LMFDB - Embedded newform 1170.2.cu.e.431.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(71,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 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("1170.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.cu (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 12x^{14} + 103x^{12} - 396x^{10} + 1089x^{8} - 1584x^{6} + 1648x^{4} - 768x^{2} + 256 $ x^16 - 12x^14 + 103x^12 - 396x^10 + 1089x^8 - 1584x^6 + 1648x^4 - 768*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			431.1
Root			$1.46923 + 0.848261i$ of defining polynomial
Character	$\chi$	$=$	1170.431
Dual form			1170.2.cu.e.1151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.47231 + 0.394504i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.47231 + 0.394504i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{10} +(1.35157 + 0.362151i) q^{11} +(-3.30591 - 1.43909i) q^{13} -1.52425i q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.431501 + 0.747382i) q^{17} +(2.02848 + 7.57039i) q^{19} +(-0.258819 - 0.965926i) q^{20} +(-0.699622 + 1.21178i) q^{22} +(-1.90032 - 3.29146i) q^{23} +1.00000i q^{25} +(2.24569 - 2.82080i) q^{26} +(1.47231 + 0.394504i) q^{28} +(-6.11051 + 3.52790i) q^{29} +(-5.72126 + 5.72126i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.610235 - 0.610235i) q^{34} +(-1.32004 - 0.762124i) q^{35} +(-0.943831 + 3.52243i) q^{37} -7.83744 q^{38} +1.00000 q^{40} +(1.69652 - 6.33150i) q^{41} +(-1.97231 - 1.13871i) q^{43} +(-0.989414 - 0.989414i) q^{44} +(3.67114 - 0.983680i) q^{46} +(6.37736 - 6.37736i) q^{47} +(-4.05012 + 2.33834i) q^{49} +(-0.965926 - 0.258819i) q^{50} +(2.14345 + 2.89924i) q^{52} +4.69722i q^{53} +(0.699622 + 1.21178i) q^{55} +(-0.762124 + 1.32004i) q^{56} +(-1.82618 - 6.81538i) q^{58} +(1.25627 + 4.68848i) q^{59} +(-6.11102 + 10.5846i) q^{61} +(-4.04554 - 7.00708i) q^{62} -1.00000i q^{64} +(-1.32004 - 3.35522i) q^{65} +(4.17588 + 1.11892i) q^{67} +(0.747382 - 0.431501i) q^{68} +(1.07781 - 1.07781i) q^{70} +(-9.99904 + 2.67923i) q^{71} +(-4.27743 - 4.27743i) q^{73} +(-3.15812 - 1.82334i) q^{74} +(2.02848 - 7.57039i) q^{76} -2.13279 q^{77} -7.74153 q^{79} +(-0.258819 + 0.965926i) q^{80} +(5.67667 + 3.27743i) q^{82} +(-6.44154 - 6.44154i) q^{83} +(-0.833596 + 0.223361i) q^{85} +(1.61038 - 1.61038i) q^{86} +(1.21178 - 0.699622i) q^{88} +(-9.45809 - 2.53429i) q^{89} +(5.43505 + 0.814595i) q^{91} +3.80065i q^{92} +(4.50948 + 7.81064i) q^{94} +(-3.91872 + 6.78742i) q^{95} +(3.30059 + 12.3180i) q^{97} +(-1.21041 - 4.51732i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} - 12 q^{13} + 8 q^{16} + 36 q^{19} + 12 q^{22} - 8 q^{28} - 12 q^{31} + 16 q^{34} + 20 q^{37} + 16 q^{40} + 32 q^{46} - 12 q^{49} - 24 q^{52} - 12 q^{55} + 32 q^{58} - 44 q^{61} + 4 q^{67} - 4 q^{70} - 24 q^{73} + 36 q^{76} - 24 q^{79} - 4 q^{85} + 12 q^{88} + 36 q^{91} + 56 q^{97}+O(q^{100}) $ 16 * q + 8 * q^7 - 12 * q^13 + 8 * q^16 + 36 * q^19 + 12 * q^22 - 8 * q^28 - 12 * q^31 + 16 * q^34 + 20 * q^37 + 16 * q^40 + 32 * q^46 - 12 * q^49 - 24 * q^52 - 12 * q^55 + 32 * q^58 - 44 * q^61 + 4 * q^67 - 4 * q^70 - 24 * q^73 + 36 * q^76 - 24 * q^79 - 4 * q^85 + 12 * q^88 + 36 * q^91 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$	−1.47231	+	0.394504i	−0.556481	+	0.149109i	−0.526089	−	0.850429i	$-0.676342\pi$
$7$	−1.47231	+	0.394504i	−0.556481	+	0.149109i	−0.0303917	+	0.999538i	$0.509675\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$	1.35157	+	0.362151i	0.407512	+	0.109193i	0.456751	−	0.889594i	$-0.349013\pi$
$11$	1.35157	+	0.362151i	0.407512	+	0.109193i	−0.0492390	+	0.998787i	$0.515680\pi$
$12$		0			0
$13$	−3.30591	−	1.43909i	−0.916893	−	0.399132i
$13$	−3.30591	−	1.43909i	−0.916893	−	0.399132i
$14$		−	1.52425i		−	0.407372i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.431501	+	0.747382i	−0.104654	+	0.181267i	−0.913597	−	0.406621i	$-0.866707\pi$
$17$	−0.431501	+	0.747382i	−0.104654	+	0.181267i	0.808943	+	0.587888i	$0.200040\pi$
$18$		0			0
$19$	2.02848	+	7.57039i	0.465365	+	1.73677i	0.655677	+	0.755042i	$0.272384\pi$
$19$	2.02848	+	7.57039i	0.465365	+	1.73677i	−0.190312	+	0.981724i	$0.560950\pi$
$20$	−0.258819	−	0.965926i	−0.0578737	−	0.215988i
$21$		0			0
$22$	−0.699622	+	1.21178i	−0.149160	+	0.258352i
$23$	−1.90032	−	3.29146i	−0.396245	−	0.686316i	0.597014	−	0.802231i	$-0.296354\pi$
$23$	−1.90032	−	3.29146i	−0.396245	−	0.686316i	−0.993259	+	0.115914i	$0.963020\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$	2.24569	−	2.82080i	0.440416	−	0.553204i
$27$		0			0
$28$	1.47231	+	0.394504i	0.278240	+	0.0745543i
$29$	−6.11051	+	3.52790i	−1.13469	+	0.655115i	−0.945111	−	0.326750i	$-0.894047\pi$
$29$	−6.11051	+	3.52790i	−1.13469	+	0.655115i	−0.189582	+	0.981865i	$0.560713\pi$
$30$		0			0
$31$	−5.72126	+	5.72126i	−1.02757	+	1.02757i	−0.0279592	+	0.999609i	$0.508901\pi$
$31$	−5.72126	+	5.72126i	−1.02757	+	1.02757i	−0.999609	+	0.0279592i	$0.991099\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		0			0
$34$	−0.610235	−	0.610235i	−0.104654	−	0.104654i
$35$	−1.32004	−	0.762124i	−0.223127	−	0.128822i
$36$		0			0
$37$	−0.943831	+	3.52243i	−0.155165	+	0.579083i	0.843926	+	0.536459i	$0.180238\pi$
$37$	−0.943831	+	3.52243i	−0.155165	+	0.579083i	−0.999091	+	0.0426240i	$0.986428\pi$
$38$	−7.83744			−1.27140
$39$		0			0
$40$	1.00000			0.158114
$41$	1.69652	−	6.33150i	0.264952	−	0.988815i	−0.697328	−	0.716753i	$-0.745628\pi$
$41$	1.69652	−	6.33150i	0.264952	−	0.988815i	0.962280	−	0.272062i	$-0.0877056\pi$
$42$		0			0
$43$	−1.97231	−	1.13871i	−0.300774	−	0.173652i	0.342016	−	0.939694i	$-0.388890\pi$
$43$	−1.97231	−	1.13871i	−0.300774	−	0.173652i	−0.642791	+	0.766042i	$0.722224\pi$
$44$	−0.989414	−	0.989414i	−0.149160	−	0.149160i
$45$		0			0
$46$	3.67114	−	0.983680i	0.541280	−	0.145036i
$47$	6.37736	−	6.37736i	0.930234	−	0.930234i	−0.0674859	−	0.997720i	$-0.521498\pi$
$47$	6.37736	−	6.37736i	0.930234	−	0.930234i	0.997720	+	0.0674859i	$0.0214978\pi$
$48$		0			0
$49$	−4.05012	+	2.33834i	−0.578588	+	0.334048i
$50$	−0.965926	−	0.258819i	−0.136603	−	0.0366025i
$51$		0			0
$52$	2.14345	+	2.89924i	0.297243	+	0.402053i
$53$			4.69722i			0.645213i	0.946533	+	0.322607i	$0.104559\pi$
$53$			4.69722i			0.645213i	−0.946533	+	0.322607i	$0.895441\pi$
$54$		0			0
$55$	0.699622	+	1.21178i	0.0943370	+	0.163396i
$56$	−0.762124	+	1.32004i	−0.101843	+	0.176397i
$57$		0			0
$58$	−1.82618	−	6.81538i	−0.239789	−	0.894904i
$59$	1.25627	+	4.68848i	0.163553	+	0.610387i	0.998220	+	0.0596333i	$0.0189931\pi$
$59$	1.25627	+	4.68848i	0.163553	+	0.610387i	−0.834668	+	0.550754i	$0.814340\pi$
$60$		0			0
$61$	−6.11102	+	10.5846i	−0.782436	+	1.35522i	0.148082	+	0.988975i	$0.452690\pi$
$61$	−6.11102	+	10.5846i	−0.782436	+	1.35522i	−0.930519	+	0.366244i	$0.880643\pi$
$62$	−4.04554	−	7.00708i	−0.513784	−	0.889900i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−1.32004	−	3.35522i	−0.163730	−	0.416164i
$66$		0			0
$67$	4.17588	+	1.11892i	0.510165	+	0.136698i	0.504714	−	0.863287i	$-0.331598\pi$
$67$	4.17588	+	1.11892i	0.510165	+	0.136698i	0.00545147	+	0.999985i	$0.498265\pi$
$68$	0.747382	−	0.431501i	0.0906334	−	0.0523272i
$69$		0			0
$70$	1.07781	−	1.07781i	0.128822	−	0.128822i
$71$	−9.99904	+	2.67923i	−1.18667	+	0.317967i	−0.797568	−	0.603229i	$-0.793880\pi$
$71$	−9.99904	+	2.67923i	−1.18667	+	0.317967i	−0.389099	+	0.921196i	$0.627214\pi$
$72$		0			0
$73$	−4.27743	−	4.27743i	−0.500635	−	0.500635i	0.411000	−	0.911635i	$-0.365180\pi$
