LMFDB - Embedded newform 240.2.s.c.61.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(61,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("240.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.s (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^18 - 4x^17 + 7x^16 + 16x^15 + 6x^14 - 36x^13 - 42x^12 + 40x^11 + 136x^10 + 80x^9 - 168x^8 - 288x^7 + 96x^6 + 512x^5 + 448x^4 - 512x^3 - 512*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.7
Root			$1.15787 + 0.811989i$ of defining polynomial
Character	$\chi$	$=$	240.61
Dual form			240.2.s.c.181.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15787 + 0.811989i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.681349 + 1.88036i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.244579 + 1.39290i) q^{6} -2.18060i q^{7} +(-0.737916 + 2.73047i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(1.15787 + 0.811989i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.681349 + 1.88036i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.244579 + 1.39290i) q^{6} -2.18060i q^{7} +(-0.737916 + 2.73047i) q^{8} +1.00000i q^{9} +(1.39290 - 0.244579i) q^{10} +(-0.00889637 + 0.00889637i) q^{11} +(-0.847831 + 1.81140i) q^{12} +(1.72965 + 1.72965i) q^{13} +(1.77062 - 2.52486i) q^{14} +1.00000 q^{15} +(-3.07153 + 2.56237i) q^{16} -5.54943 q^{17} +(-0.811989 + 1.15787i) q^{18} +(-4.94702 - 4.94702i) q^{19} +(1.81140 + 0.847831i) q^{20} +(1.54192 - 1.54192i) q^{21} +(-0.0175246 + 0.00307713i) q^{22} -3.01309i q^{23} +(-2.45252 + 1.40895i) q^{24} -1.00000i q^{25} +(0.598263 + 3.40718i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.10031 - 1.48575i) q^{28} +(3.20471 + 3.20471i) q^{29} +(1.15787 + 0.811989i) q^{30} +3.58009 q^{31} +(-5.63706 + 0.472855i) q^{32} -0.0125814 q^{33} +(-6.42554 - 4.50607i) q^{34} +(-1.54192 - 1.54192i) q^{35} +(-1.88036 + 0.681349i) q^{36} +(4.97761 - 4.97761i) q^{37} +(-1.71111 - 9.74496i) q^{38} +2.44610i q^{39} +(1.40895 + 2.45252i) q^{40} +3.76487i q^{41} +(3.03736 - 0.533328i) q^{42} +(6.81210 - 6.81210i) q^{43} +(-0.0227899 - 0.0106669i) q^{44} +(0.707107 + 0.707107i) q^{45} +(2.44659 - 3.48878i) q^{46} -10.0800 q^{47} +(-3.98376 - 0.360031i) q^{48} +2.24499 q^{49} +(0.811989 - 1.15787i) q^{50} +(-3.92404 - 3.92404i) q^{51} +(-2.07388 + 4.43087i) q^{52} +(-0.932644 + 0.932644i) q^{53} +(-1.39290 + 0.244579i) q^{54} +0.0125814i q^{55} +(5.95406 + 1.60910i) q^{56} -6.99615i q^{57} +(1.10846 + 6.31283i) q^{58} +(-4.60522 + 4.60522i) q^{59} +(0.681349 + 1.88036i) q^{60} +(4.17149 + 4.17149i) q^{61} +(4.14530 + 2.90700i) q^{62} +2.18060 q^{63} +(-6.91096 - 4.02972i) q^{64} +2.44610 q^{65} +(-0.0145676 - 0.0102159i) q^{66} +(-11.0105 - 11.0105i) q^{67} +(-3.78110 - 10.4349i) q^{68} +(2.13057 - 2.13057i) q^{69} +(-0.533328 - 3.03736i) q^{70} +12.1092i q^{71} +(-2.73047 - 0.737916i) q^{72} +7.12981i q^{73} +(9.80521 - 1.72169i) q^{74} +(0.707107 - 0.707107i) q^{75} +(5.93155 - 12.6729i) q^{76} +(0.0193994 + 0.0193994i) q^{77} +(-1.98620 + 2.83228i) q^{78} -3.41789 q^{79} +(-0.360031 + 3.98376i) q^{80} -1.00000 q^{81} +(-3.05704 + 4.35925i) q^{82} +(5.31631 + 5.31631i) q^{83} +(3.94994 + 1.84878i) q^{84} +(-3.92404 + 3.92404i) q^{85} +(13.4189 - 2.35621i) q^{86} +4.53214i q^{87} +(-0.0177265 - 0.0308561i) q^{88} +5.06405i q^{89} +(0.244579 + 1.39290i) q^{90} +(3.77168 - 3.77168i) q^{91} +(5.66569 - 2.05296i) q^{92} +(2.53151 + 2.53151i) q^{93} +(-11.6714 - 8.18483i) q^{94} -6.99615 q^{95} +(-4.32036 - 3.65164i) q^{96} -10.3646 q^{97} +(2.59942 + 1.82291i) q^{98} +(-0.00889637 - 0.00889637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) $ 20 * q + 4 * q^4 + 12 * q^8	$ 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) $ 20 * q + 4 * q^4 + 12 * q^8 + 8 * q^11 - 4 * q^14 + 20 * q^15 - 20 * q^16 - 24 * q^17 - 4 * q^18 - 4 * q^19 - 8 * q^20 + 8 * q^22 + 28 * q^26 - 8 * q^28 + 16 * q^29 - 40 * q^32 + 16 * q^33 - 44 * q^34 + 16 * q^37 - 8 * q^38 + 12 * q^40 + 12 * q^42 - 8 * q^43 + 24 * q^44 - 12 * q^46 - 16 * q^48 - 52 * q^49 + 4 * q^50 + 4 * q^51 - 56 * q^52 - 16 * q^53 + 64 * q^56 + 72 * q^58 - 16 * q^59 + 4 * q^60 - 4 * q^61 - 44 * q^62 - 8 * q^63 - 56 * q^64 - 32 * q^66 - 8 * q^67 - 32 * q^68 - 4 * q^69 + 20 * q^70 + 4 * q^72 + 60 * q^74 + 28 * q^76 - 40 * q^77 - 28 * q^78 + 56 * q^79 - 16 * q^80 - 20 * q^81 - 24 * q^82 - 48 * q^83 + 24 * q^84 + 4 * q^85 + 64 * q^86 + 40 * q^88 - 8 * q^91 + 88 * q^92 + 16 * q^93 - 20 * q^94 + 56 * q^97 - 48 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.15787	+	0.811989i	0.818741	+	0.574163i
$2$	1.15787	+	0.811989i	0.818741	+	0.574163i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	0.681349	+	1.88036i	0.340674	+	0.940181i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	0.244579	+	1.39290i	0.0998488	+	0.568651i
$7$		−	2.18060i		−	0.824189i	−0.911141	−	0.412094i	$-0.864797\pi$
$7$		−	2.18060i		−	0.824189i	0.911141	−	0.412094i	$-0.135203\pi$
$8$	−0.737916	+	2.73047i	−0.260893	+	0.965368i
$9$			1.00000i			0.333333i
$10$	1.39290	−	0.244579i	0.440475	−	0.0773425i
$11$	−0.00889637	+	0.00889637i	−0.00268236	+	0.00268236i	−0.708447	−	0.705764i	$-0.750604\pi$
$11$	−0.00889637	+	0.00889637i	−0.00268236	+	0.00268236i	0.705764	+	0.708447i	$0.250604\pi$
$12$	−0.847831	+	1.81140i	−0.244748	+	0.522907i
$13$	1.72965	+	1.72965i	0.479719	+	0.479719i	0.905042	−	0.425323i	$-0.139839\pi$
$13$	1.72965	+	1.72965i	0.479719	+	0.479719i	−0.425323	+	0.905042i	$0.639839\pi$
$14$	1.77062	−	2.52486i	0.473218	−	0.674797i
$15$	1.00000			0.258199
$16$	−3.07153	+	2.56237i	−0.767882	+	0.640592i
$17$	−5.54943			−1.34593			−0.672967	−	0.739673i	$-0.734980\pi$
$17$	−5.54943			−1.34593			−0.672967	+	0.739673i	$0.734980\pi$
$18$	−0.811989	+	1.15787i	−0.191388	+	0.272914i
$19$	−4.94702	−	4.94702i	−1.13493	−	1.13493i	−0.989347	−	0.145579i	$-0.953496\pi$
$19$	−4.94702	−	4.94702i	−1.13493	−	1.13493i	−0.145579	−	0.989347i	$-0.546504\pi$
$20$	1.81140	+	0.847831i	0.405042	+	0.189581i
$21$	1.54192	−	1.54192i	0.336474	−	0.336474i
$22$	−0.0175246	+	0.00307713i	−0.00373626	+	0.000656047i
$23$		−	3.01309i		−	0.628272i	−0.949378	−	0.314136i	$-0.898285\pi$
$23$		−	3.01309i		−	0.628272i	0.949378	−	0.314136i	$-0.101715\pi$
$24$	−2.45252	+	1.40895i	−0.500619	+	0.287601i
$25$		−	1.00000i		−	0.200000i
$26$	0.598263	+	3.40718i	0.117329	+	0.668203i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	4.10031	−	1.48575i	0.774887	−	0.280780i
$29$	3.20471	+	3.20471i	0.595099	+	0.595099i	0.939004	−	0.343905i	$-0.111750\pi$
$29$	3.20471	+	3.20471i	0.595099	+	0.595099i	−0.343905	+	0.939004i	$0.611750\pi$
$30$	1.15787	+	0.811989i	0.211398	+	0.148248i
$31$	3.58009			0.643004			0.321502	−	0.946909i	$-0.395812\pi$
$31$	3.58009			0.643004			0.321502	+	0.946909i	$0.395812\pi$
$32$	−5.63706	+	0.472855i	−0.996500	+	0.0835897i
$33$	−0.0125814			−0.00219013
$34$	−6.42554	−	4.50607i	−1.10197	−	0.772785i
$35$	−1.54192	−	1.54192i	−0.260631	−	0.260631i
$36$	−1.88036	+	0.681349i	−0.313394	+	0.113558i
$37$	4.97761	−	4.97761i	0.818314	−	0.818314i	−0.167550	−	0.985864i	$-0.553586\pi$
$37$	4.97761	−	4.97761i	0.818314	−	0.818314i	0.985864	+	0.167550i	$0.0535856\pi$
$38$	−1.71111	−	9.74496i	−0.277578	−	1.58084i
$39$			2.44610i			0.391689i
$40$	1.40895	+	2.45252i	0.222775	+	0.387778i
$41$			3.76487i			0.587975i	0.955809	+	0.293987i	$0.0949823\pi$
$41$			3.76487i			0.587975i	−0.955809	+	0.293987i	$0.905018\pi$
$42$	3.03736	−	0.533328i	0.468675	−	0.0822942i
$43$	6.81210	−	6.81210i	1.03884	−	1.03884i	0.0396204	−	0.999215i	$-0.487385\pi$
$43$	6.81210	−	6.81210i	1.03884	−	1.03884i	0.999215	−	0.0396204i	$-0.0126149\pi$
$44$	−0.0227899	−	0.0106669i	−0.00343571	−	0.00160809i
$45$	0.707107	+	0.707107i	0.105409	+	0.105409i
$46$	2.44659	−	3.48878i	0.360730	−	0.514392i
$47$	−10.0800			−1.47032			−0.735158	−	0.677896i	$-0.762892\pi$
$47$	−10.0800			−1.47032			−0.735158	+	0.677896i	$0.762892\pi$
$48$	−3.98376	−	0.360031i	−0.575007	−	0.0519660i
$49$	2.24499			0.320713
$50$	0.811989	−	1.15787i	0.114833	−	0.163748i
$51$	−3.92404	−	3.92404i	−0.549475	−	0.549475i
$52$	−2.07388	+	4.43087i	−0.287595	+	0.614451i
$53$	−0.932644	+	0.932644i	−0.128108	+	0.128108i	−0.768254	−	0.640145i	$-0.778874\pi$
$53$	−0.932644	+	0.932644i	−0.128108	+	0.128108i	0.640145	+	0.768254i	$0.278874\pi$
$54$	−1.39290	+	0.244579i	−0.189550	+	0.0332829i
$55$			0.0125814i			0.00169647i
$56$	5.95406	+	1.60910i	0.795645	+	0.215025i
$57$		−	6.99615i		−	0.926663i
$58$	1.10846	+	6.31283i	0.145548	+	0.828915i
$59$	−4.60522	+	4.60522i	−0.599548	+	0.599548i	−0.940192	−	0.340644i	$-0.889355\pi$
$59$	−4.60522	+	4.60522i	−0.599548	+	0.599548i	0.340644	+	0.940192i	$0.389355\pi$
$60$	0.681349	+	1.88036i	0.0879618	+	0.242754i
$61$	4.17149	+	4.17149i	0.534105	+	0.534105i	0.921791	−	0.387686i	$-0.126726\pi$
$61$	4.17149	+	4.17149i	0.534105	+	0.534105i	−0.387686	+	0.921791i	$0.626726\pi$
$62$	4.14530	+	2.90700i	0.526454	+	0.369189i
$63$	2.18060			0.274730
$64$	−6.91096	−	4.02972i	−0.863870	−	0.503715i
$65$	2.44610			0.303401
