LMFDB - Embedded newform 120.2.m.b.59.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,2,Mod(59,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("120.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	120.m (of order $2$, degree $1$, 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:	$0.958204824255$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 192x^{12} + 672x^{10} + 1092x^{8} + 880x^{6} + 352x^{4} + 64x^{2} + 4 $ x^16 + 24x^14 + 192x^12 + 672x^10 + 1092x^8 + 880x^6 + 352x^4 + 64*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.9
Root			$-3.49930i$ of defining polynomial
Character	$\chi$	$=$	120.59
Dual form			120.2.m.b.59.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.541196 - 1.30656i) q^{2} +(1.30656 - 1.13705i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(-2.10100 + 0.765367i) q^{5} +(-0.778527 - 2.32248i) q^{6} +2.27411 q^{7} +(-2.61313 + 1.08239i) q^{8} +(0.414214 - 2.97127i) q^{9} +O(q^{10})$	\(q+(0.541196 - 1.30656i) q^{2} +(1.30656 - 1.13705i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(-2.10100 + 0.765367i) q^{5} +(-0.778527 - 2.32248i) q^{6} +2.27411 q^{7} +(-2.61313 + 1.08239i) q^{8} +(0.414214 - 2.97127i) q^{9} +(-0.137055 + 3.15931i) q^{10} +4.20201i q^{11} +(-3.45580 - 0.239721i) q^{12} +3.21608 q^{13} +(1.23074 - 2.97127i) q^{14} +(-1.87483 + 3.38896i) q^{15} +4.00000i q^{16} +1.53073 q^{17} +(-3.65798 - 2.14923i) q^{18} -4.82843 q^{19} +(4.05366 + 1.88887i) q^{20} +(2.97127 - 2.58579i) q^{21} +(5.49019 + 2.27411i) q^{22} -1.08239i q^{23} +(-2.18347 + 4.38548i) q^{24} +(3.82843 - 3.21608i) q^{25} +(1.74053 - 4.20201i) q^{26} +(-2.83730 - 4.35313i) q^{27} +(-3.21608 - 3.21608i) q^{28} -1.74053 q^{29} +(3.41323 + 4.28367i) q^{30} +6.82843i q^{31} +(5.22625 + 2.16478i) q^{32} +(4.77791 + 5.49019i) q^{33} +(0.828427 - 2.00000i) q^{34} +(-4.77791 + 1.74053i) q^{35} +(-4.78779 + 3.61622i) q^{36} -7.76429 q^{37} +(-2.61313 + 6.30864i) q^{38} +(4.20201 - 3.65685i) q^{39} +(4.66176 - 4.27411i) q^{40} -2.46148i q^{41} +(-1.77045 - 5.28156i) q^{42} +8.70626i q^{43} +(5.94253 - 5.94253i) q^{44} +(1.40385 + 6.55967i) q^{45} +(-1.41421 - 0.585786i) q^{46} +1.08239i q^{47} +(4.54822 + 5.22625i) q^{48} -1.82843 q^{49} +(-2.13008 - 6.74261i) q^{50} +(2.00000 - 1.74053i) q^{51} +(-4.54822 - 4.54822i) q^{52} -11.0866i q^{53} +(-7.22317 + 1.35121i) q^{54} +(-3.21608 - 8.82843i) q^{55} +(-5.94253 + 2.46148i) q^{56} +(-6.30864 + 5.49019i) q^{57} +(-0.941967 + 2.27411i) q^{58} -4.20201i q^{59} +(7.44411 - 2.14130i) q^{60} -8.48528i q^{61} +(8.92177 + 3.69552i) q^{62} +(0.941967 - 6.75699i) q^{63} +(5.65685 - 5.65685i) q^{64} +(-6.75699 + 2.46148i) q^{65} +(9.75906 - 3.27137i) q^{66} +2.27411i q^{67} +(-2.16478 - 2.16478i) q^{68} +(-1.23074 - 1.41421i) q^{69} +(-0.311677 + 7.18461i) q^{70} -11.8851 q^{71} +(2.13368 + 8.21264i) q^{72} -4.54822i q^{73} +(-4.20201 + 10.1445i) q^{74} +(1.34523 - 8.55514i) q^{75} +(6.82843 + 6.82843i) q^{76} +9.55582i q^{77} +(-2.50380 - 7.46926i) q^{78} +0.485281i q^{79} +(-3.06147 - 8.40401i) q^{80} +(-8.65685 - 2.46148i) q^{81} +(-3.21608 - 1.33214i) q^{82} +6.94269 q^{83} +(-7.85886 - 0.545152i) q^{84} +(-3.21608 + 1.17157i) q^{85} +(11.3753 + 4.71179i) q^{86} +(-2.27411 + 1.97908i) q^{87} +(-4.54822 - 10.9804i) q^{88} +8.40401i q^{89} +(9.33037 + 1.71585i) q^{90} +7.31371 q^{91} +(-1.53073 + 1.53073i) q^{92} +(7.76429 + 8.92177i) q^{93} +(1.41421 + 0.585786i) q^{94} +(10.1445 - 3.69552i) q^{95} +(9.28991 - 3.11411i) q^{96} -10.9804i q^{97} +(-0.989538 + 2.38896i) q^{98} +(12.4853 + 1.74053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^9	$ 16 q - 16 q^{9} + 16 q^{10} - 32 q^{19} - 32 q^{24} + 16 q^{25} + 16 q^{30} - 32 q^{34} - 32 q^{36} + 32 q^{40} + 16 q^{49} + 32 q^{51} + 32 q^{54} + 64 q^{66} - 64 q^{70} + 32 q^{75} + 64 q^{76} - 48 q^{81} + 32 q^{84} - 16 q^{90} - 64 q^{91} + 64 q^{96} + 64 q^{99}+O(q^{100}) $ 16 * q - 16 * q^9 + 16 * q^10 - 32 * q^19 - 32 * q^24 + 16 * q^25 + 16 * q^30 - 32 * q^34 - 32 * q^36 + 32 * q^40 + 16 * q^49 + 32 * q^51 + 32 * q^54 + 64 * q^66 - 64 * q^70 + 32 * q^75 + 64 * q^76 - 48 * q^81 + 32 * q^84 - 16 * q^90 - 64 * q^91 + 64 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.541196	−	1.30656i	0.382683	−	0.923880i
$2$	0.541196	−	1.30656i	0.382683	−	0.923880i
$3$	1.30656	−	1.13705i	0.754344	−	0.656479i
$3$	1.30656	−	1.13705i	0.754344	−	0.656479i
$4$	−1.41421	−	1.41421i	−0.707107	−	0.707107i
$5$	−2.10100	+	0.765367i	−0.939597	+	0.342282i
$5$	−2.10100	+	0.765367i	−0.939597	+	0.342282i
$6$	−0.778527	−	2.32248i	−0.317832	−	0.948147i
$7$	2.27411			0.859533			0.429766	−	0.902940i	$-0.358596\pi$
$7$	2.27411			0.859533			0.429766	+	0.902940i	$0.358596\pi$
$8$	−2.61313	+	1.08239i	−0.923880	+	0.382683i
$9$	0.414214	−	2.97127i	0.138071	−	0.990422i
$10$	−0.137055	+	3.15931i	−0.0433405	+	0.999060i
$11$			4.20201i			1.26695i	0.773762	+	0.633476i	$0.218373\pi$
$11$			4.20201i			1.26695i	−0.773762	+	0.633476i	$0.781627\pi$
$12$	−3.45580	−	0.239721i	−0.997603	−	0.0692015i
$13$	3.21608			0.891979			0.445990	−	0.895038i	$-0.352852\pi$
$13$	3.21608			0.891979			0.445990	+	0.895038i	$0.352852\pi$
$14$	1.23074	−	2.97127i	0.328929	−	0.794104i
$15$	−1.87483	+	3.38896i	−0.484079	+	0.875024i
$16$			4.00000i			1.00000i
$17$	1.53073			0.371257			0.185629	−	0.982620i	$-0.440568\pi$
$17$	1.53073			0.371257			0.185629	+	0.982620i	$0.440568\pi$
$18$	−3.65798	−	2.14923i	−0.862193	−	0.506579i
$19$	−4.82843			−1.10772			−0.553859	−	0.832611i	$-0.686845\pi$
$19$	−4.82843			−1.10772			−0.553859	+	0.832611i	$0.686845\pi$
$20$	4.05366	+	1.88887i	0.906426	+	0.422365i
$21$	2.97127	−	2.58579i	0.648384	−	0.564265i
$22$	5.49019	+	2.27411i	1.17051	+	0.484842i
$23$		−	1.08239i		−	0.225694i	−0.993612	−	0.112847i	$-0.964003\pi$
$23$		−	1.08239i		−	0.225694i	0.993612	−	0.112847i	$-0.0359971\pi$
$24$	−2.18347	+	4.38548i	−0.445700	+	0.895182i
$25$	3.82843	−	3.21608i	0.765685	−	0.643215i
$26$	1.74053	−	4.20201i	0.341346	−	0.824081i
$27$	−2.83730	−	4.35313i	−0.546038	−	0.837760i
$28$	−3.21608	−	3.21608i	−0.607781	−	0.607781i
$29$	−1.74053			−0.323208			−0.161604	−	0.986856i	$-0.551667\pi$
$29$	−1.74053			−0.323208			−0.161604	+	0.986856i	$0.551667\pi$
$30$	3.41323	+	4.28367i	0.623168	+	0.782088i
$31$			6.82843i			1.22642i	0.789919	+	0.613211i	$0.210122\pi$
$31$			6.82843i			1.22642i	−0.789919	+	0.613211i	$0.789878\pi$
$32$	5.22625	+	2.16478i	0.923880	+	0.382683i
$33$	4.77791	+	5.49019i	0.831727	+	0.955719i
$34$	0.828427	−	2.00000i	0.142074	−	0.342997i
$35$	−4.77791	+	1.74053i	−0.807614	+	0.294203i
$36$	−4.78779	+	3.61622i	−0.797965	+	0.602703i
$37$	−7.76429			−1.27644			−0.638221	−	0.769853i	$-0.720329\pi$
$37$	−7.76429			−1.27644			−0.638221	+	0.769853i	$0.720329\pi$
$38$	−2.61313	+	6.30864i	−0.423905	+	1.02340i
$39$	4.20201	−	3.65685i	0.672859	−	0.585565i
$40$	4.66176	−	4.27411i	0.737089	−	0.675796i
$41$		−	2.46148i		−	0.384418i	−0.981354	−	0.192209i	$-0.938435\pi$
$41$		−	2.46148i		−	0.384418i	0.981354	−	0.192209i	$-0.0615652\pi$
$42$	−1.77045	−	5.28156i	−0.273187	−	0.814963i
$43$			8.70626i			1.32769i	0.747869	+	0.663846i	$0.231077\pi$
$43$			8.70626i			1.32769i	−0.747869	+	0.663846i	$0.768923\pi$
$44$	5.94253	−	5.94253i	0.895871	−	0.895871i
$45$	1.40385	+	6.55967i	0.209273	+	0.977857i
$46$	−1.41421	−	0.585786i	−0.208514	−	0.0863695i
$47$			1.08239i			0.157883i	0.996879	+	0.0789416i	$0.0251541\pi$
$47$			1.08239i			0.157883i	−0.996879	+	0.0789416i	$0.974846\pi$
$48$	4.54822	+	5.22625i	0.656479	+	0.754344i
$49$	−1.82843			−0.261204
$50$	−2.13008	−	6.74261i	−0.301238	−	0.953549i
$51$	2.00000	−	1.74053i	0.280056	−	0.243723i
$52$	−4.54822	−	4.54822i	−0.630724	−	0.630724i
$53$		−	11.0866i		−	1.52286i	−0.648250	−	0.761428i	$-0.724499\pi$
$53$		−	11.0866i		−	1.52286i	0.648250	−	0.761428i	$-0.275501\pi$
$54$	−7.22317	+	1.35121i	−0.982949	+	0.183876i
$55$	−3.21608	−	8.82843i	−0.433656	−	1.19042i
$56$	−5.94253	+	2.46148i	−0.794104	+	0.328929i
$57$	−6.30864	+	5.49019i	−0.835600	+	0.727193i
$58$	−0.941967	+	2.27411i	−0.123686	+	0.298605i
$59$		−	4.20201i		−	0.547055i	−0.961864	−	0.273527i	$-0.911810\pi$
$59$		−	4.20201i		−	0.547055i	0.961864	−	0.273527i	$-0.0881904\pi$
$60$	7.44411	−	2.14130i	0.961031	−	0.276440i
$61$		−	8.48528i		−	1.08643i	−0.839594	−	0.543214i	$-0.817207\pi$
$61$		−	8.48528i		−	1.08643i	0.839594	−	0.543214i	$-0.182793\pi$
$62$	8.92177	+	3.69552i	1.13307	+	0.469331i
$63$	0.941967	−	6.75699i	0.118677	−	0.851300i
$64$	5.65685	−	5.65685i	0.707107	−	0.707107i
$65$	−6.75699	+	2.46148i	−0.838101	+	0.305309i
$66$	9.75906	−	3.27137i	1.20126	−	0.402678i
$67$			2.27411i			0.277827i	0.990305	+	0.138913i	$0.0443609\pi$
