LMFDB - Embedded newform 399.2.j.g.58.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [399,2,Mod(58,399)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(399, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("399.58");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 13 x^{14} - 2 x^{13} + 118 x^{12} - 16 x^{11} + 534 x^{10} - 21 x^{9} + 1743 x^{8} - 101 x^{7} + \cdots + 256 $ x^16 + 13x^14 - 2x^13 + 118x^12 - 16x^11 + 534x^10 - 21x^9 + 1743x^8 - 101x^7 + 2902x^6 - 401x^5 + 3427x^4 - 294x^3 + 1076x^2 + 96x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			58.2
Root			$1.14143 - 1.97701i$ of defining polynomial
Character	$\chi$	$=$	399.58
Dual form			399.2.j.g.172.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14143 + 1.97701i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.60570 - 2.78116i) q^{4} +(1.27263 - 2.20425i) q^{5} -2.28285 q^{6} +(-2.54832 - 0.711380i) q^{7} +2.76546 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.14143 + 1.97701i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.60570 - 2.78116i) q^{4} +(1.27263 - 2.20425i) q^{5} -2.28285 q^{6} +(-2.54832 - 0.711380i) q^{7} +2.76546 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.90522 + 5.03198i) q^{10} +(-1.64814 - 2.85466i) q^{11} +(1.60570 - 2.78116i) q^{12} -4.96243 q^{13} +(4.31512 - 4.22606i) q^{14} +2.54525 q^{15} +(0.0548414 - 0.0949880i) q^{16} +(-2.79818 - 4.84659i) q^{17} +(-1.14143 - 1.97701i) q^{18} +(0.500000 - 0.866025i) q^{19} -8.17384 q^{20} +(-0.658087 - 2.56260i) q^{21} +7.52492 q^{22} +(2.90990 - 5.04010i) q^{23} +(1.38273 + 2.39496i) q^{24} +(-0.739156 - 1.28026i) q^{25} +(5.66425 - 9.81077i) q^{26} -1.00000 q^{27} +(2.11339 + 8.22955i) q^{28} -9.32850 q^{29} +(-2.90522 + 5.03198i) q^{30} +(3.21154 + 5.56255i) q^{31} +(2.89065 + 5.00676i) q^{32} +(1.64814 - 2.85466i) q^{33} +12.7757 q^{34} +(-4.81112 + 4.71182i) q^{35} +3.21141 q^{36} +(-3.85024 + 6.66882i) q^{37} +(1.14143 + 1.97701i) q^{38} +(-2.48122 - 4.29759i) q^{39} +(3.51940 - 6.09577i) q^{40} +6.13136 q^{41} +(5.81744 + 1.62397i) q^{42} -4.62835 q^{43} +(-5.29285 + 9.16748i) q^{44} +(1.27263 + 2.20425i) q^{45} +(6.64288 + 11.5058i) q^{46} +(3.15720 - 5.46842i) q^{47} +0.109683 q^{48} +(5.98788 + 3.62565i) q^{49} +3.37477 q^{50} +(2.79818 - 4.84659i) q^{51} +(7.96820 + 13.8013i) q^{52} +(4.58210 + 7.93643i) q^{53} +(1.14143 - 1.97701i) q^{54} -8.38987 q^{55} +(-7.04728 - 1.96729i) q^{56} +1.00000 q^{57} +(10.6478 - 18.4425i) q^{58} +(-4.90555 - 8.49667i) q^{59} +(-4.08692 - 7.07875i) q^{60} +(0.907947 - 1.57261i) q^{61} -14.6629 q^{62} +(1.89023 - 1.85122i) q^{63} -12.9785 q^{64} +(-6.31533 + 10.9385i) q^{65} +(3.76246 + 6.51677i) q^{66} +(-1.68164 - 2.91269i) q^{67} +(-8.98609 + 15.5644i) q^{68} +5.81981 q^{69} +(-3.82377 - 14.8898i) q^{70} +2.01667 q^{71} +(-1.38273 + 2.39496i) q^{72} +(2.36284 + 4.09256i) q^{73} +(-8.78953 - 15.2239i) q^{74} +(0.739156 - 1.28026i) q^{75} -3.21141 q^{76} +(2.16924 + 8.44705i) q^{77} +11.3285 q^{78} +(6.44927 - 11.1705i) q^{79} +(-0.139585 - 0.241769i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.99849 + 12.1217i) q^{82} -0.743338 q^{83} +(-6.07031 + 5.94502i) q^{84} -14.2442 q^{85} +(5.28291 - 9.15027i) q^{86} +(-4.66425 - 8.07871i) q^{87} +(-4.55787 - 7.89445i) q^{88} +(5.70242 - 9.87688i) q^{89} -5.81043 q^{90} +(12.6459 + 3.53018i) q^{91} -18.6898 q^{92} +(-3.21154 + 5.56255i) q^{93} +(7.20741 + 12.4836i) q^{94} +(-1.27263 - 2.20425i) q^{95} +(-2.89065 + 5.00676i) q^{96} -16.9210 q^{97} +(-14.0026 + 7.69967i) q^{98} +3.29628 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 10 q^{4} + 5 q^{5} + q^{7} - 6 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 - 10 * q^4 + 5 * q^5 + q^7 - 6 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} - 10 q^{4} + 5 q^{5} + q^{7} - 6 q^{8} - 8 q^{9} + 3 q^{10} + 7 q^{11} + 10 q^{12} - 12 q^{13} - 12 q^{14} + 10 q^{15} - 10 q^{16} + 8 q^{19} - 32 q^{20} - q^{21} + 36 q^{22} + 9 q^{23} - 3 q^{24} - 15 q^{25} + 12 q^{26} - 16 q^{27} - 40 q^{28} + 8 q^{29} - 3 q^{30} + 11 q^{31} + 26 q^{32} - 7 q^{33} - 32 q^{34} - 7 q^{35} + 20 q^{36} - 17 q^{37} - 6 q^{39} + 3 q^{40} - 34 q^{41} - 9 q^{42} + 16 q^{43} + 31 q^{44} + 5 q^{45} - q^{46} + 29 q^{47} - 20 q^{48} + q^{49} + 60 q^{50} + 25 q^{52} + 6 q^{53} - 42 q^{55} - 54 q^{56} + 16 q^{57} + 37 q^{58} + 7 q^{59} - 16 q^{60} + 2 q^{61} - 78 q^{62} - 2 q^{63} + 58 q^{64} + 13 q^{65} + 18 q^{66} - 13 q^{67} - 14 q^{68} + 18 q^{69} - 81 q^{70} + 36 q^{71} + 3 q^{72} + 20 q^{73} + 26 q^{74} + 15 q^{75} - 20 q^{76} + 19 q^{77} + 24 q^{78} + 3 q^{79} + 35 q^{80} - 8 q^{81} + 5 q^{82} - 72 q^{83} - 29 q^{84} + 10 q^{85} + 51 q^{86} + 4 q^{87} - 53 q^{88} + q^{89} - 6 q^{90} - 9 q^{91} + 30 q^{92} - 11 q^{93} + 30 q^{94} - 5 q^{95} - 26 q^{96} + 6 q^{97} - 75 q^{98} - 14 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 - 10 * q^4 + 5 * q^5 + q^7 - 6 * q^8 - 8 * q^9 + 3 * q^10 + 7 * q^11 + 10 * q^12 - 12 * q^13 - 12 * q^14 + 10 * q^15 - 10 * q^16 + 8 * q^19 - 32 * q^20 - q^21 + 36 * q^22 + 9 * q^23 - 3 * q^24 - 15 * q^25 + 12 * q^26 - 16 * q^27 - 40 * q^28 + 8 * q^29 - 3 * q^30 + 11 * q^31 + 26 * q^32 - 7 * q^33 - 32 * q^34 - 7 * q^35 + 20 * q^36 - 17 * q^37 - 6 * q^39 + 3 * q^40 - 34 * q^41 - 9 * q^42 + 16 * q^43 + 31 * q^44 + 5 * q^45 - q^46 + 29 * q^47 - 20 * q^48 + q^49 + 60 * q^50 + 25 * q^52 + 6 * q^53 - 42 * q^55 - 54 * q^56 + 16 * q^57 + 37 * q^58 + 7 * q^59 - 16 * q^60 + 2 * q^61 - 78 * q^62 - 2 * q^63 + 58 * q^64 + 13 * q^65 + 18 * q^66 - 13 * q^67 - 14 * q^68 + 18 * q^69 - 81 * q^70 + 36 * q^71 + 3 * q^72 + 20 * q^73 + 26 * q^74 + 15 * q^75 - 20 * q^76 + 19 * q^77 + 24 * q^78 + 3 * q^79 + 35 * q^80 - 8 * q^81 + 5 * q^82 - 72 * q^83 - 29 * q^84 + 10 * q^85 + 51 * q^86 + 4 * q^87 - 53 * q^88 + q^89 - 6 * q^90 - 9 * q^91 + 30 * q^92 - 11 * q^93 + 30 * q^94 - 5 * q^95 - 26 * q^96 + 6 * q^97 - 75 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.14143	+	1.97701i	−0.807110	+	1.39795i	0.107748	+	0.994178i	$0.465636\pi$
$2$	−1.14143	+	1.97701i	−0.807110	+	1.39795i	−0.914858	+	0.403776i	$0.867697\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.60570	−	2.78116i	−0.802852	−	1.39058i
$5$	1.27263	−	2.20425i	0.569136	−	0.985772i	−0.427516	−	0.904008i	$-0.640611\pi$
$5$	1.27263	−	2.20425i	0.569136	−	0.985772i	0.996652	−	0.0817643i	$-0.0260555\pi$
$6$	−2.28285			−0.931970
$7$	−2.54832	−	0.711380i	−0.963175	−	0.268876i
$7$	−2.54832	−	0.711380i	−0.963175	−	0.268876i
$8$	2.76546			0.977737
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	2.90522	+	5.03198i	0.918710	+	1.59125i
$11$	−1.64814	−	2.85466i	−0.496933	−	0.860713i	0.503061	−	0.864251i	$-0.332207\pi$
$11$	−1.64814	−	2.85466i	−0.496933	−	0.860713i	−0.999994	+	0.00353776i	$0.998874\pi$
$12$	1.60570	−	2.78116i	0.463527	−	0.802852i
$13$	−4.96243			−1.37633			−0.688166	−	0.725553i	$-0.741584\pi$
$13$	−4.96243			−1.37633			−0.688166	+	0.725553i	$0.741584\pi$
$14$	4.31512	−	4.22606i	1.15326	−	1.12946i
$15$	2.54525			0.657181
$16$	0.0548414	−	0.0949880i	0.0137103	−	0.0237470i
$17$	−2.79818	−	4.84659i	−0.678658	−	1.17547i	−0.975385	−	0.220508i	$-0.929228\pi$
$17$	−2.79818	−	4.84659i	−0.678658	−	1.17547i	0.296727	−	0.954962i	$-0.404105\pi$
$18$	−1.14143	−	1.97701i	−0.269037	−	0.465985i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i
$20$	−8.17384			−1.82773
$21$	−0.658087	−	2.56260i	−0.143606	−	0.559205i
$22$	7.52492			1.60432
$23$	2.90990	−	5.04010i	0.606757	−	1.05093i	−0.385014	−	0.922911i	$-0.625803\pi$
$23$	2.90990	−	5.04010i	0.606757	−	1.05093i	0.991771	−	0.128023i	$-0.0408632\pi$
$24$	1.38273	+	2.39496i	0.282248	+	0.488869i
$25$	−0.739156	−	1.28026i	−0.147831	−	0.256051i
$26$	5.66425	−	9.81077i	1.11085	−	1.92405i
$27$	−1.00000			−0.192450
$28$	2.11339	+	8.22955i	0.399392	+	1.55524i
$29$	−9.32850			−1.73226			−0.866129	−	0.499820i	$-0.833399\pi$
$29$	−9.32850			−1.73226			−0.866129	+	0.499820i	$0.833399\pi$
$30$	−2.90522	+	5.03198i	−0.530417	+	0.918710i
$31$	3.21154	+	5.56255i	0.576809	+	0.999063i	0.995842	+	0.0910919i	$0.0290357\pi$
$31$	3.21154	+	5.56255i	0.576809	+	0.999063i	−0.419033	+	0.907971i	$0.637631\pi$
$32$	2.89065	+	5.00676i	0.511000	+	0.885078i
$33$	1.64814	−	2.85466i	0.286904	−	0.496933i
$34$	12.7757			2.19101
$35$	−4.81112	+	4.71182i	−0.813228	+	0.796444i
$36$	3.21141			0.535234
$37$	−3.85024	+	6.66882i	−0.632976	+	1.09635i	0.353964	+	0.935259i	$0.384833\pi$
$37$	−3.85024	+	6.66882i	−0.632976	+	1.09635i	−0.986940	+	0.161088i	$0.948500\pi$
$38$	1.14143	+	1.97701i	0.185164	+	0.320713i
$39$	−2.48122	−	4.29759i	−0.397313	−	0.688166i
$40$	3.51940	−	6.09577i	0.556465	−	0.963826i
$41$	6.13136			0.957558			0.478779	−	0.877936i	$-0.341080\pi$
$41$	6.13136			0.957558			0.478779	+	0.877936i	$0.341080\pi$
$42$	5.81744	+	1.62397i	0.897650	+	0.250585i
$43$	−4.62835			−0.705816			−0.352908	−	0.935658i	$-0.614807\pi$
$43$	−4.62835			−0.705816			−0.352908	+	0.935658i	$0.614807\pi$
$44$	−5.29285	+	9.16748i	−0.797927	+	1.38205i
$45$	1.27263	+	2.20425i	0.189712	+	0.328591i