$66$	−0.0145676	−	0.0102159i	−0.00179315	−	0.00125749i
$67$	−11.0105	−	11.0105i	−1.34515	−	1.34515i	−0.890852	−	0.454293i	$-0.849892\pi$
$67$	−11.0105	−	11.0105i	−1.34515	−	1.34515i	−0.454293	−	0.890852i	$-0.650108\pi$
$68$	−3.78110	−	10.4349i	−0.458525	−	1.26542i
$69$	2.13057	−	2.13057i	0.256491	−	0.256491i
$70$	−0.533328	−	3.03736i	−0.0637448	−	0.363034i
$71$			12.1092i			1.43710i	0.695475	+	0.718550i	$0.255194\pi$
$71$			12.1092i			1.43710i	−0.695475	+	0.718550i	$0.744806\pi$
$72$	−2.73047	−	0.737916i	−0.321789	−	0.0869643i
$73$			7.12981i			0.834481i	0.908796	+	0.417240i	$0.137003\pi$
$73$			7.12981i			0.834481i	−0.908796	+	0.417240i	$0.862997\pi$
$74$	9.80521	−	1.72169i	1.13983	−	0.200142i
$75$	0.707107	−	0.707107i	0.0816497	−	0.0816497i
$76$	5.93155	−	12.6729i	0.680396	−	1.45368i
$77$	0.0193994	+	0.0193994i	0.00221077	+	0.00221077i
$78$	−1.98620	+	2.83228i	−0.224893	+	0.320692i
$79$	−3.41789			−0.384543			−0.192272	−	0.981342i	$-0.561585\pi$
$79$	−3.41789			−0.384543			−0.192272	+	0.981342i	$0.561585\pi$
$80$	−0.360031	+	3.98376i	−0.0402527	+	0.445398i
$81$	−1.00000			−0.111111
$82$	−3.05704	+	4.35925i	−0.337593	+	0.481399i
$83$	5.31631	+	5.31631i	0.583541	+	0.583541i	0.935875	−	0.352333i	$-0.114612\pi$
$83$	5.31631	+	5.31631i	0.583541	+	0.583541i	−0.352333	+	0.935875i	$0.614612\pi$
$84$	3.94994	+	1.84878i	0.430974	+	0.201718i
$85$	−3.92404	+	3.92404i	−0.425622	+	0.425622i
$86$	13.4189	−	2.35621i	1.44700	−	0.254077i
$87$			4.53214i			0.485896i
$88$	−0.0177265	−	0.0308561i	−0.00188965	−	0.00328927i
$89$			5.06405i			0.536788i	0.963309	+	0.268394i	$0.0864929\pi$
$89$			5.06405i			0.536788i	−0.963309	+	0.268394i	$0.913507\pi$
$90$	0.244579	+	1.39290i	0.0257808	+	0.146825i
$91$	3.77168	−	3.77168i	0.395379	−	0.395379i
$92$	5.66569	−	2.05296i	0.590689	−	0.214036i
$93$	2.53151	+	2.53151i	0.262505	+	0.262505i
$94$	−11.6714	−	8.18483i	−1.20381	−	0.844201i
$95$	−6.99615			−0.717790
$96$	−4.32036	−	3.65164i	−0.440945	−	0.372694i
$97$	−10.3646			−1.05237			−0.526184	−	0.850371i	$-0.676378\pi$
$97$	−10.3646			−1.05237			−0.526184	+	0.850371i	$0.676378\pi$
$98$	2.59942	+	1.82291i	0.262581	+	0.184142i
$99$	−0.00889637	−	0.00889637i	−0.000894119	−	0.000894119i
$100$	1.88036	−	0.681349i	0.188036	−	0.0681349i
$101$	9.96414	−	9.96414i	0.991469	−	0.991469i	−0.00849458	−	0.999964i	$-0.502704\pi$
$101$	9.96414	−	9.96414i	0.991469	−	0.991469i	0.999964	+	0.00849458i	$0.00270394\pi$
$102$	−1.35727	−	7.72982i	−0.134390	−	0.765366i
$103$			2.25154i			0.221851i	0.993829	+	0.110926i	$0.0353815\pi$
$103$			2.25154i			0.221851i	−0.993829	+	0.110926i	$0.964618\pi$
$104$	−5.99911	+	3.44643i	−0.588261	+	0.337950i
$105$		−	2.18060i		−	0.212805i
$106$	−1.83718	+	0.322589i	−0.178443	+	0.0313326i
$107$	2.51098	−	2.51098i	0.242746	−	0.242746i	−0.575239	−	0.817985i	$-0.695091\pi$
$107$	2.51098	−	2.51098i	0.242746	−	0.242746i	0.817985	+	0.575239i	$0.195091\pi$
$108$	−1.81140	−	0.847831i	−0.174302	−	0.0815825i
$109$	12.0668	+	12.0668i	1.15579	+	1.15579i	0.985372	+	0.170420i	$0.0545124\pi$
$109$	12.0668	+	12.0668i	1.15579	+	1.15579i	0.170420	+	0.985372i	$0.445488\pi$
$110$	−0.0102159	+	0.0145676i	−0.000974050	+	0.00138897i
$111$	7.03940			0.668150
$112$	5.58749	+	6.69777i	0.527968	+	0.632879i
$113$	−19.7954			−1.86219			−0.931097	−	0.364772i	$-0.881147\pi$
$113$	−19.7954			−1.86219			−0.931097	+	0.364772i	$0.881147\pi$
$114$	5.68079	−	8.10067i	0.532055	−	0.758697i
$115$	−2.13057	−	2.13057i	−0.198677	−	0.198677i
$116$	−3.84249	+	8.20953i	−0.356766	+	0.762236i
$117$	−1.72965	+	1.72965i	−0.159906	+	0.159906i
$118$	−9.07165	+	1.59288i	−0.835113	+	0.146637i
$119$			12.1011i			1.10930i
$120$	−0.737916	+	2.73047i	−0.0673622	+	0.249257i
$121$			10.9998i			0.999986i
$122$	1.44286	+	8.21727i	0.130631	+	0.743957i
$123$	−2.66217	+	2.66217i	−0.240040	+	0.240040i
$124$	2.43929	+	6.73188i	0.219055	+	0.604540i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	2.52486	+	1.77062i	0.224932	+	0.157739i
$127$	14.3984			1.27765			0.638825	−	0.769352i	$-0.279421\pi$
$127$	14.3984			1.27765			0.638825	+	0.769352i	$0.279421\pi$
$128$	−4.72994	−	10.2775i	−0.418072	−	0.908414i
$129$	9.63376			0.848205
$130$	2.83228	+	1.98620i	0.248407	+	0.174202i
$131$	−0.574754	−	0.574754i	−0.0502165	−	0.0502165i	0.681553	−	0.731769i	$-0.261305\pi$
$131$	−0.574754	−	0.574754i	−0.0502165	−	0.0502165i	−0.731769	+	0.681553i	$0.761305\pi$
$132$	−0.00857230	−	0.0236575i	−0.000746123	−	0.00205912i
$133$	−10.7875	+	10.7875i	−0.935393	+	0.935393i
$134$	−3.80838	−	21.6892i	−0.328994	−	1.87366i
$135$			1.00000i			0.0860663i
$136$	4.09501	−	15.1526i	0.351144	−	1.29932i
$137$			16.0077i			1.36763i	0.729654	+	0.683817i	$0.239681\pi$
$137$			16.0077i			1.36763i	−0.729654	+	0.683817i	$0.760319\pi$
$138$	4.19694	−	0.736936i	0.357267	−	0.0627322i
$139$	−1.52424	+	1.52424i	−0.129284	+	0.129284i	−0.768788	−	0.639504i	$-0.779140\pi$
$139$	−1.52424	+	1.52424i	−0.129284	+	0.129284i	0.639504	+	0.768788i	$0.279140\pi$
$140$	1.84878	−	3.94994i	0.156250	−	0.333831i
$141$	−7.12762	−	7.12762i	−0.600254	−	0.600254i
$142$	−9.83255	+	14.0210i	−0.825129	+	1.17661i
$143$	−0.0307753			−0.00257356
$144$	−2.56237	−	3.07153i	−0.213531	−	0.255961i
$145$	4.53214			0.376374
$146$	−5.78932	+	8.25543i	−0.479128	+	0.683224i
$147$	1.58745	+	1.58745i	0.130931	+	0.130931i
$148$	12.7512	+	5.96822i	1.04814	+	0.490585i
$149$	12.1410	−	12.1410i	0.994629	−	0.994629i	−0.00535669	−	0.999986i	$-0.501705\pi$
$149$	12.1410	−	12.1410i	0.994629	−	0.994629i	0.999986	+	0.00535669i	$0.00170510\pi$
$150$	1.39290	−	0.244579i	0.113730	−	0.0199698i
$151$			12.7940i			1.04116i	0.853813	+	0.520580i	$0.174284\pi$
$151$			12.7940i			1.04116i	−0.853813	+	0.520580i	$0.825716\pi$
$152$	17.1582	−	9.85723i	1.39171	−	0.799527i
$153$		−	5.54943i		−	0.448645i
$154$	0.00670999	+	0.0382142i	0.000540706	+	0.00307939i
$155$	2.53151	−	2.53151i	0.203336	−	0.203336i
$156$	−4.59955	+	1.66665i	−0.368259	+	0.133438i
$157$	−10.3333	−	10.3333i	−0.824686	−	0.824686i	0.162090	−	0.986776i	$-0.448177\pi$
$157$	−10.3333	−	10.3333i	−0.824686	−	0.824686i	−0.986776	+	0.162090i	$0.948177\pi$
$158$	−3.95749	−	2.77529i	−0.314841	−	0.220790i
$159$	−1.31896			−0.104600
$160$	−3.65164	+	4.32036i	−0.288688	+	0.341554i
$161$	−6.57033			−0.517814
$162$	−1.15787	−	0.811989i	−0.0909713	−	0.0637959i
$163$	13.4362	+	13.4362i	1.05241	+	1.05241i	0.998549	+	0.0538580i	$0.0171518\pi$
$163$	13.4362	+	13.4362i	1.05241	+	1.05241i	0.0538580	+	0.998549i	$0.482848\pi$
$164$	−7.07933	+	2.56519i	−0.552803	+	0.200308i
$165$	−0.00889637	+	0.00889637i	−0.000692581	+	0.000692581i
$166$	1.83884	+	10.4724i	0.142722	+	0.812817i
$167$		−	5.08389i		−	0.393403i	−0.980463	−	0.196702i	$-0.936977\pi$
$167$		−	5.08389i		−	0.393403i	0.980463	−	0.196702i	$-0.0630230\pi$
$168$	3.07235	+	5.34796i	0.237037	+	0.412604i
$169$		−	7.01660i		−	0.539739i
$170$	−7.72982	+	1.35727i	−0.592850	+	0.104098i
$171$	4.94702	−	4.94702i	0.378308	−	0.378308i
$172$	17.4506	+	8.16780i	1.33060	+	0.622789i
$173$	−10.8821	−	10.8821i	−0.827350	−	0.827350i	0.159799	−	0.987150i	$-0.448915\pi$
$173$	−10.8821	−	10.8821i	−0.827350	−	0.827350i	−0.987150	+	0.159799i	$0.948915\pi$
$174$	−3.68004	+	5.24765i	−0.278983	+	0.397823i
$175$	−2.18060			−0.164838
$176$	0.00452968	−	0.0501212i	0.000341438	−	0.00377803i
$177$	−6.51276			−0.489529
$178$	−4.11195	+	5.86353i	−0.308204	+	0.439490i
$179$	11.1719	+	11.1719i	0.835028	+	0.835028i	0.988200	−	0.153172i	$-0.0489488\pi$
$179$	11.1719	+	11.1719i	0.835028	+	0.835028i	−0.153172	+	0.988200i	$0.548949\pi$
$180$	−0.847831	+	1.81140i	−0.0631936	+	0.135014i
$181$	−10.1479	+	10.1479i	−0.754290	+	0.754290i	−0.975277	−	0.220987i	$-0.929072\pi$
$181$	−10.1479	+	10.1479i	−0.754290	+	0.754290i	0.220987	+	0.975277i	$0.429072\pi$
$182$	7.42969	−	1.30457i	0.550725	−	0.0967013i
$183$			5.89938i			0.436095i
$184$	8.22715	+	2.22340i	0.606513	+	0.163912i
$185$		−	7.03940i		−	0.517547i
$186$	0.875614	+	4.98673i	0.0642032	+	0.365645i
$187$	0.0493697	−	0.0493697i	0.00361027	−	0.00361027i
$188$	−6.86798	−	18.9540i	−0.500899	−	1.38236i
$189$	1.54192	+	1.54192i	0.112158	+	0.112158i
$190$	−8.10067	−	5.68079i	−0.587684	−	0.412128i
$191$	13.3716			0.967532			0.483766	−	0.875197i	$-0.339269\pi$
$191$	13.3716			0.967532			0.483766	+	0.875197i	$0.339269\pi$
$192$	−2.03734	−	7.73623i	−0.147033	−	0.558314i
$193$	8.32925			0.599553			0.299776	−	0.954009i	$-0.403088\pi$
$193$	8.32925			0.599553			0.299776	+	0.954009i	$0.403088\pi$
$194$	−12.0009	−	8.41596i	−0.861617	−	0.604230i
$195$	1.72965	+	1.72965i	0.123863	+	0.123863i
$196$	1.52962	+	4.22140i	0.109259	+	0.301529i
$197$	13.1995	−	13.1995i	0.940427	−	0.940427i	−0.0578960	−	0.998323i	$-0.518439\pi$
$197$	13.1995	−	13.1995i	0.940427	−	0.940427i	0.998323	+	0.0578960i	$0.0184392\pi$
$198$	−0.00307713	−	0.0175246i	−0.000218682	−	0.00124542i
$199$		−	3.66713i		−	0.259956i	−0.991517	−	0.129978i	$-0.958509\pi$
$199$		−	3.66713i		−	0.259956i	0.991517	−	0.129978i	$-0.0414906\pi$
$200$	2.73047	+	0.737916i	0.193074	+	0.0521786i
$201$		−	15.5712i		−	1.09831i
