LMFDB - Embedded newform 360.2.bm.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.a.131.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39929 - 0.204905i) q^{2} +(0.875353 - 1.49458i) q^{3} +(1.91603 + 0.573443i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.53112 + 1.91198i) q^{6} +(-1.05351 - 0.608247i) q^{7} +(-2.56358 - 1.19502i) q^{8} +(-1.46751 - 2.61656i) q^{9} +O(q^{10})$	\(q+(-1.39929 - 0.204905i) q^{2} +(0.875353 - 1.49458i) q^{3} +(1.91603 + 0.573443i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.53112 + 1.91198i) q^{6} +(-1.05351 - 0.608247i) q^{7} +(-2.56358 - 1.19502i) q^{8} +(-1.46751 - 2.61656i) q^{9} +(0.522192 + 1.31427i) q^{10} +(-2.23529 - 1.29055i) q^{11} +(2.53425 - 2.36168i) q^{12} +(-4.16652 + 2.40554i) q^{13} +(1.34954 + 1.06698i) q^{14} +(-1.73202 - 0.0107898i) q^{15} +(3.34233 + 2.19747i) q^{16} -5.97195i q^{17} +(1.51733 + 3.96203i) q^{18} +4.69437 q^{19} +(-0.461398 - 1.94605i) q^{20} +(-1.83127 + 1.04213i) q^{21} +(2.86338 + 2.26387i) q^{22} +(-0.866377 - 1.50061i) q^{23} +(-4.03008 + 2.78540i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(6.32307 - 2.51231i) q^{26} +(-5.19525 - 0.0971033i) q^{27} +(-1.66977 - 1.76955i) q^{28} +(-3.85425 + 6.67576i) q^{29} +(2.42138 + 0.369997i) q^{30} +(4.30506 - 2.48553i) q^{31} +(-4.22661 - 3.75975i) q^{32} +(-3.88549 + 2.21113i) q^{33} +(-1.22368 + 8.35649i) q^{34} +1.21649i q^{35} +(-1.31135 - 5.85494i) q^{36} -8.33096i q^{37} +(-6.56878 - 0.961899i) q^{38} +(-0.0519106 + 8.33287i) q^{39} +(0.246874 + 2.81763i) q^{40} +(-2.00948 + 1.16017i) q^{41} +(2.77601 - 1.08300i) q^{42} +(-1.97426 + 3.41951i) q^{43} +(-3.54283 - 3.75454i) q^{44} +(-1.53225 + 2.57919i) q^{45} +(0.904830 + 2.27731i) q^{46} +(3.25544 - 5.63858i) q^{47} +(6.20999 - 3.07180i) q^{48} +(-2.76007 - 4.78058i) q^{49} +(0.877098 - 1.10937i) q^{50} +(-8.92553 - 5.22756i) q^{51} +(-9.36260 + 2.21982i) q^{52} +0.0729656 q^{53} +(7.24976 + 1.20041i) q^{54} +2.58109i q^{55} +(1.97390 + 2.81826i) q^{56} +(4.10923 - 7.01609i) q^{57} +(6.76112 - 8.55158i) q^{58} +(5.32751 - 3.07584i) q^{59} +(-3.31241 - 1.01389i) q^{60} +(-9.89571 - 5.71329i) q^{61} +(-6.53333 + 2.59585i) q^{62} +(-0.0454680 + 3.64920i) q^{63} +(5.14387 + 6.12704i) q^{64} +(4.16652 + 2.40554i) q^{65} +(5.89000 - 2.29786i) q^{66} +(2.59541 + 4.49538i) q^{67} +(3.42457 - 11.4424i) q^{68} +(-3.00116 - 0.0186961i) q^{69} +(0.249266 - 1.70223i) q^{70} +9.50092 q^{71} +(0.635251 + 8.46147i) q^{72} +10.7517 q^{73} +(-1.70706 + 11.6574i) q^{74} +(0.856664 + 1.50537i) q^{75} +(8.99454 + 2.69195i) q^{76} +(1.56994 + 2.71922i) q^{77} +(1.78008 - 11.6495i) q^{78} +(9.17877 + 5.29936i) q^{79} +(0.231899 - 3.99327i) q^{80} +(-4.69280 + 7.67969i) q^{81} +(3.04957 - 1.21167i) q^{82} +(5.02858 + 2.90325i) q^{83} +(-4.10636 + 0.946616i) q^{84} +(-5.17186 + 2.98597i) q^{85} +(3.46324 - 4.38036i) q^{86} +(6.60360 + 11.6041i) q^{87} +(4.18812 + 5.97963i) q^{88} +11.5646i q^{89} +(2.67255 - 3.29506i) q^{90} +5.85265 q^{91} +(-0.799488 - 3.37203i) q^{92} +(0.0536368 - 8.60996i) q^{93} +(-5.71068 + 7.22296i) q^{94} +(-2.34718 - 4.06544i) q^{95} +(-9.31901 + 3.02588i) q^{96} +(4.84693 - 8.39513i) q^{97} +(2.88258 + 7.25498i) q^{98} +(-0.0964717 + 7.74268i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * q^96 + 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.39929	−	0.204905i	−0.989448	−	0.144890i
$2$	−1.39929	−	0.204905i	−0.989448	−	0.144890i
$3$	0.875353	−	1.49458i	0.505385	−	0.862894i
$3$	0.875353	−	1.49458i	0.505385	−	0.862894i
$4$	1.91603	+	0.573443i	0.958014	+	0.286722i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−1.53112	+	1.91198i	−0.625077	+	0.780563i
$7$	−1.05351	−	0.608247i	−0.398191	−	0.229896i	0.287512	−	0.957777i	$-0.407172\pi$
$7$	−1.05351	−	0.608247i	−0.398191	−	0.229896i	−0.685703	+	0.727881i	$0.740505\pi$
$8$	−2.56358	−	1.19502i	−0.906362	−	0.422502i
$9$	−1.46751	−	2.61656i	−0.489172	−	0.872188i
$10$	0.522192	+	1.31427i	0.165132	+	0.415610i
$11$	−2.23529	−	1.29055i	−0.673966	−	0.389115i	0.123612	−	0.992331i	$-0.460552\pi$
$11$	−2.23529	−	1.29055i	−0.673966	−	0.389115i	−0.797578	+	0.603216i	$0.793886\pi$
$12$	2.53425	−	2.36168i	0.731576	−	0.681759i
$13$	−4.16652	+	2.40554i	−1.15558	+	0.667176i	−0.950242	−	0.311514i	$-0.899164\pi$
$13$	−4.16652	+	2.40554i	−1.15558	+	0.667176i	−0.205342	+	0.978690i	$0.565831\pi$
$14$	1.34954	+	1.06698i	0.360680	+	0.285164i
$15$	−1.73202	−	0.0107898i	−0.447205	−	0.00278592i
$16$	3.34233	+	2.19747i	0.835581	+	0.549367i
$17$		−	5.97195i		−	1.44841i	−0.689584	−	0.724205i	$-0.742207\pi$
$17$		−	5.97195i		−	1.44841i	0.689584	−	0.724205i	$-0.257793\pi$
$18$	1.51733	+	3.96203i	0.357639	+	0.933860i
$19$	4.69437			1.07696			0.538481	−	0.842638i	$-0.318998\pi$
$19$	4.69437			1.07696			0.538481	+	0.842638i	$0.318998\pi$
$20$	−0.461398	−	1.94605i	−0.103172	−	0.435150i
$21$	−1.83127	+	1.04213i	−0.399615	+	0.227411i
$22$	2.86338	+	2.26387i	0.610476	+	0.482659i
$23$	−0.866377	−	1.50061i	−0.180652	−	0.312898i	0.761451	−	0.648223i	$-0.224487\pi$
$23$	−0.866377	−	1.50061i	−0.180652	−	0.312898i	−0.942103	+	0.335324i	$0.891154\pi$
$24$	−4.03008	+	2.78540i	−0.822637	+	0.568568i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	6.32307	−	2.51231i	1.24006	−	0.492704i
$27$	−5.19525	−	0.0971033i	−0.999825	−	0.0186875i
$28$	−1.66977	−	1.76955i	−0.315557	−	0.334413i
$29$	−3.85425	+	6.67576i	−0.715717	+	1.23966i	0.246965	+	0.969024i	$0.420567\pi$
$29$	−3.85425	+	6.67576i	−0.715717	+	1.23966i	−0.962682	+	0.270634i	$0.912767\pi$
$30$	2.42138	+	0.369997i	0.442082	+	0.0675519i
$31$	4.30506	−	2.48553i	0.773212	−	0.446414i	−0.0608069	−	0.998150i	$-0.519367\pi$
$31$	4.30506	−	2.48553i	0.773212	−	0.446414i	0.834019	+	0.551735i	$0.186034\pi$
$32$	−4.22661	−	3.75975i	−0.747167	−	0.664637i
$33$	−3.88549	+	2.21113i	−0.676377	+	0.384909i
$34$	−1.22368	+	8.35649i	−0.209860	+	1.43313i
$35$			1.21649i			0.205625i
$36$	−1.31135	−	5.85494i	−0.218558	−	0.975824i
$37$		−	8.33096i		−	1.36960i	−0.728730	−	0.684801i	$-0.759889\pi$
$37$		−	8.33096i		−	1.36960i	0.728730	−	0.684801i	$-0.240111\pi$
$38$	−6.56878	−	0.961899i	−1.06560	−	0.156041i
$39$	−0.0519106	+	8.33287i	−0.00831236	+	1.33433i
$40$	0.246874	+	2.81763i	0.0390342	+	0.445507i
$41$	−2.00948	+	1.16017i	−0.313827	+	0.181188i	−0.648638	−	0.761097i	$-0.724661\pi$
$41$	−2.00948	+	1.16017i	−0.313827	+	0.181188i	0.334810	+	0.942285i	$0.391328\pi$
$42$	2.77601	−	1.08300i	0.428348	−	0.167111i
$43$	−1.97426	+	3.41951i	−0.301071	+	0.521471i	−0.976379	−	0.216065i	$-0.930678\pi$
$43$	−1.97426	+	3.41951i	−0.301071	+	0.521471i	0.675307	+	0.737536i	$0.264011\pi$
$44$	−3.54283	−	3.75454i	−0.534101	−	0.566018i
$45$	−1.53225	+	2.57919i	−0.228415	+	0.384482i
$46$	0.904830	+	2.27731i	0.133410	+	0.335771i
$47$	3.25544	−	5.63858i	0.474854	−	0.822472i	−0.524731	−	0.851268i	$-0.675834\pi$
$47$	3.25544	−	5.63858i	0.474854	−	0.822472i	0.999585	+	0.0287964i	$0.00916743\pi$
$48$	6.20999	−	3.07180i	0.896336	−	0.443376i
$49$	−2.76007	−	4.78058i	−0.394296	−	0.682941i
$50$	0.877098	−	1.10937i	0.124040	−	0.156888i
$51$	−8.92553	−	5.22756i	−1.24982	−	0.732005i
$52$	−9.36260	+	2.21982i	−1.29836	+	0.307834i
$53$	0.0729656			0.0100226			0.00501130	−	0.999987i	$-0.498405\pi$
$53$	0.0729656			0.0100226			0.00501130	+	0.999987i	$0.498405\pi$
$54$	7.24976	+	1.20041i	0.986567	+	0.163355i
$55$			2.58109i			0.348035i
$56$	1.97390	+	2.81826i	0.263774	+	0.376605i
$57$	4.10923	−	7.01609i	0.544280	−	0.929303i
$58$	6.76112	−	8.55158i	0.887778	−	1.12288i
$59$	5.32751	−	3.07584i	0.693582	−	0.400440i	−0.111370	−	0.993779i	$-0.535524\pi$
$59$	5.32751	−	3.07584i	0.693582	−	0.400440i	0.804953	+	0.593339i	$0.202191\pi$
$60$	−3.31241	−	1.01389i	−0.427630	−	0.130892i
$61$	−9.89571	−	5.71329i	−1.26702	−	0.731512i	−0.292594	−	0.956237i	$-0.594518\pi$
$61$	−9.89571	−	5.71329i	−1.26702	−	0.731512i	−0.974422	+	0.224725i	$0.927852\pi$
$62$	−6.53333	+	2.59585i	−0.829734	+	0.329673i
$63$	−0.0454680	+	3.64920i	−0.00572843	+	0.459756i
$64$	5.14387	+	6.12704i	0.642983	+	0.765880i
$65$	4.16652	+	2.40554i	0.516793	+	0.298370i
$66$	5.89000	−	2.29786i	0.725009	−	0.282847i
$67$	2.59541	+	4.49538i	0.317080	+	0.549199i	0.979877	−	0.199600i	$-0.0639643\pi$
$67$	2.59541	+	4.49538i	0.317080	+	0.549199i	−0.662798	+	0.748799i	$0.730631\pi$
$68$	3.42457	−	11.4424i	0.415291	−	1.38760i
$69$	−3.00116	−	0.0186961i	−0.361297	−	0.00225074i
$70$	0.249266	−	1.70223i	0.0297929	−	0.203455i
$71$	9.50092			1.12755			0.563776	−	0.825928i	$-0.309348\pi$
$71$	9.50092			1.12755			0.563776	+	0.825928i	$0.309348\pi$
$72$	0.635251	+	8.46147i	0.0748651	+	0.997194i
$73$	10.7517			1.25839			0.629194	−	0.777248i	$-0.283385\pi$
$73$	10.7517			1.25839			0.629194	+	0.777248i	$0.283385\pi$
$74$	−1.70706	+	11.6574i	−0.198441	+	1.35515i
$75$	0.856664	+	1.50537i	0.0989191	+	0.173825i
$76$	8.99454	+	2.69195i	1.03174	+	0.308788i
$77$	1.56994	+	2.71922i	0.178912	+	0.309884i
$78$	1.78008	−	11.6495i	0.201555	−	1.31904i
$79$	9.17877	+	5.29936i	1.03269	+	0.596225i	0.917755	−	0.397148i	$-0.130000\pi$
