LMFDB - Embedded newform 300.2.x.a.233.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(17,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 13]))

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

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

chi := DirichletCharacter("300.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.x (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			233.8
Character	$\chi$	$=$	300.233
Dual form			300.2.x.a.197.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.767407 - 1.55277i) q^{3} +(1.73820 - 1.40665i) q^{5} +(-0.636300 + 0.636300i) q^{7} +(-1.82217 - 2.38321i) q^{9} +O(q^{10})$	\(q+(0.767407 - 1.55277i) q^{3} +(1.73820 - 1.40665i) q^{5} +(-0.636300 + 0.636300i) q^{7} +(-1.82217 - 2.38321i) q^{9} +(2.06892 - 0.672233i) q^{11} +(0.777501 - 0.396157i) q^{13} +(-0.850289 - 3.77849i) q^{15} +(0.108171 + 0.682968i) q^{17} +(-3.00841 + 4.14072i) q^{19} +(0.499725 + 1.47633i) q^{21} +(-4.93053 - 2.51223i) q^{23} +(1.04269 - 4.89007i) q^{25} +(-5.09892 + 1.00052i) q^{27} +(4.84938 - 3.52328i) q^{29} +(6.26107 + 4.54893i) q^{31} +(0.543881 - 3.72843i) q^{33} +(-0.210967 + 2.00107i) q^{35} +(-0.550893 - 1.08119i) q^{37} +(-0.0184796 - 1.51129i) q^{39} +(2.90898 + 0.945186i) q^{41} +(8.01220 + 8.01220i) q^{43} +(-6.51964 - 1.57934i) q^{45} +(-7.69094 - 1.21813i) q^{47} +6.19025i q^{49} +(1.14350 + 0.356149i) q^{51} +(-0.429522 + 2.71189i) q^{53} +(2.65060 - 4.07872i) q^{55} +(4.12090 + 7.84897i) q^{57} +(-3.57345 + 10.9980i) q^{59} +(2.58562 + 7.95771i) q^{61} +(2.67588 + 0.356986i) q^{63} +(0.794201 - 1.78227i) q^{65} +(-9.44650 + 1.49618i) q^{67} +(-7.68464 + 5.72807i) q^{69} +(-3.16602 - 4.35766i) q^{71} +(7.59343 - 14.9030i) q^{73} +(-6.79298 - 5.37172i) q^{75} +(-0.888711 + 1.74419i) q^{77} +(2.00608 + 2.76113i) q^{79} +(-2.35936 + 8.68524i) q^{81} +(-5.95105 + 0.942553i) q^{83} +(1.14872 + 1.03498i) q^{85} +(-1.74939 - 10.2337i) q^{87} +(4.99027 + 15.3585i) q^{89} +(-0.242649 + 0.746798i) q^{91} +(11.8682 - 6.23110i) q^{93} +(0.595312 + 11.4292i) q^{95} +(-0.0903661 + 0.570549i) q^{97} +(-5.37200 - 3.70574i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q - 2 * q^3 + 4 * q^7	$ 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) $ 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{20}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.767407	−	1.55277i	0.443062	−	0.896491i
$3$	0.767407	−	1.55277i	0.443062	−	0.896491i
$4$		0			0
$5$	1.73820	−	1.40665i	0.777347	−	0.629072i
$5$	1.73820	−	1.40665i	0.777347	−	0.629072i
$6$		0			0
$7$	−0.636300	+	0.636300i	−0.240499	+	0.240499i	−0.817056	−	0.576558i	$-0.804396\pi$
$7$	−0.636300	+	0.636300i	−0.240499	+	0.240499i	0.576558	+	0.817056i	$0.304396\pi$
$8$		0			0
$9$	−1.82217	−	2.38321i	−0.607391	−	0.794403i
$10$		0			0
$11$	2.06892	−	0.672233i	0.623803	−	0.202686i	0.0199748	−	0.999800i	$-0.493641\pi$
$11$	2.06892	−	0.672233i	0.623803	−	0.202686i	0.603828	+	0.797115i	$0.293641\pi$
$12$		0			0
$13$	0.777501	−	0.396157i	0.215640	−	0.109874i	−0.342834	−	0.939396i	$-0.611387\pi$
$13$	0.777501	−	0.396157i	0.215640	−	0.109874i	0.558474	+	0.829522i	$0.311387\pi$
$14$		0			0
$15$	−0.850289	−	3.77849i	−0.219544	−	0.975603i
$16$		0			0
$17$	0.108171	+	0.682968i	0.0262354	+	0.165644i	0.997327	−	0.0730615i	$-0.0232769\pi$
$17$	0.108171	+	0.682968i	0.0262354	+	0.165644i	−0.971092	+	0.238706i	$0.923277\pi$
$18$		0			0
$19$	−3.00841	+	4.14072i	−0.690176	+	0.949945i	−1.00000		0.000848557i	$-0.999730\pi$
$19$	−3.00841	+	4.14072i	−0.690176	+	0.949945i	0.309824	+	0.950794i	$0.399730\pi$
$20$		0			0
$21$	0.499725	+	1.47633i	0.109049	+	0.322161i
$22$		0			0
$23$	−4.93053	−	2.51223i	−1.02809	−	0.523837i	−0.143225	−	0.989690i	$-0.545747\pi$
$23$	−4.93053	−	2.51223i	−1.02809	−	0.523837i	−0.884862	+	0.465853i	$0.845747\pi$
$24$		0			0
$25$	1.04269	−	4.89007i	0.208537	−	0.978014i
$26$		0			0
$27$	−5.09892	+	1.00052i	−0.981287	+	0.192551i
$28$		0			0
$29$	4.84938	−	3.52328i	0.900507	−	0.654256i	−0.0380893	−	0.999274i	$-0.512127\pi$
$29$	4.84938	−	3.52328i	0.900507	−	0.654256i	0.938596	+	0.345018i	$0.112127\pi$
$30$		0			0
$31$	6.26107	+	4.54893i	1.12452	+	0.817012i	0.984888	−	0.173191i	$-0.0554078\pi$
$31$	6.26107	+	4.54893i	1.12452	+	0.817012i	0.139633	+	0.990203i	$0.455408\pi$
$32$		0			0
$33$	0.543881	−	3.72843i	0.0946776	−	0.649036i
$34$		0			0
$35$	−0.210967	+	2.00107i	−0.0356600	+	0.338242i
$36$		0			0
$37$	−0.550893	−	1.08119i	−0.0905663	−	0.177746i	0.841280	−	0.540600i	$-0.181803\pi$
$37$	−0.550893	−	1.08119i	−0.0905663	−	0.177746i	−0.931846	+	0.362853i	$0.881803\pi$
$38$		0			0
$39$	−0.0184796	−	1.51129i	−0.00295911	−	0.242000i
$40$		0			0
$41$	2.90898	+	0.945186i	0.454307	+	0.147613i	0.527227	−	0.849724i	$-0.323232\pi$
$41$	2.90898	+	0.945186i	0.454307	+	0.147613i	−0.0729199	+	0.997338i	$0.523232\pi$
$42$		0			0
$43$	8.01220	+	8.01220i	1.22185	+	1.22185i	0.966974	+	0.254875i	$0.0820344\pi$
$43$	8.01220	+	8.01220i	1.22185	+	1.22185i	0.254875	+	0.966974i	$0.417966\pi$
$44$		0			0
$45$	−6.51964	−	1.57934i	−0.971890	−	0.235434i
$46$		0			0
$47$	−7.69094	−	1.21813i	−1.12184	−	0.177682i	−0.432160	−	0.901797i	$-0.642248\pi$
$47$	−7.69094	−	1.21813i	−1.12184	−	0.177682i	−0.689679	+	0.724115i	$0.742248\pi$
$48$		0			0
$49$			6.19025i			0.884321i
$50$		0			0
$51$	1.14350	+	0.356149i	0.160122	+	0.0498708i
$52$		0			0
$53$	−0.429522	+	2.71189i	−0.0589994	+	0.372507i	0.940468	+	0.339881i	$0.110387\pi$
$53$	−0.429522	+	2.71189i	−0.0589994	+	0.372507i	−0.999468	+	0.0326258i	$0.989613\pi$
$54$		0			0
$55$	2.65060	−	4.07872i	0.357407	−	0.549974i
$56$		0			0
$57$	4.12090	+	7.84897i	0.545826	+	1.03962i
$58$		0			0
$59$	−3.57345	+	10.9980i	−0.465224	+	1.43181i	0.393477	+	0.919334i	$0.371272\pi$
$59$	−3.57345	+	10.9980i	−0.465224	+	1.43181i	−0.858701	+	0.512477i	$0.828728\pi$
$60$		0			0
$61$	2.58562	+	7.95771i	0.331054	+	1.01888i	0.968633	+	0.248495i	$0.0799359\pi$
$61$	2.58562	+	7.95771i	0.331054	+	1.01888i	−0.637579	+	0.770385i	$0.720064\pi$
$62$		0			0
$63$	2.67588	+	0.356986i	0.337130	+	0.0449760i
$64$		0			0
$65$	0.794201	−	1.78227i	0.0985085	−	0.221063i
$66$		0			0
$67$	−9.44650	+	1.49618i	−1.15407	+	0.182787i	−0.703997	−	0.710203i	$-0.748603\pi$
$67$	−9.44650	+	1.49618i	−1.15407	+	0.182787i	−0.450076	+	0.892990i	$0.648603\pi$
$68$		0			0
$69$	−7.68464	+	5.72807i	−0.925122	+	0.689578i
$70$		0			0
$71$	−3.16602	−	4.35766i	−0.375738	−	0.517159i	0.578711	−	0.815533i	$-0.303556\pi$
$71$	−3.16602	−	4.35766i	−0.375738	−	0.517159i	−0.954449	+	0.298374i	$0.903556\pi$
$72$		0			0
$73$	7.59343	−	14.9030i	0.888744	−	1.74426i	0.261936	−	0.965085i	$-0.415639\pi$
$73$	7.59343	−	14.9030i	0.888744	−	1.74426i	0.626808	−	0.779174i	$-0.284361\pi$
$74$		0			0
$75$	−6.79298	−	5.37172i	−0.784386	−	0.620273i
$76$		0			0
