LMFDB - Embedded newform 360.2.bm.b.11.14

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			11.14
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.b.131.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0747682 + 1.41224i) q^{2} +(-0.478797 - 1.66456i) q^{3} +(-1.98882 + 0.211181i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.31495 - 0.800631i) q^{6} +(1.88846 + 1.09030i) q^{7} +(-0.446938 - 2.79289i) q^{8} +(-2.54151 + 1.59397i) q^{9} +O(q^{10})$	\(q+(0.0747682 + 1.41224i) q^{2} +(-0.478797 - 1.66456i) q^{3} +(-1.98882 + 0.211181i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.31495 - 0.800631i) q^{6} +(1.88846 + 1.09030i) q^{7} +(-0.446938 - 2.79289i) q^{8} +(-2.54151 + 1.59397i) q^{9} +(-1.18565 + 0.770869i) q^{10} +(2.33319 + 1.34707i) q^{11} +(1.30376 + 3.20939i) q^{12} +(1.45854 - 0.842091i) q^{13} +(-1.39857 + 2.74847i) q^{14} +(1.20215 - 1.24693i) q^{15} +(3.91081 - 0.840001i) q^{16} +1.26352i q^{17} +(-2.44109 - 3.47003i) q^{18} +7.49897 q^{19} +(-1.17730 - 1.61678i) q^{20} +(0.910682 - 3.66548i) q^{21} +(-1.72793 + 3.39574i) q^{22} +(3.13519 + 5.43032i) q^{23} +(-4.43494 + 2.08118i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.29828 + 1.99685i) q^{26} +(3.87013 + 3.46729i) q^{27} +(-3.98605 - 1.76961i) q^{28} +(-1.81085 + 3.13648i) q^{29} +(1.85084 + 1.60449i) q^{30} +(-6.27015 + 3.62007i) q^{31} +(1.47868 + 5.46017i) q^{32} +(1.12515 - 4.52871i) q^{33} +(-1.78438 + 0.0944710i) q^{34} +2.18060i q^{35} +(4.71798 - 3.70684i) q^{36} -7.85016i q^{37} +(0.560685 + 10.5903i) q^{38} +(-2.10006 - 2.02464i) q^{39} +(2.19525 - 1.78351i) q^{40} +(-3.69238 + 2.13180i) q^{41} +(5.24461 + 1.01204i) q^{42} +(5.78481 - 10.0196i) q^{43} +(-4.92477 - 2.18635i) q^{44} +(-2.65117 - 1.40402i) q^{45} +(-7.43447 + 4.83365i) q^{46} +(3.33277 - 5.77252i) q^{47} +(-3.27071 - 6.10757i) q^{48} +(-1.12248 - 1.94420i) q^{49} +(-1.26042 - 0.641367i) q^{50} +(2.10320 - 0.604969i) q^{51} +(-2.72295 + 1.98278i) q^{52} -0.537500 q^{53} +(-4.60727 + 5.72477i) q^{54} +2.69414i q^{55} +(2.20107 - 5.76156i) q^{56} +(-3.59049 - 12.4825i) q^{57} +(-4.56484 - 2.32283i) q^{58} +(-4.48139 + 2.58733i) q^{59} +(-2.12753 + 2.73379i) q^{60} +(-9.13215 - 5.27245i) q^{61} +(-5.58121 - 8.58427i) q^{62} +(-6.53744 + 0.239141i) q^{63} +(-7.60049 + 2.49650i) q^{64} +(1.45854 + 0.842091i) q^{65} +(6.47973 + 1.25037i) q^{66} +(4.42845 + 7.67031i) q^{67} +(-0.266831 - 2.51291i) q^{68} +(7.53795 - 7.81873i) q^{69} +(-3.07953 + 0.163040i) q^{70} -3.23033 q^{71} +(5.58769 + 6.38575i) q^{72} +1.89706 q^{73} +(11.0863 - 0.586943i) q^{74} +(1.68095 + 0.417628i) q^{75} +(-14.9141 + 1.58364i) q^{76} +(2.93742 + 5.08777i) q^{77} +(2.70225 - 3.11715i) q^{78} +(-9.75776 - 5.63364i) q^{79} +(2.68286 + 2.96686i) q^{80} +(3.91851 - 8.10218i) q^{81} +(-3.28667 - 5.05512i) q^{82} +(-0.764471 - 0.441368i) q^{83} +(-1.03710 + 7.48230i) q^{84} +(-1.09424 + 0.631759i) q^{85} +(14.5825 + 7.42037i) q^{86} +(6.08788 + 1.51252i) q^{87} +(2.71943 - 7.11841i) q^{88} +11.4473i q^{89} +(1.78459 - 3.84906i) q^{90} +3.67253 q^{91} +(-7.38211 - 10.1378i) q^{92} +(9.02796 + 8.70375i) q^{93} +(8.40134 + 4.27505i) q^{94} +(3.74948 + 6.49430i) q^{95} +(8.38079 - 5.07567i) q^{96} +(-4.16021 + 7.20570i) q^{97} +(2.66174 - 1.73058i) q^{98} +(-8.07701 + 0.295458i) 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 $

$2$	0.0747682	+	1.41224i	0.0528691	+	0.998601i
$2$	0.0747682	+	1.41224i	0.0528691	+	0.998601i
$3$	−0.478797	−	1.66456i	−0.276434	−	0.961033i
$3$	−0.478797	−	1.66456i	−0.276434	−	0.961033i
$4$	−1.98882	+	0.211181i	−0.994410	+	0.105590i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	2.31495	−	0.800631i	0.945074	−	0.326856i
$7$	1.88846	+	1.09030i	0.713770	+	0.412095i	0.812455	−	0.583023i	$-0.198130\pi$
$7$	1.88846	+	1.09030i	0.713770	+	0.412095i	−0.0986853	+	0.995119i	$0.531464\pi$
$8$	−0.446938	−	2.79289i	−0.158016	−	0.987437i
$9$	−2.54151	+	1.59397i	−0.847169	+	0.531324i
$10$	−1.18565	+	0.770869i	−0.374935	+	0.243770i
$11$	2.33319	+	1.34707i	0.703484	+	0.406157i	0.808644	−	0.588299i	$-0.200202\pi$
$11$	2.33319	+	1.34707i	0.703484	+	0.406157i	−0.105160	+	0.994455i	$0.533535\pi$
$12$	1.30376	+	3.20939i	0.376364	+	0.926472i
$13$	1.45854	−	0.842091i	0.404527	−	0.233554i	−0.283908	−	0.958851i	$-0.591631\pi$
$13$	1.45854	−	0.842091i	0.404527	−	0.233554i	0.688436	+	0.725298i	$0.258298\pi$
$14$	−1.39857	+	2.74847i	−0.373783	+	0.734559i
$15$	1.20215	−	1.24693i	0.310394	−	0.321956i
$16$	3.91081	−	0.840001i	0.977701	−	0.210000i
$17$			1.26352i			0.306448i	0.988191	+	0.153224i	$0.0489656\pi$
$17$			1.26352i			0.306448i	−0.988191	+	0.153224i	$0.951034\pi$
$18$	−2.44109	−	3.47003i	−0.575370	−	0.817893i
$19$	7.49897			1.72038			0.860191	−	0.509972i	$-0.170344\pi$
$19$	7.49897			1.72038			0.860191	+	0.509972i	$0.170344\pi$
$20$	−1.17730	−	1.61678i	−0.263252	−	0.361522i
$21$	0.910682	−	3.66548i	0.198727	−	0.799874i
$22$	−1.72793	+	3.39574i	−0.368396	+	0.723973i
$23$	3.13519	+	5.43032i	0.653733	+	1.13230i	0.982210	+	0.187787i	$0.0601315\pi$
$23$	3.13519	+	5.43032i	0.653733	+	1.13230i	−0.328477	+	0.944512i	$0.606535\pi$
$24$	−4.43494	+	2.08118i	−0.905278	+	0.424820i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.29828	+	1.99685i	0.254614	+	0.391614i
$27$	3.87013	+	3.46729i	0.744806	+	0.667281i
$28$	−3.98605	−	1.76961i	−0.753293	−	0.334424i
$29$	−1.81085	+	3.13648i	−0.336266	+	0.582430i	−0.983727	−	0.179669i	$-0.942497\pi$
$29$	−1.81085	+	3.13648i	−0.336266	+	0.582430i	0.647461	+	0.762098i	$0.275831\pi$
$30$	1.85084	+	1.60449i	0.337916	+	0.292938i
$31$	−6.27015	+	3.62007i	−1.12615	+	0.650185i	−0.942965	−	0.332893i	$-0.891975\pi$
$31$	−6.27015	+	3.62007i	−1.12615	+	0.650185i	−0.183188	+	0.983078i	$0.558642\pi$
$32$	1.47868	+	5.46017i	0.261397	+	0.965231i
$33$	1.12515	−	4.52871i	0.195863	−	0.788347i
$34$	−1.78438	+	0.0944710i	−0.306019	+	0.0162016i
$35$			2.18060i			0.368589i
$36$	4.71798	−	3.70684i	0.786330	−	0.617807i
$37$		−	7.85016i		−	1.29056i	−0.763947	−	0.645279i	$-0.776741\pi$
$37$		−	7.85016i		−	1.29056i	0.763947	−	0.645279i	$-0.223259\pi$
$38$	0.560685	+	10.5903i	0.0909551	+	1.71798i
$39$	−2.10006	−	2.02464i	−0.336278	−	0.324202i
$40$	2.19525	−	1.78351i	0.347099	−	0.281997i
$41$	−3.69238	+	2.13180i	−0.576653	+	0.332931i	−0.759802	−	0.650154i	$-0.774704\pi$
$41$	−3.69238	+	2.13180i	−0.576653	+	0.332931i	0.183149	+	0.983085i	$0.441371\pi$
$42$	5.24461	+	1.01204i	0.809262	+	0.156160i
$43$	5.78481	−	10.0196i	0.882176	−	1.52797i	0.0332595	−	0.999447i	$-0.489411\pi$
$43$	5.78481	−	10.0196i	0.882176	−	1.52797i	0.848917	−	0.528527i	$-0.177255\pi$
$44$	−4.92477	−	2.18635i	−0.742437	−	0.329605i
$45$	−2.65117	−	1.40402i	−0.395214	−	0.209299i
$46$	−7.43447	+	4.83365i	−1.09615	+	0.712683i
$47$	3.33277	−	5.77252i	0.486134	−	0.842009i	−0.513739	−	0.857946i	$-0.671740\pi$
$47$	3.33277	−	5.77252i	0.486134	−	0.842009i	0.999873	+	0.0159379i	$0.00507339\pi$
$48$	−3.27071	−	6.10757i	−0.472087	−	0.881552i
$49$	−1.12248	−	1.94420i	−0.160355	−	0.277743i
$50$	−1.26042	−	0.641367i	−0.178250	−	0.0907029i
$51$	2.10320	−	0.604969i	0.294507	−	0.0847126i
$52$	−2.72295	+	1.98278i	−0.377605	+	0.274962i
$53$	−0.537500			−0.0738313			−0.0369157	−	0.999318i	$-0.511753\pi$
$53$	−0.537500			−0.0738313			−0.0369157	+	0.999318i	$0.511753\pi$
$54$	−4.60727	+	5.72477i	−0.626971	+	0.779043i
$55$			2.69414i			0.363278i
$56$	2.20107	−	5.76156i	0.294131	−	0.769920i
$57$	−3.59049	−	12.4825i	−0.475572	−	1.65334i
$58$	−4.56484	−	2.32283i	−0.599393	−	0.305003i
$59$	−4.48139	+	2.58733i	−0.583427	+	0.336842i	−0.762494	−	0.646995i	$-0.776025\pi$
$59$	−4.48139	+	2.58733i	−0.583427	+	0.336842i	0.179067	+	0.983837i	$0.442692\pi$
$60$	−2.12753	+	2.73379i	−0.274663	+	0.352931i
$61$	−9.13215	−	5.27245i	−1.16925	−	0.675068i	−0.215749	−	0.976449i	$-0.569219\pi$
$61$	−9.13215	−	5.27245i	−1.16925	−	0.675068i	−0.953504	+	0.301381i	$0.902553\pi$
$62$	−5.58121	−	8.58427i	−0.708814	−	1.09020i
$63$	−6.53744	+	0.239141i	−0.823640	+	0.0301289i
$64$	−7.60049	+	2.49650i	−0.950062	+	0.312062i
$65$	1.45854	+	0.842091i	0.180910	+	0.104448i
$66$	6.47973	+	1.25037i	0.797599	+	0.153910i
$67$	4.42845	+	7.67031i	0.541022	+	0.937077i	0.998846	+	0.0480343i	$0.0152957\pi$
$67$	4.42845	+	7.67031i	0.541022	+	0.937077i	−0.457824	+	0.889043i	$0.651371\pi$
$68$	−0.266831	−	2.51291i	−0.0323580	−	0.304735i
$69$	7.53795	−	7.81873i	0.907463	−	0.941265i
$70$	−3.07953	+	0.163040i	−0.368074	+	0.0194870i
$71$	−3.23033			−0.383370			−0.191685	−	0.981457i	$-0.561395\pi$
$71$	−3.23033			−0.383370			−0.191685	+	0.981457i	$0.561395\pi$
$72$	5.58769	+	6.38575i	0.658515	+	0.752567i
$73$	1.89706			0.222034			0.111017	−	0.993818i	$-0.464589\pi$
$73$	1.89706			0.222034			0.111017	+	0.993818i	$0.464589\pi$
$74$	11.0863	−	0.586943i	1.28875	−	0.0682307i
$75$	1.68095	+	0.417628i	0.194099	+	0.0482236i
$76$	−14.9141	+	1.58364i	−1.71076	+	0.181656i
$77$	2.93742	+	5.08777i	0.334751	+	0.579805i
$78$	2.70225	−	3.11715i	0.305970	−	0.352948i
$79$	−9.75776	−	5.63364i	−1.09783	−	0.633834i	−0.162182	−	0.986761i	$-0.551853\pi$