$46$	6.64288	+	11.5058i	0.979439	+	1.69644i
$47$	3.15720	−	5.46842i	0.460524	−	0.797652i	−0.538463	−	0.842649i	$-0.680995\pi$
$47$	3.15720	−	5.46842i	0.460524	−	0.797652i	0.998987	+	0.0449977i	$0.0143281\pi$
$48$	0.109683			0.0158313
$49$	5.98788	+	3.62565i	0.855411	+	0.517950i
$50$	3.37477			0.477264
$51$	2.79818	−	4.84659i	0.391824	−	0.678658i
$52$	7.96820	+	13.8013i	1.10499	+	1.91390i
$53$	4.58210	+	7.93643i	0.629400	+	1.09015i	0.987672	+	0.156535i	$0.0500325\pi$
$53$	4.58210	+	7.93643i	0.629400	+	1.09015i	−0.358273	+	0.933617i	$0.616634\pi$
$54$	1.14143	−	1.97701i	0.155328	−	0.269037i
$55$	−8.38987			−1.13129
$56$	−7.04728	−	1.96729i	−0.941732	−	0.262890i
$57$	1.00000			0.132453
$58$	10.6478	−	18.4425i	1.39812	−	2.42162i
$59$	−4.90555	−	8.49667i	−0.638649	−	1.10617i	−0.985730	−	0.168337i	$-0.946160\pi$
$59$	−4.90555	−	8.49667i	−0.638649	−	1.10617i	0.347081	−	0.937835i	$-0.387173\pi$
$60$	−4.08692	−	7.07875i	−0.527619	−	0.913863i
$61$	0.907947	−	1.57261i	0.116251	−	0.201352i	−0.802028	−	0.597286i	$-0.796246\pi$
$61$	0.907947	−	1.57261i	0.116251	−	0.201352i	0.918279	+	0.395934i	$0.129579\pi$
$62$	−14.6629			−1.86219
$63$	1.89023	−	1.85122i	0.238147	−	0.233232i
$64$	−12.9785			−1.62231
$65$	−6.31533	+	10.9385i	−0.783320	+	1.35675i
$66$	3.76246	+	6.51677i	0.463127	+	0.802159i
$67$	−1.68164	−	2.91269i	−0.205445	−	0.355842i	0.744829	−	0.667255i	$-0.232531\pi$
$67$	−1.68164	−	2.91269i	−0.205445	−	0.355842i	−0.950275	+	0.311413i	$0.899198\pi$
$68$	−8.98609	+	15.5644i	−1.08972	+	1.88746i
$69$	5.81981			0.700623
$70$	−3.82377	−	14.8898i	−0.457028	−	1.77967i
$71$	2.01667			0.239335			0.119667	−	0.992814i	$-0.461817\pi$
$71$	2.01667			0.239335			0.119667	+	0.992814i	$0.461817\pi$
$72$	−1.38273	+	2.39496i	−0.162956	+	0.282248i
$73$	2.36284	+	4.09256i	0.276550	+	0.478998i	0.970525	−	0.241001i	$-0.0774757\pi$
$73$	2.36284	+	4.09256i	0.276550	+	0.478998i	−0.693975	+	0.719999i	$0.744142\pi$
$74$	−8.78953	−	15.2239i	−1.02176	−	1.76974i
$75$	0.739156	−	1.28026i	0.0853504	−	0.147831i
$76$	−3.21141			−0.368374
$77$	2.16924	+	8.44705i	0.247208	+	0.962631i
$78$	11.3285			1.28270
$79$	6.44927	−	11.1705i	0.725599	−	1.25677i	−0.233128	−	0.972446i	$-0.574896\pi$
$79$	6.44927	−	11.1705i	0.725599	−	1.25677i	0.958727	−	0.284329i	$-0.0917707\pi$
$80$	−0.139585	−	0.241769i	−0.0156061	−	0.0270305i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.99849	+	12.1217i	−0.772854	+	1.33862i
$83$	−0.743338			−0.0815919			−0.0407960	−	0.999167i	$-0.512989\pi$
$83$	−0.743338			−0.0815919			−0.0407960	+	0.999167i	$0.512989\pi$
$84$	−6.07031	+	5.94502i	−0.662325	+	0.648655i
$85$	−14.2442			−1.54500
$86$	5.28291	−	9.15027i	0.569671	−	0.986699i
$87$	−4.66425	−	8.07871i	−0.500060	−	0.866129i
$88$	−4.55787	−	7.89445i	−0.485870	−	0.841552i
$89$	5.70242	−	9.87688i	0.604455	−	1.04695i	−0.387682	−	0.921793i	$-0.626724\pi$
$89$	5.70242	−	9.87688i	0.604455	−	1.04695i	0.992137	−	0.125154i	$-0.0399424\pi$
$90$	−5.81043			−0.612473
$91$	12.6459	+	3.53018i	1.32565	+	0.370063i
$92$	−18.6898			−1.94854
$93$	−3.21154	+	5.56255i	−0.333021	+	0.576809i
$94$	7.20741	+	12.4836i	0.743387	+	1.28758i
$95$	−1.27263	−	2.20425i	−0.130569	−	0.226152i
$96$	−2.89065	+	5.00676i	−0.295026	+	0.511000i
$97$	−16.9210			−1.71807			−0.859035	−	0.511918i	$-0.828935\pi$
$97$	−16.9210			−1.71807			−0.859035	+	0.511918i	$0.828935\pi$
$98$	−14.0026	+	7.69967i	−1.41448	+	0.777784i
$99$	3.29628			0.331289
$100$	−2.37373	+	4.11142i	−0.237373	+	0.411142i
$101$	5.42936	+	9.40393i	0.540242	+	0.935726i	0.998890	+	0.0471079i	$0.0150004\pi$
$101$	5.42936	+	9.40393i	0.540242	+	0.935726i	−0.458648	+	0.888618i	$0.651666\pi$
$102$	6.38783	+	11.0640i	0.632489	+	1.09550i
$103$	−2.08791	+	3.61637i	−0.205728	+	0.356331i	−0.950364	−	0.311139i	$-0.899290\pi$
$103$	−2.08791	+	3.61637i	−0.205728	+	0.356331i	0.744637	+	0.667470i	$0.232623\pi$
$104$	−13.7234			−1.34569
$105$	−6.48612	−	1.81064i	−0.632981	−	0.176700i
$106$	−20.9205			−2.03198
$107$	1.82373	−	3.15880i	0.176307	−	0.305373i	−0.764306	−	0.644854i	$-0.776918\pi$
$107$	1.82373	−	3.15880i	0.176307	−	0.305373i	0.940613	+	0.339481i	$0.110252\pi$
$108$	1.60570	+	2.78116i	0.154509	+	0.267617i
$109$	−7.08585	−	12.2731i	−0.678701	−	1.17555i	−0.975372	−	0.220566i	$-0.929210\pi$
$109$	−7.08585	−	12.2731i	−0.678701	−	1.17555i	0.296671	−	0.954980i	$-0.404124\pi$
$110$	9.57641	−	16.5868i	0.913075	−	1.58149i
$111$	−7.70048			−0.730898
$112$	−0.207326	+	0.203047i	−0.0195905	+	0.0191861i
$113$	−9.20761			−0.866179			−0.433089	−	0.901351i	$-0.642577\pi$
$113$	−9.20761			−0.866179			−0.433089	+	0.901351i	$0.642577\pi$
$114$	−1.14143	+	1.97701i	−0.106904	+	0.185164i
$115$	−7.40644	−	12.8283i	−0.690654	−	1.19625i
$116$	14.9788	+	25.9440i	1.39075	+	2.40884i
$117$	2.48122	−	4.29759i	0.229389	−	0.397313i
$118$	22.3973			2.06184
$119$	3.68290	+	14.3412i	0.337610	+	1.31466i
$120$	7.03879			0.642551
$121$	0.0672653	−	0.116507i	0.00611502	−	0.0105915i
$122$	2.07271	+	3.59004i	0.187654	+	0.325027i
$123$	3.06568	+	5.30991i	0.276423	+	0.478779i
$124$	10.3136	−	17.8636i	0.926184	−	1.60420i
$125$	8.96359			0.801728
$126$	1.50232	+	5.85003i	0.133837	+	0.521162i
$127$	−5.26815			−0.467472			−0.233736	−	0.972300i	$-0.575095\pi$
$127$	−5.26815			−0.467472			−0.233736	+	0.972300i	$0.575095\pi$
$128$	9.03267	−	15.6451i	0.798383	−	1.38284i
$129$	−2.31417	−	4.00826i	−0.203752	−	0.352908i
$130$	−14.4169	−	24.9709i	−1.26445	−	2.19009i
$131$	3.96817	−	6.87308i	0.346701	−	0.600503i	−0.638960	−	0.769240i	$-0.720635\pi$
$131$	3.96817	−	6.87308i	0.346701	−	0.600503i	0.985661	+	0.168736i	$0.0539686\pi$
$132$	−10.5857			−0.921367
$133$	−1.89023	+	1.85122i	−0.163904	+	0.160521i
$134$	7.67788			0.663268
$135$	−1.27263	+	2.20425i	−0.109530	+	0.189712i
$136$	−7.73825	−	13.4030i	−0.663550	−	1.14930i
$137$	−4.09826	−	7.09839i	−0.350138	−	0.606456i	0.636136	−	0.771577i	$-0.280532\pi$
$137$	−4.09826	−	7.09839i	−0.350138	−	0.606456i	−0.986273	+	0.165121i	$0.947199\pi$
$138$	−6.64288	+	11.5058i	−0.565479	+	0.979439i
$139$	9.20860			0.781063			0.390531	−	0.920590i	$-0.372291\pi$
$139$	9.20860			0.781063			0.390531	+	0.920590i	$0.372291\pi$
$140$	20.8296	+	5.81470i	1.76042	+	0.491432i
$141$	6.31439			0.531768
$142$	−2.30188	+	3.98697i	−0.193169	+	0.334579i
$143$	8.17879	+	14.1661i	0.683945	+	1.18463i
$144$	0.0548414	+	0.0949880i	0.00457011	+	0.00791567i
$145$	−11.8717	+	20.5624i	−0.985890	+	1.70761i
$146$	−10.7880			−0.892823
$147$	−0.145964	+	6.99848i	−0.0120389	+	0.577225i
$148$	24.7294			2.03274
$149$	−2.39764	+	4.15284i	−0.196423	+	0.340214i	−0.947366	−	0.320153i	$-0.896266\pi$
$149$	−2.39764	+	4.15284i	−0.196423	+	0.340214i	0.750943	+	0.660367i	$0.229599\pi$
$150$	1.68738	+	2.92263i	0.137774	+	0.238632i
$151$	−3.83040	−	6.63446i	−0.311714	−	0.539904i	0.667020	−	0.745040i	$-0.267570\pi$
$151$	−3.83040	−	6.63446i	−0.311714	−	0.539904i	−0.978734	+	0.205136i	$0.934236\pi$
$152$	1.38273	−	2.39496i	0.112154	−	0.194257i
$153$	5.59636			0.452439
$154$	−19.1759	−	5.35307i	−1.54524	−	0.431363i
$155$	16.3483			1.31313
$156$	−7.96820	+	13.8013i	−0.637966	+	1.10499i
$157$	2.46803	+	4.27475i	0.196970	+	0.341162i	0.947545	−	0.319624i	$-0.103556\pi$
$157$	2.46803	+	4.27475i	0.196970	+	0.341162i	−0.750574	+	0.660786i	$0.770223\pi$
$158$	14.7227	+	25.5005i	1.17128	+	2.02871i
$159$	−4.58210	+	7.93643i	−0.363384	+	0.629400i
$160$	14.7149			1.16331
$161$	−11.0008	+	10.7737i	−0.866984	+	0.849090i
$162$	2.28285			0.179358
$163$	−1.27555	+	2.20932i	−0.0999090	+	0.173047i	−0.911647	−	0.410975i	$-0.865189\pi$
$163$	−1.27555	+	2.20932i	−0.0999090	+	0.173047i	0.811738	+	0.584022i	$0.198522\pi$
$164$	−9.84515	−	17.0523i	−0.768777	−	1.33156i
$165$	−4.19493	−	7.26584i	−0.326575	−	0.565645i
$166$	0.848465	−	1.46958i	0.0658536	−	0.114062i
$167$	−1.94706			−0.150668			−0.0753340	−	0.997158i	$-0.524002\pi$
$167$	−1.94706			−0.150668			−0.0753340	+	0.997158i	$0.524002\pi$
$168$	−1.81991	−	7.08677i	−0.140409	−	0.546756i
$169$	11.6258			0.894289
$170$	16.2586	−	28.1608i	1.24698	−	2.15983i
$171$	0.500000	+	0.866025i	0.0382360	+	0.0662266i
$172$	7.43175	+	12.8722i	0.566665	+	0.981493i
$173$	−7.53471	+	13.0505i	−0.572853	+	0.992211i	0.423418	+	0.905935i	$0.360830\pi$
$173$	−7.53471	+	13.0505i	−0.572853	+	0.992211i	−0.996271	+	0.0862768i	$0.972503\pi$
$174$	21.2956			1.61441
$175$	0.972859	+	3.78832i	0.0735412	+	0.286370i
$176$	−0.361545			−0.0272525
$177$	4.90555	−	8.49667i	0.368724	−	0.638649i
$178$	13.0178	+	22.5474i	0.975723	+	1.69000i
$179$	−11.6786	−	20.2280i	−0.872901	−	1.51191i	−0.858982	−	0.512006i	$-0.828902\pi$
$179$	−11.6786	−	20.2280i	−0.872901	−	1.51191i	−0.0139195	−	0.999903i	$-0.504431\pi$
$180$	4.08692	−	7.07875i	0.304621	−	0.527619i
$181$	21.8279			1.62246			0.811228	−	0.584730i	$-0.198800\pi$
$181$	21.8279			1.62246			0.811228	+	0.584730i	$0.198800\pi$
$182$	−21.4135	+	20.9715i	−1.58727	+	1.55451i
$183$	1.81589			0.134235
$184$	8.04722	−	13.9382i	0.593249	−	1.02754i
$185$	9.79984	+	16.9738i	0.720499	+	1.24794i
$186$	−7.33146	−	12.6985i	−0.537569	−	0.931096i