$67$			2.27411i			0.277827i	−0.990305	+	0.138913i	$0.955639\pi$
$68$	−2.16478	−	2.16478i	−0.262519	−	0.262519i
$69$	−1.23074	−	1.41421i	−0.148164	−	0.170251i
$70$	−0.311677	+	7.18461i	−0.0372525	+	0.858725i
$71$	−11.8851			−1.41050			−0.705249	−	0.708960i	$-0.749165\pi$
$71$	−11.8851			−1.41050			−0.705249	+	0.708960i	$0.749165\pi$
$72$	2.13368	+	8.21264i	0.251457	+	0.967868i
$73$		−	4.54822i		−	0.532329i	−0.963928	−	0.266164i	$-0.914244\pi$
$73$		−	4.54822i		−	0.532329i	0.963928	−	0.266164i	$-0.0857564\pi$
$74$	−4.20201	+	10.1445i	−0.488473	+	1.17928i
$75$	1.34523	−	8.55514i	0.155333	−	0.987862i
$76$	6.82843	+	6.82843i	0.783274	+	0.783274i
$77$			9.55582i			1.08899i
$78$	−2.50380	−	7.46926i	−0.283500	−	0.845727i
$79$			0.485281i			0.0545984i	0.999627	+	0.0272992i	$0.00869069\pi$
$79$			0.485281i			0.0545984i	−0.999627	+	0.0272992i	$0.991309\pi$
$80$	−3.06147	−	8.40401i	−0.342282	−	0.939597i
$81$	−8.65685	−	2.46148i	−0.961873	−	0.273498i
$82$	−3.21608	−	1.33214i	−0.355156	−	0.147111i
$83$	6.94269			0.762060			0.381030	−	0.924563i	$-0.375569\pi$
$83$	6.94269			0.762060			0.381030	+	0.924563i	$0.375569\pi$
$84$	−7.85886	−	0.545152i	−0.857472	−	0.0594809i
$85$	−3.21608	+	1.17157i	−0.348832	+	0.127075i
$86$	11.3753	+	4.71179i	1.22663	+	0.508086i
$87$	−2.27411	+	1.97908i	−0.243810	+	0.212179i
$88$	−4.54822	−	10.9804i	−0.484842	−	1.17051i
$89$			8.40401i			0.890823i	0.895326	+	0.445412i	$0.146943\pi$
$89$			8.40401i			0.890823i	−0.895326	+	0.445412i	$0.853057\pi$
$90$	9.33037	+	1.71585i	0.983508	+	0.180867i
$91$	7.31371			0.766685
$92$	−1.53073	+	1.53073i	−0.159590	+	0.159590i
$93$	7.76429	+	8.92177i	0.805120	+	0.925144i
$94$	1.41421	+	0.585786i	0.145865	+	0.0604193i
$95$	10.1445	−	3.69552i	1.04081	−	0.379152i
$96$	9.28991	−	3.11411i	0.948147	−	0.317832i
$97$		−	10.9804i		−	1.11489i	−0.830215	−	0.557444i	$-0.811782\pi$
$97$		−	10.9804i		−	1.11489i	0.830215	−	0.557444i	$-0.188218\pi$
$98$	−0.989538	+	2.38896i	−0.0999584	+	0.241321i
$99$	12.4853	+	1.74053i	1.25482	+	0.174930i
$100$	−9.96243	−	0.865995i	−0.996243	−	0.0865995i
$101$	13.6256			1.35580			0.677899	−	0.735155i	$-0.262891\pi$
$101$	13.6256			1.35580			0.677899	+	0.735155i	$0.262891\pi$
$102$	−1.19172	−	3.55509i	−0.117998	−	0.352007i
$103$	8.70626			0.857853			0.428927	−	0.903339i	$-0.358892\pi$
$103$	8.70626			0.857853			0.428927	+	0.903339i	$0.358892\pi$
$104$	−8.40401	+	3.48106i	−0.824081	+	0.341346i
$105$	−4.26357	+	7.70685i	−0.416081	+	0.752112i
$106$	−14.4853	−	6.00000i	−1.40693	−	0.582772i
$107$	5.67459			0.548584			0.274292	−	0.961647i	$-0.411557\pi$
$107$	5.67459			0.548584			0.274292	+	0.961647i	$0.411557\pi$
$108$	−2.14371	+	10.1688i	−0.206279	+	0.978493i
$109$			16.4853i			1.57900i	0.613748	+	0.789502i	$0.289661\pi$
$109$			16.4853i			1.57900i	−0.613748	+	0.789502i	$0.710339\pi$
$110$	−13.2754	−	0.575904i	−1.26576	−	0.0549103i
$111$	−10.1445	+	8.82843i	−0.962877	+	0.837957i
$112$			9.09644i			0.859533i
$113$	−0.634051			−0.0596465			−0.0298232	−	0.999555i	$-0.509494\pi$
$113$	−0.634051			−0.0596465			−0.0298232	+	0.999555i	$0.509494\pi$
$114$	3.75906	+	11.2139i	0.352068	+	1.05028i
$115$	0.828427	+	2.27411i	0.0772512	+	0.212062i
$116$	2.46148	+	2.46148i	0.228543	+	0.228543i
$117$	1.33214	−	9.55582i	0.123157	−	0.883436i
$118$	−5.49019	−	2.27411i	−0.505413	−	0.209349i
$119$	3.48106			0.319108
$120$	1.23099	−	10.8851i	0.112373	−	0.993666i
$121$	−6.65685			−0.605169
$122$	−11.0866	−	4.59220i	−1.00373	−	0.415758i
$123$	−2.79884	−	3.21608i	−0.252362	−	0.289984i
$124$	9.65685	−	9.65685i	0.867211	−	0.867211i
$125$	−5.58206	+	9.68714i	−0.499275	+	0.866444i
$126$	−8.31864	−	4.88759i	−0.741083	−	0.435421i
$127$	−2.27411			−0.201795			−0.100897	−	0.994897i	$-0.532171\pi$
$127$	−2.27411			−0.201795			−0.100897	+	0.994897i	$0.532171\pi$
$128$	−4.32957	−	10.4525i	−0.382683	−	0.923880i
$129$	9.89949	+	11.3753i	0.871602	+	1.00154i
$130$	−0.440778	+	10.1606i	−0.0386588	+	0.891141i
$131$		−	11.1641i		−	0.975413i	−0.873008	−	0.487707i	$-0.837834\pi$
$131$		−	11.1641i		−	0.975413i	0.873008	−	0.487707i	$-0.162166\pi$
$132$	1.00731	−	14.5213i	0.0876750	−	1.26392i
$133$	−10.9804			−0.952119
$134$	2.97127	+	1.23074i	0.256678	+	0.106320i
$135$	9.29291	+	6.97437i	0.799806	+	0.600258i
$136$	−4.00000	+	1.65685i	−0.342997	+	0.142074i
$137$	8.02509			0.685629			0.342815	−	0.939403i	$-0.388620\pi$
$137$	8.02509			0.685629			0.342815	+	0.939403i	$0.388620\pi$
$138$	−2.51383	+	0.842671i	−0.213991	+	0.0717329i
$139$	−2.48528			−0.210799			−0.105399	−	0.994430i	$-0.533612\pi$
$139$	−2.48528			−0.210799			−0.105399	+	0.994430i	$0.533612\pi$
$140$	9.21846	+	4.29551i	0.779102	+	0.363037i
$141$	1.23074	+	1.41421i	0.103647	+	0.119098i
$142$	−6.43215	+	15.5286i	−0.539774	+	1.30313i
$143$			13.5140i			1.13010i
$144$	11.8851	+	1.65685i	0.990422	+	0.138071i
$145$	3.65685	−	1.33214i	0.303685	−	0.110628i
$146$	−5.94253	−	2.46148i	−0.491808	−	0.203713i
$147$	−2.38896	+	2.07902i	−0.197038	+	0.171475i
$148$	10.9804	+	10.9804i	0.902581	+	0.902581i
$149$	−0.720950			−0.0590625			−0.0295313	−	0.999564i	$-0.509401\pi$
$149$	−0.720950			−0.0590625			−0.0295313	+	0.999564i	$0.509401\pi$
$150$	−10.4498	−	6.38763i	−0.853222	−	0.521548i
$151$			2.82843i			0.230174i	0.993355	+	0.115087i	$0.0367147\pi$
$151$			2.82843i			0.230174i	−0.993355	+	0.115087i	$0.963285\pi$
$152$	12.6173	−	5.22625i	1.02340	−	0.423905i
$153$	0.634051	−	4.54822i	0.0512600	−	0.367702i
$154$	12.4853	+	5.17157i	1.00609	+	0.416737i
$155$	−5.22625	−	14.3465i	−0.419783	−	1.15234i
$156$	−11.1141	−	0.770961i	−0.889841	−	0.0617263i
$157$	23.2929			1.85897			0.929487	−	0.368854i	$-0.120250\pi$
$157$	23.2929			1.85897			0.929487	+	0.368854i	$0.120250\pi$
$158$	0.634051	+	0.262632i	0.0504424	+	0.0208939i
$159$	−12.6060	−	14.4853i	−0.999722	−	1.14876i
$160$	−12.6372	−	0.548218i	−0.999060	−	0.0433405i
$161$		−	2.46148i		−	0.193992i
$162$	−7.90113	+	9.97858i	−0.620772	+	0.783992i
$163$		−	8.70626i		−	0.681927i	−0.940077	−	0.340964i	$-0.889247\pi$
$163$		−	8.70626i		−	0.681927i	0.940077	−	0.340964i	$-0.110753\pi$
$164$	−3.48106	+	3.48106i	−0.271825	+	0.271825i
$165$	−14.2404	−	7.87804i	−1.10861	−	0.613305i
$166$	3.75736	−	9.07107i	0.291628	−	0.704051i
$167$		−	5.04054i		−	0.390049i	−0.980798	−	0.195024i	$-0.937521\pi$
$167$		−	5.04054i		−	0.390049i	0.980798	−	0.195024i	$-0.0624786\pi$
$168$	−4.96546	+	9.97306i	−0.383094	+	0.769438i
$169$	−2.65685			−0.204373
$170$	−0.209794	+	4.83606i	−0.0160905	+	0.370909i
$171$	−2.00000	+	14.3465i	−0.152944	+	1.09711i
$172$	12.3125	−	12.3125i	0.938820	−	0.938820i
$173$		−	0.262632i		−	0.0199676i	−0.999950	−	0.00998379i	$-0.996822\pi$
$173$		−	0.262632i		−	0.0199676i	0.999950	−	0.00998379i	$-0.00317799\pi$
$174$	1.35505	+	4.04233i	0.102726	+	0.306449i
$175$	8.70626	−	7.31371i	0.658132	−	0.552864i
$176$	−16.8080			−1.26695
$177$	−4.77791	−	5.49019i	−0.359130	−	0.412668i
$178$	10.9804	+	4.54822i	0.823014	+	0.340903i
$179$			7.68306i			0.574259i	0.957892	+	0.287129i	$0.0927010\pi$
$179$			7.68306i			0.574259i	−0.957892	+	0.287129i	$0.907299\pi$
$180$	7.29143	−	11.2621i	0.543471	−	0.839428i
$181$		−	21.6569i		−	1.60974i	−0.593450	−	0.804871i	$-0.702235\pi$
$181$		−	21.6569i		−	1.60974i	0.593450	−	0.804871i	$-0.297765\pi$
$182$	3.95815	−	9.55582i	0.293398	−	0.708325i
$183$	−9.64823	−	11.0866i	−0.713218	−	0.819542i
$184$	1.17157	+	2.82843i	0.0863695	+	0.208514i
$185$	16.3128	−	5.94253i	1.19934	−	0.436904i
$186$	15.8589	−	5.31611i	1.16283	−	0.389796i
$187$			6.43215i			0.470366i
$188$	1.53073	−	1.53073i	0.111640	−	0.111640i
$189$	−6.45232	−	9.89949i	−0.469337	−	0.720082i
$190$	0.661758	−	15.2545i	0.0480090	−	1.10668i
$191$	8.40401			0.608093			0.304046	−	0.952657i	$-0.401662\pi$
$191$	8.40401			0.608093			0.304046	+	0.952657i	$0.401662\pi$
$192$	0.958884	−	13.8232i	0.0692015	−	0.997603i
$193$			13.6447i			0.982164i	0.871113	+	0.491082i	$0.163398\pi$
$193$			13.6447i			0.982164i	−0.871113	+	0.491082i	$0.836602\pi$
$194$	−14.3465	−	5.94253i	−1.03002	−	0.426649i
$195$	−6.02959	+	10.8991i	−0.431788	+	0.780503i
$196$	2.58579	+	2.58579i	0.184699	+	0.184699i
$197$		−	8.02509i		−	0.571764i	−0.958265	−	0.285882i	$-0.907713\pi$
$197$		−	8.02509i		−	0.571764i	0.958265	−	0.285882i	$-0.0922865\pi$
$198$	9.03109	−	15.3708i	0.641812	−	1.09236i
$199$			14.8284i			1.05116i	0.850744	+	0.525580i	$0.176152\pi$
$199$			14.8284i			1.05116i	−0.850744	+	0.525580i	$0.823848\pi$
$200$	−6.52311	+	12.5479i	−0.461253	+	0.887269i
$201$	2.58579	+	2.97127i	0.182387	+	0.209577i
$202$	7.37412	−	17.8027i	0.518841	−	1.25259i
$203$	−3.95815			−0.277808
$204$	−5.28991	−	0.366949i	−0.370367	−	0.0256916i
$205$	1.88393	+	5.17157i	0.131580	+	0.361198i
$206$	4.71179	−	11.3753i	0.328286	−	0.792553i
