LMFDB - Embedded newform 891.2.f.e.487.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(82,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("891.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.f (of order $5$, degree $4$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			487.4
Character	$\chi$	$=$	891.487
Dual form			891.2.f.e.730.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.537447 + 0.390478i) q^{2} +(-0.481658 + 1.48239i) q^{4} +(0.903367 + 0.656335i) q^{5} +(-1.20657 + 3.71344i) q^{7} +(-0.730548 - 2.24840i) q^{8} -0.741796 q^{10} +(1.17816 + 3.10031i) q^{11} +(-2.16655 + 1.57409i) q^{13} +(-0.801549 - 2.46691i) q^{14} +(-1.25142 - 0.909207i) q^{16} +(4.48727 + 3.26019i) q^{17} +(-1.58598 - 4.88115i) q^{19} +(-1.40806 + 1.02301i) q^{20} +(-1.84380 - 1.20620i) q^{22} -2.11438 q^{23} +(-1.15979 - 3.56946i) q^{25} +(0.549758 - 1.69198i) q^{26} +(-4.92362 - 3.57722i) q^{28} +(-0.334678 + 1.03003i) q^{29} +(0.348009 - 0.252843i) q^{31} +5.75580 q^{32} -3.68470 q^{34} +(-3.52724 + 2.56269i) q^{35} +(-2.69024 + 8.27970i) q^{37} +(2.75836 + 2.00407i) q^{38} +(0.815747 - 2.51061i) q^{40} +(0.902044 + 2.77621i) q^{41} -2.23257 q^{43} +(-5.16335 + 0.253209i) q^{44} +(1.13637 - 0.825618i) q^{46} +(-3.96638 - 12.2073i) q^{47} +(-6.67071 - 4.84655i) q^{49} +(2.01712 + 1.46552i) q^{50} +(-1.28988 - 3.96985i) q^{52} +(4.56381 - 3.31581i) q^{53} +(-0.970527 + 3.57399i) q^{55} +9.23074 q^{56} +(-0.222333 - 0.684272i) q^{58} +(0.734030 - 2.25911i) q^{59} +(3.30439 + 2.40078i) q^{61} +(-0.0883065 + 0.271779i) q^{62} +(-0.590604 + 0.429099i) q^{64} -2.99032 q^{65} -9.75169 q^{67} +(-6.99421 + 5.08159i) q^{68} +(0.895028 - 2.75461i) q^{70} +(5.11062 + 3.71308i) q^{71} +(-3.60705 + 11.1014i) q^{73} +(-1.78718 - 5.50038i) q^{74} +7.99967 q^{76} +(-12.9344 + 0.634298i) q^{77} +(-3.65248 + 2.65368i) q^{79} +(-0.533744 - 1.64269i) q^{80} +(-1.56885 - 1.13983i) q^{82} +(0.389949 + 0.283315i) q^{83} +(1.91387 + 5.89030i) q^{85} +(1.19989 - 0.871768i) q^{86} +(6.11002 - 4.91390i) q^{88} -16.0830 q^{89} +(-3.23120 - 9.94461i) q^{91} +(1.01841 - 3.13433i) q^{92} +(6.89838 + 5.01197i) q^{94} +(1.77094 - 5.45040i) q^{95} +(-6.48480 + 4.71148i) q^{97} +5.47762 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28}+ \cdots + 164 q^{98}+O(q^{100}) $ 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8 - 4 * q^10 - 2 * q^11 + 11 * q^13 - 10 * q^14 + 9 * q^16 + 10 * q^17 + 4 * q^19 - 45 * q^20 + 16 * q^22 + 20 * q^23 - 11 * q^25 + 6 * q^26 - 27 * q^28 - 23 * q^29 - 3 * q^31 + 18 * q^32 - 8 * q^34 - 9 * q^35 - 21 * q^37 - q^38 + 25 * q^40 + 10 * q^41 + 8 * q^43 - 19 * q^44 - 9 * q^46 - 34 * q^47 - q^49 + 27 * q^52 - 2 * q^53 + 9 * q^55 + 114 * q^56 - q^58 - 16 * q^59 + 3 * q^61 - 92 * q^62 + 13 * q^64 + 84 * q^65 - 10 * q^67 - 23 * q^68 + 46 * q^70 + 24 * q^71 - 20 * q^73 + 68 * q^74 - 16 * q^76 - 26 * q^77 - 19 * q^79 + 28 * q^80 + 47 * q^82 + 7 * q^83 - 25 * q^85 - 77 * q^86 - 18 * q^88 + 28 * q^89 + 10 * q^91 + 50 * q^92 + 63 * q^94 - 77 * q^95 + 33 * q^97 + 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.537447	+	0.390478i	−0.380032	+	0.276109i	−0.761359	−	0.648331i	$-0.775467\pi$
$2$	−0.537447	+	0.390478i	−0.380032	+	0.276109i	0.381327	+	0.924440i	$0.375467\pi$
$3$		0			0
$3$		0			0
$4$	−0.481658	+	1.48239i	−0.240829	+	0.741196i
$5$	0.903367	+	0.656335i	0.403998	+	0.293522i	0.771168	−	0.636632i	$-0.219673\pi$
$5$	0.903367	+	0.656335i	0.403998	+	0.293522i	−0.367169	+	0.930154i	$0.619673\pi$
$6$		0			0
$7$	−1.20657	+	3.71344i	−0.456041	+	1.40355i	0.413869	+	0.910337i	$0.364177\pi$
$7$	−1.20657	+	3.71344i	−0.456041	+	1.40355i	−0.869909	+	0.493212i	$0.835823\pi$
$8$	−0.730548	−	2.24840i	−0.258288	−	0.794928i
$9$		0			0
$10$	−0.741796			−0.234576
$11$	1.17816	+	3.10031i	0.355230	+	0.934779i
$11$	1.17816	+	3.10031i	0.355230	+	0.934779i
$12$		0			0
$13$	−2.16655	+	1.57409i	−0.600893	+	0.436574i	−0.846196	−	0.532872i	$-0.821113\pi$
$13$	−2.16655	+	1.57409i	−0.600893	+	0.436574i	0.245303	+	0.969447i	$0.421113\pi$
$14$	−0.801549	−	2.46691i	−0.214223	−	0.659311i
$15$		0			0
$16$	−1.25142	−	0.909207i	−0.312854	−	0.227302i
$17$	4.48727	+	3.26019i	1.08832	+	0.790713i	0.979115	−	0.203306i	$-0.0651688\pi$
$17$	4.48727	+	3.26019i	1.08832	+	0.790713i	0.109207	+	0.994019i	$0.465169\pi$
$18$		0			0
$19$	−1.58598	−	4.88115i	−0.363849	−	1.11981i	−0.950699	−	0.310116i	$-0.899632\pi$
$19$	−1.58598	−	4.88115i	−0.363849	−	1.11981i	0.586850	−	0.809696i	$-0.300368\pi$
$20$	−1.40806	+	1.02301i	−0.314852	+	0.228753i
$21$		0			0
$22$	−1.84380	−	1.20620i	−0.393100	−	0.257164i
$23$	−2.11438			−0.440878			−0.220439	−	0.975401i	$-0.570749\pi$
$23$	−2.11438			−0.440878			−0.220439	+	0.975401i	$0.570749\pi$
$24$		0			0
$25$	−1.15979	−	3.56946i	−0.231958	−	0.713892i
$26$	0.549758	−	1.69198i	0.107816	−	0.331825i
$27$		0			0
$28$	−4.92362	−	3.57722i	−0.930476	−	0.676030i
$29$	−0.334678	+	1.03003i	−0.0621481	+	0.191272i	−0.977310	−	0.211814i	$-0.932063\pi$
$29$	−0.334678	+	1.03003i	−0.0621481	+	0.191272i	0.915162	+	0.403087i	$0.132063\pi$
$30$		0			0
$31$	0.348009	−	0.252843i	0.0625042	−	0.0454120i	−0.556094	−	0.831119i	$-0.687701\pi$
$31$	0.348009	−	0.252843i	0.0625042	−	0.0454120i	0.618599	+	0.785707i	$0.287701\pi$
$32$	5.75580			1.01749
$33$		0			0
$34$	−3.68470			−0.631921
$35$	−3.52724	+	2.56269i	−0.596212	+	0.433173i
$36$		0			0
$37$	−2.69024	+	8.27970i	−0.442273	+	1.36118i	0.443175	+	0.896435i	$0.353852\pi$
$37$	−2.69024	+	8.27970i	−0.442273	+	1.36118i	−0.885447	+	0.464740i	$0.846148\pi$
$38$	2.75836	+	2.00407i	0.447465	+	0.325102i
$39$		0			0
$40$	0.815747	−	2.51061i	0.128981	−	0.396962i
$41$	0.902044	+	2.77621i	0.140876	+	0.433571i	0.996458	−	0.0840968i	$-0.0268005\pi$
$41$	0.902044	+	2.77621i	0.140876	+	0.433571i	−0.855582	+	0.517667i	$0.826800\pi$
$42$		0			0
$43$	−2.23257			−0.340463			−0.170232	−	0.985404i	$-0.554452\pi$
$43$	−2.23257			−0.340463			−0.170232	+	0.985404i	$0.554452\pi$
$44$	−5.16335	+	0.253209i	−0.778404	+	0.0381728i
$45$		0			0
$46$	1.13637	−	0.825618i	0.167548	−	0.121731i
$47$	−3.96638	−	12.2073i	−0.578556	−	1.78061i	−0.623739	−	0.781633i	$-0.714387\pi$
$47$	−3.96638	−	12.2073i	−0.578556	−	1.78061i	0.0451833	−	0.998979i	$-0.485613\pi$
$48$		0			0
$49$	−6.67071	−	4.84655i	−0.952958	−	0.692365i
$50$	2.01712	+	1.46552i	0.285264	+	0.207256i
$51$		0			0
$52$	−1.28988	−	3.96985i	−0.178875	−	0.550519i
$53$	4.56381	−	3.31581i	0.626888	−	0.455461i	−0.228433	−	0.973560i	$-0.573360\pi$
$53$	4.56381	−	3.31581i	0.626888	−	0.455461i	0.855321	+	0.518099i	$0.173360\pi$
$54$		0			0
$55$	−0.970527	+	3.57399i	−0.130866	+	0.481917i
$56$	9.23074			1.23351
$57$		0			0
$58$	−0.222333	−	0.684272i	−0.0291938	−	0.0898493i
$59$	0.734030	−	2.25911i	0.0955625	−	0.294111i	−0.891837	−	0.452356i	$-0.850584\pi$
$59$	0.734030	−	2.25911i	0.0955625	−	0.294111i	0.987400	+	0.158245i	$0.0505836\pi$
$60$		0			0
$61$	3.30439	+	2.40078i	0.423084	+	0.307389i	0.778878	−	0.627176i	$-0.215789\pi$
$61$	3.30439	+	2.40078i	0.423084	+	0.307389i	−0.355793	+	0.934565i	$0.615789\pi$
$62$	−0.0883065	+	0.271779i	−0.0112149	+	0.0345160i
$63$		0			0
$64$	−0.590604	+	0.429099i	−0.0738255	+	0.0536374i
$65$	−2.99032			−0.370904
$66$		0			0
$67$	−9.75169			−1.19136			−0.595679	−	0.803223i	$-0.703117\pi$
$67$	−9.75169			−1.19136			−0.595679	+	0.803223i	$0.703117\pi$
$68$	−6.99421	+	5.08159i	−0.848172	+	0.616233i
$69$		0			0
$70$	0.895028	−	2.75461i	0.106976	−	0.329239i
$71$	5.11062	+	3.71308i	0.606519	+	0.440662i	0.848187	−	0.529697i	$-0.177694\pi$
