LMFDB - Embedded newform 600.2.b.i.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(251,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("600.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.b (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:	$4.79102412128$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.1
Root			$-0.528036i$ of defining polynomial
Character	$\chi$	$=$	600.251
Dual form			600.2.b.i.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30656 - 0.541196i) q^{2} +(-1.13705 + 1.30656i) q^{3} +(1.41421 + 1.41421i) q^{4} +(2.19274 - 1.09174i) q^{6} +2.27411i q^{7} +(-1.08239 - 2.61313i) q^{8} +(-0.414214 - 2.97127i) q^{9} +O(q^{10})$	\(q+(-1.30656 - 0.541196i) q^{2} +(-1.13705 + 1.30656i) q^{3} +(1.41421 + 1.41421i) q^{4} +(2.19274 - 1.09174i) q^{6} +2.27411i q^{7} +(-1.08239 - 2.61313i) q^{8} +(-0.414214 - 2.97127i) q^{9} -4.20201i q^{11} +(-3.45580 + 0.239721i) q^{12} -3.21608i q^{13} +(1.23074 - 2.97127i) q^{14} +4.00000i q^{16} -1.53073i q^{17} +(-1.06684 + 4.10632i) q^{18} +4.82843 q^{19} +(-2.97127 - 2.58579i) q^{21} +(-2.27411 + 5.49019i) q^{22} +1.08239 q^{23} +(4.64495 + 1.55705i) q^{24} +(-1.74053 + 4.20201i) q^{26} +(4.35313 + 2.83730i) q^{27} +(-3.21608 + 3.21608i) q^{28} -1.74053 q^{29} +6.82843i q^{31} +(2.16478 - 5.22625i) q^{32} +(5.49019 + 4.77791i) q^{33} +(-0.828427 + 2.00000i) q^{34} +(3.61622 - 4.78779i) q^{36} -7.76429i q^{37} +(-6.30864 - 2.61313i) q^{38} +(4.20201 + 3.65685i) q^{39} +2.46148i q^{41} +(2.48273 + 4.98653i) q^{42} +8.70626 q^{43} +(5.94253 - 5.94253i) q^{44} +(-1.41421 - 0.585786i) q^{46} +1.08239 q^{47} +(-5.22625 - 4.54822i) q^{48} +1.82843 q^{49} +(2.00000 + 1.74053i) q^{51} +(4.54822 - 4.54822i) q^{52} +11.0866 q^{53} +(-4.15211 - 6.06300i) q^{54} +(5.94253 - 2.46148i) q^{56} +(-5.49019 + 6.30864i) q^{57} +(2.27411 + 0.941967i) q^{58} -4.20201i q^{59} -8.48528i q^{61} +(3.69552 - 8.92177i) q^{62} +(6.75699 - 0.941967i) q^{63} +(-5.65685 + 5.65685i) q^{64} +(-4.58749 - 9.21391i) q^{66} -2.27411 q^{67} +(2.16478 - 2.16478i) q^{68} +(-1.23074 + 1.41421i) q^{69} +11.8851 q^{71} +(-7.31595 + 4.29847i) q^{72} -4.54822 q^{73} +(-4.20201 + 10.1445i) q^{74} +(6.82843 + 6.82843i) q^{76} +9.55582 q^{77} +(-3.51111 - 7.05202i) q^{78} -0.485281i q^{79} +(-8.65685 + 2.46148i) q^{81} +(1.33214 - 3.21608i) q^{82} +6.94269i q^{83} +(-0.545152 - 7.85886i) q^{84} +(-11.3753 - 4.71179i) q^{86} +(1.97908 - 2.27411i) q^{87} +(-10.9804 + 4.54822i) q^{88} +8.40401i q^{89} +7.31371 q^{91} +(1.53073 + 1.53073i) q^{92} +(-8.92177 - 7.76429i) q^{93} +(-1.41421 - 0.585786i) q^{94} +(4.36695 + 8.77096i) q^{96} +10.9804 q^{97} +(-2.38896 - 0.989538i) 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} + 32 q^{19} + 32 q^{24} + 32 q^{34} - 32 q^{36} - 16 q^{49} + 32 q^{51} - 32 q^{54} + 64 q^{66} + 64 q^{76} - 48 q^{81} - 32 q^{84} - 64 q^{91} + 64 q^{96} - 64 q^{99}+O(q^{100}) $ 16 * q + 16 * q^9 + 32 * q^19 + 32 * q^24 + 32 * q^34 - 32 * q^36 - 16 * q^49 + 32 * q^51 - 32 * q^54 + 64 * q^66 + 64 * q^76 - 48 * q^81 - 32 * q^84 - 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 $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	−1.30656	−	0.541196i	−0.923880	−	0.382683i
$2$	−1.30656	−	0.541196i	−0.923880	−	0.382683i
$3$	−1.13705	+	1.30656i	−0.656479	+	0.754344i
$3$	−1.13705	+	1.30656i	−0.656479	+	0.754344i
$4$	1.41421	+	1.41421i	0.707107	+	0.707107i
$5$		0			0
$5$		0			0
$6$	2.19274	−	1.09174i	0.895182	−	0.445700i
$7$			2.27411i			0.859533i	0.902940	+	0.429766i	$0.141404\pi$
$7$			2.27411i			0.859533i	−0.902940	+	0.429766i	$0.858596\pi$
$8$	−1.08239	−	2.61313i	−0.382683	−	0.923880i
$9$	−0.414214	−	2.97127i	−0.138071	−	0.990422i
$10$		0			0
$11$		−	4.20201i		−	1.26695i	−0.773762	−	0.633476i	$-0.781627\pi$
$11$		−	4.20201i		−	1.26695i	0.773762	−	0.633476i	$-0.218373\pi$
$12$	−3.45580	+	0.239721i	−0.997603	+	0.0692015i
$13$		−	3.21608i		−	0.891979i	−0.895038	−	0.445990i	$-0.852852\pi$
$13$		−	3.21608i		−	0.891979i	0.895038	−	0.445990i	$-0.147148\pi$
$14$	1.23074	−	2.97127i	0.328929	−	0.794104i
$15$		0			0
$16$			4.00000i			1.00000i
$17$		−	1.53073i		−	0.371257i	−0.982620	−	0.185629i	$-0.940568\pi$
$17$		−	1.53073i		−	0.371257i	0.982620	−	0.185629i	$-0.0594322\pi$
$18$	−1.06684	+	4.10632i	−0.251457	+	0.967868i
$19$	4.82843			1.10772			0.553859	−	0.832611i	$-0.313155\pi$
$19$	4.82843			1.10772			0.553859	+	0.832611i	$0.313155\pi$
$20$		0			0
$21$	−2.97127	−	2.58579i	−0.648384	−	0.564265i
$22$	−2.27411	+	5.49019i	−0.484842	+	1.17051i
$23$	1.08239			0.225694			0.112847	−	0.993612i	$-0.464003\pi$
$23$	1.08239			0.225694			0.112847	+	0.993612i	$0.464003\pi$
$24$	4.64495	+	1.55705i	0.948147	+	0.317832i
$25$		0			0
$26$	−1.74053	+	4.20201i	−0.341346	+	0.824081i
$27$	4.35313	+	2.83730i	0.837760	+	0.546038i
$28$	−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	$0.551667\pi$
$30$		0			0
$31$			6.82843i			1.22642i	0.789919	+	0.613211i	$0.210122\pi$
$31$			6.82843i			1.22642i	−0.789919	+	0.613211i	$0.789878\pi$
$32$	2.16478	−	5.22625i	0.382683	−	0.923880i
$33$	5.49019	+	4.77791i	0.955719	+	0.831727i
$34$	−0.828427	+	2.00000i	−0.142074	+	0.342997i
$35$		0			0
$36$	3.61622	−	4.78779i	0.602703	−	0.797965i
$37$		−	7.76429i		−	1.27644i	−0.769853	−	0.638221i	$-0.779671\pi$
$37$		−	7.76429i		−	1.27644i	0.769853	−	0.638221i	$-0.220329\pi$
$38$	−6.30864	−	2.61313i	−1.02340	−	0.423905i
$39$	4.20201	+	3.65685i	0.672859	+	0.585565i
$40$		0			0
$41$			2.46148i			0.384418i	0.981354	+	0.192209i	$0.0615652\pi$
$41$			2.46148i			0.384418i	−0.981354	+	0.192209i	$0.938435\pi$
$42$	2.48273	+	4.98653i	0.383094	+	0.769438i
$43$	8.70626			1.32769			0.663846	−	0.747869i	$-0.268923\pi$
$43$	8.70626			1.32769			0.663846	+	0.747869i	$0.268923\pi$
$44$	5.94253	−	5.94253i	0.895871	−	0.895871i
$45$		0			0
$46$	−1.41421	−	0.585786i	−0.208514	−	0.0863695i
$47$	1.08239			0.157883			0.0789416	−	0.996879i	$-0.474846\pi$
$47$	1.08239			0.157883			0.0789416	+	0.996879i	$0.474846\pi$
$48$	−5.22625	−	4.54822i	−0.754344	−	0.656479i
$49$	1.82843			0.261204
$50$		0			0
$51$	2.00000	+	1.74053i	0.280056	+	0.243723i
$52$	4.54822	−	4.54822i	0.630724	−	0.630724i
$53$	11.0866			1.52286			0.761428	−	0.648250i	$-0.224499\pi$
$53$	11.0866			1.52286			0.761428	+	0.648250i	$0.224499\pi$
$54$	−4.15211	−	6.06300i	−0.565030	−	0.825070i
$55$		0			0
$56$	5.94253	−	2.46148i	0.794104	−	0.328929i
$57$	−5.49019	+	6.30864i	−0.727193	+	0.835600i
$58$	2.27411	+	0.941967i	0.298605	+	0.123686i
$59$		−	4.20201i		−	0.547055i	−0.961864	−	0.273527i	$-0.911810\pi$
$59$		−	4.20201i		−	0.547055i	0.961864	−	0.273527i	$-0.0881904\pi$
$60$		0			0
$61$		−	8.48528i		−	1.08643i	−0.839594	−	0.543214i	$-0.817207\pi$
$61$		−	8.48528i		−	1.08643i	0.839594	−	0.543214i	$-0.182793\pi$
$62$	3.69552	−	8.92177i	0.469331	−	1.13307i
$63$	6.75699	−	0.941967i	0.851300	−	0.118677i
$64$	−5.65685	+	5.65685i	−0.707107	+	0.707107i
$65$		0			0
$66$	−4.58749	−	9.21391i	−0.564681	−	1.13415i
$67$	−2.27411			−0.277827			−0.138913	−	0.990305i	$-0.544361\pi$
$67$	−2.27411			−0.277827			−0.138913	+	0.990305i	$0.544361\pi$
$68$	2.16478	−	2.16478i	0.262519	−	0.262519i