$79$	−9.75776	−	5.63364i	−1.09783	−	0.633834i	−0.935651	+	0.352926i	$0.885187\pi$
$80$	2.68286	+	2.96686i	0.299953	+	0.331705i
$81$	3.91851	−	8.10218i	0.435390	−	0.900242i
$82$	−3.28667	−	5.05512i	−0.362952	−	0.558245i
$83$	−0.764471	−	0.441368i	−0.0839116	−	0.0484464i	0.457457	−	0.889232i	$-0.348760\pi$
$83$	−0.764471	−	0.441368i	−0.0839116	−	0.0484464i	−0.541369	+	0.840785i	$0.682094\pi$
$84$	−1.03710	+	7.48230i	−0.113157	+	0.816386i
$85$	−1.09424	+	0.631759i	−0.118687	+	0.0685239i
$86$	14.5825	+	7.42037i	1.57248	+	0.800160i
$87$	6.08788	+	1.51252i	0.652689	+	0.162159i
$88$	2.71943	−	7.11841i	0.289892	−	0.758825i
$89$			11.4473i			1.21341i	0.794925	+	0.606707i	$0.207510\pi$
$89$			11.4473i			1.21341i	−0.794925	+	0.606707i	$0.792490\pi$
$90$	1.78459	−	3.84906i	0.188112	−	0.405726i
$91$	3.67253			0.384986
$92$	−7.38211	−	10.1378i	−0.769639	−	1.05694i
$93$	9.02796	+	8.70375i	0.936155	+	0.902537i
$94$	8.40134	+	4.27505i	0.866532	+	0.440938i
$95$	3.74948	+	6.49430i	0.384689	+	0.666301i
$96$	8.38079	−	5.07567i	0.855360	−	0.518033i
$97$	−4.16021	+	7.20570i	−0.422406	+	0.731628i	−0.996174	−	0.0873894i	$-0.972148\pi$
$97$	−4.16021	+	7.20570i	−0.422406	+	0.731628i	0.573769	+	0.819017i	$0.305481\pi$
$98$	2.66174	−	1.73058i	0.268876	−	0.174815i
$99$	−8.07701	+	0.295458i	−0.811770	+	0.0296947i
$100$	0.811522	−	1.82796i	0.0811522	−	0.182796i
$101$	5.00508	−	8.66905i	0.498024	−	0.862603i	−0.501974	−	0.864883i	$-0.667393\pi$
$101$	5.00508	−	8.66905i	0.498024	−	0.862603i	0.999997	+	0.00228039i	$0.000725873\pi$
$102$	1.01161	+	2.92498i	0.100164	+	0.289616i
$103$	5.82373	−	3.36233i	0.573829	−	0.331300i	−0.184848	−	0.982767i	$-0.559179\pi$
$103$	5.82373	−	3.36233i	0.573829	−	0.331300i	0.758677	+	0.651467i	$0.225846\pi$
$104$	−3.00375	−	3.69719i	−0.294542	−	0.362540i
$105$	3.62974	−	1.04407i	0.354226	−	0.101891i
$106$	−0.0401880	−	0.759077i	−0.00390340	−	0.0737281i
$107$		−	8.72231i		−	0.843218i	−0.906778	−	0.421609i	$-0.861466\pi$
$107$		−	8.72231i		−	0.843218i	0.906778	−	0.421609i	$-0.138534\pi$
$108$	−8.42921	−	6.07853i	−0.811101	−	0.584907i
$109$		−	6.49204i		−	0.621825i	−0.950439	−	0.310913i	$-0.899365\pi$
$109$		−	6.49204i		−	0.621825i	0.950439	−	0.310913i	$-0.100635\pi$
$110$	−3.80476	+	0.201436i	−0.362769	+	0.0192062i
$111$	−13.0670	+	3.75864i	−1.24027	+	0.356754i
$112$	8.30125	+	2.67765i	0.784394	+	0.253014i
$113$	3.47461	−	2.00607i	0.326864	−	0.188715i	−0.327584	−	0.944822i	$-0.606234\pi$
$113$	3.47461	−	2.00607i	0.326864	−	0.188715i	0.654448	+	0.756107i	$0.272901\pi$
$114$	17.3597	−	6.00391i	1.62589	−	0.562317i
$115$	−3.13519	+	5.43032i	−0.292358	+	0.506380i
$116$	2.93908	−	6.62031i	0.272887	−	0.614680i
$117$	−2.36463	+	4.46506i	−0.218610	+	0.412795i
$118$	−3.98899	−	6.13533i	−0.367216	−	0.564803i
$119$	−1.37762	+	2.38610i	−0.126286	+	0.218733i
$120$	−4.01983	−	2.80018i	−0.366958	−	0.255620i
$121$	−1.87081	−	3.24034i	−0.170074	−	0.294576i
$122$	6.76315	−	13.2910i	0.612307	−	1.20331i
$123$	5.31640	+	5.12549i	0.479364	+	0.462149i
$124$	11.7057	−	8.52381i	1.05120	−	0.765461i
$125$	−1.00000			−0.0894427
$126$	−0.826516	−	9.21452i	−0.0736319	−	0.820895i
$127$		−	6.52099i		−	0.578644i	−0.957232	−	0.289322i	$-0.906570\pi$
$127$		−	6.52099i		−	0.578644i	0.957232	−	0.289322i	$-0.0934298\pi$
$128$	−4.09392	−	10.5470i	−0.361855	−	0.932235i
$129$	−19.4479	−	4.83180i	−1.71230	−	0.425417i
$130$	−1.08018	+	2.12277i	−0.0947378	+	0.186179i
$131$	−16.8066	+	9.70332i	−1.46840	+	0.847783i	−0.999373	−	0.0353995i	$-0.988730\pi$
$131$	−16.8066	+	9.70332i	−1.46840	+	0.847783i	−0.469030	+	0.883182i	$0.655396\pi$
$132$	−1.28134	+	9.24439i	−0.111526	+	0.804621i
$133$	14.1615	+	8.17614i	1.22796	+	0.708961i
$134$	−10.5012	+	6.82752i	−0.907163	+	0.589808i
$135$	−1.06770	+	5.08527i	−0.0918932	+	0.437671i
$136$	3.52887	−	0.564714i	0.302598	−	0.0484238i
$137$	−13.1121	−	7.57028i	−1.12024	−	0.646773i	−0.178780	−	0.983889i	$-0.557215\pi$
$137$	−13.1121	−	7.57028i	−1.12024	−	0.646773i	−0.941463	+	0.337117i	$0.890548\pi$
$138$	11.6055	+	10.0608i	0.987925	+	0.856430i
$139$	4.24729	+	7.35652i	0.360250	+	0.623972i	0.988002	−	0.154442i	$-0.0493580\pi$
$139$	4.24729	+	7.35652i	0.360250	+	0.623972i	−0.627752	+	0.778414i	$0.716025\pi$
$140$	−0.460502	−	4.33683i	−0.0389195	−	0.366529i
$141$	−11.2044	−	2.78371i	−0.943582	−	0.234431i
$142$	−0.241526	−	4.56199i	−0.0202684	−	0.382833i
$143$	4.53742			0.379438
$144$	−8.60040	+	8.36858i	−0.716700	+	0.697382i
$145$	−3.62170			−0.300765
$146$	0.141840	+	2.67910i	0.0117388	+	0.221724i
$147$	−2.69879	+	2.79932i	−0.222592	+	0.230884i
$148$	1.65780	+	15.6126i	0.136271	+	1.28334i
$149$	9.94067	+	17.2177i	0.814371	+	1.41053i	0.909779	+	0.415094i	$0.136251\pi$
$149$	9.94067	+	17.2177i	0.814371	+	1.41053i	−0.0954075	+	0.995438i	$0.530415\pi$
$150$	−0.464108	+	2.40512i	−0.0378943	+	0.196377i
$151$	17.7622	+	10.2550i	1.44547	+	0.834541i	0.998207	−	0.0598620i	$-0.0190661\pi$
$151$	17.7622	+	10.2550i	1.44547	+	0.834541i	0.447261	+	0.894403i	$0.352399\pi$
$152$	−3.35157	−	20.9438i	−0.271848	−	1.69877i
$153$	−2.01401	−	3.21124i	−0.162823	−	0.259613i
$154$	−6.96550	+	4.52874i	−0.561296	+	0.364936i
$155$	−6.27015	−	3.62007i	−0.503631	−	0.290771i
$156$	4.60420	+	3.58315i	0.368631	+	0.286882i
$157$	−11.0907	+	6.40323i	−0.885135	+	0.511033i	−0.872348	−	0.488885i	$-0.837404\pi$
$157$	−11.0907	+	6.40323i	−0.885135	+	0.511033i	−0.0127872	+	0.999918i	$0.504070\pi$
$158$	7.22646	−	14.2015i	0.574906	−	1.12981i
$159$	0.257354	+	0.894700i	0.0204095	+	0.0709544i
$160$	−3.98931	+	4.01066i	−0.315382	+	0.317071i
$161$			13.6732i			1.07760i
$162$	11.7352	+	4.92807i	0.922002	+	0.387186i
$163$	21.1034			1.65295			0.826474	−	0.562976i	$-0.190343\pi$
$163$	21.1034			1.65295			0.826474	+	0.562976i	$0.190343\pi$
$164$	6.89329	−	5.01952i	0.538275	−	0.391959i
$165$	4.48455	−	1.28995i	0.349122	−	0.100422i
$166$	0.566157	−	1.11261i	0.0439423	−	0.0863556i
$167$	−5.39086	−	9.33724i	−0.417157	−	0.722538i	0.578495	−	0.815686i	$-0.303640\pi$
$167$	−5.39086	−	9.33724i	−0.417157	−	0.722538i	−0.995652	+	0.0931484i	$0.970307\pi$
$168$	−10.6443	−	0.905194i	−0.821227	−	0.0698373i
$169$	−5.08177	+	8.80188i	−0.390905	+	0.677068i
$170$	−0.974007	−	1.49809i	−0.0747029	−	0.114898i
$171$	−19.0587	+	11.9531i	−1.45745	+	0.914080i
$172$	−9.38901	+	21.1488i	−0.715905	+	1.61258i
$173$	−1.79887	+	3.11574i	−0.136766	+	0.236885i	−0.926271	−	0.376859i	$-0.877004\pi$
$173$	−1.79887	+	3.11574i	−0.136766	+	0.236885i	0.789505	+	0.613744i	$0.210337\pi$
$174$	−1.68086	+	8.71061i	−0.127426	+	0.660350i
$175$	−1.88846	+	1.09030i	−0.142754	+	0.0824191i
$176$	10.2562	+	3.30824i	0.773090	+	0.249368i
$177$	6.45244	+	6.22072i	0.484995	+	0.467578i
$178$	−16.1663	+	0.855897i	−1.21172	+	0.0641522i
$179$		−	4.06880i		−	0.304116i	−0.988372	−	0.152058i	$-0.951410\pi$
$179$		−	4.06880i		−	0.304116i	0.988372	−	0.152058i	$-0.0485901\pi$
$180$	5.56921	+	2.23247i	0.415104	+	0.166399i
$181$		−	19.0648i		−	1.41708i	−0.705672	−	0.708539i	$-0.749355\pi$
$181$		−	19.0648i		−	1.41708i	0.705672	−	0.708539i	$-0.250645\pi$
$182$	0.274589	+	5.18648i	0.0203539	+	0.384447i
$183$	−4.40385	+	17.7254i	−0.325542	+	1.31030i
$184$	13.7651	−	11.1833i	1.01477	−	0.824442i
$185$	6.79844	−	3.92508i	0.499831	−	0.288578i
$186$	−11.6167	+	13.4004i	−0.851781	+	0.982563i
$187$	−1.70205	+	2.94803i	−0.124466	+	0.215581i
$188$	−5.40922	+	12.1843i	−0.394508	+	0.888633i
$189$	3.52817	+	10.7674i	0.256637	+	0.783216i
$190$	−8.89114	+	5.78072i	−0.645031	+	0.419378i
$191$	5.00614	−	8.67089i	0.362232	−	0.627404i	−0.626096	−	0.779746i	$-0.715348\pi$
$191$	5.00614	−	8.67089i	0.362232	−	0.627404i	0.988328	+	0.152342i	$0.0486816\pi$
$192$	7.79466	+	11.4561i	0.562531	+	0.826776i
$193$	−3.23846	−	5.60917i	−0.233109	−	0.403757i	0.725612	−	0.688104i	$-0.241557\pi$
$193$	−3.23846	−	5.60917i	−0.233109	−	0.403757i	−0.958721	+	0.284347i	$0.908223\pi$
$194$	−10.4872	−	5.33644i	−0.752937	−	0.383134i
$195$	0.703362	−	2.83102i	0.0503688	−	0.202734i
$196$	2.64300	+	3.62961i	0.188785	+	0.259258i
$197$	−21.2157			−1.51156			−0.755779	−	0.654827i	$-0.772742\pi$
$197$	−21.2157			−1.51156			−0.755779	+	0.654827i	$0.772742\pi$
$198$	−1.02116	−	11.3846i	−0.0725707	−	0.809065i
$199$			8.56229i			0.606964i	0.952837	+	0.303482i	$0.0981493\pi$
$199$			8.56229i			0.606964i	−0.952837	+	0.303482i	$0.901851\pi$
$200$	2.64218	+	1.00939i	0.186831	+	0.0713744i
$201$	10.6473	−	11.0439i	0.751005	−	0.778980i
$202$	12.6170	+	6.42018i	0.887726	+	0.451722i
$203$	−6.83942	+	3.94874i	−0.480033	+	0.277147i
$204$	−4.05512	+	1.64733i	−0.283915	+	0.115336i
$205$	−3.69238	−	2.13180i	−0.257887	−	0.148891i
$206$	5.18384	+	7.97308i	0.361175	+	0.555511i
$207$	−16.6239	−	8.80377i	−1.15544	−	0.611904i
$208$	4.99672	−	4.51843i	0.346460	−	0.313297i
$209$	17.4965	+	10.1016i	1.21026	+	0.698744i
$210$	1.74586	+	5.04799i	0.120476	+	0.348344i
$211$	−13.2412	−	22.9345i	−0.911564	−	1.57888i	−0.811855	−	0.583859i	$-0.801542\pi$
$211$	−13.2412	−	22.9345i	−0.911564	−	1.57888i	−0.0997092	−	0.995017i	$-0.531791\pi$
$212$	1.06899	−	0.113510i	0.0734186	−	0.00779588i
