LMFDB - Embedded newform 675.2.ba.a.518.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(32,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("675.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$12$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			518.7
Character	$\chi$	$=$	675.518
Dual form			675.2.ba.a.632.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0777805 + 0.00680491i) q^{2} +(1.54232 + 0.788185i) q^{3} +(-1.96361 - 0.346238i) q^{4} +(0.114599 + 0.0718008i) q^{6} +(-1.14874 - 0.804356i) q^{7} +(-0.301209 - 0.0807087i) q^{8} +(1.75753 + 2.43127i) q^{9} +(-1.25188 + 3.43951i) q^{11} +(-2.75563 - 2.08170i) q^{12} +(0.326983 + 3.73743i) q^{13} +(-0.0838760 - 0.0703803i) q^{14} +(3.72443 + 1.35558i) q^{16} +(-4.17846 + 1.11962i) q^{17} +(0.120157 + 0.201066i) q^{18} +(-1.40048 + 0.808565i) q^{19} +(-1.13775 - 2.14600i) q^{21} +(-0.120777 + 0.259008i) q^{22} +(3.27482 + 4.67693i) q^{23} +(-0.400948 - 0.361887i) q^{24} +0.292925i q^{26} +(0.794382 + 5.13507i) q^{27} +(1.97718 + 1.97718i) q^{28} +(3.26399 - 2.73881i) q^{29} +(0.336874 - 1.91051i) q^{31} +(0.845700 + 0.394356i) q^{32} +(-4.64178 + 4.31813i) q^{33} +(-0.332622 + 0.0586502i) q^{34} +(-2.60930 - 5.38260i) q^{36} +(2.07996 + 7.76253i) q^{37} +(-0.114432 + 0.0533605i) q^{38} +(-2.44148 + 6.02206i) q^{39} +(-2.08450 + 2.48421i) q^{41} +(-0.0738912 - 0.174659i) q^{42} +(-0.347912 - 0.746099i) q^{43} +(3.64909 - 6.32042i) q^{44} +(0.222891 + 0.386059i) q^{46} +(-0.661922 + 0.945323i) q^{47} +(4.67583 + 5.02629i) q^{48} +(-1.72153 - 4.72986i) q^{49} +(-7.32701 - 1.56659i) q^{51} +(0.651973 - 7.45209i) q^{52} +(-7.50182 + 7.50182i) q^{53} +(0.0268437 + 0.404814i) q^{54} +(0.281092 + 0.334993i) q^{56} +(-2.79729 + 0.143235i) q^{57} +(0.272512 - 0.190815i) q^{58} +(9.85710 - 3.58769i) q^{59} +(-1.72247 - 9.76861i) q^{61} +(0.0392030 - 0.146308i) q^{62} +(-0.0633310 - 4.20658i) q^{63} +(-6.80182 - 3.92703i) q^{64} +(-0.390424 + 0.304279i) q^{66} +(-14.7353 + 1.28917i) q^{67} +(8.59253 - 0.751749i) q^{68} +(1.36455 + 9.79451i) q^{69} +(8.12470 + 4.69080i) q^{71} +(-0.333158 - 0.874169i) q^{72} +(0.0713724 - 0.266365i) q^{73} +(0.108957 + 0.617928i) q^{74} +(3.02995 - 1.10281i) q^{76} +(4.20468 - 2.94415i) q^{77} +(-0.230879 + 0.451785i) q^{78} +(-7.24149 - 8.63007i) q^{79} +(-2.82219 + 8.54607i) q^{81} +(-0.179038 + 0.179038i) q^{82} +(1.48834 - 17.0118i) q^{83} +(1.49107 + 4.60784i) q^{84} +(-0.0219836 - 0.0603995i) q^{86} +(7.19282 - 1.65151i) q^{87} +(0.654676 - 0.934974i) q^{88} +(6.77753 + 11.7390i) q^{89} +(2.63061 - 4.55635i) q^{91} +(-4.81115 - 10.3175i) q^{92} +(2.02540 - 2.68110i) q^{93} +(-0.0579174 + 0.0690233i) q^{94} +(0.993517 + 1.27479i) q^{96} +(12.5700 - 5.86150i) q^{97} +(-0.101715 - 0.379605i) q^{98} +(-10.5626 + 3.00137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 12 q^{6} - 48 q^{21} + 84 q^{36} + 36 q^{41} - 84 q^{51} - 324 q^{56} + 36 q^{61} - 288 q^{66} - 144 q^{71} - 216 q^{76} - 132 q^{81} - 288 q^{86} + 36 q^{91} + 132 q^{96}+O(q^{100}) $ 144 * q + 12 * q^6 - 48 * q^21 + 84 * q^36 + 36 * q^41 - 84 * q^51 - 324 * q^56 + 36 * q^61 - 288 * q^66 - 144 * q^71 - 216 * q^76 - 132 * q^81 - 288 * q^86 + 36 * q^91 + 132 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.0777805	+	0.00680491i	0.0549991	+	0.00481180i	0.114622	−	0.993409i	$-0.463434\pi$
$2$	0.0777805	+	0.00680491i	0.0549991	+	0.00481180i	−0.0596230	+	0.998221i	$0.518990\pi$
$3$	1.54232	+	0.788185i	0.890461	+	0.455059i
$3$	1.54232	+	0.788185i	0.890461	+	0.455059i
$4$	−1.96361	−	0.346238i	−0.981806	−	0.173119i
$5$		0			0
$5$		0			0
$6$	0.114599	+	0.0718008i	0.0467849	+	0.0293126i
$7$	−1.14874	−	0.804356i	−0.434183	−	0.304018i	0.335976	−	0.941871i	$-0.390934\pi$
$7$	−1.14874	−	0.804356i	−0.434183	−	0.304018i	−0.770158	+	0.637853i	$0.779823\pi$
$8$	−0.301209	−	0.0807087i	−0.106493	−	0.0285348i
$9$	1.75753	+	2.43127i	0.585843	+	0.810425i
$10$		0			0
$11$	−1.25188	+	3.43951i	−0.377456	+	1.03705i	0.594951	+	0.803762i	$0.297171\pi$
$11$	−1.25188	+	3.43951i	−0.377456	+	1.03705i	−0.972407	+	0.233290i	$0.925051\pi$
$12$	−2.75563	−	2.08170i	−0.795481	−	0.600935i
$13$	0.326983	+	3.73743i	0.0906888	+	1.03658i	0.896097	+	0.443858i	$0.146390\pi$
$13$	0.326983	+	3.73743i	0.0906888	+	1.03658i	−0.805408	+	0.592720i	$0.798054\pi$
$14$	−0.0838760	−	0.0703803i	−0.0224168	−	0.0188099i
$15$		0			0
$16$	3.72443	+	1.35558i	0.931109	+	0.338896i
$17$	−4.17846	+	1.11962i	−1.01343	+	0.271547i	−0.727060	−	0.686574i	$-0.759114\pi$
$17$	−4.17846	+	1.11962i	−1.01343	+	0.271547i	−0.286366	+	0.958120i	$0.592447\pi$
$18$	0.120157	+	0.201066i	0.0283212	+	0.0473916i
$19$	−1.40048	+	0.808565i	−0.321291	+	0.185498i	−0.651968	−	0.758246i	$-0.726056\pi$
$19$	−1.40048	+	0.808565i	−0.321291	+	0.185498i	0.330677	+	0.943744i	$0.392723\pi$
$20$		0			0
$21$	−1.13775	−	2.14600i	−0.248277	−	0.468295i
$22$	−0.120777	+	0.259008i	−0.0257498	+	0.0552207i
$23$	3.27482	+	4.67693i	0.682847	+	0.975207i	0.999643	+	0.0267134i	$0.00850416\pi$
$23$	3.27482	+	4.67693i	0.682847	+	0.975207i	−0.316796	+	0.948494i	$0.602607\pi$
$24$	−0.400948	−	0.361887i	−0.0818432	−	0.0738699i
$25$		0			0
$26$			0.292925i			0.0574472i
$27$	0.794382	+	5.13507i	0.152879	+	0.988245i
$28$	1.97718	+	1.97718i	0.373652	+	0.373652i
$29$	3.26399	−	2.73881i	0.606107	−	0.508584i	−0.287295	−	0.957842i	$-0.592756\pi$
$29$	3.26399	−	2.73881i	0.606107	−	0.508584i	0.893402	+	0.449258i	$0.148312\pi$
$30$		0			0
$31$	0.336874	−	1.91051i	0.0605043	−	0.343137i	−0.939496	−	0.342561i	$-0.888706\pi$
$31$	0.336874	−	1.91051i	0.0605043	−	0.343137i	1.00000		0.000575745i	$-0.000183265\pi$
$32$	0.845700	+	0.394356i	0.149500	+	0.0697130i
$33$	−4.64178	+	4.31813i	−0.808029	+	0.751689i
$34$	−0.332622	+	0.0586502i	−0.0570441	+	0.0100584i
$35$		0			0
$36$	−2.60930	−	5.38260i	−0.434884	−	0.897100i
$37$	2.07996	+	7.76253i	0.341944	+	1.27615i	0.896142	+	0.443768i	$0.146358\pi$
$37$	2.07996	+	7.76253i	0.341944	+	1.27615i	−0.554198	+	0.832385i	$0.686975\pi$
$38$	−0.114432	+	0.0533605i	−0.0185633	+	0.00865621i
$39$	−2.44148	+	6.02206i	−0.390949	+	0.964301i
$40$		0			0
$41$	−2.08450	+	2.48421i	−0.325544	+	0.387968i	−0.903848	−	0.427853i	$-0.859270\pi$
$41$	−2.08450	+	2.48421i	−0.325544	+	0.387968i	0.578304	+	0.815821i	$0.303715\pi$
$42$	−0.0738912	−	0.174659i	−0.0114017	−	0.0269505i
$43$	−0.347912	−	0.746099i	−0.0530561	−	0.113779i	0.877992	−	0.478674i	$-0.158883\pi$
$43$	−0.347912	−	0.746099i	−0.0530561	−	0.113779i	−0.931049	+	0.364895i	$0.881105\pi$
$44$	3.64909	−	6.32042i	0.550122	−	0.952839i
$45$		0			0
$46$	0.222891	+	0.386059i	0.0328635	+	0.0569212i
$47$	−0.661922	+	0.945323i	−0.0965513	+	0.137889i	−0.864521	−	0.502597i	$-0.832378\pi$
$47$	−0.661922	+	0.945323i	−0.0965513	+	0.137889i	0.767970	+	0.640486i	$0.221267\pi$
$48$	4.67583	+	5.02629i	0.674899	+	0.725483i
$49$	−1.72153	−	4.72986i	−0.245932	−	0.675694i
$50$		0			0
$51$	−7.32701	−	1.56659i	−1.02599	−	0.219367i
$52$	0.651973	−	7.45209i	0.0904124	−	1.03342i
$53$	−7.50182	+	7.50182i	−1.03045	+	1.03045i	−0.0309335	+	0.999521i	$0.509848\pi$
$53$	−7.50182	+	7.50182i	−1.03045	+	1.03045i	−0.999521	+	0.0309335i	$0.990152\pi$
$54$	0.0268437	+	0.404814i	0.00365297	+	0.0550882i
$55$		0			0
$56$	0.281092	+	0.334993i	0.0375625	+	0.0447653i
$57$	−2.79729	+	0.143235i	−0.370510	+	0.0189719i
$58$	0.272512	−	0.190815i	0.0357826	−	0.0250552i
$59$	9.85710	−	3.58769i	1.28328	−	0.467077i	0.391767	−	0.920064i	$-0.371864\pi$
$59$	9.85710	−	3.58769i	1.28328	−	0.467077i	0.891517	+	0.452987i	$0.149642\pi$
$60$		0			0
$61$	−1.72247	−	9.76861i	−0.220540	−	1.25074i	−0.871031	−	0.491228i	$-0.836548\pi$
$61$	−1.72247	−	9.76861i	−0.220540	−	1.25074i	0.650491	−	0.759514i	$-0.274563\pi$
$62$	0.0392030	−	0.146308i	0.00497879	−	0.0185811i
$63$	−0.0633310	−	4.20658i	−0.00797896	−	0.529979i
$64$	−6.80182	−	3.92703i	−0.850227	−	0.490879i
$65$		0			0
$66$	−0.390424	+	0.304279i	−0.0480579	+	0.0374542i
$67$	−14.7353	+	1.28917i	−1.80020	+	0.157497i	−0.937447	−	0.348128i	$-0.886817\pi$
$67$	−14.7353	+	1.28917i	−1.80020	+	0.157497i	−0.862753	+	0.505625i	$0.831262\pi$
$68$	8.59253	−	0.751749i	1.04200	−	0.0911630i
$69$	1.36455	+	9.79451i	0.164272	+	1.17912i
$70$		0			0
$71$	8.12470	+	4.69080i	0.964224	+	0.556695i	0.897471	−	0.441074i	$-0.145403\pi$
$71$	8.12470	+	4.69080i	0.964224	+	0.556695i	0.0667536	+	0.997769i	$0.478736\pi$
$72$	−0.333158	−	0.874169i	−0.0392630	−	0.103022i
$73$	0.0713724	−	0.266365i	0.00835350	−	0.0311757i	−0.961623	−	0.274373i	$-0.911530\pi$