$187$	−9.22359	+	15.9757i	−0.674496	+	1.16826i
$188$	−20.2781			−1.47893
$189$	2.54832	+	0.711380i	0.185363	+	0.0517453i
$190$	5.81043			0.421533
$191$	5.36754	−	9.29685i	0.388381	−	0.672696i	−0.603851	−	0.797097i	$-0.706368\pi$
$191$	5.36754	−	9.29685i	0.388381	−	0.672696i	0.992232	+	0.124401i	$0.0397010\pi$
$192$	−6.48925	−	11.2397i	−0.468321	−	0.811156i
$193$	−9.01029	−	15.6063i	−0.648575	−	1.12336i	−0.983463	−	0.181107i	$-0.942032\pi$
$193$	−9.01029	−	15.6063i	−0.648575	−	1.12336i	0.334889	−	0.942258i	$-0.391301\pi$
$194$	19.3141	−	33.4530i	1.38667	−	2.40178i
$195$	−12.6307			−0.904500
$196$	0.468750	−	22.4750i	0.0334821	−	1.60535i
$197$	−3.39251			−0.241706			−0.120853	−	0.992670i	$-0.538563\pi$
$197$	−3.39251			−0.241706			−0.120853	+	0.992670i	$0.538563\pi$
$198$	−3.76246	+	6.51677i	−0.267386	+	0.463127i
$199$	−0.0554566	−	0.0960536i	−0.00393121	−	0.00680906i	0.864053	−	0.503401i	$-0.167918\pi$
$199$	−0.0554566	−	0.0960536i	−0.00393121	−	0.00680906i	−0.867984	+	0.496592i	$0.834585\pi$
$200$	−2.04411	−	3.54049i	−0.144540	−	0.250351i
$201$	1.68164	−	2.91269i	0.118614	−	0.205445i
$202$	−24.7888			−1.74414
$203$	23.7720	+	6.63610i	1.66847	+	0.465763i
$204$	−17.9722			−1.25830
$205$	7.80293	−	13.5151i	0.544980	−	0.943934i
$206$	−4.76639	−	8.25562i	−0.332090	−	0.575197i
$207$	2.90990	+	5.04010i	0.202252	+	0.350311i
$208$	−0.272147	+	0.471372i	−0.0188700	+	0.0326838i
$209$	−3.29628			−0.228009
$210$	10.9831	−	10.7564i	0.757904	−	0.742262i
$211$	11.6596			0.802681			0.401340	−	0.915929i	$-0.368544\pi$
$211$	11.6596			0.802681			0.401340	+	0.915929i	$0.368544\pi$
$212$	14.7150	−	25.4871i	1.01063	−	1.75046i
$213$	1.00834	+	1.74649i	0.0690900	+	0.119667i
$214$	4.16331	+	7.21106i	0.284598	+	0.492938i
$215$	−5.89015	+	10.2020i	−0.401705	+	0.695774i
$216$	−2.76546			−0.188166
$217$	−4.22695	−	16.4598i	−0.286944	−	1.11736i
$218$	32.3519			2.19115
$219$	−2.36284	+	4.09256i	−0.159666	+	0.276550i
$220$	13.4716	+	23.3336i	0.908258	+	1.57315i
$221$	13.8858	+	24.0509i	0.934059	+	1.61784i
$222$	8.78953	−	15.2239i	0.589914	−	1.02176i
$223$	13.8313			0.926214			0.463107	−	0.886302i	$-0.346735\pi$
$223$	13.8313			0.926214			0.463107	+	0.886302i	$0.346735\pi$
$224$	−3.80461	−	14.8152i	−0.254206	−	0.989881i
$225$	1.47831			0.0985541
$226$	10.5098	−	18.2035i	0.699101	−	1.21088i
$227$	−6.89519	−	11.9428i	−0.457650	−	0.792673i	0.541187	−	0.840903i	$-0.317975\pi$
$227$	−6.89519	−	11.9428i	−0.457650	−	0.792673i	−0.998836	+	0.0482300i	$0.984642\pi$
$228$	−1.60570	−	2.78116i	−0.106340	−	0.184187i
$229$	−6.98222	+	12.0936i	−0.461398	+	0.799165i	−0.999031	−	0.0440139i	$-0.985985\pi$
$229$	−6.98222	+	12.0936i	−0.461398	+	0.799165i	0.537633	+	0.843179i	$0.319319\pi$
$230$	33.8156			2.22973
$231$	−6.23074	+	6.10214i	−0.409953	+	0.401492i
$232$	−25.7976			−1.69369
$233$	8.49188	−	14.7084i	0.556322	−	0.963578i	−0.441478	−	0.897272i	$-0.645546\pi$
$233$	8.49188	−	14.7084i	0.556322	−	0.963578i	0.997799	−	0.0663053i	$-0.0211211\pi$
$234$	5.66425	+	9.81077i	0.370283	+	0.641350i
$235$	−8.03586	−	13.9185i	−0.524202	−	0.907944i
$236$	−15.7537	+	27.2862i	−1.02548	+	1.77618i
$237$	12.8985			0.837850
$238$	−32.5565	−	9.08834i	−2.11032	−	0.589110i
$239$	2.74352			0.177463			0.0887317	−	0.996056i	$-0.471719\pi$
$239$	2.74352			0.177463			0.0887317	+	0.996056i	$0.471719\pi$
$240$	0.139585	−	0.241769i	0.00901018	−	0.0156061i
$241$	−4.96607	−	8.60149i	−0.319893	−	0.554071i	0.660573	−	0.750762i	$-0.270314\pi$
$241$	−4.96607	−	8.60149i	−0.319893	−	0.554071i	−0.980465	+	0.196692i	$0.936980\pi$
$242$	0.153557	+	0.265968i	0.00987099	+	0.0170971i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−5.83157			−0.373328
$245$	15.6122	−	8.58471i	0.997425	−	0.548457i
$246$	−13.9970			−0.892415
$247$	−2.48122	+	4.29759i	−0.157876	+	0.273449i
$248$	8.88138	+	15.3830i	0.563968	+	0.976821i
$249$	−0.371669	−	0.643750i	−0.0235536	−	0.0407960i
$250$	−10.2313	+	17.7211i	−0.647082	+	1.12078i
$251$	0.0936224			0.00590940			0.00295470	−	0.999996i	$-0.499059\pi$
$251$	0.0936224			0.00590940			0.00295470	+	0.999996i	$0.499059\pi$
$252$	−8.18369	−	2.28453i	−0.515524	−	0.143912i
$253$	−19.1837			−1.20607
$254$	6.01319	−	10.4152i	0.377301	−	0.653505i
$255$	−7.12208	−	12.3358i	−0.446002	−	0.772498i
$256$	7.64175	+	13.2359i	0.477609	+	0.827244i
$257$	−5.33246	+	9.23609i	−0.332630	+	0.576132i	−0.983027	−	0.183463i	$-0.941269\pi$
$257$	−5.33246	+	9.23609i	−0.332630	+	0.576132i	0.650397	+	0.759595i	$0.274603\pi$
$258$	10.5658			0.657799
$259$	14.5557	−	14.2553i	0.904448	−	0.885781i
$260$	40.5621			2.51556
$261$	4.66425	−	8.07871i	0.288710	−	0.500060i
$262$	9.05874	+	15.6902i	0.559651	+	0.969344i
$263$	−1.35596	−	2.34860i	−0.0836124	−	0.144821i	0.821187	−	0.570660i	$-0.193312\pi$
$263$	−1.35596	−	2.34860i	−0.0836124	−	0.144821i	−0.904799	+	0.425839i	$0.859979\pi$
$264$	4.55787	−	7.89445i	0.280517	−	0.485870i
$265$	23.3252			1.43286
$266$	−1.50232	−	5.85003i	−0.0921129	−	0.358689i
$267$	11.4048			0.697965
$268$	−5.40044	+	9.35383i	−0.329884	+	0.571376i
$269$	0.382993	+	0.663364i	0.0233515	+	0.0404460i	0.877465	−	0.479641i	$-0.159233\pi$
$269$	0.382993	+	0.663364i	0.0233515	+	0.0404460i	−0.854113	+	0.520087i	$0.825900\pi$
$270$	−2.90522	−	5.03198i	−0.176806	−	0.306237i
$271$	−2.80999	+	4.86704i	−0.170695	+	0.295652i	−0.938663	−	0.344836i	$-0.887934\pi$
$271$	−2.80999	+	4.86704i	−0.170695	+	0.295652i	0.767968	+	0.640488i	$0.221268\pi$
$272$	−0.613824			−0.0372186
$273$	3.26572	+	12.7167i	0.197650	+	0.769652i
$274$	18.7114			1.13040
$275$	−2.43647	+	4.22008i	−0.146924	+	0.254481i
$276$	−9.34488	−	16.1858i	−0.562496	−	0.974272i
$277$	14.1778	+	24.5567i	0.851863	+	1.47547i	0.879525	+	0.475852i	$0.157860\pi$
$277$	14.1778	+	24.5567i	0.851863	+	1.47547i	−0.0276623	+	0.999617i	$0.508806\pi$
$278$	−10.5109	+	18.2055i	−0.630403	+	1.09189i
$279$	−6.42307			−0.384539
$280$	−13.3050	+	13.0304i	−0.795123	+	0.778713i
$281$	−30.7742			−1.83583			−0.917916	−	0.396774i	$-0.870130\pi$
$281$	−30.7742			−1.83583			−0.917916	+	0.396774i	$0.870130\pi$
$282$	−7.20741	+	12.4836i	−0.429195	+	0.743387i
$283$	7.70015	+	13.3370i	0.457726	+	0.792805i	0.998840	−	0.0481441i	$-0.0153307\pi$
$283$	7.70015	+	13.3370i	0.457726	+	0.792805i	−0.541114	+	0.840949i	$0.681997\pi$
$284$	−3.23818	−	5.60869i	−0.192150	−	0.332814i
$285$	1.27263	−	2.20425i	0.0753839	−	0.130569i
$286$	−37.3419			−2.20807
$287$	−15.6247	−	4.36173i	−0.922295	−	0.257465i
$288$	−5.78131			−0.340667
$289$	−7.15963	+	12.4008i	−0.421155	+	0.729461i
$290$	−27.1013	−	46.9408i	−1.59144	−	2.75646i
$291$	−8.46051	−	14.6540i	−0.495964	−	0.859035i
$292$	7.58804	−	13.1429i	0.444056	−	0.769128i
$293$	−3.63257			−0.212217			−0.106109	−	0.994355i	$-0.533839\pi$
$293$	−3.63257			−0.212217			−0.106109	+	0.994355i	$0.533839\pi$
$294$	−13.6694	−	8.27681i	−0.797217	−	0.482713i
$295$	−24.9717			−1.45391
$296$	−10.6477	+	18.4423i	−0.618884	+	1.07194i
$297$	1.64814	+	2.85466i	0.0956348	+	0.165644i
$298$	−5.47346	−	9.48031i	−0.317069	−	0.549180i
$299$	−14.4402	+	25.0112i	−0.835099	+	1.44643i
$300$	−4.74746			−0.274095
$301$	11.7945	+	3.29251i	0.679824	+	0.189777i
$302$	17.4885			1.00635
$303$	−5.42936	+	9.40393i	−0.311909	+	0.540242i
$304$	−0.0548414	−	0.0949880i	−0.00314537	−	0.00544794i
$305$	−2.31096	−	4.00269i	−0.132325	−	0.229193i
$306$	−6.38783	+	11.0640i	−0.365168	+	0.632489i
$307$	20.4805			1.16888			0.584442	−	0.811436i	$-0.301314\pi$
$307$	20.4805			1.16888			0.584442	+	0.811436i	$0.301314\pi$
$308$	20.0094	−	19.5965i	1.14014	−	1.11661i
$309$	−4.17582			−0.237554
$310$	−18.6604	+	32.3208i	−1.05984	+	1.83570i
$311$	11.4343	+	19.8048i	0.648382	+	1.12303i	0.983509	+	0.180857i	$0.0578872\pi$
$311$	11.4343	+	19.8048i	0.648382	+	1.12303i	−0.335128	+	0.942173i	$0.608779\pi$
$312$	−6.86170	−	11.8848i	−0.388468	−	0.672846i
$313$	10.7262	−	18.5783i	0.606279	−	1.05011i	−0.385569	−	0.922679i	$-0.625995\pi$
$313$	10.7262	−	18.5783i	0.606279	−	1.05011i	0.991848	−	0.127427i	$-0.0406720\pi$
$314$	−11.2683			−0.635906
$315$	−1.67500	−	6.52247i	−0.0943755	−	0.367499i
$316$	−41.4224			−2.33019
$317$	−11.3236	+	19.6130i	−0.635996	+	1.10158i	0.350307	+	0.936635i	$0.386077\pi$
$317$	−11.3236	+	19.6130i	−0.635996	+	1.10158i	−0.986303	+	0.164942i	$0.947256\pi$
$318$	−10.4602	−	18.1177i	−0.586582	−	1.01599i
$319$	15.3747	+	26.6297i	0.860816	+	1.49098i
$320$	−16.5168	+	28.6079i	−0.923316	+	1.59923i
$321$	3.64747			0.203582
$322$	−8.74319	−	34.0461i	−0.487239	−	1.89731i
$323$	−5.59636			−0.311390
$324$	−1.60570	+	2.78116i	−0.0892057	+	0.154509i
$325$	3.66801	+	6.35319i	0.203465	+	0.352411i
$326$	−2.91190	−	5.04355i	−0.161275	−	0.279337i
$327$	7.08585	−	12.2731i	0.391848	−	0.678701i
$328$	16.9560			0.936240
$329$	−11.9357	+	11.6893i	−0.658035	+	0.644454i
$330$	19.1528			1.05433
$331$	−14.3534	+	24.8609i	−0.788937	+	1.36648i	0.137682	+	0.990476i	$0.456035\pi$
$331$	−14.3534	+	24.8609i	−0.788937	+	1.36648i	−0.926619	+	0.376002i	$0.877299\pi$
$332$	1.19358	+	2.06734i	0.0655062	+	0.113460i
$333$	−3.85024	−	6.66882i	−0.210992	−	0.365449i
$334$	2.22242	−	3.84935i	0.121606	−	0.210627i