$213$	1.54667	+	5.37707i	0.105976	+	0.368431i
$214$	12.3180	−	0.652152i	0.842038	−	0.0445802i
$215$	11.5696			0.789042
$216$	7.95408	−	12.3585i	0.541206	−	0.840890i
$217$	−15.7879			−1.07175
$218$	9.16830	−	0.485399i	0.620955	−	0.0328754i
$219$	−0.908308	−	3.15777i	−0.0613778	−	0.213382i
$220$	−0.568950	−	5.35815i	−0.0383586	−	0.361247i
$221$	1.06400	+	1.84290i	0.0715721	+	0.123967i
$222$	−6.28508	−	18.1727i	−0.421827	−	1.21967i
$223$	21.2830	+	12.2878i	1.42522	+	0.822849i	0.996738	−	0.0807023i	$-0.0257163\pi$
$223$	21.2830	+	12.2878i	1.42522	+	0.822849i	0.428479	+	0.903552i	$0.359050\pi$
$224$	−3.16081	+	11.9235i	−0.211190	+	0.796674i
$225$	−0.109667	−	2.99799i	−0.00731114	−	0.199866i
$226$	3.09283	+	4.75698i	0.205732	+	0.316429i
$227$	−11.2920	−	6.51945i	−0.749478	−	0.432711i	0.0760272	−	0.997106i	$-0.475776\pi$
$227$	−11.2920	−	6.51945i	−0.749478	−	0.432711i	−0.825505	+	0.564394i	$0.809110\pi$
$228$	9.77689	+	24.0671i	0.647490	+	1.59388i
$229$	−2.80647	+	1.62032i	−0.185457	+	0.107074i	−0.589854	−	0.807510i	$-0.700815\pi$
$229$	−2.80647	+	1.62032i	−0.185457	+	0.107074i	0.404397	+	0.914584i	$0.367481\pi$
$230$	−7.90330	−	4.02162i	−0.521128	−	0.265178i
$231$	7.06245	−	7.32552i	0.464675	−	0.481984i
$232$	9.56919	+	3.65569i	0.628248	+	0.240008i
$233$			12.7387i			0.834542i	0.908782	+	0.417271i	$0.137013\pi$
$233$			12.7387i			0.834542i	−0.908782	+	0.417271i	$0.862987\pi$
$234$	−6.48251	−	3.00557i	−0.423775	−	0.196480i
$235$	6.66553			0.434811
$236$	8.36628	−	6.09212i	0.544598	−	0.396563i
$237$	−4.70554	+	18.9397i	−0.305657	+	1.23027i
$238$	−3.47274	−	1.76711i	−0.225104	−	0.114545i
$239$	−6.29182	−	10.8978i	−0.406984	−	0.704917i	0.587566	−	0.809176i	$-0.300086\pi$
$239$	−6.29182	−	10.8978i	−0.406984	−	0.704917i	−0.994550	+	0.104259i	$0.966753\pi$
$240$	3.65396	−	5.88631i	0.235862	−	0.379959i
$241$	−4.92669	+	8.53327i	−0.317356	+	0.549677i	−0.979935	−	0.199315i	$-0.936128\pi$
$241$	−4.92669	+	8.53327i	−0.317356	+	0.549677i	0.662580	+	0.748992i	$0.269462\pi$
$242$	4.43624	−	2.88430i	0.285173	−	0.185410i
$243$	−15.3627	−	2.64328i	−0.985519	−	0.169566i
$244$	19.2756	+	8.55742i	1.23400	+	0.547833i
$245$	1.12248	−	1.94420i	0.0717129	−	0.124210i
$246$	−6.84089	+	7.89124i	−0.436160	+	0.503127i
$247$	10.9376	−	6.31481i	0.695941	−	0.401802i
$248$	12.9128	+	15.8939i	0.819966	+	1.00926i
$249$	−0.368655	+	1.48383i	−0.0233626	+	0.0940340i
$250$	−0.0747682	−	1.41224i	−0.00472876	−	0.0893176i
$251$		−	22.8296i		−	1.44099i	−0.693458	−	0.720497i	$-0.743914\pi$
$251$		−	22.8296i		−	1.44099i	0.693458	−	0.720497i	$-0.256086\pi$
$252$	12.9513	−	1.85619i	0.815854	−	0.116929i
$253$			16.8933i			1.06207i
$254$	9.20917	−	0.487563i	0.577835	−	0.0305924i
$255$	1.57552	+	1.51894i	0.0986628	+	0.0951196i
$256$	14.5888	−	6.57016i	0.911800	−	0.410635i
$257$	8.31162	−	4.79872i	0.518465	−	0.299336i	−0.217841	−	0.975984i	$-0.569902\pi$
$257$	8.31162	−	4.79872i	0.518465	−	0.299336i	0.736306	+	0.676648i	$0.236568\pi$
$258$	5.36956	−	27.8264i	0.334294	−	1.73239i
$259$	8.55905	−	14.8247i	0.531833	−	0.921162i
$260$	−3.07861	−	1.36675i	−0.190927	−	0.0847622i
$261$	−0.397181	−	10.8578i	−0.0245849	−	0.672082i
$262$	−14.9600	−	23.0094i	−0.924230	−	1.42153i
$263$	2.72290	−	4.71620i	0.167901	−	0.290813i	−0.769781	−	0.638309i	$-0.779634\pi$
$263$	2.72290	−	4.71620i	0.167901	−	0.290813i	0.937682	+	0.347495i	$0.112968\pi$
$264$	−13.1511	−	1.11837i	−0.809392	−	0.0688308i
$265$	−0.268750	−	0.465489i	−0.0165092	−	0.0285948i
$266$	−10.4878	+	20.6107i	−0.643049	+	1.26372i
$267$	19.0547	−	5.48095i	1.16613	−	0.335429i
$268$	−10.4272	−	14.3197i	−0.636944	−	0.874712i
$269$	−0.945674			−0.0576588			−0.0288294	−	0.999584i	$-0.509178\pi$
$269$	−0.945674			−0.0576588			−0.0288294	+	0.999584i	$0.509178\pi$
$270$	−7.26144	−	1.12763i	−0.441917	−	0.0686254i
$271$			13.9414i			0.846880i	0.905924	+	0.423440i	$0.139178\pi$
$271$			13.9414i			0.846880i	−0.905924	+	0.423440i	$0.860822\pi$
$272$	1.06136	+	4.94137i	0.0643542	+	0.299615i
$273$	−1.75840	−	6.11314i	−0.106423	−	0.369984i
$274$	9.71065	−	19.0834i	0.586642	−	1.15287i
$275$	−2.33319	+	1.34707i	−0.140697	+	0.0812313i
$276$	−13.3405	+	17.1419i	−0.803001	+	1.03182i
$277$	10.8558	+	6.26761i	0.652263	+	0.376584i	0.789323	−	0.613979i	$-0.210432\pi$
$277$	10.8558	+	6.26761i	0.652263	+	0.376584i	−0.137060	+	0.990563i	$0.543765\pi$
$278$	−10.0716	+	6.54820i	−0.604053	+	0.392735i
$279$	10.1653	−	19.1949i	0.608583	−	1.14917i
$280$	6.09019	−	0.974594i	0.363959	−	0.0582431i
$281$	18.5010	+	10.6816i	1.10368	+	0.637209i	0.937185	−	0.348833i	$-0.113422\pi$
$281$	18.5010	+	10.6816i	1.10368	+	0.637209i	0.166494	+	0.986042i	$0.446755\pi$
$282$	3.09353	−	16.0314i	0.184217	−	0.954656i
$283$	−7.79619	−	13.5034i	−0.463435	−	0.802694i	0.535694	−	0.844412i	$-0.320050\pi$
$283$	−7.79619	−	13.5034i	−0.463435	−	0.802694i	−0.999129	+	0.0417185i	$0.986717\pi$
$284$	6.42454	−	0.682184i	0.381226	−	0.0404801i
$285$	9.01489	−	9.35069i	0.533996	−	0.553887i
$286$	0.339255	+	6.40790i	0.0200605	+	0.378907i
$287$	−9.29721			−0.548797
$288$	−12.4614	−	11.5201i	−0.734298	−	0.678828i
$289$	15.4035			0.906090
$290$	−0.270788	−	5.11469i	−0.0159012	−	0.300345i
$291$	13.9862	+	3.47485i	0.819886	+	0.203699i
$292$	−3.77291	+	0.400623i	−0.220793	+	0.0234447i
$293$	−16.0549	−	27.8079i	−0.937937	−	1.62455i	−0.769311	−	0.638874i	$-0.779401\pi$
$293$	−16.0549	−	27.8079i	−0.937937	−	1.62455i	−0.168625	−	0.985680i	$-0.553933\pi$
$294$	−4.15508	−	3.60203i	−0.242329	−	0.210074i
$295$	−4.48139	−	2.58733i	−0.260917	−	0.150640i
$296$	−21.9247	+	3.50853i	−1.27434	+	0.203929i
$297$	4.35906	+	13.3032i	0.252938	+	0.771929i
$298$	−23.5723	+	15.3259i	−1.36550	+	0.887806i
$299$	9.14564	+	5.28024i	0.528906	+	0.305364i
$300$	−3.43130	−	0.475603i	−0.198106	−	0.0274590i
$301$	21.8488	−	12.6144i	1.25934	−	0.727081i
$302$	−13.1545	+	25.8512i	−0.756954	+	1.48757i
$303$	−16.8266	−	4.18052i	−0.966660	−	0.240165i
$304$	29.3270	−	6.29914i	1.68202	−	0.361280i
$305$		−	10.5449i		−	0.603799i
$306$	4.38444	−	3.08436i	0.250642	−	0.176321i
$307$	8.20208			0.468118			0.234059	−	0.972222i	$-0.424799\pi$
$307$	8.20208			0.468118			0.234059	+	0.972222i	$0.424799\pi$
$308$	−6.91644	−	9.49832i	−0.394101	−	0.541217i
$309$	−8.38518	−	8.08406i	−0.477016	−	0.459886i
$310$	4.64359	−	9.12560i	0.263738	−	0.518299i
$311$	−1.76373	−	3.05486i	−0.100012	−	0.173225i	0.811678	−	0.584106i	$-0.198555\pi$
$311$	−1.76373	−	3.05486i	−0.100012	−	0.173225i	−0.911689	+	0.410880i	$0.865221\pi$
$312$	−4.71601	+	6.77012i	−0.266991	+	0.383282i
$313$	−1.89398	+	3.28047i	−0.107054	+	0.185423i	−0.914576	−	0.404415i	$-0.867475\pi$
$313$	−1.89398	+	3.28047i	−0.107054	+	0.185423i	0.807522	+	0.589838i	$0.200808\pi$
$314$	−9.87210	−	15.1839i	−0.557115	−	0.856880i
$315$	−3.47582	−	5.54202i	−0.195840	−	0.312257i
$316$	20.5961	+	9.14365i	1.15862	+	0.514370i
$317$	2.11485	−	3.66303i	0.118782	−	0.205736i	−0.800503	−	0.599328i	$-0.795434\pi$
$317$	2.11485	−	3.66303i	0.118782	−	0.205736i	0.919285	+	0.393592i	$0.128768\pi$
$318$	−1.24429	+	0.430339i	−0.0697761	+	0.0241322i
$319$	−8.45011	+	4.87867i	−0.473115	+	0.273153i
$320$	−5.96228	−	5.33397i	−0.333301	−	0.298178i
$321$	−14.5188	+	4.17622i	−0.810360	+	0.233094i
$322$	−19.3098	+	1.02232i	−1.07609	+	0.0569719i
$323$			9.47508i			0.527208i
$324$	−6.08218	+	16.9413i	−0.337899	+	0.941182i
$325$			1.68418i			0.0934216i
$326$	1.57787	+	29.8030i	0.0873899	+	1.65064i
$327$	−10.8064	+	3.10837i	−0.597594	+	0.171893i
$328$	7.60415	+	9.35965i	0.419869	+	0.516800i
$329$	12.5876	−	7.26744i	0.693976	−	0.400667i
$330$	2.15701	+	6.23679i	0.118739	+	0.343324i
$331$	−12.3041	+	21.3113i	−0.676293	+	1.17137i	0.299796	+	0.954003i	$0.403081\pi$
$331$	−12.3041	+	21.3113i	−0.676293	+	1.17137i	−0.976089	+	0.217371i	$0.930252\pi$
$332$	1.61360	+	0.716359i	0.0885580	+	0.0393153i
$333$	12.5129	+	19.9512i	0.685705	+	1.09332i
$334$	12.7833	−	8.31129i	0.699472	−	0.454774i
$335$	−4.42845	+	7.67031i	−0.241952	+	0.419074i
$336$	0.482491	−	15.1000i	0.0263221	−	0.823770i
$337$	9.31174	+	16.1284i	0.507243	+	0.878570i	0.999965	+	0.00838331i	$0.00266852\pi$
$337$	9.31174	+	16.1284i	0.507243	+	0.878570i	−0.492722	+	0.870187i	$0.663998\pi$
$338$	−12.8103	−	6.51855i	−0.696788	−	0.354562i
$339$	−5.00285	−	4.82319i	−0.271717	−	0.261960i
$340$	2.04283	−	1.48754i	0.110788	−	0.0806730i
$341$	−19.5060			−1.05631
$342$	−18.3056	−	26.0216i	−0.989856	−	1.40709i
$343$		−	20.1596i		−	1.08852i
$344$	−30.5691	−	11.6782i	−1.64818	−	0.629648i
$345$	10.5402	+	2.61869i	0.567465	+	0.140986i
$346$	−4.53466	−	2.30747i	−0.243785	−	0.124051i
$347$	2.82992	−	1.63386i	0.151918	−	0.0877100i	−0.422114	−	0.906543i	$-0.638712\pi$
$347$	2.82992	−	1.63386i	0.151918	−	0.0877100i	0.574032	+	0.818833i	$0.305378\pi$
$348$	−12.4271	−	1.72249i	−0.666163	−	0.0923352i
$349$	−17.9472	−	10.3618i	−0.960693	−	0.554656i	−0.0643065	−	0.997930i	$-0.520484\pi$
$349$	−17.9472	−	10.3618i	−0.960693	−	0.554656i	−0.896386	+	0.443274i	$0.853817\pi$
$350$	−1.68096	−	2.58543i	−0.0898511	−	0.138197i
$351$	8.56452	+	1.79820i	0.457140	+	0.0959811i
$352$	−3.90518	+	14.7315i	−0.208147	+	0.785193i
