LMFDB - Embedded newform 847.2.f.o.148.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.446265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 4x^{6} - 7x^{5} + 19x^{4} + 21x^{3} + 36x^{2} + 27x + 81 $ x^8 - x^7 + 4x^6 - 7x^5 + 19x^4 + 21x^3 + 36x^2 + 27x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.2
Root			$1.86298 - 1.35354i$ of defining polynomial
Character	$\chi$	$=$	847.148
Dual form			847.2.f.o.372.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.711597 + 2.19007i) q^{2} +(1.86298 + 1.35354i) q^{3} +(-2.67200 + 1.94132i) q^{4} +(1.11418 - 3.42908i) q^{5} +(-1.63865 + 5.04324i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.711597 + 2.19007i) q^{9} +O(q^{10})$	\(q+(0.711597 + 2.19007i) q^{2} +(1.86298 + 1.35354i) q^{3} +(-2.67200 + 1.94132i) q^{4} +(1.11418 - 3.42908i) q^{5} +(-1.63865 + 5.04324i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.711597 + 2.19007i) q^{9} +8.30278 q^{10} -7.60555 q^{12} +(2.04123 + 6.28225i) q^{13} +(1.86298 + 1.35354i) q^{14} +(6.71709 - 4.88025i) q^{15} +(0.0935628 - 0.287957i) q^{16} +(0.833488 - 2.56521i) q^{17} +(-4.29004 + 3.11689i) q^{18} +(2.42705 + 1.76336i) q^{19} +(3.67988 + 11.3255i) q^{20} +2.30278 q^{21} -2.69722 q^{23} +(-2.13479 - 6.57021i) q^{24} +(-6.47214 - 4.70228i) q^{25} +(-12.3060 + 8.94086i) q^{26} +(0.496143 - 1.52697i) q^{27} +(-1.02061 + 3.14113i) q^{28} +(-3.80013 + 2.76096i) q^{29} +(15.4679 + 11.2381i) q^{30} +(0.309017 + 0.951057i) q^{31} -5.30278 q^{32} +6.21110 q^{34} +(-1.11418 - 3.42908i) q^{35} +(-6.15302 - 4.47043i) q^{36} +(4.21587 - 3.06301i) q^{37} +(-2.13479 + 6.57021i) q^{38} +(-4.70049 + 14.4666i) q^{39} +(-8.75086 + 6.35787i) q^{40} +(-5.66312 - 4.11450i) q^{41} +(1.63865 + 5.04324i) q^{42} +1.69722 q^{43} +8.30278 q^{45} +(-1.91934 - 5.90711i) q^{46} +(1.54387 + 1.12169i) q^{47} +(0.564066 - 0.409818i) q^{48} +(0.309017 - 0.951057i) q^{49} +(5.69277 - 17.5206i) q^{50} +(5.02489 - 3.65079i) q^{51} +(-17.6500 - 12.8235i) q^{52} +(-3.98889 - 12.2765i) q^{53} +3.69722 q^{54} -3.00000 q^{56} +(2.13479 + 6.57021i) q^{57} +(-8.75086 - 6.35787i) q^{58} +(-5.41817 + 3.93653i) q^{59} +(-8.47393 + 26.0801i) q^{60} +(-1.32963 + 4.09218i) q^{61} +(-1.86298 + 1.35354i) q^{62} +(1.86298 + 1.35354i) q^{63} +(-3.96056 - 12.1894i) q^{64} +23.8167 q^{65} +8.51388 q^{67} +(2.75282 + 8.47232i) q^{68} +(-5.02489 - 3.65079i) q^{69} +(6.71709 - 4.88025i) q^{70} +(-1.32963 + 4.09218i) q^{71} +(2.13479 - 6.57021i) q^{72} +(4.04508 - 2.93893i) q^{73} +(9.70820 + 7.05342i) q^{74} +(-5.69277 - 17.5206i) q^{75} -9.90833 q^{76} -35.0278 q^{78} +(-2.56570 - 7.89641i) q^{79} +(-0.883182 - 0.641669i) q^{80} +(8.58007 - 6.23379i) q^{81} +(4.98118 - 15.3305i) q^{82} +(0.927051 - 2.85317i) q^{83} +(-6.15302 + 4.47043i) q^{84} +(-7.86767 - 5.71620i) q^{85} +(1.20774 + 3.71704i) q^{86} -10.8167 q^{87} -14.7250 q^{89} +(5.90823 + 18.1837i) q^{90} +(5.34400 + 3.88265i) q^{91} +(7.20699 - 5.23618i) q^{92} +(-0.711597 + 2.19007i) q^{93} +(-1.35796 + 4.17937i) q^{94} +(8.75086 - 6.35787i) q^{95} +(-9.87899 - 7.17751i) q^{96} +(-1.11418 - 3.42908i) q^{97} +2.30278 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + q^{3} - 3 q^{4} + 7 q^{6} + 2 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) $ 8 * q - q^2 + q^3 - 3 * q^4 + 7 * q^6 + 2 * q^7 - 6 * q^8 - q^9	$ 8 q - q^{2} + q^{3} - 3 q^{4} + 7 q^{6} + 2 q^{7} - 6 q^{8} - q^{9} + 52 q^{10} - 32 q^{12} - 6 q^{13} + q^{14} + 13 q^{15} + 3 q^{16} - 9 q^{17} - 7 q^{18} + 6 q^{19} - 13 q^{20} + 4 q^{21} - 36 q^{23} + 3 q^{24} - 16 q^{25} - 16 q^{26} + 4 q^{27} + 3 q^{28} - 13 q^{29} + 13 q^{30} - 2 q^{31} - 28 q^{32} - 8 q^{34} - 8 q^{36} - 4 q^{37} + 3 q^{38} + 16 q^{39} - 14 q^{41} - 7 q^{42} + 28 q^{43} + 52 q^{45} - 2 q^{46} - 7 q^{47} + 5 q^{48} - 2 q^{49} - 8 q^{50} - 2 q^{51} - 22 q^{52} + 15 q^{53} + 44 q^{54} - 24 q^{56} - 3 q^{57} - 17 q^{59} + 26 q^{60} + 5 q^{61} - q^{62} + q^{63} + 4 q^{64} + 104 q^{65} - 4 q^{67} - 7 q^{68} + 2 q^{69} + 13 q^{70} + 5 q^{71} - 3 q^{72} + 10 q^{73} + 24 q^{74} + 8 q^{75} - 36 q^{76} - 136 q^{78} + 13 q^{79} - 13 q^{80} + 14 q^{81} - 7 q^{82} - 6 q^{83} - 8 q^{84} + 13 q^{85} + 3 q^{86} + 12 q^{89} - 13 q^{90} + 6 q^{91} + 7 q^{92} + q^{93} + 16 q^{94} - 10 q^{96} + 4 q^{98}+O(q^{100}) $ 8 * q - q^2 + q^3 - 3 * q^4 + 7 * q^6 + 2 * q^7 - 6 * q^8 - q^9 + 52 * q^10 - 32 * q^12 - 6 * q^13 + q^14 + 13 * q^15 + 3 * q^16 - 9 * q^17 - 7 * q^18 + 6 * q^19 - 13 * q^20 + 4 * q^21 - 36 * q^23 + 3 * q^24 - 16 * q^25 - 16 * q^26 + 4 * q^27 + 3 * q^28 - 13 * q^29 + 13 * q^30 - 2 * q^31 - 28 * q^32 - 8 * q^34 - 8 * q^36 - 4 * q^37 + 3 * q^38 + 16 * q^39 - 14 * q^41 - 7 * q^42 + 28 * q^43 + 52 * q^45 - 2 * q^46 - 7 * q^47 + 5 * q^48 - 2 * q^49 - 8 * q^50 - 2 * q^51 - 22 * q^52 + 15 * q^53 + 44 * q^54 - 24 * q^56 - 3 * q^57 - 17 * q^59 + 26 * q^60 + 5 * q^61 - q^62 + q^63 + 4 * q^64 + 104 * q^65 - 4 * q^67 - 7 * q^68 + 2 * q^69 + 13 * q^70 + 5 * q^71 - 3 * q^72 + 10 * q^73 + 24 * q^74 + 8 * q^75 - 36 * q^76 - 136 * q^78 + 13 * q^79 - 13 * q^80 + 14 * q^81 - 7 * q^82 - 6 * q^83 - 8 * q^84 + 13 * q^85 + 3 * q^86 + 12 * q^89 - 13 * q^90 + 6 * q^91 + 7 * q^92 + q^93 + 16 * q^94 - 10 * q^96 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.711597	+	2.19007i	0.503175	+	1.54861i	0.803817	+	0.594876i	$0.202799\pi$
$2$	0.711597	+	2.19007i	0.503175	+	1.54861i	−0.300642	+	0.953737i	$0.597201\pi$
$3$	1.86298	+	1.35354i	1.07559	+	0.781465i	0.976910	−	0.213653i	$-0.0685363\pi$
$3$	1.86298	+	1.35354i	1.07559	+	0.781465i	0.0986852	+	0.995119i	$0.468536\pi$
$4$	−2.67200	+	1.94132i	−1.33600	+	0.970661i
$5$	1.11418	−	3.42908i	0.498275	−	1.53353i	−0.313515	−	0.949583i	$-0.601507\pi$
$5$	1.11418	−	3.42908i	0.498275	−	1.53353i	0.811790	−	0.583949i	$-0.198493\pi$
$6$	−1.63865	+	5.04324i	−0.668975	+	2.05889i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	−2.42705	−	1.76336i	−0.858092	−	0.623440i
$9$	0.711597	+	2.19007i	0.237199	+	0.730023i
$10$	8.30278			2.62557
$11$		0			0
$11$		0			0
$12$	−7.60555			−2.19553
$13$	2.04123	+	6.28225i	0.566135	+	1.74238i	0.664556	+	0.747239i	$0.268621\pi$
$13$	2.04123	+	6.28225i	0.566135	+	1.74238i	−0.0984213	+	0.995145i	$0.531379\pi$
$14$	1.86298	+	1.35354i	0.497904	+	0.361748i
$15$	6.71709	−	4.88025i	1.73434	−	1.26007i
$16$	0.0935628	−	0.287957i	0.0233907	−	0.0719892i
$17$	0.833488	−	2.56521i	0.202151	−	0.622155i	−0.797668	−	0.603097i	$-0.793933\pi$
$17$	0.833488	−	2.56521i	0.202151	−	0.622155i	0.999818	−	0.0190584i	$-0.00606685\pi$
$18$	−4.29004	+	3.11689i	−1.01117	+	0.734659i
$19$	2.42705	+	1.76336i	0.556804	+	0.404542i	0.830288	−	0.557335i	$-0.188176\pi$
$19$	2.42705	+	1.76336i	0.556804	+	0.404542i	−0.273484	+	0.961877i	$0.588176\pi$
$20$	3.67988	+	11.3255i	0.822845	+	2.53246i
$21$	2.30278			0.502507
$22$		0			0
$23$	−2.69722			−0.562410			−0.281205	−	0.959648i	$-0.590734\pi$
$23$	−2.69722			−0.562410			−0.281205	+	0.959648i	$0.590734\pi$
$24$	−2.13479	−	6.57021i	−0.435762	−	1.34114i
$25$	−6.47214	−	4.70228i	−1.29443	−	0.940456i
$26$	−12.3060	+	8.94086i	−2.41341	+	1.75345i
$27$	0.496143	−	1.52697i	0.0954827	−	0.293866i
$28$	−1.02061	+	3.14113i	−0.192878	+	0.593617i
$29$	−3.80013	+	2.76096i	−0.705667	+	0.512697i	−0.881773	−	0.471674i	$-0.843650\pi$
$29$	−3.80013	+	2.76096i	−0.705667	+	0.512697i	0.176106	+	0.984371i	$0.443650\pi$
$30$	15.4679	+	11.2381i	2.82405	+	2.05179i
$31$	0.309017	+	0.951057i	0.0555011	+	0.170815i	0.974964	−	0.222361i	$-0.0713764\pi$
$31$	0.309017	+	0.951057i	0.0555011	+	0.170815i	−0.919463	+	0.393176i	$0.871376\pi$
$32$	−5.30278			−0.937407
$33$		0			0
$34$	6.21110			1.06520
$35$	−1.11418	−	3.42908i	−0.188330	−	0.579621i
$36$	−6.15302	−	4.47043i	−1.02550	−	0.745072i
$37$	4.21587	−	3.06301i	0.693085	−	0.503556i	−0.184588	−	0.982816i	$-0.559095\pi$
$37$	4.21587	−	3.06301i	0.693085	−	0.503556i	0.877673	+	0.479260i	$0.159095\pi$
$38$	−2.13479	+	6.57021i	−0.346309	+	1.06583i
$39$	−4.70049	+	14.4666i	−0.752681	+	2.31651i
$40$	−8.75086	+	6.35787i	−1.38363	+	1.00527i
$41$	−5.66312	−	4.11450i	−0.884431	−	0.642576i	0.0499893	−	0.998750i	$-0.484081\pi$
$41$	−5.66312	−	4.11450i	−0.884431	−	0.642576i	−0.934420	+	0.356173i	$0.884081\pi$
$42$	1.63865	+	5.04324i	0.252849	+	0.778189i
$43$	1.69722			0.258824			0.129412	−	0.991591i	$-0.458691\pi$
$43$	1.69722			0.258824			0.129412	+	0.991591i	$0.458691\pi$
$44$		0			0
$45$	8.30278			1.23770
$46$	−1.91934	−	5.90711i	−0.282991	−	0.870956i
$47$	1.54387	+	1.12169i	0.225196	+	0.163615i	0.694663	−	0.719336i	$-0.255554\pi$
$47$	1.54387	+	1.12169i	0.225196	+	0.163615i	−0.469466	+	0.882950i	$0.655554\pi$
$48$	0.564066	−	0.409818i	0.0814160	−	0.0591522i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	5.69277	−	17.5206i	0.805080	−	2.47778i
$51$	5.02489	−	3.65079i	0.703625	−	0.511213i
$52$	−17.6500	−	12.8235i	−2.44762	−	1.77830i
