LMFDB - Embedded newform 825.2.n.o.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			751.1
Character	$\chi$	$=$	825.751
Dual form			825.2.n.o.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.20531 + 1.60225i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.67816 - 5.16484i) q^{4} +(2.20531 + 1.60225i) q^{6} +(0.150285 - 0.462529i) q^{7} +(2.88981 + 8.89393i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-2.20531 + 1.60225i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.67816 - 5.16484i) q^{4} +(2.20531 + 1.60225i) q^{6} +(0.150285 - 0.462529i) q^{7} +(2.88981 + 8.89393i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(3.06568 + 1.26554i) q^{11} -5.43063 q^{12} +(-2.92082 + 2.12210i) q^{13} +(0.409664 + 1.26082i) q^{14} +(-11.8363 - 8.59960i) q^{16} +(2.94711 + 2.14120i) q^{17} +(0.842355 - 2.59250i) q^{18} +(-0.504099 - 1.55146i) q^{19} -0.486331 q^{21} +(-8.78851 + 2.12109i) q^{22} -3.54253 q^{23} +(7.56563 - 5.49675i) q^{24} +(3.04119 - 9.35981i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-2.13668 - 1.55239i) q^{28} +(0.326342 - 1.00438i) q^{29} +(-4.93572 + 3.58601i) q^{31} +21.1784 q^{32} +(0.256251 - 3.30671i) q^{33} -9.93007 q^{34} +(1.67816 + 5.16484i) q^{36} +(2.65479 - 8.17060i) q^{37} +(3.59752 + 2.61375i) q^{38} +(2.92082 + 2.12210i) q^{39} +(3.39392 + 10.4454i) q^{41} +(1.07251 - 0.779227i) q^{42} +7.41765 q^{43} +(11.6810 - 13.7100i) q^{44} +(7.81239 - 5.67603i) q^{46} +(1.61089 + 4.95781i) q^{47} +(-4.52108 + 13.9145i) q^{48} +(5.47177 + 3.97547i) q^{49} +(1.12570 - 3.46454i) q^{51} +(6.05871 + 18.6468i) q^{52} +(1.20559 - 0.875916i) q^{53} -2.72592 q^{54} +4.54799 q^{56} +(-1.31975 + 0.958853i) q^{57} +(0.889581 + 2.73785i) q^{58} +(-2.46472 + 7.58562i) q^{59} +(8.78900 + 6.38558i) q^{61} +(5.13911 - 15.8166i) q^{62} +(0.150285 + 0.462529i) q^{63} +(-23.0323 + 16.7339i) q^{64} +(4.73308 + 7.70292i) q^{66} -0.432515 q^{67} +(16.0047 - 11.6281i) q^{68} +(1.09470 + 3.36915i) q^{69} +(-4.86481 - 3.53449i) q^{71} +(-7.56563 - 5.49675i) q^{72} +(-0.359734 + 1.10715i) q^{73} +(7.23674 + 22.2724i) q^{74} -8.85898 q^{76} +(1.04607 - 1.22777i) q^{77} -9.84148 q^{78} +(3.57985 - 2.60091i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-24.2209 - 17.5975i) q^{82} +(-2.57049 - 1.86757i) q^{83} +(-0.816141 + 2.51182i) q^{84} +(-16.3583 + 11.8850i) q^{86} -1.05606 q^{87} +(-2.39636 + 30.9231i) q^{88} +1.38354 q^{89} +(0.542578 + 1.66988i) q^{91} +(-5.94492 + 18.2966i) q^{92} +(4.93572 + 3.58601i) q^{93} +(-11.4962 - 8.35247i) q^{94} +(-6.54447 - 20.1418i) q^{96} +(1.13241 - 0.822741i) q^{97} -18.4367 q^{98} +(-3.22405 + 0.778121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9	$ 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9} - 24 q^{12} - 4 q^{13} + 2 q^{14} - 22 q^{16} - 4 q^{17} - 2 q^{18} + 8 q^{19} - 16 q^{21} + 4 q^{22} + 6 q^{24} - 38 q^{26} + 6 q^{27} - 30 q^{28} - 10 q^{31} + 56 q^{32} - 10 q^{33} + 12 q^{34} - 6 q^{36} - 10 q^{37} - 4 q^{38} + 4 q^{39} + 30 q^{41} + 8 q^{42} + 64 q^{43} + 24 q^{44} + 54 q^{46} + 8 q^{47} + 2 q^{48} + 14 q^{49} + 14 q^{51} - 14 q^{52} - 26 q^{53} - 8 q^{54} + 12 q^{56} - 8 q^{57} - 20 q^{58} - 30 q^{59} + 20 q^{61} + 50 q^{62} - 4 q^{63} - 32 q^{64} + 6 q^{66} - 20 q^{67} + 62 q^{68} - 10 q^{69} - 16 q^{71} - 6 q^{72} + 12 q^{73} + 16 q^{74} - 68 q^{76} + 2 q^{77} - 32 q^{78} + 26 q^{79} - 6 q^{81} - 56 q^{82} - 48 q^{83} - 52 q^{86} - 48 q^{88} - 20 q^{89} - 20 q^{91} - 46 q^{92} + 10 q^{93} - 36 q^{94} + 14 q^{96} + 14 q^{97} + 120 q^{98}+O(q^{100}) $ 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9 - 24 * q^12 - 4 * q^13 + 2 * q^14 - 22 * q^16 - 4 * q^17 - 2 * q^18 + 8 * q^19 - 16 * q^21 + 4 * q^22 + 6 * q^24 - 38 * q^26 + 6 * q^27 - 30 * q^28 - 10 * q^31 + 56 * q^32 - 10 * q^33 + 12 * q^34 - 6 * q^36 - 10 * q^37 - 4 * q^38 + 4 * q^39 + 30 * q^41 + 8 * q^42 + 64 * q^43 + 24 * q^44 + 54 * q^46 + 8 * q^47 + 2 * q^48 + 14 * q^49 + 14 * q^51 - 14 * q^52 - 26 * q^53 - 8 * q^54 + 12 * q^56 - 8 * q^57 - 20 * q^58 - 30 * q^59 + 20 * q^61 + 50 * q^62 - 4 * q^63 - 32 * q^64 + 6 * q^66 - 20 * q^67 + 62 * q^68 - 10 * q^69 - 16 * q^71 - 6 * q^72 + 12 * q^73 + 16 * q^74 - 68 * q^76 + 2 * q^77 - 32 * q^78 + 26 * q^79 - 6 * q^81 - 56 * q^82 - 48 * q^83 - 52 * q^86 - 48 * q^88 - 20 * q^89 - 20 * q^91 - 46 * q^92 + 10 * q^93 - 36 * q^94 + 14 * q^96 + 14 * q^97 + 120 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	−2.20531	+	1.60225i	−1.55939	+	1.13297i	−0.622888	+	0.782311i	$0.714041\pi$
$2$	−2.20531	+	1.60225i	−1.55939	+	1.13297i	−0.936505	+	0.350654i	$0.885959\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	1.67816	−	5.16484i	0.839079	−	2.58242i
$5$		0			0
$5$		0			0
$6$	2.20531	+	1.60225i	0.900316	+	0.654118i
$7$	0.150285	−	0.462529i	0.0568023	−	0.174819i	−0.918630	−	0.395119i	$-0.870703\pi$
$7$	0.150285	−	0.462529i	0.0568023	−	0.174819i	0.975432	+	0.220299i	$0.0707034\pi$
$8$	2.88981	+	8.89393i	1.02170	+	3.14448i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	3.06568	+	1.26554i	0.924338	+	0.381574i
$11$	3.06568	+	1.26554i	0.924338	+	0.381574i
$12$	−5.43063			−1.56769
$13$	−2.92082	+	2.12210i	−0.810090	+	0.588565i	−0.913857	−	0.406037i	$-0.866911\pi$
$13$	−2.92082	+	2.12210i	−0.810090	+	0.588565i	0.103766	+	0.994602i	$0.466911\pi$
$14$	0.409664	+	1.26082i	0.109487	+	0.336967i
$15$		0			0
$16$	−11.8363	−	8.59960i	−2.95908	−	2.14990i
$17$	2.94711	+	2.14120i	0.714780	+	0.519318i	0.884712	−	0.466138i	$-0.154355\pi$
$17$	2.94711	+	2.14120i	0.714780	+	0.519318i	−0.169932	+	0.985456i	$0.554355\pi$
$18$	0.842355	−	2.59250i	0.198545	−	0.611059i
$19$	−0.504099	−	1.55146i	−0.115648	−	0.355928i	0.876433	−	0.481523i	$-0.159916\pi$
$19$	−0.504099	−	1.55146i	−0.115648	−	0.355928i	−0.992082	+	0.125594i	$0.959916\pi$
$20$		0			0
$21$	−0.486331			−0.106126
$22$	−8.78851	+	2.12109i	−1.87372	+	0.452219i
$23$	−3.54253			−0.738668			−0.369334	−	0.929297i	$-0.620414\pi$
$23$	−3.54253			−0.738668			−0.369334	+	0.929297i	$0.620414\pi$
$24$	7.56563	−	5.49675i	1.54433	−	1.12202i
$25$		0			0
$26$	3.04119	−	9.35981i	0.596425	−	1.83561i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−2.13668	−	1.55239i	−0.403795	−	0.293375i
$29$	0.326342	−	1.00438i	0.0606001	−	0.186508i	−0.916174	−	0.400782i	$-0.868739\pi$
$29$	0.326342	−	1.00438i	0.0606001	−	0.186508i	0.976774	+	0.214274i	$0.0687385\pi$
$30$		0			0
$31$	−4.93572	+	3.58601i	−0.886481	+	0.644066i	−0.934958	−	0.354758i	$-0.884563\pi$
$31$	−4.93572	+	3.58601i	−0.886481	+	0.644066i	0.0484769	+	0.998824i	$0.484563\pi$
$32$	21.1784			3.74384
$33$	0.256251	−	3.30671i	0.0446075	−	0.575624i
$34$	−9.93007			−1.70299
$35$		0			0
$36$	1.67816	+	5.16484i	0.279693	+	0.860807i
$37$	2.65479	−	8.17060i	0.436445	−	1.34324i	−0.455154	−	0.890413i	$-0.650416\pi$
$37$	2.65479	−	8.17060i	0.436445	−	1.34324i	0.891599	−	0.452826i	$-0.149584\pi$
$38$	3.59752	+	2.61375i	0.583596	+	0.424007i
$39$	2.92082	+	2.12210i	0.467706	+	0.339808i
$40$		0			0
$41$	3.39392	+	10.4454i	0.530041	+	1.63130i	0.754127	+	0.656729i	$0.228061\pi$
$41$	3.39392	+	10.4454i	0.530041	+	1.63130i	−0.224085	+	0.974570i	$0.571939\pi$
$42$	1.07251	−	0.779227i	0.165492	−	0.120237i
$43$	7.41765			1.13118			0.565591	−	0.824686i	$-0.308648\pi$
$43$	7.41765			1.13118			0.565591	+	0.824686i	$0.308648\pi$
$44$	11.6810	−	13.7100i	1.76098	−	2.06686i
$45$		0			0
$46$	7.81239	−	5.67603i	1.15187	−	0.836886i
$47$	1.61089	+	4.95781i	0.234972	+	0.723170i	0.997125	+	0.0757732i	$0.0241425\pi$
$47$	1.61089	+	4.95781i	0.234972	+	0.723170i	−0.762153	+	0.647397i	$0.775858\pi$
$48$	−4.52108	+	13.9145i	−0.652562	+	2.00838i
$49$	5.47177	+	3.97547i	0.781682	+	0.567925i
$50$		0			0
$51$	1.12570	−	3.46454i	0.157629	−	0.485133i
$52$	6.05871	+	18.6468i	0.840193	+	2.58585i
$53$	1.20559	−	0.875916i	0.165601	−	0.120316i	−0.501898	−	0.864927i	$-0.667365\pi$
$53$	1.20559	−	0.875916i	0.165601	−	0.120316i	0.667499	+	0.744610i	$0.267365\pi$
$54$	−2.72592			−0.370951
$55$		0			0
$56$	4.54799			0.607751
$57$	−1.31975	+	0.958853i	−0.174805	+	0.127003i
$58$	0.889581	+	2.73785i	0.116808	+	0.359497i
$59$	−2.46472	+	7.58562i	−0.320879	+	0.987563i	0.652388	+	0.757885i	$0.273767\pi$
$59$	−2.46472	+	7.58562i	−0.320879	+	0.987563i	−0.973267	+	0.229678i	$0.926233\pi$
$60$		0			0
$61$	8.78900	+	6.38558i	1.12532	+	0.817590i	0.985007	−	0.172517i	$-0.0551900\pi$
$61$	8.78900	+	6.38558i	1.12532	+	0.817590i	0.140310	+	0.990108i	$0.455190\pi$