$353$	−3.44648	−	1.98983i	−0.183438	−	0.105908i	0.405469	−	0.914109i	$-0.367108\pi$
$353$	−3.44648	−	1.98983i	−0.183438	−	0.105908i	−0.588907	+	0.808201i	$0.700441\pi$
$354$	−8.30269	+	9.57748i	−0.441283	+	0.509037i
$355$	−1.61516	−	2.79755i	−0.0857241	−	0.148478i
$356$	−2.41746	−	22.7667i	−0.128125	−	1.20663i
$357$	4.63140	+	1.15066i	0.245120	+	0.0608995i
$358$	5.74610	−	0.304217i	0.303691	−	0.0160784i
$359$	28.0127			1.47845			0.739227	−	0.673456i	$-0.235191\pi$
$359$	28.0127			1.47845			0.739227	+	0.673456i	$0.235191\pi$
$360$	−2.73638	+	8.03195i	−0.144220	+	0.423321i
$361$	37.2345			1.95971
$362$	26.9240	−	1.42544i	1.41510	−	0.0749196i
$363$	−4.49799	+	4.66554i	−0.236083	+	0.244877i
$364$	−7.30400	+	0.775568i	−0.382834	+	0.0406508i
$365$	0.948531	+	1.64290i	0.0496484	+	0.0859935i
$366$	−25.3618	−	4.89397i	−1.32568	−	0.255812i
$367$	−16.0747	−	9.28076i	−0.839095	−	0.484452i	0.0178616	−	0.999840i	$-0.494314\pi$
$367$	−16.0747	−	9.28076i	−0.839095	−	0.484452i	−0.856956	+	0.515389i	$0.827648\pi$
$368$	16.8226	+	18.6033i	0.876939	+	0.969766i
$369$	5.98619	−	11.3035i	0.311628	−	0.588438i
$370$	6.05145	+	9.30753i	0.314600	+	0.483875i
$371$	−1.01505	−	0.586038i	−0.0526986	−	0.0304256i
$372$	−19.7930	−	15.4037i	−1.02622	−	0.798642i
$373$	−6.56377	+	3.78959i	−0.339859	+	0.196218i	−0.660210	−	0.751081i	$-0.729533\pi$
$373$	−6.56377	+	3.78959i	−0.339859	+	0.196218i	0.320351	+	0.947299i	$0.396199\pi$
$374$	−4.29057	−	2.18327i	−0.221860	−	0.112894i
$375$	0.478797	+	1.66456i	0.0247250	+	0.0859574i
$376$	−17.6116	−	6.72810i	−0.908247	−	0.346975i
$377$			6.09959i			0.314145i
$378$	−14.9424	+	5.78767i	−0.768553	+	0.297686i
$379$	−11.2694			−0.578872			−0.289436	−	0.957197i	$-0.593468\pi$
$379$	−11.2694			−0.578872			−0.289436	+	0.957197i	$0.593468\pi$
$380$	−8.82852	−	12.1242i	−0.452893	−	0.621957i
$381$	−10.8546	+	3.12223i	−0.556096	+	0.159957i
$382$	12.6196	+	6.42155i	0.645677	+	0.328555i
$383$	−15.9892	−	27.6941i	−0.817011	−	1.41510i	−0.907875	−	0.419241i	$-0.862296\pi$
$383$	−15.9892	−	27.6941i	−0.817011	−	1.41510i	0.0908637	−	0.995863i	$-0.471037\pi$
$384$	−15.5960	+	11.8645i	−0.795879	+	0.605455i
$385$	−2.93742	+	5.08777i	−0.149705	+	0.259297i
$386$	7.67934	−	4.99285i	0.390868	−	0.254129i
$387$	1.26881	+	34.6857i	0.0644971	+	1.76317i
$388$	6.75221	−	15.2094i	0.342791	−	0.772140i
$389$	−11.3067	+	19.5837i	−0.573272	+	0.992936i	0.422955	+	0.906150i	$0.360993\pi$
$389$	−11.3067	+	19.5837i	−0.573272	+	0.992936i	−0.996227	+	0.0867851i	$0.972341\pi$
$390$	4.05066	+	0.781642i	0.205113	+	0.0395800i
$391$	−6.86130	+	3.96137i	−0.346991	+	0.200335i
$392$	−4.92826	+	4.00391i	−0.248915	+	0.202228i
$393$	24.1987	+	23.3297i	1.22066	+	1.17683i
$394$	−1.58626	−	29.9616i	−0.0799148	−	1.50944i
$395$		−	11.2673i		−	0.566919i
$396$	16.0013	−	2.29332i	0.804097	−	0.115244i
$397$		−	4.60230i		−	0.230983i	−0.993308	−	0.115492i	$-0.963156\pi$
$397$		−	4.60230i		−	0.230983i	0.993308	−	0.115492i	$-0.0368443\pi$
$398$	−12.0920	+	0.640187i	−0.606116	+	0.0320897i
$399$	6.82917	−	27.4873i	0.341886	−	1.37609i
$400$	−1.22794	+	3.80686i	−0.0613970	+	0.190343i
$401$	6.92084	−	3.99575i	0.345610	−	0.199538i	−0.317140	−	0.948379i	$-0.602722\pi$
$401$	6.92084	−	3.99575i	0.345610	−	0.199538i	0.662750	+	0.748841i	$0.269389\pi$
$402$	16.3927	+	14.2108i	0.817595	+	0.708771i
$403$	−6.09686	+	10.5601i	−0.303706	+	0.526035i
$404$	−8.12346	+	18.2981i	−0.404157	+	0.910367i
$405$	8.97595	−	0.657563i	0.446018	−	0.0326746i
$406$	−6.08792	−	9.36363i	−0.302139	−	0.464709i
$407$	10.5747	−	18.3159i	0.524169	−	0.907887i
$408$	−2.62961	−	5.60362i	−0.130185	−	0.277421i
$409$	−13.4930	−	23.3706i	−0.667188	−	1.15560i	−0.978687	−	0.205357i	$-0.934164\pi$
$409$	−13.4930	−	23.3706i	−0.667188	−	1.15560i	0.311499	−	0.950246i	$-0.399169\pi$
$410$	2.73453	−	5.37391i	0.135049	−	0.265398i
$411$	−6.32312	+	25.4505i	−0.311897	+	1.25538i
$412$	−10.8723	+	7.91693i	−0.535639	+	0.390039i
$413$	−11.2839			−0.555244
$414$	11.1901	−	24.1351i	0.549961	−	1.18617i
$415$		−	0.882735i		−	0.0433318i
$416$	6.75468	+	6.71872i	0.331176	+	0.329412i
$417$	10.2118	−	10.5921i	0.500072	−	0.518699i
$418$	−12.9577	+	25.4645i	−0.633782	+	1.24551i
$419$	22.0624	−	12.7377i	1.07782	−	0.622279i	0.147511	−	0.989060i	$-0.452874\pi$
$419$	22.0624	−	12.7377i	1.07782	−	0.622279i	0.930307	+	0.366782i	$0.119540\pi$
$420$	−6.99841	+	2.84299i	−0.341488	+	0.138724i
$421$	−0.228683	−	0.132030i	−0.0111453	−	0.00643476i	0.494417	−	0.869225i	$-0.335382\pi$
$421$	−0.228683	−	0.132030i	−0.0111453	−	0.00643476i	−0.505562	+	0.862790i	$0.668715\pi$
$422$	31.3989	−	20.4145i	1.52847	−	0.993763i
$423$	0.730990	+	19.9832i	0.0355419	+	0.971618i
$424$	0.240229	+	1.50118i	0.0116666	+	0.0729038i
$425$	−1.09424	−	0.631759i	−0.0530784	−	0.0306448i
$426$	−7.47805	+	2.58630i	−0.362313	+	0.125307i
$427$	−11.4971	−	19.9136i	−0.556385	−	0.963687i
$428$	1.84198	+	17.3471i	0.0890357	+	0.838504i
$429$	−2.17250	−	7.55279i	−0.104889	−	0.364652i
$430$	0.865041	+	16.3390i	0.0417160	+	0.787939i
$431$	−23.4866			−1.13131			−0.565656	−	0.824642i	$-0.691377\pi$
$431$	−23.4866			−1.13131			−0.565656	+	0.824642i	$0.691377\pi$
$432$	18.0478	+	10.3090i	0.868327	+	0.495992i
$433$	−27.2331			−1.30874			−0.654369	−	0.756175i	$-0.727066\pi$
$433$	−27.2331			−1.30874			−0.654369	+	0.756175i	$0.727066\pi$
$434$	−1.18043	−	22.2962i	−0.0566626	−	1.07025i
$435$	1.73406	+	6.02852i	0.0831417	+	0.289046i
$436$	1.37099	+	12.9115i	0.0656588	+	0.618349i
$437$	23.5107	+	40.7218i	1.12467	+	1.94799i
$438$	4.39160	−	1.51885i	0.209839	−	0.0725733i
$439$	−6.43425	−	3.71482i	−0.307090	−	0.177298i	0.338534	−	0.940954i	$-0.390069\pi$
$439$	−6.43425	−	3.71482i	−0.307090	−	0.177298i	−0.645624	+	0.763656i	$0.723402\pi$
$440$	7.52444	−	1.20411i	0.358713	−	0.0574038i
$441$	5.95180	+	3.15199i	0.283419	+	0.150095i
$442$	−2.52305	+	1.64040i	−0.120009	+	0.0780260i
$443$	2.76333	+	1.59541i	0.131290	+	0.0758003i	0.564206	−	0.825634i	$-0.309182\pi$
$443$	2.76333	+	1.59541i	0.131290	+	0.0758003i	−0.432917	+	0.901434i	$0.642516\pi$
$444$	25.1942	−	10.2348i	1.19567	−	0.485720i
$445$	−9.91368	+	5.72366i	−0.469953	+	0.271328i
$446$	−15.7619	+	30.9754i	−0.746349	+	1.46673i
$447$	23.9004	−	24.7906i	1.13045	−	1.17256i
$448$	−17.0751	−	3.57230i	−0.806725	−	0.168775i
$449$		−	13.6098i		−	0.642286i	−0.947031	−	0.321143i	$-0.895933\pi$
$449$		−	13.6098i		−	0.642286i	0.947031	−	0.321143i	$-0.104067\pi$
$450$	4.22568	−	0.379031i	0.199200	−	0.0178677i
$451$	−11.4867			−0.540888
$452$	−6.48673	+	4.72347i	−0.305110	+	0.222174i
$453$	8.56557	−	34.4763i	0.402446	−	1.61984i
$454$	8.36272	−	16.4344i	0.392482	−	0.771307i
$455$	1.83627	+	3.18051i	0.0860855	+	0.149104i
$456$	−33.2575	+	15.6067i	−1.55742	+	0.730852i
$457$	−4.25473	+	7.36942i	−0.199028	+	0.344727i	−0.948214	−	0.317634i	$-0.897112\pi$
$457$	−4.25473	+	7.36942i	−0.199028	+	0.344727i	0.749185	+	0.662360i	$0.230445\pi$
$458$	−2.49811	−	3.84226i	−0.116729	−	0.179537i
$459$	−4.38099	+	4.88997i	−0.204487	+	0.228244i
$460$	5.08856	−	11.4620i	0.237255	−	0.534419i
$461$	12.5094	−	21.6669i	0.582620	−	1.00913i	−0.412548	−	0.910936i	$-0.635361\pi$
$461$	12.5094	−	21.6669i	0.582620	−	1.00913i	0.995168	−	0.0981910i	$-0.0313056\pi$
$462$	10.8734	+	9.42613i	0.505877	+	0.438543i
$463$	5.97172	−	3.44777i	0.277529	−	0.160232i	−0.354775	−	0.934952i	$-0.615443\pi$
$463$	5.97172	−	3.44777i	0.277529	−	0.160232i	0.632304	+	0.774720i	$0.282109\pi$
$464$	−4.44723	+	13.7873i	−0.206457	+	0.640058i
$465$	−3.02369	+	12.1703i	−0.140220	+	0.564385i
$466$	−17.9901	+	0.952453i	−0.833375	+	0.0441215i
$467$		−	27.8524i		−	1.28886i	−0.764665	−	0.644428i	$-0.777096\pi$
$467$		−	27.8524i		−	1.28886i	0.764665	−	0.644428i	$-0.222904\pi$
$468$	3.75989	−	9.37955i	0.173801	−	0.433570i
$469$			19.3134i			0.891810i
$470$	0.498370	+	9.41330i	0.0229881	+	0.434203i
$471$	15.9687	+	15.3953i	0.735801	+	0.709377i
$472$	9.22904	+	11.3597i	0.424801	+	0.522871i
$473$	26.9942	−	15.5851i	1.24119	−	0.716603i
$474$	−27.0992	−	5.22924i	−1.24471	−	0.240187i
$475$	−3.74948	+	6.49430i	−0.172038	+	0.297979i
$476$	2.23593	−	5.03645i	0.102484	−	0.230845i
$477$	1.36606	−	0.856760i	0.0625476	−	0.0392284i
$478$	14.9198	−	9.70034i	0.682414	−	0.443683i
$479$	−14.5273	+	25.1620i	−0.663770	+	1.14968i	0.315848	+	0.948810i	$0.397711\pi$
$479$	−14.5273	+	25.1620i	−0.663770	+	1.14968i	−0.979617	+	0.200873i	$0.935622\pi$
$480$	8.58605	+	4.72014i	0.391898	+	0.215444i
$481$	−6.61055	−	11.4498i	−0.301415	−	0.522066i
$482$	−12.4194	−	6.31963i	−0.565686	−	0.287851i
$483$	22.7599	−	6.54671i	1.03561	−	0.297886i
$484$	4.40500	+	6.04937i	0.200227	+	0.274971i
$485$	−8.32043			−0.377811
$486$	2.58429	−	21.8934i	0.117226	−	0.993105i
$487$			18.1895i			0.824244i	0.911129	+	0.412122i	$0.135212\pi$
$487$			18.1895i			0.824244i	−0.911129	+	0.412122i	$0.864788\pi$
$488$	−10.6439	+	27.8616i	−0.481826	+	1.26123i
$489$	−10.1043	−	35.1279i	−0.456930	−	1.58854i
$490$	2.82959	+	1.43985i	0.127828	+	0.0650457i
$491$	−1.94702	+	1.12411i	−0.0878677	+	0.0507304i	−0.543290	−	0.839545i	$-0.682822\pi$
