LMFDB - Embedded newform 465.2.o.a.26.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [465,2,Mod(26,465)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(465, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("465.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.o (of order $6$, 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:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.10
Character	$\chi$	$=$	465.26
Dual form			465.2.o.a.161.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.64741i q^{2} +(1.01103 - 1.40635i) q^{3} -0.713974 q^{4} +(-0.866025 + 0.500000i) q^{5} +(-2.31685 - 1.66558i) q^{6} +(-0.179912 + 0.311616i) q^{7} -2.11862i q^{8} +(-0.955654 - 2.84372i) q^{9} +O(q^{10})$	\(q-1.64741i q^{2} +(1.01103 - 1.40635i) q^{3} -0.713974 q^{4} +(-0.866025 + 0.500000i) q^{5} +(-2.31685 - 1.66558i) q^{6} +(-0.179912 + 0.311616i) q^{7} -2.11862i q^{8} +(-0.955654 - 2.84372i) q^{9} +(0.823707 + 1.42670i) q^{10} +(-1.04045 - 1.80210i) q^{11} +(-0.721846 + 1.00410i) q^{12} +(-3.57997 + 2.06689i) q^{13} +(0.513361 + 0.296389i) q^{14} +(-0.172398 + 1.72345i) q^{15} -4.91819 q^{16} +(2.65068 - 4.59111i) q^{17} +(-4.68478 + 1.57436i) q^{18} +(0.592325 - 1.02594i) q^{19} +(0.618320 - 0.356987i) q^{20} +(0.256347 + 0.568071i) q^{21} +(-2.96881 + 1.71404i) q^{22} +7.04783 q^{23} +(-2.97952 - 2.14198i) q^{24} +(0.500000 - 0.866025i) q^{25} +(3.40503 + 5.89769i) q^{26} +(-4.96546 - 1.53109i) q^{27} +(0.128452 - 0.222486i) q^{28} -9.84496 q^{29} +(2.83924 + 0.284011i) q^{30} +(3.11821 - 4.61268i) q^{31} +3.86506i q^{32} +(-3.58631 - 0.358741i) q^{33} +(-7.56346 - 4.36676i) q^{34} -0.359823i q^{35} +(0.682312 + 2.03034i) q^{36} +(7.48560 + 4.32181i) q^{37} +(-1.69014 - 0.975804i) q^{38} +(-0.712656 + 7.12438i) q^{39} +(1.05931 + 1.83478i) q^{40} +(8.73309 - 5.04205i) q^{41} +(0.935848 - 0.422309i) q^{42} +(8.22272 + 4.74739i) q^{43} +(0.742851 + 1.28666i) q^{44} +(2.24948 + 1.98490i) q^{45} -11.6107i q^{46} +13.1789i q^{47} +(-4.97242 + 6.91671i) q^{48} +(3.43526 + 5.95005i) q^{49} +(-1.42670 - 0.823707i) q^{50} +(-3.77681 - 8.36951i) q^{51} +(2.55600 - 1.47571i) q^{52} +(1.74736 + 3.02651i) q^{53} +(-2.52233 + 8.18017i) q^{54} +(1.80210 + 1.04045i) q^{55} +(0.660195 + 0.381164i) q^{56} +(-0.843973 - 1.87027i) q^{57} +16.2187i q^{58} +(-1.42168 - 0.820809i) q^{59} +(0.123088 - 1.23050i) q^{60} +1.28445i q^{61} +(-7.59899 - 5.13698i) q^{62} +(1.05808 + 0.213821i) q^{63} -3.46902 q^{64} +(2.06689 - 3.57997i) q^{65} +(-0.590995 + 5.90814i) q^{66} +(-2.48577 - 4.30548i) q^{67} +(-1.89252 + 3.27793i) q^{68} +(7.12554 - 9.91173i) q^{69} -0.592778 q^{70} +(4.91218 - 2.83605i) q^{71} +(-6.02475 + 2.02466i) q^{72} +(1.69784 - 0.980246i) q^{73} +(7.11982 - 12.3319i) q^{74} +(-0.712424 - 1.57875i) q^{75} +(-0.422905 + 0.732492i) q^{76} +0.748753 q^{77} +(11.7368 + 1.17404i) q^{78} +(1.40332 + 0.810208i) q^{79} +(4.25928 - 2.45909i) q^{80} +(-7.17345 + 5.43522i) q^{81} +(-8.30635 - 14.3870i) q^{82} +(-3.08573 - 5.34463i) q^{83} +(-0.183025 - 0.405588i) q^{84} +5.30135i q^{85} +(7.82092 - 13.5462i) q^{86} +(-9.95351 + 13.8455i) q^{87} +(-3.81797 + 2.20430i) q^{88} -9.99822 q^{89} +(3.26996 - 3.70582i) q^{90} -1.48743i q^{91} -5.03197 q^{92} +(-3.33446 - 9.04883i) q^{93} +21.7111 q^{94} +1.18465i q^{95} +(5.43564 + 3.90768i) q^{96} +16.7465 q^{97} +(9.80220 - 5.65930i) q^{98} +(-4.13037 + 4.68092i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 76 q^{4} + 18 q^{6}+O(q^{10}) $ 84 * q - 76 * q^4 + 18 * q^6	$ 84 q - 76 q^{4} + 18 q^{6} + 2 q^{10} - 18 q^{13} + 60 q^{16} + 10 q^{18} + 10 q^{19} - 42 q^{21} - 36 q^{24} + 42 q^{25} - 8 q^{28} - 28 q^{31} - 4 q^{33} - 18 q^{34} + 6 q^{36} + 18 q^{37} + 32 q^{39} + 24 q^{40} - 90 q^{42} + 42 q^{43} + 4 q^{45} + 48 q^{48} - 62 q^{49} - 8 q^{51} + 144 q^{52} - 12 q^{55} - 12 q^{57} - 72 q^{63} - 160 q^{64} - 76 q^{66} - 32 q^{67} + 24 q^{69} - 84 q^{72} - 30 q^{73} - 86 q^{76} + 76 q^{78} + 28 q^{81} - 36 q^{82} + 210 q^{84} - 6 q^{87} - 72 q^{88} + 8 q^{90} - 100 q^{93} + 220 q^{94} + 168 q^{96} + 12 q^{97} + 54 q^{99}+O(q^{100}) $ 84 * q - 76 * q^4 + 18 * q^6 + 2 * q^10 - 18 * q^13 + 60 * q^16 + 10 * q^18 + 10 * q^19 - 42 * q^21 - 36 * q^24 + 42 * q^25 - 8 * q^28 - 28 * q^31 - 4 * q^33 - 18 * q^34 + 6 * q^36 + 18 * q^37 + 32 * q^39 + 24 * q^40 - 90 * q^42 + 42 * q^43 + 4 * q^45 + 48 * q^48 - 62 * q^49 - 8 * q^51 + 144 * q^52 - 12 * q^55 - 12 * q^57 - 72 * q^63 - 160 * q^64 - 76 * q^66 - 32 * q^67 + 24 * q^69 - 84 * q^72 - 30 * q^73 - 86 * q^76 + 76 * q^78 + 28 * q^81 - 36 * q^82 + 210 * q^84 - 6 * q^87 - 72 * q^88 + 8 * q^90 - 100 * q^93 + 220 * q^94 + 168 * q^96 + 12 * q^97 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.64741i		−	1.16490i	−0.812867	−	0.582449i	$-0.802095\pi$
$2$		−	1.64741i		−	1.16490i	0.812867	−	0.582449i	$-0.197905\pi$
$3$	1.01103	−	1.40635i	0.583716	−	0.811958i
$3$	1.01103	−	1.40635i	0.583716	−	0.811958i
$4$	−0.713974			−0.356987
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−2.31685	−	1.66558i	−0.945848	−	0.679970i
$7$	−0.179912	+	0.311616i	−0.0680002	+	0.117780i	−0.898021	−	0.439953i	$-0.854995\pi$
$7$	−0.179912	+	0.311616i	−0.0680002	+	0.117780i	0.830021	+	0.557733i	$0.188329\pi$
$8$		−	2.11862i		−	0.749044i
$9$	−0.955654	−	2.84372i	−0.318551	−	0.947906i
$10$	0.823707	+	1.42670i	0.260479	+	0.451163i
$11$	−1.04045	−	1.80210i	−0.313706	−	0.543355i	0.665456	−	0.746437i	$-0.268237\pi$
$11$	−1.04045	−	1.80210i	−0.313706	−	0.543355i	−0.979162	+	0.203083i	$0.934904\pi$
$12$	−0.721846	+	1.00410i	−0.208379	+	0.289859i
$13$	−3.57997	+	2.06689i	−0.992904	+	0.573253i	−0.906141	−	0.422976i	$-0.860986\pi$
$13$	−3.57997	+	2.06689i	−0.992904	+	0.573253i	−0.0867630	+	0.996229i	$0.527652\pi$
$14$	0.513361	+	0.296389i	0.137201	+	0.0792133i
$15$	−0.172398	+	1.72345i	−0.0445129	+	0.444993i
$16$	−4.91819			−1.22955
$17$	2.65068	−	4.59111i	0.642884	−	1.11351i	−0.341902	−	0.939735i	$-0.611071\pi$
$17$	2.65068	−	4.59111i	0.642884	−	1.11351i	0.984786	−	0.173771i	$-0.0555954\pi$
$18$	−4.68478	+	1.57436i	−1.10421	+	0.371080i
$19$	0.592325	−	1.02594i	0.135889	−	0.235366i	−0.790048	−	0.613045i	$-0.789944\pi$
$19$	0.592325	−	1.02594i	0.135889	−	0.235366i	0.925937	+	0.377679i	$0.123278\pi$
$20$	0.618320	−	0.356987i	0.138261	−	0.0798248i
$21$	0.256347	+	0.568071i	0.0559394	+	0.123963i
$22$	−2.96881	+	1.71404i	−0.632953	+	0.365435i
$23$	7.04783			1.46957			0.734787	−	0.678298i	$-0.237282\pi$
$23$	7.04783			1.46957			0.734787	+	0.678298i	$0.237282\pi$
$24$	−2.97952	−	2.14198i	−0.608192	−	0.437229i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	3.40503	+	5.89769i	0.667782	+	1.15663i
$27$	−4.96546	−	1.53109i	−0.955603	−	0.294657i
$28$	0.128452	−	0.222486i	0.0242752	−	0.0420459i
$29$	−9.84496			−1.82816			−0.914082	−	0.405529i	$-0.867087\pi$
$29$	−9.84496			−1.82816			−0.914082	+	0.405529i	$0.867087\pi$
$30$	2.83924	+	0.284011i	0.518371	+	0.0518530i
$31$	3.11821	−	4.61268i	0.560047	−	0.828461i
$31$	3.11821	−	4.61268i	0.560047	−	0.828461i
$32$			3.86506i			0.683253i
$33$	−3.58631	−	0.358741i	−0.624296	−	0.0624488i
$34$	−7.56346	−	4.36676i	−1.29712	−	0.748894i
$35$		−	0.359823i		−	0.0608212i
$36$	0.682312	+	2.03034i	0.113719	+	0.338390i
$37$	7.48560	+	4.32181i	1.23063	+	0.710502i	0.967160	−	0.254167i	$-0.0818013\pi$
$37$	7.48560	+	4.32181i	1.23063	+	0.710502i	0.263465	+	0.964669i	$0.415135\pi$
$38$	−1.69014	−	0.975804i	−0.274177	−	0.158296i
$39$	−0.712656	+	7.12438i	−0.114116	+	1.14081i
$40$	1.05931	+	1.83478i	0.167491	+	0.290104i
$41$	8.73309	−	5.04205i	1.36388	−	0.787437i	0.373742	−	0.927533i	$-0.378074\pi$
$41$	8.73309	−	5.04205i	1.36388	−	0.787437i	0.990138	+	0.140096i	$0.0447412\pi$
$42$	0.935848	−	0.422309i	0.144405	−	0.0651637i
$43$	8.22272	+	4.74739i	1.25395	+	0.723970i	0.971892	−	0.235426i	$-0.0756485\pi$
$43$	8.22272	+	4.74739i	1.25395	+	0.723970i	0.282061	+	0.959396i	$0.408982\pi$
$44$	0.742851	+	1.28666i	0.111989	+	0.193971i
$45$	2.24948	+	1.98490i	0.335333	+	0.295892i
$46$		−	11.6107i		−	1.71190i
$47$			13.1789i			1.92234i	0.275954	+	0.961171i	$0.411006\pi$
$47$			13.1789i			1.92234i	−0.275954	+	0.961171i	$0.588994\pi$
$48$	−4.97242	+	6.91671i	−0.717706	+	0.998341i
$49$	3.43526	+	5.95005i	0.490752	+	0.850007i
$50$	−1.42670	−	0.823707i	−0.201766	−	0.116490i
$51$	−3.77681	−	8.36951i	−0.528859	−	1.17197i
$52$	2.55600	−	1.47571i	0.354454	−	0.204644i
$53$	1.74736	+	3.02651i	0.240018	+	0.415723i	0.960719	−	0.277523i	$-0.0895134\pi$
$53$	1.74736	+	3.02651i	0.240018	+	0.415723i	−0.720701	+	0.693246i	$0.756180\pi$
$54$	−2.52233	+	8.18017i	−0.343246	+	1.11318i
$55$	1.80210	+	1.04045i	0.242996	+	0.140294i
$56$	0.660195	+	0.381164i	0.0882223	+	0.0509352i
$57$	−0.843973	−	1.87027i	−0.111787	−	0.247723i
$58$			16.2187i			2.12962i
$59$	−1.42168	−	0.820809i	−0.185087	−	0.106860i	0.404593	−	0.914497i	$-0.367413\pi$
$59$	−1.42168	−	0.820809i	−0.185087	−	0.106860i	−0.589681	+	0.807636i	$0.700746\pi$
$60$	0.123088	−	1.23050i	0.0158905	−	0.158857i
$61$			1.28445i			0.164457i	0.996614	+	0.0822283i	$0.0262037\pi$
