LMFDB - Embedded newform 300.2.x.a.233.6

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			233.6
Character	$\chi$	$=$	300.233
Dual form			300.2.x.a.197.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0384027 - 1.73163i) q^{3} +(-2.22910 - 0.176414i) q^{5} +(3.29686 - 3.29686i) q^{7} +(-2.99705 + 0.132998i) q^{9} +O(q^{10})$	\(q+(-0.0384027 - 1.73163i) q^{3} +(-2.22910 - 0.176414i) q^{5} +(3.29686 - 3.29686i) q^{7} +(-2.99705 + 0.132998i) q^{9} +(-2.51720 + 0.817889i) q^{11} +(-2.61460 + 1.33221i) q^{13} +(-0.219879 + 3.86674i) q^{15} +(-1.07325 - 6.77623i) q^{17} +(0.761063 - 1.04751i) q^{19} +(-5.83553 - 5.58232i) q^{21} +(0.460230 + 0.234499i) q^{23} +(4.93776 + 0.786487i) q^{25} +(0.345398 + 5.18466i) q^{27} +(3.38873 - 2.46206i) q^{29} +(-6.95448 - 5.05272i) q^{31} +(1.51294 + 4.32744i) q^{33} +(-7.93063 + 6.76741i) q^{35} +(0.868677 + 1.70487i) q^{37} +(2.40729 + 4.47635i) q^{39} +(6.79828 + 2.20889i) q^{41} +(6.48953 + 6.48953i) q^{43} +(6.70418 + 0.232255i) q^{45} +(9.43571 + 1.49447i) q^{47} -14.7386i q^{49} +(-11.6927 + 2.11869i) q^{51} +(0.368009 - 2.32352i) q^{53} +(5.75538 - 1.37909i) q^{55} +(-1.84313 - 1.27765i) q^{57} +(0.216043 - 0.664912i) q^{59} +(-1.56100 - 4.80426i) q^{61} +(-9.44238 + 10.3193i) q^{63} +(6.06323 - 2.50837i) q^{65} +(11.0275 - 1.74659i) q^{67} +(0.388390 - 0.805952i) q^{69} +(3.02291 + 4.16068i) q^{71} +(-1.39613 + 2.74005i) q^{73} +(1.17228 - 8.58055i) q^{75} +(-5.60240 + 10.9953i) q^{77} +(1.41634 + 1.94942i) q^{79} +(8.96462 - 0.797205i) q^{81} +(0.525550 - 0.0832390i) q^{83} +(1.19696 + 15.2942i) q^{85} +(-4.39350 - 5.77346i) q^{87} +(1.78061 + 5.48014i) q^{89} +(-4.22788 + 13.0121i) q^{91} +(-8.48235 + 12.2366i) q^{93} +(-1.88128 + 2.20075i) q^{95} +(1.58455 - 10.0045i) q^{97} +(7.43541 - 2.78604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.0384027	−	1.73163i	−0.0221718	−	0.999754i
$3$	−0.0384027	−	1.73163i	−0.0221718	−	0.999754i
$4$		0			0
$5$	−2.22910	−	0.176414i	−0.996883	−	0.0788946i
$5$	−2.22910	−	0.176414i	−0.996883	−	0.0788946i
$6$		0			0
$7$	3.29686	−	3.29686i	1.24610	−	1.24610i	0.288666	−	0.957430i	$-0.406788\pi$
$7$	3.29686	−	3.29686i	1.24610	−	1.24610i	0.957430	−	0.288666i	$-0.0932116\pi$
$8$		0			0
$9$	−2.99705	+	0.132998i	−0.999017	+	0.0443328i
$10$		0			0
$11$	−2.51720	+	0.817889i	−0.758965	+	0.246603i	−0.662834	−	0.748766i	$-0.730647\pi$
$11$	−2.51720	+	0.817889i	−0.758965	+	0.246603i	−0.0961308	+	0.995369i	$0.530647\pi$
$12$		0			0
$13$	−2.61460	+	1.33221i	−0.725160	+	0.369488i	−0.777281	−	0.629153i	$-0.783402\pi$
$13$	−2.61460	+	1.33221i	−0.725160	+	0.369488i	0.0521211	+	0.998641i	$0.483402\pi$
$14$		0			0
$15$	−0.219879	+	3.86674i	−0.0567725	+	0.998387i
$16$		0			0
$17$	−1.07325	−	6.77623i	−0.260301	−	1.64348i	−0.678123	−	0.734949i	$-0.737206\pi$
$17$	−1.07325	−	6.77623i	−0.260301	−	1.64348i	0.417821	−	0.908529i	$-0.362794\pi$
$18$		0			0
$19$	0.761063	−	1.04751i	0.174600	−	0.240316i	−0.712744	−	0.701424i	$-0.752548\pi$
$19$	0.761063	−	1.04751i	0.174600	−	0.240316i	0.887344	+	0.461108i	$0.152548\pi$
$20$		0			0
$21$	−5.83553	−	5.58232i	−1.27342	−	1.21816i
$22$		0			0
$23$	0.460230	+	0.234499i	0.0959646	+	0.0488964i	0.501314	−	0.865265i	$-0.332850\pi$
$23$	0.460230	+	0.234499i	0.0959646	+	0.0488964i	−0.405349	+	0.914162i	$0.632850\pi$
$24$		0			0
$25$	4.93776	+	0.786487i	0.987551	+	0.157297i
$26$		0			0
$27$	0.345398	+	5.18466i	0.0664719	+	0.997788i
$28$		0			0
$29$	3.38873	−	2.46206i	0.629272	−	0.457193i	−0.226876	−	0.973924i	$-0.572851\pi$
$29$	3.38873	−	2.46206i	0.629272	−	0.457193i	0.856148	+	0.516731i	$0.172851\pi$
$30$		0			0
$31$	−6.95448	−	5.05272i	−1.24906	−	0.907496i	−0.250894	−	0.968015i	$-0.580725\pi$
$31$	−6.95448	−	5.05272i	−1.24906	−	0.907496i	−0.998167	+	0.0605186i	$0.980725\pi$
$32$		0			0
$33$	1.51294	+	4.32744i	0.263370	+	0.753311i
$34$		0			0
$35$	−7.93063	+	6.76741i	−1.34052	+	1.14390i
$36$		0			0
$37$	0.868677	+	1.70487i	0.142810	+	0.280280i	0.951322	−	0.308200i	$-0.0997267\pi$
$37$	0.868677	+	1.70487i	0.142810	+	0.280280i	−0.808512	+	0.588480i	$0.799727\pi$
$38$		0			0
$39$	2.40729	+	4.47635i	0.385475	+	0.716790i
$40$		0			0
$41$	6.79828	+	2.20889i	1.06171	+	0.344971i	0.787255	−	0.616628i	$-0.211502\pi$
$41$	6.79828	+	2.20889i	1.06171	+	0.344971i	0.274458	+	0.961599i	$0.411502\pi$
$42$		0			0
$43$	6.48953	+	6.48953i	0.989644	+	0.989644i	0.999947	−	0.0103030i	$-0.00327959\pi$
$43$	6.48953	+	6.48953i	0.989644	+	0.989644i	−0.0103030	+	0.999947i	$0.503280\pi$
$44$		0			0
$45$	6.70418	+	0.232255i	0.999400	+	0.0346225i
$46$		0			0
$47$	9.43571	+	1.49447i	1.37634	+	0.217991i	0.800383	−	0.599489i	$-0.204630\pi$
$47$	9.43571	+	1.49447i	1.37634	+	0.217991i	0.575957	+	0.817480i	$0.304630\pi$
$48$		0			0
$49$		−	14.7386i		−	2.10551i
$50$		0			0
$51$	−11.6927	+	2.11869i	−1.63730	+	0.296676i
$52$		0			0
$53$	0.368009	−	2.32352i	0.0505499	−	0.319159i	−0.949437	−	0.313959i	$-0.898345\pi$
$53$	0.368009	−	2.32352i	0.0505499	−	0.319159i	0.999986	−	0.00520061i	$-0.00165541\pi$
$54$		0			0
$55$	5.75538	−	1.37909i	0.776055	−	0.185956i
$56$		0			0
$57$	−1.84313	−	1.27765i	−0.244128	−	0.169229i
$58$		0			0
$59$	0.216043	−	0.664912i	0.0281264	−	0.0865641i	−0.936008	−	0.351979i	$-0.885509\pi$
$59$	0.216043	−	0.664912i	0.0281264	−	0.0865641i	0.964134	+	0.265415i	$0.0855089\pi$
$60$		0			0
$61$	−1.56100	−	4.80426i	−0.199865	−	0.615122i	−0.999885	−	0.0151489i	$-0.995178\pi$
$61$	−1.56100	−	4.80426i	−0.199865	−	0.615122i	0.800020	−	0.599974i	$-0.204822\pi$
$62$		0			0
$63$	−9.44238	+	10.3193i	−1.18963	+	1.30011i
$64$		0			0
$65$	6.06323	−	2.50837i	0.752051	−	0.311125i
$66$		0			0
$67$	11.0275	−	1.74659i	1.34723	−	0.213380i	0.559205	−	0.829029i	$-0.311106\pi$
$67$	11.0275	−	1.74659i	1.34723	−	0.213380i	0.788020	+	0.615650i	$0.211106\pi$
$68$		0			0
$69$	0.388390	−	0.805952i	0.0467567	−	0.0970252i
$70$		0			0
$71$	3.02291	+	4.16068i	0.358753	+	0.493782i	0.949801	−	0.312855i	$-0.101285\pi$
$71$	3.02291	+	4.16068i	0.358753	+	0.493782i	−0.591048	+	0.806637i	$0.701285\pi$
$72$		0			0
$73$	−1.39613	+	2.74005i	−0.163404	+	0.320699i	−0.958161	−	0.286229i	$-0.907598\pi$
$73$	−1.39613	+	2.74005i	−0.163404	+	0.320699i	0.794757	+	0.606928i	$0.207598\pi$
$74$		0			0
$75$	1.17228	−	8.58055i	0.135363	−	0.990796i
$76$		0			0
$77$	−5.60240	+	10.9953i	−0.638453	+	1.25303i
$78$		0			0
$79$	1.41634	+	1.94942i	0.159350	+	0.219327i	0.881225	−	0.472697i	$-0.156719\pi$
$79$	1.41634	+	1.94942i	0.159350	+	0.219327i	−0.721875	+	0.692024i	$0.756719\pi$
$80$		0			0
$81$	8.96462	−	0.797205i	0.996069	−	0.0885784i
$82$		0			0
$83$	0.525550	−	0.0832390i	0.0576866	−	0.00913666i	−0.127524	−	0.991835i	$-0.540703\pi$
$83$	0.525550	−	0.0832390i	0.0576866	−	0.00913666i	0.185211	+	0.982699i	$0.440703\pi$
