LMFDB - Embedded newform 675.2.u.d.49.3

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:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	675.49
Dual form			675.2.u.d.124.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19967 - 1.42971i) q^{2} +(1.58534 + 0.697646i) q^{3} +(-0.257569 + 1.46075i) q^{4} +(-0.904448 - 3.10352i) q^{6} +(3.42349 - 0.603654i) q^{7} +(-0.835177 + 0.482190i) q^{8} +(2.02658 + 2.21201i) q^{9} +O(q^{10})$	\(q+(-1.19967 - 1.42971i) q^{2} +(1.58534 + 0.697646i) q^{3} +(-0.257569 + 1.46075i) q^{4} +(-0.904448 - 3.10352i) q^{6} +(3.42349 - 0.603654i) q^{7} +(-0.835177 + 0.482190i) q^{8} +(2.02658 + 2.21201i) q^{9} +(-3.21914 - 1.17167i) q^{11} +(-1.42742 + 2.13608i) q^{12} +(1.92269 - 2.29137i) q^{13} +(-4.97011 - 4.17042i) q^{14} +(4.47899 + 1.63022i) q^{16} +(1.58484 + 0.915007i) q^{17} +(0.731301 - 5.55110i) q^{18} +(-2.83150 - 4.90430i) q^{19} +(5.84852 + 1.43139i) q^{21} +(2.18675 + 6.00805i) q^{22} +(8.37528 + 1.47679i) q^{23} +(-1.66043 + 0.181775i) q^{24} -5.58258 q^{26} +(1.66961 + 4.92061i) q^{27} +5.15634i q^{28} +(-2.71852 + 2.28111i) q^{29} +(0.629929 - 3.57251i) q^{31} +(-2.38289 - 6.54694i) q^{32} +(-4.28600 - 4.10331i) q^{33} +(-0.593087 - 3.36357i) q^{34} +(-3.75317 + 2.39058i) q^{36} +(7.14525 + 4.12531i) q^{37} +(-3.61487 + 9.93177i) q^{38} +(4.64666 - 2.29123i) q^{39} +(3.49560 + 2.93316i) q^{41} +(-4.96982 - 10.0789i) q^{42} +(2.33002 - 6.40168i) q^{43} +(2.54066 - 4.40056i) q^{44} +(-7.93619 - 13.7459i) q^{46} +(-4.24834 + 0.749097i) q^{47} +(5.96338 + 5.70919i) q^{48} +(4.77806 - 1.73907i) q^{49} +(1.87415 + 2.55625i) q^{51} +(2.85188 + 3.39874i) q^{52} -6.55503i q^{53} +(5.03206 - 8.29017i) q^{54} +(-2.56815 + 2.15493i) q^{56} +(-1.06741 - 9.75035i) q^{57} +(6.52266 + 1.15012i) q^{58} +(3.06342 - 1.11500i) q^{59} +(0.589476 + 3.34309i) q^{61} +(-5.86336 + 3.38521i) q^{62} +(8.27327 + 6.34943i) q^{63} +(-1.73511 + 3.00530i) q^{64} +(-0.724755 + 11.0504i) q^{66} +(-2.67781 + 3.19129i) q^{67} +(-1.74480 + 2.07937i) q^{68} +(12.2474 + 8.18418i) q^{69} +(4.35406 - 7.54146i) q^{71} +(-2.75916 - 0.870220i) q^{72} +(-6.87971 + 3.97200i) q^{73} +(-2.67394 - 15.1646i) q^{74} +(7.89326 - 2.87291i) q^{76} +(-11.7280 - 2.06796i) q^{77} +(-8.85027 - 3.89466i) q^{78} +(-11.2271 + 9.42064i) q^{79} +(-0.785942 + 8.96562i) q^{81} -8.51652i q^{82} +(-9.28016 - 11.0597i) q^{83} +(-3.59730 + 8.17453i) q^{84} +(-11.9478 + 4.34865i) q^{86} +(-5.90118 + 1.71976i) q^{87} +(3.25351 - 0.573682i) q^{88} +(-1.78804 - 3.09697i) q^{89} +(5.19911 - 9.00512i) q^{91} +(-4.31443 + 11.8538i) q^{92} +(3.49099 - 5.22416i) q^{93} +(6.16760 + 5.17523i) q^{94} +(0.789762 - 12.0415i) q^{96} +(1.25203 - 3.43991i) q^{97} +(-8.21846 - 4.74493i) q^{98} +(-3.93210 - 9.49523i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 12 q^{6} + 6 q^{9}+O(q^{10}) $ 84 * q - 12 * q^6 + 6 * q^9	$ 84 q - 12 q^{6} + 6 q^{9} - 12 q^{11} + 54 q^{14} - 24 q^{16} + 48 q^{19} + 24 q^{21} + 6 q^{24} - 36 q^{26} - 24 q^{31} - 102 q^{34} - 72 q^{36} + 60 q^{39} + 66 q^{41} - 24 q^{44} - 60 q^{46} - 36 q^{49} - 78 q^{51} - 60 q^{54} - 48 q^{56} + 54 q^{59} - 12 q^{61} + 126 q^{64} - 60 q^{66} - 102 q^{69} + 24 q^{71} + 144 q^{74} + 276 q^{76} + 36 q^{79} + 90 q^{81} + 102 q^{84} + 36 q^{86} - 18 q^{89} - 138 q^{91} + 66 q^{94} + 306 q^{96} + 18 q^{99}+O(q^{100}) $ 84 * q - 12 * q^6 + 6 * q^9 - 12 * q^11 + 54 * q^14 - 24 * q^16 + 48 * q^19 + 24 * q^21 + 6 * q^24 - 36 * q^26 - 24 * q^31 - 102 * q^34 - 72 * q^36 + 60 * q^39 + 66 * q^41 - 24 * q^44 - 60 * q^46 - 36 * q^49 - 78 * q^51 - 60 * q^54 - 48 * q^56 + 54 * q^59 - 12 * q^61 + 126 * q^64 - 60 * q^66 - 102 * q^69 + 24 * q^71 + 144 * q^74 + 276 * q^76 + 36 * q^79 + 90 * q^81 + 102 * q^84 + 36 * q^86 - 18 * q^89 - 138 * q^91 + 66 * q^94 + 306 * q^96 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	−1.19967	−	1.42971i	−0.848295	−	1.01096i	−0.999747	−	0.0224938i	$-0.992839\pi$
$2$	−1.19967	−	1.42971i	−0.848295	−	1.01096i	0.151452	−	0.988465i	$-0.451605\pi$
$3$	1.58534	+	0.697646i	0.915294	+	0.402786i
$3$	1.58534	+	0.697646i	0.915294	+	0.402786i
$4$	−0.257569	+	1.46075i	−0.128785	+	0.730374i
$5$		0			0
$5$		0			0
$6$	−0.904448	−	3.10352i	−0.369239	−	1.26701i
$7$	3.42349	−	0.603654i	1.29396	−	0.228160i	0.516062	−	0.856552i	$-0.327398\pi$
$7$	3.42349	−	0.603654i	1.29396	−	0.228160i	0.777897	+	0.628392i	$0.216286\pi$
$8$	−0.835177	+	0.482190i	−0.295280	+	0.170480i
$9$	2.02658	+	2.21201i	0.675527	+	0.737335i
$10$		0			0
$11$	−3.21914	−	1.17167i	−0.970606	−	0.353272i	−0.192425	−	0.981312i	$-0.561635\pi$
$11$	−3.21914	−	1.17167i	−0.970606	−	0.353272i	−0.778181	+	0.628040i	$0.783857\pi$
$12$	−1.42742	+	2.13608i	−0.412060	+	0.616634i
$13$	1.92269	−	2.29137i	0.533257	−	0.635511i	−0.430405	−	0.902636i	$-0.641629\pi$
$13$	1.92269	−	2.29137i	0.533257	−	0.635511i	0.963662	+	0.267125i	$0.0860737\pi$
$14$	−4.97011	−	4.17042i	−1.32832	−	1.11459i
$15$		0			0
$16$	4.47899	+	1.63022i	1.11975	+	0.407554i
$17$	1.58484	+	0.915007i	0.384380	+	0.221922i	0.679722	−	0.733470i	$-0.262100\pi$
$17$	1.58484	+	0.915007i	0.384380	+	0.221922i	−0.295342	+	0.955391i	$0.595434\pi$
$18$	0.731301	−	5.55110i	0.172369	−	1.30841i
$19$	−2.83150	−	4.90430i	−0.649591	−	1.12512i	−0.983221	−	0.182420i	$-0.941607\pi$
$19$	−2.83150	−	4.90430i	−0.649591	−	1.12512i	0.333630	−	0.942704i	$-0.391726\pi$
$20$		0			0
$21$	5.84852	+	1.43139i	1.27625	+	0.312355i
$22$	2.18675	+	6.00805i	0.466217	+	1.28092i
$23$	8.37528	+	1.47679i	1.74637	+	0.307931i	0.953484	−	0.301444i	$-0.0974685\pi$
$23$	8.37528	+	1.47679i	1.74637	+	0.307931i	0.792882	+	0.609375i	$0.208580\pi$
$24$	−1.66043	+	0.181775i	−0.338935	+	0.0371046i
$25$		0			0
$26$	−5.58258			−1.09483
$27$	1.66961	+	4.92061i	0.321317	+	0.946972i
$28$			5.15634i			0.974457i
$29$	−2.71852	+	2.28111i	−0.504817	+	0.423592i	−0.859301	−	0.511470i	$-0.829101\pi$
$29$	−2.71852	+	2.28111i	−0.504817	+	0.423592i	0.354484	+	0.935062i	$0.384657\pi$
$30$		0			0
$31$	0.629929	−	3.57251i	0.113139	−	0.641641i	−0.874516	−	0.484996i	$-0.838821\pi$
$31$	0.629929	−	3.57251i	0.113139	−	0.641641i	0.987655	−	0.156645i	$-0.0500679\pi$
$32$	−2.38289	−	6.54694i	−0.421240	−	1.15735i
$33$	−4.28600	−	4.10331i	−0.746097	−	0.714294i
$34$	−0.593087	−	3.36357i	−0.101714	−	0.576847i
$35$		0			0
$36$	−3.75317	+	2.39058i	−0.625528	+	0.398430i
$37$	7.14525	+	4.12531i	1.17467	+	0.678197i	0.954776	−	0.297327i	$-0.0960951\pi$
$37$	7.14525	+	4.12531i	1.17467	+	0.678197i	0.219895	+	0.975523i	$0.429428\pi$
$38$	−3.61487	+	9.93177i	−0.586409	+	1.61115i
$39$	4.64666	−	2.29123i	0.744062	−	0.366891i
$40$		0			0
$41$	3.49560	+	2.93316i	0.545921	+	0.458082i	0.873557	−	0.486722i	$-0.161808\pi$
$41$	3.49560	+	2.93316i	0.545921	+	0.458082i	−0.327636	+	0.944804i	$0.606252\pi$
$42$	−4.96982	−	10.0789i	−0.766860	−	1.55521i
$43$	2.33002	−	6.40168i	0.355325	−	0.976247i	−0.625306	−	0.780380i	$-0.715026\pi$
$43$	2.33002	−	6.40168i	0.355325	−	0.976247i	0.980630	−	0.195867i	$-0.0627521\pi$
$44$	2.54066	−	4.40056i	0.383019	−	0.663409i
$45$		0			0
$46$	−7.93619	−	13.7459i	−1.17013	−	2.02672i
$47$	−4.24834	+	0.749097i	−0.619684	+	0.109267i	−0.474672	−	0.880163i	$-0.657433\pi$
$47$	−4.24834	+	0.749097i	−0.619684	+	0.109267i	−0.145012	+	0.989430i	$0.546322\pi$
$48$	5.96338	+	5.70919i	0.860740	+	0.824051i
$49$	4.77806	−	1.73907i	0.682579	−	0.248439i
$50$		0			0
$51$	1.87415	+	2.55625i	0.262433	+	0.357946i
$52$	2.85188	+	3.39874i	0.395485	+	0.471321i
$53$		−	6.55503i		−	0.900403i	−0.892927	−	0.450201i	$-0.851352\pi$
$53$		−	6.55503i		−	0.900403i	0.892927	−	0.450201i	$-0.148648\pi$
$54$	5.03206	−	8.29017i	0.684777	−	1.12815i
$55$		0			0
$56$	−2.56815	+	2.15493i	−0.343183	+	0.287965i
$57$	−1.06741	−	9.75035i	−0.141382	−	1.29147i
$58$	6.52266	+	1.15012i	0.856467	+	0.151018i
$59$	3.06342	−	1.11500i	0.398824	−	0.145160i	−0.134818	−	0.990870i	$-0.543045\pi$
$59$	3.06342	−	1.11500i	0.398824	−	0.145160i	0.533642	+	0.845710i	$0.320823\pi$
$60$		0			0
$61$	0.589476	+	3.34309i	0.0754747	+	0.428038i	0.999008	+	0.0445212i	$0.0141762\pi$
$61$	0.589476	+	3.34309i	0.0754747	+	0.428038i	−0.923534	+	0.383517i	$0.874713\pi$
$62$	−5.86336	+	3.38521i	−0.744648	+	0.429922i
$63$	8.27327	+	6.34943i	1.04233	+	0.799953i
$64$	−1.73511	+	3.00530i	−0.216889	+	0.375663i
$65$		0			0
$66$	−0.724755	+	11.0504i	−0.0892112	+	1.36020i
$67$	−2.67781	+	3.19129i	−0.327146	+	0.389878i	−0.904399	−	0.426688i	$-0.859680\pi$
$67$	−2.67781	+	3.19129i	−0.327146	+	0.389878i	0.577253	+	0.816566i	$0.304125\pi$
