LMFDB - Embedded newform 1120.2.x.f.127.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1120,2,Mod(127,1120)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1120.127"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1120, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.x (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,0,0,-4,0,0,0,0,0,0,0,-12,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)

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

Self dual:	no
Analytic conductor:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 4 x^{18} + 16 x^{17} - 56 x^{16} - 24 x^{15} + 512 x^{14} + 856 x^{13} + 402 x^{12} + \cdots + 5000 $ x^20 - 4x^19 + 4x^18 + 16x^17 - 56x^16 - 24x^15 + 512x^14 + 856x^13 + 402x^12 - 2696x^11 - 2776x^10 + 4912x^9 + 9744x^8 + 15176x^7 + 40928x^6 + 42808x^5 + 48369x^4 + 34460x^3 + 24900x^2 + 16000*x + 5000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.6
Root			$-1.87480 + 0.776568i$ of defining polynomial
Character	$\chi$	$=$	1120.127
Dual form			1120.2.x.f.1023.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.254210 + 0.254210i) q^{3} +(-0.655120 + 2.13795i) q^{5} +(0.707107 - 0.707107i) q^{7} -2.87075i q^{9} +3.31853i q^{11} +(-4.49218 + 4.49218i) q^{13} +(-0.710025 + 0.376949i) q^{15} +(-1.16279 - 1.16279i) q^{17} -5.55688 q^{19} +0.359507 q^{21} +(3.40931 + 3.40931i) q^{23} +(-4.14164 - 2.80122i) q^{25} +(1.49240 - 1.49240i) q^{27} -2.45071i q^{29} +4.69312i q^{31} +(-0.843603 + 0.843603i) q^{33} +(1.04852 + 1.97500i) q^{35} +(-1.50708 - 1.50708i) q^{37} -2.28391 q^{39} -5.25434 q^{41} +(5.00470 + 5.00470i) q^{43} +(6.13752 + 1.88069i) q^{45} +(-4.11978 + 4.11978i) q^{47} -1.00000i q^{49} -0.591185i q^{51} +(2.04151 - 2.04151i) q^{53} +(-7.09485 - 2.17404i) q^{55} +(-1.41261 - 1.41261i) q^{57} -4.21228 q^{59} -6.22068 q^{61} +(-2.02993 - 2.02993i) q^{63} +(-6.66113 - 12.5470i) q^{65} +(-6.24893 + 6.24893i) q^{67} +1.73336i q^{69} +9.56426i q^{71} +(-3.14663 + 3.14663i) q^{73} +(-0.340746 - 1.76494i) q^{75} +(2.34656 + 2.34656i) q^{77} +3.81321 q^{79} -7.85350 q^{81} +(-5.49953 - 5.49953i) q^{83} +(3.24775 - 1.72422i) q^{85} +(0.622993 - 0.622993i) q^{87} -10.9771i q^{89} +6.35291i q^{91} +(-1.19304 + 1.19304i) q^{93} +(3.64042 - 11.8803i) q^{95} +(-5.57435 - 5.57435i) q^{97} +9.52670 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5} - 12 q^{13} + 8 q^{15} - 4 q^{17} - 24 q^{19} + 8 q^{23} + 4 q^{25} - 16 q^{33} - 4 q^{35} + 4 q^{37} + 8 q^{39} + 32 q^{41} - 8 q^{43} + 32 q^{45} + 24 q^{47} + 28 q^{53} + 24 q^{59} + 24 q^{61}+ \cdots + 4 q^{97}+O(q^{100}) $ 20 * q - 4 * q^5 - 12 * q^13 + 8 * q^15 - 4 * q^17 - 24 * q^19 + 8 * q^23 + 4 * q^25 - 16 * q^33 - 4 * q^35 + 4 * q^37 + 8 * q^39 + 32 * q^41 - 8 * q^43 + 32 * q^45 + 24 * q^47 + 28 * q^53 + 24 * q^59 + 24 * q^61 - 8 * q^63 - 12 * q^65 - 8 * q^67 + 20 * q^73 + 72 * q^75 + 8 * q^77 - 24 * q^79 - 20 * q^81 - 48 * q^83 - 20 * q^85 + 56 * q^87 - 8 * q^93 - 8 * q^95 + 4 * q^97

Character values

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

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.254210	+	0.254210i	0.146768	+	0.146768i	0.776673	−	0.629905i	$-0.216906\pi$
$3$	0.254210	+	0.254210i	0.146768	+	0.146768i	−0.629905	+	0.776673i	$0.716906\pi$
$4$		0			0
$5$	−0.655120	+	2.13795i	−0.292979	+	0.956119i
$5$	−0.655120	+	2.13795i	−0.292979	+	0.956119i
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$		0			0
$9$		−	2.87075i		−	0.956918i
$10$		0			0
$11$			3.31853i			1.00058i	0.865859	+	0.500288i	$0.166772\pi$
$11$			3.31853i			1.00058i	−0.865859	+	0.500288i	$0.833228\pi$
$12$		0			0
$13$	−4.49218	+	4.49218i	−1.24591	+	1.24591i	−0.288396	+	0.957511i	$0.593122\pi$
$13$	−4.49218	+	4.49218i	−1.24591	+	1.24591i	−0.957511	+	0.288396i	$0.906878\pi$
$14$		0			0
$15$	−0.710025	+	0.376949i	−0.183328	+	0.0973278i
$16$		0			0
$17$	−1.16279	−	1.16279i	−0.282018	−	0.282018i	0.551895	−	0.833913i	$-0.313905\pi$
$17$	−1.16279	−	1.16279i	−0.282018	−	0.282018i	−0.833913	+	0.551895i	$0.813905\pi$
$18$		0			0
$19$	−5.55688			−1.27484			−0.637418	−	0.770518i	$-0.719997\pi$
$19$	−5.55688			−1.27484			−0.637418	+	0.770518i	$0.719997\pi$
$20$		0			0
$21$	0.359507			0.0784508
$22$		0			0
$23$	3.40931	+	3.40931i	0.710890	+	0.710890i	0.966721	−	0.255832i	$-0.0823493\pi$
$23$	3.40931	+	3.40931i	0.710890	+	0.710890i	−0.255832	+	0.966721i	$0.582349\pi$
$24$		0			0
$25$	−4.14164	−	2.80122i	−0.828327	−	0.560245i
$26$		0			0
$27$	1.49240	−	1.49240i	0.287213	−	0.287213i
$28$		0			0
$29$		−	2.45071i		−	0.455085i	−0.973768	−	0.227542i	$-0.926931\pi$
$29$		−	2.45071i		−	0.455085i	0.973768	−	0.227542i	$-0.0730690\pi$
$30$		0			0
$31$			4.69312i			0.842908i	0.906850	+	0.421454i	$0.138480\pi$
$31$			4.69312i			0.842908i	−0.906850	+	0.421454i	$0.861520\pi$
$32$		0			0
$33$	−0.843603	+	0.843603i	−0.146853	+	0.146853i
$34$		0			0
$35$	1.04852	+	1.97500i	0.177232	+	0.333835i
$36$		0			0
$37$	−1.50708	−	1.50708i	−0.247763	−	0.247763i	0.572289	−	0.820052i	$-0.306055\pi$
$37$	−1.50708	−	1.50708i	−0.247763	−	0.247763i	−0.820052	+	0.572289i	$0.806055\pi$
$38$		0			0
$39$	−2.28391			−0.365719
$40$		0			0
$41$	−5.25434			−0.820590			−0.410295	−	0.911953i	$-0.634574\pi$
$41$	−5.25434			−0.820590			−0.410295	+	0.911953i	$0.634574\pi$
$42$		0			0
$43$	5.00470	+	5.00470i	0.763210	+	0.763210i	0.976901	−	0.213692i	$-0.0685488\pi$
$43$	5.00470	+	5.00470i	0.763210	+	0.763210i	−0.213692	+	0.976901i	$0.568549\pi$
$44$		0			0
$45$	6.13752	+	1.88069i	0.914928	+	0.280356i
$46$		0			0
$47$	−4.11978	+	4.11978i	−0.600931	+	0.600931i	−0.940560	−	0.339628i	$-0.889699\pi$
$47$	−4.11978	+	4.11978i	−0.600931	+	0.600931i	0.339628	+	0.940560i	$0.389699\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$		−	0.591185i		−	0.0827825i
$52$		0			0
$53$	2.04151	−	2.04151i	0.280422	−	0.280422i	−0.552855	−	0.833277i	$-0.686462\pi$
$53$	2.04151	−	2.04151i	0.280422	−	0.280422i	0.833277	+	0.552855i	$0.186462\pi$
$54$		0			0
$55$	−7.09485	−	2.17404i	−0.956669	−	0.293147i
$56$		0			0
$57$	−1.41261	−	1.41261i	−0.187105	−	0.187105i
$58$		0			0
$59$	−4.21228			−0.548393			−0.274196	−	0.961674i	$-0.588412\pi$
$59$	−4.21228			−0.548393			−0.274196	+	0.961674i	$0.588412\pi$
$60$		0			0
$61$	−6.22068			−0.796476			−0.398238	−	0.917282i	$-0.630378\pi$