$79$	9.17877	+	5.29936i	1.03269	+	0.596225i	0.114937	+	0.993373i	$0.463333\pi$
$80$	0.231899	−	3.99327i	0.0259271	−	0.446461i
$81$	−4.69280	+	7.67969i	−0.521422	+	0.853299i
$82$	3.04957	−	1.21167i	0.336768	−	0.133806i
$83$	5.02858	+	2.90325i	0.551958	+	0.318673i	0.749912	−	0.661538i	$-0.230096\pi$
$83$	5.02858	+	2.90325i	0.551958	+	0.318673i	−0.197953	+	0.980212i	$0.563429\pi$
$84$	−4.10636	+	0.946616i	−0.448041	+	0.103284i
$85$	−5.17186	+	2.98597i	−0.560967	+	0.323874i
$86$	3.46324	−	4.38036i	0.373450	−	0.472346i
$87$	6.60360	+	11.6041i	0.707981	+	1.24409i
$88$	4.18812	+	5.97963i	0.446455	+	0.637431i
$89$			11.5646i			1.22584i	0.790144	+	0.612922i	$0.210006\pi$
$89$			11.5646i			1.22584i	−0.790144	+	0.612922i	$0.789994\pi$
$90$	2.67255	−	3.29506i	0.281712	−	0.347330i
$91$	5.85265			0.613524
$92$	−0.799488	−	3.37203i	−0.0833524	−	0.351558i
$93$	0.0536368	−	8.60996i	0.00556188	−	0.892812i
$94$	−5.71068	+	7.22296i	−0.589011	+	0.744991i
$95$	−2.34718	−	4.06544i	−0.240816	−	0.417105i
$96$	−9.31901	+	3.02588i	−0.951118	+	0.308828i
$97$	4.84693	−	8.39513i	0.492131	−	0.852397i	−0.507828	−	0.861459i	$-0.669551\pi$
$97$	4.84693	−	8.39513i	0.492131	−	0.852397i	0.999959	+	0.00906220i	$0.00288463\pi$
$98$	2.88258	+	7.25498i	0.291184	+	0.732863i
$99$	−0.0964717	+	7.74268i	−0.00969577	+	0.778169i
$100$	−1.45463	+	1.37261i	−0.145463	+	0.137261i
$101$	7.59244	−	13.1505i	0.755476	−	1.30852i	−0.189662	−	0.981849i	$-0.560739\pi$
$101$	7.59244	−	13.1505i	0.755476	−	1.30852i	0.945138	−	0.326673i	$-0.105927\pi$
$102$	11.4183	+	9.14377i	1.13058	+	0.905368i
$103$	1.69567	−	0.978998i	0.167080	−	0.0964635i	−0.414128	−	0.910218i	$-0.635914\pi$
$103$	1.69567	−	0.978998i	0.167080	−	0.0964635i	0.581208	+	0.813755i	$0.302580\pi$
$104$	13.5558	−	1.18773i	1.32926	−	0.116466i
$105$	1.81814	+	1.06486i	0.177433	+	0.103920i
$106$	−0.102100	−	0.0149510i	−0.00991683	−	0.00145217i
$107$			12.6109i			1.21914i	0.792731	+	0.609571i	$0.208658\pi$
$107$			12.6109i			1.21914i	−0.792731	+	0.609571i	$0.791342\pi$
$108$	−9.89855	−	3.16523i	−0.952489	−	0.304574i
$109$		−	16.4111i		−	1.57190i	−0.618289	−	0.785951i	$-0.712174\pi$
$109$		−	16.4111i		−	1.57190i	0.618289	−	0.785951i	$-0.287826\pi$
$110$	0.528879	−	3.61170i	0.0504266	−	0.344362i
$111$	−12.4513	−	7.29253i	−1.18182	−	0.692177i
$112$	−2.18459	−	4.34802i	−0.206424	−	0.410849i
$113$	3.88446	−	2.24269i	0.365419	−	0.210975i	−0.306036	−	0.952020i	$-0.599003\pi$
$113$	3.88446	−	2.24269i	0.365419	−	0.210975i	0.671455	+	0.741045i	$0.265669\pi$
$114$	−7.18763	+	8.97554i	−0.673184	+	0.840637i
$115$	−0.866377	+	1.50061i	−0.0807900	+	0.139932i
$116$	−11.2130	+	10.5808i	−1.04110	+	0.982398i
$117$	12.4087	+	7.37179i	1.14718	+	0.681522i
$118$	−8.08498	+	3.21236i	−0.744283	+	0.295721i
$119$	−3.63242	+	6.29154i	−0.332983	+	0.576744i
$120$	4.42727	+	2.09745i	0.404152	+	0.191470i
$121$	−2.16898	−	3.75678i	−0.197180	−	0.341525i
$122$	12.6763	+	10.0222i	1.14766	+	0.907370i
$123$	−0.0250361	+	4.01887i	−0.00225743	+	0.362370i
$124$	9.67393	−	2.29364i	0.868745	−	0.205975i
$125$	1.00000			0.0894427
$126$	0.811362	−	5.09697i	0.0722819	−	0.454074i
$127$		−	7.36428i		−	0.653474i	−0.945115	−	0.326737i	$-0.894051\pi$
$127$		−	7.36428i		−	0.653474i	0.945115	−	0.326737i	$-0.105949\pi$
$128$	−5.94230	−	9.62751i	−0.525230	−	0.850960i
$129$	3.38255	+	5.94396i	0.297817	+	0.523336i
$130$	−5.33726	−	4.21979i	−0.468109	−	0.370100i
$131$	5.06837	−	2.92622i	0.442825	−	0.255665i	−0.261970	−	0.965076i	$-0.584372\pi$
$131$	5.06837	−	2.92622i	0.442825	−	0.255665i	0.704795	+	0.709411i	$0.251039\pi$
$132$	−8.71267	+	2.00848i	−0.758340	+	0.174816i
$133$	−4.94558	−	2.85533i	−0.428836	−	0.247589i
$134$	−2.71061	−	6.82216i	−0.234161	−	0.589345i
$135$	2.51353	+	4.54777i	0.216330	+	0.391409i
$136$	−7.13658	+	15.3096i	−0.611957	+	1.31278i
$137$	−4.74083	−	2.73712i	−0.405037	−	0.233848i	0.283618	−	0.958937i	$-0.408465\pi$
$137$	−4.74083	−	2.73712i	−0.405037	−	0.233848i	−0.688655	+	0.725089i	$0.741799\pi$
$138$	4.19566	+	0.641114i	0.357158	+	0.0545752i
$139$	−7.85671	−	13.6082i	−0.666397	−	1.15423i	−0.978904	−	0.204318i	$-0.934502\pi$
$139$	−7.85671	−	13.6082i	−0.666397	−	1.15423i	0.312507	−	0.949915i	$-0.398831\pi$
$140$	−0.697590	+	2.33084i	−0.0589571	+	0.196992i
$141$	−5.57763	−	9.80125i	−0.469721	−	0.825414i
$142$	−13.2945	−	1.94679i	−1.11565	−	0.163371i
$143$	12.4178			1.03843
$144$	0.844896	−	11.9702i	0.0704080	−	0.997518i
$145$	7.70851			0.640157
$146$	−15.0447	−	2.20307i	−1.24511	−	0.182328i
$147$	−9.56098	−	0.0595613i	−0.788577	−	0.00491254i
$148$	4.77733	−	15.9624i	0.392694	−	1.31210i
$149$	4.95490	+	8.58214i	0.405921	+	0.703076i	0.994428	−	0.105416i	$-0.0336174\pi$
$149$	4.95490	+	8.58214i	0.405921	+	0.703076i	−0.588507	+	0.808492i	$0.700284\pi$
$150$	−0.890265	−	2.28198i	−0.0726899	−	0.186323i
$151$	15.8283	+	9.13850i	1.28809	+	0.743681i	0.978314	−	0.207128i	$-0.0664117\pi$
$151$	15.8283	+	9.13850i	1.28809	+	0.743681i	0.309779	+	0.950809i	$0.399745\pi$
$152$	−12.0344	−	5.60985i	−0.976117	−	0.455019i
$153$	−15.6260	+	8.76392i	−1.26329	+	0.708521i
$154$	−1.63962	−	4.12667i	−0.132125	−	0.332536i
$155$	−4.30506	−	2.48553i	−0.345791	−	0.199643i
$156$	−4.87789	+	15.9362i	−0.390544	+	1.27592i
$157$	−14.0146	+	8.09131i	−1.11848	+	0.645757i	−0.941013	−	0.338369i	$-0.890125\pi$
$157$	−14.0146	+	8.09131i	−1.11848	+	0.645757i	−0.177470	+	0.984126i	$0.556791\pi$
$158$	−11.7579	−	9.29612i	−0.935408	−	0.739560i
$159$	0.0638706	−	0.109053i	0.00506527	−	0.00864843i
$160$	−1.14273	+	5.54023i	−0.0903411	+	0.437994i
$161$			2.10788i			0.166125i
$162$	8.14020	−	9.78454i	0.639554	−	0.768746i
$163$	3.31163			0.259387			0.129694	−	0.991554i	$-0.458601\pi$
$163$	3.31163			0.259387			0.129694	+	0.991554i	$0.458601\pi$
$164$	−4.51551	+	1.07060i	−0.352602	+	0.0835999i
$165$	3.85764	+	2.25937i	0.300317	+	0.175892i
$166$	−6.44155	−	5.09288i	−0.499962	−	0.395284i
$167$	−7.68558	−	13.3118i	−0.594728	−	1.03010i	−0.993585	−	0.113086i	$-0.963926\pi$
$167$	−7.68558	−	13.3118i	−0.594728	−	1.03010i	0.398857	−	0.917013i	$-0.369407\pi$
$168$	5.93996	−	0.483177i	0.458278	−	0.0372779i
$169$	5.07323	−	8.78710i	0.390249	−	0.675931i
$170$	7.84878	−	3.11851i	0.601974	−	0.239179i
$171$	−6.88905	−	12.2831i	−0.526819	−	0.939312i
$172$	−5.74363	+	5.41976i	−0.437948	+	0.413253i
$173$	−6.53975	+	11.3272i	−0.497208	+	0.861189i	−0.999995	−	0.00322120i	$-0.998975\pi$
$173$	−6.53975	+	11.3272i	−0.497208	+	0.861189i	0.502787	+	0.864410i	$0.332308\pi$
$174$	−6.86262	−	17.5907i	−0.520254	−	1.33354i
$175$	1.05351	−	0.608247i	0.0796382	−	0.0459791i
$176$	−4.63514	−	9.22541i	−0.349387	−	0.695391i
$177$	0.0663754	−	10.6548i	0.00498908	−	0.800864i
$178$	2.36964	−	16.1822i	0.177612	−	1.21291i
$179$			23.9509i			1.79018i	0.445889	+	0.895088i	$0.352888\pi$
$179$			23.9509i			1.79018i	−0.445889	+	0.895088i	$0.647112\pi$
$180$	−4.41486	+	4.06313i	−0.329064	+	0.302848i
$181$			12.1088i			0.900040i	0.893018	+	0.450020i	$0.148583\pi$
$181$			12.1088i			0.900040i	−0.893018	+	0.450020i	$0.851417\pi$
$182$	−8.18955	−	1.19924i	−0.607050	−	0.0888933i
$183$	−17.2012	+	9.78874i	−1.27155	+	0.723605i
$184$	0.427771	+	4.88226i	0.0315357	+	0.359925i
$185$	−7.21483	+	4.16548i	−0.530445	+	0.306252i
$186$	−1.83928	+	12.0368i	−0.134862	+	0.882585i
$187$	−7.70708	+	13.3491i	−0.563598	+	0.976180i
$188$	9.47091	−	8.93687i	0.690737	−	0.651788i
$189$	5.41420	+	3.26229i	0.393825	+	0.237297i
$190$	2.45136	+	6.16968i	0.177840	+	0.447596i
$191$	8.16239	−	14.1377i	0.590610	−	1.02297i	−0.403540	−	0.914962i	$-0.632221\pi$
$191$	8.16239	−	14.1377i	0.590610	−	1.02297i	0.994150	−	0.108005i	$-0.0344461\pi$
$192$	13.6600	−	2.32458i	0.985828	−	0.167762i
$193$	0.0649670	+	0.112526i	0.00467643	+	0.00809981i	0.868354	−	0.495945i	$-0.165178\pi$
$193$	0.0649670	+	0.112526i	0.00467643	+	0.00809981i	−0.863678	+	0.504044i	$0.831845\pi$
$194$	−8.50247	+	10.7541i	−0.610442	+	0.772097i
$195$	7.24243	−	4.12148i	0.518641	−	0.295145i
$196$	−2.54698	−	10.7425i	−0.181927	−	0.767320i
$197$	13.7825			0.981960			0.490980	−	0.871171i	$-0.336639\pi$
$197$	13.7825			0.981960			0.490980	+	0.871171i	$0.336639\pi$
$198$	1.72151	−	10.8145i	0.122342	−	0.768553i
$199$		−	12.6790i		−	0.898787i	−0.893334	−	0.449394i	$-0.851640\pi$
$199$		−	12.6790i		−	0.898787i	0.893334	−	0.449394i	$-0.148360\pi$
$200$	2.31670	−	1.62262i	0.163816	−	0.114736i
$201$	8.99059	+	0.0560080i	0.634148	+	0.00395050i
$202$	−13.3186	+	16.8456i	−0.937095	+	1.18525i
$203$	8.12102	−	4.68868i	0.569984	−	0.329081i
$204$	−14.1039	−	15.1344i	−0.987468	−	1.05962i
$205$	2.00948	+	1.16017i	0.140348	+	0.0810299i
$206$	−2.57334	+	1.02245i	−0.179293	+	0.0712375i
$207$	−2.65502	+	4.46909i	−0.184536	+	0.310623i
$208$	−19.2119	−	1.11568i	−1.33211	−	0.0773587i
$209$	−10.4933	−	6.05830i	−0.725836	−	0.419061i
$210$	−2.32591	−	1.86260i	−0.160503	−	0.128531i
$211$	−9.91972	−	17.1815i	−0.682902	−	1.18282i	−0.974091	−	0.226155i	$-0.927384\pi$
$211$	−9.91972	−	17.1815i	−0.682902	−	1.18282i	0.291190	−	0.956665i	$-0.405949\pi$
$212$	0.139804	+	0.0418416i	0.00960178	+	0.00287369i
$213$	8.31666	−	14.1998i	0.569848	−	0.972958i
