LMFDB - Embedded newform 675.2.u.b.574.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(49,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 9]))

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

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

chi := DirichletCharacter("675.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			574.2
Character	$\chi$	$=$	675.574
Dual form			675.2.u.b.274.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.274138 - 0.753189i) q^{2} +(-0.386327 - 1.68842i) q^{3} +(1.03995 - 0.872619i) q^{4} +(-1.16579 + 0.753837i) q^{6} +(1.52780 - 1.82076i) q^{7} +(-2.33062 - 1.34559i) q^{8} +(-2.70150 + 1.30456i) q^{9} +O(q^{10})$	\(q+(-0.274138 - 0.753189i) q^{2} +(-0.386327 - 1.68842i) q^{3} +(1.03995 - 0.872619i) q^{4} +(-1.16579 + 0.753837i) q^{6} +(1.52780 - 1.82076i) q^{7} +(-2.33062 - 1.34559i) q^{8} +(-2.70150 + 1.30456i) q^{9} +(-0.0434396 + 0.246358i) q^{11} +(-1.87510 - 1.41875i) q^{12} +(0.893351 - 2.45446i) q^{13} +(-1.79020 - 0.651581i) q^{14} +(0.0969067 - 0.549585i) q^{16} +(0.254072 - 0.146688i) q^{17} +(1.72317 + 1.67711i) q^{18} +(-1.39237 + 2.41166i) q^{19} +(-3.66443 - 1.87615i) q^{21} +(0.197463 - 0.0348180i) q^{22} +(-4.30015 - 5.12472i) q^{23} +(-1.37153 + 4.45490i) q^{24} -2.09357 q^{26} +(3.24631 + 4.05728i) q^{27} -3.22668i q^{28} +(-0.333645 + 0.121437i) q^{29} +(2.11847 - 1.77761i) q^{31} +(-5.74108 + 1.01231i) q^{32} +(0.432738 - 0.0218307i) q^{33} +(-0.180135 - 0.151151i) q^{34} +(-1.67103 + 3.71406i) q^{36} +(6.05558 - 3.49619i) q^{37} +(2.19814 + 0.387591i) q^{38} +(-4.48928 - 0.560124i) q^{39} +(9.13156 + 3.32362i) q^{41} +(-0.408537 + 3.27434i) q^{42} +(0.256746 + 0.0452712i) q^{43} +(0.169802 + 0.294106i) q^{44} +(-2.68104 + 4.64370i) q^{46} +(-7.34421 + 8.75249i) q^{47} +(-0.965367 + 0.0487006i) q^{48} +(0.234540 + 1.33014i) q^{49} +(-0.345826 - 0.372309i) q^{51} +(-1.21277 - 3.33207i) q^{52} +5.43137i q^{53} +(2.16596 - 3.55734i) q^{54} +(-6.01071 + 2.18772i) q^{56} +(4.60980 + 1.41922i) q^{57} +(0.182930 + 0.218007i) q^{58} +(-1.03788 - 5.88612i) q^{59} +(-9.07515 - 7.61495i) q^{61} +(-1.91963 - 1.10830i) q^{62} +(-1.75206 + 6.91190i) q^{63} +(1.77824 + 3.08001i) q^{64} +(-0.135073 - 0.319949i) q^{66} +(-0.619160 + 1.70113i) q^{67} +(0.136218 - 0.374256i) q^{68} +(-6.99139 + 9.24026i) q^{69} +(0.185255 + 0.320871i) q^{71} +(8.05158 + 0.594663i) q^{72} +(-4.35333 - 2.51339i) q^{73} +(-4.29336 - 3.60255i) q^{74} +(0.656467 + 3.72301i) q^{76} +(0.382193 + 0.455479i) q^{77} +(0.808804 + 3.53483i) q^{78} +(0.754406 - 0.274581i) q^{79} +(5.59624 - 7.04855i) q^{81} -7.78892i q^{82} +(0.942488 + 2.58947i) q^{83} +(-5.44798 + 1.24655i) q^{84} +(-0.0362861 - 0.205789i) q^{86} +(0.333932 + 0.516417i) q^{87} +(0.432738 - 0.515717i) q^{88} +(5.22533 - 9.05054i) q^{89} +(-3.10412 - 5.37650i) q^{91} +(-8.94385 - 1.57704i) q^{92} +(-3.81976 - 2.89012i) q^{93} +(8.60560 + 3.13218i) q^{94} +(3.92713 + 9.30225i) q^{96} +(14.6092 + 2.57600i) q^{97} +(0.937552 - 0.541296i) q^{98} +(-0.204037 - 0.722208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4}+O(q^{10}) $ 24 * q + 12 * q^4	$ 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) $ 24 * q + 12 * q^4 + 6 * q^11 - 30 * q^14 + 6 * q^19 - 24 * q^21 + 36 * q^24 - 60 * q^26 + 12 * q^29 + 6 * q^31 - 18 * q^34 + 36 * q^36 - 66 * q^39 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 24 * q^49 - 36 * q^51 + 108 * q^54 - 66 * q^56 + 24 * q^59 + 24 * q^61 - 24 * q^64 - 18 * q^66 - 18 * q^69 + 54 * q^71 - 66 * q^74 - 96 * q^76 + 84 * q^79 + 72 * q^81 - 12 * q^84 + 102 * q^86 - 18 * q^89 + 12 * q^91 + 30 * q^94 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.274138	−	0.753189i	−0.193845	−	0.532585i	0.804249	−	0.594292i	$-0.202568\pi$
$2$	−0.274138	−	0.753189i	−0.193845	−	0.532585i	−0.998094	+	0.0617072i	$0.980346\pi$
$3$	−0.386327	−	1.68842i	−0.223046	−	0.974808i
$3$	−0.386327	−	1.68842i	−0.223046	−	0.974808i
$4$	1.03995	−	0.872619i	0.519974	−	0.436310i
$5$		0			0
$5$		0			0
$6$	−1.16579	+	0.753837i	−0.475932	+	0.307753i
$7$	1.52780	−	1.82076i	0.577454	−	0.688183i	−0.395689	−	0.918385i	$-0.629494\pi$
$7$	1.52780	−	1.82076i	0.577454	−	0.688183i	0.973143	+	0.230202i	$0.0739386\pi$
$8$	−2.33062	−	1.34559i	−0.823999	−	0.475736i
$9$	−2.70150	+	1.30456i	−0.900501	+	0.434854i
$10$		0			0
$11$	−0.0434396	+	0.246358i	−0.0130975	+	0.0742798i	−0.990656	−	0.136385i	$-0.956452\pi$
$11$	−0.0434396	+	0.246358i	−0.0130975	+	0.0742798i	0.977558	+	0.210665i	$0.0675628\pi$
$12$	−1.87510	−	1.41875i	−0.541296	−	0.409557i
$13$	0.893351	−	2.45446i	0.247771	−	0.680745i	−0.751996	−	0.659167i	$-0.770909\pi$
$13$	0.893351	−	2.45446i	0.247771	−	0.680745i	0.999767	−	0.0215777i	$-0.00686892\pi$
$14$	−1.79020	−	0.651581i	−0.478452	−	0.174142i
$15$		0			0
$16$	0.0969067	−	0.549585i	0.0242267	−	0.137396i
$17$	0.254072	−	0.146688i	0.0616215	−	0.0355772i	−0.468873	−	0.883266i	$-0.655340\pi$
$17$	0.254072	−	0.146688i	0.0616215	−	0.0355772i	0.530494	+	0.847689i	$0.322006\pi$
$18$	1.72317	+	1.67711i	0.406154	+	0.395299i
$19$	−1.39237	+	2.41166i	−0.319432	+	0.553273i	−0.980370	−	0.197168i	$-0.936825\pi$
$19$	−1.39237	+	2.41166i	−0.319432	+	0.553273i	0.660937	+	0.750441i	$0.270159\pi$
$20$		0			0
$21$	−3.66443	−	1.87615i	−0.799645	−	0.409410i
$22$	0.197463	−	0.0348180i	0.0420992	−	0.00742323i
$23$	−4.30015	−	5.12472i	−0.896643	−	1.06858i	−0.997284	−	0.0736543i	$-0.976534\pi$
$23$	−4.30015	−	5.12472i	−0.896643	−	1.06858i	0.100641	−	0.994923i	$-0.467911\pi$
$24$	−1.37153	+	4.45490i	−0.279962	+	0.909352i
$25$		0			0
$26$	−2.09357			−0.410584
$27$	3.24631	+	4.05728i	0.624752	+	0.780823i
$28$		−	3.22668i		−	0.609786i
$29$	−0.333645	+	0.121437i	−0.0619562	+	0.0225502i	−0.372812	−	0.927907i	$-0.621606\pi$
$29$	−0.333645	+	0.121437i	−0.0619562	+	0.0225502i	0.310856	+	0.950457i	$0.399384\pi$
$30$		0			0
$31$	2.11847	−	1.77761i	0.380488	−	0.319268i	−0.432406	−	0.901679i	$-0.642335\pi$
$31$	2.11847	−	1.77761i	0.380488	−	0.319268i	0.812894	+	0.582411i	$0.197891\pi$
$32$	−5.74108	+	1.01231i	−1.01489	+	0.178952i
$33$	0.432738	−	0.0218307i	0.0753299	−	0.00380023i
$34$	−0.180135	−	0.151151i	−0.0308929	−	0.0259222i
$35$		0			0
$36$	−1.67103	+	3.71406i	−0.278506	+	0.619010i
$37$	6.05558	−	3.49619i	0.995531	−	0.574770i	0.0886080	−	0.996067i	$-0.471758\pi$
$37$	6.05558	−	3.49619i	0.995531	−	0.574770i	0.906923	+	0.421297i	$0.138425\pi$
$38$	2.19814	+	0.387591i	0.356585	+	0.0628756i
$39$	−4.48928	−	0.560124i	−0.718860	−	0.0896917i
$40$		0			0
$41$	9.13156	+	3.32362i	1.42611	+	0.519062i	0.935814	−	0.352494i	$-0.114666\pi$
$41$	9.13156	+	3.32362i	1.42611	+	0.519062i	0.490296	+	0.871556i	$0.336888\pi$
$42$	−0.408537	+	3.27434i	−0.0630386	+	0.505241i
$43$	0.256746	+	0.0452712i	0.0391534	+	0.00690379i	0.193191	−	0.981161i	$-0.438116\pi$
$43$	0.256746	+	0.0452712i	0.0391534	+	0.00690379i	−0.154037	+	0.988065i	$0.549228\pi$
$44$	0.169802	+	0.294106i	0.0255986	+	0.0443381i
$45$		0			0
$46$	−2.68104	+	4.64370i	−0.395298	+	0.684677i
$47$	−7.34421	+	8.75249i	−1.07126	+	1.27668i	−0.112140	+	0.993692i	$0.535770\pi$
$47$	−7.34421	+	8.75249i	−1.07126	+	1.27668i	−0.959123	+	0.282989i	$0.908674\pi$
$48$	−0.965367	+	0.0487006i	−0.139339	+	0.00702933i
$49$	0.234540	+	1.33014i	0.0335057	+	0.190020i
$50$		0			0
$51$	−0.345826	−	0.372309i	−0.0484253	−	0.0521337i
$52$	−1.21277	−	3.33207i	−0.168181	−	0.462074i
$53$			5.43137i			0.746056i	0.927820	+	0.373028i	$0.121680\pi$
$53$			5.43137i			0.746056i	−0.927820	+	0.373028i	$0.878320\pi$
$54$	2.16596	−	3.55734i	0.294750	−	0.484092i
$55$		0			0
$56$	−6.01071	+	2.18772i	−0.803215	+	0.292346i
$57$	4.60980	+	1.41922i	0.610583	+	0.187980i
$58$	0.182930	+	0.218007i	0.0240198	+	0.0286257i
$59$	−1.03788	−	5.88612i	−0.135121	−	0.766308i	−0.974776	−	0.223188i	$-0.928354\pi$
$59$	−1.03788	−	5.88612i	−0.135121	−	0.766308i	0.839655	−	0.543121i	$-0.182757\pi$
$60$		0			0
$61$	−9.07515	−	7.61495i	−1.16195	−	0.974995i	−0.162023	−	0.986787i	$-0.551802\pi$
$61$	−9.07515	−	7.61495i	−1.16195	−	0.974995i	−0.999930	+	0.0117924i	$0.996246\pi$
$62$	−1.91963	−	1.10830i	−0.243793	−	0.140754i
$63$	−1.75206	+	6.91190i	−0.220739	+	0.870817i
$64$	1.77824	+	3.08001i	0.222281	+	0.385001i
$65$		0			0
$66$	−0.135073	−	0.319949i	−0.0166263	−	0.0393829i
$67$	−0.619160	+	1.70113i	−0.0756424	+	0.207826i	−0.971751	−	0.236010i	$-0.924160\pi$
$67$	−0.619160	+	1.70113i	−0.0756424	+	0.207826i	0.896108	+	0.443835i	$0.146383\pi$
$68$	0.136218	−	0.374256i	0.0165189	−	0.0453852i
$69$	−6.99139	+	9.24026i	−0.841665	+	1.11240i
$70$		0			0
$71$	0.185255	+	0.320871i	0.0219857	+	0.0380804i	0.876809	−	0.480839i	$-0.159668\pi$
