LMFDB - Embedded newform 192.2.r.a.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.10
Character	$\chi$	$=$	192.37
Dual form			192.2.r.a.109.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.479743 - 1.33036i) q^{2} +(0.555570 - 0.831470i) q^{3} +(-1.53969 - 1.27646i) q^{4} +(0.248853 - 1.25107i) q^{5} +(-0.839620 - 1.13800i) q^{6} +(0.0439483 - 0.106101i) q^{7} +(-2.43680 + 1.43597i) q^{8} +(-0.382683 - 0.923880i) q^{9} +O(q^{10})$	\(q+(0.479743 - 1.33036i) q^{2} +(0.555570 - 0.831470i) q^{3} +(-1.53969 - 1.27646i) q^{4} +(0.248853 - 1.25107i) q^{5} +(-0.839620 - 1.13800i) q^{6} +(0.0439483 - 0.106101i) q^{7} +(-2.43680 + 1.43597i) q^{8} +(-0.382683 - 0.923880i) q^{9} +(-1.54498 - 0.931254i) q^{10} +(0.502576 - 0.335811i) q^{11} +(-1.91674 + 0.571048i) q^{12} +(0.581842 + 2.92512i) q^{13} +(-0.120068 - 0.109368i) q^{14} +(-0.901970 - 0.901970i) q^{15} +(0.741316 + 3.93071i) q^{16} +(4.49661 - 4.49661i) q^{17} +(-1.41268 + 0.0658809i) q^{18} +(-3.56740 + 0.709600i) q^{19} +(-1.98009 + 1.60861i) q^{20} +(-0.0638030 - 0.0954880i) q^{21} +(-0.205641 - 0.829708i) q^{22} +(0.433747 - 0.179664i) q^{23} +(-0.159847 + 2.82391i) q^{24} +(3.11615 + 1.29075i) q^{25} +(4.17058 + 0.629246i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(-0.203100 + 0.107264i) q^{28} +(4.44520 + 2.97019i) q^{29} +(-1.63265 + 0.767228i) q^{30} +3.80597i q^{31} +(5.58488 + 0.899513i) q^{32} -0.604443i q^{33} +(-3.82488 - 8.13931i) q^{34} +(-0.121802 - 0.0813857i) q^{35} +(-0.590077 + 1.91097i) q^{36} +(-5.55225 - 1.10441i) q^{37} +(-0.767413 + 5.08634i) q^{38} +(2.75540 + 1.14132i) q^{39} +(1.19009 + 3.40595i) q^{40} +(7.52493 - 3.11693i) q^{41} +(-0.157642 + 0.0390711i) q^{42} +(-1.41382 - 2.11593i) q^{43} +(-1.20246 - 0.124471i) q^{44} +(-1.25107 + 0.248853i) q^{45} +(-0.0309301 - 0.663231i) q^{46} +(-5.15240 + 5.15240i) q^{47} +(3.68012 + 1.56740i) q^{48} +(4.94042 + 4.94042i) q^{49} +(3.21211 - 3.52636i) q^{50} +(-1.24061 - 6.23698i) q^{51} +(2.83793 - 5.24648i) q^{52} +(1.52923 - 1.02180i) q^{53} +(-0.730064 + 1.21120i) q^{54} +(-0.295055 - 0.712325i) q^{55} +(0.0452641 + 0.321654i) q^{56} +(-1.39193 + 3.36042i) q^{57} +(6.08396 - 4.48877i) q^{58} +(1.59905 - 8.03898i) q^{59} +(0.237432 + 2.54008i) q^{60} +(-5.13608 + 7.68668i) q^{61} +(5.06330 + 1.82589i) q^{62} -0.114842 q^{63} +(3.87598 - 6.99834i) q^{64} +3.80431 q^{65} +(-0.804125 - 0.289977i) q^{66} +(-2.61967 + 3.92062i) q^{67} +(-12.6631 + 1.18368i) q^{68} +(0.0915919 - 0.460464i) q^{69} +(-0.166706 + 0.122996i) q^{70} +(-4.48669 + 10.8318i) q^{71} +(2.25919 + 1.70179i) q^{72} +(2.49380 + 6.02057i) q^{73} +(-4.13291 + 6.85664i) q^{74} +(2.80446 - 1.87388i) q^{75} +(6.39848 + 3.46107i) q^{76} +(-0.0135423 - 0.0680819i) q^{77} +(2.84025 - 3.11812i) q^{78} +(-9.80938 - 9.80938i) q^{79} +(5.10206 + 0.0507306i) q^{80} +(-0.707107 + 0.707107i) q^{81} +(-0.536595 - 11.5062i) q^{82} +(-10.9223 + 2.17257i) q^{83} +(-0.0236491 + 0.228464i) q^{84} +(-4.50657 - 6.74456i) q^{85} +(-3.49320 + 0.865779i) q^{86} +(4.93924 - 2.04590i) q^{87} +(-0.742463 + 1.53999i) q^{88} +(-16.0029 - 6.62864i) q^{89} +(-0.269128 + 1.78375i) q^{90} +(0.335927 + 0.0668201i) q^{91} +(-0.897171 - 0.277032i) q^{92} +(3.16455 + 2.11448i) q^{93} +(4.38270 + 9.32636i) q^{94} +4.63965i q^{95} +(3.85071 - 4.14392i) q^{96} -10.7554i q^{97} +(8.94265 - 4.20239i) q^{98} +(-0.502576 - 0.335811i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{16}\right)$

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 $

$2$	0.479743	−	1.33036i	0.339229	−	0.940704i
$2$	0.479743	−	1.33036i	0.339229	−	0.940704i
$3$	0.555570	−	0.831470i	0.320759	−	0.480049i
$3$	0.555570	−	0.831470i	0.320759	−	0.480049i
$4$	−1.53969	−	1.27646i	−0.769847	−	0.638228i
$5$	0.248853	−	1.25107i	0.111290	−	0.559495i	−0.884398	−	0.466734i	$-0.845431\pi$
$5$	0.248853	−	1.25107i	0.111290	−	0.559495i	0.995688	−	0.0927612i	$-0.0295693\pi$
$6$	−0.839620	−	1.13800i	−0.342773	−	0.464586i
$7$	0.0439483	−	0.106101i	0.0166109	−	0.0401022i	−0.915356	−	0.402644i	$-0.868091\pi$
$7$	0.0439483	−	0.106101i	0.0166109	−	0.0401022i	0.931967	+	0.362542i	$0.118091\pi$
$8$	−2.43680	+	1.43597i	−0.861538	+	0.507692i
$9$	−0.382683	−	0.923880i	−0.127561	−	0.307960i
$10$	−1.54498	−	0.931254i	−0.488566	−	0.294488i
$11$	0.502576	−	0.335811i	0.151532	−	0.101251i	−0.477493	−	0.878636i	$-0.658454\pi$
$11$	0.502576	−	0.335811i	0.151532	−	0.101251i	0.629025	+	0.777385i	$0.283454\pi$
$12$	−1.91674	+	0.571048i	−0.553316	+	0.164847i
$13$	0.581842	+	2.92512i	0.161374	+	0.811281i	0.973657	+	0.228018i	$0.0732245\pi$
$13$	0.581842	+	2.92512i	0.161374	+	0.811281i	−0.812283	+	0.583264i	$0.801775\pi$
$14$	−0.120068	−	0.109368i	−0.0320894	−	0.0292298i
$15$	−0.901970	−	0.901970i	−0.232888	−	0.232888i
$16$	0.741316	+	3.93071i	0.185329	+	0.982677i
$17$	4.49661	−	4.49661i	1.09059	−	1.09059i	0.0951230	−	0.995466i	$-0.469676\pi$
$17$	4.49661	−	4.49661i	1.09059	−	1.09059i	0.995466	−	0.0951230i	$-0.0303245\pi$
$18$	−1.41268	+	0.0658809i	−0.332971	+	0.0155283i
$19$	−3.56740	+	0.709600i	−0.818418	+	0.162793i	−0.586508	−	0.809944i	$-0.699498\pi$
$19$	−3.56740	+	0.709600i	−0.818418	+	0.162793i	−0.231910	+	0.972737i	$0.574498\pi$
$20$	−1.98009	+	1.60861i	−0.442762	+	0.359697i
$21$	−0.0638030	−	0.0954880i	−0.0139230	−	0.0208372i
$22$	−0.205641	−	0.829708i	−0.0438427	−	0.176894i
$23$	0.433747	−	0.179664i	0.0904425	−	0.0374625i	−0.337003	−	0.941503i	$-0.609413\pi$
$23$	0.433747	−	0.179664i	0.0904425	−	0.0374625i	0.427446	+	0.904041i	$0.359413\pi$
$24$	−0.159847	+	2.82391i	−0.0326286	+	0.576428i
$25$	3.11615	+	1.29075i	0.623231	+	0.258151i
$26$	4.17058	+	0.629246i	0.817918	+	0.123405i
$27$	−0.980785	−	0.195090i	−0.188752	−	0.0375451i
$28$	−0.203100	+	0.107264i	−0.0383822	+	0.0202710i
$29$	4.44520	+	2.97019i	0.825453	+	0.551550i	0.895019	−	0.446027i	$-0.147162\pi$
$29$	4.44520	+	2.97019i	0.825453	+	0.551550i	−0.0695665	+	0.997577i	$0.522162\pi$
$30$	−1.63265	+	0.767228i	−0.298081	+	0.140076i
$31$			3.80597i			0.683572i	0.939778	+	0.341786i	$0.111032\pi$
$31$			3.80597i			0.683572i	−0.939778	+	0.341786i	$0.888968\pi$
$32$	5.58488	+	0.899513i	0.987277	+	0.159013i
$33$		−	0.604443i		−	0.105220i
$34$	−3.82488	−	8.13931i	−0.655961	−	1.39588i
$35$	−0.121802	−	0.0813857i	−0.0205884	−	0.0137567i
$36$	−0.590077	+	1.91097i	−0.0983461	+	0.318495i
$37$	−5.55225	−	1.10441i	−0.912784	−	0.181564i	−0.283711	−	0.958910i	$-0.591566\pi$
$37$	−5.55225	−	1.10441i	−0.912784	−	0.181564i	−0.629074	+	0.777346i	$0.716566\pi$
$38$	−0.767413	+	5.08634i	−0.124491	+	0.825113i
$39$	2.75540	+	1.14132i	0.441217	+	0.182758i
$40$	1.19009	+	3.40595i	0.188170	+	0.538528i
$41$	7.52493	−	3.11693i	1.17520	−	0.486782i	0.292289	−	0.956330i	$-0.405583\pi$
$41$	7.52493	−	3.11693i	1.17520	−	0.486782i	0.882907	+	0.469548i	$0.155583\pi$
$42$	−0.157642	+	0.0390711i	−0.0243247	+	0.00602880i
$43$	−1.41382	−	2.11593i	−0.215605	−	0.322676i	0.707864	−	0.706349i	$-0.249659\pi$
$43$	−1.41382	−	2.11593i	−0.215605	−	0.322676i	−0.923469	+	0.383673i	$0.874659\pi$
$44$	−1.20246	−	0.124471i	−0.181278	−	0.0187647i
$45$	−1.25107	+	0.248853i	−0.186498	+	0.0370968i
$46$	−0.0309301	−	0.663231i	−0.00456039	−	0.0977880i
$47$	−5.15240	+	5.15240i	−0.751555	+	0.751555i	−0.974769	−	0.223214i	$-0.928345\pi$
$47$	−5.15240	+	5.15240i	−0.751555	+	0.751555i	0.223214	+	0.974769i	$0.428345\pi$
$48$	3.68012	+	1.56740i	0.531179	+	0.226235i
$49$	4.94042	+	4.94042i	0.705775	+	0.705775i
$50$	3.21211	−	3.52636i	0.454261	−	0.498703i
$51$	−1.24061	−	6.23698i	−0.173720	−	0.873352i
$52$	2.83793	−	5.24648i	0.393550	−	0.727556i
$53$	1.52923	−	1.02180i	0.210056	−	0.140355i	−0.446092	−	0.894987i	$-0.647185\pi$
$53$	1.52923	−	1.02180i	0.210056	−	0.140355i	0.656148	+	0.754632i	$0.272185\pi$
$54$	−0.730064	+	1.21120i	−0.0993491	+	0.164824i
$55$	−0.295055	−	0.712325i	−0.0397852	−	0.0960499i
$56$	0.0452641	+	0.321654i	0.00604868	+	0.0429828i
$57$	−1.39193	+	3.36042i	−0.184366	+	0.445098i
$58$	6.08396	−	4.48877i	0.798863	−	0.589405i
$59$	1.59905	−	8.03898i	0.208179	−	1.04659i	−0.725431	−	0.688295i	$-0.758360\pi$
$59$	1.59905	−	8.03898i	0.208179	−	1.04659i	0.933610	−	0.358291i	$-0.116640\pi$
$60$	0.237432	+	2.54008i	0.0306524	+	0.327923i
$61$	−5.13608	+	7.68668i	−0.657607	+	0.984179i	0.341413	+	0.939913i	$0.389095\pi$
$61$	−5.13608	+	7.68668i	−0.657607	+	0.984179i	−0.999020	+	0.0442651i	$0.985905\pi$
$62$	5.06330	+	1.82589i	0.643039	+	0.231888i
$63$	−0.114842			−0.0144688
$64$	3.87598	−	6.99834i	0.484497	−	0.874793i
$65$	3.80431			0.471867
$66$	−0.804125	−	0.289977i	−0.0989809	−	0.0356937i
$67$	−2.61967	+	3.92062i	−0.320044	+	0.478980i	−0.956255	−	0.292536i	$-0.905501\pi$
$67$	−2.61967	+	3.92062i	−0.320044	+	0.478980i	0.636211	+	0.771516i	$0.280501\pi$
$68$	−12.6631	+	1.18368i	−1.53563	+	0.143542i
$69$	0.0915919	−	0.460464i	0.0110264	−	0.0554333i
$70$	−0.166706	+	0.122996i	−0.0199251	+	0.0147009i
$71$	−4.48669	+	10.8318i	−0.532472	+	1.28550i	0.397410	+	0.917641i	$0.369909\pi$
$71$	−4.48669	+	10.8318i	−0.532472	+	1.28550i	−0.929881	+	0.367859i	$0.880091\pi$
$72$	2.25919	+	1.70179i	0.266248	+	0.200557i
$73$	2.49380	+	6.02057i	0.291877	+	0.704654i	0.999999	−	0.00143628i	$-0.000457184\pi$
$73$	2.49380	+	6.02057i	0.291877	+	0.704654i	−0.708122	+	0.706090i	$0.750457\pi$
$74$	−4.13291	+	6.85664i	−0.480441	+	0.797068i