$53$	−3.98889	−	12.2765i	−0.547917	−	1.68631i	−0.713953	−	0.700194i	$-0.753097\pi$
$53$	−3.98889	−	12.2765i	−0.547917	−	1.68631i	0.166036	−	0.986120i	$-0.446903\pi$
$54$	3.69722			0.503129
$55$		0			0
$56$	−3.00000			−0.400892
$57$	2.13479	+	6.57021i	0.282760	+	0.870245i
$58$	−8.75086	−	6.35787i	−1.14904	−	0.834829i
$59$	−5.41817	+	3.93653i	−0.705385	+	0.512493i	−0.881682	−	0.471845i	$-0.843588\pi$
$59$	−5.41817	+	3.93653i	−0.705385	+	0.512493i	0.176296	+	0.984337i	$0.443588\pi$
$60$	−8.47393	+	26.0801i	−1.09398	+	3.36692i
$61$	−1.32963	+	4.09218i	−0.170242	+	0.523950i	−0.999384	−	0.0350870i	$-0.988829\pi$
$61$	−1.32963	+	4.09218i	−0.170242	+	0.523950i	0.829142	+	0.559037i	$0.188829\pi$
$62$	−1.86298	+	1.35354i	−0.236599	+	0.171899i
$63$	1.86298	+	1.35354i	0.234714	+	0.170530i
$64$	−3.96056	−	12.1894i	−0.495070	−	1.52367i
$65$	23.8167			2.95409
$66$		0			0
$67$	8.51388			1.04014			0.520068	−	0.854125i	$-0.325907\pi$
$67$	8.51388			1.04014			0.520068	+	0.854125i	$0.325907\pi$
$68$	2.75282	+	8.47232i	0.333829	+	1.02742i
$69$	−5.02489	−	3.65079i	−0.604925	−	0.439504i
$70$	6.71709	−	4.88025i	0.802845	−	0.583301i
$71$	−1.32963	+	4.09218i	−0.157798	+	0.485653i	−0.998434	−	0.0559485i	$-0.982182\pi$
$71$	−1.32963	+	4.09218i	−0.157798	+	0.485653i	0.840636	+	0.541601i	$0.182182\pi$
$72$	2.13479	−	6.57021i	0.251587	−	0.774307i
$73$	4.04508	−	2.93893i	0.473441	−	0.343975i	−0.325340	−	0.945597i	$-0.605479\pi$
$73$	4.04508	−	2.93893i	0.473441	−	0.343975i	0.798781	+	0.601622i	$0.205479\pi$
$74$	9.70820	+	7.05342i	1.12856	+	0.819944i
$75$	−5.69277	−	17.5206i	−0.657345	−	2.02310i
$76$	−9.90833			−1.13656
$77$		0			0
$78$	−35.0278			−3.96611
$79$	−2.56570	−	7.89641i	−0.288664	−	0.888415i	−0.985277	−	0.170968i	$-0.945310\pi$
$79$	−2.56570	−	7.89641i	−0.288664	−	0.888415i	0.696613	−	0.717447i	$-0.254690\pi$
$80$	−0.883182	−	0.641669i	−0.0987428	−	0.0717408i
$81$	8.58007	−	6.23379i	0.953341	−	0.692643i
$82$	4.98118	−	15.3305i	0.550079	−	1.69297i
$83$	0.927051	−	2.85317i	0.101757	−	0.313176i	−0.887199	−	0.461388i	$-0.847352\pi$
$83$	0.927051	−	2.85317i	0.101757	−	0.313176i	0.988956	+	0.148212i	$0.0473517\pi$
$84$	−6.15302	+	4.47043i	−0.671350	+	0.487764i
$85$	−7.86767	−	5.71620i	−0.853369	−	0.620009i
$86$	1.20774	+	3.71704i	0.130234	+	0.400819i
$87$	−10.8167			−1.15967
$88$		0			0
$89$	−14.7250			−1.56084			−0.780422	−	0.625253i	$-0.784996\pi$
$89$	−14.7250			−1.56084			−0.780422	+	0.625253i	$0.784996\pi$
$90$	5.90823	+	18.1837i	0.622782	+	1.91673i
$91$	5.34400	+	3.88265i	0.560204	+	0.407012i
$92$	7.20699	−	5.23618i	0.751380	−	0.545910i
$93$	−0.711597	+	2.19007i	−0.0737892	+	0.227100i
$94$	−1.35796	+	4.17937i	−0.140063	+	0.431069i
$95$	8.75086	−	6.35787i	0.897819	−	0.652304i
$96$	−9.87899	−	7.17751i	−1.00827	−	0.732551i
$97$	−1.11418	−	3.42908i	−0.113127	−	0.348171i	0.878424	−	0.477881i	$-0.158595\pi$
$97$	−1.11418	−	3.42908i	−0.113127	−	0.348171i	−0.991552	+	0.129711i	$0.958595\pi$
$98$	2.30278			0.232615
$99$		0			0
$100$	26.4222			2.64222
$101$	−1.63865	−	5.04324i	−0.163052	−	0.501821i	0.835836	−	0.548979i	$-0.184983\pi$
$101$	−1.63865	−	5.04324i	−0.163052	−	0.501821i	−0.998887	+	0.0471583i	$0.984983\pi$
$102$	11.5712	+	8.40696i	1.14572	+	0.832413i
$103$	11.5712	−	8.40696i	1.14014	−	0.828362i	0.153004	−	0.988226i	$-0.451105\pi$
$103$	11.5712	−	8.40696i	1.14014	−	0.828362i	0.987139	+	0.159863i	$0.0511053\pi$
$104$	6.12368	−	18.8468i	0.600477	−	1.84808i
$105$	2.56570	−	7.89641i	0.250387	−	0.770611i
$106$	24.0480	−	17.4719i	2.33575	−	1.69702i
$107$	−10.0273	−	7.28527i	−0.969378	−	0.704294i	−0.0140679	−	0.999901i	$-0.504478\pi$
$107$	−10.0273	−	7.28527i	−0.969378	−	0.704294i	−0.955310	+	0.295607i	$0.904478\pi$
$108$	1.63865	+	5.04324i	0.157679	+	0.485286i
$109$	−8.00000			−0.766261			−0.383131	−	0.923694i	$-0.625154\pi$
$109$	−8.00000			−0.766261			−0.383131	+	0.923694i	$0.625154\pi$
$110$		0			0
$111$	12.0000			1.13899
$112$	−0.0935628	−	0.287957i	−0.00884086	−	0.0272094i
$113$	8.65424	+	6.28767i	0.814122	+	0.591494i	0.915023	−	0.403402i	$-0.132172\pi$
$113$	8.65424	+	6.28767i	0.814122	+	0.591494i	−0.100901	+	0.994897i	$0.532172\pi$
$114$	−12.8701	+	9.35068i	−1.20540	+	0.875771i
$115$	−3.00518	+	9.24901i	−0.280235	+	0.862474i
$116$	4.79405	−	14.7546i	0.445117	−	1.36993i
$117$	−12.3060	+	8.94086i	−1.13769	+	0.826583i
$118$	−12.4768	−	9.06494i	−1.14858	−	0.834496i
$119$	−0.833488	−	2.56521i	−0.0764057	−	0.235153i
$120$	−24.9083			−2.27381
$121$		0			0
$122$	−9.90833			−0.897058
$123$	−4.98118	−	15.3305i	−0.449138	−	1.38230i
$124$	−2.67200	−	1.94132i	−0.239953	−	0.174336i
$125$	−8.75086	+	6.35787i	−0.782700	+	0.568665i
$126$	−1.63865	+	5.04324i	−0.145982	+	0.449287i
$127$	0.618034	−	1.90211i	0.0548416	−	0.168785i	−0.919884	−	0.392191i	$-0.871717\pi$
$127$	0.618034	−	1.90211i	0.0548416	−	0.168785i	0.974726	+	0.223405i	$0.0717174\pi$
$128$	15.2972	−	11.1140i	1.35209	−	0.982351i
$129$	3.16190	+	2.29726i	0.278390	+	0.202262i
$130$	16.9479	+	52.1601i	1.48643	+	4.57475i
$131$	−6.00000			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$131$	−6.00000			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$132$		0			0
$133$	3.00000			0.260133
$134$	6.05845	+	18.6460i	0.523370	+	1.61077i
$135$	−4.68332	−	3.40263i	−0.403076	−	0.292852i
$136$	−6.54630	+	4.75617i	−0.561341	+	0.407838i
$137$	−3.12708	+	9.62415i	−0.267164	+	0.822247i	0.724023	+	0.689776i	$0.242291\pi$
$137$	−3.12708	+	9.62415i	−0.267164	+	0.822247i	−0.991187	+	0.132471i	$0.957709\pi$
$138$	4.41980	−	13.6027i	0.376238	−	1.15794i
$139$	−17.4793	+	12.6994i	−1.48257	+	1.07715i	−0.505854	+	0.862619i	$0.668823\pi$
$139$	−17.4793	+	12.6994i	−1.48257	+	1.07715i	−0.976717	+	0.214532i	$0.931177\pi$
$140$	9.63404	+	6.99954i	0.814225	+	0.591569i
$141$	1.35796	+	4.17937i	0.114361	+	0.351966i
$142$	−9.90833			−0.831488
$143$		0			0
$144$	0.697224			0.0581020
$145$	5.23354	+	16.1072i	0.434622	+	1.33763i
$146$	9.31492	+	6.76769i	0.770909	+	0.560098i
$147$	1.86298	−	1.35354i	0.153656	−	0.111638i
$148$	−5.31852	+	16.3687i	−0.437180	+	1.34550i
$149$	−1.51676	+	4.66810i	−0.124258	+	0.382425i	−0.993765	−	0.111494i	$-0.964436\pi$
$149$	−1.51676	+	4.66810i	−0.124258	+	0.382425i	0.869508	+	0.493920i	$0.164436\pi$
$150$	34.3203	−	24.9351i	2.80224	−	2.03595i
$151$	0.170786	+	0.124083i	0.0138983	+	0.0100977i	0.594713	−	0.803938i	$-0.297266\pi$
$151$	0.170786	+	0.124083i	0.0138983	+	0.0100977i	−0.580814	+	0.814036i	$0.697266\pi$
$152$	−2.78115	−	8.55951i	−0.225581	−	0.694268i
$153$	6.21110			0.502138
$154$		0			0
$155$	3.60555			0.289605
$156$	−15.5247	−	47.7800i	−1.24297	−	3.82546i
$157$	−5.83390	−	4.23858i	−0.465596	−	0.338275i	0.330126	−	0.943937i	$-0.392909\pi$
$157$	−5.83390	−	4.23858i	−0.465596	−	0.338275i	−0.795723	+	0.605661i	$0.792909\pi$
$158$	15.4679	−	11.2381i	1.23056	−	0.894057i
$159$	9.18552	−	28.2701i	0.728459	−	2.24197i
$160$	−5.90823	+	18.1837i	−0.467086	+	1.43754i
$161$	−2.18210	+	1.58539i	−0.171974	+	0.124946i
$162$	19.7580	+	14.3550i	1.55233	+	1.12784i
$163$	0.870394	+	2.67880i	0.0681745	+	0.209820i	0.979340	−	0.202221i	$-0.0648161\pi$
$163$	0.870394	+	2.67880i	0.0681745	+	0.209820i	−0.911165	+	0.412041i	$0.864816\pi$
$164$	23.1194			1.80532
$165$		0			0
$166$	6.90833			0.536190
$167$	−1.61032	−	4.95605i	−0.124610	−	0.383511i	0.869220	−	0.494426i	$-0.164622\pi$
$167$	−1.61032	−	4.95605i	−0.124610	−	0.383511i	−0.993830	+	0.110915i	$0.964622\pi$
$168$	−5.58895	−	4.06061i	−0.431197	−	0.313283i
$169$	−24.7829	+	18.0058i	−1.90637	+	1.38506i
$170$	6.92027	−	21.2984i	0.530760	−	1.63351i
$171$	−2.13479	+	6.57021i	−0.163252	+	0.502436i
$172$	−4.53499	+	3.29486i	−0.345789	+	0.251231i
$173$	1.05397	+	0.765752i	0.0801317	+	0.0582191i	0.627130	−	0.778915i	$-0.284230\pi$
$173$	1.05397	+	0.765752i	0.0801317	+	0.0582191i	−0.546998	+	0.837134i	$0.684230\pi$
$174$	−7.69710	−	23.6892i	−0.583515	−	1.79588i
$175$	−8.00000			−0.604743
$176$		0			0
$177$	−15.4222			−1.15920
$178$	−10.4782	−	32.2487i	−0.785378	−	2.41714i
$179$	5.17322	+	3.75856i	0.386664	+	0.280928i	0.764087	−	0.645113i	$-0.223190\pi$
$179$	5.17322	+	3.75856i	0.386664	+	0.280928i	−0.377423	+	0.926041i	$0.623190\pi$
$180$	−22.1850	+	16.1184i	−1.65357	+	1.20139i
$181$	−7.79066	+	23.9772i	−0.579075	+	1.78221i	0.0427881	+	0.999084i	$0.486376\pi$
$181$	−7.79066	+	23.9772i	−0.579075	+	1.78221i	−0.621863	+	0.783126i	$0.713624\pi$
$182$	−4.70049	+	14.4666i	−0.348423	+	1.07234i
$183$	−8.01600	+	5.82397i	−0.592560	+	0.430520i
$184$	6.54630	+	4.75617i	0.482600	+	0.350629i
$185$	−5.80609	−	17.8693i	−0.426872	−	1.31378i
$186$	−5.30278			−0.388818
$187$		0			0
$188$	−6.30278			−0.459677
$189$	−0.496143	−	1.52697i	−0.0360891	−	0.111071i
$190$	20.1513	+	14.6407i	1.46193	+	1.06215i
$191$	21.6951	−	15.7624i	1.56980	−	1.14053i	0.642461	−	0.766318i	$-0.277914\pi$
$191$	21.6951	−	15.7624i	1.56980	−	1.14053i	0.927343	−	0.374211i	$-0.122086\pi$