$202$	19.6280	−	3.44646i	1.38102	−	0.242492i
$203$	6.98817	−	6.98817i	0.490474	−	0.490474i
$204$	4.70497	−	10.0523i	0.329414	−	0.703798i
$205$	2.66217	+	2.66217i	0.185934	+	0.185934i
$206$	−1.82823	+	2.60700i	−0.127379	+	0.181639i
$207$	3.01309			0.209424
$208$	−9.74468	−	0.880672i	−0.675672	−	0.0610636i
$209$	0.0880211			0.00608855
$210$	1.77062	−	2.52486i	0.122184	−	0.174232i
$211$	−12.6423	−	12.6423i	−0.870332	−	0.870332i	0.122176	−	0.992508i	$-0.461013\pi$
$211$	−12.6423	−	12.6423i	−0.870332	−	0.870332i	−0.992508	+	0.122176i	$0.961013\pi$
$212$	−2.38916	−	1.11825i	−0.164088	−	0.0768019i
$213$	−8.56251	+	8.56251i	−0.586694	+	0.586694i
$214$	4.94629	−	0.868514i	0.338121	−	0.0593704i
$215$		−	9.63376i		−	0.657017i
$216$	−1.40895	−	2.45252i	−0.0958669	−	0.166873i
$217$		−	7.80675i		−	0.529956i
$218$	4.17375	+	23.7700i	0.282682	+	1.60991i
$219$	−5.04154	+	5.04154i	−0.340675	+	0.340675i
$220$	−0.0236575	+	0.00857230i	−0.00159499	+	0.000577944i
$221$	−9.59858	−	9.59858i	−0.645670	−	0.645670i
$222$	8.15074	+	5.71591i	0.547042	+	0.383627i
$223$	−5.37431			−0.359891			−0.179945	−	0.983677i	$-0.557592\pi$
$223$	−5.37431			−0.359891			−0.179945	+	0.983677i	$0.557592\pi$
$224$	1.03111	+	12.2922i	0.0688936	+	0.821304i
$225$	1.00000			0.0666667
$226$	−22.9206	−	16.0736i	−1.52465	−	1.06920i
$227$	1.92306	+	1.92306i	0.127638	+	0.127638i	0.768040	−	0.640402i	$-0.221232\pi$
$227$	1.92306	+	1.92306i	0.127638	+	0.127638i	−0.640402	+	0.768040i	$0.721232\pi$
$228$	13.1553	−	4.76682i	0.871231	−	0.315690i
$229$	5.08104	−	5.08104i	0.335765	−	0.335765i	−0.519006	−	0.854771i	$-0.673698\pi$
$229$	5.08104	−	5.08104i	0.335765	−	0.335765i	0.854771	+	0.519006i	$0.173698\pi$
$230$	−0.736936	−	4.19694i	−0.0485921	−	0.276738i
$231$			0.0274349i			0.00180508i
$232$	−11.1152	+	6.38556i	−0.729746	+	0.419232i
$233$		−	26.2417i		−	1.71915i	−0.511011	−	0.859574i	$-0.670729\pi$
$233$		−	26.2417i		−	1.71915i	0.511011	−	0.859574i	$-0.329271\pi$
$234$	−3.40718	+	0.598263i	−0.222734	+	0.0391097i
$235$	−7.12762	+	7.12762i	−0.464955	+	0.464955i
$236$	−11.7972	−	5.52172i	−0.767935	−	0.359433i
$237$	−2.41682	−	2.41682i	−0.156989	−	0.156989i
$238$	−9.82593	+	14.0115i	−0.636920	+	0.908232i
$239$	−7.40931			−0.479268			−0.239634	−	0.970863i	$-0.577027\pi$
$239$	−7.40931			−0.479268			−0.239634	+	0.970863i	$0.577027\pi$
$240$	−3.07153	+	2.56237i	−0.198266	+	0.165400i
$241$	−19.6231			−1.26404			−0.632019	−	0.774953i	$-0.717773\pi$
$241$	−19.6231			−1.26404			−0.632019	+	0.774953i	$0.717773\pi$
$242$	−8.93175	+	12.7364i	−0.574154	+	0.818729i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−5.00168	+	10.6862i	−0.320200	+	0.684112i
$245$	1.58745	−	1.58745i	0.101418	−	0.101418i
$246$	−5.24411	+	0.920808i	−0.334352	+	0.0587085i
$247$		−	17.1133i		−	1.08889i
$248$	−2.64181	+	9.77535i	−0.167755	+	0.620735i
$249$			7.51840i			0.476459i
$250$	−0.244579	−	1.39290i	−0.0154685	−	0.0880950i
$251$	1.23610	−	1.23610i	0.0780217	−	0.0780217i	−0.667019	−	0.745041i	$-0.732430\pi$
$251$	1.23610	−	1.23610i	0.0780217	−	0.0780217i	0.745041	+	0.667019i	$0.232430\pi$
$252$	1.48575	+	4.10031i	0.0935933	+	0.258296i
$253$	0.0268055	+	0.0268055i	0.00168525	+	0.00168525i
$254$	16.6715	+	11.6913i	1.04606	+	0.733579i
$255$	−5.54943			−0.347519
$256$	2.86856	−	15.7408i	0.179285	−	0.983797i
$257$	3.01050			0.187790			0.0938948	−	0.995582i	$-0.470068\pi$
$257$	3.01050			0.187790			0.0938948	+	0.995582i	$0.470068\pi$
$258$	11.1547	+	7.82250i	0.694461	+	0.487008i
$259$	−10.8542	−	10.8542i	−0.674445	−	0.674445i
$260$	1.66665	+	4.59955i	0.103361	+	0.285252i
$261$	−3.20471	+	3.20471i	−0.198366	+	0.198366i
$262$	−0.198800	−	1.13219i	−0.0122819	−	0.0699468i
$263$		−	11.9000i		−	0.733788i	−0.930263	−	0.366894i	$-0.880421\pi$
$263$		−	11.9000i		−	0.733788i	0.930263	−	0.366894i	$-0.119579\pi$
$264$	0.00928399	−	0.0343531i	0.000571390	−	0.00211429i
$265$			1.31896i			0.0810229i
$266$	−21.2498	+	3.73124i	−1.30291	+	0.228777i
$267$	−3.58082	+	3.58082i	−0.219143	+	0.219143i
$268$	13.2017	−	28.2057i	0.806424	−	1.72294i
$269$	−15.4949	−	15.4949i	−0.944742	−	0.944742i	0.0538091	−	0.998551i	$-0.482864\pi$
$269$	−15.4949	−	15.4949i	−0.944742	−	0.944742i	−0.998551	+	0.0538091i	$0.982864\pi$
$270$	−0.811989	+	1.15787i	−0.0494161	+	0.0704660i
$271$	7.30492			0.443742			0.221871	−	0.975076i	$-0.428784\pi$
$271$	7.30492			0.443742			0.221871	+	0.975076i	$0.428784\pi$
$272$	17.0452	−	14.2197i	1.03352	−	0.862194i
$273$	5.33396			0.322826
$274$	−12.9981	+	18.5350i	−0.785244	+	1.11974i
$275$	0.00889637	+	0.00889637i	0.000536471	+	0.000536471i
$276$	5.45791	+	2.55459i	0.328528	+	0.153768i
$277$	2.23718	−	2.23718i	0.134419	−	0.134419i	−0.636696	−	0.771115i	$-0.719699\pi$
$277$	2.23718	−	2.23718i	0.134419	−	0.134419i	0.771115	+	0.636696i	$0.219699\pi$
$278$	−3.00254	+	0.527212i	−0.180080	+	0.0316201i
$279$			3.58009i			0.214335i
$280$	5.34796	−	3.07235i	0.319602	−	0.183608i
$281$			4.85036i			0.289348i	0.989479	+	0.144674i	$0.0462134\pi$
$281$			4.85036i			0.289348i	−0.989479	+	0.144674i	$0.953787\pi$
$282$	−2.46535	−	14.0404i	−0.146809	−	0.836096i
$283$	11.4295	−	11.4295i	0.679414	−	0.679414i	−0.280454	−	0.959867i	$-0.590485\pi$
$283$	11.4295	−	11.4295i	0.679414	−	0.679414i	0.959867	+	0.280454i	$0.0904850\pi$
$284$	−22.7697	+	8.25060i	−1.35113	+	0.489583i
$285$	−4.94702	−	4.94702i	−0.293036	−	0.293036i
$286$	−0.0356339	−	0.0249892i	−0.00210708	−	0.00147764i
$287$	8.20968			0.484602
$288$	−0.472855	−	5.63706i	−0.0278632	−	0.332167i
$289$	13.7961			0.811537
$290$	5.24765	+	3.68004i	0.308153	+	0.216100i
$291$	−7.32890	−	7.32890i	−0.429627	−	0.429627i
$292$	−13.4066	+	4.85789i	−0.784563	+	0.284286i
$293$	−11.1686	+	11.1686i	−0.652475	+	0.652475i	−0.953588	−	0.301113i	$-0.902642\pi$
$293$	−11.1686	+	11.1686i	−0.652475	+	0.652475i	0.301113	+	0.953588i	$0.402642\pi$
$294$	0.549077	+	3.12706i	0.0320228	+	0.182374i
$295$			6.51276i			0.379188i
$296$	9.91816	+	17.2643i	0.576481	+	1.00347i
$297$		−	0.0125814i		−	0.000730045i
$298$	23.9161	−	4.19940i	1.38542	−	0.243265i
$299$	5.21159	−	5.21159i	0.301394	−	0.301394i
$300$	1.81140	+	0.847831i	0.104581	+	0.0489495i
$301$	−14.8544	−	14.8544i	−0.856196	−	0.856196i
$302$	−10.3886	+	14.8138i	−0.597795	+	0.852440i
$303$	14.0914			0.809531
$304$	27.8710	+	2.51883i	1.59851	+	0.144465i
$305$	5.89938			0.337798
$306$	4.50607	−	6.42554i	0.257595	−	0.367324i
$307$	13.5366	+	13.5366i	0.772575	+	0.772575i	0.978556	−	0.205981i	$-0.0660384\pi$
$307$	13.5366	+	13.5366i	0.772575	+	0.772575i	−0.205981	+	0.978556i	$0.566038\pi$
$308$	−0.0232602	+	0.0496957i	−0.00132537	+	0.00283167i
$309$	−1.59208	+	1.59208i	−0.0905703	+	0.0905703i
$310$	4.98673	−	0.875614i	0.283227	−	0.0497316i
$311$		−	16.4956i		−	0.935378i	−0.883893	−	0.467689i	$-0.845087\pi$
$311$		−	16.4956i		−	0.935378i	0.883893	−	0.467689i	$-0.154913\pi$
$312$	−6.67900	−	1.80502i	−0.378124	−	0.102189i
$313$		−	27.2549i		−	1.54054i	−0.637719	−	0.770269i	$-0.720122\pi$
$313$		−	27.2549i		−	1.54054i	0.637719	−	0.770269i	$-0.279878\pi$
$314$	−3.57414	−	20.3552i	−0.201701	−	1.14871i
$315$	1.54192	−	1.54192i	0.0868771	−	0.0868771i
$316$	−2.32878	−	6.42688i	−0.131004	−	0.361540i
$317$	23.2962	+	23.2962i	1.30845	+	1.30845i	0.922536	+	0.385911i	$0.126113\pi$
$317$	23.2962	+	23.2962i	1.30845	+	1.30845i	0.385911	+	0.922536i	$0.373887\pi$
$318$	−1.52719	−	1.07098i	−0.0856404	−	0.0600575i
$319$	−0.0570205			−0.00319253
$320$	−7.73623	+	2.03734i	−0.432468	+	0.113891i
$321$	3.55106			0.198201
$322$	−7.60762	−	5.33503i	−0.423956	−	0.297310i
$323$	27.4531	+	27.4531i	1.52753	+	1.52753i
$324$	−0.681349	−	1.88036i	−0.0378527	−	0.104465i
$325$	1.72965	−	1.72965i	0.0959439	−	0.0959439i
$326$	4.64741	+	26.4675i	0.257396	+	1.46590i
$327$			17.0651i			0.943700i
$328$	−10.2799	−	2.77816i	−0.567612	−	0.153398i
$329$			21.9804i			1.21182i
$330$	−0.0175246	+	0.00307713i	−0.000964699	+	0.000169391i
$331$	−15.9057	+	15.9057i	−0.874257	+	0.874257i	−0.992933	−	0.118676i	$-0.962135\pi$
$331$	−15.9057	+	15.9057i	−0.874257	+	0.874257i	0.118676	+	0.992933i	$0.462135\pi$
$332$	−6.37433	+	13.6189i	−0.349837	+	0.747432i
$333$	4.97761	+	4.97761i	0.272771	+	0.272771i
$334$	4.12806	−	5.88651i	0.225877	−	0.322096i
$335$	−15.5712			−0.850745
$336$	−0.785083	+	8.68699i	−0.0428298	+	0.473914i
$337$	7.15503			0.389759			0.194880	−	0.980827i	$-0.437568\pi$
$337$	7.15503			0.389759			0.194880	+	0.980827i	$0.437568\pi$
$338$	5.69740	−	8.12435i	0.309898	−	0.441906i
$339$	−13.9975	−	13.9975i	−0.760237	−	0.760237i
$340$	−10.0523	−	4.70497i	−0.545160	−	0.255163i
$341$	−0.0318498	+	0.0318498i	−0.00172477	+	0.00172477i
$342$	9.74496	−	1.71111i	0.526947	−	0.0925261i
$343$		−	20.1596i		−	1.08852i
$344$	13.5735	+	23.6270i	0.731833	+	1.27388i
$345$		−	3.01309i		−	0.162219i
$346$	−3.76397	−	21.4362i	−0.202352	−	1.15242i
$347$	−9.64716	+	9.64716i	−0.517887	+	0.517887i	−0.916931	−	0.399045i	$-0.869342\pi$
$347$	−9.64716	+	9.64716i	−0.517887	+	0.517887i	0.399045	+	0.916931i	$0.369342\pi$
$348$	−8.52206	+	3.08797i	−0.456830	+	0.165532i