$77$	−0.888711	+	1.74419i	−0.101278	+	0.198769i
$78$		0			0
$79$	2.00608	+	2.76113i	0.225701	+	0.310651i	0.906817	−	0.421525i	$-0.138505\pi$
$79$	2.00608	+	2.76113i	0.225701	+	0.310651i	−0.681116	+	0.732176i	$0.738505\pi$
$80$		0			0
$81$	−2.35936	+	8.68524i	−0.262151	+	0.965027i
$82$		0			0
$83$	−5.95105	+	0.942553i	−0.653212	+	0.103459i	−0.474240	−	0.880395i	$-0.657277\pi$
$83$	−5.95105	+	0.942553i	−0.653212	+	0.103459i	−0.178972	+	0.983854i	$0.557277\pi$
$84$		0			0
$85$	1.14872	+	1.03498i	0.124596	+	0.112259i
$86$		0			0
$87$	−1.74939	−	10.2337i	−0.187554	−	1.09717i
$88$		0			0
$89$	4.99027	+	15.3585i	0.528968	+	1.62800i	0.756334	+	0.654186i	$0.226989\pi$
$89$	4.99027	+	15.3585i	0.528968	+	1.62800i	−0.227366	+	0.973809i	$0.573011\pi$
$90$		0			0
$91$	−0.242649	+	0.746798i	−0.0254366	+	0.0782857i
$92$		0			0
$93$	11.8682	−	6.23110i	1.23068	−	0.646135i
$94$		0			0
$95$	0.595312	+	11.4292i	0.0610778	+	1.17261i
$96$		0			0
$97$	−0.0903661	+	0.570549i	−0.00917528	+	0.0579305i	−0.991851	−	0.127402i	$-0.959336\pi$
$97$	−0.0903661	+	0.570549i	−0.00917528	+	0.0579305i	0.982676	+	0.185332i	$0.0593362\pi$
$98$		0			0
$99$	−5.37200	−	3.70574i	−0.539906	−	0.372441i
$100$		0			0
$101$		−	10.1216i		−	1.00713i	−0.863956	−	0.503567i	$-0.832021\pi$
$101$		−	10.1216i		−	1.00713i	0.863956	−	0.503567i	$-0.167979\pi$
$102$		0			0
$103$	3.57836	+	0.566756i	0.352586	+	0.0558442i	0.330215	−	0.943906i	$-0.392879\pi$
$103$	3.57836	+	0.566756i	0.352586	+	0.0558442i	0.0223707	+	0.999750i	$0.492879\pi$
$104$		0			0
$105$	2.94529	+	1.86321i	0.287431	+	0.181831i
$106$		0			0
$107$	−1.76323	−	1.76323i	−0.170458	−	0.170458i	0.616722	−	0.787181i	$-0.288460\pi$
$107$	−1.76323	−	1.76323i	−0.170458	−	0.170458i	−0.787181	+	0.616722i	$0.788460\pi$
$108$		0			0
$109$	−5.77632	−	1.87684i	−0.553272	−	0.179769i	0.0190199	−	0.999819i	$-0.493945\pi$
$109$	−5.77632	−	1.87684i	−0.553272	−	0.179769i	−0.572291	+	0.820050i	$0.693945\pi$
$110$		0			0
$111$	−2.10159	+	0.0256976i	−0.199474	+	0.00243911i
$112$		0			0
$113$	3.00442	+	5.89650i	0.282632	+	0.554696i	0.988057	−	0.154088i	$-0.0492439\pi$
$113$	3.00442	+	5.89650i	0.282632	+	0.554696i	−0.705425	+	0.708784i	$0.749244\pi$
$114$		0			0
$115$	−12.1041	+	2.56876i	−1.12871	+	0.239538i
$116$		0			0
$117$	−2.36087	−	1.13108i	−0.218262	−	0.104569i
$118$		0			0
$119$	−0.503402	−	0.365743i	−0.0461467	−	0.0335276i
$120$		0			0
$121$	−5.07066	+	3.68405i	−0.460969	+	0.334913i
$122$		0			0
$123$	3.70003	−	3.79163i	0.333620	−	0.341880i
$124$		0			0
$125$	−5.06621	−	9.96662i	−0.453136	−	0.891442i
$126$		0			0
$127$	−10.3962	−	5.29711i	−0.922510	−	0.470042i	−0.0728321	−	0.997344i	$-0.523204\pi$
$127$	−10.3962	−	5.29711i	−0.922510	−	0.470042i	−0.849678	+	0.527302i	$0.823204\pi$
$128$		0			0
$129$	18.5897	−	6.29247i	1.63673	−	0.554021i
$130$		0			0
$131$	11.1367	−	15.3284i	0.973018	−	1.33924i	0.0325110	−	0.999471i	$-0.489650\pi$
$131$	11.1367	−	15.3284i	0.973018	−	1.33924i	0.940507	−	0.339773i	$-0.110350\pi$
$132$		0			0
$133$	−0.720488	−	4.54898i	−0.0624742	−	0.394447i
$134$		0			0
$135$	−7.45556	+	8.91149i	−0.641672	+	0.766979i
$136$		0			0
$137$	10.5280	−	5.36426i	0.899464	−	0.458300i	0.0578166	−	0.998327i	$-0.481586\pi$
$137$	10.5280	−	5.36426i	0.899464	−	0.458300i	0.841647	+	0.540027i	$0.181586\pi$
$138$		0			0
$139$	5.62085	−	1.82633i	0.476755	−	0.154907i	−0.0607756	−	0.998151i	$-0.519357\pi$
$139$	5.62085	−	1.82633i	0.476755	−	0.154907i	0.537530	+	0.843244i	$0.319357\pi$
$140$		0			0
$141$	−7.79355	+	11.0075i	−0.656335	+	0.926995i
$142$		0			0
$143$	1.34228	−	1.34228i	0.112247	−	0.112247i
$144$		0			0
$145$	3.47318	−	12.9455i	0.288432	−	1.07507i
$146$		0			0
$147$	9.61201	+	4.75044i	0.792785	+	0.391809i
$148$		0			0
$149$	−8.89212			−0.728471			−0.364236	−	0.931307i	$-0.618670\pi$
$149$	−8.89212			−0.728471			−0.364236	+	0.931307i	$0.618670\pi$
$150$		0			0
$151$	6.58968			0.536260			0.268130	−	0.963383i	$-0.413594\pi$
$151$	6.58968			0.536260			0.268130	+	0.963383i	$0.413594\pi$
$152$		0			0
$153$	1.43055	−	1.50228i	0.115653	−	0.121452i
$154$		0			0
$155$	17.2817	−	0.900156i	1.38810	−	0.0723023i
$156$		0			0
$157$	9.41818	−	9.41818i	0.751653	−	0.751653i	−0.223135	−	0.974788i	$-0.571629\pi$
$157$	9.41818	−	9.41818i	0.751653	−	0.751653i	0.974788	+	0.223135i	$0.0716290\pi$
$158$		0			0
$159$	3.88132	+	2.74807i	0.307809	+	0.217936i
$160$		0			0
$161$	4.73583	−	1.53876i	0.373236	−	0.121272i
$162$		0			0
$163$	−10.5179	+	5.35912i	−0.823823	+	0.419759i	−0.814476	−	0.580198i	$-0.802975\pi$
$163$	−10.5179	+	5.35912i	−0.823823	+	0.419759i	−0.00934719	+	0.999956i	$0.502975\pi$
$164$		0			0
$165$	−4.29921	−	7.24580i	−0.334693	−	0.564085i
$166$		0			0
$167$	−3.37212	−	21.2908i	−0.260943	−	1.64753i	−0.675394	−	0.737457i	$-0.736027\pi$
$167$	−3.37212	−	21.2908i	−0.260943	−	1.64753i	0.414452	−	0.910071i	$-0.363973\pi$
$168$		0			0
$169$	−7.19364	+	9.90120i	−0.553357	+	0.761630i
$170$		0			0
$171$	15.3500	−	0.375447i	1.17385	−	0.0287111i
$172$		0			0
$173$	−4.69375	−	2.39158i	−0.356859	−	0.181829i	0.266365	−	0.963872i	$-0.414177\pi$
$173$	−4.69375	−	2.39158i	−0.356859	−	0.181829i	−0.623224	+	0.782044i	$0.714177\pi$
$174$		0			0
$175$	2.44809	+	3.77501i	0.185058	+	0.285364i
$176$		0			0
$177$	14.3350	+	13.9886i	1.07748	+	1.05145i
$178$		0			0
$179$	16.3130	−	11.8521i	1.21929	−	0.885869i	0.223253	−	0.974761i	$-0.428332\pi$
$179$	16.3130	−	11.8521i	1.21929	−	0.885869i	0.996041	+	0.0888915i	$0.0283325\pi$
$180$		0			0
$181$	−17.8222	−	12.9486i	−1.32471	−	0.962462i	−0.999861	−	0.0166976i	$-0.994685\pi$
$181$	−17.8222	−	12.9486i	−1.32471	−	0.962462i	−0.324854	−	0.945764i	$-0.605315\pi$
$182$		0			0
$183$	14.3407	+	2.09194i	1.06009	+	0.154640i
$184$		0			0
$185$	−2.47841	−	1.10441i	−0.182217	−	0.0811979i
$186$		0			0
$187$	0.682911	+	1.34029i	0.0499394	+	0.0980116i
$188$		0			0
$189$	2.60781	−	3.88107i	0.189690	−	0.282306i
$190$		0			0
$191$	−5.98311	−	1.94403i	−0.432922	−	0.140665i	0.0844455	−	0.996428i	$-0.473088\pi$
$191$	−5.98311	−	1.94403i	−0.432922	−	0.140665i	−0.517368	+	0.855763i	$0.673088\pi$
$192$		0			0
$193$	−7.45104	−	7.45104i	−0.536338	−	0.536338i	0.386114	−	0.922451i	$-0.373817\pi$
$193$	−7.45104	−	7.45104i	−0.536338	−	0.536338i	−0.922451	+	0.386114i	$0.873817\pi$
$194$		0			0
$195$	−2.15798	−	2.60094i	−0.154536	−	0.186257i
$196$		0			0
$197$	−23.7368	−	3.75954i	−1.69118	−	0.267856i	−0.764749	−	0.644329i	$-0.777137\pi$
$197$	−23.7368	−	3.75954i	−1.69118	−	0.267856i	−0.926428	+	0.376472i	$0.877137\pi$
$198$		0			0
$199$		−	20.1941i		−	1.43152i	−0.698346	−	0.715760i	$-0.746080\pi$
$199$		−	20.1941i		−	1.43152i	0.698346	−	0.715760i	$-0.253920\pi$
$200$		0			0
$201$	−4.92609	+	15.8164i	−0.347459	+	1.11560i
$202$		0			0
$203$	−0.843796	+	5.32752i	−0.0592229	+	0.373918i
$204$		0			0
$205$	6.38594	−	2.44899i	0.446014	−	0.171045i