$207$	−3.21608	−	0.448342i	−0.223533	−	0.0311619i
$208$			12.8643i			0.891979i
$209$		−	20.2891i		−	1.40342i
$210$	7.76207	+	9.74154i	0.535633	+	0.672230i
$211$	1.51472			0.104278			0.0521388	−	0.998640i	$-0.483396\pi$
$211$	1.51472			0.104278			0.0521388	+	0.998640i	$0.483396\pi$
$212$	−15.6788	+	15.6788i	−1.07682	+	1.07682i
$213$	−15.5286	+	13.5140i	−1.06400	+	0.925962i
$214$	3.07107	−	7.41421i	0.209934	−	0.506825i
$215$	−6.66348	−	18.2919i	−0.454446	−	1.24750i
$216$	12.1260	+	8.30421i	0.825070	+	0.565030i
$217$			15.5286i			1.05415i
$218$	21.5391	+	8.92177i	1.45881	+	0.604259i
$219$	−5.17157	−	5.94253i	−0.349463	−	0.401559i
$220$	−7.93706	+	17.0335i	−0.535117	+	1.14840i
$221$	4.92296			0.331154
$222$	6.04471	+	18.0324i	0.405694	+	1.21025i
$223$	−10.5902			−0.709172			−0.354586	−	0.935023i	$-0.615378\pi$
$223$	−10.5902			−0.709172			−0.354586	+	0.935023i	$0.615378\pi$
$224$	11.8851	+	4.92296i	0.794104	+	0.328929i
$225$	−7.97003	−	12.7074i	−0.531336	−	0.847161i
$226$	−0.343146	+	0.828427i	−0.0228257	+	0.0551062i
$227$	−4.77791			−0.317121			−0.158561	−	0.987349i	$-0.550685\pi$
$227$	−4.77791			−0.317121			−0.158561	+	0.987349i	$0.550685\pi$
$228$	16.6861	+	1.15748i	1.10506	+	0.0766557i
$229$			3.31371i			0.218976i	0.993988	+	0.109488i	$0.0349211\pi$
$229$			3.31371i			0.218976i	−0.993988	+	0.109488i	$0.965079\pi$
$230$	3.41961	+	0.148347i	0.225482	+	0.00978170i
$231$	10.8655	+	12.4853i	0.714897	+	0.821471i
$232$	4.54822	−	1.88393i	0.298605	−	0.123686i
$233$	−28.0334			−1.83653			−0.918265	−	0.395967i	$-0.870410\pi$
$233$	−28.0334			−1.83653			−0.918265	+	0.395967i	$0.870410\pi$
$234$	−11.7643	−	6.91210i	−0.769058	−	0.451858i
$235$	−0.828427	−	2.27411i	−0.0540406	−	0.148347i
$236$	−5.94253	+	5.94253i	−0.386826	+	0.386826i
$237$	0.551791	+	0.634051i	0.0358427	+	0.0411860i
$238$	1.88393	−	4.54822i	0.122117	−	0.294817i
$239$	13.3270			0.862050			0.431025	−	0.902340i	$-0.358152\pi$
$239$	13.3270			0.862050			0.431025	+	0.902340i	$0.358152\pi$
$240$	−13.5558	−	7.49932i	−0.875024	−	0.484079i
$241$	10.4853			0.675416			0.337708	−	0.941251i	$-0.390348\pi$
$241$	10.4853			0.675416			0.337708	+	0.941251i	$0.390348\pi$
$242$	−3.60266	+	8.69760i	−0.231588	+	0.559103i
$243$	−14.1096	+	6.62724i	−0.905129	+	0.425138i
$244$	−12.0000	+	12.0000i	−0.768221	+	0.768221i
$245$	3.84153	−	1.39942i	0.245426	−	0.0894055i
$246$	−5.71672	+	1.91633i	−0.364485	+	0.122181i
$247$	−15.5286			−0.988060
$248$	−7.39104	−	17.8435i	−0.469331	−	1.13307i
$249$	9.07107	−	7.89422i	0.574856	−	0.500276i
$250$	9.63587	+	12.5360i	0.609426	+	0.792843i
$251$			27.9721i			1.76559i	0.469762	+	0.882793i	$0.344340\pi$
$251$			27.9721i			1.76559i	−0.469762	+	0.882793i	$0.655660\pi$
$252$	−10.8880	+	8.22368i	−0.685877	+	0.518043i
$253$	4.54822			0.285944
$254$	−1.23074	+	2.97127i	−0.0772234	+	0.186434i
$255$	−2.86986	+	5.18759i	−0.179718	+	0.324859i
$256$	−16.0000			−1.00000
$257$	−2.42742			−0.151418			−0.0757090	−	0.997130i	$-0.524122\pi$
$257$	−2.42742			−0.151418			−0.0757090	+	0.997130i	$0.524122\pi$
$258$	20.2201	−	6.77806i	1.25885	−	0.421983i
$259$	−17.6569			−1.09714
$260$	13.0369	+	6.07476i	0.808513	+	0.376741i
$261$	−0.720950	+	5.17157i	−0.0446257	+	0.320112i
$262$	−14.5866	−	6.04198i	−0.901165	−	0.373275i
$263$			27.5851i			1.70097i	0.526001	+	0.850484i	$0.323691\pi$
$263$			27.5851i			1.70097i	−0.526001	+	0.850484i	$0.676309\pi$
$264$	−18.4278	−	9.17497i	−1.13415	−	0.564681i
$265$	8.48528	+	23.2929i	0.521247	+	1.43087i
$266$	−5.94253	+	14.3465i	−0.364360	+	0.879643i
$267$	9.55582	+	10.9804i	0.584807	+	0.671988i
$268$	3.21608	−	3.21608i	0.196453	−	0.196453i
$269$	−7.68306			−0.468445			−0.234222	−	0.972183i	$-0.575254\pi$
$269$	−7.68306			−0.468445			−0.234222	+	0.972183i	$0.575254\pi$
$270$	14.1417	−	8.36727i	0.860639	−	0.509216i
$271$		−	14.1421i		−	0.859074i	−0.903049	−	0.429537i	$-0.858677\pi$
$271$		−	14.1421i		−	0.859074i	0.903049	−	0.429537i	$-0.141323\pi$
$272$			6.12293i			0.371257i
$273$	9.55582	−	8.31609i	0.578345	−	0.503312i
$274$	4.34315	−	10.4853i	0.262379	−	0.633439i
$275$	13.5140	+	16.0871i	0.814923	+	0.970087i
$276$	−0.259472	+	3.74053i	−0.0156184	+	0.225153i
$277$	−16.8607			−1.01306			−0.506532	−	0.862221i	$-0.669073\pi$
$277$	−16.8607			−1.01306			−0.506532	+	0.862221i	$0.669073\pi$
$278$	−1.34502	+	3.24718i	−0.0806692	+	0.194753i
$279$	20.2891	+	2.82843i	1.21468	+	0.169334i
$280$	10.6013	−	9.71979i	0.633552	−	0.580869i
$281$		−	5.94253i		−	0.354502i	−0.984166	−	0.177251i	$-0.943280\pi$
$281$		−	5.94253i		−	0.354502i	0.984166	−	0.177251i	$-0.0567204\pi$
$282$	2.51383	−	0.842671i	0.149696	−	0.0501803i
$283$		−	26.1188i		−	1.55260i	−0.630363	−	0.776300i	$-0.717094\pi$
$283$		−	26.1188i		−	1.55260i	0.630363	−	0.776300i	$-0.282906\pi$
$284$	16.8080	+	16.8080i	0.997373	+	0.997373i
$285$	9.05247	−	16.3633i	0.536222	−	0.969280i
$286$	17.6569	+	7.31371i	1.04407	+	0.432469i
$287$		−	5.59767i		−	0.330420i
$288$	8.59694	−	14.6319i	0.506579	−	0.862193i
$289$	−14.6569			−0.862168
$290$	0.238547	−	5.49886i	0.0140080	−	0.322904i
$291$	−12.4853	−	14.3465i	−0.731900	−	0.841009i
$292$	−6.43215	+	6.43215i	−0.376413	+	0.376413i
$293$		−	16.3128i		−	0.953004i	−0.879173	−	0.476502i	$-0.841904\pi$
$293$		−	16.3128i		−	0.953004i	0.879173	−	0.476502i	$-0.158096\pi$
$294$	1.42348	+	4.24648i	0.0830190	+	0.247660i
$295$	3.21608	+	8.82843i	0.187247	+	0.514011i
$296$	20.2891	−	8.40401i	1.17928	−	0.488473i
$297$	18.2919	−	11.9223i	1.06140	−	0.691804i
$298$	−0.390175	+	0.941967i	−0.0226023	+	0.0545667i
$299$		−	3.48106i		−	0.201315i
$300$	−14.0012	+	10.1964i	−0.808361	+	0.588687i
$301$			19.7990i			1.14119i
$302$	3.69552	+	1.53073i	0.212653	+	0.0880838i
$303$	17.8027	−	15.4930i	1.02274	−	0.890052i
$304$		−	19.3137i		−	1.10772i
$305$	6.49435	+	17.8276i	0.371866	+	1.02081i
$306$	−5.59939	−	3.28991i	−0.320096	−	0.188071i
$307$		−	17.8027i		−	1.01605i	−0.861341	−	0.508027i	$-0.830375\pi$
$307$		−	17.8027i		−	1.01605i	0.861341	−	0.508027i	$-0.169625\pi$
$308$	13.5140	−	13.5140i	0.770030	−	0.770030i
$309$	11.3753	−	9.89949i	0.647117	−	0.563163i
$310$	−21.5731	−	0.935868i	−1.22527	−	0.0531537i
$311$	−9.84591			−0.558310			−0.279155	−	0.960246i	$-0.590054\pi$
$311$	−9.84591			−0.558310			−0.279155	+	0.960246i	$0.590054\pi$
$312$	−7.02222	+	14.1040i	−0.397555	+	0.798484i
$313$		−	24.6250i		−	1.39189i	−0.718096	−	0.695944i	$-0.754986\pi$
$313$		−	24.6250i		−	1.39189i	0.718096	−	0.695944i	$-0.245014\pi$
$314$	12.6060	−	30.4336i	0.711399	−	1.71747i
$315$	3.19250	+	14.9174i	0.179877	+	0.840500i
$316$	0.686292	−	0.686292i	0.0386069	−	0.0386069i
$317$			9.81845i			0.551459i	0.961235	+	0.275730i	$0.0889194\pi$
$317$			9.81845i			0.551459i	−0.961235	+	0.275730i	$0.911081\pi$
$318$	−25.7483	+	8.63118i	−1.44389	+	0.484012i
$319$		−	7.31371i		−	0.409489i
$320$	−7.55550	+	16.2146i	−0.422365	+	0.906426i
$321$	7.41421	−	6.45232i	0.413821	−	0.360134i
$322$	−3.21608	−	1.33214i	−0.179225	−	0.0742374i
$323$	−7.39104			−0.411248
$324$	8.76158	+	15.7237i	0.486755	+	0.873539i
$325$	12.3125	−	10.3431i	0.682975	−	0.573734i
$326$	−11.3753	−	4.71179i	−0.630018	−	0.260962i
$327$	18.7447	+	21.5391i	1.03658	+	1.19111i
$328$	2.66428	+	6.43215i	0.147111	+	0.355156i
$329$			2.46148i			0.135706i
$330$	−18.0000	+	14.3424i	−0.990868	+	0.789525i
$331$	−1.51472			−0.0832565			−0.0416282	−	0.999133i	$-0.513255\pi$
$331$	−1.51472			−0.0832565			−0.0416282	+	0.999133i	$0.513255\pi$
$332$	−9.81845	−	9.81845i	−0.538858	−	0.538858i
$333$	−3.21608	+	23.0698i	−0.176240	+	1.26422i
$334$	−6.58579	−	2.72792i	−0.360358	−	0.149265i
$335$	−1.74053	−	4.77791i	−0.0950952	−	0.261045i
$336$	10.3431	+	11.8851i	0.564265	+	0.648384i
$337$			19.2965i			1.05114i	0.850749	+	0.525572i	$0.176149\pi$
$337$			19.2965i			1.05114i	−0.850749	+	0.525572i	$0.823851\pi$
$338$	−1.43788	+	3.47135i	−0.0782103	+	0.188816i
$339$	−0.828427	+	0.720950i	−0.0449940	+	0.0391566i
$340$	6.20507	+	2.89136i	0.336517	+	0.156806i
$341$	−28.6931			−1.55382
$342$	17.6623	+	10.3774i	0.955066	+	0.561147i
$343$	−20.0768			−1.08405
$344$	−9.42359	−	22.7506i	−0.508086	−	1.22663i
$345$	3.66818	+	2.02930i	0.197488	+	0.109254i
$346$	−0.343146	−	0.142136i	−0.0184476	−	0.00764126i
$347$	−15.2304			−0.817611			−0.408806	−	0.912621i	$-0.634055\pi$
$347$	−15.2304			−0.817611			−0.408806	+	0.912621i	$0.634055\pi$
$348$	6.01491	+	0.417241i	0.322433	+	0.0223665i
$349$		−	13.6569i		−	0.731035i	−0.930805	−	0.365517i	$-0.880892\pi$
$349$		−	13.6569i		−	0.731035i	0.930805	−	0.365517i	$-0.119108\pi$
$350$	−4.84403	−	15.3334i	−0.258924	−	0.819606i
$351$	−9.12496	−	14.0000i	−0.487054	−	0.747265i
$352$	−9.09644	+	21.9607i	−0.484842	+	1.17051i
$353$	26.3939			1.40481			0.702403	−	0.711780i	$-0.252111\pi$