$62$	5.13911	−	15.8166i	0.652668	−	2.00871i
$63$	0.150285	+	0.462529i	0.0189341	+	0.0582731i
$64$	−23.0323	+	16.7339i	−2.87903	+	2.09174i
$65$		0			0
$66$	4.73308	+	7.70292i	0.582602	+	0.948164i
$67$	−0.432515			−0.0528401			−0.0264201	−	0.999651i	$-0.508411\pi$
$67$	−0.432515			−0.0528401			−0.0264201	+	0.999651i	$0.508411\pi$
$68$	16.0047	−	11.6281i	1.94086	−	1.41011i
$69$	1.09470	+	3.36915i	0.131787	+	0.405597i
$70$		0			0
$71$	−4.86481	−	3.53449i	−0.577347	−	0.419467i	0.260420	−	0.965496i	$-0.416139\pi$
$71$	−4.86481	−	3.53449i	−0.577347	−	0.419467i	−0.837767	+	0.546028i	$0.816139\pi$
$72$	−7.56563	−	5.49675i	−0.891618	−	0.647798i
$73$	−0.359734	+	1.10715i	−0.0421037	+	0.129582i	−0.969899	−	0.243508i	$-0.921702\pi$
$73$	−0.359734	+	1.10715i	−0.0421037	+	0.129582i	0.927795	+	0.373090i	$0.121702\pi$
$74$	7.23674	+	22.2724i	0.841254	+	2.58911i
$75$		0			0
$76$	−8.85898			−1.01619
$77$	1.04607	−	1.22777i	0.119211	−	0.139918i
$78$	−9.84148			−1.11433
$79$	3.57985	−	2.60091i	0.402765	−	0.292626i	−0.367901	−	0.929865i	$-0.619924\pi$
$79$	3.57985	−	2.60091i	0.402765	−	0.292626i	0.770666	+	0.637239i	$0.219924\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−24.2209	−	17.5975i	−2.67475	−	1.94332i
$83$	−2.57049	−	1.86757i	−0.282148	−	0.204993i	0.437706	−	0.899118i	$-0.355791\pi$
$83$	−2.57049	−	1.86757i	−0.282148	−	0.204993i	−0.719854	+	0.694126i	$0.755791\pi$
$84$	−0.816141	+	2.51182i	−0.0890483	+	0.274062i
$85$		0			0
$86$	−16.3583	+	11.8850i	−1.76396	+	1.28159i
$87$	−1.05606			−0.113222
$88$	−2.39636	+	30.9231i	−0.255453	+	3.29642i
$89$	1.38354			0.146655			0.0733274	−	0.997308i	$-0.476638\pi$
$89$	1.38354			0.146655			0.0733274	+	0.997308i	$0.476638\pi$
$90$		0			0
$91$	0.542578	+	1.66988i	0.0568776	+	0.175051i
$92$	−5.94492	+	18.2966i	−0.619801	+	1.90755i
$93$	4.93572	+	3.58601i	0.511810	+	0.371852i
$94$	−11.4962	−	8.35247i	−1.18574	−	0.861491i
$95$		0			0
$96$	−6.54447	−	20.1418i	−0.667942	−	2.05571i
$97$	1.13241	−	0.822741i	0.114978	−	0.0835367i	−0.528810	−	0.848740i	$-0.677362\pi$
$97$	1.13241	−	0.822741i	0.114978	−	0.0835367i	0.643789	+	0.765203i	$0.277362\pi$
$98$	−18.4367			−1.86239
$99$	−3.22405	+	0.778121i	−0.324030	+	0.0782041i
$100$		0			0
$101$	0.0916009	−	0.0665520i	0.00911463	−	0.00662217i	−0.583219	−	0.812315i	$-0.698207\pi$
$101$	0.0916009	−	0.0665520i	0.00911463	−	0.00662217i	0.592333	+	0.805693i	$0.298207\pi$
$102$	3.06856	+	9.44406i	0.303833	+	0.935101i
$103$	2.23985	−	6.89355i	0.220699	−	0.679241i	−0.778001	−	0.628263i	$-0.783766\pi$
$103$	2.23985	−	6.89355i	0.220699	−	0.679241i	0.998700	−	0.0509781i	$-0.0162339\pi$
$104$	−27.3145	−	19.8451i	−2.67840	−	1.94597i
$105$		0			0
$106$	−1.25528	+	3.86334i	−0.121923	+	0.375241i
$107$	2.67571	+	8.23500i	0.258671	+	0.796108i	0.993084	+	0.117405i	$0.0374576\pi$
$107$	2.67571	+	8.23500i	0.258671	+	0.796108i	−0.734413	+	0.678703i	$0.762542\pi$
$108$	4.39348	−	3.19205i	0.422762	−	0.307155i
$109$	4.41573			0.422951			0.211475	−	0.977383i	$-0.432173\pi$
$109$	4.41573			0.422951			0.211475	+	0.977383i	$0.432173\pi$
$110$		0			0
$111$	−8.59108			−0.815429
$112$	−5.75638	+	4.18226i	−0.543927	+	0.395186i
$113$	5.67501	+	17.4659i	0.533860	+	1.64305i	0.746100	+	0.665834i	$0.231924\pi$
$113$	5.67501	+	17.4659i	0.533860	+	1.64305i	−0.212240	+	0.977218i	$0.568076\pi$
$114$	1.37413	−	4.22914i	0.128699	−	0.396096i
$115$		0			0
$116$	−4.63979	−	3.37100i	−0.430794	−	0.312990i
$117$	1.11566	−	3.43363i	0.103142	−	0.317439i
$118$	−6.71862	−	20.6778i	−0.618499	−	1.90354i
$119$	1.43327	−	1.04133i	0.131388	−	0.0954590i
$120$		0			0
$121$	7.79682	+	7.75948i	0.708802	+	0.705407i
$122$	−29.6139			−2.68111
$123$	8.88539	−	6.45562i	0.801169	−	0.582083i
$124$	10.2382	+	31.5101i	0.919422	+	2.82969i
$125$		0			0
$126$	−1.07251	−	0.779227i	−0.0955471	−	0.0694190i
$127$	8.58117	+	6.23458i	0.761456	+	0.553230i	0.899356	−	0.437216i	$-0.144036\pi$
$127$	8.58117	+	6.23458i	0.761456	+	0.553230i	−0.137901	+	0.990446i	$0.544036\pi$
$128$	10.8924	−	33.5235i	0.962764	−	2.96308i
$129$	−2.29218	−	7.05461i	−0.201815	−	0.621123i
$130$		0			0
$131$	16.5042			1.44198			0.720989	−	0.692946i	$-0.243688\pi$
$131$	16.5042			1.44198			0.720989	+	0.692946i	$0.243688\pi$
$132$	−16.6486	−	6.87268i	−1.44907	−	0.598190i
$133$	−0.793351			−0.0687923
$134$	0.953832	−	0.692999i	0.0823985	−	0.0598660i
$135$		0			0
$136$	−10.5271	+	32.3991i	−0.902692	+	2.77820i
$137$	4.92300	+	3.57677i	0.420600	+	0.305584i	0.777879	−	0.628414i	$-0.216296\pi$
$137$	4.92300	+	3.57677i	0.420600	+	0.305584i	−0.357279	+	0.933998i	$0.616296\pi$
$138$	−7.81239	−	5.67603i	−0.665035	−	0.483176i
$139$	−5.36213	+	16.5029i	−0.454810	+	1.39976i	0.416549	+	0.909113i	$0.363239\pi$
$139$	−5.36213	+	16.5029i	−0.454810	+	1.39976i	−0.871359	+	0.490647i	$0.836761\pi$
$140$		0			0
$141$	4.21736	−	3.06409i	0.355166	−	0.258043i
$142$	16.3916			1.37555
$143$	−11.6399	+	2.80928i	−0.973379	+	0.234924i
$144$	14.6305			1.21921
$145$		0			0
$146$	−0.980606	−	3.01800i	−0.0811555	−	0.249771i
$147$	2.09003	−	6.43245i	0.172383	−	0.530540i
$148$	−37.7447	−	27.4231i	−3.10260	−	2.25417i
$149$	−16.0876	−	11.6883i	−1.31795	−	0.957546i	−0.999955	−	0.00945254i	$-0.996991\pi$
$149$	−16.0876	−	11.6883i	−1.31795	−	0.957546i	−0.317993	−	0.948093i	$-0.603009\pi$
$150$		0			0
$151$	−0.0196381	−	0.0604400i	−0.00159813	−	0.00491854i	0.950254	−	0.311475i	$-0.100823\pi$
$151$	−0.0196381	−	0.0604400i	−0.00159813	−	0.00491854i	−0.951852	+	0.306557i	$0.900823\pi$
$152$	12.3418	−	8.96684i	1.00105	−	0.727306i
$153$	−3.64283			−0.294506
$154$	−0.339711	+	4.38371i	−0.0273747	+	0.353249i
$155$		0			0
$156$	15.8619	−	11.5244i	1.26997	−	0.922687i
$157$	0.301174	+	0.926920i	0.0240363	+	0.0739762i	0.962355	−	0.271795i	$-0.0876173\pi$
$157$	0.301174	+	0.926920i	0.0240363	+	0.0739762i	−0.938319	+	0.345771i	$0.887617\pi$
$158$	−3.72737	+	11.4717i	−0.296534	+	0.912637i
$159$	−1.20559	−	0.875916i	−0.0956099	−	0.0694646i
$160$		0			0
$161$	−0.532388	+	1.63852i	−0.0419580	+	0.129134i
$162$	0.842355	+	2.59250i	0.0661817	+	0.203686i
$163$	14.3303	−	10.4116i	1.12244	−	0.815500i	0.137862	−	0.990451i	$-0.455977\pi$
$163$	14.3303	−	10.4116i	1.12244	−	0.815500i	0.984577	+	0.174952i	$0.0559769\pi$
$164$	59.6444			4.65744
$165$		0			0
$166$	8.66108			0.672230
$167$	7.90573	−	5.74385i	0.611763	−	0.444472i	−0.238271	−	0.971199i	$-0.576581\pi$
$167$	7.90573	−	5.74385i	0.611763	−	0.444472i	0.850035	+	0.526726i	$0.176581\pi$
$168$	−1.40541	−	4.32540i	−0.108429	−	0.333712i
$169$	0.0106681	−	0.0328332i	0.000820626	−	0.00252563i
$170$		0			0
$171$	1.31975	+	0.958853i	0.100924	+	0.0733253i
$172$	12.4480	−	38.3110i	0.949151	−	2.92119i
$173$	2.52827	+	7.78122i	0.192221	+	0.591596i	0.999998	+	0.00210700i	$0.000670679\pi$
$173$	2.52827	+	7.78122i	0.192221	+	0.591596i	−0.807777	+	0.589489i	$0.799329\pi$
$174$	2.32895	−	1.69208i	0.176557	−	0.128276i
$175$		0			0
$176$	−25.4033	−	41.3430i	−1.91485	−	3.11635i
$177$	7.97599			0.599512
$178$	−3.05114	+	2.21678i	−0.228692	+	0.166155i
$179$	0.165620	+	0.509726i	0.0123790	+	0.0380987i	0.957055	−	0.289906i	$-0.0936239\pi$
$179$	0.165620	+	0.509726i	0.0123790	+	0.0380987i	−0.944676	+	0.328004i	$0.893624\pi$
$180$		0			0
$181$	4.12098	+	2.99406i	0.306310	+	0.222547i	0.730311	−	0.683114i	$-0.239375\pi$
$181$	4.12098	+	2.99406i	0.306310	+	0.222547i	−0.424002	+	0.905661i	$0.639375\pi$
$182$	−3.87213	−	2.81327i	−0.287022	−	0.208533i
$183$	3.35710	−	10.3321i	0.248164	−	0.763770i
$184$	−10.2372	−	31.5070i	−0.754700	−	2.32273i
$185$		0			0
$186$	−16.6305			−1.21941
$187$	6.32514	+	10.2939i	0.462540	+	0.752767i
$188$	28.3096			2.06469
$189$	0.393450	−	0.285858i	0.0286193	−	0.0207931i
$190$		0			0
$191$	3.75481	−	11.5561i	0.271689	−	0.836172i	−0.718388	−	0.695643i	$-0.755120\pi$
$191$	3.75481	−	11.5561i	0.271689	−	0.836172i	0.990077	−	0.140529i	$-0.0448804\pi$
$192$	23.0323	+	16.7339i	1.66221	+	1.20767i
$193$	7.64628	+	5.55535i	0.550391	+	0.399883i	0.827930	−	0.560832i	$-0.189519\pi$
$193$	7.64628	+	5.55535i	0.550391	+	0.399883i	−0.277538	+	0.960715i	$0.589519\pi$
$194$	−1.17907	+	3.62880i	−0.0846523	+	0.260533i
$195$		0			0
$196$	29.7152	−	21.5894i	2.12251	−	1.54210i
$197$	−7.89908			−0.562786			−0.281393	−	0.959593i	$-0.590797\pi$
$197$	−7.89908			−0.562786			−0.281393	+	0.959593i	$0.590797\pi$
$198$	5.86331	−	6.88176i	0.416687	−	0.489065i
$199$	2.60454			0.184631			0.0923155	−	0.995730i	$-0.470573\pi$