$491$	−1.94702	+	1.12411i	−0.0878677	+	0.0507304i	0.455422	+	0.890276i	$0.349488\pi$
$492$	−11.6558	−	9.07094i	−0.525483	−	0.408950i
$493$	−3.96300	−	2.28804i	−0.178484	−	0.103048i
$494$	9.73578	+	14.9743i	0.438034	+	0.673725i
$495$	−4.29438	−	6.84717i	−0.193018	−	0.307757i
$496$	−21.4805	+	19.4243i	−0.964502	+	0.872179i
$497$	−6.10034	−	3.52203i	−0.273638	−	0.157985i
$498$	−2.12308	−	0.409684i	−0.0951377	−	0.0183584i
$499$	−0.0717323	−	0.124244i	−0.00321118	−	0.00556192i	0.864415	−	0.502778i	$-0.167689\pi$
$499$	−0.0717323	−	0.124244i	−0.00321118	−	0.00556192i	−0.867627	+	0.497216i	$0.834355\pi$
$500$	1.98882	−	0.211181i	0.0889427	−	0.00944429i
$501$	−12.9613	+	13.4440i	−0.579066	+	0.600636i
$502$	32.2408	−	1.70693i	1.43898	−	0.0761841i
$503$	43.2540			1.92860			0.964299	−	0.264815i	$-0.0853108\pi$
$503$	43.2540			1.92860			0.964299	+	0.264815i	$0.0853108\pi$
$504$	3.58972	+	18.1515i	0.159899	+	0.808531i
$505$	10.0102			0.445446
$506$	−23.8573	+	1.26308i	−1.06059	+	0.0561508i
$507$	17.0844	+	4.24458i	0.758744	+	0.188508i
$508$	1.37711	+	12.9691i	0.0610992	+	0.575409i
$509$	8.03555	+	13.9180i	0.356169	+	0.616904i	0.987317	−	0.158759i	$-0.0507492\pi$
$509$	8.03555	+	13.9180i	0.356169	+	0.616904i	−0.631148	+	0.775663i	$0.717416\pi$
$510$	−2.02730	+	2.33857i	−0.0897704	+	0.103554i
$511$	3.58252	+	2.06837i	0.158481	+	0.0914993i
$512$	10.3694	+	20.1116i	0.458267	+	0.888815i
$513$	29.0219	+	26.0011i	1.28135	+	1.14798i
$514$	7.39837	+	11.3792i	0.326328	+	0.501914i
$515$	5.82373	+	3.36233i	0.256624	+	0.148162i
$516$	39.6988	+	5.50255i	1.74764	+	0.242236i
$517$	15.5520	−	8.97893i	0.683975	−	0.394893i
$518$	21.5759	+	10.9790i	0.947991	+	0.482388i
$519$	6.04762	+	1.50252i	0.265461	+	0.0659533i
$520$	1.69999	−	4.44992i	0.0745495	−	0.195142i
$521$		−	12.7366i		−	0.558002i	−0.960291	−	0.279001i	$-0.909997\pi$
$521$		−	12.7366i		−	0.558002i	0.960291	−	0.279001i	$-0.0900034\pi$
$522$	15.3041	−	1.37273i	0.669843	−	0.0600829i
$523$	4.95083			0.216485			0.108242	−	0.994125i	$-0.465478\pi$
$523$	4.95083			0.216485			0.108242	+	0.994125i	$0.465478\pi$
$524$	31.3762	−	22.8474i	1.37068	−	0.998093i
$525$	2.71906	+	2.62141i	0.118669	+	0.114408i
$526$	6.86398	+	3.49276i	0.299284	+	0.152291i
$527$	−4.57403	−	7.92245i	−0.199248	−	0.345107i
$528$	0.596118	−	18.6560i	0.0259427	−	0.811899i
$529$	−8.15889	+	14.1316i	−0.354734	+	0.614418i
$530$	0.637286	−	0.414342i	0.0276819	−	0.0179979i
$531$	7.26534	−	13.7189i	0.315289	−	0.595351i
$532$	−29.8913	−	13.2702i	−1.29595	−	0.575337i
$533$	−3.59033	+	6.21864i	−0.155515	+	0.269359i
$534$	9.16508	+	26.5000i	0.396612	+	1.14677i
$535$	7.55374	−	4.36116i	0.326577	−	0.188549i
$536$	19.4431	−	15.7963i	0.839814	−	0.682298i
$537$	−6.77275	+	1.94813i	−0.292266	+	0.0840680i
$538$	−0.0707064	−	1.33551i	−0.00304837	−	0.0575781i
$539$		−	6.04825i		−	0.260517i
$540$	1.04956	−	10.3392i	0.0451657	−	0.444927i
$541$		−	14.9473i		−	0.642633i	−0.946972	−	0.321316i	$-0.895875\pi$
$541$		−	14.9473i		−	0.642633i	0.946972	−	0.321316i	$-0.104125\pi$
$542$	−19.6885	+	1.04237i	−0.845696	+	0.0447738i
$543$	−31.7345	+	9.12819i	−1.36186	+	0.391728i
$544$	−6.89903	+	1.86834i	−0.295793	+	0.0801045i
$545$	5.62228	−	3.24602i	0.240832	−	0.139044i
$546$	8.50172	−	2.94034i	0.363840	−	0.125835i
$547$	−3.71371	+	6.43233i	−0.158787	+	0.275027i	−0.934431	−	0.356143i	$-0.884092\pi$
$547$	−3.71371	+	6.43233i	−0.158787	+	0.275027i	0.775645	+	0.631170i	$0.217425\pi$
$548$	27.6763	+	12.2869i	1.18227	+	0.524870i
$549$	31.6136	−	1.15643i	1.34923	−	0.0493552i
$550$	−2.07683	−	3.19430i	−0.0885562	−	0.136205i
$551$	−13.5795	+	23.5204i	−0.578506	+	1.00200i
$552$	−25.2059	−	17.5582i	−1.07283	−	0.747327i
$553$	−12.2847	−	21.2778i	−0.522400	−	0.904824i
$554$	−8.03967	+	15.7996i	−0.341573	+	0.671260i
$555$	−9.78860	−	9.43708i	−0.415503	−	0.400582i
$556$	−10.0006	−	13.7338i	−0.424122	−	0.582444i
$557$	41.6983			1.76681			0.883406	−	0.468608i	$-0.155244\pi$
$557$	41.6983			1.76681			0.883406	+	0.468608i	$0.155244\pi$
$558$	27.8678	+	12.9207i	1.17974	+	0.546976i
$559$		−	19.4854i		−	0.824143i
$560$	1.83171	+	8.52792i	0.0774038	+	0.360370i
$561$	5.72210	+	1.42164i	0.241587	+	0.0600219i
$562$	−13.7016	+	26.9265i	−0.577968	+	1.13582i
$563$	−36.9371	+	21.3256i	−1.55671	+	0.898768i	−0.559145	+	0.829070i	$0.688870\pi$
$563$	−36.9371	+	21.3256i	−1.55671	+	0.898768i	−0.997568	+	0.0696983i	$0.977796\pi$
$564$	22.8714	+	3.17015i	0.963061	+	0.133487i
$565$	3.47461	+	2.00607i	0.146178	+	0.0843958i
$566$	18.4871	−	12.0197i	0.777070	−	0.505225i
$567$	16.2338	−	11.0283i	0.681754	−	0.463144i
$568$	1.44376	+	9.02196i	0.0605787	+	0.378553i
$569$	−19.0811	−	11.0165i	−0.799920	−	0.461834i	0.0435235	−	0.999052i	$-0.486142\pi$
$569$	−19.0811	−	11.0165i	−0.799920	−	0.461834i	−0.843443	+	0.537219i	$0.819475\pi$
$570$	13.8794	+	12.0320i	0.581344	+	0.503966i
$571$	−2.03892	−	3.53151i	−0.0853261	−	0.147789i	0.820204	−	0.572071i	$-0.193860\pi$
$571$	−2.03892	−	3.53151i	−0.0853261	−	0.147789i	−0.905530	+	0.424282i	$0.860527\pi$
$572$	−9.02410	+	0.958215i	−0.377317	+	0.0400650i
$573$	−16.8301	−	4.18141i	−0.703089	−	0.174681i
$574$	−0.695136	−	13.1299i	−0.0290144	−	0.548030i
$575$	−6.27039			−0.261493
$576$	15.3374	−	18.4598i	0.639056	−	0.769160i
$577$	−26.9469			−1.12182			−0.560908	−	0.827878i	$-0.689548\pi$
$577$	−26.9469			−1.12182			−0.560908	+	0.827878i	$0.689548\pi$
$578$	1.15169	+	21.7534i	0.0479042	+	0.904822i
$579$	−7.78622	+	8.07625i	−0.323584	+	0.335638i
$580$	7.20290	−	0.764832i	0.299084	−	0.0317579i
$581$	−0.962448	−	1.66701i	−0.0399291	−	0.0691592i
$582$	−3.86158	+	20.0116i	−0.160068	+	0.829509i
$583$	−1.25409	−	0.724050i	−0.0519392	−	0.0299871i
$584$	−0.847868	−	5.29829i	−0.0350850	−	0.219245i
$585$	−5.04917	+	0.184699i	−0.208757	+	0.00763637i
$586$	38.0709	−	24.7524i	1.57269	−	1.02251i
$587$	19.9276	+	11.5052i	0.822501	+	0.474871i	0.851278	−	0.524715i	$-0.175828\pi$
$587$	19.9276	+	11.5052i	0.822501	+	0.474871i	−0.0287772	+	0.999586i	$0.509161\pi$
$588$	4.77624	−	6.13727i	0.196969	−	0.253097i
$589$	−47.0197	+	27.1468i	−1.93741	+	1.11857i
$590$	3.31886	−	6.52223i	0.136635	−	0.268516i
$591$	10.1580	+	35.3148i	0.417846	+	1.45266i
$592$	−6.59414	−	30.7005i	−0.271018	−	1.26178i
$593$			7.35031i			0.301841i	0.988546	+	0.150920i	$0.0482237\pi$
$593$			7.35031i			0.301841i	−0.988546	+	0.150920i	$0.951776\pi$
$594$	−18.4613	+	7.15068i	−0.757477	+	0.293396i
$595$	−2.75523			−0.112953
$596$	−23.4062	−	32.1437i	−0.958757	−	1.31666i
$597$	14.2524	−	4.09960i	0.583313	−	0.167785i
$598$	−6.77313	+	13.3106i	−0.276974	+	0.544310i
$599$	14.3954	+	24.9336i	0.588180	+	1.01876i	0.994471	+	0.105014i	$0.0334887\pi$
$599$	14.3954	+	24.9336i	0.588180	+	1.01876i	−0.406291	+	0.913744i	$0.633178\pi$
$600$	0.415112	−	4.88136i	0.0169469	−	0.199281i
$601$	1.96719	−	3.40728i	0.0802434	−	0.138986i	−0.823111	−	0.567880i	$-0.807764\pi$
$601$	1.96719	−	3.40728i	0.0802434	−	0.138986i	0.903354	+	0.428895i	$0.141097\pi$
$602$	19.4481	+	29.9124i	0.792645	+	1.21914i
$603$	−23.4812	−	12.4353i	−0.956228	−	0.506405i
$604$	−37.4915	−	16.6443i	−1.52551	−	0.677248i
$605$	1.87081	−	3.24034i	0.0760592	−	0.131738i
$606$	4.64579	−	24.0756i	0.188722	−	0.978005i
$607$	−39.1546	+	22.6059i	−1.58924	+	0.917547i	−0.595805	+	0.803129i	$0.703167\pi$
$607$	−39.1546	+	22.6059i	−1.58924	+	0.917547i	−0.993433	+	0.114418i	$0.963500\pi$
$608$	11.0886	+	40.9457i	0.449702	+	1.66057i
$609$	9.84761	+	9.49396i	0.399045	+	0.384715i
$610$	14.8919	−	0.788424i	0.602955	−	0.0319224i
$611$		−	11.2260i		−	0.454154i
$612$	4.68366	+	5.96125i	0.189326	+	0.240969i
$613$			32.1249i			1.29751i	0.760997	+	0.648756i	$0.224710\pi$
$613$			32.1249i			1.29751i	−0.760997	+	0.648756i	$0.775290\pi$
$614$	0.613255	+	11.5833i	0.0247490	+	0.467463i
$615$	−1.78060	+	7.16688i	−0.0718006	+	0.288997i
$616$	12.8967	−	10.4778i	0.519624	−	0.422163i
$617$	−25.4273	+	14.6804i	−1.02366	+	0.591013i	−0.915163	−	0.403084i	$-0.867938\pi$
$617$	−25.4273	+	14.6804i	−1.02366	+	0.591013i	−0.108501	+	0.994096i	$0.534605\pi$
$618$	10.7897	−	12.4463i	0.434024	−	0.500663i
$619$	1.13894	−	1.97270i	0.0457778	−	0.0792894i	−0.842229	−	0.539121i	$-0.818757\pi$
$619$	1.13894	−	1.97270i	0.0457778	−	0.0792894i	0.888006	+	0.459831i	$0.152090\pi$
$620$	13.2347	+	5.87554i	0.531518	+	0.235967i
$621$	−6.69491	+	31.8866i	−0.268658	+	1.27957i
$622$	4.18231	−	2.71920i	0.167696	−	0.109030i
$623$	−12.4810	+	21.6178i	−0.500042	+	0.866099i
$624$	−9.91361	−	6.15392i	−0.396862	−	0.246354i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−4.77440	−	2.42947i	−0.190823	−	0.0971011i
$627$	8.43745	−	33.9606i	0.336959	−	1.35626i
$628$	20.7052	−	15.0770i	0.826227	−	0.601638i
$629$	9.91882			0.395489
$630$	7.56675	−	5.32305i	0.301467	−	0.212075i
$631$			44.7364i			1.78093i	0.455053	+	0.890464i	$0.349620\pi$
$631$			44.7364i			1.78093i	−0.455053	+	0.890464i	$0.650380\pi$
$632$	−11.3731	+	29.7702i	−0.452396	+	1.18420i
$633$	−31.8359	+	33.0218i	−1.26536	+	1.31250i
$634$	5.33118	+	2.71279i	0.211728	+	0.107739i
$635$	5.64734	−	3.26049i	0.224108	−	0.129389i
$636$	−0.700774	−	1.72505i	−0.0277875	−	0.0684027i
