LMFDB - Embedded newform 1120.2.bz.f.271.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(271,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("1120.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bz (of order $6$, degree $2$, not 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:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.10
Character	$\chi$	$=$	1120.271
Dual form			1120.2.bz.f.591.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.908317 - 0.524417i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.14799 + 1.54472i) q^{7} +(-0.949974 + 1.64540i) q^{9} +O(q^{10})$	\(q+(0.908317 - 0.524417i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.14799 + 1.54472i) q^{7} +(-0.949974 + 1.64540i) q^{9} +(1.17590 + 2.03673i) q^{11} +1.21209 q^{13} -1.04883i q^{15} +(-4.23538 + 2.44530i) q^{17} +(2.21189 + 1.27704i) q^{19} +(2.76113 + 0.276650i) q^{21} +(7.59015 + 4.38218i) q^{23} +(-0.500000 - 0.866025i) q^{25} +5.13923i q^{27} -5.21449i q^{29} +(1.68841 + 2.92441i) q^{31} +(2.13619 + 1.23333i) q^{33} +(2.41176 - 1.08785i) q^{35} +(-6.16385 - 3.55870i) q^{37} +(1.10097 - 0.635642i) q^{39} +3.18809i q^{41} -11.6101 q^{43} +(0.949974 + 1.64540i) q^{45} +(5.01045 - 8.67836i) q^{47} +(2.22771 + 6.63606i) q^{49} +(-2.56471 + 4.44221i) q^{51} +(7.03102 - 4.05936i) q^{53} +2.35181 q^{55} +2.67880 q^{57} +(9.90904 - 5.72099i) q^{59} +(-0.560848 + 0.971417i) q^{61} +(-4.58221 + 2.06687i) q^{63} +(0.606047 - 1.04970i) q^{65} +(-0.386838 - 0.670023i) q^{67} +9.19235 q^{69} -2.53216i q^{71} +(11.1488 - 6.43675i) q^{73} +(-0.908317 - 0.524417i) q^{75} +(-0.620335 + 6.19130i) q^{77} +(-1.34425 - 0.776104i) q^{79} +(-0.154821 - 0.268158i) q^{81} -4.47506i q^{83} +4.89060i q^{85} +(-2.73457 - 4.73641i) q^{87} +(-9.58219 - 5.53228i) q^{89} +(2.60356 + 1.87234i) q^{91} +(3.06722 + 1.77086i) q^{93} +(2.21189 - 1.27704i) q^{95} +13.3588i q^{97} -4.46831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{3} + 12 q^{5} + 10 q^{7} + 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^3 + 12 * q^5 + 10 * q^7 + 12 * q^9	$ 24 q - 12 q^{3} + 12 q^{5} + 10 q^{7} + 12 q^{9} - 8 q^{11} - 20 q^{13} + 6 q^{17} - 18 q^{19} + 26 q^{21} + 18 q^{23} - 12 q^{25} - 6 q^{31} + 12 q^{33} + 8 q^{35} - 18 q^{39} - 32 q^{43} - 12 q^{45} + 8 q^{49} + 22 q^{51} - 30 q^{53} - 16 q^{55} - 44 q^{57} + 18 q^{59} - 22 q^{61} - 12 q^{63} - 10 q^{65} + 8 q^{67} + 12 q^{69} + 30 q^{73} + 12 q^{75} + 32 q^{77} + 6 q^{79} - 4 q^{81} + 14 q^{87} - 60 q^{89} - 18 q^{91} + 18 q^{93} - 18 q^{95} + 56 q^{99}+O(q^{100}) $ 24 * q - 12 * q^3 + 12 * q^5 + 10 * q^7 + 12 * q^9 - 8 * q^11 - 20 * q^13 + 6 * q^17 - 18 * q^19 + 26 * q^21 + 18 * q^23 - 12 * q^25 - 6 * q^31 + 12 * q^33 + 8 * q^35 - 18 * q^39 - 32 * q^43 - 12 * q^45 + 8 * q^49 + 22 * q^51 - 30 * q^53 - 16 * q^55 - 44 * q^57 + 18 * q^59 - 22 * q^61 - 12 * q^63 - 10 * q^65 + 8 * q^67 + 12 * q^69 + 30 * q^73 + 12 * q^75 + 32 * q^77 + 6 * q^79 - 4 * q^81 + 14 * q^87 - 60 * q^89 - 18 * q^91 + 18 * q^93 - 18 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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			0
$2$		0			0
$3$	0.908317	−	0.524417i	0.524417	−	0.302772i	−0.214323	−	0.976763i	$-0.568755\pi$
$3$	0.908317	−	0.524417i	0.524417	−	0.302772i	0.738740	+	0.673991i	$0.235421\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	2.14799	+	1.54472i	0.811863	+	0.583848i
$7$	2.14799	+	1.54472i	0.811863	+	0.583848i
$8$		0			0
$9$	−0.949974	+	1.64540i	−0.316658	+	0.548468i
$10$		0			0
$11$	1.17590	+	2.03673i	0.354549	+	0.614096i	0.987041	−	0.160471i	$-0.0513012\pi$
$11$	1.17590	+	2.03673i	0.354549	+	0.614096i	−0.632492	+	0.774567i	$0.717968\pi$
$12$		0			0
$13$	1.21209			0.336174			0.168087	−	0.985772i	$-0.446241\pi$
$13$	1.21209			0.336174			0.168087	+	0.985772i	$0.446241\pi$
$14$		0			0
$15$		−	1.04883i		−	0.270808i
$16$		0			0
$17$	−4.23538	+	2.44530i	−1.02723	+	0.593072i	−0.916190	−	0.400744i	$-0.868752\pi$
$17$	−4.23538	+	2.44530i	−1.02723	+	0.593072i	−0.111041	+	0.993816i	$0.535418\pi$
$18$		0			0
$19$	2.21189	+	1.27704i	0.507442	+	0.292972i	0.731782	−	0.681539i	$-0.238689\pi$
$19$	2.21189	+	1.27704i	0.507442	+	0.292972i	−0.224339	+	0.974511i	$0.572022\pi$
$20$		0			0
$21$	2.76113	+	0.276650i	0.602528	+	0.0603700i
$22$		0			0
$23$	7.59015	+	4.38218i	1.58266	+	0.913747i	0.994470	+	0.105021i	$0.0334909\pi$
$23$	7.59015	+	4.38218i	1.58266	+	0.913747i	0.588186	+	0.808726i	$0.299842\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$			5.13923i			0.989045i
$28$		0			0
$29$		−	5.21449i		−	0.968307i	−0.874983	−	0.484153i	$-0.839128\pi$
$29$		−	5.21449i		−	0.968307i	0.874983	−	0.484153i	$-0.160872\pi$
$30$		0			0
$31$	1.68841	+	2.92441i	0.303247	+	0.525239i	0.976869	−	0.213837i	$-0.0685961\pi$
$31$	1.68841	+	2.92441i	0.303247	+	0.525239i	−0.673623	+	0.739075i	$0.735263\pi$
$32$		0			0
$33$	2.13619	+	1.23333i	0.371863	+	0.214695i
$34$		0			0
$35$	2.41176	−	1.08785i	0.407661	−	0.183881i
$36$		0			0
$37$	−6.16385	−	3.55870i	−1.01333	−	0.585046i	−0.101165	−	0.994870i	$-0.532257\pi$
$37$	−6.16385	−	3.55870i	−1.01333	−	0.585046i	−0.912165	+	0.409823i	$0.865590\pi$
$38$		0			0
$39$	1.10097	−	0.635642i	0.176296	−	0.101784i
$40$		0			0
$41$			3.18809i			0.497897i	0.968517	+	0.248948i	$0.0800849\pi$
$41$			3.18809i			0.497897i	−0.968517	+	0.248948i	$0.919915\pi$
$42$		0			0
$43$	−11.6101			−1.77053			−0.885264	−	0.465089i	$-0.846022\pi$
$43$	−11.6101			−1.77053			−0.885264	+	0.465089i	$0.846022\pi$
$44$		0			0
$45$	0.949974	+	1.64540i	0.141614	+	0.245282i
$46$		0			0
$47$	5.01045	−	8.67836i	0.730849	−	1.26587i	−0.225671	−	0.974204i	$-0.572457\pi$
$47$	5.01045	−	8.67836i	0.730849	−	1.26587i	0.956521	−	0.291665i	$-0.0942092\pi$
$48$		0			0
$49$	2.22771	+	6.63606i	0.318244	+	0.948009i
$50$		0			0
$51$	−2.56471	+	4.44221i	−0.359132	+	0.622034i
$52$		0			0
$53$	7.03102	−	4.05936i	0.965784	−	0.557596i	0.0678359	−	0.997696i	$-0.478391\pi$
$53$	7.03102	−	4.05936i	0.965784	−	0.557596i	0.897948	+	0.440101i	$0.145057\pi$
$54$		0			0
$55$	2.35181			0.317118
$56$		0			0
$57$	2.67880			0.354815
$58$		0			0
$59$	9.90904	−	5.72099i	1.29005	−	0.744809i	0.311385	−	0.950284i	$-0.399207\pi$
$59$	9.90904	−	5.72099i	1.29005	−	0.744809i	0.978662	+	0.205475i	$0.0658738\pi$
$60$		0			0
$61$	−0.560848	+	0.971417i	−0.0718092	+	0.124377i	−0.899694	−	0.436521i	$-0.856211\pi$
$61$	−0.560848	+	0.971417i	−0.0718092	+	0.124377i	0.827885	+	0.560898i	$0.189544\pi$
$62$		0			0
$63$	−4.58221	+	2.06687i	−0.577304	+	0.260401i
$64$		0			0
$65$	0.606047	−	1.04970i	0.0751709	−	0.130200i
$66$		0			0
$67$	−0.386838	−	0.670023i	−0.0472598	−	0.0818563i	0.841428	−	0.540369i	$-0.181716\pi$