$335$	−8.56041			−0.467705
$336$	−0.279507	−	0.0780261i	−0.0152483	−	0.00425667i
$337$	27.9822			1.52428			0.762142	−	0.647409i	$-0.224148\pi$
$337$	27.9822			1.52428			0.762142	+	0.647409i	$0.224148\pi$
$338$	−13.2699	+	22.9842i	−0.721789	+	1.25018i
$339$	−4.60380	−	7.97402i	−0.250044	−	0.433089i
$340$	22.8719	+	39.6153i	1.24040	+	2.14844i
$341$	10.5861	−	18.3357i	0.573271	−	0.992935i
$342$	−2.28285			−0.123442
$343$	−12.6798	−	13.4990i	−0.684646	−	0.728876i
$344$	−12.7995			−0.690103
$345$	7.40644	−	12.8283i	0.398749	−	0.690654i
$346$	−17.2006	−	29.7923i	−0.924711	−	1.60165i
$347$	−9.05812	−	15.6891i	−0.486265	−	0.842236i	0.513610	−	0.858024i	$-0.328308\pi$
$347$	−9.05812	−	15.6891i	−0.486265	−	0.842236i	−0.999875	+	0.0157875i	$0.994974\pi$
$348$	−14.9788	+	25.9440i	−0.802948	+	1.39075i
$349$	−16.1254			−0.863170			−0.431585	−	0.902072i	$-0.642046\pi$
$349$	−16.1254			−0.863170			−0.431585	+	0.902072i	$0.642046\pi$
$350$	−8.59998	−	2.40074i	−0.459688	−	0.128325i
$351$	4.96243			0.264875
$352$	9.52841	−	16.5037i	0.507866	−	0.879649i
$353$	9.51891	+	16.4872i	0.506641	+	0.877527i	0.999970	+	0.00768495i	$0.00244622\pi$
$353$	9.51891	+	16.4872i	0.506641	+	0.877527i	−0.493330	+	0.869842i	$0.664220\pi$
$354$	11.1986	+	19.3966i	0.595201	+	1.03092i
$355$	2.56647	−	4.44526i	0.136214	−	0.235930i
$356$	−36.6256			−1.94115
$357$	−10.5784	+	10.3601i	−0.559870	+	0.548315i
$358$	53.3211			2.81811
$359$	2.58582	−	4.47877i	0.136474	−	0.236380i	−0.789685	−	0.613512i	$-0.789756\pi$
$359$	2.58582	−	4.47877i	0.136474	−	0.236380i	0.926160	+	0.377132i	$0.123090\pi$
$360$	3.51940	+	6.09577i	0.185488	+	0.321275i
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$	−24.9149	+	43.1539i	−1.30950	+	2.26812i
$363$	0.134531			0.00706102
$364$	−10.4875	−	40.8386i	−0.549696	−	2.14052i
$365$	12.0281			0.629577
$366$	−2.07271	+	3.59004i	−0.108342	+	0.187654i
$367$	−2.81392	−	4.87386i	−0.146886	−	0.254413i	0.783189	−	0.621783i	$-0.213592\pi$
$367$	−2.81392	−	4.87386i	−0.146886	−	0.254413i	−0.930075	+	0.367370i	$0.880258\pi$
$368$	−0.319166	−	0.552812i	−0.0166377	−	0.0288173i
$369$	−3.06568	+	5.30991i	−0.159593	+	0.276423i
$370$	−44.7431			−2.32609
$371$	−6.03085	−	23.4842i	−0.313106	−	1.21924i
$372$	20.6271			1.06947
$373$	−1.79728	+	3.11298i	−0.0930596	+	0.161184i	−0.908797	−	0.417238i	$-0.862998\pi$
$373$	−1.79728	+	3.11298i	−0.0930596	+	0.161184i	0.815738	+	0.578422i	$0.196331\pi$
$374$	−21.0561	−	36.4702i	−1.08878	−	1.88583i
$375$	4.48179	+	7.76269i	0.231439	+	0.400864i
$376$	8.73110	−	15.1227i	0.450272	−	0.779894i
$377$	46.2920			2.38416
$378$	−4.31512	+	4.22606i	−0.221946	+	0.217365i
$379$	8.82165			0.453138			0.226569	−	0.973995i	$-0.427249\pi$
$379$	8.82165			0.453138			0.226569	+	0.973995i	$0.427249\pi$
$380$	−4.08692	+	7.07875i	−0.209655	+	0.363132i
$381$	−2.63407	−	4.56235i	−0.134948	−	0.233736i
$382$	12.2533	+	21.2233i	0.626933	+	1.08588i
$383$	15.6624	−	27.1281i	0.800311	−	1.38618i	−0.119101	−	0.992882i	$-0.538001\pi$
$383$	15.6624	−	27.1281i	0.800311	−	1.38618i	0.919412	−	0.393297i	$-0.128665\pi$
$384$	18.0653			0.921893
$385$	21.3801	+	5.96838i	1.08963	+	0.304177i
$386$	41.1383			2.09388
$387$	2.31417	−	4.00826i	0.117636	−	0.203752i
$388$	27.1701	+	47.0600i	1.37935	+	2.38911i
$389$	0.122913	+	0.212891i	0.00623193	+	0.0107940i	0.869125	−	0.494593i	$-0.164683\pi$
$389$	0.122913	+	0.212891i	0.00623193	+	0.0107940i	−0.862893	+	0.505387i	$0.831350\pi$
$390$	14.4169	−	24.9709i	0.730030	−	1.26445i
$391$	−32.5697			−1.64712
$392$	16.5592	+	10.0266i	0.836367	+	0.506419i
$393$	7.93634			0.400336
$394$	3.87229	−	6.70701i	0.195083	−	0.337894i
$395$	−16.4150	−	28.4316i	−0.825929	−	1.43055i
$396$	−5.29285	−	9.16748i	−0.265976	−	0.460683i
$397$	0.897652	−	1.55478i	0.0450519	−	0.0780321i	−0.842620	−	0.538508i	$-0.818988\pi$
$397$	0.897652	−	1.55478i	0.0450519	−	0.0780321i	0.887672	+	0.460476i	$0.152321\pi$
$398$	0.253198			0.0126917
$399$	−2.54832	−	0.711380i	−0.127576	−	0.0356135i
$400$	−0.162145			−0.00810726
$401$	12.2512	−	21.2196i	0.611793	−	1.05966i	−0.379145	−	0.925337i	$-0.623782\pi$
$401$	12.2512	−	21.2196i	0.611793	−	1.05966i	0.990938	−	0.134320i	$-0.0428850\pi$
$402$	3.83894	+	6.64924i	0.191469	+	0.331634i
$403$	−15.9370	−	27.6038i	−0.793881	−	1.37504i
$404$	17.4359	−	30.1998i	0.867467	−	1.50250i
$405$	−2.54525			−0.126475
$406$	−40.2536	+	39.4228i	−1.99775	+	1.95652i
$407$	25.3830			1.25819
$408$	7.73825	−	13.4030i	0.383101	−	0.663550i
$409$	−13.5524	−	23.4735i	−0.670125	−	1.16069i	−0.977868	−	0.209222i	$-0.932907\pi$
$409$	−13.5524	−	23.4735i	−0.670125	−	1.16069i	0.307743	−	0.951470i	$-0.400426\pi$
$410$	17.8129	+	30.8529i	0.879718	+	1.52372i
$411$	4.09826	−	7.09839i	0.202152	−	0.350138i
$412$	13.4103			0.660676
$413$	6.45657	+	25.1419i	0.317707	+	1.23715i
$414$	−13.2858			−0.652959
$415$	−0.945992	+	1.63851i	−0.0464369	+	0.0804311i
$416$	−14.3447	−	24.8457i	−0.703306	−	1.21816i
$417$	4.60430	+	7.97488i	0.225473	+	0.390531i
$418$	3.76246	−	6.51677i	0.184028	−	0.318746i
$419$	−24.5949			−1.20154			−0.600771	−	0.799421i	$-0.705140\pi$
$419$	−24.5949			−1.20154			−0.600771	+	0.799421i	$0.705140\pi$
$420$	5.37910	+	20.9463i	0.262473	+	1.02207i
$421$	17.1191			0.834334			0.417167	−	0.908830i	$-0.363023\pi$
$421$	17.1191			0.834334			0.417167	+	0.908830i	$0.363023\pi$
$422$	−13.3086	+	23.0511i	−0.647851	+	1.12211i
$423$	3.15720	+	5.46842i	0.153508	+	0.265884i
$424$	12.6716	+	21.9479i	0.615388	+	1.06588i
$425$	−4.13658	+	7.16477i	−0.200654	+	0.347543i
$426$	−4.60376			−0.223053
$427$	−3.43246	+	3.36162i	−0.166109	+	0.162680i
$428$	−11.7135			−0.566193
$429$	−8.17879	+	14.1661i	−0.394876	+	0.683945i
$430$	−13.4463	−	23.2897i	−0.648440	−	1.12313i
$431$	9.81420	+	16.9987i	0.472733	+	0.818798i	0.999513	−	0.0312037i	$-0.00993405\pi$
$431$	9.81420	+	16.9987i	0.472733	+	0.818798i	−0.526780	+	0.850002i	$0.676601\pi$
$432$	−0.0548414	+	0.0949880i	−0.00263856	+	0.00457011i
$433$	30.0095			1.44216			0.721082	−	0.692850i	$-0.243645\pi$
$433$	30.0095			1.44216			0.721082	+	0.692850i	$0.243645\pi$
$434$	37.3658	+	10.4309i	1.79362	+	0.500699i
$435$	−23.7434			−1.13841
$436$	−22.7555	+	39.4138i	−1.08979	+	1.88758i
$437$	−2.90990	−	5.04010i	−0.139200	−	0.241101i
$438$	−5.39401	−	9.34270i	−0.257736	−	0.446412i
$439$	5.82201	−	10.0840i	0.277869	−	0.481284i	−0.692986	−	0.720951i	$-0.743705\pi$
$439$	5.82201	−	10.0840i	0.277869	−	0.481284i	0.970855	+	0.239667i	$0.0770384\pi$
$440$	−23.2018			−1.10610
$441$	−6.13384	+	3.37283i	−0.292088	+	0.160611i
$442$	−63.3984			−3.01555
$443$	9.66895	−	16.7471i	0.459386	−	0.795679i	−0.539543	−	0.841958i	$-0.681403\pi$
$443$	9.66895	−	16.7471i	0.459386	−	0.795679i	0.998929	+	0.0462788i	$0.0147363\pi$
$444$	12.3647	+	21.4163i	0.586802	+	1.01637i
$445$	−14.5141	−	25.1391i	−0.688034	−	1.19171i
$446$	−15.7874	+	27.3446i	−0.747556	+	1.29481i
$447$	−4.79529			−0.226809
$448$	33.0734	+	9.23264i	1.56257	+	0.436201i
$449$	−34.8975			−1.64692			−0.823458	−	0.567377i	$-0.807958\pi$
$449$	−34.8975			−1.64692			−0.823458	+	0.567377i	$0.807958\pi$
$450$	−1.68738	+	2.92263i	−0.0795440	+	0.137774i
$451$	−10.1053	−	17.5030i	−0.475842	−	0.824183i
$452$	14.7847	+	25.6078i	0.695413	+	1.20449i
$453$	3.83040	−	6.63446i	0.179968	−	0.311714i
$454$	31.4814			1.47749
$455$	23.8749	−	23.3821i	1.11927	−	1.09617i
$456$	2.76546			0.129504
$457$	1.55603	−	2.69512i	0.0727878	−	0.126072i	−0.827334	−	0.561710i	$-0.810144\pi$
$457$	1.55603	−	2.69512i	0.0727878	−	0.126072i	0.900122	+	0.435638i	$0.143477\pi$
$458$	−15.9394	−	27.6078i	−0.744798	−	1.29003i
$459$	2.79818	+	4.84659i	0.130608	+	0.226219i
$460$	−23.7851	+	41.1970i	−1.10899	+	1.92082i
$461$	21.6573			1.00868			0.504341	−	0.863505i	$-0.331736\pi$
$461$	21.6573			1.00868			0.504341	+	0.863505i	$0.331736\pi$
$462$	−4.95205	−	19.2834i	−0.230390	−	0.897143i
$463$	−27.4240			−1.27450			−0.637252	−	0.770656i	$-0.719929\pi$
$463$	−27.4240			−1.27450			−0.637252	+	0.770656i	$0.719929\pi$
$464$	−0.511587	+	0.886095i	−0.0237498	+	0.0411359i
$465$	8.17417	+	14.1581i	0.379068	+	0.656566i
$466$	19.3857	+	33.5770i	0.898025	+	1.55543i
$467$	13.6273	−	23.6031i	0.630595	−	1.09222i	−0.356835	−	0.934167i	$-0.616144\pi$
$467$	13.6273	−	23.6031i	0.630595	−	1.09222i	0.987430	−	0.158056i	$-0.0505225\pi$
$468$	−15.9364			−0.736660
$469$	2.21334	+	8.61876i	0.102202	+	0.397977i
$470$	36.6893			1.69235
$471$	−2.46803	+	4.27475i	−0.113721	+	0.196970i
$472$	−13.5661	−	23.4972i	−0.624431	−	1.08155i
$473$	7.62816	+	13.2124i	0.350743	+	0.607505i
$474$	−14.7227	+	25.5005i	−0.676237	+	1.17128i
$475$	−1.47831			−0.0678296
$476$	33.9716	−	33.2705i	1.55709	−	1.52495i
$477$	−9.16420			−0.419600
$478$	−3.13152	+	5.42395i	−0.143232	+	0.248086i
$479$	17.7994	+	30.8295i	0.813277	+	1.40864i	0.910559	+	0.413380i	$0.135652\pi$
$479$	17.7994	+	30.8295i	0.813277	+	1.40864i	−0.0972820	+	0.995257i	$0.531015\pi$
$480$	7.35744	+	12.7435i	0.335820	+	0.581657i
$481$	19.1066	−	33.0936i	0.871185	−	1.50894i
$482$	22.6736			1.03275
$483$	−14.8307	−	4.14009i	−0.674822	−	0.188381i