$199$	2.60454			0.184631			0.0923155	+	0.995730i	$0.470573\pi$
$200$		0			0
$201$	0.133655	+	0.411346i	0.00942726	+	0.0290141i
$202$	−0.0953757	+	0.293536i	−0.00671061	+	0.0206531i
$203$	−0.415508	−	0.301885i	−0.0291630	−	0.0211881i
$204$	−16.0047	−	11.6281i	−1.12055	−	0.814130i
$205$		0			0
$206$	6.10565	+	18.7912i	0.425401	+	1.30925i
$207$	2.86597	−	2.08225i	0.199198	−	0.144726i
$208$	52.8211			3.66248
$209$	0.418021	−	5.39423i	0.0289151	−	0.373127i
$210$		0			0
$211$	8.36799	−	6.07970i	0.576076	−	0.418544i	−0.261231	−	0.965276i	$-0.584128\pi$
$211$	8.36799	−	6.07970i	0.576076	−	0.418544i	0.837307	+	0.546732i	$0.184128\pi$
$212$	−2.50079	−	7.69663i	−0.171755	−	0.528607i
$213$	−1.85819	+	5.71893i	−0.127321	+	0.391855i
$214$	−19.0954	−	13.8736i	−1.30533	−	0.948380i
$215$		0			0
$216$	−2.88981	+	8.89393i	−0.196627	+	0.605155i
$217$	0.916869	+	2.82183i	0.0622411	+	0.191559i
$218$	−9.73808	+	7.07513i	−0.659546	+	0.479188i
$219$	1.16412			0.0786642
$220$		0			0
$221$	−13.1519			−0.884689
$222$	18.9460	−	13.7651i	1.27157	−	0.923853i
$223$	−4.44615	−	13.6838i	−0.297736	−	0.916338i	−0.982289	−	0.187374i	$-0.940002\pi$
$223$	−4.44615	−	13.6838i	−0.297736	−	0.916338i	0.684552	−	0.728964i	$-0.259998\pi$
$224$	3.18278	−	9.79559i	0.212658	−	0.654496i
$225$		0			0
$226$	−40.5000	−	29.4250i	−2.69402	−	1.95732i
$227$	0.440176	−	1.35472i	0.0292155	−	0.0899160i	−0.935386	−	0.353630i	$-0.884947\pi$
$227$	0.440176	−	1.35472i	0.0292155	−	0.0899160i	0.964601	+	0.263714i	$0.0849474\pi$
$228$	2.73758	+	8.42539i	0.181300	+	0.557985i
$229$	4.09296	−	2.97371i	0.270470	−	0.196508i	−0.444280	−	0.895888i	$-0.646540\pi$
$229$	4.09296	−	2.97371i	0.270470	−	0.196508i	0.714750	+	0.699380i	$0.246540\pi$
$230$		0			0
$231$	−1.49094	−	0.615471i	−0.0980965	−	0.0404950i
$232$	9.87592			0.648386
$233$	−16.9164	+	12.2905i	−1.10823	+	0.805178i	−0.982384	−	0.186871i	$-0.940165\pi$
$233$	−16.9164	+	12.2905i	−1.10823	+	0.805178i	−0.125848	+	0.992050i	$0.540165\pi$
$234$	3.04119	+	9.35981i	0.198808	+	0.611870i
$235$		0			0
$236$	35.0423	+	25.4597i	2.28106	+	1.65729i
$237$	−3.57985	−	2.60091i	−0.232536	−	0.168948i
$238$	−1.49234	+	4.59294i	−0.0967338	+	0.297716i
$239$	−5.72883	−	17.6315i	−0.370567	−	1.14049i	−0.946421	−	0.322935i	$-0.895330\pi$
$239$	−5.72883	−	17.6315i	−0.370567	−	1.14049i	0.575854	−	0.817552i	$-0.304670\pi$
$240$		0			0
$241$	−21.5816			−1.39019			−0.695095	−	0.718918i	$-0.744638\pi$
$241$	−21.5816			−1.39019			−0.695095	+	0.718918i	$0.744638\pi$
$242$	−29.6271	−	4.61960i	−1.90450	−	0.296959i
$243$	−1.00000			−0.0641500
$244$	47.7299	−	34.6778i	3.05559	−	2.22002i
$245$		0			0
$246$	−9.25155	+	28.4733i	−0.589857	+	1.81539i
$247$	4.76473	+	3.46178i	0.303173	+	0.220268i
$248$	−46.1570	−	33.5350i	−2.93097	−	2.12948i
$249$	−0.981841	+	3.02180i	−0.0622217	+	0.191499i
$250$		0			0
$251$	−0.508100	+	0.369156i	−0.0320710	+	0.0233009i	−0.603705	−	0.797208i	$-0.706310\pi$
$251$	−0.508100	+	0.369156i	−0.0320710	+	0.0233009i	0.571634	+	0.820509i	$0.306310\pi$
$252$	2.64109			0.166373
$253$	−10.8603	−	4.48321i	−0.682779	−	0.281857i
$254$	−28.9136			−1.81420
$255$		0			0
$256$	12.0968	+	37.2302i	0.756051	+	2.32689i
$257$	−1.05357	+	3.24256i	−0.0657199	+	0.202265i	−0.978524	−	0.206132i	$-0.933912\pi$
$257$	−1.05357	+	3.24256i	−0.0657199	+	0.202265i	0.912804	+	0.408397i	$0.133912\pi$
$258$	16.3583	+	11.8850i	1.01842	+	0.739926i
$259$	−3.38016	−	2.45583i	−0.210033	−	0.152598i
$260$		0			0
$261$	0.326342	+	1.00438i	0.0202000	+	0.0621693i
$262$	−36.3970	+	26.4439i	−2.24861	+	1.63371i
$263$	14.4795			0.892843			0.446422	−	0.894823i	$-0.352698\pi$
$263$	14.4795			0.892843			0.446422	+	0.894823i	$0.352698\pi$
$264$	30.1502	−	7.27670i	1.85561	−	0.447850i
$265$		0			0
$266$	1.74959	−	1.27115i	0.107274	−	0.0779393i
$267$	−0.427537	−	1.31582i	−0.0261648	−	0.0805270i
$268$	−0.725829	+	2.23387i	−0.0443370	+	0.136455i
$269$	24.1642	+	17.5563i	1.47332	+	1.07043i	0.979635	+	0.200789i	$0.0643505\pi$
$269$	24.1642	+	17.5563i	1.47332	+	1.07043i	0.493685	+	0.869641i	$0.335650\pi$
$270$		0			0
$271$	−0.463920	+	1.42780i	−0.0281811	+	0.0867327i	−0.964158	−	0.265329i	$-0.914519\pi$
$271$	−0.463920	+	1.42780i	−0.0281811	+	0.0867327i	0.935977	+	0.352062i	$0.114519\pi$
$272$	−16.4695	−	50.6880i	−0.998613	−	3.07341i
$273$	1.42049	−	1.03204i	0.0859718	−	0.0624622i
$274$	−16.5876			−1.00210
$275$		0			0
$276$	19.2382			1.15800
$277$	−5.11811	+	3.71852i	−0.307517	+	0.223424i	−0.730830	−	0.682559i	$-0.760867\pi$
$277$	−5.11811	+	3.71852i	−0.307517	+	0.223424i	0.423313	+	0.905983i	$0.360867\pi$
$278$	−14.6167	−	44.9856i	−0.876653	−	2.69806i
$279$	1.88528	−	5.80229i	0.112869	−	0.347374i
$280$		0			0
$281$	−10.6493	−	7.73714i	−0.635282	−	0.461559i	0.222944	−	0.974831i	$-0.428433\pi$
$281$	−10.6493	−	7.73714i	−0.635282	−	0.461559i	−0.858226	+	0.513272i	$0.828433\pi$
$282$	−4.39115	+	13.5146i	−0.261489	+	0.804781i
$283$	2.68299	+	8.25740i	0.159487	+	0.490852i	0.998588	−	0.0531248i	$-0.0169181\pi$
$283$	2.68299	+	8.25740i	0.159487	+	0.490852i	−0.839101	+	0.543976i	$0.816918\pi$
$284$	−26.4190	+	19.1945i	−1.56768	+	1.13899i
$285$		0			0
$286$	21.1685	−	24.8455i	1.25172	−	1.46914i
$287$	5.34135			0.315290
$288$	−17.1336	+	12.4483i	−1.00961	+	0.733524i
$289$	−1.15256	−	3.54721i	−0.0677976	−	0.208660i
$290$		0			0
$291$	−1.13241	−	0.822741i	−0.0663828	−	0.0482299i
$292$	5.11455	+	3.71594i	0.299306	+	0.217459i
$293$	−6.09966	+	18.7728i	−0.356346	+	1.09672i	0.598879	+	0.800839i	$0.295613\pi$
$293$	−6.09966	+	18.7728i	−0.356346	+	1.09672i	−0.955225	+	0.295880i	$0.904387\pi$
$294$	5.69725	+	17.5343i	0.332271	+	1.02262i
$295$		0			0
$296$	80.3406			4.66970
$297$	1.73632	+	2.82581i	0.100752	+	0.163970i
$298$	54.2059			3.14007
$299$	10.3471	−	7.51761i	0.598388	−	0.434754i
$300$		0			0
$301$	1.11476	−	3.43088i	0.0642536	−	0.197752i
$302$	0.140149	+	0.101824i	0.00806465	+	0.00585931i
$303$	−0.0916009	−	0.0665520i	−0.00526234	−	0.00382331i
$304$	−7.37523	+	22.6986i	−0.422998	+	1.30185i
$305$		0			0
$306$	8.03360	−	5.83675i	0.459250	−	0.333665i
$307$	−12.9484			−0.739003			−0.369501	−	0.929230i	$-0.620471\pi$
$307$	−12.9484			−0.739003			−0.369501	+	0.929230i	$0.620471\pi$
$308$	−4.58579	−	7.46320i	−0.261299	−	0.425255i
$309$	−7.24830			−0.412342
$310$		0			0
$311$	−8.80661	−	27.1039i	−0.499377	−	1.53692i	−0.810023	−	0.586398i	$-0.800545\pi$
$311$	−8.80661	−	27.1039i	−0.499377	−	1.53692i	0.310646	−	0.950526i	$-0.399455\pi$
$312$	−10.4332	+	32.1101i	−0.590663	+	1.81787i
$313$	5.49367	+	3.99139i	0.310521	+	0.225606i	0.732120	−	0.681176i	$-0.238531\pi$
$313$	5.49367	+	3.99139i	0.310521	+	0.225606i	−0.421599	+	0.906782i	$0.638531\pi$
$314$	−2.14935	−	1.56159i	−0.121295	−	0.0881257i
$315$		0			0
$316$	−7.42575	−	22.8541i	−0.417731	−	1.28564i
$317$	−24.7749	+	18.0000i	−1.39150	+	1.01098i	−0.395799	+	0.918337i	$0.629532\pi$
$317$	−24.7749	+	18.0000i	−1.39150	+	1.01098i	−0.995699	+	0.0926455i	$0.970468\pi$
$318$	4.06216			0.227794
$319$	2.27154	−	2.66610i	0.127182	−	0.149273i
$320$		0			0
$321$	7.00511	−	5.08951i	0.390987	−	0.284069i
$322$	−1.45125	−	4.46647i	−0.0808748	−	0.248907i
$323$	1.83635	−	5.65170i	0.102177	−	0.314469i
$324$	−4.39348	−	3.19205i	−0.244082	−	0.177336i
$325$		0			0
$326$	−14.9209	+	45.9217i	−0.826391	+	2.54337i
$327$	−1.36454	−	4.19961i	−0.0754590	−	0.232239i
$328$	−83.0929	+	60.3706i	−4.58804	+	3.33341i
$329$	2.53522			0.139771
$330$		0			0
$331$	−34.9532			−1.92120			−0.960601	−	0.277932i	$-0.910351\pi$
$331$	−34.9532			−1.92120			−0.960601	+	0.277932i	$0.910351\pi$
$332$	−13.9594	+	10.1421i	−0.766122	+	0.556620i
$333$	2.65479	+	8.17060i	0.145482	+	0.447746i
$334$	−8.23151	+	25.3340i	−0.450408	+	1.38621i
$335$		0			0
$336$	5.75638	+	4.18226i	0.314036	+	0.228161i
$337$	−1.79711	+	5.53092i	−0.0978946	+	0.301289i	−0.987997	−	0.154471i	$-0.950633\pi$
$337$	−1.79711	+	5.53092i	−0.0978946	+	0.301289i	0.890103	+	0.455760i	$0.150633\pi$
$338$	0.0290805	+	0.0895005i	0.00158177	+	0.00486819i
$339$	14.8574	−	10.7945i	0.806941	−	0.586277i
$340$		0			0
$341$	−19.6696	+	4.74723i	−1.06517	+	0.257077i
$342$	−4.44679			−0.240455
$343$	5.41525	−	3.93441i	0.292396	−	0.212438i
$344$	21.4356	+	65.9721i	1.15573	+	3.55698i
$345$		0			0
$346$	−18.0431	−	13.1091i	−0.970005	−	0.704750i
$347$	−22.3387	−	16.2300i	−1.19921	−	0.871274i	−0.204999	−	0.978762i	$-0.565719\pi$
$347$	−22.3387	−	16.2300i	−1.19921	−	0.871274i	−0.994206	+	0.107488i	$0.965719\pi$