$353$	26.3939			1.40481			0.702403	+	0.711780i	$0.252111\pi$
$354$	−9.75906	+	3.27137i	−0.518688	+	0.173872i
$355$	24.9706	−	9.09644i	1.32530	−	0.482789i
$356$	11.8851	−	11.8851i	0.629907	−	0.629907i
$357$	4.54822	−	3.95815i	0.240717	−	0.209488i
$358$	10.0384	+	4.15804i	0.530546	+	0.219759i
$359$	−32.1741			−1.69809			−0.849043	−	0.528323i	$-0.822821\pi$
$359$	−32.1741			−1.69809			−0.849043	+	0.528323i	$0.822821\pi$
$360$	−10.7686	−	15.6217i	−0.567553	−	0.823337i
$361$	4.31371			0.227037
$362$	−28.2960	−	11.7206i	−1.48721	−	0.616021i
$363$	−8.69760	+	7.56921i	−0.456506	+	0.397280i
$364$	−10.3431	−	10.3431i	−0.542128	−	0.542128i
$365$	3.48106	+	9.55582i	0.182207	+	0.500175i
$366$	−19.7069	+	6.60602i	−1.03009	+	0.345302i
$367$	24.2349			1.26505			0.632524	−	0.774540i	$-0.282019\pi$
$367$	24.2349			1.26505			0.632524	+	0.774540i	$0.282019\pi$
$368$	4.32957			0.225694
$369$	−7.31371	−	1.01958i	−0.380736	−	0.0530771i
$370$	1.06413	−	24.5298i	0.0553216	−	1.27524i
$371$		−	25.2120i		−	1.30894i
$372$	1.63692	−	23.5977i	0.0848702	−	1.22348i
$373$	10.4286			0.539971			0.269986	−	0.962864i	$-0.412981\pi$
$373$	10.4286			0.539971			0.269986	+	0.962864i	$0.412981\pi$
$374$	8.40401	+	3.48106i	0.434561	+	0.180001i
$375$	3.72149	+	19.0040i	0.192177	+	0.981360i
$376$	−1.17157	−	2.82843i	−0.0604193	−	0.145865i
$377$	−5.59767			−0.288295
$378$	−16.4263	+	3.07280i	−0.844877	+	0.158048i
$379$	15.1716			0.779311			0.389656	−	0.920961i	$-0.372594\pi$
$379$	15.1716			0.779311			0.389656	+	0.920961i	$0.372594\pi$
$380$	−19.5728	−	9.12029i	−1.00406	−	0.467861i
$381$	−2.97127	+	2.58579i	−0.152223	+	0.132474i
$382$	4.54822	−	10.9804i	0.232707	−	0.561805i
$383$			18.5545i			0.948091i	0.880500	+	0.474046i	$0.157207\pi$
$383$			18.5545i			0.948091i	−0.880500	+	0.474046i	$0.842793\pi$
$384$	−17.5419	−	8.73390i	−0.895182	−	0.445700i
$385$	−7.31371	−	20.0768i	−0.372741	−	1.02321i
$386$	17.8276	+	7.38443i	0.907401	+	0.375858i
$387$	25.8686	+	3.60625i	1.31498	+	0.183316i
$388$	−15.5286	+	15.5286i	−0.788345	+	0.788345i
$389$	12.6060			0.639150			0.319575	−	0.947561i	$-0.396460\pi$
$389$	12.6060			0.639150			0.319575	+	0.947561i	$0.396460\pi$
$390$	10.9772	+	13.7766i	0.555853	+	0.697606i
$391$		−	1.65685i		−	0.0837907i
$392$	4.77791	−	1.97908i	0.241321	−	0.0999584i
$393$	−12.6942	−	14.5866i	−0.640338	−	0.735798i
$394$	−10.4853	−	4.34315i	−0.528241	−	0.218805i
$395$	−0.371418	−	1.01958i	−0.0186881	−	0.0513005i
$396$	−15.1954	−	20.1183i	−0.763596	−	1.01098i
$397$	−0.551791			−0.0276936			−0.0138468	−	0.999904i	$-0.504408\pi$
$397$	−0.551791			−0.0276936			−0.0138468	+	0.999904i	$0.504408\pi$
$398$	19.3743	+	8.02509i	0.971145	+	0.402261i
$399$	−14.3465	+	12.4853i	−0.718226	+	0.625046i
$400$	12.8643	+	15.3137i	0.643215	+	0.765685i
$401$			25.2120i			1.25903i	0.776989	+	0.629514i	$0.216746\pi$
$401$			25.2120i			1.25903i	−0.776989	+	0.629514i	$0.783254\pi$
$402$	5.28156	−	1.77045i	0.263421	−	0.0883023i
$403$			21.9607i			1.09394i
$404$	−19.2695	−	19.2695i	−0.958694	−	0.958694i
$405$	20.0720	−	1.45410i	0.997386	−	0.0722546i
$406$	−2.14214	+	5.17157i	−0.106312	+	0.256661i
$407$		−	32.6256i		−	1.61719i
$408$	−3.34232	+	6.71300i	−0.165469	+	0.332343i
$409$	−7.17157			−0.354611			−0.177306	−	0.984156i	$-0.556738\pi$
$409$	−7.17157			−0.354611			−0.177306	+	0.984156i	$0.556738\pi$
$410$	7.77656	+	0.337357i	0.384057	+	0.0166609i
$411$	10.4853	−	9.12496i	0.517201	−	0.450101i
$412$	−12.3125	−	12.3125i	−0.606594	−	0.606594i
$413$		−	9.55582i		−	0.470211i
$414$	−2.32631	+	3.95937i	−0.114332	+	0.194592i
$415$	−14.5866	+	5.31371i	−0.716029	+	0.260840i
$416$	16.8080	+	6.96211i	0.824081	+	0.341346i
$417$	−3.24718	+	2.82590i	−0.159015	+	0.138385i
$418$	−26.5090	−	10.9804i	−1.29660	−	0.537067i
$419$			4.20201i			0.205281i	0.994718	+	0.102641i	$0.0327292\pi$
$419$			4.20201i			0.205281i	−0.994718	+	0.102641i	$0.967271\pi$
$420$	16.9287	−	4.86955i	0.826037	−	0.237610i
$421$			29.1716i			1.42174i	0.703326	+	0.710868i	$0.251698\pi$
$421$			29.1716i			1.42174i	−0.703326	+	0.710868i	$0.748302\pi$
$422$	0.819760	−	1.97908i	0.0399053	−	0.0963399i
$423$	3.21608	+	0.448342i	0.156371	+	0.0217991i
$424$	12.0000	+	28.9706i	0.582772	+	1.40693i
$425$	5.86030	−	4.92296i	0.284266	−	0.238798i
$426$	9.25284	+	27.6028i	0.448302	+	1.33736i
$427$		−	19.2965i		−	0.933821i
$428$	−8.02509	−	8.02509i	−0.387907	−	0.387907i
$429$	15.3661	+	17.6569i	0.741883	+	0.852481i
$430$	−27.5057	−	1.19323i	−1.32644	−	0.0575428i
$431$	21.7310			1.04674			0.523372	−	0.852104i	$-0.324674\pi$
$431$	21.7310			1.04674			0.523372	+	0.852104i	$0.324674\pi$
$432$	17.4125	−	11.3492i	0.837760	−	0.546038i
$433$			29.1732i			1.40198i	0.713173	+	0.700988i	$0.247258\pi$
$433$			29.1732i			1.40198i	−0.713173	+	0.700988i	$0.752742\pi$
$434$	20.2891	+	8.40401i	0.973907	+	0.403405i
$435$	3.26319	−	5.89857i	0.156458	−	0.282815i
$436$	23.3137	−	23.3137i	1.11652	−	1.11652i
$437$			5.22625i			0.250006i
$438$	−10.5631	+	3.54091i	−0.504726	+	0.169191i
$439$		−	11.5147i		−	0.549568i	−0.961506	−	0.274784i	$-0.911394\pi$
$439$		−	11.5147i		−	0.549568i	0.961506	−	0.274784i	$-0.0886063\pi$
$440$	17.9598	+	19.5887i	0.856201	+	0.933856i
$441$	−0.757359	+	5.43275i	−0.0360647	+	0.258702i
$442$	2.66428	−	6.43215i	0.126727	−	0.305946i
$443$	40.4650			1.92255			0.961275	−	0.275591i	$-0.0888737\pi$
$443$	40.4650			1.92255			0.961275	+	0.275591i	$0.0888737\pi$
$444$	26.8318	+	1.86126i	1.27338	+	0.0883317i
$445$	−6.43215	−	17.6569i	−0.304913	−	0.837015i
$446$	−5.73137	+	13.8368i	−0.271388	+	0.655189i
$447$	−0.941967	+	0.819760i	−0.0445535	+	0.0387733i
$448$	12.8643	−	12.8643i	0.607781	−	0.607781i
$449$			24.7897i			1.16990i	0.811070	+	0.584949i	$0.198886\pi$
$449$			24.7897i			1.16990i	−0.811070	+	0.584949i	$0.801114\pi$
$450$	−20.9164	+	3.53614i	−0.986008	+	0.166695i
$451$	10.3431			0.487040
$452$	0.896683	+	0.896683i	0.0421764	+	0.0421764i
$453$	3.21608	+	3.69552i	0.151104	+	0.173631i
$454$	−2.58579	+	6.24264i	−0.121357	+	0.292982i
$455$	−15.3661	+	5.59767i	−0.720375	+	0.262423i
$456$	10.5427	−	21.1750i	0.493709	−	0.991609i
$457$		−	12.8643i		−	0.601767i	−0.953661	−	0.300883i	$-0.902719\pi$
$457$		−	12.8643i		−	0.601767i	0.953661	−	0.300883i	$-0.0972815\pi$
$458$	4.32957	+	1.79337i	0.202307	+	0.0837985i
$459$	−4.34315	−	6.66348i	−0.202721	−	0.311025i
$460$	2.04450	−	4.38765i	0.0953255	−	0.204575i
$461$	−18.5486			−0.863892			−0.431946	−	0.901899i	$-0.642173\pi$
$461$	−18.5486			−0.863892			−0.431946	+	0.901899i	$0.642173\pi$
$462$	22.1932	−	7.43946i	1.03252	−	0.346115i
$463$	−4.93839			−0.229507			−0.114753	−	0.993394i	$-0.536608\pi$
$463$	−4.93839			−0.229507			−0.114753	+	0.993394i	$0.536608\pi$
$464$		−	6.96211i		−	0.323208i
$465$	−23.1412	−	12.8021i	−1.07315	−	0.593685i
$466$	−15.1716	+	36.6274i	−0.702810	+	1.69673i
$467$	−8.73606			−0.404257			−0.202128	−	0.979359i	$-0.564786\pi$
$467$	−8.73606			−0.404257			−0.202128	+	0.979359i	$0.564786\pi$
$468$	−15.3979	+	11.6300i	−0.711768	+	0.537599i
$469$			5.17157i			0.238801i
$470$	−3.41961	−	0.148347i	−0.157735	−	0.00684273i
$471$	30.4336	−	26.4853i	1.40231	−	1.22038i
$472$	4.54822	+	10.9804i	0.209349	+	0.505413i
$473$	−36.5838			−1.68212
$474$	1.12705	−	0.377804i	0.0517673	−	0.0173531i
$475$	−18.4853	+	15.5286i	−0.848163	+	0.712501i
$476$	−4.92296	−	4.92296i	−0.225643	−	0.225643i
$477$	−32.9411	−	4.59220i	−1.50827	−	0.210262i
$478$	7.21250	−	17.4125i	0.329892	−	0.796430i
$479$	15.3661			0.702096			0.351048	−	0.936357i	$-0.385825\pi$
$479$	15.3661			0.702096			0.351048	+	0.936357i	$0.385825\pi$
$480$	−17.1347	+	13.6529i	−0.782088	+	0.623168i
$481$	−24.9706			−1.13856
$482$	5.67459	−	13.6997i	0.258471	−	0.624003i
$483$	−2.79884	−	3.21608i	−0.127351	−	0.146337i
$484$	9.41421	+	9.41421i	0.427919	+	0.427919i
$485$	8.40401	+	23.0698i	0.381607	+	1.04755i
$486$	1.02287	+	22.0217i	0.0463982	+	0.998923i
$487$	19.6866			0.892086			0.446043	−	0.895011i	$-0.352833\pi$
$487$	19.6866			0.892086			0.446043	+	0.895011i	$0.352833\pi$
$488$	9.18440	+	22.1731i	0.415758	+	1.00373i
$489$	−9.89949	−	11.3753i	−0.447671	−	0.514408i
$490$	0.250594	−	5.77656i	0.0113207	−	0.260958i
$491$		−	14.0479i		−	0.633974i	−0.948430	−	0.316987i	$-0.897329\pi$
$491$		−	14.0479i		−	0.633974i	0.948430	−	0.316987i	$-0.102671\pi$
$492$	−0.590068	+	8.50637i	−0.0266023	+	0.383497i
$493$	−2.66428			−0.119993
$494$	−8.40401	+	20.2891i	−0.378114	+	0.912849i
$495$	−27.5638	+	5.89897i	−1.23890	+	0.265139i
$496$	−27.3137			−1.22642
$497$	−27.0279			−1.21237
$498$	−5.40507	−	16.1242i	−0.242207	−	0.722545i
$499$	25.1127			1.12420			0.562099	−	0.827070i	$-0.309994\pi$
$499$	25.1127			1.12420			0.562099	+	0.827070i	$0.309994\pi$
