LMFDB - Embedded newform 378.2.ba.a.47.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(47,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("378.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.ba (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.6
Character	$\chi$	$=$	378.47
Dual form			378.2.ba.a.185.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(0.206907 + 1.71965i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.47224 - 0.899821i) q^{5} +(0.0948504 - 1.72945i) q^{6} +(-1.11322 + 2.40015i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.91438 + 0.711614i) q^{9} +O(q^{10})$	\(q+(-0.984808 - 0.173648i) q^{2} +(0.206907 + 1.71965i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.47224 - 0.899821i) q^{5} +(0.0948504 - 1.72945i) q^{6} +(-1.11322 + 2.40015i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.91438 + 0.711614i) q^{9} +(2.27843 + 1.31545i) q^{10} +(-1.80097 - 4.94813i) q^{11} +(-0.393726 + 1.68671i) q^{12} +(2.11622 - 5.81426i) q^{13} +(1.51309 - 2.17038i) q^{14} +(1.03585 - 4.43756i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.62738 + 2.81870i) q^{17} +(2.99367 - 0.194726i) q^{18} +(-1.39478 + 0.805278i) q^{19} +(-2.01539 - 1.69111i) q^{20} +(-4.35775 - 1.41774i) q^{21} +(0.914377 + 5.18569i) q^{22} +(5.57230 - 0.982547i) q^{23} +(0.680638 - 1.59271i) q^{24} +(1.47206 + 1.23521i) q^{25} +(-3.09370 + 5.35845i) q^{26} +(-1.82673 - 4.86447i) q^{27} +(-1.86699 + 1.87466i) q^{28} +(-1.95430 - 5.36940i) q^{29} +(-1.79069 + 4.19027i) q^{30} +(-1.40997 + 3.87387i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(8.13640 - 4.12084i) q^{33} +(2.09211 - 2.49328i) q^{34} +(4.91186 - 4.93205i) q^{35} +(-2.98201 - 0.328078i) q^{36} -6.97047 q^{37} +(1.51343 - 0.550843i) q^{38} +(10.4363 + 2.43614i) q^{39} +(1.69111 + 2.01539i) q^{40} +(-8.45380 - 3.07693i) q^{41} +(4.04536 + 2.15292i) q^{42} +(0.780396 - 4.42584i) q^{43} -5.26569i q^{44} +(7.84537 + 0.863142i) q^{45} -5.65826 q^{46} +(3.82615 - 1.39261i) q^{47} +(-0.946869 + 1.45032i) q^{48} +(-4.52147 - 5.34381i) q^{49} +(-1.23521 - 1.47206i) q^{50} +(-5.18388 - 2.21531i) q^{51} +(3.97719 - 4.73983i) q^{52} +(-9.53822 + 5.50689i) q^{53} +(0.954271 + 5.10778i) q^{54} +13.8535i q^{55} +(2.16416 - 1.52198i) q^{56} +(-1.67339 - 2.23192i) q^{57} +(0.992226 + 5.62719i) q^{58} +(-5.22762 + 4.38649i) q^{59} +(2.49112 - 3.81566i) q^{60} +(3.14692 + 8.64610i) q^{61} +(2.06125 - 3.57018i) q^{62} +(1.53637 - 7.78714i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-10.4636 + 12.4700i) q^{65} +(-8.72837 + 2.64536i) q^{66} +(-1.80769 - 10.2519i) q^{67} +(-2.49328 + 2.09211i) q^{68} +(2.84258 + 9.37910i) q^{69} +(-5.69368 + 4.00419i) q^{70} +(-7.72685 + 4.46110i) q^{71} +(2.87973 + 0.840914i) q^{72} +2.74001i q^{73} +(6.86458 + 1.21041i) q^{74} +(-1.81954 + 2.78701i) q^{75} +(-1.58609 + 0.279670i) q^{76} +(13.8811 + 1.18576i) q^{77} +(-9.85476 - 4.21138i) q^{78} +(0.961277 - 5.45167i) q^{79} +(-1.31545 - 2.27843i) q^{80} +(7.98721 - 4.14782i) q^{81} +(7.79106 + 4.49817i) q^{82} +(1.10973 - 0.403910i) q^{83} +(-3.61005 - 2.82268i) q^{84} +(6.55959 - 5.50415i) q^{85} +(-1.53708 + 4.22309i) q^{86} +(8.82912 - 4.47168i) q^{87} +(-0.914377 + 5.18569i) q^{88} +(1.72098 + 2.98082i) q^{89} +(-7.57630 - 2.21236i) q^{90} +(11.5993 + 11.5518i) q^{91} +(5.57230 + 0.982547i) q^{92} +(-6.95343 - 1.62313i) q^{93} +(-4.00985 + 0.707044i) q^{94} +(4.17284 - 0.735785i) q^{95} +(1.18433 - 1.26387i) q^{96} +(1.48336 + 0.261557i) q^{97} +(3.52484 + 6.04777i) q^{98} +(8.76986 + 13.1391i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{6} + 24 q^{9}+O(q^{10}) $ 144 * q - 18 * q^6 + 24 * q^9	$ 144 q - 18 q^{6} + 24 q^{9} - 24 q^{11} + 6 q^{14} + 12 q^{15} - 30 q^{21} - 42 q^{23} - 6 q^{29} - 18 q^{30} + 6 q^{36} + 48 q^{39} - 48 q^{42} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 12 q^{50} - 36 q^{51} - 90 q^{53} + 6 q^{56} - 6 q^{57} + 18 q^{60} + 54 q^{61} - 24 q^{63} + 72 q^{64} + 78 q^{65} - 72 q^{66} - 54 q^{68} + 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} - 36 q^{74} - 6 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 36 q^{91} - 42 q^{92} + 96 q^{93} - 66 q^{95} - 108 q^{99}+O(q^{100}) $ 144 * q - 18 * q^6 + 24 * q^9 - 24 * q^11 + 6 * q^14 + 12 * q^15 - 30 * q^21 - 42 * q^23 - 6 * q^29 - 18 * q^30 + 6 * q^36 + 48 * q^39 - 48 * q^42 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 12 * q^50 - 36 * q^51 - 90 * q^53 + 6 * q^56 - 6 * q^57 + 18 * q^60 + 54 * q^61 - 24 * q^63 + 72 * q^64 + 78 * q^65 - 72 * q^66 - 54 * q^68 + 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 - 36 * q^74 - 6 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 36 * q^91 - 42 * q^92 + 96 * q^93 - 66 * q^95 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$3$	0.206907	+	1.71965i	0.119458	+	0.992839i
$3$	0.206907	+	1.71965i	0.119458	+	0.992839i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	−2.47224	−	0.899821i	−1.10562	−	0.402412i	−0.276234	−	0.961090i	$-0.589087\pi$
$5$	−2.47224	−	0.899821i	−1.10562	−	0.402412i	−0.829385	+	0.558678i	$0.811309\pi$
$6$	0.0948504	−	1.72945i	0.0387225	−	0.706046i
$7$	−1.11322	+	2.40015i	−0.420758	+	0.907173i
$7$	−1.11322	+	2.40015i	−0.420758	+	0.907173i
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−2.91438	+	0.711614i	−0.971460	+	0.237205i
$10$	2.27843	+	1.31545i	0.720502	+	0.415982i
$11$	−1.80097	−	4.94813i	−0.543013	−	1.49192i	−0.842969	−	0.537963i	$-0.819194\pi$
$11$	−1.80097	−	4.94813i	−0.543013	−	1.49192i	0.299956	−	0.953953i	$-0.403028\pi$
$12$	−0.393726	+	1.68671i	−0.113659	+	0.486910i
$13$	2.11622	−	5.81426i	0.586933	−	1.61259i	−0.189145	−	0.981949i	$-0.560571\pi$
$13$	2.11622	−	5.81426i	0.586933	−	1.61259i	0.776078	−	0.630637i	$-0.217206\pi$
$14$	1.51309	−	2.17038i	0.404391	−	0.580059i
$15$	1.03585	−	4.43756i	0.267456	−	1.14577i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−1.62738	+	2.81870i	−0.394697	+	0.683635i	−0.993062	−	0.117588i	$-0.962484\pi$
$17$	−1.62738	+	2.81870i	−0.394697	+	0.683635i	0.598366	+	0.801223i	$0.295817\pi$
$18$	2.99367	−	0.194726i	0.705616	−	0.0458973i
$19$	−1.39478	+	0.805278i	−0.319985	+	0.184744i	−0.651386	−	0.758747i	$-0.725812\pi$
$19$	−1.39478	+	0.805278i	−0.319985	+	0.184744i	0.331401	+	0.943490i	$0.392479\pi$
$20$	−2.01539	−	1.69111i	−0.450654	−	0.378144i
$21$	−4.35775	−	1.41774i	−0.950940	−	0.309377i
$22$	0.914377	+	5.18569i	0.194946	+	1.10559i
$23$	5.57230	−	0.982547i	1.16191	−	0.204875i	0.440738	−	0.897636i	$-0.354717\pi$
$23$	5.57230	−	0.982547i	1.16191	−	0.204875i	0.721167	+	0.692761i	$0.243606\pi$
$24$	0.680638	−	1.59271i	0.138935	−	0.325111i
$25$	1.47206	+	1.23521i	0.294413	+	0.247042i
$26$	−3.09370	+	5.35845i	−0.606725	+	1.05088i
$27$	−1.82673	−	4.86447i	−0.351554	−	0.936168i
$28$	−1.86699	+	1.87466i	−0.352827	+	0.354278i
$29$	−1.95430	−	5.36940i	−0.362905	−	0.997073i	−0.977997	−	0.208618i	$-0.933103\pi$
$29$	−1.95430	−	5.36940i	−0.362905	−	0.997073i	0.615092	−	0.788455i	$-0.289119\pi$
$30$	−1.79069	+	4.19027i	−0.326934	+	0.765035i
$31$	−1.40997	+	3.87387i	−0.253239	+	0.695768i	0.746306	+	0.665603i	$0.231826\pi$
$31$	−1.40997	+	3.87387i	−0.253239	+	0.695768i	−0.999545	+	0.0301652i	$0.990397\pi$
$32$	−0.642788	−	0.766044i	−0.113630	−	0.135419i
$33$	8.13640	−	4.12084i	1.41637	−	0.717345i
$34$	2.09211	−	2.49328i	0.358795	−	0.427595i
$35$	4.91186	−	4.93205i	0.830256	−	0.833669i
$36$	−2.98201	−	0.328078i	−0.497001	−	0.0546797i
$37$	−6.97047			−1.14594			−0.572969	−	0.819577i	$-0.694209\pi$
$37$	−6.97047			−1.14594			−0.572969	+	0.819577i	$0.694209\pi$
$38$	1.51343	−	0.550843i	0.245510	−	0.0893585i
$39$	10.4363	+	2.43614i	1.67115	+	0.390095i
$40$	1.69111	+	2.01539i	0.267388	+	0.318661i
$41$	−8.45380	−	3.07693i	−1.32026	−	0.480536i	−0.416719	−	0.909035i	$-0.636820\pi$
$41$	−8.45380	−	3.07693i	−1.32026	−	0.480536i	−0.903542	+	0.428499i	$0.859042\pi$
$42$	4.04536	+	2.15292i	0.624213	+	0.332203i
$43$	0.780396	−	4.42584i	0.119009	−	0.674935i	−0.865678	−	0.500602i	$-0.833112\pi$
$43$	0.780396	−	4.42584i	0.119009	−	0.674935i	0.984687	−	0.174333i	$-0.0557769\pi$
$44$		−	5.26569i		−	0.793832i
$45$	7.84537	+	0.863142i	1.16952	+	0.128670i
$46$	−5.65826			−0.834265
$47$	3.82615	−	1.39261i	0.558102	−	0.203132i	−0.0475408	−	0.998869i	$-0.515138\pi$
$47$	3.82615	−	1.39261i	0.558102	−	0.203132i	0.605642	+	0.795737i	$0.292916\pi$
$48$	−0.946869	+	1.45032i	−0.136669	+	0.209336i
$49$	−4.52147	−	5.34381i	−0.645925	−	0.763401i
$50$	−1.23521	−	1.47206i	−0.174685	−	0.208181i
$51$	−5.18388	−	2.21531i	−0.725889	−	0.310205i
$52$	3.97719	−	4.73983i	0.551537	−	0.657296i
$53$	−9.53822	+	5.50689i	−1.31018	+	0.756430i	−0.982125	−	0.188230i	$-0.939725\pi$
$53$	−9.53822	+	5.50689i	−1.31018	+	0.756430i	−0.328050	+	0.944660i	$0.606392\pi$
$54$	0.954271	+	5.10778i	0.129860	+	0.695080i
$55$			13.8535i			1.86801i
$56$	2.16416	−	1.52198i	0.289197	−	0.203384i
$57$	−1.67339	−	2.23192i	−0.221645	−	0.295625i
$58$	0.992226	+	5.62719i	0.130286	+	0.738886i
$59$	−5.22762	+	4.38649i	−0.680578	+	0.571072i	−0.916175	−	0.400778i	$-0.868740\pi$
$59$	−5.22762	+	4.38649i	−0.680578	+	0.571072i	0.235597	+	0.971851i	$0.424295\pi$
$60$	2.49112	−	3.81566i	0.321602	−	0.492600i
$61$	3.14692	+	8.64610i	0.402922	+	1.10702i	0.960835	+	0.277120i	$0.0893801\pi$
$61$	3.14692	+	8.64610i	0.402922	+	1.10702i	−0.557913	+	0.829900i	$0.688398\pi$
$62$	2.06125	−	3.57018i	0.261778	−	0.453413i
$63$	1.53637	−	7.78714i	0.193564	−	0.981088i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−10.4636	+	12.4700i	−1.29785	+	1.54672i