$69$	−1.23074	+	1.41421i	−0.148164	+	0.170251i
$70$		0			0
$71$	11.8851			1.41050			0.705249	−	0.708960i	$-0.250835\pi$
$71$	11.8851			1.41050			0.705249	+	0.708960i	$0.250835\pi$
$72$	−7.31595	+	4.29847i	−0.862193	+	0.506579i
$73$	−4.54822			−0.532329			−0.266164	−	0.963928i	$-0.585756\pi$
$73$	−4.54822			−0.532329			−0.266164	+	0.963928i	$0.585756\pi$
$74$	−4.20201	+	10.1445i	−0.488473	+	1.17928i
$75$		0			0
$76$	6.82843	+	6.82843i	0.783274	+	0.783274i
$77$	9.55582			1.08899
$78$	−3.51111	−	7.05202i	−0.397555	−	0.798484i
$79$		−	0.485281i		−	0.0545984i	−0.999627	−	0.0272992i	$-0.991309\pi$
$79$		−	0.485281i		−	0.0545984i	0.999627	−	0.0272992i	$-0.00869069\pi$
$80$		0			0
$81$	−8.65685	+	2.46148i	−0.961873	+	0.273498i
$82$	1.33214	−	3.21608i	0.147111	−	0.355156i
$83$			6.94269i			0.762060i	0.924563	+	0.381030i	$0.124431\pi$
$83$			6.94269i			0.762060i	−0.924563	+	0.381030i	$0.875569\pi$
$84$	−0.545152	−	7.85886i	−0.0594809	−	0.857472i
$85$		0			0
$86$	−11.3753	−	4.71179i	−1.22663	−	0.508086i
$87$	1.97908	−	2.27411i	0.212179	−	0.243810i
$88$	−10.9804	+	4.54822i	−1.17051	+	0.484842i
$89$			8.40401i			0.890823i	0.895326	+	0.445412i	$0.146943\pi$
$89$			8.40401i			0.890823i	−0.895326	+	0.445412i	$0.853057\pi$
$90$		0			0
$91$	7.31371			0.766685
$92$	1.53073	+	1.53073i	0.159590	+	0.159590i
$93$	−8.92177	−	7.76429i	−0.925144	−	0.805120i
$94$	−1.41421	−	0.585786i	−0.145865	−	0.0604193i
$95$		0			0
$96$	4.36695	+	8.77096i	0.445700	+	0.895182i
$97$	10.9804			1.11489			0.557444	−	0.830215i	$-0.311782\pi$
$97$	10.9804			1.11489			0.557444	+	0.830215i	$0.311782\pi$
$98$	−2.38896	−	0.989538i	−0.241321	−	0.0999584i
$99$	−12.4853	+	1.74053i	−1.25482	+	0.174930i
$100$		0			0
$101$	−13.6256			−1.35580			−0.677899	−	0.735155i	$-0.737109\pi$
$101$	−13.6256			−1.35580			−0.677899	+	0.735155i	$0.737109\pi$
$102$	−1.67116	−	3.35650i	−0.165469	−	0.332343i
$103$		−	8.70626i		−	0.857853i	−0.903339	−	0.428927i	$-0.858892\pi$
$103$		−	8.70626i		−	0.857853i	0.903339	−	0.428927i	$-0.141108\pi$
$104$	−8.40401	+	3.48106i	−0.824081	+	0.341346i
$105$		0			0
$106$	−14.4853	−	6.00000i	−1.40693	−	0.582772i
$107$		−	5.67459i		−	0.548584i	−0.961647	−	0.274292i	$-0.911557\pi$
$107$		−	5.67459i		−	0.548584i	0.961647	−	0.274292i	$-0.0884434\pi$
$108$	2.14371	+	10.1688i	0.206279	+	0.978493i
$109$		−	16.4853i		−	1.57900i	−0.613748	−	0.789502i	$-0.710339\pi$
$109$		−	16.4853i		−	1.57900i	0.613748	−	0.789502i	$-0.289661\pi$
$110$		0			0
$111$	10.1445	+	8.82843i	0.962877	+	0.837957i
$112$	−9.09644			−0.859533
$113$		−	0.634051i		−	0.0596465i	−0.999555	−	0.0298232i	$-0.990506\pi$
$113$		−	0.634051i		−	0.0596465i	0.999555	−	0.0298232i	$-0.00949444\pi$
$114$	10.5875	−	5.27137i	0.991609	−	0.493709i
$115$		0			0
$116$	−2.46148	−	2.46148i	−0.228543	−	0.228543i
$117$	−9.55582	+	1.33214i	−0.883436	+	0.123157i
$118$	−2.27411	+	5.49019i	−0.209349	+	0.505413i
$119$	3.48106			0.319108
$120$		0			0
$121$	−6.65685			−0.605169
$122$	−4.59220	+	11.0866i	−0.415758	+	1.00373i
$123$	−3.21608	−	2.79884i	−0.289984	−	0.252362i
$124$	−9.65685	+	9.65685i	−0.867211	+	0.867211i
$125$		0			0
$126$	−9.33822	−	2.42612i	−0.831914	−	0.216136i
$127$		−	2.27411i		−	0.201795i	−0.994897	−	0.100897i	$-0.967829\pi$
$127$		−	2.27411i		−	0.201795i	0.994897	−	0.100897i	$-0.0321713\pi$
$128$	10.4525	−	4.32957i	0.923880	−	0.382683i
$129$	−9.89949	+	11.3753i	−0.871602	+	1.00154i
$130$		0			0
$131$			11.1641i			0.975413i	0.873008	+	0.487707i	$0.162166\pi$
$131$			11.1641i			0.975413i	−0.873008	+	0.487707i	$0.837834\pi$
$132$	1.00731	+	14.5213i	0.0876750	+	1.26392i
$133$			10.9804i			0.952119i
$134$	2.97127	+	1.23074i	0.256678	+	0.106320i
$135$		0			0
$136$	−4.00000	+	1.65685i	−0.342997	+	0.142074i
$137$		−	8.02509i		−	0.685629i	−0.939403	−	0.342815i	$-0.888620\pi$
$137$		−	8.02509i		−	0.685629i	0.939403	−	0.342815i	$-0.111380\pi$
$138$	2.37340	−	1.18169i	0.202038	−	0.100592i
$139$	2.48528			0.210799			0.105399	−	0.994430i	$-0.466388\pi$
$139$	2.48528			0.210799			0.105399	+	0.994430i	$0.466388\pi$
$140$		0			0
$141$	−1.23074	+	1.41421i	−0.103647	+	0.119098i
$142$	−15.5286	−	6.43215i	−1.30313	−	0.539774i
$143$	−13.5140			−1.13010
$144$	11.8851	−	1.65685i	0.990422	−	0.138071i
$145$		0			0
$146$	5.94253	+	2.46148i	0.491808	+	0.203713i
$147$	−2.07902	+	2.38896i	−0.171475	+	0.197038i
$148$	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	$0.509401\pi$
$150$		0			0
$151$			2.82843i			0.230174i	0.993355	+	0.115087i	$0.0367147\pi$
$151$			2.82843i			0.230174i	−0.993355	+	0.115087i	$0.963285\pi$
$152$	−5.22625	−	12.6173i	−0.423905	−	1.02340i
$153$	−4.54822	+	0.634051i	−0.367702	+	0.0512600i
$154$	−12.4853	−	5.17157i	−1.00609	−	0.416737i
$155$		0			0
$156$	0.770961	+	11.1141i	0.0617263	+	0.889841i
$157$			23.2929i			1.85897i	0.368854	+	0.929487i	$0.379750\pi$
$157$			23.2929i			1.85897i	−0.368854	+	0.929487i	$0.620250\pi$
$158$	−0.262632	+	0.634051i	−0.0208939	+	0.0504424i
$159$	−12.6060	+	14.4853i	−0.999722	+	1.14876i
$160$		0			0
$161$			2.46148i			0.193992i
$162$	12.6429	+	1.46898i	0.993317	+	0.115414i
$163$	−8.70626			−0.681927			−0.340964	−	0.940077i	$-0.610753\pi$
$163$	−8.70626			−0.681927			−0.340964	+	0.940077i	$0.610753\pi$
$164$	−3.48106	+	3.48106i	−0.271825	+	0.271825i
$165$		0			0
$166$	3.75736	−	9.07107i	0.291628	−	0.704051i
$167$	−5.04054			−0.390049			−0.195024	−	0.980798i	$-0.562479\pi$
$167$	−5.04054			−0.390049			−0.195024	+	0.980798i	$0.562479\pi$
$168$	−3.54091	+	10.5631i	−0.273187	+	0.814963i
$169$	2.65685			0.204373
$170$		0			0
$171$	−2.00000	−	14.3465i	−0.152944	−	1.09711i
$172$	12.3125	+	12.3125i	0.938820	+	0.938820i
$173$	0.262632			0.0199676			0.00998379	−	0.999950i	$-0.496822\pi$
$173$	0.262632			0.0199676			0.00998379	+	0.999950i	$0.496822\pi$
$174$	−3.81653	+	1.90020i	−0.289330	+	0.144054i
$175$		0			0
$176$	16.8080			1.26695
$177$	5.49019	+	4.77791i	0.412668	+	0.359130i
$178$	4.54822	−	10.9804i	0.340903	−	0.823014i
$179$			7.68306i			0.574259i	0.957892	+	0.287129i	$0.0927010\pi$
$179$			7.68306i			0.574259i	−0.957892	+	0.287129i	$0.907299\pi$
$180$		0			0
$181$		−	21.6569i		−	1.60974i	−0.593450	−	0.804871i	$-0.702235\pi$
$181$		−	21.6569i		−	1.60974i	0.593450	−	0.804871i	$-0.297765\pi$
$182$	−9.55582	−	3.95815i	−0.708325	−	0.293398i
$183$	11.0866	+	9.64823i	0.819542	+	0.713218i
$184$	−1.17157	−	2.82843i	−0.0863695	−	0.208514i
$185$		0			0
$186$	7.45485	+	14.9730i	0.546616	+	1.09787i
$187$	−6.43215			−0.470366
$188$	1.53073	+	1.53073i	0.111640	+	0.111640i
$189$	−6.45232	+	9.89949i	−0.469337	+	0.720082i
$190$		0			0
$191$	−8.40401			−0.608093			−0.304046	−	0.952657i	$-0.598338\pi$
$191$	−8.40401			−0.608093			−0.304046	+	0.952657i	$0.598338\pi$
$192$	−0.958884	−	13.8232i	−0.0692015	−	0.997603i
$193$	13.6447			0.982164			0.491082	−	0.871113i	$-0.336602\pi$
$193$	13.6447			0.982164			0.491082	+	0.871113i	$0.336602\pi$
$194$	−14.3465	−	5.94253i	−1.03002	−	0.426649i
$195$		0			0
$196$	2.58579	+	2.58579i	0.184699	+	0.184699i
$197$	−8.02509			−0.571764			−0.285882	−	0.958265i	$-0.592287\pi$
$197$	−8.02509			−0.571764			−0.285882	+	0.958265i	$0.592287\pi$
$198$	17.2548	+	4.48288i	1.22624	+	0.318584i