$61$			1.28445i			0.164457i	−0.996614	+	0.0822283i	$0.973796\pi$
$62$	−7.59899	−	5.13698i	−0.965073	−	0.652397i
$63$	1.05808	+	0.213821i	0.133306	+	0.0269389i
$64$	−3.46902			−0.433628
$65$	2.06689	−	3.57997i	0.256367	−	0.444040i
$66$	−0.590995	+	5.90814i	−0.0727464	+	0.727241i
$67$	−2.48577	−	4.30548i	−0.303685	−	0.525998i	0.673283	−	0.739385i	$-0.264884\pi$
$67$	−2.48577	−	4.30548i	−0.303685	−	0.525998i	−0.976968	+	0.213387i	$0.931550\pi$
$68$	−1.89252	+	3.27793i	−0.229501	+	0.397508i
$69$	7.12554	−	9.91173i	0.857814	−	1.19323i
$70$	−0.592778			−0.0708505
$71$	4.91218	−	2.83605i	0.582969	−	0.336577i	−0.179344	−	0.983787i	$-0.557397\pi$
$71$	4.91218	−	2.83605i	0.582969	−	0.336577i	0.762312	+	0.647209i	$0.224064\pi$
$72$	−6.02475	+	2.02466i	−0.710023	+	0.238609i
$73$	1.69784	−	0.980246i	0.198717	−	0.114729i	−0.397340	−	0.917671i	$-0.630067\pi$
$73$	1.69784	−	0.980246i	0.198717	−	0.114729i	0.596057	+	0.802942i	$0.296733\pi$
$74$	7.11982	−	12.3319i	0.827662	−	1.43355i
$75$	−0.712424	−	1.57875i	−0.0822636	−	0.182298i
$76$	−0.422905	+	0.732492i	−0.0485105	+	0.0840226i
$77$	0.748753			0.0853283
$78$	11.7368	+	1.17404i	1.32893	+	0.132934i
$79$	1.40332	+	0.810208i	0.157886	+	0.0911555i	0.576861	−	0.816842i	$-0.304277\pi$
$79$	1.40332	+	0.810208i	0.157886	+	0.0911555i	−0.418975	+	0.907998i	$0.637611\pi$
$80$	4.25928	−	2.45909i	0.476202	−	0.274935i
$81$	−7.17345	+	5.43522i	−0.797050	+	0.603913i
$82$	−8.30635	−	14.3870i	−0.917283	−	1.58878i
$83$	−3.08573	−	5.34463i	−0.338702	−	0.586650i	0.645486	−	0.763772i	$-0.276655\pi$
$83$	−3.08573	−	5.34463i	−0.338702	−	0.586650i	−0.984189	+	0.177122i	$0.943321\pi$
$84$	−0.183025	−	0.405588i	−0.0199697	−	0.0442533i
$85$			5.30135i			0.575013i
$86$	7.82092	−	13.5462i	0.843352	−	1.46073i
$87$	−9.95351	+	13.8455i	−1.06713	+	1.48439i
$88$	−3.81797	+	2.20430i	−0.406997	+	0.234980i
$89$	−9.99822			−1.05981			−0.529904	−	0.848057i	$-0.677772\pi$
$89$	−9.99822			−1.05981			−0.529904	+	0.848057i	$0.677772\pi$
$90$	3.26996	−	3.70582i	0.344684	−	0.390628i
$91$		−	1.48743i		−	0.155925i
$92$	−5.03197			−0.524619
$93$	−3.33446	−	9.04883i	−0.345767	−	0.938320i
$94$	21.7111			2.23933
$95$			1.18465i			0.121542i
$96$	5.43564	+	3.90768i	0.554773	+	0.398826i
$97$	16.7465			1.70035			0.850176	−	0.526498i	$-0.176495\pi$
$97$	16.7465			1.70035			0.850176	+	0.526498i	$0.176495\pi$
$98$	9.80220	−	5.65930i	0.990172	−	0.571676i
$99$	−4.13037	+	4.68092i	−0.415118	+	0.470450i
$100$	−0.356987	+	0.618320i	−0.0356987	+	0.0618320i
$101$		−	11.1465i		−	1.10912i	−0.832145	−	0.554558i	$-0.812887\pi$
$101$		−	11.1465i		−	1.10912i	0.832145	−	0.554558i	$-0.187113\pi$
$102$	−13.7881	+	6.22197i	−1.36522	+	0.616067i
$103$	2.62079	+	4.53934i	0.258234	+	0.447274i	0.965769	−	0.259404i	$-0.0835261\pi$
$103$	2.62079	+	4.53934i	0.258234	+	0.447274i	−0.707535	+	0.706678i	$0.750193\pi$
$104$	4.37896	+	7.58458i	0.429392	+	0.743729i
$105$	−0.506038	−	0.363791i	−0.0493843	−	0.0355023i
$106$	4.98591	−	2.87862i	0.484275	−	0.279596i
$107$	−11.2964	−	6.52201i	−1.09207	−	0.630506i	−0.157942	−	0.987448i	$-0.550486\pi$
$107$	−11.2964	−	6.52201i	−1.09207	−	0.630506i	−0.934126	+	0.356942i	$0.883819\pi$
$108$	3.54521	+	1.09316i	0.341138	+	0.105189i
$109$	−8.23959			−0.789210			−0.394605	−	0.918851i	$-0.629119\pi$
$109$	−8.23959			−0.789210			−0.394605	+	0.918851i	$0.629119\pi$
$110$	1.71404	−	2.96881i	0.163428	−	0.283065i
$111$	13.6461	−	6.15793i	1.29523	−	0.584485i
$112$	0.884839	−	1.53259i	0.0836095	−	0.144816i
$113$	1.43696	−	0.829630i	0.135178	−	0.0780450i	−0.430886	−	0.902406i	$-0.641799\pi$
$113$	1.43696	−	0.829630i	0.135178	−	0.0780450i	0.566064	+	0.824361i	$0.308466\pi$
$114$	−3.08110	+	1.39037i	−0.288572	+	0.130220i
$115$	−6.10360	+	3.52392i	−0.569164	+	0.328607i
$116$	7.02905			0.652631
$117$	9.29887	+	8.20518i	0.859681	+	0.758569i
$118$	−1.35221	+	2.34210i	−0.124481	+	0.215608i
$119$	0.953775	+	1.65199i	0.0874324	+	0.151437i
$120$	3.65133	+	0.365245i	0.333319	+	0.0333422i
$121$	3.33495	−	5.77630i	0.303177	−	0.525118i
$122$	2.11602			0.191575
$123$	1.73848	−	17.3795i	0.156753	−	1.56705i
$124$	−2.22632	+	3.29333i	−0.199929	+	0.295750i
$125$			1.00000i			0.0894427i
$126$	0.352251	−	1.74310i	0.0313810	−	0.155288i
$127$	3.01997	+	1.74358i	0.267979	+	0.154718i	0.627969	−	0.778239i	$-0.283887\pi$
$127$	3.01997	+	1.74358i	0.267979	+	0.154718i	−0.359990	+	0.932956i	$0.617220\pi$
$128$			13.4450i			1.18838i
$129$	14.9899	−	6.76431i	1.31979	−	0.595564i
$130$	−5.89769	−	3.40503i	−0.517262	−	0.298641i
$131$	17.3718	+	10.0296i	1.51778	+	0.876289i	0.999781	+	0.0209056i	$0.00665495\pi$
$131$	17.3718	+	10.0296i	1.51778	+	0.876289i	0.517996	+	0.855383i	$0.326678\pi$
$132$	2.56053	+	0.256132i	0.222866	+	0.0222934i
$133$	0.213132	+	0.369156i	0.0184809	+	0.0320099i
$134$	−7.09291	+	4.09509i	−0.612734	+	0.353762i
$135$	5.06576	−	1.15677i	0.435991	−	0.0995590i
$136$	−9.72680	−	5.61577i	−0.834066	−	0.481548i
$137$	−2.73376	−	4.73502i	−0.233561	−	0.404540i	0.725292	−	0.688441i	$-0.241705\pi$
$137$	−2.73376	−	4.73502i	−0.233561	−	0.404540i	−0.958854	+	0.283901i	$0.908371\pi$
$138$	−16.3287	−	11.7387i	−1.38999	−	0.999266i
$139$		−	0.0959240i		−	0.00813617i	−0.999992	−	0.00406808i	$-0.998705\pi$
$139$		−	0.0959240i		−	0.00813617i	0.999992	−	0.00406808i	$-0.00129492\pi$
$140$			0.256905i			0.0217124i
$141$	18.5342	+	13.3242i	1.56086	+	1.12210i
$142$	−4.67215	−	8.09240i	−0.392078	−	0.679099i
$143$	7.44952	+	4.30098i	0.622960	+	0.359666i
$144$	4.70009	+	13.9859i	0.391674	+	1.16549i
$145$	8.52599	−	4.92248i	0.708045	−	0.408790i
$146$	−1.61487	−	2.79704i	−0.133648	−	0.231485i
$147$	11.8410	+	1.18446i	0.976630	+	0.0976929i
$148$	−5.34453	−	3.08566i	−0.439317	−	0.253640i
$149$	−15.4484	−	8.91912i	−1.26558	−	0.730683i	−0.291431	−	0.956592i	$-0.594132\pi$
$149$	−15.4484	−	8.91912i	−1.26558	−	0.730683i	−0.974148	+	0.225909i	$0.927465\pi$
$150$	−2.60086	+	1.17366i	−0.212359	+	0.0958287i
$151$			4.14762i			0.337528i	0.985656	+	0.168764i	$0.0539776\pi$
$151$			4.14762i			0.337528i	−0.985656	+	0.168764i	$0.946022\pi$
$152$	−2.17357	−	1.25491i	−0.176300	−	0.101787i
$153$	−15.5889	−	3.15027i	−1.26029	−	0.254684i
$154$		−	1.23351i		−	0.0993987i
$155$	−0.394109	+	5.55380i	−0.0316556	+	0.446092i
$156$	0.508818	−	5.08662i	0.0407381	−	0.407256i
$157$	−5.31849			−0.424462			−0.212231	−	0.977220i	$-0.568073\pi$
$157$	−5.31849			−0.424462			−0.212231	+	0.977220i	$0.568073\pi$
$158$	1.33475	−	2.31185i	0.106187	−	0.183921i
$159$	6.02296	+	0.602480i	0.477652	+	0.0477798i
$160$	−1.93253	−	3.34724i	−0.152780	−	0.264623i
$161$	−1.26799	+	2.19622i	−0.0999314	+	0.173086i
$162$	8.95406	+	11.8176i	0.703497	+	0.928482i
$163$	−10.5065			−0.822936			−0.411468	−	0.911424i	$-0.634984\pi$
$163$	−10.5065			−0.822936			−0.411468	+	0.911424i	$0.634984\pi$
$164$	−6.23520	+	3.59990i	−0.486888	+	0.281105i
$165$	3.28521	−	1.48248i	0.255753	−	0.115411i
$166$	−8.80483	+	5.08347i	−0.683387	+	0.394554i
$167$	−2.23171	+	3.86544i	−0.172695	+	0.299117i	−0.939361	−	0.342929i	$-0.888581\pi$
$167$	−2.23171	+	3.86544i	−0.172695	+	0.299117i	0.766666	+	0.642046i	$0.221914\pi$
$168$	1.20353	−	0.543101i	0.0928540	−	0.0419011i
$169$	2.04411	−	3.54050i	0.157239	−	0.272346i
$170$	8.73353			0.669831
$171$	−3.48353	−	0.703964i	−0.266392	−	0.0538335i
$172$	−5.87081	−	3.38952i	−0.447645	−	0.258448i
$173$	5.19202	−	2.99762i	0.394742	−	0.227905i	−0.289471	−	0.957187i	$-0.593479\pi$
$173$	5.19202	−	2.99762i	0.394742	−	0.227905i	0.684213	+	0.729282i	$0.260146\pi$
$174$	22.8093	+	16.3976i	1.72917	+	1.24310i
$175$	0.179912	+	0.311616i	0.0136000	+	0.0235560i
$176$	5.11711	+	8.86309i	0.385716	+	0.668080i
$177$	−2.59170	+	1.16953i	−0.194804	+	0.0879071i
$178$			16.4712i			1.23457i
$179$	−9.74740	+	16.8830i	−0.728555	+	1.26189i	0.228940	+	0.973441i	$0.426474\pi$
$179$	−9.74740	+	16.8830i	−0.728555	+	1.26189i	−0.957494	+	0.288453i	$0.906859\pi$
$180$	−1.60607	−	1.41717i	−0.119709	−	0.105630i
$181$	12.4107	−	7.16535i	0.922483	−	0.532596i	0.0380568	−	0.999276i	$-0.487883\pi$
$181$	12.4107	−	7.16535i	0.922483	−	0.532596i	0.884426	+	0.466680i	$0.154550\pi$
$182$	−2.45042			−0.181637
$183$	1.80638	+	1.29861i	0.133532	+	0.0959959i
$184$		−	14.9317i		−	1.10078i
$185$	−8.64363			−0.635492
$186$	−14.9072	+	5.49324i	−1.09305	+	0.402784i
$187$	−11.0315			−0.806706
$188$		−	9.40940i		−	0.686251i
$189$	1.37045	−	1.27186i	0.0996859	−	0.0925140i
$190$	1.95161			0.141585
$191$	−18.7342	+	10.8162i	−1.35556	+	0.782631i	−0.989021	−	0.147772i	$-0.952790\pi$
$191$	−18.7342	+	10.8162i	−1.35556	+	0.782631i	−0.366536	+	0.930404i	$0.619456\pi$
$192$	−3.50727	+	4.87866i	−0.253115	+	0.352087i
$193$	4.00849	−	6.94290i	0.288537	−	0.499761i	−0.684924	−	0.728615i	$-0.740164\pi$
$193$	4.00849	−	6.94290i	0.288537	−	0.499761i	0.973461	+	0.228854i	$0.0734978\pi$
$194$		−	27.5885i		−	1.98074i
$195$	−2.94501	−	6.52622i	−0.210897	−	0.467352i
$196$	−2.45269	−	4.24818i	−0.175192	−	0.303442i
$197$	9.29376	+	16.0973i	0.662153	+	1.14688i	0.980049	+	0.198757i	$0.0636903\pi$