$214$	2.58404	−	17.6463i	0.176641	−	1.20628i
$215$	3.94851			0.269286
$216$	13.2024	+	6.45734i	0.898308	+	0.439366i
$217$	−6.04726			−0.410515
$218$	−3.36272	+	22.9640i	−0.227752	+	1.55532i
$219$	9.41151	−	16.0692i	0.635971	−	1.08586i
$220$	−1.48011	+	4.94545i	−0.0997891	+	0.333422i
$221$	14.3658	+	24.8822i	0.966345	+	1.67376i
$222$	15.9287	+	12.7557i	1.06906	+	0.856106i
$223$	−3.61346	−	2.08623i	−0.241975	−	0.139704i	0.374109	−	0.927385i	$-0.377949\pi$
$223$	−3.61346	−	2.08623i	−0.241975	−	0.139704i	−0.616084	+	0.787680i	$0.711282\pi$
$224$	2.16594	+	6.53178i	0.144718	+	0.436423i
$225$	2.99977	+	0.0373763i	0.199984	+	0.00249175i
$226$	−5.89503	+	2.34224i	−0.392132	+	0.155803i
$227$	−3.92457	−	2.26585i	−0.260483	−	0.150390i	0.364072	−	0.931371i	$-0.381386\pi$
$227$	−3.92457	−	2.26585i	−0.260483	−	0.150390i	−0.624555	+	0.780981i	$0.714720\pi$
$228$	11.8967	−	11.0866i	0.787880	−	0.734229i
$229$	6.27141	−	3.62080i	0.414426	−	0.239269i	−0.278264	−	0.960505i	$-0.589759\pi$
$229$	6.27141	−	3.62080i	0.414426	−	0.239269i	0.692690	+	0.721236i	$0.256426\pi$
$230$	1.51979	−	1.92226i	0.100212	−	0.126750i
$231$	5.43833	+	0.0338788i	0.357816	+	0.00222906i
$232$	17.8583	−	12.5079i	1.17246	−	0.821187i
$233$			20.2232i			1.32487i	0.749120	+	0.662434i	$0.230476\pi$
$233$			20.2232i			1.32487i	−0.749120	+	0.662434i	$0.769524\pi$
$234$	−15.8528	−	12.8579i	−1.03633	−	0.840545i
$235$	−6.51087			−0.424723
$236$	11.9715	−	2.83837i	0.779276	−	0.184762i
$237$	15.9550	−	9.07955i	1.03639	−	0.589780i
$238$	6.37198	−	8.05939i	0.413034	−	0.522412i
$239$	−10.8002	−	18.7065i	−0.698607	−	1.21002i	−0.968950	−	0.247258i	$-0.920470\pi$
$239$	−10.8002	−	18.7065i	−0.698607	−	1.21002i	0.270343	−	0.962764i	$-0.412863\pi$
$240$	−5.76526	−	3.84211i	−0.372146	−	0.248007i
$241$	−13.3267	+	23.0825i	−0.858448	+	1.48687i	0.0149617	+	0.999888i	$0.495237\pi$
$241$	−13.3267	+	23.0825i	−0.858448	+	1.48687i	−0.873409	+	0.486987i	$0.838096\pi$
$242$	2.26525	+	5.70126i	0.145616	+	0.366491i
$243$	7.37002	+	13.7362i	0.472787	+	0.881177i
$244$	−15.6842	−	16.6215i	−1.00408	−	1.06408i
$245$	−2.76007	+	4.78058i	−0.176334	+	0.305420i
$246$	0.858520	−	5.61844i	0.0547372	−	0.358219i
$247$	−19.5591	+	11.2925i	−1.24452	+	0.718523i
$248$	−14.0066	+	1.22722i	−0.889421	+	0.0779289i
$249$	8.74091	−	4.97423i	0.553933	−	0.315229i
$250$	−1.39929	−	0.204905i	−0.0884989	−	0.0129593i
$251$		−	13.0658i		−	0.824704i	−0.911025	−	0.412352i	$-0.864707\pi$
$251$		−	13.0658i		−	0.824704i	0.911025	−	0.412352i	$-0.135293\pi$
$252$	−2.17973	+	6.96589i	−0.137310	+	0.438810i
$253$			4.47240i			0.281177i
$254$	−1.50898	+	10.3048i	−0.0946817	+	0.646579i
$255$	−0.0644362	+	10.3435i	−0.00403515	+	0.647736i
$256$	6.34228	+	14.6893i	0.396393	+	0.918081i
$257$	−8.01506	+	4.62750i	−0.499966	+	0.288655i	−0.728699	−	0.684834i	$-0.759875\pi$
$257$	−8.01506	+	4.62750i	−0.499966	+	0.288655i	0.228734	+	0.973489i	$0.426541\pi$
$258$	−3.51523	−	9.01043i	−0.218848	−	0.560965i
$259$	−5.06728	+	8.77679i	−0.314866	+	0.545363i
$260$	6.60372	+	6.99834i	0.409545	+	0.434019i
$261$	23.1237	+	0.288115i	1.43132	+	0.0178339i
$262$	−7.69172	+	3.05610i	−0.475196	+	0.188807i
$263$	−9.10142	+	15.7641i	−0.561217	+	0.972057i	0.436173	+	0.899863i	$0.356333\pi$
$263$	−9.10142	+	15.7641i	−0.561217	+	0.972057i	−0.997391	+	0.0721942i	$0.977000\pi$
$264$	12.6031	−	1.02518i	0.775667	−	0.0630954i
$265$	−0.0364828	−	0.0631900i	−0.00224112	−	0.00388173i
$266$	6.33524	+	5.00882i	0.388438	+	0.307110i
$267$	17.2841	+	10.1231i	1.05777	+	0.619523i
$268$	2.39503	+	10.1016i	0.146300	+	0.617054i
$269$	−15.7911			−0.962798			−0.481399	−	0.876502i	$-0.659871\pi$
$269$	−15.7911			−0.962798			−0.481399	+	0.876502i	$0.659871\pi$
$270$	−2.58530	−	6.87868i	−0.157336	−	0.418623i
$271$			4.97272i			0.302071i	0.988528	+	0.151035i	$0.0482608\pi$
$271$			4.97272i			0.302071i	−0.988528	+	0.151035i	$0.951739\pi$
$272$	13.1232	−	19.9602i	0.795708	−	1.21026i
$273$	5.12313	−	8.74722i	0.310066	−	0.529406i
$274$	6.07295	+	4.80145i	0.366881	+	0.290066i
$275$	2.23529	−	1.29055i	0.134793	−	0.0778229i
$276$	−5.73958	−	1.75682i	−0.345482	−	0.105748i
$277$	−5.96566	−	3.44427i	−0.358442	−	0.206946i	0.309955	−	0.950751i	$-0.399686\pi$
$277$	−5.96566	−	3.44427i	−0.358442	−	0.206946i	−0.668397	+	0.743805i	$0.733019\pi$
$278$	8.20542	+	20.6517i	0.492129	+	1.23861i
$279$	−12.8213	−	7.61692i	−0.767591	−	0.456013i
$280$	1.45373	−	3.11858i	0.0868771	−	0.186371i
$281$	−7.00122	−	4.04215i	−0.417657	−	0.241135i	0.276417	−	0.961038i	$-0.410853\pi$
$281$	−7.00122	−	4.04215i	−0.417657	−	0.241135i	−0.694075	+	0.719903i	$0.744186\pi$
$282$	5.79641	+	14.8577i	0.345171	+	0.884762i
$283$	13.9503	+	24.1626i	0.829260	+	1.43632i	0.898620	+	0.438728i	$0.144571\pi$
$283$	13.9503	+	24.1626i	0.829260	+	1.43632i	−0.0693603	+	0.997592i	$0.522096\pi$
$284$	18.2040	+	5.44824i	1.08021	+	0.323293i
$285$	−8.13072	−	0.0506513i	−0.481622	−	0.00300033i
$286$	−17.3762	−	2.54448i	−1.02747	−	0.150458i
$287$	2.82268			0.166618
$288$	−3.63501	+	16.5767i	−0.214195	+	0.976791i
$289$	−18.6642			−1.09789
$290$	−10.7864	−	1.57951i	−0.633402	−	0.0927521i
$291$	−8.30439	−	14.5928i	−0.486812	−	0.855446i
$292$	20.6005	+	6.16547i	1.20555	+	0.360807i
$293$	13.2771	+	22.9966i	0.775655	+	1.34347i	0.934425	+	0.356159i	$0.115914\pi$
$293$	13.2771	+	22.9966i	0.775655	+	1.34347i	−0.158770	+	0.987316i	$0.550753\pi$
$294$	13.3664	+	2.04244i	0.779544	+	0.119117i
$295$	−5.32751	−	3.07584i	−0.310179	−	0.179082i
$296$	−9.95565	+	21.3571i	−0.578660	+	1.24136i
$297$	11.4876	+	6.92176i	0.666577	+	0.401641i
$298$	−5.17482	−	13.0242i	−0.299769	−	0.754471i
$299$	7.21954	+	4.16821i	0.417517	+	0.241054i
$300$	0.778151	+	3.37557i	0.0449266	+	0.194889i
$301$	4.15982	−	2.40167i	0.239768	−	0.138430i
$302$	−20.2759	−	16.0307i	−1.16675	−	0.922465i
$303$	−13.0083	−	22.8588i	−0.747309	−	1.31320i
$304$	15.6901	+	10.3157i	0.899889	+	0.591647i
$305$			11.4266i			0.654284i
$306$	23.6611	−	9.06143i	1.35261	−	0.518008i
$307$	9.06253			0.517226			0.258613	−	0.965981i	$-0.416735\pi$
$307$	9.06253			0.517226			0.258613	+	0.965981i	$0.416735\pi$
$308$	1.44874	+	6.11037i	0.0825494	+	0.348171i
$309$	0.0211264	−	3.39128i	0.00120184	−	0.192923i
$310$	5.51474	+	4.36011i	0.313216	+	0.247638i
$311$	−4.69912	−	8.13912i	−0.266463	−	0.461527i	0.701483	−	0.712686i	$-0.252522\pi$
$311$	−4.69912	−	8.13912i	−0.266463	−	0.461527i	−0.967946	+	0.251159i	$0.919188\pi$
$312$	10.0910	−	21.2999i	0.571290	−	1.20587i
$313$	4.26424	−	7.38588i	0.241029	−	0.417474i	−0.719979	−	0.693996i	$-0.755848\pi$
$313$	4.26424	−	7.38588i	0.241029	−	0.417474i	0.961008	+	0.276522i	$0.0891818\pi$
$314$	21.2684	−	8.45044i	1.20025	−	0.476886i
$315$	3.18303	−	1.78522i	0.179344	−	0.100586i
$316$	14.5479	+	15.4172i	0.818383	+	0.867287i
$317$	5.99329	−	10.3807i	0.336617	−	0.583037i	−0.647177	−	0.762339i	$-0.724051\pi$
$317$	5.99329	−	10.3807i	0.336617	−	0.583037i	0.983794	+	0.179302i	$0.0573840\pi$
$318$	−0.111719	+	0.139509i	−0.00626489	+	0.00782327i
$319$	17.2308	−	9.94819i	0.964738	−	0.556992i
$320$	2.73424	−	7.51824i	0.152849	−	0.420282i
$321$	18.8480	+	11.0390i	1.05199	+	0.616137i
$322$	0.431916	−	2.94954i	0.0240697	−	0.164372i
$323$		−	28.0345i		−	1.55988i
$324$	−13.3954	+	12.0234i	−0.744189	+	0.667969i
$325$		−	4.81108i		−	0.266871i
$326$	−4.63394	−	0.678570i	−0.256650	−	0.0375825i
$327$	−24.5277	−	14.3655i	−1.35638	−	0.794416i
$328$	6.53788	−	0.572832i	0.360994	−	0.0316294i
$329$	−6.85930	+	3.96022i	−0.378165	+	0.218334i
$330$	−4.93501	−	3.95196i	−0.271663	−	0.217548i
$331$	15.9389	−	27.6071i	0.876084	−	1.51742i	0.0204800	−	0.999790i	$-0.493481\pi$
$331$	15.9389	−	27.6071i	0.876084	−	1.51742i	0.855604	−	0.517631i	$-0.173186\pi$
$332$	7.97005	+	8.44632i	0.437413	+	0.463552i
$333$	−21.7985	+	12.2258i	−1.19455	+	0.669970i
$334$	8.02670	+	20.2019i	0.439202	+	1.10540i
$335$	2.59541	−	4.49538i	0.141802	−	0.245609i
$336$	−8.41073	−	0.541022i	−0.458843	−	0.0295152i
$337$	−5.56020	−	9.63054i	−0.302883	−	0.524609i	0.673905	−	0.738818i	$-0.264616\pi$
$337$	−5.56020	−	9.63054i	−0.302883	−	0.524609i	−0.976788	+	0.214209i	$0.931283\pi$
$338$	−8.89945	+	11.2562i	−0.484066	+	0.612255i
$339$	0.0483965	−	7.76877i	0.00262854	−	0.421942i
$340$	−11.6217	+	2.75544i	−0.630276	+	0.149435i
$341$	−12.8308			−0.694825
$342$	7.12292	+	18.5992i	0.385163	+	1.00573i
$343$			15.2307i			0.822379i
$344$	9.14754	−	6.40692i	0.493202	−	0.345438i
$345$	1.48439	+	2.60843i	0.0799168	+	0.140433i
$346$	11.4720	−	14.5100i	0.616739	−	0.780061i
$347$	−3.18899	+	1.84116i	−0.171194	+	0.0988388i	−0.583149	−	0.812365i	$-0.698180\pi$
$347$	−3.18899	+	1.84116i	−0.171194	+	0.0988388i	0.411955	+	0.911204i	$0.364846\pi$
$348$	5.99838	+	26.0206i	0.321547	+	1.39485i
$349$	20.4332	+	11.7971i	1.09376	+	0.631485i	0.934576	−	0.355763i	$-0.115779\pi$
$349$	20.4332	+	11.7971i	1.09376	+	0.631485i	0.159189	+	0.987248i	$0.449112\pi$
$350$	−1.59881	+	0.635244i	−0.0854598	+	0.0339552i
$351$	21.8797	−	12.0928i	1.16785	−	0.645465i
$352$	4.59558	+	13.8588i	0.244945	+	0.738676i
$353$	10.7105	+	6.18372i	0.570064	+	0.329126i	0.757175	−	0.653212i	$-0.226579\pi$