$68$	−1.74480	+	2.07937i	−0.211588	+	0.252161i
$69$	12.2474	+	8.18418i	1.47441	+	0.985260i
$70$		0			0
$71$	4.35406	−	7.54146i	0.516732	−	0.895007i	−0.483079	−	0.875577i	$-0.660482\pi$
$71$	4.35406	−	7.54146i	0.516732	−	0.895007i	0.999811	−	0.0194298i	$-0.00618507\pi$
$72$	−2.75916	−	0.870220i	−0.325170	−	0.102556i
$73$	−6.87971	+	3.97200i	−0.805210	+	0.464888i	−0.845290	−	0.534309i	$-0.820572\pi$
$73$	−6.87971	+	3.97200i	−0.805210	+	0.464888i	0.0400800	+	0.999196i	$0.487239\pi$
$74$	−2.67394	−	15.1646i	−0.310839	−	1.76285i
$75$		0			0
$76$	7.89326	−	2.87291i	0.905419	−	0.329545i
$77$	−11.7280	−	2.06796i	−1.33653	−	0.235666i
$78$	−8.85027	−	3.89466i	−1.00210	−	0.440984i
$79$	−11.2271	+	9.42064i	−1.26315	+	1.05990i	−0.267806	+	0.963473i	$0.586299\pi$
$79$	−11.2271	+	9.42064i	−1.26315	+	1.05990i	−0.995340	+	0.0964321i	$0.969257\pi$
$80$		0			0
$81$	−0.785942	+	8.96562i	−0.0873268	+	0.996180i
$82$		−	8.51652i		−	0.940492i
$83$	−9.28016	−	11.0597i	−1.01863	−	1.21396i	−0.976650	−	0.214837i	$-0.931078\pi$
$83$	−9.28016	−	11.0597i	−1.01863	−	1.21396i	−0.0419799	−	0.999118i	$-0.513367\pi$
$84$	−3.59730	+	8.17453i	−0.392498	+	0.891915i
$85$		0			0
$86$	−11.9478	+	4.34865i	−1.28837	+	0.468927i
$87$	−5.90118	+	1.71976i	−0.632673	+	0.184378i
$88$	3.25351	−	0.573682i	0.346826	−	0.0611547i
$89$	−1.78804	−	3.09697i	−0.189531	−	0.328278i	0.755563	−	0.655076i	$-0.227364\pi$
$89$	−1.78804	−	3.09697i	−0.189531	−	0.328278i	−0.945094	+	0.326798i	$0.894030\pi$
$90$		0			0
$91$	5.19911	−	9.00512i	0.545014	−	0.943993i
$92$	−4.31443	+	11.8538i	−0.449810	+	1.23584i
$93$	3.49099	−	5.22416i	0.361999	−	0.541720i
$94$	6.16760	+	5.17523i	0.636139	+	0.533784i
$95$		0			0
$96$	0.789762	−	12.0415i	0.0806047	−	1.22898i
$97$	1.25203	−	3.43991i	0.127124	−	0.349270i	−0.859761	−	0.510697i	$-0.829387\pi$
$97$	1.25203	−	3.43991i	0.127124	−	0.349270i	0.986885	+	0.161427i	$0.0516096\pi$
$98$	−8.21846	−	4.74493i	−0.830190	−	0.479310i
$99$	−3.93210	−	9.49523i	−0.395191	−	0.954306i
$100$		0			0
$101$	0.0680401	+	0.385875i	0.00677025	+	0.0383960i	0.988006	−	0.154417i	$-0.0493500\pi$
$101$	0.0680401	+	0.385875i	0.00677025	+	0.0383960i	−0.981235	+	0.192813i	$0.938239\pi$
$102$	1.40633	−	5.74615i	0.139248	−	0.568953i
$103$	5.62618	+	15.4578i	0.554364	+	1.52310i	0.827693	+	0.561181i	$0.189653\pi$
$103$	5.62618	+	15.4578i	0.554364	+	1.52310i	−0.273330	+	0.961920i	$0.588125\pi$
$104$	−0.500909	+	2.84080i	−0.0491182	+	0.278563i
$105$		0			0
$106$	−9.37180	+	7.86388i	−0.910270	+	0.763807i
$107$		−	12.6842i		−	1.22623i	−0.789995	−	0.613113i	$-0.789917\pi$
$107$		−	12.6842i		−	1.22623i	0.789995	−	0.613113i	$-0.210083\pi$
$108$	−7.61781	+	1.17149i	−0.733024	+	0.112727i
$109$	−14.0464			−1.34540			−0.672701	−	0.739914i	$-0.734866\pi$
$109$	−14.0464			−1.34540			−0.672701	+	0.739914i	$0.734866\pi$
$110$		0			0
$111$	8.44961	+	11.5249i	0.802002	+	1.09389i
$112$	16.3179	+	2.87728i	1.54189	+	0.271877i
$113$	−2.54930	−	7.00413i	−0.239818	−	0.658893i	−0.999958	−	0.00913486i	$-0.997092\pi$
$113$	−2.54930	−	7.00413i	−0.239818	−	0.658893i	0.760141	−	0.649758i	$-0.225130\pi$
$114$	−12.6596	+	13.2233i	−1.18568	+	1.23848i
$115$		0			0
$116$	−2.63192	−	4.55862i	−0.244368	−	0.423257i
$117$	8.96499	−	0.390649i	0.828814	−	0.0361155i
$118$	−5.26922	−	3.04218i	−0.485071	−	0.280056i
$119$	5.97803	+	2.17582i	0.548005	+	0.199457i
$120$		0			0
$121$	0.563534	+	0.472862i	0.0512304	+	0.0429874i
$122$	4.07247	−	4.85338i	0.368704	−	0.439405i
$123$	3.49540	+	7.08873i	0.315169	+	0.639169i
$124$	5.05628	+	1.84034i	0.454067	+	0.165267i
$125$		0			0
$126$	−0.847341	−	19.4456i	−0.0754871	−	1.73235i
$127$	−11.1308	+	6.42637i	−0.987699	+	0.570248i	−0.904586	−	0.426292i	$-0.859820\pi$
$127$	−11.1308	+	6.42637i	−0.987699	+	0.570248i	−0.0831130	+	0.996540i	$0.526486\pi$
$128$	−7.34425	+	1.29499i	−0.649146	+	0.114462i
$129$	8.15997	−	8.52328i	0.718445	−	0.750433i
$130$		0			0
$131$	−3.04490	+	17.2685i	−0.266034	+	1.50876i	0.500040	+	0.866003i	$0.333319\pi$
$131$	−3.04490	+	17.2685i	−0.266034	+	1.50876i	−0.766074	+	0.642753i	$0.777792\pi$
$132$	7.09784	−	5.20388i	0.617787	−	0.452940i
$133$	−12.6541	−	15.0806i	−1.09725	−	1.30765i
$134$	7.77510			0.671667
$135$		0			0
$136$	−1.76483			−0.151333
$137$	6.38877	+	7.61384i	0.545830	+	0.650495i	0.966484	−	0.256726i	$-0.0826439\pi$
$137$	6.38877	+	7.61384i	0.545830	+	0.650495i	−0.420654	+	0.907221i	$0.638199\pi$
$138$	−2.99177	−	27.3285i	−0.254676	−	2.32636i
$139$	−0.556612	+	3.15670i	−0.0472112	+	0.267748i	−0.999272	−	0.0381621i	$-0.987850\pi$
$139$	−0.556612	+	3.15670i	−0.0472112	+	0.267748i	0.952060	+	0.305910i	$0.0989608\pi$
$140$		0			0
$141$	−7.25765	−	1.77627i	−0.611205	−	0.149589i
$142$	−16.0055	+	2.82221i	−1.34316	+	0.236835i
$143$	−8.87411	+	5.12347i	−0.742090	+	0.428446i
$144$	5.47098	+	13.2113i	0.455915	+	1.10094i
$145$		0			0
$146$	13.9322	+	5.07091i	1.15304	+	0.419671i
$147$	8.78808	+	0.576380i	0.724829	+	0.0475390i
$148$	−7.86643	+	9.37485i	−0.646617	+	0.770608i
$149$	−0.773640	−	0.649161i	−0.0633790	−	0.0531813i	0.610548	−	0.791979i	$-0.290949\pi$
$149$	−0.773640	−	0.649161i	−0.0633790	−	0.0531813i	−0.673927	+	0.738798i	$0.735394\pi$
$150$		0			0
$151$	11.1642	+	4.06345i	0.908533	+	0.330679i	0.753667	−	0.657257i	$-0.228283\pi$
$151$	11.1642	+	4.06345i	0.908533	+	0.330679i	0.154866	+	0.987936i	$0.450505\pi$
$152$	4.72961	+	2.73064i	0.383622	+	0.221484i
$153$	1.18780	+	5.36001i	0.0960281	+	0.433331i
$154$	11.1131	+	19.2485i	0.895520	+	1.55109i
$155$		0			0
$156$	2.15008	+	7.37776i	0.172144	+	0.590693i
$157$	6.69550	+	18.3957i	0.534359	+	1.46814i	0.853834	+	0.520545i	$0.174271\pi$
$157$	6.69550	+	18.3957i	0.534359	+	1.46814i	−0.319475	+	0.947595i	$0.603507\pi$
$158$	26.9376	+	4.74982i	2.14304	+	0.377876i
$159$	4.57309	−	10.3919i	0.362670	−	0.824134i
$160$		0			0
$161$	29.5642			2.32998
$162$	13.7611	−	9.63211i	1.08118	−	0.756770i
$163$			9.26458i			0.725658i	0.931856	+	0.362829i	$0.118189\pi$
$163$			9.26458i			0.725658i	−0.931856	+	0.362829i	$0.881811\pi$
$164$	−5.18496	+	4.35070i	−0.404877	+	0.339732i
$165$		0			0
$166$	−4.67899	+	26.5359i	−0.363160	+	2.05958i
$167$	3.48738	+	9.58151i	0.269862	+	0.741439i	0.998406	+	0.0564405i	$0.0179751\pi$
$167$	3.48738	+	9.58151i	0.269862	+	0.741439i	−0.728544	+	0.684999i	$0.759803\pi$
$168$	−5.57475	+	1.62463i	−0.430102	+	0.125343i
$169$	0.703782	+	3.99135i	0.0541371	+	0.307027i
$170$		0			0
$171$	5.11008	−	16.2023i	0.390778	−	1.23902i
$172$	8.75110	+	5.05245i	0.667265	+	0.385246i
$173$	−3.86724	+	10.6251i	−0.294021	+	0.807815i	0.701448	+	0.712721i	$0.252537\pi$
$173$	−3.86724	+	10.6251i	−0.294021	+	0.807815i	−0.995468	+	0.0950941i	$0.969685\pi$
$174$	9.53823	+	6.37383i	0.723091	+	0.483199i
$175$		0			0
$176$	−12.5084	−	10.4958i	−0.942855	−	0.791150i
$177$	5.63443	+	0.369543i	0.423510	+	0.0277765i
$178$	−2.28272	+	6.27171i	−0.171097	+	0.470085i
$179$	−12.0316	+	20.8394i	−0.899285	+	1.55761i	−0.0708754	+	0.997485i	$0.522579\pi$
$179$	−12.0316	+	20.8394i	−0.899285	+	1.55761i	−0.828410	+	0.560122i	$0.810754\pi$
$180$		0			0
$181$	−4.60686	−	7.97931i	−0.342425	−	0.593098i	0.642457	−	0.766321i	$-0.277915\pi$
$181$	−4.60686	−	7.97931i	−0.342425	−	0.593098i	−0.984882	+	0.173224i	$0.944582\pi$
$182$	−19.1119	+	3.36995i	−1.41667	+	0.249797i
$183$	−1.39777	+	5.71116i	−0.103326	+	0.422181i
$184$	−7.70693	+	2.80509i	−0.568162	+	0.206794i
$185$		0			0
$186$	−11.6571	+	1.27615i	−0.854738	+	0.0935719i
$187$	−4.02972	−	4.80244i	−0.294682	−	0.351189i
$188$		−	6.39870i		−	0.466673i
$189$	8.68626	+	15.8378i	0.631832	+	1.15203i
$190$		0			0
$191$	−1.50137	+	1.25980i	−0.108635	+	0.0911559i	−0.695487	−	0.718538i	$-0.744811\pi$
$191$	−1.50137	+	1.25980i	−0.108635	+	0.0911559i	0.586852	+	0.809694i	$0.300367\pi$
$192$	−4.84737	+	3.55392i	−0.349829	+	0.256482i
$193$	10.3977	+	1.83340i	0.748446	+	0.131971i	0.534846	−	0.844950i	$-0.320370\pi$
$193$	10.3977	+	1.83340i	0.748446	+	0.131971i	0.213601	+	0.976921i	$0.431481\pi$
$194$	−6.42010	+	2.33673i	−0.460937	+	0.167767i
$195$		0			0
$196$	1.30966	+	7.42747i	0.0935473	+	0.530533i
$197$	1.70542	−	0.984623i	0.121506	−	0.0701515i	−0.438015	−	0.898968i	$-0.644318\pi$
$197$	1.70542	−	0.984623i	0.121506	−	0.0701515i	0.559521	+	0.828816i	$0.310985\pi$
$198$	−8.85822	+	17.0129i	−0.629526	+	1.20905i
$199$	7.27018	−	12.5923i	0.515369	−	0.892646i	−0.484472	−	0.874807i	$-0.660988\pi$
$199$	7.27018	−	12.5923i	0.515369	−	0.892646i	0.999841	−	0.0178388i	$-0.00567858\pi$