$73$	−4.27743	−	4.27743i	−0.500635	−	0.500635i	−0.911635	+	0.411000i	$0.865180\pi$
$74$	−3.15812	−	1.82334i	−0.367124	−	0.211959i
$75$		0			0
$76$	2.02848	−	7.57039i	0.232682	−	0.868383i
$77$	−2.13279			−0.243054
$78$		0			0
$79$	−7.74153			−0.870990			−0.435495	−	0.900191i	$-0.643427\pi$
$79$	−7.74153			−0.870990			−0.435495	+	0.900191i	$0.643427\pi$
$80$	−0.258819	+	0.965926i	−0.0289368	+	0.107994i
$81$		0			0
$82$	5.67667	+	3.27743i	0.626883	+	0.361931i
$83$	−6.44154	−	6.44154i	−0.707051	−	0.707051i	0.258863	−	0.965914i	$-0.416652\pi$
$83$	−6.44154	−	6.44154i	−0.707051	−	0.707051i	−0.965914	+	0.258863i	$0.916652\pi$
$84$		0			0
$85$	−0.833596	+	0.223361i	−0.0904162	+	0.0242269i
$86$	1.61038	−	1.61038i	0.173652	−	0.173652i
$87$		0			0
$88$	1.21178	−	0.699622i	0.129176	−	0.0745799i
$89$	−9.45809	−	2.53429i	−1.00256	−	0.268634i	−0.280040	−	0.959988i	$-0.590348\pi$
$89$	−9.45809	−	2.53429i	−1.00256	−	0.268634i	−0.722516	+	0.691354i	$0.757014\pi$
$90$		0			0
$91$	5.43505	+	0.814595i	0.569748	+	0.0853928i
$92$			3.80065i			0.396245i
$93$		0			0
$94$	4.50948	+	7.81064i	0.465117	+	0.805607i
$95$	−3.91872	+	6.78742i	−0.402052	+	0.696375i
$96$		0			0
$97$	3.30059	+	12.3180i	0.335124	+	1.25070i	0.903735	+	0.428093i	$0.140815\pi$
$97$	3.30059	+	12.3180i	0.335124	+	1.25070i	−0.568610	+	0.822607i	$0.692519\pi$
$98$	−1.21041	−	4.51732i	−0.122270	−	0.456318i
$99$		0			0
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	3.96815	+	6.87304i	0.394846	+	0.683893i	0.993081	−	0.117427i	$-0.0374647\pi$
$101$	3.96815	+	6.87304i	0.394846	+	0.683893i	−0.598236	+	0.801320i	$0.704131\pi$
$102$		0			0
$103$		−	12.2088i		−	1.20297i	−0.798885	−	0.601484i	$-0.794576\pi$
$103$		−	12.2088i		−	1.20297i	0.798885	−	0.601484i	$-0.205424\pi$
$104$	−3.35522	+	1.32004i	−0.329006	+	0.129440i
$105$		0			0
$106$	−4.53717	−	1.21573i	−0.440689	−	0.118082i
$107$	6.02612	−	3.47918i	0.582567	−	0.336345i	−0.179586	−	0.983742i	$-0.557476\pi$
$107$	6.02612	−	3.47918i	0.582567	−	0.336345i	0.762153	+	0.647397i	$0.224143\pi$
$108$		0			0
$109$	−4.14077	+	4.14077i	−0.396614	+	0.396614i	−0.877037	−	0.480423i	$-0.840483\pi$
$109$	−4.14077	+	4.14077i	−0.396614	+	0.396614i	0.480423	+	0.877037i	$0.340483\pi$
$110$	−1.35157	+	0.362151i	−0.128867	+	0.0345297i
$111$		0			0
$112$	−1.07781	−	1.07781i	−0.101843	−	0.101843i
$113$	11.9157	+	6.87955i	1.12094	+	0.647174i	0.941640	−	0.336621i	$-0.109284\pi$
$113$	11.9157	+	6.87955i	1.12094	+	0.647174i	0.179298	+	0.983795i	$0.442617\pi$
$114$		0			0
$115$	0.983680	−	3.67114i	0.0917286	−	0.342336i
$116$	7.05580			0.655115
$117$		0			0
$118$	−4.85387			−0.446835
$119$	0.340458	−	1.27061i	0.0312097	−	0.116476i
$120$		0			0
$121$	−7.83070	−	4.52106i	−0.711882	−	0.411005i
$122$	−8.64229	−	8.64229i	−0.782436	−	0.782436i
$123$		0			0
$124$	7.81538	−	2.09413i	0.701842	−	0.188058i
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	−0.431191	+	0.248948i	−0.0382620	+	0.0220906i	−0.519009	−	0.854769i	$-0.673699\pi$
$127$	−0.431191	+	0.248948i	−0.0382620	+	0.0220906i	0.480747	+	0.876859i	$0.340366\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		0			0
$130$	3.58254	−	0.406663i	0.314210	−	0.0356667i
$131$		−	15.7546i		−	1.37649i	−0.725480	−	0.688244i	$-0.758382\pi$
$131$		−	15.7546i		−	1.37649i	0.725480	−	0.688244i	$-0.241618\pi$
$132$		0			0
$133$	−5.97310	−	10.3457i	−0.517933	−	0.897087i
$134$	−2.16160	+	3.74399i	−0.186733	+	0.323432i
$135$		0			0
$136$	0.223361	+	0.833596i	0.0191531	+	0.0714803i
$137$	2.39109	+	8.92367i	0.204285	+	0.762401i	0.989666	+	0.143389i	$0.0458000\pi$
$137$	2.39109	+	8.92367i	0.204285	+	0.762401i	−0.785382	+	0.619012i	$0.787533\pi$
$138$		0			0
$139$	8.70168	−	15.0718i	0.738067	−	1.27837i	−0.215298	−	0.976548i	$-0.569072\pi$
$139$	8.70168	−	15.0718i	0.738067	−	1.27837i	0.953365	−	0.301821i	$-0.0975945\pi$
$140$	0.762124	+	1.32004i	0.0644112	+	0.111563i
$141$		0			0
$142$		−	10.3518i		−	0.868701i
$143$	−3.94698	−	3.14226i	−0.330063	−	0.262769i
$144$		0			0
$145$	−6.81538	−	1.82618i	−0.565987	−	0.151656i
$146$	5.23876	−	3.02460i	0.433563	−	0.250317i
$147$		0			0
$148$	2.57859	−	2.57859i	0.211959	−	0.211959i
$149$	10.4871	−	2.81000i	0.859135	−	0.230204i	0.197751	−	0.980252i	$-0.436636\pi$
$149$	10.4871	−	2.81000i	0.859135	−	0.230204i	0.661384	+	0.750048i	$0.269970\pi$
$150$		0			0
$151$	7.36124	+	7.36124i	0.599049	+	0.599049i	0.940060	−	0.341010i	$-0.110769\pi$
$151$	7.36124	+	7.36124i	0.599049	+	0.599049i	−0.341010	+	0.940060i	$0.610769\pi$
$152$	6.78742	+	3.91872i	0.550533	+	0.317850i
$153$		0			0
$154$	0.552007	−	2.06012i	0.0444820	−	0.166009i
$155$	−8.09108			−0.649891
$156$		0			0
$157$	−18.3502			−1.46450			−0.732252	−	0.681034i	$-0.761531\pi$
$157$	−18.3502			−1.46450			−0.732252	+	0.681034i	$0.761531\pi$
$158$	2.00366	−	7.47774i	0.159402	−	0.594897i
$159$		0			0
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	4.09636	+	4.09636i	0.322838	+	0.322838i
$162$		0			0
$163$	6.30538	−	1.68952i	0.493875	−	0.132334i	−0.00328069	−	0.999995i	$-0.501044\pi$
$163$	6.30538	−	1.68952i	0.493875	−	0.132334i	0.497156	+	0.867661i	$0.334378\pi$
$164$	−4.63498	+	4.63498i	−0.361931	+	0.361931i
$165$		0			0
$166$	7.88924	−	4.55485i	0.612324	−	0.353525i
$167$	15.2326	+	4.08157i	1.17874	+	0.315841i	0.794425	−	0.607363i	$-0.207773\pi$
$167$	15.2326	+	4.08157i	1.17874	+	0.315841i	0.384310	+	0.923204i	$0.374439\pi$
$168$		0			0
$169$	8.85803	+	9.51501i	0.681387	+	0.731924i
$170$		−	0.863002i		−	0.0661893i
$171$		0			0
$172$	1.13871	+	1.97231i	0.0868261	+	0.150387i
$173$	−10.0015	+	17.3231i	−0.760399	+	1.31705i	0.182246	+	0.983253i	$0.441663\pi$
$173$	−10.0015	+	17.3231i	−0.760399	+	1.31705i	−0.942645	+	0.333797i	$0.891670\pi$
$174$		0			0
$175$	−0.394504	−	1.47231i	−0.0298217	−	0.111296i
$176$	0.362151	+	1.35157i	0.0272981	+	0.101878i
$177$		0			0
$178$	4.89587	−	8.47990i	0.366961	−	0.635595i
$179$	−4.16414	−	7.21249i	−0.311242	−	0.539087i	0.667389	−	0.744709i	$-0.267412\pi$
$179$	−4.16414	−	7.21249i	−0.311242	−	0.539087i	−0.978632	+	0.205622i	$0.934078\pi$
$180$		0			0
$181$			24.3005i			1.80624i	0.429386	+	0.903121i	$0.358730\pi$
$181$			24.3005i			1.80624i	−0.429386	+	0.903121i	$0.641270\pi$
$182$	−2.19353	+	5.03902i	−0.162595	+	0.373517i
$183$		0			0
$184$	−3.67114	−	0.983680i	−0.270640	−	0.0725178i
$185$	−3.15812	+	1.82334i	−0.232190	+	0.134055i
$186$		0			0
$187$	−0.853867	+	0.853867i	−0.0624409	+	0.0624409i
$188$	−8.71164	+	2.33428i	−0.635362	+	0.170245i
$189$		0			0
$190$	−5.54191	−	5.54191i	−0.402052	−	0.402052i
$191$	20.5835	+	11.8839i	1.48937	+	0.859890i	0.999926	−	0.0121439i	$-0.00386563\pi$
$191$	20.5835	+	11.8839i	1.48937	+	0.859890i	0.489446	+	0.872034i	$0.337199\pi$
$192$		0			0
$193$	6.40583	−	23.9069i	0.461102	−	1.72085i	−0.208399	−	0.978044i	$-0.566825\pi$
$193$	6.40583	−	23.9069i	0.461102	−	1.72085i	0.669501	−	0.742811i	$-0.266508\pi$
$194$	−12.7525			−0.915576
$195$		0			0
$196$	4.67667			0.334048
$197$	0.859733	−	3.20857i	0.0612534	−	0.228601i	−0.928513	−	0.371301i	$-0.878912\pi$
$197$	0.859733	−	3.20857i	0.0612534	−	0.228601i	0.989766	+	0.142700i	$0.0455785\pi$
$198$		0			0
$199$	6.71994	+	3.87976i	0.476364	+	0.275029i	0.718900	−	0.695113i	$-0.244646\pi$
$199$	6.71994	+	3.87976i	0.476364	+	0.275029i	−0.242536	+	0.970142i	$0.577979\pi$
$200$	0.707107	+	0.707107i	0.0500000	+	0.0500000i
$201$		0			0
$202$	−7.66588	+	2.05407i	−0.539369	+	0.144524i
$203$	7.60479	−	7.60479i	0.533751	−	0.533751i
$204$		0			0
$205$	5.67667	−	3.27743i	0.396476	−	0.228905i