$73$	0.0713724	−	0.266365i	0.00835350	−	0.0311757i	0.969977	+	0.243197i	$0.0781963\pi$
$74$	0.108957	+	0.617928i	0.0126660	+	0.0718326i
$75$		0			0
$76$	3.02995	−	1.10281i	0.347559	−	0.126501i
$77$	4.20468	−	2.94415i	0.479167	−	0.335517i
$78$	−0.230879	+	0.451785i	−0.0261419	+	0.0511545i
$79$	−7.24149	−	8.63007i	−0.814732	−	0.970959i	0.185199	−	0.982701i	$-0.440707\pi$
$79$	−7.24149	−	8.63007i	−0.814732	−	0.970959i	−0.999931	+	0.0117417i	$0.996262\pi$
$80$		0			0
$81$	−2.82219	+	8.54607i	−0.313577	+	0.949563i
$82$	−0.179038	+	0.179038i	−0.0197715	+	0.0197715i
$83$	1.48834	−	17.0118i	0.163366	−	1.86728i	−0.265758	−	0.964040i	$-0.585622\pi$
$83$	1.48834	−	17.0118i	0.163366	−	1.86728i	0.429125	−	0.903245i	$-0.358822\pi$
$84$	1.49107	+	4.60784i	0.162689	+	0.502756i
$85$		0			0
$86$	−0.0219836	−	0.0603995i	−0.00237055	−	0.00651304i
$87$	7.19282	−	1.65151i	0.771151	−	0.177060i
$88$	0.654676	−	0.934974i	0.0697886	−	0.0996685i
$89$	6.77753	+	11.7390i	0.718417	+	1.24433i	0.961627	+	0.274360i	$0.0884662\pi$
$89$	6.77753	+	11.7390i	0.718417	+	1.24433i	−0.243210	+	0.969974i	$0.578201\pi$
$90$		0			0
$91$	2.63061	−	4.55635i	0.275763	−	0.477635i
$92$	−4.81115	−	10.3175i	−0.501597	−	1.07568i
$93$	2.02540	−	2.68110i	0.210024	−	0.278017i
$94$	−0.0579174	+	0.0690233i	−0.00597373	+	0.00711921i
$95$		0			0
$96$	0.993517	+	1.27479i	0.101400	+	0.130108i
$97$	12.5700	−	5.86150i	1.27629	−	0.595145i	0.338051	−	0.941128i	$-0.390232\pi$
$97$	12.5700	−	5.86150i	1.27629	−	0.595145i	0.938241	+	0.345983i	$0.112454\pi$
$98$	−0.101715	−	0.379605i	−0.0102748	−	0.0383459i
$99$	−10.5626	+	3.00137i	−1.06158	+	0.301649i
$100$		0			0
$101$	6.29402	−	1.10980i	0.626278	−	0.110430i	0.148503	−	0.988912i	$-0.452555\pi$
$101$	6.29402	−	1.10980i	0.626278	−	0.110430i	0.477775	+	0.878482i	$0.341443\pi$
$102$	−0.559238	−	0.171710i	−0.0553728	−	0.0170018i
$103$	−5.42718	−	2.53074i	−0.534756	−	0.249361i	0.136430	−	0.990650i	$-0.456437\pi$
$103$	−5.42718	−	2.53074i	−0.534756	−	0.249361i	−0.671186	+	0.741289i	$0.734215\pi$
$104$	0.203153	−	1.15214i	0.0199208	−	0.112977i
$105$		0			0
$106$	−0.634545	+	0.532446i	−0.0616324	+	0.0517158i
$107$	9.48052	+	9.48052i	0.916517	+	0.916517i	0.996774	−	0.0802575i	$-0.0255743\pi$
$107$	9.48052	+	9.48052i	0.916517	+	0.916517i	−0.0802575	+	0.996774i	$0.525574\pi$
$108$	0.218097	−	10.3583i	0.0209864	−	0.996731i
$109$		−	10.7098i		−	1.02581i	−0.858444	−	0.512907i	$-0.828569\pi$
$109$		−	10.7098i		−	1.02581i	0.858444	−	0.512907i	$-0.171431\pi$
$110$		0			0
$111$	−2.91034	+	13.6117i	−0.276237	+	1.29197i
$112$	−3.18803	−	4.55299i	−0.301241	−	0.430217i
$113$	−1.87900	+	4.02953i	−0.176762	+	0.379067i	−0.974649	−	0.223740i	$-0.928173\pi$
$113$	−1.87900	+	4.02953i	−0.176762	+	0.379067i	0.797887	+	0.602807i	$0.205951\pi$
$114$	−0.218549	−	0.00789441i	−0.0204690	−	0.000739379i
$115$		0			0
$116$	−7.35749	+	4.24785i	−0.683125	+	0.394403i
$117$	−8.51205	+	7.36363i	−0.786939	+	0.680768i
$118$	0.791104	−	0.211976i	0.0728270	−	0.0195139i
$119$	5.70054	+	2.07483i	0.522567	+	0.190199i
$120$		0			0
$121$	−1.83654	−	1.54104i	−0.166958	−	0.140095i
$122$	−0.0675000	−	0.771528i	−0.00611116	−	0.0698509i
$123$	−5.17299	+	2.18848i	−0.466433	+	0.197329i
$124$	−1.32298	+	3.63485i	−0.118807	+	0.326419i
$125$		0			0
$126$	0.0236995	−	0.327621i	0.00211132	−	0.0291868i
$127$	19.7795	+	5.29991i	1.75515	+	0.470291i	0.985713	−	0.168434i	$-0.0538709\pi$
$127$	19.7795	+	5.29991i	1.75515	+	0.470291i	0.769436	+	0.638724i	$0.220538\pi$
$128$	−2.03107	−	1.42217i	−0.179523	−	0.125703i
$129$	0.0514717	−	1.42495i	0.00453183	−	0.125460i
$130$		0			0
$131$	19.0340	+	3.35621i	1.66301	+	0.293233i	0.924549	−	0.381064i	$-0.124442\pi$
$131$	19.0340	+	3.35621i	1.66301	+	0.293233i	0.738460	+	0.674297i	$0.235553\pi$
$132$	10.6097	−	6.87197i	0.923460	−	0.598128i
$133$	2.25916	+	0.197651i	0.195894	+	0.0171385i
$134$	−1.15489			−0.0997672
$135$		0			0
$136$	1.34895			0.115672
$137$	−8.99783	−	0.787208i	−0.768736	−	0.0672557i	−0.303961	−	0.952684i	$-0.598309\pi$
$137$	−8.99783	−	0.787208i	−0.768736	−	0.0672557i	−0.464775	+	0.885429i	$0.653865\pi$
$138$	0.0394845	+	0.771107i	0.00336114	+	0.0656410i
$139$	−5.38293	−	0.949156i	−0.456574	−	0.0805063i	−0.0593688	−	0.998236i	$-0.518909\pi$
$139$	−5.38293	−	0.949156i	−0.456574	−	0.0805063i	−0.397205	+	0.917730i	$0.630020\pi$
$140$		0			0
$141$	−1.76599	+	0.936277i	−0.148723	+	0.0788487i
$142$	0.600022	+	0.420140i	0.0503528	+	0.0352574i
$143$	−13.2643	−	3.55416i	−1.10922	−	0.297213i
$144$	3.25000	+	11.4376i	0.270833	+	0.953133i
$145$		0			0
$146$	0.00736397	−	0.0202323i	0.000609446	−	0.00167444i
$147$	1.07285	−	8.65185i	0.0884872	−	0.713593i
$148$	−1.39656	−	15.9628i	−0.114797	−	1.31213i
$149$	−0.505618	−	0.424264i	−0.0414218	−	0.0347570i	0.621842	−	0.783143i	$-0.286385\pi$
$149$	−0.505618	−	0.424264i	−0.0414218	−	0.0347570i	−0.663264	+	0.748386i	$0.730829\pi$
$150$		0			0
$151$	0.0862252	+	0.0313834i	0.00701691	+	0.00255395i	0.345526	−	0.938409i	$-0.387700\pi$
$151$	0.0862252	+	0.0313834i	0.00701691	+	0.00255395i	−0.338509	+	0.940963i	$0.609923\pi$
$152$	0.487094	−	0.130516i	0.0395085	−	0.0105863i
$153$	−10.0659	−	8.19123i	−0.813776	−	0.662222i
$154$	0.347076	−	0.200385i	0.0279682	−	0.0161475i
$155$		0			0
$156$	6.87918	−	10.9797i	0.550775	−	0.879076i
$157$	−6.46880	+	13.8724i	−0.516266	+	1.10714i	0.459471	+	0.888193i	$0.348039\pi$
$157$	−6.46880	+	13.8724i	−0.516266	+	1.10714i	−0.975737	+	0.218944i	$0.929739\pi$
$158$	−0.504520	−	0.720529i	−0.0401374	−	0.0573222i
$159$	−17.4831	+	5.65742i	−1.38650	+	0.448662i
$160$		0			0
$161$		−	8.00670i		−	0.631016i
$162$	−0.277667	+	0.645512i	−0.0218156	+	0.0507162i
$163$	−5.11206	−	5.11206i	−0.400408	−	0.400408i	0.477969	−	0.878377i	$-0.341373\pi$
$163$	−5.11206	−	5.11206i	−0.400408	−	0.400408i	−0.878377	+	0.477969i	$0.841373\pi$
$164$	4.95328	−	4.15629i	0.386786	−	0.324552i
$165$		0			0
$166$	0.231527	−	1.31306i	0.0179700	−	0.101913i
$167$	13.2408	+	6.17428i	1.02460	+	0.477780i	0.860924	−	0.508734i	$-0.169886\pi$
$167$	13.2408	+	6.17428i	1.02460	+	0.477780i	0.163679	+	0.986514i	$0.447664\pi$
$168$	0.169499	+	0.738220i	0.0130771	+	0.0569549i
$169$	−1.05900	+	0.186730i	−0.0814615	+	0.0143639i
$170$		0			0
$171$	−4.42722	−	1.98387i	−0.338558	−	0.151710i
$172$	0.424836	+	1.58551i	0.0323934	+	0.120894i
$173$	8.77812	−	4.09330i	0.667388	−	0.311208i	−0.0592355	−	0.998244i	$-0.518866\pi$
$173$	8.77812	−	4.09330i	0.667388	−	0.311208i	0.726623	+	0.687036i	$0.241089\pi$
$174$	0.570699	−	0.0795085i	0.0432646	−	0.00602753i
$175$		0			0
$176$	−9.32509	+	11.1132i	−0.702905	+	0.837689i
$177$	18.0306	+	2.23584i	1.35526	+	0.168056i
$178$	0.447276	+	0.959187i	0.0335248	+	0.0718941i
$179$	9.40526	−	16.2904i	0.702982	−	1.21760i	−0.264433	−	0.964404i	$-0.585185\pi$
$179$	9.40526	−	16.2904i	0.702982	−	1.21760i	0.967415	−	0.253197i	$-0.0814820\pi$
$180$		0			0
$181$	−5.53790	−	9.59192i	−0.411629	−	0.712962i	0.583439	−	0.812157i	$-0.301707\pi$
$181$	−5.53790	−	9.59192i	−0.411629	−	0.712962i	−0.995068	+	0.0991950i	$0.968373\pi$
$182$	0.235616	−	0.336494i	0.0174650	−	0.0249426i
$183$	5.04287	−	16.4240i	0.372780	−	1.21410i
$184$	−0.608936	−	1.67304i	−0.0448914	−	0.123338i
$185$		0			0
$186$	0.175781	−	0.194755i	0.0128889	−	0.0142801i
$187$	1.38000	−	15.7735i	0.100916	−	1.15347i
$188$	1.62706	−	1.62706i	0.118666	−	0.118666i
$189$	3.21789	−	6.53783i	0.234067	−	0.475557i
$190$		0			0
$191$	4.33436	+	5.16549i	0.313623	+	0.373762i	0.899711	−	0.436486i	$-0.143777\pi$
$191$	4.33436	+	5.16549i	0.313623	+	0.373762i	−0.586088	+	0.810247i	$0.699333\pi$
$192$	−7.39538	−	11.4179i	−0.533716	−	0.824012i
$193$	1.13686	−	0.796040i	0.0818332	−	0.0573002i	−0.531944	−	0.846780i	$-0.678538\pi$
$193$	1.13686	−	0.796040i	0.0818332	−	0.0573002i	0.613777	+	0.789479i	$0.289649\pi$
$194$	1.01759	−	0.370372i	0.0730586	−	0.0265912i
$195$		0			0
$196$	1.74276	+	9.88366i	0.124483	+	0.705976i
$197$	−5.85076	+	21.8353i	−0.416849	+	1.55570i	0.364253	+	0.931300i	$0.381324\pi$
$197$	−5.85076	+	21.8353i	−0.416849	+	1.55570i	−0.781102	+	0.624403i	$0.785342\pi$
$198$	−0.841989	+	0.161571i	−0.0598375	+	0.0114823i
$199$	5.40542	+	3.12082i	0.383180	+	0.221229i	0.679201	−	0.733952i	$-0.262326\pi$
$199$	5.40542	+	3.12082i	0.383180	+	0.221229i	−0.296021	+	0.955181i	$0.595660\pi$
$200$		0			0
$201$	−23.7427	−	9.62581i	−1.67468	−	0.678952i
$202$	0.497104	−	0.0434909i	0.0349761	−	0.00306001i
$203$	−5.95245	+	0.520772i	−0.417780	+	0.0365510i
$204$	13.8450	+	5.61307i	0.969343	+	0.392993i
$205$		0			0
$206$	−0.404908	−	0.233773i	−0.0282112	−	0.0162878i