$200$		0			0
$201$	−6.47161	+	3.19110i	−0.456472	+	0.225083i
$202$	0.470064	−	0.560200i	0.0330736	−	0.0394155i
$203$	−7.92984	+	9.45041i	−0.556565	+	0.663289i
$204$	−4.21676	+	2.07925i	−0.295232	+	0.145577i
$205$		0			0
$206$	15.3506	−	26.5881i	1.06953	−	1.85248i
$207$	13.7065	+	21.5190i	0.952669	+	1.49567i
$208$	12.3471	−	7.12861i	0.856118	−	0.494280i
$209$	3.36876	+	19.1052i	0.233022	+	1.32153i
$210$		0			0
$211$	−11.3530	+	4.13217i	−0.781575	+	0.284470i	−0.701829	−	0.712345i	$-0.747633\pi$
$211$	−11.3530	+	4.13217i	−0.781575	+	0.284470i	−0.0797459	+	0.996815i	$0.525411\pi$
$212$	9.57525	+	1.68837i	0.657631	+	0.115958i
$213$	12.1639	−	8.91815i	0.833458	−	0.611062i
$214$	−18.1347	+	15.2168i	−1.23966	+	1.04020i
$215$		0			0
$216$	−3.76709	−	3.30451i	−0.256318	−	0.224843i
$217$		−	12.6107i		−	0.856071i
$218$	16.8511	+	20.0823i	1.14130	+	1.36015i
$219$	−13.6777	+	1.49736i	−0.924254	+	0.101182i
$220$		0			0
$221$	5.14376	−	1.87218i	0.346007	−	0.125936i
$222$	6.34046	−	25.9065i	0.425544	−	1.73873i
$223$	20.4957	−	3.61394i	1.37249	−	0.242007i	0.561699	−	0.827342i	$-0.310148\pi$
$223$	20.4957	−	3.61394i	1.37249	−	0.242007i	0.810792	+	0.585334i	$0.199037\pi$
$224$	−12.1099	−	20.9750i	−0.809127	−	1.40145i
$225$		0			0
$226$	−6.95557	+	12.0474i	−0.462678	+	0.801381i
$227$	−2.91729	+	8.01519i	−0.193627	+	0.531987i	−0.998074	−	0.0620383i	$-0.980240\pi$
$227$	−2.91729	+	8.01519i	−0.193627	+	0.531987i	0.804446	+	0.594025i	$0.202462\pi$
$228$	14.5177	+	0.952169i	0.961461	+	0.0630589i
$229$	−12.0900	−	10.1447i	−0.798931	−	0.670383i	0.149008	−	0.988836i	$-0.452392\pi$
$229$	−12.0900	−	10.1447i	−0.798931	−	0.670383i	−0.947938	+	0.318453i	$0.896837\pi$
$230$		0			0
$231$	−17.1501	−	11.4604i	−1.12839	−	0.754037i
$232$	1.17052	−	3.21597i	0.0768483	−	0.211139i
$233$	−15.7429	−	9.08918i	−1.03135	−	0.595452i	−0.113981	−	0.993483i	$-0.536360\pi$
$233$	−15.7429	−	9.08918i	−1.03135	−	0.595452i	−0.917372	+	0.398031i	$0.869694\pi$
$234$	−11.3136	−	12.3487i	−0.739590	−	0.807260i
$235$		0			0
$236$	0.839683	+	4.76208i	0.0546587	+	0.309985i
$237$	−24.3710	+	7.10235i	−1.58306	+	0.461348i
$238$	−4.06086	−	11.1571i	−0.263227	−	0.723209i
$239$	2.15258	−	12.2079i	0.139239	−	0.789663i	−0.832575	−	0.553913i	$-0.813134\pi$
$239$	2.15258	−	12.2079i	0.139239	−	0.789663i	0.971814	−	0.235750i	$-0.0757547\pi$
$240$		0			0
$241$	−6.87075	+	5.76524i	−0.442584	+	0.371372i	−0.836675	−	0.547699i	$-0.815504\pi$
$241$	−6.87075	+	5.76524i	−0.442584	+	0.371372i	0.394091	+	0.919071i	$0.371059\pi$
$242$		−	1.37297i		−	0.0882578i
$243$	−7.50081	+	13.6652i	−0.481177	+	0.876623i
$244$	−5.03524			−0.322348
$245$		0			0
$246$	5.94151	−	13.5015i	0.378817	−	0.860827i
$247$	−16.6816	−	2.94142i	−1.06143	−	0.187158i
$248$	1.19652	+	3.28742i	0.0759793	+	0.208751i
$249$	−6.99644	−	24.0075i	−0.443382	−	1.52142i
$250$		0			0
$251$	−5.89181	−	10.2049i	−0.371888	−	0.644129i	0.617968	−	0.786203i	$-0.287956\pi$
$251$	−5.89181	−	10.2049i	−0.371888	−	0.644129i	−0.989856	+	0.142074i	$0.954623\pi$
$252$	−11.4059	+	10.4497i	−0.718502	+	0.658272i
$253$	−25.2308	−	14.5670i	−1.58625	−	0.915822i
$254$	22.5411	+	8.20430i	1.41436	+	0.514784i
$255$		0			0
$256$	15.9788	+	13.4078i	0.998677	+	0.837989i
$257$	−6.57063	+	7.83057i	−0.409865	+	0.488458i	−0.931001	−	0.365015i	$-0.881064\pi$
$257$	−6.57063	+	7.83057i	−0.409865	+	0.488458i	0.521137	+	0.853473i	$0.325508\pi$
$258$	−21.9751	−	1.44127i	−1.36811	−	0.0897297i
$259$	26.9520	+	9.80971i	1.67471	+	0.609546i
$260$		0			0
$261$	−10.5551	−	1.39053i	−0.653346	−	0.0860718i
$262$	28.3418	−	16.3632i	1.75096	−	1.01092i
$263$	22.5431	−	3.97496i	1.39007	−	0.245107i	0.572013	−	0.820245i	$-0.306163\pi$
$263$	22.5431	−	3.97496i	1.39007	−	0.245107i	0.818056	+	0.575138i	$0.195052\pi$
$264$	5.55814	+	1.36032i	0.342080	+	0.0837220i
$265$		0			0
$266$	−6.38013	+	36.1835i	−0.391191	+	2.21855i
$267$	−0.674050	−	6.15715i	−0.0412512	−	0.376811i
$268$	−3.97194	−	4.73358i	−0.242625	−	0.289149i
$269$	−0.457689			−0.0279058			−0.0139529	−	0.999903i	$-0.504441\pi$
$269$	−0.457689			−0.0279058			−0.0139529	+	0.999903i	$0.504441\pi$
$270$		0			0
$271$	−24.7898			−1.50588			−0.752938	−	0.658092i	$-0.771364\pi$
$271$	−24.7898			−1.50588			−0.752938	+	0.658092i	$0.771364\pi$
$272$	5.60681	+	6.68193i	0.339963	+	0.405152i
$273$	14.5247	−	10.6490i	0.879076	−	0.644507i
$274$	3.22118	−	18.2682i	0.194598	−	1.10362i
$275$		0			0
$276$	−15.1096	+	15.7823i	−0.909489	+	0.949983i
$277$	−6.06336	+	1.06913i	−0.364312	+	0.0642381i	−0.352808	−	0.935696i	$-0.614773\pi$
$277$	−6.06336	+	1.06913i	−0.364312	+	0.0642381i	−0.0115042	+	0.999934i	$0.503662\pi$
$278$	5.18093	−	2.99121i	0.310731	−	0.179401i
$279$	9.17901	−	5.84657i	0.549533	−	0.350025i
$280$		0			0
$281$	17.0698	+	6.21288i	1.01830	+	0.370629i	0.796613	−	0.604489i	$-0.206623\pi$
$281$	17.0698	+	6.21288i	1.01830	+	0.370629i	0.221683	+	0.975119i	$0.428845\pi$
$282$	6.16724	+	12.5073i	0.367254	+	0.744798i
$283$	4.51955	−	5.38619i	0.268659	−	0.320176i	−0.614800	−	0.788683i	$-0.710763\pi$
$283$	4.51955	−	5.38619i	0.268659	−	0.320176i	0.883460	+	0.468507i	$0.155208\pi$
$284$	9.89470	+	8.30264i	0.587142	+	0.492671i
$285$		0			0
$286$	17.9711	+	6.54094i	1.06265	+	0.386774i
$287$	13.7378	+	7.93150i	0.810915	+	0.468182i
$288$	9.65275	−	18.5389i	0.568794	−	1.09241i
$289$	−6.82553	−	11.8222i	−0.401502	−	0.695421i
$290$		0			0
$291$	4.38472	−	4.57995i	0.257037	−	0.268481i
$292$	−4.03009	−	11.0726i	−0.235843	−	0.647974i
$293$	−23.3907	−	4.12441i	−1.36650	−	0.240951i	−0.558192	−	0.829712i	$-0.688505\pi$
$293$	−23.3907	−	4.12441i	−1.36650	−	0.240951i	−0.808307	+	0.588761i	$0.799616\pi$
$294$	−9.71874	−	13.2559i	−0.566808	−	0.773099i
$295$		0			0
$296$	−7.95672			−0.462475
$297$	0.390611	−	17.7963i	0.0226656	−	1.03265i
$298$			1.88486i			0.109187i
$299$	19.4869	−	16.3514i	1.12696	−	0.945628i
$300$		0			0
$301$	4.11241	−	23.3226i	0.237035	−	1.34429i
$302$	−7.58384	−	20.8364i	−0.436401	−	1.19900i
$303$	−0.161337	+	0.659209i	−0.00926859	+	0.0378706i
$304$	−4.68717	−	26.5823i	−0.268828	−	1.52460i
$305$		0			0
$306$	6.23829	−	8.12845i	0.356619	−	0.464673i
$307$	−16.1300	−	9.31264i	−0.920585	−	0.531500i	−0.0367637	−	0.999324i	$-0.511705\pi$
$307$	−16.1300	−	9.31264i	−0.920585	−	0.531500i	−0.883822	+	0.467824i	$0.845038\pi$
$308$	6.04153	−	16.5990i	0.344248	−	0.945814i
$309$	−1.86468	+	28.4309i	−0.106078	+	1.61738i
$310$		0			0
$311$	1.48464	+	1.24576i	0.0841860	+	0.0706404i	0.683909	−	0.729567i	$-0.260278\pi$
$311$	1.48464	+	1.24576i	0.0841860	+	0.0706404i	−0.599724	+	0.800207i	$0.704723\pi$
$312$	−2.77598	+	4.15416i	−0.157159	+	0.235183i
$313$	−10.3468	+	28.4277i	−0.584838	+	1.60683i	0.194968	+	0.980810i	$0.437540\pi$
$313$	−10.3468	+	28.4277i	−0.584838	+	1.60683i	−0.779806	+	0.626021i	$0.784683\pi$
$314$	18.2682	−	31.6414i	1.03093	−	1.78563i
$315$		0			0
$316$	−10.8694	−	18.8264i	−0.611453	−	1.05907i
$317$	2.88607	−	0.508892i	0.162098	−	0.0285822i	−0.0920102	−	0.995758i	$-0.529329\pi$
$317$	2.88607	−	0.508892i	0.162098	−	0.0285822i	0.254108	+	0.967176i	$0.418218\pi$
$318$	−20.3437	+	5.92869i	−1.14082	+	0.332464i
$319$	11.4240	−	4.15799i	0.639621	−	0.232803i
$320$		0			0
$321$	8.84907	−	20.1087i	0.493907	−	1.12236i
$322$	−35.4673	−	42.2682i	−1.97651	−	2.35552i
$323$		−	10.3634i		−	0.576633i
$324$	−12.8941	−	3.45733i	−0.716337	−	0.192074i
$325$		0			0
$326$	13.2457	−	11.1144i	0.733610	−	0.615572i
$327$	−22.2683	−	9.79943i	−1.23144	−	0.541909i
$328$	−4.33378	−	0.764162i	−0.239293	−	0.0421938i
$329$	−14.0920	+	5.12906i	−0.776915	+	0.282774i
$330$		0			0
$331$	−1.87857	−	10.6539i	−0.103255	−	0.585590i	−0.991903	−	0.126999i	$-0.959465\pi$
$331$	−1.87857	−	10.6539i	−0.103255	−	0.585590i	0.888648	−	0.458591i	$-0.151646\pi$
$332$	18.5457	−	10.7073i	1.01783	−	0.587642i
$333$	5.35521	+	24.1656i	0.293464	+	1.32427i
$334$	9.51508	−	16.4806i	0.520642	−	0.901778i
$335$		0			0
$336$	23.8620	+	15.9455i	1.30178	+	0.869901i
$337$	−8.79442	+	10.4808i	−0.479063	+	0.570925i	−0.950401	−	0.311028i	$-0.899327\pi$
$337$	−8.79442	+	10.4808i	−0.479063	+	0.570925i	0.471338	+	0.881953i	$0.343771\pi$
$338$	4.86216	−	5.79450i	0.264467	−	0.315179i
$339$	0.844913	−	12.8824i	0.0458894	−	0.699676i
$340$		0			0
$341$	−6.21363	+	10.7623i	−0.336487	+	0.582812i
$342$	−29.2950	+	12.1314i	−1.58409	+	0.655992i
$343$	−5.76614	+	3.32908i	−0.311342	+	0.179754i
$344$	1.14084	+	6.47005i	0.0615102	+	0.348842i
$345$		0			0
$346$	19.8303	−	7.21764i	1.06608	−	0.388023i