$199$		−	14.8284i		−	1.05116i	−0.850744	−	0.525580i	$-0.823848\pi$
$199$		−	14.8284i		−	1.05116i	0.850744	−	0.525580i	$-0.176152\pi$
$200$		0			0
$201$	2.58579	−	2.97127i	0.182387	−	0.209577i
$202$	17.8027	+	7.37412i	1.25259	+	0.518841i
$203$		−	3.95815i		−	0.277808i
$204$	0.366949	+	5.28991i	0.0256916	+	0.370367i
$205$		0			0
$206$	−4.71179	+	11.3753i	−0.328286	+	0.792553i
$207$	−0.448342	−	3.21608i	−0.0311619	−	0.223533i
$208$	12.8643			0.891979
$209$		−	20.2891i		−	1.40342i
$210$		0			0
$211$	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
$213$	−13.5140	+	15.5286i	−0.925962	+	1.06400i
$214$	−3.07107	+	7.41421i	−0.209934	+	0.506825i
$215$		0			0
$216$	2.70242	−	14.4463i	0.183876	−	0.982949i
$217$	−15.5286			−1.05415
$218$	−8.92177	+	21.5391i	−0.604259	+	1.45881i
$219$	5.17157	−	5.94253i	0.349463	−	0.401559i
$220$		0			0
$221$	−4.92296			−0.331154
$222$	−8.47657	−	17.0251i	−0.568910	−	1.14265i
$223$			10.5902i			0.709172i	0.935023	+	0.354586i	$0.115378\pi$
$223$			10.5902i			0.709172i	−0.935023	+	0.354586i	$0.884622\pi$
$224$	11.8851	+	4.92296i	0.794104	+	0.328929i
$225$		0			0
$226$	−0.343146	+	0.828427i	−0.0228257	+	0.0551062i
$227$			4.77791i			0.317121i	0.987349	+	0.158561i	$0.0506853\pi$
$227$			4.77791i			0.317121i	−0.987349	+	0.158561i	$0.949315\pi$
$228$	−16.6861	+	1.15748i	−1.10506	+	0.0766557i
$229$		−	3.31371i		−	0.218976i	−0.993988	−	0.109488i	$-0.965079\pi$
$229$		−	3.31371i		−	0.218976i	0.993988	−	0.109488i	$-0.0349211\pi$
$230$		0			0
$231$	−10.8655	+	12.4853i	−0.714897	+	0.821471i
$232$	1.88393	+	4.54822i	0.123686	+	0.298605i
$233$		−	28.0334i		−	1.83653i	−0.395967	−	0.918265i	$-0.629590\pi$
$233$		−	28.0334i		−	1.83653i	0.395967	−	0.918265i	$-0.370410\pi$
$234$	13.2062	+	3.43105i	0.863318	+	0.224294i
$235$		0			0
$236$	5.94253	−	5.94253i	0.386826	−	0.386826i
$237$	0.634051	+	0.551791i	0.0411860	+	0.0358427i
$238$	−4.54822	−	1.88393i	−0.294817	−	0.122117i
$239$	13.3270			0.862050			0.431025	−	0.902340i	$-0.358152\pi$
$239$	13.3270			0.862050			0.431025	+	0.902340i	$0.358152\pi$
$240$		0			0
$241$	10.4853			0.675416			0.337708	−	0.941251i	$-0.390348\pi$
$241$	10.4853			0.675416			0.337708	+	0.941251i	$0.390348\pi$
$242$	8.69760	+	3.60266i	0.559103	+	0.231588i
$243$	6.62724	−	14.1096i	0.425138	−	0.905129i
$244$	12.0000	−	12.0000i	0.768221	−	0.768221i
$245$		0			0
$246$	2.68729	+	5.39738i	0.171335	+	0.344125i
$247$		−	15.5286i		−	0.988060i
$248$	17.8435	−	7.39104i	1.13307	−	0.469331i
$249$	−9.07107	−	7.89422i	−0.574856	−	0.500276i
$250$		0			0
$251$		−	27.9721i		−	1.76559i	−0.469762	−	0.882793i	$-0.655660\pi$
$251$		−	27.9721i		−	1.76559i	0.469762	−	0.882793i	$-0.344340\pi$
$252$	10.8880	+	8.22368i	0.685877	+	0.518043i
$253$		−	4.54822i		−	0.285944i
$254$	−1.23074	+	2.97127i	−0.0772234	+	0.186434i
$255$		0			0
$256$	−16.0000			−1.00000
$257$			2.42742i			0.151418i	0.997130	+	0.0757090i	$0.0241220\pi$
$257$			2.42742i			0.151418i	−0.997130	+	0.0757090i	$0.975878\pi$
$258$	19.0906	−	9.50495i	1.18853	−	0.591752i
$259$	17.6569			1.09714
$260$		0			0
$261$	0.720950	+	5.17157i	0.0446257	+	0.320112i
$262$	6.04198	−	14.5866i	0.373275	−	0.901165i
$263$	−27.5851			−1.70097			−0.850484	−	0.526001i	$-0.823691\pi$
$263$	−27.5851			−1.70097			−0.850484	+	0.526001i	$0.823691\pi$
$264$	6.54275	−	19.5181i	0.402678	−	1.20126i
$265$		0			0
$266$	5.94253	−	14.3465i	0.364360	−	0.879643i
$267$	−10.9804	−	9.55582i	−0.671988	−	0.584807i
$268$	−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	$0.575254\pi$
$270$		0			0
$271$		−	14.1421i		−	0.859074i	−0.903049	−	0.429537i	$-0.858677\pi$
$271$		−	14.1421i		−	0.859074i	0.903049	−	0.429537i	$-0.141323\pi$
$272$	6.12293			0.371257
$273$	−8.31609	+	9.55582i	−0.503312	+	0.578345i
$274$	−4.34315	+	10.4853i	−0.262379	+	0.633439i
$275$		0			0
$276$	−3.74053	+	0.259472i	−0.225153	+	0.0156184i
$277$		−	16.8607i		−	1.01306i	−0.862221	−	0.506532i	$-0.830927\pi$
$277$		−	16.8607i		−	1.01306i	0.862221	−	0.506532i	$-0.169073\pi$
$278$	−3.24718	−	1.34502i	−0.194753	−	0.0806692i
$279$	20.2891	−	2.82843i	1.21468	−	0.169334i
$280$		0			0
$281$			5.94253i			0.354502i	0.984166	+	0.177251i	$0.0567204\pi$
$281$			5.94253i			0.354502i	−0.984166	+	0.177251i	$0.943280\pi$
$282$	2.37340	−	1.18169i	0.141334	−	0.0703685i
$283$	−26.1188			−1.55260			−0.776300	−	0.630363i	$-0.782906\pi$
$283$	−26.1188			−1.55260			−0.776300	+	0.630363i	$0.782906\pi$
$284$	16.8080	+	16.8080i	0.997373	+	0.997373i
$285$		0			0
$286$	17.6569	+	7.31371i	1.04407	+	0.432469i
$287$	−5.59767			−0.330420
$288$	−16.4253	−	4.26737i	−0.967868	−	0.251457i
$289$	14.6569			0.862168
$290$		0			0
$291$	−12.4853	+	14.3465i	−0.731900	+	0.841009i
$292$	−6.43215	−	6.43215i	−0.376413	−	0.376413i
$293$	16.3128			0.953004			0.476502	−	0.879173i	$-0.341904\pi$
$293$	16.3128			0.953004			0.476502	+	0.879173i	$0.341904\pi$
$294$	4.00927	−	1.99616i	0.233825	−	0.116419i
$295$		0			0
$296$	−20.2891	+	8.40401i	−1.17928	+	0.488473i
$297$	11.9223	−	18.2919i	0.691804	−	1.06140i
$298$	0.941967	+	0.390175i	0.0545667	+	0.0226023i
$299$		−	3.48106i		−	0.201315i
$300$		0			0
$301$			19.7990i			1.14119i
$302$	1.53073	−	3.69552i	0.0880838	−	0.212653i
$303$	15.4930	−	17.8027i	0.890052	−	1.02274i
$304$			19.3137i			1.10772i
$305$		0			0
$306$	6.28568	+	1.63305i	0.359328	+	0.0933553i
$307$	17.8027			1.01605			0.508027	−	0.861341i	$-0.330375\pi$
$307$	17.8027			1.01605			0.508027	+	0.861341i	$0.330375\pi$
$308$	13.5140	+	13.5140i	0.770030	+	0.770030i
$309$	11.3753	+	9.89949i	0.647117	+	0.563163i
$310$		0			0
$311$	9.84591			0.558310			0.279155	−	0.960246i	$-0.409946\pi$
$311$	9.84591			0.558310			0.279155	+	0.960246i	$0.409946\pi$
$312$	5.00760	−	14.9385i	0.283500	−	0.845727i
$313$	−24.6250			−1.39189			−0.695944	−	0.718096i	$-0.745014\pi$
$313$	−24.6250			−1.39189			−0.695944	+	0.718096i	$0.745014\pi$
$314$	12.6060	−	30.4336i	0.711399	−	1.71747i
$315$		0			0
$316$	0.686292	−	0.686292i	0.0386069	−	0.0386069i
$317$	9.81845			0.551459			0.275730	−	0.961235i	$-0.411081\pi$
$317$	9.81845			0.551459			0.275730	+	0.961235i	$0.411081\pi$
$318$	24.3099	−	12.1036i	1.36323	−	0.678736i
$319$			7.31371i			0.409489i
$320$		0			0
$321$	7.41421	+	6.45232i	0.413821	+	0.360134i
$322$	1.33214	−	3.21608i	0.0742374	−	0.179225i
$323$		−	7.39104i		−	0.411248i
$324$	−15.7237	−	8.76158i	−0.873539	−	0.486755i
$325$		0			0
$326$	11.3753	+	4.71179i	0.630018	+	0.260962i
$327$	21.5391	+	18.7447i	1.19111	+	1.03658i
$328$	6.43215	−	2.66428i	0.355156	−	0.147111i
$329$			2.46148i			0.135706i
$330$		0			0
$331$	−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
$333$	−23.0698	+	3.21608i	−1.26422	+	0.176240i
$334$	6.58579	+	2.72792i	0.360358	+	0.149265i
$335$		0			0
$336$	10.3431	−	11.8851i	0.564265	−	0.648384i
$337$	−19.2965			−1.05114			−0.525572	−	0.850749i	$-0.676149\pi$
$337$	−19.2965			−1.05114			−0.525572	+	0.850749i	$0.676149\pi$
$338$	−3.47135	−	1.43788i	−0.188816	−	0.0782103i
$339$	0.828427	+	0.720950i	0.0449940	+	0.0391566i
$340$		0			0
$341$	28.6931			1.55382
$342$	−5.15117	+	19.8271i	−0.278543	+	1.07212i
$343$			20.0768i			1.08405i
