
$957$	−3.93450	−	2.85858i	−0.127184	−	0.0924049i
$958$	3.67472	+	11.3096i	0.118725	+	0.365397i
$959$	5.39307	−	16.5982i	0.174151	−	0.535982i
$960$	−1.00000			−0.0322749
$961$	0.0970934	−	30.9998i	0.00313204	−	0.999995i
$962$	2.44646			0.0788770
$963$	3.24385	−	9.98355i	0.104532	−	0.321715i
$964$	−5.65335	−	17.3992i	−0.182082	−	0.560392i
$965$	−2.96903	−	2.15712i	−0.0955763	−	0.0694403i
$966$	15.1688			0.488047
$967$	−7.86078			−0.252786			−0.126393	−	0.991980i	$-0.540340\pi$
$967$	−7.86078			−0.252786			−0.126393	+	0.991980i	$0.540340\pi$
$968$	−3.73429	−	2.71312i	−0.120025	−	0.0872030i
$969$	−14.4952	+	10.5314i	−0.465654	+	0.338318i
$970$	−14.0569	+	10.2130i	−0.451341	+	0.327918i
$971$	13.2086	−	40.6518i	0.423883	−	1.30458i	−0.480177	−	0.877172i	$-0.659428\pi$
$971$	13.2086	−	40.6518i	0.423883	−	1.30458i	0.904060	−	0.427406i	$-0.140572\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	22.1133	−	68.0578i	0.708920	−	2.18183i
$974$	9.74546	+	29.9934i	0.312265	+	0.961051i
$975$	−0.235118	+	0.170824i	−0.00752981	+	0.00547073i
$976$	3.85028	+	11.8500i	0.123245	+	0.379308i
$977$	−6.73261	−	20.7208i	−0.215395	−	0.662918i	−0.999125	−	0.0418168i	$-0.986685\pi$
$977$	−6.73261	−	20.7208i	−0.215395	−	0.662918i	0.783730	−	0.621102i	$-0.213315\pi$
$978$	−9.10993	+	6.61875i	−0.291303	+	0.211644i
$979$	2.74178	+	8.43835i	0.0876278	+	0.269691i
$980$	1.21972	−	3.75392i	0.0389626	−	0.119915i
$981$	−0.757997	−	0.550717i	−0.0242010	−	0.0175830i
$982$	−1.69388	+	5.21323i	−0.0540539	+	0.166361i
$983$	−25.5827	+	18.5869i	−0.815962	+	0.592831i	−0.915553	−	0.402197i	$-0.868247\pi$
$983$	−25.5827	+	18.5869i	−0.815962	+	0.592831i	0.0995908	+	0.995028i	$0.468247\pi$
$984$	6.81032	−	4.94799i	0.217105	−	0.157736i
$985$	7.91413	+	5.74995i	0.252165	+	0.183209i
$986$	−11.5678			−0.368395
$987$	−5.56699			−0.177199
$988$	−0.700942	−	0.509264i	−0.0222999	−	0.0162018i
$989$	17.8036	+	54.7940i	0.566123	+	1.74235i
$990$	0.780790	−	2.40303i	0.0248151	−	0.0763732i
$991$	37.9960			1.20698			0.603491	−	0.797370i	$-0.293776\pi$
$991$	37.9960			1.20698			0.603491	+	0.797370i	$0.293776\pi$
$992$	−3.94316	+	3.93083i	−0.125196	+	0.124804i
$993$	26.8002			0.850478
$994$	2.75919	−	8.49191i	0.0875162	−	0.269347i
$995$	−3.99449	−	12.2938i	−0.126634	−	0.389739i
$996$	−5.22607	−	3.79696i	−0.165594	−	0.120311i
$997$	18.0984			0.573182			0.286591	−	0.958053i	$-0.407478\pi$
$997$	18.0984			0.573182			0.286591	+	0.958053i	$0.407478\pi$
$998$	3.92827			0.124347
$999$	6.81031	+	4.94798i	0.215469	+	0.156547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.f.721.3	✓	12
31.4	even	5	inner	930.2.n.f.841.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.f.721.3	✓	12	1.1	even	1	trivial
930.2.n.f.841.3	yes	12	31.4	even	5	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(2.67675 + 1.94477i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(2.67675 + 1.94477i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.309017 + 0.951057i) q^{10} +(2.04414 + 1.48515i) q^{11} +(-0.309017 + 0.951057i) q^{12} +(-0.0898072 - 0.276398i) q^{13} +(-2.67675 + 1.94477i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.86217 + 3.53257i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-0.921250 + 2.83532i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(1.02243 - 3.14670i) q^{21} +(-2.04414 + 1.48515i) q^{22} +(3.70901 - 2.69475i) q^{23} +(-0.809017 - 0.587785i) q^{24} +1.00000 q^{25} +0.290622 q^{26} +(0.809017 + 0.587785i) q^{27} +(-1.02243 - 3.14670i) q^{28} +(0.594788 - 1.83057i) q^{29} +1.00000 q^{30} +(3.94316 - 3.93083i) q^{31} -1.00000 q^{32} +(0.780790 - 2.40303i) q^{33} +(-1.85718 - 5.71582i) q^{34} +(2.67675 + 1.94477i) q^{35} +1.00000 q^{36} +8.41800 q^{37} +(-2.41186 - 1.75232i) q^{38} +(-0.235118 + 