LMFDB - Embedded newform 370.2.m.c.159.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(159,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.159");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.m (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 37x^{14} + 559x^{12} + 4431x^{10} + 19684x^{8} + 48248x^{6} + 58656x^{4} + 25392x^{2} + 256 $ x^16 + 37x^14 + 559x^12 + 4431x^10 + 19684x^8 + 48248x^6 + 58656x^4 + 25392*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			159.7
Root			$2.88937i$ of defining polynomial
Character	$\chi$	$=$	370.159
Dual form			370.2.m.c.249.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(2.50227 + 1.44468i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.791839 + 2.09117i) q^{5} -2.88937i q^{6} +(0.668346 + 0.385870i) q^{7} +1.00000 q^{8} +(2.67422 + 4.63189i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(2.50227 + 1.44468i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.791839 + 2.09117i) q^{5} -2.88937i q^{6} +(0.668346 + 0.385870i) q^{7} +1.00000 q^{8} +(2.67422 + 4.63189i) q^{9} +(2.20693 - 0.359832i) q^{10} -4.03232 q^{11} +(-2.50227 + 1.44468i) q^{12} +(1.92005 - 3.32562i) q^{13} -0.771740i q^{14} +(-5.00247 + 4.08870i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.69038 + 6.39193i) q^{17} +(2.67422 - 4.63189i) q^{18} +(-2.31597 - 1.33713i) q^{19} +(-1.41509 - 1.73134i) q^{20} +(1.11492 + 1.93110i) q^{21} +(2.01616 + 3.49210i) q^{22} +4.28411 q^{23} +(2.50227 + 1.44468i) q^{24} +(-3.74598 - 3.31174i) q^{25} -3.84010 q^{26} +6.78552i q^{27} +(-0.668346 + 0.385870i) q^{28} +3.03430i q^{29} +(6.04216 + 2.28792i) q^{30} -0.197005i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-10.0899 - 5.82543i) q^{33} +(3.69038 - 6.39193i) q^{34} +(-1.33614 + 1.09208i) q^{35} -5.34844 q^{36} +(-4.87668 - 3.63566i) q^{37} +2.67425i q^{38} +(9.60895 - 5.54773i) q^{39} +(-0.791839 + 2.09117i) q^{40} +(2.56682 - 4.44586i) q^{41} +(1.11492 - 1.93110i) q^{42} +7.21634 q^{43} +(2.01616 - 3.49210i) q^{44} +(-11.8036 + 1.92454i) q^{45} +(-2.14205 - 3.71015i) q^{46} -1.03114i q^{47} -2.88937i q^{48} +(-3.20221 - 5.54639i) q^{49} +(-0.995062 + 4.89998i) q^{50} +21.3258i q^{51} +(1.92005 + 3.32562i) q^{52} +(9.81438 - 5.66633i) q^{53} +(5.87643 - 3.39276i) q^{54} +(3.19295 - 8.43227i) q^{55} +(0.668346 + 0.385870i) q^{56} +(-3.86345 - 6.69169i) q^{57} +(2.62778 - 1.51715i) q^{58} +(6.08484 - 3.51308i) q^{59} +(-1.03969 - 6.37662i) q^{60} +(5.52875 + 3.19203i) q^{61} +(-0.170612 + 0.0985027i) q^{62} +4.12761i q^{63} +1.00000 q^{64} +(5.43407 + 6.64851i) q^{65} +11.6509i q^{66} +(-5.06487 - 2.92421i) q^{67} -7.38077 q^{68} +(10.7200 + 6.18918i) q^{69} +(1.61384 + 0.611094i) q^{70} +(7.15012 - 12.3844i) q^{71} +(2.67422 + 4.63189i) q^{72} +3.22401i q^{73} +(-0.710230 + 6.04116i) q^{74} +(-4.58902 - 13.6986i) q^{75} +(2.31597 - 1.33713i) q^{76} +(-2.69499 - 1.55595i) q^{77} +(-9.60895 - 5.54773i) q^{78} +(-6.11172 - 3.52860i) q^{79} +(2.20693 - 0.359832i) q^{80} +(-1.78026 + 3.08350i) q^{81} -5.13364 q^{82} +(-12.9664 + 7.48616i) q^{83} -2.22984 q^{84} +(-16.2888 + 2.65583i) q^{85} +(-3.60817 - 6.24953i) q^{86} +(-4.38360 + 7.59262i) q^{87} -4.03232 q^{88} +(-6.24517 + 3.60565i) q^{89} +(7.56851 + 9.25996i) q^{90} +(2.56652 - 1.48178i) q^{91} +(-2.14205 + 3.71015i) q^{92} +(0.284611 - 0.492960i) q^{93} +(-0.892995 + 0.515571i) q^{94} +(4.63003 - 3.78430i) q^{95} +(-2.50227 + 1.44468i) q^{96} -15.2287 q^{97} +(-3.20221 + 5.54639i) q^{98} +(-10.7833 - 18.6773i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9}+O(q^{10}) $ 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9	$ 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} - 3 q^{12} + 6 q^{13} - 9 q^{15} - 8 q^{16} + 13 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} + 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 9 q^{30} - 8 q^{32} - 6 q^{33} + 12 q^{35} - 26 q^{36} - 16 q^{37} + 15 q^{39} + 6 q^{40} + 7 q^{41} - 6 q^{42} + 22 q^{43} + 3 q^{44} - 4 q^{45} - 11 q^{46} + 4 q^{49} - 6 q^{50} + 6 q^{52} - 3 q^{53} + 9 q^{54} - 25 q^{55} + 12 q^{56} - 18 q^{57} - 36 q^{58} + 15 q^{59} + 18 q^{60} + 12 q^{61} + 33 q^{62} + 16 q^{64} - 26 q^{65} - 24 q^{67} + 42 q^{69} - 18 q^{70} - 4 q^{71} + 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} + 24 q^{77} - 15 q^{78} - 6 q^{80} + 10 q^{81} - 14 q^{82} - 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} - 50 q^{87} - 6 q^{88} + 9 q^{89} + 5 q^{90} - 24 q^{91} - 11 q^{92} + 25 q^{93} - 27 q^{94} + 49 q^{95} - 3 q^{96} - 68 q^{97} + 4 q^{98} + 37 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 - 3 * q^12 + 6 * q^13 - 9 * q^15 - 8 * q^16 + 13 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 + 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 9 * q^30 - 8 * q^32 - 6 * q^33 + 12 * q^35 - 26 * q^36 - 16 * q^37 + 15 * q^39 + 6 * q^40 + 7 * q^41 - 6 * q^42 + 22 * q^43 + 3 * q^44 - 4 * q^45 - 11 * q^46 + 4 * q^49 - 6 * q^50 + 6 * q^52 - 3 * q^53 + 9 * q^54 - 25 * q^55 + 12 * q^56 - 18 * q^57 - 36 * q^58 + 15 * q^59 + 18 * q^60 + 12 * q^61 + 33 * q^62 + 16 * q^64 - 26 * q^65 - 24 * q^67 + 42 * q^69 - 18 * q^70 - 4 * q^71 + 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 + 24 * q^77 - 15 * q^78 - 6 * q^80 + 10 * q^81 - 14 * q^82 - 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 - 50 * q^87 - 6 * q^88 + 9 * q^89 + 5 * q^90 - 24 * q^91 - 11 * q^92 + 25 * q^93 - 27 * q^94 + 49 * q^95 - 3 * q^96 - 68 * q^97 + 4 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	2.50227	+	1.44468i	1.44468	+	0.834089i	0.998157	−	0.0606818i	$-0.0193275\pi$
$3$	2.50227	+	1.44468i	1.44468	+	0.834089i	0.446527	+	0.894770i	$0.352661\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.791839	+	2.09117i	−0.354121	+	0.935199i
$5$	−0.791839	+	2.09117i	−0.354121	+	0.935199i
$6$		−	2.88937i		−	1.17958i
$7$	0.668346	+	0.385870i	0.252611	+	0.145845i	0.620959	−	0.783843i	$-0.286743\pi$
$7$	0.668346	+	0.385870i	0.252611	+	0.145845i	−0.368348	+	0.929688i	$0.620077\pi$
$8$	1.00000			0.353553
$9$	2.67422	+	4.63189i	0.891407	+	1.54396i
$10$	2.20693	−	0.359832i	0.697891	−	0.113789i
$11$	−4.03232			−1.21579			−0.607896	−	0.794017i	$-0.707986\pi$
$11$	−4.03232			−1.21579			−0.607896	+	0.794017i	$0.707986\pi$
$12$	−2.50227	+	1.44468i	−0.722342	+	0.417044i
$13$	1.92005	−	3.32562i	0.532526	−	0.922362i	−0.466753	−	0.884388i	$-0.654576\pi$
$13$	1.92005	−	3.32562i	0.532526	−	0.922362i	0.999279	−	0.0379741i	$-0.0120905\pi$
$14$		−	0.771740i		−	0.206256i
$15$	−5.00247	+	4.08870i	−1.29163	+	1.05570i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.69038	+	6.39193i	0.895050	+	1.55027i	0.833743	+	0.552152i	$0.186193\pi$
$17$	3.69038	+	6.39193i	0.895050	+	1.55027i	0.0613065	+	0.998119i	$0.480473\pi$
$18$	2.67422	−	4.63189i	0.630320	−	1.09175i
$19$	−2.31597	−	1.33713i	−0.531320	−	0.306758i	0.210234	−	0.977651i	$-0.432577\pi$
$19$	−2.31597	−	1.33713i	−0.531320	−	0.306758i	−0.741554	+	0.670893i	$0.765911\pi$
$20$	−1.41509	−	1.73134i	−0.316423	−	0.387139i
$21$	1.11492	+	1.93110i	0.243295	+	0.421400i
$22$	2.01616	+	3.49210i	0.429847	+	0.744517i
$23$	4.28411			0.893298			0.446649	−	0.894709i	$-0.352617\pi$
$23$	4.28411			0.893298			0.446649	+	0.894709i	$0.352617\pi$
$24$	2.50227	+	1.44468i	0.510773	+	0.294895i
$25$	−3.74598	−	3.31174i	−0.749196	−	0.662348i
$26$	−3.84010			−0.753105
$27$			6.78552i			1.30587i
$28$	−0.668346	+	0.385870i	−0.126306	+	0.0729225i
$29$			3.03430i			0.563455i	0.959494	+	0.281727i	$0.0909074\pi$
$29$			3.03430i			0.563455i	−0.959494	+	0.281727i	$0.909093\pi$
$30$	6.04216	+	2.28792i	1.10314	+	0.417714i
$31$		−	0.197005i		−	0.0353832i	−0.999843	−	0.0176916i	$-0.994368\pi$
$31$		−	0.197005i		−	0.0353832i	0.999843	−	0.0176916i	$-0.00563171\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−10.0899	−	5.82543i	−1.75643	−	1.01408i
$34$	3.69038	−	6.39193i	0.632896	−	1.09621i
$35$	−1.33614	+	1.09208i	−0.225849	+	0.184595i
$36$	−5.34844			−0.891407
$37$	−4.87668	−	3.63566i	−0.801721	−	0.597698i
$37$	−4.87668	−	3.63566i	−0.801721	−	0.597698i
$38$			2.67425i			0.433821i
$39$	9.60895	−	5.54773i	1.53866	−	0.888348i
$40$	−0.791839	+	2.09117i	−0.125201	+	0.330643i
$41$	2.56682	−	4.44586i	0.400870	−	0.694327i	−0.592961	−	0.805231i	$-0.702041\pi$
$41$	2.56682	−	4.44586i	0.400870	−	0.694327i	0.993831	+	0.110904i	$0.0353746\pi$
$42$	1.11492	−	1.93110i	0.172036	−	0.297975i
$43$	7.21634			1.10048			0.550240	−	0.835006i	$-0.314536\pi$
$43$	7.21634			1.10048			0.550240	+	0.835006i	$0.314536\pi$
$44$	2.01616	−	3.49210i	0.303948	−	0.526453i
$45$	−11.8036	+	1.92454i	−1.75958	+	0.286893i
$46$	−2.14205	−	3.71015i	−0.315829	−	0.547031i
$47$		−	1.03114i		−	0.150408i	−0.997168	−	0.0752038i	$-0.976039\pi$
$47$		−	1.03114i		−	0.150408i	0.997168	−	0.0752038i	$-0.0239607\pi$
$48$		−	2.88937i		−	0.417044i
$49$	−3.20221	−	5.54639i	−0.457458	−	0.792341i
$50$	−0.995062	+	4.89998i	−0.140723	+	0.692963i
$51$			21.3258i			2.98620i
$52$	1.92005	+	3.32562i	0.266263	+	0.461181i
$53$	9.81438	−	5.66633i	1.34811	−	0.778331i	0.360127	−	0.932903i	$-0.382733\pi$