$344$	−9.42359	−	22.7506i	−0.508086	−	1.22663i
$345$		0			0
$346$	−0.343146	−	0.142136i	−0.0184476	−	0.00764126i
$347$			15.2304i			0.817611i	0.912621	+	0.408806i	$0.134055\pi$
$347$			15.2304i			0.817611i	−0.912621	+	0.408806i	$0.865945\pi$
$348$	6.01491	−	0.417241i	0.322433	−	0.0223665i
$349$			13.6569i			0.731035i	0.930805	+	0.365517i	$0.119108\pi$
$349$			13.6569i			0.731035i	−0.930805	+	0.365517i	$0.880892\pi$
$350$		0			0
$351$	9.12496	−	14.0000i	0.487054	−	0.747265i
$352$	−21.9607	−	9.09644i	−1.17051	−	0.484842i
$353$			26.3939i			1.40481i	0.711780	+	0.702403i	$0.247889\pi$
$353$			26.3939i			1.40481i	−0.711780	+	0.702403i	$0.752111\pi$
$354$	−4.58749	−	9.21391i	−0.243822	−	0.489714i
$355$		0			0
$356$	−11.8851	+	11.8851i	−0.629907	+	0.629907i
$357$	−3.95815	+	4.54822i	−0.209488	+	0.240717i
$358$	4.15804	−	10.0384i	0.219759	−	0.530546i
$359$	−32.1741			−1.69809			−0.849043	−	0.528323i	$-0.822821\pi$
$359$	−32.1741			−1.69809			−0.849043	+	0.528323i	$0.822821\pi$
$360$		0			0
$361$	4.31371			0.227037
$362$	−11.7206	+	28.2960i	−0.616021	+	1.48721i
$363$	7.56921	−	8.69760i	0.397280	−	0.456506i
$364$	10.3431	+	10.3431i	0.542128	+	0.542128i
$365$		0			0
$366$	−9.26370	−	18.6060i	−0.484221	−	0.972552i
$367$			24.2349i			1.26505i	0.774540	+	0.632524i	$0.217981\pi$
$367$			24.2349i			1.26505i	−0.774540	+	0.632524i	$0.782019\pi$
$368$			4.32957i			0.225694i
$369$	7.31371	−	1.01958i	0.380736	−	0.0530771i
$370$		0			0
$371$			25.2120i			1.30894i
$372$	−1.63692	−	23.5977i	−0.0848702	−	1.22348i
$373$		−	10.4286i		−	0.539971i	−0.962864	−	0.269986i	$-0.912981\pi$
$373$		−	10.4286i		−	0.539971i	0.962864	−	0.269986i	$-0.0870190\pi$
$374$	8.40401	+	3.48106i	0.434561	+	0.180001i
$375$		0			0
$376$	−1.17157	−	2.82843i	−0.0604193	−	0.145865i
$377$			5.59767i			0.288295i
$378$	13.7879	−	9.44234i	0.709175	−	0.485662i
$379$	−15.1716			−0.779311			−0.389656	−	0.920961i	$-0.627406\pi$
$379$	−15.1716			−0.779311			−0.389656	+	0.920961i	$0.627406\pi$
$380$		0			0
$381$	2.97127	+	2.58579i	0.152223	+	0.132474i
$382$	10.9804	+	4.54822i	0.561805	+	0.232707i
$383$	−18.5545			−0.948091			−0.474046	−	0.880500i	$-0.657207\pi$
$383$	−18.5545			−0.948091			−0.474046	+	0.880500i	$0.657207\pi$
$384$	−6.22821	+	18.5798i	−0.317832	+	0.948147i
$385$		0			0
$386$	−17.8276	−	7.38443i	−0.907401	−	0.375858i
$387$	−3.60625	−	25.8686i	−0.183316	−	1.31498i
$388$	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	$0.396460\pi$
$390$		0			0
$391$		−	1.65685i		−	0.0837907i
$392$	−1.97908	−	4.77791i	−0.0999584	−	0.241321i
$393$	−14.5866	−	12.6942i	−0.735798	−	0.640338i
$394$	10.4853	+	4.34315i	0.528241	+	0.218805i
$395$		0			0
$396$	−20.1183	−	15.1954i	−1.01098	−	0.763596i
$397$		−	0.551791i		−	0.0276936i	−0.999904	−	0.0138468i	$-0.995592\pi$
$397$		−	0.551791i		−	0.0276936i	0.999904	−	0.0138468i	$-0.00440772\pi$
$398$	−8.02509	+	19.3743i	−0.402261	+	0.971145i
$399$	−14.3465	−	12.4853i	−0.718226	−	0.625046i
$400$		0			0
$401$		−	25.2120i		−	1.25903i	−0.776989	−	0.629514i	$-0.783254\pi$
$401$		−	25.2120i		−	1.25903i	0.776989	−	0.629514i	$-0.216746\pi$
$402$	−4.98653	+	2.48273i	−0.248706	+	0.123827i
$403$	21.9607			1.09394
$404$	−19.2695	−	19.2695i	−0.958694	−	0.958694i
$405$		0			0
$406$	−2.14214	+	5.17157i	−0.106312	+	0.256661i
$407$	−32.6256			−1.61719
$408$	2.38343	−	7.11019i	0.117998	−	0.352007i
$409$	7.17157			0.354611			0.177306	−	0.984156i	$-0.443262\pi$
$409$	7.17157			0.354611			0.177306	+	0.984156i	$0.443262\pi$
$410$		0			0
$411$	10.4853	+	9.12496i	0.517201	+	0.450101i
$412$	12.3125	−	12.3125i	0.606594	−	0.606594i
$413$	9.55582			0.470211
$414$	−1.15474	+	4.44465i	−0.0567524	+	0.218442i
$415$		0			0
$416$	−16.8080	−	6.96211i	−0.824081	−	0.341346i
$417$	−2.82590	+	3.24718i	−0.138385	+	0.159015i
$418$	−10.9804	+	26.5090i	−0.537067	+	1.29660i
$419$			4.20201i			0.205281i	0.994718	+	0.102641i	$0.0327292\pi$
$419$			4.20201i			0.205281i	−0.994718	+	0.102641i	$0.967271\pi$
$420$		0			0
$421$			29.1716i			1.42174i	0.703326	+	0.710868i	$0.251698\pi$
$421$			29.1716i			1.42174i	−0.703326	+	0.710868i	$0.748302\pi$
$422$	−1.97908	−	0.819760i	−0.0963399	−	0.0399053i
$423$	−0.448342	−	3.21608i	−0.0217991	−	0.156371i
$424$	−12.0000	−	28.9706i	−0.582772	−	1.40693i
$425$		0			0
$426$	26.0609	−	12.9754i	1.26265	−	0.628659i
$427$	19.2965			0.933821
$428$	8.02509	−	8.02509i	0.387907	−	0.387907i
$429$	15.3661	−	17.6569i	0.741883	−	0.852481i
$430$		0			0
$431$	−21.7310			−1.04674			−0.523372	−	0.852104i	$-0.675326\pi$
$431$	−21.7310			−1.04674			−0.523372	+	0.852104i	$0.675326\pi$
$432$	−11.3492	+	17.4125i	−0.546038	+	0.837760i
$433$	29.1732			1.40198			0.700988	−	0.713173i	$-0.252742\pi$
$433$	29.1732			1.40198			0.700988	+	0.713173i	$0.252742\pi$
$434$	20.2891	+	8.40401i	0.973907	+	0.403405i
$435$		0			0
$436$	23.3137	−	23.3137i	1.11652	−	1.11652i
$437$	5.22625			0.250006
$438$	−9.97306	+	4.96546i	−0.476531	+	0.237259i
$439$			11.5147i			0.549568i	0.961506	+	0.274784i	$0.0886063\pi$
$439$			11.5147i			0.549568i	−0.961506	+	0.274784i	$0.911394\pi$
$440$		0			0
$441$	−0.757359	−	5.43275i	−0.0360647	−	0.258702i
$442$	6.43215	+	2.66428i	0.305946	+	0.126727i
$443$			40.4650i			1.92255i	0.275591	+	0.961275i	$0.411126\pi$
$443$			40.4650i			1.92255i	−0.275591	+	0.961275i	$0.588874\pi$
$444$	1.86126	+	26.8318i	0.0883317	+	1.27338i
$445$		0			0
$446$	5.73137	−	13.8368i	0.271388	−	0.655189i
$447$	0.819760	−	0.941967i	0.0387733	−	0.0445535i
$448$	−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	$0.801114\pi$
$450$		0			0
$451$	10.3431			0.487040
$452$	0.896683	−	0.896683i	0.0421764	−	0.0421764i
$453$	−3.69552	−	3.21608i	−0.173631	−	0.151104i
$454$	2.58579	−	6.24264i	0.121357	−	0.292982i
$455$		0			0
$456$	22.4278	+	7.51812i	1.05028	+	0.352068i
$457$	12.8643			0.601767			0.300883	−	0.953661i	$-0.402719\pi$
$457$	12.8643			0.601767			0.300883	+	0.953661i	$0.402719\pi$
$458$	−1.79337	+	4.32957i	−0.0837985	+	0.202307i
$459$	4.34315	−	6.66348i	0.202721	−	0.311025i
$460$		0			0
$461$	18.5486			0.863892			0.431946	−	0.901899i	$-0.357827\pi$
$461$	18.5486			0.863892			0.431946	+	0.901899i	$0.357827\pi$
$462$	20.9534	−	10.4324i	0.974842	−	0.485361i
$463$			4.93839i			0.229507i	0.993394	+	0.114753i	$0.0366078\pi$
$463$			4.93839i			0.229507i	−0.993394	+	0.114753i	$0.963392\pi$
$464$		−	6.96211i		−	0.323208i
$465$		0			0
$466$	−15.1716	+	36.6274i	−0.702810	+	1.69673i
$467$			8.73606i			0.404257i	0.979359	+	0.202128i	$0.0647858\pi$
$467$			8.73606i			0.404257i	−0.979359	+	0.202128i	$0.935214\pi$
$468$	−15.3979	−	11.6300i	−0.711768	−	0.537599i
$469$		−	5.17157i		−	0.238801i
$470$		0			0
$471$	−30.4336	−	26.4853i	−1.40231	−	1.22038i
$472$	−10.9804	+	4.54822i	−0.505413	+	0.209349i
$473$		−	36.5838i		−	1.68212i
$474$	−0.529800	−	1.06410i	−0.0243345	−	0.0488755i
$475$		0			0
$476$	4.92296	+	4.92296i	0.225643	+	0.225643i
$477$	−4.59220	−	32.9411i	−0.210262	−	1.50827i
$478$	−17.4125	−	7.21250i	−0.796430	−	0.329892i
$479$	15.3661			0.702096			0.351048	−	0.936357i	$-0.385825\pi$
$479$	15.3661			0.702096			0.351048	+	0.936357i	$0.385825\pi$
$480$		0			0
$481$	−24.9706			−1.13856
$482$	−13.6997	−	5.67459i	−0.624003	−	0.258471i