$206$		0			0
$207$	2.99712	+	16.3282i	0.208314	+	1.13489i
$208$		0			0
$209$	−3.44063	+	10.5892i	−0.237993	+	0.732467i
$210$		0			0
$211$	−0.979151	−	3.01352i	−0.0674075	−	0.207459i	0.911679	−	0.410903i	$-0.134787\pi$
$211$	−0.979151	−	3.01352i	−0.0674075	−	0.207459i	−0.979087	+	0.203444i	$0.934787\pi$
$212$		0			0
$213$	−9.19606	+	1.57200i	−0.630104	+	0.107712i
$214$		0			0
$215$	25.1972	+	2.65648i	1.71843	+	0.181170i
$216$		0			0
$217$	−6.87840	+	1.08943i	−0.466936	+	0.0739554i
$218$		0			0
$219$	−17.3136	−	23.2275i	−1.16994	−	1.56957i
$220$		0			0
$221$	0.354666	+	0.488156i	0.0238574	+	0.0328369i
$222$		0			0
$223$	−6.35432	+	12.4711i	−0.425517	+	0.835124i	0.574347	+	0.818612i	$0.305256\pi$
$223$	−6.35432	+	12.4711i	−0.425517	+	0.835124i	−0.999864	+	0.0165117i	$0.994744\pi$
$224$		0			0
$225$	−13.5540	+	6.42562i	−0.903601	+	0.428375i
$226$		0			0
$227$	−8.70950	+	17.0934i	−0.578070	+	1.13453i	0.398064	+	0.917358i	$0.369682\pi$
$227$	−8.70950	+	17.0934i	−0.578070	+	1.13453i	−0.976134	+	0.217169i	$0.930318\pi$
$228$		0			0
$229$	−5.96289	−	8.20721i	−0.394039	−	0.542348i	0.565197	−	0.824956i	$-0.308800\pi$
$229$	−5.96289	−	8.20721i	−0.394039	−	0.542348i	−0.959235	+	0.282609i	$0.908800\pi$
$230$		0			0
$231$	2.02632	+	2.71847i	0.133322	+	0.178862i
$232$		0			0
$233$	−21.7035	+	3.43750i	−1.42185	+	0.225198i	−0.819519	−	0.573052i	$-0.805759\pi$
$233$	−21.7035	+	3.43750i	−1.42185	+	0.225198i	−0.602326	+	0.798250i	$0.705759\pi$
$234$		0			0
$235$	−15.0819	+	8.70110i	−0.983833	+	0.567597i
$236$		0			0
$237$	5.82686	−	0.996063i	0.378495	−	0.0647012i
$238$		0			0
$239$	6.69642	+	20.6095i	0.433155	+	1.33312i	0.894965	+	0.446136i	$0.147200\pi$
$239$	6.69642	+	20.6095i	0.433155	+	1.33312i	−0.461810	+	0.886979i	$0.652800\pi$
$240$		0			0
$241$	6.18567	−	19.0375i	0.398454	−	1.22631i	−0.527785	−	0.849378i	$-0.676977\pi$
$241$	6.18567	−	19.0375i	0.398454	−	1.22631i	0.926239	−	0.376937i	$-0.123023\pi$
$242$		0			0
$243$	11.6756	+	10.3287i	0.748988	+	0.662583i
$244$		0			0
$245$	8.70749	+	10.7599i	0.556301	+	0.687424i
$246$		0			0
$247$	−0.698668	+	4.41121i	−0.0444552	+	0.280679i
$248$		0			0
$249$	−3.10331	+	9.96391i	−0.196664	+	0.631437i
$250$		0			0
$251$			11.8785i			0.749764i	0.927073	+	0.374882i	$0.122317\pi$
$251$			11.8785i			0.749764i	−0.927073	+	0.374882i	$0.877683\pi$
$252$		0			0
$253$	−11.8897	−	1.88314i	−0.747498	−	0.118392i
$254$		0			0
$255$	2.48861	−	0.989445i	0.155843	−	0.0619615i
$256$		0			0
$257$	7.36523	+	7.36523i	0.459430	+	0.459430i	0.898468	−	0.439038i	$-0.144681\pi$
$257$	7.36523	+	7.36523i	0.459430	+	0.459430i	−0.439038	+	0.898468i	$0.644681\pi$
$258$		0			0
$259$	1.03849	+	0.337427i	0.0645288	+	0.0209667i
$260$		0			0
$261$	−17.2331	−	5.13705i	−1.06670	−	0.317975i
$262$		0			0
$263$	−1.00991	−	1.98207i	−0.0622739	−	0.122219i	0.857771	−	0.514031i	$-0.171848\pi$
$263$	−1.00991	−	1.98207i	−0.0622739	−	0.122219i	−0.920045	+	0.391812i	$0.871848\pi$
$264$		0			0
$265$	3.06808	+	5.31800i	0.188471	+	0.326682i
$266$		0			0
$267$	27.6777	+	4.03747i	1.69385	+	0.247089i
$268$		0			0
$269$	−16.6826	−	12.1206i	−1.01716	−	0.739006i	−0.0514573	−	0.998675i	$-0.516387\pi$
$269$	−16.6826	−	12.1206i	−1.01716	−	0.739006i	−0.965698	+	0.259669i	$0.916387\pi$
$270$		0			0
$271$	4.83987	−	3.51637i	0.294001	−	0.213604i	−0.431000	−	0.902352i	$-0.641839\pi$
$271$	4.83987	−	3.51637i	0.294001	−	0.213604i	0.725001	+	0.688748i	$0.241839\pi$
$272$		0			0
$273$	0.973393	+	0.949876i	0.0589124	+	0.0574891i
$274$		0			0
$275$	−1.13003	−	10.8181i	−0.0681435	−	0.652356i
$276$		0			0
$277$	26.8008	+	13.6557i	1.61030	+	0.820490i	0.999590	+	0.0286381i	$0.00911705\pi$
$277$	26.8008	+	13.6557i	1.61030	+	0.820490i	0.610713	+	0.791852i	$0.290883\pi$
$278$		0			0
$279$	−0.567703	−	23.2104i	−0.0339875	−	1.38957i
$280$		0			0
$281$	−4.52028	+	6.22163i	−0.269657	+	0.371151i	−0.922274	−	0.386537i	$-0.873671\pi$
$281$	−4.52028	+	6.22163i	−0.269657	+	0.371151i	0.652617	+	0.757688i	$0.273671\pi$
$282$		0			0
$283$	1.44567	+	9.12761i	0.0859363	+	0.542580i	0.992668	+	0.120872i	$0.0385692\pi$
$283$	1.44567	+	9.12761i	0.0859363	+	0.542580i	−0.906732	+	0.421708i	$0.861431\pi$
$284$		0			0
$285$	18.2037	+	7.84643i	1.07829	+	0.464783i
$286$		0			0
$287$	−2.45241	+	1.24956i	−0.144761	+	0.0737594i
$288$		0			0
$289$	15.7132	−	5.10553i	0.924307	−	0.300326i
$290$		0			0
$291$	0.816582	+	0.578160i	0.0478689	+	0.0338924i
$292$		0			0
$293$	−14.0642	+	14.0642i	−0.821637	+	0.821637i	−0.986343	−	0.164706i	$-0.947332\pi$
$293$	−14.0642	+	14.0642i	−0.821637	+	0.821637i	0.164706	+	0.986343i	$0.447332\pi$
$294$		0			0
$295$	9.25887	+	24.1432i	0.539072	+	1.40567i
$296$		0			0
$297$	−9.87666	+	5.49766i	−0.573102	+	0.319007i
$298$		0			0
$299$	−4.82874			−0.279253
$300$		0			0
$301$	−10.1963			−0.587706
$302$		0			0
$303$	−15.7164	−	7.76735i	−0.902885	−	0.446223i
$304$		0			0
$305$	15.6880	+	10.1950i	0.898293	+	0.583767i
$306$		0			0
$307$	15.6968	−	15.6968i	0.895865	−	0.895865i	−0.0992024	−	0.995067i	$-0.531629\pi$
$307$	15.6968	−	15.6968i	0.895865	−	0.895865i	0.995067	+	0.0992024i	$0.0316291\pi$
$308$		0			0
$309$	3.62610	−	5.12143i	0.206281	−	0.291348i
$310$		0			0
$311$	−2.25244	+	0.731862i	−0.127724	+	0.0415001i	−0.372182	−	0.928160i	$-0.621390\pi$
$311$	−2.25244	+	0.731862i	−0.127724	+	0.0415001i	0.244457	+	0.969660i	$0.421390\pi$
$312$		0			0
$313$	−8.52093	+	4.34163i	−0.481632	+	0.245404i	−0.677910	−	0.735145i	$-0.737114\pi$
$313$	−8.52093	+	4.34163i	−0.481632	+	0.245404i	0.196279	+	0.980548i	$0.437114\pi$
$314$		0			0
$315$	5.15338	−	3.14351i	0.290360	−	0.177117i
$316$		0			0
$317$	−3.90141	−	24.6325i	−0.219125	−	1.38350i	−0.814551	−	0.580091i	$-0.803017\pi$
$317$	−3.90141	−	24.6325i	−0.219125	−	1.38350i	0.595426	−	0.803410i	$-0.296983\pi$
$318$		0			0
$319$	7.66451	−	10.5493i	0.429130	−	0.590647i
$320$		0			0
$321$	−4.09101	+	1.38477i	−0.228338	+	0.0772906i
$322$		0			0
$323$	−3.15340	−	1.60674i	−0.175460	−	0.0894013i
$324$		0			0
$325$	−1.12655	−	4.21511i	−0.0624895	−	0.233812i
$326$		0			0
$327$	−7.34709	+	7.52899i	−0.406295	+	0.416354i
$328$		0			0
$329$	5.66884	−	4.11865i	0.312533	−	0.227069i
$330$		0			0
$331$	−3.45492	−	2.51015i	−0.189900	−	0.137970i	0.488773	−	0.872411i	$-0.337445\pi$
$331$	−3.45492	−	2.51015i	−0.189900	−	0.137970i	−0.678673	+	0.734441i	$0.737445\pi$
$332$		0			0
$333$	−1.57287	+	3.28301i	−0.0861930	+	0.179908i
$334$		0			0
$335$	−14.3153	+	15.8885i	−0.782129	+	0.868084i
$336$		0			0
$337$	16.4657	+	32.3157i	0.896941	+	1.76035i	0.586990	+	0.809594i	$0.300313\pi$
$337$	16.4657	+	32.3157i	0.896941	+	1.76035i	0.309951	+	0.950753i	$0.399687\pi$
$338$		0			0
$339$	11.4615	−	0.140148i	0.622504	−	0.00761178i
$340$		0			0
$341$	16.0116	+	5.20248i	0.867076	+	0.281730i
$342$		0			0
$343$	−8.39295	−	8.39295i	−0.453177	−	0.453177i