$66$	−8.72837	+	2.64536i	−1.07439	+	0.325621i
$67$	−1.80769	−	10.2519i	−0.220845	−	1.25247i	−0.870471	−	0.492220i	$-0.836186\pi$
$67$	−1.80769	−	10.2519i	−0.220845	−	1.25247i	0.649626	−	0.760254i	$-0.274926\pi$
$68$	−2.49328	+	2.09211i	−0.302355	+	0.253706i
$69$	2.84258	+	9.37910i	0.342207	+	1.12911i
$70$	−5.69368	+	4.00419i	−0.680525	+	0.478592i
$71$	−7.72685	+	4.46110i	−0.917008	+	0.529435i	−0.882679	−	0.469976i	$-0.844263\pi$
$71$	−7.72685	+	4.46110i	−0.917008	+	0.529435i	−0.0343290	+	0.999411i	$0.510929\pi$
$72$	2.87973	+	0.840914i	0.339380	+	0.0991027i
$73$			2.74001i			0.320694i	0.987061	+	0.160347i	$0.0512613\pi$
$73$			2.74001i			0.320694i	−0.987061	+	0.160347i	$0.948739\pi$
$74$	6.86458	+	1.21041i	0.797991	+	0.140707i
$75$	−1.81954	+	2.78701i	−0.210103	+	0.321816i
$76$	−1.58609	+	0.279670i	−0.181937	+	0.0320804i
$77$	13.8811	+	1.18576i	1.58190	+	0.135129i
$78$	−9.85476	−	4.21138i	−1.11583	−	0.476845i
$79$	0.961277	−	5.45167i	0.108152	−	0.613361i	−0.881762	−	0.471694i	$-0.843643\pi$
$79$	0.961277	−	5.45167i	0.108152	−	0.613361i	0.989914	−	0.141667i	$-0.0452463\pi$
$80$	−1.31545	−	2.27843i	−0.147072	−	0.254736i
$81$	7.98721	−	4.14782i	0.887468	−	0.460869i
$82$	7.79106	+	4.49817i	0.860379	+	0.496740i
$83$	1.10973	−	0.403910i	0.121809	−	0.0443349i	−0.280396	−	0.959884i	$-0.590466\pi$
$83$	1.10973	−	0.403910i	0.121809	−	0.0443349i	0.402206	+	0.915549i	$0.368244\pi$
$84$	−3.61005	−	2.82268i	−0.393889	−	0.307980i
$85$	6.55959	−	5.50415i	0.711487	−	0.597009i
$86$	−1.53708	+	4.22309i	−0.165748	+	0.455388i
$87$	8.82912	−	4.47168i	0.946582	−	0.479414i
$88$	−0.914377	+	5.18569i	−0.0974729	+	0.552796i
$89$	1.72098	+	2.98082i	0.182423	+	0.315967i	0.942705	−	0.333627i	$-0.108273\pi$
$89$	1.72098	+	2.98082i	0.182423	+	0.315967i	−0.760282	+	0.649593i	$0.774939\pi$
$90$	−7.57630	−	2.21236i	−0.798612	−	0.233203i
$91$	11.5993	+	11.5518i	1.21594	+	1.21096i
$92$	5.57230	+	0.982547i	0.580953	+	0.102438i
$93$	−6.95343	−	1.62313i	−0.721037	−	0.168311i
$94$	−4.00985	+	0.707044i	−0.413584	+	0.0729260i
$95$	4.17284	−	0.735785i	0.428125	−	0.0754899i
$96$	1.18433	−	1.26387i	0.120875	−	0.128993i
$97$	1.48336	+	0.261557i	0.150613	+	0.0265571i	0.248446	−	0.968646i	$-0.420080\pi$
$97$	1.48336	+	0.261557i	0.150613	+	0.0265571i	−0.0978334	+	0.995203i	$0.531191\pi$
$98$	3.52484	+	6.04777i	0.356063	+	0.610917i
$99$	8.76986	+	13.1391i	0.881404	+	1.32053i
$100$	0.960822	+	1.66419i	0.0960822	+	0.166419i
$101$	−2.59922	+	14.7409i	−0.258632	+	1.46677i	0.527943	+	0.849280i	$0.322963\pi$
$101$	−2.59922	+	14.7409i	−0.258632	+	1.46677i	−0.786575	+	0.617495i	$0.788148\pi$
$102$	4.72045	+	3.08182i	0.467394	+	0.305146i
$103$	−0.997724	+	2.74122i	−0.0983086	+	0.270101i	−0.979092	−	0.203419i	$-0.934795\pi$
$103$	−0.997724	+	2.74122i	−0.0983086	+	0.270101i	0.880783	+	0.473520i	$0.157017\pi$
$104$	−4.73983	+	3.97719i	−0.464779	+	0.389996i
$105$	9.49769	+	7.42620i	0.926880	+	0.724722i
$106$	10.3496	−	3.76694i	1.00524	−	0.365877i
$107$	1.68427	+	0.972416i	0.162825	+	0.0940071i	0.579198	−	0.815187i	$-0.303366\pi$
$107$	1.68427	+	0.972416i	0.162825	+	0.0940071i	−0.416373	+	0.909194i	$0.636699\pi$
$108$	−0.0528179	−	5.19588i	−0.00508241	−	0.499974i
$109$	−1.57502	−	2.72801i	−0.150860	−	0.261296i	0.780684	−	0.624926i	$-0.214871\pi$
$109$	−1.57502	−	2.72801i	−0.150860	−	0.261296i	−0.931544	+	0.363629i	$0.881537\pi$
$110$	2.40564	−	13.6430i	0.229368	−	1.30081i
$111$	−1.44224	−	11.9868i	−0.136891	−	1.13773i
$112$	−2.39557	+	1.12306i	−0.226360	+	0.106119i
$113$	19.1104	−	3.36968i	1.79775	−	0.316993i	0.827937	−	0.560822i	$-0.189515\pi$
$113$	19.1104	−	3.36968i	1.79775	−	0.316993i	0.969818	+	0.243829i	$0.0784035\pi$
$114$	1.26039	+	2.48859i	0.118047	+	0.233078i
$115$	−14.6602	−	2.58498i	−1.36707	−	0.241051i
$116$		−	5.71400i		−	0.530531i
$117$	−2.02996	+	18.4509i	−0.187669	+	1.70579i
$118$	5.90990	−	3.41208i	0.544051	−	0.314108i
$119$	−4.95368	−	7.04379i	−0.454103	−	0.645703i
$120$	−3.11586	+	3.32511i	−0.284437	+	0.303540i
$121$	−12.8140	+	10.7522i	−1.16491	+	0.977472i
$122$	−1.59774	−	9.06121i	−0.144652	−	0.820363i
$123$	3.54209	−	15.1742i	0.319380	−	1.36821i
$124$	−2.64989	+	3.15801i	−0.237967	+	0.283598i
$125$	4.04943	+	7.01381i	0.362192	+	0.627334i
$126$	−2.86525	+	7.40205i	−0.255257	+	0.659427i
$127$	−2.37992	+	4.12214i	−0.211183	+	0.365780i	−0.952085	−	0.305833i	$-0.901065\pi$
$127$	−2.37992	+	4.12214i	−0.211183	+	0.365780i	0.740902	+	0.671613i	$0.234398\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$	7.77237	+	0.426269i	0.684319	+	0.0375309i
$130$	12.4700	−	10.4636i	1.09369	−	0.917718i
$131$	−1.18072	−	6.69622i	−0.103160	−	0.585051i	−0.991939	−	0.126715i	$-0.959557\pi$
$131$	−1.18072	−	6.69622i	−0.103160	−	0.585051i	0.888779	−	0.458336i	$-0.151554\pi$
$132$	9.05513	−	1.08951i	0.788148	−	0.0948293i
$133$	−0.380089	−	4.24415i	−0.0329579	−	0.368014i
$134$			10.4101i			0.899295i
$135$	0.138959	+	13.6699i	0.0119597	+	1.17651i
$136$	2.81870	−	1.62738i	0.241701	−	0.139546i
$137$	−1.63483	+	1.94832i	−0.139673	+	0.166456i	−0.831346	−	0.555755i	$-0.812429\pi$
$137$	−1.63483	+	1.94832i	−0.139673	+	0.166456i	0.691673	+	0.722211i	$0.256874\pi$
$138$	−1.17073	−	9.73022i	−0.0996594	−	0.828291i
$139$	−2.59387	−	3.09126i	−0.220010	−	0.262197i	0.644738	−	0.764403i	$-0.276966\pi$
$139$	−2.59387	−	3.09126i	−0.220010	−	0.262197i	−0.864748	+	0.502206i	$0.832522\pi$
$140$	6.30250	−	2.95466i	0.532658	−	0.249714i
$141$	3.18645	+	6.29150i	0.268347	+	0.529839i
$142$	8.38412	−	3.05157i	0.703580	−	0.256082i
$143$	−32.5809			−2.72456
$144$	−2.68996	−	1.32820i	−0.224163	−	0.110683i
$145$			15.0330i			1.24842i
$146$	0.475798	−	2.69838i	0.0393773	−	0.223320i
$147$	8.25394	−	8.88101i	0.680774	−	0.732494i
$148$	−6.55010	−	2.38404i	−0.538415	−	0.195967i
$149$	−4.50690	−	5.37111i	−0.369219	−	0.440019i	0.549161	−	0.835716i	$-0.314947\pi$
$149$	−4.50690	−	5.37111i	−0.369219	−	0.440019i	−0.918381	+	0.395698i	$0.870503\pi$
$150$	2.27586	−	2.42870i	0.185823	−	0.198303i
$151$	−4.36150	+	1.58746i	−0.354934	+	0.129185i	−0.513332	−	0.858190i	$-0.671589\pi$
$151$	−4.36150	+	1.58746i	−0.354934	+	0.129185i	0.158399	+	0.987375i	$0.449367\pi$
$152$	1.61056			0.130633
$153$	2.73697	−	9.37282i	0.221271	−	0.757747i
$154$	−13.4644	−	3.57818i	−1.08499	−	0.288338i
$155$	6.97159	−	8.30842i	0.559971	−	0.667348i
$156$	8.97375	+	5.85866i	0.718475	+	0.469069i
$157$	−10.7352	−	12.7938i	−0.856766	−	1.02105i	−0.999510	−	0.0312939i	$-0.990037\pi$
$157$	−10.7352	−	12.7938i	−0.856766	−	1.02105i	0.142745	−	0.989760i	$-0.454407\pi$
$158$	−1.89335	+	5.20193i	−0.150627	+	0.413843i
$159$	−11.4434	−	15.2630i	−0.907524	−	1.21043i
$160$	0.899821	+	2.47224i	0.0711371	+	0.195448i
$161$	−3.84494	+	14.4682i	−0.303024	+	1.14025i
$162$	−8.58613	+	2.69784i	−0.674590	+	0.211963i
$163$	10.7246	−	18.5756i	0.840018	−	1.45495i	−0.0498612	−	0.998756i	$-0.515878\pi$
$163$	10.7246	−	18.5756i	0.840018	−	1.45495i	0.889879	−	0.456197i	$-0.150789\pi$
$164$	−6.89160	−	5.78274i	−0.538143	−	0.451556i
$165$	−23.8231	+	2.86638i	−1.85463	+	0.223148i
$166$	−1.16301	+	0.205070i	−0.0902673	+	0.0159166i
$167$	−0.391559	−	2.22064i	−0.0302998	−	0.171838i	0.965903	−	0.258905i	$-0.0833618\pi$
$167$	−0.391559	−	2.22064i	−0.0302998	−	0.171838i	−0.996202	+	0.0870668i	$0.972251\pi$
$168$	3.06505	+	3.40668i	0.236474	+	0.262831i
$169$	−19.3687	−	16.2523i	−1.48990	−	1.25017i
$170$	−7.41572	+	4.28147i	−0.568760	+	0.328374i
$171$	3.49188	−	3.33943i	0.267031	−	0.255373i
$172$	2.24706	−	3.89202i	0.171337	−	0.296764i
$173$	0.948444	+	0.795839i	0.0721089	+	0.0605065i	0.678130	−	0.734942i	$-0.262791\pi$
$173$	0.948444	+	0.795839i	0.0721089	+	0.0605065i	−0.606021	+	0.795449i	$0.707235\pi$
$174$	−9.47149	+	2.87058i	−0.718032	+	0.217618i
$175$	−4.60343	+	2.15812i	−0.347986	+	0.163139i
$176$	1.80097	−	4.94813i	0.135753	−	0.372979i
$177$	−8.62485	−	8.08207i	−0.648283	−	0.607485i
$178$	−1.17722	−	3.23438i	−0.0882363	−	0.242427i
$179$	−6.44093	−	3.71868i	−0.481418	−	0.277947i	0.239589	−	0.970874i	$-0.422987\pi$
$179$	−6.44093	−	3.71868i	−0.481418	−	0.277947i	−0.721007	+	0.692928i	$0.756321\pi$
$180$	7.07702	+	3.49436i	0.527490	+	0.260454i
$181$	16.6597	+	9.61848i	1.23831	+	0.714936i	0.968748	−	0.248049i	$-0.0797893\pi$
$181$	16.6597	+	9.61848i	1.23831	+	0.714936i	0.269557	+	0.962984i	$0.413123\pi$
$182$	−9.41713	−	13.3905i	−0.698044	−	0.992571i
$183$	−14.2171	+	7.20054i	−1.05096	+	0.532279i
$184$	−5.31703	−	1.93524i	−0.391977	−	0.142668i
$185$	17.2327	+	6.27218i	1.26697	+	0.461140i
$186$	6.56594	+	2.80592i	0.481438	+	0.205740i
$187$	16.8781	+	2.97607i	1.23425	+	0.217632i
$188$	4.07171			0.296960
$189$	13.7090	+	1.03080i	0.997185	+	0.0749798i
$190$	−4.23722			−0.307400
$191$	2.34105	+	0.412790i	0.169392	+	0.0298684i	0.257701	−	0.966225i	$-0.417035\pi$
$191$	2.34105	+	0.412790i	0.169392	+	0.0298684i	−0.0883087	+	0.996093i	$0.528146\pi$
$192$	−1.38581	+	1.03901i	−0.100012	+	0.0749841i
$193$	−24.9931	−	9.09676i	−1.79905	−	0.654799i	−0.998454	−	0.0555885i	$-0.982297\pi$
$193$	−24.9931	−	9.09676i	−1.79905	−	0.654799i	−0.800592	−	0.599210i	$-0.795481\pi$
$194$	−1.41541	−	0.515166i	−0.101620	−	0.0369868i
$195$	−23.6090	−	15.4136i	−1.69068	−	1.10379i
$196$	−2.42111	−	6.56797i	−0.172936	−	0.469141i
$197$	10.8575	+	6.26858i	0.773565	+	0.446618i	0.834145	−	0.551546i	$-0.185962\pi$
$197$	10.8575	+	6.26858i	0.773565	+	0.446618i	−0.0605801	+	0.998163i	$0.519295\pi$
$198$	−6.35505	−	14.4624i	−0.451633	−	1.02780i