$500$	21.5939	−	5.80546i	0.965709	−	0.259628i
$501$	−5.73137	−	6.58579i	−0.256059	−	0.294231i
$502$	36.5474	+	15.1384i	1.63119	+	0.675660i
$503$		−	28.4818i		−	1.26994i	−0.772537	−	0.634969i	$-0.781013\pi$
$503$		−	28.4818i		−	1.26994i	0.772537	−	0.634969i	$-0.218987\pi$
$504$	4.85223	+	18.6764i	0.216136	+	0.831914i
$505$	−28.6274	+	10.4286i	−1.27390	+	0.464066i
$506$	2.46148	−	5.94253i	0.109426	−	0.264178i
$507$	−3.47135	+	3.02099i	−0.154168	+	0.134167i
$508$	3.21608	+	3.21608i	0.142690	+	0.142690i
$509$	13.6256			0.603944			0.301972	−	0.953317i	$-0.402355\pi$
$509$	13.6256			0.603944			0.301972	+	0.953317i	$0.402355\pi$
$510$	5.22475	+	6.55716i	0.231356	+	0.290356i
$511$		−	10.3431i		−	0.457554i
$512$	−8.65914	+	20.9050i	−0.382683	+	0.923880i
$513$	13.6997	+	21.0188i	0.604856	+	0.928002i
$514$	−1.31371	+	3.17157i	−0.0579452	+	0.139892i
$515$	−18.2919	+	6.66348i	−0.806037	+	0.293628i
$516$	2.08707	−	30.0871i	0.0918783	−	1.32451i
$517$	−4.54822			−0.200030
$518$	−9.55582	+	23.0698i	−0.419859	+	1.01363i
$519$	−0.298627	−	0.343146i	−0.0131083	−	0.0150624i
$520$	14.9926	−	13.7459i	0.657468	−	0.602796i
$521$			9.84591i			0.431357i	0.976464	+	0.215679i	$0.0691964\pi$
$521$			9.84591i			0.431357i	−0.976464	+	0.215679i	$0.930804\pi$
$522$	6.36681	+	3.74080i	0.278668	+	0.163730i
$523$			4.15804i			0.181819i	0.995859	+	0.0909093i	$0.0289773\pi$
$523$			4.15804i			0.181819i	−0.995859	+	0.0909093i	$0.971023\pi$
$524$	−15.7884	+	15.7884i	−0.689721	+	0.689721i
$525$	3.05919	−	19.4553i	0.133514	−	0.849100i
$526$	36.0416	+	14.9289i	1.57149	+	0.650932i
$527$			10.4525i			0.455318i
$528$	−21.9607	+	19.1116i	−0.955719	+	0.831727i
$529$	21.8284			0.949062
$530$	35.0258	+	1.51946i	1.52142	+	0.0660013i
$531$	−12.4853	−	1.74053i	−0.541815	−	0.0755325i
$532$	15.5286	+	15.5286i	0.673250	+	0.673250i
$533$		−	7.91630i		−	0.342893i
$534$	19.5181	−	6.54275i	0.844632	−	0.283132i
$535$	−11.9223	+	4.34315i	−0.515448	+	0.187771i
$536$	−2.46148	−	5.94253i	−0.106320	−	0.256678i
$537$	8.73606	+	10.0384i	0.376989	+	0.433189i
$538$	−4.15804	+	10.0384i	−0.179266	+	0.432786i
$539$		−	7.68306i		−	0.330933i
$540$	−3.27891	−	23.0054i	−0.141102	−	0.989995i
$541$			16.0000i			0.687894i	0.938989	+	0.343947i	$0.111764\pi$
$541$			16.0000i			0.687894i	−0.938989	+	0.343947i	$0.888236\pi$
$542$	−18.4776	−	7.65367i	−0.793680	−	0.328753i
$543$	−24.6250	−	28.2960i	−1.05676	−	1.21430i
$544$	8.00000	+	3.31371i	0.342997	+	0.142074i
$545$	−12.6173	−	34.6356i	−0.540465	−	1.48363i
$546$	−5.69392	−	16.9859i	−0.243677	−	0.726930i
$547$			33.3313i			1.42514i	0.701600	+	0.712571i	$0.252470\pi$
$547$			33.3313i			1.42514i	−0.701600	+	0.712571i	$0.747530\pi$
$548$	−11.3492	−	11.3492i	−0.484813	−	0.484813i
$549$	−25.2120	−	3.51472i	−1.07602	−	0.150005i
$550$	28.3325	−	8.95059i	1.20810	−	0.381655i
$551$	8.40401			0.358023
$552$	4.74681	+	2.36338i	0.202038	+	0.100592i
$553$			1.10358i			0.0469291i
$554$	−9.12496	+	22.0296i	−0.387682	+	0.935948i
$555$	14.5567	−	26.3128i	0.617898	−	1.11692i
$556$	3.51472	+	3.51472i	0.149057	+	0.149057i
$557$		−	19.3743i		−	0.820914i	−0.911880	−	0.410457i	$-0.865369\pi$
$557$		−	19.3743i		−	0.820914i	0.911880	−	0.410457i	$-0.134631\pi$
$558$	14.6759	−	24.9782i	0.621280	−	1.05741i
$559$			28.0000i			1.18427i
$560$	−6.96211	−	19.1116i	−0.294203	−	0.807614i
$561$	7.31371	+	8.40401i	0.308785	+	0.354818i
$562$	−7.76429	−	3.21608i	−0.327517	−	0.135662i
$563$	6.04601			0.254809			0.127405	−	0.991851i	$-0.459335\pi$
$563$	6.04601			0.254809			0.127405	+	0.991851i	$0.459335\pi$
$564$	0.259472	−	3.74053i	0.0109257	−	0.157505i
$565$	1.33214	−	0.485281i	0.0560437	−	0.0204159i
$566$	−34.1258	−	14.1354i	−1.43442	−	0.594155i
$567$	−19.6866	−	5.59767i	−0.826761	−	0.235080i
$568$	31.0572	−	12.8643i	1.30313	−	0.539774i
$569$			9.42359i			0.395057i	0.980297	+	0.197529i	$0.0632916\pi$
$569$			9.42359i			0.395057i	−0.980297	+	0.197529i	$0.936708\pi$
$570$	−16.4805	−	20.6834i	−0.690294	−	0.866332i
$571$	−41.1127			−1.72051			−0.860256	−	0.509862i	$-0.829697\pi$
$571$	−41.1127			−1.72051			−0.860256	+	0.509862i	$0.829697\pi$
$572$	19.1116	−	19.1116i	0.799098	−	0.799098i
$573$	10.9804	−	9.55582i	0.458712	−	0.399200i
$574$	−7.31371	−	3.02944i	−0.305268	−	0.126446i
$575$	−3.48106	−	4.14386i	−0.145170	−	0.172811i
$576$	−14.4649	−	19.1512i	−0.602703	−	0.797965i
$577$		−	15.5286i		−	0.646464i	−0.946320	−	0.323232i	$-0.895231\pi$
$577$		−	15.5286i		−	0.646464i	0.946320	−	0.323232i	$-0.104769\pi$
$578$	−7.93223	+	19.1501i	−0.329937	+	0.796539i
$579$	15.5147	+	17.8276i	0.644770	+	0.740890i
$580$	−7.05551	−	3.28764i	−0.292964	−	0.136512i
$581$	15.7884			0.655015
$582$	−25.5017	+	8.54851i	−1.05708	+	0.354347i
$583$	46.5858			1.92939
$584$	4.92296	+	11.8851i	0.203713	+	0.491808i
$585$	4.51487	+	21.0964i	0.186667	+	0.872228i
$586$	−21.3137	−	8.82843i	−0.880461	−	0.364699i
$587$	−12.1689			−0.502266			−0.251133	−	0.967953i	$-0.580803\pi$
$587$	−12.1689			−0.502266			−0.251133	+	0.967953i	$0.580803\pi$
$588$	6.31867	+	0.438312i	0.260578	+	0.0180757i
$589$		−	32.9706i		−	1.35853i
$590$	13.2754	+	0.575904i	0.546541	+	0.0237096i
$591$	−9.12496	−	10.4853i	−0.375351	−	0.431307i
$592$		−	31.0572i		−	1.27644i
$593$	39.3826			1.61725			0.808625	−	0.588325i	$-0.200212\pi$
$593$	39.3826			1.61725			0.808625	+	0.588325i	$0.200212\pi$
$594$	−5.67779	−	30.3518i	−0.232963	−	1.24535i
$595$	−7.31371	+	2.66428i	−0.299833	+	0.109225i
$596$	1.01958	+	1.01958i	0.0417635	+	0.0417635i
$597$	16.8607	+	19.3743i	0.690064	+	0.792936i
$598$	−4.54822	−	1.88393i	−0.185990	−	0.0770398i
$599$	−30.1350			−1.23128			−0.615641	−	0.788027i	$-0.711103\pi$
$599$	−30.1350			−1.23128			−0.615641	+	0.788027i	$0.711103\pi$
$600$	5.74477	+	23.8117i	0.234529	+	0.972109i
$601$	30.4853			1.24352			0.621760	−	0.783208i	$-0.286418\pi$
$601$	30.4853			1.24352			0.621760	+	0.783208i	$0.286418\pi$
$602$	25.8686	+	10.7151i	1.05433	+	0.436716i
$603$	6.75699	+	0.941967i	0.275166	+	0.0383599i
$604$	4.00000	−	4.00000i	0.162758	−	0.162758i
$605$	13.9861	−	5.09494i	0.568615	−	0.207139i
$606$	−10.6079	−	31.6451i	−0.430916	−	1.28550i
$607$	−35.2152			−1.42934			−0.714671	−	0.699461i	$-0.753424\pi$
$607$	−35.2152			−1.42934			−0.714671	+	0.699461i	$0.753424\pi$
$608$	−25.2346	−	10.4525i	−1.02340	−	0.423905i
$609$	−5.17157	+	4.50063i	−0.209563	+	0.182375i
$610$	26.8076	+	1.16295i	1.08541	+	0.0470863i
$611$			3.48106i			0.140828i
$612$	−7.32884	+	5.53547i	−0.296251	+	0.223758i
$613$	16.0804			0.649480			0.324740	−	0.945803i	$-0.394723\pi$
$613$	16.0804			0.649480			0.324740	+	0.945803i	$0.394723\pi$
$614$	−23.2603	−	9.63475i	−0.938711	−	0.388827i
$615$	8.34184	+	4.61485i	0.336375	+	0.186089i
$616$	−10.3431	−	24.9706i	−0.416737	−	1.00609i
$617$	31.0949			1.25183			0.625916	−	0.779890i	$-0.284725\pi$
$617$	31.0949			1.25183			0.625916	+	0.779890i	$0.284725\pi$
$618$	−6.77806	−	20.2201i	−0.272653	−	0.813371i
$619$	14.4853			0.582213			0.291106	−	0.956691i	$-0.405977\pi$
$619$	14.4853			0.582213			0.291106	+	0.956691i	$0.405977\pi$
$620$	−12.8980	+	27.6801i	−0.517998	+	1.11166i
$621$	−4.71179	+	3.07107i	−0.189078	+	0.123238i
$622$	−5.32857	+	12.8643i	−0.213656	+	0.515812i
$623$			19.1116i			0.765692i
$624$	14.6274	+	16.8080i	0.585565	+	0.672859i
$625$	4.31371	−	24.6250i	0.172548	−	0.985001i
$626$	−32.1741	−	13.3270i	−1.28594	−	0.532653i
$627$	−23.0698	−	26.5090i	−0.921319	−	1.05867i
$628$	−32.9411	−	32.9411i	−1.31449	−	1.31449i
$629$	−11.8851			−0.473889
$630$	21.2183	+	3.90204i	0.845357	+	0.155461i
$631$		−	26.1421i		−	1.04070i	−0.853952	−	0.520351i	$-0.825801\pi$
$631$		−	26.1421i		−	1.04070i	0.853952	−	0.520351i	$-0.174199\pi$
$632$	−0.525265	−	1.26810i	−0.0208939	−	0.0504424i
$633$	1.97908	−	1.72232i	0.0786612	−	0.0684560i
$634$	12.8284	+	5.31371i	0.509482	+	0.211034i
$635$	4.77791	−	1.74053i	0.189606	−	0.0690707i
$636$	−2.65768	+	38.3129i	−0.105384	+	1.51920i
$637$	−5.88036			−0.232988
$638$	−9.55582	−	3.95815i	−0.378319	−	0.156705i
$639$	−4.92296	+	35.3137i	−0.194749	+	1.39699i
$640$	17.0964	+	18.6470i	0.675796	+	0.737089i
$641$		−	24.7897i		−	0.979135i	−0.871965	−	0.489567i	$-0.837155\pi$
$641$		−	24.7897i		−	0.979135i	0.871965	−	0.489567i	$-0.162845\pi$
$642$	−4.41782	−	13.1791i	−0.174358	−	0.520138i
$643$			1.49376i			0.0589081i	0.999566	+	0.0294540i	$0.00937687\pi$
$643$			1.49376i			0.0589081i	−0.999566	+	0.0294540i	$0.990623\pi$
$644$	−3.48106	+	3.48106i	−0.137173	+	0.137173i
$645$	−29.5051	−	16.3227i	−1.16176	−	0.642708i
$646$	−4.00000	+	9.65685i	−0.157378	+	0.379944i
$647$			42.3671i			1.66562i	0.553556	+	0.832812i	$0.313271\pi$
$647$			42.3671i			1.66562i	−0.553556	+	0.832812i	$0.686729\pi$
$648$	25.2857	−	2.93796i	0.993317	−	0.115414i