$197$	9.29376	+	16.0973i	0.662153	+	1.14688i	−0.317896	+	0.948126i	$0.602976\pi$
$198$	7.71141	+	6.80443i	0.548026	+	0.483570i
$199$	2.95764	−	1.70760i	0.209662	−	0.121048i	−0.391492	−	0.920181i	$-0.628041\pi$
$199$	2.95764	−	1.70760i	0.209662	−	0.121048i	0.601154	+	0.799133i	$0.294708\pi$
$200$	−1.83478	−	1.05931i	−0.129738	−	0.0749044i
$201$	−8.56820	−	0.857083i	−0.604354	−	0.0604540i
$202$	−18.3629			−1.29201
$203$	1.77122	−	3.06785i	0.124316	−	0.215321i
$204$	2.69655	+	5.97562i	0.188796	+	0.418377i
$205$	−5.04205	+	8.73309i	−0.352152	+	0.609946i
$206$	7.47817	−	4.31752i	0.521029	−	0.300816i
$207$	−6.73529	−	20.0420i	−0.468135	−	1.39302i
$208$	17.6070	−	10.1654i	1.22082	−	0.704842i
$209$	−2.46513			−0.170516
$210$	−0.599314	+	0.833655i	−0.0413566	+	0.0575276i
$211$	−6.84117	+	11.8492i	−0.470965	+	0.815736i	−0.999448	−	0.0332078i	$-0.989428\pi$
$211$	−6.84117	+	11.8492i	−0.470965	+	0.815736i	0.528483	+	0.848944i	$0.322761\pi$
$212$	−1.24757	−	2.16085i	−0.0856832	−	0.148408i
$213$	0.977858	−	9.77558i	0.0670017	−	0.669812i
$214$	−10.7444	+	18.6099i	−0.734475	+	1.27215i
$215$	−9.49478			−0.647539
$216$	−3.24378	+	10.5199i	−0.220711	+	0.715789i
$217$	0.876382	+	1.80156i	0.0594927	+	0.122298i
$218$			13.5740i			0.919349i
$219$	0.337984	−	3.37881i	0.0228389	−	0.228319i
$220$	−1.28666	−	0.742851i	−0.0867463	−	0.0500830i
$221$			21.9147i			1.47414i
$222$	−10.1447	−	22.4808i	−0.680865	−	1.50881i
$223$	−20.4802	−	11.8242i	−1.37145	−	0.791809i	−0.380343	−	0.924845i	$-0.624194\pi$
$223$	−20.4802	−	11.8242i	−1.37145	−	0.791809i	−0.991111	+	0.133036i	$0.957527\pi$
$224$	−1.20442	−	0.695370i	−0.0804734	−	0.0464613i
$225$	−2.94056	−	0.594238i	−0.196037	−	0.0396159i
$226$	−1.36674	−	2.36727i	−0.0909144	−	0.157468i
$227$	2.61546	−	1.51004i	0.173594	−	0.100225i	−0.410685	−	0.911777i	$-0.634711\pi$
$227$	2.61546	−	1.51004i	0.173594	−	0.100225i	0.584279	+	0.811553i	$0.301377\pi$
$228$	0.602575	+	1.33532i	0.0399065	+	0.0884338i
$229$	3.11036	+	1.79577i	0.205539	+	0.118668i	0.599236	−	0.800572i	$-0.295471\pi$
$229$	3.11036	+	1.79577i	0.205539	+	0.118668i	−0.393698	+	0.919240i	$0.628804\pi$
$230$	5.80535	+	10.0552i	0.382793	+	0.663018i
$231$	0.757008	−	1.05301i	0.0498075	−	0.0692830i
$232$			20.8577i			1.36938i
$233$			14.2031i			0.930476i	0.885186	+	0.465238i	$0.154031\pi$
$233$			14.2031i			0.930476i	−0.885186	+	0.465238i	$0.845969\pi$
$234$	13.5173	−	15.3191i	0.883655	−	1.00144i
$235$	−6.58945	−	11.4133i	−0.429849	−	0.744520i
$236$	1.01504	+	0.586036i	0.0660738	+	0.0381477i
$237$	2.55823	−	1.15442i	0.166175	−	0.0749878i
$238$	2.72151	−	1.57126i	0.176409	−	0.101850i
$239$	−1.29960	−	2.25098i	−0.0840644	−	0.145604i	0.820928	−	0.571032i	$-0.193457\pi$
$239$	−1.29960	−	2.25098i	−0.0840644	−	0.145604i	−0.904992	+	0.425428i	$0.860123\pi$
$240$	0.847885	−	8.47625i	0.0547307	−	0.547140i
$241$	10.2337	+	5.90845i	0.659212	+	0.380597i	0.791977	−	0.610551i	$-0.209052\pi$
$241$	10.2337	+	5.90845i	0.659212	+	0.380597i	−0.132764	+	0.991148i	$0.542385\pi$
$242$	−9.51596	−	5.49404i	−0.611709	−	0.353170i
$243$	0.391287	+	15.5835i	0.0251011	+	0.999685i
$244$		−	0.917062i		−	0.0587089i
$245$	−5.95005	−	3.43526i	−0.380135	−	0.219471i
$246$	−28.6312	−	2.86399i	−1.82546	−	0.182602i
$247$			4.89709i			0.311594i
$248$	−9.77249	−	6.60629i	−0.620554	−	0.419500i
$249$	−10.6362	−	1.06394i	−0.674041	−	0.0674248i
$250$	1.64741			0.104192
$251$	2.23825	−	3.87677i	0.141277	−	0.244699i	−0.786701	−	0.617335i	$-0.788212\pi$
$251$	2.23825	−	3.87677i	0.141277	−	0.244699i	0.927978	+	0.372635i	$0.121546\pi$
$252$	−0.755443	−	0.152662i	−0.0475884	−	0.00961683i
$253$	−7.33288	−	12.7009i	−0.461014	−	0.798500i
$254$	2.87240	−	4.97514i	0.180230	−	0.312168i
$255$	7.45557	+	5.35980i	0.466886	+	0.335644i
$256$	15.2115			0.950719
$257$	4.59932	−	2.65542i	0.286898	−	0.165640i	−0.349644	−	0.936883i	$-0.613698\pi$
$257$	4.59932	−	2.65542i	0.286898	−	0.165640i	0.636542	+	0.771242i	$0.280364\pi$
$258$	−11.1436	−	24.6946i	−0.693772	−	1.53742i
$259$	−2.69349	+	1.55509i	−0.167366	+	0.0966285i
$260$	−1.47571	+	2.55600i	−0.0915196	+	0.158517i
$261$	9.40838	+	27.9963i	0.582364	+	1.73293i
$262$	16.5229	−	28.6185i	1.02079	−	1.76806i
$263$	−15.7968			−0.974072			−0.487036	−	0.873382i	$-0.661922\pi$
$263$	−15.7968			−0.974072			−0.487036	+	0.873382i	$0.661922\pi$
$264$	−0.760035	+	7.59802i	−0.0467769	+	0.467626i
$265$	−3.02651	−	1.74736i	−0.185917	−	0.107339i
$266$	0.608153	−	0.351117i	0.0372882	−	0.0215284i
$267$	−10.1085	+	14.0610i	−0.618627	+	0.860520i
$268$	1.77478	+	3.07400i	0.108412	+	0.187775i
$269$	8.53254	+	14.7788i	0.520238	+	0.901079i	0.999723	+	0.0235291i	$0.00749024\pi$
$269$	8.53254	+	14.7788i	0.520238	+	0.901079i	−0.479485	+	0.877550i	$0.659176\pi$
$270$	−1.90568	−	8.34540i	−0.115976	−	0.507885i
$271$			3.59484i			0.218371i	0.994021	+	0.109186i	$0.0348243\pi$
$271$			3.59484i			0.218371i	−0.994021	+	0.109186i	$0.965176\pi$
$272$	−13.0365	+	22.5799i	−0.790456	+	1.36911i
$273$	−2.09186	−	1.50383i	−0.126605	−	0.0910162i
$274$	−7.80053	+	4.50364i	−0.471247	+	0.272075i
$275$	−2.08089			−0.125482
$276$	−5.08745	+	7.07672i	−0.306229	+	0.425969i
$277$			10.1695i			0.611025i	0.952188	+	0.305512i	$0.0988277\pi$
$277$			10.1695i			0.611025i	−0.952188	+	0.305512i	$0.901172\pi$
$278$	−0.158027			−0.00947781
$279$	−16.0971	−	4.45918i	−0.963706	−	0.266964i
$280$	−0.762328			−0.0455578
$281$		−	18.3579i		−	1.09514i	−0.836759	−	0.547571i	$-0.815553\pi$
$281$		−	18.3579i		−	1.09514i	0.836759	−	0.547571i	$-0.184447\pi$
$282$	21.9505	−	30.5335i	1.30713	−	1.81824i
$283$	−7.23838			−0.430277			−0.215139	−	0.976584i	$-0.569020\pi$
$283$	−7.23838			−0.430277			−0.215139	+	0.976584i	$0.569020\pi$
$284$	−3.50717	+	2.02487i	−0.208112	+	0.120154i
$285$	1.66603	+	1.19771i	0.0986874	+	0.0709463i
$286$	7.08550	−	12.2724i	0.418974	−	0.725685i
$287$			3.62850i			0.214183i
$288$	10.9911	−	3.69366i	0.647659	−	0.217651i
$289$	−5.55217	−	9.61665i	−0.326598	−	0.565685i
$290$	−8.10937	−	14.0458i	−0.476199	−	0.824800i
$291$	16.9312	−	23.5515i	0.992523	−	1.38061i
$292$	−1.21221	+	0.699870i	−0.0709393	+	0.0409568i
$293$	27.8746	+	16.0934i	1.62845	+	0.940186i	0.984556	+	0.175072i	$0.0560160\pi$
$293$	27.8746	+	16.0934i	1.62845	+	0.940186i	0.643895	+	0.765114i	$0.277317\pi$
$294$	1.95130	−	19.5070i	0.113802	−	1.13767i
$295$	1.64162			0.0955787
$296$	9.15627	−	15.8591i	0.532197	−	0.921793i
$297$	2.40711	+	10.5413i	0.139675	+	0.611667i
$298$	−14.6935	+	25.4499i	−0.851171	+	1.47427i
$299$	−25.2310	+	14.5671i	−1.45915	+	0.842439i
$300$	0.508652	+	1.12719i	0.0293671	+	0.0650782i
$301$	−2.95873	+	1.70822i	−0.170538	+	0.0984603i
$302$	6.83285			0.393186
$303$	−15.6759	−	11.2694i	−0.900555	−	0.647408i
$304$	−2.91317	+	5.04575i	−0.167081	+	0.289394i
$305$	−0.642223	−	1.11236i	−0.0367736	−	0.0636937i
$306$	−5.18979	+	25.6814i	−0.296681	+	1.46811i
$307$	8.34789	−	14.4590i	0.476439	−	0.825217i	−0.523196	−	0.852212i	$-0.675261\pi$
$307$	8.34789	−	14.4590i	0.476439	−	0.825217i	0.999636	+	0.0269952i	$0.00859387\pi$
$308$	−0.534590			−0.0304611
$309$	9.03359	+	0.903636i	0.513903	+	0.0514061i
$310$	9.14941	+	0.649261i	0.519651	+	0.0368756i
$311$			10.7014i			0.606820i	0.952860	+	0.303410i	$0.0981252\pi$
$311$			10.7014i			0.606820i	−0.952860	+	0.303410i	$0.901875\pi$
$312$	15.0938	+	1.50985i	0.854520	+	0.0854782i
$313$	−3.37761	−	1.95007i	−0.190914	−	0.110224i	0.401496	−	0.915861i	$-0.368490\pi$
$313$	−3.37761	−	1.95007i	−0.190914	−	0.110224i	−0.592410	+	0.805636i	$0.701824\pi$
$314$			8.76176i			0.494455i
$315$	−1.02324	+	0.343866i	−0.0576528	+	0.0193747i
$316$	−1.00194	−	0.578468i	−0.0563633	−	0.0325413i
$317$	4.29207	+	2.47803i	0.241067	+	0.139180i	0.615667	−	0.788006i	$-0.288887\pi$
$317$	4.29207	+	2.47803i	0.241067	+	0.139180i	−0.374600	+	0.927186i	$0.622220\pi$
$318$	0.992535	−	9.92231i	0.0556586	−	0.556415i
$319$	10.2431	+	17.7416i	0.573506	+	0.993341i
$320$	3.00426	−	1.73451i	0.167943	−	0.0969621i
$321$	−20.5932	+	9.29287i	−1.14940	+	0.518677i
$322$	3.61808	+	2.08890i	0.201628	+	0.116410i
$323$	−3.14012	−	5.43885i	−0.174721	−	0.302626i
$324$	5.12166	−	3.88061i	0.284537	−	0.215589i
$325$			4.13379i			0.229301i
$326$			17.3086i			0.958636i
$327$	−8.33044	+	11.5878i	−0.460674	+	0.640805i
$328$	−10.6822	−	18.5021i	−0.589825	−	1.02161i
$329$	−4.10676	−	2.37104i	−0.226413	−	0.130720i
$330$	−2.44225	−	5.41209i	−0.134442	−	0.297926i
$331$	−13.2391	+	7.64360i	−0.727687	+	0.420130i	−0.817575	−	0.575822i	$-0.804682\pi$
$331$	−13.2391	+	7.64360i	−0.727687	+	0.420130i	0.0898886	+	0.995952i	$0.471349\pi$
$332$	2.20313	+	3.81593i	0.120912	+	0.209426i
$333$	5.13637	−	25.4171i	0.281471	−	1.39285i
$334$	6.36798	+	3.67656i	0.348440	+	0.201172i
$335$	4.30548	+	2.48577i	0.235234	+	0.135812i
$336$	−1.26076	−	2.79388i	−0.0687802	−	0.152419i
$337$			16.4069i			0.893741i	0.894599	+	0.446871i	$0.147462\pi$
$337$			16.4069i			0.893741i	−0.894599	+	0.446871i	$0.852538\pi$
$338$	−5.83267	−	3.36749i	−0.317255	−	0.183167i
$339$	0.286053	−	2.85965i	0.0155362	−	0.155315i