$75$	2.80446	−	1.87388i	0.323832	−	0.216377i
$76$	6.39848	+	3.46107i	0.733956	+	0.397011i
$77$	−0.0135423	−	0.0680819i	−0.00154329	−	0.00775865i
$78$	2.84025	−	3.11812i	0.321595	−	0.353058i
$79$	−9.80938	−	9.80938i	−1.10364	−	1.10364i	−0.993968	−	0.109673i	$-0.965020\pi$
$79$	−9.80938	−	9.80938i	−1.10364	−	1.10364i	−0.109673	−	0.993968i	$-0.534980\pi$
$80$	5.10206	+	0.0507306i	0.570428	+	0.00567186i
$81$	−0.707107	+	0.707107i	−0.0785674	+	0.0785674i
$82$	−0.536595	−	11.5062i	−0.0592570	−	1.27064i
$83$	−10.9223	+	2.17257i	−1.19887	+	0.238471i	−0.753849	−	0.657048i	$-0.771805\pi$
$83$	−10.9223	+	2.17257i	−1.19887	+	0.238471i	−0.445025	+	0.895518i	$0.646805\pi$
$84$	−0.0236491	+	0.228464i	−0.00258033	+	0.0249275i
$85$	−4.50657	−	6.74456i	−0.488807	−	0.731551i
$86$	−3.49320	+	0.865779i	−0.376682	+	0.0933594i
$87$	4.93924	−	2.04590i	0.529542	−	0.219344i
$88$	−0.742463	+	1.53999i	−0.0791468	+	0.164163i
$89$	−16.0029	−	6.62864i	−1.69631	−	0.702634i	−0.696421	−	0.717633i	$-0.745226\pi$
$89$	−16.0029	−	6.62864i	−1.69631	−	0.702634i	−0.999888	+	0.0149990i	$0.995226\pi$
$90$	−0.269128	+	1.78375i	−0.0283685	+	0.188024i
$91$	0.335927	+	0.0668201i	0.0352148	+	0.00700465i
$92$	−0.897171	−	0.277032i	−0.0935366	−	0.0288826i
$93$	3.16455	+	2.11448i	0.328148	+	0.219262i
$94$	4.38270	+	9.32636i	0.452041	+	0.961940i
$95$			4.63965i			0.476018i
$96$	3.85071	−	4.14392i	0.393011	−	0.422937i
$97$		−	10.7554i		−	1.09205i	−0.837769	−	0.546024i	$-0.816141\pi$
$97$		−	10.7554i		−	1.09205i	0.837769	−	0.546024i	$-0.183859\pi$
$98$	8.94265	−	4.20239i	0.903344	−	0.424505i
$99$	−0.502576	−	0.335811i	−0.0505108	−	0.0337503i
$100$	−3.15033	−	5.96500i	−0.315033	−	0.596500i
$101$	−9.18850	−	1.82771i	−0.914290	−	0.181864i	−0.284543	−	0.958663i	$-0.591842\pi$
$101$	−9.18850	−	1.82771i	−0.914290	−	0.181864i	−0.629748	+	0.776800i	$0.716842\pi$
$102$	−8.89258	−	1.34169i	−0.880496	−	0.132847i
$103$	16.0937	+	6.66622i	1.58576	+	0.656842i	0.989312	−	0.145812i	$-0.0465796\pi$
$103$	16.0937	+	6.66622i	1.58576	+	0.656842i	0.596444	+	0.802654i	$0.296580\pi$
$104$	−5.61821	−	6.29241i	−0.550911	−	0.617022i
$105$	−0.135340	+	0.0560595i	−0.0132078	+	0.00547084i
$106$	−0.625719	−	2.52462i	−0.0607752	−	0.245213i
$107$	−5.38973	−	8.06631i	−0.521045	−	0.779799i	0.473861	−	0.880599i	$-0.342860\pi$
$107$	−5.38973	−	8.06631i	−0.521045	−	0.779799i	−0.994907	+	0.100800i	$0.967860\pi$
$108$	1.26109	+	1.55231i	0.121348	+	0.149371i
$109$	−18.1143	+	3.60315i	−1.73503	+	0.345119i	−0.958529	−	0.284994i	$-0.908009\pi$
$109$	−18.1143	+	3.60315i	−1.73503	+	0.345119i	−0.776503	+	0.630113i	$0.783009\pi$
$110$	−1.08920	+	0.0507951i	−0.103851	+	0.00484313i
$111$	−4.00295	+	4.00295i	−0.379943	+	0.379943i
$112$	0.449630	+	0.0940937i	0.0424860	+	0.00889102i
$113$	5.41294	+	5.41294i	0.509206	+	0.509206i	0.914283	−	0.405077i	$-0.132755\pi$
$113$	5.41294	+	5.41294i	0.509206	+	0.509206i	−0.405077	+	0.914283i	$0.632755\pi$
$114$	3.80278	+	3.46390i	0.356163	+	0.324424i
$115$	−0.116833	−	0.587357i	−0.0108947	−	0.0547713i
$116$	−3.05293	−	10.2473i	−0.283458	−	0.951437i
$117$	2.47979	−	1.65695i	0.229257	−	0.153185i
$118$	−9.92757	−	5.98395i	−0.913907	−	0.550867i
$119$	−0.279475	−	0.674711i	−0.0256194	−	0.0618507i
$120$	3.49312	+	0.902717i	0.318877	+	0.0824064i
$121$	−4.06970	+	9.82513i	−0.369973	+	0.893194i
$122$	7.76203	+	10.5204i	0.702741	+	0.952476i
$123$	1.58900	−	7.98842i	0.143275	−	0.720292i
$124$	4.85816	−	5.86003i	0.436275	−	0.526246i
$125$	5.93365	−	8.88034i	0.530722	−	0.794281i
$126$	−0.0550948	+	0.152781i	−0.00490823	+	0.0136108i
$127$	10.4509			0.927370			0.463685	−	0.886000i	$-0.346527\pi$
$127$	10.4509			0.927370			0.463685	+	0.886000i	$0.346527\pi$
$128$	−7.45082	−	8.51383i	−0.658565	−	0.752523i
$129$	−2.54480			−0.224057
$130$	1.82509	−	5.06109i	0.160071	−	0.443887i
$131$	−4.34818	+	6.50752i	−0.379903	+	0.568564i	−0.971312	−	0.237807i	$-0.923572\pi$
$131$	−4.34818	+	6.50752i	−0.379903	+	0.568564i	0.591410	+	0.806371i	$0.298572\pi$
$132$	−0.771546	+	0.930658i	−0.0671545	+	0.0810034i
$133$	−0.0814922	+	0.409689i	−0.00706627	+	0.0355245i
$134$	3.95905	+	5.36599i	0.342010	+	0.463551i
$135$	−0.488143	+	1.17848i	−0.0420126	+	0.101427i
$136$	−4.50034	+	17.4143i	−0.385901	+	1.49327i
$137$	−3.78899	−	9.14744i	−0.323716	−	0.781519i	−0.999032	−	0.0439905i	$-0.985993\pi$
$137$	−3.78899	−	9.14744i	−0.323716	−	0.781519i	0.675316	−	0.737528i	$-0.264007\pi$
$138$	−0.568640	−	0.342754i	−0.0484058	−	0.0291771i
$139$	2.24134	−	1.49762i	0.190108	−	0.127026i	−0.456874	−	0.889531i	$-0.651031\pi$
$139$	2.24134	−	1.49762i	0.190108	−	0.127026i	0.646982	+	0.762505i	$0.276031\pi$
$140$	0.0836530	+	0.280785i	0.00706997	+	0.0237306i
$141$	1.42154	+	7.14659i	0.119716	+	0.601851i
$142$	12.2577	+	11.1654i	1.02865	+	0.936978i
$143$	1.27471	+	1.27471i	0.106596	+	0.106596i
$144$	3.34781	−	2.18910i	0.278984	−	0.182425i
$145$	4.82211	−	4.82211i	0.400454	−	0.400454i
$146$	9.20588	−	0.429320i	0.761884	−	0.0355308i
$147$	6.85256	−	1.36306i	0.565190	−	0.112423i
$148$	7.13904	+	8.78766i	0.586825	+	0.722342i
$149$	−5.98637	−	8.95924i	−0.490423	−	0.733969i	0.500888	−	0.865512i	$-0.333007\pi$
$149$	−5.98637	−	8.95924i	−0.490423	−	0.733969i	−0.991310	+	0.131543i	$0.958007\pi$
$150$	−1.14751	−	4.62992i	−0.0936939	−	0.378031i
$151$	6.41638	−	2.65775i	0.522157	−	0.216285i	−0.106007	−	0.994365i	$-0.533807\pi$
$151$	6.41638	−	2.65775i	0.522157	−	0.216285i	0.628164	+	0.778081i	$0.283807\pi$
$152$	7.67407	−	6.85184i	0.622449	−	0.555757i
$153$	−5.87511	−	2.43355i	−0.474974	−	0.196741i
$154$	−0.0970700	−	0.0146457i	−0.00782213	−	0.00118018i
$155$	4.76153	+	0.947127i	0.382455	+	0.0760751i
$156$	−2.78562	−	5.27444i	−0.223028	−	0.422293i
$157$	4.15362	+	2.77536i	0.331495	+	0.221498i	0.710167	−	0.704033i	$-0.248619\pi$
$157$	4.15362	+	2.77536i	0.331495	+	0.221498i	−0.378672	+	0.925531i	$0.623619\pi$
$158$	−17.7559	+	8.34399i	−1.41259	+	0.663812i
$159$		−	1.83919i		−	0.145857i
$160$	2.51517	−	6.76322i	0.198841	−	0.534679i
$161$		−	0.0539167i		−	0.00424923i
$162$	0.601475	+	1.27993i	0.0472563	+	0.100561i
$163$	18.8800	+	12.6152i	1.47879	+	0.988099i	0.993510	+	0.113742i	$0.0362837\pi$
$163$	18.8800	+	12.6152i	1.47879	+	0.988099i	0.485284	+	0.874357i	$0.338716\pi$
$164$	−15.5647	−	4.80613i	−1.21540	−	0.375296i
$165$	−0.756200	−	0.150418i	−0.0588701	−	0.0117100i
$166$	−2.34958	+	15.5728i	−0.182363	+	1.20868i
$167$	11.3761	+	4.71216i	0.880313	+	0.364638i	0.776618	−	0.629972i	$-0.216934\pi$
$167$	11.3761	+	4.71216i	0.880313	+	0.364638i	0.103695	+	0.994609i	$0.466934\pi$
$168$	0.292593	+	0.141066i	0.0225740	+	0.0108835i
$169$	3.79266	−	1.57097i	0.291743	−	0.120844i
$170$	−11.1347	+	2.75969i	−0.853990	+	0.211659i
$171$	2.02077	+	3.02430i	0.154532	+	0.231274i
$172$	−0.524043	+	5.06255i	−0.0399579	+	0.386016i
$173$	7.12584	−	1.41742i	0.541768	−	0.107764i	0.0833821	−	0.996518i	$-0.473428\pi$
$173$	7.12584	−	1.41742i	0.541768	−	0.107764i	0.458386	+	0.888753i	$0.348428\pi$
$174$	−0.352212	−	7.55245i	−0.0267011	−	0.572550i
$175$	0.273899	−	0.273899i	0.0207048	−	0.0207048i
$176$	1.69254	+	1.72654i	0.127580	+	0.130143i
$177$	−5.79578	−	5.79578i	−0.435638	−	0.435638i
$178$	−16.4957	+	18.1096i	−1.23641	+	1.35737i
$179$	1.37045	+	6.88970i	0.102432	+	0.514960i	0.997601	+	0.0692326i	$0.0220551\pi$
$179$	1.37045	+	6.88970i	0.102432	+	0.514960i	−0.895169	+	0.445728i	$0.852945\pi$
$180$	2.24391	+	1.21378i	0.167251	+	0.0904696i
$181$	3.11141	−	2.07898i	0.231270	−	0.154529i	−0.434537	−	0.900654i	$-0.643088\pi$
$181$	3.11141	−	2.07898i	0.231270	−	0.154529i	0.665806	+	0.746125i	$0.268088\pi$
$182$	0.250053	−	0.414847i	0.0185352	−	0.0307505i
$183$	3.53779	+	8.54098i	0.261521	+	0.631367i
$184$	−0.798962	+	1.06065i	−0.0589003	+	0.0781924i
$185$	−2.76339	+	6.67141i	−0.203168	+	0.490492i
$186$	4.33118	−	3.19557i	0.317578	−	0.234310i
$187$	0.749880	−	3.76990i	0.0548367	−	0.275682i
$188$	14.5099	−	1.35630i	1.05825	−	0.0989187i
$189$	−0.0638030	+	0.0954880i	−0.00464099	+	0.00694573i
$190$	6.17238	+	2.22584i	0.447792	+	0.161479i
$191$	0.180786			0.0130812			0.00654062	−	0.999979i	$-0.497918\pi$
$191$	0.180786			0.0130812			0.00654062	+	0.999979i	$0.497918\pi$
$192$	−3.66553	−	7.11083i	−0.264537	−	0.513180i
$193$	1.98607			0.142961			0.0714803	−	0.997442i	$-0.477228\pi$
$193$	1.98607			0.142961			0.0714803	+	0.997442i	$0.477228\pi$
$194$	−14.3086	−	5.15984i	−1.02729	−	0.370455i
$195$	2.11356	−	3.16317i	0.151355	−	0.226519i
$196$	−1.30050	−	13.9130i	−0.0928931	−	0.993784i
$197$	−3.14153	+	15.7935i	−0.223825	+	1.12524i	0.691454	+	0.722421i	$0.256971\pi$
$197$	−3.14153	+	15.7935i	−0.223825	+	1.12524i	−0.915278	+	0.402822i	$0.868029\pi$
$198$	−0.687855	+	0.507503i	−0.0488837	+	0.0360666i
$199$	5.32038	−	12.8445i	0.377152	−	0.910525i	−0.615345	−	0.788258i	$-0.710983\pi$
$199$	5.32038	−	12.8445i	0.377152	−	0.910525i	0.992497	−	0.122267i	$-0.0390166\pi$
$200$	−9.44692	+	1.32940i	−0.667998	+	0.0940028i
$201$	1.80446	+	4.35636i	0.127277	+	0.307274i
$202$	−6.83962	+	11.3472i	−0.481234	+	0.798383i
$203$	0.510497	−	0.341103i	0.0358299	−	0.0239408i
$204$	−6.05107	+	11.1866i	−0.423660	+	0.783221i
$205$	−2.02689	−	10.1899i	−0.141564	−	0.711691i
$206$	16.5893	−	18.2122i	1.15583	−	1.26891i
$207$	−0.331976	−	0.331976i	−0.0230739	−	0.0230739i
$208$	−11.0664	+	4.45549i	−0.767320	+	0.308932i
$209$	−1.55460	+	1.55460i	−0.107534	+	0.107534i