$71$	5.11062	+	3.71308i	0.606519	+	0.440662i	−0.241668	+	0.970359i	$0.577694\pi$
$72$		0			0
$73$	−3.60705	+	11.1014i	−0.422174	+	1.29932i	0.483501	+	0.875344i	$0.339365\pi$
$73$	−3.60705	+	11.1014i	−0.422174	+	1.29932i	−0.905675	+	0.423973i	$0.860635\pi$
$74$	−1.78718	−	5.50038i	−0.207756	−	0.639406i
$75$		0			0
$76$	7.99967			0.917625
$77$	−12.9344	+	0.634298i	−1.47401	+	0.0722850i
$78$		0			0
$79$	−3.65248	+	2.65368i	−0.410936	+	0.298562i	−0.773980	−	0.633209i	$-0.781737\pi$
$79$	−3.65248	+	2.65368i	−0.410936	+	0.298562i	0.363045	+	0.931772i	$0.381737\pi$
$80$	−0.533744	−	1.64269i	−0.0596744	−	0.183659i
$81$		0			0
$82$	−1.56885	−	1.13983i	−0.173250	−	0.125874i
$83$	0.389949	+	0.283315i	0.0428025	+	0.0310978i	0.608981	−	0.793185i	$-0.291579\pi$
$83$	0.389949	+	0.283315i	0.0428025	+	0.0310978i	−0.566178	+	0.824283i	$0.691579\pi$
$84$		0			0
$85$	1.91387	+	5.89030i	0.207589	+	0.638893i
$86$	1.19989	−	0.871768i	0.129387	−	0.0940052i
$87$		0			0
$88$	6.11002	−	4.91390i	0.651330	−	0.523824i
$89$	−16.0830			−1.70480			−0.852399	−	0.522891i	$-0.824853\pi$
$89$	−16.0830			−1.70480			−0.852399	+	0.522891i	$0.824853\pi$
$90$		0			0
$91$	−3.23120	−	9.94461i	−0.338722	−	1.04248i
$92$	1.01841	−	3.13433i	0.106176	−	0.326777i
$93$		0			0
$94$	6.89838	+	5.01197i	0.711513	+	0.516945i
$95$	1.77094	−	5.45040i	0.181695	−	0.559199i
$96$		0			0
$97$	−6.48480	+	4.71148i	−0.658432	+	0.478379i	−0.866133	−	0.499814i	$-0.833402\pi$
$97$	−6.48480	+	4.71148i	−0.658432	+	0.478379i	0.207701	+	0.978192i	$0.433402\pi$
$98$	5.47762			0.553323
$99$		0			0
$100$	5.84996			0.584996
$101$	1.42493	−	1.03527i	0.141786	−	0.103014i	−0.514631	−	0.857412i	$-0.672071\pi$
$101$	1.42493	−	1.03527i	0.141786	−	0.103014i	0.656417	+	0.754398i	$0.272071\pi$
$102$		0			0
$103$	0.830534	−	2.55612i	0.0818350	−	0.251862i	−0.901765	−	0.432227i	$-0.857728\pi$
$103$	0.830534	−	2.55612i	0.0818350	−	0.251862i	0.983600	+	0.180365i	$0.0577279\pi$
$104$	5.12195	+	3.72131i	0.502248	+	0.364905i
$105$		0			0
$106$	−1.15806	+	3.56414i	−0.112481	+	0.346179i
$107$	3.17558	+	9.77342i	0.306995	+	0.944833i	0.978925	+	0.204219i	$0.0654653\pi$
$107$	3.17558	+	9.77342i	0.306995	+	0.944833i	−0.671931	+	0.740614i	$0.734535\pi$
$108$		0			0
$109$	2.36284			0.226319			0.113160	−	0.993577i	$-0.463903\pi$
$109$	2.36284			0.226319			0.113160	+	0.993577i	$0.463903\pi$
$110$	−0.873957	−	2.29980i	−0.0833285	−	0.219277i
$111$		0			0
$112$	4.88620	−	3.55004i	0.461703	−	0.335447i
$113$	−0.473548	−	1.45743i	−0.0445476	−	0.137103i	0.926309	−	0.376765i	$-0.122964\pi$
$113$	−0.473548	−	1.45743i	−0.0445476	−	0.137103i	−0.970857	+	0.239661i	$0.922964\pi$
$114$		0			0
$115$	−1.91006	−	1.38774i	−0.178114	−	0.129407i
$116$	−1.36571	−	0.992247i	−0.126803	−	0.0921279i
$117$		0			0
$118$	0.487631	+	1.50077i	0.0448901	+	0.138157i
$119$	−17.5207	+	12.7296i	−1.60612	+	1.16692i
$120$		0			0
$121$	−8.22386	+	7.30535i	−0.747624	+	0.664123i
$122$	−2.71339			−0.245658
$123$		0			0
$124$	0.207191	+	0.637669i	0.0186063	+	0.0572644i
$125$	3.02032	−	9.29560i	0.270146	−	0.831424i
$126$		0			0
$127$	6.19006	+	4.49734i	0.549279	+	0.399074i	0.827519	−	0.561437i	$-0.189751\pi$
$127$	6.19006	+	4.49734i	0.549279	+	0.399074i	−0.278241	+	0.960511i	$0.589751\pi$
$128$	−3.40742	+	10.4869i	−0.301176	+	0.926924i
$129$		0			0
$130$	1.60714	−	1.16765i	0.140955	−	0.102410i
$131$	5.35912			0.468229			0.234114	−	0.972209i	$-0.424781\pi$
$131$	5.35912			0.468229			0.234114	+	0.972209i	$0.424781\pi$
$132$		0			0
$133$	20.0394			1.73764
$134$	5.24101	−	3.80782i	0.452754	−	0.328945i
$135$		0			0
$136$	4.05203	−	12.4709i	0.347459	−	1.06937i
$137$	13.5358	+	9.83435i	1.15644	+	0.840205i	0.989324	−	0.145731i	$-0.0465535\pi$
$137$	13.5358	+	9.83435i	1.15644	+	0.840205i	0.167119	+	0.985937i	$0.446554\pi$
$138$		0			0
$139$	4.24593	−	13.0676i	0.360135	−	1.10838i	−0.592837	−	0.805323i	$-0.701992\pi$
$139$	4.24593	−	13.0676i	0.360135	−	1.10838i	0.952972	−	0.303059i	$-0.0980079\pi$
$140$	−2.09998	−	6.46308i	−0.177481	−	0.546230i
$141$		0			0
$142$	−4.19656			−0.352168
$143$	−7.43273	−	4.86244i	−0.621556	−	0.406618i
$144$		0			0
$145$	−0.978384	+	0.710837i	−0.0812503	+	0.0590318i
$146$	−2.39624	−	7.37487i	−0.198314	−	0.610348i
$147$		0			0
$148$	−10.9780	−	7.97597i	−0.902385	−	0.655621i
$149$	4.49786	+	3.26788i	0.368479	+	0.267716i	0.756580	−	0.653901i	$-0.226869\pi$
$149$	4.49786	+	3.26788i	0.368479	+	0.267716i	−0.388101	+	0.921617i	$0.626869\pi$
$150$		0			0
$151$	−0.0506502	−	0.155885i	−0.00412186	−	0.0126858i	0.948974	−	0.315353i	$-0.102123\pi$
$151$	−0.0506502	−	0.155885i	−0.00412186	−	0.0126858i	−0.953096	+	0.302667i	$0.902123\pi$
$152$	−9.81611	+	7.13182i	−0.796192	+	0.578467i
$153$		0			0
$154$	6.70385	−	5.39148i	0.540211	−	0.434458i
$155$	0.480329			0.0385810
$156$		0			0
$157$	7.37099	+	22.6856i	0.588269	+	1.81051i	0.585727	+	0.810509i	$0.300809\pi$
$157$	7.37099	+	22.6856i	0.588269	+	1.81051i	0.00254199	+	0.999997i	$0.499191\pi$
$158$	0.926808	−	2.85242i	0.0737329	−	0.226926i
$159$		0			0
$160$	5.19960	+	3.77773i	0.411065	+	0.298656i
$161$	2.55114	−	7.85161i	0.201058	−	0.618794i
$162$		0			0
$163$	3.39466	−	2.46636i	0.265890	−	0.193180i	−0.446850	−	0.894609i	$-0.647454\pi$
$163$	3.39466	−	2.46636i	0.265890	−	0.193180i	0.712740	+	0.701429i	$0.247454\pi$
$164$	−4.54990			−0.355288
$165$		0			0
$166$	−0.320205			−0.0248527
$167$	12.8151	−	9.31075i	0.991666	−	0.720488i	0.0313807	−	0.999508i	$-0.490010\pi$
$167$	12.8151	−	9.31075i	0.991666	−	0.720488i	0.960285	+	0.279020i	$0.0900096\pi$
$168$		0			0
$169$	−1.80104	+	5.54304i	−0.138542	+	0.426387i
$170$	−3.32864	−	2.41840i	−0.255295	−	0.185482i
$171$		0			0
$172$	1.07533	−	3.30954i	0.0819935	−	0.252350i
$173$	0.804337	+	2.47549i	0.0611526	+	0.188208i	0.976966	−	0.213396i	$-0.0684526\pi$
$173$	0.804337	+	2.47549i	0.0611526	+	0.188208i	−0.915813	+	0.401605i	$0.868453\pi$
$174$		0			0
$175$	14.6543			1.10776
$176$	1.34445	−	4.95097i	0.101342	−	0.373194i
$177$		0			0
$178$	8.64378	−	6.28007i	0.647878	−	0.470711i
$179$	−2.34483	−	7.21663i	−0.175261	−	0.539396i	0.824385	−	0.566030i	$-0.191521\pi$
$179$	−2.34483	−	7.21663i	−0.175261	−	0.539396i	−0.999645	+	0.0266334i	$0.991521\pi$
$180$		0			0
$181$	1.94179	+	1.41080i	0.144332	+	0.104864i	0.657608	−	0.753360i	$-0.271568\pi$
$181$	1.94179	+	1.41080i	0.144332	+	0.104864i	−0.513276	+	0.858224i	$0.671568\pi$
$182$	5.61975	+	4.08298i	0.416563	+	0.302651i
$183$		0			0
$184$	1.54465	+	4.75396i	0.113873	+	0.350466i
$185$	−7.86453	+	5.71392i	−0.578212	+	0.420095i
$186$		0			0
$187$	−4.82087	+	17.7530i	−0.352537	+	1.29823i
$188$	20.0064			1.45911
$189$		0			0
$190$	1.17647	+	3.62081i	0.0853504	+	0.262681i
$191$	5.10442	−	15.7098i	0.369343	−	1.13672i	−0.577874	−	0.816126i	$-0.696118\pi$
$191$	5.10442	−	15.7098i	0.369343	−	1.13672i	0.947217	−	0.320594i	$-0.103882\pi$
$192$		0			0
$193$	6.58132	+	4.78161i	0.473734	+	0.344188i	0.798895	−	0.601471i	$-0.205418\pi$
$193$	6.58132	+	4.78161i	0.473734	+	0.344188i	−0.325161	+	0.945659i	$0.605418\pi$
$194$	1.64550	−	5.06434i	0.118140	−	0.363598i
$195$		0			0
$196$	10.3975	−	7.55422i	0.742678	−	0.539587i
$197$	22.9072			1.63207			0.816035	−	0.578003i	$-0.196168\pi$
$197$	22.9072			1.63207			0.816035	+	0.578003i	$0.196168\pi$
$198$		0			0
$199$	9.27177			0.657259			0.328629	−	0.944459i	$-0.393413\pi$
$199$	9.27177			0.657259			0.328629	+	0.944459i	$0.393413\pi$
$200$	−7.17828	+	5.21532i	−0.507581	+	0.368779i
$201$		0			0
$202$	−0.361574	+	1.11281i	−0.0254402	+	0.0782970i
$203$	−3.42115	−	2.48561i	−0.240118	−	0.174456i
$204$		0			0
$205$	−1.00724	+	3.09998i	−0.0703489	+	0.216512i