$348$	−1.77224	+	5.45440i	−0.0950021	+	0.292386i
$349$	3.99149	+	12.2845i	0.213659	+	0.657576i	0.999246	+	0.0388245i	$0.0123613\pi$
$349$	3.99149	+	12.2845i	0.213659	+	0.657576i	−0.785587	+	0.618752i	$0.787639\pi$
$350$		0			0
$351$	−3.61034			−0.192705
$352$	64.9261	+	26.8020i	3.46057	+	1.42855i
$353$	−10.6615			−0.567454			−0.283727	−	0.958905i	$-0.591571\pi$
$353$	−10.6615			−0.567454			−0.283727	+	0.958905i	$0.591571\pi$
$354$	−17.5896	+	12.7796i	−0.934875	+	0.679227i
$355$		0			0
$356$	2.32180	−	7.14575i	0.123055	−	0.378724i
$357$	−1.43327	−	1.04133i	−0.0758569	−	0.0551133i
$358$	−1.18196	−	0.858741i	−0.0624683	−	0.0453859i
$359$	−3.99773	+	12.3037i	−0.210992	+	0.649367i	0.788422	+	0.615135i	$0.210899\pi$
$359$	−3.99773	+	12.3037i	−0.210992	+	0.649367i	−0.999414	+	0.0342320i	$0.989101\pi$
$360$		0			0
$361$	13.2184	−	9.60375i	0.695706	−	0.505460i
$362$	−13.8853			−0.729795
$363$	4.97035	−	9.81303i	0.260876	−	0.515051i
$364$	9.53521			0.499781
$365$		0			0
$366$	9.15118	+	28.1645i	0.478340	+	1.47218i
$367$	11.2253	−	34.5479i	0.585955	−	1.80338i	−0.00944600	−	0.999955i	$-0.503007\pi$
$367$	11.2253	−	34.5479i	0.585955	−	1.80338i	0.595401	−	0.803429i	$-0.296993\pi$
$368$	41.9306	+	30.4643i	2.18578	+	1.58806i
$369$	−8.88539	−	6.45562i	−0.462555	−	0.336066i
$370$		0			0
$371$	−0.223954	−	0.689259i	−0.0116271	−	0.0357845i
$372$	26.8041	−	19.4743i	1.38973	−	1.00970i
$373$	−18.8902			−0.978099			−0.489050	−	0.872256i	$-0.662656\pi$
$373$	−18.8902			−0.978099			−0.489050	+	0.872256i	$0.662656\pi$
$374$	−30.4424	−	12.5669i	−1.57414	−	0.649818i
$375$		0			0
$376$	−39.4392	+	28.6543i	−2.03392	+	1.47773i
$377$	1.17820	+	3.62613i	0.0606805	+	0.186755i
$378$	−0.409664	+	1.26082i	−0.0210708	+	0.0648493i
$379$	−22.0130	−	15.9934i	−1.13073	−	0.821524i	−0.144929	−	0.989442i	$-0.546296\pi$
$379$	−22.0130	−	15.9934i	−1.13073	−	0.821524i	−0.985801	+	0.167918i	$0.946296\pi$
$380$		0			0
$381$	3.27772	−	10.0878i	0.167922	−	0.516812i
$382$	10.2353	+	31.5011i	0.523685	+	1.61174i
$383$	−8.83238	+	6.41710i	−0.451314	+	0.327899i	−0.790114	−	0.612960i	$-0.789979\pi$
$383$	−8.83238	+	6.41710i	−0.451314	+	0.327899i	0.338801	+	0.940858i	$0.389979\pi$
$384$	−35.2487			−1.79878
$385$		0			0
$386$	−25.7635			−1.31133
$387$	−6.00101	+	4.35999i	−0.305048	+	0.221631i
$388$	−2.34897	−	7.22938i	−0.119251	−	0.367016i
$389$	4.07092	−	12.5290i	0.206404	−	0.635246i	−0.793249	−	0.608898i	$-0.791612\pi$
$389$	4.07092	−	12.5290i	0.206404	−	0.635246i	0.999653	−	0.0263487i	$-0.00838803\pi$
$390$		0			0
$391$	−10.4402	−	7.58528i	−0.527986	−	0.383604i
$392$	−19.5452	+	60.1539i	−0.987182	+	3.03823i
$393$	−5.10008	−	15.6964i	−0.257265	−	0.791780i
$394$	17.4200	−	12.6563i	0.877605	−	0.637617i
$395$		0			0
$396$	−1.39160	+	17.9575i	−0.0699307	+	0.902400i
$397$	35.1144			1.76234			0.881170	−	0.472800i	$-0.156757\pi$
$397$	35.1144			1.76234			0.881170	+	0.472800i	$0.156757\pi$
$398$	−5.74383	+	4.17314i	−0.287912	+	0.209181i
$399$	0.245159	+	0.754522i	0.0122733	+	0.0377733i
$400$		0			0
$401$	−14.9760	−	10.8807i	−0.747863	−	0.543355i	0.147300	−	0.989092i	$-0.452942\pi$
$401$	−14.9760	−	10.8807i	−0.747863	−	0.543355i	−0.895164	+	0.445737i	$0.852942\pi$
$402$	−0.953832	−	0.692999i	−0.0475728	−	0.0345637i
$403$	6.80648	−	20.9482i	0.339055	−	1.04350i
$404$	−0.190009	−	0.584789i	−0.00945332	−	0.0290943i
$405$		0			0
$406$	1.40002			0.0694820
$407$	18.4790	−	21.6887i	0.915968	−	1.07507i
$408$	34.0664			1.68654
$409$	−8.87599	+	6.44878i	−0.438889	+	0.318872i	−0.785193	−	0.619251i	$-0.787437\pi$
$409$	−8.87599	+	6.44878i	−0.438889	+	0.318872i	0.346304	+	0.938122i	$0.387437\pi$
$410$		0			0
$411$	1.88042	−	5.78733i	0.0927541	−	0.285468i
$412$	−31.8452	−	23.1369i	−1.56890	−	1.13987i
$413$	3.13816	+	2.28000i	0.154419	+	0.112192i
$414$	−2.98407	+	9.18402i	−0.146659	+	0.451370i
$415$		0			0
$416$	−61.8582	+	44.9426i	−3.03285	+	2.20349i
$417$	17.3522			0.849741
$418$	7.72106	+	12.5657i	0.377650	+	0.614611i
$419$	−22.8017			−1.11394			−0.556969	−	0.830533i	$-0.688036\pi$
$419$	−22.8017			−1.11394			−0.556969	+	0.830533i	$0.688036\pi$
$420$		0			0
$421$	2.97363	+	9.15188i	0.144926	+	0.446035i	0.997001	−	0.0773831i	$-0.0246564\pi$
$421$	2.97363	+	9.15188i	0.144926	+	0.446035i	−0.852076	+	0.523419i	$0.824656\pi$
$422$	−8.71282	+	26.8153i	−0.424134	+	1.30535i
$423$	−4.21736	−	3.06409i	−0.205055	−	0.148981i
$424$	11.2743	+	8.19124i	0.547527	+	0.397802i
$425$		0			0
$426$	−5.06528	−	15.5893i	−0.245414	−	0.755306i
$427$	4.27437	−	3.10551i	0.206851	−	0.150286i
$428$	47.0227			2.27293
$429$	6.26871	+	10.2021i	0.302656	+	0.492562i
$430$		0			0
$431$	2.88729	−	2.09774i	0.139076	−	0.101044i	−0.516072	−	0.856545i	$-0.672606\pi$
$431$	2.88729	−	2.09774i	0.139076	−	0.101044i	0.655148	+	0.755501i	$0.272606\pi$
$432$	−4.52108	−	13.9145i	−0.217521	−	0.669459i
$433$	1.81651	−	5.59065i	0.0872959	−	0.268669i	−0.897874	−	0.440254i	$-0.854889\pi$
$433$	1.81651	−	5.59065i	0.0872959	−	0.268669i	0.985169	+	0.171584i	$0.0548886\pi$
$434$	−6.54328	−	4.75397i	−0.314088	−	0.228198i
$435$		0			0
$436$	7.41030	−	22.8066i	0.354889	−	1.09224i
$437$	1.78578	+	5.49608i	0.0854256	+	0.262913i
$438$	−2.56726	+	1.86522i	−0.122668	+	0.0891238i
$439$	2.88592			0.137737			0.0688686	−	0.997626i	$-0.478061\pi$
$439$	2.88592			0.137737			0.0688686	+	0.997626i	$0.478061\pi$
$440$		0			0
$441$	−6.76348			−0.322071
$442$	29.0040	−	21.0726i	1.37958	−	1.00232i
$443$	8.62637	+	26.5492i	0.409851	+	1.26139i	0.916776	+	0.399402i	$0.130782\pi$
$443$	8.62637	+	26.5492i	0.409851	+	1.26139i	−0.506925	+	0.861990i	$0.669218\pi$
$444$	−14.4172	+	44.3716i	−0.684210	+	2.10578i
$445$		0			0
$446$	31.7302	+	23.0533i	1.50247	+	1.09161i
$447$	−6.14492	+	18.9121i	−0.290645	+	0.894513i
$448$	4.27852	+	13.1679i	0.202141	+	0.622126i
$449$	−15.4125	+	11.1978i	−0.727359	+	0.528457i	−0.888727	−	0.458437i	$-0.848409\pi$
$449$	−15.4125	+	11.1978i	−0.727359	+	0.528457i	0.161368	+	0.986894i	$0.448409\pi$
$450$		0			0
$451$	−2.81439	+	36.3174i	−0.132524	+	1.71012i
$452$	99.7320			4.69100
$453$	−0.0514133	+	0.0373540i	−0.00241561	+	0.00175504i
$454$	1.19988	+	3.69286i	0.0563133	+	0.173315i
$455$		0			0
$456$	−12.3418	−	8.96684i	−0.577957	−	0.419911i
$457$	−17.1709	−	12.4754i	−0.803220	−	0.583573i	0.108637	−	0.994081i	$-0.465351\pi$
$457$	−17.1709	−	12.4754i	−0.803220	−	0.583573i	−0.911857	+	0.410508i	$0.865351\pi$
$458$	−4.26162	+	13.1159i	−0.199133	+	0.612867i
$459$	1.12570	+	3.46454i	0.0525431	+	0.161711i
$460$		0			0
$461$	20.7585			0.966818			0.483409	−	0.875395i	$-0.339398\pi$
$461$	20.7585			0.966818			0.483409	+	0.875395i	$0.339398\pi$
$462$	4.27413	−	1.03155i	0.198850	−	0.0479923i
$463$	−13.4393			−0.624575			−0.312288	−	0.949988i	$-0.601095\pi$
$463$	−13.4393			−0.624575			−0.312288	+	0.949988i	$0.601095\pi$
$464$	−12.4999	+	9.08173i	−0.580295	+	0.421609i
$465$		0			0
$466$	17.6135	−	54.2089i	0.815931	−	2.51118i
$467$	28.2761	+	20.5438i	1.30846	+	0.950653i	1.00000		0.000583525i	$-0.000185742\pi$
$467$	28.2761	+	20.5438i	1.30846	+	0.950653i	0.308462	+	0.951237i	$0.400186\pi$
$468$	−15.8619	−	11.5244i	−0.733218	−	0.532714i
$469$	−0.0650004	+	0.200051i	−0.00300144	+	0.00923748i
$470$		0			0
$471$	0.788485	−	0.572868i	0.0363315	−	0.0263964i
$472$	−74.5885			−3.43322
$473$	22.7402	+	9.38732i	1.04559	+	0.431630i
$474$	12.0620			0.554027
$475$		0			0
$476$	−2.97307	−	9.15016i	−0.136270	−	0.419397i
$477$	−0.460496	+	1.41726i	−0.0210847	+	0.0648919i
$478$	40.8840	+	29.7040i	1.86999	+	1.35863i
$479$	16.1380	+	11.7250i	0.737366	+	0.535727i	0.891885	−	0.452262i	$-0.149383\pi$
$479$	16.1380	+	11.7250i	0.737366	+	0.535727i	−0.154519	+	0.987990i	$0.549383\pi$
$480$		0			0
$481$	9.58468	+	29.4986i	0.437024	+	1.34502i
$482$	47.5941	−	34.5792i	2.16785	−	1.57504i
$483$	1.72284			0.0783921
$484$	53.1608	−	27.2477i	2.41640	−	1.23853i
$485$		0			0
$486$	2.20531	−	1.60225i	0.100035	−	0.0726798i
$487$	−2.08937	−	6.43042i	−0.0946784	−	0.291390i	0.892491	−	0.451065i	$-0.148956\pi$
$487$	−2.08937	−	6.43042i	−0.0946784	−	0.291390i	−0.987170	+	0.159674i	$0.948956\pi$
$488$	−31.3944	+	96.6219i	−1.42116	+	4.37387i
$489$	−14.3303	−	10.4116i	−0.648041	−	0.470829i
$490$		0			0
$491$	−1.04109	+	3.20413i	−0.0469836	+	0.144601i	−0.971796	−	0.235822i	$-0.924222\pi$
$491$	−1.04109	+	3.20413i	−0.0469836	+	0.144601i	0.924813	+	0.380423i	$0.124222\pi$
$492$	−18.4311	−	56.7252i	−0.830940	−	2.55737i