$353$	10.7105	+	6.18372i	0.570064	+	0.329126i	−0.187111	+	0.982339i	$0.559912\pi$
$354$	−2.27610	+	14.8956i	−0.120973	+	0.791690i
$355$	−4.75046	−	8.22804i	−0.252128	−	0.436699i
$356$	−6.63163	+	22.1581i	−0.351476	+	1.17438i
$357$	6.22353	+	10.9362i	0.329384	+	0.578807i
$358$	4.90766	−	33.5143i	0.259378	−	1.77129i
$359$	−33.0373			−1.74364			−0.871820	−	0.489827i	$-0.837060\pi$
$359$	−33.0373			−1.74364			−0.871820	+	0.489827i	$0.837060\pi$
$360$	7.01022	−	4.78088i	0.369471	−	0.251974i
$361$	3.03707			0.159846
$362$	2.48115	−	16.9437i	0.130407	−	0.890543i
$363$	−7.51341	−	0.0468057i	−0.394352	−	0.00245666i
$364$	11.2138	+	3.35616i	0.587765	+	0.175911i
$365$	−5.37584	−	9.31122i	−0.281384	−	0.487372i
$366$	26.0752	−	10.1727i	1.36297	−	0.531735i
$367$	9.72422	+	5.61428i	0.507600	+	0.293063i	0.731847	−	0.681469i	$-0.238659\pi$
$367$	9.72422	+	5.61428i	0.507600	+	0.293063i	−0.224247	+	0.974532i	$0.571992\pi$
$368$	0.401823	−	6.91936i	0.0209465	−	0.360696i
$369$	5.98460	+	3.55535i	0.311546	+	0.185084i
$370$	10.9492	−	4.35037i	0.569220	−	0.226165i
$371$	−0.0768703	−	0.0443811i	−0.00399091	−	0.00230415i
$372$	5.04009	−	16.4662i	0.261317	−	0.853731i
$373$	−19.9485	+	11.5173i	−1.03290	+	0.596343i	−0.917813	−	0.397013i	$-0.870047\pi$
$373$	−19.9485	+	11.5173i	−1.03290	+	0.596343i	−0.115083	+	0.993356i	$0.536713\pi$
$374$	13.5197	−	17.1000i	0.699089	−	0.884219i
$375$	0.875353	−	1.49458i	0.0452030	−	0.0771796i
$376$	−15.0838	+	10.5646i	−0.777886	+	0.544830i
$377$		−	37.0862i		−	1.91004i
$378$	−6.90758	−	5.67429i	−0.355288	−	0.291854i
$379$	−11.4156			−0.586379			−0.293189	−	0.956054i	$-0.594717\pi$
$379$	−11.4156			−0.586379			−0.293189	+	0.956054i	$0.594717\pi$
$380$	−2.16597	−	9.13547i	−0.111112	−	0.468640i
$381$	−11.0065	−	6.44634i	−0.563879	−	0.330256i
$382$	−14.3184	+	18.1102i	−0.732595	+	0.926599i
$383$	−3.00204	−	5.19968i	−0.153397	−	0.265691i	0.779077	−	0.626928i	$-0.215688\pi$
$383$	−3.00204	−	5.19968i	−0.153397	−	0.265691i	−0.932474	+	0.361237i	$0.882355\pi$
$384$	−19.5907	+	0.453753i	−0.999732	+	0.0231555i
$385$	1.56994	−	2.71922i	0.0800117	−	0.138584i
$386$	−0.0678505	−	0.170769i	−0.00345350	−	0.00869190i
$387$	11.8446	+	0.147581i	0.602096	+	0.00750196i
$388$	14.1010	−	13.3059i	0.715869	−	0.675503i
$389$	10.6451	−	18.4379i	0.539728	−	0.934836i	−0.459190	−	0.888338i	$-0.651860\pi$
$389$	10.6451	−	18.4379i	0.539728	−	0.934836i	0.998918	−	0.0464983i	$-0.0148062\pi$
$390$	−10.9788	+	4.28314i	−0.555932	+	0.216885i
$391$	−8.96156	+	5.17396i	−0.453205	+	0.261658i
$392$	1.36278	+	15.5537i	0.0688307	+	0.785582i
$393$	0.0631468	−	10.1365i	0.00318534	−	0.511321i
$394$	−19.2857	−	2.82409i	−0.971598	−	0.142276i
$395$		−	10.5987i		−	0.533280i
$396$	−4.62483	+	14.7799i	−0.232406	+	0.742717i
$397$		−	5.41338i		−	0.271690i	−0.990730	−	0.135845i	$-0.956625\pi$
$397$		−	5.41338i		−	0.271690i	0.990730	−	0.135845i	$-0.0433748\pi$
$398$	−2.59798	+	17.7415i	−0.130225	+	0.889303i
$399$	−8.59664	+	4.89213i	−0.430370	+	0.244913i
$400$	−3.57422	+	1.79581i	−0.178711	+	0.0897903i
$401$	10.6788	−	6.16543i	0.533276	−	0.307887i	−0.209074	−	0.977900i	$-0.567045\pi$
$401$	10.6788	−	6.16543i	0.533276	−	0.307887i	0.742349	+	0.670013i	$0.233712\pi$
$402$	−12.5690	−	1.92059i	−0.626883	−	0.0957903i
$403$	−11.9581	+	20.7120i	−0.595674	+	1.03174i
$404$	22.0884	−	20.8429i	1.09894	−	1.03697i
$405$	8.99721	+	0.224240i	0.447075	+	0.0111426i
$406$	−12.3244	+	4.89678i	−0.611650	+	0.243023i
$407$	−10.7515	+	18.6221i	−0.532932	+	0.923066i
$408$	16.6343	+	24.0674i	0.823519	+	1.19152i
$409$	−11.3909	−	19.7296i	−0.563242	−	0.975565i	−0.997211	−	0.0746365i	$-0.976220\pi$
$409$	−11.3909	−	19.7296i	−0.563242	−	0.975565i	0.433968	−	0.900928i	$-0.357113\pi$
$410$	−2.57412	−	2.03517i	−0.127127	−	0.100510i
$411$	−8.24074	+	4.68959i	−0.406486	+	0.231320i
$412$	3.81036	−	0.903415i	0.187723	−	0.0445080i
$413$	−7.48347			−0.368238
$414$	4.63088	−	5.70953i	0.227595	−	0.280608i
$415$		−	5.80651i		−	0.285030i
$416$	26.6545	+	5.49779i	1.30684	+	0.269551i
$417$	−27.2159	−	0.169545i	−1.33277	−	0.00830265i
$418$	13.4418	+	10.6274i	0.657459	+	0.519805i
$419$	−9.26906	+	5.35149i	−0.452823	+	0.261438i	−0.709022	−	0.705187i	$-0.750863\pi$
$419$	−9.26906	+	5.35149i	−0.452823	+	0.261438i	0.256199	+	0.966624i	$0.417530\pi$
$420$	2.87297	+	3.08291i	0.140187	+	0.150430i
$421$	−12.4216	−	7.17164i	−0.605394	−	0.349524i	0.165767	−	0.986165i	$-0.446990\pi$
$421$	−12.4216	−	7.17164i	−0.605394	−	0.349524i	−0.771160	+	0.636641i	$0.780323\pi$
$422$	10.3600	+	26.0745i	0.504317	+	1.26928i
$423$	−19.5311	−	0.243352i	−0.949635	−	0.0118322i
$424$	−0.187053	−	0.0871951i	−0.00908409	−	0.00423457i
$425$	5.17186	+	2.98597i	0.250872	+	0.144841i
$426$	−14.5470	+	18.1656i	−0.704806	+	0.880126i
$427$	6.95018	+	12.0381i	0.336343	+	0.582563i
$428$	−7.23164	+	24.1629i	−0.349555	+	1.16796i
$429$	10.8700	−	18.5594i	0.524808	−	0.896057i
$430$	−5.52512	−	0.809070i	−0.266445	−	0.0390168i
$431$	−18.6893			−0.900230			−0.450115	−	0.892971i	$-0.648617\pi$
$431$	−18.6893			−0.900230			−0.450115	+	0.892971i	$0.648617\pi$
$432$	−17.1508	−	11.7409i	−0.825169	−	0.564886i
$433$	27.7581			1.33397			0.666984	−	0.745072i	$-0.267585\pi$
$433$	27.7581			1.33397			0.666984	+	0.745072i	$0.267585\pi$
$434$	8.46188	+	1.23911i	0.406183	+	0.0594794i
$435$	6.74766	−	11.5209i	0.323526	−	0.552387i
$436$	9.41086	−	31.4442i	0.450698	−	1.50590i
$437$	−4.06709	−	7.04441i	−0.194555	−	0.336980i
$438$	−16.4621	+	20.5570i	−0.786589	+	0.982252i
$439$	26.2677	+	15.1656i	1.25369	+	0.723817i	0.971840	−	0.235642i	$-0.0757194\pi$
$439$	26.2677	+	15.1656i	1.25369	+	0.723817i	0.281848	+	0.959459i	$0.409053\pi$
$440$	3.08445	−	6.61684i	0.147045	−	0.315445i
$441$	−8.45825	+	14.2375i	−0.402774	+	0.677975i
$442$	−15.0034	−	37.7611i	−0.713638	−	1.79611i
$443$	−29.3461	−	16.9430i	−1.39427	−	0.804984i	−0.400488	−	0.916302i	$-0.631159\pi$
$443$	−29.3461	−	16.9430i	−1.39427	−	0.804984i	−0.993785	+	0.111318i	$0.964493\pi$
$444$	−19.6751	−	21.1128i	−0.933739	−	1.00197i
$445$	10.0152	−	5.78229i	0.474767	−	0.274107i
$446$	4.62880	+	3.65966i	0.219180	+	0.173290i
$447$	17.1639	+	0.106925i	0.811827	+	0.00505738i
$448$	−1.69239	−	9.58367i	−0.0799577	−	0.452786i
$449$		−	20.2689i		−	0.956550i	−0.878210	−	0.478275i	$-0.841262\pi$
$449$		−	20.2689i		−	0.956550i	0.878210	−	0.478275i	$-0.158738\pi$
$450$	−4.18989	−	0.666968i	−0.197513	−	0.0314411i
$451$	5.98902			0.282012
$452$	8.72879	−	2.06955i	0.410568	−	0.0973433i
$453$	27.5136	−	15.6573i	1.29270	−	0.735642i
$454$	5.02733	+	3.97475i	0.235944	+	0.186544i
$455$	−2.92632	−	5.06854i	−0.137188	−	0.237617i
$456$	−18.9187	+	13.0757i	−0.885948	+	0.612325i
$457$	−14.1827	+	24.5651i	−0.663437	+	1.14911i	0.316270	+	0.948669i	$0.397569\pi$
$457$	−14.1827	+	24.5651i	−0.663437	+	1.14911i	−0.979707	+	0.200437i	$0.935764\pi$
$458$	−9.51744	+	3.78151i	−0.444721	+	0.176698i
$459$	−0.579896	+	31.0257i	−0.0270672	+	1.44816i
$460$	−2.52052	+	2.37839i	−0.117520	+	0.110893i
$461$	−11.8822	+	20.5806i	−0.553411	+	0.958536i	0.444614	+	0.895722i	$0.353341\pi$
$461$	−11.8822	+	20.5806i	−0.553411	+	0.958536i	−0.998025	+	0.0628139i	$0.979993\pi$
$462$	−7.60287	−	1.16175i	−0.353717	−	0.0540494i
$463$	−17.4043	+	10.0484i	−0.808845	+	0.466987i	−0.846555	−	0.532302i	$-0.821327\pi$
$463$	−17.4043	+	10.0484i	−0.808845	+	0.466987i	0.0377098	+	0.999289i	$0.487994\pi$
$464$	−27.5519	+	13.8430i	−1.27907	+	0.642644i
$465$	−7.48326	+	4.25853i	−0.347028	+	0.197485i
$466$	4.14384	−	28.2982i	0.191960	−	1.31089i
$467$		−	3.17945i		−	0.147127i	−0.997291	−	0.0735636i	$-0.976563\pi$
$467$		−	3.17945i		−	0.147127i	0.997291	−	0.0735636i	$-0.0234372\pi$
$468$	19.5481	+	21.2402i	0.903609	+	0.981829i
$469$		−	6.31460i		−	0.291581i
$470$	9.11060	+	1.33411i	0.420241	+	0.0615379i
$471$	−0.174608	+	28.0286i	−0.00804549	+	1.29149i
$472$	−17.3332	+	1.51869i	−0.797823	+	0.0699032i
$473$	8.82609	−	5.09574i	0.405824	−	0.234303i
$474$	−24.1861	+	9.43568i	−1.11090	+	0.433395i
$475$	−2.34718	+	4.06544i	−0.107696	+	0.186535i
$476$	−10.5677	+	9.97177i	−0.484368	+	0.457055i
$477$	−0.107078	−	0.190919i	−0.00490277	−	0.00874158i
$478$	11.2796	+	28.3888i	0.515915	+	1.29847i
$479$	−2.41400	+	4.18118i	−0.110299	+	0.191043i	−0.915891	−	0.401428i	$-0.868514\pi$
$479$	−2.41400	+	4.18118i	−0.110299	+	0.191043i	0.805592	+	0.592471i	$0.201847\pi$
$480$	7.28000	+	6.55756i	0.332285	+	0.299310i
$481$	20.0405	+	34.7111i	0.913766	+	1.58269i
$482$	23.3776	−	29.5684i	1.06482	−	1.34680i
$483$	3.15039	+	1.84514i	0.143348	+	0.0839569i
$484$	−2.00152	−	8.44188i	−0.0909782	−	0.383722i
$485$	−9.69386			−0.440176
$486$	−7.49819	−	20.7311i	−0.340125	−	0.940380i
$487$			14.3517i			0.650339i	0.945656	+	0.325170i	$0.105421\pi$
$487$			14.3517i			0.650339i	−0.945656	+	0.325170i	$0.894579\pi$
$488$	18.5409	+	26.4720i	0.839309	+	1.19833i
$489$	2.89885	−	4.94949i	0.131090	−	0.223824i
$490$	4.84171	−	6.12387i	0.218726	−	0.276648i
$491$	1.35188	−	0.780507i	0.0610094	−	0.0352238i	−0.469185	−	0.883100i	$-0.655452\pi$
$491$	1.35188	−	0.780507i	0.0610094	−	0.0352238i	0.530194	+	0.847876i	$0.322119\pi$