$649$	17.6569			0.693092
$650$	−6.85049	−	21.6847i	−0.268698	−	0.850546i
$651$	17.6569	+	20.2891i	0.692027	+	0.795192i
$652$	−12.3125	+	12.3125i	−0.482195	+	0.482195i
$653$		−	37.5892i		−	1.47098i	−0.677535	−	0.735490i	$-0.736952\pi$
$653$		−	37.5892i		−	1.47098i	0.677535	−	0.735490i	$-0.263048\pi$
$654$	38.2867	−	12.8342i	1.49713	−	0.501858i
$655$	8.54465	+	23.4558i	0.333867	+	0.916496i
$656$	9.84591			0.384418
$657$	−13.5140	−	1.88393i	−0.527230	−	0.0734993i
$658$	3.21608	+	1.33214i	0.125376	+	0.0519323i
$659$			0.720950i			0.0280842i	0.999901	+	0.0140421i	$0.00446989\pi$
$659$			0.720950i			0.0280842i	−0.999901	+	0.0140421i	$0.995530\pi$
$660$	8.99775	+	31.2802i	0.350237	+	1.21758i
$661$			28.7696i			1.11901i	0.828828	+	0.559503i	$0.189008\pi$
$661$			28.7696i			1.11901i	−0.828828	+	0.559503i	$0.810992\pi$
$662$	−0.819760	+	1.97908i	−0.0318609	+	0.0769189i
$663$	6.43215	−	5.59767i	0.249804	−	0.217395i
$664$	−18.1421	+	7.51472i	−0.704051	+	0.291628i
$665$	23.0698	−	8.40401i	0.894608	−	0.325894i
$666$	28.4016	+	16.6873i	1.10054	+	0.646619i
$667$			1.88393i			0.0729462i
$668$	−7.12840	+	7.12840i	−0.275806	+	0.275806i
$669$	−13.8368	+	12.0416i	−0.534960	+	0.465556i
$670$	−7.18461	−	0.311677i	−0.277566	−	0.0120411i
$671$	35.6552			1.37645
$672$	21.1263	−	7.08182i	0.814963	−	0.273187i
$673$		−	5.65180i		−	0.217861i	−0.994049	−	0.108930i	$-0.965257\pi$
$673$		−	5.65180i		−	0.217861i	0.994049	−	0.108930i	$-0.0347426\pi$
$674$	25.2120	+	10.4432i	0.971131	+	0.402256i
$675$	−24.8624	−	7.54068i	−0.956954	−	0.290241i
$676$	3.75736	+	3.75736i	0.144514	+	0.144514i
$677$			39.3826i			1.51360i	0.653649	+	0.756798i	$0.273237\pi$
$677$			39.3826i			1.51360i	−0.653649	+	0.756798i	$0.726763\pi$
$678$	0.493625	+	1.47257i	0.0189576	+	0.0565536i
$679$		−	24.9706i		−	0.958282i
$680$	7.13591	−	6.54252i	0.273650	−	0.250894i
$681$	−6.24264	+	5.43275i	−0.239219	+	0.208183i
$682$	−15.5286	+	37.4893i	−0.594620	+	1.43554i
$683$	−21.3533			−0.817063			−0.408532	−	0.912744i	$-0.633959\pi$
$683$	−21.3533			−0.817063			−0.408532	+	0.912744i	$0.633959\pi$
$684$	23.1175	−	17.4607i	0.883920	−	0.667625i
$685$	−16.8607	+	6.14214i	−0.644215	+	0.234679i
$686$	−10.8655	+	26.2316i	−0.414846	+	1.00153i
$687$	3.76787	+	4.32957i	0.143753	+	0.165183i
$688$	−34.8250			−1.32769
$689$		−	35.6552i		−	1.35836i
$690$	4.63661	−	3.69446i	0.176513	−	0.140646i
$691$	−12.8284			−0.488016			−0.244008	−	0.969773i	$-0.578462\pi$
$691$	−12.8284			−0.488016			−0.244008	+	0.969773i	$0.578462\pi$
$692$	−0.371418	+	0.371418i	−0.0141192	+	0.0141192i
$693$	28.3929	+	3.95815i	1.07856	+	0.150358i
$694$	−8.24264	+	19.8995i	−0.312886	+	0.755374i
$695$	5.22158	−	1.90215i	0.198066	−	0.0721527i
$696$	3.80040	−	7.63305i	0.144054	−	0.289330i
$697$		−	3.76787i		−	0.142718i
$698$	−17.8435	−	7.39104i	−0.675388	−	0.279755i
$699$	−36.6274	+	31.8755i	−1.38538	+	1.20564i
$700$	−22.6557	−	1.96937i	−0.856303	−	0.0744351i
$701$	2.76011			0.104248			0.0521239	−	0.998641i	$-0.483401\pi$
$701$	2.76011			0.104248			0.0521239	+	0.998641i	$0.483401\pi$
$702$	−23.2303	+	4.34559i	−0.876770	+	0.164014i
$703$	37.4893			1.41394
$704$	23.7701	+	23.7701i	0.895871	+	0.895871i
$705$	−3.66818	−	2.02930i	−0.138152	−	0.0764279i
$706$	14.2843	−	34.4853i	0.537596	−	1.29787i
$707$	30.9861			1.16535
$708$	−1.00731	+	14.5213i	−0.0378570	+	0.545743i
$709$		−	20.2843i		−	0.761792i	−0.924618	−	0.380896i	$-0.875616\pi$
$709$		−	20.2843i		−	0.761792i	0.924618	−	0.380896i	$-0.124384\pi$
$710$	1.62890	−	37.5486i	0.0611317	−	1.40917i
$711$	1.44190	+	0.201010i	0.0540755	+	0.00753847i
$712$	−9.09644	−	21.9607i	−0.340903	−	0.823014i
$713$	7.39104			0.276796
$714$	−2.71009	−	8.08467i	−0.101423	−	0.302561i
$715$	−10.3431	−	28.3929i	−0.386812	−	1.06183i
$716$	10.8655	−	10.8655i	0.406062	−	0.406062i
$717$	17.4125	−	15.1535i	0.650283	−	0.565917i
$718$	−17.4125	+	42.0375i	−0.649830	+	1.56883i
$719$	28.6931			1.07007			0.535036	−	0.844829i	$-0.320298\pi$
$719$	28.6931			1.07007			0.535036	+	0.844829i	$0.320298\pi$
$720$	−26.2387	+	5.61538i	−0.977857	+	0.209273i
$721$	19.7990			0.737353
$722$	2.33456	−	5.63613i	0.0868834	−	0.209755i
$723$	13.6997	−	11.9223i	0.509497	−	0.443397i
$724$	−30.6274	+	30.6274i	−1.13826	+	1.13826i
$725$	−6.66348	+	5.59767i	−0.247476	+	0.207892i
$726$	5.18254	+	15.4604i	0.192342	+	0.573789i
$727$	−18.9063			−0.701195			−0.350598	−	0.936526i	$-0.614022\pi$
$727$	−18.9063			−0.701195			−0.350598	+	0.936526i	$0.614022\pi$
$728$	−19.1116	+	7.91630i	−0.708325	+	0.293398i
$729$	−10.8995	+	24.7022i	−0.403685	+	0.914898i
$730$	14.3692	+	0.623354i	0.531829	+	0.0230714i
$731$			13.3270i			0.492916i
$732$	−2.03410	+	29.3234i	−0.0751825	+	1.08382i
$733$	−38.8215			−1.43390			−0.716952	−	0.697123i	$-0.754463\pi$
$733$	−38.8215			−1.43390			−0.716952	+	0.697123i	$0.754463\pi$
$734$	13.1158	−	31.6644i	0.484113	−	1.16875i
$735$	3.42799	−	6.19646i	0.126443	−	0.228560i
$736$	2.34315	−	5.65685i	0.0863695	−	0.208514i
$737$	−9.55582			−0.351993
$738$	−5.29029	+	9.00403i	−0.194738	+	0.331443i
$739$	−32.8284			−1.20761			−0.603807	−	0.797131i	$-0.706350\pi$
$739$	−32.8284			−1.20761			−0.603807	+	0.797131i	$0.706350\pi$
$740$	−31.4738	−	14.6658i	−1.15700	−	0.539125i
$741$	−20.2891	+	17.6569i	−0.745338	+	0.648641i
$742$	−32.9411	−	13.6447i	−1.20931	−	0.500911i
$743$			0.185709i			0.00681301i	0.999994	+	0.00340650i	$0.00108433\pi$
$743$			0.185709i			0.00681301i	−0.999994	+	0.00340650i	$0.998916\pi$
$744$	−29.9459	−	14.9097i	−1.09787	−	0.546616i
$745$	1.51472	−	0.551791i	0.0554950	−	0.0202161i
$746$	5.64391	−	13.6256i	0.206638	−	0.498868i
$747$	2.87576	−	20.6286i	0.105218	−	0.754761i
$748$	9.09644	−	9.09644i	0.332599	−	0.332599i
$749$	12.9046			0.471525
$750$	26.8439	+	5.42250i	0.980202	+	0.198002i
$751$			27.1127i			0.989356i	0.869076	+	0.494678i	$0.164714\pi$
$751$			27.1127i			0.989356i	−0.869076	+	0.494678i	$0.835286\pi$
$752$	−4.32957			−0.157883
$753$	31.8059	+	36.5474i	1.15907	+	1.33186i
$754$	−3.02944	+	7.31371i	−0.110326	+	0.266350i
$755$	−2.16478	−	5.94253i	−0.0787846	−	0.216271i
$756$	−4.87504	+	23.1250i	−0.177303	+	0.841047i
$757$	36.1572			1.31416			0.657078	−	0.753823i	$-0.271792\pi$
$757$	36.1572			1.31416			0.657078	+	0.753823i	$0.271792\pi$
$758$	8.21080	−	19.8226i	0.298230	−	0.719990i
$759$	5.94253	−	5.17157i	0.215700	−	0.187716i
$760$	−22.5090	+	20.6372i	−0.816486	+	0.748591i
$761$		−	4.92296i		−	0.178457i	−0.996011	−	0.0892285i	$-0.971560\pi$
$761$		−	4.92296i		−	0.178457i	0.996011	−	0.0892285i	$-0.0284401\pi$
$762$	1.77045	+	5.28156i	0.0641368	+	0.191331i
$763$			37.4893i			1.35720i
$764$	−11.8851	−	11.8851i	−0.429987	−	0.429987i
$765$	2.14891	+	10.0411i	0.0776941	+	0.363037i
$766$	24.2426	+	10.0416i	0.875922	+	0.362819i
$767$		−	13.5140i		−	0.487961i
$768$	−20.9050	+	18.1929i	−0.754344	+	0.656479i
$769$	29.5980			1.06733			0.533665	−	0.845696i	$-0.320814\pi$
$769$	29.5980			1.06733			0.533665	+	0.845696i	$0.320814\pi$
$770$	−30.1898	−	1.30967i	−1.08796	−	0.0471972i
$771$	−3.17157	+	2.76011i	−0.114221	+	0.0994028i
$772$	19.2965	−	19.2965i	0.694495	−	0.694495i
$773$			38.1145i			1.37088i	0.728128	+	0.685442i	$0.240391\pi$
$773$			38.1145i			1.37088i	−0.728128	+	0.685442i	$0.759609\pi$
$774$	18.7118	−	31.8473i	0.672582	−	1.14473i
$775$	21.9607	+	26.1421i	0.788853	+	0.939053i
$776$	11.8851	+	28.6931i	0.426649	+	1.03002i
$777$	−23.0698	+	20.0768i	−0.827624	+	0.720251i
$778$	6.82233	−	16.4706i	0.244592	−	0.590498i
$779$			11.8851i			0.425827i
$780$	23.9408	−	6.88658i	0.857220	−	0.246579i
$781$		−	49.9411i		−	1.78703i
$782$	−2.16478	−	0.896683i	−0.0774125	−	0.0320653i
$783$	4.93839	+	7.57675i	0.176484	+	0.270771i
$784$		−	7.31371i		−	0.261204i
$785$	−48.9384	+	17.8276i	−1.74669	+	0.636294i
$786$	−25.9284	+	8.69156i	−0.924835	+	0.310018i
$787$		−	7.60268i		−	0.271006i	−0.990777	−	0.135503i	$-0.956735\pi$
$787$		−	7.60268i		−	0.271006i	0.990777	−	0.135503i	$-0.0432651\pi$
$788$	−11.3492	+	11.3492i	−0.404298	+	0.404298i
$789$	31.3657	+	36.0416i	1.11665	+	1.28312i
$790$	−1.53315	−	0.0665101i	−0.0545471	−	0.00236632i
$791$	−1.44190			−0.0512681
$792$	−34.5095	+	8.96575i	−1.22624	+	0.318584i
$793$		−	27.2893i		−	0.969072i
$794$	−0.298627	+	0.720950i	−0.0105979	+	0.0255856i
$795$	37.5718	+	20.7854i	1.33254	+	0.737182i
$796$	20.9706	−	20.9706i	0.743282	−	0.743282i
$797$		−	0.634051i		−	0.0224592i	−0.999937	−	0.0112296i	$-0.996425\pi$
$797$		−	0.634051i		−	0.0224592i	0.999937	−	0.0112296i	$-0.00357457\pi$
$798$	8.54851	+	25.5017i	0.302614	+	0.902749i
$799$			1.65685i			0.0586153i
$800$	26.9704	−	8.52030i	0.953549	−	0.301238i
$801$	24.9706	+	3.48106i	0.882291	+	0.122997i
$802$	32.9411	+	13.6447i	1.16319	+	0.481810i
$803$	19.1116			0.674435