$61$	−6.22068			−0.796476			−0.398238	+	0.917282i	$0.630378\pi$
$62$		0			0
$63$	−2.02993	−	2.02993i	−0.255747	−	0.255747i
$64$		0			0
$65$	−6.66113	−	12.5470i	−0.826212	−	1.55626i
$66$		0			0
$67$	−6.24893	+	6.24893i	−0.763429	+	0.763429i	−0.976940	−	0.213512i	$-0.931510\pi$
$67$	−6.24893	+	6.24893i	−0.763429	+	0.763429i	0.213512	+	0.976940i	$0.431510\pi$
$68$		0			0
$69$			1.73336i			0.208672i
$70$		0			0
$71$			9.56426i			1.13507i	0.823350	+	0.567534i	$0.192103\pi$
$71$			9.56426i			1.13507i	−0.823350	+	0.567534i	$0.807897\pi$
$72$		0			0
$73$	−3.14663	+	3.14663i	−0.368286	+	0.368286i	−0.866852	−	0.498566i	$-0.833860\pi$
$73$	−3.14663	+	3.14663i	−0.368286	+	0.368286i	0.498566	+	0.866852i	$0.333860\pi$
$74$		0			0
$75$	−0.340746	−	1.76494i	−0.0393460	−	0.203798i
$76$		0			0
$77$	2.34656	+	2.34656i	0.267415	+	0.267415i
$78$		0			0
$79$	3.81321			0.429019			0.214510	−	0.976722i	$-0.431185\pi$
$79$	3.81321			0.429019			0.214510	+	0.976722i	$0.431185\pi$
$80$		0			0
$81$	−7.85350			−0.872611
$82$		0			0
$83$	−5.49953	−	5.49953i	−0.603652	−	0.603652i	0.337628	−	0.941280i	$-0.390376\pi$
$83$	−5.49953	−	5.49953i	−0.603652	−	0.603652i	−0.941280	+	0.337628i	$0.890376\pi$
$84$		0			0
$85$	3.24775	−	1.72422i	0.352268	−	0.187018i
$86$		0			0
$87$	0.622993	−	0.622993i	0.0667919	−	0.0667919i
$88$		0			0
$89$		−	10.9771i		−	1.16357i	−0.813341	−	0.581787i	$-0.802354\pi$
$89$		−	10.9771i		−	1.16357i	0.813341	−	0.581787i	$-0.197646\pi$
$90$		0			0
$91$			6.35291i			0.665965i
$92$		0			0
$93$	−1.19304	+	1.19304i	−0.123712	+	0.123712i
$94$		0			0
$95$	3.64042	−	11.8803i	0.373500	−	1.21889i
$96$		0			0
$97$	−5.57435	−	5.57435i	−0.565990	−	0.565990i	0.365013	−	0.931003i	$-0.381065\pi$
$97$	−5.57435	−	5.57435i	−0.565990	−	0.565990i	−0.931003	+	0.365013i	$0.881065\pi$
$98$		0			0
$99$	9.52670			0.957469
$100$		0			0
$101$	−7.63835			−0.760044			−0.380022	−	0.924977i	$-0.624084\pi$
$101$	−7.63835			−0.760044			−0.380022	+	0.924977i	$0.624084\pi$
$102$		0			0
$103$	12.6697	+	12.6697i	1.24838	+	1.24838i	0.956436	+	0.291942i	$0.0943013\pi$
$103$	12.6697	+	12.6697i	1.24838	+	1.24838i	0.291942	+	0.956436i	$0.405699\pi$
$104$		0			0
$105$	−0.235520	+	0.768607i	−0.0229844	+	0.0750083i
$106$		0			0
$107$	9.28851	−	9.28851i	0.897954	−	0.897954i	−0.0973005	−	0.995255i	$-0.531021\pi$
$107$	9.28851	−	9.28851i	0.897954	−	0.897954i	0.995255	+	0.0973005i	$0.0310208\pi$
$108$		0			0
$109$			19.2678i			1.84552i	0.385376	+	0.922760i	$0.374072\pi$
$109$			19.2678i			1.84552i	−0.385376	+	0.922760i	$0.625928\pi$
$110$		0			0
$111$		−	0.766229i		−	0.0727273i
$112$		0			0
$113$	−4.63119	+	4.63119i	−0.435666	+	0.435666i	−0.890550	−	0.454885i	$-0.849680\pi$
$113$	−4.63119	+	4.63119i	−0.435666	+	0.435666i	0.454885	+	0.890550i	$0.349680\pi$
$114$		0			0
$115$	−9.52242	+	5.05541i	−0.887970	+	0.471420i
$116$		0			0
$117$	12.8960	+	12.8960i	1.19223	+	1.19223i
$118$		0			0
$119$	−1.64443			−0.150745
$120$		0			0
$121$	−0.0126652			−0.00115139
$122$		0			0
$123$	−1.33570	−	1.33570i	−0.120436	−	0.120436i
$124$		0			0
$125$	8.70214	−	7.01946i	0.778343	−	0.627840i
$126$		0			0
$127$	7.98110	−	7.98110i	0.708208	−	0.708208i	−0.257950	−	0.966158i	$-0.583047\pi$
$127$	7.98110	−	7.98110i	0.708208	−	0.708208i	0.966158	+	0.257950i	$0.0830471\pi$
$128$		0			0
$129$			2.54449i			0.224030i
$130$		0			0
$131$		−	1.55532i		−	0.135889i	−0.997689	−	0.0679443i	$-0.978356\pi$
$131$		−	1.55532i		−	0.135889i	0.997689	−	0.0679443i	$-0.0216440\pi$
$132$		0			0
$133$	−3.92931	+	3.92931i	−0.340714	+	0.340714i
$134$		0			0
$135$	2.21298	+	4.16838i	0.190463	+	0.358757i
$136$		0			0
$137$	15.8901	+	15.8901i	1.35758	+	1.35758i	0.876887	+	0.480697i	$0.159616\pi$
$137$	15.8901	+	15.8901i	1.35758	+	1.35758i	0.480697	+	0.876887i	$0.340384\pi$
$138$		0			0
$139$	21.5437			1.82731			0.913656	−	0.406488i	$-0.133247\pi$
$139$	21.5437			1.82731			0.913656	+	0.406488i	$0.133247\pi$
$140$		0			0
$141$	−2.09457			−0.176395
$142$		0			0
$143$	−14.9075	−	14.9075i	−1.24662	−	1.24662i
$144$		0			0
$145$	5.23948	+	1.60551i	0.435115	+	0.133330i
$146$		0			0
$147$	0.254210	−	0.254210i	0.0209669	−	0.0209669i
$148$		0			0
$149$		−	5.14952i		−	0.421865i	−0.977501	−	0.210933i	$-0.932350\pi$
$149$		−	5.14952i		−	0.421865i	0.977501	−	0.210933i	$-0.0676501\pi$
$150$		0			0
$151$			9.45373i			0.769333i	0.923056	+	0.384667i	$0.125684\pi$
$151$			9.45373i			0.769333i	−0.923056	+	0.384667i	$0.874316\pi$
$152$		0			0
$153$	−3.33809	+	3.33809i	−0.269868	+	0.269868i
$154$		0			0
$155$	−10.0336	−	3.07455i	−0.805921	−	0.246954i
$156$		0			0
$157$	7.78569	+	7.78569i	0.621365	+	0.621365i	0.945880	−	0.324515i	$-0.105201\pi$
$157$	7.78569	+	7.78569i	0.621365	+	0.621365i	−0.324515	+	0.945880i	$0.605201\pi$
$158$		0			0
$159$	1.03794			0.0823141
$160$		0			0
$161$	4.82149			0.379986
$162$		0			0
$163$	6.12207	+	6.12207i	0.479517	+	0.479517i	0.904977	−	0.425460i	$-0.139888\pi$
$163$	6.12207	+	6.12207i	0.479517	+	0.479517i	−0.425460	+	0.904977i	$0.639888\pi$
$164$		0			0
$165$	−1.25092	−	2.35624i	−0.0973839	−	0.183433i
$166$		0			0
$167$	0.311698	−	0.311698i	0.0241199	−	0.0241199i	−0.694944	−	0.719064i	$-0.744571\pi$
$167$	0.311698	−	0.311698i	0.0241199	−	0.0241199i	0.719064	+	0.694944i	$0.244571\pi$
$168$		0			0
$169$		−	27.3594i		−	2.10457i
$170$		0			0
$171$			15.9524i			1.21991i
$172$		0			0
$173$	13.4563	−	13.4563i	1.02307	−	1.02307i	0.0233381	−	0.999728i	$-0.492571\pi$
$173$	13.4563	−	13.4563i	1.02307	−	1.02307i	0.999728	−	0.0233381i	$-0.00742941\pi$
$174$		0			0
$175$	−4.90934	+	0.947815i	−0.371111	+	0.0716481i
$176$		0			0
$177$	−1.07080	−	1.07080i	−0.0804865	−	0.0804865i
$178$		0			0
$179$	−17.3632			−1.29779			−0.648894	−	0.760879i	$-0.724768\pi$
$179$	−17.3632			−1.29779			−0.648894	+	0.760879i	$0.724768\pi$
$180$		0			0
$181$	−5.72430			−0.425484			−0.212742	−	0.977108i	$-0.568239\pi$
$181$	−5.72430			−0.425484			−0.212742	+	0.977108i	$0.568239\pi$
$182$		0			0
$183$	−1.58136	−	1.58136i	−0.116897	−	0.116897i
$184$		0			0
$185$	4.20938	−	2.23474i	0.309480	−	0.164301i
$186$		0			0
$187$	3.85876	−	3.85876i	0.282181	−	0.282181i
$188$		0			0
$189$		−	2.11058i		−	0.153522i
$190$		0			0
$191$		−	20.6512i		−	1.49426i	−0.664675	−	0.747132i	$-0.731430\pi$
$191$		−	20.6512i		−	1.49426i	0.664675	−	0.747132i	$-0.268570\pi$
$192$		0			0