$71$	0.185255	+	0.320871i	0.0219857	+	0.0380804i	−0.854823	+	0.518919i	$0.826334\pi$
$72$	8.05158	+	0.594663i	0.948888	+	0.0700817i
$73$	−4.35333	−	2.51339i	−0.509518	−	0.294171i	0.223117	−	0.974792i	$-0.428377\pi$
$73$	−4.35333	−	2.51339i	−0.509518	−	0.294171i	−0.732636	+	0.680621i	$0.761710\pi$
$74$	−4.29336	−	3.60255i	−0.499093	−	0.418789i
$75$		0			0
$76$	0.656467	+	3.72301i	0.0753019	+	0.427059i
$77$	0.382193	+	0.455479i	0.0435549	+	0.0519067i
$78$	0.808804	+	3.53483i	0.0915790	+	0.400240i
$79$	0.754406	−	0.274581i	0.0848773	−	0.0308928i	−0.299233	−	0.954180i	$-0.596731\pi$
$79$	0.754406	−	0.274581i	0.0848773	−	0.0308928i	0.384110	+	0.923287i	$0.374508\pi$
$80$		0			0
$81$	5.59624	−	7.04855i	0.621804	−	0.783173i
$82$		−	7.78892i		−	0.860143i
$83$	0.942488	+	2.58947i	0.103452	+	0.284231i	0.980610	−	0.195971i	$-0.0627858\pi$
$83$	0.942488	+	2.58947i	0.103452	+	0.284231i	−0.877158	+	0.480201i	$0.840564\pi$
$84$	−5.44798	+	1.24655i	−0.594424	+	0.136010i
$85$		0			0
$86$	−0.0362861	−	0.205789i	−0.00391283	−	0.0221908i
$87$	0.333932	+	0.516417i	0.0358012	+	0.0553657i
$88$	0.432738	−	0.515717i	0.0461300	−	0.0549756i
$89$	5.22533	−	9.05054i	0.553884	−	0.959356i	−0.444105	−	0.895975i	$-0.646478\pi$
$89$	5.22533	−	9.05054i	0.553884	−	0.959356i	0.997989	−	0.0633809i	$-0.0201883\pi$
$90$		0			0
$91$	−3.10412	−	5.37650i	−0.325401	−	0.563611i
$92$	−8.94385	−	1.57704i	−0.932461	−	0.164418i
$93$	−3.81976	−	2.89012i	−0.396091	−	0.299692i
$94$	8.60560	+	3.13218i	0.887600	+	0.323060i
$95$		0			0
$96$	3.92713	+	9.30225i	0.400811	+	0.949407i
$97$	14.6092	+	2.57600i	1.48334	+	0.261553i	0.855913	−	0.517120i	$-0.172996\pi$
$97$	14.6092	+	2.57600i	1.48334	+	0.261553i	0.627430	+	0.778673i	$0.284107\pi$
$98$	0.937552	−	0.541296i	0.0947070	−	0.0546791i
$99$	−0.204037	−	0.722208i	−0.0205065	−	0.0725846i
$100$		0			0
$101$	3.06826	+	2.57457i	0.305303	+	0.256180i	0.782548	−	0.622591i	$-0.213920\pi$
$101$	3.06826	+	2.57457i	0.305303	+	0.256180i	−0.477244	+	0.878771i	$0.658364\pi$
$102$	−0.185615	+	0.362537i	−0.0183786	+	0.0358965i
$103$	5.82943	−	1.02789i	0.574391	−	0.101281i	0.121095	−	0.992641i	$-0.461359\pi$
$103$	5.82943	−	1.02789i	0.574391	−	0.101281i	0.453296	+	0.891360i	$0.350248\pi$
$104$	−5.38475	+	4.51834i	−0.528018	+	0.443060i
$105$		0			0
$106$	4.09085	−	1.48895i	0.397338	−	0.144619i
$107$			0.258978i			0.0250364i	0.999922	+	0.0125182i	$0.00398477\pi$
$107$			0.258978i			0.0250364i	−0.999922	+	0.0125182i	$0.996015\pi$
$108$	6.91645	+	1.38656i	0.665535	+	0.133422i
$109$	8.55787			0.819695			0.409848	−	0.912154i	$-0.365582\pi$
$109$	8.55787			0.819695			0.409848	+	0.912154i	$0.365582\pi$
$110$		0			0
$111$	−8.24246	−	8.87367i	−0.782340	−	0.842251i
$112$	−0.852609	−	1.01610i	−0.0805640	−	0.0960124i
$113$	3.07179	−	0.541640i	0.288970	−	0.0509532i	−0.0272843	−	0.999628i	$-0.508686\pi$
$113$	3.07179	−	0.541640i	0.288970	−	0.0509532i	0.316254	+	0.948675i	$0.397575\pi$
$114$	−0.194784	−	3.86111i	−0.0182432	−	0.361626i
$115$		0			0
$116$	−0.241005	+	0.417432i	−0.0223767	+	0.0387576i
$117$	0.788606	+	7.79617i	0.0729066	+	0.720756i
$118$	−4.14884	+	2.39533i	−0.381932	+	0.220508i
$119$	0.121086	−	0.686714i	0.0111000	−	0.0629510i
$120$		0			0
$121$	10.2778	+	3.74082i	0.934347	+	0.340074i
$122$	−3.24765	+	8.92285i	−0.294029	+	0.807837i
$123$	2.08388	−	16.7019i	0.187897	−	1.50596i
$124$	0.651922	−	3.69724i	0.0585444	−	0.332022i
$125$		0			0
$126$	5.68627	−	0.575183i	0.506573	−	0.0512414i
$127$	−15.9821	−	9.22726i	−1.41818	−	0.818787i	−0.422042	−	0.906576i	$-0.638686\pi$
$127$	−15.9821	−	9.22726i	−1.41818	−	0.818787i	−0.996139	+	0.0877893i	$0.972020\pi$
$128$	−5.66210	+	6.74783i	−0.500464	+	0.596430i
$129$	−0.0227511	−	0.450983i	−0.00200312	−	0.0397069i
$130$		0			0
$131$	10.8973	−	9.14396i	0.952105	−	0.798911i	−0.0275454	−	0.999621i	$-0.508769\pi$
$131$	10.8973	−	9.14396i	0.952105	−	0.798911i	0.979651	+	0.200709i	$0.0643246\pi$
$132$	0.430974	−	0.400318i	0.0375115	−	0.0348432i
$133$	2.26379	+	6.21971i	0.196295	+	0.539317i
$134$	1.45101			0.125348
$135$		0			0
$136$	−0.789527			−0.0677014
$137$	−6.73287	−	18.4984i	−0.575228	−	1.58042i	−0.796128	−	0.605128i	$-0.793122\pi$
$137$	−6.73287	−	18.4984i	−0.575228	−	1.58042i	0.220900	−	0.975296i	$-0.429100\pi$
$138$	8.87627	+	2.73273i	0.755598	+	0.232626i
$139$	13.7206	−	11.5129i	1.16377	−	0.976515i	0.163815	−	0.986491i	$-0.447620\pi$
$139$	13.7206	−	11.5129i	1.16377	−	0.976515i	0.999950	+	0.00997617i	$0.00317556\pi$
$140$		0			0
$141$	17.6151	+	9.01876i	1.48346	+	0.759517i
$142$	0.190891	−	0.227495i	0.0160192	−	0.0190910i
$143$	0.565870	+	0.326705i	0.0473205	+	0.0273205i
$144$	0.455174	+	1.61113i	0.0379312	+	0.134261i
$145$		0			0
$146$	−0.699647	+	3.96789i	−0.0579032	+	0.328385i
$147$	2.15522	−	0.909870i	0.177760	−	0.0750449i
$148$	3.24664	−	8.92007i	0.266872	−	0.733225i
$149$	15.3071	+	5.57132i	1.25401	+	0.456421i	0.881753	−	0.471711i	$-0.156363\pi$
$149$	15.3071	+	5.57132i	1.25401	+	0.456421i	0.372252	+	0.928132i	$0.378586\pi$
$150$		0			0
$151$	2.47880	−	14.0580i	0.201722	−	1.14402i	−0.700793	−	0.713365i	$-0.747170\pi$
$151$	2.47880	−	14.0580i	0.201722	−	1.14402i	0.902515	−	0.430659i	$-0.141719\pi$
$152$	6.49019	−	3.74711i	0.526424	−	0.303931i
$153$	−0.495012	+	0.727731i	−0.0400193	+	0.0588336i
$154$	0.238288	−	0.412728i	0.0192018	−	0.0332585i
$155$		0			0
$156$	−5.15739	+	3.33493i	−0.412922	+	0.267008i
$157$	0.751757	−	0.132555i	0.0599968	−	0.0105790i	−0.143569	−	0.989640i	$-0.545858\pi$
$157$	0.751757	−	0.132555i	0.0599968	−	0.0105790i	0.203566	+	0.979061i	$0.434747\pi$
$158$	−0.413623	−	0.492937i	−0.0329061	−	0.0392159i
$159$	9.17041	−	2.09828i	0.727261	−	0.166405i
$160$		0			0
$161$	−15.9006			−1.25315
$162$	−6.84304	−	2.28275i	−0.537640	−	0.179349i
$163$			5.12834i			0.401682i	0.979624	+	0.200841i	$0.0643675\pi$
$163$			5.12834i			0.401682i	−0.979624	+	0.200841i	$0.935632\pi$
$164$	12.3966	−	4.51199i	0.968011	−	0.352327i
$165$		0			0
$166$	1.69198	−	1.41974i	0.131323	−	0.110193i
$167$	8.76590	−	1.54566i	0.678325	−	0.119607i	0.176137	−	0.984366i	$-0.443640\pi$
$167$	8.76590	−	1.54566i	0.678325	−	0.119607i	0.502188	+	0.864759i	$0.332529\pi$
$168$	6.01588	+	9.30341i	0.464135	+	0.717774i
$169$	4.73227	+	3.97085i	0.364021	+	0.305450i
$170$		0			0
$171$	0.615340	−	8.33154i	0.0470562	−	0.637129i
$172$	0.306507	−	0.176962i	0.0233709	−	0.0134932i
$173$	−6.70776	−	1.18276i	−0.509982	−	0.0899235i	−0.0872644	−	0.996185i	$-0.527812\pi$
$173$	−6.70776	−	1.18276i	−0.509982	−	0.0899235i	−0.422717	+	0.906262i	$0.638924\pi$
$174$	0.297416	−	0.393083i	0.0225470	−	0.0297996i
$175$		0			0
$176$	0.131185	+	0.0477476i	0.00988847	+	0.00359911i
$177$	−9.53727	+	4.02635i	−0.716865	+	0.302639i
$178$	−8.24923	−	1.45456i	−0.618306	−	0.109024i
$179$	−9.17382	−	15.8895i	−0.685684	−	1.18764i	−0.973221	−	0.229870i	$-0.926170\pi$
$179$	−9.17382	−	15.8895i	−0.685684	−	1.18764i	0.287538	−	0.957769i	$-0.407163\pi$
$180$		0			0
$181$	−5.66282	+	9.80830i	−0.420914	+	0.729045i	−0.996029	−	0.0890276i	$-0.971624\pi$
$181$	−5.66282	+	9.80830i	−0.420914	+	0.729045i	0.575115	+	0.818073i	$0.304957\pi$
$182$	−3.19856	+	3.81190i	−0.237093	+	0.282557i
$183$	−9.35124	+	18.2645i	−0.691264	+	1.35015i
$184$	3.12628	+	17.7300i	0.230472	+	1.30707i
$185$		0			0
$186$	−1.12966	+	3.66930i	−0.0828310	+	0.269046i
$187$	0.0251011	+	0.0689648i	0.00183558	+	0.00504321i
$188$			15.5108i			1.13124i
$189$	12.3470	+	0.287957i	0.898115	+	0.0209458i
$190$		0			0
$191$	−6.44480	+	2.34571i	−0.466329	+	0.169730i	−0.564489	−	0.825441i	$-0.690927\pi$
$191$	−6.44480	+	2.34571i	−0.466329	+	0.169730i	0.0981596	+	0.995171i	$0.468704\pi$
$192$	4.51336	−	4.19231i	0.325724	−	0.302554i
$193$	13.1211	+	15.6371i	0.944477	+	1.12558i	0.991940	+	0.126711i	$0.0404420\pi$
$193$	13.1211	+	15.6371i	0.944477	+	1.12558i	−0.0474627	+	0.998873i	$0.515114\pi$
$194$	−2.06474	−	11.7097i	−0.148239	−	0.840707i
$195$		0			0
$196$	1.40462	+	1.17861i	0.100330	+	0.0841866i
$197$	2.62902	+	1.51786i	0.187310	+	0.108143i	0.590723	−	0.806875i	$-0.298843\pi$
$197$	2.62902	+	1.51786i	0.187310	+	0.108143i	−0.403413	+	0.915018i	$0.632176\pi$
$198$	−0.488024	+	0.351663i	−0.0346824	+	0.0249916i
$199$	−1.13124	−	1.95936i	−0.0801912	−	0.138895i	0.823141	−	0.567837i	$-0.192220\pi$
$199$	−1.13124	−	1.95936i	−0.0801912	−	0.138895i	−0.903332	+	0.428942i	$0.858886\pi$
$200$		0			0
$201$	3.11141	+	0.388209i	0.219462	+	0.0273821i
$202$	1.09801	−	3.01677i	0.0772560	−	0.212259i
$203$	−0.288635	+	0.793018i	−0.0202582	+	0.0556589i
$204$	−0.684525	−	0.0854077i	−0.0479263	−	0.00597974i
$205$		0			0
$206$	−2.37226	−	4.10888i	−0.165283	−	0.286279i