$192$	9.12029	−	28.0694i	0.658200	−	2.02573i
$193$	−0.654940	+	2.01570i	−0.0471436	+	0.145093i	−0.971857	−	0.235570i	$-0.924304\pi$
$193$	−0.654940	+	2.01570i	−0.0471436	+	0.145093i	0.924714	+	0.380663i	$0.124304\pi$
$194$	6.71709	−	4.88025i	0.482259	−	0.350381i
$195$	44.3701	+	32.2367i	3.17741	+	2.30852i
$196$	1.02061	+	3.14113i	0.0729010	+	0.224366i
$197$	−10.6056			−0.755614			−0.377807	−	0.925884i	$-0.623322\pi$
$197$	−10.6056			−0.755614			−0.377807	+	0.925884i	$0.623322\pi$
$198$		0			0
$199$	19.4222			1.37680			0.688402	−	0.725330i	$-0.258313\pi$
$199$	19.4222			1.37680			0.688402	+	0.725330i	$0.258313\pi$
$200$	7.41641	+	22.8254i	0.524419	+	1.61400i
$201$	15.8612	+	11.5239i	1.11876	+	0.812830i
$202$	9.87899	−	7.17751i	0.695083	−	0.505008i
$203$	−1.45152	+	4.46733i	−0.101877	+	0.313545i
$204$	−6.33914	+	19.5099i	−0.443828	+	1.36596i
$205$	−20.4187	+	14.8350i	−1.42610	+	1.03612i
$206$	26.6459	+	19.3593i	1.85650	+	1.34883i
$207$	−1.91934	−	5.90711i	−0.133403	−	0.410572i
$208$	2.00000			0.138675
$209$		0			0
$210$	19.1194			1.31937
$211$	4.79405	+	14.7546i	0.330036	+	1.01575i	0.969116	+	0.246606i	$0.0793154\pi$
$211$	4.79405	+	14.7546i	0.330036	+	1.01575i	−0.639080	+	0.769141i	$0.720685\pi$
$212$	34.4911	+	25.0592i	2.36886	+	1.72107i
$213$	−8.01600	+	5.82397i	−0.549248	+	0.399052i
$214$	8.81985	−	27.1447i	0.602913	−	1.85557i
$215$	1.89101	−	5.81992i	0.128966	−	0.396915i
$216$	−3.89675	+	2.83116i	−0.265141	+	0.192636i
$217$	0.809017	+	0.587785i	0.0549197	+	0.0399015i
$218$	−5.69277	−	17.5206i	−0.385563	−	1.18664i
$219$	11.5139			0.778036
$220$		0			0
$221$	17.8167			1.19848
$222$	8.53916	+	26.2808i	0.573111	+	1.76385i
$223$	−11.2521	−	8.17511i	−0.753495	−	0.547446i	0.143414	−	0.989663i	$-0.454192\pi$
$223$	−11.2521	−	8.17511i	−0.753495	−	0.547446i	−0.896908	+	0.442217i	$0.854192\pi$
$224$	−4.29004	+	3.11689i	−0.286640	+	0.208256i
$225$	5.69277	−	17.5206i	0.379518	−	1.16804i
$226$	−7.61211	+	23.4277i	−0.506350	+	1.55839i
$227$	−5.26984	+	3.82876i	−0.349771	+	0.254124i	−0.748773	−	0.662826i	$-0.769357\pi$
$227$	−5.26984	+	3.82876i	−0.349771	+	0.254124i	0.399002	+	0.916950i	$0.369357\pi$
$228$	−18.4591	−	13.4113i	−1.22248	−	0.888185i
$229$	−0.805160	−	2.47803i	−0.0532064	−	0.163753i	0.920922	−	0.389746i	$-0.127437\pi$
$229$	−0.805160	−	2.47803i	−0.0532064	−	0.163753i	−0.974129	+	0.225993i	$0.927437\pi$
$230$	−22.3944			−1.47665
$231$		0			0
$232$	14.0917			0.925164
$233$	5.56231	+	17.1190i	0.364399	+	1.12150i	0.950357	+	0.311163i	$0.100718\pi$
$233$	5.56231	+	17.1190i	0.364399	+	1.12150i	−0.585958	+	0.810341i	$0.699282\pi$
$234$	−28.3381	−	20.5888i	−1.85252	−	1.34593i
$235$	5.56650	−	4.04430i	0.363118	−	0.263821i
$236$	6.83528	−	21.0368i	0.444939	−	1.36938i
$237$	5.90823	−	18.1837i	0.383781	−	1.18116i
$238$	5.02489	−	3.65079i	0.325715	−	0.236646i
$239$	−21.3018	−	15.4767i	−1.37790	−	1.00110i	−0.997073	−	0.0764590i	$-0.975639\pi$
$239$	−21.3018	−	15.4767i	−1.37790	−	1.00110i	−0.380829	−	0.924645i	$-0.624361\pi$
$240$	−0.776831	−	2.39084i	−0.0501442	−	0.154328i
$241$	0.486122			0.0313139			0.0156569	−	0.999877i	$-0.495016\pi$
$241$	0.486122			0.0313139			0.0156569	+	0.999877i	$0.495016\pi$
$242$		0			0
$243$	19.6056			1.25770
$244$	−4.39147	−	13.5156i	−0.281135	−	0.865245i
$245$	−2.91695	−	2.11929i	−0.186357	−	0.135396i
$246$	30.0302	−	21.8183i	1.91466	−	1.39108i
$247$	−6.12368	+	18.8468i	−0.389641	+	1.19919i
$248$	0.927051	−	2.85317i	0.0588678	−	0.181176i
$249$	5.58895	−	4.06061i	0.354186	−	0.257331i
$250$	−20.1513	−	14.6407i	−1.27448	−	0.925962i
$251$	1.35796	+	4.17937i	0.0857136	+	0.263799i	0.984722	−	0.174131i	$-0.0557116\pi$
$251$	1.35796	+	4.17937i	0.0857136	+	0.263799i	−0.899009	+	0.437930i	$0.855712\pi$
$252$	−7.60555			−0.479105
$253$		0			0
$254$	4.60555			0.288978
$255$	−6.92027	−	21.2984i	−0.433364	−	1.33376i
$256$	14.4881	+	10.5263i	0.905509	+	0.657891i
$257$	−5.24738	+	3.81245i	−0.327323	+	0.237814i	−0.739294	−	0.673383i	$-0.764840\pi$
$257$	−5.24738	+	3.81245i	−0.327323	+	0.237814i	0.411971	+	0.911197i	$0.364840\pi$
$258$	−2.78115	+	8.55951i	−0.173147	+	0.532892i
$259$	1.61032	−	4.95605i	0.100060	−	0.307954i
$260$	−63.6381	+	46.2358i	−3.94667	+	2.86742i
$261$	−8.75086	−	6.35787i	−0.541664	−	0.393542i
$262$	−4.26958	−	13.1404i	−0.263776	−	0.811818i
$263$	20.2389			1.24798			0.623991	−	0.781432i	$-0.285510\pi$
$263$	20.2389			1.24798			0.623991	+	0.781432i	$0.285510\pi$
$264$		0			0
$265$	−46.5416			−2.85903
$266$	2.13479	+	6.57021i	0.130892	+	0.402845i
$267$	−27.4324	−	19.9308i	−1.67884	−	1.21975i
$268$	−22.7491	+	16.5282i	−1.38962	+	1.00962i
$269$	4.98118	−	15.3305i	0.303708	−	0.934716i	−0.676448	−	0.736490i	$-0.736482\pi$
$269$	4.98118	−	15.3305i	0.303708	−	0.934716i	0.980156	−	0.198226i	$-0.0635181\pi$
$270$	4.11936	−	12.6781i	0.250696	−	0.771564i
$271$	23.0682	−	16.7600i	1.40129	−	1.01810i	0.406777	−	0.913528i	$-0.366653\pi$
$271$	23.0682	−	16.7600i	1.40129	−	1.01810i	0.994517	−	0.104572i	$-0.0333473\pi$
$272$	−0.660687	−	0.480017i	−0.0400600	−	0.0291053i
$273$	4.70049	+	14.4666i	0.284487	+	0.875560i
$274$	−23.3028			−1.40777
$275$		0			0
$276$	20.5139			1.23479
$277$	9.25076	+	28.4709i	0.555824	+	1.71065i	0.693757	+	0.720209i	$0.255954\pi$
$277$	9.25076	+	28.4709i	0.555824	+	1.71065i	−0.137933	+	0.990442i	$0.544046\pi$
$278$	−40.2508	−	29.2439i	−2.41408	−	1.75393i
$279$	−1.86298	+	1.35354i	−0.111534	+	0.0810342i
$280$	−3.34253	+	10.2872i	−0.199754	+	0.614781i
$281$	1.97599	−	6.08148i	0.117878	−	0.362791i	−0.874659	−	0.484740i	$-0.838914\pi$
$281$	1.97599	−	6.08148i	0.117878	−	0.362791i	0.992536	+	0.121949i	$0.0389144\pi$
$282$	−8.18679	+	5.94805i	−0.487516	+	0.354201i
$283$	−3.55518	−	2.58299i	−0.211334	−	0.153543i	0.477083	−	0.878858i	$-0.341694\pi$
$283$	−3.55518	−	2.58299i	−0.211334	−	0.153543i	−0.688417	+	0.725315i	$0.741694\pi$
$284$	−4.39147	−	13.5156i	−0.260586	−	0.802001i
$285$	24.9083			1.47544
$286$		0			0
$287$	−7.00000			−0.413197
$288$	−3.77344	−	11.6134i	−0.222352	−	0.684329i
$289$	7.86767	+	5.71620i	0.462804	+	0.336247i
$290$	−31.5517	+	22.9236i	−1.85278	+	1.34612i
$291$	2.56570	−	7.89641i	0.150404	−	0.462896i
$292$	−5.10307	+	15.7056i	−0.298635	+	0.919103i
$293$	−3.89675	+	2.83116i	−0.227651	+	0.165398i	−0.695764	−	0.718271i	$-0.744934\pi$
$293$	−3.89675	+	2.83116i	−0.227651	+	0.165398i	0.468113	+	0.883669i	$0.344934\pi$
$294$	4.29004	+	3.11689i	0.250200	+	0.181781i
$295$	7.46189	+	22.9653i	0.434448	+	1.33709i
$296$	−15.6333			−0.908668
$297$		0			0
$298$	−11.3028			−0.654752
$299$	−5.50565	−	16.9446i	−0.318400	−	0.979934i
$300$	49.2242	+	35.7634i	2.84196	+	2.06480i
$301$	1.37308	−	0.997603i	0.0791432	−	0.0575009i
$302$	−0.150220	+	0.462329i	−0.00864418	+	0.0266041i
$303$	3.77344	−	11.6134i	0.216778	−	0.667175i
$304$	0.734852	−	0.533901i	0.0421466	−	0.0306213i
$305$	12.5510	+	9.11883i	0.718668	+	0.522143i
$306$	4.41980	+	13.6027i	0.252663	+	0.777617i
$307$	−16.6333			−0.949313			−0.474657	−	0.880171i	$-0.657428\pi$
$307$	−16.6333			−0.949313			−0.474657	+	0.880171i	$0.657428\pi$
$308$		0			0
$309$	32.9361			1.87367
$310$	2.56570	+	7.89641i	0.145722	+	0.448486i
$311$	−5.17322	−	3.75856i	−0.293346	−	0.213129i	0.431371	−	0.902174i	$-0.358030\pi$
$311$	−5.17322	−	3.75856i	−0.293346	−	0.213129i	−0.724718	+	0.689046i	$0.758030\pi$
$312$	36.9181	−	26.8226i	2.09008	−	1.51853i
$313$	4.72882	−	14.5538i	0.267289	−	0.822630i	−0.723869	−	0.689938i	$-0.757638\pi$
$313$	4.72882	−	14.5538i	0.267289	−	0.822630i	0.991157	−	0.132692i	$-0.0423621\pi$
$314$	5.13140	−	15.7928i	0.289582	−	0.891240i
$315$	6.71709	−	4.88025i	0.378465	−	0.274971i
$316$	22.1850	+	16.1184i	1.24801	+	0.906729i
$317$	5.34685	+	16.4559i	0.300309	+	0.924256i	0.981386	+	0.192045i	$0.0615119\pi$
$317$	5.34685	+	16.4559i	0.300309	+	0.924256i	−0.681077	+	0.732212i	$0.738488\pi$
$318$	68.4500			3.83848
$319$		0			0
$320$	−46.2111			−2.58328
$321$	−8.81985	−	27.1447i	−0.492276	−	1.51507i
$322$	−5.02489	−	3.65079i	−0.280026	−	0.203451i
$323$	6.54630	−	4.75617i	0.364246	−	0.264640i
$324$	−10.8242	+	33.3134i	−0.601343	+	1.85074i
$325$	16.3298	−	50.2580i	0.905815	−	2.78781i
$326$	−5.24738	+	3.81245i	−0.290626	+	0.211152i
$327$	−14.9039	−	10.8283i	−0.824186	−	0.598806i
$328$	6.48936	+	19.9722i	0.358315	+	1.10278i
$329$	1.90833			0.105209
$330$		0			0
$331$	23.8167			1.30908			0.654541	−	0.756027i	$-0.272862\pi$
$331$	23.8167			1.30908			0.654541	+	0.756027i	$0.272862\pi$
$332$	3.06184	+	9.42338i	0.168040	+	0.517175i
$333$	9.70820	+	7.05342i	0.532006	+	0.386525i
$334$	9.70820	−	7.05342i	0.531209	−	0.385946i
$335$	9.48596	−	29.1948i	0.518274	−	1.59508i
$336$	0.215454	−	0.663100i	0.0117540	−	0.0361751i
$337$	−9.53742	+	6.92934i	−0.519536	+	0.377465i	−0.816429	−	0.577446i	$-0.804050\pi$
$337$	−9.53742	+	6.92934i	−0.519536	+	0.377465i	0.296893	+	0.954911i	$0.404050\pi$
$338$	−57.0694	−	41.4633i	−3.10417	−	2.25531i
