LMFDB - Embedded newform 360.2.bm.b.11.7

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			11.7
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.b.131.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877098 - 1.10937i) q^{2} +(0.875353 - 1.49458i) q^{3} +(-0.461398 + 1.94605i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.42581 + 0.339801i) q^{6} +(1.05351 + 0.608247i) q^{7} +(2.56358 - 1.19502i) q^{8} +(-1.46751 - 2.61656i) q^{9} +O(q^{10})$	\(q+(-0.877098 - 1.10937i) q^{2} +(0.875353 - 1.49458i) q^{3} +(-0.461398 + 1.94605i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.42581 + 0.339801i) 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} +(2.50463 + 2.39307i) q^{12} +(4.16652 - 2.40554i) q^{13} +(-0.249266 - 1.70223i) q^{14} +(1.73202 + 0.0107898i) q^{15} +(-3.57422 - 1.79581i) q^{16} -5.97195i q^{17} +(-1.61558 + 3.92300i) q^{18} +4.69437 q^{19} +(-1.91603 + 0.573443i) q^{20} +(1.83127 - 1.04213i) q^{21} +(0.528879 + 3.61170i) q^{22} +(0.866377 + 1.50061i) q^{23} +(0.457991 - 4.87752i) 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} +(-1.50718 - 1.93091i) q^{30} +(-4.30506 + 2.48553i) q^{31} +(1.14273 + 5.54023i) q^{32} +(-3.88549 + 2.21113i) q^{33} +(-6.62509 + 5.23799i) q^{34} +1.21649i q^{35} +(5.76907 - 1.64858i) q^{36} +8.33096i q^{37} +(-4.11742 - 5.20778i) q^{38} +(0.0519106 - 8.33287i) q^{39} +(2.31670 + 1.62262i) q^{40} +(-2.00948 + 1.16017i) q^{41} +(-2.76230 - 1.11750i) 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} +(-5.81268 + 3.76999i) q^{48} +(-2.76007 - 4.78058i) q^{49} +(1.39929 - 0.204905i) q^{50} +(-8.92553 - 5.22756i) q^{51} +(2.75888 + 9.21816i) q^{52} -0.0729656 q^{53} +(4.44902 + 5.84861i) q^{54} -2.58109i q^{55} +(3.42763 + 0.300321i) q^{56} +(4.10923 - 7.01609i) q^{57} +(-10.7864 + 1.57951i) q^{58} +(5.32751 - 3.07584i) q^{59} +(-0.820146 + 3.36561i) 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} +(5.86092 + 2.37106i) q^{66} +(2.59541 + 4.49538i) q^{67} +(11.6217 + 2.75544i) q^{68} +(3.00116 + 0.0186961i) q^{69} +(1.34954 - 1.06698i) q^{70} -9.50092 q^{71} +(-6.88893 - 4.95406i) q^{72} +10.7517 q^{73} +(9.24211 - 7.30707i) q^{74} +(0.856664 + 1.50537i) q^{75} +(-2.16597 + 9.13547i) q^{76} +(-1.56994 - 2.71922i) q^{77} +(-9.28975 + 7.25116i) 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} +(1.18309 + 4.04458i) q^{84} +(5.17186 - 2.98597i) q^{85} +(5.52512 - 0.809070i) q^{86} +(-6.60360 - 11.6041i) q^{87} +(-7.27257 - 0.637205i) q^{88} +11.5646i q^{89} +(-4.20520 + 0.562367i) q^{90} +5.85265 q^{91} +(-3.32000 + 0.993636i) q^{92} +(-0.0536368 + 8.60996i) q^{93} +(9.11060 - 1.33411i) q^{94} +(2.34718 + 4.06544i) q^{95} +(9.28059 + 3.14175i) 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} - q^{6} + 6 q^{8}+O(q^{10}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * 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 $

$2$	−0.877098	−	1.10937i	−0.620202	−	0.784442i
$2$	−0.877098	−	1.10937i	−0.620202	−	0.784442i
$3$	0.875353	−	1.49458i	0.505385	−	0.862894i
$3$	0.875353	−	1.49458i	0.505385	−	0.862894i
$4$	−0.461398	+	1.94605i	−0.230699	+	0.973025i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−2.42581	+	0.339801i	−0.990331	+	0.138723i
$7$	1.05351	+	0.608247i	0.398191	+	0.229896i	0.685703	−	0.727881i	$-0.259495\pi$
$7$	1.05351	+	0.608247i	0.398191	+	0.229896i	−0.287512	+	0.957777i	$0.592828\pi$
$8$	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	$0.793886\pi$
$12$	2.50463	+	2.39307i	0.723026	+	0.690821i
$13$	4.16652	−	2.40554i	1.15558	−	0.667176i	0.205342	−	0.978690i	$-0.434169\pi$
$13$	4.16652	−	2.40554i	1.15558	−	0.667176i	0.950242	+	0.311514i	$0.100836\pi$
$14$	−0.249266	−	1.70223i	−0.0666190	−	0.454940i
$15$	1.73202	+	0.0107898i	0.447205	+	0.00278592i
$16$	−3.57422	−	1.79581i	−0.893556	−	0.448951i
$17$		−	5.97195i		−	1.44841i	−0.689584	−	0.724205i	$-0.742207\pi$
$17$		−	5.97195i		−	1.44841i	0.689584	−	0.724205i	$-0.257793\pi$
$18$	−1.61558	+	3.92300i	−0.380795	+	0.924659i
$19$	4.69437			1.07696			0.538481	−	0.842638i	$-0.318998\pi$
$19$	4.69437			1.07696			0.538481	+	0.842638i	$0.318998\pi$
$20$	−1.91603	+	0.573443i	−0.428437	+	0.128226i
$21$	1.83127	−	1.04213i	0.399615	−	0.227411i
$22$	0.528879	+	3.61170i	0.112757	+	0.770017i
$23$	0.866377	+	1.50061i	0.180652	+	0.312898i	0.942103	−	0.335324i	$-0.108846\pi$
$23$	0.866377	+	1.50061i	0.180652	+	0.312898i	−0.761451	+	0.648223i	$0.775513\pi$
$24$	0.457991	−	4.87752i	0.0934871	−	0.995620i
$25$	−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	$-0.579433\pi$
$29$	3.85425	−	6.67576i	0.715717	−	1.23966i	0.962682	−	0.270634i	$-0.0872332\pi$
$30$	−1.50718	−	1.93091i	−0.275172	−	0.352534i
$31$	−4.30506	+	2.48553i	−0.773212	+	0.446414i	−0.834019	−	0.551735i	$-0.813966\pi$
$31$	−4.30506	+	2.48553i	−0.773212	+	0.446414i	0.0608069	+	0.998150i	$0.480633\pi$
$32$	1.14273	+	5.54023i	0.202009	+	0.979384i
$33$	−3.88549	+	2.21113i	−0.676377	+	0.384909i
$34$	−6.62509	+	5.23799i	−1.13619	+	0.898307i
$35$			1.21649i			0.205625i
$36$	5.76907	−	1.64858i	0.961512	−	0.274764i
$37$			8.33096i			1.36960i	0.728730	+	0.684801i	$0.240111\pi$
$37$			8.33096i			1.36960i	−0.728730	+	0.684801i	$0.759889\pi$
$38$	−4.11742	−	5.20778i	−0.667934	−	0.844814i
$39$	0.0519106	−	8.33287i	0.00831236	−	1.33433i
$40$	2.31670	+	1.62262i	0.366303	+	0.256558i
$41$	−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	$0.391328\pi$
$42$	−2.76230	−	1.11750i	−0.426233	−	0.172435i
$43$	−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	−0.999585	−	0.0287964i	$-0.990833\pi$
$47$	−3.25544	+	5.63858i	−0.474854	+	0.822472i	0.524731	+	0.851268i	$0.324166\pi$
$48$	−5.81268	+	3.76999i	−0.838988	+	0.544151i
$49$	−2.76007	−	4.78058i	−0.394296	−	0.682941i
$50$	1.39929	−	0.204905i	0.197890	−	0.0289779i
$51$	−8.92553	−	5.22756i	−1.24982	−	0.732005i
$52$	2.75888	+	9.21816i	0.382588	+	1.27833i
$53$	−0.0729656			−0.0100226			−0.00501130	−	0.999987i	$-0.501595\pi$
$53$	−0.0729656			−0.0100226			−0.00501130	+	0.999987i	$0.501595\pi$
$54$	4.44902	+	5.84861i	0.605434	+	0.795895i
$55$		−	2.58109i		−	0.348035i
$56$	3.42763	+	0.300321i	0.458037	+	0.0401320i
$57$	4.10923	−	7.01609i	0.544280	−	0.929303i
$58$	−10.7864	+	1.57951i	−1.41633	+	0.207400i
$59$	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	$0.202191\pi$
$60$	−0.820146	+	3.36561i	−0.105880	+	0.434499i
$61$	9.89571	+	5.71329i	1.26702	+	0.731512i	0.974422	−	0.224725i	$-0.0721484\pi$
$61$	9.89571	+	5.71329i	1.26702	+	0.731512i	0.292594	+	0.956237i	$0.405482\pi$
$62$	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
$66$	5.86092	+	2.37106i	0.721429	+	0.291858i
$67$	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	$0.730631\pi$
$68$	11.6217	+	2.75544i	1.40934	+	0.334147i
$69$	3.00116	+	0.0186961i	0.361297	+	0.00225074i
$70$	1.34954	−	1.06698i	0.161301	−	0.127529i
$71$	−9.50092			−1.12755			−0.563776	−	0.825928i	$-0.690652\pi$
$71$	−9.50092			−1.12755			−0.563776	+	0.825928i	$0.690652\pi$
$72$	−6.88893	−	4.95406i	−0.811868	−	0.583841i