$53$	9.81438	−	5.66633i	1.34811	−	0.778331i	0.987981	+	0.154573i	$0.0494000\pi$
$54$	5.87643	−	3.39276i	0.799681	−	0.461696i
$55$	3.19295	−	8.43227i	0.430538	−	1.13701i
$56$	0.668346	+	0.385870i	0.0893115	+	0.0515640i
$57$	−3.86345	−	6.69169i	−0.511726	−	0.886336i
$58$	2.62778	−	1.51715i	0.345044	−	0.199211i
$59$	6.08484	−	3.51308i	0.792178	−	0.457364i	−0.0485504	−	0.998821i	$-0.515460\pi$
$59$	6.08484	−	3.51308i	0.792178	−	0.457364i	0.840729	+	0.541456i	$0.182127\pi$
$60$	−1.03969	−	6.37662i	−0.134223	−	0.823218i
$61$	5.52875	+	3.19203i	0.707884	+	0.408697i	0.810277	−	0.586047i	$-0.199317\pi$
$61$	5.52875	+	3.19203i	0.707884	+	0.408697i	−0.102393	+	0.994744i	$0.532650\pi$
$62$	−0.170612	+	0.0985027i	−0.0216677	+	0.0125099i
$63$			4.12761i			0.520030i
$64$	1.00000			0.125000
$65$	5.43407	+	6.64851i	0.674014	+	0.824646i
$66$			11.6509i			1.43412i
$67$	−5.06487	−	2.92421i	−0.618773	−	0.357249i	0.157618	−	0.987500i	$-0.449618\pi$
$67$	−5.06487	−	2.92421i	−0.618773	−	0.357249i	−0.776391	+	0.630251i	$0.782952\pi$
$68$	−7.38077			−0.895050
$69$	10.7200	+	6.18918i	1.29053	+	0.745090i
$70$	1.61384	+	0.611094i	0.192891	+	0.0730397i
$71$	7.15012	−	12.3844i	0.848563	−	1.46975i	−0.0339275	−	0.999424i	$-0.510802\pi$
$71$	7.15012	−	12.3844i	0.848563	−	1.46975i	0.882491	−	0.470330i	$-0.155865\pi$
$72$	2.67422	+	4.63189i	0.315160	+	0.545873i
$73$			3.22401i			0.377342i	0.982040	+	0.188671i	$0.0604180\pi$
$73$			3.22401i			0.377342i	−0.982040	+	0.188671i	$0.939582\pi$
$74$	−0.710230	+	6.04116i	−0.0825625	+	0.702270i
$75$	−4.58902	−	13.6986i	−0.529894	−	1.58178i
$76$	2.31597	−	1.33713i	0.265660	−	0.153379i
$77$	−2.69499	−	1.55595i	−0.307122	−	0.177317i
$78$	−9.60895	−	5.54773i	−1.08800	−	0.628157i
$79$	−6.11172	−	3.52860i	−0.687622	−	0.396999i	0.115098	−	0.993354i	$-0.463282\pi$
$79$	−6.11172	−	3.52860i	−0.687622	−	0.396999i	−0.802721	+	0.596355i	$0.796615\pi$
$80$	2.20693	−	0.359832i	0.246742	−	0.0402304i
$81$	−1.78026	+	3.08350i	−0.197807	+	0.342611i
$82$	−5.13364			−0.566916
$83$	−12.9664	+	7.48616i	−1.42325	+	0.821713i	−0.996575	−	0.0826926i	$-0.973648\pi$
$83$	−12.9664	+	7.48616i	−1.42325	+	0.821713i	−0.426674	+	0.904406i	$0.640315\pi$
$84$	−2.22984			−0.243295
$85$	−16.2888	+	2.65583i	−1.76677	+	0.288066i
$86$	−3.60817	−	6.24953i	−0.389079	−	0.673904i
$87$	−4.38360	+	7.59262i	−0.469971	+	0.814014i
$88$	−4.03232			−0.429847
$89$	−6.24517	+	3.60565i	−0.661986	+	0.382198i	−0.793033	−	0.609178i	$-0.791499\pi$
$89$	−6.24517	+	3.60565i	−0.661986	+	0.382198i	0.131047	+	0.991376i	$0.458166\pi$
$90$	7.56851	+	9.25996i	0.797791	+	0.976086i
$91$	2.56652	−	1.48178i	0.269044	−	0.155333i
$92$	−2.14205	+	3.71015i	−0.223325	+	0.386809i
$93$	0.284611	−	0.492960i	0.0295127	−	0.0511176i
$94$	−0.892995	+	0.515571i	−0.0921054	+	0.0531771i
$95$	4.63003	−	3.78430i	0.475031	−	0.388261i
$96$	−2.50227	+	1.44468i	−0.255386	+	0.147447i
$97$	−15.2287			−1.54624			−0.773122	−	0.634258i	$-0.781306\pi$
$97$	−15.2287			−1.54624			−0.773122	+	0.634258i	$0.781306\pi$
$98$	−3.20221	+	5.54639i	−0.323472	+	0.560270i
$99$	−10.7833	−	18.6773i	−1.08377	−	1.87714i
$100$	4.74104	−	1.58824i	0.474104	−	0.158824i
$101$	−2.16416			−0.215342			−0.107671	−	0.994187i	$-0.534339\pi$
$101$	−2.16416			−0.215342			−0.107671	+	0.994187i	$0.534339\pi$
$102$	18.4686	−	10.6629i	1.82867	−	1.05578i
$103$	2.94790			0.290465			0.145233	−	0.989398i	$-0.453607\pi$
$103$	2.94790			0.290465			0.145233	+	0.989398i	$0.453607\pi$
$104$	1.92005	−	3.32562i	0.188276	−	0.326104i
$105$	−4.92109	+	0.802367i	−0.480249	+	0.0783030i
$106$	−9.81438	−	5.66633i	−0.953257	−	0.550363i
$107$	−13.0801	−	7.55178i	−1.26450	−	0.730058i	−0.290556	−	0.956858i	$-0.593840\pi$
$107$	−13.0801	−	7.55178i	−1.26450	−	0.730058i	−0.973941	+	0.226800i	$0.927174\pi$
$108$	−5.87643	−	3.39276i	−0.565460	−	0.326468i
$109$	5.54882	−	3.20361i	0.531480	−	0.306850i	−0.210139	−	0.977672i	$-0.567392\pi$
$109$	5.54882	−	3.20361i	0.531480	−	0.306850i	0.741619	+	0.670821i	$0.234058\pi$
$110$	−8.89904	+	1.45096i	−0.848490	+	0.138343i
$111$	−6.95038	−	16.1426i	−0.659701	−	1.53219i
$112$		−	0.771740i		−	0.0729225i
$113$	6.03232	+	10.4483i	0.567473	+	0.982893i	0.996815	+	0.0797504i	$0.0254123\pi$
$113$	6.03232	+	10.4483i	0.567473	+	0.982893i	−0.429342	+	0.903142i	$0.641254\pi$
$114$	−3.86345	+	6.69169i	−0.361845	+	0.626734i
$115$	−3.39233	+	8.95880i	−0.316336	+	0.835412i
$116$	−2.62778	−	1.51715i	−0.243983	−	0.140864i
$117$	20.5386			1.89879
$118$	−6.08484	−	3.51308i	−0.560155	−	0.323406i
$119$			5.69603i			0.522154i
$120$	−5.00247	+	4.08870i	−0.456661	+	0.373246i
$121$	5.25964			0.478149
$122$		−	6.38405i		−	0.577985i
$123$	12.8457	−	7.41649i	1.15826	−	0.668722i
$124$	0.170612	+	0.0985027i	0.0153214	+	0.00884581i
$125$	9.89163	−	5.21111i	0.884734	−	0.466096i
$126$	3.57461	−	2.06380i	0.318452	−	0.183858i
$127$	15.9727	−	9.22183i	1.41735	−	0.818305i	0.421281	−	0.906930i	$-0.361580\pi$
$127$	15.9727	−	9.22183i	1.41735	−	0.818305i	0.996065	+	0.0886247i	$0.0282472\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	18.0572	+	10.4253i	1.58985	+	0.917899i
$130$	3.04074	−	8.03030i	0.266691	−	0.704304i
$131$	−12.7079	+	7.33693i	−1.11030	+	0.641031i	−0.938906	−	0.344172i	$-0.888160\pi$
$131$	−12.7079	+	7.33693i	−1.11030	+	0.641031i	−0.171391	+	0.985203i	$0.554826\pi$
$132$	10.0899	−	5.82543i	0.878217	−	0.507039i
$133$	−1.03191	−	1.78733i	−0.0894782	−	0.154981i
$134$			5.84841i			0.505226i
$135$	−14.1897	−	5.37304i	−1.22125	−	0.462438i
$136$	3.69038	+	6.39193i	0.316448	+	0.548104i
$137$			21.6785i			1.85212i	0.377381	+	0.926058i	$0.376825\pi$
$137$			21.6785i			1.85212i	−0.377381	+	0.926058i	$0.623175\pi$
$138$		−	12.3784i		−	1.05372i
$139$	−2.89685	−	5.01749i	−0.245707	−	0.425578i	0.716623	−	0.697461i	$-0.245687\pi$
$139$	−2.89685	−	5.01749i	−0.245707	−	0.425578i	−0.962330	+	0.271883i	$0.912354\pi$
$140$	−0.277696	−	1.70317i	−0.0234696	−	0.143944i
$141$	1.48967	−	2.58019i	0.125453	−	0.217291i
$142$	−14.3002			−1.20005
$143$	−7.74226	+	13.4100i	−0.647441	+	1.12140i
$144$	2.67422	−	4.63189i	0.222852	−	0.385991i
$145$	−6.34523	−	2.40268i	−0.526943	−	0.199531i
$146$	2.79208	−	1.61201i	0.231074	−	0.133411i
$147$		−	18.5047i		−	1.52624i
$148$	5.58691	−	2.40550i	0.459241	−	0.197731i
$149$	−3.77909			−0.309595			−0.154797	−	0.987946i	$-0.549472\pi$
$149$	−3.77909			−0.309595			−0.154797	+	0.987946i	$0.549472\pi$
$150$	−9.56884	+	10.8235i	−0.781292	+	0.883736i
$151$	−2.51580	+	4.35750i	−0.204733	+	0.354608i	−0.950048	−	0.312105i	$-0.898966\pi$
$151$	−2.51580	+	4.35750i	−0.204733	+	0.354608i	0.745315	+	0.666713i	$0.232299\pi$
$152$	−2.31597	−	1.33713i	−0.187850	−	0.108455i
$153$	−19.7378	+	34.1869i	−1.59571	+	2.76385i
$154$			3.11190i			0.250764i
$155$	0.411972	+	0.155997i	0.0330904	+	0.0125300i
$156$			11.0955i			0.888348i
$157$	17.5159	−	10.1128i	1.39792	−	0.807091i	0.403748	−	0.914870i	$-0.367707\pi$
$157$	17.5159	−	10.1128i	1.39792	−	0.807091i	0.994175	+	0.107779i	$0.0343739\pi$
$158$			7.05721i			0.561441i
$159$	32.7442			2.59679
$160$	−1.41509	−	1.73134i	−0.111872	−	0.136874i
$161$	2.86327	+	1.65311i	0.225657	+	0.130283i
$162$	3.56052			0.279741
$163$	−0.833476	−	1.44362i	−0.0652829	−	0.113073i	0.831537	−	0.555470i	$-0.187462\pi$
$163$	−0.833476	−	1.44362i	−0.0652829	−	0.113073i	−0.896819	+	0.442397i	$0.854128\pi$
$164$	2.56682	+	4.44586i	0.200435	+	0.347164i
$165$	20.1716	−	16.4870i	1.57036	−	1.28351i
$166$	12.9664	+	7.48616i	1.00639	+	0.581039i
$167$	−7.47097	+	12.9401i	−0.578121	+	1.00133i	0.417574	+	0.908643i	$0.362880\pi$
$167$	−7.47097	+	12.9401i	−0.578121	+	1.00133i	−0.995695	+	0.0926917i	$0.970453\pi$
$168$	1.11492	+	1.93110i	0.0860179	+	0.148987i
$169$	−0.873181	−	1.51239i	−0.0671677	−	0.116338i
$170$	10.4444	+	12.7786i	0.801051	+	0.980074i
$171$		−	14.3031i		−	1.09378i
$172$	−3.60817	+	6.24953i	−0.275120	+	0.476522i
$173$	−20.3104	+	11.7262i	−1.54417	+	0.891526i	−0.545599	+	0.838046i	$0.683698\pi$
$173$	−20.3104	+	11.7262i	−1.54417	+	0.891526i	−0.998569	+	0.0534796i	$0.982969\pi$
$174$	8.76720			0.664640
$175$	−1.22571	−	3.65885i	−0.0926550	−	0.276583i
$176$	2.01616	+	3.49210i	0.151974	+	0.263227i
$177$	20.3012			1.52593
$178$	6.24517	+	3.60565i	0.468095	+	0.270255i
$179$		−	12.6892i		−	0.948433i	−0.880408	−	0.474216i	$-0.842731\pi$
$179$		−	12.6892i		−	0.948433i	0.880408	−	0.474216i	$-0.157269\pi$
$180$	4.23511	−	11.1845i	0.315666	−	0.833644i
$181$	−9.15095	+	15.8499i	−0.680185	+	1.17811i	0.294740	+	0.955578i	$0.404767\pi$
$181$	−9.15095	+	15.8499i	−0.680185	+	1.17811i	−0.974924	+	0.222537i	$0.928566\pi$
$182$	−2.56652	−	1.48178i	−0.190243	−	0.109837i
$183$	9.22294	+	15.9746i	0.681779	+	1.18088i
$184$	4.28411			0.315829
$185$	11.4643	−	7.31911i	0.842874	−	0.538112i
$186$	−0.569221			−0.0417373
$187$	−14.8808	−	25.7743i	−1.08819	−	1.88481i
$188$	0.892995	+	0.515571i	0.0651284	+	0.0376019i
$189$	−2.61833	+	4.53507i	−0.190455	+	0.329878i
$190$	−5.59231	−	2.11758i	−0.405709	−	0.153625i
$191$			5.40053i			0.390769i	0.980727	+	0.195384i	$0.0625955\pi$
$191$			5.40053i			0.390769i	−0.980727	+	0.195384i	$0.937405\pi$