$67$	−0.386838	−	0.670023i	−0.0472598	−	0.0818563i	−0.888688	+	0.458513i	$0.848382\pi$
$68$		0			0
$69$	9.19235			1.10663
$70$		0			0
$71$		−	2.53216i		−	0.300512i	−0.988647	−	0.150256i	$-0.951990\pi$
$71$		−	2.53216i		−	0.300512i	0.988647	−	0.150256i	$-0.0480097\pi$
$72$		0			0
$73$	11.1488	−	6.43675i	1.30487	−	0.753365i	0.323631	−	0.946183i	$-0.395096\pi$
$73$	11.1488	−	6.43675i	1.30487	−	0.753365i	0.981234	+	0.192819i	$0.0617629\pi$
$74$		0			0
$75$	−0.908317	−	0.524417i	−0.104883	−	0.0605545i
$76$		0			0
$77$	−0.620335	+	6.19130i	−0.0706937	+	0.705565i
$78$		0			0
$79$	−1.34425	−	0.776104i	−0.151240	−	0.0873186i	0.422470	−	0.906377i	$-0.361163\pi$
$79$	−1.34425	−	0.776104i	−0.151240	−	0.0873186i	−0.573710	+	0.819058i	$0.694496\pi$
$80$		0			0
$81$	−0.154821	−	0.268158i	−0.0172023	−	0.0297953i
$82$		0			0
$83$		−	4.47506i		−	0.491202i	−0.969371	−	0.245601i	$-0.921015\pi$
$83$		−	4.47506i		−	0.491202i	0.969371	−	0.245601i	$-0.0789853\pi$
$84$		0			0
$85$			4.89060i			0.530460i
$86$		0			0
$87$	−2.73457	−	4.73641i	−0.293176	−	0.507796i
$88$		0			0
$89$	−9.58219	−	5.53228i	−1.01571	−	0.586420i	−0.102851	−	0.994697i	$-0.532797\pi$
$89$	−9.58219	−	5.53228i	−1.01571	−	0.586420i	−0.912858	+	0.408276i	$0.866130\pi$
$90$		0			0
$91$	2.60356	+	1.87234i	0.272928	+	0.196275i
$92$		0			0
$93$	3.06722	+	1.77086i	0.318055	+	0.183629i
$94$		0			0
$95$	2.21189	−	1.27704i	0.226935	−	0.131021i
$96$		0			0
$97$			13.3588i			1.35638i	0.734888	+	0.678189i	$0.237235\pi$
$97$			13.3588i			1.35638i	−0.734888	+	0.678189i	$0.762765\pi$
$98$		0			0
$99$	−4.46831			−0.449082
$100$		0			0
$101$	0.799019	+	1.38394i	0.0795054	+	0.137707i	0.903037	−	0.429564i	$-0.141333\pi$
$101$	0.799019	+	1.38394i	0.0795054	+	0.137707i	−0.823531	+	0.567271i	$0.807999\pi$
$102$		0			0
$103$	1.77318	−	3.07124i	0.174717	−	0.302618i	−0.765346	−	0.643619i	$-0.777432\pi$
$103$	1.77318	−	3.07124i	0.174717	−	0.302618i	0.940063	+	0.341000i	$0.110766\pi$
$104$		0			0
$105$	1.62015	−	2.25288i	0.158110	−	0.219859i
$106$		0			0
$107$	−4.99959	+	8.65954i	−0.483329	+	0.837150i	−0.999817	−	0.0191446i	$-0.993906\pi$
$107$	−4.99959	+	8.65954i	−0.483329	+	0.837150i	0.516488	+	0.856294i	$0.327239\pi$
$108$		0			0
$109$	−4.17287	+	2.40921i	−0.399689	+	0.230760i	−0.686350	−	0.727272i	$-0.740788\pi$
$109$	−4.17287	+	2.40921i	−0.399689	+	0.230760i	0.286661	+	0.958032i	$0.407455\pi$
$110$		0			0
$111$	−7.46497			−0.708543
$112$		0			0
$113$	8.76609			0.824644			0.412322	−	0.911038i	$-0.364718\pi$
$113$	8.76609			0.824644			0.412322	+	0.911038i	$0.364718\pi$
$114$		0			0
$115$	7.59015	−	4.38218i	0.707785	−	0.408640i
$116$		0			0
$117$	−1.15146	+	1.99438i	−0.106452	+	0.184381i
$118$		0			0
$119$	−12.8748	−	1.28999i	−1.18024	−	0.118253i
$120$		0			0
$121$	2.73450	−	4.73629i	0.248591	−	0.430571i
$122$		0			0
$123$	1.67189	+	2.89580i	0.150749	+	0.261105i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$			2.51008i			0.222734i	0.993779	+	0.111367i	$0.0355229\pi$
$127$			2.51008i			0.222734i	−0.993779	+	0.111367i	$0.964477\pi$
$128$		0			0
$129$	−10.5457	+	6.08855i	−0.928495	+	0.536067i
$130$		0			0
$131$	−4.72620	−	2.72867i	−0.412930	−	0.238405i	0.279118	−	0.960257i	$-0.409958\pi$
$131$	−4.72620	−	2.72867i	−0.412930	−	0.238405i	−0.692048	+	0.721852i	$0.743291\pi$
$132$		0			0
$133$	2.77846	+	6.15980i	0.240923	+	0.534122i
$134$		0			0
$135$	4.45070	+	2.56962i	0.383056	+	0.221157i
$136$		0			0
$137$	−7.53495	−	13.0509i	−0.643754	−	1.11502i	−0.984588	−	0.174891i	$-0.944043\pi$
$137$	−7.53495	−	13.0509i	−0.643754	−	1.11502i	0.340833	−	0.940124i	$-0.389291\pi$
$138$		0			0
$139$			15.2747i			1.29558i	0.761819	+	0.647789i	$0.224306\pi$
$139$			15.2747i			1.29558i	−0.761819	+	0.647789i	$0.775694\pi$
$140$		0			0
$141$		−	10.5103i		−	0.885124i
$142$		0			0
$143$	1.42531	+	2.46870i	0.119190	+	0.206443i
$144$		0			0
$145$	−4.51588	−	2.60725i	−0.375024	−	0.216520i
$146$		0			0
$147$	5.50353	+	4.85940i	0.453923	+	0.400797i
$148$		0			0
$149$	3.67599	+	2.12234i	0.301149	+	0.173869i	0.642959	−	0.765901i	$-0.277707\pi$
$149$	3.67599	+	2.12234i	0.301149	+	0.173869i	−0.341810	+	0.939769i	$0.611040\pi$
$150$		0			0
$151$	1.03731	−	0.598892i	0.0844152	−	0.0487371i	−0.457198	−	0.889365i	$-0.651147\pi$
$151$	1.03731	−	0.598892i	0.0844152	−	0.0487371i	0.541613	+	0.840628i	$0.317814\pi$
$152$		0			0
$153$		−	9.29188i		−	0.751204i
$154$		0			0
$155$	3.37681			0.271232
$156$		0			0
$157$	5.51369	+	9.54999i	0.440040	+	0.762172i	0.997692	−	0.0679028i	$-0.0216308\pi$
$157$	5.51369	+	9.54999i	0.440040	+	0.762172i	−0.557652	+	0.830075i	$0.688297\pi$
$158$		0			0
$159$	4.25759	−	7.37437i	0.337649	−	0.584825i
$160$		0			0
$161$	9.53434	+	21.1375i	0.751411	+	1.66587i
$162$		0			0
$163$	6.36400	−	11.0228i	0.498467	−	0.863370i	−0.501532	−	0.865139i	$-0.667230\pi$
$163$	6.36400	−	11.0228i	0.498467	−	0.863370i	0.999998	+	0.00176946i	$0.000563235\pi$
$164$		0			0
$165$	2.13619	−	1.23333i	0.166302	−	0.0960145i
$166$		0			0
$167$	−15.0560			−1.16507			−0.582535	−	0.812805i	$-0.697939\pi$
$167$	−15.0560			−1.16507			−0.582535	+	0.812805i	$0.697939\pi$
$168$		0			0
$169$	−11.5308			−0.886987
$170$		0			0
$171$	−4.20247	+	2.42630i	−0.321371	+	0.185544i
$172$		0			0
$173$	6.09623	−	10.5590i	0.463488	−	0.802784i	−0.535644	−	0.844444i	$-0.679931\pi$
$173$	6.09623	−	10.5590i	0.463488	−	0.802784i	0.999132	+	0.0416597i	$0.0132645\pi$
$174$		0			0
$175$	0.263769	−	2.63257i	0.0199391	−	0.199004i
$176$		0			0
$177$	6.00037	−	10.3929i	0.451015	−	0.781181i
$178$		0			0
$179$	0.698646	+	1.21009i	0.0522192	+	0.0904464i	0.890953	−	0.454095i	$-0.150037\pi$
$179$	0.698646	+	1.21009i	0.0522192	+	0.0904464i	−0.838734	+	0.544541i	$0.816704\pi$
$180$		0			0
$181$	−25.6584			−1.90717			−0.953587	−	0.301118i	$-0.902640\pi$
$181$	−25.6584			−1.90717			−0.953587	+	0.301118i	$0.902640\pi$
$182$		0			0
$183$			1.17647i			0.0869674i
$184$		0			0
$185$	−6.16385	+	3.55870i	−0.453175	+	0.261641i
$186$		0			0
$187$	−9.96081	−	5.75088i	−0.728407	−	0.420546i
$188$		0			0
$189$	−7.93865	+	11.0390i	−0.577452	+	0.802970i
$190$		0			0
$191$	−6.13554	−	3.54235i	−0.443952	−	0.256316i	0.261321	−	0.965252i	$-0.415842\pi$
$191$	−6.13554	−	3.54235i	−0.443952	−	0.256316i	−0.705273	+	0.708936i	$0.749175\pi$
$192$		0			0
$193$	−9.51108	−	16.4737i	−0.684622	−	1.18580i	−0.973555	−	0.228451i	$-0.926634\pi$
$193$	−9.51108	−	16.4737i	−0.684622	−	1.18580i	0.288933	−	0.957349i	$-0.406699\pi$
$194$		0			0
$195$		−	1.27128i		−	0.0910386i
$196$		0			0
$197$		−	25.7446i		−	1.83423i	−0.398626	−	0.917113i	$-0.630513\pi$
$197$		−	25.7446i		−	1.83423i	0.398626	−	0.917113i	$-0.369487\pi$