$206$	11.7928	+	3.15987i	0.821642	+	0.220158i
$207$		0			0
$208$	−0.406663	−	3.58254i	−0.0281970	−	0.248405i
$209$			10.9665i			0.758568i
$210$		0			0
$211$	8.45747	+	14.6488i	0.582236	+	1.00846i	0.995214	+	0.0977216i	$0.0311555\pi$
$211$	8.45747	+	14.6488i	0.582236	+	1.00846i	−0.412978	+	0.910741i	$0.635511\pi$
$212$	2.34861	−	4.06791i	0.161303	−	0.279385i
$213$		0			0
$214$	1.80096	+	6.72126i	0.123111	+	0.459456i
$215$	−0.589442	−	2.19983i	−0.0401996	−	0.150027i
$216$		0			0
$217$	6.16640	−	10.6805i	0.418603	−	0.725041i
$218$	−2.92797	−	5.07139i	−0.198307	−	0.343478i
$219$		0			0
$220$		−	1.39924i		−	0.0943370i
$221$	2.50205	−	1.84980i	0.168306	−	0.124431i
$222$		0			0
$223$	−7.83487	−	2.09935i	−0.524661	−	0.140583i	−0.0132395	−	0.999912i	$-0.504214\pi$
$223$	−7.83487	−	2.09935i	−0.524661	−	0.140583i	−0.511422	+	0.859330i	$0.670881\pi$
$224$	1.32004	−	0.762124i	0.0881987	−	0.0509215i
$225$		0			0
$226$	−9.72916	+	9.72916i	−0.647174	+	0.647174i
$227$	6.48293	−	1.73710i	0.430287	−	0.115295i	−0.0371739	−	0.999309i	$-0.511836\pi$
$227$	6.48293	−	1.73710i	0.430287	−	0.115295i	0.467461	+	0.884014i	$0.345169\pi$
$228$		0			0
$229$	−7.92188	−	7.92188i	−0.523493	−	0.523493i	0.395132	−	0.918624i	$-0.370699\pi$
$229$	−7.92188	−	7.92188i	−0.523493	−	0.523493i	−0.918624	+	0.395132i	$0.870699\pi$
$230$	3.29146	+	1.90032i	0.217032	+	0.125304i
$231$		0			0
$232$	−1.82618	+	6.81538i	−0.119894	+	0.447452i
$233$	9.48072			0.621102			0.310551	−	0.950557i	$-0.399486\pi$
$233$	9.48072			0.621102			0.310551	+	0.950557i	$0.399486\pi$
$234$		0			0
$235$	9.01896			0.588332
$236$	1.25627	−	4.68848i	0.0817764	−	0.305194i
$237$		0			0
$238$	1.13919	+	0.657714i	0.0738430	+	0.0426333i
$239$	3.11155	+	3.11155i	0.201270	+	0.201270i	0.800544	−	0.599274i	$-0.204544\pi$
$239$	3.11155	+	3.11155i	0.201270	+	0.201270i	−0.599274	+	0.800544i	$0.704544\pi$
$240$		0			0
$241$	12.3375	−	3.30581i	0.794725	−	0.212946i	0.161458	−	0.986880i	$-0.448380\pi$
$241$	12.3375	−	3.30581i	0.794725	−	0.212946i	0.633267	+	0.773934i	$0.281714\pi$
$242$	6.39374	−	6.39374i	0.411005	−	0.411005i
$243$		0			0
$244$	10.5846	−	6.11102i	0.677610	−	0.391218i
$245$	−4.51732	−	1.21041i	−0.288601	−	0.0773303i
$246$		0			0
$247$	4.18852	−	27.9462i	0.266509	−	1.77817i
$248$			8.09108i			0.513784i
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−0.756351	+	1.31004i	−0.0477405	+	0.0826889i	−0.888908	−	0.458085i	$-0.848535\pi$
$251$	−0.756351	+	1.31004i	−0.0477405	+	0.0826889i	0.841168	+	0.540774i	$0.181869\pi$
$252$		0			0
$253$	−1.37641	−	5.13682i	−0.0865340	−	0.322949i
$254$	−0.128865	−	0.480931i	−0.00808572	−	0.0301763i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.11439	+	8.85838i	0.319027	+	0.552571i	0.980285	−	0.197587i	$-0.0633106\pi$
$257$	5.11439	+	8.85838i	0.319027	+	0.552571i	−0.661258	+	0.750158i	$0.729977\pi$
$258$		0			0
$259$		−	5.55845i		−	0.345385i
$260$	−0.534425	+	3.56572i	−0.0331436	+	0.221137i
$261$		0			0
$262$	15.2178	+	4.07759i	0.940158	+	0.251915i
$263$	−8.02732	+	4.63457i	−0.494986	+	0.285780i	−0.726640	−	0.687018i	$-0.758919\pi$
$263$	−8.02732	+	4.63457i	−0.494986	+	0.285780i	0.231655	+	0.972798i	$0.425586\pi$
$264$		0			0
$265$	−3.32144	+	3.32144i	−0.204034	+	0.204034i
$266$	11.5391	−	3.09190i	0.707510	−	0.189577i
$267$		0			0
$268$	−3.05696	−	3.05696i	−0.186733	−	0.186733i
$269$	19.7102	+	11.3797i	1.20175	+	0.693831i	0.960944	−	0.276742i	$-0.0892548\pi$
$269$	19.7102	+	11.3797i	1.20175	+	0.693831i	0.240806	+	0.970573i	$0.422588\pi$
$270$		0			0
$271$	1.32539	−	4.94642i	0.0805116	−	0.300473i	−0.913915	−	0.405906i	$-0.866956\pi$
$271$	1.32539	−	4.94642i	0.0805116	−	0.300473i	0.994426	+	0.105433i	$0.0336227\pi$
$272$	−0.863002			−0.0523272
$273$		0			0
$274$	−9.23846			−0.558116
$275$	−0.362151	+	1.35157i	−0.0218385	+	0.0815024i
$276$		0			0
$277$	1.83975	+	1.06218i	0.110540	+	0.0638201i	0.554251	−	0.832350i	$-0.313005\pi$
$277$	1.83975	+	1.06218i	0.110540	+	0.0638201i	−0.443711	+	0.896170i	$0.646338\pi$
$278$	12.3060	+	12.3060i	0.738067	+	0.738067i
$279$		0			0
$280$	−1.47231	+	0.394504i	−0.0879873	+	0.0235761i
$281$	7.20895	−	7.20895i	0.430050	−	0.430050i	−0.458595	−	0.888645i	$-0.651647\pi$
$281$	7.20895	−	7.20895i	0.430050	−	0.430050i	0.888645	+	0.458595i	$0.151647\pi$
$282$		0			0
$283$	−12.0480	+	6.95589i	−0.716177	+	0.413485i	−0.813344	−	0.581783i	$-0.802355\pi$
$283$	−12.0480	+	6.95589i	−0.716177	+	0.413485i	0.0971670	+	0.995268i	$0.469022\pi$
$284$	9.99904	+	2.67923i	0.593334	+	0.158983i
$285$		0			0
$286$	4.05675	−	2.99921i	0.239880	−	0.177347i
$287$			9.99122i			0.589763i
$288$		0			0
$289$	8.12761	+	14.0774i	0.478095	+	0.828085i
$290$	3.52790	−	6.11051i	0.207166	−	0.358821i
$291$		0			0
$292$	1.56565	+	5.84307i	0.0916226	+	0.341940i
$293$	−0.629010	−	2.34750i	−0.0367471	−	0.137142i	0.945115	−	0.326737i	$-0.105949\pi$
$293$	−0.629010	−	2.34750i	−0.0367471	−	0.137142i	−0.981862	+	0.189595i	$0.939283\pi$
$294$		0			0
$295$	−2.42693	+	4.20357i	−0.141302	+	0.244741i
$296$	1.82334	+	3.15812i	0.105980	+	0.183562i
$297$		0			0
$298$			10.8570i			0.628930i
$299$	1.54558	+	13.6160i	0.0893833	+	0.787433i
$300$		0			0
$301$	3.35308	+	0.898455i	0.193268	+	0.0517861i
$302$	−9.01564	+	5.20518i	−0.518792	+	0.299525i
$303$		0			0
$304$	−5.54191	+	5.54191i	−0.317850	+	0.317850i
$305$	−11.8056	+	3.16330i	−0.675986	+	0.181130i
$306$		0			0
$307$	17.8111	+	17.8111i	1.01653	+	1.01653i	0.999861	+	0.0166732i	$0.00530750\pi$
$307$	17.8111	+	17.8111i	1.01653	+	1.01653i	0.0166732	+	0.999861i	$0.494692\pi$
$308$	1.84705	+	1.06640i	0.105246	+	0.0607636i
$309$		0			0
$310$	2.09413	−	7.81538i	0.118938	−	0.443884i
$311$	7.46564			0.423338			0.211669	−	0.977341i	$-0.432110\pi$
$311$	7.46564			0.423338			0.211669	+	0.977341i	$0.432110\pi$
$312$		0			0
$313$	−23.4344			−1.32459			−0.662296	−	0.749242i	$-0.730418\pi$
$313$	−23.4344			−1.32459			−0.662296	+	0.749242i	$0.730418\pi$
$314$	4.74938	−	17.7249i	0.268023	−	1.00028i
$315$		0			0
$316$	6.70436	+	3.87076i	0.377150	+	0.217748i
$317$	0.210690	+	0.210690i	0.0118335	+	0.0118335i	0.712999	−	0.701165i	$-0.247336\pi$
$317$	0.210690	+	0.210690i	0.0118335	+	0.0118335i	−0.701165	+	0.712999i	$0.747336\pi$
$318$		0			0
$319$	−9.53638	+	2.55527i	−0.533935	+	0.143067i
$320$	0.707107	−	0.707107i	0.0395285	−	0.0395285i
$321$		0			0
$322$	−5.01699	+	2.89656i	−0.279586	+	0.161419i
$323$	−6.53326	−	1.75058i	−0.363520	−	0.0974050i
$324$		0			0
$325$	1.43909	−	3.30591i	0.0798265	−	0.183379i
$326$			6.52781i			0.361542i
$327$		0			0
$328$	−3.27743	−	5.67667i	−0.180966	−	0.313442i
$329$	−6.87356	+	11.9054i	−0.378952	+	0.656363i
$330$		0			0
$331$	6.36217	+	23.7439i	0.349697	+	1.30509i	0.887029	+	0.461715i	$0.152766\pi$
$331$	6.36217	+	23.7439i	0.349697	+	1.30509i	−0.537332	+	0.843371i	$0.680568\pi$
$332$	2.35777	+	8.79930i	0.129399	+	0.482924i
$333$		0			0
$334$	−7.88498	+	13.6572i	−0.431447	+	0.747288i
$335$	2.16160	+	3.74399i	0.118101	+	0.204556i
$336$		0			0
$337$			1.32314i			0.0720759i	0.999350	+	0.0360379i	$0.0114737\pi$
$337$			1.32314i			0.0720759i	−0.999350	+	0.0360379i	$0.988526\pi$
$338$	−11.4834	+	6.09353i	−0.624615	+	0.331445i
$339$		0			0
$340$	0.833596	+	0.223361i	0.0452081	+	0.0121135i
$341$	−9.80461	+	5.66069i	−0.530949	+	0.306544i
$342$		0			0
$343$	12.5852	−	12.5852i	0.679536	−	0.679536i
$344$	−2.19983	+	0.589442i	−0.118607	+	0.0317806i
$345$		0			0
$346$	−14.1442	−	14.1442i	−0.760399	−	0.760399i
$347$	13.3649	+	7.71623i	0.717466	+	0.414229i	0.813819	−	0.581118i	$-0.197385\pi$