$193$	−0.417957	+	0.417957i	−0.0300852	+	0.0300852i	−0.721989	−	0.691904i	$-0.756772\pi$
$193$	−0.417957	+	0.417957i	−0.0300852	+	0.0300852i	0.691904	+	0.721989i	$0.256772\pi$
$194$		0			0
$195$	1.49624	−	4.88289i	0.107148	−	0.349671i
$196$		0			0
$197$	4.65803	+	4.65803i	0.331871	+	0.331871i	0.853297	−	0.521426i	$-0.174600\pi$
$197$	4.65803	+	4.65803i	0.331871	+	0.331871i	−0.521426	+	0.853297i	$0.674600\pi$
$198$		0			0
$199$	−22.3934			−1.58743			−0.793713	−	0.608293i	$-0.791855\pi$
$199$	−22.3934			−1.58743			−0.793713	+	0.608293i	$0.791855\pi$
$200$		0			0
$201$	−3.17708			−0.224094
$202$		0			0
$203$	−1.73291	−	1.73291i	−0.121626	−	0.121626i
$204$		0			0
$205$	3.44222	−	11.2335i	0.240415	−	0.784582i
$206$		0			0
$207$	9.78728	−	9.78728i	0.680263	−	0.680263i
$208$		0			0
$209$		−	18.4407i		−	1.27557i
$210$		0			0
$211$		−	28.6661i		−	1.97346i	−0.162384	−	0.986728i	$-0.551918\pi$
$211$		−	28.6661i		−	1.97346i	0.162384	−	0.986728i	$-0.448082\pi$
$212$		0			0
$213$	−2.43133	+	2.43133i	−0.166592	+	0.166592i
$214$		0			0
$215$	−13.9785	+	7.42111i	−0.953323	+	0.506115i
$216$		0			0
$217$	3.31853	+	3.31853i	0.225277	+	0.225277i
$218$		0			0
$219$	−1.59981			−0.108105
$220$		0			0
$221$	10.4469			0.702737
$222$		0			0
$223$	6.72214	+	6.72214i	0.450148	+	0.450148i	0.895403	−	0.445256i	$-0.146887\pi$
$223$	6.72214	+	6.72214i	0.450148	+	0.450148i	−0.445256	+	0.895403i	$0.646887\pi$
$224$		0			0
$225$	−8.04163	+	11.8896i	−0.536108	+	0.792641i
$226$		0			0
$227$	12.2339	−	12.2339i	0.811993	−	0.811993i	−0.172940	−	0.984932i	$-0.555327\pi$
$227$	12.2339	−	12.2339i	0.811993	−	0.811993i	0.984932	+	0.172940i	$0.0553266\pi$
$228$		0			0
$229$			22.3611i			1.47767i	0.673889	+	0.738833i	$0.264623\pi$
$229$			22.3611i			1.47767i	−0.673889	+	0.738833i	$0.735377\pi$
$230$		0			0
$231$			1.19304i			0.0784960i
$232$		0			0
$233$	5.75039	−	5.75039i	0.376720	−	0.376720i	−0.493197	−	0.869918i	$-0.664172\pi$
$233$	5.75039	−	5.75039i	0.376720	−	0.376720i	0.869918	+	0.493197i	$0.164172\pi$
$234$		0			0
$235$	−6.10892	−	11.5068i	−0.398502	−	0.750622i
$236$		0			0
$237$	0.969354	+	0.969354i	0.0629663	+	0.0629663i
$238$		0			0
$239$	−15.6017			−1.00919			−0.504594	−	0.863357i	$-0.668358\pi$
$239$	−15.6017			−1.00919			−0.504594	+	0.863357i	$0.668358\pi$
$240$		0			0
$241$	15.6819			1.01016			0.505080	−	0.863073i	$-0.331463\pi$
$241$	15.6819			1.01016			0.505080	+	0.863073i	$0.331463\pi$
$242$		0			0
$243$	−6.47364	−	6.47364i	−0.415284	−	0.415284i
$244$		0			0
$245$	2.13795	+	0.655120i	0.136588	+	0.0418541i
$246$		0			0
$247$	24.9625	−	24.9625i	1.58833	−	1.58833i
$248$		0			0
$249$		−	2.79607i		−	0.177194i
$250$		0			0
$251$			17.8444i			1.12633i	0.826344	+	0.563166i	$0.190417\pi$
$251$			17.8444i			1.12633i	−0.826344	+	0.563166i	$0.809583\pi$
$252$		0			0
$253$	−11.3139	+	11.3139i	−0.711299	+	0.711299i
$254$		0			0
$255$	1.26392	+	0.387297i	0.0791499	+	0.0242535i
$256$		0			0
$257$	20.3587	+	20.3587i	1.26994	+	1.26994i	0.946118	+	0.323822i	$0.104968\pi$
$257$	20.3587	+	20.3587i	1.26994	+	1.26994i	0.323822	+	0.946118i	$0.395032\pi$
$258$		0			0
$259$	−2.13133			−0.132435
$260$		0			0
$261$	−7.03537			−0.435479
$262$		0			0
$263$	21.0482	+	21.0482i	1.29789	+	1.29789i	0.929785	+	0.368104i	$0.119993\pi$
$263$	21.0482	+	21.0482i	1.29789	+	1.29789i	0.368104	+	0.929785i	$0.380007\pi$
$264$		0			0
$265$	3.02720	+	5.70206i	0.185959	+	0.350275i
$266$		0			0
$267$	2.79050	−	2.79050i	0.170776	−	0.170776i
$268$		0			0
$269$			19.6406i			1.19751i	0.800932	+	0.598755i	$0.204338\pi$
$269$			19.6406i			1.19751i	−0.800932	+	0.598755i	$0.795662\pi$
$270$		0			0
$271$		−	6.47759i		−	0.393486i	−0.980455	−	0.196743i	$-0.936964\pi$
$271$		−	6.47759i		−	0.393486i	0.980455	−	0.196743i	$-0.0630364\pi$
$272$		0			0
$273$	−1.61497	+	1.61497i	−0.0977424	+	0.0977424i
$274$		0			0
$275$	9.29595	−	13.7442i	0.560567	−	0.828804i
$276$		0			0
$277$	0.354423	+	0.354423i	0.0212952	+	0.0212952i	0.717674	−	0.696379i	$-0.245207\pi$
$277$	0.354423	+	0.354423i	0.0212952	+	0.0212952i	−0.696379	+	0.717674i	$0.745207\pi$
$278$		0			0
$279$	13.4728			0.806594
$280$		0			0
$281$	4.02107			0.239877			0.119938	−	0.992781i	$-0.461730\pi$
$281$	4.02107			0.239877			0.119938	+	0.992781i	$0.461730\pi$
$282$		0			0
$283$	18.7541	+	18.7541i	1.11482	+	1.11482i	0.992490	+	0.122328i	$0.0390359\pi$
$283$	18.7541	+	18.7541i	1.11482	+	1.11482i	0.122328	+	0.992490i	$0.460964\pi$
$284$		0			0
$285$	3.94552	−	2.09466i	0.233713	−	0.124077i
$286$		0			0
$287$	−3.71538	+	3.71538i	−0.219312	+	0.219312i
$288$		0			0
$289$		−	14.2958i		−	0.840931i
$290$		0			0
$291$		−	2.83411i		−	0.166138i
$292$		0			0
$293$	14.1778	−	14.1778i	0.828275	−	0.828275i	−0.159003	−	0.987278i	$-0.550828\pi$
$293$	14.1778	−	14.1778i	0.828275	−	0.828275i	0.987278	+	0.159003i	$0.0508279\pi$
$294$		0			0
$295$	2.75955	−	9.00564i	0.160667	−	0.524329i
$296$		0			0
$297$	4.95259	+	4.95259i	0.287378	+	0.287378i
$298$		0			0
$299$	−30.6305			−1.77141
$300$		0			0
$301$	7.07771			0.407953
$302$		0			0
$303$	−1.94174	−	1.94174i	−0.111550	−	0.111550i
$304$		0			0
$305$	4.07529	−	13.2995i	0.233350	−	0.761526i
$306$		0			0
$307$	18.0261	−	18.0261i	1.02880	−	1.02880i	0.0292309	−	0.999573i	$-0.490694\pi$
$307$	18.0261	−	18.0261i	1.02880	−	1.02880i	0.999573	−	0.0292309i	$-0.00930582\pi$
$308$		0			0
$309$			6.44150i			0.366444i
$310$		0			0
$311$		−	10.5871i		−	0.600338i	−0.953886	−	0.300169i	$-0.902957\pi$
$311$		−	10.5871i		−	0.600338i	0.953886	−	0.300169i	$-0.0970432\pi$
$312$		0			0
$313$	−14.4178	+	14.4178i	−0.814944	+	0.814944i	−0.985370	−	0.170426i	$-0.945485\pi$
$313$	−14.4178	+	14.4178i	−0.814944	+	0.814944i	0.170426	+	0.985370i	$0.445485\pi$
$314$		0			0
$315$	5.66973	−	3.01004i	0.319453	−	0.169596i
$316$		0			0
$317$	−22.6954	−	22.6954i	−1.27470	−	1.27470i	−0.943594	−	0.331104i	$-0.892579\pi$
$317$	−22.6954	−	22.6954i	−1.27470	−	1.27470i	−0.331104	−	0.943594i	$-0.607421\pi$
$318$		0			0
$319$	8.13275			0.455346
$320$		0			0
$321$	4.72246			0.263582
$322$		0			0
$323$	6.46149	+	6.46149i	0.359527	+	0.359527i
$324$		0			0
$325$	31.1886	−	6.02138i	1.73003	−	0.334006i
$326$		0			0
$327$	−4.89806	+	4.89806i	−0.270863	+	0.270863i
$328$		0			0
$329$			5.82625i			0.321211i
$330$		0			0
$331$			17.8219i			0.979582i	0.871840	+	0.489791i	$0.162927\pi$
$331$			17.8219i			0.979582i	−0.871840	+	0.489791i	$0.837073\pi$