$73$	10.7517			1.25839			0.629194	−	0.777248i	$-0.283385\pi$
$73$	10.7517			1.25839			0.629194	+	0.777248i	$0.283385\pi$
$74$	9.24211	−	7.30707i	1.07437	−	0.849430i
$75$	0.856664	+	1.50537i	0.0989191	+	0.173825i
$76$	−2.16597	+	9.13547i	−0.248454	+	1.04791i
$77$	−1.56994	−	2.71922i	−0.178912	−	0.309884i
$78$	−9.28975	+	7.25116i	−1.05186	+	0.821032i
$79$	−9.17877	−	5.29936i	−1.03269	−	0.596225i	−0.114937	−	0.993373i	$-0.536667\pi$
$79$	−9.17877	−	5.29936i	−1.03269	−	0.596225i	−0.917755	+	0.397148i	$0.870000\pi$
$80$	−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	$0.563429\pi$
$84$	1.18309	+	4.04458i	0.129086	+	0.441299i
$85$	5.17186	−	2.98597i	0.560967	−	0.323874i
$86$	5.52512	−	0.809070i	0.595789	−	0.0872443i
$87$	−6.60360	−	11.6041i	−0.707981	−	1.24409i
$88$	−7.27257	−	0.637205i	−0.775259	−	0.0679262i
$89$			11.5646i			1.22584i	0.790144	+	0.612922i	$0.210006\pi$
$89$			11.5646i			1.22584i	−0.790144	+	0.612922i	$0.789994\pi$
$90$	−4.20520	+	0.562367i	−0.443267	+	0.0592787i
$91$	5.85265			0.613524
$92$	−3.32000	+	0.993636i	−0.346134	+	0.103594i
$93$	−0.0536368	+	8.60996i	−0.00556188	+	0.892812i
$94$	9.11060	−	1.33411i	0.939687	−	0.137603i
$95$	2.34718	+	4.06544i	0.240816	+	0.417105i
$96$	9.28059	+	3.14175i	0.947196	+	0.320654i
$97$	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	$0.439261\pi$
$101$	−7.59244	+	13.1505i	−0.755476	+	1.30852i	−0.945138	+	0.326673i	$0.894073\pi$
$102$	2.02927	+	14.4868i	0.200928	+	1.43441i
$103$	−1.69567	+	0.978998i	−0.167080	+	0.0964635i	−0.581208	−	0.813755i	$-0.697420\pi$
$103$	−1.69567	+	0.978998i	−0.167080	+	0.0964635i	0.414128	+	0.910218i	$0.364086\pi$
$104$	7.80653	−	11.1458i	0.765493	−	1.09294i
$105$	1.81814	+	1.06486i	0.177433	+	0.103920i
$106$	0.0639980	+	0.0809457i	0.00621603	+	0.00786214i
$107$			12.6109i			1.21914i	0.792731	+	0.609571i	$0.208658\pi$
$107$			12.6109i			1.21914i	−0.792731	+	0.609571i	$0.791342\pi$
$108$	2.58604	−	10.0654i	0.248842	−	0.968544i
$109$			16.4111i			1.57190i	0.618289	+	0.785951i	$0.287826\pi$
$109$			16.4111i			1.57190i	−0.618289	+	0.785951i	$0.712174\pi$
$110$	−2.86338	+	2.26387i	−0.273013	+	0.215852i
$111$	12.4513	+	7.29253i	1.18182	+	0.692177i
$112$	−2.67320	−	4.06592i	−0.252594	−	0.384193i
$113$	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	$0.265669\pi$
$114$	−11.3876	+	1.59515i	−1.06655	+	0.149399i
$115$	−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
$120$	4.45306	−	2.04213i	0.406507	−	0.186420i
$121$	−2.16898	−	3.75678i	−0.197180	−	0.341525i
$122$	−2.34136	−	15.9891i	−0.211977	−	1.44759i
$123$	−0.0250361	+	4.01887i	−0.00225743	+	0.362370i
$124$	−2.85062	−	9.52469i	−0.255993	−	0.855342i
$125$	−1.00000			−0.0894427
$126$	−4.08819	+	3.15026i	−0.364205	+	0.280648i
$127$			7.36428i			0.653474i	0.945115	+	0.326737i	$0.105949\pi$
$127$			7.36428i			0.653474i	−0.945115	+	0.326737i	$0.894051\pi$
$128$	−11.3088	−	0.332429i	−0.999568	−	0.0293829i
$129$	3.38255	+	5.94396i	0.297817	+	0.523336i
$130$	−0.985814	−	6.73210i	−0.0864616	−	0.590444i
$131$	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	$0.251039\pi$
$132$	−2.51022	−	8.58157i	−0.218486	−	0.746930i
$133$	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	$0.741799\pi$
$138$	−2.61157	−	3.34579i	−0.222312	−	0.284813i
$139$	−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	$-0.398831\pi$
$140$	−2.36736	−	0.561287i	−0.200078	−	0.0474374i
$141$	5.57763	+	9.80125i	0.469721	+	0.825414i
$142$	8.33324	+	10.5400i	0.699310	+	0.884499i
$143$	−12.4178			−1.03843
$144$	0.546388	+	11.9876i	0.0455324	+	0.998963i
$145$	7.70851			0.640157
$146$	−9.43027	−	11.9276i	−0.780455	−	0.987133i
$147$	−9.56098	−	0.0595613i	−0.788577	−	0.00491254i
$148$	−16.2125	−	3.84389i	−1.33266	−	0.315966i
$149$	−4.95490	−	8.58214i	−0.405921	−	0.703076i	0.588507	−	0.808492i	$-0.299716\pi$
$149$	−4.95490	−	8.58214i	−0.405921	−	0.703076i	−0.994428	+	0.105416i	$0.966383\pi$
$150$	0.918627	−	2.27071i	0.0750056	−	0.185403i
$151$	−15.8283	−	9.13850i	−1.28809	−	0.743681i	−0.309779	−	0.950809i	$-0.600255\pi$
$151$	−15.8283	−	9.13850i	−1.28809	−	0.743681i	−0.978314	+	0.207128i	$0.933588\pi$
$152$	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
$156$	16.1922	+	3.94579i	1.29642	+	0.315916i
$157$	14.0146	−	8.09131i	1.11848	−	0.645757i	0.177470	−	0.984126i	$-0.443209\pi$
$157$	14.0146	−	8.09131i	1.11848	−	0.645757i	0.941013	+	0.338369i	$0.109875\pi$
$158$	2.17173	+	14.8307i	0.172774	+	1.17987i
$159$	−0.0638706	+	0.109053i	−0.00506527	+	0.00864843i
$160$	−4.22661	+	3.75975i	−0.334143	+	0.297235i
$161$			2.10788i			0.166125i
$162$	12.6357	−	1.52979i	0.992751	−	0.120192i
$163$	3.31163			0.259387			0.129694	−	0.991554i	$-0.458601\pi$
$163$	3.31163			0.259387			0.129694	+	0.991554i	$0.458601\pi$
$164$	−1.33059	−	4.44584i	−0.103901	−	0.347162i
$165$	−3.85764	−	2.25937i	−0.300317	−	0.175892i
$166$	−1.18978	−	8.12499i	−0.0923450	−	0.630621i
$167$	7.68558	+	13.3118i	0.594728	+	1.03010i	0.993585	+	0.113086i	$0.0360736\pi$
$167$	7.68558	+	13.3118i	0.594728	+	1.03010i	−0.398857	+	0.917013i	$0.630593\pi$
$168$	3.44924	−	4.85997i	0.266115	−	0.374955i
$169$	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	−0.502787	−	0.864410i	$-0.667692\pi$
$173$	6.53975	−	11.3272i	0.497208	−	0.861189i	0.999995	+	0.00322120i	$0.00102534\pi$
$174$	−7.08124	+	17.5038i	−0.536828	+	1.32696i
$175$	−1.05351	+	0.608247i	−0.0796382	+	0.0459791i
$176$	5.67187	+	8.62686i	0.427533	+	0.650274i
$177$	0.0663754	−	10.6548i	0.00498908	−	0.800864i
$178$	12.8294	−	10.1433i	0.961603	−	0.760271i
$179$			23.9509i			1.79018i	0.445889	+	0.895088i	$0.352888\pi$
$179$			23.9509i			1.79018i	−0.445889	+	0.895088i	$0.647112\pi$
$180$	4.31225	+	4.17187i	0.321416	+	0.310953i
$181$		−	12.1088i		−	0.900040i	−0.893018	−	0.450020i	$-0.851417\pi$
$181$		−	12.1088i		−	0.900040i	0.893018	−	0.450020i	$-0.148583\pi$
$182$	−5.13335	−	6.49274i	−0.380509	−	0.481274i
$183$	17.2012	−	9.78874i	1.27155	−	0.723605i
$184$	4.01428	+	2.81159i	0.295936	+	0.207273i
$185$	−7.21483	+	4.16548i	−0.530445	+	0.306252i
$186$	9.59867	−	7.49228i	0.703808	−	0.549361i
$187$	−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	$0.367779\pi$
$191$	−8.16239	+	14.1377i	−0.590610	+	1.02297i	−0.994150	+	0.108005i	$0.965554\pi$
$192$	−4.65463	−	13.0512i	−0.335919	−	0.941891i
$193$	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	$0.831845\pi$
$194$	−13.5645	+	1.98632i	−0.973877	+	0.142610i
$195$	7.24243	−	4.12148i	0.518641	−	0.295145i
$196$	10.5767	−	3.16549i	0.755482	−	0.226106i
$197$	−13.7825			−0.981960			−0.490980	−	0.871171i	$-0.663361\pi$
$197$	−13.7825			−0.981960			−0.490980	+	0.871171i	$0.663361\pi$
$198$	8.67410	−	6.68407i	0.616442	−	0.475016i
$199$			12.6790i			0.898787i	0.893334	+	0.449394i	$0.148360\pi$
$199$			12.6790i			0.898787i	−0.893334	+	0.449394i	$0.851640\pi$
$200$	−0.246874	+	2.81763i	−0.0174566	+	0.199237i
$201$	8.99059	+	0.0560080i	0.634148	+	0.00395050i
$202$	21.2480	−	3.11146i	1.49501	−	0.218921i
$203$	8.12102	−	4.68868i	0.569984	−	0.329081i