$198$		0			0
$199$	3.38261	+	5.85886i	0.239787	+	0.415323i	0.960653	−	0.277751i	$-0.0895891\pi$
$199$	3.38261	+	5.85886i	0.239787	+	0.415323i	−0.720866	+	0.693074i	$0.756256\pi$
$200$		0			0
$201$	−0.702743	−	0.405729i	−0.0495676	−	0.0286179i
$202$		0			0
$203$	8.05491	−	11.2007i	0.565344	−	0.786132i
$204$		0			0
$205$	2.76097	+	1.59405i	0.192835	+	0.111333i
$206$		0			0
$207$	−14.4209	+	8.32590i	−1.00232	+	0.578690i
$208$		0			0
$209$			6.00669i			0.415491i
$210$		0			0
$211$	−14.7573			−1.01593			−0.507967	−	0.861377i	$-0.669603\pi$
$211$	−14.7573			−1.01593			−0.507967	+	0.861377i	$0.669603\pi$
$212$		0			0
$213$	−1.32791	−	2.30000i	−0.0909866	−	0.157593i
$214$		0			0
$215$	−5.80506	+	10.0547i	−0.395902	+	0.685723i
$216$		0			0
$217$	−0.890699	+	8.88969i	−0.0604646	+	0.603472i
$218$		0			0
$219$	6.75108	−	11.6932i	0.456196	−	0.790154i
$220$		0			0
$221$	−5.13368	+	2.96393i	−0.345329	+	0.199376i
$222$		0			0
$223$	14.4522			0.967791			0.483896	−	0.875126i	$-0.339221\pi$
$223$	14.4522			0.967791			0.483896	+	0.875126i	$0.339221\pi$
$224$		0			0
$225$	1.89995			0.126663
$226$		0			0
$227$	3.97850	−	2.29699i	0.264062	−	0.152456i	−0.362124	−	0.932130i	$-0.617948\pi$
$227$	3.97850	−	2.29699i	0.264062	−	0.152456i	0.626186	+	0.779673i	$0.284615\pi$
$228$		0			0
$229$	−6.54085	+	11.3291i	−0.432232	+	0.748647i	−0.997065	−	0.0765577i	$-0.975607\pi$
$229$	−6.54085	+	11.3291i	−0.432232	+	0.748647i	0.564833	+	0.825205i	$0.308940\pi$
$230$		0			0
$231$	2.68336	+	5.94898i	0.176552	+	0.391414i
$232$		0			0
$233$	10.4329	−	18.0703i	0.683483	−	1.18383i	−0.290428	−	0.956897i	$-0.593798\pi$
$233$	10.4329	−	18.0703i	0.683483	−	1.18383i	0.973911	−	0.226931i	$-0.0728691\pi$
$234$		0			0
$235$	−5.01045	−	8.67836i	−0.326846	−	0.566114i
$236$		0			0
$237$	−1.62801			−0.105751
$238$		0			0
$239$			2.94959i			0.190793i	0.995439	+	0.0953964i	$0.0304119\pi$
$239$			2.94959i			0.190793i	−0.995439	+	0.0953964i	$0.969588\pi$
$240$		0			0
$241$	0.798690	−	0.461124i	0.0514481	−	0.0297036i	−0.474055	−	0.880495i	$-0.657210\pi$
$241$	0.798690	−	0.461124i	0.0514481	−	0.0297036i	0.525503	+	0.850791i	$0.323877\pi$
$242$		0			0
$243$	−13.6334	−	7.87123i	−0.874581	−	0.504940i
$244$		0			0
$245$	6.86085	+	1.38878i	0.438324	+	0.0887260i
$246$		0			0
$247$	2.68102	+	1.54789i	0.170589	+	0.0984896i
$248$		0			0
$249$	−2.34680	−	4.06478i	−0.148722	−	0.257595i
$250$		0			0
$251$			9.30464i			0.587304i	0.955912	+	0.293652i	$0.0948706\pi$
$251$			9.30464i			0.587304i	−0.955912	+	0.293652i	$0.905129\pi$
$252$		0			0
$253$			20.6121i			1.29587i
$254$		0			0
$255$	2.56471	+	4.44221i	0.160609	+	0.278182i
$256$		0			0
$257$	26.0684	+	15.0506i	1.62610	+	0.938832i	0.985240	+	0.171178i	$0.0547575\pi$
$257$	26.0684	+	15.0506i	1.62610	+	0.938832i	0.640865	+	0.767654i	$0.278576\pi$
$258$		0			0
$259$	−7.74269	−	17.1654i	−0.481107	−	1.06661i
$260$		0			0
$261$	8.57994	+	4.95363i	0.531085	+	0.306622i
$262$		0			0
$263$	15.2475	−	8.80316i	0.940202	−	0.542826i	0.0501785	−	0.998740i	$-0.484021\pi$
$263$	15.2475	−	8.80316i	0.940202	−	0.542826i	0.890024	+	0.455914i	$0.150688\pi$
$264$		0			0
$265$		−	8.11872i		−	0.498729i
$266$		0			0
$267$	−11.6049			−0.710207
$268$		0			0
$269$	−4.10363	−	7.10769i	−0.250202	−	0.433363i	0.713379	−	0.700778i	$-0.247164\pi$
$269$	−4.10363	−	7.10769i	−0.250202	−	0.433363i	−0.963581	+	0.267415i	$0.913831\pi$
$270$		0			0
$271$	−7.40183	+	12.8204i	−0.449629	+	0.778781i	−0.998362	−	0.0572171i	$-0.981777\pi$
$271$	−7.40183	+	12.8204i	−0.449629	+	0.778781i	0.548732	+	0.835998i	$0.315111\pi$
$272$		0			0
$273$	3.34675	+	0.335326i	0.202554	+	0.0202948i
$274$		0			0
$275$	1.17590	−	2.03673i	0.0709097	−	0.122819i
$276$		0			0
$277$	−5.53090	+	3.19327i	−0.332320	+	0.191865i	−0.656870	−	0.754003i	$-0.728120\pi$
$277$	−5.53090	+	3.19327i	−0.332320	+	0.191865i	0.324551	+	0.945868i	$0.394787\pi$
$278$		0			0
$279$	−6.41577			−0.384102
$280$		0			0
$281$	−12.2559			−0.731128			−0.365564	−	0.930786i	$-0.619124\pi$
$281$	−12.2559			−0.731128			−0.365564	+	0.930786i	$0.619124\pi$
$282$		0			0
$283$	14.5951	−	8.42649i	0.867589	−	0.500903i	0.00104298	−	0.999999i	$-0.499668\pi$
$283$	14.5951	−	8.42649i	0.867589	−	0.500903i	0.866546	+	0.499096i	$0.166335\pi$
$284$		0			0
$285$	1.33940	−	2.31990i	0.0793391	−	0.137419i
$286$		0			0
$287$	−4.92470	+	6.84799i	−0.290696	+	0.404224i
$288$		0			0
$289$	3.45898	−	5.99113i	0.203469	−	0.352419i
$290$		0			0
$291$	7.00556	+	12.1340i	0.410673	+	0.711307i
$292$		0			0
$293$	−27.0419			−1.57980			−0.789902	−	0.613233i	$-0.789869\pi$
$293$	−27.0419			−1.57980			−0.789902	+	0.613233i	$0.789869\pi$
$294$		0			0
$295$		−	11.4420i		−	0.666178i
$296$		0			0
$297$	−10.4672	+	6.04325i	−0.607369	+	0.350665i
$298$		0			0
$299$	9.19997	+	5.31161i	0.532048	+	0.307178i
$300$		0			0
$301$	−24.9384	−	17.9343i	−1.43743	−	1.03372i
$302$		0			0
$303$	1.45153	+	0.838038i	0.0833879	+	0.0481441i
$304$		0			0
$305$	0.560848	+	0.971417i	0.0321141	+	0.0556232i
$306$		0			0
$307$		−	3.32341i		−	0.189677i	−0.995493	−	0.0948386i	$-0.969766\pi$
$307$		−	3.32341i		−	0.189677i	0.995493	−	0.0948386i	$-0.0302335\pi$
$308$		0			0
$309$		−	3.71955i		−	0.211598i
$310$		0			0
$311$	−17.2937	−	29.9536i	−0.980637	−	1.69851i	−0.659915	−	0.751340i	$-0.729408\pi$
$311$	−17.2937	−	29.9536i	−0.980637	−	1.69851i	−0.320723	−	0.947173i	$-0.603926\pi$
$312$		0			0
$313$	−12.5334	−	7.23619i	−0.708432	−	0.409014i	0.102048	−	0.994779i	$-0.467461\pi$
$313$	−12.5334	−	7.23619i	−0.708432	−	0.409014i	−0.810480	+	0.585766i	$0.800794\pi$
$314$		0			0
$315$	−0.501147	+	5.00174i	−0.0282365	+	0.281816i
$316$		0			0
$317$	−13.1460	−	7.58984i	−0.738352	−	0.426288i	0.0831178	−	0.996540i	$-0.473512\pi$
$317$	−13.1460	−	7.58984i	−0.738352	−	0.426288i	−0.821470	+	0.570252i	$0.806846\pi$
$318$		0			0
$319$	10.6205	−	6.13174i	0.594633	−	0.343312i
$320$		0			0
$321$			10.4875i			0.585354i
$322$		0			0
$323$	−12.4909			−0.695014
$324$		0			0
$325$	−0.606047	−	1.04970i	−0.0336174	−	0.0582271i
$326$		0			0
$327$	−2.52686	+	4.37665i	−0.139736	+	0.242029i
$328$		0			0
$329$	24.1680	−	10.9013i	1.33242	−	0.601007i
$330$		0			0
$331$	−8.23079	+	14.2562i	−0.452405	+	0.783589i	−0.998535	−	0.0541118i	$-0.982767\pi$
$331$	−8.23079	+	14.2562i	−0.452405	+	0.783589i	0.546130	+	0.837701i	$0.316101\pi$
$332$		0			0
$333$	11.7110	−	6.76134i	0.641758	−	0.370519i
$334$		0			0
$335$	−0.773676			−0.0422704
$336$		0			0
$337$	−28.2883			−1.54096			−0.770482	−	0.637462i	$-0.779984\pi$
$337$	−28.2883			−1.54096			−0.770482	+	0.637462i	$0.779984\pi$
$338$		0			0
$339$	7.96238	−	4.59708i	0.432457	−	0.249679i