$84$		0			0
$85$	1.19696	+	15.2942i	0.129828	+	1.65889i
$86$		0			0
$87$	−4.39350	−	5.77346i	−0.471032	−	0.618980i
$88$		0			0
$89$	1.78061	+	5.48014i	0.188744	+	0.580894i	0.999993	−	0.00380724i	$-0.00121189\pi$
$89$	1.78061	+	5.48014i	0.188744	+	0.580894i	−0.811249	+	0.584701i	$0.801212\pi$
$90$		0			0
$91$	−4.22788	+	13.0121i	−0.443202	+	1.36404i
$92$		0			0
$93$	−8.48235	+	12.2366i	−0.879579	+	1.26887i
$94$		0			0
$95$	−1.88128	+	2.20075i	−0.193015	+	0.225792i
$96$		0			0
$97$	1.58455	−	10.0045i	0.160887	−	1.01580i	−0.766649	−	0.642066i	$-0.778077\pi$
$97$	1.58455	−	10.0045i	0.160887	−	1.01580i	0.927536	−	0.373733i	$-0.121923\pi$
$98$		0			0
$99$	7.43541	−	2.78604i	0.747287	−	0.280007i
$100$		0			0
$101$			2.41412i			0.240214i	0.992761	+	0.120107i	$0.0383238\pi$
$101$			2.41412i			0.240214i	−0.992761	+	0.120107i	$0.961676\pi$
$102$		0			0
$103$	−13.7381	−	2.17590i	−1.35366	−	0.214398i	−0.562897	−	0.826527i	$-0.690313\pi$
$103$	−13.7381	−	2.17590i	−1.35366	−	0.214398i	−0.790758	+	0.612129i	$0.790313\pi$
$104$		0			0
$105$	12.0232	+	13.4730i	1.17334	+	1.31483i
$106$		0			0
$107$	11.6789	+	11.6789i	1.12905	+	1.12905i	0.990333	+	0.138713i	$0.0442964\pi$
$107$	11.6789	+	11.6789i	1.12905	+	1.12905i	0.138713	+	0.990333i	$0.455704\pi$
$108$		0			0
$109$	−10.3444	−	3.36109i	−0.990810	−	0.321934i	−0.231623	−	0.972806i	$-0.574403\pi$
$109$	−10.3444	−	3.36109i	−0.990810	−	0.321934i	−0.759187	+	0.650872i	$0.774403\pi$
$110$		0			0
$111$	2.91884	−	1.56969i	0.277044	−	0.148989i
$112$		0			0
$113$	−8.87975	−	17.4275i	−0.835336	−	1.63944i	−0.766884	−	0.641785i	$-0.778194\pi$
$113$	−8.87975	−	17.4275i	−0.835336	−	1.63944i	−0.0684521	−	0.997654i	$-0.521806\pi$
$114$		0			0
$115$	−0.984529	−	0.603912i	−0.0918078	−	0.0563151i
$116$		0			0
$117$	7.65891	−	4.34043i	0.708067	−	0.401273i
$118$		0			0
$119$	−25.8786	−	18.8019i	−2.37229	−	1.72357i
$120$		0			0
$121$	−3.23182	+	2.34805i	−0.293802	+	0.213459i
$122$		0			0
$123$	3.56390	−	11.8569i	0.321346	−	1.06910i
$124$		0			0
$125$	−10.8680	−	2.62425i	−0.972063	−	0.234720i
$126$		0			0
$127$	−2.04315	−	1.04104i	−0.181300	−	0.0923770i	0.360985	−	0.932572i	$-0.382441\pi$
$127$	−2.04315	−	1.04104i	−0.181300	−	0.0923770i	−0.542285	+	0.840195i	$0.682441\pi$
$128$		0			0
$129$	10.9882	−	11.4866i	0.967458	−	1.01134i
$130$		0			0
$131$	−0.615704	+	0.847443i	−0.0537943	+	0.0740415i	−0.835067	−	0.550149i	$-0.814571\pi$
$131$	−0.615704	+	0.847443i	−0.0537943	+	0.0740415i	0.781272	+	0.624190i	$0.214571\pi$
$132$		0			0
$133$	−0.944386	−	5.96262i	−0.0818887	−	0.517025i
$134$		0			0
$135$	0.144719	−	11.6180i	0.0124554	−	0.999922i
$136$		0			0
$137$	13.3366	−	6.79532i	1.13942	−	0.580564i	0.220649	−	0.975353i	$-0.429183\pi$
$137$	13.3366	−	6.79532i	1.13942	−	0.580564i	0.918771	+	0.394790i	$0.129183\pi$
$138$		0			0
$139$	7.95528	−	2.58483i	0.674758	−	0.219242i	0.0484593	−	0.998825i	$-0.484569\pi$
$139$	7.95528	−	2.58483i	0.674758	−	0.219242i	0.626299	+	0.779583i	$0.284569\pi$
$140$		0			0
$141$	2.22550	−	16.3965i	0.187421	−	1.38083i
$142$		0			0
$143$	5.49189	−	5.49189i	0.459255	−	0.459255i
$144$		0			0
$145$	−7.98815	+	4.89035i	−0.663380	+	0.406121i
$146$		0			0
$147$	−25.5217	+	0.566001i	−2.10499	+	0.0466830i
$148$		0			0
$149$	−16.5905			−1.35914			−0.679572	−	0.733609i	$-0.737834\pi$
$149$	−16.5905			−1.35914			−0.679572	+	0.733609i	$0.737834\pi$
$150$		0			0
$151$	6.48124			0.527436			0.263718	−	0.964600i	$-0.415051\pi$
$151$	6.48124			0.527436			0.263718	+	0.964600i	$0.415051\pi$
$152$		0			0
$153$	4.11781	+	20.1660i	0.332905	+	1.63032i
$154$		0			0
$155$	14.6108	+	12.4899i	1.17357	+	1.00321i
$156$		0			0
$157$	−2.84503	+	2.84503i	−0.227058	+	0.227058i	−0.811462	−	0.584405i	$-0.801328\pi$
$157$	−2.84503	+	2.84503i	−0.227058	+	0.227058i	0.584405	+	0.811462i	$0.301328\pi$
$158$		0			0
$159$	−4.03759	−	0.548024i	−0.320202	−	0.0434611i
$160$		0			0
$161$	2.29042	−	0.744204i	0.180511	−	0.0586515i
$162$		0			0
$163$	−4.72683	+	2.40844i	−0.370234	+	0.188644i	−0.629201	−	0.777243i	$-0.716618\pi$
$163$	−4.72683	+	2.40844i	−0.370234	+	0.188644i	0.258967	+	0.965886i	$0.416618\pi$
$164$		0			0
$165$	−2.60908	−	9.91320i	−0.203117	−	0.771741i
$166$		0			0
$167$	0.192101	+	1.21288i	0.0148653	+	0.0938555i	0.994006	−	0.109330i	$-0.0348705\pi$
$167$	0.192101	+	1.21288i	0.0148653	+	0.0938555i	−0.979140	+	0.203186i	$0.934871\pi$
$168$		0			0
$169$	−2.57984	+	3.55084i	−0.198449	+	0.273142i
$170$		0			0
$171$	−2.14163	+	3.24067i	−0.163774	+	0.247820i
$172$		0			0
$173$	4.94847	+	2.52137i	0.376225	+	0.191696i	0.631870	−	0.775075i	$-0.282288\pi$
$173$	4.94847	+	2.52137i	0.376225	+	0.191696i	−0.255645	+	0.966771i	$0.582288\pi$
$174$		0			0
$175$	18.8720	−	13.6861i	1.42659	−	1.03458i
$176$		0			0
$177$	−1.15967	−	0.348571i	−0.0871665	−	0.0262002i
$178$		0			0
$179$	8.40448	−	6.10621i	0.628180	−	0.456400i	−0.227589	−	0.973757i	$-0.573084\pi$
$179$	8.40448	−	6.10621i	0.628180	−	0.456400i	0.855769	+	0.517358i	$0.173084\pi$
$180$		0			0
$181$	−10.6877	−	7.76504i	−0.794408	−	0.577171i	0.114861	−	0.993382i	$-0.463358\pi$
$181$	−10.6877	−	7.76504i	−0.794408	−	0.577171i	−0.909268	+	0.416211i	$0.863358\pi$
$182$		0			0
$183$	−8.25923	+	2.88756i	−0.610540	+	0.213455i
$184$		0			0
$185$	−1.63560	−	3.95358i	−0.120252	−	0.290673i
$186$		0			0
$187$	8.24379	+	16.1794i	0.602846	+	1.18315i
$188$		0			0
$189$	18.2318	+	15.9544i	1.32617	+	1.16051i
$190$		0			0
$191$	−17.2545	−	5.60632i	−1.24849	−	0.405659i	−0.391111	−	0.920344i	$-0.627909\pi$
$191$	−17.2545	−	5.60632i	−1.24849	−	0.405659i	−0.857380	+	0.514684i	$0.827909\pi$
$192$		0			0
$193$	16.4813	+	16.4813i	1.18635	+	1.18635i	0.978068	+	0.208285i	$0.0667882\pi$
$193$	16.4813	+	16.4813i	1.18635	+	1.18635i	0.208285	+	0.978068i	$0.433212\pi$
$194$		0			0
$195$	−4.57640	−	10.4029i	−0.327723	−	0.744967i
$196$		0			0
$197$	−19.3571	−	3.06586i	−1.37914	−	0.218434i	−0.577570	−	0.816341i	$-0.695999\pi$
$197$	−19.3571	−	3.06586i	−1.37914	−	0.218434i	−0.801565	+	0.597907i	$0.795999\pi$
$198$		0			0
$199$			17.0715i			1.21017i	0.796161	+	0.605085i	$0.206861\pi$
$199$			17.0715i			1.21017i	−0.796161	+	0.605085i	$0.793139\pi$
$200$		0			0
$201$	−3.44792	−	19.0284i	−0.243198	−	1.34216i
$202$		0			0
$203$	3.05511	−	19.2892i	0.214427	−	1.35384i
$204$		0			0
$205$	−14.7643	−	6.12315i	−1.03119	−	0.427659i
$206$		0			0
$207$	−1.41052	−	0.641596i	−0.0980380	−	0.0445940i
$208$		0			0
$209$	−1.05900	+	3.25927i	−0.0732526	+	0.225448i
$210$		0			0
$211$	2.31272	+	7.11781i	0.159214	+	0.490010i	0.998563	−	0.0535819i	$-0.0170638\pi$
$211$	2.31272	+	7.11781i	0.159214	+	0.490010i	−0.839349	+	0.543592i	$0.817064\pi$
$212$		0			0
$213$	7.08865	−	5.39433i	0.485706	−	0.369613i