$206$	0.551741	+	1.69808i	0.0384416	+	0.118311i
$207$		0			0
$208$	4.14243			0.287226
$209$	13.2645	−	10.6678i	0.917527	−	0.737909i
$210$		0			0
$211$	−3.40643	+	2.47491i	−0.234508	+	0.170380i	−0.698833	−	0.715285i	$-0.746297\pi$
$211$	−3.40643	+	2.47491i	−0.234508	+	0.170380i	0.464325	+	0.885665i	$0.346297\pi$
$212$	2.71712	+	8.36244i	0.186613	+	0.574335i
$213$		0			0
$214$	−5.52301	−	4.01270i	−0.377545	−	0.274303i
$215$	−2.01683	−	1.46531i	−0.137547	−	0.0999334i
$216$		0			0
$217$	0.519021	+	1.59738i	0.0352335	+	0.108437i
$218$	−1.26990	+	0.922637i	−0.0860086	+	0.0624889i
$219$		0			0
$220$	−4.83059	−	3.16014i	−0.325678	−	0.213057i
$221$	−14.8537			−0.999170
$222$		0			0
$223$	−2.11957	−	6.52335i	−0.141937	−	0.436836i	0.854668	−	0.519175i	$-0.173761\pi$
$223$	−2.11957	−	6.52335i	−0.141937	−	0.436836i	−0.996604	+	0.0823393i	$0.973761\pi$
$224$	−6.94477	+	21.3738i	−0.464017	+	1.42810i
$225$		0			0
$226$	0.823601	+	0.598381i	0.0547851	+	0.0398037i
$227$	−8.69262	+	26.7531i	−0.576950	+	1.77567i	0.0524933	+	0.998621i	$0.483283\pi$
$227$	−8.69262	+	26.7531i	−0.576950	+	1.77567i	−0.629443	+	0.777047i	$0.716717\pi$
$228$		0			0
$229$	11.3543	−	8.24939i	0.750314	−	0.545135i	−0.145610	−	0.989342i	$-0.546515\pi$
$229$	11.3543	−	8.24939i	0.750314	−	0.545135i	0.895924	+	0.444207i	$0.146515\pi$
$230$	1.56844			0.103420
$231$		0			0
$232$	2.56042			0.168100
$233$	−11.7385	+	8.52854i	−0.769017	+	0.558723i	−0.901663	−	0.432440i	$-0.857653\pi$
$233$	−11.7385	+	8.52854i	−0.769017	+	0.558723i	0.132646	+	0.991163i	$0.457653\pi$
$234$		0			0
$235$	4.42895	−	13.6309i	0.288913	−	0.889182i
$236$	2.99534	+	2.17624i	0.194980	+	0.141661i
$237$		0			0
$238$	4.44585	−	13.6829i	0.288181	−	0.886931i
$239$	7.77120	+	23.9173i	0.502677	+	1.54708i	0.804641	+	0.593762i	$0.202358\pi$
$239$	7.77120	+	23.9173i	0.502677	+	1.54708i	−0.301964	+	0.953319i	$0.597642\pi$
$240$		0			0
$241$	17.7422			1.14288			0.571438	−	0.820645i	$-0.306386\pi$
$241$	17.7422			1.14288			0.571438	+	0.820645i	$0.306386\pi$
$242$	1.56731	−	7.13747i	0.100750	−	0.458814i
$243$		0			0
$244$	−5.15048	+	3.74205i	−0.329726	+	0.239560i
$245$	−2.84514	−	8.75643i	−0.181769	−	0.559428i
$246$		0			0
$247$	11.1195	+	8.07877i	0.707515	+	0.514040i
$248$	−0.822729	−	0.597747i	−0.0522433	−	0.0379570i
$249$		0			0
$250$	2.00646	+	6.17526i	0.126900	+	0.390558i
$251$	−17.6993	+	12.8593i	−1.11717	+	0.811670i	−0.983777	−	0.179394i	$-0.942586\pi$
$251$	−17.6993	+	12.8593i	−1.11717	+	0.811670i	−0.133390	+	0.991064i	$0.542586\pi$
$252$		0			0
$253$	−2.49108	−	6.55523i	−0.156613	−	0.412124i
$254$	−5.08294			−0.318932
$255$		0			0
$256$	−2.71480	−	8.35529i	−0.169675	−	0.522205i
$257$	−1.59568	+	4.91099i	−0.0995356	+	0.306339i	−0.988409	−	0.151814i	$-0.951489\pi$
$257$	−1.59568	+	4.91099i	−0.0995356	+	0.306339i	0.888874	+	0.458153i	$0.151489\pi$
$258$		0			0
$259$	−27.5002	−	19.9801i	−1.70878	−	1.24150i
$260$	1.44031	−	4.43283i	0.0893244	−	0.274912i
$261$		0			0
$262$	−2.88024	+	2.09262i	−0.177942	+	0.129282i
$263$	27.8981			1.72027			0.860135	−	0.510066i	$-0.170379\pi$
$263$	27.8981			1.72027			0.860135	+	0.510066i	$0.170379\pi$
$264$		0			0
$265$	6.29908			0.386949
$266$	−10.7701	+	7.82496i	−0.660359	+	0.479779i
$267$		0			0
$268$	4.69698	−	14.4558i	0.286914	−	0.883029i
$269$	2.44290	+	1.77487i	0.148946	+	0.108216i	0.659763	−	0.751474i	$-0.270657\pi$
$269$	2.44290	+	1.77487i	0.148946	+	0.108216i	−0.510816	+	0.859690i	$0.670657\pi$
$270$		0			0
$271$	−7.84125	+	24.1329i	−0.476322	+	1.46597i	0.367845	+	0.929887i	$0.380096\pi$
$271$	−7.84125	+	24.1329i	−0.476322	+	1.46597i	−0.844167	+	0.536081i	$0.819904\pi$
$272$	−2.65125	−	8.15971i	−0.160756	−	0.494755i
$273$		0			0
$274$	−11.1149			−0.671474
$275$	9.70002	−	7.80111i	0.584933	−	0.470425i
$276$		0			0
$277$	8.54677	−	6.20959i	0.513525	−	0.373098i	−0.300634	−	0.953740i	$-0.597198\pi$
$277$	8.54677	−	6.20959i	0.513525	−	0.373098i	0.814159	+	0.580642i	$0.197198\pi$
$278$	2.82066	+	8.68109i	0.169172	+	0.520657i
$279$		0			0
$280$	8.33875	+	6.05845i	0.498335	+	0.362062i
$281$	−18.2599	−	13.2666i	−1.08930	−	0.791420i	−0.110016	−	0.993930i	$-0.535090\pi$
$281$	−18.2599	−	13.2666i	−1.08930	−	0.791420i	−0.979280	+	0.202510i	$0.935090\pi$
$282$		0			0
$283$	−1.81616	−	5.58958i	−0.107960	−	0.332266i	0.882454	−	0.470399i	$-0.155890\pi$
$283$	−1.81616	−	5.58958i	−0.107960	−	0.332266i	−0.990414	+	0.138133i	$0.955890\pi$
$284$	−7.96581	+	5.78750i	−0.472684	+	0.343425i
$285$		0			0
$286$	5.89337	−	0.289010i	0.348482	−	0.0170895i
$287$	−11.3977			−0.672782
$288$		0			0
$289$	4.25344	+	13.0907i	0.250202	+	0.770044i
$290$	0.248263	−	0.764074i	0.0145785	−	0.0448680i
$291$		0			0
$292$	−14.7192	−	10.6941i	−0.861376	−	0.625827i
$293$	−2.19220	+	6.74690i	−0.128070	+	0.394158i	−0.994448	−	0.105230i	$-0.966442\pi$
$293$	−2.19220	+	6.74690i	−0.128070	+	0.394158i	0.866378	+	0.499389i	$0.166442\pi$
$294$		0			0
$295$	2.14583	−	1.55904i	0.124935	−	0.0907707i
$296$	20.5814			1.19627
$297$		0			0
$298$	−3.69339			−0.213953
$299$	4.58091	−	3.32822i	0.264921	−	0.192476i
$300$		0			0
$301$	2.69375	−	8.29051i	0.155265	−	0.477857i
$302$	0.0880915	+	0.0640022i	0.00506910	+	0.00368292i
$303$		0			0
$304$	−2.45325	+	7.55033i	−0.140704	+	0.433041i
$305$	1.40936	+	4.33757i	0.0806999	+	0.248369i
$306$		0			0
$307$	−18.5370			−1.05796			−0.528981	−	0.848633i	$-0.677426\pi$
$307$	−18.5370			−1.05796			−0.528981	+	0.848633i	$0.677426\pi$
$308$	5.28966	−	19.4793i	0.301406	−	1.10994i
$309$		0			0
$310$	−0.258151	+	0.187558i	−0.0146620	+	0.0106526i
$311$	−2.12487	−	6.53969i	−0.120491	−	0.370832i	0.872562	−	0.488503i	$-0.162457\pi$
$311$	−2.12487	−	6.53969i	−0.120491	−	0.370832i	−0.993053	+	0.117672i	$0.962457\pi$
$312$		0			0
$313$	20.4890	+	14.8861i	1.15811	+	0.841414i	0.989537	−	0.144276i	$-0.0460853\pi$
$313$	20.4890	+	14.8861i	1.15811	+	0.841414i	0.168569	+	0.985690i	$0.446085\pi$
$314$	−12.8197	−	9.31407i	−0.723459	−	0.525624i
$315$		0			0
$316$	−2.17455	−	6.69256i	−0.122328	−	0.376486i
$317$	8.88241	−	6.45345i	0.498886	−	0.362462i	−0.309705	−	0.950833i	$-0.600230\pi$
$317$	8.88241	−	6.45345i	0.498886	−	0.362462i	0.808591	+	0.588371i	$0.200230\pi$
$318$		0			0
$319$	−3.58773	+	0.175942i	−0.200874	+	0.00985083i
$320$	−0.815165			−0.0455691
$321$		0			0
$322$	1.69478	+	5.21599i	0.0944463	+	0.290676i
$323$	8.79675	−	27.0736i	0.489464	−	1.50642i
$324$		0			0
$325$	8.13140	+	5.90780i	0.451049	+	0.327706i
$326$	−0.861386	+	2.65107i	−0.0477078	+	0.146829i
$327$		0			0
$328$	5.58302	−	4.05630i	0.308271	−	0.223972i
$329$	50.1166			2.76302
$330$		0			0
$331$	−3.71025			−0.203934			−0.101967	−	0.994788i	$-0.532514\pi$
$331$	−3.71025			−0.203934			−0.101967	+	0.994788i	$0.532514\pi$
$332$	−0.607805	+	0.441596i	−0.0333576	+	0.0242357i
$333$		0			0
$334$	−3.25182	+	10.0081i	−0.177931	+	0.547617i
$335$	−8.80935	−	6.40037i	−0.481306	−	0.349690i
$336$		0			0
$337$	−9.94885	+	30.6194i	−0.541948	+	1.66795i	0.186189	+	0.982514i	$0.440386\pi$
$337$	−9.94885	+	30.6194i	−0.541948	+	1.66795i	−0.728137	+	0.685432i	$0.759614\pi$
$338$	−1.19647	−	3.68235i	−0.0650793	−	0.200294i
$339$		0			0
$340$	−9.65356			−0.523538
$341$	1.19390	+	0.781045i	0.0646535	+	0.0422960i
$342$		0			0
$343$	3.93417	−	2.85834i	0.212425	−	0.154336i
$344$	1.63100	+	5.01970i	0.0879375	+	0.270644i
$345$		0			0
$346$	−1.39891	−	1.01637i	−0.0752061	−	0.0546404i
$347$	−17.4121	−	12.6506i	−0.934728	−	0.679120i	0.0124177	−	0.999923i	$-0.496047\pi$
$347$	−17.4121	−	12.6506i	−0.934728	−	0.679120i	−0.947146	+	0.320803i	$0.896047\pi$
$348$		0			0