$344$		0			0
$345$	−5.30007	+	20.7661i	−0.285346	+	1.11801i
$346$		0			0
$347$	−3.51964	−	0.557457i	−0.188944	−	0.0299258i	0.0612451	−	0.998123i	$-0.480493\pi$
$347$	−3.51964	−	0.557457i	−0.188944	−	0.0299258i	−0.250189	+	0.968197i	$0.580493\pi$
$348$		0			0
$349$			6.07476i			0.325174i	0.986694	+	0.162587i	$0.0519839\pi$
$349$			6.07476i			0.325174i	−0.986694	+	0.162587i	$0.948016\pi$
$350$		0			0
$351$	−3.56805	+	2.79788i	−0.190449	+	0.149340i
$352$		0			0
$353$	−3.37712	+	21.3223i	−0.179746	+	1.13487i	0.718549	+	0.695476i	$0.244807\pi$
$353$	−3.37712	+	21.3223i	−0.179746	+	1.13487i	−0.898295	+	0.439394i	$0.855193\pi$
$354$		0			0
$355$	−11.6329	−	3.12101i	−0.617409	−	0.165646i
$356$		0			0
$357$	−0.954227	+	0.500992i	−0.0505030	+	0.0265153i
$358$		0			0
$359$	−0.695103	+	2.13931i	−0.0366861	+	0.112908i	−0.967723	−	0.252018i	$-0.918906\pi$
$359$	−0.695103	+	2.13931i	−0.0366861	+	0.112908i	0.931036	+	0.364926i	$0.118906\pi$
$360$		0			0
$361$	−2.22370	−	6.84384i	−0.117037	−	0.360202i
$362$		0			0
$363$	1.82921	+	10.7007i	0.0960088	+	0.561642i
$364$		0			0
$365$	−7.76429	−	36.5856i	−0.406401	−	1.91498i
$366$		0			0
$367$	0.0910705	−	0.0144241i	0.00475384	−	0.000752934i	−0.154057	−	0.988062i	$-0.549234\pi$
$367$	0.0910705	−	0.0144241i	0.00475384	−	0.000752934i	0.158811	+	0.987309i	$0.449234\pi$
$368$		0			0
$369$	−3.04810	−	8.65501i	−0.158678	−	0.450562i
$370$		0			0
$371$	−1.45227	−	1.99888i	−0.0753982	−	0.103777i
$372$		0			0
$373$	−9.29049	+	18.2336i	−0.481043	+	0.944101i	0.515164	+	0.857092i	$0.327731\pi$
$373$	−9.29049	+	18.2336i	−0.481043	+	0.944101i	−0.996208	+	0.0870092i	$0.972269\pi$
$374$		0			0
$375$	−19.3637	+	0.218194i	−0.999937	+	0.0112675i
$376$		0			0
$377$	2.37463	−	4.66047i	0.122300	−	0.240026i
$378$		0			0
$379$	−13.7712	−	18.9544i	−0.707377	−	0.973620i	−0.999850	−	0.0173466i	$-0.994478\pi$
$379$	−13.7712	−	18.9544i	−0.707377	−	0.973620i	0.292473	−	0.956274i	$-0.405522\pi$
$380$		0			0
$381$	−16.2033	+	12.0778i	−0.830118	+	0.618764i
$382$		0			0
$383$	26.5323	−	4.20230i	1.35574	−	0.214728i	0.564093	−	0.825711i	$-0.309226\pi$
$383$	26.5323	−	4.20230i	1.35574	−	0.214728i	0.791643	+	0.610984i	$0.209226\pi$
$384$		0			0
$385$	0.908707	+	4.28186i	0.0463120	+	0.218224i
$386$		0			0
$387$	4.49512	−	33.6944i	0.228500	−	1.71278i
$388$		0			0
$389$	6.63326	+	20.4151i	0.336319	+	1.03508i	0.966068	+	0.258286i	$0.0831577\pi$
$389$	6.63326	+	20.4151i	0.336319	+	1.03508i	−0.629749	+	0.776799i	$0.716842\pi$
$390$		0			0
$391$	1.18243	−	3.63915i	0.0597981	−	0.184040i
$392$		0			0
$393$	−15.2550	−	29.0558i	−0.769513	−	1.46567i
$394$		0			0
$395$	7.37089	+	1.97755i	0.370870	+	0.0995014i
$396$		0			0
$397$	2.70917	−	17.1050i	0.135969	−	0.858477i	−0.821556	−	0.570128i	$-0.806894\pi$
$397$	2.70917	−	17.1050i	0.135969	−	0.858477i	0.957525	−	0.288349i	$-0.0931063\pi$
$398$		0			0
$399$	−7.61642	−	2.37217i	−0.381298	−	0.118757i
$400$		0			0
$401$		−	38.7468i		−	1.93492i	−0.253022	−	0.967460i	$-0.581425\pi$
$401$		−	38.7468i		−	1.93492i	0.253022	−	0.967460i	$-0.418575\pi$
$402$		0			0
$403$	6.67008	+	1.05644i	0.332260	+	0.0526249i
$404$		0			0
$405$	8.11602	+	18.4155i	0.403288	+	0.915073i
$406$		0			0
$407$	−1.86656	−	1.86656i	−0.0925221	−	0.0925221i
$408$		0			0
$409$	23.7030	+	7.70156i	1.17204	+	0.380818i	0.829403	−	0.558651i	$-0.188681\pi$
$409$	23.7030	+	7.70156i	1.17204	+	0.380818i	0.342634	+	0.939469i	$0.388681\pi$
$410$		0			0
$411$	−0.250228	−	20.4640i	−0.0123428	−	1.00942i
$412$		0			0
$413$	−4.72421	−	9.27178i	−0.232463	−	0.456234i
$414$		0			0
$415$	−9.01828	+	10.0094i	−0.442690	+	0.491341i
$416$		0			0
$417$	1.47762	−	10.1294i	0.0723594	−	0.496040i
$418$		0			0
$419$	−16.0365	−	11.6512i	−0.783434	−	0.569198i	0.122574	−	0.992459i	$-0.460885\pi$
$419$	−16.0365	−	11.6512i	−0.783434	−	0.569198i	−0.906008	+	0.423261i	$0.860885\pi$
$420$		0			0
$421$	−28.5140	+	20.7166i	−1.38968	+	1.00967i	−0.393785	+	0.919203i	$0.628835\pi$
$421$	−28.5140	+	20.7166i	−1.38968	+	1.00967i	−0.995900	+	0.0904626i	$0.971165\pi$
$422$		0			0
$423$	11.1112	+	20.5488i	0.540245	+	0.999115i
$424$		0			0
$425$	3.45255	+	0.183155i	0.167473	+	0.00888431i
$426$		0			0
$427$	−6.70871	−	3.41826i	−0.324657	−	0.165421i
$428$		0			0
$429$	−1.05417	−	3.11432i	−0.0508959	−	0.150361i
$430$		0			0
$431$	−5.84421	+	8.04387i	−0.281506	+	0.387459i	−0.926232	−	0.376954i	$-0.876971\pi$
$431$	−5.84421	+	8.04387i	−0.281506	+	0.387459i	0.644726	+	0.764414i	$0.276971\pi$
$432$		0			0
$433$	−1.00246	−	6.32931i	−0.0481753	−	0.304167i	0.951822	−	0.306652i	$-0.0992089\pi$
$433$	−1.00246	−	6.32931i	−0.0481753	−	0.304167i	−0.999997	+	0.00248534i	$0.999209\pi$
$434$		0			0
$435$	−17.4361	−	15.3275i	−0.835995	−	0.734899i
$436$		0			0
$437$	25.2355	−	12.8581i	1.20718	−	0.615087i
$438$		0			0
$439$	13.3636	−	4.34210i	0.637811	−	0.207237i	0.0277788	−	0.999614i	$-0.491157\pi$
$439$	13.3636	−	4.34210i	0.637811	−	0.207237i	0.610032	+	0.792377i	$0.291157\pi$
$440$		0			0
$441$	14.7526	−	11.2797i	0.702507	−	0.537129i
$442$		0			0
$443$	−4.23679	+	4.23679i	−0.201296	+	0.201296i	−0.800555	−	0.599259i	$-0.795462\pi$
$443$	−4.23679	+	4.23679i	−0.201296	+	0.201296i	0.599259	+	0.800555i	$0.295462\pi$
$444$		0			0
$445$	30.2781	+	19.6766i	1.43532	+	0.932759i
$446$		0			0
$447$	−6.82387	+	13.8074i	−0.322758	+	0.653068i
$448$		0			0
$449$	2.90528			0.137109			0.0685544	−	0.997647i	$-0.478161\pi$
$449$	2.90528			0.137109			0.0685544	+	0.997647i	$0.478161\pi$
$450$		0			0
$451$	6.65384			0.313317
$452$		0			0
$453$	5.05696	−	10.2322i	0.237597	−	0.480752i
$454$		0			0
$455$	0.628708	+	1.63941i	0.0294743	+	0.0768566i
$456$		0			0
$457$	−0.266668	+	0.266668i	−0.0124742	+	0.0124742i	−0.713316	−	0.700842i	$-0.752808\pi$
$457$	−0.266668	+	0.266668i	−0.0124742	+	0.0124742i	0.700842	+	0.713316i	$0.252808\pi$
$458$		0			0
$459$	−1.23488	−	3.37417i	−0.0576394	−	0.157493i
$460$		0			0
$461$	7.84012	−	2.54741i	0.365151	−	0.118645i	−0.120694	−	0.992690i	$-0.538512\pi$
$461$	7.84012	−	2.54741i	0.365151	−	0.118645i	0.485845	+	0.874045i	$0.338512\pi$
$462$		0			0
$463$	25.2437	−	12.8623i	1.17318	−	0.597763i	0.244861	−	0.969558i	$-0.421258\pi$
$463$	25.2437	−	12.8623i	1.17318	−	0.597763i	0.928315	+	0.371795i	$0.121258\pi$
$464$		0			0
$465$	11.8644	−	27.5253i	0.550198	−	1.27646i
$466$		0			0
$467$	−2.43120	−	15.3500i	−0.112502	−	0.710312i	−0.977876	−	0.209185i	$-0.932919\pi$
$467$	−2.43120	−	15.3500i	−0.112502	−	0.710312i	0.865374	−	0.501127i	$-0.167081\pi$
$468$		0			0
$469$	5.05878	−	6.96282i	0.233593	−	0.321513i
$470$		0			0
$471$	−7.39667	−	21.8518i	−0.340821	−	1.00688i
$472$		0			0
$473$	21.9627	+	11.1905i	1.00984	+	0.514541i
$474$		0			0
$475$	17.1116	+	19.0288i	0.785133	+	0.873101i
$476$		0			0
$477$	7.24567	−	3.91790i	0.331757	−	0.179388i
$478$		0			0