$192$	2.50227	+	1.44468i	0.180585	+	0.104261i
$193$	21.2813			1.53186			0.765931	−	0.642923i	$-0.222279\pi$
$193$	21.2813			1.53186			0.765931	+	0.642923i	$0.222279\pi$
$194$	7.61437	+	13.1885i	0.546680	+	0.946877i
$195$	3.99250	+	24.4869i	0.285909	+	1.75354i
$196$	6.40442			0.457458
$197$	11.5610	−	6.67476i	0.823688	−	0.475557i	−0.0279984	−	0.999608i	$-0.508913\pi$
$197$	11.5610	−	6.67476i	0.823688	−	0.475557i	0.851687	+	0.524051i	$0.175580\pi$
$198$	−10.7833	+	18.6773i	−0.766338	+	1.32734i
$199$		−	0.220135i		−	0.0156049i	−0.999970	−	0.00780247i	$-0.997516\pi$
$199$		−	0.220135i		−	0.0156049i	0.999970	−	0.00780247i	$-0.00248363\pi$
$200$	−3.74598	−	3.31174i	−0.264881	−	0.234175i
$201$	−8.44911	−	14.6343i	−0.595954	−	1.03222i
$202$	1.08208	+	1.87422i	0.0761348	+	0.131869i
$203$	−1.17084	+	2.02796i	−0.0821771	+	0.142335i
$204$	−18.4686	−	10.6629i	−1.29306	−	0.746551i
$205$	7.26454	+	8.88807i	0.507378	+	0.620769i
$206$	−1.47395	−	2.55296i	−0.102695	−	0.177873i
$207$	11.4567	+	19.8435i	0.796293	+	1.37922i
$208$	−3.84010			−0.266263
$209$	9.33874	+	5.39172i	0.645974	+	0.372953i
$210$	3.15541	+	3.86061i	0.217744	+	0.266407i
$211$	−15.1410			−1.04235			−0.521175	−	0.853450i	$-0.674506\pi$
$211$	−15.1410			−1.04235			−0.521175	+	0.853450i	$0.674506\pi$
$212$			11.3327i			0.778331i
$213$	35.7830	−	20.6593i	2.45181	−	1.41555i
$214$			15.1036i			1.03246i
$215$	−5.71418	+	15.0906i	−0.389704	+	1.02917i
$216$			6.78552i			0.461696i
$217$	0.0760185	−	0.131668i	0.00516047	−	0.00893819i
$218$	−5.54882	−	3.20361i	−0.375813	−	0.216976i
$219$	−4.65768	+	8.06733i	−0.314737	+	0.545140i
$220$	5.70609	+	6.98132i	0.384704	+	0.470680i
$221$	28.3429			1.90655
$222$	−10.5047	+	14.0905i	−0.705032	+	0.945694i
$223$		−	13.4593i		−	0.901303i	−0.892700	−	0.450651i	$-0.851192\pi$
$223$		−	13.4593i		−	0.901303i	0.892700	−	0.450651i	$-0.148808\pi$
$224$	−0.668346	+	0.385870i	−0.0446558	+	0.0257820i
$225$	5.32203	−	26.2073i	0.354802	−	1.74715i
$226$	6.03232	−	10.4483i	0.401264	−	0.695010i
$227$	1.02793	−	1.78043i	0.0682261	−	0.118171i	−0.829894	−	0.557920i	$-0.811599\pi$
$227$	1.02793	−	1.78043i	0.0682261	−	0.118171i	0.898121	+	0.439749i	$0.144933\pi$
$228$	7.72689			0.511726
$229$	1.14384	−	1.98119i	0.0755872	−	0.130921i	−0.825754	−	0.564030i	$-0.809250\pi$
$229$	1.14384	−	1.98119i	0.0755872	−	0.130921i	0.901341	+	0.433109i	$0.142584\pi$
$230$	9.45471	−	1.54156i	0.623425	−	0.101647i
$231$	−4.49572	−	7.78681i	−0.295796	−	0.512335i
$232$			3.03430i			0.199211i
$233$		−	4.43799i		−	0.290743i	−0.989377	−	0.145371i	$-0.953562\pi$
$233$		−	4.43799i		−	0.290743i	0.989377	−	0.145371i	$-0.0464377\pi$
$234$	−10.2693	−	17.7869i	−0.671324	−	1.16277i
$235$	2.15629	+	0.816499i	0.140661	+	0.0532625i
$236$			7.02617i			0.457364i
$237$	−10.1954	−	17.6590i	−0.662265	−	1.14708i
$238$	4.93291	−	2.84802i	0.319753	−	0.184609i
$239$	7.26013	−	4.19164i	0.469619	−	0.271135i	−0.246461	−	0.969153i	$-0.579268\pi$
$239$	7.26013	−	4.19164i	0.469619	−	0.271135i	0.716080	+	0.698018i	$0.245935\pi$
$240$	6.04216	+	2.28792i	0.390020	+	0.147684i
$241$	10.4145	+	6.01284i	0.670860	+	0.387321i	0.796402	−	0.604767i	$-0.206734\pi$
$241$	10.4145	+	6.01284i	0.670860	+	0.387321i	−0.125543	+	0.992088i	$0.540067\pi$
$242$	−2.62982	−	4.55498i	−0.169051	−	0.292805i
$243$	8.71992	−	5.03445i	0.559383	−	0.322960i
$244$	−5.52875	+	3.19203i	−0.353942	+	0.204349i
$245$	14.1341	−	2.30451i	0.902993	−	0.147230i
$246$	−12.8457	−	7.41649i	−0.819014	−	0.472858i
$247$	−8.89355	+	5.13469i	−0.565883	+	0.326713i
$248$		−	0.197005i		−	0.0125099i
$249$	−43.2605			−2.74153
$250$	−9.45877	−	5.96084i	−0.598225	−	0.376997i
$251$		−	17.4114i		−	1.09900i	−0.835495	−	0.549499i	$-0.814819\pi$
$251$		−	17.4114i		−	1.09900i	0.835495	−	0.549499i	$-0.185181\pi$
$252$	−3.57461	−	2.06380i	−0.225179	−	0.130007i
$253$	−17.2749			−1.08606
$254$	−15.9727	−	9.22183i	−1.00222	−	0.578629i
$255$	−44.5958	−	16.8866i	−2.79270	−	1.05748i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.631635	+	1.09402i	0.0394003	+	0.0682433i	0.885053	−	0.465490i	$-0.154122\pi$
$257$	0.631635	+	1.09402i	0.0394003	+	0.0682433i	−0.845653	+	0.533733i	$0.820789\pi$
$258$		−	20.8506i		−	1.29810i
$259$	−1.85642	−	4.31164i	−0.115352	−	0.267912i
$260$	−8.47481	+	1.38179i	−0.525586	+	0.0856949i
$261$	−14.0545	+	8.11438i	−0.869953	+	0.502268i
$262$	12.7079	+	7.33693i	0.785099	+	0.453277i
$263$	−6.52258	−	3.76581i	−0.402199	−	0.232210i	0.285233	−	0.958458i	$-0.407929\pi$
$263$	−6.52258	−	3.76581i	−0.402199	−	0.232210i	−0.687432	+	0.726248i	$0.741262\pi$
$264$	−10.0899	−	5.82543i	−0.620993	−	0.358531i
$265$	4.07785	+	25.0104i	0.250500	+	1.53637i
$266$	−1.03191	+	1.78733i	−0.0632706	+	0.109588i
$267$	−20.8361			−1.27515
$268$	5.06487	−	2.92421i	0.309386	−	0.178624i
$269$	−25.5664			−1.55881			−0.779407	−	0.626518i	$-0.784479\pi$
$269$	−25.5664			−1.55881			−0.779407	+	0.626518i	$0.784479\pi$
$270$	2.44164	+	14.9751i	0.148594	+	0.911358i
$271$	7.65037	+	13.2508i	0.464727	+	0.804930i	0.999189	−	0.0402618i	$-0.0128192\pi$
$271$	7.65037	+	13.2508i	0.464727	+	0.804930i	−0.534462	+	0.845192i	$0.679486\pi$
$272$	3.69038	−	6.39193i	0.223762	−	0.387568i
$273$	8.56280			0.518244
$274$	18.7741	−	10.8392i	1.13418	−	0.654822i
$275$	15.1050	+	13.3540i	0.910866	+	0.805277i
$276$	−10.7200	+	6.18918i	−0.645267	+	0.372545i
$277$	2.59810	−	4.50004i	0.156105	−	0.270381i	−0.777356	−	0.629061i	$-0.783440\pi$
$277$	2.59810	−	4.50004i	0.156105	−	0.270381i	0.933461	+	0.358680i	$0.116773\pi$
$278$	−2.89685	+	5.01749i	−0.173741	+	0.300929i
$279$	0.912507	−	0.526836i	0.0546304	−	0.0315409i
$280$	−1.33614	+	1.09208i	−0.0798498	+	0.0652642i
$281$	−15.8995	+	9.17961i	−0.948487	+	0.547609i	−0.892611	−	0.450828i	$-0.851129\pi$
$281$	−15.8995	+	9.17961i	−0.948487	+	0.547609i	−0.0558767	+	0.998438i	$0.517795\pi$
$282$	−2.97935			−0.177418
$283$	1.21268	−	2.10042i	0.0720861	−	0.124857i	−0.827729	−	0.561128i	$-0.810368\pi$
$283$	1.21268	−	2.10042i	0.0720861	−	0.124857i	0.899815	+	0.436271i	$0.143701\pi$
$284$	7.15012	+	12.3844i	0.424282	+	0.734877i
$285$	17.0527	−	2.78038i	1.01011	−	0.164696i
$286$	15.4845			0.915619
$287$	3.43105	−	1.98092i	0.202528	−	0.116930i
$288$	−5.34844			−0.315160
$289$	−18.7379	+	32.4549i	−1.10223	+	1.90911i
$290$	1.09184	+	6.69647i	0.0641148	+	0.393230i
$291$	−38.1063	−	22.0007i	−2.23383	−	1.28970i
$292$	−2.79208	−	1.61201i	−0.163394	−	0.0943355i
$293$	6.43891	+	3.71751i	0.376165	+	0.217179i	0.676149	−	0.736765i	$-0.263648\pi$
$293$	6.43891	+	3.71751i	0.376165	+	0.217179i	−0.299983	+	0.953944i	$0.596981\pi$
$294$	−16.0256	+	9.25236i	−0.934629	+	0.539608i
$295$	2.52824	+	15.5062i	0.147200	+	0.902807i
$296$	−4.87668	−	3.63566i	−0.283451	−	0.211318i
$297$		−	27.3614i		−	1.58767i
$298$	1.88954	+	3.27279i	0.109458	+	0.189587i
$299$	8.22570	−	14.2473i	0.475704	−	0.823944i
$300$	14.1579	+	2.87510i	0.817404	+	0.165994i
$301$	4.82301	+	2.78457i	0.277994	+	0.160500i
$302$	5.03161			0.289536
$303$	−5.41530	−	3.12653i	−0.311101	−	0.179614i
$304$			2.67425i			0.153379i
$305$	−11.0530	+	9.03399i	−0.632890	+	0.517285i
$306$	39.4756			2.25667
$307$			30.5748i			1.74500i	0.488618	+	0.872498i	$0.337501\pi$
$307$			30.5748i			1.74500i	−0.488618	+	0.872498i	$0.662499\pi$
$308$	2.69499	−	1.55595i	0.153561	−	0.0886586i
$309$	7.37643	+	4.25878i	0.419630	+	0.242274i
$310$	−0.0708888	−	0.434776i	−0.00402621	−	0.0246936i
$311$	−10.1909	+	5.88374i	−0.577875	+	0.333636i	−0.760289	−	0.649586i	$-0.774942\pi$
$311$	−10.1909	+	5.88374i	−0.577875	+	0.333636i	0.182413	+	0.983222i	$0.441609\pi$
$312$	9.60895	−	5.54773i	0.544000	−	0.314078i
$313$	11.7805	+	20.4044i	0.665872	+	1.15332i	0.979048	+	0.203629i	$0.0652737\pi$
$313$	11.7805	+	20.4044i	0.665872	+	1.15332i	−0.313176	+	0.949695i	$0.601393\pi$
$314$	−17.5159	−	10.1128i	−0.988481	−	0.570700i
$315$	−8.63152	−	3.26840i	−0.486331	−	0.184154i
$316$	6.11172	−	3.52860i	0.343811	−	0.198499i
$317$	−16.8102	+	9.70539i	−0.944157	+	0.545109i	−0.891261	−	0.453491i	$-0.850178\pi$
$317$	−16.8102	+	9.70539i	−0.944157	+	0.545109i	−0.0528957	+	0.998600i	$0.516845\pi$
$318$	−16.3721	−	28.3573i	−0.918103	−	1.59020i
$319$		−	12.2353i		−	0.685043i
$320$	−0.791839	+	2.09117i	−0.0442652	+	0.116900i
$321$	−21.8199	−	37.7931i	−1.21787	−	2.10941i
$322$		−	3.30622i		−	0.184248i
$323$		−	19.7380i		−	1.09825i
$324$	−1.78026	−	3.08350i	−0.0989034	−	0.171306i
$325$	−18.2061	+	6.09901i	−1.00989	+	0.338312i
$326$	−0.833476	+	1.44362i	−0.0461620	+	0.0799549i
$327$	18.5128			1.02376
$328$	2.56682	−	4.44586i	0.141729	−	0.245482i
$329$	0.397887	−	0.689160i	0.0219362	−	0.0379946i
$330$	−24.3639	−	9.22562i	−1.34119	−	0.507853i
$331$	20.1775	−	11.6495i	1.10906	−	0.640314i	0.170472	−	0.985363i	$-0.445471\pi$
$331$	20.1775	−	11.6495i	1.10906	−	0.640314i	0.938585	+	0.345048i	$0.112138\pi$
$332$		−	14.9723i		−	0.821713i
$333$	3.79862	−	32.3108i	0.208163	−	1.77062i
$334$	14.9419			0.817586
$335$	10.1256	−	8.27601i	0.553220	−	0.452167i
$336$	1.11492	−	1.93110i	0.0608239	−	0.105350i
$337$	−11.6219	−	6.70991i	−0.633085	−	0.365512i	0.148861	−	0.988858i	$-0.452439\pi$