$637$	−3.27438	−	1.89047i	−0.129736	−	0.0749030i
$638$	−7.52164	−	11.5688i	−0.297784	−	0.458012i
$639$	8.20990	−	5.14906i	0.324779	−	0.203693i
$640$	7.08704	−	8.81895i	0.280140	−	0.348600i
$641$	−39.0229	−	22.5299i	−1.54131	−	0.889877i	−0.998756	−	0.0498579i	$-0.984123\pi$
$641$	−39.0229	−	22.5299i	−1.54131	−	0.889877i	−0.542556	−	0.840019i	$-0.682543\pi$
$642$	−6.98335	−	20.1917i	−0.275611	−	0.796903i
$643$	14.6383	+	25.3544i	0.577280	+	0.999878i	0.995790	+	0.0916659i	$0.0292192\pi$
$643$	14.6383	+	25.3544i	0.577280	+	0.999878i	−0.418510	+	0.908212i	$0.637447\pi$
$644$	−2.88752	−	27.1936i	−0.113784	−	1.07158i
$645$	−5.53951	−	19.2583i	−0.218118	−	0.758296i
$646$	−13.3810	+	0.708435i	−0.526470	+	0.0278730i
$647$	−25.0609			−0.985247			−0.492623	−	0.870243i	$-0.663962\pi$
$647$	−25.0609			−0.985247			−0.492623	+	0.870243i	$0.663962\pi$
$648$	−24.3798	−	7.32280i	−0.957731	−	0.287667i
$649$	−13.9413			−0.547242
$650$	−2.37846	+	0.125923i	−0.0932909	+	0.00493912i
$651$	7.55920	+	26.2799i	0.296269	+	1.02999i
$652$	−41.9709	+	4.45664i	−1.64371	+	0.174535i
$653$	−19.8556	−	34.3910i	−0.777011	−	1.34582i	−0.933657	−	0.358167i	$-0.883402\pi$
$653$	−19.8556	−	34.3910i	−0.777011	−	1.34582i	0.156647	−	0.987655i	$-0.449932\pi$
$654$	−5.19773	−	15.0288i	−0.203247	−	0.587671i
$655$	−16.8066	−	9.70332i	−0.656690	−	0.379140i
$656$	−12.6495	+	11.4387i	−0.493879	+	0.446604i
$657$	−4.82139	+	3.02386i	−0.188100	+	0.117972i
$658$	11.2045	+	17.2333i	0.436797	+	0.671822i
$659$	31.6828	+	18.2921i	1.23419	+	0.712557i	0.967900	−	0.251337i	$-0.0808702\pi$
$659$	31.6828	+	18.2921i	1.23419	+	0.712557i	0.266286	+	0.963894i	$0.414204\pi$
$660$	−8.64655	+	3.51252i	−0.336566	+	0.136725i
$661$	16.9843	−	9.80587i	0.660611	−	0.381404i	−0.131899	−	0.991263i	$-0.542107\pi$
$661$	16.9843	−	9.80587i	0.660611	−	0.381404i	0.792510	+	0.609859i	$0.208774\pi$
$662$	−31.0165	−	15.7828i	−1.20549	−	0.613418i
$663$	2.55817	−	2.65346i	0.0993510	−	0.103052i
$664$	−0.891021	+	2.33235i	−0.0345783	+	0.0905127i
$665$			16.3523i			0.634114i
$666$	−27.2403	+	19.1629i	−1.05554	+	0.742549i
$667$	−22.7094			−0.879313
$668$	12.6933	+	17.4316i	0.491118	+	0.674451i
$669$	10.2634	−	41.3102i	0.396807	−	1.59714i
$670$	−11.1634	−	5.68053i	−0.431279	−	0.219458i
$671$	−14.2047	−	24.6033i	−0.548367	−	0.949799i
$672$	21.3608	−	0.447606i	0.824010	−	0.0172668i
$673$	8.86138	−	15.3484i	0.341581	−	0.591636i	−0.643145	−	0.765744i	$-0.722371\pi$
$673$	8.86138	−	15.3484i	0.341581	−	0.591636i	0.984727	+	0.174108i	$0.0557042\pi$
$674$	−22.0809	+	14.3563i	−0.850524	+	0.552982i
$675$	−4.93783	+	1.61798i	−0.190057	+	0.0622761i
$676$	8.24793	−	18.5785i	0.317228	−	0.714558i
$677$	12.8826	−	22.3134i	0.495120	−	0.857574i	−0.504864	−	0.863199i	$-0.668457\pi$
$677$	12.8826	−	22.3134i	0.495120	−	0.857574i	0.999984	+	0.00562533i	$0.00179061\pi$
$678$	6.43742	−	7.42582i	0.247228	−	0.285187i
$679$	−15.7128	+	9.07178i	−0.603001	+	0.348143i
$680$	2.25349	+	2.77373i	0.0864174	+	0.106368i
$681$	−5.44542	+	21.9177i	−0.208669	+	0.839889i
$682$	−1.45843	−	27.5470i	−0.0558460	−	1.05483i
$683$		−	2.71884i		−	0.104034i	−0.998646	−	0.0520168i	$-0.983435\pi$
$683$		−	2.71884i		−	0.104034i	0.998646	−	0.0520168i	$-0.0165649\pi$
$684$	35.3800	−	27.7975i	1.35279	−	1.06286i
$685$		−	15.1406i		−	0.578491i
$686$	28.4701	−	1.50730i	1.08699	−	0.0575489i
$687$	4.04085	+	3.89574i	0.154168	+	0.148632i
$688$	14.2068	−	44.0439i	0.541630	−	1.67916i
$689$	−0.783968	+	0.452624i	−0.0298668	+	0.0172436i
$690$	−2.91014	+	15.0810i	−0.110787	+	0.574125i
$691$	−5.22034	+	9.04189i	−0.198591	+	0.343970i	−0.948072	−	0.318056i	$-0.896970\pi$
$691$	−5.22034	+	9.04189i	−0.198591	+	0.343970i	0.749481	+	0.662026i	$0.230303\pi$
$692$	2.91965	−	6.57653i	0.110988	−	0.250002i
$693$	−15.5752	−	8.24842i	−0.591654	−	0.313332i
$694$	2.51898	+	3.87436i	0.0956192	+	0.147069i
$695$	−4.24729	+	7.35652i	−0.161109	+	0.279049i
$696$	1.50341	−	17.6788i	0.0569866	−	0.670113i
$697$	−2.69356	−	4.66539i	−0.102026	−	0.176714i
$698$	13.2915	−	26.1204i	0.503089	−	0.988673i
$699$	21.2044	−	6.09927i	0.802023	−	0.230696i
$700$	3.52555	−	2.56722i	0.133253	−	0.0970318i
$701$	36.1705			1.36614			0.683070	−	0.730353i	$-0.260644\pi$
$701$	36.1705			1.36614			0.683070	+	0.730353i	$0.260644\pi$
$702$	−1.89913	+	12.2296i	−0.0716782	+	0.461575i
$703$		−	58.8681i		−	2.22025i
$704$	−21.0964	−	4.41358i	−0.795099	−	0.166343i
$705$	−3.19144	−	11.0952i	−0.120197	−	0.417868i
$706$	2.55242	−	5.01602i	0.0960614	−	0.188780i
$707$	18.9038	−	10.9141i	0.710949	−	0.410467i
$708$	−14.1464	−	11.0093i	−0.531655	−	0.413753i
$709$	7.25864	+	4.19078i	0.272604	+	0.157388i	0.630070	−	0.776538i	$-0.283026\pi$
$709$	7.25864	+	4.19078i	0.272604	+	0.157388i	−0.357467	+	0.933926i	$0.616359\pi$
$710$	3.83003	−	2.49016i	0.143739	−	0.0934541i
$711$	33.7793	−	1.23565i	1.26682	−	0.0463405i
$712$	31.9712	−	5.11624i	1.19817	−	0.191739i
$713$	−39.3163	−	22.6993i	−1.47241	−	0.850095i
$714$	−1.27873	+	6.62666i	−0.0478551	+	0.247997i
$715$	2.26871	+	3.92952i	0.0848449	+	0.146956i
$716$	0.859252	+	8.09210i	0.0321117	+	0.302416i
$717$	−15.1274	+	15.6909i	−0.564944	+	0.585988i
$718$	2.09446	+	39.5606i	0.0781646	+	1.47639i
$719$	16.3120			0.608334			0.304167	−	0.952619i	$-0.401622\pi$
$719$	16.3120			0.608334			0.304167	+	0.952619i	$0.401622\pi$
$720$	−11.5476	−	3.26387i	−0.430354	−	0.121637i
$721$	14.6638			0.546110
$722$	2.78396	+	52.5839i	0.103608	+	1.95697i
$723$	16.5630	+	4.11505i	0.615985	+	0.153040i
$724$	4.02612	+	37.9165i	0.149630	+	1.40916i
$725$	−1.81085	−	3.13648i	−0.0672532	−	0.116486i
$726$	−6.92514	−	6.00339i	−0.257016	−	0.222807i
$727$	29.0047	+	16.7459i	1.07573	+	0.621071i	0.929740	−	0.368216i	$-0.120031\pi$
$727$	29.0047	+	16.7459i	1.07573	+	0.621071i	0.145986	+	0.989287i	$0.453364\pi$
$728$	−1.64139	−	10.2570i	−0.0608340	−	0.380149i
$729$	2.95574	+	26.8377i	0.109472	+	0.993990i
$730$	−2.24925	+	1.46239i	−0.0832484	+	0.0541253i
$731$	12.6599	+	7.30922i	0.468245	+	0.270341i
$732$	5.01519	−	36.1827i	0.185367	−	1.33735i
$733$	17.5157	−	10.1127i	0.646958	−	0.373522i	−0.140332	−	0.990105i	$-0.544817\pi$
$733$	17.5157	−	10.1127i	0.646958	−	0.373522i	0.787290	+	0.616583i	$0.211484\pi$
$734$	11.9047	−	23.3952i	0.439412	−	0.863534i
$735$	−3.77367	−	0.937562i	−0.139194	−	0.0345825i
$736$	−25.0145	+	25.1484i	−0.922047	+	0.926983i
$737$			23.8617i			0.878958i
$738$	16.4108	+	7.60876i	0.604091	+	0.280082i
$739$	−34.1590			−1.25656			−0.628280	−	0.777988i	$-0.716241\pi$
$739$	−34.1590			−1.25656			−0.628280	+	0.777988i	$0.716241\pi$
$740$	−12.6920	+	9.24198i	−0.466566	+	0.339742i
$741$	−15.7482	−	15.1827i	−0.578526	−	0.557751i
$742$	0.751730	−	1.47730i	0.0275969	−	0.0542335i
$743$	0.546838	+	0.947152i	0.0200616	+	0.0347476i	0.875882	−	0.482526i	$-0.160280\pi$
$743$	0.546838	+	0.947152i	0.0200616	+	0.0347476i	−0.855820	+	0.517273i	$0.826947\pi$
$744$	20.2737	−	29.1041i	0.743270	−	1.06701i
$745$	−9.94067	+	17.2177i	−0.364198	+	0.630809i
$746$	−5.84256	−	8.98625i	−0.213911	−	0.329010i
$747$	2.64644	−	0.0968070i	0.0968280	−	0.00354198i
$748$	2.76249	−	6.22254i	0.101007	−	0.227519i
$749$	9.50995	−	16.4717i	0.347486	−	0.601864i
$750$	−2.31495	+	0.800631i	−0.0845300	+	0.0292349i
$751$	−1.78017	+	1.02778i	−0.0649593	+	0.0375043i	−0.532128	−	0.846664i	$-0.678607\pi$
$751$	−1.78017	+	1.02778i	−0.0649593	+	0.0375043i	0.467169	+	0.884168i	$0.345274\pi$
$752$	8.18488	−	25.3747i	0.298472	−	0.925321i
$753$	−38.0013	+	10.9308i	−1.38484	+	0.398339i
$754$	−8.61406	+	0.456056i	−0.313706	+	0.0166086i
$755$			20.5100i			0.746436i
$756$	−9.29077	−	20.6694i	−0.337902	−	0.751740i
$757$			41.2969i			1.50096i	0.660892	+	0.750481i	$0.270178\pi$
$757$			41.2969i			1.50096i	−0.660892	+	0.750481i	$0.729822\pi$
$758$	−0.842596	−	15.9151i	−0.0306045	−	0.578063i
$759$	28.1199	−	8.08846i	1.02069	−	0.293593i
$760$	16.4621	−	13.3745i	0.597143	−	0.485142i
$761$	−1.05524	+	0.609244i	−0.0382525	+	0.0220851i	−0.519004	−	0.854772i	$-0.673697\pi$
$761$	−1.05524	+	0.609244i	−0.0382525	+	0.0220851i	0.480752	+	0.876857i	$0.340364\pi$
$762$	−5.22090	−	15.0958i	−0.189133	−	0.546861i
$763$	7.07829	−	12.2600i	0.256251	−	0.443840i
$764$	−8.12519	+	18.3020i	−0.293959	+	0.662145i
$765$	1.77401	−	3.34980i	0.0641394	−	0.121112i
$766$	37.9152	−	24.6512i	1.36993	−	0.890684i
$767$	−4.35753	+	7.54747i	−0.157341	+	0.272523i
$768$	−17.9215	−	21.1381i	−0.646686	−	0.762756i
$769$	22.2813	+	38.5924i	0.803485	+	1.39168i	0.917309	+	0.398176i	$0.130357\pi$
$769$	22.2813	+	38.5924i	0.803485	+	1.39168i	−0.113824	+	0.993501i	$0.536310\pi$
$770$	−7.40475	−	3.76793i	−0.266849	−	0.135787i
$771$	−11.9673	−	11.5376i	−0.430993	−	0.415515i
$772$	7.62525	+	10.4717i	0.274439	+	0.376886i
$773$	−51.6358			−1.85721			−0.928606	−	0.371068i	$-0.878992\pi$
$773$	−51.6358			−1.85721			−0.928606	+	0.371068i	$0.878992\pi$
$774$	−48.8895	+	4.38524i	−1.75730	+	0.157624i
$775$		−	7.24015i		−	0.260074i
$776$	21.9841	+	8.39853i	0.789183	+	0.301490i
$777$	−28.7746	−	7.14900i	−1.03228	−	0.256469i
$778$	−28.5023	−	14.5035i	−1.02186	−	0.519974i