$204$	14.2913	−	14.9576i	1.00059	−	1.04724i
$205$	−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
$210$	−0.413366	−	2.95098i	−0.0285249	−	0.203637i
$211$	−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	$-0.405949\pi$
$212$	0.0336661	−	0.141995i	0.00231220	−	0.00975223i
$213$	−8.31666	+	14.1998i	−0.569848	+	0.972958i
$214$	13.9902	−	11.0610i	0.956347	−	0.756115i
$215$	−3.94851			−0.269286
$216$	−13.4345	+	5.95948i	−0.914099	+	0.405491i
$217$	−6.04726			−0.410515
$218$	18.2060	−	14.3942i	1.23307	−	0.974897i
$219$	9.41151	−	16.0692i	0.635971	−	1.08586i
$220$	5.02294	+	1.19091i	0.338646	+	0.0802912i
$221$	−14.3658	−	24.8822i	−0.966345	−	1.67376i
$222$	−2.83087	−	20.2093i	−0.189995	−	1.35636i
$223$	3.61346	+	2.08623i	0.241975	+	0.139704i	0.616084	−	0.787680i	$-0.288718\pi$
$223$	3.61346	+	2.08623i	0.241975	+	0.139704i	−0.374109	+	0.927385i	$0.622051\pi$
$224$	−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	$0.714720\pi$
$228$	11.7577	+	11.2340i	0.778671	+	0.743988i
$229$	−6.27141	+	3.62080i	−0.414426	+	0.239269i	−0.692690	−	0.721236i	$-0.743574\pi$
$229$	−6.27141	+	3.62080i	−0.414426	+	0.239269i	0.278264	+	0.960505i	$0.410241\pi$
$230$	2.42463	−	0.355050i	0.159875	−	0.0234113i
$231$	−5.43833	−	0.0338788i	−0.357816	−	0.00222906i
$232$	1.90303	−	21.7197i	0.124940	−	1.42597i
$233$			20.2232i			1.32487i	0.749120	+	0.662434i	$0.230476\pi$
$233$			20.2232i			1.32487i	−0.749120	+	0.662434i	$0.769524\pi$
$234$	2.70559	+	20.2316i	0.176870	+	1.32258i
$235$	−6.51087			−0.424723
$236$	3.52764	+	11.7868i	0.229629	+	0.767254i
$237$	−15.9550	+	9.07955i	−1.03639	+	0.589780i
$238$	−10.1656	+	1.48860i	−0.658939	+	0.0964917i
$239$	10.8002	+	18.7065i	0.698607	+	1.21002i	0.968950	+	0.247258i	$0.0795296\pi$
$239$	10.8002	+	18.7065i	0.698607	+	1.21002i	−0.270343	+	0.962764i	$0.587137\pi$
$240$	−6.17124	−	3.14893i	−0.398352	−	0.203263i
$241$	−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
$246$	4.48037	−	3.49717i	0.285658	−	0.222972i
$247$	19.5591	−	11.2925i	1.24452	−	0.718523i
$248$	−8.06612	+	11.5165i	−0.512199	+	0.731297i
$249$	8.74091	−	4.97423i	0.553933	−	0.315229i
$250$	0.877098	+	1.10937i	0.0554726	+	0.0701626i
$251$		−	13.0658i		−	0.824704i	−0.911025	−	0.412352i	$-0.864707\pi$
$251$		−	13.0658i		−	0.824704i	0.911025	−	0.412352i	$-0.135293\pi$
$252$	7.08054	+	1.77221i	0.446032	+	0.111639i
$253$		−	4.47240i		−	0.281177i
$254$	8.16970	−	6.45920i	0.512613	−	0.405286i
$255$	0.0644362	−	10.3435i	0.00403515	−	0.647736i
$256$	9.55016	+	12.8372i	0.596885	+	0.802327i
$257$	−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	$0.426541\pi$
$258$	3.62721	−	8.96593i	0.225820	−	0.558195i
$259$	−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	$-0.643667\pi$
$263$	9.10142	−	15.7641i	0.561217	−	0.972057i	0.997391	−	0.0721942i	$-0.0230001\pi$
$264$	−7.31842	+	10.3116i	−0.450418	+	0.634637i
$265$	−0.0364828	−	0.0631900i	−0.00224112	−	0.00388173i
$266$	−1.17014	−	7.99088i	−0.0717461	−	0.489952i
$267$	17.2841	+	10.1231i	1.05777	+	0.619523i
$268$	−9.94576	+	2.97664i	−0.607534	+	0.181827i
$269$	15.7911			0.962798			0.481399	−	0.876502i	$-0.340129\pi$
$269$	15.7911			0.962798			0.481399	+	0.876502i	$0.340129\pi$
$270$	−2.84054	+	6.77727i	−0.172870	+	0.412451i
$271$		−	4.97272i		−	0.302071i	−0.988528	−	0.151035i	$-0.951739\pi$
$271$		−	4.97272i		−	0.302071i	0.988528	−	0.151035i	$-0.0482608\pi$
$272$	−10.7245	+	21.3451i	−0.650266	+	1.29424i
$273$	5.12313	−	8.74722i	0.310066	−	0.529406i
$274$	1.12170	+	7.66006i	0.0677644	+	0.462761i
$275$	2.23529	−	1.29055i	0.134793	−	0.0778229i
$276$	−1.42111	+	5.83178i	−0.0855408	+	0.351032i
$277$	5.96566	+	3.44427i	0.358442	+	0.206946i	0.668397	−	0.743805i	$-0.266981\pi$
$277$	5.96566	+	3.44427i	0.358442	+	0.206946i	−0.309955	+	0.950751i	$0.600314\pi$
$278$	−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	$0.744186\pi$
$282$	5.98106	−	14.7843i	0.356167	−	0.880393i
$283$	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	$0.522096\pi$
$284$	4.38370	−	18.4893i	0.260125	−	1.09714i
$285$	8.13072	+	0.0506513i	0.481622	+	0.00300033i
$286$	10.8917	+	13.7760i	0.644038	+	0.814590i
$287$	−2.82268			−0.166618
$288$	12.8194	−	11.1204i	0.755389	−	0.655276i
$289$	−18.6642			−1.09789
$290$	−6.76112	−	8.55158i	−0.397026	−	0.502166i
$291$	−8.30439	−	14.5928i	−0.486812	−	0.855446i
$292$	−4.96080	+	20.9233i	−0.290309	+	1.22444i
$293$	−13.2771	−	22.9966i	−0.775655	−	1.34347i	−0.934425	−	0.356159i	$-0.884086\pi$
$293$	−13.2771	−	22.9966i	−0.775655	−	1.34347i	0.158770	−	0.987316i	$-0.449247\pi$
$294$	8.31984	+	10.6589i	0.485223	+	0.621639i
$295$	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
$300$	−3.32478	+	0.972540i	−0.191956	+	0.0561496i
$301$	−4.15982	+	2.40167i	−0.239768	+	0.138430i
$302$	3.74505	+	25.5748i	0.215503	+	1.47167i
$303$	13.0083	+	22.8588i	0.747309	+	1.31320i
$304$	−16.7787	−	8.43017i	−0.962326	−	0.483503i
$305$			11.4266i			0.654284i
$306$	23.4279	+	9.64815i	1.33929	+	0.551548i
$307$	9.06253			0.517226			0.258613	−	0.965981i	$-0.416735\pi$
$307$	9.06253			0.517226			0.258613	+	0.965981i	$0.416735\pi$
$308$	6.01611	−	1.80055i	0.342800	−	0.102596i
$309$	−0.0211264	+	3.39128i	−0.00120184	+	0.192923i
$310$	1.01860	+	6.95596i	0.0578523	+	0.395072i
$311$	4.69912	+	8.13912i	0.266463	+	0.461527i	0.967946	−	0.251159i	$-0.0808117\pi$
$311$	4.69912	+	8.13912i	0.266463	+	0.461527i	−0.701483	+	0.712686i	$0.747478\pi$
$312$	−9.82485	−	21.4240i	−0.556222	−	1.21290i
$313$	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	−0.983794	−	0.179302i	$-0.942616\pi$
$317$	−5.99329	+	10.3807i	−0.336617	+	0.583037i	0.647177	+	0.762339i	$0.275949\pi$
$318$	0.177000	−	0.0247938i	0.00992568	−	0.00139036i
$319$	−17.2308	+	9.94819i	−0.964738	+	0.556992i
$320$	7.87811	+	1.39120i	0.440400	+	0.0777704i
$321$	18.8480	+	11.0390i	1.05199	+	0.616137i
$322$	2.33842	−	1.84882i	0.130315	−	0.103031i
$323$		−	28.0345i		−	1.55988i
$324$	−12.7798	−	12.6758i	−0.709990	−	0.704212i
$325$			4.81108i			0.266871i
$326$	−2.90463	−	3.67382i	−0.160873	−	0.203474i
$327$	24.5277	+	14.3655i	1.35638	+	0.794416i
$328$	−3.76502	+	5.37555i	−0.207889	+	0.296815i
$329$	−6.85930	+	3.96022i	−0.378165	+	0.218334i
$330$	0.877058	+	6.26123i	0.0482805	+	0.344670i
$331$	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
$336$	−8.41682	+	0.436193i	−0.459175	+	0.0237963i
$337$	−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	$0.931283\pi$
$338$	−14.1979	+	2.07906i	−0.772262	+	0.113086i
$339$	0.0483965	−	7.76877i	0.00262854	−	0.421942i
$340$	3.42457	+	11.4424i	0.185724	+	0.620552i
$341$	12.8308			0.694825
$342$	−7.58412	+	18.4160i	−0.410102	+	0.995822i
$343$		−	15.2307i		−	0.822379i
$344$	−0.974785	+	11.1255i	−0.0525569	+	0.599845i
$345$	1.48439	+	2.60843i	0.0799168	+	0.140433i
$346$	−18.3020	+	2.68005i	−0.983922	+	0.144081i
$347$	−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	$0.364846\pi$
$348$	25.6291	−	7.49683i	1.37386	−	0.401872i
$349$	−20.4332	−	11.7971i	−1.09376	−	0.631485i	−0.159189	−	0.987248i	$-0.550888\pi$