$337$	−11.6219	−	6.70991i	−0.633085	−	0.365512i	−0.781946	+	0.623346i	$0.785773\pi$
$338$	−0.873181	+	1.51239i	−0.0474948	+	0.0822634i
$339$			34.8592i			1.89329i
$340$	5.84438	−	15.4344i	0.316956	−	0.837050i
$341$			0.794390i			0.0430186i
$342$	−12.3868	+	7.15154i	−0.669803	+	0.386711i
$343$		−	10.3447i		−	0.558562i
$344$	7.21634			0.389079
$345$	−21.4311	+	17.5164i	−1.15381	+	0.943054i
$346$	20.3104	+	11.7262i	1.09189	+	0.630404i
$347$	−32.3638			−1.73738			−0.868691	−	0.495355i	$-0.835038\pi$
$347$	−32.3638			−1.73738			−0.868691	+	0.495355i	$0.835038\pi$
$348$	−4.38360	−	7.59262i	−0.234986	−	0.407007i
$349$	−0.0141987	−	0.0245929i	−0.000760039	−	0.00131643i	0.865645	−	0.500658i	$-0.166909\pi$
$349$	−0.0141987	−	0.0245929i	−0.000760039	−	0.00131643i	−0.866405	+	0.499342i	$0.833575\pi$
$350$	−2.55580	+	2.89092i	−0.136613	+	0.154526i
$351$	22.5661	+	13.0285i	1.20449	+	0.695412i
$352$	2.01616	−	3.49210i	0.107462	−	0.186129i
$353$	0.762087	+	1.31997i	0.0405618	+	0.0702551i	0.885594	−	0.464461i	$-0.153752\pi$
$353$	0.762087	+	1.31997i	0.0405618	+	0.0702551i	−0.845032	+	0.534716i	$0.820419\pi$
$354$	−10.1506	−	17.5813i	−0.539498	−	0.934437i
$355$	20.2361	+	24.7585i	1.07402	+	1.31405i
$356$		−	7.21130i		−	0.382198i
$357$	−8.22896	+	14.2530i	−0.435523	+	0.754348i
$358$	−10.9891	+	6.34458i	−0.580794	+	0.335322i
$359$	14.3290			0.756254			0.378127	−	0.925754i	$-0.376568\pi$
$359$	14.3290			0.756254			0.378127	+	0.925754i	$0.376568\pi$
$360$	−11.8036	+	1.92454i	−0.622105	+	0.101432i
$361$	−5.92419	−	10.2610i	−0.311799	−	0.540053i
$362$	18.3019			0.961926
$363$	13.1610	+	7.59851i	0.690774	+	0.398819i
$364$			2.96356i			0.155333i
$365$	−6.74195	−	2.55290i	−0.352890	−	0.133625i
$366$	9.22294	−	15.9746i	0.482091	−	0.835006i
$367$	−32.0645	−	18.5125i	−1.67376	−	0.966343i	−0.965506	−	0.260380i	$-0.916152\pi$
$367$	−32.0645	−	18.5125i	−1.67376	−	0.966343i	−0.708249	−	0.705963i	$-0.750515\pi$
$368$	−2.14205	−	3.71015i	−0.111662	−	0.193405i
$369$	27.4570			1.42935
$370$	−12.0707	−	6.26884i	−0.627526	−	0.325901i
$371$	8.74587			0.454063
$372$	0.284611	+	0.492960i	0.0147564	+	0.0255588i
$373$	19.2967	+	11.1410i	0.999146	+	0.576857i	0.907996	−	0.418980i	$-0.137612\pi$
$373$	19.2967	+	11.1410i	0.999146	+	0.576857i	0.0911507	+	0.995837i	$0.470946\pi$
$374$	−14.8808	+	25.7743i	−0.769469	+	1.33276i
$375$	32.2799	+	1.25068i	1.66693	+	0.0645851i
$376$		−	1.03114i		−	0.0531771i
$377$	10.0909	+	5.82600i	0.519709	+	0.300054i
$378$	5.23665			0.269344
$379$	−9.18488	−	15.9087i	−0.471795	−	0.817174i	0.527684	−	0.849441i	$-0.323061\pi$
$379$	−9.18488	−	15.9087i	−0.471795	−	0.817174i	−0.999479	+	0.0322671i	$0.989727\pi$
$380$	0.962280	+	5.90187i	0.0493639	+	0.302760i
$381$	53.2905			2.73016
$382$	4.67700	−	2.70027i	0.239296	−	0.138158i
$383$	8.94728	−	15.4971i	0.457185	−	0.791867i	−0.541626	−	0.840619i	$-0.682191\pi$
$383$	8.94728	−	15.4971i	0.457185	−	0.791867i	0.998811	+	0.0487523i	$0.0155245\pi$
$384$		−	2.88937i		−	0.147447i
$385$	5.38776	−	4.40361i	0.274586	−	0.224429i
$386$	−10.6406	−	18.4301i	−0.541595	−	0.938069i
$387$	19.2981	+	33.4253i	0.980977	+	1.69910i
$388$	7.61437	−	13.1885i	0.386561	−	0.669543i
$389$	−12.6393	−	7.29728i	−0.640836	−	0.369987i	0.144101	−	0.989563i	$-0.453971\pi$
$389$	−12.6393	−	7.29728i	−0.640836	−	0.369987i	−0.784936	+	0.619576i	$0.787304\pi$
$390$	19.2100	−	15.7010i	0.972735	−	0.795053i
$391$	15.8100	+	27.3837i	0.799546	+	1.38485i
$392$	−3.20221	−	5.54639i	−0.161736	−	0.280135i
$393$	−42.3982			−2.13871
$394$	−11.5610	−	6.67476i	−0.582436	−	0.336269i
$395$	12.2184	−	9.98656i	0.614775	−	0.502478i
$396$	21.5667			1.08377
$397$			6.56464i			0.329470i	0.986338	+	0.164735i	$0.0526769\pi$
$397$			6.56464i			0.329470i	−0.986338	+	0.164735i	$0.947323\pi$
$398$	−0.190642	+	0.110067i	−0.00955604	+	0.00551718i
$399$		−	5.96315i		−	0.298531i
$400$	−0.995062	+	4.89998i	−0.0497531	+	0.244999i
$401$			22.1050i			1.10387i	0.833887	+	0.551935i	$0.186110\pi$
$401$			22.1050i			1.10387i	−0.833887	+	0.551935i	$0.813890\pi$
$402$	−8.44911	+	14.6343i	−0.421403	+	0.729892i
$403$	−0.655166	−	0.378260i	−0.0326361	−	0.0188425i
$404$	1.08208	−	1.87422i	0.0538355	−	0.0932458i
$405$	−5.03845	−	6.16447i	−0.250362	−	0.306315i
$406$	2.34169			0.116216
$407$	19.6644	+	14.6601i	0.974726	+	0.726676i
$408$			21.3258i			1.05578i
$409$	−0.493221	+	0.284761i	−0.0243882	+	0.0140805i	−0.512145	−	0.858899i	$-0.671149\pi$
$409$	−0.493221	+	0.284761i	−0.0243882	+	0.0140805i	0.487756	+	0.872980i	$0.337815\pi$
$410$	4.06502	−	10.7353i	0.200757	−	0.530179i
$411$	−31.3185	+	54.2453i	−1.54483	+	2.67572i
$412$	−1.47395	+	2.55296i	−0.0726163	+	0.125775i
$413$	5.42237			0.266817
$414$	11.4567	−	19.8435i	0.563064	−	0.975255i
$415$	−5.38752	−	33.0428i	−0.264463	−	1.62201i
$416$	1.92005	+	3.32562i	0.0941382	+	0.163052i
$417$		−	16.7401i		−	0.819767i
$418$		−	10.7834i		−	0.527436i
$419$	9.29139	+	16.0932i	0.453914	+	0.786202i	0.998625	−	0.0524216i	$-0.0166940\pi$
$419$	9.29139	+	16.0932i	0.453914	+	0.786202i	−0.544711	+	0.838624i	$0.683361\pi$
$420$	1.76567	−	4.66297i	0.0861561	−	0.227530i
$421$			5.98487i			0.291685i	0.989308	+	0.145842i	$0.0465893\pi$
$421$			5.98487i			0.291685i	−0.989308	+	0.145842i	$0.953411\pi$
$422$	7.57051	+	13.1125i	0.368527	+	0.638307i
$423$	4.77614	−	2.75750i	0.232224	−	0.134074i
$424$	9.81438	−	5.66633i	0.476628	−	0.275181i
$425$	7.34432	−	36.1657i	0.356252	−	1.75429i
$426$	−35.7830	−	20.6593i	−1.73369	−	1.00095i
$427$	2.46341	+	4.26676i	0.119213	+	0.206483i
$428$	13.0801	−	7.55178i	0.632249	−	0.365029i
$429$	−38.7464	+	22.3702i	−1.87069	+	1.08005i
$430$	15.9259	−	2.59667i	0.768016	−	0.125222i
$431$	−15.2869	−	8.82589i	−0.736343	−	0.425128i	0.0843950	−	0.996432i	$-0.473104\pi$
$431$	−15.2869	−	8.82589i	−0.736343	−	0.425128i	−0.820738	+	0.571304i	$0.806438\pi$
$432$	5.87643	−	3.39276i	0.282730	−	0.163234i
$433$			7.99321i			0.384129i	0.981382	+	0.192065i	$0.0615183\pi$
$433$			7.99321i			0.384129i	−0.981382	+	0.192065i	$0.938482\pi$
$434$	−0.152037			−0.00729800
$435$	−12.4063	−	15.1790i	−0.594839	−	0.727776i
$436$			6.40722i			0.306850i
$437$	−9.92186	−	5.72839i	−0.474627	−	0.274026i
$438$	9.31535			0.445105
$439$	8.78855	+	5.07407i	0.419455	+	0.242172i	0.694844	−	0.719161i	$-0.255473\pi$
$439$	8.78855	+	5.07407i	0.419455	+	0.242172i	−0.275389	+	0.961333i	$0.588807\pi$
$440$	3.19295	−	8.43227i	0.152218	−	0.401993i
$441$	17.1268	−	29.6646i	0.815564	−	1.41260i
$442$	−14.1714	−	24.5457i	−0.674067	−	1.16752i
$443$			3.13738i			0.149062i	0.997219	+	0.0745308i	$0.0237459\pi$
$443$			3.13738i			0.149062i	−0.997219	+	0.0745308i	$0.976254\pi$
$444$	17.4551	+	2.05211i	0.828383	+	0.0973890i
$445$	−2.59485	−	15.9148i	−0.123008	−	0.754434i
$446$	−11.6561	+	6.72966i	−0.551933	+	0.318659i
$447$	−9.45628	−	5.45959i	−0.447267	−	0.258230i
$448$	0.668346	+	0.385870i	0.0315764	+	0.0182306i
$449$	12.8216	+	7.40258i	0.605091	+	0.349349i	0.771042	−	0.636785i	$-0.219736\pi$
$449$	12.8216	+	7.40258i	0.605091	+	0.349349i	−0.165951	+	0.986134i	$0.553069\pi$
$450$	−25.3572	+	8.49463i	−1.19535	+	0.400441i
$451$	−10.3503	+	17.9272i	−0.487374	+	0.844157i
$452$	−12.0646			−0.567473
$453$	−12.5904	+	7.26908i	−0.591549	+	0.341531i
$454$	−2.05586			−0.0964863
$455$	1.06638	+	6.54035i	0.0499927	+	0.306616i
$456$	−3.86345	−	6.69169i	−0.180922	−	0.313367i
$457$	−7.65510	+	13.2590i	−0.358091	+	0.620231i	−0.987642	−	0.156728i	$-0.949905\pi$
$457$	−7.65510	+	13.2590i	−0.358091	+	0.620231i	0.629551	+	0.776959i	$0.283239\pi$
$458$	−2.28768			−0.106896
$459$	−43.3726	+	25.0412i	−2.02446	+	1.16882i
$460$	−6.06238	−	7.41724i	−0.282660	−	0.345831i
$461$	10.5942	−	6.11657i	0.493422	−	0.284877i	−0.232571	−	0.972579i	$-0.574714\pi$
$461$	10.5942	−	6.11657i	0.493422	−	0.284877i	0.725993	+	0.687702i	$0.241380\pi$
$462$	−4.49572	+	7.78681i	−0.209160	+	0.362275i
$463$	16.2153	−	28.0858i	0.753591	−	1.30526i	−0.192481	−	0.981301i	$-0.561653\pi$
$463$	16.2153	−	28.0858i	0.753591	−	1.30526i	0.946072	−	0.323957i	$-0.105013\pi$
$464$	2.62778	−	1.51715i	0.121992	−	0.0704318i
$465$	0.805497	+	0.985514i	0.0373540	+	0.0457021i
$466$	−3.84342	+	2.21900i	−0.178043	+	0.102793i
$467$	−27.2218			−1.25967			−0.629837	−	0.776727i	$-0.716878\pi$
$467$	−27.2218			−1.25967			−0.629837	+	0.776727i	$0.716878\pi$
$468$	−10.2693	+	17.7869i	−0.474698	+	0.822200i
$469$	−2.25673	−	3.90876i	−0.104206	−	0.180490i
$470$	−0.371038	−	2.27565i	−0.0171147	−	0.104968i
$471$	58.4393			2.69274
$472$	6.08484	−	3.51308i	0.280077	−	0.161703i
$473$	−29.0986			−1.33796
$474$	−10.1954	+	17.6590i	−0.468292	+	0.811105i
$475$	4.24736	+	12.6787i	0.194882	+	0.581740i
$476$	−4.93291	−	2.84802i	−0.226099	−	0.130539i
$477$	52.4916	+	30.3061i	2.40343	+	1.38762i
$478$	−7.26013	−	4.19164i	−0.332071	−	0.191721i
$479$	−21.8198	+	12.5977i	−0.996971	+	0.575602i	−0.907351	−	0.420374i	$-0.861899\pi$
$479$	−21.8198	+	12.5977i	−0.996971	+	0.575602i	−0.0896204	+	0.995976i	$0.528565\pi$
$480$	−1.03969	−	6.37662i	−0.0474550	−	0.291052i
$481$	−21.4543	+	9.23736i	−0.978231	+	0.421188i
$482$		−	12.0257i		−	0.547755i