$332$		0			0
$333$	−4.32646	+	4.32646i	−0.237089	+	0.237089i
$334$		0			0
$335$	−9.26609	−	17.4537i	−0.506260	−	0.953597i
$336$		0			0
$337$	16.2021	+	16.2021i	0.882586	+	0.882586i	0.993797	−	0.111211i	$-0.0354730\pi$
$337$	16.2021	+	16.2021i	0.882586	+	0.882586i	−0.111211	+	0.993797i	$0.535473\pi$
$338$		0			0
$339$	−2.35459			−0.127884
$340$		0			0
$341$	−15.5743			−0.843393
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$		0			0
$345$	−3.70583	−	1.13556i	−0.199515	−	0.0611363i
$346$		0			0
$347$	−13.2131	+	13.2131i	−0.709318	+	0.709318i	−0.966392	−	0.257074i	$-0.917242\pi$
$347$	−13.2131	+	13.2131i	−0.709318	+	0.709318i	0.257074	+	0.966392i	$0.417242\pi$
$348$		0			0
$349$		−	12.4841i		−	0.668256i	−0.942528	−	0.334128i	$-0.891558\pi$
$349$		−	12.4841i		−	0.668256i	0.942528	−	0.334128i	$-0.108442\pi$
$350$		0			0
$351$			13.4083i			0.715682i
$352$		0			0
$353$	−3.51115	+	3.51115i	−0.186880	+	0.186880i	−0.794346	−	0.607466i	$-0.792186\pi$
$353$	−3.51115	+	3.51115i	−0.186880	+	0.186880i	0.607466	+	0.794346i	$0.292186\pi$
$354$		0			0
$355$	−20.4479	−	6.26574i	−1.08526	−	0.332551i
$356$		0			0
$357$	−0.418031	−	0.418031i	−0.0221246	−	0.0221246i
$358$		0			0
$359$	10.7418			0.566930			0.283465	−	0.958983i	$-0.408516\pi$
$359$	10.7418			0.566930			0.283465	+	0.958983i	$0.408516\pi$
$360$		0			0
$361$	11.8789			0.625206
$362$		0			0
$363$	−0.00321963	−	0.00321963i	−0.000168987	−	0.000168987i
$364$		0			0
$365$	−4.66591	−	8.78876i	−0.244225	−	0.460025i
$366$		0			0
$367$	−14.4828	+	14.4828i	−0.755998	+	0.755998i	−0.975591	−	0.219594i	$-0.929527\pi$
$367$	−14.4828	+	14.4828i	−0.755998	+	0.755998i	0.219594	+	0.975591i	$0.429527\pi$
$368$		0			0
$369$			15.0839i			0.785238i
$370$		0			0
$371$		−	2.88713i		−	0.149892i
$372$		0			0
$373$	−6.19138	+	6.19138i	−0.320577	+	0.320577i	−0.848989	−	0.528411i	$-0.822788\pi$
$373$	−6.19138	+	6.19138i	−0.320577	+	0.320577i	0.528411	+	0.848989i	$0.322788\pi$
$374$		0			0
$375$	3.99658	+	0.427752i	0.206383	+	0.0220890i
$376$		0			0
$377$	11.0090	+	11.0090i	0.566993	+	0.566993i
$378$		0			0
$379$	22.1164			1.13604			0.568021	−	0.823014i	$-0.307709\pi$
$379$	22.1164			1.13604			0.568021	+	0.823014i	$0.307709\pi$
$380$		0			0
$381$	4.05774			0.207885
$382$		0			0
$383$	−8.15912	−	8.15912i	−0.416911	−	0.416911i	0.467226	−	0.884138i	$-0.345253\pi$
$383$	−8.15912	−	8.15912i	−0.416911	−	0.416911i	−0.884138	+	0.467226i	$0.845253\pi$
$384$		0			0
$385$	−6.55409	+	3.47954i	−0.334027	+	0.177334i
$386$		0			0
$387$	14.3673	−	14.3673i	0.730329	−	0.730329i
$388$		0			0
$389$		−	33.6009i		−	1.70363i	−0.523841	−	0.851816i	$-0.675501\pi$
$389$		−	33.6009i		−	1.70363i	0.523841	−	0.851816i	$-0.324499\pi$
$390$		0			0
$391$		−	7.92862i		−	0.400968i
$392$		0			0
$393$	0.395377	−	0.395377i	0.0199441	−	0.0199441i
$394$		0			0
$395$	−2.49811	+	8.15243i	−0.125693	+	0.410193i
$396$		0			0
$397$	−10.3392	−	10.3392i	−0.518909	−	0.518909i	0.398332	−	0.917241i	$-0.369589\pi$
$397$	−10.3392	−	10.3392i	−0.518909	−	0.518909i	−0.917241	+	0.398332i	$0.869589\pi$
$398$		0			0
$399$	−1.99774			−0.100012
$400$		0			0
$401$	−28.8499			−1.44069			−0.720347	−	0.693613i	$-0.756018\pi$
$401$	−28.8499			−1.44069			−0.720347	+	0.693613i	$0.756018\pi$
$402$		0			0
$403$	−21.0823	−	21.0823i	−1.05019	−	1.05019i
$404$		0			0
$405$	5.14498	−	16.7904i	0.255656	−	0.834320i
$406$		0			0
$407$	5.00130	−	5.00130i	0.247905	−	0.247905i
$408$		0			0
$409$			23.8384i			1.17873i	0.807866	+	0.589366i	$0.200623\pi$
$409$			23.8384i			1.17873i	−0.807866	+	0.589366i	$0.799377\pi$
$410$		0			0
$411$			8.07884i			0.398500i
$412$		0			0
$413$	−2.97853	+	2.97853i	−0.146564	+	0.146564i
$414$		0			0
$415$	15.3606	−	8.15485i	0.754020	−	0.400306i
$416$		0			0
$417$	5.47662	+	5.47662i	0.268191	+	0.268191i
$418$		0			0
$419$	16.3859			0.800503			0.400251	−	0.916405i	$-0.368923\pi$
$419$	16.3859			0.800503			0.400251	+	0.916405i	$0.368923\pi$
$420$		0			0
$421$	−18.0450			−0.879459			−0.439730	−	0.898130i	$-0.644926\pi$
$421$	−18.0450			−0.879459			−0.439730	+	0.898130i	$0.644926\pi$
$422$		0			0
$423$	11.8269	+	11.8269i	0.575042	+	0.575042i
$424$		0			0
$425$	1.55862	+	8.07309i	0.0756042	+	0.391603i
$426$		0			0
$427$	−4.39868	+	4.39868i	−0.212867	+	0.212867i
$428$		0			0
$429$		−	7.57924i		−	0.365929i
$430$		0			0
$431$			33.9777i			1.63665i	0.574757	+	0.818324i	$0.305097\pi$
$431$			33.9777i			1.63665i	−0.574757	+	0.818324i	$0.694903\pi$
$432$		0			0
$433$	4.14241	−	4.14241i	0.199071	−	0.199071i	−0.600530	−	0.799602i	$-0.705044\pi$
$433$	4.14241	−	4.14241i	0.199071	−	0.199071i	0.799602	+	0.600530i	$0.205044\pi$
$434$		0			0
$435$	0.923791	+	1.74006i	0.0442924	+	0.0834296i
$436$		0			0
$437$	−18.9451	−	18.9451i	−0.906268	−	0.906268i
$438$		0			0
$439$	20.1293			0.960720			0.480360	−	0.877071i	$-0.340506\pi$
$439$	20.1293			0.960720			0.480360	+	0.877071i	$0.340506\pi$
$440$		0			0
$441$	−2.87075			−0.136703
$442$		0			0
$443$	−2.24706	−	2.24706i	−0.106761	−	0.106761i	0.651709	−	0.758469i	$-0.274053\pi$
$443$	−2.24706	−	2.24706i	−0.106761	−	0.106761i	−0.758469	+	0.651709i	$0.774053\pi$
$444$		0			0
$445$	23.4685	+	7.19134i	1.11252	+	0.340902i
$446$		0			0
$447$	1.30906	−	1.30906i	0.0619163	−	0.0619163i
$448$		0			0
$449$		−	12.9572i		−	0.611489i	−0.952114	−	0.305744i	$-0.901095\pi$
$449$		−	12.9572i		−	0.611489i	0.952114	−	0.305744i	$-0.0989053\pi$
$450$		0			0
$451$		−	17.4367i		−	0.821062i
$452$		0			0
$453$	−2.40323	+	2.40323i	−0.112914	+	0.112914i
$454$		0			0
$455$	−13.5822	−	4.16191i	−0.636742	−	0.195114i
$456$		0			0
$457$	2.31835	+	2.31835i	0.108448	+	0.108448i	0.759249	−	0.650801i	$-0.225567\pi$
$457$	2.31835	+	2.31835i	0.108448	+	0.108448i	−0.650801	+	0.759249i	$0.725567\pi$
$458$		0			0
$459$	−3.47071			−0.161999
$460$		0			0
$461$	−24.5541			−1.14360			−0.571800	−	0.820393i	$-0.693755\pi$
$461$	−24.5541			−1.14360			−0.571800	+	0.820393i	$0.693755\pi$
$462$		0			0
$463$	−13.9838	−	13.9838i	−0.649882	−	0.649882i	0.303083	−	0.952964i	$-0.401984\pi$
$463$	−13.9838	−	13.9838i	−0.649882	−	0.649882i	−0.952964	+	0.303083i	$0.901984\pi$
$464$		0			0
$465$	−1.76907	−	3.33223i	−0.0820385	−	0.154528i
$466$		0			0
$467$	−5.95676	+	5.95676i	−0.275646	+	0.275646i	−0.831368	−	0.555722i	$-0.812442\pi$