$210$	0.00965092	+	0.206944i	0.000665977	+	0.0142805i
$211$	−15.3000	+	3.04337i	−1.05330	+	0.209514i	−0.691228	−	0.722637i	$-0.742930\pi$
$211$	−15.3000	+	3.04337i	−1.05330	+	0.209514i	−0.362070	+	0.932151i	$0.617930\pi$
$212$	−3.65883	−	0.378738i	−0.251289	−	0.0260118i
$213$	6.51366	+	9.74838i	0.446309	+	0.667948i
$214$	−13.3167	+	3.30051i	−0.910314	+	0.225619i
$215$	−2.99900	+	1.24223i	−0.204530	+	0.0847191i
$216$	2.67012	−	0.932983i	0.181679	−	0.0634815i
$217$	0.403815	+	0.167266i	0.0274128	+	0.0113547i
$218$	−3.89671	+	25.8270i	−0.263919	+	1.74923i
$219$	6.39140	+	1.27133i	0.431891	+	0.0859084i
$220$	−0.454958	+	1.47339i	−0.0306733	+	0.0993357i
$221$	15.7694	+	10.5368i	1.06077	+	0.708782i
$222$	3.40496	+	7.24573i	0.228526	+	0.486302i
$223$		−	21.8061i		−	1.46025i	−0.683315	−	0.730124i	$-0.739462\pi$
$223$		−	21.8061i		−	1.46025i	0.683315	−	0.730124i	$-0.260538\pi$
$224$	0.340885	−	0.553027i	0.0227763	−	0.0369506i
$225$		−	3.37290i		−	0.224860i
$226$	9.79795	−	4.60432i	0.651750	−	0.306275i
$227$	19.9542	+	13.3330i	1.32441	+	0.884941i	0.998177	−	0.0603491i	$-0.0192214\pi$
$227$	19.9542	+	13.3330i	1.32441	+	0.884941i	0.326231	+	0.945290i	$0.394221\pi$
$228$	6.43258	−	3.39728i	0.426008	−	0.224990i
$229$	2.89887	+	0.576621i	0.191563	+	0.0381042i	0.289939	−	0.957045i	$-0.406365\pi$
$229$	2.89887	+	0.576621i	0.191563	+	0.0381042i	−0.0983764	+	0.995149i	$0.531365\pi$
$230$	−0.837444	−	0.126351i	−0.0552194	−	0.00833136i
$231$	−0.0641318	−	0.0265642i	−0.00421956	−	0.00174780i
$232$	−15.0972	−	0.854573i	−0.991177	−	0.0561054i
$233$	−9.69807	+	4.01707i	−0.635342	+	0.263167i	−0.677021	−	0.735964i	$-0.736729\pi$
$233$	−9.69807	+	4.01707i	−0.635342	+	0.263167i	0.0416789	+	0.999131i	$0.486729\pi$
$234$	−1.01466	−	4.09392i	−0.0663307	−	0.267628i
$235$	5.16382	+	7.72820i	0.336850	+	0.504132i
$236$	−12.7235	+	10.3364i	−0.828227	+	0.672845i
$237$	−13.6060	+	2.70640i	−0.883804	+	0.175800i
$238$	−1.03168	+	0.0481129i	−0.0668740	+	0.00311870i
$239$	5.37906	−	5.37906i	0.347942	−	0.347942i	−0.511400	−	0.859343i	$-0.670873\pi$
$239$	5.37906	−	5.37906i	0.347942	−	0.347942i	0.859343	+	0.511400i	$0.170873\pi$
$240$	2.87673	−	4.21402i	0.185692	−	0.272014i
$241$	12.9797	+	12.9797i	0.836097	+	0.836097i	0.988343	−	0.152246i	$-0.0486506\pi$
$241$	12.9797	+	12.9797i	0.836097	+	0.836097i	−0.152246	+	0.988343i	$0.548651\pi$
$242$	11.1185	+	10.1277i	0.714725	+	0.651033i
$243$	0.195090	+	0.980785i	0.0125150	+	0.0629174i
$244$	17.7197	−	5.27916i	1.13439	−	0.337963i
$245$	7.41024	−	4.95137i	0.473423	−	0.316331i
$246$	−9.86514	−	5.94632i	−0.628978	−	0.379123i
$247$	−4.15133	−	10.0222i	−0.264143	−	0.637697i
$248$	−5.46526	−	9.27438i	−0.347044	−	0.588924i
$249$	−4.26165	+	10.2885i	−0.270071	+	0.652010i
$250$	−8.96738	−	12.1541i	−0.567147	−	0.768695i
$251$	4.85663	−	24.4159i	0.306548	−	1.54112i	−0.453503	−	0.891255i	$-0.649826\pi$
$251$	4.85663	−	24.4159i	0.306548	−	1.54112i	0.760051	−	0.649864i	$-0.225174\pi$
$252$	0.176822	+	0.146591i	0.0111387	+	0.00923439i
$253$	0.157658	−	0.235952i	0.00991187	−	0.0148342i
$254$	5.01375	−	13.9035i	0.314591	−	0.872380i
$255$	−8.11162			−0.507969
$256$	−14.9009	+	5.82779i	−0.931306	+	0.364237i
$257$	4.59417			0.286577			0.143288	−	0.989681i	$-0.454232\pi$
$257$	4.59417			0.286577			0.143288	+	0.989681i	$0.454232\pi$
$258$	−1.22085	+	3.38549i	−0.0760068	+	0.210772i
$259$	−0.361191	+	0.540560i	−0.0224433	+	0.0335888i
$260$	−5.85748	−	4.85604i	−0.363266	−	0.301159i
$261$	1.04299	−	5.24347i	0.0645595	−	0.324563i
$262$	6.57130	+	8.90656i	0.405977	+	0.550249i
$263$	−6.94109	+	16.7573i	−0.428006	+	1.03330i	0.551913	+	0.833902i	$0.313898\pi$
$263$	−6.94109	+	16.7573i	−0.428006	+	1.03330i	−0.979919	+	0.199396i	$0.936102\pi$
$264$	0.867963	+	1.47291i	0.0534194	+	0.0906512i
$265$	−0.897786	−	2.16745i	−0.0551506	−	0.133145i
$266$	0.505937	+	0.304959i	0.0310210	+	0.0186982i
$267$	−14.4023	+	9.62329i	−0.881405	+	0.588936i
$268$	9.03800	−	2.69265i	0.552084	−	0.164480i
$269$	−1.00325	−	5.04369i	−0.0611693	−	0.307519i	0.938073	−	0.346437i	$-0.112609\pi$
$269$	−1.00325	−	5.04369i	−0.0611693	−	0.307519i	−0.999242	+	0.0389185i	$0.987609\pi$
$270$	1.33362	+	1.21477i	0.0811613	+	0.0739286i
$271$	−19.7002	−	19.7002i	−1.19670	−	1.19670i	−0.975149	−	0.221552i	$-0.928888\pi$
$271$	−19.7002	−	19.7002i	−1.19670	−	1.19670i	−0.221552	−	0.975149i	$-0.571112\pi$
$272$	21.0083	+	14.3414i	1.27381	+	0.869578i
$273$	0.242190	−	0.242190i	0.0146580	−	0.0146580i
$274$	−13.9871	+	0.652294i	−0.844991	+	0.0394065i
$275$	1.99955	−	0.397736i	0.120578	−	0.0239844i
$276$	−0.728785	+	0.592060i	−0.0438677	+	0.0356378i
$277$	−17.2568	−	25.8266i	−1.03686	−	1.55177i	−0.817334	−	0.576163i	$-0.804549\pi$
$277$	−17.2568	−	25.8266i	−1.03686	−	1.55177i	−0.219525	−	0.975607i	$-0.570451\pi$
$278$	−0.917096	−	3.70025i	−0.0550038	−	0.221926i
$279$	3.51626	−	1.45648i	0.210513	−	0.0871973i
$280$	0.413675	+	0.0234160i	0.0247218	+	0.00139938i
$281$	−20.9151	−	8.66330i	−1.24769	−	0.516809i	−0.341578	−	0.939853i	$-0.610961\pi$
$281$	−20.9151	−	8.66330i	−1.24769	−	0.516809i	−0.906109	+	0.423044i	$0.860961\pi$
$282$	10.1895	+	1.53736i	0.606775	+	0.0915486i
$283$	14.2324	+	2.83100i	0.846029	+	0.168286i	0.599026	−	0.800729i	$-0.295554\pi$
$283$	14.2324	+	2.83100i	0.846029	+	0.168286i	0.247002	+	0.969015i	$0.420554\pi$
$284$	20.7345	−	10.9506i	1.23036	−	0.649800i
$285$	3.85773	+	2.57765i	0.228512	+	0.152687i
$286$	2.30734	−	1.08428i	0.136436	−	0.0641149i
$287$		−	0.935383i		−	0.0552139i
$288$	−1.30620	−	5.50398i	−0.0769685	−	0.324325i
$289$		−	23.4390i		−	1.37877i
$290$	−4.10175	−	8.72849i	−0.240863	−	0.512555i
$291$	−8.94282	−	5.97540i	−0.524237	−	0.350284i
$292$	3.84530	−	12.4531i	0.225029	−	0.728760i
$293$	5.62575	+	1.11903i	0.328660	+	0.0653745i	0.356662	−	0.934233i	$-0.383915\pi$
$293$	5.62575	+	1.11903i	0.328660	+	0.0653745i	−0.0280026	+	0.999608i	$0.508915\pi$
$294$	1.47411	−	9.77026i	0.0859719	−	0.569813i
$295$	−9.65938	−	4.00105i	−0.562391	−	0.232950i
$296$	15.1156	−	5.28164i	0.878578	−	0.306989i
$297$	−0.558433	+	0.231310i	−0.0324036	+	0.0134220i
$298$	−14.7909	+	3.66588i	−0.856813	+	0.212359i
$299$	0.777910	+	1.16423i	0.0449877	+	0.0673289i
$300$	−6.70995	−	0.694570i	−0.387399	−	0.0401010i
$301$	−0.286636	+	0.0570154i	−0.0165214	+	0.00328631i
$302$	−0.457545	−	9.81110i	−0.0263288	−	0.564566i
$303$	−6.62454	+	6.62454i	−0.380570	+	0.380570i
$304$	−5.43380	−	13.4964i	−0.311650	−	0.774070i
$305$	8.33843	+	8.33843i	0.477457	+	0.477457i
$306$	−6.05602	+	6.64851i	−0.346200	+	0.380070i
$307$	−3.49140	−	17.5524i	−0.199265	−	1.00177i	−0.942872	−	0.333154i	$-0.891887\pi$
$307$	−3.49140	−	17.5524i	−0.199265	−	1.00177i	0.743608	−	0.668616i	$-0.233113\pi$
$308$	−0.0660526	+	0.122112i	−0.00376369	+	0.00695795i
$309$	14.4839	−	9.67785i	0.823962	−	0.550554i
$310$	3.54432	−	5.88015i	0.201304	−	0.333970i
$311$	−10.7808	−	26.0272i	−0.611325	−	1.47587i	−0.861546	−	0.507679i	$-0.830503\pi$
$311$	−10.7808	−	26.0272i	−0.611325	−	1.47587i	0.250222	−	0.968189i	$-0.419497\pi$
$312$	−8.35326	+	1.17550i	−0.472910	+	0.0665494i
$313$	3.49291	−	8.43262i	0.197431	−	0.476640i	−0.793897	−	0.608052i	$-0.791951\pi$
$313$	3.49291	−	8.43262i	0.197431	−	0.476640i	0.991328	+	0.131412i	$0.0419512\pi$
$314$	5.68489	−	4.19434i	0.320817	−	0.236700i
$315$	−0.0285789	+	0.143676i	−0.00161024	+	0.00809521i
$316$	2.58219	+	27.6247i	0.145260	+	1.55401i
$317$	3.75613	−	5.62144i	0.210965	−	0.315732i	−0.710863	−	0.703331i	$-0.751695\pi$
$317$	3.75613	−	5.62144i	0.210965	−	0.315732i	0.921828	+	0.387599i	$0.126695\pi$
$318$	−2.44678	−	0.882337i	−0.137208	−	0.0494790i
$319$	3.23147			0.180928
$320$	−7.79086	−	6.59067i	−0.435522	−	0.368430i
$321$	−9.70127			−0.541472
$322$	−0.0717284	−	0.0258661i	−0.00399727	−	0.00144146i
$323$	−12.8504	+	19.2320i	−0.715017	+	1.07010i
$324$	1.99132	−	0.186137i	0.110629	−	0.0103409i
$325$	−1.96249	+	9.86613i	−0.108860	+	0.547274i
$326$	25.8402	−	19.0650i	1.43116	−	1.05592i
$327$	−7.06784	+	17.0633i	−0.390852	+	0.943601i
$328$	−13.8609	+	18.4009i	−0.765341	+	1.01602i
$329$	0.320233	+	0.773112i	0.0176550	+	0.0426230i
$330$	−0.562890	+	0.933854i	−0.0309861	+	0.0514069i
$331$	−25.7444	+	17.2019i	−1.41504	+	0.945500i	−0.415688	+	0.909507i	$0.636459\pi$
$331$	−25.7444	+	17.2019i	−1.41504	+	0.945500i	−0.999352	+	0.0359928i	$0.988541\pi$
$332$	19.5901	+	10.5967i	1.07515	+	0.581569i
$333$	1.10441	+	5.55225i	0.0605214	+	0.304261i
$334$	11.7265	−	12.8737i	0.641644	−	0.704418i
$335$	4.25305	+	4.25305i	0.232369	+	0.232369i
$336$	0.328037	−	0.321578i	0.0178959	−	0.0175435i
$337$	−11.8008	+	11.8008i	−0.642832	+	0.642832i	−0.951251	−	0.308419i	$-0.900200\pi$
$337$	−11.8008	+	11.8008i	−0.642832	+	0.642832i	0.308419	+	0.951251i	$0.400200\pi$
$338$	−0.270451	−	5.79926i	−0.0147106	−	0.315438i
$339$	7.50796	−	1.49343i	0.407776	−	0.0811118i
$340$	−1.67040	+	16.1370i	−0.0905901	+	0.875152i
$341$	1.27809	+	1.91279i	0.0692122	+	0.103583i
$342$	4.99284	−	1.23746i	0.269982	−	0.0669142i
$343$	1.48401	−	0.614696i	0.0801289	−	0.0331905i
$344$	6.48359	+	3.12589i	0.349572	+	0.168536i
$345$	−0.553278	−	0.229175i	−0.0297875	−	0.0123384i
$346$	1.53290	−	10.1599i	0.0824092	−	0.546200i
$347$	11.0918	+	2.20629i	0.595438	+	0.118440i	0.483604	−	0.875287i	$-0.339328\pi$
$347$	11.0918	+	2.20629i	0.595438	+	0.118440i	0.111834	+	0.993727i	$0.464328\pi$