$207$	−5.61531	+	16.1818i	−0.390291	+	1.12471i
$208$	−3.84858	+	14.3631i	−0.266851	+	0.995901i
$209$	−1.02784	−	5.82918i	−0.0710973	−	0.403213i
$210$		0			0
$211$	0.707308	−	0.257439i	0.0486931	−	0.0177228i	−0.317559	−	0.948239i	$-0.602863\pi$
$211$	0.707308	−	0.257439i	0.0486931	−	0.0177228i	0.366252	+	0.930516i	$0.380641\pi$
$212$	17.3281	−	12.1333i	1.19010	−	0.833316i
$213$	8.83370	+	13.6385i	0.605275	+	0.934494i
$214$	0.672885	+	0.801914i	0.0459975	+	0.0548177i
$215$		0			0
$216$	0.175170	−	1.61084i	0.0119188	−	0.109604i
$217$	−1.92371	+	1.92371i	−0.130590	+	0.130590i
$218$	0.0728793	−	0.833014i	0.00493601	−	0.0564188i
$219$	0.320025	−	0.354567i	0.0216253	−	0.0239594i
$220$		0			0
$221$	−5.55078	−	15.2506i	−0.373386	−	1.02587i
$222$	−0.318994	+	1.03892i	−0.0214095	+	0.0697280i
$223$	2.77332	−	3.96071i	0.185715	−	0.265229i	−0.715489	−	0.698624i	$-0.753796\pi$
$223$	2.77332	−	3.96071i	0.185715	−	0.265229i	0.901204	+	0.433396i	$0.142685\pi$
$224$	−0.654286	−	1.13326i	−0.0437163	−	0.0757189i
$225$		0			0
$226$	−0.173570	+	0.300633i	−0.0115457	+	0.0199978i
$227$	−5.43745	−	11.6607i	−0.360896	−	0.773945i	−0.999988	−	0.00481463i	$-0.998467\pi$
$227$	−5.43745	−	11.6607i	−0.360896	−	0.773945i	0.639092	−	0.769130i	$-0.279310\pi$
$228$	5.54238	+	0.687269i	0.367053	+	0.0455155i
$229$	0.424504	−	0.505904i	0.0280520	−	0.0334311i	−0.751836	−	0.659350i	$-0.770832\pi$
$229$	0.424504	−	0.505904i	0.0280520	−	0.0334311i	0.779888	+	0.625919i	$0.215276\pi$
$230$		0			0
$231$	8.80551	−	1.22676i	0.579360	−	0.0807151i
$232$	−1.20419	+	0.561522i	−0.0790588	+	0.0368657i
$233$	−2.52986	−	9.44157i	−0.165737	−	0.618538i	−0.997945	−	0.0640748i	$-0.979590\pi$
$233$	−2.52986	−	9.44157i	−0.165737	−	0.618538i	0.832208	−	0.554463i	$-0.187076\pi$
$234$	−0.712180	+	0.514823i	−0.0465567	+	0.0336550i
$235$		0			0
$236$	−20.5977	+	3.63193i	−1.34080	+	0.236419i
$237$	−4.36663	−	19.0180i	−0.283643	−	1.23535i
$238$	0.429271	+	0.200173i	0.0278255	+	0.0129753i
$239$	−3.56341	+	20.2091i	−0.230498	+	1.30722i	0.621392	+	0.783499i	$0.286567\pi$
$239$	−3.56341	+	20.2091i	−0.230498	+	1.30722i	−0.851891	+	0.523720i	$0.824544\pi$
$240$		0			0
$241$	3.96082	−	3.32352i	0.255139	−	0.214087i	−0.506243	−	0.862391i	$-0.668966\pi$
$241$	3.96082	−	3.32352i	0.255139	−	0.214087i	0.761381	+	0.648304i	$0.224522\pi$
$242$	−0.132360	−	0.132360i	−0.00850845	−	0.00850845i
$243$	−11.0886	+	10.9564i	−0.711335	+	0.702853i
$244$			19.7781i			1.26617i
$245$		0			0
$246$	−0.417250	+	0.135020i	−0.0266029	+	0.00860854i
$247$	−3.47989	−	4.96980i	−0.221420	−	0.316221i
$248$	−0.255664	+	0.548272i	−0.0162347	+	0.0348153i
$249$	15.7039	−	25.0646i	0.995196	−	1.58840i
$250$		0			0
$251$	−6.01963	+	3.47543i	−0.379955	+	0.219367i	−0.677799	−	0.735247i	$-0.737066\pi$
$251$	−6.01963	+	3.47543i	−0.379955	+	0.219367i	0.297843	+	0.954615i	$0.403733\pi$
$252$	−1.33212	+	8.28202i	−0.0839157	+	0.521718i
$253$	−20.1860	+	5.40883i	−1.26908	+	0.340050i
$254$	1.50240	+	0.546827i	0.0942687	+	0.0343110i
$255$		0			0
$256$	11.8848	+	9.97255i	0.742802	+	0.623285i
$257$	−2.15005	−	24.5752i	−0.134117	−	1.53296i	−0.703385	−	0.710809i	$-0.748329\pi$
$257$	−2.15005	−	24.5752i	−0.134117	−	1.53296i	0.569268	−	0.822152i	$-0.307227\pi$
$258$	0.0137001	−	0.110483i	0.000852933	−	0.00687835i
$259$	3.85451	−	10.5902i	0.239507	−	0.658041i
$260$		0			0
$261$	12.3954	+	3.12211i	0.767253	+	0.193254i
$262$	1.45764	+	0.390572i	0.0900530	+	0.0241296i
$263$	8.76805	+	6.13946i	0.540661	+	0.378575i	0.811773	−	0.583973i	$-0.198502\pi$
$263$	8.76805	+	6.13946i	0.540661	+	0.378575i	−0.271112	+	0.962548i	$0.587391\pi$
$264$	1.74665	−	0.926027i	0.107499	−	0.0569930i
$265$		0			0
$266$	0.174373	+	0.0307467i	0.0106915	+	0.00188520i
$267$	1.20062	+	23.4473i	0.0734767	+	1.43495i
$268$	29.3807	+	2.57048i	1.79471	+	0.157017i
$269$	−25.6878			−1.56621			−0.783106	−	0.621888i	$-0.786366\pi$
$269$	−25.6878			−1.56621			−0.783106	+	0.621888i	$0.786366\pi$
$270$		0			0
$271$	−3.84439			−0.233530			−0.116765	−	0.993160i	$-0.537252\pi$
$271$	−3.84439			−0.233530			−0.116765	+	0.993160i	$0.537252\pi$
$272$	−17.0801	−	1.49432i	−1.03564	−	0.0906064i
$273$	7.64850	−	4.95396i	0.462909	−	0.299827i
$274$	−0.694499	−	0.122459i	−0.0419562	−	0.00739801i
$275$		0			0
$276$	0.711784	−	19.7051i	0.0428444	−	1.18611i
$277$	−17.6146	−	12.3338i	−1.05836	−	0.741069i	−0.0913494	−	0.995819i	$-0.529118\pi$
$277$	−17.6146	−	12.3338i	−1.05836	−	0.741069i	−0.967007	+	0.254750i	$0.918007\pi$
$278$	−0.412228	−	0.110456i	−0.0247238	−	0.00662472i
$279$	5.23703	−	2.53873i	0.313533	−	0.151990i
$280$		0			0
$281$	4.61880	−	12.6900i	0.275534	−	0.757024i	−0.722320	−	0.691558i	$-0.756924\pi$
$281$	4.61880	−	12.6900i	0.275534	−	0.757024i	0.997855	−	0.0654659i	$-0.0208534\pi$
$282$	−0.143731	+	0.0608067i	−0.00855904	+	0.00362098i
$283$	−1.82816	−	20.8960i	−0.108673	−	1.24214i	−0.833232	−	0.552923i	$-0.813512\pi$
$283$	−1.82816	−	20.8960i	−0.108673	−	1.24214i	0.724560	−	0.689212i	$-0.242043\pi$
$284$	−14.3296	−	12.0240i	−0.850307	−	0.713492i
$285$		0			0
$286$	−1.00752	−	0.366706i	−0.0595757	−	0.0216838i
$287$	4.39274	−	1.17703i	0.259295	−	0.0694779i
$288$	0.527552	+	2.74922i	0.0310863	+	0.161999i
$289$	1.48357	−	0.856540i	0.0872689	−	0.0503847i
$290$		0			0
$291$	24.0070	+	0.867178i	1.40731	+	0.0508349i
$292$	−0.232373	+	0.498326i	−0.0135986	+	0.0291623i
$293$	16.2974	+	23.2751i	0.952105	+	1.35975i	0.932980	+	0.359929i	$0.117199\pi$
$293$	16.2974	+	23.2751i	0.952105	+	1.35975i	0.0191252	+	0.999817i	$0.493912\pi$
$294$	0.142322	−	0.665645i	0.00830038	−	0.0388212i
$295$		0			0
$296$		−	2.50602i		−	0.145659i
$297$	−18.6566	−	3.69620i	−1.08257	−	0.214475i
$298$	−0.0364401	−	0.0364401i	−0.00211092	−	0.00211092i
$299$	−16.4089	+	13.7687i	−0.948952	+	0.796265i
$300$		0			0
$301$	−0.200470	+	1.13692i	−0.0115549	+	0.0655309i
$302$	0.00649308	+	0.00302777i	0.000373634	+	0.000174229i
$303$	10.5821	+	3.24917i	0.607928	+	0.186660i
$304$	−6.31206	+	1.11299i	−0.362021	+	0.0638342i
$305$		0			0
$306$	−0.727186	−	0.705615i	−0.0415705	−	0.0403373i
$307$	6.71325	+	25.0542i	0.383146	+	1.42992i	0.841069	+	0.540927i	$0.181927\pi$
$307$	6.71325	+	25.0542i	0.383146	+	1.42992i	−0.457924	+	0.888991i	$0.651407\pi$
$308$	−9.27573	+	4.32534i	−0.528534	+	0.246459i
$309$	−6.37579	−	8.18085i	−0.362706	−	0.465392i
$310$		0			0
$311$	−14.3581	+	17.1114i	−0.814176	+	0.970297i	−0.999924	−	0.0123005i	$-0.996085\pi$
$311$	−14.3581	+	17.1114i	−0.814176	+	0.970297i	0.185749	+	0.982597i	$0.440529\pi$
$312$	1.22143	−	1.61685i	0.0691497	−	0.0915361i
$313$	11.3289	+	24.2949i	0.640346	+	1.37323i	0.911744	+	0.410760i	$0.134737\pi$
$313$	11.3289	+	24.2949i	0.640346	+	1.37323i	−0.271397	+	0.962467i	$0.587486\pi$
$314$	−0.597547	+	1.03498i	−0.0337215	+	0.0584074i
$315$		0			0
$316$	11.2314	+	19.4534i	0.631817	+	1.09434i
$317$	−11.9984	+	17.1355i	−0.673896	+	0.962423i	0.325959	+	0.945384i	$0.394313\pi$
$317$	−11.9984	+	17.1355i	−0.673896	+	0.962423i	−0.999855	+	0.0170391i	$0.994576\pi$
$318$	−1.39834	+	0.321066i	−0.0784150	+	0.0180045i
$319$	5.33405	+	14.6552i	0.298649	+	0.820533i
$320$		0			0
$321$	7.14963	+	22.0944i	0.399053	+	1.23319i
$322$	0.0544849	−	0.622765i	0.00303632	−	0.0347053i
$323$	4.94655	−	4.94655i	0.275234	−	0.275234i
$324$	8.50066	−	15.8040i	0.472259	−	0.878000i
$325$		0			0
$326$	−0.362832	−	0.432406i	−0.0200954	−	0.0239487i
$327$	8.44132	−	16.5180i	0.466806	−	0.913448i
$328$	0.828367	−	0.580029i	0.0457389	−	0.0320267i
$329$	1.52075	−	0.553509i	0.0838418	−	0.0305159i
$330$		0			0
$331$	2.07689	+	11.7786i	0.114156	+	0.647411i	0.987165	+	0.159706i	$0.0510547\pi$
$331$	2.07689	+	11.7786i	0.114156	+	0.647411i	−0.873009	+	0.487705i	$0.837834\pi$
$332$	−8.81264	+	32.8892i	−0.483656	+	1.80503i
$333$	−15.2173	+	18.6998i	−0.833901	+	1.02474i
$334$	0.987859	+	0.570341i	0.0540533	+	0.0312077i
$335$		0			0
$336$	−1.32839	−	9.53494i	−0.0724694	−	0.520174i
$337$	−18.9713	+	1.65977i	−1.03343	+	0.0904136i	−0.591231	−	0.806502i	$-0.701358\pi$
$337$	−18.9713	+	1.65977i	−1.03343	+	0.0904136i	−0.442201	+	0.896916i	$0.645802\pi$
$338$	−0.0836401	+	0.00731756i	−0.00454942	+	0.000398023i
$339$	−6.07405	+	4.73385i	−0.329897	+	0.257107i
$340$		0			0
$341$	6.14948	+	3.55040i	0.333013	+	0.192265i
$342$	−0.330851	−	0.184433i	−0.0178904	−	0.00997299i
$343$	−4.36759	+	16.3001i	−0.235828	+	0.880121i
$344$	0.0445774	+	0.252811i	0.00240345	+	0.0136307i
$345$		0			0
$346$	0.710621	−	0.258645i	0.0382032	−	0.0139048i
$347$	16.8906	−	11.8269i	0.906735	−	0.634903i	−0.0243506	−	0.999703i	$-0.507752\pi$