$483$	4.77644	+	8.27303i	0.217335	+	0.376436i
$484$	−2.62982	+	4.55498i	−0.119537	+	0.207045i
$485$	12.0587	−	31.8459i	0.547558	−	1.44605i
$486$	−8.71992	−	5.03445i	−0.395544	−	0.228367i
$487$	−15.8772			−0.719463			−0.359732	−	0.933056i	$-0.617132\pi$
$487$	−15.8772			−0.719463			−0.359732	+	0.933056i	$0.617132\pi$
$488$	5.52875	+	3.19203i	0.250275	+	0.144496i
$489$		−	4.81644i		−	0.217807i
$490$	−9.06280	−	11.0882i	−0.409416	−	0.500914i
$491$	−19.2000			−0.866482			−0.433241	−	0.901278i	$-0.642630\pi$
$491$	−19.2000			−0.866482			−0.433241	+	0.901278i	$0.642630\pi$
$492$			14.8330i			0.668722i
$493$	−19.3950	+	11.1977i	−0.873508	+	0.504320i
$494$	8.89355	+	5.13469i	0.400140	+	0.231021i
$495$	47.5960	−	7.76037i	2.13928	−	0.348803i
$496$	−0.170612	+	0.0985027i	−0.00766069	+	0.00442290i
$497$	9.55751	−	5.51803i	0.428713	−	0.247518i
$498$	21.6303	+	37.4647i	0.969276	+	1.67883i
$499$	−26.7701	−	15.4557i	−1.19840	−	0.691894i	−0.238199	−	0.971216i	$-0.576557\pi$
$499$	−26.7701	−	15.4557i	−1.19840	−	0.691894i	−0.960197	+	0.279322i	$0.909890\pi$
$500$	−0.432858	+	11.1720i	−0.0193580	+	0.499625i
$501$	−37.3887	+	21.5864i	−1.67040	+	0.964408i
$502$	−15.0787	+	8.70570i	−0.672996	+	0.388554i
$503$	7.18212	+	12.4398i	0.320235	+	0.554663i	0.980536	−	0.196338i	$-0.0629049\pi$
$503$	7.18212	+	12.4398i	0.320235	+	0.554663i	−0.660302	+	0.751000i	$0.729572\pi$
$504$			4.12761i			0.183858i
$505$	1.71367	−	4.52562i	0.0762572	−	0.201388i
$506$	8.63746	+	14.9605i	0.383982	+	0.665076i
$507$		−	5.04588i		−	0.224095i
$508$			18.4437i			0.818305i
$509$	−21.1337	−	36.6047i	−0.936735	−	1.62247i	−0.771510	−	0.636217i	$-0.780498\pi$
$509$	−21.1337	−	36.6047i	−0.936735	−	1.62247i	−0.165225	−	0.986256i	$-0.552835\pi$
$510$	7.67368	+	47.0644i	0.339796	+	2.08404i
$511$	−1.24405	+	2.15476i	−0.0550335	+	0.0953208i
$512$	1.00000			0.0441942
$513$	9.07309	−	15.7151i	0.400587	−	0.693837i
$514$	0.631635	−	1.09402i	0.0278602	−	0.0482553i
$515$	−2.33426	+	6.16456i	−0.102860	+	0.271643i
$516$	−18.0572	+	10.4253i	−0.794923	+	0.458949i
$517$			4.15790i			0.182864i
$518$	−2.80578	+	3.76353i	−0.123279	+	0.165360i
$519$	−67.7626			−2.97445
$520$	5.43407	+	6.64851i	0.238300	+	0.291556i
$521$	18.1837	−	31.4952i	0.796644	−	1.37983i	−0.125146	−	0.992138i	$-0.539940\pi$
$521$	18.1837	−	31.4952i	0.796644	−	1.37983i	0.921790	−	0.387689i	$-0.126727\pi$
$522$	14.0545	+	8.11438i	0.615150	+	0.355157i
$523$	8.38265	−	14.5192i	0.366548	−	0.634879i	−0.622476	−	0.782639i	$-0.713873\pi$
$523$	8.38265	−	14.5192i	0.366548	−	0.634879i	0.989023	+	0.147760i	$0.0472064\pi$
$524$		−	14.6739i		−	0.641031i
$525$	2.21883	−	10.9262i	0.0968376	−	0.476858i
$526$			7.53162i			0.328394i
$527$	1.25925	−	0.727026i	0.0548536	−	0.0316697i
$528$			11.6509i			0.507039i
$529$	−4.64642			−0.202018
$530$	19.6207	−	16.0367i	0.852268	−	0.696590i
$531$	32.5444	+	18.7895i	1.41231	+	0.815396i
$532$	2.06383			0.0894782
$533$	−9.85684	−	17.0726i	−0.426947	−	0.739494i
$534$	10.4180	+	18.0446i	0.450833	+	0.780866i
$535$	26.1494	−	21.3728i	1.13054	−	0.924028i
$536$	−5.06487	−	2.92421i	−0.218769	−	0.126306i
$537$	18.3318	−	31.7517i	0.791077	−	1.37019i
$538$	12.7832	+	22.1412i	0.551124	+	0.954574i
$539$	12.9123	+	22.3648i	0.556174	+	0.963322i
$540$	11.7480	−	9.60209i	0.505554	−	0.413208i
$541$		−	3.11854i		−	0.134076i	−0.997750	−	0.0670382i	$-0.978645\pi$
$541$		−	3.11854i		−	0.134076i	0.997750	−	0.0670382i	$-0.0213549\pi$
$542$	7.65037	−	13.2508i	0.328611	−	0.569172i
$543$	−45.7962	+	26.4404i	−1.96530	+	1.13467i
$544$	−7.38077			−0.316448
$545$	2.30552	+	14.1403i	0.0987577	+	0.605702i
$546$	−4.28140	−	7.41561i	−0.183227	−	0.317359i
$547$	31.4065			1.34284			0.671422	−	0.741075i	$-0.265684\pi$
$547$	31.4065			1.34284			0.671422	+	0.741075i	$0.265684\pi$
$548$	−18.7741	−	10.8392i	−0.801990	−	0.463029i
$549$			34.1448i			1.45726i
$550$	4.01241	−	19.7583i	0.171090	−	0.842498i
$551$	4.05724	−	7.02734i	0.172844	−	0.299375i
$552$	10.7200	+	6.18918i	0.456272	+	0.263429i
$553$	−2.72316	−	4.71666i	−0.115801	−	0.200573i
$554$	−5.19620			−0.220765
$555$	39.2606	−	1.75204i	1.66652	−	0.0743701i
$556$	5.79369			0.245707
$557$	−1.02909	−	1.78243i	−0.0436038	−	0.0755240i	0.843400	−	0.537286i	$-0.180551\pi$
$557$	−1.02909	−	1.78243i	−0.0436038	−	0.0755240i	−0.887004	+	0.461762i	$0.847217\pi$
$558$	−0.912507	−	0.526836i	−0.0386295	−	0.0223028i
$559$	13.8557	−	23.9988i	0.586035	−	1.01504i
$560$	1.61384	+	0.611094i	0.0681971	+	0.0258234i
$561$		−	85.9923i		−	3.63060i
$562$	15.8995	+	9.17961i	0.670682	+	0.387218i
$563$	40.6022			1.71118			0.855590	−	0.517654i	$-0.173195\pi$
$563$	40.6022			1.71118			0.855590	+	0.517654i	$0.173195\pi$
$564$	1.48967	+	2.58019i	0.0627266	+	0.108646i
$565$	−26.6258	+	4.34124i	−1.12016	+	0.182637i
$566$	−2.42535			−0.101945
$567$	−2.37966	+	1.37390i	−0.0999364	+	0.0576983i
$568$	7.15012	−	12.3844i	0.300012	−	0.519637i
$569$			25.5058i			1.06926i	0.845087	+	0.534629i	$0.179549\pi$
$569$			25.5058i			1.06926i	−0.845087	+	0.534629i	$0.820451\pi$
$570$	−10.9342	−	13.3779i	−0.457984	−	0.560337i
$571$	1.22775	+	2.12653i	0.0513798	+	0.0889923i	0.890571	−	0.454843i	$-0.150305\pi$
$571$	1.22775	+	2.12653i	0.0513798	+	0.0889923i	−0.839192	+	0.543836i	$0.816971\pi$
$572$	−7.74226	−	13.4100i	−0.323720	−	0.560700i
$573$	−7.80206	+	13.5136i	−0.325936	+	0.564537i
$574$	−3.43105	−	1.98092i	−0.143209	−	0.0826819i
$575$	−16.0482	−	14.1879i	−0.669256	−	0.591675i
$576$	2.67422	+	4.63189i	0.111426	+	0.192995i
$577$	11.5125	+	19.9402i	0.479272	+	0.830123i	0.999717	−	0.0237719i	$-0.00756756\pi$
$577$	11.5125	+	19.9402i	0.479272	+	0.830123i	−0.520446	+	0.853895i	$0.674234\pi$
$578$	37.4757			1.55879
$579$	53.2514	+	30.7447i	2.21305	+	1.27771i
$580$	5.25339	−	4.29379i	0.218135	−	0.178290i
$581$	−11.5547			−0.479371
$582$			44.0014i			1.82392i
$583$	−39.5748	+	22.8485i	−1.63902	+	0.946288i
$584$			3.22401i			0.133411i
$585$	−16.2632	+	42.9496i	−0.672402	+	1.77575i
$586$		−	7.43502i		−	0.307138i
$587$	13.1526	−	22.7809i	0.542865	−	0.940270i	−0.455873	−	0.890045i	$-0.650673\pi$
$587$	13.1526	−	22.7809i	0.542865	−	0.940270i	0.998738	−	0.0502252i	$-0.0159939\pi$
$588$	16.0256	+	9.25236i	0.660883	+	0.381561i
$589$	−0.263421	+	0.456259i	−0.0108541	+	0.0187998i
$590$	12.1647	−	9.94263i	0.500811	−	0.409332i
$591$	38.5716			1.58663
$592$	−0.710230	+	6.04116i	−0.0291903	+	0.248290i
$593$			36.7926i			1.51089i	0.655211	+	0.755446i	$0.272580\pi$
$593$			36.7926i			1.51089i	−0.655211	+	0.755446i	$0.727420\pi$
$594$	−23.6957	+	13.6807i	−0.972245	+	0.561326i
$595$	−11.9114	−	4.51034i	−0.488318	−	0.184906i
$596$	1.88954	−	3.27279i	0.0773987	−	0.134059i
$597$	0.318025	−	0.550836i	0.0130159	−	0.0225442i
$598$	−16.4514			−0.672748
$599$	19.4894	−	33.7566i	0.796314	−	1.37926i	−0.125688	−	0.992070i	$-0.540114\pi$
$599$	19.4894	−	33.7566i	0.796314	−	1.37926i	0.922002	−	0.387186i	$-0.126553\pi$
$600$	−4.58902	−	13.6986i	−0.187346	−	0.559244i
$601$	4.29903	+	7.44614i	0.175361	+	0.303734i	0.940286	−	0.340385i	$-0.110557\pi$
$601$	4.29903	+	7.44614i	0.175361	+	0.303734i	−0.764925	+	0.644119i	$0.777224\pi$
$602$		−	5.56913i		−	0.226981i
$603$		−	31.2799i		−	1.27382i
$604$	−2.51580	−	4.35750i	−0.102367	−	0.177304i
$605$	−4.16479	+	10.9988i	−0.169323	+	0.447165i
$606$			6.25305i			0.254013i
$607$	11.7140	+	20.2892i	0.475456	+	0.823515i	0.999605	−	0.0281123i	$-0.00894961\pi$
$607$	11.7140	+	20.2892i	0.475456	+	0.823515i	−0.524148	+	0.851627i	$0.675616\pi$
$608$	2.31597	−	1.33713i	0.0939250	−	0.0542276i
$609$	−5.85952	+	3.38300i	−0.237440	+	0.137086i
$610$	13.3501	+	5.05515i	0.540531	+	0.204677i
$611$	−3.42919	−	1.97984i	−0.138730	−	0.0800959i
$612$	−19.7378	−	34.1869i	−0.797854	−	1.38192i
$613$	−34.2200	+	19.7569i	−1.38213	+	0.797975i	−0.992412	−	0.122957i	$-0.960762\pi$
$613$	−34.2200	+	19.7569i	−1.38213	+	0.797975i	−0.389722	+	0.920933i	$0.627429\pi$
$614$	26.4786	−	15.2874i	1.06859	−	0.616949i
$615$	5.33737	+	32.7353i	0.215224	+	1.32001i
$616$	−2.69499	−	1.55595i	−0.108584	−	0.0626911i
$617$	28.9902	−	16.7375i	1.16710	−	0.673825i	0.214105	−	0.976811i	$-0.431317\pi$
$617$	28.9902	−	16.7375i	1.16710	−	0.673825i	0.952995	+	0.302985i	$0.0979833\pi$
$618$		−	8.51756i		−	0.342627i
$619$	−12.4754			−0.501428			−0.250714	−	0.968061i	$-0.580665\pi$
$619$	−12.4754			−0.501428			−0.250714	+	0.968061i	$0.580665\pi$
$620$	−0.341083	+	0.278780i	−0.0136982	+	0.0111961i
$621$			29.0699i			1.16653i
$622$	10.1909	+	5.88374i	0.408619	+	0.235917i
$623$	−5.56525			−0.222967
$624$	−9.60895	−	5.54773i	−0.384666	−	0.222087i
$625$	3.06474	+	24.8114i	0.122590	+	0.992457i
$626$	11.7805	−	20.4044i	0.470843	−	0.815524i
$627$	15.5787	+	26.9831i	0.622152	+	1.07760i
$628$			20.2256i			0.807091i
$629$	5.24204	−	44.5884i	0.209014	−	1.77786i
$630$	1.48524	+	9.10932i	0.0591735	+	0.362924i
$631$	25.1859	−	14.5411i	1.00264	−	0.578872i	0.0936090	−	0.995609i	$-0.470160\pi$
$631$	25.1859	−	14.5411i	1.00264	−	0.578872i	0.909027	+	0.416737i	$0.136826\pi$
$632$	−6.11172	−	3.52860i	−0.243111	−	0.140360i
$633$	−37.8869	−	21.8740i	−1.50587	−	0.869413i