$348$	−10.2164	−	3.15467i	−0.547658	−	0.169108i
$349$	14.4007	+	9.62227i	0.770854	+	0.515068i	0.877702	−	0.479207i	$-0.159076\pi$
$349$	14.4007	+	9.62227i	0.770854	+	0.515068i	−0.106848	+	0.994275i	$0.534076\pi$
$350$	−0.232982	−	0.495784i	−0.0124534	−	0.0265008i
$351$		−	2.98242i		−	0.159190i
$352$	3.10889	−	1.42339i	0.165705	−	0.0758669i
$353$			7.16105i			0.381144i	0.981673	+	0.190572i	$0.0610343\pi$
$353$			7.16105i			0.381144i	−0.981673	+	0.190572i	$0.938966\pi$
$354$	−10.4909	+	4.92997i	−0.557587	+	0.262025i
$355$	12.4348	+	8.30868i	0.659972	+	0.440979i
$356$	16.1785	+	30.6331i	0.857457	+	1.62355i
$357$	−0.716270	−	0.142475i	−0.0379090	−	0.00754057i
$358$	9.82322	+	1.48210i	0.519173	+	0.0783315i
$359$	−32.4110	−	13.4251i	−1.71059	−	0.708548i	−0.999988	−	0.00495054i	$-0.998424\pi$
$359$	−32.4110	−	13.4251i	−1.71059	−	0.708548i	−0.710599	−	0.703598i	$-0.751576\pi$
$360$	2.69126	−	2.40290i	0.141842	−	0.126644i
$361$	−5.33090	+	2.20813i	−0.280573	+	0.116217i
$362$	−1.27311	−	5.13666i	−0.0669130	−	0.269977i
$363$	5.90829	+	8.84239i	0.310105	+	0.464105i
$364$	−0.431932	−	0.531679i	−0.0226394	−	0.0278676i
$365$	8.15273	−	1.62168i	0.426733	−	0.0848826i
$366$	13.0598	−	0.609048i	0.682645	−	0.0318355i
$367$	−14.2045	+	14.2045i	−0.741469	+	0.741469i	−0.972861	−	0.231392i	$-0.925672\pi$
$367$	−14.2045	+	14.2045i	−0.741469	+	0.741469i	0.231392	+	0.972861i	$0.425672\pi$
$368$	1.02775	+	1.57174i	0.0535752	+	0.0819329i
$369$	−5.75933	−	5.75933i	−0.299819	−	0.299819i
$370$	7.54963	+	6.87685i	0.392487	+	0.357510i
$371$	−0.0412064	−	0.207158i	−0.00213933	−	0.0107551i
$372$	−2.17339	−	7.29507i	−0.112685	−	0.378232i
$373$	3.84920	−	2.57196i	0.199304	−	0.133171i	−0.451914	−	0.892062i	$-0.649258\pi$
$373$	3.84920	−	2.57196i	0.199304	−	0.133171i	0.651218	+	0.758891i	$0.274258\pi$
$374$	−4.65556	−	2.80619i	−0.240733	−	0.145105i
$375$	−4.08717	−	9.86730i	−0.211061	−	0.509545i
$376$	5.15667	−	19.9541i	0.265935	−	1.02905i
$377$	−6.10174	+	14.7309i	−0.314256	+	0.758680i
$378$	0.0964240	+	0.130690i	0.00495951	+	0.00672199i
$379$	−6.96001	+	34.9903i	−0.357512	+	1.79733i	0.214104	+	0.976811i	$0.431317\pi$
$379$	−6.96001	+	34.9903i	−0.357512	+	1.79733i	−0.571616	+	0.820522i	$0.693683\pi$
$380$	5.92231	−	7.14364i	0.303808	−	0.366461i
$381$	5.80622	−	8.68963i	0.297462	−	0.445183i
$382$	0.0867309	−	0.240510i	0.00443754	−	0.0123056i
$383$	32.1551			1.64305			0.821523	−	0.570175i	$-0.193124\pi$
$383$	32.1551			1.64305			0.821523	+	0.570175i	$0.193124\pi$
$384$	−11.2184	+	1.46510i	−0.572489	+	0.0747654i
$385$	−0.0885452			−0.00451268
$386$	0.952803	−	2.64218i	0.0484964	−	0.134484i
$387$	−1.41382	+	2.11593i	−0.0718683	+	0.107559i
$388$	−13.7288	+	16.5601i	−0.696977	+	0.840711i
$389$	−3.67153	+	18.4580i	−0.186154	+	0.935860i	0.768887	+	0.639385i	$0.220811\pi$
$389$	−3.67153	+	18.4580i	−0.186154	+	0.935860i	−0.955041	+	0.296475i	$0.904189\pi$
$390$	−3.19418	−	4.32930i	−0.161743	−	0.219223i
$391$	1.14251	−	2.75827i	0.0577794	−	0.139492i
$392$	−19.1331	−	4.94451i	−0.966368	−	0.249736i
$393$	2.99508	+	7.23076i	0.151082	+	0.364744i
$394$	19.5039	+	11.7562i	0.982592	+	0.592268i
$395$	−14.7133	+	9.83111i	−0.740306	+	0.494657i
$396$	0.345166	+	1.15856i	0.0173452	+	0.0582200i
$397$	−4.91471	−	24.7079i	−0.246662	−	1.24005i	−0.883269	−	0.468866i	$-0.844663\pi$
$397$	−4.91471	−	24.7079i	−0.246662	−	1.24005i	0.636607	−	0.771188i	$-0.280337\pi$
$398$	−14.5354	−	13.2401i	−0.728593	−	0.663665i
$399$	0.295369	+	0.295369i	0.0147870	+	0.0147870i
$400$	−2.76352	+	13.2055i	−0.138176	+	0.660277i
$401$	−12.8717	+	12.8717i	−0.642783	+	0.642783i	−0.951239	−	0.308456i	$-0.900188\pi$
$401$	−12.8717	+	12.8717i	−0.642783	+	0.642783i	0.308456	+	0.951239i	$0.400188\pi$
$402$	6.66119	−	0.310647i	0.332230	−	0.0154937i
$403$	−11.1329	+	2.21447i	−0.554570	+	0.110311i
$404$	11.8145	+	14.5428i	0.587793	+	0.723533i
$405$	0.708673	+	1.06060i	0.0352143	+	0.0527019i
$406$	−0.208882	−	0.842785i	−0.0103666	−	0.0418267i
$407$	−3.16130	+	1.30945i	−0.156700	+	0.0649073i
$408$	11.9792	+	13.4168i	0.593061	+	0.664230i
$409$	12.9312	+	5.35630i	0.639409	+	0.264852i	0.678745	−	0.734374i	$-0.262524\pi$
$409$	12.9312	+	5.35630i	0.639409	+	0.264852i	−0.0393360	+	0.999226i	$0.512524\pi$
$410$	−14.5285	−	2.19202i	−0.717513	−	0.108256i
$411$	−9.71087	−	1.93161i	−0.479002	−	0.0952794i
$412$	−16.2702	−	30.8068i	−0.801575	−	1.51774i
$413$	−0.782664	−	0.522960i	−0.0385124	−	0.0257332i
$414$	−0.600909	+	0.282383i	−0.0295331	+	0.0138784i
$415$			14.2051i			0.697303i
$416$	0.618338	+	16.8598i	0.0303165	+	0.826620i
$417$		−	2.69564i		−	0.132006i
$418$	1.32236	+	2.81398i	0.0646789	+	0.137636i
$419$	−10.0989	−	6.74787i	−0.493364	−	0.329655i	0.283875	−	0.958861i	$-0.408380\pi$
$419$	−10.0989	−	6.74787i	−0.493364	−	0.329655i	−0.777238	+	0.629206i	$0.783380\pi$
$420$	0.279939	+	0.0864406i	0.0136596	+	0.00421787i
$421$	34.8889	+	6.93984i	1.70038	+	0.338227i	0.947458	−	0.319881i	$-0.103643\pi$
$421$	34.8889	+	6.93984i	1.70038	+	0.338227i	0.752924	+	0.658108i	$0.228643\pi$
$422$	−3.29132	+	21.8145i	−0.160219	+	1.06191i
$423$	6.73194	+	2.78846i	0.327318	+	0.135580i
$424$	−2.25915	+	4.68585i	−0.109714	+	0.227565i
$425$	19.8161	−	8.20812i	0.961224	−	0.398152i
$426$	16.0937	−	3.98877i	0.779742	−	0.193257i
$427$	0.589839	+	0.882757i	0.0285443	+	0.0427196i
$428$	−1.99775	+	19.2994i	−0.0965649	+	0.932872i
$429$	1.76807	−	0.351691i	0.0853631	−	0.0169798i
$430$	0.213855	+	4.58569i	0.0103130	+	0.221141i
$431$	−2.49598	+	2.49598i	−0.120227	+	0.120227i	−0.764661	−	0.644433i	$-0.777093\pi$
$431$	−2.49598	+	2.49598i	−0.120227	+	0.120227i	0.644433	+	0.764661i	$0.277093\pi$
$432$	0.0397707	−	3.99980i	0.00191347	−	0.192441i
$433$	5.88846	+	5.88846i	0.282981	+	0.282981i	0.834297	−	0.551316i	$-0.185874\pi$
$433$	5.88846	+	5.88846i	0.282981	+	0.282981i	−0.551316	+	0.834297i	$0.685874\pi$
$434$	0.416251	−	0.456974i	0.0199807	−	0.0219354i
$435$	−1.33042	−	6.68846i	−0.0637886	−	0.320687i
$436$	32.4897	+	17.5743i	1.55598	+	0.841658i
$437$	−1.41986	+	0.948720i	−0.0679211	+	0.0453835i
$438$	4.75755	−	7.89293i	0.227324	−	0.377139i
$439$	0.312067	+	0.753395i	0.0148941	+	0.0359576i	0.931152	−	0.364632i	$-0.118805\pi$
$439$	0.312067	+	0.753395i	0.0148941	+	0.0359576i	−0.916258	+	0.400590i	$0.868805\pi$
$440$	1.74187	+	1.31210i	0.0830402	+	0.0625520i
$441$	2.67374	−	6.45497i	0.127321	−	0.307380i
$442$	21.5830	−	15.9240i	1.02660	−	0.757428i
$443$	5.39469	−	27.1209i	0.256310	−	1.28856i	−0.611336	−	0.791371i	$-0.709367\pi$
$443$	5.39469	−	27.1209i	0.256310	−	1.28856i	0.867645	−	0.497184i	$-0.165633\pi$
$444$	11.2729	−	1.05373i	0.534989	−	0.0500076i
$445$	−12.2753	+	18.3712i	−0.581903	+	0.870879i
$446$	−29.0099	−	10.4613i	−1.37366	−	0.495358i
$447$	−10.7752			−0.509649
$448$	−0.572185	−	0.718808i	−0.0270332	−	0.0339605i
$449$	−22.6219			−1.06759			−0.533796	−	0.845613i	$-0.679235\pi$
$449$	−22.6219			−1.06759			−0.533796	+	0.845613i	$0.679235\pi$
$450$	−4.48716	−	1.61812i	−0.211527	−	0.0762791i
$451$	2.73515	−	4.09345i	0.128793	−	0.192753i
$452$	−1.42489	−	15.2436i	−0.0670211	−	0.717001i
$453$	1.35491	−	6.81159i	0.0636592	−	0.320036i
$454$	27.3105	−	20.1498i	1.28175	−	0.945678i
$455$	0.167193	−	0.403640i	0.00783813	−	0.0189229i
$456$	−1.43361	−	10.1874i	−0.0671348	−	0.477070i
$457$	1.70969	+	4.12755i	0.0799759	+	0.193079i	0.958810	−	0.284049i	$-0.0916779\pi$
$457$	1.70969	+	4.12755i	0.0799759	+	0.193079i	−0.878834	+	0.477128i	$0.841678\pi$
$458$	2.15782	−	3.57990i	0.100828	−	0.167278i
$459$	−5.28746	+	3.53297i	−0.246797	+	0.164905i
$460$	−0.569850	+	1.05348i	−0.0265694	+	0.0491189i
$461$	3.16990	+	15.9362i	0.147637	+	0.742222i	0.981682	+	0.190526i	$0.0610193\pi$
$461$	3.16990	+	15.9362i	0.147637	+	0.742222i	−0.834045	+	0.551696i	$0.813981\pi$
$462$	−0.0661066	+	0.0725741i	−0.00307556	+	0.00337645i
$463$	−9.04107	−	9.04107i	−0.420174	−	0.420174i	0.465090	−	0.885264i	$-0.346022\pi$
$463$	−9.04107	−	9.04107i	−0.420174	−	0.420174i	−0.885264	+	0.465090i	$0.846022\pi$
$464$	−8.37964	+	19.6746i	−0.389015	+	0.913371i
$465$	3.43287	−	3.43287i	0.159196	−	0.159196i
$466$	0.691559	+	14.8291i	0.0320359	+	0.686943i
$467$	2.47304	−	0.491919i	0.114439	−	0.0227633i	−0.137539	−	0.990496i	$-0.543919\pi$
$467$	2.47304	−	0.491919i	0.114439	−	0.0227633i	0.251977	+	0.967733i	$0.418919\pi$
$468$	−5.93314	−	0.614161i	−0.274260	−	0.0283896i
$469$	0.300850	+	0.450253i	0.0138919	+	0.0207908i
$470$	12.7586	−	3.16217i	0.588508	−	0.145860i
$471$	4.61526	−	1.91170i	0.212660	−	0.0880866i
$472$	7.64717	+	21.8856i	0.351990	+	1.00736i
$473$	−1.42110	−	0.588639i	−0.0653423	−	0.0270657i
$474$	−2.92690	+	19.3992i	−0.134437	+	0.891034i
$475$	−12.0325	−	2.39341i	−0.552088	−	0.109817i
$476$	−0.430934	+	1.39559i	−0.0197518	+	0.0639666i
$477$	−1.52923	−	1.02180i	−0.0700186	−	0.0467849i
$478$	−4.57550	−	9.73662i	−0.209278	−	0.445343i
$479$		−	27.1259i		−	1.23941i	−0.784833	−	0.619707i	$-0.787251\pi$
$479$		−	27.1259i		−	1.23941i	0.784833	−	0.619707i	$-0.212749\pi$
$480$	−4.22606	−	5.84873i	−0.192892	−	0.266957i
$481$		−	16.8836i		−	0.769825i
$482$	23.4946	−	11.0407i	1.07015	−	0.502891i
$483$	−0.0448301	−	0.0299545i	−0.00203984	−	0.00136298i
$484$	18.8075	−	9.93290i	0.854884	−	0.451495i
$485$	−13.4558	−	2.67652i	−0.610996	−	0.121535i
$486$	1.39839	+	0.210985i	0.0634321	+	0.00957047i