$349$	20.3332	+	20.3332i	1.08841	+	1.08841i	0.995692	+	0.0927209i	$0.0295564\pi$
$349$	20.3332	+	20.3332i	1.08841	+	1.08841i	0.0927209	+	0.995692i	$0.470444\pi$
$350$	−2.52486	−	1.77062i	−0.134959	−	0.0946437i
$351$	−2.44610			−0.130563
$352$	0.0459426	−	0.0543560i	0.00244875	−	0.00289719i
$353$	32.1660			1.71202			0.856010	−	0.516958i	$-0.172936\pi$
$353$	32.1660			1.71202			0.856010	+	0.516958i	$0.172936\pi$
$354$	−7.54096	−	5.28829i	−0.400798	−	0.281069i
$355$	8.56251	+	8.56251i	0.454451	+	0.454451i
$356$	−9.52225	+	3.45038i	−0.504678	+	0.182870i
$357$	−8.55675	+	8.55675i	−0.452871	+	0.452871i
$358$	3.86421	+	22.0071i	0.204230	+	1.16311i
$359$		−	15.8239i		−	0.835155i	−0.908641	−	0.417578i	$-0.862879\pi$
$359$		−	15.8239i		−	0.835155i	0.908641	−	0.417578i	$-0.137121\pi$
$360$	−2.45252	+	1.40895i	−0.129259	+	0.0742582i
$361$			29.9461i			1.57611i
$362$	−19.9901	+	3.51003i	−1.05065	+	0.184483i
$363$	−7.77806	+	7.77806i	−0.408242	+	0.408242i
$364$	9.66195	+	4.52229i	0.506424	+	0.237033i
$365$	5.04154	+	5.04154i	0.263886	+	0.263886i
$366$	−4.79023	+	6.83075i	−0.250389	+	0.357049i
$367$	4.34838			0.226984			0.113492	−	0.993539i	$-0.463796\pi$
$367$	4.34838			0.226984			0.113492	+	0.993539i	$0.463796\pi$
$368$	7.72063	+	9.25477i	0.402466	+	0.482438i
$369$	−3.76487			−0.195992
$370$	5.71591	−	8.15074i	0.297156	−	0.423737i
$371$	2.03372	+	2.03372i	0.105586	+	0.105586i
$372$	−3.03531	+	6.48500i	−0.157374	+	0.336231i
$373$	−17.3659	+	17.3659i	−0.899171	+	0.899171i	−0.995363	−	0.0961919i	$-0.969334\pi$
$373$	−17.3659	+	17.3659i	−0.899171	+	0.899171i	0.0961919	+	0.995363i	$0.469334\pi$
$374$	0.0972517	−	0.0170763i	0.00502876	−	0.000882996i
$375$		−	1.00000i		−	0.0516398i
$376$	7.43818	−	27.5231i	0.383595	−	1.41940i
$377$			11.0861i			0.570961i
$378$	0.533328	+	3.03736i	0.0274314	+	0.156225i
$379$	−15.3936	+	15.3936i	−0.790717	+	0.790717i	−0.981611	−	0.190893i	$-0.938862\pi$
$379$	−15.3936	+	15.3936i	−0.790717	+	0.790717i	0.190893	+	0.981611i	$0.438862\pi$
$380$	−4.76682	−	13.1553i	−0.244533	−	0.674853i
$381$	10.1812	+	10.1812i	0.521598	+	0.521598i
$382$	15.4826	+	10.8576i	0.792159	+	0.555521i
$383$	−15.6393			−0.799129			−0.399564	−	0.916705i	$-0.630839\pi$
$383$	−15.6393			−0.799129			−0.399564	+	0.916705i	$0.630839\pi$
$384$	3.92274	−	10.6119i	0.200181	−	0.541536i
$385$	0.0274349			0.00139821
$386$	9.64423	+	6.76326i	0.490879	+	0.344241i
$387$	6.81210	+	6.81210i	0.346278	+	0.346278i
$388$	−7.06193	−	19.4893i	−0.358515	−	0.989417i
$389$	17.0067	−	17.0067i	0.862276	−	0.862276i	−0.129326	−	0.991602i	$-0.541281\pi$
$389$	17.0067	−	17.0067i	0.862276	−	0.862276i	0.991602	+	0.129326i	$0.0412813\pi$
$390$	0.598263	+	3.40718i	0.0302942	+	0.172529i
$391$			16.7209i			0.845612i
$392$	−1.65662	+	6.12989i	−0.0836717	+	0.309606i
$393$		−	0.812825i		−	0.0410016i
$394$	26.0012	−	4.56553i	1.30992	−	0.230008i
$395$	−2.41682	+	2.41682i	−0.121603	+	0.121603i
$396$	0.0106669	−	0.0227899i	0.000536030	−	0.00114524i
$397$	−12.5043	−	12.5043i	−0.627572	−	0.627572i	0.319884	−	0.947457i	$-0.396356\pi$
$397$	−12.5043	−	12.5043i	−0.627572	−	0.627572i	−0.947457	+	0.319884i	$0.896356\pi$
$398$	2.97767	−	4.24608i	0.149257	−	0.212837i
$399$	−15.2558			−0.763745
$400$	2.56237	+	3.07153i	0.128118	+	0.153576i
$401$	−14.6398			−0.731079			−0.365539	−	0.930796i	$-0.619115\pi$
$401$	−14.6398			−0.731079			−0.365539	+	0.930796i	$0.619115\pi$
$402$	12.6436	−	18.0295i	0.630607	−	0.899229i
$403$	6.19232	+	6.19232i	0.308461	+	0.308461i
$404$	25.5253	+	11.9471i	1.26993	+	0.594393i
$405$	−0.707107	+	0.707107i	−0.0351364	+	0.0351364i
$406$	13.7657	−	2.41711i	0.683183	−	0.119959i
$407$			0.0885653i			0.00439002i
$408$	13.6101	−	7.81886i	0.673800	−	0.387091i
$409$		−	33.5504i		−	1.65896i	−0.558537	−	0.829479i	$-0.688637\pi$
$409$		−	33.5504i		−	1.65896i	0.558537	−	0.829479i	$-0.311363\pi$
$410$	0.920808	+	5.24411i	0.0454754	+	0.258988i
$411$	−11.3192	+	11.3192i	−0.558334	+	0.558334i
$412$	−4.23372	+	1.53409i	−0.208580	+	0.0755790i
$413$	10.0421	+	10.0421i	0.494141	+	0.494141i
$414$	3.48878	+	2.44659i	0.171464	+	0.120243i
$415$	7.51840			0.369064
$416$	−10.5680	−	8.93227i	−0.518140	−	0.437941i
$417$	−2.15559			−0.105560
$418$	0.101917	+	0.0714721i	0.00498495	+	0.00349582i
$419$	16.5641	+	16.5641i	0.809211	+	0.809211i	0.984514	−	0.175303i	$-0.0560906\pi$
$419$	16.5641	+	16.5641i	0.809211	+	0.809211i	−0.175303	+	0.984514i	$0.556091\pi$
$420$	4.10031	−	1.48575i	0.200075	−	0.0724971i
$421$	14.1472	−	14.1472i	0.689492	−	0.689492i	−0.272628	−	0.962120i	$-0.587893\pi$
$421$	14.1472	−	14.1472i	0.689492	−	0.689492i	0.962120	+	0.272628i	$0.0878928\pi$
$422$	−4.37280	−	24.9036i	−0.212865	−	1.21229i
$423$		−	10.0800i		−	0.490105i
$424$	−1.85834	−	3.23477i	−0.0902492	−	0.157094i
$425$			5.54943i			0.269187i
$426$	−16.8670	+	2.96166i	−0.817208	+	0.143493i
$427$	9.09635	−	9.09635i	0.440203	−	0.440203i
$428$	6.43241	+	3.01070i	0.310922	+	0.145528i
$429$	−0.0217614	−	0.0217614i	−0.00105065	−	0.00105065i
$430$	7.82250	−	11.1547i	0.377235	−	0.537927i
$431$	13.1169			0.631819			0.315909	−	0.948789i	$-0.397690\pi$
$431$	13.1169			0.631819			0.315909	+	0.948789i	$0.397690\pi$
$432$	0.360031	−	3.98376i	0.0173220	−	0.191669i
$433$	0.300976			0.0144640			0.00723199	−	0.999974i	$-0.497698\pi$
$433$	0.300976			0.0144640			0.00723199	+	0.999974i	$0.497698\pi$
$434$	6.33899	−	9.03924i	0.304281	−	0.433897i
$435$	3.20471	+	3.20471i	0.153654	+	0.153654i
$436$	−14.4683	+	30.9117i	−0.692905	+	1.48040i
$437$	−14.9058	+	14.9058i	−0.713041	+	0.713041i
$438$	−9.93114	+	1.74380i	−0.474528	+	0.0833219i
$439$		−	30.3358i		−	1.44785i	−0.689879	−	0.723925i	$-0.742336\pi$
$439$		−	30.3358i		−	1.44785i	0.689879	−	0.723925i	$-0.257664\pi$
$440$	−0.0343531	−	0.00928399i	−0.00163772	−	0.000442597i
$441$			2.24499i			0.106904i
$442$	−3.32002	−	18.9079i	−0.157917	−	0.899357i
$443$	−3.99367	+	3.99367i	−0.189745	+	0.189745i	−0.795586	−	0.605841i	$-0.792837\pi$
$443$	−3.99367	+	3.99367i	−0.189745	+	0.189745i	0.605841	+	0.795586i	$0.292837\pi$
$444$	4.79629	+	13.2366i	0.227622	+	0.628182i
$445$	3.58082	+	3.58082i	0.169747	+	0.169747i
$446$	−6.22278	−	4.36388i	−0.294657	−	0.206636i
$447$	17.1700			0.812111
$448$	−8.78720	+	15.0700i	−0.415156	+	0.711992i
$449$	−10.4806			−0.494610			−0.247305	−	0.968938i	$-0.579545\pi$
$449$	−10.4806			−0.494610			−0.247305	+	0.968938i	$0.579545\pi$
$450$	1.15787	+	0.811989i	0.0545828	+	0.0382775i
$451$	−0.0334937	−	0.0334937i	−0.00157716	−	0.00157716i
$452$	−13.4876	−	37.2225i	−0.634402	−	1.75080i
$453$	−9.04671	+	9.04671i	−0.425052	+	0.425052i
$454$	0.665160	+	3.78816i	0.0312175	+	0.177787i
$455$		−	5.33396i		−	0.250060i
$456$	19.1028	+	5.16257i	0.894570	+	0.241760i
$457$			5.70188i			0.266723i	0.991067	+	0.133361i	$0.0425771\pi$
$457$			5.70188i			0.266723i	−0.991067	+	0.133361i	$0.957423\pi$
$458$	10.0090	−	1.75746i	0.467688	−	0.0821208i
$459$	3.92404	−	3.92404i	0.183158	−	0.183158i
$460$	2.55459	−	5.45791i	0.119108	−	0.254477i
$461$	1.78282	+	1.78282i	0.0830341	+	0.0830341i	0.747404	−	0.664370i	$-0.231300\pi$
$461$	1.78282	+	1.78282i	0.0830341	+	0.0830341i	−0.664370	+	0.747404i	$0.731300\pi$
$462$	−0.0222768	+	0.0317662i	−0.00103641	+	0.00147790i
$463$	−37.2015			−1.72890			−0.864451	−	0.502717i	$-0.832334\pi$
$463$	−37.2015			−1.72890			−0.864451	+	0.502717i	$0.832334\pi$
$464$	−18.0550	−	1.63171i	−0.838181	−	0.0757503i
$465$	3.58009			0.166023
$466$	21.3079	−	30.3846i	0.987071	−	1.40754i
$467$	−14.3669	−	14.3669i	−0.664822	−	0.664822i	0.291691	−	0.956513i	$-0.405782\pi$
$467$	−14.3669	−	14.3669i	−0.664822	−	0.664822i	−0.956513	+	0.291691i	$0.905782\pi$
$468$	−4.43087	−	2.07388i	−0.204817	−	0.0958650i
$469$	−24.0094	+	24.0094i	−1.10865	+	1.10865i
$470$	−14.0404	+	2.46535i	−0.647637	+	0.113718i
$471$		−	14.6135i		−	0.673353i
$472$	−9.17616	−	15.9727i	−0.422367	−	0.735202i
$473$			0.121206i			0.00557305i
$474$	−0.835944	−	4.76080i	−0.0383962	−	0.218671i
$475$	−4.94702	+	4.94702i	−0.226985	+	0.226985i
$476$	−22.7544	+	8.24505i	−1.04295	+	0.377911i
$477$	−0.932644	−	0.932644i	−0.0427028	−	0.0427028i
$478$	−8.57905	−	6.01627i	−0.392397	−	0.275178i
$479$	−36.6561			−1.67486			−0.837431	−	0.546544i	$-0.815943\pi$
$479$	−36.6561			−1.67486			−0.837431	+	0.546544i	$0.815943\pi$
$480$	−5.63706	+	0.472855i	−0.257295	+	0.0215828i
$481$	17.2191			0.785122
$482$	−22.7211	−	15.9338i	−1.03492	−	0.725763i
$483$	−4.64592	−	4.64592i	−0.211397	−	0.211397i
$484$	−20.6837	+	7.49473i	−0.940168	+	0.340670i
$485$	−7.32890	+	7.32890i	−0.332788	+	0.332788i
$486$	−0.244579	−	1.39290i	−0.0110943	−	0.0631834i
$487$			34.3322i			1.55574i	0.628425	+	0.777870i	$0.283700\pi$
$487$			34.3322i			1.55574i	−0.628425	+	0.777870i	$0.716300\pi$
$488$	−14.4684	+	8.31194i	−0.654952	+	0.376264i
$489$			19.0017i			0.859286i
$490$	3.12706	−	0.549077i	0.141266	−	0.0248048i
$491$	17.6224	−	17.6224i	0.795287	−	0.795287i	−0.187061	−	0.982348i	$-0.559896\pi$
$491$	17.6224	−	17.6224i	0.795287	−	0.795287i	0.982348	+	0.187061i	$0.0598963\pi$