$340$		−	3.78503i		−	0.205272i
$341$	−11.5568	−	0.820098i	−0.625838	−	0.0444108i
$342$	−1.15972	+	5.73882i	−0.0627105	+	0.310320i
$343$	−4.99094			−0.269485
$344$	10.0579	−	17.4208i	0.542286	−	0.939267i
$345$	−1.21503	+	12.1466i	−0.0654150	+	0.653950i
$346$	−4.93832	−	8.55342i	−0.265486	−	0.459834i
$347$	−6.14789	+	10.6485i	−0.330036	+	0.571639i	−0.982519	−	0.186165i	$-0.940394\pi$
$347$	−6.14789	+	10.6485i	−0.330036	+	0.571639i	0.652483	+	0.757804i	$0.273728\pi$
$348$	7.10655	−	9.88532i	0.380951	−	0.529909i
$349$	−3.87208			−0.207268			−0.103634	−	0.994616i	$-0.533047\pi$
$349$	−3.87208			−0.207268			−0.103634	+	0.994616i	$0.533047\pi$
$350$	0.513361	−	0.296389i	0.0274403	−	0.0158427i
$351$	20.9408	−	4.78185i	1.11774	−	0.255236i
$352$	6.96524	−	4.02138i	0.371249	−	0.214340i
$353$	13.4142	−	23.2341i	0.713966	−	1.23663i	−0.249391	−	0.968403i	$-0.580230\pi$
$353$	13.4142	−	23.2341i	0.713966	−	1.23663i	0.963357	−	0.268223i	$-0.0864363\pi$
$354$	1.92670	+	4.26961i	0.102403	+	0.226927i
$355$	−2.83605	+	4.91218i	−0.150522	+	0.260712i
$356$	7.13847			0.378338
$357$	3.28757	+	0.328858i	0.173997	+	0.0174050i
$358$	27.8133	+	16.0580i	1.46998	+	0.848692i
$359$	9.90283	−	5.71740i	0.522651	−	0.301753i	−0.215367	−	0.976533i	$-0.569095\pi$
$359$	9.90283	−	5.71740i	0.522651	−	0.301753i	0.738019	+	0.674780i	$0.235762\pi$
$360$	4.20525	−	4.76578i	0.221636	−	0.251179i
$361$	8.79830	+	15.2391i	0.463069	+	0.802058i
$362$	−11.8043	−	20.4456i	−0.620420	−	1.07460i
$363$	−4.75179	−	10.5301i	−0.249405	−	0.552687i
$364$			1.06199i			0.0556634i
$365$	−0.980246	+	1.69784i	−0.0513084	+	0.0888688i
$366$	2.13935	−	2.97586i	0.111825	−	0.155551i
$367$	−3.84786	+	2.22156i	−0.200857	+	0.115965i	−0.597055	−	0.802200i	$-0.703663\pi$
$367$	−3.84786	+	2.22156i	−0.200857	+	0.115965i	0.396198	+	0.918165i	$0.370329\pi$
$368$	−34.6626			−1.80691
$369$	−22.6840	−	20.0160i	−1.18088	−	1.04199i
$370$			14.2396i			0.740283i
$371$	−1.25748			−0.0652850
$372$	2.38072	+	6.46063i	0.123434	+	0.334968i
$373$	31.2831			1.61978			0.809890	−	0.586582i	$-0.199527\pi$
$373$	31.2831			1.61978			0.809890	+	0.586582i	$0.199527\pi$
$374$			18.1735i			0.939730i
$375$	1.40635	+	1.01103i	0.0726237	+	0.0522091i
$376$	27.9211			1.43992
$377$	35.2446	−	20.3485i	1.81519	−	1.04800i
$378$	−2.09528	−	2.25771i	−0.107769	−	0.116124i
$379$	8.35325	−	14.4683i	0.429078	−	0.743184i	−0.567714	−	0.823226i	$-0.692172\pi$
$379$	8.35325	−	14.4683i	0.429078	−	0.743184i	0.996792	+	0.0800417i	$0.0255054\pi$
$380$		−	0.845809i		−	0.0433891i
$381$	5.50535	−	2.48433i	0.282048	−	0.127276i
$382$	17.8187	+	30.8630i	0.911686	+	1.57909i
$383$	9.37986	+	16.2464i	0.479289	+	0.830152i	0.999718	−	0.0237527i	$-0.00756142\pi$
$383$	9.37986	+	16.2464i	0.479289	+	0.830152i	−0.520429	+	0.853905i	$0.674228\pi$
$384$	18.9085	+	13.5933i	0.964918	+	0.693679i
$385$	−0.648439	+	0.374376i	−0.0330475	+	0.0190800i
$386$	−11.4378	−	6.60364i	−0.582171	−	0.336116i
$387$	5.64216	−	27.9200i	0.286807	−	1.41925i
$388$	−11.9566			−0.607004
$389$	−4.77251	+	8.26623i	−0.241976	+	0.419115i	−0.961277	−	0.275584i	$-0.911129\pi$
$389$	−4.77251	+	8.26623i	−0.241976	+	0.419115i	0.719301	+	0.694698i	$0.244462\pi$
$390$	−10.7514	+	4.85165i	−0.544418	+	0.245673i
$391$	18.6815	−	32.3573i	0.944765	−	1.63638i
$392$	12.6059	−	7.27801i	0.636693	−	0.367595i
$393$	31.6684	−	14.2906i	1.59746	−	0.720867i
$394$	26.5189	−	15.3107i	1.33600	−	0.771340i
$395$	−1.62042			−0.0815320
$396$	2.94898	−	3.34206i	0.148192	−	0.167945i
$397$	−0.802862	+	1.39060i	−0.0402945	+	0.0697921i	−0.885469	−	0.464698i	$-0.846163\pi$
$397$	−0.802862	+	1.39060i	−0.0402945	+	0.0697921i	0.845175	+	0.534490i	$0.179496\pi$
$398$	−2.81312	−	4.87246i	−0.141009	−	0.244235i
$399$	0.734645	+	0.0734871i	0.0367783	+	0.00367895i
$400$	−2.45909	+	4.25928i	−0.122955	+	0.212964i
$401$	−34.7065			−1.73316			−0.866580	−	0.499039i	$-0.833687\pi$
$401$	−34.7065			−1.73316			−0.866580	+	0.499039i	$0.833687\pi$
$402$	−1.41197	+	14.1154i	−0.0704227	+	0.704011i
$403$	−1.62916	+	22.9582i	−0.0811545	+	1.14363i
$404$			7.95830i			0.395940i
$405$	3.49478	−	8.29376i	0.173657	−	0.412120i
$406$	−5.05402	−	2.91794i	−0.250827	−	0.144815i
$407$		−	17.9864i		−	0.891555i
$408$	−17.7318	+	8.00162i	−0.877855	+	0.396139i
$409$	−28.1942	−	16.2779i	−1.39411	−	0.804892i	−0.400346	−	0.916364i	$-0.631110\pi$
$409$	−28.1942	−	16.2779i	−1.39411	−	0.804892i	−0.993768	+	0.111472i	$0.964443\pi$
$410$	14.3870	+	8.30635i	0.710524	+	0.410222i
$411$	−9.42301	−	0.942590i	−0.464803	−	0.0464945i
$412$	−1.87118	−	3.24097i	−0.0921862	−	0.159671i
$413$	0.511555	−	0.295346i	0.0251720	−	0.0145330i
$414$	−33.0175	+	11.0958i	−1.62272	+	0.545329i
$415$	5.34463	+	3.08573i	0.262358	+	0.151472i
$416$	−7.98868	−	13.8368i	−0.391677	−	0.678405i
$417$	−0.134903	−	0.0969817i	−0.00660623	−	0.00474921i
$418$			4.06108i			0.198634i
$419$		−	7.27771i		−	0.355540i	−0.984072	−	0.177770i	$-0.943112\pi$
$419$		−	7.27771i		−	0.355540i	0.984072	−	0.177770i	$-0.0568882\pi$
$420$	0.361298	+	0.259737i	0.0176296	+	0.0126739i
$421$	−9.94892	−	17.2320i	−0.484881	−	0.839838i	0.514968	−	0.857209i	$-0.327804\pi$
$421$	−9.94892	−	17.2320i	−0.484881	−	0.839838i	−0.999849	+	0.0173711i	$0.994470\pi$
$422$	19.5206	+	11.2702i	0.950249	+	0.548627i
$423$	37.4771	−	12.5945i	1.82220	−	0.612364i
$424$	6.41201	−	3.70198i	0.311395	−	0.179784i
$425$	−2.65068	−	4.59111i	−0.128577	−	0.222701i
$426$	−16.1044	−	1.61094i	−0.780262	−	0.0780501i
$427$	−0.400254	−	0.231087i	−0.0193697	−	0.0111831i
$428$	8.06537	+	4.65654i	0.389854	+	0.225083i
$429$	13.5803	−	6.12824i	0.655665	−	0.295874i
$430$			15.6418i			0.754317i
$431$	−16.2175	−	9.36319i	−0.781171	−	0.451009i	0.0556742	−	0.998449i	$-0.482269\pi$
$431$	−16.2175	−	9.36319i	−0.781171	−	0.451009i	−0.836845	+	0.547440i	$0.815603\pi$
$432$	24.4211	+	7.53017i	1.17496	+	0.362295i
$433$			28.7876i			1.38344i	0.722165	+	0.691721i	$0.243147\pi$
$433$			28.7876i			1.38344i	−0.722165	+	0.691721i	$0.756853\pi$
$434$	2.96791	−	1.44376i	0.142464	−	0.0693029i
$435$	1.69725	−	16.9673i	0.0813769	−	0.813520i
$436$	5.88286			0.281738
$437$	4.17460	−	7.23063i	0.199698	−	0.345888i
$438$	−5.56630	−	0.556800i	−0.265968	−	0.0266050i
$439$	−12.7539	−	22.0904i	−0.608711	−	1.05432i	−0.991453	−	0.130464i	$-0.958353\pi$
$439$	−12.7539	−	22.0904i	−0.608711	−	1.05432i	0.382742	−	0.923855i	$-0.374980\pi$
$440$	2.20430	−	3.81797i	0.105086	−	0.182014i
$441$	13.6373	−	15.4551i	0.649397	−	0.735957i
$442$	36.1026			1.71722
$443$	−11.8700	+	6.85316i	−0.563962	+	0.325604i	−0.754734	−	0.656031i	$-0.772234\pi$
$443$	−11.8700	+	6.85316i	−0.563962	+	0.325604i	0.190772	+	0.981634i	$0.438901\pi$
$444$	−9.74299	+	4.39660i	−0.462382	+	0.208654i
$445$	8.65871	−	4.99911i	0.410462	−	0.236980i
$446$	−19.4794	+	33.7393i	−0.922377	+	1.59760i
$447$	−28.1621	+	12.7084i	−1.33202	+	0.601086i
$448$	0.624117	−	1.08100i	0.0294868	−	0.0510726i
$449$	26.7192			1.26096			0.630478	−	0.776207i	$-0.282859\pi$
$449$	26.7192			1.26096			0.630478	+	0.776207i	$0.282859\pi$
$450$	−0.978956	+	4.84432i	−0.0461484	+	0.228363i
$451$	−18.1726	−	10.4920i	−0.855715	−	0.494047i
$452$	−1.02595	+	0.592334i	−0.0482568	+	0.0278611i
$453$	5.83301	+	4.19335i	0.274059	+	0.197021i
$454$	−2.48766	−	4.30875i	−0.116751	−	0.202219i
$455$	0.743717	+	1.28816i	0.0348660	+	0.0603897i
$456$	−3.96238	+	1.78806i	−0.185555	+	0.0837334i
$457$			17.5365i			0.820324i	0.912013	+	0.410162i	$0.134528\pi$
$457$			17.5365i			0.820324i	−0.912013	+	0.410162i	$0.865472\pi$
$458$	2.95838	−	5.12406i	0.138236	−	0.239432i
$459$	−20.1912	+	18.7385i	−0.942444	+	0.874640i
$460$	4.35781	−	2.51599i	0.203184	−	0.117308i
$461$	−24.4017			−1.13650			−0.568251	−	0.822855i	$-0.692380\pi$
$461$	−24.4017			−1.13650			−0.568251	+	0.822855i	$0.692380\pi$
$462$	−1.73474	−	1.24711i	−0.0807076	−	0.0580206i
$463$			1.85686i			0.0862955i	0.999069	+	0.0431478i	$0.0137386\pi$
$463$			1.85686i			0.0862955i	−0.999069	+	0.0431478i	$0.986261\pi$
$464$	48.4194			2.24781
$465$	7.41214	+	6.16929i	0.343730	+	0.286094i
$466$	23.3984			1.08391
$467$			41.9621i			1.94177i	0.239538	+	0.970887i	$0.423004\pi$
$467$			41.9621i			1.94177i	−0.239538	+	0.970887i	$0.576996\pi$
$468$	−6.63916	−	5.85828i	−0.306895	−	0.270799i
$469$	1.78888			0.0826026
$470$	−18.8024	+	10.8556i	−0.867289	+	0.500730i
$471$	−5.37714	+	7.47968i	−0.247765	+	0.344645i
$472$	−1.73898	+	3.01200i	−0.0800430	+	0.138639i
$473$		−	19.7576i		−	0.908455i
$474$	−1.90181	−	4.21447i	−0.0873532	−	0.193577i
$475$	−0.592325	−	1.02594i	−0.0271777	−	0.0470732i
$476$	−0.680971	−	1.17948i	−0.0312123	−	0.0540612i
$477$	6.93667	−	7.86128i	0.317608	−	0.359943i
$478$	−3.70830	+	2.14099i	−0.169614	+	0.0979264i
$479$	−22.1755	−	12.8031i	−1.01323	−	0.584986i	−0.101091	−	0.994877i	$-0.532233\pi$
$479$	−22.1755	−	12.8031i	−1.01323	−	0.584986i	−0.912135	+	0.409891i	$0.865567\pi$
$480$	−6.66124	−	0.666328i	−0.304043	−	0.0304136i
$481$	−35.7309			−1.62919
$482$	9.73366	−	16.8592i	0.443356	−	0.767915i
$483$	1.80669	+	4.00367i	0.0822072	+	0.182173i
$484$	−2.38107	+	4.12413i	−0.108230	+	0.187460i