$340$		0			0
$341$	−3.97081	+	6.87764i	−0.215031	+	0.372445i
$342$		0			0
$343$	−5.46574	+	17.6954i	−0.295122	+	0.955459i
$344$		0			0
$345$	4.59617	−	7.96081i	0.247450	−	0.428595i
$346$		0			0
$347$	−0.490872	−	0.850215i	−0.0263514	−	0.0456420i	0.852549	−	0.522647i	$-0.175056\pi$
$347$	−0.490872	−	0.850215i	−0.0263514	−	0.0456420i	−0.878900	+	0.477005i	$0.841722\pi$
$348$		0			0
$349$	−25.8547			−1.38397			−0.691985	−	0.721912i	$-0.743264\pi$
$349$	−25.8547			−1.38397			−0.691985	+	0.721912i	$0.743264\pi$
$350$		0			0
$351$			6.22923i			0.332492i
$352$		0			0
$353$	11.4688	−	6.62150i	0.610421	−	0.352427i	−0.162709	−	0.986674i	$-0.552023\pi$
$353$	11.4688	−	6.62150i	0.610421	−	0.352427i	0.773130	+	0.634247i	$0.218690\pi$
$354$		0			0
$355$	−2.19291	−	1.26608i	−0.116388	−	0.0671965i
$356$		0			0
$357$	−12.3709	+	5.58007i	−0.654739	+	0.295329i
$358$		0			0
$359$	4.64380	+	2.68110i	0.245090	+	0.141503i	0.617514	−	0.786560i	$-0.288140\pi$
$359$	4.64380	+	2.68110i	0.245090	+	0.141503i	−0.372424	+	0.928063i	$0.621473\pi$
$360$		0			0
$361$	−6.23836	−	10.8052i	−0.328335	−	0.568693i
$362$		0			0
$363$		−	5.73606i		−	0.301065i
$364$		0			0
$365$		−	12.8735i		−	0.673830i
$366$		0			0
$367$	10.6905	+	18.5165i	0.558041	+	0.966556i	0.997660	+	0.0683713i	$0.0217803\pi$
$367$	10.6905	+	18.5165i	0.558041	+	0.966556i	−0.439619	+	0.898185i	$0.644886\pi$
$368$		0			0
$369$	−5.24570	−	3.02861i	−0.273080	−	0.157663i
$370$		0			0
$371$	21.3731	+	2.14147i	1.10964	+	0.111179i
$372$		0			0
$373$	7.38217	+	4.26210i	0.382234	+	0.220683i	0.678790	−	0.734333i	$-0.262505\pi$
$373$	7.38217	+	4.26210i	0.382234	+	0.220683i	−0.296556	+	0.955016i	$0.595838\pi$
$374$		0			0
$375$	−0.908317	+	0.524417i	−0.0469053	+	0.0270808i
$376$		0			0
$377$		−	6.32045i		−	0.325520i
$378$		0			0
$379$	4.45055			0.228609			0.114305	−	0.993446i	$-0.463536\pi$
$379$	4.45055			0.228609			0.114305	+	0.993446i	$0.463536\pi$
$380$		0			0
$381$	1.31633	+	2.27995i	0.0674376	+	0.116805i
$382$		0			0
$383$	−5.77418	+	10.0012i	−0.295047	+	0.511036i	−0.974996	−	0.222223i	$-0.928669\pi$
$383$	−5.77418	+	10.0012i	−0.295047	+	0.511036i	0.679949	+	0.733259i	$0.262002\pi$
$384$		0			0
$385$	5.05166	+	3.63288i	0.257456	+	0.185149i
$386$		0			0
$387$	11.0293	−	19.1033i	0.560652	−	0.971077i
$388$		0			0
$389$	8.52646	−	4.92276i	0.432309	−	0.249594i	−0.268021	−	0.963413i	$-0.586370\pi$
$389$	8.52646	−	4.92276i	0.432309	−	0.249594i	0.700330	+	0.713819i	$0.253036\pi$
$390$		0			0
$391$	−42.8629			−2.16767
$392$		0			0
$393$	−5.72385			−0.288730
$394$		0			0
$395$	−1.34425	+	0.776104i	−0.0676367	+	0.0390500i
$396$		0			0
$397$	13.9206	−	24.1113i	0.698657	−	1.21011i	−0.270275	−	0.962783i	$-0.587115\pi$
$397$	13.9206	−	24.1113i	0.698657	−	1.21011i	0.968932	−	0.247327i	$-0.0795521\pi$
$398$		0			0
$399$	5.75402	+	4.13798i	0.288061	+	0.207158i
$400$		0			0
$401$	−18.2301	+	31.5755i	−0.910370	+	1.57681i	−0.0968267	+	0.995301i	$0.530869\pi$
$401$	−18.2301	+	31.5755i	−0.910370	+	1.57681i	−0.813543	+	0.581505i	$0.802464\pi$
$402$		0			0
$403$	2.04651	+	3.54465i	0.101944	+	0.176572i
$404$		0			0
$405$	−0.309642			−0.0153862
$406$		0			0
$407$		−	16.7388i		−	0.829709i
$408$		0			0
$409$	3.55633	−	2.05325i	0.175849	−	0.101527i	−0.409492	−	0.912314i	$-0.634294\pi$
$409$	3.55633	−	2.05325i	0.175849	−	0.101527i	0.585341	+	0.810787i	$0.300961\pi$
$410$		0			0
$411$	−13.6882	−	7.90291i	−0.675191	−	0.389822i
$412$		0			0
$413$	30.1218	+	3.01804i	1.48220	+	0.148508i
$414$		0			0
$415$	−3.87552	−	2.23753i	−0.190242	−	0.109836i
$416$		0			0
$417$	8.01029	+	13.8742i	0.392265	+	0.679424i
$418$		0			0
$419$			39.8516i			1.94688i	0.228943	+	0.973440i	$0.426473\pi$
$419$			39.8516i			1.94688i	−0.228943	+	0.973440i	$0.573527\pi$
$420$		0			0
$421$		−	10.2595i		−	0.500020i	−0.968243	−	0.250010i	$-0.919566\pi$
$421$		−	10.2595i		−	0.500020i	0.968243	−	0.250010i	$-0.0804339\pi$
$422$		0			0
$423$	9.51959	+	16.4884i	0.462859	+	0.801694i
$424$		0			0
$425$	4.23538	+	2.44530i	0.205446	+	0.118614i
$426$		0			0
$427$	−2.70526	+	1.22024i	−0.130917	+	0.0590517i
$428$		0			0
$429$	2.58926	+	1.49491i	0.125011	+	0.0721749i
$430$		0			0
$431$	13.6969	−	7.90789i	0.659755	−	0.380909i	−0.132429	−	0.991193i	$-0.542278\pi$
$431$	13.6969	−	7.90789i	0.659755	−	0.380909i	0.792183	+	0.610283i	$0.208944\pi$
$432$		0			0
$433$			32.7619i			1.57443i	0.616676	+	0.787217i	$0.288479\pi$
$433$			32.7619i			1.57443i	−0.616676	+	0.787217i	$0.711521\pi$
$434$		0			0
$435$	−5.46913			−0.262225
$436$		0			0
$437$	11.1924	+	19.3858i	0.535404	+	0.927347i
$438$		0			0
$439$	−0.202051	+	0.349962i	−0.00964336	+	0.0167028i	−0.870807	−	0.491625i	$-0.836403\pi$
$439$	−0.202051	+	0.349962i	−0.00964336	+	0.0167028i	0.861163	+	0.508328i	$0.169736\pi$
$440$		0			0
$441$	−13.0353	−	2.63861i	−0.620727	−	0.125648i
$442$		0			0
$443$	16.1659	−	28.0002i	0.768066	−	1.33033i	−0.170544	−	0.985350i	$-0.554553\pi$
$443$	16.1659	−	28.0002i	0.768066	−	1.33033i	0.938610	−	0.344979i	$-0.112114\pi$
$444$		0			0
$445$	−9.58219	+	5.53228i	−0.454239	+	0.262255i
$446$		0			0
$447$	4.45196			0.210570
$448$		0			0
$449$	4.91848			0.232117			0.116059	−	0.993242i	$-0.462974\pi$
$449$	4.91848			0.232117			0.116059	+	0.993242i	$0.462974\pi$
$450$		0			0
$451$	−6.49328	+	3.74889i	−0.305756	+	0.176529i
$452$		0			0
$453$	0.628138	−	1.08797i	0.0295125	−	0.0511172i
$454$		0			0
$455$	2.92328	−	1.31858i	0.137045	−	0.0618160i
$456$		0			0
$457$	10.7472	−	18.6147i	0.502733	−	0.870759i	−0.497262	−	0.867601i	$-0.665661\pi$
$457$	10.7472	−	18.6147i	0.502733	−	0.870759i	0.999995	−	0.00315885i	$-0.00100550\pi$
$458$		0			0
$459$	−12.5670	−	21.7666i	−0.586575	−	1.01598i
$460$		0			0
$461$	27.8967			1.29928			0.649639	−	0.760243i	$-0.274920\pi$
$461$	27.8967			1.29928			0.649639	+	0.760243i	$0.274920\pi$
$462$		0			0
$463$		−	38.9342i		−	1.80942i	−0.426024	−	0.904712i	$-0.640086\pi$
$463$		−	38.9342i		−	1.80942i	0.426024	−	0.904712i	$-0.359914\pi$
$464$		0			0
$465$	3.06722	−	1.77086i	0.142239	−	0.0821216i
$466$		0			0
$467$	21.6588	+	12.5047i	1.00225	+	0.578650i	0.908914	−	0.416984i	$-0.136913\pi$
$467$	21.6588	+	12.5047i	1.00225	+	0.578650i	0.0933379	+	0.995634i	$0.470246\pi$
$468$		0			0
$469$	0.204072	−	2.03676i	0.00942316	−	0.0940486i
$470$		0			0
$471$	10.0164	+	5.78295i	0.461529	+	0.266464i
$472$		0			0
$473$	−13.6524	−	23.6467i	−0.627738	−	1.08727i
$474$		0			0
$475$		−	2.55407i		−	0.117189i
$476$		0			0
$477$			15.4251i			0.706268i
$478$		0			0
$479$	−4.29962	−	7.44716i	−0.196455	−	0.340269i	0.750922	−	0.660391i	$-0.229609\pi$
$479$	−4.29962	−	7.44716i	−0.196455	−	0.340269i	−0.947376	+	0.320122i	$0.896276\pi$