$487$	27.2489	+	11.2869i	1.23477	+	0.511457i	0.902075	−	0.431580i	$-0.142044\pi$
$487$	27.2489	+	11.2869i	1.23477	+	0.511457i	0.332690	+	0.943036i	$0.392044\pi$
$488$	1.47773	−	26.1061i	0.0668939	−	1.18177i
$489$	20.9783	−	8.68950i	0.948672	−	0.392953i
$490$	−3.03207	−	12.2336i	−0.136975	−	0.552660i
$491$	1.60938	+	2.40861i	0.0726305	+	0.108699i	0.866007	−	0.500032i	$-0.166679\pi$
$491$	1.60938	+	2.40861i	0.0726305	+	0.108699i	−0.793376	+	0.608732i	$0.791679\pi$
$492$	−12.6434	+	10.2714i	−0.570010	+	0.463072i
$493$	33.3441	−	6.63256i	1.50174	−	0.298715i
$494$	−15.3246	+	0.714672i	−0.689489	+	0.0321546i
$495$	−0.545190	+	0.545190i	−0.0245045	+	0.0245045i
$496$	−14.9601	+	2.82143i	−0.671731	+	0.126686i
$497$	0.952080	+	0.952080i	0.0427066	+	0.0427066i
$498$	11.6429	+	10.6054i	0.521732	+	0.475238i
$499$	−0.115462	−	0.580465i	−0.00516877	−	0.0259852i	0.978115	−	0.208066i	$-0.0667168\pi$
$499$	−0.115462	−	0.580465i	−0.00516877	−	0.0259852i	−0.983284	+	0.182081i	$0.941717\pi$
$500$	−20.4714	+	6.09895i	−0.915508	+	0.272753i
$501$	10.2383	−	6.84099i	0.457412	−	0.305633i
$502$	−30.1519	−	18.1744i	−1.34575	−	0.811163i
$503$	−6.01458	−	14.5205i	−0.268177	−	0.647436i	0.731221	−	0.682141i	$-0.238951\pi$
$503$	−6.01458	−	14.5205i	−0.268177	−	0.647436i	−0.999398	+	0.0347049i	$0.988951\pi$
$504$	0.279848	−	0.164910i	0.0124654	−	0.00734569i
$505$	−4.57317	+	11.0406i	−0.203504	+	0.491301i
$506$	−0.238265	−	0.322937i	−0.0105922	−	0.0143563i
$507$	0.800875	−	4.02627i	0.0355681	−	0.178813i
$508$	−16.0912	−	13.3402i	−0.713933	−	0.591874i
$509$	18.1864	−	27.2179i	0.806100	−	1.20641i	−0.169212	−	0.985580i	$-0.554122\pi$
$509$	18.1864	−	27.2179i	0.806100	−	1.20641i	0.975312	−	0.220833i	$-0.0708777\pi$
$510$	−3.89149	+	10.7913i	−0.172318	+	0.477849i
$511$	0.748384			0.0331065
$512$	0.604442	+	22.6193i	0.0267128	+	0.999643i
$513$	3.63729			0.160590
$514$	2.20402	−	6.11188i	0.0972151	−	0.269584i
$515$	12.3449	−	18.4754i	0.543979	−	0.814122i
$516$	3.91822	+	3.24833i	0.172490	+	0.143000i
$517$	−0.859243	+	4.31971i	−0.0377895	+	0.189981i
$518$	0.545859	+	0.739842i	0.0239836	+	0.0325068i
$519$	2.78037	−	6.71240i	0.122045	−	0.294642i
$520$	−9.27035	+	5.46288i	−0.406532	+	0.239563i
$521$	−7.49599	−	18.0969i	−0.328405	−	0.792840i	−0.998711	−	0.0507553i	$-0.983837\pi$
$521$	−7.49599	−	18.0969i	−0.328405	−	0.792840i	0.670306	−	0.742085i	$-0.266163\pi$
$522$	−6.47532	−	3.90307i	−0.283417	−	0.170833i
$523$	11.4984	−	7.68297i	0.502789	−	0.335953i	−0.278173	−	0.960531i	$-0.589729\pi$
$523$	11.4984	−	7.68297i	0.502789	−	0.335953i	0.780962	+	0.624578i	$0.214729\pi$
$524$	15.0014	−	4.46932i	0.655341	−	0.195243i
$525$	−0.0755686	−	0.379909i	−0.00329808	−	0.0165806i
$526$	18.9632	+	17.2733i	0.826835	+	0.753151i
$527$	17.1140	+	17.1140i	0.745496	+	0.745496i
$528$	2.37589	−	0.448084i	0.103397	−	0.0195003i
$529$	−16.1076	+	16.1076i	−0.700330	+	0.700330i
$530$	−3.31418	+	0.154558i	−0.143959	+	0.00671359i
$531$	−8.03898	+	1.59905i	−0.348862	+	0.0693930i
$532$	0.648423	−	0.526774i	0.0281127	−	0.0228386i
$533$	13.4957	+	20.1977i	0.584564	+	0.874861i
$534$	5.89302	+	23.7768i	0.255016	+	1.02892i
$535$	−11.4328	+	4.73560i	−0.494281	+	0.204738i
$536$	0.753724	−	13.3155i	0.0325559	−	0.575144i
$537$	6.48996	+	2.68823i	0.280062	+	0.116006i
$538$	−7.19120	−	1.08499i	−0.310035	−	0.0467772i
$539$	4.14199	+	0.823892i	0.178408	+	0.0354875i
$540$	2.25587	−	1.19141i	0.0970772	−	0.0512700i
$541$	−27.7191	−	18.5213i	−1.19174	−	0.796293i	−0.208392	−	0.978045i	$-0.566823\pi$
$541$	−27.7191	−	18.5213i	−1.19174	−	0.796293i	−0.983344	+	0.181753i	$0.941823\pi$
$542$	−35.6593	+	16.7572i	−1.53170	+	0.719785i
$543$		−	3.74207i		−	0.160587i
$544$	29.1578	−	21.0683i	1.25013	−	0.903295i
$545$			23.5589i			1.00915i
$546$	−0.206010	−	0.438388i	−0.00881642	−	0.0187613i
$547$	−13.6261	−	9.10467i	−0.582610	−	0.389288i	0.229053	−	0.973414i	$-0.426437\pi$
$547$	−13.6261	−	9.10467i	−0.582610	−	0.389288i	−0.811663	+	0.584126i	$0.801437\pi$
$548$	−5.84242	+	18.9208i	−0.249576	+	0.808254i
$549$	9.06706	+	1.80355i	0.386973	+	0.0769736i
$550$	0.430141	−	2.85093i	0.0183413	−	0.121564i
$551$	−17.9655	−	7.44153i	−0.765354	−	0.317020i
$552$	0.438021	+	1.25358i	0.0186434	+	0.0533559i
$553$	−1.47189	+	0.609675i	−0.0625909	+	0.0259260i
$554$	−42.6374	+	10.5675i	−1.81149	+	0.448972i
$555$	4.01182	+	6.00411i	0.170292	+	0.254860i
$556$	−5.36262	−	0.555104i	−0.227426	−	0.0235417i
$557$	−32.9643	+	6.55700i	−1.39674	+	0.277829i	−0.835348	−	0.549721i	$-0.814734\pi$
$557$	−32.9643	+	6.55700i	−1.39674	+	0.277829i	−0.561392	+	0.827550i	$0.689734\pi$
$558$	−0.250741	−	5.37661i	−0.0106147	−	0.227610i
$559$	5.36671	−	5.36671i	0.226988	−	0.226988i
$560$	0.229609	−	0.539102i	0.00970276	−	0.0227812i
$561$	−2.71795	−	2.71795i	−0.114752	−	0.114752i
$562$	−21.5591	+	23.6683i	−0.909416	+	0.998388i
$563$	1.88685	+	9.48584i	0.0795213	+	0.399781i	0.999960	+	0.00889464i	$0.00283129\pi$
$563$	1.88685	+	9.48584i	0.0795213	+	0.399781i	−0.920439	+	0.390886i	$0.872169\pi$
$564$	6.93357	−	12.8181i	0.291956	−	0.539739i
$565$	8.11898	−	5.42493i	0.341568	−	0.228228i
$566$	10.5941	−	17.5760i	0.445305	−	0.738775i
$567$	0.0439483	+	0.106101i	0.00184565	+	0.00445580i
$568$	−4.62102	−	32.8377i	−0.193894	−	1.37784i
$569$	11.9817	−	28.9264i	0.502300	−	1.21266i	−0.445928	−	0.895069i	$-0.647126\pi$
$569$	11.9817	−	28.9264i	0.502300	−	1.21266i	0.948228	−	0.317590i	$-0.102874\pi$
$570$	5.27991	−	3.89554i	0.221151	−	0.163166i
$571$	−5.36833	+	26.9884i	−0.224658	+	1.12943i	0.689567	+	0.724222i	$0.257801\pi$
$571$	−5.36833	+	26.9884i	−0.224658	+	1.12943i	−0.914224	+	0.405208i	$0.867199\pi$
$572$	−0.335550	−	3.58976i	−0.0140301	−	0.150096i
$573$	0.100440	−	0.150318i	0.00419592	−	0.00627964i
$574$	−1.24439	−	0.448743i	−0.0519399	−	0.0187302i
$575$	1.58352			0.0660375
$576$	−7.94890	−	0.902785i	−0.331204	−	0.0376160i
$577$	−22.7355			−0.946491			−0.473246	−	0.880930i	$-0.656918\pi$
$577$	−22.7355			−0.946491			−0.473246	+	0.880930i	$0.656918\pi$
$578$	−31.1823	−	11.2447i	−1.29701	−	0.467718i
$579$	1.10340	−	1.65136i	0.0458559	−	0.0686281i
$580$	−13.5798	+	1.26936i	−0.563870	+	0.0527073i
$581$	−0.249503	+	1.25434i	−0.0103511	+	0.0520387i
$582$	−12.2397	+	9.03048i	−0.507350	+	0.374325i
$583$	0.425424	−	1.02706i	0.0176192	−	0.0425366i
$584$	−14.7222	−	11.0899i	−0.609211	−	0.458903i
$585$	−1.45585	−	3.51473i	−0.0601919	−	0.145316i
$586$	4.18762	−	6.94740i	0.172989	−	0.286995i
$587$	16.1701	−	10.8045i	0.667410	−	0.445949i	−0.175157	−	0.984540i	$-0.556043\pi$
$587$	16.1701	−	10.8045i	0.667410	−	0.445949i	0.842567	+	0.538592i	$0.181043\pi$
$588$	−12.2907	−	6.64830i	−0.506861	−	0.274171i
$589$	−2.70072	−	13.5774i	−0.111281	−	0.559448i
$590$	−9.95684	+	10.9309i	−0.409916	+	0.450020i
$591$	11.3865	+	11.3865i	0.468378	+	0.468378i
$592$	0.225143	−	22.6430i	0.00925332	−	0.930621i
$593$	−4.92657	+	4.92657i	−0.202310	+	0.202310i	−0.800989	−	0.598679i	$-0.795692\pi$
$593$	−4.92657	+	4.92657i	−0.202310	+	0.202310i	0.598679	+	0.800989i	$0.295692\pi$
$594$	0.0398213	+	0.853884i	0.00163389	+	0.0350353i
$595$	−0.913658	+	0.181738i	−0.0374563	+	0.00745053i
$596$	−2.21890	+	21.4358i	−0.0908896	+	0.878046i
$597$	−7.72400	−	11.5598i	−0.316122	−	0.473110i
$598$	1.92203	−	0.476369i	0.0785977	−	0.0194802i
$599$	24.1037	−	9.98408i	0.984850	−	0.407938i	0.168630	−	0.985679i	$-0.446066\pi$
$599$	24.1037	−	9.98408i	0.984850	−	0.407938i	0.816220	+	0.577741i	$0.196066\pi$
$600$	−4.14307	+	8.59340i	−0.169140	+	0.350824i
$601$	43.2509	+	17.9151i	1.76424	+	0.730772i	0.995872	+	0.0907646i	$0.0289311\pi$
$601$	43.2509	+	17.9151i	1.76424	+	0.730772i	0.768368	+	0.640008i	$0.221069\pi$
$602$	−0.0616606	+	0.408680i	−0.00251310	+	0.0166566i
$603$	4.62469	+	0.919907i	0.188332	+	0.0374615i
$604$	−13.2718	−	4.09811i	−0.540020	−	0.166750i
$605$	11.2792	+	7.53649i	0.458563	+	0.306402i
$606$	5.63492	+	11.9911i	0.228903	+	0.487104i
$607$			40.3915i			1.63944i	0.572764	+	0.819720i	$0.305871\pi$
$607$			40.3915i			1.63944i	−0.572764	+	0.819720i	$0.694129\pi$
$608$	−20.5618	+	0.754109i	−0.833891	+	0.0305832i
$609$		−	0.613970i		−	0.0248793i
$610$	15.0934	−	7.09278i	0.611113	−	0.287178i
$611$	−18.0693	−	12.0735i	−0.731004	−	0.488441i
$612$	5.93955	+	11.2462i	0.240092	+	0.454602i
$613$	11.9238	+	2.37180i	0.481599	+	0.0957959i	0.429918	−	0.902868i	$-0.358542\pi$
$613$	11.9238	+	2.37180i	0.481599	+	0.0957959i	0.0516803	+	0.998664i	$0.483542\pi$
$614$	−25.0260	−	3.77585i	−1.00997	−	0.152381i
$615$	−9.59864	−	3.97589i	−0.387054	−	0.160323i
$616$	0.130764	+	0.146456i	0.00526862	+	0.00590086i
$617$	10.5994	−	4.39041i	0.426716	−	0.176751i	−0.158981	−	0.987282i	$-0.550821\pi$
$617$	10.5994	−	4.39041i	0.426716	−	0.176751i	0.585697	+	0.810530i	$0.300821\pi$
$618$	−5.92643	−	23.9116i	−0.238396	−	0.961868i
$619$	−2.45349	−	3.67191i	−0.0986143	−	0.147587i	0.778881	−	0.627171i	$-0.215787\pi$
$619$	−2.45349	−	3.67191i	−0.0986143	−	0.147587i	−0.877496	+	0.479585i	$0.840787\pi$
$620$	−6.12233	−	7.53617i	−0.245879	−	0.302660i
$621$	−0.460464	+	0.0915919i	−0.0184778	+	0.00367546i
$622$	−39.7975	+	1.85597i	−1.59573	+	0.0744177i
$623$	−1.40660	+	1.40660i	−0.0563544	+	0.0563544i
$624$	−2.44359	+	11.6767i	−0.0978218	+	0.467444i
$625$	2.29170	+	2.29170i	0.0916681	+	0.0916681i
$626$	−9.54269	−	8.69229i	−0.381403	−	0.347414i
$627$	0.428913	+	2.15629i	0.0171291	+	0.0861140i