$199$	16.9933	+	9.81111i	1.20463	+	0.695491i	0.961580	−	0.274524i	$-0.0885203\pi$
$199$	16.9933	+	9.81111i	1.20463	+	0.695491i	0.243045	+	0.970015i	$0.421854\pi$
$200$	−0.657241	−	1.80575i	−0.0464740	−	0.127686i
$201$	17.2557	−	5.22979i	1.21712	−	0.368881i
$202$	5.11946	−	14.0656i	0.360204	−	0.989652i
$203$	15.0630	+	1.28671i	1.05721	+	0.0903093i
$204$	−4.11358	−	3.85470i	−0.288008	−	0.269883i
$205$	18.1311	+	15.2138i	1.26633	+	1.06258i
$206$	1.45857	−	2.52632i	0.101624	−	0.176017i
$207$	−15.5406	+	6.82884i	−1.08015	+	0.474637i
$208$	5.35845	−	3.09370i	0.371542	−	0.214510i
$209$	6.49658	+	5.45128i	0.449378	+	0.377073i
$210$	−8.06385	−	8.96263i	−0.556459	−	0.618480i
$211$	−2.96613	−	16.8217i	−0.204197	−	1.15806i	−0.898699	−	0.438566i	$-0.855487\pi$
$211$	−2.96613	−	16.8217i	−0.204197	−	1.15806i	0.694502	−	0.719490i	$-0.255625\pi$
$212$	−10.8465	+	1.91252i	−0.744938	+	0.131353i
$213$	−9.27026	−	12.3644i	−0.635188	−	0.847197i
$214$	−1.48983	−	1.25011i	−0.101843	−	0.0854561i
$215$	−5.91180	+	10.2395i	−0.403181	+	0.698330i
$216$	−0.850240	+	5.12612i	−0.0578515	+	0.348788i
$217$	−7.72828	−	7.69664i	−0.524630	−	0.522482i
$218$	1.07738	+	2.96007i	0.0729692	+	0.200481i
$219$	−4.71186	+	0.566927i	−0.318398	+	0.0383094i
$220$	−4.73818	+	13.0180i	−0.319448	+	0.877676i
$221$	12.9448	+	15.4270i	0.870759	+	1.03773i
$222$	−0.661152	+	12.0551i	−0.0443736	+	0.809085i
$223$	−3.34646	+	3.98816i	−0.224096	+	0.267067i	−0.866364	−	0.499413i	$-0.833549\pi$
$223$	−3.34646	+	3.98816i	−0.224096	+	0.267067i	0.642268	+	0.766480i	$0.277994\pi$
$224$	2.55419	−	0.690012i	0.170659	−	0.0461033i
$225$	−5.16915	−	2.55233i	−0.344610	−	0.170155i
$226$	−19.4052			−1.29082
$227$	15.3989	−	5.60475i	1.02206	−	0.372000i	0.224009	−	0.974587i	$-0.428085\pi$
$227$	15.3989	−	5.60475i	1.02206	−	0.372000i	0.798053	+	0.602587i	$0.205863\pi$
$228$	−0.809107	−	2.66965i	−0.0535844	−	0.176802i
$229$	−11.1081	−	13.2381i	−0.734042	−	0.874797i	0.261873	−	0.965102i	$-0.415660\pi$
$229$	−11.1081	−	13.2381i	−0.734042	−	0.874797i	−0.995914	+	0.0903059i	$0.971216\pi$
$230$	13.9886	+	5.09143i	0.922380	+	0.335719i
$231$	0.833019	+	24.1160i	0.0548087	+	1.58672i
$232$	−0.992226	+	5.62719i	−0.0651428	+	0.369443i
$233$		−	15.5579i		−	1.01923i	−0.860401	−	0.509617i	$-0.829787\pi$
$233$		−	15.5579i		−	1.01923i	0.860401	−	0.509617i	$-0.170213\pi$
$234$	5.20308	−	17.8181i	0.340136	−	1.16480i
$235$	−10.7123			−0.698791
$236$	−6.41262	+	2.33400i	−0.417426	+	0.151931i
$237$	9.57386	+	0.525071i	0.621889	+	0.0341070i
$238$	3.65528	+	7.79697i	0.236937	+	0.505403i
$239$	9.18136	+	10.9419i	0.593893	+	0.707774i	0.976349	−	0.216200i	$-0.0693662\pi$
$239$	9.18136	+	10.9419i	0.593893	+	0.707774i	−0.382456	+	0.923974i	$0.624922\pi$
$240$	3.64592	−	2.73353i	0.235343	−	0.176449i
$241$	13.1859	−	15.7144i	0.849381	−	1.01225i	−0.150340	−	0.988634i	$-0.548037\pi$
$241$	13.1859	−	15.7144i	0.849381	−	1.01225i	0.999721	−	0.0236181i	$-0.00751859\pi$
$242$	14.4864	−	8.36372i	0.931220	−	0.537640i
$243$	8.78540	+	12.8770i	0.563584	+	0.826059i
$244$			9.20099i			0.589033i
$245$	6.36969	+	17.2797i	0.406945	+	1.10396i
$246$	−6.12325	+	14.3286i	−0.390404	+	0.913557i
$247$	1.73043	+	9.81378i	0.110105	+	0.624436i
$248$	3.15801	−	2.64989i	0.200534	−	0.168268i
$249$	0.924194	+	1.82478i	0.0585684	+	0.115641i
$250$	−2.76997	−	7.61043i	−0.175188	−	0.481326i
$251$	−3.46248	+	5.99718i	−0.218550	+	0.378539i	−0.954365	−	0.298643i	$-0.903466\pi$
$251$	−3.46248	+	5.99718i	−0.218550	+	0.378539i	0.735815	+	0.677182i	$0.236799\pi$
$252$	4.10707	−	6.79205i	0.258721	−	0.427859i
$253$	−14.8973	−	25.8029i	−0.936586	−	1.62221i
$254$	3.05956	−	3.64624i	0.191974	−	0.228786i
$255$	10.8224	+	10.1413i	0.677726	+	0.635075i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−9.42259	+	7.90649i	−0.587765	+	0.493193i	−0.887487	−	0.460833i	$-0.847551\pi$
$257$	−9.42259	+	7.90649i	−0.587765	+	0.493193i	0.299722	+	0.954027i	$0.403106\pi$
$258$	−7.58026	−	1.76945i	−0.471927	−	0.110161i
$259$	7.75968	−	16.7302i	0.482163	−	1.03956i
$260$	−14.0976	+	8.13923i	−0.874294	+	0.504774i
$261$	9.51652	+	14.2578i	0.589058	+	0.882534i
$262$			6.79952i			0.420076i
$263$	13.5471	+	2.38871i	0.835348	+	0.147294i	0.574931	−	0.818202i	$-0.305029\pi$
$263$	13.5471	+	2.38871i	0.835348	+	0.147294i	0.260417	+	0.965496i	$0.416140\pi$
$264$	−9.10675	−	0.499452i	−0.560482	−	0.0307392i
$265$	28.5360	−	5.03166i	1.75295	−	0.309093i
$266$	−0.362674	+	4.24567i	−0.0222370	+	0.260319i
$267$	−4.76989	+	3.57623i	−0.291912	+	0.218862i
$268$	1.80769	−	10.2519i	0.110422	−	0.626237i
$269$	−1.56667	−	2.71355i	−0.0955214	−	0.165448i	0.814305	−	0.580438i	$-0.197118\pi$
$269$	−1.56667	−	2.71355i	−0.0955214	−	0.165448i	−0.909826	+	0.414990i	$0.863785\pi$
$270$	2.23690	−	13.4863i	0.136133	−	0.820751i
$271$	−22.1014	−	12.7603i	−1.34257	−	0.775131i	−0.355383	−	0.934721i	$-0.615649\pi$
$271$	−22.1014	−	12.7603i	−1.34257	−	0.775131i	−0.987183	+	0.159590i	$0.948983\pi$
$272$	−3.05847	+	1.11319i	−0.185447	+	0.0674971i
$273$	−17.4651	+	22.3369i	−1.05703	+	1.35189i
$274$	1.94832	−	1.63483i	0.117702	−	0.0987639i
$275$	3.46082	−	9.50854i	0.208696	−	0.573386i
$276$	−0.536689	+	9.78569i	−0.0323049	+	0.589030i
$277$	1.12454	−	6.37757i	0.0675669	−	0.383191i	−0.932207	−	0.361926i	$-0.882119\pi$
$277$	1.12454	−	6.37757i	0.0675669	−	0.383191i	0.999774	−	0.0212653i	$-0.00676948\pi$
$278$	2.01768	+	3.49472i	0.121012	+	0.209599i
$279$	1.35250	−	12.2933i	0.0809721	−	0.735980i
$280$	−6.71982	+	1.81535i	−0.401586	+	0.108488i
$281$	−27.4797	−	4.84541i	−1.63930	−	0.289053i	−0.723392	−	0.690438i	$-0.757418\pi$
$281$	−27.4797	−	4.84541i	−1.63930	−	0.289053i	−0.915909	+	0.401385i	$0.868529\pi$
$282$	−2.04553	−	6.74923i	−0.121810	−	0.401911i
$283$	18.8071	−	3.31620i	1.11797	−	0.197128i	0.416018	−	0.909356i	$-0.363425\pi$
$283$	18.8071	−	3.31620i	1.11797	−	0.197128i	0.701947	+	0.712229i	$0.252314\pi$
$284$	−8.78665	+	1.54932i	−0.521392	+	0.0919354i
$285$	2.12868	+	7.02358i	0.126092	+	0.416041i
$286$	32.0860	+	5.65762i	1.89728	+	0.334542i
$287$	16.7961	−	16.8651i	0.991440	−	0.995516i
$288$	2.41845	+	1.77513i	0.142509	+	0.104600i
$289$	3.20329	+	5.54827i	0.188429	+	0.326369i
$290$	2.61045	−	14.8046i	0.153291	−	0.869355i
$291$	−0.142868	+	2.60498i	−0.00837507	+	0.152707i
$292$	−0.937139	+	2.57477i	−0.0548419	+	0.150677i
$293$	−1.09863	+	0.921862i	−0.0641828	+	0.0538558i	−0.674315	−	0.738444i	$-0.735561\pi$
$293$	−1.09863	+	0.921862i	−0.0641828	+	0.0538558i	0.610132	+	0.792300i	$0.291116\pi$
$294$	−9.67072	+	7.31281i	−0.564008	+	0.426492i
$295$	16.8710	−	6.14053i	0.982266	−	0.357516i
$296$	6.03661	+	3.48524i	0.350871	+	0.202575i
$297$	−20.7801	+	17.7997i	−1.20578	+	1.03284i
$298$	3.50574	+	6.07213i	0.203082	+	0.351749i
$299$	6.07942	−	34.4781i	0.351582	−	1.99392i
$300$	−2.66303	+	1.99661i	−0.153750	+	0.115274i
$301$	9.75395	+	6.80002i	0.562209	+	0.391946i
$302$	4.57090	−	0.805972i	0.263025	−	0.0463785i
$303$	−25.8870	−	1.41975i	−1.48717	−	0.0815625i
$304$	−1.58609	−	0.279670i	−0.0909684	−	0.0160402i
$305$		−	24.2069i		−	1.38608i
$306$	−4.32296	+	8.75515i	−0.247127	+	0.500499i
$307$	12.7043	−	7.33486i	0.725075	−	0.418622i	−0.0915425	−	0.995801i	$-0.529180\pi$
$307$	12.7043	−	7.33486i	0.725075	−	0.418622i	0.816618	+	0.577179i	$0.195846\pi$
$308$	12.6385	+	5.86188i	0.720143	+	0.334011i
$309$	−4.92037	−	1.14856i	−0.279910	−	0.0653391i
$310$	−8.30842	+	6.97159i	−0.471886	+	0.395960i
$311$	−0.651092	−	3.69253i	−0.0369200	−	0.209384i	0.960767	−	0.277356i	$-0.0894582\pi$
$311$	−0.651092	−	3.69253i	−0.0369200	−	0.209384i	−0.997687	+	0.0679722i	$0.978347\pi$
$312$	−7.82007	−	7.32793i	−0.442724	−	0.414862i
$313$	−16.7741	+	19.9906i	−0.948131	+	1.12994i	0.0432682	+	0.999063i	$0.486223\pi$
$313$	−16.7741	+	19.9906i	−0.948131	+	1.12994i	−0.991399	+	0.130875i	$0.958221\pi$
$314$	8.35054	+	14.4636i	0.471248	+	0.816225i
$315$	−10.8053	+	17.8692i	−0.608810	+	1.00682i
$316$	2.76789	−	4.79412i	0.155706	−	0.269690i
$317$	−1.46853	−	4.03474i	−0.0824806	−	0.226614i	0.891596	−	0.452832i	$-0.149586\pi$
$317$	−1.46853	−	4.03474i	−0.0824806	−	0.226614i	−0.974077	+	0.226218i	$0.927364\pi$
$318$	8.61920	+	17.0182i	0.483341	+	0.954335i
$319$	−23.0488	+	19.3403i	−1.29049	+	1.08285i
$320$	−0.456851	−	2.59093i	−0.0255388	−	0.144838i
$321$	−1.32373	+	3.09756i	−0.0738832	+	0.172889i
$322$	6.29890	−	13.5807i	0.351024	−	0.756823i
$323$		−	5.24196i		−	0.291671i
$324$	8.92416	−	1.16589i	0.495787	−	0.0647718i
$325$	10.2970	−	5.94500i	0.571177	−	0.329769i
$326$	−13.7873	+	16.4311i	−0.763609	+	0.910033i
$327$	4.36534	−	3.27292i	0.241404	−	0.180993i
$328$	5.78274	+	6.89160i	0.319298	+	0.380525i
$329$	−0.916889	+	10.7336i	−0.0505497	+	0.591764i
$330$	23.9590	+	1.31401i	1.31890	+	0.0723339i
$331$	−15.5502	+	5.65982i	−0.854718	+	0.311092i	−0.731962	−	0.681345i	$-0.761395\pi$
$331$	−15.5502	+	5.65982i	−0.854718	+	0.311092i	−0.122755	+	0.992437i	$0.539173\pi$
$332$	1.18095			0.0648133
$333$	20.3146	−	4.96028i	1.11323	−	0.271822i
$334$			2.25490i			0.123383i
$335$	−4.75586	+	26.9718i	−0.259841	+	1.47363i
$336$	−2.42693	−	3.88716i	−0.132400	−	0.212062i
$337$	6.82488	+	2.48405i	0.371775	+	0.135315i	0.521149	−	0.853466i	$-0.325504\pi$
$337$	6.82488	+	2.48405i	0.371775	+	0.135315i	−0.149374	+	0.988781i	$0.547726\pi$
$338$	16.2523	+	19.3687i	0.884006	+	1.05352i
$339$	9.74873	+	32.1659i	0.529478	+	1.74701i
$340$	8.04653	−	2.92870i	0.436384	−	0.158831i
$341$	21.7077			1.17554
$342$	−4.01872	+	2.68234i	−0.217307	+	0.145044i
$343$	17.8594	−	4.90339i	0.964315	−	0.264758i