$480$		0			0
$481$	−7.47116	−	4.31348i	−0.340655	−	0.196678i
$482$		0			0
$483$	19.7451	+	14.1996i	0.898431	+	0.646103i
$484$		0			0
$485$	11.5690	+	6.67938i	0.525323	+	0.303295i
$486$		0			0
$487$	12.9204	−	7.45959i	0.585478	−	0.338026i	−0.177829	−	0.984061i	$-0.556907\pi$
$487$	12.9204	−	7.45959i	0.585478	−	0.338026i	0.763308	+	0.646035i	$0.223574\pi$
$488$		0			0
$489$		−	13.3496i		−	0.603688i
$490$		0			0
$491$	−3.92024			−0.176918			−0.0884589	−	0.996080i	$-0.528194\pi$
$491$	−3.92024			−0.176918			−0.0884589	+	0.996080i	$0.528194\pi$
$492$		0			0
$493$	12.7510	+	22.0854i	0.574276	+	0.994675i
$494$		0			0
$495$	−2.23416	+	3.86967i	−0.100418	+	0.173929i
$496$		0			0
$497$	3.91146	−	5.43904i	0.175453	−	0.243974i
$498$		0			0
$499$	−5.70995	+	9.88993i	−0.255613	+	0.442734i	−0.965062	−	0.262023i	$-0.915610\pi$
$499$	−5.70995	+	9.88993i	−0.255613	+	0.442734i	0.709449	+	0.704757i	$0.248944\pi$
$500$		0			0
$501$	−13.6756	+	7.89564i	−0.610983	+	0.352751i
$502$		0			0
$503$	22.9658			1.02399			0.511997	−	0.858987i	$-0.328906\pi$
$503$	22.9658			1.02399			0.511997	+	0.858987i	$0.328906\pi$
$504$		0			0
$505$	1.59804			0.0711118
$506$		0			0
$507$	−10.4736	+	6.04696i	−0.465151	+	0.268555i
$508$		0			0
$509$	12.4956	−	21.6429i	0.553856	−	0.959306i	−0.444136	−	0.895959i	$-0.646489\pi$
$509$	12.4956	−	21.6429i	0.553856	−	0.959306i	0.997992	−	0.0633469i	$-0.0201774\pi$
$510$		0			0
$511$	33.8904	+	3.39563i	1.49922	+	0.150214i
$512$		0			0
$513$	−6.56298	+	11.3674i	−0.289763	+	0.501883i
$514$		0			0
$515$	−1.77318	−	3.07124i	−0.0781357	−	0.135335i
$516$		0			0
$517$	23.5673			1.03649
$518$		0			0
$519$		−	12.7879i		−	0.561325i
$520$		0			0
$521$	14.0875	−	8.13341i	0.617184	−	0.356331i	−0.158588	−	0.987345i	$-0.550694\pi$
$521$	14.0875	−	8.13341i	0.617184	−	0.356331i	0.775772	+	0.631014i	$0.217361\pi$
$522$		0			0
$523$	16.4913	+	9.52126i	0.721114	+	0.416336i	0.815163	−	0.579232i	$-0.196647\pi$
$523$	16.4913	+	9.52126i	0.721114	+	0.416336i	−0.0940483	+	0.995568i	$0.529981\pi$
$524$		0			0
$525$	−1.14098	−	2.52953i	−0.0497964	−	0.110398i
$526$		0			0
$527$	−14.3021	−	8.25732i	−0.623009	−	0.359694i
$528$		0			0
$529$	26.9069	+	46.6042i	1.16987	+	2.02627i
$530$		0			0
$531$			21.7392i			0.943399i
$532$		0			0
$533$			3.86427i			0.167380i
$534$		0			0
$535$	4.99959	+	8.65954i	0.216151	+	0.374385i
$536$		0			0
$537$	1.26918	+	0.732763i	0.0547693	+	0.0316211i
$538$		0			0
$539$	−10.8963	+	12.3406i	−0.469336	+	0.531548i
$540$		0			0
$541$	33.7035	+	19.4587i	1.44902	+	0.836595i	0.998423	−	0.0561307i	$-0.0178764\pi$
$541$	33.7035	+	19.4587i	1.44902	+	0.836595i	0.450601	+	0.892725i	$0.351210\pi$
$542$		0			0
$543$	−23.3060	+	13.4557i	−1.00015	+	0.577439i
$544$		0			0
$545$			4.81842i			0.206398i
$546$		0			0
$547$	1.29047			0.0551764			0.0275882	−	0.999619i	$-0.491217\pi$
$547$	1.29047			0.0551764			0.0275882	+	0.999619i	$0.491217\pi$
$548$		0			0
$549$	−1.06558	−	1.84564i	−0.0454779	−	0.0787701i
$550$		0			0
$551$	6.65909	−	11.5339i	0.283687	−	0.491360i
$552$		0			0
$553$	−1.68858	−	3.74355i	−0.0718056	−	0.159192i
$554$		0			0
$555$	−3.73248	+	6.46485i	−0.158435	+	0.274418i
$556$		0			0
$557$	5.64503	−	3.25916i	0.239188	−	0.138095i	−0.375616	−	0.926776i	$-0.622569\pi$
$557$	5.64503	−	3.25916i	0.239188	−	0.138095i	0.614803	+	0.788680i	$0.289235\pi$
$558$		0			0
$559$	−14.0726			−0.595206
$560$		0			0
$561$	−12.0634			−0.509319
$562$		0			0
$563$	−24.9474	+	14.4034i	−1.05141	+	0.607030i	−0.923043	−	0.384697i	$-0.874306\pi$
$563$	−24.9474	+	14.4034i	−1.05141	+	0.607030i	−0.128364	+	0.991727i	$0.540973\pi$
$564$		0			0
$565$	4.38304	−	7.59165i	0.184396	−	0.319383i
$566$		0			0
$567$	0.0816740	−	0.815154i	0.00342999	−	0.0342333i
$568$		0			0
$569$	5.68292	−	9.84310i	0.238240	−	0.412644i	−0.721969	−	0.691925i	$-0.756763\pi$
$569$	5.68292	−	9.84310i	0.238240	−	0.412644i	0.960209	+	0.279281i	$0.0900961\pi$
$570$		0			0
$571$	1.36107	+	2.35745i	0.0569592	+	0.0986562i	0.893099	−	0.449860i	$-0.148526\pi$
$571$	1.36107	+	2.35745i	0.0569592	+	0.0986562i	−0.836140	+	0.548516i	$0.815193\pi$
$572$		0			0
$573$	−7.43068			−0.310421
$574$		0			0
$575$		−	8.76435i		−	0.365499i
$576$		0			0
$577$	−8.29404	+	4.78857i	−0.345285	+	0.199351i	−0.662607	−	0.748967i	$-0.730550\pi$
$577$	−8.29404	+	4.78857i	−0.345285	+	0.199351i	0.317321	+	0.948318i	$0.397217\pi$
$578$		0			0
$579$	−17.2781	−	9.97554i	−0.718055	−	0.414569i
$580$		0			0
$581$	6.91270	−	9.61238i	0.286787	−	0.398789i
$582$		0			0
$583$	16.5356	+	9.54684i	0.684835	+	0.395390i
$584$		0			0
$585$	1.15146	+	1.99438i	0.0476069	+	0.0824576i
$586$		0			0
$587$			37.9535i			1.56651i	0.621703	+	0.783253i	$0.286441\pi$
$587$			37.9535i			1.56651i	−0.621703	+	0.783253i	$0.713559\pi$
$588$		0			0
$589$			8.62461i			0.355371i
$590$		0			0
$591$	−13.5009	−	23.3843i	−0.555353	−	0.961900i
$592$		0			0
$593$	22.1702	+	12.7999i	0.910419	+	0.525631i	0.880566	−	0.473923i	$-0.157163\pi$
$593$	22.1702	+	12.7999i	0.910419	+	0.525631i	0.0298534	+	0.999554i	$0.490496\pi$
$594$		0			0
$595$	−7.55459	+	10.5049i	−0.309708	+	0.430661i
$596$		0			0
$597$	6.14497	+	3.54780i	0.251497	+	0.145202i
$598$		0			0
$599$	28.0612	−	16.2011i	1.14655	−	0.661960i	0.198504	−	0.980100i	$-0.436392\pi$
$599$	28.0612	−	16.2011i	1.14655	−	0.661960i	0.948044	+	0.318140i	$0.103058\pi$
$600$		0			0
$601$			22.3390i			0.911226i	0.890178	+	0.455613i	$0.150580\pi$
$601$			22.3390i			0.911226i	−0.890178	+	0.455613i	$0.849420\pi$
$602$		0			0
$603$	1.46994			0.0598607
$604$		0			0
$605$	−2.73450	−	4.73629i	−0.111173	−	0.192557i
$606$		0			0
$607$	14.9462	−	25.8877i	0.606649	−	1.05075i	−0.385139	−	0.922858i	$-0.625847\pi$
$607$	14.9462	−	25.8877i	0.606649	−	1.05075i	0.991789	−	0.127889i	$-0.0408201\pi$
$608$		0			0
$609$	1.44259	−	14.3979i	0.0584566	−	0.583432i
$610$		0			0
$611$	6.07314	−	10.5190i	0.245693	−	0.425552i
$612$		0			0
$613$	7.53192	−	4.34856i	0.304211	−	0.175637i	−0.340122	−	0.940381i	$-0.610468\pi$
$613$	7.53192	−	4.34856i	0.304211	−	0.175637i	0.644333	+	0.764745i	$0.277135\pi$
$614$		0			0
$615$	3.34378			0.134834
$616$		0			0
$617$	14.2056			0.571897			0.285948	−	0.958245i	$-0.407691\pi$
$617$	14.2056			0.571897			0.285948	+	0.958245i	$0.407691\pi$
$618$		0			0
$619$	−16.3642	+	9.44785i	−0.657731	+	0.379741i	−0.791412	−	0.611283i	$-0.790654\pi$
$619$	−16.3642	+	9.44785i	−0.657731	+	0.379741i	0.133681	+	0.991024i	$0.457320\pi$
$620$		0			0
$621$	−22.5210	+	39.0075i	−0.903737	+	1.56532i
$622$		0			0
$623$	−12.0366	−	26.6850i	−0.482237	−	1.06911i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	3.15001	+	5.45597i	0.125799	+	0.217891i
$628$		0			0