$339$	7.61211	+	23.4277i	0.413433	+	1.27242i
$340$	32.1194			1.74192
$341$		0			0
$342$	−15.9083			−0.860224
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	−4.11925	−	2.99281i	−0.222095	−	0.161362i
$345$	−18.1175	+	13.1631i	−0.975413	+	0.708679i
$346$	−0.927051	+	2.85317i	−0.0498386	+	0.153387i
$347$	2.96828	−	9.13542i	0.159346	−	0.490415i	−0.839230	−	0.543777i	$-0.816994\pi$
$347$	2.96828	−	9.13542i	0.159346	−	0.490415i	0.998575	+	0.0533619i	$0.0169937\pi$
$348$	28.9021	−	20.9986i	1.54932	−	1.12564i
$349$	3.80013	+	2.76096i	0.203417	+	0.147791i	0.684830	−	0.728703i	$-0.259876\pi$
$349$	3.80013	+	2.76096i	0.203417	+	0.147791i	−0.481413	+	0.876494i	$0.659876\pi$
$350$	−5.69277	−	17.5206i	−0.304292	−	0.936513i
$351$	10.6056			0.566082
$352$		0			0
$353$	5.09167			0.271002			0.135501	−	0.990777i	$-0.456736\pi$
$353$	5.09167			0.271002			0.135501	+	0.990777i	$0.456736\pi$
$354$	−10.9744	−	33.7757i	−0.583282	−	1.79516i
$355$	12.5510	+	9.11883i	0.666137	+	0.483977i
$356$	39.3452	−	28.5859i	2.08529	−	1.51505i
$357$	1.91934	−	5.90711i	0.101582	−	0.312637i
$358$	−4.55027	+	14.0043i	−0.240489	+	0.740150i
$359$	27.4549	−	19.9471i	1.44901	−	1.05277i	0.462952	−	0.886383i	$-0.346790\pi$
$359$	27.4549	−	19.9471i	1.44901	−	1.05277i	0.986061	−	0.166386i	$-0.0532097\pi$
$360$	−20.1513	−	14.6407i	−1.06206	−	0.771635i
$361$	−3.09017	−	9.51057i	−0.162641	−	0.500556i
$362$	−58.0555			−3.05133
$363$		0			0
$364$	−21.8167			−1.14350
$365$	−5.57088	−	17.1454i	−0.291593	−	0.897432i
$366$	−18.4591	−	13.4113i	−0.964871	−	0.701019i
$367$	14.2656	−	10.3646i	0.744661	−	0.541028i	−0.149507	−	0.988761i	$-0.547769\pi$
$367$	14.2656	−	10.3646i	0.744661	−	0.541028i	0.894167	+	0.447733i	$0.147769\pi$
$368$	−0.252360	+	0.776684i	−0.0131552	+	0.0404874i
$369$	4.98118	−	15.3305i	0.259310	−	0.798073i
$370$	35.0034	−	25.4315i	1.81974	−	1.32212i
$371$	−10.4431	−	7.58732i	−0.542176	−	0.393914i
$372$	−2.35024	−	7.23331i	−0.121855	−	0.375030i
$373$	−20.1194			−1.04174			−0.520872	−	0.853635i	$-0.674393\pi$
$373$	−20.1194			−1.04174			−0.520872	+	0.853635i	$0.674393\pi$
$374$		0			0
$375$	−24.9083			−1.28626
$376$	−1.76912	−	5.44478i	−0.0912352	−	0.280793i
$377$	−25.1020	−	18.2377i	−1.29282	−	0.939287i
$378$	2.99112	−	2.17317i	0.153846	−	0.111776i
$379$	−4.88761	+	15.0425i	−0.251060	+	0.772683i	0.743521	+	0.668713i	$0.233155\pi$
$379$	−4.88761	+	15.0425i	−0.251060	+	0.772683i	−0.994580	+	0.103970i	$0.966845\pi$
$380$	−11.0396	+	33.9765i	−0.566321	+	1.74296i
$381$	3.72597	−	2.70708i	0.190887	−	0.138688i
$382$	49.9590	+	36.2973i	2.55613	+	1.85713i
$383$	11.9383	+	36.7425i	0.610021	+	1.87745i	0.457661	+	0.889127i	$0.348687\pi$
$383$	11.9383	+	36.7425i	0.610021	+	1.87745i	0.152361	+	0.988325i	$0.451313\pi$
$384$	43.5416			2.22197
$385$		0			0
$386$	−4.88057			−0.248414
$387$	1.20774	+	3.71704i	0.0613928	+	0.188948i
$388$	9.63404	+	6.99954i	0.489094	+	0.355348i
$389$	6.32381	−	4.59451i	0.320630	−	0.232951i	−0.415814	−	0.909449i	$-0.636503\pi$
$389$	6.32381	−	4.59451i	0.320630	−	0.232951i	0.736444	+	0.676498i	$0.236503\pi$
$390$	−39.0271	+	120.113i	−1.97621	+	6.08216i
$391$	−2.24810	+	6.91895i	−0.113692	+	0.349907i
$392$	−2.42705	+	1.76336i	−0.122585	+	0.0890629i
$393$	−11.1779	−	8.12123i	−0.563851	−	0.409662i
$394$	−7.54688	−	23.2269i	−0.380206	−	1.17015i
$395$	−29.9361			−1.50625
$396$		0			0
$397$	30.2111			1.51625			0.758126	−	0.652108i	$-0.226115\pi$
$397$	30.2111			1.51625			0.758126	+	0.652108i	$0.226115\pi$
$398$	13.8208	+	42.5360i	0.692773	+	2.13214i
$399$	5.58895	+	4.06061i	0.279798	+	0.203285i
$400$	−1.95961	+	1.42374i	−0.0979803	+	0.0711868i
$401$	−6.55459	+	20.1730i	−0.327321	+	1.00739i	0.643062	+	0.765815i	$0.277664\pi$
$401$	−6.55459	+	20.1730i	−0.327321	+	1.00739i	−0.970382	+	0.241575i	$0.922336\pi$
$402$	−13.9512	+	42.9375i	−0.695825	+	2.14153i
$403$	−5.34400	+	3.88265i	−0.266204	+	0.193408i
$404$	14.1690	+	10.2944i	0.704935	+	0.512166i
$405$	−11.8165	−	36.3673i	−0.587164	−	1.80711i
$406$	−10.8167			−0.536822
$407$		0			0
$408$	−18.6333			−0.922486
$409$	6.36747	+	19.5970i	0.314851	+	0.969011i	0.975816	+	0.218595i	$0.0701472\pi$
$409$	6.36747	+	19.5970i	0.314851	+	0.969011i	−0.660965	+	0.750417i	$0.729853\pi$
$410$	−47.0196	−	34.1617i	−2.32213	−	1.68713i
$411$	−18.8523	+	13.6970i	−0.929917	+	0.675625i
$412$	−14.5976	+	44.9268i	−0.719173	+	2.21339i
$413$	−2.06956	+	6.36944i	−0.101836	+	0.313420i
$414$	11.5712	−	8.40696i	0.568693	−	0.413180i
$415$	−8.75086	−	6.35787i	−0.429563	−	0.312096i
$416$	−10.8242	−	33.3134i	−0.530699	−	1.63332i
$417$	−49.7527			−2.43640
$418$		0			0
$419$	−38.4222			−1.87705			−0.938524	−	0.345215i	$-0.887806\pi$
$419$	−38.4222			−1.87705			−0.938524	+	0.345215i	$0.887806\pi$
$420$	8.47393	+	26.0801i	0.413485	+	1.27258i
$421$	17.6500	+	12.8235i	0.860210	+	0.624980i	0.927942	−	0.372724i	$-0.121576\pi$
$421$	17.6500	+	12.8235i	0.860210	+	0.624980i	−0.0677317	+	0.997704i	$0.521576\pi$
$422$	−28.9021	+	20.9986i	−1.40693	+	1.02220i
$423$	−1.35796	+	4.17937i	−0.0660262	+	0.203208i
$424$	−11.9667	+	36.8296i	−0.581153	+	1.78861i
$425$	−17.4568	+	12.6831i	−0.846779	+	0.615221i
$426$	−18.4591	−	13.4113i	−0.894344	−	0.649779i
$427$	1.32963	+	4.09218i	0.0643453	+	0.198035i
$428$	40.9361			1.97872
$429$		0			0
$430$	14.0917			0.679561
$431$	−0.963957	−	2.96675i	−0.0464322	−	0.142903i	0.925153	−	0.379595i	$-0.123937\pi$
$431$	−0.963957	−	2.96675i	−0.0464322	−	0.142903i	−0.971585	+	0.236692i	$0.923937\pi$
$432$	−0.393281	−	0.285735i	−0.0189217	−	0.0137474i
$433$	−23.5806	+	17.1323i	−1.13321	+	0.823325i	−0.986159	−	0.165804i	$-0.946978\pi$
$433$	−23.5806	+	17.1323i	−1.13321	+	0.823325i	−0.147051	+	0.989129i	$0.546978\pi$
$434$	−0.711597	+	2.19007i	−0.0341577	+	0.105127i
$435$	−12.0517	+	37.0912i	−0.577833	+	1.77839i
$436$	21.3760	−	15.5306i	1.02373	−	0.743780i
$437$	−6.54630	−	4.75617i	−0.313152	−	0.227518i
$438$	8.19324	+	25.2162i	0.391488	+	1.20488i
$439$	27.7250			1.32324			0.661621	−	0.749839i	$-0.269869\pi$
$439$	27.7250			1.32324			0.661621	+	0.749839i	$0.269869\pi$
$440$		0			0
$441$	2.30278			0.109656
$442$	12.6783	+	39.0197i	0.603044	+	1.85598i
$443$	−21.7917	−	15.8326i	−1.03536	−	0.752231i	−0.0659834	−	0.997821i	$-0.521018\pi$
$443$	−21.7917	−	15.8326i	−1.03536	−	0.752231i	−0.969374	+	0.245590i	$0.921018\pi$
$444$	−32.0640	+	23.2959i	−1.52169	+	1.10557i
$445$	−16.4062	+	50.4932i	−0.777730	+	2.39361i
$446$	9.89712	−	30.4602i	0.468642	−	1.44233i
$447$	−9.14414	+	6.64360i	−0.432503	+	0.314232i
$448$	−10.3689	−	7.53344i	−0.489884	−	0.355922i
$449$	12.4628	+	38.3566i	0.588157	+	1.81016i	0.586205	+	0.810162i	$0.300621\pi$
$449$	12.4628	+	38.3566i	0.588157	+	1.81016i	0.00195147	+	0.999998i	$0.499379\pi$
$450$	42.4222			1.99980
$451$		0			0
$452$	−35.3305			−1.66181
$453$	0.150220	+	0.462329i	0.00705795	+	0.0217221i
$454$	−12.1353	−	8.81678i	−0.569536	−	0.413792i
$455$	19.2681	−	13.9991i	0.903301	−	0.656287i
$456$	6.40437	−	19.7106i	0.299912	−	0.923035i
$457$	6.52626	−	20.0858i	0.305286	−	0.939573i	−0.674285	−	0.738471i	$-0.735548\pi$
$457$	6.52626	−	20.0858i	0.305286	−	0.939573i	0.979570	−	0.201101i	$-0.0644520\pi$
$458$	4.85410	−	3.52671i	0.226817	−	0.164792i
$459$	−3.50347	−	2.54542i	−0.163528	−	0.118810i
$460$	−9.92545	−	30.5474i	−0.462776	−	1.42428i
$461$	8.09167			0.376867			0.188433	−	0.982086i	$-0.439659\pi$
$461$	8.09167			0.376867			0.188433	+	0.982086i	$0.439659\pi$
$462$		0			0
$463$	−30.8167			−1.43217			−0.716086	−	0.698012i	$-0.754068\pi$
$463$	−30.8167			−1.43217			−0.716086	+	0.698012i	$0.754068\pi$
$464$	0.439486	+	1.35260i	0.0204026	+	0.0627928i
$465$	6.71709	+	4.88025i	0.311497	+	0.226316i
$466$	−33.5337	+	24.3637i	−1.55342	+	1.12863i
$467$	−4.18460	+	12.8789i	−0.193640	+	0.595963i	0.806350	+	0.591439i	$0.201440\pi$
$467$	−4.18460	+	12.8789i	−0.193640	+	0.595963i	−0.999990	+	0.00452363i	$0.998560\pi$
$468$	15.5247	−	47.7800i	0.717628	−	2.20863i
$469$	6.88787	−	5.00433i	0.318052	−	0.231079i
$470$	12.8184	+	9.31311i	0.591269	+	0.429582i
$471$	−5.13140	−	15.7928i	−0.236442	−	0.727695i
$472$	20.0917			0.924794
$473$		0			0
$474$	44.0278			2.02226
$475$	−7.41641	−	22.8254i	−0.340288	−	1.04730i
$476$	7.20699	+	5.23618i	0.330332	+	0.240000i
$477$	24.0480	−	17.4719i	1.10108	−	0.799984i
$478$	18.7367	−	57.6657i	0.856998	−	2.63757i
$479$	−8.84818	+	27.2319i	−0.404284	+	1.24426i	0.517208	+	0.855860i	$0.326971\pi$
$479$	−8.84818	+	27.2319i	−0.404284	+	1.24426i	−0.921492	+	0.388397i	$0.873029\pi$
$480$	−35.6192	+	25.8789i	−1.62579	+	1.18120i
$481$	27.8481	+	20.2329i	1.26977	+	0.922539i
$482$	0.345923	+	1.06464i	0.0157563	+	0.0484931i
$483$	−6.21110			−0.282615
$484$		0			0
$485$	−13.0000			−0.590300
$486$	13.9512	+	42.9375i	0.632841	+	1.94769i
$487$	2.27872	+	1.65559i	0.103259	+	0.0750218i	0.638216	−	0.769857i	$-0.279672\pi$
$487$	2.27872	+	1.65559i	0.103259	+	0.0750218i	−0.534958	+	0.844879i	$0.679672\pi$