$479$	27.1035	−	19.6918i	1.23839	−	0.899743i	0.240900	−	0.970550i	$-0.422558\pi$
$479$	27.1035	−	19.6918i	1.23839	−	0.899743i	0.997490	+	0.0708073i	$0.0225576\pi$
$480$		0			0
$481$	−0.856641	−	0.622386i	−0.0390594	−	0.0283783i
$482$		0			0
$483$	1.24496	−	8.53450i	0.0566478	−	0.388333i
$484$		0			0
$485$	0.645487	+	1.11884i	0.0293100	+	0.0508040i
$486$		0			0
$487$	4.96474	+	9.74384i	0.224974	+	0.441536i	0.975710	−	0.219066i	$-0.0703011\pi$
$487$	4.96474	+	9.74384i	0.224974	+	0.441536i	−0.750736	+	0.660602i	$0.770301\pi$
$488$		0			0
$489$	0.249988	+	20.4444i	0.0113048	+	0.924529i
$490$		0			0
$491$	−29.5939	−	9.61564i	−1.33555	−	0.433948i	−0.447746	−	0.894161i	$-0.647773\pi$
$491$	−29.5939	−	9.61564i	−1.33555	−	0.433948i	−0.887809	+	0.460213i	$0.847773\pi$
$492$		0			0
$493$	2.93085	+	2.93085i	0.131999	+	0.131999i
$494$		0			0
$495$	−14.5503	+	1.11519i	−0.653987	+	0.0501240i
$496$		0			0
$497$	4.78732	+	0.758236i	0.214740	+	0.0340115i
$498$		0			0
$499$			18.3818i			0.822881i	0.911437	+	0.411441i	$0.134974\pi$
$499$			18.3818i			0.822881i	−0.911437	+	0.411441i	$0.865026\pi$
$500$		0			0
$501$	−35.6474	−	11.1025i	−1.59261	−	0.496025i
$502$		0			0
$503$	6.37553	−	40.2535i	0.284271	−	1.79481i	−0.270403	−	0.962747i	$-0.587157\pi$
$503$	6.37553	−	40.2535i	0.284271	−	1.79481i	0.554674	−	0.832068i	$-0.312843\pi$
$504$		0			0
$505$	−14.2375	−	17.5933i	−0.633559	−	0.782892i
$506$		0			0
$507$	9.85381	+	18.7683i	0.437623	+	0.833529i
$508$		0			0
$509$	−8.19240	+	25.2136i	−0.363122	+	1.11757i	0.588027	+	0.808841i	$0.299905\pi$
$509$	−8.19240	+	25.2136i	−0.363122	+	1.11757i	−0.951149	+	0.308733i	$0.900095\pi$
$510$		0			0
$511$	4.65104	+	14.3144i	0.205750	+	0.633234i
$512$		0			0
$513$	11.1967	−	24.1231i	0.494348	−	1.06506i
$514$		0			0
$515$	7.01713	−	4.04835i	0.309212	−	0.178392i
$516$		0			0
$517$	−16.7308	+	2.64990i	−0.735820	+	0.116542i
$518$		0			0
$519$	−7.31559	+	5.45298i	−0.321119	+	0.239359i
$520$		0			0
$521$	−1.98068	−	2.72618i	−0.0867754	−	0.119436i	0.763422	−	0.645900i	$-0.223518\pi$
$521$	−1.98068	−	2.72618i	−0.0867754	−	0.119436i	−0.850198	+	0.526464i	$0.823518\pi$
$522$		0			0
$523$	−6.15343	+	12.0768i	−0.269071	+	0.528081i	−0.985520	−	0.169558i	$-0.945766\pi$
$523$	−6.15343	+	12.0768i	−0.269071	+	0.528081i	0.716449	+	0.697639i	$0.245766\pi$
$524$		0			0
$525$	7.74040	−	0.904346i	0.337819	−	0.0394689i
$526$		0			0
$527$	−2.42950	+	4.76817i	−0.105831	+	0.207705i
$528$		0			0
$529$	4.47979	+	6.16590i	0.194773	+	0.268083i
$530$		0			0
$531$	32.7219	−	11.5239i	1.42001	−	0.500095i
$532$		0			0
$533$	2.63618	−	0.417530i	0.114186	−	0.0180852i
$534$		0			0
$535$	−5.54510	−	0.584607i	−0.239736	−	0.0252748i
$536$		0			0
$537$	−5.88485	−	34.4258i	−0.253950	−	1.48558i
$538$		0			0
$539$	4.16129	+	12.8071i	0.179239	+	0.551642i
$540$		0			0
$541$	3.66203	−	11.2706i	0.157443	−	0.484559i	−0.840957	−	0.541101i	$-0.818007\pi$
$541$	3.66203	−	11.2706i	0.157443	−	0.484559i	0.998400	+	0.0565420i	$0.0180075\pi$
$542$		0			0
$543$	−33.7830	+	17.7369i	−1.44977	+	0.761164i
$544$		0			0
$545$	−12.6805	+	4.86292i	−0.543172	+	0.208305i
$546$		0			0
$547$	−2.04796	+	12.9303i	−0.0875642	+	0.552859i	0.904435	+	0.426612i	$0.140293\pi$
$547$	−2.04796	+	12.9303i	−0.0875642	+	0.552859i	−0.991999	+	0.126247i	$0.959707\pi$
$548$		0			0
$549$	14.2534	−	20.6624i	0.608322	−	0.881849i
$550$		0			0
$551$			30.6793i			1.30698i
$552$		0			0
$553$	−3.03337	−	0.480438i	−0.128992	−	0.0204303i
$554$		0			0
$555$	−3.61685	+	3.00087i	−0.153527	+	0.127380i
$556$		0			0
$557$	16.6516	+	16.6516i	0.705552	+	0.705552i	0.965597	−	0.260045i	$-0.0837374\pi$
$557$	16.6516	+	16.6516i	0.705552	+	0.705552i	−0.260045	+	0.965597i	$0.583737\pi$
$558$		0			0
$559$	9.40359	+	3.05541i	0.397729	+	0.129230i
$560$		0			0
$561$	2.60523	−	0.0318559i	0.109993	−	0.00134496i
$562$		0			0
$563$	9.45734	+	18.5611i	0.398579	+	0.782256i	0.999859	−	0.0167826i	$-0.00534231\pi$
$563$	9.45734	+	18.5611i	0.398579	+	0.782256i	−0.601280	+	0.799039i	$0.705342\pi$
$564$		0			0
$565$	13.5166	+	6.02315i	0.568647	+	0.253396i
$566$		0			0
$567$	−4.02515	−	7.02768i	−0.169041	−	0.295135i
$568$		0			0
$569$	−23.7171	−	17.2314i	−0.994271	−	0.722380i	−0.0334184	−	0.999441i	$-0.510639\pi$
$569$	−23.7171	−	17.2314i	−0.994271	−	0.722380i	−0.960852	+	0.277062i	$0.910639\pi$
$570$		0			0
$571$	7.34646	−	5.33751i	0.307440	−	0.223368i	−0.423357	−	0.905963i	$-0.639149\pi$
$571$	7.34646	−	5.33751i	0.307440	−	0.223368i	0.730797	+	0.682595i	$0.239149\pi$
$572$		0			0
$573$	−7.61010	+	7.79851i	−0.317917	+	0.325788i
$574$		0			0
$575$	−17.4260	+	21.4912i	−0.726714	+	0.896245i
$576$		0			0
$577$	−16.0285	−	8.16690i	−0.667273	−	0.339993i	0.0873249	−	0.996180i	$-0.472168\pi$
$577$	−16.0285	−	8.16690i	−0.667273	−	0.339993i	−0.754598	+	0.656187i	$0.772168\pi$
$578$		0			0
$579$	−17.2877	+	5.85176i	−0.718453	+	0.243191i
$580$		0			0
$581$	3.18690	−	4.38639i	0.132215	−	0.181978i
$582$		0			0
$583$	0.934378	+	5.89943i	0.0386980	+	0.244329i
$584$		0			0
$585$	−5.69469	+	1.35486i	−0.235447	+	0.0560166i
$586$		0			0
$587$	−12.3163	+	6.27549i	−0.508350	+	0.259017i	−0.689301	−	0.724475i	$-0.742082\pi$
$587$	−12.3163	+	6.27549i	−0.508350	+	0.259017i	0.180951	+	0.983492i	$0.442082\pi$
$588$		0			0
$589$	−37.6717	+	12.2403i	−1.55223	+	0.504351i
$590$		0			0
$591$	−24.0535	+	33.9726i	−0.989427	+	1.39745i
$592$		0			0
$593$	−0.149745	+	0.149745i	−0.00614930	+	0.00614930i	−0.710175	−	0.704025i	$-0.751384\pi$
$593$	−0.149745	+	0.149745i	−0.00614930	+	0.00614930i	0.704025	+	0.710175i	$0.251384\pi$
$594$		0			0
$595$	−1.38948	+	0.0723742i	−0.0569633	+	0.00296705i
$596$		0			0
$597$	−31.3567	−	15.4971i	−1.28334	−	0.634253i
$598$		0			0
$599$	−4.89253			−0.199903			−0.0999517	−	0.994992i	$-0.531869\pi$
$599$	−4.89253			−0.199903			−0.0999517	+	0.994992i	$0.531869\pi$
$600$		0			0
$601$	37.0254			1.51030			0.755148	−	0.655554i	$-0.227565\pi$
$601$	37.0254			1.51030			0.755148	+	0.655554i	$0.227565\pi$
$602$		0			0
$603$	20.7789	+	19.7867i	0.846181	+	0.805776i
$604$		0			0
$605$	−3.63166	+	13.5362i	−0.147648	+	0.550326i
$606$		0			0
$607$	25.1008	−	25.1008i	1.01881	−	1.01881i	0.0189918	−	0.999820i	$-0.493954\pi$
$607$	25.1008	−	25.1008i	1.01881	−	1.01881i	0.999820	−	0.0189918i	$-0.00604565\pi$
$608$		0			0
$609$	7.62486	+	5.39859i	0.308975	+	0.218762i
$610$		0			0
$611$	−6.46229	+	2.09973i	−0.261436	+	0.0849458i
$612$		0			0
$613$	18.3061	−	9.32741i	0.739375	−	0.376731i	−0.0433812	−	0.999059i	$-0.513813\pi$
$613$	18.3061	−	9.32741i	0.739375	−	0.376731i	0.782757	+	0.622328i	$0.213813\pi$
$614$		0			0
$615$	1.09790	−	11.7953i	0.0442717	−	0.475631i
$616$		0			0
$617$	5.07305	+	32.0300i	0.204233	+	1.28948i	0.850341	+	0.526232i	$0.176396\pi$
$617$	5.07305	+	32.0300i	0.204233	+	1.28948i	−0.646108	+	0.763246i	$0.723604\pi$