$347$	13.3649	+	7.71623i	0.717466	+	0.414229i	−0.0963534	+	0.995347i	$0.530718\pi$
$348$		0			0
$349$	3.29516	−	12.2977i	0.176386	−	0.658281i	−0.819926	−	0.572470i	$-0.805985\pi$
$349$	3.29516	−	12.2977i	0.176386	−	0.658281i	0.996311	−	0.0858107i	$-0.0273480\pi$
$350$	1.52425			0.0814744
$351$		0			0
$352$	−1.39924			−0.0745799
$353$	4.16209	−	15.5331i	0.221526	−	0.826745i	−0.762241	−	0.647293i	$-0.775901\pi$
$353$	4.16209	−	15.5331i	0.221526	−	0.826745i	0.983767	−	0.179452i	$-0.0574324\pi$
$354$		0			0
$355$	−8.96489	−	5.17588i	−0.475807	−	0.274707i
$356$	6.92381	+	6.92381i	0.366961	+	0.366961i
$357$		0			0
$358$	8.04449	−	2.15552i	0.425165	−	0.113923i
$359$	22.6408	−	22.6408i	1.19494	−	1.19494i	0.219273	−	0.975663i	$-0.429631\pi$
$359$	22.6408	−	22.6408i	1.19494	−	1.19494i	0.975663	−	0.219273i	$-0.0703687\pi$
$360$		0			0
$361$	−36.7415	+	21.2127i	−1.93377	+	1.11646i
$362$	−23.4725	−	6.28943i	−1.23369	−	0.330565i
$363$		0			0
$364$	−4.29959	−	3.42298i	−0.225360	−	0.179413i
$365$		−	6.04920i		−	0.316629i
$366$		0			0
$367$	2.86624	+	4.96447i	0.149616	+	0.259143i	0.931086	−	0.364801i	$-0.118863\pi$
$367$	2.86624	+	4.96447i	0.149616	+	0.259143i	−0.781469	+	0.623944i	$0.785529\pi$
$368$	1.90032	−	3.29146i	0.0990612	−	0.171579i
$369$		0			0
$370$	−0.943831	−	3.52243i	−0.0490674	−	0.183122i
$371$	−1.85307	−	6.91577i	−0.0962068	−	0.359049i
$372$		0			0
$373$	9.39587	−	16.2741i	0.486500	−	0.842642i	−0.513380	−	0.858161i	$-0.671607\pi$
$373$	9.39587	−	16.2741i	0.486500	−	0.842642i	0.999880	+	0.0155193i	$0.00494013\pi$
$374$	−0.603775	−	1.04577i	−0.0312205	−	0.0540754i
$375$		0			0
$376$		−	9.01896i		−	0.465117i
$377$	25.2777	−	2.86933i	1.30187	−	0.147778i
$378$		0			0
$379$	11.4618	+	3.07117i	0.588752	+	0.157756i	0.540883	−	0.841098i	$-0.318090\pi$
$379$	11.4618	+	3.07117i	0.588752	+	0.157756i	0.0478693	+	0.998854i	$0.484757\pi$
$380$	6.78742	−	3.91872i	0.348187	−	0.201026i
$381$		0			0
$382$	−16.8064	+	16.8064i	−0.859890	+	0.859890i
$383$	−30.5921	+	8.19714i	−1.56319	+	0.418854i	−0.933670	−	0.358134i	$-0.883413\pi$
$383$	−30.5921	+	8.19714i	−1.56319	+	0.418854i	−0.629515	+	0.776988i	$0.716746\pi$
$384$		0			0
$385$	−1.50811	−	1.50811i	−0.0768605	−	0.0768605i
$386$	21.4343	+	12.3751i	1.09098	+	0.629877i
$387$		0			0
$388$	3.30059	−	12.3180i	0.167562	−	0.625350i
$389$	4.71902			0.239264			0.119632	−	0.992818i	$-0.461829\pi$
$389$	4.71902			0.239264			0.119632	+	0.992818i	$0.461829\pi$
$390$		0			0
$391$	3.27997			0.165875
$392$	−1.21041	+	4.51732i	−0.0611350	+	0.228159i
$393$		0			0
$394$	2.87672	+	1.66088i	0.144927	+	0.0836737i
$395$	−5.47409	−	5.47409i	−0.275431	−	0.275431i
$396$		0			0
$397$	−3.37761	+	0.905027i	−0.169517	+	0.0454220i	−0.342579	−	0.939489i	$-0.611301\pi$
$397$	−3.37761	+	0.905027i	−0.169517	+	0.0454220i	0.173062	+	0.984911i	$0.444634\pi$
$398$	−5.48681	+	5.48681i	−0.275029	+	0.275029i
$399$		0			0
$400$	−0.866025	+	0.500000i	−0.0433013	+	0.0250000i
$401$	−4.05072	−	1.08539i	−0.202283	−	0.0542016i	0.156255	−	0.987717i	$-0.450058\pi$
$401$	−4.05072	−	1.08539i	−0.202283	−	0.0542016i	−0.358538	+	0.933515i	$0.616725\pi$
$402$		0			0
$403$	27.1474	−	10.6805i	1.35231	−	0.532035i
$404$		−	7.93630i		−	0.394846i
$405$		0			0
$406$	5.37740	+	9.31392i	0.266876	+	0.462242i
$407$	−2.55130	+	4.41898i	−0.126463	+	0.219041i
$408$		0			0
$409$	4.06359	+	15.1655i	0.200932	+	0.749887i	0.990651	+	0.136419i	$0.0435593\pi$
$409$	4.06359	+	15.1655i	0.200932	+	0.749887i	−0.789720	+	0.613468i	$0.789774\pi$
$410$	1.69652	+	6.33150i	0.0837852	+	0.312691i
$411$		0			0
$412$	−6.10439	+	10.5731i	−0.300742	+	0.520900i
$413$	−3.69925	−	6.40728i	−0.182028	−	0.315282i
$414$		0			0
$415$		−	9.10971i		−	0.447178i
$416$	3.56572	+	0.534425i	0.174824	+	0.0262023i
$417$		0			0
$418$	−10.5928	−	2.83834i	−0.518111	−	0.138828i
$419$	8.98610	−	5.18812i	0.439000	−	0.253456i	−0.264174	−	0.964475i	$-0.585099\pi$
$419$	8.98610	−	5.18812i	0.439000	−	0.253456i	0.703173	+	0.711019i	$0.251766\pi$
$420$		0			0
$421$	8.69941	−	8.69941i	0.423983	−	0.423983i	−0.462589	−	0.886573i	$-0.653080\pi$
$421$	8.69941	−	8.69941i	0.423983	−	0.423983i	0.886573	+	0.462589i	$0.153080\pi$
$422$	−16.3386	+	4.37791i	−0.795350	+	0.213113i
$423$		0			0
$424$	3.32144	+	3.32144i	0.161303	+	0.161303i
$425$	−0.747382	−	0.431501i	−0.0362533	−	0.0209309i
$426$		0			0
$427$	4.82165	−	17.9946i	0.233336	−	0.870822i
$428$	−6.95836			−0.336345
$429$		0			0
$430$	2.27743			0.109827
$431$	3.55832	−	13.2798i	0.171398	−	0.639666i	−0.825739	−	0.564052i	$-0.809242\pi$
$431$	3.55832	−	13.2798i	0.171398	−	0.639666i	0.997137	−	0.0756139i	$-0.0240917\pi$
$432$		0			0
$433$	7.51405	+	4.33824i	0.361102	+	0.208482i	0.669564	−	0.742754i	$-0.266481\pi$
$433$	7.51405	+	4.33824i	0.361102	+	0.208482i	−0.308462	+	0.951237i	$0.599814\pi$
$434$	8.72061	+	8.72061i	0.418603	+	0.418603i
$435$		0			0
$436$	5.65640	−	1.51563i	0.270892	−	0.0725854i
$437$	21.0628	−	21.0628i	1.00757	−	1.00757i
$438$		0			0
$439$	6.49527	−	3.75004i	0.310002	−	0.178980i	−0.336925	−	0.941531i	$-0.609387\pi$
$439$	6.49527	−	3.75004i	0.310002	−	0.178980i	0.646927	+	0.762552i	$0.276054\pi$
$440$	1.35157	+	0.362151i	0.0644333	+	0.0172649i
$441$		0			0
$442$	1.13919	+	2.89556i	0.0541860	+	0.137728i
$443$			8.57341i			0.407335i	0.979040	+	0.203668i	$0.0652862\pi$
$443$			8.57341i			0.407335i	−0.979040	+	0.203668i	$0.934714\pi$
$444$		0			0
$445$	−4.89587	−	8.47990i	−0.232087	−	0.401986i
$446$	4.05563	−	7.02455i	0.192039	−	0.332622i
$447$		0			0
$448$	0.394504	+	1.47231i	0.0186386	+	0.0695601i
$449$	−0.689391	−	2.57284i	−0.0325344	−	0.121420i	0.947749	−	0.319017i	$-0.103353\pi$
$449$	−0.689391	−	2.57284i	−0.0325344	−	0.121420i	−0.980283	+	0.197597i	$0.936686\pi$
$450$		0			0
$451$	4.58592	−	7.94304i	0.215942	−	0.374023i
$452$	−6.87955	−	11.9157i	−0.323587	−	0.560469i
$453$		0			0
$454$			6.71162i			0.314992i
$455$	3.26715	+	4.41916i	0.153166	+	0.207174i
$456$		0			0
$457$	−35.0828	−	9.40040i	−1.64110	−	0.439732i	−0.684000	−	0.729482i	$-0.739761\pi$
$457$	−35.0828	−	9.40040i	−1.64110	−	0.439732i	−0.957102	+	0.289750i	$0.906428\pi$
$458$	9.70228	−	5.60161i	0.453358	−	0.261746i
$459$		0			0
$460$	−2.68746	+	2.68746i	−0.125304	+	0.125304i
$461$	−31.0267	+	8.31357i	−1.44506	+	0.387202i	−0.894301	−	0.447465i	$-0.852327\pi$
$461$	−31.0267	+	8.31357i	−1.44506	+	0.387202i	−0.550755	+	0.834667i	$0.685660\pi$
$462$		0			0
$463$	−6.22741	−	6.22741i	−0.289412	−	0.289412i	0.547436	−	0.836848i	$-0.315604\pi$
$463$	−6.22741	−	6.22741i	−0.289412	−	0.289412i	−0.836848	+	0.547436i	$0.815604\pi$
$464$	−6.11051	−	3.52790i	−0.283673	−	0.163779i
$465$		0			0
$466$	−2.45379	+	9.15767i	−0.113670	+	0.424221i
$467$	−39.9714			−1.84966			−0.924829	−	0.380384i	$-0.875792\pi$
$467$	−39.9714			−1.84966			−0.924829	+	0.380384i	$0.875792\pi$
$468$		0			0
$469$	−6.58961			−0.304280
$470$	−2.33428	+	8.71164i	−0.107672	+	0.401838i
$471$		0			0
$472$	4.20357	+	2.42693i	0.193485	+	0.111709i
$473$	−2.25332	−	2.25332i	−0.103608	−	0.103608i
$474$		0			0
$475$	−7.57039	+	2.02848i	−0.347353	+	0.0930730i
$476$	−0.930149	+	0.930149i	−0.0426333	+	0.0426333i
$477$		0			0
$478$	−3.81086	+	2.20020i	−0.174305	+	0.100635i
$479$	−8.95885	−	2.40052i	−0.409340	−	0.109682i	0.0482719	−	0.998834i	$-0.484629\pi$
$479$	−8.95885	−	2.40052i	−0.409340	−	0.109682i	−0.457612	+	0.889152i	$0.651295\pi$
$480$		0			0
$481$	8.18931	−	10.2865i	0.373400	−	0.469026i
$482$			12.7727i			0.581779i
$483$		0			0