$207$	18.3024	+	8.23463i	1.27210	+	0.572346i
$208$	−1.26236	−	0.728826i	−0.0875292	−	0.0505350i
$209$	−0.533649	−	0.447784i	−0.0369132	−	0.0309739i
$210$		0			0
$211$	4.41601	+	25.0445i	0.304011	+	1.72413i	0.628124	+	0.778113i	$0.283823\pi$
$211$	4.41601	+	25.0445i	0.304011	+	1.72413i	−0.324113	+	0.946018i	$0.605066\pi$
$212$	4.73952	+	5.64834i	0.325511	+	0.387929i
$213$	0.470195	−	0.436749i	0.0322172	−	0.0299255i
$214$	0.195060	−	0.0709959i	0.0133340	−	0.00485318i
$215$		0			0
$216$	−2.10650	−	13.8242i	−0.143329	−	0.940615i
$217$		−	6.57305i		−	0.446208i
$218$	−2.34604	−	6.44569i	−0.158894	−	0.436557i
$219$	−2.56185	+	8.32122i	−0.173114	+	0.562296i
$220$		0			0
$221$	−0.133066	−	0.754654i	−0.00895097	−	0.0507635i
$222$	−4.42398	+	8.64074i	−0.296918	+	0.579929i
$223$	2.46274	−	2.93497i	0.164917	−	0.196540i	−0.677257	−	0.735747i	$-0.736831\pi$
$223$	2.46274	−	2.93497i	0.164917	−	0.196540i	0.842174	+	0.539206i	$0.181276\pi$
$224$	−6.92805	+	11.9997i	−0.462900	+	0.801766i
$225$		0			0
$226$	−1.25005	−	2.16515i	−0.0831523	−	0.144024i
$227$	−2.47777	−	0.436897i	−0.164455	−	0.0289979i	0.0908142	−	0.995868i	$-0.471053\pi$
$227$	−2.47777	−	0.436897i	−0.164455	−	0.0289979i	−0.255269	+	0.966870i	$0.582164\pi$
$228$	6.03238	−	2.54669i	0.399504	−	0.168659i
$229$	−14.9783	−	5.45167i	−0.989797	−	0.360257i	−0.204155	−	0.978939i	$-0.565445\pi$
$229$	−14.9783	−	5.45167i	−0.989797	−	0.360257i	−0.785642	+	0.618682i	$0.787667\pi$
$230$		0			0
$231$	0.621388	−	0.821264i	0.0408843	−	0.0540352i
$232$	0.941003	+	0.165924i	0.0617799	+	0.0108935i
$233$	24.3598	−	14.0641i	1.59586	−	0.921372i	0.603590	−	0.797295i	$-0.293736\pi$
$233$	24.3598	−	14.0641i	1.59586	−	0.921372i	0.992273	−	0.124077i	$-0.0395971\pi$
$234$	5.65580	−	2.73120i	0.369731	−	0.178544i
$235$		0			0
$236$	−6.21569	−	5.21558i	−0.404607	−	0.339505i
$237$	−0.755055	−	1.16767i	−0.0490461	−	0.0758485i
$238$	−0.550420	+	0.0970539i	−0.0356784	+	0.00629107i
$239$	11.2653	−	9.45270i	0.728691	−	0.611444i	−0.201083	−	0.979574i	$-0.564446\pi$
$239$	11.2653	−	9.45270i	0.728691	−	0.611444i	0.929774	+	0.368130i	$0.120002\pi$
$240$		0			0
$241$	−7.93378	+	2.88766i	−0.511059	+	0.186010i	−0.584662	−	0.811277i	$-0.698773\pi$
$241$	−7.93378	+	2.88766i	−0.511059	+	0.186010i	0.0736022	+	0.997288i	$0.476550\pi$
$242$		−	8.76664i		−	0.563541i
$243$	−14.0629	−	6.72574i	−0.902134	−	0.431456i
$244$	−16.0826			−1.02958
$245$		0			0
$246$	−13.1509	+	3.00907i	−0.838474	+	0.191851i
$247$	4.67545	+	5.57198i	0.297492	+	0.354537i
$248$	−7.32927	+	1.29235i	−0.465409	+	0.0820642i
$249$	4.00799	−	2.59169i	0.253996	−	0.164242i
$250$		0			0
$251$	11.6102	−	20.1095i	0.732832	−	1.26930i	−0.222835	−	0.974856i	$-0.571531\pi$
$251$	11.6102	−	20.1095i	0.732832	−	1.26930i	0.955668	−	0.294447i	$-0.0951354\pi$
$252$	4.20940	+	8.71689i	0.265168	+	0.549112i
$253$	1.44931	−	0.836762i	0.0911176	−	0.0526067i
$254$	−2.56857	+	14.5671i	−0.161166	+	0.914020i
$255$		0			0
$256$	13.3186	+	4.84758i	0.832413	+	0.302973i
$257$	−2.34804	+	6.45118i	−0.146466	+	0.402413i	−0.991132	−	0.132881i	$-0.957577\pi$
$257$	−2.34804	+	6.45118i	−0.146466	+	0.402413i	0.844666	+	0.535294i	$0.179799\pi$
$258$	−0.333439	+	0.140768i	−0.0207590	+	0.00876382i
$259$	2.88598	−	16.3672i	0.179326	−	1.01701i
$260$		0			0
$261$	0.742920	−	0.763321i	0.0459856	−	0.0472484i
$262$	−9.87451	−	5.70105i	−0.610049	−	0.352212i
$263$	−2.15523	+	2.56850i	−0.132897	+	0.158381i	−0.828389	−	0.560154i	$-0.810742\pi$
$263$	−2.15523	+	2.56850i	−0.132897	+	0.158381i	0.695492	+	0.718534i	$0.255187\pi$
$264$	−1.03792	−	0.531406i	−0.0638797	−	0.0327058i
$265$		0			0
$266$	4.06402	−	3.41012i	0.249181	−	0.209088i
$267$	−17.2998	−	5.32607i	−1.05873	−	0.325950i
$268$	0.840543	+	2.30937i	0.0513444	+	0.141067i
$269$	−12.7416			−0.776869			−0.388434	−	0.921476i	$-0.626984\pi$
$269$	−12.7416			−0.776869			−0.388434	+	0.921476i	$0.626984\pi$
$270$		0			0
$271$	−23.5566			−1.43096			−0.715481	−	0.698632i	$-0.753792\pi$
$271$	−23.5566			−1.43096			−0.715481	+	0.698632i	$0.753792\pi$
$272$	−0.0559965	−	0.153849i	−0.00339529	−	0.00932848i
$273$	−7.87857	+	7.31814i	−0.476833	+	0.442914i
$274$	−12.0871	+	10.1422i	−0.730206	+	0.612715i
$275$		0			0
$276$	0.792545	+	15.7102i	0.0477056	+	0.945643i
$277$	2.68763	−	3.20300i	0.161484	−	0.192450i	−0.679235	−	0.733921i	$-0.737688\pi$
$277$	2.68763	−	3.20300i	0.161484	−	0.192450i	0.840719	+	0.541472i	$0.182133\pi$
$278$	−12.4328	−	7.17806i	−0.745667	−	0.430511i
$279$	−3.40406	+	7.56589i	−0.203795	+	0.452958i
$280$		0			0
$281$	−3.75705	+	21.3073i	−0.224127	+	1.27109i	0.640220	+	0.768192i	$0.278843\pi$
$281$	−3.75705	+	21.3073i	−0.224127	+	1.27109i	−0.864347	+	0.502896i	$0.832268\pi$
$282$	1.96386	−	15.7399i	0.116946	−	0.937297i
$283$	1.78785	−	4.91209i	0.106277	−	0.291993i	−0.875143	−	0.483864i	$-0.839233\pi$
$283$	1.78785	−	4.91209i	0.106277	−	0.291993i	0.981420	+	0.191870i	$0.0614553\pi$
$284$	0.472654	+	0.172032i	0.0280468	+	0.0102082i
$285$		0			0
$286$	0.0909441	−	0.515770i	0.00537764	−	0.0304981i
$287$	20.0027	−	11.5486i	1.18072	−	0.681690i
$288$	14.1889	−	10.2243i	0.836090	−	0.602475i
$289$	−8.45697	+	14.6479i	−0.497469	+	0.861641i
$290$		0			0
$291$	−1.29457	−	25.6617i	−0.0758893	−	1.50431i
$292$	−6.72047	+	1.18500i	−0.393285	+	0.0693468i
$293$	−3.94811	−	4.70517i	−0.230651	−	0.274879i	0.638289	−	0.769797i	$-0.279643\pi$
$293$	−3.94811	−	4.70517i	−0.230651	−	0.274879i	−0.868940	+	0.494918i	$0.835198\pi$
$294$	−1.27613	−	1.37386i	−0.0744257	−	0.0801252i
$295$		0			0
$296$	−18.8177			−1.09376
$297$	−1.14056	+	0.623508i	−0.0661821	+	0.0361796i
$298$		−	13.0564i		−	0.756339i
$299$	−16.4200	+	5.97638i	−0.949591	+	0.345623i
$300$		0			0
$301$	0.474684	−	0.398307i	0.0273603	−	0.0229580i
$302$	−11.2679	+	1.98683i	−0.648393	+	0.114329i
$303$	3.16160	−	6.17513i	0.181629	−	0.354752i
$304$	1.19048	+	0.998934i	0.0682789	+	0.0572928i
$305$		0			0
$306$	0.683821	+	0.173338i	0.0390914	+	0.00990909i
$307$	−16.4578	+	9.50194i	−0.939298	+	0.542304i	−0.889740	−	0.456467i	$-0.849115\pi$
$307$	−16.4578	+	9.50194i	−0.939298	+	0.542304i	−0.0495580	+	0.998771i	$0.515781\pi$
$308$	0.794920	+	0.140166i	0.0452948	+	0.00798669i
$309$	−3.98757	−	9.44541i	−0.226845	−	0.537331i
$310$		0			0
$311$	20.2475	+	7.36948i	1.14813	+	0.417885i	0.844843	−	0.535015i	$-0.179694\pi$
$311$	20.2475	+	7.36948i	1.14813	+	0.417885i	0.303286	+	0.952900i	$0.401916\pi$
$312$	9.70912	+	7.34615i	0.549671	+	0.415894i
$313$	−3.75568	−	0.662228i	−0.212284	−	0.0374313i	0.0664949	−	0.997787i	$-0.478818\pi$
$313$	−3.75568	−	0.662228i	−0.212284	−	0.0374313i	−0.278778	+	0.960355i	$0.589930\pi$
$314$	−0.305925	−	0.529877i	−0.0172643	−	0.0299027i
$315$		0			0
$316$	0.544937	−	0.943859i	0.0306551	−	0.0530962i
$317$	2.73473	−	3.25913i	0.153598	−	0.183051i	−0.683758	−	0.729709i	$-0.739656\pi$
$317$	2.73473	−	3.25913i	0.153598	−	0.183051i	0.837356	+	0.546658i	$0.184100\pi$
$318$	−4.09437	−	6.33183i	−0.229601	−	0.355072i
$319$	−0.0154235	−	0.0874713i	−0.000863553	−	0.00489745i
$320$		0			0
$321$	0.437264	−	0.100050i	0.0244057	−	0.00558426i
$322$	4.35898	+	11.9762i	0.242916	+	0.667407i
$323$			0.816980i			0.0454580i
$324$	−0.330912	−	12.2135i	−0.0183840	−	0.678528i
$325$		0			0
$326$	3.86261	−	1.40587i	0.213930	−	0.0778642i
$327$	−3.30614	−	14.4493i	−0.182830	−	0.799046i
$328$	−16.8100	−	20.0334i	−0.928178	−	1.10616i
$329$	4.71570	+	26.7441i	0.259985	+	1.47445i
$330$		0			0
$331$	−10.9497	−	9.18787i	−0.601849	−	0.505011i	0.290191	−	0.956969i	$-0.406281\pi$
$331$	−10.9497	−	9.18787i	−0.601849	−	0.505011i	−0.892039	+	0.451958i	$0.850726\pi$
$332$	3.23976	+	1.87047i	0.177805	+	0.102656i
$333$	−11.7982	+	17.3448i	−0.646536	+	0.950491i
$334$	−3.56725	−	6.17865i	−0.195191	−	0.338081i
$335$		0			0
$336$	−1.38621	+	1.83211i	−0.0756242	+	0.0999496i
$337$	−12.2164	+	33.5644i	−0.665472	+	1.82837i	−0.115278	+	0.993333i	$0.536776\pi$
$337$	−12.2164	+	33.5644i	−0.665472	+	1.82837i	−0.550194	+	0.835037i	$0.685446\pi$
$338$	1.69350	−	4.65286i	0.0921143	−	0.253082i
$339$	−2.10123	−	4.97721i	−0.114123	−	0.270325i
$340$		0			0
$341$	0.345903	+	0.599121i	0.0187317	+	0.0324442i
$342$	−6.44391	+	1.82053i	−0.348447	+	0.0984429i
$343$	17.1890	+	9.92407i	0.928118	+	0.535849i
$344$	−0.537461	−	0.450983i	−0.0289780	−	0.0243154i
$345$		0			0
$346$	0.948013	+	5.37645i	0.0509655	+	0.289040i
$347$	12.4968	+	14.8931i	0.670862	+	0.799502i	0.988901	−	0.148575i	$-0.0474688\pi$
$347$	12.4968	+	14.8931i	0.670862	+	0.799502i	−0.318039	+	0.948078i	$0.603024\pi$
$348$	0.797906	+	0.245651i	0.0427723	+	0.0131683i
$349$	−7.53700	+	2.74324i	−0.403446	+	0.146842i	−0.535770	−	0.844364i	$-0.679978\pi$