$618$		0			0
$619$	−0.306242	+	0.421506i	−0.0123089	+	0.0169418i	−0.815127	−	0.579282i	$-0.803333\pi$
$619$	−0.306242	+	0.421506i	−0.0123089	+	0.0169418i	0.802818	+	0.596224i	$0.203333\pi$
$620$		0			0
$621$	27.6539	+	7.87655i	1.10971	+	0.316075i
$622$		0			0
$623$	−12.9479	−	6.59729i	−0.518747	−	0.264315i
$624$		0			0
$625$	−22.8256	−	10.1976i	−0.913024	−	0.407905i
$626$		0			0
$627$	13.8021	+	13.4687i	0.551204	+	0.537887i
$628$		0			0
$629$	0.678826	−	0.493196i	0.0270666	−	0.0196650i
$630$		0			0
$631$	−8.26187	−	6.00260i	−0.328900	−	0.238960i	0.411064	−	0.911607i	$-0.365157\pi$
$631$	−8.26187	−	6.00260i	−0.328900	−	0.238960i	−0.739964	+	0.672647i	$0.765157\pi$
$632$		0			0
$633$	−5.43070	−	0.792199i	−0.215851	−	0.0314871i
$634$		0			0
$635$	−25.5218	+	5.41629i	−1.01280	+	0.214939i
$636$		0			0
$637$	2.45231	+	4.81293i	0.0971640	+	0.190695i
$638$		0			0
$639$	−4.61616	+	15.4857i	−0.182612	+	0.612605i
$640$		0			0
$641$	17.1276	+	5.56508i	0.676498	+	0.219807i	0.627061	−	0.778970i	$-0.284258\pi$
$641$	17.1276	+	5.56508i	0.676498	+	0.219807i	0.0494363	+	0.998777i	$0.484258\pi$
$642$		0			0
$643$	−6.99059	−	6.99059i	−0.275682	−	0.275682i	0.555700	−	0.831383i	$-0.312450\pi$
$643$	−6.99059	−	6.99059i	−0.275682	−	0.275682i	−0.831383	+	0.555700i	$0.812450\pi$
$644$		0			0
$645$	23.4614	−	37.0867i	0.923790	−	1.46029i
$646$		0			0
$647$	−17.5984	−	2.78732i	−0.691865	−	0.109581i	−0.199407	−	0.979917i	$-0.563902\pi$
$647$	−17.5984	−	2.78732i	−0.691865	−	0.109581i	−0.492458	+	0.870336i	$0.663902\pi$
$648$		0			0
$649$			25.1561i			0.987462i
$650$		0			0
$651$	−3.58689	+	11.5166i	−0.140581	+	0.451371i
$652$		0			0
$653$	−2.53429	+	16.0009i	−0.0991746	+	0.626164i	0.887167	+	0.461449i	$0.152670\pi$
$653$	−2.53429	+	16.0009i	−0.0991746	+	0.626164i	−0.986341	+	0.164715i	$0.947330\pi$
$654$		0			0
$655$	−2.20376	−	42.3092i	−0.0861082	−	1.65316i
$656$		0			0
$657$	−49.3534	+	9.05904i	−1.92546	+	0.353427i
$658$		0			0
$659$	9.69034	−	29.8238i	0.377482	−	1.16177i	−0.564307	−	0.825565i	$-0.690856\pi$
$659$	9.69034	−	29.8238i	0.377482	−	1.16177i	0.941789	−	0.336205i	$-0.109144\pi$
$660$		0			0
$661$	12.1139	+	37.2828i	0.471177	+	1.45013i	0.851046	+	0.525092i	$0.175969\pi$
$661$	12.1139	+	37.2828i	0.471177	+	1.45013i	−0.379869	+	0.925040i	$0.624031\pi$
$662$		0			0
$663$	1.03017	−	0.176100i	0.0400083	−	0.00683915i
$664$		0			0
$665$	−7.65117	−	6.89357i	−0.296700	−	0.267321i
$666$		0			0
$667$	−32.7613	+	5.18888i	−1.26852	+	0.200914i
$668$		0			0
$669$	14.4883	+	19.4372i	0.560150	+	0.751484i
$670$		0			0
$671$	10.6989	+	14.7257i	0.413025	+	0.568480i
$672$		0			0
$673$	11.9112	−	23.3771i	0.459145	−	0.901122i	−0.539120	−	0.842229i	$-0.681243\pi$
$673$	11.9112	−	23.3771i	0.459145	−	0.901122i	0.998264	−	0.0588931i	$-0.0187571\pi$
$674$		0			0
$675$	−0.423941	+	25.9773i	−0.0163175	+	0.999867i
$676$		0			0
$677$	−5.68410	+	11.1557i	−0.218458	+	0.428748i	−0.974062	−	0.226281i	$-0.927343\pi$
$677$	−5.68410	+	11.1557i	−0.218458	+	0.428748i	0.755604	+	0.655028i	$0.227343\pi$
$678$		0			0
$679$	−0.305540	−	0.420540i	−0.0117256	−	0.0161388i
$680$		0			0
$681$	19.8583	+	26.6414i	0.760971	+	1.02090i
$682$		0			0
$683$	−3.16982	+	0.502051i	−0.121290	+	0.0192104i	−0.216784	−	0.976220i	$-0.569557\pi$
$683$	−3.16982	+	0.502051i	−0.121290	+	0.0192104i	0.0954943	+	0.995430i	$0.469557\pi$
$684$		0			0
$685$	10.7541	−	24.1333i	0.410892	−	0.922086i
$686$		0			0
$687$	−17.3198	+	2.96071i	−0.660793	+	0.112958i
$688$		0			0
$689$	0.740381	+	2.27866i	0.0282063	+	0.0868100i
$690$		0			0
$691$	−5.16372	+	15.8923i	−0.196437	+	0.604571i	0.803520	+	0.595278i	$0.202958\pi$
$691$	−5.16372	+	15.8923i	−0.196437	+	0.604571i	−0.999957	+	0.00929313i	$0.997042\pi$
$692$		0			0
$693$	5.77616	−	1.06024i	0.219418	−	0.0402752i
$694$		0			0
$695$	7.20118	−	11.0811i	0.273156	−	0.420329i
$696$		0			0
$697$	−0.330863	+	2.08899i	−0.0125323	+	0.0791260i
$698$		0			0
$699$	−11.3178	+	36.3385i	−0.428078	+	1.37445i
$700$		0			0
$701$			10.1389i			0.382941i	0.981498	+	0.191470i	$0.0613256\pi$
$701$			10.1389i			0.382941i	−0.981498	+	0.191470i	$0.938674\pi$
$702$		0			0
$703$	6.13421	+	0.971563i	0.231356	+	0.0366432i
$704$		0			0
$705$	1.93685	+	30.0959i	0.0729459	+	1.13348i
$706$		0			0
$707$	6.44035	+	6.44035i	0.242214	+	0.242214i
$708$		0			0
$709$	−4.38945	−	1.42622i	−0.164849	−	0.0535627i	0.225430	−	0.974259i	$-0.427621\pi$
$709$	−4.38945	−	1.42622i	−0.164849	−	0.0535627i	−0.390279	+	0.920697i	$0.627621\pi$
$710$		0			0
$711$	2.92492	−	9.81215i	0.109693	−	0.367984i
$712$		0			0
$713$	−19.4424	−	38.1579i	−0.728125	−	1.42903i
$714$		0			0
$715$	0.445037	−	4.22126i	0.0166435	−	0.157866i
$716$		0			0
$717$	37.1406	+	5.41785i	1.38704	+	0.202333i
$718$		0			0
$719$	−4.62038	−	3.35690i	−0.172311	−	0.125191i	0.498287	−	0.867012i	$-0.333963\pi$
$719$	−4.62038	−	3.35690i	−0.172311	−	0.125191i	−0.670598	+	0.741821i	$0.733963\pi$
$720$		0			0
$721$	−2.63754	+	1.91628i	−0.0982269	+	0.0713660i
$722$		0			0
$723$	−24.8139	−	24.2144i	−0.922840	−	0.900544i
$724$		0			0
$725$	−12.1727	−	27.3875i	−0.452083	−	1.01715i
$726$		0			0
$727$	−19.0304	−	9.69647i	−0.705798	−	0.359622i	0.0639646	−	0.997952i	$-0.479626\pi$
$727$	−19.0304	−	9.69647i	−0.705798	−	0.359622i	−0.769763	+	0.638330i	$0.779626\pi$
$728$		0			0
$729$	24.9979	−	10.2032i	0.925848	−	0.377895i
$730$		0			0
$731$	−4.60538	+	6.33877i	−0.170336	+	0.234448i
$732$		0			0
$733$	4.21301	+	26.5999i	0.155611	+	0.982489i	0.934664	+	0.355531i	$0.115700\pi$
$733$	4.21301	+	26.5999i	0.155611	+	0.982489i	−0.779053	+	0.626958i	$0.784300\pi$
$734$		0			0
$735$	23.3898	−	5.26350i	0.862746	−	0.194147i
$736$		0			0
$737$	−18.5383	+	9.44572i	−0.682866	+	0.347937i
$738$		0			0
$739$	−31.2236	+	10.1452i	−1.14858	+	0.373196i	−0.820608	−	0.571491i	$-0.806365\pi$
$739$	−31.2236	+	10.1452i	−1.14858	+	0.373196i	−0.327972	+	0.944688i	$0.606365\pi$
$740$		0			0
$741$	6.31343	+	4.47006i	0.231930	+	0.164212i
$742$		0			0
$743$	3.67463	−	3.67463i	0.134809	−	0.134809i	−0.636482	−	0.771291i	$-0.719611\pi$
$743$	3.67463	−	3.67463i	0.134809	−	0.134809i	0.771291	+	0.636482i	$0.219611\pi$
$744$		0			0
$745$	−15.4563	+	12.5081i	−0.566275	+	0.458261i
$746$		0			0
$747$	13.0901	+	12.4651i	0.478943	+	0.456074i
$748$		0			0
$749$	2.24389			0.0819899
$750$		0			0
$751$	30.6986			1.12021			0.560105	−	0.828422i	$-0.310761\pi$
$751$	30.6986			1.12021			0.560105	+	0.828422i	$0.310761\pi$
$752$		0			0
$753$	18.4445	+	9.11563i	0.672156	+	0.332192i
$754$		0			0
$755$	11.4542	−	9.26935i	0.416860	−	0.337346i
$756$		0			0
$757$	12.7050	−	12.7050i	0.461771	−	0.461771i	−0.437465	−	0.899236i	$-0.644124\pi$
$757$	12.7050	−	12.7050i	0.461771	−	0.461771i	0.899236	+	0.437465i	$0.144124\pi$
$758$		0			0
$759$	−12.0483	+	17.0168i	−0.437326	+	0.617670i
$760$		0			0