$634$	16.8102	+	9.70539i	0.667620	+	0.385450i
$635$	6.63662	+	40.7038i	0.263366	+	1.61528i
$636$	−16.3721	+	28.3573i	−0.649197	+	1.12444i
$637$	−24.5936			−0.974434
$638$	−10.5961	+	6.11763i	−0.419502	+	0.242199i
$639$	76.4840			3.02566
$640$	2.20693	−	0.359832i	0.0872364	−	0.0142236i
$641$	−3.08912	−	5.35051i	−0.122013	−	0.211333i	0.798548	−	0.601931i	$-0.205602\pi$
$641$	−3.08912	−	5.35051i	−0.122013	−	0.211333i	−0.920561	+	0.390598i	$0.872268\pi$
$642$	−21.8199	+	37.7931i	−0.861161	+	1.49157i
$643$	−15.9159			−0.627662			−0.313831	−	0.949479i	$-0.601613\pi$
$643$	−15.9159			−0.627662			−0.313831	+	0.949479i	$0.601613\pi$
$644$	−2.86327	+	1.65311i	−0.112829	+	0.0651416i
$645$	−36.0995	+	29.5055i	−1.42142	+	1.16178i
$646$	−17.0936	+	9.86901i	−0.672540	+	0.388291i
$647$	−17.5322	+	30.3667i	−0.689262	+	1.19384i	0.282814	+	0.959175i	$0.408732\pi$
$647$	−17.5322	+	30.3667i	−0.689262	+	1.19384i	−0.972077	+	0.234663i	$0.924601\pi$
$648$	−1.78026	+	3.08350i	−0.0699353	+	0.121131i
$649$	−24.5360	+	14.1659i	−0.963124	+	0.556060i
$650$	14.3849	+	12.7174i	0.564224	+	0.498818i
$651$	0.380437	−	0.219645i	0.0149105	−	0.00860858i
$652$	1.66695			0.0652829
$653$	−4.34715	+	7.52948i	−0.170117	+	0.294651i	−0.938461	−	0.345386i	$-0.887748\pi$
$653$	−4.34715	+	7.52948i	−0.170117	+	0.294651i	0.768344	+	0.640038i	$0.221081\pi$
$654$	−9.25641	−	16.0326i	−0.361954	−	0.626923i
$655$	−5.28012	−	32.3841i	−0.206311	−	1.26535i
$656$	−5.13364			−0.200435
$657$	−14.9333	+	8.62172i	−0.582602	+	0.336365i
$658$	−0.795773			−0.0310225
$659$	−2.45842	+	4.25810i	−0.0957663	+	0.165872i	−0.909928	−	0.414766i	$-0.863863\pi$
$659$	−2.45842	+	4.25810i	−0.0957663	+	0.165872i	0.814162	+	0.580638i	$0.197197\pi$
$660$	4.19235	+	25.7126i	0.163187	+	1.00086i
$661$	18.3304	+	10.5831i	0.712969	+	0.411633i	0.812159	−	0.583436i	$-0.198292\pi$
$661$	18.3304	+	10.5831i	0.712969	+	0.411633i	−0.0991902	+	0.995068i	$0.531625\pi$
$662$	−20.1775	−	11.6495i	−0.784221	−	0.452770i
$663$	70.9214	+	40.9465i	2.75436	+	1.59023i
$664$	−12.9664	+	7.48616i	−0.503194	+	0.290519i
$665$	4.55471	−	0.742630i	0.176624	−	0.0287980i
$666$	−29.8813	+	12.8657i	−1.15788	+	0.498535i
$667$			12.9993i			0.503333i
$668$	−7.47097	−	12.9401i	−0.289060	−	0.500667i
$669$	19.4445	−	33.6788i	0.751766	−	1.30210i
$670$	−12.2300	−	4.63100i	−0.472487	−	0.178911i
$671$	−22.2937	−	12.8713i	−0.860640	−	0.496891i
$672$	−2.22984			−0.0860179
$673$	−1.84857	−	1.06727i	−0.0712573	−	0.0411404i	0.463948	−	0.885862i	$-0.346432\pi$
$673$	−1.84857	−	1.06727i	−0.0712573	−	0.0411404i	−0.535205	+	0.844722i	$0.679766\pi$
$674$			13.4198i			0.516912i
$675$	22.4719	−	25.4184i	0.864943	−	0.978355i
$676$	1.74636			0.0671677
$677$		−	48.0304i		−	1.84596i	−0.384850	−	0.922979i	$-0.625747\pi$
$677$		−	48.0304i		−	1.84596i	0.384850	−	0.922979i	$-0.374253\pi$
$678$	30.1890	−	17.4296i	1.15940	−	0.669380i
$679$	−10.1781	−	5.87631i	−0.390598	−	0.225512i
$680$	−16.2888	+	2.65583i	−0.624647	+	0.101847i
$681$	5.14431	−	2.97007i	0.197130	−	0.113813i
$682$	0.687962	−	0.397195i	0.0263434	−	0.0152094i
$683$	−20.8320	−	36.0821i	−0.797114	−	1.38064i	−0.921488	−	0.388407i	$-0.873026\pi$
$683$	−20.8320	−	36.0821i	−0.797114	−	1.38064i	0.124374	−	0.992235i	$-0.460308\pi$
$684$	12.3868	+	7.15154i	0.473622	+	0.273446i
$685$	−45.3333	−	17.1659i	−1.73210	−	0.655874i
$686$	−8.95879	+	5.17236i	−0.342048	+	0.197482i
$687$	5.72439	−	3.30498i	0.218399	−	0.126093i
$688$	−3.60817	−	6.24953i	−0.137560	−	0.238261i
$689$		−	43.5186i		−	1.65793i
$690$	25.8853	+	9.80168i	0.985435	+	0.373143i
$691$	−7.77914	−	13.4739i	−0.295932	−	0.512570i	0.679269	−	0.733889i	$-0.262297\pi$
$691$	−7.77914	−	13.4739i	−0.295932	−	0.512570i	−0.975201	+	0.221320i	$0.928964\pi$
$692$		−	23.4524i		−	0.891526i
$693$		−	16.6438i		−	0.632247i
$694$	16.1819	+	28.0279i	0.614257	+	1.06392i
$695$	12.7863	−	2.08475i	0.485010	−	0.0790793i
$696$	−4.38360	+	7.59262i	−0.166160	+	0.287797i
$697$	37.8902			1.43519
$698$	−0.0141987	+	0.0245929i	−0.000537429	+	0.000930854i
$699$	6.41150	−	11.1050i	0.242505	−	0.420031i
$700$	3.78151	+	0.767929i	0.142928	+	0.0290250i
$701$	−5.01561	+	2.89577i	−0.189437	+	0.109372i	−0.591719	−	0.806144i	$-0.701550\pi$
$701$	−5.01561	+	2.89577i	−0.189437	+	0.109372i	0.402282	+	0.915516i	$0.368217\pi$
$702$		−	26.0571i		−	0.983460i
$703$	6.43292	+	14.9408i	0.242622	+	0.563503i
$704$	−4.03232			−0.151974
$705$	4.21604	+	5.15826i	0.158785	+	0.194271i
$706$	0.762087	−	1.31997i	0.0286815	−	0.0496779i
$707$	−1.44641	−	0.835084i	−0.0543977	−	0.0314065i
$708$	−10.1506	+	17.5813i	−0.381482	+	0.660747i
$709$		−	36.7426i		−	1.37990i	−0.723859	−	0.689948i	$-0.757633\pi$
$709$		−	36.7426i		−	1.37990i	0.723859	−	0.689948i	$-0.242367\pi$
$710$	11.3235	−	29.9042i	0.424963	−	1.12229i
$711$		−	37.7451i		−	1.41555i
$712$	−6.24517	+	3.60565i	−0.234048	+	0.135127i
$713$		−	0.843993i		−	0.0316078i
$714$	16.4579			0.615922
$715$	−21.9119	−	26.8089i	−0.819460	−	1.00260i
$716$	10.9891	+	6.34458i	0.410683	+	0.237108i
$717$	24.2224			0.904601
$718$	−7.16449	−	12.4093i	−0.267376	−	0.463109i
$719$	10.4176	+	18.0439i	0.388512	+	0.672922i	0.992250	−	0.124261i	$-0.0396559\pi$
$719$	10.4176	+	18.0439i	0.388512	+	0.672922i	−0.603738	+	0.797183i	$0.706323\pi$
$720$	7.56851	+	9.25996i	0.282062	+	0.345098i
$721$	1.97022	+	1.13751i	0.0733747	+	0.0423629i
$722$	−5.92419	+	10.2610i	−0.220476	+	0.381875i
$723$	17.3733	+	30.0914i	0.646120	+	1.11911i
$724$	−9.15095	−	15.8499i	−0.340092	−	0.589057i
$725$	10.0488	−	11.3664i	0.373203	−	0.422138i
$726$		−	15.1970i		−	0.564015i
$727$	1.21854	−	2.11056i	0.0451930	−	0.0782765i	−0.842544	−	0.538627i	$-0.818943\pi$
$727$	1.21854	−	2.11056i	0.0451930	−	0.0782765i	0.887737	+	0.460351i	$0.152276\pi$
$728$	2.56652	−	1.48178i	0.0951214	−	0.0549184i
$729$	39.7743			1.47312
$730$	1.16010	+	7.11515i	0.0429373	+	0.263344i
$731$	26.6311	+	46.1263i	0.984985	+	1.70604i
$732$	−18.4459			−0.681779
$733$	6.76694	+	3.90689i	0.249942	+	0.144304i	0.619738	−	0.784809i	$-0.287239\pi$
$733$	6.76694	+	3.90689i	0.249942	+	0.144304i	−0.369795	+	0.929113i	$0.620572\pi$
$734$			37.0249i			1.36662i
$735$	38.6965	+	14.6528i	1.42734	+	0.540475i
$736$	−2.14205	+	3.71015i	−0.0789572	+	0.136758i
$737$	20.4232	+	11.7913i	0.752299	+	0.434340i
$738$	−13.7285	−	23.7785i	−0.505353	−	0.875297i
$739$	−36.1759			−1.33075			−0.665375	−	0.746509i	$-0.731728\pi$
$739$	−36.1759			−1.33075			−0.665375	+	0.746509i	$0.731728\pi$
$740$	0.606376	+	13.5879i	0.0222908	+	0.499503i
$741$	−29.6720			−1.09003
$742$	−4.37293	−	7.57414i	−0.160535	−	0.278056i
$743$	−10.8402	−	6.25858i	−0.397688	−	0.229605i	0.287798	−	0.957691i	$-0.407077\pi$
$743$	−10.8402	−	6.25858i	−0.397688	−	0.229605i	−0.685486	+	0.728086i	$0.740410\pi$
$744$	0.284611	−	0.492960i	0.0104343	−	0.0180728i
$745$	2.99243	−	7.90271i	0.109634	−	0.289533i
$746$		−	22.2819i		−	0.815799i
$747$	−69.3501	−	40.0393i	−2.53739	−	1.46496i
$748$	29.7617			1.08819
$749$	−5.82801	−	10.0944i	−0.212951	−	0.368841i
$750$	−15.0568	−	28.5805i	−0.549797	−	1.04361i
$751$	13.8046			0.503738			0.251869	−	0.967761i	$-0.418955\pi$
$751$	13.8046			0.503738			0.251869	+	0.967761i	$0.418955\pi$
$752$	−0.892995	+	0.515571i	−0.0325642	+	0.0188009i
$753$	25.1540	−	43.5679i	0.916661	−	1.58770i
$754$		−	11.6520i		−	0.424341i
$755$	−7.12016	−	8.71141i	−0.259129	−	0.317041i
$756$	−2.61833	−	4.53507i	−0.0952276	−	0.164939i
$757$	3.40675	+	5.90067i	0.123821	+	0.214464i	0.921271	−	0.388921i	$-0.127152\pi$
$757$	3.40675	+	5.90067i	0.123821	+	0.214464i	−0.797451	+	0.603384i	$0.793819\pi$
$758$	−9.18488	+	15.9087i	−0.333610	+	0.577829i
$759$	−43.2264	−	24.9568i	−1.56902	−	0.905874i
$760$	4.63003	−	3.78430i	0.167949	−	0.137271i
$761$	−3.89614	−	6.74831i	−0.141235	−	0.244626i	0.786727	−	0.617301i	$-0.211774\pi$
$761$	−3.89614	−	6.74831i	−0.141235	−	0.244626i	−0.927962	+	0.372675i	$0.878441\pi$
$762$	−26.6453	−	46.1510i	−0.965256	−	1.67187i
$763$	4.94471			0.179010
$764$	−4.67700	−	2.70027i	−0.169208	−	0.0976922i
$765$	−55.8614	−	68.3457i	−2.01967	−	2.47104i
$766$	−17.8946			−0.646557
$767$		−	26.9812i		−	0.974234i
$768$	−2.50227	+	1.44468i	−0.0902927	+	0.0521305i
$769$			13.9995i			0.504836i	0.967618	+	0.252418i	$0.0812258\pi$
$769$			13.9995i			0.504836i	−0.967618	+	0.252418i	$0.918774\pi$
$770$	−6.50752	−	2.46413i	−0.234515	−	0.0888010i
$771$			3.65005i			0.131453i
$772$	−10.6406	+	18.4301i	−0.382965	+	0.663315i
$773$	7.99336	+	4.61497i	0.287501	+	0.165989i	0.636814	−	0.771017i	$-0.280252\pi$
$773$	7.99336	+	4.61497i	0.287501	+	0.165989i	−0.349313	+	0.937006i	$0.613585\pi$
$774$	19.2981	−	33.4253i	0.693655	−	1.20145i
$775$	−0.652431	+	0.737979i	−0.0234360	+	0.0265090i
$776$	−15.2287			−0.546680
$777$	1.58370	−	13.4708i	0.0568148	−	0.483263i
$778$			14.5946i			0.523240i
$779$	−11.8894	+	6.86432i	−0.425980	+	0.245940i
$780$	−23.2025	−	8.78582i	−0.830782	−	0.314583i
$781$	−28.8316	+	49.9378i	−1.03168	+	1.78691i
$782$	15.8100	−	27.3837i	0.565365	−	0.979240i
$783$	−20.5893			−0.735801
$784$	−3.20221	+	5.54639i	−0.114365	+	0.198085i
$785$	7.27783	+	44.6365i	0.259757	+	1.59315i