$488$	10.4431	−	7.58732i	0.472735	−	0.343462i
$489$	−2.00432	+	6.16867i	−0.0906386	+	0.278957i
$490$	2.56570	−	7.89641i	0.115906	−	0.356723i
$491$	10.2723	−	7.46324i	0.463581	−	0.336811i	−0.331353	−	0.943507i	$-0.607505\pi$
$491$	10.2723	−	7.46324i	0.463581	−	0.336811i	0.794934	+	0.606695i	$0.207505\pi$
$492$	43.0711	+	31.2930i	1.94180	+	1.41080i
$493$	3.91508	+	12.0494i	0.176326	+	0.542677i
$494$	−45.6333			−2.05314
$495$		0			0
$496$	0.302776			0.0135950
$497$	1.32963	+	4.09218i	0.0596421	+	0.183559i
$498$	12.8701	+	9.35068i	0.576723	+	0.419014i
$499$	−2.35289	+	1.70947i	−0.105330	+	0.0765265i	−0.639203	−	0.769038i	$-0.720736\pi$
$499$	−2.35289	+	1.70947i	−0.105330	+	0.0765265i	0.533874	+	0.845564i	$0.320736\pi$
$500$	11.0396	−	33.9765i	0.493707	−	1.51947i
$501$	3.70820	−	11.4127i	0.165670	−	0.509881i
$502$	−8.18679	+	5.94805i	−0.365394	+	0.265475i
$503$	−4.51253	−	3.27855i	−0.201204	−	0.146183i	0.482621	−	0.875829i	$-0.339685\pi$
$503$	−4.51253	−	3.27855i	−0.201204	−	0.146183i	−0.683825	+	0.729646i	$0.739685\pi$
$504$	−2.13479	−	6.57021i	−0.0950911	−	0.292660i
$505$	−19.1194			−0.850803
$506$		0			0
$507$	−70.5416			−3.13286
$508$	2.04123	+	6.28225i	0.0905648	+	0.278730i
$509$	−18.0433	−	13.1092i	−0.799756	−	0.581057i	0.111086	−	0.993811i	$-0.464567\pi$
$509$	−18.0433	−	13.1092i	−0.799756	−	0.581057i	−0.910843	+	0.412754i	$0.864567\pi$
$510$	41.7205	−	30.3117i	1.84742	−	1.34223i
$511$	1.54508	−	4.75528i	0.0683505	−	0.210361i
$512$	−1.05752	+	3.25471i	−0.0467362	+	0.143839i
$513$	3.89675	−	2.83116i	0.172046	−	0.124999i
$514$	−12.0835	−	8.77921i	−0.532982	−	0.387234i
$515$	−15.9358	−	49.0454i	−0.702216	−	2.16120i
$516$	−12.9083			−0.568257
$517$		0			0
$518$	12.0000			0.527250
$519$	0.927051	+	2.85317i	0.0406930	+	0.125240i
$520$	−57.8042	−	41.9972i	−2.53488	−	1.84170i
$521$	−6.00469	+	4.36266i	−0.263070	+	0.191132i	−0.711499	−	0.702687i	$-0.751984\pi$
$521$	−6.00469	+	4.36266i	−0.263070	+	0.191132i	0.448429	+	0.893818i	$0.351984\pi$
$522$	7.69710	−	23.6892i	0.336893	−	1.03685i
$523$	−13.7641	+	42.3616i	−0.601863	+	1.85234i	−0.0847974	+	0.996398i	$0.527024\pi$
$523$	−13.7641	+	42.3616i	−0.601863	+	1.85234i	−0.517066	+	0.855946i	$0.672976\pi$
$524$	16.0320	−	11.6479i	0.700362	−	0.508842i
$525$	−14.9039	−	10.8283i	−0.650459	−	0.472586i
$526$	14.4019	+	44.3245i	0.627953	+	1.93264i
$527$	2.69722			0.117493
$528$		0			0
$529$	−15.7250			−0.683695
$530$	−33.1189	−	101.929i	−1.43859	−	4.42753i
$531$	−12.4768	−	9.06494i	−0.541448	−	0.393385i
$532$	−8.01600	+	5.82397i	−0.347538	+	0.252501i
$533$	14.2886	−	43.9758i	0.618908	−	1.90480i
$534$	24.1291	−	74.2616i	1.04417	−	3.21361i
$535$	−36.1540	+	26.2674i	−1.56307	+	1.13564i
$536$	−20.6636	−	15.0130i	−0.892532	−	0.648463i
$537$	4.55027	+	14.0043i	0.196359	+	0.604330i
$538$	37.1194			1.60033
$539$		0			0
$540$	19.1194			0.822769
$541$	−10.0104	−	30.8090i	−0.430382	−	1.32458i	−0.897745	−	0.440515i	$-0.854796\pi$
$541$	−10.0104	−	30.8090i	−0.430382	−	1.32458i	0.467363	−	0.884065i	$-0.345204\pi$
$542$	53.1209	+	38.5946i	2.28174	+	1.65778i
$543$	−46.9679	+	34.1242i	−2.01559	+	1.46441i
$544$	−4.41980	+	13.6027i	−0.189497	+	0.583213i
$545$	−8.91341	+	27.4327i	−0.381809	+	1.17509i
$546$	−28.3381	+	20.5888i	−1.21276	+	0.881119i
$547$	24.2188	+	17.5960i	1.03552	+	0.752350i	0.969406	−	0.245462i	$-0.0789396\pi$
$547$	24.2188	+	17.5960i	1.03552	+	0.752350i	0.0661149	+	0.997812i	$0.478940\pi$
$548$	−10.3280	−	31.7864i	−0.441192	−	1.35785i
$549$	−9.90833			−0.422877
$550$		0			0
$551$	−14.0917			−0.600325
$552$	5.75801	+	17.7213i	0.245077	+	0.754270i
$553$	−6.71709	−	4.88025i	−0.285640	−	0.207529i
$554$	−55.7705	+	40.5196i	−2.36946	+	1.72151i
$555$	13.3701	−	41.1490i	0.567530	−	1.74668i
$556$	22.0509	−	67.8658i	0.935167	−	2.87815i
$557$	−5.85636	+	4.25489i	−0.248142	+	0.180286i	−0.704903	−	0.709304i	$-0.749009\pi$
$557$	−5.85636	+	4.25489i	−0.248142	+	0.180286i	0.456761	+	0.889589i	$0.349009\pi$
$558$	−4.29004	−	3.11689i	−0.181612	−	0.131949i
$559$	3.46442	+	10.6624i	0.146529	+	0.450971i
$560$	−1.09167			−0.0461316
$561$		0			0
$562$	14.7250			0.621136
$563$	−0.0935628	−	0.287957i	−0.00394320	−	0.0121359i	0.949066	−	0.315079i	$-0.102031\pi$
$563$	−0.0935628	−	0.287957i	−0.00394320	−	0.0121359i	−0.953009	+	0.302943i	$0.902031\pi$
$564$	−11.7420	−	8.53104i	−0.494426	−	0.359222i
$565$	31.2033	−	22.6705i	1.31273	−	0.953756i
$566$	3.12708	−	9.62415i	0.131441	−	0.404533i
$567$	3.27730	−	10.0865i	0.137633	−	0.423592i
$568$	10.4431	−	7.58732i	0.438181	−	0.318357i
$569$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$569$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$570$	17.7247	+	54.5510i	0.742405	+	2.28489i
$571$	25.8444			1.08155			0.540777	−	0.841166i	$-0.318130\pi$
$571$	25.8444			1.08155			0.540777	+	0.841166i	$0.318130\pi$
$572$		0			0
$573$	61.7527			2.57976
$574$	−4.98118	−	15.3305i	−0.207910	−	0.639882i
$575$	17.4568	+	12.6831i	0.727999	+	0.528922i
$576$	23.8772	−	17.3478i	0.994885	−	0.722826i
$577$	0.683268	−	2.10288i	0.0284448	−	0.0875442i	−0.935826	−	0.352462i	$-0.885345\pi$
$577$	0.683268	−	2.10288i	0.0284448	−	0.0875442i	0.964271	+	0.264917i	$0.0853447\pi$
$578$	−6.92027	+	21.2984i	−0.287845	+	0.885896i
$579$	−3.94846	+	2.86873i	−0.164093	+	0.119220i
$580$	−45.2532	−	32.8784i	−1.87904	−	1.36520i
$581$	−0.927051	−	2.85317i	−0.0384606	−	0.118369i
$582$	19.1194			0.792526
$583$		0			0
$584$	−15.0000			−0.620704
$585$	16.9479	+	52.1601i	0.700708	+	2.15656i
$586$	−8.97335	−	6.51952i	−0.370686	−	0.269319i
$587$	11.0071	−	7.99714i	0.454313	−	0.330077i	−0.336984	−	0.941511i	$-0.609407\pi$
$587$	11.0071	−	7.99714i	0.454313	−	0.330077i	0.791296	+	0.611433i	$0.209407\pi$
$588$	−2.35024	+	7.23331i	−0.0969225	+	0.298297i
$589$	−0.927051	+	2.85317i	−0.0381985	+	0.117563i
$590$	−44.9858	+	32.6841i	−1.85204	+	1.34558i
$591$	−19.7580	−	14.3550i	−0.812735	−	0.590486i
$592$	−0.487565	−	1.50057i	−0.0200388	−	0.0616731i
$593$	22.6056			0.928299			0.464149	−	0.885757i	$-0.346360\pi$
$593$	22.6056			0.928299			0.464149	+	0.885757i	$0.346360\pi$
$594$		0			0
$595$	−9.72498			−0.398685
$596$	−5.00951	−	15.4177i	−0.205197	−	0.631533i
$597$	36.1833	+	26.2887i	1.48088	+	1.07592i
$598$	33.1922	−	24.1155i	1.35733	−	0.986157i
$599$	−4.57002	+	14.0651i	−0.186726	+	0.574683i	−0.999974	−	0.00723398i	$-0.997697\pi$
$599$	−4.57002	+	14.0651i	−0.186726	+	0.574683i	0.813248	+	0.581917i	$0.197697\pi$
$600$	−17.0783	+	52.5617i	−0.697220	+	2.14582i
$601$	4.70577	−	3.41894i	0.191952	−	0.139462i	−0.487658	−	0.873035i	$-0.662149\pi$
$601$	4.70577	−	3.41894i	0.191952	−	0.139462i	0.679611	+	0.733573i	$0.262149\pi$
$602$	3.16190	+	2.29726i	0.128870	+	0.0936292i
$603$	6.05845	+	18.6460i	0.246719	+	0.759323i
$604$	−0.697224			−0.0283697
$605$		0			0
$606$	28.1194			1.14227
$607$	−6.34771	−	19.5363i	−0.257646	−	0.792952i	−0.993297	−	0.115591i	$-0.963124\pi$
$607$	−6.34771	−	19.5363i	−0.257646	−	0.792952i	0.735651	−	0.677361i	$-0.236876\pi$
$608$	−12.8701	−	9.35068i	−0.521952	−	0.379220i
$609$	−8.75086	+	6.35787i	−0.354603	+	0.257634i
$610$	−11.0396	+	33.9765i	−0.446981	+	1.37567i
$611$	−3.89533	+	11.9886i	−0.157588	+	0.485007i
$612$	−16.5961	+	12.0578i	−0.670857	+	0.487406i
$613$	26.7425	+	19.4295i	1.08012	+	0.784752i	0.977704	−	0.209990i	$-0.0673431\pi$
$613$	26.7425	+	19.4295i	1.08012	+	0.784752i	0.102415	+	0.994742i	$0.467343\pi$
$614$	−11.8362	−	36.4281i	−0.477671	−	1.47012i
$615$	−58.1194			−2.34360
$616$		0			0
$617$	21.6333			0.870924			0.435462	−	0.900207i	$-0.356585\pi$
$617$	21.6333			0.870924			0.435462	+	0.900207i	$0.356585\pi$
$618$	23.4372	+	72.1323i	0.942783	+	2.90159i
$619$	−32.2123	−	23.4036i	−1.29472	−	0.940672i	−0.294834	−	0.955548i	$-0.595264\pi$
$619$	−32.2123	−	23.4036i	−1.29472	−	0.940672i	−0.999889	+	0.0148766i	$0.995264\pi$
$620$	−9.63404	+	6.99954i	−0.386912	+	0.281108i
$621$	−1.33821	+	4.11858i	−0.0537004	+	0.165273i
$622$	4.55027	−	14.0043i	0.182449	−	0.561521i
$623$	−11.9128	+	8.65513i	−0.477275	+	0.346760i
$624$	3.72597	+	2.70708i	0.149158	+	0.108370i
$625$	−0.309017	−	0.951057i	−0.0123607	−	0.0380423i
$626$	35.2389			1.40843
$627$		0			0
$628$	23.8167			0.950388
$629$	−4.34339	−	13.3676i	−0.173182	−	0.533001i
$630$	15.4679	+	11.2381i	0.616258	+	0.447737i
$631$	25.1244	−	18.2540i	1.00019	−	0.726679i	0.0380596	−	0.999275i	$-0.487882\pi$
$631$	25.1244	−	18.2540i	1.00019	−	0.726679i	0.962129	+	0.272596i	$0.0878823\pi$
$632$	−7.69710	+	23.6892i	−0.306174	+	0.942307i
$633$	−11.0396	+	33.9765i	−0.438786	+	1.35044i
$634$	−32.2348	+	23.4200i	−1.28021	+	0.930125i
$635$	−5.83390	−	4.23858i	−0.231511	−	0.168203i
$636$	30.3377	+	93.3699i	1.20297	+	3.70236i
$637$	6.60555			0.261721
$638$		0			0
$639$	−9.90833			−0.391967
$640$	−21.0672	−	64.8382i	−0.832755	−	2.56296i
$641$	23.3132	+	16.9380i	0.920815	+	0.669011i	0.943727	−	0.330727i	$-0.107294\pi$