$492$	−6.81971	−	3.19198i	−0.307456	−	0.143905i
$493$	−17.7843	−	17.7843i	−0.800963	−	0.800963i
$494$	13.8958	−	19.8150i	0.625201	−	0.891520i
$495$	−0.0125814			−0.000565490
$496$	−10.9964	+	9.17351i	−0.493751	+	0.411903i
$497$	26.4053			1.18444
$498$	−6.10486	+	8.70537i	−0.273565	+	0.390097i
$499$	−14.6801	−	14.6801i	−0.657173	−	0.657173i	0.297537	−	0.954710i	$-0.403835\pi$
$499$	−14.6801	−	14.6801i	−0.657173	−	0.657173i	−0.954710	+	0.297537i	$0.903835\pi$
$500$	0.847831	−	1.81140i	0.0379161	−	0.0810084i
$501$	3.59485	−	3.59485i	0.160606	−	0.160606i
$502$	2.43494	−	0.427549i	0.108677	−	0.0190824i
$503$		−	13.0618i		−	0.582398i	−0.956663	−	0.291199i	$-0.905946\pi$
$503$		−	13.0618i		−	0.582398i	0.956663	−	0.291199i	$-0.0940541\pi$
$504$	−1.60910	+	5.95406i	−0.0716749	+	0.265215i
$505$		−	14.0914i		−	0.627060i
$506$	0.00927166	+	0.0528032i	0.000412176	+	0.00234739i
$507$	4.96149	−	4.96149i	0.220347	−	0.220347i
$508$	9.81032	+	27.0742i	0.435263	+	1.20122i
$509$	−22.0202	−	22.0202i	−0.976027	−	0.976027i	0.0236921	−	0.999719i	$-0.492458\pi$
$509$	−22.0202	−	22.0202i	−0.976027	−	0.976027i	−0.999719	+	0.0236921i	$0.992458\pi$
$510$	−6.42554	−	4.50607i	−0.284528	−	0.199532i
$511$	15.5472			0.687770
$512$	16.1027	−	15.8966i	0.711648	−	0.702537i
$513$	6.99615			0.308888
$514$	3.48578	+	2.44449i	0.153751	+	0.107822i
$515$	1.59208	+	1.59208i	0.0701555	+	0.0701555i
$516$	6.56395	+	18.1150i	0.288962	+	0.797467i
$517$	0.0896752	−	0.0896752i	0.00394391	−	0.00394391i
$518$	−3.75431	−	21.3812i	−0.164955	−	0.939437i
$519$		−	15.3896i		−	0.675529i
$520$	−1.80502	+	6.67900i	−0.0791552	+	0.292894i
$521$			22.0123i			0.964375i	0.876068	+	0.482188i	$0.160158\pi$
$521$			22.0123i			0.964375i	−0.876068	+	0.482188i	$0.839842\pi$
$522$	−6.31283	+	1.10846i	−0.276305	+	0.0485161i
$523$	−14.7575	+	14.7575i	−0.645299	+	0.645299i	−0.951853	−	0.306554i	$-0.900824\pi$
$523$	−14.7575	+	14.7575i	−0.645299	+	0.645299i	0.306554	+	0.951853i	$0.400824\pi$
$524$	0.689138	−	1.47235i	0.0301051	−	0.0643201i
$525$	−1.54192	−	1.54192i	−0.0672947	−	0.0672947i
$526$	9.66269	−	13.7788i	0.421313	−	0.600782i
$527$	−19.8675			−0.865441
$528$	0.0386440	−	0.0322381i	0.00168176	−	0.00140298i
$529$	13.9213			0.605275
$530$	−1.07098	+	1.52719i	−0.0465203	+	0.0663368i
$531$	−4.60522	−	4.60522i	−0.199849	−	0.199849i
$532$	−27.6344	−	12.9343i	−1.19810	−	0.560774i
$533$	−6.51192	+	6.51192i	−0.282063	+	0.282063i
$534$	−7.05373	+	1.23856i	−0.305245	+	0.0535976i
$535$		−	3.55106i		−	0.153526i
$536$	38.1887	−	21.9390i	1.64950	−	0.947621i
$537$			15.7995i			0.681797i
$538$	−5.35948	−	30.5229i	−0.231064	−	1.31593i
$539$	−0.0199723	+	0.0199723i	−0.000860267	+	0.000860267i
$540$	−1.88036	+	0.681349i	−0.0809179	+	0.0293206i
$541$	8.39925	+	8.39925i	0.361112	+	0.361112i	0.864222	−	0.503110i	$-0.167811\pi$
$541$	8.39925	+	8.39925i	0.361112	+	0.361112i	−0.503110	+	0.864222i	$0.667811\pi$
$542$	8.45818	+	5.93151i	0.363310	+	0.254780i
$543$	−14.3513			−0.615875
$544$	31.2824	−	2.62407i	1.34122	−	0.112506i
$545$	17.0651			0.730987
$546$	6.17605	+	4.33111i	0.264311	+	0.185354i
$547$	−8.81903	−	8.81903i	−0.377074	−	0.377074i	0.492971	−	0.870046i	$-0.335911\pi$
$547$	−8.81903	−	8.81903i	−0.377074	−	0.377074i	−0.870046	+	0.492971i	$0.835911\pi$
$548$	−30.1003	+	10.9069i	−1.28582	+	0.465918i
$549$	−4.17149	+	4.17149i	−0.178035	+	0.178035i
$550$	0.00307713	+	0.0175246i	0.000131209	+	0.000747253i
$551$		−	31.7075i		−	1.35079i
$552$	4.24529	+	7.38965i	0.180691	+	0.314525i
$553$			7.45305i			0.316936i
$554$	4.40694	−	0.773810i	0.187233	−	0.0328760i
$555$	4.97761	−	4.97761i	0.211288	−	0.211288i
$556$	−3.90465	−	1.82758i	−0.165594	−	0.0775066i
$557$	6.98592	+	6.98592i	0.296003	+	0.296003i	0.839446	−	0.543443i	$-0.182880\pi$
$557$	6.98592	+	6.98592i	0.296003	+	0.296003i	−0.543443	+	0.839446i	$0.682880\pi$
$558$	−2.90700	+	4.14530i	−0.123063	+	0.175485i
$559$	23.5651			0.996699
$560$	8.68699	+	0.785083i	0.367092	+	0.0331758i
$561$	0.0698194			0.00294778
$562$	−3.93844	+	5.61612i	−0.166133	+	0.236902i
$563$	3.94396	+	3.94396i	0.166218	+	0.166218i	0.785315	−	0.619097i	$-0.212501\pi$
$563$	3.94396	+	3.94396i	0.166218	+	0.166218i	−0.619097	+	0.785315i	$0.712501\pi$
$564$	8.54612	−	18.2589i	0.359856	−	0.768839i
$565$	−13.9975	+	13.9975i	−0.588877	+	0.588877i
$566$	22.5146	−	3.95331i	0.946358	−	0.166170i
$567$			2.18060i			0.0915765i
$568$	−33.0639	−	8.93559i	−1.38733	−	0.374929i
$569$		−	31.6307i		−	1.32603i	−0.748607	−	0.663014i	$-0.769277\pi$
$569$		−	31.6307i		−	1.32603i	0.748607	−	0.663014i	$-0.230723\pi$
$570$	−1.71111	−	9.74496i	−0.0716704	−	0.408172i
$571$	5.70590	−	5.70590i	0.238785	−	0.238785i	−0.577562	−	0.816347i	$-0.695996\pi$
$571$	5.70590	−	5.70590i	0.238785	−	0.238785i	0.816347	+	0.577562i	$0.195996\pi$
$572$	−0.0209687	−	0.0578686i	−0.000876745	−	0.00241961i
$573$	9.45512	+	9.45512i	0.394993	+	0.394993i
$574$	9.50578	+	6.66616i	0.396764	+	0.278240i
$575$	−3.01309			−0.125654
$576$	4.02972	−	6.91096i	0.167905	−	0.287957i
$577$	21.9772			0.914921			0.457461	−	0.889230i	$-0.348759\pi$
$577$	21.9772			0.914921			0.457461	+	0.889230i	$0.348759\pi$
$578$	15.9742	+	11.2023i	0.664439	+	0.465954i
$579$	5.88967	+	5.88967i	0.244766	+	0.244766i
$580$	3.08797	+	8.52206i	0.128221	+	0.353859i
$581$	11.5927	−	11.5927i	0.480948	−	0.480948i
$582$	−2.53497	−	14.4369i	−0.105078	−	0.598430i
$583$		−	0.0165943i		−	0.000687265i
$584$	−19.4677	−	5.26120i	−0.805581	−	0.217710i
$585$			2.44610i			0.101134i
$586$	−22.0006	+	3.86306i	−0.908835	+	0.159581i
$587$	−15.3747	+	15.3747i	−0.634583	+	0.634583i	−0.949214	−	0.314631i	$-0.898119\pi$
$587$	−15.3747	+	15.3747i	−0.634583	+	0.634583i	0.314631	+	0.949214i	$0.398119\pi$
$588$	−1.90337	+	4.06659i	−0.0784938	+	0.167703i
$589$	−17.7108	−	17.7108i	−0.729761	−	0.729761i
$590$	−5.28829	+	7.54096i	−0.217715	+	0.310457i
$591$	18.6669			0.767855
$592$	−2.53440	+	28.0433i	−0.104163	+	1.15257i
$593$	−16.9206			−0.694846			−0.347423	−	0.937708i	$-0.612943\pi$
$593$	−16.9206			−0.694846			−0.347423	+	0.937708i	$0.612943\pi$
$594$	0.0102159	−	0.0145676i	0.000419165	−	0.000597718i
$595$	8.55675	+	8.55675i	0.350792	+	0.350792i
$596$	31.1017	+	14.5572i	1.27398	+	0.596287i
$597$	2.59305	−	2.59305i	0.106127	−	0.106127i
$598$	10.2661	−	1.80262i	0.419813	−	0.0737145i
$599$			19.1715i			0.783327i	0.920109	+	0.391663i	$0.128100\pi$
$599$			19.1715i			0.783327i	−0.920109	+	0.391663i	$0.871900\pi$
$600$	1.40895	+	2.45252i	0.0575201	+	0.100124i
$601$			10.1428i			0.413735i	0.978369	+	0.206867i	$0.0663269\pi$
$601$			10.1428i			0.413735i	−0.978369	+	0.206867i	$0.933673\pi$
$602$	−5.13795	−	29.2612i	−0.209407	−	1.19260i
$603$	11.0105	−	11.0105i	0.448382	−	0.448382i
$604$	−24.0573	+	8.71717i	−0.978879	+	0.354696i
$605$	7.77806	+	7.77806i	0.316223	+	0.316223i
$606$	16.3161	+	11.4421i	0.662797	+	0.464803i
$607$	6.80048			0.276023			0.138011	−	0.990431i	$-0.455929\pi$
$607$	6.80048			0.276023			0.138011	+	0.990431i	$0.455929\pi$
$608$	30.2259	+	25.5474i	1.22582	+	1.03609i
$609$	9.88277			0.400470
$610$	6.83075	+	4.79023i	0.276569	+	0.193951i
$611$	−17.4349	−	17.4349i	−0.705339	−	0.705339i
$612$	10.4349	−	3.78110i	0.421807	−	0.152842i
$613$	18.1431	−	18.1431i	0.732793	−	0.732793i	−0.238379	−	0.971172i	$-0.576616\pi$
$613$	18.1431	−	18.1431i	0.732793	−	0.732793i	0.971172	+	0.238379i	$0.0766161\pi$
$614$	4.68213	+	26.6653i	0.188955	+	1.07612i
$615$			3.76487i			0.151814i
$616$	−0.0672847	+	0.0386544i	−0.00271098	+	0.00155743i
$617$			30.4488i			1.22582i	0.790151	+	0.612912i	$0.210002\pi$
$617$			30.4488i			1.22582i	−0.790151	+	0.612912i	$0.789998\pi$
$618$	−3.13618	+	0.550679i	−0.126156	+	0.0221516i
$619$	−12.1946	+	12.1946i	−0.490143	+	0.490143i	−0.908351	−	0.418208i	$-0.862658\pi$
$619$	−12.1946	+	12.1946i	−0.490143	+	0.490143i	0.418208	+	0.908351i	$0.362658\pi$
$620$	6.48500	+	3.03531i	0.260444	+	0.121901i
$621$	2.13057	+	2.13057i	0.0854969	+	0.0854969i
$622$	13.3942	−	19.0998i	0.537059	−	0.765833i
$623$	11.0427			0.442415
$624$	−6.26780	−	7.51326i	−0.250913	−	0.300771i
$625$	−1.00000			−0.0400000
$626$	22.1307	−	31.5578i	0.884519	−	1.26130i
$627$	0.0622403	+	0.0622403i	0.00248564	+	0.00248564i
$628$	12.3898	−	26.4709i	0.494405	−	1.05630i
$629$	−27.6229	+	27.6229i	−1.10140	+	1.10140i
$630$	3.03736	−	0.533328i	0.121011	−	0.0212483i
$631$			27.9943i			1.11444i	0.830366	+	0.557218i	$0.188131\pi$
$631$			27.9943i			1.11444i	−0.830366	+	0.557218i	$0.811869\pi$
$632$	2.52212	−	9.33246i	0.100324	−	0.371225i
$633$		−	17.8789i		−	0.710623i
$634$	8.05785	+	45.8904i	0.320018	+	1.82254i
$635$	10.1812	−	10.1812i	0.404028	−	0.404028i
$636$	−0.898670	−	2.48012i	−0.0356346	−	0.0983431i
$637$	3.88306	+	3.88306i	0.153852	+	0.153852i
$638$	−0.0660226	−	0.0463000i	−0.00261386	−	0.00183303i
$639$	−12.1092			−0.479033
$640$	−10.6119	−	3.92274i	−0.419472	−	0.155060i
$641$	5.01913			0.198244			0.0991219	−	0.995075i	$-0.468397\pi$
$641$	5.01913			0.198244			0.0991219	+	0.995075i	$0.468397\pi$
$642$	4.11169	+	2.88342i	0.162275	+	0.113800i