$349$	−20.4332	−	11.7971i	−1.09376	−	0.631485i	−0.934576	+	0.355763i	$0.884221\pi$
$350$	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	$0.559912\pi$
$354$	−11.8783	+	9.27167i	−0.631326	+	0.492784i
$355$	−4.75046	−	8.22804i	−0.252128	−	0.436699i
$356$	−22.5053	−	5.33587i	−1.19278	−	0.282801i
$357$	−6.22353	−	10.9362i	−0.329384	−	0.578807i
$358$	26.5704	−	21.0073i	1.40429	−	1.11027i
$359$	33.0373			1.74364			0.871820	−	0.489827i	$-0.162940\pi$
$359$	33.0373			1.74364			0.871820	+	0.489827i	$0.162940\pi$
$360$	0.845877	−	8.44301i	0.0445816	−	0.444986i
$361$	3.03707			0.159846
$362$	−13.4331	+	10.6206i	−0.706029	+	0.558207i
$363$	−7.51341	−	0.0468057i	−0.394352	−	0.00245666i
$364$	−2.70040	+	11.3895i	−0.141539	+	0.596974i
$365$	5.37584	+	9.31122i	0.281384	+	0.487372i
$366$	−25.9465	−	10.4968i	−1.35624	−	0.548675i
$367$	−9.72422	−	5.61428i	−0.507600	−	0.293063i	0.224247	−	0.974532i	$-0.428008\pi$
$367$	−9.72422	−	5.61428i	−0.507600	−	0.293063i	−0.731847	+	0.681469i	$0.761341\pi$
$368$	−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
$372$	−16.7307	−	4.07700i	−0.867445	−	0.211382i
$373$	19.9485	−	11.5173i	1.03290	−	0.596343i	0.115083	−	0.993356i	$-0.463287\pi$
$373$	19.9485	−	11.5173i	1.03290	−	0.596343i	0.917813	+	0.397013i	$0.129953\pi$
$374$	21.5689	−	3.15844i	1.11530	−	0.163319i
$375$	−0.875353	+	1.49458i	−0.0452030	+	0.0771796i
$376$	−1.60736	+	18.3452i	−0.0828935	+	0.946084i
$377$		−	37.0862i		−	1.91004i
$378$	1.12970	+	8.86770i	0.0581057	+	0.456105i
$379$	−11.4156			−0.586379			−0.293189	−	0.956054i	$-0.594717\pi$
$379$	−11.4156			−0.586379			−0.293189	+	0.956054i	$0.594717\pi$
$380$	−8.99454	+	2.69195i	−0.461410	+	0.138094i
$381$	11.0065	+	6.44634i	0.563879	+	0.330256i
$382$	22.8431	−	3.34503i	1.16876	−	0.171147i
$383$	3.00204	+	5.19968i	0.153397	+	0.265691i	0.932474	−	0.361237i	$-0.117645\pi$
$383$	3.00204	+	5.19968i	0.153397	+	0.265691i	−0.779077	+	0.626928i	$0.784312\pi$
$384$	−10.3961	+	16.6109i	−0.530521	+	0.847672i
$385$	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	$0.348140\pi$
$389$	−10.6451	+	18.4379i	−0.539728	+	0.934836i	−0.998918	+	0.0464983i	$0.985194\pi$
$390$	−10.9246	−	4.41959i	−0.553187	−	0.223794i
$391$	8.96156	−	5.17396i	0.453205	−	0.261658i
$392$	−12.7885	−	8.95707i	−0.645919	−	0.452400i
$393$	0.0631468	−	10.1365i	0.00318534	−	0.511321i
$394$	12.0886	+	15.2898i	0.609013	+	0.770291i
$395$		−	10.5987i		−	0.533280i
$396$	−15.0231	−	3.76019i	−0.754941	−	0.188957i
$397$			5.41338i			0.271690i	0.990730	+	0.135845i	$0.0433748\pi$
$397$			5.41338i			0.271690i	−0.990730	+	0.135845i	$0.956625\pi$
$398$	14.0656	−	11.1207i	0.705046	−	0.557430i
$399$	8.59664	−	4.89213i	0.430370	−	0.244913i
$400$	3.34233	−	2.19747i	0.167116	−	0.109873i
$401$	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	$0.233712\pi$
$402$	−7.82350	−	10.0230i	−0.390201	−	0.499902i
$403$	−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
$408$	−29.1283	−	2.73510i	−1.44207	−	0.135408i
$409$	−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	$-0.357113\pi$
$410$	0.475450	+	3.24683i	0.0234808	+	0.160350i
$411$	−8.24074	+	4.68959i	−0.406486	+	0.231320i
$412$	−1.12280	−	3.75157i	−0.0553164	−	0.184827i
$413$	7.48347			0.368238
$414$	−7.28658	+	0.974443i	−0.358116	+	0.0478913i
$415$			5.80651i			0.285030i
$416$	18.0885	+	20.3346i	0.886860	+	0.996984i
$417$	−27.2159	−	0.169545i	−1.33277	−	0.00830265i
$418$	2.48275	+	16.9546i	0.121435	+	0.829279i
$419$	−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	$0.417530\pi$
$420$	−2.91116	+	3.04687i	−0.142050	+	0.148672i
$421$	12.4216	+	7.17164i	0.605394	+	0.349524i	0.771160	−	0.636641i	$-0.219677\pi$
$421$	12.4216	+	7.17164i	0.605394	+	0.349524i	−0.165767	+	0.986165i	$0.553010\pi$
$422$	−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
$426$	23.0474	−	3.22842i	1.11665	−	0.156418i
$427$	6.95018	+	12.0381i	0.336343	+	0.582563i
$428$	−24.5415	−	5.81864i	−1.18626	−	0.281255i
$429$	−10.8700	+	18.5594i	−0.524808	+	0.896057i
$430$	3.46324	+	4.38036i	0.167012	+	0.211240i
$431$	18.6893			0.900230			0.450115	−	0.892971i	$-0.351383\pi$
$431$	18.6893			0.900230			0.450115	+	0.892971i	$0.351383\pi$
$432$	18.3946	+	9.67672i	0.885010	+	0.465571i
$433$	27.7581			1.33397			0.666984	−	0.745072i	$-0.267585\pi$
$433$	27.7581			1.33397			0.666984	+	0.745072i	$0.267585\pi$
$434$	5.30404	+	6.70865i	0.254602	+	0.322025i
$435$	6.74766	−	11.5209i	0.323526	−	0.552387i
$436$	−31.9369	−	7.57206i	−1.52950	−	0.362636i
$437$	4.06709	+	7.04441i	0.194555	+	0.336980i
$438$	−26.0815	+	3.65343i	−1.24622	+	0.174568i
$439$	−26.2677	−	15.1656i	−1.25369	−	0.723817i	−0.281848	−	0.959459i	$-0.590947\pi$
$439$	−26.2677	−	15.1656i	−1.25369	−	0.723817i	−0.971840	+	0.235642i	$0.924281\pi$
$440$	−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	$0.964493\pi$
$444$	−19.9366	+	20.8660i	−0.946150	+	0.990258i
$445$	−10.0152	+	5.78229i	−0.474767	+	0.274107i
$446$	−0.854959	−	5.83849i	−0.0404835	−	0.276460i
$447$	−17.1639	−	0.106925i	−0.811827	−	0.00505738i
$448$	9.14589	−	3.32618i	0.432103	−	0.157147i
$449$		−	20.2689i		−	0.956550i	−0.878210	−	0.478275i	$-0.841262\pi$
$449$		−	20.2689i		−	0.956550i	0.878210	−	0.478275i	$-0.158738\pi$
$450$	−2.58963	−	3.36063i	−0.122076	−	0.158422i
$451$	5.98902			0.282012
$452$	2.57212	+	8.59413i	0.120982	+	0.404234i
$453$	−27.5136	+	15.6573i	−1.29270	+	0.735642i
$454$	0.928569	+	6.34117i	0.0435799	+	0.297606i
$455$	2.92632	+	5.06854i	0.137188	+	0.237617i
$456$	2.14998	−	22.8969i	0.100682	−	1.07224i
$457$	−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	$-0.646659\pi$
$461$	11.8822	−	20.5806i	0.553411	−	0.958536i	0.998025	−	0.0628139i	$-0.0200075\pi$
$462$	4.73237	+	6.06283i	0.220170	+	0.282069i
$463$	17.4043	−	10.0484i	0.808845	−	0.466987i	−0.0377098	−	0.999289i	$-0.512006\pi$
$463$	17.4043	−	10.0484i	0.808845	−	0.466987i	0.846555	+	0.532302i	$0.178673\pi$
$464$	−25.7643	+	16.9392i	−1.19608	+	0.786382i
$465$	−7.48326	+	4.25853i	−0.347028	+	0.197485i
$466$	22.4350	−	17.7378i	1.03928	−	0.821686i
$467$		−	3.17945i		−	0.147127i	−0.997291	−	0.0735636i	$-0.976563\pi$
$467$		−	3.17945i		−	0.147127i	0.997291	−	0.0735636i	$-0.0234372\pi$
$468$	20.0712	−	20.7466i	0.927791	−	0.959010i
$469$			6.31460i			0.291581i
$470$	5.71068	+	7.22296i	0.263414	+	0.333170i
$471$	0.174608	−	28.0286i	0.00804549	−	1.29149i
$472$	9.98180	−	14.2516i	0.459450	−	0.655983i
$473$	8.82609	−	5.09574i	0.405824	−	0.234303i
$474$	24.0666	+	9.73628i	1.10542	+	0.447202i
$475$	−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	−0.805592	−	0.592471i	$-0.798153\pi$
$479$	2.41400	−	4.18118i	0.110299	−	0.191043i	0.915891	+	0.401428i	$0.131486\pi$
$480$	1.91946	+	9.60810i	0.0876109	+	0.438548i
$481$	20.0405	+	34.7111i	0.913766	+	1.58269i
$482$	37.2958	−	5.46141i	1.69878	−	0.248760i
$483$	3.15039	+	1.84514i	0.143348	+	0.0839569i
$484$	8.31164	−	2.48757i	0.377802	−	0.113071i
$485$	9.69386			0.440176
$486$	8.77426	−	20.2241i	0.398009	−	0.917382i