$349$	−5.19765	−	15.9967i	−0.278224	−	0.856285i	−0.988348	−	0.152209i	$-0.951361\pi$
$349$	−5.19765	−	15.9967i	−0.278224	−	0.856285i	0.710124	−	0.704076i	$-0.248639\pi$
$350$	−7.87593	+	5.72219i	−0.420986	+	0.305864i
$351$		0			0
$352$	6.78127	+	17.8448i	0.361443	+	0.951129i
$353$	−3.13085			−0.166639			−0.0833193	−	0.996523i	$-0.526552\pi$
$353$	−3.13085			−0.166639			−0.0833193	+	0.996523i	$0.526552\pi$
$354$		0			0
$355$	2.17974	+	6.70855i	0.115689	+	0.356053i
$356$	7.74653	−	23.8414i	0.410565	−	1.26359i
$357$		0			0
$358$	4.07815	+	2.96295i	0.215537	+	0.156597i
$359$	−2.62315	+	8.07323i	−0.138445	+	0.426089i	−0.996110	−	0.0881197i	$-0.971914\pi$
$359$	−2.62315	+	8.07323i	−0.138445	+	0.426089i	0.857665	+	0.514208i	$0.171914\pi$
$360$		0			0
$361$	−5.93893	+	4.31489i	−0.312575	+	0.227099i
$362$	−1.59449			−0.0838048
$363$		0			0
$364$	16.2981			0.854254
$365$	−10.5447	+	7.66118i	−0.551935	+	0.401004i
$366$		0			0
$367$	−3.40258	+	10.4720i	−0.177613	+	0.546637i	−0.999743	−	0.0226630i	$-0.992786\pi$
$367$	−3.40258	+	10.4720i	−0.177613	+	0.546637i	0.822130	+	0.569300i	$0.192786\pi$
$368$	2.64596	+	1.92241i	0.137930	+	0.100212i
$369$		0			0
$370$	1.99561	−	6.14185i	0.103747	−	0.319300i
$371$	6.80648	+	20.9482i	0.353375	+	1.08758i
$372$		0			0
$373$	11.0068			0.569912			0.284956	−	0.958541i	$-0.408021\pi$
$373$	11.0068			0.569912			0.284956	+	0.958541i	$0.408021\pi$
$374$	−4.34118	−	11.4237i	−0.224477	−	0.590706i
$375$		0			0
$376$	−24.5491	+	17.8360i	−1.26602	+	0.919820i
$377$	−0.896269	−	2.75843i	−0.0461602	−	0.142067i
$378$		0			0
$379$	−20.5384	−	14.9220i	−1.05499	−	0.766492i	−0.0818315	−	0.996646i	$-0.526077\pi$
$379$	−20.5384	−	14.9220i	−1.05499	−	0.766492i	−0.973154	+	0.230154i	$0.926077\pi$
$380$	7.22664	+	5.25046i	0.370719	+	0.269343i
$381$		0			0
$382$	3.39097	+	10.4363i	0.173497	+	0.533969i
$383$	−9.80103	+	7.12086i	−0.500809	+	0.363859i	−0.809326	−	0.587360i	$-0.800167\pi$
$383$	−9.80103	+	7.12086i	−0.500809	+	0.363859i	0.308517	+	0.951219i	$0.400167\pi$
$384$		0			0
$385$	−12.1008	−	7.91626i	−0.616713	−	0.403450i
$386$	−5.40422			−0.275068
$387$		0			0
$388$	−3.86080	−	11.8823i	−0.196003	−	0.603234i
$389$	−4.43473	+	13.6487i	−0.224850	+	0.692016i	0.773457	+	0.633849i	$0.218526\pi$
$389$	−4.43473	+	13.6487i	−0.224850	+	0.692016i	−0.998307	+	0.0581676i	$0.981474\pi$
$390$		0			0
$391$	−9.48778	−	6.89328i	−0.479818	−	0.348608i
$392$	−6.02370	+	18.5390i	−0.304243	+	0.936362i
$393$		0			0
$394$	−12.3114	+	8.94475i	−0.620239	+	0.450630i
$395$	−5.04123			−0.253652
$396$		0			0
$397$	−5.03882			−0.252891			−0.126446	−	0.991974i	$-0.540357\pi$
$397$	−5.03882			−0.252891			−0.126446	+	0.991974i	$0.540357\pi$
$398$	−4.98308	+	3.62042i	−0.249779	+	0.181475i
$399$		0			0
$400$	−1.79400	+	5.52136i	−0.0897000	+	0.276068i
$401$	−14.7243	−	10.6978i	−0.735294	−	0.534223i	0.155940	−	0.987767i	$-0.450159\pi$
$401$	−14.7243	−	10.6978i	−0.735294	−	0.534223i	−0.891234	+	0.453544i	$0.850159\pi$
$402$		0			0
$403$	−0.355980	+	1.09560i	−0.0177327	+	0.0545755i
$404$	0.848352	+	2.61096i	0.0422071	+	0.129900i
$405$		0			0
$406$	2.80926			0.139421
$407$	−28.8392	+	1.41427i	−1.42951	+	0.0701027i
$408$		0			0
$409$	−13.2925	+	9.65758i	−0.657273	+	0.477537i	−0.865741	−	0.500493i	$-0.833152\pi$
$409$	−13.2925	+	9.65758i	−0.657273	+	0.477537i	0.208468	+	0.978029i	$0.433152\pi$
$410$	−0.669133	−	2.05938i	−0.0330461	−	0.101705i
$411$		0			0
$412$	3.38914	+	2.46235i	0.166971	+	0.121311i
$413$	7.50342	+	5.45155i	0.369219	+	0.268253i
$414$		0			0
$415$	0.166318	+	0.511874i	0.00816423	+	0.0251269i
$416$	−12.4702	+	9.06015i	−0.611403	+	0.444211i
$417$		0			0
$418$	−2.96343	+	10.9129i	−0.144946	+	0.533767i
$419$	17.4065			0.850362			0.425181	−	0.905108i	$-0.360210\pi$
$419$	17.4065			0.850362			0.425181	+	0.905108i	$0.360210\pi$
$420$		0			0
$421$	1.40561	+	4.32602i	0.0685052	+	0.210837i	0.979449	−	0.201694i	$-0.0646447\pi$
$421$	1.40561	+	4.32602i	0.0685052	+	0.210837i	−0.910943	+	0.412531i	$0.864645\pi$
$422$	0.864374	−	2.66027i	0.0420771	−	0.129500i
$423$		0			0
$424$	−10.7893	−	7.83890i	−0.523976	−	0.380691i
$425$	6.43284	−	19.7983i	0.312039	−	0.960356i
$426$		0			0
$427$	−12.9021	+	9.37395i	−0.624378	+	0.453637i
$428$	−16.0176			−0.774239
$429$		0			0
$430$	1.65611			0.0798647
$431$	10.1004	−	7.33838i	0.486520	−	0.353477i	−0.317325	−	0.948317i	$-0.602784\pi$
$431$	10.1004	−	7.33838i	0.486520	−	0.353477i	0.803844	+	0.594840i	$0.202784\pi$
$432$		0			0
$433$	8.86451	−	27.2822i	0.426001	−	1.31110i	−0.476031	−	0.879428i	$-0.657925\pi$
$433$	8.86451	−	27.2822i	0.426001	−	1.31110i	0.902032	−	0.431668i	$-0.142075\pi$
$434$	−0.902689	−	0.655842i	−0.0433304	−	0.0314814i
$435$		0			0
$436$	−1.13808	+	3.50266i	−0.0545042	+	0.167747i
$437$	3.35336	+	10.3206i	0.160413	+	0.493701i
$438$		0			0
$439$	−4.10807			−0.196068			−0.0980338	−	0.995183i	$-0.531255\pi$
$439$	−4.10807			−0.196068			−0.0980338	+	0.995183i	$0.531255\pi$
$440$	8.74476	−	0.428841i	0.416890	−	0.0204442i
$441$		0			0
$442$	7.98309	−	5.80005i	0.379717	−	0.275880i
$443$	6.56034	+	20.1906i	0.311691	+	0.959287i	0.977095	+	0.212803i	$0.0682593\pi$
$443$	6.56034	+	20.1906i	0.311691	+	0.959287i	−0.665404	+	0.746483i	$0.731741\pi$
$444$		0			0
$445$	−14.5289	−	10.5559i	−0.688736	−	0.500396i
$446$	3.68638	+	2.67831i	0.174555	+	0.126822i
$447$		0			0
$448$	−0.880828	−	2.71091i	−0.0416152	−	0.128078i
$449$	20.9494	−	15.2206i	0.988663	−	0.718306i	0.0290350	−	0.999578i	$-0.490757\pi$
$449$	20.9494	−	15.2206i	0.988663	−	0.718306i	0.959628	+	0.281273i	$0.0907566\pi$
$450$		0			0
$451$	−7.54435	+	6.06744i	−0.355249	+	0.285705i
$452$	2.38857			0.112349
$453$		0			0
$454$	−5.77469	−	17.7727i	−0.271019	−	0.834112i
$455$	3.60803	−	11.1044i	0.169147	−	0.520581i
$456$		0			0
$457$	8.33600	+	6.05645i	0.389941	+	0.283309i	0.765431	−	0.643517i	$-0.222526\pi$
$457$	8.33600	+	6.05645i	0.389941	+	0.283309i	−0.375490	+	0.926826i	$0.622526\pi$
$458$	−2.88113	+	8.86721i	−0.134626	+	0.414338i
$459$		0			0
$460$	2.97717	−	2.16304i	0.138811	−	0.100852i
$461$	25.4532			1.18548			0.592738	−	0.805395i	$-0.298047\pi$
$461$	25.4532			1.18548			0.592738	+	0.805395i	$0.298047\pi$
$462$		0			0
$463$	−39.8554			−1.85224			−0.926119	−	0.377231i	$-0.876876\pi$
$463$	−39.8554			−1.85224			−0.926119	+	0.377231i	$0.876876\pi$
$464$	1.35533	−	0.984708i	0.0629198	−	0.0457139i
$465$		0			0
$466$	2.97863	−	9.16727i	0.137982	−	0.424666i
$467$	−14.0582	−	10.2139i	−0.650537	−	0.472643i	0.212917	−	0.977070i	$-0.431704\pi$
$467$	−14.0582	−	10.2139i	−0.650537	−	0.472643i	−0.863454	+	0.504427i	$0.831704\pi$
$468$		0			0
$469$	11.7661	−	36.2123i	0.543308	−	1.67213i
$470$	2.94224	+	9.05529i	0.135716	+	0.417689i
$471$		0			0
$472$	−5.61562			−0.258480
$473$	−2.63033	−	6.92165i	−0.120943	−	0.318258i
$474$		0			0
$475$	−15.5837	+	11.3222i	−0.715027	+	0.519498i
$476$	−10.4312	−	32.1039i	−0.478112	−	1.47148i
$477$		0			0
$478$	−13.5158	−	9.81979i	−0.618197	−	0.449147i
$479$	−17.7142	−	12.8701i	−0.809383	−	0.588051i	0.104269	−	0.994549i	$-0.466750\pi$
$479$	−17.7142	−	12.8701i	−0.809383	−	0.588051i	−0.913652	+	0.406498i	$0.866750\pi$
$480$		0			0
$481$	−7.20447	−	22.1731i	−0.328496	−	1.01101i
$482$	−9.53548	+	6.92794i	−0.434329	+	0.315559i
$483$		0			0
$484$	−6.86830	−	15.7097i	−0.312195	−	0.714075i
$485$	−8.95046			−0.406420
$486$		0			0
$487$	1.01084	+	3.11106i	0.0458057	+	0.140975i	0.971344	−	0.237679i	$-0.0763867\pi$
$487$	1.01084	+	3.11106i	0.0458057	+	0.140975i	−0.925538	+	0.378655i	$0.876387\pi$
$488$	2.98389	−	9.18347i	0.135074	−	0.415716i