$484$	−0.432032			−0.0196378
$485$	−21.5341	+	37.2982i	−0.977815	+	1.69362i
$486$	1.14143	+	1.97701i	0.0517761	+	0.0896788i
$487$	−10.7802	−	18.6719i	−0.488498	−	0.846104i	0.511414	−	0.859334i	$-0.329122\pi$
$487$	−10.7802	−	18.6719i	−0.488498	−	0.846104i	−0.999912	+	0.0132307i	$0.995788\pi$
$488$	2.51089	−	4.34899i	0.113663	−	0.196870i
$489$	−2.55111			−0.115365
$490$	−0.848114	+	40.6642i	−0.0383139	+	1.83702i
$491$	4.06065			0.183255			0.0916273	−	0.995793i	$-0.470793\pi$
$491$	4.06065			0.183255			0.0916273	+	0.995793i	$0.470793\pi$
$492$	9.84515	−	17.0523i	0.443853	−	0.768777i
$493$	26.1028	+	45.2114i	1.17561	+	2.03622i
$494$	−5.66425	−	9.81077i	−0.254847	−	0.441407i
$495$	4.19493	−	7.26584i	0.188548	−	0.326575i
$496$	0.704500			0.0316330
$497$	−5.13913	−	1.43462i	−0.230521	−	0.0643515i
$498$	1.69693			0.0760412
$499$	6.84108	−	11.8491i	0.306249	−	0.530439i	−0.671290	−	0.741195i	$-0.734259\pi$
$499$	6.84108	−	11.8491i	0.306249	−	0.530439i	0.977539	+	0.210756i	$0.0675926\pi$
$500$	−14.3929	−	24.9292i	−0.643668	−	1.11487i
$501$	−0.973530	−	1.68620i	−0.0434941	−	0.0753340i
$502$	−0.106863	+	0.185092i	−0.00476953	+	0.00826107i
$503$	16.8353			0.750650			0.375325	−	0.926893i	$-0.377531\pi$
$503$	16.8353			0.750650			0.375325	+	0.926893i	$0.377531\pi$
$504$	5.22736	−	5.11948i	0.232845	−	0.228040i
$505$	27.6382			1.22988
$506$	21.8968	−	37.9263i	0.973431	−	1.68603i
$507$	5.81288	+	10.0682i	0.258159	+	0.447144i
$508$	8.45908	+	14.6516i	0.375311	+	0.650057i
$509$	−2.09067	+	3.62115i	−0.0926673	+	0.160504i	−0.908633	−	0.417596i	$-0.862873\pi$
$509$	−2.09067	+	3.62115i	−0.0926673	+	0.160504i	0.815965	+	0.578101i	$0.196206\pi$
$510$	32.5173			1.43989
$511$	−3.10991	−	12.1100i	−0.137574	−	0.535716i
$512$	1.24076			0.0548342
$513$	−0.500000	+	0.866025i	−0.0220755	+	0.0382360i
$514$	−12.1732	−	21.0846i	−0.536937	−	0.930003i
$515$	5.31426	+	9.20457i	0.234174	+	0.405602i
$516$	−7.43175	+	12.8722i	−0.327164	+	0.566665i
$517$	−20.8140			−0.915399
$518$	11.5686	+	45.0481i	0.508293	+	1.97930i
$519$	−15.0694			−0.661474
$520$	−17.4648	+	30.2499i	−0.765881	+	1.32654i
$521$	6.38585	+	11.0606i	0.279769	+	0.484575i	0.971327	−	0.237746i	$-0.0764087\pi$
$521$	6.38585	+	11.0606i	0.279769	+	0.484575i	−0.691558	+	0.722321i	$0.743075\pi$
$522$	10.6478	+	18.4425i	0.466041	+	0.807206i
$523$	12.9659	−	22.4575i	0.566957	−	0.981999i	−0.429907	−	0.902873i	$-0.641454\pi$
$523$	12.9659	−	22.4575i	0.566957	−	0.981999i	0.996865	−	0.0791260i	$-0.0252129\pi$
$524$	−25.4868			−1.11340
$525$	−2.79435	+	2.73668i	−0.121956	+	0.119439i
$526$	6.19093			0.269937
$527$	17.9729	−	31.1300i	0.782913	−	1.35604i
$528$	−0.180773	−	0.313107i	−0.00786711	−	0.0136262i
$529$	−5.43508	−	9.41384i	−0.236308	−	0.409298i
$530$	−26.6240	+	46.1141i	−1.15647	+	2.00307i
$531$	9.81110			0.425766
$532$	8.18369	+	2.28453i	0.354808	+	0.0990469i
$533$	−30.4265			−1.31792
$534$	−13.0178	+	22.5474i	−0.563334	+	0.975723i
$535$	−4.64186	−	8.03994i	−0.200685	−	0.347597i
$536$	−4.65051	−	8.05493i	−0.200872	−	0.347920i
$537$	11.6786	−	20.2280i	0.503970	−	0.872901i
$538$	−1.74863			−0.0753889
$539$	0.481138	−	23.0690i	0.0207241	−	0.993650i
$540$	8.17384			0.351746
$541$	11.4156	−	19.7724i	0.490795	−	0.850082i	−0.509149	−	0.860678i	$-0.670040\pi$
$541$	11.4156	−	19.7724i	0.490795	−	0.850082i	0.999944	+	0.0105967i	$0.00337311\pi$
$542$	−6.41478	−	11.1107i	−0.275538	−	0.477247i
$543$	10.9140	+	18.9035i	0.468363	+	0.811228i
$544$	16.1771	−	28.0196i	0.693589	−	1.20133i
$545$	−36.0706			−1.54509
$546$	−28.8686	−	8.05886i	−1.23546	−	0.344887i
$547$	−21.0599			−0.900455			−0.450227	−	0.892914i	$-0.648657\pi$
$547$	−21.0599			−0.900455			−0.450227	+	0.892914i	$0.648657\pi$
$548$	−13.1612	+	22.7958i	−0.562217	+	0.973788i
$549$	0.907947	+	1.57261i	0.0387502	+	0.0671174i
$550$	−5.56209	−	9.63382i	−0.237168	−	0.410787i
$551$	−4.66425	+	8.07871i	−0.198704	+	0.344165i
$552$	16.0944			0.685025
$553$	−24.3812	+	23.8780i	−1.03680	+	1.01540i
$554$	−64.7317			−2.75019
$555$	−9.79984	+	16.9738i	−0.415980	+	0.720499i
$556$	−14.7863	−	25.6106i	−0.627078	−	1.08613i
$557$	−21.7768	−	37.7185i	−0.922713	−	1.59819i	−0.795199	−	0.606348i	$-0.792634\pi$
$557$	−21.7768	−	37.7185i	−0.922713	−	1.59819i	−0.127514	−	0.991837i	$-0.540700\pi$
$558$	7.33146	−	12.6985i	0.310365	−	0.537569i
$559$	22.9679			0.971437
$560$	0.183718	+	0.715402i	0.00776352	+	0.0302312i
$561$	−18.4472			−0.778841
$562$	35.1264	−	60.8407i	1.48172	−	2.56641i
$563$	10.7691	+	18.6526i	0.453862	+	0.786112i	0.998622	−	0.0524800i	$-0.0167126\pi$
$563$	10.7691	+	18.6526i	0.453862	+	0.786112i	−0.544760	+	0.838592i	$0.683379\pi$
$564$	−10.1390	−	17.5613i	−0.426931	−	0.739465i
$565$	−11.7178	+	20.2959i	−0.492973	+	0.853855i
$566$	−35.1566			−1.47774
$567$	0.658087	+	2.56260i	0.0276371	+	0.107619i
$568$	5.57702			0.234007
$569$	−6.91119	+	11.9705i	−0.289732	+	0.501831i	−0.973746	−	0.227639i	$-0.926900\pi$
$569$	−6.91119	+	11.9705i	−0.289732	+	0.501831i	0.684014	+	0.729469i	$0.260233\pi$
$570$	2.90522	+	5.03198i	0.121686	+	0.210767i
$571$	3.18585	+	5.51805i	0.133324	+	0.230923i	0.924956	−	0.380075i	$-0.124102\pi$
$571$	3.18585	+	5.51805i	0.133324	+	0.230923i	−0.791632	+	0.610998i	$0.790768\pi$
$572$	26.2654	−	45.4930i	1.09821	−	1.90216i
$573$	10.7351			0.448464
$574$	26.4576	−	25.9115i	1.10432	−	1.08153i
$575$	−8.60349			−0.358790
$576$	6.48925	−	11.2397i	0.270385	−	0.468321i
$577$	−9.19733	−	15.9302i	−0.382890	−	0.663185i	0.608584	−	0.793489i	$-0.291738\pi$
$577$	−9.19733	−	15.9302i	−0.382890	−	0.663185i	−0.991474	+	0.130305i	$0.958405\pi$
$578$	−16.3444	−	28.3093i	−0.679836	−	1.17751i
$579$	9.01029	−	15.6063i	0.374455	−	0.648575i
$580$	76.2496			3.16609
$581$	1.89426	+	0.528796i	0.0785873	+	0.0219381i
$582$	38.6282			1.60119
$583$	15.1039	−	26.1607i	0.625539	−	1.08347i
$584$	6.53434	+	11.3178i	0.270393	+	0.468334i
$585$	−6.31533	−	10.9385i	−0.261107	−	0.452250i
$586$	4.14631	−	7.18162i	0.171282	−	0.296670i
$587$	−28.7021			−1.18466			−0.592331	−	0.805695i	$-0.701792\pi$
$587$	−28.7021			−1.18466			−0.592331	+	0.805695i	$0.701792\pi$
$588$	19.6983	−	10.8315i	0.812342	−	0.446685i
$589$	6.42307			0.264658
$590$	28.5034	−	49.3693i	1.17347	−	2.03250i
$591$	−1.69625	−	2.93800i	−0.0697745	−	0.120853i
$592$	0.422305	+	0.731454i	0.0173566	+	0.0300626i
$593$	−16.3272	+	28.2795i	−0.670478	+	1.16130i	0.307291	+	0.951616i	$0.400577\pi$
$593$	−16.3272	+	28.2795i	−0.670478	+	1.16130i	−0.977769	+	0.209686i	$0.932756\pi$
$594$	−7.52492			−0.308751
$595$	36.2987	+	10.1330i	1.48810	+	0.415413i
$596$	15.3996			0.630793
$597$	0.0554566	−	0.0960536i	0.00226969	−	0.00393121i
$598$	−32.9648	−	57.0968i	−1.34803	−	2.33486i
$599$	−4.63577	−	8.02939i	−0.189412	−	0.328072i	0.755642	−	0.654985i	$-0.227325\pi$
$599$	−4.63577	−	8.02939i	−0.189412	−	0.328072i	−0.945054	+	0.326913i	$0.893992\pi$
$600$	2.04411	−	3.54049i	0.0834503	−	0.144540i
$601$	6.44868			0.263047			0.131524	−	0.991313i	$-0.458013\pi$
$601$	6.44868			0.263047			0.131524	+	0.991313i	$0.458013\pi$
$602$	−19.9719	+	19.5597i	−0.813992	+	0.797192i
$603$	3.36328			0.136964
$604$	−12.3010	+	21.3059i	−0.500520	+	0.866926i
$605$	−0.171207	−	0.296539i	−0.00696056	−	0.0120560i
$606$	−12.3944	−	21.4678i	−0.503489	−	0.872068i
$607$	4.88593	−	8.46267i	0.198314	−	0.343489i	−0.749668	−	0.661814i	$-0.769787\pi$
$607$	4.88593	−	8.46267i	0.198314	−	0.343489i	0.947982	+	0.318325i	$0.103120\pi$
$608$	5.78131			0.234463
$609$	6.13897	+	23.9052i	0.248763	+	0.968688i
$610$	10.5511			0.427203
$611$	−15.6674	+	27.1367i	−0.633834	+	1.09783i
$612$	−8.98609	−	15.5644i	−0.363241	−	0.629152i
$613$	22.3319	+	38.6801i	0.901979	+	1.56227i	0.824922	+	0.565246i	$0.191219\pi$
$613$	22.3319	+	38.6801i	0.901979	+	1.56227i	0.0770563	+	0.997027i	$0.475448\pi$
$614$	−23.3770	+	40.4901i	−0.943417	+	1.63405i
$615$	15.6059			0.629289
$616$	5.99895	+	23.3600i	0.241705	+	0.941200i
$617$	−25.1695			−1.01329			−0.506643	−	0.862156i	$-0.669114\pi$
$617$	−25.1695			−1.01329			−0.506643	+	0.862156i	$0.669114\pi$
$618$	4.76639	−	8.25562i	0.191732	−	0.332090i
$619$	19.7418	+	34.1938i	0.793490	+	1.37436i	0.923794	+	0.382891i	$0.125071\pi$
$619$	19.7418	+	34.1938i	0.793490	+	1.37436i	−0.130304	+	0.991474i	$0.541595\pi$
$620$	−26.2506	−	45.4674i	−1.05425	−	1.82601i
$621$	−2.90990	+	5.04010i	−0.116770	+	0.202252i
$622$	−52.2058			−2.09326
$623$	−21.5578	+	21.1129i	−0.863695	+	0.845869i
$624$	−0.544293			−0.0217892
$625$	15.1031	−	26.1593i	0.604123	−	1.04637i
$626$	24.4863	+	42.4114i	0.978668	+	1.69510i
$627$	−1.64814	−	2.85466i	−0.0658204	−	0.114004i
$628$	7.92584	−	13.7280i	0.316276	−	0.547805i
$629$	43.0947			1.71830
$630$	14.8068	+	4.13342i	0.589919	+	0.164680i
$631$	5.92164			0.235737			0.117868	−	0.993029i	$-0.462394\pi$
$631$	5.92164			0.235737			0.117868	+	0.993029i	$0.462394\pi$
$632$	17.8352	−	30.8914i	0.709446	−	1.22880i
$633$	5.82980	+	10.0975i	0.231714	+	0.401340i
$634$	−25.8501	−	44.7736i	−1.02664	−	1.77819i
$635$	−6.70438	+	11.6123i	−0.266055	+	0.460821i
$636$	29.4300			1.16697
$637$	−29.7145	−	17.9920i	−1.17733	−	0.712871i