$493$	3.11234	−	2.26125i	0.140173	−	0.101841i
$494$	−16.0544			−0.722321
$495$		0			0
$496$	89.2591			4.00785
$497$	−2.36591	+	1.71893i	−0.106126	+	0.0771047i
$498$	−2.67642	−	8.23717i	−0.119933	−	0.369117i
$499$	5.43299	−	16.7210i	0.243214	−	0.748536i	−0.752711	−	0.658351i	$-0.771254\pi$
$499$	5.43299	−	16.7210i	0.243214	−	0.748536i	0.995925	−	0.0901847i	$-0.0287457\pi$
$500$		0			0
$501$	−7.90573	−	5.74385i	−0.353202	−	0.256616i
$502$	0.529038	−	1.62821i	0.0236121	−	0.0726706i
$503$	−10.2313	−	31.4887i	−0.456191	−	1.40401i	−0.869732	−	0.493525i	$-0.835708\pi$
$503$	−10.2313	−	31.4887i	−0.456191	−	1.40401i	0.413541	−	0.910486i	$-0.364292\pi$
$504$	−3.67940	+	2.67324i	−0.163894	+	0.119076i
$505$		0			0
$506$	31.1336	−	7.51404i	1.38406	−	0.334040i
$507$	−0.0345228			−0.00153321
$508$	46.6012	−	33.8578i	2.06759	−	1.50219i
$509$	−9.18163	−	28.2582i	−0.406969	−	1.25252i	−0.919240	−	0.393697i	$-0.871196\pi$
$509$	−9.18163	−	28.2582i	−0.406969	−	1.25252i	0.512271	−	0.858824i	$-0.328804\pi$
$510$		0			0
$511$	0.458025	+	0.332775i	0.0202618	+	0.0147211i
$512$	−29.2960	−	21.2848i	−1.29471	−	0.940663i
$513$	0.504099	−	1.55146i	0.0222565	−	0.0684985i
$514$	−2.87195	−	8.83895i	−0.126676	−	0.389869i
$515$		0			0
$516$	−40.2826			−1.77334
$517$	−1.33582	+	17.2377i	−0.0587493	+	0.758113i
$518$	11.3892			0.500412
$519$	6.61910	−	4.80906i	0.290546	−	0.211094i
$520$		0			0
$521$	10.3127	−	31.7394i	0.451810	−	1.39053i	−0.423031	−	0.906115i	$-0.639034\pi$
$521$	10.3127	−	31.7394i	0.451810	−	1.39053i	0.874840	−	0.484412i	$-0.160966\pi$
$522$	−2.32895	−	1.69208i	−0.101935	−	0.0740605i
$523$	1.36785	+	0.993798i	0.0598117	+	0.0434557i	0.617289	−	0.786736i	$-0.288231\pi$
$523$	1.36785	+	0.993798i	0.0598117	+	0.0434557i	−0.557478	+	0.830192i	$0.688231\pi$
$524$	27.6967	−	85.2416i	1.20993	−	3.72380i
$525$		0			0
$526$	−31.9318	+	23.1998i	−1.39229	+	1.01156i
$527$	−22.2245			−0.968115
$528$	−31.4695	+	36.9357i	−1.36953	+	1.60742i
$529$	−10.4505			−0.454369
$530$		0			0
$531$	−2.46472	−	7.58562i	−0.106960	−	0.329188i
$532$	−1.33137	+	4.09753i	−0.0577222	+	0.177651i
$533$	−32.0793	−	23.3069i	−1.38951	−	1.00954i
$534$	3.05114	+	2.21678i	0.132036	+	0.0959295i
$535$		0			0
$536$	−1.24989	−	3.84676i	−0.0539869	−	0.166155i
$537$	0.433599	−	0.315028i	0.0187112	−	0.0135945i
$538$	−81.4195			−3.51024
$539$	11.7436	+	19.1123i	0.505833	+	0.823224i
$540$		0			0
$541$	35.8405	−	26.0396i	1.54090	−	1.11953i	0.591135	−	0.806572i	$-0.298680\pi$
$541$	35.8405	−	26.0396i	1.54090	−	1.11953i	0.949767	−	0.312959i	$-0.101320\pi$
$542$	−1.26461	−	3.89207i	−0.0543196	−	0.167179i
$543$	1.57407	−	4.84450i	0.0675499	−	0.207897i
$544$	62.4150	+	45.3472i	2.67602	+	1.94424i
$545$		0			0
$546$	−1.47902	+	4.55197i	−0.0632964	+	0.194806i
$547$	−11.5627	−	35.5864i	−0.494386	−	1.52156i	−0.817912	−	0.575344i	$-0.804868\pi$
$547$	−11.5627	−	35.5864i	−0.494386	−	1.52156i	0.323526	−	0.946219i	$-0.395132\pi$
$548$	26.7350	−	19.4241i	1.14206	−	0.829757i
$549$	−10.8638			−0.463656
$550$		0			0
$551$	−1.72275			−0.0733918
$552$	−26.8015	+	19.4724i	−1.14075	+	0.828800i
$553$	−0.665001	−	2.04666i	−0.0282787	−	0.0870329i
$554$	5.32902	−	16.4010i	0.226408	−	0.696813i
$555$		0			0
$556$	76.2365	+	55.3891i	3.23315	+	2.34902i
$557$	−1.86934	+	5.75323i	−0.0792064	+	0.243772i	−0.982817	−	0.184583i	$-0.940907\pi$
$557$	−1.86934	+	5.75323i	−0.0792064	+	0.243772i	0.903611	+	0.428355i	$0.140907\pi$
$558$	5.13911	+	15.8166i	0.217556	+	0.669568i
$559$	−21.6656	+	15.7410i	−0.916359	+	0.665774i
$560$		0			0
$561$	7.83554	−	9.19657i	0.330817	−	0.388279i
$562$	35.8818			1.51358
$563$	8.64183	−	6.27866i	0.364210	−	0.264614i	−0.390596	−	0.920562i	$-0.627731\pi$
$563$	8.64183	−	6.27866i	0.364210	−	0.264614i	0.754806	+	0.655948i	$0.227731\pi$
$564$	−8.74815	−	26.9240i	−0.368364	−	1.13371i
$565$		0			0
$566$	−19.1473	−	13.9113i	−0.804821	−	0.584737i
$567$	−0.393450	−	0.285858i	−0.0165234	−	0.0120049i
$568$	17.3771	−	53.4813i	0.729128	−	2.24403i
$569$	8.28385	+	25.4951i	0.347277	+	1.06881i	0.960353	+	0.278786i	$0.0899319\pi$
$569$	8.28385	+	25.4951i	0.347277	+	1.06881i	−0.613076	+	0.790024i	$0.710068\pi$
$570$		0			0
$571$	9.73293			0.407310			0.203655	−	0.979043i	$-0.434718\pi$
$571$	9.73293			0.407310			0.203655	+	0.979043i	$0.434718\pi$
$572$	−5.02416	+	64.8327i	−0.210071	+	2.71079i
$573$	−12.1508			−0.507608
$574$	−11.7794	+	8.55821i	−0.491661	+	0.357213i
$575$		0			0
$576$	8.79754	−	27.0760i	0.366564	−	1.12817i
$577$	−1.02947	−	0.747953i	−0.0428574	−	0.0311377i	0.566150	−	0.824302i	$-0.308432\pi$
$577$	−1.02947	−	0.747953i	−0.0428574	−	0.0311377i	−0.609008	+	0.793164i	$0.708432\pi$
$578$	8.22530	+	5.97603i	0.342127	+	0.248570i
$579$	2.92062	−	8.98874i	0.121377	−	0.373559i
$580$		0			0
$581$	−1.25011	+	0.908259i	−0.0518634	+	0.0376809i
$582$	3.81555			0.158160
$583$	4.80448	−	1.15955i	0.198981	−	0.0480238i
$584$	−10.8865			−0.450485
$585$		0			0
$586$	−16.6272	−	51.1732i	−0.686862	−	2.11394i
$587$	4.64365	−	14.2917i	0.191664	−	0.589881i	−0.808335	−	0.588722i	$-0.799631\pi$
$587$	4.64365	−	14.2917i	0.191664	−	0.589881i	0.999999	−	0.00115896i	$-0.000368908\pi$
$588$	−29.7152	−	21.5894i	−1.22543	−	0.890330i
$589$	8.05163	+	5.84985i	0.331761	+	0.241039i
$590$		0			0
$591$	2.44095	+	7.51247i	0.100407	+	0.309022i
$592$	−101.687	+	73.8799i	−4.17931	+	3.03644i
$593$	−11.4115			−0.468615			−0.234307	−	0.972163i	$-0.575282\pi$
$593$	−11.4115			−0.468615			−0.234307	+	0.972163i	$0.575282\pi$
$594$	−8.35680	−	3.44976i	−0.342884	−	0.141545i
$595$		0			0
$596$	−87.3659	+	63.4751i	−3.57865	+	2.60004i
$597$	−0.804848	−	2.47707i	−0.0329402	−	0.101380i
$598$	−10.7735	+	33.1574i	−0.440561	+	1.35591i
$599$	10.7661	+	7.82202i	0.439890	+	0.319599i	0.785591	−	0.618746i	$-0.212359\pi$
$599$	10.7661	+	7.82202i	0.439890	+	0.319599i	−0.345701	+	0.938345i	$0.612359\pi$
$600$		0			0
$601$	−11.0156	+	33.9026i	−0.449337	+	1.38292i	0.428319	+	0.903627i	$0.359106\pi$
$601$	−11.0156	+	33.9026i	−0.449337	+	1.38292i	−0.877657	+	0.479290i	$0.840894\pi$
$602$	3.03874	+	9.35229i	0.123850	+	0.381171i
$603$	0.349912	−	0.254226i	0.0142495	−	0.0103529i
$604$	−0.345119			−0.0140427
$605$		0			0
$606$	0.308642			0.0125377
$607$	−24.2966	+	17.6525i	−0.986167	+	0.716492i	−0.959078	−	0.283141i	$-0.908624\pi$
$607$	−24.2966	+	17.6525i	−0.986167	+	0.716492i	−0.0270884	+	0.999633i	$0.508624\pi$
$608$	−10.6760	−	32.8573i	−0.432968	−	1.33254i
$609$	−0.158710	+	0.488460i	−0.00643126	+	0.0197934i
$610$		0			0
$611$	−15.2261	−	11.0624i	−0.615982	−	0.447537i
$612$	−6.11325	+	18.8147i	−0.247114	+	0.760537i
$613$	12.5953	+	38.7644i	0.508720	+	1.56568i	0.794426	+	0.607361i	$0.207772\pi$
$613$	12.5953	+	38.7644i	0.508720	+	1.56568i	−0.285706	+	0.958317i	$0.592228\pi$
$614$	28.5552	−	20.7466i	1.15240	−	0.837264i
$615$		0			0
$616$	13.9427	+	5.75566i	0.561767	+	0.231902i
$617$	−38.2194			−1.53865			−0.769327	−	0.638855i	$-0.779408\pi$
$617$	−38.2194			−1.53865			−0.769327	+	0.638855i	$0.779408\pi$
$618$	15.9848	−	11.6136i	0.643003	−	0.467169i
$619$	−4.08228	−	12.5640i	−0.164081	−	0.504988i	0.834887	−	0.550422i	$-0.185533\pi$
$619$	−4.08228	−	12.5640i	−0.164081	−	0.504988i	−0.998967	+	0.0454334i	$0.985533\pi$
$620$		0			0
$621$	−2.86597	−	2.08225i	−0.115007	−	0.0835577i
$622$	62.8488	+	45.6623i	2.52001	+	1.83089i
$623$	0.207924	−	0.639926i	0.00833032	−	0.0256381i
$624$	−16.3226	−	50.2358i	−0.653428	−	2.01104i
$625$		0			0
$626$	−18.5105			−0.739828
$627$	−5.25939	+	1.26935i	−0.210040	+	0.0506928i
$628$	5.29281			0.211206
$629$	25.3189	−	18.3953i	1.00953	−	0.733467i
$630$		0			0
$631$	−12.8518	+	39.5539i	−0.511624	+	1.57462i	0.277719	+	0.960662i	$0.410422\pi$
$631$	−12.8518	+	39.5539i	−0.511624	+	1.57462i	−0.789342	+	0.613953i	$0.789578\pi$
$632$	33.4775	+	24.3228i	1.33166	+	0.967509i
$633$	−8.36799	−	6.07970i	−0.332598	−	0.241646i
$634$	25.7959	−	79.3915i	1.02448	−	3.15304i
$635$		0			0
$636$	−6.54714	+	4.75678i	−0.259611	+	0.188619i
$637$	−24.4184			−0.967494
$638$	−0.737680	+	9.51917i	−0.0292050	+	0.376868i
$639$	6.01324			0.237880
$640$		0			0
$641$	−10.5846	−	32.5761i	−0.418067	−	1.28668i	−0.909478	−	0.415751i	$-0.863519\pi$
$641$	−10.5846	−	32.5761i	−0.418067	−	1.28668i	0.491411	−	0.870928i	$-0.336481\pi$
$642$	−7.29378	+	22.4480i	−0.287863	+	0.885950i
$643$	31.8092	+	23.1107i	1.25443	+	0.911398i	0.998470	−	0.0552896i	$-0.0176082\pi$
$643$	31.8092	+	23.1107i	1.25443	+	0.911398i	0.255961	+	0.966687i	$0.417608\pi$