$487$		−	14.3517i		−	0.650339i	−0.945656	−	0.325170i	$-0.894579\pi$
$487$		−	14.3517i		−	0.650339i	0.945656	−	0.325170i	$-0.105421\pi$
$488$	32.1959	+	2.82092i	1.45744	+	0.127697i
$489$	2.89885	−	4.94949i	0.131090	−	0.223824i
$490$	−7.72428	+	1.13110i	−0.348948	+	0.0510981i
$491$	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	$0.322119\pi$
$492$	−7.80938	−	1.90302i	−0.352074	−	0.0857948i
$493$	−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
$498$	−13.1849	−	5.33401i	−0.590829	−	0.239023i
$499$	−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	$0.924613\pi$
$500$	0.461398	−	1.94605i	0.0206343	−	0.0870300i
$501$	26.6231	+	0.165852i	1.18943	+	0.00740972i
$502$	−14.4948	+	11.4600i	−0.646933	+	0.511483i
$503$	−32.7222			−1.45901			−0.729505	−	0.683976i	$-0.760249\pi$
$503$	−32.7222			−1.45901			−0.729505	+	0.683976i	$0.760249\pi$
$504$	−4.24429	−	9.40934i	−0.189056	−	0.419125i
$505$	−15.1849			−0.675718
$506$	−4.96154	+	3.92273i	−0.220567	+	0.174387i
$507$	−8.69212	−	15.2741i	−0.386031	−	0.678349i
$508$	−14.3313	−	3.39786i	−0.635847	−	0.150756i
$509$	−5.41863	−	9.38534i	−0.240176	−	0.415998i	0.720588	−	0.693364i	$-0.243872\pi$
$509$	−5.41863	−	9.38534i	−0.240176	−	0.415998i	−0.960764	+	0.277366i	$0.910539\pi$
$510$	−11.5313	+	9.00080i	−0.510614	+	0.398562i
$511$	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
$516$	−13.1279	+	3.84009i	−0.577926	+	0.169050i
$517$	14.5537	−	8.40259i	0.640071	−	0.369545i
$518$	14.1812	−	2.07662i	0.623086	−	0.0912416i
$519$	−11.2047	−	19.6894i	−0.491833	−	0.864270i
$520$	13.5558	+	1.18773i	0.594463	+	0.0520854i
$521$		−	36.1420i		−	1.58341i	−0.610903	−	0.791706i	$-0.709193\pi$
$521$		−	36.1420i		−	1.58341i	0.610903	−	0.791706i	$-0.290807\pi$
$522$	19.9622	+	25.9054i	0.873720	+	1.13385i
$523$	−38.6056			−1.68810			−0.844052	−	0.536262i	$-0.819836\pi$
$523$	−38.6056			−1.68810			−0.844052	+	0.536262i	$0.819836\pi$
$524$	3.35605	+	11.2135i	0.146610	+	0.489862i
$525$	−0.0131257	+	2.10699i	−0.000572854	+	0.0919565i
$526$	−25.4710	+	3.72985i	−1.11059	+	0.162629i
$527$	14.8435	+	25.7096i	0.646591	+	1.11993i
$528$	17.8584	−	0.925492i	0.777186	−	0.0402769i
$529$	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
$534$	−3.92966	−	28.0534i	−0.170053	−	1.21399i
$535$	−10.9214	+	6.30546i	−0.472172	+	0.272609i
$536$	12.0256	+	8.42271i	0.519427	+	0.363806i
$537$	35.7965	+	20.9655i	1.54473	+	0.904729i
$538$	−13.8503	−	17.5181i	−0.597129	−	0.755259i
$539$			14.2480i			0.613705i
$540$	10.0099	−	2.79313i	0.430758	−	0.120197i
$541$			8.66994i			0.372750i	0.982479	+	0.186375i	$0.0596739\pi$
$541$			8.66994i			0.372750i	−0.982479	+	0.186375i	$0.940326\pi$
$542$	−5.51657	+	4.36156i	−0.236957	+	0.187345i
$543$	−18.0975	−	10.5995i	−0.776639	−	0.454867i
$544$	33.0860	−	6.82436i	1.41855	−	0.292592i
$545$	−14.2125	+	8.20557i	−0.608795	+	0.351488i
$546$	−14.1974	+	1.98873i	−0.607592	+	0.0851100i
$547$	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
$552$	7.71605	−	3.53851i	0.328417	−	0.150609i
$553$	−6.44664	−	11.1659i	−0.274139	−	0.474823i
$554$	−1.41150	−	9.63908i	−0.0599688	−	0.409525i
$555$	−0.0898896	+	14.4294i	−0.00381560	+	0.612493i
$556$	30.1073	−	9.01075i	1.27684	−	0.382141i
$557$	7.87236			0.333563			0.166781	−	0.985994i	$-0.446663\pi$
$557$	7.87236			0.333563			0.166781	+	0.985994i	$0.446663\pi$
$558$	−2.79556	−	20.9043i	−0.118345	−	0.884951i
$559$			18.9966i			0.803471i
$560$	2.18459	−	4.34802i	0.0923156	−	0.183737i
$561$	13.2048	+	23.2040i	0.557506	+	0.979672i
$562$	1.65651	+	11.3123i	0.0698759	+	0.477180i
$563$	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	$-0.0715998\pi$
$564$	−21.6472	+	6.33208i	−0.911513	+	0.266629i
$565$	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	$0.381920\pi$
$570$	−7.07525	−	9.06440i	−0.296350	−	0.379666i
$571$	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	$0.747457\pi$
$572$	5.72956	−	24.1658i	0.239565	−	1.01042i
$573$	13.9849	+	24.5748i	0.584226	+	1.02663i
$574$	2.47577	+	3.13140i	0.103337	+	0.130702i
$575$	−1.73275			−0.0722608
$576$	−23.5805	−	4.46773i	−0.982520	−	0.186155i
$577$	−1.47556			−0.0614283			−0.0307141	−	0.999528i	$-0.509778\pi$
$577$	−1.47556			−0.0614283			−0.0307141	+	0.999528i	$0.509778\pi$
$578$	16.3703	+	20.7055i	0.680916	+	0.861234i
$579$	0.225048	+	0.00140196i	0.00935267	+	5.82636e-5i
$580$	−3.55669	+	15.0011i	−0.147683	+	0.622889i
$581$	3.53179	+	6.11724i	0.146523	+	0.253786i
$582$	−8.90504	+	22.0120i	−0.369126	+	0.912425i
$583$	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	$0.359833\pi$
$588$	4.52732	−	18.5787i	0.186704	−	0.766172i
$589$	−20.2095	+	11.6680i	−0.832720	+	0.480771i
$590$	−1.26051	−	8.60798i	−0.0518943	−	0.354385i
$591$	−12.0645	+	20.5989i	−0.496268	+	0.847327i
$592$	14.9608	−	29.7767i	0.614885	−	1.22382i
$593$		−	15.7328i		−	0.646070i	−0.946387	−	0.323035i	$-0.895297\pi$
$593$		−	15.7328i		−	0.646070i	0.946387	−	0.323035i	$-0.104703\pi$
$594$	−2.39695	−	18.8150i	−0.0983480	−	0.771990i
$595$	7.26484			0.297829
$596$	18.9875	−	5.68271i	0.777757	−	0.232773i
$597$	18.9497	+	11.0986i	0.775558	+	0.454234i
$598$	−1.70817	−	11.6651i	−0.0698523	−	0.477020i
$599$	−11.0081	−	19.0666i	−0.449778	−	0.779039i	0.548593	−	0.836090i	$-0.315164\pi$
$599$	−11.0081	−	19.0666i	−0.449778	−	0.779039i	−0.998371	+	0.0570507i	$0.981830\pi$
$600$	3.99506	+	2.83539i	0.163098	+	0.115754i
$601$	−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
$606$	13.9492	−	34.4804i	0.566649	−	1.40067i
$607$	−7.15706	+	4.13213i	−0.290496	+	0.167718i	−0.638166	−	0.769899i	$-0.720306\pi$
$607$	−7.15706	+	4.13213i	−0.290496	+	0.167718i	0.347669	+	0.937617i	$0.386973\pi$
$608$	5.36442	+	26.0079i	0.217556	+	1.05476i
$609$	0.101180	−	16.2417i	0.00410002	−	0.658148i
$610$	12.6763	−	10.0222i	0.513248	−	0.405788i
$611$			31.3243i			1.26725i
$612$	−9.84525	−	34.4526i	−0.397971	−	1.39266i
$613$		−	15.5613i		−	0.628514i	−0.949338	−	0.314257i	$-0.898245\pi$
$613$		−	15.5613i		−	0.628514i	0.949338	−	0.314257i	$-0.101755\pi$
$614$	−7.94873	−	10.0537i	−0.320784	−	0.405734i
$615$	−3.49297	+	1.98776i	−0.140850	+	0.0801540i
$616$	−7.27419	−	5.09483i	−0.293085	−	0.205276i
$617$	−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	$0.337878\pi$
$618$	3.78071	−	2.95105i	0.152083	−	0.118709i
$619$	−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
$624$	−15.1498	+	29.6903i	−0.606476	+	1.18856i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−11.9338	+	1.74753i	−0.476971	+	0.0698452i
$627$	−18.2399	+	10.3799i	−0.728432	+	0.414532i
$628$	9.27982	+	31.0064i	0.370305	+	1.23729i
$629$	49.7521			1.98375
$630$	−4.77230	−	1.96534i	−0.190133	−	0.0783011i
$631$		−	11.4322i		−	0.455108i	−0.973765	−	0.227554i	$-0.926927\pi$
$631$		−	11.4322i		−	0.455108i	0.973765	−	0.227554i	$-0.0730728\pi$
$632$	−29.8633	−	2.61655i	−1.18790	−	0.104081i
$633$	−34.3623	−	0.214064i	−1.36578	−	0.00850828i
$634$	16.7727	−	2.45611i	0.666129	−	0.0975446i
$635$	−6.37765	+	3.68214i	−0.253089	+	0.146121i
$636$	−0.182752	−	0.174612i	−0.00724659	−	0.00692382i