$484$	4.52106	+	7.83070i	0.205503	+	0.355941i
$485$	−6.37625	+	11.0440i	−0.289531	+	0.501482i
$486$		0			0
$487$	−0.998378	−	3.72600i	−0.0452408	−	0.168841i	0.939609	−	0.342249i	$-0.111189\pi$
$487$	−0.998378	−	3.72600i	−0.0452408	−	0.168841i	−0.984850	+	0.173408i	$0.944522\pi$
$488$	3.16330	+	11.8056i	0.143196	+	0.534414i
$489$		0			0
$490$	2.33834	−	4.05012i	0.105635	−	0.182966i
$491$	−14.5477	−	25.1973i	−0.656527	−	1.13714i	−0.981509	−	0.191417i	$-0.938692\pi$
$491$	−14.5477	−	25.1973i	−0.656527	−	1.13714i	0.324982	−	0.945720i	$-0.394642\pi$
$492$		0			0
$493$		−	6.08918i		−	0.274243i
$494$	25.9098	+	11.2788i	1.16574	+	0.507457i
$495$		0			0
$496$	−7.81538	−	2.09413i	−0.350921	−	0.0940290i
$497$	13.6647	−	7.88932i	0.612946	−	0.353885i
$498$		0			0
$499$	21.9762	−	21.9762i	0.983790	−	0.983790i	−0.0160805	−	0.999871i	$-0.505119\pi$
$499$	21.9762	−	21.9762i	0.983790	−	0.983790i	0.999871	+	0.0160805i	$0.00511881\pi$
$500$	0.965926	−	0.258819i	0.0431975	−	0.0115747i
$501$		0			0
$502$	−1.06964	−	1.06964i	−0.0477405	−	0.0477405i
$503$	−37.3168	−	21.5449i	−1.66387	−	0.960639i	−0.970838	−	0.239736i	$-0.922939\pi$
$503$	−37.3168	−	21.5449i	−1.66387	−	0.960639i	−0.693037	−	0.720902i	$-0.743728\pi$
$504$		0			0
$505$	−2.05407	+	7.66588i	−0.0914047	+	0.341127i
$506$	5.31803			0.236415
$507$		0			0
$508$	0.497897			0.0220906
$509$	8.52002	−	31.7971i	0.377643	−	1.40938i	−0.471801	−	0.881705i	$-0.656396\pi$
$509$	8.52002	−	31.7971i	0.377643	−	1.40938i	0.849444	−	0.527679i	$-0.176937\pi$
$510$		0			0
$511$	7.98516	+	4.61023i	0.353243	+	0.203945i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−9.88024	+	2.64740i	−0.435799	+	0.116772i
$515$	8.63291	−	8.63291i	0.380412	−	0.380412i
$516$		0			0
$517$	10.9290	−	6.30986i	0.480657	−	0.277507i
$518$	5.36905	+	1.43863i	0.235902	+	0.0632098i
$519$		0			0
$520$	−3.30591	−	1.43909i	−0.144974	−	0.0631084i
$521$			25.0972i			1.09953i	0.835320	+	0.549764i	$0.185282\pi$
$521$			25.0972i			1.09953i	−0.835320	+	0.549764i	$0.814718\pi$
$522$		0			0
$523$	7.34971	+	12.7301i	0.321380	+	0.556647i	0.980773	−	0.195152i	$-0.0625199\pi$
$523$	7.34971	+	12.7301i	0.321380	+	0.556647i	−0.659393	+	0.751799i	$0.729187\pi$
$524$	−7.87731	+	13.6439i	−0.344122	+	0.596036i
$525$		0			0
$526$	−2.39903	−	8.95331i	−0.104603	−	0.390383i
$527$	−1.80724	−	6.74469i	−0.0787244	−	0.293803i
$528$		0			0
$529$	4.27754	−	7.40892i	0.185980	−	0.322127i
$530$	−2.34861	−	4.06791i	−0.102017	−	0.176699i
$531$		0			0
$532$			11.9462i			0.517933i
$533$	−14.7202	+	18.4899i	−0.637601	+	0.800887i
$534$		0			0
$535$	6.72126	+	1.80096i	0.290585	+	0.0778621i
$536$	3.74399	−	2.16160i	0.161716	−	0.0933667i
$537$		0			0
$538$	−16.0933	+	16.0933i	−0.693831	+	0.693831i
$539$	−6.32082	+	1.69366i	−0.272257	+	0.0729511i
$540$		0			0
$541$	−2.02274	−	2.02274i	−0.0869644	−	0.0869644i	0.662286	−	0.749251i	$-0.269586\pi$
$541$	−2.02274	−	2.02274i	−0.0869644	−	0.0869644i	−0.749251	+	0.662286i	$0.769586\pi$
$542$	4.43483	+	2.56045i	0.190492	+	0.109981i
$543$		0			0
$544$	0.223361	−	0.833596i	0.00957654	−	0.0357401i
$545$	−5.85594			−0.250841
$546$		0			0
$547$	16.4927			0.705178			0.352589	−	0.935778i	$-0.385301\pi$
$547$	16.4927			0.705178			0.352589	+	0.935778i	$0.385301\pi$
$548$	2.39109	−	8.92367i	0.102142	−	0.381200i
$549$		0			0
$550$	−1.21178	−	0.699622i	−0.0516705	−	0.0298320i
$551$	−39.1026	−	39.1026i	−1.66583	−	1.66583i
$552$		0			0
$553$	11.3979	−	3.05407i	0.484689	−	0.129872i
$554$	−1.50215	+	1.50215i	−0.0638201	+	0.0638201i
$555$		0			0
$556$	−15.0718	+	8.70168i	−0.639185	+	0.369033i
$557$	11.6760	+	3.12859i	0.494730	+	0.132562i	0.497553	−	0.867434i	$-0.334232\pi$
$557$	11.6760	+	3.12859i	0.494730	+	0.132562i	−0.00282317	+	0.999996i	$0.500899\pi$
$558$		0			0
$559$	4.88156	+	6.60282i	0.206468	+	0.279269i
$560$		−	1.52425i		−	0.0644112i
$561$		0			0
$562$	5.09750	+	8.82913i	0.215025	+	0.372434i
$563$	−1.15276	+	1.99663i	−0.0485829	+	0.0841480i	−0.889294	−	0.457336i	$-0.848804\pi$
$563$	−1.15276	+	1.99663i	−0.0485829	+	0.0841480i	0.840711	+	0.541484i	$0.182137\pi$
$564$		0			0
$565$	3.56112	+	13.2903i	0.149817	+	0.559126i
$566$	−3.60064	−	13.4378i	−0.151346	−	0.564831i
$567$		0			0
$568$	−5.17588	+	8.96489i	−0.217175	+	0.376158i
$569$	−16.3433	−	28.3075i	−0.685149	−	1.18671i	−0.973390	−	0.229155i	$-0.926404\pi$
$569$	−16.3433	−	28.3075i	−0.685149	−	1.18671i	0.288241	−	0.957558i	$-0.406930\pi$
$570$		0			0
$571$			15.0864i			0.631344i	0.948868	+	0.315672i	$0.102230\pi$
$571$			15.0864i			0.631344i	−0.948868	+	0.315672i	$0.897770\pi$
$572$	1.84705	+	4.69477i	0.0772291	+	0.196298i
$573$		0			0
$574$	−9.65078	−	2.58592i	−0.402816	−	0.107934i
$575$	3.29146	−	1.90032i	0.137263	−	0.0792490i
$576$		0			0
$577$	−10.7578	+	10.7578i	−0.447851	+	0.447851i	−0.894640	−	0.446788i	$-0.852568\pi$
$577$	−10.7578	+	10.7578i	−0.447851	+	0.447851i	0.446788	+	0.894640i	$0.352568\pi$
$578$	−15.7013	+	4.20716i	−0.653090	+	0.174995i
$579$		0			0
$580$	4.98921	+	4.98921i	0.207166	+	0.207166i
$581$	12.0252	+	6.94272i	0.498887	+	0.288033i
$582$		0			0
$583$	−1.70110	+	6.34860i	−0.0704525	+	0.262932i
$584$	−6.04920			−0.250317
$585$		0			0
$586$	2.43031			0.100395
$587$	9.06480	−	33.8303i	0.374144	−	1.39633i	−0.480447	−	0.877024i	$-0.659526\pi$
$587$	9.06480	−	33.8303i	0.374144	−	1.39633i	0.854591	−	0.519301i	$-0.173808\pi$
$588$		0			0
$589$	−54.9176	−	31.7067i	−2.26284	−	1.30645i
$590$	−3.43220	−	3.43220i	−0.141302	−	0.141302i
$591$		0			0
$592$	−3.52243	+	0.943831i	−0.144771	+	0.0387912i
$593$	−17.3353	+	17.3353i	−0.711875	+	0.711875i	−0.966927	−	0.255052i	$-0.917907\pi$
$593$	−17.3353	+	17.3353i	−0.711875	+	0.711875i	0.255052	+	0.966927i	$0.417907\pi$
$594$		0			0
$595$	1.13919	−	0.657714i	0.0467024	−	0.0269637i
$596$	−10.4871	−	2.81000i	−0.429567	−	0.115102i
$597$		0			0
$598$	−13.5521	−	2.03116i	−0.554185	−	0.0830603i
$599$		−	25.7906i		−	1.05377i	−0.849935	−	0.526887i	$-0.823359\pi$
$599$		−	25.7906i		−	1.05377i	0.849935	−	0.526887i	$-0.176641\pi$
$600$		0			0
$601$	14.9846	+	25.9541i	0.611236	+	1.05869i	0.991032	+	0.133622i	$0.0426607\pi$
$601$	14.9846	+	25.9541i	0.611236	+	1.05869i	−0.379796	+	0.925070i	$0.624006\pi$
$602$	−1.73568	+	3.00629i	−0.0707411	+	0.122527i
$603$		0			0
$604$	−2.69440	−	10.0556i	−0.109634	−	0.409158i
$605$	−2.34027	−	8.73402i	−0.0951456	−	0.355088i
$606$		0			0
$607$	14.3192	−	24.8016i	0.581200	−	1.00667i	−0.414138	−	0.910214i	$-0.635917\pi$
$607$	14.3192	−	24.8016i	0.581200	−	1.00667i	0.995337	−	0.0964535i	$-0.0307499\pi$
$608$	−3.91872	−	6.78742i	−0.158925	−	0.275266i
$609$		0			0
$610$		−	12.2220i		−	0.494856i
$611$	−30.2606	+	11.9054i	−1.22421	+	0.481639i
$612$		0			0
$613$	9.67014	+	2.59110i	0.390573	+	0.104654i	0.448761	−	0.893652i	$-0.351866\pi$
$613$	9.67014	+	2.59110i	0.390573	+	0.104654i	−0.0581877	+	0.998306i	$0.518532\pi$
$614$	−21.8141	+	12.5944i	−0.880344	+	0.508267i
$615$		0			0
$616$	−1.50811	+	1.50811i	−0.0607636	+	0.0607636i
$617$	−44.4206	+	11.9025i	−1.78831	+	0.479175i	−0.992057	−	0.125792i	$-0.959853\pi$
$617$	−44.4206	+	11.9025i	−1.78831	+	0.479175i	−0.796250	+	0.604967i	$0.793186\pi$
$618$		0			0
$619$	4.18163	+	4.18163i	0.168074	+	0.168074i	0.786132	−	0.618058i	$-0.212080\pi$
$619$	4.18163	+	4.18163i	0.168074	+	0.168074i	−0.618058	+	0.786132i	$0.712080\pi$
$620$	7.00708	+	4.04554i	0.281411	+	0.162473i
$621$		0			0
$622$	−1.93225	+	7.21125i	−0.0774762	+	0.289145i
$623$	14.9250			0.597959