$467$	−5.95676	+	5.95676i	−0.275646	+	0.275646i	0.555722	+	0.831368i	$0.312442\pi$
$468$		0			0
$469$			8.83732i			0.408070i
$470$		0			0
$471$			3.95839i			0.182393i
$472$		0			0
$473$	−16.6083	+	16.6083i	−0.763649	+	0.763649i
$474$		0			0
$475$	23.0146	+	15.5661i	1.05598	+	0.714220i
$476$		0			0
$477$	−5.86066	−	5.86066i	−0.268341	−	0.268341i
$478$		0			0
$479$	−38.9952			−1.78174			−0.890869	−	0.454260i	$-0.849904\pi$
$479$	−38.9952			−1.78174			−0.890869	+	0.454260i	$0.849904\pi$
$480$		0			0
$481$	13.5402			0.617378
$482$		0			0
$483$	1.22567	+	1.22567i	0.0557699	+	0.0557699i
$484$		0			0
$485$	15.5695	−	8.26580i	0.706977	−	0.375331i
$486$		0			0
$487$	−13.2329	+	13.2329i	−0.599639	+	0.599639i	−0.940216	−	0.340578i	$-0.889377\pi$
$487$	−13.2329	+	13.2329i	−0.599639	+	0.599639i	0.340578	+	0.940216i	$0.389377\pi$
$488$		0			0
$489$			3.11258i			0.140756i
$490$		0			0
$491$			22.7401i			1.02625i	0.858315	+	0.513123i	$0.171512\pi$
$491$			22.7401i			1.02625i	−0.858315	+	0.513123i	$0.828488\pi$
$492$		0			0
$493$	−2.84966	+	2.84966i	−0.128342	+	0.128342i
$494$		0			0
$495$	−6.24113	+	20.3676i	−0.280518	+	0.915454i
$496$		0			0
$497$	6.76295	+	6.76295i	0.303360	+	0.303360i
$498$		0			0
$499$	−30.0436			−1.34494			−0.672468	−	0.740126i	$-0.734766\pi$
$499$	−30.0436			−1.34494			−0.672468	+	0.740126i	$0.734766\pi$
$500$		0			0
$501$	0.158473			0.00708006
$502$		0			0
$503$	−2.00745	−	2.00745i	−0.0895080	−	0.0895080i	0.660935	−	0.750443i	$-0.270160\pi$
$503$	−2.00745	−	2.00745i	−0.0895080	−	0.0895080i	−0.750443	+	0.660935i	$0.770160\pi$
$504$		0			0
$505$	5.00403	−	16.3304i	0.222677	−	0.726693i
$506$		0			0
$507$	6.95503	−	6.95503i	0.308884	−	0.308884i
$508$		0			0
$509$			8.34006i			0.369667i	0.982770	+	0.184833i	$0.0591745\pi$
$509$			8.34006i			0.369667i	−0.982770	+	0.184833i	$0.940825\pi$
$510$		0			0
$511$			4.45001i			0.196857i
$512$		0			0
$513$	−8.29310	+	8.29310i	−0.366150	+	0.366150i
$514$		0			0
$515$	−35.3872	+	18.7869i	−1.55935	+	0.827850i
$516$		0			0
$517$	−13.6716	−	13.6716i	−0.601277	−	0.601277i
$518$		0			0
$519$	6.84146			0.300307
$520$		0			0
$521$	−12.2561			−0.536948			−0.268474	−	0.963287i	$-0.586519\pi$
$521$	−12.2561			−0.536948			−0.268474	+	0.963287i	$0.586519\pi$
$522$		0			0
$523$	3.94245	+	3.94245i	0.172391	+	0.172391i	0.788029	−	0.615638i	$-0.211102\pi$
$523$	3.94245	+	3.94245i	0.172391	+	0.172391i	−0.615638	+	0.788029i	$0.711102\pi$
$524$		0			0
$525$	−1.48895	−	1.00706i	−0.0649829	−	0.0439517i
$526$		0			0
$527$	5.45711	−	5.45711i	0.237716	−	0.237716i
$528$		0			0
$529$			0.246744i			0.0107280i
$530$		0			0
$531$			12.0924i			0.524767i
$532$		0			0
$533$	23.6035	−	23.6035i	1.02238	−	1.02238i
$534$		0			0
$535$	13.7733	+	25.9434i	0.595470	+	1.12163i
$536$		0			0
$537$	−4.41390	−	4.41390i	−0.190474	−	0.190474i
$538$		0			0
$539$	3.31853			0.142939
$540$		0			0
$541$	−43.8017			−1.88318			−0.941591	−	0.336758i	$-0.890670\pi$
$541$	−43.8017			−1.88318			−0.941591	+	0.336758i	$0.890670\pi$
$542$		0			0
$543$	−1.45517	−	1.45517i	−0.0624474	−	0.0624474i
$544$		0			0
$545$	−41.1935	−	12.6227i	−1.76454	−	0.540698i
$546$		0			0
$547$	−27.8081	+	27.8081i	−1.18899	+	1.18899i	−0.211640	+	0.977348i	$0.567880\pi$
$547$	−27.8081	+	27.8081i	−1.18899	+	1.18899i	−0.977348	+	0.211640i	$0.932120\pi$
$548$		0			0
$549$			17.8580i			0.762162i
$550$		0			0
$551$			13.6183i			0.580158i
$552$		0			0
$553$	2.69634	−	2.69634i	0.114660	−	0.114660i
$554$		0			0
$555$	1.63816	+	0.501972i	0.0695359	+	0.0213075i
$556$		0			0
$557$	−3.94318	−	3.94318i	−0.167078	−	0.167078i	0.618616	−	0.785694i	$-0.287694\pi$
$557$	−3.94318	−	3.94318i	−0.167078	−	0.167078i	−0.785694	+	0.618616i	$0.787694\pi$
$558$		0			0
$559$	−44.9641			−1.90178
$560$		0			0
$561$	1.96187			0.0828302
$562$		0			0
$563$	13.3253	+	13.3253i	0.561593	+	0.561593i	0.929760	−	0.368167i	$-0.120015\pi$
$563$	13.3253	+	13.3253i	0.561593	+	0.561593i	−0.368167	+	0.929760i	$0.620015\pi$
$564$		0			0
$565$	−6.86725	−	12.9352i	−0.288908	−	0.544189i
$566$		0			0
$567$	−5.55326	+	5.55326i	−0.233215	+	0.233215i
$568$		0			0
$569$		−	16.5792i		−	0.695037i	−0.937673	−	0.347519i	$-0.887024\pi$
$569$		−	16.5792i		−	0.695037i	0.937673	−	0.347519i	$-0.112976\pi$
$570$		0			0
$571$		−	1.75641i		−	0.0735033i	−0.999324	−	0.0367516i	$-0.988299\pi$
$571$		−	1.75641i		−	0.0735033i	0.999324	−	0.0367516i	$-0.0117010\pi$
$572$		0			0
$573$	5.24972	−	5.24972i	0.219310	−	0.219310i
$574$		0			0
$575$	−4.56988	−	23.6703i	−0.190577	−	0.987121i
$576$		0			0
$577$	22.6219	+	22.6219i	0.941760	+	0.941760i	0.998395	−	0.0566345i	$-0.0180370\pi$
$577$	22.6219	+	22.6219i	0.941760	+	0.941760i	−0.0566345	+	0.998395i	$0.518037\pi$
$578$		0			0
$579$	−0.212498			−0.00883110
$580$		0			0
$581$	−7.77751			−0.322666
$582$		0			0
$583$	6.77481	+	6.77481i	0.280584	+	0.280584i
$584$		0			0
$585$	−36.0193	+	19.1225i	−1.48921	+	0.790617i
$586$		0			0
$587$	1.89960	−	1.89960i	0.0784051	−	0.0784051i	−0.666817	−	0.745222i	$-0.732344\pi$
$587$	1.89960	−	1.89960i	0.0784051	−	0.0784051i	0.745222	+	0.666817i	$0.232344\pi$
$588$		0			0
$589$		−	26.0791i		−	1.07457i
$590$		0			0
$591$			2.36823i			0.0974161i
$592$		0			0
$593$	4.90801	−	4.90801i	0.201548	−	0.201548i	−0.599115	−	0.800663i	$-0.704481\pi$
$593$	4.90801	−	4.90801i	0.201548	−	0.201548i	0.800663	+	0.599115i	$0.204481\pi$
$594$		0			0
$595$	1.07730	−	3.51571i	0.0441651	−	0.144130i
$596$		0			0
$597$	−5.69262	−	5.69262i	−0.232983	−	0.232983i
$598$		0			0
$599$	41.9543			1.71421			0.857104	−	0.515144i	$-0.172261\pi$
$599$	41.9543			1.71421			0.857104	+	0.515144i	$0.172261\pi$
$600$		0			0
$601$	8.00006			0.326329			0.163165	−	0.986599i	$-0.447830\pi$
$601$	8.00006			0.326329			0.163165	+	0.986599i	$0.447830\pi$
$602$		0			0
$603$	17.9392	+	17.9392i	0.730539	+	0.730539i
$604$		0			0
$605$	0.00829725	−	0.0270776i	0.000337331	−	0.00110086i
$606$		0			0
$607$	26.8075	−	26.8075i	1.08808	−	1.08808i	0.0923578	−	0.995726i	$-0.470560\pi$
$607$	26.8075	−	26.8075i	1.08808	−	1.08808i	0.995726	−	0.0923578i	$-0.0294404\pi$
$608$		0			0
$609$		−	0.881045i		−	0.0357018i
$610$		0			0
$611$		−	37.0136i		−	1.49741i
$612$		0			0
$613$	−26.2065	+	26.2065i	−1.05847	+	1.05847i	−0.0602885	+	0.998181i	$0.519202\pi$
$613$	−26.2065	+	26.2065i	−1.05847	+	1.05847i	−0.998181	+	0.0602885i	$0.980798\pi$
$614$		0			0