$628$	−2.85268	−	9.57512i	−0.113834	−	0.382089i
$629$	−29.9324	+	20.0002i	−1.19348	+	0.797461i
$630$	0.177429	+	0.106947i	0.00706895	+	0.00426089i
$631$	4.04950	+	9.77637i	0.161208	+	0.389191i	0.983757	−	0.179503i	$-0.0574489\pi$
$631$	4.04950	+	9.77637i	0.161208	+	0.389191i	−0.822549	+	0.568694i	$0.807449\pi$
$632$	37.9894	+	9.81750i	1.51114	+	0.390519i
$633$	−5.96978	+	14.4123i	−0.237277	+	0.572838i
$634$	−5.67655	−	7.69383i	−0.225444	−	0.305561i
$635$	2.60074	−	13.0748i	0.103207	−	0.518858i
$636$	−2.34764	+	2.83179i	−0.0930902	+	0.112288i
$637$	−11.5768	+	17.3259i	−0.458688	+	0.686475i
$638$	1.55028	−	4.29901i	0.0613760	−	0.170199i
$639$	11.7243			0.463805
$640$	−12.5055	+	7.20279i	−0.494325	+	0.284715i
$641$	−2.69030			−0.106261			−0.0531303	−	0.998588i	$-0.516920\pi$
$641$	−2.69030			−0.106261			−0.0531303	+	0.998588i	$0.516920\pi$
$642$	−4.65411	+	12.9061i	−0.183683	+	0.509365i
$643$	22.0513	−	33.0021i	0.869619	−	1.30148i	−0.0827634	−	0.996569i	$-0.526375\pi$
$643$	22.0513	−	33.0021i	0.869619	−	1.30148i	0.952382	−	0.304907i	$-0.0986254\pi$
$644$	−0.0688224	+	0.0830153i	−0.00271198	+	0.00327126i
$645$	−0.633281	+	3.18372i	−0.0249354	+	0.125359i
$646$	19.4205	+	26.3220i	0.764091	+	1.03563i
$647$	−1.83521	+	4.43060i	−0.0721497	+	0.174185i	−0.955840	−	0.293887i	$-0.905051\pi$
$647$	−1.83521	+	4.43060i	−0.0721497	+	0.174185i	0.883691	+	0.468072i	$0.155051\pi$
$648$	0.707692	−	2.73846i	0.0278008	−	0.107577i
$649$	−1.89593	−	4.57718i	−0.0744218	−	0.179670i
$650$	12.1840	+	7.34402i	0.477895	+	0.288056i
$651$	0.363424	−	0.242832i	0.0142437	−	0.00951735i
$652$	−12.9666	−	43.5230i	−0.507813	−	1.70449i
$653$	−6.51196	−	32.7378i	−0.254833	−	1.28113i	−0.870125	−	0.492832i	$-0.835962\pi$
$653$	−6.51196	−	32.7378i	−0.254833	−	1.28113i	0.615292	−	0.788299i	$-0.289038\pi$
$654$	19.3095	+	17.5887i	0.755061	+	0.687773i
$655$	7.05929	+	7.05929i	0.275829	+	0.275829i
$656$	17.8301	+	27.2677i	0.696148	+	1.06462i
$657$	4.60794	−	4.60794i	0.179773	−	0.179773i
$658$	1.18214	−	0.0551298i	0.0460848	−	0.00214918i
$659$	37.2979	−	7.41902i	1.45292	−	0.289004i	0.595390	−	0.803437i	$-0.296998\pi$
$659$	37.2979	−	7.41902i	1.45292	−	0.289004i	0.857531	+	0.514433i	$0.171998\pi$
$660$	0.972315	+	1.19685i	0.0378473	+	0.0465875i
$661$	1.53528	+	2.29771i	0.0597154	+	0.0893704i	0.860126	−	0.510082i	$-0.170385\pi$
$661$	1.53528	+	2.29771i	0.0597154	+	0.0893704i	−0.800410	+	0.599453i	$0.795385\pi$
$662$	10.5339	+	42.5017i	0.409412	+	1.65188i
$663$	17.5221	−	7.25787i	0.680500	−	0.281872i
$664$	23.4956	−	20.9782i	0.911806	−	0.814111i
$665$	0.492269	+	0.203905i	0.0190894	+	0.00790708i
$666$	7.91630	+	1.19439i	0.306751	+	0.0462817i
$667$	2.46173	+	0.489668i	0.0953185	+	0.0189600i
$668$	−11.5009	−	21.7764i	−0.444984	−	0.842556i
$669$	−18.1311	−	12.1148i	−0.700990	−	0.468387i
$670$	7.69844	−	3.61770i	0.297417	−	0.139764i
$671$			5.58789i			0.215718i
$672$	−0.270440	−	0.590680i	−0.0104324	−	0.0227860i
$673$		−	11.0365i		−	0.425426i	−0.977115	−	0.212713i	$-0.931770\pi$
$673$		−	11.0365i		−	0.425426i	0.977115	−	0.212713i	$-0.0682299\pi$
$674$	10.0379	+	21.3607i	0.386647	+	0.822782i
$675$	−2.80446	−	1.87388i	−0.107944	−	0.0721258i
$676$	−7.84482	−	2.42235i	−0.301724	−	0.0931675i
$677$	−39.3877	−	7.83469i	−1.51379	−	0.301112i	−0.632826	−	0.774294i	$-0.718105\pi$
$677$	−39.3877	−	7.83469i	−1.51379	−	0.301112i	−0.880965	+	0.473182i	$0.843105\pi$
$678$	1.61510	−	10.7047i	0.0620275	−	0.411112i
$679$	−1.14116	−	0.472683i	−0.0437936	−	0.0181399i
$680$	20.6666	+	9.96384i	0.792528	+	0.382096i
$681$	22.1719	−	9.18392i	0.849631	−	0.351928i
$682$	3.15784	−	0.782662i	0.120920	−	0.0299697i
$683$	12.2521	+	18.3366i	0.468815	+	0.701632i	0.988244	−	0.152882i	$-0.0488554\pi$
$683$	12.2521	+	18.3366i	0.468815	+	0.701632i	−0.519429	+	0.854513i	$0.673855\pi$
$684$	0.749015	−	7.23592i	0.0286393	−	0.276672i
$685$	−12.3870	+	2.46392i	−0.473282	+	0.0941417i
$686$	−0.105823	−	2.26915i	−0.00404034	−	0.0866367i
$687$	2.08997	−	2.08997i	0.0797373	−	0.0797373i
$688$	7.26900	−	7.12587i	0.277128	−	0.271671i
$689$	3.87865	+	3.87865i	0.147765	+	0.147765i
$690$	−0.570316	+	0.626112i	−0.0217116	+	0.0238357i
$691$	−6.10019	−	30.6677i	−0.232062	−	1.16665i	−0.904491	−	0.426493i	$-0.859749\pi$
$691$	−6.10019	−	30.6677i	−0.232062	−	1.16665i	0.672429	−	0.740162i	$-0.265251\pi$
$692$	−12.7809	−	6.91344i	−0.485857	−	0.262810i
$693$	−0.0577171	+	0.0385653i	−0.00219249	+	0.00146497i
$694$	8.25635	−	13.6976i	0.313407	−	0.519952i
$695$	−1.31586	−	3.17676i	−0.0499132	−	0.120501i
$696$	−9.09808	+	12.0781i	−0.344862	+	0.457817i
$697$	19.8211	−	47.8523i	0.750777	−	1.81254i
$698$	19.7097	−	14.5419i	0.746023	−	0.550419i
$699$	−2.04789	+	10.2954i	−0.0774582	+	0.389409i
$700$	−0.771341	+	0.0721005i	−0.0291540	+	0.00272514i
$701$	−7.92921	+	11.8669i	−0.299482	+	0.448206i	−0.950440	−	0.310907i	$-0.899367\pi$
$701$	−7.92921	+	11.8669i	−0.299482	+	0.448206i	0.650958	+	0.759113i	$0.274367\pi$
$702$	−3.96768	−	1.43080i	−0.149751	−	0.0540019i
$703$	20.5908			0.776597
$704$	−0.402145	−	4.81880i	−0.0151564	−	0.181615i
$705$	9.29463			0.350056
$706$	9.52674	+	3.43546i	0.358544	+	0.129295i
$707$	−0.597740	+	0.894581i	−0.0224803	+	0.0336442i
$708$	1.52567	+	16.3218i	0.0573380	+	0.613411i
$709$	−6.11756	+	30.7551i	−0.229750	+	1.15503i	0.677852	+	0.735198i	$0.262911\pi$
$709$	−6.11756	+	30.7551i	−0.229750	+	1.15503i	−0.907602	+	0.419832i	$0.862089\pi$
$710$	17.0190	−	12.5567i	0.638712	−	0.471245i
$711$	−5.30880	+	12.8166i	−0.199095	+	0.480659i
$712$	48.5145	−	6.82711i	1.81816	−	0.255857i
$713$	0.683796	+	1.65083i	0.0256083	+	0.0618240i
$714$	−0.533167	+	0.884542i	−0.0199533	+	0.0331032i
$715$	1.91196	−	1.27753i	0.0715032	−	0.0477769i
$716$	6.68434	−	12.3573i	0.249805	−	0.461816i
$717$	−1.48408	−	7.46097i	−0.0554239	−	0.278635i
$718$	−33.4091	+	36.6776i	−1.24681	+	1.36879i
$719$	20.9840	+	20.9840i	0.782570	+	0.782570i	0.980264	−	0.197694i	$-0.0633452\pi$
$719$	20.9840	+	20.9840i	0.782570	+	0.782570i	−0.197694	+	0.980264i	$0.563345\pi$
$720$	−1.90561	−	4.73310i	−0.0710177	−	0.176392i
$721$	1.41458	−	1.41458i	0.0526817	−	0.0526817i
$722$	0.380140	+	8.15132i	0.0141474	+	0.303361i
$723$	18.0034	−	3.58109i	0.669553	−	0.133182i
$724$	−7.44435	−	0.770592i	−0.276667	−	0.0286388i
$725$	10.0181	+	14.9932i	0.372065	+	0.556834i
$726$	14.5980	−	3.61807i	0.541782	−	0.134279i
$727$	−38.7094	+	16.0340i	−1.43565	+	0.594667i	−0.958740	−	0.284284i	$-0.908244\pi$
$727$	−38.7094	+	16.0340i	−1.43565	+	0.594667i	−0.476913	+	0.878951i	$0.658244\pi$
$728$	−0.914539	+	0.319555i	−0.0338951	+	0.0118435i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	1.75380	−	11.6240i	0.0649111	−	0.430224i
$731$	−15.8719	−	3.15711i	−0.587043	−	0.116770i
$732$	5.45508	−	17.6663i	0.201625	−	0.652967i
$733$	9.37507	+	6.26422i	0.346276	+	0.231374i	0.716530	−	0.697556i	$-0.245729\pi$
$733$	9.37507	+	6.26422i	0.346276	+	0.231374i	−0.370254	+	0.928931i	$0.620729\pi$
$734$	12.0825	+	25.7115i	0.445974	+	0.949030i
$735$		−	8.91222i		−	0.328732i
$736$	2.58404	−	0.613241i	0.0952488	−	0.0226043i
$737$			2.85013i			0.104986i
$738$	−10.4250	+	4.89896i	−0.383748	+	0.180333i
$739$	27.6208	+	18.4556i	1.01605	+	0.678901i	0.947832	−	0.318770i	$-0.103270\pi$
$739$	27.6208	+	18.4556i	1.01605	+	0.678901i	0.0682148	+	0.997671i	$0.478270\pi$
$740$	12.7705	−	6.74458i	0.469454	−	0.247936i
$741$	−10.6395	−	2.11633i	−0.390852	−	0.0777453i
$742$	−0.295363	−	0.0445635i	−0.0108431	−	0.00163598i
$743$	−2.77328	−	1.14873i	−0.101742	−	0.0421428i	0.331232	−	0.943549i	$-0.392536\pi$
$743$	−2.77328	−	1.14873i	−0.101742	−	0.0421428i	−0.432974	+	0.901407i	$0.642536\pi$
$744$	−10.7477	−	0.608372i	−0.394030	−	0.0223040i
$745$	−12.6983	+	5.25983i	−0.465231	+	0.192705i
$746$	−1.57499	−	6.35469i	−0.0576645	−	0.232662i
$747$	6.18696	+	9.25944i	0.226369	+	0.338785i
$748$	−5.96670	+	4.84731i	−0.218164	+	0.177235i
$749$	−1.09271	+	0.217353i	−0.0399267	+	0.00794192i
$750$	−15.0878	+	0.703627i	−0.550929	+	0.0256928i
$751$	2.89918	−	2.89918i	0.105793	−	0.105793i	−0.652229	−	0.758022i	$-0.726166\pi$
$751$	2.89918	−	2.89918i	0.105793	−	0.105793i	0.758022	+	0.652229i	$0.226166\pi$
$752$	−24.0721	−	16.4330i	−0.877821	−	0.599251i
$753$	−17.6029	−	17.6029i	−0.641485	−	0.641485i
$754$	16.6701	+	15.1845i	0.607089	+	0.552988i
$755$	−1.72829	−	8.68872i	−0.0628990	−	0.316215i
$756$	0.220123	−	0.0655805i	0.00800581	−	0.00238514i
$757$	−16.0269	+	10.7088i	−0.582508	+	0.389219i	−0.811624	−	0.584180i	$-0.801416\pi$
$757$	−16.0269	+	10.7088i	−0.582508	+	0.389219i	0.229116	+	0.973399i	$0.426416\pi$
$758$	43.2106	+	26.0456i	1.56948	+	0.946020i
$759$	−0.108597	−	0.262176i	−0.00394181	−	0.00951637i
$760$	−6.66240	−	11.3059i	−0.241671	−	0.410108i
$761$	−10.1938	+	24.6099i	−0.369524	+	0.892109i	0.624305	+	0.781181i	$0.285382\pi$
$761$	−10.1938	+	24.6099i	−0.369524	+	0.892109i	−0.993828	+	0.110928i	$0.964618\pi$
$762$	−8.77480	−	11.8931i	−0.317878	−	0.430843i
$763$	−0.413795	+	2.08029i	−0.0149804	+	0.0753114i
$764$	−0.278356	−	0.230766i	−0.0100706	−	0.00834882i
$765$	−4.50657	+	6.74456i	−0.162936	+	0.243850i
$766$	15.4262	−	42.7777i	0.557370	−	1.54562i
$767$	24.4454			0.882670
$768$	−3.43286	+	15.6274i	−0.123873	+	0.563905i
$769$	−46.8147			−1.68818			−0.844090	−	0.536202i	$-0.819859\pi$
$769$	−46.8147			−1.68818			−0.844090	+	0.536202i	$0.819859\pi$