$344$	−2.88877	+	3.44270i	−0.155752	+	0.185618i
$345$	1.41197	−	25.7452i	0.0760182	−	1.38607i
$346$	−0.795839	−	0.948444i	−0.0427846	−	0.0509887i
$347$	−6.34378	+	17.4294i	−0.340552	+	0.935659i	0.644683	+	0.764450i	$0.276989\pi$
$347$	−6.34378	+	17.4294i	−0.340552	+	0.935659i	−0.985235	+	0.171209i	$0.945233\pi$
$348$	9.82607	−	1.18226i	0.526733	−	0.0633761i
$349$	6.14180	+	16.8745i	0.328763	+	0.903269i	0.988425	+	0.151707i	$0.0484771\pi$
$349$	6.14180	+	16.8745i	0.328763	+	0.903269i	−0.659662	+	0.751562i	$0.729301\pi$
$350$	4.90824	−	1.32596i	0.262357	−	0.0708754i
$351$	−32.1491	+	0.326806i	−1.71599	+	0.0174436i
$352$	−2.63284	+	4.56022i	−0.140331	+	0.243060i
$353$	−22.2455	−	18.6662i	−1.18401	−	0.993501i	−0.999944	−	0.0105863i	$-0.996630\pi$
$353$	−22.2455	−	18.6662i	−1.18401	−	0.993501i	−0.184064	−	0.982914i	$-0.558925\pi$
$354$	7.09038	+	9.45697i	0.376850	+	0.502632i
$355$	23.1168	−	4.07612i	1.22691	−	0.216338i
$356$	0.597690	+	3.38967i	0.0316775	+	0.179652i
$357$	11.0879	−	9.97599i	0.586833	−	0.527985i
$358$	5.69734	+	4.78064i	0.301114	+	0.252665i
$359$	13.1560	−	7.59563i	0.694348	−	0.400882i	−0.110891	−	0.993833i	$-0.535370\pi$
$359$	13.1560	−	7.59563i	0.694348	−	0.400882i	0.805239	+	0.592950i	$0.202037\pi$
$360$	−6.36272	−	4.67019i	−0.335345	−	0.246140i
$361$	−8.20305	+	14.2081i	−0.431740	+	0.747795i
$362$	−14.7364	−	12.3653i	−0.774526	−	0.649904i
$363$	−21.1413	−	19.8108i	−1.10963	−	1.03980i
$364$	6.94883	+	14.8223i	0.364217	+	0.776902i
$365$	2.46552	−	6.77396i	0.129051	−	0.354565i
$366$	15.2515	−	4.62237i	0.797209	−	0.241615i
$367$	1.93563	+	5.31811i	0.101039	+	0.277603i	0.979905	−	0.199467i	$-0.0639211\pi$
$367$	1.93563	+	5.31811i	0.101039	+	0.277603i	−0.878865	+	0.477070i	$0.841699\pi$
$368$	4.90020	+	2.82913i	0.255441	+	0.147479i
$369$	26.8272	+	2.95151i	1.39657	+	0.153649i
$370$	−15.8817	−	9.16932i	−0.825651	−	0.476690i
$371$	−2.59924	−	29.0236i	−0.134946	−	1.50683i
$372$	−5.97895	−	3.90346i	−0.309994	−	0.202385i
$373$	25.2705	+	9.19770i	1.30846	+	0.476239i	0.899742	−	0.436423i	$-0.143755\pi$
$373$	25.2705	+	9.19770i	1.30846	+	0.476239i	0.408715	+	0.912662i	$0.365977\pi$
$374$	−16.1049	−	5.86171i	−0.832766	−	0.303102i
$375$	−11.2234	+	8.41479i	−0.579576	+	0.434538i
$376$	−4.00985	−	0.707044i	−0.206792	−	0.0364630i
$377$	−35.3548			−1.82087
$378$	−13.3218	−	3.39569i	−0.685197	−	0.174655i
$379$	−3.92061			−0.201388			−0.100694	−	0.994917i	$-0.532106\pi$
$379$	−3.92061			−0.201388			−0.100694	+	0.994917i	$0.532106\pi$
$380$	4.17284	+	0.735785i	0.214062	+	0.0377450i
$381$	−7.58105	−	3.23972i	−0.388389	−	0.165976i
$382$	−2.23380	−	0.813037i	−0.114291	−	0.0415986i
$383$	2.54905	+	0.927779i	0.130250	+	0.0474073i	0.406323	−	0.913730i	$-0.366811\pi$
$383$	2.54905	+	0.927779i	0.130250	+	0.0474073i	−0.276073	+	0.961137i	$0.589033\pi$
$384$	1.54517	−	0.782583i	0.0788518	−	0.0399360i
$385$	−33.2505	−	15.4220i	−1.69460	−	0.785979i
$386$	23.0338	+	13.2986i	1.17239	+	0.676879i
$387$	0.875122	+	13.4539i	0.0444849	+	0.683902i
$388$	1.30445	+	0.753123i	0.0662232	+	0.0382340i
$389$	1.69903	+	4.66805i	0.0861443	+	0.236680i	0.975283	−	0.220957i	$-0.0709182\pi$
$389$	1.69903	+	4.66805i	0.0861443	+	0.236680i	−0.889139	+	0.457637i	$0.848696\pi$
$390$	20.5738	+	19.2791i	1.04180	+	0.976234i
$391$	−6.29873	+	17.3056i	−0.318540	+	0.875182i
$392$	1.24381	+	6.88861i	0.0628218	+	0.347927i
$393$	11.2708	−	3.41592i	0.568539	−	0.172310i
$394$	−9.60402	−	8.05873i	−0.483844	−	0.405993i
$395$	−7.28204	+	12.6129i	−0.366399	+	0.634622i
$396$	3.74713	+	15.3462i	0.188301	+	0.771176i
$397$	−9.94147	+	5.73971i	−0.498948	+	0.288068i	−0.728279	−	0.685281i	$-0.759680\pi$
$397$	−9.94147	+	5.73971i	−0.498948	+	0.288068i	0.229331	+	0.973349i	$0.426346\pi$
$398$	−15.0315	−	12.6129i	−0.753460	−	0.632228i
$399$	7.21980	−	1.53176i	0.361442	−	0.0766840i
$400$	0.333690	+	1.89245i	0.0166845	+	0.0946225i
$401$	−9.44450	+	1.66532i	−0.471636	+	0.0831621i	−0.404414	−	0.914576i	$-0.632525\pi$
$401$	−9.44450	+	1.66532i	−0.471636	+	0.0831621i	−0.0672216	+	0.997738i	$0.521413\pi$
$402$	−17.9017	+	2.15392i	−0.892855	+	0.107428i
$403$	19.5399	+	16.3959i	0.973352	+	0.816739i
$404$	−7.48415	+	12.9629i	−0.372350	+	0.644930i
$405$	−23.4786	+	3.06735i	−1.16666	+	0.152418i
$406$	−14.6107	−	3.88282i	−0.725116	−	0.192701i
$407$	12.5536	+	34.4908i	0.622260	+	1.70964i
$408$	3.38172	+	4.51045i	0.167420	+	0.223301i
$409$	1.55818	−	4.28107i	0.0770472	−	0.211685i	−0.895189	−	0.445686i	$-0.852960\pi$
$409$	1.55818	−	4.28107i	0.0770472	−	0.211685i	0.972236	+	0.234001i	$0.0751819\pi$
$410$	−15.2138	−	18.1311i	−0.751357	−	0.895432i
$411$	−3.68868	−	2.40822i	−0.181949	−	0.118789i
$412$	−1.87511	+	2.23467i	−0.0923799	+	0.110094i
$413$	−4.70876	−	17.4302i	−0.231703	−	0.857685i
$414$	16.4903	−	4.02650i	0.810455	−	0.197892i
$415$	−3.10697			−0.152515
$416$	−5.81426	+	2.11622i	−0.285068	+	0.103756i
$417$	4.77919	−	5.10015i	0.234038	−	0.249756i
$418$	−5.45128	−	6.49658i	−0.266631	−	0.317758i
$419$	−3.57531	−	1.30131i	−0.174666	−	0.0635730i	0.253207	−	0.967412i	$-0.418515\pi$
$419$	−3.57531	−	1.30131i	−0.174666	−	0.0635730i	−0.427873	+	0.903839i	$0.640737\pi$
$420$	6.38500	+	10.2267i	0.311556	+	0.499014i
$421$	−5.77200	+	32.7346i	−0.281310	+	1.59539i	0.436866	+	0.899527i	$0.356089\pi$
$421$	−5.77200	+	32.7346i	−0.281310	+	1.59539i	−0.718176	+	0.695862i	$0.755023\pi$
$422$			17.0812i			0.831502i
$423$	−10.1599	+	6.78132i	−0.493989	+	0.329719i
$424$	11.0138			0.534877
$425$	−5.87728	+	2.13916i	−0.285090	+	0.103764i
$426$	6.98236	+	13.7864i	0.338296	+	0.667951i
$427$	−24.2552	−	2.07193i	−1.17379	−	0.100268i
$428$	1.25011	+	1.48983i	0.0604266	+	0.0720136i
$429$	−6.74122	−	56.0278i	−0.325469	−	2.70505i
$430$	7.60006	−	9.05740i	0.366507	−	0.436786i
$431$	33.8133	−	19.5221i	1.62873	−	0.940347i	0.644256	−	0.764810i	$-0.277167\pi$
$431$	33.8133	−	19.5221i	1.62873	−	0.940347i	0.984473	−	0.175537i	$-0.0561660\pi$
$432$	1.72746	−	4.90060i	0.0831127	−	0.235780i
$433$		−	32.4403i		−	1.55898i	−0.626414	−	0.779491i	$-0.715478\pi$
$433$		−	32.4403i		−	1.55898i	0.626414	−	0.779491i	$-0.284522\pi$
$434$	6.27436	+	8.92171i	0.301179	+	0.428256i
$435$	−25.8514	+	3.11042i	−1.23948	+	0.149133i
$436$	−0.546999	−	3.10218i	−0.0261965	−	0.148568i
$437$	−6.98093	+	5.85769i	−0.333943	+	0.280211i
$438$	4.73872	+	0.259891i	0.226425	+	0.0124181i
$439$	−7.54734	−	20.7361i	−0.360215	−	0.989682i	−0.978953	−	0.204085i	$-0.934578\pi$
$439$	−7.54734	−	20.7361i	−0.360215	−	0.989682i	0.618738	−	0.785597i	$-0.287644\pi$
$440$	6.92675	−	11.9975i	0.330220	−	0.571958i
$441$	16.9800	+	12.3563i	0.808572	+	0.588397i
$442$	−10.0692	−	17.4404i	−0.478945	−	0.829557i
$443$	0.421665	−	0.502521i	0.0200339	−	0.0238755i	−0.755934	−	0.654647i	$-0.772817\pi$
$443$	0.421665	−	0.502521i	0.0200339	−	0.0238755i	0.775968	+	0.630772i	$0.217262\pi$
$444$	2.74445	−	11.7571i	0.130246	−	0.557970i
$445$	−1.57246	−	8.91788i	−0.0745419	−	0.422748i
$446$	3.98816	−	3.34646i	0.188845	−	0.158460i
$447$	8.30391	−	8.86160i	0.392762	−	0.419139i
$448$	−2.63520	+	0.235998i	−0.124502	+	0.0111499i
$449$	15.6143	−	9.01493i	0.736885	−	0.425441i	−0.0840508	−	0.996461i	$-0.526786\pi$
$449$	15.6143	−	9.01493i	0.736885	−	0.425441i	0.820936	+	0.571021i	$0.193452\pi$
$450$	4.64741	+	3.41116i	0.219081	+	0.160804i
$451$			47.3719i			2.23066i
$452$	19.1104	+	3.36968i	0.898877	+	0.158496i
$453$	−3.63229	−	7.17179i	−0.170660	−	0.336960i
$454$	−16.1382	+	2.84561i	−0.757405	+	0.133551i
$455$	−18.2817	−	38.9961i	−0.857058	−	1.82817i
$456$	0.333235	+	2.76959i	0.0156052	+	0.129698i
$457$	2.22611	−	12.6249i	0.104133	−	0.590567i	−0.887430	−	0.460942i	$-0.847512\pi$
$457$	2.22611	−	12.6249i	0.104133	−	0.590567i	0.991563	−	0.129625i	$-0.0413773\pi$
$458$	8.64054	+	14.9659i	0.403746	+	0.699308i
$459$	16.6842	+	2.76732i	0.778754	+	0.129168i
$460$	−12.8919	−	7.44317i	−0.601090	−	0.347039i
$461$	−7.87279	+	2.86546i	−0.366673	+	0.133458i	−0.518784	−	0.854905i	$-0.673615\pi$
$461$	−7.87279	+	2.86546i	−0.366673	+	0.133458i	0.152111	+	0.988363i	$0.451393\pi$
$462$	3.36734	−	23.8943i	0.156663	−	1.11166i
$463$	9.95309	−	8.35164i	0.462559	−	0.388133i	−0.381512	−	0.924364i	$-0.624597\pi$
$463$	9.95309	−	8.35164i	0.462559	−	0.388133i	0.844072	+	0.536230i	$0.180152\pi$
$464$	1.95430	−	5.36940i	0.0907262	−	0.249268i
$465$	15.7300	+	10.2696i	0.729462	+	0.476242i
$466$	−2.70161	+	15.3216i	−0.125149	+	0.709758i
$467$	−6.82839	−	11.8271i	−0.315980	−	0.547293i	0.663665	−	0.748030i	$-0.269000\pi$
$467$	−6.82839	−	11.8271i	−0.315980	−	0.547293i	−0.979645	+	0.200736i	$0.935667\pi$
$468$	−8.21811	+	16.6439i	−0.379882	+	0.769364i
$469$	26.6186	+	7.07394i	1.22913	+	0.326644i
$470$	10.5495	+	1.86016i	0.486613	+	0.0858030i
$471$	19.7796	−	21.1080i	0.911395	−	0.972603i
$472$	6.72049	−	1.18500i	0.309336	−	0.0545442i
$473$	−23.3051	+	4.10932i	−1.07157	+	0.188947i
$474$	−9.33723	−	2.17958i	−0.428873	−	0.100111i
$475$	−3.04790	−	0.537427i	−0.139847	−	0.0246588i
$476$	−2.24582	−	8.31325i	−0.102937	−	0.381037i
$477$	23.8792	−	22.8367i	1.09335	−	1.04562i
$478$	−7.14183	−	12.3700i	−0.326660	−	0.565791i
$479$	−3.45014	+	19.5667i	−0.157641	+	0.894027i	0.798690	+	0.601742i	$0.205527\pi$
$479$	−3.45014	+	19.5667i	−0.157641	+	0.894027i	−0.956331	+	0.292285i	$0.905585\pi$
$480$	−4.06520	+	2.05890i	−0.185550	+	0.0939755i
$481$	−14.7510	+	40.5282i	−0.672590	+	1.84793i
$482$	−15.7144	+	13.1859i	−0.715771	+	0.600603i
$483$	−25.6757	−	3.61839i	−1.16829	−	0.164642i
$484$	−15.7187	+	5.72112i	−0.714484	+	0.260051i