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	6.06528	−	22.6359i	0.242417	−	0.904713i
$627$		0			0
$628$	15.8917	+	9.17509i	0.634149	+	0.366126i
$629$	−2.22533	−	2.22533i	−0.0887298	−	0.0887298i
$630$		0			0
$631$	−26.5725	+	7.12008i	−1.05783	+	0.283446i	−0.745486	−	0.666522i	$-0.767782\pi$
$631$	−26.5725	+	7.12008i	−1.05783	+	0.283446i	−0.312349	+	0.949968i	$0.601116\pi$
$632$	−5.47409	+	5.47409i	−0.217748	+	0.217748i
$633$		0			0
$634$	−0.258041	+	0.148980i	−0.0102481	+	0.00591676i
$635$	−0.480931	−	0.128865i	−0.0190852	−	0.00511386i
$636$		0			0
$637$	16.7544	−	1.90183i	0.663833	−	0.0753532i
$638$		−	9.87279i		−	0.390867i
$639$		0			0
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−5.66029	+	9.80390i	−0.223568	+	0.387231i	−0.955889	−	0.293729i	$-0.905104\pi$
$641$	−5.66029	+	9.80390i	−0.223568	+	0.387231i	0.732321	+	0.680960i	$0.238437\pi$
$642$		0			0
$643$	0.703879	+	2.62691i	0.0277583	+	0.103595i	0.978415	−	0.206649i	$-0.0662558\pi$
$643$	0.703879	+	2.62691i	0.0277583	+	0.103595i	−0.950657	+	0.310244i	$0.899589\pi$
$644$	−1.49937	−	5.59573i	−0.0590835	−	0.220503i
$645$		0			0
$646$	3.38186	−	5.85756i	0.133058	−	0.230463i
$647$	10.9801	+	19.0181i	0.431673	+	0.747679i	0.997018	−	0.0771756i	$-0.0245902\pi$
$647$	10.9801	+	19.0181i	0.431673	+	0.747679i	−0.565345	+	0.824855i	$0.691257\pi$
$648$		0			0
$649$			6.79174i			0.266599i
$650$	2.82080	+	2.24569i	0.110641	+	0.0880831i
$651$		0			0
$652$	−6.30538	−	1.68952i	−0.246938	−	0.0661668i
$653$	−36.4401	+	21.0387i	−1.42601	+	0.823308i	−0.996803	−	0.0798969i	$-0.974541\pi$
$653$	−36.4401	+	21.0387i	−1.42601	+	0.823308i	−0.429209	+	0.903205i	$0.641208\pi$
$654$		0			0
$655$	11.1402	−	11.1402i	0.435283	−	0.435283i
$656$	6.33150	−	1.69652i	0.247204	−	0.0662380i
$657$		0			0
$658$	−9.72068	−	9.72068i	−0.378952	−	0.378952i
$659$	20.6684	+	11.9329i	0.805128	+	0.464841i	0.845261	−	0.534353i	$-0.179445\pi$
$659$	20.6684	+	11.9329i	0.805128	+	0.464841i	−0.0401329	+	0.999194i	$0.512778\pi$
$660$		0			0
$661$	−4.77664	+	17.8267i	−0.185790	+	0.693377i	0.808670	+	0.588262i	$0.200188\pi$
$661$	−4.77664	+	17.8267i	−0.185790	+	0.693377i	−0.994460	+	0.105115i	$0.966479\pi$
$662$	−24.5815			−0.955389
$663$		0			0
$664$	−9.10971			−0.353525
$665$	3.09190	−	11.5391i	0.119899	−	0.447469i
$666$		0			0
$667$	23.2239	+	13.4083i	0.899232	+	0.519172i
$668$	−11.1510	−	11.1510i	−0.431447	−	0.431447i
$669$		0			0
$670$	−4.17588	+	1.11892i	−0.161328	+	0.0432278i
$671$	−12.0927	+	12.0927i	−0.466832	+	0.466832i
$672$		0			0
$673$	−28.1091	+	16.2288i	−1.08353	+	0.625574i	−0.931845	−	0.362856i	$-0.881802\pi$
$673$	−28.1091	+	16.2288i	−1.08353	+	0.625574i	−0.151681	+	0.988430i	$0.548468\pi$
$674$	−1.27805	−	0.342453i	−0.0492288	−	0.0131908i
$675$		0			0
$676$	−2.91377	−	12.6693i	−0.112068	−	0.487279i
$677$		−	22.0711i		−	0.848262i	−0.905601	−	0.424131i	$-0.860580\pi$
$677$		−	22.0711i		−	0.848262i	0.905601	−	0.424131i	$-0.139420\pi$
$678$		0			0
$679$	−9.71898	−	16.8338i	−0.372980	−	0.646021i
$680$	−0.431501	+	0.747382i	−0.0165473	+	0.0286608i
$681$		0			0
$682$	−2.93019	−	10.9356i	−0.112203	−	0.418747i
$683$	−7.14894	−	26.6802i	−0.273547	−	1.02089i	−0.956809	−	0.290717i	$-0.906106\pi$
$683$	−7.14894	−	26.6802i	−0.273547	−	1.02089i	0.683262	−	0.730173i	$-0.260561\pi$
$684$		0			0
$685$	−4.61923	+	8.00074i	−0.176492	+	0.305693i
$686$	8.89907	+	15.4136i	0.339768	+	0.588495i
$687$		0			0
$688$		−	2.27743i		−	0.0868261i
$689$	6.75973	−	15.5286i	0.257525	−	0.591592i
$690$		0			0
$691$	22.7854	+	6.10532i	0.866796	+	0.232257i	0.664702	−	0.747109i	$-0.268559\pi$
$691$	22.7854	+	6.10532i	0.866796	+	0.232257i	0.202094	+	0.979366i	$0.435225\pi$
$692$	17.3231	−	10.0015i	0.658525	−	0.380200i
$693$		0			0
$694$	−10.9124	+	10.9124i	−0.414229	+	0.414229i
$695$	16.8104	−	4.50432i	0.637653	−	0.170859i
$696$		0			0
$697$	4.00000	+	4.00000i	0.151511	+	0.151511i
$698$	11.0258	+	6.36576i	0.417333	+	0.240947i
$699$		0			0
$700$	−0.394504	+	1.47231i	−0.0149109	+	0.0556481i
$701$	−15.5374			−0.586838			−0.293419	−	0.955984i	$-0.594793\pi$
$701$	−15.5374			−0.586838			−0.293419	+	0.955984i	$0.594793\pi$
$702$		0			0
$703$	−28.5807			−1.07794
$704$	0.362151	−	1.35157i	0.0136491	−	0.0509390i
$705$		0			0
$706$	13.9266	+	8.04054i	0.524135	+	0.302610i
$707$	−8.55379	−	8.55379i	−0.321698	−	0.321698i
$708$		0			0
$709$	−13.4708	+	3.60950i	−0.505908	+	0.135558i	−0.502741	−	0.864437i	$-0.667675\pi$
$709$	−13.4708	+	3.60950i	−0.505908	+	0.135558i	−0.00316760	+	0.999995i	$0.501008\pi$
$710$	7.31980	−	7.31980i	0.274707	−	0.274707i
$711$		0			0
$712$	−8.47990	+	4.89587i	−0.317798	+	0.183480i
$713$	29.7035	+	7.95903i	1.11241	+	0.298068i
$714$		0			0
$715$	−0.569020	−	5.01285i	−0.0212801	−	0.187470i
$716$			8.32827i			0.311242i
$717$		0			0
$718$	16.0095	+	27.7292i	0.597468	+	1.03485i
$719$	−21.2897	+	36.8748i	−0.793970	+	1.37520i	0.129520	+	0.991577i	$0.458656\pi$
$719$	−21.2897	+	36.8748i	−0.793970	+	1.37520i	−0.923491	+	0.383620i	$0.874677\pi$
$720$		0			0
$721$	4.81642	+	17.9751i	0.179373	+	0.669428i
$722$	−10.9805	−	40.9799i	−0.408653	−	1.52511i
$723$		0			0
$724$	12.1502	−	21.0449i	0.451560	−	0.782126i
$725$	−3.52790	−	6.11051i	−0.131023	−	0.226938i
$726$		0			0
$727$			29.5299i			1.09520i	0.836739	+	0.547602i	$0.184459\pi$
$727$			29.5299i			1.09520i	−0.836739	+	0.547602i	$0.815541\pi$
$728$	4.41916	−	3.26715i	0.163785	−	0.121089i
$729$		0			0
$730$	5.84307	+	1.56565i	0.216262	+	0.0579472i
$731$	1.70211	−	0.982712i	0.0629547	−	0.0363469i
$732$		0			0
$733$	−30.0045	+	30.0045i	−1.10824	+	1.10824i	−0.114861	+	0.993382i	$0.536642\pi$
$733$	−30.0045	+	30.0045i	−1.10824	+	1.10824i	−0.993382	+	0.114861i	$0.963358\pi$
$734$	−5.53714	+	1.48367i	−0.204380	+	0.0547634i
$735$		0			0
$736$	2.68746	+	2.68746i	0.0990612	+	0.0990612i
$737$	5.23876	+	3.02460i	0.192972	+	0.111412i
$738$		0			0
$739$	7.60296	−	28.3746i	0.279679	−	1.04378i	−0.672961	−	0.739678i	$-0.734978\pi$
$739$	7.60296	−	28.3746i	0.279679	−	1.04378i	0.952640	−	0.304099i	$-0.0983555\pi$
$740$	3.64668			0.134055
$741$		0			0
$742$	7.15973			0.262842
$743$	4.43565	−	16.5541i	0.162728	−	0.607310i	−0.835591	−	0.549352i	$-0.814874\pi$
$743$	4.43565	−	16.5541i	0.162728	−	0.607310i	0.998319	−	0.0579577i	$-0.0184589\pi$
$744$		0			0
$745$	9.40246	+	5.42851i	0.344479	+	0.198885i
$746$	13.2878	+	13.2878i	0.486500	+	0.486500i
$747$		0			0
$748$	1.16640	−	0.312537i	0.0426479	−	0.0114275i
$749$	−7.49976	+	7.49976i	−0.274035	+	0.274035i
$750$		0			0
$751$	0.0370080	−	0.0213666i	0.00135044	−	0.000779678i	−0.499325	−	0.866415i	$-0.666418\pi$
$751$	0.0370080	−	0.0213666i	0.00135044	−	0.000779678i	0.500675	+	0.865635i	$0.333085\pi$
$752$	8.71164	+	2.33428i	0.317681	+	0.0851223i
$753$		0			0
$754$	−3.77080	+	25.1591i	−0.137324	+	0.916239i
$755$			10.4104i			0.378872i
$756$		0			0
$757$	−18.0155	−	31.2038i	−0.654786	−	1.13412i	−0.981947	−	0.189154i	$-0.939426\pi$
$757$	−18.0155	−	31.2038i	−0.654786	−	1.13412i	0.327162	−	0.944968i	$-0.393908\pi$
$758$	−5.93305	+	10.2764i	−0.215498	+	0.373254i
$759$		0			0
$760$	2.02848	+	7.57039i	0.0735807	+	0.274607i
$761$	2.75831	+	10.2942i	0.0999887	+	0.373163i	0.997729	−	0.0673632i	$-0.0214586\pi$
$761$	2.75831	+	10.2942i	0.0999887	+	0.373163i	−0.897740	+	0.440526i	$0.854792\pi$
$762$		0			0
$763$	4.46295	−	7.73005i	0.161570	−	0.279847i
$764$	−11.8839	−	20.5835i	−0.429945	−	0.744686i
$765$		0			0
$766$		−	31.6713i		−	1.14433i
$767$	2.59403	−	17.3076i	0.0936649	−	0.624939i
$768$		0			0