$485$	−14.5029	+	8.37327i	−0.658544	+	0.380210i
$486$	25.6726	−	0.644612i	1.16453	−	0.0292402i
$487$	16.5539	−	9.55742i	0.750131	−	0.433088i	−0.0756105	−	0.997137i	$-0.524091\pi$
$487$	16.5539	−	9.55742i	0.750131	−	0.433088i	0.825741	+	0.564049i	$0.190757\pi$
$488$	2.72125			0.123185
$489$	−10.6224	+	14.7759i	−0.480361	+	0.668189i
$490$	−5.65930	+	9.80220i	−0.255661	+	0.442818i
$491$	3.70316	+	6.41407i	0.167121	+	0.289463i	0.937407	−	0.348237i	$-0.113219\pi$
$491$	3.70316	+	6.41407i	0.167121	+	0.289463i	−0.770285	+	0.637700i	$0.779886\pi$
$492$	−1.24123	+	12.4085i	−0.0559589	+	0.559418i
$493$	−26.0958	+	45.1993i	−1.17530	+	2.03567i
$494$	8.06754			0.362976
$495$	1.23654	−	6.11898i	0.0555785	−	0.275028i
$496$	−15.3359	+	22.6860i	−0.688604	+	1.01863i
$497$			2.04095i			0.0915493i
$498$	−1.75276	+	17.5222i	−0.0785430	+	0.785189i
$499$	10.5308	+	6.07995i	0.471422	+	0.272176i	0.716835	−	0.697243i	$-0.245590\pi$
$499$	10.5308	+	6.07995i	0.471422	+	0.272176i	−0.245413	+	0.969419i	$0.578923\pi$
$500$		−	0.713974i		−	0.0319299i
$501$	3.17985	+	7.04663i	0.142065	+	0.314820i
$502$	−6.38664	−	3.68733i	−0.285050	−	0.164574i
$503$	−2.11601	−	1.22168i	−0.0943480	−	0.0544718i	0.452084	−	0.891976i	$-0.350681\pi$
$503$	−2.11601	−	1.22168i	−0.0943480	−	0.0544718i	−0.546432	+	0.837504i	$0.684014\pi$
$504$	0.453004	−	2.24167i	0.0201784	−	0.0998519i
$505$	5.57324	+	9.65313i	0.248006	+	0.429559i
$506$	−20.9237	+	12.0803i	−0.930171	+	0.537035i
$507$	−2.91254	−	6.45427i	−0.129351	−	0.286644i
$508$	−2.15618	−	1.24487i	−0.0956649	−	0.0552322i
$509$	−1.18244	−	2.04804i	−0.0524105	−	0.0907777i	0.838630	−	0.544702i	$-0.183357\pi$
$509$	−1.18244	−	2.04804i	−0.0524105	−	0.0907777i	−0.891040	+	0.453924i	$0.850024\pi$
$510$	8.82982	−	12.2824i	0.390991	−	0.543874i
$511$			0.705430i			0.0312064i
$512$			1.83042i			0.0808937i
$513$	−4.51196	+	4.18735i	−0.199208	+	0.184876i
$514$	−4.37458	−	7.57699i	−0.192954	−	0.334207i
$515$	−4.53934	−	2.62079i	−0.200027	−	0.115486i
$516$	−10.7024	+	4.82954i	−0.471147	+	0.212609i
$517$	23.7498	−	13.7119i	1.04451	−	0.603050i
$518$	2.56188	+	4.43730i	0.112562	+	0.194964i
$519$	1.03357	−	10.3325i	0.0453685	−	0.453546i
$520$	−7.58458	−	4.37896i	−0.332606	−	0.192030i
$521$	21.6877	+	12.5214i	0.950154	+	0.548572i	0.893129	−	0.449801i	$-0.148505\pi$
$521$	21.6877	+	12.5214i	0.950154	+	0.548572i	0.0570251	+	0.998373i	$0.481838\pi$
$522$	46.1215	−	15.4995i	2.01868	−	0.678395i
$523$		−	35.6968i		−	1.56091i	−0.625212	−	0.780455i	$-0.714987\pi$
$523$		−	35.6968i		−	1.56091i	0.625212	−	0.780455i	$-0.285013\pi$
$524$	−12.4030	−	7.16087i	−0.541827	−	0.312824i
$525$	0.620137	+	0.0620327i	0.0270650	+	0.00270733i
$526$			26.0239i			1.13469i
$527$	−12.9119	−	26.5427i	−0.562452	−	1.15622i
$528$	17.6381	+	1.76436i	0.767602	+	0.0767837i
$529$	26.6719			1.15965
$530$	−2.87862	+	4.98591i	−0.125039	+	0.216574i
$531$	−0.975512	+	4.82727i	−0.0423336	+	0.209486i
$532$	−0.152171	−	0.263568i	−0.00659745	−	0.0114271i
$533$	−20.8428	+	36.1008i	−0.902801	+	1.56370i
$534$	23.1643	+	16.6528i	1.00242	+	0.720638i
$535$	13.0440			0.563942
$536$	−9.12167	+	5.26640i	−0.393996	+	0.227474i
$537$	13.8886	+	30.7774i	0.599335	+	1.32814i
$538$	24.3468	−	14.0566i	1.04967	−	0.606025i
$539$	7.14841	−	12.3814i	0.307904	−	0.533305i
$540$	−3.61682	+	0.825905i	−0.155643	+	0.0355413i
$541$	21.1575	−	36.6459i	0.909633	−	1.57553i	0.0950591	−	0.995472i	$-0.469696\pi$
$541$	21.1575	−	36.6459i	0.909633	−	1.57553i	0.814574	−	0.580059i	$-0.196971\pi$
$542$	5.92220			0.254380
$543$	2.47058	−	24.6982i	0.106023	−	1.05990i
$544$	17.7449	+	10.2450i	0.760807	+	0.439252i
$545$	7.13570	−	4.11980i	0.305660	−	0.176473i
$546$	−2.47744	+	3.44615i	−0.106025	+	0.147482i
$547$	−11.7023	−	20.2689i	−0.500352	−	0.866636i	−1.00000		0.000407072i	$-0.999870\pi$
$547$	−11.7023	−	20.2689i	−0.500352	−	0.866636i	0.499647	−	0.866229i	$-0.333463\pi$
$548$	1.95184	+	3.38068i	0.0833783	+	0.144415i
$549$	3.65260	−	1.22749i	0.155889	−	0.0523878i
$550$			3.42809i			0.146174i
$551$	−5.83142	+	10.1003i	−0.248427	+	0.430288i
$552$	−20.9992	−	15.0963i	−0.893784	−	0.642541i
$553$	−0.504948	+	0.291532i	−0.0214726	+	0.0123972i
$554$	16.7533			0.711781
$555$	−8.73893	+	12.1560i	−0.370947	+	0.515993i
$556$			0.0684873i			0.00290451i
$557$	26.1777			1.10918			0.554592	−	0.832123i	$-0.312874\pi$
$557$	26.1777			1.10918			0.554592	+	0.832123i	$0.312874\pi$
$558$	−7.34612	+	26.5185i	−0.310986	+	1.12262i
$559$	−39.2494			−1.66007
$560$			1.76968i			0.0747826i
$561$	−11.1532	+	15.5142i	−0.470887	+	0.655011i
$562$	−30.2431			−1.27573
$563$	6.86504	−	3.96353i	0.289327	−	0.167043i	−0.348311	−	0.937379i	$-0.613245\pi$
$563$	6.86504	−	3.96353i	0.289327	−	0.167043i	0.637638	+	0.770336i	$0.279911\pi$
$564$	−13.2329	−	9.51315i	−0.557207	−	0.400576i
$565$	−0.829630	+	1.43696i	−0.0349028	+	0.0604534i
$566$			11.9246i			0.501229i
$567$	−0.403114	−	3.21322i	−0.0169292	−	0.134943i
$568$	−6.00850	−	10.4070i	−0.252111	−	0.436669i
$569$	15.3485	+	26.5844i	0.643443	+	1.11448i	0.984659	+	0.174491i	$0.0558280\pi$
$569$	15.3485	+	26.5844i	0.643443	+	1.11448i	−0.341216	+	0.939985i	$0.610839\pi$
$570$	1.97313	−	2.74465i	0.0826452	−	0.114961i
$571$	−17.2465	+	9.95726i	−0.721743	+	0.416699i	−0.815394	−	0.578907i	$-0.803480\pi$
$571$	−17.2465	+	9.95726i	−0.721743	+	0.416699i	0.0936509	+	0.995605i	$0.470146\pi$
$572$	−5.31876	−	3.07079i	−0.222389	−	0.128396i
$573$	−3.72937	+	37.2823i	−0.155797	+	1.55749i
$574$	5.97764			0.249502
$575$	3.52392	−	6.10360i	0.146957	−	0.254538i
$576$	3.31518	+	9.86491i	0.138133	+	0.411038i
$577$	7.43741	−	12.8820i	0.309624	−	0.536284i	−0.668656	−	0.743571i	$-0.733130\pi$
$577$	7.43741	−	12.8820i	0.309624	−	0.536284i	0.978280	+	0.207288i	$0.0664636\pi$
$578$	−15.8426	+	9.14673i	−0.658965	+	0.380454i
$579$	−5.71148	−	12.6568i	−0.237361	−	0.525999i
$580$	−6.08734	+	3.51453i	−0.252763	+	0.145933i
$581$	2.22063			0.0921273
$582$	−38.7991	−	27.8927i	−1.60828	−	1.15619i
$583$	3.63605	−	6.29783i	0.150590	−	0.260829i
$584$	−2.07677	−	3.59706i	−0.0859372	−	0.148848i
$585$	−12.1556	−	2.45645i	−0.502574	−	0.101562i
$586$	26.5125	−	45.9210i	1.09522	−	1.89698i
$587$	4.71197			0.194484			0.0972419	−	0.995261i	$-0.468998\pi$
$587$	4.71197			0.194484			0.0972419	+	0.995261i	$0.468998\pi$
$588$	−8.45418	−	0.845677i	−0.348644	−	0.0348751i
$589$	−2.88532	−	5.93129i	−0.118888	−	0.244394i
$590$		−	2.70442i		−	0.111339i
$591$	32.0346	+	3.20445i	1.31773	+	0.131813i
$592$	−36.8156	−	21.2555i	−1.51311	−	0.873596i
$593$		−	9.70917i		−	0.398708i	−0.979928	−	0.199354i	$-0.936116\pi$
$593$		−	9.70917i		−	0.398708i	0.979928	−	0.199354i	$-0.0638843\pi$
$594$	17.3659	−	3.96551i	0.712530	−	0.162707i
$595$	−1.65199	−	0.953775i	−0.0677249	−	0.0391010i
$596$	11.0297	+	6.36802i	0.451796	+	0.260844i
$597$	0.588772	−	5.88591i	0.0240968	−	0.240894i
$598$	23.9981	+	41.5659i	0.981355	+	1.69976i
$599$	22.9673	−	13.2602i	0.938420	−	0.541797i	0.0489554	−	0.998801i	$-0.484411\pi$
$599$	22.9673	−	13.2602i	0.938420	−	0.541797i	0.889465	+	0.457004i	$0.151077\pi$
$600$	−3.34477	+	1.50935i	−0.136550	+	0.0616191i
$601$	17.1832	+	9.92074i	0.700919	+	0.404676i	0.807689	−	0.589608i	$-0.200718\pi$
$601$	17.1832	+	9.92074i	0.700919	+	0.404676i	−0.106771	+	0.994284i	$0.534051\pi$
$602$	2.81415	+	4.87425i	0.114696	+	0.198660i
$603$	−9.86803	+	11.1834i	−0.401857	+	0.455422i
$604$		−	2.96129i		−	0.120493i
$605$			6.66990i			0.271170i
$606$	−18.5653	+	25.8247i	−0.754165	+	1.04905i
$607$	−16.0608	−	27.8181i	−0.651886	−	1.12910i	−0.982665	−	0.185392i	$-0.940645\pi$
$607$	−16.0608	−	27.8181i	−0.651886	−	1.12910i	0.330778	−	0.943708i	$-0.392689\pi$
$608$	3.96531	+	2.28937i	0.160814	+	0.0928463i
$609$	−2.52372	−	5.59264i	−0.102266	−	0.226625i
$610$	−1.83252	+	1.05801i	−0.0741967	+	0.0428375i
$611$	−27.2394	−	47.1801i	−1.10199	−	1.90870i
$612$	11.1301	+	2.24921i	0.449908	+	0.0909189i
$613$	36.0192	+	20.7957i	1.45480	+	0.839931i	0.998748	−	0.0500212i	$-0.0159289\pi$
$613$	36.0192	+	20.7957i	1.45480	+	0.839931i	0.456054	+	0.889952i	$0.349262\pi$
$614$	−23.8199	−	13.7524i	−0.961294	−	0.555003i
$615$	7.18416	+	15.9203i	0.289693	+	0.641968i
$616$		−	1.58632i		−	0.0639147i
$617$	2.25012	+	1.29911i	0.0905864	+	0.0523001i	0.544609	−	0.838690i	$-0.316678\pi$
$617$	2.25012	+	1.29911i	0.0905864	+	0.0523001i	−0.454022	+	0.890990i	$0.650011\pi$
$618$	1.48866	−	14.8821i	0.0598828	−	0.598645i
$619$			21.5641i			0.866732i	0.901218	+	0.433366i	$0.142674\pi$
$619$			21.5641i			0.866732i	−0.901218	+	0.433366i	$0.857326\pi$
$620$	0.281384	−	3.96527i	0.0113006	−	0.159249i
$621$	−34.9957	−	10.7908i	−1.40433	−	0.433021i
$622$	17.6296			0.706883
$623$	1.79880	−	3.11561i	0.0720672	−	0.124824i
$624$	3.50498	−	35.0390i	0.140311	−	1.40268i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−3.21257	+	5.56433i	−0.128400	+	0.222395i
$627$	−2.49231	+	3.46683i	−0.0995331	+	0.138452i
$628$	3.79727			0.151528
$629$	39.6838	−	22.9115i	1.58230	−	0.913540i
$630$	0.566491	+	1.68569i	0.0225695	+	0.0671596i