$643$	1.55218	+	1.55218i	0.0612118	+	0.0612118i	0.737050	−	0.675838i	$-0.236218\pi$
$643$	1.55218	+	1.55218i	0.0612118	+	0.0612118i	−0.675838	+	0.737050i	$0.736218\pi$
$644$	−4.47669	−	12.3546i	−0.176406	−	0.486839i
$645$	6.81210	−	6.81210i	0.268226	−	0.268226i
$646$	9.49567	+	54.0790i	0.373602	+	2.12771i
$647$		−	24.6915i		−	0.970722i	−0.874314	−	0.485361i	$-0.838688\pi$
$647$		−	24.6915i		−	0.970722i	0.874314	−	0.485361i	$-0.161312\pi$
$648$	0.737916	−	2.73047i	0.0289881	−	0.107263i
$649$		−	0.0819394i		−	0.00321640i
$650$	3.40718	−	0.598263i	0.133641	−	0.0234658i
$651$	5.52020	−	5.52020i	0.216354	−	0.216354i
$652$	−16.1102	+	34.4197i	−0.630925	+	1.34798i
$653$	−10.4301	−	10.4301i	−0.408161	−	0.408161i	0.472936	−	0.881097i	$-0.343194\pi$
$653$	−10.4301	−	10.4301i	−0.408161	−	0.408161i	−0.881097	+	0.472936i	$0.843194\pi$
$654$	−13.8566	+	19.7592i	−0.541837	+	0.772646i
$655$	−0.812825			−0.0317597
$656$	−9.64699	−	11.5639i	−0.376652	−	0.451495i
$657$	−7.12981			−0.278160
$658$	−17.8478	+	25.4505i	−0.695781	+	0.992165i
$659$	−15.4151	−	15.4151i	−0.600487	−	0.600487i	0.339955	−	0.940442i	$-0.389588\pi$
$659$	−15.4151	−	15.4151i	−0.600487	−	0.600487i	−0.940442	+	0.339955i	$0.889588\pi$
$660$	−0.0227899	−	0.0106669i	−0.000887097	−	0.000415207i
$661$	17.9150	−	17.9150i	0.696813	−	0.696813i	−0.266909	−	0.963722i	$-0.586002\pi$
$661$	17.9150	−	17.9150i	0.696813	−	0.696813i	0.963722	+	0.266909i	$0.0860022\pi$
$662$	−31.3321	+	5.50157i	−1.21776	+	0.213825i
$663$		−	13.5744i		−	0.527188i
$664$	−18.4390	+	10.5931i	−0.715574	+	0.411090i
$665$			15.2558i			0.591594i
$666$	1.72169	+	9.80521i	0.0667140	+	0.379944i
$667$	9.65605	−	9.65605i	0.373884	−	0.373884i
$668$	9.55956	−	3.46390i	0.369870	−	0.134022i
$669$	−3.80021	−	3.80021i	−0.146925	−	0.146925i
$670$	−18.0295	−	12.6436i	−0.696540	−	0.488466i
$671$	−0.0742223			−0.00286532
$672$	−7.96276	+	9.42097i	−0.307170	+	0.363422i
$673$	28.8891			1.11359			0.556796	−	0.830649i	$-0.312030\pi$
$673$	28.8891			1.11359			0.556796	+	0.830649i	$0.312030\pi$
$674$	8.28463	+	5.80981i	0.319112	+	0.223785i
$675$	0.707107	+	0.707107i	0.0272166	+	0.0272166i
$676$	13.1938	−	4.78076i	0.507452	−	0.183875i
$677$	10.8421	−	10.8421i	0.416695	−	0.416695i	−0.467368	−	0.884063i	$-0.654798\pi$
$677$	10.8421	−	10.8421i	0.416695	−	0.416695i	0.884063	+	0.467368i	$0.154798\pi$
$678$	−4.84153	−	27.5731i	−0.185938	−	1.05894i
$679$			22.6011i			0.867350i
$680$	−7.81886	−	13.6101i	−0.299840	−	0.521923i
$681$			2.71961i			0.104216i
$682$	−0.0627398	+	0.0110164i	−0.00240243	+	0.000421841i
$683$	−2.04256	+	2.04256i	−0.0781564	+	0.0781564i	−0.745104	−	0.666948i	$-0.767600\pi$
$683$	−2.04256	+	2.04256i	−0.0781564	+	0.0781564i	0.666948	+	0.745104i	$0.267600\pi$
$684$	12.6729	+	5.93155i	0.484559	+	0.226799i
$685$	11.3192	+	11.3192i	0.432484	+	0.432484i
$686$	16.3694	−	23.3423i	0.624986	−	0.891214i
$687$	7.18568			0.274151
$688$	−3.46845	+	38.3786i	−0.132234	+	1.46317i
$689$	−3.22630			−0.122912
$690$	2.44659	−	3.48878i	0.0931401	−	0.132815i
$691$	33.4347	+	33.4347i	1.27192	+	1.27192i	0.945081	+	0.326837i	$0.105983\pi$
$691$	33.4347	+	33.4347i	1.27192	+	1.27192i	0.326837	+	0.945081i	$0.394017\pi$
$692$	13.0478	−	27.8768i	0.496002	−	1.05972i
$693$	−0.0193994	+	0.0193994i	−0.000736922	+	0.000736922i
$694$	−19.0036	+	3.33682i	−0.721366	+	0.126664i
$695$			2.15559i			0.0817664i
$696$	−12.3749	−	3.34434i	−0.469068	−	0.126767i
$697$		−	20.8929i		−	0.791375i
$698$	7.03299	+	40.0537i	0.266203	+	1.51605i
$699$	18.5557	−	18.5557i	0.701839	−	0.701839i
$700$	−1.48575	−	4.10031i	−0.0561560	−	0.154977i
$701$	4.02037	+	4.02037i	0.151847	+	0.151847i	0.778943	−	0.627095i	$-0.215756\pi$
$701$	4.02037	+	4.02037i	0.151847	+	0.151847i	−0.627095	+	0.778943i	$0.715756\pi$
$702$	−2.83228	−	1.98620i	−0.106897	−	0.0749644i
$703$	−49.2487			−1.85745
$704$	0.0973323	−	0.0256326i	0.00366835	−	0.000966064i
$705$	−10.0800			−0.379634
$706$	37.2442	+	26.1184i	1.40170	+	0.982978i
$707$	−21.7278	−	21.7278i	−0.817158	−	0.817158i
$708$	−4.43746	−	12.2464i	−0.166770	−	0.460246i
$709$	18.0101	−	18.0101i	0.676385	−	0.676385i	−0.282795	−	0.959180i	$-0.591262\pi$
$709$	18.0101	−	18.0101i	0.676385	−	0.676385i	0.959180	+	0.282795i	$0.0912617\pi$
$710$	2.96166	+	16.8670i	0.111149	+	0.633006i
$711$		−	3.41789i		−	0.128181i
$712$	−13.8272	−	3.73684i	−0.518198	−	0.140044i
$713$		−	10.7871i		−	0.403981i
$714$	−16.8556	+	2.95966i	−0.630806	+	0.110763i
$715$	−0.0217614	+	0.0217614i	−0.000813830	+	0.000813830i
$716$	−13.3953	+	28.6192i	−0.500605	+	1.06955i
$717$	−5.23917	−	5.23917i	−0.195660	−	0.195660i
$718$	12.8489	−	18.3221i	0.479515	−	0.683776i
$719$	50.2917			1.87556			0.937782	−	0.347224i	$-0.112876\pi$
$719$	50.2917			1.87556			0.937782	+	0.347224i	$0.112876\pi$
$720$	−3.98376	−	0.360031i	−0.148466	−	0.0134176i
$721$	4.90971			0.182847
$722$	−24.3159	+	34.6739i	−0.904944	+	1.29043i
$723$	−13.8757	−	13.8757i	−0.516041	−	0.516041i
$724$	−25.9961	−	12.1675i	−0.966137	−	0.452202i
$725$	3.20471	−	3.20471i	0.119020	−	0.119020i
$726$	−15.3217	+	2.69033i	−0.568642	+	0.0998474i
$727$			15.1799i			0.562991i	0.959562	+	0.281496i	$0.0908305\pi$
$727$			15.1799i			0.562991i	−0.959562	+	0.281496i	$0.909169\pi$
$728$	7.51528	+	13.0816i	0.278535	+	0.484838i
$729$		−	1.00000i		−	0.0370370i
$730$	1.74380	+	9.93114i	0.0645409	+	0.367568i
$731$	−37.8032	+	37.8032i	−1.39820	+	1.39820i
$732$	−11.0930	+	4.01954i	−0.410008	+	0.148566i
$733$	−12.1524	−	12.1524i	−0.448859	−	0.448859i	0.446116	−	0.894975i	$-0.352807\pi$
$733$	−12.1524	−	12.1524i	−0.448859	−	0.448859i	−0.894975	+	0.446116i	$0.852807\pi$
$734$	5.03488	+	3.53084i	0.185841	+	0.130326i
$735$	2.24499			0.0828078
$736$	1.42475	+	16.9849i	0.0525170	+	0.626073i
$737$	0.195907			0.00721632
$738$	−4.35925	−	3.05704i	−0.160466	−	0.112531i
$739$	−17.9947	−	17.9947i	−0.661947	−	0.661947i	0.293892	−	0.955839i	$-0.405050\pi$
$739$	−17.9947	−	17.9947i	−0.661947	−	0.661947i	−0.955839	+	0.293892i	$0.905050\pi$
$740$	13.2366	−	4.79629i	0.486588	−	0.176315i
$741$	12.1009	−	12.1009i	0.444538	−	0.444538i
$742$	0.703436	+	4.00615i	0.0258240	+	0.147070i
$743$			19.2456i			0.706051i	0.935614	+	0.353026i	$0.114847\pi$
$743$			19.2456i			0.706051i	−0.935614	+	0.353026i	$0.885153\pi$
$744$	−8.78026	+	5.04417i	−0.321900	+	0.184928i
$745$		−	17.1700i		−	0.629059i
$746$	−34.2084	+	6.00662i	−1.25246	+	0.219918i
$747$	−5.31631	+	5.31631i	−0.194514	+	0.194514i
$748$	0.126471	+	0.0591950i	0.00462424	+	0.00216438i
$749$	−5.47544	−	5.47544i	−0.200068	−	0.200068i
$750$	0.811989	−	1.15787i	0.0296496	−	0.0422796i
$751$	−53.5813			−1.95521			−0.977604	−	0.210451i	$-0.932507\pi$
$751$	−53.5813			−1.95521			−0.977604	+	0.210451i	$0.932507\pi$
$752$	30.9609	−	25.8286i	1.12903	−	0.941872i
$753$	1.74810			0.0637044
$754$	−9.00175	+	12.8363i	−0.327824	+	0.467469i
$755$	9.04671	+	9.04671i	0.329244	+	0.329244i
$756$	−1.84878	+	3.94994i	−0.0672394	+	0.143658i
$757$	10.4133	−	10.4133i	0.378477	−	0.378477i	−0.492076	−	0.870552i	$-0.663762\pi$
$757$	10.4133	−	10.4133i	0.378477	−	0.378477i	0.870552	+	0.492076i	$0.163762\pi$
$758$	−30.3233	+	5.32445i	−1.10139	+	0.193393i
$759$			0.0379087i			0.00137600i
$760$	5.16257	−	19.1028i	0.187266	−	0.692931i
$761$		−	38.1651i		−	1.38348i	−0.722145	−	0.691742i	$-0.756844\pi$
$761$		−	38.1651i		−	1.38348i	0.722145	−	0.691742i	$-0.243156\pi$
$762$	3.52154	+	20.0556i	0.127572	+	0.726536i
$763$	26.3129	−	26.3129i	0.952590	−	0.952590i
$764$	9.11070	+	25.1434i	0.329614	+	0.909656i
$765$	−3.92404	−	3.92404i	−0.141874	−	0.141874i
$766$	−18.1083	−	12.6989i	−0.654279	−	0.458830i
$767$	−15.9309			−0.575230
$768$	13.1588	−	9.10202i	0.474826	−	0.328441i
$769$	−38.1071			−1.37418			−0.687089	−	0.726573i	$-0.741112\pi$
$769$	−38.1071			−1.37418			−0.687089	+	0.726573i	$0.741112\pi$
$770$	0.0317662	+	0.0222768i	0.00114477	+	0.000802801i
$771$	2.12874	+	2.12874i	0.0766648	+	0.0766648i
$772$	5.67513	+	15.6620i	0.204252	+	0.563688i
$773$	−32.9401	+	32.9401i	−1.18477	+	1.18477i	−0.206280	+	0.978493i	$0.566136\pi$
$773$	−32.9401	+	32.9401i	−1.18477	+	1.18477i	−0.978493	+	0.206280i	$0.933864\pi$
$774$	2.35621	+	13.4189i	0.0846923	+	0.482333i
$775$		−	3.58009i		−	0.128601i
$776$	7.64822	−	28.3003i	0.274555	−	1.01592i
$777$		−	15.3501i		−	0.550682i
$778$	33.5010	−	5.88240i	1.20107	−	0.210894i
$779$	18.6249	−	18.6249i	0.667307	−	0.667307i
$780$	−2.07388	+	4.43087i	−0.0742567	+	0.158651i
$781$	−0.107728	−	0.107728i	−0.00385481	−	0.00385481i
$782$	−13.5772	+	19.3607i	−0.485519	+	0.692337i
$783$	−4.53214			−0.161965
$784$	−6.89556	+	5.75249i	−0.246270	+	0.205446i
$785$	−14.6135			−0.521577
$786$	0.660005	−	0.941150i	0.0235416	−	0.0335697i
$787$	21.5631	+	21.5631i	0.768642	+	0.768642i	0.977867	−	0.209225i	$-0.0670942\pi$
$787$	21.5631	+	21.5631i	0.768642	+	0.768642i	−0.209225	+	0.977867i	$0.567094\pi$
$788$	33.8134	+	15.8264i	1.20455	+	0.563792i
$789$	8.41460	−	8.41460i	0.299568	−	0.299568i
$790$	−4.76080	+	0.835944i	−0.169382	+	0.0297415i
$791$			43.1658i			1.53480i
$792$	0.0308561	−	0.0177265i	0.00109642	−	0.000629884i