$483$	−3.21608	−	2.79884i	−0.146337	−	0.127351i
$484$	−9.41421	−	9.41421i	−0.427919	−	0.427919i
$485$		0			0
$486$	−16.2949	+	14.8484i	−0.739154	+	0.673537i
$487$			19.6866i			0.892086i	0.895011	+	0.446043i	$0.147167\pi$
$487$			19.6866i			0.892086i	−0.895011	+	0.446043i	$0.852833\pi$
$488$	−22.1731	+	9.18440i	−1.00373	+	0.415758i
$489$	9.89949	−	11.3753i	0.447671	−	0.514408i
$490$		0			0
$491$			14.0479i			0.633974i	0.948430	+	0.316987i	$0.102671\pi$
$491$			14.0479i			0.633974i	−0.948430	+	0.316987i	$0.897329\pi$
$492$	−0.590068	−	8.50637i	−0.0266023	−	0.383497i
$493$			2.66428i			0.119993i
$494$	−8.40401	+	20.2891i	−0.378114	+	0.912849i
$495$		0			0
$496$	−27.3137			−1.22642
$497$			27.0279i			1.21237i
$498$	7.57960	+	15.2235i	0.339650	+	0.682183i
$499$	−25.1127			−1.12420			−0.562099	−	0.827070i	$-0.690006\pi$
$499$	−25.1127			−1.12420			−0.562099	+	0.827070i	$0.690006\pi$
$500$		0			0
$501$	5.73137	−	6.58579i	0.256059	−	0.294231i
$502$	−15.1384	+	36.5474i	−0.675660	+	1.63119i
$503$	28.4818			1.26994			0.634969	−	0.772537i	$-0.281013\pi$
$503$	28.4818			1.26994			0.634969	+	0.772537i	$0.281013\pi$
$504$	−9.77519	−	16.6373i	−0.435421	−	0.741083i
$505$		0			0
$506$	−2.46148	+	5.94253i	−0.109426	+	0.264178i
$507$	−3.02099	+	3.47135i	−0.134167	+	0.154168i
$508$	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	$0.402355\pi$
$510$		0			0
$511$		−	10.3431i		−	0.457554i
$512$	20.9050	+	8.65914i	0.923880	+	0.382683i
$513$	21.0188	+	13.6997i	0.928002	+	0.604856i
$514$	1.31371	−	3.17157i	0.0579452	−	0.139892i
$515$		0			0
$516$	−30.0871	+	2.08707i	−1.32451	+	0.0918783i
$517$		−	4.54822i		−	0.200030i
$518$	−23.0698	−	9.55582i	−1.01363	−	0.419859i
$519$	−0.298627	+	0.343146i	−0.0131083	+	0.0150624i
$520$		0			0
$521$		−	9.84591i		−	0.431357i	−0.976464	−	0.215679i	$-0.930804\pi$
$521$		−	9.84591i		−	0.431357i	0.976464	−	0.215679i	$-0.0691964\pi$
$522$	1.85687	−	7.14716i	0.0812729	−	0.312823i
$523$	4.15804			0.181819			0.0909093	−	0.995859i	$-0.471023\pi$
$523$	4.15804			0.181819			0.0909093	+	0.995859i	$0.471023\pi$
$524$	−15.7884	+	15.7884i	−0.689721	+	0.689721i
$525$		0			0
$526$	36.0416	+	14.9289i	1.57149	+	0.650932i
$527$	10.4525			0.455318
$528$	−19.1116	+	21.9607i	−0.831727	+	0.955719i
$529$	−21.8284			−0.949062
$530$		0			0
$531$	−12.4853	+	1.74053i	−0.541815	+	0.0755325i
$532$	−15.5286	+	15.5286i	−0.673250	+	0.673250i
$533$	7.91630			0.342893
$534$	9.17497	+	18.4278i	0.397040	+	0.797450i
$535$		0			0
$536$	2.46148	+	5.94253i	0.106320	+	0.256678i
$537$	−10.0384	−	8.73606i	−0.433189	−	0.376989i
$538$	10.0384	+	4.15804i	0.432786	+	0.179266i
$539$		−	7.68306i		−	0.330933i
$540$		0			0
$541$			16.0000i			0.687894i	0.938989	+	0.343947i	$0.111764\pi$
$541$			16.0000i			0.687894i	−0.938989	+	0.343947i	$0.888236\pi$
$542$	−7.65367	+	18.4776i	−0.328753	+	0.793680i
$543$	28.2960	+	24.6250i	1.21430	+	1.05676i
$544$	−8.00000	−	3.31371i	−0.342997	−	0.142074i
$545$		0			0
$546$	16.0371	−	7.98465i	0.686323	−	0.341711i
$547$	−33.3313			−1.42514			−0.712571	−	0.701600i	$-0.752470\pi$
$547$	−33.3313			−1.42514			−0.712571	+	0.701600i	$0.752470\pi$
$548$	11.3492	−	11.3492i	0.484813	−	0.484813i
$549$	−25.2120	+	3.51472i	−1.07602	+	0.150005i
$550$		0			0
$551$	−8.40401			−0.358023
$552$	5.02766	+	1.68534i	0.213991	+	0.0717329i
$553$	1.10358			0.0469291
$554$	−9.12496	+	22.0296i	−0.387682	+	0.935948i
$555$		0			0
$556$	3.51472	+	3.51472i	0.149057	+	0.149057i
$557$	−19.3743			−0.820914			−0.410457	−	0.911880i	$-0.634631\pi$
$557$	−19.3743			−0.820914			−0.410457	+	0.911880i	$0.634631\pi$
$558$	−28.0397	−	7.28485i	−1.18701	−	0.308392i
$559$		−	28.0000i		−	1.18427i
$560$		0			0
$561$	7.31371	−	8.40401i	0.308785	−	0.354818i
$562$	3.21608	−	7.76429i	0.135662	−	0.327517i
$563$			6.04601i			0.254809i	0.991851	+	0.127405i	$0.0406646\pi$
$563$			6.04601i			0.254809i	−0.991851	+	0.127405i	$0.959335\pi$
$564$	−3.74053	+	0.259472i	−0.157505	+	0.0109257i
$565$		0			0
$566$	34.1258	+	14.1354i	1.43442	+	0.594155i
$567$	−5.59767	−	19.6866i	−0.235080	−	0.826761i
$568$	−12.8643	−	31.0572i	−0.539774	−	1.30313i
$569$			9.42359i			0.395057i	0.980297	+	0.197529i	$0.0632916\pi$
$569$			9.42359i			0.395057i	−0.980297	+	0.197529i	$0.936708\pi$
$570$		0			0
$571$	−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
$573$	9.55582	−	10.9804i	0.399200	−	0.458712i
$574$	7.31371	+	3.02944i	0.305268	+	0.126446i
$575$		0			0
$576$	19.1512	+	14.4649i	0.797965	+	0.602703i
$577$	15.5286			0.646464			0.323232	−	0.946320i	$-0.395231\pi$
$577$	15.5286			0.646464			0.323232	+	0.946320i	$0.395231\pi$
$578$	−19.1501	−	7.93223i	−0.796539	−	0.329937i
$579$	−15.5147	+	17.8276i	−0.644770	+	0.740890i
$580$		0			0
$581$	−15.7884			−0.655015
$582$	24.0771	−	11.9877i	0.998028	−	0.496905i
$583$		−	46.5858i		−	1.92939i
$584$	4.92296	+	11.8851i	0.203713	+	0.491808i
$585$		0			0
$586$	−21.3137	−	8.82843i	−0.880461	−	0.364699i
$587$			12.1689i			0.502266i	0.967953	+	0.251133i	$0.0808032\pi$
$587$			12.1689i			0.502266i	−0.967953	+	0.251133i	$0.919197\pi$
$588$	−6.31867	+	0.438312i	−0.260578	+	0.0180757i
$589$			32.9706i			1.35853i
$590$		0			0
$591$	9.12496	−	10.4853i	0.375351	−	0.431307i
$592$	31.0572			1.27644
$593$			39.3826i			1.61725i	0.588325	+	0.808625i	$0.299788\pi$
$593$			39.3826i			1.61725i	−0.588325	+	0.808625i	$0.700212\pi$
$594$	−25.4768	+	17.4472i	−1.04532	+	0.715866i
$595$		0			0
$596$	−1.01958	−	1.01958i	−0.0417635	−	0.0417635i
$597$	19.3743	+	16.8607i	0.792936	+	0.690064i
$598$	−1.88393	+	4.54822i	−0.0770398	+	0.185990i
$599$	−30.1350			−1.23128			−0.615641	−	0.788027i	$-0.711103\pi$
$599$	−30.1350			−1.23128			−0.615641	+	0.788027i	$0.711103\pi$
$600$		0			0
$601$	30.4853			1.24352			0.621760	−	0.783208i	$-0.286418\pi$
$601$	30.4853			1.24352			0.621760	+	0.783208i	$0.286418\pi$
$602$	10.7151	−	25.8686i	0.436716	−	1.05433i
$603$	0.941967	+	6.75699i	0.0383599	+	0.275166i
$604$	−4.00000	+	4.00000i	−0.162758	+	0.162758i
$605$		0			0
$606$	−29.8774	+	14.8756i	−1.21369	+	0.604279i
$607$		−	35.2152i		−	1.42934i	−0.699461	−	0.714671i	$-0.746576\pi$
$607$		−	35.2152i		−	1.42934i	0.699461	−	0.714671i	$-0.253424\pi$
$608$	10.4525	−	25.2346i	0.423905	−	1.02340i
$609$	5.17157	+	4.50063i	0.209563	+	0.182375i
$610$		0			0
$611$		−	3.48106i		−	0.140828i
$612$	−7.32884	−	5.53547i	−0.296251	−	0.223758i
$613$		−	16.0804i		−	0.649480i	−0.945803	−	0.324740i	$-0.894723\pi$
$613$		−	16.0804i		−	0.649480i	0.945803	−	0.324740i	$-0.105277\pi$
$614$	−23.2603	−	9.63475i	−0.938711	−	0.388827i
$615$		0			0
$616$	−10.3431	−	24.9706i	−0.416737	−	1.00609i
$617$		−	31.0949i		−	1.25183i	−0.779890	−	0.625916i	$-0.784725\pi$
$617$		−	31.0949i		−	1.25183i	0.779890	−	0.625916i	$-0.215275\pi$
$618$	−9.50495	−	19.0906i	−0.382345	−	0.767935i
$619$	−14.4853			−0.582213			−0.291106	−	0.956691i	$-0.594023\pi$
$619$	−14.4853			−0.582213			−0.291106	+	0.956691i	$0.594023\pi$
$620$		0			0
$621$	4.71179	+	3.07107i	0.189078	+	0.123238i
$622$	−12.8643	−	5.32857i	−0.515812	−	0.213656i
$623$	−19.1116			−0.765692
$624$	−14.6274	+	16.8080i	−0.585565	+	0.672859i
$625$		0			0