$631$	−22.8437	+	13.1888i	−0.909394	+	0.525039i	−0.880236	−	0.474536i	$-0.842616\pi$
$631$	−22.8437	+	13.1888i	−0.909394	+	0.525039i	−0.0291580	+	0.999575i	$0.509283\pi$
$632$	1.71652	−	2.97310i	0.0682795	−	0.118264i
$633$	9.74762	+	21.6010i	0.387433	+	0.858562i
$634$	4.08234	−	7.07083i	0.162131	−	0.280818i
$635$	−3.48716			−0.138384
$636$	−4.30024	−	0.430156i	−0.170515	−	0.0170568i
$637$	−24.5963	−	14.2007i	−0.974539	−	0.562650i
$638$	29.2278	−	16.8747i	1.15714	−	0.668076i
$639$	−12.7593	−	11.2586i	−0.504749	−	0.445382i
$640$	−6.72252	−	11.6437i	−0.265731	−	0.460259i
$641$	−9.22971	−	15.9863i	−0.364552	−	0.631422i	0.624152	−	0.781303i	$-0.285444\pi$
$641$	−9.22971	−	15.9863i	−0.364552	−	0.631422i	−0.988704	+	0.149881i	$0.952111\pi$
$642$	15.3092	+	33.9256i	0.604206	+	1.33894i
$643$			26.3443i			1.03892i	0.854496	+	0.519458i	$0.173866\pi$
$643$			26.3443i			1.03892i	−0.854496	+	0.519458i	$0.826134\pi$
$644$	0.905310	−	1.56804i	0.0356742	−	0.0617895i
$645$	−9.59947	+	13.3530i	−0.377979	+	0.525774i
$646$	−8.96004	+	5.17308i	−0.352528	+	0.203532i
$647$	20.6197			0.810642			0.405321	−	0.914174i	$-0.367160\pi$
$647$	20.6197			0.810642			0.405321	+	0.914174i	$0.367160\pi$
$648$	11.5151	+	15.1978i	0.452358	+	0.597026i
$649$			3.41603i			0.134091i
$650$	6.81006			0.267113
$651$	3.41967	+	0.588919i	0.134027	+	0.0230816i
$652$	7.50140			0.293777
$653$		−	24.0235i		−	0.940111i	−0.882637	−	0.470056i	$-0.844234\pi$
$653$		−	24.0235i		−	0.940111i	0.882637	−	0.470056i	$-0.155766\pi$
$654$	19.0899	+	13.7237i	0.746473	+	0.536639i
$655$	−20.0592			−0.783777
$656$	−42.9510	+	24.7978i	−1.67696	+	0.968190i
$657$	−4.41008	−	3.89139i	−0.172054	−	0.151817i
$658$	−3.90608	+	6.76554i	−0.152275	+	0.263748i
$659$			22.6042i			0.880536i	0.897866	+	0.440268i	$0.145117\pi$
$659$			22.6042i			0.880536i	−0.897866	+	0.440268i	$0.854883\pi$
$660$	−2.34555	+	1.05845i	−0.0913005	+	0.0412001i
$661$	−20.8193	−	36.0601i	−0.809778	−	1.40258i	−0.913018	−	0.407920i	$-0.866254\pi$
$661$	−20.8193	−	36.0601i	−0.809778	−	1.40258i	0.103240	−	0.994656i	$-0.467079\pi$
$662$	12.5922	+	21.8103i	0.489409	+	0.847681i
$663$	30.8198	+	22.1563i	1.19694	+	0.860480i
$664$	−11.3232	+	6.53747i	−0.439427	+	0.253703i
$665$	−0.369156	−	0.213132i	−0.0143153	−	0.00826491i
$666$	−41.8725	−	8.46173i	−1.62253	−	0.327885i
$667$	−69.3856			−2.68662
$668$	1.59339	−	2.75982i	0.0616499	−	0.106781i
$669$	−37.3350	+	16.8477i	−1.44346	+	0.651371i
$670$	4.09509	−	7.09291i	0.158207	−	0.274023i
$671$	2.31471	−	1.33640i	0.0893582	−	0.0515910i
$672$	−2.19563	+	0.990796i	−0.0846983	+	0.0382208i
$673$	−38.5175	+	22.2381i	−1.48474	+	0.857216i	−0.999849	−	0.0173586i	$-0.994474\pi$
$673$	−38.5175	+	22.2381i	−1.48474	+	0.857216i	−0.484892	+	0.874574i	$0.661141\pi$
$674$	27.0290			1.04112
$675$	−3.80869	+	3.53467i	−0.146596	+	0.136050i
$676$	−1.45944	+	2.52782i	−0.0561323	+	0.0972240i
$677$	−17.7374	−	30.7220i	−0.681702	−	1.18074i	−0.974461	−	0.224557i	$-0.927907\pi$
$677$	−17.7374	−	30.7220i	−0.681702	−	1.18074i	0.292759	−	0.956186i	$-0.405427\pi$
$678$	−4.71103	−	0.471247i	−0.180926	−	0.0180981i
$679$	−3.01290	+	5.21849i	−0.115624	+	0.200267i
$680$	11.2315			0.430710
$681$	0.520654	−	5.20494i	0.0199515	−	0.199454i
$682$	−1.35104	+	19.0389i	−0.0517340	+	0.729038i
$683$		−	14.7506i		−	0.564418i	−0.959353	−	0.282209i	$-0.908933\pi$
$683$		−	14.7506i		−	0.564418i	0.959353	−	0.282209i	$-0.0910671\pi$
$684$	2.48715	+	0.502612i	0.0950986	+	0.0192179i
$685$	4.73502	+	2.73376i	0.180916	+	0.104452i
$686$			8.22214i			0.313923i
$687$	5.67014	−	2.55870i	0.216329	−	0.0976204i
$688$	−40.4409	−	23.3486i	−1.54180	−	0.890156i
$689$	−12.5109	−	7.22320i	−0.476629	−	0.275182i
$690$	20.0105	+	2.00166i	0.761785	+	0.0762019i
$691$	−11.3297	−	19.6236i	−0.431002	−	0.746517i	0.565958	−	0.824434i	$-0.308506\pi$
$691$	−11.3297	−	19.6236i	−0.431002	−	0.746517i	−0.996960	+	0.0779171i	$0.975173\pi$
$692$	−3.70697	+	2.14022i	−0.140918	+	0.0813590i
$693$	−0.715548	−	2.12924i	−0.0271814	−	0.0808832i
$694$	17.5424	+	10.1281i	0.665901	+	0.384458i
$695$	0.0479620	+	0.0830726i	0.00181930	+	0.00315112i
$696$	29.3333	+	21.0877i	1.11188	+	0.799327i
$697$		−	53.4594i		−	2.02492i
$698$			6.37892i			0.241446i
$699$	19.9746	+	14.3597i	0.755507	+	0.543134i
$700$	−0.128452	−	0.222486i	−0.00485504	−	0.00840918i
$701$	0.901706	+	0.520600i	0.0340570	+	0.0196628i	0.516932	−	0.856027i	$-0.327074\pi$
$701$	0.901706	+	0.520600i	0.0340570	+	0.0196628i	−0.482875	+	0.875689i	$0.660407\pi$
$702$	−7.87768	−	34.4981i	−0.297324	−	1.30205i
$703$	8.86781	−	5.11983i	0.334456	−	0.193098i
$704$	3.60932	+	6.25153i	0.136032	+	0.235614i
$705$	−22.7132	−	2.27202i	−0.855428	−	0.0855690i
$706$	−38.2762	−	22.0988i	−1.44054	−	0.831698i
$707$	3.47342	+	2.00538i	0.130631	+	0.0754201i
$708$	1.85041	−	0.835013i	0.0695427	−	0.0313817i
$709$			9.89713i			0.371695i	0.982579	+	0.185847i	$0.0595030\pi$
$709$			9.89713i			0.371695i	−0.982579	+	0.185847i	$0.940497\pi$
$710$	8.09240	+	4.67215i	0.303702	+	0.175343i
$711$	0.962913	−	4.76493i	0.0361120	−	0.178699i
$712$			21.1824i			0.793844i
$713$	21.9766	−	32.5094i	0.823030	−	1.21749i
$714$	0.541765	−	5.41599i	0.0202750	−	0.202688i
$715$	−8.60196			−0.321695
$716$	6.95939	−	12.0540i	0.260085	−	0.450480i
$717$	−4.47960	−	0.448098i	−0.167294	−	0.0167345i
$718$	−9.41893	−	16.3141i	−0.351511	−	0.608836i
$719$	−12.6929	+	21.9847i	−0.473364	+	0.819891i	−0.999535	−	0.0304879i	$-0.990294\pi$
$719$	−12.6929	+	21.9847i	−0.473364	+	0.819891i	0.526171	+	0.850379i	$0.323627\pi$
$720$	−11.0634	−	9.76213i	−0.412307	−	0.363813i
$721$	−1.88604			−0.0702398
$722$	25.1051	−	14.4945i	0.934316	−	0.539428i
$723$	18.6559	−	8.41864i	0.693821	−	0.313093i
$724$	−8.86095	+	5.11587i	−0.329315	+	0.190130i
$725$	−4.92248	+	8.52599i	−0.182816	+	0.316647i
$726$	−17.3474	+	7.82817i	−0.643824	+	0.290531i
$727$	15.2782	−	26.4626i	0.566636	−	0.981442i	−0.430260	−	0.902705i	$-0.641578\pi$
$727$	15.2782	−	26.4626i	0.566636	−	0.981442i	0.996895	−	0.0787367i	$-0.0250887\pi$
$728$	−3.15130			−0.116795
$729$	22.3116	+	15.2051i	0.826354	+	0.563151i
$730$	2.79704	+	1.61487i	0.103523	+	0.0597691i
$731$	43.5916	−	25.1676i	1.61229	−	0.930857i
$732$	−1.28971	−	0.927173i	−0.0476691	−	0.0342693i
$733$	−13.5381	−	23.4486i	−0.500040	−	0.866095i	−1.00000		4.65302e-5i	$-0.999985\pi$
$733$	−13.5381	−	23.4486i	−0.500040	−	0.866095i	0.499960	−	0.866049i	$-0.333348\pi$
$734$	3.65984	+	6.33902i	0.135087	+	0.233978i
$735$	−10.8468	+	4.89473i	−0.400092	+	0.180545i
$736$			27.2403i			1.00409i
$737$	−5.17261	+	8.95923i	−0.190536	+	0.330018i
$738$	−32.9746	+	37.3699i	−1.21381	+	1.37561i
$739$	−28.9121	+	16.6924i	−1.06355	+	0.614041i	−0.926412	−	0.376512i	$-0.877124\pi$
$739$	−28.9121	+	16.6924i	−1.06355	+	0.614041i	−0.137137	+	0.990552i	$0.543790\pi$
$740$	6.17133			0.226863
$741$	6.88704	+	4.95109i	0.253002	+	0.181883i
$742$			2.07159i			0.0760504i
$743$	−23.8025			−0.873229			−0.436615	−	0.899649i	$-0.643823\pi$
$743$	−23.8025			−0.873229			−0.436615	+	0.899649i	$0.643823\pi$
$744$	−19.1710	+	7.06444i	−0.702843	+	0.258995i
$745$	17.8382			0.653543
$746$		−	51.5363i		−	1.88688i
$747$	−12.2497	+	13.8826i	−0.448195	+	0.507936i
$748$	7.87623			0.287984
$749$	4.06472	−	2.34677i	0.148522	−	0.0857491i
$750$	1.66558	−	2.31685i	0.0608183	−	0.0845992i
$751$	−7.96371	+	13.7936i	−0.290600	+	0.503334i	−0.973952	−	0.226755i	$-0.927188\pi$
$751$	−7.96371	+	13.7936i	−0.290600	+	0.503334i	0.683352	+	0.730089i	$0.260522\pi$
$752$		−	64.8164i		−	2.36361i
$753$	−3.18917	−	7.06728i	−0.116220	−	0.257546i
$754$	−33.5224	−	58.0625i	−1.22081	−	2.11451i
$755$	−2.07381	−	3.59194i	−0.0754736	−	0.130724i
$756$	−0.978469	+	0.908073i	−0.0355866	+	0.0330263i
$757$	5.95353	−	3.43727i	0.216385	−	0.124930i	−0.387890	−	0.921705i	$-0.626796\pi$
$757$	5.95353	−	3.43727i	0.216385	−	0.124930i	0.604275	+	0.796776i	$0.293463\pi$
$758$	−23.8352	−	13.7613i	−0.865734	−	0.499832i
$759$	−25.2757	−	2.52835i	−0.917450	−	0.0917731i
$760$	2.50982			0.0910407
$761$	−10.5999	+	18.3596i	−0.384246	+	0.665533i	−0.991664	−	0.128849i	$-0.958872\pi$
$761$	−10.5999	+	18.3596i	−0.384246	+	0.665533i	0.607418	+	0.794382i	$0.292205\pi$
$762$	−4.09273	−	9.06959i	−0.148264	−	0.328557i
$763$	1.48240	−	2.56759i	0.0536664	−	0.0929530i
$764$	13.3757	−	7.72248i	0.483917	−	0.279389i
$765$	15.0755	−	5.06626i	0.545058	−	0.183171i
$766$	26.7645	−	15.4525i	0.967042	−	0.558322i
$767$	6.78610			0.245032
$768$	15.3792	−	21.3927i	0.554950	−	0.771944i
$769$	5.36071	−	9.28502i	0.193312	−	0.334826i	−0.753034	−	0.657982i	$-0.771410\pi$
$769$	5.36071	−	9.28502i	0.193312	−	0.334826i	0.946346	+	0.323156i	$0.104744\pi$
$770$	0.616753	+	1.06825i	0.0222262	+	0.0384970i
$771$	0.915577	−	9.15296i	0.0329737	−	0.329636i
$772$	−2.86196	+	4.95705i	−0.103004	+	0.178408i
$773$	6.36471			0.228923			0.114461	−	0.993428i	$-0.463486\pi$
$773$	6.36471			0.228923			0.114461	+	0.993428i	$0.463486\pi$
$774$	−45.9957	−	9.29498i	−1.65328	−	0.334101i
$775$	−2.43559	−	5.00679i	−0.0874890	−	0.179849i
$776$		−	35.4795i		−	1.27364i