$793$			14.4305i			0.512441i
$794$	−4.32506	−	24.6317i	−0.153491	−	0.874148i
$795$	−0.932644	+	0.932644i	−0.0330775	+	0.0330775i
$796$	6.89553	−	2.49859i	0.244406	−	0.0885603i
$797$	7.81695	+	7.81695i	0.276891	+	0.276891i	0.831866	−	0.554976i	$-0.187273\pi$
$797$	7.81695	+	7.81695i	0.276891	+	0.276891i	−0.554976	+	0.831866i	$0.687273\pi$
$798$	−17.6643	−	12.3875i	−0.625309	−	0.438514i
$799$	55.9381			1.97895
$800$	0.472855	+	5.63706i	0.0167179	+	0.199300i
$801$	−5.06405			−0.178929
$802$	−16.9511	−	11.8874i	−0.598564	−	0.419758i
$803$	−0.0634294	−	0.0634294i	−0.00223837	−	0.00223837i
$804$	29.2795	−	10.6094i	1.03261	−	0.374165i
$805$	−4.64592	+	4.64592i	−0.163747	+	0.163747i
$806$	2.14184	+	12.1980i	0.0754430	+	0.429657i
$807$		−	21.9131i		−	0.771379i
$808$	19.8541	+	34.5595i	0.698465	+	1.21580i
$809$			8.21009i			0.288651i	0.989530	+	0.144326i	$0.0461013\pi$
$809$			8.21009i			0.288651i	−0.989530	+	0.144326i	$0.953899\pi$
$810$	−1.39290	+	0.244579i	−0.0489417	+	0.00859362i
$811$	−0.466318	+	0.466318i	−0.0163746	+	0.0163746i	−0.715247	−	0.698872i	$-0.753686\pi$
$811$	−0.466318	+	0.466318i	−0.0163746	+	0.0163746i	0.698872	+	0.715247i	$0.253686\pi$
$812$	17.9017	+	8.37892i	0.628226	+	0.294042i
$813$	5.16536	+	5.16536i	0.181157	+	0.181157i
$814$	−0.0719140	+	0.102547i	−0.00252058	+	0.00359429i
$815$	19.0017			0.665600
$816$	22.1076	+	1.99797i	0.773921	+	0.0699428i
$817$	−67.3992			−2.35800
$818$	27.2425	−	38.8471i	0.952512	−	1.35826i
$819$	3.77168	+	3.77168i	0.131793	+	0.131793i
$820$	−3.19198	+	6.81971i	−0.111469	+	0.238154i
$821$	22.1688	−	22.1688i	0.773696	−	0.773696i	−0.205054	−	0.978751i	$-0.565737\pi$
$821$	22.1688	−	22.1688i	0.773696	−	0.773696i	0.978751	+	0.205054i	$0.0657371\pi$
$822$	−22.2972	+	3.91515i	−0.777706	+	0.136557i
$823$		−	14.7926i		−	0.515636i	−0.966193	−	0.257818i	$-0.916996\pi$
$823$		−	14.7926i		−	0.515636i	0.966193	−	0.257818i	$-0.0830035\pi$
$824$	−6.14777	−	1.66145i	−0.214168	−	0.0578793i
$825$			0.0125814i			0.000438027i
$826$	3.47344	+	19.7816i	0.120856	+	0.688291i
$827$	27.9227	−	27.9227i	0.970967	−	0.970967i	−0.0286237	−	0.999590i	$-0.509112\pi$
$827$	27.9227	−	27.9227i	0.970967	−	0.970967i	0.999590	+	0.0286237i	$0.00911246\pi$
$828$	2.05296	+	5.66569i	0.0713454	+	0.196896i
$829$	−0.798074	−	0.798074i	−0.0277182	−	0.0277182i	0.693112	−	0.720830i	$-0.256239\pi$
$829$	−0.798074	−	0.798074i	−0.0277182	−	0.0277182i	−0.720830	+	0.693112i	$0.756239\pi$
$830$	8.70537	+	6.10486i	0.302168	+	0.211903i
$831$	3.16385			0.109753
$832$	−4.98354	−	18.9236i	−0.172773	−	0.656057i
$833$	−12.4584			−0.431659
$834$	−2.49591	−	1.75032i	−0.0864263	−	0.0606086i
$835$	−3.59485	−	3.59485i	−0.124405	−	0.124405i
$836$	0.0599731	+	0.165512i	0.00207421	+	0.00572434i
$837$	−2.53151	+	2.53151i	−0.0875018	+	0.0875018i
$838$	5.72931	+	32.6291i	0.197916	+	1.12715i
$839$			29.3983i			1.01494i	0.861669	+	0.507470i	$0.169419\pi$
$839$			29.3983i			1.01494i	−0.861669	+	0.507470i	$0.830581\pi$
$840$	5.95406	+	1.60910i	0.205435	+	0.0555192i
$841$		−	8.45973i		−	0.291715i
$842$	27.8680	−	4.89332i	0.960396	−	0.168635i
$843$	−3.42973	+	3.42973i	−0.118126	+	0.118126i
$844$	15.1583	−	32.3859i	0.521770	−	1.11477i
$845$	−4.96149	−	4.96149i	−0.170680	−	0.170680i
$846$	8.18483	−	11.6714i	0.281400	−	0.401270i
$847$	23.9862			0.824177
$848$	0.474866	−	5.25441i	0.0163070	−	0.180437i
$849$	16.1638			0.554739
$850$	−4.50607	+	6.42554i	−0.154557	+	0.220394i
$851$	−14.9980	−	14.9980i	−0.514123	−	0.514123i
$852$	−21.9347	−	10.2666i	−0.751470	−	0.351727i
$853$	24.2137	−	24.2137i	0.829060	−	0.829060i	−0.158326	−	0.987387i	$-0.550610\pi$
$853$	24.2137	−	24.2137i	0.829060	−	0.829060i	0.987387	+	0.158326i	$0.0506098\pi$
$854$	17.9186	−	3.14630i	0.613161	−	0.107664i
$855$		−	6.99615i		−	0.239263i
$856$	5.00327	+	8.70906i	0.171008	+	0.297669i
$857$			16.2011i			0.553419i	0.960954	+	0.276709i	$0.0892440\pi$
$857$			16.2011i			0.553419i	−0.960954	+	0.276709i	$0.910756\pi$
$858$	−0.00752697	−	0.0428670i	−0.000256966	−	0.00146345i
$859$	0.266646	−	0.266646i	0.00909783	−	0.00909783i	−0.702543	−	0.711641i	$-0.747952\pi$
$859$	0.266646	−	0.266646i	0.00909783	−	0.00909783i	0.711641	+	0.702543i	$0.247952\pi$
$860$	18.1150	−	6.56395i	0.617715	−	0.223829i
$861$	5.80512	+	5.80512i	0.197838	+	0.197838i
$862$	15.1877	+	10.6508i	0.517296	+	0.362767i
$863$	10.2561			0.349121			0.174560	−	0.984646i	$-0.444150\pi$
$863$	10.2561			0.349121			0.174560	+	0.984646i	$0.444150\pi$
$864$	3.65164	−	4.32036i	0.124231	−	0.146982i
$865$	−15.3896			−0.523262
$866$	0.348492	+	0.244389i	0.0118422	+	0.00830467i
$867$	9.75534	+	9.75534i	0.331309	+	0.331309i
$868$	14.6795	−	5.31912i	0.498255	−	0.180543i
$869$	0.0304068	−	0.0304068i	0.00103148	−	0.00103148i
$870$	1.10846	+	6.31283i	0.0375804	+	0.214025i
$871$		−	38.0886i		−	1.29058i
$872$	−41.8524	+	24.0438i	−1.41730	+	0.814226i
$873$		−	10.3646i		−	0.350789i
$874$	−29.3624	+	5.15572i	−0.993198	+	0.174395i
$875$	−1.54192	+	1.54192i	−0.0521263	+	0.0521263i
$876$	−12.9150	−	6.04487i	−0.436356	−	0.204237i
$877$	−20.4974	−	20.4974i	−0.692149	−	0.692149i	0.270555	−	0.962704i	$-0.412793\pi$
$877$	−20.4974	−	20.4974i	−0.692149	−	0.692149i	−0.962704	+	0.270555i	$0.912793\pi$
$878$	24.6323	−	35.1251i	0.831301	−	1.18541i
$879$	−15.7948			−0.532744
$880$	−0.0322381	−	0.0386440i	−0.00108675	−	0.00130269i
$881$	−56.8144			−1.91413			−0.957063	−	0.289881i	$-0.906384\pi$
$881$	−56.8144			−1.91413			−0.957063	+	0.289881i	$0.906384\pi$
$882$	−1.82291	+	2.59942i	−0.0613805	+	0.0875270i
$883$	26.2082	+	26.2082i	0.881978	+	0.881978i	0.993735	−	0.111758i	$-0.0356481\pi$
$883$	26.2082	+	26.2082i	0.881978	+	0.881978i	−0.111758	+	0.993735i	$0.535648\pi$
$884$	11.5088	−	24.5888i	0.387084	−	0.827011i
$885$	−4.60522	+	4.60522i	−0.154803	+	0.154803i
$886$	−7.86698	+	1.38136i	−0.264296	+	0.0464075i
$887$			26.0161i			0.873537i	0.899574	+	0.436768i	$0.143877\pi$
$887$			26.0161i			0.873537i	−0.899574	+	0.436768i	$0.856123\pi$
$888$	−5.19449	+	19.2209i	−0.174316	+	0.645011i
$889$		−	31.3971i		−	1.05302i
$890$	1.23856	+	7.05373i	0.0415165	+	0.236442i
$891$	0.00889637	−	0.00889637i	0.000298040	−	0.000298040i
$892$	−3.66178	−	10.1057i	−0.122606	−	0.338362i
$893$	49.8659	+	49.8659i	1.66870	+	1.66870i
$894$	19.8807	+	13.9418i	0.664909	+	0.466284i
$895$	15.7995			0.528118
$896$	−22.4112	+	10.3141i	−0.748704	+	0.344570i
$897$	7.37030			0.246087
$898$	−12.1352	−	8.51013i	−0.404958	−	0.283987i
$899$	11.4731	+	11.4731i	0.382651	+	0.382651i
$900$	0.681349	+	1.88036i	0.0227116	+	0.0626788i
$901$	5.17564	−	5.17564i	0.172425	−	0.172425i
$902$	−0.0115850	−	0.0659780i	−0.000385739	−	0.00219683i
$903$		−	21.0074i		−	0.699081i
$904$	14.6073	−	54.0508i	0.485833	−	1.79770i
$905$			14.3513i			0.477055i
$906$	−17.8208	+	3.12913i	−0.592056	+	0.103959i
$907$	−27.6233	+	27.6233i	−0.917218	+	0.917218i	−0.996826	−	0.0796085i	$-0.974633\pi$
$907$	−27.6233	+	27.6233i	−0.917218	+	0.917218i	0.0796085	+	0.996826i	$0.474633\pi$
$908$	−2.30577	+	4.92632i	−0.0765198	+	0.163486i
$909$	9.96414	+	9.96414i	0.330490	+	0.330490i
$910$	4.33111	−	6.17605i	0.143575	−	0.204734i
$911$	−5.83194			−0.193221			−0.0966104	−	0.995322i	$-0.530800\pi$
$911$	−5.83194			−0.193221			−0.0966104	+	0.995322i	$0.530800\pi$
$912$	17.9267	+	21.4889i	0.593612	+	0.711567i
$913$	−0.0945918			−0.00313053
$914$	−4.62986	+	6.60207i	−0.153142	+	0.218377i
$915$	4.17149	+	4.17149i	0.137905	+	0.137905i
$916$	13.0162	+	6.09224i	0.430066	+	0.201293i
$917$	−1.25331	+	1.25331i	−0.0413879	+	0.0413879i
$918$	7.72982	−	1.35727i	0.255122	−	0.0447966i
$919$			11.8292i			0.390208i	0.980783	+	0.195104i	$0.0625045\pi$
$919$			11.8292i			0.390208i	−0.980783	+	0.195104i	$0.937496\pi$
$920$	7.38965	−	4.24529i	0.243630	−	0.139963i
$921$			19.1437i			0.630805i
$922$	0.616653	+	3.51191i	0.0203084	+	0.115659i
$923$	−20.9447	+	20.9447i	−0.689405	+	0.689405i
$924$	−0.0515876	+	0.0186927i	−0.00169711	+	0.000614946i
$925$	−4.97761	−	4.97761i	−0.163663	−	0.163663i
$926$	−43.0747	−	30.2072i	−1.41552	−	0.992671i
$927$	−2.25154			−0.0739503
$928$	−19.5805	−	16.5497i	−0.642760	−	0.543272i
$929$	−45.8141			−1.50311			−0.751556	−	0.659669i	$-0.770696\pi$
$929$	−45.8141			−1.50311			−0.751556	+	0.659669i	$0.770696\pi$
$930$	4.14530	+	2.90700i	0.135930	+	0.0953242i
$931$	−11.1060	−	11.1060i	−0.363986	−	0.363986i
$932$	49.3438	−	17.8797i	1.61631	−	0.585670i
$933$	11.6641	−	11.6641i	0.381867	−	0.381867i
$934$	−4.96932	−	28.3009i	−0.162601	−	0.926033i
$935$		−	0.0698194i		−	0.00228334i
$936$	−3.44643	−	5.99911i	−0.112650	−	0.196087i
$937$		−	6.21014i		−	0.202876i	−0.994842	−	0.101438i	$-0.967656\pi$
$937$		−	6.21014i		−	0.202876i	0.994842	−	0.101438i	$-0.0323444\pi$
$938$	−47.2953	+	8.30454i	−1.54425	+	0.271153i
$939$	19.2721	−	19.2721i	0.628922	−	0.628922i
$940$	−18.2589	−	8.54612i	−0.595540	−	0.278744i
$941$	−2.43886	−	2.43886i	−0.0795045	−	0.0795045i	0.666236	−	0.745741i	$-0.267904\pi$
$941$	−2.43886	−	2.43886i	−0.0795045	−	0.0795045i	−0.745741	+	0.666236i	$0.767904\pi$