$214$		0			0
$215$	−13.3210	−	15.6106i	−0.908482	−	1.06464i
$216$		0			0
$217$	−39.5860	+	6.26981i	−2.68728	+	0.425623i
$218$		0			0
$219$	4.79836	+	2.31234i	0.324243	+	0.156254i
$220$		0			0
$221$	11.8335	+	16.2874i	0.796005	+	1.09561i
$222$		0			0
$223$	0.771097	−	1.51336i	0.0516365	−	0.101342i	−0.863746	−	0.503927i	$-0.831888\pi$
$223$	0.771097	−	1.51336i	0.0516365	−	0.101342i	0.915383	+	0.402585i	$0.131888\pi$
$224$		0			0
$225$	−14.9033	−	1.70043i	−0.993554	−	0.113362i
$226$		0			0
$227$	9.28911	−	18.2309i	0.616540	−	1.21003i	−0.345834	−	0.938296i	$-0.612404\pi$
$227$	9.28911	−	18.2309i	0.616540	−	1.21003i	0.962373	−	0.271731i	$-0.0875962\pi$
$228$		0			0
$229$	6.08934	+	8.38126i	0.402395	+	0.553849i	0.961343	−	0.275353i	$-0.0887948\pi$
$229$	6.08934	+	8.38126i	0.402395	+	0.553849i	−0.558948	+	0.829203i	$0.688795\pi$
$230$		0			0
$231$	19.2549	+	9.27900i	1.26688	+	0.610514i
$232$		0			0
$233$	10.4859	−	1.66080i	0.686955	−	0.108803i	0.196807	−	0.980442i	$-0.436943\pi$
$233$	10.4859	−	1.66080i	0.686955	−	0.108803i	0.490148	+	0.871639i	$0.336943\pi$
$234$		0			0
$235$	−20.7695	−	4.99591i	−1.35485	−	0.325897i
$236$		0			0
$237$	3.32128	−	2.52743i	0.215740	−	0.164174i
$238$		0			0
$239$	6.75814	+	20.7994i	0.437148	+	1.34540i	0.890870	+	0.454259i	$0.150096\pi$
$239$	6.75814	+	20.7994i	0.437148	+	1.34540i	−0.453722	+	0.891143i	$0.649904\pi$
$240$		0			0
$241$	3.43227	−	10.5634i	0.221092	−	0.680451i	−0.777573	−	0.628793i	$-0.783549\pi$
$241$	3.43227	−	10.5634i	0.221092	−	0.680451i	0.998665	−	0.0516582i	$-0.0164506\pi$
$242$		0			0
$243$	−1.72473	−	15.4928i	−0.110641	−	0.993860i
$244$		0			0
$245$	−2.60008	+	32.8537i	−0.166113	+	2.09895i
$246$		0			0
$247$	−0.594373	+	3.75272i	−0.0378191	+	0.238780i
$248$		0			0
$249$	−0.164321	−	0.906859i	−0.0104134	−	0.0574699i
$250$		0			0
$251$			10.0302i			0.633100i	0.948576	+	0.316550i	$0.102524\pi$
$251$			10.0302i			0.633100i	−0.948576	+	0.316550i	$0.897476\pi$
$252$		0			0
$253$	−1.35029	−	0.213864i	−0.0848918	−	0.0134455i
$254$		0			0
$255$	26.4379	−	2.66002i	1.65561	−	0.166577i
$256$		0			0
$257$	14.2299	+	14.2299i	0.887636	+	0.887636i	0.994296	−	0.106659i	$-0.0340154\pi$
$257$	14.2299	+	14.2299i	0.887636	+	0.887636i	−0.106659	+	0.994296i	$0.534015\pi$
$258$		0			0
$259$	8.48463	+	2.75682i	0.527209	+	0.171301i
$260$		0			0
$261$	−9.82875	+	7.82960i	−0.608384	+	0.484640i
$262$		0			0
$263$	9.27721	+	18.2076i	0.572057	+	1.12273i	0.977957	+	0.208808i	$0.0669583\pi$
$263$	9.27721	+	18.2076i	0.572057	+	1.12273i	−0.405899	+	0.913918i	$0.633042\pi$
$264$		0			0
$265$	−1.23023	+	5.11442i	−0.0755723	+	0.314177i
$266$		0			0
$267$	9.42117	−	3.29379i	0.576566	−	0.201577i
$268$		0			0
$269$	−9.47744	−	6.88577i	−0.577850	−	0.419833i	0.260098	−	0.965582i	$-0.416245\pi$
$269$	−9.47744	−	6.88577i	−0.577850	−	0.419833i	−0.837948	+	0.545750i	$0.816245\pi$
$270$		0			0
$271$	−1.24045	+	0.901239i	−0.0753519	+	0.0547463i	−0.624823	−	0.780766i	$-0.714829\pi$
$271$	−1.24045	+	0.901239i	−0.0753519	+	0.0547463i	0.549472	+	0.835512i	$0.314829\pi$
$272$		0			0
$273$	22.6944	+	6.82140i	1.37353	+	0.412850i
$274$		0			0
$275$	−13.0726	+	2.05879i	−0.788307	+	0.124150i
$276$		0			0
$277$	−7.36701	−	3.75368i	−0.442641	−	0.225537i	0.218442	−	0.975850i	$-0.429903\pi$
$277$	−7.36701	−	3.75368i	−0.442641	−	0.225537i	−0.661082	+	0.750313i	$0.729903\pi$
$278$		0			0
$279$	21.5149	+	14.2183i	1.28806	+	0.851229i
$280$		0			0
$281$	−16.4737	+	22.6741i	−0.982737	+	1.35262i	−0.0473952	+	0.998876i	$0.515092\pi$
$281$	−16.4737	+	22.6741i	−0.982737	+	1.35262i	−0.935342	+	0.353745i	$0.884908\pi$
$282$		0			0
$283$	−2.95822	−	18.6774i	−0.175848	−	1.11026i	−0.904845	−	0.425742i	$-0.860013\pi$
$283$	−2.95822	−	18.6774i	−0.175848	−	1.11026i	0.728997	−	0.684517i	$-0.239987\pi$
$284$		0			0
$285$	3.88312	+	3.17316i	0.230016	+	0.187962i
$286$		0			0
$287$	29.6954	−	15.1305i	1.75286	−	0.893128i
$288$		0			0
$289$	−28.5975	+	9.29189i	−1.68221	+	0.546582i
$290$		0			0
$291$	−17.3848	−	2.35965i	−1.01912	−	0.138325i
$292$		0			0
$293$	2.21527	−	2.21527i	0.129417	−	0.129417i	−0.639431	−	0.768848i	$-0.720830\pi$
$293$	2.21527	−	2.21527i	0.129417	−	0.129417i	0.768848	+	0.639431i	$0.220830\pi$
$294$		0			0
$295$	−0.598880	+	1.44404i	−0.0348682	+	0.0840753i
$296$		0			0
$297$	−5.10991	−	12.7683i	−0.296507	−	0.740895i
$298$		0			0
$299$	−1.51572			−0.0876564
$300$		0			0
$301$	42.7901			2.46638
$302$		0			0
$303$	4.18035	−	0.0927089i	0.240155	−	0.00532599i
$304$		0			0
$305$	2.63208	+	10.9845i	0.150713	+	0.628973i
$306$		0			0
$307$	5.97093	−	5.97093i	0.340779	−	0.340779i	−0.515881	−	0.856660i	$-0.672535\pi$
$307$	5.97093	−	5.97093i	0.340779	−	0.340779i	0.856660	+	0.515881i	$0.172535\pi$
$308$		0			0
$309$	−3.24026	+	23.8728i	−0.184332	+	1.35808i
$310$		0			0
$311$	24.1306	−	7.84050i	1.36832	−	0.444594i	0.469508	−	0.882928i	$-0.344431\pi$
$311$	24.1306	−	7.84050i	1.36832	−	0.444594i	0.898812	+	0.438334i	$0.144431\pi$
$312$		0			0
$313$	18.5441	−	9.44868i	1.04817	−	0.534071i	0.156936	−	0.987609i	$-0.449838\pi$
$313$	18.5441	−	9.44868i	1.04817	−	0.534071i	0.891237	+	0.453538i	$0.149838\pi$
$314$		0			0
$315$	22.8685	−	21.3370i	1.28849	−	1.20221i
$316$		0			0
$317$	−1.87932	−	11.8655i	−0.105553	−	0.666435i	−0.982558	−	0.185955i	$-0.940462\pi$
$317$	−1.87932	−	11.8655i	−0.105553	−	0.666435i	0.877005	−	0.480481i	$-0.159538\pi$
$318$		0			0
$319$	−6.51643	+	8.96910i	−0.364850	+	0.502173i
$320$		0			0
$321$	19.7750	−	20.6720i	1.10373	−	1.15380i
$322$		0			0
$323$	−7.91500	−	4.03290i	−0.440403	−	0.224396i
$324$		0			0
$325$	−13.9580	+	4.52176i	−0.774252	+	0.250822i
$326$		0			0
$327$	−5.42289	+	18.0416i	−0.299886	+	0.997704i
$328$		0			0
$329$	36.0353	−	26.1811i	1.98669	−	1.44341i
$330$		0			0
$331$	8.81611	+	6.40528i	0.484577	+	0.352066i	0.803095	−	0.595851i	$-0.203185\pi$
$331$	8.81611	+	6.40528i	0.484577	+	0.352066i	−0.318518	+	0.947917i	$0.603185\pi$
$332$		0			0
$333$	−2.83021	−	4.99406i	−0.155095	−	0.273673i
$334$		0			0
$335$	−24.8895	+	1.94791i	−1.35986	+	0.106426i
$336$		0			0
$337$	3.69026	+	7.24255i	0.201021	+	0.394527i	0.969406	−	0.245461i	$-0.0789393\pi$
$337$	3.69026	+	7.24255i	0.201021	+	0.394527i	−0.768385	+	0.639988i	$0.778939\pi$
$338$		0			0
$339$	−29.8369	+	16.0457i	−1.62052	+	0.871480i
$340$		0			0
$341$	21.6384	+	7.03074i	1.17178	+	0.380736i
$342$		0			0
$343$	−25.5129	−	25.5129i	−1.37757	−	1.37757i
$344$		0			0
$345$	−1.00794	+	1.72803i	−0.0542657	+	0.0930339i
$346$		0			0
$347$	−23.9622	−	3.79524i	−1.28636	−	0.203739i	−0.524460	−	0.851435i	$-0.675733\pi$
$347$	−23.9622	−	3.79524i	−1.28636	−	0.203739i	−0.761899	+	0.647696i	$0.775733\pi$
$348$		0			0
$349$			0.686028i			0.0367222i	0.999831	+	0.0183611i	$0.00584486\pi$