$777$	−0.536188	+	5.36024i	−0.0192356	+	0.192297i
$778$	13.6179	+	7.86230i	0.488226	+	0.281877i
$779$		−	11.9461i		−	0.428015i
$780$	2.10266	+	4.65955i	0.0752874	+	0.166839i
$781$	−10.2217	−	5.90151i	−0.365762	−	0.211173i
$782$	−53.3060	−	30.7762i	−1.90622	−	1.10055i
$783$	48.8848	+	15.0735i	1.74700	+	0.538682i
$784$	−16.8953	−	29.2635i	−0.603403	−	1.04512i
$785$	4.60595	−	2.65925i	0.164393	−	0.0949126i
$786$	−23.5426	−	52.1710i	−0.839737	−	1.86088i
$787$	−6.74778	−	3.89583i	−0.240533	−	0.138872i	0.374889	−	0.927070i	$-0.377681\pi$
$787$	−6.74778	−	3.89583i	−0.240533	−	0.138872i	−0.615421	+	0.788198i	$0.711014\pi$
$788$	−6.63550	−	11.4930i	−0.236380	−	0.409422i
$789$	−15.9710	+	22.2159i	−0.568582	+	0.790906i
$790$			2.66950i			0.0949764i
$791$			0.597040i			0.0212283i
$792$	9.91707	+	8.75067i	0.352388	+	0.310941i
$793$	−2.65482	−	4.59828i	−0.0942753	−	0.163290i
$794$	2.29089	+	1.32265i	0.0813006	+	0.0469389i
$795$	−5.51727	+	2.48972i	−0.195678	+	0.0883011i
$796$	−2.11168	+	1.21918i	−0.0748466	+	0.0432127i
$797$	15.2894	+	26.4820i	0.541579	+	0.938042i	0.998814	+	0.0486959i	$0.0155065\pi$
$797$	15.2894	+	26.4820i	0.541579	+	0.938042i	−0.457235	+	0.889346i	$0.651160\pi$
$798$	0.121064	−	1.21027i	0.00428561	−	0.0428429i
$799$	60.5058	+	34.9330i	2.14054	+	1.23584i
$800$	3.34724	+	1.93253i	0.118343	+	0.0683253i
$801$	9.55483	+	28.4321i	0.337603	+	1.00460i
$802$			57.1760i			2.01895i
$803$	−3.53301	−	2.03978i	−0.124677	−	0.0719824i
$804$	6.11748	+	0.611935i	0.215747	+	0.0215813i
$805$		−	2.53597i		−	0.0893813i
$806$	37.8217	+	2.68391i	1.33221	+	0.0945367i
$807$	29.4108	+	2.94198i	1.03531	+	0.103563i
$808$	−23.6151			−0.830777
$809$	3.15675	−	5.46766i	0.110986	−	0.192233i	−0.805182	−	0.593027i	$-0.797933\pi$
$809$	3.15675	−	5.46766i	0.110986	−	0.192233i	0.916168	+	0.400795i	$0.131266\pi$
$810$	−13.6633	−	5.75735i	−0.480078	−	0.202293i
$811$	−3.64030	−	6.30519i	−0.127828	−	0.221405i	0.795007	−	0.606601i	$-0.207467\pi$
$811$	−3.64030	−	6.30519i	−0.127828	−	0.221405i	−0.922835	+	0.385196i	$0.874134\pi$
$812$	−1.26461	+	2.19037i	−0.0443790	+	0.0768668i
$813$	5.05562	+	3.63448i	0.177308	+	0.127467i
$814$	−29.6311			−1.03857
$815$	9.09893	−	5.25327i	0.318722	−	0.184014i
$816$	18.5751	+	41.1628i	0.650258	+	1.44099i
$817$	9.74105	−	5.62400i	0.340796	−	0.196759i
$818$	−26.8165	+	46.4475i	−0.937617	+	1.62400i
$819$	−4.22984	+	1.42147i	−0.147803	+	0.0496702i
$820$	3.59990	−	6.23520i	0.125714	−	0.217743i
$821$	−38.8919			−1.35734			−0.678669	−	0.734444i	$-0.737443\pi$
$821$	−38.8919			−1.35734			−0.678669	+	0.734444i	$0.737443\pi$
$822$	−1.55284	+	15.5236i	−0.0541614	+	0.541448i
$823$	17.2906	+	9.98274i	0.602713	+	0.347977i	0.770108	−	0.637913i	$-0.220202\pi$
$823$	17.2906	+	9.98274i	0.602713	+	0.347977i	−0.167395	+	0.985890i	$0.553536\pi$
$824$	9.61712	−	5.55245i	0.335028	−	0.193429i
$825$	−2.10383	+	2.92646i	−0.0732461	+	0.101886i
$826$	−0.486557	−	0.842742i	−0.0169295	−	0.0293228i
$827$	16.7496	+	29.0112i	0.582441	+	1.00882i	0.995189	+	0.0979722i	$0.0312356\pi$
$827$	16.7496	+	29.0112i	0.582441	+	1.00882i	−0.412748	+	0.910845i	$0.635431\pi$
$828$	4.80882	+	14.3095i	0.167118	+	0.497289i
$829$			46.0636i			1.59985i	0.600097	+	0.799927i	$0.295128\pi$
$829$			46.0636i			1.59985i	−0.600097	+	0.799927i	$0.704872\pi$
$830$	5.08347	−	8.80483i	0.176450	−	0.305620i
$831$	14.3019	+	10.2816i	0.496126	+	0.356665i
$832$	12.4190	−	7.17010i	0.430551	−	0.248578i
$833$	36.4231			1.26199
$834$	−0.159769	+	0.222241i	−0.00553235	+	0.00769558i
$835$		−	4.46342i		−	0.154463i
$836$	1.76004			0.0608721
$837$	−22.5457	+	18.1298i	−0.779294	+	0.626658i
$838$	−11.9894			−0.414167
$839$			11.0940i			0.383008i	0.981492	+	0.191504i	$0.0613365\pi$
$839$			11.0940i			0.383008i	−0.981492	+	0.191504i	$0.938664\pi$
$840$	−0.770733	+	1.07210i	−0.0265928	+	0.0369910i
$841$	67.9233			2.34218
$842$	−28.3883	+	16.3900i	−0.978326	+	0.564837i
$843$	−25.8177	−	18.5603i	−0.889209	−	0.639252i
$844$	4.88442	−	8.46006i	0.168129	−	0.291207i
$845$			4.08821i			0.140639i
$846$	−20.7483	−	61.7403i	−0.713342	−	2.12268i
$847$	1.19999	+	2.07845i	0.0412322	+	0.0714163i
$848$	−8.59382	−	14.8849i	−0.295113	−	0.511151i
$849$	−7.31819	+	10.1797i	−0.251160	+	0.349367i
$850$	−7.56346	+	4.36676i	−0.259424	+	0.149779i
$851$	52.7572	+	30.4594i	1.80850	+	1.04414i
$852$	−0.698165	+	6.97951i	−0.0239187	+	0.239114i
$853$	38.6121			1.32205			0.661026	−	0.750363i	$-0.270121\pi$
$853$	38.6121			1.32205			0.661026	+	0.750363i	$0.270121\pi$
$854$	−0.380696	+	0.659385i	−0.0130271	+	0.0225637i
$855$	3.36881	−	1.13211i	0.115211	−	0.0387175i
$856$	−13.8176	+	23.9328i	−0.472277	+	0.818008i
$857$	−13.4243	+	7.75052i	−0.458565	+	0.264753i	−0.711441	−	0.702746i	$-0.751957\pi$
$857$	−13.4243	+	7.75052i	−0.458565	+	0.264753i	0.252875	+	0.967499i	$0.418624\pi$
$858$	−10.0958	−	22.3725i	−0.344663	−	0.763783i
$859$	14.9430	−	8.62736i	0.509850	−	0.294362i	−0.222922	−	0.974836i	$-0.571560\pi$
$859$	14.9430	−	8.62736i	0.509850	−	0.294362i	0.732772	+	0.680474i	$0.238226\pi$
$860$	6.77903			0.231163
$861$	5.10294	+	3.66850i	0.173908	+	0.125022i
$862$	−15.4251	+	26.7170i	−0.525380	+	0.909984i
$863$	0.688727	+	1.19291i	0.0234445	+	0.0406071i	0.877510	−	0.479559i	$-0.159203\pi$
$863$	0.688727	+	1.19291i	0.0234445	+	0.0406071i	−0.854065	+	0.520166i	$0.825870\pi$
$864$	5.91774	−	19.1918i	0.201326	−	0.652918i
$865$	−2.99762	+	5.19202i	−0.101922	+	0.176534i
$866$	47.4250			1.61157
$867$	−19.1378	−	1.91437i	−0.649953	−	0.0650153i
$868$	−0.625714	−	1.28627i	−0.0212381	−	0.0436587i
$869$		−	3.37191i		−	0.114384i
$870$	−27.9522	−	2.79607i	−0.947668	−	0.0947958i
$871$	17.7979	+	10.2757i	0.603061	+	0.348177i
$872$			17.4565i			0.591153i
$873$	−16.0039	−	47.6224i	−0.541650	−	1.61177i
$874$	−11.9118	−	6.87730i	−0.402924	−	0.232628i
$875$	−0.311616	−	0.179912i	−0.0105345	−	0.00608212i
$876$	−0.241312	+	2.41238i	−0.00815318	+	0.0815068i
$877$	−4.50813	−	7.80831i	−0.152229	−	0.263668i	0.779818	−	0.626007i	$-0.215312\pi$
$877$	−4.50813	−	7.80831i	−0.152229	−	0.263668i	−0.932047	+	0.362339i	$0.881978\pi$
$878$	−36.3921	+	21.0110i	−1.22817	+	0.709087i
$879$	50.8149	−	22.9306i	1.71394	−	0.773431i
$880$	−8.86309	−	5.11711i	−0.298775	−	0.172498i
$881$	−10.5103	−	18.2044i	−0.354102	−	0.613322i	0.632862	−	0.774265i	$-0.281880\pi$
$881$	−10.5103	−	18.2044i	−0.354102	−	0.613322i	−0.986964	+	0.160942i	$0.948547\pi$
$882$	−25.4610	−	22.4663i	−0.857315	−	0.756481i
$883$			34.8507i			1.17282i	0.810014	+	0.586410i	$0.199459\pi$
$883$			34.8507i			1.17282i	−0.810014	+	0.586410i	$0.800541\pi$
$884$		−	15.6465i		−	0.526249i
$885$	1.65972	−	2.30869i	0.0557908	−	0.0776059i
$886$	11.2900	+	19.5549i	0.379295	+	0.656958i
$887$	−36.8135	−	21.2543i	−1.23608	−	0.713650i	−0.267787	−	0.963478i	$-0.586292\pi$
$887$	−36.8135	−	21.2543i	−1.23608	−	0.713650i	−0.968290	+	0.249829i	$0.919626\pi$
$888$	−13.0463	−	28.9109i	−0.437805	−	0.970187i
$889$	−1.08665	+	0.627380i	−0.0364452	+	0.0210416i
$890$	−8.23560	−	14.2645i	−0.276058	−	0.478147i
$891$	17.2584	+	7.27226i	0.578178	+	0.243630i
$892$	14.6223	+	8.44220i	0.489592	+	0.282666i
$893$	13.5207	+	7.80619i	0.452454	+	0.261224i
$894$	20.9360	+	46.3947i	0.700204	+	1.55167i
$895$		−	19.4948i		−	0.651639i
$896$	−4.18969	−	2.41892i	−0.139968	−	0.0808104i
$897$	−5.02268	+	50.2114i	−0.167702	+	1.67651i
$898$		−	44.0176i		−	1.46889i
$899$	−30.6986	+	45.4116i	−1.02386	+	1.51456i
$900$	2.09948	+	0.424271i	0.0699828	+	0.0141424i
$901$	18.5267			0.617214
$902$	−17.2846	+	29.9378i	−0.575514	+	0.996820i
$903$	−0.588987	+	5.88807i	−0.0196003	+	0.195943i
$904$	−1.75767	−	3.04437i	−0.0584592	−	0.101254i
$905$	−7.16535	+	12.4107i	−0.238184	+	0.412547i
$906$	6.90818	−	9.60939i	0.229509	−	0.319251i
$907$	−24.8730			−0.825894			−0.412947	−	0.910755i	$-0.635501\pi$
$907$	−24.8730			−0.825894			−0.412947	+	0.910755i	$0.635501\pi$
$908$	−1.86737	+	1.07813i	−0.0619709	+	0.0357789i
$909$	−31.6974	+	10.6522i	−1.05134	+	0.353310i
$910$	2.12213	−	1.22521i	0.0703478	−	0.0406153i
$911$	−18.3064	+	31.7076i	−0.606517	+	1.05052i	0.385293	+	0.922794i	$0.374101\pi$
$911$	−18.3064	+	31.7076i	−0.606517	+	1.05052i	−0.991810	+	0.127724i	$0.959233\pi$
$912$	4.15082	+	9.19832i	0.137447	+	0.304587i
$913$	−6.42106	+	11.1216i	−0.212506	+	0.368071i
$914$	28.8899			0.955594
$915$	−2.21368	−	0.221436i	−0.0731820	−	0.00732044i
$916$	−2.22072	−	1.28213i	−0.0733747	−	0.0423629i
$917$	−6.25076	+	3.60888i	−0.206418	+	0.119176i
$918$	30.8701	+	33.2633i	1.01887	+	1.09785i
$919$	23.8501	+	41.3096i	0.786743	+	1.36268i	0.927952	+	0.372699i	$0.121568\pi$
$919$	23.8501	+	41.3096i	0.786743	+	1.36268i	−0.141209	+	0.989980i	$0.545099\pi$
$920$	7.46583	+	12.9312i	0.246141	+	0.426329i
$921$	−11.8945	−	26.3585i	−0.391936	−	0.868541i
$922$			40.1998i			1.32391i
$923$	−11.7236	+	20.3059i	−0.385888	+	0.668378i
$924$	−0.540484	+	0.751822i	−0.0177806	+	0.0247331i
$925$	7.48560	−	4.32181i	0.246125	−	0.142100i
$926$	3.05901			0.100525
$927$	10.4040	−	11.7908i	0.341713	−	0.387261i
$928$		−	38.0514i		−	1.24910i