$349$	−7.53700	+	2.74324i	−0.403446	+	0.146842i	0.132323	+	0.991207i	$0.457756\pi$
$350$		0			0
$351$	12.8585	−	4.34336i	0.686337	−	0.231832i
$352$		−	1.45834i		−	0.0777296i
$353$	−2.99398	−	8.22589i	−0.159354	−	0.437820i	0.834162	−	0.551520i	$-0.185952\pi$
$353$	−2.99398	−	8.22589i	−0.159354	−	0.437820i	−0.993515	+	0.113700i	$0.963730\pi$
$354$	5.64713	+	6.07959i	0.300142	+	0.323127i
$355$		0			0
$356$	−2.46361	−	13.9718i	−0.130571	−	0.740505i
$357$	−1.20624	+	0.0608521i	−0.0638409	+	0.00322063i
$358$	−9.45292	+	11.2656i	−0.499602	+	0.595403i
$359$	−4.13896	+	7.16888i	−0.218446	+	0.378359i	−0.954333	−	0.298745i	$-0.903432\pi$
$359$	−4.13896	+	7.16888i	−0.218446	+	0.378359i	0.735887	+	0.677104i	$0.236765\pi$
$360$		0			0
$361$	5.62260	+	9.73862i	0.295926	+	0.512559i
$362$	8.93990	+	1.57635i	0.469871	+	0.0828509i
$363$	2.34547	−	18.7984i	0.123105	−	0.986661i
$364$	−7.91977	−	2.88256i	−0.415108	−	0.151087i
$365$		0			0
$366$	16.3201	+	2.03625i	0.853068	+	0.106437i
$367$	14.5750	+	2.56997i	0.760809	+	0.134151i	0.540575	−	0.841296i	$-0.318207\pi$
$367$	14.5750	+	2.56997i	0.760809	+	0.134151i	0.220234	+	0.975447i	$0.429318\pi$
$368$	−3.23318	+	1.86668i	−0.168541	+	0.0973074i
$369$	−29.0048	+	2.93392i	−1.50993	+	0.152734i
$370$		0			0
$371$	9.88922	+	8.29804i	0.513423	+	0.430813i
$372$	−6.49433	+	0.327625i	−0.336715	+	0.0169865i
$373$	−25.1455	+	4.43383i	−1.30198	+	0.229575i	−0.781290	−	0.624168i	$-0.785438\pi$
$373$	−25.1455	+	4.43383i	−1.30198	+	0.229575i	−0.520694	+	0.853743i	$0.674327\pi$
$374$	0.0450623	−	0.0378118i	0.00233012	−	0.00195520i
$375$		0			0
$376$	28.8938	−	10.5165i	1.49008	−	0.542346i
$377$			0.927403i			0.0477637i
$378$	−3.16791	−	9.37859i	−0.162940	−	0.482383i
$379$	−20.1244			−1.03372			−0.516861	−	0.856070i	$-0.672899\pi$
$379$	−20.1244			−1.03372			−0.516861	+	0.856070i	$0.672899\pi$
$380$		0			0
$381$	−9.40516	+	30.5492i	−0.481841	+	1.56508i
$382$	3.53353	+	4.21110i	0.180791	+	0.215459i
$383$	23.4987	−	4.14346i	1.20073	−	0.211721i	0.462716	−	0.886507i	$-0.346875\pi$
$383$	23.4987	−	4.14346i	1.20073	−	0.211721i	0.738014	+	0.674785i	$0.235764\pi$
$384$	13.5806	+	6.95312i	0.693031	+	0.354825i
$385$		0			0
$386$	8.18070	−	14.1694i	0.416387	−	0.721203i
$387$	−0.752659	+	0.212640i	−0.0382598	+	0.0108091i
$388$	17.4407	−	10.0694i	0.885418	−	0.511196i
$389$	−6.59400	+	37.3964i	−0.334329	+	1.89607i	0.0994307	+	0.995044i	$0.468298\pi$
$389$	−6.59400	+	37.3964i	−0.334329	+	1.89607i	−0.433760	+	0.901029i	$0.642813\pi$
$390$		0			0
$391$	−1.84428	−	0.671264i	−0.0932694	−	0.0339473i
$392$	1.24320	−	3.41565i	0.0627908	−	0.172516i
$393$	−19.6487	−	14.8667i	−0.991148	−	0.749926i
$394$	0.422524	−	2.39625i	0.0212864	−	0.120721i
$395$		0			0
$396$	−0.842400	−	0.573011i	−0.0423322	−	0.0287949i
$397$	17.6230	+	10.1747i	0.884474	+	0.510651i	0.872131	−	0.489272i	$-0.162738\pi$
$397$	17.6230	+	10.1747i	0.884474	+	0.510651i	0.0123433	+	0.999924i	$0.496071\pi$
$398$	−1.16565	+	1.38917i	−0.0584289	+	0.0696328i
$399$	9.62690	−	6.22506i	0.481948	−	0.311643i
$400$		0			0
$401$	5.32015	−	4.46414i	0.265676	−	0.222928i	−0.500212	−	0.865903i	$-0.666744\pi$
$401$	5.32015	−	4.46414i	0.265676	−	0.222928i	0.765887	+	0.642975i	$0.222300\pi$
$402$	−0.560563	−	2.44990i	−0.0279583	−	0.122190i
$403$	−2.47053	−	6.78773i	−0.123066	−	0.338121i
$404$	5.43745			0.270523
$405$		0			0
$406$	0.676418			0.0335701
$407$	0.598264	+	1.64372i	0.0296548	+	0.0814760i
$408$	0.305015	+	1.33305i	0.0151005	+	0.0659958i
$409$	8.35444	−	7.01021i	0.413101	−	0.346633i	−0.412431	−	0.910989i	$-0.635320\pi$
$409$	8.35444	−	7.01021i	0.413101	−	0.346633i	0.825531	+	0.564356i	$0.190876\pi$
$410$		0			0
$411$	−28.6319	+	18.5143i	−1.41231	+	0.913244i
$412$	5.16535	−	6.15582i	0.254478	−	0.303276i
$413$	−12.3029	−	7.10308i	−0.605386	−	0.349520i
$414$	1.18485	−	16.0426i	0.0582322	−	0.788449i
$415$		0			0
$416$	−2.64413	+	14.9956i	−0.129639	+	0.735220i
$417$	−24.7393	−	18.7183i	−1.21149	−	0.916640i
$418$	−0.190973	+	0.524693i	−0.00934078	+	0.0256636i
$419$	−9.46194	−	3.44386i	−0.462246	−	0.168244i	0.100391	−	0.994948i	$-0.467991\pi$
$419$	−9.46194	−	3.44386i	−0.462246	−	0.168244i	−0.562637	+	0.826704i	$0.690213\pi$
$420$		0			0
$421$	−0.539623	+	3.06035i	−0.0262996	+	0.149152i	−0.995130	−	0.0985733i	$-0.968572\pi$
$421$	−0.539623	+	3.06035i	−0.0262996	+	0.149152i	0.968830	+	0.247726i	$0.0796832\pi$
$422$	17.6526	−	10.1917i	0.859315	−	0.496126i
$423$	8.42224	−	33.2258i	0.409504	−	1.61550i
$424$	7.30837	−	12.6585i	0.354926	−	0.614750i
$425$		0			0
$426$	−0.457853	−	0.234416i	−0.0221830	−	0.0113575i
$427$	−27.7300	+	4.88955i	−1.34195	+	0.236622i
$428$	0.225990	+	0.269324i	0.0109236	+	0.0130183i
$429$	0.333004	−	1.08164i	0.0160776	−	0.0522221i
$430$		0			0
$431$	−28.0701			−1.35209			−0.676044	−	0.736862i	$-0.736307\pi$
$431$	−28.0701			−1.35209			−0.676044	+	0.736862i	$0.736307\pi$
$432$	2.54441	−	1.39095i	0.122418	−	0.0669219i
$433$			19.5251i			0.938317i	0.883114	+	0.469158i	$0.155443\pi$
$433$			19.5251i			0.938317i	−0.883114	+	0.469158i	$0.844557\pi$
$434$	−4.95075	+	1.80193i	−0.237644	+	0.0864952i
$435$		0			0
$436$	8.89973	−	7.46776i	0.426220	−	0.357641i
$437$	18.3465	−	3.23498i	0.877631	−	0.154750i
$438$	6.96975	−	0.351609i	0.333028	−	0.0168005i
$439$	−11.2069	−	9.40371i	−0.534876	−	0.448815i	0.334905	−	0.942252i	$-0.391296\pi$
$439$	−11.2069	−	9.40371i	−0.534876	−	0.448815i	−0.869781	+	0.493437i	$0.835740\pi$
$440$		0			0
$441$	−2.36886	−	3.28741i	−0.112803	−	0.156543i
$442$	−0.531918	+	0.307103i	−0.0253008	+	0.0146074i
$443$	18.0771	+	3.18748i	0.858868	+	0.151442i	0.585703	−	0.810526i	$-0.300818\pi$
$443$	18.0771	+	3.18748i	0.858868	+	0.151442i	0.273165	+	0.961967i	$0.411930\pi$
$444$	−16.3151	−	2.03562i	−0.774278	−	0.0966062i
$445$		0			0
$446$	−2.88572	−	1.05032i	−0.136643	−	0.0497339i
$447$	3.49318	−	27.9971i	0.165222	−	1.32422i
$448$	8.32476	+	1.46788i	0.393308	+	0.0693508i
$449$	6.92969	+	12.0026i	0.327032	+	0.566437i	0.981922	−	0.189288i	$-0.0606180\pi$
$449$	6.92969	+	12.0026i	0.327032	+	0.566437i	−0.654889	+	0.755725i	$0.727285\pi$
$450$		0			0
$451$	−1.21547	+	2.10526i	−0.0572344	+	0.0991328i
$452$	2.72185	−	3.24378i	0.128025	−	0.152575i
$453$	−24.6934	+	1.24573i	−1.16020	+	0.0585294i
$454$	0.350185	+	1.98600i	0.0164350	+	0.0932075i
$455$		0			0
$456$	−8.83402	−	9.51053i	−0.413691	−	0.445372i
$457$	6.03602	+	16.5838i	0.282353	+	0.775758i	0.997081	+	0.0763555i	$0.0243284\pi$
$457$	6.03602	+	16.5838i	0.282353	+	0.775758i	−0.714728	+	0.699403i	$0.753449\pi$
$458$			12.7760i			0.596985i
$459$	1.41995	+	0.554644i	0.0662776	+	0.0258886i
$460$		0			0
$461$	−24.0919	+	8.76872i	−1.12207	+	0.408400i	−0.835407	−	0.549631i	$-0.814768\pi$
$461$	−24.0919	+	8.76872i	−1.12207	+	0.408400i	−0.286663	+	0.958032i	$0.592546\pi$
$462$	−0.788913	−	0.242882i	−0.0367036	−	0.0112999i
$463$	11.7935	+	14.0549i	0.548090	+	0.653189i	0.966981	−	0.254848i	$-0.0820255\pi$
$463$	11.7935	+	14.0549i	0.548090	+	0.653189i	−0.418891	+	0.908037i	$0.637581\pi$
$464$	0.0344074	+	0.195134i	0.00159732	+	0.00905888i
$465$		0			0
$466$	−17.2709	−	14.4920i	−0.800059	−	0.671329i
$467$	−14.0832	−	8.13092i	−0.651692	−	0.376254i	0.137412	−	0.990514i	$-0.456121\pi$
$467$	−14.0832	−	8.13092i	−0.651692	−	0.376254i	−0.789104	+	0.614260i	$0.789455\pi$
$468$	7.62319	+	7.41945i	0.352382	+	0.342964i
$469$	2.15139	+	3.72632i	0.0993421	+	0.172066i
$470$		0			0
$471$	−0.514232	−	1.21807i	−0.0236946	−	0.0561257i
$472$	−5.50137	+	15.1149i	−0.253221	+	0.695719i
$473$	−0.0223059	+	0.0612849i	−0.00102563	+	0.00281788i
$474$	−0.672489	+	0.888803i	−0.0308884	+	0.0408241i
$475$		0			0
$476$	−0.473317	−	0.819809i	−0.0216944	−	0.0375759i
$477$	−7.08555	−	14.6729i	−0.324425	−	0.671824i
$478$	−10.2079	−	5.89354i	−0.466899	−	0.269564i
$479$	7.25575	+	6.08830i	0.331524	+	0.278181i	0.793320	−	0.608804i	$-0.208351\pi$
$479$	7.25575	+	6.08830i	0.331524	+	0.278181i	−0.461797	+	0.886986i	$0.652795\pi$
$480$		0			0
$481$	−3.17151	−	17.9865i	−0.144608	−	0.820114i
$482$	4.34990	+	5.18401i	0.198133	+	0.236125i
$483$	6.14284	+	26.8469i	0.279509	+	1.22158i
$484$	13.9527	−	5.07836i	0.634213	−	0.230835i
$485$		0			0
$486$	−1.21058	+	12.4358i	−0.0549129	+	0.564099i
$487$			0.467564i			0.0211874i	0.999944	+	0.0105937i	$0.00337214\pi$
$487$			0.467564i			0.0211874i	−0.999944	+	0.0105937i	$0.996628\pi$
$488$	10.9042	+	29.9590i	0.493608	+	1.35618i
$489$	8.65877	−	1.98121i	0.391563	−	0.0895936i
$490$		0			0
$491$	4.34936	+	24.6665i	0.196284	+	1.11318i	0.910578	+	0.413337i	$0.135637\pi$
$491$	4.34936	+	24.6665i	0.196284	+	1.11318i	−0.714294	+	0.699846i	$0.753252\pi$