$349$			0.686028i			0.0367222i	−0.999831	+	0.0183611i	$0.994155\pi$
$350$		0			0
$351$	−7.81012	−	13.0957i	−0.416873	−	0.698996i
$352$		0			0
$353$	−0.458795	+	2.89672i	−0.0244192	+	0.154177i	−0.996885	−	0.0788690i	$-0.974869\pi$
$353$	−0.458795	+	2.89672i	−0.0244192	+	0.154177i	0.972466	+	0.233046i	$0.0748691\pi$
$354$		0			0
$355$	−6.00436	−	9.80784i	−0.318678	−	0.520546i
$356$		0			0
$357$	−31.5641	+	45.5341i	−1.67055	+	2.40992i
$358$		0			0
$359$	−7.07630	+	21.7786i	−0.373473	+	1.14943i	0.571031	+	0.820929i	$0.306544\pi$
$359$	−7.07630	+	21.7786i	−0.373473	+	1.14943i	−0.944503	+	0.328502i	$0.893456\pi$
$360$		0			0
$361$	5.35326	+	16.4756i	0.281750	+	0.867138i
$362$		0			0
$363$	4.19006	+	5.50612i	0.219921	+	0.288997i
$364$		0			0
$365$	3.59548	−	5.86155i	0.188196	−	0.306807i
$366$		0			0
$367$	7.75783	−	1.22872i	0.404955	−	0.0641386i	0.0493656	−	0.998781i	$-0.484280\pi$
$367$	7.75783	−	1.22872i	0.404955	−	0.0641386i	0.355590	+	0.934642i	$0.384280\pi$
$368$		0			0
$369$	−20.6686	−	5.71601i	−1.07596	−	0.297563i
$370$		0			0
$371$	−6.44703	−	8.87358i	−0.334713	−	0.460693i
$372$		0			0
$373$	8.90498	−	17.4770i	0.461082	−	0.904925i	−0.537033	−	0.843561i	$-0.680455\pi$
$373$	8.90498	−	17.4770i	0.461082	−	0.904925i	0.998115	−	0.0613640i	$-0.0195451\pi$
$374$		0			0
$375$	−4.12685	+	18.9201i	−0.213110	+	0.977028i
$376$		0			0
$377$	−5.58022	+	10.9518i	−0.287396	+	0.564046i
$378$		0			0
$379$	10.7496	+	14.7956i	0.552172	+	0.760000i	0.990305	−	0.138910i	$-0.0443600\pi$
$379$	10.7496	+	14.7956i	0.552172	+	0.760000i	−0.438133	+	0.898910i	$0.644360\pi$
$380$		0			0
$381$	−1.72422	+	3.57794i	−0.0883345	+	0.183304i
$382$		0			0
$383$	4.77981	−	0.757047i	0.244237	−	0.0386833i	−0.0331158	−	0.999452i	$-0.510543\pi$
$383$	4.77981	−	0.757047i	0.244237	−	0.0386833i	0.277353	+	0.960768i	$0.410543\pi$
$384$		0			0
$385$	14.4280	−	23.5213i	0.735320	−	1.19876i
$386$		0			0
$387$	−20.3125	−	18.5864i	−1.03254	−	0.944797i
$388$		0			0
$389$	−4.33329	−	13.3365i	−0.219707	−	0.676188i	−0.998786	−	0.0492621i	$-0.984313\pi$
$389$	−4.33329	−	13.3365i	−0.219707	−	0.676188i	0.779079	−	0.626926i	$-0.215687\pi$
$390$		0			0
$391$	1.09508	−	3.37030i	0.0553805	−	0.170444i
$392$		0			0
$393$	1.49110	+	1.03362i	0.0752160	+	0.0521394i
$394$		0			0
$395$	−2.81325	−	4.59531i	−0.141550	−	0.231215i
$396$		0			0
$397$	−2.55903	+	16.1570i	−0.128434	+	0.810899i	0.836416	+	0.548096i	$0.184647\pi$
$397$	−2.55903	+	16.1570i	−0.128434	+	0.810899i	−0.964849	+	0.262803i	$0.915353\pi$
$398$		0			0
$399$	−10.2888	+	1.86430i	−0.515082	+	0.0933319i
$400$		0			0
$401$			21.7930i			1.08829i	0.838991	+	0.544145i	$0.183146\pi$
$401$			21.7930i			1.08829i	−0.838991	+	0.544145i	$0.816854\pi$
$402$		0			0
$403$	24.9145	+	3.94606i	1.24108	+	0.196567i
$404$		0			0
$405$	−20.1237	+	0.195566i	−0.999953	+	0.00971774i
$406$		0			0
$407$	−3.58103	−	3.58103i	−0.177505	−	0.177505i
$408$		0			0
$409$	12.1283	+	3.94072i	0.599705	+	0.194856i	0.593109	−	0.805122i	$-0.297900\pi$
$409$	12.1283	+	3.94072i	0.599705	+	0.194856i	0.00659637	+	0.999978i	$0.497900\pi$
$410$		0			0
$411$	−12.2791	−	22.8330i	−0.605684	−	1.12627i
$412$		0			0
$413$	−1.47986	−	2.90438i	−0.0728190	−	0.142915i
$414$		0			0
$415$	−1.18619	+	0.0928335i	−0.0582276	+	0.00455702i
$416$		0			0
$417$	−4.78146	−	13.6763i	−0.234149	−	0.669731i
$418$		0			0
$419$	−22.6925	−	16.4871i	−1.10860	−	0.805447i	−0.126160	−	0.992010i	$-0.540265\pi$
$419$	−22.6925	−	16.4871i	−1.10860	−	0.805447i	−0.982443	+	0.186563i	$0.940265\pi$
$420$		0			0
$421$	4.60347	−	3.34462i	0.224360	−	0.163007i	−0.469927	−	0.882705i	$-0.655720\pi$
$421$	4.60347	−	3.34462i	0.224360	−	0.163007i	0.694287	+	0.719698i	$0.255720\pi$
$422$		0			0
$423$	−28.4781	−	3.22407i	−1.38465	−	0.156760i
$424$		0			0
$425$	0.0299739	−	34.3035i	0.00145395	−	1.66396i
$426$		0			0
$427$	−20.9854	−	10.6926i	−1.01555	−	0.517450i
$428$		0			0
$429$	−9.72080	−	9.29899i	−0.469324	−	0.448959i
$430$		0			0
$431$	12.4959	−	17.1991i	0.601904	−	0.828450i	−0.393977	−	0.919120i	$-0.628901\pi$
$431$	12.4959	−	17.1991i	0.601904	−	0.828450i	0.995881	+	0.0906706i	$0.0289010\pi$
$432$		0			0
$433$	3.63581	+	22.9556i	0.174726	+	1.10318i	0.906679	+	0.421821i	$0.138609\pi$
$433$	3.63581	+	22.9556i	0.174726	+	1.10318i	−0.731953	+	0.681355i	$0.761391\pi$
$434$		0			0
$435$	8.77502	+	13.6447i	0.420730	+	0.654213i
$436$		0			0
$437$	0.595905	−	0.303629i	0.0285060	−	0.0145245i
$438$		0			0
$439$	24.5061	−	7.96251i	1.16961	−	0.380030i	0.341114	−	0.940022i	$-0.389196\pi$
$439$	24.5061	−	7.96251i	1.16961	−	0.380030i	0.828498	+	0.559992i	$0.189196\pi$
$440$		0			0
$441$	1.96020	+	44.1722i	0.0933430	+	2.10344i
$442$		0			0
$443$	−9.30295	+	9.30295i	−0.441997	+	0.441997i	−0.892683	−	0.450686i	$-0.851179\pi$
$443$	−9.30295	+	9.30295i	−0.441997	+	0.441997i	0.450686	+	0.892683i	$0.351179\pi$
$444$		0			0
$445$	−3.00237	−	12.5299i	−0.142326	−	0.593974i
$446$		0			0
$447$	0.637119	+	28.7285i	0.0301347	+	1.35881i
$448$		0			0
$449$	−22.1737			−1.04644			−0.523221	−	0.852197i	$-0.675270\pi$
$449$	−22.1737			−1.04644			−0.523221	+	0.852197i	$0.675270\pi$
$450$		0			0
$451$	−18.9193			−0.890874
$452$		0			0
$453$	−0.248898	−	11.2231i	−0.0116942	−	0.527306i
$454$		0			0
$455$	11.7199	−	28.2593i	0.549436	−	1.32482i
$456$		0			0
$457$	10.0840	−	10.0840i	0.471711	−	0.471711i	−0.430757	−	0.902468i	$-0.641753\pi$
$457$	10.0840	−	10.0840i	0.471711	−	0.471711i	0.902468	+	0.430757i	$0.141753\pi$
$458$		0			0
$459$	34.7618	−	7.90493i	1.62254	−	0.368971i
$460$		0			0
$461$	−24.5459	+	7.97544i	−1.14322	+	0.371453i	−0.818584	−	0.574387i	$-0.805240\pi$
$461$	−24.5459	+	7.97544i	−1.14322	+	0.371453i	−0.324632	+	0.945841i	$0.605240\pi$
$462$		0			0
$463$	20.3415	−	10.3645i	0.945350	−	0.481680i	0.0878325	−	0.996135i	$-0.472006\pi$
$463$	20.3415	−	10.3645i	0.945350	−	0.481680i	0.857517	+	0.514456i	$0.172006\pi$
$464$		0			0
$465$	21.0667	−	25.7801i	0.976945	−	1.19553i
$466$		0			0
$467$	−2.18498	−	13.7954i	−0.101109	−	0.638376i	−0.985245	−	0.171148i	$-0.945252\pi$
$467$	−2.18498	−	13.7954i	−0.101109	−	0.638376i	0.884136	−	0.467229i	$-0.154748\pi$
$468$		0			0
$469$	30.5979	−	42.1144i	1.41288	−	1.94466i
$470$		0			0
$471$	5.03578	+	4.81726i	0.232036	+	0.221968i
$472$		0			0
$473$	−21.6432	−	11.0277i	−0.995154	−	0.507056i
$474$		0			0
$475$	4.58180	−	4.57380i	0.210227	−	0.209860i
$476$		0			0
$477$	−0.793917	+	7.01264i	−0.0363510	+	0.321087i
$478$		0			0
$479$	−2.14256	+	1.55666i	−0.0978960	+	0.0711256i	−0.635656	−	0.771972i	$-0.719270\pi$
$479$	−2.14256	+	1.55666i	−0.0978960	+	0.0711256i	0.537760	+	0.843098i	$0.319270\pi$
$480$		0			0
$481$	−4.54249	−	3.30031i	−0.207120	−	0.150481i
$482$		0			0