$761$	9.26623	−	3.01078i	0.335901	−	0.109141i	−0.136210	−	0.990680i	$-0.543492\pi$
$761$	9.26623	−	3.01078i	0.335901	−	0.109141i	0.472111	+	0.881539i	$0.343492\pi$
$762$		0			0
$763$	4.86971	−	2.48124i	0.176295	−	0.0898269i
$764$		0			0
$765$	0.373399	−	4.62354i	0.0135003	−	0.167165i
$766$		0			0
$767$	1.57855	+	9.96657i	0.0569981	+	0.359872i
$768$		0			0
$769$	−12.7156	+	17.5015i	−0.458535	+	0.631119i	−0.974204	−	0.225669i	$-0.927543\pi$
$769$	−12.7156	+	17.5015i	−0.458535	+	0.631119i	0.515669	+	0.856788i	$0.327543\pi$
$770$		0			0
$771$	17.0886	−	5.78436i	0.615431	−	0.208319i
$772$		0			0
$773$	32.7902	+	16.7075i	1.17938	+	0.600926i	0.930029	−	0.367487i	$-0.119782\pi$
$773$	32.7902	+	16.7075i	1.17938	+	0.600926i	0.249354	+	0.968412i	$0.419782\pi$
$774$		0			0
$775$	28.7729	−	25.8740i	1.03355	−	0.929420i
$776$		0			0
$777$	1.32089	−	1.35359i	0.0473867	−	0.0485599i
$778$		0			0
$779$	−12.6652	+	9.20177i	−0.453776	+	0.329688i
$780$		0			0
$781$	−9.47961	−	6.88734i	−0.339207	−	0.246448i
$782$		0			0
$783$	−21.2015	+	22.8168i	−0.757678	+	0.815407i
$784$		0			0
$785$	3.12263	−	29.6188i	0.111452	−	1.05714i
$786$		0			0
$787$	−1.07205	−	2.10401i	−0.0382144	−	0.0750000i	0.871110	−	0.491088i	$-0.163401\pi$
$787$	−1.07205	−	2.10401i	−0.0382144	−	0.0750000i	−0.909324	+	0.416088i	$0.863401\pi$
$788$		0			0
$789$	−3.85270	+	0.0471096i	−0.137160	+	0.00167715i
$790$		0			0
$791$	−5.66365	−	1.84023i	−0.201376	−	0.0654311i
$792$		0			0
$793$	5.16282	+	5.16282i	0.183337	+	0.183337i
$794$		0			0
$795$	10.6121	−	0.682950i	0.376372	−	0.0242217i
$796$		0			0
$797$	39.2063	+	6.20967i	1.38876	+	0.219958i	0.805628	−	0.592421i	$-0.201828\pi$
$797$	39.2063	+	6.20967i	1.38876	+	0.219958i	0.583130	+	0.812379i	$0.301828\pi$
$798$		0			0
$799$		−	5.38443i		−	0.190488i
$800$		0			0
$801$	27.5093	−	39.8787i	0.971994	−	1.40904i
$802$		0			0
$803$	5.69195	−	35.9376i	0.200865	−	1.26821i
$804$		0			0
$805$	6.06732	−	9.33632i	0.213845	−	0.329062i
$806$		0			0
$807$	−31.6228	+	16.6027i	−1.11318	+	0.584444i
$808$		0			0
$809$	14.9484	−	46.0064i	0.525557	−	1.61750i	−0.237655	−	0.971350i	$-0.576379\pi$
$809$	14.9484	−	46.0064i	0.525557	−	1.61750i	0.763212	−	0.646149i	$-0.223621\pi$
$810$		0			0
$811$	1.26259	+	3.88586i	0.0443356	+	0.136451i	0.970774	−	0.239995i	$-0.0771459\pi$
$811$	1.26259	+	3.88586i	0.0443356	+	0.136451i	−0.926438	+	0.376446i	$0.877146\pi$
$812$		0			0
$813$	−1.74596	−	10.2137i	−0.0612334	−	0.358209i
$814$		0			0
$815$	−10.7438	+	24.1102i	−0.376338	+	0.844542i
$816$		0			0
$817$	−57.2802	+	9.07229i	−2.00398	+	0.317399i
$818$		0			0
$819$	2.22193	−	0.782512i	0.0776404	−	0.0273432i
$820$		0			0
$821$	2.89947	+	3.99078i	0.101192	+	0.139279i	0.856610	−	0.515964i	$-0.172566\pi$
$821$	2.89947	+	3.99078i	0.101192	+	0.139279i	−0.755418	+	0.655243i	$0.772566\pi$
$822$		0			0
$823$	8.52446	−	16.7302i	0.297144	−	0.583178i	−0.693371	−	0.720580i	$-0.743875\pi$
$823$	8.52446	−	16.7302i	0.297144	−	0.583178i	0.990515	+	0.137403i	$0.0438754\pi$
$824$		0			0
$825$	−17.6652	−	6.54720i	−0.615023	−	0.227944i
$826$		0			0
$827$	−13.8719	+	27.2251i	−0.482373	+	0.946711i	0.513682	+	0.857980i	$0.328281\pi$
$827$	−13.8719	+	27.2251i	−0.482373	+	0.946711i	−0.996056	+	0.0887303i	$0.971719\pi$
$828$		0			0
$829$	−18.2599	−	25.1326i	−0.634193	−	0.872892i	0.364096	−	0.931361i	$-0.381378\pi$
$829$	−18.2599	−	25.1326i	−0.634193	−	0.872892i	−0.998289	+	0.0584697i	$0.981378\pi$
$830$		0			0
$831$	41.7712	−	31.1359i	1.44903	−	1.08009i
$832$		0			0
$833$	−4.22774	+	0.669608i	−0.146482	+	0.0232005i
$834$		0			0
$835$	−35.8100	−	32.2642i	−1.23926	−	1.11655i
$836$		0			0
$837$	−36.4760	−	16.9303i	−1.26079	−	0.585196i
$838$		0			0
$839$	−7.58657	−	23.3491i	−0.261918	−	0.806100i	−0.992387	−	0.123155i	$-0.960699\pi$
$839$	−7.58657	−	23.3491i	−0.261918	−	0.806100i	0.730470	−	0.682945i	$-0.239301\pi$
$840$		0			0
$841$	2.14147	−	6.59078i	0.0738439	−	0.227268i
$842$		0			0
$843$	6.19185	+	11.7935i	0.213259	+	0.406188i
$844$		0			0
$845$	1.42350	+	27.3292i	0.0489698	+	0.940153i
$846$		0			0
$847$	0.882299	−	5.57061i	0.0303161	−	0.191409i
$848$		0			0
$849$	15.2825	+	4.75980i	0.524493	+	0.163356i
$850$		0			0
$851$			6.71481i			0.230181i
$852$		0			0
$853$	30.8235	+	4.88197i	1.05538	+	0.167155i	0.659926	−	0.751331i	$-0.270588\pi$
$853$	30.8235	+	4.88197i	1.05538	+	0.167155i	0.395452	+	0.918486i	$0.370588\pi$
$854$		0			0
$855$	26.1533	−	22.2447i	0.894425	−	0.760752i
$856$		0			0
$857$	14.2236	+	14.2236i	0.485870	+	0.485870i	0.907000	−	0.421130i	$-0.138366\pi$
$857$	14.2236	+	14.2236i	0.485870	+	0.485870i	−0.421130	+	0.907000i	$0.638366\pi$
$858$		0			0
$859$	−22.7703	−	7.39851i	−0.776912	−	0.252434i	−0.106391	−	0.994324i	$-0.533929\pi$
$859$	−22.7703	−	7.39851i	−0.776912	−	0.252434i	−0.670521	+	0.741890i	$0.733929\pi$
$860$		0			0
$861$	0.0582887	+	4.76694i	0.00198647	+	0.162457i
$862$		0			0
$863$	−12.7944	−	25.1105i	−0.435527	−	0.854770i	−0.999579	−	0.0290305i	$-0.990758\pi$
$863$	−12.7944	−	25.1105i	−0.435527	−	0.854770i	0.564051	−	0.825740i	$-0.309242\pi$
$864$		0			0
$865$	−11.5228	+	2.44539i	−0.391787	+	0.0831459i
$866$		0			0
$867$	4.13072	−	28.3170i	0.140287	−	0.961696i
$868$		0			0
$869$	6.00653	+	4.36400i	0.203758	+	0.148039i
$870$		0			0
$871$	−6.75194	+	4.90557i	−0.228781	+	0.166219i
$872$		0			0
$873$	1.52440	−	0.824278i	0.0515931	−	0.0278976i
$874$		0			0
$875$	9.56538	+	3.11813i	0.323369	+	0.105412i
$876$		0			0
$877$	−30.3131	−	15.4453i	−1.02360	−	0.521550i	−0.140177	−	0.990127i	$-0.544767\pi$
$877$	−30.3131	−	15.4453i	−1.02360	−	0.521550i	−0.883423	+	0.468577i	$0.844767\pi$
$878$		0			0
$879$	11.0454	+	32.6313i	0.372553	+	1.10063i
$880$		0			0
$881$	−15.5491	+	21.4016i	−0.523864	+	0.721037i	−0.986180	−	0.165678i	$-0.947019\pi$
$881$	−15.5491	+	21.4016i	−0.523864	+	0.721037i	0.462316	+	0.886715i	$0.347019\pi$
$882$		0			0
$883$	−6.05676	−	38.2409i	−0.203826	−	1.28691i	−0.851243	−	0.524772i	$-0.824151\pi$
$883$	−6.05676	−	38.2409i	−0.203826	−	1.28691i	0.647417	−	0.762136i	$-0.275849\pi$
$884$		0			0
$885$	44.5942	+	4.15082i	1.49902	+	0.139528i
$886$		0			0
$887$	40.6858	−	20.7304i	1.36609	−	0.696060i	0.391530	−	0.920166i	$-0.371946\pi$
$887$	40.6858	−	20.7304i	1.36609	−	0.696060i	0.974565	+	0.224106i	$0.0719461\pi$
$888$		0			0
$889$	9.98562	−	3.24453i	0.334907	−	0.108818i
$890$		0			0
$891$	0.957170	+	19.5551i	0.0320664	+	0.655121i
$892$		0			0
$893$	28.1814	−	28.1814i	0.943055	−	0.943055i
$894$		0			0
$895$	11.6836	−	43.5481i	0.390540	−	1.45565i
$896$		0			0
$897$	−3.70560	+	7.49790i	−0.123726	+	0.250348i
$898$		0			0
$899$	46.3894			1.54717
$900$		0			0
$901$	−1.89860			−0.0632515
$902$		0			0
$903$	−7.82472	+	15.8325i	−0.260391	+	0.526873i
$904$		0			0
$905$	−49.1927	+	2.56231i	−1.63522	+	0.0851740i
$906$		0			0