$492$	−12.4073	−	19.1875i	−0.559363	−	0.865040i
$493$	−0.0669563	+	0.0797954i	−0.00301556	+	0.00359380i
$494$	2.91504	−	5.04899i	0.131154	−	0.227165i
$495$		0			0
$496$	−0.771653	−	1.33654i	−0.0346482	−	0.0600125i
$497$	0.867261	+	0.152922i	0.0389020	+	0.00685947i
$498$	−3.05078	−	2.30829i	−0.136709	−	0.103437i
$499$	−13.1878	−	4.79996i	−0.590367	−	0.214876i	0.0295240	−	0.999564i	$-0.490601\pi$
$499$	−13.1878	−	4.79996i	−0.590367	−	0.214876i	−0.619891	+	0.784688i	$0.712823\pi$
$500$		0			0
$501$	−5.99623	−	14.2034i	−0.267892	−	0.634559i
$502$	−18.3291	−	3.23191i	−0.818068	−	0.144247i
$503$	24.5186	−	14.1558i	1.09323	−	0.631176i	0.158794	−	0.987312i	$-0.449239\pi$
$503$	24.5186	−	14.1558i	1.09323	−	0.631176i	0.934434	+	0.356136i	$0.115906\pi$
$504$	13.3839	−	13.7515i	0.596168	−	0.612539i
$505$		0			0
$506$	−1.02755	−	0.862218i	−0.0456803	−	0.0383303i
$507$	4.87624	−	9.52410i	0.216562	−	0.422980i
$508$	−24.6724	+	4.35041i	−1.09466	+	0.193018i
$509$	21.9759	−	18.4399i	0.974063	−	0.817336i	−0.00912008	−	0.999958i	$-0.502903\pi$
$509$	21.9759	−	18.4399i	0.974063	−	0.817336i	0.983183	+	0.182622i	$0.0584586\pi$
$510$		0			0
$511$	−11.2273	+	4.08640i	−0.496666	+	0.180772i
$512$			6.25700i			0.276523i
$513$	−14.3048	+	2.17975i	−0.631574	+	0.0962382i
$514$	5.50264			0.242711
$515$		0			0
$516$	−0.417197	−	0.449146i	−0.0183661	−	0.0197725i
$517$	−1.83722	−	2.18951i	−0.0808008	−	0.0962946i
$518$	−13.1188	+	2.31319i	−0.576406	+	0.101636i
$519$	0.594397	+	11.7824i	0.0260911	+	0.517191i
$520$		0			0
$521$	12.4548	−	21.5724i	0.545655	−	0.945102i	−0.452910	−	0.891556i	$-0.649614\pi$
$521$	12.4548	−	21.5724i	0.545655	−	0.945102i	0.998565	−	0.0535462i	$-0.0170525\pi$
$522$	−0.778588	−	0.350304i	−0.0340779	−	0.0153324i
$523$	−22.3995	+	12.9324i	−0.979464	+	0.565494i	−0.902108	−	0.431510i	$-0.857981\pi$
$523$	−22.3995	+	12.9324i	−0.979464	+	0.565494i	−0.0773554	+	0.997004i	$0.524648\pi$
$524$	3.35347	−	19.0185i	0.146497	−	0.830826i
$525$		0			0
$526$	2.52540	+	0.919169i	0.110113	+	0.0400777i
$527$	0.277489	−	0.762395i	0.0120876	−	0.0332104i
$528$	0.0299374	−	0.239942i	0.00130286	−	0.0104421i
$529$	−3.77754	+	21.4235i	−0.164241	+	0.931456i
$530$		0			0
$531$	10.4827	+	14.5474i	0.454908	+	0.631303i
$532$	7.78166	+	4.49274i	0.337378	+	0.194785i
$533$	16.3154	−	19.4439i	0.706698	−	0.842209i
$534$	0.730992	+	14.4901i	0.0316331	+	0.627047i
$535$		0			0
$536$	3.73204	−	3.13155i	0.161200	−	0.135262i
$537$	−23.2841	+	21.6278i	−1.00478	+	0.933308i
$538$	3.49296	+	9.59683i	0.150592	+	0.413749i
$539$	−0.337880			−0.0145535
$540$		0			0
$541$	−21.9158			−0.942232			−0.471116	−	0.882071i	$-0.656149\pi$
$541$	−21.9158			−0.942232			−0.471116	+	0.882071i	$0.656149\pi$
$542$	6.45777	+	17.7426i	0.277385	+	0.762109i
$543$	18.7482	+	5.77200i	0.804562	+	0.247700i
$544$	−1.31015	+	1.09935i	−0.0561723	+	0.0471342i
$545$		0			0
$546$	7.67176	+	3.92787i	0.328321	+	0.168097i
$547$	−6.41248	+	7.64210i	−0.274178	+	0.326752i	−0.885509	−	0.464623i	$-0.846190\pi$
$547$	−6.41248	+	7.64210i	−0.274178	+	0.326752i	0.611331	+	0.791375i	$0.290634\pi$
$548$	−23.1439	−	13.3621i	−0.988658	−	0.570802i
$549$	34.4507	+	8.73273i	1.47032	+	0.372704i
$550$		0			0
$551$	0.171694	−	0.973722i	0.00731439	−	0.0414820i
$552$	28.7278	−	12.1280i	1.22274	−	0.516203i
$553$	0.652634	−	1.79310i	0.0277528	−	0.0762502i
$554$	−3.14925	−	1.14623i	−0.133799	−	0.0486987i
$555$		0			0
$556$	4.22227	−	23.9457i	0.179064	−	1.01552i
$557$	16.0500	−	9.26650i	0.680062	−	0.392634i	−0.119816	−	0.992796i	$-0.538231\pi$
$557$	16.0500	−	9.26650i	0.680062	−	0.392634i	0.799879	+	0.600162i	$0.204897\pi$
$558$	6.63172	+	0.489797i	0.280743	+	0.0207348i
$559$	0.340480	−	0.589729i	0.0144008	−	0.0249429i
$560$		0			0
$561$	0.106744	−	0.0690241i	0.00450674	−	0.00291420i
$562$	17.0784	−	3.01138i	0.720408	−	0.127027i
$563$	28.0789	+	33.4632i	1.18339	+	1.41031i	0.890999	+	0.454005i	$0.150005\pi$
$563$	28.0789	+	33.4632i	1.18339	+	1.41031i	0.292388	+	0.956300i	$0.405550\pi$
$564$	26.1887	−	5.99225i	1.10274	−	0.252319i
$565$		0			0
$566$	−4.18985			−0.176113
$567$	−4.28380	−	20.9582i	−0.179903	−	0.880161i
$568$		−	0.997105i		−	0.0418376i
$569$	12.7485	−	4.64008i	0.534446	−	0.194522i	−0.0606766	−	0.998157i	$-0.519326\pi$
$569$	12.7485	−	4.64008i	0.534446	−	0.194522i	0.595122	+	0.803635i	$0.297104\pi$
$570$		0			0
$571$	18.1926	−	15.2654i	0.761335	−	0.638836i	−0.177139	−	0.984186i	$-0.556684\pi$
$571$	18.1926	−	15.2654i	0.761335	−	0.638836i	0.938474	+	0.345350i	$0.112240\pi$
$572$	0.873565	−	0.154033i	0.0365256	−	0.00644044i
$573$	6.45034	+	9.97529i	0.269467	+	0.416724i
$574$	−14.1818	−	11.8999i	−0.591935	−	0.496693i
$575$		0			0
$576$	−8.82200	−	6.00083i	−0.367583	−	0.250034i
$577$	7.03128	−	4.05951i	0.292716	−	0.169000i	−0.346450	−	0.938068i	$-0.612613\pi$
$577$	7.03128	−	4.05951i	0.292716	−	0.169000i	0.639166	+	0.769069i	$0.279280\pi$
$578$	13.3510	+	2.35414i	0.555329	+	0.0979194i
$579$	21.3329	−	28.1949i	0.886566	−	1.17174i
$580$		0			0
$581$	6.15473	+	2.24014i	0.255341	+	0.0929366i
$582$	−18.9732	+	8.00990i	−0.786464	+	0.332021i
$583$	−1.33806	−	0.235937i	−0.0554169	−	0.00977150i
$584$	6.76397	+	11.7155i	0.279895	+	0.484793i
$585$		0			0
$586$	−2.46156	+	4.26354i	−0.101686	+	0.176125i
$587$	−2.37317	+	2.82823i	−0.0979511	+	0.116734i	−0.812793	−	0.582552i	$-0.802054\pi$
$587$	−2.37317	+	2.82823i	−0.0979511	+	0.116734i	0.714842	+	0.699286i	$0.246499\pi$
$588$	1.44735	−	2.82691i	0.0596877	−	0.116580i
$589$	1.33729	+	7.58412i	0.0551019	+	0.312498i
$590$		0			0
$591$	1.54713	−	5.02527i	0.0636403	−	0.206712i
$592$	−1.33463	−	3.66686i	−0.0548529	−	0.150707i
$593$			29.4590i			1.20974i	0.796325	+	0.604869i	$0.206774\pi$
$593$			29.4590i			1.20974i	−0.796325	+	0.604869i	$0.793226\pi$
$594$	0.782291	+	0.688131i	0.0320978	+	0.0282344i
$595$		0			0
$596$	20.7802	−	7.56338i	0.851190	−	0.309808i
$597$	−2.87119	+	2.66695i	−0.117510	+	0.109151i
$598$	9.00268	+	10.7290i	0.368147	+	0.438740i
$599$	3.79862	+	21.5431i	0.155207	+	0.880225i	0.958596	+	0.284770i	$0.0919172\pi$
$599$	3.79862	+	21.5431i	0.155207	+	0.880225i	−0.803388	+	0.595455i	$0.796972\pi$
$600$		0			0
$601$	27.9764	+	23.4750i	1.14118	+	0.957566i	0.999477	−	0.0323424i	$-0.0102967\pi$
$601$	27.9764	+	23.4750i	1.14118	+	0.957566i	0.141706	+	0.989909i	$0.454741\pi$
$602$	−0.430130	−	0.248335i	−0.0175308	−	0.0101214i
$603$	−0.546563	−	5.40333i	−0.0222578	−	0.220041i
$604$	−9.68946	−	16.7826i	−0.394258	−	0.682876i
$605$		0			0
$606$	−5.51775	−	0.688447i	−0.224143	−	0.0279662i
$607$	2.25077	−	6.18395i	0.0913561	−	0.250999i	−0.885596	−	0.464456i	$-0.846250\pi$
$607$	2.25077	−	6.18395i	0.0913561	−	0.250999i	0.976953	+	0.213457i	$0.0684722\pi$
$608$	5.55238	−	15.2550i	0.225179	−	0.618674i
$609$	1.45045	+	0.180972i	0.0587753	+	0.00733335i
$610$		0			0
$611$	14.9217	+	25.8451i	0.603667	+	1.04558i
$612$	0.120247	+	1.18876i	0.00486068	+	0.0480527i
$613$	6.19093	+	3.57434i	0.250049	+	0.144366i	0.619787	−	0.784770i	$-0.287219\pi$
$613$	6.19093	+	3.57434i	0.250049	+	0.144366i	−0.369737	+	0.929136i	$0.620552\pi$
$614$	11.6685	+	9.79101i	0.470901	+	0.395133i
$615$		0			0
$616$	−0.277860	−	1.57582i	−0.0111953	−	0.0634917i
$617$	−10.6301	−	12.6684i	−0.427951	−	0.510012i	0.508379	−	0.861133i	$-0.330245\pi$
$617$	−10.6301	−	12.6684i	−0.427951	−	0.510012i	−0.936330	+	0.351121i	$0.885800\pi$
$618$	−6.02103	+	5.59274i	−0.242202	+	0.224973i
$619$	−1.40893	+	0.512808i	−0.0566296	+	0.0206115i	−0.370180	−	0.928960i	$-0.620704\pi$
$619$	−1.40893	+	0.512808i	−0.0566296	+	0.0206115i	0.313550	+	0.949572i	$0.398482\pi$
$620$		0			0
$621$	6.83279	−	34.0833i	0.274190	−	1.36772i
$622$		−	17.2704i		−	0.692481i
$623$	−8.49561	−	23.3415i	−0.340369	−	0.935157i
$624$	−0.742878	+	2.41296i	−0.0297389	+	0.0965958i
$625$		0			0
$626$	0.530793	+	3.01028i	0.0212148	+	0.120315i
$627$	−0.549884	+	1.07401i	−0.0219602	+	0.0428919i
$628$	0.666118	−	0.793848i	0.0265810	−	0.0316780i
$629$	1.02570	−	1.77657i	0.0408974	−	0.0708363i
$630$		0			0
$631$	17.9456	+	31.0827i	0.714404	+	1.23738i	0.963189	+	0.268826i	$0.0866356\pi$
$631$	17.9456	+	31.0827i	0.714404	+	1.23738i	−0.248785	+	0.968559i	$0.580031\pi$
$632$	−2.12771	−	0.375172i	−0.0846356	−	0.0149235i
$633$	40.5795	−	17.1314i	1.61289	−	0.680913i
$634$	−3.20443	−	1.16632i	−0.127264	−	0.0463204i
$635$		0			0
$636$	7.70574	−	10.1844i	0.305553	−	0.403837i
$637$	3.47431	+	0.612614i	0.137657	+	0.0242727i
$638$	−0.0616542	+	0.0355961i	−0.00244091	+	0.00140926i
$639$	−0.919063	−	0.625157i	−0.0363576	−	0.0247308i
$640$		0			0
$641$	30.0504	+	25.2152i	1.18692	+	0.995942i	0.999908	+	0.0135840i	$0.00432406\pi$