$492$	−2.35257	+	7.68592i	−0.106062	+	0.346508i
$493$	39.8673	+	23.0174i	1.79553	+	1.03665i
$494$	29.6828	−	11.7937i	1.33549	−	0.530623i
$495$	6.75359	−	3.78779i	0.303552	−	0.170249i
$496$	19.8508	+	1.15278i	0.891327	+	0.0517615i
$497$	−10.0094	−	5.77891i	−0.448981	−	0.259219i
$498$	−13.2503	+	5.16933i	−0.593761	+	0.231643i
$499$	−6.31836	−	10.9437i	−0.282849	−	0.489908i	0.689237	−	0.724536i	$-0.257946\pi$
$499$	−6.31836	−	10.9437i	−0.282849	−	0.489908i	−0.972085	+	0.234628i	$0.924613\pi$
$500$	1.91603	+	0.573443i	0.0856874	+	0.0256452i
$501$	−26.6231	−	0.165852i	−1.18943	−	0.00740972i
$502$	−2.67724	+	18.2828i	−0.119491	+	0.816002i
$503$	32.7222			1.45901			0.729505	−	0.683976i	$-0.239751\pi$
$503$	32.7222			1.45901			0.729505	+	0.683976i	$0.239751\pi$
$504$	4.47742	−	9.30067i	0.199440	−	0.414285i
$505$	−15.1849			−0.675718
$506$	0.916417	−	6.25819i	0.0407397	−	0.278210i
$507$	−8.69212	−	15.2741i	−0.386031	−	0.678349i
$508$	4.22300	−	14.1102i	0.187365	−	0.626037i
$509$	5.41863	+	9.38534i	0.240176	+	0.415998i	0.960764	−	0.277366i	$-0.0894614\pi$
$509$	5.41863	+	9.38534i	0.240176	+	0.415998i	−0.720588	+	0.693364i	$0.756128\pi$
$510$	2.20960	−	14.4604i	0.0978429	−	0.640317i
$511$	−11.3270	−	6.53967i	−0.501079	−	0.289298i
$512$	−5.86479	−	21.8542i	−0.259189	−	0.965826i
$513$	−24.3884	−	0.455839i	−1.07677	−	0.0201258i
$514$	12.1636	−	4.83289i	0.536513	−	0.213169i
$515$	−1.69567	−	0.978998i	−0.0747203	−	0.0431398i
$516$	3.07254	+	13.3285i	0.135261	+	0.586754i
$517$	−14.5537	+	8.40259i	−0.640071	+	0.369545i
$518$	8.88901	−	11.2430i	0.390561	−	0.493988i
$519$	11.2047	+	19.6894i	0.491833	+	0.864270i
$520$	−7.80653	−	11.1458i	−0.342339	−	0.488778i
$521$		−	36.1420i		−	1.58341i	−0.610903	−	0.791706i	$-0.709193\pi$
$521$		−	36.1420i		−	1.58341i	0.610903	−	0.791706i	$-0.290807\pi$
$522$	−32.2978	−	5.14132i	−1.41364	−	0.225030i
$523$	−38.6056			−1.68810			−0.844052	−	0.536262i	$-0.819836\pi$
$523$	−38.6056			−1.68810			−0.844052	+	0.536262i	$0.819836\pi$
$524$	11.3892	−	2.70031i	0.497538	−	0.117963i
$525$	0.0131257	−	2.10699i	0.000572854	−	0.0919565i
$526$	15.9657	−	20.1936i	0.696136	−	0.880485i
$527$	−14.8435	−	25.7096i	−0.646591	−	1.11993i
$528$	−17.8455	−	1.14791i	−0.776624	−	0.0499565i
$529$	9.99878	−	17.3184i	0.434730	−	0.752974i
$530$	0.0381021	+	0.0958967i	0.00165505	+	0.00416549i
$531$	−15.8663	−	9.42592i	−0.688539	−	0.409050i
$532$	−7.83850	−	8.30691i	−0.339842	−	0.360150i
$533$	5.58168	−	9.66775i	0.241769	−	0.418757i
$534$	−22.1113	−	17.7068i	−0.956848	−	0.766246i
$535$	10.9214	−	6.30546i	0.472172	−	0.272609i
$536$	−1.28148	−	14.6258i	−0.0553514	−	0.631740i
$537$	35.7965	+	20.9655i	1.54473	+	0.904729i
$538$	22.0963	+	3.23567i	0.952638	+	0.139499i
$539$			14.2480i			0.613705i
$540$	2.20811	+	10.1550i	0.0950217	+	0.437002i
$541$		−	8.66994i		−	0.372750i	−0.982479	−	0.186375i	$-0.940326\pi$
$541$		−	8.66994i		−	0.372750i	0.982479	−	0.186375i	$-0.0596739\pi$
$542$	1.01893	−	6.95827i	0.0437670	−	0.298883i
$543$	18.0975	+	10.5995i	0.776639	+	0.454867i
$544$	−22.4531	+	25.2411i	−0.962667	+	1.08220i
$545$	−14.2125	+	8.20557i	−0.608795	+	0.351488i
$546$	−8.96110	+	11.1902i	−0.383500	+	0.478894i
$547$	12.8154	−	22.1968i	0.547945	−	0.949068i	−0.450470	−	0.892791i	$-0.648744\pi$
$547$	12.8154	−	22.1968i	0.547945	−	0.949068i	0.998415	−	0.0562770i	$-0.0179230\pi$
$548$	−7.51399	−	7.96300i	−0.320982	−	0.340163i
$549$	−0.427083	+	34.2771i	−0.0182275	+	1.46291i
$550$	−3.39226	+	1.34783i	−0.144647	+	0.0574716i
$551$	−18.0933	+	31.3385i	−0.770800	+	1.33506i
$552$	7.67136	+	3.63437i	0.326515	+	0.154689i
$553$	−6.44664	−	11.1659i	−0.274139	−	0.474823i
$554$	7.64194	+	6.04193i	0.324675	+	0.256697i
$555$	−0.0898896	+	14.4294i	−0.00381560	+	0.612493i
$556$	−7.25013	−	30.5791i	−0.307474	−	1.29684i
$557$	−7.87236			−0.333563			−0.166781	−	0.985994i	$-0.553337\pi$
$557$	−7.87236			−0.333563			−0.166781	+	0.985994i	$0.553337\pi$
$558$	16.3800	+	13.2854i	0.693419	+	0.562417i
$559$		−	18.9966i		−	0.803471i
$560$	−2.67320	+	4.06592i	−0.112963	+	0.171816i
$561$	13.2048	+	23.2040i	0.557506	+	0.979672i
$562$	8.96848	+	7.09073i	0.378312	+	0.299104i
$563$	39.2781	−	22.6772i	1.65538	−	0.955731i	0.680567	−	0.732686i	$-0.261734\pi$
$563$	39.2781	−	22.6772i	1.65538	−	0.955731i	0.974808	−	0.223045i	$-0.0715998\pi$
$564$	−5.06644	−	21.9779i	−0.213336	−	0.925437i
$565$	−3.88446	−	2.24269i	−0.163421	−	0.0943509i
$566$	−14.5695	−	36.6690i	−0.612401	−	1.54131i
$567$	9.61508	−	5.23628i	0.403795	−	0.219903i
$568$	−24.3564	−	11.3538i	−1.02197	−	0.476393i
$569$	32.2236	+	18.6043i	1.35088	+	0.779933i	0.988373	−	0.152046i	$-0.0485863\pi$
$569$	32.2236	+	18.6043i	1.35088	+	0.779933i	0.362511	+	0.931980i	$0.381920\pi$
$570$	11.3669	+	1.73690i	0.476106	+	0.0727508i
$571$	6.36881	+	11.0311i	0.266527	+	0.461637i	0.967962	−	0.251095i	$-0.0807907\pi$
$571$	6.36881	+	11.0311i	0.266527	+	0.461637i	−0.701436	+	0.712733i	$0.747457\pi$
$572$	23.7929	+	7.12093i	0.994833	+	0.297741i
$573$	−13.9849	−	24.5748i	−0.584226	−	1.02663i
$574$	−3.94975	−	0.578382i	−0.164860	−	0.0241412i
$575$	1.73275			0.0722608
$576$	8.48308	−	22.4508i	0.353462	−	0.935449i
$577$	−1.47556			−0.0614283			−0.0307141	−	0.999528i	$-0.509778\pi$
$577$	−1.47556			−0.0614283			−0.0307141	+	0.999528i	$0.509778\pi$
$578$	26.1166	+	3.82438i	1.08631	+	0.159073i
$579$	0.225048	+	0.00140196i	0.00935267	+	5.82636e-5i
$580$	14.7697	+	4.42039i	0.613279	+	0.183547i
$581$	−3.53179	−	6.11724i	−0.146523	−	0.253786i
$582$	8.63011	+	22.1212i	0.357730	+	0.916953i
$583$	−0.163099	−	0.0941655i	−0.00675489	−	0.00389994i
$584$	−27.5628	−	12.8484i	−1.14056	−	0.531672i
$585$	0.179820	−	14.4321i	0.00743465	−	0.596694i
$586$	−13.8664	−	34.8994i	−0.572815	−	1.44168i
$587$	34.4715	+	19.9021i	1.42279	+	0.821448i	0.996537	−	0.0831555i	$-0.0264998\pi$
$587$	34.4715	+	19.9021i	1.42279	+	0.821448i	0.426253	+	0.904604i	$0.359833\pi$
$588$	−18.2850	−	5.59680i	−0.754059	−	0.230808i
$589$	20.2095	−	11.6680i	0.832720	−	0.480771i
$590$	6.82447	+	5.39562i	0.280959	+	0.222134i
$591$	12.0645	−	20.5989i	0.496268	−	0.847327i
$592$	18.3070	−	27.8448i	0.752414	−	1.14441i
$593$		−	15.7328i		−	0.646070i	−0.946387	−	0.323035i	$-0.895297\pi$
$593$		−	15.7328i		−	0.646070i	0.946387	−	0.323035i	$-0.104703\pi$
$594$	−14.6562	−	12.0394i	−0.601349	−	0.493983i
$595$	7.26484			0.297829
$596$	4.57236	+	19.2850i	0.187291	+	0.789943i
$597$	−18.9497	−	11.0986i	−0.775558	−	0.454234i
$598$	−9.24815	−	7.31185i	−0.378185	−	0.299004i
$599$	11.0081	+	19.0666i	0.449778	+	0.779039i	0.998371	−	0.0570507i	$-0.0181697\pi$
$599$	11.0081	+	19.0666i	0.449778	+	0.779039i	−0.548593	+	0.836090i	$0.684836\pi$
$600$	−0.397188	−	4.88285i	−0.0162151	−	0.199342i
$601$	−21.5225	+	37.2780i	−0.877921	+	1.52060i	−0.0243020	+	0.999705i	$0.507736\pi$
$601$	−21.5225	+	37.2780i	−0.877921	+	1.52060i	−0.853619	+	0.520898i	$0.825597\pi$
$602$	−6.31291	+	2.50827i	−0.257295	+	0.102229i
$603$	7.95365	−	13.3881i	0.323898	−	0.545205i
$604$	25.0871	+	26.5863i	1.02078	+	1.08178i
$605$	−2.16898	+	3.75678i	−0.0881814	+	0.152735i
$606$	13.5186	+	34.6516i	0.549154	+	1.40762i
$607$	7.15706	−	4.13213i	0.290496	−	0.167718i	−0.347669	−	0.937617i	$-0.613027\pi$
$607$	7.15706	−	4.13213i	0.290496	−	0.167718i	0.638166	+	0.769899i	$0.279694\pi$
$608$	−19.8413	−	17.6497i	−0.804670	−	0.715788i
$609$	0.101180	−	16.2417i	0.00410002	−	0.658148i
$610$	2.34136	−	15.9891i	0.0947990	−	0.647380i
$611$			31.3243i			1.26725i
$612$	−34.9654	+	7.83131i	−1.41339	+	0.316562i
$613$			15.5613i			0.628514i	0.949338	+	0.314257i	$0.101755\pi$
$613$			15.5613i			0.628514i	−0.949338	+	0.314257i	$0.898245\pi$
$614$	−12.6811	−	1.85696i	−0.511768	−	0.0749407i
$615$	3.49297	−	1.98776i	0.140850	−	0.0801540i
$616$	−0.775156	−	8.84704i	−0.0312319	−	0.356457i
$617$	−0.614243	+	0.354633i	−0.0247285	+	0.0142770i	−0.512313	−	0.858799i	$-0.671211\pi$
$617$	−0.614243	+	0.354633i	−0.0247285	+	0.0142770i	0.487585	+	0.873076i	$0.337878\pi$
$618$	−0.724453	+	4.74106i	−0.0291418	+	0.190713i
$619$	−4.20556	+	7.28425i	−0.169036	+	0.292779i	−0.938081	−	0.346416i	$-0.887399\pi$
$619$	−4.20556	+	7.28425i	−0.169036	+	0.292779i	0.769045	+	0.639194i	$0.220732\pi$
$620$	−6.82331	−	7.23106i	−0.274031	−	0.290406i
$621$	4.35532	+	7.88016i	0.174773	+	0.316220i
$622$	4.90769	+	12.3519i	0.196780	+	0.495265i
$623$	7.03412	−	12.1835i	0.281816	−	0.488120i
$624$	−18.4847	+	27.7371i	−0.739980	+	1.11037i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.48031	+	9.46122i	−0.298973	+	0.378147i
$627$	−18.2399	+	10.3799i	−0.728432	+	0.414532i
$628$	−31.4922	+	7.46662i	−1.25668	+	0.297951i
$629$	−49.7521			−1.98375
$630$	−4.81979	+	1.84583i	−0.192025	+	0.0735395i
$631$			11.4322i			0.455108i	0.973765	+	0.227554i	$0.0730728\pi$
$631$			11.4322i			0.455108i	−0.973765	+	0.227554i	$0.926927\pi$
$632$	−17.1977	−	24.5541i	−0.684086	−	0.976710i
$633$	−34.3623	−	0.214064i	−1.36578	−	0.00850828i
$634$	−10.5134	+	13.2975i	−0.417541	+	0.528113i
$635$	−6.37765	+	3.68214i	−0.253089	+	0.146121i
$636$	0.184913	−	0.172322i	0.00733229	−	0.00683300i