$489$		0			0
$490$	4.94830	+	3.59515i	0.223542	+	0.162412i
$491$	2.23231	−	6.87034i	0.100743	−	0.310054i	−0.887965	−	0.459911i	$-0.847881\pi$
$491$	2.23231	−	6.87034i	0.100743	−	0.310054i	0.988708	+	0.149857i	$0.0478813\pi$
$492$		0			0
$493$	−4.85989	+	3.53092i	−0.218879	+	0.159025i
$494$	−9.13071			−0.410810
$495$		0			0
$496$	−0.665390			−0.0298769
$497$	−19.9546	+	14.4979i	−0.895087	+	0.650319i
$498$		0			0
$499$	4.58412	−	14.1085i	0.205213	−	0.631581i	−0.794491	−	0.607275i	$-0.792262\pi$
$499$	4.58412	−	14.1085i	0.205213	−	0.631581i	0.999705	−	0.0243059i	$-0.00773756\pi$
$500$	12.3250	+	8.95460i	0.551189	+	0.400462i
$501$		0			0
$502$	4.49115	−	13.8223i	0.200450	−	0.616921i
$503$	10.1918	+	31.3671i	0.454430	+	1.39859i	0.871803	+	0.489856i	$0.162951\pi$
$503$	10.1918	+	31.3671i	0.454430	+	1.39859i	−0.417374	+	0.908735i	$0.637049\pi$
$504$		0			0
$505$	1.96673			0.0875181
$506$	3.89850	+	2.55037i	0.173309	+	0.113378i
$507$		0			0
$508$	−9.64831	+	7.00990i	−0.428074	+	0.311014i
$509$	−11.9495	−	36.7768i	−0.529652	−	1.63010i	−0.754929	−	0.655807i	$-0.772329\pi$
$509$	−11.9495	−	36.7768i	−0.529652	−	1.63010i	0.225277	−	0.974295i	$-0.427671\pi$
$510$		0			0
$511$	−36.8721	−	26.7892i	−1.63113	−	1.18508i
$512$	−13.1198	−	9.53213i	−0.579821	−	0.421264i
$513$		0			0
$514$	−1.06004	−	3.26247i	−0.0467564	−	0.143901i
$515$	2.42795	−	1.76401i	0.106988	−	0.0777315i
$516$		0			0
$517$	33.1733	−	26.6792i	1.45896	−	1.17335i
$518$	22.5817			0.992182
$519$		0			0
$520$	2.18457	+	6.72343i	0.0957999	+	0.294842i
$521$	5.40297	−	16.6286i	0.236708	−	0.728514i	−0.760182	−	0.649710i	$-0.774890\pi$
$521$	5.40297	−	16.6286i	0.236708	−	0.728514i	0.996890	−	0.0788032i	$-0.0251099\pi$
$522$		0			0
$523$	−11.7211	−	8.51591i	−0.512530	−	0.372375i	0.301253	−	0.953544i	$-0.402595\pi$
$523$	−11.7211	−	8.51591i	−0.512530	−	0.372375i	−0.813782	+	0.581170i	$0.802595\pi$
$524$	−2.58126	+	7.94431i	−0.112763	+	0.347049i
$525$		0			0
$526$	−14.9937	+	10.8936i	−0.653758	+	0.474983i
$527$	2.38593			0.103933
$528$		0			0
$529$	−18.5294			−0.805626
$530$	−3.38542	+	2.45965i	−0.147053	+	0.106840i
$531$		0			0
$532$	−9.65216	+	29.7063i	−0.418474	+	1.28793i
$533$	−6.32433	−	4.59489i	−0.273937	−	0.199027i
$534$		0			0
$535$	−3.54592	+	10.9132i	−0.153304	+	0.471820i
$536$	7.12408	+	21.9256i	0.307713	+	0.947044i
$537$		0			0
$538$	−2.00597			−0.0864837
$539$	7.16664	−	26.3913i	0.308689	−	1.13675i
$540$		0			0
$541$	−26.7771	+	19.4547i	−1.15124	+	0.836422i	−0.988645	−	0.150272i	$-0.951985\pi$
$541$	−26.7771	+	19.4547i	−1.15124	+	0.836422i	−0.162591	+	0.986694i	$0.551985\pi$
$542$	−5.20910	−	16.0320i	−0.223750	−	0.688632i
$543$		0			0
$544$	25.8278	+	18.7650i	1.10736	+	0.804543i
$545$	2.13451	+	1.55082i	0.0914325	+	0.0664296i
$546$		0			0
$547$	2.84732	+	8.76316i	0.121743	+	0.374686i	0.993294	−	0.115619i	$-0.0368853\pi$
$547$	2.84732	+	8.76316i	0.121743	+	0.374686i	−0.871551	+	0.490305i	$0.836885\pi$
$548$	−21.0980	+	15.3286i	−0.901262	+	0.654805i
$549$		0			0
$550$	−2.16708	+	7.98032i	−0.0924046	+	0.340282i
$551$	5.55853			0.236802
$552$		0			0
$553$	−5.44731	−	16.7651i	−0.231643	−	0.712925i
$554$	−2.16872	+	6.67464i	−0.0921402	+	0.283578i
$555$		0			0
$556$	17.3262	+	12.5883i	0.734796	+	0.533861i
$557$	−11.4496	+	35.2384i	−0.485137	+	1.49310i	0.346645	+	0.937996i	$0.387321\pi$
$557$	−11.4496	+	35.2384i	−0.485137	+	1.49310i	−0.831782	+	0.555102i	$0.812679\pi$
$558$		0			0
$559$	4.83697	−	3.51427i	0.204582	−	0.148638i
$560$	6.74405			0.284988
$561$		0			0
$562$	14.9941			0.632486
$563$	−21.8387	+	15.8667i	−0.920390	+	0.668702i	−0.943621	−	0.331028i	$-0.892605\pi$
$563$	−21.8387	+	15.8667i	−0.920390	+	0.668702i	0.0232313	+	0.999730i	$0.492605\pi$
$564$		0			0
$565$	0.528774	−	1.62740i	0.0222457	−	0.0684652i
$566$	3.15870	+	2.29493i	0.132770	+	0.0964630i
$567$		0			0
$568$	4.61492	−	14.2033i	0.193638	−	0.595956i
$569$	8.49046	+	26.1310i	0.355939	+	1.09547i	0.955463	+	0.295110i	$0.0953564\pi$
$569$	8.49046	+	26.1310i	0.355939	+	1.09547i	−0.599524	+	0.800356i	$0.704644\pi$
$570$		0			0
$571$	−39.0103			−1.63253			−0.816266	−	0.577676i	$-0.803960\pi$
$571$	−39.0103			−1.63253			−0.816266	+	0.577676i	$0.803960\pi$
$572$	10.7881	−	8.67617i	0.451072	−	0.362769i
$573$		0			0
$574$	6.12563	−	4.45053i	0.255679	−	0.185762i
$575$	2.45223	+	7.54719i	0.102265	+	0.314739i
$576$		0			0
$577$	23.5957	+	17.1433i	0.982302	+	0.713684i	0.958222	−	0.286026i	$-0.0923344\pi$
$577$	23.5957	+	17.1433i	0.982302	+	0.713684i	0.0240800	+	0.999710i	$0.492334\pi$
$578$	−7.39764	−	5.37470i	−0.307701	−	0.223558i
$579$		0			0
$580$	−0.582493	−	1.79273i	−0.0241867	−	0.0744390i
$581$	−1.52257	+	1.10621i	−0.0631670	+	0.0458935i
$582$		0			0
$583$	15.6569	+	10.2427i	0.648445	+	0.424209i
$584$	27.5954			1.14191
$585$		0			0
$586$	−1.45632	−	4.48210i	−0.0601602	−	0.185154i
$587$	1.57226	−	4.83891i	0.0648940	−	0.199723i	−0.913352	−	0.407170i	$-0.866516\pi$
$587$	1.57226	−	4.83891i	0.0648940	−	0.199723i	0.978246	+	0.207447i	$0.0665155\pi$
$588$		0			0
$589$	−1.78610	−	1.29768i	−0.0735950	−	0.0534699i
$590$	−0.544500	+	1.67580i	−0.0224167	+	0.0689916i
$591$		0			0
$592$	10.8946	−	7.91537i	0.447764	−	0.325320i
$593$	−3.46422			−0.142258			−0.0711292	−	0.997467i	$-0.522660\pi$
$593$	−3.46422			−0.142258			−0.0711292	+	0.997467i	$0.522660\pi$
$594$		0			0
$595$	−24.1825			−0.991386
$596$	−7.01071	+	5.09358i	−0.287170	+	0.208641i
$597$		0			0
$598$	−1.16240	+	3.57748i	−0.0475339	+	0.146294i
$599$	20.1242	+	14.6211i	0.822251	+	0.597400i	0.917356	−	0.398067i	$-0.130319\pi$
$599$	20.1242	+	14.6211i	0.822251	+	0.597400i	−0.0951054	+	0.995467i	$0.530319\pi$
$600$		0			0
$601$	3.42024	−	10.5264i	0.139514	−	0.429381i	−0.856750	−	0.515731i	$-0.827520\pi$
$601$	3.42024	−	10.5264i	0.139514	−	0.429381i	0.996265	+	0.0863500i	$0.0275203\pi$
$602$	1.78951	+	5.50755i	0.0729351	+	0.224471i
$603$		0			0
$604$	0.255479			0.0103953
$605$	−12.2239	+	1.20181i	−0.496973	+	0.0488604i
$606$		0			0
$607$	22.6209	−	16.4351i	0.918155	−	0.667079i	−0.0249090	−	0.999690i	$-0.507930\pi$
$607$	22.6209	−	16.4351i	0.918155	−	0.667079i	0.943064	+	0.332611i	$0.107930\pi$
$608$	−9.12859	−	28.0949i	−0.370213	−	1.13940i
$609$		0			0
$610$	−2.45118	−	1.78089i	−0.0992455	−	0.0721061i
$611$	27.8087	+	20.2042i	1.12502	+	0.817375i
$612$		0			0
$613$	3.39680	+	10.4543i	0.137196	+	0.422245i	0.995925	−	0.0901845i	$-0.0287457\pi$
$613$	3.39680	+	10.4543i	0.137196	+	0.422245i	−0.858729	+	0.512429i	$0.828746\pi$
$614$	9.96265	−	7.23829i	0.402060	−	0.292114i
$615$		0			0
$616$	10.8753	+	28.6182i	0.438179	+	1.15306i
$617$	−18.6262			−0.749864			−0.374932	−	0.927052i	$-0.622334\pi$
$617$	−18.6262			−0.749864			−0.374932	+	0.927052i	$0.622334\pi$
$618$		0			0
$619$	0.830787	+	2.55690i	0.0333921	+	0.102770i	0.966363	−	0.257180i	$-0.0827935\pi$
$619$	0.830787	+	2.55690i	0.0333921	+	0.102770i	−0.932971	+	0.359951i	$0.882793\pi$
$620$	−0.231355	+	0.712036i	−0.00929142	+	0.0285961i
$621$		0			0
$622$	3.69561	+	2.68502i	0.148180	+	0.107659i
$623$	19.4053	−	59.7234i	0.777457	−	2.39277i
$624$		0			0
$625$	−6.35233	+	4.61524i	−0.254093	+	0.184610i
$626$	−16.8244			−0.672440
$627$		0			0
$628$	−37.1792			−1.48361
$629$	−39.0652	+	28.3826i	−1.55763	+	1.13169i
$630$		0			0
$631$	−12.1224	+	37.3089i	−0.482585	+	1.48524i	0.352863	+	0.935675i	$0.385208\pi$
$631$	−12.1224	+	37.3089i	−0.482585	+	1.48524i	−0.835448	+	0.549569i	$0.814792\pi$
$632$	8.63483	+	6.27357i	0.343475	+	0.249549i
$633$		0			0
$634$	−2.25389	+	6.93677i	−0.0895135	+	0.275494i
$635$	2.64013	+	8.12550i	0.104771	+	0.322451i