$483$	−1.37664	−	3.93758i	−0.0626393	−	0.179166i
$484$		0			0
$485$	−5.29705	+	22.0214i	−0.240526	+	0.999940i
$486$		0			0
$487$	2.86281	+	5.61858i	0.129726	+	0.254602i	0.946729	−	0.322032i	$-0.104366\pi$
$487$	2.86281	+	5.61858i	0.129726	+	0.254602i	−0.817002	+	0.576634i	$0.804366\pi$
$488$		0			0
$489$	4.35204	+	8.09261i	0.196806	+	0.365960i
$490$		0			0
$491$	17.2145	+	5.59334i	0.776881	+	0.252424i	0.670508	−	0.741902i	$-0.266076\pi$
$491$	17.2145	+	5.59334i	0.776881	+	0.252424i	0.106373	+	0.994326i	$0.466076\pi$
$492$		0			0
$493$	−20.3204	−	20.3204i	−0.915186	−	0.915186i
$494$		0			0
$495$	−17.0657	+	4.89864i	−0.767048	+	0.220178i
$496$		0			0
$497$	23.6833	+	3.75106i	1.06234	+	0.168258i
$498$		0			0
$499$			25.8514i			1.15727i	0.815587	+	0.578634i	$0.196414\pi$
$499$			25.8514i			1.15727i	−0.815587	+	0.578634i	$0.803586\pi$
$500$		0			0
$501$	2.09288	−	0.379225i	0.0935028	−	0.0169425i
$502$		0			0
$503$	−2.21885	+	14.0093i	−0.0989337	+	0.624643i	0.887541	+	0.460729i	$0.152412\pi$
$503$	−2.21885	+	14.0093i	−0.0989337	+	0.624643i	−0.986475	+	0.163914i	$0.947588\pi$
$504$		0			0
$505$	0.425884	−	5.38131i	0.0189516	−	0.239465i
$506$		0			0
$507$	6.24780	+	4.33095i	0.277474	+	0.192344i
$508$		0			0
$509$	7.07081	−	21.7617i	0.313408	−	0.964571i	−0.662997	−	0.748622i	$-0.730716\pi$
$509$	7.07081	−	21.7617i	0.313408	−	0.964571i	0.976405	−	0.215949i	$-0.0692844\pi$
$510$		0			0
$511$	4.43073	+	13.6364i	0.196004	+	0.603239i
$512$		0			0
$513$	5.69387	+	3.58404i	0.251390	+	0.158239i
$514$		0			0
$515$	30.2397	+	7.27389i	1.33252	+	0.320526i
$516$		0			0
$517$	−24.9739	+	3.95548i	−1.09835	+	0.173962i
$518$		0			0
$519$	4.17603	−	8.66572i	0.183308	−	0.380383i
$520$		0			0
$521$	−21.3145	−	29.3369i	−0.933805	−	1.28527i	−0.958357	−	0.285574i	$-0.907816\pi$
$521$	−21.3145	−	29.3369i	−0.933805	−	1.28527i	0.0245518	−	0.999699i	$-0.492184\pi$
$522$		0			0
$523$	−8.90012	+	17.4675i	−0.389175	+	0.763799i	−0.999600	−	0.0282747i	$-0.990999\pi$
$523$	−8.90012	+	17.4675i	−0.389175	+	0.763799i	0.610425	+	0.792074i	$0.290999\pi$
$524$		0			0
$525$	−24.4240	−	32.1537i	−1.06595	−	1.40330i
$526$		0			0
$527$	−26.7745	+	52.5480i	−1.16632	+	2.28903i
$528$		0			0
$529$	−13.3622	−	18.3915i	−0.580967	−	0.799632i
$530$		0			0
$531$	−0.559059	+	2.02151i	−0.0242611	+	0.0877259i
$532$		0			0
$533$	−20.7175	+	3.28133i	−0.897374	+	0.142130i
$534$		0			0
$535$	−23.9732	−	28.0938i	−1.03645	−	1.21460i
$536$		0			0
$537$	−10.8964	−	14.3189i	−0.470215	−	0.617907i
$538$		0			0
$539$	12.0545	+	37.0999i	0.519224	+	1.59801i
$540$		0			0
$541$	13.0093	−	40.0384i	0.559312	−	1.72138i	−0.124964	−	0.992161i	$-0.539881\pi$
$541$	13.0093	−	40.0384i	0.559312	−	1.72138i	0.684275	−	0.729224i	$-0.260119\pi$
$542$		0			0
$543$	−13.0357	+	18.8052i	−0.559416	+	0.807009i
$544$		0			0
$545$	22.4657	+	9.31708i	0.962323	+	0.399100i
$546$		0			0
$547$	3.47779	−	21.9579i	0.148699	−	0.938851i	−0.794654	−	0.607062i	$-0.792348\pi$
$547$	3.47779	−	21.9579i	0.148699	−	0.938851i	0.943354	−	0.331789i	$-0.107652\pi$
$548$		0			0
$549$	5.31735	+	14.1910i	0.226939	+	0.605657i
$550$		0			0
$551$		−	5.42352i		−	0.231050i
$552$		0			0
$553$	11.0964	+	1.75750i	0.471868	+	0.0747366i
$554$		0			0
$555$	−6.78330	+	2.98408i	−0.287935	+	0.126667i
$556$		0			0
$557$	0.749164	+	0.749164i	0.0317431	+	0.0317431i	0.722800	−	0.691057i	$-0.242855\pi$
$557$	0.749164	+	0.749164i	0.0317431	+	0.0317431i	−0.691057	+	0.722800i	$0.742855\pi$
$558$		0			0
$559$	−25.6129	−	8.32215i	−1.08331	−	0.351989i
$560$		0			0
$561$	27.7000	−	14.8965i	1.16949	−	0.628930i
$562$		0			0
$563$	−0.652641	−	1.28088i	−0.0275055	−	0.0539827i	0.876845	−	0.480773i	$-0.159644\pi$
$563$	−0.652641	−	1.28088i	−0.0275055	−	0.0539827i	−0.904350	+	0.426791i	$0.859644\pi$
$564$		0			0
$565$	16.7194	+	40.4141i	0.703390	+	1.70023i
$566$		0			0
$567$	26.9268	−	32.1834i	1.13082	−	1.35157i
$568$		0			0
$569$	−6.70335	−	4.87027i	−0.281019	−	0.204172i	0.438343	−	0.898808i	$-0.355566\pi$
$569$	−6.70335	−	4.87027i	−0.281019	−	0.204172i	−0.719362	+	0.694636i	$0.755566\pi$
$570$		0			0
$571$	−5.69591	+	4.13832i	−0.238366	+	0.173183i	−0.700555	−	0.713598i	$-0.747064\pi$
$571$	−5.69591	+	4.13832i	−0.238366	+	0.173183i	0.462189	+	0.886781i	$0.347064\pi$
$572$		0			0
$573$	−9.04543	+	30.0936i	−0.377878	+	1.25718i
$574$		0			0
$575$	2.08807	+	1.51986i	0.0870787	+	0.0633827i
$576$		0			0
$577$	18.4348	+	9.39300i	0.767451	+	0.391036i	0.793457	−	0.608626i	$-0.208279\pi$
$577$	18.4348	+	9.39300i	0.767451	+	0.391036i	−0.0260065	+	0.999662i	$0.508279\pi$
$578$		0			0
$579$	27.9066	−	29.1724i	1.15976	−	1.21237i
$580$		0			0
$581$	1.45824	−	2.00709i	0.0604979	−	0.0832682i
$582$		0			0
$583$	0.974025	+	6.14975i	0.0403400	+	0.254697i
$584$		0			0
$585$	−17.8382	+	8.32410i	−0.737518	+	0.344159i
$586$		0			0
$587$	−0.296037	+	0.150838i	−0.0122187	+	0.00622576i	−0.460089	−	0.887873i	$-0.652183\pi$
$587$	−0.296037	+	0.150838i	−0.0122187	+	0.00622576i	0.447870	+	0.894098i	$0.352183\pi$
$588$		0			0
$589$	−10.5856	+	3.43947i	−0.436172	+	0.141721i
$590$		0			0
$591$	−4.56556	+	33.6370i	−0.187802	+	1.38364i
$592$		0			0
$593$	27.1484	−	27.1484i	1.11485	−	1.11485i	0.122365	−	0.992485i	$-0.460952\pi$
$593$	27.1484	−	27.1484i	1.11485	−	1.11485i	0.992485	−	0.122365i	$-0.0390480\pi$
$594$		0			0
$595$	54.3691	+	46.4767i	2.22892	+	1.90536i
$596$		0			0
$597$	29.5615	−	0.655594i	1.20987	−	0.0268317i
$598$		0			0
$599$	−15.8427			−0.647315			−0.323657	−	0.946174i	$-0.604913\pi$
$599$	−15.8427			−0.647315			−0.323657	+	0.946174i	$0.604913\pi$
$600$		0			0
$601$	−10.1851			−0.415459			−0.207729	−	0.978186i	$-0.566607\pi$
$601$	−10.1851			−0.415459			−0.207729	+	0.978186i	$0.566607\pi$
$602$		0			0
$603$	−32.8177	+	6.70125i	−1.33644	+	0.272896i
$604$		0			0
$605$	7.61827	−	4.66390i	0.309727	−	0.189615i
$606$		0			0
$607$	15.8821	−	15.8821i	0.644635	−	0.644635i	−0.307056	−	0.951691i	$-0.599344\pi$
$607$	15.8821	−	15.8821i	0.644635	−	0.644635i	0.951691	+	0.307056i	$0.0993441\pi$
$608$		0			0
$609$	−33.5190	−	4.54955i	−1.35826	−	0.184357i
$610$		0			0
$611$	−26.6616	+	8.66287i	−1.07861	+	0.350462i
$612$		0			0
$613$	−14.2208	+	7.24586i	−0.574373	+	0.292658i	−0.716948	−	0.697126i	$-0.754462\pi$
$613$	−14.2208	+	7.24586i	−0.574373	+	0.292658i	0.142576	+	0.989784i	$0.454462\pi$
$614$		0			0
$615$	−10.0360	+	25.8015i	−0.404691	+	1.04041i
$616$		0			0
$617$	−1.40300	−	8.85819i	−0.0564826	−	0.356617i	−0.999701	−	0.0244446i	$-0.992218\pi$
$617$	−1.40300	−	8.85819i	−0.0564826	−	0.356617i	0.943219	−	0.332173i	$-0.107782\pi$
$618$		0			0
$619$	−8.67904	+	11.9457i	−0.348840	+	0.480137i	−0.946997	−	0.321242i	$-0.895900\pi$
$619$	−8.67904	+	11.9457i	−0.348840	+	0.480137i	0.598157	+	0.801379i	$0.295900\pi$