$786$	21.1991	+	36.7179i	0.756146	+	1.30968i
$787$			2.72141i			0.0970076i	0.998823	+	0.0485038i	$0.0154453\pi$
$787$			2.72141i			0.0970076i	−0.998823	+	0.0485038i	$0.984555\pi$
$788$			13.3495i			0.475557i
$789$	−10.8808	−	18.8461i	−0.387367	−	0.670940i
$790$	−14.7578	−	5.58818i	−0.525060	−	0.198818i
$791$			9.31077i			0.331053i
$792$	−10.7833	−	18.6773i	−0.383169	−	0.663668i
$793$	21.2310	−	12.2577i	0.753934	−	0.435284i
$794$	5.68514	−	3.28232i	0.201758	−	0.116485i
$795$	−25.9282	+	68.4738i	−0.919578	+	2.42851i
$796$	0.190642	+	0.110067i	0.00675714	+	0.00390124i
$797$	24.3169	+	42.1181i	0.861349	+	1.49190i	0.870627	+	0.491944i	$0.163714\pi$
$797$	24.3169	+	42.1181i	0.861349	+	1.49190i	−0.00927734	+	0.999957i	$0.502953\pi$
$798$	−5.16424	+	2.98158i	−0.182812	+	0.105547i
$799$	6.59099	−	3.80531i	0.233173	−	0.134622i
$800$	4.74104	−	1.58824i	0.167621	−	0.0561529i
$801$	−33.4019	−	19.2846i	−1.18020	−	0.681388i
$802$	19.1435	−	11.0525i	0.675980	−	0.390277i
$803$		−	13.0003i		−	0.458769i
$804$	16.8982			0.595954
$805$	−5.72418	+	4.67858i	−0.201751	+	0.164898i
$806$			0.756520i			0.0266473i
$807$	−63.9740	−	36.9354i	−2.25199	−	1.30019i
$808$	−2.16416			−0.0761348
$809$	28.8517	+	16.6575i	1.01437	+	0.585648i	0.912469	−	0.409146i	$-0.134173\pi$
$809$	28.8517	+	16.6575i	1.01437	+	0.585648i	0.101903	+	0.994794i	$0.467507\pi$
$810$	−2.81936	+	7.44566i	−0.0990623	+	0.261614i
$811$	23.9189	−	41.4288i	0.839908	−	1.45476i	−0.0500635	−	0.998746i	$-0.515942\pi$
$811$	23.9189	−	41.4288i	0.839908	−	1.45476i	0.889971	−	0.456017i	$-0.150724\pi$
$812$	−1.17084	−	2.02796i	−0.0410886	−	0.0711675i
$813$			44.2095i			1.55049i
$814$	2.86388	−	24.3599i	0.100379	−	0.853814i
$815$	3.67884	−	0.599822i	0.128864	−	0.0210109i
$816$	18.4686	−	10.6629i	0.646532	−	0.373275i
$817$	−16.7128	−	9.64915i	−0.584707	−	0.337581i
$818$	0.493221	+	0.284761i	0.0172451	+	0.00995645i
$819$	13.7269	+	7.92521i	0.479655	+	0.276929i
$820$	−11.3296	+	1.84725i	−0.395646	+	0.0645086i
$821$	−26.1992	+	45.3784i	−0.914359	+	1.58372i	−0.106521	+	0.994310i	$0.533971\pi$
$821$	−26.1992	+	45.3784i	−0.914359	+	1.58372i	−0.807837	+	0.589405i	$0.799362\pi$
$822$	62.6370			2.18472
$823$	−8.52802	+	4.92365i	−0.297268	+	0.171628i	−0.641215	−	0.767361i	$-0.721569\pi$
$823$	−8.52802	+	4.92365i	−0.297268	+	0.171628i	0.343947	+	0.938989i	$0.388236\pi$
$824$	2.94790			0.102695
$825$	18.5044	+	55.2373i	0.644241	+	1.92311i
$826$	−2.71119	−	4.69591i	−0.0943342	−	0.163392i
$827$	7.18531	−	12.4453i	0.249858	−	0.432766i	−0.713628	−	0.700524i	$-0.752949\pi$
$827$	7.18531	−	12.4453i	0.249858	−	0.432766i	0.963486	+	0.267758i	$0.0862828\pi$
$828$	−22.9133			−0.796293
$829$	10.0198	−	5.78491i	0.348000	−	0.200918i	−0.315804	−	0.948825i	$-0.602274\pi$
$829$	10.0198	−	5.78491i	0.348000	−	0.200918i	0.663804	+	0.747906i	$0.268941\pi$
$830$	−25.9222	+	21.1871i	−0.899771	+	0.735416i
$831$	13.0023	−	7.50686i	0.451044	−	0.260410i
$832$	1.92005	−	3.32562i	0.0665657	−	0.115295i
$833$	23.6348	−	40.9366i	0.818896	−	1.41837i
$834$	−14.4974	+	8.37006i	−0.502003	+	0.289831i
$835$	−21.1441	−	25.8695i	−0.731723	−	0.895252i
$836$	−9.33874	+	5.39172i	−0.322987	+	0.186477i
$837$	1.33678			0.0462060
$838$	9.29139	−	16.0932i	0.320966	−	0.555929i
$839$	9.59263	+	16.6149i	0.331174	+	0.573611i	0.982742	−	0.184979i	$-0.0592218\pi$
$839$	9.59263	+	16.6149i	0.331174	+	0.573611i	−0.651568	+	0.758590i	$0.725889\pi$
$840$	−4.92109	+	0.802367i	−0.169794	+	0.0276843i
$841$	19.7930			0.682519
$842$	5.18305	−	2.99244i	0.178620	−	0.103126i
$843$	−53.0465			−1.82702
$844$	7.57051	−	13.1125i	0.260588	−	0.451351i
$845$	3.85409	−	0.628396i	0.132585	−	0.0216175i
$846$	−4.77614	−	2.75750i	−0.164207	−	0.0948049i
$847$	3.51526	+	2.02954i	0.120786	+	0.0697357i
$848$	−9.81438	−	5.66633i	−0.337027	−	0.194583i
$849$	6.06888	−	3.50387i	0.208283	−	0.120252i
$850$	−34.9925	+	11.7225i	−1.20023	+	0.402077i
$851$	−20.8922	−	15.5755i	−0.716176	−	0.533923i
$852$			41.3186i			1.41555i
$853$	−15.4403	−	26.7435i	−0.528667	−	0.915678i	−0.999441	−	0.0334246i	$-0.989359\pi$
$853$	−15.4403	−	26.7435i	−0.528667	−	0.915678i	0.470774	−	0.882254i	$-0.343975\pi$
$854$	2.46341	−	4.26676i	0.0842963	−	0.146005i
$855$	29.9102	+	11.3257i	1.02291	+	0.387332i
$856$	−13.0801	−	7.55178i	−0.447067	−	0.258114i
$857$	0.242847			0.00829548			0.00414774	−	0.999991i	$-0.498680\pi$
$857$	0.242847			0.00829548			0.00414774	+	0.999991i	$0.498680\pi$
$858$	38.7464	+	22.3702i	1.32278	+	0.763707i
$859$			17.2506i			0.588583i	0.955716	+	0.294291i	$0.0950836\pi$
$859$			17.2506i			0.588583i	−0.955716	+	0.294291i	$0.904916\pi$
$860$	−10.2117	−	12.4939i	−0.348217	−	0.426039i
$861$	11.4472			0.390119
$862$			17.6518i			0.601222i
$863$	1.69420	−	0.978147i	0.0576713	−	0.0332965i	−0.470887	−	0.882193i	$-0.656066\pi$
$863$	1.69420	−	0.978147i	0.0576713	−	0.0332965i	0.528558	+	0.848897i	$0.322733\pi$
$864$	−5.87643	−	3.39276i	−0.199920	−	0.115424i
$865$	−8.43891	−	51.7577i	−0.286932	−	1.75981i
$866$	6.92232	−	3.99660i	0.235230	−	0.135810i
$867$	−93.7743	+	54.1406i	−3.18474	+	1.83871i
$868$	0.0760185	+	0.131668i	0.00258023	+	0.00446910i
$869$	24.6444	+	14.2285i	0.836005	+	0.482668i
$870$	−6.94221	+	18.3337i	−0.235363	+	0.621571i
$871$	−19.4496	+	11.2292i	−0.659025	+	0.380488i
$872$	5.54882	−	3.20361i	0.187907	−	0.108488i
$873$	−40.7250	−	70.5378i	−1.37833	−	2.38734i
$874$			11.4568i			0.387531i
$875$	8.62184	+	0.334053i	0.291471	+	0.0112931i
$876$	−4.65768	−	8.06733i	−0.157368	−	0.272570i
$877$		−	18.8974i		−	0.638121i	−0.947734	−	0.319060i	$-0.896633\pi$
$877$		−	18.8974i		−	0.638121i	0.947734	−	0.319060i	$-0.103367\pi$
$878$		−	10.1481i		−	0.342483i
$879$	10.7412	+	18.6044i	0.362293	+	0.627510i
$880$	−8.89904	+	1.45096i	−0.299987	+	0.0489118i
$881$	9.90951	−	17.1638i	0.333860	−	0.578262i	−0.649405	−	0.760442i	$-0.724982\pi$
$881$	9.90951	−	17.1638i	0.333860	−	0.578262i	0.983265	+	0.182180i	$0.0583154\pi$
$882$	−34.2537			−1.15338
$883$	−12.0776	+	20.9190i	−0.406443	+	0.703980i	−0.994488	−	0.104848i	$-0.966564\pi$
$883$	−12.0776	+	20.9190i	−0.406443	+	0.703980i	0.588045	+	0.808828i	$0.299898\pi$
$884$	−14.1714	+	24.5457i	−0.476637	+	0.825560i
$885$	−16.0753	+	42.4532i	−0.540364	+	1.42705i
$886$	2.71705	−	1.56869i	0.0912812	−	0.0527012i
$887$			17.1861i			0.577054i	0.957472	+	0.288527i	$0.0931655\pi$
$887$			17.1861i			0.577054i	−0.957472	+	0.288527i	$0.906835\pi$
$888$	−6.95038	−	16.1426i	−0.233239	−	0.541711i
$889$	14.2337			0.477383
$890$	−12.4852	+	10.2046i	−0.418505	+	0.342059i
$891$	7.17859	−	12.4337i	0.240492	−	0.416544i
$892$	11.6561	+	6.72966i	0.390276	+	0.225326i
$893$	−1.37877	+	2.38809i	−0.0461387	+	0.0799145i
$894$			10.9192i			0.365192i
$895$	26.5352	+	10.0478i	0.886974	+	0.335860i
$896$		−	0.771740i		−	0.0257820i
$897$	41.1658	−	23.7671i	1.37449	−	0.793559i
$898$		−	14.8052i		−	0.494054i
$899$	0.597773			0.0199368
$900$	20.0352	+	17.7127i	0.667839	+	0.590422i
$901$	72.4376	+	41.8219i	2.41325	+	1.39329i
$902$	20.7005			0.689251
$903$	8.04564	+	13.9354i	0.267742	+	0.463743i
$904$	6.03232	+	10.4483i	0.200632	+	0.347505i
$905$	−25.8988	−	31.6868i	−0.860904	−	1.05330i
$906$	12.5904	+	7.26908i	0.418288	+	0.241499i
$907$	8.84542	−	15.3207i	0.293707	−	0.508716i	−0.680976	−	0.732306i	$-0.738444\pi$
$907$	8.84542	−	15.3207i	0.293707	−	0.508716i	0.974683	+	0.223590i	$0.0717775\pi$
$908$	1.02793	+	1.78043i	0.0341130	+	0.0590855i
$909$	−5.78744	−	10.0241i	−0.191957	−	0.332480i
$910$	5.13092	−	4.19369i	0.170088	−	0.139019i
$911$		−	32.5046i		−	1.07693i	−0.842649	−	0.538463i	$-0.819005\pi$
$911$		−	32.5046i		−	1.07693i	0.842649	−	0.538463i	$-0.180995\pi$
$912$	−3.86345	+	6.69169i	−0.127932	+	0.221584i
$913$	52.2848	−	30.1866i	1.73037	−	0.999032i
$914$	15.3102			0.506417
$915$	−40.7087	+	6.63741i	−1.34579	+	0.219426i
$916$	1.14384	+	1.98119i	0.0377936	+	0.0654604i
$917$	−11.3244			−0.373965
$918$	43.3726	+	25.0412i	1.43151	+	0.826482i
$919$			23.2134i			0.765740i	0.923802	+	0.382870i	$0.125064\pi$
$919$			23.2134i			0.765740i	−0.923802	+	0.382870i	$0.874936\pi$
$920$	−3.39233	+	8.95880i	−0.111842	+	0.295363i
$921$	−44.1709	+	76.5063i	−1.45548	+	2.52097i
$922$	−10.5942	−	6.11657i	−0.348902	−	0.201439i
$923$	−27.4572	−	47.5572i	−0.903764	−	1.56536i
$924$	8.99144			0.295796
$925$	6.22760	+	29.7694i	0.204762	+	0.978812i
$926$	−32.4307			−1.06574
$927$	7.88334	+	13.6543i	0.258923	+	0.448467i
$928$	−2.62778	−	1.51715i	−0.0862610	−	0.0498028i
$929$	17.9995	−	31.1760i	0.590543	−	1.02285i	−0.403617	−	0.914928i	$-0.632247\pi$
$929$	17.9995	−	31.1760i	0.590543	−	1.02285i	0.994159	−	0.107922i	$-0.0344197\pi$
$930$	0.450732	−	1.19034i	0.0147801	−	0.0390327i
$931$			17.1270i			0.561315i
$932$	3.84342	+	2.21900i	0.125895	+	0.0726857i
$933$	−34.0006			−1.11313
$934$	13.6109	+	23.5748i	0.445362	+	0.771390i
$935$	65.6818	−	10.7092i	2.14802	−	0.350228i
$936$	20.5386			0.671324
$937$	13.7906	−	7.96202i	0.450520	−	0.260108i	−0.257530	−	0.966270i	$-0.582909\pi$
$937$	13.7906	−	7.96202i	0.450520	−	0.260108i	0.708050	+	0.706163i	$0.249575\pi$
$938$	−2.25673	+	3.90876i	−0.0736847	+	0.127626i