$347$	17.7155	+	3.12373i	0.951020	+	0.167691i	0.627575	−	0.778556i	$-0.284048\pi$
$347$	17.7155	+	3.12373i	0.951020	+	0.167691i	0.323445	+	0.946247i	$0.395159\pi$
$348$	−0.992176	−	9.06309i	−0.0531862	−	0.485833i
$349$	−2.87063	+	2.40875i	−0.153661	+	0.128937i	−0.716377	−	0.697713i	$-0.754201\pi$
$349$	−2.87063	+	2.40875i	−0.153661	+	0.128937i	0.562716	+	0.826650i	$0.309757\pi$
$350$		0			0
$351$	14.4851	+	5.63508i	0.773156	+	0.300778i
$352$			23.8675i			1.27214i
$353$	−0.210170	−	0.250470i	−0.0111862	−	0.0133312i	0.760422	−	0.649429i	$-0.224992\pi$
$353$	−0.210170	−	0.250470i	−0.0111862	−	0.0133312i	−0.771609	+	0.636098i	$0.780548\pi$
$354$	−6.23111	−	8.49893i	−0.331180	−	0.451713i
$355$		0			0
$356$	4.98443	−	1.81418i	0.264174	−	0.0961516i
$357$	7.95923	+	7.61996i	0.421247	+	0.403291i
$358$	44.2282	−	7.79863i	2.33754	−	0.412171i
$359$	−3.20577	−	5.55255i	−0.169194	−	0.293053i	0.768943	−	0.639318i	$-0.220783\pi$
$359$	−3.20577	−	5.55255i	−0.169194	−	0.293053i	−0.938137	+	0.346265i	$0.887450\pi$
$360$		0			0
$361$	−6.53480	+	11.3186i	−0.343937	+	0.595716i
$362$	−5.88140	+	16.1590i	−0.309120	+	0.849299i
$363$	0.563502	+	1.14279i	0.0295762	+	0.0599810i
$364$	11.8151	+	9.91402i	0.619278	+	0.519636i
$365$		0			0
$366$	9.84218	−	4.85310i	0.514459	−	0.253676i
$367$	2.78980	−	7.66491i	0.145626	−	0.400105i	−0.845338	−	0.534232i	$-0.820601\pi$
$367$	2.78980	−	7.66491i	0.145626	−	0.400105i	0.990964	+	0.134127i	$0.0428230\pi$
$368$	35.1053	+	20.2680i	1.82999	+	1.05654i
$369$	0.595955	+	13.6766i	0.0310242	+	0.711973i
$370$		0			0
$371$	−3.95697	−	22.4411i	−0.205436	−	1.16508i
$372$	6.73200	+	6.44504i	0.349038	+	0.334160i
$373$	−0.286390	−	0.786850i	−0.0148287	−	0.0407415i	0.932057	−	0.362311i	$-0.118012\pi$
$373$	−0.286390	−	0.786850i	−0.0148287	−	0.0407415i	−0.946886	+	0.321569i	$0.895790\pi$
$374$	−2.03176	+	11.5227i	−0.105060	+	0.595823i
$375$		0			0
$376$	3.18691	−	2.67413i	0.164352	−	0.137908i
$377$			10.6150i			0.546700i
$378$	12.2228	−	31.4190i	0.628675	−	1.61602i
$379$	7.38310			0.379245			0.189622	−	0.981857i	$-0.439274\pi$
$379$	7.38310			0.379245			0.189622	+	0.981857i	$0.439274\pi$
$380$		0			0
$381$	−22.1294	+	2.42260i	−1.13372	+	0.124114i
$382$	3.60230	+	0.635182i	0.184310	+	0.0324988i
$383$	−5.86435	−	16.1122i	−0.299654	−	0.823293i	−0.994557	−	0.104190i	$-0.966775\pi$
$383$	−5.86435	−	16.1122i	−0.299654	−	0.823293i	0.694903	−	0.719103i	$-0.255447\pi$
$384$	−12.5465	−	3.07069i	−0.640263	−	0.156701i
$385$		0			0
$386$	−9.85263	−	17.0653i	−0.501486	−	0.868599i
$387$	18.8825	−	7.81950i	0.959853	−	0.397488i
$388$	4.70236	+	2.71491i	0.238726	+	0.137829i
$389$	−6.10545	−	2.22220i	−0.309558	−	0.112670i	0.182569	−	0.983193i	$-0.441559\pi$
$389$	−6.10545	−	2.22220i	−0.309558	−	0.112670i	−0.492128	+	0.870523i	$0.663781\pi$
$390$		0			0
$391$	11.9222	+	10.0039i	0.602931	+	0.505919i
$392$	−3.15196	+	3.75636i	−0.159198	+	0.189725i
$393$	−16.8745	+	25.2521i	−0.851205	+	1.27380i
$394$	−3.45366	−	1.25703i	−0.173993	−	0.0633283i
$395$		0			0
$396$	14.8829	−	3.29812i	0.747895	−	0.165737i
$397$	−6.24602	+	3.60614i	−0.313479	+	0.180987i	−0.648482	−	0.761230i	$-0.724596\pi$
$397$	−6.24602	+	3.60614i	−0.313479	+	0.180987i	0.335003	+	0.942217i	$0.391263\pi$
$398$	−26.7252	+	4.71237i	−1.33961	+	0.236210i
$399$	−9.54012	−	32.7359i	−0.477604	−	1.63885i
$400$		0			0
$401$	−1.84693	+	10.4745i	−0.0922313	+	0.523070i	0.903329	+	0.428948i	$0.141115\pi$
$401$	−1.84693	+	10.4745i	−0.0922313	+	0.523070i	−0.995561	+	0.0941220i	$0.969996\pi$
$402$	12.3262	+	5.42427i	0.614773	+	0.270538i
$403$	−6.97477	−	8.31221i	−0.347438	−	0.414060i
$404$	−0.581191			−0.0289153
$405$		0			0
$406$	23.0245			1.14269
$407$	−18.1680	−	21.6518i	−0.900555	−	1.07324i
$408$	−2.79784	−	1.23122i	−0.138514	−	0.0609547i
$409$	−1.72049	+	9.75737i	−0.0850727	+	0.482471i	0.912268	+	0.409593i	$0.134329\pi$
$409$	−1.72049	+	9.75737i	−0.0850727	+	0.482471i	−0.997341	+	0.0728778i	$0.976782\pi$
$410$		0			0
$411$	4.81659	+	16.5276i	0.237585	+	0.815246i
$412$	−24.0291	+	4.23697i	−1.18383	+	0.208741i
$413$	9.81454	−	5.66643i	0.482942	−	0.278827i
$414$	14.3227	−	45.4120i	0.703920	−	2.23188i
$415$		0			0
$416$	−19.5830	−	7.12763i	−0.960135	−	0.349461i
$417$	−3.08468	+	4.61612i	−0.151057	+	0.226052i
$418$	23.2735	−	27.7363i	1.13834	−	1.35663i
$419$	8.15754	+	6.84499i	0.398522	+	0.334400i	0.819922	−	0.572475i	$-0.194017\pi$
$419$	8.15754	+	6.84499i	0.398522	+	0.334400i	−0.421400	+	0.906875i	$0.638461\pi$
$420$		0			0
$421$	−36.2626	−	13.1985i	−1.76733	−	0.643255i	−0.999998	−	0.00200391i	$-0.999362\pi$
$421$	−36.2626	−	13.1985i	−1.76733	−	0.643255i	−0.767331	−	0.641251i	$-0.778416\pi$
$422$	19.5277	+	11.2743i	0.950594	+	0.548826i
$423$	−10.2666	−	7.87925i	−0.499180	−	0.383102i
$424$	3.16077	+	5.47461i	0.153500	+	0.265871i
$425$		0			0
$426$	−27.3431	−	6.69205i	−1.32478	−	0.324231i
$427$	4.03614	+	11.0892i	0.195322	+	0.536644i
$428$	18.5284	+	3.26706i	0.895604	+	0.157919i
$429$	−17.6428	+	1.93144i	−0.851803	+	0.0932506i
$430$		0			0
$431$	−24.1205			−1.16184			−0.580922	−	0.813960i	$-0.697308\pi$
$431$	−24.1205			−1.16184			−0.580922	+	0.813960i	$0.697308\pi$
$432$	−0.543482	+	24.7612i	−0.0261483	+	1.19132i
$433$		−	9.73516i		−	0.467842i	−0.972256	−	0.233921i	$-0.924844\pi$
$433$		−	9.73516i		−	0.467842i	0.972256	−	0.233921i	$-0.0751557\pi$
$434$	−18.0297	+	15.1287i	−0.865452	+	0.726201i
$435$		0			0
$436$	3.61793	−	20.5183i	0.173267	−	0.982647i
$437$	−16.4720	−	45.2564i	−0.787962	−	2.16491i
$438$	18.5495	+	17.7588i	0.886331	+	0.848550i
$439$	−4.96370	−	28.1505i	−0.236904	−	1.34355i	−0.838566	−	0.544800i	$-0.816606\pi$
$439$	−4.96370	−	28.1505i	−0.236904	−	1.34355i	0.601662	−	0.798751i	$-0.294506\pi$
$440$		0			0
$441$	13.5299	+	7.04472i	0.644283	+	0.335463i
$442$	−8.84749	−	5.10810i	−0.420832	−	0.242967i
$443$	10.0280	−	27.5517i	0.476444	−	1.30902i	−0.436048	−	0.899924i	$-0.643622\pi$
$443$	10.0280	−	27.5517i	0.476444	−	1.30902i	0.912492	−	0.409096i	$-0.134156\pi$
$444$	−19.0113	+	9.37430i	−0.902235	+	0.444885i
$445$		0			0
$446$	−29.7549	−	24.9673i	−1.40894	−	1.18224i
$447$	−0.773594	−	1.56886i	−0.0365898	−	0.0742047i
$448$	−4.12598	+	11.3360i	−0.194934	+	0.535578i
$449$	−13.6125	+	23.5775i	−0.642413	+	1.11269i	0.342480	+	0.939525i	$0.388733\pi$
$449$	−13.6125	+	23.5775i	−0.642413	+	1.11269i	−0.984893	+	0.173167i	$0.944600\pi$
$450$		0			0
$451$	−7.81612	−	13.5379i	−0.368047	−	0.637475i
$452$	10.8879	−	1.91983i	0.512123	−	0.0903012i
$453$	14.8642	+	14.2306i	0.698382	+	0.668613i
$454$	14.9592	−	5.44470i	0.702070	−	0.255533i
$455$		0			0
$456$	5.59300	+	7.62857i	0.261916	+	0.357241i
$457$	21.0933	+	25.1380i	0.986704	+	1.17591i	0.984406	+	0.175911i	$0.0562870\pi$
$457$	21.0933	+	25.1380i	0.986704	+	1.17591i	0.00229800	+	0.999997i	$0.499269\pi$
$458$			29.4556i			1.37637i
$459$	−1.85632	+	9.32607i	−0.0866456	+	0.435304i
$460$		0			0
$461$	4.81252	−	4.03819i	0.224142	−	0.188077i	−0.523801	−	0.851841i	$-0.675486\pi$
$461$	4.81252	−	4.03819i	0.224142	−	0.188077i	0.747942	+	0.663764i	$0.231042\pi$
$462$	4.18940	+	38.2683i	0.194909	+	1.78040i
$463$	−24.5024	−	4.32044i	−1.13872	−	0.200788i	−0.427677	−	0.903932i	$-0.640668\pi$
$463$	−24.5024	−	4.32044i	−1.13872	−	0.200788i	−0.711047	+	0.703144i	$0.751779\pi$
$464$	−15.8949	+	5.78528i	−0.737904	+	0.268575i
$465$		0			0
$466$	5.89141	+	33.4118i	0.272914	+	1.54777i
$467$	26.1809	−	15.1156i	1.21151	−	0.699464i	0.248420	−	0.968652i	$-0.420089\pi$
$467$	26.1809	−	15.1156i	1.21151	−	0.699464i	0.963088	+	0.269188i	$0.0867553\pi$
$468$	−1.73847	+	13.1962i	−0.0803607	+	0.609995i
$469$	−7.24102	+	12.5418i	−0.334359	+	0.579127i
$470$		0			0
$471$	−2.21909	+	33.8345i	−0.102250	+	1.55901i
$472$	−2.02086	+	2.40837i	−0.0930177	+	0.110854i
$473$	−15.0013	+	17.8779i	−0.689761	+	0.822025i
$474$	39.3914	+	26.3230i	1.80931	+	1.20905i
$475$		0			0
$476$	−4.71809	+	8.17197i	−0.216253	+	0.374561i
$477$	14.4998	−	13.2843i	0.663899	−	0.608246i
$478$	−20.0361	+	11.5679i	−0.916432	+	0.529102i
$479$	1.45847	+	8.27140i	0.0666392	+	0.377930i	0.999828	+	0.0185434i	$0.00590289\pi$
$479$	1.45847	+	8.27140i	0.0666392	+	0.377930i	−0.933189	+	0.359386i	$0.882986\pi$
$480$		0			0
$481$	23.1907	−	8.44071i	1.05740	−	0.384863i
$482$	16.4853	+	2.90680i	0.750883	+	0.132401i
$483$	46.8691	+	20.6253i	2.13262	+	0.938485i
$484$	−0.835881	+	0.701387i	−0.0379946	+	0.0318812i
$485$		0			0
$486$	28.5358	−	5.66975i	1.29441	−	0.257185i
$487$		−	25.5873i		−	1.15947i	−0.814805	−	0.579735i	$-0.803156\pi$