$637$	−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	$0.621461\pi$
$642$	−4.28520	−	30.5916i	−0.169123	−	1.20736i
$643$	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	$0.723711\pi$
$644$	−4.10205	−	0.972572i	−0.161643	−	0.0383247i
$645$	−3.45634	+	5.90136i	−0.136093	+	0.232366i
$646$	−31.1006	+	24.5890i	−1.22364	+	0.967442i
$647$	−33.0387			−1.29889			−0.649443	−	0.760411i	$-0.724998\pi$
$647$	−33.0387			−1.29889			−0.649443	+	0.760411i	$0.724998\pi$
$648$	−2.85300	+	25.2955i	−0.112076	+	0.993700i
$649$	−15.8780			−0.623268
$650$	5.33726	−	4.21979i	0.209345	−	0.165514i
$651$	−5.29349	+	9.03810i	−0.207468	+	0.354231i
$652$	−1.52798	+	6.44461i	−0.0598403	+	0.252390i
$653$	8.35904	+	14.4783i	0.327115	+	0.566579i	0.981938	−	0.189203i	$-0.0605903\pi$
$653$	8.35904	+	14.4783i	0.327115	+	0.566579i	−0.654823	+	0.755782i	$0.727257\pi$
$654$	−5.57652	−	39.8102i	−0.218059	−	1.55670i
$655$	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	$0.912588\pi$
$660$	6.17675	−	6.46470i	0.240430	−	0.251638i
$661$	12.5998	−	7.27451i	0.490076	−	0.282945i	−0.234530	−	0.972109i	$-0.575355\pi$
$661$	12.5998	−	7.27451i	0.490076	−	0.282945i	0.724606	+	0.689163i	$0.242022\pi$
$662$	−44.6064	+	6.53194i	−1.73368	+	0.253871i
$663$	−49.7635	−	0.310008i	−1.93265	−	0.0120397i
$664$	16.3606	+	1.43347i	0.634914	+	0.0556296i
$665$			5.71067i			0.221450i
$666$	−32.6824	−	13.4593i	−1.26642	−	0.521538i
$667$	13.3569			0.517183
$668$	−29.4516	+	8.81449i	−1.13952	+	0.341043i
$669$	6.28108	−	3.57440i	0.242841	−	0.138194i
$670$	7.26347	−	1.06363i	0.280612	−	0.0410914i
$671$	−14.7465	−	25.5418i	−0.569284	−	0.986029i
$672$	7.86628	+	8.95477i	0.303448	+	0.345438i
$673$	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	$0.388183\pi$
$677$	−16.6806	+	28.8917i	−0.641088	+	1.11040i	−0.985190	+	0.171465i	$0.945150\pi$
$678$	−8.66088	+	6.76029i	−0.332619	+	0.259627i
$679$	10.2126	−	5.89626i	0.391925	−	0.226278i
$680$	9.69018	−	13.8352i	0.371601	−	0.530557i
$681$	−6.82187	+	3.88215i	−0.261415	+	0.148764i
$682$	−11.2538	−	14.2341i	−0.430932	−	0.545050i
$683$		−	30.0087i		−	1.14825i	−0.818767	−	0.574126i	$-0.805342\pi$
$683$		−	30.0087i		−	1.14825i	0.818767	−	0.574126i	$-0.194658\pi$
$684$	27.0821	−	7.73905i	1.03551	−	0.295910i
$685$		−	5.47424i		−	0.209160i
$686$	−16.8964	+	13.3588i	−0.645109	+	0.510041i
$687$	−0.0781355	+	12.5426i	−0.00298106	+	0.478529i
$688$	13.1972	−	8.67673i	0.503139	−	0.330797i
$689$	−0.304012	+	0.175521i	−0.0115819	+	0.00668684i
$690$	1.59175	−	3.93458i	0.0605970	−	0.149787i
$691$	−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
$696$	−30.7960	−	21.8567i	−1.16732	−	0.828474i
$697$	6.92849	+	12.0005i	0.262435	+	0.454551i
$698$	4.83458	+	33.0152i	0.182991	+	1.24964i
$699$	30.2251	+	17.7025i	1.14322	+	0.669568i
$700$	−0.697590	−	2.33084i	−0.0263664	−	0.0880973i
$701$	7.04424			0.266057			0.133029	−	0.991112i	$-0.457530\pi$
$701$	7.04424			0.266057			0.133029	+	0.991112i	$0.457530\pi$
$702$	32.6060	+	13.6660i	1.23063	+	0.515792i
$703$			39.1086i			1.47501i
$704$	−19.4053	+	7.05733i	−0.731364	+	0.265983i
$705$	−5.69931	+	9.73100i	−0.214649	+	0.366490i
$706$	−2.53415	−	17.3057i	−0.0953740	−	0.651307i
$707$	−15.9975	+	9.23615i	−0.601647	+	0.347361i
$708$	20.7042	+	5.04527i	0.778110	+	0.189613i
$709$	−3.17078	−	1.83065i	−0.119081	−	0.0687516i	0.439276	−	0.898352i	$-0.355235\pi$
$709$	−3.17078	−	1.83065i	−0.119081	−	0.0687516i	−0.558358	+	0.829600i	$0.688568\pi$
$710$	−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
$714$	−6.67368	+	16.4963i	−0.249756	+	0.617360i
$715$	−6.20892	−	10.7542i	−0.232201	−	0.402183i
$716$	−46.6097	−	11.0509i	−1.74189	−	0.412992i
$717$	37.4123	+	0.233064i	1.39719	+	0.00870395i
$718$	−28.9769	−	36.6505i	−1.08141	−	1.36778i
$719$	−20.0716			−0.748545			−0.374272	−	0.927319i	$-0.622107\pi$
$719$	−20.0716			−0.748545			−0.374272	+	0.927319i	$0.622107\pi$
$720$	−10.1083	+	6.46696i	−0.376715	+	0.241009i
$721$	−2.38189			−0.0887062
$722$	−2.66381	−	3.36923i	−0.0991368	−	0.125390i
$723$	22.8330	+	40.1231i	0.849168	+	1.49219i
$724$	23.5643	+	5.58697i	0.875762	+	0.207638i
$725$	3.85425	+	6.67576i	0.143143	+	0.247932i
$726$	6.53807	+	8.37619i	0.242651	+	0.310870i
$727$	−22.2080	−	12.8218i	−0.823648	−	0.475533i	0.0280248	−	0.999607i	$-0.491078\pi$
$727$	−22.2080	−	12.8218i	−0.823648	−	0.475533i	−0.851673	+	0.524074i	$0.824412\pi$
$728$	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
$732$	11.1128	+	37.9909i	0.410741	+	1.40418i
$733$	−34.1239	+	19.7014i	−1.26039	+	0.727689i	−0.973151	−	0.230169i	$-0.926072\pi$
$733$	−34.1239	+	19.7014i	−1.26039	+	0.727689i	−0.287243	+	0.957858i	$0.592739\pi$
$734$	2.30079	+	15.7120i	0.0849236	+	0.579941i
$735$	−4.72891	−	8.30983i	−0.174428	−	0.306513i
$736$	−7.32368	+	6.51472i	−0.269954	+	0.240136i
$737$		−	13.3980i		−	0.493522i
$738$	−1.30488	−	9.75752i	−0.0480335	−	0.359179i
$739$	19.4393			0.715086			0.357543	−	0.933897i	$-0.383615\pi$
$739$	19.4393			0.715086			0.357543	+	0.933897i	$0.383615\pi$
$740$	−4.77733	−	15.9624i	−0.175618	−	0.586788i
$741$	0.243688	−	39.1175i	0.00895209	−	1.43702i
$742$	0.0181878	+	0.124204i	0.000667695	+	0.00455967i
$743$	1.32397	+	2.29319i	0.0485718	+	0.0841289i	0.889289	−	0.457345i	$-0.151200\pi$
$743$	1.32397	+	2.29319i	0.0485718	+	0.0841289i	−0.840717	+	0.541474i	$0.817866\pi$
$744$	10.1516	+	22.1364i	0.372174	+	0.811560i
$745$	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
$750$	2.42581	−	0.339801i	0.0885779	−	0.0124078i
$751$	−35.7172	+	20.6213i	−1.30334	+	0.752483i	−0.980975	−	0.194133i	$-0.937811\pi$
$751$	−35.7172	+	20.6213i	−1.30334	+	0.752483i	−0.322364	+	0.946616i	$0.604477\pi$
$752$	21.7615	−	14.3074i	0.793559	−	0.521738i
$753$	−19.5278	−	11.4372i	−0.711632	−	0.416793i
$754$	−41.1423	+	32.5283i	−1.49831	+	1.18461i
$755$		−	18.2770i		−	0.665168i
$756$	8.84668	−	9.03110i	0.321751	−	0.328458i
$757$		−	7.94389i		−	0.288725i	−0.989525	−	0.144363i	$-0.953887\pi$
$757$		−	7.94389i		−	0.288725i	0.989525	−	0.144363i	$-0.0461132\pi$
$758$	10.0126	+	12.6641i	0.363673	+	0.459980i
$759$	−6.68434	−	3.91493i	−0.242626	−	0.142103i
$760$	10.8755	+	7.61715i	0.394494	+	0.276303i
$761$	−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	$0.343951\pi$
$762$	−2.50239	−	17.8643i	−0.0906520	−	0.647156i
$763$	−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
$768$	27.5460	−	3.03634i	0.993980	−	0.109564i
$769$	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	$0.660670\pi$
$770$	−4.39361	+	0.643378i	−0.158335	+	0.0231857i
$771$	−0.0998596	+	16.0298i	−0.00359636	+	0.577299i
$772$	−0.248957	+	0.0745098i	−0.00896016	+	0.00268166i
$773$	0.438719			0.0157796			0.00788981	−	0.999969i	$-0.497489\pi$
$773$	0.438719			0.0157796			0.00788981	+	0.999969i	$0.497489\pi$
$774$	−10.2252	−	13.2695i	−0.367536	−	0.476962i
$775$		−	4.97106i		−	0.178566i
$776$	2.39316	−	27.3137i	0.0859095	−	0.980506i
$777$	8.68192	+	15.2562i	0.311462	+	0.547314i
$778$	29.7912	−	4.36247i	1.06807	−	0.156402i
$779$	−9.43322	+	5.44627i	−0.337980	+	0.195133i