$620$		0			0
$621$	−1.05683	+	2.46713i	−0.0424093	+	0.0990026i
$622$		0			0
$623$	23.9377	+	12.1968i	0.959042	+	0.488656i
$624$		0			0
$625$	23.7629	+	7.76696i	0.950515	+	0.310679i
$626$		0			0
$627$	5.68450	+	1.70863i	0.227017	+	0.0682360i
$628$		0			0
$629$	10.6203	−	7.71611i	0.423460	−	0.307661i
$630$		0			0
$631$	5.22678	+	3.79747i	0.208075	+	0.151175i	0.686942	−	0.726712i	$-0.258953\pi$
$631$	5.22678	+	3.79747i	0.208075	+	0.151175i	−0.478868	+	0.877887i	$0.658953\pi$
$632$		0			0
$633$	12.2366	−	4.27810i	0.486360	−	0.170039i
$634$		0			0
$635$	4.37072	+	2.68101i	0.173447	+	0.106393i
$636$		0			0
$637$	19.6348	+	38.5355i	0.777959	+	1.52683i
$638$		0			0
$639$	−9.61317	−	12.0677i	−0.380291	−	0.477392i
$640$		0			0
$641$	10.6889	+	3.47304i	0.422187	+	0.137177i	0.512402	−	0.858745i	$-0.328756\pi$
$641$	10.6889	+	3.47304i	0.422187	+	0.137177i	−0.0902157	+	0.995922i	$0.528756\pi$
$642$		0			0
$643$	−8.44140	−	8.44140i	−0.332896	−	0.332896i	0.520789	−	0.853685i	$-0.325638\pi$
$643$	−8.44140	−	8.44140i	−0.332896	−	0.332896i	−0.853685	+	0.520789i	$0.825638\pi$
$644$		0			0
$645$	−26.5202	+	23.6664i	−1.04423	+	0.931863i
$646$		0			0
$647$	12.8707	+	2.03852i	0.506001	+	0.0801427i	0.404216	−	0.914664i	$-0.367545\pi$
$647$	12.8707	+	2.03852i	0.506001	+	0.0801427i	0.101785	+	0.994806i	$0.467545\pi$
$648$		0			0
$649$			1.85042i			0.0726352i
$650$		0			0
$651$	12.3772	+	68.3074i	0.485100	+	2.67718i
$652$		0			0
$653$	−1.55677	+	9.82909i	−0.0609213	+	0.384642i	0.938323	+	0.345761i	$0.112379\pi$
$653$	−1.55677	+	9.82909i	−0.0609213	+	0.384642i	−0.999244	+	0.0388808i	$0.987621\pi$
$654$		0			0
$655$	1.52196	−	1.78042i	0.0594681	−	0.0695666i
$656$		0			0
$657$	3.81984	−	8.39775i	0.149026	−	0.327628i
$658$		0			0
$659$	−12.8415	+	39.5220i	−0.500232	+	1.53956i	0.308408	+	0.951254i	$0.400204\pi$
$659$	−12.8415	+	39.5220i	−0.500232	+	1.53956i	−0.808641	+	0.588303i	$0.799796\pi$
$660$		0			0
$661$	−0.168013	−	0.517089i	−0.00653493	−	0.0201124i	0.947736	−	0.319056i	$-0.103366\pi$
$661$	−0.168013	−	0.517089i	−0.00653493	−	0.0201124i	−0.954271	+	0.298943i	$0.903366\pi$
$662$		0			0
$663$	27.7492	−	21.1166i	1.07769	−	0.820101i
$664$		0			0
$665$	1.05324	+	13.4579i	0.0408429	+	0.521874i
$666$		0			0
$667$	2.13695	−	0.338459i	0.0827429	−	0.0131052i
$668$		0			0
$669$	−2.65019	−	1.27713i	−0.102462	−	0.0493768i
$670$		0			0
$671$	7.85870	+	10.8166i	0.303382	+	0.417569i
$672$		0			0
$673$	−8.48836	+	16.6593i	−0.327202	+	0.642170i	−0.994743	−	0.102403i	$-0.967347\pi$
$673$	−8.48836	+	16.6593i	−0.327202	+	0.642170i	0.667541	+	0.744573i	$0.267347\pi$
$674$		0			0
$675$	−2.37218	+	25.8722i	−0.0913051	+	0.995823i
$676$		0			0
$677$	−2.20359	+	4.32479i	−0.0846909	+	0.166215i	−0.929468	−	0.368904i	$-0.879733\pi$
$677$	−2.20359	+	4.32479i	−0.0846909	+	0.166215i	0.844777	+	0.535119i	$0.179733\pi$
$678$		0			0
$679$	−27.7593	−	38.2074i	−1.06530	−	1.46626i
$680$		0			0
$681$	−31.9258	−	15.3851i	−1.22340	−	0.589560i
$682$		0			0
$683$	37.0496	−	5.86808i	1.41766	−	0.224536i	0.599893	−	0.800080i	$-0.295210\pi$
$683$	37.0496	−	5.86808i	1.41766	−	0.224536i	0.817770	+	0.575545i	$0.195210\pi$
$684$		0			0
$685$	−30.9273	+	12.7947i	−1.18167	+	0.488860i
$686$		0			0
$687$	14.2794	−	10.8663i	0.544791	−	0.414576i
$688$		0			0
$689$	2.13321	+	6.56534i	0.0812687	+	0.250119i
$690$		0			0
$691$	10.4266	−	32.0898i	0.396647	−	1.22075i	−0.531025	−	0.847356i	$-0.678193\pi$
$691$	10.4266	−	32.0898i	0.396647	−	1.22075i	0.927672	−	0.373397i	$-0.121807\pi$
$692$		0			0
$693$	15.3283	−	33.6987i	0.582274	−	1.28011i
$694$		0			0
$695$	−18.1891	+	4.35841i	−0.689952	+	0.165324i
$696$		0			0
$697$	7.67173	−	48.4374i	0.290587	−	1.83470i
$698$		0			0
$699$	−3.27858	−	18.0939i	−0.124007	−	0.684373i
$700$		0			0
$701$		−	50.3263i		−	1.90080i	−0.311032	−	0.950399i	$-0.600675\pi$
$701$		−	50.3263i		−	1.90080i	0.311032	−	0.950399i	$-0.399325\pi$
$702$		0			0
$703$	2.44700	+	0.387566i	0.0922902	+	0.0146173i
$704$		0			0
$705$	−7.85343	+	36.1568i	−0.295777	+	1.36174i
$706$		0			0
$707$	7.95902	+	7.95902i	0.299330	+	0.299330i
$708$		0			0
$709$	36.5771	+	11.8846i	1.37368	+	0.446337i	0.900588	−	0.434675i	$-0.143137\pi$
$709$	36.5771	+	11.8846i	1.37368	+	0.446337i	0.473095	+	0.881011i	$0.343137\pi$
$710$		0			0
$711$	−4.50411	−	5.65415i	−0.168917	−	0.212047i
$712$		0			0
$713$	−2.01580	−	3.95623i	−0.0754924	−	0.148162i
$714$		0			0
$715$	−13.2108	+	11.2731i	−0.494056	+	0.421591i
$716$		0			0
$717$	35.7573	−	12.5013i	1.33538	−	0.466870i
$718$		0			0
$719$	41.8068	+	30.3745i	1.55913	+	1.13278i	0.936716	+	0.350089i	$0.113849\pi$
$719$	41.8068	+	30.3745i	1.55913	+	1.13278i	0.622416	+	0.782687i	$0.286151\pi$
$720$		0			0
$721$	−52.4662	+	38.1189i	−1.95394	+	1.41962i
$722$		0			0
$723$	−18.4237	−	5.53774i	−0.685186	−	0.205951i
$724$		0			0
$725$	18.6691	−	9.49184i	0.693353	−	0.352518i
$726$		0			0
$727$	−28.7844	−	14.6664i	−1.06755	−	0.543946i	−0.170269	−	0.985398i	$-0.554464\pi$
$727$	−28.7844	−	14.6664i	−1.06755	−	0.543946i	−0.897285	+	0.441452i	$0.854464\pi$
$728$		0			0
$729$	−26.7614	+	3.58154i	−0.991163	+	0.132650i
$730$		0			0
$731$	37.0097	−	50.9394i	1.36885	−	1.88406i
$732$		0			0
$733$	5.26046	+	33.2132i	0.194300	+	1.22676i	0.871291	+	0.490768i	$0.163284\pi$
$733$	5.26046	+	33.2132i	0.194300	+	1.22676i	−0.676991	+	0.735991i	$0.736716\pi$
$734$		0			0
$735$	56.9901	+	3.24070i	2.10211	+	0.119535i
$736$		0			0
$737$	−26.3300	+	13.4158i	−0.969877	+	0.494177i
$738$		0			0
$739$	−22.5536	+	7.32812i	−0.829649	+	0.269569i	−0.692897	−	0.721036i	$-0.743666\pi$
$739$	−22.5536	+	7.32812i	−0.829649	+	0.269569i	−0.136751	+	0.990605i	$0.543666\pi$
$740$		0			0
$741$	6.52114	+	0.885116i	0.239560	+	0.0325156i
$742$		0			0
$743$	−16.0850	+	16.0850i	−0.590100	+	0.590100i	−0.937658	−	0.347559i	$-0.887011\pi$
$743$	−16.0850	+	16.0850i	−0.590100	+	0.590100i	0.347559	+	0.937658i	$0.387011\pi$
$744$		0			0
$745$	36.9818	+	2.92679i	1.35491	+	0.107229i
$746$		0			0
$747$	−1.56403	+	0.319369i	−0.0572249	+	0.0116851i
$748$		0			0
$749$	77.0076			2.81380
$750$		0			0
$751$	−36.4969			−1.33179			−0.665896	−	0.746045i	$-0.731951\pi$
$751$	−36.4969			−1.33179			−0.665896	+	0.746045i	$0.731951\pi$
$752$		0			0
$753$	17.3685	−	0.385187i	0.632944	−	0.0140370i
$754$		0			0
$755$	−14.4473	−	1.14338i	−0.525792	−	0.0416119i
$756$		0			0
$757$	30.7730	−	30.7730i	1.11846	−	1.11846i	0.126497	−	0.991967i	$-0.459626\pi$
$757$	30.7730	−	30.7730i	1.11846	−	1.11846i	0.991967	−	0.126497i	$-0.0403735\pi$
$758$		0			0
$759$	−0.318478	+	2.34640i	−0.0115600	+	0.0851691i
$760$		0			0
$761$	−26.0146	+	8.45266i	−0.943029	+	0.306409i	−0.739880	−	0.672739i	$-0.765118\pi$