$637$	22.9998	+	13.2789i	0.911284	+	0.526130i
$638$	−26.1493	+	10.3897i	−1.03526	+	0.411334i
$639$	−13.9427	−	24.8598i	−0.551566	−	0.983437i
$640$	−5.36652	+	9.95994i	−0.212130	+	0.393701i
$641$	6.20681	+	3.58350i	0.245154	+	0.141540i	0.617543	−	0.786537i	$-0.288128\pi$
$641$	6.20681	+	3.58350i	0.245154	+	0.141540i	−0.372389	+	0.928077i	$0.621461\pi$
$642$	−24.1118	−	19.3088i	−0.951618	−	0.762058i
$643$	8.56125	+	14.8285i	0.337623	+	0.584779i	0.983985	−	0.178251i	$-0.0570439\pi$
$643$	8.56125	+	14.8285i	0.337623	+	0.584779i	−0.646362	+	0.763030i	$0.723711\pi$
$644$	−1.20875	+	4.03876i	−0.0476315	+	0.159150i
$645$	3.45634	−	5.90136i	0.136093	−	0.232366i
$646$	−5.74441	+	39.2284i	−0.226011	+	1.54342i
$647$	33.0387			1.29889			0.649443	−	0.760411i	$-0.275002\pi$
$647$	33.0387			1.29889			0.649443	+	0.760411i	$0.275002\pi$
$648$	21.2077	−	14.0795i	0.833118	−	0.553095i
$649$	−15.8780			−0.623268
$650$	−0.985814	+	6.73210i	−0.0386668	+	0.264055i
$651$	−5.29349	+	9.03810i	−0.207468	+	0.354231i
$652$	6.34518	+	1.89903i	0.248497	+	0.0743719i
$653$	−8.35904	−	14.4783i	−0.327115	−	0.566579i	0.654823	−	0.755782i	$-0.272743\pi$
$653$	−8.35904	−	14.4783i	−0.327115	−	0.566579i	−0.981938	+	0.189203i	$0.939410\pi$
$654$	31.3778	+	25.1274i	1.22697	+	0.982560i
$655$	−5.06837	−	2.92622i	−0.198038	−	0.114337i
$656$	−9.26576	−	0.538085i	−0.361767	−	0.0210087i
$657$	−15.7782	−	28.1324i	−0.615568	−	1.09755i
$658$	10.4096	−	4.13599i	0.405809	−	0.161238i
$659$	−31.0349	−	17.9180i	−1.20895	−	0.697987i	−0.246420	−	0.969163i	$-0.579254\pi$
$659$	−31.0349	−	17.9180i	−1.20895	−	0.697987i	−0.962530	+	0.271176i	$0.912588\pi$
$660$	6.09573	+	6.54115i	0.237276	+	0.254614i
$661$	−12.5998	+	7.27451i	−0.490076	+	0.282945i	−0.724606	−	0.689163i	$-0.757978\pi$
$661$	−12.5998	+	7.27451i	−0.490076	+	0.282945i	0.234530	+	0.972109i	$0.424645\pi$
$662$	−27.9600	+	35.3643i	−1.08670	+	1.37447i
$663$	49.7635	+	0.310008i	1.93265	+	0.0120397i
$664$	−9.42172	−	13.4520i	−0.365634	−	0.522037i
$665$			5.71067i			0.221450i
$666$	33.0076	−	12.6408i	1.27902	−	0.489823i
$667$	13.3569			0.517183
$668$	−7.09222	−	29.9131i	−0.274406	−	1.15737i
$669$	−6.28108	+	3.57440i	−0.242841	+	0.138194i
$670$	−4.55286	+	5.75854i	−0.175892	+	0.222472i
$671$	14.7465	+	25.5418i	0.569284	+	0.986029i
$672$	11.6582	+	2.48045i	0.449725	+	0.0956854i
$673$	3.53592	−	6.12439i	0.136300	−	0.236078i	−0.789794	−	0.613373i	$-0.789812\pi$
$673$	3.53592	−	6.12439i	0.136300	−	0.236078i	0.926093	+	0.377295i	$0.123146\pi$
$674$	5.80698	+	14.6152i	0.223677	+	0.562958i
$675$	2.68172	−	4.45066i	0.103219	−	0.171306i
$676$	14.7594	−	13.9271i	0.567668	−	0.535658i
$677$	16.6806	−	28.8917i	0.641088	−	1.11040i	−0.344102	−	0.938932i	$-0.611817\pi$
$677$	16.6806	−	28.8917i	0.641088	−	1.11040i	0.985190	−	0.171465i	$-0.0548499\pi$
$678$	−1.65958	+	10.8609i	−0.0637358	+	0.417109i
$679$	−10.2126	+	5.89626i	−0.391925	+	0.226278i
$680$	16.8268	−	1.47432i	0.645277	−	0.0565375i
$681$	−6.82187	+	3.88215i	−0.261415	+	0.148764i
$682$	17.9540	+	2.62909i	0.687493	+	0.100673i
$683$		−	30.0087i		−	1.14825i	−0.818767	−	0.574126i	$-0.805342\pi$
$683$		−	30.0087i		−	1.14825i	0.818767	−	0.574126i	$-0.194658\pi$
$684$	−6.15595	−	27.4852i	−0.235379	−	1.05092i
$685$			5.47424i			0.209160i
$686$	3.12084	−	21.3121i	0.119154	−	0.813701i
$687$	0.0781355	−	12.5426i	0.00298106	−	0.478529i
$688$	−14.1129	+	7.09077i	−0.538048	+	0.270333i
$689$	−0.304012	+	0.175521i	−0.0115819	+	0.00668684i
$690$	−1.54261	−	3.95411i	−0.0587262	−	0.150530i
$691$	−14.9186	+	25.8397i	−0.567529	+	0.982989i	0.429281	+	0.903171i	$0.358767\pi$
$691$	−14.9186	+	25.8397i	−0.567529	+	0.982989i	−0.996809	+	0.0798177i	$0.974566\pi$
$692$	−19.0258	+	17.9530i	−0.723253	+	0.682471i
$693$	4.81110	−	8.09835i	0.182758	−	0.307631i
$694$	4.83959	−	1.92288i	0.183708	−	0.0729916i
$695$	−7.85671	+	13.6082i	−0.298022	+	0.516189i
$696$	−3.06173	−	37.6395i	−0.116054	−	1.42672i
$697$	6.92849	+	12.0005i	0.262435	+	0.454551i
$698$	−26.1747	−	20.6945i	−0.990728	−	0.783297i
$699$	30.2251	+	17.7025i	1.14322	+	0.669568i
$700$	2.36736	−	0.561287i	0.0894777	−	0.0212147i
$701$	−7.04424			−0.266057			−0.133029	−	0.991112i	$-0.542470\pi$
$701$	−7.04424			−0.266057			−0.133029	+	0.991112i	$0.542470\pi$
$702$	−33.0939	+	12.4381i	−1.24905	+	0.469444i
$703$		−	39.1086i		−	1.47501i
$704$	−3.59082	−	20.3341i	−0.135334	−	0.766372i
$705$	−5.69931	+	9.73100i	−0.214649	+	0.366490i
$706$	−13.7201	−	10.8475i	−0.516361	−	0.408250i
$707$	−15.9975	+	9.23615i	−0.601647	+	0.347361i
$708$	6.23710	−	20.3768i	0.234405	−	0.765809i
$709$	3.17078	+	1.83065i	0.119081	+	0.0687516i	0.558358	−	0.829600i	$-0.311432\pi$
$709$	3.17078	+	1.83065i	0.119081	+	0.0687516i	−0.439276	+	0.898352i	$0.644765\pi$
$710$	4.96131	+	12.4868i	0.186195	+	0.468622i
$711$	0.396141	−	31.7937i	0.0148565	−	1.19236i
$712$	13.8199	−	29.6467i	0.517922	−	1.11106i
$713$	−7.45962	−	4.30681i	−0.279365	−	0.161291i
$714$	−6.46764	−	16.5782i	−0.242045	−	0.620424i
$715$	−6.20892	−	10.7542i	−0.232201	−	0.402183i
$716$	−13.7345	+	45.8907i	−0.513282	+	1.71501i
$717$	−37.4123	−	0.233064i	−1.39719	−	0.00870395i
$718$	46.2287	+	6.76950i	1.72524	+	0.252635i
$719$	20.0716			0.748545			0.374272	−	0.927319i	$-0.377893\pi$
$719$	20.0716			0.748545			0.374272	+	0.927319i	$0.377893\pi$
$720$	−10.7890	+	5.25341i	−0.402081	+	0.195783i
$721$	−2.38189			−0.0887062
$722$	−4.24975	−	0.622311i	−0.158159	−	0.0231600i
$723$	22.8330	+	40.1231i	0.849168	+	1.49219i
$724$	−6.94371	+	23.2008i	−0.258061	+	0.862251i
$725$	−3.85425	−	6.67576i	−0.143143	−	0.247932i
$726$	10.5039	+	1.60503i	0.389835	+	0.0595682i
$727$	22.2080	+	12.8218i	0.823648	+	0.475533i	0.851673	−	0.524074i	$-0.175588\pi$
$727$	22.2080	+	12.8218i	0.823648	+	0.475533i	−0.0280248	+	0.999607i	$0.508922\pi$
$728$	−15.0037	−	6.99401i	−0.556075	−	0.259215i
$729$	26.9811	+	1.00895i	0.999302	+	0.0373686i
$730$	5.61444	+	14.1306i	0.207800	+	0.522999i
$731$	20.4212	+	11.7902i	0.755304	+	0.436075i
$732$	−38.5712	+	8.89161i	−1.42563	+	0.328643i
$733$	34.1239	−	19.7014i	1.26039	−	0.727689i	0.287243	−	0.957858i	$-0.407261\pi$
$733$	34.1239	−	19.7014i	1.26039	−	0.727689i	0.973151	+	0.230169i	$0.0739278\pi$
$734$	−12.4566	−	9.84855i	−0.459782	−	0.363516i
$735$	4.72891	+	8.30983i	0.174428	+	0.306513i
$736$	−1.98008	+	9.59985i	−0.0729866	+	0.353855i
$737$		−	13.3980i		−	0.493522i
$738$	−7.64568	−	6.20124i	−0.281441	−	0.228271i
$739$	19.4393			0.715086			0.357543	−	0.933897i	$-0.383615\pi$
$739$	19.4393			0.715086			0.357543	+	0.933897i	$0.383615\pi$
$740$	−16.2125	+	3.84389i	−0.595983	+	0.141304i
$741$	−0.243688	+	39.1175i	−0.00895209	+	1.43702i
$742$	0.0984699	+	0.0778531i	0.00361495	+	0.00285808i
$743$	−1.32397	−	2.29319i	−0.0485718	−	0.0841289i	0.840717	−	0.541474i	$-0.182134\pi$
$743$	−1.32397	−	2.29319i	−0.0485718	−	0.0841289i	−0.889289	+	0.457345i	$0.848800\pi$
$744$	−10.4266	+	22.0082i	−0.382256	+	0.806860i
$745$	4.95490	−	8.58214i	0.181534	−	0.314425i
$746$	30.2737	−	12.0285i	1.10840	−	0.440394i
$747$	0.217026	−	17.4182i	0.00794055	−	0.637297i
$748$	−22.4219	+	21.1576i	−0.819826	+	0.773598i
$749$	7.67055	−	13.2858i	0.280276	−	0.485452i
$750$	−1.53112	+	1.91198i	−0.0559086	+	0.0698157i
$751$	35.7172	−	20.6213i	1.30334	−	0.752483i	0.322364	−	0.946616i	$-0.395523\pi$
$751$	35.7172	−	20.6213i	1.30334	−	0.752483i	0.980975	+	0.194133i	$0.0621892\pi$
$752$	23.2713	−	11.6923i	0.848618	−	0.426373i
$753$	−19.5278	−	11.4372i	−0.711632	−	0.416793i
$754$	−7.59915	+	51.8944i	−0.276745	+	1.88988i
$755$		−	18.2770i		−	0.665168i
$756$	8.50303	+	9.35538i	0.309252	+	0.340252i
$757$			7.94389i			0.288725i	0.989525	+	0.144363i	$0.0461132\pi$
$757$			7.94389i			0.288725i	−0.989525	+	0.144363i	$0.953887\pi$
$758$	15.9737	+	2.33911i	0.580191	+	0.0849602i
$759$	6.68434	+	3.91493i	0.242626	+	0.142103i
$760$	1.15892	+	13.2270i	0.0420383	+	0.479794i
$761$	−1.59354	+	0.920033i	−0.0577659	+	0.0333512i	−0.528605	−	0.848868i	$-0.677285\pi$
$761$	−1.59354	+	0.920033i	−0.0577659	+	0.0333512i	0.470839	+	0.882219i	$0.343951\pi$
$762$	14.0804	+	11.2756i	0.510078	+	0.408471i
$763$	−9.98203	+	17.2894i	−0.361374	+	0.625917i
$764$	23.7465	−	22.4075i	0.859119	−	0.810675i
$765$	15.4028	+	9.15053i	0.556888	+	0.330838i
$766$	3.13528	+	7.89100i	0.113282	+	0.285113i
$767$	−14.7981	+	25.6310i	−0.534328	+	0.925483i
$768$	27.5060	+	3.37929i	0.992538	+	0.121940i
$769$	14.3154	+	24.7949i	0.516225	+	0.894128i	0.999823	+	0.0188374i	$0.00599650\pi$
$769$	14.3154	+	24.7949i	0.516225	+	0.894128i	−0.483598	+	0.875290i	$0.660670\pi$
$770$	−2.75399	+	3.48329i	−0.0992468	+	0.125529i
$771$	−0.0998596	+	16.0298i	−0.00359636	+	0.577299i
$772$	0.0599512	+	0.252858i	0.00215769	+	0.00910056i
$773$	−0.438719			−0.0157796			−0.00788981	−	0.999969i	$-0.502511\pi$
$773$	−0.438719			−0.0157796			−0.00788981	+	0.999969i	$0.502511\pi$
$774$	−16.5438	−	2.63353i	−0.594656	−	0.0946603i
$775$			4.97106i			0.178566i
$776$	−22.4578	+	15.7294i	−0.806189	+	0.564653i
$777$	8.68192	+	15.2562i	0.311462	+	0.547314i
$778$	−18.6736	+	23.6187i	−0.669481	+	0.846771i