$615$	3.73071	−	1.98062i	0.150437	−	0.0798662i
$616$		0			0
$617$	−5.79622	−	5.79622i	−0.233347	−	0.233347i	0.580741	−	0.814088i	$-0.302763\pi$
$617$	−5.79622	−	5.79622i	−0.233347	−	0.233347i	−0.814088	+	0.580741i	$0.802763\pi$
$618$		0			0
$619$	−27.3240			−1.09825			−0.549123	−	0.835742i	$-0.685038\pi$
$619$	−27.3240			−1.09825			−0.549123	+	0.835742i	$0.685038\pi$
$620$		0			0
$621$	10.1761			0.408354
$622$		0			0
$623$	−7.76201	−	7.76201i	−0.310978	−	0.310978i
$624$		0			0
$625$	9.30630	+	23.2033i	0.372252	+	0.928132i
$626$		0			0
$627$	4.68780	−	4.68780i	0.187213	−	0.187213i
$628$		0			0
$629$			3.50484i			0.139747i
$630$		0			0
$631$			9.21022i			0.366653i	0.983052	+	0.183326i	$0.0586865\pi$
$631$			9.21022i			0.366653i	−0.983052	+	0.183326i	$0.941313\pi$
$632$		0			0
$633$	7.28720	−	7.28720i	0.289640	−	0.289640i
$634$		0			0
$635$	11.8346	+	22.2917i	0.469641	+	0.884621i
$636$		0			0
$637$	4.49218	+	4.49218i	0.177987	+	0.177987i
$638$		0			0
$639$	27.4566			1.08617
$640$		0			0
$641$	39.9767			1.57898			0.789491	−	0.613761i	$-0.210344\pi$
$641$	39.9767			1.57898			0.789491	+	0.613761i	$0.210344\pi$
$642$		0			0
$643$	25.2629	+	25.2629i	0.996271	+	0.996271i	0.999993	−	0.00372195i	$-0.00118474\pi$
$643$	25.2629	+	25.2629i	0.996271	+	0.996271i	−0.00372195	+	0.999993i	$0.501185\pi$
$644$		0			0
$645$	−5.43998	−	1.66694i	−0.214199	−	0.0656358i
$646$		0			0
$647$	−21.8082	+	21.8082i	−0.857370	+	0.857370i	−0.991028	−	0.133657i	$-0.957328\pi$
$647$	−21.8082	+	21.8082i	−0.857370	+	0.857370i	0.133657	+	0.991028i	$0.457328\pi$
$648$		0			0
$649$		−	13.9786i		−	0.548708i
$650$		0			0
$651$			1.68721i			0.0661269i
$652$		0			0
$653$	26.1270	−	26.1270i	1.02243	−	1.02243i	0.0226855	−	0.999743i	$-0.492778\pi$
$653$	26.1270	−	26.1270i	1.02243	−	1.02243i	0.999743	−	0.0226855i	$-0.00722165\pi$
$654$		0			0
$655$	3.32519	+	1.01892i	0.129926	+	0.0398125i
$656$		0			0
$657$	9.03321	+	9.03321i	0.352419	+	0.352419i
$658$		0			0
$659$	5.98250			0.233045			0.116523	−	0.993188i	$-0.462825\pi$
$659$	5.98250			0.233045			0.116523	+	0.993188i	$0.462825\pi$
$660$		0			0
$661$	−36.5857			−1.42302			−0.711509	−	0.702677i	$-0.751988\pi$
$661$	−36.5857			−1.42302			−0.711509	+	0.702677i	$0.751988\pi$
$662$		0			0
$663$	2.65571	+	2.65571i	0.103139	+	0.103139i
$664$		0			0
$665$	−5.82649	−	10.9748i	−0.225941	−	0.425585i
$666$		0			0
$667$	8.35521	−	8.35521i	0.323515	−	0.323515i
$668$		0			0
$669$			3.41767i			0.132135i
$670$		0			0
$671$		−	20.6435i		−	0.796934i
$672$		0			0
$673$	−19.2576	+	19.2576i	−0.742327	+	0.742327i	−0.973025	−	0.230698i	$-0.925899\pi$
$673$	−19.2576	+	19.2576i	−0.742327	+	0.742327i	0.230698	+	0.973025i	$0.425899\pi$
$674$		0			0
$675$	−10.3615	+	2.00044i	−0.398816	+	0.0769968i
$676$		0			0
$677$	−2.98190	−	2.98190i	−0.114604	−	0.114604i	0.647479	−	0.762083i	$-0.275823\pi$
$677$	−2.98190	−	2.98190i	−0.114604	−	0.114604i	−0.762083	+	0.647479i	$0.775823\pi$
$678$		0			0
$679$	−7.88333			−0.302534
$680$		0			0
$681$	6.21995			0.238349
$682$		0			0
$683$	−35.3071	−	35.3071i	−1.35099	−	1.35099i	−0.884558	−	0.466430i	$-0.845540\pi$
$683$	−35.3071	−	35.3071i	−1.35099	−	1.35099i	−0.466430	−	0.884558i	$-0.654460\pi$
$684$		0			0
$685$	−44.3821	+	23.5623i	−1.69575	+	0.900269i
$686$		0			0
$687$	−5.68442	+	5.68442i	−0.216874	+	0.216874i
$688$		0			0
$689$			18.3416i			0.698761i
$690$		0			0
$691$			18.0502i			0.686662i	0.939214	+	0.343331i	$0.111555\pi$
$691$			18.0502i			0.686662i	−0.939214	+	0.343331i	$0.888445\pi$
$692$		0			0
$693$	6.73639	−	6.73639i	0.255894	−	0.255894i
$694$		0			0
$695$	−14.1137	+	46.0593i	−0.535363	+	1.74713i
$696$		0			0
$697$	6.10970	+	6.10970i	0.231421	+	0.231421i
$698$		0			0
$699$	2.92361			0.110581
$700$		0			0
$701$	−1.96936			−0.0743819			−0.0371909	−	0.999308i	$-0.511841\pi$
$701$	−1.96936			−0.0743819			−0.0371909	+	0.999308i	$0.511841\pi$
$702$		0			0
$703$	8.37467	+	8.37467i	0.315857	+	0.315857i
$704$		0			0
$705$	1.37220	−	4.47809i	0.0516800	−	0.168655i
$706$		0			0
$707$	−5.40113	+	5.40113i	−0.203130	+	0.203130i
$708$		0			0
$709$			31.1106i			1.16838i	0.811616	+	0.584191i	$0.198588\pi$
$709$			31.1106i			1.16838i	−0.811616	+	0.584191i	$0.801412\pi$
$710$		0			0
$711$		−	10.9468i		−	0.410536i
$712$		0			0
$713$	−16.0003	+	16.0003i	−0.599215	+	0.599215i
$714$		0			0
$715$	41.6375	−	22.1052i	1.55716	−	0.826687i
$716$		0			0
$717$	−3.96609	−	3.96609i	−0.148117	−	0.148117i
$718$		0			0
$719$	0.367206			0.0136945			0.00684724	−	0.999977i	$-0.497820\pi$
$719$	0.367206			0.0136945			0.00684724	+	0.999977i	$0.497820\pi$
$720$		0			0
$721$	17.9176			0.667286
$722$		0			0
$723$	3.98649	+	3.98649i	0.148259	+	0.148259i
$724$		0			0
$725$	−6.86497	+	10.1499i	−0.254959	+	0.376959i
$726$		0			0
$727$	−21.4892	+	21.4892i	−0.796991	+	0.796991i	−0.982620	−	0.185629i	$-0.940568\pi$
$727$	−21.4892	+	21.4892i	−0.796991	+	0.796991i	0.185629	+	0.982620i	$0.440568\pi$
$728$		0			0
$729$			20.2692i			0.750710i
$730$		0			0
$731$		−	11.6388i		−	0.430478i
$732$		0			0
$733$	−7.63767	+	7.63767i	−0.282104	+	0.282104i	−0.833947	−	0.551844i	$-0.813924\pi$
$733$	−7.63767	+	7.63767i	−0.282104	+	0.282104i	0.551844	+	0.833947i	$0.313924\pi$
$734$		0			0
$735$	0.376949	+	0.710025i	0.0139040	+	0.0261897i
$736$		0			0
$737$	−20.7373	−	20.7373i	−0.763868	−	0.763868i
$738$		0			0
$739$	4.12185			0.151625			0.0758123	−	0.997122i	$-0.475845\pi$
$739$	4.12185			0.151625			0.0758123	+	0.997122i	$0.475845\pi$
$740$		0			0
$741$	12.6914			0.466231
$742$		0			0
$743$	−15.2432	−	15.2432i	−0.559217	−	0.559217i	0.369867	−	0.929085i	$-0.379403\pi$
$743$	−15.2432	−	15.2432i	−0.559217	−	0.559217i	−0.929085	+	0.369867i	$0.879403\pi$
$744$		0			0
$745$	11.0094	+	3.37355i	0.403353	+	0.123597i
$746$		0			0
$747$	−15.7878	+	15.7878i	−0.577646	+	0.577646i
$748$		0			0
$749$		−	13.1359i		−	0.479977i
$750$		0			0
$751$			33.0872i			1.20737i	0.797223	+	0.603685i	$0.206301\pi$
$751$			33.0872i			1.20737i	−0.797223	+	0.603685i	$0.793699\pi$
$752$		0			0
$753$	−4.53623	+	4.53623i	−0.165309	+	0.165309i
$754$		0			0
$755$	−20.2116	−	6.19332i	−0.735574	−	0.225398i
$756$		0			0
$757$	−6.89322	−	6.89322i	−0.250539	−	0.250539i	0.570653	−	0.821191i	$-0.306690\pi$
$757$	−6.89322	−	6.89322i	−0.250539	−	0.250539i	−0.821191	+	0.570653i	$0.806690\pi$
$758$		0			0
$759$	−5.75221			−0.208792