$761$	−26.0146	+	8.45266i	−0.943029	+	0.306409i	−0.203149	+	0.979148i	$0.565118\pi$
$762$		0			0
$763$	−45.1849	+	23.0229i	−1.63580	+	0.833484i
$764$		0			0
$765$	−5.62145	−	45.6784i	−0.203244	−	1.65150i
$766$		0			0
$767$	0.320933	+	2.02629i	0.0115882	+	0.0731652i
$768$		0			0
$769$	−1.09156	+	1.50240i	−0.0393625	+	0.0541779i	−0.828245	−	0.560367i	$-0.810660\pi$
$769$	−1.09156	+	1.50240i	−0.0393625	+	0.0541779i	0.788882	+	0.614545i	$0.210660\pi$
$770$		0			0
$771$	24.0944	−	25.1873i	0.867738	−	0.907099i
$772$		0			0
$773$	13.8988	+	7.08181i	0.499906	+	0.254715i	0.685714	−	0.727871i	$-0.259490\pi$
$773$	13.8988	+	7.08181i	0.499906	+	0.254715i	−0.185808	+	0.982586i	$0.559490\pi$
$774$		0			0
$775$	−30.3656	−	30.4187i	−1.09077	−	1.09267i
$776$		0			0
$777$	4.44795	−	14.7981i	0.159569	−	0.530878i
$778$		0			0
$779$	7.48776	−	5.44018i	0.268277	−	0.194915i
$780$		0			0
$781$	−11.0122	−	8.00087i	−0.394049	−	0.286294i
$782$		0			0
$783$	13.9354	+	16.7190i	0.498010	+	0.597489i
$784$		0			0
$785$	6.84375	−	5.83994i	0.244264	−	0.208437i
$786$		0			0
$787$	20.3851	+	40.0079i	0.726649	+	1.42613i	0.897583	+	0.440846i	$0.145321\pi$
$787$	20.3851	+	40.0079i	0.726649	+	1.42613i	−0.170934	+	0.985282i	$0.554679\pi$
$788$		0			0
$789$	31.1724	−	16.7639i	1.10977	−	0.596810i
$790$		0			0
$791$	−86.7312	−	28.1807i	−3.08381	−	1.00199i
$792$		0			0
$793$	10.4817	+	10.4817i	0.372215	+	0.372215i
$794$		0			0
$795$	8.90351	+	1.93389i	0.315775	+	0.0685879i
$796$		0			0
$797$	−41.9364	−	6.64208i	−1.48546	−	0.235275i	−0.639615	−	0.768696i	$-0.720906\pi$
$797$	−41.9364	−	6.64208i	−1.48546	−	0.235275i	−0.845850	+	0.533421i	$0.820906\pi$
$798$		0			0
$799$		−	65.5425i		−	2.31873i
$800$		0			0
$801$	−6.06541	−	16.1874i	−0.214311	−	0.571955i
$802$		0			0
$803$	1.27327	−	8.03914i	0.0449329	−	0.283695i
$804$		0			0
$805$	−5.23687	+	1.25484i	−0.184575	+	0.0442273i
$806$		0			0
$807$	−11.5596	+	16.6758i	−0.406917	+	0.587016i
$808$		0			0
$809$	−3.06477	+	9.43238i	−0.107751	+	0.331625i	−0.990366	−	0.138472i	$-0.955781\pi$
$809$	−3.06477	+	9.43238i	−0.107751	+	0.331625i	0.882615	+	0.470097i	$0.155781\pi$
$810$		0			0
$811$	0.305962	+	0.941654i	0.0107438	+	0.0330660i	0.956285	−	0.292437i	$-0.0944663\pi$
$811$	0.305962	+	0.941654i	0.0107438	+	0.0330660i	−0.945541	+	0.325503i	$0.894466\pi$
$812$		0			0
$813$	1.60824	+	2.11338i	0.0564036	+	0.0741195i
$814$		0			0
$815$	10.9614	−	4.53477i	0.383963	−	0.158846i
$816$		0			0
$817$	11.7368	−	1.85893i	0.410619	−	0.0650357i
$818$		0			0
$819$	10.9406	−	39.5601i	0.382295	−	1.38234i
$820$		0			0
$821$	9.68607	+	13.3317i	0.338046	+	0.465281i	0.943870	−	0.330319i	$-0.107156\pi$
$821$	9.68607	+	13.3317i	0.338046	+	0.465281i	−0.605823	+	0.795599i	$0.707156\pi$
$822$		0			0
$823$	−16.4813	+	32.3464i	−0.574503	+	1.12753i	0.402723	+	0.915322i	$0.368064\pi$
$823$	−16.4813	+	32.3464i	−0.574503	+	1.12753i	−0.977226	+	0.212203i	$0.931936\pi$
$824$		0			0
$825$	4.06707	+	22.5578i	0.141597	+	0.785361i
$826$		0			0
$827$	24.7130	−	48.5020i	0.859356	−	1.68658i	0.142007	−	0.989866i	$-0.454644\pi$
$827$	24.7130	−	48.5020i	0.859356	−	1.68658i	0.717348	−	0.696715i	$-0.245356\pi$
$828$		0			0
$829$	20.2093	+	27.8157i	0.701898	+	0.966079i	0.999934	+	0.0115244i	$0.00366843\pi$
$829$	20.2093	+	27.8157i	0.701898	+	0.966079i	−0.298036	+	0.954555i	$0.596332\pi$
$830$		0			0
$831$	−6.21705	+	12.9010i	−0.215667	+	0.447532i
$832$		0			0
$833$	−99.8719	+	15.8182i	−3.46036	+	0.548067i
$834$		0			0
$835$	−0.214244	−	2.73752i	−0.00741422	−	0.0947357i
$836$		0			0
$837$	23.7946	−	37.8018i	0.822461	−	1.30662i
$838$		0			0
$839$	−0.440558	−	1.35590i	−0.0152097	−	0.0468108i	0.943164	−	0.332329i	$-0.107834\pi$
$839$	−0.440558	−	1.35590i	−0.0152097	−	0.0468108i	−0.958373	+	0.285518i	$0.907834\pi$
$840$		0			0
$841$	−3.53972	+	10.8941i	−0.122059	+	0.375660i
$842$		0			0
$843$	39.8956	+	27.6555i	1.37408	+	0.952505i
$844$		0			0
$845$	6.37712	−	7.46005i	0.219380	−	0.256634i
$846$		0			0
$847$	−2.91365	+	18.3960i	−0.100114	+	0.632096i
$848$		0			0
$849$	−32.2287	+	5.83979i	−1.10609	+	0.200421i
$850$		0			0
$851$			0.988338i			0.0338798i
$852$		0			0
$853$	−2.88397	−	0.456776i	−0.0987454	−	0.0156397i	0.106866	−	0.994273i	$-0.465918\pi$
$853$	−2.88397	−	0.456776i	−0.0987454	−	0.0156397i	−0.205612	+	0.978634i	$0.565918\pi$
$854$		0			0
$855$	5.34559	−	6.84596i	0.182815	−	0.234127i
$856$		0			0
$857$	−24.5977	−	24.5977i	−0.840242	−	0.840242i	0.148648	−	0.988890i	$-0.452508\pi$
$857$	−24.5977	−	24.5977i	−0.840242	−	0.840242i	−0.988890	+	0.148648i	$0.952508\pi$
$858$		0			0
$859$	−1.91026	−	0.620681i	−0.0651772	−	0.0211774i	0.276247	−	0.961087i	$-0.410909\pi$
$859$	−1.91026	−	0.620681i	−0.0651772	−	0.0211774i	−0.341424	+	0.939909i	$0.610909\pi$
$860$		0			0
$861$	−27.3408	−	50.8402i	−0.931772	−	1.73263i
$862$		0			0
$863$	10.1861	+	19.9914i	0.346740	+	0.680516i	0.996849	−	0.0793253i	$-0.0252766\pi$
$863$	10.1861	+	19.9914i	0.346740	+	0.680516i	−0.650108	+	0.759841i	$0.725277\pi$
$864$		0			0
$865$	−10.5858	−	6.49336i	−0.359929	−	0.220781i
$866$		0			0
$867$	17.1883	+	49.1633i	0.583745	+	1.66967i
$868$		0			0
$869$	−5.15962	−	3.74868i	−0.175028	−	0.127165i
$870$		0			0
$871$	−26.5058	+	19.2576i	−0.898113	+	0.652517i
$872$		0			0
$873$	−3.41840	+	30.1946i	−0.115695	+	1.02193i
$874$		0			0
$875$	−44.4820	+	27.1785i	−1.50377	+	0.918800i
$876$		0			0
$877$	31.6567	+	16.1299i	1.06897	+	0.544669i	0.897724	−	0.440559i	$-0.145220\pi$
$877$	31.6567	+	16.1299i	1.06897	+	0.544669i	0.171249	+	0.985228i	$0.445220\pi$
$878$		0			0
$879$	−3.92109	−	3.75094i	−0.132255	−	0.126516i
$880$		0			0
$881$	−16.5746	+	22.8130i	−0.558413	+	0.768590i	−0.991124	−	0.132943i	$-0.957557\pi$
$881$	−16.5746	+	22.8130i	−0.558413	+	0.768590i	0.432710	+	0.901533i	$0.357557\pi$
$882$		0			0
$883$	4.01887	+	25.3742i	0.135246	+	0.853908i	0.958262	+	0.285891i	$0.0922895\pi$
$883$	4.01887	+	25.3742i	0.135246	+	0.853908i	−0.823016	+	0.568018i	$0.807711\pi$
$884$		0			0
$885$	2.52353	+	0.981581i	0.0848277	+	0.0329955i
$886$		0			0
$887$	−5.79025	+	2.95028i	−0.194417	+	0.0990606i	−0.548489	−	0.836158i	$-0.684797\pi$
$887$	−5.79025	+	2.95028i	−0.194417	+	0.0990606i	0.354072	+	0.935218i	$0.384797\pi$
$888$		0			0
$889$	−10.1681	+	3.30382i	−0.341028	+	0.110807i
$890$		0			0
$891$	−21.9138	+	9.33879i	−0.734138	+	0.312861i
$892$		0			0
$893$	8.74665	−	8.74665i	0.292695	−	0.292695i
$894$		0			0
$895$	−19.8116	+	12.1287i	−0.662230	+	0.405417i
$896$		0			0
$897$	0.0582078	+	2.62466i	0.00194350	+	0.0876348i
$898$		0			0
$899$	−36.0069			−1.20090
$900$		0			0
$901$	−16.1397			−0.537690
$902$		0			0
$903$	−1.64326	−	74.0965i	−0.0546842	−	2.46578i
$904$		0			0
$905$	22.4540	+	19.1945i	0.746396	+	0.638046i
$906$		0			0