$629$	34.8083			1.38790
$630$		0			0
$631$			3.99376i			0.158989i	0.996835	+	0.0794945i	$0.0253306\pi$
$631$			3.99376i			0.158989i	−0.996835	+	0.0794945i	$0.974669\pi$
$632$		0			0
$633$	−13.4043	+	7.73897i	−0.532773	+	0.307596i
$634$		0			0
$635$	2.17379	+	1.25504i	0.0862644	+	0.0498048i
$636$		0			0
$637$	2.70019	+	8.04353i	0.106985	+	0.318696i
$638$		0			0
$639$	4.16642	+	2.40548i	0.164821	+	0.0951594i
$640$		0			0
$641$	9.65359	+	16.7205i	0.381294	+	0.660420i	0.991247	−	0.132017i	$-0.0421453\pi$
$641$	9.65359	+	16.7205i	0.381294	+	0.660420i	−0.609954	+	0.792437i	$0.708812\pi$
$642$		0			0
$643$		−	21.3394i		−	0.841544i	−0.907166	−	0.420772i	$-0.861759\pi$
$643$		−	21.3394i		−	0.841544i	0.907166	−	0.420772i	$-0.138241\pi$
$644$		0			0
$645$			12.1771i			0.479473i
$646$		0			0
$647$	11.9178	+	20.6422i	0.468535	+	0.811527i	0.999353	−	0.0359589i	$-0.0114485\pi$
$647$	11.9178	+	20.6422i	0.468535	+	0.811527i	−0.530818	+	0.847486i	$0.678115\pi$
$648$		0			0
$649$	23.3042	+	13.4547i	0.914769	+	0.528142i
$650$		0			0
$651$	3.85287	+	8.54176i	0.151006	+	0.334778i
$652$		0			0
$653$	3.56712	+	2.05948i	0.139592	+	0.0805936i	0.568170	−	0.822911i	$-0.307652\pi$
$653$	3.56712	+	2.05948i	0.139592	+	0.0805936i	−0.428577	+	0.903505i	$0.640985\pi$
$654$		0			0
$655$	−4.72620	+	2.72867i	−0.184668	+	0.106618i
$656$		0			0
$657$			24.4590i			0.954235i
$658$		0			0
$659$	−39.8908			−1.55393			−0.776963	−	0.629546i	$-0.783241\pi$
$659$	−39.8908			−1.55393			−0.776963	+	0.629546i	$0.783241\pi$
$660$		0			0
$661$	−20.1318	−	34.8692i	−0.783035	−	1.35626i	−0.930166	−	0.367139i	$-0.880337\pi$
$661$	−20.1318	−	34.8692i	−0.783035	−	1.35626i	0.147132	−	0.989117i	$-0.452996\pi$
$662$		0			0
$663$	−3.10867	+	5.38438i	−0.120731	+	0.209112i
$664$		0			0
$665$	6.72377	+	0.673685i	0.260737	+	0.0261244i
$666$		0			0
$667$	22.8508	−	39.5788i	0.884787	−	1.53250i
$668$		0			0
$669$	13.1272	−	7.57898i	0.507526	−	0.293020i
$670$		0			0
$671$	−2.63802			−0.101839
$672$		0			0
$673$	−23.6181			−0.910412			−0.455206	−	0.890386i	$-0.650434\pi$
$673$	−23.6181			−0.910412			−0.455206	+	0.890386i	$0.650434\pi$
$674$		0			0
$675$	4.45070	−	2.56962i	0.171308	−	0.0989045i
$676$		0			0
$677$	−12.2908	+	21.2883i	−0.472374	+	0.818175i	−0.999500	−	0.0316116i	$-0.989936\pi$
$677$	−12.2908	+	21.2883i	−0.472374	+	0.818175i	0.527127	+	0.849787i	$0.323269\pi$
$678$		0			0
$679$	−20.6355	+	28.6945i	−0.791918	+	1.10119i
$680$		0			0
$681$	2.40916	−	4.17279i	0.0923192	−	0.159902i
$682$		0			0
$683$	10.5724	+	18.3120i	0.404543	+	0.700688i	0.994268	−	0.106915i	$-0.0340974\pi$
$683$	10.5724	+	18.3120i	0.404543	+	0.700688i	−0.589726	+	0.807604i	$0.700764\pi$
$684$		0			0
$685$	−15.0699			−0.575791
$686$		0			0
$687$			13.7205i			0.523471i
$688$		0			0
$689$	8.52225	−	4.92032i	0.324672	−	0.187449i
$690$		0			0
$691$	1.87978	+	1.08529i	0.0715102	+	0.0412864i	0.535329	−	0.844644i	$-0.320188\pi$
$691$	1.87978	+	1.08529i	0.0715102	+	0.0412864i	−0.463819	+	0.885930i	$0.653521\pi$
$692$		0			0
$693$	−9.59789	−	6.90228i	−0.364594	−	0.262196i
$694$		0			0
$695$	13.2282	+	7.63733i	0.501776	+	0.289700i
$696$		0			0
$697$	−7.79584	−	13.5028i	−0.295289	−	0.511455i
$698$		0			0
$699$		−	21.8848i		−	0.827759i
$700$		0			0
$701$		−	45.6142i		−	1.72283i	−0.507906	−	0.861413i	$-0.669580\pi$
$701$		−	45.6142i		−	1.72283i	0.507906	−	0.861413i	$-0.330420\pi$
$702$		0			0
$703$	−9.08916	−	15.7429i	−0.342804	−	0.593754i
$704$		0			0
$705$	−9.10216	−	5.25513i	−0.342807	−	0.197920i
$706$		0			0
$707$	−0.421513	+	4.20695i	−0.0158526	+	0.158219i
$708$		0			0
$709$	22.2197	+	12.8285i	0.834477	+	0.481785i	0.855383	−	0.517996i	$-0.173322\pi$
$709$	22.2197	+	12.8285i	0.834477	+	0.481785i	−0.0209062	+	0.999781i	$0.506655\pi$
$710$		0			0
$711$	2.55401	−	1.47456i	0.0957828	−	0.0553002i
$712$		0			0
$713$			29.5956i			1.10836i
$714$		0			0
$715$	2.85061			0.106607
$716$		0			0
$717$	1.54681	+	2.67916i	0.0577668	+	0.100055i
$718$		0			0
$719$	−11.6722	+	20.2169i	−0.435301	+	0.753964i	−0.997320	−	0.0731603i	$-0.976692\pi$
$719$	−11.6722	+	20.2169i	−0.435301	+	0.753964i	0.562019	+	0.827124i	$0.310025\pi$
$720$		0			0
$721$	8.55297	−	3.85793i	0.318529	−	0.143677i
$722$		0			0
$723$	0.483642	−	0.837693i	0.0179868	−	0.0311541i
$724$		0			0
$725$	−4.51588	+	2.60725i	−0.167716	+	0.0968307i
$726$		0			0
$727$	−17.2636			−0.640273			−0.320136	−	0.947371i	$-0.603729\pi$
$727$	−17.2636			−0.640273			−0.320136	+	0.947371i	$0.603729\pi$
$728$		0			0
$729$	−15.5823			−0.577122
$730$		0			0
$731$	49.1733	−	28.3902i	1.81874	−	1.05005i
$732$		0			0
$733$	13.4244	−	23.2518i	0.495843	−	0.858825i	−0.504146	−	0.863619i	$-0.668193\pi$
$733$	13.4244	−	23.2518i	0.495843	−	0.858825i	0.999989	+	0.00479386i	$0.00152594\pi$
$734$		0			0
$735$	6.96013	−	2.33649i	0.256728	−	0.0861829i
$736$		0			0
$737$	0.909769	−	1.57577i	0.0335118	−	0.0580441i
$738$		0			0
$739$	6.14064	+	10.6359i	0.225887	+	0.391248i	0.956585	−	0.291453i	$-0.0941386\pi$
$739$	6.14064	+	10.6359i	0.225887	+	0.391248i	−0.730698	+	0.682701i	$0.760805\pi$
$740$		0			0
$741$	3.24695			0.119280
$742$		0			0
$743$		−	24.4507i		−	0.897009i	−0.893781	−	0.448505i	$-0.851957\pi$
$743$		−	24.4507i		−	0.897009i	0.893781	−	0.448505i	$-0.148043\pi$
$744$		0			0
$745$	3.67599	−	2.12234i	0.134678	−	0.0777564i
$746$		0			0
$747$	7.36328	+	4.25119i	0.269408	+	0.155543i
$748$		0			0
$749$	−24.1156	+	10.8777i	−0.881165	+	0.397461i
$750$		0			0
$751$	31.9771	+	18.4620i	1.16686	+	0.673687i	0.952938	−	0.303164i	$-0.0980430\pi$
$751$	31.9771	+	18.4620i	1.16686	+	0.673687i	0.213921	+	0.976851i	$0.431376\pi$
$752$		0			0
$753$	4.87951	+	8.45156i	0.177819	+	0.307992i
$754$		0			0
$755$		−	1.19778i		−	0.0435918i
$756$		0			0
$757$		−	14.6178i		−	0.531293i	−0.964071	−	0.265646i	$-0.914415\pi$
$757$		−	14.6178i		−	0.531293i	0.964071	−	0.265646i	$-0.0855854\pi$
$758$		0			0
$759$	10.8093	+	18.7223i	0.392354	+	0.679577i
$760$		0			0
$761$	−15.3433	−	8.85843i	−0.556193	−	0.321118i	0.195423	−	0.980719i	$-0.437392\pi$
$761$	−15.3433	−	8.85843i	−0.556193	−	0.321118i	−0.751616	+	0.659601i	$0.770725\pi$
$762$		0			0
$763$	−12.6848	−	1.27095i	−0.459221	−	0.0460115i
$764$		0			0
$765$	−8.04700	−	4.64594i	−0.290940	−	0.167974i
$766$		0			0
$767$	12.0107	−	6.93437i	0.433681	−	0.250386i
$768$		0			0
$769$			3.82227i			0.137834i	0.997622	+	0.0689172i	$0.0219544\pi$
$769$			3.82227i			0.137834i	−0.997622	+	0.0689172i	$0.978046\pi$
$770$		0			0
$771$	31.5712			1.13701
$772$		0			0
$773$	−22.2173	−	38.4815i	−0.799101	−	1.38408i	−0.920202	−	0.391443i	$-0.871976\pi$
$773$	−22.2173	−	38.4815i	−0.799101	−	1.38408i	0.121102	−	0.992640i	$-0.461357\pi$