$760$		0			0
$761$	28.8931			1.04737			0.523687	−	0.851911i	$-0.324556\pi$
$761$	28.8931			1.04737			0.523687	+	0.851911i	$0.324556\pi$
$762$		0			0
$763$	13.6244	+	13.6244i	0.493236	+	0.493236i
$764$		0			0
$765$	−4.94981	−	9.32350i	−0.178961	−	0.337092i
$766$		0			0
$767$	18.9223	−	18.9223i	0.683246	−	0.683246i
$768$		0			0
$769$		−	50.7158i		−	1.82886i	−0.404745	−	0.914429i	$-0.632640\pi$
$769$		−	50.7158i		−	1.82886i	0.404745	−	0.914429i	$-0.367360\pi$
$770$		0			0
$771$			10.3508i			0.372773i
$772$		0			0
$773$	16.8457	−	16.8457i	0.605899	−	0.605899i	−0.335973	−	0.941872i	$-0.609065\pi$
$773$	16.8457	−	16.8457i	0.605899	−	0.605899i	0.941872	+	0.335973i	$0.109065\pi$
$774$		0			0
$775$	13.1465	−	19.4372i	0.472235	−	0.698204i
$776$		0			0
$777$	−0.541806	−	0.541806i	−0.0194372	−	0.0194372i
$778$		0			0
$779$	29.1977			1.04612
$780$		0			0
$781$	−31.7393			−1.13572
$782$		0			0
$783$	−3.65744	−	3.65744i	−0.130706	−	0.130706i
$784$		0			0
$785$	−21.7459	+	11.5448i	−0.776146	+	0.412053i
$786$		0			0
$787$	11.9165	−	11.9165i	0.424776	−	0.424776i	−0.462068	−	0.886844i	$-0.652892\pi$
$787$	11.9165	−	11.9165i	0.424776	−	0.424776i	0.886844	+	0.462068i	$0.152892\pi$
$788$		0			0
$789$			10.7013i			0.380977i
$790$		0			0
$791$			6.54949i			0.232873i
$792$		0			0
$793$	27.9444	−	27.9444i	0.992335	−	0.992335i
$794$		0			0
$795$	−0.679976	+	2.21906i	−0.0241163	+	0.0787021i
$796$		0			0
$797$	14.5745	+	14.5745i	0.516254	+	0.516254i	0.916436	−	0.400182i	$-0.131053\pi$
$797$	14.5745	+	14.5745i	0.516254	+	0.516254i	−0.400182	+	0.916436i	$0.631053\pi$
$798$		0			0
$799$	9.58088			0.338947
$800$		0			0
$801$	−31.5127			−1.11345
$802$		0			0
$803$	−10.4422	−	10.4422i	−0.368498	−	0.368498i
$804$		0			0
$805$	−3.15865	+	10.3081i	−0.111328	+	0.363312i
$806$		0			0
$807$	−4.99284	+	4.99284i	−0.175756	+	0.175756i
$808$		0			0
$809$		−	43.7779i		−	1.53915i	−0.638556	−	0.769575i	$-0.720468\pi$
$809$		−	43.7779i		−	1.53915i	0.638556	−	0.769575i	$-0.279532\pi$
$810$		0			0
$811$		−	8.35872i		−	0.293514i	−0.989173	−	0.146757i	$-0.953116\pi$
$811$		−	8.35872i		−	0.293514i	0.989173	−	0.146757i	$-0.0468836\pi$
$812$		0			0
$813$	1.64667	−	1.64667i	0.0577511	−	0.0577511i
$814$		0			0
$815$	−17.0993	+	9.07797i	−0.598964	+	0.317987i
$816$		0			0
$817$	−27.8105	−	27.8105i	−0.972967	−	0.972967i
$818$		0			0
$819$	18.2376			0.637275
$820$		0			0
$821$	35.0507			1.22328			0.611638	−	0.791137i	$-0.290511\pi$
$821$	35.0507			1.22328			0.611638	+	0.791137i	$0.290511\pi$
$822$		0			0
$823$	14.2699	+	14.2699i	0.497416	+	0.497416i	0.910633	−	0.413217i	$-0.135595\pi$
$823$	14.2699	+	14.2699i	0.497416	+	0.497416i	−0.413217	+	0.910633i	$0.635595\pi$
$824$		0			0
$825$	5.85702	−	1.13078i	0.203915	−	0.0393686i
$826$		0			0
$827$	−3.39513	+	3.39513i	−0.118060	+	0.118060i	−0.763669	−	0.645608i	$-0.776604\pi$
$827$	−3.39513	+	3.39513i	−0.118060	+	0.118060i	0.645608	+	0.763669i	$0.276604\pi$
$828$		0			0
$829$			26.0300i			0.904058i	0.892003	+	0.452029i	$0.149300\pi$
$829$			26.0300i			0.904058i	−0.892003	+	0.452029i	$0.850700\pi$
$830$		0			0
$831$			0.180196i			0.00625092i
$832$		0			0
$833$	−1.16279	+	1.16279i	−0.0402883	+	0.0402883i
$834$		0			0
$835$	0.462194	+	0.870593i	0.0159949	+	0.0301281i
$836$		0			0
$837$	7.00402	+	7.00402i	0.242094	+	0.242094i
$838$		0			0
$839$	−32.4541			−1.12044			−0.560220	−	0.828344i	$-0.689284\pi$
$839$	−32.4541			−1.12044			−0.560220	+	0.828344i	$0.689284\pi$
$840$		0			0
$841$	22.9940			0.792898
$842$		0			0
$843$	1.02219	+	1.02219i	0.0352062	+	0.0352062i
$844$		0			0
$845$	58.4930	+	17.9237i	2.01222	+	0.616594i
$846$		0			0
$847$	−0.00895568	+	0.00895568i	−0.000307721	+	0.000307721i
$848$		0			0
$849$			9.53497i			0.327239i
$850$		0			0
$851$		−	10.2762i		−	0.352264i
$852$		0			0
$853$	−1.65477	+	1.65477i	−0.0566581	+	0.0566581i	−0.734868	−	0.678210i	$-0.762756\pi$
$853$	−1.65477	+	1.65477i	−0.0566581	+	0.0566581i	0.678210	+	0.734868i	$0.262756\pi$
$854$		0			0
$855$	−34.1055	−	10.4508i	−1.16638	−	0.357409i
$856$		0			0
$857$	−29.3328	−	29.3328i	−1.00199	−	1.00199i	−0.999998	−	0.00199077i	$-0.999366\pi$
$857$	−29.3328	−	29.3328i	−1.00199	−	1.00199i	−0.00199077	−	0.999998i	$-0.500634\pi$
$858$		0			0
$859$	−23.2213			−0.792300			−0.396150	−	0.918186i	$-0.629654\pi$
$859$	−23.2213			−0.792300			−0.396150	+	0.918186i	$0.629654\pi$
$860$		0			0
$861$	−1.88897			−0.0643760
$862$		0			0
$863$	1.92038	+	1.92038i	0.0653705	+	0.0653705i	0.739036	−	0.673666i	$-0.235281\pi$
$863$	1.92038	+	1.92038i	0.0653705	+	0.0653705i	−0.673666	+	0.739036i	$0.735281\pi$
$864$		0			0
$865$	19.9534	+	37.5844i	0.678436	+	1.27791i
$866$		0			0
$867$	3.63414	−	3.63414i	0.123422	−	0.123422i
$868$		0			0
$869$			12.6543i			0.429266i
$870$		0			0
$871$		−	56.1427i		−	1.90232i
$872$		0			0
$873$	−16.0026	+	16.0026i	−0.541606	+	0.541606i
$874$		0			0
$875$	1.18983	−	11.1168i	0.0402236	−	0.375818i
$876$		0			0
$877$	−26.3659	−	26.3659i	−0.890313	−	0.890313i	0.104239	−	0.994552i	$-0.466759\pi$
$877$	−26.3659	−	26.3659i	−0.890313	−	0.890313i	−0.994552	+	0.104239i	$0.966759\pi$
$878$		0			0
$879$	7.20826			0.243129
$880$		0			0
$881$	4.76864			0.160660			0.0803298	−	0.996768i	$-0.474403\pi$
$881$	4.76864			0.160660			0.0803298	+	0.996768i	$0.474403\pi$
$882$		0			0
$883$	2.15889	+	2.15889i	0.0726524	+	0.0726524i	0.742499	−	0.669847i	$-0.233640\pi$
$883$	2.15889	+	2.15889i	0.0726524	+	0.0726524i	−0.669847	+	0.742499i	$0.733640\pi$
$884$		0			0
$885$	2.99083	−	1.58782i	0.100536	−	0.0533739i
$886$		0			0
$887$	5.11095	−	5.11095i	0.171609	−	0.171609i	−0.616077	−	0.787686i	$-0.711279\pi$
$887$	5.11095	−	5.11095i	0.171609	−	0.171609i	0.787686	+	0.616077i	$0.211279\pi$
$888$		0			0
$889$		−	11.2870i		−	0.378553i
$890$		0			0
$891$		−	26.0621i		−	0.873113i
$892$		0			0
$893$	22.8931	−	22.8931i	0.766089	−	0.766089i
$894$		0			0
$895$	11.3750	−	37.1216i	0.380224	−	1.24084i
$896$		0			0
$897$	−7.78656	−	7.78656i	−0.259986	−	0.259986i
$898$		0			0
$899$	11.5014			0.383595
$900$		0			0
$901$	−4.74769			−0.158168
$902$		0			0
$903$	1.79922	+	1.79922i	0.0598744	+	0.0598744i
$904$		0			0
$905$	3.75010	−	12.2382i	0.124658	−	0.406813i
$906$		0			0
$907$	−26.3613	+	26.3613i	−0.875314	+	0.875314i	−0.993045	−	0.117731i	$-0.962438\pi$
$907$	−26.3613	+	26.3613i	−0.875314	+	0.875314i	0.117731	+	0.993045i	$0.462438\pi$