$769$	−49.0270	−	13.1368i	−1.76796	−	0.473723i	−0.779654	−	0.626210i	$-0.784605\pi$
$769$	−49.0270	−	13.1368i	−1.76796	−	0.473723i	−0.988305	+	0.152487i	$0.951272\pi$
$770$	1.84705	−	1.06640i	0.0665632	−	0.0384303i
$771$		0			0
$772$	−17.5011	+	17.5011i	−0.629877	+	0.629877i
$773$	13.4423	−	3.60186i	0.483487	−	0.129550i	−0.00883893	−	0.999961i	$-0.502814\pi$
$773$	13.4423	−	3.60186i	0.483487	−	0.129550i	0.492326	+	0.870411i	$0.336147\pi$
$774$		0			0
$775$	−5.72126	−	5.72126i	−0.205514	−	0.205514i
$776$	11.0440	+	6.37625i	0.396456	+	0.228894i
$777$		0			0
$778$	−1.22137	+	4.55823i	−0.0437884	+	0.163420i
$779$	51.3733			1.84064
$780$		0			0
$781$	−14.4846			−0.518301
$782$	−0.848918	+	3.16820i	−0.0303572	+	0.113295i
$783$		0			0
$784$	−4.05012	−	2.33834i	−0.144647	−	0.0835120i
$785$	−12.9755	−	12.9755i	−0.463117	−	0.463117i
$786$		0			0
$787$	−46.5856	+	12.4826i	−1.66060	+	0.444956i	−0.962552	−	0.271097i	$-0.912613\pi$
$787$	−46.5856	+	12.4826i	−1.66060	+	0.444956i	−0.698046	+	0.716053i	$0.745947\pi$
$788$	−2.34883	+	2.34883i	−0.0836737	+	0.0836737i
$789$		0			0
$790$	6.70436	−	3.87076i	0.238530	−	0.137716i
$791$	−20.2577	−	5.42803i	−0.720280	−	0.192998i
$792$		0			0
$793$	35.4347	−	26.1974i	1.25832	−	0.930296i
$794$		−	3.49676i		−	0.124095i
$795$		0			0
$796$	−3.87976	−	6.71994i	−0.137514	−	0.238182i
$797$	−20.4594	+	35.4366i	−0.724708	+	1.25523i	0.234387	+	0.972143i	$0.424692\pi$
$797$	−20.4594	+	35.4366i	−0.724708	+	1.25523i	−0.959094	+	0.283087i	$0.908642\pi$
$798$		0			0
$799$	2.01449	+	7.51817i	0.0712674	+	0.265974i
$800$	−0.258819	−	0.965926i	−0.00915064	−	0.0341506i
$801$		0			0
$802$	2.09681	−	3.63178i	0.0740408	−	0.128242i
$803$	−4.23215	−	7.33030i	−0.149349	−	0.258680i
$804$		0			0
$805$			5.79313i			0.204181i
$806$	3.29034	+	28.9867i	0.115897	+	1.02101i
$807$		0			0
$808$	7.66588	+	2.05407i	0.269685	+	0.0722618i
$809$	−26.0180	+	15.0215i	−0.914745	+	0.528128i	−0.881955	−	0.471334i	$-0.843773\pi$
$809$	−26.0180	+	15.0215i	−0.914745	+	0.528128i	−0.0327903	+	0.999462i	$0.510439\pi$
$810$		0			0
$811$	−2.06570	+	2.06570i	−0.0725365	+	0.0725365i	−0.742444	−	0.669908i	$-0.766334\pi$
$811$	−2.06570	+	2.06570i	−0.0725365	+	0.0725365i	0.669908	+	0.742444i	$0.266334\pi$
$812$	−10.3883	+	2.78354i	−0.364559	+	0.0976833i
$813$		0			0
$814$	−3.60808	−	3.60808i	−0.126463	−	0.126463i
$815$	5.65325	+	3.26390i	0.198025	+	0.114330i
$816$		0			0
$817$	4.61971	−	17.2410i	0.161623	−	0.603186i
$818$	−15.7005			−0.548955
$819$		0			0
$820$	−6.55485			−0.228905
$821$	2.81246	−	10.4962i	0.0981556	−	0.366322i	−0.899323	−	0.437284i	$-0.855940\pi$
$821$	2.81246	−	10.4962i	0.0981556	−	0.366322i	0.997479	+	0.0709626i	$0.0226071\pi$
$822$		0			0
$823$	26.9741	+	15.5735i	0.940258	+	0.542858i	0.890041	−	0.455880i	$-0.150675\pi$
$823$	26.9741	+	15.5735i	0.940258	+	0.542858i	0.0502168	+	0.998738i	$0.484009\pi$
$824$	−8.63291	−	8.63291i	−0.300742	−	0.300742i
$825$		0			0
$826$	7.14640	−	1.91487i	0.248655	−	0.0666269i
$827$	10.4562	−	10.4562i	0.363596	−	0.363596i	−0.501539	−	0.865135i	$-0.667233\pi$
$827$	10.4562	−	10.4562i	0.363596	−	0.363596i	0.865135	+	0.501539i	$0.167233\pi$
$828$		0			0
$829$	9.25539	−	5.34360i	0.321453	−	0.185591i	−0.330587	−	0.943775i	$-0.607247\pi$
$829$	9.25539	−	5.34360i	0.321453	−	0.185591i	0.652040	+	0.758185i	$0.273913\pi$
$830$	8.79930	+	2.35777i	0.305428	+	0.0818393i
$831$		0			0
$832$	−1.43909	+	3.30591i	−0.0498915	+	0.114612i
$833$		−	4.03598i		−	0.139838i
$834$		0			0
$835$	7.88498	+	13.6572i	0.272871	+	0.472626i
$836$	5.48324	−	9.49725i	0.189642	−	0.328469i
$837$		0			0
$838$	2.68557	+	10.0227i	0.0927715	+	0.346228i
$839$	13.8616	+	51.7320i	0.478554	+	1.78599i	0.607481	+	0.794334i	$0.292180\pi$
$839$	13.8616	+	51.7320i	0.478554	+	1.78599i	−0.128926	+	0.991654i	$0.541153\pi$
$840$		0			0
$841$	10.3922	−	17.9998i	0.358351	−	0.620683i
$842$	6.15141	+	10.6546i	0.211992	+	0.367180i
$843$		0			0
$844$		−	16.9149i		−	0.582236i
$845$	−0.464553	+	12.9917i	−0.0159811	+	0.446928i
$846$		0			0
$847$	13.3128	+	3.56715i	0.457433	+	0.122569i
$848$	−4.06791	+	2.34861i	−0.139693	+	0.0806516i
$849$		0			0
$850$	0.610235	−	0.610235i	0.0209309	−	0.0209309i
$851$	13.3875	−	3.58717i	0.458917	−	0.122967i
$852$		0			0
$853$	39.1661	+	39.1661i	1.34102	+	1.34102i	0.895043	+	0.445979i	$0.147144\pi$
$853$	39.1661	+	39.1661i	1.34102	+	1.34102i	0.445979	+	0.895043i	$0.352856\pi$
$854$	16.1336	+	9.31471i	0.552079	+	0.318743i
$855$		0			0
$856$	1.80096	−	6.72126i	0.0615554	−	0.229728i
$857$	47.7248			1.63025			0.815124	−	0.579287i	$-0.196669\pi$
$857$	47.7248			1.63025			0.815124	+	0.579287i	$0.196669\pi$
$858$		0			0
$859$	40.2327			1.37272			0.686361	−	0.727261i	$-0.259207\pi$
$859$	40.2327			1.37272			0.686361	+	0.727261i	$0.259207\pi$
$860$	−0.589442	+	2.19983i	−0.0200998	+	0.0750134i
$861$		0			0
$862$	11.9064	+	6.87414i	0.405532	+	0.234134i
$863$	3.57930	+	3.57930i	0.121841	+	0.121841i	0.765398	−	0.643557i	$-0.222542\pi$
$863$	3.57930	+	3.57930i	0.121841	+	0.121841i	−0.643557	+	0.765398i	$0.722542\pi$
$864$		0			0
$865$	−19.3214	+	5.17715i	−0.656947	+	0.176028i
$866$	−6.13520	+	6.13520i	−0.208482	+	0.208482i
$867$		0			0
$868$	−10.6805	+	6.16640i	−0.362521	+	0.209301i
$869$	−10.4632	−	2.80360i	−0.354939	−	0.0951056i
$870$		0			0
$871$	−12.1948	−	9.70854i	−0.413206	−	0.328961i
$872$			5.85594i			0.198307i
$873$		0			0
$874$	14.8937	+	25.7966i	0.503786	+	0.872583i
$875$	0.762124	−	1.32004i	0.0257645	−	0.0446254i
$876$		0			0
$877$	−2.16946	−	8.09654i	−0.0732575	−	0.273401i	0.919575	−	0.392914i	$-0.128533\pi$
$877$	−2.16946	−	8.09654i	−0.0732575	−	0.273401i	−0.992833	+	0.119514i	$0.961866\pi$
$878$	1.94117	+	7.24453i	0.0655112	+	0.244491i
$879$		0			0
$880$	−0.699622	+	1.21178i	−0.0235842	+	0.0408491i
$881$	3.48542	+	6.03693i	0.117427	+	0.203389i	0.918747	−	0.394846i	$-0.129202\pi$
$881$	3.48542	+	6.03693i	0.117427	+	0.203389i	−0.801320	+	0.598235i	$0.795869\pi$
$882$		0			0
$883$			48.1939i			1.62185i	0.585148	+	0.810926i	$0.301036\pi$
$883$			48.1939i			1.62185i	−0.585148	+	0.810926i	$0.698964\pi$
$884$	−3.09174	+	0.350951i	−0.103987	+	0.0118038i
$885$		0			0
$886$	−8.28128	−	2.21896i	−0.278215	−	0.0745475i
$887$	10.3657	−	5.98462i	0.348045	−	0.200944i	−0.315779	−	0.948833i	$-0.602266\pi$
$887$	10.3657	−	5.98462i	0.348045	−	0.200944i	0.663824	+	0.747889i	$0.268932\pi$
$888$		0			0
$889$	0.536636	−	0.536636i	0.0179982	−	0.0179982i
$890$	9.45809	−	2.53429i	0.317036	−	0.0849496i
$891$		0			0
$892$	5.73552	+	5.73552i	0.192039	+	0.192039i
$893$	61.2155	+	35.3428i	2.04850	+	1.18270i
$894$		0			0
$895$	2.15552	−	8.04449i	0.0720509	−	0.268898i
$896$	−1.52425			−0.0509215
$897$		0			0
$898$	2.66360			0.0888855
$899$	14.7757	−	55.1438i	0.492799	−	1.83915i
$900$		0			0
$901$	−3.51062	−	2.02686i	−0.116956	−	0.0675244i
$902$	6.48547	+	6.48547i	0.215942	+	0.215942i
$903$		0			0
$904$	13.2903	−	3.56112i	0.442028	−	0.118441i
$905$	−17.1830	+	17.1830i	−0.571184	+	0.571184i
$906$		0			0
$907$	0.305802	−	0.176555i	0.0101540	−	0.00586242i	−0.494914	−	0.868942i	$-0.664801\pi$
$907$	0.305802	−	0.176555i	0.0101540	−	0.00586242i	0.505068	+	0.863079i	$0.331467\pi$
$908$	−6.48293	−	1.73710i	−0.215143	−	0.0576475i
$909$		0			0
$910$	−5.11419	+	2.01206i	−0.169534	+	0.0666992i
$911$			0.0349872i			0.00115918i	1.00000		0.000579589i	$0.000184489\pi$
$911$			0.0349872i			0.00115918i	−1.00000		0.000579589i	$0.999816\pi$
$912$		0			0
$913$	−6.37335	−	11.0390i	−0.210927	−	0.365336i
$914$	18.1602	−	31.4543i	0.600685	−	1.04042i