$641$	23.3132	+	16.9380i	0.920815	+	0.669011i	−0.0229121	+	0.999737i	$0.507294\pi$
$642$	53.1726	−	38.6322i	2.09856	−	1.52469i
$643$	−0.382828	+	1.17822i	−0.0150973	+	0.0464647i	−0.958321	−	0.285692i	$-0.907776\pi$
$643$	−0.382828	+	1.17822i	−0.0150973	+	0.0464647i	0.943224	+	0.332157i	$0.107776\pi$
$644$	2.75282	−	8.47232i	0.108476	−	0.333856i
$645$	11.4004	−	8.28288i	0.448890	−	0.326138i
$646$	15.0747	+	10.9524i	0.593105	+	0.430916i
$647$	3.27730	+	10.0865i	0.128844	+	0.396540i	0.994582	−	0.103957i	$-0.0331505\pi$
$647$	3.27730	+	10.0865i	0.128844	+	0.396540i	−0.865738	+	0.500497i	$0.833150\pi$
$648$	−31.8167			−1.24988
$649$		0			0
$650$	121.689			4.77303
$651$	0.711597	+	2.19007i	0.0278897	+	0.0858356i
$652$	−7.52610	−	5.46803i	−0.294745	−	0.214145i
$653$	5.51479	−	4.00673i	0.215810	−	0.156795i	−0.474628	−	0.880186i	$-0.657418\pi$
$653$	5.51479	−	4.00673i	0.215810	−	0.156795i	0.690439	+	0.723391i	$0.257418\pi$
$654$	13.1092	−	40.3459i	0.512610	−	1.57765i
$655$	−6.68506	+	20.5745i	−0.261207	+	0.803912i
$656$	−1.71465	+	1.24577i	−0.0669460	+	0.0486391i
$657$	9.31492	+	6.76769i	0.363410	+	0.264033i
$658$	1.35796	+	4.17937i	0.0529388	+	0.162929i
$659$	4.63331			0.180488			0.0902440	−	0.995920i	$-0.471235\pi$
$659$	4.63331			0.180488			0.0902440	+	0.995920i	$0.471235\pi$
$660$		0			0
$661$	−18.3028			−0.711895			−0.355948	−	0.934506i	$-0.615842\pi$
$661$	−18.3028			−0.711895			−0.355948	+	0.934506i	$0.615842\pi$
$662$	16.9479	+	52.1601i	0.658697	+	2.02726i
$663$	33.1922	+	24.1155i	1.28908	+	0.936569i
$664$	−7.28115	+	5.29007i	−0.282564	+	0.205294i
$665$	3.34253	−	10.2872i	0.129618	−	0.398922i
$666$	−8.53916	+	26.2808i	−0.330886	+	1.01836i
$667$	10.2498	−	7.44693i	0.396874	−	0.288346i
$668$	13.9241	+	10.1164i	0.538739	+	0.391417i
$669$	−9.89712	−	30.4602i	−0.382645	−	1.17766i
$670$	70.6888			2.73095
$671$		0			0
$672$	−12.2111			−0.471054
$673$	−2.60260	−	8.00999i	−0.100323	−	0.308763i	0.888281	−	0.459300i	$-0.151900\pi$
$673$	−2.60260	−	8.00999i	−0.100323	−	0.308763i	−0.988604	+	0.150537i	$0.951900\pi$
$674$	−21.9625	−	15.9567i	−0.845965	−	0.614630i
$675$	−10.3913	+	7.54975i	−0.399963	+	0.290590i
$676$	31.2648	−	96.2231i	1.20249	−	3.70089i
$677$	3.18373	−	9.79852i	0.122361	−	0.376588i	−0.871050	−	0.491194i	$-0.836561\pi$
$677$	3.18373	−	9.79852i	0.122361	−	0.376588i	0.993411	+	0.114606i	$0.0365606\pi$
$678$	−45.8915	+	33.3421i	−1.76245	+	1.28050i
$679$	−2.91695	−	2.11929i	−0.111942	−	0.0813309i
$680$	9.01555	+	27.7470i	0.345731	+	1.06405i
$681$	−15.0000			−0.574801
$682$		0			0
$683$	15.6972			0.600638			0.300319	−	0.953839i	$-0.402907\pi$
$683$	15.6972			0.600638			0.300319	+	0.953839i	$0.402907\pi$
$684$	−7.05073	−	21.6999i	−0.269592	−	0.829717i
$685$	29.5179	+	21.4460i	1.12782	+	0.819410i
$686$	1.86298	−	1.35354i	0.0711291	−	0.0516783i
$687$	1.85410	−	5.70634i	0.0707384	−	0.217710i
$688$	0.158797	−	0.488727i	0.00605408	−	0.0186325i
$689$	68.9821	−	50.1185i	2.62801	−	1.90936i
$690$	−41.7205	−	30.3117i	−1.58827	−	1.15395i
$691$	−5.26187	−	16.1944i	−0.200171	−	0.616062i	−0.999877	−	0.0156711i	$-0.995012\pi$
$691$	−5.26187	−	16.1944i	−0.200171	−	0.616062i	0.799706	−	0.600391i	$-0.204988\pi$
$692$	−4.30278			−0.163567
$693$		0			0
$694$	22.1194			0.839642
$695$	24.0724	+	74.0872i	0.913118	+	2.81029i
$696$	26.2526	+	19.0736i	0.995101	+	0.722983i
$697$	−15.2747	+	11.0977i	−0.578571	+	0.420356i
$698$	−3.34253	+	10.2872i	−0.126517	+	0.389378i
$699$	−12.8087	+	39.4213i	−0.484471	+	1.49105i
$700$	21.3760	−	15.5306i	0.807937	−	0.587001i
$701$	25.1761	+	18.2915i	0.950890	+	0.690862i	0.951017	−	0.309138i	$-0.100040\pi$
$701$	25.1761	+	18.2915i	0.950890	+	0.690862i	−0.000127232		1.00000i	$0.500040\pi$
$702$	7.54688	+	23.2269i	0.284838	+	0.876643i
$703$	15.6333			0.589621
$704$		0			0
$705$	15.8444			0.596735
$706$	3.62322	+	11.1511i	0.136362	+	0.419678i
$707$	−4.29004	−	3.11689i	−0.161343	−	0.117223i
$708$	41.2082	−	29.9395i	1.54870	−	1.12519i
$709$	7.82756	−	24.0908i	0.293970	−	0.904748i	−0.689595	−	0.724195i	$-0.742211\pi$
$709$	7.82756	−	24.0908i	0.293970	−	0.904748i	0.983565	−	0.180553i	$-0.0577886\pi$
$710$	−11.0396	+	33.9765i	−0.414310	+	1.27511i
$711$	15.4679	−	11.2381i	0.580093	−	0.421462i
$712$	35.7383	+	25.9654i	1.33935	+	0.973094i
$713$	−0.833488	−	2.56521i	−0.0312144	−	0.0960680i
$714$	14.3028			0.535268
$715$		0			0
$716$	−21.1194			−0.789270
$717$	−18.7367	−	57.6657i	−0.699736	−	2.15357i
$718$	63.2224	+	45.9338i	2.35944	+	1.71423i
$719$	−17.1826	+	12.4839i	−0.640803	+	0.465570i	−0.860126	−	0.510082i	$-0.829615\pi$
$719$	−17.1826	+	12.4839i	−0.640803	+	0.465570i	0.219323	+	0.975652i	$0.429615\pi$
$720$	0.776831	−	2.39084i	0.0289508	−	0.0891014i
$721$	4.41980	−	13.6027i	0.164602	−	0.506593i
$722$	18.6298	−	13.5354i	0.693331	−	0.503735i
$723$	0.905637	+	0.657984i	0.0336810	+	0.0244707i
$724$	−25.7308	−	79.1913i	−0.956278	−	2.94312i
$725$	37.5778			1.39560
$726$		0			0
$727$	24.1194			0.894540			0.447270	−	0.894399i	$-0.352396\pi$
$727$	24.1194			0.894540			0.447270	+	0.894399i	$0.352396\pi$
$728$	−6.12368	−	18.8468i	−0.226959	−	0.698507i
$729$	10.7846	+	7.83549i	0.399431	+	0.290203i
$730$	33.5854	−	24.4012i	1.24305	−	0.903131i
$731$	1.41462	−	4.35374i	0.0523215	−	0.161029i
$732$	10.1126	−	31.1233i	0.373772	−	1.15035i
$733$	5.49233	−	3.99041i	0.202864	−	0.147389i	−0.481715	−	0.876328i	$-0.659986\pi$
$733$	5.49233	−	3.99041i	0.202864	−	0.147389i	0.684579	+	0.728939i	$0.259986\pi$
$734$	32.8506	+	23.8673i	1.21254	+	0.880960i
$735$	−2.56570	−	7.89641i	−0.0946372	−	0.291263i
$736$	14.3028			0.527207
$737$		0			0
$738$	37.1194			1.36639
$739$	−13.3246	−	41.0090i	−0.490155	−	1.50854i	−0.824374	−	0.566046i	$-0.808473\pi$
$739$	−13.3246	−	41.0090i	−0.490155	−	1.50854i	0.334219	−	0.942495i	$-0.391527\pi$
$740$	50.2040	+	36.4753i	1.84553	+	1.34086i
$741$	−36.9181	+	26.8226i	−1.35622	+	0.985352i
$742$	9.18552	−	28.2701i	0.337211	−	1.03783i
$743$	13.8860	−	42.7368i	0.509428	−	1.56786i	−0.283768	−	0.958893i	$-0.591584\pi$
$743$	13.8860	−	42.7368i	0.509428	−	1.56786i	0.793196	−	0.608966i	$-0.208416\pi$
$744$	5.58895	−	4.06061i	0.204901	−	0.148869i
$745$	14.3174	+	10.4022i	0.524547	+	0.381106i
$746$	−14.3169	−	44.0630i	−0.524180	−	1.61326i
$747$	6.90833			0.252762
$748$		0			0
$749$	−12.3944			−0.452883
$750$	−17.7247	−	54.5510i	−0.647214	−	1.99192i
$751$	−6.17548	−	4.48675i	−0.225346	−	0.163724i	0.469384	−	0.882994i	$-0.344476\pi$
$751$	−6.17548	−	4.48675i	−0.225346	−	0.163724i	−0.694730	+	0.719271i	$0.744476\pi$
$752$	0.467446	−	0.339619i	0.0170460	−	0.0123846i
$753$	−3.12708	+	9.62415i	−0.113957	+	0.350723i
$754$	22.0793	−	67.9530i	0.804079	−	2.47470i
$755$	0.615776	−	0.447387i	0.0224104	−	0.0162821i
$756$	4.29004	+	3.11689i	0.156027	+	0.113360i
$757$	−7.35975	−	22.6510i	−0.267495	−	0.823264i	−0.991108	−	0.133059i	$-0.957520\pi$
$757$	−7.35975	−	22.6510i	−0.267495	−	0.823264i	0.723613	−	0.690205i	$-0.242480\pi$
$758$	−36.4222			−1.32291
$759$		0			0
$760$	−32.4500			−1.17708
$761$	12.9787	+	39.9444i	0.470478	+	1.44798i	0.851960	+	0.523606i	$0.175414\pi$
$761$	12.9787	+	39.9444i	0.470478	+	1.44798i	−0.381482	+	0.924376i	$0.624586\pi$
$762$	8.58007	+	6.23379i	0.310823	+	0.225826i
$763$	−6.47214	+	4.70228i	−0.234307	+	0.170234i
$764$	−27.3694	+	84.2345i	−0.990192	+	3.04750i
$765$	6.92027	−	21.2984i	0.250203	−	0.770045i
$766$	−71.9733	+	52.2916i	−2.60050	+	1.88937i
$767$	−35.7900	−	26.0029i	−1.29230	−	0.938912i
$768$	12.7435	+	39.2205i	0.459842	+	1.41525i
$769$	−39.3305			−1.41830			−0.709148	−	0.705060i	$-0.750920\pi$
$769$	−39.3305			−1.41830			−0.709148	+	0.705060i	$0.750920\pi$
$770$		0			0
$771$	−14.9361			−0.537910
$772$	−2.16312	−	6.65740i	−0.0778524	−	0.239605i
$773$	−24.7829	−	18.0058i	−0.891378	−	0.647624i	0.0448591	−	0.998993i	$-0.485716\pi$
$773$	−24.7829	−	18.0058i	−0.891378	−	0.647624i	−0.936237	+	0.351369i	$0.885716\pi$
$774$	−7.28115	+	5.29007i	−0.261716	+	0.190148i
$775$	2.47214	−	7.60845i	0.0888017	−	0.273304i
$776$	−3.34253	+	10.2872i	−0.119990	+	0.369291i
$777$	9.70820	−	7.05342i	0.348280	−	0.253040i
$778$	14.5623	+	10.5801i	0.522084	+	0.379316i
$779$	−6.48936	−	19.9722i	−0.232505	−	0.715578i
$780$	−181.139			−6.48581
$781$		0			0
$782$	−16.7527			−0.599077
$783$	2.33049	+	7.17252i	0.0832850	+	0.256325i
$784$	−0.244951	−	0.177967i	−0.00874824	−	0.00635597i
$785$	−21.0344	+	15.2824i	−0.750751	+	0.545453i
$786$	9.83189	−	30.2594i	0.350692	−	1.07932i
$787$	−6.94859	+	21.3856i	−0.247691	+	0.762313i	0.747492	+	0.664271i	$0.231258\pi$
$787$	−6.94859	+	21.3856i	−0.247691	+	0.762313i	−0.995182	+	0.0980421i	$0.968742\pi$
$788$	28.3381	−	20.5888i	1.00950	−	0.733446i
$789$	37.7047	+	27.3941i	1.34232	+	0.975254i
$790$	−21.3024	−	65.5621i	−0.757906	−	2.33260i
$791$	10.6972			0.380350
$792$		0			0
$793$	−28.4222			−1.00930
$794$	21.4981	+	66.1644i	0.762940	+	2.34809i