$638$	−70.1962			−2.77909
$639$	−1.00834	+	1.74649i	−0.0398891	+	0.0690900i
$640$	−22.9904	−	39.8206i	−0.908777	−	1.57405i
$641$	7.56670	+	13.1059i	0.298867	+	0.517652i	0.975877	−	0.218321i	$-0.0700581\pi$
$641$	7.56670	+	13.1059i	0.298867	+	0.517652i	−0.677010	+	0.735973i	$0.736725\pi$
$642$	−4.16331	+	7.21106i	−0.164313	+	0.284598i
$643$	14.5709			0.574619			0.287310	−	0.957838i	$-0.407239\pi$
$643$	14.5709			0.574619			0.287310	+	0.957838i	$0.407239\pi$
$644$	47.6275	+	13.2955i	1.87679	+	0.523917i
$645$	−11.7803			−0.463849
$646$	6.38783	−	11.0640i	0.251326	−	0.435309i
$647$	1.45937	+	2.52771i	0.0573739	+	0.0993745i	0.893286	−	0.449489i	$-0.148394\pi$
$647$	1.45937	+	2.52771i	0.0573739	+	0.0993745i	−0.835912	+	0.548864i	$0.815061\pi$
$648$	−1.38273	−	2.39496i	−0.0543187	−	0.0940828i
$649$	−16.1701	+	28.0074i	−0.634731	+	1.09939i
$650$	−16.7471			−0.656873
$651$	12.1411	−	11.8905i	0.475848	−	0.466027i
$652$	8.19264			0.320848
$653$	13.8699	−	24.0233i	0.542770	−	0.940106i	−0.455973	−	0.889993i	$-0.650709\pi$
$653$	13.8699	−	24.0233i	0.542770	−	0.940106i	0.998744	−	0.0501122i	$-0.0159579\pi$
$654$	16.1759	+	28.0175i	0.632529	+	1.09557i
$655$	−10.1000	−	17.4937i	−0.394640	−	0.683536i
$656$	0.336252	−	0.582406i	0.0131284	−	0.0227391i
$657$	−4.72568			−0.184366
$658$	−9.48621	−	36.9394i	−0.369811	−	1.44005i
$659$	14.7834			0.575880			0.287940	−	0.957648i	$-0.407030\pi$
$659$	14.7834			0.575880			0.287940	+	0.957648i	$0.407030\pi$
$660$	−13.4716	+	23.3336i	−0.524383	+	0.908258i
$661$	−17.6266	−	30.5302i	−0.685596	−	1.18749i	−0.973249	−	0.229752i	$-0.926208\pi$
$661$	−17.6266	−	30.5302i	−0.685596	−	1.18749i	0.287654	−	0.957735i	$-0.407125\pi$
$662$	−32.7668	−	56.7537i	−1.27352	−	2.20580i
$663$	−13.8858	+	24.0509i	−0.539279	+	0.934059i
$664$	−2.05567			−0.0797755
$665$	1.67500	+	6.52247i	0.0649537	+	0.252930i
$666$	17.5791			0.681175
$667$	−27.1450	+	47.0166i	−1.05106	+	1.82049i
$668$	3.12640	+	5.41508i	0.120964	+	0.209516i
$669$	6.91566	+	11.9783i	0.267375	+	0.463107i
$670$	9.77107	−	16.9240i	0.377489	−	0.653831i
$671$	−5.98570			−0.231075
$672$	10.9280	−	10.7025i	0.421558	−	0.412857i
$673$	−22.4607			−0.865796			−0.432898	−	0.901443i	$-0.642509\pi$
$673$	−22.4607			−0.865796			−0.432898	+	0.901443i	$0.642509\pi$
$674$	−31.9395	+	55.3209i	−1.23026	+	2.13088i
$675$	0.739156	+	1.28026i	0.0284501	+	0.0492771i
$676$	−18.6675	−	32.3331i	−0.717981	−	1.24358i
$677$	4.64321	−	8.04228i	0.178453	−	0.309090i	−0.762898	−	0.646519i	$-0.776224\pi$
$677$	4.64321	−	8.04228i	0.178453	−	0.309090i	0.941351	+	0.337429i	$0.109557\pi$
$678$	21.0196			0.807253
$679$	43.1202	+	12.0373i	1.65480	+	0.461948i
$680$	−39.3916			−1.51060
$681$	6.89519	−	11.9428i	0.264224	−	0.457650i
$682$	24.1666	+	41.8577i	0.925385	+	1.60281i
$683$	−9.61953	−	16.6615i	−0.368081	−	0.637535i	0.621184	−	0.783664i	$-0.286652\pi$
$683$	−9.61953	−	16.6615i	−0.368081	−	0.637535i	−0.989266	+	0.146129i	$0.953318\pi$
$684$	1.60570	−	2.78116i	0.0613956	−	0.106340i
$685$	−20.8622			−0.797103
$686$	41.1606	−	9.66003i	1.57152	−	0.368822i
$687$	−13.9644			−0.532777
$688$	−0.253825	+	0.439637i	−0.00967698	+	0.0167610i
$689$	−22.7384	−	39.3840i	−0.866263	−	1.50041i
$690$	16.9078	+	29.2852i	0.643669	+	1.11487i
$691$	−11.5353	+	19.9797i	−0.438823	+	0.760064i	−0.997599	−	0.0692547i	$-0.977938\pi$
$691$	−11.5353	+	19.9797i	−0.438823	+	0.760064i	0.558776	+	0.829319i	$0.311271\pi$
$692$	48.3940			1.83967
$693$	−8.39998	−	2.34491i	−0.319089	−	0.0890757i
$694$	41.3567			1.56988
$695$	11.7191	−	20.2981i	0.444531	−	0.769950i
$696$	−12.8988	−	22.3414i	−0.488927	−	0.846847i
$697$	−17.1567	−	29.7162i	−0.649855	−	1.12558i
$698$	18.4059	−	31.8799i	0.696673	−	1.20667i
$699$	16.9838			0.642385
$700$	8.97381	−	8.78860i	0.339178	−	0.332178i
$701$	−18.6485			−0.704344			−0.352172	−	0.935935i	$-0.614557\pi$
$701$	−18.6485			−0.704344			−0.352172	+	0.935935i	$0.614557\pi$
$702$	−5.66425	+	9.81077i	−0.213783	+	0.370283i
$703$	3.85024	+	6.66882i	0.145215	+	0.251519i
$704$	21.3904	+	37.0492i	0.806180	+	1.39635i
$705$	8.03586	−	13.9185i	0.302648	−	0.524202i
$706$	−43.4605			−1.63566
$707$	−7.14599	−	27.8266i	−0.268753	−	1.04653i
$708$	−31.5074			−1.18412
$709$	−22.2557	+	38.5481i	−0.835832	+	1.44770i	0.0575196	+	0.998344i	$0.481681\pi$
$709$	−22.2557	+	38.5481i	−0.835832	+	1.44770i	−0.893351	+	0.449359i	$0.851653\pi$
$710$	5.85887	+	10.1479i	0.219879	+	0.380842i
$711$	6.44927	+	11.1705i	0.241866	+	0.418925i
$712$	15.7698	−	27.3141i	0.590998	−	1.02364i
$713$	37.3811			1.39993
$714$	−8.40750	−	32.7389i	−0.314643	−	1.22522i
$715$	41.6342			1.55703
$716$	−37.5048	+	64.9602i	−1.40162	+	2.42768i
$717$	1.37176	+	2.37596i	0.0512293	+	0.0887317i
$718$	5.90304	+	10.2244i	0.220299	+	0.381570i
$719$	−11.8983	+	20.6085i	−0.443733	+	0.768567i	−0.997963	−	0.0637960i	$-0.979679\pi$
$719$	−11.8983	+	20.6085i	−0.443733	+	0.768567i	0.554230	+	0.832363i	$0.313013\pi$
$720$	0.279170			0.0104041
$721$	7.89327	−	7.73036i	0.293961	−	0.287894i
$722$	2.28285			0.0849589
$723$	4.96607	−	8.60149i	0.184690	−	0.319893i
$724$	−35.0491	−	60.7069i	−1.30259	−	2.25615i
$725$	6.89521	+	11.9429i	0.256082	+	0.443547i
$726$	−0.153557	+	0.265968i	−0.00569902	+	0.00987099i
$727$	−28.5209			−1.05778			−0.528891	−	0.848689i	$-0.677392\pi$
$727$	−28.5209			−1.05778			−0.528891	+	0.848689i	$0.677392\pi$
$728$	34.9717	+	9.76256i	1.29614	+	0.361824i
$729$	1.00000			0.0370370
$730$	−13.7291	+	23.7795i	−0.508138	+	0.880120i
$731$	12.9509	+	22.4317i	0.479008	+	0.829666i
$732$	−2.91579	−	5.05029i	−0.107771	−	0.186664i
$733$	8.13938	−	14.0978i	0.300635	−	0.520715i	−0.675645	−	0.737227i	$-0.736135\pi$
$733$	8.13938	−	14.0978i	0.300635	−	0.520715i	0.976280	+	0.216512i	$0.0694681\pi$
$734$	12.8475			0.474211
$735$	15.2407	+	9.22819i	0.562160	+	0.340387i
$736$	33.6461			1.24021
$737$	−5.54317	+	9.60105i	−0.204185	+	0.353659i
$738$	−6.99849	−	12.1217i	−0.257618	−	0.446207i
$739$	−26.2459	−	45.4592i	−0.965470	−	1.67224i	−0.708348	−	0.705863i	$-0.750559\pi$
$739$	−26.2459	−	45.4592i	−0.965470	−	1.67224i	−0.257121	−	0.966379i	$-0.582774\pi$
$740$	31.4713	−	54.5098i	1.15691	−	2.00382i
$741$	−4.96243			−0.182300
$742$	53.3121	+	14.8824i	1.95715	+	0.546351i
$743$	−31.9433			−1.17189			−0.585944	−	0.810352i	$-0.699276\pi$
$743$	−31.9433			−1.17189			−0.585944	+	0.810352i	$0.699276\pi$
$744$	−8.88138	+	15.3830i	−0.325607	+	0.563968i
$745$	6.10261	+	10.5700i	0.223582	+	0.387256i
$746$	−4.10292	−	7.10647i	−0.150219	−	0.260186i
$747$	0.371669	−	0.643750i	0.0135987	−	0.0235536i
$748$	59.2414			2.16608
$749$	−6.89456	+	6.75226i	−0.251922	+	0.246722i
$750$	−20.4625			−0.747186
$751$	3.40492	−	5.89749i	0.124247	−	0.215202i	−0.797191	−	0.603727i	$-0.793682\pi$
$751$	3.40492	−	5.89749i	0.124247	−	0.215202i	0.921438	+	0.388524i	$0.127015\pi$
$752$	−0.346290	−	0.599792i	−0.0126279	−	0.0218721i
$753$	0.0468112	+	0.0810794i	0.00170590	+	0.00295470i
$754$	−52.8389	+	91.5197i	−1.92428	+	3.33295i
$755$	−19.4987			−0.709630
$756$	−2.11339	−	8.22955i	−0.0768631	−	0.299306i
$757$	9.00239			0.327198			0.163599	−	0.986527i	$-0.447690\pi$
$757$	9.00239			0.327198			0.163599	+	0.986527i	$0.447690\pi$
$758$	−10.0693	+	17.4405i	−0.365732	+	0.633466i
$759$	−9.59186	−	16.6136i	−0.348163	−	0.603035i
$760$	−3.51940	−	6.09577i	−0.127662	−	0.221117i
$761$	−2.58982	+	4.48569i	−0.0938808	+	0.162606i	−0.909141	−	0.416489i	$-0.863261\pi$
$761$	−2.58982	+	4.48569i	−0.0938808	+	0.162606i	0.815260	+	0.579095i	$0.196594\pi$
$762$	12.0264			0.435670
$763$	9.32622	+	36.3164i	0.337632	+	1.31474i
$764$	−34.4747			−1.24725
$765$	7.12208	−	12.3358i	0.257499	−	0.446002i
$766$	35.7549	+	61.9293i	1.29188	+	2.23760i
$767$	24.3435	+	42.1641i	0.878992	+	1.52246i
$768$	−7.64175	+	13.2359i	−0.275748	+	0.477609i
$769$	41.5253			1.49744			0.748720	−	0.662886i	$-0.230669\pi$
$769$	41.5253			1.49744			0.748720	+	0.662886i	$0.230669\pi$
$770$	−36.2033	+	35.4561i	−1.30468	+	1.27775i
$771$	−10.6649			−0.384088
$772$	−28.9357	+	50.1181i	−1.04142	+	1.80379i
$773$	1.41901	+	2.45780i	0.0510382	+	0.0884008i	0.890416	−	0.455148i	$-0.150414\pi$
$773$	1.41901	+	2.45780i	0.0510382	+	0.0884008i	−0.839378	+	0.543549i	$0.817080\pi$
$774$	5.28291	+	9.15027i	0.189890	+	0.328900i
$775$	4.74765	−	8.22318i	0.170541	−	0.295385i
$776$	−46.7944			−1.67982
$777$	19.6233	+	5.47797i	0.703982	+	0.196521i
$778$	−0.561183			−0.0201194
$779$	3.06568	−	5.30991i	0.109839	−	0.190247i
$780$	20.2811	+	35.1279i	0.726179	+	1.25778i
$781$	−3.32376	−	5.75692i	−0.118933	−	0.205999i
$782$	37.1759	−	64.3906i	1.32941	−	2.30260i
$783$	9.32850			0.333373
$784$	0.672776	−	0.369941i	0.0240277	−	0.0132122i
$785$	12.5635			0.448411
$786$	−9.05874	+	15.6902i	−0.323115	+	0.559651i
$787$	20.7488	+	35.9379i	0.739614	+	1.28105i	0.952669	+	0.304009i	$0.0983251\pi$
$787$	20.7488	+	35.9379i	0.739614	+	1.28105i	−0.213056	+	0.977040i	$0.568342\pi$
$788$	5.44736	+	9.43510i	0.194054	+	0.336111i
$789$	1.35596	−	2.34860i	0.0482736	−	0.0836124i
$790$	74.9461			2.66646
$791$	23.4639	+	6.55011i	0.834282	+	0.232895i