$770$	−0.0424789	+	0.117797i	−0.00153083	+	0.00424510i
$771$	2.55238	−	3.81991i	0.0919219	−	0.137571i
$772$	−3.05794	−	2.53514i	−0.110058	−	0.0912415i
$773$	0.720233	−	3.62086i	0.0259050	−	0.130233i	−0.965669	−	0.259776i	$-0.916351\pi$
$773$	0.720233	−	3.62086i	0.0259050	−	0.130233i	0.991574	+	0.129543i	$0.0413511\pi$
$774$	2.13667	+	2.89598i	0.0768009	+	0.104094i
$775$	−4.91257	+	11.8600i	−0.176465	+	0.426023i
$776$	15.4445	+	26.2088i	0.554425	+	0.940842i
$777$	0.248792	+	0.600638i	0.00892538	+	0.0215478i
$778$	22.7944	+	13.7396i	0.817218	+	0.492587i
$779$	−24.6327	+	16.4590i	−0.882557	+	0.589706i
$780$	−7.29189	+	2.17244i	−0.261092	+	0.0777860i
$781$	1.38254	+	6.95049i	0.0494711	+	0.248708i
$782$	−3.12137	−	2.84321i	−0.111620	−	0.101673i
$783$	−3.78033	−	3.78033i	−0.135098	−	0.135098i
$784$	−15.7569	+	23.0818i	−0.562748	+	0.824349i
$785$	4.50581	−	4.50581i	0.160819	−	0.160819i
$786$	11.0564	−	0.515618i	0.394367	−	0.0183915i
$787$	−13.4135	+	2.66811i	−0.478140	+	0.0951080i	−0.428276	−	0.903648i	$-0.640879\pi$
$787$	−13.4135	+	2.66811i	−0.478140	+	0.0951080i	−0.0498643	+	0.998756i	$0.515879\pi$
$788$	24.9968	−	20.3072i	0.890472	−	0.723413i
$789$	10.0769	+	15.0811i	0.358747	+	0.536903i
$790$	6.02028	+	24.2903i	0.214192	+	0.864211i
$791$	0.812205	−	0.336426i	0.0288787	−	0.0119619i
$792$	1.70689	+	0.0966184i	0.0606518	+	0.00343318i
$793$	−25.4728	−	10.5512i	−0.904566	−	0.374684i
$794$	−35.2281	−	5.31512i	−1.25020	−	0.188627i
$795$	−2.30095	−	0.457687i	−0.0816063	−	0.0162325i
$796$	−24.5873	+	12.9854i	−0.871472	+	0.460256i
$797$	−40.4755	−	27.0449i	−1.43372	−	0.957979i	−0.998332	−	0.0577343i	$-0.981612\pi$
$797$	−40.4755	−	27.0449i	−1.43372	−	0.957979i	−0.435385	−	0.900245i	$-0.643388\pi$
$798$	0.534647	−	0.251245i	0.0189263	−	0.00889398i
$799$			46.3367i			1.63927i
$800$	16.2423	+	10.0117i	0.574252	+	0.353968i
$801$			17.3215i			0.612024i
$802$	10.9488	+	23.2991i	0.386617	+	0.822719i
$803$	3.27510	+	2.18835i	0.115576	+	0.0772252i
$804$	2.78238	−	9.01078i	0.0981271	−	0.317786i
$805$	−0.0674535	−	0.0134173i	−0.00237742	−	0.000472899i
$806$	−2.39489	+	15.8731i	−0.0843565	+	0.559106i
$807$	−4.75105	−	1.96795i	−0.167245	−	0.0692751i
$808$	25.0151	−	8.74067i	0.880027	−	0.307496i
$809$	13.8245	−	5.72627i	0.486042	−	0.201325i	−0.126186	−	0.992007i	$-0.540274\pi$
$809$	13.8245	−	5.72627i	0.486042	−	0.201325i	0.612228	+	0.790682i	$0.290274\pi$
$810$	1.75096	−	0.433971i	0.0615225	−	0.0152482i
$811$	−15.3374	−	22.9540i	−0.538569	−	0.806025i	0.457986	−	0.888959i	$-0.348571\pi$
$811$	−15.3374	−	22.9540i	−0.538569	−	0.806025i	−0.996555	+	0.0829340i	$0.973571\pi$
$812$	−1.22141	−	0.126433i	−0.0428632	−	0.00443692i
$813$	−27.3249	+	5.43527i	−0.958327	+	0.190623i
$814$	0.225429	+	4.83386i	0.00790129	+	0.169427i
$815$	20.4808	−	20.4808i	0.717412	−	0.717412i
$816$	23.5960	−	9.50006i	0.826027	−	0.332569i
$817$	6.54511	+	6.54511i	0.228984	+	0.228984i
$818$	13.3294	−	14.6335i	0.466053	−	0.511649i
$819$	−0.0668201	−	0.335927i	−0.00233488	−	0.0117383i
$820$	−9.88612	+	18.2765i	−0.345238	+	0.638243i
$821$	−7.95160	+	5.31309i	−0.277513	+	0.185428i	−0.686536	−	0.727096i	$-0.740870\pi$
$821$	−7.95160	+	5.31309i	−0.277513	+	0.185428i	0.409023	+	0.912524i	$0.365870\pi$
$822$	−7.22845	+	11.9922i	−0.252121	+	0.418277i
$823$	3.22145	+	7.77727i	0.112293	+	0.271098i	0.970028	−	0.242993i	$-0.0781292\pi$
$823$	3.22145	+	7.77727i	0.112293	+	0.271098i	−0.857735	+	0.514091i	$0.828129\pi$
$824$	−48.7895	+	6.86581i	−1.69966	+	0.239182i
$825$	0.780187	−	1.88354i	0.0271626	−	0.0655764i
$826$	−1.07120	+	0.790336i	−0.0372718	+	0.0274993i
$827$	−2.35617	+	11.8453i	−0.0819322	+	0.411901i	0.917952	+	0.396691i	$0.129842\pi$
$827$	−2.35617	+	11.8453i	−0.0819322	+	0.411901i	−0.999884	+	0.0152097i	$0.995158\pi$
$828$	0.0873884	+	0.934894i	0.00303696	+	0.0324898i
$829$	−17.6812	+	26.4617i	−0.614092	+	0.919054i	−0.999994	−	0.00348602i	$-0.998890\pi$
$829$	−17.6812	+	26.4617i	−0.614092	+	0.919054i	0.385902	+	0.922540i	$0.373890\pi$
$830$	18.8979	+	6.81481i	0.655956	+	0.236546i
$831$	−31.0614			−1.07751
$832$	22.7262	+	7.26575i	0.787888	+	0.251895i
$833$	44.4303			1.53942
$834$	−3.58616	−	1.29321i	−0.124178	−	0.0447803i
$835$	8.72622	−	13.0597i	0.301983	−	0.451950i
$836$	4.37799	−	0.409229i	0.151416	−	0.0141535i
$837$	0.742508	−	3.73284i	0.0256648	−	0.129026i
$838$	−13.8219	+	10.1979i	−0.477471	+	0.352280i
$839$	4.25717	−	10.2777i	0.146974	−	0.354826i	−0.833198	−	0.552974i	$-0.813493\pi$
$839$	4.25717	−	10.2777i	0.146974	−	0.354826i	0.980172	+	0.198148i	$0.0634928\pi$
$840$	0.249295	−	0.330949i	0.00860151	−	0.0114188i
$841$	−0.160033	−	0.386354i	−0.00551838	−	0.0133226i
$842$	25.9701	−	43.0853i	0.894990	−	1.48482i
$843$	−18.8231	+	12.5772i	−0.648300	+	0.433180i
$844$	27.4421	+	14.8440i	0.944596	+	0.510951i
$845$	−1.02158	−	5.13582i	−0.0351434	−	0.176678i
$846$	6.93924	−	7.61813i	0.238576	−	0.261917i
$847$	0.863595	+	0.863595i	0.0296735	+	0.0296735i
$848$	5.15003	+	5.25348i	0.176853	+	0.180405i
$849$	10.2610	−	10.2610i	0.352156	−	0.352156i
$850$	−1.41307	−	30.3003i	−0.0484679	−	1.03929i
$851$	−2.60670	+	0.518504i	−0.0893564	+	0.0177741i
$852$	2.41434	−	23.3239i	0.0827140	−	0.799065i
$853$	2.39490	+	3.58422i	0.0819997	+	0.122721i	0.870202	−	0.492695i	$-0.163988\pi$
$853$	2.39490	+	3.58422i	0.0819997	+	0.122721i	−0.788203	+	0.615416i	$0.788988\pi$
$854$	1.45735	−	0.361200i	0.0498695	−	0.0123600i
$855$	4.28648	−	1.77552i	0.146594	−	0.0607214i
$856$	24.7167	+	11.9165i	0.844799	+	0.407296i
$857$	12.1010	+	5.01240i	0.413362	+	0.171220i	0.579666	−	0.814854i	$-0.303183\pi$
$857$	12.1010	+	5.01240i	0.413362	+	0.171220i	−0.166304	+	0.986075i	$0.553183\pi$
$858$	0.380344	−	2.52088i	0.0129847	−	0.0860614i
$859$	14.4830	+	2.88084i	0.494152	+	0.0982930i	0.435875	−	0.900007i	$-0.356439\pi$
$859$	14.4830	+	2.88084i	0.494152	+	0.0982930i	0.0582777	+	0.998300i	$0.481439\pi$
$860$	6.20319	+	1.91544i	0.211527	+	0.0653161i
$861$	−0.777742	−	0.519671i	−0.0265054	−	0.0177103i
$862$	2.12312	+	4.51797i	0.0723136	+	0.153883i
$863$			0.559064i			0.0190307i	0.999955	+	0.00951537i	$0.00302888\pi$
$863$			0.559064i			0.0190307i	−0.999955	+	0.00951537i	$0.996971\pi$
$864$	−5.30208	−	1.97178i	−0.180380	−	0.0670815i
$865$		−	9.26765i		−	0.315109i
$866$	10.6587	−	5.00880i	0.362197	−	0.170206i
$867$	−19.4888	−	13.0220i	−0.661876	−	0.442251i
$868$	−0.408245	−	0.772991i	−0.0138567	−	0.0262370i
$869$	−8.22405	−	1.63587i	−0.278982	−	0.0554930i
$870$	−9.53629	−	1.43881i	−0.323310	−	0.0487802i
$871$	−12.9925	−	5.38167i	−0.440234	−	0.182351i
$872$	38.9668	−	34.7917i	1.31958	−	1.17820i
$873$	−9.93673	+	4.11593i	−0.336307	+	0.139303i
$874$	0.580968	+	2.34406i	0.0196515	+	0.0792891i
$875$	−0.681435	−	1.01984i	−0.0230367	−	0.0344768i
$876$	−8.21801	−	10.1158i	−0.277661	−	0.341781i
$877$	−0.811394	+	0.161396i	−0.0273988	+	0.00544997i	−0.208771	−	0.977965i	$-0.566946\pi$
$877$	−0.811394	+	0.161396i	−0.0273988	+	0.00544997i	0.181372	+	0.983415i	$0.441946\pi$
$878$	1.15200	−	0.0537238i	0.0388780	−	0.00181309i
$879$	4.05594	−	4.05594i	0.136803	−	0.136803i
$880$	2.58121	−	1.68783i	0.0870126	−	0.0568968i
$881$	−9.58605	−	9.58605i	−0.322962	−	0.322962i	0.526940	−	0.849902i	$-0.323339\pi$
$881$	−9.58605	−	9.58605i	−0.322962	−	0.322962i	−0.849902	+	0.526940i	$0.823339\pi$
$882$	−7.30471	−	6.65375i	−0.245962	−	0.224043i
$883$	0.679748	+	3.41732i	0.0228753	+	0.115002i	0.990536	−	0.137254i	$-0.0438276\pi$
$883$	0.679748	+	3.41732i	0.0228753	+	0.115002i	−0.967661	+	0.252256i	$0.918828\pi$
$884$	−10.8303	−	36.3524i	−0.364264	−	1.22267i
$885$	−8.69322	+	5.80862i	−0.292219	+	0.195255i
$886$	−33.4925	−	20.1879i	−1.12520	−	0.678227i
$887$	21.5254	+	51.9668i	0.722751	+	1.74487i	0.665360	+	0.746523i	$0.268278\pi$
$887$	21.5254	+	51.9668i	0.722751	+	1.74487i	0.0573913	+	0.998352i	$0.481722\pi$
$888$	4.00626	−	15.5025i	0.134441	−	0.520230i
$889$	0.459300	−	1.10885i	0.0154044	−	0.0371896i
$890$	18.5513	+	25.1439i	0.621841	+	0.842826i
$891$	−0.117921	+	0.592829i	−0.00395050	+	0.0198605i
$892$	−27.8346	+	33.5748i	−0.931971	+	1.12417i
$893$	14.7245	−	22.0368i	0.492738	−	0.737434i
$894$	−5.16931	+	14.3348i	−0.172888	+	0.479428i
$895$	8.96053			0.299517
$896$	−1.23077	+	0.416367i	−0.0411172	+	0.0139099i
$897$	1.40020			0.0467514
$898$	−10.8527	+	30.0951i	−0.362158	+	1.00429i
$899$	−11.3044	+	16.9183i	−0.377024	+	0.564257i
$900$	−4.30536	+	5.19323i	−0.143512	+	0.173108i
$901$	2.28172	−	11.4710i	0.0760151	−	0.382154i
$902$	−4.13357	−	5.60253i	−0.137633	−	0.186544i
$903$	−0.111840	+	0.270005i	−0.00372179	+	0.00898520i
$904$	−20.9631	−	5.41742i	−0.697221	−	0.180181i
$905$	−1.82666	−	4.40995i	−0.0607203	−	0.146592i
$906$	−8.41183	−	5.07032i	−0.279464	−	0.168450i
$907$	38.7268	−	25.8764i	1.28590	−	0.859212i	0.290677	−	0.956821i	$-0.406120\pi$
$907$	38.7268	−	25.8764i	1.28590	−	0.859212i	0.995225	+	0.0976092i	$0.0311195\pi$
$908$	−13.7044	−	45.9994i	−0.454797	−	1.52654i
$909$	1.82771	+	9.18850i	0.0606212	+	0.304763i
$910$	−0.456775	−	0.416069i	−0.0151419	−	0.0137926i
$911$	−11.3071	−	11.3071i	−0.374620	−	0.374620i	0.494537	−	0.869157i	$-0.335338\pi$
$911$	−11.3071	−	11.3071i	−0.374620	−	0.374620i	−0.869157	+	0.494537i	$0.835338\pi$
$912$	−14.2407	−	2.98014i	−0.471556	−	0.0986822i
$913$	−4.75970	+	4.75970i	−0.157523	+	0.157523i
$914$	6.31133	−	0.294331i	0.208760	−	0.00973562i