$347$	16.8906	−	11.8269i	0.906735	−	0.634903i	0.931086	+	0.364801i	$0.118863\pi$
$348$	−14.6957	+	0.752494i	−0.787773	+	0.0403379i
$349$	22.8800	+	27.2673i	1.22474	+	1.45959i	0.845234	+	0.534396i	$0.179461\pi$
$349$	22.8800	+	27.2673i	1.22474	+	1.45959i	0.379503	+	0.925190i	$0.376095\pi$
$350$		0			0
$351$	−18.9322	+	4.64803i	−1.01053	+	0.248094i
$352$	−2.41511	+	2.41511i	−0.128726	+	0.128726i
$353$	−1.01031	+	11.5479i	−0.0537734	+	0.614632i	0.920721	+	0.390221i	$0.127601\pi$
$353$	−1.01031	+	11.5479i	−0.0537734	+	0.614632i	−0.974495	+	0.224411i	$0.927954\pi$
$354$	1.38721	+	0.296601i	0.0737296	+	0.0157642i
$355$		0			0
$356$	−9.24394	−	25.3975i	−0.489928	−	1.34607i
$357$	7.15673	+	7.69313i	0.378774	+	0.407164i
$358$	0.842400	−	1.20307i	0.0445222	−	0.0635844i
$359$	8.36957	+	14.4965i	0.441729	+	0.765097i	0.997818	−	0.0660256i	$-0.0210319\pi$
$359$	8.36957	+	14.4965i	0.441729	+	0.765097i	−0.556089	+	0.831123i	$0.687699\pi$
$360$		0			0
$361$	−8.19244	+	14.1897i	−0.431181	+	0.746828i
$362$	−0.365468	−	0.783749i	−0.0192086	−	0.0411929i
$363$	−1.61792	−	3.82432i	−0.0849185	−	0.200725i
$364$	−6.74308	+	8.03609i	−0.353433	+	0.421206i
$365$		0			0
$366$	0.504001	−	1.24315i	0.0263445	−	0.0649805i
$367$	7.42555	−	3.46259i	0.387611	−	0.180746i	−0.219037	−	0.975716i	$-0.570292\pi$
$367$	7.42555	−	3.46259i	0.387611	−	0.180746i	0.606648	+	0.794971i	$0.292514\pi$
$368$	5.85689	+	21.8582i	0.305312	+	1.13944i
$369$	−9.70336	−	0.701923i	−0.505137	−	0.0365407i
$370$		0			0
$371$	14.6518	−	2.58351i	0.760683	−	0.134129i
$372$	−4.90540	+	4.56337i	−0.254333	+	0.236600i
$373$	2.33425	+	1.08848i	0.120863	+	0.0563592i	0.482109	−	0.876111i	$-0.339871\pi$
$373$	2.33425	+	1.08848i	0.120863	+	0.0563592i	−0.361246	+	0.932470i	$0.617649\pi$
$374$	0.214674	−	1.21748i	0.0111005	−	0.0629543i
$375$		0			0
$376$	0.275673	−	0.231317i	0.0142167	−	0.0119292i
$377$	11.3034	+	11.3034i	0.582155	+	0.582155i
$378$	0.294778	−	0.486618i	0.0151618	−	0.0250289i
$379$		−	9.64972i		−	0.495673i	−0.968802	−	0.247836i	$-0.920280\pi$
$379$		−	9.64972i		−	0.495673i	0.968802	−	0.247836i	$-0.0797195\pi$
$380$		0			0
$381$	26.3291	+	23.7641i	1.34888	+	1.21747i
$382$	0.301978	+	0.431269i	0.0154505	+	0.0220656i
$383$	−6.52445	+	13.9917i	−0.333384	+	0.714944i	−0.999523	−	0.0308834i	$-0.990168\pi$
$383$	−6.52445	+	13.9917i	−0.333384	+	0.714944i	0.666139	+	0.745828i	$0.267946\pi$
$384$	−2.01163	−	3.79431i	−0.102656	−	0.193627i
$385$		0			0
$386$	0.0938427	−	0.0541801i	0.00477647	−	0.00275770i
$387$	1.20251	−	2.15716i	0.0611269	−	0.109655i
$388$	−26.7121	+	7.15749i	−1.35610	+	0.363366i
$389$	−9.45615	−	3.44176i	−0.479446	−	0.174504i	0.0909807	−	0.995853i	$-0.471000\pi$
$389$	−9.45615	−	3.44176i	−0.479446	−	0.174504i	−0.570426	+	0.821349i	$0.693222\pi$
$390$		0			0
$391$	−18.9201	−	15.8758i	−0.956829	−	0.802875i
$392$	0.136799	+	1.56362i	0.00690938	+	0.0789746i
$393$	26.7113	+	20.1787i	1.34741	+	1.01788i
$394$	−0.603662	+	1.65855i	−0.0304121	+	0.0835565i
$395$		0			0
$396$	21.7801	−	2.23636i	1.09449	−	0.112381i
$397$	2.60816	+	0.698855i	0.130900	+	0.0350745i	0.323674	−	0.946169i	$-0.395082\pi$
$397$	2.60816	+	0.698855i	0.130900	+	0.0350745i	−0.192774	+	0.981243i	$0.561748\pi$
$398$	0.399199	+	0.279522i	0.0200100	+	0.0140112i
$399$	3.32857	+	2.08548i	0.166637	+	0.104404i
$400$		0			0
$401$	31.5922	+	5.57055i	1.57764	+	0.278180i	0.892778	−	0.450496i	$-0.148753\pi$
$401$	31.5922	+	5.57055i	1.57764	+	0.278180i	0.684858	+	0.728676i	$0.259864\pi$
$402$	−1.78121	−	0.910267i	−0.0888389	−	0.0454000i
$403$	7.25054	+	0.634340i	0.361175	+	0.0315987i
$404$	−12.7433			−0.634001
$405$		0			0
$406$	−0.466528			−0.0231534
$407$	−29.3032	−	2.56370i	−1.45250	−	0.127078i
$408$	2.08052	+	1.06322i	0.103001	+	0.0526375i
$409$	32.0488	+	5.65107i	1.58471	+	0.279427i	0.895476	−	0.445110i	$-0.146836\pi$
$409$	32.0488	+	5.65107i	1.58471	+	0.279427i	0.689235	+	0.724538i	$0.257947\pi$
$410$		0			0
$411$	−13.2571	−	8.30609i	−0.653925	−	0.409709i
$412$	9.78065	+	6.84848i	0.481858	+	0.337401i
$413$	−14.2090	−	3.80730i	−0.699180	−	0.187345i
$414$	−0.546877	+	1.22042i	−0.0268776	+	0.0599803i
$415$		0			0
$416$	−1.19735	+	3.28969i	−0.0587050	+	0.161291i
$417$	−7.55411	−	5.70665i	−0.369926	−	0.279456i
$418$	−0.0402790	−	0.460391i	−0.00197011	−	0.0225184i
$419$	−17.2393	−	14.4655i	−0.842197	−	0.706687i	0.115860	−	0.993266i	$-0.463038\pi$
$419$	−17.2393	−	14.4655i	−0.842197	−	0.706687i	−0.958057	+	0.286578i	$0.907482\pi$
$420$		0			0
$421$	−28.8586	−	10.5037i	−1.40648	−	0.511918i	−0.476388	−	0.879235i	$-0.658054\pi$
$421$	−28.8586	−	10.5037i	−1.40648	−	0.511918i	−0.930096	+	0.367316i	$0.880277\pi$
$422$	0.0567666	−	0.0152106i	0.00276336	−	0.000740439i
$423$	−3.46169	+	0.0521164i	−0.168313	+	0.00253399i
$424$	2.86508	−	1.65415i	0.139141	−	0.0803328i
$425$		0			0
$426$	0.594281	+	1.12092i	0.0287930	+	0.0543088i
$427$	−5.87877	+	12.6071i	−0.284494	+	0.610099i
$428$	−15.3336	−	21.8986i	−0.741175	−	1.05851i
$429$	−17.6565	−	15.9364i	−0.852464	−	0.769416i
$430$		0			0
$431$		−	17.0982i		−	0.823592i	−0.911276	−	0.411796i	$-0.864902\pi$
$431$		−	17.0982i		−	0.823592i	0.911276	−	0.411796i	$-0.135098\pi$
$432$	−4.00239	+	20.2021i	−0.192565	+	0.971973i
$433$	7.53063	+	7.53063i	0.361899	+	0.361899i	0.864512	−	0.502613i	$-0.167628\pi$
$433$	7.53063	+	7.53063i	0.361899	+	0.361899i	−0.502613	+	0.864512i	$0.667628\pi$
$434$	−0.162718	+	0.136536i	−0.00781069	+	0.00655395i
$435$		0			0
$436$	−3.70814	+	21.0299i	−0.177588	+	1.00715i
$437$	−8.36791	−	3.90202i	−0.400292	−	0.186659i
$438$	0.0273045	−	0.0254007i	0.00130466	−	0.00121369i
$439$	12.4586	−	2.19679i	0.594617	−	0.104847i	0.131763	−	0.991281i	$-0.457936\pi$
$439$	12.4586	−	2.19679i	0.594617	−	0.104847i	0.462855	+	0.886434i	$0.346825\pi$
$440$		0			0
$441$	8.47395	−	12.4984i	0.403521	−	0.595160i
$442$	−0.327963	−	1.22397i	−0.0155996	−	0.0582185i
$443$	28.9199	−	13.4856i	1.37403	−	0.640719i	0.411375	−	0.911466i	$-0.365049\pi$
$443$	28.9199	−	13.4856i	1.37403	−	0.640719i	0.962650	+	0.270747i	$0.0872708\pi$
$444$	10.4277	−	25.7205i	0.494875	−	1.22064i
$445$		0			0
$446$	0.242662	−	0.289194i	0.0114904	−	0.0136937i
$447$	−0.445428	−	1.05287i	−0.0210680	−	0.0497992i
$448$	4.65479	+	9.98223i	0.219918	+	0.471616i
$449$	−13.3782	+	23.1718i	−0.631358	+	1.09354i	0.355916	+	0.934518i	$0.384169\pi$
$449$	−13.3782	+	23.1718i	−0.631358	+	1.09354i	−0.987274	+	0.159026i	$0.949165\pi$
$450$		0			0
$451$	−5.93492	−	10.2796i	−0.279465	−	0.484047i
$452$	5.08481	−	7.26186i	0.239169	−	0.341569i
$453$	0.108251	+	0.116365i	0.00508609	+	0.00546730i
$454$	−0.343578	−	0.943973i	−0.0161249	−	0.0443028i
$455$		0			0
$456$	0.854128	+	0.182622i	0.0399982	+	0.00855205i
$457$	1.87432	−	21.4236i	0.0876772	−	1.00215i	−0.817164	−	0.576405i	$-0.804455\pi$
$457$	1.87432	−	21.4236i	0.0876772	−	1.00215i	0.904841	−	0.425750i	$-0.139990\pi$
$458$	0.0364607	−	0.0364607i	0.00170370	−	0.00170370i
$459$	−9.06860	−	20.5673i	−0.423286	−	0.959999i
$460$		0			0
$461$	−15.4953	−	18.4666i	−0.721687	−	0.860073i	0.273107	−	0.961984i	$-0.411949\pi$
$461$	−15.4953	−	18.4666i	−0.721687	−	0.860073i	−0.994794	+	0.101911i	$0.967504\pi$
$462$	0.693244	−	0.0354976i	0.0322527	−	0.00165150i
$463$	21.4684	−	15.0323i	0.997720	−	0.698611i	0.0439142	−	0.999035i	$-0.486017\pi$
$463$	21.4684	−	15.0323i	0.997720	−	0.698611i	0.953806	+	0.300424i	$0.0971283\pi$
$464$	15.8692	−	5.77592i	0.736709	−	0.268140i
$465$		0			0
$466$	−0.132525	−	0.751585i	−0.00613909	−	0.0348165i
$467$	3.07154	−	11.4631i	0.142134	−	0.530451i	−0.857732	−	0.514096i	$-0.828127\pi$
$467$	3.07154	−	11.4631i	0.142134	−	0.530451i	0.999866	−	0.0163543i	$-0.00520595\pi$
$468$	19.2639	−	11.5121i	0.890475	−	0.532148i
$469$	17.9640	+	10.3715i	0.829498	+	0.478911i
$470$		0			0
$471$	−20.9110	+	16.2971i	−0.963528	+	0.750931i
$472$	−3.25860	+	0.285091i	−0.149989	+	0.0131224i
$473$	3.00176	−	0.262620i	0.138021	−	0.0120753i
$474$	−0.210223	−	1.50894i	−0.00965585	−	0.0693081i
$475$		0			0
$476$	−10.4753	−	6.04789i	−0.480133	−	0.277205i
$477$	−31.4237	−	5.05433i	−1.43879	−	0.231422i
$478$	−0.414685	+	1.54763i	−0.0189673	+	0.0707868i
$479$	2.62132	+	14.8663i	0.119771	+	0.679256i	0.984277	+	0.176633i	$0.0565206\pi$
$479$	2.62132	+	14.8663i	0.119771	+	0.679256i	−0.864506	+	0.502623i	$0.832368\pi$
$480$		0			0
$481$	−28.3319	+	10.3120i	−1.29182	+	0.470184i
$482$	0.330691	−	0.231552i	0.0150625	−	0.0105469i
$483$	6.31076	−	12.3489i	0.287150	−	0.561896i
$484$	3.07269	+	3.66189i	0.139668	+	0.166449i
$485$		0			0