$626$	32.1741	+	13.3270i	1.28594	+	0.532653i
$627$	26.5090	+	23.0698i	1.05867	+	0.921319i
$628$	−32.9411	+	32.9411i	−1.31449	+	1.31449i
$629$	−11.8851			−0.473889
$630$		0			0
$631$		−	26.1421i		−	1.04070i	−0.853952	−	0.520351i	$-0.825801\pi$
$631$		−	26.1421i		−	1.04070i	0.853952	−	0.520351i	$-0.174199\pi$
$632$	−1.26810	+	0.525265i	−0.0504424	+	0.0208939i
$633$	−1.72232	+	1.97908i	−0.0684560	+	0.0786612i
$634$	−12.8284	−	5.31371i	−0.509482	−	0.211034i
$635$		0			0
$636$	−38.3129	+	2.65768i	−1.51920	+	0.105384i
$637$		−	5.88036i		−	0.232988i
$638$	3.95815	−	9.55582i	0.156705	−	0.378319i
$639$	−4.92296	−	35.3137i	−0.194749	−	1.39699i
$640$		0			0
$641$			24.7897i			0.979135i	0.871965	+	0.489567i	$0.162845\pi$
$641$			24.7897i			0.979135i	−0.871965	+	0.489567i	$0.837155\pi$
$642$	−6.19516	−	12.4429i	−0.244504	−	0.491082i
$643$	1.49376			0.0589081			0.0294540	−	0.999566i	$-0.490623\pi$
$643$	1.49376			0.0589081			0.0294540	+	0.999566i	$0.490623\pi$
$644$	−3.48106	+	3.48106i	−0.137173	+	0.137173i
$645$		0			0
$646$	−4.00000	+	9.65685i	−0.157378	+	0.379944i
$647$	42.3671			1.66562			0.832812	−	0.553556i	$-0.186729\pi$
$647$	42.3671			1.66562			0.832812	+	0.553556i	$0.186729\pi$
$648$	15.8023	+	19.9572i	0.620772	+	0.783992i
$649$	−17.6569			−0.693092
$650$		0			0
$651$	17.6569	−	20.2891i	0.692027	−	0.795192i
$652$	−12.3125	−	12.3125i	−0.482195	−	0.482195i
$653$	37.5892			1.47098			0.735490	−	0.677535i	$-0.236952\pi$
$653$	37.5892			1.47098			0.735490	+	0.677535i	$0.236952\pi$
$654$	−17.9976	−	36.1479i	−0.703762	−	1.41350i
$655$		0			0
$656$	−9.84591			−0.384418
$657$	1.88393	+	13.5140i	0.0734993	+	0.527230i
$658$	1.33214	−	3.21608i	0.0519323	−	0.125376i
$659$			0.720950i			0.0280842i	0.999901	+	0.0140421i	$0.00446989\pi$
$659$			0.720950i			0.0280842i	−0.999901	+	0.0140421i	$0.995530\pi$
$660$		0			0
$661$			28.7696i			1.11901i	0.828828	+	0.559503i	$0.189008\pi$
$661$			28.7696i			1.11901i	−0.828828	+	0.559503i	$0.810992\pi$
$662$	1.97908	+	0.819760i	0.0769189	+	0.0318609i
$663$	5.59767	−	6.43215i	0.217395	−	0.249804i
$664$	18.1421	−	7.51472i	0.704051	−	0.291628i
$665$		0			0
$666$	31.8827	+	8.28328i	1.23543	+	0.320970i
$667$	−1.88393			−0.0729462
$668$	−7.12840	−	7.12840i	−0.275806	−	0.275806i
$669$	−13.8368	−	12.0416i	−0.534960	−	0.465556i
$670$		0			0
$671$	−35.6552			−1.37645
$672$	−19.9461	+	9.93092i	−0.769438	+	0.383094i
$673$	−5.65180			−0.217861			−0.108930	−	0.994049i	$-0.534743\pi$
$673$	−5.65180			−0.217861			−0.108930	+	0.994049i	$0.534743\pi$
$674$	25.2120	+	10.4432i	0.971131	+	0.402256i
$675$		0			0
$676$	3.75736	+	3.75736i	0.144514	+	0.144514i
$677$	39.3826			1.51360			0.756798	−	0.653649i	$-0.226763\pi$
$677$	39.3826			1.51360			0.756798	+	0.653649i	$0.226763\pi$
$678$	−0.692217	−	1.39031i	−0.0265844	−	0.0533945i
$679$			24.9706i			0.958282i
$680$		0			0
$681$	−6.24264	−	5.43275i	−0.239219	−	0.208183i
$682$	−37.4893	−	15.5286i	−1.43554	−	0.594620i
$683$		−	21.3533i		−	0.817063i	−0.912744	−	0.408532i	$-0.866041\pi$
$683$		−	21.3533i		−	0.817063i	0.912744	−	0.408532i	$-0.133959\pi$
$684$	17.4607	−	23.1175i	0.667625	−	0.883920i
$685$		0			0
$686$	10.8655	−	26.2316i	0.414846	−	1.00153i
$687$	4.32957	+	3.76787i	0.165183	+	0.143753i
$688$			34.8250i			1.32769i
$689$		−	35.6552i		−	1.35836i
$690$		0			0
$691$	−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
$693$	−3.95815	−	28.3929i	−0.150358	−	1.07856i
$694$	8.24264	−	19.8995i	0.312886	−	0.755374i
$695$		0			0
$696$	−8.08467	−	2.71009i	−0.306449	−	0.102726i
$697$	3.76787			0.142718
$698$	7.39104	−	17.8435i	0.279755	−	0.675388i
$699$	36.6274	+	31.8755i	1.38538	+	1.20564i
$700$		0			0
$701$	−2.76011			−0.104248			−0.0521239	−	0.998641i	$-0.516599\pi$
$701$	−2.76011			−0.104248			−0.0521239	+	0.998641i	$0.516599\pi$
$702$	−19.4991	+	13.3535i	−0.735945	+	0.503995i
$703$		−	37.4893i		−	1.41394i
$704$	23.7701	+	23.7701i	0.895871	+	0.895871i
$705$		0			0
$706$	14.2843	−	34.4853i	0.537596	−	1.29787i
$707$		−	30.9861i		−	1.16535i
$708$	1.00731	+	14.5213i	0.0378570	+	0.545743i
$709$			20.2843i			0.761792i	0.924618	+	0.380896i	$0.124384\pi$
$709$			20.2843i			0.761792i	−0.924618	+	0.380896i	$0.875616\pi$
$710$		0			0
$711$	−1.44190	+	0.201010i	−0.0540755	+	0.00753847i
$712$	21.9607	−	9.09644i	0.823014	−	0.340903i
$713$			7.39104i			0.276796i
$714$	7.63305	−	3.80040i	0.285660	−	0.142226i
$715$		0			0
$716$	−10.8655	+	10.8655i	−0.406062	+	0.406062i
$717$	−15.1535	+	17.4125i	−0.565917	+	0.650283i
$718$	42.0375	+	17.4125i	1.56883	+	0.649830i
$719$	28.6931			1.07007			0.535036	−	0.844829i	$-0.320298\pi$
$719$	28.6931			1.07007			0.535036	+	0.844829i	$0.320298\pi$
$720$		0			0
$721$	19.7990			0.737353
$722$	−5.63613	−	2.33456i	−0.209755	−	0.0868834i
$723$	−11.9223	+	13.6997i	−0.443397	+	0.509497i
$724$	30.6274	−	30.6274i	1.13826	−	1.13826i
$725$		0			0
$726$	−14.5968	+	7.26754i	−0.541736	+	0.269724i
$727$		−	18.9063i		−	0.701195i	−0.936526	−	0.350598i	$-0.885978\pi$
$727$		−	18.9063i		−	0.701195i	0.936526	−	0.350598i	$-0.114022\pi$
$728$	−7.91630	−	19.1116i	−0.293398	−	0.708325i
$729$	10.8995	+	24.7022i	0.403685	+	0.914898i
$730$		0			0
$731$		−	13.3270i		−	0.492916i
$732$	2.03410	+	29.3234i	0.0751825	+	1.08382i
$733$			38.8215i			1.43390i	0.697123	+	0.716952i	$0.254463\pi$
$733$			38.8215i			1.43390i	−0.697123	+	0.716952i	$0.745537\pi$
$734$	13.1158	−	31.6644i	0.484113	−	1.16875i
$735$		0			0
$736$	2.34315	−	5.65685i	0.0863695	−	0.208514i
$737$			9.55582i			0.351993i
$738$	−10.1076	−	2.62601i	−0.372066	−	0.0966647i
$739$	32.8284			1.20761			0.603807	−	0.797131i	$-0.293650\pi$
$739$	32.8284			1.20761			0.603807	+	0.797131i	$0.293650\pi$
$740$		0			0
$741$	20.2891	+	17.6569i	0.745338	+	0.648641i
$742$	13.6447	−	32.9411i	0.500911	−	1.20931i
$743$	−0.185709			−0.00681301			−0.00340650	−	0.999994i	$-0.501084\pi$
$743$	−0.185709			−0.00681301			−0.00340650	+	0.999994i	$0.501084\pi$
$744$	−10.6322	+	31.7177i	−0.389796	+	1.16283i
$745$		0			0
$746$	−5.64391	+	13.6256i	−0.206638	+	0.498868i
$747$	20.6286	−	2.87576i	0.754761	−	0.105218i
$748$	−9.09644	−	9.09644i	−0.332599	−	0.332599i
$749$	12.9046			0.471525
$750$		0			0
$751$			27.1127i			0.989356i	0.869076	+	0.494678i	$0.164714\pi$
$751$			27.1127i			0.989356i	−0.869076	+	0.494678i	$0.835286\pi$
$752$			4.32957i			0.157883i
$753$	36.5474	+	31.8059i	1.33186	+	1.15907i
$754$	3.02944	−	7.31371i	0.110326	−	0.266350i
$755$		0			0
$756$	−23.1250	+	4.87504i	−0.841047	+	0.177303i
$757$			36.1572i			1.31416i	0.753823	+	0.657078i	$0.228208\pi$
$757$			36.1572i			1.31416i	−0.753823	+	0.657078i	$0.771792\pi$
$758$	19.8226	+	8.21080i	0.719990	+	0.298230i
$759$	5.94253	+	5.17157i	0.215700	+	0.187716i
$760$		0			0
$761$			4.92296i			0.178457i	0.996011	+	0.0892285i	$0.0284401\pi$
$761$			4.92296i			0.178457i	−0.996011	+	0.0892285i	$0.971560\pi$
$762$	−2.48273	−	4.98653i	−0.0899398	−	0.180643i
$763$	37.4893			1.35720
$764$	−11.8851	−	11.8851i	−0.429987	−	0.429987i
$765$		0			0
$766$	24.2426	+	10.0416i	0.875922	+	0.362819i
$767$	−13.5140			−0.487961
$768$	18.1929	−	20.9050i	0.656479	−	0.754344i
$769$	−29.5980			−1.06733			−0.533665	−	0.845696i	$-0.679186\pi$