$487$		−	25.5873i		−	1.15947i	0.814805	−	0.579735i	$-0.196844\pi$
$488$	−2.10432	−	2.50783i	−0.0952580	−	0.113524i
$489$	−6.46340	+	14.6875i	−0.292285	+	0.664191i
$490$		0			0
$491$	2.22987	−	0.811607i	0.100633	−	0.0366273i	−0.291213	−	0.956658i	$-0.594059\pi$
$491$	2.22987	−	0.811607i	0.100633	−	0.0366273i	0.391846	+	0.920031i	$0.371837\pi$
$492$	−11.2551	+	3.28005i	−0.507421	+	0.147876i
$493$	−6.39565	+	1.12773i	−0.288045	+	0.0507902i
$494$	15.8071	+	27.3787i	0.711194	+	1.23182i
$495$		0			0
$496$	8.64541	−	14.9743i	0.388190	−	0.672366i
$497$	10.3537	−	28.4465i	0.464426	−	1.27600i
$498$	−25.9304	+	38.8040i	−1.16197	+	1.73885i
$499$	−1.12305	−	0.942347i	−0.0502744	−	0.0421853i	0.617304	−	0.786725i	$-0.288225\pi$
$499$	−1.12305	−	0.942347i	−0.0502744	−	0.0421853i	−0.667579	+	0.744539i	$0.732669\pi$
$500$		0			0
$501$	−1.15582	+	17.6229i	−0.0516384	+	0.787332i
$502$	−7.52186	+	20.6661i	−0.335717	+	0.922374i
$503$	23.5654	+	13.6055i	1.05073	+	0.606640i	0.922854	−	0.385150i	$-0.125850\pi$
$503$	23.5654	+	13.6055i	1.05073	+	0.606640i	0.127877	+	0.991790i	$0.459184\pi$
$504$	−9.97127	−	1.31361i	−0.444156	−	0.0585130i
$505$		0			0
$506$	9.44204	+	53.5485i	0.419750	+	2.38052i
$507$	−1.66881	+	6.81861i	−0.0741147	+	0.302825i
$508$	−6.52035	−	17.9145i	−0.289294	−	0.794828i
$509$	0.472987	−	2.68244i	0.0209648	−	0.118897i	−0.972529	−	0.232780i	$-0.925218\pi$
$509$	0.472987	−	2.68244i	0.0209648	−	0.118897i	0.993494	+	0.113883i	$0.0363289\pi$
$510$		0			0
$511$	−21.1549	+	17.7511i	−0.935839	+	0.785262i
$512$		−	24.0150i		−	1.06132i
$513$	19.4046	−	22.1210i	0.856736	−	0.976666i
$514$	19.0781			0.841497
$515$		0			0
$516$	10.3486	+	14.1150i	0.455572	+	0.621378i
$517$	14.5537	+	2.56621i	0.640070	+	0.112862i
$518$	−18.3084	−	50.3019i	−0.804425	−	2.21014i
$519$	−13.5435	+	14.1465i	−0.594492	+	0.620961i
$520$		0			0
$521$	2.22878	+	3.86036i	0.0976447	+	0.169126i	0.910709	−	0.413048i	$-0.135536\pi$
$521$	2.22878	+	3.86036i	0.0976447	+	0.169126i	−0.813065	+	0.582173i	$0.802202\pi$
$522$	10.6746	+	16.7590i	0.467215	+	0.733520i
$523$	31.6140	+	18.2523i	1.38238	+	0.798119i	0.992441	−	0.122721i	$-0.0391620\pi$
$523$	31.6140	+	18.2523i	1.38238	+	0.798119i	0.389941	+	0.920840i	$0.372495\pi$
$524$	−24.4406	−	8.89566i	−1.06769	−	0.388609i
$525$		0			0
$526$	−32.7274	−	27.4615i	−1.42698	−	1.19738i
$527$	4.26720	−	5.08545i	0.185882	−	0.221526i
$528$	−12.5077	−	25.3658i	−0.544326	−	1.10390i
$529$	46.3514	+	16.8705i	2.01528	+	0.733502i
$530$		0			0
$531$	8.67465	+	4.51668i	0.376448	+	0.196007i
$532$	25.2883	−	14.6002i	1.09639	−	0.632998i
$533$	13.4419	−	2.37016i	0.582232	−	0.102663i
$534$	−7.99431	+	8.35024i	−0.345948	+	0.361350i
$535$		0			0
$536$	0.697638	−	3.95650i	0.0301334	−	0.170895i
$537$	−33.6127	+	24.6436i	−1.45049	+	1.06345i
$538$	0.549076	+	0.654364i	0.0236724	+	0.0282116i
$539$	−17.4188			−0.750282
$540$		0			0
$541$	−5.40959			−0.232577			−0.116288	−	0.993216i	$-0.537100\pi$
$541$	−5.40959			−0.232577			−0.116288	+	0.993216i	$0.537100\pi$
$542$	29.7396	+	35.4423i	1.27743	+	1.52238i
$543$	−1.73668	−	15.8638i	−0.0745283	−	0.680783i
$544$	2.21400	−	12.5562i	0.0949243	−	0.538343i
$545$		0			0
$546$	−32.6499	−	7.99085i	−1.39728	−	0.341977i
$547$	21.3180	−	3.75894i	0.911492	−	0.160721i	0.301811	−	0.953368i	$-0.402409\pi$
$547$	21.3180	−	3.75894i	0.911492	−	0.160721i	0.609681	+	0.792647i	$0.291298\pi$
$548$	−12.7675	+	7.37129i	−0.545399	+	0.314886i
$549$	−6.20031	+	8.07896i	−0.264623	+	0.344802i
$550$		0			0
$551$	18.8848	+	6.87349i	0.804518	+	0.292820i
$552$	−14.1750	−	0.929692i	−0.603330	−	0.0395703i
$553$	−32.7490	+	39.0288i	−1.39263	+	1.65967i
$554$	8.80259	+	7.38625i	0.373986	+	0.313812i
$555$		0			0
$556$	−4.46778	−	1.62614i	−0.189476	−	0.0689637i
$557$	−4.55373	−	2.62910i	−0.192948	−	0.111399i	0.400414	−	0.916334i	$-0.368866\pi$
$557$	−4.55373	−	2.62910i	−0.192948	−	0.111399i	−0.593362	+	0.804936i	$0.702200\pi$
$558$	−19.3707	−	6.10938i	−0.820026	−	0.258631i
$559$	−10.1887	−	17.6473i	−0.430936	−	0.746403i
$560$		0			0
$561$	−3.03806	−	10.4248i	−0.128267	−	0.440135i
$562$	−11.5954	−	31.8582i	−0.489124	−	1.34386i
$563$	23.4191	+	4.12942i	0.986998	+	0.174034i	0.643771	−	0.765218i	$-0.277369\pi$
$563$	23.4191	+	4.12942i	0.986998	+	0.174034i	0.343227	+	0.939253i	$0.388480\pi$
$564$	4.46403	−	10.1441i	0.187969	−	0.427143i
$565$		0			0
$566$	−13.1227			−0.551587
$567$	2.72147	+	31.1682i	0.114291	+	1.30894i
$568$			8.39794i			0.352370i
$569$	23.3095	−	19.5590i	0.977185	−	0.819955i	−0.00647745	−	0.999979i	$-0.502062\pi$
$569$	23.3095	−	19.5590i	0.977185	−	0.819955i	0.983662	+	0.180024i	$0.0576174\pi$
$570$		0			0
$571$	3.24490	−	18.4027i	0.135795	−	0.770130i	−0.838508	−	0.544889i	$-0.816572\pi$
$571$	3.24490	−	18.4027i	0.135795	−	0.770130i	0.974303	−	0.225241i	$-0.0723170\pi$
$572$	−5.19840	−	14.2825i	−0.217356	−	0.597181i
$573$	−3.25907	+	0.949781i	−0.136150	+	0.0396777i
$574$	−5.14103	−	29.1562i	−0.214582	−	1.21696i
$575$		0			0
$576$	−10.1641	+	2.25241i	−0.423504	+	0.0938504i
$577$	16.0058	+	9.24093i	0.666329	+	0.384705i	0.794684	−	0.607023i	$-0.207637\pi$
$577$	16.0058	+	9.24093i	0.666329	+	0.384705i	−0.128355	+	0.991728i	$0.540970\pi$
$578$	−8.71389	+	23.9412i	−0.362450	+	0.995823i
$579$	15.2049	+	10.1605i	0.631892	+	0.422256i
$580$		0			0
$581$	−38.4468	−	32.2607i	−1.59504	−	1.33840i
$582$	−11.8082	−	0.774461i	−0.489467	−	0.0321025i
$583$	−7.68033	+	21.1015i	−0.318087	+	0.873936i
$584$	3.83052	−	6.63465i	0.158508	−	0.274544i
$585$		0			0
$586$	22.1644	+	38.3899i	0.915603	+	1.58587i
$587$	26.2382	−	4.62650i	1.08297	−	0.190956i	0.396440	−	0.918061i	$-0.370246\pi$
$587$	26.2382	−	4.62650i	1.08297	−	0.190956i	0.686527	+	0.727105i	$0.259135\pi$
$588$	−3.10548	+	12.6887i	−0.128068	+	0.523274i
$589$	−19.3043	+	7.02619i	−0.795420	+	0.289509i
$590$		0			0
$591$	3.39058	−	0.371181i	0.139470	−	0.0152684i
$592$	25.2783	+	30.1255i	1.03893	+	1.23815i
$593$		−	4.62357i		−	0.189867i	−0.995484	−	0.0949337i	$-0.969736\pi$
$593$		−	4.62357i		−	0.189867i	0.995484	−	0.0949337i	$-0.0302639\pi$
$594$	−25.9122	+	20.7913i	−1.06319	+	0.853076i
$595$		0			0
$596$	1.14753	−	0.962888i	0.0470045	−	0.0394414i
$597$	20.3107	−	14.8910i	0.831260	−	0.609450i
$598$	−46.7557	−	8.24429i	−1.91198	−	0.337134i
$599$	7.29668	−	2.65577i	0.298134	−	0.108512i	−0.188622	−	0.982050i	$-0.560402\pi$
$599$	7.29668	−	2.65577i	0.298134	−	0.108512i	0.486756	+	0.873538i	$0.338180\pi$
$600$		0			0
$601$	−2.59767	−	14.7321i	−0.105961	−	0.600936i	−0.990832	−	0.135099i	$-0.956865\pi$
$601$	−2.59767	−	14.7321i	−0.105961	−	0.600936i	0.884871	−	0.465837i	$-0.154247\pi$
$602$	−38.2782	+	22.0999i	−1.56010	+	0.900725i
$603$	−12.4859	+	0.544074i	−0.508467	+	0.0221564i
$604$	−8.81124	+	15.2615i	−0.358524	+	0.620982i
$605$		0			0
$606$	1.13603	−	0.560167i	0.0461481	−	0.0227552i
$607$	16.5405	−	19.7122i	0.671359	−	0.800094i	−0.317610	−	0.948222i	$-0.602880\pi$
$607$	16.5405	−	19.7122i	0.671359	−	0.800094i	0.988968	+	0.148128i	$0.0473246\pi$
$608$	−25.3610	+	30.2241i	−1.02853	+	1.22575i
$609$	−19.1645	+	9.44986i	−0.776585	+	0.382928i
$610$		0			0
$611$	−6.45177	+	11.1748i	−0.261011	+	0.452084i
$612$	−8.13556	+	0.354506i	−0.328860	+	0.0143301i
$613$	25.2399	−	14.5722i	1.01943	−	0.588567i	0.105490	−	0.994420i	$-0.466359\pi$
$613$	25.2399	−	14.5722i	1.01943	−	0.588567i	0.913938	+	0.405853i	$0.133026\pi$
$614$	6.03625	+	34.2333i	0.243603	+	1.38154i
$615$		0			0
$616$	10.7921	−	3.92799i	0.434825	−	0.158263i
$617$	−8.43098	−	1.48661i	−0.339418	−	0.0598486i	0.00134119	−	0.999999i	$-0.499573\pi$
$617$	−8.43098	−	1.48661i	−0.339418	−	0.0598486i	−0.340760	+	0.940150i	$0.610684\pi$
$618$	42.8849	−	31.4417i	1.72509	−	1.26477i
$619$	−16.6721	+	13.9895i	−0.670108	+	0.562287i	−0.913097	−	0.407741i	$-0.866316\pi$
$619$	−16.6721	+	13.9895i	−0.670108	+	0.562287i	0.242989	+	0.970029i	$0.421872\pi$
$620$		0			0
$621$	6.71679	+	43.6771i	0.269536	+	1.75270i
$622$		−	3.61710i		−	0.145032i
$623$	−7.99082	−	9.52309i	−0.320146	−	0.381535i
$624$	24.5476	−	2.68733i	0.982689	−	0.107579i
$625$		0			0
$626$	53.0562	−	19.3109i	2.12055	−	0.771819i
$627$	−7.98804	+	32.6384i	−0.319012	+	1.30345i
$628$	−28.5961	+	5.04226i	−1.14111	+	0.201208i
$629$	7.54937	+	13.0759i	0.301013	+	0.521370i
$630$		0			0
$631$	22.3730	−	38.7512i	0.890657	−	1.54266i	0.0515673	−	0.998670i	$-0.483578\pi$
$631$	22.3730	−	38.7512i	0.890657	−	1.54266i	0.839090	−	0.543993i	$-0.183088\pi$
$632$	4.83407	−	13.2815i	0.192289	−	0.528309i