$486$	−0.937035	+	0.776736i	−0.0425048	+	0.0352335i
$487$	17.5079	−	17.5079i	0.793360	−	0.793360i	−0.188679	−	0.982039i	$-0.560421\pi$
$487$	17.5079	−	17.5079i	0.793360	−	0.793360i	0.982039	+	0.188679i	$0.0604207\pi$
$488$	−0.269588	+	3.08141i	−0.0122037	+	0.139489i
$489$	−3.85521	−	11.9137i	−0.174338	−	0.538757i
$490$		0			0
$491$	−14.3755	−	39.4964i	−0.648758	−	1.78245i	−0.622274	−	0.782799i	$-0.713791\pi$
$491$	−14.3755	−	39.4964i	−0.648758	−	1.78245i	−0.0264842	−	0.999649i	$-0.508431\pi$
$492$	10.9155	−	2.50625i	0.492108	−	0.112990i
$493$	−10.5720	+	15.0984i	−0.476140	+	0.679999i
$494$	−0.236849	−	0.410234i	−0.0106563	−	0.0184573i
$495$		0			0
$496$	3.84451	−	6.65889i	0.172624	−	0.298993i
$497$	−5.56009	−	11.9237i	−0.249404	−	0.534849i
$498$	1.39202	−	1.84267i	0.0623780	−	0.0825721i
$499$	14.9078	−	17.7664i	0.667366	−	0.795336i	−0.321057	−	0.947060i	$-0.604038\pi$
$499$	14.9078	−	17.7664i	0.667366	−	0.795336i	0.988423	+	0.151724i	$0.0484826\pi$
$500$		0			0
$501$	15.5551	+	19.9589i	0.694951	+	0.891700i
$502$	−0.491859	+	0.229358i	−0.0219528	+	0.0102367i
$503$	−6.80105	−	25.3819i	−0.303244	−	1.13172i	−0.934447	−	0.356103i	$-0.884105\pi$
$503$	−6.80105	−	25.3819i	−0.303244	−	1.13172i	0.631203	−	0.775618i	$-0.282561\pi$
$504$	−0.320432	+	1.27217i	−0.0142732	+	0.0566670i
$505$		0			0
$506$	−1.60689	+	0.283337i	−0.0714348	+	0.0125959i
$507$	−1.78050	−	0.546689i	−0.0790747	−	0.0242793i
$508$	−37.0043	−	17.2554i	−1.64180	−	0.765584i
$509$	−7.00772	+	39.7428i	−0.310612	+	1.76157i	0.285224	+	0.958461i	$0.407932\pi$
$509$	−7.00772	+	39.7428i	−0.310612	+	1.76157i	−0.595836	+	0.803106i	$0.703179\pi$
$510$		0			0
$511$	−0.296241	+	0.248576i	−0.0131049	+	0.0109963i
$512$	4.36306	+	4.36306i	0.192822	+	0.192822i
$513$	−5.26455	−	6.54924i	−0.232436	−	0.289156i
$514$		−	1.92610i		−	0.0849568i
$515$		0			0
$516$	−0.594441	+	2.78022i	−0.0261688	+	0.122392i
$517$	−2.42280	−	3.46012i	−0.106555	−	0.152176i
$518$	0.371870	−	0.797479i	0.0163390	−	0.0350392i
$519$	16.7650	+	0.605583i	0.735901	+	0.0265821i
$520$		0			0
$521$	18.5284	−	10.6974i	0.811746	−	0.468662i	−0.0358161	−	0.999358i	$-0.511403\pi$
$521$	18.5284	−	10.6974i	0.811746	−	0.468662i	0.847562	+	0.530697i	$0.178070\pi$
$522$	0.942871	+	0.327189i	0.0412683	+	0.0143207i
$523$	25.2654	−	6.76985i	1.10478	−	0.296025i	0.340071	−	0.940400i	$-0.389549\pi$
$523$	25.2654	−	6.76985i	1.10478	−	0.296025i	0.764710	+	0.644375i	$0.222882\pi$
$524$	−36.2134	−	13.1806i	−1.58199	−	0.575796i
$525$		0			0
$526$	0.640205	+	0.537196i	0.0279143	+	0.0234228i
$527$	0.731418	+	8.36014i	0.0318611	+	0.364173i
$528$	−23.1416	+	9.79027i	−1.00711	+	0.426067i
$529$	−3.28275	+	9.01929i	−0.142728	+	0.392143i
$530$		0			0
$531$	26.0468	+	17.6598i	1.13033	+	0.766372i
$532$	−4.36767	−	1.17031i	−0.189363	−	0.0507396i
$533$	−9.96617	−	6.97839i	−0.431683	−	0.302267i
$534$	−0.0661722	+	1.83191i	−0.00286355	+	0.0792747i
$535$		0			0
$536$	4.54244	+	0.800955i	0.196204	+	0.0345960i
$537$	27.3458	−	17.7120i	1.18006	−	0.764328i
$538$	−1.99801	−	0.174803i	−0.0861403	−	0.00753630i
$539$	18.4235			0.793558
$540$		0			0
$541$	−8.34293			−0.358691			−0.179345	−	0.983786i	$-0.557398\pi$
$541$	−8.34293			−0.358691			−0.179345	+	0.983786i	$0.557398\pi$
$542$	−0.299018	−	0.0261607i	−0.0128439	−	0.00112370i
$543$	−0.981022	−	19.1587i	−0.0420997	−	0.822180i
$544$	−3.97525	−	0.700944i	−0.170437	−	0.0300527i
$545$		0			0
$546$	0.628616	−	0.333274i	0.0269023	−	0.0142628i
$547$	−0.804110	−	0.563044i	−0.0343812	−	0.0240740i	0.556259	−	0.831009i	$-0.312236\pi$
$547$	−0.804110	−	0.563044i	−0.0343812	−	0.0240740i	−0.590641	+	0.806935i	$0.701125\pi$
$548$	17.3957	+	4.66116i	0.743107	+	0.199115i
$549$	20.7229	−	21.3564i	0.884431	−	0.911469i
$550$		0			0
$551$	−2.35663	+	6.47479i	−0.100396	+	0.275835i
$552$	0.379488	−	3.06032i	0.0161521	−	0.130256i
$553$	1.37694	+	15.7385i	0.0585533	+	0.669267i
$554$	−1.28614	−	1.07920i	−0.0546428	−	0.0458507i
$555$		0			0
$556$	10.2414	+	3.72755i	0.434330	+	0.158083i
$557$	4.49123	−	1.20342i	0.190299	−	0.0509906i	−0.162411	−	0.986723i	$-0.551927\pi$
$557$	4.49123	−	1.20342i	0.190299	−	0.0509906i	0.352710	+	0.935733i	$0.385260\pi$
$558$	0.424614	−	0.161826i	0.0179754	−	0.00685066i
$559$	2.67474	−	1.54426i	0.113129	−	0.0653152i
$560$		0			0
$561$	14.5608	−	23.2401i	0.614759	−	0.981199i
$562$	0.445607	−	0.955607i	0.0187968	−	0.0403098i
$563$	4.48288	+	6.40221i	0.188931	+	0.269821i	0.902431	−	0.430833i	$-0.141780\pi$
$563$	4.48288	+	6.40221i	0.188931	+	0.269821i	−0.713501	+	0.700654i	$0.752891\pi$
$564$	3.79189	−	1.22703i	0.159667	−	0.0516674i
$565$		0			0
$566$		−	1.63774i		−	0.0688392i
$567$	10.1160	−	7.54716i	0.424834	−	0.316951i
$568$	−2.06864	−	2.06864i	−0.0867983	−	0.0867983i
$569$	−13.8060	+	11.5846i	−0.578776	+	0.485651i	−0.884545	−	0.466455i	$-0.845531\pi$
$569$	−13.8060	+	11.5846i	−0.578776	+	0.485651i	0.305769	+	0.952106i	$0.401087\pi$
$570$		0			0
$571$	3.14824	−	17.8546i	0.131750	−	0.747190i	−0.845318	−	0.534263i	$-0.820589\pi$
$571$	3.14824	−	17.8546i	0.131750	−	0.747190i	0.977068	−	0.212927i	$-0.0682997\pi$
$572$	24.8153	+	11.5716i	1.03758	+	0.483832i
$573$	2.61362	+	11.3831i	0.109186	+	0.475537i
$574$	0.349679	−	0.0616578i	0.0145953	−	0.00257355i
$575$		0			0
$576$	−2.40669	−	23.4390i	−0.100279	−	0.976623i
$577$	−1.79688	−	6.70605i	−0.0748051	−	0.279177i	0.918384	−	0.395691i	$-0.129495\pi$
$577$	−1.79688	−	6.70605i	−0.0748051	−	0.279177i	−0.993189	+	0.116514i	$0.962828\pi$
$578$	0.121222	−	0.0565265i	0.00504215	−	0.00235119i
$579$	2.38084	−	0.331693i	0.0989443	−	0.0137847i
$580$		0			0
$581$	−15.3932	+	18.3450i	−0.638619	+	0.761077i
$582$	1.86137	+	0.230815i	0.0771564	+	0.00956759i
$583$	−16.4112	−	35.1940i	−0.679683	−	1.45759i
$584$	−0.0429960	+	0.0744712i	−0.00177919	+	0.00308164i
$585$		0			0
$586$	1.10924	+	1.92125i	0.0458221	+	0.0793662i
$587$	16.0612	−	22.9378i	0.662918	−	0.946745i	−0.337068	−	0.941480i	$-0.609435\pi$
$587$	16.0612	−	22.9378i	0.662918	−	0.946745i	0.999986	−	0.00526447i	$-0.00167574\pi$
$588$	−5.10226	+	16.6174i	−0.210414	+	0.685291i
$589$	1.07298	+	2.94800i	0.0442116	+	0.121470i
$590$		0			0
$591$	−26.2341	+	29.0657i	−1.07913	+	1.19560i
$592$	−2.77607	+	31.7306i	−0.114096	+	1.30412i
$593$	−16.2602	+	16.2602i	−0.667726	+	0.667726i	−0.957189	−	0.289463i	$-0.906523\pi$
$593$	−16.2602	+	16.2602i	−0.667726	+	0.667726i	0.289463	+	0.957189i	$0.406523\pi$
$594$	−1.42597	−	0.414449i	−0.0585081	−	0.0170050i
$595$		0			0
$596$	0.845941	+	1.00815i	0.0346511	+	0.0412956i
$597$	5.87712	+	9.07379i	0.240535	+	0.371365i
$598$	−1.36999	+	0.959276i	−0.0560230	+	0.0392277i
$599$	7.68065	−	2.79553i	0.313823	−	0.114222i	−0.180307	−	0.983610i	$-0.557709\pi$
$599$	7.68065	−	2.79553i	0.313823	−	0.114222i	0.494130	+	0.869388i	$0.335487\pi$
$600$		0			0
$601$	0.950433	+	5.39018i	0.0387690	+	0.219870i	0.998037	−	0.0626279i	$-0.0199481\pi$
$601$	0.950433	+	5.39018i	0.0387690	+	0.219870i	−0.959268	+	0.282498i	$0.908837\pi$
$602$	−0.0233292	+	0.0870659i	−0.000950829	+	0.00354854i
$603$	−29.0320	−	33.5597i	−1.18227	−	1.36666i
$604$	−0.158447	−	0.0914792i	−0.00644710	−	0.00372224i
$605$		0			0
$606$	0.800974	+	0.324733i	0.0325373	+	0.0131914i
$607$	−4.31710	+	0.377697i	−0.175226	+	0.0153303i	−0.174431	−	0.984669i	$-0.555809\pi$
$607$	−4.31710	+	0.377697i	−0.175226	+	0.0153303i	−0.000794827		1.00000i	$0.500253\pi$
$608$	−1.50324	+	0.131517i	−0.0609646	+	0.00533371i
$609$	−9.59108	−	3.88844i	−0.388650	−	0.157567i
$610$		0			0
$611$	−3.74952	−	2.16479i	−0.151689	−	0.0875779i
$612$	16.9293	+	19.5696i	0.684327	+	0.791053i
$613$	9.89430	−	36.9260i	0.399627	−	1.49143i	−0.414127	−	0.910219i	$-0.635913\pi$
$613$	9.89430	−	36.9260i	0.399627	−	1.49143i	0.813754	−	0.581209i	$-0.197420\pi$
$614$	0.351668	+	1.99441i	0.0141922	+	0.0804879i
$615$		0			0
$616$	−1.50410	+	0.547449i	−0.0606021	+	0.0220573i
$617$	−12.9164	+	9.04416i	−0.519995	+	0.364104i	−0.803915	−	0.594744i	$-0.797254\pi$
$617$	−12.9164	+	9.04416i	−0.519995	+	0.364104i	0.283921	+	0.958848i	$0.408365\pi$
$618$	−0.440242	−	0.679697i	−0.0177091	−	0.0273414i
$619$	−13.8731	−	16.5333i	−0.557608	−	0.664531i	0.411431	−	0.911441i	$-0.365029\pi$
$619$	−13.8731	−	16.5333i	−0.557608	−	0.664531i	−0.969038	+	0.246910i	$0.920585\pi$
$620$		0			0
$621$	−21.4149	+	20.5317i	−0.859351	+	0.823909i
$622$	−1.23322	+	1.23322i	−0.0494478	+	0.0494478i
$623$	1.65674	−	18.9366i	0.0663759	−	0.758680i
$624$	−17.2565	+	19.1191i	−0.690814	+	0.765378i
$625$		0			0
$626$	0.715842	+	1.96676i	0.0286108	+	0.0786075i