$907$	−0.298353	+	0.298353i	−0.00990666	+	0.00990666i	−0.712043	−	0.702136i	$-0.752230\pi$
$907$	−0.298353	+	0.298353i	−0.00990666	+	0.00990666i	0.702136	+	0.712043i	$0.252230\pi$
$908$		0			0
$909$	−24.1218	+	18.4432i	−0.800069	+	0.611724i
$910$		0			0
$911$	−20.9701	+	6.81358i	−0.694769	+	0.225744i	−0.635050	−	0.772471i	$-0.719020\pi$
$911$	−20.9701	+	6.81358i	−0.694769	+	0.225744i	−0.0597191	+	0.998215i	$0.519020\pi$
$912$		0			0
$913$	−11.6786	+	5.95056i	−0.386506	+	0.196935i
$914$		0			0
$915$	27.8696	−	16.5361i	0.921341	−	0.546666i
$916$		0			0
$917$	2.66715	+	16.8397i	0.0880770	+	0.556096i
$918$		0			0
$919$	−19.4520	+	26.7734i	−0.641662	+	0.883172i	−0.998703	−	0.0509169i	$-0.983786\pi$
$919$	−19.4520	+	26.7734i	−0.641662	+	0.883172i	0.357041	+	0.934089i	$0.383786\pi$
$920$		0			0
$921$	−12.3277	−	36.4194i	−0.406211	−	1.20006i
$922$		0			0
$923$	−4.18790	−	2.13384i	−0.137847	−	0.0702363i
$924$		0			0
$925$	−5.86150	+	1.56657i	−0.192725	+	0.0515084i
$926$		0			0
$927$	−5.16969	−	9.56070i	−0.169795	−	0.314015i
$928$		0			0
$929$	−1.80163	+	1.30896i	−0.0591096	+	0.0429457i	−0.616948	−	0.787004i	$-0.711631\pi$
$929$	−1.80163	+	1.30896i	−0.0591096	+	0.0429457i	0.557838	+	0.829950i	$0.311631\pi$
$930$		0			0
$931$	−25.6320	−	18.6228i	−0.840056	−	0.610337i
$932$		0			0
$933$	−0.592126	+	4.05915i	−0.0193853	+	0.132891i
$934$		0			0
$935$	3.07235	+	1.36908i	0.100477	+	0.0447736i
$936$		0			0
$937$	16.4846	+	32.3528i	0.538528	+	1.05692i	0.986636	+	0.162941i	$0.0520982\pi$
$937$	16.4846	+	32.3528i	0.538528	+	1.05692i	−0.448108	+	0.893980i	$0.647902\pi$
$938$		0			0
$939$	0.202525	+	16.5628i	0.00660915	+	0.540507i
$940$		0			0
$941$	18.5804	+	6.03715i	0.605705	+	0.196806i	0.595783	−	0.803145i	$-0.296842\pi$
$941$	18.5804	+	6.03715i	0.605705	+	0.196806i	0.00992184	+	0.999951i	$0.496842\pi$
$942$		0			0
$943$	−11.9683	−	11.9683i	−0.389742	−	0.389742i
$944$		0			0
$945$	−0.926406	−	10.4143i	−0.0301360	−	0.338779i
$946$		0			0
$947$	−11.2253	−	1.77791i	−0.364773	−	0.0577744i	−0.0286423	−	0.999590i	$-0.509118\pi$
$947$	−11.2253	−	1.77791i	−0.364773	−	0.0577744i	−0.336131	+	0.941815i	$0.609118\pi$
$948$		0			0
$949$		−	14.5953i		−	0.473782i
$950$		0			0
$951$	−41.2426	−	12.8452i	−1.33738	−	0.416534i
$952$		0			0
$953$	0.193828	−	1.22378i	0.00627872	−	0.0396423i	−0.984350	−	0.176224i	$-0.943612\pi$
$953$	0.193828	−	1.22378i	0.00627872	−	0.0396423i	0.990629	+	0.136582i	$0.0436117\pi$
$954$		0			0
$955$	−13.1344	+	5.03701i	−0.425019	+	0.162994i
$956$		0			0
$957$	−10.4988	−	19.9968i	−0.339378	−	0.646405i
$958$		0			0
$959$	−3.28566	+	10.1122i	−0.106099	+	0.326540i
$960$		0			0
$961$	8.92866	+	27.4796i	0.288021	+	0.886438i
$962$		0			0
$963$	−0.989234	+	7.41507i	−0.0318776	+	0.238947i
$964$		0			0
$965$	−23.4324	−	2.47042i	−0.754315	−	0.0795256i
$966$		0			0
$967$	2.01341	−	0.318893i	0.0647469	−	0.0102549i	−0.123977	−	0.992285i	$-0.539565\pi$
$967$	2.01341	−	0.318893i	0.0647469	−	0.0102549i	0.188724	+	0.982030i	$0.439565\pi$
$968$		0			0
$969$	−4.91483	+	3.66348i	−0.157887	+	0.117688i
$970$		0			0
$971$	13.6798	+	18.8287i	0.439007	+	0.604241i	0.969991	−	0.243141i	$-0.0781777\pi$
$971$	13.6798	+	18.8287i	0.439007	+	0.604241i	−0.530984	+	0.847382i	$0.678178\pi$
$972$		0			0
$973$	−2.41446	+	4.73864i	−0.0774039	+	0.151914i
$974$		0			0
$975$	−7.40960	−	1.48544i	−0.237297	−	0.0475721i
$976$		0			0
$977$	15.7500	−	30.9112i	0.503889	−	0.988937i	−0.489266	−	0.872134i	$-0.662735\pi$
$977$	15.7500	−	30.9112i	0.503889	−	0.988937i	0.993155	−	0.116803i	$-0.0372646\pi$
$978$		0			0
$979$	20.6489	+	28.4208i	0.659943	+	0.908334i
$980$		0			0
$981$	6.05256	+	17.1861i	0.193244	+	0.548711i
$982$		0			0
$983$	38.1077	−	6.03567i	1.21545	−	0.192508i	0.484407	−	0.874843i	$-0.339035\pi$
$983$	38.1077	−	6.03567i	1.21545	−	0.192508i	0.731040	+	0.682335i	$0.239035\pi$
$984$		0			0
$985$	−46.5477	+	26.8545i	−1.48313	+	0.855654i
$986$		0			0
$987$	−2.04500	−	11.9631i	−0.0650932	−	0.380789i
$988$		0			0
$989$	−19.3759	−	59.6329i	−0.616118	−	1.89622i
$990$		0			0
$991$	3.50349	−	10.7826i	0.111292	−	0.342522i	−0.879864	−	0.475226i	$-0.842366\pi$
$991$	3.50349	−	10.7826i	0.111292	−	0.342522i	0.991156	+	0.132705i	$0.0423662\pi$
$992$		0			0
$993$	−6.54901	+	3.43839i	−0.207827	+	0.109114i
$994$		0			0
$995$	−28.4059	−	35.1014i	−0.900529	−	1.11279i
$996$		0			0
$997$	8.21324	−	51.8564i	0.260116	−	1.64231i	−0.418791	−	0.908083i	$-0.637546\pi$
$997$	8.21324	−	51.8564i	0.260116	−	1.64231i	0.678907	−	0.734225i	$-0.262454\pi$
$998$		0			0
$999$	3.89071	+	4.96171i	0.123097	+	0.156982i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.x.a.233.8	yes	80
3.2	odd	2	inner	300.2.x.a.233.7	yes	80
25.22	odd	20	inner	300.2.x.a.197.7	✓	80
75.47	even	20	inner	300.2.x.a.197.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.197.7	✓	80	25.22	odd	20	inner
300.2.x.a.197.8	yes	80	75.47	even	20	inner
300.2.x.a.233.7	yes	80	3.2	odd	2	inner
300.2.x.a.233.8	yes	80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.767407 - 1.55277i) q^{3} +(1.73820 - 1.40665i) q^{5} +(-0.636300 + 0.636300i) q^{7} +(-1.82217 - 2.38321i) q^{9} +O(q^{10})\)	\(q+(0.767407 - 1.55277i) q^{3} +(1.73820 - 1.40665i) q^{5} +(-0.636300 + 0.636300i) q^{7} +(-1.82217 - 2.38321i) q^{9} +(2.06892 - 0.672233i) q^{11} +(0.777501 - 0.396157i) q^{13} +(-0.850289 - 3.77849i) q^{15} +(0.108171 + 0.682968i) q^{17} +(-3.00841 + 4.14072i) q^{19} +(0.499725 + 1.47633i) q^{21} +(-4.93053 - 2.51223i) q^{23} +(1.04269 - 4.89007i) q^{25} +(-5.09892 + 1.00052i) q^{27} +(4.84938 - 3.52328i) q^{29} +(6.26107 + 4.54893i) q^{31} +(0.543881 - 3.72843i) q^{33} +(-0.210967 + 2.00107i) q^{35} +(-0.550893 - 1.08119i) q^{37} +(-0.0184796 - 1.51129i) q^{39} +(2.90898 + 0.945186i) q^{41} +(8.01220 + 8.01220i) q^{43} +(-6.51964 - 1.57934i) q^{45} +(-7.69094 - 1.21813i) q^{47} +6.19025i q^{49} +(1.14350 + 0.356149i) q^{51} +(-0.429522 + 2.71189i) q^{53} +(2.65060 - 4.07872i) q^{55} +(4.12090 + 7.84897i) q^{57} +(-3.57345 + 10.9980i) q^{59} +(2.58562 + 7.95771i) q^{61} +(2.67588 + 0.356986i) q^{63} +(0.794201 - 1.78227i) q^{65} +(-9.44650 + 1.49618i) q^{67} +(-7.68464 + 5.72807i) q^{69} +(-3.16602 - 4.35766i) q^{71} +(7.59343 - 14.9030i) q^{73} +(-6.79298 - 5.37172i) q^{75} +(-0.888711 + 1.74419i) q^{77} +(2.00608 + 2.76113i) q^{79} +(-2.35936 + 8.68524i) q^{81} +(-5.95105 + 0.942553i) q^{83} +(1.14872 + 1.03498i) q^{85} +(-1.74939 - 10.2337i) q^{87} +(4.99027 + 15.3585i) q^{89} +(-0.242649 + 0.746798i) q^{91} +(11.8682 - 6.23110i) q^{93} +(0.595312 + 11.4292i) q^{95} +(-0.0903661 + 0.570549i) q^{97} +(-5.37200 - 3.70574i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q - 2 * q^3 + 4 * q^7	\( 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) \) 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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