$792$	9.11573			0.323913
$793$	−4.50563	+	7.80398i	−0.160000	+	0.277127i
$794$	2.04921	+	3.54933i	0.0727236	+	0.125961i
$795$	11.6626	+	20.2002i	0.413630	+	0.716428i
$796$	−0.178094	+	0.308467i	−0.00631236	+	0.0109333i
$797$	−34.7178			−1.22977			−0.614884	−	0.788618i	$-0.710797\pi$
$797$	−34.7178			−1.22977			−0.614884	+	0.788618i	$0.710797\pi$
$798$	4.31512	−	4.22606i	0.152754	−	0.149601i
$799$	−35.3376			−1.25016
$800$	4.27329	−	7.40155i	0.151084	−	0.261684i
$801$	5.70242	+	9.87688i	0.201485	+	0.348982i
$802$	27.9676	+	48.4412i	0.987569	+	1.71052i
$803$	7.78859	−	13.4902i	0.274853	−	0.476060i
$804$	−10.8009			−0.380917
$805$	9.74817	+	37.9595i	0.343578	+	1.33790i
$806$	72.7638			2.56299
$807$	−0.382993	+	0.663364i	−0.0134820	+	0.0233515i
$808$	15.0147	+	26.0062i	0.528214	+	0.914894i
$809$	18.4335	+	31.9278i	0.648087	+	1.12252i	0.983579	+	0.180477i	$0.0577642\pi$
$809$	18.4335	+	31.9278i	0.648087	+	1.12252i	−0.335492	+	0.942043i	$0.608902\pi$
$810$	2.90522	−	5.03198i	0.102079	−	0.176806i
$811$	−45.4803			−1.59703			−0.798515	−	0.601974i	$-0.794381\pi$
$811$	−45.4803			−1.59703			−0.798515	+	0.601974i	$0.794381\pi$
$812$	−19.7147	−	76.7693i	−0.691851	−	2.69408i
$813$	−5.61998			−0.197101
$814$	−28.9728	+	50.1823i	−1.01549	+	1.75889i
$815$	3.24660	+	5.62328i	0.113724	+	0.196975i
$816$	−0.306912	−	0.531587i	−0.0107441	−	0.0186093i
$817$	−2.31417	+	4.00826i	−0.0809626	+	0.140231i
$818$	61.8764			2.16346
$819$	−9.38016	+	9.18656i	−0.327769	+	0.321004i
$820$	−50.1168			−1.75015
$821$	−12.7761	+	22.1288i	−0.445888	+	0.772301i	−0.998114	−	0.0613939i	$-0.980445\pi$
$821$	−12.7761	+	22.1288i	−0.445888	+	0.772301i	0.552226	+	0.833695i	$0.313779\pi$
$822$	9.35570	+	16.2046i	0.326318	+	0.565199i
$823$	−3.77591	−	6.54008i	−0.131620	−	0.227973i	0.792681	−	0.609636i	$-0.208685\pi$
$823$	−3.77591	−	6.54008i	−0.131620	−	0.227973i	−0.924301	+	0.381664i	$0.875351\pi$
$824$	−5.77403	+	10.0009i	−0.201148	+	0.348398i
$825$	−4.87293			−0.169654
$826$	−57.0755	−	15.9330i	−1.98591	−	0.554379i
$827$	−30.8901			−1.07415			−0.537077	−	0.843533i	$-0.680472\pi$
$827$	−30.8901			−1.07415			−0.537077	+	0.843533i	$0.680472\pi$
$828$	9.34488	−	16.1858i	0.324757	−	0.562496i
$829$	−13.1893	−	22.8446i	−0.458084	−	0.793424i	0.540776	−	0.841167i	$-0.318131\pi$
$829$	−13.1893	−	22.8446i	−0.458084	−	0.793424i	−0.998860	+	0.0477425i	$0.984797\pi$
$830$	−2.15956	−	3.74046i	−0.0749593	−	0.129833i
$831$	−14.1778	+	24.5567i	−0.491823	+	0.851863i
$832$	64.4049			2.23284
$833$	0.816867	−	39.1660i	0.0283028	−	1.35702i
$834$	−21.0218			−0.727927
$835$	−2.47788	+	4.29181i	−0.0857506	+	0.148524i
$836$	5.29285	+	9.16748i	0.183057	+	0.317064i
$837$	−3.21154	−	5.56255i	−0.111007	−	0.192270i
$838$	28.0733	−	48.6244i	0.969776	−	1.67970i
$839$	−2.55457			−0.0881935			−0.0440968	−	0.999027i	$-0.514041\pi$
$839$	−2.55457			−0.0881935			−0.0440968	+	0.999027i	$0.514041\pi$
$840$	−17.9371	−	5.00725i	−0.618889	−	0.172767i
$841$	58.0208			2.00072
$842$	−19.5402	+	33.8446i	−0.673399	+	1.16636i
$843$	−15.3871	−	26.6512i	−0.529959	−	0.917916i
$844$	−18.7219	−	32.4272i	−0.644433	−	1.11619i
$845$	14.7952	−	25.6261i	0.508972	−	0.881565i
$846$	−14.4148			−0.495591
$847$	−0.254294	+	0.249046i	−0.00873765	+	0.00855731i
$848$	1.00515			0.0345171
$849$	−7.70015	+	13.3370i	−0.264268	+	0.457726i
$850$	−9.44320	−	16.3561i	−0.323899	−	0.561010i
$851$	22.4077	+	38.8112i	0.768125	+	1.33043i
$852$	3.23818	−	5.60869i	0.110938	−	0.192150i
$853$	−52.1083			−1.78416			−0.892078	−	0.451882i	$-0.850753\pi$
$853$	−52.1083			−1.78416			−0.892078	+	0.451882i	$0.850753\pi$
$854$	−2.72805	−	10.6230i	−0.0933518	−	0.363513i
$855$	2.54525			0.0870458
$856$	5.04346	−	8.73553i	0.172382	−	0.298574i
$857$	3.72754	+	6.45628i	0.127330	+	0.220542i	0.922641	−	0.385659i	$-0.126026\pi$
$857$	3.72754	+	6.45628i	0.127330	+	0.220542i	−0.795311	+	0.606201i	$0.792693\pi$
$858$	−18.6710	−	32.3390i	−0.637416	−	1.10404i
$859$	14.9701	−	25.9289i	0.510772	−	0.884684i	−0.489150	−	0.872200i	$-0.662693\pi$
$859$	14.9701	−	25.9289i	0.510772	−	0.884684i	0.999922	−	0.0124838i	$-0.00397382\pi$
$860$	37.8314			1.29004
$861$	−4.03497	−	15.7122i	−0.137511	−	0.535471i
$862$	−44.8087			−1.52619
$863$	7.19480	−	12.4618i	0.244914	−	0.424204i	−0.717193	−	0.696874i	$-0.754574\pi$
$863$	7.19480	−	12.4618i	0.244914	−	0.424204i	0.962107	+	0.272671i	$0.0879069\pi$
$864$	−2.89065	−	5.00676i	−0.0983420	−	0.170333i
$865$	19.1777	+	33.2168i	0.652063	+	1.12941i
$866$	−34.2536	+	59.3289i	−1.16398	+	2.01608i
$867$	−14.3193			−0.486308
$868$	−38.9900	+	38.1853i	−1.32341	+	1.29609i
$869$	−42.5172			−1.44230
$870$	27.1013	−	46.9408i	0.918820	−	1.59144i
$871$	8.34504	+	14.4540i	0.282761	+	0.489756i
$872$	−19.5956	−	33.9406i	−0.663592	−	1.14937i
$873$	8.46051	−	14.6540i	0.286345	−	0.495964i
$874$	13.2858			0.449397
$875$	−22.8421	−	6.37651i	−0.772204	−	0.215566i
$876$	15.1761			0.512752
$877$	−27.3998	+	47.4579i	−0.925226	+	1.60254i	−0.134029	+	0.990977i	$0.542792\pi$
$877$	−27.3998	+	47.4579i	−0.925226	+	1.60254i	−0.791197	+	0.611561i	$0.790542\pi$
$878$	13.2908	+	23.0203i	0.448542	+	0.776898i
$879$	−1.81629	−	3.14590i	−0.0612618	−	0.106109i
$880$	−0.460112	+	0.796937i	−0.0155104	+	0.0268647i
$881$	−20.3805			−0.686638			−0.343319	−	0.939219i	$-0.611551\pi$
$881$	−20.3805			−0.686638			−0.343319	+	0.939219i	$0.611551\pi$
$882$	0.333214	−	15.9765i	0.0112199	−	0.537956i
$883$	−20.1615			−0.678488			−0.339244	−	0.940698i	$-0.610171\pi$
$883$	−20.1615			−0.678488			−0.339244	+	0.940698i	$0.610171\pi$
$884$	44.5929	−	77.2372i	1.49982	−	2.59777i
$885$	−12.4859	−	21.6262i	−0.419708	−	0.726956i
$886$	22.0728	+	38.2312i	0.741549	+	1.28440i
$887$	22.5022	−	38.9749i	0.755549	−	1.30865i	−0.189552	−	0.981871i	$-0.560704\pi$
$887$	22.5022	−	38.9749i	0.755549	−	1.30865i	0.945101	−	0.326778i	$-0.105963\pi$
$888$	−21.2954			−0.714626
$889$	13.4249	+	3.74765i	0.450258	+	0.125692i
$890$	66.2670			2.22128
$891$	−1.64814	+	2.85466i	−0.0552148	+	0.0956348i
$892$	−22.2090	−	38.4671i	−0.743613	−	1.28797i
$893$	−3.15720	−	5.46842i	−0.105652	−	0.182994i
$894$	5.47346	−	9.48031i	0.183060	−	0.317069i
$895$	−59.4501			−1.98720
$896$	−34.1477	+	33.4429i	−1.14080	+	1.11725i
$897$	−28.8804			−0.964289
$898$	39.8329	−	68.9927i	1.32924	−	2.30231i
$899$	−29.9588	−	51.8902i	−0.999182	−	1.73063i
$900$	−2.37373	−	4.11142i	−0.0791243	−	0.137047i
$901$	25.6431	−	44.4151i	0.854295	−	1.47968i
$902$	46.1380			1.53623
$903$	3.04586	+	11.8606i	0.101360	+	0.394696i
$904$	−25.4633			−0.846895
$905$	27.7788	−	48.1142i	0.923398	−	1.59937i
$906$	8.74424	+	15.1455i	0.290508	+	0.503175i
$907$	12.9338	+	22.4020i	0.429459	+	0.743846i	0.996825	−	0.0796203i	$-0.0253708\pi$
$907$	12.9338	+	22.4020i	0.429459	+	0.743846i	−0.567366	+	0.823466i	$0.692037\pi$
$908$	−22.1433	+	38.3532i	−0.734850	+	1.27280i
$909$	−10.8587			−0.360161
$910$	18.9752	+	73.8897i	0.629022	+	2.44942i
$911$	−8.50711			−0.281853			−0.140927	−	0.990020i	$-0.545008\pi$
$911$	−8.50711			−0.281853			−0.140927	+	0.990020i	$0.545008\pi$
$912$	0.0548414	−	0.0949880i	0.00181598	−	0.00314537i
$913$	1.22513	+	2.12198i	0.0405457	+	0.0702273i
$914$	3.55218	+	6.15255i	0.117496	+	0.203508i
$915$	2.31096	−	4.00269i	0.0763978	−	0.132325i
$916$	44.8455			1.48174
$917$	−15.0015	+	14.6919i	−0.495395	+	0.485170i
$918$	−12.7757			−0.421659
$919$	−13.8584	+	24.0034i	−0.457146	+	0.791800i	−0.998809	−	0.0487956i	$-0.984462\pi$
$919$	−13.8584	+	24.0034i	−0.457146	+	0.791800i	0.541663	+	0.840596i	$0.317795\pi$
$920$	−20.4822	−	35.4762i	−0.675279	−	1.16962i
$921$	10.2402	+	17.7366i	0.337428	+	0.584442i
$922$	−24.7202	+	42.8166i	−0.814116	+	1.41009i
$923$	−10.0076			−0.329404
$924$	26.9758	+	7.53045i	0.887437	+	0.247734i
$925$	11.3837			0.374294
$926$	31.3025	−	54.2175i	1.02866	−	1.78170i
$927$	−2.08791	−	3.61637i	−0.0685760	−	0.118777i
$928$	−26.9655	−	46.7055i	−0.885184	−	1.53318i
$929$	9.84267	−	17.0480i	0.322928	−	0.559327i	−0.658163	−	0.752875i	$-0.728666\pi$
$929$	9.84267	−	17.0480i	0.322928	−	0.559327i	0.981091	+	0.193548i	$0.0619996\pi$
$930$	−37.3208			−1.22380
$931$	6.13384	−	3.37283i	0.201029	−	0.110540i
$932$	−54.5418			−1.78658
$933$	−11.4343	+	19.8048i	−0.374343	+	0.648382i
$934$	31.1090	+	53.8824i	1.01792	+	1.76309i
$935$	23.4764	+	40.6623i	0.767759	+	1.32980i
$936$	6.86170	−	11.8848i	0.224282	−	0.388468i
$937$	39.0825			1.27677			0.638385	−	0.769717i	$-0.279603\pi$
$937$	39.0825			1.27677			0.638385	+	0.769717i	$0.279603\pi$
$938$	−19.5657	−	5.46189i	−0.638843	−	0.178337i
$939$	21.4524			0.700071
$940$	−25.8064	+	44.6980i	−0.841713	+	1.45789i
$941$	−23.0669	−	39.9530i	−0.751958	−	1.30243i	−0.946872	−	0.321610i	$-0.895776\pi$
$941$	−23.0669	−	39.9530i	−0.751958	−	1.30243i	0.194914	−	0.980820i	$-0.437557\pi$
$942$	−5.63414	−	9.75862i	−0.183570	−	0.317953i
$943$	17.8417	−	30.9027i	0.581005	−	1.00633i
$944$	−1.07611			−0.0350244
$945$	4.81112	−	4.71182i	0.156506	−	0.153276i
$946$	−34.8279			−1.13235
$947$	−4.92484	+	8.53007i	−0.160036	+	0.277190i	−0.934881	−	0.354961i	$-0.884494\pi$