$774$		0			0
$775$	1.68841	−	2.92441i	0.0606493	−	0.105048i
$776$		0			0
$777$	−16.0347	−	11.5313i	−0.575240	−	0.413681i
$778$		0			0
$779$	−4.07131	+	7.05171i	−0.145870	+	0.252654i
$780$		0			0
$781$	5.15731	−	2.97758i	0.184543	−	0.106546i
$782$		0			0
$783$	26.7985			0.957699
$784$		0			0
$785$	11.0274			0.393584
$786$		0			0
$787$	−46.4327	+	26.8079i	−1.65515	+	0.955600i	−0.680240	+	0.732989i	$0.738125\pi$
$787$	−46.4327	+	26.8079i	−1.65515	+	0.955600i	−0.974907	+	0.222611i	$0.928542\pi$
$788$		0			0
$789$	9.23305	−	15.9921i	0.328705	−	0.569334i
$790$		0			0
$791$	18.8294	+	13.5411i	0.669498	+	0.481466i
$792$		0			0
$793$	−0.679800	+	1.17745i	−0.0241404	+	0.0418124i
$794$		0			0
$795$	−4.25759	−	7.37437i	−0.151001	−	0.261542i
$796$		0			0
$797$	−30.6896			−1.08708			−0.543541	−	0.839383i	$-0.682917\pi$
$797$	−30.6896			−1.08708			−0.543541	+	0.839383i	$0.682917\pi$
$798$		0			0
$799$			49.0082i			1.73379i
$800$		0			0
$801$	18.2057	−	10.5110i	0.643265	−	0.371389i
$802$		0			0
$803$	26.2198	+	15.1380i	0.925277	+	0.534209i
$804$		0			0
$805$	23.0728	+	2.31176i	0.813208	+	0.0814790i
$806$		0			0
$807$	−7.45478	−	4.30402i	−0.262421	−	0.151509i
$808$		0			0
$809$	−4.24657	−	7.35528i	−0.149302	−	0.258598i	0.781668	−	0.623695i	$-0.214369\pi$
$809$	−4.24657	−	7.35528i	−0.149302	−	0.258598i	−0.930970	+	0.365097i	$0.881036\pi$
$810$		0			0
$811$		−	21.1581i		−	0.742961i	−0.928441	−	0.371480i	$-0.878850\pi$
$811$		−	21.1581i		−	0.742961i	0.928441	−	0.371480i	$-0.121150\pi$
$812$		0			0
$813$			15.5266i			0.544541i
$814$		0			0
$815$	−6.36400	−	11.0228i	−0.222921	−	0.386111i
$816$		0			0
$817$	−25.6803	−	14.8265i	−0.898441	−	0.518715i
$818$		0			0
$819$	−5.55407	+	2.50524i	−0.194075	+	0.0875400i
$820$		0			0
$821$	15.7431	+	9.08930i	0.549439	+	0.317219i	0.748896	−	0.662688i	$-0.230584\pi$
$821$	15.7431	+	9.08930i	0.549439	+	0.317219i	−0.199457	+	0.979907i	$0.563918\pi$
$822$		0			0
$823$	−29.4225	+	16.9871i	−1.02561	+	0.592133i	−0.915723	−	0.401811i	$-0.868381\pi$
$823$	−29.4225	+	16.9871i	−1.02561	+	0.592133i	−0.109883	+	0.993945i	$0.535048\pi$
$824$		0			0
$825$		−	2.46666i		−	0.0858780i
$826$		0			0
$827$	29.9169			1.04031			0.520157	−	0.854071i	$-0.325874\pi$
$827$	29.9169			1.04031			0.520157	+	0.854071i	$0.325874\pi$
$828$		0			0
$829$	−7.84211	−	13.5829i	−0.272368	−	0.471755i	0.697100	−	0.716974i	$-0.254473\pi$
$829$	−7.84211	−	13.5829i	−0.272368	−	0.471755i	−0.969468	+	0.245219i	$0.921140\pi$
$830$		0			0
$831$	−3.34921	+	5.80099i	−0.116183	+	0.201234i
$832$		0			0
$833$	−25.6623	−	22.6589i	−0.889148	−	0.785083i
$834$		0			0
$835$	−7.52802	+	13.0389i	−0.260518	+	0.451230i
$836$		0			0
$837$	−15.0292	+	8.67711i	−0.519485	+	0.299925i
$838$		0			0
$839$	10.8159			0.373405			0.186702	−	0.982417i	$-0.440220\pi$
$839$	10.8159			0.373405			0.186702	+	0.982417i	$0.440220\pi$
$840$		0			0
$841$	1.80909			0.0623823
$842$		0			0
$843$	−11.1323	+	6.42722i	−0.383416	+	0.221365i
$844$		0			0
$845$	−5.76541	+	9.98599i	−0.198336	+	0.343529i
$846$		0			0
$847$	13.1899	−	5.94947i	0.453210	−	0.204426i
$848$		0			0
$849$	8.83799	−	15.3078i	0.303319	−	0.525364i
$850$		0			0
$851$	−31.1897	−	54.0221i	−1.06917	−	1.85185i
$852$		0			0
$853$	−37.5530			−1.28579			−0.642894	−	0.765955i	$-0.722267\pi$
$853$	−37.5530			−1.28579			−0.642894	+	0.765955i	$0.722267\pi$
$854$		0			0
$855$			4.85260i			0.165955i
$856$		0			0
$857$	4.42892	−	2.55704i	0.151289	−	0.0873467i	−0.422444	−	0.906389i	$-0.638828\pi$
$857$	4.42892	−	2.55704i	0.151289	−	0.0873467i	0.573733	+	0.819042i	$0.305495\pi$
$858$		0			0
$859$	29.0706	+	16.7839i	0.991876	+	0.572660i	0.905835	−	0.423631i	$-0.139245\pi$
$859$	29.0706	+	16.7839i	0.991876	+	0.572660i	0.0860417	+	0.996292i	$0.472578\pi$
$860$		0			0
$861$	−0.881986	+	8.80274i	−0.0300580	+	0.299997i
$862$		0			0
$863$	−12.8472	−	7.41734i	−0.437324	−	0.252489i	0.265138	−	0.964210i	$-0.414582\pi$
$863$	−12.8472	−	7.41734i	−0.437324	−	0.252489i	−0.702462	+	0.711721i	$0.747916\pi$
$864$		0			0
$865$	−6.09623	−	10.5590i	−0.207278	−	0.359016i
$866$		0			0
$867$		−	7.25579i		−	0.246419i
$868$		0			0
$869$		−	3.65050i		−	0.123835i
$870$		0			0
$871$	−0.468884	−	0.812130i	−0.0158875	−	0.0275180i
$872$		0			0
$873$	−21.9805	−	12.6905i	−0.743929	−	0.429507i
$874$		0			0
$875$	−2.14799	−	1.54472i	−0.0726153	−	0.0522209i
$876$		0			0
$877$	−19.7181	−	11.3843i	−0.665833	−	0.384419i	0.128663	−	0.991688i	$-0.458931\pi$
$877$	−19.7181	−	11.3843i	−0.665833	−	0.384419i	−0.794496	+	0.607270i	$0.792265\pi$
$878$		0			0
$879$	−24.5626	+	14.1812i	−0.828476	+	0.478321i
$880$		0			0
$881$		−	46.0172i		−	1.55036i	−0.631742	−	0.775179i	$-0.717660\pi$
$881$		−	46.0172i		−	1.55036i	0.631742	−	0.775179i	$-0.282340\pi$
$882$		0			0
$883$	48.2392			1.62338			0.811689	−	0.584090i	$-0.198548\pi$
$883$	48.2392			1.62338			0.811689	+	0.584090i	$0.198548\pi$
$884$		0			0
$885$	−6.00037	−	10.3929i	−0.201700	−	0.349355i
$886$		0			0
$887$	26.5340	−	45.9583i	0.890926	−	1.54313i	0.0521586	−	0.998639i	$-0.483390\pi$
$887$	26.5340	−	45.9583i	0.890926	−	1.54313i	0.838767	−	0.544490i	$-0.183277\pi$
$888$		0			0
$889$	−3.87736	+	5.39162i	−0.130043	+	0.180829i
$890$		0			0
$891$	0.364110	−	0.630656i	0.0121981	−	0.0211278i
$892$		0			0
$893$	22.1651	−	12.7970i	0.741728	−	0.428237i
$894$		0			0
$895$	1.39729			0.0467063
$896$		0			0
$897$	11.1420			0.372020
$898$		0			0
$899$	15.2493	−	8.80418i	0.508592	−	0.293636i
$900$		0			0
$901$	−19.8527	+	34.3859i	−0.661389	+	1.14556i
$902$		0			0
$903$	−32.0571	−	3.21194i	−1.06679	−	0.106887i
$904$		0			0
$905$	−12.8292	+	22.2208i	−0.426457	+	0.738645i
$906$		0			0
$907$	−19.4872	−	33.7529i	−0.647063	−	1.12075i	−0.983821	−	0.179155i	$-0.942664\pi$
$907$	−19.4872	−	33.7529i	−0.647063	−	1.12075i	0.336758	−	0.941591i	$-0.390670\pi$
$908$		0			0
$909$	−3.03619			−0.100704
$910$		0			0
$911$			23.8599i			0.790512i	0.918571	+	0.395256i	$0.129344\pi$
$911$			23.8599i			0.790512i	−0.918571	+	0.395256i	$0.870656\pi$
$912$		0			0
$913$	9.11448	−	5.26225i	0.301645	−	0.174155i
$914$		0			0
$915$	1.01886	+	0.588237i	0.0336823	+	0.0194465i
$916$		0			0
$917$	−5.93680	−	13.1618i	−0.196050	−	0.434641i
$918$		0			0
$919$	−23.6619	−	13.6612i	−0.780535	−	0.450642i	0.0560847	−	0.998426i	$-0.482138\pi$
$919$	−23.6619	−	13.6612i	−0.780535	−	0.450642i	−0.836620	+	0.547784i	$0.815472\pi$
$920$		0			0
$921$	−1.74285	−	3.01871i	−0.0574290	−	0.0994699i
$922$		0			0
$923$		−	3.06921i		−	0.101024i
$924$		0			0
$925$			7.11740i			0.234019i
$926$		0			0
$927$	3.36895	+	5.83520i	0.110651	+	0.191653i
$928$		0			0
$929$	14.1805	+	8.18709i	0.465246	+	0.268610i	0.714247	−	0.699893i	$-0.246769\pi$