$485$	−3.43187	−	1.98139i	−0.155833	−	0.0899704i
$486$	−6.41587	−	14.2069i	−0.291030	−	0.644439i
$487$	16.1938	+	28.0486i	0.733813	+	1.27100i	0.955242	+	0.295825i	$0.0955947\pi$
$487$	16.1938	+	28.0486i	0.733813	+	1.27100i	−0.221429	+	0.975177i	$0.571072\pi$
$488$	1.59774	−	9.06121i	0.0723261	−	0.410182i
$489$	34.1625	+	14.5992i	1.54488	+	0.660197i
$490$	−3.27234	−	18.1233i	−0.147829	−	0.818725i
$491$	18.4073	−	3.24570i	0.830710	−	0.146477i	0.257907	−	0.966170i	$-0.416967\pi$
$491$	18.4073	−	3.24570i	0.830710	−	0.146477i	0.572803	+	0.819693i	$0.305856\pi$
$492$	8.51836	−	13.0476i	0.384037	−	0.588232i
$493$	18.3151	+	3.22945i	0.824871	+	0.145447i
$494$		−	9.96517i		−	0.448354i
$495$	−9.85834	−	40.3744i	−0.443099	−	1.81469i
$496$	−3.57018	+	2.06125i	−0.160306	+	0.0925526i
$497$	−2.10563	−	23.5118i	−0.0944502	−	1.05465i
$498$	−0.593284	−	1.95754i	−0.0265857	−	0.0877195i
$499$	8.20058	−	6.88110i	0.367108	−	0.308040i	−0.440508	−	0.897749i	$-0.645202\pi$
$499$	8.20058	−	6.88110i	0.367108	−	0.308040i	0.807616	+	0.589708i	$0.200757\pi$
$500$	1.40635	+	7.97581i	0.0628939	+	0.356689i
$501$	3.73771	−	1.13281i	0.166988	−	0.0506102i
$502$	4.45127	−	5.30482i	0.198670	−	0.236766i
$503$	10.9676	+	18.9965i	0.489023	+	0.847013i	0.999920	−	0.0126291i	$-0.00402006\pi$
$503$	10.9676	+	18.9965i	0.489023	+	0.847013i	−0.510897	+	0.859642i	$0.670687\pi$
$504$	−5.22410	+	5.97568i	−0.232700	+	0.266178i
$505$	19.6901	−	34.1042i	0.876196	−	1.51762i
$506$	10.1904	+	27.9978i	0.453017	+	1.24465i
$507$	23.9407	−	36.6700i	1.06324	−	1.62857i
$508$	−3.64624	+	3.05956i	−0.161776	+	0.135746i
$509$	−3.97942	−	22.5684i	−0.176385	−	1.00033i	−0.936534	−	0.350578i	$-0.885985\pi$
$509$	−3.97942	−	22.5684i	−0.176385	−	1.00033i	0.760149	−	0.649749i	$-0.225126\pi$
$510$	−8.89698	−	11.8666i	−0.393965	−	0.525460i
$511$	−6.57645	−	3.05024i	−0.290925	−	0.134935i
$512$		−	1.00000i		−	0.0441942i
$513$	6.46514	+	5.31385i	0.285443	+	0.234612i
$514$	10.6524	−	6.15016i	0.469857	−	0.271272i
$515$	4.93322	−	5.87918i	0.217384	−	0.259068i
$516$	7.15784	+	3.05887i	0.315106	+	0.134659i
$517$	−13.7816	−	16.4242i	−0.606113	−	0.722337i
$518$	−10.5470	+	15.1286i	−0.463407	+	0.664712i
$519$	−1.17232	+	1.79566i	−0.0514593	+	0.0788205i
$520$	15.2968	−	5.56756i	0.670807	−	0.244154i
$521$	−6.60011			−0.289156			−0.144578	−	0.989493i	$-0.546182\pi$
$521$	−6.60011			−0.289156			−0.144578	+	0.989493i	$0.546182\pi$
$522$	−6.89611	−	15.6937i	−0.301834	−	0.686894i
$523$			8.42832i			0.368545i	0.982875	+	0.184272i	$0.0589929\pi$
$523$			8.42832i			0.368545i	−0.982875	+	0.184272i	$0.941007\pi$
$524$	1.18072	−	6.69622i	0.0515802	−	0.292526i
$525$	−4.66369	−	7.46974i	−0.203540	−	0.326006i
$526$	−12.9265	−	4.70484i	−0.563620	−	0.205141i
$527$	−8.62472	−	10.2785i	−0.375699	−	0.447740i
$528$	8.88167	+	2.07323i	0.386525	+	0.0902260i
$529$	8.47221	−	3.08363i	0.368357	−	0.134071i
$530$	−28.9762			−1.25865
$531$	12.1138	−	16.5039i	0.525693	−	0.716210i
$532$	1.09442	−	4.11819i	0.0474490	−	0.178546i
$533$	−35.7802	+	42.6411i	−1.54981	+	1.84699i
$534$	5.31843	−	2.69362i	0.230151	−	0.116564i
$535$	−3.28893	−	3.91959i	−0.142193	−	0.169459i
$536$	−3.56046	+	9.78229i	−0.153789	+	0.422530i
$537$	5.06214	−	11.8456i	0.218447	−	0.511174i
$538$	1.07166	+	2.94437i	0.0462027	+	0.126941i
$539$	−18.2988	+	31.9969i	−0.788184	+	1.37820i
$540$	−4.54479	+	12.8930i	−0.195577	+	0.554826i
$541$	−4.97897	+	8.62383i	−0.214063	+	0.370767i	−0.952982	−	0.303026i	$-0.902003\pi$
$541$	−4.97897	+	8.62383i	−0.214063	+	0.370767i	0.738920	+	0.673794i	$0.235336\pi$
$542$	19.5499	+	16.4043i	0.839738	+	0.704624i
$543$	−13.0934	+	30.6389i	−0.561891	+	1.31484i
$544$	3.20531	−	0.565182i	0.137426	−	0.0242320i
$545$	1.43910	+	8.16154i	0.0616443	+	0.349602i
$546$	21.0785	−	18.9647i	0.902077	−	0.811616i
$547$	8.51278	+	7.14307i	0.363980	+	0.305416i	0.806375	−	0.591405i	$-0.201426\pi$
$547$	8.51278	+	7.14307i	0.363980	+	0.305416i	−0.442394	+	0.896821i	$0.645871\pi$
$548$	−2.20261	+	1.27167i	−0.0940906	+	0.0543233i
$549$	−15.3240	−	22.9586i	−0.654013	−	0.979850i
$550$	−5.05939	+	8.76311i	−0.215733	+	0.373660i
$551$	7.04969	+	5.91539i	0.300327	+	0.252004i
$552$	2.22780	−	9.54383i	0.0948216	−	0.406212i
$553$	12.0147	+	8.37614i	0.510919	+	0.356190i
$554$	−2.21491	+	6.08541i	−0.0941024	+	0.258544i
$555$	−7.22039	+	30.9319i	−0.306488	+	1.31299i
$556$	−1.38017	−	3.79199i	−0.0585323	−	0.160816i
$557$	2.46024	+	1.42042i	0.104244	+	0.0601851i	0.551215	−	0.834363i	$-0.314164\pi$
$557$	2.46024	+	1.42042i	0.104244	+	0.0601851i	−0.446972	+	0.894548i	$0.647498\pi$
$558$	−3.46666	+	11.8717i	−0.146755	+	0.502568i
$559$	−24.0815	−	13.9035i	−1.01854	−	0.588055i
$560$	6.93297	−	0.620889i	0.292971	−	0.0262373i
$561$	−1.62559	+	29.6402i	−0.0686326	+	1.25141i
$562$	26.2208	+	9.54360i	1.10606	+	0.402572i
$563$	−5.18299	−	1.88645i	−0.218437	−	0.0795045i	0.230484	−	0.973076i	$-0.425969\pi$
$563$	−5.18299	−	1.88645i	−0.218437	−	0.0795045i	−0.448921	+	0.893572i	$0.648191\pi$
$564$	0.842463	+	7.00190i	0.0354741	+	0.294833i
$565$	−50.2776	−	8.86529i	−2.11519	−	0.372966i
$566$	−19.0972			−0.802716
$567$	1.06387	+	23.7880i	0.0446785	+	0.999001i
$568$	8.92220			0.374367
$569$	−0.451625	−	0.0796336i	−0.0189331	−	0.00333842i	0.164174	−	0.986431i	$-0.447504\pi$
$569$	−0.451625	−	0.0796336i	−0.0189331	−	0.00333842i	−0.183107	+	0.983093i	$0.558615\pi$
$570$	−0.876709	−	7.28652i	−0.0367213	−	0.305199i
$571$	−23.0773	−	8.39945i	−0.965755	−	0.351506i	−0.189469	−	0.981887i	$-0.560677\pi$
$571$	−23.0773	−	8.39945i	−0.965755	−	0.351506i	−0.776286	+	0.630380i	$0.782899\pi$
$572$	−30.6161	−	11.1433i	−1.28012	−	0.465926i
$573$	−0.225475	+	4.11119i	−0.00941934	+	0.171747i
$574$	−19.4695	+	13.6923i	−0.812641	+	0.571505i
$575$	9.41644	+	5.43658i	0.392693	+	0.226721i
$576$	−2.07347	−	2.16812i	−0.0863944	−	0.0903383i
$577$	−16.7736	−	9.68425i	−0.698294	−	0.403160i	0.108417	−	0.994105i	$-0.465422\pi$
$577$	−16.7736	−	9.68425i	−0.698294	−	0.403160i	−0.806712	+	0.590945i	$0.798755\pi$
$578$	−2.19118	−	6.02022i	−0.0911412	−	0.250408i
$579$	10.4720	−	44.8616i	0.435200	−	1.86438i
$580$	−5.14158	+	14.1264i	−0.213492	+	0.586566i
$581$	−0.265934	+	3.11317i	−0.0110328	+	0.129156i
$582$	0.593047	−	2.54059i	0.0245826	−	0.105311i
$583$	44.4269	+	37.2786i	1.83997	+	1.54392i
$584$	1.37001	−	2.37292i	0.0566912	−	0.0981921i
$585$	21.6210	−	43.7884i	0.893920	−	1.81043i
$586$	1.24202	−	0.717081i	0.0513074	−	0.0296224i
$587$	3.88418	+	3.25921i	0.160317	+	0.134522i	0.719417	−	0.694578i	$-0.244409\pi$
$587$	3.88418	+	3.25921i	0.160317	+	0.134522i	−0.559100	+	0.829100i	$0.688853\pi$
$588$	10.7937	−	5.52241i	0.445123	−	0.227740i
$589$	−1.15294	−	6.53863i	−0.0475060	−	0.269420i
$590$	−17.6810	+	3.11763i	−0.727914	+	0.128351i
$591$	−8.53326	+	19.9681i	−0.351011	+	0.821377i
$592$	−5.33969	−	4.48053i	−0.219460	−	0.184149i
$593$	18.8157	−	32.5898i	0.772669	−	1.33830i	−0.163426	−	0.986556i	$-0.552254\pi$
$593$	18.8157	−	32.5898i	0.772669	−	1.33830i	0.936095	−	0.351747i	$-0.114412\pi$
$594$	23.5553	−	13.9208i	0.966486	−	0.571178i
$595$	5.90852	+	21.8714i	0.242226	+	0.896638i
$596$	−2.39807	−	6.58864i	−0.0982288	−	0.269881i
$597$	−13.3556	+	31.2525i	−0.546609	+	1.27908i
$598$	−11.9741	+	32.8986i	−0.489658	+	1.34532i
$599$	−11.7728	−	14.0303i	−0.481025	−	0.573263i	0.469886	−	0.882727i	$-0.344295\pi$
$599$	−11.7728	−	14.0303i	−0.481025	−	0.573263i	−0.950911	+	0.309464i	$0.899850\pi$
$600$	2.96928	−	1.50385i	0.121220	−	0.0613943i
$601$	−10.8069	+	12.8792i	−0.440824	+	0.525353i	−0.940013	−	0.341140i	$-0.889187\pi$
$601$	−10.8069	+	12.8792i	−0.440824	+	0.525353i	0.499189	+	0.866493i	$0.333631\pi$
$602$	−8.42496	−	8.39047i	−0.343376	−	0.341970i
$603$	12.5637	+	28.5917i	0.511634	+	1.16434i
$604$	−4.64141			−0.188856
$605$	41.3542	−	15.0517i	1.68129	−	0.611939i
$606$	25.2471	+	5.89340i	1.02559	+	0.239403i
$607$	25.9117	+	30.8804i	1.05172	+	1.25340i	0.966400	+	0.257044i	$0.0827485\pi$
$607$	25.9117	+	30.8804i	1.05172	+	1.25340i	0.0853252	+	0.996353i	$0.472807\pi$
$608$	1.51343	+	0.550843i	0.0613776	+	0.0223396i
$609$	0.903942	+	26.1692i	0.0366296	+	1.06043i
$610$	−4.20348	+	23.8391i	−0.170194	+	0.965219i
$611$		−	25.1933i		−	1.01921i
$612$	5.77760	−	7.87147i	0.233546	−	0.318185i
$613$	10.0672			0.406612			0.203306	−	0.979115i	$-0.434831\pi$
$613$	10.0672			0.406612			0.203306	+	0.979115i	$0.434831\pi$
$614$	−13.7850	+	5.01734i	−0.556318	+	0.202483i
$615$	−22.4110	+	34.3270i	−0.903697	+	1.38420i
$616$	−11.4285	−	7.96746i	−0.460469	−	0.321018i
$617$	14.1881	+	16.9087i	0.571190	+	0.680718i	0.971875	−	0.235498i	$-0.0756721\pi$
$617$	14.1881	+	16.9087i	0.571190	+	0.680718i	−0.400684	+	0.916216i	$0.631228\pi$
$618$	4.64618	+	1.98552i	0.186897	+	0.0798694i
$619$	12.7940	−	15.2473i	0.514235	−	0.612842i	−0.444972	−	0.895544i	$-0.646786\pi$
$619$	12.7940	−	15.2473i	0.514235	−	0.612842i	0.959208	+	0.282703i	$0.0912309\pi$
$620$	9.39280	−	5.42293i	0.377224	−	0.217790i
$621$	−14.9587	−	25.3114i	−0.600270	−	1.01571i
$622$			3.74949i			0.150341i
$623$	−9.07027	+	0.812297i	−0.363393	+	0.0325440i
$624$	6.42878	+	8.57455i	0.257357	+	0.343257i
$625$	−5.36842	−	30.4458i	−0.214737	−	1.21783i
$626$	19.9906	−	16.7741i	0.798987	−	0.670430i
$627$	−8.03009	+	12.2997i	−0.320691	+	0.491204i
$628$	−5.71210	−	15.6939i	−0.227938	−	0.626254i
$629$	11.3436	−	19.6477i	0.452298	−	0.783404i
$630$	13.7441	−	15.7214i	0.547578	−	0.626356i
$631$	−11.6127	−	20.1137i	−0.462292	−	0.800714i	0.536782	−	0.843721i	$-0.319640\pi$