$915$		0			0
$916$	2.89961	+	10.8215i	0.0958058	+	0.357552i
$917$	6.21526	+	23.1957i	0.205246	+	0.765989i
$918$		0			0
$919$	16.6952	−	28.9169i	0.550724	−	0.953882i	−0.447499	−	0.894285i	$-0.647685\pi$
$919$	16.6952	−	28.9169i	0.550724	−	0.953882i	0.998223	−	0.0595972i	$-0.0189816\pi$
$920$	−1.90032	−	3.29146i	−0.0626518	−	0.108516i
$921$		0			0
$922$		−	32.1212i		−	1.05785i
$923$	36.9115	+	5.53224i	1.21496	+	0.182096i
$924$		0			0
$925$	−3.52243	−	0.943831i	−0.115817	−	0.0310330i
$926$	7.62699	−	4.40344i	0.250638	−	0.144706i
$927$		0			0
$928$	4.98921	−	4.98921i	0.163779	−	0.163779i
$929$	39.0790	−	10.4712i	1.28214	−	0.343549i	0.447471	−	0.894299i	$-0.352325\pi$
$929$	39.0790	−	10.4712i	1.28214	−	0.343549i	0.834670	+	0.550750i	$0.185658\pi$
$930$		0			0
$931$	−25.9177	−	25.9177i	−0.849417	−	0.849417i
$932$	−8.21054	−	4.74036i	−0.268945	−	0.155276i
$933$		0			0
$934$	10.3454	−	38.6094i	0.338511	−	1.26334i
$935$	−1.20755			−0.0394911
$936$		0			0
$937$	38.3649			1.25333			0.626664	−	0.779290i	$-0.284420\pi$
$937$	38.3649			1.25333			0.626664	+	0.779290i	$0.284420\pi$
$938$	1.70552	−	6.36508i	0.0556871	−	0.207827i
$939$		0			0
$940$	−7.81064	−	4.50948i	−0.254755	−	0.147083i
$941$	−15.8665	−	15.8665i	−0.517233	−	0.517233i	0.399500	−	0.916733i	$-0.369184\pi$
$941$	−15.8665	−	15.8665i	−0.517233	−	0.517233i	−0.916733	+	0.399500i	$0.869184\pi$
$942$		0			0
$943$	−24.0638	+	6.44788i	−0.783625	+	0.209972i
$944$	−3.43220	+	3.43220i	−0.111709	+	0.111709i
$945$		0			0
$946$	2.75974	−	1.59334i	0.0897269	−	0.0518039i
$947$	16.3183	+	4.37248i	0.530274	+	0.142087i	0.514015	−	0.857781i	$-0.328158\pi$
$947$	16.3183	+	4.37248i	0.530274	+	0.142087i	0.0162593	+	0.999868i	$0.494824\pi$
$948$		0			0
$949$	7.98516	+	20.2964i	0.259209	+	0.658848i
$950$		−	7.83744i		−	0.254280i
$951$		0			0
$952$	−0.657714	−	1.13919i	−0.0213166	−	0.0369215i
$953$	6.73104	−	11.6585i	0.218040	−	0.377656i	−0.736169	−	0.676798i	$-0.763367\pi$
$953$	6.73104	−	11.6585i	0.218040	−	0.377656i	0.954209	+	0.299142i	$0.0967004\pi$
$954$		0			0
$955$	6.15156	+	22.9580i	0.199060	+	0.742902i
$956$	−1.13891	−	4.25046i	−0.0368349	−	0.137470i
$957$		0			0
$958$	4.63744	−	8.03229i	0.149829	−	0.259511i
$959$	−7.04085	−	12.1951i	−0.227361	−	0.393801i
$960$		0			0
$961$		−	34.4656i		−	1.11179i
$962$	7.81649	+	10.5726i	0.252014	+	0.340875i
$963$		0			0
$964$	−12.3375	−	3.30581i	−0.397363	−	0.106473i
$965$	21.4343	−	12.3751i	0.689995	−	0.398369i
$966$		0			0
$967$	−23.1158	+	23.1158i	−0.743354	+	0.743354i	−0.973222	−	0.229868i	$-0.926171\pi$
$967$	−23.1158	+	23.1158i	−0.743354	+	0.743354i	0.229868	+	0.973222i	$0.426171\pi$
$968$	−8.73402	+	2.34027i	−0.280722	+	0.0752192i
$969$		0			0
$970$	−9.01738	−	9.01738i	−0.289531	−	0.289531i
$971$	−31.4889	−	18.1801i	−1.01053	−	0.583428i	−0.0991808	−	0.995069i	$-0.531622\pi$
$971$	−31.4889	−	18.1801i	−1.01053	−	0.583428i	−0.911346	+	0.411642i	$0.864956\pi$
$972$		0			0
$973$	−6.86570	+	25.6231i	−0.220104	+	0.821440i
$974$	3.85744			0.123600
$975$		0			0
$976$	−12.2220			−0.391218
$977$	−11.2196	+	41.8720i	−0.358945	+	1.33960i	0.516501	+	0.856287i	$0.327234\pi$
$977$	−11.2196	+	41.8720i	−0.358945	+	1.33960i	−0.875446	+	0.483316i	$0.839432\pi$
$978$		0			0
$979$	−11.8654	−	6.85051i	−0.379221	−	0.218943i
$980$	3.30691	+	3.30691i	0.105635	+	0.105635i
$981$		0			0
$982$	28.1039	−	7.53042i	0.896832	−	0.240305i
$983$	26.2139	−	26.2139i	0.836093	−	0.836093i	−0.152249	−	0.988342i	$-0.548652\pi$
$983$	26.2139	−	26.2139i	0.836093	−	0.836093i	0.988342	+	0.152249i	$0.0486515\pi$
$984$		0			0
$985$	2.87672	−	1.66088i	0.0916600	−	0.0529199i
$986$	5.88169	+	1.57599i	0.187311	+	0.0501899i
$987$		0			0
$988$	−17.6004	+	22.1078i	−0.559945	+	0.703343i
$989$			8.65570i			0.275235i
$990$		0			0
$991$	−15.8129	−	27.3888i	−0.502314	−	0.870033i	−0.999996	−	0.00267380i	$-0.999149\pi$
$991$	−15.8129	−	27.3888i	−0.502314	−	0.870033i	0.497683	−	0.867359i	$-0.334184\pi$
$992$	4.04554	−	7.00708i	0.128446	−	0.222475i
$993$		0			0
$994$	4.08381	+	15.2410i	0.129531	+	0.483415i
$995$	2.00831	+	7.49512i	0.0636678	+	0.237611i
$996$		0			0
$997$	−6.39203	+	11.0713i	−0.202438	+	0.350633i	−0.949313	−	0.314331i	$-0.898220\pi$
$997$	−6.39203	+	11.0713i	−0.202438	+	0.350633i	0.746876	+	0.664964i	$0.231553\pi$
$998$	15.5395	+	26.9152i	0.491895	+	0.851987i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.cu.e.431.1	✓	16
3.2	odd	2	inner	1170.2.cu.e.431.3	yes	16
13.7	odd	12	inner	1170.2.cu.e.1151.3	yes	16
39.20	even	12	inner	1170.2.cu.e.1151.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.cu.e.431.1	✓	16	1.1	even	1	trivial
1170.2.cu.e.431.3	yes	16	3.2	odd	2	inner
1170.2.cu.e.1151.1	yes	16	39.20	even	12	inner
1170.2.cu.e.1151.3	yes	16	13.7	odd	12	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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.cu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.47231 + 0.394504i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.707107 + 0.707107i) q^{5} +(-1.47231 + 0.394504i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{10} +(1.35157 + 0.362151i) q^{11} +(-3.30591 - 1.43909i) q^{13} -1.52425i q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.431501 + 0.747382i) q^{17} +(2.02848 + 7.57039i) q^{19} +(-0.258819 - 0.965926i) q^{20} +(-0.699622 + 1.21178i) q^{22} +(-1.90032 - 3.29146i) q^{23} +1.00000i q^{25} +(2.24569 - 2.82080i) q^{26} +(1.47231 + 0.394504i) q^{28} +(-6.11051 + 3.52790i) q^{29} +(-5.72126 + 5.72126i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.610235 - 0.610235i) q^{34} +(-1.32004 - 0.762124i) q^{35} +(-0.943831 + 3.52243i) q^{37} -7.83744 q^{38} +1.00000 q^{40} +(1.69652 - 6.33150i) q^{41} +(-1.97231 - 1.13871i) q^{43} +(-0.989414 - 0.989414i) q^{44} +(3.67114 - 0.983680i) q^{46} +(6.37736 - 6.37736i) q^{47} +(-4.05012 + 2.33834i) q^{49} +(-0.965926 - 0.258819i) q^{50} +(2.14345 + 2.89924i) q^{52} +4.69722i q^{53} +(0.699622 + 1.21178i) q^{55} +(-0.762124 + 1.32004i) q^{56} +(-1.82618 - 6.81538i) q^{58} +(1.25627 + 4.68848i) q^{59} +(-6.11102 + 10.5846i) q^{61} +(-4.04554 - 7.00708i) q^{62} -1.00000i q^{64} +(-1.32004 - 3.35522i) q^{65} +(4.17588 + 1.11892i) q^{67} +(0.747382 - 0.431501i) q^{68} +(1.07781 - 1.07781i) q^{70} +(-9.99904 + 2.67923i) q^{71} +(-4.27743 - 4.27743i) q^{73} +(-3.15812 - 1.82334i) q^{74} +(2.02848 - 7.57039i) q^{76} -2.13279 q^{77} -7.74153 q^{79} +(-0.258819 + 0.965926i) q^{80} +(5.67667 + 3.27743i) q^{82} +(-6.44154 - 6.44154i) q^{83} +(-0.833596 + 0.223361i) q^{85} +(1.61038 - 1.61038i) q^{86} +(1.21178 - 0.699622i) q^{88} +(-9.45809 - 2.53429i) q^{89} +(5.43505 + 0.814595i) q^{91} +3.80065i q^{92} +(4.50948 + 7.81064i) q^{94} +(-3.91872 + 6.78742i) q^{95} +(3.30059 + 12.3180i) q^{97} +(-1.21041 - 4.51732i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} - 12 q^{13} + 8 q^{16} + 36 q^{19} + 12 q^{22} - 8 q^{28} - 12 q^{31} + 16 q^{34} + 20 q^{37} + 16 q^{40} + 32 q^{46} - 12 q^{49} - 24 q^{52} - 12 q^{55} + 32 q^{58} - 44 q^{61} + 4 q^{67} - 4 q^{70} - 24 q^{73} + 36 q^{76} - 24 q^{79} - 4 q^{85} + 12 q^{88} + 36 q^{91} + 56 q^{97}+O(q^{100}) \) 16 * q + 8 * q^7 - 12 * q^13 + 8 * q^16 + 36 * q^19 + 12 * q^22 - 8 * q^28 - 12 * q^31 + 16 * q^34 + 20 * q^37 + 16 * q^40 + 32 * q^46 - 12 * q^49 - 24 * q^52 - 12 * q^55 + 32 * q^58 - 44 * q^61 + 4 * q^67 - 4 * q^70 - 24 * q^73 + 36 * q^76 - 24 * q^79 - 4 * q^85 + 12 * q^88 + 36 * q^91 + 56 * q^97

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