$769$	−29.5980			−1.06733			−0.533665	+	0.845696i	$0.679186\pi$
$770$		0			0
$771$	−3.17157	−	2.76011i	−0.114221	−	0.0994028i
$772$	19.2965	+	19.2965i	0.694495	+	0.694495i
$773$	−38.1145			−1.37088			−0.685442	−	0.728128i	$-0.740391\pi$
$773$	−38.1145			−1.37088			−0.685442	+	0.728128i	$0.740391\pi$
$774$	−9.28821	+	35.7507i	−0.333858	+	1.28503i
$775$		0			0
$776$	−11.8851	−	28.6931i	−0.426649	−	1.03002i
$777$	−20.0768	+	23.0698i	−0.720251	+	0.827624i
$778$	−16.4706	−	6.82233i	−0.590498	−	0.244592i
$779$			11.8851i			0.425827i
$780$		0			0
$781$		−	49.9411i		−	1.78703i
$782$	−0.896683	+	2.16478i	−0.0320653	+	0.0774125i
$783$	−7.57675	−	4.93839i	−0.270771	−	0.176484i
$784$			7.31371i			0.261204i
$785$		0			0
$786$	12.1883	+	24.4800i	0.434742	+	0.873173i
$787$	7.60268			0.271006			0.135503	−	0.990777i	$-0.456735\pi$
$787$	7.60268			0.271006			0.135503	+	0.990777i	$0.456735\pi$
$788$	−11.3492	−	11.3492i	−0.404298	−	0.404298i
$789$	31.3657	−	36.0416i	1.11665	−	1.28312i
$790$		0			0
$791$	1.44190			0.0512681
$792$	18.0622	+	30.7417i	0.641812	+	1.09236i
$793$	−27.2893			−0.969072
$794$	−0.298627	+	0.720950i	−0.0105979	+	0.0255856i
$795$		0			0
$796$	20.9706	−	20.9706i	0.743282	−	0.743282i
$797$	−0.634051			−0.0224592			−0.0112296	−	0.999937i	$-0.503575\pi$
$797$	−0.634051			−0.0224592			−0.0112296	+	0.999937i	$0.503575\pi$
$798$	11.9877	+	24.0771i	0.424359	+	0.852320i
$799$		−	1.65685i		−	0.0586153i
$800$		0			0
$801$	24.9706	−	3.48106i	0.882291	−	0.122997i
$802$	−13.6447	+	32.9411i	−0.481810	+	1.16319i
$803$			19.1116i			0.674435i
$804$	7.85886	−	0.545152i	0.277161	−	0.0192260i
$805$		0			0
$806$	−28.6931	−	11.8851i	−1.01067	−	0.418634i
$807$	8.73606	−	10.0384i	0.307524	−	0.353369i
$808$	14.7482	+	35.6054i	0.518841	+	1.25259i
$809$		−	40.5782i		−	1.42665i	−0.700832	−	0.713326i	$-0.747188\pi$
$809$		−	40.5782i		−	1.42665i	0.700832	−	0.713326i	$-0.252812\pi$
$810$		0			0
$811$	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
$813$	18.4776	+	16.0804i	0.648037	+	0.563964i
$814$	42.6274	+	17.6569i	1.49409	+	0.618872i
$815$		0			0
$816$	−6.96211	+	8.00000i	−0.243723	+	0.280056i
$817$	42.0375			1.47071
$818$	−9.37011	−	3.88123i	−0.327618	−	0.135704i
$819$	−3.02944	−	21.7310i	−0.105857	−	0.759342i
$820$		0			0
$821$	31.4532			1.09772			0.548862	−	0.835913i	$-0.315061\pi$
$821$	31.4532			1.09772			0.548862	+	0.835913i	$0.315061\pi$
$822$	−8.76129	−	17.5969i	−0.305585	−	0.613763i
$823$			48.0795i			1.67595i	0.545711	+	0.837973i	$0.316260\pi$
$823$			48.0795i			1.67595i	−0.545711	+	0.837973i	$0.683740\pi$
$824$	−22.7506	+	9.42359i	−0.792553	+	0.328286i
$825$		0			0
$826$	−12.4853	−	5.17157i	−0.434418	−	0.179942i
$827$		−	17.7666i		−	0.617806i	−0.951094	−	0.308903i	$-0.900038\pi$
$827$		−	17.7666i		−	0.617806i	0.951094	−	0.308903i	$-0.0999618\pi$
$828$	3.91417	−	5.18227i	0.136027	−	0.180096i
$829$		−	10.8284i		−	0.376087i	−0.982161	−	0.188043i	$-0.939785\pi$
$829$		−	10.8284i		−	0.376087i	0.982161	−	0.188043i	$-0.0602146\pi$
$830$		0			0
$831$	22.0296	+	19.1716i	0.764199	+	0.665054i
$832$	18.1929	+	18.1929i	0.630724	+	0.630724i
$833$		−	2.79884i		−	0.0969739i
$834$	5.44958	−	2.71327i	0.188703	−	0.0939530i
$835$		0			0
$836$	28.6931	−	28.6931i	0.992371	−	0.992371i
$837$	−19.3743	+	29.7250i	−0.669673	+	1.02745i
$838$	2.27411	−	5.49019i	0.0785578	−	0.189655i
$839$	−5.52021			−0.190579			−0.0952894	−	0.995450i	$-0.530378\pi$
$839$	−5.52021			−0.190579			−0.0952894	+	0.995450i	$0.530378\pi$
$840$		0			0
$841$	−25.9706			−0.895537
$842$	15.7875	−	38.1145i	0.544075	−	1.31351i
$843$	−7.76429	−	6.75699i	−0.267417	−	0.232723i
$844$	2.14214	+	2.14214i	0.0737353	+	0.0737353i
$845$		0			0
$846$	−1.15474	+	4.44465i	−0.0397008	+	0.152810i
$847$		−	15.1384i		−	0.520162i
$848$			44.3462i			1.52286i
$849$	29.6985	−	34.1258i	1.01925	−	1.17120i
$850$		0			0
$851$		−	8.40401i		−	0.288086i
$852$	−41.0724	+	2.84910i	−1.40712	+	0.0976086i
$853$		−	6.98394i		−	0.239126i	−0.992827	−	0.119563i	$-0.961851\pi$
$853$		−	6.98394i		−	0.239126i	0.992827	−	0.119563i	$-0.0381493\pi$
$854$	−25.2120	−	10.4432i	−0.862738	−	0.357358i
$855$		0			0
$856$	−14.8284	+	6.14214i	−0.506825	+	0.209934i
$857$		−	27.1367i		−	0.926973i	−0.886104	−	0.463486i	$-0.846598\pi$
$857$		−	27.1367i		−	0.926973i	0.886104	−	0.463486i	$-0.153402\pi$
$858$	−29.6326	+	14.7537i	−1.01164	+	0.503683i
$859$	−32.1421			−1.09668			−0.548338	−	0.836257i	$-0.684739\pi$
$859$	−32.1421			−1.09668			−0.548338	+	0.836257i	$0.684739\pi$
$860$		0			0
$861$	6.36486	−	7.31371i	0.216914	−	0.249251i
$862$	28.3929	+	11.7607i	0.967066	+	0.400572i
$863$	32.8113			1.11691			0.558455	−	0.829535i	$-0.311394\pi$
$863$	32.8113			1.11691			0.558455	+	0.829535i	$0.311394\pi$
$864$	24.2520	−	16.6084i	0.825070	−	0.565030i
$865$		0			0
$866$	−38.1167	−	15.7884i	−1.29526	−	0.536513i
$867$	−16.6656	+	19.1501i	−0.565995	+	0.650372i
$868$	−21.9607	−	21.9607i	−0.745396	−	0.745396i
$869$	−2.03916			−0.0691736
$870$		0			0
$871$			7.31371i			0.247816i
$872$	−43.0781	+	17.8435i	−1.45881	+	0.604259i
$873$	−4.54822	−	32.6256i	−0.153934	−	1.10421i
$874$	−6.82843	−	2.82843i	−0.230975	−	0.0956730i
$875$		0			0
$876$	15.7177	−	1.09030i	0.531053	−	0.0368379i
$877$		−	33.4929i		−	1.13098i	−0.824757	−	0.565488i	$-0.808688\pi$
$877$		−	33.4929i		−	1.13098i	0.824757	−	0.565488i	$-0.191312\pi$
$878$	6.23172	−	15.0447i	0.210310	−	0.507734i
$879$	−18.5486	+	21.3137i	−0.625627	+	0.718894i
$880$		0			0
$881$			12.3074i			0.414647i	0.978272	+	0.207323i	$0.0664752\pi$
$881$			12.3074i			0.414647i	−0.978272	+	0.207323i	$0.933525\pi$
$882$	−1.95064	+	7.50810i	−0.0656816	+	0.252811i
$883$	−12.4741			−0.419788			−0.209894	−	0.977724i	$-0.567312\pi$
$883$	−12.4741			−0.419788			−0.209894	+	0.977724i	$0.567312\pi$
$884$	−6.96211	−	6.96211i	−0.234161	−	0.234161i
$885$		0			0
$886$	21.8995	−	52.8701i	0.735728	−	1.77620i
$887$	−37.6662			−1.26471			−0.632353	−	0.774680i	$-0.717911\pi$
$887$	−37.6662			−1.26471			−0.632353	+	0.774680i	$0.717911\pi$
$888$	12.0894	−	36.0648i	0.405694	−	1.21025i
$889$	5.17157			0.173449
$890$		0			0
$891$	10.3431	+	36.3762i	0.346508	+	1.21865i
$892$	−14.9768	+	14.9768i	−0.501460	+	0.501460i
$893$	5.22625			0.174890
$894$	−1.58086	+	0.787088i	−0.0528718	+	0.0263242i
$895$		0			0
$896$	9.84591	+	23.7701i	0.328929	+	0.794104i
$897$	4.54822	+	3.95815i	0.151861	+	0.132159i
$898$	13.4161	−	32.3893i	0.447701	−	1.08085i
$899$		−	11.8851i		−	0.396389i
$900$		0			0
$901$		−	16.9706i		−	0.565371i
$902$	−13.5140	−	5.59767i	−0.449966	−	0.186382i
$903$	−25.8686	−	22.5125i	−0.860854	−	0.749170i
$904$	−1.65685	+	0.686292i	−0.0551062	+	0.0228257i
$905$		0			0
$906$	3.08790	+	6.20201i	0.102589	+	0.206048i
$907$	−46.1956			−1.53390			−0.766950	−	0.641707i	$-0.778226\pi$
$907$	−46.1956			−1.53390			−0.766950	+	0.641707i	$0.778226\pi$
$908$	−6.75699	+	6.75699i	−0.224238	+	0.224238i
$909$	5.64391	+	40.4853i	0.187197	+	1.34281i
$910$		0			0
$911$	28.6931			0.950645			0.475322	−	0.879812i	$-0.342331\pi$
$911$	28.6931			0.950645			0.475322	+	0.879812i	$0.342331\pi$
$912$	−25.2346	−	21.9607i	−0.835600	−	0.727193i
$913$	29.1732			0.965493