$779$	−27.6891	+	15.9863i	−0.992064	+	0.572768i
$780$	−0.801002	+	5.77893i	−0.0286805	+	0.206919i
$781$	−7.53698	−	4.35148i	−0.269694	−	0.155708i
$782$	−6.10740	−	9.39359i	−0.218400	−	0.335914i
$783$	−17.8833	+	5.85983i	−0.639097	+	0.209413i
$784$	−6.02294	−	6.66050i	−0.215105	−	0.237875i
$785$	−11.0907	−	6.40323i	−0.395845	−	0.228541i
$786$	−31.1377	+	35.9186i	−1.11065	+	1.28117i
$787$	−2.65188	−	4.59319i	−0.0945294	−	0.163730i	0.814883	−	0.579626i	$-0.196801\pi$
$787$	−2.65188	−	4.59319i	−0.0945294	−	0.163730i	−0.909412	+	0.415896i	$0.863468\pi$
$788$	42.1943	−	4.48035i	1.50311	−	0.159606i
$789$	−9.15411	−	2.27432i	−0.325895	−	0.0809680i
$790$	15.9121	−	0.842435i	0.566126	−	0.0299725i
$791$	8.74887			0.311074
$792$	4.43510	+	22.4262i	0.157595	+	0.796879i
$793$	−17.7595			−0.630659
$794$	6.49954	−	0.344106i	0.230660	−	0.0122119i
$795$	−0.646156	+	0.670225i	−0.0229168	+	0.0237704i
$796$	−1.80819	−	17.0288i	−0.0640896	−	0.603571i
$797$	−4.76269	−	8.24922i	−0.168703	−	0.292202i	0.769261	−	0.638935i	$-0.220625\pi$
$797$	−4.76269	−	8.24922i	−0.168703	−	0.292202i	−0.937964	+	0.346732i	$0.887291\pi$
$798$	39.3292	+	7.58922i	1.39224	+	0.268656i
$799$	7.29368	+	4.21101i	0.258032	+	0.148975i
$800$	−5.46799	−	1.44951i	−0.193323	−	0.0512479i
$801$	−18.2467	−	29.0935i	−0.644716	−	1.02797i
$802$	6.16040	+	9.47510i	0.217531	+	0.334577i
$803$	4.42621	+	2.55547i	0.156198	+	0.0901807i
$804$	−18.8434	+	24.2129i	−0.664554	+	0.853924i
$805$	−11.8414	+	6.83662i	−0.417353	+	0.240959i
$806$	−15.3692	−	7.82065i	−0.541356	−	0.275471i
$807$	0.452786	+	1.57413i	0.0159388	+	0.0554120i
$808$	−26.4487	−	10.1041i	−0.930461	−	0.355462i
$809$			1.79483i			0.0631027i	0.999502	+	0.0315513i	$0.0100448\pi$
$809$			1.79483i			0.0631027i	−0.999502	+	0.0315513i	$0.989955\pi$
$810$	1.59975	+	12.6270i	0.0562095	+	0.443667i
$811$	22.9076			0.804395			0.402197	−	0.915553i	$-0.368247\pi$
$811$	22.9076			0.804395			0.402197	+	0.915553i	$0.368247\pi$
$812$	12.7685	−	9.29769i	0.448086	−	0.326285i
$813$	23.2063	−	6.67511i	0.813880	−	0.234106i
$814$	26.6571	+	13.5645i	0.934330	+	0.475437i
$815$	10.5517	+	18.2761i	0.369610	+	0.640184i
$816$	7.71703	−	4.13260i	0.270150	−	0.144670i
$817$	43.3801	−	75.1366i	1.51768	−	2.62870i
$818$	31.9960	−	20.8027i	1.11871	−	0.727351i
$819$	−9.33376	+	5.85391i	−0.326148	+	0.204552i
$820$	7.79368	+	3.46000i	0.272167	+	0.120828i
$821$	−23.4828	+	40.6733i	−0.819554	+	1.41951i	0.0864575	+	0.996256i	$0.472445\pi$
$821$	−23.4828	+	40.6733i	−0.819554	+	1.41951i	−0.906011	+	0.423253i	$0.860888\pi$
$822$	−36.4149	−	7.02685i	−1.27011	−	0.245090i
$823$	19.4949	−	11.2554i	0.679550	−	0.392338i	−0.120136	−	0.992757i	$-0.538333\pi$
$823$	19.4949	−	11.2554i	0.679550	−	0.392338i	0.799685	+	0.600419i	$0.205000\pi$
$824$	−11.9935	−	14.7623i	−0.417813	−	0.514269i
$825$	3.35940	+	3.23876i	0.116959	+	0.112759i
$826$	−0.843676	−	15.9355i	−0.0293553	−	0.554467i
$827$			45.2544i			1.57365i	0.617175	+	0.786826i	$0.288277\pi$
$827$			45.2544i			1.57365i	−0.617175	+	0.786826i	$0.711723\pi$
$828$	34.9211	+	13.9985i	1.21359	+	0.486480i
$829$		−	55.5430i		−	1.92909i	−0.263923	−	0.964544i	$-0.585017\pi$
$829$		−	55.5430i		−	1.92909i	0.263923	−	0.964544i	$-0.414983\pi$
$830$	1.24663	−	0.0660006i	0.0432712	−	0.00229091i
$831$	5.23506	−	21.0710i	0.181602	−	0.730947i
$832$	−8.98337	+	10.0416i	−0.311442	+	0.348128i
$833$	2.45653	−	1.41828i	0.0851137	−	0.0491404i
$834$	15.7221	+	13.6295i	0.544412	+	0.471949i
$835$	5.39086	−	9.33724i	0.186558	−	0.323129i
$836$	−36.9307	−	16.3954i	−1.27728	−	0.567046i
$837$	−36.8181	−	7.73033i	−1.27262	−	0.267199i
$838$	19.6382	+	30.2049i	0.678392	+	1.04341i
$839$	−19.6977	+	34.1174i	−0.680041	+	1.17786i	0.294927	+	0.955520i	$0.404705\pi$
$839$	−19.6977	+	34.1174i	−0.680041	+	1.17786i	−0.974968	+	0.222345i	$0.928629\pi$
$840$	−4.53824	−	9.67084i	−0.156584	−	0.333676i
$841$	7.94166	+	13.7554i	0.273850	+	0.474323i
$842$	0.169360	−	0.332826i	0.00583651	−	0.0114699i
$843$	8.92186	−	35.9104i	0.307285	−	1.23682i
$844$	31.1778	+	42.8163i	1.07318	+	1.47380i
$845$	−10.1635			−0.349636
$846$	−28.1664	+	2.52644i	−0.968380	+	0.0868608i
$847$		−	8.15899i		−	0.280346i
$848$	−2.10206	+	0.451501i	−0.0721850	+	0.0155046i
$849$	−18.7444	+	19.4426i	−0.643306	+	0.667268i
$850$	0.810378	−	1.59256i	0.0277957	−	0.0546243i
$851$	42.6289	−	24.6118i	1.46130	−	0.843681i
$852$	−4.21159	−	10.3674i	−0.144287	−	0.355181i
$853$	26.0648	+	15.0485i	0.892442	+	0.515252i	0.874741	−	0.484592i	$-0.161032\pi$
$853$	26.0648	+	15.0485i	0.892442	+	0.515252i	0.0177016	+	0.999843i	$0.494365\pi$
$854$	27.2631	−	17.7256i	0.932924	−	0.606556i
$855$	−19.8811	−	10.5287i	−0.679918	−	0.360075i
$856$	−24.3605	+	3.89833i	−0.832624	+	0.133242i
$857$	−4.11389	−	2.37516i	−0.140528	−	0.0811338i	0.428088	−	0.903737i	$-0.359187\pi$
$857$	−4.11389	−	2.37516i	−0.140528	−	0.0811338i	−0.568616	+	0.822603i	$0.692521\pi$
$858$	10.5039	−	3.63280i	0.358597	−	0.124022i
$859$	21.8732	+	37.8854i	0.746303	+	1.29263i	0.949584	+	0.313514i	$0.101506\pi$
$859$	21.8732	+	37.8854i	0.746303	+	1.29263i	−0.203281	+	0.979121i	$0.565160\pi$
$860$	−23.0099	+	2.44328i	−0.784631	+	0.0833153i
$861$	4.45148	+	15.4757i	0.151706	+	0.527412i
$862$	−1.75605	−	33.1687i	−0.0598114	−	1.12973i
$863$	2.88754			0.0982929			0.0491464	−	0.998792i	$-0.484350\pi$
$863$	2.88754			0.0982929			0.0491464	+	0.998792i	$0.484350\pi$
$864$	−13.2093	+	26.2586i	−0.449391	+	0.893335i
$865$	−3.59774			−0.122327
$866$	−2.03617	−	38.4595i	−0.0691918	−	1.30691i
$867$	−7.37517	−	25.6401i	−0.250474	−	0.870782i
$868$	31.3993	−	3.33410i	1.06576	−	0.113167i
$869$	−15.1778	−	26.2887i	−0.514872	−	0.891785i
$870$	−8.38404	+	2.89964i	−0.284246	+	0.0983070i
$871$	12.9182	+	7.45832i	0.437716	+	0.252715i
$872$	−18.1316	+	2.90154i	−0.614013	+	0.0982585i
$873$	−0.912477	−	24.9446i	−0.0308827	−	0.844247i
$874$	−55.7509	+	36.2474i	−1.88580	+	1.22609i
$875$	−1.88846	−	1.09030i	−0.0638415	−	0.0368589i
$876$	2.47332	+	6.08841i	0.0835658	+	0.205708i
$877$	18.5515	−	10.7107i	0.626440	−	0.361675i	−0.152932	−	0.988237i	$-0.548872\pi$
$877$	18.5515	−	10.7107i	0.626440	−	0.361675i	0.779372	+	0.626561i	$0.215538\pi$
$878$	4.76512	−	9.36443i	0.160815	−	0.316034i
$879$	−38.6008	+	40.0386i	−1.30197	+	1.35047i
$880$	2.26308	+	10.5362i	0.0762884	+	0.355177i
$881$			30.8096i			1.03800i	0.854774	+	0.519001i	$0.173696\pi$
$881$			30.8096i			1.03800i	−0.854774	+	0.519001i	$0.826304\pi$
$882$	−4.00634	+	8.64101i	−0.134901	+	0.290958i
$883$	5.84845			0.196816			0.0984080	−	0.995146i	$-0.468625\pi$
$883$	5.84845			0.196816			0.0984080	+	0.995146i	$0.468625\pi$
$884$	−2.50528	−	3.44049i	−0.0842617	−	0.115716i
$885$	−2.16108	+	8.69834i	−0.0726441	+	0.292391i
$886$	−2.04649	+	4.02176i	−0.0687531	+	0.135114i
$887$	11.4920	+	19.9047i	0.385864	+	0.668336i	0.991889	−	0.127110i	$-0.0405701\pi$
$887$	11.4920	+	19.9047i	0.385864	+	0.668336i	−0.606025	+	0.795446i	$0.707237\pi$
$888$	16.3376	+	34.8150i	0.548255	+	1.16831i
$889$	7.10984	−	12.3146i	0.238456	−	0.413019i
$890$	−8.82439	−	13.5725i	−0.295794	−	0.454951i
$891$	20.0568	−	13.6254i	0.671929	−	0.456469i
$892$	−44.9230	−	19.9436i	−1.50413	−	0.667760i
$893$	24.9923	−	43.2879i	0.836336	−	1.44858i
$894$	36.7972	+	31.8994i	1.23068	+	1.06688i
$895$	3.52368	−	2.03440i	0.117784	−	0.0680024i
$896$	3.76825	−	24.3812i	0.125889	−	0.814520i
$897$	4.41035	−	17.7516i	0.147257	−	0.592709i
$898$	19.2202	−	1.01758i	0.641388	−	0.0339571i
$899$		−	26.2216i		−	0.874540i
$900$	0.851227	+	5.93931i	0.0283742	+	0.197977i
$901$		−	0.679141i		−	0.0226255i
$902$	−0.858842	−	16.2220i	−0.0285963	−	0.540132i
$903$	−31.4585	−	30.3288i	−1.04687	−	1.00928i
$904$	−7.15566	−	8.80762i	−0.237994	−	0.292937i
$905$	16.5106	−	9.53241i	0.548832	−	0.316868i
$906$	49.3291	+	9.51887i	1.63885	+	0.316243i
$907$	6.44710	−	11.1667i	0.214072	−	0.370784i	−0.738913	−	0.673801i	$-0.764660\pi$
$907$	6.44710	−	11.1667i	0.214072	−	0.370784i	0.952985	+	0.303017i	$0.0979938\pi$
$908$	23.8346	+	10.5814i	0.790978	+	0.351155i
$909$	1.09778	+	30.0104i	0.0364112	+	0.995382i
$910$	−4.35433	+	2.83104i	−0.144345	+	0.0938481i
$911$	−2.81659	+	4.87848i	−0.0933179	+	0.161631i	−0.908905	−	0.417003i	$-0.863081\pi$
$911$	−2.81659	+	4.87848i	−0.0933179	+	0.161631i	0.815587	+	0.578634i	$0.196414\pi$
$912$	−24.5270	−	45.8005i	−0.812169	−	1.51661i
$913$	−1.18911	−	2.05959i	−0.0393536	−	0.0681625i
$914$	−10.7255	−	5.45769i	−0.354767	−	0.180524i
$915$	−17.5526	+	5.04887i	−0.580271	+	0.166911i
$916$	5.23939	−	3.81520i	0.173114	−	0.126058i
$917$	−42.3182			−1.39747
$918$	−7.23335	−	5.82137i	−0.238736	−	0.192134i
$919$			4.44179i			0.146521i	0.997313	+	0.0732606i	$0.0233405\pi$
$919$			4.44179i			0.146521i	−0.997313	+	0.0732606i	$0.976660\pi$
$920$	16.5675	+	6.32925i	0.546215	+	0.208669i
$921$	−3.92714	−	13.6528i	−0.129404	−	0.449876i
$922$	31.5340	+	16.0462i	1.03852	+	0.528453i
$923$	−4.71158	+	2.72023i	−0.155083	+	0.0895375i
$924$	−12.4989	+	16.0606i	−0.411185	+	0.528355i
$925$	6.79844	+	3.92508i	0.223531	+	0.129056i
$926$	5.31556	+	8.17569i	0.174680	+	0.268670i
$927$	−9.44158	+	17.8283i	−0.310102	+	0.585557i