$947$	−4.92484	+	8.53007i	−0.160036	+	0.277190i	0.774846	+	0.632151i	$0.217828\pi$
$948$	−20.7112	−	35.8729i	−0.672669	−	1.16510i
$949$	−11.7254	−	20.3091i	−0.380624	−	0.659260i
$950$	1.68738	−	2.92263i	0.0547459	−	0.0948227i
$951$	−22.6472			−0.734385
$952$	10.1849	+	39.6601i	0.330094	+	1.28539i
$953$	23.5275			0.762131			0.381066	−	0.924548i	$-0.375557\pi$
$953$	23.5275			0.762131			0.381066	+	0.924548i	$0.375557\pi$
$954$	10.4602	−	18.1177i	0.338663	−	0.586582i
$955$	−13.6617	−	23.6628i	−0.442083	−	0.765711i
$956$	−4.40528	−	7.63016i	−0.142477	−	0.246777i
$957$	−15.3747	+	26.6297i	−0.496993	+	0.860816i
$958$	−81.2669			−2.62561
$959$	5.39402	+	21.0044i	0.174182	+	0.678267i
$960$	−33.0336			−1.06615
$961$	−5.12794	+	8.88186i	−0.165418	+	0.286512i
$962$	43.6175	+	75.5476i	1.40628	+	2.43575i
$963$	1.82373	+	3.15880i	0.0587690	+	0.101791i
$964$	−15.9481	+	27.6229i	−0.513653	+	0.889673i
$965$	−45.8669			−1.47651
$966$	25.1132	−	24.5949i	0.808003	−	0.791327i
$967$	19.3664			0.622783			0.311391	−	0.950282i	$-0.399205\pi$
$967$	19.3664			0.622783			0.311391	+	0.950282i	$0.399205\pi$
$968$	0.186019	−	0.322195i	0.00597889	−	0.0103557i
$969$	−2.79818	−	4.84659i	−0.0898905	−	0.155695i
$970$	−49.1592	−	85.1462i	−1.57841	−	2.73388i
$971$	19.5531	−	33.8669i	0.627488	−	1.08684i	−0.360566	−	0.932734i	$-0.617416\pi$
$971$	19.5531	−	33.8669i	0.627488	−	1.08684i	0.988054	−	0.154108i	$-0.0492503\pi$
$972$	−3.21141			−0.103006
$973$	−23.4665	−	6.55081i	−0.752300	−	0.210009i
$974$	49.2192			1.57709
$975$	−3.66801	+	6.35319i	−0.117470	+	0.203465i
$976$	−0.0995861	−	0.172488i	−0.00318767	−	0.00552121i
$977$	−21.6273	−	37.4595i	−0.691917	−	1.19844i	−0.971209	−	0.238230i	$-0.923433\pi$
$977$	−21.6273	−	37.4595i	−0.691917	−	1.19844i	0.279291	−	0.960206i	$-0.409900\pi$
$978$	2.91190	−	5.04355i	0.0931122	−	0.161275i
$979$	−37.5935			−1.20149
$980$	−48.9440	−	29.6355i	−1.56346	−	0.946670i
$981$	14.1717			0.452468
$982$	−4.63493	+	8.02793i	−0.147907	+	0.256182i
$983$	0.0719590	+	0.124637i	0.00229513	+	0.00397529i	0.867171	−	0.498011i	$-0.165936\pi$
$983$	0.0719590	+	0.124637i	0.00229513	+	0.00397529i	−0.864876	+	0.501986i	$0.832603\pi$
$984$	8.47801	+	14.6844i	0.270269	+	0.468120i
$985$	−4.31739	+	7.47794i	−0.137564	+	0.238267i
$986$	−119.178			−3.79539
$987$	−16.0911	−	4.49193i	−0.512185	−	0.142980i
$988$	15.9364			0.507004
$989$	−13.4680	+	23.3273i	−0.428259	+	0.741766i
$990$	9.57641	+	16.5868i	0.304358	+	0.527164i
$991$	−6.34137	−	10.9836i	−0.201440	−	0.348905i	0.747552	−	0.664203i	$-0.231229\pi$
$991$	−6.34137	−	10.9836i	−0.201440	−	0.348905i	−0.948993	+	0.315298i	$0.897896\pi$
$992$	−18.5669	+	32.1588i	−0.589499	+	1.02104i
$993$	−28.7069			−0.910986
$994$	8.70218	−	8.52258i	0.276016	−	0.270320i
$995$	−0.282302			−0.00894958
$996$	−1.19358	+	2.06734i	−0.0378200	+	0.0655062i
$997$	11.1801	+	19.3645i	0.354078	+	0.613281i	0.986960	−	0.160967i	$-0.0514614\pi$
$997$	11.1801	+	19.3645i	0.354078	+	0.613281i	−0.632882	+	0.774248i	$0.718128\pi$
$998$	15.6172	+	27.0497i	0.494353	+	0.856245i
$999$	3.85024	−	6.66882i	0.121816	−	0.210992i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.j.g.58.2	✓	16
3.2	odd	2		1197.2.j.m.856.7		16
7.2	even	3		2793.2.a.bm.1.7		8
7.4	even	3	inner	399.2.j.g.172.2	yes	16
7.5	odd	6		2793.2.a.bn.1.7		8
21.2	odd	6		8379.2.a.cr.1.2		8
21.5	even	6		8379.2.a.cq.1.2		8
21.11	odd	6		1197.2.j.m.172.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.j.g.58.2	✓	16	1.1	even	1	trivial
399.2.j.g.172.2	yes	16	7.4	even	3	inner
1197.2.j.m.172.7		16	21.11	odd	6
1197.2.j.m.856.7		16	3.2	odd	2
2793.2.a.bm.1.7		8	7.2	even	3
2793.2.a.bn.1.7		8	7.5	odd	6
8379.2.a.cq.1.2		8	21.5	even	6
8379.2.a.cr.1.2		8	21.2	odd	6

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:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14143 + 1.97701i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.60570 - 2.78116i) q^{4} +(1.27263 - 2.20425i) q^{5} -2.28285 q^{6} +(-2.54832 - 0.711380i) q^{7} +2.76546 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.14143 + 1.97701i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.60570 - 2.78116i) q^{4} +(1.27263 - 2.20425i) q^{5} -2.28285 q^{6} +(-2.54832 - 0.711380i) q^{7} +2.76546 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.90522 + 5.03198i) q^{10} +(-1.64814 - 2.85466i) q^{11} +(1.60570 - 2.78116i) q^{12} -4.96243 q^{13} +(4.31512 - 4.22606i) q^{14} +2.54525 q^{15} +(0.0548414 - 0.0949880i) q^{16} +(-2.79818 - 4.84659i) q^{17} +(-1.14143 - 1.97701i) q^{18} +(0.500000 - 0.866025i) q^{19} -8.17384 q^{20} +(-0.658087 - 2.56260i) q^{21} +7.52492 q^{22} +(2.90990 - 5.04010i) q^{23} +(1.38273 + 2.39496i) q^{24} +(-0.739156 - 1.28026i) q^{25} +(5.66425 - 9.81077i) q^{26} -1.00000 q^{27} +(2.11339 + 8.22955i) q^{28} -9.32850 q^{29} +(-2.90522 + 5.03198i) q^{30} +(3.21154 + 5.56255i) q^{31} +(2.89065 + 5.00676i) q^{32} +(1.64814 - 2.85466i) q^{33} +12.7757 q^{34} +(-4.81112 + 4.71182i) q^{35} +3.21141 q^{36} +(-3.85024 + 6.66882i) q^{37} +(1.14143 + 1.97701i) q^{38} +(-2.48122 - 4.29759i) q^{39} +(3.51940 - 6.09577i) q^{40} +6.13136 q^{41} +(5.81744 + 1.62397i) q^{42} -4.62835 q^{43} +(-5.29285 + 9.16748i) q^{44} +(1.27263 + 2.20425i) q^{45} +(6.64288 + 11.5058i) q^{46} +(3.15720 - 5.46842i) q^{47} +0.109683 q^{48} +(5.98788 + 3.62565i) q^{49} +3.37477 q^{50} +(2.79818 - 4.84659i) q^{51} +(7.96820 + 13.8013i) q^{52} +(4.58210 + 7.93643i) q^{53} +(1.14143 - 1.97701i) q^{54} -8.38987 q^{55} +(-7.04728 - 1.96729i) q^{56} +1.00000 q^{57} +(10.6478 - 18.4425i) q^{58} +(-4.90555 - 8.49667i) q^{59} +(-4.08692 - 7.07875i) q^{60} +(0.907947 - 1.57261i) q^{61} -14.6629 q^{62} +(1.89023 - 1.85122i) q^{63} -12.9785 q^{64} +(-6.31533 + 10.9385i) q^{65} +(3.76246 + 6.51677i) q^{66} +(-1.68164 - 2.91269i) q^{67} +(-8.98609 + 15.5644i) q^{68} +5.81981 q^{69} +(-3.82377 - 14.8898i) q^{70} +2.01667 q^{71} +(-1.38273 + 2.39496i) q^{72} +(2.36284 + 4.09256i) q^{73} +(-8.78953 - 15.2239i) q^{74} +(0.739156 - 1.28026i) q^{75} -3.21141 q^{76} +(2.16924 + 8.44705i) q^{77} +11.3285 q^{78} +(6.44927 - 11.1705i) q^{79} +(-0.139585 - 0.241769i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.99849 + 12.1217i) q^{82} -0.743338 q^{83} +(-6.07031 + 5.94502i) q^{84} -14.2442 q^{85} +(5.28291 - 9.15027i) q^{86} +(-4.66425 - 8.07871i) q^{87} +(-4.55787 - 7.89445i) q^{88} +(5.70242 - 9.87688i) q^{89} -5.81043 q^{90} +(12.6459 + 3.53018i) q^{91} -18.6898 q^{92} +(-3.21154 + 5.56255i) q^{93} +(7.20741 + 12.4836i) q^{94} +(-1.27263 - 2.20425i) q^{95} +(-2.89065 + 5.00676i) q^{96} -16.9210 q^{97} +(-14.0026 + 7.69967i) q^{98} +3.29628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 10 q^{4} + 5 q^{5} + q^{7} - 6 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 - 10 * q^4 + 5 * q^5 + q^7 - 6 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} - 10 q^{4} + 5 q^{5} + q^{7} - 6 q^{8} - 8 q^{9} + 3 q^{10} + 7 q^{11} + 10 q^{12} - 12 q^{13} - 12 q^{14} + 10 q^{15} - 10 q^{16} + 8 q^{19} - 32 q^{20} - q^{21} + 36 q^{22} + 9 q^{23} - 3 q^{24} - 15 q^{25} + 12 q^{26} - 16 q^{27} - 40 q^{28} + 8 q^{29} - 3 q^{30} + 11 q^{31} + 26 q^{32} - 7 q^{33} - 32 q^{34} - 7 q^{35} + 20 q^{36} - 17 q^{37} - 6 q^{39} + 3 q^{40} - 34 q^{41} - 9 q^{42} + 16 q^{43} + 31 q^{44} + 5 q^{45} - q^{46} + 29 q^{47} - 20 q^{48} + q^{49} + 60 q^{50} + 25 q^{52} + 6 q^{53} - 42 q^{55} - 54 q^{56} + 16 q^{57} + 37 q^{58} + 7 q^{59} - 16 q^{60} + 2 q^{61} - 78 q^{62} - 2 q^{63} + 58 q^{64} + 13 q^{65} + 18 q^{66} - 13 q^{67} - 14 q^{68} + 18 q^{69} - 81 q^{70} + 36 q^{71} + 3 q^{72} + 20 q^{73} + 26 q^{74} + 15 q^{75} - 20 q^{76} + 19 q^{77} + 24 q^{78} + 3 q^{79} + 35 q^{80} - 8 q^{81} + 5 q^{82} - 72 q^{83} - 29 q^{84} + 10 q^{85} + 51 q^{86} + 4 q^{87} - 53 q^{88} + q^{89} - 6 q^{90} - 9 q^{91} + 30 q^{92} - 11 q^{93} + 30 q^{94} - 5 q^{95} - 26 q^{96} + 6 q^{97} - 75 q^{98} - 14 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 - 10 * q^4 + 5 * q^5 + q^7 - 6 * q^8 - 8 * q^9 + 3 * q^10 + 7 * q^11 + 10 * q^12 - 12 * q^13 - 12 * q^14 + 10 * q^15 - 10 * q^16 + 8 * q^19 - 32 * q^20 - q^21 + 36 * q^22 + 9 * q^23 - 3 * q^24 - 15 * q^25 + 12 * q^26 - 16 * q^27 - 40 * q^28 + 8 * q^29 - 3 * q^30 + 11 * q^31 + 26 * q^32 - 7 * q^33 - 32 * q^34 - 7 * q^35 + 20 * q^36 - 17 * q^37 - 6 * q^39 + 3 * q^40 - 34 * q^41 - 9 * q^42 + 16 * q^43 + 31 * q^44 + 5 * q^45 - q^46 + 29 * q^47 - 20 * q^48 + q^49 + 60 * q^50 + 25 * q^52 + 6 * q^53 - 42 * q^55 - 54 * q^56 + 16 * q^57 + 37 * q^58 + 7 * q^59 - 16 * q^60 + 2 * q^61 - 78 * q^62 - 2 * q^63 + 58 * q^64 + 13 * q^65 + 18 * q^66 - 13 * q^67 - 14 * q^68 + 18 * q^69 - 81 * q^70 + 36 * q^71 + 3 * q^72 + 20 * q^73 + 26 * q^74 + 15 * q^75 - 20 * q^76 + 19 * q^77 + 24 * q^78 + 3 * q^79 + 35 * q^80 - 8 * q^81 + 5 * q^82 - 72 * q^83 - 29 * q^84 + 10 * q^85 + 51 * q^86 + 4 * q^87 - 53 * q^88 + q^89 - 6 * q^90 - 9 * q^91 + 30 * q^92 - 11 * q^93 + 30 * q^94 - 5 * q^95 - 26 * q^96 + 6 * q^97 - 75 * q^98 - 14 * q^99

Introduction

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