$804$	0.545152	−	7.85886i	0.0192260	−	0.277161i
$805$	1.88393	+	5.17157i	0.0663999	+	0.182274i
$806$	28.6931	+	11.8851i	1.01067	+	0.418634i
$807$	−10.0384	+	8.73606i	−0.353369	+	0.307524i
$808$	−35.6054	+	14.7482i	−1.25259	+	0.518841i
$809$		−	40.5782i		−	1.42665i	−0.700832	−	0.713326i	$-0.747188\pi$
$809$		−	40.5782i		−	1.42665i	0.700832	−	0.713326i	$-0.252812\pi$
$810$	8.96303	−	27.0123i	0.314929	−	0.949115i
$811$	2.48528			0.0872700			0.0436350	−	0.999048i	$-0.486106\pi$
$811$	2.48528			0.0872700			0.0436350	+	0.999048i	$0.486106\pi$
$812$	5.59767	+	5.59767i	0.196440	+	0.196440i
$813$	−16.0804	−	18.4776i	−0.563964	−	0.648037i
$814$	−42.6274	−	17.6569i	−1.49409	−	0.618872i
$815$	6.66348	+	18.2919i	0.233412	+	0.640737i
$816$	6.96211	+	8.00000i	0.243723	+	0.280056i
$817$		−	42.0375i		−	1.47071i
$818$	−3.88123	+	9.37011i	−0.135704	+	0.327618i
$819$	3.02944	−	21.7310i	0.105857	−	0.759342i
$820$	4.64942	−	9.97799i	0.162365	−	0.348447i
$821$	−31.4532			−1.09772			−0.548862	−	0.835913i	$-0.684939\pi$
$821$	−31.4532			−1.09772			−0.548862	+	0.835913i	$0.684939\pi$
$822$	−6.24774	−	18.6381i	−0.217915	−	0.650077i
$823$	−48.0795			−1.67595			−0.837973	−	0.545711i	$-0.816260\pi$
$823$	−48.0795			−1.67595			−0.837973	+	0.545711i	$0.816260\pi$
$824$	−22.7506	+	9.42359i	−0.792553	+	0.328286i
$825$	35.9487	+	5.65265i	1.25157	+	0.196800i
$826$	−12.4853	−	5.17157i	−0.434418	−	0.179942i
$827$	17.7666			0.617806			0.308903	−	0.951094i	$-0.400038\pi$
$827$	17.7666			0.617806			0.308903	+	0.951094i	$0.400038\pi$
$828$	3.91417	+	5.18227i	0.136027	+	0.180096i
$829$			10.8284i			0.376087i	0.982161	+	0.188043i	$0.0602146\pi$
$829$			10.8284i			0.376087i	−0.982161	+	0.188043i	$0.939785\pi$
$830$	−0.951528	+	21.9341i	−0.0330280	+	0.761344i
$831$	−22.0296	+	19.1716i	−0.764199	+	0.665054i
$832$	18.1929	−	18.1929i	0.630724	−	0.630724i
$833$	−2.79884			−0.0969739
$834$	1.93486	+	5.77201i	0.0669986	+	0.199868i
$835$	3.85786	+	10.5902i	0.133507	+	0.366489i
$836$	−28.6931	+	28.6931i	−0.992371	+	0.992371i
$837$	29.7250	−	19.3743i	1.02745	−	0.669673i
$838$	5.49019	+	2.27411i	0.189655	+	0.0785578i
$839$	−5.52021			−0.190579			−0.0952894	−	0.995450i	$-0.530378\pi$
$839$	−5.52021			−0.190579			−0.0952894	+	0.995450i	$0.530378\pi$
$840$	2.79939	−	24.7538i	0.0965883	−	0.854088i
$841$	−25.9706			−0.895537
$842$	38.1145	+	15.7875i	1.31351	+	0.544075i
$843$	−6.75699	−	7.76429i	−0.232723	−	0.267417i
$844$	−2.14214	−	2.14214i	−0.0737353	−	0.0737353i
$845$	5.58206	−	2.03347i	0.192029	−	0.0699534i
$846$	2.32631	−	3.95937i	0.0799803	−	0.136126i
$847$	−15.1384			−0.520162
$848$	44.3462			1.52286
$849$	−29.6985	−	34.1258i	−1.01925	−	1.17120i
$850$	−3.26058	−	10.3211i	−0.111837	−	0.354012i
$851$			8.40401i			0.288086i
$852$	41.0724	+	2.84910i	1.40712	+	0.0976086i
$853$	6.98394			0.239126			0.119563	−	0.992827i	$-0.461851\pi$
$853$	6.98394			0.239126			0.119563	+	0.992827i	$0.461851\pi$
$854$	−25.2120	−	10.4432i	−0.862738	−	0.357358i
$855$	−6.77836	−	31.6729i	−0.231815	−	1.08319i
$856$	−14.8284	+	6.14214i	−0.506825	+	0.209934i
$857$	27.1367			0.926973			0.463486	−	0.886104i	$-0.346598\pi$
$857$	27.1367			0.926973			0.463486	+	0.886104i	$0.346598\pi$
$858$	31.3859	−	10.5210i	1.07150	−	0.359181i
$859$	32.1421			1.09668			0.548338	−	0.836257i	$-0.315261\pi$
$859$	32.1421			1.09668			0.548338	+	0.836257i	$0.315261\pi$
$860$	−16.4450	+	35.2922i	−0.560771	+	1.20345i
$861$	−6.36486	−	7.31371i	−0.216914	−	0.249251i
$862$	11.7607	−	28.3929i	0.400572	−	0.967066i
$863$		−	32.8113i		−	1.11691i	−0.829535	−	0.558455i	$-0.811394\pi$
$863$		−	32.8113i		−	1.11691i	0.829535	−	0.558455i	$-0.188606\pi$
$864$	−5.40484	−	28.8927i	−0.183876	−	0.982949i
$865$	0.201010	+	0.551791i	0.00683455	+	0.0187615i
$866$	38.1167	+	15.7884i	1.29526	+	0.536513i
$867$	−19.1501	+	16.6656i	−0.650372	+	0.565995i
$868$	21.9607	−	21.9607i	0.745396	−	0.745396i
$869$	−2.03916			−0.0691736
$870$	−5.94083	−	7.45585i	−0.201413	−	0.252777i
$871$			7.31371i			0.247816i
$872$	−17.8435	−	43.0781i	−0.604259	−	1.45881i
$873$	−32.6256	−	4.54822i	−1.10421	−	0.153934i
$874$	6.82843	+	2.82843i	0.230975	+	0.0956730i
$875$	−12.6942	+	22.0296i	−0.429143	+	0.744737i
$876$	−1.09030	+	15.7177i	−0.0368379	+	0.531053i
$877$	−33.4929			−1.13098			−0.565488	−	0.824757i	$-0.691312\pi$
$877$	−33.4929			−1.13098			−0.565488	+	0.824757i	$0.691312\pi$
$878$	−15.0447	−	6.23172i	−0.507734	−	0.210310i
$879$	−18.5486	−	21.3137i	−0.625627	−	0.718894i
$880$	35.3137	−	12.8643i	1.19042	−	0.433656i
$881$		−	12.3074i		−	0.414647i	−0.978272	−	0.207323i	$-0.933525\pi$
$881$		−	12.3074i		−	0.414647i	0.978272	−	0.207323i	$-0.0664752\pi$
$882$	6.68834	+	3.92972i	0.225208	+	0.132320i
$883$		−	12.4741i		−	0.419788i	−0.977724	−	0.209894i	$-0.932688\pi$
$883$		−	12.4741i		−	0.419788i	0.977724	−	0.209894i	$-0.0673119\pi$
$884$	−6.96211	−	6.96211i	−0.234161	−	0.234161i
$885$	14.2404	+	7.87804i	0.478686	+	0.264817i
$886$	21.8995	−	52.8701i	0.735728	−	1.77620i
$887$		−	37.6662i		−	1.26471i	−0.774680	−	0.632353i	$-0.782089\pi$
$887$		−	37.6662i		−	1.26471i	0.774680	−	0.632353i	$-0.217911\pi$
$888$	16.9531	−	34.0502i	0.568910	−	1.14265i
$889$	−5.17157			−0.173449
$890$	−26.5508	−	1.15181i	−0.889986	−	0.0386087i
$891$	10.3431	−	36.3762i	0.346508	−	1.21865i
$892$	14.9768	+	14.9768i	0.501460	+	0.501460i
$893$		−	5.22625i		−	0.174890i
$894$	0.561279	+	1.67439i	0.0187720	+	0.0560000i
$895$	−5.88036	−	16.1421i	−0.196559	−	0.539572i
$896$	−9.84591	−	23.7701i	−0.328929	−	0.794104i
$897$	−3.95815	−	4.54822i	−0.132159	−	0.151861i
$898$	32.3893	+	13.4161i	1.08085	+	0.447701i
$899$		−	11.8851i		−	0.396389i
$900$	−6.69968	+	29.2423i	−0.223323	+	0.974745i
$901$		−	16.9706i		−	0.565371i
$902$	5.59767	−	13.5140i	0.186382	−	0.449966i
$903$	22.5125	+	25.8686i	0.749170	+	0.860854i
$904$	1.65685	−	0.686292i	0.0551062	−	0.0228257i
$905$	16.5754	+	45.5011i	0.550986	+	1.51251i
$906$	6.56895	−	2.20201i	0.218239	−	0.0731567i
$907$			46.1956i			1.53390i	0.641707	+	0.766950i	$0.278226\pi$
$907$			46.1956i			1.53390i	−0.641707	+	0.766950i	$0.721774\pi$
$908$	6.75699	+	6.75699i	0.224238	+	0.224238i
$909$	5.64391	−	40.4853i	0.187197	−	1.34281i
$910$	−1.00238	+	23.1062i	−0.0332285	+	0.765965i
$911$	−28.6931			−0.950645			−0.475322	−	0.879812i	$-0.657669\pi$
$911$	−28.6931			−0.950645			−0.475322	+	0.879812i	$0.657669\pi$
$912$	−21.9607	−	25.2346i	−0.727193	−	0.835600i
$913$			29.1732i			0.965493i
$914$	−16.8080	−	6.96211i	−0.555960	−	0.230286i
$915$	28.7562	+	15.9084i	0.950652	+	0.525917i
$916$	4.68629	−	4.68629i	0.154839	−	0.154839i
$917$		−	25.3884i		−	0.838400i
$918$	−11.0568	+	2.06834i	−0.364927	+	0.0682655i
$919$		−	22.1421i		−	0.730402i	−0.930929	−	0.365201i	$-0.881000\pi$
$919$		−	22.1421i		−	0.730402i	0.930929	−	0.365201i	$-0.119000\pi$
$920$	−4.62626	−	5.04585i	−0.152523	−	0.166357i
$921$	−20.2426	−	23.2603i	−0.667018	−	0.766454i
$922$	−10.0384	+	24.2349i	−0.330597	+	0.798132i
$923$	−38.2233			−1.25813
$924$	2.29073	−	33.0230i	0.0753595	−	1.08638i
$925$	−29.7250	+	24.9706i	−0.977353	+	0.821027i
$926$	−2.67264	+	6.45232i	−0.0878284	+	0.212036i
$927$	3.60625	−	25.8686i	0.118445	−	0.849637i
$928$	−9.09644	−	3.76787i	−0.298605	−	0.123686i
$929$			56.3666i			1.84933i	0.380784	+	0.924664i	$0.375654\pi$
$929$			56.3666i			1.84933i	−0.380784	+	0.924664i	$0.624346\pi$
$930$	−29.2507	+	23.3070i	−0.959169	+	0.764267i
$931$	8.82843			0.289340
$932$	39.6452	+	39.6452i	1.29862	+	1.29862i
$933$	−12.8643	+	11.1953i	−0.421158	+	0.366519i
$934$	−4.72792	+	11.4142i	−0.154702	+	0.373484i
$935$	−4.92296	−	13.5140i	−0.160998	−	0.441954i
$936$	6.86209	+	26.4125i	0.224294	+	0.863318i
$937$			32.9411i			1.07614i	0.842900	+	0.538070i	$0.180846\pi$
$937$			32.9411i			1.07614i	−0.842900	+	0.538070i	$0.819154\pi$
$938$	6.75699	+	2.79884i	0.220623	+	0.0913852i
$939$	−28.0000	−	32.1741i	−0.913745	−	1.04996i
$940$	−2.04450	+	4.38765i	−0.0666843	+	0.143109i
$941$	−3.18243			−0.103744			−0.0518721	−	0.998654i	$-0.516519\pi$
$941$	−3.18243			−0.103744			−0.0518721	+	0.998654i	$0.516519\pi$
$942$	−18.1341	−	54.0972i	−0.590842	−	1.76258i
$943$	−2.66428			−0.0867610
$944$	16.8080			0.547055
$945$	21.1331	+	15.8605i	0.687460	+	0.515941i
$946$	−19.7990	+	47.7990i	−0.643721	+	1.55408i
$947$	−36.5068			−1.18631			−0.593156	−	0.805087i	$-0.702118\pi$
$947$	−36.5068			−1.18631			−0.593156	+	0.805087i	$0.702118\pi$
$948$	0.116332	−	1.67703i	0.00377829	−	0.0544675i
$949$		−	14.6274i		−	0.474826i
$950$	10.2849	+	32.5562i	0.333687	+	1.05626i
$951$	11.1641	+	12.8284i	0.362021	+	0.415990i
$952$	−9.09644	+	3.76787i	−0.294817	+	0.122117i
$953$	−39.9079			−1.29274			−0.646371	−	0.763023i	$-0.723714\pi$