$644$	7.56927	+	5.49939i	0.298271	+	0.216706i
$645$		0			0
$646$	5.00574	+	15.4061i	0.196948	+	0.606144i
$647$	11.8489	−	8.60874i	0.465829	−	0.338444i	−0.329985	−	0.943986i	$-0.607044\pi$
$647$	11.8489	−	8.60874i	0.465829	−	0.338444i	0.795813	+	0.605542i	$0.207044\pi$
$648$	9.35163			0.367367
$649$	−17.1559	+	20.1359i	−0.673429	+	0.790403i
$650$		0			0
$651$	2.40039	−	1.74399i	0.0940789	−	0.0683523i
$652$	−29.7257	−	91.4863i	−1.16415	−	3.58288i
$653$	10.9489	−	33.6971i	0.428462	−	1.31867i	−0.471178	−	0.882038i	$-0.656171\pi$
$653$	10.9489	−	33.6971i	0.428462	−	1.31867i	0.899640	−	0.436632i	$-0.143829\pi$
$654$	9.73808	+	7.07513i	0.380789	+	0.276660i
$655$		0			0
$656$	49.6548	−	152.822i	1.93869	−	5.96669i
$657$	−0.359734	−	1.10715i	−0.0140346	−	0.0431940i
$658$	−5.59096	+	4.06207i	−0.217958	+	0.158356i
$659$	−39.2826			−1.53023			−0.765116	−	0.643893i	$-0.777318\pi$
$659$	−39.2826			−1.53023			−0.765116	+	0.643893i	$0.777318\pi$
$660$		0			0
$661$	−29.7431			−1.15687			−0.578436	−	0.815728i	$-0.696337\pi$
$661$	−29.7431			−1.15687			−0.578436	+	0.815728i	$0.696337\pi$
$662$	77.0828	−	56.0039i	2.99591	−	2.17665i
$663$	4.06415	+	12.5082i	0.157838	+	0.485776i
$664$	9.18182	−	28.2587i	0.356324	−	1.09665i
$665$		0			0
$666$	−18.9460	−	13.7651i	−0.734144	−	0.533387i
$667$	−1.15607	+	3.55803i	−0.0447634	+	0.137768i
$668$	−16.3990	−	50.4709i	−0.634496	−	1.95278i
$669$	−11.6402	+	8.45708i	−0.450035	+	0.326970i
$670$		0			0
$671$	18.8631	+	30.6990i	0.728202	+	1.18512i
$672$	−10.2997			−0.397319
$673$	−36.1148	+	26.2389i	−1.39212	+	1.01144i	−0.396493	+	0.918038i	$0.629773\pi$
$673$	−36.1148	+	26.2389i	−1.39212	+	1.01144i	−0.995629	+	0.0933980i	$0.970227\pi$
$674$	−4.89877	−	15.0769i	−0.188693	−	0.580739i
$675$		0			0
$676$	−0.151675	−	0.110198i	−0.00583366	−	0.00423840i
$677$	−20.9207	−	15.1998i	−0.804049	−	0.584176i	0.108050	−	0.994145i	$-0.465539\pi$
$677$	−20.9207	−	15.1998i	−0.804049	−	0.584176i	−0.912099	+	0.409969i	$0.865539\pi$
$678$	−15.4696	+	47.6106i	−0.594107	+	1.82847i
$679$	−0.210358	−	0.647415i	−0.00807280	−	0.0248455i
$680$		0			0
$681$	−1.42444			−0.0545846
$682$	35.7714	−	41.9848i	1.36976	−	1.60768i
$683$	36.8419			1.40972			0.704858	−	0.709348i	$-0.251011\pi$
$683$	36.8419			1.40972			0.704858	+	0.709348i	$0.251011\pi$
$684$	7.16707	−	5.20718i	0.274040	−	0.199101i
$685$		0			0
$686$	−5.63840	+	17.3532i	−0.215275	+	0.662549i
$687$	−4.09296	−	2.97371i	−0.156156	−	0.113454i
$688$	−87.7978	−	63.7889i	−3.34726	−	2.43193i
$689$	−1.66255	+	5.11679i	−0.0633379	+	0.194934i
$690$		0			0
$691$	32.0604	−	23.2932i	1.21963	−	0.886116i	0.223564	−	0.974689i	$-0.428231\pi$
$691$	32.0604	−	23.2932i	1.21963	−	0.886116i	0.996070	+	0.0885737i	$0.0282309\pi$
$692$	44.4316			1.68904
$693$	−0.124623	+	1.60816i	−0.00473403	+	0.0610888i
$694$	75.2686			2.85716
$695$		0			0
$696$	−3.05183	−	9.39255i	−0.115679	−	0.356024i
$697$	−12.3635	+	38.0509i	−0.468300	+	1.44128i
$698$	−28.4854	−	20.6959i	−1.07819	−	0.783351i
$699$	16.9164	+	12.2905i	0.639838	+	0.464870i
$700$		0			0
$701$	6.72817	+	20.7072i	0.254119	+	0.782099i	0.994002	+	0.109363i	$0.0348810\pi$
$701$	6.72817	+	20.7072i	0.254119	+	0.782099i	−0.739883	+	0.672736i	$0.765119\pi$
$702$	7.96193	−	5.78468i	0.300504	−	0.218329i
$703$	−14.0146			−0.528571
$704$	−91.7870	+	22.1527i	−3.45935	+	0.834910i
$705$		0			0
$706$	23.5120	−	17.0824i	0.884884	−	0.642906i
$707$	−0.0170160	−	0.0523698i	−0.000639952	−	0.00196957i
$708$	13.3850	−	41.1947i	0.503038	−	1.54819i
$709$	30.3030	+	22.0164i	1.13805	+	0.826844i	0.986847	−	0.161658i	$-0.0516840\pi$
$709$	30.3030	+	22.0164i	1.13805	+	0.826844i	0.151207	+	0.988502i	$0.451684\pi$
$710$		0			0
$711$	−1.36738	+	4.20837i	−0.0512808	+	0.157826i
$712$	3.99817	+	12.3051i	0.149838	+	0.461153i
$713$	17.4849	−	12.7035i	0.654816	−	0.475751i
$714$	4.82930			0.180732
$715$		0			0
$716$	2.91059			0.108774
$717$	−14.9983	+	10.8969i	−0.560120	+	0.406951i
$718$	−10.8975	−	33.5390i	−0.406691	−	1.25167i
$719$	4.02749	−	12.3953i	0.150200	−	0.462268i	−0.847443	−	0.530886i	$-0.821859\pi$
$719$	4.02749	−	12.3953i	0.150200	−	0.462268i	0.997643	+	0.0686183i	$0.0218591\pi$
$720$		0			0
$721$	−2.85185	−	2.07199i	−0.106208	−	0.0771649i
$722$	−13.7631	+	42.3586i	−0.512211	+	1.57642i
$723$	6.66907	+	20.5253i	0.248025	+	0.763344i
$724$	22.3795	−	16.2597i	0.831728	−	0.604286i
$725$		0			0
$726$	4.76178	+	29.6046i	0.176726	+	1.09873i
$727$	−50.8515			−1.88598			−0.942989	−	0.332824i	$-0.891998\pi$
$727$	−50.8515			−1.88598			−0.942989	+	0.332824i	$0.891998\pi$
$728$	−13.2839	+	9.65130i	−0.492333	+	0.357701i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	21.8607	+	15.8827i	0.808546	+	0.587443i
$732$	−47.7299	−	34.6778i	−1.76415	−	1.28173i
$733$	4.57209	−	14.0715i	0.168874	−	0.519741i	−0.830427	−	0.557128i	$-0.811903\pi$
$733$	4.57209	−	14.0715i	0.168874	−	0.519741i	0.999301	+	0.0373868i	$0.0119034\pi$
$734$	30.5992	+	94.1747i	1.12944	+	3.47605i
$735$		0			0
$736$	−75.0249			−2.76546
$737$	−1.32595	−	0.547365i	−0.0488421	−	0.0201624i
$738$	29.9386			1.10206
$739$	2.51477	−	1.82709i	0.0925074	−	0.0672106i	−0.540570	−	0.841299i	$-0.681791\pi$
$739$	2.51477	−	1.82709i	0.0925074	−	0.0672106i	0.633078	+	0.774088i	$0.281791\pi$
$740$		0			0
$741$	1.81997	−	5.60128i	0.0668581	−	0.205768i
$742$	1.59826	+	1.16120i	0.0586738	+	0.0426290i
$743$	−4.75035	−	3.45133i	−0.174273	−	0.126617i	0.497229	−	0.867619i	$-0.334351\pi$
$743$	−4.75035	−	3.45133i	−0.174273	−	0.126617i	−0.671503	+	0.741002i	$0.734351\pi$
$744$	−17.6304	+	54.2608i	−0.646362	+	1.98930i
$745$		0			0
$746$	41.6589	−	30.2670i	1.52524	−	1.10815i
$747$	3.17731			0.116252
$748$	63.7811	−	15.3935i	2.33207	−	0.562842i
$749$	4.21104			0.153868
$750$		0			0
$751$	5.42674	+	16.7018i	0.198025	+	0.609457i	0.999928	+	0.0120034i	$0.00382089\pi$
$751$	5.42674	+	16.7018i	0.198025	+	0.609457i	−0.801903	+	0.597454i	$0.796179\pi$
$752$	23.5681	−	72.5353i	0.859442	−	2.64509i
$753$	0.508100	+	0.369156i	0.0185162	+	0.0134528i
$754$	−8.40830	−	6.10899i	−0.306212	−	0.222476i
$755$		0			0
$756$	−0.816141	−	2.51182i	−0.0296828	−	0.0913541i
$757$	9.67574	−	7.02984i	0.351671	−	0.255504i	−0.397899	−	0.917429i	$-0.630261\pi$
$757$	9.67574	−	7.02984i	0.351671	−	0.255504i	0.749570	+	0.661926i	$0.230261\pi$
$758$	74.1710			2.69401
$759$	−0.907775	+	11.7141i	−0.0329502	+	0.425196i
$760$		0			0
$761$	12.8097	−	9.30679i	0.464351	−	0.337371i	−0.330885	−	0.943671i	$-0.607347\pi$
$761$	12.8097	−	9.30679i	0.464351	−	0.337371i	0.795236	+	0.606300i	$0.207347\pi$
$762$	8.93479	+	27.4984i	0.323673	+	0.996164i
$763$	0.663617	−	2.04240i	0.0240245	−	0.0739399i
$764$	−53.3844	−	38.7860i	−1.93138	−	1.40323i
$765$		0			0
$766$	9.19635	−	28.3035i	0.332278	−	1.02265i
$767$	−8.89845	−	27.3866i	−0.321305	−	0.988874i
$768$	31.6699	−	23.0095i	1.14279	−	0.830284i
$769$	36.6876			1.32299			0.661494	−	0.749950i	$-0.269923\pi$
$769$	36.6876			1.32299			0.661494	+	0.749950i	$0.269923\pi$
$770$		0			0
$771$	3.40943			0.122787
$772$	41.5242	−	30.1691i	1.49449	−	1.08581i
$773$	−0.515861	−	1.58766i	−0.0185542	−	0.0571040i	0.941351	−	0.337430i	$-0.109558\pi$
$773$	−0.515861	−	1.58766i	−0.0185542	−	0.0571040i	−0.959905	+	0.280326i	$0.909558\pi$
$774$	6.24830	−	19.2303i	0.224590	−	0.691218i
$775$		0			0
$776$	10.5898	+	7.69397i	0.380153	+	0.276197i
$777$	−1.29111	+	3.97362i	−0.0463182	+	0.142553i
$778$	11.0970	+	34.1531i	0.397847	+	1.22445i
$779$	14.4947	−	10.5310i	0.519327	−	0.377313i
$780$		0			0
$781$	−10.4409	−	16.9922i	−0.373606	−	0.608030i
$782$	35.1776			1.25795
$783$	0.854373	−	0.620739i	0.0305328	−	0.0221834i
$784$	−30.5782	−	94.1101i	−1.09208	−	3.36108i
$785$		0			0
$786$	36.3970	+	26.4439i	1.29824	+	0.943224i
$787$	28.1087	+	20.4221i	1.00197	+	0.727971i	0.962509	−	0.271251i	$-0.0874372\pi$
$787$	28.1087	+	20.4221i	1.00197	+	0.727971i	0.0394570	+	0.999221i	$0.487437\pi$
$788$	−13.2559	+	40.7975i	−0.472222	+	1.45335i
$789$	−4.47441	−	13.7708i	−0.159293	−	0.490254i
$790$		0			0
$791$	8.93133			0.317562
$792$	−16.2375	−	26.4259i	−0.576973	−	0.939003i
$793$	−39.2220			−1.39281
$794$	−77.4382	+	56.2622i	−2.74818	+	1.99667i
$795$		0			0
$796$	4.37083	−	13.4520i	0.154920	−	0.476795i
$797$	24.5424	+	17.8311i	0.869337	+	0.631611i	0.930409	−	0.366523i	$-0.119452\pi$
$797$	24.5424	+	17.8311i	0.869337	+	0.631611i	−0.0610717	+	0.998133i	$0.519452\pi$
$798$	−1.74959	−	1.27115i	−0.0619348	−	0.0449982i
$799$	−5.86820	+	18.0605i	−0.207602	+	0.638933i