$780$	4.67896	+	15.9958i	0.167534	+	0.572741i
$781$	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
$786$	−11.3005	+	8.82069i	−0.403077	+	0.314624i
$787$	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	$0.745478\pi$
$788$	6.35919	−	26.8214i	0.226537	−	0.955472i
$789$	−15.5937	−	27.4019i	−0.555151	−	0.975534i
$790$	−11.7579	+	9.29612i	−0.418327	+	0.330741i
$791$	5.45645			0.194009
$792$	9.00532	+	19.9643i	0.319990	+	0.709399i
$793$	54.9742			1.95219
$794$	6.00543	−	4.74806i	0.213125	−	0.168502i
$795$	−0.126378		0.000787285i	−0.00448215		2.79221e-5i
$796$	−24.6739	−	5.85004i	−0.874543	−	0.207349i
$797$	−17.6568	−	30.5824i	−0.625435	−	1.08328i	−0.988457	−	0.151504i	$-0.951588\pi$
$797$	−17.6568	−	30.5824i	−0.625435	−	1.08328i	0.363022	−	0.931781i	$-0.381745\pi$
$798$	−12.9673	−	5.24597i	−0.459036	−	0.185705i
$799$	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
$804$	−4.25723	+	17.4703i	−0.150141	+	0.616130i
$805$	−1.82548	+	1.05394i	−0.0643397	+	0.0371466i
$806$	33.4657	−	4.90054i	1.17878	−	0.172614i
$807$	13.8227	−	23.6009i	0.486584	−	0.830792i
$808$	−3.74875	+	42.7854i	−0.131880	+	1.50518i
$809$			22.5085i			0.791358i	0.918389	+	0.395679i	$0.129491\pi$
$809$			22.5085i			0.791358i	−0.918389	+	0.395679i	$0.870509\pi$
$810$	7.64267	+	10.1779i	0.268536	+	0.357615i
$811$	52.4632			1.84223			0.921116	−	0.389289i	$-0.127279\pi$
$811$	52.4632			1.84223			0.921116	+	0.389289i	$0.127279\pi$
$812$	5.37738	+	17.9673i	0.188709	+	0.630527i
$813$	−7.43210	−	4.35288i	−0.260655	−	0.152662i
$814$	−30.0889	+	4.40607i	−1.05462	+	0.154433i
$815$	1.65582	+	2.86796i	0.0580008	+	0.100460i
$816$	22.5142	+	34.7130i	0.788154	+	1.21520i
$817$	−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	$0.583662\pi$
$821$	−27.6844	+	47.9508i	−0.966193	+	1.67350i	−0.706375	+	0.707838i	$0.749671\pi$
$822$	12.4304	+	5.02879i	0.433561	+	0.175399i
$823$	32.2602	−	18.6255i	1.12452	−	0.649243i	0.181970	−	0.983304i	$-0.441753\pi$
$823$	32.2602	−	18.6255i	1.12452	−	0.649243i	0.942551	+	0.334061i	$0.108419\pi$
$824$	−3.17707	+	4.53610i	−0.110679	+	0.158022i
$825$	0.0278495	−	4.47050i	0.000969596	−	0.155643i
$826$	−6.56374	−	8.30193i	−0.228382	−	0.288861i
$827$		−	11.9636i		−	0.416016i	−0.978127	−	0.208008i	$-0.933302\pi$
$827$		−	11.9636i		−	0.416016i	0.978127	−	0.208008i	$-0.0666981\pi$
$828$	7.47206	+	7.22882i	0.259672	+	0.251219i
$829$		−	14.2267i		−	0.494113i	−0.969001	−	0.247056i	$-0.920537\pi$
$829$		−	14.2267i		−	0.494113i	0.969001	−	0.247056i	$-0.0794633\pi$
$830$	6.44155	−	5.09288i	0.223590	−	0.176776i
$831$	10.3698	−	5.90117i	0.359724	−	0.204709i
$832$	6.69317	−	37.9022i	0.232044	−	1.31402i
$833$	−28.5494	+	16.4830i	−0.989178	+	0.571102i
$834$	23.6829	+	30.3412i	0.820073	+	1.05063i
$835$	−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	$0.339430\pi$
$839$	−14.9605	+	25.9124i	−0.516494	+	0.894594i	−0.999817	+	0.0191519i	$0.993903\pi$
$840$	5.93348	+	0.557144i	0.204724	+	0.0192233i
$841$	−15.2105	−	26.3454i	−0.524501	−	0.908463i
$842$	−2.93901	−	20.0704i	−0.101285	−	0.691672i
$843$	−12.1698	+	6.92554i	−0.419152	+	0.238528i
$844$	38.0129	−	11.3768i	1.30846	−	0.391605i
$845$	10.1465			0.349049
$846$	−16.8607	−	21.8806i	−0.579684	−	0.752272i
$847$		−	5.27709i		−	0.181323i
$848$	0.260795	+	0.131032i	0.00895575	+	0.00449966i
$849$	48.3243	+	0.301042i	1.65849	+	0.0103318i
$850$	−1.22368	−	8.35649i	−0.0419720	−	0.286625i
$851$	−12.5015	+	7.21775i	−0.428546	+	0.247421i
$852$	−23.7963	−	22.7364i	−0.815249	−	0.778937i
$853$	43.9084	+	25.3505i	1.50339	+	0.867985i	0.999992	+	0.00393313i	$0.00125196\pi$
$853$	43.9084	+	25.3505i	1.50339	+	0.867985i	0.503402	+	0.864052i	$0.332081\pi$
$854$	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	$0.464392\pi$
$858$	30.1233	−	4.21959i	1.02839	−	0.144055i
$859$	−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	$0.904388\pi$
$860$	1.82184	−	7.68401i	0.0621241	−	0.262023i
$861$	−2.47084	+	4.21872i	−0.0842061	+	0.143773i
$862$	−16.3923	−	20.7333i	−0.558324	−	0.706178i
$863$	−25.0943			−0.854220			−0.427110	−	0.904200i	$-0.640468\pi$
$863$	−25.0943			−0.854220			−0.427110	+	0.904200i	$0.640468\pi$
$864$	−5.39881	−	28.8938i	−0.183671	−	0.982988i
$865$	13.0795			0.444716
$866$	−24.3466	−	30.7940i	−0.827330	−	1.04642i
$867$	−16.3377	+	27.8950i	−0.554859	+	0.947365i
$868$	2.79019	−	11.7683i	0.0947053	−	0.399442i
$869$	13.6782	+	23.6913i	0.464000	+	0.803671i
$870$	−18.6993	+	2.61936i	−0.633967	+	0.0888045i
$871$	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
$876$	26.9290	+	25.7296i	0.909847	+	0.869321i
$877$	−29.8243	+	17.2191i	−1.00710	+	0.581447i	−0.910340	−	0.413861i	$-0.864180\pi$
$877$	−29.8243	+	17.2191i	−1.00710	+	0.581447i	−0.0967563	+	0.995308i	$0.530847\pi$
$878$	6.21503	+	42.4423i	0.209747	+	1.43236i
$879$	−45.9923	−	0.286515i	−1.55128	−	0.00966390i
$880$	−4.63514	+	9.22541i	−0.156251	+	0.310989i
$881$			11.0595i			0.372603i	0.982493	+	0.186301i	$0.0596501\pi$
$881$			11.0595i			0.372603i	−0.982493	+	0.186301i	$0.940350\pi$
$882$	23.2133	−	3.10435i	0.781633	−	0.104529i
$883$	−28.7514			−0.967563			−0.483782	−	0.875189i	$-0.660737\pi$
$883$	−28.7514			−0.967563			−0.483782	+	0.875189i	$0.660737\pi$
$884$	55.0504	−	16.4759i	1.85154	−	0.554144i
$885$	9.26052	−	5.26992i	0.311289	−	0.177146i
$886$	6.94339	+	47.4162i	0.233268	+	1.59298i
$887$	−23.0648	−	39.9494i	−0.774440	−	1.34137i	−0.935109	−	0.354361i	$-0.884698\pi$
$887$	−23.0648	−	39.9494i	−0.774440	−	1.34137i	0.160668	−	0.987008i	$-0.448635\pi$
$888$	40.6345	+	3.81551i	1.36360	+	0.128040i
$889$	−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
$894$	14.9358	+	19.1349i	0.499529	+	0.639968i
$895$	−20.7421	+	11.9755i	−0.693332	+	0.400296i
$896$	−11.7118	−	7.22878i	−0.391264	−	0.241496i
$897$	12.5493	−	7.14151i	0.419011	−	0.238448i
$898$	−22.4857	+	17.7778i	−0.750358	+	0.593254i
$899$			38.3195i			1.27803i
$900$	−1.45682	+	5.82045i	−0.0485607	+	0.194015i
$901$			0.435747i			0.0145168i
$902$	−5.25296	−	6.64404i	−0.174905	−	0.221222i
$903$	−0.0518272	+	8.31947i	−0.00172470	+	0.276855i
$904$	7.27806	−	10.3913i	0.242065	−	0.345610i
$905$	10.4865	−	6.05440i	0.348584	−	0.201255i
$906$	41.5018	+	16.7897i	1.37880	+	0.557802i
$907$	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	−0.684079	−	0.729408i	$-0.739796\pi$
$911$	8.74232	−	15.1421i	0.289646	−	0.501681i	0.973725	+	0.227726i	$0.0731291\pi$
$912$	−27.2868	+	17.6977i	−0.903557	+	0.586029i
$913$	−7.49357	−	12.9792i	−0.248001	−	0.429550i
$914$	39.6913	−	5.81219i	1.31287	−	0.192250i
$915$	17.0779	+	10.0023i	0.564578	+	0.330666i
$916$	−4.15264	−	13.8751i	−0.137207	−	0.458446i
$917$	7.11947			0.235106
$918$	34.9276	−	26.5693i	1.15278	−	0.876918i
$919$		−	17.5577i		−	0.579174i	−0.957152	−	0.289587i	$-0.906482\pi$
$919$		−	17.5577i		−	0.579174i	0.957152	−	0.289587i	$-0.0935179\pi$
$920$	−0.427771	+	4.88226i	−0.0141032	+	0.160963i
$921$	7.93291	−	13.5446i	0.261398	−	0.446311i
$922$	−33.2534	+	4.86946i	−1.09514	+	0.160367i
$923$	−39.5857	+	22.8548i	−1.30298	+	0.752276i