$795$	−86.7063	−	62.9959i	−3.07516	−	2.23423i
$796$	−51.8962	+	37.7048i	−1.83941	+	1.33641i
$797$	−8.84818	+	27.2319i	−0.313419	+	0.964603i	0.662982	+	0.748635i	$0.269291\pi$
$797$	−8.84818	+	27.2319i	−0.313419	+	0.964603i	−0.976400	+	0.215968i	$0.930709\pi$
$798$	−4.91594	+	15.1297i	−0.174023	+	0.535586i
$799$	4.16416	−	3.02544i	0.147317	−	0.107032i
$800$	34.3203	+	24.9351i	1.21341	+	0.881591i
$801$	−10.4782	−	32.2487i	−0.370231	−	1.13945i
$802$	−48.8444			−1.72476
$803$		0			0
$804$	−64.7527			−2.28365
$805$	3.00518	+	9.24901i	0.105919	+	0.325985i
$806$	−12.3060	−	8.94086i	−0.433462	−	0.314928i
$807$	30.0302	−	21.8183i	1.05711	−	0.768039i
$808$	−4.91594	+	15.1297i	−0.172942	+	0.532262i
$809$	2.50046	−	7.69564i	0.0879117	−	0.270564i	−0.897430	−	0.441157i	$-0.854568\pi$
$809$	2.50046	−	7.69564i	0.0879117	−	0.270564i	0.985342	+	0.170593i	$0.0545682\pi$
$810$	71.2384	−	51.7577i	2.50306	−	1.81858i
$811$	33.0438	+	24.0077i	1.16033	+	0.843026i	0.989819	−	0.142331i	$-0.0454597\pi$
$811$	33.0438	+	24.0077i	1.16033	+	0.843026i	0.170506	+	0.985357i	$0.445460\pi$
$812$	−4.79405	−	14.7546i	−0.168238	−	0.517784i
$813$	65.6611			2.30283
$814$		0			0
$815$	10.1556			0.355735
$816$	−0.581128	−	1.78853i	−0.0203436	−	0.0626110i
$817$	4.11925	+	2.99281i	0.144114	+	0.104705i
$818$	−38.3878	+	27.8904i	−1.34220	+	0.975165i
$819$	−4.70049	+	14.4666i	−0.164248	+	0.505505i
$820$	25.7591	−	79.2784i	0.899548	−	2.76852i
$821$	22.1850	−	16.1184i	0.774263	−	0.562535i	−0.128989	−	0.991646i	$-0.541173\pi$
$821$	22.1850	−	16.1184i	0.774263	−	0.562535i	0.903252	+	0.429111i	$0.141173\pi$
$822$	−43.4127	−	31.5412i	−1.51419	−	1.10013i
$823$	10.8808	+	33.4877i	0.379282	+	1.16731i	0.940544	+	0.339672i	$0.110316\pi$
$823$	10.8808	+	33.4877i	0.379282	+	1.16731i	−0.561262	+	0.827638i	$0.689684\pi$
$824$	−42.9083			−1.49478
$825$		0			0
$826$	−15.4222			−0.536607
$827$	−4.38290	−	13.4892i	−0.152408	−	0.469064i	0.845481	−	0.534006i	$-0.179314\pi$
$827$	−4.38290	−	13.4892i	−0.152408	−	0.469064i	−0.997889	+	0.0649415i	$0.979314\pi$
$828$	16.5961	+	12.0578i	0.576754	+	0.419036i
$829$	−10.7397	+	7.80286i	−0.373006	+	0.271005i	−0.758456	−	0.651724i	$-0.774046\pi$
$829$	−10.7397	+	7.80286i	−0.373006	+	0.271005i	0.385450	+	0.922729i	$0.374046\pi$
$830$	7.69710	−	23.6892i	0.267170	−	0.822265i
$831$	−21.3024	+	65.5621i	−0.738973	+	2.27432i
$832$	68.4922	−	49.7625i	2.37454	−	1.72521i
$833$	−2.18210	−	1.58539i	−0.0756053	−	0.0549305i
$834$	−35.4039	−	108.962i	−1.22594	−	3.77304i
$835$	−18.7889			−0.650217
$836$		0			0
$837$	1.60555			0.0554960
$838$	−27.3411	−	84.1473i	−0.944483	−	2.90682i
$839$	−34.1495	−	24.8111i	−1.17897	−	0.856573i	−0.186916	−	0.982376i	$-0.559849\pi$
$839$	−34.1495	−	24.8111i	−1.17897	−	0.856573i	−0.992055	+	0.125803i	$0.959849\pi$
$840$	−20.1513	+	14.6407i	−0.695285	+	0.505154i
$841$	−2.14337	+	6.59661i	−0.0739092	+	0.227469i
$842$	−15.5247	+	47.7800i	−0.535015	+	1.64661i
$843$	11.9128	−	8.65513i	0.410297	−	0.298098i
$844$	−41.4531	−	30.1174i	−1.42687	−	1.03669i
$845$	34.1309	+	105.044i	1.17414	+	3.61363i
$846$	−10.1194			−0.347913
$847$		0			0
$848$	−3.90833			−0.134212
$849$	−3.12708	−	9.62415i	−0.107321	−	0.330300i
$850$	−40.1991	−	29.2064i	−1.37882	−	1.00177i
$851$	−11.3711	+	8.26162i	−0.389798	+	0.283205i
$852$	10.1126	−	31.1233i	0.346451	−	1.06627i
$853$	−14.1298	+	43.4870i	−0.483795	+	1.48897i	0.349924	+	0.936778i	$0.386208\pi$
$853$	−14.1298	+	43.4870i	−0.483795	+	1.48897i	−0.833719	+	0.552190i	$0.813792\pi$
$854$	−8.01600	+	5.82397i	−0.274302	+	0.199292i
$855$	20.1513	+	14.6407i	0.689159	+	0.500703i
$856$	11.4903	+	35.3635i	0.392730	+	1.20870i
$857$	35.3583			1.20782			0.603908	−	0.797054i	$-0.293609\pi$
$857$	35.3583			1.20782			0.603908	+	0.797054i	$0.293609\pi$
$858$		0			0
$859$	−25.3028			−0.863320			−0.431660	−	0.902036i	$-0.642072\pi$
$859$	−25.3028			−0.863320			−0.431660	+	0.902036i	$0.642072\pi$
$860$	6.24557	+	19.2219i	0.212972	+	0.655461i
$861$	−13.0409	−	9.47476i	−0.444432	−	0.322899i
$862$	5.81145	−	4.22226i	0.197939	−	0.143811i
$863$	9.71000	−	29.8843i	0.330532	−	1.01727i	−0.638349	−	0.769747i	$-0.720382\pi$
$863$	9.71000	−	29.8843i	0.330532	−	1.01727i	0.968881	−	0.247526i	$-0.0796176\pi$
$864$	−2.63093	+	8.09718i	−0.0895062	+	0.275472i
$865$	3.80013	−	2.76096i	0.129208	−	0.0938754i
$866$	−54.3008	−	39.4518i	−1.84521	−	1.34063i
$867$	6.92027	+	21.2984i	0.235025	+	0.723331i
$868$	−3.30278			−0.112104
$869$		0			0
$870$	−89.8082			−3.04478
$871$	17.3788	+	53.4863i	0.588857	+	1.81232i
$872$	19.4164	+	14.1068i	0.657523	+	0.477718i
$873$	6.71709	−	4.88025i	0.227339	−	0.165171i
$874$	5.75801	−	17.7213i	0.194768	−	0.599433i
$875$	−3.34253	+	10.2872i	−0.112998	+	0.347772i
$876$	−30.7651	+	22.3522i	−1.03946	+	0.755209i
$877$	−38.0687	−	27.6585i	−1.28549	−	0.933962i	−0.285785	−	0.958294i	$-0.592254\pi$
$877$	−38.0687	−	27.6585i	−1.28549	−	0.933962i	−0.999704	+	0.0243313i	$0.992254\pi$
$878$	19.7290	+	60.7196i	0.665822	+	2.04919i
$879$	−11.0917			−0.374113
$880$		0			0
$881$	34.3305			1.15663			0.578313	−	0.815815i	$-0.303711\pi$
$881$	34.3305			1.15663			0.578313	+	0.815815i	$0.303711\pi$
$882$	1.63865	+	5.04324i	0.0551761	+	0.169815i
$883$	6.24964	+	4.54063i	0.210317	+	0.152804i	0.687957	−	0.725751i	$-0.258508\pi$
$883$	6.24964	+	4.54063i	0.210317	+	0.152804i	−0.477640	+	0.878556i	$0.658508\pi$
$884$	−47.6061	+	34.5879i	−1.60117	+	1.16332i
$885$	−17.1831	+	52.8840i	−0.577602	+	1.77768i
$886$	19.1676	−	58.9919i	0.643949	−	1.98187i
$887$	−35.6934	+	25.9327i	−1.19847	+	0.870737i	−0.994133	−	0.108165i	$-0.965503\pi$
$887$	−35.6934	+	25.9327i	−1.19847	+	0.870737i	−0.204333	+	0.978901i	$0.565503\pi$
$888$	−29.1246	−	21.1603i	−0.977358	−	0.710092i
$889$	−0.618034	−	1.90211i	−0.0207282	−	0.0637948i
$890$	−122.258			−4.09810
$891$		0			0
$892$	45.9361			1.53805
$893$	1.76912	+	5.44478i	0.0592012	+	0.182203i
$894$	−21.0569	−	15.2987i	−0.704248	−	0.511666i
$895$	18.6523	−	13.5517i	0.623478	−	0.452983i
$896$	5.84299	−	17.9829i	0.195201	−	0.600766i
$897$	12.6783	−	39.0197i	0.423315	−	1.30283i
$898$	−75.1352	+	54.5889i	−2.50729	+	1.82165i
$899$	−3.80013	−	2.76096i	−0.126742	−	0.0920831i
$900$	18.8020	+	57.8665i	0.626732	+	1.92888i
$901$	−34.8167			−1.15991
$902$		0			0
$903$	3.90833			0.130061
$904$	−9.91687	−	30.5210i	−0.329830	−	1.01511i
$905$	73.5396	+	53.4296i	2.44454	+	1.77606i
$906$	−0.905637	+	0.657984i	−0.0300878	+	0.0218601i
$907$	0.121891	−	0.375143i	0.00404734	−	0.0124564i	−0.949012	−	0.315239i	$-0.897915\pi$
$907$	0.121891	−	0.375143i	0.00404734	−	0.0124564i	0.953060	+	0.302782i	$0.0979155\pi$
$908$	6.64815	−	20.4609i	0.220627	−	0.679019i
$909$	9.87899	−	7.17751i	0.327665	−	0.238063i
$910$	44.3701	+	32.2367i	1.47085	+	1.06864i
$911$	−15.5899	−	47.9808i	−0.516516	−	1.58967i	−0.780506	−	0.625148i	$-0.785039\pi$
$911$	−15.5899	−	47.9808i	−0.516516	−	1.58967i	0.263990	−	0.964525i	$-0.414961\pi$
$912$	2.09167			0.0692622
$913$		0			0
$914$	48.6333			1.60865
$915$	11.0396	+	33.9765i	0.364959	+	1.12323i
$916$	6.96204	+	5.05822i	0.230032	+	0.167128i
$917$	−4.85410	+	3.52671i	−0.160297	+	0.116462i
$918$	3.08159	−	9.48417i	0.101708	−	0.313024i
$919$	17.1436	−	52.7624i	0.565514	−	1.74047i	−0.100906	−	0.994896i	$-0.532174\pi$
$919$	17.1436	−	52.7624i	0.565514	−	1.74047i	0.666420	−	0.745577i	$-0.267826\pi$
$920$	23.6030	−	17.1486i	0.778169	−	0.565373i
$921$	−30.9876	−	22.5138i	−1.02108	−	0.741855i
$922$	5.75801	+	17.7213i	0.189630	+	0.583621i
$923$	−28.4222			−0.935528
$924$		0			0
$925$	−41.6888			−1.37072
$926$	−21.9290	−	67.4906i	−0.720633	−	2.21788i
$927$	26.6459	+	19.3593i	0.875165	+	0.635844i
$928$	20.1513	−	14.6407i	0.661498	−	0.480606i
$929$	−8.53916	+	26.2808i	−0.280161	+	0.862246i	0.707647	+	0.706566i	$0.249757\pi$
$929$	−8.53916	+	26.2808i	−0.280161	+	0.862246i	−0.987808	+	0.155680i	$0.950243\pi$
$930$	−5.90823	+	18.1837i	−0.193738	+	0.596266i
$931$	2.42705	−	1.76336i	0.0795434	−	0.0577917i
$932$	−48.0960	−	34.9438i	−1.57544	−	1.14462i
$933$	−4.55027	−	14.0043i	−0.148969	−	0.458480i
$934$	−31.1833			−1.02035
$935$		0			0
$936$	45.6333			1.49157
$937$	9.76665	+	30.0587i	0.319063	+	0.981974i	0.974050	+	0.226334i	$0.0726740\pi$
$937$	9.76665	+	30.0587i	0.319063	+	0.981974i	−0.654987	+	0.755640i	$0.727326\pi$
$938$	15.8612	+	11.5239i	0.517887	+	0.376267i
$939$	28.5088	−	20.7129i	0.930351	−	0.675939i
$940$	−7.02241	+	21.6127i	−0.229046	+	0.704930i
$941$	11.5641	−	35.5906i	0.376979	−	1.16022i	−0.565155	−	0.824985i	$-0.691184\pi$
$941$	11.5641	−	35.5906i	0.376979	−	1.16022i	0.942134	−	0.335237i	$-0.108816\pi$
$942$	30.9359	−	22.4762i	1.00795	−	0.732315i
$943$	15.2747	+	11.0977i	0.497413	+	0.361392i
$944$	0.626611	+	1.92851i	0.0203945	+	0.0627677i
$945$	−5.78890			−0.188313
$946$		0			0
$947$	46.6611			1.51628			0.758140	−	0.652091i	$-0.226108\pi$
$947$	46.6611			1.51628			0.758140	+	0.652091i	$0.226108\pi$