$939$			68.0763i			2.22159i
$940$	−1.78526	+	1.45916i	−0.0582286	+	0.0475924i
$941$	−30.2937	−	52.4703i	−0.987548	−	1.71048i	−0.630018	−	0.776581i	$-0.716952\pi$
$941$	−30.2937	−	52.4703i	−0.987548	−	1.71048i	−0.357530	−	0.933902i	$-0.616381\pi$
$942$	−29.2197	−	50.6099i	−0.952028	−	1.64896i
$943$	10.9965	−	19.0466i	0.358096	−	0.620241i
$944$	−6.08484	−	3.51308i	−0.198045	−	0.114341i
$945$	−7.41032	−	9.06642i	−0.241058	−	0.294931i
$946$	14.5493	+	25.2001i	0.473039	+	0.819327i
$947$	16.2294	+	28.1101i	0.527384	+	0.913455i	0.999491	+	0.0319140i	$0.0101603\pi$
$947$	16.2294	+	28.1101i	0.527384	+	0.913455i	−0.472107	+	0.881541i	$0.656506\pi$
$948$	20.3909			0.662265
$949$	10.7218	+	6.19026i	0.348046	+	0.200944i
$950$	8.85643	−	10.0177i	0.287340	−	0.325017i
$951$	−56.0849			−1.81868
$952$			5.69603i			0.184609i
$953$	0.505671	−	0.291949i	0.0163803	−	0.00945717i	−0.491787	−	0.870715i	$-0.663656\pi$
$953$	0.505671	−	0.291949i	0.0163803	−	0.00945717i	0.508168	+	0.861258i	$0.330323\pi$
$954$		−	60.6121i		−	1.96239i
$955$	−11.2934	−	4.27636i	−0.365447	−	0.138380i
$956$			8.38328i			0.271135i
$957$	17.6761	−	30.6159i	0.571387	−	0.989671i
$958$	21.8198	+	12.5977i	0.704965	+	0.407012i
$959$	−8.36506	+	14.4887i	−0.270122	+	0.467865i
$960$	−5.00247	+	4.08870i	−0.161454	+	0.131962i
$961$	30.9612			0.998748
$962$	18.7269	+	13.9613i	0.603781	+	0.450130i
$963$		−	80.7805i		−	2.60312i
$964$	−10.4145	+	6.01284i	−0.335430	+	0.193661i
$965$	−16.8514	+	44.5028i	−0.542465	+	1.43260i
$966$	4.77644	−	8.27303i	0.153679	−	0.266180i
$967$	16.7138	−	28.9491i	0.537480	−	0.930942i	−0.461559	−	0.887109i	$-0.652710\pi$
$967$	16.7138	−	28.9491i	0.537480	−	0.930942i	0.999039	−	0.0438325i	$-0.0139568\pi$
$968$	5.25964			0.169051
$969$	28.5152	−	49.3898i	0.916040	−	1.58663i
$970$	−33.6087	+	5.47978i	−1.07911	+	0.175945i
$971$	0.0961475	+	0.166532i	0.00308552	+	0.00534428i	0.867564	−	0.497325i	$-0.165685\pi$
$971$	0.0961475	+	0.166532i	0.00308552	+	0.00534428i	−0.864479	+	0.502670i	$0.832351\pi$
$972$			10.0689i			0.322960i
$973$		−	4.47122i		−	0.143341i
$974$	7.93858	+	13.7500i	0.254369	+	0.440579i
$975$	−54.3676	−	11.0407i	−1.74116	−	0.353584i
$976$		−	6.38405i		−	0.204349i
$977$	−4.06298	−	7.03729i	−0.129986	−	0.225143i	0.793685	−	0.608329i	$-0.208160\pi$
$977$	−4.06298	−	7.03729i	−0.129986	−	0.225143i	−0.923671	+	0.383187i	$0.874827\pi$
$978$	−4.17116	+	2.40822i	−0.133379	+	0.0770064i
$979$	25.1825	−	14.5391i	0.804838	−	0.464673i
$980$	−5.07127	+	13.3927i	−0.161996	+	0.427815i
$981$	29.6775	+	17.1343i	0.947531	+	0.547057i
$982$	9.59998	+	16.6277i	0.306348	+	0.530610i
$983$	−41.5447	+	23.9858i	−1.32507	+	0.765029i	−0.984532	−	0.175202i	$-0.943942\pi$
$983$	−41.5447	+	23.9858i	−1.32507	+	0.765029i	−0.340536	+	0.940231i	$0.610609\pi$
$984$	12.8457	−	7.41649i	0.409507	−	0.236429i
$985$	4.80358	+	29.4614i	0.153055	+	0.938718i
$986$	19.3950	+	11.1977i	0.617663	+	0.356608i
$987$	1.99124	−	1.14964i	0.0633818	−	0.0365935i
$988$		−	10.2694i		−	0.326713i
$989$	30.9156			0.983058
$990$	−30.5187	−	37.3392i	−0.969947	−	1.18672i
$991$			12.5205i			0.397727i	0.980027	+	0.198864i	$0.0637251\pi$
$991$			12.5205i			0.397727i	−0.980027	+	0.198864i	$0.936275\pi$
$992$	0.170612	+	0.0985027i	0.00541693	+	0.00312746i
$993$	67.3193			2.13631
$994$	−9.55751	−	5.51803i	−0.303146	−	0.175021i
$995$	0.460339	+	0.174311i	0.0145937	+	0.00552605i
$996$	21.6303	−	37.4647i	0.685381	−	1.18712i
$997$	−0.817867	−	1.41659i	−0.0259021	−	0.0448637i	0.852784	−	0.522264i	$-0.174912\pi$
$997$	−0.817867	−	1.41659i	−0.0259021	−	0.0448637i	−0.878686	+	0.477400i	$0.841579\pi$
$998$			30.9115i			0.978486i
$999$	24.6698	−	33.0908i	0.780518	−	1.04695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.m.c.159.7	✓	16
5.4	even	2		370.2.m.d.159.2	yes	16
37.27	even	6		370.2.m.d.249.2	yes	16
185.64	even	6	inner	370.2.m.c.249.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.m.c.159.7	✓	16	1.1	even	1	trivial
370.2.m.c.249.7	yes	16	185.64	even	6	inner
370.2.m.d.159.2	yes	16	5.4	even	2
370.2.m.d.249.2	yes	16	37.27	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(2.50227 + 1.44468i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.791839 + 2.09117i) q^{5} -2.88937i q^{6} +(0.668346 + 0.385870i) q^{7} +1.00000 q^{8} +(2.67422 + 4.63189i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(2.50227 + 1.44468i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.791839 + 2.09117i) q^{5} -2.88937i q^{6} +(0.668346 + 0.385870i) q^{7} +1.00000 q^{8} +(2.67422 + 4.63189i) q^{9} +(2.20693 - 0.359832i) q^{10} -4.03232 q^{11} +(-2.50227 + 1.44468i) q^{12} +(1.92005 - 3.32562i) q^{13} -0.771740i q^{14} +(-5.00247 + 4.08870i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.69038 + 6.39193i) q^{17} +(2.67422 - 4.63189i) q^{18} +(-2.31597 - 1.33713i) q^{19} +(-1.41509 - 1.73134i) q^{20} +(1.11492 + 1.93110i) q^{21} +(2.01616 + 3.49210i) q^{22} +4.28411 q^{23} +(2.50227 + 1.44468i) q^{24} +(-3.74598 - 3.31174i) q^{25} -3.84010 q^{26} +6.78552i q^{27} +(-0.668346 + 0.385870i) q^{28} +3.03430i q^{29} +(6.04216 + 2.28792i) q^{30} -0.197005i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-10.0899 - 5.82543i) q^{33} +(3.69038 - 6.39193i) q^{34} +(-1.33614 + 1.09208i) q^{35} -5.34844 q^{36} +(-4.87668 - 3.63566i) q^{37} +2.67425i q^{38} +(9.60895 - 5.54773i) q^{39} +(-0.791839 + 2.09117i) q^{40} +(2.56682 - 4.44586i) q^{41} +(1.11492 - 1.93110i) q^{42} +7.21634 q^{43} +(2.01616 - 3.49210i) q^{44} +(-11.8036 + 1.92454i) q^{45} +(-2.14205 - 3.71015i) q^{46} -1.03114i q^{47} -2.88937i q^{48} +(-3.20221 - 5.54639i) q^{49} +(-0.995062 + 4.89998i) q^{50} +21.3258i q^{51} +(1.92005 + 3.32562i) q^{52} +(9.81438 - 5.66633i) q^{53} +(5.87643 - 3.39276i) q^{54} +(3.19295 - 8.43227i) q^{55} +(0.668346 + 0.385870i) q^{56} +(-3.86345 - 6.69169i) q^{57} +(2.62778 - 1.51715i) q^{58} +(6.08484 - 3.51308i) q^{59} +(-1.03969 - 6.37662i) q^{60} +(5.52875 + 3.19203i) q^{61} +(-0.170612 + 0.0985027i) q^{62} +4.12761i q^{63} +1.00000 q^{64} +(5.43407 + 6.64851i) q^{65} +11.6509i q^{66} +(-5.06487 - 2.92421i) q^{67} -7.38077 q^{68} +(10.7200 + 6.18918i) q^{69} +(1.61384 + 0.611094i) q^{70} +(7.15012 - 12.3844i) q^{71} +(2.67422 + 4.63189i) q^{72} +3.22401i q^{73} +(-0.710230 + 6.04116i) q^{74} +(-4.58902 - 13.6986i) q^{75} +(2.31597 - 1.33713i) q^{76} +(-2.69499 - 1.55595i) q^{77} +(-9.60895 - 5.54773i) q^{78} +(-6.11172 - 3.52860i) q^{79} +(2.20693 - 0.359832i) q^{80} +(-1.78026 + 3.08350i) q^{81} -5.13364 q^{82} +(-12.9664 + 7.48616i) q^{83} -2.22984 q^{84} +(-16.2888 + 2.65583i) q^{85} +(-3.60817 - 6.24953i) q^{86} +(-4.38360 + 7.59262i) q^{87} -4.03232 q^{88} +(-6.24517 + 3.60565i) q^{89} +(7.56851 + 9.25996i) q^{90} +(2.56652 - 1.48178i) q^{91} +(-2.14205 + 3.71015i) q^{92} +(0.284611 - 0.492960i) q^{93} +(-0.892995 + 0.515571i) q^{94} +(4.63003 - 3.78430i) q^{95} +(-2.50227 + 1.44468i) q^{96} -15.2287 q^{97} +(-3.20221 + 5.54639i) q^{98} +(-10.7833 - 18.6773i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9}+O(q^{10}) \) 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9	\( 16 q - 8 q^{2} + 3 q^{3} - 8 q^{4} + 6 q^{5} + 12 q^{7} + 16 q^{8} + 13 q^{9} - 6 q^{10} - 6 q^{11} - 3 q^{12} + 6 q^{13} - 9 q^{15} - 8 q^{16} + 13 q^{18} - 3 q^{19} - 6 q^{21} + 3 q^{22} + 22 q^{23} + 3 q^{24} - 6 q^{25} - 12 q^{26} - 12 q^{28} - 9 q^{30} - 8 q^{32} - 6 q^{33} + 12 q^{35} - 26 q^{36} - 16 q^{37} + 15 q^{39} + 6 q^{40} + 7 q^{41} - 6 q^{42} + 22 q^{43} + 3 q^{44} - 4 q^{45} - 11 q^{46} + 4 q^{49} - 6 q^{50} + 6 q^{52} - 3 q^{53} + 9 q^{54} - 25 q^{55} + 12 q^{56} - 18 q^{57} - 36 q^{58} + 15 q^{59} + 18 q^{60} + 12 q^{61} + 33 q^{62} + 16 q^{64} - 26 q^{65} - 24 q^{67} + 42 q^{69} - 18 q^{70} - 4 q^{71} + 13 q^{72} + 5 q^{74} - 10 q^{75} + 3 q^{76} + 24 q^{77} - 15 q^{78} - 6 q^{80} + 10 q^{81} - 14 q^{82} - 6 q^{83} + 12 q^{84} - 26 q^{85} - 11 q^{86} - 50 q^{87} - 6 q^{88} + 9 q^{89} + 5 q^{90} - 24 q^{91} - 11 q^{92} + 25 q^{93} - 27 q^{94} + 49 q^{95} - 3 q^{96} - 68 q^{97} + 4 q^{98} + 37 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 + 3 * q^3 - 8 * q^4 + 6 * q^5 + 12 * q^7 + 16 * q^8 + 13 * q^9 - 6 * q^10 - 6 * q^11 - 3 * q^12 + 6 * q^13 - 9 * q^15 - 8 * q^16 + 13 * q^18 - 3 * q^19 - 6 * q^21 + 3 * q^22 + 22 * q^23 + 3 * q^24 - 6 * q^25 - 12 * q^26 - 12 * q^28 - 9 * q^30 - 8 * q^32 - 6 * q^33 + 12 * q^35 - 26 * q^36 - 16 * q^37 + 15 * q^39 + 6 * q^40 + 7 * q^41 - 6 * q^42 + 22 * q^43 + 3 * q^44 - 4 * q^45 - 11 * q^46 + 4 * q^49 - 6 * q^50 + 6 * q^52 - 3 * q^53 + 9 * q^54 - 25 * q^55 + 12 * q^56 - 18 * q^57 - 36 * q^58 + 15 * q^59 + 18 * q^60 + 12 * q^61 + 33 * q^62 + 16 * q^64 - 26 * q^65 - 24 * q^67 + 42 * q^69 - 18 * q^70 - 4 * q^71 + 13 * q^72 + 5 * q^74 - 10 * q^75 + 3 * q^76 + 24 * q^77 - 15 * q^78 - 6 * q^80 + 10 * q^81 - 14 * q^82 - 6 * q^83 + 12 * q^84 - 26 * q^85 - 11 * q^86 - 50 * q^87 - 6 * q^88 + 9 * q^89 + 5 * q^90 - 24 * q^91 - 11 * q^92 + 25 * q^93 - 27 * q^94 + 49 * q^95 - 3 * q^96 - 68 * q^97 + 4 * q^98 + 37 * q^99

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