$924$	2.57516	−	10.5676i	0.0847167	−	0.347650i
$925$	−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	$0.878352\pi$
$930$	11.2878	+	4.56655i	0.370143	+	0.149743i
$931$	−12.9568	−	22.4418i	−0.424641	−	0.735501i
$932$	−39.3554	−	9.33095i	−1.28913	−	0.305645i
$933$	16.2779	+	0.101405i	0.532915	+	0.00331986i
$934$	−3.52718	+	2.78869i	−0.115413	+	0.0912486i
$935$	−15.4142			−0.504097
$936$	−40.6200	−	4.06958i	−1.32771	−	0.133018i
$937$	0.778145			0.0254209			0.0127104	−	0.999919i	$-0.495954\pi$
$937$	0.778145			0.0254209			0.0127104	+	0.999919i	$0.495954\pi$
$938$	7.00522	−	5.53853i	0.228729	−	0.180839i
$939$	−7.30604	−	12.8385i	−0.238424	−	0.418968i
$940$	3.00410	−	12.6705i	0.0979830	−	0.413266i
$941$	−4.49598	−	7.78726i	−0.146565	−	0.253857i	0.783391	−	0.621529i	$-0.213488\pi$
$941$	−4.49598	−	7.78726i	−0.146565	−	0.253857i	−0.929956	+	0.367672i	$0.880155\pi$
$942$	−31.2472	+	24.3901i	−1.01809	+	0.794673i
$943$	−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	$0.504839\pi$
$948$	−10.3077	−	35.2384i	−0.334778	−	1.14449i
$949$	44.7970	−	25.8636i	1.45417	−	0.839567i
$950$	6.56878	−	0.961899i	0.213119	−	0.0312081i
$951$	10.2685	+	18.0442i	0.332978	+	0.585123i
$952$	1.79350	−	20.4696i	0.0581276	−	0.663425i
$953$			6.56079i			0.212525i	0.994338	+	0.106262i	$0.0338884\pi$
$953$			6.56079i			0.212525i	−0.994338	+	0.106262i	$0.966112\pi$
$954$	0.117882	−	0.286244i	0.00381656	−	0.00926748i
$955$	−16.3248			−0.528258
$956$	−41.3870	+	12.3866i	−1.33855	+	0.400611i
$957$	−0.214678	+	34.4609i	−0.00693956	+	1.11396i
$958$	−6.75578	+	0.989282i	−0.218269	+	0.0319623i
$959$	−3.32969	−	5.76720i	−0.107521	−	0.186232i
$960$	8.97538	−	10.5566i	0.289679	−	0.340714i
$961$	−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
$966$	−0.716261	−	5.11332i	−0.0230453	−	0.164518i
$967$	27.1073	−	15.6504i	0.871712	−	0.503283i	0.00379555	−	0.999993i	$-0.498792\pi$
$967$	27.1073	−	15.6504i	0.871712	−	0.503283i	0.867917	+	0.496709i	$0.165459\pi$
$968$	−10.0498	−	7.03883i	−0.323011	−	0.226237i
$969$	−41.8997	−	24.5401i	−1.34601	−	0.788341i
$970$	−8.50247	−	10.7541i	−0.272998	−	0.345292i
$971$			38.5329i			1.23658i	0.785950	+	0.618290i	$0.212174\pi$
$971$			38.5329i			1.23658i	−0.785950	+	0.618290i	$0.787826\pi$
$972$	−30.1318	+	8.00459i	−0.966479	+	0.256747i
$973$		−	19.1153i		−	0.612807i
$974$	−15.9214	+	12.5879i	−0.510154	+	0.403342i
$975$	7.19052	+	4.21139i	0.230281	+	0.134872i
$976$	−25.1095	−	38.1914i	−0.803736	−	1.22248i
$977$	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	$0.323418\pi$
$978$	−8.03338	+	1.12530i	−0.256879	+	0.0359830i
$979$	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	−0.946037	−	0.324059i	$-0.894952\pi$
$983$	−6.03150	+	10.4469i	−0.192375	+	0.333203i	0.753662	+	0.657262i	$0.228286\pi$
$984$	4.73844	+	10.3326i	0.151056	+	0.329392i
$985$	−6.89123	−	11.9360i	−0.219573	−	0.380311i
$986$	9.43276	+	64.4161i	0.300400	+	2.05143i
$987$	−0.0854601	+	13.7183i	−0.00272022	+	0.436659i
$988$	12.9512	+	43.2734i	0.412032	+	1.37671i
$989$	−6.84180			−0.217557
$990$	10.1256	+	4.16996i	0.321813	+	0.132530i
$991$		−	41.3228i		−	1.31266i	−0.754473	−	0.656331i	$-0.772107\pi$
$991$		−	41.3228i		−	1.31266i	0.754473	−	0.656331i	$-0.227893\pi$
$992$	−18.6900	−	21.0107i	−0.593407	−	0.667092i
$993$	−27.3087	−	47.9879i	−0.866614	−	1.52285i
$994$	2.36825	+	16.1727i	0.0751164	+	0.512968i
$995$	−10.9803	+	6.33948i	−0.348099	+	0.200975i
$996$	5.64706	+	19.3054i	0.178934	+	0.611714i
$997$	−31.8106	−	18.3659i	−1.00745	−	0.581653i	−0.0970082	−	0.995284i	$-0.530927\pi$
$997$	−31.8106	−	18.3659i	−1.00745	−	0.581653i	−0.910445	+	0.413630i	$0.864261\pi$
$998$	−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.b.11.7	yes	48
3.2	odd	2		1080.2.bm.a.251.18		48
4.3	odd	2		1440.2.cc.b.911.8		48
8.3	odd	2		360.2.bm.a.11.2	✓	48
8.5	even	2		1440.2.cc.a.911.8		48
9.4	even	3		1080.2.bm.b.611.23		48
9.5	odd	6		360.2.bm.a.131.2	yes	48
12.11	even	2		4320.2.cc.a.1871.10		48
24.5	odd	2		4320.2.cc.b.1871.15		48
24.11	even	2		1080.2.bm.b.251.23		48
36.23	even	6		1440.2.cc.a.1391.8		48
36.31	odd	6		4320.2.cc.b.3311.15		48
72.5	odd	6		1440.2.cc.b.1391.8		48
72.13	even	6		4320.2.cc.a.3311.10		48
72.59	even	6	inner	360.2.bm.b.131.7	yes	48
72.67	odd	6		1080.2.bm.a.611.18		48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.877098 - 1.10937i) q^{2} +(0.875353 - 1.49458i) q^{3} +(-0.461398 + 1.94605i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.42581 + 0.339801i) q^{6} +(1.05351 + 0.608247i) q^{7} +(2.56358 - 1.19502i) q^{8} +(-1.46751 - 2.61656i) q^{9} +O(q^{10})\)	\(q+(-0.877098 - 1.10937i) q^{2} +(0.875353 - 1.49458i) q^{3} +(-0.461398 + 1.94605i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.42581 + 0.339801i) 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} +(2.50463 + 2.39307i) q^{12} +(4.16652 - 2.40554i) q^{13} +(-0.249266 - 1.70223i) q^{14} +(1.73202 + 0.0107898i) q^{15} +(-3.57422 - 1.79581i) q^{16} -5.97195i q^{17} +(-1.61558 + 3.92300i) q^{18} +4.69437 q^{19} +(-1.91603 + 0.573443i) q^{20} +(1.83127 - 1.04213i) q^{21} +(0.528879 + 3.61170i) q^{22} +(0.866377 + 1.50061i) q^{23} +(0.457991 - 4.87752i) 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} +(-1.50718 - 1.93091i) q^{30} +(-4.30506 + 2.48553i) q^{31} +(1.14273 + 5.54023i) q^{32} +(-3.88549 + 2.21113i) q^{33} +(-6.62509 + 5.23799i) q^{34} +1.21649i q^{35} +(5.76907 - 1.64858i) q^{36} +8.33096i q^{37} +(-4.11742 - 5.20778i) q^{38} +(0.0519106 - 8.33287i) q^{39} +(2.31670 + 1.62262i) q^{40} +(-2.00948 + 1.16017i) q^{41} +(-2.76230 - 1.11750i) 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} +(-5.81268 + 3.76999i) q^{48} +(-2.76007 - 4.78058i) q^{49} +(1.39929 - 0.204905i) q^{50} +(-8.92553 - 5.22756i) q^{51} +(2.75888 + 9.21816i) q^{52} -0.0729656 q^{53} +(4.44902 + 5.84861i) q^{54} -2.58109i q^{55} +(3.42763 + 0.300321i) q^{56} +(4.10923 - 7.01609i) q^{57} +(-10.7864 + 1.57951i) q^{58} +(5.32751 - 3.07584i) q^{59} +(-0.820146 + 3.36561i) 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} +(5.86092 + 2.37106i) q^{66} +(2.59541 + 4.49538i) q^{67} +(11.6217 + 2.75544i) q^{68} +(3.00116 + 0.0186961i) q^{69} +(1.34954 - 1.06698i) q^{70} -9.50092 q^{71} +(-6.88893 - 4.95406i) q^{72} +10.7517 q^{73} +(9.24211 - 7.30707i) q^{74} +(0.856664 + 1.50537i) q^{75} +(-2.16597 + 9.13547i) q^{76} +(-1.56994 - 2.71922i) q^{77} +(-9.28975 + 7.25116i) 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} +(1.18309 + 4.04458i) q^{84} +(5.17186 - 2.98597i) q^{85} +(5.52512 - 0.809070i) q^{86} +(-6.60360 - 11.6041i) q^{87} +(-7.27257 - 0.637205i) q^{88} +11.5646i q^{89} +(-4.20520 + 0.562367i) q^{90} +5.85265 q^{91} +(-3.32000 + 0.993636i) q^{92} +(-0.0536368 + 8.60996i) q^{93} +(9.11060 - 1.33411i) q^{94} +(2.34718 + 4.06544i) q^{95} +(9.28059 + 3.14175i) q^{96} +(4.84693 - 8.39513i) q^{97} +(-2.88258 + 7.25498i) q^{98} +(-0.0964717 + 7.74268i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

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