$641$	30.0504	+	25.2152i	1.18692	+	0.995942i	0.187010	+	0.982358i	$0.440120\pi$
$642$	−0.195227	−	0.301914i	−0.00770501	−	0.0119156i
$643$	10.2602	−	1.80915i	0.404624	−	0.0713461i	0.0323674	−	0.999476i	$-0.489695\pi$
$643$	10.2602	−	1.80915i	0.404624	−	0.0713461i	0.372256	+	0.928130i	$0.378584\pi$
$644$	−16.5358	+	13.8752i	−0.651603	+	0.546760i
$645$		0			0
$646$	0.615340	−	0.223965i	0.0242102	−	0.00881180i
$647$			39.1517i			1.53921i	0.638519	+	0.769606i	$0.279547\pi$
$647$			39.1517i			1.53921i	−0.638519	+	0.769606i	$0.720453\pi$
$648$	−22.5271	+	8.89730i	−0.884950	+	0.349519i
$649$	1.49518			0.0586910
$650$		0			0
$651$	−11.0981	+	2.53935i	−0.434967	+	0.0995248i
$652$	4.47509	+	5.33320i	0.175258	+	0.208864i
$653$	−32.4099	+	5.71474i	−1.26830	+	0.223635i	−0.767004	−	0.641642i	$-0.778253\pi$
$653$	−32.4099	+	5.71474i	−1.26830	+	0.223635i	−0.501294	+	0.865277i	$0.667142\pi$
$654$	−9.97668	+	6.45124i	−0.390119	+	0.252263i
$655$		0			0
$656$	2.71152	−	4.69649i	0.105867	−	0.183367i
$657$	15.0394	+	1.11076i	0.586743	+	0.0433349i
$658$	18.8506	−	10.8834i	0.734873	−	0.424279i
$659$	3.74532	−	21.2407i	0.145897	−	0.827422i	−0.820746	−	0.571293i	$-0.806442\pi$
$659$	3.74532	−	21.2407i	0.145897	−	0.827422i	0.966643	−	0.256128i	$-0.0824470\pi$
$660$		0			0
$661$	−24.7105	−	8.99389i	−0.961127	−	0.349822i	−0.186652	−	0.982426i	$-0.559764\pi$
$661$	−24.7105	−	8.99389i	−0.961127	−	0.349822i	−0.774475	+	0.632604i	$0.781986\pi$
$662$	−3.91848	+	10.7659i	−0.152296	+	0.418430i
$663$	−1.22276	+	0.516213i	−0.0474882	+	0.0200481i
$664$	1.28776	−	7.30326i	0.0499749	−	0.283422i
$665$		0			0
$666$	16.2983	+	4.13136i	0.631545	+	0.160087i
$667$	2.05705	+	1.18764i	0.0796493	+	0.0459855i
$668$	7.76729	−	9.25670i	0.300526	−	0.358152i
$669$	−5.90688	−	3.02427i	−0.228373	−	0.116925i
$670$		0			0
$671$	2.27023	−	1.90495i	0.0876412	−	0.0735397i
$672$	22.9370	+	7.06161i	0.884815	+	0.272408i
$673$	−3.94080	−	10.8272i	−0.151907	−	0.417360i	0.840275	−	0.542160i	$-0.182393\pi$
$673$	−3.94080	−	10.8272i	−0.151907	−	0.417360i	−0.992182	+	0.124800i	$0.960171\pi$
$674$	28.6293			1.10276
$675$		0			0
$676$	8.38635			0.322552
$677$	−11.6030	−	31.8791i	−0.445941	−	1.22521i	−0.935526	−	0.353257i	$-0.885074\pi$
$677$	−11.6030	−	31.8791i	−0.445941	−	1.22521i	0.489585	−	0.871955i	$-0.337148\pi$
$678$	−3.17275	+	2.94707i	−0.121849	+	0.113181i
$679$	27.0103	−	22.6643i	1.03656	−	0.869776i
$680$		0			0
$681$	0.219563	+	4.35229i	0.00841369	+	0.166780i
$682$	0.356426	−	0.424772i	0.0136483	−	0.0162654i
$683$	−31.8310	−	18.3777i	−1.21798	−	0.703201i	−0.253495	−	0.967337i	$-0.581580\pi$
$683$	−31.8310	−	18.3777i	−1.21798	−	0.703201i	−0.964486	+	0.264135i	$0.914913\pi$
$684$	−6.63034	−	9.20132i	−0.253518	−	0.351821i
$685$		0			0
$686$	2.76254	−	15.6671i	0.105474	−	0.598174i
$687$	−3.41816	+	27.3958i	−0.130411	+	1.04522i
$688$	0.0497608	−	0.136717i	0.00189711	−	0.00521227i
$689$	13.3311	+	4.85212i	0.507874	+	0.184851i
$690$		0			0
$691$	2.32309	−	13.1749i	0.0883744	−	0.501196i	−0.908203	−	0.418530i	$-0.862545\pi$
$691$	2.32309	−	13.1749i	0.0883744	−	0.501196i	0.996577	−	0.0826660i	$-0.0263435\pi$
$692$	−8.00781	+	4.62331i	−0.304411	+	0.175752i
$693$	−1.62670	−	0.731885i	−0.0617930	−	0.0278020i
$694$	7.79146	−	13.4952i	0.295760	−	0.512271i
$695$		0			0
$696$	−0.0833854	−	1.65291i	−0.00316072	−	0.0626532i
$697$	2.80761	−	0.495057i	0.106346	−	0.0187516i
$698$	4.13236	+	4.92475i	0.156412	+	0.186405i
$699$	−33.1570	−	35.6961i	−1.25411	−	1.35015i
$700$		0			0
$701$	5.00452			0.189018			0.0945091	−	0.995524i	$-0.469872\pi$
$701$	5.00452			0.189018			0.0945091	+	0.995524i	$0.469872\pi$
$702$	−6.79639	−	8.49421i	−0.256513	−	0.320593i
$703$			19.4720i			0.734400i
$704$	−0.836033	+	0.304291i	−0.0315092	+	0.0114684i
$705$		0			0
$706$	−5.37489	+	4.51007i	−0.202287	+	0.169739i
$707$	9.37537	−	1.65313i	0.352597	−	0.0621724i
$708$	−6.40479	+	12.5096i	−0.240707	+	0.470139i
$709$	−13.1330	−	11.0199i	−0.493218	−	0.413859i	0.361960	−	0.932194i	$-0.382108\pi$
$709$	−13.1330	−	11.0199i	−0.493218	−	0.413859i	−0.855178	+	0.518334i	$0.826552\pi$
$710$		0			0
$711$	−1.67982	+	1.72595i	−0.0629982	+	0.0647282i
$712$	−24.3566	+	14.0623i	−0.912800	+	0.527006i
$713$	−18.2195	−	3.21258i	−0.682324	−	0.120312i
$714$	0.376509	+	0.891844i	0.0140905	+	0.0333764i
$715$		0			0
$716$	−23.4058	−	8.51902i	−0.874716	−	0.318371i
$717$	−20.3122	−	15.3687i	−0.758572	−	0.573954i
$718$	6.53417	+	1.15215i	0.243853	+	0.0429979i
$719$	−21.6760	−	37.5439i	−0.808377	−	1.40015i	−0.913987	−	0.405742i	$-0.867013\pi$
$719$	−21.6760	−	37.5439i	−0.808377	−	1.40015i	0.105610	−	0.994408i	$-0.466320\pi$
$720$		0			0
$721$	7.03467	−	12.1844i	0.261985	−	0.453771i
$722$	5.79365	−	6.90461i	0.215617	−	0.256963i
$723$	7.94060	+	12.2799i	0.295314	+	0.456696i
$724$	2.66987	+	15.1416i	0.0992251	+	0.562733i
$725$		0			0
$726$	−14.8017	+	3.38679i	−0.549344	+	0.125695i
$727$	−12.4303	−	34.1521i	−0.461016	−	1.26663i	−0.924722	−	0.380642i	$-0.875703\pi$
$727$	−12.4303	−	34.1521i	−0.461016	−	1.26663i	0.463706	−	0.885989i	$-0.346519\pi$
$728$			16.7075i			0.619220i
$729$	−5.92298	+	26.3423i	−0.219370	+	0.975642i
$730$		0			0
$731$	0.0718726	−	0.0261595i	0.00265830	−	0.000967544i
$732$	6.21315	+	27.1542i	0.229645	+	1.00365i
$733$	2.49119	+	2.96889i	0.0920143	+	0.109658i	0.810087	−	0.586310i	$-0.199420\pi$
$733$	2.49119	+	2.96889i	0.0920143	+	0.109658i	−0.718073	+	0.695968i	$0.754975\pi$
$734$	−2.05990	−	11.6823i	−0.0760322	−	0.431200i
$735$		0			0
$736$	29.8753	+	25.0683i	1.10122	+	0.924031i
$737$	−0.392191	−	0.226432i	−0.0144465	−	0.00834071i
$738$	10.1611	+	21.0418i	0.374036	+	0.774559i
$739$	13.2241	+	22.9048i	0.486456	+	0.842567i	0.999879	−	0.0155689i	$-0.00495594\pi$
$739$	13.2241	+	22.9048i	0.486456	+	0.842567i	−0.513422	+	0.858136i	$0.671623\pi$
$740$		0			0
$741$	7.60158	−	10.0467i	0.279251	−	0.369075i
$742$	3.53898	−	9.72326i	0.129920	−	0.356952i
$743$	−4.60474	+	12.6514i	−0.168932	+	0.464136i	−0.995052	−	0.0993584i	$-0.968321\pi$
$743$	−4.60474	+	12.6514i	−0.168932	+	0.464136i	0.826120	+	0.563494i	$0.190543\pi$
$744$	5.01352	+	11.8756i	0.183805	+	0.435381i
$745$		0			0
$746$	10.2329	+	17.7238i	0.374651	+	0.648915i
$747$	−5.92425	−	5.76591i	−0.216757	−	0.210964i
$748$	0.0862839	+	0.0498160i	0.00315485	+	0.00182145i
$749$	0.471538	+	0.395667i	0.0172296	+	0.0144574i
$750$		0			0
$751$	0.654359	+	3.71106i	0.0238779	+	0.135418i	0.994416	−	0.105528i	$-0.0336533\pi$
$751$	0.654359	+	3.71106i	0.0238779	+	0.135418i	−0.970538	+	0.240946i	$0.922542\pi$
$752$	4.09854	+	4.88444i	0.149458	+	0.178117i
$753$	−38.4386	−	11.8341i	−1.40078	−	0.431258i
$754$	0.698510	−	0.254237i	0.0254382	−	0.00925876i
$755$		0			0
$756$	13.0915	−	10.4748i	0.476135	−	0.380965i
$757$			33.7073i			1.22511i	0.790427	+	0.612556i	$0.209859\pi$
$757$			33.7073i			1.22511i	−0.790427	+	0.612556i	$0.790141\pi$
$758$	5.51687	+	15.1575i	0.200382	+	0.550544i
$759$	−1.97271	−	2.12378i	−0.0716049	−	0.0770884i
$760$		0			0
$761$	−1.67665	−	9.50874i	−0.0607784	−	0.344692i	−0.999999	−	0.00137744i	$-0.999562\pi$
$761$	−1.67665	−	9.50874i	−0.0607784	−	0.344692i	0.939221	−	0.343314i	$-0.111550\pi$
$762$	25.5876	−	1.29084i	0.926941	−	0.0467621i
$763$	13.0747	−	15.5818i	0.473336	−	0.564100i
$764$	−4.65533	+	8.06327i	−0.168424	+	0.291719i
$765$		0			0
$766$	−9.56272	−	16.5631i	−0.345515	−	0.598450i
$767$	−15.3745	−	2.71093i	−0.555139	−	0.0978861i
$768$	3.03939	−	24.3601i	0.109675	−	0.879019i
$769$	36.3764	+	13.2399i	1.31177	+	0.477445i	0.900812	−	0.434210i	$-0.142973\pi$
$769$	36.3764	+	13.2399i	1.31177	+	0.477445i	0.410957	+	0.911655i	$0.365195\pi$
$770$		0			0
$771$	11.7994	+	1.47220i	0.424944	+	0.0530200i
$772$	27.2905	+	4.81205i	0.982206	+	0.173189i
$773$	21.0478	−	12.1519i	0.757036	−	0.437075i	−0.0711944	−	0.997462i	$-0.522681\pi$
$773$	21.0478	−	12.1519i	0.757036	−	0.437075i	0.828231	+	0.560387i	$0.189348\pi$
$774$	0.366491	+	0.508601i	0.0131732	+	0.0182813i
$775$		0			0
$776$	−30.5824	−	25.6617i	−1.09784	−	0.921200i
$777$	−28.7496	+	1.45036i	−1.03139	+	0.0520312i
$778$	29.9742	−	5.28527i	1.07463	−	0.189486i
$779$	−20.7300	+	17.3945i	−0.742728	+	0.623223i
$780$		0			0
$781$	−0.0870967	+	0.0317006i	−0.00311656	+	0.00113434i
$782$			1.57311i			0.0562544i
$783$	−1.57581	−	0.959467i	−0.0563150	−	0.0342886i
$784$	0.753755			0.0269198
$785$		0			0
$786$	−5.81096	+	18.8748i	−0.207270	+	0.673240i
$787$	−13.4604	−	16.0414i	−0.479810	−	0.571816i	0.470785	−	0.882248i	$-0.343971\pi$
$787$	−13.4604	−	16.0414i	−0.479810	−	0.571816i	−0.950596	+	0.310432i	$0.899526\pi$
$788$	4.05856	−	0.715633i	0.144580	−	0.0254934i