$953$	−39.9079			−1.29274			−0.646371	+	0.763023i	$0.723714\pi$
$954$	−23.8276	+	40.5544i	−0.771447	+	1.31300i
$955$	−17.6569	+	6.43215i	−0.571362	+	0.208140i
$956$	−18.8472	−	18.8472i	−0.609561	−	0.609561i
$957$	−8.31609	−	9.55582i	−0.268821	−	0.308896i
$958$	8.31609	−	20.0768i	0.268681	−	0.648652i
$959$	18.2499			0.589321
$960$	8.56519	+	29.7765i	0.276440	+	0.961031i
$961$	−15.6274			−0.504110
$962$	−13.5140	+	32.6256i	−0.435708	+	1.05189i
$963$	2.35049	−	16.8607i	0.0757436	−	0.543329i
$964$	−14.8284	−	14.8284i	−0.477591	−	0.477591i
$965$	−10.4432	−	28.6675i	−0.336177	−	0.922838i
$966$	−5.71672	+	1.91633i	−0.183933	+	0.0616568i
$967$	51.8474			1.66730			0.833650	−	0.552293i	$-0.186247\pi$
$967$	51.8474			1.66730			0.833650	+	0.552293i	$0.186247\pi$
$968$	17.3952	−	7.20533i	0.559103	−	0.231588i
$969$	−9.65685	+	8.40401i	−0.310223	+	0.269976i
$970$	34.6904	+	1.50491i	1.11384	+	0.0483198i
$971$		−	48.2612i		−	1.54878i	−0.632711	−	0.774388i	$-0.718058\pi$
$971$		−	48.2612i		−	1.54878i	0.632711	−	0.774388i	$-0.281942\pi$
$972$	29.3263	+	10.5816i	0.940640	+	0.339405i
$973$	−5.65180			−0.181188
$974$	10.6543	−	25.7218i	0.341387	−	0.824180i
$975$	4.32635	−	27.5140i	0.138554	−	0.881152i
$976$	33.9411			1.08643
$977$	13.7766			0.440753			0.220376	−	0.975415i	$-0.429271\pi$
$977$	13.7766			0.440753			0.220376	+	0.975415i	$0.429271\pi$
$978$	−20.2201	+	6.77806i	−0.646567	+	0.216738i
$979$	−35.3137			−1.12863
$980$	−7.41182	−	3.45367i	−0.236762	−	0.110323i
$981$	48.9822	+	6.82843i	1.56388	+	0.218015i
$982$	−18.3545	−	7.60268i	−0.585715	−	0.242611i
$983$			1.97908i			0.0631227i	0.999502	+	0.0315613i	$0.0100480\pi$
$983$			1.97908i			0.0631227i	−0.999502	+	0.0315613i	$0.989952\pi$
$984$	10.7948	+	5.37457i	0.344125	+	0.171335i
$985$	6.14214	+	16.8607i	0.195705	+	0.537228i
$986$	−1.44190	+	3.48106i	−0.0459195	+	0.110859i
$987$	2.79884	+	3.21608i	0.0890879	+	0.102369i
$988$	21.9607	+	21.9607i	0.698664	+	0.698664i
$989$	9.42359			0.299653
$990$	−7.21003	+	39.2063i	−0.229150	+	1.24606i
$991$		−	19.7990i		−	0.628936i	−0.949268	−	0.314468i	$-0.898174\pi$
$991$		−	19.7990i		−	0.628936i	0.949268	−	0.314468i	$-0.101826\pi$
$992$	−14.7821	+	35.6871i	−0.469331	+	1.13307i
$993$	−1.97908	+	1.72232i	−0.0628041	+	0.0546561i
$994$	−14.6274	+	35.3137i	−0.463953	+	1.12008i
$995$	−11.3492	−	31.1546i	−0.359793	−	0.987666i
$996$	−23.9925	−	1.66431i	−0.760233	−	0.0527357i
$997$	12.3125			0.389941			0.194971	−	0.980809i	$-0.437539\pi$
$997$	12.3125			0.389941			0.194971	+	0.980809i	$0.437539\pi$
$998$	13.5909	−	32.8113i	0.430212	−	1.03862i
$999$	22.0296	+	33.7990i	0.696986	+	1.06935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.2.m.b.59.9	yes	16
3.2	odd	2	inner	120.2.m.b.59.7	yes	16
4.3	odd	2		480.2.m.b.239.3		16
5.2	odd	4		600.2.b.i.251.15		16
5.3	odd	4		600.2.b.i.251.2		16
5.4	even	2	inner	120.2.m.b.59.8	yes	16
8.3	odd	2	inner	120.2.m.b.59.11	yes	16
8.5	even	2		480.2.m.b.239.4		16
12.11	even	2		480.2.m.b.239.16		16
15.2	even	4		600.2.b.i.251.1		16
15.8	even	4		600.2.b.i.251.16		16
15.14	odd	2	inner	120.2.m.b.59.10	yes	16
20.3	even	4		2400.2.b.i.2351.6		16
20.7	even	4		2400.2.b.i.2351.11		16
20.19	odd	2		480.2.m.b.239.13		16
24.5	odd	2		480.2.m.b.239.15		16
24.11	even	2	inner	120.2.m.b.59.5	✓	16
40.3	even	4		600.2.b.i.251.14		16
40.13	odd	4		2400.2.b.i.2351.5		16
40.19	odd	2	inner	120.2.m.b.59.6	yes	16
40.27	even	4		600.2.b.i.251.3		16
40.29	even	2		480.2.m.b.239.14		16
40.37	odd	4		2400.2.b.i.2351.12		16
60.23	odd	4		2400.2.b.i.2351.8		16
60.47	odd	4		2400.2.b.i.2351.9		16
60.59	even	2		480.2.m.b.239.2		16
120.29	odd	2		480.2.m.b.239.1		16
120.53	even	4		2400.2.b.i.2351.7		16
120.59	even	2	inner	120.2.m.b.59.12	yes	16
120.77	even	4		2400.2.b.i.2351.10		16
120.83	odd	4		600.2.b.i.251.4		16
120.107	odd	4		600.2.b.i.251.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.m.b.59.5	✓	16	24.11	even	2	inner
120.2.m.b.59.6	yes	16	40.19	odd	2	inner
120.2.m.b.59.7	yes	16	3.2	odd	2	inner
120.2.m.b.59.8	yes	16	5.4	even	2	inner
120.2.m.b.59.9	yes	16	1.1	even	1	trivial
120.2.m.b.59.10	yes	16	15.14	odd	2	inner
120.2.m.b.59.11	yes	16	8.3	odd	2	inner
120.2.m.b.59.12	yes	16	120.59	even	2	inner
480.2.m.b.239.1		16	120.29	odd	2
480.2.m.b.239.2		16	60.59	even	2
480.2.m.b.239.3		16	4.3	odd	2
480.2.m.b.239.4		16	8.5	even	2
480.2.m.b.239.13		16	20.19	odd	2
480.2.m.b.239.14		16	40.29	even	2
480.2.m.b.239.15		16	24.5	odd	2
480.2.m.b.239.16		16	12.11	even	2
600.2.b.i.251.1		16	15.2	even	4
600.2.b.i.251.2		16	5.3	odd	4
600.2.b.i.251.3		16	40.27	even	4
600.2.b.i.251.4		16	120.83	odd	4
600.2.b.i.251.13		16	120.107	odd	4
600.2.b.i.251.14		16	40.3	even	4
600.2.b.i.251.15		16	5.2	odd	4
600.2.b.i.251.16		16	15.8	even	4
2400.2.b.i.2351.5		16	40.13	odd	4
2400.2.b.i.2351.6		16	20.3	even	4
2400.2.b.i.2351.7		16	120.53	even	4
2400.2.b.i.2351.8		16	60.23	odd	4
2400.2.b.i.2351.9		16	60.47	odd	4
2400.2.b.i.2351.10		16	120.77	even	4
2400.2.b.i.2351.11		16	20.7	even	4
2400.2.b.i.2351.12		16	40.37	odd	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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	120.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.541196 - 1.30656i) q^{2} +(1.30656 - 1.13705i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(-2.10100 + 0.765367i) q^{5} +(-0.778527 - 2.32248i) q^{6} +2.27411 q^{7} +(-2.61313 + 1.08239i) q^{8} +(0.414214 - 2.97127i) q^{9} +O(q^{10})\)	\(q+(0.541196 - 1.30656i) q^{2} +(1.30656 - 1.13705i) q^{3} +(-1.41421 - 1.41421i) q^{4} +(-2.10100 + 0.765367i) q^{5} +(-0.778527 - 2.32248i) q^{6} +2.27411 q^{7} +(-2.61313 + 1.08239i) q^{8} +(0.414214 - 2.97127i) q^{9} +(-0.137055 + 3.15931i) q^{10} +4.20201i q^{11} +(-3.45580 - 0.239721i) q^{12} +3.21608 q^{13} +(1.23074 - 2.97127i) q^{14} +(-1.87483 + 3.38896i) q^{15} +4.00000i q^{16} +1.53073 q^{17} +(-3.65798 - 2.14923i) q^{18} -4.82843 q^{19} +(4.05366 + 1.88887i) q^{20} +(2.97127 - 2.58579i) q^{21} +(5.49019 + 2.27411i) q^{22} -1.08239i q^{23} +(-2.18347 + 4.38548i) q^{24} +(3.82843 - 3.21608i) q^{25} +(1.74053 - 4.20201i) q^{26} +(-2.83730 - 4.35313i) q^{27} +(-3.21608 - 3.21608i) q^{28} -1.74053 q^{29} +(3.41323 + 4.28367i) q^{30} +6.82843i q^{31} +(5.22625 + 2.16478i) q^{32} +(4.77791 + 5.49019i) q^{33} +(0.828427 - 2.00000i) q^{34} +(-4.77791 + 1.74053i) q^{35} +(-4.78779 + 3.61622i) q^{36} -7.76429 q^{37} +(-2.61313 + 6.30864i) q^{38} +(4.20201 - 3.65685i) q^{39} +(4.66176 - 4.27411i) q^{40} -2.46148i q^{41} +(-1.77045 - 5.28156i) q^{42} +8.70626i q^{43} +(5.94253 - 5.94253i) q^{44} +(1.40385 + 6.55967i) q^{45} +(-1.41421 - 0.585786i) q^{46} +1.08239i q^{47} +(4.54822 + 5.22625i) q^{48} -1.82843 q^{49} +(-2.13008 - 6.74261i) q^{50} +(2.00000 - 1.74053i) q^{51} +(-4.54822 - 4.54822i) q^{52} -11.0866i q^{53} +(-7.22317 + 1.35121i) q^{54} +(-3.21608 - 8.82843i) q^{55} +(-5.94253 + 2.46148i) q^{56} +(-6.30864 + 5.49019i) q^{57} +(-0.941967 + 2.27411i) q^{58} -4.20201i q^{59} +(7.44411 - 2.14130i) q^{60} -8.48528i q^{61} +(8.92177 + 3.69552i) q^{62} +(0.941967 - 6.75699i) q^{63} +(5.65685 - 5.65685i) q^{64} +(-6.75699 + 2.46148i) q^{65} +(9.75906 - 3.27137i) q^{66} +2.27411i q^{67} +(-2.16478 - 2.16478i) q^{68} +(-1.23074 - 1.41421i) q^{69} +(-0.311677 + 7.18461i) q^{70} -11.8851 q^{71} +(2.13368 + 8.21264i) q^{72} -4.54822i q^{73} +(-4.20201 + 10.1445i) q^{74} +(1.34523 - 8.55514i) q^{75} +(6.82843 + 6.82843i) q^{76} +9.55582i q^{77} +(-2.50380 - 7.46926i) q^{78} +0.485281i q^{79} +(-3.06147 - 8.40401i) q^{80} +(-8.65685 - 2.46148i) q^{81} +(-3.21608 - 1.33214i) q^{82} +6.94269 q^{83} +(-7.85886 - 0.545152i) q^{84} +(-3.21608 + 1.17157i) q^{85} +(11.3753 + 4.71179i) q^{86} +(-2.27411 + 1.97908i) q^{87} +(-4.54822 - 10.9804i) q^{88} +8.40401i q^{89} +(9.33037 + 1.71585i) q^{90} +7.31371 q^{91} +(-1.53073 + 1.53073i) q^{92} +(7.76429 + 8.92177i) q^{93} +(1.41421 + 0.585786i) q^{94} +(10.1445 - 3.69552i) q^{95} +(9.28991 - 3.11411i) q^{96} -10.9804i q^{97} +(-0.989538 + 2.38896i) q^{98} +(12.4853 + 1.74053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^9	\( 16 q - 16 q^{9} + 16 q^{10} - 32 q^{19} - 32 q^{24} + 16 q^{25} + 16 q^{30} - 32 q^{34} - 32 q^{36} + 32 q^{40} + 16 q^{49} + 32 q^{51} + 32 q^{54} + 64 q^{66} - 64 q^{70} + 32 q^{75} + 64 q^{76} - 48 q^{81} + 32 q^{84} - 16 q^{90} - 64 q^{91} + 64 q^{96} + 64 q^{99}+O(q^{100}) \) 16 * q - 16 * q^9 + 16 * q^10 - 32 * q^19 - 32 * q^24 + 16 * q^25 + 16 * q^30 - 32 * q^34 - 32 * q^36 + 32 * q^40 + 16 * q^49 + 32 * q^51 + 32 * q^54 + 64 * q^66 - 64 * q^70 + 32 * q^75 + 64 * q^76 - 48 * q^81 + 32 * q^84 - 16 * q^90 - 64 * q^91 + 64 * q^96 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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