$800$		0			0
$801$	−1.11931	+	0.813223i	−0.0395487	+	0.0287338i
$802$	50.4603			1.78181
$803$	−2.50397	+	2.93891i	−0.0883632	+	0.103712i
$804$	2.34883			0.0828369
$805$		0			0
$806$	18.5539	+	57.1031i	0.653534	+	2.01137i
$807$	9.22992	−	28.4068i	0.324909	−	0.999966i
$808$	0.856618	+	0.622370i	0.0301357	+	0.0218949i
$809$	4.44684	+	3.23082i	0.156343	+	0.113589i	0.663206	−	0.748437i	$-0.269195\pi$
$809$	4.44684	+	3.23082i	0.156343	+	0.113589i	−0.506864	+	0.862026i	$0.669195\pi$
$810$		0			0
$811$	5.09871	+	15.6922i	0.179040	+	0.551028i	0.999795	−	0.0202524i	$-0.00644697\pi$
$811$	5.09871	+	15.6922i	0.179040	+	0.551028i	−0.820755	+	0.571280i	$0.806447\pi$
$812$	−2.25647	+	1.63942i	−0.0791867	+	0.0575325i
$813$	1.50128			0.0526521
$814$	−6.00103	+	77.4385i	−0.210336	+	2.71422i
$815$		0			0
$816$	−43.1178	+	31.3269i	−1.50943	+	1.09666i
$817$	−3.73923	−	11.5082i	−0.130819	−	0.402620i
$818$	9.24175	−	28.4432i	0.323130	−	0.994493i
$819$	−1.42049	−	1.03204i	−0.0496359	−	0.0360626i
$820$		0			0
$821$	−14.6733	+	45.1598i	−0.512102	+	1.57609i	0.276392	+	0.961045i	$0.410861\pi$
$821$	−14.6733	+	45.1598i	−0.512102	+	1.57609i	−0.788494	+	0.615042i	$0.789139\pi$
$822$	5.12587	+	15.7758i	0.178785	+	0.550244i
$823$	−22.3129	+	16.2113i	−0.777780	+	0.565090i	−0.904312	−	0.426872i	$-0.859615\pi$
$823$	−22.3129	+	16.2113i	−0.777780	+	0.565090i	0.126532	+	0.991963i	$0.459615\pi$
$824$	67.7835			2.36135
$825$		0			0
$826$	−10.5738			−0.367908
$827$	−23.3764	+	16.9839i	−0.812875	+	0.590589i	−0.914663	−	0.404218i	$-0.867544\pi$
$827$	−23.3764	+	16.9839i	−0.812875	+	0.590589i	0.101787	+	0.994806i	$0.467544\pi$
$828$	−5.94492	−	18.2966i	−0.206600	−	0.635851i
$829$	−1.01777	+	3.13237i	−0.0353485	+	0.108792i	−0.967174	−	0.254115i	$-0.918216\pi$
$829$	−1.01777	+	3.13237i	−0.0353485	+	0.108792i	0.931825	+	0.362907i	$0.118216\pi$
$830$		0			0
$831$	5.11811	+	3.71852i	0.177545	+	0.128994i
$832$	31.7621	−	97.7536i	1.10115	−	3.38900i
$833$	7.61363	+	23.4324i	0.263797	+	0.811883i
$834$	−38.2671	+	27.8027i	−1.32508	+	0.962727i
$835$		0			0
$836$	−27.1588	−	11.2114i	−0.939308	−	0.387754i
$837$	−6.10088			−0.210877
$838$	50.2850	−	36.5342i	1.73707	−	1.26205i
$839$	−2.00175	−	6.16077i	−0.0691082	−	0.212693i	0.910538	−	0.413426i	$-0.135668\pi$
$839$	−2.00175	−	6.16077i	−0.0691082	−	0.212693i	−0.979646	+	0.200732i	$0.935668\pi$
$840$		0			0
$841$	22.5592	+	16.3902i	0.777904	+	0.565180i
$842$	−21.2214	−	15.4183i	−0.731339	−	0.531349i
$843$	−4.06766	+	12.5190i	−0.140098	+	0.431176i
$844$	−17.3579	−	53.4220i	−0.597483	−	1.83886i
$845$		0			0
$846$	14.2101			0.488552
$847$	4.76072	−	2.44012i	0.163580	−	0.0838436i
$848$	−21.8024			−0.748696
$849$	7.02416	−	5.10335i	0.241069	−	0.175147i
$850$		0			0
$851$	−9.40467	+	28.9446i	−0.322388	+	0.992208i
$852$	26.4190	+	19.1945i	0.905100	+	0.657594i
$853$	35.7108	+	25.9454i	1.22271	+	0.888353i	0.996322	−	0.0856837i	$-0.0273074\pi$
$853$	35.7108	+	25.9454i	1.22271	+	0.888353i	0.226391	+	0.974037i	$0.427307\pi$
$854$	−4.45051	+	13.6973i	−0.152293	+	0.468710i
$855$		0			0
$856$	−65.5092	+	47.5952i	−2.23906	+	1.62677i
$857$	16.2984			0.556744			0.278372	−	0.960473i	$-0.410205\pi$
$857$	16.2984			0.556744			0.278372	+	0.960473i	$0.410205\pi$
$858$	−30.1709	−	12.4548i	−1.03002	−	0.425199i
$859$	−41.9250			−1.43046			−0.715231	−	0.698888i	$-0.753679\pi$
$859$	−41.9250			−1.43046			−0.715231	+	0.698888i	$0.753679\pi$
$860$		0			0
$861$	−1.65057	−	5.07993i	−0.0562512	−	0.173124i
$862$	−3.00627	+	9.25234i	−0.102394	+	0.315136i
$863$	−21.9612	−	15.9557i	−0.747567	−	0.543139i	0.147505	−	0.989061i	$-0.452876\pi$
$863$	−21.9612	−	15.9557i	−0.747567	−	0.543139i	−0.895072	+	0.445922i	$0.852876\pi$
$864$	17.1336	+	12.4483i	0.582898	+	0.423501i
$865$		0			0
$866$	4.95166	+	15.2396i	0.168264	+	0.517864i
$867$	−3.01744	+	2.19230i	−0.102478	+	0.0744544i
$868$	16.1130			0.546910
$869$	14.2662	−	3.44314i	0.483949	−	0.116800i
$870$		0			0
$871$	1.26330	−	0.917841i	0.0428053	−	0.0310999i
$872$	12.7606	+	39.2732i	0.432130	+	1.32996i
$873$	−0.432540	+	1.33122i	−0.0146393	+	0.0450550i
$874$	−12.7443	−	9.25930i	−0.431084	−	0.313201i
$875$		0			0
$876$	1.95358	−	6.01252i	0.0660055	−	0.203144i
$877$	7.60649	+	23.4104i	0.256853	+	0.790512i	0.993459	+	0.114190i	$0.0364272\pi$
$877$	7.60649	+	23.4104i	0.256853	+	0.790512i	−0.736606	+	0.676322i	$0.763573\pi$
$878$	−6.36435	+	4.62397i	−0.214786	+	0.156052i
$879$	19.7389			0.665777
$880$		0			0
$881$	−27.3598			−0.921777			−0.460888	−	0.887458i	$-0.652469\pi$
$881$	−27.3598			−0.921777			−0.460888	+	0.887458i	$0.652469\pi$
$882$	14.9156	−	10.8368i	0.502235	−	0.364895i
$883$	−18.2683	−	56.2239i	−0.614776	−	1.89209i	−0.404915	−	0.914354i	$-0.632699\pi$
$883$	−18.2683	−	56.2239i	−0.614776	−	1.89209i	−0.209861	−	0.977731i	$-0.567301\pi$
$884$	−22.0709	+	67.9272i	−0.742324	+	2.28464i
$885$		0			0
$886$	−61.5625	−	44.7278i	−2.06823	−	1.50266i
$887$	1.89608	−	5.83552i	0.0636640	−	0.195938i	−0.914165	−	0.405342i	$-0.867152\pi$
$887$	1.89608	−	5.83552i	0.0636640	−	0.195938i	0.977829	+	0.209404i	$0.0671525\pi$
$888$	−24.8266	−	76.4085i	−0.833127	−	2.56410i
$889$	4.17329	−	3.03207i	0.139968	−	0.101692i
$890$		0			0
$891$	2.15095	−	2.52456i	0.0720594	−	0.0845761i
$892$	−78.1362			−2.61619
$893$	6.87977	−	4.99845i	0.230223	−	0.167267i
$894$	−16.7506	−	51.5529i	−0.560222	−	1.72419i
$895$		0			0
$896$	−13.8686	−	10.0761i	−0.463317	−	0.336620i
$897$	−10.3471	−	7.51761i	−0.345480	−	0.251006i
$898$	16.0476	−	49.3894i	0.535515	−	1.64814i
$899$	1.99097	+	6.12758i	0.0664026	+	0.204366i
$900$		0			0
$901$	5.42854			0.180851
$902$	−51.9832	−	84.6008i	−1.73085	−	2.81690i
$903$	−3.60744			−0.120048
$904$	−138.941	+	100.946i	−4.62110	+	3.35742i
$905$		0			0
$906$	0.0535320	−	0.164755i	0.00177848	−	0.00547360i
$907$	0.00159270	+	0.00115716i	5.28846e−5	+	3.84229e-5i	0.587812	−	0.808998i	$-0.299990\pi$
$907$	0.00159270	+	0.00115716i	5.28846e−5	+	3.84229e-5i	−0.587759	+	0.809036i	$0.699990\pi$
$908$	−6.25823	−	4.54687i	−0.207687	−	0.150893i
$909$	−0.0349884	+	0.107683i	−0.00116049	+	0.00357163i
$910$		0			0
$911$	33.9149	−	24.6406i	1.12365	−	0.816379i	0.138892	−	0.990308i	$-0.455646\pi$
$911$	33.9149	−	24.6406i	1.12365	−	0.816379i	0.984758	+	0.173928i	$0.0556460\pi$
$912$	23.8667			0.790307
$913$	−5.51683	−	8.97845i	−0.182581	−	0.297143i
$914$	57.8559			1.91370
$915$		0			0
$916$	−8.49010	−	26.1298i	−0.280521	−	0.863354i
$917$	2.48033	−	7.63366i	0.0819076	−	0.252086i
$918$	−8.03360	−	5.83675i	−0.265148	−	0.192641i
$919$	14.1448	+	10.2768i	0.466592	+	0.338999i	0.796112	−	0.605150i	$-0.206887\pi$
$919$	14.1448	+	10.2768i	0.466592	+	0.338999i	−0.329519	+	0.944149i	$0.606887\pi$
$920$		0			0
$921$	4.00127	+	12.3146i	0.131846	+	0.405781i
$922$	−45.7789	+	33.2603i	−1.50765	+	1.09537i
$923$	21.7098			0.714587
$924$	−5.68084	+	6.66760i	−0.186886	+	0.219348i
$925$		0			0
$926$	29.6378	−	21.5331i	0.973958	−	0.707622i
$927$	2.23985	+	6.89355i	0.0735663	+	0.226414i
$928$	6.91138	−	21.2710i	0.226877	−	0.698256i
$929$	−35.6438	−	25.8968i	−1.16944	−	0.849645i	−0.178495	−	0.983941i	$-0.557123\pi$
$929$	−35.6438	−	25.8968i	−1.16944	−	0.849645i	−0.990941	+	0.134295i	$0.957123\pi$
$930$		0			0
$931$	3.40946	−	10.4932i	0.111741	−	0.343902i
$932$	35.0901	+	107.996i	1.14941	+	3.53753i
$933$	−23.0560	+	16.7512i	−0.754819	+	0.548408i
$934$	−95.2741			−3.11746
$935$		0			0
$936$	33.7625			1.10356
$937$	−11.3473	+	8.24433i	−0.370702	+	0.269330i	−0.757502	−	0.652833i	$-0.773580\pi$
$937$	−11.3473	+	8.24433i	−0.370702	+	0.269330i	0.386800	+	0.922164i	$0.373580\pi$
$938$	−0.177186	−	0.545322i	−0.00578532	−	0.0178054i
$939$	2.09840	−	6.45820i	0.0684785	−	0.210755i
$940$		0			0
$941$	−0.721160	−	0.523953i	−0.0235091	−	0.0170804i	0.575969	−	0.817472i	$-0.304625\pi$
$941$	−0.721160	−	0.523953i	−0.0235091	−	0.0170804i	−0.599478	+	0.800391i	$0.704625\pi$
$942$	−0.820977	+	2.52671i	−0.0267489	+	0.0823246i
$943$	−12.0231	−	37.0032i	−0.391525	−	1.20499i
$944$	94.4065	−	68.5904i	3.07267	−	2.23243i
$945$		0			0
$946$	−65.1901	+	15.7335i	−2.11951	+	0.511542i
$947$	5.19472			0.168806			0.0844029	−	0.996432i	$-0.473102\pi$
$947$	5.19472			0.168806			0.0844029	+	0.996432i	$0.473102\pi$
$948$	−19.4409	+	14.1246i	−0.631410	+	0.458746i
$949$	−1.29876	−	3.99718i	−0.0421596	−	0.129754i
$950$		0			0
$951$	24.7749	+	18.0000i	0.803382	+	0.583691i
$952$	13.4034	+	9.73818i	0.434408	+	0.315616i