$631$	−11.6127	−	20.1137i	−0.462292	−	0.800714i	−0.999075	+	0.0430068i	$0.986306\pi$
$632$	−3.55833	+	4.24065i	−0.141543	+	0.168684i
$633$	28.3138	−	8.58122i	1.12537	−	0.341073i
$634$	0.745590	+	4.22845i	0.0296112	+	0.167933i
$635$	9.59291	−	8.04941i	0.380683	−	0.319431i
$636$	−5.53308	−	18.2564i	−0.219401	−	0.723913i
$637$	−40.6387	+	14.9804i	−1.61016	+	0.593544i
$638$	26.0571	−	15.0441i	1.03161	−	0.595600i
$639$	19.3444	−	18.4999i	0.765252	−	0.731843i
$640$			2.63090i			0.103996i
$641$	−40.7526	−	7.18579i	−1.60963	−	0.283822i	−0.704741	−	0.709465i	$-0.748937\pi$
$641$	−40.7526	−	7.18579i	−1.60963	−	0.283822i	−0.904891	+	0.425643i	$0.860048\pi$
$642$	1.84150	−	2.82064i	0.0726783	−	0.111322i
$643$	−11.7591	+	2.07345i	−0.463734	+	0.0817688i	−0.400633	−	0.916238i	$-0.631210\pi$
$643$	−11.7591	+	2.07345i	−0.463734	+	0.0817688i	−0.0631003	+	0.998007i	$0.520099\pi$
$644$	−8.56147	+	12.2806i	−0.337369	+	0.483923i
$645$	−18.8316	−	8.04758i	−0.741493	−	0.316873i
$646$	−0.910257	+	5.16233i	−0.0358136	+	0.203109i
$647$	−24.6767	−	42.7412i	−0.970139	−	1.68033i	−0.695122	−	0.718892i	$-0.744650\pi$
$647$	−24.6767	−	42.7412i	−0.970139	−	1.68033i	−0.275017	−	0.961439i	$-0.588684\pi$
$648$	−8.99104	−	0.401486i	−0.353201	−	0.0157718i
$649$	31.1197	+	17.9670i	1.22155	+	0.705265i
$650$	−11.1729	+	4.06662i	−0.438239	+	0.159506i
$651$	11.6365	−	14.8824i	0.456069	−	0.583287i
$652$	16.4311	−	13.7873i	0.643491	−	0.539953i
$653$	7.22078	−	19.8389i	0.282571	−	0.776357i	−0.714483	−	0.699653i	$-0.753338\pi$
$653$	7.22078	−	19.8389i	0.282571	−	0.776357i	0.997054	−	0.0767042i	$-0.0244397\pi$
$654$	−4.86736	+	2.46517i	−0.190329	+	0.0963957i
$655$	−3.10637	+	17.6171i	−0.121376	+	0.688357i
$656$	−4.49817	−	7.79106i	−0.175624	−	0.304190i
$657$	−1.94983	−	7.98543i	−0.0760701	−	0.311541i
$658$	2.76683	−	10.4113i	0.107862	−	0.405877i
$659$	−5.78715	−	1.02043i	−0.225436	−	0.0397504i	0.0597893	−	0.998211i	$-0.480957\pi$
$659$	−5.78715	−	1.02043i	−0.225436	−	0.0397504i	−0.285225	+	0.958461i	$0.592068\pi$
$660$	−23.3668	−	5.45448i	−0.909551	−	0.212315i
$661$	−42.5379	+	7.50059i	−1.65453	+	0.291739i	−0.921478	−	0.388430i	$-0.873018\pi$
$661$	−42.5379	+	7.50059i	−1.65453	+	0.291739i	−0.733055	+	0.680169i	$0.761906\pi$
$662$	16.2968	−	2.87357i	0.633393	−	0.111684i
$663$	−23.8506	+	25.4524i	−0.926281	+	0.988489i
$664$	−1.16301	−	0.205070i	−0.0451336	−	0.00795828i
$665$	−2.87930	+	10.8346i	−0.111655	+	0.420146i
$666$	−20.8673	+	1.35733i	−0.808592	+	0.0525955i
$667$	−16.1657	−	27.9997i	−0.625937	−	1.08415i
$668$	0.391559	−	2.22064i	0.0151499	−	0.0859192i
$669$	−7.55064	−	4.92956i	−0.291925	−	0.190588i
$670$	9.36722	−	25.7362i	0.361887	−	0.994278i
$671$	37.1145	−	31.1428i	1.43279	−	1.20225i
$672$	1.71506	+	4.24954i	0.0661597	+	0.163930i
$673$	−11.1730	+	4.06664i	−0.430688	+	0.156758i	−0.548262	−	0.836307i	$-0.684710\pi$
$673$	−11.1730	+	4.06664i	−0.430688	+	0.156758i	0.117574	+	0.993064i	$0.462488\pi$
$674$	−6.28984	−	3.63144i	−0.242276	−	0.139878i
$675$	3.31957	−	9.41721i	0.127770	−	0.362468i
$676$	−12.6420	−	21.8966i	−0.486231	−	0.842177i
$677$	1.36758	−	7.75592i	0.0525603	−	0.298084i	−0.947184	−	0.320690i	$-0.896085\pi$
$677$	1.36758	−	7.75592i	0.0525603	−	0.298084i	0.999744	+	0.0226060i	$0.00719632\pi$
$678$	−4.01507	−	33.3701i	−0.154198	−	1.28157i
$679$	−2.27909	+	3.26913i	−0.0874633	+	0.125458i
$680$	−8.43284	+	1.48694i	−0.323385	+	0.0570215i
$681$	12.8243	+	25.3211i	0.491430	+	0.970306i
$682$	−21.3779	−	3.76951i	−0.818604	−	0.144342i
$683$			17.2052i			0.658340i	0.944271	+	0.329170i	$0.106769\pi$
$683$			17.2052i			0.658340i	−0.944271	+	0.329170i	$0.893231\pi$
$684$	4.42345	−	1.94375i	0.169135	−	0.0743210i
$685$	5.79484	−	3.34565i	0.221409	−	0.127831i
$686$	−18.4395	+	1.72765i	−0.704023	+	0.0659621i
$687$	20.4665	−	21.8410i	0.780846	−	0.833286i
$688$	3.44270	−	2.88877i	0.131252	−	0.110133i
$689$	11.8336	+	67.1115i	0.450823	+	2.55674i
$690$	−5.86113	+	25.1089i	−0.223129	+	0.955879i
$691$	−18.0849	+	21.5528i	−0.687983	+	0.819906i	−0.991110	−	0.133044i	$-0.957525\pi$
$691$	−18.0849	+	21.5528i	−0.687983	+	0.819906i	0.303127	+	0.952950i	$0.401969\pi$
$692$	0.619053	+	1.07223i	0.0235329	+	0.0407601i
$693$	−41.2987	+	6.42227i	−1.56881	+	0.243962i
$694$	9.27398	−	16.0630i	0.352036	−	0.609744i
$695$	3.63110	+	9.97636i	0.137735	+	0.378425i
$696$	−9.88209	−	0.541975i	−0.374579	−	0.0205435i
$697$	22.4304	−	18.8214i	0.849614	−	0.712911i
$698$	−3.11828	−	17.6846i	−0.118028	−	0.669373i
$699$	26.7542	−	3.21904i	1.01194	−	0.121755i
$700$	−5.06393	+	0.453505i	−0.191398	+	0.0171409i
$701$		−	33.4406i		−	1.26303i	−0.775363	−	0.631516i	$-0.782433\pi$
$701$		−	33.4406i		−	1.26303i	0.775363	−	0.631516i	$-0.217567\pi$
$702$	31.7174	+	5.26078i	1.19710	+	0.198556i
$703$	9.72230	−	5.61317i	0.366683	−	0.211705i
$704$	3.38472	−	4.03375i	0.127566	−	0.152028i
$705$	−2.21644	−	18.4213i	−0.0834759	−	0.693787i
$706$	18.6662	+	22.2455i	0.702511	+	0.837220i
$707$	−32.4869	−	22.6484i	−1.22180	−	0.851781i
$708$	−5.34048	−	10.5445i	−0.200707	−	0.396288i
$709$	−7.25175	+	2.63942i	−0.272345	+	0.0991256i	−0.474583	−	0.880211i	$-0.657401\pi$
$709$	−7.25175	+	2.63942i	−0.272345	+	0.0991256i	0.202237	+	0.979337i	$0.435179\pi$
$710$	−23.4734			−0.880942
$711$	1.07796	+	16.5723i	0.0404266	+	0.621510i
$712$		−	3.44196i		−	0.128993i
$713$	−4.05054	+	22.9718i	−0.151694	+	0.860299i
$714$	−12.6518	+	7.89904i	−0.473480	+	0.295614i
$715$	80.5479	+	29.3170i	3.01232	+	1.09639i
$716$	−4.78064	−	5.69734i	−0.178661	−	0.212920i
$717$	−16.9166	+	18.0527i	−0.631761	+	0.674189i
$718$	−14.2751	+	5.19572i	−0.532743	+	0.193902i
$719$	−25.5365			−0.952350			−0.476175	−	0.879351i	$-0.657977\pi$
$719$	−25.5365			−0.952350			−0.476175	+	0.879351i	$0.657977\pi$
$720$	5.45508	+	5.70411i	0.203299	+	0.212580i
$721$	−5.46867	−	5.44628i	−0.203664	−	0.202830i
$722$	10.5456	−	12.5678i	0.392468	−	0.467725i
$723$	29.7515	+	19.4238i	1.10647	+	0.722377i
$724$	12.3653	+	14.7364i	0.459552	+	0.547673i
$725$	3.75547	−	10.3181i	0.139475	−	0.383204i
$726$	17.3800	+	23.1810i	0.645032	+	0.860327i
$727$	−8.31250	−	22.8384i	−0.308293	−	0.847029i	−0.992990	−	0.118201i	$-0.962287\pi$
$727$	−8.31250	−	22.8384i	−0.308293	−	0.847029i	0.684696	−	0.728828i	$-0.259935\pi$
$728$	−4.26938	−	15.8038i	−0.158234	−	0.585728i
$729$	−20.3261	+	17.7721i	−0.752819	+	0.658227i
$730$	−3.60435	+	6.24292i	−0.133403	+	0.231061i
$731$	11.2051	+	9.40221i	0.414436	+	0.347753i
$732$	−15.8225	+	1.90375i	−0.584815	+	0.0703645i
$733$	13.0926	−	2.30859i	0.483588	−	0.0852696i	0.0734611	−	0.997298i	$-0.476596\pi$
$733$	13.0926	−	2.30859i	0.483588	−	0.0852696i	0.410127	+	0.912028i	$0.365484\pi$
$734$	−0.982747	−	5.57343i	−0.0362738	−	0.205719i
$735$	−28.3970	+	14.5289i	−1.04744	+	0.535907i
$736$	−4.33448	−	3.63706i	−0.159771	−	0.134064i
$737$	−47.4723	+	27.4081i	−1.74866	+	1.00959i
$738$	−25.9071	−	7.56515i	−0.953652	−	0.278477i
$739$	−7.15492	+	12.3927i	−0.263198	+	0.455872i	−0.967090	−	0.254435i	$-0.918111\pi$
$739$	−7.15492	+	12.3927i	−0.263198	+	0.455872i	0.703892	+	0.710307i	$0.251444\pi$
$740$	14.0482	+	11.7878i	0.516422	+	0.433330i
$741$	−16.5182	+	5.00627i	−0.606811	+	0.183910i
$742$	−2.48014	+	29.0340i	−0.0910490	+	1.06587i
$743$	12.5638	−	34.5187i	0.460921	−	1.26637i	−0.463873	−	0.885902i	$-0.653541\pi$
$743$	12.5638	−	34.5187i	0.460921	−	1.26637i	0.924794	−	0.380468i	$-0.124237\pi$
$744$	5.21028	+	4.88239i	0.191018	+	0.178997i
$745$	6.30909	+	17.3341i	0.231147	+	0.635071i
$746$	−23.2894	−	13.4461i	−0.852686	−	0.492298i
$747$	−2.94676	+	1.96685i	−0.107816	+	0.0719632i
$748$	14.8424	+	8.56925i	0.542691	+	0.313323i
$749$	−4.20892	+	2.96000i	−0.153791	+	0.108156i
$750$	12.5141	−	6.33802i	0.456952	−	0.231432i
$751$	41.5158	+	15.1105i	1.51493	+	0.551391i	0.959877	−	0.280422i	$-0.0904744\pi$
$751$	41.5158	+	15.1105i	1.51493	+	0.551391i	0.555057	+	0.831813i	$0.312697\pi$
$752$	3.82615	+	1.39261i	0.139525	+	0.0507831i
$753$	−11.0295	−	4.71338i	−0.401936	−	0.171765i
$754$	34.8177	+	6.13930i	1.26799	+	0.223580i
$755$	12.2111			0.444407
$756$	12.5297	+	5.65740i	0.455701	+	0.205758i
$757$	−11.0138			−0.400302			−0.200151	−	0.979765i	$-0.564143\pi$
$757$	−11.0138			−0.400302			−0.200151	+	0.979765i	$0.564143\pi$
$758$	3.86105	+	0.680807i	0.140240	+	0.0247280i
$759$	41.2896	−	30.9569i	1.49872	−	1.12367i
$760$	−3.98168	−	1.44921i	−0.144431	−	0.0525685i
$761$	−11.4921	−	4.18280i	−0.416590	−	0.151626i	0.125217	−	0.992129i	$-0.460037\pi$
$761$	−11.4921	−	4.18280i	−0.416590	−	0.151626i	−0.541807	+	0.840503i	$0.682260\pi$
$762$	6.90330	+	4.50694i	0.250080	+	0.163269i
$763$	8.30100	−	0.743405i	0.300516	−	0.0269131i
$764$	2.05868	+	1.18858i	0.0744805	+	0.0430013i
$765$	−15.2003	+	20.7091i	−0.549568	+	0.748738i
$766$	−2.34922	−	1.35632i	−0.0848807	−	0.0490059i
$767$	14.4414	+	39.6775i	0.521450	+	1.43267i
$768$	−1.65759	+	0.502377i	−0.0598133	+	0.0181280i
$769$	15.2561	−	41.9157i	0.550148	−	1.51152i	−0.283361	−	0.959013i	$-0.591450\pi$
$769$	15.2561	−	41.9157i	0.550148	−	1.51152i	0.833509	−	0.552506i	$-0.186328\pi$
$770$	30.0674	+	20.9616i	1.08355	+	0.755404i
$771$	−15.5460	−	14.5676i	−0.559875	−	0.524640i
$772$	−20.3746	−	17.0963i	−0.733298	−	0.615310i
$773$	3.33806	−	5.78169i	0.120062	−	0.207953i	−0.799730	−	0.600360i	$-0.795024\pi$
$773$	3.33806	−	5.78169i	0.120062	−	0.207953i	0.919792	+	0.392407i	$0.128357\pi$
$774$	1.47442	−	13.4015i	0.0529971	−	0.481707i
$775$	−6.86062	+	3.96098i	−0.246441	+	0.142283i
$776$	−1.15385	−	0.968196i	−0.0414208	−	0.0347562i