$779$	−9.43322	+	5.44627i	−0.337980	+	0.195133i
$780$	16.2401	−	3.74375i	0.581490	−	0.134048i
$781$	−21.2373	−	12.2614i	−0.759932	−	0.438747i
$782$	13.6000	−	5.40360i	0.486335	−	0.193232i
$783$	20.6720	−	34.3080i	0.738758	−	1.22607i
$784$	1.28011	−	22.0434i	0.0457184	−	0.787265i
$785$	14.0146	+	8.09131i	0.500201	+	0.288791i
$786$	−2.16539	+	14.1710i	−0.0772369	+	0.505464i
$787$	7.64503	+	13.2416i	0.272516	+	0.472011i	0.969505	−	0.245070i	$-0.0788110\pi$
$787$	7.64503	+	13.2416i	0.272516	+	0.472011i	−0.696990	+	0.717081i	$0.745478\pi$
$788$	26.4076	+	7.90346i	0.940731	+	0.281549i
$789$	15.5937	+	27.4019i	0.555151	+	0.975534i
$790$	−2.17173	+	14.8307i	−0.0772668	+	0.527653i
$791$	−5.45645			−0.194009
$792$	9.49995	−	19.7337i	0.337566	−	0.701206i
$793$	54.9742			1.95219
$794$	−1.10923	+	7.57489i	−0.0393650	+	0.268823i
$795$	−0.126378		0.000787285i	−0.00448215		2.79221e-5i
$796$	7.27066	−	24.2932i	0.257702	−	0.861051i
$797$	17.6568	+	30.5824i	0.625435	+	1.08328i	0.988457	+	0.151504i	$0.0484116\pi$
$797$	17.6568	+	30.5824i	0.625435	+	1.08328i	−0.363022	+	0.931781i	$0.618255\pi$
$798$	13.0316	−	5.08401i	0.461314	−	0.179972i
$799$	−33.6733	−	19.4413i	−1.19128	−	0.687784i
$800$	5.36935	−	1.78048i	0.189835	−	0.0629494i
$801$	30.2595	−	16.9712i	1.06917	−	0.599648i
$802$	−16.2061	+	6.43908i	−0.572258	+	0.227372i
$803$	−24.0331	−	13.8755i	−0.848111	−	0.489657i
$804$	17.1941	+	5.26291i	0.606389	+	0.185608i
$805$	1.82548	−	1.05394i	0.0643397	−	0.0371466i
$806$	20.9768	−	26.5318i	0.738877	−	0.934544i
$807$	−13.8227	+	23.6009i	−0.486584	+	0.830792i
$808$	−35.1789	+	24.6392i	−1.23759	+	0.866804i
$809$			22.5085i			0.791358i	0.918389	+	0.395679i	$0.129491\pi$
$809$			22.5085i			0.791358i	−0.918389	+	0.395679i	$0.870509\pi$
$810$	−12.5438	−	2.15735i	−0.440743	−	0.0758015i
$811$	52.4632			1.84223			0.921116	−	0.389289i	$-0.127279\pi$
$811$	52.4632			1.84223			0.921116	+	0.389289i	$0.127279\pi$
$812$	18.2488	−	4.32669i	0.640407	−	0.151837i
$813$	7.43210	+	4.35288i	0.260655	+	0.152662i
$814$	18.8602	−	23.8548i	0.661051	−	0.836109i
$815$	−1.65582	−	2.86796i	−0.0580008	−	0.100460i
$816$	−18.3446	−	37.0858i	−0.642191	−	1.29826i
$817$	−9.26789	+	16.0525i	−0.324242	+	0.561604i
$818$	11.8965	+	29.9415i	0.415950	+	1.04688i
$819$	−8.58885	−	15.3138i	−0.300119	−	0.535108i
$820$	3.18492	+	3.37524i	0.111222	+	0.117869i
$821$	27.6844	−	47.9508i	0.966193	−	1.67350i	0.259818	−	0.965658i	$-0.416338\pi$
$821$	27.6844	−	47.9508i	0.966193	−	1.67350i	0.706375	−	0.707838i	$-0.250329\pi$
$822$	12.4921	−	4.87353i	0.435712	−	0.169984i
$823$	−32.2602	+	18.6255i	−1.12452	+	0.649243i	−0.942551	−	0.334061i	$-0.891581\pi$
$823$	−32.2602	+	18.6255i	−1.12452	+	0.649243i	−0.181970	+	0.983304i	$0.558247\pi$
$824$	−5.51691	+	0.483378i	−0.192191	+	0.0168393i
$825$	0.0278495	−	4.47050i	0.000969596	−	0.155643i
$826$	10.4716	+	1.53340i	0.364352	+	0.0533538i
$827$		−	11.9636i		−	0.416016i	−0.978127	−	0.208008i	$-0.933302\pi$
$827$		−	11.9636i		−	0.416016i	0.978127	−	0.208008i	$-0.0666981\pi$
$828$	−7.64985	+	7.04041i	−0.265851	+	0.244671i
$829$			14.2267i			0.494113i	0.969001	+	0.247056i	$0.0794633\pi$
$829$			14.2267i			0.494113i	−0.969001	+	0.247056i	$0.920537\pi$
$830$	−1.18978	+	8.12499i	−0.0412979	+	0.282022i
$831$	−10.3698	+	5.90117i	−0.359724	+	0.204709i
$832$	−36.1708	−	13.1546i	−1.25400	−	0.456055i
$833$	−28.5494	+	16.4830i	−0.989178	+	0.571102i
$834$	38.0482	+	5.81392i	1.31750	+	0.201319i
$835$	−7.68558	+	13.3118i	−0.265970	+	0.460674i
$836$	−16.6313	−	17.6252i	−0.575207	−	0.609579i
$837$	−22.6072	+	12.4949i	−0.781420	+	0.431887i
$838$	14.0667	−	5.58902i	0.485925	−	0.193069i
$839$	14.9605	−	25.9124i	0.516494	−	0.894594i	−0.483322	−	0.875442i	$-0.660570\pi$
$839$	14.9605	−	25.9124i	0.516494	−	0.894594i	0.999817	−	0.0191519i	$-0.00609660\pi$
$840$	−3.38842	−	4.90257i	−0.116912	−	0.169155i
$841$	−15.2105	−	26.3454i	−0.524501	−	0.908463i
$842$	15.9120	+	12.5805i	0.548363	+	0.433551i
$843$	−12.1698	+	6.92554i	−0.419152	+	0.238528i
$844$	−9.15387	−	38.6086i	−0.315089	−	1.32896i
$845$	−10.1465			−0.349049
$846$	27.2798	+	4.34254i	0.937900	+	0.149300i
$847$			5.27709i			0.181323i
$848$	0.243875	+	0.160339i	0.00837469	+	0.00550608i
$849$	48.3243	+	0.301042i	1.65849	+	0.0103318i
$850$	−6.62509	−	5.23799i	−0.227239	−	0.179661i
$851$	−12.5015	+	7.21775i	−0.428546	+	0.247421i
$852$	24.0778	−	22.4382i	0.824890	−	0.768719i
$853$	−43.9084	−	25.3505i	−1.50339	−	0.867985i	−0.999992	−	0.00393313i	$-0.998748\pi$
$853$	−43.9084	−	25.3505i	−1.50339	−	0.867985i	−0.503402	−	0.864052i	$-0.667919\pi$
$854$	−7.25866	−	18.2689i	−0.248386	−	0.625148i
$855$	−7.19295	+	12.1076i	−0.245994	+	0.414073i
$856$	15.0703	−	32.3291i	0.515091	−	1.10498i
$857$	30.0961	+	17.3760i	1.02806	+	0.593552i	0.916429	−	0.400198i	$-0.131059\pi$
$857$	30.0961	+	17.3760i	1.02806	+	0.593552i	0.111633	+	0.993750i	$0.464392\pi$
$858$	−19.0132	+	23.7427i	−0.649100	+	0.810562i
$859$	−6.48824	−	11.2380i	−0.221376	−	0.383434i	0.733850	−	0.679311i	$-0.237721\pi$
$859$	−6.48824	−	11.2380i	−0.221376	−	0.383434i	−0.955226	+	0.295877i	$0.904388\pi$
$860$	7.56546	+	2.26425i	0.257980	+	0.0772102i
$861$	2.47084	−	4.21872i	0.0842061	−	0.143773i
$862$	26.1517	+	3.82952i	0.890730	+	0.130434i
$863$	25.0943			0.854220			0.427110	−	0.904200i	$-0.359532\pi$
$863$	25.0943			0.854220			0.427110	+	0.904200i	$0.359532\pi$
$864$	21.5932	+	19.9433i	0.734616	+	0.678483i
$865$	13.0795			0.444716
$866$	−38.8416	−	5.68777i	−1.31989	−	0.193278i
$867$	−16.3377	+	27.8950i	−0.554859	+	0.947365i
$868$	−11.5867	−	3.46776i	−0.393279	−	0.117704i
$869$	−13.6782	−	23.6913i	−0.464000	−	0.803671i
$870$	−11.8026	+	14.7385i	−0.400147	+	0.499683i
$871$	−21.6276	−	12.4867i	−0.732825	−	0.423097i
$872$	−19.6116	+	42.0712i	−0.664133	+	1.42471i
$873$	−29.0793	−	0.362321i	−0.984186	−	0.0122627i
$874$	4.24761	+	10.6905i	0.143677	+	0.361613i
$875$	−1.05351	−	0.608247i	−0.0356153	−	0.0205625i
$876$	27.2475	−	25.3921i	0.920607	−	0.857918i
$877$	29.8243	−	17.2191i	1.00710	−	0.581447i	0.0967563	−	0.995308i	$-0.469153\pi$
$877$	29.8243	−	17.2191i	1.00710	−	0.581447i	0.910340	+	0.413861i	$0.135820\pi$
$878$	−33.6486	−	26.6035i	−1.13558	−	0.897825i
$879$	45.9923	+	0.286515i	1.55128	+	0.00966390i
$880$	−5.67187	+	8.62686i	−0.191199	+	0.290811i
$881$			11.0595i			0.372603i	0.982493	+	0.186301i	$0.0596501\pi$
$881$			11.0595i			0.372603i	−0.982493	+	0.186301i	$0.940350\pi$
$882$	14.7529	−	18.1892i	0.496755	−	0.612463i
$883$	−28.7514			−0.967563			−0.483782	−	0.875189i	$-0.660737\pi$
$883$	−28.7514			−0.967563			−0.483782	+	0.875189i	$0.660737\pi$
$884$	13.2567	+	55.9130i	0.445869	+	1.88056i
$885$	−9.26052	+	5.26992i	−0.311289	+	0.177146i
$886$	37.5920	+	29.7213i	1.26293	+	0.998505i
$887$	23.0648	+	39.9494i	0.774440	+	1.34137i	0.935109	+	0.354361i	$0.115302\pi$
$887$	23.0648	+	39.9494i	0.774440	+	1.34137i	−0.160668	+	0.987008i	$0.551365\pi$
$888$	23.2051	+	33.5745i	0.778711	+	1.12668i
$889$	−4.47930	+	7.75838i	−0.150231	+	0.260208i
$890$	−15.1990	+	6.03894i	−0.509473	+	0.202426i
$891$	20.4008	−	11.1101i	0.683452	−	0.372202i
$892$	−5.72715	−	6.06939i	−0.191759	−	0.203218i
$893$	15.2822	−	26.4696i	0.511400	−	0.885770i
$894$	−23.9954	−	3.66660i	−0.802528	−	0.122629i
$895$	20.7421	−	11.9755i	0.693332	−	0.400296i
$896$	0.404398	+	13.7571i	0.0135100	+	0.459593i
$897$	12.5493	−	7.14151i	0.419011	−	0.238448i
$898$	−4.15320	+	28.3621i	−0.138594	+	0.946456i
$899$			38.3195i			1.27803i
$900$	5.72620	+	1.79181i	0.190873	+	0.0597270i
$901$		−	0.435747i		−	0.0145168i
$902$	−8.38039	−	1.22718i	−0.279036	−	0.0408607i
$903$	0.0518272	−	8.31947i	0.00172470	−	0.276855i
$904$	−12.6382	+	1.10733i	−0.420340	+	0.0368291i
$905$	10.4865	−	6.05440i	0.348584	−	0.201255i
$906$	−41.7077	+	16.2714i	−1.38565	+	0.540580i
$907$	19.7183	−	34.1532i	0.654737	−	1.13404i	−0.327223	−	0.944947i	$-0.606113\pi$
$907$	19.7183	−	34.1532i	0.654737	−	1.13404i	0.981960	−	0.189090i	$-0.0605539\pi$
$908$	−6.22025	−	6.59195i	−0.206426	−	0.218762i
$909$	−45.5511	−	0.567554i	−1.51083	−	0.0188246i
$910$	3.05621	+	7.69198i	0.101312	+	0.254987i
$911$	−8.74232	+	15.1421i	−0.289646	+	0.501681i	−0.973725	−	0.227726i	$-0.926871\pi$
$911$	−8.74232	+	15.1421i	−0.289646	+	0.501681i	0.684079	+	0.729408i	$0.260204\pi$
$912$	29.1520	−	14.4202i	0.965319	−	0.477499i
$913$	−7.49357	−	12.9792i	−0.248001	−	0.429550i
$914$	24.8792	−	31.4676i	0.822930	−	1.04086i
$915$	17.0779	+	10.0023i	0.564578	+	0.330666i
$916$	14.0925	−	3.34126i	0.465630	−	0.110398i
$917$	−7.11947			−0.235106
$918$	7.16877	−	43.2952i	0.236605	−	1.42895i
$919$			17.5577i			0.579174i	0.957152	+	0.289587i	$0.0935179\pi$
$919$			17.5577i			0.579174i	−0.957152	+	0.289587i	$0.906482\pi$
$920$	4.01428	−	2.81159i	0.132347	−	0.0926954i
$921$	7.93291	−	13.5446i	0.261398	−	0.446311i
$922$	20.8438	−	26.3636i	0.686453	−	0.868238i
$923$	−39.5857	+	22.8548i	−1.30298	+	0.752276i
$924$	10.4006	+	3.18349i	0.342154	+	0.104729i
$925$	7.21483	+	4.16548i	0.237222	+	0.136960i
$926$	26.4126	−	10.4944i	0.867971	−	0.344866i
$927$	−5.05004	−	3.00014i	−0.165865	−	0.0985377i