$789$	5.16932	+	2.64664i	0.184033	+	0.0942229i
$790$		0			0
$791$	3.70688	−	6.42051i	0.131802	−	0.228287i
$792$	−0.496258	+	1.95774i	−0.0176338	+	0.0695654i
$793$	−26.7979	+	15.4718i	−0.951621	+	0.549419i
$794$	2.83229	−	16.0627i	0.100514	−	0.570045i
$795$		0			0
$796$	−2.88620	−	1.05049i	−0.102299	−	0.0372337i
$797$	−4.08261	+	11.2169i	−0.144614	+	0.397322i	−0.990760	−	0.135628i	$-0.956695\pi$
$797$	−4.08261	+	11.2169i	−0.144614	+	0.397322i	0.846146	+	0.532951i	$0.178917\pi$
$798$	−7.32775	−	5.54435i	−0.259400	−	0.196268i
$799$	−0.582068	+	3.30107i	−0.0205921	+	0.116783i
$800$		0			0
$801$	−2.30926	+	31.2668i	−0.0815939	+	1.10476i
$802$	−4.82080	−	2.78329i	−0.170228	−	0.0982814i
$803$	0.808303	−	0.963297i	0.0285244	−	0.0339940i
$804$	3.57446	−	2.31136i	0.126062	−	0.0815154i
$805$		0			0
$806$	−4.43518	+	3.72155i	−0.156222	+	0.131086i
$807$	4.92242	+	21.5131i	0.173277	+	0.757298i
$808$	−3.68664	−	10.1290i	−0.129696	−	0.356336i
$809$	−8.60808			−0.302644			−0.151322	−	0.988485i	$-0.548353\pi$
$809$	−8.60808			−0.302644			−0.151322	+	0.988485i	$0.548353\pi$
$810$		0			0
$811$	1.53770			0.0539958			0.0269979	−	0.999635i	$-0.491405\pi$
$811$	1.53770			0.0539958			0.0269979	+	0.999635i	$0.491405\pi$
$812$	0.391837	+	1.07656i	0.0137508	+	0.0377800i
$813$	9.10055	+	39.7734i	0.319170	+	1.39491i
$814$	1.07402	−	0.901211i	0.0376444	−	0.0315874i
$815$		0			0
$816$	−0.238129	+	0.153982i	−0.00833617	+	0.00539043i
$817$	−0.466665	+	0.556149i	−0.0163265	+	0.0194572i
$818$	−7.57029	−	4.37071i	−0.264689	−	0.152818i
$819$	15.3998	+	10.4751i	0.538112	+	0.366030i
$820$		0			0
$821$	5.03168	−	28.5361i	0.175607	−	0.995915i	−0.761835	−	0.647772i	$-0.775701\pi$
$821$	5.03168	−	28.5361i	0.175607	−	0.995915i	0.937441	−	0.348144i	$-0.113188\pi$
$822$	21.7939	+	16.4898i	0.760149	+	0.575147i
$823$	−3.85004	+	10.5779i	−0.134204	+	0.368722i	−0.988532	−	0.151012i	$-0.951747\pi$
$823$	−3.85004	+	10.5779i	−0.134204	+	0.368722i	0.854328	+	0.519734i	$0.173969\pi$
$824$	−14.9693	−	5.44838i	−0.521481	−	0.189803i
$825$		0			0
$826$	−1.97727	+	11.2136i	−0.0687979	+	0.390172i
$827$	−26.7844	+	15.4640i	−0.931383	+	0.537734i	−0.887249	−	0.461291i	$-0.847386\pi$
$827$	−26.7844	+	15.4640i	−0.931383	+	0.537734i	−0.0441346	+	0.999026i	$0.514053\pi$
$828$	26.2192	−	7.40742i	0.911180	−	0.257426i
$829$	−4.91762	+	8.51757i	−0.170796	+	0.295827i	−0.938698	−	0.344739i	$-0.887967\pi$
$829$	−4.91762	+	8.51757i	−0.170796	+	0.295827i	0.767902	+	0.640567i	$0.221301\pi$
$830$		0			0
$831$	−6.44630	−	3.30044i	−0.223620	−	0.114491i
$832$	9.14836	−	1.61310i	0.317162	−	0.0559243i
$833$	0.254706	+	0.303547i	0.00882505	+	0.0105173i
$834$	−7.31644	+	23.7648i	−0.253348	+	0.822906i
$835$		0			0
$836$	−0.945711			−0.0327081
$837$	14.0894	+	2.82456i	0.487003	+	0.0976310i
$838$			8.07072i			0.278798i
$839$	−12.3506	+	4.49524i	−0.426389	+	0.155193i	−0.546296	−	0.837592i	$-0.683963\pi$
$839$	−12.3506	+	4.49524i	−0.426389	+	0.155193i	0.119907	+	0.992785i	$0.461740\pi$
$840$		0			0
$841$	−22.1187	+	18.5598i	−0.762714	+	0.639993i
$842$	2.45296	−	0.432522i	0.0845344	−	0.0149057i
$843$	37.4271	−	1.88811i	1.28906	−	0.0650301i
$844$	26.4467	+	22.1914i	0.910333	+	0.763860i
$845$		0			0
$846$	−27.3342	+	2.76494i	−0.939769	+	0.0950604i
$847$	22.5136	−	12.9982i	0.773575	−	0.446624i
$848$	2.98500	+	0.526336i	0.102505	+	0.0180745i
$849$	−8.98435	−	1.12097i	−0.308342	−	0.0384717i
$850$		0			0
$851$	−43.9569	−	15.9990i	−1.50682	−	0.548438i
$852$	0.107863	−	0.864497i	0.00369531	−	0.0296172i
$853$	15.2077	+	2.68153i	0.520703	+	0.0918139i	0.427821	−	0.903863i	$-0.359281\pi$
$853$	15.2077	+	2.68153i	0.520703	+	0.0918139i	0.0928812	+	0.995677i	$0.470392\pi$
$854$	11.2846	+	19.5455i	0.386151	+	0.668834i
$855$		0			0
$856$	0.348478	−	0.603581i	0.0119107	−	0.0206300i
$857$	14.1302	−	16.8398i	0.482680	−	0.575235i	−0.468660	−	0.883378i	$-0.655263\pi$
$857$	14.1302	−	16.8398i	0.482680	−	0.575235i	0.951340	+	0.308143i	$0.0997076\pi$
$858$	−0.905968	+	0.0457041i	−0.0309293	+	0.00156031i
$859$	−3.39772	−	19.2694i	−0.115929	−	0.657464i	−0.986286	−	0.165044i	$-0.947223\pi$
$859$	−3.39772	−	19.2694i	−0.115929	−	0.657464i	0.870358	−	0.492420i	$-0.163888\pi$
$860$		0			0
$861$	−27.2264	−	29.3114i	−0.927873	−	0.998929i
$862$	7.69508	+	21.1421i	0.262095	+	0.720101i
$863$			21.8676i			0.744383i	0.928156	+	0.372191i	$0.121393\pi$
$863$			21.8676i			0.744383i	−0.928156	+	0.372191i	$0.878607\pi$
$864$	−22.7445	−	20.0069i	−0.773784	−	0.680648i
$865$		0			0
$866$	14.7061	−	5.35258i	0.499733	−	0.181888i
$867$	27.9989	+	8.62001i	0.950893	+	0.292751i
$868$	−5.73577	−	6.83563i	−0.194685	−	0.232016i
$869$	0.0348743	+	0.197782i	0.00118303	+	0.00670929i
$870$		0			0
$871$	3.62223	+	3.03941i	0.122734	+	0.102986i
$872$	−19.9452	−	11.5153i	−0.675428	−	0.389959i
$873$	−42.8275	+	12.0996i	−1.44949	+	0.409508i
$874$	−7.46602	−	12.9315i	−0.252542	−	0.437416i
$875$		0			0
$876$	4.59707	+	10.8891i	0.155321	+	0.367910i
$877$	13.3729	−	36.7419i	0.451572	−	1.24068i	−0.480045	−	0.877244i	$-0.659380\pi$
$877$	13.3729	−	36.7419i	0.451572	−	1.24068i	0.931617	−	0.363441i	$-0.118398\pi$
$878$	−4.01053	+	11.0188i	−0.135349	+	0.371868i
$879$	−6.41903	+	8.48379i	−0.216509	+	0.286151i
$880$		0			0
$881$	3.65254	+	6.32639i	0.123057	+	0.213141i	0.920972	−	0.389629i	$-0.127397\pi$
$881$	3.65254	+	6.32639i	0.123057	+	0.213141i	−0.797915	+	0.602771i	$0.794063\pi$
$882$	−1.82665	+	2.68541i	−0.0615063	+	0.0904223i
$883$	3.02496	+	1.74646i	0.101798	+	0.0587732i	0.550035	−	0.835142i	$-0.314614\pi$
$883$	3.02496	+	1.74646i	0.101798	+	0.0587732i	−0.448237	+	0.893915i	$0.647948\pi$
$884$	−0.796907	−	0.668684i	−0.0268029	−	0.0224903i
$885$		0			0
$886$	−2.55485	−	14.4893i	−0.0858318	−	0.486776i
$887$	−18.2688	−	21.7720i	−0.613408	−	0.731031i	0.366514	−	0.930413i	$-0.380551\pi$
$887$	−18.2688	−	21.7720i	−0.613408	−	0.731031i	−0.979922	+	0.199381i	$0.936107\pi$
$888$	7.26978	+	31.7721i	0.243958	+	1.06620i
$889$	−41.2181	+	15.0021i	−1.38241	+	0.503156i
$890$		0			0
$891$	1.49337	+	1.68487i	0.0500298	+	0.0564452i
$892$		−	5.20125i		−	0.174151i
$893$	−10.8821	−	29.8985i	−0.364157	−	1.00051i
$894$	−22.0447	+	5.04405i	−0.737286	+	0.168698i
$895$		0			0
$896$	3.63563	+	20.6187i	0.121458	+	0.688821i
$897$	16.4341	+	25.4149i	0.548718	+	0.848579i
$898$	7.14052	−	8.50974i	0.238282	−	0.283974i
$899$	−0.490949	+	0.850349i	−0.0163741	+	0.0283607i
$900$		0			0
$901$	0.796719	+	1.37996i	0.0265426	+	0.0459731i
$902$	1.91887	+	0.338348i	0.0638913	+	0.0112658i
$903$	−0.855892	−	0.647588i	−0.0284823	−	0.0215504i
$904$	−7.88800	−	2.87100i	−0.262351	−	0.0954880i
$905$		0			0
$906$	7.70767	+	18.2573i	0.256070	+	0.606558i
$907$	−52.3097	−	9.22362i	−1.73692	−	0.306265i	−0.786579	−	0.617489i	$-0.788150\pi$
$907$	−52.3097	−	9.22362i	−1.73692	−	0.306265i	−0.950337	+	0.311224i	$0.899261\pi$
$908$	−2.95799	+	1.70780i	−0.0981644	+	0.0566753i
$909$	−11.6476	−	2.95249i	−0.386327	−	0.0979279i
$910$		0			0
$911$	−6.18649	−	5.19108i	−0.204968	−	0.171988i	0.534526	−	0.845152i	$-0.320490\pi$
$911$	−6.18649	−	5.19108i	−0.204968	−	0.171988i	−0.739493	+	0.673164i	$0.764935\pi$
$912$	1.22670	−	2.39595i	0.0406201	−	0.0793377i
$913$	−0.678878	+	0.119704i	−0.0224676	+	0.00396164i
$914$	10.8360	−	9.09252i	0.358424	−	0.300754i
$915$		0			0
$916$	−20.3339	+	7.40094i	−0.671852	+	0.244534i
$917$		−	33.8116i		−	1.11656i
$918$	0.0284888	−	1.22154i	0.000940269	−	0.0403168i
$919$	47.9961			1.58325			0.791623	−	0.611009i	$-0.209236\pi$
$919$	47.9961			1.58325			0.791623	+	0.611009i	$0.209236\pi$
$920$		0			0
$921$	22.4013	+	24.1168i	0.738149	+	0.794677i
$922$	13.2090	+	15.7419i	0.435016	+	0.518431i
$923$	0.953063	−	0.168051i	0.0313705	−	0.00553146i
$924$	−0.0704406	−	1.39631i	−0.00231732	−	0.0459351i
$925$		0			0
$926$	7.35298	−	12.7357i	0.241634	−	0.418522i
$927$	−14.4073	+	10.3817i	−0.473197	+	0.340979i
$928$	1.79255	−	1.03493i	0.0588433	−	0.0339732i
$929$	5.03474	−	28.5534i	0.165185	−	0.936808i	−0.783689	−	0.621153i	$-0.786665\pi$
$929$	5.03474	−	28.5534i	0.165185	−	0.936808i	0.948874	−	0.315655i	$-0.102224\pi$
$930$		0			0
$931$	−3.53442	−	1.28642i	−0.115836	−	0.0421608i
$932$	13.0603	−	35.8828i	0.427803	−	1.17538i
$933$	4.62061	−	37.0332i	0.151272	−	1.21241i
$934$	−2.26338	+	12.8363i	−0.0740602	+	0.420016i
$935$		0			0
$936$	8.65246	−	19.2311i	0.282815	−	0.628587i
$937$	4.35481	+	2.51425i	0.142265	+	0.0821369i	0.569443	−	0.822031i	$-0.307159\pi$
$937$	4.35481	+	2.51425i	0.142265	+	0.0821369i	−0.427178	+	0.904168i	$0.640492\pi$
$938$	2.21685	−	2.64193i	0.0723826	−	0.0862622i
$939$	0.332803	+	6.59699i	0.0108606	+	0.215285i
$940$		0			0