$777$	30.3756	+	9.88233i	1.08972	+	0.354527i
$778$	−0.862621	−	4.89217i	−0.0309265	−	0.175393i
$779$	14.2690	−	2.51601i	0.511240	−	0.0901454i
$780$	−16.9135	−	22.5588i	−0.605600	−	0.807734i
$781$	35.9899	+	30.1991i	1.28782	+	1.08061i
$782$	9.20812	−	15.9489i	0.329282	−	0.570333i
$783$	−22.5493	+	19.3151i	−0.805847	+	0.690265i
$784$	−0.0287179	−	6.99994i	−0.00102564	−	0.249998i
$785$	15.0280	+	41.2890i	0.536372	+	1.47367i
$786$	−11.6928	+	1.40687i	−0.417068	+	0.0501812i
$787$	−13.3206	+	36.5980i	−0.474828	+	1.30458i	0.439004	+	0.898485i	$0.355331\pi$
$787$	−13.3206	+	36.5980i	−0.474828	+	1.30458i	−0.913832	+	0.406093i	$0.866891\pi$
$788$	8.05873	+	9.60402i	0.287080	+	0.342129i
$789$	−1.30477	+	23.7904i	−0.0464509	+	0.846961i
$790$	9.36161	−	11.1567i	0.333071	−	0.396939i
$791$	−13.1864	+	49.6191i	−0.468853	+	1.76425i
$792$	−1.02537	−	15.7637i	−0.0364348	−	0.560140i
$793$	56.9303			2.02165
$794$	10.7871	−	3.92619i	0.382821	−	0.139335i
$795$	14.5570	+	48.0308i	0.516283	+	1.70348i
$796$	12.6129	+	15.0315i	0.447053	+	0.532777i
$797$	−30.8542	−	11.2300i	−1.09291	−	0.397788i	−0.268214	−	0.963359i	$-0.586433\pi$
$797$	−30.8542	−	11.2300i	−1.09291	−	0.397788i	−0.824699	+	0.565572i	$0.808656\pi$
$798$	−7.37610	+	0.254786i	−0.261111	+	0.00901934i
$799$	−2.30125	+	13.0511i	−0.0814125	+	0.461713i
$800$		−	1.92164i		−	0.0679404i
$801$	−7.13678	−	7.46258i	−0.252166	−	0.263677i
$802$	9.59019			0.338642
$803$	13.5579	−	4.93468i	0.478449	−	0.174141i
$804$	18.0038	+	0.987401i	0.634943	+	0.0348230i
$805$	22.5244	−	32.3090i	0.793880	−	1.13874i
$806$	−16.3959	−	19.5399i	−0.577522	−	0.688264i
$807$	4.34219	−	3.25557i	0.152852	−	0.114601i
$808$	9.62144	−	11.4664i	0.338481	−	0.403386i
$809$	8.89967	−	5.13823i	0.312896	−	0.180650i	−0.335326	−	0.942102i	$-0.608846\pi$
$809$	8.89967	−	5.13823i	0.312896	−	0.180650i	0.648222	+	0.761452i	$0.275513\pi$
$810$	23.6545	+	1.05627i	0.831136	+	0.0371135i
$811$			33.4628i			1.17504i	0.809210	+	0.587520i	$0.199896\pi$
$811$			33.4628i			1.17504i	−0.809210	+	0.587520i	$0.800104\pi$
$812$	13.7145	+	6.36095i	0.481284	+	0.223226i
$813$	17.3702	−	40.6469i	0.609201	−	1.42555i
$814$	−6.37364	−	36.1467i	−0.223396	−	1.26694i
$815$	−43.2286	+	36.2731i	−1.51423	+	1.27059i
$816$	−2.54711	−	5.02916i	−0.0891668	−	0.176056i
$817$	2.47555	+	6.80153i	0.0866087	+	0.237955i
$818$	−2.27791	+	3.94546i	−0.0796453	+	0.137950i
$819$	−42.0252	−	25.4121i	−1.46848	−	0.887972i
$820$	11.8342	+	20.4975i	0.413270	+	0.715804i
$821$	27.1980	−	32.4133i	0.949215	−	1.13123i	−0.0420193	−	0.999117i	$-0.513379\pi$
$821$	27.1980	−	32.4133i	0.949215	−	1.13123i	0.991235	−	0.132114i	$-0.0421764\pi$
$822$	3.21446	+	3.01216i	0.112117	+	0.105061i
$823$	−2.10169	−	11.9193i	−0.0732602	−	0.415479i	−0.999278	−	0.0379989i	$-0.987902\pi$
$823$	−2.10169	−	11.9193i	−0.0732602	−	0.415479i	0.926018	−	0.377480i	$-0.123209\pi$
$824$	2.23467	−	1.87511i	0.0778483	−	0.0653224i
$825$	17.0674	+	3.98402i	0.594211	+	0.138706i
$826$	1.61049	+	17.9831i	0.0560362	+	0.625711i
$827$	−8.24247	+	4.75879i	−0.286619	+	0.165479i	−0.636416	−	0.771346i	$-0.719584\pi$
$827$	−8.24247	+	4.75879i	−0.286619	+	0.165479i	0.349797	+	0.936825i	$0.386250\pi$
$828$	−16.9390	+	1.10181i	−0.588671	+	0.0382906i
$829$		−	39.8072i		−	1.38256i	−0.722587	−	0.691280i	$-0.757047\pi$
$829$		−	39.8072i		−	1.38256i	0.722587	−	0.691280i	$-0.242953\pi$
$830$	3.05977	+	0.539520i	0.106206	+	0.0187270i
$831$	11.1999	+	0.614247i	0.388519	+	0.0213080i
$832$	6.09341	−	1.07443i	0.211251	−	0.0372492i
$833$	22.4207	−	4.04829i	0.776832	−	0.140265i
$834$	−5.59221	+	4.19277i	−0.193643	+	0.145184i
$835$	−1.03015	+	5.84229i	−0.0356499	+	0.202181i
$836$	4.24034	+	7.34449i	0.146655	+	0.254014i
$837$	21.4200	−	0.217741i	0.740383	−	0.00752624i
$838$	3.29503	+	1.90238i	0.113825	+	0.0657168i
$839$	−35.6950	+	12.9919i	−1.23233	+	0.448531i	−0.874394	−	0.485216i	$-0.838741\pi$
$839$	−35.6950	+	12.9919i	−1.23233	+	0.448531i	−0.357934	+	0.933747i	$0.616519\pi$
$840$	−4.51214	−	11.1801i	−0.155684	−	0.385751i
$841$	−2.79590	+	2.34604i	−0.0964103	+	0.0808978i
$842$	11.3686	−	31.2350i	0.391789	−	1.07643i
$843$	2.64667	−	48.2579i	0.0911561	−	1.66209i
$844$	2.96613	−	16.8217i	0.102098	−	0.579028i
$845$	33.2599	+	57.6078i	1.14418	+	1.98177i
$846$	11.1831	−	4.91406i	0.384482	−	0.168949i
$847$	−11.5421	−	42.7251i	−0.396592	−	1.46805i
$848$	−10.8465	−	1.91252i	−0.372469	−	0.0656764i
$849$	9.59401	+	31.6554i	0.329266	+	1.08641i
$850$	6.15946	−	1.08608i	0.211268	−	0.0372522i
$851$	−38.8416	+	6.84882i	−1.33147	+	0.234774i
$852$	−4.48231	−	14.7894i	−0.153561	−	0.506676i
$853$	5.17392	+	0.912302i	0.177152	+	0.0312366i	0.261520	−	0.965198i	$-0.415776\pi$
$853$	5.17392	+	0.912302i	0.177152	+	0.0312366i	−0.0843685	+	0.996435i	$0.526887\pi$
$854$	23.5269	+	6.25232i	0.805075	+	0.213950i
$855$	−11.6377	+	5.11381i	−0.397999	+	0.174889i
$856$	−0.972416	−	1.68427i	−0.0332365	−	0.0575673i
$857$	9.35366	−	53.0472i	0.319515	−	1.81206i	−0.226192	−	0.974083i	$-0.572628\pi$
$857$	9.35366	−	53.0472i	0.319515	−	1.81206i	0.545707	−	0.837976i	$-0.316261\pi$
$858$	−3.09032	+	56.3472i	−0.105502	+	1.92366i
$859$	−7.73892	+	21.2625i	−0.264049	+	0.725468i	0.734836	+	0.678245i	$0.237259\pi$
$859$	−7.73892	+	21.2625i	−0.264049	+	0.725468i	−0.998884	+	0.0472227i	$0.984963\pi$
$860$	−9.05740	+	7.60006i	−0.308855	+	0.259160i
$861$	32.4773	+	25.3938i	1.10682	+	0.865419i
$862$	−36.6896	+	13.3539i	−1.24965	+	0.454836i
$863$	40.3685	+	23.3068i	1.37416	+	0.793371i	0.991449	−	0.130497i	$-0.0416572\pi$
$863$	40.3685	+	23.3068i	1.37416	+	0.793371i	0.382711	+	0.923868i	$0.374991\pi$
$864$	−2.55220	+	4.52618i	−0.0868276	+	0.153984i
$865$	−1.62867	−	2.82094i	−0.0553764	−	0.0959147i
$866$	−5.63320	+	31.9475i	−0.191424	+	1.08562i
$867$	−8.87829	+	6.65651i	−0.301522	+	0.226067i
$868$	−4.62980	−	9.87570i	−0.157146	−	0.335203i
$869$	−28.7068	+	5.06178i	−0.973812	+	0.171709i
$870$	25.9988	+	1.42588i	0.881442	+	0.0483420i
$871$	−63.4329	−	11.1849i	−2.14934	−	0.378987i
$872$			3.15004i			0.106674i
$873$	−4.50921	+	0.293305i	−0.152614	+	0.00992687i
$874$	7.89205	−	4.55648i	0.266953	−	0.154125i
$875$	−21.3421	+	1.91132i	−0.721496	+	0.0646143i
$876$	−4.62160	−	1.07881i	−0.156149	−	0.0364497i
$877$	−38.5648	+	32.3597i	−1.30224	+	1.09271i	−0.312489	+	0.949921i	$0.601163\pi$
$877$	−38.5648	+	32.3597i	−1.30224	+	1.09271i	−0.989753	+	0.142789i	$0.954393\pi$
$878$	3.83188	+	21.7317i	0.129320	+	0.733409i
$879$	−1.81259	−	1.69852i	−0.0611372	−	0.0572897i
$880$	−8.90486	+	10.6124i	−0.300183	+	0.357744i
$881$	4.98011	+	8.62581i	0.167784	+	0.290611i	0.937641	−	0.347606i	$-0.113005\pi$
$881$	4.98011	+	8.62581i	0.167784	+	0.290611i	−0.769856	+	0.638217i	$0.779672\pi$
$882$	−14.5764	−	15.1172i	−0.490813	−	0.509021i
$883$	−10.9714	+	19.0030i	−0.369216	+	0.639501i	−0.989443	−	0.144921i	$-0.953707\pi$
$883$	−10.9714	+	19.0030i	−0.369216	+	0.639501i	0.620227	+	0.784422i	$0.287041\pi$
$884$	6.88777	+	18.9240i	0.231661	+	0.636482i
$885$	14.0503	+	27.7416i	0.472295	+	0.932524i
$886$	−0.502521	+	0.421665i	−0.0168825	+	0.0141661i
$887$	−2.52798	−	14.3369i	−0.0848811	−	0.481385i	−0.997382	−	0.0723104i	$-0.976963\pi$
$887$	−2.52798	−	14.3369i	−0.0848811	−	0.481385i	0.912501	−	0.409074i	$-0.134148\pi$
$888$	−4.74437	+	11.1020i	−0.159211	+	0.372557i
$889$	−7.24439	−	10.3010i	−0.242969	−	0.345485i
$890$			9.05545i			0.303540i
$891$	−34.9087	−	32.0516i	−1.16948	−	1.07377i
$892$	−4.50868	+	2.60309i	−0.150962	+	0.0871578i
$893$	−4.21522	+	5.02350i	−0.141057	+	0.168105i
$894$	−9.71656	+	7.28501i	−0.324970	+	0.243647i
$895$	12.5774	+	14.9891i	0.420416	+	0.501032i
$896$	2.63615	+	0.225185i	0.0880676	+	0.00752292i
$897$	60.5481	+	3.32071i	2.02164	+	0.110875i
$898$	−16.9425	+	6.16657i	−0.565379	+	0.205781i
$899$	23.5559			0.785633
$900$	−3.98446	−	4.16635i	−0.132815	−	0.138878i
$901$		−	35.8472i		−	1.19424i
$902$	8.22605	−	46.6522i	0.273897	−	1.55335i
$903$	−9.67548	+	18.1803i	−0.321980	+	0.605004i
$904$	−18.2349	−	6.63697i	−0.606485	−	0.220742i
$905$	−32.5318	−	38.7699i	−1.08139	−	1.28876i
$906$	2.33174	+	7.69357i	0.0774668	+	0.255602i
$907$	21.5510	−	7.84392i	0.715589	−	0.260453i	0.0415371	−	0.999137i	$-0.486775\pi$
$907$	21.5510	−	7.84392i	0.715589	−	0.260453i	0.674052	+	0.738684i	$0.264552\pi$
$908$	16.3872			0.543828
$909$	−2.91472	−	44.8102i	−0.0966750	−	1.48626i
$910$	11.2323	+	41.5783i	0.372348	+	1.37831i
$911$	27.3407	−	32.5833i	0.905837	−	1.07953i	−0.0906583	−	0.995882i	$-0.528897\pi$
$911$	27.3407	−	32.5833i	0.905837	−	1.07953i	0.996495	−	0.0836521i	$-0.0266584\pi$
$912$	0.152762	−	2.78538i	0.00505845	−	0.0922331i
$913$	−3.99719	−	4.76367i	−0.132288	−	0.157654i
$914$	−4.38458	+	12.0465i	−0.145029	+	0.398464i
$915$	41.6274	−	5.00857i	1.37616	−	0.165578i
$916$	−5.91048	−	16.2389i	−0.195288	−	0.536548i
$917$	17.3864	+	4.62046i	0.574148	+	0.152581i
$918$	−15.9502	−	5.62247i	−0.526436	−	0.185569i
$919$	−26.6455	+	46.1514i	−0.878954	+	1.52239i	−0.0264644	+	0.999650i	$0.508425\pi$
$919$	−26.6455	+	46.1514i	−0.878954	+	1.52239i	−0.852490	+	0.522744i	$0.824908\pi$
$920$	11.4036	+	9.56875i	0.375965	+	0.315472i
$921$	15.2420	+	20.3294i	0.502241	+	0.669876i
$922$	8.25077	−	1.45483i	0.271725	−	0.0479124i
$923$	9.58630	+	54.3666i	0.315537	+	1.78950i
$924$	−7.46538	+	22.9466i	−0.245593	+	0.754886i
$925$	−10.2610	−	8.60999i	−0.337379	−	0.283095i
$926$	−11.2521	+	6.49642i	−0.369768	+	0.213486i
$927$	0.957053	−	8.69896i	0.0314338	−	0.285711i
$928$	−2.85700	+	4.94847i	−0.0937856	+	0.162441i