$627$	3.00921	−	9.80061i	0.120176	−	0.391399i
$628$	17.5054	−	25.0002i	0.698540	−	0.997618i
$629$	−17.3821	−	30.1067i	−0.693070	−	1.20043i
$630$		0			0
$631$	−6.83945	+	11.8463i	−0.272274	+	0.471593i	−0.969444	−	0.245314i	$-0.921109\pi$
$631$	−6.83945	+	11.8463i	−0.272274	+	0.471593i	0.697170	+	0.716906i	$0.254442\pi$
$632$	1.48468	+	3.18391i	0.0590574	+	0.126649i
$633$	1.29381	+	0.160435i	0.0514243	+	0.00637673i
$634$	−1.04984	+	1.25116i	−0.0416947	+	0.0496897i
$635$		0			0
$636$	36.2888	−	5.05567i	1.43894	−	0.200470i
$637$	17.1146	−	7.98068i	0.678106	−	0.316206i
$638$	0.315158	+	1.17618i	0.0124772	+	0.0465656i
$639$	2.87477	+	27.9976i	0.113724	+	1.10757i
$640$		0			0
$641$	13.5589	−	2.39080i	0.535545	−	0.0944310i	0.100667	−	0.994920i	$-0.467902\pi$
$641$	13.5589	−	2.39080i	0.535545	−	0.0944310i	0.434878	+	0.900489i	$0.356791\pi$
$642$	0.405751	+	1.76717i	0.0160137	+	0.0697446i
$643$	16.5953	+	7.73851i	0.654455	+	0.305177i	0.721338	−	0.692584i	$-0.243528\pi$
$643$	16.5953	+	7.73851i	0.654455	+	0.305177i	−0.0668830	+	0.997761i	$0.521305\pi$
$644$	−2.77222	+	15.7221i	−0.109241	+	0.619536i
$645$		0			0
$646$	0.418406	−	0.351084i	0.0164620	−	0.0138132i
$647$	−1.94056	−	1.94056i	−0.0762913	−	0.0762913i	0.667931	−	0.744223i	$-0.267180\pi$
$647$	−1.94056	−	1.94056i	−0.0762913	−	0.0762913i	−0.744223	+	0.667931i	$0.767180\pi$
$648$	1.53981	−	2.34638i	0.0604895	−	0.0921743i
$649$			38.3949i			1.50713i
$650$		0			0
$651$	−4.48322	+	1.45074i	−0.175711	+	0.0568591i
$652$	8.26812	+	11.8081i	0.323805	+	0.462441i
$653$	1.44008	−	3.08827i	0.0563549	−	0.120853i	−0.876114	−	0.482105i	$-0.839873\pi$
$653$	1.44008	−	3.08827i	0.0563549	−	0.120853i	0.932469	+	0.361251i	$0.117650\pi$
$654$	0.768973	−	1.22734i	0.0300692	−	0.0479926i
$655$		0			0
$656$	−11.1311	+	6.42656i	−0.434598	+	0.250915i
$657$	0.773046	−	0.294619i	0.0301594	−	0.0114942i
$658$	0.122051	−	0.0327036i	0.00475806	−	0.00127492i
$659$	35.1988	+	12.8113i	1.37115	+	0.499058i	0.919484	−	0.393128i	$-0.128607\pi$
$659$	35.1988	+	12.8113i	1.37115	+	0.499058i	0.451668	+	0.892186i	$0.350829\pi$
$660$		0			0
$661$	17.3498	+	14.5582i	0.674830	+	0.566250i	0.914491	−	0.404607i	$-0.132592\pi$
$661$	17.3498	+	14.5582i	0.674830	+	0.566250i	−0.239661	+	0.970857i	$0.577036\pi$
$662$	0.0813889	+	0.930279i	0.00316327	+	0.0361563i
$663$	3.45923	−	27.8965i	0.134345	−	1.08341i
$664$	−1.82130	+	5.00398i	−0.0706801	+	0.194192i
$665$		0			0
$666$	−1.31086	+	1.35093i	−0.0507946	+	0.0523475i
$667$	23.4982	+	6.29633i	0.909854	+	0.243795i
$668$	−23.8620	−	16.7084i	−0.923248	−	0.646466i
$669$	7.39913	−	3.92281i	0.286067	−	0.151665i
$670$		0			0
$671$	35.7556	+	6.30467i	1.38033	+	0.243389i
$672$	−0.115905	−	2.26355i	−0.00447113	−	0.0873182i
$673$	−28.7132	−	2.51208i	−1.10681	−	0.0968335i	−0.480936	−	0.876756i	$-0.659703\pi$
$673$	−28.7132	−	2.51208i	−1.10681	−	0.0968335i	−0.625876	+	0.779922i	$0.715258\pi$
$674$	−1.48689			−0.0572729
$675$		0			0
$676$	2.14412			0.0824660
$677$	31.1016	+	2.72104i	1.19533	+	0.104578i	0.667393	−	0.744705i	$-0.267410\pi$
$677$	31.1016	+	2.72104i	1.19533	+	0.104578i	0.527937	+	0.849283i	$0.322966\pi$
$678$	−0.504656	+	0.326867i	−0.0193812	+	0.0125533i
$679$	−19.1544	−	3.37744i	−0.735079	−	0.129614i
$680$		0			0
$681$	0.804443	−	22.2702i	0.0308263	−	0.853397i
$682$	0.454149	+	0.317999i	0.0173903	+	0.0121768i
$683$	−13.2286	−	3.54459i	−0.506178	−	0.135630i	−0.00331227	−	0.999995i	$-0.501054\pi$
$683$	−13.2286	−	3.54459i	−0.506178	−	0.135630i	−0.502866	+	0.864365i	$0.667721\pi$
$684$	8.00645	+	5.42841i	0.306134	+	0.207561i
$685$		0			0
$686$	−0.450634	+	1.23811i	−0.0172053	+	0.0472711i
$687$	1.05347	−	0.445680i	0.0401923	−	0.0170038i
$688$	−0.284375	−	3.25042i	−0.0108417	−	0.123921i
$689$	−30.4906	−	25.5846i	−1.16160	−	0.974696i
$690$		0			0
$691$	22.4334	+	8.16509i	0.853407	+	0.310615i	0.731429	−	0.681918i	$-0.238854\pi$
$691$	22.4334	+	8.16509i	0.853407	+	0.310615i	0.121978	+	0.992533i	$0.461076\pi$
$692$	−18.6541	+	4.99834i	−0.709122	+	0.190009i
$693$	14.5479	+	5.04830i	0.552628	+	0.191769i
$694$	1.39424	−	0.804965i	0.0529246	−	0.0305561i
$695$		0			0
$696$	−2.29983	−	0.0830743i	−0.0871749	−	0.00314892i
$697$	5.92864	−	12.7140i	0.224563	−	0.481578i
$698$	1.59407	+	2.27656i	0.0603363	+	0.0861691i
$699$	3.53984	−	16.5560i	0.133889	−	0.626204i
$700$		0			0
$701$			30.4193i			1.14892i	0.818532	+	0.574461i	$0.194788\pi$
$701$			30.4193i			1.14892i	−0.818532	+	0.574461i	$0.805212\pi$
$702$	−1.50419	+	0.232694i	−0.0567719	+	0.00878247i
$703$	−9.18946	−	9.18946i	−0.346587	−	0.346587i
$704$	22.0221	−	18.4788i	0.829990	−	0.696444i
$705$		0			0
$706$	−0.157165	+	0.891326i	−0.00591497	+	0.0335455i
$707$	−8.12286	−	3.78775i	−0.305492	−	0.142453i
$708$	−34.6310	−	10.6332i	−1.30151	−	0.399620i
$709$	16.6287	−	2.93209i	0.624503	−	0.110117i	0.147563	−	0.989053i	$-0.452857\pi$
$709$	16.6287	−	2.93209i	0.624503	−	0.110117i	0.476940	+	0.878936i	$0.341746\pi$
$710$		0			0
$711$	8.25496	−	32.7737i	0.309585	−	1.22911i
$712$	−1.09401	−	4.08290i	−0.0409998	−	0.153013i
$713$	10.0385	−	4.68103i	0.375945	−	0.175306i
$714$	0.504303	+	0.647076i	0.0188730	+	0.0242162i
$715$		0			0
$716$	−24.1086	+	28.7315i	−0.900982	+	1.07375i
$717$	−21.4245	+	28.3604i	−0.800112	+	1.05914i
$718$	0.552342	+	1.18450i	0.0206132	+	0.0442052i
$719$	−5.81196	+	10.0666i	−0.216749	+	0.375421i	−0.953812	−	0.300403i	$-0.902879\pi$
$719$	−5.81196	+	10.0666i	−0.216749	+	0.375421i	0.737063	+	0.675824i	$0.236212\pi$
$720$		0			0
$721$	4.19881	+	7.27255i	0.156372	+	0.270844i
$722$	−0.733772	+	1.04794i	−0.0273082	+	0.0390001i
$723$	8.72842	−	2.00409i	0.324613	−	0.0745328i
$724$	7.55320	+	20.7522i	0.280712	+	0.771251i
$725$		0			0
$726$	−0.0998181	−	0.308467i	−0.00370460	−	0.0114483i
$727$	2.70998	−	30.9752i	0.100508	−	1.14881i	−0.763666	−	0.645612i	$-0.776602\pi$
$727$	2.70998	−	30.9752i	0.100508	−	1.14881i	0.864173	−	0.503194i	$-0.167842\pi$
$728$	−1.16010	+	1.16010i	−0.0429962	+	0.0429962i
$729$	−25.7379	+	8.15842i	−0.953256	+	0.302164i
$730$		0			0
$731$	2.28908	+	2.72802i	0.0846647	+	0.100899i
$732$	−15.5888	+	30.5043i	−0.576180	+	1.12747i
$733$	−23.6376	+	16.5512i	−0.873073	+	0.611332i	−0.921880	−	0.387476i	$-0.873347\pi$
$733$	−23.6376	+	16.5512i	−0.873073	+	0.611332i	0.0488066	+	0.998808i	$0.484458\pi$
$734$	0.601125	−	0.218792i	0.0221879	−	0.00807575i
$735$		0			0
$736$	0.925139	+	5.24672i	0.0341011	+	0.193397i
$737$	14.0127	−	52.2960i	0.516164	−	1.92635i
$738$	−0.749956	−	0.120626i	−0.0276062	−	0.00444032i
$739$	−10.6803	−	6.16626i	−0.392881	−	0.226830i	0.290527	−	0.956867i	$-0.406169\pi$
$739$	−10.6803	−	6.16626i	−0.392881	−	0.226830i	−0.683408	+	0.730037i	$0.739503\pi$
$740$		0			0
$741$	−1.45000	−	10.4078i	−0.0532670	−	0.382342i
$742$	1.15720	−	0.101242i	0.0424823	−	0.00371672i
$743$	17.8818	−	1.56446i	0.656020	−	0.0573943i	0.245714	−	0.969342i	$-0.420977\pi$
$743$	17.8818	−	1.56446i	0.656020	−	0.0573943i	0.410306	+	0.911948i	$0.365422\pi$
$744$	−0.826457	+	0.644104i	−0.0302994	+	0.0236140i
$745$		0			0
$746$	0.174152	+	0.100547i	0.00637615	+	0.00368127i
$747$	43.9761	−	26.2801i	1.60900	−	0.961539i
$748$	−8.17116	+	30.4952i	−0.298767	+	1.11501i
$749$	−3.26494	−	18.5164i	−0.119298	−	0.676574i
$750$		0			0
$751$	47.0846	−	17.1374i	1.71814	−	0.625352i	0.720464	−	0.693492i	$-0.243929\pi$
$751$	47.0846	−	17.1374i	1.71814	−	0.625352i	0.997676	+	0.0681401i	$0.0217065\pi$
$752$	−3.74675	+	2.62350i	−0.136630	+	0.0956693i
$753$	−12.0235	+	0.615663i	−0.438161	+	0.0224360i
$754$	0.802265	+	0.956102i	0.0292168	+	0.0348192i
$755$		0			0
$756$	−8.58233	+	11.7236i	−0.312136	+	0.426383i
$757$	−30.6375	+	30.6375i	−1.11354	+	1.11354i	−0.120869	+	0.992668i	$0.538568\pi$
$757$	−30.6375	+	30.6375i	−1.11354	+	1.11354i	−0.992668	+	0.120869i	$0.961432\pi$
$758$	0.0656655	−	0.750560i	0.00238508	−	0.0272616i
$759$	−35.3966	−	7.56816i	−1.28481	−	0.274707i
$760$		0			0
$761$	−16.5112	−	45.3641i	−0.598530	−	1.64445i	−0.754205	−	0.656638i	$-0.771978\pi$
$761$	−16.5112	−	45.3641i	−0.598530	−	1.64445i	0.155676	−	0.987808i	$-0.450244\pi$
$762$	1.88618	+	2.02755i	0.0683291	+	0.0734504i
$763$	−8.61450	+	12.3028i	−0.311866	+	0.445391i
$764$	−6.72251	−	11.6437i	−0.243212	−	0.421256i
$765$		0			0
$766$	−0.602688	+	1.04389i	−0.0217760	+	0.0377171i
$767$	16.6319	+	35.6671i	0.600542	+	1.28787i
$768$	10.4700	+	24.7484i	0.377805	+	0.893029i
$769$	−18.0088	+	21.4621i	−0.649414	+	0.773942i	−0.985826	−	0.167773i	$-0.946342\pi$
$769$	−18.0088	+	21.4621i	−0.649414	+	0.773942i	0.336411	+	0.941715i	$0.390787\pi$
$770$		0			0