$928$	−19.8034	−	5.24968i	−0.650078	−	0.172329i
$929$	−30.1957	−	17.4335i	−0.990688	−	0.571974i	−0.0852080	−	0.996363i	$-0.527155\pi$
$929$	−30.1957	−	17.4335i	−0.990688	−	0.571974i	−0.905480	+	0.424389i	$0.860489\pi$
$930$	−17.4134	−	3.36021i	−0.571009	−	0.110186i
$931$	−8.41747	−	14.5795i	−0.275871	−	0.477823i
$932$	−2.69018	−	25.3350i	−0.0881197	−	0.829877i
$933$	−4.24053	+	4.39848i	−0.138829	+	0.144000i
$934$	39.3342	−	2.08248i	1.28705	−	0.0681407i
$935$	−3.40409			−0.111326
$936$	13.5273	+	4.60855i	0.442152	+	0.150635i
$937$	34.8699			1.13915			0.569574	−	0.821940i	$-0.307108\pi$
$937$	34.8699			1.13915			0.569574	+	0.821940i	$0.307108\pi$
$938$	−27.2751	+	1.44403i	−0.890563	+	0.0471492i
$939$	6.36736	+	1.58196i	0.207791	+	0.0516252i
$940$	−13.2565	+	1.40763i	−0.432381	+	0.0459119i
$941$	15.9221	+	27.5780i	0.519047	+	0.899016i	0.999755	+	0.0221350i	$0.00704636\pi$
$941$	15.9221	+	27.5780i	0.519047	+	0.899016i	−0.480708	+	0.876881i	$0.659620\pi$
$942$	−20.5478	+	23.7027i	−0.669484	+	0.772276i
$943$	−23.1527	−	13.3672i	−0.753955	−	0.435296i
$944$	−15.3525	+	13.8829i	−0.499681	+	0.451850i
$945$	−7.56080	+	8.43921i	−0.245953	+	0.274527i
$946$	24.0281	+	36.9569i	0.781222	+	1.20157i
$947$	28.9826	+	16.7331i	0.941807	+	0.543753i	0.890526	−	0.454932i	$-0.150336\pi$
$947$	28.9826	+	16.7331i	0.941807	+	0.543753i	0.0512809	+	0.998684i	$0.483670\pi$
$948$	5.35876	−	38.6614i	0.174044	−	1.25566i
$949$	2.76695	−	1.59750i	0.0898189	−	0.0518570i
$950$	−9.45182	−	4.80959i	−0.306658	−	0.156044i
$951$	−7.10990	−	1.76644i	−0.230554	−	0.0572808i
$952$	7.27983	+	2.78109i	0.235941	+	0.0901358i
$953$		−	50.9115i		−	1.64919i	−0.565726	−	0.824593i	$-0.691404\pi$
$953$		−	50.9115i		−	1.64919i	0.565726	−	0.824593i	$-0.308596\pi$
$954$	1.31209	+	1.86514i	0.0424803	+	0.0603862i
$955$	10.0123			0.323990
$956$	14.8147	+	20.3450i	0.479141	+	0.658003i
$957$	12.1667	+	11.7298i	0.393294	+	0.379171i
$958$	−36.6209	−	18.6347i	−1.18317	−	0.602059i
$959$	−16.5078	−	28.5923i	−0.533064	−	0.923294i
$960$	−6.02398	+	12.4784i	−0.194423	+	0.402740i
$961$	10.7099	−	18.5501i	0.345480	−	0.598389i
$962$	15.6756	−	10.1917i	0.505400	−	0.328595i
$963$	13.9031	+	22.1678i	0.448022	+	0.714348i
$964$	7.99623	−	18.0116i	0.257541	−	0.580113i
$965$	3.23846	−	5.60917i	0.104250	−	0.180566i
$966$	10.9472	+	31.6528i	0.352221	+	1.01841i
$967$	18.2319	−	10.5262i	0.586298	−	0.338499i	−0.177334	−	0.984151i	$-0.556747\pi$
$967$	18.2319	−	10.5262i	0.586298	−	0.338499i	0.763632	+	0.645651i	$0.223414\pi$
$968$	−8.21378	+	6.67320i	−0.264001	+	0.214485i
$969$	15.7718	−	4.53664i	0.506664	−	0.145738i
$970$	−0.622104	−	11.7504i	−0.0199745	−	0.377283i
$971$			12.5056i			0.401325i	0.979660	+	0.200662i	$0.0643094\pi$
$971$			12.5056i			0.401325i	−0.979660	+	0.200662i	$0.935691\pi$
$972$	31.1119	+	2.01270i	0.997914	+	0.0645572i
$973$			18.5233i			0.593830i
$974$	−25.6878	+	1.36000i	−0.823092	+	0.0435771i
$975$	2.80342	−	0.806381i	0.0897812	−	0.0258249i
$976$	−40.1429	−	12.9485i	−1.28494	−	0.414472i
$977$	30.7013	−	17.7254i	0.982221	−	0.567085i	0.0792809	−	0.996852i	$-0.474738\pi$
$977$	30.7013	−	17.7254i	0.982221	−	0.567085i	0.902940	+	0.429767i	$0.141404\pi$
$978$	48.8533	−	16.8960i	1.56216	−	0.540276i
$979$	−15.4203	+	26.7088i	−0.492836	+	0.853617i
$980$	−1.82184	+	4.10371i	−0.0581965	+	0.131088i
$981$	10.3481	+	16.4996i	0.330391	+	0.526791i
$982$	−1.73309	−	2.66560i	−0.0553050	−	0.0850627i
$983$	−5.87250	+	10.1715i	−0.187304	+	0.324420i	−0.944350	−	0.328941i	$-0.893308\pi$
$983$	−5.87250	+	10.1715i	−0.187304	+	0.324420i	0.757047	+	0.653361i	$0.226642\pi$
$984$	11.9388	−	17.1389i	0.380596	−	0.546369i
$985$	−10.6079	−	18.3734i	−0.337995	−	0.585424i
$986$	2.93494	−	5.76776i	0.0934676	−	0.183683i
$987$	−18.1240	−	17.4731i	−0.576893	−	0.556176i
$988$	−20.4193	+	14.8688i	−0.649624	+	0.473040i
$989$	72.5461			2.30683
$990$	9.34873	−	6.57663i	0.297122	−	0.209019i
$991$		−	8.64694i		−	0.274679i	−0.990524	−	0.137340i	$-0.956145\pi$
$991$		−	8.64694i		−	0.274679i	0.990524	−	0.137340i	$-0.0438551\pi$
$992$	−29.0378	−	28.8832i	−0.921951	−	0.917042i
$993$	41.3650	+	10.2771i	1.31268	+	0.326133i
$994$	4.51783	−	8.87846i	0.143297	−	0.281608i
$995$	−7.41516	+	4.28114i	−0.235076	+	0.135721i
$996$	0.419832	−	3.02893i	0.0133029	−	0.0959752i
$997$	−2.11722	−	1.22238i	−0.0670530	−	0.0387131i	0.466099	−	0.884733i	$-0.345659\pi$
$997$	−2.11722	−	1.22238i	−0.0670530	−	0.0387131i	−0.533152	+	0.846020i	$0.678992\pi$
$998$	0.170098	−	0.110592i	0.00538437	−	0.00350074i
$999$	27.2188	−	30.3811i	0.861165	−	0.961216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.b.11.14	yes	48
3.2	odd	2		1080.2.bm.a.251.11		48
4.3	odd	2		1440.2.cc.b.911.15		48
8.3	odd	2		360.2.bm.a.11.21	✓	48
8.5	even	2		1440.2.cc.a.911.15		48
9.4	even	3		1080.2.bm.b.611.4		48
9.5	odd	6		360.2.bm.a.131.21	yes	48
12.11	even	2		4320.2.cc.a.1871.7		48
24.5	odd	2		4320.2.cc.b.1871.18		48
24.11	even	2		1080.2.bm.b.251.4		48
36.23	even	6		1440.2.cc.a.1391.15		48
36.31	odd	6		4320.2.cc.b.3311.18		48
72.5	odd	6		1440.2.cc.b.1391.15		48
72.13	even	6		4320.2.cc.a.3311.7		48
72.59	even	6	inner	360.2.bm.b.131.14	yes	48
72.67	odd	6		1080.2.bm.a.611.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.21	✓	48	8.3	odd	2
360.2.bm.a.131.21	yes	48	9.5	odd	6
360.2.bm.b.11.14	yes	48	1.1	even	1	trivial
360.2.bm.b.131.14	yes	48	72.59	even	6	inner
1080.2.bm.a.251.11		48	3.2	odd	2
1080.2.bm.a.611.11		48	72.67	odd	6
1080.2.bm.b.251.4		48	24.11	even	2
1080.2.bm.b.611.4		48	9.4	even	3
1440.2.cc.a.911.15		48	8.5	even	2
1440.2.cc.a.1391.15		48	36.23	even	6
1440.2.cc.b.911.15		48	4.3	odd	2
1440.2.cc.b.1391.15		48	72.5	odd	6
4320.2.cc.a.1871.7		48	12.11	even	2
4320.2.cc.a.3311.7		48	72.13	even	6
4320.2.cc.b.1871.18		48	24.5	odd	2
4320.2.cc.b.3311.18		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)

\(f(q)\)	\(=\)	\(q+(0.0747682 + 1.41224i) q^{2} +(-0.478797 - 1.66456i) q^{3} +(-1.98882 + 0.211181i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.31495 - 0.800631i) q^{6} +(1.88846 + 1.09030i) q^{7} +(-0.446938 - 2.79289i) q^{8} +(-2.54151 + 1.59397i) q^{9} +O(q^{10})\)	\(q+(0.0747682 + 1.41224i) q^{2} +(-0.478797 - 1.66456i) q^{3} +(-1.98882 + 0.211181i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.31495 - 0.800631i) q^{6} +(1.88846 + 1.09030i) q^{7} +(-0.446938 - 2.79289i) q^{8} +(-2.54151 + 1.59397i) q^{9} +(-1.18565 + 0.770869i) q^{10} +(2.33319 + 1.34707i) q^{11} +(1.30376 + 3.20939i) q^{12} +(1.45854 - 0.842091i) q^{13} +(-1.39857 + 2.74847i) q^{14} +(1.20215 - 1.24693i) q^{15} +(3.91081 - 0.840001i) q^{16} +1.26352i q^{17} +(-2.44109 - 3.47003i) q^{18} +7.49897 q^{19} +(-1.17730 - 1.61678i) q^{20} +(0.910682 - 3.66548i) q^{21} +(-1.72793 + 3.39574i) q^{22} +(3.13519 + 5.43032i) q^{23} +(-4.43494 + 2.08118i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.29828 + 1.99685i) q^{26} +(3.87013 + 3.46729i) q^{27} +(-3.98605 - 1.76961i) q^{28} +(-1.81085 + 3.13648i) q^{29} +(1.85084 + 1.60449i) q^{30} +(-6.27015 + 3.62007i) q^{31} +(1.47868 + 5.46017i) q^{32} +(1.12515 - 4.52871i) q^{33} +(-1.78438 + 0.0944710i) q^{34} +2.18060i q^{35} +(4.71798 - 3.70684i) q^{36} -7.85016i q^{37} +(0.560685 + 10.5903i) q^{38} +(-2.10006 - 2.02464i) q^{39} +(2.19525 - 1.78351i) q^{40} +(-3.69238 + 2.13180i) q^{41} +(5.24461 + 1.01204i) q^{42} +(5.78481 - 10.0196i) q^{43} +(-4.92477 - 2.18635i) q^{44} +(-2.65117 - 1.40402i) q^{45} +(-7.43447 + 4.83365i) q^{46} +(3.33277 - 5.77252i) q^{47} +(-3.27071 - 6.10757i) q^{48} +(-1.12248 - 1.94420i) q^{49} +(-1.26042 - 0.641367i) q^{50} +(2.10320 - 0.604969i) q^{51} +(-2.72295 + 1.98278i) q^{52} -0.537500 q^{53} +(-4.60727 + 5.72477i) q^{54} +2.69414i q^{55} +(2.20107 - 5.76156i) q^{56} +(-3.59049 - 12.4825i) q^{57} +(-4.56484 - 2.32283i) q^{58} +(-4.48139 + 2.58733i) q^{59} +(-2.12753 + 2.73379i) q^{60} +(-9.13215 - 5.27245i) q^{61} +(-5.58121 - 8.58427i) q^{62} +(-6.53744 + 0.239141i) q^{63} +(-7.60049 + 2.49650i) q^{64} +(1.45854 + 0.842091i) q^{65} +(6.47973 + 1.25037i) q^{66} +(4.42845 + 7.67031i) q^{67} +(-0.266831 - 2.51291i) q^{68} +(7.53795 - 7.81873i) q^{69} +(-3.07953 + 0.163040i) q^{70} -3.23033 q^{71} +(5.58769 + 6.38575i) q^{72} +1.89706 q^{73} +(11.0863 - 0.586943i) q^{74} +(1.68095 + 0.417628i) q^{75} +(-14.9141 + 1.58364i) q^{76} +(2.93742 + 5.08777i) q^{77} +(2.70225 - 3.11715i) q^{78} +(-9.75776 - 5.63364i) q^{79} +(2.68286 + 2.96686i) q^{80} +(3.91851 - 8.10218i) q^{81} +(-3.28667 - 5.05512i) q^{82} +(-0.764471 - 0.441368i) q^{83} +(-1.03710 + 7.48230i) q^{84} +(-1.09424 + 0.631759i) q^{85} +(14.5825 + 7.42037i) q^{86} +(6.08788 + 1.51252i) q^{87} +(2.71943 - 7.11841i) q^{88} +11.4473i q^{89} +(1.78459 - 3.84906i) q^{90} +3.67253 q^{91} +(-7.38211 - 10.1378i) q^{92} +(9.02796 + 8.70375i) q^{93} +(8.40134 + 4.27505i) q^{94} +(3.74948 + 6.49430i) q^{95} +(8.38079 - 5.07567i) q^{96} +(-4.16021 + 7.20570i) q^{97} +(2.66174 - 1.73058i) q^{98} +(-8.07701 + 0.295458i) 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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