$633$	−20.8812	−	1.36952i	−0.829952	−	0.0544337i
$634$	−4.18990	−	3.51574i	−0.166402	−	0.139628i
$635$		0			0
$636$	14.0021	+	9.35677i	0.555219	+	0.371020i
$637$	5.20185	−	14.2920i	0.206105	−	0.566268i
$638$	−19.6498	−	11.3448i	−0.777941	−	0.449145i
$639$	25.5056	−	5.65216i	1.00899	−	0.223596i
$640$		0			0
$641$	4.57420	+	25.9416i	0.180670	+	1.02463i	0.931393	+	0.364014i	$0.118594\pi$
$641$	4.57420	+	25.9416i	0.180670	+	1.02463i	−0.750723	+	0.660617i	$0.770295\pi$
$642$	−39.3656	+	11.4722i	−1.55364	+	0.452771i
$643$	−12.4278	−	34.1452i	−0.490106	−	1.34656i	−0.900583	−	0.434684i	$-0.856860\pi$
$643$	−12.4278	−	34.1452i	−0.490106	−	1.34656i	0.410477	−	0.911871i	$-0.365362\pi$
$644$	−7.61482	+	43.1858i	−0.300066	+	1.70176i
$645$		0			0
$646$	−14.8166	+	12.4326i	−0.582952	+	0.489155i
$647$			39.1069i			1.53745i	0.639580	+	0.768725i	$0.279108\pi$
$647$			39.1069i			1.53745i	−0.639580	+	0.768725i	$0.720892\pi$
$648$	−3.66673	−	7.86685i	−0.144043	−	0.309039i
$649$	−11.1680			−0.438382
$650$		0			0
$651$	8.79781	−	19.9922i	0.344813	−	0.783557i
$652$	−13.5332	−	2.38627i	−0.530002	−	0.0934536i
$653$	5.00203	+	13.7430i	0.195744	+	0.537804i	0.998269	−	0.0588158i	$-0.0187325\pi$
$653$	5.00203	+	13.7430i	0.195744	+	0.537804i	−0.802524	+	0.596619i	$0.796510\pi$
$654$	12.7043	+	43.5933i	0.496776	+	1.70463i
$655$		0			0
$656$	10.8751	+	18.8362i	0.424600	+	0.735428i
$657$	−22.7284	−	7.16838i	−0.886719	−	0.279665i
$658$	24.2388	+	13.9943i	0.944926	+	0.545553i
$659$	−19.5964	−	7.13252i	−0.763369	−	0.277844i	−0.0691489	−	0.997606i	$-0.522028\pi$
$659$	−19.5964	−	7.13252i	−0.763369	−	0.277844i	−0.694220	+	0.719763i	$0.744251\pi$
$660$		0			0
$661$	13.5383	+	11.3600i	0.526580	+	0.441853i	0.866918	−	0.498450i	$-0.166097\pi$
$661$	13.5383	+	11.3600i	0.526580	+	0.441853i	−0.340339	+	0.940303i	$0.610542\pi$
$662$	−12.9783	+	15.4669i	−0.504416	+	0.601140i
$663$	9.46070	+	0.620495i	0.367423	+	0.0240980i
$664$	13.0834	+	4.76198i	0.507735	+	0.184801i
$665$		0			0
$666$	28.1253	−	36.6471i	1.08983	−	1.42005i
$667$	−26.1371	+	15.0903i	−1.01203	+	0.584297i
$668$	−14.8944	+	2.62629i	−0.576282	+	0.101614i
$669$	35.0138	+	8.56941i	1.35371	+	0.331312i
$670$		0			0
$671$	2.01939	−	11.4525i	0.0779576	−	0.442120i
$672$	−4.56517	−	41.7008i	−0.176105	−	1.60864i
$673$	−15.1265	−	18.0270i	−0.583082	−	0.694890i	0.391179	−	0.920315i	$-0.372067\pi$
$673$	−15.1265	−	18.0270i	−0.583082	−	0.694890i	−0.974261	+	0.225425i	$0.927623\pi$
$674$	25.5349			0.983567
$675$		0			0
$676$	−6.01162			−0.231216
$677$	−24.5727	−	29.2846i	−0.944407	−	1.12550i	−0.991950	−	0.126631i	$-0.959584\pi$
$677$	−24.5727	−	29.2846i	−0.944407	−	1.12550i	0.0475429	−	0.998869i	$-0.484861\pi$
$678$	−19.4317	+	14.2467i	−0.746271	+	0.547140i
$679$	2.20978	−	12.5323i	0.0848038	−	0.480946i
$680$		0			0
$681$	−10.2167	+	10.6715i	−0.391503	+	0.408934i
$682$	22.8413	−	4.02754i	0.874639	−	0.154222i
$683$	4.80646	−	2.77501i	0.183914	−	0.106183i	−0.405216	−	0.914221i	$-0.632804\pi$
$683$	4.80646	−	2.77501i	0.183914	−	0.106183i	0.589130	+	0.808038i	$0.299470\pi$
$684$	22.3512	+	11.6377i	0.854620	+	0.444980i
$685$		0			0
$686$	11.6771	+	4.25011i	0.445833	+	0.162270i
$687$	−12.0893	−	24.5174i	−0.461236	−	0.935395i
$688$	20.8723	−	24.8746i	0.795748	−	0.948335i
$689$	−15.0200	−	12.6033i	−0.572216	−	0.480146i
$690$		0			0
$691$	28.6323	+	10.4213i	1.08922	+	0.396445i	0.823333	−	0.567559i	$-0.192112\pi$
$691$	28.6323	+	10.4213i	1.08922	+	0.396445i	0.265890	+	0.964003i	$0.414334\pi$
$692$	−14.5246	−	8.38577i	−0.552142	−	0.318779i
$693$	−19.1933	−	30.1332i	−0.729095	−	1.14467i
$694$	−16.7868	−	29.0756i	−0.637217	−	1.10369i
$695$		0			0
$696$	4.09928	−	4.28179i	0.155383	−	0.162301i
$697$	2.85610	+	7.84707i	0.108183	+	0.297229i
$698$	6.88762	+	1.21447i	0.260700	+	0.0459685i
$699$	−18.6168	−	25.3924i	−0.704152	−	0.960428i
$700$		0			0
$701$	−9.84780			−0.371946			−0.185973	−	0.982555i	$-0.559544\pi$
$701$	−9.84780			−0.371946			−0.185973	+	0.982555i	$0.559544\pi$
$702$	−9.32076	−	27.4697i	−0.351789	−	1.03678i
$703$		−	46.7233i		−	1.76220i
$704$	9.10678	−	7.64150i	0.343225	−	0.288000i
$705$		0			0
$706$	−0.105966	+	0.600964i	−0.00398809	+	0.0226176i
$707$	0.465870	+	1.27997i	0.0175208	+	0.0481381i
$708$	−1.99106	+	8.13529i	−0.0748288	+	0.305743i
$709$	7.42637	+	42.1171i	0.278903	+	1.58174i	0.726284	+	0.687395i	$0.241246\pi$
$709$	7.42637	+	42.1171i	0.278903	+	1.58174i	−0.447380	+	0.894344i	$0.647643\pi$
$710$		0			0
$711$	−43.5911	−	5.74269i	−1.63479	−	0.215368i
$712$	2.98665	+	1.72434i	0.111929	+	0.0646225i
$713$	10.5517	−	28.9905i	0.395163	−	1.08570i
$714$	1.34589	−	20.5208i	0.0503687	−	0.767973i
$715$		0			0
$716$	−27.3421	−	22.9427i	−1.02182	−	0.857410i
$717$	11.9293	−	17.8519i	0.445510	−	0.666690i
$718$	−4.09268	+	11.2446i	−0.152738	+	0.419643i
$719$	−5.28698	+	9.15732i	−0.197171	+	0.341510i	−0.947610	−	0.319429i	$-0.896509\pi$
$719$	−5.28698	+	9.15732i	−0.197171	+	0.341510i	0.750439	+	0.660940i	$0.229842\pi$
$720$		0			0
$721$	28.5923	+	49.5234i	1.06483	+	1.84435i
$722$	24.0219	−	4.23571i	0.894004	−	0.157637i
$723$	−14.9145	+	4.34650i	−0.554678	+	0.161648i
$724$	12.8423	−	4.67423i	0.477282	−	0.173716i
$725$		0			0
$726$	0.957846	−	2.17662i	0.0355490	−	0.0807819i
$727$	−25.8811	−	30.8438i	−0.959875	−	1.14393i	−0.989523	−	0.144374i	$-0.953883\pi$
$727$	−25.8811	−	30.8438i	−0.959875	−	1.14393i	0.0296480	−	0.999560i	$-0.490561\pi$
$728$			10.0278i			0.371656i
$729$	−21.4248	+	16.4310i	−0.793510	+	0.608557i
$730$		0			0
$731$	9.55028	−	8.01364i	0.353230	−	0.296395i
$732$	−7.98254	−	3.51281i	−0.295043	−	0.129837i
$733$	44.0263	+	7.76303i	1.62615	+	0.286734i	0.911052	−	0.412290i	$-0.135271\pi$
$733$	44.0263	+	7.76303i	1.62615	+	0.286734i	0.715098	+	0.699025i	$0.246382\pi$
$734$	−14.3054	+	5.20676i	−0.528024	+	0.192185i
$735$		0			0
$736$	−10.2889	−	58.3515i	−0.379255	−	2.15086i
$737$	12.3594	−	7.13568i	0.455263	−	0.262846i
$738$	18.8386	−	17.2594i	0.693458	−	0.635328i
$739$	7.15194	−	12.3875i	0.263088	−	0.455682i	−0.703973	−	0.710227i	$-0.748592\pi$
$739$	7.15194	−	12.3875i	0.263088	−	0.455682i	0.967061	+	0.254545i	$0.0819256\pi$
$740$		0			0
$741$	−24.3939	−	16.3010i	−0.896134	−	0.598833i
$742$	−27.3372	+	32.5792i	−1.00358	+	1.19602i
$743$	−14.0804	+	16.7804i	−0.516560	+	0.615612i	−0.959764	−	0.280809i	$-0.909397\pi$
$743$	−14.0804	+	16.7804i	−0.516560	+	0.615612i	0.443204	+	0.896421i	$0.353842\pi$
$744$	−0.396564	+	6.04642i	−0.0145387	+	0.221672i
$745$		0			0
$746$	−0.781395	+	1.35342i	−0.0286089	+	0.0495521i
$747$	5.65705	−	42.9411i	0.206981	−	1.57113i
$748$	8.05308	−	4.64945i	0.294450	−	0.170001i
$749$	−7.65686	−	43.4242i	−0.279776	−	1.58669i
$750$		0			0
$751$	−2.77841	+	1.01126i	−0.101386	+	0.0369014i	−0.392215	−	0.919874i	$-0.628291\pi$
$751$	−2.77841	+	1.01126i	−0.101386	+	0.0369014i	0.290829	+	0.956775i	$0.406069\pi$
$752$	−20.2495	−	3.57053i	−0.738422	−	0.130204i
$753$	−2.22108	−	20.2886i	−0.0809408	−	0.739359i
$754$	15.1764	−	12.7345i	0.552691	−	0.463763i
$755$		0			0
$756$	−25.3723	+	8.60910i	−0.922783	+	0.313110i
$757$		−	31.6130i		−	1.14899i	−0.818507	−	0.574497i	$-0.805198\pi$
$757$		−	31.6130i		−	1.14899i	0.818507	−	0.574497i	$-0.194802\pi$
$758$	−8.85729	−	10.5557i	−0.321711	−	0.383401i
$759$	−29.8367	−	40.6958i	−1.08301	−	1.47717i
$760$		0			0
$761$	15.9097	−	5.79066i	0.576727	−	0.209911i	−0.0371547	−	0.999310i	$-0.511829\pi$
$761$	15.9097	−	5.79066i	0.576727	−	0.209911i	0.613882	+	0.789398i	$0.289607\pi$
$762$	30.0116	+	28.7323i	1.08720	+	1.04086i
$763$	−48.0878	+	8.47918i	−1.74090	+	0.306967i
$764$	−1.45354	−	2.51761i	−0.0525873	−	0.0910839i
$765$		0			0
$766$	−16.0005	+	27.7136i	−0.578120	+	1.00133i
$767$	3.33514	−	9.16321i	0.120425	−	0.330864i
$768$	15.9779	+	32.4035i	0.576553	+	1.16926i
$769$	15.8071	+	13.2638i	0.570020	+	0.478303i	0.881653	−	0.471899i	$-0.156431\pi$
$769$	15.8071	+	13.2638i	0.570020	+	0.478303i	−0.311633	+	0.950203i	$0.600876\pi$
$770$		0			0
$771$	−15.8796	+	7.83012i	−0.571891	+	0.281995i
$772$	−5.35628	+	14.7163i	−0.192777	+	0.529650i
$773$	−12.4042	−	7.16157i	−0.446148	−	0.257584i	0.260054	−	0.965594i	$-0.416260\pi$
$773$	−12.4042	−	7.16157i	−0.446148	−	0.257584i	−0.706202	+	0.708010i	$0.749593\pi$
$774$	−33.8324	−	17.6157i	−1.21608	−	0.633185i
$775$		0			0
$776$	0.613027	+	3.47665i	0.0220064	+	0.124804i
$777$	35.8842	+	34.3546i	1.28734	+	1.23246i
$778$	4.14742	+	11.3949i	0.148692	+	0.408528i
$779$	4.48729	−	25.4487i	0.160774	−	0.911795i
$780$		0			0