$636$		0			0
$637$	22.0813			0.874895
$638$	1.85951	−	1.49549i	0.0736187	−	0.0592069i
$639$		0			0
$640$	−9.96109	+	7.23716i	−0.393747	+	0.286074i
$641$	−7.95687	−	24.4887i	−0.314277	−	0.967246i	−0.976051	−	0.217542i	$-0.930196\pi$
$641$	−7.95687	−	24.4887i	−0.314277	−	0.967246i	0.661773	−	0.749704i	$-0.269804\pi$
$642$		0			0
$643$	10.7859	+	7.83639i	0.425353	+	0.309037i	0.779788	−	0.626044i	$-0.215327\pi$
$643$	10.7859	+	7.83639i	0.425353	+	0.309037i	−0.354435	+	0.935081i	$0.615327\pi$
$644$	10.4104	+	7.56359i	0.410227	+	0.298047i
$645$		0			0
$646$	5.84386	+	17.9856i	0.229924	+	0.707632i
$647$	19.2955	−	14.0190i	0.758585	−	0.551145i	−0.139891	−	0.990167i	$-0.544675\pi$
$647$	19.2955	−	14.0190i	0.758585	−	0.551145i	0.898476	+	0.439022i	$0.144675\pi$
$648$		0			0
$649$	7.86876	−	0.385882i	0.308876	−	0.0151472i
$650$	−6.67706			−0.261896
$651$		0			0
$652$	2.02105	+	6.22015i	0.0791504	+	0.243600i
$653$	−3.93222	+	12.1021i	−0.153880	+	0.473593i	−0.998046	−	0.0624889i	$-0.980096\pi$
$653$	−3.93222	+	12.1021i	−0.153880	+	0.473593i	0.844166	+	0.536082i	$0.180096\pi$
$654$		0			0
$655$	4.84125	+	3.51738i	0.189163	+	0.137435i
$656$	1.39531	−	4.29433i	0.0544778	−	0.167666i
$657$		0			0
$658$	−26.9350	+	19.5694i	−1.05004	+	0.762896i
$659$	27.2527			1.06161			0.530806	−	0.847493i	$-0.321889\pi$
$659$	27.2527			1.06161			0.530806	+	0.847493i	$0.321889\pi$
$660$		0			0
$661$	43.6440			1.69755			0.848777	−	0.528751i	$-0.177339\pi$
$661$	43.6440			1.69755			0.848777	+	0.528751i	$0.177339\pi$
$662$	1.99406	−	1.44877i	0.0775014	−	0.0563081i
$663$		0			0
$664$	0.352127	−	1.08373i	0.0136652	−	0.0420571i
$665$	18.1030	+	13.1526i	0.702003	+	0.510035i
$666$		0			0
$667$	0.707636	−	2.17788i	0.0273998	−	0.0843278i
$668$	7.62965	+	23.4817i	0.295200	+	0.908533i
$669$		0			0
$670$	7.23376			0.279465
$671$	−3.55005	+	13.0732i	−0.137048	+	0.504684i
$672$		0			0
$673$	21.5900	−	15.6860i	0.832233	−	0.604652i	−0.0879575	−	0.996124i	$-0.528034\pi$
$673$	21.5900	−	15.6860i	0.832233	−	0.604652i	0.920190	+	0.391472i	$0.128034\pi$
$674$	−6.60922	−	20.3411i	−0.254578	−	0.783510i
$675$		0			0
$676$	−7.34946	−	5.33970i	−0.282672	−	0.205373i
$677$	21.9107	+	15.9190i	0.842095	+	0.611818i	0.922955	−	0.384908i	$-0.125767\pi$
$677$	21.9107	+	15.9190i	0.842095	+	0.611818i	−0.0808602	+	0.996725i	$0.525767\pi$
$678$		0			0
$679$	−9.67144	−	29.7656i	−0.371156	−	1.14230i
$680$	11.8455	−	8.60629i	0.454256	−	0.330036i
$681$		0			0
$682$	−0.946640	+	0.0464231i	−0.0362487	+	0.00177763i
$683$	16.7343			0.640322			0.320161	−	0.947363i	$-0.396263\pi$
$683$	16.7343			0.640322			0.320161	+	0.947363i	$0.396263\pi$
$684$		0			0
$685$	5.77319	+	17.7681i	0.220582	+	0.678883i
$686$	−0.998288	+	3.07242i	−0.0381148	+	0.117305i
$687$		0			0
$688$	2.79387	+	2.02987i	0.106515	+	0.0773879i
$689$	−4.66836	+	14.3677i	−0.177850	+	0.547367i
$690$		0			0
$691$	30.3540	−	22.0534i	1.15472	−	0.838953i	0.165618	−	0.986190i	$-0.447038\pi$
$691$	30.3540	−	22.0534i	1.15472	−	0.838953i	0.989101	+	0.147237i	$0.0470381\pi$
$692$	−4.05707			−0.154226
$693$		0			0
$694$	14.2978			0.542738
$695$	12.4124	−	9.01811i	0.470828	−	0.342077i
$696$		0			0
$697$	−5.00325	+	15.3984i	−0.189512	+	0.583257i
$698$	9.03983	+	6.56782i	0.342163	+	0.248596i
$699$		0			0
$700$	−7.05838	+	21.7235i	−0.266782	+	0.821070i
$701$	−3.15219	−	9.70143i	−0.119056	−	0.366418i	0.873715	−	0.486438i	$-0.161704\pi$
$701$	−3.15219	−	9.70143i	−0.119056	−	0.366418i	−0.992771	+	0.120020i	$0.961704\pi$
$702$		0			0
$703$	44.6811			1.68518
$704$	−2.02617	−	1.32551i	−0.0763641	−	0.0499569i
$705$		0			0
$706$	1.68267	−	1.22253i	0.0633280	−	0.0460105i
$707$	2.12515	+	6.54054i	0.0799245	+	0.245982i
$708$		0			0
$709$	11.7289	+	8.52152i	0.440487	+	0.320032i	0.785828	−	0.618445i	$-0.212237\pi$
$709$	11.7289	+	8.52152i	0.440487	+	0.320032i	−0.345342	+	0.938477i	$0.612237\pi$
$710$	−3.79104	−	2.75435i	−0.142275	−	0.103369i
$711$		0			0
$712$	11.7494	+	36.1610i	0.440329	+	1.35519i
$713$	−0.735822	+	0.534606i	−0.0275568	+	0.0200212i
$714$		0			0
$715$	−3.52309	−	9.27093i	−0.131756	−	0.346713i
$716$	11.8273			0.442006
$717$		0			0
$718$	−1.74261	−	5.36321i	−0.0650337	−	0.200153i
$719$	−5.94135	+	18.2856i	−0.221575	+	0.681938i	0.777046	+	0.629444i	$0.216717\pi$
$719$	−5.94135	+	18.2856i	−0.221575	+	0.681938i	−0.998621	+	0.0524943i	$0.983283\pi$
$720$		0			0
$721$	8.48991	+	6.16828i	0.316181	+	0.229719i
$722$	1.50699	−	4.63804i	0.0560844	−	0.172610i
$723$		0			0
$724$	−3.02663	+	2.19898i	−0.112484	+	0.0817243i
$725$	4.06482			0.150964
$726$		0			0
$727$	0.726827			0.0269565			0.0134783	−	0.999909i	$-0.495710\pi$
$727$	0.726827			0.0269565			0.0134783	+	0.999909i	$0.495710\pi$
$728$	−19.9989	+	14.5300i	−0.741207	+	0.538519i
$729$		0			0
$730$	2.67570	−	8.23495i	0.0990320	−	0.304789i
$731$	−10.0181	−	7.27860i	−0.370534	−	0.269209i
$732$		0			0
$733$	−0.579681	+	1.78408i	−0.0214110	+	0.0658964i	−0.961191	−	0.275883i	$-0.911030\pi$
$733$	−0.579681	+	1.78408i	−0.0214110	+	0.0658964i	0.939780	+	0.341780i	$0.111030\pi$
$734$	−2.26040	−	6.95680i	−0.0834329	−	0.256780i
$735$		0			0
$736$	−12.1699			−0.448590
$737$	−11.4891	−	30.2333i	−0.423206	−	1.11366i
$738$		0			0
$739$	42.5402	−	30.9073i	1.56487	−	1.13694i	0.632993	−	0.774157i	$-0.281826\pi$
$739$	42.5402	−	30.9073i	1.56487	−	1.13694i	0.931873	−	0.362784i	$-0.118174\pi$
$740$	−4.68224	−	14.4105i	−0.172123	−	0.529739i
$741$		0			0
$742$	−11.8379	−	8.60076i	−0.434584	−	0.315744i
$743$	−26.9668	−	19.5925i	−0.989316	−	0.718780i	−0.0295450	−	0.999563i	$-0.509406\pi$
$743$	−26.9668	−	19.5925i	−0.989316	−	0.718780i	−0.959771	+	0.280783i	$0.909406\pi$
$744$		0			0
$745$	1.91839	+	5.90420i	0.0702844	+	0.216313i
$746$	−5.91558	+	4.29792i	−0.216585	+	0.157358i
$747$		0			0
$748$	−23.9948	−	15.6973i	−0.877338	−	0.573949i
$749$	−40.1246			−1.46612
$750$		0			0
$751$	−7.21990	−	22.2206i	−0.263458	−	0.810840i	−0.992045	−	0.125886i	$-0.959823\pi$
$751$	−7.21990	−	22.2206i	−0.263458	−	0.810840i	0.728587	−	0.684953i	$-0.240177\pi$
$752$	−6.13533	+	18.8826i	−0.223732	+	0.688578i
$753$		0			0
$754$	1.55880	+	1.13254i	0.0567683	+	0.0412446i
$755$	0.0565572	−	0.174065i	0.00205833	−	0.00633488i
$756$		0			0
$757$	27.3472	−	19.8689i	0.993952	−	0.722148i	0.0331687	−	0.999450i	$-0.489440\pi$
$757$	27.3472	−	19.8689i	0.993952	−	0.722148i	0.960783	+	0.277302i	$0.0894401\pi$
$758$	16.8650			0.612564
$759$		0			0
$760$	−13.5484			−0.491453
$761$	16.2709	−	11.8215i	0.589819	−	0.428528i	−0.252432	−	0.967615i	$-0.581230\pi$
$761$	16.2709	−	11.8215i	0.589819	−	0.428528i	0.842251	+	0.539086i	$0.181230\pi$
$762$		0			0
$763$	−2.85093	+	8.77427i	−0.103211	+	0.317650i
$764$	20.8294	+	15.1335i	0.753583	+	0.547510i
$765$		0			0
$766$	2.48699	−	7.65417i	0.0898586	−	0.276556i
$767$	1.96573	+	6.04991i	0.0709786	+	0.218450i
$768$		0			0
$769$	0.626999			0.0226102			0.0113051	−	0.999936i	$-0.496401\pi$
$769$	0.626999			0.0226102			0.0113051	+	0.999936i	$0.496401\pi$
$770$	9.59465	−	0.470520i	0.345767	−	0.0169564i
$771$		0			0
$772$	−10.2582	+	7.45299i	−0.369199	+	0.268239i
$773$	−8.88046	−	27.3313i	−0.319408	−	0.983037i	−0.973902	−	0.226970i	$-0.927118\pi$
$773$	−8.88046	−	27.3313i	−0.319408	−	0.983037i	0.654494	−	0.756067i	$-0.272882\pi$
$774$		0			0
$775$	−1.30613	−	0.948959i	−0.0469176	−	0.0340876i
$776$	15.3307	+	11.1384i	0.550341	+	0.399846i
$777$		0			0
$778$	−2.94608	−	9.06711i	−0.105622	−	0.325072i
$779$	12.1204	−	8.80602i	0.434260	−	0.315508i
$780$		0			0
$781$	−5.49056	+	20.2191i	−0.196468	+	0.723497i
$782$	7.79085			0.278600
$783$		0			0