$948$	19.5136	+	60.0565i	0.633771	+	1.95055i
$949$	26.7200	+	19.4132i	0.867368	+	0.630180i
$950$	44.7116	−	32.4849i	1.45064	−	1.05395i
$951$	−12.3126	+	37.8943i	−0.399263	+	1.22881i
$952$	−2.50046	+	7.69564i	−0.0810405	+	0.249417i
$953$	4.87656	−	3.54303i	0.157967	−	0.114770i	−0.505994	−	0.862537i	$-0.668874\pi$
$953$	4.87656	−	3.54303i	0.157967	−	0.114770i	0.663961	+	0.747767i	$0.268874\pi$
$954$	55.3772	+	40.2339i	1.79290	+	1.30262i
$955$	−29.8785	−	91.9565i	−0.966845	−	2.97564i
$956$	86.9638			2.81261
$957$		0			0
$958$	−65.9361			−2.13030
$959$	3.12708	+	9.62415i	0.100979	+	0.310780i
$960$	−86.0906	−	62.5485i	−2.77856	−	2.01874i
$961$	24.2705	−	17.6336i	0.782920	−	0.568824i
$962$	−24.4947	+	75.3870i	−0.789742	+	2.43058i
$963$	8.81985	−	27.1447i	0.284216	−	0.874726i
$964$	−1.29892	+	0.943719i	−0.0418353	+	0.0303952i
$965$	6.18227	+	4.49169i	0.199014	+	0.144592i
$966$	−4.41980	−	13.6027i	−0.142205	−	0.437661i
$967$	40.5139			1.30284			0.651419	−	0.758718i	$-0.274174\pi$
$967$	40.5139			1.30284			0.651419	+	0.758718i	$0.274174\pi$
$968$		0			0
$969$	18.6333			0.598588
$970$	−9.25076	−	28.4709i	−0.297024	−	0.914146i
$971$	5.15076	+	3.74225i	0.165296	+	0.120094i	0.667358	−	0.744737i	$-0.267425\pi$
$971$	5.15076	+	3.74225i	0.165296	+	0.120094i	−0.502062	+	0.864832i	$0.667425\pi$
$972$	−52.3861	+	38.0607i	−1.68028	+	1.22080i
$973$	−6.67648	+	20.5481i	−0.214038	+	0.658742i
$974$	−2.00432	+	6.16867i	−0.0642226	+	0.197657i
$975$	98.4483	−	71.5269i	3.15287	−	2.29069i
$976$	1.05397	+	0.765752i	0.0337367	+	0.0245111i
$977$	12.3693	+	38.0687i	0.395728	+	1.21792i	0.928393	+	0.371599i	$0.121190\pi$
$977$	12.3693	+	38.0687i	0.395728	+	1.21792i	−0.532666	+	0.846326i	$0.678810\pi$
$978$	−14.9361			−0.477603
$979$		0			0
$980$	11.9083			0.380398
$981$	−5.69277	−	17.5206i	−0.181756	−	0.559388i
$982$	23.6547	+	17.1862i	0.754853	+	0.548433i
$983$	7.50365	−	5.45172i	0.239329	−	0.173883i	−0.461655	−	0.887059i	$-0.652744\pi$
$983$	7.50365	−	5.45172i	0.239329	−	0.173883i	0.700984	+	0.713177i	$0.252744\pi$
$984$	−14.9435	+	45.9915i	−0.476382	+	1.46615i
$985$	−11.8165	+	36.3673i	−0.376504	+	1.15876i
$986$	−23.6030	+	17.1486i	−0.751673	+	0.546123i
$987$	3.55518	+	2.58299i	0.113163	+	0.0822175i
$988$	−20.2252	−	62.2466i	−0.643448	−	1.98033i
$989$	−4.57779			−0.145565
$990$		0			0
$991$	−43.7250			−1.38897			−0.694485	−	0.719507i	$-0.744368\pi$
$991$	−43.7250			−1.38897			−0.694485	+	0.719507i	$0.744368\pi$
$992$	−1.63865	−	5.04324i	−0.0520271	−	0.160123i
$993$	44.3701	+	32.2367i	1.40804	+	1.02300i
$994$	−8.01600	+	5.82397i	−0.254252	+	0.184725i
$995$	21.6398	−	66.6004i	0.686027	−	2.11137i
$996$	−7.05073	+	21.6999i	−0.223411	+	0.687589i
$997$	−36.9698	+	26.8602i	−1.17085	+	0.850670i	−0.991110	−	0.133045i	$-0.957524\pi$
$997$	−36.9698	+	26.8602i	−1.17085	+	0.850670i	−0.179736	+	0.983715i	$0.557524\pi$
$998$	−5.41817	−	3.93653i	−0.171509	−	0.124609i
$999$	−2.58545	−	7.95720i	−0.0818000	−	0.251755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.o.148.2		8
11.2	odd	10		847.2.f.r.372.1		8
11.3	even	5		847.2.a.g.1.2	yes	2
11.4	even	5	inner	847.2.f.o.729.1		8
11.5	even	5	inner	847.2.f.o.323.1		8
11.6	odd	10		847.2.f.r.323.2		8
11.7	odd	10		847.2.f.r.729.2		8
11.8	odd	10		847.2.a.e.1.1	✓	2
11.9	even	5	inner	847.2.f.o.372.2		8
11.10	odd	2		847.2.f.r.148.1		8
33.8	even	10		7623.2.a.bs.1.2		2
33.14	odd	10		7623.2.a.bc.1.1		2
77.41	even	10		5929.2.a.k.1.1		2
77.69	odd	10		5929.2.a.p.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.e.1.1	✓	2	11.8	odd	10
847.2.a.g.1.2	yes	2	11.3	even	5
847.2.f.o.148.2		8	1.1	even	1	trivial
847.2.f.o.323.1		8	11.5	even	5	inner
847.2.f.o.372.2		8	11.9	even	5	inner
847.2.f.o.729.1		8	11.4	even	5	inner
847.2.f.r.148.1		8	11.10	odd	2
847.2.f.r.323.2		8	11.6	odd	10
847.2.f.r.372.1		8	11.2	odd	10
847.2.f.r.729.2		8	11.7	odd	10
5929.2.a.k.1.1		2	77.41	even	10
5929.2.a.p.1.2		2	77.69	odd	10
7623.2.a.bc.1.1		2	33.14	odd	10
7623.2.a.bs.1.2		2	33.8	even	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.711597 + 2.19007i) q^{2} +(1.86298 + 1.35354i) q^{3} +(-2.67200 + 1.94132i) q^{4} +(1.11418 - 3.42908i) q^{5} +(-1.63865 + 5.04324i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.711597 + 2.19007i) q^{9} +O(q^{10})\)	\(q+(0.711597 + 2.19007i) q^{2} +(1.86298 + 1.35354i) q^{3} +(-2.67200 + 1.94132i) q^{4} +(1.11418 - 3.42908i) q^{5} +(-1.63865 + 5.04324i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.42705 - 1.76336i) q^{8} +(0.711597 + 2.19007i) q^{9} +8.30278 q^{10} -7.60555 q^{12} +(2.04123 + 6.28225i) q^{13} +(1.86298 + 1.35354i) q^{14} +(6.71709 - 4.88025i) q^{15} +(0.0935628 - 0.287957i) q^{16} +(0.833488 - 2.56521i) q^{17} +(-4.29004 + 3.11689i) q^{18} +(2.42705 + 1.76336i) q^{19} +(3.67988 + 11.3255i) q^{20} +2.30278 q^{21} -2.69722 q^{23} +(-2.13479 - 6.57021i) q^{24} +(-6.47214 - 4.70228i) q^{25} +(-12.3060 + 8.94086i) q^{26} +(0.496143 - 1.52697i) q^{27} +(-1.02061 + 3.14113i) q^{28} +(-3.80013 + 2.76096i) q^{29} +(15.4679 + 11.2381i) q^{30} +(0.309017 + 0.951057i) q^{31} -5.30278 q^{32} +6.21110 q^{34} +(-1.11418 - 3.42908i) q^{35} +(-6.15302 - 4.47043i) q^{36} +(4.21587 - 3.06301i) q^{37} +(-2.13479 + 6.57021i) q^{38} +(-4.70049 + 14.4666i) q^{39} +(-8.75086 + 6.35787i) q^{40} +(-5.66312 - 4.11450i) q^{41} +(1.63865 + 5.04324i) q^{42} +1.69722 q^{43} +8.30278 q^{45} +(-1.91934 - 5.90711i) q^{46} +(1.54387 + 1.12169i) q^{47} +(0.564066 - 0.409818i) q^{48} +(0.309017 - 0.951057i) q^{49} +(5.69277 - 17.5206i) q^{50} +(5.02489 - 3.65079i) q^{51} +(-17.6500 - 12.8235i) q^{52} +(-3.98889 - 12.2765i) q^{53} +3.69722 q^{54} -3.00000 q^{56} +(2.13479 + 6.57021i) q^{57} +(-8.75086 - 6.35787i) q^{58} +(-5.41817 + 3.93653i) q^{59} +(-8.47393 + 26.0801i) q^{60} +(-1.32963 + 4.09218i) q^{61} +(-1.86298 + 1.35354i) q^{62} +(1.86298 + 1.35354i) q^{63} +(-3.96056 - 12.1894i) q^{64} +23.8167 q^{65} +8.51388 q^{67} +(2.75282 + 8.47232i) q^{68} +(-5.02489 - 3.65079i) q^{69} +(6.71709 - 4.88025i) q^{70} +(-1.32963 + 4.09218i) q^{71} +(2.13479 - 6.57021i) q^{72} +(4.04508 - 2.93893i) q^{73} +(9.70820 + 7.05342i) q^{74} +(-5.69277 - 17.5206i) q^{75} -9.90833 q^{76} -35.0278 q^{78} +(-2.56570 - 7.89641i) q^{79} +(-0.883182 - 0.641669i) q^{80} +(8.58007 - 6.23379i) q^{81} +(4.98118 - 15.3305i) q^{82} +(0.927051 - 2.85317i) q^{83} +(-6.15302 + 4.47043i) q^{84} +(-7.86767 - 5.71620i) q^{85} +(1.20774 + 3.71704i) q^{86} -10.8167 q^{87} -14.7250 q^{89} +(5.90823 + 18.1837i) q^{90} +(5.34400 + 3.88265i) q^{91} +(7.20699 - 5.23618i) q^{92} +(-0.711597 + 2.19007i) q^{93} +(-1.35796 + 4.17937i) q^{94} +(8.75086 - 6.35787i) q^{95} +(-9.87899 - 7.17751i) q^{96} +(-1.11418 - 3.42908i) q^{97} +2.30278 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + q^{3} - 3 q^{4} + 7 q^{6} + 2 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) \) 8 * q - q^2 + q^3 - 3 * q^4 + 7 * q^6 + 2 * q^7 - 6 * q^8 - q^9	\( 8 q - q^{2} + q^{3} - 3 q^{4} + 7 q^{6} + 2 q^{7} - 6 q^{8} - q^{9} + 52 q^{10} - 32 q^{12} - 6 q^{13} + q^{14} + 13 q^{15} + 3 q^{16} - 9 q^{17} - 7 q^{18} + 6 q^{19} - 13 q^{20} + 4 q^{21} - 36 q^{23} + 3 q^{24} - 16 q^{25} - 16 q^{26} + 4 q^{27} + 3 q^{28} - 13 q^{29} + 13 q^{30} - 2 q^{31} - 28 q^{32} - 8 q^{34} - 8 q^{36} - 4 q^{37} + 3 q^{38} + 16 q^{39} - 14 q^{41} - 7 q^{42} + 28 q^{43} + 52 q^{45} - 2 q^{46} - 7 q^{47} + 5 q^{48} - 2 q^{49} - 8 q^{50} - 2 q^{51} - 22 q^{52} + 15 q^{53} + 44 q^{54} - 24 q^{56} - 3 q^{57} - 17 q^{59} + 26 q^{60} + 5 q^{61} - q^{62} + q^{63} + 4 q^{64} + 104 q^{65} - 4 q^{67} - 7 q^{68} + 2 q^{69} + 13 q^{70} + 5 q^{71} - 3 q^{72} + 10 q^{73} + 24 q^{74} + 8 q^{75} - 36 q^{76} - 136 q^{78} + 13 q^{79} - 13 q^{80} + 14 q^{81} - 7 q^{82} - 6 q^{83} - 8 q^{84} + 13 q^{85} + 3 q^{86} + 12 q^{89} - 13 q^{90} + 6 q^{91} + 7 q^{92} + q^{93} + 16 q^{94} - 10 q^{96} + 4 q^{98}+O(q^{100}) \) 8 * q - q^2 + q^3 - 3 * q^4 + 7 * q^6 + 2 * q^7 - 6 * q^8 - q^9 + 52 * q^10 - 32 * q^12 - 6 * q^13 + q^14 + 13 * q^15 + 3 * q^16 - 9 * q^17 - 7 * q^18 + 6 * q^19 - 13 * q^20 + 4 * q^21 - 36 * q^23 + 3 * q^24 - 16 * q^25 - 16 * q^26 + 4 * q^27 + 3 * q^28 - 13 * q^29 + 13 * q^30 - 2 * q^31 - 28 * q^32 - 8 * q^34 - 8 * q^36 - 4 * q^37 + 3 * q^38 + 16 * q^39 - 14 * q^41 - 7 * q^42 + 28 * q^43 + 52 * q^45 - 2 * q^46 - 7 * q^47 + 5 * q^48 - 2 * q^49 - 8 * q^50 - 2 * q^51 - 22 * q^52 + 15 * q^53 + 44 * q^54 - 24 * q^56 - 3 * q^57 - 17 * q^59 + 26 * q^60 + 5 * q^61 - q^62 + q^63 + 4 * q^64 + 104 * q^65 - 4 * q^67 - 7 * q^68 + 2 * q^69 + 13 * q^70 + 5 * q^71 - 3 * q^72 + 10 * q^73 + 24 * q^74 + 8 * q^75 - 36 * q^76 - 136 * q^78 + 13 * q^79 - 13 * q^80 + 14 * q^81 - 7 * q^82 - 6 * q^83 - 8 * q^84 + 13 * q^85 + 3 * q^86 + 12 * q^89 - 13 * q^90 + 6 * q^91 + 7 * q^92 + q^93 + 16 * q^94 - 10 * q^96 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more