$942$	11.8660	−	16.9206i	0.386614	−	0.551302i
$943$	11.3439			0.369408
$944$	2.34480	−	25.9453i	0.0763167	−	0.844448i
$945$	2.18060			0.0709349
$946$	−0.0984178	+	0.140341i	−0.00319984	+	0.00456289i
$947$	−33.4856	−	33.4856i	−1.08814	−	1.08814i	−0.995720	−	0.0924159i	$-0.970541\pi$
$947$	−33.4856	−	33.4856i	−1.08814	−	1.08814i	−0.0924159	−	0.995720i	$-0.529459\pi$
$948$	2.89779	−	6.19118i	0.0941160	−	0.201080i
$949$	−12.3321	+	12.3321i	−0.400317	+	0.400317i
$950$	−9.74496	+	1.71111i	−0.316168	+	0.0555157i
$951$			32.9459i			1.06834i
$952$	−33.0416	−	8.92957i	−1.07089	−	0.289409i
$953$		−	14.3013i		−	0.463266i	−0.972803	−	0.231633i	$-0.925593\pi$
$953$		−	14.3013i		−	0.463266i	0.972803	−	0.231633i	$-0.0744068\pi$
$954$	−0.322589	−	1.83718i	−0.0104442	−	0.0594809i
$955$	9.45512	−	9.45512i	0.305961	−	0.305961i
$956$	−5.04832	−	13.9322i	−0.163274	−	0.450599i
$957$	−0.0403196	−	0.0403196i	−0.00130335	−	0.00130335i
$958$	−42.4432	−	29.7644i	−1.37128	−	0.961643i
$959$	34.9064			1.12719
$960$	−6.91096	−	4.02972i	−0.223050	−	0.130059i
$961$	−18.1829			−0.586546
$962$	19.9375	+	13.9817i	0.642811	+	0.450787i
$963$	2.51098	+	2.51098i	0.0809152	+	0.0809152i
$964$	−13.3702	−	36.8986i	−0.430625	−	1.18842i
$965$	5.88967	−	5.88967i	0.189595	−	0.189595i
$966$	−1.60696	−	9.15183i	−0.0517031	−	0.294455i
$967$			53.0546i			1.70612i	0.521812	+	0.853060i	$0.325256\pi$
$967$			53.0546i			1.70612i	−0.521812	+	0.853060i	$0.674744\pi$
$968$	−30.0348	−	8.11696i	−0.965354	−	0.260889i
$969$			38.8246i			1.24723i
$970$	−14.4369	+	2.53497i	−0.463542	+	0.0813928i
$971$	4.58090	−	4.58090i	0.147008	−	0.147008i	−0.629772	−	0.776780i	$-0.716852\pi$
$971$	4.58090	−	4.58090i	0.147008	−	0.147008i	0.776780	+	0.629772i	$0.216852\pi$
$972$	0.847831	−	1.81140i	0.0271942	−	0.0581008i
$973$	3.32375	+	3.32375i	0.106554	+	0.106554i
$974$	−27.8774	+	39.7524i	−0.893248	+	1.27375i
$975$	2.44610			0.0783378
$976$	−23.5018	−	2.12396i	−0.752273	−	0.0679864i
$977$	11.2092			0.358614			0.179307	−	0.983793i	$-0.442615\pi$
$977$	11.2092			0.358614			0.179307	+	0.983793i	$0.442615\pi$
$978$	−15.4292	+	22.0016i	−0.493370	+	0.703533i
$979$	−0.0450516	−	0.0450516i	−0.00143986	−	0.00143986i
$980$	4.06659	+	1.90337i	0.129902	+	0.0608010i
$981$	−12.0668	+	12.0668i	−0.385264	+	0.385264i
$982$	34.7137	−	6.09534i	1.10776	−	0.194510i
$983$			20.1018i			0.641147i	0.947224	+	0.320573i	$0.103876\pi$
$983$			20.1018i			0.641147i	−0.947224	+	0.320573i	$0.896124\pi$
$984$	−5.30452	−	9.23343i	−0.169102	−	0.294351i
$985$		−	18.6669i		−	0.594778i
$986$	−6.15134	−	35.0326i	−0.195899	−	1.11567i
$987$	−15.5425	+	15.5425i	−0.494723	+	0.494723i
$988$	32.1791	−	11.6601i	1.02376	−	0.370957i
$989$	−20.5254	−	20.5254i	−0.652671	−	0.652671i
$990$	−0.0145676	−	0.0102159i	−0.000462990	−	0.000324683i
$991$	20.7088			0.657835			0.328918	−	0.944359i	$-0.393316\pi$
$991$	20.7088			0.657835			0.328918	+	0.944359i	$0.393316\pi$
$992$	−20.1812	+	1.69286i	−0.640754	+	0.0537485i
$993$	−22.4941			−0.713828
$994$	30.5741	+	21.4408i	0.969751	+	0.680062i
$995$	−2.59305	−	2.59305i	−0.0822052	−	0.0822052i
$996$	−14.1373	+	5.12266i	−0.447958	+	0.162318i
$997$	0.704128	−	0.704128i	0.0223000	−	0.0223000i	−0.695869	−	0.718169i	$-0.744981\pi$
$997$	0.704128	−	0.704128i	0.0223000	−	0.0223000i	0.718169	+	0.695869i	$0.244981\pi$
$998$	−5.07766	−	28.9179i	−0.160730	−	0.915379i
$999$			7.03940i			0.222717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.s.c.61.7	✓	20
3.2	odd	2		720.2.t.d.541.4		20
4.3	odd	2		960.2.s.c.721.4		20
8.3	odd	2		1920.2.s.f.1441.9		20
8.5	even	2		1920.2.s.e.1441.2		20
12.11	even	2		2880.2.t.d.721.4		20
16.3	odd	4		1920.2.s.f.481.7		20
16.5	even	4	inner	240.2.s.c.181.7	yes	20
16.11	odd	4		960.2.s.c.241.2		20
16.13	even	4		1920.2.s.e.481.4		20
48.5	odd	4		720.2.t.d.181.4		20
48.11	even	4		2880.2.t.d.2161.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.s.c.61.7	✓	20	1.1	even	1	trivial
240.2.s.c.181.7	yes	20	16.5	even	4	inner
720.2.t.d.181.4		20	48.5	odd	4
720.2.t.d.541.4		20	3.2	odd	2
960.2.s.c.241.2		20	16.11	odd	4
960.2.s.c.721.4		20	4.3	odd	2
1920.2.s.e.481.4		20	16.13	even	4
1920.2.s.e.1441.2		20	8.5	even	2
1920.2.s.f.481.7		20	16.3	odd	4
1920.2.s.f.1441.9		20	8.3	odd	2
2880.2.t.d.721.4		20	12.11	even	2
2880.2.t.d.2161.2		20	48.11	even	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15787 + 0.811989i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.681349 + 1.88036i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.244579 + 1.39290i) q^{6} -2.18060i q^{7} +(-0.737916 + 2.73047i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(1.15787 + 0.811989i) q^{2} +(0.707107 + 0.707107i) q^{3} +(0.681349 + 1.88036i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.244579 + 1.39290i) q^{6} -2.18060i q^{7} +(-0.737916 + 2.73047i) q^{8} +1.00000i q^{9} +(1.39290 - 0.244579i) q^{10} +(-0.00889637 + 0.00889637i) q^{11} +(-0.847831 + 1.81140i) q^{12} +(1.72965 + 1.72965i) q^{13} +(1.77062 - 2.52486i) q^{14} +1.00000 q^{15} +(-3.07153 + 2.56237i) q^{16} -5.54943 q^{17} +(-0.811989 + 1.15787i) q^{18} +(-4.94702 - 4.94702i) q^{19} +(1.81140 + 0.847831i) q^{20} +(1.54192 - 1.54192i) q^{21} +(-0.0175246 + 0.00307713i) q^{22} -3.01309i q^{23} +(-2.45252 + 1.40895i) q^{24} -1.00000i q^{25} +(0.598263 + 3.40718i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.10031 - 1.48575i) q^{28} +(3.20471 + 3.20471i) q^{29} +(1.15787 + 0.811989i) q^{30} +3.58009 q^{31} +(-5.63706 + 0.472855i) q^{32} -0.0125814 q^{33} +(-6.42554 - 4.50607i) q^{34} +(-1.54192 - 1.54192i) q^{35} +(-1.88036 + 0.681349i) q^{36} +(4.97761 - 4.97761i) q^{37} +(-1.71111 - 9.74496i) q^{38} +2.44610i q^{39} +(1.40895 + 2.45252i) q^{40} +3.76487i q^{41} +(3.03736 - 0.533328i) q^{42} +(6.81210 - 6.81210i) q^{43} +(-0.0227899 - 0.0106669i) q^{44} +(0.707107 + 0.707107i) q^{45} +(2.44659 - 3.48878i) q^{46} -10.0800 q^{47} +(-3.98376 - 0.360031i) q^{48} +2.24499 q^{49} +(0.811989 - 1.15787i) q^{50} +(-3.92404 - 3.92404i) q^{51} +(-2.07388 + 4.43087i) q^{52} +(-0.932644 + 0.932644i) q^{53} +(-1.39290 + 0.244579i) q^{54} +0.0125814i q^{55} +(5.95406 + 1.60910i) q^{56} -6.99615i q^{57} +(1.10846 + 6.31283i) q^{58} +(-4.60522 + 4.60522i) q^{59} +(0.681349 + 1.88036i) q^{60} +(4.17149 + 4.17149i) q^{61} +(4.14530 + 2.90700i) q^{62} +2.18060 q^{63} +(-6.91096 - 4.02972i) q^{64} +2.44610 q^{65} +(-0.0145676 - 0.0102159i) q^{66} +(-11.0105 - 11.0105i) q^{67} +(-3.78110 - 10.4349i) q^{68} +(2.13057 - 2.13057i) q^{69} +(-0.533328 - 3.03736i) q^{70} +12.1092i q^{71} +(-2.73047 - 0.737916i) q^{72} +7.12981i q^{73} +(9.80521 - 1.72169i) q^{74} +(0.707107 - 0.707107i) q^{75} +(5.93155 - 12.6729i) q^{76} +(0.0193994 + 0.0193994i) q^{77} +(-1.98620 + 2.83228i) q^{78} -3.41789 q^{79} +(-0.360031 + 3.98376i) q^{80} -1.00000 q^{81} +(-3.05704 + 4.35925i) q^{82} +(5.31631 + 5.31631i) q^{83} +(3.94994 + 1.84878i) q^{84} +(-3.92404 + 3.92404i) q^{85} +(13.4189 - 2.35621i) q^{86} +4.53214i q^{87} +(-0.0177265 - 0.0308561i) q^{88} +5.06405i q^{89} +(0.244579 + 1.39290i) q^{90} +(3.77168 - 3.77168i) q^{91} +(5.66569 - 2.05296i) q^{92} +(2.53151 + 2.53151i) q^{93} +(-11.6714 - 8.18483i) q^{94} -6.99615 q^{95} +(-4.32036 - 3.65164i) q^{96} -10.3646 q^{97} +(2.59942 + 1.82291i) q^{98} +(-0.00889637 - 0.00889637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{4} + 12 q^{8}+O(q^{10}) \) 20 * q + 4 * q^4 + 12 * q^8	\( 20 q + 4 q^{4} + 12 q^{8} + 8 q^{11} - 4 q^{14} + 20 q^{15} - 20 q^{16} - 24 q^{17} - 4 q^{18} - 4 q^{19} - 8 q^{20} + 8 q^{22} + 28 q^{26} - 8 q^{28} + 16 q^{29} - 40 q^{32} + 16 q^{33} - 44 q^{34} + 16 q^{37} - 8 q^{38} + 12 q^{40} + 12 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} - 16 q^{48} - 52 q^{49} + 4 q^{50} + 4 q^{51} - 56 q^{52} - 16 q^{53} + 64 q^{56} + 72 q^{58} - 16 q^{59} + 4 q^{60} - 4 q^{61} - 44 q^{62} - 8 q^{63} - 56 q^{64} - 32 q^{66} - 8 q^{67} - 32 q^{68} - 4 q^{69} + 20 q^{70} + 4 q^{72} + 60 q^{74} + 28 q^{76} - 40 q^{77} - 28 q^{78} + 56 q^{79} - 16 q^{80} - 20 q^{81} - 24 q^{82} - 48 q^{83} + 24 q^{84} + 4 q^{85} + 64 q^{86} + 40 q^{88} - 8 q^{91} + 88 q^{92} + 16 q^{93} - 20 q^{94} + 56 q^{97} - 48 q^{98} + 8 q^{99}+O(q^{100}) \) 20 * q + 4 * q^4 + 12 * q^8 + 8 * q^11 - 4 * q^14 + 20 * q^15 - 20 * q^16 - 24 * q^17 - 4 * q^18 - 4 * q^19 - 8 * q^20 + 8 * q^22 + 28 * q^26 - 8 * q^28 + 16 * q^29 - 40 * q^32 + 16 * q^33 - 44 * q^34 + 16 * q^37 - 8 * q^38 + 12 * q^40 + 12 * q^42 - 8 * q^43 + 24 * q^44 - 12 * q^46 - 16 * q^48 - 52 * q^49 + 4 * q^50 + 4 * q^51 - 56 * q^52 - 16 * q^53 + 64 * q^56 + 72 * q^58 - 16 * q^59 + 4 * q^60 - 4 * q^61 - 44 * q^62 - 8 * q^63 - 56 * q^64 - 32 * q^66 - 8 * q^67 - 32 * q^68 - 4 * q^69 + 20 * q^70 + 4 * q^72 + 60 * q^74 + 28 * q^76 - 40 * q^77 - 28 * q^78 + 56 * q^79 - 16 * q^80 - 20 * q^81 - 24 * q^82 - 48 * q^83 + 24 * q^84 + 4 * q^85 + 64 * q^86 + 40 * q^88 - 8 * q^91 + 88 * q^92 + 16 * q^93 - 20 * q^94 + 56 * q^97 - 48 * q^98 + 8 * q^99

Introduction

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