$771$	16.0538	−	39.5976i	0.578162	−	1.42607i
$772$	−2.50798	+	1.16949i	−0.0902641	+	0.0420908i
$773$	−1.04175	−	3.88787i	−0.0374692	−	0.139837i	0.944657	−	0.328059i	$-0.106394\pi$
$773$	−1.04175	−	3.88787i	−0.0374692	−	0.139837i	−0.982127	+	0.188222i	$0.939728\pi$
$774$	0.108211	−	0.159602i	0.00388956	−	0.00573677i
$775$		0			0
$776$	−4.25927	+	0.751025i	−0.152899	+	0.0269602i
$777$	14.2919	−	13.2954i	0.512719	−	0.476970i
$778$	−0.712083	−	0.332050i	−0.0255294	−	0.0119046i
$779$	0.910646	−	5.16453i	0.0326273	−	0.185039i
$780$		0			0
$781$	−26.3052	+	22.0727i	−0.941273	+	0.789822i
$782$	−1.36358	−	1.36358i	−0.0487615	−	0.0487615i
$783$	16.6568	+	14.5851i	0.595267	+	0.521231i
$784$		−	19.9497i		−	0.712490i
$785$		0			0
$786$	1.94030	+	1.75128i	0.0692083	+	0.0624659i
$787$	−7.13138	−	10.1847i	−0.254206	−	0.363044i	0.671683	−	0.740838i	$-0.265572\pi$
$787$	−7.13138	−	10.1847i	−0.254206	−	0.363044i	−0.925890	+	0.377794i	$0.876683\pi$
$788$	19.0488	−	40.8504i	0.678587	−	1.45523i
$789$	8.68415	+	16.3799i	0.309164	+	0.583139i
$790$		0			0
$791$	5.39967	−	3.11750i	0.191990	−	0.110846i
$792$	3.42379	−	0.0515459i	0.121659	−	0.00183160i
$793$	35.9463	−	9.63179i	1.27649	−	0.342035i
$794$	0.198109	+	0.0721056i	0.00703061	+	0.00255893i
$795$		0			0
$796$	−9.53360	−	7.99964i	−0.337909	−	0.283540i
$797$	−0.644697	−	7.36893i	−0.0228364	−	0.261021i	−0.999027	−	0.0441058i	$-0.985956\pi$
$797$	−0.644697	−	7.36893i	−0.0228364	−	0.261021i	0.976191	−	0.216915i	$-0.0695994\pi$
$798$	0.244706	+	0.184860i	0.00866250	+	0.00654397i
$799$	1.70742	−	4.69109i	0.0604041	−	0.165959i
$800$		0			0
$801$	−16.6291	+	37.1097i	−0.587560	+	1.31121i
$802$	2.41935	+	0.648262i	0.0854301	+	0.0228909i
$803$	0.826817	+	0.578943i	0.0291777	+	0.0204305i
$804$	43.2886	+	27.1220i	1.52667	+	0.956518i
$805$		0			0
$806$	0.559634	+	0.0986785i	0.0197123	+	0.00347580i
$807$	−39.6189	−	20.2467i	−1.39465	−	0.712719i
$808$	−1.98538	−	0.173699i	−0.0698456	−	0.00611070i
$809$	16.5770			0.582817			0.291408	−	0.956599i	$-0.405876\pi$
$809$	16.5770			0.582817			0.291408	+	0.956599i	$0.405876\pi$
$810$		0			0
$811$	16.0416			0.563298			0.281649	−	0.959518i	$-0.409119\pi$
$811$	16.0416			0.563298			0.281649	+	0.959518i	$0.409119\pi$
$812$	11.8686	+	1.03837i	0.416507	+	0.0364396i
$813$	−5.92929	−	3.03009i	−0.207949	−	0.106270i
$814$	−2.26177	−	0.398811i	−0.0792750	−	0.0139783i
$815$		0			0
$816$	−25.1653	−	15.7670i	−0.880962	−	0.551957i
$817$	1.09051	+	0.763585i	0.0381522	+	0.0267145i
$818$	2.45432	+	0.657632i	0.0858131	+	0.0229936i
$819$	15.7011	−	1.61218i	0.548641	−	0.0563340i
$820$		0			0
$821$	−5.82610	+	16.0071i	−0.203332	+	0.558651i	−0.998884	−	0.0472350i	$-0.984959\pi$
$821$	−5.82610	+	16.0071i	−0.203332	+	0.558651i	0.795551	+	0.605886i	$0.207181\pi$
$822$	−0.974622	−	0.736265i	−0.0339938	−	0.0256802i
$823$	3.22849	+	36.9018i	0.112538	+	1.28632i	0.817026	+	0.576601i	$0.195621\pi$
$823$	3.22849	+	36.9018i	0.112538	+	1.28632i	−0.704488	+	0.709716i	$0.748823\pi$
$824$	1.43046	+	1.20030i	0.0498326	+	0.0418145i
$825$		0			0
$826$	−1.07928	−	0.392824i	−0.0375528	−	0.0136681i
$827$	−22.3705	+	5.99415i	−0.777897	+	0.208437i	−0.625858	−	0.779937i	$-0.715251\pi$
$827$	−22.3705	+	5.99415i	−0.777897	+	0.208437i	−0.152040	+	0.988374i	$0.548584\pi$
$828$	16.6291	−	29.8306i	0.577899	−	1.03668i
$829$	−11.9738	+	6.91310i	−0.415868	+	0.240102i	−0.693308	−	0.720641i	$-0.743847\pi$
$829$	−11.9738	+	6.91310i	−0.415868	+	0.240102i	0.277440	+	0.960743i	$0.410514\pi$
$830$		0			0
$831$	−17.4460	−	32.9063i	−0.605195	−	1.14151i
$832$	12.4529	−	26.7054i	0.431728	−	0.925844i
$833$	12.4890	+	17.8361i	0.432717	+	0.617983i
$834$	−0.548729	−	0.495271i	−0.0190009	−	0.0171498i
$835$		0			0
$836$			11.8021i			0.408185i
$837$	10.0782	+	0.212198i	0.348353	+	0.00733465i
$838$	−1.24245	−	1.24245i	−0.0429196	−	0.0429196i
$839$	15.9236	−	13.3615i	0.549744	−	0.461290i	−0.325110	−	0.945676i	$-0.605401\pi$
$839$	15.9236	−	13.3615i	0.549744	−	0.461290i	0.874854	+	0.484386i	$0.160957\pi$
$840$		0			0
$841$	−1.88327	+	10.6805i	−0.0649402	+	0.368294i
$842$	−2.17316	−	1.01336i	−0.0748921	−	0.0349228i
$843$	17.1258	−	15.9317i	0.589843	−	0.548717i
$844$	−1.47801	+	0.260614i	−0.0508753	+	0.00897069i
$845$		0			0
$846$	−0.269606	−	0.0195028i	−0.00926925	−	0.000670521i
$847$	0.870162	+	3.24749i	0.0298991	+	0.111585i
$848$	−38.1094	+	17.7707i	−1.30868	+	0.610249i
$849$	13.6503	−	33.6693i	0.468476	−	1.15553i
$850$		0			0
$851$	−29.4933	+	35.1488i	−1.01102	+	1.20488i
$852$	−12.6238	−	29.8393i	−0.432484	−	1.02228i
$853$	−11.3440	−	24.3274i	−0.388413	−	0.832954i	−0.999154	−	0.0411237i	$-0.986906\pi$
$853$	−11.3440	−	24.3274i	−0.388413	−	0.832954i	0.610741	−	0.791830i	$-0.290872\pi$
$854$	−0.543044	+	0.940580i	−0.0185826	+	0.0321860i
$855$		0			0
$856$	−2.09046	−	3.62078i	−0.0714503	−	0.123756i
$857$	−9.01794	+	12.8789i	−0.308047	+	0.439936i	−0.943089	−	0.332541i	$-0.892094\pi$
$857$	−9.01794	+	12.8789i	−0.308047	+	0.439936i	0.635042	+	0.772478i	$0.280983\pi$
$858$	−1.26489	−	1.35969i	−0.0431825	−	0.0464191i
$859$	−16.8242	−	46.2242i	−0.574035	−	1.57715i	−0.798068	−	0.602567i	$-0.794144\pi$
$859$	−16.8242	−	46.2242i	−0.574035	−	1.57715i	0.224033	−	0.974582i	$-0.428078\pi$
$860$		0			0
$861$	7.70274	+	1.64693i	0.262509	+	0.0561272i
$862$	0.116352	−	1.32991i	0.00396296	−	0.0452968i
$863$	−5.61483	+	5.61483i	−0.191131	+	0.191131i	−0.796185	−	0.605054i	$-0.793152\pi$
$863$	−5.61483	+	5.61483i	−0.191131	+	0.191131i	0.605054	+	0.796185i	$0.293152\pi$
$864$	−1.35324	+	4.65600i	−0.0460381	+	0.158400i
$865$		0			0
$866$	0.534491	+	0.636981i	0.0181627	+	0.0216455i
$867$	2.96326	−	0.151734i	0.100638	−	0.00515314i
$868$	4.44347	−	3.11135i	0.150821	−	0.105606i
$869$	38.7487	−	14.1034i	1.31446	−	0.478424i
$870$		0			0
$871$	−9.63637	−	54.6506i	−0.326516	−	1.85176i
$872$	−0.864375	+	3.22589i	−0.0292714	+	0.109242i
$873$	36.3431	+	20.2594i	1.23003	+	0.685678i
$874$	−0.624307	−	0.360444i	−0.0211175	−	0.0121922i
$875$		0			0
$876$	−0.751169	+	0.585427i	−0.0253796	+	0.0197798i
$877$	16.1776	−	1.41536i	0.546279	−	0.0477932i	0.189324	−	0.981915i	$-0.439370\pi$
$877$	16.1776	−	1.41536i	0.546279	−	0.0477932i	0.356955	+	0.934122i	$0.383815\pi$
$878$	0.983986	−	0.0860876i	0.0332079	−	0.00290532i
$879$	6.79078	+	48.7431i	0.229047	+	1.64407i
$880$		0			0
$881$	−23.5094	−	13.5731i	−0.792051	−	0.457291i	0.0486330	−	0.998817i	$-0.484514\pi$
$881$	−23.5094	−	13.5731i	−0.792051	−	0.457291i	−0.840684	+	0.541526i	$0.817847\pi$
$882$	0.744158	−	0.914464i	0.0250571	−	0.0307916i
$883$	8.38602	−	31.2970i	0.282212	−	1.05323i	−0.668641	−	0.743586i	$-0.733124\pi$
$883$	8.38602	−	31.2970i	0.282212	−	1.05323i	0.950853	−	0.309644i	$-0.100210\pi$
$884$	5.61923	+	31.8682i	0.188995	+	1.07184i
$885$		0			0
$886$	2.34117	−	0.852117i	0.0786532	−	0.0286274i
$887$	−24.1100	+	16.8820i	−0.809534	+	0.566842i	−0.903428	−	0.428740i	$-0.858957\pi$
$887$	−24.1100	+	16.8820i	−0.809534	+	0.566842i	0.0938937	+	0.995582i	$0.470069\pi$
$888$	1.97520	−	3.86509i	0.0662835	−	0.129704i
$889$	−18.4585	−	21.9980i	−0.619079	−	0.737789i
$890$		0			0
$891$	−25.8612	−	20.4056i	−0.866384	−	0.683613i
$892$	−6.81707	+	6.81707i	−0.228252	+	0.228252i
$893$	0.162651	−	1.85911i	0.00544291	−	0.0622127i
$894$	−0.0274809	−	0.0849240i	−0.000919099	−	0.00284028i
$895$		0			0
$896$	1.18924	+	3.26741i	0.0397297	+	0.109156i
$897$	−36.1601	+	8.30255i	−1.20735	+	0.277214i
$898$	−1.19825	+	1.71127i	−0.0399860	+	0.0571060i
$899$	−4.13296	−	7.15850i	−0.137842	−	0.238749i
$900$		0			0
$901$	22.9469	−	39.7452i	0.764473	−	1.32411i
$902$	−0.391669	−	0.839938i	−0.0130412	−	0.0279669i
$903$	−1.20529	+	1.59549i	−0.0401096	+	0.0530946i
$904$	0.891191	−	1.06208i	0.0296406	−	0.0353242i
$905$		0			0
$906$	0.00762798	+	0.00978755i	0.000253423	+	0.000325170i
$907$	−28.5940	+	13.3336i	−0.949447	+	0.442735i	−0.834727	−	0.550663i	$-0.814375\pi$
$907$	−28.5940	+	13.3336i	−0.949447	+	0.442735i	−0.114720	+	0.993398i	$0.536597\pi$
$908$	6.63969	+	24.7797i	0.220346	+	0.822342i
$909$	13.7601	+	13.3520i	0.456395	+	0.442857i
$910$		0			0
$911$	−4.44253	+	0.783337i	−0.147187	+	0.0259531i	−0.246756	−	0.969078i	$-0.579365\pi$
$911$	−4.44253	+	0.783337i	−0.147187	+	0.0259531i	0.0995689	+	0.995031i	$0.468254\pi$
$912$	−10.6125	−	3.25849i	−0.351414	−	0.107899i
$913$	56.6490	+	26.4158i	1.87481	+	0.874237i
$914$	0.291572	−	1.65359i	0.00964433	−	0.0546957i
$915$		0			0
$916$	−1.00872	+	0.846419i	−0.0333292	+	0.0279665i
$917$	−19.1655	−	19.1655i	−0.632902	−	0.632902i
$918$	−0.565402	−	1.66145i	−0.0186610	−	0.0548359i