$784$	3.94131	+	12.1301i	0.140761	+	0.433218i
$785$	−8.23062	+	25.3312i	−0.293763	+	0.904110i
$786$		0			0
$787$	11.4095	+	8.28950i	0.406705	+	0.295489i	0.772267	−	0.635298i	$-0.219123\pi$
$787$	11.4095	+	8.28950i	0.406705	+	0.295489i	−0.365561	+	0.930787i	$0.619123\pi$
$788$	−11.0334	+	33.9574i	−0.393050	+	1.20968i
$789$		0			0
$790$	2.70939	−	1.96849i	0.0963958	−	0.0700357i
$791$	5.98345			0.212747
$792$		0			0
$793$	−10.9382			−0.388426
$794$	2.70810	−	1.96755i	0.0961068	−	0.0698257i
$795$		0			0
$796$	−4.46582	+	13.7444i	−0.158287	+	0.487157i
$797$	21.1596	+	15.3733i	0.749511	+	0.544552i	0.895675	−	0.444709i	$-0.146693\pi$
$797$	21.1596	+	15.3733i	0.749511	+	0.544552i	−0.146164	+	0.989260i	$0.546693\pi$
$798$		0			0
$799$	21.9998	−	67.7084i	0.778297	−	2.39535i
$800$	−6.67551	−	20.5451i	−0.236015	−	0.726379i
$801$		0			0
$802$	12.0908			0.426939
$803$	−38.6674	+	1.89624i	−1.36454	+	0.0669169i
$804$		0			0
$805$	7.45791	−	5.41849i	0.262857	−	0.190977i
$806$	−0.236485	−	0.727826i	−0.00832983	−	0.0256366i
$807$		0			0
$808$	−3.36869	−	2.44750i	−0.118510	−	0.0861026i
$809$	12.8256	+	9.31836i	0.450925	+	0.327616i	0.789961	−	0.613157i	$-0.210101\pi$
$809$	12.8256	+	9.31836i	0.450925	+	0.327616i	−0.339036	+	0.940773i	$0.610101\pi$
$810$		0			0
$811$	−11.2255	−	34.5484i	−0.394179	−	1.21316i	−0.929599	−	0.368573i	$-0.879846\pi$
$811$	−11.2255	−	34.5484i	−0.394179	−	1.21316i	0.535420	−	0.844586i	$-0.320154\pi$
$812$	5.33248	−	3.87427i	0.187133	−	0.135960i
$813$		0			0
$814$	14.9473	−	12.0212i	0.523902	−	0.421342i
$815$	4.68538			0.164122
$816$		0			0
$817$	3.54081	+	10.8975i	0.123877	+	0.381255i
$818$	3.37295	−	10.3809i	0.117932	−	0.362958i
$819$		0			0
$820$	−4.11023	−	2.98626i	−0.143535	−	0.104285i
$821$	5.05451	−	15.5562i	0.176404	−	0.542914i	−0.823291	−	0.567619i	$-0.807865\pi$
$821$	5.05451	−	15.5562i	0.176404	−	0.542914i	0.999695	+	0.0247048i	$0.00786458\pi$
$822$		0			0
$823$	21.1756	−	15.3850i	0.738136	−	0.536287i	−0.153991	−	0.988072i	$-0.549213\pi$
$823$	21.1756	−	15.3850i	0.738136	−	0.536287i	0.892127	+	0.451785i	$0.149213\pi$
$824$	−6.35392			−0.221349
$825$		0			0
$826$	−6.16139			−0.214382
$827$	4.48139	−	3.25592i	0.155833	−	0.113219i	−0.507136	−	0.861866i	$-0.669296\pi$
$827$	4.48139	−	3.25592i	0.155833	−	0.113219i	0.662969	+	0.748647i	$0.269296\pi$
$828$		0			0
$829$	5.71784	−	17.5977i	0.198589	−	0.611194i	−0.801327	−	0.598227i	$-0.795872\pi$
$829$	5.71784	−	17.5977i	0.198589	−	0.611194i	0.999916	−	0.0129672i	$-0.00412771\pi$
$830$	−0.289263	−	0.210162i	−0.0100405	−	0.00729481i
$831$		0			0
$832$	0.604133	−	1.85933i	0.0209445	−	0.0644606i
$833$	−14.1326	−	43.4956i	−0.489664	−	1.50703i
$834$		0			0
$835$	17.6878			0.612110
$836$	9.42492	+	24.8015i	0.325968	+	0.857776i
$837$		0			0
$838$	−9.35505	+	6.79684i	−0.323165	+	0.234793i
$839$	5.55158	+	17.0860i	0.191662	+	0.589875i	0.999999	+	0.00115518i	$0.000367705\pi$
$839$	5.55158	+	17.0860i	0.191662	+	0.589875i	−0.808337	+	0.588719i	$0.799632\pi$
$840$		0			0
$841$	22.5125	+	16.3563i	0.776294	+	0.564011i
$842$	−2.44465	−	1.77614i	−0.0842483	−	0.0612100i
$843$		0			0
$844$	−2.02806	−	6.24172i	−0.0698086	−	0.214849i
$845$	−5.26509	+	3.82531i	−0.181125	+	0.131595i
$846$		0			0
$847$	−17.2053	−	39.3532i	−0.591182	−	1.35219i
$848$	−8.72598			−0.299651
$849$		0			0
$850$	4.27347	+	13.1524i	0.146579	+	0.451123i
$851$	5.68818	−	17.5064i	0.194988	−	0.600112i
$852$		0			0
$853$	−22.5822	−	16.4069i	−0.773199	−	0.561762i	0.129732	−	0.991549i	$-0.458588\pi$
$853$	−22.5822	−	16.4069i	−0.773199	−	0.561762i	−0.902930	+	0.429788i	$0.858588\pi$
$854$	3.27389	−	10.0760i	0.112030	−	0.344794i
$855$		0			0
$856$	19.6546	−	14.2799i	0.671781	−	0.488077i
$857$	8.49967			0.290343			0.145172	−	0.989406i	$-0.453627\pi$
$857$	8.49967			0.290343			0.145172	+	0.989406i	$0.453627\pi$
$858$		0			0
$859$	27.8517			0.950289			0.475145	−	0.879908i	$-0.342396\pi$
$859$	27.8517			0.950289			0.475145	+	0.879908i	$0.342396\pi$
$860$	3.14359	−	2.28395i	0.107195	−	0.0778820i
$861$		0			0
$862$	−2.56296	+	7.88797i	−0.0872947	+	0.268665i
$863$	10.9978	+	7.99035i	0.374368	+	0.271995i	0.759020	−	0.651067i	$-0.225678\pi$
$863$	10.9978	+	7.99035i	0.374368	+	0.271995i	−0.384652	+	0.923062i	$0.625678\pi$
$864$		0			0
$865$	−0.898141	+	2.76419i	−0.0305377	+	0.0939854i
$866$	5.88887	+	18.1241i	0.200112	+	0.615882i
$867$		0			0
$868$	−2.61794			−0.0888586
$869$	−12.5304	−	8.19734i	−0.425066	−	0.278076i
$870$		0			0
$871$	21.1275	−	15.3500i	0.715879	−	0.520117i
$872$	−1.72617	−	5.31260i	−0.0584555	−	0.179907i
$873$		0			0
$874$	−5.83221	−	4.23735i	−0.197278	−	0.143331i
$875$	30.8744	+	22.4316i	1.04375	+	0.758326i
$876$		0			0
$877$	11.1796	+	34.4073i	0.377509	+	1.16185i	0.941771	+	0.336256i	$0.109161\pi$
$877$	11.1796	+	34.4073i	0.377509	+	1.16185i	−0.564262	+	0.825596i	$0.690839\pi$
$878$	2.20787	−	1.60411i	0.0745120	−	0.0541361i
$879$		0			0
$880$	4.46403	−	3.59014i	0.150482	−	0.121023i
$881$	−26.6423			−0.897601			−0.448800	−	0.893632i	$-0.648149\pi$
$881$	−26.6423			−0.897601			−0.448800	+	0.893632i	$0.648149\pi$
$882$		0			0
$883$	−6.32757	−	19.4743i	−0.212940	−	0.655361i	−0.999293	−	0.0375844i	$-0.988034\pi$
$883$	−6.32757	−	19.4743i	−0.212940	−	0.655361i	0.786354	−	0.617776i	$-0.211966\pi$
$884$	7.15442	−	22.0190i	0.240629	−	0.740581i
$885$		0			0
$886$	−11.4098	−	8.28973i	−0.383321	−	0.278499i
$887$	9.88890	−	30.4349i	0.332037	−	1.02190i	−0.636126	−	0.771585i	$-0.719464\pi$
$887$	9.88890	−	30.4349i	0.332037	−	1.02190i	0.968163	−	0.250320i	$-0.0805357\pi$
$888$		0			0
$889$	−24.1693	+	17.5600i	−0.810613	+	0.588945i
$890$	11.9303			0.399906
$891$		0			0
$892$	10.6911			0.357963
$893$	−53.2948	+	38.7209i	−1.78344	+	1.29575i
$894$		0			0
$895$	2.61829	−	8.05826i	0.0875197	−	0.269358i
$896$	−34.8314	−	25.3065i	−1.16363	−	0.845430i
$897$		0			0
$898$	−5.31586	+	16.3605i	−0.177393	+	0.545958i
$899$	0.143966	+	0.443082i	0.00480153	+	0.0147776i
$900$		0			0
$901$	31.2892			1.04239
$902$	1.68548	−	6.20683i	0.0561204	−	0.206665i
$903$		0			0
$904$	−2.93093	+	2.12944i	−0.0974813	+	0.0708243i
$905$	0.828198	+	2.54893i	0.0275302	+	0.0847294i
$906$		0			0
$907$	39.6825	+	28.8310i	1.31764	+	0.957318i	0.999958	+	0.00911935i	$0.00290282\pi$
$907$	39.6825	+	28.8310i	1.31764	+	0.957318i	0.317677	+	0.948199i	$0.397097\pi$
$908$	−35.4717	−	25.7717i	−1.17717	−	0.855265i
$909$		0			0
$910$	2.39689	+	7.37687i	0.0794561	+	0.244541i
$911$	−18.9159	+	13.7432i	−0.626710	+	0.455332i	−0.855259	−	0.518201i	$-0.826602\pi$
$911$	−18.9159	+	13.7432i	−0.626710	+	0.455332i	0.228549	+	0.973532i	$0.426602\pi$
$912$		0			0
$913$	−0.418940	+	1.54275i	−0.0138649	+	0.0510577i
$914$	−6.84506			−0.226415
$915$		0			0
$916$	6.75993	+	20.8049i	0.223354	+	0.687414i
$917$	−6.46615	+	19.9008i	−0.213531	+	0.657181i
$918$		0			0
$919$	6.14797	+	4.46676i	0.202803	+	0.147345i	0.684551	−	0.728965i	$-0.259998\pi$
$919$	6.14797	+	4.46676i	0.202803	+	0.147345i	−0.481749	+	0.876309i	$0.659998\pi$
$920$	−1.72480	+	5.30838i	−0.0568649	+	0.175012i
$921$		0			0
$922$	−13.6798	+	9.93893i	−0.450519	+	0.327321i
$923$	−16.9171			−0.556835
$924$		0			0
$925$	32.6742			1.07432
$926$	21.4202	−	15.5627i	0.703910	−	0.511421i
$927$		0			0
$928$	−1.92634	+	5.92866i	−0.0632352	+	0.194618i
$929$	−12.0355	−	8.74433i	−0.394873	−	0.286892i	0.372576	−	0.928002i	$-0.378475\pi$
$929$	−12.0355	−	8.74433i	−0.394873	−	0.286892i	−0.767450	+	0.641109i	$0.778475\pi$
$930$		0			0
$931$	−13.0771	+	40.2472i	−0.428585	+	1.31905i
$932$	−6.98867	−	21.5089i	−0.228922	−	0.704548i
$933$		0			0