$941$	−42.7767	+	35.8939i	−1.39448	+	1.17011i	−0.430995	+	0.902354i	$0.641837\pi$
$941$	−42.7767	+	35.8939i	−1.39448	+	1.17011i	−0.963487	+	0.267755i	$0.913718\pi$
$942$	−0.776466	+	0.721234i	−0.0252986	+	0.0234991i
$943$	−22.2345	−	61.0887i	−0.724054	−	1.98932i
$944$	−3.33551			−0.108561
$945$		0			0
$946$	0.0522740			0.00169957
$947$	14.5459	+	39.9645i	0.472678	+	1.29867i	0.915592	+	0.402109i	$0.131723\pi$
$947$	14.5459	+	39.9645i	0.472678	+	1.29867i	−0.442914	+	0.896564i	$0.646055\pi$
$948$	−1.80415	−	0.555443i	−0.0585961	−	0.0180400i
$949$	−10.0581	+	8.43973i	−0.326499	+	0.273965i
$950$		0			0
$951$	−6.55926	−	3.35828i	−0.212699	−	0.108900i
$952$	−1.20624	+	1.43754i	−0.0390944	+	0.0465909i
$953$	−18.8922	−	10.9074i	−0.611977	−	0.353325i	0.161762	−	0.986830i	$-0.448282\pi$
$953$	−18.8922	−	10.9074i	−0.611977	−	0.353325i	−0.773739	+	0.633505i	$0.781616\pi$
$954$	−9.10901	+	9.35916i	−0.294915	+	0.303014i
$955$		0			0
$956$	3.46670	−	19.6606i	0.112121	−	0.635870i
$957$	−0.141729	+	0.0598339i	−0.00458146	+	0.00193415i
$958$	2.59656	−	7.13399i	0.0838910	−	0.230489i
$959$	−43.9676	−	16.0029i	−1.41979	−	0.516761i
$960$		0			0
$961$	−4.05507	+	22.9974i	−0.130809	+	0.741852i
$962$	−12.6778	+	7.31954i	−0.408749	+	0.235991i
$963$	−0.337853	−	0.699631i	−0.0108872	−	0.0225453i
$964$	−5.73088	+	9.92618i	−0.184579	+	0.319701i
$965$		0			0
$966$	18.5368	−	11.9865i	0.596412	−	0.385659i
$967$	4.55827	−	0.803746i	0.146584	−	0.0258467i	−0.0998746	−	0.995000i	$-0.531844\pi$
$967$	4.55827	−	0.803746i	0.146584	−	0.0258467i	0.246459	+	0.969153i	$0.420733\pi$
$968$	−18.9201	−	22.5481i	−0.608115	−	0.724724i
$969$	1.37940	−	0.315621i	0.0443128	−	0.0101392i
$970$		0			0
$971$	−21.6509			−0.694809			−0.347405	−	0.937715i	$-0.612937\pi$
$971$	−21.6509			−0.694809			−0.347405	+	0.937715i	$0.612937\pi$
$972$	−20.4937	+	5.27712i	−0.657334	+	0.169264i
$973$		−	42.5714i		−	1.36478i
$974$	0.352164	−	0.128177i	0.0112841	−	0.00410707i
$975$		0			0
$976$	−5.06451	+	4.24963i	−0.162111	+	0.136027i
$977$	−21.7493	+	3.83499i	−0.695822	+	0.122692i	−0.510362	−	0.859960i	$-0.670489\pi$
$977$	−21.7493	+	3.83499i	−0.695822	+	0.122692i	−0.185460	+	0.982652i	$0.559377\pi$
$978$	−3.86593	−	5.97856i	−0.123619	−	0.191173i
$979$	2.00269	+	1.68046i	0.0640063	+	0.0537076i
$980$		0			0
$981$	−23.1191	+	11.1643i	−0.738137	+	0.356448i
$982$	17.3862	−	10.0379i	0.554815	−	0.320323i
$983$	−13.6524	−	2.40729i	−0.435445	−	0.0767807i	−0.0483713	−	0.998829i	$-0.515403\pi$
$983$	−13.6524	−	2.40729i	−0.435445	−	0.0767807i	−0.387074	+	0.922049i	$0.626514\pi$
$984$	−27.3306	+	36.1217i	−0.871266	+	1.15152i
$985$		0			0
$986$	0.0784563	+	0.0285558i	0.00249856	+	0.000909401i
$987$	43.3334	−	18.2940i	1.37932	−	0.582305i
$988$	9.72444	+	1.71468i	0.309376	+	0.0545513i
$989$	−0.872042	−	1.51042i	−0.0277293	−	0.0480286i
$990$		0			0
$991$	−17.4112	+	30.1570i	−0.553084	+	0.957970i	0.444966	+	0.895548i	$0.353216\pi$
$991$	−17.4112	+	30.1570i	−0.553084	+	0.957970i	−0.998050	+	0.0624224i	$0.980117\pi$
$992$	−10.3628	+	12.3499i	−0.329020	+	0.392111i
$993$	−11.2828	+	22.0371i	−0.358049	+	0.699328i
$994$	−0.122571	−	0.695133i	−0.00388771	−	0.0220483i
$995$		0			0
$996$	1.90653	−	6.19267i	0.0604109	−	0.196222i
$997$	−8.46492	−	23.2572i	−0.268087	−	0.736562i	−0.998561	−	0.0536221i	$-0.982923\pi$
$997$	−8.46492	−	23.2572i	−0.268087	−	0.736562i	0.730475	−	0.682940i	$-0.239299\pi$
$998$			11.2488i			0.356073i
$999$	33.8433	+	13.2195i	1.07075	+	0.418245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.b.574.2		24
5.2	odd	4		27.2.e.a.7.2	yes	12
5.3	odd	4		675.2.l.c.601.1		12
5.4	even	2	inner	675.2.u.b.574.3		24
15.2	even	4		81.2.e.a.19.1		12
20.7	even	4		432.2.u.c.385.2		12
27.4	even	9	inner	675.2.u.b.274.3		24
45.2	even	12		243.2.e.a.136.2		12
45.7	odd	12		243.2.e.d.136.1		12
45.22	odd	12		243.2.e.c.217.1		12
45.32	even	12		243.2.e.b.217.2		12
135.2	even	36		729.2.a.d.1.4		6
135.4	even	18	inner	675.2.u.b.274.2		24
135.7	odd	36		729.2.c.e.487.4		12
135.22	odd	36		243.2.e.c.28.1		12
135.32	even	36		243.2.e.b.28.2		12
135.47	even	36		729.2.c.b.487.3		12
135.52	odd	36		729.2.a.a.1.3		6
135.58	odd	36		675.2.l.c.301.1		12
135.67	odd	36		243.2.e.d.109.1		12
135.77	even	36		81.2.e.a.64.1		12
135.92	even	36		729.2.c.b.244.3		12
135.97	odd	36		729.2.c.e.244.4		12
135.112	odd	36		27.2.e.a.4.2	✓	12
135.122	even	36		243.2.e.a.109.2		12
540.247	even	36		432.2.u.c.193.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.2	✓	12	135.112	odd	36
27.2.e.a.7.2	yes	12	5.2	odd	4
81.2.e.a.19.1		12	15.2	even	4
81.2.e.a.64.1		12	135.77	even	36
243.2.e.a.109.2		12	135.122	even	36
243.2.e.a.136.2		12	45.2	even	12
243.2.e.b.28.2		12	135.32	even	36
243.2.e.b.217.2		12	45.32	even	12
243.2.e.c.28.1		12	135.22	odd	36
243.2.e.c.217.1		12	45.22	odd	12
243.2.e.d.109.1		12	135.67	odd	36
243.2.e.d.136.1		12	45.7	odd	12
432.2.u.c.193.2		12	540.247	even	36
432.2.u.c.385.2		12	20.7	even	4
675.2.l.c.301.1		12	135.58	odd	36
675.2.l.c.601.1		12	5.3	odd	4
675.2.u.b.274.2		24	135.4	even	18	inner
675.2.u.b.274.3		24	27.4	even	9	inner
675.2.u.b.574.2		24	1.1	even	1	trivial
675.2.u.b.574.3		24	5.4	even	2	inner
729.2.a.a.1.3		6	135.52	odd	36
729.2.a.d.1.4		6	135.2	even	36
729.2.c.b.244.3		12	135.92	even	36
729.2.c.b.487.3		12	135.47	even	36
729.2.c.e.244.4		12	135.97	odd	36
729.2.c.e.487.4		12	135.7	odd	36

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.274138 - 0.753189i) q^{2} +(-0.386327 - 1.68842i) q^{3} +(1.03995 - 0.872619i) q^{4} +(-1.16579 + 0.753837i) q^{6} +(1.52780 - 1.82076i) q^{7} +(-2.33062 - 1.34559i) q^{8} +(-2.70150 + 1.30456i) q^{9} +O(q^{10})\)	\(q+(-0.274138 - 0.753189i) q^{2} +(-0.386327 - 1.68842i) q^{3} +(1.03995 - 0.872619i) q^{4} +(-1.16579 + 0.753837i) q^{6} +(1.52780 - 1.82076i) q^{7} +(-2.33062 - 1.34559i) q^{8} +(-2.70150 + 1.30456i) q^{9} +(-0.0434396 + 0.246358i) q^{11} +(-1.87510 - 1.41875i) q^{12} +(0.893351 - 2.45446i) q^{13} +(-1.79020 - 0.651581i) q^{14} +(0.0969067 - 0.549585i) q^{16} +(0.254072 - 0.146688i) q^{17} +(1.72317 + 1.67711i) q^{18} +(-1.39237 + 2.41166i) q^{19} +(-3.66443 - 1.87615i) q^{21} +(0.197463 - 0.0348180i) q^{22} +(-4.30015 - 5.12472i) q^{23} +(-1.37153 + 4.45490i) q^{24} -2.09357 q^{26} +(3.24631 + 4.05728i) q^{27} -3.22668i q^{28} +(-0.333645 + 0.121437i) q^{29} +(2.11847 - 1.77761i) q^{31} +(-5.74108 + 1.01231i) q^{32} +(0.432738 - 0.0218307i) q^{33} +(-0.180135 - 0.151151i) q^{34} +(-1.67103 + 3.71406i) q^{36} +(6.05558 - 3.49619i) q^{37} +(2.19814 + 0.387591i) q^{38} +(-4.48928 - 0.560124i) q^{39} +(9.13156 + 3.32362i) q^{41} +(-0.408537 + 3.27434i) q^{42} +(0.256746 + 0.0452712i) q^{43} +(0.169802 + 0.294106i) q^{44} +(-2.68104 + 4.64370i) q^{46} +(-7.34421 + 8.75249i) q^{47} +(-0.965367 + 0.0487006i) q^{48} +(0.234540 + 1.33014i) q^{49} +(-0.345826 - 0.372309i) q^{51} +(-1.21277 - 3.33207i) q^{52} +5.43137i q^{53} +(2.16596 - 3.55734i) q^{54} +(-6.01071 + 2.18772i) q^{56} +(4.60980 + 1.41922i) q^{57} +(0.182930 + 0.218007i) q^{58} +(-1.03788 - 5.88612i) q^{59} +(-9.07515 - 7.61495i) q^{61} +(-1.91963 - 1.10830i) q^{62} +(-1.75206 + 6.91190i) q^{63} +(1.77824 + 3.08001i) q^{64} +(-0.135073 - 0.319949i) q^{66} +(-0.619160 + 1.70113i) q^{67} +(0.136218 - 0.374256i) q^{68} +(-6.99139 + 9.24026i) q^{69} +(0.185255 + 0.320871i) q^{71} +(8.05158 + 0.594663i) q^{72} +(-4.35333 - 2.51339i) q^{73} +(-4.29336 - 3.60255i) q^{74} +(0.656467 + 3.72301i) q^{76} +(0.382193 + 0.455479i) q^{77} +(0.808804 + 3.53483i) q^{78} +(0.754406 - 0.274581i) q^{79} +(5.59624 - 7.04855i) q^{81} -7.78892i q^{82} +(0.942488 + 2.58947i) q^{83} +(-5.44798 + 1.24655i) q^{84} +(-0.0362861 - 0.205789i) q^{86} +(0.333932 + 0.516417i) q^{87} +(0.432738 - 0.515717i) q^{88} +(5.22533 - 9.05054i) q^{89} +(-3.10412 - 5.37650i) q^{91} +(-8.94385 - 1.57704i) q^{92} +(-3.81976 - 2.89012i) q^{93} +(8.60560 + 3.13218i) q^{94} +(3.92713 + 9.30225i) q^{96} +(14.6092 + 2.57600i) q^{97} +(0.937552 - 0.541296i) q^{98} +(-0.204037 - 0.722208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4}+O(q^{10}) \) 24 * q + 12 * q^4	\( 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) \) 24 * q + 12 * q^4 + 6 * q^11 - 30 * q^14 + 6 * q^19 - 24 * q^21 + 36 * q^24 - 60 * q^26 + 12 * q^29 + 6 * q^31 - 18 * q^34 + 36 * q^36 - 66 * q^39 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 24 * q^49 - 36 * q^51 + 108 * q^54 - 66 * q^56 + 24 * q^59 + 24 * q^61 - 24 * q^64 - 18 * q^66 - 18 * q^69 + 54 * q^71 - 66 * q^74 - 96 * q^76 + 84 * q^79 + 72 * q^81 - 12 * q^84 + 102 * q^86 - 18 * q^89 + 12 * q^91 + 30 * q^94 + 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more