$929$	−18.2395			−0.598419			−0.299209	−	0.954187i	$-0.596723\pi$
$929$	−18.2395			−0.598419			−0.299209	+	0.954187i	$0.596723\pi$
$930$	10.1634	−	12.2109i	0.333270	−	0.400410i
$931$	8.13917			0.266750
$932$		−	10.1406i		−	0.332168i
$933$	15.0499	+	10.8194i	0.492712	+	0.354210i
$934$	69.1290			2.26197
$935$	9.55359	−	5.51577i	0.312436	−	0.180385i
$936$	17.3836	−	19.7008i	0.568202	−	0.643939i
$937$	8.17673	−	14.1625i	0.267122	−	0.462669i	−0.700995	−	0.713166i	$-0.747261\pi$
$937$	8.17673	−	14.1625i	0.267122	−	0.462669i	0.968117	+	0.250497i	$0.0805940\pi$
$938$		−	2.94702i		−	0.0962236i
$939$	−6.15733	+	2.77855i	−0.200937	+	0.0906744i
$940$	4.70470	+	8.14878i	0.153450	+	0.265784i
$941$	−5.55329	−	9.61858i	−0.181032	−	0.313557i	0.761200	−	0.648517i	$-0.224610\pi$
$941$	−5.55329	−	9.61858i	−0.181032	−	0.313557i	−0.942232	+	0.334960i	$0.891277\pi$
$942$	12.3221	+	8.85837i	0.401477	+	0.288621i
$943$	61.5494	−	35.5355i	2.00432	−	1.15720i
$944$	6.99210	+	4.03689i	0.227574	+	0.131390i
$945$	−0.550920	+	1.78669i	−0.0179214	+	0.0581210i
$946$	−32.5490			−1.05826
$947$	−19.8607	+	34.3997i	−0.645385	+	1.11784i	0.338828	+	0.940848i	$0.389970\pi$
$947$	−19.8607	+	34.3997i	−0.645385	+	1.11784i	−0.984213	+	0.176991i	$0.943364\pi$
$948$	−1.82651	+	0.824228i	−0.0593223	+	0.0267697i
$949$	−4.05213	+	7.01849i	−0.131538	+	0.227830i
$950$	−1.69014	+	0.975804i	−0.0548355	+	0.0316593i
$951$	7.82438	−	3.53082i	0.253723	−	0.114495i
$952$	3.49993	−	2.02068i	0.113433	−	0.0654908i
$953$	13.7796			0.446366			0.223183	−	0.974777i	$-0.428355\pi$
$953$	13.7796			0.446366			0.223183	+	0.974777i	$0.428355\pi$
$954$	−12.9508	−	11.4276i	−0.419297	−	0.369981i
$955$	10.8162	−	18.7342i	0.350003	−	0.606224i
$956$	0.927884	+	1.60714i	0.0300099	+	0.0519787i
$957$	35.3071	+	3.53179i	1.14132	+	0.114167i
$958$	−21.0919	+	36.5323i	−0.681449	+	1.18030i
$959$	1.96734			0.0635288
$960$	0.598052	−	5.97868i	0.0193020	−	0.192961i
$961$	−11.5536	−	28.7666i	−0.372695	−	0.927954i
$962$			58.8637i			1.89784i
$963$	−7.75125	+	38.3567i	−0.249780	+	1.23603i
$964$	−7.30662	−	4.21848i	−0.235330	−	0.135868i
$965$			8.01697i			0.258076i
$966$	6.59570	−	2.97636i	0.212213	−	0.0957630i
$967$	27.7154	+	16.0015i	0.891266	+	0.514573i	0.874357	−	0.485284i	$-0.161284\pi$
$967$	27.7154	+	16.0015i	0.891266	+	0.514573i	0.0169099	+	0.999857i	$0.494617\pi$
$968$	−12.2378	−	7.06548i	−0.393337	−	0.227093i
$969$	−10.8237	−	1.08270i	−0.347707	−	0.0347814i
$970$	13.7942	+	23.8923i	0.442906	+	0.767136i
$971$	26.6034	−	15.3595i	0.853744	−	0.492909i	−0.00816867	−	0.999967i	$-0.502600\pi$
$971$	26.6034	−	15.3595i	0.853744	−	0.492909i	0.861912	+	0.507058i	$0.169267\pi$
$972$	−0.279369	−	11.1263i	−0.00896077	−	0.356875i
$973$	0.0298915	+	0.0172578i	0.000958277	+	0.000553261i
$974$	−15.7450	−	27.2712i	−0.504503	−	0.873825i
$975$	5.81356	+	4.17937i	0.186183	+	0.133847i
$976$		−	6.31715i		−	0.202207i
$977$		−	45.1169i		−	1.44342i	−0.692196	−	0.721709i	$-0.743357\pi$
$977$		−	45.1169i		−	1.44342i	0.692196	−	0.721709i	$-0.256643\pi$
$978$	24.3420	+	17.4995i	0.778372	+	0.559571i
$979$	10.4026	+	18.0178i	0.332468	+	0.575852i
$980$	4.24818	+	2.45269i	0.135703	+	0.0783483i
$981$	7.87420	+	23.4311i	0.251404	+	0.748096i
$982$	10.5666	−	6.10065i	0.337195	−	0.194679i
$983$	11.5974	+	20.0873i	0.369899	+	0.640684i	0.989549	−	0.144194i	$-0.0460588\pi$
$983$	11.5974	+	20.0873i	0.369899	+	0.640684i	−0.619650	+	0.784878i	$0.712726\pi$
$984$	−36.8204	−	3.68317i	−1.17379	−	0.117415i
$985$	−16.0973	−	9.29376i	−0.512901	−	0.296124i
$986$	74.4619	+	42.9906i	2.37135	+	1.36910i
$987$	−7.48656	+	3.37837i	−0.238300	+	0.107535i
$988$		−	3.49640i		−	0.111235i
$989$	57.9524	+	33.4588i	1.84278	+	1.06393i
$990$	−10.0805	−	2.03710i	−0.320379	−	0.0647433i
$991$			55.1905i			1.75318i	0.481234	+	0.876592i	$0.340189\pi$
$991$			55.1905i			1.75318i	−0.481234	+	0.876592i	$0.659811\pi$
$992$	17.8283	+	12.0521i	0.566048	+	0.382653i
$993$	−2.63548	+	26.3467i	−0.0836344	+	0.836088i
$994$	3.36230			0.106646
$995$	−1.70760	+	2.95764i	−0.0541344	+	0.0937636i
$996$	7.59397	+	0.759629i	0.240624	+	0.0240698i
$997$	7.59254	+	13.1507i	0.240458	+	0.416486i	0.960845	−	0.277087i	$-0.0893690\pi$
$997$	7.59254	+	13.1507i	0.240458	+	0.416486i	−0.720387	+	0.693573i	$0.756036\pi$
$998$	10.0162	−	17.3486i	0.317057	−	0.549159i
$999$	−30.5524	−	32.9209i	−0.966634	−	1.04157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.o.a.26.10	✓	84
3.2	odd	2	inner	465.2.o.a.26.33	yes	84
31.6	odd	6	inner	465.2.o.a.161.10	yes	84
93.68	even	6	inner	465.2.o.a.161.33	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.o.a.26.10	✓	84	1.1	even	1	trivial
465.2.o.a.26.33	yes	84	3.2	odd	2	inner
465.2.o.a.161.10	yes	84	31.6	odd	6	inner
465.2.o.a.161.33	yes	84	93.68	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.64741i q^{2} +(1.01103 - 1.40635i) q^{3} -0.713974 q^{4} +(-0.866025 + 0.500000i) q^{5} +(-2.31685 - 1.66558i) q^{6} +(-0.179912 + 0.311616i) q^{7} -2.11862i q^{8} +(-0.955654 - 2.84372i) q^{9} +O(q^{10})\)	\(q-1.64741i q^{2} +(1.01103 - 1.40635i) q^{3} -0.713974 q^{4} +(-0.866025 + 0.500000i) q^{5} +(-2.31685 - 1.66558i) q^{6} +(-0.179912 + 0.311616i) q^{7} -2.11862i q^{8} +(-0.955654 - 2.84372i) q^{9} +(0.823707 + 1.42670i) q^{10} +(-1.04045 - 1.80210i) q^{11} +(-0.721846 + 1.00410i) q^{12} +(-3.57997 + 2.06689i) q^{13} +(0.513361 + 0.296389i) q^{14} +(-0.172398 + 1.72345i) q^{15} -4.91819 q^{16} +(2.65068 - 4.59111i) q^{17} +(-4.68478 + 1.57436i) q^{18} +(0.592325 - 1.02594i) q^{19} +(0.618320 - 0.356987i) q^{20} +(0.256347 + 0.568071i) q^{21} +(-2.96881 + 1.71404i) q^{22} +7.04783 q^{23} +(-2.97952 - 2.14198i) q^{24} +(0.500000 - 0.866025i) q^{25} +(3.40503 + 5.89769i) q^{26} +(-4.96546 - 1.53109i) q^{27} +(0.128452 - 0.222486i) q^{28} -9.84496 q^{29} +(2.83924 + 0.284011i) q^{30} +(3.11821 - 4.61268i) q^{31} +3.86506i q^{32} +(-3.58631 - 0.358741i) q^{33} +(-7.56346 - 4.36676i) q^{34} -0.359823i q^{35} +(0.682312 + 2.03034i) q^{36} +(7.48560 + 4.32181i) q^{37} +(-1.69014 - 0.975804i) q^{38} +(-0.712656 + 7.12438i) q^{39} +(1.05931 + 1.83478i) q^{40} +(8.73309 - 5.04205i) q^{41} +(0.935848 - 0.422309i) q^{42} +(8.22272 + 4.74739i) q^{43} +(0.742851 + 1.28666i) q^{44} +(2.24948 + 1.98490i) q^{45} -11.6107i q^{46} +13.1789i q^{47} +(-4.97242 + 6.91671i) q^{48} +(3.43526 + 5.95005i) q^{49} +(-1.42670 - 0.823707i) q^{50} +(-3.77681 - 8.36951i) q^{51} +(2.55600 - 1.47571i) q^{52} +(1.74736 + 3.02651i) q^{53} +(-2.52233 + 8.18017i) q^{54} +(1.80210 + 1.04045i) q^{55} +(0.660195 + 0.381164i) q^{56} +(-0.843973 - 1.87027i) q^{57} +16.2187i q^{58} +(-1.42168 - 0.820809i) q^{59} +(0.123088 - 1.23050i) q^{60} +1.28445i q^{61} +(-7.59899 - 5.13698i) q^{62} +(1.05808 + 0.213821i) q^{63} -3.46902 q^{64} +(2.06689 - 3.57997i) q^{65} +(-0.590995 + 5.90814i) q^{66} +(-2.48577 - 4.30548i) q^{67} +(-1.89252 + 3.27793i) q^{68} +(7.12554 - 9.91173i) q^{69} -0.592778 q^{70} +(4.91218 - 2.83605i) q^{71} +(-6.02475 + 2.02466i) q^{72} +(1.69784 - 0.980246i) q^{73} +(7.11982 - 12.3319i) q^{74} +(-0.712424 - 1.57875i) q^{75} +(-0.422905 + 0.732492i) q^{76} +0.748753 q^{77} +(11.7368 + 1.17404i) q^{78} +(1.40332 + 0.810208i) q^{79} +(4.25928 - 2.45909i) q^{80} +(-7.17345 + 5.43522i) q^{81} +(-8.30635 - 14.3870i) q^{82} +(-3.08573 - 5.34463i) q^{83} +(-0.183025 - 0.405588i) q^{84} +5.30135i q^{85} +(7.82092 - 13.5462i) q^{86} +(-9.95351 + 13.8455i) q^{87} +(-3.81797 + 2.20430i) q^{88} -9.99822 q^{89} +(3.26996 - 3.70582i) q^{90} -1.48743i q^{91} -5.03197 q^{92} +(-3.33446 - 9.04883i) q^{93} +21.7111 q^{94} +1.18465i q^{95} +(5.43564 + 3.90768i) q^{96} +16.7465 q^{97} +(9.80220 - 5.65930i) q^{98} +(-4.13037 + 4.68092i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 76 q^{4} + 18 q^{6}+O(q^{10}) \) 84 * q - 76 * q^4 + 18 * q^6	\( 84 q - 76 q^{4} + 18 q^{6} + 2 q^{10} - 18 q^{13} + 60 q^{16} + 10 q^{18} + 10 q^{19} - 42 q^{21} - 36 q^{24} + 42 q^{25} - 8 q^{28} - 28 q^{31} - 4 q^{33} - 18 q^{34} + 6 q^{36} + 18 q^{37} + 32 q^{39} + 24 q^{40} - 90 q^{42} + 42 q^{43} + 4 q^{45} + 48 q^{48} - 62 q^{49} - 8 q^{51} + 144 q^{52} - 12 q^{55} - 12 q^{57} - 72 q^{63} - 160 q^{64} - 76 q^{66} - 32 q^{67} + 24 q^{69} - 84 q^{72} - 30 q^{73} - 86 q^{76} + 76 q^{78} + 28 q^{81} - 36 q^{82} + 210 q^{84} - 6 q^{87} - 72 q^{88} + 8 q^{90} - 100 q^{93} + 220 q^{94} + 168 q^{96} + 12 q^{97} + 54 q^{99}+O(q^{100}) \) 84 * q - 76 * q^4 + 18 * q^6 + 2 * q^10 - 18 * q^13 + 60 * q^16 + 10 * q^18 + 10 * q^19 - 42 * q^21 - 36 * q^24 + 42 * q^25 - 8 * q^28 - 28 * q^31 - 4 * q^33 - 18 * q^34 + 6 * q^36 + 18 * q^37 + 32 * q^39 + 24 * q^40 - 90 * q^42 + 42 * q^43 + 4 * q^45 + 48 * q^48 - 62 * q^49 - 8 * q^51 + 144 * q^52 - 12 * q^55 - 12 * q^57 - 72 * q^63 - 160 * q^64 - 76 * q^66 - 32 * q^67 + 24 * q^69 - 84 * q^72 - 30 * q^73 - 86 * q^76 + 76 * q^78 + 28 * q^81 - 36 * q^82 + 210 * q^84 - 6 * q^87 - 72 * q^88 + 8 * q^90 - 100 * q^93 + 220 * q^94 + 168 * q^96 + 12 * q^97 + 54 * q^99

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