$914$	−16.8080	−	6.96211i	−0.555960	−	0.230286i
$915$		0			0
$916$	4.68629	−	4.68629i	0.154839	−	0.154839i
$917$	−25.3884			−0.838400
$918$	−9.28084	+	6.35577i	−0.306314	+	0.209772i
$919$			22.1421i			0.730402i	0.930929	+	0.365201i	$0.119000\pi$
$919$			22.1421i			0.730402i	−0.930929	+	0.365201i	$0.881000\pi$
$920$		0			0
$921$	−20.2426	+	23.2603i	−0.667018	+	0.766454i
$922$	−24.2349	−	10.0384i	−0.798132	−	0.330597i
$923$		−	38.2233i		−	1.25813i
$924$	−33.0230	+	2.29073i	−1.08638	+	0.0753595i
$925$		0			0
$926$	2.67264	−	6.45232i	0.0878284	−	0.212036i
$927$	−25.8686	+	3.60625i	−0.849637	+	0.118445i
$928$	−3.76787	+	9.09644i	−0.123686	+	0.298605i
$929$			56.3666i			1.84933i	0.380784	+	0.924664i	$0.375654\pi$
$929$			56.3666i			1.84933i	−0.380784	+	0.924664i	$0.624346\pi$
$930$		0			0
$931$	8.82843			0.289340
$932$	39.6452	−	39.6452i	1.29862	−	1.29862i
$933$	−11.1953	+	12.8643i	−0.366519	+	0.421158i
$934$	4.72792	−	11.4142i	0.154702	−	0.373484i
$935$		0			0
$936$	13.8242	+	23.5287i	0.451858	+	0.769058i
$937$	−32.9411			−1.07614			−0.538070	−	0.842900i	$-0.680846\pi$
$937$	−32.9411			−1.07614			−0.538070	+	0.842900i	$0.680846\pi$
$938$	−2.79884	+	6.75699i	−0.0913852	+	0.220623i
$939$	28.0000	−	32.1741i	0.913745	−	1.04996i
$940$		0			0
$941$	3.18243			0.103744			0.0518721	−	0.998654i	$-0.483481\pi$
$941$	3.18243			0.103744			0.0518721	+	0.998654i	$0.483481\pi$
$942$	25.4297	+	51.0752i	0.828545	+	1.66412i
$943$			2.66428i			0.0867610i
$944$	16.8080			0.547055
$945$		0			0
$946$	−19.7990	+	47.7990i	−0.643721	+	1.55408i
$947$			36.5068i			1.18631i	0.805087	+	0.593156i	$0.202118\pi$
$947$			36.5068i			1.18631i	−0.805087	+	0.593156i	$0.797882\pi$
$948$	0.116332	+	1.67703i	0.00377829	+	0.0544675i
$949$			14.6274i			0.474826i
$950$		0			0
$951$	−11.1641	+	12.8284i	−0.362021	+	0.415990i
$952$	−3.76787	−	9.09644i	−0.122117	−	0.294817i
$953$		−	39.9079i		−	1.29274i	−0.763023	−	0.646371i	$-0.776286\pi$
$953$		−	39.9079i		−	1.29274i	0.763023	−	0.646371i	$-0.223714\pi$
$954$	−11.8276	+	45.5249i	−0.382933	+	1.47392i
$955$		0			0
$956$	18.8472	+	18.8472i	0.609561	+	0.609561i
$957$	−9.55582	−	8.31609i	−0.308896	−	0.268821i
$958$	−20.0768	−	8.31609i	−0.648652	−	0.268681i
$959$	18.2499			0.589321
$960$		0			0
$961$	−15.6274			−0.504110
$962$	32.6256	+	13.5140i	1.05189	+	0.435708i
$963$	−16.8607	+	2.35049i	−0.543329	+	0.0757436i
$964$	14.8284	+	14.8284i	0.477591	+	0.477591i
$965$		0			0
$966$	2.68729	+	5.39738i	0.0864621	+	0.173658i
$967$			51.8474i			1.66730i	0.552293	+	0.833650i	$0.313753\pi$
$967$			51.8474i			1.66730i	−0.552293	+	0.833650i	$0.686247\pi$
$968$	7.20533	+	17.3952i	0.231588	+	0.559103i
$969$	9.65685	+	8.40401i	0.310223	+	0.269976i
$970$		0			0
$971$			48.2612i			1.54878i	0.632711	+	0.774388i	$0.281942\pi$
$971$			48.2612i			1.54878i	−0.632711	+	0.774388i	$0.718058\pi$
$972$	29.3263	−	10.5816i	0.940640	−	0.339405i
$973$			5.65180i			0.181188i
$974$	10.6543	−	25.7218i	0.341387	−	0.824180i
$975$		0			0
$976$	33.9411			1.08643
$977$		−	13.7766i		−	0.440753i	−0.975415	−	0.220376i	$-0.929271\pi$
$977$		−	13.7766i		−	0.440753i	0.975415	−	0.220376i	$-0.0707285\pi$
$978$	−19.0906	+	9.50495i	−0.610449	+	0.303935i
$979$	35.3137			1.12863
$980$		0			0
$981$	−48.9822	+	6.82843i	−1.56388	+	0.218015i
$982$	7.60268	−	18.3545i	0.242611	−	0.585715i
$983$	−1.97908			−0.0631227			−0.0315613	−	0.999502i	$-0.510048\pi$
$983$	−1.97908			−0.0631227			−0.0315613	+	0.999502i	$0.510048\pi$
$984$	−3.83265	+	11.4334i	−0.122181	+	0.364485i
$985$		0			0
$986$	1.44190	−	3.48106i	0.0459195	−	0.110859i
$987$	−3.21608	−	2.79884i	−0.102369	−	0.0890879i
$988$	21.9607	−	21.9607i	0.698664	−	0.698664i
$989$	9.42359			0.299653
$990$		0			0
$991$		−	19.7990i		−	0.628936i	−0.949268	−	0.314468i	$-0.898174\pi$
$991$		−	19.7990i		−	0.628936i	0.949268	−	0.314468i	$-0.101826\pi$
$992$	35.6871	+	14.7821i	1.13307	+	0.469331i
$993$	1.72232	−	1.97908i	0.0546561	−	0.0628041i
$994$	14.6274	−	35.3137i	0.463953	−	1.12008i
$995$		0			0
$996$	−1.66431	−	23.9925i	−0.0527357	−	0.760233i
$997$			12.3125i			0.389941i	0.980809	+	0.194971i	$0.0624611\pi$
$997$			12.3125i			0.389941i	−0.980809	+	0.194971i	$0.937539\pi$
$998$	32.8113	+	13.5909i	1.03862	+	0.430212i
$999$	22.0296	−	33.7990i	0.696986	−	1.06935i

Twists

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

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

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30656 - 0.541196i) q^{2} +(-1.13705 + 1.30656i) q^{3} +(1.41421 + 1.41421i) q^{4} +(2.19274 - 1.09174i) q^{6} +2.27411i q^{7} +(-1.08239 - 2.61313i) q^{8} +(-0.414214 - 2.97127i) q^{9} +O(q^{10})\)	\(q+(-1.30656 - 0.541196i) q^{2} +(-1.13705 + 1.30656i) q^{3} +(1.41421 + 1.41421i) q^{4} +(2.19274 - 1.09174i) q^{6} +2.27411i q^{7} +(-1.08239 - 2.61313i) q^{8} +(-0.414214 - 2.97127i) q^{9} -4.20201i q^{11} +(-3.45580 + 0.239721i) q^{12} -3.21608i q^{13} +(1.23074 - 2.97127i) q^{14} +4.00000i q^{16} -1.53073i q^{17} +(-1.06684 + 4.10632i) q^{18} +4.82843 q^{19} +(-2.97127 - 2.58579i) q^{21} +(-2.27411 + 5.49019i) q^{22} +1.08239 q^{23} +(4.64495 + 1.55705i) q^{24} +(-1.74053 + 4.20201i) q^{26} +(4.35313 + 2.83730i) q^{27} +(-3.21608 + 3.21608i) q^{28} -1.74053 q^{29} +6.82843i q^{31} +(2.16478 - 5.22625i) q^{32} +(5.49019 + 4.77791i) q^{33} +(-0.828427 + 2.00000i) q^{34} +(3.61622 - 4.78779i) q^{36} -7.76429i q^{37} +(-6.30864 - 2.61313i) q^{38} +(4.20201 + 3.65685i) q^{39} +2.46148i q^{41} +(2.48273 + 4.98653i) q^{42} +8.70626 q^{43} +(5.94253 - 5.94253i) q^{44} +(-1.41421 - 0.585786i) q^{46} +1.08239 q^{47} +(-5.22625 - 4.54822i) q^{48} +1.82843 q^{49} +(2.00000 + 1.74053i) q^{51} +(4.54822 - 4.54822i) q^{52} +11.0866 q^{53} +(-4.15211 - 6.06300i) q^{54} +(5.94253 - 2.46148i) q^{56} +(-5.49019 + 6.30864i) q^{57} +(2.27411 + 0.941967i) q^{58} -4.20201i q^{59} -8.48528i q^{61} +(3.69552 - 8.92177i) q^{62} +(6.75699 - 0.941967i) q^{63} +(-5.65685 + 5.65685i) q^{64} +(-4.58749 - 9.21391i) q^{66} -2.27411 q^{67} +(2.16478 - 2.16478i) q^{68} +(-1.23074 + 1.41421i) q^{69} +11.8851 q^{71} +(-7.31595 + 4.29847i) q^{72} -4.54822 q^{73} +(-4.20201 + 10.1445i) q^{74} +(6.82843 + 6.82843i) q^{76} +9.55582 q^{77} +(-3.51111 - 7.05202i) q^{78} -0.485281i q^{79} +(-8.65685 + 2.46148i) q^{81} +(1.33214 - 3.21608i) q^{82} +6.94269i q^{83} +(-0.545152 - 7.85886i) q^{84} +(-11.3753 - 4.71179i) q^{86} +(1.97908 - 2.27411i) q^{87} +(-10.9804 + 4.54822i) q^{88} +8.40401i q^{89} +7.31371 q^{91} +(1.53073 + 1.53073i) q^{92} +(-8.92177 - 7.76429i) q^{93} +(-1.41421 - 0.585786i) q^{94} +(4.36695 + 8.77096i) q^{96} +10.9804 q^{97} +(-2.38896 - 0.989538i) 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	\( 16 q + 16 q^{9} + 32 q^{19} + 32 q^{24} + 32 q^{34} - 32 q^{36} - 16 q^{49} + 32 q^{51} - 32 q^{54} + 64 q^{66} + 64 q^{76} - 48 q^{81} - 32 q^{84} - 64 q^{91} + 64 q^{96} - 64 q^{99}+O(q^{100}) \) 16 * q + 16 * q^9 + 32 * q^19 + 32 * q^24 + 32 * q^34 - 32 * q^36 - 16 * q^49 + 32 * q^51 - 32 * q^54 + 64 * q^66 + 64 * q^76 - 48 * q^81 - 32 * q^84 - 64 * q^91 + 64 * q^96 - 64 * q^99

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