$928$	41.3897	−	13.7248i	1.35868	−	0.450539i
$929$	−32.5770	−	18.8083i	−1.06882	−	0.617081i	−0.140958	−	0.990016i	$-0.545018\pi$
$929$	−32.5770	−	18.8083i	−1.06882	−	0.617081i	−0.927858	+	0.372935i	$0.878352\pi$
$930$	11.3439	−	4.42556i	0.371980	−	0.145120i
$931$	−12.9568	−	22.4418i	−0.424641	−	0.735501i
$932$	−11.5969	+	38.7483i	−0.379868	+	1.26924i
$933$	−16.2779	−	0.101405i	−0.532915	−	0.00331986i
$934$	−0.651485	+	4.44897i	−0.0213172	+	0.145575i
$935$	15.4142			0.504097
$936$	−23.0012	−	33.7267i	−0.751817	−	1.10239i
$937$	0.778145			0.0254209			0.0127104	−	0.999919i	$-0.495954\pi$
$937$	0.778145			0.0254209			0.0127104	+	0.999919i	$0.495954\pi$
$938$	−1.29389	+	8.83596i	−0.0422471	+	0.288504i
$939$	−7.30604	−	12.8385i	−0.238424	−	0.418968i
$940$	−12.4750	−	3.73362i	−0.406890	−	0.121777i
$941$	4.49598	+	7.78726i	0.146565	+	0.253857i	0.929956	−	0.367672i	$-0.119845\pi$
$941$	4.49598	+	7.78726i	0.146565	+	0.253857i	−0.783391	+	0.621529i	$0.786512\pi$
$942$	5.98752	−	39.1844i	0.195084	−	1.27670i
$943$	3.48193	+	2.01029i	0.113387	+	0.0654641i
$944$	24.5653	+	1.42656i	0.799533	+	0.0464307i
$945$	0.118126	−	6.31998i	0.00384263	−	0.205589i
$946$	−13.3944	+	5.32192i	−0.435490	+	0.173030i
$947$	25.9458	+	14.9798i	0.843124	+	0.486778i	0.858325	−	0.513107i	$-0.171505\pi$
$947$	25.9458	+	14.9798i	0.843124	+	0.486778i	−0.0152009	+	0.999884i	$0.504839\pi$
$948$	35.7768	−	8.24741i	1.16198	−	0.267863i
$949$	−44.7970	+	25.8636i	−1.45417	+	0.839567i
$950$	4.11742	−	5.20778i	0.133587	−	0.168963i
$951$	−10.2685	−	18.0442i	−0.332978	−	0.585123i
$952$	16.8305	−	11.7880i	0.545479	−	0.382053i
$953$			6.56079i			0.212525i	0.994338	+	0.106262i	$0.0338884\pi$
$953$			6.56079i			0.212525i	−0.994338	+	0.106262i	$0.966112\pi$
$954$	0.110713	+	0.289092i	0.00358447	+	0.00935970i
$955$	−16.3248			−0.528258
$956$	−9.96637	−	42.0355i	−0.322335	−	1.35952i
$957$	0.214678	−	34.4609i	0.00693956	−	1.11396i
$958$	4.23464	−	5.35604i	0.136815	−	0.173046i
$959$	3.32969	+	5.76720i	0.107521	+	0.186232i
$960$	−8.84316	−	10.6676i	−0.285412	−	0.344297i
$961$	−3.14428	+	5.44605i	−0.101428	+	0.175679i
$962$	−20.9299	−	52.6773i	−0.674809	−	1.69838i
$963$	32.9972	−	18.5067i	1.06332	−	0.596370i
$964$	−38.7708	+	36.5846i	−1.24872	+	1.17831i
$965$	0.0649670	−	0.112526i	0.00209136	−	0.00362234i
$966$	−4.03024	−	3.22742i	−0.129671	−	0.103841i
$967$	−27.1073	+	15.6504i	−0.871712	+	0.503283i	−0.867917	−	0.496709i	$-0.834541\pi$
$967$	−27.1073	+	15.6504i	−0.871712	+	0.503283i	−0.00379555	+	0.999993i	$0.501208\pi$
$968$	1.07093	+	12.2228i	0.0344209	+	0.392854i
$969$	−41.8997	−	24.5401i	−1.34601	−	0.788341i
$970$	13.5645	+	1.98632i	0.435531	+	0.0637769i
$971$			38.5329i			1.23658i	0.785950	+	0.618290i	$0.212174\pi$
$971$			38.5329i			1.23658i	−0.785950	+	0.618290i	$0.787826\pi$
$972$	6.24425	+	30.5452i	0.200284	+	0.979738i
$973$			19.1153i			0.612807i
$974$	2.94074	−	20.0822i	0.0942275	−	0.643477i
$975$	−7.19052	−	4.21139i	−0.230281	−	0.134872i
$976$	−20.5199	−	40.8412i	−0.656827	−	1.30729i
$977$	1.68613	−	0.973486i	0.0539440	−	0.0311446i	−0.472785	−	0.881178i	$-0.656751\pi$
$977$	1.68613	−	0.973486i	0.0539440	−	0.0311446i	0.526729	+	0.850033i	$0.323418\pi$
$978$	−5.07051	+	6.33179i	−0.162137	+	0.202468i
$979$	14.9246	−	25.8502i	0.476994	−	0.826177i
$980$	−8.02977	+	7.57699i	−0.256501	+	0.242038i
$981$	−42.9408	+	24.0836i	−1.37099	+	0.768930i
$982$	−2.05160	+	0.815150i	−0.0654692	+	0.0260125i
$983$	6.03150	−	10.4469i	0.192375	−	0.333203i	−0.753662	−	0.657262i	$-0.771714\pi$
$983$	6.03150	−	10.4469i	0.192375	−	0.333203i	0.946037	+	0.324059i	$0.105048\pi$
$984$	4.86681	−	10.2728i	0.155148	−	0.327484i
$985$	−6.89123	−	11.9360i	−0.219573	−	0.380311i
$986$	−51.0696	−	40.3771i	−1.62639	−	1.28587i
$987$	−0.0854601	+	13.7183i	−0.00272022	+	0.436659i
$988$	−43.9515	+	10.4206i	−1.39828	+	0.331525i
$989$	6.84180			0.217557
$990$	−10.2264	+	3.91638i	−0.325016	+	0.124471i
$991$			41.3228i			1.31266i	0.754473	+	0.656331i	$0.227893\pi$
$991$			41.3228i			1.31266i	−0.754473	+	0.656331i	$0.772107\pi$
$992$	−27.5408	−	5.68060i	−0.874422	−	0.180359i
$993$	−27.3087	−	47.9879i	−0.866614	−	1.52285i
$994$	12.8219	+	10.1373i	0.406685	+	0.321537i
$995$	−10.9803	+	6.33948i	−0.348099	+	0.200975i
$996$	19.6003	−	4.51834i	0.621058	−	0.143169i
$997$	31.8106	+	18.3659i	1.00745	+	0.581653i	0.910445	−	0.413630i	$-0.135739\pi$
$997$	31.8106	+	18.3659i	1.00745	+	0.581653i	0.0970082	+	0.995284i	$0.469073\pi$
$998$	6.59880	+	16.6081i	0.208881	+	0.525720i
$999$	−0.808964	+	43.2814i	−0.0255945	+	1.36936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.a.11.2	✓	48
3.2	odd	2		1080.2.bm.b.251.23		48
4.3	odd	2		1440.2.cc.a.911.8		48
8.3	odd	2		360.2.bm.b.11.7	yes	48
8.5	even	2		1440.2.cc.b.911.8		48
9.4	even	3		1080.2.bm.a.611.18		48
9.5	odd	6		360.2.bm.b.131.7	yes	48
12.11	even	2		4320.2.cc.b.1871.15		48
24.5	odd	2		4320.2.cc.a.1871.10		48
24.11	even	2		1080.2.bm.a.251.18		48
36.23	even	6		1440.2.cc.b.1391.8		48
36.31	odd	6		4320.2.cc.a.3311.10		48
72.5	odd	6		1440.2.cc.a.1391.8		48
72.13	even	6		4320.2.cc.b.3311.15		48
72.59	even	6	inner	360.2.bm.a.131.2	yes	48
72.67	odd	6		1080.2.bm.b.611.23		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.2	✓	48	1.1	even	1	trivial
360.2.bm.a.131.2	yes	48	72.59	even	6	inner
360.2.bm.b.11.7	yes	48	8.3	odd	2
360.2.bm.b.131.7	yes	48	9.5	odd	6
1080.2.bm.a.251.18		48	24.11	even	2
1080.2.bm.a.611.18		48	9.4	even	3
1080.2.bm.b.251.23		48	3.2	odd	2
1080.2.bm.b.611.23		48	72.67	odd	6
1440.2.cc.a.911.8		48	4.3	odd	2
1440.2.cc.a.1391.8		48	72.5	odd	6
1440.2.cc.b.911.8		48	8.5	even	2
1440.2.cc.b.1391.8		48	36.23	even	6
4320.2.cc.a.1871.10		48	24.5	odd	2
4320.2.cc.a.3311.10		48	36.31	odd	6
4320.2.cc.b.1871.15		48	12.11	even	2
4320.2.cc.b.3311.15		48	72.13	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39929 - 0.204905i) q^{2} +(0.875353 - 1.49458i) q^{3} +(1.91603 + 0.573443i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.53112 + 1.91198i) q^{6} +(-1.05351 - 0.608247i) q^{7} +(-2.56358 - 1.19502i) q^{8} +(-1.46751 - 2.61656i) q^{9} +O(q^{10})\)	\(q+(-1.39929 - 0.204905i) q^{2} +(0.875353 - 1.49458i) q^{3} +(1.91603 + 0.573443i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.53112 + 1.91198i) q^{6} +(-1.05351 - 0.608247i) q^{7} +(-2.56358 - 1.19502i) q^{8} +(-1.46751 - 2.61656i) q^{9} +(0.522192 + 1.31427i) q^{10} +(-2.23529 - 1.29055i) q^{11} +(2.53425 - 2.36168i) q^{12} +(-4.16652 + 2.40554i) q^{13} +(1.34954 + 1.06698i) q^{14} +(-1.73202 - 0.0107898i) q^{15} +(3.34233 + 2.19747i) q^{16} -5.97195i q^{17} +(1.51733 + 3.96203i) q^{18} +4.69437 q^{19} +(-0.461398 - 1.94605i) q^{20} +(-1.83127 + 1.04213i) q^{21} +(2.86338 + 2.26387i) q^{22} +(-0.866377 - 1.50061i) q^{23} +(-4.03008 + 2.78540i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(6.32307 - 2.51231i) q^{26} +(-5.19525 - 0.0971033i) q^{27} +(-1.66977 - 1.76955i) q^{28} +(-3.85425 + 6.67576i) q^{29} +(2.42138 + 0.369997i) q^{30} +(4.30506 - 2.48553i) q^{31} +(-4.22661 - 3.75975i) q^{32} +(-3.88549 + 2.21113i) q^{33} +(-1.22368 + 8.35649i) q^{34} +1.21649i q^{35} +(-1.31135 - 5.85494i) q^{36} -8.33096i q^{37} +(-6.56878 - 0.961899i) q^{38} +(-0.0519106 + 8.33287i) q^{39} +(0.246874 + 2.81763i) q^{40} +(-2.00948 + 1.16017i) q^{41} +(2.77601 - 1.08300i) q^{42} +(-1.97426 + 3.41951i) q^{43} +(-3.54283 - 3.75454i) q^{44} +(-1.53225 + 2.57919i) q^{45} +(0.904830 + 2.27731i) q^{46} +(3.25544 - 5.63858i) q^{47} +(6.20999 - 3.07180i) q^{48} +(-2.76007 - 4.78058i) q^{49} +(0.877098 - 1.10937i) q^{50} +(-8.92553 - 5.22756i) q^{51} +(-9.36260 + 2.21982i) q^{52} +0.0729656 q^{53} +(7.24976 + 1.20041i) q^{54} +2.58109i q^{55} +(1.97390 + 2.81826i) q^{56} +(4.10923 - 7.01609i) q^{57} +(6.76112 - 8.55158i) q^{58} +(5.32751 - 3.07584i) q^{59} +(-3.31241 - 1.01389i) q^{60} +(-9.89571 - 5.71329i) q^{61} +(-6.53333 + 2.59585i) q^{62} +(-0.0454680 + 3.64920i) q^{63} +(5.14387 + 6.12704i) q^{64} +(4.16652 + 2.40554i) q^{65} +(5.89000 - 2.29786i) q^{66} +(2.59541 + 4.49538i) q^{67} +(3.42457 - 11.4424i) q^{68} +(-3.00116 - 0.0186961i) q^{69} +(0.249266 - 1.70223i) q^{70} +9.50092 q^{71} +(0.635251 + 8.46147i) q^{72} +10.7517 q^{73} +(-1.70706 + 11.6574i) q^{74} +(0.856664 + 1.50537i) q^{75} +(8.99454 + 2.69195i) q^{76} +(1.56994 + 2.71922i) q^{77} +(1.78008 - 11.6495i) q^{78} +(9.17877 + 5.29936i) q^{79} +(0.231899 - 3.99327i) q^{80} +(-4.69280 + 7.67969i) q^{81} +(3.04957 - 1.21167i) q^{82} +(5.02858 + 2.90325i) q^{83} +(-4.10636 + 0.946616i) q^{84} +(-5.17186 + 2.98597i) q^{85} +(3.46324 - 4.38036i) q^{86} +(6.60360 + 11.6041i) q^{87} +(4.18812 + 5.97963i) q^{88} +11.5646i q^{89} +(2.67255 - 3.29506i) q^{90} +5.85265 q^{91} +(-0.799488 - 3.37203i) q^{92} +(0.0536368 - 8.60996i) q^{93} +(-5.71068 + 7.22296i) q^{94} +(-2.34718 - 4.06544i) q^{95} +(-9.31901 + 3.02588i) q^{96} +(4.84693 - 8.39513i) q^{97} +(2.88258 + 7.25498i) q^{98} +(-0.0964717 + 7.74268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * q^96 + 42 * q^98 - 16 * q^99

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