$781$	−22.8524	+	19.1755i	−0.817724	+	0.686152i
$782$		−	29.0467i		−	1.03871i
$783$	−15.7633	−	9.56821i	−0.563336	−	0.341940i
$784$	24.2359			0.865568
$785$		0			0
$786$	56.3470	−	6.16855i	2.00983	−	0.220025i
$787$	−30.2590	−	5.33548i	−1.07862	−	0.190189i	−0.394013	−	0.919105i	$-0.628914\pi$
$787$	−30.2590	−	5.33548i	−1.07862	−	0.190189i	−0.684603	+	0.728916i	$0.740025\pi$
$788$	0.999023	+	2.74479i	0.0355887	+	0.0977792i
$789$	38.5116	+	9.42547i	1.37105	+	0.335556i
$790$		0			0
$791$	−12.9556	−	22.4397i	−0.460647	−	0.797864i
$792$	7.86250	+	6.03418i	0.279382	+	0.214415i
$793$	8.79362	+	5.07700i	0.312270	+	0.180289i
$794$	12.6489	+	4.60382i	0.448893	+	0.163384i
$795$		0			0
$796$	16.5216	+	13.8633i	0.585594	+	0.491371i
$797$	−19.9050	+	23.7219i	−0.705071	+	0.840271i	−0.993090	−	0.117354i	$-0.962559\pi$
$797$	−19.9050	+	23.7219i	−0.705071	+	0.840271i	0.288019	+	0.957625i	$0.407003\pi$
$798$	−35.3579	+	52.9119i	−1.25166	+	1.87306i
$799$	−7.41836	−	2.70006i	−0.262443	−	0.0955213i
$800$		0			0
$801$	3.22691	−	10.2314i	0.114017	−	0.361509i
$802$	17.1912	−	9.92532i	0.607041	−	0.350475i
$803$	26.8006	−	4.72567i	0.945773	−	0.166765i
$804$	−2.99451	−	10.2753i	−0.105608	−	0.362383i
$805$		0			0
$806$	−3.51663	+	19.9438i	−0.123868	+	0.702491i
$807$	−0.725591	−	0.319305i	−0.0255420	−	0.0112401i
$808$	−0.242890	−	0.289465i	−0.00854485	−	0.0101834i
$809$	2.58326			0.0908226			0.0454113	−	0.998968i	$-0.485540\pi$
$809$	2.58326			0.0908226			0.0454113	+	0.998968i	$0.485540\pi$
$810$		0			0
$811$	−24.6638			−0.866064			−0.433032	−	0.901379i	$-0.642556\pi$
$811$	−24.6638			−0.866064			−0.433032	+	0.901379i	$0.642556\pi$
$812$	−11.7622	−	14.0176i	−0.412772	−	0.491922i
$813$	−39.3002	−	17.2945i	−1.37832	−	0.606546i
$814$	−9.16019	+	51.9500i	−0.321065	+	1.82085i
$815$		0			0
$816$	4.22705	+	14.5047i	0.147976	+	0.507765i
$817$	−37.9932	+	6.69923i	−1.32922	+	0.234376i
$818$	16.0142	−	9.24583i	0.559925	−	0.323273i
$819$	30.4558	−	6.74914i	1.06421	−	0.235834i
$820$		0			0
$821$	−21.3469	−	7.76964i	−0.745013	−	0.271162i	−0.0585070	−	0.998287i	$-0.518634\pi$
$821$	−21.3469	−	7.76964i	−0.745013	−	0.271162i	−0.686505	+	0.727125i	$0.740856\pi$
$822$	17.8514	−	26.7140i	0.622638	−	0.931758i
$823$	−17.1816	+	20.4763i	−0.598914	+	0.713758i	−0.977293	−	0.211893i	$-0.932037\pi$
$823$	−17.1816	+	20.4763i	−0.598914	+	0.713758i	0.378379	+	0.925651i	$0.376482\pi$
$824$	−12.1524	−	10.1971i	−0.423350	−	0.355233i
$825$		0			0
$826$	−19.8756	−	7.23411i	−0.691559	−	0.251707i
$827$	13.3792	+	7.72449i	0.465241	+	0.268607i	0.714245	−	0.699895i	$-0.246770\pi$
$827$	13.3792	+	7.72449i	0.465241	+	0.268607i	−0.249005	+	0.968502i	$0.580103\pi$
$828$	−34.9642	+	14.4791i	−1.21509	+	0.503184i
$829$	−6.87832	−	11.9136i	−0.238894	−	0.413776i	0.721503	−	0.692411i	$-0.243451\pi$
$829$	−6.87832	−	11.9136i	−0.238894	−	0.413776i	−0.960397	+	0.278635i	$0.910118\pi$
$830$		0			0
$831$	−10.3583	−	2.53514i	−0.359327	−	0.0879431i
$832$	3.55018	+	9.75403i	0.123080	+	0.338160i
$833$	9.16370	+	1.61581i	0.317504	+	0.0559844i
$834$	10.3003	−	1.12762i	0.356671	−	0.0390463i
$835$		0			0
$836$	−28.7756			−0.995224
$837$	18.6306	−	2.86507i	0.643969	−	0.0990315i
$838$		−	19.8747i		−	0.686559i
$839$	−7.36180	+	6.17729i	−0.254158	+	0.213264i	−0.760960	−	0.648799i	$-0.775272\pi$
$839$	−7.36180	+	6.17729i	−0.254158	+	0.213264i	0.506803	+	0.862062i	$0.330827\pi$
$840$		0			0
$841$	−2.84890	+	16.1569i	−0.0982380	+	0.557135i
$842$	24.6331	+	67.6788i	0.848912	+	2.33237i
$843$	22.7269	+	21.7581i	0.782756	+	0.749390i
$844$	−3.11186	−	17.6482i	−0.107115	−	0.607477i
$845$		0			0
$846$	1.05150	+	24.1308i	0.0361512	+	0.829634i
$847$	2.21470	+	1.27866i	0.0760980	+	0.0439352i
$848$	10.6861	−	29.3599i	0.366963	−	1.00822i
$849$	10.9227	−	5.38588i	0.374865	−	0.184843i
$850$		0			0
$851$	53.7512	+	45.1026i	1.84257	+	1.54610i
$852$	9.89412	+	20.0655i	0.338967	+	0.687431i
$853$	−7.03097	+	19.3174i	−0.240736	+	0.661416i	0.759208	+	0.650848i	$0.225586\pi$
$853$	−7.03097	+	19.3174i	−0.240736	+	0.661416i	−0.999944	+	0.0105685i	$0.996636\pi$
$854$	11.0123	−	19.0739i	0.376834	−	0.652695i
$855$		0			0
$856$	6.11618	+	10.5935i	0.209047	+	0.362080i
$857$	−39.8901	+	7.03369i	−1.36262	+	0.240266i	−0.806695	−	0.590967i	$-0.798746\pi$
$857$	−39.8901	+	7.03369i	−1.36262	+	0.240266i	−0.555923	+	0.831234i	$0.687635\pi$
$858$	23.9269	+	22.9070i	0.816853	+	0.782033i
$859$	23.7524	−	8.64516i	0.810421	−	0.294969i	0.0966234	−	0.995321i	$-0.469196\pi$
$859$	23.7524	−	8.64516i	0.810421	−	0.294969i	0.713798	+	0.700352i	$0.246974\pi$
$860$		0			0
$861$	16.2456	+	22.1582i	0.553649	+	0.755149i
$862$	28.9366	+	34.4853i	0.985585	+	1.17458i
$863$			47.4531i			1.61532i	0.589648	+	0.807661i	$0.299267\pi$
$863$			47.4531i			1.61532i	−0.589648	+	0.807661i	$0.700733\pi$
$864$	28.2364	−	22.6561i	0.960623	−	0.770778i
$865$		0			0
$866$	−13.9185	+	11.6790i	−0.472969	+	0.396868i
$867$	−2.57307	−	23.5039i	−0.0873862	−	0.798234i
$868$	18.4211	+	3.24813i	0.625252	+	0.110249i
$869$	47.1794	−	17.1719i	1.60045	−	0.582516i
$870$		0			0
$871$	2.16383	+	12.2717i	0.0733185	+	0.415810i
$872$	11.7312	−	6.77304i	0.397270	−	0.229364i
$873$	10.1464	−	4.20177i	0.343405	−	0.142209i
$874$	−44.9427	+	77.8430i	−1.52021	+	2.63308i
$875$		0			0
$876$	1.33569	−	20.3654i	0.0451289	−	0.688082i
$877$	−2.17496	+	2.59201i	−0.0734430	+	0.0875260i	−0.801515	−	0.597975i	$-0.795972\pi$
$877$	−2.17496	+	2.59201i	−0.0734430	+	0.0875260i	0.728072	+	0.685501i	$0.240417\pi$
$878$	−34.2923	+	40.8680i	−1.15731	+	1.37923i
$879$	−34.2047	−	22.8570i	−1.15370	−	0.770948i
$880$		0			0
$881$	−11.9030	+	20.6166i	−0.401022	+	0.694591i	−0.993850	−	0.110738i	$-0.964678\pi$
$881$	−11.9030	+	20.6166i	−0.401022	+	0.694591i	0.592827	+	0.805330i	$0.298012\pi$
$882$	−6.15956	−	27.7953i	−0.207403	−	0.935915i
$883$	20.2353	−	11.6829i	0.680972	−	0.393159i	−0.119249	−	0.992864i	$-0.538049\pi$
$883$	20.2353	−	11.6829i	0.680972	−	0.393159i	0.800221	+	0.599705i	$0.204715\pi$
$884$	1.40990	+	7.99595i	0.0474201	+	0.268933i
$885$		0			0
$886$	−51.4212	+	18.7158i	−1.72753	+	0.628769i
$887$	−30.4018	−	5.36066i	−1.02079	−	0.179993i	−0.361890	−	0.932221i	$-0.617868\pi$
$887$	−30.4018	−	5.36066i	−1.02079	−	0.179993i	−0.658903	+	0.752228i	$0.728979\pi$
$888$	−12.6141	−	5.55098i	−0.423301	−	0.186279i
$889$	−34.2269	+	28.7198i	−1.14793	+	0.963231i
$890$		0			0
$891$	13.0348	−	27.9407i	0.436682	−	0.936048i
$892$			30.8698i			1.03360i
$893$	15.7030	+	18.7141i	0.525480	+	0.626243i
$894$	−1.31496	+	2.98814i	−0.0439790	+	0.0999382i
$895$		0			0
$896$	−24.3613	+	8.86677i	−0.813853	+	0.296218i
$897$	42.3008	−	12.3276i	1.41238	−	0.411606i
$898$	50.0395	−	8.82332i	1.66984	−	0.294438i
$899$	6.43681	+	11.1489i	0.214680	+	0.371836i
$900$		0			0
$901$	5.99790	−	10.3887i	0.199819	−	0.346097i
$902$	−9.97854	+	27.4158i	−0.332249	+	0.912847i
$903$	22.7905	−	34.1052i	0.758420	−	1.13495i
$904$	5.50643	+	4.62045i	0.183141	+	0.153674i
$905$		0			0
$906$	2.51351	−	38.3236i	0.0835059	−	1.27322i
$907$	3.83144	−	10.5268i	0.127221	−	0.349537i	−0.859687	−	0.510821i	$-0.829341\pi$
$907$	3.83144	−	10.5268i	0.127221	−	0.349537i	0.986908	+	0.161284i	$0.0515636\pi$
$908$	−10.9568	−	6.32589i	−0.363613	−	0.209932i
$909$	−0.715668	+	0.932511i	−0.0237372	+	0.0309295i
$910$		0			0
$911$	−4.51397	−	25.6000i	−0.149555	−	0.848166i	−0.963597	−	0.267360i	$-0.913849\pi$
$911$	−4.51397	−	25.6000i	−0.149555	−	0.848166i	0.814042	−	0.580806i	$-0.197262\pi$
$912$	11.1143	−	45.4118i	0.368030	−	1.50374i
$913$	16.9158	+	46.4758i	0.559832	+	1.53813i
$914$	10.6351	−	60.3147i	0.351778	−	1.99503i
$915$		0			0
$916$	17.9329	−	15.0475i	0.592520	−	0.497183i
$917$			60.9566i			2.01296i
$918$	15.5606	−	8.53421i	0.513575	−	0.281671i
$919$	9.14191			0.301564			0.150782	−	0.988567i	$-0.451821\pi$
$919$	9.14191			0.301564			0.150782	+	0.988567i	$0.451821\pi$
$920$		0			0
$921$	−19.0745	−	26.0167i	−0.628526	−	0.857278i
$922$	−11.5469	−	2.03603i	−0.380276	−	0.0670530i
$923$	−8.90876	−	24.4766i	−0.293235	−	0.805657i
$924$	21.1580	−	22.1001i	0.696049	−	0.727039i
$925$		0			0
$926$	23.2178	+	40.2145i	0.762986	+	1.32153i
$927$	−22.7908	+	43.7716i	−0.748549	+	1.43765i
$928$	21.4122	+	12.3624i	0.702891	+	0.405814i
$929$	−51.0829	−	18.5927i	−1.67598	−	0.610005i	−0.683226	−	0.730207i	$-0.739424\pi$
$929$	−51.0829	−	18.5927i	−1.67598	−	0.610005i	−0.992749	+	0.120202i	$0.961646\pi$
$930$		0			0
$931$	−22.0580	−	18.5089i	−0.722922	−	0.606603i
$932$	17.3319	−	20.6553i	0.567725	−	0.676588i