$915$	11.5657	−	2.30057i	0.382352	−	0.0760545i
$916$	−3.72734	−	4.58810i	−0.123155	−	0.151595i
$917$	0.499356	+	0.747339i	0.0164902	+	0.0246793i
$918$	2.16348	+	8.72911i	0.0714056	+	0.288104i
$919$	−33.8759	+	14.0319i	−1.11746	+	0.462869i	−0.863502	−	0.504345i	$-0.831734\pi$
$919$	−33.8759	+	14.0319i	−1.11746	+	0.462869i	−0.253962	+	0.967214i	$0.581734\pi$
$920$	1.12813	+	1.26350i	0.0371932	+	0.0416565i
$921$	−16.5340	−	6.84862i	−0.544815	−	0.225670i
$922$	22.7215	+	3.42816i	0.748294	+	0.112901i
$923$	−34.2949	−	6.82168i	−1.12883	−	0.224538i
$924$	0.0648352	+	0.122762i	0.00213292	+	0.00403858i
$925$	−15.8761	−	10.6081i	−0.522004	−	0.348792i
$926$	−16.3652	+	7.69046i	−0.537795	+	0.252724i
$927$		−	17.4197i		−	0.572137i
$928$	22.1542	+	20.5867i	0.727247	+	0.675790i
$929$			12.7842i			0.419435i	0.977762	+	0.209717i	$0.0672544\pi$
$929$			12.7842i			0.419435i	−0.977762	+	0.209717i	$0.932746\pi$
$930$	−2.92005	−	6.21383i	−0.0957521	−	0.203760i
$931$	−21.1302	−	14.1187i	−0.692514	−	0.462723i
$932$	20.0597	+	6.19411i	0.657077	+	0.202895i
$933$	−27.6303	−	5.49602i	−0.904577	−	0.179932i
$934$	0.531997	−	3.52602i	0.0174075	−	0.115375i
$935$	−4.52979	−	1.87630i	−0.148140	−	0.0613616i
$936$	−3.66343	+	7.59856i	−0.119743	+	0.248367i
$937$	−15.3253	+	6.34795i	−0.500656	+	0.207379i	−0.618696	−	0.785630i	$-0.712339\pi$
$937$	−15.3253	+	6.34795i	−0.500656	+	0.207379i	0.118040	+	0.993009i	$0.462339\pi$
$938$	0.743327	−	0.184231i	0.0242705	−	0.00601537i
$939$	−5.07091	−	7.58916i	−0.165483	−	0.247663i
$940$	1.91401	−	18.4905i	0.0624282	−	0.603092i
$941$	5.92737	−	1.17903i	0.193227	−	0.0384352i	−0.0975282	−	0.995233i	$-0.531094\pi$
$941$	5.92737	−	1.17903i	0.193227	−	0.0384352i	0.290755	+	0.956798i	$0.406094\pi$
$942$	−0.329109	−	7.05706i	−0.0107229	−	0.229931i
$943$	2.70392	−	2.70392i	0.0880517	−	0.0880517i
$944$	32.7843	+	0.325979i	1.06704	+	0.0106097i
$945$	0.103584	+	0.103584i	0.00336960	+	0.00336960i
$946$	−1.46486	+	1.60817i	−0.0476268	+	0.0522863i
$947$	−1.78007	−	8.94903i	−0.0578446	−	0.290804i	0.941025	−	0.338337i	$-0.109864\pi$
$947$	−1.78007	−	8.94903i	−0.0578446	−	0.290804i	−0.998870	+	0.0475323i	$0.984864\pi$
$948$	24.4037	+	13.2004i	0.792594	+	0.428730i
$949$	−16.1599	+	10.7977i	−0.524571	+	0.350507i
$950$	−8.95658	+	14.8593i	−0.290590	+	0.482098i
$951$	−2.58727	−	6.24621i	−0.0838979	−	0.202547i
$952$	1.64989	+	1.24282i	0.0534732	+	0.0402800i
$953$	13.0915	−	31.6057i	0.424076	−	1.02381i	−0.557057	−	0.830474i	$-0.688070\pi$
$953$	13.0915	−	31.6057i	0.424076	−	1.02381i	0.981133	−	0.193335i	$-0.0619304\pi$
$954$	−2.09299	+	1.54422i	−0.0677631	+	0.0499959i
$955$	0.0449892	−	0.226176i	0.00145582	−	0.00731889i
$956$	−15.1482	+	1.41597i	−0.489929	+	0.0457957i
$957$	1.79531	−	2.68687i	0.0580341	−	0.0868542i
$958$	−36.0871	−	13.0135i	−1.16592	−	0.420446i
$959$	−1.13707			−0.0367179
$960$	−9.80831	+	2.81628i	−0.316562	+	0.0908951i
$961$	16.5146			0.532729
$962$	−22.4612	−	8.09977i	−0.724177	−	0.261147i
$963$	−5.38973	+	8.06631i	−0.173682	+	0.259933i
$964$	−3.41674	−	36.5528i	−0.110046	−	1.17729i
$965$	0.494240	−	2.48471i	0.0159101	−	0.0799857i
$966$	−0.0613571	+	0.0452696i	−0.00197413	+	0.00145652i
$967$	10.2665	−	24.7856i	0.330150	−	0.797052i	−0.668430	−	0.743775i	$-0.733033\pi$
$967$	10.2665	−	24.7856i	0.330150	−	0.797052i	0.998580	−	0.0532769i	$-0.0169666\pi$
$968$	−4.19156	−	29.7858i	−0.134722	−	0.957353i
$969$	8.85152	+	21.3695i	0.284352	+	0.686486i
$970$	−10.0160	+	16.6169i	−0.321596	+	0.533538i
$971$	30.1222	−	20.1270i	0.966669	−	0.645908i	0.0312735	−	0.999511i	$-0.490044\pi$
$971$	30.1222	−	20.1270i	0.966669	−	0.645908i	0.935395	+	0.353603i	$0.115044\pi$
$972$	0.951551	−	1.75913i	0.0305210	−	0.0564242i
$973$	−0.0603948	−	0.303625i	−0.00193617	−	0.00973377i
$974$	28.0880	−	30.8359i	0.899998	−	0.988047i
$975$	7.11308	+	7.11308i	0.227801	+	0.227801i
$976$	−34.0215	−	14.4901i	−1.08900	−	0.463818i
$977$	17.6946	−	17.6946i	0.566101	−	0.566101i	−0.364933	−	0.931034i	$-0.618908\pi$
$977$	17.6946	−	17.6946i	0.566101	−	0.566101i	0.931034	+	0.364933i	$0.118908\pi$
$978$	−1.49594	−	32.0773i	−0.0478349	−	1.02572i
$979$	−10.2687	+	2.04257i	−0.328188	+	0.0652807i
$980$	−17.7297	−	1.83527i	−0.566355	−	0.0586254i
$981$	10.2609	+	15.3565i	0.327606	+	0.490297i
$982$	3.97641	−	0.985540i	0.126892	−	0.0314498i
$983$	−37.7618	+	15.6415i	−1.20442	+	0.498885i	−0.892423	−	0.451199i	$-0.850996\pi$
$983$	−37.7618	+	15.6415i	−1.20442	+	0.498885i	−0.311993	+	0.950085i	$0.600996\pi$
$984$	7.59908	+	21.7479i	0.242250	+	0.693299i
$985$	18.9770	+	7.86053i	0.604658	+	0.250457i
$986$	7.17293	−	47.5415i	0.228433	−	1.51403i
$987$	0.820731	+	0.163254i	0.0261242	+	0.00519642i
$988$	−6.40112	+	20.7301i	−0.203647	+	0.659512i
$989$	−0.993394	−	0.663765i	−0.0315881	−	0.0211065i
$990$	0.463746	+	0.986847i	0.0147388	+	0.0313641i
$991$		−	17.3744i		−	0.551917i	−0.961169	−	0.275959i	$-0.911005\pi$
$991$		−	17.3744i		−	0.551917i	0.961169	−	0.275959i	$-0.0889953\pi$
$992$	−3.42352	+	21.2559i	−0.108697	+	0.674875i
$993$			30.9625i			0.982566i
$994$	1.72336	−	0.809852i	0.0546616	−	0.0256869i
$995$	−14.7454	−	9.85256i	−0.467461	−	0.312347i
$996$	19.6945	−	10.4014i	0.624045	−	0.329581i
$997$	45.0240	+	8.95583i	1.42592	+	0.283634i	0.846933	−	0.531700i	$-0.178447\pi$
$997$	45.0240	+	8.95583i	1.42592	+	0.283634i	0.578991	+	0.815334i	$0.303447\pi$
$998$	−0.827617	−	0.124869i	−0.0261978	−	0.00395265i
$999$	5.23011	+	2.16638i	0.165473	+	0.0685413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.37.10	✓	128
3.2	odd	2		576.2.bd.b.37.7		128
4.3	odd	2		768.2.r.a.241.6		128
64.19	odd	16		768.2.r.a.529.6		128
64.45	even	16	inner	192.2.r.a.109.10	yes	128
192.173	odd	16		576.2.bd.b.109.7		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.37.10	✓	128	1.1	even	1	trivial
192.2.r.a.109.10	yes	128	64.45	even	16	inner
576.2.bd.b.37.7		128	3.2	odd	2
576.2.bd.b.109.7		128	192.173	odd	16
768.2.r.a.241.6		128	4.3	odd	2
768.2.r.a.529.6		128	64.19	odd	16

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.479743 - 1.33036i) q^{2} +(0.555570 - 0.831470i) q^{3} +(-1.53969 - 1.27646i) q^{4} +(0.248853 - 1.25107i) q^{5} +(-0.839620 - 1.13800i) q^{6} +(0.0439483 - 0.106101i) q^{7} +(-2.43680 + 1.43597i) q^{8} +(-0.382683 - 0.923880i) q^{9} +O(q^{10})\)	\(q+(0.479743 - 1.33036i) q^{2} +(0.555570 - 0.831470i) q^{3} +(-1.53969 - 1.27646i) q^{4} +(0.248853 - 1.25107i) q^{5} +(-0.839620 - 1.13800i) q^{6} +(0.0439483 - 0.106101i) q^{7} +(-2.43680 + 1.43597i) q^{8} +(-0.382683 - 0.923880i) q^{9} +(-1.54498 - 0.931254i) q^{10} +(0.502576 - 0.335811i) q^{11} +(-1.91674 + 0.571048i) q^{12} +(0.581842 + 2.92512i) q^{13} +(-0.120068 - 0.109368i) q^{14} +(-0.901970 - 0.901970i) q^{15} +(0.741316 + 3.93071i) q^{16} +(4.49661 - 4.49661i) q^{17} +(-1.41268 + 0.0658809i) q^{18} +(-3.56740 + 0.709600i) q^{19} +(-1.98009 + 1.60861i) q^{20} +(-0.0638030 - 0.0954880i) q^{21} +(-0.205641 - 0.829708i) q^{22} +(0.433747 - 0.179664i) q^{23} +(-0.159847 + 2.82391i) q^{24} +(3.11615 + 1.29075i) q^{25} +(4.17058 + 0.629246i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(-0.203100 + 0.107264i) q^{28} +(4.44520 + 2.97019i) q^{29} +(-1.63265 + 0.767228i) q^{30} +3.80597i q^{31} +(5.58488 + 0.899513i) q^{32} -0.604443i q^{33} +(-3.82488 - 8.13931i) q^{34} +(-0.121802 - 0.0813857i) q^{35} +(-0.590077 + 1.91097i) q^{36} +(-5.55225 - 1.10441i) q^{37} +(-0.767413 + 5.08634i) q^{38} +(2.75540 + 1.14132i) q^{39} +(1.19009 + 3.40595i) q^{40} +(7.52493 - 3.11693i) q^{41} +(-0.157642 + 0.0390711i) q^{42} +(-1.41382 - 2.11593i) q^{43} +(-1.20246 - 0.124471i) q^{44} +(-1.25107 + 0.248853i) q^{45} +(-0.0309301 - 0.663231i) q^{46} +(-5.15240 + 5.15240i) q^{47} +(3.68012 + 1.56740i) q^{48} +(4.94042 + 4.94042i) q^{49} +(3.21211 - 3.52636i) q^{50} +(-1.24061 - 6.23698i) q^{51} +(2.83793 - 5.24648i) q^{52} +(1.52923 - 1.02180i) q^{53} +(-0.730064 + 1.21120i) q^{54} +(-0.295055 - 0.712325i) q^{55} +(0.0452641 + 0.321654i) q^{56} +(-1.39193 + 3.36042i) q^{57} +(6.08396 - 4.48877i) q^{58} +(1.59905 - 8.03898i) q^{59} +(0.237432 + 2.54008i) q^{60} +(-5.13608 + 7.68668i) q^{61} +(5.06330 + 1.82589i) q^{62} -0.114842 q^{63} +(3.87598 - 6.99834i) q^{64} +3.80431 q^{65} +(-0.804125 - 0.289977i) q^{66} +(-2.61967 + 3.92062i) q^{67} +(-12.6631 + 1.18368i) q^{68} +(0.0915919 - 0.460464i) q^{69} +(-0.166706 + 0.122996i) q^{70} +(-4.48669 + 10.8318i) q^{71} +(2.25919 + 1.70179i) q^{72} +(2.49380 + 6.02057i) q^{73} +(-4.13291 + 6.85664i) q^{74} +(2.80446 - 1.87388i) q^{75} +(6.39848 + 3.46107i) q^{76} +(-0.0135423 - 0.0680819i) q^{77} +(2.84025 - 3.11812i) q^{78} +(-9.80938 - 9.80938i) q^{79} +(5.10206 + 0.0507306i) q^{80} +(-0.707107 + 0.707107i) q^{81} +(-0.536595 - 11.5062i) q^{82} +(-10.9223 + 2.17257i) q^{83} +(-0.0236491 + 0.228464i) q^{84} +(-4.50657 - 6.74456i) q^{85} +(-3.49320 + 0.865779i) q^{86} +(4.93924 - 2.04590i) q^{87} +(-0.742463 + 1.53999i) q^{88} +(-16.0029 - 6.62864i) q^{89} +(-0.269128 + 1.78375i) q^{90} +(0.335927 + 0.0668201i) q^{91} +(-0.897171 - 0.277032i) q^{92} +(3.16455 + 2.11448i) q^{93} +(4.38270 + 9.32636i) q^{94} +4.63965i q^{95} +(3.85071 - 4.14392i) q^{96} -10.7554i q^{97} +(8.94265 - 4.20239i) q^{98} +(-0.502576 - 0.335811i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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