$908$		0			0
$909$			21.9278i			0.727300i
$910$		0			0
$911$		−	18.5614i		−	0.614965i	−0.951554	−	0.307482i	$-0.900513\pi$
$911$		−	18.5614i		−	0.614965i	0.951554	−	0.307482i	$-0.0994865\pi$
$912$		0			0
$913$	18.2504	−	18.2504i	0.603999	−	0.603999i
$914$		0			0
$915$	4.41683	−	2.34488i	0.146016	−	0.0775193i
$916$		0			0
$917$	−1.09978	−	1.09978i	−0.0363178	−	0.0363178i
$918$		0			0
$919$	32.3872			1.06836			0.534178	−	0.845372i	$-0.320621\pi$
$919$	32.3872			1.06836			0.534178	+	0.845372i	$0.320621\pi$
$920$		0			0
$921$	9.16482			0.301991
$922$		0			0
$923$	−42.9644	−	42.9644i	−1.41419	−	1.41419i
$924$		0			0
$925$	2.02011	+	10.4634i	0.0664208	+	0.344036i
$926$		0			0
$927$	36.3715	−	36.3715i	1.19460	−	1.19460i
$928$		0			0
$929$			21.0620i			0.691023i	0.938415	+	0.345511i	$0.112295\pi$
$929$			21.0620i			0.691023i	−0.938415	+	0.345511i	$0.887705\pi$
$930$		0			0
$931$			5.55688i			0.182119i
$932$		0			0
$933$	2.69134	−	2.69134i	0.0881105	−	0.0881105i
$934$		0			0
$935$	5.72188	+	10.7778i	0.187125	+	0.352471i
$936$		0			0
$937$	17.4722	+	17.4722i	0.570793	+	0.570793i	0.932350	−	0.361557i	$-0.117755\pi$
$937$	17.4722	+	17.4722i	0.570793	+	0.570793i	−0.361557	+	0.932350i	$0.617755\pi$
$938$		0			0
$939$	−7.33031			−0.239215
$940$		0			0
$941$	17.3939			0.567025			0.283512	−	0.958969i	$-0.408500\pi$
$941$	17.3939			0.567025			0.283512	+	0.958969i	$0.408500\pi$
$942$		0			0
$943$	−17.9137	−	17.9137i	−0.583349	−	0.583349i
$944$		0			0
$945$	4.51230	+	1.38268i	0.146785	+	0.0449786i
$946$		0			0
$947$	−30.2742	+	30.2742i	−0.983778	+	0.983778i	−0.999871	−	0.0160928i	$-0.994877\pi$
$947$	−30.2742	+	30.2742i	−0.983778	+	0.983778i	0.0160928	+	0.999871i	$0.494877\pi$
$948$		0			0
$949$		−	28.2705i		−	0.917699i
$950$		0			0
$951$		−	11.5388i		−	0.374170i
$952$		0			0
$953$	−16.0684	+	16.0684i	−0.520506	+	0.520506i	−0.917724	−	0.397218i	$-0.869976\pi$
$953$	−16.0684	+	16.0684i	−0.520506	+	0.520506i	0.397218	+	0.917724i	$0.369976\pi$
$954$		0			0
$955$	44.1511	+	13.5290i	1.42870	+	0.437787i
$956$		0			0
$957$	2.06742	+	2.06742i	0.0668303	+	0.0668303i
$958$		0			0
$959$	22.4720			0.725659
$960$		0			0
$961$	8.97467			0.289505
$962$		0			0
$963$	−26.6650	−	26.6650i	−0.859269	−	0.859269i
$964$		0			0
$965$	−0.619759	−	1.16738i	−0.0199507	−	0.0375794i
$966$		0			0
$967$	−37.0970	+	37.0970i	−1.19296	+	1.19296i	−0.216727	+	0.976232i	$0.569538\pi$
$967$	−37.0970	+	37.0970i	−1.19296	+	1.19296i	−0.976232	+	0.216727i	$0.930462\pi$
$968$		0			0
$969$			3.28515i			0.105534i
$970$		0			0
$971$			6.28649i			0.201743i	0.994899	+	0.100872i	$0.0321631\pi$
$971$			6.28649i			0.201743i	−0.994899	+	0.100872i	$0.967837\pi$
$972$		0			0
$973$	15.2337	−	15.2337i	0.488370	−	0.488370i
$974$		0			0
$975$	9.45914	+	6.39775i	0.302935	+	0.204892i
$976$		0			0
$977$	−27.1175	−	27.1175i	−0.867565	−	0.867565i	0.124637	−	0.992202i	$-0.460223\pi$
$977$	−27.1175	−	27.1175i	−0.867565	−	0.867565i	−0.992202	+	0.124637i	$0.960223\pi$
$978$		0			0
$979$	36.4280			1.16424
$980$		0			0
$981$	55.3131			1.76601
$982$		0			0
$983$	−12.4725	−	12.4725i	−0.397810	−	0.397810i	0.479650	−	0.877460i	$-0.340764\pi$
$983$	−12.4725	−	12.4725i	−0.397810	−	0.397810i	−0.877460	+	0.479650i	$0.840764\pi$
$984$		0			0
$985$	−13.0102	+	6.90706i	−0.414539	+	0.220077i
$986$		0			0
$987$	−1.48109	+	1.48109i	−0.0471436	+	0.0471436i
$988$		0			0
$989$			34.1251i			1.08512i
$990$		0			0
$991$		−	3.78381i		−	0.120197i	−0.998192	−	0.0600984i	$-0.980859\pi$
$991$		−	3.78381i		−	0.120197i	0.998192	−	0.0600984i	$-0.0191414\pi$
$992$		0			0
$993$	−4.53051	+	4.53051i	−0.143771	+	0.143771i
$994$		0			0
$995$	14.6704	−	47.8759i	0.465082	−	1.51777i
$996$		0			0
$997$	−11.1149	−	11.1149i	−0.352012	−	0.352012i	0.508846	−	0.860858i	$-0.330072\pi$
$997$	−11.1149	−	11.1149i	−0.352012	−	0.352012i	−0.860858	+	0.508846i	$0.830072\pi$
$998$		0			0
$999$	−4.49834			−0.142321

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.x.f.127.6	yes	20
4.3	odd	2		1120.2.x.e.127.5	✓	20
5.3	odd	4		1120.2.x.e.1023.5	yes	20
20.3	even	4	inner	1120.2.x.f.1023.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1120.2.x.e.127.5	✓	20	4.3	odd	2
1120.2.x.e.1023.5	yes	20	5.3	odd	4
1120.2.x.f.127.6	yes	20	1.1	even	1	trivial
1120.2.x.f.1023.6	yes	20	20.3	even	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.254210 + 0.254210i) q^{3} +(-0.655120 + 2.13795i) q^{5} +(0.707107 - 0.707107i) q^{7} -2.87075i q^{9} +3.31853i q^{11} +(-4.49218 + 4.49218i) q^{13} +(-0.710025 + 0.376949i) q^{15} +(-1.16279 - 1.16279i) q^{17} -5.55688 q^{19} +0.359507 q^{21} +(3.40931 + 3.40931i) q^{23} +(-4.14164 - 2.80122i) q^{25} +(1.49240 - 1.49240i) q^{27} -2.45071i q^{29} +4.69312i q^{31} +(-0.843603 + 0.843603i) q^{33} +(1.04852 + 1.97500i) q^{35} +(-1.50708 - 1.50708i) q^{37} -2.28391 q^{39} -5.25434 q^{41} +(5.00470 + 5.00470i) q^{43} +(6.13752 + 1.88069i) q^{45} +(-4.11978 + 4.11978i) q^{47} -1.00000i q^{49} -0.591185i q^{51} +(2.04151 - 2.04151i) q^{53} +(-7.09485 - 2.17404i) q^{55} +(-1.41261 - 1.41261i) q^{57} -4.21228 q^{59} -6.22068 q^{61} +(-2.02993 - 2.02993i) q^{63} +(-6.66113 - 12.5470i) q^{65} +(-6.24893 + 6.24893i) q^{67} +1.73336i q^{69} +9.56426i q^{71} +(-3.14663 + 3.14663i) q^{73} +(-0.340746 - 1.76494i) q^{75} +(2.34656 + 2.34656i) q^{77} +3.81321 q^{79} -7.85350 q^{81} +(-5.49953 - 5.49953i) q^{83} +(3.24775 - 1.72422i) q^{85} +(0.622993 - 0.622993i) q^{87} -10.9771i q^{89} +6.35291i q^{91} +(-1.19304 + 1.19304i) q^{93} +(3.64042 - 11.8803i) q^{95} +(-5.57435 - 5.57435i) q^{97} +9.52670 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5} - 12 q^{13} + 8 q^{15} - 4 q^{17} - 24 q^{19} + 8 q^{23} + 4 q^{25} - 16 q^{33} - 4 q^{35} + 4 q^{37} + 8 q^{39} + 32 q^{41} - 8 q^{43} + 32 q^{45} + 24 q^{47} + 28 q^{53} + 24 q^{59} + 24 q^{61}+ \cdots + 4 q^{97}+O(q^{100}) \) 20 * q - 4 * q^5 - 12 * q^13 + 8 * q^15 - 4 * q^17 - 24 * q^19 + 8 * q^23 + 4 * q^25 - 16 * q^33 - 4 * q^35 + 4 * q^37 + 8 * q^39 + 32 * q^41 - 8 * q^43 + 32 * q^45 + 24 * q^47 + 28 * q^53 + 24 * q^59 + 24 * q^61 - 8 * q^63 - 12 * q^65 - 8 * q^67 + 20 * q^73 + 72 * q^75 + 8 * q^77 - 24 * q^79 - 20 * q^81 - 48 * q^83 - 20 * q^85 + 56 * q^87 - 8 * q^93 - 8 * q^95 + 4 * q^97

Introduction

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