$953$	−6.82545	+	21.0066i	−0.221098	+	0.680470i	0.777566	+	0.628801i	$0.216454\pi$
$953$	−6.82545	+	21.0066i	−0.221098	+	0.680470i	−0.998664	+	0.0516686i	$0.983546\pi$
$954$	−1.25528	−	3.86334i	−0.0406410	−	0.125080i
$955$		0			0
$956$	−100.678			−3.25615
$957$	−3.23756	−	1.33649i	−0.104655	−	0.0432026i
$958$	−54.3758			−1.75680
$959$	2.39421	−	1.73949i	0.0773130	−	0.0561712i
$960$		0			0
$961$	1.92233	−	5.91632i	0.0620106	−	0.190849i
$962$	−68.4016	−	49.6966i	−2.20535	−	1.60228i
$963$	−7.00511	−	5.08951i	−0.225737	−	0.164007i
$964$	−36.2173	+	111.465i	−1.16648	+	3.59006i
$965$		0			0
$966$	−3.79941	+	2.76043i	−0.122244	+	0.0888155i
$967$	3.71338			0.119414			0.0597072	−	0.998216i	$-0.480983\pi$
$967$	3.71338			0.119414			0.0597072	+	0.998216i	$0.480983\pi$
$968$	−46.4809	+	91.7679i	−1.49395	+	2.94953i
$969$	−5.94255			−0.190902
$970$		0			0
$971$	2.36096	+	7.26629i	0.0757668	+	0.233186i	0.981766	−	0.190093i	$-0.0608789\pi$
$971$	2.36096	+	7.26629i	0.0757668	+	0.233186i	−0.905999	+	0.423279i	$0.860879\pi$
$972$	−1.67816	+	5.16484i	−0.0538270	+	0.165662i
$973$	6.82723	+	4.96027i	0.218871	+	0.159019i
$974$	14.9109	+	10.8334i	0.477776	+	0.347125i
$975$		0			0
$976$	−49.1161	−	151.164i	−1.57217	−	4.83864i
$977$	23.4636	−	17.0473i	0.750667	−	0.545392i	−0.145366	−	0.989378i	$-0.546436\pi$
$977$	23.4636	−	17.0473i	0.750667	−	0.545392i	0.896034	+	0.443986i	$0.146436\pi$
$978$	48.2850			1.54398
$979$	4.24149	+	1.75092i	0.135559	+	0.0559597i
$980$		0			0
$981$	−3.57240	+	2.59550i	−0.114058	+	0.0828680i
$982$	−2.83792	−	8.73421i	−0.0905616	−	0.278720i
$983$	2.78758	−	8.57928i	0.0889099	−	0.273637i	−0.896709	−	0.442621i	$-0.854049\pi$
$983$	2.78758	−	8.57928i	0.0889099	−	0.273637i	0.985619	+	0.168984i	$0.0540487\pi$
$984$	83.0929	+	60.3706i	2.64891	+	1.92454i
$985$		0			0
$986$	−3.24059	+	9.97352i	−0.103202	+	0.317622i
$987$	−0.783426	−	2.41114i	−0.0249367	−	0.0767473i
$988$	25.8755	−	18.7997i	0.823210	−	0.598097i
$989$	−26.2772			−0.835568
$990$		0			0
$991$	−14.7651			−0.469028			−0.234514	−	0.972113i	$-0.575350\pi$
$991$	−14.7651			−0.469028			−0.234514	+	0.972113i	$0.575350\pi$
$992$	−104.530	+	75.9458i	−3.31884	+	2.41128i
$993$	10.8011	+	33.2425i	0.342764	+	1.05492i
$994$	2.46341	−	7.58158i	0.0781345	−	0.240473i
$995$		0			0
$996$	13.9594	+	10.1421i	0.442321	+	0.321365i
$997$	13.8848	−	42.7329i	0.439735	−	1.35337i	−0.448420	−	0.893823i	$-0.648013\pi$
$997$	13.8848	−	42.7329i	0.439735	−	1.35337i	0.888155	−	0.459543i	$-0.151987\pi$
$998$	14.8099	+	45.5801i	0.468799	+	1.44281i
$999$	6.95033	−	5.04971i	0.219899	−	0.159766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.o.751.1		24
5.2	odd	4		165.2.s.a.124.1	yes	48
5.3	odd	4		165.2.s.a.124.12	yes	48
5.4	even	2		825.2.n.p.751.6		24
11.2	odd	10		9075.2.a.dx.1.1		12
11.4	even	5	inner	825.2.n.o.301.1		24
11.9	even	5		9075.2.a.dz.1.12		12
15.2	even	4		495.2.ba.c.289.12		48
15.8	even	4		495.2.ba.c.289.1		48
55.2	even	20		1815.2.c.k.364.1		24
55.4	even	10		825.2.n.p.301.6		24
55.9	even	10		9075.2.a.dy.1.1		12
55.13	even	20		1815.2.c.k.364.24		24
55.24	odd	10		9075.2.a.ea.1.12		12
55.37	odd	20		165.2.s.a.4.12	yes	48
55.42	odd	20		1815.2.c.j.364.24		24
55.48	odd	20		165.2.s.a.4.1	✓	48
55.53	odd	20		1815.2.c.j.364.1		24
165.92	even	20		495.2.ba.c.334.1		48
165.158	even	20		495.2.ba.c.334.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.4.1	✓	48	55.48	odd	20
165.2.s.a.4.12	yes	48	55.37	odd	20
165.2.s.a.124.1	yes	48	5.2	odd	4
165.2.s.a.124.12	yes	48	5.3	odd	4
495.2.ba.c.289.1		48	15.8	even	4
495.2.ba.c.289.12		48	15.2	even	4
495.2.ba.c.334.1		48	165.92	even	20
495.2.ba.c.334.12		48	165.158	even	20
825.2.n.o.301.1		24	11.4	even	5	inner
825.2.n.o.751.1		24	1.1	even	1	trivial
825.2.n.p.301.6		24	55.4	even	10
825.2.n.p.751.6		24	5.4	even	2
1815.2.c.j.364.1		24	55.53	odd	20
1815.2.c.j.364.24		24	55.42	odd	20
1815.2.c.k.364.1		24	55.2	even	20
1815.2.c.k.364.24		24	55.13	even	20
9075.2.a.dx.1.1		12	11.2	odd	10
9075.2.a.dy.1.1		12	55.9	even	10
9075.2.a.dz.1.12		12	11.9	even	5
9075.2.a.ea.1.12		12	55.24	odd	10

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.20531 + 1.60225i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.67816 - 5.16484i) q^{4} +(2.20531 + 1.60225i) q^{6} +(0.150285 - 0.462529i) q^{7} +(2.88981 + 8.89393i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-2.20531 + 1.60225i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.67816 - 5.16484i) q^{4} +(2.20531 + 1.60225i) q^{6} +(0.150285 - 0.462529i) q^{7} +(2.88981 + 8.89393i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(3.06568 + 1.26554i) q^{11} -5.43063 q^{12} +(-2.92082 + 2.12210i) q^{13} +(0.409664 + 1.26082i) q^{14} +(-11.8363 - 8.59960i) q^{16} +(2.94711 + 2.14120i) q^{17} +(0.842355 - 2.59250i) q^{18} +(-0.504099 - 1.55146i) q^{19} -0.486331 q^{21} +(-8.78851 + 2.12109i) q^{22} -3.54253 q^{23} +(7.56563 - 5.49675i) q^{24} +(3.04119 - 9.35981i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-2.13668 - 1.55239i) q^{28} +(0.326342 - 1.00438i) q^{29} +(-4.93572 + 3.58601i) q^{31} +21.1784 q^{32} +(0.256251 - 3.30671i) q^{33} -9.93007 q^{34} +(1.67816 + 5.16484i) q^{36} +(2.65479 - 8.17060i) q^{37} +(3.59752 + 2.61375i) q^{38} +(2.92082 + 2.12210i) q^{39} +(3.39392 + 10.4454i) q^{41} +(1.07251 - 0.779227i) q^{42} +7.41765 q^{43} +(11.6810 - 13.7100i) q^{44} +(7.81239 - 5.67603i) q^{46} +(1.61089 + 4.95781i) q^{47} +(-4.52108 + 13.9145i) q^{48} +(5.47177 + 3.97547i) q^{49} +(1.12570 - 3.46454i) q^{51} +(6.05871 + 18.6468i) q^{52} +(1.20559 - 0.875916i) q^{53} -2.72592 q^{54} +4.54799 q^{56} +(-1.31975 + 0.958853i) q^{57} +(0.889581 + 2.73785i) q^{58} +(-2.46472 + 7.58562i) q^{59} +(8.78900 + 6.38558i) q^{61} +(5.13911 - 15.8166i) q^{62} +(0.150285 + 0.462529i) q^{63} +(-23.0323 + 16.7339i) q^{64} +(4.73308 + 7.70292i) q^{66} -0.432515 q^{67} +(16.0047 - 11.6281i) q^{68} +(1.09470 + 3.36915i) q^{69} +(-4.86481 - 3.53449i) q^{71} +(-7.56563 - 5.49675i) q^{72} +(-0.359734 + 1.10715i) q^{73} +(7.23674 + 22.2724i) q^{74} -8.85898 q^{76} +(1.04607 - 1.22777i) q^{77} -9.84148 q^{78} +(3.57985 - 2.60091i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-24.2209 - 17.5975i) q^{82} +(-2.57049 - 1.86757i) q^{83} +(-0.816141 + 2.51182i) q^{84} +(-16.3583 + 11.8850i) q^{86} -1.05606 q^{87} +(-2.39636 + 30.9231i) q^{88} +1.38354 q^{89} +(0.542578 + 1.66988i) q^{91} +(-5.94492 + 18.2966i) q^{92} +(4.93572 + 3.58601i) q^{93} +(-11.4962 - 8.35247i) q^{94} +(-6.54447 - 20.1418i) q^{96} +(1.13241 - 0.822741i) q^{97} -18.4367 q^{98} +(-3.22405 + 0.778121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9	\( 24 q - 2 q^{2} + 6 q^{3} - 6 q^{4} + 2 q^{6} - 4 q^{7} - 6 q^{8} - 6 q^{9} - 24 q^{12} - 4 q^{13} + 2 q^{14} - 22 q^{16} - 4 q^{17} - 2 q^{18} + 8 q^{19} - 16 q^{21} + 4 q^{22} + 6 q^{24} - 38 q^{26} + 6 q^{27} - 30 q^{28} - 10 q^{31} + 56 q^{32} - 10 q^{33} + 12 q^{34} - 6 q^{36} - 10 q^{37} - 4 q^{38} + 4 q^{39} + 30 q^{41} + 8 q^{42} + 64 q^{43} + 24 q^{44} + 54 q^{46} + 8 q^{47} + 2 q^{48} + 14 q^{49} + 14 q^{51} - 14 q^{52} - 26 q^{53} - 8 q^{54} + 12 q^{56} - 8 q^{57} - 20 q^{58} - 30 q^{59} + 20 q^{61} + 50 q^{62} - 4 q^{63} - 32 q^{64} + 6 q^{66} - 20 q^{67} + 62 q^{68} - 10 q^{69} - 16 q^{71} - 6 q^{72} + 12 q^{73} + 16 q^{74} - 68 q^{76} + 2 q^{77} - 32 q^{78} + 26 q^{79} - 6 q^{81} - 56 q^{82} - 48 q^{83} - 52 q^{86} - 48 q^{88} - 20 q^{89} - 20 q^{91} - 46 q^{92} + 10 q^{93} - 36 q^{94} + 14 q^{96} + 14 q^{97} + 120 q^{98}+O(q^{100}) \) 24 * q - 2 * q^2 + 6 * q^3 - 6 * q^4 + 2 * q^6 - 4 * q^7 - 6 * q^8 - 6 * q^9 - 24 * q^12 - 4 * q^13 + 2 * q^14 - 22 * q^16 - 4 * q^17 - 2 * q^18 + 8 * q^19 - 16 * q^21 + 4 * q^22 + 6 * q^24 - 38 * q^26 + 6 * q^27 - 30 * q^28 - 10 * q^31 + 56 * q^32 - 10 * q^33 + 12 * q^34 - 6 * q^36 - 10 * q^37 - 4 * q^38 + 4 * q^39 + 30 * q^41 + 8 * q^42 + 64 * q^43 + 24 * q^44 + 54 * q^46 + 8 * q^47 + 2 * q^48 + 14 * q^49 + 14 * q^51 - 14 * q^52 - 26 * q^53 - 8 * q^54 + 12 * q^56 - 8 * q^57 - 20 * q^58 - 30 * q^59 + 20 * q^61 + 50 * q^62 - 4 * q^63 - 32 * q^64 + 6 * q^66 - 20 * q^67 + 62 * q^68 - 10 * q^69 - 16 * q^71 - 6 * q^72 + 12 * q^73 + 16 * q^74 - 68 * q^76 + 2 * q^77 - 32 * q^78 + 26 * q^79 - 6 * q^81 - 56 * q^82 - 48 * q^83 - 52 * q^86 - 48 * q^88 - 20 * q^89 - 20 * q^91 - 46 * q^92 + 10 * q^93 - 36 * q^94 + 14 * q^96 + 14 * q^97 + 120 * q^98

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