$929$	14.1805	+	8.18709i	0.465246	+	0.268610i	−0.249002	+	0.968503i	$0.580102\pi$
$930$		0			0
$931$	−3.54704	+	17.5231i	−0.116250	+	0.574296i
$932$		0			0
$933$	−31.4164	−	18.1382i	−1.02853	−	0.593820i
$934$		0			0
$935$	−9.96081	+	5.75088i	−0.325753	+	0.188074i
$936$		0			0
$937$		−	9.65373i		−	0.315374i	−0.987489	−	0.157687i	$-0.949596\pi$
$937$		−	9.65373i		−	0.315374i	0.987489	−	0.157687i	$-0.0504036\pi$
$938$		0			0
$939$	−15.1791			−0.495352
$940$		0			0
$941$	14.1753	+	24.5524i	0.462103	+	0.800385i	0.999066	−	0.0432207i	$-0.0137619\pi$
$941$	14.1753	+	24.5524i	0.462103	+	0.800385i	−0.536963	+	0.843606i	$0.680429\pi$
$942$		0			0
$943$	−13.9708	+	24.1981i	−0.454951	+	0.787999i
$944$		0			0
$945$	5.59074	+	12.3946i	0.181867	+	0.403196i
$946$		0			0
$947$	1.38549	−	2.39973i	0.0450223	−	0.0779808i	−0.842636	−	0.538483i	$-0.818997\pi$
$947$	1.38549	−	2.39973i	0.0450223	−	0.0779808i	0.887658	+	0.460503i	$0.152331\pi$
$948$		0			0
$949$	13.5134	−	7.80194i	0.438662	−	0.253262i
$950$		0			0
$951$	−15.9210			−0.516272
$952$		0			0
$953$	−10.6334			−0.344451			−0.172225	−	0.985058i	$-0.555096\pi$
$953$	−10.6334			−0.344451			−0.172225	+	0.985058i	$0.555096\pi$
$954$		0			0
$955$	−6.13554	+	3.54235i	−0.198541	+	0.114628i
$956$		0			0
$957$	6.43118	−	11.1391i	0.207891	−	0.360077i
$958$		0			0
$959$	3.97497	−	39.6726i	0.128359	−	1.28109i
$960$		0			0
$961$	9.79857	−	16.9716i	0.316083	−	0.547472i
$962$		0			0
$963$	−9.49896	−	16.4527i	−0.306100	−	0.530180i
$964$		0			0
$965$	−19.0222			−0.612345
$966$		0			0
$967$			7.65003i			0.246008i	0.992406	+	0.123004i	$0.0392528\pi$
$967$			7.65003i			0.246008i	−0.992406	+	0.123004i	$0.960747\pi$
$968$		0			0
$969$	−11.3457	+	6.55046i	−0.364477	+	0.210431i
$970$		0			0
$971$	−26.8992	−	15.5302i	−0.863235	−	0.498389i	0.00185907	−	0.999998i	$-0.499408\pi$
$971$	−26.8992	−	15.5302i	−0.863235	−	0.498389i	−0.865094	+	0.501609i	$0.832742\pi$
$972$		0			0
$973$	−23.5950	+	32.8098i	−0.756421	+	1.05183i
$974$		0			0
$975$	−1.10097	−	0.635642i	−0.0352591	−	0.0203569i
$976$		0			0
$977$	2.12922	+	3.68791i	0.0681197	+	0.117987i	0.898074	−	0.439845i	$-0.144967\pi$
$977$	2.12922	+	3.68791i	0.0681197	+	0.117987i	−0.829954	+	0.557832i	$0.811633\pi$
$978$		0			0
$979$		−	26.0217i		−	0.831658i
$980$		0			0
$981$		−	9.15474i		−	0.292288i
$982$		0			0
$983$	3.78011	+	6.54734i	0.120567	+	0.208828i	0.919991	−	0.391939i	$-0.128195\pi$
$983$	3.78011	+	6.54734i	0.120567	+	0.208828i	−0.799425	+	0.600767i	$0.794862\pi$
$984$		0			0
$985$	−22.2955	−	12.8723i	−0.710393	−	0.410146i
$986$		0			0
$987$	16.2354	−	22.5759i	0.516778	−	0.718599i
$988$		0			0
$989$	−88.1226	−	50.8776i	−2.80214	−	1.61781i
$990$		0			0
$991$	−36.3263	+	20.9730i	−1.15394	+	0.666229i	−0.949845	−	0.312722i	$-0.898759\pi$
$991$	−36.3263	+	20.9730i	−1.15394	+	0.666229i	−0.204097	+	0.978951i	$0.565426\pi$
$992$		0			0
$993$			17.2655i			0.547903i
$994$		0			0
$995$	6.76522			0.214472
$996$		0			0
$997$	7.07310	+	12.2510i	0.224007	+	0.387992i	0.956021	−	0.293298i	$-0.0947527\pi$
$997$	7.07310	+	12.2510i	0.224007	+	0.387992i	−0.732014	+	0.681290i	$0.761419\pi$
$998$		0			0
$999$	18.2890	−	31.6774i	0.578637	−	1.00223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bz.f.271.10		24
4.3	odd	2		280.2.bj.e.131.1	✓	24
7.3	odd	6		1120.2.bz.e.591.10		24
8.3	odd	2		1120.2.bz.e.271.10		24
8.5	even	2		280.2.bj.f.131.7	yes	24
28.3	even	6		280.2.bj.f.171.7	yes	24
56.3	even	6	inner	1120.2.bz.f.591.10		24
56.45	odd	6		280.2.bj.e.171.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.1	✓	24	4.3	odd	2
280.2.bj.e.171.1	yes	24	56.45	odd	6
280.2.bj.f.131.7	yes	24	8.5	even	2
280.2.bj.f.171.7	yes	24	28.3	even	6
1120.2.bz.e.271.10		24	8.3	odd	2
1120.2.bz.e.591.10		24	7.3	odd	6
1120.2.bz.f.271.10		24	1.1	even	1	trivial
1120.2.bz.f.591.10		24	56.3	even	6	inner

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:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.908317 - 0.524417i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.14799 + 1.54472i) q^{7} +(-0.949974 + 1.64540i) q^{9} +O(q^{10})\)	\(q+(0.908317 - 0.524417i) q^{3} +(0.500000 - 0.866025i) q^{5} +(2.14799 + 1.54472i) q^{7} +(-0.949974 + 1.64540i) q^{9} +(1.17590 + 2.03673i) q^{11} +1.21209 q^{13} -1.04883i q^{15} +(-4.23538 + 2.44530i) q^{17} +(2.21189 + 1.27704i) q^{19} +(2.76113 + 0.276650i) q^{21} +(7.59015 + 4.38218i) q^{23} +(-0.500000 - 0.866025i) q^{25} +5.13923i q^{27} -5.21449i q^{29} +(1.68841 + 2.92441i) q^{31} +(2.13619 + 1.23333i) q^{33} +(2.41176 - 1.08785i) q^{35} +(-6.16385 - 3.55870i) q^{37} +(1.10097 - 0.635642i) q^{39} +3.18809i q^{41} -11.6101 q^{43} +(0.949974 + 1.64540i) q^{45} +(5.01045 - 8.67836i) q^{47} +(2.22771 + 6.63606i) q^{49} +(-2.56471 + 4.44221i) q^{51} +(7.03102 - 4.05936i) q^{53} +2.35181 q^{55} +2.67880 q^{57} +(9.90904 - 5.72099i) q^{59} +(-0.560848 + 0.971417i) q^{61} +(-4.58221 + 2.06687i) q^{63} +(0.606047 - 1.04970i) q^{65} +(-0.386838 - 0.670023i) q^{67} +9.19235 q^{69} -2.53216i q^{71} +(11.1488 - 6.43675i) q^{73} +(-0.908317 - 0.524417i) q^{75} +(-0.620335 + 6.19130i) q^{77} +(-1.34425 - 0.776104i) q^{79} +(-0.154821 - 0.268158i) q^{81} -4.47506i q^{83} +4.89060i q^{85} +(-2.73457 - 4.73641i) q^{87} +(-9.58219 - 5.53228i) q^{89} +(2.60356 + 1.87234i) q^{91} +(3.06722 + 1.77086i) q^{93} +(2.21189 - 1.27704i) q^{95} +13.3588i q^{97} -4.46831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{3} + 12 q^{5} + 10 q^{7} + 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^3 + 12 * q^5 + 10 * q^7 + 12 * q^9	\( 24 q - 12 q^{3} + 12 q^{5} + 10 q^{7} + 12 q^{9} - 8 q^{11} - 20 q^{13} + 6 q^{17} - 18 q^{19} + 26 q^{21} + 18 q^{23} - 12 q^{25} - 6 q^{31} + 12 q^{33} + 8 q^{35} - 18 q^{39} - 32 q^{43} - 12 q^{45} + 8 q^{49} + 22 q^{51} - 30 q^{53} - 16 q^{55} - 44 q^{57} + 18 q^{59} - 22 q^{61} - 12 q^{63} - 10 q^{65} + 8 q^{67} + 12 q^{69} + 30 q^{73} + 12 q^{75} + 32 q^{77} + 6 q^{79} - 4 q^{81} + 14 q^{87} - 60 q^{89} - 18 q^{91} + 18 q^{93} - 18 q^{95} + 56 q^{99}+O(q^{100}) \) 24 * q - 12 * q^3 + 12 * q^5 + 10 * q^7 + 12 * q^9 - 8 * q^11 - 20 * q^13 + 6 * q^17 - 18 * q^19 + 26 * q^21 + 18 * q^23 - 12 * q^25 - 6 * q^31 + 12 * q^33 + 8 * q^35 - 18 * q^39 - 32 * q^43 - 12 * q^45 + 8 * q^49 + 22 * q^51 - 30 * q^53 - 16 * q^55 - 44 * q^57 + 18 * q^59 - 22 * q^61 - 12 * q^63 - 10 * q^65 + 8 * q^67 + 12 * q^69 + 30 * q^73 + 12 * q^75 + 32 * q^77 + 6 * q^79 - 4 * q^81 + 14 * q^87 - 60 * q^89 - 18 * q^91 + 18 * q^93 - 18 * q^95 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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