$933$	1.48455	+	3.01069i	0.0486019	+	0.0985657i
$934$	−53.0193	−	19.2975i	−1.73485	−	0.631432i
$935$		0			0
$936$	−7.29899	+	4.64909i	−0.238575	+	0.151960i
$937$	0.889623	−	0.513624i	0.0290627	−	0.0167794i	−0.485398	−	0.874293i	$-0.661325\pi$
$937$	0.889623	−	0.513624i	0.0290627	−	0.0167794i	0.514461	+	0.857514i	$0.327992\pi$
$938$	26.6180	−	4.69347i	0.869109	−	0.153247i
$939$	−36.2357	+	37.8491i	−1.18251	+	1.23516i
$940$		0			0
$941$	8.92999	−	50.6445i	0.291109	−	1.65096i	−0.391499	−	0.920179i	$-0.628043\pi$
$941$	8.92999	−	50.6445i	0.291109	−	1.65096i	0.682608	−	0.730785i	$-0.260846\pi$
$942$	51.0357	−	37.4176i	1.66283	−	1.21913i
$943$	24.9450	+	29.7283i	0.812320	+	0.968085i
$944$	15.5387			0.505742
$945$		0			0
$946$	43.5568			1.41615
$947$	17.5068	+	20.8637i	0.568893	+	0.677980i	0.971403	−	0.237435i	$-0.0763067\pi$
$947$	17.5068	+	20.8637i	0.568893	+	0.677980i	−0.402510	+	0.915415i	$0.631862\pi$
$948$	−4.09754	−	37.4292i	−0.133082	−	1.21564i
$949$	−4.12620	+	23.4009i	−0.133942	+	0.759624i
$950$		0			0
$951$	4.93041	+	1.20669i	0.159880	+	0.0391296i
$952$	−6.04187	+	1.06534i	−0.195818	+	0.0345280i
$953$	−11.4390	+	6.60432i	−0.370546	+	0.213935i	−0.673697	−	0.739008i	$-0.735295\pi$
$953$	−11.4390	+	6.60432i	−0.370546	+	0.213935i	0.303151	+	0.952943i	$0.401961\pi$
$954$	−36.3877	−	4.79370i	−1.17809	−	0.155202i
$955$		0			0
$956$	17.2782	+	6.28875i	0.558817	+	0.203393i
$957$	21.0117	+	1.37808i	0.679211	+	0.0445471i
$958$	10.0760	−	12.0081i	0.325542	−	0.387965i
$959$	26.4680	+	22.2093i	0.854698	+	0.717177i
$960$		0			0
$961$	16.7645	+	6.10177i	0.540790	+	0.196831i
$962$	−39.8889	−	23.0299i	−1.28607	−	0.742513i
$963$	28.0575	−	25.7055i	0.904140	−	0.828349i
$964$	−6.65187	−	11.5214i	−0.214242	−	0.371079i
$965$		0			0
$966$	−26.7393	−	91.7529i	−0.860322	−	2.95210i
$967$	−2.96338	−	8.14181i	−0.0952958	−	0.261823i	0.882881	−	0.469596i	$-0.155601\pi$
$967$	−2.96338	−	8.14181i	−0.0952958	−	0.261823i	−0.978177	+	0.207773i	$0.933378\pi$
$968$	−0.698660	−	0.123193i	−0.0224558	−	0.00395956i
$969$	7.22996	−	16.4294i	0.232260	−	0.527789i
$970$		0			0
$971$	27.5409			0.883831			0.441915	−	0.897057i	$-0.354299\pi$
$971$	27.5409			0.883831			0.441915	+	0.897057i	$0.354299\pi$
$972$	−18.0294	−	14.4765i	−0.578295	−	0.464335i
$973$			11.1430i			0.357227i
$974$	−36.5824	+	30.6963i	−1.17218	+	0.983572i
$975$		0			0
$976$	−2.80970	+	15.9346i	−0.0899364	+	0.510055i
$977$	2.26275	+	6.21685i	0.0723917	+	0.198895i	0.970611	−	0.240652i	$-0.0773613\pi$
$977$	2.26275	+	6.21685i	0.0723917	+	0.198895i	−0.898220	+	0.439547i	$0.855139\pi$
$978$	28.7528	−	8.37933i	0.919413	−	0.267942i
$979$	2.12730	+	12.0645i	0.0679889	+	0.385584i
$980$		0			0
$981$	−28.4662	−	31.0708i	−0.908856	−	0.992013i
$982$	−3.83548	−	2.21441i	−0.122395	−	0.0706648i
$983$	12.7593	−	35.0558i	0.406958	−	1.11811i	−0.551823	−	0.833961i	$-0.686068\pi$
$983$	12.7593	−	35.0558i	0.406958	−	1.11811i	0.958781	−	0.284147i	$-0.0917102\pi$
$984$	−6.33738	−	4.23490i	−0.202028	−	0.135004i
$985$		0			0
$986$	9.28499	+	7.79103i	0.295694	+	0.248117i
$987$	−25.9188	−	1.69992i	−0.825004	−	0.0541092i
$988$	8.59336	−	23.6101i	0.273391	−	0.751136i
$989$	28.9685	−	50.1749i	0.921144	−	1.59547i
$990$		0			0
$991$	20.4866	+	35.4838i	0.650777	+	1.12718i	0.982935	+	0.183955i	$0.0588900\pi$
$991$	20.4866	+	35.4838i	0.650777	+	1.12718i	−0.332158	+	0.943224i	$0.607777\pi$
$992$	−24.8900	+	4.38879i	−0.790260	+	0.139344i
$993$	4.45447	−	18.2005i	0.141358	−	0.577577i
$994$	−53.0912	+	19.3236i	−1.68395	+	0.612908i
$995$		0			0
$996$	36.8710	−	4.03643i	1.16830	−	0.127899i
$997$	14.8855	+	17.7398i	0.471428	+	0.561826i	0.948393	−	0.317096i	$-0.102708\pi$
$997$	14.8855	+	17.7398i	0.471428	+	0.561826i	−0.476965	+	0.878922i	$0.658263\pi$
$998$			2.73614i			0.0866109i
$999$	−8.36923	+	42.0466i	−0.264791	+	1.33030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.d.49.3		84
5.2	odd	4		135.2.k.b.76.6	yes	42
5.3	odd	4		675.2.l.e.76.2		42
5.4	even	2	inner	675.2.u.d.49.12		84
15.2	even	4		405.2.k.b.361.2		42
27.16	even	9	inner	675.2.u.d.124.12		84
135.43	odd	36		675.2.l.e.151.2		42
135.77	even	36		3645.2.a.k.1.5		21
135.92	even	36		405.2.k.b.46.2		42
135.97	odd	36		135.2.k.b.16.6	✓	42
135.112	odd	36		3645.2.a.l.1.17		21
135.124	even	18	inner	675.2.u.d.124.3		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.k.b.16.6	✓	42	135.97	odd	36
135.2.k.b.76.6	yes	42	5.2	odd	4
405.2.k.b.46.2		42	135.92	even	36
405.2.k.b.361.2		42	15.2	even	4
675.2.l.e.76.2		42	5.3	odd	4
675.2.l.e.151.2		42	135.43	odd	36
675.2.u.d.49.3		84	1.1	even	1	trivial
675.2.u.d.49.12		84	5.4	even	2	inner
675.2.u.d.124.3		84	135.124	even	18	inner
675.2.u.d.124.12		84	27.16	even	9	inner
3645.2.a.k.1.5		21	135.77	even	36
3645.2.a.l.1.17		21	135.112	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)

\(f(q)\)	\(=\)	\(q+(-1.19967 - 1.42971i) q^{2} +(1.58534 + 0.697646i) q^{3} +(-0.257569 + 1.46075i) q^{4} +(-0.904448 - 3.10352i) q^{6} +(3.42349 - 0.603654i) q^{7} +(-0.835177 + 0.482190i) q^{8} +(2.02658 + 2.21201i) q^{9} +O(q^{10})\)	\(q+(-1.19967 - 1.42971i) q^{2} +(1.58534 + 0.697646i) q^{3} +(-0.257569 + 1.46075i) q^{4} +(-0.904448 - 3.10352i) q^{6} +(3.42349 - 0.603654i) q^{7} +(-0.835177 + 0.482190i) q^{8} +(2.02658 + 2.21201i) q^{9} +(-3.21914 - 1.17167i) q^{11} +(-1.42742 + 2.13608i) q^{12} +(1.92269 - 2.29137i) q^{13} +(-4.97011 - 4.17042i) q^{14} +(4.47899 + 1.63022i) q^{16} +(1.58484 + 0.915007i) q^{17} +(0.731301 - 5.55110i) q^{18} +(-2.83150 - 4.90430i) q^{19} +(5.84852 + 1.43139i) q^{21} +(2.18675 + 6.00805i) q^{22} +(8.37528 + 1.47679i) q^{23} +(-1.66043 + 0.181775i) q^{24} -5.58258 q^{26} +(1.66961 + 4.92061i) q^{27} +5.15634i q^{28} +(-2.71852 + 2.28111i) q^{29} +(0.629929 - 3.57251i) q^{31} +(-2.38289 - 6.54694i) q^{32} +(-4.28600 - 4.10331i) q^{33} +(-0.593087 - 3.36357i) q^{34} +(-3.75317 + 2.39058i) q^{36} +(7.14525 + 4.12531i) q^{37} +(-3.61487 + 9.93177i) q^{38} +(4.64666 - 2.29123i) q^{39} +(3.49560 + 2.93316i) q^{41} +(-4.96982 - 10.0789i) q^{42} +(2.33002 - 6.40168i) q^{43} +(2.54066 - 4.40056i) q^{44} +(-7.93619 - 13.7459i) q^{46} +(-4.24834 + 0.749097i) q^{47} +(5.96338 + 5.70919i) q^{48} +(4.77806 - 1.73907i) q^{49} +(1.87415 + 2.55625i) q^{51} +(2.85188 + 3.39874i) q^{52} -6.55503i q^{53} +(5.03206 - 8.29017i) q^{54} +(-2.56815 + 2.15493i) q^{56} +(-1.06741 - 9.75035i) q^{57} +(6.52266 + 1.15012i) q^{58} +(3.06342 - 1.11500i) q^{59} +(0.589476 + 3.34309i) q^{61} +(-5.86336 + 3.38521i) q^{62} +(8.27327 + 6.34943i) q^{63} +(-1.73511 + 3.00530i) q^{64} +(-0.724755 + 11.0504i) q^{66} +(-2.67781 + 3.19129i) q^{67} +(-1.74480 + 2.07937i) q^{68} +(12.2474 + 8.18418i) q^{69} +(4.35406 - 7.54146i) q^{71} +(-2.75916 - 0.870220i) q^{72} +(-6.87971 + 3.97200i) q^{73} +(-2.67394 - 15.1646i) q^{74} +(7.89326 - 2.87291i) q^{76} +(-11.7280 - 2.06796i) q^{77} +(-8.85027 - 3.89466i) q^{78} +(-11.2271 + 9.42064i) q^{79} +(-0.785942 + 8.96562i) q^{81} -8.51652i q^{82} +(-9.28016 - 11.0597i) q^{83} +(-3.59730 + 8.17453i) q^{84} +(-11.9478 + 4.34865i) q^{86} +(-5.90118 + 1.71976i) q^{87} +(3.25351 - 0.573682i) q^{88} +(-1.78804 - 3.09697i) q^{89} +(5.19911 - 9.00512i) q^{91} +(-4.31443 + 11.8538i) q^{92} +(3.49099 - 5.22416i) q^{93} +(6.16760 + 5.17523i) q^{94} +(0.789762 - 12.0415i) q^{96} +(1.25203 - 3.43991i) q^{97} +(-8.21846 - 4.74493i) q^{98} +(-3.93210 - 9.49523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 12 q^{6} + 6 q^{9}+O(q^{10}) \) 84 * q - 12 * q^6 + 6 * q^9	\( 84 q - 12 q^{6} + 6 q^{9} - 12 q^{11} + 54 q^{14} - 24 q^{16} + 48 q^{19} + 24 q^{21} + 6 q^{24} - 36 q^{26} - 24 q^{31} - 102 q^{34} - 72 q^{36} + 60 q^{39} + 66 q^{41} - 24 q^{44} - 60 q^{46} - 36 q^{49} - 78 q^{51} - 60 q^{54} - 48 q^{56} + 54 q^{59} - 12 q^{61} + 126 q^{64} - 60 q^{66} - 102 q^{69} + 24 q^{71} + 144 q^{74} + 276 q^{76} + 36 q^{79} + 90 q^{81} + 102 q^{84} + 36 q^{86} - 18 q^{89} - 138 q^{91} + 66 q^{94} + 306 q^{96} + 18 q^{99}+O(q^{100}) \) 84 * q - 12 * q^6 + 6 * q^9 - 12 * q^11 + 54 * q^14 - 24 * q^16 + 48 * q^19 + 24 * q^21 + 6 * q^24 - 36 * q^26 - 24 * q^31 - 102 * q^34 - 72 * q^36 + 60 * q^39 + 66 * q^41 - 24 * q^44 - 60 * q^46 - 36 * q^49 - 78 * q^51 - 60 * q^54 - 48 * q^56 + 54 * q^59 - 12 * q^61 + 126 * q^64 - 60 * q^66 - 102 * q^69 + 24 * q^71 + 144 * q^74 + 276 * q^76 + 36 * q^79 + 90 * q^81 + 102 * q^84 + 36 * q^86 - 18 * q^89 - 138 * q^91 + 66 * q^94 + 306 * q^96 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more