$929$	17.2684	+	14.4899i	0.566559	+	0.475399i	0.880502	−	0.474042i	$-0.157206\pi$
$929$	17.2684	+	14.4899i	0.566559	+	0.475399i	−0.313943	+	0.949442i	$0.601650\pi$
$930$	−13.7077	−	12.8451i	−0.449495	−	0.421207i
$931$	10.6097	+	3.81240i	0.347720	+	0.124947i
$932$	5.32112	−	14.6197i	0.174299	−	0.478883i
$933$	6.21513	−	1.88366i	0.203474	−	0.0616682i
$934$	4.67089	+	12.8332i	0.152836	+	0.419914i
$935$	−39.0488	−	22.5449i	−1.27703	−	0.737296i
$936$	10.9834	−	14.9640i	0.359005	−	0.489113i
$937$	20.6698	+	11.9337i	0.675251	+	0.389857i	0.798063	−	0.602573i	$-0.205858\pi$
$937$	20.6698	+	11.9337i	0.675251	+	0.389857i	−0.122812	+	0.992430i	$0.539191\pi$
$938$	−24.9858	−	11.5887i	−0.815816	−	0.378386i
$939$	−37.8476	−	24.7094i	−1.23511	−	0.806362i
$940$	−10.0662	−	3.66381i	−0.328324	−	0.119500i
$941$	24.5495	+	8.93530i	0.800292	+	0.291283i	0.709608	−	0.704597i	$-0.248872\pi$
$941$	24.5495	+	8.93530i	0.800292	+	0.291283i	0.0906847	+	0.995880i	$0.471094\pi$
$942$	−23.1444	+	17.3526i	−0.754087	+	0.565378i
$943$	−50.1303	−	8.83933i	−1.63247	−	0.287848i
$944$	−6.82417			−0.222108
$945$	−32.9645	−	14.8841i	−1.07233	−	0.484179i
$946$	23.6646			0.769403
$947$	25.6011	+	4.51416i	0.831923	+	0.146691i	0.573360	−	0.819304i	$-0.305640\pi$
$947$	25.6011	+	4.51416i	0.831923	+	0.146691i	0.258564	+	0.965994i	$0.416751\pi$
$948$	8.81690	+	3.76786i	0.286360	+	0.122374i
$949$	15.9311	+	5.79846i	0.517147	+	0.188226i
$950$	2.90827	+	1.05852i	0.0943567	+	0.0343430i
$951$	6.63449	−	3.36016i	0.215138	−	0.108961i
$952$	0.768117	+	8.57694i	0.0248948	+	0.277980i
$953$	29.2909	+	16.9111i	0.948825	+	0.547804i	0.892716	−	0.450620i	$-0.148797\pi$
$953$	29.2909	+	16.9111i	0.948825	+	0.547804i	0.0561092	+	0.998425i	$0.482130\pi$
$954$	−27.4820	+	18.3432i	−0.889762	+	0.593882i
$955$	−5.41619	−	3.12704i	−0.175264	−	0.101189i
$956$	4.88530	+	13.4223i	0.158002	+	0.434107i
$957$	−38.0274	−	35.6343i	−1.22925	−	1.15189i
$958$	6.79545	−	18.6704i	0.219551	−	0.603212i
$959$	−2.85633	−	6.09276i	−0.0922358	−	0.196746i
$960$	4.36097	−	1.32170i	0.140750	−	0.0426578i
$961$	10.7285	+	9.00229i	0.346081	+	0.290396i
$962$	21.5646	−	37.3510i	0.695270	−	1.20424i
$963$	−5.60060	−	1.63544i	−0.180477	−	0.0527012i
$964$	17.7654	−	10.2568i	0.572184	−	0.330350i
$965$	53.6035	+	44.9787i	1.72556	+	1.44792i
$966$	24.6573	+	8.02196i	0.793336	+	0.258102i
$967$	6.28098	+	35.6212i	0.201983	+	1.14550i	0.902118	+	0.431490i	$0.142012\pi$
$967$	6.28098	+	35.6212i	0.201983	+	1.14550i	−0.700135	+	0.714010i	$0.746877\pi$
$968$	16.4733	−	2.90469i	0.529472	−	0.0933603i
$969$	9.01433	−	1.08460i	0.289582	−	0.0348423i
$970$	3.03567	+	2.54723i	0.0974694	+	0.0817866i
$971$	−8.78451	+	15.2152i	−0.281908	+	0.488279i	−0.971855	−	0.235581i	$-0.924301\pi$
$971$	−8.78451	+	15.2152i	−0.281908	+	0.488279i	0.689946	+	0.723860i	$0.257634\pi$
$972$	3.85139	+	15.1052i	0.123533	+	0.484499i
$973$	10.3071	−	2.78444i	0.330429	−	0.0892651i
$974$	−11.0772	−	30.4345i	−0.354938	−	0.975184i
$975$	12.3538	+	16.4772i	0.395639	+	0.527694i
$976$	−3.14692	+	8.64610i	−0.100731	+	0.276755i
$977$	10.7048	+	12.7575i	0.342477	+	0.408149i	0.909600	−	0.415485i	$-0.136388\pi$
$977$	10.7048	+	12.7575i	0.342477	+	0.408149i	−0.567123	+	0.823633i	$0.691944\pi$
$978$	−31.1084	−	20.3096i	−0.994736	−	0.649430i
$979$	11.6501	−	13.8840i	0.372337	−	0.443734i
$980$	0.0755539	+	18.4162i	0.00241348	+	0.588283i
$981$	6.53150	+	6.82966i	0.208535	+	0.218054i
$982$	−18.6913			−0.596462
$983$	15.2702	−	5.55790i	0.487044	−	0.177270i	−0.0868136	−	0.996225i	$-0.527668\pi$
$983$	15.2702	−	5.55790i	0.487044	−	0.177270i	0.573858	+	0.818955i	$0.305446\pi$
$984$	−10.6546	+	11.3702i	−0.339657	+	0.362469i
$985$	−21.2017	−	25.2672i	−0.675543	−	0.805081i
$986$	−17.4761	−	6.36077i	−0.556552	−	0.202568i
$987$	−18.6478	+	0.644135i	−0.593565	+	0.0205030i
$988$	−1.73043	+	9.81378i	−0.0550524	+	0.312218i
$989$		−	25.4289i		−	0.808593i
$990$	2.69764	+	41.4729i	0.0857365	+	1.31809i
$991$	3.66318			0.116365			0.0581824	−	0.998306i	$-0.481469\pi$
$991$	3.66318			0.116365			0.0581824	+	0.998306i	$0.481469\pi$
$992$	3.87387	−	1.40997i	0.122996	−	0.0447667i
$993$	−12.9503	−	25.5699i	−0.410967	−	0.811435i
$994$	−2.00915	+	23.5203i	−0.0637263	+	0.746017i
$995$	−33.1833	−	39.5464i	−1.05198	−	1.25370i
$996$	0.244347	+	2.03082i	0.00774244	+	0.0643492i
$997$	−6.05196	+	7.21245i	−0.191668	+	0.228421i	−0.853317	−	0.521393i	$-0.825412\pi$
$997$	−6.05196	+	7.21245i	−0.191668	+	0.228421i	0.661649	+	0.749814i	$0.269857\pi$
$998$	−9.27088	+	5.35255i	−0.293465	+	0.169432i
$999$	12.7332	+	33.9077i	0.402860	+	1.07279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.ba.a.47.6	✓	144
7.3	odd	6		378.2.bf.a.101.14	yes	144
27.23	odd	18		378.2.bf.a.131.14	yes	144
189.185	even	18	inner	378.2.ba.a.185.6	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.6	✓	144	1.1	even	1	trivial
378.2.ba.a.185.6	yes	144	189.185	even	18	inner
378.2.bf.a.101.14	yes	144	7.3	odd	6
378.2.bf.a.131.14	yes	144	27.23	odd	18

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(0.206907 + 1.71965i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.47224 - 0.899821i) q^{5} +(0.0948504 - 1.72945i) q^{6} +(-1.11322 + 2.40015i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.91438 + 0.711614i) q^{9} +O(q^{10})\)	\(q+(-0.984808 - 0.173648i) q^{2} +(0.206907 + 1.71965i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.47224 - 0.899821i) q^{5} +(0.0948504 - 1.72945i) q^{6} +(-1.11322 + 2.40015i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-2.91438 + 0.711614i) q^{9} +(2.27843 + 1.31545i) q^{10} +(-1.80097 - 4.94813i) q^{11} +(-0.393726 + 1.68671i) q^{12} +(2.11622 - 5.81426i) q^{13} +(1.51309 - 2.17038i) q^{14} +(1.03585 - 4.43756i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.62738 + 2.81870i) q^{17} +(2.99367 - 0.194726i) q^{18} +(-1.39478 + 0.805278i) q^{19} +(-2.01539 - 1.69111i) q^{20} +(-4.35775 - 1.41774i) q^{21} +(0.914377 + 5.18569i) q^{22} +(5.57230 - 0.982547i) q^{23} +(0.680638 - 1.59271i) q^{24} +(1.47206 + 1.23521i) q^{25} +(-3.09370 + 5.35845i) q^{26} +(-1.82673 - 4.86447i) q^{27} +(-1.86699 + 1.87466i) q^{28} +(-1.95430 - 5.36940i) q^{29} +(-1.79069 + 4.19027i) q^{30} +(-1.40997 + 3.87387i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(8.13640 - 4.12084i) q^{33} +(2.09211 - 2.49328i) q^{34} +(4.91186 - 4.93205i) q^{35} +(-2.98201 - 0.328078i) q^{36} -6.97047 q^{37} +(1.51343 - 0.550843i) q^{38} +(10.4363 + 2.43614i) q^{39} +(1.69111 + 2.01539i) q^{40} +(-8.45380 - 3.07693i) q^{41} +(4.04536 + 2.15292i) q^{42} +(0.780396 - 4.42584i) q^{43} -5.26569i q^{44} +(7.84537 + 0.863142i) q^{45} -5.65826 q^{46} +(3.82615 - 1.39261i) q^{47} +(-0.946869 + 1.45032i) q^{48} +(-4.52147 - 5.34381i) q^{49} +(-1.23521 - 1.47206i) q^{50} +(-5.18388 - 2.21531i) q^{51} +(3.97719 - 4.73983i) q^{52} +(-9.53822 + 5.50689i) q^{53} +(0.954271 + 5.10778i) q^{54} +13.8535i q^{55} +(2.16416 - 1.52198i) q^{56} +(-1.67339 - 2.23192i) q^{57} +(0.992226 + 5.62719i) q^{58} +(-5.22762 + 4.38649i) q^{59} +(2.49112 - 3.81566i) q^{60} +(3.14692 + 8.64610i) q^{61} +(2.06125 - 3.57018i) q^{62} +(1.53637 - 7.78714i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-10.4636 + 12.4700i) q^{65} +(-8.72837 + 2.64536i) q^{66} +(-1.80769 - 10.2519i) q^{67} +(-2.49328 + 2.09211i) q^{68} +(2.84258 + 9.37910i) q^{69} +(-5.69368 + 4.00419i) q^{70} +(-7.72685 + 4.46110i) q^{71} +(2.87973 + 0.840914i) q^{72} +2.74001i q^{73} +(6.86458 + 1.21041i) q^{74} +(-1.81954 + 2.78701i) q^{75} +(-1.58609 + 0.279670i) q^{76} +(13.8811 + 1.18576i) q^{77} +(-9.85476 - 4.21138i) q^{78} +(0.961277 - 5.45167i) q^{79} +(-1.31545 - 2.27843i) q^{80} +(7.98721 - 4.14782i) q^{81} +(7.79106 + 4.49817i) q^{82} +(1.10973 - 0.403910i) q^{83} +(-3.61005 - 2.82268i) q^{84} +(6.55959 - 5.50415i) q^{85} +(-1.53708 + 4.22309i) q^{86} +(8.82912 - 4.47168i) q^{87} +(-0.914377 + 5.18569i) q^{88} +(1.72098 + 2.98082i) q^{89} +(-7.57630 - 2.21236i) q^{90} +(11.5993 + 11.5518i) q^{91} +(5.57230 + 0.982547i) q^{92} +(-6.95343 - 1.62313i) q^{93} +(-4.00985 + 0.707044i) q^{94} +(4.17284 - 0.735785i) q^{95} +(1.18433 - 1.26387i) q^{96} +(1.48336 + 0.261557i) q^{97} +(3.52484 + 6.04777i) q^{98} +(8.76986 + 13.1391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{6} + 24 q^{9}+O(q^{10}) \) 144 * q - 18 * q^6 + 24 * q^9	\( 144 q - 18 q^{6} + 24 q^{9} - 24 q^{11} + 6 q^{14} + 12 q^{15} - 30 q^{21} - 42 q^{23} - 6 q^{29} - 18 q^{30} + 6 q^{36} + 48 q^{39} - 48 q^{42} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 12 q^{50} - 36 q^{51} - 90 q^{53} + 6 q^{56} - 6 q^{57} + 18 q^{60} + 54 q^{61} - 24 q^{63} + 72 q^{64} + 78 q^{65} - 72 q^{66} - 54 q^{68} + 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} - 36 q^{74} - 6 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 36 q^{91} - 42 q^{92} + 96 q^{93} - 66 q^{95} - 108 q^{99}+O(q^{100}) \) 144 * q - 18 * q^6 + 24 * q^9 - 24 * q^11 + 6 * q^14 + 12 * q^15 - 30 * q^21 - 42 * q^23 - 6 * q^29 - 18 * q^30 + 6 * q^36 + 48 * q^39 - 48 * q^42 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 12 * q^50 - 36 * q^51 - 90 * q^53 + 6 * q^56 - 6 * q^57 + 18 * q^60 + 54 * q^61 - 24 * q^63 + 72 * q^64 + 78 * q^65 - 72 * q^66 - 54 * q^68 + 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 - 36 * q^74 - 6 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 36 * q^91 - 42 * q^92 + 96 * q^93 - 66 * q^95 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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