$934$	11.5438			0.377726
$935$	−16.0069	+	12.8733i	−0.523482	+	0.421003i
$936$		0			0
$937$	−14.4192	+	10.4762i	−0.471056	+	0.342242i	−0.797853	−	0.602853i	$-0.794031\pi$
$937$	−14.4192	+	10.4762i	−0.471056	+	0.342242i	0.326797	+	0.945095i	$0.394031\pi$
$938$	7.81646	+	24.0566i	0.255216	+	0.785475i
$939$		0			0
$940$	18.0731	+	13.1309i	0.589479	+	0.428282i
$941$	34.5120	+	25.0744i	1.12506	+	0.817402i	0.984968	−	0.172737i	$-0.0552609\pi$
$941$	34.5120	+	25.0744i	1.12506	+	0.817402i	0.140090	+	0.990139i	$0.455261\pi$
$942$		0			0
$943$	−1.90726	−	5.86995i	−0.0621090	−	0.191152i
$944$	−2.97257	+	2.15970i	−0.0967491	+	0.0702923i
$945$		0			0
$946$	4.11641	+	2.69293i	0.133836	+	0.0875548i
$947$	−6.89340			−0.224006			−0.112003	−	0.993708i	$-0.535727\pi$
$947$	−6.89340			−0.224006			−0.112003	+	0.993708i	$0.535727\pi$
$948$		0			0
$949$	−9.65971	−	29.7295i	−0.313567	−	0.965061i
$950$	3.95432	−	12.1701i	0.128295	−	0.394852i
$951$		0			0
$952$	41.4208	+	30.0940i	1.34246	+	0.975351i
$953$	7.31766	−	22.5214i	0.237042	−	0.729541i	−0.759802	−	0.650155i	$-0.774704\pi$
$953$	7.31766	−	22.5214i	0.237042	−	0.729541i	0.996844	−	0.0793863i	$-0.0252960\pi$
$954$		0			0
$955$	14.9220	−	10.8415i	0.482866	−	0.350822i
$956$	−39.1978			−1.26775
$957$		0			0
$958$	14.5459			0.469958
$959$	−52.8512	+	38.3986i	−1.70665	+	1.23996i
$960$		0			0
$961$	−9.52235	+	29.3068i	−0.307172	+	0.945380i
$962$	12.5301	+	9.10366i	0.403987	+	0.293514i
$963$		0			0
$964$	−8.54567	+	26.3009i	−0.275238	+	0.847094i
$965$	2.80701	+	8.63910i	0.0903610	+	0.278102i
$966$		0			0
$967$	−31.1399			−1.00139			−0.500696	−	0.865623i	$-0.666923\pi$
$967$	−31.1399			−1.00139			−0.500696	+	0.865623i	$0.666923\pi$
$968$	22.4332	+	13.1536i	0.721032	+	0.422772i
$969$		0			0
$970$	4.81040	−	3.49496i	0.154453	−	0.112216i
$971$	−4.12687	−	12.7012i	−0.132438	−	0.407601i	0.862745	−	0.505639i	$-0.168743\pi$
$971$	−4.12687	−	12.7012i	−0.132438	−	0.407601i	−0.995183	+	0.0980383i	$0.968743\pi$
$972$		0			0
$973$	43.4028	+	31.5340i	1.39143	+	1.01093i
$974$	−1.75807	−	1.27732i	−0.0563323	−	0.0409278i
$975$		0			0
$976$	−1.95236	−	6.00875i	−0.0624936	−	0.192335i
$977$	−7.21314	+	5.24065i	−0.230769	+	0.167663i	−0.697161	−	0.716915i	$-0.745554\pi$
$977$	−7.21314	+	5.24065i	−0.230769	+	0.167663i	0.466392	+	0.884578i	$0.345554\pi$
$978$		0			0
$979$	−18.9485	−	49.8624i	−0.605595	−	1.59361i
$980$	14.3508			0.458421
$981$		0			0
$982$	1.48297	+	4.56411i	0.0473234	+	0.145647i
$983$	5.20958	−	16.0334i	0.166160	−	0.511387i	−0.832960	−	0.553333i	$-0.813356\pi$
$983$	5.20958	−	16.0334i	0.166160	−	0.511387i	0.999120	+	0.0419459i	$0.0133557\pi$
$984$		0			0
$985$	20.6936	+	15.0348i	0.659353	+	0.479048i
$986$	1.23319	−	3.79536i	0.0392727	−	0.120869i
$987$		0			0
$988$	−17.3317	+	12.5922i	−0.551394	+	0.400612i
$989$	4.72049			0.150103
$990$		0			0
$991$	−33.5356			−1.06529			−0.532647	−	0.846338i	$-0.678803\pi$
$991$	−33.5356			−1.06529			−0.532647	+	0.846338i	$0.678803\pi$
$992$	2.00307	−	1.45531i	0.0635975	−	0.0462063i
$993$		0			0
$994$	5.06344	−	15.5837i	0.160603	−	0.494284i
$995$	8.37582	+	6.08539i	0.265531	+	0.192920i
$996$		0			0
$997$	−1.00235	+	3.08492i	−0.0317447	+	0.0977003i	−0.965673	−	0.259759i	$-0.916357\pi$
$997$	−1.00235	+	3.08492i	−0.0317447	+	0.0977003i	0.933929	+	0.357459i	$0.116357\pi$
$998$	3.04532	+	9.37254i	0.0963980	+	0.296682i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.f.e.487.4		36
3.2	odd	2		891.2.f.f.487.6		36
9.2	odd	6		99.2.m.b.58.4	yes	72
9.4	even	3		297.2.n.b.289.4		72
9.5	odd	6		99.2.m.b.25.6	yes	72
9.7	even	3		297.2.n.b.91.6		72
11.2	odd	10		9801.2.a.cn.1.8		18
11.4	even	5	inner	891.2.f.e.730.4		36
11.9	even	5		9801.2.a.cp.1.11		18
33.2	even	10		9801.2.a.co.1.11		18
33.20	odd	10		9801.2.a.cm.1.8		18
33.26	odd	10		891.2.f.f.730.6		36
99.2	even	30		1089.2.e.o.364.8		36
99.4	even	15		297.2.n.b.235.6		72
99.20	odd	30		1089.2.e.p.364.11		36
99.59	odd	30		99.2.m.b.70.4	yes	72
99.68	even	30		1089.2.e.o.727.8		36
99.70	even	15		297.2.n.b.37.4		72
99.86	odd	30		1089.2.e.p.727.11		36
99.92	odd	30		99.2.m.b.4.6	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.6	✓	72	99.92	odd	30
99.2.m.b.25.6	yes	72	9.5	odd	6
99.2.m.b.58.4	yes	72	9.2	odd	6
99.2.m.b.70.4	yes	72	99.59	odd	30
297.2.n.b.37.4		72	99.70	even	15
297.2.n.b.91.6		72	9.7	even	3
297.2.n.b.235.6		72	99.4	even	15
297.2.n.b.289.4		72	9.4	even	3
891.2.f.e.487.4		36	1.1	even	1	trivial
891.2.f.e.730.4		36	11.4	even	5	inner
891.2.f.f.487.6		36	3.2	odd	2
891.2.f.f.730.6		36	33.26	odd	10
1089.2.e.o.364.8		36	99.2	even	30
1089.2.e.o.727.8		36	99.68	even	30
1089.2.e.p.364.11		36	99.20	odd	30
1089.2.e.p.727.11		36	99.86	odd	30
9801.2.a.cm.1.8		18	33.20	odd	10
9801.2.a.cn.1.8		18	11.2	odd	10
9801.2.a.co.1.11		18	33.2	even	10
9801.2.a.cp.1.11		18	11.9	even	5

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.537447 + 0.390478i) q^{2} +(-0.481658 + 1.48239i) q^{4} +(0.903367 + 0.656335i) q^{5} +(-1.20657 + 3.71344i) q^{7} +(-0.730548 - 2.24840i) q^{8} -0.741796 q^{10} +(1.17816 + 3.10031i) q^{11} +(-2.16655 + 1.57409i) q^{13} +(-0.801549 - 2.46691i) q^{14} +(-1.25142 - 0.909207i) q^{16} +(4.48727 + 3.26019i) q^{17} +(-1.58598 - 4.88115i) q^{19} +(-1.40806 + 1.02301i) q^{20} +(-1.84380 - 1.20620i) q^{22} -2.11438 q^{23} +(-1.15979 - 3.56946i) q^{25} +(0.549758 - 1.69198i) q^{26} +(-4.92362 - 3.57722i) q^{28} +(-0.334678 + 1.03003i) q^{29} +(0.348009 - 0.252843i) q^{31} +5.75580 q^{32} -3.68470 q^{34} +(-3.52724 + 2.56269i) q^{35} +(-2.69024 + 8.27970i) q^{37} +(2.75836 + 2.00407i) q^{38} +(0.815747 - 2.51061i) q^{40} +(0.902044 + 2.77621i) q^{41} -2.23257 q^{43} +(-5.16335 + 0.253209i) q^{44} +(1.13637 - 0.825618i) q^{46} +(-3.96638 - 12.2073i) q^{47} +(-6.67071 - 4.84655i) q^{49} +(2.01712 + 1.46552i) q^{50} +(-1.28988 - 3.96985i) q^{52} +(4.56381 - 3.31581i) q^{53} +(-0.970527 + 3.57399i) q^{55} +9.23074 q^{56} +(-0.222333 - 0.684272i) q^{58} +(0.734030 - 2.25911i) q^{59} +(3.30439 + 2.40078i) q^{61} +(-0.0883065 + 0.271779i) q^{62} +(-0.590604 + 0.429099i) q^{64} -2.99032 q^{65} -9.75169 q^{67} +(-6.99421 + 5.08159i) q^{68} +(0.895028 - 2.75461i) q^{70} +(5.11062 + 3.71308i) q^{71} +(-3.60705 + 11.1014i) q^{73} +(-1.78718 - 5.50038i) q^{74} +7.99967 q^{76} +(-12.9344 + 0.634298i) q^{77} +(-3.65248 + 2.65368i) q^{79} +(-0.533744 - 1.64269i) q^{80} +(-1.56885 - 1.13983i) q^{82} +(0.389949 + 0.283315i) q^{83} +(1.91387 + 5.89030i) q^{85} +(1.19989 - 0.871768i) q^{86} +(6.11002 - 4.91390i) q^{88} -16.0830 q^{89} +(-3.23120 - 9.94461i) q^{91} +(1.01841 - 3.13433i) q^{92} +(6.89838 + 5.01197i) q^{94} +(1.77094 - 5.45040i) q^{95} +(-6.48480 + 4.71148i) q^{97} +5.47762 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28}+ \cdots + 164 q^{98}+O(q^{100}) \) 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8 - 4 * q^10 - 2 * q^11 + 11 * q^13 - 10 * q^14 + 9 * q^16 + 10 * q^17 + 4 * q^19 - 45 * q^20 + 16 * q^22 + 20 * q^23 - 11 * q^25 + 6 * q^26 - 27 * q^28 - 23 * q^29 - 3 * q^31 + 18 * q^32 - 8 * q^34 - 9 * q^35 - 21 * q^37 - q^38 + 25 * q^40 + 10 * q^41 + 8 * q^43 - 19 * q^44 - 9 * q^46 - 34 * q^47 - q^49 + 27 * q^52 - 2 * q^53 + 9 * q^55 + 114 * q^56 - q^58 - 16 * q^59 + 3 * q^61 - 92 * q^62 + 13 * q^64 + 84 * q^65 - 10 * q^67 - 23 * q^68 + 46 * q^70 + 24 * q^71 - 20 * q^73 + 68 * q^74 - 16 * q^76 - 26 * q^77 - 19 * q^79 + 28 * q^80 + 47 * q^82 + 7 * q^83 - 25 * q^85 - 77 * q^86 - 18 * q^88 + 28 * q^89 + 10 * q^91 + 50 * q^92 + 63 * q^94 - 77 * q^95 + 33 * q^97 + 164 * q^98

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