$907$	−10.3156	+	10.3156i	−0.342524	+	0.342524i	−0.857315	−	0.514792i	$-0.827869\pi$
$907$	−10.3156	+	10.3156i	−0.342524	+	0.342524i	0.514792	+	0.857315i	$0.327869\pi$
$908$		0			0
$909$	−0.321074	−	7.23524i	−0.0106494	−	0.239978i
$910$		0			0
$911$	54.8554	−	17.8236i	1.81744	−	0.590522i	0.817548	−	0.575861i	$-0.195333\pi$
$911$	54.8554	−	17.8236i	1.81744	−	0.590522i	0.999893	−	0.0146615i	$-0.00466706\pi$
$912$		0			0
$913$	−1.25484	+	0.639371i	−0.0415290	+	0.0211601i
$914$		0			0
$915$	18.9200	−	4.97961i	0.625477	−	0.164621i
$916$		0			0
$917$	0.764013	+	4.82379i	0.0252299	+	0.159296i
$918$		0			0
$919$	11.8043	−	16.2472i	0.389387	−	0.535945i	−0.568654	−	0.822577i	$-0.692536\pi$
$919$	11.8043	−	16.2472i	0.389387	−	0.535945i	0.958041	+	0.286632i	$0.0925356\pi$
$920$		0			0
$921$	−10.5687	−	10.1101i	−0.348251	−	0.333140i
$922$		0			0
$923$	−13.4466	−	6.85138i	−0.442600	−	0.225516i
$924$		0			0
$925$	2.94845	+	9.10145i	0.0969445	+	0.299254i
$926$		0			0
$927$	41.4632	+	4.69414i	1.36183	+	0.154176i
$928$		0			0
$929$	−9.26961	+	6.73476i	−0.304126	+	0.220960i	−0.729372	−	0.684117i	$-0.760188\pi$
$929$	−9.26961	+	6.73476i	−0.304126	+	0.220960i	0.425246	+	0.905078i	$0.360188\pi$
$930$		0			0
$931$	−15.4388	−	11.2170i	−0.505987	−	0.367621i
$932$		0			0
$933$	−14.5035	−	41.4840i	−0.474823	−	1.35813i
$934$		0			0
$935$	−15.5220	−	37.5197i	−0.507622	−	1.22703i
$936$		0			0
$937$	−15.0819	−	29.5998i	−0.492703	−	0.966984i	−0.994769	−	0.102155i	$-0.967426\pi$
$937$	−15.0819	−	29.5998i	−0.492703	−	0.966984i	0.502065	−	0.864830i	$-0.332574\pi$
$938$		0			0
$939$	−17.0737	−	31.7485i	−0.557180	−	1.03607i
$940$		0			0
$941$	24.7821	+	8.05220i	0.807874	+	0.262494i	0.683697	−	0.729766i	$-0.260371\pi$
$941$	24.7821	+	8.05220i	0.807874	+	0.262494i	0.124177	+	0.992260i	$0.460371\pi$
$942$		0			0
$943$	2.61079	+	2.61079i	0.0850190	+	0.0850190i
$944$		0			0
$945$	−37.8259	−	38.7802i	−1.23048	−	1.26152i
$946$		0			0
$947$	−37.3955	−	5.92286i	−1.21519	−	0.192467i	−0.484262	−	0.874923i	$-0.660912\pi$
$947$	−37.3955	−	5.92286i	−1.21519	−	0.192467i	−0.730927	+	0.682456i	$0.760912\pi$
$948$		0			0
$949$		−	9.02407i		−	0.292934i
$950$		0			0
$951$	−20.4745	+	3.70994i	−0.663931	+	0.120303i
$952$		0			0
$953$	−7.51528	+	47.4496i	−0.243444	+	1.53704i	0.498683	+	0.866785i	$0.333817\pi$
$953$	−7.51528	+	47.4496i	−0.243444	+	1.53704i	−0.742127	+	0.670260i	$0.766183\pi$
$954$		0			0
$955$	37.4729	+	15.5410i	1.21259	+	0.502894i
$956$		0			0
$957$	15.7814	+	10.9396i	0.510139	+	0.353627i
$958$		0			0
$959$	21.5656	−	66.3720i	0.696389	−	2.14326i
$960$		0			0
$961$	13.2552	+	40.7954i	0.427588	+	1.31598i
$962$		0			0
$963$	−36.5556	−	33.4491i	−1.17799	−	1.07788i
$964$		0			0
$965$	−33.8310	−	39.6461i	−1.08906	−	1.27625i
$966$		0			0
$967$	−24.1259	+	3.82116i	−0.775835	+	0.122880i	−0.531782	−	0.846882i	$-0.678477\pi$
$967$	−24.1259	+	3.82116i	−0.775835	+	0.122880i	−0.244054	+	0.969762i	$0.578477\pi$
$968$		0			0
$969$	−6.67951	+	13.8607i	−0.214577	+	0.445270i
$970$		0			0
$971$	1.91914	+	2.64147i	0.0615880	+	0.0847687i	0.838700	−	0.544594i	$-0.183316\pi$
$971$	1.91914	+	2.64147i	0.0615880	+	0.0847687i	−0.777112	+	0.629362i	$0.783316\pi$
$972$		0			0
$973$	17.7056	−	34.7493i	0.567617	−	1.11401i
$974$		0			0
$975$	8.36602	+	23.9964i	0.267927	+	0.768501i
$976$		0			0
$977$	1.06879	−	2.09762i	0.0341937	−	0.0671089i	−0.873278	−	0.487223i	$-0.838010\pi$
$977$	1.06879	−	2.09762i	0.0341937	−	0.0671089i	0.907471	+	0.420114i	$0.138010\pi$
$978$		0			0
$979$	−8.96429	−	12.3383i	−0.286500	−	0.394333i
$980$		0			0
$981$	31.4496	+	8.69756i	1.00411	+	0.277692i
$982$		0			0
$983$	23.4380	−	3.71221i	0.747556	−	0.118401i	0.228978	−	0.973432i	$-0.426462\pi$
$983$	23.4380	−	3.71221i	0.747556	−	0.118401i	0.518578	+	0.855030i	$0.326462\pi$
$984$		0			0
$985$	42.6080	+	10.2490i	1.35760	+	0.326559i
$986$		0			0
$987$	−46.7198	−	61.3941i	−1.48711	−	1.95420i
$988$		0			0
$989$	1.46489	+	4.50847i	0.0465808	+	0.143361i
$990$		0			0
$991$	14.8809	−	45.7986i	0.472706	−	1.45484i	−0.376321	−	0.926489i	$-0.622811\pi$
$991$	14.8809	−	45.7986i	0.472706	−	1.45484i	0.849027	−	0.528350i	$-0.177189\pi$
$992$		0			0
$993$	10.7530	−	15.5122i	0.341235	−	0.492264i
$994$		0			0
$995$	3.01166	−	38.0541i	0.0954759	−	1.20640i
$996$		0			0
$997$	−1.07371	+	6.77915i	−0.0340048	+	0.214698i	−0.998840	−	0.0481589i	$-0.984665\pi$
$997$	−1.07371	+	6.77915i	−0.0340048	+	0.214698i	0.964835	+	0.262857i	$0.0846646\pi$
$998$		0			0
$999$	−8.53915	+	5.09265i	−0.270167	+	0.161124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.x.a.233.6	yes	80
3.2	odd	2	inner	300.2.x.a.233.5	yes	80
25.22	odd	20	inner	300.2.x.a.197.5	✓	80
75.47	even	20	inner	300.2.x.a.197.6	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.197.5	✓	80	25.22	odd	20	inner
300.2.x.a.197.6	yes	80	75.47	even	20	inner
300.2.x.a.233.5	yes	80	3.2	odd	2	inner
300.2.x.a.233.6	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)

\(f(q)\)	\(=\)	\(q+(-0.0384027 - 1.73163i) q^{3} +(-2.22910 - 0.176414i) q^{5} +(3.29686 - 3.29686i) q^{7} +(-2.99705 + 0.132998i) q^{9} +O(q^{10})\)	\(q+(-0.0384027 - 1.73163i) q^{3} +(-2.22910 - 0.176414i) q^{5} +(3.29686 - 3.29686i) q^{7} +(-2.99705 + 0.132998i) q^{9} +(-2.51720 + 0.817889i) q^{11} +(-2.61460 + 1.33221i) q^{13} +(-0.219879 + 3.86674i) q^{15} +(-1.07325 - 6.77623i) q^{17} +(0.761063 - 1.04751i) q^{19} +(-5.83553 - 5.58232i) q^{21} +(0.460230 + 0.234499i) q^{23} +(4.93776 + 0.786487i) q^{25} +(0.345398 + 5.18466i) q^{27} +(3.38873 - 2.46206i) q^{29} +(-6.95448 - 5.05272i) q^{31} +(1.51294 + 4.32744i) q^{33} +(-7.93063 + 6.76741i) q^{35} +(0.868677 + 1.70487i) q^{37} +(2.40729 + 4.47635i) q^{39} +(6.79828 + 2.20889i) q^{41} +(6.48953 + 6.48953i) q^{43} +(6.70418 + 0.232255i) q^{45} +(9.43571 + 1.49447i) q^{47} -14.7386i q^{49} +(-11.6927 + 2.11869i) q^{51} +(0.368009 - 2.32352i) q^{53} +(5.75538 - 1.37909i) q^{55} +(-1.84313 - 1.27765i) q^{57} +(0.216043 - 0.664912i) q^{59} +(-1.56100 - 4.80426i) q^{61} +(-9.44238 + 10.3193i) q^{63} +(6.06323 - 2.50837i) q^{65} +(11.0275 - 1.74659i) q^{67} +(0.388390 - 0.805952i) q^{69} +(3.02291 + 4.16068i) q^{71} +(-1.39613 + 2.74005i) q^{73} +(1.17228 - 8.58055i) q^{75} +(-5.60240 + 10.9953i) q^{77} +(1.41634 + 1.94942i) q^{79} +(8.96462 - 0.797205i) q^{81} +(0.525550 - 0.0832390i) q^{83} +(1.19696 + 15.2942i) q^{85} +(-4.39350 - 5.77346i) q^{87} +(1.78061 + 5.48014i) q^{89} +(-4.22788 + 13.0121i) q^{91} +(-8.48235 + 12.2366i) q^{93} +(-1.88128 + 2.20075i) q^{95} +(1.58455 - 10.0045i) q^{97} +(7.43541 - 2.78604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 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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