0.170824i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-2.60131 + 8.00601i) q^{41} +(2.67675 + 1.94477i) q^{42} +(-3.88337 + 11.9518i) q^{43} +(-0.780790 - 2.40303i) q^{44} +(-0.809017 + 0.587785i) q^{45} +(1.41672 + 4.36020i) q^{46} +(-0.519940 - 1.60021i) q^{47} +(0.809017 - 0.587785i) q^{48} +(1.21972 + 3.75392i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(4.86217 + 3.53257i) q^{51} +(-0.0898072 + 0.276398i) q^{52} +(-2.35647 + 1.71207i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(2.04414 + 1.48515i) q^{55} +3.30864 q^{56} +2.98123 q^{57} +(1.55718 + 1.13135i) q^{58} +(-1.25881 - 3.87422i) q^{59} +(-0.309017 + 0.951057i) q^{60} +12.4598 q^{61} +(2.51994 + 4.96487i) q^{62} -3.30864 q^{63} +(0.309017 - 0.951057i) q^{64} +(-0.0898072 - 0.276398i) q^{65} +(2.04414 + 1.48515i) q^{66} -1.95352 q^{67} +6.00997 q^{68} +(-3.70901 - 2.69475i) q^{69} +(-2.67675 + 1.94477i) q^{70} +(-2.18327 + 1.58624i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(6.06027 + 4.40304i) q^{73} +(-2.60131 + 8.00600i) q^{74} +(-0.309017 - 0.951057i) q^{75} +(2.41186 - 1.75232i) q^{76} +(2.58335 + 7.95075i) q^{77} +(-0.0898072 - 0.276398i) q^{78} +(6.45966 - 4.69321i) q^{79} +(0.309017 + 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-6.81032 - 4.94799i) q^{82} +(-1.99618 + 6.14362i) q^{83} +(-2.67675 + 1.94477i) q^{84} +(-4.86217 + 3.53257i) q^{85} +(-10.1668 - 7.38660i) q^{86} -1.92478 q^{87} +2.52669 q^{88} +(2.84090 + 2.06404i) q^{89} +(-0.309017 - 0.951057i) q^{90} +(0.297140 - 0.914502i) q^{91} -4.58459 q^{92} +(-4.95695 - 2.53548i) q^{93} +1.68256 q^{94} +(-0.921250 + 2.83532i) q^{95} +(0.309017 + 0.951057i) q^{96} +(14.0569 + 10.2130i) q^{97} -3.94710 q^{98} -2.52669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 3 q^{15} - 3 q^{16} - 7 q^{17} + 3 q^{18} + 12 q^{19} - 3 q^{20} + q^{21} - 14 q^{22} - 6 q^{23} - 3 q^{24} + 12 q^{25} + 6 q^{26} + 3 q^{27} - q^{28} - 23 q^{29} + 12 q^{30} + 34 q^{31} - 12 q^{32} + 11 q^{33} - 3 q^{34} - q^{35} + 12 q^{36} + 22 q^{37} + 8 q^{38} + q^{39} + 3 q^{40} + 15 q^{41} - q^{42} - 17 q^{43} - 11 q^{44} - 3 q^{45} + 6 q^{46} - 2 q^{47} + 3 q^{48} - 8 q^{49} + 3 q^{50} + 7 q^{51} + 4 q^{52} - 21 q^{53} - 3 q^{54} + 14 q^{55} - 4 q^{56} + 8 q^{57} - 17 q^{58} - 15 q^{59} + 3 q^{60} + 16 q^{61} + 26 q^{62} + 4 q^{63} - 3 q^{64} + 4 q^{65} + 14 q^{66} + 24 q^{67} + 8 q^{68} + 6 q^{69} + q^{70} + 23 q^{71} + 3 q^{72} + 56 q^{73} + 8 q^{74} + 3 q^{75} - 8 q^{76} - 8 q^{77} + 4 q^{78} - 9 q^{79} - 3 q^{80} - 3 q^{81} + 15 q^{82} - 24 q^{83} + q^{84} - 7 q^{85} - 18 q^{86} - 12 q^{87} + 6 q^{88} - 27 q^{89} + 3 q^{90} - 3 q^{91} + 24 q^{92} + 11 q^{93} - 28 q^{94} + 12 q^{95} - 3 q^{96} + 38 q^{97} - 52 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 3 * q^15 - 3 * q^16 - 7 * q^17 + 3 * q^18 + 12 * q^19 - 3 * q^20 + q^21 - 14 * q^22 - 6 * q^23 - 3 * q^24 + 12 * q^25 + 6 * q^26 + 3 * q^27 - q^28 - 23 * q^29 + 12 * q^30 + 34 * q^31 - 12 * q^32 + 11 * q^33 - 3 * q^34 - q^35 + 12 * q^36 + 22 * q^37 + 8 * q^38 + q^39 + 3 * q^40 + 15 * q^41 - q^42 - 17 * q^43 - 11 * q^44 - 3 * q^45 + 6 * q^46 - 2 * q^47 + 3 * q^48 - 8 * q^49 + 3 * q^50 + 7 * q^51 + 4 * q^52 - 21 * q^53 - 3 * q^54 + 14 * q^55 - 4 * q^56 + 8 * q^57 - 17 * q^58 - 15 * q^59 + 3 * q^60 + 16 * q^61 + 26 * q^62 + 4 * q^63 - 3 * q^64 + 4 * q^65 + 14 * q^66 + 24 * q^67 + 8 * q^68 + 6 * q^69 + q^70 + 23 * q^71 + 3 * q^72 + 56 * q^73 + 8 * q^74 + 3 * q^75 - 8 * q^76 - 8 * q^77 + 4 * q^78 - 9 * q^79 - 3 * q^80 - 3 * q^81 + 15 * q^82 - 24 * q^83 + q^84 - 7 * q^85 - 18 * q^86 - 12 * q^87 + 6 * q^88 - 27 * q^89 + 3 * q^90 - 3 * q^91 + 24 * q^92 + 11 * q^93 - 28 * q^94 + 12 * q^95 - 3 * q^96 + 38 * q^97 - 52 * q^98 - 6 * q^99

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