$919$		−	42.2613i		−	1.39407i	−0.717036	−	0.697037i	$-0.754502\pi$
$919$		−	42.2613i		−	1.39407i	0.717036	−	0.697037i	$-0.245498\pi$
$920$		0			0
$921$	−9.39334	+	43.9330i	−0.309521	+	1.44764i
$922$	−1.07957	−	1.54178i	−0.0355536	−	0.0507759i
$923$	−14.8749	+	31.8993i	−0.489613	+	1.04998i
$924$	−17.7153	−	0.639912i	−0.582792	−	0.0210516i
$925$		0			0
$926$	1.77211	−	1.02313i	0.0582353	−	0.0336222i
$927$	−3.38551	−	17.6428i	−0.111195	−	0.579466i
$928$	3.84042	−	1.02904i	0.126068	−	0.0337798i
$929$	12.2132	+	4.44523i	0.400701	+	0.145843i	0.534507	−	0.845164i	$-0.320497\pi$
$929$	12.2132	+	4.44523i	0.400701	+	0.145843i	−0.133805	+	0.991008i	$0.542720\pi$
$930$		0			0
$931$	6.23535	+	5.23208i	0.204355	+	0.171475i
$932$	1.69864	+	19.4155i	0.0556407	+	0.635976i
$933$	−35.6318	+	15.0744i	−1.16653	+	0.493514i
$934$	0.316911	−	0.870707i	0.0103697	−	0.0284904i
$935$		0			0
$936$	3.15821	−	1.53099i	0.103229	−	0.0500421i
$937$	−20.7151	−	5.55061i	−0.676734	−	0.181330i	−0.0959478	−	0.995386i	$-0.530588\pi$
$937$	−20.7151	−	5.55061i	−0.676734	−	0.181330i	−0.580786	+	0.814056i	$0.697255\pi$
$938$	1.32667	+	0.928943i	0.0433172	+	0.0303311i
$939$	−1.67605	+	46.3998i	−0.0546958	+	1.51420i
$940$		0			0
$941$	56.2257	+	9.91411i	1.83291	+	0.323191i	0.980019	−	0.198904i	$-0.0637383\pi$
$941$	56.2257	+	9.91411i	1.83291	+	0.323191i	0.852887	+	0.522095i	$0.174849\pi$
$942$	−1.73737	+	1.12530i	−0.0566065	+	0.0366642i
$943$	−18.4448	−	1.61371i	−0.600647	−	0.0525498i
$944$	41.5755			1.35317
$945$		0			0
$946$	0.235265			0.00764914
$947$	24.4864	+	2.14228i	0.795702	+	0.0696149i	0.477754	−	0.878493i	$-0.341451\pi$
$947$	24.4864	+	2.14228i	0.795702	+	0.0696149i	0.317947	+	0.948108i	$0.397006\pi$
$948$	1.98961	+	38.8559i	0.0646197	+	1.26198i
$949$	1.01886	+	0.179653i	0.0330736	+	0.00583177i
$950$		0			0
$951$	−32.0113	+	16.9715i	−1.03804	+	0.550338i
$952$	−1.54960	−	1.08504i	−0.0502227	−	0.0351663i
$953$	18.6903	+	5.00806i	0.605439	+	0.162227i	0.548500	−	0.836151i	$-0.315199\pi$
$953$	18.6903	+	5.00806i	0.605439	+	0.162227i	0.0569395	+	0.998378i	$0.481866\pi$
$954$	−2.40975	−	0.606964i	−0.0780186	−	0.0196512i
$955$		0			0
$956$	13.9943	−	38.4491i	0.452609	−	1.24353i
$957$	−3.32417	+	26.8073i	−0.107455	+	0.866556i
$958$	0.102724	+	1.17414i	0.00331887	+	0.0379348i
$959$	9.70297	+	8.14176i	0.313325	+	0.262911i
$960$		0			0
$961$	25.5939	+	9.31543i	0.825610	+	0.300498i
$962$	−2.27384	+	0.609273i	−0.0733114	+	0.0196437i
$963$	−6.38747	+	39.7120i	−0.205833	+	1.27970i
$964$	−8.92824	+	5.15472i	−0.287559	+	0.166022i
$965$		0			0
$966$	0.574887	−	0.917561i	0.0184967	−	0.0295220i
$967$	−15.5485	+	33.3438i	−0.500005	+	1.07226i	0.480720	+	0.876874i	$0.340375\pi$
$967$	−15.5485	+	33.3438i	−0.500005	+	1.07226i	−0.980726	+	0.195390i	$0.937403\pi$
$968$	0.428807	+	0.612400i	0.0137824	+	0.0196833i
$969$	11.5280	−	3.73039i	0.370332	−	0.119837i
$970$		0			0
$971$			31.1249i			0.998846i	0.866358	+	0.499423i	$0.166455\pi$
$971$			31.1249i			0.998846i	−0.866358	+	0.499423i	$0.833545\pi$
$972$	25.5673	−	17.6748i	0.820070	−	0.566920i
$973$	5.42013	+	5.42013i	0.173761	+	0.173761i
$974$	1.48091	−	1.24263i	0.0474515	−	0.0398166i
$975$		0			0
$976$	6.82694	−	38.7175i	0.218525	−	1.23932i
$977$	−43.0480	−	20.0736i	−1.37723	−	0.642211i	−0.413845	−	0.910347i	$-0.635815\pi$
$977$	−43.0480	−	20.0736i	−1.37723	−	0.642211i	−0.963381	+	0.268136i	$0.913592\pi$
$978$	−0.218788	−	0.952889i	−0.00699607	−	0.0304700i
$979$	−48.8611	+	8.61554i	−1.56161	+	0.275354i
$980$		0			0
$981$	26.0385	−	18.8228i	0.831345	−	0.600965i
$982$	−0.849365	−	3.16987i	−0.0271043	−	0.101155i
$983$	2.95806	−	1.37937i	0.0943476	−	0.0439950i	−0.374872	−	0.927077i	$-0.622313\pi$
$983$	2.95806	−	1.37937i	0.0943476	−	0.0439950i	0.469219	+	0.883082i	$0.344535\pi$
$984$	1.73478	−	0.241686i	0.0553028	−	0.00770466i
$985$		0			0
$986$	−0.925041	+	1.10242i	−0.0294593	+	0.0351082i
$987$	2.78176	+	0.344945i	0.0885444	+	0.0109797i
$988$	5.11243	+	10.9636i	0.162648	+	0.348800i
$989$	2.35011	−	4.07050i	0.0747290	−	0.129434i
$990$		0			0
$991$	−14.1507	−	24.5098i	−0.449513	−	0.778579i	0.548841	−	0.835927i	$-0.315069\pi$
$991$	−14.1507	−	24.5098i	−0.449513	−	0.778579i	−0.998354	+	0.0573473i	$0.981736\pi$
$992$	1.03831	−	1.48287i	0.0329665	−	0.0470810i
$993$	−6.08050	+	19.8034i	−0.192959	+	0.628442i
$994$	−0.351327	−	0.965264i	−0.0111434	−	0.0306163i
$995$		0			0
$996$	−39.5147	+	43.7798i	−1.25207	+	1.38722i
$997$	−4.65748	+	53.2353i	−0.147504	+	1.68598i	0.457071	+	0.889430i	$0.348899\pi$
$997$	−4.65748	+	53.2353i	−0.147504	+	1.68598i	−0.604575	+	0.796548i	$0.706657\pi$
$998$	1.28044	−	1.28044i	0.0405315	−	0.0405315i
$999$	−38.2089	+	16.8472i	−1.20888	+	0.533021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.a.518.7	yes	144
5.2	odd	4	inner	675.2.ba.a.32.6	✓	144
5.3	odd	4	inner	675.2.ba.a.32.7	yes	144
5.4	even	2	inner	675.2.ba.a.518.6	yes	144
27.11	odd	18	inner	675.2.ba.a.443.6	yes	144
135.38	even	36	inner	675.2.ba.a.632.6	yes	144
135.92	even	36	inner	675.2.ba.a.632.7	yes	144
135.119	odd	18	inner	675.2.ba.a.443.7	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.ba.a.32.6	✓	144	5.2	odd	4	inner
675.2.ba.a.32.7	yes	144	5.3	odd	4	inner
675.2.ba.a.443.6	yes	144	27.11	odd	18	inner
675.2.ba.a.443.7	yes	144	135.119	odd	18	inner
675.2.ba.a.518.6	yes	144	5.4	even	2	inner
675.2.ba.a.518.7	yes	144	1.1	even	1	trivial
675.2.ba.a.632.6	yes	144	135.38	even	36	inner
675.2.ba.a.632.7	yes	144	135.92	even	36	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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0777805 + 0.00680491i) q^{2} +(1.54232 + 0.788185i) q^{3} +(-1.96361 - 0.346238i) q^{4} +(0.114599 + 0.0718008i) q^{6} +(-1.14874 - 0.804356i) q^{7} +(-0.301209 - 0.0807087i) q^{8} +(1.75753 + 2.43127i) q^{9} +(-1.25188 + 3.43951i) q^{11} +(-2.75563 - 2.08170i) q^{12} +(0.326983 + 3.73743i) q^{13} +(-0.0838760 - 0.0703803i) q^{14} +(3.72443 + 1.35558i) q^{16} +(-4.17846 + 1.11962i) q^{17} +(0.120157 + 0.201066i) q^{18} +(-1.40048 + 0.808565i) q^{19} +(-1.13775 - 2.14600i) q^{21} +(-0.120777 + 0.259008i) q^{22} +(3.27482 + 4.67693i) q^{23} +(-0.400948 - 0.361887i) q^{24} +0.292925i q^{26} +(0.794382 + 5.13507i) q^{27} +(1.97718 + 1.97718i) q^{28} +(3.26399 - 2.73881i) q^{29} +(0.336874 - 1.91051i) q^{31} +(0.845700 + 0.394356i) q^{32} +(-4.64178 + 4.31813i) q^{33} +(-0.332622 + 0.0586502i) q^{34} +(-2.60930 - 5.38260i) q^{36} +(2.07996 + 7.76253i) q^{37} +(-0.114432 + 0.0533605i) q^{38} +(-2.44148 + 6.02206i) q^{39} +(-2.08450 + 2.48421i) q^{41} +(-0.0738912 - 0.174659i) q^{42} +(-0.347912 - 0.746099i) q^{43} +(3.64909 - 6.32042i) q^{44} +(0.222891 + 0.386059i) q^{46} +(-0.661922 + 0.945323i) q^{47} +(4.67583 + 5.02629i) q^{48} +(-1.72153 - 4.72986i) q^{49} +(-7.32701 - 1.56659i) q^{51} +(0.651973 - 7.45209i) q^{52} +(-7.50182 + 7.50182i) q^{53} +(0.0268437 + 0.404814i) q^{54} +(0.281092 + 0.334993i) q^{56} +(-2.79729 + 0.143235i) q^{57} +(0.272512 - 0.190815i) q^{58} +(9.85710 - 3.58769i) q^{59} +(-1.72247 - 9.76861i) q^{61} +(0.0392030 - 0.146308i) q^{62} +(-0.0633310 - 4.20658i) q^{63} +(-6.80182 - 3.92703i) q^{64} +(-0.390424 + 0.304279i) q^{66} +(-14.7353 + 1.28917i) q^{67} +(8.59253 - 0.751749i) q^{68} +(1.36455 + 9.79451i) q^{69} +(8.12470 + 4.69080i) q^{71} +(-0.333158 - 0.874169i) q^{72} +(0.0713724 - 0.266365i) q^{73} +(0.108957 + 0.617928i) q^{74} +(3.02995 - 1.10281i) q^{76} +(4.20468 - 2.94415i) q^{77} +(-0.230879 + 0.451785i) q^{78} +(-7.24149 - 8.63007i) q^{79} +(-2.82219 + 8.54607i) q^{81} +(-0.179038 + 0.179038i) q^{82} +(1.48834 - 17.0118i) q^{83} +(1.49107 + 4.60784i) q^{84} +(-0.0219836 - 0.0603995i) q^{86} +(7.19282 - 1.65151i) q^{87} +(0.654676 - 0.934974i) q^{88} +(6.77753 + 11.7390i) q^{89} +(2.63061 - 4.55635i) q^{91} +(-4.81115 - 10.3175i) q^{92} +(2.02540 - 2.68110i) q^{93} +(-0.0579174 + 0.0690233i) q^{94} +(0.993517 + 1.27479i) q^{96} +(12.5700 - 5.86150i) q^{97} +(-0.101715 - 0.379605i) q^{98} +(-10.5626 + 3.00137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 12 q^{6} - 48 q^{21} + 84 q^{36} + 36 q^{41} - 84 q^{51} - 324 q^{56} + 36 q^{61} - 288 q^{66} - 144 q^{71} - 216 q^{76} - 132 q^{81} - 288 q^{86} + 36 q^{91} + 132 q^{96}+O(q^{100}) \) 144 * q + 12 * q^6 - 48 * q^21 + 84 * q^36 + 36 * q^41 - 84 * q^51 - 324 * q^56 + 36 * q^61 - 288 * q^66 - 144 * q^71 - 216 * q^76 - 132 * q^81 - 288 * q^86 + 36 * q^91 + 132 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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